LMFDB - Embedded newform 2013.4.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.33494 q^{2} +3.00000 q^{3} +3.12184 q^{4} +0.253130 q^{5} -10.0048 q^{6} -0.691781 q^{7} +16.2684 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.33494 q^{2} +3.00000 q^{3} +3.12184 q^{4} +0.253130 q^{5} -10.0048 q^{6} -0.691781 q^{7} +16.2684 q^{8} +9.00000 q^{9} -0.844174 q^{10} +11.0000 q^{11} +9.36553 q^{12} +22.1328 q^{13} +2.30705 q^{14} +0.759390 q^{15} -79.2288 q^{16} +110.686 q^{17} -30.0145 q^{18} +32.5537 q^{19} +0.790232 q^{20} -2.07534 q^{21} -36.6844 q^{22} -160.925 q^{23} +48.8051 q^{24} -124.936 q^{25} -73.8115 q^{26} +27.0000 q^{27} -2.15963 q^{28} +40.8490 q^{29} -2.53252 q^{30} -207.706 q^{31} +134.077 q^{32} +33.0000 q^{33} -369.133 q^{34} -0.175110 q^{35} +28.0966 q^{36} -109.736 q^{37} -108.565 q^{38} +66.3983 q^{39} +4.11801 q^{40} -179.467 q^{41} +6.92115 q^{42} +108.910 q^{43} +34.3403 q^{44} +2.27817 q^{45} +536.676 q^{46} -284.638 q^{47} -237.687 q^{48} -342.521 q^{49} +416.654 q^{50} +332.059 q^{51} +69.0950 q^{52} +414.165 q^{53} -90.0435 q^{54} +2.78443 q^{55} -11.2542 q^{56} +97.6611 q^{57} -136.229 q^{58} -170.894 q^{59} +2.37069 q^{60} +61.0000 q^{61} +692.689 q^{62} -6.22603 q^{63} +186.693 q^{64} +5.60246 q^{65} -110.053 q^{66} -497.617 q^{67} +345.546 q^{68} -482.775 q^{69} +0.583983 q^{70} -257.916 q^{71} +146.415 q^{72} +1179.63 q^{73} +365.964 q^{74} -374.808 q^{75} +101.628 q^{76} -7.60959 q^{77} -221.434 q^{78} -736.662 q^{79} -20.0552 q^{80} +81.0000 q^{81} +598.514 q^{82} -637.080 q^{83} -6.47890 q^{84} +28.0180 q^{85} -363.209 q^{86} +122.547 q^{87} +178.952 q^{88} -349.810 q^{89} -7.59756 q^{90} -15.3110 q^{91} -502.383 q^{92} -623.119 q^{93} +949.252 q^{94} +8.24031 q^{95} +402.230 q^{96} +758.074 q^{97} +1142.29 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9}+O(q^{10}) $ 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9} - 161 q^{10} + 396 q^{11} + 438 q^{12} - 233 q^{13} - 264 q^{14} - 195 q^{15} + 574 q^{16} - 556 q^{17} - 126 q^{18} - 615 q^{19} - 136 q^{20} - 315 q^{21} - 154 q^{22} - 457 q^{23} - 567 q^{24} + 863 q^{25} + 115 q^{26} + 972 q^{27} - 424 q^{28} - 754 q^{29} - 483 q^{30} - 508 q^{31} - 1511 q^{32} + 1188 q^{33} - 860 q^{34} - 826 q^{35} + 1314 q^{36} - 412 q^{37} - 599 q^{38} - 699 q^{39} - 2791 q^{40} - 2066 q^{41} - 792 q^{42} - 2063 q^{43} + 1606 q^{44} - 585 q^{45} - 787 q^{46} - 1815 q^{47} + 1722 q^{48} + 2825 q^{49} + 808 q^{50} - 1668 q^{51} - 2882 q^{52} - 759 q^{53} - 378 q^{54} - 715 q^{55} - 1749 q^{56} - 1845 q^{57} - 335 q^{58} - 2337 q^{59} - 408 q^{60} + 2196 q^{61} - 1689 q^{62} - 945 q^{63} + 4723 q^{64} - 3550 q^{65} - 462 q^{66} - 1331 q^{67} - 6166 q^{68} - 1371 q^{69} - 1750 q^{70} - 361 q^{71} - 1701 q^{72} - 4627 q^{73} - 3394 q^{74} + 2589 q^{75} - 7214 q^{76} - 1155 q^{77} + 345 q^{78} - 2583 q^{79} - 2643 q^{80} + 2916 q^{81} + 1090 q^{82} - 6123 q^{83} - 1272 q^{84} + 295 q^{85} + 613 q^{86} - 2262 q^{87} - 2079 q^{88} - 2485 q^{89} - 1449 q^{90} - 3156 q^{91} - 6291 q^{92} - 1524 q^{93} - 1744 q^{94} - 5572 q^{95} - 4533 q^{96} - 2558 q^{97} - 2314 q^{98} + 3564 q^{99}+O(q^{100}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9 - 161 * q^10 + 396 * q^11 + 438 * q^12 - 233 * q^13 - 264 * q^14 - 195 * q^15 + 574 * q^16 - 556 * q^17 - 126 * q^18 - 615 * q^19 - 136 * q^20 - 315 * q^21 - 154 * q^22 - 457 * q^23 - 567 * q^24 + 863 * q^25 + 115 * q^26 + 972 * q^27 - 424 * q^28 - 754 * q^29 - 483 * q^30 - 508 * q^31 - 1511 * q^32 + 1188 * q^33 - 860 * q^34 - 826 * q^35 + 1314 * q^36 - 412 * q^37 - 599 * q^38 - 699 * q^39 - 2791 * q^40 - 2066 * q^41 - 792 * q^42 - 2063 * q^43 + 1606 * q^44 - 585 * q^45 - 787 * q^46 - 1815 * q^47 + 1722 * q^48 + 2825 * q^49 + 808 * q^50 - 1668 * q^51 - 2882 * q^52 - 759 * q^53 - 378 * q^54 - 715 * q^55 - 1749 * q^56 - 1845 * q^57 - 335 * q^58 - 2337 * q^59 - 408 * q^60 + 2196 * q^61 - 1689 * q^62 - 945 * q^63 + 4723 * q^64 - 3550 * q^65 - 462 * q^66 - 1331 * q^67 - 6166 * q^68 - 1371 * q^69 - 1750 * q^70 - 361 * q^71 - 1701 * q^72 - 4627 * q^73 - 3394 * q^74 + 2589 * q^75 - 7214 * q^76 - 1155 * q^77 + 345 * q^78 - 2583 * q^79 - 2643 * q^80 + 2916 * q^81 + 1090 * q^82 - 6123 * q^83 - 1272 * q^84 + 295 * q^85 + 613 * q^86 - 2262 * q^87 - 2079 * q^88 - 2485 * q^89 - 1449 * q^90 - 3156 * q^91 - 6291 * q^92 - 1524 * q^93 - 1744 * q^94 - 5572 * q^95 - 4533 * q^96 - 2558 * q^97 - 2314 * q^98 + 3564 * 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 $

$2$	−3.33494	−1.17908	−0.589540	−	0.807739i	$-0.700691\pi$
$2$	−3.33494	−1.17908	−0.589540	+	0.807739i	$0.700691\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	3.12184	0.390230
$5$	0.253130	0.0226406	0.0113203	−	0.999936i	$-0.496397\pi$
$5$	0.253130	0.0226406	0.0113203	+	0.999936i	$0.496397\pi$
$6$	−10.0048	−0.680742
$7$	−0.691781	−0.0373527	−0.0186763	−	0.999826i	$-0.505945\pi$
$7$	−0.691781	−0.0373527	−0.0186763	+	0.999826i	$0.505945\pi$
$8$	16.2684	0.718967
$9$	9.00000	0.333333
$10$	−0.844174	−0.0266951
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	9.36553	0.225300
$13$	22.1328	0.472194	0.236097	−	0.971730i	$-0.424132\pi$
$13$	22.1328	0.472194	0.236097	+	0.971730i	$0.424132\pi$
$14$	2.30705	0.0440418
$15$	0.759390	0.0130716
$16$	−79.2288	−1.23795
$17$	110.686	1.57914	0.789571	−	0.613659i	$-0.210303\pi$
$17$	110.686	1.57914	0.789571	+	0.613659i	$0.210303\pi$
$18$	−30.0145	−0.393027
$19$	32.5537	0.393070	0.196535	−	0.980497i	$-0.437031\pi$
$19$	32.5537	0.393070	0.196535	+	0.980497i	$0.437031\pi$
$20$	0.790232	0.00883506
$21$	−2.07534	−0.0215656
$22$	−36.6844	−0.355506
$23$	−160.925	−1.45892	−0.729461	−	0.684022i	$-0.760229\pi$
$23$	−160.925	−1.45892	−0.729461	+	0.684022i	$0.760229\pi$
$24$	48.8051	0.415096
$25$	−124.936	−0.999487
$26$	−73.8115	−0.556755
$27$	27.0000	0.192450
$28$	−2.15963	−0.0145761
$29$	40.8490	0.261568	0.130784	−	0.991411i	$-0.458251\pi$
$29$	40.8490	0.261568	0.130784	+	0.991411i	$0.458251\pi$
$30$	−2.53252	−0.0154124
$31$	−207.706	−1.20339	−0.601696	−	0.798725i	$-0.705508\pi$
$31$	−207.706	−1.20339	−0.601696	+	0.798725i	$0.705508\pi$
$32$	134.077	0.740676
$33$	33.0000	0.174078
$34$	−369.133	−1.86193
$35$	−0.175110	−0.000845688 0
$36$	28.0966	0.130077
$37$	−109.736	−0.487581	−0.243791	−	0.969828i	$-0.578391\pi$
$37$	−109.736	−0.487581	−0.243791	+	0.969828i	$0.578391\pi$
$38$	−108.565	−0.463461
$39$	66.3983	0.272621
$40$	4.11801	0.0162779
$41$	−179.467	−0.683612	−0.341806	−	0.939770i	$-0.611039\pi$
$41$	−179.467	−0.683612	−0.341806	+	0.939770i	$0.611039\pi$
$42$	6.92115	0.0254275
$43$	108.910	0.386248	0.193124	−	0.981174i	$-0.438138\pi$
$43$	108.910	0.386248	0.193124	+	0.981174i	$0.438138\pi$
$44$	34.3403	0.117659
$45$	2.27817	0.00754687
$46$	536.676	1.72019
$47$	−284.638	−0.883378	−0.441689	−	0.897168i	$-0.645620\pi$
$47$	−284.638	−0.883378	−0.441689	+	0.897168i	$0.645620\pi$
$48$	−237.687	−0.714731
$49$	−342.521	−0.998605
$50$	416.654	1.17848
$51$	332.059	0.911718
$52$	69.0950	0.184264
$53$	414.165	1.07340	0.536698	−	0.843775i	$-0.319672\pi$
$53$	414.165	1.07340	0.536698	+	0.843775i	$0.319672\pi$
$54$	−90.0435	−0.226914
$55$	2.78443	0.00682640
$56$	−11.2542	−0.0268554
$57$	97.6611	0.226939
$58$	−136.229	−0.308409
$59$	−170.894	−0.377093	−0.188546	−	0.982064i	$-0.560378\pi$
$59$	−170.894	−0.377093	−0.188546	+	0.982064i	$0.560378\pi$
$60$	2.37069	0.00510092
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	692.689	1.41890
$63$	−6.22603	−0.0124509
$64$	186.693	0.364634
$65$	5.60246	0.0106908
$66$	−110.053	−0.205252
$67$	−497.617	−0.907368	−0.453684	−	0.891163i	$-0.649890\pi$
$67$	−497.617	−0.907368	−0.453684	+	0.891163i	$0.649890\pi$
$68$	345.546	0.616229
$69$	−482.775	−0.842309
$70$	0.583983	0.000997134 0
$71$	−257.916	−0.431113	−0.215557	−	0.976491i	$-0.569157\pi$
$71$	−257.916	−0.431113	−0.215557	+	0.976491i	$0.569157\pi$
$72$	146.415	0.239656
$73$	1179.63	1.89131	0.945654	−	0.325174i	$-0.105423\pi$
$73$	1179.63	1.89131	0.945654	+	0.325174i	$0.105423\pi$
$74$	365.964	0.574897
$75$	−374.808	−0.577054
$76$	101.628	0.153388
$77$	−7.60959	−0.0112623
$78$	−221.434	−0.321442
$79$	−736.662	−1.04913	−0.524563	−	0.851372i	$-0.675771\pi$
$79$	−736.662	−1.04913	−0.524563	+	0.851372i	$0.675771\pi$
$80$	−20.0552	−0.0280280
$81$	81.0000	0.111111
$82$	598.514	0.806034
$83$	−637.080	−0.842513	−0.421256	−	0.906942i	$-0.638411\pi$
$83$	−637.080	−0.842513	−0.421256	+	0.906942i	$0.638411\pi$
$84$	−6.47890	−0.00841554
$85$	28.0180	0.0357528
$86$	−363.209	−0.455417
$87$	122.547	0.151016
$88$	178.952	0.216777
$89$	−349.810	−0.416627	−0.208313	−	0.978062i	$-0.566797\pi$
$89$	−349.810	−0.416627	−0.208313	+	0.978062i	$0.566797\pi$
$90$	−7.59756	−0.00889837
$91$	−15.3110	−0.0176377
$92$	−502.383	−0.569316
$93$	−623.119	−0.694779
$94$	949.252	1.04157
$95$	8.24031	0.00889935
$96$	402.230	0.427629
$97$	758.074	0.793513	0.396757	−	0.917924i	$-0.370136\pi$
$97$	758.074	0.793513	0.396757	+	0.917924i	$0.370136\pi$
$98$	1142.29	1.17744
$99$	99.0000	0.100504
$100$	−390.030	−0.390030
$101$	180.350	0.177678	0.0888388	−	0.996046i	$-0.471684\pi$
$101$	180.350	0.177678	0.0888388	+	0.996046i	$0.471684\pi$
$102$	−1107.40	−1.07499
$103$	212.422	0.203209	0.101605	−	0.994825i	$-0.467602\pi$
$103$	212.422	0.203209	0.101605	+	0.994825i	$0.467602\pi$
$104$	360.064	0.339492
$105$	−0.525331	−0.000488258 0
$106$	−1381.22	−1.26562
$107$	1001.94	0.905244	0.452622	−	0.891703i	$-0.350489\pi$
$107$	1001.94	0.905244	0.452622	+	0.891703i	$0.350489\pi$
$108$	84.2897	0.0750999
$109$	−1081.93	−0.950733	−0.475366	−	0.879788i	$-0.657684\pi$
$109$	−1081.93	−0.950733	−0.475366	+	0.879788i	$0.657684\pi$
$110$	−9.28591	−0.00804888
$111$	−329.208	−0.281505
$112$	54.8090	0.0462408
$113$	717.788	0.597556	0.298778	−	0.954323i	$-0.403421\pi$
$113$	717.788	0.597556	0.298778	+	0.954323i	$0.403421\pi$
$114$	−325.694	−0.267579
$115$	−40.7350	−0.0330309
$116$	127.524	0.102072
$117$	199.195	0.157398
$118$	569.921	0.444623
$119$	−76.5708	−0.0589852
$120$	12.3540	0.00939803
$121$	121.000	0.0909091
$122$	−203.432	−0.150966
$123$	−538.402	−0.394684
$124$	−648.426	−0.469600
$125$	−63.2662	−0.0452696
$126$	20.7635	0.0146806
$127$	1102.24	0.770143	0.385071	−	0.922887i	$-0.374177\pi$
$127$	1102.24	0.770143	0.385071	+	0.922887i	$0.374177\pi$
$128$	−1695.22	−1.17061
$129$	326.731	0.223000
$130$	−18.6839	−0.0126053
$131$	−1178.83	−0.786221	−0.393111	−	0.919491i	$-0.628601\pi$
$131$	−1178.83	−0.786221	−0.393111	+	0.919491i	$0.628601\pi$
$132$	103.021	0.0679304
$133$	−22.5200	−0.0146822
$134$	1659.53	1.06986
$135$	6.83451	0.00435719
$136$	1800.69	1.13535
$137$	−2569.62	−1.60246	−0.801232	−	0.598353i	$-0.795822\pi$
$137$	−2569.62	−1.60246	−0.801232	+	0.598353i	$0.795822\pi$
$138$	1610.03	0.993150
$139$	−347.338	−0.211948	−0.105974	−	0.994369i	$-0.533796\pi$
$139$	−347.338	−0.211948	−0.105974	+	0.994369i	$0.533796\pi$
$140$	−0.546667	−0.000330013 0
$141$	−853.915	−0.510018
$142$	860.137	0.508317
$143$	243.460	0.142372
$144$	−713.060	−0.412650
$145$	10.3401	0.00592205
$146$	−3934.01	−2.23000
$147$	−1027.56	−0.576545
$148$	−342.579	−0.190269
$149$	781.597	0.429738	0.214869	−	0.976643i	$-0.431068\pi$
$149$	781.597	0.429738	0.214869	+	0.976643i	$0.431068\pi$
$150$	1249.96	0.680393
$151$	−401.532	−0.216399	−0.108199	−	0.994129i	$-0.534508\pi$
$151$	−401.532	−0.216399	−0.108199	+	0.994129i	$0.534508\pi$
$152$	529.596	0.282604
$153$	996.178	0.526381
$154$	25.3776	0.0132791
$155$	−52.5767	−0.0272455
$156$	207.285	0.106385
$157$	341.477	0.173585	0.0867925	−	0.996226i	$-0.472338\pi$
$157$	341.477	0.173585	0.0867925	+	0.996226i	$0.472338\pi$
$158$	2456.72	1.23700
$159$	1242.49	0.619725
$160$	33.9388	0.0167694
$161$	111.325	0.0544947
$162$	−270.130	−0.131009
$163$	−2733.09	−1.31332	−0.656662	−	0.754185i	$-0.728032\pi$
$163$	−2733.09	−1.31332	−0.656662	+	0.754185i	$0.728032\pi$
$164$	−560.269	−0.266766
$165$	8.35329	0.00394123
$166$	2124.62	0.993390
$167$	−3275.07	−1.51756	−0.758781	−	0.651346i	$-0.774205\pi$
$167$	−3275.07	−1.51756	−0.758781	+	0.651346i	$0.774205\pi$
$168$	−33.7625	−0.0155049
$169$	−1707.14	−0.777033
$170$	−93.4386	−0.0421554
$171$	292.983	0.131023
$172$	340.000	0.150726
$173$	−810.864	−0.356352	−0.178176	−	0.983999i	$-0.557020\pi$
$173$	−810.864	−0.356352	−0.178176	+	0.983999i	$0.557020\pi$
$174$	−408.687	−0.178060
$175$	86.4283	0.0373335
$176$	−871.517	−0.373256
$177$	−512.681	−0.217715
$178$	1166.60	0.491236
$179$	−366.674	−0.153109	−0.0765545	−	0.997065i	$-0.524392\pi$
$179$	−366.674	−0.153109	−0.0765545	+	0.997065i	$0.524392\pi$
$180$	7.11208	0.00294502
$181$	560.819	0.230306	0.115153	−	0.993348i	$-0.463264\pi$
$181$	560.819	0.230306	0.115153	+	0.993348i	$0.463264\pi$
$182$	51.0614	0.0207963
$183$	183.000	0.0739221
$184$	−2617.99	−1.04892
$185$	−27.7775	−0.0110391
$186$	2078.07	0.819200
$187$	1217.55	0.476129
$188$	−888.596	−0.344721
$189$	−18.6781	−0.00718853
$190$	−27.4810	−0.0104930
$191$	4537.55	1.71898	0.859491	−	0.511151i	$-0.170781\pi$
$191$	4537.55	1.71898	0.859491	+	0.511151i	$0.170781\pi$
$192$	560.079	0.210522
$193$	3426.28	1.27787	0.638935	−	0.769261i	$-0.279375\pi$
$193$	3426.28	1.27787	0.638935	+	0.769261i	$0.279375\pi$
$194$	−2528.13	−0.935616
$195$	16.8074	0.00617232
$196$	−1069.30	−0.389686
$197$	−67.8824	−0.0245504	−0.0122752	−	0.999925i	$-0.503907\pi$
$197$	−67.8824	−0.0245504	−0.0122752	+	0.999925i	$0.503907\pi$
$198$	−330.159	−0.118502
$199$	4102.72	1.46148	0.730739	−	0.682657i	$-0.239176\pi$
$199$	4102.72	1.46148	0.730739	+	0.682657i	$0.239176\pi$
$200$	−2032.50	−0.718599
$201$	−1492.85	−0.523869
$202$	−601.455	−0.209496
$203$	−28.2585	−0.00977025
$204$	1036.64	0.355780
$205$	−45.4286	−0.0154774
$206$	−708.415	−0.239600
$207$	−1448.33	−0.486307
$208$	−1753.55	−0.584553
$209$	358.091	0.118515
$210$	1.75195	0.000575696 0
$211$	−3323.08	−1.08422	−0.542110	−	0.840308i	$-0.682374\pi$
$211$	−3323.08	−1.08422	−0.542110	+	0.840308i	$0.682374\pi$
$212$	1292.96	0.418871
$213$	−773.749	−0.248903
$214$	−3341.41	−1.06736
$215$	27.5684	0.00874489
$216$	439.246	0.138365
$217$	143.687	0.0449499
$218$	3608.17	1.12099
$219$	3538.90	1.09195
$220$	8.69255	0.00266387
$221$	2449.80	0.745661
$222$	1097.89	0.331917
$223$	2881.35	0.865243	0.432622	−	0.901576i	$-0.357589\pi$
$223$	2881.35	0.865243	0.432622	+	0.901576i	$0.357589\pi$
$224$	−92.7517	−0.0276662
$225$	−1124.42	−0.333162
$226$	−2393.78	−0.704567
$227$	−4171.00	−1.21955	−0.609777	−	0.792573i	$-0.708741\pi$
$227$	−4171.00	−1.21955	−0.609777	+	0.792573i	$0.708741\pi$
$228$	304.883	0.0885585
$229$	287.979	0.0831012	0.0415506	−	0.999136i	$-0.486770\pi$
$229$	287.979	0.0831012	0.0415506	+	0.999136i	$0.486770\pi$
$230$	135.849	0.0389461
$231$	−22.8288	−0.00650227
$232$	664.546	0.188059
$233$	1567.38	0.440698	0.220349	−	0.975421i	$-0.429280\pi$
$233$	1567.38	0.440698	0.220349	+	0.975421i	$0.429280\pi$
$234$	−664.303	−0.185585
$235$	−72.0504	−0.0200002
$236$	−533.503	−0.147153
$237$	−2209.99	−0.605713
$238$	255.359	0.0695483
$239$	−1335.13	−0.361349	−0.180674	−	0.983543i	$-0.557828\pi$
$239$	−1335.13	−0.361349	−0.180674	+	0.983543i	$0.557828\pi$
$240$	−60.1656	−0.0161820
$241$	1510.96	0.403856	0.201928	−	0.979400i	$-0.435279\pi$
$241$	1510.96	0.403856	0.201928	+	0.979400i	$0.435279\pi$
$242$	−403.528	−0.107189
$243$	243.000	0.0641500
$244$	190.432	0.0499639
$245$	−86.7024	−0.0226090
$246$	1795.54	0.465364
$247$	720.503	0.185605
$248$	−3379.04	−0.865200
$249$	−1911.24	−0.486425
$250$	210.989	0.0533765
$251$	−3712.62	−0.933620	−0.466810	−	0.884358i	$-0.654597\pi$
$251$	−3712.62	−0.933620	−0.466810	+	0.884358i	$0.654597\pi$
$252$	−19.4367	−0.00485872
$253$	−1770.18	−0.439882
$254$	−3675.91	−0.908060
$255$	84.0541	0.0206419
$256$	4159.93	1.01561
$257$	−3028.93	−0.735172	−0.367586	−	0.929989i	$-0.619816\pi$
$257$	−3028.93	−0.735172	−0.367586	+	0.929989i	$0.619816\pi$
$258$	−1089.63	−0.262935
$259$	75.9134	0.0182125
$260$	17.4900	0.00417186
$261$	367.641	0.0871892
$262$	3931.34	0.927018
$263$	−4853.86	−1.13803	−0.569015	−	0.822327i	$-0.692675\pi$
$263$	−4853.86	−1.13803	−0.569015	+	0.822327i	$0.692675\pi$
$264$	536.856	0.125156
$265$	104.838	0.0243023
$266$	75.1030	0.0173115
$267$	−1049.43	−0.240540
$268$	−1553.48	−0.354082
$269$	2852.26	0.646487	0.323244	−	0.946316i	$-0.395227\pi$
$269$	2852.26	0.646487	0.323244	+	0.946316i	$0.395227\pi$
$270$	−22.7927	−0.00513748
$271$	−2838.78	−0.636324	−0.318162	−	0.948036i	$-0.603066\pi$
$271$	−2838.78	−0.636324	−0.318162	+	0.948036i	$0.603066\pi$
$272$	−8769.56	−1.95490
$273$	−45.9331	−0.0101831
$274$	8569.54	1.88943
$275$	−1374.30	−0.301357
$276$	−1507.15	−0.328695
$277$	8456.57	1.83432	0.917159	−	0.398521i	$-0.130476\pi$
$277$	8456.57	1.83432	0.917159	+	0.398521i	$0.130476\pi$
$278$	1158.35	0.249904
$279$	−1869.36	−0.401131
$280$	−2.84876	−0.000608022 0
$281$	−7140.76	−1.51595	−0.757975	−	0.652284i	$-0.773811\pi$
$281$	−7140.76	−1.51595	−0.757975	+	0.652284i	$0.773811\pi$
$282$	2847.76	0.601353
$283$	4635.38	0.973656	0.486828	−	0.873498i	$-0.338154\pi$
$283$	4635.38	0.973656	0.486828	+	0.873498i	$0.338154\pi$
$284$	−805.175	−0.168234
$285$	24.7209	0.00513804
$286$	−811.926	−0.167868
$287$	124.152	0.0255348
$288$	1206.69	0.246892
$289$	7338.49	1.49369
$290$	−34.4836	−0.00698258
$291$	2274.22	0.458135
$292$	3682.63	0.738046
$293$	3592.91	0.716383	0.358191	−	0.933648i	$-0.383394\pi$
$293$	3592.91	0.716383	0.358191	+	0.933648i	$0.383394\pi$
$294$	3426.87	0.679793
$295$	−43.2583	−0.00853761
$296$	−1785.23	−0.350555
$297$	297.000	0.0580259
$298$	−2606.58	−0.506695
$299$	−3561.72	−0.688894
$300$	−1170.09	−0.225184
$301$	−75.3420	−0.0144274
$302$	1339.08	0.255151
$303$	541.049	0.102582
$304$	−2579.19	−0.486601
$305$	15.4409	0.00289883
$306$	−3322.20	−0.620645
$307$	6477.18	1.20414	0.602072	−	0.798442i	$-0.294342\pi$
$307$	6477.18	1.20414	0.602072	+	0.798442i	$0.294342\pi$
$308$	−23.7560	−0.00439487
$309$	637.266	0.117323
$310$	175.340	0.0321247
$311$	−8928.71	−1.62798	−0.813989	−	0.580881i	$-0.802708\pi$
$311$	−8928.71	−1.62798	−0.813989	+	0.580881i	$0.802708\pi$
$312$	1080.19	0.196006
$313$	−9734.57	−1.75792	−0.878962	−	0.476892i	$-0.841763\pi$
$313$	−9734.57	−1.75792	−0.878962	+	0.476892i	$0.841763\pi$
$314$	−1138.81	−0.204671
$315$	−1.57599	−0.000281896 0
$316$	−2299.74	−0.409401
$317$	7047.73	1.24871	0.624353	−	0.781142i	$-0.285363\pi$
$317$	7047.73	1.24871	0.624353	+	0.781142i	$0.285363\pi$
$318$	−4143.65	−0.730705
$319$	449.339	0.0788656
$320$	47.2575	0.00825555
$321$	3005.82	0.522643
$322$	−371.262	−0.0642536
$323$	3603.25	0.620713
$324$	252.869	0.0433589
$325$	−2765.18	−0.471952
$326$	9114.68	1.54851
$327$	−3245.78	−0.548906
$328$	−2919.64	−0.491495
$329$	196.907	0.0329965
$330$	−27.8577	−0.00464702
$331$	−3896.13	−0.646981	−0.323491	−	0.946231i	$-0.604856\pi$
$331$	−3896.13	−0.646981	−0.323491	+	0.946231i	$0.604856\pi$
$332$	−1988.86	−0.328774
$333$	−987.625	−0.162527
$334$	10922.2	1.78933
$335$	−125.962	−0.0205434
$336$	164.427	0.0266971
$337$	−8028.72	−1.29778	−0.648890	−	0.760882i	$-0.724767\pi$
$337$	−8028.72	−1.29778	−0.648890	+	0.760882i	$0.724767\pi$
$338$	5693.22	0.916184
$339$	2153.37	0.344999
$340$	87.4679	0.0139518
$341$	−2284.77	−0.362836
$342$	−977.082	−0.154487
$343$	474.231	0.0746532
$344$	1771.79	0.277699
$345$	−122.205	−0.0190704
$346$	2704.18	0.420167
$347$	−11403.6	−1.76421	−0.882103	−	0.471056i	$-0.843873\pi$
$347$	−11403.6	−1.76421	−0.882103	+	0.471056i	$0.843873\pi$
$348$	382.572	0.0589311
$349$	−2689.93	−0.412575	−0.206288	−	0.978491i	$-0.566138\pi$
$349$	−2689.93	−0.412575	−0.206288	+	0.978491i	$0.566138\pi$
$350$	−288.234	−0.0440192
$351$	597.584	0.0908738
$352$	1474.84	0.223322
$353$	3392.14	0.511460	0.255730	−	0.966748i	$-0.417684\pi$
$353$	3392.14	0.511460	0.255730	+	0.966748i	$0.417684\pi$
$354$	1709.76	0.256703
$355$	−65.2864	−0.00976068
$356$	−1092.05	−0.162580
$357$	−229.712	−0.0340551
$358$	1222.84	0.180528
$359$	890.915	0.130977	0.0654884	−	0.997853i	$-0.479139\pi$
$359$	890.915	0.130977	0.0654884	+	0.997853i	$0.479139\pi$
$360$	37.0621	0.00542596
$361$	−5799.26	−0.845496
$362$	−1870.30	−0.271549
$363$	363.000	0.0524864
$364$	−47.7986	−0.00688277
$365$	298.600	0.0428204
$366$	−610.295	−0.0871601
$367$	4350.95	0.618850	0.309425	−	0.950924i	$-0.399863\pi$
$367$	4350.95	0.618850	0.309425	+	0.950924i	$0.399863\pi$
$368$	12749.9	1.80607
$369$	−1615.21	−0.227871
$370$	92.6363	0.0130160
$371$	−286.512	−0.0400942
$372$	−1945.28	−0.271124
$373$	6564.57	0.911261	0.455631	−	0.890169i	$-0.349414\pi$
$373$	6564.57	0.911261	0.455631	+	0.890169i	$0.349414\pi$
$374$	−4060.46	−0.561394
$375$	−189.799	−0.0261364
$376$	−4630.60	−0.635120
$377$	904.100	0.123511
$378$	62.2904	0.00847585
$379$	−3358.15	−0.455137	−0.227568	−	0.973762i	$-0.573077\pi$
$379$	−3358.15	−0.455137	−0.227568	+	0.973762i	$0.573077\pi$
$380$	25.7250	0.00347280
$381$	3306.73	0.444642
$382$	−15132.5	−2.02682
$383$	−7955.29	−1.06135	−0.530674	−	0.847576i	$-0.678061\pi$
$383$	−7955.29	−1.06135	−0.530674	+	0.847576i	$0.678061\pi$
$384$	−5085.67	−0.675851
$385$	−1.92622	−0.000254984 0
$386$	−11426.4	−1.50671
$387$	980.192	0.128749
$388$	2366.59	0.309653
$389$	9810.96	1.27875	0.639377	−	0.768893i	$-0.279192\pi$
$389$	9810.96	1.27875	0.639377	+	0.768893i	$0.279192\pi$
$390$	−56.0517	−0.00727766
$391$	−17812.2	−2.30384
$392$	−5572.27	−0.717964
$393$	−3536.49	−0.453925
$394$	226.384	0.0289468
$395$	−186.471	−0.0237529
$396$	309.062	0.0392196
$397$	3646.53	0.460992	0.230496	−	0.973073i	$-0.425965\pi$
$397$	3646.53	0.460992	0.230496	+	0.973073i	$0.425965\pi$
$398$	−13682.3	−1.72320
$399$	−67.5601	−0.00847678
$400$	9898.53	1.23732
$401$	−12801.8	−1.59424	−0.797118	−	0.603823i	$-0.793643\pi$
$401$	−12801.8	−1.59424	−0.797118	+	0.603823i	$0.793643\pi$
$402$	4978.58	0.617684
$403$	−4597.11	−0.568234
$404$	563.023	0.0693352
$405$	20.5035	0.00251562
$406$	94.2406	0.0115199
$407$	−1207.10	−0.147011
$408$	5402.07	0.655495
$409$	7102.31	0.858647	0.429324	−	0.903151i	$-0.358752\pi$
$409$	7102.31	0.858647	0.429324	+	0.903151i	$0.358752\pi$
$410$	151.502	0.0182491
$411$	−7708.87	−0.925183
$412$	663.148	0.0792984
$413$	118.221	0.0140854
$414$	4830.08	0.573395
$415$	−161.264	−0.0190750
$416$	2967.48	0.349743
$417$	−1042.01	−0.122368
$418$	−1194.21	−0.139739
$419$	−10229.4	−1.19270	−0.596349	−	0.802725i	$-0.703383\pi$
$419$	−10229.4	−1.19270	−0.596349	+	0.802725i	$0.703383\pi$
$420$	−1.64000	−0.000190533 0
$421$	−7486.41	−0.866663	−0.433332	−	0.901235i	$-0.642662\pi$
$421$	−7486.41	−0.866663	−0.433332	+	0.901235i	$0.642662\pi$
$422$	11082.3	1.27838
$423$	−2561.74	−0.294459
$424$	6737.79	0.771736
$425$	−13828.7	−1.57833
$426$	2580.41	0.293477
$427$	−42.1987	−0.00478252
$428$	3127.90	0.353254
$429$	730.381	0.0821984
$430$	−91.9391	−0.0103109
$431$	−15357.9	−1.71639	−0.858197	−	0.513321i	$-0.828415\pi$
$431$	−15357.9	−1.71639	−0.858197	+	0.513321i	$0.828415\pi$
$432$	−2139.18	−0.238244
$433$	−10429.8	−1.15757	−0.578783	−	0.815481i	$-0.696472\pi$
$433$	−10429.8	−1.15757	−0.578783	+	0.815481i	$0.696472\pi$
$434$	−479.189	−0.0529996
$435$	31.0203	0.00341910
$436$	−3377.61	−0.371005
$437$	−5238.71	−0.573458
$438$	−11802.0	−1.28749
$439$	−13322.0	−1.44835	−0.724176	−	0.689615i	$-0.757780\pi$
$439$	−13322.0	−1.44835	−0.724176	+	0.689615i	$0.757780\pi$
$440$	45.2981	0.00490796
$441$	−3082.69	−0.332868
$442$	−8169.93	−0.879194
$443$	−8311.32	−0.891383	−0.445691	−	0.895187i	$-0.647042\pi$
$443$	−8311.32	−0.891383	−0.445691	+	0.895187i	$0.647042\pi$
$444$	−1027.74	−0.109852
$445$	−88.5473	−0.00943269
$446$	−9609.12	−1.02019
$447$	2344.79	0.248109
$448$	−129.151	−0.0136201
$449$	−2417.77	−0.254124	−0.127062	−	0.991895i	$-0.540555\pi$
$449$	−2417.77	−0.254124	−0.127062	+	0.991895i	$0.540555\pi$
$450$	3749.89	0.392825
$451$	−1974.14	−0.206117
$452$	2240.82	0.233185
$453$	−1204.59	−0.124938
$454$	13910.0	1.43795
$455$	−3.87568	−0.000399329 0
$456$	1588.79	0.163162
$457$	−989.498	−0.101284	−0.0506420	−	0.998717i	$-0.516127\pi$
$457$	−989.498	−0.101284	−0.0506420	+	0.998717i	$0.516127\pi$
$458$	−960.393	−0.0979830
$459$	2988.53	0.303906
$460$	−127.168	−0.0128897
$461$	3021.14	0.305225	0.152612	−	0.988286i	$-0.451231\pi$
$461$	3021.14	0.305225	0.152612	+	0.988286i	$0.451231\pi$
$462$	76.1327	0.00766669
$463$	8252.36	0.828336	0.414168	−	0.910200i	$-0.364073\pi$
$463$	8252.36	0.828336	0.414168	+	0.910200i	$0.364073\pi$
$464$	−3236.42	−0.323808
$465$	−157.730	−0.0157302
$466$	−5227.13	−0.519619
$467$	1594.22	0.157970	0.0789848	−	0.996876i	$-0.474832\pi$
$467$	1594.22	0.157970	0.0789848	+	0.996876i	$0.474832\pi$
$468$	621.855	0.0614215
$469$	344.242	0.0338926
$470$	240.284	0.0235819
$471$	1024.43	0.100219
$472$	−2780.16	−0.271117
$473$	1198.01	0.116458
$474$	7370.17	0.714184
$475$	−4067.13	−0.392868
$476$	−239.042	−0.0230178
$477$	3727.48	0.357798
$478$	4452.58	0.426059
$479$	−4067.27	−0.387972	−0.193986	−	0.981004i	$-0.562142\pi$
$479$	−4067.27	−0.387972	−0.193986	+	0.981004i	$0.562142\pi$
$480$	101.816	0.00968179
$481$	−2428.76	−0.230233
$482$	−5038.96	−0.476179
$483$	333.975	0.0314625
$484$	377.743	0.0354755
$485$	191.891	0.0179656
$486$	−810.391	−0.0756380
$487$	10352.9	0.963318	0.481659	−	0.876359i	$-0.340034\pi$
$487$	10352.9	0.963318	0.481659	+	0.876359i	$0.340034\pi$
$488$	992.371	0.0920543
$489$	−8199.26	−0.758248
$490$	289.148	0.0266579
$491$	−2327.78	−0.213954	−0.106977	−	0.994261i	$-0.534117\pi$
$491$	−2327.78	−0.213954	−0.106977	+	0.994261i	$0.534117\pi$
$492$	−1680.81	−0.154018
$493$	4521.43	0.413052
$494$	−2402.84	−0.218843
$495$	25.0599	0.00227547
$496$	16456.3	1.48974
$497$	178.422	0.0161032
$498$	6373.87	0.573534
$499$	−16136.6	−1.44764	−0.723821	−	0.689988i	$-0.757616\pi$
$499$	−16136.6	−1.44764	−0.723821	+	0.689988i	$0.757616\pi$
$500$	−197.507	−0.0176656
$501$	−9825.22	−0.876164
$502$	12381.4	1.10081
$503$	−18821.9	−1.66844	−0.834221	−	0.551430i	$-0.814083\pi$
$503$	−18821.9	−1.66844	−0.834221	+	0.551430i	$0.814083\pi$
$504$	−101.287	−0.00895179
$505$	45.6518	0.00402273
$506$	5903.44	0.518656
$507$	−5121.42	−0.448620
$508$	3441.03	0.300533
$509$	−11260.9	−0.980607	−0.490304	−	0.871552i	$-0.663114\pi$
$509$	−11260.9	−0.980607	−0.490304	+	0.871552i	$0.663114\pi$
$510$	−280.316	−0.0243384
$511$	−816.048	−0.0706454
$512$	−311.340	−0.0268739
$513$	878.950	0.0756463
$514$	10101.3	0.866827
$515$	53.7703	0.00460079
$516$	1020.00	0.0870214
$517$	−3131.02	−0.266348
$518$	−253.167	−0.0214740
$519$	−2432.59	−0.205740
$520$	91.1429	0.00768631
$521$	−11963.4	−1.00600	−0.502999	−	0.864287i	$-0.667770\pi$
$521$	−11963.4	−1.00600	−0.502999	+	0.864287i	$0.667770\pi$
$522$	−1226.06	−0.102803
$523$	4524.81	0.378310	0.189155	−	0.981947i	$-0.439425\pi$
$523$	4524.81	0.378310	0.189155	+	0.981947i	$0.439425\pi$
$524$	−3680.13	−0.306807
$525$	259.285	0.0215545
$526$	16187.3	1.34183
$527$	−22990.3	−1.90033
$528$	−2614.55	−0.215500
$529$	13729.9	1.12845
$530$	−349.627	−0.0286544
$531$	−1538.04	−0.125698
$532$	−70.3040	−0.00572945
$533$	−3972.11	−0.322798
$534$	3499.79	0.283615
$535$	253.621	0.0204953
$536$	−8095.43	−0.652368
$537$	−1100.02	−0.0883975
$538$	−9512.11	−0.762261
$539$	−3767.74	−0.301091
$540$	21.3363	0.00170031
$541$	−21733.9	−1.72719	−0.863597	−	0.504183i	$-0.831794\pi$
$541$	−21733.9	−1.72719	−0.863597	+	0.504183i	$0.831794\pi$
$542$	9467.18	0.750277
$543$	1682.46	0.132967
$544$	14840.5	1.16963
$545$	−273.868	−0.0215252
$546$	153.184	0.0120067
$547$	11362.4	0.888156	0.444078	−	0.895988i	$-0.353531\pi$
$547$	11362.4	0.888156	0.444078	+	0.895988i	$0.353531\pi$
$548$	−8021.96	−0.625330
$549$	549.000	0.0426790
$550$	4583.20	0.355324
$551$	1329.78	0.102814
$552$	−7853.97	−0.605593
$553$	509.609	0.0391877
$554$	−28202.2	−2.16281
$555$	−83.3324	−0.00637345
$556$	−1084.33	−0.0827086
$557$	2922.73	0.222334	0.111167	−	0.993802i	$-0.464541\pi$
$557$	2922.73	0.222334	0.111167	+	0.993802i	$0.464541\pi$
$558$	6234.20	0.472965
$559$	2410.48	0.182384
$560$	13.8738	0.00104692
$561$	3652.65	0.274893
$562$	23814.0	1.78743
$563$	13086.2	0.979606	0.489803	−	0.871833i	$-0.337069\pi$
$563$	13086.2	0.979606	0.489803	+	0.871833i	$0.337069\pi$
$564$	−2665.79	−0.199025
$565$	181.694	0.0135290
$566$	−15458.7	−1.14802
$567$	−56.0343	−0.00415030
$568$	−4195.88	−0.309957
$569$	−1824.88	−0.134452	−0.0672259	−	0.997738i	$-0.521415\pi$
$569$	−1824.88	−0.134452	−0.0672259	+	0.997738i	$0.521415\pi$
$570$	−82.4429	−0.00605816
$571$	21267.7	1.55871	0.779356	−	0.626581i	$-0.215546\pi$
$571$	21267.7	1.55871	0.779356	+	0.626581i	$0.215546\pi$
$572$	760.045	0.0555578
$573$	13612.7	0.992455
$574$	−414.041	−0.0301075
$575$	20105.3	1.45817
$576$	1680.24	0.121545
$577$	−24654.8	−1.77884	−0.889422	−	0.457087i	$-0.848893\pi$
$577$	−24654.8	−1.77884	−0.889422	+	0.457087i	$0.848893\pi$
$578$	−24473.5	−1.76118
$579$	10278.8	0.737779
$580$	32.2801	0.00231096
$581$	440.720	0.0314701
$582$	−7584.40	−0.540178
$583$	4555.81	0.323641
$584$	19190.7	1.35979
$585$	50.4221	0.00356359
$586$	−11982.2	−0.844673
$587$	−13213.9	−0.929121	−0.464561	−	0.885541i	$-0.653788\pi$
$587$	−13213.9	−0.929121	−0.464561	+	0.885541i	$0.653788\pi$
$588$	−3207.89	−0.224985
$589$	−6761.61	−0.473017
$590$	144.264	0.0100665
$591$	−203.647	−0.0141742
$592$	8694.26	0.603601
$593$	−12177.8	−0.843312	−0.421656	−	0.906756i	$-0.638551\pi$
$593$	−12177.8	−0.843312	−0.421656	+	0.906756i	$0.638551\pi$
$594$	−990.478	−0.0684172
$595$	−19.3824	−0.00133546
$596$	2440.02	0.167697
$597$	12308.2	0.843785
$598$	11878.1	0.812262
$599$	−10903.9	−0.743772	−0.371886	−	0.928278i	$-0.621289\pi$
$599$	−10903.9	−0.743772	−0.371886	+	0.928278i	$0.621289\pi$
$600$	−6097.51	−0.414883
$601$	−17261.5	−1.17157	−0.585784	−	0.810467i	$-0.699213\pi$
$601$	−17261.5	−1.17157	−0.585784	+	0.810467i	$0.699213\pi$
$602$	251.261	0.0170110
$603$	−4478.56	−0.302456
$604$	−1253.52	−0.0844453
$605$	30.6287	0.00205824
$606$	−1804.37	−0.120953
$607$	25161.0	1.68246	0.841229	−	0.540679i	$-0.181833\pi$
$607$	25161.0	1.68246	0.841229	+	0.540679i	$0.181833\pi$
$608$	4364.69	0.291137
$609$	−84.7756	−0.00564086
$610$	−51.4946	−0.00341796
$611$	−6299.83	−0.417126
$612$	3109.91	0.205410
$613$	−26637.3	−1.75509	−0.877544	−	0.479496i	$-0.840820\pi$
$613$	−26637.3	−1.75509	−0.877544	+	0.479496i	$0.840820\pi$
$614$	−21601.0	−1.41978
$615$	−136.286	−0.00893589
$616$	−123.796	−0.00809720
$617$	−19726.3	−1.28712	−0.643559	−	0.765396i	$-0.722543\pi$
$617$	−19726.3	−1.28712	−0.643559	+	0.765396i	$0.722543\pi$
$618$	−2125.25	−0.138333
$619$	−5180.02	−0.336353	−0.168177	−	0.985757i	$-0.553788\pi$
$619$	−5180.02	−0.336353	−0.168177	+	0.985757i	$0.553788\pi$
$620$	−164.136	−0.0106320
$621$	−4344.98	−0.280770
$622$	29776.7	1.91952
$623$	241.992	0.0155621
$624$	−5260.66	−0.337492
$625$	15601.0	0.998462
$626$	32464.2	2.07273
$627$	1074.27	0.0684247
$628$	1066.04	0.0677381
$629$	−12146.3	−0.769960
$630$	5.25585	0.000332378 0
$631$	−5133.33	−0.323859	−0.161929	−	0.986802i	$-0.551772\pi$
$631$	−5133.33	−0.323859	−0.161929	+	0.986802i	$0.551772\pi$
$632$	−11984.3	−0.754287
$633$	−9969.24	−0.625974
$634$	−23503.8	−1.47232
$635$	279.010	0.0174365
$636$	3878.87	0.241835
$637$	−7580.94	−0.471535
$638$	−1498.52	−0.0929889
$639$	−2321.25	−0.143704
$640$	−429.112	−0.0265033
$641$	−1644.18	−0.101312	−0.0506562	−	0.998716i	$-0.516131\pi$
$641$	−1644.18	−0.101312	−0.0506562	+	0.998716i	$0.516131\pi$
$642$	−10024.2	−0.616238
$643$	11691.0	0.717027	0.358513	−	0.933525i	$-0.383284\pi$
$643$	11691.0	0.717027	0.358513	+	0.933525i	$0.383284\pi$
$644$	347.539	0.0212655
$645$	82.7053	0.00504886
$646$	−12016.6	−0.731871
$647$	5097.37	0.309735	0.154867	−	0.987935i	$-0.450505\pi$
$647$	5097.37	0.309735	0.154867	+	0.987935i	$0.450505\pi$
$648$	1317.74	0.0798853
$649$	−1879.83	−0.113698
$650$	9221.70	0.556469
$651$	431.062	0.0259518
$652$	−8532.26	−0.512499
$653$	4888.75	0.292973	0.146487	−	0.989213i	$-0.453203\pi$
$653$	4888.75	0.292973	0.146487	+	0.989213i	$0.453203\pi$
$654$	10824.5	0.647204
$655$	−298.397	−0.0178005
$656$	14219.0	0.846278
$657$	10616.7	0.630436
$658$	−656.675	−0.0389055
$659$	19899.3	1.17628	0.588139	−	0.808760i	$-0.299861\pi$
$659$	19899.3	1.17628	0.588139	+	0.808760i	$0.299861\pi$
$660$	26.0776	0.00153799
$661$	1324.93	0.0779636	0.0389818	−	0.999240i	$-0.487589\pi$
$661$	1324.93	0.0779636	0.0389818	+	0.999240i	$0.487589\pi$
$662$	12993.4	0.762843
$663$	7349.39	0.430508
$664$	−10364.2	−0.605739
$665$	−5.70049	−0.000332415 0
$666$	3293.67	0.191632
$667$	−6573.62	−0.381607
$668$	−10224.3	−0.592198
$669$	8644.04	0.499548
$670$	420.075	0.0242223
$671$	671.000	0.0386046
$672$	−278.255	−0.0159731
$673$	1819.19	0.104197	0.0520986	−	0.998642i	$-0.483409\pi$
$673$	1819.19	0.104197	0.0520986	+	0.998642i	$0.483409\pi$
$674$	26775.3	1.53019
$675$	−3373.27	−0.192351
$676$	−5329.43	−0.303222
$677$	10138.6	0.575566	0.287783	−	0.957696i	$-0.407082\pi$
$677$	10138.6	0.575566	0.287783	+	0.957696i	$0.407082\pi$
$678$	−7181.35	−0.406782
$679$	−524.422	−0.0296398
$680$	455.808	0.0257051
$681$	−12513.0	−0.704110
$682$	7619.57	0.427813
$683$	24389.8	1.36640	0.683198	−	0.730233i	$-0.260588\pi$
$683$	24389.8	1.36640	0.683198	+	0.730233i	$0.260588\pi$
$684$	914.648	0.0511293
$685$	−650.448	−0.0362808
$686$	−1581.53	−0.0880222
$687$	863.936	0.0479785
$688$	−8628.83	−0.478156
$689$	9166.61	0.506851
$690$	407.546	0.0224855
$691$	17614.9	0.969755	0.484877	−	0.874582i	$-0.338864\pi$
$691$	17614.9	0.969755	0.484877	+	0.874582i	$0.338864\pi$
$692$	−2531.39	−0.139059
$693$	−68.4863	−0.00375409
$694$	38030.5	2.08014
$695$	−87.9216	−0.00479864
$696$	1993.64	0.108576
$697$	−19864.6	−1.07952
$698$	8970.77	0.486459
$699$	4702.15	0.254437
$700$	269.816	0.0145687
$701$	23977.8	1.29191	0.645955	−	0.763375i	$-0.276459\pi$
$701$	23977.8	1.29191	0.645955	+	0.763375i	$0.276459\pi$
$702$	−1992.91	−0.107147
$703$	−3572.31	−0.191653
$704$	2053.62	0.109941
$705$	−216.151	−0.0115471
$706$	−11312.6	−0.603052
$707$	−124.762	−0.00663674
$708$	−1600.51	−0.0849588
$709$	13806.9	0.731352	0.365676	−	0.930742i	$-0.380838\pi$
$709$	13806.9	0.731352	0.365676	+	0.930742i	$0.380838\pi$
$710$	217.726	0.0115086
$711$	−6629.96	−0.349709
$712$	−5690.84	−0.299541
$713$	33425.2	1.75566
$714$	766.078	0.0401537
$715$	61.6271	0.00322339
$716$	−1144.70	−0.0597478
$717$	−4005.39	−0.208625
$718$	−2971.15	−0.154432
$719$	−9171.76	−0.475729	−0.237864	−	0.971298i	$-0.576447\pi$
$719$	−9171.76	−0.475729	−0.237864	+	0.971298i	$0.576447\pi$
$720$	−180.497	−0.00934266
$721$	−146.950	−0.00759041
$722$	19340.2	0.996908
$723$	4532.88	0.233167
$724$	1750.79	0.0898723
$725$	−5103.50	−0.261434
$726$	−1210.58	−0.0618857
$727$	16459.9	0.839703	0.419851	−	0.907593i	$-0.362082\pi$
$727$	16459.9	0.839703	0.419851	+	0.907593i	$0.362082\pi$
$728$	−249.085	−0.0126809
$729$	729.000	0.0370370
$730$	−995.815	−0.0504887
$731$	12054.9	0.609940
$732$	571.297	0.0288467
$733$	12963.5	0.653228	0.326614	−	0.945158i	$-0.394092\pi$
$733$	12963.5	0.653228	0.326614	+	0.945158i	$0.394092\pi$
$734$	−14510.2	−0.729674
$735$	−260.107	−0.0130533
$736$	−21576.3	−1.08059
$737$	−5473.79	−0.273582
$738$	5386.62	0.268678
$739$	28043.6	1.39594	0.697972	−	0.716125i	$-0.254086\pi$
$739$	28043.6	1.39594	0.697972	+	0.716125i	$0.254086\pi$
$740$	−86.7169	−0.00430781
$741$	2161.51	0.107159
$742$	955.500	0.0472743
$743$	8762.79	0.432673	0.216336	−	0.976319i	$-0.430589\pi$
$743$	8762.79	0.432673	0.216336	+	0.976319i	$0.430589\pi$
$744$	−10137.1	−0.499523
$745$	197.846	0.00972953
$746$	−21892.5	−1.07445
$747$	−5733.72	−0.280838
$748$	3801.00	0.185800
$749$	−693.123	−0.0338133
$750$	632.968	0.0308170
$751$	1921.19	0.0933490	0.0466745	−	0.998910i	$-0.485138\pi$
$751$	1921.19	0.0933490	0.0466745	+	0.998910i	$0.485138\pi$
$752$	22551.6	1.09358
$753$	−11137.9	−0.539025
$754$	−3015.12	−0.145629
$755$	−101.640	−0.00489940
$756$	−58.3101	−0.00280518
$757$	23964.5	1.15060	0.575301	−	0.817942i	$-0.304885\pi$
$757$	23964.5	1.15060	0.575301	+	0.817942i	$0.304885\pi$
$758$	11199.2	0.536643
$759$	−5310.53	−0.253966
$760$	134.056	0.00639834
$761$	21297.2	1.01448	0.507242	−	0.861804i	$-0.330665\pi$
$761$	21297.2	1.01448	0.507242	+	0.861804i	$0.330665\pi$
$762$	−11027.7	−0.524269
$763$	748.457	0.0355124
$764$	14165.5	0.670799
$765$	252.162	0.0119176
$766$	26530.4	1.25142
$767$	−3782.35	−0.178061
$768$	12479.8	0.586361
$769$	22817.3	1.06998	0.534988	−	0.844860i	$-0.320316\pi$
$769$	22817.3	1.06998	0.534988	+	0.844860i	$0.320316\pi$
$770$	6.42382	0.000300647 0
$771$	−9086.78	−0.424452
$772$	10696.3	0.498664
$773$	36028.0	1.67637	0.838187	−	0.545383i	$-0.183616\pi$
$773$	36028.0	1.67637	0.838187	+	0.545383i	$0.183616\pi$
$774$	−3268.88	−0.151806
$775$	25950.0	1.20278
$776$	12332.6	0.570510
$777$	227.740	0.0105150
$778$	−32719.0	−1.50775
$779$	−5842.33	−0.268708
$780$	52.4700	0.00240862
$781$	−2837.08	−0.129986
$782$	59402.8	2.71642
$783$	1102.92	0.0503387
$784$	27137.6	1.23622
$785$	86.4381	0.00393007
$786$	11794.0	0.535214
$787$	−7451.50	−0.337506	−0.168753	−	0.985658i	$-0.553974\pi$
$787$	−7451.50	−0.337506	−0.168753	+	0.985658i	$0.553974\pi$
$788$	−211.918	−0.00958029
$789$	−14561.6	−0.657042
$790$	621.870	0.0280065
$791$	−496.553	−0.0223203
$792$	1610.57	0.0722589
$793$	1350.10	0.0604582
$794$	−12161.0	−0.543547
$795$	314.513	0.0140310
$796$	12808.0	0.570313
$797$	−7856.68	−0.349182	−0.174591	−	0.984641i	$-0.555860\pi$
$797$	−7856.68	−0.349182	−0.174591	+	0.984641i	$0.555860\pi$
$798$	225.309	0.00999481
$799$	−31505.6	−1.39498
$800$	−16751.0	−0.740296
$801$	−3148.29	−0.138876
$802$	42693.1	1.87973
$803$	12976.0	0.570251
$804$	−4660.45	−0.204430
$805$	28.1797	0.00123379
$806$	15331.1	0.669994
$807$	8556.77	0.373250
$808$	2933.99	0.127744
$809$	−4666.39	−0.202795	−0.101398	−	0.994846i	$-0.532331\pi$
$809$	−4666.39	−0.202795	−0.101398	+	0.994846i	$0.532331\pi$
$810$	−68.3781	−0.00296612
$811$	32077.0	1.38887	0.694437	−	0.719553i	$-0.255653\pi$
$811$	32077.0	1.38887	0.694437	+	0.719553i	$0.255653\pi$
$812$	−88.2187	−0.00381265
$813$	−8516.35	−0.367382
$814$	4025.60	0.173338
$815$	−691.826	−0.0297345
$816$	−26308.7	−1.12866
$817$	3545.43	0.151822
$818$	−23685.8	−1.01241
$819$	−137.799	−0.00587924
$820$	−141.821	−0.00603976
$821$	22045.3	0.937134	0.468567	−	0.883428i	$-0.344770\pi$
$821$	22045.3	0.937134	0.468567	+	0.883428i	$0.344770\pi$
$822$	25708.6	1.09087
$823$	−32122.9	−1.36055	−0.680276	−	0.732956i	$-0.738140\pi$
$823$	−32122.9	−1.36055	−0.680276	+	0.732956i	$0.738140\pi$
$824$	3455.76	0.146101
$825$	−4122.89	−0.173988
$826$	−394.261	−0.0166078
$827$	−14515.5	−0.610341	−0.305170	−	0.952298i	$-0.598713\pi$
$827$	−14515.5	−0.610341	−0.305170	+	0.952298i	$0.598713\pi$
$828$	−4521.45	−0.189772
$829$	−8504.35	−0.356295	−0.178147	−	0.984004i	$-0.557010\pi$
$829$	−8504.35	−0.356295	−0.178147	+	0.984004i	$0.557010\pi$
$830$	537.806	0.0224910
$831$	25369.7	1.05904
$832$	4132.03	0.172178
$833$	−37912.5	−1.57694
$834$	3475.05	0.144282
$835$	−829.019	−0.0343585
$836$	1117.90	0.0462482
$837$	−5608.07	−0.231593
$838$	34114.6	1.40629
$839$	1910.68	0.0786223	0.0393111	−	0.999227i	$-0.487484\pi$
$839$	1910.68	0.0786223	0.0393111	+	0.999227i	$0.487484\pi$
$840$	−8.54629	−0.000351042 0
$841$	−22720.4	−0.931582
$842$	24966.7	1.02187
$843$	−21422.3	−0.875234
$844$	−10374.1	−0.423095
$845$	−432.128	−0.0175925
$846$	8543.27	0.347191
$847$	−83.7055	−0.00339570
$848$	−32813.8	−1.32881
$849$	13906.1	0.562140
$850$	46118.0	1.86098
$851$	17659.3	0.711343
$852$	−2415.52	−0.0971297
$853$	−16163.3	−0.648795	−0.324397	−	0.945921i	$-0.605162\pi$
$853$	−16163.3	−0.648795	−0.324397	+	0.945921i	$0.605162\pi$
$854$	140.730	0.00563898
$855$	74.1628	0.00296645
$856$	16299.9	0.650841
$857$	−13344.6	−0.531907	−0.265954	−	0.963986i	$-0.585687\pi$
$857$	−13344.6	−0.531907	−0.265954	+	0.963986i	$0.585687\pi$
$858$	−2435.78	−0.0969185
$859$	−15309.4	−0.608091	−0.304045	−	0.952658i	$-0.598337\pi$
$859$	−15309.4	−0.608091	−0.304045	+	0.952658i	$0.598337\pi$
$860$	86.0643	0.00341252
$861$	372.457	0.0147425
$862$	51217.8	2.02377
$863$	−3552.16	−0.140112	−0.0700562	−	0.997543i	$-0.522318\pi$
$863$	−3552.16	−0.140112	−0.0700562	+	0.997543i	$0.522318\pi$
$864$	3620.07	0.142543
$865$	−205.254	−0.00806802
$866$	34782.9	1.36486
$867$	22015.5	0.862382
$868$	448.569	0.0175408
$869$	−8103.28	−0.316323
$870$	−103.451	−0.00403139
$871$	−11013.6	−0.428454
$872$	−17601.2	−0.683546
$873$	6822.67	0.264504
$874$	17470.8	0.676154
$875$	43.7664	0.00169094
$876$	11047.9	0.426111
$877$	11411.7	0.439393	0.219696	−	0.975568i	$-0.429493\pi$
$877$	11411.7	0.439393	0.219696	+	0.975568i	$0.429493\pi$
$878$	44428.3	1.70772
$879$	10778.7	0.413604
$880$	−220.607	−0.00845075
$881$	−26137.3	−0.999531	−0.499765	−	0.866161i	$-0.666580\pi$
$881$	−26137.3	−0.999531	−0.499765	+	0.866161i	$0.666580\pi$
$882$	10280.6	0.392478
$883$	11479.3	0.437495	0.218748	−	0.975781i	$-0.429803\pi$
$883$	11479.3	0.437495	0.218748	+	0.975781i	$0.429803\pi$
$884$	7647.88	0.290980
$885$	−129.775	−0.00492919
$886$	27717.8	1.05101
$887$	1165.61	0.0441233	0.0220617	−	0.999757i	$-0.492977\pi$
$887$	1165.61	0.0441233	0.0220617	+	0.999757i	$0.492977\pi$
$888$	−5355.68	−0.202393
$889$	−762.510	−0.0287669
$890$	295.300	0.0111219
$891$	891.000	0.0335013
$892$	8995.11	0.337644
$893$	−9266.02	−0.347229
$894$	−7819.75	−0.292541
$895$	−92.8162	−0.00346648
$896$	1172.72	0.0437254
$897$	−10685.1	−0.397733
$898$	8063.13	0.299633
$899$	−8484.58	−0.314768
$900$	−3510.27	−0.130010
$901$	45842.5	1.69504
$902$	6583.65	0.243028
$903$	−226.026	−0.00832965
$904$	11677.3	0.429623
$905$	141.960	0.00521426
$906$	4017.25	0.147312
$907$	−15556.4	−0.569507	−0.284753	−	0.958601i	$-0.591912\pi$
$907$	−15556.4	−0.569507	−0.284753	+	0.958601i	$0.591912\pi$
$908$	−13021.2	−0.475907
$909$	1623.15	0.0592259
$910$	12.9252	0.000470841 0
$911$	−12940.5	−0.470623	−0.235311	−	0.971920i	$-0.575611\pi$
$911$	−12940.5	−0.470623	−0.235311	+	0.971920i	$0.575611\pi$
$912$	−7737.57	−0.280939
$913$	−7007.88	−0.254027
$914$	3299.92	0.119422
$915$	46.3228	0.00167364
$916$	899.025	0.0324286
$917$	815.494	0.0293675
$918$	−9966.59	−0.358330
$919$	−49602.6	−1.78046	−0.890228	−	0.455516i	$-0.849455\pi$
$919$	−49602.6	−1.78046	−0.890228	+	0.455516i	$0.849455\pi$
$920$	−662.692	−0.0237481
$921$	19431.6	0.695213
$922$	−10075.3	−0.359884
$923$	−5708.40	−0.203569
$924$	−71.2679	−0.00253738
$925$	13710.0	0.487331
$926$	−27521.1	−0.976675
$927$	1911.80	0.0677364
$928$	5476.89	0.193737
$929$	11218.6	0.396199	0.198100	−	0.980182i	$-0.436523\pi$
$929$	11218.6	0.396199	0.198100	+	0.980182i	$0.436523\pi$
$930$	526.020	0.0185472
$931$	−11150.3	−0.392522
$932$	4893.12	0.171974
$933$	−26786.1	−0.939913
$934$	−5316.64	−0.186259
$935$	308.199	0.0107799
$936$	3240.58	0.113164
$937$	−18009.9	−0.627917	−0.313958	−	0.949437i	$-0.601655\pi$
$937$	−18009.9	−0.627917	−0.313958	+	0.949437i	$0.601655\pi$
$938$	−1148.03	−0.0399621
$939$	−29203.7	−1.01494
$940$	−224.930	−0.00780469
$941$	36553.8	1.26633	0.633167	−	0.774015i	$-0.281755\pi$
$941$	36553.8	1.26633	0.633167	+	0.774015i	$0.281755\pi$
$942$	−3416.42	−0.118167
$943$	28880.8	0.997337
$944$	13539.7	0.466822
$945$	−4.72798	−0.000162753 0
$946$	−3995.30	−0.137313
$947$	−51828.5	−1.77846	−0.889228	−	0.457463i	$-0.848758\pi$
$947$	−51828.5	−1.77846	−0.889228	+	0.457463i	$0.848758\pi$
$948$	−6899.23	−0.236368
$949$	26108.5	0.893064
$950$	13563.6	0.463223
$951$	21143.2	0.720941
$952$	−1245.68	−0.0424084
$953$	−32965.0	−1.12051	−0.560253	−	0.828322i	$-0.689296\pi$
$953$	−32965.0	−1.12051	−0.560253	+	0.828322i	$0.689296\pi$
$954$	−12430.9	−0.421873
$955$	1148.59	0.0389188
$956$	−4168.06	−0.141009
$957$	1348.02	0.0455331
$958$	13564.1	0.457450
$959$	1777.62	0.0598563
$960$	141.773	0.00476634
$961$	13350.9	0.448152
$962$	8099.78	0.271463
$963$	9017.45	0.301748
$964$	4716.97	0.157597
$965$	867.293	0.0289318
$966$	−1113.79	−0.0370968
$967$	47083.6	1.56578	0.782888	−	0.622162i	$-0.213746\pi$
$967$	47083.6	1.56578	0.782888	+	0.622162i	$0.213746\pi$
$968$	1968.47	0.0653607
$969$	10809.8	0.358369
$970$	−639.946	−0.0211829
$971$	833.515	0.0275477	0.0137738	−	0.999905i	$-0.495616\pi$
$971$	833.515	0.0275477	0.0137738	+	0.999905i	$0.495616\pi$
$972$	758.608	0.0250333
$973$	240.282	0.00791683
$974$	−34526.4	−1.13583
$975$	−8295.53	−0.272482
$976$	−4832.96	−0.158503
$977$	−27792.2	−0.910084	−0.455042	−	0.890470i	$-0.650376\pi$
$977$	−27792.2	−0.910084	−0.455042	+	0.890470i	$0.650376\pi$
$978$	27344.0	0.894035
$979$	−3847.91	−0.125618
$980$	−270.671	−0.00882273
$981$	−9737.35	−0.316911
$982$	7763.02	0.252269
$983$	9081.47	0.294663	0.147332	−	0.989087i	$-0.452932\pi$
$983$	9081.47	0.294663	0.147332	+	0.989087i	$0.452932\pi$
$984$	−8758.93	−0.283765
$985$	−17.1831	−0.000555835 0
$986$	−15078.7	−0.487022
$987$	590.722	0.0190506
$988$	2249.30	0.0724288
$989$	−17526.4	−0.563505
$990$	−83.5732	−0.00268296
$991$	−29230.5	−0.936969	−0.468484	−	0.883472i	$-0.655200\pi$
$991$	−29230.5	−0.936969	−0.468484	+	0.883472i	$0.655200\pi$
$992$	−27848.6	−0.891323
$993$	−11688.4	−0.373535
$994$	−595.026	−0.0189870
$995$	1038.52	0.0330888
$996$	−5966.59	−0.189818
$997$	−27479.9	−0.872915	−0.436457	−	0.899725i	$-0.643767\pi$
$997$	−27479.9	−0.872915	−0.436457	+	0.899725i	$0.643767\pi$
$998$	53814.6	1.70689
$999$	−2962.87	−0.0938350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.a.1.10	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.a.1.10	✓	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-3.33494 q^{2} +3.00000 q^{3} +3.12184 q^{4} +0.253130 q^{5} -10.0048 q^{6} -0.691781 q^{7} +16.2684 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.33494 q^{2} +3.00000 q^{3} +3.12184 q^{4} +0.253130 q^{5} -10.0048 q^{6} -0.691781 q^{7} +16.2684 q^{8} +9.00000 q^{9} -0.844174 q^{10} +11.0000 q^{11} +9.36553 q^{12} +22.1328 q^{13} +2.30705 q^{14} +0.759390 q^{15} -79.2288 q^{16} +110.686 q^{17} -30.0145 q^{18} +32.5537 q^{19} +0.790232 q^{20} -2.07534 q^{21} -36.6844 q^{22} -160.925 q^{23} +48.8051 q^{24} -124.936 q^{25} -73.8115 q^{26} +27.0000 q^{27} -2.15963 q^{28} +40.8490 q^{29} -2.53252 q^{30} -207.706 q^{31} +134.077 q^{32} +33.0000 q^{33} -369.133 q^{34} -0.175110 q^{35} +28.0966 q^{36} -109.736 q^{37} -108.565 q^{38} +66.3983 q^{39} +4.11801 q^{40} -179.467 q^{41} +6.92115 q^{42} +108.910 q^{43} +34.3403 q^{44} +2.27817 q^{45} +536.676 q^{46} -284.638 q^{47} -237.687 q^{48} -342.521 q^{49} +416.654 q^{50} +332.059 q^{51} +69.0950 q^{52} +414.165 q^{53} -90.0435 q^{54} +2.78443 q^{55} -11.2542 q^{56} +97.6611 q^{57} -136.229 q^{58} -170.894 q^{59} +2.37069 q^{60} +61.0000 q^{61} +692.689 q^{62} -6.22603 q^{63} +186.693 q^{64} +5.60246 q^{65} -110.053 q^{66} -497.617 q^{67} +345.546 q^{68} -482.775 q^{69} +0.583983 q^{70} -257.916 q^{71} +146.415 q^{72} +1179.63 q^{73} +365.964 q^{74} -374.808 q^{75} +101.628 q^{76} -7.60959 q^{77} -221.434 q^{78} -736.662 q^{79} -20.0552 q^{80} +81.0000 q^{81} +598.514 q^{82} -637.080 q^{83} -6.47890 q^{84} +28.0180 q^{85} -363.209 q^{86} +122.547 q^{87} +178.952 q^{88} -349.810 q^{89} -7.59756 q^{90} -15.3110 q^{91} -502.383 q^{92} -623.119 q^{93} +949.252 q^{94} +8.24031 q^{95} +402.230 q^{96} +758.074 q^{97} +1142.29 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9}+O(q^{10}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9	\( 36 q - 14 q^{2} + 108 q^{3} + 146 q^{4} - 65 q^{5} - 42 q^{6} - 105 q^{7} - 189 q^{8} + 324 q^{9} - 161 q^{10} + 396 q^{11} + 438 q^{12} - 233 q^{13} - 264 q^{14} - 195 q^{15} + 574 q^{16} - 556 q^{17} - 126 q^{18} - 615 q^{19} - 136 q^{20} - 315 q^{21} - 154 q^{22} - 457 q^{23} - 567 q^{24} + 863 q^{25} + 115 q^{26} + 972 q^{27} - 424 q^{28} - 754 q^{29} - 483 q^{30} - 508 q^{31} - 1511 q^{32} + 1188 q^{33} - 860 q^{34} - 826 q^{35} + 1314 q^{36} - 412 q^{37} - 599 q^{38} - 699 q^{39} - 2791 q^{40} - 2066 q^{41} - 792 q^{42} - 2063 q^{43} + 1606 q^{44} - 585 q^{45} - 787 q^{46} - 1815 q^{47} + 1722 q^{48} + 2825 q^{49} + 808 q^{50} - 1668 q^{51} - 2882 q^{52} - 759 q^{53} - 378 q^{54} - 715 q^{55} - 1749 q^{56} - 1845 q^{57} - 335 q^{58} - 2337 q^{59} - 408 q^{60} + 2196 q^{61} - 1689 q^{62} - 945 q^{63} + 4723 q^{64} - 3550 q^{65} - 462 q^{66} - 1331 q^{67} - 6166 q^{68} - 1371 q^{69} - 1750 q^{70} - 361 q^{71} - 1701 q^{72} - 4627 q^{73} - 3394 q^{74} + 2589 q^{75} - 7214 q^{76} - 1155 q^{77} + 345 q^{78} - 2583 q^{79} - 2643 q^{80} + 2916 q^{81} + 1090 q^{82} - 6123 q^{83} - 1272 q^{84} + 295 q^{85} + 613 q^{86} - 2262 q^{87} - 2079 q^{88} - 2485 q^{89} - 1449 q^{90} - 3156 q^{91} - 6291 q^{92} - 1524 q^{93} - 1744 q^{94} - 5572 q^{95} - 4533 q^{96} - 2558 q^{97} - 2314 q^{98} + 3564 q^{99}+O(q^{100}) \) 36 * q - 14 * q^2 + 108 * q^3 + 146 * q^4 - 65 * q^5 - 42 * q^6 - 105 * q^7 - 189 * q^8 + 324 * q^9 - 161 * q^10 + 396 * q^11 + 438 * q^12 - 233 * q^13 - 264 * q^14 - 195 * q^15 + 574 * q^16 - 556 * q^17 - 126 * q^18 - 615 * q^19 - 136 * q^20 - 315 * q^21 - 154 * q^22 - 457 * q^23 - 567 * q^24 + 863 * q^25 + 115 * q^26 + 972 * q^27 - 424 * q^28 - 754 * q^29 - 483 * q^30 - 508 * q^31 - 1511 * q^32 + 1188 * q^33 - 860 * q^34 - 826 * q^35 + 1314 * q^36 - 412 * q^37 - 599 * q^38 - 699 * q^39 - 2791 * q^40 - 2066 * q^41 - 792 * q^42 - 2063 * q^43 + 1606 * q^44 - 585 * q^45 - 787 * q^46 - 1815 * q^47 + 1722 * q^48 + 2825 * q^49 + 808 * q^50 - 1668 * q^51 - 2882 * q^52 - 759 * q^53 - 378 * q^54 - 715 * q^55 - 1749 * q^56 - 1845 * q^57 - 335 * q^58 - 2337 * q^59 - 408 * q^60 + 2196 * q^61 - 1689 * q^62 - 945 * q^63 + 4723 * q^64 - 3550 * q^65 - 462 * q^66 - 1331 * q^67 - 6166 * q^68 - 1371 * q^69 - 1750 * q^70 - 361 * q^71 - 1701 * q^72 - 4627 * q^73 - 3394 * q^74 + 2589 * q^75 - 7214 * q^76 - 1155 * q^77 + 345 * q^78 - 2583 * q^79 - 2643 * q^80 + 2916 * q^81 + 1090 * q^82 - 6123 * q^83 - 1272 * q^84 + 295 * q^85 + 613 * q^86 - 2262 * q^87 - 2079 * q^88 - 2485 * q^89 - 1449 * q^90 - 3156 * q^91 - 6291 * q^92 - 1524 * q^93 - 1744 * q^94 - 5572 * q^95 - 4533 * q^96 - 2558 * q^97 - 2314 * q^98 + 3564 * q^99

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