LMFDB - Embedded newform 667.4.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,4,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	667.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:	$39.3542739738$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.110439 q^{2} +4.20263 q^{3} -7.98780 q^{4} -3.45054 q^{5} -0.464136 q^{6} -7.85612 q^{7} +1.76568 q^{8} -9.33789 q^{9} +O(q^{10})$	\(q-0.110439 q^{2} +4.20263 q^{3} -7.98780 q^{4} -3.45054 q^{5} -0.464136 q^{6} -7.85612 q^{7} +1.76568 q^{8} -9.33789 q^{9} +0.381076 q^{10} +35.6867 q^{11} -33.5698 q^{12} +0.661917 q^{13} +0.867625 q^{14} -14.5014 q^{15} +63.7074 q^{16} +114.800 q^{17} +1.03127 q^{18} +71.2702 q^{19} +27.5623 q^{20} -33.0164 q^{21} -3.94122 q^{22} -23.0000 q^{23} +7.42051 q^{24} -113.094 q^{25} -0.0731017 q^{26} -152.715 q^{27} +62.7532 q^{28} +29.0000 q^{29} +1.60152 q^{30} -236.014 q^{31} -21.1613 q^{32} +149.978 q^{33} -12.6784 q^{34} +27.1079 q^{35} +74.5892 q^{36} -205.453 q^{37} -7.87104 q^{38} +2.78179 q^{39} -6.09257 q^{40} -286.082 q^{41} +3.64631 q^{42} -440.240 q^{43} -285.058 q^{44} +32.2208 q^{45} +2.54011 q^{46} -56.3533 q^{47} +267.739 q^{48} -281.281 q^{49} +12.4900 q^{50} +482.462 q^{51} -5.28726 q^{52} -234.635 q^{53} +16.8657 q^{54} -123.139 q^{55} -13.8714 q^{56} +299.522 q^{57} -3.20274 q^{58} +332.601 q^{59} +115.834 q^{60} +145.796 q^{61} +26.0652 q^{62} +73.3596 q^{63} -507.322 q^{64} -2.28397 q^{65} -16.5635 q^{66} +82.6146 q^{67} -917.000 q^{68} -96.6605 q^{69} -2.99378 q^{70} -761.095 q^{71} -16.4878 q^{72} -1005.46 q^{73} +22.6901 q^{74} -475.291 q^{75} -569.292 q^{76} -280.359 q^{77} -0.307220 q^{78} +286.628 q^{79} -219.825 q^{80} -389.681 q^{81} +31.5947 q^{82} +1256.65 q^{83} +263.728 q^{84} -396.122 q^{85} +48.6198 q^{86} +121.876 q^{87} +63.0114 q^{88} -60.2062 q^{89} -3.55845 q^{90} -5.20010 q^{91} +183.719 q^{92} -991.880 q^{93} +6.22362 q^{94} -245.921 q^{95} -88.9330 q^{96} -723.526 q^{97} +31.0645 q^{98} -333.238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) $ 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9 + 30 * q^10 - 100 * q^11 - 173 * q^12 - 160 * q^13 - 304 * q^14 - 208 * q^15 + 552 * q^16 - 666 * q^17 - 315 * q^18 - 252 * q^19 - 747 * q^20 - 470 * q^21 - 323 * q^22 - 874 * q^23 - 114 * q^24 + 910 * q^25 - 119 * q^26 - 526 * q^27 - 619 * q^28 + 1102 * q^29 - 533 * q^30 + 358 * q^31 - 1272 * q^32 - 604 * q^33 - 553 * q^34 + 16 * q^35 + 1230 * q^36 - 1206 * q^37 - 2010 * q^38 - 240 * q^39 - 418 * q^40 - 1094 * q^41 - 1184 * q^42 - 936 * q^43 - 2153 * q^44 - 3654 * q^45 + 184 * q^46 - 1702 * q^47 - 1319 * q^48 + 1920 * q^49 - 1255 * q^50 - 270 * q^51 - 2202 * q^52 - 4640 * q^53 - 1529 * q^54 - 318 * q^55 - 2435 * q^56 - 1980 * q^57 - 232 * q^58 + 318 * q^59 - 3279 * q^60 - 2212 * q^61 - 541 * q^62 - 1044 * q^63 + 1186 * q^64 - 2438 * q^65 - 3503 * q^66 - 496 * q^67 - 6099 * q^68 + 368 * q^69 + 4068 * q^70 + 870 * q^71 - 3869 * q^72 - 2810 * q^73 - 2793 * q^74 - 3638 * q^75 + 1548 * q^76 - 6072 * q^77 + 2170 * q^78 - 3084 * q^79 - 6702 * q^80 + 362 * q^81 - 1183 * q^82 - 5566 * q^83 - 6518 * q^84 - 120 * q^85 - 2095 * q^86 - 464 * q^87 - 1220 * q^88 - 6506 * q^89 + 165 * q^90 + 44 * q^91 - 3496 * q^92 - 5928 * q^93 + 135 * q^94 - 2024 * q^95 - 3164 * q^96 - 7472 * q^97 - 6422 * q^98 - 944 * 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 $

$2$	−0.110439	−0.0390462	−0.0195231	−	0.999809i	$-0.506215\pi$
$2$	−0.110439	−0.0390462	−0.0195231	+	0.999809i	$0.506215\pi$
$3$	4.20263	0.808797	0.404398	−	0.914583i	$-0.367481\pi$
$3$	4.20263	0.808797	0.404398	+	0.914583i	$0.367481\pi$
$4$	−7.98780	−0.998475
$5$	−3.45054	−0.308626	−0.154313	−	0.988022i	$-0.549316\pi$
$5$	−3.45054	−0.308626	−0.154313	+	0.988022i	$0.549316\pi$
$6$	−0.464136	−0.0315805
$7$	−7.85612	−0.424191	−0.212095	−	0.977249i	$-0.568029\pi$
$7$	−7.85612	−0.424191	−0.212095	+	0.977249i	$0.568029\pi$
$8$	1.76568	0.0780329
$9$	−9.33789	−0.345848
$10$	0.381076	0.0120507
$11$	35.6867	0.978177	0.489088	−	0.872234i	$-0.337330\pi$
$11$	35.6867	0.978177	0.489088	+	0.872234i	$0.337330\pi$
$12$	−33.5698	−0.807564
$13$	0.661917	0.0141218	0.00706088	−	0.999975i	$-0.497752\pi$
$13$	0.661917	0.0141218	0.00706088	+	0.999975i	$0.497752\pi$
$14$	0.867625	0.0165630
$15$	−14.5014	−0.249616
$16$	63.7074	0.995429
$17$	114.800	1.63783	0.818914	−	0.573916i	$-0.194576\pi$
$17$	114.800	1.63783	0.818914	+	0.573916i	$0.194576\pi$
$18$	1.03127	0.0135040
$19$	71.2702	0.860553	0.430277	−	0.902697i	$-0.358416\pi$
$19$	71.2702	0.860553	0.430277	+	0.902697i	$0.358416\pi$
$20$	27.5623	0.308156
$21$	−33.0164	−0.343084
$22$	−3.94122	−0.0381941
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	7.42051	0.0631128
$25$	−113.094	−0.904750
$26$	−0.0731017	−0.000551401 0
$27$	−152.715	−1.08852
$28$	62.7532	0.423544
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	1.60152	0.00974655
$31$	−236.014	−1.36740	−0.683699	−	0.729764i	$-0.739630\pi$
$31$	−236.014	−1.36740	−0.683699	+	0.729764i	$0.739630\pi$
$32$	−21.1613	−0.116901
$33$	149.978	0.791146
$34$	−12.6784	−0.0639510
$35$	27.1079	0.130916
$36$	74.5892	0.345320
$37$	−205.453	−0.912871	−0.456435	−	0.889757i	$-0.650874\pi$
$37$	−205.453	−0.912871	−0.456435	+	0.889757i	$0.650874\pi$
$38$	−7.87104	−0.0336013
$39$	2.78179	0.0114216
$40$	−6.09257	−0.0240830
$41$	−286.082	−1.08972	−0.544859	−	0.838527i	$-0.683417\pi$
$41$	−286.082	−1.08972	−0.544859	+	0.838527i	$0.683417\pi$
$42$	3.64631	0.0133961
$43$	−440.240	−1.56130	−0.780650	−	0.624968i	$-0.785112\pi$
$43$	−440.240	−1.56130	−0.780650	+	0.624968i	$0.785112\pi$
$44$	−285.058	−0.976686
$45$	32.2208	0.106738
$46$	2.54011	0.00814170
$47$	−56.3533	−0.174893	−0.0874465	−	0.996169i	$-0.527871\pi$
$47$	−56.3533	−0.174893	−0.0874465	+	0.996169i	$0.527871\pi$
$48$	267.739	0.805099
$49$	−281.281	−0.820062
$50$	12.4900	0.0353271
$51$	482.462	1.32467
$52$	−5.28726	−0.0141002
$53$	−234.635	−0.608105	−0.304053	−	0.952655i	$-0.598340\pi$
$53$	−234.635	−0.608105	−0.304053	+	0.952655i	$0.598340\pi$
$54$	16.8657	0.0425025
$55$	−123.139	−0.301891
$56$	−13.8714	−0.0331008
$57$	299.522	0.696013
$58$	−3.20274	−0.00725070
$59$	332.601	0.733914	0.366957	−	0.930238i	$-0.380400\pi$
$59$	332.601	0.733914	0.366957	+	0.930238i	$0.380400\pi$
$60$	115.834	0.249235
$61$	145.796	0.306020	0.153010	−	0.988225i	$-0.451103\pi$
$61$	145.796	0.306020	0.153010	+	0.988225i	$0.451103\pi$
$62$	26.0652	0.0533917
$63$	73.3596	0.146705
$64$	−507.322	−0.990864
$65$	−2.28397	−0.00435834
$66$	−16.5635	−0.0308913
$67$	82.6146	0.150641	0.0753207	−	0.997159i	$-0.476002\pi$
$67$	82.6146	0.150641	0.0753207	+	0.997159i	$0.476002\pi$
$68$	−917.000	−1.63533
$69$	−96.6605	−0.168646
$70$	−2.99378	−0.00511179
$71$	−761.095	−1.27219	−0.636094	−	0.771612i	$-0.719451\pi$
$71$	−761.095	−1.27219	−0.636094	+	0.771612i	$0.719451\pi$
$72$	−16.4878	−0.0269875
$73$	−1005.46	−1.61205	−0.806025	−	0.591881i	$-0.798385\pi$
$73$	−1005.46	−1.61205	−0.806025	+	0.591881i	$0.798385\pi$
$74$	22.6901	0.0356442
$75$	−475.291	−0.731759
$76$	−569.292	−0.859241
$77$	−280.359	−0.414934
$78$	−0.307220	−0.000445971 0
$79$	286.628	0.408205	0.204102	−	0.978950i	$-0.434572\pi$
$79$	286.628	0.408205	0.204102	+	0.978950i	$0.434572\pi$
$80$	−219.825	−0.307215
$81$	−389.681	−0.534542
$82$	31.5947	0.0425494
$83$	1256.65	1.66187	0.830937	−	0.556367i	$-0.187805\pi$
$83$	1256.65	1.66187	0.830937	+	0.556367i	$0.187805\pi$
$84$	263.728	0.342561
$85$	−396.122	−0.505477
$86$	48.6198	0.0609629
$87$	121.876	0.150190
$88$	63.0114	0.0763300
$89$	−60.2062	−0.0717061	−0.0358531	−	0.999357i	$-0.511415\pi$
$89$	−60.2062	−0.0717061	−0.0358531	+	0.999357i	$0.511415\pi$
$90$	−3.55845	−0.00416770
$91$	−5.20010	−0.00599032
$92$	183.719	0.208197
$93$	−991.880	−1.10595
$94$	6.22362	0.00682891
$95$	−245.921	−0.265589
$96$	−88.9330	−0.0945488
$97$	−723.526	−0.757350	−0.378675	−	0.925530i	$-0.623620\pi$
$97$	−723.526	−0.757350	−0.378675	+	0.925530i	$0.623620\pi$
$98$	31.0645	0.0320203
$99$	−333.238	−0.338300
$100$	903.371	0.903371
$101$	1335.46	1.31567	0.657836	−	0.753161i	$-0.271472\pi$
$101$	1335.46	1.31567	0.657836	+	0.753161i	$0.271472\pi$
$102$	−53.2828	−0.0517234
$103$	980.265	0.937751	0.468876	−	0.883264i	$-0.344659\pi$
$103$	980.265	0.937751	0.468876	+	0.883264i	$0.344659\pi$
$104$	1.16874	0.00110196
$105$	113.925	0.105885
$106$	25.9129	0.0237442
$107$	−1439.29	−1.30039	−0.650196	−	0.759767i	$-0.725313\pi$
$107$	−1439.29	−1.30039	−0.650196	+	0.759767i	$0.725313\pi$
$108$	1219.86	1.08686
$109$	1000.77	0.879413	0.439706	−	0.898142i	$-0.355083\pi$
$109$	1000.77	0.879413	0.439706	+	0.898142i	$0.355083\pi$
$110$	13.5993	0.0117877
$111$	−863.442	−0.738327
$112$	−500.493	−0.422252
$113$	1505.67	1.25347	0.626733	−	0.779234i	$-0.284392\pi$
$113$	1505.67	1.25347	0.626733	+	0.779234i	$0.284392\pi$
$114$	−33.0791	−0.0271767
$115$	79.3625	0.0643530
$116$	−231.646	−0.185412
$117$	−6.18091	−0.00488398
$118$	−36.7322	−0.0286566
$119$	−901.883	−0.694752
$120$	−25.6048	−0.0194782
$121$	−57.4592	−0.0431699
$122$	−16.1016	−0.0119489
$123$	−1202.30	−0.881361
$124$	1885.23	1.36531
$125$	821.553	0.587855
$126$	−8.10179	−0.00572829
$127$	−2331.74	−1.62920	−0.814600	−	0.580024i	$-0.803043\pi$
$127$	−2331.74	−1.62920	−0.814600	+	0.580024i	$0.803043\pi$
$128$	225.319	0.155590
$129$	−1850.16	−1.26277
$130$	0.252241	0.000170177 0
$131$	−363.088	−0.242161	−0.121081	−	0.992643i	$-0.538636\pi$
$131$	−363.088	−0.242161	−0.121081	+	0.992643i	$0.538636\pi$
$132$	−1198.00	−0.789940
$133$	−559.908	−0.365039
$134$	−9.12390	−0.00588198
$135$	526.949	0.335945
$136$	202.700	0.127805
$137$	2106.07	1.31338	0.656692	−	0.754159i	$-0.271955\pi$
$137$	2106.07	1.31338	0.656692	+	0.754159i	$0.271955\pi$
$138$	10.6751	0.00658498
$139$	1085.51	0.662389	0.331194	−	0.943563i	$-0.392548\pi$
$139$	1085.51	0.662389	0.331194	+	0.943563i	$0.392548\pi$
$140$	−216.533	−0.130717
$141$	−236.832	−0.141453
$142$	84.0548	0.0496741
$143$	23.6216	0.0138136
$144$	−594.893	−0.344267
$145$	−100.066	−0.0573104
$146$	111.042	0.0629445
$147$	−1182.12	−0.663264
$148$	1641.12	0.911479
$149$	971.844	0.534340	0.267170	−	0.963649i	$-0.413912\pi$
$149$	971.844	0.534340	0.267170	+	0.963649i	$0.413912\pi$
$150$	52.4909	0.0285724
$151$	−2606.93	−1.40496	−0.702481	−	0.711702i	$-0.747924\pi$
$151$	−2606.93	−1.40496	−0.702481	+	0.711702i	$0.747924\pi$
$152$	125.841	0.0671515
$153$	−1071.99	−0.566439
$154$	30.9627	0.0162016
$155$	814.376	0.422015
$156$	−22.2204	−0.0114042
$157$	−1723.06	−0.875893	−0.437947	−	0.899001i	$-0.644294\pi$
$157$	−1723.06	−0.875893	−0.437947	+	0.899001i	$0.644294\pi$
$158$	−31.6550	−0.0159388
$159$	−986.084	−0.491834
$160$	73.0179	0.0360786
$161$	180.691	0.0884499
$162$	43.0361	0.0208718
$163$	−2370.59	−1.13914	−0.569568	−	0.821944i	$-0.692889\pi$
$163$	−2370.59	−1.13914	−0.569568	+	0.821944i	$0.692889\pi$
$164$	2285.17	1.08806
$165$	−517.506	−0.244168
$166$	−138.784	−0.0648899
$167$	−1246.97	−0.577806	−0.288903	−	0.957358i	$-0.593290\pi$
$167$	−1246.97	−0.577806	−0.288903	+	0.957358i	$0.593290\pi$
$168$	−58.2965	−0.0267719
$169$	−2196.56	−0.999801
$170$	43.7475	0.0197369
$171$	−665.513	−0.297620
$172$	3516.55	1.55892
$173$	−3035.82	−1.33416	−0.667078	−	0.744988i	$-0.732455\pi$
$173$	−3035.82	−1.33416	−0.667078	+	0.744988i	$0.732455\pi$
$174$	−13.4599	−0.00586434
$175$	888.478	0.383787
$176$	2273.51	0.973705
$177$	1397.80	0.593588
$178$	6.64914	0.00279985
$179$	2148.80	0.897255	0.448627	−	0.893719i	$-0.351913\pi$
$179$	2148.80	0.897255	0.448627	+	0.893719i	$0.351913\pi$
$180$	−257.373	−0.106575
$181$	−781.942	−0.321112	−0.160556	−	0.987027i	$-0.551329\pi$
$181$	−781.942	−0.321112	−0.160556	+	0.987027i	$0.551329\pi$
$182$	0.574296	0.000233899 0
$183$	612.725	0.247508
$184$	−40.6107	−0.0162710
$185$	708.924	0.281736
$186$	109.543	0.0431831
$187$	4096.83	1.60209
$188$	450.139	0.174626
$189$	1199.75	0.461739
$190$	27.1594	0.0103702
$191$	−1719.31	−0.651336	−0.325668	−	0.945484i	$-0.605589\pi$
$191$	−1719.31	−0.651336	−0.325668	+	0.945484i	$0.605589\pi$
$192$	−2132.09	−0.801408
$193$	1655.79	0.617545	0.308772	−	0.951136i	$-0.400082\pi$
$193$	1655.79	0.617545	0.308772	+	0.951136i	$0.400082\pi$
$194$	79.9058	0.0295716
$195$	−9.59870	−0.00352501
$196$	2246.82	0.818812
$197$	−3425.83	−1.23899	−0.619494	−	0.785001i	$-0.712662\pi$
$197$	−3425.83	−1.23899	−0.619494	+	0.785001i	$0.712662\pi$
$198$	36.8027	0.0132093
$199$	−1023.27	−0.364510	−0.182255	−	0.983251i	$-0.558340\pi$
$199$	−1023.27	−0.364510	−0.182255	+	0.983251i	$0.558340\pi$
$200$	−199.688	−0.0706003
$201$	347.199	0.121838
$202$	−147.487	−0.0513720
$203$	−227.828	−0.0787702
$204$	−3853.81	−1.32265
$205$	987.138	0.336316
$206$	−108.260	−0.0366156
$207$	214.771	0.0721142
$208$	42.1690	0.0140572
$209$	2543.40	0.841773
$210$	−12.5818	−0.00413440
$211$	−1868.18	−0.609528	−0.304764	−	0.952428i	$-0.598578\pi$
$211$	−1868.18	−0.609528	−0.304764	+	0.952428i	$0.598578\pi$
$212$	1874.22	0.607178
$213$	−3198.60	−1.02894
$214$	158.955	0.0507754
$215$	1519.07	0.481858
$216$	−269.646	−0.0849402
$217$	1854.15	0.580038
$218$	−110.524	−0.0343377
$219$	−4225.56	−1.30382
$220$	983.606	0.301431
$221$	75.9881	0.0231290
$222$	95.3580	0.0288289
$223$	−3791.46	−1.13854	−0.569271	−	0.822150i	$-0.692775\pi$
$223$	−3791.46	−1.13854	−0.569271	+	0.822150i	$0.692775\pi$
$224$	166.246	0.0495882
$225$	1056.06	0.312906
$226$	−166.285	−0.0489431
$227$	−798.986	−0.233615	−0.116807	−	0.993155i	$-0.537266\pi$
$227$	−798.986	−0.233615	−0.116807	+	0.993155i	$0.537266\pi$
$228$	−2392.53	−0.694951
$229$	−144.212	−0.0416149	−0.0208074	−	0.999784i	$-0.506624\pi$
$229$	−144.212	−0.0416149	−0.0208074	+	0.999784i	$0.506624\pi$
$230$	−8.76475	−0.00251274
$231$	−1178.25	−0.335597
$232$	51.2048	0.0144903
$233$	−3597.41	−1.01148	−0.505739	−	0.862687i	$-0.668780\pi$
$233$	−3597.41	−1.01148	−0.505739	+	0.862687i	$0.668780\pi$
$234$	0.682616	0.000190701 0
$235$	194.449	0.0539765
$236$	−2656.75	−0.732795
$237$	1204.59	0.330155
$238$	99.6034	0.0271274
$239$	2218.12	0.600326	0.300163	−	0.953888i	$-0.402959\pi$
$239$	2218.12	0.600326	0.300163	+	0.953888i	$0.402959\pi$
$240$	−923.845	−0.248475
$241$	−488.166	−0.130479	−0.0652396	−	0.997870i	$-0.520781\pi$
$241$	−488.166	−0.130479	−0.0652396	+	0.997870i	$0.520781\pi$
$242$	6.34576	0.00168562
$243$	2485.61	0.656182
$244$	−1164.59	−0.305553
$245$	970.574	0.253093
$246$	132.781	0.0344138
$247$	47.1750	0.0121525
$248$	−416.726	−0.106702
$249$	5281.25	1.34412
$250$	−90.7318	−0.0229535
$251$	1661.52	0.417827	0.208913	−	0.977934i	$-0.433007\pi$
$251$	1661.52	0.417827	0.208913	+	0.977934i	$0.433007\pi$
$252$	−585.982	−0.146482
$253$	−820.794	−0.203964
$254$	257.516	0.0636141
$255$	−1664.76	−0.408828
$256$	4033.69	0.984789
$257$	3991.49	0.968803	0.484402	−	0.874846i	$-0.339037\pi$
$257$	3991.49	0.968803	0.484402	+	0.874846i	$0.339037\pi$
$258$	204.331	0.0493066
$259$	1614.06	0.387231
$260$	18.2439	0.00435170
$261$	−270.799	−0.0642223
$262$	40.0992	0.00945548
$263$	−7810.36	−1.83121	−0.915604	−	0.402082i	$-0.868287\pi$
$263$	−7810.36	−1.83121	−0.915604	+	0.402082i	$0.868287\pi$
$264$	264.814	0.0617354
$265$	809.618	0.187677
$266$	61.8358	0.0142534
$267$	−253.025	−0.0579957
$268$	−659.909	−0.150412
$269$	3338.26	0.756645	0.378322	−	0.925674i	$-0.376501\pi$
$269$	3338.26	0.756645	0.378322	+	0.925674i	$0.376501\pi$
$270$	−58.1959	−0.0131174
$271$	−488.204	−0.109433	−0.0547164	−	0.998502i	$-0.517425\pi$
$271$	−488.204	−0.109433	−0.0547164	+	0.998502i	$0.517425\pi$
$272$	7313.61	1.63034
$273$	−21.8541	−0.00484495
$274$	−232.593	−0.0512827
$275$	−4035.94	−0.885006
$276$	772.105	0.168389
$277$	−3517.70	−0.763025	−0.381512	−	0.924364i	$-0.624597\pi$
$277$	−3517.70	−0.763025	−0.381512	+	0.924364i	$0.624597\pi$
$278$	−119.883	−0.0258638
$279$	2203.87	0.472912
$280$	47.8640	0.0102158
$281$	−7771.51	−1.64986	−0.824928	−	0.565238i	$-0.808784\pi$
$281$	−7771.51	−1.64986	−0.824928	+	0.565238i	$0.808784\pi$
$282$	26.1556	0.00552320
$283$	6286.76	1.32053	0.660264	−	0.751034i	$-0.270444\pi$
$283$	6286.76	1.32053	0.660264	+	0.751034i	$0.270444\pi$
$284$	6079.47	1.27025
$285$	−1033.52	−0.214808
$286$	−2.60876	−0.000539368 0
$287$	2247.49	0.462249
$288$	197.602	0.0404298
$289$	8266.04	1.68248
$290$	11.0512	0.00223776
$291$	−3040.71	−0.612542
$292$	8031.38	1.60959
$293$	4145.56	0.826574	0.413287	−	0.910601i	$-0.364381\pi$
$293$	4145.56	0.826574	0.413287	+	0.910601i	$0.364381\pi$
$294$	130.553	0.0258979
$295$	−1147.65	−0.226505
$296$	−362.764	−0.0712340
$297$	−5449.89	−1.06476
$298$	−107.330	−0.0208639
$299$	−15.2241	−0.00294459
$300$	3796.53	0.730643
$301$	3458.58	0.662289
$302$	287.908	0.0548585
$303$	5612.43	1.06411
$304$	4540.44	0.856619
$305$	−503.074	−0.0944457
$306$	118.390	0.0221173
$307$	−619.109	−0.115096	−0.0575479	−	0.998343i	$-0.518328\pi$
$307$	−619.109	−0.115096	−0.0575479	+	0.998343i	$0.518328\pi$
$308$	2239.45	0.414301
$309$	4119.69	0.758450
$310$	−89.9392	−0.0164781
$311$	1005.49	0.183331	0.0916654	−	0.995790i	$-0.470781\pi$
$311$	1005.49	0.183331	0.0916654	+	0.995790i	$0.470781\pi$
$312$	4.91177	0.000891263 0
$313$	1286.73	0.232365	0.116183	−	0.993228i	$-0.462934\pi$
$313$	1286.73	0.232365	0.116183	+	0.993228i	$0.462934\pi$
$314$	190.294	0.0342003
$315$	−253.131	−0.0452771
$316$	−2289.53	−0.407582
$317$	6520.15	1.15523	0.577616	−	0.816309i	$-0.303983\pi$
$317$	6520.15	1.15523	0.577616	+	0.816309i	$0.303983\pi$
$318$	108.903	0.0192042
$319$	1034.91	0.181643
$320$	1750.54	0.305806
$321$	−6048.83	−1.05175
$322$	−19.9554	−0.00345363
$323$	8181.82	1.40944
$324$	3112.69	0.533727
$325$	−74.8587	−0.0127767
$326$	261.807	0.0444789
$327$	4205.85	0.711266
$328$	−505.130	−0.0850339
$329$	442.718	0.0741880
$330$	57.1530	0.00953385
$331$	816.048	0.135511	0.0677554	−	0.997702i	$-0.478416\pi$
$331$	816.048	0.135511	0.0677554	+	0.997702i	$0.478416\pi$
$332$	−10037.9	−1.65934
$333$	1918.49	0.315714
$334$	137.715	0.0225611
$335$	−285.065	−0.0464919
$336$	−2103.39	−0.341516
$337$	2560.49	0.413883	0.206942	−	0.978353i	$-0.433649\pi$
$337$	2560.49	0.413883	0.206942	+	0.978353i	$0.433649\pi$
$338$	242.587	0.0390384
$339$	6327.78	1.01380
$340$	3164.15	0.504706
$341$	−8422.56	−1.33756
$342$	73.4989	0.0116209
$343$	4904.43	0.772054
$344$	−777.324	−0.121833
$345$	333.531	0.0520485
$346$	335.274	0.0520937
$347$	−5511.10	−0.852597	−0.426299	−	0.904582i	$-0.640183\pi$
$347$	−5511.10	−0.852597	−0.426299	+	0.904582i	$0.640183\pi$
$348$	−973.524	−0.149961
$349$	376.361	0.0577254	0.0288627	−	0.999583i	$-0.490811\pi$
$349$	376.361	0.0577254	0.0288627	+	0.999583i	$0.490811\pi$
$350$	−98.1230	−0.0149854
$351$	−101.085	−0.0153718
$352$	−755.176	−0.114349
$353$	2282.38	0.344133	0.172067	−	0.985085i	$-0.444956\pi$
$353$	2282.38	0.344133	0.172067	+	0.985085i	$0.444956\pi$
$354$	−154.372	−0.0231773
$355$	2626.19	0.392630
$356$	480.915	0.0715968
$357$	−3790.28	−0.561913
$358$	−237.312	−0.0350344
$359$	7436.18	1.09322	0.546611	−	0.837387i	$-0.315918\pi$
$359$	7436.18	1.09322	0.546611	+	0.837387i	$0.315918\pi$
$360$	56.8917	0.00832905
$361$	−1779.56	−0.259448
$362$	86.3572	0.0125382
$363$	−241.480	−0.0349157
$364$	41.5374	0.00598118
$365$	3469.37	0.497521
$366$	−67.6689	−0.00966424
$367$	−3654.64	−0.519810	−0.259905	−	0.965634i	$-0.583691\pi$
$367$	−3654.64	−0.519810	−0.259905	+	0.965634i	$0.583691\pi$
$368$	−1465.27	−0.207561
$369$	2671.40	0.376877
$370$	−78.2931	−0.0110007
$371$	1843.32	0.257953
$372$	7922.94	1.10426
$373$	2291.96	0.318158	0.159079	−	0.987266i	$-0.449147\pi$
$373$	2291.96	0.318158	0.159079	+	0.987266i	$0.449147\pi$
$374$	−452.452	−0.0625554
$375$	3452.68	0.475456
$376$	−99.5020	−0.0136474
$377$	19.1956	0.00262234
$378$	−132.499	−0.0180292
$379$	−4798.72	−0.650379	−0.325190	−	0.945649i	$-0.605428\pi$
$379$	−4798.72	−0.650379	−0.325190	+	0.945649i	$0.605428\pi$
$380$	1964.37	0.265184
$381$	−9799.44	−1.31769
$382$	189.880	0.0254322
$383$	−6009.08	−0.801697	−0.400848	−	0.916144i	$-0.631285\pi$
$383$	−6009.08	−0.801697	−0.400848	+	0.916144i	$0.631285\pi$
$384$	946.931	0.125841
$385$	967.392	0.128059
$386$	−182.864	−0.0241128
$387$	4110.91	0.539972
$388$	5779.38	0.756195
$389$	−3726.56	−0.485717	−0.242858	−	0.970062i	$-0.578085\pi$
$389$	−3726.56	−0.485717	−0.242858	+	0.970062i	$0.578085\pi$
$390$	1.06007	0.000137638 0
$391$	−2640.40	−0.341511
$392$	−496.654	−0.0639918
$393$	−1525.92	−0.195859
$394$	378.347	0.0483778
$395$	−989.022	−0.125983
$396$	2661.84	0.337785
$397$	7833.46	0.990303	0.495151	−	0.868807i	$-0.335113\pi$
$397$	7833.46	0.990303	0.495151	+	0.868807i	$0.335113\pi$
$398$	113.009	0.0142327
$399$	−2353.09	−0.295242
$400$	−7204.91	−0.900614
$401$	11103.4	1.38274	0.691370	−	0.722501i	$-0.257008\pi$
$401$	11103.4	1.38274	0.691370	+	0.722501i	$0.257008\pi$
$402$	−38.3444	−0.00475733
$403$	−156.222	−0.0193101
$404$	−10667.4	−1.31367
$405$	1344.61	0.164973
$406$	25.1611	0.00307568
$407$	−7331.93	−0.892949
$408$	851.875	0.103368
$409$	5674.54	0.686034	0.343017	−	0.939329i	$-0.388551\pi$
$409$	5674.54	0.686034	0.343017	+	0.939329i	$0.388551\pi$
$410$	−109.019	−0.0131319
$411$	8851.04	1.06226
$412$	−7830.17	−0.936322
$413$	−2612.95	−0.311320
$414$	−23.7192	−0.00281579
$415$	−4336.13	−0.512897
$416$	−14.0070	−0.00165084
$417$	4562.01	0.535738
$418$	−280.891	−0.0328681
$419$	12811.5	1.49375	0.746877	−	0.664962i	$-0.231552\pi$
$419$	12811.5	1.49375	0.746877	+	0.664962i	$0.231552\pi$
$420$	−910.007	−0.105723
$421$	−12342.2	−1.42879	−0.714397	−	0.699741i	$-0.753299\pi$
$421$	−12342.2	−1.42879	−0.714397	+	0.699741i	$0.753299\pi$
$422$	206.320	0.0237998
$423$	526.221	0.0604864
$424$	−414.291	−0.0474522
$425$	−12983.2	−1.48183
$426$	353.251	0.0401763
$427$	−1145.39	−0.129811
$428$	11496.8	1.29841
$429$	99.2730	0.0111724
$430$	−167.765	−0.0188147
$431$	1215.74	0.135871	0.0679353	−	0.997690i	$-0.478359\pi$
$431$	1215.74	0.135871	0.0679353	+	0.997690i	$0.478359\pi$
$432$	−9729.06	−1.08354
$433$	13356.8	1.48241	0.741206	−	0.671277i	$-0.234254\pi$
$433$	13356.8	1.48241	0.741206	+	0.671277i	$0.234254\pi$
$434$	−204.772	−0.0226483
$435$	−420.540	−0.0463525
$436$	−7993.92	−0.878072
$437$	−1639.21	−0.179438
$438$	466.668	0.0509093
$439$	−11276.3	−1.22595	−0.612973	−	0.790104i	$-0.710026\pi$
$439$	−11276.3	−1.22595	−0.612973	+	0.790104i	$0.710026\pi$
$440$	−217.424	−0.0235574
$441$	2626.57	0.283617
$442$	−8.39208	−0.000903100 0
$443$	15440.3	1.65596	0.827981	−	0.560756i	$-0.189490\pi$
$443$	15440.3	1.65596	0.827981	+	0.560756i	$0.189490\pi$
$444$	6897.01	0.737201
$445$	207.744	0.0221304
$446$	418.727	0.0444558
$447$	4084.30	0.432172
$448$	3985.59	0.420315
$449$	−4370.71	−0.459391	−0.229695	−	0.973263i	$-0.573773\pi$
$449$	−4370.71	−0.459391	−0.229695	+	0.973263i	$0.573773\pi$
$450$	−116.630	−0.0122178
$451$	−10209.3	−1.06594
$452$	−12027.0	−1.25156
$453$	−10956.0	−1.13633
$454$	88.2395	0.00912178
$455$	17.9432	0.00184877
$456$	528.862	0.0543119
$457$	11860.8	1.21406	0.607032	−	0.794678i	$-0.292360\pi$
$457$	11860.8	1.21406	0.607032	+	0.794678i	$0.292360\pi$
$458$	15.9267	0.00162490
$459$	−17531.7	−1.78280
$460$	−633.932	−0.0642549
$461$	5157.41	0.521051	0.260526	−	0.965467i	$-0.416104\pi$
$461$	5157.41	0.521051	0.260526	+	0.965467i	$0.416104\pi$
$462$	130.125	0.0131038
$463$	3264.51	0.327677	0.163839	−	0.986487i	$-0.447612\pi$
$463$	3264.51	0.327677	0.163839	+	0.986487i	$0.447612\pi$
$464$	1847.52	0.184846
$465$	3422.52	0.341324
$466$	397.296	0.0394944
$467$	−13171.5	−1.30515	−0.652575	−	0.757724i	$-0.726311\pi$
$467$	−13171.5	−1.30515	−0.652575	+	0.757724i	$0.726311\pi$
$468$	49.3719	0.00487653
$469$	−649.030	−0.0639007
$470$	−21.4749	−0.00210758
$471$	−7241.39	−0.708420
$472$	587.268	0.0572695
$473$	−15710.7	−1.52723
$474$	−133.034	−0.0128913
$475$	−8060.22	−0.778585
$476$	7204.06	0.693693
$477$	2190.99	0.210312
$478$	−244.967	−0.0234405
$479$	−19235.9	−1.83489	−0.917444	−	0.397864i	$-0.869752\pi$
$479$	−19235.9	−1.83489	−0.917444	+	0.397864i	$0.869752\pi$
$480$	306.867	0.0291802
$481$	−135.993	−0.0128913
$482$	53.9127	0.00509472
$483$	759.377	0.0715380
$484$	458.973	0.0431041
$485$	2496.56	0.233738
$486$	−274.510	−0.0256214
$487$	−17743.5	−1.65100	−0.825500	−	0.564402i	$-0.809107\pi$
$487$	−17743.5	−1.65100	−0.825500	+	0.564402i	$0.809107\pi$
$488$	257.429	0.0238796
$489$	−9962.72	−0.921329
$490$	−107.190	−0.00988231
$491$	−16676.0	−1.53274	−0.766372	−	0.642397i	$-0.777940\pi$
$491$	−16676.0	−1.53274	−0.766372	+	0.642397i	$0.777940\pi$
$492$	9603.71	0.880017
$493$	3329.20	0.304137
$494$	−5.20997	−0.000474510 0
$495$	1149.85	0.104408
$496$	−15035.8	−1.36115
$497$	5979.25	0.539650
$498$	−583.258	−0.0524827
$499$	20334.6	1.82425	0.912125	−	0.409913i	$-0.134441\pi$
$499$	20334.6	1.82425	0.912125	+	0.409913i	$0.134441\pi$
$500$	−6562.40	−0.586959
$501$	−5240.56	−0.467327
$502$	−183.498	−0.0163146
$503$	10130.0	0.897963	0.448981	−	0.893541i	$-0.351787\pi$
$503$	10130.0	0.897963	0.448981	+	0.893541i	$0.351787\pi$
$504$	129.530	0.0114478
$505$	−4608.05	−0.406051
$506$	90.6480	0.00796402
$507$	−9231.34	−0.808635
$508$	18625.5	1.62672
$509$	304.237	0.0264933	0.0132466	−	0.999912i	$-0.495783\pi$
$509$	304.237	0.0264933	0.0132466	+	0.999912i	$0.495783\pi$
$510$	183.855	0.0159632
$511$	7898.98	0.683817
$512$	−2248.03	−0.194042
$513$	−10884.0	−0.936727
$514$	−440.818	−0.0378281
$515$	−3382.45	−0.289415
$516$	14778.8	1.26085
$517$	−2011.06	−0.171076
$518$	−178.256	−0.0151199
$519$	−12758.4	−1.07906
$520$	−4.03277	−0.000340094 0
$521$	−13136.8	−1.10467	−0.552335	−	0.833622i	$-0.686263\pi$
$521$	−13136.8	−1.10467	−0.552335	+	0.833622i	$0.686263\pi$
$522$	29.9068	0.00250764
$523$	1423.77	0.119039	0.0595194	−	0.998227i	$-0.481043\pi$
$523$	1423.77	0.119039	0.0595194	+	0.998227i	$0.481043\pi$
$524$	2900.27	0.241792
$525$	3733.95	0.310405
$526$	862.572	0.0715017
$527$	−27094.4	−2.23956
$528$	9554.72	0.787530
$529$	529.000	0.0434783
$530$	−89.4137	−0.00732808
$531$	−3105.79	−0.253823
$532$	4472.43	0.364482
$533$	−189.362	−0.0153887
$534$	27.9439	0.00226451
$535$	4966.35	0.401335
$536$	145.871	0.0117550
$537$	9030.60	0.725697
$538$	−368.676	−0.0295441
$539$	−10038.0	−0.802166
$540$	−4209.16	−0.335433
$541$	−6709.28	−0.533187	−0.266594	−	0.963809i	$-0.585898\pi$
$541$	−6709.28	−0.533187	−0.266594	+	0.963809i	$0.585898\pi$
$542$	53.9170	0.00427294
$543$	−3286.22	−0.259715
$544$	−2429.31	−0.191463
$545$	−3453.19	−0.271410
$546$	2.41355	0.000189177 0
$547$	11624.0	0.908606	0.454303	−	0.890847i	$-0.349888\pi$
$547$	11624.0	0.908606	0.454303	+	0.890847i	$0.349888\pi$
$548$	−16822.9	−1.31138
$549$	−1361.42	−0.105836
$550$	445.727	0.0345561
$551$	2066.84	0.159801
$552$	−170.672	−0.0131599
$553$	−2251.78	−0.173157
$554$	388.492	0.0297932
$555$	2979.34	0.227867
$556$	−8670.87	−0.661379
$557$	6177.60	0.469934	0.234967	−	0.972003i	$-0.424502\pi$
$557$	6177.60	0.469934	0.234967	+	0.972003i	$0.424502\pi$
$558$	−243.394	−0.0184654
$559$	−291.402	−0.0220483
$560$	1726.97	0.130318
$561$	17217.5	1.29576
$562$	858.281	0.0644206
$563$	21570.5	1.61472	0.807359	−	0.590061i	$-0.200896\pi$
$563$	21570.5	1.61472	0.807359	+	0.590061i	$0.200896\pi$
$564$	1891.77	0.141237
$565$	−5195.39	−0.386852
$566$	−694.306	−0.0515616
$567$	3061.38	0.226748
$568$	−1343.85	−0.0992725
$569$	−5304.99	−0.390856	−0.195428	−	0.980718i	$-0.562610\pi$
$569$	−5304.99	−0.390856	−0.195428	+	0.980718i	$0.562610\pi$
$570$	114.141	0.00838742
$571$	197.077	0.0144438	0.00722191	−	0.999974i	$-0.497701\pi$
$571$	197.077	0.0144438	0.00722191	+	0.999974i	$0.497701\pi$
$572$	−188.685	−0.0137925
$573$	−7225.64	−0.526798
$574$	−248.212	−0.0180491
$575$	2601.16	0.188653
$576$	4737.32	0.342688
$577$	−23750.9	−1.71363	−0.856815	−	0.515625i	$-0.827560\pi$
$577$	−23750.9	−1.71363	−0.856815	+	0.515625i	$0.827560\pi$
$578$	−912.896	−0.0656946
$579$	6958.66	0.499468
$580$	799.306	0.0572230
$581$	−9872.41	−0.704951
$582$	335.814	0.0239175
$583$	−8373.35	−0.594835
$584$	−1775.32	−0.125793
$585$	21.3275	0.00150732
$586$	−457.833	−0.0322746
$587$	9332.96	0.656240	0.328120	−	0.944636i	$-0.393585\pi$
$587$	9332.96	0.656240	0.328120	+	0.944636i	$0.393585\pi$
$588$	9442.56	0.662252
$589$	−16820.8	−1.17672
$590$	126.746	0.00884417
$591$	−14397.5	−1.00209
$592$	−13088.9	−0.908698
$593$	−19174.0	−1.32779	−0.663896	−	0.747825i	$-0.731098\pi$
$593$	−19174.0	−1.32779	−0.663896	+	0.747825i	$0.731098\pi$
$594$	601.882	0.0415749
$595$	3111.99	0.214418
$596$	−7762.90	−0.533525
$597$	−4300.42	−0.294815
$598$	1.68134	0.000114975 0
$599$	10745.2	0.732951	0.366476	−	0.930428i	$-0.380564\pi$
$599$	10745.2	0.732951	0.366476	+	0.930428i	$0.380564\pi$
$600$	−839.214	−0.0571013
$601$	8314.12	0.564293	0.282146	−	0.959371i	$-0.408954\pi$
$601$	8314.12	0.564293	0.282146	+	0.959371i	$0.408954\pi$
$602$	−381.963	−0.0258599
$603$	−771.446	−0.0520990
$604$	20823.7	1.40282
$605$	198.265	0.0133234
$606$	−619.833	−0.0415495
$607$	1875.94	0.125440	0.0627200	−	0.998031i	$-0.480023\pi$
$607$	1875.94	0.125440	0.0627200	+	0.998031i	$0.480023\pi$
$608$	−1508.17	−0.100599
$609$	−957.475	−0.0637091
$610$	55.5592	0.00368775
$611$	−37.3012	−0.00246980
$612$	8562.84	0.565576
$613$	13838.4	0.911793	0.455896	−	0.890033i	$-0.349319\pi$
$613$	13838.4	0.911793	0.455896	+	0.890033i	$0.349319\pi$
$614$	68.3740	0.00449406
$615$	4148.58	0.272011
$616$	−495.025	−0.0323785
$617$	3100.27	0.202289	0.101144	−	0.994872i	$-0.467750\pi$
$617$	3100.27	0.202289	0.101144	+	0.994872i	$0.467750\pi$
$618$	−454.976	−0.0296146
$619$	29257.9	1.89980	0.949899	−	0.312556i	$-0.101185\pi$
$619$	29257.9	1.89980	0.949899	+	0.312556i	$0.101185\pi$
$620$	−6505.08	−0.421371
$621$	3512.44	0.226972
$622$	−111.045	−0.00715837
$623$	472.987	0.0304171
$624$	177.221	0.0113694
$625$	11301.9	0.723322
$626$	−142.106	−0.00907298
$627$	10689.0	0.680823
$628$	13763.5	0.874558
$629$	−23586.0	−1.49513
$630$	27.9556	0.00176790
$631$	−27212.9	−1.71685	−0.858423	−	0.512942i	$-0.828556\pi$
$631$	−27212.9	−1.71685	−0.858423	+	0.512942i	$0.828556\pi$
$632$	506.094	0.0318534
$633$	−7851.25	−0.492985
$634$	−720.082	−0.0451074
$635$	8045.77	0.502813
$636$	7876.65	0.491084
$637$	−186.185	−0.0115807
$638$	−114.295	−0.00709247
$639$	7107.02	0.439983
$640$	−777.472	−0.0480192
$641$	−3211.63	−0.197897	−0.0989483	−	0.995093i	$-0.531548\pi$
$641$	−3211.63	−0.197897	−0.0989483	+	0.995093i	$0.531548\pi$
$642$	668.029	0.0410670
$643$	−1507.09	−0.0924321	−0.0462161	−	0.998931i	$-0.514716\pi$
$643$	−1507.09	−0.0924321	−0.0462161	+	0.998931i	$0.514716\pi$
$644$	−1443.32	−0.0883150
$645$	6384.08	0.389725
$646$	−903.595	−0.0550332
$647$	−12053.4	−0.732407	−0.366204	−	0.930535i	$-0.619343\pi$
$647$	−12053.4	−0.732407	−0.366204	+	0.930535i	$0.619343\pi$
$648$	−688.053	−0.0417118
$649$	11869.4	0.717898
$650$	8.26735	0.000498880 0
$651$	7792.33	0.469133
$652$	18935.8	1.13740
$653$	23252.2	1.39346	0.696729	−	0.717335i	$-0.254638\pi$
$653$	23252.2	1.39346	0.696729	+	0.717335i	$0.254638\pi$
$654$	−464.491	−0.0277722
$655$	1252.85	0.0747373
$656$	−18225.5	−1.08474
$657$	9388.83	0.557524
$658$	−48.8935	−0.00289676
$659$	−3413.81	−0.201795	−0.100898	−	0.994897i	$-0.532171\pi$
$659$	−3413.81	−0.201795	−0.100898	+	0.994897i	$0.532171\pi$
$660$	4133.74	0.243796
$661$	−26199.8	−1.54169	−0.770844	−	0.637024i	$-0.780165\pi$
$661$	−26199.8	−1.54169	−0.770844	+	0.637024i	$0.780165\pi$
$662$	−90.1238	−0.00529118
$663$	319.350	0.0187067
$664$	2218.85	0.129681
$665$	1931.99	0.112660
$666$	−211.877	−0.0123274
$667$	−667.000	−0.0387202
$668$	9960.56	0.576925
$669$	−15934.1	−0.920850
$670$	31.4824	0.00181533
$671$	5202.96	0.299341
$672$	698.669	0.0401067
$673$	3701.42	0.212005	0.106003	−	0.994366i	$-0.466195\pi$
$673$	3701.42	0.212005	0.106003	+	0.994366i	$0.466195\pi$
$674$	−282.779	−0.0161606
$675$	17271.1	0.984836
$676$	17545.7	0.998276
$677$	12168.6	0.690811	0.345406	−	0.938454i	$-0.387741\pi$
$677$	12168.6	0.690811	0.345406	+	0.938454i	$0.387741\pi$
$678$	−698.837	−0.0395850
$679$	5684.11	0.321261
$680$	−699.427	−0.0394438
$681$	−3357.84	−0.188947
$682$	930.182	0.0522266
$683$	−15357.7	−0.860387	−0.430194	−	0.902737i	$-0.641555\pi$
$683$	−15357.7	−0.860387	−0.430194	+	0.902737i	$0.641555\pi$
$684$	5315.99	0.297167
$685$	−7267.09	−0.405345
$686$	−541.642	−0.0301458
$687$	−606.071	−0.0336580
$688$	−28046.5	−1.55416
$689$	−155.309	−0.00858751
$690$	−36.8350	−0.00203230
$691$	31921.7	1.75739	0.878696	−	0.477382i	$-0.158414\pi$
$691$	31921.7	1.75739	0.878696	+	0.477382i	$0.158414\pi$
$692$	24249.5	1.33212
$693$	2617.96	0.143504
$694$	608.642	0.0332907
$695$	−3745.61	−0.204430
$696$	215.195	0.0117197
$697$	−32842.2	−1.78477
$698$	−41.5651	−0.00225396
$699$	−15118.6	−0.818080
$700$	−7096.99	−0.383201
$701$	−6059.23	−0.326468	−0.163234	−	0.986587i	$-0.552193\pi$
$701$	−6059.23	−0.326468	−0.163234	+	0.986587i	$0.552193\pi$
$702$	11.1637	0.000600210 0
$703$	−14642.7	−0.785574
$704$	−18104.7	−0.969240
$705$	817.200	0.0436561
$706$	−252.065	−0.0134371
$707$	−10491.5	−0.558096
$708$	−11165.3	−0.592683
$709$	−6153.31	−0.325941	−0.162971	−	0.986631i	$-0.552108\pi$
$709$	−6153.31	−0.325941	−0.162971	+	0.986631i	$0.552108\pi$
$710$	−290.035	−0.0153307
$711$	−2676.50	−0.141177
$712$	−106.305	−0.00559544
$713$	5428.32	0.285122
$714$	418.596	0.0219406
$715$	−81.5075	−0.00426323
$716$	−17164.2	−0.895887
$717$	9321.93	0.485542
$718$	−821.247	−0.0426862
$719$	−12515.8	−0.649181	−0.324590	−	0.945855i	$-0.605226\pi$
$719$	−12515.8	−0.649181	−0.324590	+	0.945855i	$0.605226\pi$
$720$	2052.70	0.106250
$721$	−7701.08	−0.397785
$722$	196.533	0.0101305
$723$	−2051.58	−0.105531
$724$	6246.00	0.320623
$725$	−3279.72	−0.168008
$726$	26.6689	0.00136333
$727$	38371.9	1.95755	0.978773	−	0.204946i	$-0.0657019\pi$
$727$	38371.9	1.95755	0.978773	+	0.204946i	$0.0657019\pi$
$728$	−9.18173	−0.000467442 0
$729$	20967.5	1.06526
$730$	−383.155	−0.0194263
$731$	−50539.5	−2.55714
$732$	−4894.33	−0.247130
$733$	33761.4	1.70123	0.850617	−	0.525786i	$-0.176229\pi$
$733$	33761.4	1.70123	0.850617	+	0.525786i	$0.176229\pi$
$734$	403.616	0.0202966
$735$	4078.96	0.204700
$736$	486.709	0.0243755
$737$	2948.24	0.147354
$738$	−295.028	−0.0147156
$739$	26953.1	1.34166	0.670830	−	0.741611i	$-0.265938\pi$
$739$	26953.1	1.34166	0.670830	+	0.741611i	$0.265938\pi$
$740$	−5662.74	−0.281306
$741$	198.259	0.00982892
$742$	−203.575	−0.0100721
$743$	−21668.3	−1.06990	−0.534948	−	0.844885i	$-0.679669\pi$
$743$	−21668.3	−1.06990	−0.534948	+	0.844885i	$0.679669\pi$
$744$	−1751.34	−0.0863003
$745$	−3353.39	−0.164911
$746$	−253.122	−0.0124229
$747$	−11734.5	−0.574755
$748$	−32724.7	−1.59964
$749$	11307.3	0.551614
$750$	−381.312	−0.0185647
$751$	1551.44	0.0753834	0.0376917	−	0.999289i	$-0.488000\pi$
$751$	1551.44	0.0753834	0.0376917	+	0.999289i	$0.488000\pi$
$752$	−3590.12	−0.174093
$753$	6982.78	0.337937
$754$	−2.11995	−0.000102393 0
$755$	8995.34	0.433608
$756$	−9583.33	−0.461035
$757$	27669.2	1.32847	0.664236	−	0.747523i	$-0.268757\pi$
$757$	27669.2	1.32847	0.664236	+	0.747523i	$0.268757\pi$
$758$	529.968	0.0253949
$759$	−3449.50	−0.164965
$760$	−434.219	−0.0207247
$761$	8313.63	0.396017	0.198008	−	0.980200i	$-0.436553\pi$
$761$	8313.63	0.396017	0.198008	+	0.980200i	$0.436553\pi$
$762$	1082.24	0.0514509
$763$	−7862.14	−0.373039
$764$	13733.5	0.650343
$765$	3698.95	0.174818
$766$	663.639	0.0313032
$767$	220.154	0.0103642
$768$	16952.1	0.796494
$769$	−1685.58	−0.0790425	−0.0395213	−	0.999219i	$-0.512583\pi$
$769$	−1685.58	−0.0790425	−0.0395213	+	0.999219i	$0.512583\pi$
$770$	−106.838	−0.00500023
$771$	16774.8	0.783565
$772$	−13226.1	−0.616603
$773$	11903.5	0.553865	0.276932	−	0.960889i	$-0.410682\pi$
$773$	11903.5	0.553865	0.276932	+	0.960889i	$0.410682\pi$
$774$	−454.006	−0.0210839
$775$	26691.7	1.23715
$776$	−1277.52	−0.0590982
$777$	6783.31	0.313191
$778$	411.559	0.0189654
$779$	−20389.1	−0.937761
$780$	76.6725	0.00351964
$781$	−27161.0	−1.24442
$782$	291.604	0.0133347
$783$	−4428.73	−0.202133
$784$	−17919.7	−0.816313
$785$	5945.50	0.270324
$786$	168.522	0.00764756
$787$	−1847.34	−0.0836728	−0.0418364	−	0.999124i	$-0.513321\pi$
$787$	−1847.34	−0.0836728	−0.0418364	+	0.999124i	$0.513321\pi$
$788$	27364.9	1.23710
$789$	−32824.1	−1.48107
$790$	109.227	0.00491914
$791$	−11828.7	−0.531709
$792$	−588.394	−0.0263986
$793$	96.5045	0.00432153
$794$	−865.123	−0.0386676
$795$	3402.53	0.151793
$796$	8173.66	0.363954
$797$	−31277.5	−1.39009	−0.695047	−	0.718964i	$-0.744616\pi$
$797$	−31277.5	−1.39009	−0.695047	+	0.718964i	$0.744616\pi$
$798$	259.873	0.0115281
$799$	−6469.36	−0.286445
$800$	2393.21	0.105766
$801$	562.199	0.0247994
$802$	−1226.26	−0.0539907
$803$	−35881.4	−1.57687
$804$	−2773.35	−0.121653
$805$	−623.482	−0.0272979
$806$	17.2530	0.000753985 0
$807$	14029.5	0.611972
$808$	2357.99	0.102666
$809$	−34142.2	−1.48378	−0.741888	−	0.670524i	$-0.766069\pi$
$809$	−34142.2	−1.48378	−0.741888	+	0.670524i	$0.766069\pi$
$810$	−148.498	−0.00644159
$811$	36824.6	1.59444	0.797218	−	0.603692i	$-0.206304\pi$
$811$	36824.6	1.59444	0.797218	+	0.603692i	$0.206304\pi$
$812$	1819.84	0.0786502
$813$	−2051.74	−0.0885089
$814$	809.734	0.0348663
$815$	8179.83	0.351567
$816$	30736.4	1.31861
$817$	−31376.0	−1.34358
$818$	−626.693	−0.0267870
$819$	48.5580	0.00207174
$820$	−7885.06	−0.335803
$821$	−23999.8	−1.02022	−0.510110	−	0.860109i	$-0.670395\pi$
$821$	−23999.8	−1.02022	−0.510110	+	0.860109i	$0.670395\pi$
$822$	−977.503	−0.0414773
$823$	8120.07	0.343922	0.171961	−	0.985104i	$-0.444990\pi$
$823$	8120.07	0.343922	0.171961	+	0.985104i	$0.444990\pi$
$824$	1730.84	0.0731755
$825$	−16961.6	−0.715790
$826$	288.573	0.0121559
$827$	10913.2	0.458876	0.229438	−	0.973323i	$-0.426311\pi$
$827$	10913.2	0.458876	0.229438	+	0.973323i	$0.426311\pi$
$828$	−1715.55	−0.0720043
$829$	−13916.2	−0.583027	−0.291513	−	0.956567i	$-0.594159\pi$
$829$	−13916.2	−0.583027	−0.291513	+	0.956567i	$0.594159\pi$
$830$	478.880	0.0200267
$831$	−14783.6	−0.617132
$832$	−335.805	−0.0139927
$833$	−32291.1	−1.34312
$834$	−503.826	−0.0209185
$835$	4302.73	0.178326
$836$	−20316.2	−0.840490
$837$	36042.8	1.48844
$838$	−1414.89	−0.0583254
$839$	29867.7	1.22902	0.614510	−	0.788909i	$-0.289354\pi$
$839$	29867.7	1.22902	0.614510	+	0.788909i	$0.289354\pi$
$840$	201.155	0.00826249
$841$	841.000	0.0344828
$842$	1363.06	0.0557890
$843$	−32660.8	−1.33440
$844$	14922.6	0.608599
$845$	7579.33	0.308565
$846$	−58.1155	−0.00236176
$847$	451.406	0.0183123
$848$	−14948.0	−0.605325
$849$	26421.0	1.06804
$850$	1433.85	0.0578597
$851$	4725.41	0.190347
$852$	25549.8	1.02737
$853$	33382.8	1.33998	0.669992	−	0.742369i	$-0.266298\pi$
$853$	33382.8	1.33998	0.669992	+	0.742369i	$0.266298\pi$
$854$	126.496	0.00506862
$855$	2296.38	0.0918534
$856$	−2541.34	−0.101473
$857$	7567.33	0.301628	0.150814	−	0.988562i	$-0.451811\pi$
$857$	7567.33	0.301628	0.150814	+	0.988562i	$0.451811\pi$
$858$	−10.9637	−0.000436239 0
$859$	−22714.0	−0.902201	−0.451100	−	0.892473i	$-0.648968\pi$
$859$	−22714.0	−0.902201	−0.451100	+	0.892473i	$0.648968\pi$
$860$	−12134.0	−0.481123
$861$	9445.39	0.373865
$862$	−134.266	−0.00530523
$863$	−22878.9	−0.902442	−0.451221	−	0.892412i	$-0.649011\pi$
$863$	−22878.9	−0.902442	−0.451221	+	0.892412i	$0.649011\pi$
$864$	3231.64	0.127248
$865$	10475.2	0.411755
$866$	−1475.11	−0.0578826
$867$	34739.1	1.36079
$868$	−14810.6	−0.579153
$869$	10228.8	0.399296
$870$	46.4441	0.00180989
$871$	54.6840	0.00212732
$872$	1767.04	0.0686231
$873$	6756.21	0.261928
$874$	181.034	0.00700636
$875$	−6454.22	−0.249363
$876$	33752.9	1.30183
$877$	6862.15	0.264217	0.132109	−	0.991235i	$-0.457825\pi$
$877$	6862.15	0.264217	0.132109	+	0.991235i	$0.457825\pi$
$878$	1245.35	0.0478685
$879$	17422.3	0.668530
$880$	−7844.84	−0.300511
$881$	23037.7	0.880998	0.440499	−	0.897753i	$-0.354801\pi$
$881$	23037.7	0.880998	0.440499	+	0.897753i	$0.354801\pi$
$882$	−290.077	−0.0110742
$883$	47072.5	1.79402	0.897009	−	0.442013i	$-0.145736\pi$
$883$	47072.5	1.79402	0.897009	+	0.442013i	$0.145736\pi$
$884$	−606.978	−0.0230937
$885$	−4823.17	−0.183197
$886$	−1705.22	−0.0646590
$887$	−9127.99	−0.345533	−0.172767	−	0.984963i	$-0.555271\pi$
$887$	−9127.99	−0.345533	−0.172767	+	0.984963i	$0.555271\pi$
$888$	−1524.56	−0.0576138
$889$	18318.4	0.691091
$890$	−22.9431	−0.000864108 0
$891$	−13906.4	−0.522876
$892$	30285.4	1.13681
$893$	−4016.31	−0.150505
$894$	−451.068	−0.0168747
$895$	−7414.52	−0.276916
$896$	−1770.13	−0.0659999
$897$	−63.9813	−0.00238157
$898$	482.698	0.0179375
$899$	−6844.40	−0.253920
$900$	−8435.57	−0.312429
$901$	−26936.1	−0.995972
$902$	1127.51	0.0416208
$903$	14535.1	0.535657
$904$	2658.54	0.0978116
$905$	2698.13	0.0991036
$906$	1209.97	0.0443693
$907$	20081.6	0.735168	0.367584	−	0.929990i	$-0.380185\pi$
$907$	20081.6	0.735168	0.367584	+	0.929990i	$0.380185\pi$
$908$	6382.14	0.233259
$909$	−12470.3	−0.455022
$910$	−1.98163	−7.21874e−5 0
$911$	35869.3	1.30450	0.652252	−	0.758003i	$-0.273825\pi$
$911$	35869.3	1.30450	0.652252	+	0.758003i	$0.273825\pi$
$912$	19081.8	0.692831
$913$	44845.8	1.62561
$914$	−1309.90	−0.0474046
$915$	−2114.23	−0.0763873
$916$	1151.94	0.0415514
$917$	2852.46	0.102723
$918$	1936.18	0.0696118
$919$	−50041.2	−1.79620	−0.898100	−	0.439792i	$-0.855052\pi$
$919$	−50041.2	−1.79620	−0.898100	+	0.439792i	$0.855052\pi$
$920$	140.129	0.00502165
$921$	−2601.89	−0.0930891
$922$	−569.581	−0.0203451
$923$	−503.782	−0.0179655
$924$	9411.60	0.335085
$925$	23235.4	0.825920
$926$	−360.530	−0.0127946
$927$	−9153.61	−0.324319
$928$	−613.677	−0.0217079
$929$	−3690.58	−0.130338	−0.0651690	−	0.997874i	$-0.520759\pi$
$929$	−3690.58	−0.130338	−0.0651690	+	0.997874i	$0.520759\pi$
$930$	−377.981	−0.0133274
$931$	−20047.0	−0.705707
$932$	28735.4	1.00994
$933$	4225.69	0.148277
$934$	1454.65	0.0509611
$935$	−14136.3	−0.494446
$936$	−10.9135	−0.000381111 0
$937$	−35134.6	−1.22497	−0.612485	−	0.790482i	$-0.709830\pi$
$937$	−35134.6	−1.22497	−0.612485	+	0.790482i	$0.709830\pi$
$938$	71.6785	0.00249508
$939$	5407.65	0.187936
$940$	−1553.22	−0.0538942
$941$	356.116	0.0123369	0.00616847	−	0.999981i	$-0.498037\pi$
$941$	356.116	0.0123369	0.00616847	+	0.999981i	$0.498037\pi$
$942$	799.735	0.0276611
$943$	6579.88	0.227222
$944$	21189.1	0.730559
$945$	−4139.78	−0.142505
$946$	1735.08	0.0596325
$947$	−23476.1	−0.805567	−0.402783	−	0.915295i	$-0.631957\pi$
$947$	−23476.1	−0.805567	−0.402783	+	0.915295i	$0.631957\pi$
$948$	−9622.04	−0.329651
$949$	−665.528	−0.0227650
$950$	890.165	0.0304008
$951$	27401.8	0.934347
$952$	−1592.44	−0.0542135
$953$	−45430.5	−1.54421	−0.772107	−	0.635492i	$-0.780797\pi$
$953$	−45430.5	−1.54421	−0.772107	+	0.635492i	$0.780797\pi$
$954$	−241.972	−0.00821188
$955$	5932.57	0.201019
$956$	−17717.9	−0.599411
$957$	4349.36	0.146912
$958$	2124.40	0.0716455
$959$	−16545.5	−0.557126
$960$	7356.87	0.247335
$961$	25911.6	0.869778
$962$	15.0189	0.000503358 0
$963$	13440.0	0.449737
$964$	3899.37	0.130280
$965$	−5713.36	−0.190590
$966$	−83.8651	−0.00279329
$967$	−48708.3	−1.61981	−0.809903	−	0.586564i	$-0.800480\pi$
$967$	−48708.3	−1.61981	−0.809903	+	0.586564i	$0.800480\pi$
$968$	−101.455	−0.00336868
$969$	34385.2	1.13995
$970$	−275.718	−0.00912658
$971$	−21624.0	−0.714674	−0.357337	−	0.933976i	$-0.616315\pi$
$971$	−21624.0	−0.714674	−0.357337	+	0.933976i	$0.616315\pi$
$972$	−19854.6	−0.655181
$973$	−8527.92	−0.280979
$974$	1959.59	0.0644653
$975$	−314.603	−0.0103337
$976$	9288.26	0.304621
$977$	−26178.2	−0.857231	−0.428615	−	0.903487i	$-0.640998\pi$
$977$	−26178.2	−0.857231	−0.428615	+	0.903487i	$0.640998\pi$
$978$	1100.28	0.0359744
$979$	−2148.56	−0.0701413
$980$	−7752.75	−0.252707
$981$	−9345.04	−0.304143
$982$	1841.69	0.0598478
$983$	33548.1	1.08852	0.544262	−	0.838915i	$-0.316810\pi$
$983$	33548.1	1.08852	0.544262	+	0.838915i	$0.316810\pi$
$984$	−2122.87	−0.0687752
$985$	11821.0	0.382384
$986$	−367.675	−0.0118754
$987$	1860.58	0.0600030
$988$	−376.824	−0.0121340
$989$	10125.5	0.325554
$990$	−126.989	−0.00407675
$991$	21297.5	0.682681	0.341340	−	0.939940i	$-0.389119\pi$
$991$	21297.5	0.682681	0.341340	+	0.939940i	$0.389119\pi$
$992$	4994.35	0.159850
$993$	3429.55	0.109601
$994$	−660.345	−0.0210713
$995$	3530.83	0.112497
$996$	−42185.6	−1.34207
$997$	43247.7	1.37379	0.686895	−	0.726757i	$-0.258973\pi$
$997$	43247.7	1.37379	0.686895	+	0.726757i	$0.258973\pi$
$998$	−2245.74	−0.0712300
$999$	31375.7	0.993676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.b.1.20	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.b.1.20	✓	38	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-0.110439 q^{2} +4.20263 q^{3} -7.98780 q^{4} -3.45054 q^{5} -0.464136 q^{6} -7.85612 q^{7} +1.76568 q^{8} -9.33789 q^{9} +O(q^{10})\)	\(q-0.110439 q^{2} +4.20263 q^{3} -7.98780 q^{4} -3.45054 q^{5} -0.464136 q^{6} -7.85612 q^{7} +1.76568 q^{8} -9.33789 q^{9} +0.381076 q^{10} +35.6867 q^{11} -33.5698 q^{12} +0.661917 q^{13} +0.867625 q^{14} -14.5014 q^{15} +63.7074 q^{16} +114.800 q^{17} +1.03127 q^{18} +71.2702 q^{19} +27.5623 q^{20} -33.0164 q^{21} -3.94122 q^{22} -23.0000 q^{23} +7.42051 q^{24} -113.094 q^{25} -0.0731017 q^{26} -152.715 q^{27} +62.7532 q^{28} +29.0000 q^{29} +1.60152 q^{30} -236.014 q^{31} -21.1613 q^{32} +149.978 q^{33} -12.6784 q^{34} +27.1079 q^{35} +74.5892 q^{36} -205.453 q^{37} -7.87104 q^{38} +2.78179 q^{39} -6.09257 q^{40} -286.082 q^{41} +3.64631 q^{42} -440.240 q^{43} -285.058 q^{44} +32.2208 q^{45} +2.54011 q^{46} -56.3533 q^{47} +267.739 q^{48} -281.281 q^{49} +12.4900 q^{50} +482.462 q^{51} -5.28726 q^{52} -234.635 q^{53} +16.8657 q^{54} -123.139 q^{55} -13.8714 q^{56} +299.522 q^{57} -3.20274 q^{58} +332.601 q^{59} +115.834 q^{60} +145.796 q^{61} +26.0652 q^{62} +73.3596 q^{63} -507.322 q^{64} -2.28397 q^{65} -16.5635 q^{66} +82.6146 q^{67} -917.000 q^{68} -96.6605 q^{69} -2.99378 q^{70} -761.095 q^{71} -16.4878 q^{72} -1005.46 q^{73} +22.6901 q^{74} -475.291 q^{75} -569.292 q^{76} -280.359 q^{77} -0.307220 q^{78} +286.628 q^{79} -219.825 q^{80} -389.681 q^{81} +31.5947 q^{82} +1256.65 q^{83} +263.728 q^{84} -396.122 q^{85} +48.6198 q^{86} +121.876 q^{87} +63.0114 q^{88} -60.2062 q^{89} -3.55845 q^{90} -5.20010 q^{91} +183.719 q^{92} -991.880 q^{93} +6.22362 q^{94} -245.921 q^{95} -88.9330 q^{96} -723.526 q^{97} +31.0645 q^{98} -333.238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9 + 30 * q^10 - 100 * q^11 - 173 * q^12 - 160 * q^13 - 304 * q^14 - 208 * q^15 + 552 * q^16 - 666 * q^17 - 315 * q^18 - 252 * q^19 - 747 * q^20 - 470 * q^21 - 323 * q^22 - 874 * q^23 - 114 * q^24 + 910 * q^25 - 119 * q^26 - 526 * q^27 - 619 * q^28 + 1102 * q^29 - 533 * q^30 + 358 * q^31 - 1272 * q^32 - 604 * q^33 - 553 * q^34 + 16 * q^35 + 1230 * q^36 - 1206 * q^37 - 2010 * q^38 - 240 * q^39 - 418 * q^40 - 1094 * q^41 - 1184 * q^42 - 936 * q^43 - 2153 * q^44 - 3654 * q^45 + 184 * q^46 - 1702 * q^47 - 1319 * q^48 + 1920 * q^49 - 1255 * q^50 - 270 * q^51 - 2202 * q^52 - 4640 * q^53 - 1529 * q^54 - 318 * q^55 - 2435 * q^56 - 1980 * q^57 - 232 * q^58 + 318 * q^59 - 3279 * q^60 - 2212 * q^61 - 541 * q^62 - 1044 * q^63 + 1186 * q^64 - 2438 * q^65 - 3503 * q^66 - 496 * q^67 - 6099 * q^68 + 368 * q^69 + 4068 * q^70 + 870 * q^71 - 3869 * q^72 - 2810 * q^73 - 2793 * q^74 - 3638 * q^75 + 1548 * q^76 - 6072 * q^77 + 2170 * q^78 - 3084 * q^79 - 6702 * q^80 + 362 * q^81 - 1183 * q^82 - 5566 * q^83 - 6518 * q^84 - 120 * q^85 - 2095 * q^86 - 464 * q^87 - 1220 * q^88 - 6506 * q^89 + 165 * q^90 + 44 * q^91 - 3496 * q^92 - 5928 * q^93 + 135 * q^94 - 2024 * q^95 - 3164 * q^96 - 7472 * q^97 - 6422 * q^98 - 944 * q^99

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