LMFDB - Embedded newform 143.4.b.a.12.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(12,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("143.12");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			12.6
Character	$\chi$	$=$	143.12
Dual form			143.4.b.a.12.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.27424i q^{2} +4.33951 q^{3} -10.2691 q^{4} +0.295728i q^{5} -18.5481i q^{6} -11.5737i q^{7} +9.69883i q^{8} -8.16862 q^{9} +O(q^{10})$	\(q-4.27424i q^{2} +4.33951 q^{3} -10.2691 q^{4} +0.295728i q^{5} -18.5481i q^{6} -11.5737i q^{7} +9.69883i q^{8} -8.16862 q^{9} +1.26401 q^{10} -11.0000i q^{11} -44.5631 q^{12} +(-1.44705 - 46.8498i) q^{13} -49.4689 q^{14} +1.28331i q^{15} -40.6979 q^{16} -39.7079 q^{17} +34.9147i q^{18} -68.1624i q^{19} -3.03687i q^{20} -50.2243i q^{21} -47.0167 q^{22} +83.5604 q^{23} +42.0882i q^{24} +124.913 q^{25} +(-200.247 + 6.18503i) q^{26} -152.615 q^{27} +118.852i q^{28} +198.255 q^{29} +5.48519 q^{30} +191.091i q^{31} +251.543i q^{32} -47.7347i q^{33} +169.721i q^{34} +3.42267 q^{35} +83.8847 q^{36} +196.760i q^{37} -291.343 q^{38} +(-6.27949 - 203.305i) q^{39} -2.86821 q^{40} +55.2695i q^{41} -214.671 q^{42} +240.921 q^{43} +112.960i q^{44} -2.41569i q^{45} -357.157i q^{46} -476.074i q^{47} -176.609 q^{48} +209.049 q^{49} -533.906i q^{50} -172.313 q^{51} +(14.8599 + 481.107i) q^{52} -39.3242 q^{53} +652.312i q^{54} +3.25300 q^{55} +112.252 q^{56} -295.792i q^{57} -847.389i q^{58} -353.223i q^{59} -13.1785i q^{60} +62.6336 q^{61} +816.771 q^{62} +94.5414i q^{63} +749.574 q^{64} +(13.8548 - 0.427932i) q^{65} -204.029 q^{66} +781.242i q^{67} +407.766 q^{68} +362.611 q^{69} -14.6293i q^{70} -575.874i q^{71} -79.2261i q^{72} -526.139i q^{73} +840.998 q^{74} +542.060 q^{75} +699.969i q^{76} -127.311 q^{77} +(-868.976 + 26.8400i) q^{78} +886.680 q^{79} -12.0355i q^{80} -441.721 q^{81} +236.235 q^{82} -111.859i q^{83} +515.760i q^{84} -11.7427i q^{85} -1029.75i q^{86} +860.330 q^{87} +106.687 q^{88} -433.213i q^{89} -10.3252 q^{90} +(-542.227 + 16.7477i) q^{91} -858.093 q^{92} +829.244i q^{93} -2034.86 q^{94} +20.1575 q^{95} +1091.58i q^{96} +1029.26i q^{97} -893.526i q^{98} +89.8548i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) $ 36 * q - 152 * q^4 + 360 * q^9	$ 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) $ 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	4.27424i		−	1.51117i	−0.655049	−	0.755586i	$-0.727352\pi$
$2$		−	4.27424i		−	1.51117i	0.655049	−	0.755586i	$-0.272648\pi$
$3$	4.33951			0.835140			0.417570	−	0.908645i	$-0.362882\pi$
$3$	4.33951			0.835140			0.417570	+	0.908645i	$0.362882\pi$
$4$	−10.2691			−1.28364
$5$			0.295728i			0.0264507i	0.999913	+	0.0132253i	$0.00420988\pi$
$5$			0.295728i			0.0264507i	−0.999913	+	0.0132253i	$0.995790\pi$
$6$		−	18.5481i		−	1.26204i
$7$		−	11.5737i		−	0.624922i	−0.949931	−	0.312461i	$-0.898847\pi$
$7$		−	11.5737i		−	0.624922i	0.949931	−	0.312461i	$-0.101153\pi$
$8$			9.69883i			0.428632i
$9$	−8.16862			−0.302542
$10$	1.26401			0.0399715
$11$		−	11.0000i		−	0.301511i
$11$		−	11.0000i		−	0.301511i
$12$	−44.5631			−1.07202
$13$	−1.44705	−	46.8498i	−0.0308722	−	0.999523i
$13$	−1.44705	−	46.8498i	−0.0308722	−	0.999523i
$14$	−49.4689			−0.944365
$15$			1.28331i			0.0220900i
$16$	−40.6979			−0.635905
$17$	−39.7079			−0.566505			−0.283252	−	0.959045i	$-0.591413\pi$
$17$	−39.7079			−0.566505			−0.283252	+	0.959045i	$0.591413\pi$
$18$			34.9147i			0.457192i
$19$		−	68.1624i		−	0.823028i	−0.911403	−	0.411514i	$-0.865000\pi$
$19$		−	68.1624i		−	0.823028i	0.911403	−	0.411514i	$-0.135000\pi$
$20$		−	3.03687i		−	0.0339532i
$21$		−	50.2243i		−	0.521897i
$22$	−47.0167			−0.455636
$23$	83.5604			0.757545			0.378773	−	0.925490i	$-0.376346\pi$
$23$	83.5604			0.757545			0.378773	+	0.925490i	$0.376346\pi$
$24$			42.0882i			0.357968i
$25$	124.913			0.999300
$26$	−200.247	+	6.18503i	−1.51045	+	0.0466533i
$27$	−152.615			−1.08780
$28$			118.852i			0.802176i
$29$	198.255			1.26948			0.634742	−	0.772724i	$-0.281107\pi$
$29$	198.255			1.26948			0.634742	+	0.772724i	$0.281107\pi$
$30$	5.48519			0.0333818
$31$			191.091i			1.10713i	0.832806	+	0.553565i	$0.186733\pi$
$31$			191.091i			1.10713i	−0.832806	+	0.553565i	$0.813267\pi$
$32$			251.543i			1.38959i
$33$		−	47.7347i		−	0.251804i
$34$			169.721i			0.856086i
$35$	3.42267			0.0165296
$36$	83.8847			0.388355
$37$			196.760i			0.874246i	0.899402	+	0.437123i	$0.144003\pi$
$37$			196.760i			0.874246i	−0.899402	+	0.437123i	$0.855997\pi$
$38$	−291.343			−1.24374
$39$	−6.27949	−	203.305i	−0.0257826	−	0.834742i
$40$	−2.86821			−0.0113376
$41$			55.2695i			0.210528i	0.994444	+	0.105264i	$0.0335688\pi$
$41$			55.2695i			0.210528i	−0.994444	+	0.105264i	$0.966431\pi$
$42$	−214.671			−0.788677
$43$	240.921			0.854421			0.427210	−	0.904152i	$-0.359496\pi$
$43$	240.921			0.854421			0.427210	+	0.904152i	$0.359496\pi$
$44$			112.960i			0.387033i
$45$		−	2.41569i		−	0.00800243i
$46$		−	357.157i		−	1.14478i
$47$		−	476.074i		−	1.47750i	−0.673978	−	0.738751i	$-0.735416\pi$
$47$		−	476.074i		−	1.47750i	0.673978	−	0.738751i	$-0.264584\pi$
$48$	−176.609			−0.531070
$49$	209.049			0.609472
$50$		−	533.906i		−	1.51012i
$51$	−172.313			−0.473111
$52$	14.8599	+	481.107i	0.0396289	+	1.28303i
$53$	−39.3242			−0.101917			−0.0509585	−	0.998701i	$-0.516228\pi$
$53$	−39.3242			−0.101917			−0.0509585	+	0.998701i	$0.516228\pi$
$54$			652.312i			1.64386i
$55$	3.25300			0.00797518
$56$	112.252			0.267862
$57$		−	295.792i		−	0.687344i
$58$		−	847.389i		−	1.91841i
$59$		−	353.223i		−	0.779419i	−0.920938	−	0.389710i	$-0.872575\pi$
$59$		−	353.223i		−	0.779419i	0.920938	−	0.389710i	$-0.127425\pi$
$60$		−	13.1785i		−	0.0283557i
$61$	62.6336			0.131466			0.0657329	−	0.997837i	$-0.479061\pi$
$61$	62.6336			0.131466			0.0657329	+	0.997837i	$0.479061\pi$
$62$	816.771			1.67306
$63$			94.5414i			0.189065i
$64$	749.574			1.46401
$65$	13.8548	−	0.427932i	0.0264381	−	0.000816592i
$66$	−204.029			−0.380519
$67$			781.242i			1.42454i	0.701908	+	0.712268i	$0.252332\pi$
$67$			781.242i			1.42454i	−0.701908	+	0.712268i	$0.747668\pi$
$68$	407.766			0.727189
$69$	362.611			0.632656
$70$		−	14.6293i		−	0.0249791i
$71$		−	575.874i		−	0.962586i	−0.876560	−	0.481293i	$-0.840167\pi$
$71$		−	575.874i		−	0.962586i	0.876560	−	0.481293i	$-0.159833\pi$
$72$		−	79.2261i		−	0.129679i
$73$		−	526.139i		−	0.843560i	−0.906698	−	0.421780i	$-0.861405\pi$
$73$		−	526.139i		−	0.843560i	0.906698	−	0.421780i	$-0.138595\pi$
$74$	840.998			1.32114
$75$	542.060			0.834555
$76$			699.969i			1.05647i
$77$	−127.311			−0.188421
$78$	−868.976	+	26.8400i	−1.26144	+	0.0389620i
$79$	886.680			1.26278			0.631388	−	0.775467i	$-0.282486\pi$
$79$	886.680			1.26278			0.631388	+	0.775467i	$0.282486\pi$
$80$		−	12.0355i		−	0.0168201i
$81$	−441.721			−0.605927
$82$	236.235			0.318144
$83$		−	111.859i		−	0.147929i	−0.997261	−	0.0739647i	$-0.976435\pi$
$83$		−	111.859i		−	0.147929i	0.997261	−	0.0739647i	$-0.0235652\pi$
$84$			515.760i			0.669929i
$85$		−	11.7427i		−	0.0149844i
$86$		−	1029.75i		−	1.29118i
$87$	860.330			1.06020
$88$	106.687			0.129237
$89$		−	433.213i		−	0.515960i	−0.966150	−	0.257980i	$-0.916943\pi$
$89$		−	433.213i		−	0.515960i	0.966150	−	0.257980i	$-0.0830569\pi$
$90$	−10.3252			−0.0120931
$91$	−542.227	+	16.7477i	−0.624624	+	0.0192927i
$92$	−858.093			−0.972417
$93$			829.244i			0.924608i
$94$	−2034.86			−2.23276
$95$	20.1575			0.0217697
$96$			1091.58i			1.16051i
$97$			1029.26i			1.07738i	0.842505	+	0.538689i	$0.181080\pi$
$97$			1029.26i			1.07738i	−0.842505	+	0.538689i	$0.818920\pi$
$98$		−	893.526i		−	0.921017i
$99$			89.8548i			0.0912197i
$100$	−1282.74			−1.28274
$101$	1182.09			1.16458			0.582290	−	0.812981i	$-0.302157\pi$
$101$	1182.09			1.16458			0.582290	+	0.812981i	$0.302157\pi$
$102$			736.507i			0.714952i
$103$	−1425.70			−1.36387			−0.681934	−	0.731414i	$-0.738861\pi$
$103$	−1425.70			−1.36387			−0.681934	+	0.731414i	$0.738861\pi$
$104$	454.389	−	14.0347i	0.428428	−	0.0132328i
$105$	14.8527			0.0138045
$106$			168.081i			0.154014i
$107$	−1691.61			−1.52835			−0.764176	−	0.645008i	$-0.776854\pi$
$107$	−1691.61			−1.52835			−0.764176	+	0.645008i	$0.776854\pi$
$108$	1567.22			1.39635
$109$			1202.17i			1.05639i	0.849122	+	0.528196i	$0.177131\pi$
$109$			1202.17i			1.05639i	−0.849122	+	0.528196i	$0.822869\pi$
$110$		−	13.9041i		−	0.0120519i
$111$			853.842i			0.730118i
$112$			471.027i			0.397391i
$113$	382.151			0.318139			0.159070	−	0.987267i	$-0.449151\pi$
$113$	382.151			0.318139			0.159070	+	0.987267i	$0.449151\pi$
$114$	−1264.29			−1.03869
$115$			24.7111i			0.0200376i
$116$	−2035.91			−1.62956
$117$	11.8204	+	382.698i	0.00934013	+	0.302397i
$118$	−1509.76			−1.17784
$119$			459.568i			0.354021i
$120$	−12.4466			−0.00946849
$121$	−121.000			−0.0909091
$122$		−	267.711i		−	0.198667i
$123$			239.843i			0.175820i
$124$		−	1962.34i		−	1.42116i
$125$			73.9060i			0.0528829i
$126$	404.093			0.285710
$127$	−1181.10			−0.825244			−0.412622	−	0.910902i	$-0.635387\pi$
$127$	−1181.10			−0.825244			−0.412622	+	0.910902i	$0.635387\pi$
$128$		−	1191.51i		−	0.822779i
$129$	1045.48			0.713561
$130$	−1.82909	−	59.2187i	−0.00123401	−	0.0399525i
$131$	2140.49			1.42760			0.713801	−	0.700349i	$-0.246972\pi$
$131$	2140.49			1.42760			0.713801	+	0.700349i	$0.246972\pi$
$132$			490.194i			0.323226i
$133$	−788.893			−0.514329
$134$	3339.22			2.15272
$135$		−	45.1324i		−	0.0287732i
$136$		−	385.120i		−	0.242822i
$137$		−	843.457i		−	0.525996i	−0.964796	−	0.262998i	$-0.915289\pi$
$137$		−	843.457i		−	0.525996i	0.964796	−	0.262998i	$-0.0847112\pi$
$138$		−	1549.89i		−	0.956052i
$139$	2046.42			1.24874			0.624371	−	0.781128i	$-0.285355\pi$
$139$	2046.42			1.24874			0.624371	+	0.781128i	$0.285355\pi$
$140$	−35.1479			−0.0212181
$141$		−	2065.93i		−	1.23392i
$142$	−2461.42			−1.45463
$143$	−515.348	+	15.9175i	−0.301368	+	0.00930833i
$144$	332.446			0.192388
$145$			58.6295i			0.0335787i
$146$	−2248.84			−1.27476
$147$	907.171			0.508994
$148$		−	2020.55i		−	1.12222i
$149$			717.397i			0.394439i	0.980359	+	0.197220i	$0.0631912\pi$
$149$			717.397i			0.394439i	−0.980359	+	0.197220i	$0.936809\pi$
$150$		−	2316.89i		−	1.26116i
$151$			2010.44i			1.08349i	0.840542	+	0.541747i	$0.182237\pi$
$151$			2010.44i			1.08349i	−0.840542	+	0.541747i	$0.817763\pi$
$152$	661.096			0.352776
$153$	324.359			0.171391
$154$			544.158i			0.284737i
$155$	−56.5110			−0.0292844
$156$	64.4849	+	2087.77i	0.0330957	+	1.07151i
$157$	390.900			0.198709			0.0993543	−	0.995052i	$-0.468322\pi$
$157$	390.900			0.198709			0.0993543	+	0.995052i	$0.468322\pi$
$158$		−	3789.88i		−	1.90827i
$159$	−170.648			−0.0851149
$160$	−74.3884			−0.0367557
$161$		−	967.104i		−	0.473407i
$162$			1888.02i			0.915660i
$163$		−	607.427i		−	0.291885i	−0.989293	−	0.145943i	$-0.953378\pi$
$163$		−	607.427i		−	0.291885i	0.989293	−	0.145943i	$-0.0466215\pi$
$164$		−	567.570i		−	0.270243i
$165$	14.1165			0.00666039
$166$	−478.113			−0.223547
$167$			3446.58i			1.59703i	0.601975	+	0.798515i	$0.294381\pi$
$167$			3446.58i			1.59703i	−0.601975	+	0.798515i	$0.705619\pi$
$168$	487.117			0.223702
$169$	−2192.81	+	135.588i	−0.998094	+	0.0617150i
$170$	−50.1912			−0.0226441
$171$			556.793i			0.249000i
$172$	−2474.05			−1.09677
$173$	66.7622			0.0293401			0.0146700	−	0.999892i	$-0.495330\pi$
$173$	66.7622			0.0293401			0.0146700	+	0.999892i	$0.495330\pi$
$174$		−	3677.26i		−	1.60214i
$175$		−	1445.70i		−	0.624485i
$176$			447.677i			0.191733i
$177$		−	1532.82i		−	0.650924i
$178$	−1851.66			−0.779705
$179$	2614.66			1.09178			0.545891	−	0.837856i	$-0.316191\pi$
$179$	2614.66			1.09178			0.545891	+	0.837856i	$0.316191\pi$
$180$			24.8070i			0.0102723i
$181$	−3968.01			−1.62950			−0.814750	−	0.579812i	$-0.803126\pi$
$181$	−3968.01			−1.62950			−0.814750	+	0.579812i	$0.803126\pi$
$182$	71.5839	+	2317.61i	0.0291547	+	0.943915i
$183$	271.799			0.109792
$184$			810.438i			0.324708i
$185$	−58.1873			−0.0231244
$186$	3544.39			1.39724
$187$			436.787i			0.170808i
$188$			4888.87i			1.89658i
$189$			1766.32i			0.679793i
$190$		−	86.1581i		−	0.0328977i
$191$	−950.221			−0.359977			−0.179988	−	0.983669i	$-0.557606\pi$
$191$	−950.221			−0.359977			−0.179988	+	0.983669i	$0.557606\pi$
$192$	3252.79			1.22265
$193$			903.572i			0.336997i	0.985702	+	0.168499i	$0.0538919\pi$
$193$			903.572i			0.336997i	−0.985702	+	0.168499i	$0.946108\pi$
$194$	4399.31			1.62810
$195$	60.1230	−	1.85702i	0.0220795	−	0.000681968i
$196$	−2146.75			−0.782344
$197$		−	3014.55i		−	1.09024i	−0.838358	−	0.545121i	$-0.816484\pi$
$197$		−	3014.55i		−	1.09024i	0.838358	−	0.545121i	$-0.183516\pi$
$198$	384.061			0.137849
$199$	2400.72			0.855189			0.427594	−	0.903971i	$-0.359361\pi$
$199$	2400.72			0.855189			0.427594	+	0.903971i	$0.359361\pi$
$200$			1211.51i			0.428332i
$201$			3390.21i			1.18969i
$202$		−	5052.55i		−	1.75988i
$203$		−	2294.55i		−	0.793328i
$204$	1769.51			0.607305
$205$	−16.3447			−0.00556861
$206$			6093.79i			2.06104i
$207$	−682.573			−0.229189
$208$	58.8919	+	1906.69i	0.0196318	+	0.635602i
$209$	−749.787			−0.248152
$210$		−	63.4841i		−	0.0208610i
$211$	832.376			0.271579			0.135789	−	0.990738i	$-0.456643\pi$
$211$	832.376			0.271579			0.135789	+	0.990738i	$0.456643\pi$
$212$	403.826			0.130825
$213$		−	2499.01i		−	0.803894i
$214$			7230.33i			2.30960i
$215$			71.2470i			0.0226000i
$216$		−	1480.18i		−	0.466268i
$217$	2211.64			0.691870
$218$	5138.35			1.59639
$219$		−	2283.19i		−	0.704490i
$220$	−33.4055			−0.0102373
$221$	57.4592	+	1860.31i	0.0174893	+	0.566235i
$222$	3649.52			1.10333
$223$		−	426.781i		−	0.128159i	−0.997945	−	0.0640794i	$-0.979589\pi$
$223$		−	426.781i		−	0.128159i	0.997945	−	0.0640794i	$-0.0204111\pi$
$224$	2911.29			0.868389
$225$	−1020.36			−0.302330
$226$		−	1633.40i		−	0.480763i
$227$		−	2730.32i		−	0.798316i	−0.916882	−	0.399158i	$-0.869302\pi$
$227$		−	2730.32i		−	0.798316i	0.916882	−	0.399158i	$-0.130698\pi$
$228$			3037.53i			0.882303i
$229$		−	877.843i		−	0.253317i	−0.991946	−	0.126658i	$-0.959575\pi$
$229$		−	877.843i		−	0.253317i	0.991946	−	0.126658i	$-0.0404252\pi$
$230$	105.621			0.0302802
$231$	−552.468			−0.157358
$232$			1922.84i			0.544141i
$233$	−4594.32			−1.29178			−0.645888	−	0.763432i	$-0.723513\pi$
$233$	−4594.32			−1.29178			−0.645888	+	0.763432i	$0.723513\pi$
$234$	1635.75	−	50.5232i	0.456974	−	0.0141145i
$235$	140.788			0.0390809
$236$			3627.30i			1.00050i
$237$	3847.76			1.05459
$238$	1964.31			0.534987
$239$		−	3058.65i		−	0.827813i	−0.910319	−	0.413907i	$-0.864164\pi$
$239$		−	3058.65i		−	0.827813i	0.910319	−	0.413907i	$-0.135836\pi$
$240$		−	52.2282i		−	0.0140472i
$241$			246.112i			0.0657820i	0.999459	+	0.0328910i	$0.0104714\pi$
$241$			246.112i			0.0657820i	−0.999459	+	0.0328910i	$0.989529\pi$
$242$			517.183i			0.137379i
$243$	2203.74			0.581770
$244$	−643.193			−0.168755
$245$			61.8215i			0.0161210i
$246$	1025.15			0.265695
$247$	−3193.40	+	98.6344i	−0.822636	+	0.0254087i
$248$	−1853.36			−0.474551
$249$		−	485.414i		−	0.123542i
$250$	315.892			0.0799151
$251$	−5506.45			−1.38472			−0.692359	−	0.721553i	$-0.743429\pi$
$251$	−5506.45			−1.38472			−0.692359	+	0.721553i	$0.743429\pi$
$252$		−	970.858i		−	0.242692i
$253$		−	919.164i		−	0.228408i
$254$			5048.32i			1.24709i
$255$		−	50.9577i		−	0.0125141i
$256$	903.783			0.220650
$257$	−1094.53			−0.265660			−0.132830	−	0.991139i	$-0.542407\pi$
$257$	−1094.53			−0.265660			−0.132830	+	0.991139i	$0.542407\pi$
$258$		−	4468.63i		−	1.07831i
$259$	2277.24			0.546336
$260$	−142.277	+	4.39449i	−0.0339370	+	0.00104821i
$261$	−1619.47			−0.384071
$262$		−	9148.98i		−	2.15735i
$263$	−1468.52			−0.344307			−0.172153	−	0.985070i	$-0.555072\pi$
$263$	−1468.52			−0.344307			−0.172153	+	0.985070i	$0.555072\pi$
$264$	462.970			0.107931
$265$		−	11.6293i		−	0.00269577i
$266$			3371.92i			0.777239i
$267$		−	1879.93i		−	0.430899i
$268$		−	8022.68i		−	1.82859i
$269$	−6900.60			−1.56408			−0.782039	−	0.623229i	$-0.785820\pi$
$269$	−6900.60			−1.56408			−0.782039	+	0.623229i	$0.785820\pi$
$270$	−192.907			−0.0434812
$271$			554.284i			0.124245i	0.998069	+	0.0621224i	$0.0197869\pi$
$271$			554.284i			0.124245i	−0.998069	+	0.0621224i	$0.980213\pi$
$272$	1616.03			0.360243
$273$	−2353.00	+	72.6770i	−0.521649	+	0.0161121i
$274$	−3605.14			−0.794870
$275$		−	1374.04i		−	0.301300i
$276$	−3723.70			−0.812104
$277$	−8531.36			−1.85054			−0.925270	−	0.379310i	$-0.876162\pi$
$277$	−8531.36			−1.85054			−0.925270	+	0.379310i	$0.876162\pi$
$278$		−	8746.89i		−	1.88706i
$279$		−	1560.95i		−	0.334953i
$280$			33.1959i			0.00708512i
$281$			261.071i			0.0554242i	0.999616	+	0.0277121i	$0.00882216\pi$
$281$			261.071i			0.0554242i	−0.999616	+	0.0277121i	$0.991178\pi$
$282$	−8830.29			−1.86467
$283$	5786.71			1.21549			0.607746	−	0.794131i	$-0.292074\pi$
$283$	5786.71			1.21549			0.607746	+	0.794131i	$0.292074\pi$
$284$			5913.72i			1.23562i
$285$	87.4738			0.0181807
$286$	68.0354	+	2202.72i	0.0140665	+	0.455418i
$287$	639.674			0.131564
$288$		−	2054.76i		−	0.420410i
$289$	−3336.28			−0.679072
$290$	250.596			0.0507432
$291$			4466.49i			0.899761i
$292$			5402.99i			1.08283i
$293$		−	4466.22i		−	0.890509i	−0.895404	−	0.445255i	$-0.853113\pi$
$293$		−	4466.22i		−	0.890509i	0.895404	−	0.445255i	$-0.146887\pi$
$294$		−	3877.47i		−	0.769178i
$295$	104.458			0.0206162
$296$	−1908.34			−0.374730
$297$			1678.76i			0.327985i
$298$	3066.33			0.596065
$299$	−120.916	−	3914.79i	−0.0233871	−	0.757184i
$300$	−5566.48			−1.07127
$301$		−	2788.35i		−	0.533947i
$302$	8593.12			1.63735
$303$	5129.70			0.972587
$304$			2774.07i			0.523368i
$305$			18.5225i			0.00347736i
$306$		−	1386.39i		−	0.259002i
$307$		−	2578.45i		−	0.479348i	−0.970853	−	0.239674i	$-0.922959\pi$
$307$		−	2578.45i		−	0.479348i	0.970853	−	0.239674i	$-0.0770405\pi$
$308$	1307.37			0.241865
$309$	−6186.84			−1.13902
$310$			241.542i			0.0442537i
$311$	4244.93			0.773981			0.386990	−	0.922084i	$-0.373515\pi$
$311$	4244.93			0.773981			0.386990	+	0.922084i	$0.373515\pi$
$312$	1971.83	−	60.9037i	0.357797	−	0.0110513i
$313$	5516.53			0.996207			0.498103	−	0.867118i	$-0.334030\pi$
$313$	5516.53			0.996207			0.498103	+	0.867118i	$0.334030\pi$
$314$		−	1670.80i		−	0.300283i
$315$	−27.9585			−0.00500090
$316$	−9105.44			−1.62095
$317$			8229.05i			1.45801i	0.684508	+	0.729005i	$0.260017\pi$
$317$			8229.05i			1.45801i	−0.684508	+	0.729005i	$0.739983\pi$
$318$			729.391i			0.128623i
$319$		−	2180.80i		−	0.382764i
$320$			221.670i			0.0387241i
$321$	−7340.75			−1.27639
$322$	−4133.64			−0.715399
$323$			2706.59i			0.466249i
$324$	4536.09			0.777793
$325$	−180.754	−	5852.13i	−0.0308506	−	0.998824i
$326$	−2596.29			−0.441089
$327$			5216.82i			0.882235i
$328$	−536.050			−0.0902390
$329$	−5509.95			−0.923324
$330$		−	60.3371i		−	0.0100650i
$331$			9065.84i			1.50545i	0.658336	+	0.752724i	$0.271261\pi$
$331$			9065.84i			1.50545i	−0.658336	+	0.752724i	$0.728739\pi$
$332$			1148.70i			0.189888i
$333$		−	1607.26i		−	0.264496i
$334$	14731.5			2.41339
$335$	−231.035			−0.0376799
$336$			2044.03i			0.331877i
$337$	−1819.38			−0.294089			−0.147045	−	0.989130i	$-0.546976\pi$
$337$	−1819.38			−0.294089			−0.147045	+	0.989130i	$0.546976\pi$
$338$	579.535	+	9372.61i	0.0932620	+	1.50829i
$339$	1658.35			0.265691
$340$			120.588i			0.0192347i
$341$	2102.01			0.333812
$342$	2379.87			0.376282
$343$		−	6389.26i		−	1.00580i
$344$			2336.65i			0.366232i
$345$			107.234i			0.0167342i
$346$		−	285.358i		−	0.0443379i
$347$	6353.91			0.982985			0.491492	−	0.870882i	$-0.336452\pi$
$347$	6353.91			0.982985			0.491492	+	0.870882i	$0.336452\pi$
$348$	−8834.84			−1.36091
$349$			3814.24i			0.585019i	0.956263	+	0.292509i	$0.0944903\pi$
$349$			3814.24i			0.585019i	−0.956263	+	0.292509i	$0.905510\pi$
$350$	−6179.28			−0.943705
$351$	220.841	+	7149.97i	0.0335829	+	1.08729i
$352$	2766.98			0.418978
$353$			10332.2i			1.55786i	0.627110	+	0.778931i	$0.284238\pi$
$353$			10332.2i			1.55786i	−0.627110	+	0.778931i	$0.715762\pi$
$354$	−6551.63			−0.983659
$355$	170.302			0.0254611
$356$			4448.72i			0.662308i
$357$			1994.30i			0.295657i
$358$		−	11175.7i		−	1.64987i
$359$		−	5905.08i		−	0.868128i	−0.900882	−	0.434064i	$-0.857079\pi$
$359$		−	5905.08i		−	0.868128i	0.900882	−	0.434064i	$-0.142921\pi$
$360$	23.4293			0.00343010
$361$	2212.88			0.322624
$362$			16960.2i			2.46246i
$363$	−525.081			−0.0759218
$364$	5568.20	−	171.985i	0.801794	−	0.0247650i
$365$	155.594			0.0223127
$366$		−	1161.74i		−	0.165915i
$367$	13851.8			1.97018			0.985090	−	0.172038i	$-0.0550351\pi$
$367$	13851.8			1.97018			0.985090	+	0.172038i	$0.0550351\pi$
$368$	−3400.73			−0.481727
$369$		−	451.476i		−	0.0636935i
$370$			248.707i			0.0349450i
$371$			455.128i			0.0636902i
$372$		−	8515.62i		−	1.18687i
$373$	−11878.0			−1.64885			−0.824424	−	0.565972i	$-0.808501\pi$
$373$	−11878.0			−1.64885			−0.824424	+	0.565972i	$0.808501\pi$
$374$	1866.93			0.258120
$375$			320.716i			0.0441646i
$376$	4617.37			0.633304
$377$	−286.884	−	9288.21i	−0.0391918	−	1.26888i
$378$	7549.68			1.02728
$379$			4585.38i			0.621464i	0.950497	+	0.310732i	$0.100574\pi$
$379$			4585.38i			0.621464i	−0.950497	+	0.310732i	$0.899426\pi$
$380$	−207.000			−0.0279445
$381$	−5125.42			−0.689194
$382$			4061.47i			0.543987i
$383$			2738.17i			0.365311i	0.983177	+	0.182655i	$0.0584692\pi$
$383$			2738.17i			0.365311i	−0.983177	+	0.182655i	$0.941531\pi$
$384$		−	5170.58i		−	0.687136i
$385$		−	37.6494i		−	0.00498387i
$386$	3862.08			0.509261
$387$	−1967.99			−0.258498
$388$		−	10569.6i		−	1.38297i
$389$	73.0815			0.00952540			0.00476270	−	0.999989i	$-0.498484\pi$
$389$	73.0815			0.00952540			0.00476270	+	0.999989i	$0.498484\pi$
$390$	−7.93734	−	256.980i	−0.00103057	−	0.0333659i
$391$	−3318.01			−0.429153
$392$			2027.53i			0.261239i
$393$	9288.70			1.19225
$394$	−12884.9			−1.64754
$395$			262.216i			0.0334013i
$396$		−	922.731i		−	0.117093i
$397$			3133.25i			0.396104i	0.980191	+	0.198052i	$0.0634616\pi$
$397$			3133.25i			0.396104i	−0.980191	+	0.198052i	$0.936538\pi$
$398$		−	10261.3i		−	1.29234i
$399$	−3423.41			−0.429536
$400$	−5083.68			−0.635460
$401$		−	9195.25i		−	1.14511i	−0.819867	−	0.572555i	$-0.805952\pi$
$401$		−	9195.25i		−	1.14511i	0.819867	−	0.572555i	$-0.194048\pi$
$402$	14490.6			1.79782
$403$	8952.60	−	276.519i	1.10660	−	0.0341796i
$404$	−12139.1			−1.49490
$405$		−	130.629i		−	0.0160272i
$406$	−9807.45			−1.19886
$407$	2164.36			0.263595
$408$		−	1671.23i		−	0.202790i
$409$		−	218.502i		−	0.0264162i	−0.999913	−	0.0132081i	$-0.995796\pi$
$409$		−	218.502i		−	0.0264162i	0.999913	−	0.0132081i	$-0.00420439\pi$
$410$			69.8613i			0.00841513i
$411$		−	3660.19i		−	0.439280i
$412$	14640.7			1.75072
$413$	−4088.11			−0.487077
$414$			2917.48i			0.346344i
$415$	33.0798			0.00391283
$416$	11784.8	−	363.996i	1.38893	−	0.0428999i
$417$	8880.47			1.04287
$418$			3204.77i			0.375001i
$419$	15977.6			1.86290			0.931450	−	0.363869i	$-0.118544\pi$
$419$	15977.6			1.86290			0.931450	+	0.363869i	$0.118544\pi$
$420$	−152.525			−0.0177201
$421$			4043.12i			0.468051i	0.972230	+	0.234025i	$0.0751899\pi$
$421$			4043.12i			0.468051i	−0.972230	+	0.234025i	$0.924810\pi$
$422$		−	3557.78i		−	0.410403i
$423$			3888.87i			0.447006i
$424$		−	381.399i		−	0.0436848i
$425$	−4960.01			−0.566108
$426$	−10681.4			−1.21482
$427$		−	724.904i		−	0.0821559i
$428$	17371.3			1.96186
$429$	−2236.36	+	69.0743i	−0.251684	+	0.00777375i
$430$	304.527			0.0341525
$431$			14547.9i			1.62587i	0.582358	+	0.812933i	$0.302130\pi$
$431$			14547.9i			1.62587i	−0.582358	+	0.812933i	$0.697870\pi$
$432$	6211.10			0.691740
$433$	5626.97			0.624515			0.312258	−	0.949997i	$-0.398915\pi$
$433$	5626.97			0.624515			0.312258	+	0.949997i	$0.398915\pi$
$434$		−	9453.08i		−	1.04554i
$435$			254.423i			0.0280429i
$436$		−	12345.2i		−	1.35603i
$437$		−	5695.68i		−	0.623481i
$438$	−9758.89			−1.06461
$439$	−4393.73			−0.477679			−0.238840	−	0.971059i	$-0.576767\pi$
$439$	−4393.73			−0.477679			−0.238840	+	0.971059i	$0.576767\pi$
$440$			31.5503i			0.00341842i
$441$	−1707.64			−0.184391
$442$	7951.40	−	245.595i	0.855678	−	0.0264293i
$443$	10180.2			1.09182			0.545912	−	0.837843i	$-0.316183\pi$
$443$	10180.2			1.09182			0.545912	+	0.837843i	$0.316183\pi$
$444$		−	8768.21i		−	0.937210i
$445$	128.113			0.0136475
$446$	−1824.17			−0.193670
$447$			3113.15i			0.329412i
$448$		−	8675.36i		−	0.914893i
$449$			4141.65i			0.435316i	0.976025	+	0.217658i	$0.0698417\pi$
$449$			4141.65i			0.435316i	−0.976025	+	0.217658i	$0.930158\pi$
$450$			4361.28i			0.456873i
$451$	607.965			0.0634766
$452$	−3924.36			−0.408377
$453$			8724.34i			0.904869i
$454$	−11670.0			−1.20639
$455$	−4.95277	−	160.351i	−0.000510306	−	0.0165217i
$456$	2868.84			0.294617
$457$			12713.7i			1.30136i	0.759352	+	0.650680i	$0.225516\pi$
$457$			12713.7i			1.30136i	−0.759352	+	0.650680i	$0.774484\pi$
$458$	−3752.11			−0.382805
$459$	6060.01			0.616246
$460$		−	253.762i		−	0.0257211i
$461$		−	17549.9i		−	1.77306i	−0.462673	−	0.886529i	$-0.653110\pi$
$461$		−	17549.9i		−	1.77306i	0.462673	−	0.886529i	$-0.346890\pi$
$462$			2361.38i			0.237795i
$463$		−	10960.0i		−	1.10012i	−0.835125	−	0.550060i	$-0.814605\pi$
$463$		−	10960.0i		−	1.10012i	0.835125	−	0.550060i	$-0.185395\pi$
$464$	−8068.57			−0.807271
$465$	−245.230			−0.0244565
$466$			19637.2i			1.95210i
$467$	−7368.99			−0.730184			−0.365092	−	0.930971i	$-0.618963\pi$
$467$	−7368.99			−0.730184			−0.365092	+	0.930971i	$0.618963\pi$
$468$	−121.385	−	3929.98i	−0.0119894	−	0.388170i
$469$	9041.88			0.890224
$470$		−	601.763i		−	0.0590580i
$471$	1696.32			0.165949
$472$	3425.85			0.334084
$473$		−	2650.13i		−	0.257618i
$474$		−	16446.3i		−	1.59367i
$475$		−	8514.34i		−	0.822452i
$476$		−	4719.37i		−	0.454437i
$477$	321.225			0.0308341
$478$	−13073.4			−1.25097
$479$		−	10106.7i		−	0.964065i	−0.876153	−	0.482032i	$-0.839899\pi$
$479$		−	10106.7i		−	0.964065i	0.876153	−	0.482032i	$-0.160101\pi$
$480$	−322.809			−0.0306962
$481$	9218.16	−	284.721i	0.873829	−	0.0269899i
$482$	1051.94			0.0994079
$483$		−	4196.76i		−	0.395361i
$484$	1242.57			0.116695
$485$	−304.381			−0.0284974
$486$		−	9419.33i		−	0.879155i
$487$			16640.4i			1.54835i	0.632969	+	0.774177i	$0.281836\pi$
$487$			16640.4i			1.54835i	−0.632969	+	0.774177i	$0.718164\pi$
$488$			607.473i			0.0563504i
$489$		−	2635.94i		−	0.243765i
$490$	264.240			0.0243615
$491$	13448.1			1.23605			0.618027	−	0.786157i	$-0.287932\pi$
$491$	13448.1			1.23605			0.618027	+	0.786157i	$0.287932\pi$
$492$		−	2462.98i		−	0.225690i
$493$	−7872.29			−0.719168
$494$	421.587	+	13649.4i	0.0383970	+	1.24314i
$495$	−26.5726			−0.00241282
$496$		−	7777.03i		−	0.704030i
$497$	−6665.00			−0.601542
$498$	−2074.78			−0.186693
$499$			19287.6i			1.73032i	0.501496	+	0.865160i	$0.332783\pi$
$499$			19287.6i			1.73032i	−0.501496	+	0.865160i	$0.667217\pi$
$500$		−	758.951i		−	0.0678827i
$501$			14956.5i			1.33374i
$502$			23535.9i			2.09255i
$503$	−2212.03			−0.196083			−0.0980413	−	0.995182i	$-0.531258\pi$
$503$	−2212.03			−0.196083			−0.0980413	+	0.995182i	$0.531258\pi$
$504$	−916.941			−0.0810393
$505$			349.577i			0.0308039i
$506$	−3928.73			−0.345165
$507$	−9515.74	+	588.386i	−0.833548	+	0.0515407i
$508$	12128.9			1.05932
$509$			10398.3i			0.905493i	0.891639	+	0.452747i	$0.149556\pi$
$509$			10398.3i			0.905493i	−0.891639	+	0.452747i	$0.850444\pi$
$510$	−217.806			−0.0189110
$511$	−6089.38			−0.527159
$512$		−	13395.1i		−	1.15622i
$513$			10402.6i			0.895294i
$514$			4678.27i			0.401459i
$515$		−	421.619i		−	0.0360752i
$516$	−10736.2			−0.915957
$517$	−5236.82			−0.445484
$518$		−	9733.48i		−	0.825608i
$519$	289.716			0.0245031
$520$	4.15044	+	134.375i	0.000350017	+	0.0113322i
$521$	−20957.7			−1.76233			−0.881166	−	0.472807i	$-0.843241\pi$
$521$	−20957.7			−1.76233			−0.881166	+	0.472807i	$0.843241\pi$
$522$			6922.00i			0.580398i
$523$	21443.2			1.79282			0.896409	−	0.443228i	$-0.146167\pi$
$523$	21443.2			1.79282			0.896409	+	0.443228i	$0.146167\pi$
$524$	−21981.0			−1.83253
$525$		−	6273.65i		−	0.521532i
$526$			6276.80i			0.520307i
$527$		−	7587.84i		−	0.627194i
$528$			1942.70i			0.160124i
$529$	−5184.67			−0.426125
$530$	−49.7062			−0.00407378
$531$			2885.35i			0.235807i
$532$	8101.25			0.660214
$533$	2589.37	−	79.9777i	0.210428	−	0.00649947i
$534$	−8035.29			−0.651163
$535$		−	500.255i		−	0.0404260i
$536$	−7577.13			−0.610601
$537$	11346.4			0.911790
$538$			29494.8i			2.36359i
$539$		−	2299.54i		−	0.183763i
$540$			463.471i			0.0369344i
$541$			12626.1i			1.00340i	0.865042	+	0.501699i	$0.167292\pi$
$541$			12626.1i			1.00340i	−0.865042	+	0.501699i	$0.832708\pi$
$542$	2369.14			0.187755
$543$	−17219.2			−1.36086
$544$		−	9988.26i		−	0.787212i
$545$	−355.514			−0.0279423
$546$	310.639	+	10057.3i	0.0243482	+	0.788301i
$547$	17202.2			1.34463			0.672317	−	0.740264i	$-0.265299\pi$
$547$	17202.2			1.34463			0.672317	+	0.740264i	$0.265299\pi$
$548$			8661.57i			0.675190i
$549$	−511.630			−0.0397739
$550$	−5872.97			−0.455317
$551$		−	13513.5i		−	1.04482i
$552$			3516.91i			0.271177i
$553$		−	10262.2i		−	0.789137i
$554$			36465.1i			2.79648i
$555$	−252.505			−0.0193121
$556$	−21015.0			−1.60294
$557$		−	21165.4i		−	1.61007i	−0.593231	−	0.805033i	$-0.702148\pi$
$557$		−	21165.4i		−	1.61007i	0.593231	−	0.805033i	$-0.297852\pi$
$558$	−6671.89			−0.506172
$559$	−348.624	−	11287.1i	−0.0263779	−	0.854014i
$560$	−139.296			−0.0105113
$561$			1895.44i			0.142648i
$562$	1115.88			0.0837555
$563$	−12181.9			−0.911908			−0.455954	−	0.890003i	$-0.650702\pi$
$563$	−12181.9			−0.911908			−0.455954	+	0.890003i	$0.650702\pi$
$564$			21215.3i			1.58391i
$565$			113.013i			0.00841500i
$566$		−	24733.8i		−	1.83682i
$567$			5112.35i			0.378657i
$568$	5585.30			0.412595
$569$	14988.3			1.10429			0.552147	−	0.833747i	$-0.313809\pi$
$569$	14988.3			1.10429			0.552147	+	0.833747i	$0.313809\pi$
$570$		−	373.884i		−	0.0274742i
$571$	−144.731			−0.0106073			−0.00530367	−	0.999986i	$-0.501688\pi$
$571$	−144.731			−0.0106073			−0.00530367	+	0.999986i	$0.501688\pi$
$572$	5292.18	−	163.459i	0.386848	−	0.0119486i
$573$	−4123.50			−0.300631
$574$		−	2734.12i		−	0.198815i
$575$	10437.7			0.757015
$576$	−6122.98			−0.442924
$577$		−	8362.30i		−	0.603340i	−0.953412	−	0.301670i	$-0.902456\pi$
$577$		−	8362.30i		−	0.603340i	0.953412	−	0.301670i	$-0.0975441\pi$
$578$			14260.1i			1.02620i
$579$			3921.06i			0.281440i
$580$		−	602.074i		−	0.0431030i
$581$	−1294.63			−0.0924444
$582$	19090.9			1.35969
$583$			432.566i			0.0307291i
$584$	5102.93			0.361577
$585$	−113.175	+	3.49562i	−0.00799862	+	0.000247053i
$586$	−19089.7			−1.34571
$587$		−	17166.0i		−	1.20701i	−0.797359	−	0.603505i	$-0.793770\pi$
$587$		−	17166.0i		−	1.20701i	0.797359	−	0.603505i	$-0.206230\pi$
$588$	−9315.86			−0.653367
$589$	13025.3			0.911199
$590$		−	446.478i		−	0.0311546i
$591$		−	13081.7i		−	0.910504i
$592$		−	8007.72i		−	0.555938i
$593$		−	4113.76i		−	0.284877i	−0.989804	−	0.142438i	$-0.954506\pi$
$593$		−	4113.76i		−	0.284877i	0.989804	−	0.142438i	$-0.0454943\pi$
$594$	7175.43			0.495642
$595$	−135.907			−0.00936411
$596$		−	7367.04i		−	0.506318i
$597$	10418.0			0.714202
$598$	−16732.7	+	516.824i	−1.14424	+	0.0353420i
$599$	−14840.9			−1.01233			−0.506163	−	0.862438i	$-0.668937\pi$
$599$	−14840.9			−1.01233			−0.506163	+	0.862438i	$0.668937\pi$
$600$			5257.35i			0.357717i
$601$	9244.34			0.627429			0.313714	−	0.949517i	$-0.398427\pi$
$601$	9244.34			0.627429			0.313714	+	0.949517i	$0.398427\pi$
$602$	−11918.1			−0.806885
$603$		−	6381.67i		−	0.430981i
$604$		−	20645.5i		−	1.39082i
$605$		−	35.7830i		−	0.00240461i
$606$		−	21925.6i		−	1.46975i
$607$	−19407.7			−1.29775			−0.648876	−	0.760894i	$-0.724761\pi$
$607$	−19407.7			−1.29775			−0.648876	+	0.760894i	$0.724761\pi$
$608$	17145.8			1.14368
$609$		−	9957.22i		−	0.662540i
$610$	79.1696			0.00525489
$611$	−22304.0	+	688.903i	−1.47680	+	0.0456138i
$612$	−3330.88			−0.220005
$613$		−	11289.4i		−	0.743842i	−0.928264	−	0.371921i	$-0.878699\pi$
$613$		−	11289.4i		−	0.743842i	0.928264	−	0.371921i	$-0.121301\pi$
$614$	−11020.9			−0.724377
$615$	−70.9281			−0.00465057
$616$		−	1234.77i		−	0.0807633i
$617$		−	11589.4i		−	0.756193i	−0.925766	−	0.378097i	$-0.876579\pi$
$617$		−	11589.4i		−	0.756193i	0.925766	−	0.378097i	$-0.123421\pi$
$618$			26444.1i			1.72126i
$619$			15574.1i			1.01127i	0.862747	+	0.505635i	$0.168742\pi$
$619$			15574.1i			1.01127i	−0.862747	+	0.505635i	$0.831258\pi$
$620$	580.319			0.0375906
$621$	−12752.5			−0.824061
$622$		−	18143.9i		−	1.16962i
$623$	−5013.89			−0.322435
$624$	255.562	+	8274.11i	0.0163953	+	0.530817i
$625$	15592.2			0.997902
$626$		−	23579.0i		−	1.50544i
$627$	−3253.71			−0.207242
$628$	−4014.21			−0.255071
$629$		−	7812.92i		−	0.495264i
$630$			119.501i			0.00755722i
$631$		−	27292.4i		−	1.72186i	−0.508725	−	0.860929i	$-0.669883\pi$
$631$		−	27292.4i		−	1.72186i	0.508725	−	0.860929i	$-0.330117\pi$
$632$			8599.76i			0.541266i
$633$	3612.11			0.226806
$634$	35172.9			2.20331
$635$		−	349.285i		−	0.0218283i
$636$	1752.41			0.109257
$637$	−302.504	−	9793.91i	−0.0188158	−	0.609182i
$638$	−9321.28			−0.578422
$639$			4704.09i			0.291222i
$640$	352.363			0.0217631
$641$	−8093.08			−0.498686			−0.249343	−	0.968415i	$-0.580215\pi$
$641$	−8093.08			−0.498686			−0.249343	+	0.968415i	$0.580215\pi$
$642$			31376.1i			1.92884i
$643$			23867.9i			1.46385i	0.681384	+	0.731926i	$0.261379\pi$
$643$			23867.9i			1.46385i	−0.681384	+	0.731926i	$0.738621\pi$
$644$			9931.33i			0.607685i
$645$			309.177i			0.0188742i
$646$	11568.6			0.704583
$647$	18520.7			1.12538			0.562692	−	0.826667i	$-0.309766\pi$
$647$	18520.7			1.12538			0.562692	+	0.826667i	$0.309766\pi$
$648$		−	4284.18i		−	0.259720i
$649$	−3885.46			−0.235004
$650$	−25013.4	+	772.588i	−1.50940	+	0.0466206i
$651$	9597.44			0.577808
$652$			6237.75i			0.374676i
$653$	7350.61			0.440508			0.220254	−	0.975443i	$-0.429311\pi$
$653$	7350.61			0.440508			0.220254	+	0.975443i	$0.429311\pi$
$654$	22297.9			1.33321
$655$			633.003i			0.0377610i
$656$		−	2249.36i		−	0.133876i
$657$			4297.83i			0.255212i
$658$			23550.9i			1.39530i
$659$	−6793.50			−0.401574			−0.200787	−	0.979635i	$-0.564350\pi$
$659$	−6793.50			−0.401574			−0.200787	+	0.979635i	$0.564350\pi$
$660$	−144.964			−0.00854956
$661$		−	2867.64i		−	0.168742i	−0.996434	−	0.0843709i	$-0.973112\pi$
$661$		−	2867.64i		−	0.168742i	0.996434	−	0.0843709i	$-0.0268880\pi$
$662$	38749.6			2.27499
$663$	249.345	+	8072.83i	0.0146060	+	0.472885i
$664$	1084.90			0.0634072
$665$		−	233.298i		−	0.0136043i
$666$	−6869.80			−0.399699
$667$	16566.3			0.961691
$668$		−	35393.3i		−	2.05001i
$669$		−	1852.02i		−	0.107030i
$670$			987.499i			0.0569409i
$671$		−	688.970i		−	0.0396384i
$672$	12633.6			0.725226
$673$	33234.8			1.90358			0.951788	−	0.306756i	$-0.0992434\pi$
$673$	33234.8			1.90358			0.951788	+	0.306756i	$0.0992434\pi$
$674$			7776.47i			0.444419i
$675$	−19063.5			−1.08704
$676$	22518.3	−	1392.37i	1.28120	−	0.0792200i
$677$	−10422.3			−0.591669			−0.295835	−	0.955239i	$-0.595598\pi$
$677$	−10422.3			−0.591669			−0.295835	+	0.955239i	$0.595598\pi$
$678$		−	7088.18i		−	0.401504i
$679$	11912.4			0.673277
$680$	113.891			0.00642281
$681$		−	11848.3i		−	0.666705i
$682$		−	8984.48i		−	0.504448i
$683$			31006.8i			1.73710i	0.495600	+	0.868551i	$0.334948\pi$
$683$			31006.8i			1.73710i	−0.495600	+	0.868551i	$0.665052\pi$
$684$		−	5717.79i		−	0.319627i
$685$	249.434			0.0139129
$686$	−27309.2			−1.51993
$687$		−	3809.41i		−	0.211555i
$688$	−9804.99			−0.543331
$689$	56.9040	+	1842.33i	0.00314640	+	0.101868i
$690$	458.345			0.0252882
$691$		−	5840.00i		−	0.321511i	−0.986994	−	0.160755i	$-0.948607\pi$
$691$		−	5840.00i		−	0.321511i	0.986994	−	0.160755i	$-0.0513930\pi$
$692$	−685.590			−0.0376622
$693$	1039.95			0.0570052
$694$		−	27158.1i		−	1.48546i
$695$			605.183i			0.0330301i
$696$			8344.20i			0.454434i
$697$		−	2194.64i		−	0.119265i
$698$	16303.0			0.884064
$699$	−19937.1			−1.07881
$700$			14846.1i			0.801615i
$701$	−21174.3			−1.14086			−0.570431	−	0.821346i	$-0.693224\pi$
$701$	−21174.3			−1.14086			−0.570431	+	0.821346i	$0.693224\pi$
$702$	30560.7	−	943.927i	1.64308	−	0.0507496i
$703$	13411.6			0.719529
$704$		−	8245.31i		−	0.441416i
$705$	610.953			0.0326380
$706$	44162.1			2.35420
$707$		−	13681.2i		−	0.727772i
$708$			15740.7i			0.835554i
$709$			36423.9i			1.92938i	0.263391	+	0.964689i	$0.415159\pi$
$709$			36423.9i			1.92938i	−0.263391	+	0.964689i	$0.584841\pi$
$710$		−	727.911i		−	0.0384761i
$711$	−7242.95			−0.382042
$712$	4201.66			0.221157
$713$			15967.7i			0.838701i
$714$	8524.13			0.446789
$715$	−4.70725	−	152.403i	−0.000246212	−	0.00797138i
$716$	−26850.3			−1.40146
$717$		−	13273.0i		−	0.691340i
$718$	−25239.7			−1.31189
$719$	1016.87			0.0527440			0.0263720	−	0.999652i	$-0.491605\pi$
$719$	1016.87			0.0527440			0.0263720	+	0.999652i	$0.491605\pi$
$720$			98.3135i			0.00508879i
$721$			16500.7i			0.852311i
$722$		−	9458.39i		−	0.487541i
$723$			1068.01i			0.0549371i
$724$	40748.0			2.09170
$725$	24764.5			1.26860
$726$			2244.32i			0.114731i
$727$	12283.3			0.626633			0.313316	−	0.949649i	$-0.398560\pi$
$727$	12283.3			0.626633			0.313316	+	0.949649i	$0.398560\pi$
$728$	−162.433	−	5258.97i	−0.00826949	−	0.267734i
$729$	21489.6			1.09179
$730$		−	665.045i		−	0.0337184i
$731$	−9566.46			−0.484033
$732$	−2791.15			−0.140934
$733$			33618.5i			1.69404i	0.531565	+	0.847018i	$0.321604\pi$
$733$			33618.5i			1.69404i	−0.531565	+	0.847018i	$0.678396\pi$
$734$		−	59205.8i		−	2.97728i
$735$			268.275i			0.0134633i
$736$			21019.1i			1.05268i
$737$	8593.66			0.429514
$738$	−1929.72			−0.0962518
$739$		−	22942.0i		−	1.14199i	−0.820952	−	0.570997i	$-0.806557\pi$
$739$		−	22942.0i		−	1.14199i	0.820952	−	0.570997i	$-0.193443\pi$
$740$	597.533			0.0296835
$741$	−13857.8	+	428.025i	−0.687016	+	0.0212198i
$742$	1945.32			0.0962468
$743$			11157.6i			0.550917i	0.961313	+	0.275458i	$0.0888297\pi$
$743$			11157.6i			0.550917i	−0.961313	+	0.275458i	$0.911170\pi$
$744$	−8042.70			−0.396317
$745$	−212.154			−0.0104332
$746$			50769.5i			2.49169i
$747$			913.735i			0.0447548i
$748$		−	4485.42i		−	0.219256i
$749$			19578.2i			0.955102i
$750$	1370.82			0.0667403
$751$	8534.37			0.414678			0.207339	−	0.978269i	$-0.433520\pi$
$751$	8534.37			0.414678			0.207339	+	0.978269i	$0.433520\pi$
$752$			19375.2i			0.939551i
$753$	−23895.3			−1.15643
$754$	−39700.0	+	1226.21i	−1.91749	+	0.0592255i
$755$	−594.544			−0.0286591
$756$		−	18138.6i		−	0.872611i
$757$	−34403.9			−1.65182			−0.825912	−	0.563799i	$-0.809339\pi$
$757$	−34403.9			−1.65182			−0.825912	+	0.563799i	$0.809339\pi$
$758$	19599.0			0.939140
$759$		−	3988.72i		−	0.190753i
$760$			195.504i			0.00933117i
$761$			9083.21i			0.432676i	0.976319	+	0.216338i	$0.0694113\pi$
$761$			9083.21i			0.432676i	−0.976319	+	0.216338i	$0.930589\pi$
$762$			21907.3i			1.04149i
$763$	13913.5			0.660163
$764$	9757.95			0.462082
$765$			95.9219i			0.00453341i
$766$	11703.6			0.552047
$767$	−16548.4	+	511.131i	−0.779048	+	0.0240624i
$768$	3921.98			0.184274
$769$			5495.59i			0.257706i	0.991664	+	0.128853i	$0.0411296\pi$
$769$			5495.59i			0.257706i	−0.991664	+	0.128853i	$0.958870\pi$
$770$	−160.922			−0.00753148
$771$	−4749.72			−0.221864
$772$		−	9278.90i		−	0.432584i
$773$			7785.64i			0.362264i	0.983459	+	0.181132i	$0.0579761\pi$
$773$			7785.64i			0.362264i	−0.983459	+	0.181132i	$0.942024\pi$
$774$			8411.67i			0.390635i
$775$			23869.7i			1.10636i
$776$	−9982.63			−0.461798
$777$	9882.13			0.456267
$778$		−	312.368i		−	0.0143945i
$779$	3767.30			0.173270
$780$	−617.412	+	19.0700i	−0.0283422	+	0.000875403i
$781$	−6334.61			−0.290231
$782$			14182.0i			0.648524i
$783$	−30256.6			−1.38095
$784$	−8507.86			−0.387567
$785$			115.600i			0.00525598i
$786$		−	39702.1i		−	1.80169i
$787$		−	18657.7i		−	0.845075i	−0.906345	−	0.422537i	$-0.861140\pi$
$787$		−	18657.7i		−	0.845075i	0.906345	−	0.422537i	$-0.138860\pi$
$788$			30956.8i			1.39948i
$789$	−6372.65			−0.287544
$790$	1120.77			0.0504751
$791$		−	4422.91i		−	0.198812i
$792$	−871.487			−0.0390997
$793$	−90.6339	−	2934.37i	−0.00405864	−	0.131403i
$794$	13392.3			0.598582
$795$		−	50.4653i		−	0.00225135i
$796$	−24653.3			−1.09776
$797$	11130.4			0.494679			0.247340	−	0.968929i	$-0.420444\pi$
$797$	11130.4			0.494679			0.247340	+	0.968929i	$0.420444\pi$
$798$			14632.5i			0.649104i
$799$			18903.9i			0.837012i
$800$			31420.9i			1.38862i
$801$			3538.75i			0.156099i
$802$	−39302.7			−1.73046
$803$	−5787.52			−0.254343
$804$		−	34814.5i		−	1.52713i
$805$	285.999			0.0125219
$806$	−1181.91	−	38265.6i	−0.0516512	−	1.67227i
$807$	−29945.3			−1.30622
$808$			11464.9i			0.499176i
$809$	30801.9			1.33861			0.669307	−	0.742986i	$-0.266591\pi$
$809$	30801.9			1.33861			0.669307	+	0.742986i	$0.266591\pi$
$810$	−558.340			−0.0242198
$811$		−	33447.1i		−	1.44820i	−0.689697	−	0.724098i	$-0.742256\pi$
$811$		−	33447.1i		−	1.44820i	0.689697	−	0.724098i	$-0.257744\pi$
$812$			23563.0i			1.01835i
$813$			2405.32i			0.103762i
$814$		−	9250.98i		−	0.398338i
$815$	179.633			0.00772057
$816$	7012.78			0.300854
$817$		−	16421.8i		−	0.703213i
$818$	−933.931			−0.0399195
$819$	4429.25	−	136.806i	0.188975	−	0.00583686i
$820$	167.846			0.00714810
$821$		−	3022.20i		−	0.128472i	−0.997935	−	0.0642360i	$-0.979539\pi$
$821$		−	3022.20i		−	0.128472i	0.997935	−	0.0642360i	$-0.0204610\pi$
$822$	−15644.5			−0.663828
$823$	−16292.5			−0.690060			−0.345030	−	0.938592i	$-0.612131\pi$
$823$	−16292.5			−0.690060			−0.345030	+	0.938592i	$0.612131\pi$
$824$		−	13827.6i		−	0.584597i
$825$		−	5962.66i		−	0.251628i
$826$			17473.6i			0.736057i
$827$		−	11340.8i		−	0.476856i	−0.971160	−	0.238428i	$-0.923368\pi$
$827$		−	11340.8i		−	0.476856i	0.971160	−	0.238428i	$-0.0766321\pi$
$828$	7009.43			0.294196
$829$	−9566.57			−0.400797			−0.200399	−	0.979714i	$-0.564224\pi$
$829$	−9566.57			−0.400797			−0.200399	+	0.979714i	$0.564224\pi$
$830$		−	141.391i		−	0.00591296i
$831$	−37021.9			−1.54546
$832$	−1084.67	−	35117.4i	−0.0451973	−	1.46331i
$833$	−8300.89			−0.345269
$834$		−	37957.3i		−	1.57596i
$835$	−1019.25			−0.0422425
$836$	7699.66			0.318539
$837$		−	29163.4i		−	1.20434i
$838$		−	68292.0i		−	2.81516i
$839$			21117.2i			0.868946i	0.900685	+	0.434473i	$0.143065\pi$
$839$			21117.2i			0.868946i	−0.900685	+	0.434473i	$0.856935\pi$
$840$			144.054i			0.00591707i
$841$	14916.0			0.611588
$842$	17281.3			0.707306
$843$			1132.92i			0.0462869i
$844$	−8547.78			−0.348610
$845$	−40.0971	−	648.475i	−0.00163240	−	0.0264003i
$846$	16622.0			0.675503
$847$			1400.42i			0.0568111i
$848$	1600.41			0.0648095
$849$	25111.5			1.01511
$850$			21200.3i			0.855487i
$851$			16441.3i			0.662281i
$852$			25662.7i			1.03191i
$853$			15065.9i			0.604742i	0.953190	+	0.302371i	$0.0977782\pi$
$853$			15065.9i			0.604742i	−0.953190	+	0.302371i	$0.902222\pi$
$854$	−3098.42			−0.124152
$855$	−164.659			−0.00658623
$856$		−	16406.6i		−	0.655101i
$857$	24221.6			0.965454			0.482727	−	0.875771i	$-0.339646\pi$
$857$	24221.6			0.965454			0.482727	+	0.875771i	$0.339646\pi$
$858$	295.240	+	9558.74i	0.0117475	+	0.380338i
$859$	−12928.4			−0.513517			−0.256758	−	0.966476i	$-0.582654\pi$
$859$	−12928.4			−0.513517			−0.256758	+	0.966476i	$0.582654\pi$
$860$		−	731.645i		−	0.0290103i
$861$	2775.87			0.109874
$862$	62181.2			2.45696
$863$			1369.14i			0.0540047i	0.999635	+	0.0270024i	$0.00859616\pi$
$863$			1369.14i			0.0540047i	−0.999635	+	0.0270024i	$0.991404\pi$
$864$		−	38389.2i		−	1.51161i
$865$			19.7434i			0.000776066i
$866$		−	24051.0i		−	0.943750i
$867$	−14477.8			−0.567120
$868$	−22711.6			−0.888114
$869$		−	9753.48i		−	0.380741i
$870$	1087.47			0.0423777
$871$	36601.0	−	1130.49i	1.42386	−	0.0439786i
$872$	−11659.6			−0.452803
$873$		−	8407.65i		−	0.325952i
$874$	−24344.7			−0.942187
$875$	855.368			0.0330477
$876$			23446.3i			0.904313i
$877$		−	21506.7i		−	0.828085i	−0.910258	−	0.414042i	$-0.864117\pi$
$877$		−	21506.7i		−	0.828085i	0.910258	−	0.414042i	$-0.135883\pi$
$878$			18779.8i			0.721855i
$879$		−	19381.2i		−	0.743700i
$880$	−132.391			−0.00507146
$881$	5767.13			0.220544			0.110272	−	0.993901i	$-0.464828\pi$
$881$	5767.13			0.220544			0.110272	+	0.993901i	$0.464828\pi$
$882$			7298.87i			0.278646i
$883$	−40233.2			−1.53336			−0.766680	−	0.642030i	$-0.778092\pi$
$883$	−40233.2			−1.53336			−0.766680	+	0.642030i	$0.778092\pi$
$884$	−590.057	−	19103.8i	−0.0224500	−	0.726843i
$885$	453.296			0.0172174
$886$		−	43512.8i		−	1.64993i
$887$	−31997.0			−1.21122			−0.605611	−	0.795761i	$-0.707071\pi$
$887$	−31997.0			−1.21122			−0.605611	+	0.795761i	$0.707071\pi$
$888$	−8281.27			−0.312952
$889$			13669.8i			0.515714i
$890$		−	547.586i		−	0.0206237i
$891$			4858.93i			0.182694i
$892$			4382.68i			0.164510i
$893$	−32450.4			−1.21603
$894$	13306.4			0.497798
$895$			773.227i			0.0288784i
$896$	−13790.2			−0.514173
$897$	−524.716	−	16988.3i	−0.0195315	−	0.632355i
$898$	17702.4			0.657837
$899$			37884.8i			1.40548i
$900$	10478.2			0.388083
$901$	1561.48			0.0577364
$902$		−	2598.59i		−	0.0959240i
$903$		−	12100.1i		−	0.445920i
$904$			3706.42i			0.136365i
$905$		−	1173.45i		−	0.0431014i
$906$	37290.0			1.36741
$907$	−19192.1			−0.702605			−0.351302	−	0.936262i	$-0.614261\pi$
$907$	−19192.1			−0.702605			−0.351302	+	0.936262i	$0.614261\pi$
$908$			28038.0i			1.02475i
$909$	−9656.06			−0.352334
$910$	−685.381	+	21.1693i	−0.0249672	+	0.000771161i
$911$	−3361.95			−0.122268			−0.0611341	−	0.998130i	$-0.519472\pi$
$911$	−3361.95			−0.122268			−0.0611341	+	0.998130i	$0.519472\pi$
$912$			12038.1i			0.437085i
$913$	−1230.45			−0.0446024
$914$	54341.4			1.96658
$915$			80.3786i			0.00290408i
$916$			9014.69i			0.325168i
$917$		−	24773.5i		−	0.892140i
$918$		−	25901.9i		−	0.931254i
$919$	25861.9			0.928298			0.464149	−	0.885757i	$-0.346360\pi$
$919$	25861.9			0.928298			0.464149	+	0.885757i	$0.346360\pi$
$920$	−239.669			−0.00858875
$921$		−	11189.2i		−	0.400323i
$922$	−75012.4			−2.67940
$923$	−26979.6	+	833.317i	−0.962127	+	0.0297172i
$924$	5673.36			0.201991
$925$			24577.8i			0.873634i
$926$	−46845.8			−1.66247
$927$	11646.0			0.412627
$928$			49869.7i			1.76407i
$929$			41969.4i			1.48221i	0.671390	+	0.741104i	$0.265698\pi$
$929$			41969.4i			1.48221i	−0.671390	+	0.741104i	$0.734302\pi$
$930$			1048.17i			0.0369580i
$931$		−	14249.3i		−	0.501613i
$932$	47179.7			1.65818
$933$	18420.9			0.646382
$934$			31496.8i			1.10343i
$935$	−129.170			−0.00451798
$936$	−3711.73	+	114.644i	−0.129617	+	0.00400348i
$937$	4940.31			0.172244			0.0861221	−	0.996285i	$-0.472552\pi$
$937$	4940.31			0.172244			0.0861221	+	0.996285i	$0.472552\pi$
$938$		−	38647.2i		−	1.34528i
$939$	23939.1			0.831972
$940$	−1445.77			−0.0501659
$941$			39192.7i			1.35775i	0.734252	+	0.678877i	$0.237533\pi$
$941$			39192.7i			1.35775i	−0.734252	+	0.678877i	$0.762467\pi$
$942$		−	7250.47i		−	0.250778i
$943$			4618.34i			0.159484i
$944$			14375.5i			0.495637i
$945$	−522.350			−0.0179810
$946$	−11327.3			−0.389305
$947$			36734.5i			1.26052i	0.776385	+	0.630259i	$0.217051\pi$
$947$			36734.5i			1.26052i	−0.776385	+	0.630259i	$0.782949\pi$
$948$	−39513.2			−1.35372
$949$	−24649.5	+	761.348i	−0.843158	+	0.0260426i
$950$	−36392.4			−1.24287
$951$			35710.1i			1.21764i
$952$	−4457.27			−0.151745
$953$	−6994.80			−0.237758			−0.118879	−	0.992909i	$-0.537930\pi$
$953$	−6994.80			−0.237758			−0.118879	+	0.992909i	$0.537930\pi$
$954$		−	1372.99i		−	0.0465956i
$955$		−	281.007i		−	0.00952164i
$956$			31409.7i			1.06262i
$957$		−	9463.63i		−	0.319661i
$958$	−43198.5			−1.45687
$959$	−9761.94			−0.328706
$960$			961.939i			0.0323400i
$961$	−6724.94			−0.225737
$962$	−1216.97	−	39400.6i	−0.0407864	−	1.32051i
$963$	13818.1			0.462390
$964$		−	2527.35i		−	0.0844405i
$965$	−267.211			−0.00891381
$966$	−17938.0			−0.597458
$967$		−	16441.3i		−	0.546758i	−0.961906	−	0.273379i	$-0.911859\pi$
$967$		−	16441.3i		−	0.546758i	0.961906	−	0.273379i	$-0.0881413\pi$
$968$		−	1173.56i		−	0.0389665i
$969$			11745.3i			0.389383i
$970$			1301.00i			0.0430645i
$971$	−815.576			−0.0269548			−0.0134774	−	0.999909i	$-0.504290\pi$
$971$	−815.576			−0.0269548			−0.0134774	+	0.999909i	$0.504290\pi$
$972$	−22630.5			−0.746785
$973$		−	23684.7i		−	0.780366i
$974$	71125.1			2.33983
$975$	−784.387	−	25395.4i	−0.0257646	−	0.834158i
$976$	−2549.06			−0.0835998
$977$			14340.9i			0.469606i	0.972043	+	0.234803i	$0.0754444\pi$
$977$			14340.9i			0.469606i	−0.972043	+	0.234803i	$0.924556\pi$
$978$	−11266.6			−0.368371
$979$	−4765.34			−0.155568
$980$		−	634.854i		−	0.0206935i
$981$		−	9820.05i		−	0.319602i
$982$		−	57480.3i		−	1.86789i
$983$			5189.65i			0.168387i	0.996449	+	0.0841933i	$0.0268313\pi$
$983$			5189.65i			0.168387i	−0.996449	+	0.0841933i	$0.973169\pi$
$984$	−2326.20			−0.0753622
$985$	891.485			0.0288376
$986$			33648.0i			1.08679i
$987$	−23910.5			−0.771105
$988$	32793.4	−	1012.89i	1.05597	−	0.0326157i
$989$	20131.4			0.647262
$990$			113.578i			0.00364619i
$991$	−9352.86			−0.299802			−0.149901	−	0.988701i	$-0.547895\pi$
$991$	−9352.86			−0.299802			−0.149901	+	0.988701i	$0.547895\pi$
$992$	−48067.8			−1.53846
$993$			39341.3i			1.25726i
$994$			28487.8i			0.909033i
$995$			709.959i			0.0226203i
$996$			4984.79i			0.158583i
$997$	−43798.5			−1.39129			−0.695644	−	0.718387i	$-0.744881\pi$
$997$	−43798.5			−1.39129			−0.695644	+	0.718387i	$0.744881\pi$
$998$	82439.6			2.61481
$999$		−	30028.4i		−	0.951008i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.b.a.12.6	✓	36
13.5	odd	4		1859.4.a.k.1.3		18
13.8	odd	4		1859.4.a.j.1.16		18
13.12	even	2	inner	143.4.b.a.12.31	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.6	✓	36	1.1	even	1	trivial
143.4.b.a.12.31	yes	36	13.12	even	2	inner
1859.4.a.j.1.16		18	13.8	odd	4
1859.4.a.k.1.3		18	13.5	odd	4

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.27424i q^{2} +4.33951 q^{3} -10.2691 q^{4} +0.295728i q^{5} -18.5481i q^{6} -11.5737i q^{7} +9.69883i q^{8} -8.16862 q^{9} +O(q^{10})\)	\(q-4.27424i q^{2} +4.33951 q^{3} -10.2691 q^{4} +0.295728i q^{5} -18.5481i q^{6} -11.5737i q^{7} +9.69883i q^{8} -8.16862 q^{9} +1.26401 q^{10} -11.0000i q^{11} -44.5631 q^{12} +(-1.44705 - 46.8498i) q^{13} -49.4689 q^{14} +1.28331i q^{15} -40.6979 q^{16} -39.7079 q^{17} +34.9147i q^{18} -68.1624i q^{19} -3.03687i q^{20} -50.2243i q^{21} -47.0167 q^{22} +83.5604 q^{23} +42.0882i q^{24} +124.913 q^{25} +(-200.247 + 6.18503i) q^{26} -152.615 q^{27} +118.852i q^{28} +198.255 q^{29} +5.48519 q^{30} +191.091i q^{31} +251.543i q^{32} -47.7347i q^{33} +169.721i q^{34} +3.42267 q^{35} +83.8847 q^{36} +196.760i q^{37} -291.343 q^{38} +(-6.27949 - 203.305i) q^{39} -2.86821 q^{40} +55.2695i q^{41} -214.671 q^{42} +240.921 q^{43} +112.960i q^{44} -2.41569i q^{45} -357.157i q^{46} -476.074i q^{47} -176.609 q^{48} +209.049 q^{49} -533.906i q^{50} -172.313 q^{51} +(14.8599 + 481.107i) q^{52} -39.3242 q^{53} +652.312i q^{54} +3.25300 q^{55} +112.252 q^{56} -295.792i q^{57} -847.389i q^{58} -353.223i q^{59} -13.1785i q^{60} +62.6336 q^{61} +816.771 q^{62} +94.5414i q^{63} +749.574 q^{64} +(13.8548 - 0.427932i) q^{65} -204.029 q^{66} +781.242i q^{67} +407.766 q^{68} +362.611 q^{69} -14.6293i q^{70} -575.874i q^{71} -79.2261i q^{72} -526.139i q^{73} +840.998 q^{74} +542.060 q^{75} +699.969i q^{76} -127.311 q^{77} +(-868.976 + 26.8400i) q^{78} +886.680 q^{79} -12.0355i q^{80} -441.721 q^{81} +236.235 q^{82} -111.859i q^{83} +515.760i q^{84} -11.7427i q^{85} -1029.75i q^{86} +860.330 q^{87} +106.687 q^{88} -433.213i q^{89} -10.3252 q^{90} +(-542.227 + 16.7477i) q^{91} -858.093 q^{92} +829.244i q^{93} -2034.86 q^{94} +20.1575 q^{95} +1091.58i q^{96} +1029.26i q^{97} -893.526i q^{98} +89.8548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) \) 36 * q - 152 * q^4 + 360 * q^9	\( 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) \) 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Introduction

L-functions

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