LMFDB - Embedded newform 252.4.e.a.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(71,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("252.71");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.e (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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.1
Character	$\chi$	$=$	252.71
Dual form			252.4.e.a.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82720 - 0.0833946i) q^{2} +(7.98609 + 0.471546i) q^{4} -8.62666i q^{5} -7.00000i q^{7} +(-22.5389 - 1.99915i) q^{8} +O(q^{10})$	\(q+(-2.82720 - 0.0833946i) q^{2} +(7.98609 + 0.471546i) q^{4} -8.62666i q^{5} -7.00000i q^{7} +(-22.5389 - 1.99915i) q^{8} +(-0.719417 + 24.3893i) q^{10} -44.2558 q^{11} -3.70463 q^{13} +(-0.583762 + 19.7904i) q^{14} +(63.5553 + 7.53161i) q^{16} -35.8211i q^{17} +88.8088i q^{19} +(4.06787 - 68.8933i) q^{20} +(125.120 + 3.69069i) q^{22} -41.2086 q^{23} +50.5807 q^{25} +(10.4737 + 0.308946i) q^{26} +(3.30082 - 55.9026i) q^{28} -12.7794i q^{29} +67.8021i q^{31} +(-179.055 - 26.5935i) q^{32} +(-2.98728 + 101.273i) q^{34} -60.3866 q^{35} -339.755 q^{37} +(7.40617 - 251.080i) q^{38} +(-17.2460 + 194.436i) q^{40} +450.831i q^{41} -60.2125i q^{43} +(-353.431 - 20.8686i) q^{44} +(116.505 + 3.43658i) q^{46} -243.426 q^{47} -49.0000 q^{49} +(-143.002 - 4.21816i) q^{50} +(-29.5855 - 1.74690i) q^{52} +587.360i q^{53} +381.780i q^{55} +(-13.9940 + 157.773i) q^{56} +(-1.06573 + 36.1298i) q^{58} -393.669 q^{59} -890.660 q^{61} +(5.65432 - 191.690i) q^{62} +(504.007 + 90.1174i) q^{64} +31.9586i q^{65} +497.143i q^{67} +(16.8913 - 286.070i) q^{68} +(170.725 + 5.03592i) q^{70} -94.3384 q^{71} -636.939 q^{73} +(960.556 + 28.3338i) q^{74} +(-41.8774 + 709.235i) q^{76} +309.791i q^{77} -1118.13i q^{79} +(64.9727 - 548.270i) q^{80} +(37.5968 - 1274.59i) q^{82} +1167.84 q^{83} -309.016 q^{85} +(-5.02139 + 170.233i) q^{86} +(997.479 + 88.4740i) q^{88} -328.229i q^{89} +25.9324i q^{91} +(-329.096 - 19.4318i) q^{92} +(688.213 + 20.3004i) q^{94} +766.124 q^{95} -467.361 q^{97} +(138.533 + 4.08633i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 24 q^{4}+O(q^{10}) $ 36 * q - 24 * q^4	$ 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64} - 504 q^{70} - 2520 q^{76} + 1032 q^{82} - 3144 q^{85} + 2748 q^{88} + 5496 q^{94}+O(q^{100}) $ 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−2.82720	−	0.0833946i	−0.999565	−	0.0294844i
$2$	−2.82720	−	0.0833946i	−0.999565	−	0.0294844i
$3$		0			0
$3$		0			0
$4$	7.98609	+	0.471546i	0.998261	+	0.0589432i
$5$		−	8.62666i		−	0.771592i	−0.922584	−	0.385796i	$-0.873927\pi$
$5$		−	8.62666i		−	0.771592i	0.922584	−	0.385796i	$-0.126073\pi$
$6$		0			0
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$	−22.5389	−	1.99915i	−0.996089	−	0.0883508i
$9$		0			0
$10$	−0.719417	+	24.3893i	−0.0227500	+	0.771257i
$11$	−44.2558			−1.21306			−0.606529	−	0.795062i	$-0.707438\pi$
$11$	−44.2558			−1.21306			−0.606529	+	0.795062i	$0.707438\pi$
$12$		0			0
$13$	−3.70463			−0.0790368			−0.0395184	−	0.999219i	$-0.512582\pi$
$13$	−3.70463			−0.0790368			−0.0395184	+	0.999219i	$0.512582\pi$
$14$	−0.583762	+	19.7904i	−0.0111441	+	0.377800i
$15$		0			0
$16$	63.5553	+	7.53161i	0.993051	+	0.117681i
$17$		−	35.8211i		−	0.511052i	−0.966802	−	0.255526i	$-0.917751\pi$
$17$		−	35.8211i		−	0.511052i	0.966802	−	0.255526i	$-0.0822486\pi$
$18$		0			0
$19$			88.8088i			1.07232i	0.844115	+	0.536162i	$0.180126\pi$
$19$			88.8088i			1.07232i	−0.844115	+	0.536162i	$0.819874\pi$
$20$	4.06787	−	68.8933i	0.0454801	−	0.770251i
$21$		0			0
$22$	125.120	+	3.69069i	1.21253	+	0.0357663i
$23$	−41.2086			−0.373591			−0.186796	−	0.982399i	$-0.559810\pi$
$23$	−41.2086			−0.373591			−0.186796	+	0.982399i	$0.559810\pi$
$24$		0			0
$25$	50.5807			0.404646
$26$	10.4737	+	0.308946i	0.0790024	+	0.00233035i
$27$		0			0
$28$	3.30082	−	55.9026i	0.0222784	−	0.377307i
$29$		−	12.7794i		−	0.0818299i	−0.999163	−	0.0409149i	$-0.986973\pi$
$29$		−	12.7794i		−	0.0818299i	0.999163	−	0.0409149i	$-0.0130273\pi$
$30$		0			0
$31$			67.8021i			0.392826i	0.980521	+	0.196413i	$0.0629293\pi$
$31$			67.8021i			0.392826i	−0.980521	+	0.196413i	$0.937071\pi$
$32$	−179.055	−	26.5935i	−0.989150	−	0.146910i
$33$		0			0
$34$	−2.98728	+	101.273i	−0.0150681	+	0.510830i
$35$	−60.3866			−0.291634
$36$		0			0
$37$	−339.755			−1.50961			−0.754803	−	0.655951i	$-0.772268\pi$
$37$	−339.755			−1.50961			−0.754803	+	0.655951i	$0.772268\pi$
$38$	7.40617	−	251.080i	0.0316168	−	1.07186i
$39$		0			0
$40$	−17.2460	+	194.436i	−0.0681707	+	0.768575i
$41$			450.831i			1.71727i	0.512590	+	0.858634i	$0.328686\pi$
$41$			450.831i			1.71727i	−0.512590	+	0.858634i	$0.671314\pi$
$42$		0			0
$43$		−	60.2125i		−	0.213542i	−0.994284	−	0.106771i	$-0.965949\pi$
$43$		−	60.2125i		−	0.213542i	0.994284	−	0.106771i	$-0.0340512\pi$
$44$	−353.431	−	20.8686i	−1.21095	−	0.0715015i
$45$		0			0
$46$	116.505	+	3.43658i	0.373429	+	0.0110151i
$47$	−243.426			−0.755474			−0.377737	−	0.925913i	$-0.623298\pi$
$47$	−243.426			−0.755474			−0.377737	+	0.925913i	$0.623298\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	−143.002	−	4.21816i	−0.404470	−	0.0119307i
$51$		0			0
$52$	−29.5855	−	1.74690i	−0.0788994	−	0.00465868i
$53$			587.360i			1.52227i	0.648596	+	0.761133i	$0.275356\pi$
$53$			587.360i			1.52227i	−0.648596	+	0.761133i	$0.724644\pi$
$54$		0			0
$55$			381.780i			0.935985i
$56$	−13.9940	+	157.773i	−0.0333934	+	0.376486i
$57$		0			0
$58$	−1.06573	+	36.1298i	−0.00241271	+	0.0817943i
$59$	−393.669			−0.868667			−0.434333	−	0.900752i	$-0.643016\pi$
$59$	−393.669			−0.868667			−0.434333	+	0.900752i	$0.643016\pi$
$60$		0			0
$61$	−890.660			−1.86946			−0.934732	−	0.355353i	$-0.884361\pi$
$61$	−890.660			−1.86946			−0.934732	+	0.355353i	$0.884361\pi$
$62$	5.65432	−	191.690i	0.0115823	−	0.392655i
$63$		0			0
$64$	504.007	+	90.1174i	0.984388	+	0.176011i
$65$			31.9586i			0.0609842i
$66$		0			0
$67$			497.143i			0.906502i	0.891383	+	0.453251i	$0.149736\pi$
$67$			497.143i			0.906502i	−0.891383	+	0.453251i	$0.850264\pi$
$68$	16.8913	−	286.070i	0.0301231	−	0.510163i
$69$		0			0
$70$	170.725	+	5.03592i	0.291508	+	0.00859867i
$71$	−94.3384			−0.157689			−0.0788444	−	0.996887i	$-0.525123\pi$
$71$	−94.3384			−0.157689			−0.0788444	+	0.996887i	$0.525123\pi$
$72$		0			0
$73$	−636.939			−1.02121			−0.510603	−	0.859817i	$-0.670578\pi$
$73$	−636.939			−1.02121			−0.510603	+	0.859817i	$0.670578\pi$
$74$	960.556	+	28.3338i	1.50895	+	0.0445099i
$75$		0			0
$76$	−41.8774	+	709.235i	−0.0632062	+	1.07046i
$77$			309.791i			0.458492i
$78$		0			0
$79$		−	1118.13i		−	1.59240i	−0.605036	−	0.796198i	$-0.706841\pi$
$79$		−	1118.13i		−	1.59240i	0.605036	−	0.796198i	$-0.293159\pi$
$80$	64.9727	−	548.270i	0.0908021	−	0.766231i
$81$		0			0
$82$	37.5968	−	1274.59i	0.0506326	−	1.71652i
$83$	1167.84			1.54442			0.772209	−	0.635369i	$-0.219152\pi$
$83$	1167.84			1.54442			0.772209	+	0.635369i	$0.219152\pi$
$84$		0			0
$85$	−309.016			−0.394324
$86$	−5.02139	+	170.233i	−0.00629617	+	0.213449i
$87$		0			0
$88$	997.479	+	88.4740i	1.20831	+	0.107175i
$89$		−	328.229i		−	0.390923i	−0.980711	−	0.195462i	$-0.937380\pi$
$89$		−	328.229i		−	0.390923i	0.980711	−	0.195462i	$-0.0626205\pi$
$90$		0			0
$91$			25.9324i			0.0298731i
$92$	−329.096	−	19.4318i	−0.372942	−	0.0220207i
$93$		0			0
$94$	688.213	+	20.3004i	0.755146	+	0.0222747i
$95$	766.124			0.827396
$96$		0			0
$97$	−467.361			−0.489209			−0.244605	−	0.969623i	$-0.578658\pi$
$97$	−467.361			−0.489209			−0.244605	+	0.969623i	$0.578658\pi$
$98$	138.533	+	4.08633i	0.142795	+	0.00421206i
$99$		0			0
$100$	403.942	+	23.8511i	0.403942	+	0.0238511i
$101$			162.896i			0.160483i	0.996775	+	0.0802414i	$0.0255691\pi$
$101$			162.896i			0.160483i	−0.996775	+	0.0802414i	$0.974431\pi$
$102$		0			0
$103$		−	973.199i		−	0.930991i	−0.885050	−	0.465496i	$-0.845876\pi$
$103$		−	973.199i		−	0.930991i	0.885050	−	0.465496i	$-0.154124\pi$
$104$	83.4983	+	7.40610i	0.0787277	+	0.00698296i
$105$		0			0
$106$	48.9826	−	1660.58i	0.0448831	−	1.52160i
$107$	940.544			0.849774			0.424887	−	0.905246i	$-0.360314\pi$
$107$	940.544			0.849774			0.424887	+	0.905246i	$0.360314\pi$
$108$		0			0
$109$	35.7699			0.0314324			0.0157162	−	0.999876i	$-0.494997\pi$
$109$	35.7699			0.0314324			0.0157162	+	0.999876i	$0.494997\pi$
$110$	31.8384	−	1079.37i	0.0275970	−	0.935578i
$111$		0			0
$112$	52.7213	−	444.887i	0.0444794	−	0.375338i
$113$			466.240i			0.388143i	0.980987	+	0.194071i	$0.0621693\pi$
$113$			466.240i			0.388143i	−0.980987	+	0.194071i	$0.937831\pi$
$114$		0			0
$115$			355.493i			0.288260i
$116$	6.02605	−	102.057i	0.00482332	−	0.0816876i
$117$		0			0
$118$	1112.98	+	32.8298i	0.868289	+	0.0256121i
$119$	−250.747			−0.193159
$120$		0			0
$121$	627.577			0.471508
$122$	2518.07	+	74.2762i	1.86865	+	0.0551201i
$123$		0			0
$124$	−31.9718	+	541.473i	−0.0231544	+	0.392143i
$125$		−	1514.68i		−	1.08381i
$126$		0			0
$127$		−	1364.63i		−	0.953475i	−0.879046	−	0.476737i	$-0.841819\pi$
$127$		−	1364.63i		−	0.953475i	0.879046	−	0.476737i	$-0.158181\pi$
$128$	−1417.41	−	296.811i	−0.978771	−	0.204958i
$129$		0			0
$130$	2.66517	−	90.3531i	0.00179808	−	0.0609576i
$131$	−1237.31			−0.825220			−0.412610	−	0.910908i	$-0.635383\pi$
$131$	−1237.31			−0.825220			−0.412610	+	0.910908i	$0.635383\pi$
$132$		0			0
$133$	621.662			0.405300
$134$	41.4590	−	1405.52i	0.0267277	−	0.906108i
$135$		0			0
$136$	−71.6117	+	807.368i	−0.0451518	+	0.509053i
$137$			425.810i			0.265543i	0.991147	+	0.132772i	$0.0423877\pi$
$137$			425.810i			0.265543i	−0.991147	+	0.132772i	$0.957612\pi$
$138$		0			0
$139$			1410.05i			0.860421i	0.902729	+	0.430211i	$0.141561\pi$
$139$			1410.05i			0.860421i	−0.902729	+	0.430211i	$0.858439\pi$
$140$	−482.253	−	28.4751i	−0.291127	−	0.0171899i
$141$		0			0
$142$	266.713	+	7.86731i	0.157620	+	0.00464937i
$143$	163.951			0.0958761
$144$		0			0
$145$	−110.243			−0.0631393
$146$	1800.75	+	53.1172i	1.02076	+	0.0301097i
$147$		0			0
$148$	−2713.32	−	160.210i	−1.50698	−	0.0889811i
$149$			2815.26i			1.54789i	0.633255	+	0.773943i	$0.281718\pi$
$149$			2815.26i			1.54789i	−0.633255	+	0.773943i	$0.718282\pi$
$150$		0			0
$151$			1650.97i			0.889762i	0.895590	+	0.444881i	$0.146754\pi$
$151$			1650.97i			0.889762i	−0.895590	+	0.444881i	$0.853246\pi$
$152$	177.542	−	2001.66i	0.0947406	−	1.06813i
$153$		0			0
$154$	25.8349	−	875.839i	0.0135184	−	0.458293i
$155$	584.905			0.303102
$156$		0			0
$157$	1773.44			0.901500			0.450750	−	0.892650i	$-0.351157\pi$
$157$	1773.44			0.901500			0.450750	+	0.892650i	$0.351157\pi$
$158$	−93.2459	+	3161.17i	−0.0469509	+	1.59170i
$159$		0			0
$160$	−229.413	+	1544.65i	−0.113354	+	0.763220i
$161$			288.461i			0.141204i
$162$		0			0
$163$		−	2642.80i		−	1.26994i	−0.772536	−	0.634971i	$-0.781012\pi$
$163$		−	2642.80i		−	1.26994i	0.772536	−	0.634971i	$-0.218988\pi$
$164$	−212.587	+	3600.38i	−0.101221	+	1.71428i
$165$		0			0
$166$	−3301.70	−	97.3912i	−1.54375	−	0.0455363i
$167$	2462.44			1.14101			0.570507	−	0.821293i	$-0.306747\pi$
$167$	2462.44			1.14101			0.570507	+	0.821293i	$0.306747\pi$
$168$		0			0
$169$	−2183.28			−0.993753
$170$	873.650	+	25.7703i	0.394152	+	0.0116264i
$171$		0			0
$172$	28.3929	−	480.862i	0.0125869	−	0.213171i
$173$		−	3762.50i		−	1.65351i	−0.562560	−	0.826756i	$-0.690184\pi$
$173$		−	3762.50i		−	1.65351i	0.562560	−	0.826756i	$-0.309816\pi$
$174$		0			0
$175$		−	354.065i		−	0.152942i
$176$	−2812.69	−	333.318i	−1.20463	−	0.142754i
$177$		0			0
$178$	−27.3725	+	927.967i	−0.0115261	+	0.390753i
$179$	−449.960			−0.187886			−0.0939429	−	0.995578i	$-0.529947\pi$
$179$	−449.960			−0.187886			−0.0939429	+	0.995578i	$0.529947\pi$
$180$		0			0
$181$	−728.531			−0.299178			−0.149589	−	0.988748i	$-0.547795\pi$
$181$	−728.531			−0.299178			−0.149589	+	0.988748i	$0.547795\pi$
$182$	2.16262	−	73.3160i	0.000880791	−	0.0298601i
$183$		0			0
$184$	928.799	+	82.3823i	0.372130	+	0.0330071i
$185$			2930.95i			1.16480i
$186$		0			0
$187$			1585.29i			0.619935i
$188$	−1944.02	−	114.786i	−0.754161	−	0.0445301i
$189$		0			0
$190$	−2165.98	−	63.8905i	−0.827036	−	0.0243953i
$191$	−3611.80			−1.36827			−0.684137	−	0.729353i	$-0.739821\pi$
$191$	−3611.80			−1.36827			−0.684137	+	0.729353i	$0.739821\pi$
$192$		0			0
$193$	1871.03			0.697823			0.348912	−	0.937156i	$-0.386551\pi$
$193$	1871.03			0.697823			0.348912	+	0.937156i	$0.386551\pi$
$194$	1321.32	+	38.9754i	0.488997	+	0.0144241i
$195$		0			0
$196$	−391.318	−	23.1057i	−0.142609	−	0.00842046i
$197$		−	3659.98i		−	1.32367i	−0.749650	−	0.661835i	$-0.769778\pi$
$197$		−	3659.98i		−	1.32367i	0.749650	−	0.661835i	$-0.230222\pi$
$198$		0			0
$199$		−	3946.37i		−	1.40578i	−0.711297	−	0.702892i	$-0.751892\pi$
$199$		−	3946.37i		−	1.40578i	0.711297	−	0.702892i	$-0.248108\pi$
$200$	−1140.04	−	101.118i	−0.403063	−	0.0357508i
$201$		0			0
$202$	13.5846	−	460.539i	0.00473174	−	0.160413i
$203$	−89.4555			−0.0309288
$204$		0			0
$205$	3889.17			1.32503
$206$	−81.1595	+	2751.42i	−0.0274498	+	0.930587i
$207$		0			0
$208$	−235.449	−	27.9018i	−0.0784876	−	0.00930117i
$209$		−	3930.31i		−	1.30079i
$210$		0			0
$211$			4492.02i			1.46561i	0.680440	+	0.732804i	$0.261789\pi$
$211$			4492.02i			1.46561i	−0.680440	+	0.732804i	$0.738211\pi$
$212$	−276.967	+	4690.71i	−0.0897272	+	1.51962i
$213$		0			0
$214$	−2659.10	−	78.4363i	−0.849405	−	0.0250551i
$215$	−519.433			−0.164768
$216$		0			0
$217$	474.614			0.148474
$218$	−101.129	−	2.98301i	−0.0314188	−	0.000926767i
$219$		0			0
$220$	−180.027	+	3048.93i	−0.0551700	+	0.934358i
$221$			132.704i			0.0403919i
$222$		0			0
$223$			5398.26i			1.62105i	0.585704	+	0.810525i	$0.300818\pi$
$223$			5398.26i			1.62105i	−0.585704	+	0.810525i	$0.699182\pi$
$224$	−186.155	+	1253.39i	−0.0555267	+	0.373864i
$225$		0			0
$226$	38.8819	−	1318.15i	0.0114442	−	0.387974i
$227$	−5620.96			−1.64351			−0.821754	−	0.569843i	$-0.807004\pi$
$227$	−5620.96			−1.64351			−0.821754	+	0.569843i	$0.807004\pi$
$228$		0			0
$229$	−1480.78			−0.427305			−0.213652	−	0.976910i	$-0.568536\pi$
$229$	−1480.78			−0.427305			−0.213652	+	0.976910i	$0.568536\pi$
$230$	29.6462	−	1005.05i	0.00849918	−	0.288135i
$231$		0			0
$232$	−25.5478	+	288.033i	−0.00722973	+	0.0815099i
$233$			42.8997i			0.0120620i	0.999982	+	0.00603102i	$0.00191974\pi$
$233$			42.8997i			0.0120620i	−0.999982	+	0.00603102i	$0.998080\pi$
$234$		0			0
$235$			2099.95i			0.582918i
$236$	−3143.88	−	185.633i	−0.867156	−	0.0512020i
$237$		0			0
$238$	708.913	+	20.9110i	0.193076	+	0.00569520i
$239$	−162.709			−0.0440367			−0.0220184	−	0.999758i	$-0.507009\pi$
$239$	−162.709			−0.0440367			−0.0220184	+	0.999758i	$0.507009\pi$
$240$		0			0
$241$	4633.53			1.23847			0.619236	−	0.785205i	$-0.287443\pi$
$241$	4633.53			1.23847			0.619236	+	0.785205i	$0.287443\pi$
$242$	−1774.28	−	52.3365i	−0.471303	−	0.0139021i
$243$		0			0
$244$	−7112.89	−	419.987i	−1.86621	−	0.110192i
$245$			422.706i			0.110227i
$246$		0			0
$247$		−	329.003i		−	0.0847530i
$248$	135.546	−	1528.19i	0.0347065	−	0.391290i
$249$		0			0
$250$	−126.316	+	4282.29i	−0.0319556	+	1.08334i
$251$	−4459.19			−1.12136			−0.560680	−	0.828032i	$-0.689460\pi$
$251$	−4459.19			−1.12136			−0.560680	+	0.828032i	$0.689460\pi$
$252$		0			0
$253$	1823.72			0.453187
$254$	−113.803	+	3858.08i	−0.0281127	+	0.953060i
$255$		0			0
$256$	3982.55	+	957.348i	0.972302	+	0.233728i
$257$		−	6877.12i		−	1.66919i	−0.550861	−	0.834597i	$-0.685701\pi$
$257$		−	6877.12i		−	1.66919i	0.550861	−	0.834597i	$-0.314299\pi$
$258$		0			0
$259$			2378.29i			0.570578i
$260$	−15.0699	+	255.224i	−0.00359460	+	0.0608781i
$261$		0			0
$262$	3498.11	+	103.185i	0.824862	+	0.0243312i
$263$	5906.74			1.38489			0.692443	−	0.721473i	$-0.256534\pi$
$263$	5906.74			1.38489			0.692443	+	0.721473i	$0.256534\pi$
$264$		0			0
$265$	5066.95			1.17457
$266$	−1757.56	−	51.8432i	−0.405124	−	0.0119500i
$267$		0			0
$268$	−234.426	+	3970.23i	−0.0534322	+	0.904926i
$269$			1366.13i			0.309645i	0.987942	+	0.154823i	$0.0494806\pi$
$269$			1366.13i			0.309645i	−0.987942	+	0.154823i	$0.950519\pi$
$270$		0			0
$271$		−	5728.00i		−	1.28395i	−0.766724	−	0.641977i	$-0.778114\pi$
$271$		−	5728.00i		−	1.28395i	0.766724	−	0.641977i	$-0.221886\pi$
$272$	269.790	−	2276.62i	0.0601414	−	0.507501i
$273$		0			0
$274$	35.5102	−	1203.85i	0.00782939	−	0.265428i
$275$	−2238.49			−0.490858
$276$		0			0
$277$	6438.08			1.39649			0.698243	−	0.715860i	$-0.253965\pi$
$277$	6438.08			1.39649			0.698243	+	0.715860i	$0.253965\pi$
$278$	117.590	−	3986.48i	0.0253690	−	0.860047i
$279$		0			0
$280$	1361.05	+	120.722i	0.290494	+	0.0257661i
$281$		−	8186.44i		−	1.73794i	−0.494861	−	0.868972i	$-0.664781\pi$
$281$		−	8186.44i		−	1.73794i	0.494861	−	0.868972i	$-0.335219\pi$
$282$		0			0
$283$		−	6518.84i		−	1.36928i	−0.728884	−	0.684638i	$-0.759960\pi$
$283$		−	6518.84i		−	1.36928i	0.728884	−	0.684638i	$-0.240040\pi$
$284$	−753.395	−	44.4849i	−0.157415	−	0.00929469i
$285$		0			0
$286$	−463.522	−	13.6726i	−0.0958345	−	0.00282685i
$287$	3155.82			0.649066
$288$		0			0
$289$	3629.85			0.738826
$290$	311.679	+	9.19368i	0.0631118	+	0.00186163i
$291$		0			0
$292$	−5086.65	−	300.346i	−1.01943	−	0.0601932i
$293$			5776.02i			1.15167i	0.817567	+	0.575834i	$0.195322\pi$
$293$			5776.02i			1.15167i	−0.817567	+	0.575834i	$0.804678\pi$
$294$		0			0
$295$			3396.05i			0.670256i
$296$	7657.72	+	679.222i	1.50370	+	0.133375i
$297$		0			0
$298$	234.777	−	7959.29i	0.0456385	−	1.54721i
$299$	152.663			0.0295274
$300$		0			0
$301$	−421.487			−0.0807114
$302$	137.682	−	4667.62i	0.0262341	−	0.889375i
$303$		0			0
$304$	−668.874	+	5644.27i	−0.126193	+	1.06487i
$305$			7683.42i			1.44246i
$306$		0			0
$307$		−	7138.73i		−	1.32713i	−0.748119	−	0.663564i	$-0.769043\pi$
$307$		−	7138.73i		−	1.32713i	0.748119	−	0.663564i	$-0.230957\pi$
$308$	−146.080	+	2474.02i	−0.0270250	+	0.457695i
$309$		0			0
$310$	−1653.64	−	48.7779i	−0.302970	−	0.00893678i
$311$	2455.56			0.447724			0.223862	−	0.974621i	$-0.428133\pi$
$311$	2455.56			0.447724			0.223862	+	0.974621i	$0.428133\pi$
$312$		0			0
$313$	−9841.00			−1.77715			−0.888573	−	0.458736i	$-0.848302\pi$
$313$	−9841.00			−1.77715			−0.888573	+	0.458736i	$0.848302\pi$
$314$	−5013.85	−	147.895i	−0.901109	−	0.0265802i
$315$		0			0
$316$	527.249	−	8929.48i	0.0938610	−	1.58963i
$317$		−	220.937i		−	0.0391453i	−0.999808	−	0.0195727i	$-0.993769\pi$
$317$		−	220.937i		−	0.0391453i	0.999808	−	0.0195727i	$-0.00623057\pi$
$318$		0			0
$319$			565.561i			0.0992643i
$320$	777.412	−	4347.90i	0.135808	−	0.759546i
$321$		0			0
$322$	24.0560	−	815.535i	0.00416333	−	0.141143i
$323$	3181.23			0.548013
$324$		0			0
$325$	−187.383			−0.0319819
$326$	−220.396	+	7471.73i	−0.0374435	+	1.26939i
$327$		0			0
$328$	901.278	−	10161.2i	0.151722	−	1.71055i
$329$			1703.98i			0.285542i
$330$		0			0
$331$			5852.38i			0.971831i	0.874006	+	0.485916i	$0.161514\pi$
$331$			5852.38i			0.971831i	−0.874006	+	0.485916i	$0.838486\pi$
$332$	9326.44	+	550.688i	1.54173	+	0.0910329i
$333$		0			0
$334$	−6961.80	−	205.354i	−1.14052	−	0.0336421i
$335$	4288.68			0.699450
$336$		0			0
$337$	−336.910			−0.0544589			−0.0272294	−	0.999629i	$-0.508668\pi$
$337$	−336.910			−0.0544589			−0.0272294	+	0.999629i	$0.508668\pi$
$338$	6172.55	+	182.073i	0.993321	+	0.0293002i
$339$		0			0
$340$	−2467.83	−	145.715i	−0.393638	−	0.0232427i
$341$		−	3000.63i		−	0.476520i
$342$		0			0
$343$			343.000i			0.0539949i
$344$	−120.374	+	1357.13i	−0.0188666	+	0.212707i
$345$		0			0
$346$	−313.772	+	10637.3i	−0.0487529	+	1.65279i
$347$	−1531.16			−0.236878			−0.118439	−	0.992961i	$-0.537789\pi$
$347$	−1531.16			−0.236878			−0.118439	+	0.992961i	$0.537789\pi$
$348$		0			0
$349$	−7302.37			−1.12002			−0.560010	−	0.828486i	$-0.689203\pi$
$349$	−7302.37			−1.12002			−0.560010	+	0.828486i	$0.689203\pi$
$350$	−29.5271	+	1001.01i	−0.00450940	+	0.152875i
$351$		0			0
$352$	7924.24	+	1176.92i	1.19990	+	0.178210i
$353$		−	2246.03i		−	0.338651i	−0.985560	−	0.169326i	$-0.945841\pi$
$353$		−	2246.03i		−	0.338651i	0.985560	−	0.169326i	$-0.0541589\pi$
$354$		0			0
$355$			813.826i			0.121671i
$356$	154.775	−	2621.26i	0.0230423	−	0.390243i
$357$		0			0
$358$	1272.13	+	37.5242i	0.187804	+	0.00553971i
$359$	−8.54625			−0.00125642			−0.000628208	−	1.00000i	$-0.500200\pi$
$359$	−8.54625			−0.00125642			−0.000628208		1.00000i	$0.500200\pi$
$360$		0			0
$361$	−1028.01			−0.149877
$362$	2059.70	+	60.7555i	0.299048	+	0.00882111i
$363$		0			0
$364$	−12.2283	+	207.098i	−0.00176082	+	0.0298212i
$365$			5494.65i			0.787954i
$366$		0			0
$367$		−	12889.8i		−	1.83336i	−0.399621	−	0.916681i	$-0.630858\pi$
$367$		−	12889.8i		−	1.83336i	0.399621	−	0.916681i	$-0.369142\pi$
$368$	−2619.03	−	310.368i	−0.370995	−	0.0439648i
$369$		0			0
$370$	244.426	−	8286.39i	0.0343435	−	1.16429i
$371$	4111.52			0.575362
$372$		0			0
$373$	−12579.3			−1.74620			−0.873101	−	0.487540i	$-0.837894\pi$
$373$	−12579.3			−1.74620			−0.873101	+	0.487540i	$0.837894\pi$
$374$	132.205	−	4481.93i	0.0182784	−	0.619666i
$375$		0			0
$376$	5486.55	+	486.644i	0.752520	+	0.0667467i
$377$			47.3427i			0.00646757i
$378$		0			0
$379$			9627.78i			1.30487i	0.757845	+	0.652435i	$0.226252\pi$
$379$			9627.78i			1.30487i	−0.757845	+	0.652435i	$0.773748\pi$
$380$	6118.33	+	361.262i	0.825957	+	0.0487694i
$381$		0			0
$382$	10211.3	+	301.204i	1.36768	+	0.0403428i
$383$	6174.08			0.823710			0.411855	−	0.911249i	$-0.364881\pi$
$383$	6174.08			0.823710			0.411855	+	0.911249i	$0.364881\pi$
$384$		0			0
$385$	2672.46			0.353769
$386$	−5289.78	−	156.034i	−0.697520	−	0.0205749i
$387$		0			0
$388$	−3732.39	−	220.382i	−0.488359	−	0.0288356i
$389$			2164.47i			0.282116i	0.990001	+	0.141058i	$0.0450503\pi$
$389$			2164.47i			0.282116i	−0.990001	+	0.141058i	$0.954950\pi$
$390$		0			0
$391$			1476.14i			0.190925i
$392$	1104.41	+	97.9583i	0.142298	+	0.0126215i
$393$		0			0
$394$	−305.223	+	10347.5i	−0.0390276	+	1.32309i
$395$	−9645.72			−1.22868
$396$		0			0
$397$	−739.413			−0.0934762			−0.0467381	−	0.998907i	$-0.514883\pi$
$397$	−739.413			−0.0934762			−0.0467381	+	0.998907i	$0.514883\pi$
$398$	−329.106	+	11157.2i	−0.0414487	+	1.40517i
$399$		0			0
$400$	3214.67	+	380.954i	0.401834	+	0.0476193i
$401$			9286.61i			1.15649i	0.815864	+	0.578243i	$0.196262\pi$
$401$			9286.61i			1.15649i	−0.815864	+	0.578243i	$0.803738\pi$
$402$		0			0
$403$		−	251.181i		−	0.0310477i
$404$	−76.8130	+	1300.90i	−0.00945937	+	0.160204i
$405$		0			0
$406$	252.908	+	7.46010i	0.0309153	+	0.000911918i
$407$	15036.1			1.83124
$408$		0			0
$409$	−11569.9			−1.39877			−0.699383	−	0.714747i	$-0.746542\pi$
$409$	−11569.9			−1.39877			−0.699383	+	0.714747i	$0.746542\pi$
$410$	−10995.4	−	324.335i	−1.32445	−	0.0390677i
$411$		0			0
$412$	458.908	−	7772.05i	0.0548756	−	0.929373i
$413$			2755.68i			0.328325i
$414$		0			0
$415$		−	10074.5i		−	1.19166i
$416$	663.333	+	98.5191i	0.0781792	+	0.0116113i
$417$		0			0
$418$	−327.766	+	11111.8i	−0.0383530	+	1.30022i
$419$	−8586.92			−1.00119			−0.500595	−	0.865682i	$-0.666885\pi$
$419$	−8586.92			−1.00119			−0.500595	+	0.865682i	$0.666885\pi$
$420$		0			0
$421$	−5371.55			−0.621837			−0.310918	−	0.950437i	$-0.600637\pi$
$421$	−5371.55			−0.621837			−0.310918	+	0.950437i	$0.600637\pi$
$422$	374.610	−	12699.8i	0.0432126	−	1.46497i
$423$		0			0
$424$	1174.22	−	13238.5i	0.134493	−	1.51631i
$425$		−	1811.85i		−	0.206795i
$426$		0			0
$427$			6234.62i			0.706591i
$428$	7511.27	+	443.510i	0.848297	+	0.0500884i
$429$		0			0
$430$	1468.54	+	43.3179i	0.164696	+	0.00485808i
$431$	11094.9			1.23996			0.619978	−	0.784619i	$-0.287141\pi$
$431$	11094.9			1.23996			0.619978	+	0.784619i	$0.287141\pi$
$432$		0			0
$433$	−9455.94			−1.04948			−0.524738	−	0.851263i	$-0.675837\pi$
$433$	−9455.94			−1.04948			−0.524738	+	0.851263i	$0.675837\pi$
$434$	−1341.83	−	39.5803i	−0.148410	−	0.00437768i
$435$		0			0
$436$	285.662	+	16.8671i	0.0313778	+	0.00185273i
$437$		−	3659.69i		−	0.400610i
$438$		0			0
$439$		−	1277.44i		−	0.138881i	−0.997586	−	0.0694407i	$-0.977879\pi$
$439$		−	1277.44i		−	0.138881i	0.997586	−	0.0694407i	$-0.0221215\pi$
$440$	763.235	−	8604.91i	0.0826950	−	0.932325i
$441$		0			0
$442$	11.0668	−	375.179i	0.00119093	−	0.0403743i
$443$	−7948.67			−0.852489			−0.426245	−	0.904608i	$-0.640164\pi$
$443$	−7948.67			−0.852489			−0.426245	+	0.904608i	$0.640164\pi$
$444$		0			0
$445$	−2831.52			−0.301633
$446$	450.185	−	15261.9i	0.0477957	−	1.62034i
$447$		0			0
$448$	630.822	−	3528.05i	0.0665257	−	0.372064i
$449$			10690.8i			1.12368i	0.827247	+	0.561839i	$0.189906\pi$
$449$			10690.8i			1.12368i	−0.827247	+	0.561839i	$0.810094\pi$
$450$		0			0
$451$		−	19951.9i		−	2.08314i
$452$	−219.853	+	3723.43i	−0.0228784	+	0.387468i
$453$		0			0
$454$	15891.6	+	468.757i	1.64279	+	0.0484579i
$455$	223.710			0.0230498
$456$		0			0
$457$	11479.3			1.17500			0.587502	−	0.809222i	$-0.300111\pi$
$457$	11479.3			1.17500			0.587502	+	0.809222i	$0.300111\pi$
$458$	4186.46	+	123.489i	0.427119	+	0.0125988i
$459$		0			0
$460$	−167.631	+	2839.00i	−0.0169910	+	0.287759i
$461$		−	7324.06i		−	0.739947i	−0.929042	−	0.369973i	$-0.879367\pi$
$461$		−	7324.06i		−	0.739947i	0.929042	−	0.369973i	$-0.120633\pi$
$462$		0			0
$463$			11018.2i			1.10596i	0.833196	+	0.552978i	$0.186509\pi$
$463$			11018.2i			1.10596i	−0.833196	+	0.552978i	$0.813491\pi$
$464$	96.2492	−	812.196i	0.00962986	−	0.0812613i
$465$		0			0
$466$	3.57760	−	121.286i	0.000355642	−	0.0120568i
$467$	−11040.0			−1.09394			−0.546969	−	0.837153i	$-0.684218\pi$
$467$	−11040.0			−1.09394			−0.546969	+	0.837153i	$0.684218\pi$
$468$		0			0
$469$	3480.00			0.342626
$470$	175.125	−	5936.98i	0.0171870	−	0.582664i
$471$		0			0
$472$	8872.88	+	787.003i	0.865270	+	0.0767474i
$473$			2664.75i			0.259039i
$474$		0			0
$475$			4492.01i			0.433911i
$476$	−2002.49	−	118.239i	−0.192824	−	0.0113854i
$477$		0			0
$478$	460.011	+	13.5691i	0.0440176	+	0.00129840i
$479$	−16926.4			−1.61459			−0.807295	−	0.590148i	$-0.799069\pi$
$479$	−16926.4			−1.61459			−0.807295	+	0.590148i	$0.799069\pi$
$480$		0			0
$481$	1258.67			0.119314
$482$	−13099.9	−	386.411i	−1.23793	−	0.0365156i
$483$		0			0
$484$	5011.88	+	295.931i	0.470688	+	0.0277922i
$485$			4031.76i			0.377470i
$486$		0			0
$487$			9639.43i			0.896929i	0.893801	+	0.448464i	$0.148029\pi$
$487$			9639.43i			0.896929i	−0.893801	+	0.448464i	$0.851971\pi$
$488$	20074.5	+	1780.56i	1.86215	+	0.165169i
$489$		0			0
$490$	35.2514	−	1195.07i	0.00324999	−	0.110180i
$491$	4791.74			0.440424			0.220212	−	0.975452i	$-0.429325\pi$
$491$	4791.74			0.440424			0.220212	+	0.975452i	$0.429325\pi$
$492$		0			0
$493$	−457.770			−0.0418193
$494$	−27.4371	+	930.158i	−0.00249889	+	0.0847161i
$495$		0			0
$496$	−510.659	+	4309.18i	−0.0462284	+	0.390097i
$497$			660.369i			0.0596008i
$498$		0			0
$499$			2224.16i			0.199533i	0.995011	+	0.0997664i	$0.0318096\pi$
$499$			2224.16i			0.199533i	−0.995011	+	0.0997664i	$0.968190\pi$
$500$	714.239	−	12096.3i	0.0638835	−	1.08193i
$501$		0			0
$502$	12607.0	+	371.872i	1.12087	+	0.0330627i
$503$	9038.06			0.801167			0.400584	−	0.916260i	$-0.368807\pi$
$503$	9038.06			0.801167			0.400584	+	0.916260i	$0.368807\pi$
$504$		0			0
$505$	1405.25			0.123827
$506$	−5156.02	−	152.089i	−0.452990	−	0.0133620i
$507$		0			0
$508$	643.485	−	10898.1i	0.0562009	−	0.951817i
$509$			4178.67i			0.363883i	0.983309	+	0.181942i	$0.0582382\pi$
$509$			4178.67i			0.363883i	−0.983309	+	0.181942i	$0.941762\pi$
$510$		0			0
$511$			4458.57i			0.385980i
$512$	−11179.6	−	3038.73i	−0.964988	−	0.262294i
$513$		0			0
$514$	−573.514	+	19443.0i	−0.0492152	+	1.66847i
$515$	−8395.46			−0.718346
$516$		0			0
$517$	10773.0			0.916433
$518$	198.336	−	6723.89i	0.0168232	−	0.570330i
$519$		0			0
$520$	63.8899	−	720.312i	0.00538800	−	0.0607457i
$521$			15973.1i			1.34317i	0.740925	+	0.671587i	$0.234387\pi$
$521$			15973.1i			1.34317i	−0.740925	+	0.671587i	$0.765613\pi$
$522$		0			0
$523$			7772.55i			0.649847i	0.945740	+	0.324923i	$0.105339\pi$
$523$			7772.55i			0.649847i	−0.945740	+	0.324923i	$0.894661\pi$
$524$	−9881.23	−	583.446i	−0.823786	−	0.0486412i
$525$		0			0
$526$	−16699.5	−	492.590i	−1.38428	−	0.0408326i
$527$	2428.74			0.200755
$528$		0			0
$529$	−10468.8			−0.860430
$530$	−14325.3	−	422.556i	−1.17406	−	0.0346315i
$531$		0			0
$532$	4964.65	+	293.142i	0.404595	+	0.0238897i
$533$		−	1670.16i		−	0.135727i
$534$		0			0
$535$		−	8113.76i		−	0.655679i
$536$	993.863	−	11205.1i	0.0800902	−	0.902957i
$537$		0			0
$538$	113.928	−	3862.33i	0.00912972	−	0.309511i
$539$	2168.53			0.173294
$540$		0			0
$541$	−1207.74			−0.0959793			−0.0479897	−	0.998848i	$-0.515281\pi$
$541$	−1207.74			−0.0959793			−0.0479897	+	0.998848i	$0.515281\pi$
$542$	−477.684	+	16194.2i	−0.0378566	+	1.28340i
$543$		0			0
$544$	−952.608	+	6413.95i	−0.0750786	+	0.505507i
$545$		−	308.575i		−	0.0242530i
$546$		0			0
$547$			22972.7i			1.79569i	0.440315	+	0.897843i	$0.354867\pi$
$547$			22972.7i			1.79569i	−0.440315	+	0.897843i	$0.645133\pi$
$548$	−200.789	+	3400.56i	−0.0156520	+	0.265081i
$549$		0			0
$550$	6328.65	+	186.678i	0.490645	+	0.0144727i
$551$	1134.92			0.0877481
$552$		0			0
$553$	−7826.90			−0.601869
$554$	−18201.7	−	536.901i	−1.39588	−	0.0411746i
$555$		0			0
$556$	−664.901	+	11260.8i	−0.0507160	+	0.858925i
$557$		−	3082.31i		−	0.234473i	−0.993104	−	0.117237i	$-0.962596\pi$
$557$		−	3082.31i		−	0.234473i	0.993104	−	0.117237i	$-0.0374036\pi$
$558$		0			0
$559$			223.065i			0.0168777i
$560$	−3837.89	−	454.809i	−0.289608	−	0.0343200i
$561$		0			0
$562$	−682.705	+	23144.7i	−0.0512423	+	1.73719i
$563$	−23690.8			−1.77344			−0.886721	−	0.462306i	$-0.847022\pi$
$563$	−23690.8			−1.77344			−0.886721	+	0.462306i	$0.847022\pi$
$564$		0			0
$565$	4022.09			0.299488
$566$	−543.636	+	18430.1i	−0.0403723	+	1.36868i
$567$		0			0
$568$	2126.29	+	188.597i	0.157072	+	0.0139319i
$569$		−	21184.2i		−	1.56079i	−0.625289	−	0.780393i	$-0.715019\pi$
$569$		−	21184.2i		−	1.56079i	0.625289	−	0.780393i	$-0.284981\pi$
$570$		0			0
$571$			14344.6i			1.05132i	0.850695	+	0.525660i	$0.176182\pi$
$571$			14344.6i			1.05132i	−0.850695	+	0.525660i	$0.823818\pi$
$572$	1309.33	+	77.3105i	0.0957094	+	0.00565125i
$573$		0			0
$574$	−8922.12	−	263.178i	−0.648784	−	0.0191373i
$575$	−2084.36			−0.151172
$576$		0			0
$577$	−4374.69			−0.315634			−0.157817	−	0.987468i	$-0.550446\pi$
$577$	−4374.69			−0.315634			−0.157817	+	0.987468i	$0.550446\pi$
$578$	−10262.3	−	302.710i	−0.738505	−	0.0217839i
$579$		0			0
$580$	−880.412	−	51.9847i	−0.0630295	−	0.00372163i
$581$		−	8174.85i		−	0.583735i
$582$		0			0
$583$		−	25994.1i		−	1.84659i
$584$	14355.9	+	1273.34i	1.01721	+	0.0902243i
$585$		0			0
$586$	481.689	−	16329.9i	0.0339563	−	1.15117i
$587$	−4899.69			−0.344518			−0.172259	−	0.985052i	$-0.555107\pi$
$587$	−4899.69			−0.344518			−0.172259	+	0.985052i	$0.555107\pi$
$588$		0			0
$589$	−6021.42			−0.421236
$590$	283.212	−	9601.30i	0.0197621	−	0.669965i
$591$		0			0
$592$	−21593.3	−	2558.91i	−1.49912	−	0.177653i
$593$			23704.4i			1.64152i	0.571271	+	0.820761i	$0.306450\pi$
$593$			23704.4i			1.64152i	−0.571271	+	0.820761i	$0.693550\pi$
$594$		0			0
$595$			2163.11i			0.149040i
$596$	−1327.52	+	22482.9i	−0.0912374	+	1.54519i
$597$		0			0
$598$	−431.607	−	12.7312i	−0.0295146	−	0.000870600i
$599$	5334.79			0.363896			0.181948	−	0.983308i	$-0.441760\pi$
$599$	5334.79			0.363896			0.181948	+	0.983308i	$0.441760\pi$
$600$		0			0
$601$	300.297			0.0203817			0.0101908	−	0.999948i	$-0.496756\pi$
$601$	300.297			0.0203817			0.0101908	+	0.999948i	$0.496756\pi$
$602$	1191.63	+	35.1498i	0.0806763	+	0.00237973i
$603$		0			0
$604$	−778.508	+	13184.8i	−0.0524454	+	0.888215i
$605$		−	5413.89i		−	0.363812i
$606$		0			0
$607$		−	12004.3i		−	0.802702i	−0.915924	−	0.401351i	$-0.868541\pi$
$607$		−	12004.3i		−	0.802702i	0.915924	−	0.401351i	$-0.131459\pi$
$608$	2361.74	−	15901.7i	0.157535	−	1.06069i
$609$		0			0
$610$	640.756	−	21722.5i	0.0425302	−	1.44184i
$611$	901.801			0.0597103
$612$		0			0
$613$	−3051.53			−0.201060			−0.100530	−	0.994934i	$-0.532054\pi$
$613$	−3051.53			−0.201060			−0.100530	+	0.994934i	$0.532054\pi$
$614$	−595.331	+	20182.6i	−0.0391296	+	1.32655i
$615$		0			0
$616$	619.318	−	6982.35i	0.0405082	−	0.456700i
$617$		−	6684.09i		−	0.436129i	−0.975934	−	0.218064i	$-0.930026\pi$
$617$		−	6684.09i		−	0.436129i	0.975934	−	0.218064i	$-0.0699743\pi$
$618$		0			0
$619$			5493.15i			0.356686i	0.983968	+	0.178343i	$0.0570736\pi$
$619$			5493.15i			0.356686i	−0.983968	+	0.178343i	$0.942926\pi$
$620$	4671.11	+	275.810i	0.302575	+	0.0178658i
$621$		0			0
$622$	−6942.36	−	204.781i	−0.447530	−	0.0132009i
$623$	−2297.60			−0.147755
$624$		0			0
$625$	−6744.00			−0.431616
$626$	27822.5	+	820.686i	1.77637	+	0.0523981i
$627$		0			0
$628$	14162.8	+	836.256i	0.899933	+	0.0531373i
$629$			12170.4i			0.771487i
$630$		0			0
$631$		−	20126.1i		−	1.26974i	−0.772619	−	0.634870i	$-0.781053\pi$
$631$		−	20126.1i		−	1.26974i	0.772619	−	0.634870i	$-0.218947\pi$
$632$	−2235.31	+	25201.4i	−0.140689	+	1.58617i
$633$		0			0
$634$	−18.4250	+	624.633i	−0.00115418	+	0.0391283i
$635$	−11772.2			−0.735693
$636$		0			0
$637$	181.527			0.0112910
$638$	47.1647	−	1598.95i	0.00292675	−	0.0992212i
$639$		0			0
$640$	−2560.49	+	12227.5i	−0.158144	+	0.755212i
$641$		−	29220.8i		−	1.80055i	−0.435323	−	0.900275i	$-0.643366\pi$
$641$		−	29220.8i		−	1.80055i	0.435323	−	0.900275i	$-0.356634\pi$
$642$		0			0
$643$			13497.5i			0.827821i	0.910318	+	0.413911i	$0.135837\pi$
$643$			13497.5i			0.827821i	−0.910318	+	0.413911i	$0.864163\pi$
$644$	−136.022	+	2303.67i	−0.00832303	+	0.140959i
$645$		0			0
$646$	−8993.95	−	265.297i	−0.547775	−	0.0161578i
$647$	5544.47			0.336902			0.168451	−	0.985710i	$-0.446123\pi$
$647$	5544.47			0.336902			0.168451	+	0.985710i	$0.446123\pi$
$648$		0			0
$649$	17422.1			1.05374
$650$	529.768	+	15.6267i	0.0319680	+	0.000942968i
$651$		0			0
$652$	1246.20	−	21105.7i	0.0748544	−	1.26773i
$653$			9054.79i			0.542636i	0.962490	+	0.271318i	$0.0874595\pi$
$653$			9054.79i			0.542636i	−0.962490	+	0.271318i	$0.912540\pi$
$654$		0			0
$655$			10673.8i			0.636734i
$656$	−3395.48	+	28652.7i	−0.202091	+	1.70533i
$657$		0			0
$658$	142.103	−	4817.49i	0.00841905	−	0.285418i
$659$	−154.743			−0.00914709			−0.00457354	−	0.999990i	$-0.501456\pi$
$659$	−154.743			−0.00914709			−0.00457354	+	0.999990i	$0.501456\pi$
$660$		0			0
$661$	19351.7			1.13872			0.569360	−	0.822088i	$-0.307191\pi$
$661$	19351.7			1.13872			0.569360	+	0.822088i	$0.307191\pi$
$662$	488.057	−	16545.8i	0.0286539	−	0.971409i
$663$		0			0
$664$	−26321.8	−	2334.68i	−1.53838	−	0.136450i
$665$		−	5362.87i		−	0.312726i
$666$		0			0
$667$			526.620i			0.0305709i
$668$	19665.3	+	1161.15i	1.13903	+	0.0672550i
$669$		0			0
$670$	−12125.0	−	357.653i	−0.699146	−	0.0206229i
$671$	39416.9			2.26777
$672$		0			0
$673$	8696.70			0.498117			0.249059	−	0.968488i	$-0.419879\pi$
$673$	8696.70			0.498117			0.249059	+	0.968488i	$0.419879\pi$
$674$	952.511	+	28.0964i	0.0544352	+	0.00160569i
$675$		0			0
$676$	−17435.8	−	1029.51i	−0.992025	−	0.0585750i
$677$		−	11717.8i		−	0.665218i	−0.943065	−	0.332609i	$-0.892071\pi$
$677$		−	11717.8i		−	0.665218i	0.943065	−	0.332609i	$-0.107929\pi$
$678$		0			0
$679$			3271.53i			0.184904i
$680$	6964.89	+	617.770i	0.392782	+	0.0348388i
$681$		0			0
$682$	−250.237	+	8483.39i	−0.0140499	+	0.476313i
$683$	17566.1			0.984112			0.492056	−	0.870564i	$-0.336246\pi$
$683$	17566.1			0.984112			0.492056	+	0.870564i	$0.336246\pi$
$684$		0			0
$685$	3673.32			0.204891
$686$	28.6043	−	969.729i	0.00159201	−	0.0539714i
$687$		0			0
$688$	453.497	−	3826.82i	0.0251300	−	0.212058i
$689$		−	2175.95i		−	0.120315i
$690$		0			0
$691$		−	22587.0i		−	1.24349i	−0.783222	−	0.621743i	$-0.786425\pi$
$691$		−	22587.0i		−	1.24349i	0.783222	−	0.621743i	$-0.213575\pi$
$692$	1774.19	−	30047.7i	0.0974633	−	1.65064i
$693$		0			0
$694$	4328.88	+	127.690i	0.236775	+	0.00698422i
$695$	12164.0			0.663894
$696$		0			0
$697$	16149.2			0.877613
$698$	20645.2	+	608.978i	1.11953	+	0.0330231i
$699$		0			0
$700$	166.958	−	2827.59i	0.00901488	−	0.152676i
$701$		−	4908.37i		−	0.264460i	−0.991219	−	0.132230i	$-0.957786\pi$
$701$		−	4908.37i		−	0.264460i	0.991219	−	0.132230i	$-0.0422138\pi$
$702$		0			0
$703$		−	30173.3i		−	1.61879i
$704$	−22305.2	−	3988.22i	−1.19412	−	0.213511i
$705$		0			0
$706$	−187.306	+	6349.96i	−0.00998494	+	0.338504i
$707$	1140.27			0.0606568
$708$		0			0
$709$	−8955.08			−0.474351			−0.237176	−	0.971467i	$-0.576222\pi$
$709$	−8955.08			−0.474351			−0.237176	+	0.971467i	$0.576222\pi$
$710$	67.8686	−	2300.85i	0.00358741	−	0.121619i
$711$		0			0
$712$	−656.178	+	7397.92i	−0.0345384	+	0.389394i
$713$		−	2794.03i		−	0.146756i
$714$		0			0
$715$		−	1414.35i		−	0.0739773i
$716$	−3593.42	−	212.177i	−0.187559	−	0.0110746i
$717$		0			0
$718$	24.1619	+	0.712711i	0.00125587	+	3.70447e-5i
$719$	−22577.2			−1.17105			−0.585527	−	0.810653i	$-0.699112\pi$
$719$	−22577.2			−1.17105			−0.585527	+	0.810653i	$0.699112\pi$
$720$		0			0
$721$	−6812.39			−0.351882
$722$	2906.37	+	85.7300i	0.149812	+	0.00441903i
$723$		0			0
$724$	−5818.12	−	343.536i	−0.298658	−	0.0176345i
$725$		−	646.389i		−	0.0331121i
$726$		0			0
$727$			9030.29i			0.460681i	0.973110	+	0.230340i	$0.0739840\pi$
$727$			9030.29i			0.460681i	−0.973110	+	0.230340i	$0.926016\pi$
$728$	51.8427	−	584.488i	0.00263931	−	0.0297563i
$729$		0			0
$730$	458.224	−	15534.5i	0.0232324	−	0.787612i
$731$	−2156.88			−0.109131
$732$		0			0
$733$	19124.7			0.963694			0.481847	−	0.876255i	$-0.339966\pi$
$733$	19124.7			0.963694			0.481847	+	0.876255i	$0.339966\pi$
$734$	−1074.94	+	36442.1i	−0.0540556	+	1.83256i
$735$		0			0
$736$	7378.63	+	1095.88i	0.369538	+	0.0548842i
$737$		−	22001.5i		−	1.09964i
$738$		0			0
$739$			35083.3i			1.74636i	0.487398	+	0.873180i	$0.337946\pi$
$739$			35083.3i			1.74636i	−0.487398	+	0.873180i	$0.662054\pi$
$740$	−1382.08	+	23406.9i	−0.0686571	+	1.16278i
$741$		0			0
$742$	−11624.1	−	342.878i	−0.575112	−	0.0169642i
$743$	30463.7			1.50418			0.752090	−	0.659060i	$-0.229046\pi$
$743$	30463.7			1.50418			0.752090	+	0.659060i	$0.229046\pi$
$744$		0			0
$745$	24286.3			1.19434
$746$	35564.3	+	1049.05i	1.74544	+	0.0514858i
$747$		0			0
$748$	−747.537	+	12660.3i	−0.0365410	+	0.618857i
$749$		−	6583.81i		−	0.321184i
$750$		0			0
$751$		−	36497.4i		−	1.77338i	−0.462365	−	0.886690i	$-0.652999\pi$
$751$		−	36497.4i		−	1.77338i	0.462365	−	0.886690i	$-0.347001\pi$
$752$	−15471.0	−	1833.39i	−0.750225	−	0.0889053i
$753$		0			0
$754$	3.94813	−	133.847i	0.000190693	−	0.00646476i
$755$	14242.4			0.686533
$756$		0			0
$757$	27788.7			1.33421			0.667105	−	0.744964i	$-0.267533\pi$
$757$	27788.7			1.33421			0.667105	+	0.744964i	$0.267533\pi$
$758$	802.904	−	27219.6i	0.0384733	−	1.30430i
$759$		0			0
$760$	−17267.6	−	1531.60i	−0.824160	−	0.0731011i
$761$			30159.1i			1.43662i	0.695724	+	0.718310i	$0.255084\pi$
$761$			30159.1i			1.43662i	−0.695724	+	0.718310i	$0.744916\pi$
$762$		0			0
$763$		−	250.389i		−	0.0118803i
$764$	−28844.1	−	1703.13i	−1.36590	−	0.0806505i
$765$		0			0
$766$	−17455.3	−	514.885i	−0.823352	−	0.0242866i
$767$	1458.40			0.0686566
$768$		0			0
$769$	35782.2			1.67794			0.838972	−	0.544175i	$-0.183157\pi$
$769$	35782.2			1.67794			0.838972	+	0.544175i	$0.183157\pi$
$770$	−7555.57	−	222.869i	−0.353615	−	0.0104307i
$771$		0			0
$772$	14942.2	+	882.277i	0.696610	+	0.0411319i
$773$		−	21533.3i		−	1.00194i	−0.865465	−	0.500969i	$-0.832977\pi$
$773$		−	21533.3i		−	1.00194i	0.865465	−	0.500969i	$-0.167023\pi$
$774$		0			0
$775$			3429.48i			0.158955i
$776$	10533.8	+	934.324i	0.487296	+	0.0432220i
$777$		0			0
$778$	180.505	−	6119.38i	0.00831802	−	0.281993i
$779$	−40037.8			−1.84147
$780$		0			0
$781$	4175.02			0.191286
$782$	123.102	−	4173.33i	0.00562930	−	0.190842i
$783$		0			0
$784$	−3114.21	−	369.049i	−0.141864	−	0.0168116i
$785$		−	15298.8i		−	0.695591i
$786$		0			0
$787$		−	15807.3i		−	0.715970i	−0.933727	−	0.357985i	$-0.883464\pi$
$787$		−	15807.3i		−	0.715970i	0.933727	−	0.357985i	$-0.116536\pi$
$788$	1725.85	−	29228.9i	0.0780213	−	1.32137i
$789$		0			0
$790$	27270.4	+	804.401i	1.22815	+	0.0362270i
$791$	3263.68			0.146704
$792$		0			0
$793$	3299.56			0.147756
$794$	2090.47	+	61.6630i	0.0934356	+	0.00275609i
$795$		0			0
$796$	1860.89	−	31516.1i	0.0828614	−	1.40334i
$797$			12689.5i			0.563972i	0.959419	+	0.281986i	$0.0909931\pi$
$797$			12689.5i			0.563972i	−0.959419	+	0.281986i	$0.909007\pi$
$798$		0			0
$799$			8719.77i			0.386087i
$800$	−9056.74	−	1345.12i	−0.400255	−	0.0594464i
$801$		0			0
$802$	774.453	−	26255.1i	0.0340984	−	1.15598i
$803$	28188.2			1.23878
$804$		0			0
$805$	2488.45			0.108952
$806$	−20.9471	+	710.139i	−0.000915424	+	0.0310342i
$807$		0			0
$808$	325.654	−	3671.50i	0.0141788	−	0.159855i
$809$		−	17538.6i		−	0.762206i	−0.924533	−	0.381103i	$-0.875544\pi$
$809$		−	17538.6i		−	0.762206i	0.924533	−	0.381103i	$-0.124456\pi$
$810$		0			0
$811$			36604.2i			1.58489i	0.609943	+	0.792445i	$0.291192\pi$
$811$			36604.2i			1.58489i	−0.609943	+	0.792445i	$0.708808\pi$
$812$	−714.400	−	42.1824i	−0.0308750	−	0.00182304i
$813$		0			0
$814$	−42510.2	−	1253.93i	−1.83044	−	0.0539930i
$815$	−22798.6			−0.979877
$816$		0			0
$817$	5347.40			0.228986
$818$	32710.4	+	964.867i	1.39816	+	0.0412418i
$819$		0			0
$820$	31059.2	+	1833.92i	1.32273	+	0.0781015i
$821$		−	22161.7i		−	0.942079i	−0.882112	−	0.471040i	$-0.843879\pi$
$821$		−	22161.7i		−	0.942079i	0.882112	−	0.471040i	$-0.156121\pi$
$822$		0			0
$823$		−	25053.2i		−	1.06112i	−0.847648	−	0.530560i	$-0.821982\pi$
$823$		−	25053.2i		−	1.06112i	0.847648	−	0.530560i	$-0.178018\pi$
$824$	−1945.57	+	21934.9i	−0.0822538	+	0.927351i
$825$		0			0
$826$	229.809	−	7790.86i	0.00968048	−	0.328182i
$827$	−16191.1			−0.680800			−0.340400	−	0.940281i	$-0.610562\pi$
$827$	−16191.1			−0.680800			−0.340400	+	0.940281i	$0.610562\pi$
$828$		0			0
$829$	−28983.6			−1.21428			−0.607142	−	0.794593i	$-0.707684\pi$
$829$	−28983.6			−1.21428			−0.607142	+	0.794593i	$0.707684\pi$
$830$	−840.161	+	28482.7i	−0.0351354	+	1.19114i
$831$		0			0
$832$	−1867.16	−	333.851i	−0.0778029	−	0.0139113i
$833$			1755.23i			0.0730074i
$834$		0			0
$835$		−	21242.6i		−	0.880397i
$836$	1853.32	−	31387.8i	0.0766727	−	1.29853i
$837$		0			0
$838$	24276.9	+	716.102i	1.00075	+	0.0295195i
$839$	−4683.71			−0.192729			−0.0963644	−	0.995346i	$-0.530721\pi$
$839$	−4683.71			−0.192729			−0.0963644	+	0.995346i	$0.530721\pi$
$840$		0			0
$841$	24225.7			0.993304
$842$	15186.4	+	447.958i	0.621566	+	0.0183345i
$843$		0			0
$844$	−2118.19	+	35873.6i	−0.0863876	+	1.46306i
$845$			18834.4i			0.766772i
$846$		0			0
$847$		−	4393.04i		−	0.178213i
$848$	−4423.77	+	37329.8i	−0.179142	+	1.51169i
$849$		0			0
$850$	−151.099	+	5122.47i	−0.00609723	+	0.206705i
$851$	14000.9			0.563976
$852$		0			0
$853$	−21447.0			−0.860880			−0.430440	−	0.902619i	$-0.641642\pi$
$853$	−21447.0			−0.860880			−0.430440	+	0.902619i	$0.641642\pi$
$854$	519.933	−	17626.5i	0.0208334	−	0.706284i
$855$		0			0
$856$	−21198.9	−	1880.29i	−0.846451	−	0.0750782i
$857$		−	24566.0i		−	0.979182i	−0.871952	−	0.489591i	$-0.837146\pi$
$857$		−	24566.0i		−	0.979182i	0.871952	−	0.489591i	$-0.162854\pi$
$858$		0			0
$859$			9680.45i			0.384509i	0.981345	+	0.192254i	$0.0615798\pi$
$859$			9680.45i			0.384509i	−0.981345	+	0.192254i	$0.938420\pi$
$860$	−4148.24	−	244.936i	−0.164481	−	0.00971193i
$861$		0			0
$862$	−31367.4	−	925.252i	−1.23942	−	0.0365594i
$863$	2384.05			0.0940372			0.0470186	−	0.998894i	$-0.485028\pi$
$863$	2384.05			0.0940372			0.0470186	+	0.998894i	$0.485028\pi$
$864$		0			0
$865$	−32457.8			−1.27584
$866$	26733.8	+	788.574i	1.04902	+	0.0309432i
$867$		0			0
$868$	3790.31	+	223.802i	0.148216	+	0.00875155i
$869$			49483.7i			1.93167i
$870$		0			0
$871$		−	1841.73i		−	0.0716470i
$872$	−806.215	−	71.5093i	−0.0313095	−	0.00277708i
$873$		0			0
$874$	−305.198	+	10346.7i	−0.0118118	+	0.400436i
$875$	−10602.7			−0.409643
$876$		0			0
$877$	−23220.5			−0.894073			−0.447037	−	0.894516i	$-0.647521\pi$
$877$	−23220.5			−0.894073			−0.447037	+	0.894516i	$0.647521\pi$
$878$	−106.532	+	3611.58i	−0.00409484	+	0.138821i
$879$		0			0
$880$	−2875.42	+	24264.1i	−0.110148	+	0.929481i
$881$		−	8670.93i		−	0.331590i	−0.986160	−	0.165795i	$-0.946981\pi$
$881$		−	8670.93i		−	0.331590i	0.986160	−	0.165795i	$-0.0530191\pi$
$882$		0			0
$883$			9683.52i			0.369056i	0.982827	+	0.184528i	$0.0590756\pi$
$883$			9683.52i			0.369056i	−0.982827	+	0.184528i	$0.940924\pi$
$884$	−62.5758	+	1059.78i	−0.00238083	+	0.0403217i
$885$		0			0
$886$	22472.5	+	662.876i	0.852118	+	0.0251352i
$887$	17369.1			0.657494			0.328747	−	0.944418i	$-0.393374\pi$
$887$	17369.1			0.657494			0.328747	+	0.944418i	$0.393374\pi$
$888$		0			0
$889$	−9552.41			−0.360380
$890$	8005.26	+	236.133i	0.301502	+	0.00889348i
$891$		0			0
$892$	−2545.53	+	43111.0i	−0.0955499	+	1.61823i
$893$		−	21618.3i		−	0.810112i
$894$		0			0
$895$			3881.65i			0.144971i
$896$	−2077.68	+	9921.88i	−0.0774669	+	0.369941i
$897$		0			0
$898$	891.557	−	30225.1i	0.0331310	−	1.12319i
$899$	866.467			0.0321449
$900$		0			0
$901$	21039.8			0.777957
$902$	−1663.88	+	56407.9i	−0.0614203	+	2.08224i
$903$		0			0
$904$	932.083	−	10508.5i	0.0342927	−	0.386625i
$905$			6284.79i			0.230844i
$906$		0			0
$907$		−	16471.6i		−	0.603011i	−0.953464	−	0.301505i	$-0.902511\pi$
$907$		−	16471.6i		−	0.603011i	0.953464	−	0.301505i	$-0.0974891\pi$
$908$	−44889.5	−	2650.54i	−1.64065	−	0.0968736i
$909$		0			0
$910$	−632.472	−	18.6562i	−0.0230398	−	0.000679612i
$911$	−2224.30			−0.0808939			−0.0404469	−	0.999182i	$-0.512878\pi$
$911$	−2224.30			−0.0808939			−0.0404469	+	0.999182i	$0.512878\pi$
$912$		0			0
$913$	−51683.5			−1.87347
$914$	−32454.1	−	957.308i	−1.17449	−	0.0346443i
$915$		0			0
$916$	−11825.7	−	698.256i	−0.426562	−	0.0251867i
$917$			8661.14i			0.311904i
$918$		0			0
$919$			47222.7i			1.69503i	0.530770	+	0.847516i	$0.321903\pi$
$919$			47222.7i			1.69503i	−0.530770	+	0.847516i	$0.678097\pi$
$920$	710.684	−	8012.43i	0.0254680	−	0.287133i
$921$		0			0
$922$	−610.787	+	20706.6i	−0.0218169	+	0.739625i
$923$	349.488			0.0124632
$924$		0			0
$925$	−17185.1			−0.610856
$926$	918.856	−	31150.6i	0.0326085	−	1.10548i
$927$		0			0
$928$	−339.848	+	2288.21i	−0.0120216	+	0.0809420i
$929$			14515.2i			0.512625i	0.966594	+	0.256313i	$0.0825077\pi$
$929$			14515.2i			0.512625i	−0.966594	+	0.256313i	$0.917492\pi$
$930$		0			0
$931$		−	4351.63i		−	0.153189i
$932$	−20.2292	+	342.601i	−0.000710975	+	0.0120411i
$933$		0			0
$934$	31212.2	+	920.673i	1.09346	+	0.0322541i
$935$	13675.8			0.478337
$936$		0			0
$937$	−11232.1			−0.391608			−0.195804	−	0.980643i	$-0.562732\pi$
$937$	−11232.1			−0.391608			−0.195804	+	0.980643i	$0.562732\pi$
$938$	−9838.65	−	290.213i	−0.342477	−	0.0101021i
$939$		0			0
$940$	−990.223	+	16770.4i	−0.0343591	+	0.581904i
$941$		−	7300.76i		−	0.252920i	−0.991972	−	0.126460i	$-0.959638\pi$
$941$		−	7300.76i		−	0.252920i	0.991972	−	0.126460i	$-0.0403616\pi$
$942$		0			0
$943$		−	18578.1i		−	0.641556i
$944$	−25019.7	−	2964.96i	−0.862631	−	0.102226i
$945$		0			0
$946$	222.226	−	7533.78i	0.00763762	−	0.258926i
$947$	−32290.7			−1.10803			−0.554016	−	0.832506i	$-0.686905\pi$
$947$	−32290.7			−1.10803			−0.554016	+	0.832506i	$0.686905\pi$
$948$		0			0
$949$	2359.62			0.0807128
$950$	374.609	−	12699.8i	0.0127936	−	0.433722i
$951$		0			0
$952$	5651.58	+	501.282i	0.192404	+	0.0170658i
$953$			36928.6i			1.25523i	0.778524	+	0.627615i	$0.215969\pi$
$953$			36928.6i			1.25523i	−0.778524	+	0.627615i	$0.784031\pi$
$954$		0			0
$955$			31157.7i			1.05575i
$956$	−1299.41	−	76.7248i	−0.0439602	−	0.00259567i
$957$		0			0
$958$	47854.4	+	1411.57i	1.61389	+	0.0476053i
$959$	2980.67			0.100366
$960$		0			0
$961$	25193.9			0.845688
$962$	−3558.50	−	104.966i	−0.119263	−	0.00351792i
$963$		0			0
$964$	37003.8	+	2184.92i	1.23632	+	0.0729995i
$965$		−	16140.8i		−	0.538435i
$966$		0			0
$967$		−	6532.84i		−	0.217251i	−0.994083	−	0.108626i	$-0.965355\pi$
$967$		−	6532.84i		−	0.217251i	0.994083	−	0.108626i	$-0.0346450\pi$
$968$	−14144.9	−	1254.62i	−0.469664	−	0.0416581i
$969$		0			0
$970$	336.227	−	11398.6i	0.0111295	−	0.377306i
$971$	−48395.7			−1.59948			−0.799739	−	0.600348i	$-0.795029\pi$
$971$	−48395.7			−1.59948			−0.799739	+	0.600348i	$0.795029\pi$
$972$		0			0
$973$	9870.32			0.325209
$974$	803.876	−	27252.6i	0.0264454	−	0.896539i
$975$		0			0
$976$	−56606.1	−	6708.11i	−1.85647	−	0.220001i
$977$			37053.8i			1.21336i	0.794944	+	0.606682i	$0.207500\pi$
$977$			37053.8i			1.21336i	−0.794944	+	0.606682i	$0.792500\pi$
$978$		0			0
$979$			14526.0i			0.474212i
$980$	−199.325	+	3375.77i	−0.00649716	+	0.110036i
$981$		0			0
$982$	−13547.2	−	399.605i	−0.440232	−	0.0129856i
$983$	27818.2			0.902608			0.451304	−	0.892370i	$-0.350959\pi$
$983$	27818.2			0.902608			0.451304	+	0.892370i	$0.350959\pi$
$984$		0			0
$985$	−31573.4			−1.02133
$986$	1294.21	+	38.1755i	0.0418011	+	0.00123302i
$987$		0			0
$988$	155.140	−	2627.45i	0.00499561	−	0.0846056i
$989$			2481.28i			0.0797775i
$990$		0			0
$991$			42743.2i			1.37011i	0.728490	+	0.685057i	$0.240223\pi$
$991$			42743.2i			1.37011i	−0.728490	+	0.685057i	$0.759777\pi$
$992$	1803.10	−	12140.3i	0.0577100	−	0.388564i
$993$		0			0
$994$	55.0712	−	1866.99i	0.00175730	−	0.0595749i
$995$	−34044.0			−1.08469
$996$		0			0
$997$	−10810.6			−0.343407			−0.171703	−	0.985149i	$-0.554927\pi$
$997$	−10810.6			−0.343407			−0.171703	+	0.985149i	$0.554927\pi$
$998$	185.482	−	6288.13i	0.00588311	−	0.199446i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.e.a.71.1	✓	36
3.2	odd	2	inner	252.4.e.a.71.36	yes	36
4.3	odd	2	inner	252.4.e.a.71.35	yes	36
12.11	even	2	inner	252.4.e.a.71.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.e.a.71.1	✓	36	1.1	even	1	trivial
252.4.e.a.71.2	yes	36	12.11	even	2	inner
252.4.e.a.71.35	yes	36	4.3	odd	2	inner
252.4.e.a.71.36	yes	36	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82720 - 0.0833946i) q^{2} +(7.98609 + 0.471546i) q^{4} -8.62666i q^{5} -7.00000i q^{7} +(-22.5389 - 1.99915i) q^{8} +O(q^{10})\)	\(q+(-2.82720 - 0.0833946i) q^{2} +(7.98609 + 0.471546i) q^{4} -8.62666i q^{5} -7.00000i q^{7} +(-22.5389 - 1.99915i) q^{8} +(-0.719417 + 24.3893i) q^{10} -44.2558 q^{11} -3.70463 q^{13} +(-0.583762 + 19.7904i) q^{14} +(63.5553 + 7.53161i) q^{16} -35.8211i q^{17} +88.8088i q^{19} +(4.06787 - 68.8933i) q^{20} +(125.120 + 3.69069i) q^{22} -41.2086 q^{23} +50.5807 q^{25} +(10.4737 + 0.308946i) q^{26} +(3.30082 - 55.9026i) q^{28} -12.7794i q^{29} +67.8021i q^{31} +(-179.055 - 26.5935i) q^{32} +(-2.98728 + 101.273i) q^{34} -60.3866 q^{35} -339.755 q^{37} +(7.40617 - 251.080i) q^{38} +(-17.2460 + 194.436i) q^{40} +450.831i q^{41} -60.2125i q^{43} +(-353.431 - 20.8686i) q^{44} +(116.505 + 3.43658i) q^{46} -243.426 q^{47} -49.0000 q^{49} +(-143.002 - 4.21816i) q^{50} +(-29.5855 - 1.74690i) q^{52} +587.360i q^{53} +381.780i q^{55} +(-13.9940 + 157.773i) q^{56} +(-1.06573 + 36.1298i) q^{58} -393.669 q^{59} -890.660 q^{61} +(5.65432 - 191.690i) q^{62} +(504.007 + 90.1174i) q^{64} +31.9586i q^{65} +497.143i q^{67} +(16.8913 - 286.070i) q^{68} +(170.725 + 5.03592i) q^{70} -94.3384 q^{71} -636.939 q^{73} +(960.556 + 28.3338i) q^{74} +(-41.8774 + 709.235i) q^{76} +309.791i q^{77} -1118.13i q^{79} +(64.9727 - 548.270i) q^{80} +(37.5968 - 1274.59i) q^{82} +1167.84 q^{83} -309.016 q^{85} +(-5.02139 + 170.233i) q^{86} +(997.479 + 88.4740i) q^{88} -328.229i q^{89} +25.9324i q^{91} +(-329.096 - 19.4318i) q^{92} +(688.213 + 20.3004i) q^{94} +766.124 q^{95} -467.361 q^{97} +(138.533 + 4.08633i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 24 q^{4}+O(q^{10}) \) 36 * q - 24 * q^4	\( 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64} - 504 q^{70} - 2520 q^{76} + 1032 q^{82} - 3144 q^{85} + 2748 q^{88} + 5496 q^{94}+O(q^{100}) \) 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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