LMFDB - Embedded newform 322.3.b.a.139.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,3,Mod(139,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("322.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	322.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:	$8.77386451240$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.19
Character	$\chi$	$=$	322.139
Dual form			322.3.b.a.139.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} -4.52542i q^{3} +2.00000 q^{4} -5.90217i q^{5} -6.39991i q^{6} +(4.60838 - 5.26905i) q^{7} +2.82843 q^{8} -11.4794 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} -4.52542i q^{3} +2.00000 q^{4} -5.90217i q^{5} -6.39991i q^{6} +(4.60838 - 5.26905i) q^{7} +2.82843 q^{8} -11.4794 q^{9} -8.34694i q^{10} +0.565088 q^{11} -9.05084i q^{12} +13.3802i q^{13} +(6.51723 - 7.45156i) q^{14} -26.7098 q^{15} +4.00000 q^{16} +21.1333i q^{17} -16.2343 q^{18} +0.528172i q^{19} -11.8043i q^{20} +(-23.8447 - 20.8548i) q^{21} +0.799156 q^{22} +4.79583 q^{23} -12.7998i q^{24} -9.83567 q^{25} +18.9224i q^{26} +11.2204i q^{27} +(9.21675 - 10.5381i) q^{28} +18.5594 q^{29} -37.7734 q^{30} -13.9857i q^{31} +5.65685 q^{32} -2.55726i q^{33} +29.8870i q^{34} +(-31.0988 - 27.1994i) q^{35} -22.9588 q^{36} -13.8215 q^{37} +0.746948i q^{38} +60.5509 q^{39} -16.6939i q^{40} +22.3110i q^{41} +(-33.7214 - 29.4932i) q^{42} -36.8879 q^{43} +1.13018 q^{44} +67.7535i q^{45} +6.78233 q^{46} -65.8669i q^{47} -18.1017i q^{48} +(-6.52576 - 48.5635i) q^{49} -13.9097 q^{50} +95.6371 q^{51} +26.7604i q^{52} +36.3186 q^{53} +15.8680i q^{54} -3.33525i q^{55} +(13.0345 - 14.9031i) q^{56} +2.39020 q^{57} +26.2470 q^{58} +99.0116i q^{59} -53.4196 q^{60} +9.72880i q^{61} -19.7788i q^{62} +(-52.9014 + 60.4856i) q^{63} +8.00000 q^{64} +78.9722 q^{65} -3.61651i q^{66} -43.7345 q^{67} +42.2666i q^{68} -21.7031i q^{69} +(-43.9804 - 38.4658i) q^{70} +82.5321 q^{71} -32.4687 q^{72} +10.2133i q^{73} -19.5466 q^{74} +44.5105i q^{75} +1.05634i q^{76} +(2.60414 - 2.97748i) q^{77} +85.6319 q^{78} +120.957 q^{79} -23.6087i q^{80} -52.5378 q^{81} +31.5525i q^{82} -3.16821i q^{83} +(-47.6893 - 41.7097i) q^{84} +124.732 q^{85} -52.1674 q^{86} -83.9893i q^{87} +1.59831 q^{88} -147.109i q^{89} +95.8179i q^{90} +(70.5008 + 61.6609i) q^{91} +9.59166 q^{92} -63.2913 q^{93} -93.1499i q^{94} +3.11736 q^{95} -25.5996i q^{96} -39.3242i q^{97} +(-9.22881 - 68.6792i) q^{98} -6.48688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} - 12 q^{7} - 128 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 - 12 * q^7 - 128 * q^9	$ 32 q + 64 q^{4} - 12 q^{7} - 128 q^{9} + 24 q^{11} - 8 q^{14} + 16 q^{15} + 128 q^{16} + 84 q^{21} + 16 q^{22} - 224 q^{25} - 24 q^{28} + 96 q^{30} + 32 q^{35} - 256 q^{36} - 128 q^{39} - 80 q^{42} + 144 q^{43} + 48 q^{44} + 40 q^{49} - 224 q^{50} - 200 q^{51} + 232 q^{53} - 16 q^{56} - 200 q^{57} + 224 q^{58} + 32 q^{60} - 168 q^{63} + 256 q^{64} - 144 q^{67} - 208 q^{70} + 224 q^{71} + 160 q^{74} + 240 q^{77} + 128 q^{78} - 232 q^{79} + 560 q^{81} + 168 q^{84} + 416 q^{85} + 96 q^{86} + 32 q^{88} - 316 q^{91} - 496 q^{93} + 64 q^{95} + 144 q^{98} - 32 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 - 12 * q^7 - 128 * q^9 + 24 * q^11 - 8 * q^14 + 16 * q^15 + 128 * q^16 + 84 * q^21 + 16 * q^22 - 224 * q^25 - 24 * q^28 + 96 * q^30 + 32 * q^35 - 256 * q^36 - 128 * q^39 - 80 * q^42 + 144 * q^43 + 48 * q^44 + 40 * q^49 - 224 * q^50 - 200 * q^51 + 232 * q^53 - 16 * q^56 - 200 * q^57 + 224 * q^58 + 32 * q^60 - 168 * q^63 + 256 * q^64 - 144 * q^67 - 208 * q^70 + 224 * q^71 + 160 * q^74 + 240 * q^77 + 128 * q^78 - 232 * q^79 + 560 * q^81 + 168 * q^84 + 416 * q^85 + 96 * q^86 + 32 * q^88 - 316 * q^91 - 496 * q^93 + 64 * q^95 + 144 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$		−	4.52542i		−	1.50847i	−0.656603	−	0.754236i	$-0.728007\pi$
$3$		−	4.52542i		−	1.50847i	0.656603	−	0.754236i	$-0.271993\pi$
$4$	2.00000			0.500000
$5$		−	5.90217i		−	1.18043i	−0.807244	−	0.590217i	$-0.799042\pi$
$5$		−	5.90217i		−	1.18043i	0.807244	−	0.590217i	$-0.200958\pi$
$6$		−	6.39991i		−	1.06665i
$7$	4.60838	−	5.26905i	0.658339	−	0.752721i
$7$	4.60838	−	5.26905i	0.658339	−	0.752721i
$8$	2.82843			0.353553
$9$	−11.4794			−1.27549
$10$		−	8.34694i		−	0.834694i
$11$	0.565088			0.0513717			0.0256858	−	0.999670i	$-0.491823\pi$
$11$	0.565088			0.0513717			0.0256858	+	0.999670i	$0.491823\pi$
$12$		−	9.05084i		−	0.754236i
$13$			13.3802i			1.02924i	0.857417	+	0.514622i	$0.172068\pi$
$13$			13.3802i			1.02924i	−0.857417	+	0.514622i	$0.827932\pi$
$14$	6.51723	−	7.45156i	0.465516	−	0.532254i
$15$	−26.7098			−1.78065
$16$	4.00000			0.250000
$17$			21.1333i			1.24314i	0.783360	+	0.621568i	$0.213504\pi$
$17$			21.1333i			1.24314i	−0.783360	+	0.621568i	$0.786496\pi$
$18$	−16.2343			−0.901908
$19$			0.528172i			0.0277985i	0.999903	+	0.0138993i	$0.00442441\pi$
$19$			0.528172i			0.0277985i	−0.999903	+	0.0138993i	$0.995576\pi$
$20$		−	11.8043i		−	0.590217i
$21$	−23.8447	−	20.8548i	−1.13546	−	0.993087i
$22$	0.799156			0.0363253
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$		−	12.7998i		−	0.533326i
$25$	−9.83567			−0.393427
$26$			18.9224i			0.727786i
$27$			11.2204i			0.415570i
$28$	9.21675	−	10.5381i	0.329170	−	0.376361i
$29$	18.5594			0.639981			0.319990	−	0.947421i	$-0.396320\pi$
$29$	18.5594			0.639981			0.319990	+	0.947421i	$0.396320\pi$
$30$	−37.7734			−1.25911
$31$		−	13.9857i		−	0.451153i	−0.974225	−	0.225576i	$-0.927573\pi$
$31$		−	13.9857i		−	0.451153i	0.974225	−	0.225576i	$-0.0724266\pi$
$32$	5.65685			0.176777
$33$		−	2.55726i		−	0.0774928i
$34$			29.8870i			0.879030i
$35$	−31.0988	−	27.1994i	−0.888539	−	0.777127i
$36$	−22.9588			−0.637745
$37$	−13.8215			−0.373554			−0.186777	−	0.982402i	$-0.559804\pi$
$37$	−13.8215			−0.373554			−0.186777	+	0.982402i	$0.559804\pi$
$38$			0.746948i			0.0196565i
$39$	60.5509			1.55259
$40$		−	16.6939i		−	0.417347i
$41$			22.3110i			0.544170i	0.962273	+	0.272085i	$0.0877133\pi$
$41$			22.3110i			0.544170i	−0.962273	+	0.272085i	$0.912287\pi$
$42$	−33.7214	−	29.4932i	−0.802891	−	0.702219i
$43$	−36.8879			−0.857858			−0.428929	−	0.903338i	$-0.641109\pi$
$43$	−36.8879			−0.857858			−0.428929	+	0.903338i	$0.641109\pi$
$44$	1.13018			0.0256858
$45$			67.7535i			1.50563i
$46$	6.78233			0.147442
$47$		−	65.8669i		−	1.40142i	−0.713444	−	0.700712i	$-0.752866\pi$
$47$		−	65.8669i		−	1.40142i	0.713444	−	0.700712i	$-0.247134\pi$
$48$		−	18.1017i		−	0.377118i
$49$	−6.52576	−	48.5635i	−0.133179	−	0.991092i
$50$	−13.9097			−0.278195
$51$	95.6371			1.87524
$52$			26.7604i			0.514622i
$53$	36.3186			0.685256			0.342628	−	0.939471i	$-0.388683\pi$
$53$	36.3186			0.685256			0.342628	+	0.939471i	$0.388683\pi$
$54$			15.8680i			0.293852i
$55$		−	3.33525i		−	0.0606409i
$56$	13.0345	−	14.9031i	0.232758	−	0.266127i
$57$	2.39020			0.0419333
$58$	26.2470			0.452535
$59$			99.0116i			1.67816i	0.544007	+	0.839081i	$0.316907\pi$
$59$			99.0116i			1.67816i	−0.544007	+	0.839081i	$0.683093\pi$
$60$	−53.4196			−0.890327
$61$			9.72880i			0.159489i	0.996815	+	0.0797443i	$0.0254104\pi$
$61$			9.72880i			0.159489i	−0.996815	+	0.0797443i	$0.974590\pi$
$62$		−	19.7788i		−	0.319013i
$63$	−52.9014	+	60.4856i	−0.839705	+	0.960089i
$64$	8.00000			0.125000
$65$	78.9722			1.21496
$66$		−	3.61651i		−	0.0547957i
$67$	−43.7345			−0.652753			−0.326377	−	0.945240i	$-0.605828\pi$
$67$	−43.7345			−0.652753			−0.326377	+	0.945240i	$0.605828\pi$
$68$			42.2666i			0.621568i
$69$		−	21.7031i		−	0.314538i
$70$	−43.9804	−	38.4658i	−0.628292	−	0.549512i
$71$	82.5321			1.16242			0.581212	−	0.813752i	$-0.302579\pi$
$71$	82.5321			1.16242			0.581212	+	0.813752i	$0.302579\pi$
$72$	−32.4687			−0.450954
$73$			10.2133i			0.139908i	0.997550	+	0.0699539i	$0.0222852\pi$
$73$			10.2133i			0.139908i	−0.997550	+	0.0699539i	$0.977715\pi$
$74$	−19.5466			−0.264143
$75$			44.5105i			0.593474i
$76$			1.05634i			0.0138993i
$77$	2.60414	−	2.97748i	0.0338200	−	0.0386686i
$78$	85.6319			1.09785
$79$	120.957			1.53110			0.765549	−	0.643378i	$-0.222468\pi$
$79$	120.957			1.53110			0.765549	+	0.643378i	$0.222468\pi$
$80$		−	23.6087i		−	0.295109i
$81$	−52.5378			−0.648615
$82$			31.5525i			0.384787i
$83$		−	3.16821i		−	0.0381712i	−0.999818	−	0.0190856i	$-0.993924\pi$
$83$		−	3.16821i		−	0.0381712i	0.999818	−	0.0190856i	$-0.00607551\pi$
$84$	−47.6893	−	41.7097i	−0.567730	−	0.496543i
$85$	124.732			1.46744
$86$	−52.1674			−0.606597
$87$		−	83.9893i		−	0.965394i
$88$	1.59831			0.0181626
$89$		−	147.109i		−	1.65291i	−0.562999	−	0.826457i	$-0.690353\pi$
$89$		−	147.109i		−	1.65291i	0.562999	−	0.826457i	$-0.309647\pi$
$90$			95.8179i			1.06464i
$91$	70.5008	+	61.6609i	0.774735	+	0.677592i
$92$	9.59166			0.104257
$93$	−63.2913			−0.680552
$94$		−	93.1499i		−	0.990956i
$95$	3.11736			0.0328143
$96$		−	25.5996i		−	0.266663i
$97$		−	39.3242i		−	0.405404i	−0.979240	−	0.202702i	$-0.935028\pi$
$97$		−	39.3242i		−	0.405404i	0.979240	−	0.202702i	$-0.0649723\pi$
$98$	−9.22881	−	68.6792i	−0.0941716	−	0.700808i
$99$	−6.48688			−0.0655241
$100$	−19.6713			−0.196713
$101$			198.469i			1.96504i	0.186149	+	0.982522i	$0.440399\pi$
$101$			198.469i			1.96504i	−0.186149	+	0.982522i	$0.559601\pi$
$102$	135.251			1.32599
$103$			39.0946i			0.379559i	0.981827	+	0.189779i	$0.0607773\pi$
$103$			39.0946i			0.379559i	−0.981827	+	0.189779i	$0.939223\pi$
$104$			37.8449i			0.363893i
$105$	−123.089	+	140.735i	−1.17227	+	1.34034i
$106$	51.3622			0.484549
$107$	212.780			1.98860			0.994300	−	0.106619i	$-0.0340025\pi$
$107$	212.780			1.98860			0.994300	+	0.106619i	$0.0340025\pi$
$108$			22.4408i			0.207785i
$109$	−192.228			−1.76356			−0.881780	−	0.471661i	$-0.843655\pi$
$109$	−192.228			−1.76356			−0.881780	+	0.471661i	$0.843655\pi$
$110$		−	4.71676i		−	0.0428796i
$111$			62.5481i			0.563497i
$112$	18.4335	−	21.0762i	0.164585	−	0.188180i
$113$	89.1676			0.789093			0.394547	−	0.918876i	$-0.370902\pi$
$113$	89.1676			0.789093			0.394547	+	0.918876i	$0.370902\pi$
$114$	3.38025			0.0296513
$115$		−	28.3058i		−	0.246138i
$116$	37.1189			0.319990
$117$		−	153.597i		−	1.31279i
$118$			140.023i			1.18664i
$119$	111.352	+	97.3902i	0.935735	+	0.818405i
$120$	−75.5468			−0.629556
$121$	−120.681			−0.997361
$122$			13.7586i			0.112775i
$123$	100.967			0.820866
$124$		−	27.9715i		−	0.225576i
$125$		−	89.5025i		−	0.716020i
$126$	−74.8139	+	85.5395i	−0.593761	+	0.678885i
$127$	−65.2346			−0.513658			−0.256829	−	0.966457i	$-0.582678\pi$
$127$	−65.2346			−0.513658			−0.256829	+	0.966457i	$0.582678\pi$
$128$	11.3137			0.0883883
$129$			166.933i			1.29406i
$130$	111.684			0.859104
$131$		−	16.1145i		−	0.123011i	−0.998107	−	0.0615056i	$-0.980410\pi$
$131$		−	16.1145i		−	0.123011i	0.998107	−	0.0615056i	$-0.0195902\pi$
$132$		−	5.11452i		−	0.0387464i
$133$	2.78296	+	2.43401i	0.0209245	+	0.0183009i
$134$	−61.8499			−0.461566
$135$	66.2246			0.490553
$136$			59.7740i			0.439515i
$137$	−260.749			−1.90328			−0.951638	−	0.307223i	$-0.900600\pi$
$137$	−260.749			−1.90328			−0.951638	+	0.307223i	$0.900600\pi$
$138$		−	30.6929i		−	0.222412i
$139$			233.529i			1.68006i	0.542538	+	0.840031i	$0.317463\pi$
$139$			233.529i			1.68006i	−0.542538	+	0.840031i	$0.682537\pi$
$140$	−62.1977	−	54.3989i	−0.444269	−	0.388563i
$141$	−298.075			−2.11401
$142$	116.718			0.821958
$143$			7.56099i			0.0528740i
$144$	−45.9176			−0.318873
$145$		−	109.541i		−	0.755456i
$146$			14.4438i			0.0989298i
$147$	−219.770	+	29.5318i	−1.49504	+	0.200896i
$148$	−27.6430			−0.186777
$149$	−53.7828			−0.360959			−0.180479	−	0.983579i	$-0.557765\pi$
$149$	−53.7828			−0.360959			−0.180479	+	0.983579i	$0.557765\pi$
$150$			62.9474i			0.419649i
$151$	11.6259			0.0769926			0.0384963	−	0.999259i	$-0.487743\pi$
$151$	11.6259			0.0769926			0.0384963	+	0.999259i	$0.487743\pi$
$152$			1.49390i			0.00982826i
$153$		−	242.598i		−	1.58561i
$154$	3.68281	−	4.21079i	0.0239143	−	0.0273428i
$155$	−82.5463			−0.532557
$156$	121.102			0.776294
$157$		−	16.2339i		−	0.103401i	−0.998663	−	0.0517003i	$-0.983536\pi$
$157$		−	16.2339i		−	0.103401i	0.998663	−	0.0517003i	$-0.0164641\pi$
$158$	171.059			1.08265
$159$		−	164.357i		−	1.03369i
$160$		−	33.3877i		−	0.208673i
$161$	22.1010	−	25.2695i	0.137273	−	0.156953i
$162$	−74.2997			−0.458640
$163$	113.767			0.697959			0.348979	−	0.937130i	$-0.386528\pi$
$163$	113.767			0.697959			0.348979	+	0.937130i	$0.386528\pi$
$164$			44.6220i			0.272085i
$165$	−15.0934			−0.0914752
$166$		−	4.48053i		−	0.0269911i
$167$		−	0.699844i		−	0.00419068i	−0.999998	−	0.00209534i	$-0.999333\pi$
$167$		−	0.699844i		−	0.00419068i	0.999998	−	0.00209534i	$-0.000666968\pi$
$168$	−67.4429	−	58.9864i	−0.401446	−	0.351109i
$169$	−10.0293			−0.0593450
$170$	176.398			1.03764
$171$		−	6.06310i		−	0.0354567i
$172$	−73.7758			−0.428929
$173$			178.441i			1.03145i	0.856753	+	0.515726i	$0.172478\pi$
$173$			178.441i			1.03145i	−0.856753	+	0.515726i	$0.827522\pi$
$174$		−	118.779i		−	0.682637i
$175$	−45.3265	+	51.8246i	−0.259008	+	0.296141i
$176$	2.26035			0.0128429
$177$	448.069			2.53146
$178$		−	208.044i		−	1.16879i
$179$	216.642			1.21029			0.605145	−	0.796116i	$-0.293115\pi$
$179$	216.642			1.21029			0.605145	+	0.796116i	$0.293115\pi$
$180$			135.507i			0.752817i
$181$		−	82.7225i		−	0.457030i	−0.973540	−	0.228515i	$-0.926613\pi$
$181$		−	82.7225i		−	0.457030i	0.973540	−	0.228515i	$-0.0733871\pi$
$182$	99.7032	+	87.2017i	0.547820	+	0.479130i
$183$	44.0269			0.240584
$184$	13.5647			0.0737210
$185$			81.5770i			0.440957i
$186$	−89.5075			−0.481223
$187$			11.9422i			0.0638620i
$188$		−	131.734i		−	0.700712i
$189$	59.1207	+	51.7077i	0.312808	+	0.273586i
$190$	4.40862			0.0232032
$191$	−137.430			−0.719529			−0.359765	−	0.933043i	$-0.617143\pi$
$191$	−137.430			−0.719529			−0.359765	+	0.933043i	$0.617143\pi$
$192$		−	36.2033i		−	0.188559i
$193$	263.652			1.36607			0.683037	−	0.730384i	$-0.260659\pi$
$193$	263.652			1.36607			0.683037	+	0.730384i	$0.260659\pi$
$194$		−	55.6128i		−	0.286664i
$195$		−	357.382i		−	1.83273i
$196$	−13.0515	−	97.1270i	−0.0665894	−	0.495546i
$197$	−222.241			−1.12813			−0.564064	−	0.825731i	$-0.690763\pi$
$197$	−222.241			−1.12813			−0.564064	+	0.825731i	$0.690763\pi$
$198$	−9.17384			−0.0463325
$199$		−	58.9179i		−	0.296070i	−0.988982	−	0.148035i	$-0.952705\pi$
$199$		−	58.9179i		−	0.296070i	0.988982	−	0.148035i	$-0.0472948\pi$
$200$	−27.8195			−0.139097
$201$			197.917i			0.984660i
$202$			280.678i			1.38950i
$203$	85.5289	−	97.7906i	0.421325	−	0.481727i
$204$	191.274			0.937618
$205$	131.683			0.642358
$206$			55.2881i			0.268389i
$207$	−55.0533			−0.265958
$208$			53.5207i			0.257311i
$209$			0.298464i			0.00142806i
$210$	−174.074	+	199.030i	−0.828923	+	0.947761i
$211$	−322.986			−1.53074			−0.765370	−	0.643591i	$-0.777444\pi$
$211$	−322.986			−1.53074			−0.765370	+	0.643591i	$0.777444\pi$
$212$	72.6371			0.342628
$213$		−	373.492i		−	1.75348i
$214$	300.917			1.40615
$215$			217.719i			1.01265i
$216$			31.7360i			0.146926i
$217$	−73.6916	−	64.4516i	−0.339592	−	0.297012i
$218$	−271.852			−1.24703
$219$	46.2193			0.211047
$220$		−	6.67050i		−	0.0303205i
$221$	−282.768			−1.27949
$222$			88.4564i			0.398452i
$223$		−	268.175i		−	1.20258i	−0.799031	−	0.601290i	$-0.794654\pi$
$223$		−	268.175i		−	1.20258i	0.799031	−	0.601290i	$-0.205346\pi$
$224$	26.0689	−	29.8062i	0.116379	−	0.133064i
$225$	112.908			0.501812
$226$	126.102			0.557973
$227$		−	67.9381i		−	0.299287i	−0.988740	−	0.149643i	$-0.952187\pi$
$227$		−	67.9381i		−	0.299287i	0.988740	−	0.149643i	$-0.0478126\pi$
$228$	4.78040			0.0209667
$229$		−	203.514i		−	0.888707i	−0.895852	−	0.444353i	$-0.853433\pi$
$229$		−	203.514i		−	0.888707i	0.895852	−	0.444353i	$-0.146567\pi$
$230$		−	40.0305i		−	0.174046i
$231$	−13.4743	−	11.7848i	−0.0583305	−	0.0510165i
$232$	52.4940			0.226267
$233$	178.189			0.764760			0.382380	−	0.924005i	$-0.375104\pi$
$233$	178.189			0.764760			0.382380	+	0.924005i	$0.375104\pi$
$234$		−	217.218i		−	0.928284i
$235$	−388.758			−1.65429
$236$			198.023i			0.839081i
$237$		−	547.380i		−	2.30962i
$238$	157.476	+	137.731i	0.661664	+	0.578700i
$239$	−153.434			−0.641985			−0.320993	−	0.947082i	$-0.604016\pi$
$239$	−153.434			−0.641985			−0.320993	+	0.947082i	$0.604016\pi$
$240$	−106.839			−0.445164
$241$		−	165.696i		−	0.687535i	−0.939055	−	0.343768i	$-0.888297\pi$
$241$		−	165.696i		−	0.687535i	0.939055	−	0.343768i	$-0.111703\pi$
$242$	−170.668			−0.705241
$243$			338.739i			1.39399i
$244$			19.4576i			0.0797443i
$245$	−286.630	+	38.5162i	−1.16992	+	0.157209i
$246$	142.788			0.580440
$247$	−7.06704			−0.0286115
$248$		−	39.5577i		−	0.159507i
$249$	−14.3375			−0.0575803
$250$		−	126.576i		−	0.506303i
$251$			59.0113i			0.235105i	0.993067	+	0.117552i	$0.0375048\pi$
$251$			59.0113i			0.235105i	−0.993067	+	0.117552i	$0.962495\pi$
$252$	−105.803	+	120.971i	−0.419853	+	0.480044i
$253$	2.71007			0.0107117
$254$	−92.2557			−0.363211
$255$		−	564.467i		−	2.21359i
$256$	16.0000			0.0625000
$257$			170.227i			0.662361i	0.943567	+	0.331181i	$0.107447\pi$
$257$			170.227i			0.662361i	−0.943567	+	0.331181i	$0.892553\pi$
$258$			236.079i			0.915036i
$259$	−63.6947	+	72.8262i	−0.245925	+	0.281182i
$260$	157.944			0.607478
$261$	−213.052			−0.816290
$262$		−	22.7893i		−	0.0869820i
$263$	243.521			0.925937			0.462969	−	0.886375i	$-0.346784\pi$
$263$	243.521			0.925937			0.462969	+	0.886375i	$0.346784\pi$
$264$		−	7.23303i		−	0.0273978i
$265$		−	214.358i		−	0.808900i
$266$	3.93570	+	3.44222i	0.0147959	+	0.0129407i
$267$	−665.732			−2.49338
$268$	−87.4689			−0.326377
$269$			12.1393i			0.0451275i	0.999745	+	0.0225638i	$0.00718288\pi$
$269$			12.1393i			0.0451275i	−0.999745	+	0.0225638i	$0.992817\pi$
$270$	93.6558			0.346873
$271$			207.337i			0.765082i	0.923939	+	0.382541i	$0.124951\pi$
$271$			207.337i			0.765082i	−0.923939	+	0.382541i	$0.875049\pi$
$272$			84.5332i			0.310784i
$273$	279.041	−	319.046i	1.02213	−	1.16867i
$274$	−368.754			−1.34582
$275$	−5.55802			−0.0202110
$276$		−	43.4063i		−	0.157269i
$277$	−484.370			−1.74863			−0.874315	−	0.485360i	$-0.838689\pi$
$277$	−484.370			−1.74863			−0.874315	+	0.485360i	$0.838689\pi$
$278$			330.259i			1.18798i
$279$			160.548i			0.575441i
$280$	−87.9608	−	76.9316i	−0.314146	−	0.274756i
$281$	−106.393			−0.378624			−0.189312	−	0.981917i	$-0.560626\pi$
$281$	−106.393			−0.378624			−0.189312	+	0.981917i	$0.560626\pi$
$282$	−421.542			−1.49483
$283$		−	124.329i		−	0.439325i	−0.975576	−	0.219662i	$-0.929504\pi$
$283$		−	124.329i		−	0.439325i	0.975576	−	0.219662i	$-0.0704956\pi$
$284$	165.064			0.581212
$285$		−	14.1074i		−	0.0494995i
$286$			10.6928i			0.0373876i
$287$	117.558	+	102.817i	0.409609	+	0.358249i
$288$	−64.9374			−0.225477
$289$	−157.617			−0.545386
$290$		−	154.915i		−	0.534188i
$291$	−177.959			−0.611541
$292$			20.4265i			0.0699539i
$293$			526.180i			1.79584i	0.440163	+	0.897918i	$0.354921\pi$
$293$			526.180i			1.79584i	−0.440163	+	0.897918i	$0.645079\pi$
$294$	−310.802	+	41.7642i	−1.05715	+	0.142055i
$295$	584.384			1.98096
$296$	−39.0931			−0.132071
$297$			6.34051i			0.0213485i
$298$	−76.0604			−0.255236
$299$			64.1691i			0.214612i
$300$			89.0210i			0.296737i
$301$	−169.993	+	194.364i	−0.564762	+	0.645728i
$302$	16.4415			0.0544420
$303$	898.157			2.96421
$304$			2.11269i			0.00694963i
$305$	57.4211			0.188266
$306$		−	343.085i		−	1.12119i
$307$			502.510i			1.63684i	0.574621	+	0.818420i	$0.305149\pi$
$307$			502.510i			1.63684i	−0.574621	+	0.818420i	$0.694851\pi$
$308$	5.20828	−	5.95496i	0.0169100	−	0.0193343i
$309$	176.919			0.572554
$310$	−116.738			−0.376575
$311$			336.473i			1.08191i	0.841053	+	0.540953i	$0.181936\pi$
$311$			336.473i			1.08191i	−0.841053	+	0.540953i	$0.818064\pi$
$312$	171.264			0.548923
$313$		−	488.503i		−	1.56071i	−0.625336	−	0.780356i	$-0.715038\pi$
$313$		−	488.503i		−	1.56071i	0.625336	−	0.780356i	$-0.284962\pi$
$314$		−	22.9582i		−	0.0731153i
$315$	356.997	+	312.234i	1.13332	+	0.991218i
$316$	241.913			0.765549
$317$	306.073			0.965531			0.482765	−	0.875750i	$-0.339632\pi$
$317$	306.073			0.965531			0.482765	+	0.875750i	$0.339632\pi$
$318$		−	232.435i		−	0.730929i
$319$	10.4877			0.0328769
$320$		−	47.2174i		−	0.147554i
$321$		−	962.919i		−	2.99975i
$322$	31.2555	−	35.7364i	0.0970668	−	0.110983i
$323$	−11.1620			−0.0345573
$324$	−105.076			−0.324307
$325$		−	131.603i		−	0.404932i
$326$	160.891			0.493531
$327$			869.912i			2.66028i
$328$			63.1050i			0.192393i
$329$	−347.056	−	303.539i	−1.05488	−	0.922612i
$330$	−21.3453			−0.0646827
$331$	−594.339			−1.79559			−0.897793	−	0.440417i	$-0.854831\pi$
$331$	−594.339			−1.79559			−0.897793	+	0.440417i	$0.854831\pi$
$332$		−	6.33643i		−	0.0190856i
$333$	158.663			0.476465
$334$		−	0.989729i		−	0.00296326i
$335$			258.128i			0.770533i
$336$	−95.3786	−	83.4193i	−0.283865	−	0.248272i
$337$	−9.48712			−0.0281517			−0.0140758	−	0.999901i	$-0.504481\pi$
$337$	−9.48712			−0.0281517			−0.0140758	+	0.999901i	$0.504481\pi$
$338$	−14.1836			−0.0419632
$339$		−	403.521i		−	1.19033i
$340$	249.465			0.733720
$341$		−	7.90318i		−	0.0231765i
$342$		−	8.57452i		−	0.0250717i
$343$	−285.957	−	189.414i	−0.833693	−	0.552228i
$344$	−104.335			−0.303299
$345$	−128.096			−0.371292
$346$			252.354i			0.729347i
$347$	343.233			0.989143			0.494572	−	0.869137i	$-0.335325\pi$
$347$	343.233			0.989143			0.494572	+	0.869137i	$0.335325\pi$
$348$		−	167.979i		−	0.482697i
$349$			663.685i			1.90168i	0.309687	+	0.950839i	$0.399776\pi$
$349$			663.685i			1.90168i	−0.309687	+	0.950839i	$0.600224\pi$
$350$	−64.1013	+	73.2911i	−0.183147	+	0.209403i
$351$	−150.131			−0.427723
$352$	3.19662			0.00908131
$353$			319.400i			0.904815i	0.891811	+	0.452407i	$0.149435\pi$
$353$			319.400i			0.904815i	−0.891811	+	0.452407i	$0.850565\pi$
$354$	633.665			1.79001
$355$		−	487.119i		−	1.37217i
$356$		−	294.219i		−	0.826457i
$357$	440.731	−	503.916i	1.23454	−	1.41153i
$358$	306.378			0.855804
$359$	602.658			1.67871			0.839356	−	0.543582i	$-0.182932\pi$
$359$	602.658			1.67871			0.839356	+	0.543582i	$0.182932\pi$
$360$			191.636i			0.532322i
$361$	360.721			0.999227
$362$		−	116.987i		−	0.323169i
$363$			546.131i			1.50449i
$364$	141.002	+	123.322i	0.387367	+	0.338796i
$365$	60.2805			0.165152
$366$	62.2634			0.170119
$367$			177.054i			0.482437i	0.970471	+	0.241218i	$0.0775470\pi$
$367$			177.054i			0.482437i	−0.970471	+	0.241218i	$0.922453\pi$
$368$	19.1833			0.0521286
$369$		−	256.117i		−	0.694084i
$370$			115.367i			0.311803i
$371$	167.370	−	191.364i	0.451131	−	0.515807i
$372$	−126.583			−0.340276
$373$	480.550			1.28834			0.644169	−	0.764883i	$-0.277203\pi$
$373$	480.550			1.28834			0.644169	+	0.764883i	$0.277203\pi$
$374$			16.8888i			0.0451572i
$375$	−405.036			−1.08010
$376$		−	186.300i		−	0.495478i
$377$			248.329i			0.658697i
$378$	83.6093	+	73.1257i	0.221189	+	0.193454i
$379$	−537.095			−1.41714			−0.708568	−	0.705642i	$-0.750659\pi$
$379$	−537.095			−1.41714			−0.708568	+	0.705642i	$0.750659\pi$
$380$	6.23472			0.0164072
$381$			295.214i			0.774840i
$382$	−194.355			−0.508784
$383$			611.959i			1.59780i	0.601461	+	0.798902i	$0.294585\pi$
$383$			611.959i			1.59780i	−0.601461	+	0.798902i	$0.705415\pi$
$384$		−	51.1993i		−	0.133331i
$385$	−17.5736	−	15.3701i	−0.0456457	−	0.0399223i
$386$	372.861			0.965960
$387$	423.452			1.09419
$388$		−	78.6484i		−	0.202702i
$389$	134.682			0.346227			0.173114	−	0.984902i	$-0.444617\pi$
$389$	134.682			0.346227			0.173114	+	0.984902i	$0.444617\pi$
$390$		−	505.415i		−	1.29594i
$391$			101.352i			0.259212i
$392$	−18.4576	−	137.358i	−0.0470858	−	0.350404i
$393$	−72.9247			−0.185559
$394$	−314.296			−0.797707
$395$		−	713.908i		−	1.80736i
$396$	−12.9738			−0.0327620
$397$		−	118.701i		−	0.298996i	−0.988762	−	0.149498i	$-0.952234\pi$
$397$		−	118.701i		−	0.298996i	0.988762	−	0.149498i	$-0.0477658\pi$
$398$		−	83.3225i		−	0.209353i
$399$	11.0149	−	12.5941i	0.0276063	−	0.0315641i
$400$	−39.3427			−0.0983567
$401$	660.066			1.64605			0.823025	−	0.568005i	$-0.192285\pi$
$401$	660.066			1.64605			0.823025	+	0.568005i	$0.192285\pi$
$402$			279.897i			0.696260i
$403$	187.132			0.464347
$404$			396.939i			0.982522i
$405$			310.087i			0.765648i
$406$	120.956	−	138.297i	0.297922	−	0.340633i
$407$	−7.81038			−0.0191901
$408$	270.502			0.662996
$409$			236.476i			0.578180i	0.957302	+	0.289090i	$0.0933528\pi$
$409$			236.476i			0.578180i	−0.957302	+	0.289090i	$0.906647\pi$
$410$	186.228			0.454216
$411$			1180.00i			2.87104i
$412$			78.1891i			0.189779i
$413$	521.697	+	456.282i	1.26319	+	1.10480i
$414$	−77.8572			−0.188061
$415$	−18.6993			−0.0450587
$416$			75.6897i			0.181947i
$417$	1056.81			2.53433
$418$			0.422092i			0.00100979i
$419$			59.5798i			0.142195i	0.997469	+	0.0710976i	$0.0226502\pi$
$419$			59.5798i			0.142195i	−0.997469	+	0.0710976i	$0.977350\pi$
$420$	−246.178	+	281.471i	−0.586137	+	0.670168i
$421$	−635.568			−1.50966			−0.754831	−	0.655919i	$-0.772281\pi$
$421$	−635.568			−1.50966			−0.754831	+	0.655919i	$0.772281\pi$
$422$	−456.771			−1.08240
$423$			756.114i			1.78750i
$424$	102.724			0.242275
$425$		−	207.860i		−	0.489083i
$426$		−	528.198i		−	1.23990i
$427$	51.2615	+	44.8340i	0.120050	+	0.104998i
$428$	425.560			0.994300
$429$	34.2166			0.0797590
$430$			307.901i			0.716049i
$431$	−34.5398			−0.0801389			−0.0400694	−	0.999197i	$-0.512758\pi$
$431$	−34.5398			−0.0801389			−0.0400694	+	0.999197i	$0.512758\pi$
$432$			44.8815i			0.103892i
$433$		−	297.608i		−	0.687317i	−0.939095	−	0.343659i	$-0.888334\pi$
$433$		−	297.608i		−	0.687317i	0.939095	−	0.343659i	$-0.111666\pi$
$434$	−104.216	−	91.1483i	−0.240128	−	0.210019i
$435$	−495.719			−1.13958
$436$	−384.456			−0.881780
$437$			2.53302i			0.00579639i
$438$	65.3640			0.149233
$439$		−	202.378i		−	0.460997i	−0.973073	−	0.230498i	$-0.925964\pi$
$439$		−	202.378i		−	0.460997i	0.973073	−	0.230498i	$-0.0740356\pi$
$440$		−	9.43351i		−	0.0214398i
$441$	74.9118	+	557.481i	0.169868	+	1.26413i
$442$	−399.894			−0.904737
$443$	−660.196			−1.49028			−0.745142	−	0.666906i	$-0.767618\pi$
$443$	−660.196			−1.49028			−0.745142	+	0.666906i	$0.767618\pi$
$444$			125.096i			0.281748i
$445$	−868.265			−1.95116
$446$		−	379.257i		−	0.850352i
$447$			243.390i			0.544496i
$448$	36.8670	−	42.1524i	0.0822924	−	0.0940902i
$449$	−559.694			−1.24654			−0.623268	−	0.782009i	$-0.714195\pi$
$449$	−559.694			−1.24654			−0.623268	+	0.782009i	$0.714195\pi$
$450$	159.676			0.354835
$451$			12.6077i			0.0279549i
$452$	178.335			0.394547
$453$		−	52.6120i		−	0.116141i
$454$		−	96.0790i		−	0.211628i
$455$	363.933	−	416.108i	0.799854	−	0.914524i
$456$	6.76050			0.0148257
$457$	−744.256			−1.62857			−0.814285	−	0.580466i	$-0.802871\pi$
$457$	−744.256			−1.62857			−0.814285	+	0.580466i	$0.802871\pi$
$458$		−	287.812i		−	0.628411i
$459$	−237.124			−0.516609
$460$		−	56.6117i		−	0.123069i
$461$			590.952i			1.28189i	0.767586	+	0.640945i	$0.221458\pi$
$461$			590.952i			1.28189i	−0.767586	+	0.640945i	$0.778542\pi$
$462$	−19.0556	−	16.6663i	−0.0412459	−	0.0360741i
$463$	564.691			1.21963			0.609817	−	0.792542i	$-0.291243\pi$
$463$	564.691			1.21963			0.609817	+	0.792542i	$0.291243\pi$
$464$	74.2378			0.159995
$465$			373.557i			0.803347i
$466$	251.998			0.540767
$467$		−	742.966i		−	1.59093i	−0.605998	−	0.795467i	$-0.707226\pi$
$467$		−	742.966i		−	1.59093i	0.605998	−	0.795467i	$-0.292774\pi$
$468$		−	307.193i		−	0.656396i
$469$	−201.545	+	230.439i	−0.429733	+	0.491341i
$470$	−549.787			−1.16976
$471$	−73.4652			−0.155977
$472$			280.047i			0.593320i
$473$	−20.8449			−0.0440696
$474$		−	774.112i		−	1.63315i
$475$		−	5.19492i		−	0.0109367i
$476$	222.705	+	194.780i	0.467867	+	0.409203i
$477$	−416.916			−0.874037
$478$	−216.989			−0.453952
$479$			318.312i			0.664535i	0.943185	+	0.332267i	$0.107814\pi$
$479$			318.312i			0.664535i	−0.943185	+	0.332267i	$0.892186\pi$
$480$	−151.094			−0.314778
$481$		−	184.934i		−	0.384479i
$482$		−	234.330i		−	0.486161i
$483$	−114.355	−	100.016i	−0.236760	−	0.207073i
$484$	−241.361			−0.498680
$485$	−232.098			−0.478553
$486$			479.049i			0.985698i
$487$	−301.614			−0.619330			−0.309665	−	0.950846i	$-0.600217\pi$
$487$	−301.614			−0.619330			−0.309665	+	0.950846i	$0.600217\pi$
$488$			27.5172i			0.0563877i
$489$		−	514.845i		−	1.05285i
$490$	−405.357	+	54.4701i	−0.827258	+	0.111163i
$491$	756.976			1.54170			0.770851	−	0.637015i	$-0.219831\pi$
$491$	756.976			1.54170			0.770851	+	0.637015i	$0.219831\pi$
$492$	201.933			0.410433
$493$			392.223i			0.795583i
$494$	−9.99430			−0.0202314
$495$			38.2867i			0.0773469i
$496$		−	55.9430i		−	0.112788i
$497$	380.339	−	434.866i	0.765269	−	0.874981i
$498$	−20.2763			−0.0407154
$499$	−715.336			−1.43354			−0.716770	−	0.697310i	$-0.754380\pi$
$499$	−715.336			−1.43354			−0.716770	+	0.697310i	$0.754380\pi$
$500$		−	179.005i		−	0.358010i
$501$	−3.16709			−0.00632153
$502$			83.4546i			0.166244i
$503$			736.550i			1.46431i	0.681136	+	0.732157i	$0.261486\pi$
$503$			736.550i			1.46431i	−0.681136	+	0.732157i	$0.738514\pi$
$504$	−149.628	+	171.079i	−0.296881	+	0.339443i
$505$	1171.40			2.31961
$506$	3.83262			0.00757434
$507$			45.3868i			0.0895203i
$508$	−130.469			−0.256829
$509$			182.737i			0.359012i	0.983757	+	0.179506i	$0.0574500\pi$
$509$			182.737i			0.359012i	−0.983757	+	0.179506i	$0.942550\pi$
$510$		−	798.276i		−	1.56525i
$511$	53.8142	+	47.0666i	0.105312	+	0.0921069i
$512$	22.6274			0.0441942
$513$	−5.92629			−0.0115522
$514$			240.737i			0.468360i
$515$	230.743			0.448045
$516$			333.866i			0.647028i
$517$		−	37.2206i		−	0.0719935i
$518$	−90.0779	+	102.992i	−0.173896	+	0.198826i
$519$	807.522			1.55592
$520$	223.367			0.429552
$521$			650.832i			1.24920i	0.780945	+	0.624599i	$0.214738\pi$
$521$			650.832i			1.24920i	−0.780945	+	0.624599i	$0.785262\pi$
$522$	−301.300			−0.577204
$523$		−	705.142i		−	1.34826i	−0.738611	−	0.674132i	$-0.764518\pi$
$523$		−	705.142i		−	1.34826i	0.738611	−	0.674132i	$-0.235482\pi$
$524$		−	32.2289i		−	0.0615056i
$525$	234.528	+	205.121i	0.446720	+	0.390707i
$526$	344.391			0.654736
$527$	295.565			0.560844
$528$		−	10.2290i		−	0.0193732i
$529$	23.0000			0.0434783
$530$		−	303.149i		−	0.571979i
$531$		−	1136.59i		−	2.14048i
$532$	5.56593	+	4.86803i	0.0104623	+	0.00915043i
$533$	−298.525			−0.560085
$534$	−941.487			−1.76308
$535$		−	1255.87i		−	2.34741i
$536$	−123.700			−0.230783
$537$		−	980.395i		−	1.82569i
$538$			17.1676i			0.0319100i
$539$	−3.68763	−	27.4427i	−0.00684161	−	0.0509141i
$540$	132.449			0.245276
$541$	50.7402			0.0937897			0.0468948	−	0.998900i	$-0.485067\pi$
$541$	50.7402			0.0937897			0.0468948	+	0.998900i	$0.485067\pi$
$542$			293.219i			0.540995i
$543$	−374.354			−0.689418
$544$			119.548i			0.219757i
$545$			1134.56i			2.08177i
$546$	394.624	−	451.199i	0.722755	−	0.826372i
$547$	−2.84213			−0.00519586			−0.00259793	−	0.999997i	$-0.500827\pi$
$547$	−2.84213			−0.00519586			−0.00259793	+	0.999997i	$0.500827\pi$
$548$	−521.497			−0.951638
$549$		−	111.681i		−	0.203426i
$550$	−7.86023			−0.0142913
$551$			9.80258i			0.0177905i
$552$		−	61.3858i		−	0.111206i
$553$	557.414	−	637.327i	1.00798	−	1.15249i
$554$	−685.003			−1.23647
$555$	369.170			0.665171
$556$			467.057i			0.840031i
$557$	−322.717			−0.579384			−0.289692	−	0.957120i	$-0.593553\pi$
$557$	−322.717			−0.579384			−0.289692	+	0.957120i	$0.593553\pi$
$558$			227.049i			0.406898i
$559$		−	493.567i		−	0.882946i
$560$	−124.395	−	108.798i	−0.222135	−	0.194282i
$561$	54.0434			0.0963340
$562$	−150.463			−0.267728
$563$		−	715.794i		−	1.27139i	−0.771939	−	0.635697i	$-0.780713\pi$
$563$		−	715.794i		−	1.27139i	0.771939	−	0.635697i	$-0.219287\pi$
$564$	−596.151			−1.05700
$565$		−	526.283i		−	0.931474i
$566$		−	175.828i		−	0.310649i
$567$	−242.114	+	276.824i	−0.427009	+	0.488226i
$568$	233.436			0.410979
$569$	−1008.72			−1.77279			−0.886393	−	0.462933i	$-0.846797\pi$
$569$	−1008.72			−1.77279			−0.886393	+	0.462933i	$0.846797\pi$
$570$		−	19.9508i		−	0.0350015i
$571$	492.252			0.862088			0.431044	−	0.902331i	$-0.358145\pi$
$571$	492.252			0.862088			0.431044	+	0.902331i	$0.358145\pi$
$572$			15.1220i			0.0264370i
$573$			621.929i			1.08539i
$574$	166.252	+	145.406i	0.289637	+	0.253320i
$575$	−47.1702			−0.0820351
$576$	−91.8353			−0.159436
$577$		−	621.807i		−	1.07765i	−0.842416	−	0.538827i	$-0.818867\pi$
$577$		−	621.807i		−	1.07765i	0.842416	−	0.538827i	$-0.181133\pi$
$578$	−222.904			−0.385646
$579$		−	1193.14i		−	2.06069i
$580$		−	219.082i		−	0.377728i
$581$	−16.6935	−	14.6003i	−0.0287323	−	0.0251296i
$582$	−251.671			−0.432425
$583$	20.5232			0.0352027
$584$			28.8875i			0.0494649i
$585$	−906.554			−1.54967
$586$			744.131i			1.26985i
$587$		−	510.624i		−	0.869887i	−0.900458	−	0.434944i	$-0.856768\pi$
$587$		−	510.624i		−	0.869887i	0.900458	−	0.434944i	$-0.143232\pi$
$588$	−439.540	+	59.0636i	−0.747518	+	0.100448i
$589$	7.38688			0.0125414
$590$	826.443			1.40075
$591$			1005.73i			1.70175i
$592$	−55.2860			−0.0933886
$593$		−	392.534i		−	0.661946i	−0.943640	−	0.330973i	$-0.892623\pi$
$593$		−	392.534i		−	0.661946i	0.943640	−	0.330973i	$-0.107377\pi$
$594$			8.96683i			0.0150957i
$595$	574.814	−	657.221i	0.966074	−	1.10457i
$596$	−107.566			−0.180479
$597$	−266.628			−0.446614
$598$			90.7488i			0.151754i
$599$	87.3551			0.145835			0.0729175	−	0.997338i	$-0.476769\pi$
$599$	87.3551			0.145835			0.0729175	+	0.997338i	$0.476769\pi$
$600$			125.895i			0.209825i
$601$		−	277.245i		−	0.461305i	−0.973036	−	0.230653i	$-0.925914\pi$
$601$		−	277.245i		−	0.461305i	0.973036	−	0.230653i	$-0.0740861\pi$
$602$	−240.407	+	274.872i	−0.399347	+	0.456599i
$603$	502.046			0.832580
$604$	23.2518			0.0384963
$605$			712.278i			1.17732i
$606$	1270.19			2.09602
$607$		−	251.624i		−	0.414536i	−0.978284	−	0.207268i	$-0.933543\pi$
$607$		−	251.624i		−	0.414536i	0.978284	−	0.207268i	$-0.0664573\pi$
$608$			2.98779i			0.00491413i
$609$	−442.544	−	387.054i	−0.726673	−	0.635557i
$610$	81.2057			0.133124
$611$	881.312			1.44241
$612$		−	485.196i		−	0.792804i
$613$	299.119			0.487960			0.243980	−	0.969780i	$-0.421547\pi$
$613$	299.119			0.487960			0.243980	+	0.969780i	$0.421547\pi$
$614$			710.656i			1.15742i
$615$		−	595.922i		−	0.968979i
$616$	7.36562	−	8.42158i	0.0119572	−	0.0136714i
$617$	−70.9878			−0.115053			−0.0575266	−	0.998344i	$-0.518321\pi$
$617$	−70.9878			−0.115053			−0.0575266	+	0.998344i	$0.518321\pi$
$618$	250.202			0.404857
$619$		−	788.506i		−	1.27384i	−0.770930	−	0.636920i	$-0.780208\pi$
$619$		−	788.506i		−	1.27384i	0.770930	−	0.636920i	$-0.219792\pi$
$620$	−165.093			−0.266278
$621$			53.8110i			0.0866522i
$622$			475.845i			0.765024i
$623$	−775.127	−	677.935i	−1.24418	−	1.08818i
$624$	242.204			0.388147
$625$	−774.151			−1.23864
$626$		−	690.847i		−	1.10359i
$627$	1.35067			0.00215418
$628$		−	32.4678i		−	0.0517003i
$629$		−	292.094i		−	0.464379i
$630$	504.869	+	441.565i	0.801380	+	0.700897i
$631$	47.3975			0.0751148			0.0375574	−	0.999294i	$-0.488042\pi$
$631$	47.3975			0.0751148			0.0375574	+	0.999294i	$0.488042\pi$
$632$	342.117			0.541325
$633$			1461.65i			2.30908i
$634$	432.853			0.682733
$635$			385.026i			0.606340i
$636$		−	328.713i		−	0.516845i
$637$	649.789	−	87.3158i	1.02008	−	0.137073i
$638$	14.8319			0.0232475
$639$	−947.420			−1.48266
$640$		−	66.7755i		−	0.104337i
$641$	−798.674			−1.24598			−0.622991	−	0.782229i	$-0.714083\pi$
$641$	−798.674			−1.24598			−0.622991	+	0.782229i	$0.714083\pi$
$642$		−	1361.77i		−	2.12114i
$643$			454.236i			0.706433i	0.935542	+	0.353217i	$0.114912\pi$
$643$			454.236i			0.706433i	−0.935542	+	0.353217i	$0.885088\pi$
$644$	44.2020	−	50.5389i	0.0686366	−	0.0784766i
$645$	985.269			1.52755
$646$	−15.7855			−0.0244357
$647$		−	1118.96i		−	1.72947i	−0.502232	−	0.864733i	$-0.667488\pi$
$647$		−	1118.96i		−	1.72947i	0.502232	−	0.864733i	$-0.332512\pi$
$648$	−148.599			−0.229320
$649$			55.9503i			0.0862100i
$650$		−	186.115i		−	0.286330i
$651$	−291.670	+	333.485i	−0.448034	+	0.512266i
$652$	227.535			0.348979
$653$	112.638			0.172493			0.0862465	−	0.996274i	$-0.472513\pi$
$653$	112.638			0.172493			0.0862465	+	0.996274i	$0.472513\pi$
$654$			1230.24i			1.88110i
$655$	−95.1104			−0.145207
$656$			89.2439i			0.136043i
$657$		−	117.242i		−	0.178451i
$658$	−490.811	−	429.270i	−0.745914	−	0.652386i
$659$	262.518			0.398358			0.199179	−	0.979963i	$-0.436172\pi$
$659$	262.518			0.398358			0.199179	+	0.979963i	$0.436172\pi$
$660$	−30.1868			−0.0457376
$661$		−	216.363i		−	0.327326i	−0.986516	−	0.163663i	$-0.947669\pi$
$661$		−	216.363i		−	0.327326i	0.986516	−	0.163663i	$-0.0523310\pi$
$662$	−840.522			−1.26967
$663$			1279.64i			1.93008i
$664$		−	8.96106i		−	0.0134956i
$665$	14.3660	−	16.4255i	0.0216030	−	0.0247001i
$666$	224.383			0.336912
$667$	89.0080			0.133445
$668$		−	1.39969i		−	0.00209534i
$669$	−1213.61			−1.81406
$670$			365.049i			0.544849i
$671$			5.49763i			0.00819319i
$672$	−134.886	−	117.973i	−0.200723	−	0.175555i
$673$	−216.954			−0.322368			−0.161184	−	0.986924i	$-0.551531\pi$
$673$	−216.954			−0.322368			−0.161184	+	0.986924i	$0.551531\pi$
$674$	−13.4168			−0.0199063
$675$		−	110.360i		−	0.163496i
$676$	−20.0586			−0.0296725
$677$		−	163.962i		−	0.242189i	−0.992641	−	0.121094i	$-0.961360\pi$
$677$		−	163.962i		−	0.242189i	0.992641	−	0.121094i	$-0.0386404\pi$
$678$		−	570.664i		−	0.841688i
$679$	−207.201	−	181.221i	−0.305156	−	0.266894i
$680$	352.797			0.518819
$681$	−307.449			−0.451466
$682$		−	11.1768i		−	0.0163882i
$683$	−267.489			−0.391639			−0.195819	−	0.980640i	$-0.562737\pi$
$683$	−267.489			−0.391639			−0.195819	+	0.980640i	$0.562737\pi$
$684$		−	12.1262i		−	0.0177284i
$685$			1538.98i			2.24669i
$686$	−404.404	−	267.872i	−0.589510	−	0.390484i
$687$	−920.986			−1.34059
$688$	−147.552			−0.214465
$689$			485.949i			0.705296i
$690$	−181.155			−0.262543
$691$		−	8.19050i		−	0.0118531i	−0.999982	−	0.00592656i	$-0.998114\pi$
$691$		−	8.19050i		−	0.0118531i	0.999982	−	0.00592656i	$-0.00188649\pi$
$692$			356.883i			0.515726i
$693$	−29.8940	+	34.1797i	−0.0431371	+	0.0493214i
$694$	485.404			0.699430
$695$	1378.33			1.98320
$696$		−	237.558i		−	0.341318i
$697$	−471.505			−0.676478
$698$			938.593i			1.34469i
$699$		−	806.381i		−	1.15362i
$700$	−90.6529	+	103.649i	−0.129504	+	0.148070i
$701$	87.2198			0.124422			0.0622110	−	0.998063i	$-0.480185\pi$
$701$	87.2198			0.124422			0.0622110	+	0.998063i	$0.480185\pi$
$702$	−212.317			−0.302446
$703$		−	7.30013i		−	0.0103843i
$704$	4.52071			0.00642146
$705$			1759.29i			2.49545i
$706$			451.699i			0.639801i
$707$	1045.74	+	914.621i	1.47913	+	1.29367i
$708$	896.137			1.26573
$709$	−297.848			−0.420096			−0.210048	−	0.977691i	$-0.567362\pi$
$709$	−297.848			−0.420096			−0.210048	+	0.977691i	$0.567362\pi$
$710$		−	688.890i		−	0.970268i
$711$	−1388.51			−1.95290
$712$		−	416.088i		−	0.584394i
$713$		−	67.0733i		−	0.0940719i
$714$	623.288	−	712.645i	0.872953	−	0.998103i
$715$	44.6263			0.0624144
$716$	433.284			0.605145
$717$			694.355i			0.968417i
$718$	852.287			1.18703
$719$		−	217.264i		−	0.302175i	−0.988520	−	0.151088i	$-0.951722\pi$
$719$		−	217.264i		−	0.302175i	0.988520	−	0.151088i	$-0.0482776\pi$
$720$			271.014i			0.376408i
$721$	205.991	+	180.162i	0.285702	+	0.249878i
$722$	510.137			0.706560
$723$	−749.844			−1.03713
$724$		−	165.445i		−	0.228515i
$725$	−182.545			−0.251786
$726$			772.345i			1.06384i
$727$			192.244i			0.264434i	0.991221	+	0.132217i	$0.0422096\pi$
$727$			192.244i			0.264434i	−0.991221	+	0.132217i	$0.957790\pi$
$728$	199.406	+	174.403i	0.273910	+	0.239565i
$729$	1060.10			1.45418
$730$	85.2496			0.116780
$731$		−	779.563i		−	1.06643i
$732$	88.0538			0.120292
$733$			761.669i			1.03911i	0.854437	+	0.519556i	$0.173903\pi$
$733$			761.669i			1.03911i	−0.854437	+	0.519556i	$0.826097\pi$
$734$			250.392i			0.341134i
$735$	174.302	+	1297.12i	0.237145	+	1.76479i
$736$	27.1293			0.0368605
$737$	−24.7138			−0.0335330
$738$		−	362.204i		−	0.490792i
$739$	145.360			0.196698			0.0983491	−	0.995152i	$-0.468644\pi$
$739$	145.360			0.196698			0.0983491	+	0.995152i	$0.468644\pi$
$740$			163.154i			0.220478i
$741$			31.9813i			0.0431596i
$742$	236.696	−	270.630i	0.318998	−	0.364730i
$743$	−922.603			−1.24173			−0.620864	−	0.783919i	$-0.713218\pi$
$743$	−922.603			−1.24173			−0.620864	+	0.783919i	$0.713218\pi$
$744$	−179.015			−0.240611
$745$			317.436i			0.426088i
$746$	679.601			0.910993
$747$			36.3692i			0.0486871i
$748$			23.8844i			0.0319310i
$749$	980.571	−	1121.15i	1.30917	−	1.49686i
$750$	−572.808			−0.763744
$751$	327.925			0.436652			0.218326	−	0.975876i	$-0.429940\pi$
$751$	327.925			0.436652			0.218326	+	0.975876i	$0.429940\pi$
$752$		−	263.468i		−	0.350356i
$753$	267.051			0.354649
$754$			351.190i			0.465769i
$755$		−	68.6180i		−	0.0908847i
$756$	118.241	+	103.415i	0.156404	+	0.136793i
$757$	1208.33			1.59620			0.798102	−	0.602523i	$-0.205838\pi$
$757$	1208.33			1.59620			0.798102	+	0.602523i	$0.205838\pi$
$758$	−759.567			−1.00207
$759$		−	12.2642i		−	0.0161584i
$760$	8.81723			0.0116016
$761$		−	30.4800i		−	0.0400526i	−0.999799	−	0.0200263i	$-0.993625\pi$
$761$		−	30.4800i		−	0.0400526i	0.999799	−	0.0200263i	$-0.00637499\pi$
$762$			417.496i			0.547894i
$763$	−885.859	+	1012.86i	−1.16102	+	1.32747i
$764$	−274.860			−0.359765
$765$	−1431.86			−1.87171
$766$			865.441i			1.12982i
$767$	−1324.79			−1.72724
$768$		−	72.4067i		−	0.0942796i
$769$			909.204i			1.18232i	0.806554	+	0.591160i	$0.201330\pi$
$769$			909.204i			1.18232i	−0.806554	+	0.591160i	$0.798670\pi$
$770$	−24.8528	−	21.7366i	−0.0322764	−	0.0282293i
$771$	770.348			0.999154
$772$	527.305			0.683037
$773$		−	272.377i		−	0.352364i	−0.984358	−	0.176182i	$-0.943625\pi$
$773$		−	272.377i		−	0.352364i	0.984358	−	0.176182i	$-0.0563747\pi$
$774$	598.851			0.773709
$775$			137.559i			0.177496i
$776$		−	111.226i		−	0.143332i
$777$	329.569	+	288.245i	0.424156	+	0.370972i
$778$	190.470			0.244820
$779$	−11.7840			−0.0151271
$780$		−	714.764i		−	0.916365i
$781$	46.6379			0.0597157
$782$			143.333i			0.183290i
$783$			208.244i			0.265957i
$784$	−26.1030	−	194.254i	−0.0332947	−	0.247773i
$785$	−95.8153			−0.122058
$786$	−103.131			−0.131210
$787$		−	1348.95i		−	1.71404i	−0.515287	−	0.857018i	$-0.672314\pi$
$787$		−	1348.95i		−	1.71404i	0.515287	−	0.857018i	$-0.327686\pi$
$788$	−444.482			−0.564064
$789$		−	1102.04i		−	1.39675i
$790$		−	1009.62i		−	1.27800i
$791$	410.918	−	469.828i	0.519491	−	0.593967i
$792$	−18.3477			−0.0231663
$793$	−130.173			−0.164153
$794$		−	167.869i		−	0.211422i
$795$	−970.062			−1.22020
$796$		−	117.836i		−	0.148035i
$797$		−	962.121i		−	1.20718i	−0.797296	−	0.603589i	$-0.793737\pi$
$797$		−	962.121i		−	1.20718i	0.797296	−	0.603589i	$-0.206263\pi$
$798$	15.5775	−	17.8107i	0.0195206	−	0.0223192i
$799$	1391.99			1.74216
$800$	−55.6389			−0.0695487
$801$			1688.73i			2.10828i
$802$	933.474			1.16393
$803$			5.77140i			0.00718730i
$804$			395.833i			0.492330i
$805$	−149.145	−	130.444i	−0.185273	−	0.162042i
$806$	264.644			0.328343
$807$	54.9355			0.0680737
$808$			561.356i			0.694748i
$809$	866.938			1.07162			0.535808	−	0.844340i	$-0.320007\pi$
$809$	866.938			1.07162			0.535808	+	0.844340i	$0.320007\pi$
$810$			438.530i			0.541395i
$811$		−	731.198i		−	0.901600i	−0.892625	−	0.450800i	$-0.851139\pi$
$811$		−	731.198i		−	0.901600i	0.892625	−	0.450800i	$-0.148861\pi$
$812$	171.058	−	195.581i	0.210662	−	0.240864i
$813$	938.288			1.15411
$814$	−11.0455			−0.0135695
$815$		−	671.474i		−	0.823895i
$816$	382.548			0.468809
$817$		−	19.4832i		−	0.0238472i
$818$			334.427i			0.408835i
$819$	−809.308	−	707.831i	−0.988166	−	0.864262i
$820$	263.367			0.321179
$821$	−808.173			−0.984376			−0.492188	−	0.870489i	$-0.663803\pi$
$821$	−808.173			−0.984376			−0.492188	+	0.870489i	$0.663803\pi$
$822$			1668.77i			2.03013i
$823$	360.613			0.438169			0.219084	−	0.975706i	$-0.429693\pi$
$823$	360.613			0.438169			0.219084	+	0.975706i	$0.429693\pi$
$824$			110.576i			0.134194i
$825$			25.1524i			0.0304877i
$826$	737.791	+	645.281i	0.893209	+	0.781212i
$827$	−728.430			−0.880810			−0.440405	−	0.897799i	$-0.645165\pi$
$827$	−728.430			−0.880810			−0.440405	+	0.897799i	$0.645165\pi$
$828$	−110.107			−0.132979
$829$		−	969.401i		−	1.16936i	−0.811263	−	0.584681i	$-0.801220\pi$
$829$		−	969.401i		−	1.16936i	0.811263	−	0.584681i	$-0.198780\pi$
$830$	−26.4449			−0.0318613
$831$			2191.98i			2.63776i
$832$			107.041i			0.128656i
$833$	1026.31	−	137.911i	1.23206	−	0.165559i
$834$	1494.56			1.79204
$835$	−4.13060			−0.00494683
$836$			0.596928i			0.000714028i
$837$	156.925			0.187485
$838$			84.2586i			0.100547i
$839$			562.743i			0.670731i	0.942088	+	0.335366i	$0.108860\pi$
$839$			562.743i			0.670731i	−0.942088	+	0.335366i	$0.891140\pi$
$840$	−348.148	+	398.060i	−0.414462	+	0.473880i
$841$	−496.547			−0.590424
$842$	−898.829			−1.06749
$843$			481.475i			0.571144i
$844$	−645.972			−0.765370
$845$			59.1947i			0.0700529i
$846$			1069.31i			1.26396i
$847$	−556.142	+	635.872i	−0.656602	+	0.750735i
$848$	145.274			0.171314
$849$	−562.640			−0.662709
$850$		−	293.959i		−	0.345834i
$851$	−66.2856			−0.0778915
$852$		−	746.984i		−	0.876742i
$853$			1530.54i			1.79430i	0.441725	+	0.897151i	$0.354367\pi$
$853$			1530.54i			1.79430i	−0.441725	+	0.897151i	$0.645633\pi$
$854$	72.4948	+	63.4048i	0.0848885	+	0.0742445i
$855$	−35.7855			−0.0418544
$856$	601.833			0.703076
$857$		−	414.479i		−	0.483640i	−0.970321	−	0.241820i	$-0.922256\pi$
$857$		−	414.479i		−	0.483640i	0.970321	−	0.241820i	$-0.0777443\pi$
$858$	48.3896			0.0563982
$859$		−	1034.92i		−	1.20479i	−0.798198	−	0.602396i	$-0.794213\pi$
$859$		−	1034.92i		−	1.20479i	0.798198	−	0.602396i	$-0.205787\pi$
$860$			435.438i			0.506323i
$861$	465.292	−	531.998i	0.540409	−	0.617884i
$862$	−48.8467			−0.0566667
$863$	596.009			0.690624			0.345312	−	0.938488i	$-0.387773\pi$
$863$	596.009			0.690624			0.345312	+	0.938488i	$0.387773\pi$
$864$			63.4720i			0.0734630i
$865$	1053.19			1.21756
$866$		−	420.882i		−	0.486007i
$867$			713.281i			0.822700i
$868$	−147.383	−	128.903i	−0.169796	−	0.148506i
$869$	68.3512			0.0786550
$870$	−701.053			−0.805808
$871$		−	585.175i		−	0.671843i
$872$	−543.703			−0.623513
$873$			451.419i			0.517089i
$874$			3.58224i			0.00409867i
$875$	−471.593	−	412.461i	−0.538964	−	0.471384i
$876$	92.4387			0.105524
$877$	165.386			0.188581			0.0942906	−	0.995545i	$-0.469942\pi$
$877$	165.386			0.188581			0.0942906	+	0.995545i	$0.469942\pi$
$878$		−	286.205i		−	0.325974i
$879$	2381.18			2.70897
$880$		−	13.3410i		−	0.0151602i
$881$		−	1028.56i		−	1.16749i	−0.811938	−	0.583744i	$-0.801587\pi$
$881$		−	1028.56i		−	1.16749i	0.811938	−	0.583744i	$-0.198413\pi$
$882$	105.941	+	788.397i	0.120115	+	0.893874i
$883$	−237.756			−0.269260			−0.134630	−	0.990896i	$-0.542985\pi$
$883$	−237.756			−0.269260			−0.134630	+	0.990896i	$0.542985\pi$
$884$	−565.535			−0.639745
$885$		−	2644.58i		−	2.98823i
$886$	−933.658			−1.05379
$887$		−	517.823i		−	0.583791i	−0.956450	−	0.291896i	$-0.905714\pi$
$887$		−	517.823i		−	0.583791i	0.956450	−	0.291896i	$-0.0942860\pi$
$888$			176.913i			0.199226i
$889$	−300.626	+	343.724i	−0.338162	+	0.386642i
$890$	−1227.91			−1.37968
$891$	−29.6885			−0.0333204
$892$		−	536.351i		−	0.601290i
$893$	34.7891			0.0389575
$894$			344.205i			0.385017i
$895$		−	1278.66i		−	1.42867i
$896$	52.1378	−	59.6125i	0.0581895	−	0.0665318i
$897$	290.392			0.323737
$898$	−791.527			−0.881434
$899$		−	259.568i		−	0.288729i
$900$	225.815			0.250906
$901$			767.531i			0.851866i
$902$			17.8300i			0.0197671i
$903$	879.579	+	769.291i	0.974063	+	0.851928i
$904$	252.204			0.278987
$905$	−488.243			−0.539495
$906$		−	74.4046i		−	0.0821242i
$907$	−19.4359			−0.0214287			−0.0107144	−	0.999943i	$-0.503411\pi$
$907$	−19.4359			−0.0214287			−0.0107144	+	0.999943i	$0.503411\pi$
$908$		−	135.876i		−	0.149643i
$909$		−	2278.31i		−	2.50639i
$910$	514.680	−	588.466i	0.565582	−	0.646666i
$911$	−993.058			−1.09007			−0.545037	−	0.838412i	$-0.683485\pi$
$911$	−993.058			−1.09007			−0.545037	+	0.838412i	$0.683485\pi$
$912$	9.56079			0.0104833
$913$		−	1.79032i		−	0.00196092i
$914$	−1052.54			−1.15157
$915$		−	259.854i		−	0.283994i
$916$		−	407.028i		−	0.444353i
$917$	−84.9079	−	74.2615i	−0.0925931	−	0.0809831i
$918$	−335.344			−0.365298
$919$	−746.942			−0.812777			−0.406389	−	0.913700i	$-0.633212\pi$
$919$	−746.942			−0.812777			−0.406389	+	0.913700i	$0.633212\pi$
$920$		−	80.0610i		−	0.0870228i
$921$	2274.07			2.46913
$922$			835.732i			0.906434i
$923$			1104.29i			1.19642i
$924$	−26.9487	−	23.5696i	−0.0291652	−	0.0255083i
$925$	135.944			0.146966
$926$	798.593			0.862412
$927$		−	448.783i		−	0.484124i
$928$	104.988			0.113134
$929$		−	1232.17i		−	1.32634i	−0.748470	−	0.663169i	$-0.769211\pi$
$929$		−	1232.17i		−	1.32634i	0.748470	−	0.663169i	$-0.230789\pi$
$930$			528.289i			0.568052i
$931$	25.6499	−	3.44672i	0.0275509	−	0.00370217i
$932$	356.378			0.382380
$933$	1522.68			1.63203
$934$		−	1050.71i		−	1.12496i
$935$	70.4849			0.0753849
$936$		−	434.437i		−	0.464142i
$937$			192.970i			0.205945i	0.994684	+	0.102972i	$0.0328353\pi$
$937$			192.970i			0.205945i	−0.994684	+	0.102972i	$0.967165\pi$
$938$	−285.027	+	325.890i	−0.303867	+	0.347431i
$939$	−2210.68			−2.35429
$940$	−777.516			−0.827145
$941$		−	1230.83i		−	1.30800i	−0.756494	−	0.654000i	$-0.773089\pi$
$941$		−	1230.83i		−	1.30800i	0.756494	−	0.654000i	$-0.226911\pi$
$942$	−103.895			−0.110292
$943$			107.000i			0.113467i
$944$			396.046i			0.419540i
$945$	305.188	−	348.941i	0.322950	−	0.369250i
$946$	−29.4792			−0.0311619
$947$	1795.76			1.89626			0.948130	−	0.317884i	$-0.102972\pi$
$947$	1795.76			1.89626			0.948130	+	0.317884i	$0.102972\pi$
$948$		−	1094.76i		−	1.15481i
$949$	−136.655			−0.143999
$950$		−	7.34673i		−	0.00773340i
$951$		−	1385.11i		−	1.45648i
$952$	314.952	+	275.461i	0.330832	+	0.289350i
$953$	1089.89			1.14364			0.571821	−	0.820378i	$-0.306237\pi$
$953$	1089.89			1.14364			0.571821	+	0.820378i	$0.306237\pi$
$954$	−589.608			−0.618038
$955$			811.136i			0.849357i
$956$	−306.869			−0.320993
$957$		−	47.4614i		−	0.0495939i
$958$			450.161i			0.469897i
$959$	−1201.63	+	1373.90i	−1.25300	+	1.43264i
$960$	−213.678			−0.222582
$961$	765.399			0.796461
$962$		−	261.537i		−	0.271868i
$963$	−2442.59			−2.53644
$964$		−	331.392i		−	0.343768i
$965$		−	1556.12i		−	1.61256i
$966$	−161.722	−	141.444i	−0.167414	−	0.146423i
$967$	1370.99			1.41777			0.708887	−	0.705322i	$-0.249198\pi$
$967$	1370.99			1.41777			0.708887	+	0.705322i	$0.249198\pi$
$968$	−341.336			−0.352620
$969$			50.5128i			0.0521288i
$970$	−328.237			−0.338388
$971$		−	1394.36i		−	1.43600i	−0.696041	−	0.718002i	$-0.745057\pi$
$971$		−	1394.36i		−	1.43600i	0.696041	−	0.718002i	$-0.254943\pi$
$972$			677.478i			0.696994i
$973$	1230.47	+	1076.19i	1.26462	+	1.10605i
$974$	−426.546			−0.437933
$975$	−595.559			−0.610830
$976$			38.9152i			0.0398721i
$977$	−847.241			−0.867186			−0.433593	−	0.901109i	$-0.642754\pi$
$977$	−847.241			−0.867186			−0.433593	+	0.901109i	$0.642754\pi$
$978$		−	728.100i		−	0.744479i
$979$		−	83.1298i		−	0.0849130i
$980$	−573.261	+	77.0323i	−0.584960	+	0.0786044i
$981$	2206.67			2.24940
$982$	1070.53			1.09015
$983$			956.388i			0.972927i	0.873701	+	0.486464i	$0.161713\pi$
$983$			956.388i			0.972927i	−0.873701	+	0.486464i	$0.838287\pi$
$984$	285.577			0.290220
$985$			1311.71i			1.33168i
$986$			554.686i			0.562562i
$987$	−1373.64	+	1570.57i	−1.39174	+	1.59126i
$988$	−14.1341			−0.0143057
$989$	−176.908			−0.178876
$990$			54.1456i			0.0546925i
$991$	−354.719			−0.357941			−0.178970	−	0.983854i	$-0.557277\pi$
$991$	−354.719			−0.357941			−0.178970	+	0.983854i	$0.557277\pi$
$992$		−	79.1153i		−	0.0797533i
$993$			2689.63i			2.70859i
$994$	537.880	−	614.993i	0.541127	−	0.618705i
$995$	−347.744			−0.349491
$996$	−28.6750			−0.0287901
$997$			764.770i			0.767071i	0.923526	+	0.383536i	$0.125294\pi$
$997$			764.770i			0.767071i	−0.923526	+	0.383536i	$0.874706\pi$
$998$	−1011.64			−1.01367
$999$		−	155.083i		−	0.155238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.3.b.a.139.19	✓	32
7.6	odd	2	inner	322.3.b.a.139.30	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.3.b.a.139.19	✓	32	1.1	even	1	trivial
322.3.b.a.139.30	yes	32	7.6	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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	322.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} -4.52542i q^{3} +2.00000 q^{4} -5.90217i q^{5} -6.39991i q^{6} +(4.60838 - 5.26905i) q^{7} +2.82843 q^{8} -11.4794 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} -4.52542i q^{3} +2.00000 q^{4} -5.90217i q^{5} -6.39991i q^{6} +(4.60838 - 5.26905i) q^{7} +2.82843 q^{8} -11.4794 q^{9} -8.34694i q^{10} +0.565088 q^{11} -9.05084i q^{12} +13.3802i q^{13} +(6.51723 - 7.45156i) q^{14} -26.7098 q^{15} +4.00000 q^{16} +21.1333i q^{17} -16.2343 q^{18} +0.528172i q^{19} -11.8043i q^{20} +(-23.8447 - 20.8548i) q^{21} +0.799156 q^{22} +4.79583 q^{23} -12.7998i q^{24} -9.83567 q^{25} +18.9224i q^{26} +11.2204i q^{27} +(9.21675 - 10.5381i) q^{28} +18.5594 q^{29} -37.7734 q^{30} -13.9857i q^{31} +5.65685 q^{32} -2.55726i q^{33} +29.8870i q^{34} +(-31.0988 - 27.1994i) q^{35} -22.9588 q^{36} -13.8215 q^{37} +0.746948i q^{38} +60.5509 q^{39} -16.6939i q^{40} +22.3110i q^{41} +(-33.7214 - 29.4932i) q^{42} -36.8879 q^{43} +1.13018 q^{44} +67.7535i q^{45} +6.78233 q^{46} -65.8669i q^{47} -18.1017i q^{48} +(-6.52576 - 48.5635i) q^{49} -13.9097 q^{50} +95.6371 q^{51} +26.7604i q^{52} +36.3186 q^{53} +15.8680i q^{54} -3.33525i q^{55} +(13.0345 - 14.9031i) q^{56} +2.39020 q^{57} +26.2470 q^{58} +99.0116i q^{59} -53.4196 q^{60} +9.72880i q^{61} -19.7788i q^{62} +(-52.9014 + 60.4856i) q^{63} +8.00000 q^{64} +78.9722 q^{65} -3.61651i q^{66} -43.7345 q^{67} +42.2666i q^{68} -21.7031i q^{69} +(-43.9804 - 38.4658i) q^{70} +82.5321 q^{71} -32.4687 q^{72} +10.2133i q^{73} -19.5466 q^{74} +44.5105i q^{75} +1.05634i q^{76} +(2.60414 - 2.97748i) q^{77} +85.6319 q^{78} +120.957 q^{79} -23.6087i q^{80} -52.5378 q^{81} +31.5525i q^{82} -3.16821i q^{83} +(-47.6893 - 41.7097i) q^{84} +124.732 q^{85} -52.1674 q^{86} -83.9893i q^{87} +1.59831 q^{88} -147.109i q^{89} +95.8179i q^{90} +(70.5008 + 61.6609i) q^{91} +9.59166 q^{92} -63.2913 q^{93} -93.1499i q^{94} +3.11736 q^{95} -25.5996i q^{96} -39.3242i q^{97} +(-9.22881 - 68.6792i) q^{98} -6.48688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} - 12 q^{7} - 128 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 - 12 * q^7 - 128 * q^9	\( 32 q + 64 q^{4} - 12 q^{7} - 128 q^{9} + 24 q^{11} - 8 q^{14} + 16 q^{15} + 128 q^{16} + 84 q^{21} + 16 q^{22} - 224 q^{25} - 24 q^{28} + 96 q^{30} + 32 q^{35} - 256 q^{36} - 128 q^{39} - 80 q^{42} + 144 q^{43} + 48 q^{44} + 40 q^{49} - 224 q^{50} - 200 q^{51} + 232 q^{53} - 16 q^{56} - 200 q^{57} + 224 q^{58} + 32 q^{60} - 168 q^{63} + 256 q^{64} - 144 q^{67} - 208 q^{70} + 224 q^{71} + 160 q^{74} + 240 q^{77} + 128 q^{78} - 232 q^{79} + 560 q^{81} + 168 q^{84} + 416 q^{85} + 96 q^{86} + 32 q^{88} - 316 q^{91} - 496 q^{93} + 64 q^{95} + 144 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 - 12 * q^7 - 128 * q^9 + 24 * q^11 - 8 * q^14 + 16 * q^15 + 128 * q^16 + 84 * q^21 + 16 * q^22 - 224 * q^25 - 24 * q^28 + 96 * q^30 + 32 * q^35 - 256 * q^36 - 128 * q^39 - 80 * q^42 + 144 * q^43 + 48 * q^44 + 40 * q^49 - 224 * q^50 - 200 * q^51 + 232 * q^53 - 16 * q^56 - 200 * q^57 + 224 * q^58 + 32 * q^60 - 168 * q^63 + 256 * q^64 - 144 * q^67 - 208 * q^70 + 224 * q^71 + 160 * q^74 + 240 * q^77 + 128 * q^78 - 232 * q^79 + 560 * q^81 + 168 * q^84 + 416 * q^85 + 96 * q^86 + 32 * q^88 - 316 * q^91 - 496 * q^93 + 64 * q^95 + 144 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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