LMFDB - Embedded newform 690.3.b.a.599.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(599,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("690.599");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.18
Character	$\chi$	$=$	690.599
Dual form			690.3.b.a.599.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-1.23483 + 2.73408i) q^{3} +2.00000 q^{4} +(4.77075 + 1.49664i) q^{5} +(1.74631 - 3.86657i) q^{6} -2.54772i q^{7} -2.82843 q^{8} +(-5.95040 - 6.75224i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-1.23483 + 2.73408i) q^{3} +2.00000 q^{4} +(4.77075 + 1.49664i) q^{5} +(1.74631 - 3.86657i) q^{6} -2.54772i q^{7} -2.82843 q^{8} +(-5.95040 - 6.75224i) q^{9} +(-6.74686 - 2.11656i) q^{10} +15.8694i q^{11} +(-2.46966 + 5.46816i) q^{12} -23.6018i q^{13} +3.60302i q^{14} +(-9.98298 + 11.1955i) q^{15} +4.00000 q^{16} +32.3944 q^{17} +(8.41514 + 9.54911i) q^{18} +2.70349 q^{19} +(9.54151 + 2.99327i) q^{20} +(6.96567 + 3.14599i) q^{21} -22.4428i q^{22} -4.79583 q^{23} +(3.49262 - 7.73315i) q^{24} +(20.5202 + 14.2802i) q^{25} +33.3780i q^{26} +(25.8089 - 7.93103i) q^{27} -5.09544i q^{28} +13.8764i q^{29} +(14.1181 - 15.8329i) q^{30} +16.4061 q^{31} -5.65685 q^{32} +(-43.3883 - 19.5960i) q^{33} -45.8126 q^{34} +(3.81301 - 12.1545i) q^{35} +(-11.9008 - 13.5045i) q^{36} -8.63454i q^{37} -3.82331 q^{38} +(64.5293 + 29.1442i) q^{39} +(-13.4937 - 4.23313i) q^{40} -59.3900i q^{41} +(-9.85095 - 4.44911i) q^{42} -51.2988i q^{43} +31.7389i q^{44} +(-18.2822 - 41.1188i) q^{45} +6.78233 q^{46} -38.9126 q^{47} +(-4.93931 + 10.9363i) q^{48} +42.5091 q^{49} +(-29.0199 - 20.1952i) q^{50} +(-40.0015 + 88.5689i) q^{51} -47.2036i q^{52} +85.0310 q^{53} +(-36.4993 + 11.2162i) q^{54} +(-23.7508 + 75.7091i) q^{55} +7.20604i q^{56} +(-3.33834 + 7.39155i) q^{57} -19.6241i q^{58} +78.7364i q^{59} +(-19.9660 + 22.3911i) q^{60} -68.8771 q^{61} -23.2018 q^{62} +(-17.2028 + 15.1600i) q^{63} +8.00000 q^{64} +(35.3233 - 112.598i) q^{65} +(61.3604 + 27.7130i) q^{66} +66.3843i q^{67} +64.7888 q^{68} +(5.92203 - 13.1122i) q^{69} +(-5.39241 + 17.1891i) q^{70} +88.6614i q^{71} +(16.8303 + 19.0982i) q^{72} +37.1977i q^{73} +12.2111i q^{74} +(-64.3820 + 38.4702i) q^{75} +5.40697 q^{76} +40.4309 q^{77} +(-91.2581 - 41.2161i) q^{78} +104.696 q^{79} +(19.0830 + 5.98654i) q^{80} +(-10.1854 + 80.3571i) q^{81} +83.9902i q^{82} +76.6784 q^{83} +(13.9313 + 6.29199i) q^{84} +(154.546 + 48.4826i) q^{85} +72.5475i q^{86} +(-37.9391 - 17.1349i) q^{87} -44.8855i q^{88} +76.2385i q^{89} +(25.8550 + 58.1508i) q^{90} -60.1308 q^{91} -9.59166 q^{92} +(-20.2588 + 44.8557i) q^{93} +55.0308 q^{94} +(12.8977 + 4.04613i) q^{95} +(6.98524 - 15.4663i) q^{96} +73.6041i q^{97} -60.1170 q^{98} +(107.154 - 94.4295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 176 q^{4} + 8 q^{9}+O(q^{10}) $ 88 * q + 176 * q^4 + 8 * q^9	$ 88 q + 176 q^{4} + 8 q^{9} + 32 q^{10} - 12 q^{15} + 352 q^{16} - 16 q^{19} - 176 q^{21} + 72 q^{25} - 72 q^{30} + 32 q^{31} + 160 q^{34} + 16 q^{36} + 144 q^{39} + 64 q^{40} + 92 q^{45} - 360 q^{49} + 48 q^{51} - 144 q^{54} + 16 q^{55} - 24 q^{60} + 208 q^{61} + 704 q^{64} + 512 q^{66} + 304 q^{70} + 536 q^{75} - 32 q^{76} + 448 q^{79} - 24 q^{81} - 352 q^{84} - 96 q^{85} + 32 q^{90} - 64 q^{91} + 160 q^{94} + 296 q^{99}+O(q^{100}) $ 88 * q + 176 * q^4 + 8 * q^9 + 32 * q^10 - 12 * q^15 + 352 * q^16 - 16 * q^19 - 176 * q^21 + 72 * q^25 - 72 * q^30 + 32 * q^31 + 160 * q^34 + 16 * q^36 + 144 * q^39 + 64 * q^40 + 92 * q^45 - 360 * q^49 + 48 * q^51 - 144 * q^54 + 16 * q^55 - 24 * q^60 + 208 * q^61 + 704 * q^64 + 512 * q^66 + 304 * q^70 + 536 * q^75 - 32 * q^76 + 448 * q^79 - 24 * q^81 - 352 * q^84 - 96 * q^85 + 32 * q^90 - 64 * q^91 + 160 * q^94 + 296 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−1.23483	+	2.73408i	−0.411609	+	0.911360i
$3$	−1.23483	+	2.73408i	−0.411609	+	0.911360i
$4$	2.00000			0.500000
$5$	4.77075	+	1.49664i	0.954151	+	0.299327i
$5$	4.77075	+	1.49664i	0.954151	+	0.299327i
$6$	1.74631	−	3.86657i	0.291052	−	0.644429i
$7$		−	2.54772i		−	0.363960i	−0.983302	−	0.181980i	$-0.941749\pi$
$7$		−	2.54772i		−	0.363960i	0.983302	−	0.181980i	$-0.0582506\pi$
$8$	−2.82843			−0.353553
$9$	−5.95040	−	6.75224i	−0.661156	−	0.750249i
$10$	−6.74686	−	2.11656i	−0.674686	−	0.211656i
$11$			15.8694i			1.44268i	0.692583	+	0.721338i	$0.256473\pi$
$11$			15.8694i			1.44268i	−0.692583	+	0.721338i	$0.743527\pi$
$12$	−2.46966	+	5.46816i	−0.205805	+	0.455680i
$13$		−	23.6018i		−	1.81552i	−0.419486	−	0.907762i	$-0.637790\pi$
$13$		−	23.6018i		−	1.81552i	0.419486	−	0.907762i	$-0.362210\pi$
$14$			3.60302i			0.257358i
$15$	−9.98298	+	11.1955i	−0.665532	+	0.746369i
$16$	4.00000			0.250000
$17$	32.3944			1.90555			0.952776	−	0.303673i	$-0.0982131\pi$
$17$	32.3944			1.90555			0.952776	+	0.303673i	$0.0982131\pi$
$18$	8.41514	+	9.54911i	0.467508	+	0.530506i
$19$	2.70349			0.142289			0.0711444	−	0.997466i	$-0.477335\pi$
$19$	2.70349			0.142289			0.0711444	+	0.997466i	$0.477335\pi$
$20$	9.54151	+	2.99327i	0.477075	+	0.149664i
$21$	6.96567	+	3.14599i	0.331699	+	0.149809i
$22$		−	22.4428i		−	1.02013i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$	3.49262	−	7.73315i	0.145526	−	0.322215i
$25$	20.5202	+	14.2802i	0.820806	+	0.571206i
$26$			33.3780i			1.28377i
$27$	25.8089	−	7.93103i	0.955885	−	0.293742i
$28$		−	5.09544i		−	0.181980i
$29$			13.8764i			0.478495i	0.970959	+	0.239248i	$0.0769008\pi$
$29$			13.8764i			0.478495i	−0.970959	+	0.239248i	$0.923099\pi$
$30$	14.1181	−	15.8329i	0.470602	−	0.527763i
$31$	16.4061			0.529230			0.264615	−	0.964354i	$-0.414755\pi$
$31$	16.4061			0.529230			0.264615	+	0.964354i	$0.414755\pi$
$32$	−5.65685			−0.176777
$33$	−43.3883	−	19.5960i	−1.31480	−	0.593819i
$34$	−45.8126			−1.34743
$35$	3.81301	−	12.1545i	0.108943	−	0.347272i
$36$	−11.9008	−	13.5045i	−0.330578	−	0.375124i
$37$		−	8.63454i		−	0.233366i	−0.993169	−	0.116683i	$-0.962774\pi$
$37$		−	8.63454i		−	0.233366i	0.993169	−	0.116683i	$-0.0372261\pi$
$38$	−3.82331			−0.100613
$39$	64.5293	+	29.1442i	1.65460	+	0.747286i
$40$	−13.4937	−	4.23313i	−0.337343	−	0.105828i
$41$		−	59.3900i		−	1.44854i	−0.689518	−	0.724269i	$-0.742178\pi$
$41$		−	59.3900i		−	1.44854i	0.689518	−	0.724269i	$-0.257822\pi$
$42$	−9.85095	−	4.44911i	−0.234546	−	0.105931i
$43$		−	51.2988i		−	1.19300i	−0.802615	−	0.596498i	$-0.796558\pi$
$43$		−	51.2988i		−	1.19300i	0.802615	−	0.596498i	$-0.203442\pi$
$44$			31.7389i			0.721338i
$45$	−18.2822	−	41.1188i	−0.406272	−	0.913752i
$46$	6.78233			0.147442
$47$	−38.9126			−0.827928			−0.413964	−	0.910293i	$-0.635856\pi$
$47$	−38.9126			−0.827928			−0.413964	+	0.910293i	$0.635856\pi$
$48$	−4.93931	+	10.9363i	−0.102902	+	0.227840i
$49$	42.5091			0.867533
$50$	−29.0199	−	20.1952i	−0.580398	−	0.403904i
$51$	−40.0015	+	88.5689i	−0.784343	+	1.73665i
$52$		−	47.2036i		−	0.907762i
$53$	85.0310			1.60436			0.802180	−	0.597083i	$-0.203674\pi$
$53$	85.0310			1.60436			0.802180	+	0.597083i	$0.203674\pi$
$54$	−36.4993	+	11.2162i	−0.675913	+	0.207707i
$55$	−23.7508	+	75.7091i	−0.431832	+	1.37653i
$56$			7.20604i			0.128679i
$57$	−3.33834	+	7.39155i	−0.0585674	+	0.129676i
$58$		−	19.6241i		−	0.338347i
$59$			78.7364i			1.33452i	0.744827	+	0.667258i	$0.232532\pi$
$59$			78.7364i			1.33452i	−0.744827	+	0.667258i	$0.767468\pi$
$60$	−19.9660	+	22.3911i	−0.332766	+	0.373185i
$61$	−68.8771			−1.12913			−0.564567	−	0.825387i	$-0.690957\pi$
$61$	−68.8771			−1.12913			−0.564567	+	0.825387i	$0.690957\pi$
$62$	−23.2018			−0.374222
$63$	−17.2028	+	15.1600i	−0.273060	+	0.240634i
$64$	8.00000			0.125000
$65$	35.3233	−	112.598i	0.543436	−	1.73228i
$66$	61.3604	+	27.7130i	0.929702	+	0.419893i
$67$			66.3843i			0.990810i	0.868662	+	0.495405i	$0.164980\pi$
$67$			66.3843i			0.990810i	−0.868662	+	0.495405i	$0.835020\pi$
$68$	64.7888			0.952776
$69$	5.92203	−	13.1122i	0.0858265	−	0.190032i
$70$	−5.39241	+	17.1891i	−0.0770344	+	0.245559i
$71$			88.6614i			1.24875i	0.781124	+	0.624376i	$0.214647\pi$
$71$			88.6614i			1.24875i	−0.781124	+	0.624376i	$0.785353\pi$
$72$	16.8303	+	19.0982i	0.233754	+	0.265253i
$73$			37.1977i			0.509557i	0.966999	+	0.254778i	$0.0820025\pi$
$73$			37.1977i			0.509557i	−0.966999	+	0.254778i	$0.917997\pi$
$74$			12.2111i			0.165015i
$75$	−64.3820	+	38.4702i	−0.858426	+	0.512937i
$76$	5.40697			0.0711444
$77$	40.4309			0.525076
$78$	−91.2581	−	41.2161i	−1.16998	−	0.528411i
$79$	104.696			1.32526			0.662631	−	0.748946i	$-0.269440\pi$
$79$	104.696			1.32526			0.662631	+	0.748946i	$0.269440\pi$
$80$	19.0830	+	5.98654i	0.238538	+	0.0748318i
$81$	−10.1854	+	80.3571i	−0.125746	+	0.992062i
$82$			83.9902i			1.02427i
$83$	76.6784			0.923836			0.461918	−	0.886923i	$-0.347161\pi$
$83$	76.6784			0.923836			0.461918	+	0.886923i	$0.347161\pi$
$84$	13.9313	+	6.29199i	0.165849	+	0.0749046i
$85$	154.546	+	48.4826i	1.81818	+	0.570384i
$86$			72.5475i			0.843575i
$87$	−37.9391	−	17.1349i	−0.436082	−	0.196953i
$88$		−	44.8855i		−	0.510063i
$89$			76.2385i			0.856612i	0.903634	+	0.428306i	$0.140889\pi$
$89$			76.2385i			0.856612i	−0.903634	+	0.428306i	$0.859111\pi$
$90$	25.8550	+	58.1508i	0.287278	+	0.646120i
$91$	−60.1308			−0.660778
$92$	−9.59166			−0.104257
$93$	−20.2588	+	44.8557i	−0.217836	+	0.482320i
$94$	55.0308			0.585434
$95$	12.8977	+	4.04613i	0.135765	+	0.0425909i
$96$	6.98524	−	15.4663i	0.0727629	−	0.161107i
$97$			73.6041i			0.758805i	0.925232	+	0.379403i	$0.123870\pi$
$97$			73.6041i			0.758805i	−0.925232	+	0.379403i	$0.876130\pi$
$98$	−60.1170			−0.613439
$99$	107.154	−	94.4295i	1.08237	−	0.953833i
$100$	41.0403	+	28.5603i	0.410403	+	0.285603i
$101$			4.51645i			0.0447173i	0.999750	+	0.0223587i	$0.00711758\pi$
$101$			4.51645i			0.0447173i	−0.999750	+	0.0223587i	$0.992882\pi$
$102$	56.5707	−	125.255i	0.554614	−	1.22799i
$103$			45.2000i			0.438835i	0.975631	+	0.219417i	$0.0704156\pi$
$103$			45.2000i			0.438835i	−0.975631	+	0.219417i	$0.929584\pi$
$104$			66.7560i			0.641884i
$105$	28.5231	+	25.4338i	0.271648	+	0.242227i
$106$	−120.252			−1.13445
$107$	25.9543			0.242563			0.121282	−	0.992618i	$-0.461300\pi$
$107$	25.9543			0.242563			0.121282	+	0.992618i	$0.461300\pi$
$108$	51.6178	−	15.8621i	0.477942	−	0.146871i
$109$	53.8738			0.494255			0.247128	−	0.968983i	$-0.420513\pi$
$109$	53.8738			0.494255			0.247128	+	0.968983i	$0.420513\pi$
$110$	33.5887	−	107.069i	0.305351	−	0.973354i
$111$	23.6075	+	10.6622i	0.212680	+	0.0960556i
$112$		−	10.1909i		−	0.0909900i
$113$	−82.8476			−0.733165			−0.366582	−	0.930386i	$-0.619472\pi$
$113$	−82.8476			−0.733165			−0.366582	+	0.930386i	$0.619472\pi$
$114$	4.72112	−	10.4532i	0.0414134	−	0.0916950i
$115$	−22.8797	−	7.17762i	−0.198954	−	0.0624140i
$116$			27.7527i			0.239248i
$117$	−159.365	+	140.440i	−1.36209	+	1.20034i
$118$		−	111.350i		−	0.943645i
$119$		−	82.5318i		−	0.693545i
$120$	28.2361	−	31.6658i	0.235301	−	0.263881i
$121$	−130.839			−1.08131
$122$	97.4070			0.798418
$123$	162.377	+	73.3365i	1.32014	+	0.596231i
$124$	32.8123			0.264615
$125$	76.5244	+	98.8383i	0.612195	+	0.790707i
$126$	24.3284	−	21.4394i	0.193083	−	0.170154i
$127$		−	90.0823i		−	0.709310i	−0.934997	−	0.354655i	$-0.884598\pi$
$127$		−	90.0823i		−	0.709310i	0.934997	−	0.354655i	$-0.115402\pi$
$128$	−11.3137			−0.0883883
$129$	140.255	+	63.3452i	1.08725	+	0.491048i
$130$	−49.9547	+	159.238i	−0.384267	+	1.22491i
$131$		−	135.317i		−	1.03296i	−0.856300	−	0.516478i	$-0.827243\pi$
$131$		−	135.317i		−	1.03296i	0.856300	−	0.516478i	$-0.172757\pi$
$132$	−86.7767	−	39.1920i	−0.657399	−	0.296909i
$133$		−	6.88772i		−	0.0517874i
$134$		−	93.8815i		−	0.700609i
$135$	134.998	+	0.789532i	0.999983	+	0.00584839i
$136$	−91.6252			−0.673715
$137$	117.874			0.860392			0.430196	−	0.902736i	$-0.358444\pi$
$137$	117.874			0.860392			0.430196	+	0.902736i	$0.358444\pi$
$138$	−8.37501	+	18.5434i	−0.0606885	+	0.134373i
$139$	−183.405			−1.31946			−0.659729	−	0.751504i	$-0.729329\pi$
$139$	−183.405			−1.31946			−0.659729	+	0.751504i	$0.729329\pi$
$140$	7.62602	−	24.3091i	0.0544715	−	0.173636i
$141$	48.0504	−	106.390i	0.340783	−	0.754541i
$142$		−	125.386i		−	0.883001i
$143$	374.547			2.61921
$144$	−23.8016	−	27.0090i	−0.165289	−	0.187562i
$145$	−20.7679	+	66.2007i	−0.143227	+	0.456556i
$146$		−	52.6054i		−	0.360311i
$147$	−52.4914	+	116.223i	−0.357085	+	0.790635i
$148$		−	17.2691i		−	0.116683i
$149$			24.5997i			0.165099i	0.996587	+	0.0825493i	$0.0263062\pi$
$149$			24.5997i			0.165099i	−0.996587	+	0.0825493i	$0.973694\pi$
$150$	91.0499	−	54.4051i	0.606999	−	0.362701i
$151$	−32.5412			−0.215505			−0.107752	−	0.994178i	$-0.534365\pi$
$151$	−32.5412			−0.215505			−0.107752	+	0.994178i	$0.534365\pi$
$152$	−7.64661			−0.0503067
$153$	−192.760	−	218.735i	−1.25987	−	1.42964i
$154$	−57.1779			−0.371285
$155$	78.2696	+	24.5540i	0.504965	+	0.158413i
$156$	129.059	+	58.2883i	0.827298	+	0.373643i
$157$			3.81607i			0.0243062i	0.999926	+	0.0121531i	$0.00386855\pi$
$157$			3.81607i			0.0243062i	−0.999926	+	0.0121531i	$0.996131\pi$
$158$	−148.062			−0.937101
$159$	−104.999	+	232.482i	−0.660369	+	1.46215i
$160$	−26.9875	−	8.46625i	−0.168672	−	0.0529141i
$161$			12.2184i			0.0758909i
$162$	14.4044	−	113.642i	0.0889160	−	0.701494i
$163$		−	176.476i		−	1.08268i	−0.840805	−	0.541338i	$-0.817918\pi$
$163$		−	176.476i		−	1.08268i	0.840805	−	0.541338i	$-0.182082\pi$
$164$		−	118.780i		−	0.724269i
$165$	−177.667	−	158.424i	−1.07677	−	0.960147i
$166$	−108.440			−0.653251
$167$	−157.350			−0.942215			−0.471107	−	0.882076i	$-0.656146\pi$
$167$	−157.350			−0.942215			−0.471107	+	0.882076i	$0.656146\pi$
$168$	−19.7019	−	8.89821i	−0.117273	−	0.0529656i
$169$	−388.045			−2.29613
$170$	−218.561	−	68.5648i	−1.28565	−	0.403322i
$171$	−16.0868	−	18.2546i	−0.0940750	−	0.106752i
$172$		−	102.598i		−	0.596498i
$173$	−248.801			−1.43815			−0.719077	−	0.694930i	$-0.755435\pi$
$173$	−248.801			−1.43815			−0.719077	+	0.694930i	$0.755435\pi$
$174$	53.6540	+	24.2324i	0.308356	+	0.139267i
$175$	36.3818	−	52.2796i	0.207896	−	0.298741i
$176$			63.4777i			0.360669i
$177$	−215.272	−	97.2259i	−1.21622	−	0.549299i
$178$		−	107.817i		−	0.605716i
$179$			111.059i			0.620442i	0.950664	+	0.310221i	$0.100403\pi$
$179$			111.059i			0.620442i	−0.950664	+	0.310221i	$0.899597\pi$
$180$	−36.5645	−	82.2377i	−0.203136	−	0.456876i
$181$	219.405			1.21218			0.606092	−	0.795395i	$-0.292736\pi$
$181$	219.405			1.21218			0.606092	+	0.795395i	$0.292736\pi$
$182$	85.0377			0.467240
$183$	85.0514	−	188.316i	0.464762	−	1.02905i
$184$	13.5647			0.0737210
$185$	12.9228	−	41.1933i	0.0698528	−	0.222666i
$186$	28.6502	−	63.4356i	0.154033	−	0.341051i
$187$			514.081i			2.74909i
$188$	−77.8252			−0.413964
$189$	−20.2060	−	65.7538i	−0.106910	−	0.347904i
$190$	−18.2400	−	5.72210i	−0.0960003	−	0.0301163i
$191$		−	23.6963i		−	0.124065i	−0.998074	−	0.0620323i	$-0.980242\pi$
$191$		−	23.6963i		−	0.124065i	0.998074	−	0.0620323i	$-0.0197582\pi$
$192$	−9.87862	+	21.8727i	−0.0514512	+	0.113920i
$193$			98.0811i			0.508192i	0.967179	+	0.254096i	$0.0817780\pi$
$193$			98.0811i			0.508192i	−0.967179	+	0.254096i	$0.918222\pi$
$194$		−	104.092i		−	0.536556i
$195$	264.235	+	235.616i	1.35505	+	1.20829i
$196$	85.0183			0.433767
$197$	316.042			1.60428			0.802138	−	0.597139i	$-0.203696\pi$
$197$	316.042			1.60428			0.802138	+	0.597139i	$0.203696\pi$
$198$	−151.539	+	133.543i	−0.765348	+	0.674462i
$199$	168.719			0.847835			0.423918	−	0.905701i	$-0.360655\pi$
$199$	168.719			0.847835			0.423918	+	0.905701i	$0.360655\pi$
$200$	−58.0398	−	40.3904i	−0.290199	−	0.201952i
$201$	−181.500	−	81.9731i	−0.902985	−	0.407827i
$202$		−	6.38723i		−	0.0316199i
$203$	35.3531			0.174153
$204$	−80.0030	+	177.138i	−0.392171	+	0.868323i
$205$	88.8853	−	283.335i	0.433587	−	1.38212i
$206$		−	63.9224i		−	0.310303i
$207$	28.5371	+	32.3826i	0.137860	+	0.156438i
$208$		−	94.4072i		−	0.453881i
$209$			42.9028i			0.205277i
$210$	−40.3377	−	35.9689i	−0.192084	−	0.171280i
$211$	168.980			0.800852			0.400426	−	0.916329i	$-0.368862\pi$
$211$	168.980			0.800852			0.400426	+	0.916329i	$0.368862\pi$
$212$	170.062			0.802180
$213$	−242.408	−	109.482i	−1.13806	−	0.513998i
$214$	−36.7049			−0.171518
$215$	76.7756	−	244.734i	0.357096	−	1.13830i
$216$	−72.9986	+	22.4323i	−0.337956	+	0.103853i
$217$		−	41.7982i		−	0.192619i
$218$	−76.1891			−0.349491
$219$	−101.701	−	45.9327i	−0.464390	−	0.209738i
$220$	−47.5015	+	151.418i	−0.215916	+	0.688265i
$221$		−	764.566i		−	3.45958i
$222$	−33.3861	−	15.0786i	−0.150388	−	0.0679215i
$223$			256.517i			1.15030i	0.818048	+	0.575151i	$0.195057\pi$
$223$			256.517i			1.15030i	−0.818048	+	0.575151i	$0.804943\pi$
$224$			14.4121i			0.0643396i
$225$	−25.6801	−	223.530i	−0.114134	−	0.993465i
$226$	117.164			0.518426
$227$	319.013			1.40534			0.702672	−	0.711514i	$-0.251990\pi$
$227$	319.013			1.40534			0.702672	+	0.711514i	$0.251990\pi$
$228$	−6.67668	+	14.7831i	−0.0292837	+	0.0648382i
$229$	88.2037			0.385169			0.192584	−	0.981280i	$-0.438313\pi$
$229$	88.2037			0.385169			0.192584	+	0.981280i	$0.438313\pi$
$230$	32.3568	+	10.1507i	0.140682	+	0.0441334i
$231$	−49.9251	+	110.541i	−0.216126	+	0.478534i
$232$		−	39.2483i		−	0.169174i
$233$	−442.366			−1.89857			−0.949283	−	0.314423i	$-0.898189\pi$
$233$	−442.366			−1.89857			−0.949283	+	0.314423i	$0.898189\pi$
$234$	225.376	−	198.612i	0.963146	−	0.848771i
$235$	−185.642	−	58.2380i	−0.789968	−	0.247821i
$236$			157.473i			0.667258i
$237$	−129.281	+	286.246i	−0.545490	+	1.20779i
$238$			116.718i			0.490410i
$239$		−	69.6082i		−	0.291248i	−0.989340	−	0.145624i	$-0.953481\pi$
$239$		−	69.6082i		−	0.291248i	0.989340	−	0.145624i	$-0.0465189\pi$
$240$	−39.9319	+	44.7822i	−0.166383	+	0.186592i
$241$	−37.8588			−0.157090			−0.0785452	−	0.996911i	$-0.525028\pi$
$241$	−37.8588			−0.157090			−0.0785452	+	0.996911i	$0.525028\pi$
$242$	185.034			0.764604
$243$	−207.125	−	127.075i	−0.852368	−	0.522942i
$244$	−137.754			−0.564567
$245$	202.801	+	63.6207i	0.827757	+	0.259676i
$246$	−229.636	−	103.713i	−0.933480	−	0.421599i
$247$		−	63.8071i		−	0.258329i
$248$	−46.4036			−0.187111
$249$	−94.6846	+	209.645i	−0.380260	+	0.841948i
$250$	−108.222	−	139.779i	−0.432887	−	0.559114i
$251$		−	38.2880i		−	0.152542i	−0.997087	−	0.0762709i	$-0.975699\pi$
$251$		−	38.2880i		−	0.152542i	0.997087	−	0.0762709i	$-0.0243014\pi$
$252$	−34.4056	+	30.3199i	−0.136530	+	0.120317i
$253$		−	76.1071i		−	0.300819i
$254$			127.396i			0.501558i
$255$	−323.393	+	362.673i	−1.26821	+	1.42225i
$256$	16.0000			0.0625000
$257$	−5.46616			−0.0212691			−0.0106346	−	0.999943i	$-0.503385\pi$
$257$	−5.46616			−0.0212691			−0.0106346	+	0.999943i	$0.503385\pi$
$258$	−198.351	−	89.5836i	−0.768801	−	0.347223i
$259$	−21.9984			−0.0849358
$260$	70.6466	−	225.197i	0.271718	−	0.866141i
$261$	93.6965	−	82.5699i	0.358990	−	0.316360i
$262$			191.368i			0.730411i
$263$	−485.162			−1.84472			−0.922361	−	0.386329i	$-0.873743\pi$
$263$	−485.162			−1.84472			−0.922361	+	0.386329i	$0.873743\pi$
$264$	122.721	+	55.4259i	0.464851	+	0.209947i
$265$	405.662	+	127.261i	1.53080	+	0.480228i
$266$			9.74071i			0.0366192i
$267$	−208.442	−	94.1414i	−0.780682	−	0.352589i
$268$			132.769i			0.495405i
$269$		−	268.151i		−	0.996844i	−0.866935	−	0.498422i	$-0.833913\pi$
$269$		−	268.151i		−	0.996844i	0.866935	−	0.498422i	$-0.166087\pi$
$270$	−190.916	−	1.11657i	−0.707095	−	0.00413544i
$271$	129.334			0.477246			0.238623	−	0.971112i	$-0.423304\pi$
$271$	129.334			0.477246			0.238623	+	0.971112i	$0.423304\pi$
$272$	129.578			0.476388
$273$	74.2511	−	164.402i	0.271982	−	0.602207i
$274$	−166.699			−0.608389
$275$	−226.618	+	325.643i	−0.824066	+	1.18416i
$276$	11.8441	−	26.2244i	0.0429132	−	0.0950159i
$277$		−	403.297i		−	1.45595i	−0.685605	−	0.727974i	$-0.740462\pi$
$277$		−	403.297i		−	1.45595i	0.685605	−	0.727974i	$-0.259538\pi$
$278$	259.373			0.932997
$279$	−97.6231	−	110.778i	−0.349904	−	0.397054i
$280$	−10.7848	+	34.3782i	−0.0385172	+	0.122779i
$281$			128.348i			0.456755i	0.973573	+	0.228378i	$0.0733421\pi$
$281$			128.348i			0.456755i	−0.973573	+	0.228378i	$0.926658\pi$
$282$	−67.9535	+	150.459i	−0.240970	+	0.533541i
$283$		−	351.650i		−	1.24258i	−0.783581	−	0.621289i	$-0.786609\pi$
$283$		−	351.650i		−	1.24258i	0.783581	−	0.621289i	$-0.213391\pi$
$284$			177.323i			0.624376i
$285$	−26.9889	+	30.2670i	−0.0946977	+	0.106200i
$286$	−529.690			−1.85206
$287$	−151.309			−0.527209
$288$	33.6606	+	38.1964i	0.116877	+	0.132626i
$289$	760.397			2.63113
$290$	29.3702	−	93.6219i	0.101277	−	0.322834i
$291$	−201.240	−	90.8884i	−0.691545	−	0.312331i
$292$			74.3953i			0.254778i
$293$	246.993			0.842979			0.421489	−	0.906833i	$-0.361507\pi$
$293$	246.993			0.842979			0.421489	+	0.906833i	$0.361507\pi$
$294$	74.2341	−	164.365i	0.252497	−	0.559064i
$295$	−117.840	+	375.632i	−0.399457	+	1.27333i
$296$			24.4222i			0.0825073i
$297$	125.861	+	409.572i	0.423774	+	1.37903i
$298$		−	34.7892i		−	0.116742i
$299$			113.190i			0.378563i
$300$	−128.764	+	76.9405i	−0.429213	+	0.256468i
$301$	−130.695			−0.434202
$302$	46.0202			0.152385
$303$	−12.3483	−	5.57704i	−0.0407536	−	0.0184061i
$304$	10.8139			0.0355722
$305$	−328.596	−	103.084i	−1.07736	−	0.337980i
$306$	272.603	+	309.338i	0.890860	+	1.01091i
$307$			322.299i			1.04983i	0.851154	+	0.524917i	$0.175903\pi$
$307$			322.299i			1.04983i	−0.851154	+	0.524917i	$0.824097\pi$
$308$	80.8617			0.262538
$309$	−123.580	−	55.8142i	−0.399936	−	0.180628i
$310$	−110.690	−	34.7246i	−0.357064	−	0.112015i
$311$		−	197.270i		−	0.634308i	−0.948374	−	0.317154i	$-0.897273\pi$
$311$		−	197.270i		−	0.634308i	0.948374	−	0.317154i	$-0.102727\pi$
$312$	−182.516	−	82.4321i	−0.584988	−	0.264206i
$313$		−	542.137i		−	1.73207i	−0.499987	−	0.866033i	$-0.666662\pi$
$313$		−	542.137i		−	1.73207i	0.499987	−	0.866033i	$-0.333338\pi$
$314$		−	5.39674i		−	0.0171871i
$315$	−104.759	+	46.5780i	−0.332569	+	0.147867i
$316$	209.391			0.662631
$317$	−96.0108			−0.302873			−0.151437	−	0.988467i	$-0.548390\pi$
$317$	−96.0108			−0.302873			−0.151437	+	0.988467i	$0.548390\pi$
$318$	148.491	−	328.779i	0.466951	−	1.03390i
$319$	−220.210			−0.690314
$320$	38.1660	+	11.9731i	0.119269	+	0.0374159i
$321$	−32.0490	+	70.9611i	−0.0998413	+	0.221063i
$322$		−	17.2795i		−	0.0536630i
$323$	87.5778			0.271139
$324$	−20.3709	+	160.714i	−0.0628731	+	0.496031i
$325$	337.038	−	484.313i	1.03704	−	1.49019i
$326$			249.575i			0.765567i
$327$	−66.5249	+	147.295i	−0.203440	+	0.450444i
$328$			167.980i			0.512135i
$329$			99.1384i			0.301333i
$330$	251.259	+	224.046i	0.761391	+	0.678927i
$331$	246.600			0.745016			0.372508	−	0.928029i	$-0.378498\pi$
$331$	246.600			0.745016			0.372508	+	0.928029i	$0.378498\pi$
$332$	153.357			0.461918
$333$	−58.3025	+	51.3790i	−0.175083	+	0.154291i
$334$	222.526			0.666246
$335$	−99.3531	+	316.703i	−0.296576	+	0.945382i
$336$	27.8627	+	12.5840i	0.0829247	+	0.0374523i
$337$		−	136.820i		−	0.405994i	−0.979179	−	0.202997i	$-0.934932\pi$
$337$		−	136.820i		−	0.405994i	0.979179	−	0.202997i	$-0.0650682\pi$
$338$	548.779			1.62361
$339$	102.303	−	226.512i	0.301777	−	0.668177i
$340$	309.091	+	96.9652i	0.909092	+	0.285192i
$341$			260.356i			0.763508i
$342$	22.7502	+	25.8159i	0.0665211	+	0.0754850i
$343$		−	233.140i		−	0.679707i
$344$			145.095i			0.421788i
$345$	47.8767	−	53.6919i	0.138773	−	0.155629i
$346$	351.857			1.01693
$347$	351.266			1.01229			0.506147	−	0.862447i	$-0.331069\pi$
$347$	351.266			1.01229			0.506147	+	0.862447i	$0.331069\pi$
$348$	−75.8782	−	34.2698i	−0.218041	−	0.0984765i
$349$	−210.440			−0.602979			−0.301489	−	0.953470i	$-0.597484\pi$
$349$	−210.440			−0.602979			−0.301489	+	0.953470i	$0.597484\pi$
$350$	−51.4517	+	73.9345i	−0.147005	+	0.211241i
$351$	−187.187	−	609.136i	−0.533295	−	1.73543i
$352$		−	89.7711i		−	0.255031i
$353$	−479.609			−1.35867			−0.679333	−	0.733830i	$-0.737731\pi$
$353$	−479.609			−1.35867			−0.679333	+	0.733830i	$0.737731\pi$
$354$	304.440	+	137.498i	0.860001	+	0.388413i
$355$	−132.694	+	422.982i	−0.373786	+	1.19150i
$356$			152.477i			0.428306i
$357$	225.649	+	101.913i	0.632069	+	0.285469i
$358$		−	157.061i		−	0.438719i
$359$		−	666.963i		−	1.85783i	−0.370288	−	0.928917i	$-0.620741\pi$
$359$		−	666.963i		−	1.85783i	0.370288	−	0.928917i	$-0.379259\pi$
$360$	51.7100	+	116.302i	0.143639	+	0.323060i
$361$	−353.691			−0.979754
$362$	−310.286			−0.857143
$363$	161.564	−	357.724i	0.445079	−	0.985467i
$364$	−120.262			−0.330389
$365$	−55.6714	+	177.461i	−0.152524	+	0.486194i
$366$	−120.281	+	266.319i	−0.328636	+	0.727647i
$367$			503.975i			1.37323i	0.727022	+	0.686614i	$0.240904\pi$
$367$			503.975i			1.37323i	−0.727022	+	0.686614i	$0.759096\pi$
$368$	−19.1833			−0.0521286
$369$	−401.016	+	353.395i	−1.08676	+	0.957709i
$370$	−18.2756	+	58.2561i	−0.0493934	+	0.157449i
$371$		−	216.635i		−	0.583922i
$372$	−40.5175	+	89.7114i	−0.108918	+	0.241160i
$373$		−	632.077i		−	1.69458i	−0.531133	−	0.847288i	$-0.678234\pi$
$373$		−	632.077i		−	1.69458i	0.531133	−	0.847288i	$-0.321766\pi$
$374$		−	727.020i		−	1.94390i
$375$	−364.726	+	87.1756i	−0.972604	+	0.232468i
$376$	110.062			0.292717
$377$	327.507			0.868719
$378$	28.5757	+	92.9899i	0.0755970	+	0.246005i
$379$	567.452			1.49724			0.748618	−	0.663002i	$-0.230718\pi$
$379$	567.452			1.49724			0.748618	+	0.663002i	$0.230718\pi$
$380$	25.7953	+	8.09227i	0.0678824	+	0.0212954i
$381$	246.292	+	111.236i	0.646437	+	0.291958i
$382$			33.5117i			0.0877269i
$383$	−75.9370			−0.198269			−0.0991345	−	0.995074i	$-0.531607\pi$
$383$	−75.9370			−0.198269			−0.0991345	+	0.995074i	$0.531607\pi$
$384$	13.9705	−	30.9326i	0.0363815	−	0.0805536i
$385$	192.886	+	60.5103i	0.501002	+	0.157170i
$386$		−	138.708i		−	0.359346i
$387$	−346.382	+	305.248i	−0.895043	+	0.788756i
$388$			147.208i			0.379403i
$389$		−	216.366i		−	0.556210i	−0.960551	−	0.278105i	$-0.910294\pi$
$389$		−	216.366i		−	0.556210i	0.960551	−	0.278105i	$-0.0897063\pi$
$390$	−373.685	−	333.212i	−0.958166	−	0.854390i
$391$	−155.358			−0.397335
$392$	−120.234			−0.306719
$393$	369.969	+	167.094i	0.941396	+	0.425175i
$394$	−446.951			−1.13439
$395$	499.477	+	156.691i	1.26450	+	0.396687i
$396$	214.308	−	188.859i	0.541183	−	0.476917i
$397$		−	723.583i		−	1.82263i	−0.411712	−	0.911314i	$-0.635069\pi$
$397$		−	723.583i		−	1.82263i	0.411712	−	0.911314i	$-0.364931\pi$
$398$	−238.605			−0.599510
$399$	18.8316	+	8.50515i	0.0471970	+	0.0213162i
$400$	82.0806	+	57.1206i	0.205202	+	0.142802i
$401$			258.627i			0.644955i	0.946577	+	0.322478i	$0.104516\pi$
$401$			258.627i			0.644955i	−0.946577	+	0.322478i	$0.895484\pi$
$402$	256.680	+	115.928i	0.638507	+	0.288377i
$403$		−	387.215i		−	0.960830i
$404$			9.03290i			0.0223587i
$405$	−168.858	+	368.120i	−0.416932	+	0.908938i
$406$	−49.9968			−0.123145
$407$	137.025			0.336671
$408$	113.141	−	250.511i	0.277307	−	0.613997i
$409$	−399.257			−0.976178			−0.488089	−	0.872794i	$-0.662306\pi$
$409$	−399.257			−0.976178			−0.488089	+	0.872794i	$0.662306\pi$
$410$	−125.703	+	400.696i	−0.306592	+	0.977308i
$411$	−145.554	+	322.276i	−0.354145	+	0.784127i
$412$			90.3999i			0.219417i
$413$	200.598			0.485710
$414$	−40.3576	−	45.7959i	−0.0974821	−	0.110618i
$415$	365.814	+	114.760i	0.881479	+	0.276529i
$416$			133.512i			0.320942i
$417$	226.473	−	501.443i	0.543101	−	1.20250i
$418$		−	60.6737i		−	0.145152i
$419$			447.017i			1.06687i	0.845842	+	0.533434i	$0.179099\pi$
$419$			447.017i			1.06687i	−0.845842	+	0.533434i	$0.820901\pi$
$420$	57.0462	+	50.8677i	0.135824	+	0.121113i
$421$	272.776			0.647923			0.323962	−	0.946070i	$-0.394985\pi$
$421$	272.776			0.647923			0.323962	+	0.946070i	$0.394985\pi$
$422$	−238.973			−0.566288
$423$	231.546	+	262.747i	0.547389	+	0.621152i
$424$	−240.504			−0.567227
$425$	664.738	+	462.597i	1.56409	+	1.08846i
$426$	342.816	+	154.830i	0.804732	+	0.363451i
$427$			175.480i			0.410959i
$428$	51.9085			0.121282
$429$	−462.501	+	1024.04i	−1.07809	+	2.38705i
$430$	−108.577	+	346.106i	−0.252505	+	0.804898i
$431$		−	436.879i		−	1.01364i	−0.862052	−	0.506820i	$-0.830821\pi$
$431$		−	436.879i		−	1.01364i	0.862052	−	0.506820i	$-0.169179\pi$
$432$	103.236	−	31.7241i	0.238971	−	0.0734355i
$433$		−	81.5626i		−	0.188366i	−0.995555	−	0.0941832i	$-0.969976\pi$
$433$		−	81.5626i		−	0.188366i	0.995555	−	0.0941832i	$-0.0300239\pi$
$434$			59.1116i			0.136202i
$435$	−155.353	−	138.527i	−0.357134	−	0.318454i
$436$	107.748			0.247128
$437$	−12.9655			−0.0296693
$438$	143.828	+	64.9586i	0.328373	+	0.148307i
$439$	−459.523			−1.04675			−0.523375	−	0.852103i	$-0.675327\pi$
$439$	−459.523			−1.04675			−0.523375	+	0.852103i	$0.675327\pi$
$440$	67.1773	−	214.138i	0.152676	−	0.486677i
$441$	−252.946	−	287.032i	−0.573575	−	0.650866i
$442$			1081.26i			2.44629i
$443$	341.453			0.770773			0.385387	−	0.922755i	$-0.374068\pi$
$443$	341.453			0.770773			0.385387	+	0.922755i	$0.374068\pi$
$444$	47.2151	+	21.3243i	0.106340	+	0.0480278i
$445$	−114.101	+	363.715i	−0.256407	+	0.817337i
$446$		−	362.770i		−	0.813386i
$447$	−67.2575	−	30.3764i	−0.150464	−	0.0679561i
$448$		−	20.3818i		−	0.0454950i
$449$			51.7486i			0.115253i	0.998338	+	0.0576264i	$0.0183532\pi$
$449$			51.7486i			0.115253i	−0.998338	+	0.0576264i	$0.981647\pi$
$450$	36.3172	+	316.119i	0.0807049	+	0.702486i
$451$	942.486			2.08977
$452$	−165.695			−0.366582
$453$	40.1828	−	88.9703i	0.0887037	−	0.196402i
$454$	−451.152			−0.993728
$455$	−286.869	−	89.9939i	−0.630481	−	0.197789i
$456$	9.44225	−	20.9065i	0.0207067	−	0.0458475i
$457$			408.775i			0.894474i	0.894416	+	0.447237i	$0.147592\pi$
$457$			408.775i			0.894474i	−0.894416	+	0.447237i	$0.852408\pi$
$458$	−124.739			−0.272356
$459$	836.063	−	256.921i	1.82149	−	0.559741i
$460$	−45.7595	−	14.3552i	−0.0994771	−	0.0312070i
$461$		−	274.701i		−	0.595882i	−0.954584	−	0.297941i	$-0.903700\pi$
$461$		−	274.701i		−	0.595882i	0.954584	−	0.297941i	$-0.0962998\pi$
$462$	70.6048	−	156.329i	0.152824	−	0.338374i
$463$		−	25.3001i		−	0.0546439i	−0.999627	−	0.0273219i	$-0.991302\pi$
$463$		−	25.3001i		−	0.0546439i	0.999627	−	0.0273219i	$-0.00869793\pi$
$464$			55.5054i			0.119624i
$465$	−163.782	+	183.676i	−0.352220	+	0.395001i
$466$	625.600			1.34249
$467$	−745.058			−1.59541			−0.797706	−	0.603046i	$-0.793953\pi$
$467$	−745.058			−1.59541			−0.797706	+	0.603046i	$0.793953\pi$
$468$	−318.730	+	280.880i	−0.681047	+	0.600172i
$469$	169.128			0.360615
$470$	262.538	+	82.3610i	0.558592	+	0.175236i
$471$	−10.4335	−	4.71219i	−0.0221517	−	0.0100047i
$472$		−	222.700i		−	0.471822i
$473$	814.083			1.72111
$474$	182.831	−	404.814i	0.385720	−	0.854037i
$475$	55.4760	+	38.6062i	0.116791	+	0.0812762i
$476$		−	165.064i		−	0.346772i
$477$	−505.969	−	574.150i	−1.06073	−	1.20367i
$478$			98.4409i			0.205943i
$479$			168.038i			0.350810i	0.984496	+	0.175405i	$0.0561235\pi$
$479$			168.038i			0.350810i	−0.984496	+	0.175405i	$0.943876\pi$
$480$	56.4723	−	63.3315i	0.117651	−	0.131941i
$481$	−203.791			−0.423681
$482$	53.5404			0.111080
$483$	−33.4062	−	15.0877i	−0.0691639	−	0.0312374i
$484$	−261.678			−0.540657
$485$	−110.159	+	351.147i	−0.227131	+	0.724014i
$486$	292.920	+	179.711i	0.602715	+	0.369776i
$487$		−	256.289i		−	0.526261i	−0.964760	−	0.263131i	$-0.915245\pi$
$487$		−	256.289i		−	0.526261i	0.964760	−	0.263131i	$-0.0847550\pi$
$488$	194.814			0.399209
$489$	482.500	+	217.918i	0.986707	+	0.445639i
$490$	−286.803	−	89.9733i	−0.585313	−	0.183619i
$491$			631.851i			1.28686i	0.765503	+	0.643432i	$0.222490\pi$
$491$			631.851i			1.28686i	−0.765503	+	0.643432i	$0.777510\pi$
$492$	324.754	+	146.673i	0.660070	+	0.298116i
$493$			449.516i			0.911798i
$494$			90.2369i			0.182666i
$495$	652.533	−	290.129i	1.31825	−	0.586119i
$496$	65.6246			0.132308
$497$	225.884			0.454496
$498$	133.904	−	296.483i	0.268884	−	0.595347i
$499$	539.468			1.08110			0.540550	−	0.841312i	$-0.318216\pi$
$499$	539.468			1.08110			0.540550	+	0.841312i	$0.318216\pi$
$500$	153.049	+	197.677i	0.306098	+	0.395353i
$501$	194.300	−	430.207i	0.387824	−	0.858697i
$502$			54.1474i			0.107863i
$503$	−294.962			−0.586406			−0.293203	−	0.956050i	$-0.594721\pi$
$503$	−294.962			−0.586406			−0.293203	+	0.956050i	$0.594721\pi$
$504$	48.6569	−	42.8788i	0.0965414	−	0.0850770i
$505$	−6.75949	+	21.5469i	−0.0133851	+	0.0426671i
$506$			107.632i			0.212711i
$507$	479.169	−	1060.95i	0.945106	−	2.09260i
$508$		−	180.165i		−	0.354655i
$509$			145.947i			0.286733i	0.989670	+	0.143367i	$0.0457928\pi$
$509$			145.947i			0.286733i	−0.989670	+	0.143367i	$0.954207\pi$
$510$	457.346	−	512.897i	0.896757	−	1.00568i
$511$	94.7692			0.185458
$512$	−22.6274			−0.0441942
$513$	69.7740	−	21.4414i	0.136012	−	0.0417962i
$514$	7.73032			0.0150395
$515$	−67.6479	+	215.638i	−0.131355	+	0.418714i
$516$	280.510	+	126.690i	0.543624	+	0.245524i
$517$		−	617.521i		−	1.19443i
$518$	31.1104			0.0600587
$519$	307.226	−	680.241i	0.591958	−	1.31068i
$520$	−99.9094	+	318.476i	−0.192134	+	0.612454i
$521$			699.345i			1.34231i	0.741316	+	0.671156i	$0.234202\pi$
$521$			699.345i			1.34231i	−0.741316	+	0.671156i	$0.765798\pi$
$522$	−132.507	+	116.772i	−0.253845	+	0.223700i
$523$		−	807.343i		−	1.54368i	−0.635819	−	0.771839i	$-0.719337\pi$
$523$		−	807.343i		−	1.54368i	0.635819	−	0.771839i	$-0.280663\pi$
$524$		−	270.635i		−	0.516478i
$525$	98.0114	+	164.027i	0.186688	+	0.312433i
$526$	686.123			1.30442
$527$	531.467			1.00848
$528$	−173.553	−	78.3841i	−0.328699	−	0.148455i
$529$	23.0000			0.0434783
$530$	−573.693	−	179.974i	−1.08244	−	0.339573i
$531$	531.647	−	468.513i	1.00122	−	0.882323i
$532$		−	13.7754i		−	0.0258937i
$533$	−1401.71			−2.62985
$534$	294.782	+	133.136i	0.552026	+	0.249318i
$535$	123.821	+	38.8441i	0.231442	+	0.0726058i
$536$		−	187.763i		−	0.350304i
$537$	−303.645	−	137.139i	−0.565446	−	0.255380i
$538$			379.223i			0.704875i
$539$			674.596i			1.25157i
$540$	269.995	+	1.57906i	0.499991	+	0.00292419i
$541$	−91.7399			−0.169575			−0.0847873	−	0.996399i	$-0.527021\pi$
$541$	−91.7399			−0.169575			−0.0847873	+	0.996399i	$0.527021\pi$
$542$	−182.906			−0.337464
$543$	−270.928	+	599.872i	−0.498946	+	1.10474i
$544$	−183.250			−0.336857
$545$	257.019	+	80.6295i	0.471594	+	0.147944i
$546$	−105.007	+	232.500i	−0.192320	+	0.425824i
$547$			865.481i			1.58223i	0.611666	+	0.791116i	$0.290500\pi$
$547$			865.481i			1.58223i	−0.611666	+	0.791116i	$0.709500\pi$
$548$	235.747			0.430196
$549$	409.847	+	465.075i	0.746533	+	0.847131i
$550$	320.486	−	460.529i	0.582703	−	0.837326i
$551$			37.5145i			0.0680845i
$552$	−16.7500	+	37.0869i	−0.0303442	+	0.0671864i
$553$		−	266.735i		−	0.482342i
$554$			570.349i			1.02951i
$555$	96.6683	+	86.1985i	0.174177	+	0.155313i
$556$	−366.809			−0.659729
$557$	−399.268			−0.716819			−0.358410	−	0.933564i	$-0.616681\pi$
$557$	−399.268			−0.716819			−0.358410	+	0.933564i	$0.616681\pi$
$558$	138.060	+	156.664i	0.247419	+	0.280760i
$559$	−1210.74			−2.16591
$560$	15.2520	−	48.6181i	0.0272358	−	0.0868181i
$561$	−1405.54	−	634.801i	−2.50542	−	1.13155i
$562$		−	181.512i		−	0.322975i
$563$	−766.176			−1.36088			−0.680440	−	0.732804i	$-0.738211\pi$
$563$	−766.176			−1.36088			−0.680440	+	0.732804i	$0.738211\pi$
$564$	96.1008	−	212.781i	0.170391	−	0.377270i
$565$	−395.246	−	123.993i	−0.699550	−	0.219456i
$566$			497.308i			0.878636i
$567$	204.727	+	25.9497i	0.361071	+	0.0457666i
$568$		−	250.772i		−	0.441501i
$569$			783.307i			1.37664i	0.725408	+	0.688319i	$0.241651\pi$
$569$			783.307i			1.37664i	−0.725408	+	0.688319i	$0.758349\pi$
$570$	38.1680	−	42.8040i	0.0669614	−	0.0750947i
$571$	88.9855			0.155841			0.0779207	−	0.996960i	$-0.475172\pi$
$571$	88.9855			0.155841			0.0779207	+	0.996960i	$0.475172\pi$
$572$	749.095			1.30961
$573$	64.7877	+	29.2609i	0.113068	+	0.0510661i
$574$	213.983			0.372793
$575$	−98.4112	−	68.4853i	−0.171150	−	0.119105i
$576$	−47.6032	−	54.0179i	−0.0826445	−	0.0937811i
$577$			459.789i			0.796861i	0.917199	+	0.398431i	$0.130445\pi$
$577$			459.789i			0.796861i	−0.917199	+	0.398431i	$0.869555\pi$
$578$	−1075.36			−1.86049
$579$	−268.162	−	121.113i	−0.463147	−	0.209177i
$580$	−41.5357	+	132.401i	−0.0716133	+	0.228278i
$581$		−	195.355i		−	0.336239i
$582$	284.596	+	128.536i	0.488996	+	0.220852i
$583$			1349.39i			2.31457i
$584$		−	105.211i		−	0.180156i
$585$	−970.479	+	431.494i	−1.65894	+	0.737597i
$586$	−349.301			−0.596076
$587$	294.716			0.502072			0.251036	−	0.967978i	$-0.419229\pi$
$587$	294.716			0.502072			0.251036	+	0.967978i	$0.419229\pi$
$588$	−104.983	+	232.447i	−0.178542	+	0.395318i
$589$	44.3538			0.0753035
$590$	166.651	−	531.224i	0.282459	−	0.900379i
$591$	−390.258	+	864.085i	−0.660334	+	1.46207i
$592$		−	34.5382i		−	0.0583415i
$593$	−882.001			−1.48735			−0.743677	−	0.668539i	$-0.766920\pi$
$593$	−882.001			−1.48735			−0.743677	+	0.668539i	$0.766920\pi$
$594$	−177.994	−	579.223i	−0.299654	−	0.975123i
$595$	123.520	−	393.739i	0.207597	−	0.661746i
$596$			49.1994i			0.0825493i
$597$	−208.339	+	461.292i	−0.348977	+	0.772683i
$598$		−	160.075i		−	0.267684i
$599$			615.514i			1.02757i	0.857919	+	0.513785i	$0.171757\pi$
$599$			615.514i			1.02757i	−0.857919	+	0.513785i	$0.828243\pi$
$600$	182.100	−	108.810i	0.303500	−	0.181350i
$601$	−16.1189			−0.0268201			−0.0134101	−	0.999910i	$-0.504269\pi$
$601$	−16.1189			−0.0268201			−0.0134101	+	0.999910i	$0.504269\pi$
$602$	184.831			0.307027
$603$	448.242	−	395.013i	0.743354	−	0.655080i
$604$	−65.0824			−0.107752
$605$	−624.200	−	195.818i	−1.03174	−	0.323667i
$606$	17.4632	+	7.88712i	0.0288172	+	0.0130151i
$607$			189.949i			0.312931i	0.987683	+	0.156465i	$0.0500100\pi$
$607$			189.949i			0.312931i	−0.987683	+	0.156465i	$0.949990\pi$
$608$	−15.2932			−0.0251533
$609$	−43.6549	+	96.6582i	−0.0716830	+	0.158716i
$610$	464.705	+	145.783i	0.761811	+	0.238988i
$611$			918.408i			1.50312i
$612$	−385.519	−	437.469i	−0.629933	−	0.714819i
$613$		−	448.071i		−	0.730947i	−0.930822	−	0.365474i	$-0.880907\pi$
$613$		−	448.071i		−	0.730947i	0.930822	−	0.365474i	$-0.119093\pi$
$614$		−	455.799i		−	0.742344i
$615$	664.903	+	592.890i	1.08114	+	0.964048i
$616$	−114.356			−0.185642
$617$	−884.688			−1.43385			−0.716927	−	0.697148i	$-0.754452\pi$
$617$	−884.688			−1.43385			−0.716927	+	0.697148i	$0.754452\pi$
$618$	174.769	+	78.9331i	0.282798	+	0.127724i
$619$	−869.748			−1.40509			−0.702543	−	0.711641i	$-0.747952\pi$
$619$	−869.748			−1.40509			−0.702543	+	0.711641i	$0.747952\pi$
$620$	156.539	+	49.1080i	0.252483	+	0.0792065i
$621$	−123.775	+	38.0359i	−0.199316	+	0.0612494i
$622$			278.981i			0.448523i
$623$	194.234			0.311772
$624$	258.117	+	116.577i	0.413649	+	0.186822i
$625$	217.154	+	586.062i	0.347446	+	0.937700i
$626$			766.697i			1.22476i
$627$	−117.300	−	52.9776i	−0.187081	−	0.0844937i
$628$			7.63215i			0.0121531i
$629$		−	279.711i		−	0.444691i
$630$	148.152	−	65.8713i	0.235162	−	0.104558i
$631$	326.782			0.517880			0.258940	−	0.965893i	$-0.416627\pi$
$631$	326.782			0.517880			0.258940	+	0.965893i	$0.416627\pi$
$632$	−296.124			−0.468551
$633$	−208.661	+	462.004i	−0.329638	+	0.729865i
$634$	135.780			0.214164
$635$	134.820	−	429.761i	0.212316	−	0.676788i
$636$	−209.997	+	464.964i	−0.330185	+	0.731075i
$637$		−	1003.29i		−	1.57503i
$638$	311.424			0.488125
$639$	598.663	−	527.571i	0.936875	−	0.825620i
$640$	−53.9749	−	16.9325i	−0.0843358	−	0.0264570i
$641$			219.166i			0.341913i	0.985279	+	0.170957i	$0.0546858\pi$
$641$			219.166i			0.341913i	−0.985279	+	0.170957i	$0.945314\pi$
$642$	45.3242	−	100.354i	0.0705984	−	0.156315i
$643$		−	707.067i		−	1.09964i	−0.835284	−	0.549819i	$-0.814697\pi$
$643$		−	707.067i		−	1.09964i	0.835284	−	0.549819i	$-0.185303\pi$
$644$			24.4369i			0.0379454i
$645$	574.318	+	512.115i	0.890415	+	0.793977i
$646$	−123.854			−0.191724
$647$	127.046			0.196361			0.0981807	−	0.995169i	$-0.468698\pi$
$647$	127.046			0.196361			0.0981807	+	0.995169i	$0.468698\pi$
$648$	28.8088	−	227.284i	0.0444580	−	0.350747i
$649$	−1249.50			−1.92527
$650$	−476.643	+	684.922i	−0.733297	+	1.05373i
$651$	114.280	+	51.6136i	0.175545	+	0.0792836i
$652$		−	352.952i		−	0.541338i
$653$	35.8607			0.0549169			0.0274585	−	0.999623i	$-0.491259\pi$
$653$	35.8607			0.0549169			0.0274585	+	0.999623i	$0.491259\pi$
$654$	94.0804	−	208.307i	0.143854	−	0.318512i
$655$	202.521	−	645.566i	0.309192	−	0.985596i
$656$		−	237.560i		−	0.362134i
$657$	251.167	−	221.341i	0.382294	−	0.336896i
$658$		−	140.203i		−	0.213074i
$659$		−	152.748i		−	0.231788i	−0.993262	−	0.115894i	$-0.963027\pi$
$659$		−	152.748i		−	0.231788i	0.993262	−	0.115894i	$-0.0369733\pi$
$660$	−355.334	−	316.849i	−0.538384	−	0.480074i
$661$	−96.2217			−0.145570			−0.0727850	−	0.997348i	$-0.523189\pi$
$661$	−96.2217			−0.145570			−0.0727850	+	0.997348i	$0.523189\pi$
$662$	−348.746			−0.526806
$663$	2090.39	+	944.107i	3.15292	+	1.42399i
$664$	−216.879			−0.326625
$665$	10.3084	−	32.8596i	0.0155014	−	0.0494130i
$666$	82.4521	−	72.6609i	0.123802	−	0.109100i
$667$		−	66.5487i		−	0.0997732i
$668$	−314.700			−0.471107
$669$	−701.339	−	316.755i	−1.04834	−	0.473475i
$670$	140.507	−	447.886i	0.209711	−	0.668486i
$671$		−	1093.04i		−	1.62897i
$672$	−39.4038	−	17.7964i	−0.0586366	−	0.0264828i
$673$		−	1060.82i		−	1.57626i	−0.615508	−	0.788130i	$-0.711049\pi$
$673$		−	1060.82i		−	1.57626i	0.615508	−	0.788130i	$-0.288951\pi$
$674$			193.493i			0.287081i
$675$	642.859	+	205.809i	0.952384	+	0.304902i
$676$	−776.090			−1.14806
$677$	1107.81			1.63634			0.818172	−	0.574973i	$-0.194987\pi$
$677$	1107.81			1.63634			0.818172	+	0.574973i	$0.194987\pi$
$678$	−144.678	+	320.337i	−0.213389	+	0.472473i
$679$	187.523			0.276175
$680$	−437.121	−	137.130i	−0.642825	−	0.201661i
$681$	−393.926	+	872.207i	−0.578452	+	1.28077i
$682$		−	368.199i		−	0.539882i
$683$	−637.718			−0.933701			−0.466850	−	0.884336i	$-0.654611\pi$
$683$	−637.718			−0.933701			−0.466850	+	0.884336i	$0.654611\pi$
$684$	−32.1737	−	36.5092i	−0.0470375	−	0.0533760i
$685$	562.346	+	176.414i	0.820943	+	0.257539i
$686$			329.709i			0.480626i
$687$	−108.916	+	241.156i	−0.158539	+	0.351028i
$688$		−	205.195i		−	0.298249i
$689$		−	2006.89i		−	2.91275i
$690$	−67.7079	+	75.9318i	−0.0981274	+	0.110046i
$691$	−1182.13			−1.71075			−0.855376	−	0.518008i	$-0.826674\pi$
$691$	−1182.13			−1.71075			−0.855376	+	0.518008i	$0.826674\pi$
$692$	−497.601			−0.719077
$693$	−240.580	−	272.999i	−0.347157	−	0.393938i
$694$	−496.765			−0.715800
$695$	−874.978	−	274.490i	−1.25896	−	0.394950i
$696$	107.308	+	48.4649i	0.154178	+	0.0696334i
$697$		−	1923.90i		−	2.76026i
$698$	297.607			0.426370
$699$	546.246	−	1209.46i	0.781467	−	1.73028i
$700$	72.7637	−	104.559i	0.103948	−	0.149370i
$701$		−	245.292i		−	0.349917i	−0.984576	−	0.174958i	$-0.944021\pi$
$701$		−	245.292i		−	0.349917i	0.984576	−	0.174958i	$-0.0559791\pi$
$702$	264.722	+	861.449i	0.377097	+	1.22714i
$703$		−	23.3434i		−	0.0332053i
$704$			126.955i			0.180334i
$705$	388.464	−	435.648i	0.551013	−	0.617940i
$706$	678.269			0.960721
$707$	11.5066			0.0162753
$708$	−430.544	−	194.452i	−0.608112	−	0.274649i
$709$	1079.15			1.52207			0.761034	−	0.648712i	$-0.224692\pi$
$709$	1079.15			1.52207			0.761034	+	0.648712i	$0.224692\pi$
$710$	187.657	−	598.186i	0.264306	−	0.842516i
$711$	−622.981	−	706.930i	−0.876204	−	0.994276i
$712$		−	215.635i		−	0.302858i
$713$	−78.6811			−0.110352
$714$	−319.115	−	144.126i	−0.446940	−	0.201857i
$715$	1786.87	+	560.561i	2.49912	+	0.784002i
$716$			222.118i			0.310221i
$717$	190.315	+	85.9542i	0.265432	+	0.119880i
$718$			943.227i			1.31369i
$719$		−	111.651i		−	0.155287i	−0.996981	−	0.0776433i	$-0.975260\pi$
$719$		−	111.651i		−	0.155287i	0.996981	−	0.0776433i	$-0.0247395\pi$
$720$	−73.1290	−	164.475i	−0.101568	−	0.228438i
$721$	115.157			0.159718
$722$	500.195			0.692791
$723$	46.7491	−	103.509i	0.0646599	−	0.143166i
$724$	438.810			0.606092
$725$	−198.157	+	284.745i	−0.273320	+	0.392752i
$726$	−228.485	+	505.899i	−0.314718	+	0.696830i
$727$			699.812i			0.962602i	0.876555	+	0.481301i	$0.159836\pi$
$727$			699.812i			0.962602i	−0.876555	+	0.481301i	$0.840164\pi$
$728$	170.075			0.233620
$729$	603.198	−	409.382i	0.827431	−	0.561567i
$730$	78.7312	−	250.967i	0.107851	−	0.343791i
$731$		−	1661.79i		−	2.27332i
$732$	170.103	−	376.631i	0.232381	−	0.514524i
$733$			1137.24i			1.55148i	0.631052	+	0.775740i	$0.282623\pi$
$733$			1137.24i			1.55148i	−0.631052	+	0.775740i	$0.717377\pi$
$734$		−	712.728i		−	0.971019i
$735$	−424.368	+	475.913i	−0.577371	+	0.647500i
$736$	27.1293			0.0368605
$737$	−1053.48			−1.42942
$738$	567.122	−	499.775i	0.768458	−	0.677202i
$739$	−143.147			−0.193704			−0.0968519	−	0.995299i	$-0.530877\pi$
$739$	−143.147			−0.193704			−0.0968519	+	0.995299i	$0.530877\pi$
$740$	25.8455	−	82.3865i	0.0349264	−	0.111333i
$741$	174.454	+	78.7908i	0.235430	+	0.106330i
$742$			306.368i			0.412895i
$743$	−516.019			−0.694508			−0.347254	−	0.937771i	$-0.612886\pi$
$743$	−516.019			−0.694508			−0.347254	+	0.937771i	$0.612886\pi$
$744$	57.3004	−	126.871i	0.0770167	−	0.170526i
$745$	−36.8168	+	117.359i	−0.0494185	+	0.157529i
$746$			893.892i			1.19825i
$747$	−456.267	−	517.751i	−0.610800	−	0.693107i
$748$			1028.16i			1.37455i
$749$		−	66.1242i		−	0.0882833i
$750$	515.801	−	123.285i	0.687735	−	0.164380i
$751$	456.997			0.608518			0.304259	−	0.952589i	$-0.401591\pi$
$751$	456.997			0.608518			0.304259	+	0.952589i	$0.401591\pi$
$752$	−155.650			−0.206982
$753$	104.683	+	47.2791i	0.139021	+	0.0627876i
$754$	−463.165			−0.614277
$755$	−155.246	−	48.7024i	−0.205624	−	0.0645064i
$756$	−40.4121	−	131.508i	−0.0534551	−	0.173952i
$757$			1156.06i			1.52716i	0.645711	+	0.763582i	$0.276561\pi$
$757$			1156.06i			1.52716i	−0.645711	+	0.763582i	$0.723439\pi$
$758$	−802.499			−1.05871
$759$	208.083	+	93.9792i	0.274154	+	0.123820i
$760$	−36.4801	−	11.4442i	−0.0480001	−	0.0150582i
$761$		−	146.174i		−	0.192081i	−0.995377	−	0.0960405i	$-0.969382\pi$
$761$		−	146.174i		−	0.192081i	0.995377	−	0.0960405i	$-0.0306178\pi$
$762$	−348.310	−	157.312i	−0.457100	−	0.206446i
$763$		−	137.255i		−	0.179889i
$764$		−	47.3927i		−	0.0620323i
$765$	−592.242	−	1332.02i	−0.774173	−	1.74120i
$766$	107.391			0.140197
$767$	1858.32			2.42284
$768$	−19.7572	+	43.7453i	−0.0257256	+	0.0569600i
$769$	292.979			0.380986			0.190493	−	0.981689i	$-0.438991\pi$
$769$	292.979			0.380986			0.190493	+	0.981689i	$0.438991\pi$
$770$	−272.781	−	85.5745i	−0.354262	−	0.111136i
$771$	6.74977	−	14.9449i	0.00875457	−	0.0193838i
$772$			196.162i			0.254096i
$773$	43.2864			0.0559979			0.0279990	−	0.999608i	$-0.491086\pi$
$773$	43.2864			0.0559979			0.0279990	+	0.999608i	$0.491086\pi$
$774$	489.858	−	431.687i	0.632891	−	0.557735i
$775$	336.657	+	234.282i	0.434396	+	0.302300i
$776$		−	208.184i		−	0.268278i
$777$	27.1642	−	60.1454i	0.0349604	−	0.0774072i
$778$			305.987i			0.393300i
$779$		−	160.560i		−	0.206111i
$780$	528.470	+	471.233i	0.677525	+	0.604145i
$781$	−1407.01			−1.80154
$782$	219.709			0.280958
$783$	110.054	+	358.133i	0.140554	+	0.457386i
$784$	170.037			0.216883
$785$	−5.71127	+	18.2055i	−0.00727551	+	0.0231918i
$786$	−523.215	−	236.306i	−0.665668	−	0.300644i
$787$			117.711i			0.149569i	0.997200	+	0.0747845i	$0.0238269\pi$
$787$			117.711i			0.149569i	−0.997200	+	0.0747845i	$0.976173\pi$
$788$	632.084			0.802138
$789$	599.091	−	1326.47i	0.759305	−	1.68121i
$790$	−706.367	−	221.595i	−0.894136	−	0.280500i
$791$			211.072i			0.266843i
$792$	−303.078	+	267.087i	−0.382674	+	0.337231i
$793$			1625.63i			2.04997i
$794$			1023.30i			1.28879i
$795$	−848.863	+	951.968i	−1.06775	+	1.19744i
$796$	337.438			0.423918
$797$	−257.448			−0.323022			−0.161511	−	0.986871i	$-0.551637\pi$
$797$	−257.448			−0.323022			−0.161511	+	0.986871i	$0.551637\pi$
$798$	−26.6319	−	12.0281i	−0.0333733	−	0.0150728i
$799$	−1260.55			−1.57766
$800$	−116.080	−	80.7808i	−0.145099	−	0.100976i
$801$	514.780	−	453.650i	0.642672	−	0.566354i
$802$		−	365.754i		−	0.456052i
$803$	−590.306			−0.735126
$804$	−363.000	−	163.946i	−0.451493	−	0.203913i
$805$	−18.2865	+	58.2911i	−0.0227162	+	0.0724113i
$806$			547.604i			0.679409i
$807$	733.146	+	331.120i	0.908484	+	0.410310i
$808$		−	12.7745i		−	0.0158100i
$809$		−	454.140i		−	0.561360i	−0.959801	−	0.280680i	$-0.909440\pi$
$809$		−	454.140i		−	0.561360i	0.959801	−	0.280680i	$-0.0905600\pi$
$810$	238.801	−	520.600i	0.294816	−	0.642716i
$811$	−1201.93			−1.48204			−0.741018	−	0.671486i	$-0.765657\pi$
$811$	−1201.93			−1.48204			−0.741018	+	0.671486i	$0.765657\pi$
$812$	70.7061			0.0870765
$813$	−159.705	+	353.609i	−0.196439	+	0.434943i
$814$	−193.783			−0.238063
$815$	264.120	−	841.924i	0.324074	−	1.03304i
$816$	−160.006	+	354.276i	−0.196086	+	0.434161i
$817$		−	138.686i		−	0.169750i
$818$	564.634			0.690262
$819$	357.802	+	406.017i	0.436877	+	0.495748i
$820$	177.771	−	566.670i	0.216793	−	0.691061i
$821$		−	8.09816i		−	0.00986378i	−0.999988	−	0.00493189i	$-0.998430\pi$
$821$		−	8.09816i		−	0.00986378i	0.999988	−	0.00493189i	$-0.00156988\pi$
$822$	205.844	−	455.767i	0.250418	−	0.554461i
$823$			98.7169i			0.119948i	0.998200	+	0.0599738i	$0.0191017\pi$
$823$			98.7169i			0.119948i	−0.998200	+	0.0599738i	$0.980898\pi$
$824$		−	127.845i		−	0.155151i
$825$	−610.501	−	1021.71i	−0.740001	−	1.23843i
$826$	−283.689			−0.343449
$827$	−768.746			−0.929559			−0.464780	−	0.885426i	$-0.653866\pi$
$827$	−768.746			−0.929559			−0.464780	+	0.885426i	$0.653866\pi$
$828$	57.0742	+	64.7652i	0.0689302	+	0.0782188i
$829$	−292.269			−0.352556			−0.176278	−	0.984340i	$-0.556406\pi$
$829$	−292.269			−0.352556			−0.176278	+	0.984340i	$0.556406\pi$
$830$	−517.339	−	162.295i	−0.623300	−	0.195536i
$831$	1102.65	+	498.003i	1.32689	+	0.599281i
$832$		−	188.814i		−	0.226940i
$833$	1377.06			1.65313
$834$	−320.281	+	709.148i	−0.384030	+	0.850297i
$835$	−750.677	−	235.495i	−0.899015	−	0.282031i
$836$			85.8056i			0.102638i
$837$	423.424	−	130.118i	0.505883	−	0.155457i
$838$		−	632.178i		−	0.754389i
$839$		−	721.813i		−	0.860325i	−0.902751	−	0.430163i	$-0.858456\pi$
$839$		−	721.813i		−	0.860325i	0.902751	−	0.430163i	$-0.141544\pi$
$840$	−80.6755	−	71.9377i	−0.0960422	−	0.0856402i
$841$	648.447			0.771042
$842$	−385.763			−0.458151
$843$	−350.914	−	158.488i	−0.416268	−	0.188005i
$844$	337.959			0.400426
$845$	−1851.27	−	580.762i	−2.19085	−	0.687293i
$846$	−327.455	−	371.581i	−0.387063	−	0.439221i
$847$			333.341i			0.393555i
$848$	340.124			0.401090
$849$	961.439	+	434.227i	1.13244	+	0.511457i
$850$	−940.082	−	654.211i	−1.10598	−	0.769660i
$851$			41.4098i			0.0486602i
$852$	−484.815	−	218.963i	−0.569032	−	0.256999i
$853$		−	57.1658i		−	0.0670174i	−0.999438	−	0.0335087i	$-0.989332\pi$
$853$		−	57.1658i		−	0.0670174i	0.999438	−	0.0335087i	$-0.0106681\pi$
$854$		−	248.166i		−	0.290592i
$855$	−49.4258	−	111.164i	−0.0578080	−	0.130017i
$856$	−73.4097			−0.0857590
$857$	35.9851			0.0419896			0.0209948	−	0.999780i	$-0.493317\pi$
$857$	35.9851			0.0419896			0.0209948	+	0.999780i	$0.493317\pi$
$858$	654.076	−	1448.22i	0.762326	−	1.68790i
$859$	−1394.03			−1.62286			−0.811428	−	0.584453i	$-0.801309\pi$
$859$	−1394.03			−1.62286			−0.811428	+	0.584453i	$0.801309\pi$
$860$	153.551	−	489.468i	0.178548	−	0.569149i
$861$	186.841	−	413.691i	0.217004	−	0.480478i
$862$			617.840i			0.716752i
$863$	188.479			0.218400			0.109200	−	0.994020i	$-0.465171\pi$
$863$	188.479			0.218400			0.109200	+	0.994020i	$0.465171\pi$
$864$	−145.997	+	44.8647i	−0.168978	+	0.0519267i
$865$	−1186.97	−	372.364i	−1.37222	−	0.430479i
$866$			115.347i			0.133195i
$867$	−938.959	+	2078.99i	−1.08300	+	2.39791i
$868$		−	83.5965i		−	0.0963093i
$869$			1661.46i			1.91192i
$870$	219.703	+	195.907i	0.252532	+	0.225181i
$871$	1566.79			1.79884
$872$	−152.378			−0.174746
$873$	496.993	−	437.974i	0.569293	−	0.501688i
$874$	18.3359			0.0209793
$875$	251.812	−	194.963i	0.287785	−	0.222814i
$876$	−203.403	−	91.8654i	−0.232195	−	0.104869i
$877$		−	1178.69i		−	1.34400i	−0.740550	−	0.672001i	$-0.765435\pi$
$877$		−	1178.69i		−	1.34400i	0.740550	−	0.672001i	$-0.234565\pi$
$878$	649.864			0.740164
$879$	−304.994	+	675.298i	−0.346978	+	0.768258i
$880$	−95.0031	+	302.837i	−0.107958	+	0.344132i
$881$			231.820i			0.263133i	0.991307	+	0.131567i	$0.0420007\pi$
$881$			231.820i			0.263133i	−0.991307	+	0.131567i	$0.957999\pi$
$882$	357.720	+	405.924i	0.405578	+	0.460232i
$883$		−	52.4255i		−	0.0593721i	−0.999559	−	0.0296860i	$-0.990549\pi$
$883$		−	52.4255i		−	0.0593721i	0.999559	−	0.0296860i	$-0.00945075\pi$
$884$		−	1529.13i		−	1.72979i
$885$	−881.496	−	786.024i	−0.996041	−	0.888163i
$886$	−482.887			−0.545019
$887$	1387.44			1.56420			0.782098	−	0.623155i	$-0.214150\pi$
$887$	1387.44			1.56420			0.782098	+	0.623155i	$0.214150\pi$
$888$	−66.7722	−	30.1572i	−0.0751939	−	0.0339608i
$889$	−229.504			−0.258160
$890$	161.364	−	514.371i	0.181307	−	0.577944i
$891$	−1275.22	−	161.637i	−1.43122	−	0.181411i
$892$			513.034i			0.575151i
$893$	−105.200			−0.117805
$894$	95.1165	+	42.9587i	0.106394	+	0.0480522i
$895$	−166.215	+	529.836i	−0.185715	+	0.591995i
$896$			28.8241i			0.0321698i
$897$	−309.471	−	139.770i	−0.345007	−	0.155820i
$898$		−	73.1835i		−	0.0814961i
$899$			227.658i			0.253234i
$900$	−51.3603	−	447.059i	−0.0570670	−	0.496733i
$901$	2754.53			3.05719
$902$	−1332.88			−1.47769
$903$	161.386	−	357.331i	0.178722	−	0.395715i
$904$	234.328			0.259213
$905$	1046.73	+	328.370i	1.15661	+	0.362840i
$906$	−56.8270	+	125.823i	−0.0627230	+	0.138878i
$907$		−	456.201i		−	0.502978i	−0.967860	−	0.251489i	$-0.919080\pi$
$907$		−	456.201i		−	0.502978i	0.967860	−	0.251489i	$-0.0809203\pi$
$908$	638.026			0.702672
$909$	30.4962	−	26.8747i	0.0335491	−	0.0295651i
$910$	405.694	+	127.271i	0.445818	+	0.139858i
$911$		−	583.845i		−	0.640883i	−0.947268	−	0.320442i	$-0.896169\pi$
$911$		−	583.845i		−	0.640883i	0.947268	−	0.320442i	$-0.103831\pi$
$912$	−13.3534	+	29.5662i	−0.0146418	+	0.0324191i
$913$			1216.84i			1.33280i
$914$		−	578.095i		−	0.632489i
$915$	687.599	−	771.117i	0.751475	−	0.842751i
$916$	176.407			0.192584
$917$	−344.751			−0.375955
$918$	−1182.37	+	363.341i	−1.28799	+	0.395796i
$919$	87.9255			0.0956752			0.0478376	−	0.998855i	$-0.484767\pi$
$919$	87.9255			0.0956752			0.0478376	+	0.998855i	$0.484767\pi$
$920$	64.7136	+	20.3014i	0.0703409	+	0.0220667i
$921$	−881.191	−	397.983i	−0.956776	−	0.432121i
$922$			388.486i			0.421352i
$923$	2092.57			2.26714
$924$	−99.8503	+	221.083i	−0.108063	+	0.239267i
$925$	123.303	−	177.182i	0.133300	−	0.191548i
$926$			35.7798i			0.0386391i
$927$	305.201	−	268.958i	0.329235	−	0.290138i
$928$		−	78.4966i		−	0.0845868i
$929$			1379.83i			1.48529i	0.669685	+	0.742645i	$0.266429\pi$
$929$			1379.83i			1.48529i	−0.669685	+	0.742645i	$0.733571\pi$
$930$	231.623	−	259.756i	0.249057	−	0.279308i
$931$	114.923			0.123440
$932$	−884.732			−0.949283
$933$	539.351	+	243.594i	0.578083	+	0.261087i
$934$	1053.67			1.12813
$935$	−769.392	+	2452.55i	−0.822879	+	2.62305i
$936$	450.752	−	397.225i	0.481573	−	0.424386i
$937$			718.493i			0.766801i	0.923582	+	0.383400i	$0.125247\pi$
$937$			718.493i			0.766801i	−0.923582	+	0.383400i	$0.874753\pi$
$938$	−239.184			−0.254993
$939$	1482.25	+	669.445i	1.57854	+	0.712934i
$940$	−371.285	−	116.476i	−0.394984	−	0.123911i
$941$		−	451.724i		−	0.480047i	−0.970767	−	0.240023i	$-0.922845\pi$
$941$		−	451.724i		−	0.480047i	0.970767	−	0.240023i	$-0.0771551\pi$
$942$	14.7551	+	6.66405i	0.0156636	+	0.00707436i
$943$			284.825i			0.302041i
$944$			314.946i			0.333629i
$945$	2.01151	−	343.936i	0.00212858	−	0.363954i
$946$	−1151.29			−1.21701
$947$	−1844.99			−1.94825			−0.974126	−	0.226008i	$-0.927433\pi$
$947$	−1844.99			−1.94825			−0.974126	+	0.226008i	$0.927433\pi$
$948$	−258.562	+	572.493i	−0.272745	+	0.603895i
$949$	877.932			0.925113
$950$	−78.4549	−	54.5974i	−0.0825841	−	0.0574710i
$951$	118.557	−	262.501i	0.124665	−	0.276027i
$952$			233.435i			0.245205i
$953$	16.3417			0.0171477			0.00857384	−	0.999963i	$-0.497271\pi$
$953$	16.3417			0.0171477			0.00857384	+	0.999963i	$0.497271\pi$
$954$	715.548	+	811.970i	0.750050	+	0.851122i
$955$	35.4648	−	113.049i	0.0371359	−	0.118376i
$956$		−	139.216i		−	0.145624i
$957$	271.921	−	602.072i	0.284139	−	0.629124i
$958$		−	237.642i		−	0.248060i
$959$		−	300.309i		−	0.313148i
$960$	−79.8639	+	89.5643i	−0.0831915	+	0.0932961i
$961$	−691.839			−0.719915
$962$	288.204			0.299588
$963$	−154.438	−	175.249i	−0.160372	−	0.181983i
$964$	−75.7176			−0.0785452
$965$	−146.792	+	467.921i	−0.152116	+	0.484892i
$966$	47.2435	+	21.3372i	0.0489063	+	0.0220882i
$967$		−	489.265i		−	0.505961i	−0.967471	−	0.252981i	$-0.918589\pi$
$967$		−	489.265i		−	0.505961i	0.967471	−	0.252981i	$-0.0814109\pi$
$968$	370.069			0.382302
$969$	−108.143	+	239.445i	−0.111603	+	0.247105i
$970$	155.788	−	496.597i	0.160606	−	0.511956i
$971$		−	409.567i		−	0.421799i	−0.977508	−	0.210900i	$-0.932361\pi$
$971$		−	409.567i		−	0.421799i	0.977508	−	0.210900i	$-0.0676393\pi$
$972$	−414.251	−	254.150i	−0.426184	−	0.261471i
$973$			467.263i			0.480230i
$974$			362.448i			0.372123i
$975$	907.967	+	1519.53i	0.931248	+	1.55849i
$976$	−275.509			−0.282283
$977$	1697.21			1.73717			0.868584	−	0.495542i	$-0.165030\pi$
$977$	1697.21			1.73717			0.868584	+	0.495542i	$0.165030\pi$
$978$	−682.358	−	308.182i	−0.697708	−	0.315114i
$979$	−1209.86			−1.23581
$980$	405.601	+	127.241i	0.413879	+	0.129838i
$981$	−320.571	−	363.769i	−0.326780	−	0.370814i
$982$		−	893.572i		−	0.909951i
$983$	−122.701			−0.124823			−0.0624116	−	0.998050i	$-0.519879\pi$
$983$	−122.701			−0.124823			−0.0624116	+	0.998050i	$0.519879\pi$
$984$	−459.272	−	207.427i	−0.466740	−	0.210800i
$985$	1507.76	+	473.000i	1.53072	+	0.480203i
$986$		−	635.712i		−	0.644738i
$987$	−271.053	−	122.419i	−0.274623	−	0.124031i
$988$		−	127.614i		−	0.129164i
$989$			246.020i			0.248757i
$990$	−922.821	+	410.304i	−0.932142	+	0.414449i
$991$	−303.360			−0.306115			−0.153057	−	0.988217i	$-0.548912\pi$
$991$	−303.360			−0.306115			−0.153057	+	0.988217i	$0.548912\pi$
$992$	−92.8071			−0.0935556
$993$	−304.509	+	674.226i	−0.306656	+	0.678978i
$994$	−319.449			−0.321377
$995$	804.918	+	252.511i	0.808962	+	0.253780i
$996$	−189.369	+	419.290i	−0.190130	+	0.420974i
$997$			718.407i			0.720569i	0.932843	+	0.360284i	$0.117320\pi$
$997$			718.407i			0.720569i	−0.932843	+	0.360284i	$0.882680\pi$
$998$	−762.924			−0.764453
$999$	−68.4808	−	222.848i	−0.0685494	−	0.223071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.b.a.599.18	yes	88
3.2	odd	2	inner	690.3.b.a.599.72	yes	88
5.4	even	2	inner	690.3.b.a.599.71	yes	88
15.14	odd	2	inner	690.3.b.a.599.17	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.b.a.599.17	✓	88	15.14	odd	2	inner
690.3.b.a.599.18	yes	88	1.1	even	1	trivial
690.3.b.a.599.71	yes	88	5.4	even	2	inner
690.3.b.a.599.72	yes	88	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-1.23483 + 2.73408i) q^{3} +2.00000 q^{4} +(4.77075 + 1.49664i) q^{5} +(1.74631 - 3.86657i) q^{6} -2.54772i q^{7} -2.82843 q^{8} +(-5.95040 - 6.75224i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-1.23483 + 2.73408i) q^{3} +2.00000 q^{4} +(4.77075 + 1.49664i) q^{5} +(1.74631 - 3.86657i) q^{6} -2.54772i q^{7} -2.82843 q^{8} +(-5.95040 - 6.75224i) q^{9} +(-6.74686 - 2.11656i) q^{10} +15.8694i q^{11} +(-2.46966 + 5.46816i) q^{12} -23.6018i q^{13} +3.60302i q^{14} +(-9.98298 + 11.1955i) q^{15} +4.00000 q^{16} +32.3944 q^{17} +(8.41514 + 9.54911i) q^{18} +2.70349 q^{19} +(9.54151 + 2.99327i) q^{20} +(6.96567 + 3.14599i) q^{21} -22.4428i q^{22} -4.79583 q^{23} +(3.49262 - 7.73315i) q^{24} +(20.5202 + 14.2802i) q^{25} +33.3780i q^{26} +(25.8089 - 7.93103i) q^{27} -5.09544i q^{28} +13.8764i q^{29} +(14.1181 - 15.8329i) q^{30} +16.4061 q^{31} -5.65685 q^{32} +(-43.3883 - 19.5960i) q^{33} -45.8126 q^{34} +(3.81301 - 12.1545i) q^{35} +(-11.9008 - 13.5045i) q^{36} -8.63454i q^{37} -3.82331 q^{38} +(64.5293 + 29.1442i) q^{39} +(-13.4937 - 4.23313i) q^{40} -59.3900i q^{41} +(-9.85095 - 4.44911i) q^{42} -51.2988i q^{43} +31.7389i q^{44} +(-18.2822 - 41.1188i) q^{45} +6.78233 q^{46} -38.9126 q^{47} +(-4.93931 + 10.9363i) q^{48} +42.5091 q^{49} +(-29.0199 - 20.1952i) q^{50} +(-40.0015 + 88.5689i) q^{51} -47.2036i q^{52} +85.0310 q^{53} +(-36.4993 + 11.2162i) q^{54} +(-23.7508 + 75.7091i) q^{55} +7.20604i q^{56} +(-3.33834 + 7.39155i) q^{57} -19.6241i q^{58} +78.7364i q^{59} +(-19.9660 + 22.3911i) q^{60} -68.8771 q^{61} -23.2018 q^{62} +(-17.2028 + 15.1600i) q^{63} +8.00000 q^{64} +(35.3233 - 112.598i) q^{65} +(61.3604 + 27.7130i) q^{66} +66.3843i q^{67} +64.7888 q^{68} +(5.92203 - 13.1122i) q^{69} +(-5.39241 + 17.1891i) q^{70} +88.6614i q^{71} +(16.8303 + 19.0982i) q^{72} +37.1977i q^{73} +12.2111i q^{74} +(-64.3820 + 38.4702i) q^{75} +5.40697 q^{76} +40.4309 q^{77} +(-91.2581 - 41.2161i) q^{78} +104.696 q^{79} +(19.0830 + 5.98654i) q^{80} +(-10.1854 + 80.3571i) q^{81} +83.9902i q^{82} +76.6784 q^{83} +(13.9313 + 6.29199i) q^{84} +(154.546 + 48.4826i) q^{85} +72.5475i q^{86} +(-37.9391 - 17.1349i) q^{87} -44.8855i q^{88} +76.2385i q^{89} +(25.8550 + 58.1508i) q^{90} -60.1308 q^{91} -9.59166 q^{92} +(-20.2588 + 44.8557i) q^{93} +55.0308 q^{94} +(12.8977 + 4.04613i) q^{95} +(6.98524 - 15.4663i) q^{96} +73.6041i q^{97} -60.1170 q^{98} +(107.154 - 94.4295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 176 q^{4} + 8 q^{9}+O(q^{10}) \) 88 * q + 176 * q^4 + 8 * q^9	\( 88 q + 176 q^{4} + 8 q^{9} + 32 q^{10} - 12 q^{15} + 352 q^{16} - 16 q^{19} - 176 q^{21} + 72 q^{25} - 72 q^{30} + 32 q^{31} + 160 q^{34} + 16 q^{36} + 144 q^{39} + 64 q^{40} + 92 q^{45} - 360 q^{49} + 48 q^{51} - 144 q^{54} + 16 q^{55} - 24 q^{60} + 208 q^{61} + 704 q^{64} + 512 q^{66} + 304 q^{70} + 536 q^{75} - 32 q^{76} + 448 q^{79} - 24 q^{81} - 352 q^{84} - 96 q^{85} + 32 q^{90} - 64 q^{91} + 160 q^{94} + 296 q^{99}+O(q^{100}) \) 88 * q + 176 * q^4 + 8 * q^9 + 32 * q^10 - 12 * q^15 + 352 * q^16 - 16 * q^19 - 176 * q^21 + 72 * q^25 - 72 * q^30 + 32 * q^31 + 160 * q^34 + 16 * q^36 + 144 * q^39 + 64 * q^40 + 92 * q^45 - 360 * q^49 + 48 * q^51 - 144 * q^54 + 16 * q^55 - 24 * q^60 + 208 * q^61 + 704 * q^64 + 512 * q^66 + 304 * q^70 + 536 * q^75 - 32 * q^76 + 448 * q^79 - 24 * q^81 - 352 * q^84 - 96 * q^85 + 32 * q^90 - 64 * q^91 + 160 * q^94 + 296 * q^99

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