LMFDB - Embedded newform 36.4.h.b.23.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [36,4,Mod(11,36)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(36, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("36.11"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	36.h (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.12406876021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.11
Character	$\chi$	$=$	36.23
Dual form			36.4.h.b.11.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.66543 - 0.946295i) q^{2} +(-2.90476 - 4.30841i) q^{3} +(6.20905 - 5.04457i) q^{4} +(2.08666 + 1.20474i) q^{5} +(-11.8195 - 8.73501i) q^{6} +(2.30362 - 1.33000i) q^{7} +(11.7761 - 19.3216i) q^{8} +(-10.1248 + 25.0298i) q^{9} +(6.70190 + 1.23654i) q^{10} +(24.1428 + 41.8166i) q^{11} +(-39.7699 - 12.0979i) q^{12} +(-20.3570 + 35.2594i) q^{13} +(4.88158 - 5.72493i) q^{14} +(-0.870754 - 12.4897i) q^{15} +(13.1046 - 62.6440i) q^{16} +36.3729i q^{17} +(-3.30137 + 76.2961i) q^{18} -125.173i q^{19} +(19.0336 - 3.04606i) q^{20} +(-12.4216 - 6.06163i) q^{21} +(103.922 + 88.6131i) q^{22} +(-97.0560 + 168.106i) q^{23} +(-117.452 + 5.38796i) q^{24} +(-59.5972 - 103.225i) q^{25} +(-20.8944 + 113.245i) q^{26} +(137.248 - 29.0836i) q^{27} +(7.59405 - 19.8788i) q^{28} +(153.593 - 88.6772i) q^{29} +(-14.1399 - 32.4664i) q^{30} +(-152.058 - 87.7909i) q^{31} +(-24.3503 - 179.374i) q^{32} +(110.034 - 225.484i) q^{33} +(34.4195 + 96.9496i) q^{34} +6.40918 q^{35} +(63.3991 + 206.486i) q^{36} +199.364 q^{37} +(-118.451 - 333.641i) q^{38} +(211.044 - 14.7136i) q^{39} +(47.8502 - 26.1304i) q^{40} +(-201.816 - 116.518i) q^{41} +(-38.8451 - 4.40233i) q^{42} +(-252.553 + 145.812i) q^{43} +(360.851 + 137.851i) q^{44} +(-51.2813 + 40.0310i) q^{45} +(-99.6182 + 539.918i) q^{46} +(-30.9476 - 53.6029i) q^{47} +(-307.962 + 125.506i) q^{48} +(-167.962 + 290.919i) q^{49} +(-256.534 - 218.744i) q^{50} +(156.709 - 105.655i) q^{51} +(51.4707 + 321.620i) q^{52} +352.175i q^{53} +(338.305 - 207.398i) q^{54} +116.343i q^{55} +(1.43018 - 60.1718i) q^{56} +(-539.298 + 363.598i) q^{57} +(325.478 - 381.708i) q^{58} +(70.7911 - 122.614i) q^{59} +(-68.4116 - 73.1564i) q^{60} +(-7.71518 - 13.3631i) q^{61} +(-488.377 - 90.1086i) q^{62} +(9.96583 + 71.1251i) q^{63} +(-234.645 - 455.067i) q^{64} +(-84.9565 + 49.0496i) q^{65} +(79.9135 - 705.138i) q^{66} +(131.657 + 76.0120i) q^{67} +(183.486 + 225.841i) q^{68} +(1006.19 - 70.1497i) q^{69} +(17.0832 - 6.06498i) q^{70} +28.0331 q^{71} +(364.383 + 490.381i) q^{72} +124.499 q^{73} +(531.392 - 188.657i) q^{74} +(-271.622 + 556.614i) q^{75} +(-631.445 - 777.207i) q^{76} +(111.232 + 64.2199i) q^{77} +(548.600 - 238.928i) q^{78} +(648.411 - 374.360i) q^{79} +(102.814 - 114.929i) q^{80} +(-523.978 - 506.842i) q^{81} +(-648.187 - 119.595i) q^{82} +(-174.444 - 302.146i) q^{83} +(-107.705 + 25.0248i) q^{84} +(-43.8198 + 75.8981i) q^{85} +(-535.182 + 627.641i) q^{86} +(-828.210 - 404.158i) q^{87} +(1092.27 + 25.9614i) q^{88} -416.864i q^{89} +(-98.8056 + 155.227i) q^{90} +108.299i q^{91} +(245.397 + 1533.38i) q^{92} +(63.4532 + 910.140i) q^{93} +(-133.213 - 113.589i) q^{94} +(150.801 - 261.195i) q^{95} +(-702.085 + 625.949i) q^{96} +(-752.565 - 1303.48i) q^{97} +(-172.396 + 934.367i) q^{98} +(-1291.10 + 180.905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28}+ \cdots + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.66543	−	0.946295i	0.942372	−	0.334566i
$2$	2.66543	−	0.946295i	0.942372	−	0.334566i
$3$	−2.90476	−	4.30841i	−0.559021	−	0.829154i
$3$	−2.90476	−	4.30841i	−0.559021	−	0.829154i
$4$	6.20905	−	5.04457i	0.776131	−	0.630571i
$5$	2.08666	+	1.20474i	0.186637	+	0.107755i	0.590407	−	0.807106i	$-0.298967\pi$
$5$	2.08666	+	1.20474i	0.186637	+	0.107755i	−0.403770	+	0.914860i	$0.632301\pi$
$6$	−11.8195	−	8.73501i	−0.804212	−	0.594342i
$7$	2.30362	−	1.33000i	0.124384	−	0.0718131i	−0.436517	−	0.899696i	$-0.643788\pi$
$7$	2.30362	−	1.33000i	0.124384	−	0.0718131i	0.560901	+	0.827883i	$0.310455\pi$
$8$	11.7761	−	19.3216i	0.520437	−	0.853900i
$9$	−10.1248	+	25.0298i	−0.374992	+	0.927028i
$10$	6.70190	+	1.23654i	0.211933	+	0.0391029i
$11$	24.1428	+	41.8166i	0.661758	+	1.14620i	0.980153	+	0.198241i	$0.0635229\pi$
$11$	24.1428	+	41.8166i	0.661758	+	1.14620i	−0.318395	+	0.947958i	$0.603144\pi$
$12$	−39.7699	−	12.0979i	−0.956714	−	0.291030i
$13$	−20.3570	+	35.2594i	−0.434309	+	0.752245i	−0.997239	−	0.0742593i	$-0.976341\pi$
$13$	−20.3570	+	35.2594i	−0.434309	+	0.752245i	0.562930	+	0.826505i	$0.309674\pi$
$14$	4.88158	−	5.72493i	0.0931898	−	0.109289i
$15$	−0.870754	−	12.4897i	−0.0149885	−	0.214988i
$16$	13.1046	−	62.6440i	0.204759	−	0.978812i
$17$			36.3729i			0.518925i	0.965753	+	0.259463i	$0.0835455\pi$
$17$			36.3729i			0.518925i	−0.965753	+	0.259463i	$0.916455\pi$
$18$	−3.30137	+	76.2961i	−0.0432300	+	0.999065i
$19$		−	125.173i		−	1.51141i	−0.654914	−	0.755703i	$-0.727295\pi$
$19$		−	125.173i		−	1.51141i	0.654914	−	0.755703i	$-0.272705\pi$
$20$	19.0336	−	3.04606i	0.212802	−	0.0340560i
$21$	−12.4216	−	6.06163i	−0.129077	−	0.0629884i
$22$	103.922	+	88.6131i	1.00710	+	0.858745i
$23$	−97.0560	+	168.106i	−0.879894	+	1.52402i	−0.0284384	+	0.999596i	$0.509053\pi$
$23$	−97.0560	+	168.106i	−0.879894	+	1.52402i	−0.851456	+	0.524426i	$0.824280\pi$
$24$	−117.452	+	5.38796i	−0.998949	+	0.0458255i
$25$	−59.5972	−	103.225i	−0.476778	−	0.825803i
$26$	−20.8944	+	113.245i	−0.157605	+	0.854200i
$27$	137.248	−	29.0836i	0.978277	−	0.207302i
$28$	7.59405	−	19.8788i	0.0512550	−	0.134169i
$29$	153.593	−	88.6772i	0.983503	−	0.567826i	0.0801773	−	0.996781i	$-0.474451\pi$
$29$	153.593	−	88.6772i	0.983503	−	0.567826i	0.903326	+	0.428955i	$0.141118\pi$
$30$	−14.1399	−	32.4664i	−0.0860524	−	0.197584i
$31$	−152.058	−	87.7909i	−0.880983	−	0.508636i	−0.0100006	−	0.999950i	$-0.503183\pi$
$31$	−152.058	−	87.7909i	−0.880983	−	0.508636i	−0.870982	+	0.491314i	$0.836517\pi$
$32$	−24.3503	−	179.374i	−0.134518	−	0.990911i
$33$	110.034	−	225.484i	0.580439	−	1.18945i
$34$	34.4195	+	96.9496i	0.173615	+	0.489021i
$35$	6.40918			0.0309529
$36$	63.3991	+	206.486i	0.293514	+	0.955955i
$37$	199.364			0.885818			0.442909	−	0.896566i	$-0.353946\pi$
$37$	199.364			0.885818			0.442909	+	0.896566i	$0.353946\pi$
$38$	−118.451	−	333.641i	−0.505665	−	1.42431i
$39$	211.044	−	14.7136i	0.866515	−	0.0604117i
$40$	47.8502	−	26.1304i	0.189145	−	0.103290i
$41$	−201.816	−	116.518i	−0.768740	−	0.443832i	0.0636849	−	0.997970i	$-0.479715\pi$
$41$	−201.816	−	116.518i	−0.768740	−	0.443832i	−0.832425	+	0.554138i	$0.813048\pi$
$42$	−38.8451	−	4.40233i	−0.142713	−	0.0161737i
$43$	−252.553	+	145.812i	−0.895674	+	0.517118i	−0.875794	−	0.482685i	$-0.839662\pi$
$43$	−252.553	+	145.812i	−0.895674	+	0.517118i	−0.0198798	+	0.999802i	$0.506328\pi$
$44$	360.851	+	137.851i	1.23637	+	0.472315i
$45$	−51.2813	+	40.0310i	−0.169879	+	0.132610i
$46$	−99.6182	+	539.918i	−0.319302	+	1.73058i
$47$	−30.9476	−	53.6029i	−0.0960463	−	0.166357i	0.813998	−	0.580867i	$-0.197286\pi$
$47$	−30.9476	−	53.6029i	−0.0960463	−	0.166357i	−0.910045	+	0.414510i	$0.863953\pi$
$48$	−307.962	+	125.506i	−0.926051	+	0.377399i
$49$	−167.962	+	290.919i	−0.489686	+	0.848161i
$50$	−256.534	−	218.744i	−0.725588	−	0.618701i
$51$	156.709	−	105.655i	0.430269	−	0.290090i
$52$	51.4707	+	321.620i	0.137264	+	0.857704i
$53$			352.175i			0.912735i	0.889791	+	0.456367i	$0.150850\pi$
$53$			352.175i			0.912735i	−0.889791	+	0.456367i	$0.849150\pi$
$54$	338.305	−	207.398i	0.852545	−	0.522654i
$55$			116.343i			0.285231i
$56$	1.43018	−	60.1718i	0.00341278	−	0.143586i
$57$	−539.298	+	363.598i	−1.25319	+	0.844907i
$58$	325.478	−	381.708i	0.736851	−	0.864150i
$59$	70.7911	−	122.614i	0.156207	−	0.270559i	−0.777291	−	0.629141i	$-0.783407\pi$
$59$	70.7911	−	122.614i	0.156207	−	0.270559i	0.933498	+	0.358583i	$0.116740\pi$
$60$	−68.4116	−	73.1564i	−0.147198	−	0.157407i
$61$	−7.71518	−	13.3631i	−0.0161939	−	0.0280486i	0.857815	−	0.513959i	$-0.171822\pi$
$61$	−7.71518	−	13.3631i	−0.0161939	−	0.0280486i	−0.874009	+	0.485910i	$0.838488\pi$
$62$	−488.377	−	90.1086i	−1.00039	−	0.184577i
$63$	9.96583	+	71.1251i	0.0199298	+	0.142237i
$64$	−234.645	−	455.067i	−0.458291	−	0.888802i
$65$	−84.9565	+	49.0496i	−0.162116	+	0.0935978i
$66$	79.9135	−	705.138i	0.149041	−	1.31510i
$67$	131.657	+	76.0120i	0.240066	+	0.138602i	0.615207	−	0.788366i	$-0.289072\pi$
$67$	131.657	+	76.0120i	0.240066	+	0.138602i	−0.375141	+	0.926968i	$0.622406\pi$
$68$	183.486	+	225.841i	0.327220	+	0.402754i
$69$	1006.19	−	70.1497i	1.75553	−	0.122392i
$70$	17.0832	−	6.06498i	0.0291691	−	0.0103558i
$71$	28.0331			0.0468580			0.0234290	−	0.999726i	$-0.492542\pi$
$71$	28.0331			0.0468580			0.0234290	+	0.999726i	$0.492542\pi$
$72$	364.383	+	490.381i	0.596430	+	0.802665i
$73$	124.499			0.199609			0.0998047	−	0.995007i	$-0.468178\pi$
$73$	124.499			0.199609			0.0998047	+	0.995007i	$0.468178\pi$
$74$	531.392	−	188.657i	0.834771	−	0.296365i
$75$	−271.622	+	556.614i	−0.418189	+	0.856963i
$76$	−631.445	−	777.207i	−0.953049	−	1.17305i
$77$	111.232	+	64.2199i	0.164624	+	0.0950459i
$78$	548.600	−	238.928i	0.796368	−	0.346837i
$79$	648.411	−	374.360i	0.923443	−	0.533150i	0.0387108	−	0.999250i	$-0.487675\pi$
$79$	648.411	−	374.360i	0.923443	−	0.533150i	0.884732	+	0.466101i	$0.154342\pi$
$80$	102.814	−	114.929i	0.143687	−	0.160619i
$81$	−523.978	−	506.842i	−0.718762	−	0.695256i
$82$	−648.187	−	119.595i	−0.872931	−	0.161061i
$83$	−174.444	−	302.146i	−0.230695	−	0.399576i	0.727318	−	0.686301i	$-0.240767\pi$
$83$	−174.444	−	302.146i	−0.230695	−	0.399576i	−0.958013	+	0.286725i	$0.907433\pi$
$84$	−107.705	+	25.0248i	−0.139900	+	0.0325052i
$85$	−43.8198	+	75.8981i	−0.0559167	+	0.0968506i
$86$	−535.182	+	627.641i	−0.671048	+	0.786979i
$87$	−828.210	−	404.158i	−1.02061	−	0.498049i
$88$	1092.27	+	25.9614i	1.32314	+	0.0314488i
$89$		−	416.864i		−	0.496488i	−0.968698	−	0.248244i	$-0.920146\pi$
$89$		−	416.864i		−	0.496488i	0.968698	−	0.248244i	$-0.0798535\pi$
$90$	−98.8056	+	155.227i	−0.115722	+	0.181804i
$91$			108.299i			0.124756i
$92$	245.397	+	1533.38i	0.278091	+	1.73768i
$93$	63.4532	+	910.140i	0.0707504	+	1.01481i
$94$	−133.213	−	113.589i	−0.146169	−	0.124637i
$95$	150.801	−	261.195i	0.162861	−	0.282084i
$96$	−702.085	+	625.949i	−0.746420	+	0.665476i
$97$	−752.565	−	1303.48i	−0.787747	−	1.36442i	−0.927344	−	0.374209i	$-0.877914\pi$
$97$	−752.565	−	1303.48i	−0.787747	−	1.36442i	0.139598	−	0.990208i	$-0.455419\pi$
$98$	−172.396	+	934.367i	−0.177701	+	0.963115i
$99$	−1291.10	+	180.905i	−1.31071	+	0.183653i
$100$	−890.770	−	340.289i	−0.890770	−	0.340289i
$101$	377.088	−	217.712i	0.371502	−	0.214487i	−0.302613	−	0.953114i	$-0.597859\pi$
$101$	377.088	−	217.712i	0.371502	−	0.214487i	0.674114	+	0.738627i	$0.264526\pi$
$102$	317.718	−	429.908i	0.308419	−	0.417326i
$103$	1511.52	+	872.679i	1.44597	+	0.834831i	0.998238	−	0.0593366i	$-0.0188985\pi$
$103$	1511.52	+	872.679i	1.44597	+	0.834831i	0.447732	+	0.894168i	$0.352232\pi$
$104$	441.539	+	808.548i	0.416312	+	0.762353i
$105$	−18.6171	−	27.6134i	−0.0173033	−	0.0256647i
$106$	333.261	+	938.698i	0.305370	+	0.860136i
$107$	783.805			0.708161			0.354081	−	0.935215i	$-0.384794\pi$
$107$	783.805			0.708161			0.354081	+	0.935215i	$0.384794\pi$
$108$	705.468	−	872.941i	0.628553	−	0.777767i
$109$	1581.89			1.39007			0.695035	−	0.718976i	$-0.255389\pi$
$109$	1581.89			1.39007			0.695035	+	0.718976i	$0.255389\pi$
$110$	110.095	+	310.104i	0.0954285	+	0.268794i
$111$	−579.105	−	858.943i	−0.495191	−	0.734480i
$112$	−53.1283	−	161.737i	−0.0448228	−	0.136453i
$113$	−384.367	−	221.914i	−0.319984	−	0.184743i	0.331401	−	0.943490i	$-0.392479\pi$
$113$	−384.367	−	221.914i	−0.319984	−	0.184743i	−0.651386	+	0.758747i	$0.725812\pi$
$114$	−1093.39	+	1479.48i	−0.898293	+	1.21549i
$115$	−405.046	+	233.854i	−0.328442	+	0.189626i
$116$	506.331	−	1325.41i	0.405273	−	1.06088i
$117$	−676.423	−	866.524i	−0.534490	−	0.684703i
$118$	72.6600	−	393.808i	0.0566855	−	0.307228i
$119$	48.3759	+	83.7895i	0.0372657	+	0.0645460i
$120$	−251.574	−	130.256i	−0.191379	−	0.0990889i
$121$	−500.254	+	866.466i	−0.375848	+	0.650989i
$122$	−33.2097	−	28.3175i	−0.0246448	−	0.0210143i
$123$	84.2167	+	1207.96i	0.0617363	+	0.885515i
$124$	−1387.00	+	221.971i	−1.00449	+	0.160755i
$125$		−	588.380i		−	0.421010i
$126$	93.8686	+	180.148i	0.0663689	+	0.127372i
$127$			425.829i			0.297529i	0.988873	+	0.148765i	$0.0475297\pi$
$127$			425.829i			0.297529i	−0.988873	+	0.148765i	$0.952470\pi$
$128$	−1056.06	−	990.906i	−0.729244	−	0.684254i
$129$	1361.82	+	664.555i	0.929470	+	0.453572i
$130$	−180.030	+	211.132i	−0.121459	+	0.142443i
$131$	871.836	−	1510.06i	0.581471	−	1.00714i	−0.413835	−	0.910352i	$-0.635811\pi$
$131$	871.836	−	1510.06i	0.581471	−	1.00714i	0.995305	−	0.0967846i	$-0.0308558\pi$
$132$	−454.265	−	1955.12i	−0.299535	−	1.28918i
$133$	−166.480	−	288.352i	−0.108539	−	0.187995i
$134$	422.851	+	78.0187i	0.272603	+	0.0502969i
$135$	321.430	+	104.660i	0.204920	+	0.0667239i
$136$	702.782	+	428.333i	0.443110	+	0.270068i
$137$	−1274.32	+	735.731i	−0.794692	+	0.458816i	−0.841612	−	0.540083i	$-0.818393\pi$
$137$	−1274.32	+	735.731i	−0.794692	+	0.458816i	0.0469195	+	0.998899i	$0.485060\pi$
$138$	2615.56	−	1139.13i	1.61341	−	0.702678i
$139$	−1107.04	−	639.151i	−0.675526	−	0.390015i	0.122641	−	0.992451i	$-0.460864\pi$
$139$	−1107.04	−	639.151i	−0.675526	−	0.390015i	−0.798167	+	0.602436i	$0.794197\pi$
$140$	39.7949	−	32.3316i	0.0240235	−	0.0195180i
$141$	−141.048	+	289.038i	−0.0842438	+	0.172634i
$142$	74.7204	−	26.5276i	0.0441577	−	0.0156771i
$143$	−1965.90			−1.14963
$144$	1435.28	+	962.262i	0.830603	+	0.556865i
$145$	427.331			0.244744
$146$	331.843	−	117.813i	0.188106	−	0.0667825i
$147$	1741.29	−	121.399i	0.977000	−	0.0681145i
$148$	1237.86	−	1005.71i	0.687511	−	0.558572i
$149$	1861.15	+	1074.53i	1.02330	+	0.590800i	0.915057	−	0.403325i	$-0.132146\pi$
$149$	1861.15	+	1074.53i	1.02330	+	0.590800i	0.108239	+	0.994125i	$0.465479\pi$
$150$	−197.269	+	1740.65i	−0.107379	+	0.947490i
$151$	−828.626	+	478.407i	−0.446574	+	0.257829i	−0.706382	−	0.707831i	$-0.749674\pi$
$151$	−828.626	+	478.407i	−0.446574	+	0.257829i	0.259808	+	0.965660i	$0.416341\pi$
$152$	−2418.54	−	1474.06i	−1.29059	−	0.786592i
$153$	−910.406	−	368.268i	−0.481058	−	0.194593i
$154$	357.252	+	65.9152i	0.186936	+	0.0344909i
$155$	−211.530	−	366.380i	−0.109616	−	0.189860i
$156$	1236.16	−	1155.98i	0.634435	−	0.593287i
$157$	−1046.60	+	1812.77i	−0.532024	+	0.921493i	0.467277	+	0.884111i	$0.345235\pi$
$157$	−1046.60	+	1812.77i	−0.532024	+	0.921493i	−0.999301	+	0.0373822i	$0.988098\pi$
$158$	1374.04	−	1611.42i	0.691853	−	0.811378i
$159$	1517.31	−	1022.98i	0.756798	−	0.510238i
$160$	165.288	−	403.629i	0.0816696	−	0.199436i
$161$			516.337i			0.252752i
$162$	−1876.25	−	855.114i	−0.909951	−	0.414717i
$163$		−	1468.60i		−	0.705703i	−0.935679	−	0.352851i	$-0.885212\pi$
$163$		−	1468.60i		−	0.705703i	0.935679	−	0.352851i	$-0.114788\pi$
$164$	−1840.87	+	294.606i	−0.876511	+	0.140273i
$165$	501.253	−	337.948i	0.236500	−	0.159450i
$166$	−750.887	−	640.273i	−0.351085	−	0.299366i
$167$	−1524.19	+	2639.98i	−0.706261	+	1.22328i	0.259974	+	0.965616i	$0.416286\pi$
$167$	−1524.19	+	2639.98i	−0.706261	+	1.22328i	−0.966235	+	0.257664i	$0.917047\pi$
$168$	−263.399	+	168.623i	−0.120962	+	0.0774376i
$169$	269.685	+	467.108i	0.122751	+	0.212612i
$170$	−44.9766	+	243.768i	−0.0202915	+	0.109977i
$171$	3133.06	+	1267.35i	1.40112	+	0.566765i
$172$	−832.558	+	2179.37i	−0.369081	+	0.966137i
$173$	−2403.71	+	1387.79i	−1.05636	+	0.609892i	−0.924424	−	0.381365i	$-0.875454\pi$
$173$	−2403.71	+	1387.79i	−1.05636	+	0.609892i	−0.131940	+	0.991258i	$0.542121\pi$
$174$	−2589.99	−	293.524i	−1.12843	−	0.127885i
$175$	−274.579	−	158.528i	−0.118607	−	0.0684778i
$176$	2935.94	−	964.414i	1.25742	−	0.413042i
$177$	−733.901	+	51.1661i	−0.311658	+	0.0217281i
$178$	−394.476	−	1111.12i	−0.166108	−	0.467877i
$179$	477.618			0.199435			0.0997174	−	0.995016i	$-0.468206\pi$
$179$	477.618			0.199435			0.0997174	+	0.995016i	$0.468206\pi$
$180$	−116.469	+	507.247i	−0.0482281	+	0.210044i
$181$	−732.350			−0.300747			−0.150373	−	0.988629i	$-0.548048\pi$
$181$	−732.350			−0.300747			−0.150373	+	0.988629i	$0.548048\pi$
$182$	102.483	+	288.664i	0.0417392	+	0.117567i
$183$	−35.1629	+	72.0566i	−0.0142039	+	0.0291070i
$184$	2105.12	+	3854.91i	0.843433	+	1.54450i
$185$	416.006	+	240.181i	0.165326	+	0.0954512i
$186$	1030.39	+	2365.87i	0.406193	+	0.932657i
$187$	−1520.99	+	878.146i	−0.594792	+	0.343403i
$188$	−462.559	−	176.705i	−0.179445	−	0.0685509i
$189$	277.488	−	249.538i	0.106795	−	0.0960381i
$190$	154.782	−	838.898i	0.0591003	−	0.320316i
$191$	1543.00	+	2672.55i	0.584542	+	1.01246i	0.994932	+	0.100546i	$0.0320590\pi$
$191$	1543.00	+	2672.55i	0.584542	+	1.01246i	−0.410391	+	0.911910i	$0.634608\pi$
$192$	−1279.03	+	2332.80i	−0.480760	+	0.876852i
$193$	817.160	−	1415.36i	0.304769	−	0.527876i	−0.672441	−	0.740151i	$-0.734754\pi$
$193$	817.160	−	1415.36i	0.304769	−	0.527876i	0.977210	+	0.212275i	$0.0680873\pi$
$194$	−3239.39	−	2762.19i	−1.19884	−	1.02224i
$195$	458.104	+	223.550i	0.168233	+	0.0820961i
$196$	424.676	+	2653.63i	0.154765	+	0.967066i
$197$		−	3350.67i		−	1.21181i	−0.795539	−	0.605903i	$-0.792812\pi$
$197$		−	3350.67i		−	1.21181i	0.795539	−	0.605903i	$-0.207188\pi$
$198$	−3270.15	+	1703.95i	−1.17374	+	0.611590i
$199$		−	1046.61i		−	0.372826i	−0.982471	−	0.186413i	$-0.940314\pi$
$199$		−	1046.61i		−	0.372826i	0.982471	−	0.186413i	$-0.0596863\pi$
$200$	−2696.30	−	64.0864i	−0.953286	−	0.0226580i
$201$	−54.9396	−	788.027i	−0.0192793	−	0.276533i
$202$	799.083	−	937.133i	0.278333	−	0.326418i
$203$	235.881	−	408.558i	0.0815547	−	0.141257i
$204$	440.035	−	1446.55i	0.151023	−	0.496463i
$205$	−280.748	−	486.270i	−0.0956502	−	0.165671i
$206$	4854.68	+	895.718i	1.64195	+	0.302950i
$207$	−3224.98	−	4131.32i	−1.08286	−	1.38718i
$208$	1942.02	+	1737.30i	0.647378	+	0.579136i
$209$	5234.33	−	3022.04i	1.73237	−	1.00019i
$210$	−75.7531	−	55.9843i	−0.0248927	−	0.0183966i
$211$	−4570.77	−	2638.94i	−1.49130	−	0.861004i	−0.491352	−	0.870961i	$-0.663497\pi$
$211$	−4570.77	−	2638.94i	−1.49130	−	0.861004i	−0.999950	+	0.00995667i	$0.996831\pi$
$212$	1776.57	+	2186.67i	0.575544	+	0.708402i
$213$	−81.4294	−	120.778i	−0.0261946	−	0.0388525i
$214$	2089.18	−	741.711i	0.667352	−	0.236927i
$215$	−702.658			−0.222888
$216$	1054.32	−	2994.35i	0.332116	−	0.943238i
$217$	−467.047			−0.146107
$218$	4216.42	−	1496.94i	1.30996	−	0.465070i
$219$	−361.639	−	536.392i	−0.111586	−	0.165507i
$220$	586.901	+	722.380i	0.179858	+	0.221377i
$221$	−1282.49	−	740.444i	−0.390359	−	0.225374i
$222$	−2356.38	−	1741.45i	−0.712386	−	0.526479i
$223$	4122.02	−	2379.85i	1.23781	−	0.714648i	0.269161	−	0.963095i	$-0.413254\pi$
$223$	4122.02	−	2379.85i	1.23781	−	0.714648i	0.968645	+	0.248447i	$0.0799202\pi$
$224$	−294.661	−	380.824i	−0.0878923	−	0.113593i
$225$	3187.12	−	446.569i	0.944331	−	0.132317i
$226$	−1234.50	−	227.773i	−0.363353	−	0.0670409i
$227$	1115.23	+	1931.63i	0.326080	+	0.564788i	0.981730	−	0.190277i	$-0.0609387\pi$
$227$	1115.23	+	1931.63i	0.326080	+	0.564788i	−0.655650	+	0.755065i	$0.727605\pi$
$228$	−1514.33	+	4978.12i	−0.439864	+	1.44598i
$229$	2917.29	−	5052.89i	0.841833	−	1.45810i	−0.0465095	−	0.998918i	$-0.514810\pi$
$229$	2917.29	−	5052.89i	0.841833	−	1.45810i	0.888343	−	0.459181i	$-0.151857\pi$
$230$	−858.329	+	1006.61i	−0.246072	+	0.288583i
$231$	−46.4166	−	665.776i	−0.0132207	−	0.189631i
$232$	95.3568	−	4011.94i	0.0269848	−	1.13533i
$233$			3080.09i			0.866022i	0.901389	+	0.433011i	$0.142549\pi$
$233$			3080.09i			0.866022i	−0.901389	+	0.433011i	$0.857451\pi$
$234$	−2622.95	−	1669.57i	−0.732767	−	0.466423i
$235$		−	149.135i		−	0.0413978i
$236$	−178.988	−	1118.43i	−0.0493693	−	0.308489i
$237$	−3496.37	−	1706.20i	−0.958287	−	0.467634i
$238$	208.232	+	177.557i	0.0567130	+	0.0483586i
$239$	−2645.73	+	4582.53i	−0.716058	+	1.24025i	0.246492	+	0.969145i	$0.420722\pi$
$239$	−2645.73	+	4582.53i	−0.716058	+	1.24025i	−0.962550	+	0.271104i	$0.912611\pi$
$240$	−793.813	−	109.125i	−0.213502	−	0.0293499i
$241$	2501.61	+	4332.91i	0.668642	+	1.15812i	0.978284	+	0.207268i	$0.0664573\pi$
$241$	2501.61	+	4332.91i	0.668642	+	1.15812i	−0.309642	+	0.950853i	$0.600209\pi$
$242$	−513.461	+	2782.89i	−0.136391	+	0.739220i
$243$	−661.654	+	3729.76i	−0.174671	+	0.984627i
$244$	−115.315	−	44.0523i	−0.0302553	−	0.0115580i
$245$	−700.961	+	404.700i	−0.182787	+	0.105532i
$246$	1367.56	+	3140.05i	0.354442	+	0.813830i
$247$	4413.53	+	2548.15i	1.13695	+	0.656417i
$248$	−3486.92	+	1904.16i	−0.892820	+	0.487559i
$249$	−795.050	+	1629.23i	−0.202346	+	0.414653i
$250$	−556.781	−	1568.29i	−0.140856	−	0.396748i
$251$	2577.68			0.648215			0.324107	−	0.946020i	$-0.394936\pi$
$251$	2577.68			0.648215			0.324107	+	0.946020i	$0.394936\pi$
$252$	420.674	+	391.346i	0.105159	+	0.0978272i
$253$	−9372.83			−2.32911
$254$	402.960	+	1135.02i	0.0995432	+	0.280383i
$255$	454.286	−	31.6719i	0.111563	−	0.00777792i
$256$	−3752.54	−	1641.85i	−0.916147	−	0.400842i
$257$	−753.933	−	435.283i	−0.182992	−	0.105651i	0.405705	−	0.914004i	$-0.367026\pi$
$257$	−753.933	−	435.283i	−0.182992	−	0.105651i	−0.588698	+	0.808353i	$0.700359\pi$
$258$	4258.71	+	482.641i	1.02766	+	0.116465i
$259$	459.260	−	265.154i	0.110182	−	0.0636134i
$260$	−280.065	+	733.121i	−0.0668033	+	0.174870i
$261$	664.469	+	4742.25i	0.157585	+	1.12467i
$262$	894.852	−	4849.99i	0.211008	−	1.14364i
$263$	−2155.19	−	3732.90i	−0.505304	−	0.875212i	−0.999981	−	0.00613515i	$-0.998047\pi$
$263$	−2155.19	−	3732.90i	−0.505304	−	0.875212i	0.494677	−	0.869077i	$-0.335286\pi$
$264$	−3060.93	−	4781.37i	−0.713588	−	1.11467i
$265$	−424.278	+	734.871i	−0.0983516	+	0.170350i
$266$	−716.608	−	611.043i	−0.165181	−	0.140848i
$267$	−1796.02	+	1210.89i	−0.411665	+	0.277547i
$268$	1200.91	−	192.189i	0.273721	−	0.0438052i
$269$			5603.52i			1.27008i	0.772478	+	0.635042i	$0.219017\pi$
$269$			5603.52i			1.27008i	−0.772478	+	0.635042i	$0.780983\pi$
$270$	955.788	−	25.2022i	0.215435	−	0.00568058i
$271$			2149.22i			0.481756i	0.970555	+	0.240878i	$0.0774353\pi$
$271$			2149.22i			0.481756i	−0.970555	+	0.240878i	$0.922565\pi$
$272$	2278.55	+	476.653i	0.507931	+	0.106255i
$273$	466.597	−	314.582i	0.103442	−	0.0697414i
$274$	−2700.40	+	3166.93i	−0.595392	+	0.698252i
$275$	2877.69	−	4984.31i	0.631023	−	1.09296i
$276$	5893.63	−	5511.37i	1.28534	−	1.20198i
$277$	1604.99	+	2779.93i	0.348140	+	0.602995i	0.985919	−	0.167224i	$-0.0534802\pi$
$277$	1604.99	+	2779.93i	0.348140	+	0.602995i	−0.637779	+	0.770219i	$0.720147\pi$
$278$	−3555.57	−	656.025i	−0.767083	−	0.141531i
$279$	3736.94	−	2917.12i	0.801881	−	0.625962i
$280$	75.4755	−	123.835i	0.0161090	−	0.0264306i
$281$	−814.389	+	470.188i	−0.172891	+	0.0998187i	−0.583948	−	0.811791i	$-0.698493\pi$
$281$	−814.389	+	470.188i	−0.172891	+	0.0998187i	0.411057	+	0.911610i	$0.365160\pi$
$282$	−102.438	+	903.885i	−0.0216315	+	0.190871i
$283$	−1775.44	−	1025.05i	−0.372929	−	0.215310i	0.301809	−	0.953369i	$-0.402410\pi$
$283$	−1775.44	−	1025.05i	−0.372929	−	0.215310i	−0.674737	+	0.738058i	$0.735743\pi$
$284$	174.059	−	141.415i	0.0363680	−	0.0295473i
$285$	−1563.37	+	108.995i	−0.324934	+	0.0226537i
$286$	−5239.98	+	1860.33i	−1.08338	+	0.384627i
$287$	−619.877			−0.127492
$288$	4736.23	+	1206.64i	0.969046	+	0.246882i
$289$	3590.01			0.730716
$290$	1139.02	−	404.381i	0.230640	−	0.0818830i
$291$	−3429.91	+	7028.65i	−0.690945	+	1.41590i
$292$	773.020	−	628.043i	0.154923	−	0.125868i
$293$	−3842.30	−	2218.35i	−0.766108	−	0.442312i	0.0653767	−	0.997861i	$-0.479175\pi$
$293$	−3842.30	−	2218.35i	−0.766108	−	0.442312i	−0.831484	+	0.555548i	$0.812508\pi$
$294$	4526.40	−	1971.35i	0.897909	−	0.391060i
$295$	295.434	−	170.569i	0.0583080	−	0.0336641i
$296$	2347.74	−	3852.03i	0.461013	−	0.756400i
$297$	4529.75	+	5037.11i	0.884992	+	0.984117i
$298$	5977.58	+	1102.90i	1.16199	+	0.214394i
$299$	−3951.54	−	6844.26i	−0.764292	−	1.32379i
$300$	1121.36	+	4826.26i	0.215807	+	0.928814i
$301$	−387.858	+	671.790i	−0.0742716	+	0.128642i
$302$	−1755.93	+	2059.29i	−0.334578	+	0.392380i
$303$	−2033.34	−	992.250i	−0.385519	−	0.188130i
$304$	−7841.35	−	1640.35i	−1.47938	−	0.309475i
$305$		−	37.1790i		−	0.00697988i
$306$	−2775.11	−	120.080i	−0.518440	−	0.0224332i
$307$			7392.80i			1.37436i	0.726486	+	0.687181i	$0.241152\pi$
$307$			7392.80i			1.37436i	−0.726486	+	0.687181i	$0.758848\pi$
$308$	1014.61	−	162.374i	0.187703	−	0.0300393i
$309$	−630.751	−	9047.19i	−0.116124	−	1.66562i
$310$	−910.522	−	776.392i	−0.166820	−	0.142245i
$311$	2448.25	−	4240.50i	0.446391	−	0.773172i	−0.551757	−	0.834005i	$-0.686042\pi$
$311$	2448.25	−	4240.50i	0.446391	−	0.773172i	0.998148	+	0.0608332i	$0.0193758\pi$
$312$	2200.99	−	4250.97i	0.399381	−	0.771357i
$313$	−340.861	−	590.388i	−0.0615546	−	0.106616i	0.833606	−	0.552360i	$-0.186273\pi$
$313$	−340.861	−	590.388i	−0.0615546	−	0.106616i	−0.895160	+	0.445744i	$0.852939\pi$
$314$	−1074.23	+	5822.20i	−0.193065	+	1.04639i
$315$	−64.8916	+	160.420i	−0.0116071	+	0.0286942i
$316$	2137.53	−	5595.38i	0.380524	−	0.996091i
$317$	1344.13	−	776.034i	0.238151	−	0.137497i	−0.376176	−	0.926548i	$-0.622761\pi$
$317$	1344.13	−	776.034i	0.238151	−	0.137497i	0.614327	+	0.789052i	$0.289428\pi$
$318$	3076.25	−	4162.52i	0.542477	−	0.734032i
$319$	7416.37	+	4281.84i	1.30168	+	0.751527i
$320$	58.6103	−	1232.26i	0.0102388	−	0.215266i
$321$	−2276.76	−	3376.95i	−0.395877	−	0.587175i
$322$	488.607	+	1376.26i	0.0845621	+	0.238186i
$323$	4552.92			0.784307
$324$	−5810.20	−	503.763i	−0.996262	−	0.0863792i
$325$	4852.88			0.828276
$326$	−1389.73	−	3914.45i	−0.236104	−	0.665035i
$327$	−4595.01	−	6815.43i	−0.777078	−	1.15258i
$328$	−4627.93	+	2527.26i	−0.779069	+	0.425441i
$329$	−142.583	−	82.3206i	−0.0238932	−	0.0137948i
$330$	1016.26	−	1375.11i	0.169525	−	0.229386i
$331$	−6410.22	+	3700.94i	−1.06446	+	0.614569i	−0.926664	−	0.375891i	$-0.877337\pi$
$331$	−6410.22	+	3700.94i	−1.06446	+	0.614569i	−0.137801	+	0.990460i	$0.544003\pi$
$332$	−2607.33	−	996.043i	−0.431011	−	0.164653i
$333$	−2018.52	+	4990.04i	−0.332175	+	0.821178i
$334$	−1564.43	+	8479.02i	−0.256293	+	1.38908i
$335$	183.149	+	317.223i	0.0298701	+	0.0517365i
$336$	−542.506	+	698.706i	−0.0880836	+	0.113445i
$337$	4871.58	−	8437.83i	0.787454	−	1.36391i	−0.140068	−	0.990142i	$-0.544732\pi$
$337$	4871.58	−	8437.83i	0.787454	−	1.36391i	0.927522	−	0.373769i	$-0.121935\pi$
$338$	1160.85	+	989.842i	0.186810	+	0.159291i
$339$	160.394	+	2300.62i	0.0256974	+	0.368591i
$340$	110.794	+	692.307i	0.0176725	+	0.110428i
$341$		−	8478.09i		−	1.34638i
$342$	9550.24	+	413.243i	1.50999	+	0.0653381i
$343$			1805.94i			0.284290i
$344$	−156.795	+	6596.82i	−0.0245750	+	1.03394i
$345$	2184.10	+	1065.82i	0.340835	+	0.166324i
$346$	−5093.68	+	5973.67i	−0.791439	+	0.928169i
$347$	3523.75	−	6103.31i	0.545143	−	0.944216i	−0.453455	−	0.891279i	$-0.649809\pi$
$347$	3523.75	−	6103.31i	0.545143	−	0.944216i	0.998598	−	0.0529363i	$-0.0168580\pi$
$348$	−7181.20	+	1668.53i	−1.10619	+	0.257018i
$349$	603.773	+	1045.77i	0.0926052	+	0.160397i	0.908607	−	0.417653i	$-0.137147\pi$
$349$	603.773	+	1045.77i	0.0926052	+	0.160397i	−0.816001	+	0.578050i	$0.803814\pi$
$350$	−881.886	−	162.713i	−0.134682	−	0.0248497i
$351$	−1768.50	+	5431.35i	−0.268933	+	0.825937i
$352$	6912.94	−	5348.85i	1.04676	−	0.809928i
$353$	1316.47	−	760.063i	0.198494	−	0.114601i	−0.397459	−	0.917620i	$-0.630108\pi$
$353$	1316.47	−	760.063i	0.198494	−	0.114601i	0.595953	+	0.803019i	$0.296774\pi$
$354$	−1907.75	+	830.867i	−0.286428	+	0.124746i
$355$	58.4957	+	33.7725i	0.00874544	+	0.00504918i
$356$	−2102.90	−	2588.33i	−0.313071	−	0.385340i
$357$	220.479	−	451.811i	0.0326863	−	0.0669815i
$358$	1273.06	−	451.968i	0.187942	−	0.0667241i
$359$	−6515.20			−0.957825			−0.478912	−	0.877863i	$-0.658969\pi$
$359$	−6515.20			−0.957825			−0.478912	+	0.877863i	$0.658969\pi$
$360$	169.566	+	1462.24i	0.0248247	+	0.214075i
$361$	−8809.35			−1.28435
$362$	−1952.03	+	693.020i	−0.283415	+	0.100620i
$363$	5186.21	−	361.572i	0.749877	−	0.0522799i
$364$	546.322	+	672.434i	0.0786678	+	0.0968273i
$365$	259.787	+	149.988i	0.0372545	+	0.0215089i
$366$	−25.5375	+	225.337i	−0.00364717	+	0.0321818i
$367$	3492.35	−	2016.31i	0.496729	−	0.286786i	−0.230633	−	0.973041i	$-0.574080\pi$
$367$	3492.35	−	2016.31i	0.496729	−	0.286786i	0.727362	+	0.686254i	$0.240746\pi$
$368$	9258.94	+	8282.93i	1.31156	+	1.17331i
$369$	4959.77	−	3871.68i	0.699716	−	0.546210i
$370$	1336.12	+	246.522i	0.187734	+	0.0346380i
$371$	468.392	+	811.278i	0.0655463	+	0.113530i
$372$	4985.25	+	5331.01i	0.694821	+	0.743011i
$373$	−1227.68	+	2126.40i	−0.170420	+	0.295176i	−0.938567	−	0.345098i	$-0.887846\pi$
$373$	−1227.68	+	2126.40i	−0.170420	+	0.295176i	0.768147	+	0.640274i	$0.221179\pi$
$374$	−3223.12	+	3779.95i	−0.445624	+	0.522611i
$375$	−2534.98	+	1709.10i	−0.349082	+	0.235353i
$376$	−1400.14	−	33.2788i	−0.192038	−	0.00456442i
$377$			7220.81i			0.986448i
$378$	503.488	−	927.711i	0.0685095	−	0.126234i
$379$		−	9518.27i		−	1.29003i	−0.764171	−	0.645014i	$-0.776851\pi$
$379$		−	9518.27i		−	1.29003i	0.764171	−	0.645014i	$-0.223149\pi$
$380$	−381.285	−	2382.50i	−0.0514724	−	0.321630i
$381$	1834.65	−	1236.93i	0.246698	−	0.166325i
$382$	6641.78	+	5663.37i	0.889589	+	0.758543i
$383$	−4727.72	+	8188.65i	−0.630744	+	1.09248i	0.356655	+	0.934236i	$0.383917\pi$
$383$	−4727.72	+	8188.65i	−0.630744	+	1.09248i	−0.987400	+	0.158245i	$0.949416\pi$
$384$	−1201.64	+	7428.27i	−0.159690	+	0.987167i
$385$	154.736	+	268.011i	0.0204833	+	0.0354781i
$386$	838.733	−	4545.83i	0.110597	−	0.599421i
$387$	−1092.58	−	7797.65i	−0.143512	−	1.02423i
$388$	−11248.2	−	4297.01i	−1.47176	−	0.562236i
$389$	−2568.69	+	1483.04i	−0.334802	+	0.193298i	−0.657971	−	0.753043i	$-0.728585\pi$
$389$	−2568.69	+	1483.04i	−0.334802	+	0.193298i	0.323169	+	0.946341i	$0.395252\pi$
$390$	1432.59	+	162.356i	0.186005	+	0.0210800i
$391$	−6114.50	−	3530.21i	−0.790854	−	0.456600i
$392$	3643.06	+	6671.20i	0.469394	+	0.859557i
$393$	−9038.44	+	630.142i	−1.16013	+	0.0808816i
$394$	−3170.73	−	8930.99i	−0.405429	−	1.14197i
$395$	1804.02			0.229798
$396$	−7103.92	+	7636.30i	−0.901479	+	0.969037i
$397$	1296.85			0.163947			0.0819733	−	0.996635i	$-0.473878\pi$
$397$	1296.85			0.163947			0.0819733	+	0.996635i	$0.473878\pi$
$398$	−990.405	−	2789.68i	−0.124735	−	0.351341i
$399$	−758.754	+	1554.86i	−0.0952011	+	0.195088i
$400$	−7247.45	+	2380.68i	−0.905931	+	0.297585i
$401$	−1782.15	−	1028.93i	−0.221936	−	0.128135i	0.384910	−	0.922954i	$-0.374232\pi$
$401$	−1782.15	−	1028.93i	−0.221936	−	0.128135i	−0.606847	+	0.794819i	$0.707566\pi$
$402$	−892.144	−	2048.44i	−0.110687	−	0.254147i
$403$	6190.90	−	3574.32i	0.765238	−	0.441810i
$404$	1243.10	−	3254.03i	0.153085	−	0.400728i
$405$	−482.755	−	1688.86i	−0.0592303	−	0.207211i
$406$	242.108	−	1312.20i	0.0295951	−	0.160402i
$407$	4813.22	+	8336.74i	0.586198	+	1.01532i
$408$	−195.976	−	4272.07i	−0.0237800	−	0.518380i
$409$	−2897.54	+	5018.69i	−0.350304	+	0.606744i	−0.986303	−	0.164946i	$-0.947255\pi$
$409$	−2897.54	+	5018.69i	−0.350304	+	0.606744i	0.635999	+	0.771690i	$0.280588\pi$
$410$	−1208.47	−	1030.45i	−0.145566	−	0.124122i
$411$	6871.43	+	3353.19i	0.824678	+	0.402435i
$412$	13787.4	−	2206.48i	1.64868	−	0.263849i
$413$		−	376.608i		−	0.0448709i
$414$	−12505.4	−	7959.98i	−1.48456	−	0.944955i
$415$		−	840.635i		−	0.0994341i
$416$	6820.32	+	2792.94i	0.803830	+	0.329171i
$417$	461.963	+	6626.17i	0.0542504	+	0.778141i
$418$	11092.0	−	13008.3i	1.29791	−	1.52214i
$419$	−7052.61	+	12215.5i	−0.822298	+	1.42426i	0.0816695	+	0.996659i	$0.473975\pi$
$419$	−7052.61	+	12215.5i	−0.822298	+	1.42426i	−0.903967	+	0.427602i	$0.859359\pi$
$420$	−254.892	−	77.5375i	−0.0296130	−	0.00900820i
$421$	−3210.43	−	5560.63i	−0.371655	−	0.643726i	0.618165	−	0.786048i	$-0.287876\pi$
$421$	−3210.43	−	5560.63i	−0.371655	−	0.643726i	−0.989820	+	0.142323i	$0.954543\pi$
$422$	−14680.3	−	2708.60i	−1.69343	−	0.312447i
$423$	1655.01	−	231.894i	0.190234	−	0.0266551i
$424$	6804.57	+	4147.26i	0.779384	+	0.475021i
$425$	3754.61	−	2167.73i	0.428530	−	0.247412i
$426$	−331.336	−	244.870i	−0.0376838	−	0.0278497i
$427$	−35.5457	−	20.5223i	−0.00402852	−	0.00232587i
$428$	4866.68	−	3953.96i	0.549626	−	0.446546i
$429$	5710.47	+	8469.92i	0.642667	+	0.953221i
$430$	−1872.89	+	664.922i	−0.210043	+	0.0745707i
$431$	1119.73			0.125140			0.0625700	−	0.998041i	$-0.480070\pi$
$431$	1119.73			0.125140			0.0625700	+	0.998041i	$0.480070\pi$
$432$	−23.3280	−	8978.92i	−0.00259808	−	0.999997i
$433$	−299.833			−0.0332773			−0.0166387	−	0.999862i	$-0.505296\pi$
$433$	−299.833			−0.0332773			−0.0166387	+	0.999862i	$0.505296\pi$
$434$	−1244.88	+	441.964i	−0.137687	+	0.0488824i
$435$	−1241.29	−	1841.12i	−0.136817	−	0.202930i
$436$	9822.04	−	7979.96i	1.07888	−	0.876539i
$437$	21042.4	+	12148.8i	2.30342	+	1.32988i
$438$	−1471.51	−	1087.50i	−0.160528	−	0.118636i
$439$	2090.02	−	1206.67i	0.227224	−	0.131188i	−0.382067	−	0.924135i	$-0.624788\pi$
$439$	2090.02	−	1206.67i	0.227224	−	0.131188i	0.609291	+	0.792947i	$0.291454\pi$
$440$	2247.93	+	1370.07i	0.243559	+	0.148445i
$441$	−5581.05	−	7149.55i	−0.602640	−	0.772006i
$442$	−4119.06	−	759.992i	−0.443266	−	0.0817853i
$443$	2409.36	+	4173.14i	0.258402	+	0.447566i	0.965814	−	0.259236i	$-0.0834706\pi$
$443$	2409.36	+	4173.14i	0.258402	+	0.447566i	−0.707412	+	0.706802i	$0.750137\pi$
$444$	−7928.69	−	2411.88i	−0.847475	−	0.257800i
$445$	502.211	−	869.854i	0.0534990	−	0.0926630i
$446$	8734.92	−	10244.0i	0.927378	−	1.08759i
$447$	−776.647	−	11139.8i	−0.0821793	−	1.17874i
$448$	−1145.77	−	736.225i	−0.120832	−	0.0776415i
$449$		−	8677.13i		−	0.912024i	−0.889974	−	0.456012i	$-0.849277\pi$
$449$		−	8677.13i		−	0.912024i	0.889974	−	0.456012i	$-0.150723\pi$
$450$	8072.45	−	4206.25i	0.845642	−	0.440633i
$451$		−	11252.3i		−	1.17484i
$452$	−3506.02	+	561.089i	−0.364843	+	0.0583881i
$453$	4468.13	+	2180.40i	0.463424	+	0.226146i
$454$	4800.46	+	4093.29i	0.496248	+	0.423145i
$455$	−130.472	+	225.984i	−0.0134431	+	0.0232841i
$456$	674.428	+	14701.8i	0.0692610	+	1.50982i
$457$	3460.04	+	5992.97i	0.354166	+	0.613434i	0.986975	−	0.160874i	$-0.0514313\pi$
$457$	3460.04	+	5992.97i	0.354166	+	0.613434i	−0.632809	+	0.774308i	$0.718098\pi$
$458$	2994.30	−	16228.8i	0.305491	−	1.65572i
$459$	1057.86	+	4992.13i	0.107574	+	0.507653i
$460$	−1335.26	+	3495.29i	−0.135341	+	0.354280i
$461$	−13470.8	+	7777.39i	−1.36095	+	0.785747i	−0.989751	−	0.142805i	$-0.954388\pi$
$461$	−13470.8	+	7777.39i	−1.36095	+	0.785747i	−0.371203	+	0.928552i	$0.621055\pi$
$462$	−753.741	−	1730.66i	−0.0759031	−	0.174280i
$463$	−9994.39	−	5770.27i	−1.00319	−	0.579194i	−0.0940023	−	0.995572i	$-0.529966\pi$
$463$	−9994.39	−	5770.27i	−1.00319	−	0.579194i	−0.909192	+	0.416378i	$0.863299\pi$
$464$	−3542.31	−	10783.8i	−0.354413	−	1.07893i
$465$	−964.074	+	1975.60i	−0.0961459	+	0.197024i
$466$	2914.67	+	8209.76i	0.289742	+	0.816116i
$467$	7.01271			0.000694881			0.000347441	−	1.00000i	$-0.499889\pi$
$467$	7.01271			0.000694881			0.000347441		1.00000i	$0.499889\pi$
$468$	−8571.19	−	1968.03i	−0.846588	−	0.194385i
$469$	404.383			0.0398138
$470$	−141.126	−	397.509i	−0.0138503	−	0.0390122i
$471$	10850.3	−	756.458i	1.06147	−	0.0740037i
$472$	−1535.44	−	2811.71i	−0.149734	−	0.274194i
$473$	−12194.7	−	7040.61i	−1.18544	−	0.684414i
$474$	−10933.9	−	1239.14i	−1.05952	−	0.120075i
$475$	−12921.1	+	7459.98i	−1.24812	+	0.720605i
$476$	723.051	+	276.218i	0.0696239	+	0.0265975i
$477$	−8814.85	−	3565.69i	−0.846131	−	0.342268i
$478$	−2715.57	+	14718.1i	−0.259848	+	1.40834i
$479$	2830.70	+	4902.92i	0.270017	+	0.467683i	0.968866	−	0.247586i	$-0.0796373\pi$
$479$	2830.70	+	4902.92i	0.270017	+	0.467683i	−0.698849	+	0.715269i	$0.746304\pi$
$480$	−2219.12	+	460.318i	−0.211018	+	0.0437719i
$481$	−4058.46	+	7029.46i	−0.384719	+	0.666353i
$482$	10768.1	+	9181.81i	1.01758	+	0.867677i
$483$	2224.59	−	1499.83i	0.209570	−	0.141293i
$484$	1264.84	+	7903.50i	0.118787	+	0.742252i
$485$		−	3626.57i		−	0.339534i
$486$	1765.86	+	10567.5i	0.164817	+	0.986324i
$487$			9082.26i			0.845085i	0.906343	+	0.422542i	$0.138862\pi$
$487$			9082.26i			0.845085i	−0.906343	+	0.422542i	$0.861138\pi$
$488$	−349.051	−	8.29632i	−0.0323786	−	0.000769584i
$489$	−6327.33	+	4265.92i	−0.585136	+	0.394502i
$490$	−1485.40	+	1742.02i	−0.136946	+	0.160605i
$491$	5098.79	−	8831.36i	0.468646	−	0.811718i	−0.530712	−	0.847552i	$-0.678075\pi$
$491$	5098.79	−	8831.36i	0.468646	−	0.811718i	0.999358	+	0.0358342i	$0.0114088\pi$
$492$	6616.56	+	7075.47i	0.606296	+	0.648347i
$493$	3225.45	+	5586.65i	0.294659	+	0.510365i
$494$	14175.3	+	2615.42i	1.29104	+	0.238205i
$495$	−2912.04	−	1177.95i	−0.264417	−	0.106959i
$496$	−7492.24	+	8375.07i	−0.678249	+	0.758169i
$497$	64.5778	−	37.2840i	0.00582839	−	0.00336502i
$498$	−577.414	+	5094.97i	−0.0519569	+	0.458456i
$499$	−2353.15	−	1358.59i	−0.211105	−	0.121881i	0.390720	−	0.920510i	$-0.372226\pi$
$499$	−2353.15	−	1358.59i	−0.211105	−	0.121881i	−0.601825	+	0.798628i	$0.705559\pi$
$500$	−2968.12	−	3653.28i	−0.265477	−	0.326759i
$501$	15801.5	−	1101.65i	1.40910	−	0.0982397i
$502$	6870.64	−	2439.25i	0.610860	−	0.216871i
$503$	−8294.45			−0.735251			−0.367626	−	0.929974i	$-0.619829\pi$
$503$	−8294.45			−0.735251			−0.367626	+	0.929974i	$0.619829\pi$
$504$	1491.61	+	645.024i	0.131828	+	0.0570072i
$505$	1049.14			0.0924479
$506$	−24982.6	+	8869.47i	−2.19489	+	0.779241i
$507$	1229.12	−	2518.75i	0.107667	−	0.220634i
$508$	2148.13	+	2643.99i	0.187613	+	0.230922i
$509$	2866.64	+	1655.05i	0.249629	+	0.144124i	0.619595	−	0.784922i	$-0.287297\pi$
$509$	2866.64	+	1655.05i	0.249629	+	0.144124i	−0.369965	+	0.929046i	$0.620630\pi$
$510$	1180.90	−	514.308i	0.102531	−	0.0446548i
$511$	286.798	−	165.583i	0.0248282	−	0.0143346i
$512$	−11555.8	−	825.228i	−0.997460	−	0.0712310i
$513$	−3640.49	−	17179.8i	−0.313317	−	1.47857i
$514$	−2421.46	−	446.775i	−0.207794	−	0.0383393i
$515$	2102.70	+	3641.98i	0.179914	+	0.311621i
$516$	11808.0	−	2743.55i	1.00740	−	0.234066i
$517$	1494.33	−	2588.25i	0.127119	−	0.220176i
$518$	973.212	−	1141.35i	0.0825492	−	0.0968105i
$519$	12961.4	+	6325.01i	1.09622	+	0.534946i
$520$	−52.7443	+	2219.11i	−0.00444806	+	0.187143i
$521$			5030.71i			0.423031i	0.977375	+	0.211516i	$0.0678400\pi$
$521$			5030.71i			0.423031i	−0.977375	+	0.211516i	$0.932160\pi$
$522$	6258.66	+	12011.3i	0.524778	+	1.00713i
$523$			9680.16i			0.809338i	0.914463	+	0.404669i	$0.132613\pi$
$523$			9680.16i			0.809338i	−0.914463	+	0.404669i	$0.867387\pi$
$524$	−2204.35	−	13774.1i	−0.183774	−	1.14833i
$525$	114.580	+	1643.49i	0.00952515	+	0.136624i
$526$	−9276.95	−	7910.35i	−0.769000	−	0.655718i
$527$	3193.21	−	5530.81i	0.263944	−	0.457164i
$528$	−12683.3	−	9847.86i	−1.04540	−	0.811692i
$529$	−12756.2	−	22094.4i	−1.04843	−	1.81593i
$530$	−435.479	+	2360.24i	−0.0356905	+	0.193438i
$531$	2352.25	+	3013.32i	0.192239	+	0.246266i
$532$	−2488.30	−	950.571i	−0.202784	−	0.0774671i
$533$	8216.73	−	4743.93i	0.667742	−	0.385521i
$534$	−3641.31	+	4927.10i	−0.295084	+	0.399282i
$535$	1635.54	+	944.278i	0.132169	+	0.0763078i
$536$	3019.08	−	1648.68i	0.243291	−	0.132859i
$537$	−1387.36	−	2057.77i	−0.111488	−	0.165362i
$538$	5302.58	+	14935.8i	0.424927	+	1.19689i
$539$	−16220.3			−1.29621
$540$	2523.74	−	971.633i	0.201119	−	0.0774304i
$541$	18659.8			1.48290			0.741449	−	0.671009i	$-0.234139\pi$
$541$	18659.8			1.48290			0.741449	+	0.671009i	$0.234139\pi$
$542$	2033.80	+	5728.60i	0.161179	+	0.453993i
$543$	2127.30	+	3155.26i	0.168124	+	0.249365i
$544$	6524.36	−	885.691i	0.514209	−	0.0698046i
$545$	3300.88	+	1905.76i	0.259438	+	0.149787i
$546$	945.994	−	1280.04i	0.0741480	−	0.100331i
$547$	3928.78	−	2268.28i	0.307098	−	0.177303i	−0.338529	−	0.940956i	$-0.609929\pi$
$547$	3928.78	−	2268.28i	0.307098	−	0.177303i	0.645627	+	0.763653i	$0.276596\pi$
$548$	−4200.89	+	10996.6i	−0.327469	+	0.857212i
$549$	412.589	−	57.8108i	0.0320745	−	0.00449418i
$550$	2953.66	−	16008.5i	0.228990	−	1.24110i
$551$	−11100.0	−	19225.8i	−0.858216	−	1.48647i
$552$	10493.7	−	20267.3i	0.809131	−	1.56274i
$553$	995.797	−	1724.77i	0.0765743	−	0.132631i
$554$	6908.63	+	5890.91i	0.529819	+	0.451771i
$555$	−173.597	−	2489.99i	−0.0132771	−	0.190440i
$556$	−10097.9	+	1616.03i	−0.770229	+	0.123264i
$557$		−	17657.1i		−	1.34319i	−0.740918	−	0.671596i	$-0.765609\pi$
$557$		−	17657.1i		−	1.34319i	0.740918	−	0.671596i	$-0.234391\pi$
$558$	7200.11	−	11311.6i	0.546245	−	0.858171i
$559$		−	11873.1i		−	0.898355i
$560$	83.9898	−	401.497i	0.00633789	−	0.0302970i
$561$	8201.53	+	4002.26i	0.617235	+	0.301204i
$562$	−1725.76	+	2023.91i	−0.129532	+	0.151910i
$563$	−4972.47	+	8612.57i	−0.372229	+	0.644719i	−0.989908	−	0.141711i	$-0.954740\pi$
$563$	−4972.47	+	8612.57i	−0.372229	+	0.644719i	0.617679	+	0.786430i	$0.288073\pi$
$564$	582.302	+	2506.18i	0.0434740	+	0.187109i
$565$	−534.697	−	926.122i	−0.0398139	−	0.0689597i
$566$	−5702.30	−	1052.11i	−0.423473	−	0.0781334i
$567$	−1881.15	−	470.683i	−0.139331	−	0.0348622i
$568$	330.122	−	541.643i	0.0243866	−	0.0400121i
$569$	−4084.02	+	2357.91i	−0.300898	+	0.173724i	−0.642846	−	0.765995i	$-0.722247\pi$
$569$	−4084.02	+	2357.91i	−0.300898	+	0.173724i	0.341948	+	0.939719i	$0.388913\pi$
$570$	−4063.92	+	1769.93i	−0.298630	+	0.130060i
$571$	7993.20	+	4614.88i	0.585823	+	0.338225i	0.763444	−	0.645874i	$-0.223507\pi$
$571$	7993.20	+	4614.88i	0.585823	+	0.338225i	−0.177621	+	0.984099i	$0.556840\pi$
$572$	−12206.4	+	9917.14i	−0.892264	+	0.724924i
$573$	7032.41	−	14411.0i	0.512711	−	1.05066i
$574$	−1652.24	+	586.587i	−0.120145	+	0.0426545i
$575$	23137.1			1.67806
$576$	13765.9	−	1265.65i	0.995800	−	0.0915547i
$577$	4076.34			0.294108			0.147054	−	0.989128i	$-0.453021\pi$
$577$	4076.34			0.294108			0.147054	+	0.989128i	$0.453021\pi$
$578$	9568.92	−	3397.21i	0.688607	−	0.244473i
$579$	−8471.61	+	590.624i	−0.608063	+	0.0423929i
$580$	2653.32	−	2155.70i	0.189953	−	0.154329i
$581$	−803.706	−	464.020i	−0.0573896	−	0.0331339i
$582$	−2491.01	+	21980.1i	−0.177415	+	1.56547i
$583$	−14726.8	+	8502.51i	−1.04618	+	0.604010i
$584$	1466.12	−	2405.51i	0.103884	−	0.170447i
$585$	−367.535	−	2623.06i	−0.0259755	−	0.185385i
$586$	−12340.6	−	2276.92i	−0.869941	−	0.160509i
$587$	−4317.74	−	7478.55i	−0.303599	−	0.525848i	0.673350	−	0.739324i	$-0.264855\pi$
$587$	−4317.74	−	7478.55i	−0.303599	−	0.525848i	−0.976948	+	0.213476i	$0.931522\pi$
$588$	10199.3	−	9537.82i	0.715329	−	0.668934i
$589$	−10989.1	+	19033.6i	−0.768755	+	1.33152i
$590$	626.052	−	734.209i	0.0436850	−	0.0512320i
$591$	−14436.1	+	9732.89i	−1.00477	+	0.677424i
$592$	2612.59	−	12489.0i	0.181380	−	0.867050i
$593$			24260.9i			1.68006i	0.542537	+	0.840032i	$0.317464\pi$
$593$			24260.9i			1.68006i	−0.542537	+	0.840032i	$0.682536\pi$
$594$	16840.3	+	9139.59i	1.16324	+	0.631316i
$595$			233.121i			0.0160622i
$596$	16976.5	−	2716.85i	1.16675	−	0.186723i
$597$	−4509.24	+	3040.16i	−0.309130	+	0.208418i
$598$	−17009.2	−	14503.6i	−1.16314	−	0.991800i
$599$	7549.02	−	13075.3i	0.514932	−	0.891889i	−0.484917	−	0.874560i	$-0.661150\pi$
$599$	7549.02	−	13075.3i	0.514932	−	0.891889i	0.999850	−	0.0173291i	$-0.00551631\pi$
$600$	7555.99	+	11802.9i	0.514120	+	0.803087i
$601$	−2964.13	−	5134.03i	−0.201180	−	0.348455i	0.747729	−	0.664004i	$-0.231144\pi$
$601$	−2964.13	−	5134.03i	−0.201180	−	0.348455i	−0.948909	+	0.315550i	$0.897811\pi$
$602$	−398.097	+	2157.64i	−0.0269522	+	0.146078i
$603$	−3235.56	+	2525.73i	−0.218511	+	0.170573i
$604$	−2731.62	+	7150.52i	−0.184020	+	0.481706i
$605$	−2087.73	+	1205.35i	−0.140294	+	0.0809990i
$606$	−6358.69	−	720.633i	−0.426245	−	0.0483064i
$607$	16115.3	+	9304.20i	1.07760	+	0.622151i	0.930247	−	0.366933i	$-0.119592\pi$
$607$	16115.3	+	9304.20i	1.07760	+	0.622151i	0.147350	+	0.989084i	$0.452926\pi$
$608$	−22452.8	+	3048.00i	−1.49767	+	0.203311i
$609$	−2445.41	+	170.489i	−0.162714	+	0.0113441i
$610$	−35.1823	−	99.0981i	−0.00233523	−	0.00657765i
$611$	2520.01			0.166855
$612$	−7510.51	+	2306.01i	−0.496069	+	0.152312i
$613$	7939.25			0.523105			0.261552	−	0.965189i	$-0.415766\pi$
$613$	7939.25			0.523105			0.261552	+	0.965189i	$0.415766\pi$
$614$	6995.77	+	19705.0i	0.459815	+	1.29516i
$615$	−1279.54	+	2622.07i	−0.0838963	+	0.171922i
$616$	2550.71	−	1392.91i	0.166836	−	0.0911073i
$617$	−25269.7	−	14589.5i	−1.64882	−	0.951946i	−0.977542	−	0.210740i	$-0.932413\pi$
$617$	−25269.7	−	14589.5i	−1.64882	−	0.951946i	−0.671277	−	0.741206i	$-0.734254\pi$
$618$	−10242.5	−	23517.8i	−0.666691	−	1.53078i
$619$	14117.6	−	8150.83i	0.916698	−	0.529256i	0.0341179	−	0.999418i	$-0.489138\pi$
$619$	14117.6	−	8150.83i	0.916698	−	0.529256i	0.882580	+	0.470162i	$0.155804\pi$
$620$	−3161.63	−	1207.80i	−0.204797	−	0.0782359i
$621$	−8431.65	+	25895.0i	−0.544848	+	1.67332i
$622$	2512.88	−	13619.5i	0.161990	−	0.877963i
$623$	−554.427	−	960.297i	−0.0356544	−	0.0617552i
$624$	1843.93	−	13413.4i	0.118295	−	0.860525i
$625$	−6740.81	+	11675.4i	−0.431412	+	0.747227i
$626$	−1467.22	−	1251.08i	−0.0936774	−	0.0798776i
$627$	−28224.6	−	13773.3i	−1.79774	−	0.877279i
$628$	2646.23	+	16535.2i	0.168147	+	1.05068i
$629$			7251.46i			0.459674i
$630$	−21.1591	+	488.996i	−0.00133809	+	0.0309239i
$631$		−	2517.83i		−	0.158848i	−0.996841	−	0.0794242i	$-0.974692\pi$
$631$		−	2517.83i		−	0.158848i	0.996841	−	0.0794242i	$-0.0253082\pi$
$632$	402.559	−	16936.8i	0.0253369	−	1.06600i
$633$	1907.36	+	27358.2i	0.119764	+	1.71784i
$634$	2848.33	−	3340.41i	0.178425	−	0.209250i
$635$	−513.012	+	888.562i	−0.0320602	+	0.0555300i
$636$	4260.57	−	14005.9i	0.265633	−	0.873226i
$637$	−6838.42	−	11844.5i	−0.425350	−	0.736728i
$638$	23819.7	+	4394.88i	1.47811	+	0.272720i
$639$	−283.829	+	701.662i	−0.0175714	+	0.0434387i
$640$	−1009.86	−	3339.96i	−0.0623720	−	0.206287i
$641$	14572.0	−	8413.13i	0.897907	−	0.518407i	0.0213863	−	0.999771i	$-0.493192\pi$
$641$	14572.0	−	8413.13i	0.897907	−	0.518407i	0.876520	+	0.481365i	$0.159859\pi$
$642$	−9264.15	−	6846.54i	−0.569512	−	0.420890i
$643$	17687.6	+	10211.9i	1.08481	+	0.626313i	0.932189	−	0.361973i	$-0.117897\pi$
$643$	17687.6	+	10211.9i	1.08481	+	0.626313i	0.152617	+	0.988285i	$0.451230\pi$
$644$	2604.70	+	3205.96i	0.159378	+	0.196169i
$645$	2041.05	+	3027.34i	0.124599	+	0.184808i
$646$	12135.5	−	4308.41i	0.739109	−	0.262402i
$647$	21477.2			1.30503			0.652515	−	0.757776i	$-0.273714\pi$
$647$	21477.2			1.30503			0.652515	+	0.757776i	$0.273714\pi$
$648$	−15963.4	+	4155.42i	−0.967750	+	0.251914i
$649$	6836.40			0.413485
$650$	12935.0	−	4592.26i	0.780544	−	0.277113i
$651$	1356.66	+	2012.23i	0.0816768	+	0.121145i
$652$	−7408.45	−	9118.60i	−0.444996	−	0.547718i
$653$	21836.5	+	12607.3i	1.30862	+	0.755533i	0.981866	−	0.189576i	$-0.0607113\pi$
$653$	21836.5	+	12607.3i	1.30862	+	0.755533i	0.326756	+	0.945109i	$0.394045\pi$
$654$	−18697.1	−	13817.8i	−1.11791	−	0.826178i
$655$	3638.46	−	2100.66i	0.217048	−	0.125313i
$656$	−9943.90	+	11115.6i	−0.591835	+	0.661573i
$657$	−1260.52	+	3116.18i	−0.0748519	+	0.185044i
$658$	−457.946	−	84.4938i	−0.0271316	−	0.00500595i
$659$	6865.03	+	11890.6i	0.405802	+	0.702870i	0.994415	−	0.105545i	$-0.0336588\pi$
$659$	6865.03	+	11890.6i	0.405802	+	0.702870i	−0.588612	+	0.808416i	$0.700325\pi$
$660$	1407.50	−	4626.95i	0.0830106	−	0.272884i
$661$	−772.039	+	1337.21i	−0.0454294	+	0.0786860i	−0.887846	−	0.460141i	$-0.847799\pi$
$661$	−772.039	+	1337.21i	−0.0454294	+	0.0786860i	0.842417	+	0.538827i	$0.181132\pi$
$662$	−13583.8	+	15930.6i	−0.797508	+	0.935286i
$663$	535.175	+	7676.29i	0.0313491	+	0.449657i
$664$	−7892.20	−	187.584i	−0.461260	−	0.0109633i
$665$		−	802.258i		−	0.0467823i
$666$	−658.175	+	15210.7i	−0.0382939	+	0.884990i
$667$			34426.6i			1.99851i
$668$	3853.77	+	24080.7i	0.223214	+	1.39477i
$669$	−22226.8	−	10846.5i	−1.28451	−	0.626829i
$670$	788.357	+	672.223i	0.0454580	+	0.0387616i
$671$	372.533	−	645.246i	0.0214329	−	0.0371229i
$672$	−784.830	+	2375.72i	−0.0450528	+	0.136377i
$673$	2684.11	+	4649.02i	0.153737	+	0.266280i	0.932598	−	0.360916i	$-0.117536\pi$
$673$	2684.11	+	4649.02i	0.153737	+	0.266280i	−0.778861	+	0.627196i	$0.784202\pi$
$674$	5000.19	−	27100.4i	0.285757	−	1.54877i
$675$	−11181.8	−	12434.2i	−0.637611	−	0.709028i
$676$	4030.84	+	1539.85i	0.229338	+	0.0876110i
$677$	−16713.8	+	9649.71i	−0.948838	+	0.547812i	−0.892720	−	0.450612i	$-0.851206\pi$
$677$	−16713.8	+	9649.71i	−0.948838	+	0.547812i	−0.0561181	+	0.998424i	$0.517872\pi$
$678$	2604.58	+	5980.36i	0.147535	+	0.338753i
$679$	−3467.25	−	2001.82i	−0.195966	−	0.113141i
$680$	950.441	+	1740.45i	0.0535996	+	0.0981520i
$681$	5082.79	−	10415.8i	0.286010	−	0.586099i
$682$	−8022.78	−	22597.8i	−0.450452	−	1.26879i
$683$	−7466.11			−0.418276			−0.209138	−	0.977886i	$-0.567066\pi$
$683$	−7466.11			−0.418276			−0.209138	+	0.977886i	$0.567066\pi$
$684$	25846.6	−	7935.87i	1.44484	−	0.443619i
$685$	−3545.45			−0.197759
$686$	1708.95	+	4813.60i	0.0951136	+	0.267907i
$687$	−30243.9	+	2108.55i	−1.67959	+	0.117098i
$688$	5824.61	+	17731.7i	0.322763	+	0.982581i
$689$	−12417.5	−	7169.23i	−0.686600	−	0.396409i
$690$	6830.14	+	774.062i	0.376839	+	0.0427073i
$691$	20587.2	−	11886.0i	1.13339	−	0.654364i	0.188606	−	0.982053i	$-0.439603\pi$
$691$	20587.2	−	11886.0i	1.13339	−	0.654364i	0.944786	+	0.327689i	$0.106270\pi$
$692$	−7924.00	+	20742.5i	−0.435297	+	1.13947i
$693$	−2733.61	+	2133.90i	−0.149843	+	0.116970i
$694$	3616.77	−	19602.5i	0.197825	−	1.07219i
$695$	−1540.02	−	2667.39i	−0.0840520	−	0.145582i
$696$	−17562.1	+	11242.9i	−0.956449	+	0.612299i
$697$	4238.12	−	7340.64i	0.230316	−	0.398919i
$698$	2598.92	+	2216.07i	0.140932	+	0.120171i
$699$	13270.3	−	8946.90i	0.718066	−	0.484124i
$700$	−2504.58	+	400.823i	−0.135235	+	0.0216424i
$701$		−	3501.89i		−	0.188680i	−0.995540	−	0.0943399i	$-0.969926\pi$
$701$		−	3501.89i		−	0.188680i	0.995540	−	0.0943399i	$-0.0300740\pi$
$702$	425.854	+	16150.4i	0.0228957	+	0.868316i
$703$		−	24955.1i		−	1.33883i
$704$	13364.4	−	20798.7i	0.715467	−	1.11346i
$705$	−642.535	+	433.201i	−0.0343252	+	0.0231422i
$706$	2789.71	−	3271.66i	0.148714	−	0.174406i
$707$	579.113	−	1003.05i	0.0308059	−	0.0533574i
$708$	−4298.72	+	4019.91i	−0.228186	+	0.213386i
$709$	−2079.38	−	3601.59i	−0.110145	−	0.190777i	0.805684	−	0.592346i	$-0.201798\pi$
$709$	−2079.38	−	3601.59i	−0.110145	−	0.190777i	−0.915829	+	0.401569i	$0.868465\pi$
$710$	187.875	+	34.6641i	0.00993074	+	0.00183228i
$711$	2805.13	+	20019.9i	0.147961	+	1.05598i
$712$	−8054.45	−	4909.04i	−0.423951	−	0.258391i
$713$	29516.3	−	17041.3i	1.55034	−	0.895091i
$714$	160.126	−	1412.91i	0.00839293	−	0.0740572i
$715$	−4102.18	−	2368.40i	−0.214564	−	0.123878i
$716$	2965.55	−	2409.38i	0.154788	−	0.125758i
$717$	27428.6	−	1912.27i	1.42865	−	0.0996025i
$718$	−17365.8	+	6165.30i	−0.902627	+	0.320455i
$719$	−20077.1			−1.04137			−0.520687	−	0.853748i	$-0.674324\pi$
$719$	−20077.1			−1.04137			−0.520687	+	0.853748i	$0.674324\pi$
$720$	1835.68	+	3737.05i	0.0950164	+	0.193433i
$721$	4642.64			0.239807
$722$	−23480.7	+	8336.24i	−1.21033	+	0.429699i
$723$	11401.4	−	23364.0i	0.586476	−	1.20182i
$724$	−4547.20	+	3694.39i	−0.233419	+	0.189642i
$725$	−18307.5	−	10569.8i	−0.937825	−	0.541454i
$726$	13481.3	−	5871.43i	0.689172	−	0.300150i
$727$	−31220.9	+	18025.4i	−1.59274	+	0.919566i	−0.599900	+	0.800075i	$0.704793\pi$
$727$	−31220.9	+	18025.4i	−1.59274	+	0.919566i	−0.992835	+	0.119491i	$0.961874\pi$
$728$	2092.51	+	1275.35i	0.106529	+	0.0649278i
$729$	17991.3	−	7983.37i	0.914052	−	0.405597i
$730$	834.378	+	153.948i	0.0423037	+	0.00780530i
$731$	−5303.59	−	9186.10i	−0.268345	−	0.464788i
$732$	145.167	+	624.785i	0.00732993	+	0.0315474i
$733$	10850.9	−	18794.4i	0.546779	−	0.947049i	−0.451714	−	0.892163i	$-0.649187\pi$
$733$	10850.9	−	18794.4i	0.546779	−	0.947049i	0.998493	−	0.0548859i	$-0.0174795\pi$
$734$	7400.60	−	8679.14i	0.372154	−	0.436448i
$735$	3779.74	+	1844.47i	0.189684	+	0.0925638i
$736$	32517.2	+	13315.9i	1.62853	+	0.666889i
$737$			7340.58i			0.366884i
$738$	9556.18	−	15013.1i	0.476650	−	0.748835i
$739$		−	26112.0i		−	1.29979i	−0.760024	−	0.649895i	$-0.774813\pi$
$739$		−	26112.0i		−	1.29979i	0.760024	−	0.649895i	$-0.225187\pi$
$740$	3794.61	−	607.275i	0.188504	−	0.0301674i
$741$	−1841.74	−	26417.1i	−0.0913065	−	1.30966i
$742$	2016.18	+	1719.17i	0.0997522	+	0.0850576i
$743$	2806.43	−	4860.88i	0.138570	−	0.240011i	−0.788385	−	0.615182i	$-0.789083\pi$
$743$	2806.43	−	4860.88i	0.138570	−	0.240011i	0.926956	+	0.375171i	$0.122416\pi$
$744$	18332.6	+	9491.93i	0.903366	+	0.467730i
$745$	2589.06	+	4484.38i	0.127323	+	0.220530i
$746$	−1260.09	+	6829.51i	−0.0618432	+	0.335182i
$747$	9328.84	−	1307.13i	0.456927	−	0.0640232i
$748$	−5014.06	+	13125.2i	−0.245096	+	0.641585i
$749$	1805.59	−	1042.46i	0.0880839	−	0.0508553i
$750$	−5139.50	+	6954.33i	−0.250224	+	0.338582i
$751$	−24027.9	−	13872.5i	−1.16750	−	0.674056i	−0.214409	−	0.976744i	$-0.568783\pi$
$751$	−24027.9	−	13872.5i	−1.16750	−	0.674056i	−0.953090	+	0.302688i	$0.902116\pi$
$752$	−3763.46	+	1236.24i	−0.182499	+	0.0599481i
$753$	−7487.54	−	11105.7i	−0.362365	−	0.537470i
$754$	6833.02	+	19246.6i	0.330032	+	0.929601i
$755$	−2305.42			−0.111129
$756$	464.123	−	2949.20i	0.0223280	−	0.141880i
$757$	−22792.6			−1.09433			−0.547167	−	0.837023i	$-0.684294\pi$
$757$	−22792.6			−1.09433			−0.547167	+	0.837023i	$0.684294\pi$
$758$	−9007.10	−	25370.3i	−0.431600	−	1.21569i
$759$	27225.8	+	40382.0i	1.30202	+	1.93119i
$760$	−3270.83	−	5989.57i	−0.156113	−	0.285874i
$761$	27979.1	+	16153.7i	1.33277	+	0.769477i	0.985724	−	0.168370i	$-0.0538505\pi$
$761$	27979.1	+	16153.7i	1.33277	+	0.769477i	0.347049	+	0.937847i	$0.387184\pi$
$762$	3719.62	−	5033.07i	0.176834	−	0.239277i
$763$	3644.08	−	2103.91i	0.172902	−	0.0998253i
$764$	23062.4	+	8810.24i	1.09211	+	0.417203i
$765$	−1456.05	−	1865.25i	−0.0688149	−	0.0881546i
$766$	−4852.53	+	26300.1i	−0.228889	+	1.24055i
$767$	2882.19	+	4992.10i	0.135684	+	0.235012i
$768$	3826.45	+	20936.6i	0.179785	+	0.983706i
$769$	1200.97	−	2080.14i	0.0563174	−	0.0975446i	−0.836492	−	0.547979i	$-0.815397\pi$
$769$	1200.97	−	2080.14i	0.0563174	−	0.0975446i	0.892810	+	0.450434i	$0.148731\pi$
$770$	666.055	+	567.938i	0.0311727	+	0.0265806i
$771$	314.612	+	4512.64i	0.0146958	+	0.210790i
$772$	−2066.11	−	12910.3i	−0.0963224	−	0.601880i
$773$		−	21135.4i		−	0.983424i	−0.870758	−	0.491712i	$-0.836371\pi$
$773$		−	21135.4i		−	0.983424i	0.870758	−	0.491712i	$-0.163629\pi$
$774$	−10291.1	−	19750.2i	−0.477914	−	0.917192i
$775$			20928.4i			0.970025i
$776$	−34047.6	−	809.252i	−1.57505	−	0.0374362i
$777$	−2476.43	−	1208.47i	−0.114339	−	0.0557963i
$778$	−5443.29	+	6383.68i	−0.250837	+	0.294172i
$779$	−14585.0	+	25262.0i	−0.670811	+	1.16188i
$780$	3972.10	−	922.904i	0.182339	−	0.0423657i
$781$	676.799	+	1172.25i	0.0310087	+	0.0537086i
$782$	−19638.4	−	3623.41i	−0.898041	−	0.165694i
$783$	18501.4	−	16637.9i	0.844427	−	0.759373i
$784$	16023.3	+	14334.2i	0.729922	+	0.652979i
$785$	−4367.81	+	2521.76i	−0.198591	+	0.114656i
$786$	−23495.1	+	10232.6i	−1.06621	+	0.464359i
$787$	3776.51	+	2180.37i	0.171052	+	0.0987570i	0.583082	−	0.812413i	$-0.301847\pi$
$787$	3776.51	+	2180.37i	0.171052	+	0.0987570i	−0.412030	+	0.911170i	$0.635180\pi$
$788$	−16902.7	−	20804.5i	−0.764130	−	0.940520i
$789$	−9822.57	+	20128.6i	−0.443210	+	0.908236i
$790$	4808.50	−	1707.14i	0.216555	−	0.0768826i
$791$	−1180.58			−0.0530679
$792$	−11708.8	+	27076.5i	−0.525322	+	1.21480i
$793$	628.232			0.0281326
$794$	3456.65	−	1227.20i	0.154499	−	0.0548510i
$795$	4398.55	−	306.658i	0.196227	−	0.0136805i
$796$	−5279.71	−	6498.47i	−0.235094	−	0.289362i
$797$	−17755.1	−	10250.9i	−0.789106	−	0.455590i	0.0505420	−	0.998722i	$-0.483905\pi$
$797$	−17755.1	−	10250.9i	−0.789106	−	0.455590i	−0.839648	+	0.543132i	$0.817238\pi$
$798$	−551.054	+	4862.37i	−0.0244450	+	0.215697i
$799$	1949.69	−	1125.66i	0.0863270	−	0.0498409i
$800$	−17064.8	+	13203.8i	−0.754163	+	0.583530i
$801$	10434.0	+	4220.65i	0.460258	+	0.186179i
$802$	−5723.88	−	1056.09i	−0.252016	−	0.0464985i
$803$	3005.76	+	5206.12i	0.132093	+	0.228792i
$804$	−4316.38	−	4615.75i	−0.189337	−	0.202469i
$805$	−622.050	+	1077.42i	−0.0272352	+	0.0471728i
$806$	13119.1	−	15385.5i	0.573324	−	0.672372i
$807$	24142.3	−	16276.9i	1.05309	−	0.710003i
$808$	234.111	−	9849.74i	0.0101931	−	0.428852i
$809$			34550.7i			1.50153i	0.660568	+	0.750766i	$0.270315\pi$
$809$			34550.7i			1.50153i	−0.660568	+	0.750766i	$0.729685\pi$
$810$	−2884.91	−	4044.72i	−0.125143	−	0.175453i
$811$			19709.5i			0.853384i	0.904397	+	0.426692i	$0.140321\pi$
$811$			19709.5i			0.853384i	−0.904397	+	0.426692i	$0.859679\pi$
$812$	−596.402	−	3726.68i	−0.0257754	−	0.161060i
$813$	9259.72	−	6242.96i	0.399449	−	0.269311i
$814$	20718.3	+	17666.3i	0.892109	+	0.760692i
$815$	1769.27	−	3064.47i	0.0760429	−	0.131710i
$816$	−4565.00	−	11201.5i	−0.195842	−	0.480551i
$817$	18251.7	+	31612.9i	0.781575	+	1.35373i
$818$	−2974.03	+	16118.9i	−0.127121	+	0.688978i
$819$	−2710.70	−	1096.50i	−0.115653	−	0.0467826i
$820$	−4196.20	−	1603.02i	−0.178704	−	0.0682682i
$821$	−28891.8	+	16680.7i	−1.22817	+	0.709086i	−0.966648	−	0.256110i	$-0.917559\pi$
$821$	−28891.8	+	16680.7i	−1.22817	+	0.709086i	−0.261526	+	0.965196i	$0.584226\pi$
$822$	21488.4	+	2435.29i	0.911795	+	0.103334i
$823$	−36540.4	−	21096.6i	−1.54765	−	0.893537i	−0.998321	−	0.0579313i	$-0.981550\pi$
$823$	−36540.4	−	21096.6i	−1.54765	−	0.893537i	−0.549330	−	0.835605i	$-0.685117\pi$
$824$	34661.4	−	18928.2i	1.46540	−	0.800237i
$825$	−29833.5	+	2079.93i	−1.25899	+	0.0877743i
$826$	−356.382	−	1003.82i	−0.0150123	−	0.0422851i
$827$	13992.0			0.588329			0.294165	−	0.955755i	$-0.404959\pi$
$827$	13992.0			0.588329			0.294165	+	0.955755i	$0.404959\pi$
$828$	−40864.8	−	9382.96i	−1.71516	−	0.393817i
$829$	−23454.8			−0.982653			−0.491327	−	0.870975i	$-0.663488\pi$
$829$	−23454.8			−0.982653			−0.491327	+	0.870975i	$0.663488\pi$
$830$	−795.489	−	2240.66i	−0.0332673	−	0.0937039i
$831$	7314.96	−	14990.0i	0.305359	−	0.625748i
$832$	20822.0	+	990.366i	0.867637	+	0.0412678i
$833$	−10581.6	−	6109.28i	−0.440132	−	0.254110i
$834$	7501.64	+	17224.4i	0.311464	+	0.715148i
$835$	−6360.95	+	3672.50i	−0.263629	+	0.152206i
$836$	17255.3	−	45168.9i	0.713860	−	1.86866i
$837$	−23423.0	−	7626.76i	−0.967287	−	0.314957i
$838$	−7238.80	+	39233.4i	−0.298401	+	1.61730i
$839$	−4579.55	−	7932.02i	−0.188443	−	0.326393i	0.756288	−	0.654238i	$-0.227011\pi$
$839$	−4579.55	−	7932.02i	−0.188443	−	0.326393i	−0.944731	+	0.327846i	$0.893677\pi$
$840$	−752.771	+	34.5324i	−0.0309203	+	0.00141843i
$841$	3532.81	−	6119.00i	0.144852	−	0.250892i
$842$	−13819.2	−	11783.5i	−0.565606	−	0.482286i
$843$	4391.36	+	2142.94i	0.179415	+	0.0875525i
$844$	−41692.5	+	6672.30i	−1.70037	+	0.272121i
$845$			1299.60i			0.0529082i
$846$	4191.86	−	2184.22i	0.170354	−	0.0887649i
$847$			2661.35i			0.107963i
$848$	22061.6	+	4615.11i	0.893396	+	0.186891i
$849$	740.881	+	10626.8i	0.0299493	+	0.429578i
$850$	7956.35	−	9330.90i	0.321059	−	0.376526i
$851$	−19349.5	+	33514.3i	−0.779427	+	1.35001i
$852$	−1114.87	−	339.141i	−0.0448297	−	0.0136371i
$853$	16740.3	+	28995.1i	0.671955	+	1.16386i	0.977349	+	0.211634i	$0.0678784\pi$
$853$	16740.3	+	28995.1i	0.671955	+	1.16386i	−0.305394	+	0.952226i	$0.598788\pi$
$854$	−114.165	−	21.0641i	−0.00457452	−	0.000844028i
$855$	5010.81	+	6419.04i	0.200428	+	0.256756i
$856$	9230.20	−	15144.3i	0.368553	−	0.604699i
$857$	26803.0	−	15474.7i	1.06835	−	0.616811i	0.140618	−	0.990064i	$-0.455091\pi$
$857$	26803.0	−	15474.7i	1.06835	−	0.616811i	0.927730	+	0.373253i	$0.121758\pi$
$858$	23235.9	+	17172.2i	0.924547	+	0.683274i
$859$	−5321.93	−	3072.62i	−0.211388	−	0.122045i	0.390568	−	0.920574i	$-0.372278\pi$
$859$	−5321.93	−	3072.62i	−0.211388	−	0.122045i	−0.601956	+	0.798529i	$0.705612\pi$
$860$	−4362.84	+	3544.61i	−0.172990	+	0.140547i
$861$	1800.59	+	2670.68i	0.0712706	+	0.105710i
$862$	2984.56	−	1059.59i	0.117929	−	0.0418676i
$863$	13685.9			0.539830			0.269915	−	0.962884i	$-0.413004\pi$
$863$	13685.9			0.539830			0.269915	+	0.962884i	$0.413004\pi$
$864$	−8558.89	−	23910.6i	−0.337013	−	0.941500i
$865$	−6687.66			−0.262875
$866$	−799.185	+	283.731i	−0.0313596	+	0.0111335i
$867$	−10428.1	−	15467.2i	−0.408486	−	0.605876i
$868$	−2899.92	+	2356.05i	−0.113398	+	0.0921308i
$869$	31309.0	+	18076.3i	1.22219	+	0.705633i
$870$	−5050.82	−	3732.74i	−0.196826	−	0.145462i
$871$	−5360.27	+	3094.75i	−0.208526	+	0.120392i
$872$	18628.6	−	30564.6i	0.723444	−	1.18698i
$873$	40245.4	−	5639.06i	1.56025	−	0.218618i
$874$	67583.3	+	12469.5i	2.61561	+	0.482595i
$875$	−782.544	−	1355.41i	−0.0302341	−	0.0523669i
$876$	−4951.30	−	1506.17i	−0.190969	−	0.0580923i
$877$	2574.73	−	4459.56i	0.0991361	−	0.171709i	−0.812191	−	0.583391i	$-0.801725\pi$
$877$	2574.73	−	4459.56i	0.0991361	−	0.171709i	0.911327	+	0.411683i	$0.135059\pi$
$878$	4428.94	−	5194.08i	0.170238	−	0.199649i
$879$	1603.37	+	22998.0i	0.0615249	+	0.882483i
$880$	7288.19	+	1524.63i	0.279187	+	0.0584037i
$881$		−	26936.4i		−	1.03009i	−0.857162	−	0.515046i	$-0.827775\pi$
$881$		−	26936.4i		−	1.03009i	0.857162	−	0.515046i	$-0.172225\pi$
$882$	−21641.5	−	13775.3i	−0.826199	−	0.525894i
$883$		−	37301.8i		−	1.42164i	−0.703376	−	0.710818i	$-0.748325\pi$
$883$		−	37301.8i		−	1.42164i	0.703376	−	0.710818i	$-0.251675\pi$
$884$	−11698.2	+	1872.14i	−0.445084	+	0.0712295i
$885$	−1593.05	−	777.391i	−0.0605081	−	0.0295274i
$886$	10371.0	+	8843.25i	0.393252	+	0.335321i
$887$	17421.8	−	30175.4i	0.659488	−	1.14227i	−0.321261	−	0.946991i	$-0.604107\pi$
$887$	17421.8	−	30175.4i	0.659488	−	1.14227i	0.980748	−	0.195276i	$-0.0625601\pi$
$888$	−23415.7	+	1074.17i	−0.884888	+	0.0405931i
$889$	566.352	+	980.950i	0.0213665	+	0.0370079i
$890$	515.469	−	2793.78i	0.0194141	−	0.105222i
$891$	8544.11	−	34147.6i	0.321255	−	1.28394i
$892$	13588.5	−	35570.4i	0.510064	−	1.33519i
$893$	−6709.65	+	3873.82i	−0.251433	+	0.145165i
$894$	−12611.7	−	28957.5i	−0.471809	−	1.08332i
$895$	996.628	+	575.404i	0.0372219	+	0.0214901i
$896$	−3750.66	−	878.120i	−0.139845	−	0.0327410i
$897$	−18009.6	+	36905.8i	−0.670373	+	1.37374i
$898$	−8211.12	−	23128.3i	−0.305132	−	0.859466i
$899$	−31140.2			−1.15527
$900$	17536.2	−	18850.4i	0.649489	−	0.698163i
$901$	−12809.6			−0.473641
$902$	−10648.0	−	29992.4i	−0.393061	−	1.10714i
$903$	4020.98	−	280.335i	0.148184	−	0.0103311i
$904$	−8814.09	+	4813.27i	−0.324284	+	0.177087i
$905$	−1528.17	−	882.289i	−0.0561304	−	0.0324069i
$906$	13972.8	+	1583.54i	0.512379	+	0.0580681i
$907$	−7693.07	+	4441.59i	−0.281636	+	0.162603i	−0.634164	−	0.773199i	$-0.718656\pi$
$907$	−7693.07	+	4441.59i	−0.281636	+	0.162603i	0.352528	+	0.935801i	$0.385322\pi$
$908$	16668.8	+	6367.75i	0.609220	+	0.232732i
$909$	1631.34	+	11642.7i	0.0595250	+	0.424823i
$910$	−133.916	+	725.809i	−0.00487833	+	0.0264399i
$911$	22256.0	+	38548.6i	0.809413	+	1.40194i	0.913271	+	0.407352i	$0.133548\pi$
$911$	22256.0	+	38548.6i	0.809413	+	1.40194i	−0.103858	+	0.994592i	$0.533119\pi$
$912$	15709.9	+	38548.6i	0.570403	+	1.39964i
$913$	8423.14	−	14589.3i	0.305329	−	0.528845i
$914$	14893.6	+	12699.6i	0.538991	+	0.459591i
$915$	−160.182	+	107.996i	−0.00578740	+	0.00390190i
$916$	−7376.08	−	46090.1i	−0.266062	−	1.66251i
$917$		−	4638.16i		−	0.167029i
$918$	7543.68	+	12305.1i	0.271218	+	0.442407i
$919$		−	7223.63i		−	0.259288i	−0.991561	−	0.129644i	$-0.958617\pi$
$919$		−	7223.63i		−	0.259288i	0.991561	−	0.129644i	$-0.0413834\pi$
$920$	−251.469	+	10580.0i	−0.00901160	+	0.379145i
$921$	31851.2	−	21474.3i	1.13956	−	0.768297i
$922$	−28545.9	+	33477.5i	−1.01964	+	1.19579i
$923$	−570.670	+	988.430i	−0.0203509	+	0.0352487i
$924$	−3646.76	−	3899.69i	−0.129837	−	0.138842i
$925$	−11881.6	−	20579.5i	−0.422339	−	0.731512i
$926$	−32099.7	−	5922.60i	−1.13916	−	0.210182i
$927$	−37146.8	+	28997.4i	−1.31614	+	1.02740i
$928$	−19646.4	−	25391.4i	−0.694964	−	0.898182i
$929$	−30912.2	+	17847.2i	−1.09171	+	0.630298i	−0.934031	−	0.357193i	$-0.883734\pi$
$929$	−30912.2	+	17847.2i	−1.09171	+	0.630298i	−0.157677	+	0.987491i	$0.550401\pi$
$930$	−700.169	+	6178.13i	−0.0246876	+	0.217837i
$931$	36415.3	+	21024.4i	1.28192	+	0.740114i
$932$	15537.7	+	19124.4i	0.546089	+	0.672147i
$933$	−25381.4	+	1769.54i	−0.890620	+	0.0620922i
$934$	18.6919	−	6.63610i	0.000654837	−	0.000232484i
$935$	−4231.74			−0.148014
$936$	−24708.3	+	2865.23i	−0.862836	+	0.100057i
$937$	−4657.90			−0.162398			−0.0811991	−	0.996698i	$-0.525875\pi$
$937$	−4657.90			−0.162398			−0.0811991	+	0.996698i	$0.525875\pi$
$938$	1077.85	−	382.666i	0.0375194	−	0.0133203i
$939$	−1553.52	+	3183.50i	−0.0539905	+	0.110639i
$940$	−752.322	−	925.987i	−0.0261043	−	0.0321302i
$941$	22129.9	+	12776.7i	0.766645	+	0.442623i	0.831676	−	0.555260i	$-0.187381\pi$
$941$	22129.9	+	12776.7i	0.766645	+	0.442623i	−0.0650314	+	0.997883i	$0.520715\pi$
$942$	28204.8	−	12283.8i	0.975543	−	0.424872i
$943$	39174.9	−	22617.6i	1.35282	−	0.781051i
$944$	−6753.33	−	6041.44i	−0.232841	−	0.208297i
$945$	879.651	−	186.402i	0.0302805	−	0.00641658i
$946$	−39166.6	−	7226.48i	−1.34611	−	0.248365i
$947$	26469.6	+	45846.6i	0.908285	+	1.57319i	0.816447	+	0.577421i	$0.195941\pi$
$947$	26469.6	+	45846.6i	0.908285	+	1.57319i	0.0918380	+	0.995774i	$0.470726\pi$
$948$	−30316.2	+	7043.86i	−1.03863	+	0.241323i
$949$	−2534.42	+	4389.75i	−0.0866922	+	0.150155i
$950$	−27380.9	+	32111.2i	−0.935108	+	1.09666i
$951$	−7247.85	−	3536.88i	−0.247137	−	0.120600i
$952$	2188.63	+	52.0198i	0.0745103	+	0.00177098i
$953$		−	744.138i		−	0.0252938i	−0.999920	−	0.0126469i	$-0.995974\pi$
$953$		−	744.138i		−	0.0252938i	0.999920	−	0.0126469i	$-0.00402574\pi$
$954$	−26869.6	−	1162.66i	−0.911882	−	0.0394575i
$955$			7435.63i			0.251949i
$956$	6689.46	+	41799.7i	0.226310	+	1.41412i
$957$	−3094.81	−	44390.5i	−0.104536	−	1.49941i
$958$	12184.7	+	10389.7i	0.410927	+	0.350393i
$959$	−1957.04	+	3389.70i	−0.0658980	+	0.114139i
$960$	−5479.31	+	3326.89i	−0.184213	+	0.111849i
$961$	518.981	+	898.901i	0.0174207	+	0.0301736i
$962$	−4165.60	+	22577.0i	−0.139610	+	0.756666i
$963$	−7935.85	+	19618.4i	−0.265555	+	0.656486i
$964$	37390.3	+	14283.7i	1.24923	+	0.477228i
$965$	3410.28	−	1968.92i	0.113762	−	0.0656807i
$966$	4510.21	−	6102.82i	0.150221	−	0.203266i
$967$	−14044.5	−	8108.61i	−0.467054	−	0.269654i	0.247952	−	0.968772i	$-0.420243\pi$
$967$	−14044.5	−	8108.61i	−0.467054	−	0.269654i	−0.715006	+	0.699119i	$0.753576\pi$
$968$	10850.4	+	19869.3i	0.360274	+	0.659736i
$969$	−13225.1	−	19615.8i	−0.438444	−	0.650311i
$970$	−3431.81	−	9666.37i	−0.113597	−	0.319968i
$971$	−33620.7			−1.11116			−0.555582	−	0.831462i	$-0.687504\pi$
$971$	−33620.7			−1.11116			−0.555582	+	0.831462i	$0.687504\pi$
$972$	14706.8	+	26496.0i	0.485310	+	0.874342i
$973$	−3400.28			−0.112033
$974$	8594.50	+	24208.1i	0.282737	+	0.796385i
$975$	−14096.4	−	20908.2i	−0.463023	−	0.686768i
$976$	−938.221	+	308.192i	−0.0307702	+	0.0101076i
$977$	18376.3	+	10609.6i	0.601751	+	0.347421i	0.769730	−	0.638369i	$-0.220391\pi$
$977$	18376.3	+	10609.6i	0.601751	+	0.347421i	−0.167979	+	0.985791i	$0.553724\pi$
$978$	−12828.2	+	17358.0i	−0.419429	+	0.567535i
$979$	17431.8	−	10064.3i	0.569074	−	0.328555i
$980$	−2310.77	+	6048.85i	−0.0753211	+	0.197167i
$981$	−16016.3	+	39594.4i	−0.521265	+	1.28863i
$982$	5233.39	−	28364.3i	0.170065	−	0.921733i
$983$	−19149.3	−	33167.6i	−0.621331	−	1.07618i	−0.989238	−	0.146314i	$-0.953259\pi$
$983$	−19149.3	−	33167.6i	−0.621331	−	1.07618i	0.367907	−	0.929862i	$-0.380074\pi$
$984$	24331.5	+	12597.9i	0.788271	+	0.408138i
$985$	4036.68	−	6991.73i	0.130578	−	0.226168i
$986$	13883.8	+	11838.6i	0.448429	+	0.382371i
$987$	59.4993	+	853.429i	0.00191883	+	0.0275227i
$988$	40258.2	−	6442.76i	1.29634	−	0.207461i
$989$		−	56607.5i		−	1.82004i
$990$	−8876.53	−	384.091i	−0.284964	−	0.0123305i
$991$		−	17803.2i		−	0.570674i	−0.958427	−	0.285337i	$-0.907894\pi$
$991$		−	17803.2i		−	0.570674i	0.958427	−	0.285337i	$-0.0921055\pi$
$992$	−12044.7	+	29413.0i	−0.385505	+	0.941396i
$993$	34565.3	+	16867.5i	1.10463	+	0.539048i
$994$	136.846	−	160.488i	0.00436669	−	0.00512108i
$995$	1260.89	−	2183.93i	0.0401738	−	0.0695831i
$996$	3282.28	+	14126.7i	0.104421	+	0.449419i
$997$	−4517.89	−	7825.21i	−0.143513	−	0.248573i	0.785304	−	0.619110i	$-0.212507\pi$
$997$	−4517.89	−	7825.21i	−0.143513	−	0.248573i	−0.928817	+	0.370538i	$0.879173\pi$
$998$	−7557.78	−	1394.46i	−0.239717	−	0.0442292i
$999$	27362.4	−	5798.24i	0.866576	−	0.183632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.4.h.b.23.11	yes	24
3.2	odd	2		108.4.h.b.71.2		24
4.3	odd	2	inner	36.4.h.b.23.10	yes	24
9.2	odd	6	inner	36.4.h.b.11.10	✓	24
9.4	even	3		324.4.b.c.323.12		24
9.5	odd	6		324.4.b.c.323.13		24
9.7	even	3		108.4.h.b.35.3		24
12.11	even	2		108.4.h.b.71.3		24
36.7	odd	6		108.4.h.b.35.2		24
36.11	even	6	inner	36.4.h.b.11.11	yes	24
36.23	even	6		324.4.b.c.323.11		24
36.31	odd	6		324.4.b.c.323.14		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.10	✓	24	9.2	odd	6	inner
36.4.h.b.11.11	yes	24	36.11	even	6	inner
36.4.h.b.23.10	yes	24	4.3	odd	2	inner
36.4.h.b.23.11	yes	24	1.1	even	1	trivial
108.4.h.b.35.2		24	36.7	odd	6
108.4.h.b.35.3		24	9.7	even	3
108.4.h.b.71.2		24	3.2	odd	2
108.4.h.b.71.3		24	12.11	even	2
324.4.b.c.323.11		24	36.23	even	6
324.4.b.c.323.12		24	9.4	even	3
324.4.b.c.323.13		24	9.5	odd	6
324.4.b.c.323.14		24	36.31	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	36.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.66543 - 0.946295i) q^{2} +(-2.90476 - 4.30841i) q^{3} +(6.20905 - 5.04457i) q^{4} +(2.08666 + 1.20474i) q^{5} +(-11.8195 - 8.73501i) q^{6} +(2.30362 - 1.33000i) q^{7} +(11.7761 - 19.3216i) q^{8} +(-10.1248 + 25.0298i) q^{9} +(6.70190 + 1.23654i) q^{10} +(24.1428 + 41.8166i) q^{11} +(-39.7699 - 12.0979i) q^{12} +(-20.3570 + 35.2594i) q^{13} +(4.88158 - 5.72493i) q^{14} +(-0.870754 - 12.4897i) q^{15} +(13.1046 - 62.6440i) q^{16} +36.3729i q^{17} +(-3.30137 + 76.2961i) q^{18} -125.173i q^{19} +(19.0336 - 3.04606i) q^{20} +(-12.4216 - 6.06163i) q^{21} +(103.922 + 88.6131i) q^{22} +(-97.0560 + 168.106i) q^{23} +(-117.452 + 5.38796i) q^{24} +(-59.5972 - 103.225i) q^{25} +(-20.8944 + 113.245i) q^{26} +(137.248 - 29.0836i) q^{27} +(7.59405 - 19.8788i) q^{28} +(153.593 - 88.6772i) q^{29} +(-14.1399 - 32.4664i) q^{30} +(-152.058 - 87.7909i) q^{31} +(-24.3503 - 179.374i) q^{32} +(110.034 - 225.484i) q^{33} +(34.4195 + 96.9496i) q^{34} +6.40918 q^{35} +(63.3991 + 206.486i) q^{36} +199.364 q^{37} +(-118.451 - 333.641i) q^{38} +(211.044 - 14.7136i) q^{39} +(47.8502 - 26.1304i) q^{40} +(-201.816 - 116.518i) q^{41} +(-38.8451 - 4.40233i) q^{42} +(-252.553 + 145.812i) q^{43} +(360.851 + 137.851i) q^{44} +(-51.2813 + 40.0310i) q^{45} +(-99.6182 + 539.918i) q^{46} +(-30.9476 - 53.6029i) q^{47} +(-307.962 + 125.506i) q^{48} +(-167.962 + 290.919i) q^{49} +(-256.534 - 218.744i) q^{50} +(156.709 - 105.655i) q^{51} +(51.4707 + 321.620i) q^{52} +352.175i q^{53} +(338.305 - 207.398i) q^{54} +116.343i q^{55} +(1.43018 - 60.1718i) q^{56} +(-539.298 + 363.598i) q^{57} +(325.478 - 381.708i) q^{58} +(70.7911 - 122.614i) q^{59} +(-68.4116 - 73.1564i) q^{60} +(-7.71518 - 13.3631i) q^{61} +(-488.377 - 90.1086i) q^{62} +(9.96583 + 71.1251i) q^{63} +(-234.645 - 455.067i) q^{64} +(-84.9565 + 49.0496i) q^{65} +(79.9135 - 705.138i) q^{66} +(131.657 + 76.0120i) q^{67} +(183.486 + 225.841i) q^{68} +(1006.19 - 70.1497i) q^{69} +(17.0832 - 6.06498i) q^{70} +28.0331 q^{71} +(364.383 + 490.381i) q^{72} +124.499 q^{73} +(531.392 - 188.657i) q^{74} +(-271.622 + 556.614i) q^{75} +(-631.445 - 777.207i) q^{76} +(111.232 + 64.2199i) q^{77} +(548.600 - 238.928i) q^{78} +(648.411 - 374.360i) q^{79} +(102.814 - 114.929i) q^{80} +(-523.978 - 506.842i) q^{81} +(-648.187 - 119.595i) q^{82} +(-174.444 - 302.146i) q^{83} +(-107.705 + 25.0248i) q^{84} +(-43.8198 + 75.8981i) q^{85} +(-535.182 + 627.641i) q^{86} +(-828.210 - 404.158i) q^{87} +(1092.27 + 25.9614i) q^{88} -416.864i q^{89} +(-98.8056 + 155.227i) q^{90} +108.299i q^{91} +(245.397 + 1533.38i) q^{92} +(63.4532 + 910.140i) q^{93} +(-133.213 - 113.589i) q^{94} +(150.801 - 261.195i) q^{95} +(-702.085 + 625.949i) q^{96} +(-752.565 - 1303.48i) q^{97} +(-172.396 + 934.367i) q^{98} +(-1291.10 + 180.905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28}+ \cdots + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Introduction

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