LMFDB - Embedded newform 72.3.j.a.5.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,3,Mod(5,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("72.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	72.j (of order $6$, degree $2$, 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:	$1.96185790339$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	72.5
Dual form			72.3.j.a.29.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.405893 + 1.95838i) q^{2} +(-0.340809 + 2.98058i) q^{3} +(-3.67050 - 1.58979i) q^{4} +(-1.53127 + 2.65223i) q^{5} +(-5.69877 - 1.87723i) q^{6} +(-0.720479 - 1.24791i) q^{7} +(4.60324 - 6.54295i) q^{8} +(-8.76770 - 2.03162i) q^{9} +O(q^{10})$	\(q+(-0.405893 + 1.95838i) q^{2} +(-0.340809 + 2.98058i) q^{3} +(-3.67050 - 1.58979i) q^{4} +(-1.53127 + 2.65223i) q^{5} +(-5.69877 - 1.87723i) q^{6} +(-0.720479 - 1.24791i) q^{7} +(4.60324 - 6.54295i) q^{8} +(-8.76770 - 2.03162i) q^{9} +(-4.57254 - 4.07532i) q^{10} +(8.82792 + 15.2904i) q^{11} +(5.98942 - 10.3984i) q^{12} +(-8.00003 - 4.61882i) q^{13} +(2.73631 - 0.904455i) q^{14} +(-7.38331 - 5.46796i) q^{15} +(10.9452 + 11.6706i) q^{16} +4.69563i q^{17} +(7.53743 - 16.3459i) q^{18} +16.8874i q^{19} +(9.83699 - 7.30063i) q^{20} +(3.96503 - 1.72215i) q^{21} +(-33.5276 + 11.0821i) q^{22} +(33.8361 + 19.5353i) q^{23} +(17.9330 + 15.9502i) q^{24} +(7.81045 + 13.5281i) q^{25} +(12.2926 - 13.7924i) q^{26} +(9.04351 - 25.4404i) q^{27} +(0.660616 + 5.72585i) q^{28} +(-7.60350 - 13.1696i) q^{29} +(13.7052 - 12.2399i) q^{30} +(24.3515 - 42.1781i) q^{31} +(-27.2981 + 16.6978i) q^{32} +(-48.5829 + 21.1012i) q^{33} +(-9.19582 - 1.90592i) q^{34} +4.41298 q^{35} +(28.9520 + 21.3958i) q^{36} -14.1853i q^{37} +(-33.0719 - 6.85447i) q^{38} +(16.4932 - 22.2706i) q^{39} +(10.3046 + 22.2278i) q^{40} +(8.78457 + 5.07177i) q^{41} +(1.76324 + 8.46404i) q^{42} +(-19.3522 + 11.1730i) q^{43} +(-8.09442 - 70.1579i) q^{44} +(18.8140 - 20.1430i) q^{45} +(-51.9914 + 58.3347i) q^{46} +(-36.8675 + 21.2854i) q^{47} +(-38.5154 + 28.6455i) q^{48} +(23.4618 - 40.6371i) q^{49} +(-29.6634 + 9.80487i) q^{50} +(-13.9957 - 1.60031i) q^{51} +(22.0212 + 29.6717i) q^{52} -71.2201 q^{53} +(46.1513 + 28.0367i) q^{54} -54.0715 q^{55} +(-11.4815 - 1.03035i) q^{56} +(-50.3342 - 5.75538i) q^{57} +(28.8774 - 9.54507i) q^{58} +(34.9993 - 60.6205i) q^{59} +(18.4076 + 31.8080i) q^{60} +(89.7576 - 51.8216i) q^{61} +(72.7166 + 64.8093i) q^{62} +(3.78167 + 12.4050i) q^{63} +(-21.6204 - 60.2375i) q^{64} +(24.5003 - 14.1453i) q^{65} +(-21.6047 - 103.709i) q^{66} +(10.5162 + 6.07152i) q^{67} +(7.46504 - 17.2353i) q^{68} +(-69.7582 + 94.1934i) q^{69} +(-1.79120 + 8.64229i) q^{70} +112.880i q^{71} +(-53.6526 + 48.0146i) q^{72} +84.0137 q^{73} +(27.7801 + 5.75770i) q^{74} +(-42.9834 + 18.6692i) q^{75} +(26.8473 - 61.9852i) q^{76} +(12.7207 - 22.0328i) q^{77} +(36.9198 + 41.3395i) q^{78} +(-22.9826 - 39.8070i) q^{79} +(-47.7131 + 11.1583i) q^{80} +(72.7450 + 35.6252i) q^{81} +(-13.4981 + 15.1449i) q^{82} +(25.7884 + 44.6669i) q^{83} +(-17.2915 + 0.0175934i) q^{84} +(-12.4539 - 7.19025i) q^{85} +(-14.0261 - 42.4340i) q^{86} +(41.8445 - 18.1745i) q^{87} +(140.681 + 12.6247i) q^{88} -105.051i q^{89} +(31.8112 + 45.0208i) q^{90} +13.3111i q^{91} +(-93.1386 - 125.497i) q^{92} +(117.416 + 86.9563i) q^{93} +(-26.7207 - 80.8401i) q^{94} +(-44.7892 - 25.8591i) q^{95} +(-40.4655 - 87.0548i) q^{96} +(19.4321 + 33.6574i) q^{97} +(70.0598 + 62.4415i) q^{98} +(-46.3362 - 151.997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) $ 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.405893	+	1.95838i	−0.202947	+	0.979190i
$2$	−0.405893	+	1.95838i	−0.202947	+	0.979190i
$3$	−0.340809	+	2.98058i	−0.113603	+	0.993526i
$3$	−0.340809	+	2.98058i	−0.113603	+	0.993526i
$4$	−3.67050	−	1.58979i	−0.917625	−	0.397446i
$5$	−1.53127	+	2.65223i	−0.306253	+	0.530446i	−0.977540	−	0.210752i	$-0.932409\pi$
$5$	−1.53127	+	2.65223i	−0.306253	+	0.530446i	0.671286	+	0.741198i	$0.265742\pi$
$6$	−5.69877	−	1.87723i	−0.949795	−	0.312872i
$7$	−0.720479	−	1.24791i	−0.102926	−	0.178272i	0.809963	−	0.586481i	$-0.199487\pi$
$7$	−0.720479	−	1.24791i	−0.102926	−	0.178272i	−0.912889	+	0.408208i	$0.866154\pi$
$8$	4.60324	−	6.54295i	0.575404	−	0.817869i
$9$	−8.76770	−	2.03162i	−0.974189	−	0.225735i
$10$	−4.57254	−	4.07532i	−0.457254	−	0.407532i
$11$	8.82792	+	15.2904i	0.802538	+	1.39004i	0.917941	+	0.396718i	$0.129851\pi$
$11$	8.82792	+	15.2904i	0.802538	+	1.39004i	−0.115403	+	0.993319i	$0.536816\pi$
$12$	5.98942	−	10.3984i	0.499119	−	0.866534i
$13$	−8.00003	−	4.61882i	−0.615387	−	0.355294i	0.159684	−	0.987168i	$-0.448953\pi$
$13$	−8.00003	−	4.61882i	−0.615387	−	0.355294i	−0.775071	+	0.631874i	$0.782286\pi$
$14$	2.73631	−	0.904455i	0.195451	−	0.0646039i
$15$	−7.38331	−	5.46796i	−0.492221	−	0.364531i
$16$	10.9452	+	11.6706i	0.684073	+	0.729414i
$17$			4.69563i			0.276213i	0.990417	+	0.138107i	$0.0441017\pi$
$17$			4.69563i			0.276213i	−0.990417	+	0.138107i	$0.955898\pi$
$18$	7.53743	−	16.3459i	0.418746	−	0.908103i
$19$			16.8874i			0.888810i	0.895826	+	0.444405i	$0.146585\pi$
$19$			16.8874i			0.888810i	−0.895826	+	0.444405i	$0.853415\pi$
$20$	9.83699	−	7.30063i	0.491849	−	0.365031i
$21$	3.96503	−	1.72215i	0.188811	−	0.0820070i
$22$	−33.5276	+	11.0821i	−1.52398	+	0.503734i
$23$	33.8361	+	19.5353i	1.47114	+	0.849361i	0.999474	−	0.0324187i	$-0.0103210\pi$
$23$	33.8361	+	19.5353i	1.47114	+	0.849361i	0.471662	+	0.881780i	$0.343654\pi$
$24$	17.9330	+	15.9502i	0.747207	+	0.664592i
$25$	7.81045	+	13.5281i	0.312418	+	0.541124i
$26$	12.2926	−	13.7924i	0.472791	−	0.530475i
$27$	9.04351	−	25.4404i	0.334945	−	0.942238i
$28$	0.660616	+	5.72585i	0.0235934	+	0.204495i
$29$	−7.60350	−	13.1696i	−0.262190	−	0.454126i	0.704634	−	0.709571i	$-0.251111\pi$
$29$	−7.60350	−	13.1696i	−0.262190	−	0.454126i	−0.966823	+	0.255445i	$0.917778\pi$
$30$	13.7052	−	12.2399i	0.456839	−	0.407997i
$31$	24.3515	−	42.1781i	0.785533	−	1.36058i	−0.143147	−	0.989701i	$-0.545722\pi$
$31$	24.3515	−	42.1781i	0.785533	−	1.36058i	0.928680	−	0.370881i	$-0.120944\pi$
$32$	−27.2981	+	16.6978i	−0.853065	+	0.521805i
$33$	−48.5829	+	21.1012i	−1.47221	+	0.639430i
$34$	−9.19582	−	1.90592i	−0.270465	−	0.0560565i
$35$	4.41298			0.126085
$36$	28.9520	+	21.3958i	0.804222	+	0.594328i
$37$		−	14.1853i		−	0.383386i	−0.981455	−	0.191693i	$-0.938602\pi$
$37$		−	14.1853i		−	0.383386i	0.981455	−	0.191693i	$-0.0613977\pi$
$38$	−33.0719	−	6.85447i	−0.870314	−	0.180381i
$39$	16.4932	−	22.2706i	0.422904	−	0.571041i
$40$	10.3046	+	22.2278i	0.257616	+	0.555696i
$41$	8.78457	+	5.07177i	0.214258	+	0.123702i	0.603289	−	0.797523i	$-0.293857\pi$
$41$	8.78457	+	5.07177i	0.214258	+	0.123702i	−0.389031	+	0.921225i	$0.627190\pi$
$42$	1.76324	+	8.46404i	0.0419819	+	0.201525i
$43$	−19.3522	+	11.1730i	−0.450051	+	0.259837i	−0.707852	−	0.706361i	$-0.750336\pi$
$43$	−19.3522	+	11.1730i	−0.450051	+	0.259837i	0.257801	+	0.966198i	$0.417002\pi$
$44$	−8.09442	−	70.1579i	−0.183964	−	1.59450i
$45$	18.8140	−	20.1430i	0.418089	−	0.447622i
$46$	−51.9914	+	58.3347i	−1.13025	+	1.26815i
$47$	−36.8675	+	21.2854i	−0.784414	+	0.452882i	−0.837992	−	0.545682i	$-0.816271\pi$
$47$	−36.8675	+	21.2854i	−0.784414	+	0.452882i	0.0535784	+	0.998564i	$0.482937\pi$
$48$	−38.5154	+	28.6455i	−0.802405	+	0.596780i
$49$	23.4618	−	40.6371i	0.478813	−	0.829328i
$50$	−29.6634	+	9.80487i	−0.593267	+	0.196097i
$51$	−13.9957	−	1.60031i	−0.274425	−	0.0313787i
$52$	22.0212	+	29.6717i	0.423484	+	0.570610i
$53$	−71.2201			−1.34378			−0.671888	−	0.740653i	$-0.734516\pi$
$53$	−71.2201			−1.34378			−0.671888	+	0.740653i	$0.734516\pi$
$54$	46.1513	+	28.0367i	0.854654	+	0.519199i
$55$	−54.0715			−0.983119
$56$	−11.4815	−	1.03035i	−0.205027	−	0.0183991i
$57$	−50.3342	−	5.75538i	−0.883056	−	0.100972i
$58$	28.8774	−	9.54507i	0.497886	−	0.164570i
$59$	34.9993	−	60.6205i	0.593208	−	1.02747i	−0.400589	−	0.916258i	$-0.631195\pi$
$59$	34.9993	−	60.6205i	0.593208	−	1.02747i	0.993797	−	0.111208i	$-0.0354721\pi$
$60$	18.4076	+	31.8080i	0.306793	+	0.530134i
$61$	89.7576	−	51.8216i	1.47144	−	0.849534i	0.471951	−	0.881625i	$-0.343550\pi$
$61$	89.7576	−	51.8216i	1.47144	−	0.849534i	0.999485	+	0.0320909i	$0.0102166\pi$
$62$	72.7166	+	64.8093i	1.17285	+	1.04531i
$63$	3.78167	+	12.4050i	0.0600266	+	0.196905i
$64$	−21.6204	−	60.2375i	−0.337819	−	0.941211i
$65$	24.5003	−	14.1453i	0.376928	−	0.217620i
$66$	−21.6047	−	103.709i	−0.327344	−	1.57134i
$67$	10.5162	+	6.07152i	0.156958	+	0.0906197i	0.576422	−	0.817152i	$-0.304449\pi$
$67$	10.5162	+	6.07152i	0.156958	+	0.0906197i	−0.419464	+	0.907772i	$0.637782\pi$
$68$	7.46504	−	17.2353i	0.109780	−	0.253460i
$69$	−69.7582	+	94.1934i	−1.01099	+	1.36512i
$70$	−1.79120	+	8.64229i	−0.0255885	+	0.123461i
$71$			112.880i			1.58985i	0.606705	+	0.794927i	$0.292491\pi$
$71$			112.880i			1.58985i	−0.606705	+	0.794927i	$0.707509\pi$
$72$	−53.6526	+	48.0146i	−0.745174	+	0.666870i
$73$	84.0137			1.15087			0.575436	−	0.817847i	$-0.304832\pi$
$73$	84.0137			1.15087			0.575436	+	0.817847i	$0.304832\pi$
$74$	27.7801	+	5.75770i	0.375407	+	0.0778068i
$75$	−42.9834	+	18.6692i	−0.573113	+	0.248922i
$76$	26.8473	−	61.9852i	0.353254	−	0.815594i
$77$	12.7207	−	22.0328i	0.165203	−	0.286141i
$78$	36.9198	+	41.3395i	0.473330	+	0.529994i
$79$	−22.9826	−	39.8070i	−0.290918	−	0.503886i	0.683109	−	0.730317i	$-0.260627\pi$
$79$	−22.9826	−	39.8070i	−0.290918	−	0.503886i	−0.974027	+	0.226431i	$0.927294\pi$
$80$	−47.7131	+	11.1583i	−0.596414	+	0.139478i
$81$	72.7450	+	35.6252i	0.898087	+	0.439818i
$82$	−13.4981	+	15.1449i	−0.164610	+	0.184694i
$83$	25.7884	+	44.6669i	0.310704	+	0.538155i	0.978515	−	0.206176i	$-0.0661019\pi$
$83$	25.7884	+	44.6669i	0.310704	+	0.538155i	−0.667811	+	0.744331i	$0.732769\pi$
$84$	−17.2915	+	0.0175934i	−0.205851	+	0.000209446i
$85$	−12.4539	−	7.19025i	−0.146516	−	0.0845912i
$86$	−14.0261	−	42.4340i	−0.163094	−	0.493419i
$87$	41.8445	−	18.1745i	0.480971	−	0.208902i
$88$	140.681	+	12.6247i	1.59865	+	0.143462i
$89$		−	105.051i		−	1.18035i	−0.807275	−	0.590176i	$-0.799058\pi$
$89$		−	105.051i		−	1.18035i	0.807275	−	0.590176i	$-0.200942\pi$
$90$	31.8112	+	45.0208i	0.353457	+	0.500232i
$91$			13.3111i			0.146275i
$92$	−93.1386	−	125.497i	−1.01238	−	1.36409i
$93$	117.416	+	86.9563i	1.26254	+	0.935014i
$94$	−26.7207	−	80.8401i	−0.284263	−	0.860001i
$95$	−44.7892	−	25.8591i	−0.471465	−	0.272201i
$96$	−40.4655	−	87.0548i	−0.421516	−	0.906821i
$97$	19.4321	+	33.6574i	0.200331	+	0.346984i	0.948635	−	0.316372i	$-0.102465\pi$
$97$	19.4321	+	33.6574i	0.200331	+	0.346984i	−0.748304	+	0.663356i	$0.769131\pi$
$98$	70.0598	+	62.4415i	0.714896	+	0.637158i
$99$	−46.3362	−	151.997i	−0.468043	−	1.53532i
$100$	−7.16150	−	62.0719i	−0.0716150	−	0.620719i
$101$	56.5720	+	97.9855i	0.560118	+	0.970153i	0.997486	+	0.0708705i	$0.0225777\pi$
$101$	56.5720	+	97.9855i	0.560118	+	0.970153i	−0.437367	+	0.899283i	$0.644089\pi$
$102$	8.81477	−	26.7593i	0.0864194	−	0.262346i
$103$	−15.2049	+	26.3357i	−0.147621	+	0.255686i	−0.930348	−	0.366679i	$-0.880495\pi$
$103$	−15.2049	+	26.3357i	−0.147621	+	0.255686i	0.782727	+	0.622365i	$0.213828\pi$
$104$	−67.0468	+	31.0823i	−0.644680	+	0.298868i
$105$	−1.50399	+	13.1532i	−0.0143237	+	0.125269i
$106$	28.9078	−	139.476i	0.272715	−	1.31581i
$107$	−32.1820			−0.300767			−0.150383	−	0.988628i	$-0.548051\pi$
$107$	−32.1820			−0.300767			−0.150383	+	0.988628i	$0.548051\pi$
$108$	−73.6390	+	79.0018i	−0.681843	+	0.731499i
$109$			111.285i			1.02096i	0.859890	+	0.510480i	$0.170532\pi$
$109$			111.285i			1.02096i	−0.859890	+	0.510480i	$0.829468\pi$
$110$	21.9473	−	105.893i	0.199521	−	0.962660i
$111$	42.2803	+	4.83447i	0.380904	+	0.0435538i
$112$	6.67808	−	22.0670i	0.0596258	−	0.197027i
$113$	−90.1185	−	52.0300i	−0.797509	−	0.460442i	0.0450902	−	0.998983i	$-0.485642\pi$
$113$	−90.1185	−	52.0300i	−0.797509	−	0.460442i	−0.842599	+	0.538541i	$0.818976\pi$
$114$	31.7015	−	96.2374i	0.278084	−	0.844187i
$115$	−103.624	+	59.8275i	−0.901080	+	0.520239i
$116$	6.97174	+	60.4271i	0.0601012	+	0.520924i
$117$	60.7582	+	56.7494i	0.519301	+	0.485038i
$118$	104.512	+	93.1473i	0.885695	+	0.789384i
$119$	5.85970	−	3.38310i	0.0492412	−	0.0284294i
$120$	−69.7637	+	23.1383i	−0.581364	+	0.192819i
$121$	−95.3642	+	165.176i	−0.788134	+	1.36509i
$122$	65.0543	+	196.813i	0.533232	+	1.61323i
$123$	−18.1107	+	24.4546i	−0.147241	+	0.198818i
$124$	−156.436	+	116.101i	−1.26158	+	0.936298i
$125$	−124.403			−0.995222
$126$	−25.8287	+	2.37084i	−0.204989	+	0.0188162i
$127$	−215.952			−1.70041			−0.850203	−	0.526455i	$-0.823521\pi$
$127$	−215.952			−1.70041			−0.850203	+	0.526455i	$0.823521\pi$
$128$	126.743	−	17.8911i	0.990183	−	0.139774i
$129$	−26.7066	−	61.4886i	−0.207028	−	0.476656i
$130$	17.7573	+	53.7224i	0.136595	+	0.413250i
$131$	34.6904	−	60.0855i	0.264812	−	0.458668i	−0.702702	−	0.711484i	$-0.748023\pi$
$131$	34.6904	−	60.0855i	0.264812	−	0.458668i	0.967514	+	0.252816i	$0.0813567\pi$
$132$	211.870	−	0.215570i	1.60507	−	0.00163310i
$133$	21.0739	−	12.1670i	0.158450	−	0.0914813i
$134$	−16.1588	+	18.1303i	−0.120588	+	0.135301i
$135$	53.6258	+	62.9415i	0.397228	+	0.466233i
$136$	30.7233	+	21.6151i	0.225906	+	0.158934i
$137$	74.6700	−	43.1107i	0.545036	−	0.314677i	−0.202081	−	0.979369i	$-0.564771\pi$
$137$	74.6700	−	43.1107i	0.545036	−	0.314677i	0.747118	+	0.664692i	$0.231437\pi$
$138$	−156.152	−	174.845i	−1.13154	−	1.26700i
$139$	11.1876	+	6.45914i	0.0804861	+	0.0464686i	0.539703	−	0.841856i	$-0.318537\pi$
$139$	11.1876	+	6.45914i	0.0804861	+	0.0464686i	−0.459217	+	0.888324i	$0.651870\pi$
$140$	−16.1978	−	7.01569i	−0.115699	−	0.0501121i
$141$	−50.8781	−	117.141i	−0.360838	−	0.830784i
$142$	−221.061	−	45.8171i	−1.55677	−	0.322655i
$143$		−	163.098i		−	1.14055i
$144$	−72.2536	−	124.561i	−0.501761	−	0.865006i
$145$	46.5719			0.321185
$146$	−34.1006	+	164.531i	−0.233566	+	1.12692i
$147$	113.126	+	83.7793i	0.769564	+	0.569927i
$148$	−22.5515	+	52.0670i	−0.152375	+	0.351804i
$149$	44.5743	−	77.2049i	0.299156	−	0.518154i	−0.676787	−	0.736179i	$-0.736628\pi$
$149$	44.5743	−	77.2049i	0.299156	−	0.518154i	0.975943	+	0.218025i	$0.0699615\pi$
$150$	−19.1146	−	91.7556i	−0.127431	−	0.611704i
$151$	112.524	+	194.896i	0.745189	+	1.29070i	0.950107	+	0.311926i	$0.100974\pi$
$151$	112.524	+	194.896i	0.745189	+	1.29070i	−0.204918	+	0.978779i	$0.565693\pi$
$152$	110.493	+	77.7366i	0.726930	+	0.511425i
$153$	9.53972	−	41.1698i	0.0623511	−	0.269084i
$154$	37.9854	+	33.8549i	0.246659	+	0.219837i
$155$	74.5773	+	129.172i	0.481144	+	0.833365i
$156$	−95.9439	+	55.5235i	−0.615025	+	0.355920i
$157$	−140.012	−	80.8359i	−0.891795	−	0.514878i	−0.0172660	−	0.999851i	$-0.505496\pi$
$157$	−140.012	−	80.8359i	−0.891795	−	0.514878i	−0.874529	+	0.484973i	$0.838830\pi$
$158$	87.2856	−	28.8512i	0.552440	−	0.182603i
$159$	24.2725	−	212.277i	0.152657	−	1.33508i
$160$	−2.48569	−	97.9695i	−0.0155356	−	0.612309i
$161$		−	56.2991i		−	0.349684i
$162$	−99.2945	+	128.002i	−0.612929	+	0.790138i
$163$		−	181.252i		−	1.11197i	−0.831191	−	0.555987i	$-0.812340\pi$
$163$		−	181.252i		−	1.11197i	0.831191	−	0.555987i	$-0.187660\pi$
$164$	−24.1807	−	32.5815i	−0.147444	−	0.198668i
$165$	18.4281	−	161.164i	0.111685	−	0.976754i
$166$	−97.9420	+	32.3735i	−0.590012	+	0.195021i
$167$	7.64909	+	4.41620i	0.0458029	+	0.0264443i	0.522727	−	0.852500i	$-0.324915\pi$
$167$	7.64909	+	4.41620i	0.0458029	+	0.0264443i	−0.476924	+	0.878945i	$0.658248\pi$
$168$	6.98404	−	33.8705i	0.0415717	−	0.201610i
$169$	−41.8330	−	72.4569i	−0.247533	−	0.428739i
$170$	19.1362	−	21.4709i	0.112566	−	0.126300i
$171$	34.3087	−	148.064i	0.200636	−	0.865868i
$172$	88.7950	−	10.2447i	0.516250	−	0.0595620i
$173$	−25.6412	−	44.4119i	−0.148215	−	0.256716i	0.782353	−	0.622836i	$-0.214019\pi$
$173$	−25.6412	−	44.4119i	−0.148215	−	0.256716i	−0.930568	+	0.366120i	$0.880686\pi$
$174$	18.6081	+	89.3243i	0.106943	+	0.513358i
$175$	11.2545	−	19.4934i	0.0643117	−	0.111391i
$176$	−81.8255	+	270.383i	−0.464918	+	1.53627i
$177$	168.756	+	124.978i	0.953424	+	0.706091i
$178$	205.730	+	42.6396i	1.15579	+	0.239548i
$179$	−11.7809			−0.0658149			−0.0329074	−	0.999458i	$-0.510477\pi$
$179$	−11.7809			−0.0658149			−0.0329074	+	0.999458i	$0.510477\pi$
$180$	−101.080	+	44.0247i	−0.561555	+	0.244582i
$181$		−	215.066i		−	1.18821i	−0.804387	−	0.594105i	$-0.797506\pi$
$181$		−	215.066i		−	1.18821i	0.804387	−	0.594105i	$-0.202494\pi$
$182$	−26.0681	−	5.40287i	−0.143231	−	0.0296861i
$183$	123.868	+	285.191i	0.676874	+	1.55842i
$184$	283.574	−	131.463i	1.54116	−	0.714471i
$185$	37.6226	+	21.7214i	0.203365	+	0.117413i
$186$	−217.952	+	194.650i	−1.17178	+	1.04650i
$187$	−71.7980	+	41.4526i	−0.383947	+	0.221672i
$188$	169.161	−	19.5169i	0.899794	−	0.103813i
$189$	−38.2629	+	7.04383i	−0.202449	+	0.0372689i
$190$	68.8215	−	77.2183i	0.362218	−	0.406412i
$191$	55.6159	−	32.1098i	0.291183	−	0.168114i	−0.347292	−	0.937757i	$-0.612899\pi$
$191$	55.6159	−	32.1098i	0.291183	−	0.168114i	0.638475	+	0.769642i	$0.279566\pi$
$192$	186.911	−	43.9119i	0.973495	−	0.228708i
$193$	−100.634	+	174.304i	−0.521421	+	0.903127i	0.478269	+	0.878213i	$0.341264\pi$
$193$	−100.634	+	174.304i	−0.521421	+	0.903127i	−0.999690	+	0.0249138i	$0.992069\pi$
$194$	−73.8014	+	24.3942i	−0.380420	+	0.125743i
$195$	33.8112	+	77.8460i	0.173391	+	0.399210i
$196$	−150.721	+	111.859i	−0.768984	+	0.570710i
$197$	159.855			0.811448			0.405724	−	0.913996i	$-0.367019\pi$
$197$	159.855			0.811448			0.405724	+	0.913996i	$0.367019\pi$
$198$	316.475	−	29.0496i	1.59836	−	0.146715i
$199$	252.515			1.26892			0.634461	−	0.772955i	$-0.281222\pi$
$199$	252.515			1.26892			0.634461	+	0.772955i	$0.281222\pi$
$200$	124.467	+	11.1696i	0.622335	+	0.0558481i
$201$	−21.6807	+	29.2751i	−0.107864	+	0.145647i
$202$	−214.855	+	71.0177i	−1.06364	+	0.351573i
$203$	−10.9563	+	18.9769i	−0.0539720	+	0.0934823i
$204$	48.8270	+	28.1241i	0.239348	+	0.137863i
$205$	−26.9030	+	15.5325i	−0.131234	+	0.0757681i
$206$	−45.4037	−	40.4665i	−0.220406	−	0.196439i
$207$	−256.977	−	240.022i	−1.24143	−	1.15953i
$208$	−33.6571	−	143.919i	−0.161813	−	0.691919i
$209$	−258.215	+	149.080i	−1.23548	+	0.713304i
$210$	−25.1486	−	8.28418i	−0.119755	−	0.0394485i
$211$	298.780	+	172.501i	1.41602	+	0.817539i	0.995946	−	0.0899512i	$-0.0286711\pi$
$211$	298.780	+	172.501i	1.41602	+	0.817539i	0.420073	+	0.907490i	$0.362004\pi$
$212$	261.414	+	113.225i	1.23308	+	0.534079i
$213$	−336.447	−	38.4705i	−1.57956	−	0.180612i
$214$	13.0625	−	63.0246i	0.0610395	−	0.294508i
$215$		−	68.4353i		−	0.318304i
$216$	−124.826	−	176.280i	−0.577898	−	0.816109i
$217$	−70.1791			−0.323406
$218$	−217.938	−	45.1697i	−0.999713	−	0.207200i
$219$	−28.6327	+	250.409i	−0.130743	+	1.14342i
$220$	198.470	+	85.9621i	0.902135	+	0.390737i
$221$	21.6883	−	37.5652i	0.0981369	−	0.169978i
$222$	−26.6290	+	80.8386i	−0.119951	+	0.364138i
$223$	−40.4737	−	70.1025i	−0.181496	−	0.314361i	0.760894	−	0.648876i	$-0.224761\pi$
$223$	−40.4737	−	70.1025i	−0.181496	−	0.314361i	−0.942390	+	0.334515i	$0.891427\pi$
$224$	40.5049	+	22.0351i	0.180826	+	0.0983708i
$225$	−40.9957	−	134.478i	−0.182203	−	0.597681i
$226$	138.473	−	155.368i	0.612712	−	0.687468i
$227$	−82.8163	−	143.442i	−0.364829	−	0.631903i	0.623919	−	0.781489i	$-0.285539\pi$
$227$	−82.8163	−	143.442i	−0.364829	−	0.631903i	−0.988749	+	0.149586i	$0.952206\pi$
$228$	175.602	+	101.146i	0.770184	+	0.443622i
$229$	8.73696	+	5.04428i	0.0381527	+	0.0220274i	0.518955	−	0.854802i	$-0.326321\pi$
$229$	8.73696	+	5.04428i	0.0381527	+	0.0220274i	−0.480802	+	0.876829i	$0.659655\pi$
$230$	−75.1045	−	227.219i	−0.326541	−	0.987909i
$231$	61.3353	+	45.4239i	0.265521	+	0.196640i
$232$	−121.169	−	10.8737i	−0.522280	−	0.0468692i
$233$			219.759i			0.943170i	0.881821	+	0.471585i	$0.156318\pi$
$233$			219.759i			0.943170i	−0.881821	+	0.471585i	$0.843682\pi$
$234$	−135.798	+	95.9534i	−0.580334	+	0.410057i
$235$		−	130.375i		−	0.554785i
$236$	−224.838	+	166.866i	−0.952705	+	0.707061i
$237$	126.480	−	54.9347i	0.533673	−	0.231792i
$238$	4.24698	+	12.8487i	0.0178445	+	0.0539861i
$239$	−40.2815	−	23.2565i	−0.168542	−	0.0973076i	0.413356	−	0.910569i	$-0.364356\pi$
$239$	−40.2815	−	23.2565i	−0.168542	−	0.0973076i	−0.581898	+	0.813262i	$0.697690\pi$
$240$	−16.9970	−	146.016i	−0.0708208	−	0.608398i
$241$	−236.902	−	410.326i	−0.982995	−	1.70260i	−0.650529	−	0.759481i	$-0.725453\pi$
$241$	−236.902	−	410.326i	−0.982995	−	1.70260i	−0.332465	−	0.943115i	$-0.607880\pi$
$242$	−284.769	−	253.803i	−1.17673	−	1.04877i
$243$	−130.976	+	204.681i	−0.538996	+	0.842308i
$244$	−411.841	+	47.5158i	−1.68787	+	0.194737i
$245$	71.8525	+	124.452i	0.293276	+	0.507968i
$246$	−40.5404	−	45.3935i	−0.164798	−	0.184527i
$247$	77.9998	−	135.100i	0.315789	−	0.546962i
$248$	−163.873	−	353.486i	−0.660779	−	1.42535i
$249$	−141.922	+	61.6415i	−0.569968	+	0.247556i
$250$	50.4942	−	243.628i	0.201977	−	0.974511i
$251$	−151.118			−0.602065			−0.301033	−	0.953614i	$-0.597331\pi$
$251$	−151.118			−0.602065			−0.301033	+	0.953614i	$0.597331\pi$
$252$	5.84067	−	51.5447i	0.0231772	−	0.204542i
$253$			689.824i			2.72658i
$254$	87.6533	−	422.915i	0.345092	−	1.66502i
$255$	25.6755	−	34.6693i	0.100688	−	0.135958i
$256$	−16.4068	+	255.474i	−0.0640892	+	0.997944i
$257$	260.239	+	150.249i	1.01260	+	0.584626i	0.911952	−	0.410296i	$-0.134575\pi$
$257$	260.239	+	150.249i	1.01260	+	0.584626i	0.100649	+	0.994922i	$0.467908\pi$
$258$	131.258	−	27.3438i	0.508752	−	0.105984i
$259$	−17.7019	+	10.2202i	−0.0683471	+	0.0394602i
$260$	−112.417	+	12.9700i	−0.432371	+	0.0498845i
$261$	39.9095	+	130.915i	0.152910	+	0.501590i
$262$	103.590	+	92.3253i	0.395381	+	0.352387i
$263$	42.6088	−	24.6002i	0.162011	−	0.0935369i	−0.416803	−	0.908997i	$-0.636849\pi$
$263$	42.6088	−	24.6002i	0.162011	−	0.0935369i	0.578813	+	0.815460i	$0.303516\pi$
$264$	−85.5744	+	415.009i	−0.324145	+	1.57200i
$265$	109.057	−	188.892i	0.411536	−	0.712801i
$266$	15.2739	+	46.2092i	0.0574206	+	0.173719i
$267$	313.114	+	35.8025i	1.17271	+	0.134092i
$268$	−28.9472	−	39.0040i	−0.108012	−	0.145537i
$269$	−151.922			−0.564767			−0.282383	−	0.959302i	$-0.591125\pi$
$269$	−151.922			−0.564767			−0.282383	+	0.959302i	$0.591125\pi$
$270$	−145.030	+	79.4722i	−0.537147	+	0.294341i
$271$	114.040			0.420811			0.210405	−	0.977614i	$-0.432522\pi$
$271$	114.040			0.420811			0.210405	+	0.977614i	$0.432522\pi$
$272$	−54.8009	+	51.3944i	−0.201474	+	0.188950i
$273$	−39.6747	−	4.53653i	−0.145328	−	0.0166173i
$274$	54.1191	+	163.730i	0.197515	+	0.597556i
$275$	−137.900	+	238.850i	−0.501455	+	0.868545i
$276$	405.795	−	234.837i	1.47027	−	0.850857i
$277$	113.520	−	65.5405i	0.409818	−	0.236608i	−0.280894	−	0.959739i	$-0.590631\pi$
$277$	113.520	−	65.5405i	0.409818	−	0.236608i	0.690711	+	0.723130i	$0.257297\pi$
$278$	−17.1904	+	19.2878i	−0.0618360	+	0.0693805i
$279$	−299.197	+	320.332i	−1.07239	+	1.14814i
$280$	20.3140	−	28.8739i	0.0725499	−	0.103121i
$281$	−150.809	+	87.0694i	−0.536686	+	0.309856i	−0.743735	−	0.668475i	$-0.766947\pi$
$281$	−150.809	+	87.0694i	−0.536686	+	0.309856i	0.207049	+	0.978331i	$0.433614\pi$
$282$	250.057	−	52.0921i	0.886726	−	0.184724i
$283$	102.291	+	59.0577i	0.361452	+	0.208685i	0.669718	−	0.742616i	$-0.266415\pi$
$283$	102.291	+	59.0577i	0.361452	+	0.208685i	−0.308265	+	0.951300i	$0.599748\pi$
$284$	179.454	−	414.325i	0.631882	−	1.45889i
$285$	92.3396	−	124.685i	0.323999	−	0.437490i
$286$	319.408	+	66.2005i	1.11681	+	0.231470i
$287$		−	14.6164i		−	0.0509283i
$288$	273.265	−	90.9416i	0.948836	−	0.315769i
$289$	266.951			0.923706
$290$	−18.9032	+	91.2054i	−0.0651835	+	0.314502i
$291$	−106.941	+	46.4482i	−0.367496	+	0.159616i
$292$	−308.372	−	133.564i	−1.05607	−	0.457410i
$293$	16.3661	−	28.3470i	0.0558571	−	0.0967473i	−0.836745	−	0.547593i	$-0.815544\pi$
$293$	16.3661	−	28.3470i	0.0558571	−	0.0967473i	0.892602	+	0.450846i	$0.148878\pi$
$294$	−209.989	+	187.538i	−0.714247	+	0.637885i
$295$	107.186	+	185.652i	0.363343	+	0.629329i
$296$	−92.8135	−	65.2981i	−0.313559	−	0.220602i
$297$	468.830	−	86.3069i	1.57855	−	0.290596i
$298$	133.104	+	118.630i	0.446658	+	0.398088i
$299$	−180.460	−	312.566i	−0.603545	−	1.04537i
$300$	187.451	−	0.190724i	0.624836	−	0.000635747i
$301$	27.8857	+	16.0998i	0.0926436	+	0.0534878i
$302$	−427.354	+	141.257i	−1.41508	+	0.467737i
$303$	−311.334	+	135.223i	−1.02750	+	0.446280i
$304$	−197.086	+	184.835i	−0.648310	+	0.608010i
$305$			317.410i			1.04069i
$306$	76.7541	+	35.3930i	0.250830	+	0.115663i
$307$		−	309.352i		−	1.00766i	−0.863802	−	0.503831i	$-0.831923\pi$
$307$		−	309.352i		−	1.00766i	0.863802	−	0.503831i	$-0.168077\pi$
$308$	−81.7187	+	60.6484i	−0.265320	+	0.196910i
$309$	−73.3136	−	54.2949i	−0.237261	−	0.175712i
$310$	−283.237	+	93.6207i	−0.913669	+	0.302002i
$311$	109.674	+	63.3205i	0.352651	+	0.203603i	0.665852	−	0.746084i	$-0.268068\pi$
$311$	109.674	+	63.3205i	0.352651	+	0.203603i	−0.313201	+	0.949687i	$0.601402\pi$
$312$	−69.7931	−	210.431i	−0.223696	−	0.674459i
$313$	−98.6327	−	170.837i	−0.315120	−	0.545804i	0.664343	−	0.747428i	$-0.268712\pi$
$313$	−98.6327	−	170.837i	−0.315120	−	0.545804i	−0.979463	+	0.201624i	$0.935378\pi$
$314$	215.137	−	241.386i	0.685150	−	0.768744i
$315$	−38.6917	−	8.96549i	−0.122831	−	0.0284619i
$316$	21.0730	+	182.649i	0.0666866	+	0.578003i
$317$	−95.6999	−	165.757i	−0.301892	−	0.522893i	0.674672	−	0.738118i	$-0.264285\pi$
$317$	−95.6999	−	165.757i	−0.301892	−	0.522893i	−0.976565	+	0.215224i	$0.930952\pi$
$318$	405.867	+	133.697i	1.27631	+	0.420430i
$319$	134.246	−	232.521i	0.420834	−	0.728906i
$320$	192.870	+	34.8972i	0.602720	+	0.109054i
$321$	10.9679	−	95.9210i	0.0341680	−	0.298819i
$322$	110.255	+	22.8514i	0.342407	+	0.0709672i
$323$	−79.2969			−0.245501
$324$	−210.374	−	246.412i	−0.649303	−	0.760529i
$325$		−	144.300i		−	0.444001i
$326$	354.960	+	73.5688i	1.08883	+	0.225671i
$327$	−331.693	−	37.9269i	−1.01435	−	0.115984i
$328$	73.6218	−	34.1305i	0.224457	−	0.104056i
$329$	53.1245	+	30.6714i	0.161473	+	0.0932262i
$330$	308.141	+	101.505i	0.933762	+	0.307590i
$331$	325.099	−	187.696i	0.982171	−	0.567057i	0.0792463	−	0.996855i	$-0.474749\pi$
$331$	325.099	−	187.696i	0.982171	−	0.567057i	0.902925	+	0.429798i	$0.141415\pi$
$332$	−23.6457	−	204.948i	−0.0712220	−	0.617313i
$333$	−28.8191	+	124.372i	−0.0865437	+	0.373490i
$334$	−11.7533	+	13.1873i	−0.0351896	+	0.0394830i
$335$	−32.2061	+	18.5942i	−0.0961377	+	0.0555051i
$336$	63.4964	+	27.4252i	0.188977	+	0.0816226i
$337$	−11.6541	+	20.1854i	−0.0345818	+	0.0598974i	−0.882798	−	0.469752i	$-0.844343\pi$
$337$	−11.6541	+	20.1854i	−0.0345818	+	0.0598974i	0.848217	+	0.529650i	$0.177677\pi$
$338$	158.878	−	52.5151i	0.470053	−	0.155370i
$339$	185.793	−	250.873i	0.548061	−	0.740039i
$340$	34.2810	+	46.1908i	0.100827	+	0.135855i
$341$	859.893			2.52168
$342$	276.039	+	127.287i	0.807131	+	0.372186i
$343$	−138.222			−0.402980
$344$	−15.9783	+	178.053i	−0.0464487	+	0.517595i
$345$	−143.004	−	329.250i	−0.414505	−	0.954347i
$346$	97.3829	−	32.1887i	0.281453	−	0.0930310i
$347$	−33.4878	+	58.0026i	−0.0965067	+	0.167154i	−0.910236	−	0.414089i	$-0.864100\pi$
$347$	−33.4878	+	58.0026i	−0.0965067	+	0.167154i	0.813730	+	0.581243i	$0.197434\pi$
$348$	−182.484	+	0.185670i	−0.524379	+	0.000533536i
$349$	−300.105	+	173.265i	−0.859898	+	0.496463i	−0.863978	−	0.503529i	$-0.832035\pi$
$349$	−300.105	+	173.265i	−0.859898	+	0.496463i	0.00407991	+	0.999992i	$0.498701\pi$
$350$	33.6074	+	29.9529i	0.0960212	+	0.0855797i
$351$	−189.853	+	161.754i	−0.540892	+	0.460837i
$352$	−496.301	−	269.992i	−1.40994	−	0.767023i
$353$	509.538	−	294.182i	1.44345	−	0.833377i	0.445374	−	0.895345i	$-0.353071\pi$
$353$	509.538	−	294.182i	1.44345	−	0.833377i	0.998078	+	0.0619676i	$0.0197376\pi$
$354$	−313.251	+	279.761i	−0.884891	+	0.790284i
$355$	−299.383	−	172.849i	−0.843332	−	0.486898i
$356$	−167.009	+	385.591i	−0.469127	+	1.08312i
$357$	8.08656	+	18.6183i	0.0226514	+	0.0521521i
$358$	4.78177	−	23.0714i	0.0133569	−	0.0644453i
$359$			325.201i			0.905854i	0.891548	+	0.452927i	$0.149620\pi$
$359$			325.201i			0.905854i	−0.891548	+	0.452927i	$0.850380\pi$
$360$	−45.1894	−	215.822i	−0.125526	−	0.599506i
$361$	75.8162			0.210017
$362$	421.181	+	87.2939i	1.16348	+	0.241143i
$363$	−459.818	−	340.534i	−1.26672	−	0.938110i
$364$	21.1617	−	48.8583i	0.0581366	−	0.134226i
$365$	−128.647	+	222.824i	−0.352458	+	0.610476i
$366$	−608.789	+	126.824i	−1.66336	+	0.346513i
$367$	102.698	+	177.879i	0.279832	+	0.484683i	0.971343	−	0.237683i	$-0.0763879\pi$
$367$	102.698	+	177.879i	0.279832	+	0.484683i	−0.691511	+	0.722366i	$0.743055\pi$
$368$	142.353	+	608.706i	0.386828	+	1.65409i
$369$	−66.7165	−	62.3147i	−0.180804	−	0.168874i
$370$	−57.8095	+	64.8627i	−0.156242	+	0.175305i
$371$	51.3126	+	88.8761i	0.138309	+	0.239558i
$372$	−292.733	−	505.839i	−0.786917	−	1.35978i
$373$	−329.480	−	190.225i	−0.883325	−	0.509988i	−0.0115716	−	0.999933i	$-0.503683\pi$
$373$	−329.480	−	190.225i	−0.883325	−	0.509988i	−0.871753	+	0.489945i	$0.837017\pi$
$374$	−52.0376	−	157.433i	−0.139138	−	0.420944i
$375$	42.3976	−	370.792i	0.113060	−	0.988779i
$376$	−30.4400	+	339.204i	−0.0809574	+	0.902138i
$377$			140.477i			0.372617i
$378$	1.73617	−	77.7924i	0.00459303	−	0.205800i
$379$		−	122.536i		−	0.323315i	−0.986847	−	0.161658i	$-0.948316\pi$
$379$		−	122.536i		−	0.323315i	0.986847	−	0.161658i	$-0.0516840\pi$
$380$	123.289	+	166.121i	0.324443	+	0.437161i
$381$	73.5984	−	643.661i	0.193172	−	1.68940i
$382$	40.3092	+	121.950i	0.105521	+	0.319241i
$383$	−140.462	−	81.0958i	−0.366742	−	0.211738i	0.305292	−	0.952259i	$-0.401246\pi$
$383$	−140.462	−	81.0958i	−0.366742	−	0.211738i	−0.672034	+	0.740520i	$0.734579\pi$
$384$	10.1303	+	383.866i	0.0263810	+	0.999652i
$385$	38.9574	+	67.4762i	0.101188	+	0.175263i
$386$	−300.506	−	267.829i	−0.778513	−	0.693857i
$387$	192.374	−	58.6452i	0.497089	−	0.151538i
$388$	−17.8176	−	154.433i	−0.0459215	−	0.398022i
$389$	129.033	+	223.492i	0.331704	+	0.574528i	0.982846	−	0.184428i	$-0.0590431\pi$
$389$	129.033	+	223.492i	0.331704	+	0.574528i	−0.651142	+	0.758956i	$0.725710\pi$
$390$	−166.176	+	34.6179i	−0.426092	+	0.0887639i
$391$	−91.7305	+	158.882i	−0.234605	+	0.406347i
$392$	−157.886	−	340.572i	−0.402771	−	0.868805i
$393$	167.267	+	123.875i	0.425615	+	0.315204i
$394$	−64.8841	+	313.057i	−0.164681	+	0.794561i
$395$	140.770			0.356379
$396$	−71.5647	+	631.568i	−0.180719	+	1.59487i
$397$			214.037i			0.539137i	0.962981	+	0.269568i	$0.0868810\pi$
$397$			214.037i			0.539137i	−0.962981	+	0.269568i	$0.913119\pi$
$398$	−102.494	+	494.521i	−0.257523	+	1.24252i
$399$	29.0826	+	66.9590i	0.0728886	+	0.167817i
$400$	−72.3947	+	239.220i	−0.180987	+	0.598050i
$401$	−234.012	−	135.107i	−0.583572	−	0.336925i	0.178980	−	0.983853i	$-0.442720\pi$
$401$	−234.012	−	135.107i	−0.583572	−	0.336925i	−0.762551	+	0.646928i	$0.776054\pi$
$402$	−48.5317	−	54.3415i	−0.120726	−	0.135178i
$403$	−389.626	+	224.951i	−0.966814	+	0.558190i
$404$	−51.8715	−	449.593i	−0.128395	−	1.11285i
$405$	−205.878	+	138.385i	−0.508341	+	0.341691i
$406$	−32.7169	−	29.1592i	−0.0805835	−	0.0718208i
$407$	216.898	−	125.226i	0.532920	−	0.307681i
$408$	−74.8962	+	84.2065i	−0.183569	+	0.206388i
$409$	−5.82738	+	10.0933i	−0.0142479	+	0.0246781i	−0.873061	−	0.487610i	$-0.837869\pi$
$409$	−5.82738	+	10.0933i	−0.0142479	+	0.0246781i	0.858814	+	0.512288i	$0.171202\pi$
$410$	−19.4987	−	58.9908i	−0.0475578	−	0.143880i
$411$	103.047	+	237.252i	0.250722	+	0.577256i
$412$	97.6778	−	72.4926i	0.237082	−	0.175953i
$413$	−100.865			−0.244225
$414$	574.359	−	405.835i	1.38734	−	0.980277i
$415$	−157.956			−0.380616
$416$	295.509	−	7.49769i	0.710359	−	0.0180233i
$417$	−23.0648	+	31.1441i	−0.0553113	+	0.0746860i
$418$	−187.148	−	566.194i	−0.447724	−	1.35453i
$419$	136.041	−	235.630i	0.324681	−	0.562363i	−0.656767	−	0.754094i	$-0.728077\pi$
$419$	136.041	−	235.630i	0.324681	−	0.562363i	0.981448	+	0.191730i	$0.0614099\pi$
$420$	26.4312	−	45.8879i	0.0629314	−	0.109257i
$421$	434.012	−	250.577i	1.03091	−	0.595195i	0.113663	−	0.993519i	$-0.463742\pi$
$421$	434.012	−	250.577i	1.03091	−	0.595195i	0.917245	+	0.398325i	$0.130408\pi$
$422$	−459.095	+	515.108i	−1.08790	+	1.22063i
$423$	366.487	−	111.724i	0.866398	−	0.264122i
$424$	−327.843	+	465.990i	−0.773215	+	1.09903i
$425$	−63.5229	+	36.6750i	−0.149466	+	0.0862940i
$426$	211.901	−	643.275i	0.497421	−	1.51004i
$427$	−129.337	−	74.6727i	−0.302897	−	0.174878i
$428$	118.124	+	51.1625i	0.275991	+	0.119539i
$429$	486.127	+	55.5854i	1.13316	+	0.129570i
$430$	134.022	+	27.7774i	0.311680	+	0.0645987i
$431$		−	701.705i		−	1.62809i	−0.580805	−	0.814043i	$-0.697262\pi$
$431$		−	701.705i		−	1.62809i	0.580805	−	0.814043i	$-0.302738\pi$
$432$	395.888	−	172.906i	0.916408	−	0.400246i
$433$	−387.204			−0.894236			−0.447118	−	0.894475i	$-0.647550\pi$
$433$	−387.204			−0.894236			−0.447118	+	0.894475i	$0.647550\pi$
$434$	28.4852	−	137.437i	0.0656341	−	0.316676i
$435$	−15.8721	+	138.811i	−0.0364877	+	0.319106i
$436$	176.919	−	408.470i	0.405777	−	0.936859i
$437$	−329.900	+	571.404i	−0.754920	+	1.30756i
$438$	−478.775	−	157.713i	−1.09309	−	0.360076i
$439$	162.134	+	280.825i	0.369327	+	0.639693i	0.989460	−	0.144803i	$-0.0462550\pi$
$439$	162.134	+	280.825i	0.369327	+	0.639693i	−0.620134	+	0.784496i	$0.712922\pi$
$440$	−248.904	+	353.787i	−0.565691	+	0.804062i
$441$	−288.265	+	308.628i	−0.653663	+	0.699837i
$442$	64.7637	+	57.7213i	0.146524	+	0.130591i
$443$	−5.05092	−	8.74845i	−0.0114016	−	0.0197482i	0.860268	−	0.509842i	$-0.170296\pi$
$443$	−5.05092	−	8.74845i	−0.0114016	−	0.0197482i	−0.871670	+	0.490093i	$0.836963\pi$
$444$	−147.504	−	84.9616i	−0.332216	−	0.191355i
$445$	278.620	+	160.861i	0.626113	+	0.361486i
$446$	153.715	−	50.8088i	0.344653	−	0.113921i
$447$	214.924	+	159.169i	0.480814	+	0.356084i
$448$	−59.5937	+	70.3802i	−0.133022	+	0.157099i
$449$		−	71.1875i		−	0.158547i	−0.996853	−	0.0792734i	$-0.974740\pi$
$449$		−	71.1875i		−	0.158547i	0.996853	−	0.0792734i	$-0.0252600\pi$
$450$	279.999	−	25.7015i	0.622220	−	0.0571144i
$451$			179.093i			0.397102i
$452$	248.064	+	334.245i	0.548814	+	0.739481i
$453$	−619.253	+	268.963i	−1.36700	+	0.593736i
$454$	314.528	−	103.964i	0.692794	−	0.228995i
$455$	−35.3040	−	20.3828i	−0.0775912	−	0.0447973i
$456$	−269.357	+	302.841i	−0.590696	+	0.664125i
$457$	167.424	+	289.988i	0.366355	+	0.634546i	0.988993	−	0.147964i	$-0.0472721\pi$
$457$	167.424	+	289.988i	0.366355	+	0.634546i	−0.622637	+	0.782511i	$0.713939\pi$
$458$	−13.4249	+	15.0628i	−0.0293120	+	0.0328883i
$459$	119.459	+	42.4650i	0.260259	+	0.0925163i
$460$	475.466	−	54.8565i	1.03362	−	0.119253i
$461$	−405.586	−	702.496i	−0.879796	−	1.52385i	−0.851564	−	0.524250i	$-0.824346\pi$
$461$	−405.586	−	702.496i	−0.879796	−	1.52385i	−0.0282317	−	0.999601i	$-0.508988\pi$
$462$	−113.853	+	101.680i	−0.246435	+	0.220088i
$463$	51.1602	−	88.6121i	0.110497	−	0.191387i	−0.805474	−	0.592632i	$-0.798089\pi$
$463$	51.1602	−	88.6121i	0.110497	−	0.191387i	0.915971	+	0.401245i	$0.131422\pi$
$464$	70.4764	−	232.881i	0.151889	−	0.501900i
$465$	−410.423	+	178.261i	−0.882630	+	0.383356i
$466$	−430.371	−	89.1985i	−0.923542	−	0.191413i
$467$	211.289			0.452439			0.226220	−	0.974076i	$-0.427363\pi$
$467$	211.289			0.452439			0.226220	+	0.974076i	$0.427363\pi$
$468$	−132.794	−	304.891i	−0.283747	−	0.651477i
$469$		−	17.4976i		−	0.0373084i
$470$	255.323	+	52.9181i	0.543240	+	0.112592i
$471$	288.655	−	389.767i	0.612856	−	0.827530i
$472$	−235.527	−	508.049i	−0.498998	−	1.07637i
$473$	−341.679	−	197.269i	−0.722367	−	0.417058i
$474$	56.2455	+	269.994i	0.118661	+	0.569608i
$475$	−228.454	+	131.898i	−0.480956	+	0.277680i
$476$	−26.8865	+	3.10201i	−0.0564842	+	0.00651682i
$477$	624.437	+	144.692i	1.30909	+	0.303338i
$478$	61.8950	−	69.4467i	0.129488	−	0.145286i
$479$	−400.335	+	231.133i	−0.835772	+	0.482533i	−0.855825	−	0.517266i	$-0.826950\pi$
$479$	−400.335	+	231.133i	−0.835772	+	0.482533i	0.0200529	+	0.999799i	$0.493617\pi$
$480$	292.853	+	25.9801i	0.610110	+	0.0541253i
$481$	−65.5192	+	113.483i	−0.136215	+	0.235931i
$482$	899.730	−	297.395i	1.86666	−	0.617002i
$483$	167.804	+	19.1873i	0.347420	+	0.0397252i
$484$	612.628	−	454.669i	1.26576	−	0.939399i
$485$	−119.023			−0.245408
$486$	−347.681	−	339.579i	−0.715392	−	0.698723i
$487$	−581.940			−1.19495			−0.597474	−	0.801888i	$-0.703829\pi$
$487$	−581.940			−1.19495			−0.597474	+	0.801888i	$0.703829\pi$
$488$	74.1093	−	825.826i	0.151863	−	1.69227i
$489$	540.235	+	61.7723i	1.10478	+	0.126324i
$490$	−272.889	+	90.2002i	−0.556917	+	0.184082i
$491$	−289.089	+	500.718i	−0.588777	+	1.01979i	0.405616	+	0.914044i	$0.367057\pi$
$491$	−289.089	+	500.718i	−0.588777	+	1.01979i	−0.994393	+	0.105748i	$0.966276\pi$
$492$	105.353	−	60.9685i	0.214132	−	0.123920i
$493$	61.8397	−	35.7032i	0.125436	−	0.0724203i
$494$	232.917	+	207.589i	0.471491	+	0.420221i
$495$	474.083	+	109.853i	0.957743	+	0.221925i
$496$	758.776	−	177.448i	1.52979	−	0.357759i
$497$	140.863	−	81.3275i	0.283427	−	0.163637i
$498$	−63.1123	−	302.957i	−0.126732	−	0.608347i
$499$	691.923	+	399.482i	1.38662	+	0.800565i	0.992933	−	0.118680i	$-0.0378663\pi$
$499$	691.923	+	399.482i	1.38662	+	0.800565i	0.393686	+	0.919245i	$0.371200\pi$
$500$	456.621	+	197.774i	0.913241	+	0.395547i
$501$	−15.7697	+	21.2936i	−0.0314765	+	0.0425022i
$502$	61.3379	−	295.947i	0.122187	−	0.589536i
$503$			252.819i			0.502622i	0.967906	+	0.251311i	$0.0808616\pi$
$503$			252.819i			0.502622i	−0.967906	+	0.251311i	$0.919138\pi$
$504$	98.5733	+	32.3599i	0.195582	+	0.0642061i
$505$	−346.507			−0.686152
$506$	−1350.94	−	279.995i	−2.66984	−	0.553349i
$507$	230.220	−	99.9925i	0.454084	−	0.197224i
$508$	792.651	+	343.317i	1.56034	+	0.675821i
$509$	230.691	−	399.569i	0.453224	−	0.785007i	−0.545360	−	0.838202i	$-0.683607\pi$
$509$	230.691	−	399.569i	0.453224	−	0.785007i	0.998584	+	0.0531949i	$0.0169405\pi$
$510$	57.4741	+	64.3544i	0.112694	+	0.126185i
$511$	−60.5301	−	104.841i	−0.118454	−	0.205169i
$512$	−493.655	−	135.826i	−0.964170	−	0.265285i
$513$	429.622	+	152.721i	0.837470	+	0.297702i
$514$	−399.873	+	448.661i	−0.777963	+	0.872881i
$515$	−46.5655	−	80.6539i	−0.0904185	−	0.156609i
$516$	0.272835	+	268.152i	0.000528749	+	0.519674i
$517$	−650.926	−	375.812i	−1.25904	−	0.726909i
$518$	−12.8299	−	38.8153i	−0.0247682	−	0.0749331i
$519$	141.112	−	61.2896i	0.271892	−	0.118092i
$520$	20.2290	−	225.419i	0.0389018	−	0.433497i
$521$		−	765.575i		−	1.46943i	−0.678374	−	0.734717i	$-0.737315\pi$
$521$		−	765.575i		−	1.46943i	0.678374	−	0.734717i	$-0.262685\pi$
$522$	−272.580	+	25.0204i	−0.522184	+	0.0479319i
$523$			1007.67i			1.92671i	0.268222	+	0.963357i	$0.413564\pi$
$523$			1007.67i			1.92671i	−0.268222	+	0.963357i	$0.586436\pi$
$524$	−222.854	+	165.394i	−0.425295	+	0.315637i
$525$	54.2661	+	40.1886i	0.103364	+	0.0765497i
$526$	30.8819	+	93.4292i	0.0587109	+	0.177622i
$527$	198.052	+	114.346i	0.375811	+	0.216975i
$528$	−778.011	−	336.036i	−1.47351	−	0.636433i
$529$	498.756	+	863.870i	0.942828	+	1.63303i
$530$	325.657	+	290.245i	0.614447	+	0.547632i
$531$	−430.021	+	460.397i	−0.809832	+	0.867038i
$532$	−96.6947	+	11.1561i	−0.181757	+	0.0209701i
$533$	−46.8512	−	81.1487i	−0.0879010	−	0.152249i
$534$	−197.206	+	598.664i	−0.369299	+	1.12109i
$535$	49.2792	−	85.3541i	0.0921107	−	0.159540i
$536$	88.1341	−	40.8582i	0.164429	−	0.0762281i
$537$	4.01503	−	35.1138i	0.00747678	−	0.0653888i
$538$	61.6642	−	297.521i	0.114617	−	0.553014i
$539$	828.476			1.53706
$540$	−96.7701	−	316.280i	−0.179204	−	0.585704i
$541$		−	367.842i		−	0.679930i	−0.940438	−	0.339965i	$-0.889585\pi$
$541$		−	367.842i		−	0.679930i	0.940438	−	0.339965i	$-0.110415\pi$
$542$	−46.2880	+	223.333i	−0.0854021	+	0.412054i
$543$	641.022	+	73.2966i	1.18052	+	0.134985i
$544$	−78.4064	−	128.182i	−0.144129	−	0.235628i
$545$	−295.152	−	170.406i	−0.541564	−	0.312672i
$546$	24.9879	−	75.8567i	0.0457654	−	0.138932i
$547$	584.021	−	337.185i	1.06768	−	0.616426i	0.140134	−	0.990133i	$-0.455247\pi$
$547$	584.021	−	337.185i	1.06768	−	0.616426i	0.927547	+	0.373707i	$0.121913\pi$
$548$	−342.613	+	39.5287i	−0.625206	+	0.0721327i
$549$	−892.249	+	272.003i	−1.62523	+	0.495451i
$550$	−411.786	−	367.008i	−0.748702	−	0.667288i
$551$	222.401	−	128.403i	0.403631	−	0.233037i
$552$	295.190	+	890.019i	0.534764	+	1.61235i
$553$	−33.1169	+	57.3602i	−0.0598859	+	0.103725i
$554$	82.2765	+	248.917i	0.148513	+	0.449308i
$555$	−77.5645	+	104.734i	−0.139756	+	0.188710i
$556$	−30.7953	−	41.4941i	−0.0553872	−	0.0746297i
$557$	−552.503			−0.991927			−0.495963	−	0.868344i	$-0.665185\pi$
$557$	−552.503			−0.991927			−0.495963	+	0.868344i	$0.665185\pi$
$558$	−505.889	−	715.961i	−0.906611	−	1.28308i
$559$	206.424			0.369274
$560$	48.3008	+	51.5022i	0.0862514	+	0.0919682i
$561$	−99.0833	−	228.127i	−0.176619	−	0.406644i
$562$	−109.303	−	330.681i	−0.194489	−	0.588401i
$563$	−72.4729	+	125.527i	−0.128726	+	0.222960i	−0.923183	−	0.384360i	$-0.874422\pi$
$563$	−72.4729	+	125.527i	−0.128726	+	0.222960i	0.794457	+	0.607320i	$0.207756\pi$
$564$	0.519771	+	510.850i	0.000921580	+	0.905763i
$565$	275.991	−	159.343i	0.488479	−	0.282024i
$566$	−157.177	+	176.353i	−0.277697	+	0.311578i
$567$	−7.95432	−	116.446i	−0.0140288	−	0.205373i
$568$	738.566	+	519.612i	1.30029	+	0.914809i
$569$	−540.788	+	312.224i	−0.950419	+	0.548725i	−0.893211	−	0.449638i	$-0.851553\pi$
$569$	−540.788	+	312.224i	−0.950419	+	0.548725i	−0.0572079	+	0.998362i	$0.518220\pi$
$570$	206.700	+	231.445i	0.362632	+	0.406043i
$571$	−452.320	−	261.147i	−0.792153	−	0.457350i	0.0485668	−	0.998820i	$-0.484535\pi$
$571$	−452.320	−	261.147i	−0.792153	−	0.457350i	−0.840720	+	0.541470i	$0.817868\pi$
$572$	−259.291	+	598.652i	−0.453306	+	1.04660i
$573$	76.7515	+	176.711i	0.133947	+	0.308396i
$574$	28.6245	+	5.93271i	0.0498685	+	0.0103357i
$575$			610.318i			1.06142i
$576$	67.1819	+	572.069i	0.116635	+	0.993175i
$577$	17.0045			0.0294706			0.0147353	−	0.999891i	$-0.495309\pi$
$577$	17.0045			0.0294706			0.0147353	+	0.999891i	$0.495309\pi$
$578$	−108.354	+	522.792i	−0.187463	+	0.904484i
$579$	−485.228	−	359.352i	−0.838046	−	0.620643i
$580$	−170.942	−	74.0393i	−0.294728	−	0.127654i
$581$	37.1600	−	64.3631i	0.0639588	−	0.110780i
$582$	−47.5565	−	228.285i	−0.0817122	−	0.392242i
$583$	−628.726	−	1088.98i	−1.07843	−	1.86790i
$584$	386.735	−	549.698i	0.662217	−	0.941263i
$585$	−243.549	+	74.2462i	−0.416324	+	0.126917i
$586$	48.8712	+	43.5569i	0.0833980	+	0.0743292i
$587$	61.1119	+	105.849i	0.104109	+	0.180322i	0.913374	−	0.407122i	$-0.133468\pi$
$587$	61.1119	+	105.849i	0.104109	+	0.180322i	−0.809265	+	0.587444i	$0.800134\pi$
$588$	−282.038	−	487.358i	−0.479656	−	0.828840i
$589$	712.277	+	411.234i	1.20930	+	0.698189i
$590$	−407.084	+	134.557i	−0.689972	+	0.228062i
$591$	−54.4802	+	476.461i	−0.0921830	+	0.806195i
$592$	165.551	−	155.260i	0.279647	−	0.262264i
$593$		−	811.371i		−	1.36825i	−0.729366	−	0.684124i	$-0.760185\pi$
$593$		−	811.371i		−	1.36825i	0.729366	−	0.684124i	$-0.239815\pi$
$594$	−21.2730	+	953.178i	−0.0358131	+	1.60468i
$595$			20.7217i			0.0348264i
$596$	−286.349	+	212.517i	−0.480452	+	0.356573i
$597$	−86.0596	+	752.642i	−0.144154	+	1.26071i
$598$	685.370	−	226.541i	1.14610	−	0.378831i
$599$	−868.850	−	501.631i	−1.45050	−	0.837447i	−0.451992	−	0.892022i	$-0.649286\pi$
$599$	−868.850	−	501.631i	−1.45050	−	0.837447i	−0.998510	+	0.0545746i	$0.982620\pi$
$600$	−75.7115	+	367.177i	−0.126186	+	0.611962i
$601$	−204.405	−	354.041i	−0.340109	−	0.589086i	0.644344	−	0.764736i	$-0.277131\pi$
$601$	−204.405	−	354.041i	−0.340109	−	0.589086i	−0.984453	+	0.175650i	$0.943797\pi$
$602$	−42.8482	+	48.0760i	−0.0711764	+	0.0798605i
$603$	−79.8677	−	74.5981i	−0.132451	−	0.123712i
$604$	−103.174	−	894.256i	−0.170818	−	1.48056i
$605$	−292.056	−	505.856i	−0.482737	−	0.836125i
$606$	−138.449	−	664.596i	−0.228464	−	1.09669i
$607$	−317.988	+	550.771i	−0.523868	+	0.907365i	0.475746	+	0.879583i	$0.342178\pi$
$607$	−317.988	+	550.771i	−0.523868	+	0.907365i	−0.999614	+	0.0277829i	$0.991155\pi$
$608$	−281.981	−	460.993i	−0.463785	−	0.758212i
$609$	−52.8282	−	39.1237i	−0.0867457	−	0.0642425i
$610$	−621.610	−	128.835i	−1.01903	−	0.211204i
$611$	393.254			0.643624
$612$	−100.467	+	135.948i	−0.164161	+	0.222137i
$613$		−	1029.22i		−	1.67899i	−0.543367	−	0.839495i	$-0.682851\pi$
$613$		−	1029.22i		−	1.67899i	0.543367	−	0.839495i	$-0.317149\pi$
$614$	605.829	+	125.564i	0.986693	+	0.204502i
$615$	−37.1269	−	85.4802i	−0.0603690	−	0.138992i
$616$	−85.6036	−	184.653i	−0.138967	−	0.299761i
$617$	461.455	+	266.421i	0.747902	+	0.431801i	0.824935	−	0.565227i	$-0.191211\pi$
$617$	461.455	+	266.421i	0.747902	+	0.431801i	−0.0770334	+	0.997029i	$0.524545\pi$
$618$	136.088	−	121.538i	0.220206	−	0.196663i
$619$	−77.1070	+	44.5178i	−0.124567	+	0.0719188i	−0.560989	−	0.827823i	$-0.689579\pi$
$619$	−77.1070	+	44.5178i	−0.124567	+	0.0719188i	0.436422	+	0.899742i	$0.356246\pi$
$620$	−68.3808	−	592.687i	−0.110292	−	0.955946i
$621$	802.984	−	684.138i	1.29305	−	1.10167i
$622$	−168.522	+	189.083i	−0.270935	+	0.303991i
$623$	−131.094	+	75.6873i	−0.210424	+	0.121488i
$624$	440.433	−	51.2688i	0.705822	−	0.0821615i
$625$	−4.76767	+	8.25785i	−0.00762828	+	0.0132126i
$626$	374.598	−	123.819i	0.598399	−	0.197793i
$627$	−356.344	−	820.438i	−0.568332	−	1.30851i
$628$	385.402	+	519.297i	0.613697	+	0.826906i
$629$	66.6087			0.105896
$630$	33.2625	−	72.1340i	0.0527977	−	0.114498i
$631$	8.45150			0.0133938			0.00669691	−	0.999978i	$-0.497868\pi$
$631$	8.45150			0.0133938			0.00669691	+	0.999978i	$0.497868\pi$
$632$	−366.249	−	32.8670i	−0.579508	−	0.0520048i
$633$	−615.979	+	831.748i	−0.973111	+	1.31398i
$634$	363.459	−	120.137i	0.573280	−	0.189491i
$635$	330.679	−	572.753i	0.520755	−	0.901974i
$636$	−426.568	+	740.576i	−0.670704	+	1.16443i
$637$	−375.391	+	216.732i	−0.589310	+	0.340238i
$638$	400.875	+	357.283i	0.628331	+	0.560005i
$639$	229.328	−	989.695i	0.358886	−	1.54882i
$640$	−146.627	+	363.549i	−0.229104	+	0.568045i
$641$	−537.918	+	310.567i	−0.839186	+	0.484504i	−0.856987	−	0.515337i	$-0.827667\pi$
$641$	−537.918	+	310.567i	−0.839186	+	0.484504i	0.0178015	+	0.999842i	$0.494333\pi$
$642$	183.398	+	60.4131i	0.285667	+	0.0941014i
$643$	−806.653	−	465.722i	−1.25452	−	0.724295i	−0.282513	−	0.959264i	$-0.591168\pi$
$643$	−806.653	−	465.722i	−1.25452	−	0.724295i	−0.972003	+	0.234969i	$0.924501\pi$
$644$	−89.5035	+	206.646i	−0.138981	+	0.320879i
$645$	203.977	+	23.3234i	0.316243	+	0.0361603i
$646$	32.1861	−	155.293i	0.0498236	−	0.240392i
$647$		−	168.057i		−	0.259749i	−0.991530	−	0.129874i	$-0.958543\pi$
$647$		−	168.057i		−	0.259749i	0.991530	−	0.129874i	$-0.0414574\pi$
$648$	567.957	−	311.976i	0.876477	−	0.481444i
$649$	1235.88			1.90429
$650$	282.595	+	58.5705i	0.434761	+	0.0901085i
$651$	23.9177	−	209.174i	0.0367399	−	0.321312i
$652$	−288.151	+	665.285i	−0.441950	+	1.02038i
$653$	−60.5851	+	104.936i	−0.0927796	+	0.160699i	−0.908680	−	0.417494i	$-0.862909\pi$
$653$	−60.5851	+	104.936i	−0.0927796	+	0.160699i	0.815900	+	0.578193i	$0.196242\pi$
$654$	208.907	−	634.186i	0.319430	−	0.969703i
$655$	106.240	+	184.014i	0.162199	+	0.280937i
$656$	36.9578	+	158.033i	0.0563381	+	0.240904i
$657$	−736.607	−	170.684i	−1.12117	−	0.259793i
$658$	−81.6292	+	91.5886i	−0.124056	+	0.139192i
$659$	−81.6226	−	141.374i	−0.123858	−	0.214529i	0.797428	−	0.603414i	$-0.206193\pi$
$659$	−81.6226	−	141.374i	−0.123858	−	0.214529i	−0.921286	+	0.388886i	$0.872860\pi$
$660$	−323.857	+	562.258i	−0.490693	+	0.851906i
$661$	206.669	+	119.321i	0.312661	+	0.180515i	0.648117	−	0.761541i	$-0.275557\pi$
$661$	206.669	+	119.321i	0.312661	+	0.180515i	−0.335455	+	0.942056i	$0.608890\pi$
$662$	235.624	+	712.851i	0.355928	+	1.07681i
$663$	104.574	+	77.4461i	0.157729	+	0.116812i
$664$	410.963	+	36.8796i	0.618921	+	0.0555416i
$665$			74.5237i			0.112066i
$666$	−231.870	−	106.920i	−0.348154	−	0.160541i
$667$		−	594.146i		−	0.890774i
$668$	−21.0552	−	28.3701i	−0.0315197	−	0.0424702i
$669$	222.740	−	96.7435i	0.332945	−	0.144609i
$670$	−23.3423	−	70.6191i	−0.0348392	−	0.105402i
$671$	1584.75	+	914.953i	2.36177	+	1.36357i
$672$	−79.4817	+	113.218i	−0.118276	+	0.168480i
$673$	95.1072	+	164.730i	0.141318	+	0.244770i	0.927993	−	0.372597i	$-0.121533\pi$
$673$	95.1072	+	164.730i	0.141318	+	0.244770i	−0.786675	+	0.617367i	$0.788199\pi$
$674$	−34.8004	−	31.0162i	−0.0516327	−	0.0460181i
$675$	414.794	−	76.3596i	0.614510	−	0.113125i
$676$	38.3572	+	332.459i	0.0567414	+	0.491803i
$677$	628.159	+	1088.00i	0.927857	+	1.60709i	0.786901	+	0.617079i	$0.211684\pi$
$677$	628.159	+	1088.00i	0.927857	+	1.60709i	0.140955	+	0.990016i	$0.454983\pi$
$678$	415.893	+	465.680i	0.613411	+	0.686844i
$679$	28.0009	−	48.4990i	0.0412384	−	0.0714271i
$680$	−104.374	+	48.3867i	−0.153491	+	0.0711569i
$681$	455.765	−	197.954i	0.669258	−	0.290681i
$682$	−349.025	+	1684.00i	−0.511766	+	2.46920i
$683$	−415.707			−0.608648			−0.304324	−	0.952569i	$-0.598431\pi$
$683$	−415.707			−0.608648			−0.304324	+	0.952569i	$0.598431\pi$
$684$	−361.320	+	488.924i	−0.528245	+	0.714801i
$685$			264.056i			0.385483i
$686$	56.1034	−	270.691i	0.0817833	−	0.394593i
$687$	−18.0125	+	24.3220i	−0.0262191	+	0.0354033i
$688$	−342.209	−	103.562i	−0.497397	−	0.150526i
$689$	569.763	+	328.953i	0.826943	+	0.477436i
$690$	702.841	−	146.417i	1.01861	−	0.212198i
$691$	−528.226	+	304.971i	−0.764436	+	0.441348i	−0.830886	−	0.556442i	$-0.812166\pi$
$691$	−528.226	+	304.971i	−0.764436	+	0.441348i	0.0664499	+	0.997790i	$0.478833\pi$
$692$	23.5107	+	203.778i	0.0339750	+	0.294477i
$693$	−156.293	+	167.334i	−0.225531	+	0.241463i
$694$	−99.9986	−	89.1247i	−0.144090	−	0.128422i
$695$	−34.2622	+	19.7813i	−0.0492982	+	0.0284623i
$696$	73.7053	−	357.448i	0.105898	−	0.513575i
$697$	−23.8152	+	41.2491i	−0.0341681	+	0.0591809i
$698$	−217.509	−	658.046i	−0.311618	−	0.942759i
$699$	−655.008	−	74.8958i	−0.937064	−	0.107147i
$700$	−72.3002	+	53.6584i	−0.103286	+	0.0766548i
$701$	−922.743			−1.31632			−0.658162	−	0.752877i	$-0.728666\pi$
$701$	−922.743			−1.31632			−0.658162	+	0.752877i	$0.728666\pi$
$702$	−239.715	−	437.459i	−0.341475	−	0.623161i
$703$	239.552			0.340757
$704$	730.192	−	862.357i	1.03720	−	1.22494i
$705$	388.592	+	44.4329i	0.551194	+	0.0630254i
$706$	369.302	+	1117.28i	0.523091	+	1.58254i
$707$	81.5178	−	141.193i	0.115301	−	0.199707i
$708$	−420.731	−	727.018i	−0.594253	−	1.02686i
$709$	226.420	−	130.724i	0.319351	−	0.184377i	−0.331752	−	0.943367i	$-0.607640\pi$
$709$	226.420	−	130.724i	0.319351	−	0.184377i	0.651103	+	0.758989i	$0.274306\pi$
$710$	460.021	−	516.147i	0.647917	−	0.726968i
$711$	120.632	+	395.707i	0.169665	+	0.556550i
$712$	−687.346	−	483.576i	−0.965373	−	0.679180i
$713$	1647.92	−	951.428i	2.31125	−	1.33440i
$714$	−39.7440	+	8.27951i	−0.0556638	+	0.0115960i
$715$	432.574	+	249.747i	0.604999	+	0.349296i
$716$	43.2417	+	18.7291i	0.0603934	+	0.0261579i
$717$	83.0462	−	112.136i	0.115824	−	0.156396i
$718$	−636.868	−	131.997i	−0.887003	−	0.183840i
$719$			995.870i			1.38508i	0.721381	+	0.692538i	$0.243508\pi$
$719$			995.870i			1.38508i	−0.721381	+	0.692538i	$0.756492\pi$
$720$	441.004	−	0.897410i	0.612505	−	0.00124640i
$721$	43.8193			0.0607757
$722$	−30.7733	+	148.477i	−0.0426223	+	0.205647i
$723$	1303.75	−	566.261i	1.80325	−	0.783211i
$724$	−341.909	+	789.401i	−0.472250	+	1.09033i
$725$	118.774	−	205.722i	0.163826	−	0.283754i
$726$	853.532	−	762.278i	1.17566	−	1.04997i
$727$	−409.161	−	708.688i	−0.562807	−	0.974811i	−0.997250	−	0.0741116i	$-0.976388\pi$
$727$	−409.161	−	708.688i	−0.562807	−	0.974811i	0.434442	−	0.900700i	$-0.356945\pi$
$728$	87.0936	+	61.2739i	0.119634	+	0.0841675i
$729$	−565.430	−	460.142i	−0.775624	−	0.631196i
$730$	−384.156	−	342.383i	−0.526241	−	0.469018i
$731$	−52.4642	−	90.8707i	−0.0717705	−	0.124310i
$732$	−1.26544	−	1243.72i	−0.00172874	−	1.69907i
$733$	569.802	+	328.975i	0.777356	+	0.448807i	0.835492	−	0.549502i	$-0.185183\pi$
$733$	569.802	+	328.975i	0.777356	+	0.448807i	−0.0581366	+	0.998309i	$0.518516\pi$
$734$	−390.039	+	128.923i	−0.531388	+	0.175644i
$735$	−395.428	+	171.748i	−0.537997	+	0.233670i
$736$	−1249.86	+	31.7115i	−1.69818	+	0.0430862i
$737$			214.396i			0.290903i
$738$	149.116	−	105.363i	0.202054	−	0.142769i
$739$			971.543i			1.31467i	0.753597	+	0.657336i	$0.228317\pi$
$739$			971.543i			1.31467i	−0.753597	+	0.657336i	$0.771683\pi$
$740$	−103.561	−	139.540i	−0.139948	−	0.188568i
$741$	376.092	+	278.528i	0.507547	+	0.375881i
$742$	−194.881	+	64.4154i	−0.262642	+	0.0868132i
$743$	−779.126	−	449.829i	−1.04862	−	0.605422i	−0.126359	−	0.991985i	$-0.540329\pi$
$743$	−779.126	−	449.829i	−1.04862	−	0.605422i	−0.922263	+	0.386562i	$0.873662\pi$
$744$	1109.44	−	367.966i	1.49119	−	0.494578i
$745$	136.510	+	236.442i	0.183235	+	0.317372i
$746$	506.267	−	568.036i	0.678643	−	0.761442i
$747$	−135.359	−	444.018i	−0.181204	−	0.594401i
$748$	329.435	−	38.0084i	0.440422	−	0.0508133i
$749$	23.1865	+	40.1602i	0.0309566	+	0.0536184i
$750$	708.943	+	233.533i	0.945257	+	0.311377i
$751$	−398.684	+	690.541i	−0.530871	+	0.919496i	0.468480	+	0.883474i	$0.344802\pi$
$751$	−398.684	+	690.541i	−0.530871	+	0.919496i	−0.999351	+	0.0360217i	$0.988531\pi$
$752$	−651.934	−	197.294i	−0.866934	−	0.262358i
$753$	51.5026	−	450.420i	0.0683965	−	0.598167i
$754$	−275.107	−	57.0186i	−0.364863	−	0.0756214i
$755$	−689.213			−0.912865
$756$	151.642	+	34.9755i	0.200585	+	0.0462639i
$757$		−	577.348i		−	0.762680i	−0.924435	−	0.381340i	$-0.875463\pi$
$757$		−	577.348i		−	0.762680i	0.924435	−	0.381340i	$-0.124537\pi$
$758$	239.973	+	49.7367i	0.316587	+	0.0656157i
$759$	−2056.07	−	235.099i	−2.70893	−	0.309748i
$760$	−375.370	+	174.018i	−0.493908	+	0.228972i
$761$	−596.940	−	344.643i	−0.784415	−	0.452882i	0.0535776	−	0.998564i	$-0.482938\pi$
$761$	−596.940	−	344.643i	−0.784415	−	0.452882i	−0.837993	+	0.545681i	$0.816271\pi$
$762$	1230.66	+	405.391i	1.61504	+	0.532009i
$763$	138.873	−	80.1783i	0.182009	−	0.105083i
$764$	−255.186	+	29.4419i	−0.334013	+	0.0385365i
$765$	94.5840	+	88.3435i	0.123639	+	0.115482i
$766$	215.829	−	242.162i	0.281761	−	0.316138i
$767$	−559.990	+	323.311i	−0.730105	+	0.421526i
$768$	−755.868	−	135.970i	−0.984203	−	0.177044i
$769$	752.692	−	1303.70i	0.978793	−	1.69532i	0.311991	−	0.950085i	$-0.399004\pi$
$769$	752.692	−	1303.70i	0.978793	−	1.69532i	0.666802	−	0.745235i	$-0.267663\pi$
$770$	−147.957	+	48.9053i	−0.192151	+	0.0635133i
$771$	−536.520	+	724.455i	−0.695876	+	0.939631i
$772$	646.483	−	479.795i	0.837414	−	0.621496i
$773$	584.466			0.756101			0.378051	−	0.925785i	$-0.376595\pi$
$773$	584.466			0.756101			0.378051	+	0.925785i	$0.376595\pi$
$774$	36.7664	+	400.544i	0.0475019	+	0.517499i
$775$	760.786			0.981659
$776$	309.670	+	27.7896i	0.399059	+	0.0358114i
$777$	−24.4291	−	56.2450i	−0.0314403	−	0.0723874i
$778$	−490.055	+	161.982i	−0.629891	+	0.208203i
$779$	−85.6490	+	148.348i	−0.109947	+	0.190434i
$780$	−0.345415	−	339.487i	−0.000442840	−	0.435239i
$781$	−1725.98	+	996.492i	−2.20996	+	1.27592i
$782$	−273.918	−	244.132i	−0.350279	−	0.312189i
$783$	−403.804	+	74.3363i	−0.515713	+	0.0949378i
$784$	731.053	−	170.965i	0.932466	−	0.218068i
$785$	428.791	−	247.562i	0.546230	−	0.315366i
$786$	−310.487	+	277.292i	−0.395022	+	0.352789i
$787$	−222.873	−	128.676i	−0.283193	−	0.163501i	0.351675	−	0.936122i	$-0.385612\pi$
$787$	−222.873	−	128.676i	−0.283193	−	0.163501i	−0.634868	+	0.772621i	$0.718945\pi$
$788$	−586.749	−	254.136i	−0.744605	−	0.322507i
$789$	58.8013	+	135.383i	0.0745264	+	0.171588i
$790$	−57.1374	+	275.680i	−0.0723258	+	0.348962i
$791$			149.946i			0.189565i
$792$	−1207.80	−	396.500i	−1.52500	−	0.500632i
$793$	−957.418			−1.20734
$794$	−419.166	−	86.8763i	−0.527917	−	0.109416i
$795$	525.840	+	389.429i	0.661434	+	0.489848i
$796$	−926.858	−	401.445i	−1.16439	−	0.504328i
$797$	−446.828	+	773.930i	−0.560638	+	0.971053i	0.436803	+	0.899557i	$0.356111\pi$
$797$	−446.828	+	773.930i	−0.560638	+	0.971053i	−0.997441	+	0.0714962i	$0.977223\pi$
$798$	−142.936	+	29.7765i	−0.179117	+	0.0373139i
$799$	−99.9484	−	173.116i	−0.125092	−	0.216666i
$800$	−439.099	−	238.874i	−0.548874	−	0.298593i
$801$	−213.424	+	921.058i	−0.266447	+	1.14989i
$802$	359.575	−	403.446i	0.448348	−	0.503049i
$803$	741.666	+	1284.60i	0.923619	+	1.59976i
$804$	126.120	−	72.9866i	0.156866	−	0.0907794i
$805$	149.318	+	86.2089i	0.185488	+	0.107092i
$806$	−282.392	−	854.341i	−0.350363	−	1.05998i
$807$	51.7765	−	452.816i	0.0641593	−	0.561111i
$808$	901.528	+	80.9027i	1.11575	+	0.100127i
$809$			1243.52i			1.53711i	0.639784	+	0.768554i	$0.279024\pi$
$809$			1243.52i			1.53711i	−0.639784	+	0.768554i	$0.720976\pi$
$810$	−187.445	−	459.357i	−0.231414	−	0.567108i
$811$			257.659i			0.317705i	0.987302	+	0.158852i	$0.0507794\pi$
$811$			257.659i			0.317705i	−0.987302	+	0.158852i	$0.949221\pi$
$812$	70.3844	−	52.2366i	0.0866803	−	0.0643308i
$813$	−38.8658	+	339.904i	−0.0478055	+	0.418087i
$814$	157.203	+	475.598i	0.193124	+	0.584273i
$815$	480.721	+	277.545i	0.589842	+	0.340545i
$816$	−134.508	−	180.854i	−0.164839	−	0.221635i
$817$	−188.683	−	326.808i	−0.230946	−	0.400010i
$818$	−17.4013	−	15.5090i	−0.0212729	−	0.0189597i
$819$	27.0430	−	116.707i	0.0330195	−	0.142500i
$820$	123.441	−	14.2419i	0.150538	−	0.0173682i
$821$	498.892	+	864.106i	0.607664	+	1.05250i	0.991624	+	0.129155i	$0.0412265\pi$
$821$	498.892	+	864.106i	0.607664	+	1.05250i	−0.383961	+	0.923350i	$0.625440\pi$
$822$	−506.456	+	105.505i	−0.616126	+	0.128352i
$823$	159.307	−	275.927i	0.193568	−	0.335270i	−0.752862	−	0.658178i	$-0.771327\pi$
$823$	159.307	−	275.927i	0.193568	−	0.335270i	0.946430	+	0.322908i	$0.104661\pi$
$824$	102.321	+	220.714i	0.124176	+	0.267857i
$825$	−664.913	−	492.424i	−0.805955	−	0.596878i
$826$	40.9404	−	197.532i	0.0495646	−	0.239143i
$827$	−279.151			−0.337547			−0.168773	−	0.985655i	$-0.553981\pi$
$827$	−279.151			−0.337547			−0.168773	+	0.985655i	$0.553981\pi$
$828$	561.650	+	1289.54i	0.678321	+	1.55741i
$829$			444.345i			0.536001i	0.963419	+	0.268000i	$0.0863628\pi$
$829$			444.345i			0.536001i	−0.963419	+	0.268000i	$0.913637\pi$
$830$	64.1131	−	309.337i	0.0772447	−	0.372695i
$831$	156.660	+	360.691i	0.188520	+	0.434044i
$832$	−105.262	+	581.763i	−0.126517	+	0.699234i
$833$	190.816	+	110.168i	0.229071	+	0.132254i
$834$	−51.6301	−	57.8108i	−0.0619066	−	0.0693175i
$835$	−23.4256	+	13.5248i	−0.0280546	+	0.0161973i
$836$	1184.78	−	136.694i	1.41721	−	0.163509i
$837$	−852.804	−	1000.95i	−1.01888	−	1.19588i
$838$	406.235	+	362.061i	0.484768	+	0.432054i
$839$	98.5038	−	56.8712i	0.117406	−	0.0677845i	−0.440147	−	0.897926i	$-0.645074\pi$
$839$	98.5038	−	56.8712i	0.117406	−	0.0677845i	0.557553	+	0.830141i	$0.311740\pi$
$840$	79.1378	+	70.3879i	0.0942116	+	0.0837952i
$841$	304.874	−	528.057i	0.362513	−	0.627891i
$842$	314.562	+	951.668i	0.373589	+	1.13025i
$843$	−208.120	−	479.171i	−0.246880	−	0.568412i
$844$	−822.433	−	1108.16i	−0.974447	−	1.31299i
$845$	256.230			0.303230
$846$	70.0429	+	763.068i	0.0827930	+	0.901971i
$847$	274.832			0.324477
$848$	−779.516	−	831.183i	−0.919241	−	0.980169i
$849$	−210.888	+	284.759i	−0.248396	+	0.335405i
$850$	−46.0400	−	139.288i	−0.0541647	−	0.163868i
$851$	277.113	−	479.974i	0.325633	−	0.564012i
$852$	1173.77	+	676.084i	1.37766	+	0.793526i
$853$	635.397	−	366.847i	0.744897	−	0.430067i	−0.0789500	−	0.996879i	$-0.525157\pi$
$853$	635.397	−	366.847i	0.744897	−	0.430067i	0.823847	+	0.566812i	$0.191823\pi$
$854$	198.735	−	222.982i	0.232710	−	0.261103i
$855$	340.163	+	317.719i	0.397851	+	0.371601i
$856$	−148.141	+	210.565i	−0.173062	+	0.245988i
$857$	−828.678	+	478.437i	−0.966952	+	0.558270i	−0.898306	−	0.439371i	$-0.855201\pi$
$857$	−828.678	+	478.437i	−0.966952	+	0.558270i	−0.0686463	+	0.997641i	$0.521868\pi$
$858$	−306.173	+	929.460i	−0.356845	+	1.08329i
$859$	−715.227	−	412.936i	−0.832627	−	0.480717i	0.0221243	−	0.999755i	$-0.492957\pi$
$859$	−715.227	−	412.936i	−0.832627	−	0.480717i	−0.854751	+	0.519038i	$0.826290\pi$
$860$	−108.798	+	251.192i	−0.126509	+	0.292084i
$861$	43.5654	+	4.98142i	0.0505986	+	0.00578562i
$862$	1374.21	+	284.817i	1.59421	+	0.330415i
$863$		−	945.401i		−	1.09548i	−0.836648	−	0.547741i	$-0.815488\pi$
$863$		−	945.401i		−	1.09548i	0.836648	−	0.547741i	$-0.184512\pi$
$864$	177.927	+	845.481i	0.205934	+	0.978566i
$865$	157.054			0.181565
$866$	157.163	−	758.293i	0.181482	−	0.875627i
$867$	−90.9795	+	795.669i	−0.104936	+	0.917726i
$868$	257.592	+	111.570i	0.296765	+	0.128536i
$869$	405.776	−	702.825i	0.466946	−	0.808774i
$870$	−265.403	−	87.4262i	−0.305060	−	0.100490i
$871$	−56.0865	−	97.1447i	−0.0643933	−	0.111532i
$872$	728.130	+	512.269i	0.835011	+	0.587465i
$873$	−101.996	−	334.577i	−0.116834	−	0.383250i
$874$	−985.121	−	877.999i	−1.12714	−	1.00458i
$875$	89.6296	+	155.243i	0.102434	+	0.177421i
$876$	503.194	−	873.609i	0.574422	−	0.997270i
$877$	733.997	+	423.773i	0.836941	+	0.483208i	0.856223	−	0.516606i	$-0.172805\pi$
$877$	733.997	+	423.773i	0.836941	+	0.483208i	−0.0192825	+	0.999814i	$0.506138\pi$
$878$	−615.771	+	203.536i	−0.701334	+	0.231818i
$879$	78.9126	+	58.4414i	0.0897755	+	0.0664863i
$880$	−591.822	−	631.048i	−0.672525	−	0.717100i
$881$			716.539i			0.813324i	0.913579	+	0.406662i	$0.133307\pi$
$881$			716.539i			0.813324i	−0.913579	+	0.406662i	$0.866693\pi$
$882$	−487.406	−	689.803i	−0.552614	−	0.782089i
$883$		−	915.122i		−	1.03638i	−0.855266	−	0.518189i	$-0.826606\pi$
$883$		−	915.122i		−	1.03638i	0.855266	−	0.518189i	$-0.173394\pi$
$884$	−139.327	+	103.403i	−0.157610	+	0.116972i
$885$	−589.881	+	256.205i	−0.666532	+	0.289497i
$886$	19.1829	−	6.34068i	0.0216511	−	0.00715652i
$887$	−49.5294	−	28.5958i	−0.0558392	−	0.0322388i	0.471820	−	0.881695i	$-0.343597\pi$
$887$	−49.5294	−	28.5958i	−0.0558392	−	0.0322388i	−0.527660	+	0.849456i	$0.676930\pi$
$888$	226.258	−	254.384i	0.254795	−	0.286468i
$889$	155.589	+	269.487i	0.175015	+	0.303136i
$890$	−428.118	+	480.352i	−0.481031	+	0.539721i
$891$	97.4630	+	1426.80i	0.109386	+	1.60134i
$892$	37.1108	+	321.656i	0.0416041	+	0.360601i
$893$	−359.455	−	622.595i	−0.402526	−	0.697195i
$894$	−398.950	+	356.297i	−0.446253	+	0.398543i
$895$	18.0396	−	31.2456i	0.0201560	−	0.0349112i
$896$	−113.642	−	145.274i	−0.126833	−	0.162136i
$897$	993.130	−	431.350i	1.10717	−	0.480881i
$898$	139.412	+	28.8945i	0.155247	+	0.0321765i
$899$	−740.627			−0.823834
$900$	−63.3165	+	558.777i	−0.0703517	+	0.620863i
$901$		−	334.423i		−	0.371169i
$902$	−350.732	−	72.6925i	−0.388838	−	0.0805904i
$903$	−57.4905	+	77.6286i	−0.0636662	+	0.0859675i
$904$	−755.266	+	350.135i	−0.835472	+	0.387318i
$905$	570.405	+	329.323i	0.630282	+	0.363893i
$906$	−275.380	−	1321.90i	−0.303952	−	1.45905i
$907$	1333.52	−	769.909i	1.47025	−	0.848852i	0.470812	−	0.882234i	$-0.343961\pi$
$907$	1333.52	−	769.909i	1.47025	−	0.848852i	0.999443	+	0.0333818i	$0.0106277\pi$
$908$	75.9352	+	658.164i	0.0836291	+	0.724850i
$909$	−296.937	−	974.040i	−0.326663	−	1.07155i
$910$	54.2468	−	60.8654i	0.0596119	−	0.0668850i
$911$	769.095	−	444.037i	0.844232	−	0.487418i	−0.0144685	−	0.999895i	$-0.504606\pi$
$911$	769.095	−	444.037i	0.844232	−	0.487418i	0.858701	+	0.512478i	$0.171272\pi$
$912$	−483.747	−	650.425i	−0.530424	−	0.713185i
$913$	−455.316	+	788.631i	−0.498703	+	0.863779i
$914$	−635.862	+	210.177i	−0.695692	+	0.229953i
$915$	−946.066	−	108.176i	−1.03395	−	0.118226i
$916$	−24.0497	−	32.4049i	−0.0262551	−	0.0353766i
$917$	−99.9749			−0.109024
$918$	−131.650	+	216.709i	−0.143410	+	0.236067i
$919$	1135.32			1.23539			0.617695	−	0.786418i	$-0.288067\pi$
$919$	1135.32			1.23539			0.617695	+	0.786418i	$0.288067\pi$
$920$	−85.5584	+	953.408i	−0.0929982	+	1.03631i
$921$	922.049	+	105.430i	1.00114	+	0.114474i
$922$	1540.38	−	509.153i	1.67069	−	0.552227i
$923$	521.371	−	903.041i	0.564866	−	0.978376i
$924$	−152.917	−	264.239i	−0.165494	−	0.285972i
$925$	191.900	−	110.793i	0.207459	−	0.119777i
$926$	152.771	+	136.158i	0.164979	+	0.147039i
$927$	186.816	−	200.013i	0.201528	−	0.215764i
$928$	427.464	+	232.545i	0.460630	+	0.250587i
$929$	−1052.57	+	607.703i	−1.13302	+	0.654148i	−0.944692	−	0.327959i	$-0.893639\pi$
$929$	−1052.57	+	607.703i	−1.13302	+	0.654148i	−0.188325	+	0.982107i	$0.560306\pi$
$930$	−182.514	−	876.118i	−0.196252	−	0.942063i
$931$	686.254	+	396.209i	0.737115	+	0.425573i
$932$	349.369	−	806.624i	0.374859	−	0.865476i
$933$	−226.110	+	305.313i	−0.242347	+	0.327238i
$934$	−85.7608	+	413.784i	−0.0918210	+	0.443024i
$935$		−	253.900i		−	0.271551i
$936$	650.993	−	136.307i	0.695505	−	0.145627i
$937$	−551.201			−0.588262			−0.294131	−	0.955765i	$-0.595030\pi$
$937$	−551.201			−0.588262			−0.294131	+	0.955765i	$0.595030\pi$
$938$	34.2670	+	7.10216i	0.0365320	+	0.00757160i
$939$	542.807	−	235.760i	0.578070	−	0.251075i
$940$	−207.268	+	478.540i	−0.220497	+	0.509085i
$941$	684.618	−	1185.79i	0.727543	−	1.26014i	−0.230375	−	0.973102i	$-0.573995\pi$
$941$	684.618	−	1185.79i	0.727543	−	1.26014i	0.957918	−	0.287040i	$-0.0926714\pi$
$942$	646.148	+	723.500i	0.685932	+	0.768047i
$943$	198.157	+	343.218i	0.210135	+	0.363964i
$944$	1090.55	−	255.038i	1.15525	−	0.270167i
$945$	39.9088	−	112.268i	0.0422316	−	0.118802i
$946$	525.012	−	589.068i	0.554981	−	0.622693i
$947$	−462.419	−	800.933i	−0.488299	−	0.845758i	0.511611	−	0.859217i	$-0.329049\pi$
$947$	−462.419	−	800.933i	−0.488299	−	0.845758i	−0.999909	+	0.0134593i	$0.995716\pi$
$948$	−551.581	+	0.561213i	−0.581837	+	0.000591997i
$949$	−672.112	−	388.044i	−0.708232	−	0.408898i
$950$	−165.579	−	500.937i	−0.174293	−	0.527302i
$951$	526.668	−	228.750i	0.553804	−	0.240536i
$952$	4.83812	−	53.9130i	0.00508206	−	0.0566313i
$953$		−	279.545i		−	0.293331i	−0.989186	−	0.146666i	$-0.953146\pi$
$953$		−	279.545i		−	0.293331i	0.989186	−	0.146666i	$-0.0468541\pi$
$954$	−536.817	+	1164.15i	−0.562701	+	1.22029i
$955$			196.675i			0.205942i
$956$	110.880	+	149.402i	0.115984	+	0.156278i
$957$	647.295	+	479.376i	0.676379	+	0.500916i
$958$	−290.154	−	877.823i	−0.302874	−	0.916308i
$959$	−107.596	−	62.1208i	−0.112196	−	0.0647766i
$960$	−169.746	+	562.972i	−0.176819	+	0.586429i
$961$	−705.493	−	1221.95i	−0.734124	−	1.27154i
$962$	−195.648	−	174.373i	−0.203376	−	0.181261i
$963$	282.162	+	65.3816i	0.293003	+	0.0678937i
$964$	217.218	+	1882.72i	0.225330	+	1.95303i
$965$	−308.195	−	533.810i	−0.319373	−	0.553171i
$966$	−105.686	+	320.836i	−0.109406	+	0.332128i
$967$	−1.28361	+	2.22327i	−0.00132741	+	0.00229914i	−0.866688	−	0.498850i	$-0.833756\pi$
$967$	−1.28361	+	2.22327i	−0.00132741	+	0.00229914i	0.865361	+	0.501149i	$0.167089\pi$
$968$	641.753	+	1384.31i	0.662968	+	1.43007i
$969$	27.0251	−	236.351i	0.0278897	−	0.243912i
$970$	48.3106	−	233.092i	0.0498048	−	0.240301i
$971$	−1053.61			−1.08508			−0.542540	−	0.840030i	$-0.682537\pi$
$971$	−1053.61			−1.08508			−0.542540	+	0.840030i	$0.682537\pi$
$972$	806.147	−	543.058i	0.829369	−	0.558701i
$973$		−	18.6147i		−	0.0191313i
$974$	236.205	−	1139.66i	0.242511	−	1.17008i
$975$	430.098	+	49.1789i	0.441127	+	0.0504399i
$976$	1587.20	+	480.331i	1.62623	+	0.492143i
$977$	−683.177	−	394.432i	−0.699260	−	0.403718i	0.107812	−	0.994171i	$-0.465616\pi$
$977$	−683.177	−	394.432i	−0.699260	−	0.403718i	−0.807072	+	0.590453i	$0.798949\pi$
$978$	−340.251	+	1032.91i	−0.347905	+	1.05615i
$979$	1606.28	−	927.384i	1.64073	−	0.947277i
$980$	−65.8824	−	571.032i	−0.0672270	−	0.582686i
$981$	226.088	−	975.710i	0.230467	−	0.994607i
$982$	−863.256	−	769.385i	−0.879079	−	0.783488i
$983$	471.949	−	272.480i	0.480111	−	0.277192i	−0.240352	−	0.970686i	$-0.577263\pi$
$983$	471.949	−	272.480i	0.480111	−	0.277192i	0.720463	+	0.693494i	$0.243929\pi$
$984$	76.6375	+	231.068i	0.0778836	+	0.234825i
$985$	−244.781	+	423.973i	−0.248508	+	0.430429i
$986$	44.8201	+	135.597i	0.0454565	+	0.137523i
$987$	−109.524	+	147.889i	−0.110966	+	0.149836i
$988$	−501.078	+	371.880i	−0.507164	+	0.376397i
$989$	−873.072			−0.882782
$990$	−407.560	+	883.846i	−0.411677	+	0.892773i
$991$	830.022			0.837560			0.418780	−	0.908088i	$-0.362458\pi$
$991$	830.022			0.837560			0.418780	+	0.908088i	$0.362458\pi$
$992$	39.5296	+	1558.00i	0.0398484	+	1.57056i
$993$	448.645	+	1032.95i	0.451808	+	1.04023i
$994$	102.095	+	308.874i	0.102711	+	0.310738i
$995$	−386.668	+	669.729i	−0.388611	+	0.673094i
$996$	618.922	−	0.629730i	0.621407	−	0.000632259i
$997$	−1110.73	+	641.280i	−1.11407	+	0.643210i	−0.939881	−	0.341502i	$-0.889064\pi$
$997$	−1110.73	+	641.280i	−1.11407	+	0.643210i	−0.174191	+	0.984712i	$0.555731\pi$
$998$	−1063.18	+	1192.90i	−1.06531	+	1.19529i
$999$	−360.879	−	128.285i	−0.361240	−	0.128413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.3.j.a.5.11	yes	44
3.2	odd	2		216.3.j.a.125.12		44
4.3	odd	2		288.3.n.a.113.13		44
8.3	odd	2		288.3.n.a.113.10		44
8.5	even	2	inner	72.3.j.a.5.3	✓	44
9.2	odd	6	inner	72.3.j.a.29.3	yes	44
9.4	even	3		648.3.h.a.485.9		44
9.5	odd	6		648.3.h.a.485.36		44
9.7	even	3		216.3.j.a.197.20		44
12.11	even	2		864.3.n.a.17.15		44
24.5	odd	2		216.3.j.a.125.20		44
24.11	even	2		864.3.n.a.17.8		44
36.7	odd	6		864.3.n.a.305.8		44
36.11	even	6		288.3.n.a.209.10		44
36.23	even	6		2592.3.h.a.1457.16		44
36.31	odd	6		2592.3.h.a.1457.29		44
72.5	odd	6		648.3.h.a.485.10		44
72.11	even	6		288.3.n.a.209.13		44
72.13	even	6		648.3.h.a.485.35		44
72.29	odd	6	inner	72.3.j.a.29.11	yes	44
72.43	odd	6		864.3.n.a.305.15		44
72.59	even	6		2592.3.h.a.1457.30		44
72.61	even	6		216.3.j.a.197.12		44
72.67	odd	6		2592.3.h.a.1457.15		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.3	✓	44	8.5	even	2	inner
72.3.j.a.5.11	yes	44	1.1	even	1	trivial
72.3.j.a.29.3	yes	44	9.2	odd	6	inner
72.3.j.a.29.11	yes	44	72.29	odd	6	inner
216.3.j.a.125.12		44	3.2	odd	2
216.3.j.a.125.20		44	24.5	odd	2
216.3.j.a.197.12		44	72.61	even	6
216.3.j.a.197.20		44	9.7	even	3
288.3.n.a.113.10		44	8.3	odd	2
288.3.n.a.113.13		44	4.3	odd	2
288.3.n.a.209.10		44	36.11	even	6
288.3.n.a.209.13		44	72.11	even	6
648.3.h.a.485.9		44	9.4	even	3
648.3.h.a.485.10		44	72.5	odd	6
648.3.h.a.485.35		44	72.13	even	6
648.3.h.a.485.36		44	9.5	odd	6
864.3.n.a.17.8		44	24.11	even	2
864.3.n.a.17.15		44	12.11	even	2
864.3.n.a.305.8		44	36.7	odd	6
864.3.n.a.305.15		44	72.43	odd	6
2592.3.h.a.1457.15		44	72.67	odd	6
2592.3.h.a.1457.16		44	36.23	even	6
2592.3.h.a.1457.29		44	36.31	odd	6
2592.3.h.a.1457.30		44	72.59	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.405893 + 1.95838i) q^{2} +(-0.340809 + 2.98058i) q^{3} +(-3.67050 - 1.58979i) q^{4} +(-1.53127 + 2.65223i) q^{5} +(-5.69877 - 1.87723i) q^{6} +(-0.720479 - 1.24791i) q^{7} +(4.60324 - 6.54295i) q^{8} +(-8.76770 - 2.03162i) q^{9} +O(q^{10})\)	\(q+(-0.405893 + 1.95838i) q^{2} +(-0.340809 + 2.98058i) q^{3} +(-3.67050 - 1.58979i) q^{4} +(-1.53127 + 2.65223i) q^{5} +(-5.69877 - 1.87723i) q^{6} +(-0.720479 - 1.24791i) q^{7} +(4.60324 - 6.54295i) q^{8} +(-8.76770 - 2.03162i) q^{9} +(-4.57254 - 4.07532i) q^{10} +(8.82792 + 15.2904i) q^{11} +(5.98942 - 10.3984i) q^{12} +(-8.00003 - 4.61882i) q^{13} +(2.73631 - 0.904455i) q^{14} +(-7.38331 - 5.46796i) q^{15} +(10.9452 + 11.6706i) q^{16} +4.69563i q^{17} +(7.53743 - 16.3459i) q^{18} +16.8874i q^{19} +(9.83699 - 7.30063i) q^{20} +(3.96503 - 1.72215i) q^{21} +(-33.5276 + 11.0821i) q^{22} +(33.8361 + 19.5353i) q^{23} +(17.9330 + 15.9502i) q^{24} +(7.81045 + 13.5281i) q^{25} +(12.2926 - 13.7924i) q^{26} +(9.04351 - 25.4404i) q^{27} +(0.660616 + 5.72585i) q^{28} +(-7.60350 - 13.1696i) q^{29} +(13.7052 - 12.2399i) q^{30} +(24.3515 - 42.1781i) q^{31} +(-27.2981 + 16.6978i) q^{32} +(-48.5829 + 21.1012i) q^{33} +(-9.19582 - 1.90592i) q^{34} +4.41298 q^{35} +(28.9520 + 21.3958i) q^{36} -14.1853i q^{37} +(-33.0719 - 6.85447i) q^{38} +(16.4932 - 22.2706i) q^{39} +(10.3046 + 22.2278i) q^{40} +(8.78457 + 5.07177i) q^{41} +(1.76324 + 8.46404i) q^{42} +(-19.3522 + 11.1730i) q^{43} +(-8.09442 - 70.1579i) q^{44} +(18.8140 - 20.1430i) q^{45} +(-51.9914 + 58.3347i) q^{46} +(-36.8675 + 21.2854i) q^{47} +(-38.5154 + 28.6455i) q^{48} +(23.4618 - 40.6371i) q^{49} +(-29.6634 + 9.80487i) q^{50} +(-13.9957 - 1.60031i) q^{51} +(22.0212 + 29.6717i) q^{52} -71.2201 q^{53} +(46.1513 + 28.0367i) q^{54} -54.0715 q^{55} +(-11.4815 - 1.03035i) q^{56} +(-50.3342 - 5.75538i) q^{57} +(28.8774 - 9.54507i) q^{58} +(34.9993 - 60.6205i) q^{59} +(18.4076 + 31.8080i) q^{60} +(89.7576 - 51.8216i) q^{61} +(72.7166 + 64.8093i) q^{62} +(3.78167 + 12.4050i) q^{63} +(-21.6204 - 60.2375i) q^{64} +(24.5003 - 14.1453i) q^{65} +(-21.6047 - 103.709i) q^{66} +(10.5162 + 6.07152i) q^{67} +(7.46504 - 17.2353i) q^{68} +(-69.7582 + 94.1934i) q^{69} +(-1.79120 + 8.64229i) q^{70} +112.880i q^{71} +(-53.6526 + 48.0146i) q^{72} +84.0137 q^{73} +(27.7801 + 5.75770i) q^{74} +(-42.9834 + 18.6692i) q^{75} +(26.8473 - 61.9852i) q^{76} +(12.7207 - 22.0328i) q^{77} +(36.9198 + 41.3395i) q^{78} +(-22.9826 - 39.8070i) q^{79} +(-47.7131 + 11.1583i) q^{80} +(72.7450 + 35.6252i) q^{81} +(-13.4981 + 15.1449i) q^{82} +(25.7884 + 44.6669i) q^{83} +(-17.2915 + 0.0175934i) q^{84} +(-12.4539 - 7.19025i) q^{85} +(-14.0261 - 42.4340i) q^{86} +(41.8445 - 18.1745i) q^{87} +(140.681 + 12.6247i) q^{88} -105.051i q^{89} +(31.8112 + 45.0208i) q^{90} +13.3111i q^{91} +(-93.1386 - 125.497i) q^{92} +(117.416 + 86.9563i) q^{93} +(-26.7207 - 80.8401i) q^{94} +(-44.7892 - 25.8591i) q^{95} +(-40.4655 - 87.0548i) q^{96} +(19.4321 + 33.6574i) q^{97} +(70.0598 + 62.4415i) q^{98} +(-46.3362 - 151.997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 44 q - 3 q^{2} - q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} + 4 q^{10} + 14 q^{12} - 48 q^{14} + 14 q^{15} - q^{16} - 38 q^{18} - 66 q^{20} + 7 q^{22} - 6 q^{23} - 47 q^{24} - 72 q^{25} + 28 q^{28} + 16 q^{30} - 2 q^{31} - 93 q^{32} + 30 q^{33} + 9 q^{34} - 105 q^{36} + 99 q^{38} - 118 q^{39} - 56 q^{40} + 66 q^{41} + 236 q^{42} + 72 q^{46} - 6 q^{47} + 117 q^{48} - 72 q^{49} + 189 q^{50} - 42 q^{52} + 139 q^{54} + 92 q^{55} + 270 q^{56} - 8 q^{57} - 38 q^{58} + 456 q^{60} - 226 q^{63} + 2 q^{64} - 6 q^{65} - 258 q^{66} + 387 q^{68} - 4 q^{70} + 259 q^{72} - 8 q^{73} - 432 q^{74} - 63 q^{76} - 620 q^{78} - 2 q^{79} - 44 q^{81} + 186 q^{82} - 232 q^{84} - 615 q^{86} + 174 q^{87} - 77 q^{88} - 554 q^{90} - 624 q^{92} - 186 q^{94} + 144 q^{95} - 794 q^{96} - 2 q^{97}+O(q^{100}) \) 44 * q - 3 * q^2 - q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 + 4 * q^10 + 14 * q^12 - 48 * q^14 + 14 * q^15 - q^16 - 38 * q^18 - 66 * q^20 + 7 * q^22 - 6 * q^23 - 47 * q^24 - 72 * q^25 + 28 * q^28 + 16 * q^30 - 2 * q^31 - 93 * q^32 + 30 * q^33 + 9 * q^34 - 105 * q^36 + 99 * q^38 - 118 * q^39 - 56 * q^40 + 66 * q^41 + 236 * q^42 + 72 * q^46 - 6 * q^47 + 117 * q^48 - 72 * q^49 + 189 * q^50 - 42 * q^52 + 139 * q^54 + 92 * q^55 + 270 * q^56 - 8 * q^57 - 38 * q^58 + 456 * q^60 - 226 * q^63 + 2 * q^64 - 6 * q^65 - 258 * q^66 + 387 * q^68 - 4 * q^70 + 259 * q^72 - 8 * q^73 - 432 * q^74 - 63 * q^76 - 620 * q^78 - 2 * q^79 - 44 * q^81 + 186 * q^82 - 232 * q^84 - 615 * q^86 + 174 * q^87 - 77 * q^88 - 554 * q^90 - 624 * q^92 - 186 * q^94 + 144 * q^95 - 794 * q^96 - 2 * q^97

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