LMFDB - Embedded newform 128.4.k.a.101.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

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

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.37
Character	$\chi$	$=$	128.101
Dual form			128.4.k.a.109.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.02139 - 1.97838i) q^{2} +(8.86876 - 4.74045i) q^{3} +(0.172010 - 7.99815i) q^{4} +(4.99248 + 6.08336i) q^{5} +(8.54877 - 27.1281i) q^{6} +(-23.7013 + 15.8367i) q^{7} +(-15.4757 - 16.5077i) q^{8} +(41.1826 - 61.6341i) q^{9} +(22.1269 + 2.41978i) q^{10} +(13.1684 - 3.99460i) q^{11} +(-36.3893 - 71.7491i) q^{12} +(27.1522 + 22.2832i) q^{13} +(-16.5785 + 78.9024i) q^{14} +(73.1150 + 30.2852i) q^{15} +(-63.9408 - 2.75153i) q^{16} +(-77.0427 + 31.9121i) q^{17} +(-38.6899 - 206.061i) q^{18} +(8.99475 + 91.3252i) q^{19} +(49.5144 - 38.8842i) q^{20} +(-135.128 + 252.807i) q^{21} +(18.7157 - 34.1269i) q^{22} +(64.7828 - 12.8861i) q^{23} +(-215.504 - 73.0407i) q^{24} +(12.3039 - 61.8560i) q^{25} +(98.9697 - 8.67437i) q^{26} +(46.4518 - 471.633i) q^{27} +(122.588 + 192.291i) q^{28} +(-39.5737 + 130.457i) q^{29} +(207.709 - 83.4312i) q^{30} +(110.784 + 110.784i) q^{31} +(-134.693 + 120.937i) q^{32} +(97.8515 - 97.8515i) q^{33} +(-92.5987 + 216.927i) q^{34} +(-214.669 - 65.1191i) q^{35} +(-485.875 - 339.986i) q^{36} +(-230.214 - 22.6741i) q^{37} +(198.858 + 166.809i) q^{38} +(346.438 + 68.9109i) q^{39} +(23.1598 - 176.558i) q^{40} +(-36.1462 - 181.719i) q^{41} +(227.002 + 778.355i) q^{42} +(276.260 + 147.664i) q^{43} +(-29.6843 - 106.010i) q^{44} +(580.546 - 57.1788i) q^{45} +(105.458 - 154.213i) q^{46} +(-141.593 - 341.837i) q^{47} +(-580.119 + 278.706i) q^{48} +(179.690 - 433.811i) q^{49} +(-97.5038 - 149.377i) q^{50} +(-531.995 + 648.238i) q^{51} +(182.895 - 213.334i) q^{52} +(-16.0278 - 52.8365i) q^{53} +(-839.173 - 1045.25i) q^{54} +(90.0439 + 60.1654i) q^{55} +(628.221 + 146.169i) q^{56} +(512.695 + 767.302i) q^{57} +(178.100 + 341.996i) q^{58} +(-580.900 + 476.732i) q^{59} +(254.802 - 579.575i) q^{60} +(-243.880 - 456.268i) q^{61} +(443.112 + 4.76428i) q^{62} +2113.01i q^{63} +(-33.0056 + 510.935i) q^{64} +276.425i q^{65} +(4.20811 - 391.384i) q^{66} +(190.568 + 356.527i) q^{67} +(241.986 + 621.688i) q^{68} +(513.457 - 421.384i) q^{69} +(-562.759 + 293.066i) q^{70} +(32.6973 + 48.9349i) q^{71} +(-1654.76 + 274.003i) q^{72} +(174.966 + 116.909i) q^{73} +(-510.210 + 409.618i) q^{74} +(-184.105 - 606.912i) q^{75} +(731.980 - 56.2325i) q^{76} +(-248.848 + 303.222i) q^{77} +(836.618 - 546.092i) q^{78} +(227.033 - 548.106i) q^{79} +(-302.485 - 402.712i) q^{80} +(-1057.87 - 2553.93i) q^{81} +(-432.575 - 295.814i) q^{82} +(1164.97 - 114.740i) q^{83} +(1998.74 + 1124.26i) q^{84} +(-578.767 - 309.358i) q^{85} +(850.563 - 248.061i) q^{86} +(267.455 + 1344.59i) q^{87} +(-269.732 - 155.561i) q^{88} +(113.358 + 22.5483i) q^{89} +(1060.39 - 1264.12i) q^{90} +(-996.435 - 98.1402i) q^{91} +(-91.9217 - 520.359i) q^{92} +(1507.69 + 457.352i) q^{93} +(-962.498 - 410.858i) q^{94} +(-510.658 + 510.658i) q^{95} +(-621.259 + 1711.07i) q^{96} +(-857.577 - 857.577i) q^{97} +(-495.020 - 1232.40i) q^{98} +(296.107 - 976.134i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100}) $ 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	2.02139	−	1.97838i	0.714668	−	0.699464i
$2$	2.02139	−	1.97838i	0.714668	−	0.699464i
$3$	8.86876	−	4.74045i	1.70679	−	0.912300i	0.734476	−	0.678634i	$-0.237428\pi$
$3$	8.86876	−	4.74045i	1.70679	−	0.912300i	0.972317	−	0.233666i	$-0.0750722\pi$
$4$	0.172010	−	7.99815i	0.0215013	−	0.999769i
$5$	4.99248	+	6.08336i	0.446541	+	0.544112i	0.946825	−	0.321749i	$-0.104271\pi$
$5$	4.99248	+	6.08336i	0.446541	+	0.544112i	−0.500284	+	0.865862i	$0.666771\pi$
$6$	8.54877	−	27.1281i	0.581670	−	1.84583i
$7$	−23.7013	+	15.8367i	−1.27975	+	0.855102i	−0.994641	−	0.103393i	$-0.967030\pi$
$7$	−23.7013	+	15.8367i	−1.27975	+	0.855102i	−0.285110	+	0.958495i	$0.592030\pi$
$8$	−15.4757	−	16.5077i	−0.683936	−	0.729542i
$9$	41.1826	−	61.6341i	1.52528	−	2.28275i
$10$	22.1269	+	2.41978i	0.699716	+	0.0765203i
$11$	13.1684	−	3.99460i	0.360949	−	0.109493i	−0.104601	−	0.994514i	$-0.533357\pi$
$11$	13.1684	−	3.99460i	0.360949	−	0.109493i	0.465550	+	0.885022i	$0.345857\pi$
$12$	−36.3893	−	71.7491i	−0.875391	−	1.72601i
$13$	27.1522	+	22.2832i	0.579281	+	0.475404i	0.877818	−	0.478994i	$-0.158999\pi$
$13$	27.1522	+	22.2832i	0.579281	+	0.475404i	−0.298537	+	0.954398i	$0.596499\pi$
$14$	−16.5785	+	78.9024i	−0.316484	+	1.50625i
$15$	73.1150	+	30.2852i	1.25855	+	0.521307i
$16$	−63.9408	−	2.75153i	−0.999075	−	0.0429926i
$17$	−77.0427	+	31.9121i	−1.09915	+	0.455284i	−0.857189	−	0.515001i	$-0.827791\pi$
$17$	−77.0427	+	31.9121i	−1.09915	+	0.455284i	−0.241963	+	0.970285i	$0.577791\pi$
$18$	−38.6899	−	206.061i	−0.506627	−	2.69829i
$19$	8.99475	+	91.3252i	0.108607	+	1.10271i	0.882797	+	0.469754i	$0.155658\pi$
$19$	8.99475	+	91.3252i	0.108607	+	1.10271i	−0.774190	+	0.632953i	$0.781842\pi$
$20$	49.5144	−	38.8842i	0.553588	−	0.434739i
$21$	−135.128	+	252.807i	−1.40416	+	2.62700i
$22$	18.7157	−	34.1269i	0.181372	−	0.330721i
$23$	64.7828	−	12.8861i	0.587311	−	0.116823i	0.107515	−	0.994203i	$-0.465711\pi$
$23$	64.7828	−	12.8861i	0.587311	−	0.116823i	0.479796	+	0.877380i	$0.340711\pi$
$24$	−215.504	−	73.0407i	−1.83290	−	0.621223i
$25$	12.3039	−	61.8560i	0.0984314	−	0.494848i
$26$	98.9697	−	8.67437i	0.746522	−	0.0654302i
$27$	46.4518	−	471.633i	0.331098	−	3.36170i
$28$	122.588	+	192.291i	0.827388	+	1.29784i
$29$	−39.5737	+	130.457i	−0.253402	+	0.835353i	0.734276	+	0.678851i	$0.237522\pi$
$29$	−39.5737	+	130.457i	−0.253402	+	0.835353i	−0.987678	+	0.156502i	$0.949978\pi$
$30$	207.709	−	83.4312i	1.26408	−	0.507746i
$31$	110.784	+	110.784i	0.641853	+	0.641853i	0.951011	−	0.309157i	$-0.100047\pi$
$31$	110.784	+	110.784i	0.641853	+	0.641853i	−0.309157	+	0.951011i	$0.600047\pi$
$32$	−134.693	+	120.937i	−0.744079	+	0.668091i
$33$	97.8515	−	97.8515i	0.516175	−	0.516175i
$34$	−92.5987	+	216.927i	−0.467075	+	1.09419i
$35$	−214.669	−	65.1191i	−1.03673	−	0.314489i
$36$	−485.875	−	339.986i	−2.24942	−	1.57401i
$37$	−230.214	−	22.6741i	−1.02289	−	0.100746i	−0.427362	−	0.904080i	$-0.640557\pi$
$37$	−230.214	−	22.6741i	−1.02289	−	0.100746i	−0.595528	+	0.803334i	$0.703057\pi$
$38$	198.858	+	166.809i	0.848922	+	0.712103i
$39$	346.438	+	68.9109i	1.42242	+	0.282938i
$40$	23.1598	−	176.558i	0.0915473	−	0.697909i
$41$	−36.1462	−	181.719i	−0.137685	−	0.692189i	−0.986534	−	0.163554i	$-0.947704\pi$
$41$	−36.1462	−	181.719i	−0.137685	−	0.692189i	0.848849	−	0.528635i	$-0.177296\pi$
$42$	227.002	+	778.355i	0.833982	+	2.85959i
$43$	276.260	+	147.664i	0.979749	+	0.523687i	0.881860	−	0.471511i	$-0.156291\pi$
$43$	276.260	+	147.664i	0.979749	+	0.523687i	0.0978887	+	0.995197i	$0.468791\pi$
$44$	−29.6843	−	106.010i	−0.101706	−	0.363219i
$45$	580.546	−	57.1788i	1.92317	−	0.189416i
$46$	105.458	−	154.213i	0.338019	−	0.494293i
$47$	−141.593	−	341.837i	−0.439436	−	1.06089i	−0.976144	−	0.217125i	$-0.930332\pi$
$47$	−141.593	−	341.837i	−0.439436	−	1.06089i	0.536707	−	0.843768i	$-0.319668\pi$
$48$	−580.119	+	278.706i	−1.74444	+	0.838077i
$49$	179.690	−	433.811i	0.523879	−	1.26475i
$50$	−97.5038	−	149.377i	−0.275782	−	0.422501i
$51$	−531.995	+	648.238i	−1.46067	+	1.77983i
$52$	182.895	−	213.334i	0.487749	−	0.568926i
$53$	−16.0278	−	52.8365i	−0.0415394	−	0.136937i	0.933718	−	0.358009i	$-0.116544\pi$
$53$	−16.0278	−	52.8365i	−0.0415394	−	0.136937i	−0.975257	+	0.221072i	$0.929044\pi$
$54$	−839.173	−	1045.25i	−2.11476	−	2.63409i
$55$	90.0439	+	60.1654i	0.220755	+	0.147504i
$56$	628.221	+	146.169i	1.49910	+	0.348797i
$57$	512.695	+	767.302i	1.19137	+	1.78301i
$58$	178.100	+	341.996i	0.403201	+	0.774245i
$59$	−580.900	+	476.732i	−1.28181	+	1.05195i	−0.286216	+	0.958165i	$0.592398\pi$
$59$	−580.900	+	476.732i	−1.28181	+	1.05195i	−0.995592	+	0.0937882i	$0.970102\pi$
$60$	254.802	−	579.575i	0.548247	−	1.24705i
$61$	−243.880	−	456.268i	−0.511896	−	0.957690i	−0.996551	−	0.0829843i	$-0.973555\pi$
$61$	−243.880	−	456.268i	−0.511896	−	0.957690i	0.484655	−	0.874705i	$-0.338945\pi$
$62$	443.112	+	4.76428i	0.907665	+	0.00975910i
$63$			2113.01i			4.22562i
$64$	−33.0056	+	510.935i	−0.0644640	+	0.997920i
$65$			276.425i			0.527481i
$66$	4.20811	−	391.384i	0.00784821	−	0.729939i
$67$	190.568	+	356.527i	0.347486	+	0.650100i	0.993577	−	0.113160i	$-0.0360974\pi$
$67$	190.568	+	356.527i	0.347486	+	0.650100i	−0.646091	+	0.763260i	$0.723597\pi$
$68$	241.986	+	621.688i	0.431546	+	1.10869i
$69$	513.457	−	421.384i	0.895841	−	0.735197i
$70$	−562.759	+	293.066i	−0.960894	+	0.500401i
$71$	32.6973	+	48.9349i	0.0546543	+	0.0817959i	0.857790	−	0.514000i	$-0.171837\pi$
$71$	32.6973	+	48.9349i	0.0546543	+	0.0817959i	−0.803136	+	0.595796i	$0.796837\pi$
$72$	−1654.76	+	274.003i	−2.70855	+	0.448493i
$73$	174.966	+	116.909i	0.280524	+	0.187440i	0.687870	−	0.725834i	$-0.258546\pi$
$73$	174.966	+	116.909i	0.280524	+	0.187440i	−0.407347	+	0.913274i	$0.633546\pi$
$74$	−510.210	+	409.618i	−0.801495	+	0.643475i
$75$	−184.105	−	606.912i	−0.283448	−	0.934402i
$76$	731.980	−	56.2325i	1.10479	−	0.0848725i
$77$	−248.848	+	303.222i	−0.368297	+	0.448771i
$78$	836.618	−	546.092i	1.21447	−	0.792727i
$79$	227.033	−	548.106i	0.323332	−	0.780592i	−0.675724	−	0.737154i	$-0.736169\pi$
$79$	227.033	−	548.106i	0.323332	−	0.780592i	0.999056	−	0.0434375i	$-0.0138310\pi$
$80$	−302.485	−	402.712i	−0.422736	−	0.562807i
$81$	−1057.87	−	2553.93i	−1.45113	−	3.50333i
$82$	−432.575	−	295.814i	−0.582560	−	0.398380i
$83$	1164.97	−	114.740i	1.54063	−	0.151739i	0.708258	−	0.705953i	$-0.249481\pi$
$83$	1164.97	−	114.740i	1.54063	−	0.151739i	0.832374	+	0.554214i	$0.186981\pi$
$84$	1998.74	+	1124.26i	2.59620	+	1.46032i
$85$	−578.767	−	309.358i	−0.738543	−	0.394759i
$86$	850.563	−	248.061i	1.06650	−	0.311037i
$87$	267.455	+	1344.59i	0.329588	+	1.65695i
$88$	−269.732	−	155.561i	−0.326745	−	0.188441i
$89$	113.358	+	22.5483i	0.135011	+	0.0268553i	0.262133	−	0.965032i	$-0.415574\pi$
$89$	113.358	+	22.5483i	0.135011	+	0.0268553i	−0.127122	+	0.991887i	$0.540574\pi$
$90$	1060.39	−	1264.12i	1.24194	−	1.48056i
$91$	−996.435	−	98.1402i	−1.14785	−	0.113054i
$92$	−91.9217	−	520.359i	−0.104169	−	0.589687i
$93$	1507.69	+	457.352i	1.68107	+	0.509948i
$94$	−962.498	−	410.858i	−1.05611	−	0.450817i
$95$	−510.658	+	510.658i	−0.551499	+	0.551499i
$96$	−621.259	+	1711.07i	−0.660489	+	1.81912i
$97$	−857.577	−	857.577i	−0.897668	−	0.897668i	0.0975615	−	0.995230i	$-0.468896\pi$
$97$	−857.577	−	857.577i	−0.897668	−	0.897668i	−0.995230	+	0.0975615i	$0.968896\pi$
$98$	−495.020	−	1232.40i	−0.510251	−	1.27031i
$99$	296.107	−	976.134i	0.300605	−	0.990961i
$100$	−492.617	−	109.049i	−0.492617	−	0.109049i
$101$	86.4083	−	877.318i	0.0851281	−	0.864321i	−0.853890	−	0.520453i	$-0.825763\pi$
$101$	86.4083	−	877.318i	0.0851281	−	0.864321i	0.939018	−	0.343867i	$-0.111737\pi$
$102$	207.094	+	2362.83i	0.201033	+	2.29368i
$103$	−88.9878	+	447.372i	−0.0851284	+	0.427969i	0.914593	+	0.404375i	$0.132511\pi$
$103$	−88.9878	+	447.372i	−0.0851284	+	0.427969i	−0.999722	+	0.0235942i	$0.992489\pi$
$104$	−52.3551	−	793.067i	−0.0493639	−	0.747756i
$105$	−2212.54	+	440.101i	−2.05640	+	0.409043i
$106$	−136.929	−	75.0940i	−0.125469	−	0.0688092i
$107$	350.071	−	654.936i	0.316286	−	0.591729i	−0.672669	−	0.739943i	$-0.734852\pi$
$107$	350.071	−	654.936i	0.316286	−	0.591729i	0.988955	+	0.148214i	$0.0473524\pi$
$108$	−3764.20	−	452.654i	−3.35380	−	0.403302i
$109$	104.133	+	1057.28i	0.0915054	+	0.929070i	0.925866	+	0.377852i	$0.123337\pi$
$109$	104.133	+	1057.28i	0.0915054	+	0.929070i	−0.834361	+	0.551219i	$0.814163\pi$
$110$	301.044	−	56.5236i	0.260940	−	0.0489938i
$111$	−2149.20	+	890.227i	−1.83777	+	0.761231i
$112$	1559.06	−	947.398i	1.31533	−	0.799292i
$113$	−1323.33	−	548.143i	−1.10167	−	0.456327i	−0.243609	−	0.969874i	$-0.578331\pi$
$113$	−1323.33	−	548.143i	−1.10167	−	0.456327i	−0.858062	+	0.513547i	$0.828331\pi$
$114$	2554.37	+	536.708i	2.09859	+	0.440942i
$115$	401.818	+	329.764i	0.325824	+	0.267397i
$116$	1036.61	+	338.956i	0.829711	+	0.271304i
$117$	2491.60	−	755.820i	1.96879	−	0.597227i
$118$	−231.065	+	2112.90i	−0.180265	+	1.64838i
$119$	1320.63	−	1976.46i	1.01733	−	1.52254i
$120$	−631.567	−	1675.64i	−0.480450	−	1.27470i
$121$	−949.235	+	634.259i	−0.713174	+	0.476528i
$122$	−1395.65	−	439.805i	−1.03570	−	0.326378i
$123$	−1182.00	−	1440.27i	−0.866484	−	1.05581i
$124$	905.126	−	867.014i	0.655506	−	0.627904i
$125$	1305.28	−	697.685i	0.933980	−	0.499223i
$126$	4180.33	+	4271.20i	2.95567	+	3.01991i
$127$	−2624.65			−1.83386			−0.916929	−	0.399051i	$-0.869340\pi$
$127$	−2624.65			−1.83386			−0.916929	+	0.399051i	$0.869340\pi$
$128$	944.108	+	1098.10i	0.651938	+	0.758272i
$129$	3150.07			2.14999
$130$	546.874	+	558.762i	0.368954	+	0.376974i
$131$	393.949	−	210.570i	0.262744	−	0.140440i	−0.334765	−	0.942302i	$-0.608657\pi$
$131$	393.949	−	210.570i	0.262744	−	0.140440i	0.597510	+	0.801862i	$0.296157\pi$
$132$	−765.800	−	799.463i	−0.504957	−	0.527154i
$133$	−1659.48	−	2022.08i	−1.08192	−	1.31832i
$134$	1090.56	+	343.663i	0.703058	+	0.221552i
$135$	3101.02	−	2072.04i	1.97699	−	1.32098i
$136$	1719.08	+	777.932i	1.08390	+	0.490493i
$137$	1180.01	−	1766.01i	0.735875	−	1.10131i	−0.255054	−	0.966927i	$-0.582093\pi$
$137$	1180.01	−	1766.01i	0.735875	−	1.10131i	0.990929	−	0.134388i	$-0.0429069\pi$
$138$	204.238	−	1867.59i	0.125985	−	1.15203i
$139$	−738.951	+	224.158i	−0.450914	+	0.136783i	−0.507570	−	0.861611i	$-0.669456\pi$
$139$	−738.951	+	224.158i	−0.450914	+	0.136783i	0.0566563	+	0.998394i	$0.481956\pi$
$140$	−557.757	+	1705.75i	−0.336708	+	1.02973i
$141$	−2876.22	−	2360.45i	−1.71788	−	1.40983i
$142$	162.906	+	34.2287i	0.0962729	+	0.0202283i
$143$	446.564	+	184.973i	0.261144	+	0.108169i
$144$	−2802.84	+	3827.62i	−1.62201	+	2.21506i
$145$	−991.187	+	410.563i	−0.567680	+	0.235141i
$146$	584.964	−	109.832i	0.331589	−	0.0622587i
$147$	−462.829	−	4699.18i	−0.259683	−	2.63661i
$148$	−220.950	+	1837.39i	−0.122716	+	1.02049i
$149$	−1192.34	+	2230.71i	−0.655573	+	1.22649i	0.306023	+	0.952024i	$0.401002\pi$
$149$	−1192.34	+	2230.71i	−0.655573	+	1.22649i	−0.961596	+	0.274468i	$0.911498\pi$
$150$	−1572.85	−	862.575i	−0.856152	−	0.469526i
$151$	−2395.39	+	476.472i	−1.29095	+	0.256787i	−0.792362	−	0.610051i	$-0.791149\pi$
$151$	−2395.39	+	476.472i	−1.29095	+	0.256787i	−0.498591	+	0.866837i	$0.666149\pi$
$152$	1368.37	−	1561.80i	0.730192	−	0.833415i
$153$	−1205.94	+	6062.68i	−0.637220	+	3.20352i
$154$	96.8712	+	1105.25i	0.0506890	+	0.578333i
$155$	−120.852	+	1227.03i	−0.0626262	+	0.635854i
$156$	610.751	−	2759.01i	0.313456	−	1.41601i
$157$	61.7028	−	203.407i	0.0313657	−	0.103399i	−0.939860	−	0.341560i	$-0.889045\pi$
$157$	61.7028	−	203.407i	0.0313657	−	0.103399i	0.971226	+	0.238161i	$0.0765447\pi$
$158$	−625.442	−	1557.09i	−0.314921	−	0.784023i
$159$	−392.616	−	392.616i	−0.195827	−	0.195827i
$160$	−1408.16	−	215.606i	−0.695779	−	0.106532i
$161$	−1331.36	+	1331.36i	−0.651716	+	0.651716i
$162$	−7191.01	−	3069.60i	−3.48753	−	1.48871i
$163$	1267.19	+	384.398i	0.608921	+	0.184714i	0.579661	−	0.814858i	$-0.303185\pi$
$163$	1267.19	+	384.398i	0.608921	+	0.184714i	0.0292598	+	0.999572i	$0.490685\pi$
$164$	−1459.63	+	257.845i	−0.694990	+	0.122770i
$165$	1083.79	+	106.744i	0.511350	+	0.0503636i
$166$	2127.86	−	2536.70i	0.994905	−	1.18606i
$167$	2161.15	+	429.879i	1.00140	+	0.199192i	0.668455	−	0.743753i	$-0.266956\pi$
$167$	2161.15	+	429.879i	1.00140	+	0.199192i	0.332950	+	0.942945i	$0.391956\pi$
$168$	6264.45	−	1681.71i	2.87686	−	0.772304i
$169$	−187.915	−	944.711i	−0.0855324	−	0.430000i
$170$	−1781.94	+	519.691i	−0.803933	+	0.234462i
$171$	5999.18	+	3206.63i	2.68286	+	1.43402i
$172$	1228.56	−	2184.17i	0.544632	−	0.968263i
$173$	2610.30	−	257.092i	1.14715	−	0.112985i	0.493476	−	0.869759i	$-0.335726\pi$
$173$	2610.30	−	257.092i	1.14715	−	0.112985i	0.653676	+	0.756775i	$0.273226\pi$
$174$	3200.74	+	2188.80i	1.39452	+	0.953636i
$175$	687.977	+	1660.92i	0.297178	+	0.717451i
$176$	−852.992	+	219.185i	−0.365322	+	0.0938732i
$177$	−2891.93	+	6981.75i	−1.22809	+	2.96486i
$178$	273.750	−	178.687i	0.115272	−	0.0752423i
$179$	−133.627	+	162.825i	−0.0557973	+	0.0679893i	−0.800161	−	0.599785i	$-0.795253\pi$
$179$	−133.627	+	162.825i	−0.0557973	+	0.0679893i	0.744364	+	0.667774i	$0.232753\pi$
$180$	−357.465	−	4653.13i	−0.148021	−	1.92680i
$181$	−651.864	−	2148.91i	−0.267694	−	0.882470i	−0.982992	−	0.183650i	$-0.941209\pi$
$181$	−651.864	−	2148.91i	−0.267694	−	0.882470i	0.715298	−	0.698820i	$-0.246291\pi$
$182$	−2208.34	+	1772.95i	−0.899412	+	0.722086i
$183$	−4325.83	−	2890.43i	−1.74740	−	1.16758i
$184$	−1215.28	−	869.991i	−0.486911	−	0.348569i
$185$	−1011.41	−	1513.67i	−0.401946	−	0.601554i
$186$	3952.44	−	2058.30i	1.55810	−	0.811406i
$187$	−887.056	+	727.988i	−0.346888	+	0.284683i
$188$	−2758.42	+	1073.69i	−1.07010	+	0.416524i
$189$	6368.15	+	11914.0i	2.45087	+	4.58526i
$190$	−21.9609	+	2042.51i	−0.00838531	+	0.779892i
$191$			2633.80i			0.997777i	0.866666	+	0.498888i	$0.166258\pi$
$191$			2633.80i			0.997777i	−0.866666	+	0.498888i	$0.833742\pi$
$192$	2129.34	+	4687.82i	0.800376	+	1.76205i
$193$		−	1625.00i		−	0.606061i	−0.952981	−	0.303030i	$-0.902002\pi$
$193$		−	1625.00i		−	0.606061i	0.952981	−	0.303030i	$-0.0979984\pi$
$194$	−3430.11	−	36.8801i	−1.26942	−	0.0136487i
$195$	1310.38	+	2451.55i	0.481221	+	0.900302i
$196$	−3438.78	−	1511.81i	−1.25320	−	0.550951i
$197$	405.808	−	333.038i	0.146765	−	0.120447i	−0.558146	−	0.829743i	$-0.688487\pi$
$197$	405.808	−	333.038i	0.146765	−	0.120447i	0.704911	+	0.709296i	$0.250987\pi$
$198$	−1332.62	−	2558.96i	−0.478309	−	0.918471i
$199$	88.5482	+	132.522i	0.0315428	+	0.0472071i	0.846906	−	0.531743i	$-0.178463\pi$
$199$	88.5482	+	132.522i	0.0315428	+	0.0472071i	−0.815363	+	0.578950i	$0.803463\pi$
$200$	−1211.51	+	754.156i	−0.428333	+	0.266634i
$201$	3380.20	+	2258.58i	1.18617	+	0.792575i
$202$	−1561.00	−	1944.35i	−0.543722	−	0.677246i
$203$	−1128.06	−	3718.72i	−0.390021	−	1.28573i
$204$	5093.20	+	4366.48i	1.74801	+	1.49860i
$205$	925.003	−	1127.12i	0.315147	−	0.384007i
$206$	705.193	+	1080.36i	0.238510	+	0.365400i
$207$	1873.70	−	4523.52i	0.629137	−	1.51887i
$208$	−1674.82	−	1499.52i	−0.558307	−	0.499869i
$209$	483.255	+	1166.68i	0.159940	+	0.386129i
$210$	−3601.71	+	5266.86i	−1.18353	+	1.73071i
$211$	583.137	−	57.4340i	0.190260	−	0.0187389i	−0.00243847	−	0.999997i	$-0.500776\pi$
$211$	583.137	−	57.4340i	0.190260	−	0.0187389i	0.192698	+	0.981258i	$0.438276\pi$
$212$	−425.352	+	119.104i	−0.137798	+	0.0385854i
$213$	521.958	+	278.992i	0.167906	+	0.0897476i
$214$	−588.085	−	2016.45i	−0.187854	−	0.644121i
$215$	480.930	+	2417.80i	0.152554	+	0.766941i
$216$	−8504.43	+	6532.04i	−2.67895	+	2.05763i
$217$	−4380.19	−	871.275i	−1.37026	−	0.272562i
$218$	2302.19	+	1931.15i	0.715247	+	0.599972i
$219$	2105.93	+	207.416i	0.649797	+	0.0639994i
$220$	496.700	−	709.835i	0.152216	−	0.217532i
$221$	−2802.98	−	850.275i	−0.853162	−	0.258804i
$222$	−2583.15	+	6051.43i	−0.780945	+	1.82948i
$223$	−1796.58	+	1796.58i	−0.539497	+	0.539497i	−0.923381	−	0.383884i	$-0.874586\pi$
$223$	−1796.58	+	1796.58i	−0.539497	+	0.539497i	0.383884	+	0.923381i	$0.374586\pi$
$224$	1277.14	−	4999.47i	0.380949	−	1.49125i
$225$	−3305.73	−	3305.73i	−0.979477	−	0.979477i
$226$	−3759.41	+	1510.05i	−1.10651	+	0.444456i
$227$	−809.215	+	2667.62i	−0.236606	+	0.779984i	0.755563	+	0.655076i	$0.227364\pi$
$227$	−809.215	+	2667.62i	−0.236606	+	0.779984i	−0.992168	+	0.124908i	$0.960136\pi$
$228$	6225.19	−	3968.63i	1.80822	−	1.15276i
$229$	190.712	−	1936.33i	0.0550331	−	0.558761i	−0.927648	−	0.373456i	$-0.878173\pi$
$229$	190.712	−	1936.33i	0.0550331	−	0.558761i	0.982681	−	0.185305i	$-0.0593273\pi$
$230$	1464.63	−	128.370i	0.419890	−	0.0368020i
$231$	−769.563	+	3868.86i	−0.219193	+	1.10196i
$232$	2765.97	−	1365.64i	0.782736	−	0.386460i
$233$	1947.50	−	387.383i	0.547576	−	0.108920i	0.0864531	−	0.996256i	$-0.472447\pi$
$233$	1947.50	−	387.383i	0.547576	−	0.108920i	0.461123	+	0.887336i	$0.347447\pi$
$234$	3541.19	−	6457.15i	0.989295	−	1.80392i
$235$	1372.61	−	2567.98i	0.381018	−	0.712835i
$236$	3713.05	+	4728.13i	1.02415	+	1.30413i
$237$	−584.769	−	5937.26i	−0.160274	−	1.62728i
$238$	−1240.69	−	6607.90i	−0.337908	−	1.79969i
$239$	1405.98	−	582.375i	0.380523	−	0.157618i	−0.184219	−	0.982885i	$-0.558976\pi$
$239$	1405.98	−	582.375i	0.380523	−	0.157618i	0.564742	+	0.825267i	$0.308976\pi$
$240$	−4591.70	−	2137.64i	−1.23497	−	0.574934i
$241$	−1199.44	−	496.824i	−0.320592	−	0.132794i	0.216583	−	0.976264i	$-0.430509\pi$
$241$	−1199.44	−	496.824i	−0.320592	−	0.132794i	−0.537176	+	0.843470i	$0.680509\pi$
$242$	−663.966	+	3160.03i	−0.176369	+	0.839399i
$243$	−11597.6	−	9517.88i	−3.06166	−	2.51264i
$244$	−3691.25	+	1872.11i	−0.968475	+	0.491186i
$245$	3536.13	−	1072.67i	0.922102	−	0.279717i
$246$	−5238.69	−	572.899i	−1.35775	−	0.148483i
$247$	−1790.79	+	2680.11i	−0.461317	+	0.690410i
$248$	114.325	−	3543.25i	0.0292728	−	0.907246i
$249$	9787.95	−	6540.10i	2.49111	−	1.66451i
$250$	1258.18	−	3992.63i	0.318298	−	1.01006i
$251$	3778.11	+	4603.64i	0.950088	+	1.15769i	0.987378	+	0.158381i	$0.0506274\pi$
$251$	3778.11	+	4603.64i	0.950088	+	1.15769i	−0.0372903	+	0.999304i	$0.511873\pi$
$252$	16900.1	+	363.459i	4.22464	+	0.0908561i
$253$	801.614	−	428.472i	0.199198	−	0.106473i
$254$	−5305.43	+	5192.56i	−1.31060	+	1.28272i
$255$	−6599.44			−1.62068
$256$	4080.86	+	351.870i	0.996303	+	0.0859057i
$257$	3227.16			0.783288			0.391644	−	0.920117i	$-0.371906\pi$
$257$	3227.16			0.783288			0.391644	+	0.920117i	$0.371906\pi$
$258$	6367.52	−	6232.05i	1.53653	−	1.50384i
$259$	5815.46	−	3108.43i	1.39519	−	0.745746i
$260$	2210.89	+	47.5479i	0.527359	+	0.0113415i
$261$	6410.85	+	7811.64i	1.52039	+	1.85260i
$262$	379.736	−	1205.03i	0.0895426	−	0.284148i
$263$	3207.92	−	2143.46i	0.752125	−	0.502554i	−0.119435	−	0.992842i	$-0.538108\pi$
$263$	3207.92	−	2143.46i	0.752125	−	0.502554i	0.871560	+	0.490288i	$0.163108\pi$
$264$	−3129.62	−	100.979i	−0.729602	−	0.0235410i
$265$	241.405	−	361.288i	0.0559600	−	0.0837501i
$266$	−7354.90	−	804.325i	−1.69533	−	0.185400i
$267$	1112.23	−	337.393i	0.254935	−	0.0773337i
$268$	2884.34	−	1462.86i	0.657421	−	0.333427i
$269$	−5053.55	−	4147.35i	−1.14543	−	0.940030i	−0.146639	−	0.989190i	$-0.546846\pi$
$269$	−5053.55	−	4147.35i	−1.14543	−	0.940030i	−0.998791	+	0.0491600i	$0.984346\pi$
$270$	2169.09	−	10323.4i	0.488912	−	2.32690i
$271$	2034.68	+	842.791i	0.456081	+	0.188915i	0.598883	−	0.800836i	$-0.295611\pi$
$271$	2034.68	+	842.791i	0.456081	+	0.188915i	−0.142802	+	0.989751i	$0.545611\pi$
$272$	5013.98	−	1828.50i	1.11771	−	0.407608i
$273$	−9302.37	+	3853.17i	−2.06229	+	0.854228i
$274$	−1108.58	−	5904.29i	−0.244423	−	1.30179i
$275$	−85.0667	−	863.697i	−0.0186535	−	0.189392i
$276$	−3281.97	−	4179.19i	−0.715766	−	0.911441i
$277$	−1162.17	+	2174.27i	−0.252087	+	0.471622i	−0.975854	−	0.218422i	$-0.929909\pi$
$277$	−1162.17	+	2174.27i	−0.252087	+	0.471622i	0.723767	+	0.690044i	$0.242409\pi$
$278$	−1050.23	+	1915.04i	−0.226579	+	0.413152i
$279$	11390.5	−	2265.71i	2.44420	−	0.486181i
$280$	2247.19	+	4551.44i	0.479625	+	0.971431i
$281$	−77.5903	+	390.073i	−0.0164721	+	0.0828107i	−0.988147	−	0.153511i	$-0.950942\pi$
$281$	−77.5903	+	390.073i	−0.0164721	+	0.0828107i	0.971675	+	0.236322i	$0.0759419\pi$
$282$	−10483.8	+	918.872i	−2.21384	+	0.194036i
$283$	381.075	−	3869.12i	0.0800444	−	0.812705i	−0.868422	−	0.495826i	$-0.834865\pi$
$283$	381.075	−	3869.12i	0.0800444	−	0.812705i	0.948466	−	0.316878i	$-0.102635\pi$
$284$	397.013	−	253.100i	0.0829521	−	0.0528829i
$285$	−2108.15	+	6949.65i	−0.438162	+	1.44443i
$286$	1268.63	−	509.573i	0.262292	−	0.105356i
$287$	3734.54	+	3734.54i	0.768095	+	0.768095i
$288$	1906.88	+	13282.2i	0.390152	+	2.71757i
$289$	1443.18	−	1443.18i	0.293746	−	0.293746i
$290$	−1191.32	+	2790.85i	−0.241230	+	0.565119i
$291$	−11671.0	−	3540.34i	−2.35108	−	0.713191i
$292$	965.148	−	1379.30i	0.193428	−	0.276429i
$293$	1894.27	+	186.569i	0.377694	+	0.0371997i	0.285083	−	0.958503i	$-0.407979\pi$
$293$	1894.27	+	186.569i	0.377694	+	0.0371997i	0.0926110	+	0.995702i	$0.470479\pi$
$294$	−10232.3	−	8583.20i	−2.02980	−	1.70266i
$295$	−5800.27	−	1153.74i	−1.14476	−	0.227707i
$296$	3188.43	+	4151.19i	0.626093	+	0.815146i
$297$	−1272.29	−	6396.23i	−0.248571	−	1.24965i
$298$	2003.02	+	6868.05i	0.389369	+	1.33508i
$299$	2046.14	+	1093.68i	0.395757	+	0.211536i
$300$	−4885.84	+	1368.10i	−0.940281	+	0.263292i
$301$	−8886.23	+	875.217i	−1.70164	+	0.167597i
$302$	−3899.36	+	5702.13i	−0.742990	+	1.08649i
$303$	−3392.55	−	8190.33i	−0.643224	−	1.55288i
$304$	−323.848	−	5864.16i	−0.0610986	−	1.10636i
$305$	1558.07	−	3761.52i	0.292508	−	0.706177i
$306$	9556.63	+	14640.8i	1.78535	+	2.73517i
$307$	4318.82	−	5262.50i	0.802894	−	0.978329i	−0.197104	−	0.980383i	$-0.563154\pi$
$307$	4318.82	−	5262.50i	0.802894	−	0.978329i	0.999998	+	0.00205384i	$0.000653758\pi$
$308$	2382.41	+	2042.48i	0.440749	+	0.377861i
$309$	1331.53	+	4389.47i	0.245140	+	0.808118i
$310$	2183.25	+	2719.39i	0.400000	+	0.498230i
$311$	4290.20	+	2866.62i	0.782234	+	0.522672i	0.881384	−	0.472401i	$-0.156612\pi$
$311$	4290.20	+	2866.62i	0.782234	+	0.522672i	−0.0991502	+	0.995072i	$0.531612\pi$
$312$	−4223.82	−	6785.33i	−0.766432	−	1.23123i
$313$	3299.26	+	4937.68i	0.595798	+	0.891675i	0.999733	−	0.0231125i	$-0.00735760\pi$
$313$	3299.26	+	4937.68i	0.595798	+	0.891675i	−0.403934	+	0.914788i	$0.632358\pi$
$314$	−277.691	−	533.236i	−0.0499077	−	0.0958351i
$315$	−12854.2	+	10549.2i	−2.29921	+	1.88691i
$316$	−4344.78	−	1910.12i	−0.773459	−	0.340041i
$317$	1282.62	+	2399.61i	0.227252	+	0.425159i	0.969544	−	0.244918i	$-0.0787610\pi$
$317$	1282.62	+	2399.61i	0.227252	+	0.425159i	−0.742292	+	0.670077i	$0.766261\pi$
$318$	−1570.37	−	16.8844i	−0.276925	−	0.00297746i
$319$			1876.00i			0.329265i
$320$	−3272.98	+	2350.05i	−0.571766	+	0.410537i
$321$		−	7467.96i		−	1.29851i
$322$	−57.2553	+	5325.15i	−0.00990905	+	0.921612i
$323$	−3607.36	−	6748.90i	−0.621421	−	1.16260i
$324$	−20608.7	+	8021.72i	−3.53372	+	1.37547i
$325$	1712.43	−	1405.35i	0.292272	−	0.239862i
$326$	3321.97	−	1729.97i	0.564377	−	0.293909i
$327$	5935.49	+	8883.09i	1.00377	+	1.50225i
$328$	−2440.37	+	3408.92i	−0.410814	+	0.573860i
$329$	8769.51	+	5859.60i	1.46954	+	0.981916i
$330$	2401.94	−	1928.38i	0.400673	−	0.321678i
$331$	1709.98	+	5637.06i	0.283955	+	0.936075i	0.976649	+	0.214843i	$0.0689239\pi$
$331$	1709.98	+	5637.06i	0.283955	+	0.936075i	−0.692693	+	0.721232i	$0.743576\pi$
$332$	−717.320	−	9337.37i	−0.118578	−	1.54354i
$333$	−10878.3	+	13255.3i	−1.79017	+	2.18133i
$334$	5218.98	−	3406.62i	0.855000	−	0.558090i
$335$	−1217.48	+	2939.25i	−0.198561	+	0.479368i
$336$	9335.80	−	15792.9i	1.51580	−	2.56420i
$337$	3361.28	+	8114.84i	0.543325	+	1.31170i	0.922364	+	0.386321i	$0.126254\pi$
$337$	3361.28	+	8114.84i	0.543325	+	1.31170i	−0.379040	+	0.925380i	$0.623746\pi$
$338$	−2248.85	−	1537.86i	−0.361897	−	0.247481i
$339$	−14334.8	+	1411.85i	−2.29663	+	0.226198i
$340$	−2573.84	+	4575.86i	−0.410548	+	0.729884i
$341$	1901.40	+	1016.32i	0.301954	+	0.161398i
$342$	18470.6	−	5386.83i	2.92040	−	0.851715i
$343$	703.779	+	3538.13i	0.110789	+	0.556972i
$344$	−1837.73	−	6845.60i	−0.288034	−	1.07294i
$345$	5126.86	+	1019.79i	0.800060	+	0.159142i
$346$	4767.79	−	5683.85i	0.740804	−	0.883137i
$347$	−2523.33	−	248.526i	−0.390373	−	0.0384484i	−0.0990730	−	0.995080i	$-0.531588\pi$
$347$	−2523.33	−	248.526i	−0.390373	−	0.0384484i	−0.291300	+	0.956632i	$0.594088\pi$
$348$	10800.2	−	1907.86i	1.66366	−	0.293886i
$349$	−6403.68	−	1942.53i	−0.982180	−	0.297941i	−0.241946	−	0.970290i	$-0.577786\pi$
$349$	−6403.68	−	1942.53i	−0.982180	−	0.297941i	−0.740235	+	0.672349i	$0.765286\pi$
$350$	4676.61	+	1996.29i	0.714215	+	0.304874i
$351$	11770.8	−	11770.8i	1.78996	−	1.78996i
$352$	−1290.60	+	2130.60i	−0.195423	+	0.322618i
$353$	3409.89	+	3409.89i	0.514137	+	0.514137i	0.915791	−	0.401655i	$-0.131565\pi$
$353$	3409.89	+	3409.89i	0.514137	+	0.514137i	−0.401655	+	0.915791i	$0.631565\pi$
$354$	7966.85	+	19834.2i	1.19614	+	2.97789i
$355$	−134.448	+	443.216i	−0.0201008	+	0.0662633i
$356$	199.844	−	902.777i	0.0297519	−	0.134402i
$357$	2343.03	−	23789.1i	0.347356	−	3.52676i
$358$	52.0180	+	593.496i	0.00767943	+	0.0876180i
$359$	990.433	−	4979.24i	0.145607	−	0.732018i	−0.837129	−	0.547006i	$-0.815768\pi$
$359$	990.433	−	4979.24i	0.145607	−	0.732018i	0.982736	−	0.185012i	$-0.0592324\pi$
$360$	−9928.24	−	8698.58i	−1.45351	−	1.27349i
$361$	−1532.19	+	304.771i	−0.223384	+	0.0444338i
$362$	−5569.03	−	3054.14i	−0.808568	−	0.443431i
$363$	−5411.86	+	10124.9i	−0.782505	+	1.46396i
$364$	−956.337	+	7952.75i	−0.137708	+	1.14516i
$365$	162.318	+	1648.05i	0.0232771	+	0.236336i
$366$	−14462.5	+	2715.47i	−2.06549	+	0.387814i
$367$	11170.8	−	4627.09i	1.58886	−	0.658126i	0.599072	−	0.800695i	$-0.295536\pi$
$367$	11170.8	−	4627.09i	1.58886	−	0.658126i	0.989785	+	0.142569i	$0.0455363\pi$
$368$	−4177.72	+	645.697i	−0.591791	+	0.0914654i
$369$	−12688.7	−	5255.83i	−1.79010	−	0.741484i
$370$	−5039.07	−	1058.78i	−0.708023	−	0.148765i
$371$	1216.64	+	998.468i	0.170255	+	0.139725i
$372$	3917.31	−	11980.0i	0.545976	−	1.66972i
$373$	−8155.78	+	2474.03i	−1.13215	+	0.343432i	−0.800121	−	0.599839i	$-0.795231\pi$
$373$	−8155.78	+	2474.03i	−1.13215	+	0.343432i	−0.332024	+	0.943271i	$0.607731\pi$
$374$	−352.845	+	3226.48i	−0.0487839	+	0.446089i
$375$	8268.84	−	12375.2i	1.13867	−	1.70414i
$376$	−3451.67	+	7627.53i	−0.473420	+	1.04617i
$377$	−3981.51	+	2660.36i	−0.543921	+	0.363436i
$378$	36442.9	+	11484.1i	4.95878	+	1.56264i
$379$	5577.36	+	6796.03i	0.755909	+	0.921078i	0.998800	−	0.0489757i	$-0.0155957\pi$
$379$	5577.36	+	6796.03i	0.755909	+	0.921078i	−0.242891	+	0.970054i	$0.578096\pi$
$380$	3996.48	+	4172.16i	0.539514	+	0.563230i
$381$	−23277.4	+	12442.0i	−3.13002	+	1.67303i
$382$	5210.67	+	5323.94i	0.697909	+	0.713079i
$383$	−6459.16			−0.861743			−0.430871	−	0.902413i	$-0.641794\pi$
$383$	−6459.16			−0.861743			−0.430871	+	0.902413i	$0.641794\pi$
$384$	13578.5	+	5263.24i	1.80450	+	0.699450i
$385$	−3086.98			−0.408642
$386$	−3214.86	−	3284.75i	−0.423918	−	0.433132i
$387$	20478.2	−	10945.8i	2.68984	−	1.43775i
$388$	−7006.55	+	6711.52i	−0.916762	+	0.878160i
$389$	184.136	+	224.370i	0.0240002	+	0.0292443i	0.784872	−	0.619658i	$-0.212729\pi$
$389$	184.136	+	224.370i	0.0240002	+	0.0292443i	−0.760872	+	0.648902i	$0.775229\pi$
$390$	7498.88	+	2363.09i	0.973642	+	0.306820i
$391$	−4579.82	+	3060.14i	−0.592357	+	0.395800i
$392$	−9942.04	+	3747.26i	−1.28099	+	0.482819i
$393$	2495.64	−	3735.00i	0.320327	−	0.479404i
$394$	161.419	−	1476.04i	0.0206400	−	0.188736i
$395$	4467.79	−	1355.29i	0.569111	−	0.172638i
$396$	−7756.33	−	2536.21i	−0.984269	−	0.321842i
$397$	8692.55	+	7133.79i	1.09891	+	0.901851i	0.995684	−	0.0928076i	$-0.0295841\pi$
$397$	8692.55	+	7133.79i	1.09891	+	0.901851i	0.103224	+	0.994658i	$0.467084\pi$
$398$	441.169	+	92.6956i	0.0555623	+	0.0116744i
$399$	−24303.1	−	10066.7i	−3.04931	−	1.26307i
$400$	−956.922	+	3921.27i	−0.119615	+	0.490159i
$401$	5157.21	−	2136.19i	0.642241	−	0.266025i	−0.0377030	−	0.999289i	$-0.512004\pi$
$401$	5157.21	−	2136.19i	0.642241	−	0.266025i	0.679944	+	0.733264i	$0.262004\pi$
$402$	11301.0	−	2121.87i	1.40210	−	0.263256i
$403$	539.404	+	5476.67i	0.0666741	+	0.676953i
$404$	−7002.06	−	842.014i	−0.862290	−	0.103692i
$405$	10255.1	−	19185.9i	1.25822	−	2.35396i
$406$	−9637.29	−	5285.23i	−1.17806	−	0.646063i
$407$	−3122.13	+	621.031i	−0.380242	+	0.0756348i
$408$	18933.9	−	1249.94i	2.29747	−	0.151670i
$409$	−372.889	+	1874.64i	−0.0450811	+	0.226638i	−0.996757	−	0.0804647i	$-0.974360\pi$
$409$	−372.889	+	1874.64i	−0.0450811	+	0.226638i	0.951676	+	0.307103i	$0.0993596\pi$
$410$	−360.084	−	4108.36i	−0.0433738	−	0.494871i
$411$	2093.54	−	21256.1i	0.251257	−	2.55106i
$412$	3562.84	+	788.690i	0.426040	+	0.0943106i
$413$	6218.22	−	20498.7i	0.740868	−	2.44231i
$414$	−5161.77	−	12850.7i	−0.612771	−	1.52555i
$415$	6514.12	+	6514.12i	0.770519	+	0.770519i
$416$	−6352.07	+	282.329i	−0.748644	+	0.0332748i
$417$	−5490.96	+	5490.96i	−0.644829	+	0.644829i
$418$	3284.99	+	1402.25i	0.384387	+	0.164082i
$419$	11949.2	+	3624.76i	1.39322	+	0.422628i	0.895635	−	0.444789i	$-0.146721\pi$
$419$	11949.2	+	3624.76i	1.39322	+	0.422628i	0.497582	+	0.867417i	$0.334221\pi$
$420$	3139.42	+	17771.9i	0.364733	+	2.06472i
$421$	1336.38	+	131.622i	0.154706	+	0.0152372i	0.175073	−	0.984555i	$-0.443984\pi$
$421$	1336.38	+	131.622i	0.154706	+	0.0152372i	−0.0203678	+	0.999793i	$0.506484\pi$
$422$	1065.12	−	1269.76i	0.122865	−	0.146472i
$423$	−26900.0	−	5350.74i	−3.09201	−	0.615040i
$424$	−624.166	+	1082.26i	−0.0714910	+	0.123961i
$425$	1026.03	+	5158.20i	0.117105	+	0.588728i
$426$	1607.03	−	468.681i	0.182772	−	0.0533044i
$427$	13006.1	+	6951.88i	1.47402	+	0.787881i
$428$	−5178.06	−	2912.57i	−0.584792	−	0.328936i
$429$	4837.33	−	476.435i	0.544402	−	0.0536189i
$430$	5755.47	+	3935.84i	0.645473	+	0.441402i
$431$	2089.12	+	5043.58i	0.233479	+	0.563668i	0.996582	−	0.0826090i	$-0.0263252\pi$
$431$	2089.12	+	5043.58i	0.233479	+	0.563668i	−0.763103	+	0.646277i	$0.776325\pi$
$432$	−4267.88	+	30028.8i	−0.475320	+	3.34435i
$433$	6618.73	−	15979.0i	0.734586	−	1.77345i	0.107920	−	0.994160i	$-0.465581\pi$
$433$	6618.73	−	15979.0i	0.734586	−	1.77345i	0.626666	−	0.779288i	$-0.284419\pi$
$434$	−10577.8	+	6904.51i	−1.16993	+	0.763657i
$435$	−6844.34	+	8339.86i	−0.754393	+	0.919231i
$436$	8474.16	−	651.006i	0.930823	−	0.0715081i
$437$	1759.53	+	5800.40i	0.192608	+	0.634945i
$438$	4667.25	−	3747.07i	0.509155	−	0.408771i
$439$	−13554.0	−	9056.51i	−1.47357	−	0.984610i	−0.994263	−	0.106964i	$-0.965887\pi$
$439$	−13554.0	−	9056.51i	−1.47357	−	0.984610i	−0.479310	−	0.877646i	$-0.659113\pi$
$440$	−400.302	−	2417.51i	−0.0433719	−	0.261933i
$441$	−19337.4	−	28940.5i	−2.08805	−	3.12499i
$442$	−7348.08	+	3826.63i	−0.790752	+	0.411797i
$443$	−3536.85	+	2902.62i	−0.379325	+	0.311304i	−0.804664	−	0.593730i	$-0.797655\pi$
$443$	−3536.85	+	2902.62i	−0.379325	+	0.311304i	0.425339	+	0.905034i	$0.360155\pi$
$444$	6750.49	+	17342.7i	0.721540	+	1.85372i
$445$	428.769	+	802.170i	0.0456755	+	0.0854528i
$446$	−77.2620	+	7185.91i	−0.00820282	+	0.762920i
$447$			25435.9i			2.69145i
$448$	−7309.25	−	12632.5i	−0.770826	−	1.33221i
$449$			5933.34i			0.623634i	0.950142	+	0.311817i	$0.100938\pi$
$449$			5933.34i			0.623634i	−0.950142	+	0.311817i	$0.899062\pi$
$450$	−13222.2	−	142.163i	−1.38511	−	0.0148925i
$451$	−1201.88	−	2248.57i	−0.125487	−	0.234769i
$452$	−4611.76	+	10489.9i	−0.479909	+	1.09160i
$453$	−18985.4	+	15580.9i	−1.96912	+	1.61602i
$454$	3641.84	+	6993.24i	0.376476	+	0.722927i
$455$	−4377.66	−	6551.63i	−0.451050	−	0.675045i
$456$	4732.05	−	20337.9i	0.485962	−	2.08862i
$457$	5651.96	+	3776.52i	0.578529	+	0.386560i	0.810130	−	0.586250i	$-0.199396\pi$
$457$	5651.96	+	3776.52i	0.578529	+	0.386560i	−0.231601	+	0.972811i	$0.574396\pi$
$458$	−3445.30	−	4291.37i	−0.351502	−	0.437822i
$459$	11472.0	+	37818.2i	1.16660	+	3.84576i
$460$	2706.62	−	3157.08i	0.274340	−	0.319999i
$461$	10634.8	−	12958.5i	1.07443	−	1.30920i	0.126061	−	0.992022i	$-0.459767\pi$
$461$	10634.8	−	12958.5i	1.07443	−	1.30920i	0.948368	−	0.317173i	$-0.102733\pi$
$462$	6098.49	+	9342.95i	0.614129	+	0.940851i
$463$	−595.051	+	1436.58i	−0.0597287	+	0.144198i	−0.950926	−	0.309417i	$-0.899866\pi$
$463$	−595.051	+	1436.58i	−0.0597287	+	0.144198i	0.891198	+	0.453615i	$0.149866\pi$
$464$	2889.33	−	8232.63i	0.289081	−	0.823686i
$465$	4744.87	+	11455.1i	0.473200	+	1.14241i
$466$	3170.27	−	4635.96i	0.315150	−	0.460851i
$467$	−4369.80	+	430.388i	−0.432998	+	0.0426466i	−0.312169	−	0.950027i	$-0.601055\pi$
$467$	−4369.80	+	430.388i	−0.432998	+	0.0426466i	−0.120829	+	0.992673i	$0.538555\pi$
$468$	−5616.58	−	20058.2i	−0.554757	−	1.98118i
$469$	−10162.9	−	5432.19i	−1.00060	−	0.534830i
$470$	−2305.86	−	7906.43i	−0.226301	−	0.775949i
$471$	−417.013	−	2096.47i	−0.0407961	−	0.205096i
$472$	16859.6	+	2211.53i	1.64412	+	0.215665i
$473$	4227.77	+	840.956i	0.410979	+	0.0817488i
$474$	−12928.2	−	10844.6i	−1.25277	−	1.05086i
$475$	5759.69	+	567.280i	0.556363	+	0.0547970i
$476$	−15580.9	−	10902.6i	−1.50031	−	1.04983i
$477$	−3916.60	−	1188.09i	−0.375951	−	0.114044i
$478$	1689.86	−	3958.76i	0.161700	−	0.378807i
$479$	−3557.55	+	3557.55i	−0.339350	+	0.339350i	−0.856123	−	0.516773i	$-0.827133\pi$
$479$	−3557.55	+	3557.55i	−0.339350	+	0.339350i	0.516773	+	0.856123i	$0.327133\pi$
$480$	−13510.7	+	4763.14i	−1.28474	+	0.452931i
$481$	−5745.56	−	5745.56i	−0.544646	−	0.544646i
$482$	−3407.44	+	1368.68i	−0.322001	+	0.129339i
$483$	−5496.28	+	18118.8i	−0.517784	+	1.70690i
$484$	4909.62	+	7701.22i	0.461084	+	0.723255i
$485$	935.510	−	9498.39i	0.0875862	−	0.889278i
$486$	−42273.2	+	3705.10i	−3.94558	+	0.345817i
$487$	−477.355	+	2399.82i	−0.0444169	+	0.223299i	−0.996618	−	0.0821728i	$-0.973814\pi$
$487$	−477.355	+	2399.82i	−0.0444169	+	0.223299i	0.952201	+	0.305471i	$0.0988140\pi$
$488$	−3757.69	+	11086.9i	−0.348571	+	1.02845i
$489$	13060.6	−	2597.92i	1.20782	−	0.240250i
$490$	5025.73	−	9164.10i	0.463345	−	0.844881i
$491$	1810.88	−	3387.92i	0.166444	−	0.311394i	−0.784847	−	0.619690i	$-0.787259\pi$
$491$	1810.88	−	3387.92i	0.166444	−	0.311394i	0.951291	+	0.308295i	$0.0997585\pi$
$492$	−11722.8	+	9206.09i	−1.07420	+	0.843582i
$493$	−1114.30	−	11313.6i	−0.101796	−	1.03355i
$494$	1682.40	+	8960.41i	0.153228	+	0.816089i
$495$	7416.48	−	3072.01i	0.673426	−	0.278942i
$496$	−6778.82	−	7388.47i	−0.613665	−	0.668855i
$497$	−1549.94	−	642.005i	−0.139888	−	0.0579434i
$498$	6846.42	−	32584.4i	0.616055	−	2.93201i
$499$	7730.86	+	6344.55i	0.693548	+	0.569181i	0.913752	−	0.406274i	$-0.133172\pi$
$499$	7730.86	+	6344.55i	0.693548	+	0.569181i	−0.220203	+	0.975454i	$0.570672\pi$
$500$	−5355.67	−	10559.8i	−0.479025	−	0.944498i
$501$	21204.5	−	6432.32i	1.89091	−	0.573602i
$502$	16744.8	+	1831.19i	1.48876	+	0.162809i
$503$	4402.20	−	6588.36i	0.390228	−	0.584017i	−0.583393	−	0.812190i	$-0.698275\pi$
$503$	4402.20	−	6588.36i	0.390228	−	0.584017i	0.973621	+	0.228173i	$0.0732752\pi$
$504$	34880.8	−	32700.3i	3.08277	−	2.89005i
$505$	5768.43	−	3854.34i	0.508301	−	0.339636i
$506$	772.692	−	2452.01i	0.0678861	−	0.215425i
$507$	−6144.92	−	7487.61i	−0.538275	−	0.655890i
$508$	−451.466	+	20992.3i	−0.0394302	+	1.83343i
$509$	16257.7	−	8689.93i	1.41574	−	0.756728i	0.426701	−	0.904393i	$-0.359676\pi$
$509$	16257.7	−	8689.93i	1.41574	−	0.756728i	0.989037	+	0.147665i	$0.0471757\pi$
$510$	−13340.0	+	13056.2i	−1.15825	+	1.13361i
$511$	−5998.37			−0.519280
$512$	8945.13	−	7362.23i	0.772114	−	0.635484i
$513$	43489.8			3.74293
$514$	6523.35	−	6384.56i	0.559791	−	0.547881i
$515$	−3165.79	+	1692.15i	−0.270877	+	0.144787i
$516$	541.845	−	25194.8i	0.0462275	−	2.14949i
$517$	−3230.07	−	3935.85i	−0.274774	−	0.334813i
$518$	5605.63	−	17788.5i	0.475478	−	1.50885i
$519$	21931.4	−	14654.1i	1.85487	−	1.23939i
$520$	4563.13	−	4277.87i	0.384820	−	0.360763i
$521$	−6840.53	+	10237.6i	−0.575219	+	0.860876i	−0.998992	−	0.0448923i	$-0.985706\pi$
$521$	−6840.53	+	10237.6i	−0.575219	+	0.860876i	0.423773	+	0.905769i	$0.360706\pi$
$522$	28413.2	+	3107.24i	2.38240	+	0.260537i
$523$	−15261.6	+	4629.54i	−1.27599	+	0.387067i	−0.854350	−	0.519698i	$-0.826044\pi$
$523$	−15261.6	+	4629.54i	−1.27599	+	0.387067i	−0.421637	+	0.906765i	$0.638544\pi$
$524$	−1616.41	−	3187.09i	−0.134758	−	0.265703i
$525$	13975.0	+	11469.0i	1.16175	+	0.953425i
$526$	2243.86	−	10679.3i	0.186002	−	0.885243i
$527$	−12070.5	−	4999.76i	−0.997720	−	0.413269i
$528$	−6525.95	+	5987.47i	−0.537889	+	0.493506i
$529$	−7210.08	+	2986.51i	−0.592593	+	0.245460i
$530$	−226.793	−	1207.90i	−0.0185873	−	0.0989955i
$531$	5460.00	+	55436.3i	0.446222	+	4.53057i
$532$	−16458.4	+	12924.9i	−1.34128	+	1.05332i
$533$	3067.84	−	5739.52i	0.249311	−	0.466428i
$534$	1580.77	−	2882.43i	0.128102	−	0.233586i
$535$	5731.93	−	1140.15i	0.463202	−	0.0921366i
$536$	2936.26	−	8663.33i	0.236618	−	0.698132i
$537$	−413.241	+	2077.50i	−0.0332079	+	0.166948i
$538$	−18420.2	+	1614.47i	−1.47612	+	0.129377i
$539$	633.340	−	6430.41i	0.0506120	−	0.513872i
$540$	−16039.1	−	25158.9i	−1.27817	−	2.00493i
$541$	1209.12	−	3985.92i	0.0960887	−	0.316762i	−0.895698	−	0.444662i	$-0.853324\pi$
$541$	1209.12	−	3985.92i	0.0960887	−	0.316762i	0.991787	+	0.127900i	$0.0408237\pi$
$542$	5780.24	−	2321.76i	0.458086	−	0.184001i
$543$	−15968.0	−	15968.0i	−1.26198	−	1.26198i
$544$	6517.72	−	13615.7i	0.513685	−	1.07310i
$545$	−5911.91	+	5911.91i	−0.464657	+	0.464657i
$546$	−11180.6	+	26192.4i	−0.876351	+	2.05299i
$547$	−10547.1	−	3199.44i	−0.824430	−	0.250088i	−0.150243	−	0.988649i	$-0.548006\pi$
$547$	−10547.1	−	3199.44i	−0.824430	−	0.250088i	−0.674187	+	0.738561i	$0.735506\pi$
$548$	−13921.8	−	9741.65i	−1.08524	−	0.759385i
$549$	−38165.3	−	3758.95i	−2.96695	−	0.292219i
$550$	−1880.67	−	1577.57i	−0.145804	−	0.122305i
$551$	−12270.0	−	2440.65i	−0.948671	−	0.188702i
$552$	−14902.2	−	1954.77i	−1.14906	−	0.150726i
$553$	3299.22	+	16586.3i	0.253702	+	1.27544i
$554$	1952.34	+	6694.26i	0.149724	+	0.513379i
$555$	−16145.4	−	8629.90i	−1.23484	−	0.660034i
$556$	1665.74	+	5948.80i	0.127056	+	0.453750i
$557$	−8834.36	+	870.109i	−0.672036	+	0.0661897i	−0.428279	−	0.903647i	$-0.640880\pi$
$557$	−8834.36	+	870.109i	−0.672036	+	0.0661897i	−0.243757	+	0.969836i	$0.578380\pi$
$558$	18542.1	−	27114.6i	1.40672	−	2.05708i
$559$	4210.62	+	10165.3i	0.318588	+	0.769138i
$560$	13546.9	+	4754.43i	1.02225	+	0.358771i
$561$	−4416.09	+	10661.4i	−0.332349	+	0.802361i
$562$	614.873	+	941.992i	0.0461510	+	0.0707038i
$563$	7599.31	−	9259.79i	0.568868	−	0.693168i	−0.406525	−	0.913640i	$-0.633260\pi$
$563$	7599.31	−	9259.79i	0.568868	−	0.693168i	0.975393	+	0.220472i	$0.0707596\pi$
$564$	−19374.0	+	22598.4i	−1.44644	+	1.68717i
$565$	−3272.17	−	10786.9i	−0.243648	−	0.803201i
$566$	−6884.30	−	8574.91i	−0.511252	−	0.636802i
$567$	65518.8	+	43778.2i	4.85279	+	3.24253i
$568$	301.788	−	1297.06i	0.0222936	−	0.0958157i
$569$	12955.1	+	19388.7i	0.954495	+	1.42850i	0.902908	+	0.429834i	$0.141428\pi$
$569$	12955.1	+	19388.7i	0.954495	+	1.42850i	0.0515869	+	0.998669i	$0.483572\pi$
$570$	9487.67	+	18218.7i	0.697184	+	1.33877i
$571$	8191.72	−	6722.77i	0.600372	−	0.492713i	−0.284419	−	0.958700i	$-0.591801\pi$
$571$	8191.72	−	6722.77i	0.600372	−	0.492713i	0.884791	+	0.465987i	$0.154301\pi$
$572$	1556.26	−	3539.87i	0.113759	−	0.258758i
$573$	12485.4	+	23358.6i	0.910272	+	1.70300i
$574$	14937.3	+	160.604i	1.08619	+	0.0116785i
$575$		−	4165.76i		−	0.302129i
$576$	30131.8	+	23075.9i	2.17967	+	1.66926i
$577$		−	23574.4i		−	1.70089i	−0.526060	−	0.850447i	$-0.676331\pi$
$577$		−	23574.4i		−	1.70089i	0.526060	−	0.850447i	$-0.323669\pi$
$578$	62.0638	−	5772.37i	0.00446629	−	0.415396i
$579$	−7703.21	−	14411.7i	−0.552909	−	1.03442i
$580$	3113.25	+	7998.28i	0.222881	+	0.572605i
$581$	−25794.3	+	21168.8i	−1.84187	+	1.51159i
$582$	−30595.7	+	15933.2i	−2.17909	+	1.13480i
$583$	−422.122	−	631.750i	−0.0299872	−	0.0448790i
$584$	−777.835	−	4697.52i	−0.0551148	−	0.332851i
$585$	17037.2	+	11383.9i	1.20411	+	0.804558i
$586$	4198.16	−	3370.46i	0.295946	−	0.237598i
$587$	−7706.03	−	25403.4i	−0.541843	−	1.78622i	−0.614566	−	0.788866i	$-0.710669\pi$
$587$	−7706.03	−	25403.4i	−0.541843	−	1.78622i	0.0727223	−	0.997352i	$-0.476831\pi$
$588$	−37664.3	+	2893.47i	−2.64158	+	0.202933i
$589$	−9120.93	+	11113.9i	−0.638067	+	0.777487i
$590$	−14007.1	+	9142.98i	−0.977397	+	0.637984i
$591$	2020.26	−	4877.35i	0.140613	−	0.339471i
$592$	14657.7	+	2083.24i	1.01761	+	0.144629i
$593$	3870.96	+	9345.32i	0.268063	+	0.647161i	0.999392	−	0.0348636i	$-0.0110997\pi$
$593$	3870.96	+	9345.32i	0.268063	+	0.647161i	−0.731329	+	0.682025i	$0.761100\pi$
$594$	−15226.0	−	10412.2i	−1.05173	−	0.719220i
$595$	18616.7	−	1833.59i	1.28271	−	0.126336i
$596$	17636.5	+	9920.24i	1.21211	+	0.681793i
$597$	1413.53	+	755.545i	0.0969041	+	0.0517963i
$598$	6299.76	−	1837.28i	0.430797	−	0.125639i
$599$	−717.166	−	3605.44i	−0.0489192	−	0.245934i	0.948587	−	0.316518i	$-0.102514\pi$
$599$	−717.166	−	3605.44i	−0.0489192	−	0.245934i	−0.997506	+	0.0705842i	$0.977514\pi$
$600$	−7169.55	+	12431.5i	−0.487826	+	0.845858i
$601$	−23262.8	−	4627.25i	−1.57888	−	0.314059i	−0.673674	−	0.739029i	$-0.735285\pi$
$601$	−23262.8	−	4627.25i	−1.57888	−	0.314059i	−0.905208	+	0.424970i	$0.860285\pi$
$602$	−16231.0	+	19349.5i	−1.09888	+	1.31001i
$603$	29822.3	+	2937.24i	2.01403	+	0.198364i
$604$	3398.87	+	19240.6i	0.228970	+	1.29618i
$605$	−8597.46	−	2608.01i	−0.577746	−	0.175257i
$606$	−23061.3	−	9844.08i	−1.54587	−	0.659882i
$607$	−5501.96	+	5501.96i	−0.367904	+	0.367904i	−0.866712	−	0.498809i	$-0.833771\pi$
$607$	−5501.96	+	5501.96i	−0.367904	+	0.367904i	0.498809	+	0.866712i	$0.333771\pi$
$608$	−12256.2	−	11213.0i	−0.817522	−	0.747942i
$609$	−27632.9	−	27632.9i	−1.83865	−	1.83865i
$610$	−4292.25	−	10685.9i	−0.284899	−	0.709281i
$611$	3772.65	−	12436.8i	0.249795	−	0.823465i
$612$	48282.8	+	10688.2i	3.18908	+	0.705953i
$613$	−1700.13	+	17261.7i	−0.112019	+	1.13735i	0.760693	+	0.649112i	$0.224859\pi$
$613$	−1700.13	+	17261.7i	−0.112019	+	1.13735i	−0.872712	+	0.488235i	$0.837641\pi$
$614$	−1681.23	−	19181.8i	−0.110503	−	1.26078i
$615$	2860.58	−	14381.1i	0.187560	−	0.942929i
$616$	8856.59	−	584.677i	0.579289	−	0.0382424i
$617$	−1810.05	+	360.041i	−0.118103	+	0.0234922i	−0.253788	−	0.967260i	$-0.581677\pi$
$617$	−1810.05	+	360.041i	−0.118103	+	0.0234922i	0.135685	+	0.990752i	$0.456677\pi$
$618$	11375.6	+	6238.54i	0.740443	+	0.406070i
$619$	−10729.5	+	20073.5i	−0.696698	+	1.30343i	0.245833	+	0.969312i	$0.420939\pi$
$619$	−10729.5	+	20073.5i	−0.696698	+	1.30343i	−0.942531	+	0.334119i	$0.891561\pi$
$620$	9793.18	+	1177.65i	0.634361	+	0.0762834i
$621$	−3068.23	−	31152.3i	−0.198267	−	2.01304i
$622$	14343.4	−	2693.10i	0.924628	−	0.173607i
$623$	−3043.83	+	1260.79i	−0.195744	+	0.0810797i
$624$	−21961.9	−	5359.45i	−1.40894	−	0.343830i
$625$	3477.45	+	1440.41i	0.222557	+	0.0921861i
$626$	16437.7	+	3453.78i	1.04949	+	0.220513i
$627$	9816.47	+	8056.17i	0.625250	+	0.513130i
$628$	−1616.27	−	528.496i	−0.102701	−	0.0335817i
$629$	18459.9	−	5599.74i	1.17018	−	0.354970i
$630$	−5113.02	+	46754.4i	−0.323345	+	2.95673i
$631$	3467.66	−	5189.72i	0.218772	−	0.327416i	−0.705808	−	0.708403i	$-0.749416\pi$
$631$	3467.66	−	5189.72i	0.218772	−	0.327416i	0.924580	+	0.380987i	$0.124416\pi$
$632$	−12561.4	+	4734.54i	−0.790613	+	0.297990i
$633$	4899.44	−	3273.70i	0.307638	−	0.205557i
$634$	7340.01	+	2313.03i	0.459793	+	0.144893i
$635$	−13103.5	−	15966.7i	−0.818893	−	0.997824i
$636$	−3207.73	+	3072.66i	−0.199992	+	0.191571i
$637$	14545.7	−	7774.83i	0.904742	−	0.483595i
$638$	3711.44	+	3792.11i	0.230309	+	0.235315i
$639$	4362.62			0.270082
$640$	−1966.66	+	11225.6i	−0.121468	+	0.693327i
$641$	−11062.6			−0.681662			−0.340831	−	0.940124i	$-0.610708\pi$
$641$	−11062.6			−0.681662			−0.340831	+	0.940124i	$0.610708\pi$
$642$	−14774.5	−	15095.6i	−0.908259	−	0.928002i
$643$	19311.1	−	10322.0i	1.18438	−	0.633064i	0.242873	−	0.970058i	$-0.421910\pi$
$643$	19311.1	−	10322.0i	1.18438	−	0.633064i	0.941507	+	0.336994i	$0.109410\pi$
$644$	10419.4	+	10877.5i	0.637552	+	0.665578i
$645$	15726.7	+	19163.0i	0.960059	+	1.16984i
$646$	−20643.8	−	6505.40i	−1.25730	−	0.396210i
$647$	−7012.39	+	4685.53i	−0.426098	+	0.284710i	−0.750072	−	0.661356i	$-0.769981\pi$
$647$	−7012.39	+	4685.53i	−0.426098	+	0.284710i	0.323974	+	0.946066i	$0.394981\pi$
$648$	−25788.1	+	56986.8i	−1.56335	+	3.45471i
$649$	−5745.19	+	8598.29i	−0.347486	+	0.520050i
$650$	681.154	−	6228.60i	0.0411032	−	0.375855i
$651$	−42977.1	+	13037.0i	−2.58741	+	0.784883i
$652$	3292.45	−	10069.1i	0.197764	−	0.604808i
$653$	340.125	+	279.133i	0.0203830	+	0.0167279i	0.644530	−	0.764579i	$-0.277053\pi$
$653$	340.125	+	279.133i	0.0203830	+	0.0167279i	−0.624147	+	0.781307i	$0.714553\pi$
$654$	29572.1	+	6213.49i	1.76813	+	0.371509i
$655$	3247.76	+	1345.27i	0.193741	+	0.0802503i
$656$	1811.21	+	11718.7i	0.107799	+	0.697469i
$657$	14411.1	−	5969.28i	0.855755	−	0.354465i
$658$	29319.1	−	5504.93i	1.73705	−	0.326146i
$659$	−3183.68	−	32324.5i	−0.188192	−	1.91075i	−0.372759	−	0.927928i	$-0.621588\pi$
$659$	−3183.68	−	32324.5i	−0.188192	−	1.91075i	0.184567	−	0.982820i	$-0.440912\pi$
$660$	1040.18	−	8649.94i	0.0613466	−	0.510149i
$661$	223.137	−	417.460i	0.0131301	−	0.0245648i	−0.875271	−	0.483633i	$-0.839317\pi$
$661$	223.137	−	417.460i	0.0131301	−	0.0245648i	0.888401	+	0.459069i	$0.151817\pi$
$662$	14608.8	+	8011.68i	0.857684	+	0.470367i
$663$	−28889.6	+	5746.51i	−1.69228	+	0.336615i
$664$	−19922.9	−	17455.3i	−1.16439	−	1.02018i
$665$	4016.12	−	20190.4i	0.234193	−	1.17737i
$666$	4234.69	+	48315.5i	0.246383	+	2.81109i
$667$	−882.613	+	8961.32i	−0.0512367	+	0.520215i
$668$	3809.98	−	17211.2i	0.220677	−	0.996890i
$669$	−7416.84	+	24450.0i	−0.428627	+	1.41299i
$670$	3353.96	+	8349.99i	0.193395	+	0.481475i
$671$	−5034.13	−	5034.13i	−0.289628	−	0.289628i
$672$	−12373.1	−	50393.3i	−0.710269	−	2.89280i
$673$	−8130.54	+	8130.54i	−0.465690	+	0.465690i	−0.900515	−	0.434825i	$-0.856810\pi$
$673$	−8130.54	+	8130.54i	−0.465690	+	0.465690i	0.434825	+	0.900515i	$0.356810\pi$
$674$	22848.7	+	9753.34i	1.30578	+	0.557396i
$675$	−28601.8	−	8676.26i	−1.63094	−	0.494740i
$676$	−7588.26	+	1340.47i	−0.431740	+	0.0762671i
$677$	−17252.1	−	1699.18i	−0.979395	−	0.0964620i	−0.404368	−	0.914596i	$-0.632509\pi$
$677$	−17252.1	−	1699.18i	−0.979395	−	0.0964620i	−0.575027	+	0.818134i	$0.695009\pi$
$678$	−26182.9	+	31213.6i	−1.48311	+	1.76807i
$679$	33906.9	+	6744.51i	1.91639	+	0.381193i
$680$	3850.06	+	14341.6i	0.217122	+	0.808788i
$681$	5469.01	+	27494.6i	0.307743	+	1.54713i
$682$	5854.12	−	1707.32i	0.328689	−	0.0958601i
$683$	8688.26	+	4643.97i	0.486745	+	0.260171i	0.696465	−	0.717591i	$-0.254755\pi$
$683$	8688.26	+	4643.97i	0.486745	+	0.260171i	−0.209720	+	0.977762i	$0.567255\pi$
$684$	26679.0	−	47430.8i	1.49137	−	2.65140i
$685$	16634.4	−	1638.35i	0.927838	−	0.0913840i
$686$	8422.39	+	5759.59i	0.468758	+	0.320557i
$687$	−7487.69	−	18076.9i	−0.415827	−	1.00390i
$688$	−17258.0	−	10201.9i	−0.956329	−	0.565325i
$689$	742.178	−	1791.78i	0.0410374	−	0.0990730i
$690$	12380.9	−	8081.48i	0.683091	−	0.445879i
$691$	1418.57	−	1728.53i	0.0780967	−	0.0951611i	−0.732496	−	0.680771i	$-0.761645\pi$
$691$	1418.57	−	1728.53i	0.0780967	−	0.0951611i	0.810593	+	0.585610i	$0.199145\pi$
$692$	−1607.26	−	20921.8i	−0.0882932	−	1.14932i
$693$	8440.63	+	27825.0i	0.462674	+	1.52523i
$694$	−5592.30	+	4489.74i	−0.305880	+	0.245574i
$695$	−5052.83	−	3376.20i	−0.275777	−	0.184268i
$696$	18056.9	−	25223.5i	0.983400	−	1.37370i
$697$	8583.84	+	12846.6i	0.466479	+	0.698136i
$698$	−16787.4	+	8742.31i	−0.910332	+	0.474070i
$699$	15435.6	−	12667.6i	0.835232	−	0.685457i
$700$	13402.6	−	5216.84i	0.723675	−	0.281683i
$701$	2219.22	+	4151.88i	0.119571	+	0.223701i	0.934585	−	0.355740i	$-0.115771\pi$
$701$	2219.22	+	4151.88i	0.119571	+	0.223701i	−0.815015	+	0.579441i	$0.803271\pi$
$702$	506.202	−	47080.3i	0.0272156	−	2.53124i
$703$		−	21228.3i		−	1.13889i
$704$	1606.35	+	6860.06i	0.0859966	+	0.367256i
$705$		−	29281.6i		−	1.56427i
$706$	13638.8	+	146.642i	0.727057	+	0.00781722i
$707$	11845.8	+	22162.0i	0.630139	+	1.17891i
$708$	55343.6	+	24331.1i	2.93777	+	1.29155i
$709$	−23338.7	+	19153.6i	−1.23625	+	1.01457i	−0.237183	+	0.971465i	$0.576224\pi$
$709$	−23338.7	+	19153.6i	−1.23625	+	1.01457i	−0.999071	+	0.0431017i	$0.986276\pi$
$710$	605.079	+	1161.90i	0.0319834	+	0.0614160i
$711$	−24432.2	−	36565.4i	−1.28872	−	1.92871i
$712$	−1382.08	−	2220.23i	−0.0727464	−	0.116863i
$713$	8604.50	+	5749.34i	0.451951	+	0.301984i
$714$	−42327.8	−	52722.5i	−2.21860	−	2.76343i
$715$	1104.21	+	3640.09i	0.0577553	+	0.190394i
$716$	1279.31	+	1096.77i	0.0667738	+	0.0572463i
$717$	9708.55	−	11829.9i	0.505680	−	0.616173i
$718$	−7848.79	−	12024.4i	−0.407959	−	0.624997i
$719$	−11408.3	+	27542.0i	−0.591733	+	1.42857i	0.290095	+	0.956998i	$0.406313\pi$
$719$	−11408.3	+	27542.0i	−0.591733	+	1.42857i	−0.881828	+	0.471572i	$0.843687\pi$
$720$	−37277.9	+	2058.67i	−1.92954	+	0.106559i
$721$	−4975.77	−	12012.6i	−0.257014	−	0.620487i
$722$	−2494.19	+	3647.32i	−0.128565	+	0.188004i
$723$	−12992.7	+	1279.67i	−0.668332	+	0.0658250i
$724$	−17299.4	+	4844.07i	−0.888021	+	0.248658i
$725$	7582.63	+	4053.00i	0.388430	+	0.207620i
$726$	9091.42	+	31173.0i	0.464758	+	1.59358i
$727$	2009.33	+	10101.6i	0.102506	+	0.515332i	0.997587	+	0.0694283i	$0.0221175\pi$
$727$	2009.33	+	10101.6i	0.102506	+	0.515332i	−0.895081	+	0.445903i	$0.852882\pi$
$728$	13800.5	+	17967.6i	0.702581	+	0.914730i
$729$	−74771.7	−	14873.0i	−3.79879	−	0.755627i
$730$	3588.57	+	3010.21i	0.181944	+	0.152620i
$731$	−25996.1	−	2560.39i	−1.31532	−	0.129548i
$732$	−23862.1	+	34101.4i	−1.20488	+	1.72189i
$733$	−5885.56	−	1785.37i	−0.296573	−	0.0899645i	0.138492	−	0.990364i	$-0.455775\pi$
$733$	−5885.56	−	1785.37i	−0.296573	−	0.0899645i	−0.435065	+	0.900399i	$0.643275\pi$
$734$	13426.3	−	31453.2i	0.675170	−	1.58169i
$735$	26276.1	−	26276.1i	1.31865	−	1.31865i
$736$	−7167.36	+	9570.34i	−0.358957	+	0.479303i
$737$	3933.66	+	3933.66i	0.196606	+	0.196606i
$738$	−36046.8	+	14479.0i	−1.79797	+	0.722195i
$739$	1382.86	−	4558.69i	0.0688355	−	0.226920i	−0.915773	−	0.401697i	$-0.868420\pi$
$739$	1382.86	−	4558.69i	0.0688355	−	0.226920i	0.984608	+	0.174777i	$0.0559205\pi$
$740$	−12280.6	+	7829.00i	−0.610058	+	0.388919i
$741$	−3177.18	+	32258.4i	−0.157512	+	1.59925i
$742$	4434.64	−	388.682i	0.219408	−	0.0192304i
$743$	−7497.17	+	37690.8i	−0.370181	+	1.86103i	0.124887	+	0.992171i	$0.460143\pi$
$743$	−7497.17	+	37690.8i	−0.370181	+	1.86103i	−0.495068	+	0.868854i	$0.664857\pi$
$744$	−15782.7	−	31966.2i	−0.777718	−	1.57519i
$745$	−19523.0	+	3883.36i	−0.960090	+	0.190974i
$746$	−11591.4	+	21136.2i	−0.568890	+	1.03733i
$747$	40904.8	−	76527.4i	2.00352	−	3.74832i
$748$	5669.98	+	7220.03i	0.277159	+	0.352928i
$749$	2074.90	+	21066.8i	0.101222	+	1.02772i
$750$	−7768.33	−	41374.0i	−0.378213	−	2.01435i
$751$	−14644.8	+	6066.09i	−0.711582	+	0.294747i	−0.708959	−	0.705250i	$-0.750835\pi$
$751$	−14644.8	+	6066.09i	−0.711582	+	0.294747i	−0.00262287	+	0.999997i	$0.500835\pi$
$752$	8113.02	+	22246.9i	0.393420	+	1.07880i
$753$	55330.4	+	22918.6i	2.67776	+	1.10916i
$754$	−2784.96	+	13254.6i	−0.134512	+	0.640189i
$755$	−14857.5	−	12193.2i	−0.716185	−	0.587758i
$756$	96385.1	−	48884.1i	4.63689	−	2.35171i
$757$	5175.28	−	1569.90i	0.248479	−	0.0753753i	−0.163588	−	0.986529i	$-0.552307\pi$
$757$	5175.28	−	1569.90i	0.248479	−	0.0753753i	0.412067	+	0.911153i	$0.364807\pi$
$758$	24719.1	+	2703.26i	1.18448	+	0.129534i
$759$	5078.17	−	7600.03i	0.242854	−	0.363456i
$760$	16332.6	+	526.979i	0.779532	+	0.0251520i
$761$	−18367.4	+	12272.7i	−0.874924	+	0.584606i	−0.909921	−	0.414782i	$-0.863858\pi$
$761$	−18367.4	+	12272.7i	−0.874924	+	0.584606i	0.0349967	+	0.999387i	$0.488858\pi$
$762$	−22437.5	+	71201.7i	−1.06670	+	3.38499i
$763$	−19211.8	−	23409.7i	−0.911554	−	1.11073i
$764$	21065.6	+	453.041i	0.997546	+	0.0214535i
$765$	−42902.1	+	22931.7i	−2.02762	+	1.08379i
$766$	−13056.5	+	12778.7i	−0.615860	+	0.602758i
$767$	−26395.8			−1.24263
$768$	37860.2	−	16224.5i	1.77886	−	0.762304i
$769$	−1764.68			−0.0827514			−0.0413757	−	0.999144i	$-0.513174\pi$
$769$	−1764.68			−0.0827514			−0.0413757	+	0.999144i	$0.513174\pi$
$770$	−6239.98	+	6107.22i	−0.292043	+	0.285830i
$771$	28620.9	−	15298.2i	1.33691	−	0.714594i
$772$	−12997.0	−	279.516i	−0.605921	−	0.0130311i
$773$	−8646.51	−	10535.8i	−0.402320	−	0.490228i	0.531960	−	0.846770i	$-0.321456\pi$
$773$	−8646.51	−	10535.8i	−0.402320	−	0.490228i	−0.934279	+	0.356542i	$0.883956\pi$
$774$	19739.4	−	62639.6i	0.916689	−	2.90896i
$775$	8215.76	−	5489.60i	0.380798	−	0.254441i
$776$	−884.987	+	27428.2i	−0.0409396	+	1.26883i
$777$	36840.5	−	55135.8i	1.70096	−	2.54567i
$778$	816.100	+	89.2480i	0.0376075	+	0.00411272i
$779$	16270.4	−	4935.58i	0.748329	−	0.227003i
$780$	19833.2	−	10058.9i	0.910441	−	0.461752i
$781$	626.048	+	513.784i	0.0286834	+	0.0235399i
$782$	−3203.47	+	15246.4i	−0.146491	+	0.697198i
$783$	59689.5	+	24724.2i	2.72430	+	1.12844i
$784$	−12683.2	+	27243.8i	−0.577769	+	1.24106i
$785$	1545.45	−	640.145i	0.0702667	−	0.0291054i
$786$	−2344.59	−	12487.2i	−0.106398	−	0.566672i
$787$	810.733	+	8231.51i	0.0367211	+	0.372836i	0.995929	+	0.0901358i	$0.0287301\pi$
$787$	810.733	+	8231.51i	0.0367211	+	0.372836i	−0.959208	+	0.282700i	$0.908770\pi$
$788$	−2593.89	−	3303.00i	−0.117263	−	0.149320i
$789$	18289.3	−	34216.9i	0.825242	−	1.54392i
$790$	6349.85	−	11578.5i	0.285971	−	0.521451i
$791$	40045.5	−	7965.55i	1.80007	−	0.358056i
$792$	−20696.1	+	10218.3i	−0.928542	+	0.458450i
$793$	3545.23	−	17823.1i	0.158758	−	0.798129i
$794$	31684.4	−	2777.03i	1.41617	−	0.124122i
$795$	428.295	−	4348.55i	0.0191070	−	0.193996i
$796$	1075.16	−	685.427i	0.0478744	−	0.0305205i
$797$	598.558	−	1973.18i	0.0266023	−	0.0876959i	−0.942634	−	0.333828i	$-0.891660\pi$
$797$	598.558	−	1973.18i	0.0266023	−	0.0876959i	0.969236	+	0.246132i	$0.0791596\pi$
$798$	−69041.7	+	27732.2i	−3.06272	+	1.23021i
$799$	21817.5	+	21817.5i	0.966015	+	0.966015i
$800$	5823.46	+	9819.56i	0.257363	+	0.433967i
$801$	6058.13	−	6058.13i	0.267233	−	0.267233i
$802$	6198.52	−	14521.0i	0.272914	−	0.639344i
$803$	2771.03	+	840.584i	0.121778	+	0.0369409i
$804$	18645.9	−	26646.8i	0.817896	−	1.16886i
$805$	−14746.0	−	1452.35i	−0.645624	−	0.0635885i
$806$	11925.3	+	10003.3i	0.521154	+	0.437161i
$807$	−64479.0	−	12825.7i	−2.81260	−	0.559461i
$808$	−15819.7	+	12150.7i	−0.688781	+	0.529035i
$809$	1639.10	+	8240.29i	0.0712331	+	0.358113i	0.999919	−	0.0127552i	$-0.00406023\pi$
$809$	1639.10	+	8240.29i	0.0712331	+	0.358113i	−0.928686	+	0.370868i	$0.879060\pi$
$810$	−17227.5	−	59070.5i	−0.747301	−	2.56238i
$811$	−23193.7	−	12397.3i	−1.00424	−	0.536779i	−0.114589	−	0.993413i	$-0.536555\pi$
$811$	−23193.7	−	12397.3i	−1.00424	−	0.536779i	−0.889655	+	0.456634i	$0.849055\pi$
$812$	−29936.9	+	8382.74i	−1.29382	+	0.362286i
$813$	22040.3	−	2170.78i	0.950783	−	0.0936439i
$814$	−5082.41	+	7432.12i	−0.218843	+	0.320019i
$815$	3988.00	+	9627.88i	0.171403	+	0.413804i
$816$	35799.9	−	39985.1i	1.53584	−	1.71539i
$817$	−11000.6	+	26557.7i	−0.471066	+	1.13725i
$818$	2955.00	+	4527.09i	0.126307	+	0.193504i
$819$	−47084.6	+	57372.7i	−2.00887	+	2.44782i
$820$	−8855.76	−	7592.19i	−0.377142	−	0.323330i
$821$	2474.64	+	8157.80i	0.105196	+	0.346783i	0.993698	−	0.112088i	$-0.0357539\pi$
$821$	2474.64	+	8157.80i	0.105196	+	0.346783i	−0.888503	+	0.458871i	$0.848254\pi$
$822$	−37820.7	−	47108.5i	−1.60481	−	1.99890i
$823$	−23394.7	−	15631.8i	−0.990871	−	0.662079i	−0.0492617	−	0.998786i	$-0.515687\pi$
$823$	−23394.7	−	15631.8i	−0.990871	−	0.662079i	−0.941609	+	0.336707i	$0.890687\pi$
$824$	8762.21	−	5454.41i	0.370444	−	0.230599i
$825$	−4848.75	−	7256.66i	−0.204620	−	0.306236i
$826$	−27984.9	−	53737.9i	−1.17884	−	2.26365i
$827$	1779.72	−	1460.58i	0.0748330	−	0.0614138i	−0.596233	−	0.802811i	$-0.703337\pi$
$827$	1779.72	−	1460.58i	0.0748330	−	0.0614138i	0.671066	+	0.741397i	$0.265837\pi$
$828$	−35857.5	−	15764.2i	−1.50499	−	0.661649i
$829$	−11642.5	−	21781.6i	−0.487771	−	0.912555i	−0.998601	−	0.0528732i	$-0.983162\pi$
$829$	−11642.5	−	21781.6i	−0.487771	−	0.912555i	0.510831	−	0.859681i	$-0.329338\pi$
$830$	26055.0	+	280.140i	1.08962	+	0.0117154i
$831$			24792.3i			1.03494i
$832$	−12281.4	+	13137.5i	−0.511758	+	0.547430i
$833$			39156.3i			1.62867i
$834$	−236.139	+	21962.6i	−0.00980434	+	0.911873i
$835$	8174.39	+	15293.2i	0.338786	+	0.633824i
$836$	9414.42	−	3664.47i	0.389479	−	0.151601i
$837$	57395.7	−	47103.4i	2.37023	−	1.94520i
$838$	31325.2	−	16313.1i	1.29130	−	0.672466i
$839$	−14871.1	−	22256.2i	−0.611928	−	0.915815i	0.388055	−	0.921636i	$-0.373147\pi$
$839$	−14871.1	−	22256.2i	−0.611928	−	0.915815i	−0.999983	+	0.00582106i	$0.998147\pi$
$840$	41505.6	+	29713.0i	1.70486	+	1.22047i
$841$	4825.79	+	3224.49i	0.197868	+	0.132211i
$842$	2961.73	−	2377.81i	0.121221	−	0.0973214i
$843$	1160.99	+	3827.28i	0.0474338	+	0.156368i
$844$	−359.060	−	4673.89i	−0.0146438	−	0.190619i
$845$	4808.85	−	5859.60i	0.195775	−	0.238552i
$846$	−64961.1	+	42402.5i	−2.63996	+	1.72320i
$847$	12453.5	−	30065.5i	0.505205	−	1.21967i
$848$	879.449	+	3422.51i	0.0356137	+	0.138596i
$849$	−14961.7	−	36120.8i	−0.604811	−	1.46014i
$850$	12278.9	+	8396.84i	0.495485	+	0.338834i
$851$	−15206.1	+	1497.67i	−0.612524	+	0.0603284i
$852$	2321.20	−	4126.71i	0.0933370	−	0.165937i
$853$	−1075.97	−	575.117i	−0.0431893	−	0.0230851i	0.449661	−	0.893199i	$-0.351545\pi$
$853$	−1075.97	−	575.117i	−0.0431893	−	0.0230851i	−0.492850	+	0.870114i	$0.664045\pi$
$854$	40043.7	−	11678.5i	1.60453	−	0.467951i
$855$	10443.7	+	52504.2i	0.417741	+	2.10012i
$856$	−16229.0	+	4356.74i	−0.648011	+	0.173961i
$857$	−3621.54	−	720.369i	−0.144352	−	0.0287133i	0.122385	−	0.992483i	$-0.460946\pi$
$857$	−3621.54	−	720.369i	−0.144352	−	0.0287133i	−0.266737	+	0.963769i	$0.585946\pi$
$858$	8835.54	−	10533.1i	0.351562	−	0.419109i
$859$	−37363.2	−	3679.95i	−1.48407	−	0.146168i	−0.676719	−	0.736241i	$-0.736599\pi$
$859$	−37363.2	−	3679.95i	−1.48407	−	0.146168i	−0.807350	+	0.590073i	$0.799099\pi$
$860$	19420.6	−	3430.66i	0.770044	−	0.136029i
$861$	50824.2	+	15417.4i	2.01171	+	0.610246i
$862$	14201.0	+	6061.95i	0.561125	+	0.239525i
$863$	25331.6	−	25331.6i	0.999188	−	0.999188i	−0.000812091	−	1.00000i	$-0.500258\pi$
$863$	25331.6	−	25331.6i	0.999188	−	0.999188i	1.00000		0.000812091i	$0.000258497\pi$
$864$	50781.4	+	69143.3i	1.99956	+	2.72257i
$865$	14595.8	+	14595.8i	0.573727	+	0.573727i
$866$	−18233.6	−	45394.2i	−0.715477	−	1.78124i
$867$	5957.88	−	19640.5i	0.233380	−	0.769349i
$868$	−7722.02	+	34883.6i	−0.301961	+	1.36409i
$869$	800.205	−	8124.61i	0.0312371	−	0.317156i
$870$	2664.36	+	30398.8i	0.103828	+	1.18462i
$871$	−2770.24	+	13926.9i	−0.107768	+	0.541787i
$872$	15841.6	−	18081.1i	0.615212	−	0.702181i
$873$	−88173.3	+	17538.8i	−3.41834	+	0.679951i
$874$	15032.1	+	8243.83i	0.581772	+	0.319052i
$875$	−19887.7	+	37207.3i	−0.768375	+	1.43753i
$876$	2021.19	−	16807.9i	0.0779561	−	0.648271i
$877$	−3799.10	−	38572.9i	−0.146279	−	1.48519i	−0.735668	−	0.677343i	$-0.763131\pi$
$877$	−3799.10	−	38572.9i	−0.146279	−	1.48519i	0.589389	−	0.807849i	$-0.299369\pi$
$878$	−45315.2	+	8508.33i	−1.74181	+	0.327041i
$879$	17684.3	−	7325.06i	0.678584	−	0.281079i
$880$	−5591.93	−	4094.78i	−0.214209	−	0.156858i
$881$	−12763.7	−	5286.89i	−0.488103	−	0.202179i	0.125038	−	0.992152i	$-0.460095\pi$
$881$	−12763.7	−	5286.89i	−0.488103	−	0.202179i	−0.613142	+	0.789973i	$0.710095\pi$
$882$	−96343.9	−	20243.2i	−3.67808	−	0.772815i
$883$	14427.8	+	11840.6i	0.549869	+	0.451266i	0.867847	−	0.496832i	$-0.165504\pi$
$883$	14427.8	+	11840.6i	0.549869	+	0.451266i	−0.317977	+	0.948098i	$0.603004\pi$
$884$	−7282.77	+	22272.4i	−0.277088	+	0.847400i
$885$	−56910.4	+	17263.6i	−2.16161	+	0.655717i
$886$	−1406.86	+	12864.6i	−0.0533457	+	0.487803i
$887$	−148.059	+	221.586i	−0.00560467	+	0.00838799i	−0.834261	−	0.551369i	$-0.814106\pi$
$887$	−148.059	+	221.586i	−0.00560467	+	0.00838799i	0.828657	+	0.559757i	$0.189106\pi$
$888$	47955.9	+	21701.3i	1.81227	+	0.820101i
$889$	62207.6	−	41565.8i	2.34688	−	1.56813i
$890$	2453.71	+	773.228i	0.0924140	+	0.0291221i
$891$	−24132.5	−	29405.5i	−0.907371	−	1.10564i
$892$	14060.3	+	14678.4i	0.527773	+	0.550973i
$893$	29944.7	−	16005.8i	1.12213	−	0.599791i
$894$	50321.9	+	51415.8i	1.88257	+	1.92349i
$895$	−1657.65			−0.0619096
$896$	−39766.8	−	11074.7i	−1.48272	−	0.412925i
$897$	23331.3			0.868459
$898$	11738.4	+	11993.6i	0.436209	+	0.445691i
$899$	−18836.7	+	10068.4i	−0.698821	+	0.373527i
$900$	−27008.4	+	25871.1i	−1.00031	+	0.958190i
$901$	2920.95	+	3559.19i	0.108003	+	0.131602i
$902$	−6878.00	−	2167.44i	−0.253894	−	0.0800087i
$903$	−74660.9	+	49886.8i	−2.75145	+	1.83846i
$904$	11431.0	+	30328.0i	0.420562	+	1.11581i
$905$	9818.15	−	14693.9i	0.360626	−	0.539715i
$906$	−7551.85	+	69055.5i	−0.276924	+	2.53225i
$907$	21108.0	−	6403.04i	0.772745	−	0.234410i	0.120801	−	0.992677i	$-0.461454\pi$
$907$	21108.0	−	6403.04i	0.772745	−	0.234410i	0.651944	+	0.758267i	$0.273954\pi$
$908$	21196.9	+	6931.08i	0.774717	+	0.253322i
$909$	−50514.2	−	41455.9i	−1.84318	−	1.51266i
$910$	−21810.6	−	4582.70i	−0.794521	−	0.166940i
$911$	32196.7	+	13336.3i	1.17094	+	0.485018i	0.881502	−	0.472180i	$-0.156533\pi$
$911$	32196.7	+	13336.3i	1.17094	+	0.485018i	0.289435	+	0.957198i	$0.406533\pi$
$912$	−30670.9	−	50472.6i	−1.11361	−	1.83258i
$913$	14882.6	−	6164.56i	0.539475	−	0.223458i
$914$	18896.2	−	3547.93i	0.683841	−	0.128397i
$915$	−4013.13	−	40746.0i	−0.144994	−	1.47215i
$916$	−15454.2	−	1858.41i	−0.557448	−	0.0670345i
$917$	−6002.38	+	11229.7i	−0.216157	+	0.404401i
$918$	98008.4	+	53749.2i	3.52370	+	1.93245i
$919$	−36631.4	+	7286.43i	−1.31486	+	0.261542i	−0.802203	−	0.597051i	$-0.796339\pi$
$919$	−36631.4	+	7286.43i	−1.31486	+	0.261542i	−0.512657	+	0.858593i	$0.671339\pi$
$920$	−774.791	−	11736.4i	−0.0277653	−	0.420584i
$921$	13356.0	−	67145.0i	0.477844	−	2.40228i
$922$	−4139.90	−	47233.9i	−0.147874	−	1.68716i
$923$	−202.625	+	2057.29i	−0.00722589	+	0.0733657i
$924$	30811.3	+	6820.57i	1.09699	+	0.242836i
$925$	−4235.07	+	13961.1i	−0.150538	+	0.496259i
$926$	1639.28	+	4081.12i	0.0581749	+	0.144832i
$927$	23908.6	+	23908.6i	0.847100	+	0.847100i
$928$	−10446.8	−	22357.5i	−0.369541	−	0.790864i
$929$	−22301.6	+	22301.6i	−0.787611	+	0.787611i	−0.981102	−	0.193491i	$-0.938019\pi$
$929$	−22301.6	+	22301.6i	−0.787611	+	0.787611i	0.193491	+	0.981102i	$0.438019\pi$
$930$	32253.8	+	13768.1i	1.13725	+	0.485455i
$931$	41234.2	+	12508.2i	1.45155	+	0.440324i
$932$	−2763.35	−	15643.1i	−0.0971209	−	0.549791i
$933$	51637.8	+	5085.88i	1.81195	+	0.178461i
$934$	−7981.58	+	9515.11i	−0.279620	+	0.333345i
$935$	−8857.23	−	1761.81i	−0.309799	−	0.0616229i
$936$	−51036.1	−	29433.7i	−1.78223	−	1.02785i
$937$	664.507	+	3340.70i	0.0231681	+	0.116474i	0.990639	−	0.136509i	$-0.0435883\pi$
$937$	664.507	+	3340.70i	0.0231681	+	0.116474i	−0.967471	+	0.252983i	$0.918588\pi$
$938$	−31290.1	+	9125.57i	−1.08919	+	0.317655i
$939$	52667.1	+	28151.2i	1.83038	+	0.978359i
$940$	−20303.0	−	11420.1i	−0.704478	−	0.396257i
$941$	−17359.6	+	1709.77i	−0.601388	+	0.0592316i	−0.394130	−	0.919055i	$-0.628954\pi$
$941$	−17359.6	+	1709.77i	−0.601388	+	0.0592316i	−0.207258	+	0.978286i	$0.566454\pi$
$942$	−4990.55	−	3412.76i	−0.172613	−	0.118040i
$943$	−4683.30	−	11306.5i	−0.161728	−	0.390446i
$944$	38455.0	−	28884.3i	1.32585	−	0.995872i
$945$	−40684.1	+	98220.0i	−1.40048	+	3.38105i
$946$	10209.7	−	6664.25i	0.350894	−	0.229042i
$947$	−7166.32	+	8732.18i	−0.245907	+	0.299639i	−0.881307	−	0.472545i	$-0.843335\pi$
$947$	−7166.32	+	8732.18i	−0.245907	+	0.299639i	0.635399	+	0.772184i	$0.280835\pi$
$948$	−47587.7	+	3655.80i	−1.63035	+	0.125248i
$949$	2145.61	+	7073.12i	0.0733924	+	0.241942i
$950$	12764.9	−	10248.2i	0.435944	−	0.349994i
$951$	22750.4	+	15201.4i	0.775745	+	0.518336i
$952$	−53064.4	+	8786.62i	−1.80654	+	0.299135i
$953$	17722.7	+	26523.9i	0.602407	+	0.901566i	0.999871	−	0.0160518i	$-0.00510966\pi$
$953$	17722.7	+	26523.9i	0.602407	+	0.901566i	−0.397464	+	0.917618i	$0.630110\pi$
$954$	−10267.5	+	5346.95i	−0.348450	+	0.181461i
$955$	−16022.4	+	13149.2i	−0.542903	+	0.445549i
$956$	−4416.08	−	11345.4i	−0.149400	−	0.383824i
$957$	8893.06	+	16637.7i	0.300389	+	0.561987i
$958$	−152.993	+	14229.4i	−0.00515967	+	0.479886i
$959$			60544.1i			2.03866i
$960$	−17887.0	+	36357.4i	−0.601354	+	1.22232i
$961$		−	5244.66i		−	0.176048i
$962$	−22980.9	−	247.088i	−0.770202	−	0.00828111i
$963$	−25949.6	−	48548.3i	−0.868342	−	1.62455i
$964$	−4179.99	+	9507.85i	−0.139656	+	0.317663i
$965$	9885.43	−	8112.77i	0.329765	−	0.270631i
$966$	24735.8	+	47498.9i	0.823874	+	1.58204i
$967$	−16567.0	−	24794.3i	−0.550941	−	0.824542i	0.446592	−	0.894738i	$-0.352638\pi$
$967$	−16567.0	−	24794.3i	−0.550941	−	0.824542i	−0.997533	+	0.0701958i	$0.977638\pi$
$968$	25160.2	+	5854.05i	0.835413	+	0.194376i
$969$	−63985.7	−	42753.8i	−2.12127	−	1.41739i
$970$	−16900.4	−	21050.7i	−0.559423	−	0.696802i
$971$	10941.2	+	36068.4i	0.361607	+	1.19206i	0.929458	+	0.368927i	$0.120275\pi$
$971$	10941.2	+	36068.4i	0.361607	+	1.19206i	−0.567851	+	0.823131i	$0.692225\pi$
$972$	−78120.3	+	91121.9i	−2.57789	+	3.00693i
$973$	13964.2	−	17015.4i	0.460093	−	0.560625i
$974$	3782.85	+	5795.36i	0.124446	+	0.190652i
$975$	8525.11	−	20581.4i	0.280022	−	0.676034i
$976$	14338.5	+	29845.2i	0.470249	+	0.978812i
$977$	1792.30	+	4326.99i	0.0586906	+	0.141692i	0.950504	−	0.310711i	$-0.100567\pi$
$977$	1792.30	+	4326.99i	0.0586906	+	0.141692i	−0.891814	+	0.452402i	$0.850567\pi$
$978$	21260.9	−	31090.3i	0.695142	−	1.01652i
$979$	1582.82	−	155.894i	0.0516723	−	0.00508928i
$980$	−7971.15	−	28467.0i	−0.259826	−	0.927903i
$981$	69452.7	+	37123.3i	2.26040	+	1.20821i
$982$	−3042.11	−	10430.9i	−0.0988569	−	0.338965i
$983$	−9069.85	−	45597.2i	−0.294286	−	1.47948i	−0.791136	−	0.611640i	$-0.790510\pi$
$983$	−9069.85	−	45597.2i	−0.294286	−	1.47948i	0.496850	−	0.867837i	$-0.334490\pi$
$984$	−5483.24	+	41801.3i	−0.177642	+	1.35425i
$985$	4051.98	+	805.989i	0.131073	+	0.0260720i
$986$	−24635.1	−	20664.7i	−0.795681	−	0.667443i
$987$	105552.	+	10396.0i	3.40400	+	0.335265i
$988$	21127.9	+	14784.0i	0.680332	+	0.476055i
$989$	19799.7	+	6006.17i	0.636596	+	0.193109i
$990$	8913.98	−	20882.4i	0.286166	−	0.670389i
$991$	−18042.8	+	18042.8i	−0.578354	+	0.578354i	−0.934449	−	0.356096i	$-0.884108\pi$
$991$	−18042.8	+	18042.8i	−0.578354	+	0.578354i	0.356096	+	0.934449i	$0.384108\pi$
$992$	−28319.8	−	1523.87i	−0.906406	−	0.0487730i
$993$	41887.6	+	41887.6i	1.33863	+	1.33863i
$994$	−4403.15	+	1768.63i	−0.140503	+	0.0564361i
$995$	−364.102	+	1200.28i	−0.0116008	+	0.0382428i
$996$	−50625.1	−	79410.5i	−1.61056	−	2.52632i
$997$	−4202.56	+	42669.3i	−0.133497	+	1.35542i	0.662021	+	0.749485i	$0.269699\pi$
$997$	−4202.56	+	42669.3i	−0.133497	+	1.35542i	−0.795518	+	0.605930i	$0.792801\pi$
$998$	28179.0	−	2469.80i	0.893778	−	0.0783367i
$999$	−21387.7	+	107523.i	−0.677354	+	3.40529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.101.37	✓	752
128.109	even	32	inner	128.4.k.a.109.37	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.101.37	✓	752	1.1	even	1	trivial
128.4.k.a.109.37	yes	752	128.109	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.02139 - 1.97838i) q^{2} +(8.86876 - 4.74045i) q^{3} +(0.172010 - 7.99815i) q^{4} +(4.99248 + 6.08336i) q^{5} +(8.54877 - 27.1281i) q^{6} +(-23.7013 + 15.8367i) q^{7} +(-15.4757 - 16.5077i) q^{8} +(41.1826 - 61.6341i) q^{9} +(22.1269 + 2.41978i) q^{10} +(13.1684 - 3.99460i) q^{11} +(-36.3893 - 71.7491i) q^{12} +(27.1522 + 22.2832i) q^{13} +(-16.5785 + 78.9024i) q^{14} +(73.1150 + 30.2852i) q^{15} +(-63.9408 - 2.75153i) q^{16} +(-77.0427 + 31.9121i) q^{17} +(-38.6899 - 206.061i) q^{18} +(8.99475 + 91.3252i) q^{19} +(49.5144 - 38.8842i) q^{20} +(-135.128 + 252.807i) q^{21} +(18.7157 - 34.1269i) q^{22} +(64.7828 - 12.8861i) q^{23} +(-215.504 - 73.0407i) q^{24} +(12.3039 - 61.8560i) q^{25} +(98.9697 - 8.67437i) q^{26} +(46.4518 - 471.633i) q^{27} +(122.588 + 192.291i) q^{28} +(-39.5737 + 130.457i) q^{29} +(207.709 - 83.4312i) q^{30} +(110.784 + 110.784i) q^{31} +(-134.693 + 120.937i) q^{32} +(97.8515 - 97.8515i) q^{33} +(-92.5987 + 216.927i) q^{34} +(-214.669 - 65.1191i) q^{35} +(-485.875 - 339.986i) q^{36} +(-230.214 - 22.6741i) q^{37} +(198.858 + 166.809i) q^{38} +(346.438 + 68.9109i) q^{39} +(23.1598 - 176.558i) q^{40} +(-36.1462 - 181.719i) q^{41} +(227.002 + 778.355i) q^{42} +(276.260 + 147.664i) q^{43} +(-29.6843 - 106.010i) q^{44} +(580.546 - 57.1788i) q^{45} +(105.458 - 154.213i) q^{46} +(-141.593 - 341.837i) q^{47} +(-580.119 + 278.706i) q^{48} +(179.690 - 433.811i) q^{49} +(-97.5038 - 149.377i) q^{50} +(-531.995 + 648.238i) q^{51} +(182.895 - 213.334i) q^{52} +(-16.0278 - 52.8365i) q^{53} +(-839.173 - 1045.25i) q^{54} +(90.0439 + 60.1654i) q^{55} +(628.221 + 146.169i) q^{56} +(512.695 + 767.302i) q^{57} +(178.100 + 341.996i) q^{58} +(-580.900 + 476.732i) q^{59} +(254.802 - 579.575i) q^{60} +(-243.880 - 456.268i) q^{61} +(443.112 + 4.76428i) q^{62} +2113.01i q^{63} +(-33.0056 + 510.935i) q^{64} +276.425i q^{65} +(4.20811 - 391.384i) q^{66} +(190.568 + 356.527i) q^{67} +(241.986 + 621.688i) q^{68} +(513.457 - 421.384i) q^{69} +(-562.759 + 293.066i) q^{70} +(32.6973 + 48.9349i) q^{71} +(-1654.76 + 274.003i) q^{72} +(174.966 + 116.909i) q^{73} +(-510.210 + 409.618i) q^{74} +(-184.105 - 606.912i) q^{75} +(731.980 - 56.2325i) q^{76} +(-248.848 + 303.222i) q^{77} +(836.618 - 546.092i) q^{78} +(227.033 - 548.106i) q^{79} +(-302.485 - 402.712i) q^{80} +(-1057.87 - 2553.93i) q^{81} +(-432.575 - 295.814i) q^{82} +(1164.97 - 114.740i) q^{83} +(1998.74 + 1124.26i) q^{84} +(-578.767 - 309.358i) q^{85} +(850.563 - 248.061i) q^{86} +(267.455 + 1344.59i) q^{87} +(-269.732 - 155.561i) q^{88} +(113.358 + 22.5483i) q^{89} +(1060.39 - 1264.12i) q^{90} +(-996.435 - 98.1402i) q^{91} +(-91.9217 - 520.359i) q^{92} +(1507.69 + 457.352i) q^{93} +(-962.498 - 410.858i) q^{94} +(-510.658 + 510.658i) q^{95} +(-621.259 + 1711.07i) q^{96} +(-857.577 - 857.577i) q^{97} +(-495.020 - 1232.40i) q^{98} +(296.107 - 976.134i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18}+ \cdots - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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