LMFDB - Embedded newform 140.3.x.a.103.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,3,Mod(3,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("140.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	140.x (of order $12$, degree $4$, 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:	$3.81472370104$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.37
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68350 + 1.07974i) q^{2} +(0.0423311 - 0.157982i) q^{3} +(1.66834 + 3.63547i) q^{4} +(2.84692 - 4.11036i) q^{5} +(0.241843 - 0.220256i) q^{6} +(4.44939 - 5.40398i) q^{7} +(-1.11671 + 7.92168i) q^{8} +(7.77106 + 4.48662i) q^{9} +O(q^{10})$	\(q+(1.68350 + 1.07974i) q^{2} +(0.0423311 - 0.157982i) q^{3} +(1.66834 + 3.63547i) q^{4} +(2.84692 - 4.11036i) q^{5} +(0.241843 - 0.220256i) q^{6} +(4.44939 - 5.40398i) q^{7} +(-1.11671 + 7.92168i) q^{8} +(7.77106 + 4.48662i) q^{9} +(9.23089 - 3.84587i) q^{10} +(-14.5887 + 8.42276i) q^{11} +(0.644960 - 0.109673i) q^{12} +(8.25329 - 8.25329i) q^{13} +(13.3254 - 4.29342i) q^{14} +(-0.528849 - 0.623757i) q^{15} +(-10.4333 + 12.1304i) q^{16} +(-5.56191 + 20.7573i) q^{17} +(8.23820 + 15.9439i) q^{18} +(-15.8331 - 9.14124i) q^{19} +(19.6927 + 3.49241i) q^{20} +(-0.665382 - 0.931678i) q^{21} +(-33.6544 - 1.57219i) q^{22} +(-1.98419 - 7.40511i) q^{23} +(1.20421 + 0.511752i) q^{24} +(-8.79013 - 23.4037i) q^{25} +(22.8058 - 4.98303i) q^{26} +(2.07862 - 2.07862i) q^{27} +(27.0691 + 7.15996i) q^{28} -38.9914i q^{29} +(-0.216823 - 1.62111i) q^{30} +(0.979045 + 1.69575i) q^{31} +(-30.6621 + 9.15628i) q^{32} +(0.713089 + 2.66128i) q^{33} +(-31.7759 + 28.9396i) q^{34} +(-9.54526 - 33.6733i) q^{35} +(-3.34624 + 35.7367i) q^{36} +(-1.92842 - 7.19696i) q^{37} +(-16.7849 - 32.4848i) q^{38} +(-0.954498 - 1.65324i) q^{39} +(29.3818 + 27.1424i) q^{40} +13.1587i q^{41} +(-0.114203 - 2.28692i) q^{42} +(-45.1891 + 45.1891i) q^{43} +(-54.9595 - 38.9846i) q^{44} +(40.5652 - 19.1688i) q^{45} +(4.65518 - 14.6089i) q^{46} +(-5.09175 - 19.0027i) q^{47} +(1.47473 + 2.16176i) q^{48} +(-9.40592 - 48.0888i) q^{49} +(10.4717 - 48.8911i) q^{50} +(3.04384 + 1.75736i) q^{51} +(43.7739 + 16.2353i) q^{52} +(-21.8030 + 81.3701i) q^{53} +(5.74371 - 1.25499i) q^{54} +(-6.91209 + 83.9435i) q^{55} +(37.8399 + 41.2813i) q^{56} +(-2.11438 + 2.11438i) q^{57} +(42.1005 - 65.6421i) q^{58} +(67.5099 - 38.9769i) q^{59} +(1.38535 - 2.96325i) q^{60} +(-76.0891 - 43.9301i) q^{61} +(-0.182748 + 3.91191i) q^{62} +(58.8221 - 22.0319i) q^{63} +(-61.5059 - 17.6924i) q^{64} +(-10.4276 - 57.4204i) q^{65} +(-1.67300 + 5.25022i) q^{66} +(4.77110 - 17.8060i) q^{67} +(-84.7419 + 14.4101i) q^{68} -1.25387 q^{69} +(20.2888 - 66.9953i) q^{70} +20.3435i q^{71} +(-44.2196 + 56.5496i) q^{72} +(-2.08127 - 0.557675i) q^{73} +(4.52433 - 14.1983i) q^{74} +(-4.06945 + 0.397976i) q^{75} +(6.81777 - 72.8114i) q^{76} +(-19.3941 + 116.313i) q^{77} +(0.178166 - 3.81383i) q^{78} +(4.23975 - 7.34345i) q^{79} +(20.1575 + 77.4188i) q^{80} +(40.1392 + 69.5232i) q^{81} +(-14.2079 + 22.1526i) q^{82} +(81.8188 + 81.8188i) q^{83} +(2.27701 - 3.97333i) q^{84} +(69.4859 + 81.9559i) q^{85} +(-124.868 + 27.2835i) q^{86} +(-6.15994 - 1.65055i) q^{87} +(-50.4312 - 124.972i) q^{88} +(-29.9452 + 51.8666i) q^{89} +(88.9888 + 11.5291i) q^{90} +(-7.87851 - 81.3227i) q^{91} +(23.6108 - 19.5677i) q^{92} +(0.309342 - 0.0828880i) q^{93} +(11.9459 - 37.4887i) q^{94} +(-82.6493 + 39.0554i) q^{95} +(0.148566 + 5.23164i) q^{96} +(56.1594 + 56.1594i) q^{97} +(36.0883 - 91.1133i) q^{98} -151.159 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.68350	+	1.07974i	0.841749	+	0.539868i
$2$	1.68350	+	1.07974i	0.841749	+	0.539868i
$3$	0.0423311	−	0.157982i	0.0141104	−	0.0526606i	−0.958512	−	0.285053i	$-0.907989\pi$
$3$	0.0423311	−	0.157982i	0.0141104	−	0.0526606i	0.972622	+	0.232393i	$0.0746554\pi$
$4$	1.66834	+	3.63547i	0.417084	+	0.908868i
$5$	2.84692	−	4.11036i	0.569383	−	0.822072i
$5$	2.84692	−	4.11036i	0.569383	−	0.822072i
$6$	0.241843	−	0.220256i	0.0403072	−	0.0367093i
$7$	4.44939	−	5.40398i	0.635627	−	0.771997i
$7$	4.44939	−	5.40398i	0.635627	−	0.771997i
$8$	−1.11671	+	7.92168i	−0.139588	+	0.990210i
$9$	7.77106	+	4.48662i	0.863451	+	0.498514i
$10$	9.23089	−	3.84587i	0.923089	−	0.384587i
$11$	−14.5887	+	8.42276i	−1.32624	+	0.765706i	−0.984716	−	0.174167i	$-0.944277\pi$
$11$	−14.5887	+	8.42276i	−1.32624	+	0.765706i	−0.341525	+	0.939873i	$0.610943\pi$
$12$	0.644960	−	0.109673i	0.0537467	−	0.00913945i
$13$	8.25329	−	8.25329i	0.634869	−	0.634869i	−0.314417	−	0.949285i	$-0.601809\pi$
$13$	8.25329	−	8.25329i	0.634869	−	0.634869i	0.949285	+	0.314417i	$0.101809\pi$
$14$	13.3254	−	4.29342i	0.951815	−	0.306673i
$15$	−0.528849	−	0.623757i	−0.0352566	−	0.0415838i
$16$	−10.4333	+	12.1304i	−0.652081	+	0.758149i
$17$	−5.56191	+	20.7573i	−0.327171	+	1.22102i	0.584940	+	0.811077i	$0.301118\pi$
$17$	−5.56191	+	20.7573i	−0.327171	+	1.22102i	−0.912111	+	0.409943i	$0.865549\pi$
$18$	8.23820	+	15.9439i	0.457678	+	0.885774i
$19$	−15.8331	−	9.14124i	−0.833320	−	0.481118i	0.0216678	−	0.999765i	$-0.493102\pi$
$19$	−15.8331	−	9.14124i	−0.833320	−	0.481118i	−0.854988	+	0.518647i	$0.826436\pi$
$20$	19.6927	+	3.49241i	0.984636	+	0.174621i
$21$	−0.665382	−	0.931678i	−0.0316849	−	0.0443656i
$22$	−33.6544	−	1.57219i	−1.52974	−	0.0714632i
$23$	−1.98419	−	7.40511i	−0.0862693	−	0.321961i	0.909282	−	0.416180i	$-0.136631\pi$
$23$	−1.98419	−	7.40511i	−0.0862693	−	0.321961i	−0.995552	+	0.0942187i	$0.969965\pi$
$24$	1.20421	+	0.511752i	0.0501754	+	0.0213230i
$25$	−8.79013	−	23.4037i	−0.351605	−	0.936148i
$26$	22.8058	−	4.98303i	0.877146	−	0.191655i
$27$	2.07862	−	2.07862i	0.0769858	−	0.0769858i
$28$	27.0691	+	7.15996i	0.966753	+	0.255713i
$29$		−	38.9914i		−	1.34453i	−0.740309	−	0.672266i	$-0.765321\pi$
$29$		−	38.9914i		−	1.34453i	0.740309	−	0.672266i	$-0.234679\pi$
$30$	−0.216823	−	1.62111i	−0.00722745	−	0.0540370i
$31$	0.979045	+	1.69575i	0.0315821	+	0.0547018i	0.881384	−	0.472400i	$-0.156612\pi$
$31$	0.979045	+	1.69575i	0.0315821	+	0.0547018i	−0.849802	+	0.527101i	$0.823279\pi$
$32$	−30.6621	+	9.15628i	−0.958190	+	0.286134i
$33$	0.713089	+	2.66128i	0.0216088	+	0.0806450i
$34$	−31.7759	+	28.9396i	−0.934586	+	0.851164i
$35$	−9.54526	−	33.6733i	−0.272722	−	0.962093i
$36$	−3.34624	+	35.7367i	−0.0929511	+	0.992685i
$37$	−1.92842	−	7.19696i	−0.0521194	−	0.194512i	0.934957	−	0.354760i	$-0.115437\pi$
$37$	−1.92842	−	7.19696i	−0.0521194	−	0.194512i	−0.987077	+	0.160248i	$0.948771\pi$
$38$	−16.7849	−	32.4848i	−0.441707	−	0.854864i
$39$	−0.954498	−	1.65324i	−0.0244743	−	0.0423908i
$40$	29.3818	+	27.1424i	0.734545	+	0.678561i
$41$			13.1587i			0.320943i	0.987040	+	0.160471i	$0.0513014\pi$
$41$			13.1587i			0.320943i	−0.987040	+	0.160471i	$0.948699\pi$
$42$	−0.114203	−	2.28692i	−0.00271913	−	0.0544504i
$43$	−45.1891	+	45.1891i	−1.05091	+	1.05091i	−0.0522775	+	0.998633i	$0.516648\pi$
$43$	−45.1891	+	45.1891i	−1.05091	+	1.05091i	−0.998633	+	0.0522775i	$0.983352\pi$
$44$	−54.9595	−	38.9846i	−1.24908	−	0.886014i
$45$	40.5652	−	19.1688i	0.901449	−	0.425974i
$46$	4.65518	−	14.6089i	0.101200	−	0.317585i
$47$	−5.09175	−	19.0027i	−0.108335	−	0.404312i	0.890367	−	0.455243i	$-0.150448\pi$
$47$	−5.09175	−	19.0027i	−0.108335	−	0.404312i	−0.998702	+	0.0509312i	$0.983781\pi$
$48$	1.47473	+	2.16176i	0.0307235	+	0.0450367i
$49$	−9.40592	−	48.0888i	−0.191958	−	0.981403i
$50$	10.4717	−	48.8911i	0.209433	−	0.977823i
$51$	3.04384	+	1.75736i	0.0596831	+	0.0344581i
$52$	43.7739	+	16.2353i	0.841805	+	0.312218i
$53$	−21.8030	+	81.3701i	−0.411378	+	1.53528i	0.380603	+	0.924739i	$0.375717\pi$
$53$	−21.8030	+	81.3701i	−0.411378	+	1.53528i	−0.791981	+	0.610546i	$0.790950\pi$
$54$	5.74371	−	1.25499i	0.106365	−	0.0232406i
$55$	−6.91209	+	83.9435i	−0.125674	+	1.52625i
$56$	37.8399	+	41.2813i	0.675712	+	0.737165i
$57$	−2.11438	+	2.11438i	−0.0370944	+	0.0370944i
$58$	42.1005	−	65.6421i	0.725871	−	1.13176i
$59$	67.5099	−	38.9769i	1.14424	−	0.660625i	0.196760	−	0.980452i	$-0.436958\pi$
$59$	67.5099	−	38.9769i	1.14424	−	0.660625i	0.947476	+	0.319827i	$0.103625\pi$
$60$	1.38535	−	2.96325i	0.0230892	−	0.0493875i
$61$	−76.0891	−	43.9301i	−1.24736	−	0.720165i	−0.276780	−	0.960933i	$-0.589267\pi$
$61$	−76.0891	−	43.9301i	−1.24736	−	0.720165i	−0.970583	+	0.240768i	$0.922601\pi$
$62$	−0.182748	+	3.91191i	−0.00294755	+	0.0630954i
$63$	58.8221	−	22.0319i	0.933684	−	0.349713i
$64$	−61.5059	−	17.6924i	−0.961030	−	0.276443i
$65$	−10.4276	−	57.4204i	−0.160424	−	0.883391i
$66$	−1.67300	+	5.25022i	−0.0253485	+	0.0795488i
$67$	4.77110	−	17.8060i	0.0712104	−	0.265761i	−0.921137	−	0.389239i	$-0.872738\pi$
$67$	4.77110	−	17.8060i	0.0712104	−	0.265761i	0.992347	+	0.123478i	$0.0394048\pi$
$68$	−84.7419	+	14.4101i	−1.24620	+	0.211913i
$69$	−1.25387			−0.0181720
$70$	20.2888	−	66.9953i	0.289840	−	0.957075i
$71$			20.3435i			0.286528i	0.989684	+	0.143264i	$0.0457599\pi$
$71$			20.3435i			0.286528i	−0.989684	+	0.143264i	$0.954240\pi$
$72$	−44.2196	+	56.5496i	−0.614161	+	0.785411i
$73$	−2.08127	−	0.557675i	−0.0285106	−	0.00763938i	0.244536	−	0.969640i	$-0.421365\pi$
$73$	−2.08127	−	0.557675i	−0.0285106	−	0.00763938i	−0.273046	+	0.962001i	$0.588031\pi$
$74$	4.52433	−	14.1983i	0.0611396	−	0.191868i
$75$	−4.06945	+	0.397976i	−0.0542594	+	0.00530634i
$76$	6.81777	−	72.8114i	0.0897075	−	0.958045i
$77$	−19.3941	+	116.313i	−0.251872	+	1.51056i
$78$	0.178166	−	3.81383i	0.00228418	−	0.0488953i
$79$	4.23975	−	7.34345i	0.0536677	−	0.0929551i	−0.837943	−	0.545757i	$-0.816242\pi$
$79$	4.23975	−	7.34345i	0.0536677	−	0.0929551i	0.891611	+	0.452802i	$0.149576\pi$
$80$	20.1575	+	77.4188i	0.251969	+	0.967735i
$81$	40.1392	+	69.5232i	0.495546	+	0.858311i
$82$	−14.2079	+	22.1526i	−0.173267	+	0.270153i
$83$	81.8188	+	81.8188i	0.985769	+	0.985769i	0.999900	−	0.0141315i	$-0.00449836\pi$
$83$	81.8188	+	81.8188i	0.985769	+	0.985769i	−0.0141315	+	0.999900i	$0.504498\pi$
$84$	2.27701	−	3.97333i	0.0271072	−	0.0473016i
$85$	69.4859	+	81.9559i	0.817481	+	0.964187i
$86$	−124.868	+	27.2835i	−1.45196	+	0.317250i
$87$	−6.15994	−	1.65055i	−0.0708039	−	0.0189718i
$88$	−50.4312	−	124.972i	−0.573081	−	1.42014i
$89$	−29.9452	+	51.8666i	−0.336463	+	0.582771i	−0.983765	−	0.179463i	$-0.942564\pi$
$89$	−29.9452	+	51.8666i	−0.336463	+	0.582771i	0.647302	+	0.762234i	$0.275897\pi$
$90$	88.9888	+	11.5291i	0.988764	+	0.128101i
$91$	−7.87851	−	81.3227i	−0.0865770	−	0.893656i
$92$	23.6108	−	19.5677i	0.256639	−	0.212692i
$93$	0.309342	−	0.0828880i	0.00332626	−	0.000891269i
$94$	11.9459	−	37.4887i	0.127084	−	0.398816i
$95$	−82.6493	+	39.0554i	−0.869992	+	0.411109i
$96$	0.148566	+	5.23164i	0.00154756	+	0.0544963i
$97$	56.1594	+	56.1594i	0.578963	+	0.578963i	0.934618	−	0.355654i	$-0.115742\pi$
$97$	56.1594	+	56.1594i	0.578963	+	0.578963i	−0.355654	+	0.934618i	$0.615742\pi$
$98$	36.0883	−	91.1133i	0.368248	−	0.929727i
$99$	−151.159			−1.52686
$100$	70.4186	−	71.0016i	0.704186	−	0.710016i
$101$	−55.2929	+	31.9234i	−0.547455	+	0.316073i	−0.748095	−	0.663592i	$-0.769031\pi$
$101$	−55.2929	+	31.9234i	−0.547455	+	0.316073i	0.200640	+	0.979665i	$0.435698\pi$
$102$	3.22681	+	6.24506i	0.0316354	+	0.0612261i
$103$	169.039	−	45.2938i	1.64115	−	0.439746i	0.684036	−	0.729448i	$-0.260223\pi$
$103$	169.039	−	45.2938i	1.64115	−	0.439746i	0.957117	+	0.289703i	$0.0935565\pi$
$104$	56.1634	+	74.5964i	0.540033	+	0.717273i
$105$	−5.72382	+	0.0825515i	−0.0545126	+	0.000786205i
$106$	−124.564	+	113.445i	−1.17513	+	1.07023i
$107$	109.081	−	29.2283i	1.01945	−	0.273161i	0.289879	−	0.957063i	$-0.406385\pi$
$107$	109.081	−	29.2283i	1.01945	−	0.273161i	0.729574	+	0.683902i	$0.239718\pi$
$108$	11.0246	+	4.08892i	0.102080	+	0.0378604i
$109$	49.8043	−	28.7545i	0.456920	−	0.263803i	−0.253828	−	0.967249i	$-0.581690\pi$
$109$	49.8043	−	28.7545i	0.456920	−	0.263803i	0.710748	+	0.703446i	$0.248356\pi$
$110$	−102.273	+	133.856i	−0.929758	+	1.21687i
$111$	−1.21862			−0.0109786
$112$	19.1305	+	110.354i	0.170808	+	0.985304i
$113$	34.5282	+	34.5282i	0.305559	+	0.305559i	0.843184	−	0.537625i	$-0.180678\pi$
$113$	34.5282	+	34.5282i	0.305559	+	0.305559i	−0.537625	+	0.843184i	$0.680678\pi$
$114$	−5.84253	+	1.27658i	−0.0512503	+	0.0111981i
$115$	−36.0865	−	12.9260i	−0.313796	−	0.112400i
$116$	141.752	−	65.0509i	1.22200	−	0.560784i
$117$	101.166	−	27.1074i	0.864669	−	0.231687i
$118$	155.738	+	7.27541i	1.31981	+	0.0616560i
$119$	87.4251	+	122.414i	0.734664	+	1.02869i
$120$	5.53177	−	3.49282i	0.0460981	−	0.0291068i
$121$	81.3859	−	140.964i	0.672611	−	1.16500i
$122$	−80.6630	−	156.112i	−0.661172	−	1.27961i
$123$	2.07883	+	0.557020i	0.0169010	+	0.00452862i
$124$	−4.53149	+	6.38838i	−0.0365443	+	0.0515192i
$125$	−121.222	−	30.4978i	−0.969780	−	0.243982i
$126$	122.816	+	26.4217i	0.974727	+	0.209696i
$127$	91.5843	+	91.5843i	0.721136	+	0.721136i	0.968837	−	0.247701i	$-0.0796749\pi$
$127$	91.5843	+	91.5843i	0.721136	+	0.721136i	−0.247701	+	0.968837i	$0.579675\pi$
$128$	−84.4421	−	96.1953i	−0.659704	−	0.751526i
$129$	5.22615	+	9.05196i	0.0405128	+	0.0701702i
$130$	44.4441	−	107.926i	0.341878	−	0.830202i
$131$	10.5807	−	18.3263i	0.0807685	−	0.139895i	−0.822812	−	0.568314i	$-0.807596\pi$
$131$	10.5807	−	18.3263i	0.0807685	−	0.139895i	0.903580	+	0.428419i	$0.140929\pi$
$132$	−8.48535	+	7.03234i	−0.0642830	+	0.0532753i
$133$	−119.847	+	44.8887i	−0.901102	+	0.337509i
$134$	27.2579	−	24.8248i	0.203417	−	0.185260i
$135$	−2.62622	−	14.4615i	−0.0194535	−	0.107122i
$136$	−158.222	−	67.2395i	−1.16340	−	0.494408i
$137$	27.4738	+	7.36158i	0.200539	+	0.0537342i	0.357690	−	0.933840i	$-0.383564\pi$
$137$	27.4738	+	7.36158i	0.200539	+	0.0537342i	−0.157151	+	0.987575i	$0.550231\pi$
$138$	−2.11088	−	1.35384i	−0.0152962	−	0.00981046i
$139$		−	243.325i		−	1.75054i	−0.483637	−	0.875269i	$-0.660685\pi$
$139$		−	243.325i		−	1.75054i	0.483637	−	0.875269i	$-0.339315\pi$
$140$	106.493	−	90.8799i	0.760667	−	0.649142i
$141$	−3.21761			−0.0228200
$142$	−21.9656	+	34.2483i	−0.154688	+	0.241185i
$143$	−50.8889	+	189.920i	−0.355866	+	1.32811i
$144$	−135.502	+	47.4557i	−0.940988	+	0.329553i
$145$	−160.269	−	111.005i	−1.10530	−	0.765554i
$146$	−2.90168	−	3.18607i	−0.0198745	−	0.0218224i
$147$	−7.99531	−	0.549685i	−0.0543898	−	0.00373936i
$148$	22.9471	−	19.0177i	0.155048	−	0.128498i
$149$	111.482	+	64.3639i	0.748199	+	0.431973i	0.825043	−	0.565070i	$-0.191151\pi$
$149$	111.482	+	64.3639i	0.748199	+	0.431973i	−0.0768439	+	0.997043i	$0.524484\pi$
$150$	−7.28063	−	3.72395i	−0.0485375	−	0.0248263i
$151$	−185.748	+	107.242i	−1.23012	+	0.710211i	−0.967055	−	0.254567i	$-0.918067\pi$
$151$	−185.748	+	107.242i	−1.23012	+	0.710211i	−0.263066	+	0.964778i	$0.584734\pi$
$152$	90.0948	−	115.217i	0.592729	−	0.758003i
$153$	−136.352	+	136.352i	−0.891192	+	0.891192i
$154$	−158.237	+	174.872i	−1.02751	+	1.13553i
$155$	9.75742	+	0.803447i	0.0629511	+	0.00518353i
$156$	4.41788	−	6.22821i	0.0283197	−	0.0399244i
$157$	54.2669	−	202.527i	0.345649	−	1.28998i	−0.546203	−	0.837653i	$-0.683927\pi$
$157$	54.2669	−	202.527i	0.345649	−	1.28998i	0.891852	−	0.452328i	$-0.149406\pi$
$158$	15.0666	−	7.78489i	0.0953583	−	0.0492715i
$159$	11.9320	+	6.88896i	0.0750442	+	0.0433268i
$160$	−49.6568	+	152.099i	−0.310355	+	0.950621i
$161$	−48.8455	−	22.2257i	−0.303388	−	0.138048i
$162$	−7.49238	+	160.382i	−0.0462492	+	0.990012i
$163$	4.46452	+	16.6618i	0.0273897	+	0.102220i	0.978268	−	0.207347i	$-0.0664828\pi$
$163$	4.46452	+	16.6618i	0.0273897	+	0.102220i	−0.950878	+	0.309566i	$0.899816\pi$
$164$	−47.8379	+	21.9531i	−0.291695	+	0.133860i
$165$	12.9689	+	4.64540i	0.0785997	+	0.0281540i
$166$	49.3991	+	226.085i	0.297585	+	1.36196i
$167$	−75.2662	+	75.2662i	−0.450696	+	0.450696i	−0.895585	−	0.444890i	$-0.853243\pi$
$167$	−75.2662	+	75.2662i	−0.450696	+	0.450696i	0.444890	+	0.895585i	$0.353243\pi$
$168$	8.12349	−	4.23053i	0.0483541	−	0.0251817i
$169$			32.7664i			0.193884i
$170$	28.4886	+	212.999i	0.167580	+	1.25294i
$171$	−82.0266	−	142.074i	−0.479688	−	0.830844i
$172$	−239.675	−	88.8931i	−1.39346	−	0.516820i
$173$	−53.5429	−	199.825i	−0.309496	−	1.15506i	−0.929005	−	0.370067i	$-0.879335\pi$
$173$	−53.5429	−	199.825i	−0.309496	−	1.15506i	0.619509	−	0.784990i	$-0.287332\pi$
$174$	−8.58809	−	9.42981i	−0.0493568	−	0.0541943i
$175$	−165.584	−	56.6305i	−0.946193	−	0.323603i
$176$	50.0364	−	264.843i	0.284298	−	1.50479i
$177$	−3.29986	−	12.3153i	−0.0186433	−	0.0695777i
$178$	−106.415	+	54.9845i	−0.597837	+	0.308901i
$179$	−94.1653	−	163.099i	−0.526063	−	0.911168i	−0.999539	−	0.0303611i	$-0.990334\pi$
$179$	−94.1653	−	163.099i	−0.526063	−	0.911168i	0.473476	−	0.880807i	$-0.342999\pi$
$180$	137.364	+	115.494i	0.763134	+	0.641631i
$181$		−	202.623i		−	1.11946i	−0.828674	−	0.559732i	$-0.810904\pi$
$181$		−	202.623i		−	1.11946i	0.828674	−	0.559732i	$-0.189096\pi$
$182$	74.5436	−	145.413i	0.409580	−	0.798974i
$183$	−10.1611	+	10.1611i	−0.0555250	+	0.0555250i
$184$	60.8767	−	7.44881i	0.330851	−	0.0404826i
$185$	−35.0721	−	12.5626i	−0.189579	−	0.0679062i
$186$	0.610275	+	0.194466i	0.00328105	+	0.00104552i
$187$	−93.6933	−	349.668i	−0.501034	−	1.86988i
$188$	60.5889	−	50.2138i	0.322281	−	0.267095i
$189$	−1.98423	−	20.4814i	−0.0104986	−	0.108367i
$190$	−181.309	−	23.4898i	−0.954260	−	0.123630i
$191$	220.891	+	127.531i	1.15650	+	0.667703i	0.950462	−	0.310842i	$-0.100611\pi$
$191$	220.891	+	127.531i	1.15650	+	0.667703i	0.206034	+	0.978545i	$0.433944\pi$
$192$	−5.39868	+	8.96787i	−0.0281181	+	0.0467077i
$193$	7.02235	−	26.2078i	0.0363852	−	0.135792i	−0.945344	−	0.326075i	$-0.894274\pi$
$193$	7.02235	−	26.2078i	0.0363852	−	0.135792i	0.981729	+	0.190283i	$0.0609406\pi$
$194$	33.9070	+	155.182i	0.174778	+	0.799906i
$195$	−9.51279	−	0.783303i	−0.0487835	−	0.00401694i
$196$	159.133	−	114.423i	0.811903	−	0.583792i
$197$	−44.6523	+	44.6523i	−0.226661	+	0.226661i	−0.811296	−	0.584635i	$-0.801238\pi$
$197$	−44.6523	+	44.6523i	−0.226661	+	0.226661i	0.584635	+	0.811296i	$0.301238\pi$
$198$	−254.476	−	163.212i	−1.28523	−	0.824303i
$199$	15.9630	−	9.21626i	0.0802163	−	0.0463129i	−0.459355	−	0.888253i	$-0.651920\pi$
$199$	15.9630	−	9.21626i	0.0802163	−	0.0463129i	0.539572	+	0.841940i	$0.318586\pi$
$200$	195.213	−	43.4975i	0.976063	−	0.217488i
$201$	−2.61105	−	1.50749i	−0.0129903	−	0.00749996i
$202$	−127.554	−	5.95881i	−0.631458	−	0.0294991i
$203$	−210.709	−	173.488i	−1.03797	−	0.854621i
$204$	−1.31068	+	13.9977i	−0.00642492	+	0.0686160i
$205$	54.0868	+	37.4616i	0.263838	+	0.182739i
$206$	333.482	+	106.265i	1.61884	+	0.515851i
$207$	17.8047	−	66.4479i	0.0860129	−	0.321004i
$208$	14.0066	+	186.225i	0.0673392	+	0.895311i
$209$	307.978			1.47358
$210$	−9.72518	−	6.04124i	−0.0463104	−	0.0287678i
$211$			171.174i			0.811252i	0.914039	+	0.405626i	$0.132946\pi$
$211$			171.174i			0.811252i	−0.914039	+	0.405626i	$0.867054\pi$
$212$	−332.193	+	56.4884i	−1.56695	+	0.266455i
$213$	3.21390	+	0.861163i	0.0150887	+	0.00404302i
$214$	215.197	+	68.5734i	1.00559	+	0.320437i
$215$	57.0939	+	314.393i	0.265553	+	1.46229i
$216$	14.1449	+	18.7873i	0.0654858	+	0.0869784i
$217$	13.5200	+	2.25434i	0.0623040	+	0.0103886i
$218$	114.893	+	5.36731i	0.527031	+	0.0246207i
$219$	−0.176205	+	0.305196i	−0.000804589	+	0.00139359i
$220$	−316.706	+	114.917i	−1.43957	+	0.522352i
$221$	125.412	+	217.220i	0.567476	+	0.982898i
$222$	−2.05154	−	1.31579i	−0.00924119	−	0.00592697i
$223$	−15.1317	−	15.1317i	−0.0678550	−	0.0678550i	0.672365	−	0.740220i	$-0.265279\pi$
$223$	−15.1317	−	15.1317i	−0.0678550	−	0.0678550i	−0.740220	+	0.672365i	$0.765279\pi$
$224$	−86.9471	+	206.437i	−0.388157	+	0.921593i
$225$	36.6950	−	221.310i	0.163089	−	0.983599i
$226$	20.8468	+	95.4095i	0.0922425	+	0.422166i
$227$	144.303	+	38.6658i	0.635695	+	0.170334i	0.562253	−	0.826965i	$-0.309935\pi$
$227$	144.303	+	38.6658i	0.635695	+	0.170334i	0.0734426	+	0.997299i	$0.476601\pi$
$228$	−11.2143	−	4.15927i	−0.0491854	−	0.0182424i
$229$	−2.87117	+	4.97301i	−0.0125378	+	0.0217162i	−0.872226	−	0.489103i	$-0.837324\pi$
$229$	−2.87117	+	4.97301i	−0.0125378	+	0.0217162i	0.859688	+	0.510819i	$0.170658\pi$
$230$	−46.7949	−	60.7248i	−0.203456	−	0.264021i
$231$	17.5543	+	7.98757i	0.0759928	+	0.0345782i
$232$	308.878	+	43.5420i	1.33137	+	0.187681i
$233$	40.0577	−	10.7334i	0.171921	−	0.0460662i	−0.171831	−	0.985126i	$-0.554968\pi$
$233$	40.0577	−	10.7334i	0.171921	−	0.0460662i	0.343753	+	0.939060i	$0.388302\pi$
$234$	199.582	+	63.5976i	0.852915	+	0.271785i
$235$	−92.6036	−	33.1701i	−0.394058	−	0.141149i
$236$	254.329	+	180.404i	1.07766	+	0.764423i
$237$	−0.980659	−	0.980659i	−0.00413780	−	0.00413780i
$238$	15.0053	+	300.480i	0.0630474	+	1.26252i
$239$	176.284			0.737589			0.368795	−	0.929511i	$-0.379771\pi$
$239$	176.284			0.737589			0.368795	+	0.929511i	$0.379771\pi$
$240$	13.0840	+	0.0927004i	0.0545169	+	0.000386252i
$241$	61.1770	−	35.3206i	0.253847	−	0.146558i	−0.367678	−	0.929953i	$-0.619847\pi$
$241$	61.1770	−	35.3206i	0.253847	−	0.146558i	0.621524	+	0.783395i	$0.286514\pi$
$242$	289.218	−	149.438i	1.19511	−	0.617513i
$243$	38.2375	−	10.2457i	0.157356	−	0.0421634i
$244$	32.7642	−	349.910i	0.134279	−	1.43406i
$245$	−224.440	−	98.2430i	−0.916082	−	0.400992i
$246$	2.89827	+	3.18233i	0.0117816	+	0.0129363i
$247$	−206.120	+	55.2298i	−0.834495	+	0.223602i
$248$	−14.5265	+	5.86201i	−0.0585747	+	0.0236372i
$249$	16.3893	−	9.46240i	0.0658207	−	0.0380016i
$250$	−171.148	−	182.231i	−0.684593	−	0.728925i
$251$	−322.565			−1.28512			−0.642560	−	0.766235i	$-0.722128\pi$
$251$	−322.565			−1.28512			−0.642560	+	0.766235i	$0.722128\pi$
$252$	178.231	+	177.089i	0.707268	+	0.702735i
$253$	91.3182	+	91.3182i	0.360942	+	0.360942i
$254$	55.2951	+	253.069i	0.217697	+	0.996334i
$255$	15.8889	−	7.50821i	0.0623096	−	0.0294440i
$256$	−38.2925	−	253.120i	−0.149580	−	0.988750i
$257$	−318.353	+	85.3023i	−1.23873	+	0.331916i	−0.817971	−	0.575259i	$-0.804901\pi$
$257$	−318.353	+	85.3023i	−1.23873	+	0.331916i	−0.420755	+	0.907175i	$0.638235\pi$
$258$	−0.975512	+	20.8818i	−0.00378105	+	0.0809373i
$259$	−47.4725	−	21.6009i	−0.183291	−	0.0834012i
$260$	191.354	−	133.706i	0.735975	−	0.514253i
$261$	174.940	−	303.005i	0.670268	−	1.16094i
$262$	37.6001	−	19.4279i	0.143512	−	0.0741523i
$263$	147.732	+	39.5848i	0.561720	+	0.150512i	0.528497	−	0.848935i	$-0.322756\pi$
$263$	147.732	+	39.5848i	0.561720	+	0.150512i	0.0332237	+	0.999448i	$0.489423\pi$
$264$	−21.8782	+	2.67699i	−0.0828718	+	0.0101401i
$265$	272.389	+	321.272i	1.02788	+	1.21235i
$266$	−250.230	−	53.8326i	−0.940713	−	0.202378i
$267$	6.92636	+	6.92636i	0.0259414	+	0.0259414i
$268$	72.6929	−	12.3612i	0.271242	−	0.0461239i
$269$	207.781	+	359.887i	0.772420	+	1.33787i	0.936233	+	0.351379i	$0.114287\pi$
$269$	207.781	+	359.887i	0.772420	+	1.33787i	−0.163813	+	0.986491i	$0.552379\pi$
$270$	11.1934	−	27.1816i	0.0414570	−	0.100673i
$271$	170.570	−	295.436i	0.629410	−	1.09017i	−0.358260	−	0.933622i	$-0.616630\pi$
$271$	170.570	−	295.436i	0.629410	−	1.09017i	0.987670	−	0.156549i	$-0.0500368\pi$
$272$	−193.765	−	284.036i	−0.712373	−	1.04425i
$273$	−13.1810	−	2.19782i	−0.0482820	−	0.00805061i
$274$	38.3035	+	42.0577i	0.139794	+	0.153495i
$275$	325.360	+	267.391i	1.18313	+	0.972332i
$276$	−2.09187	−	4.55839i	−0.00757924	−	0.0165159i
$277$	88.0275	+	23.5869i	0.317789	+	0.0851512i	0.414188	−	0.910192i	$-0.364066\pi$
$277$	88.0275	+	23.5869i	0.317789	+	0.0851512i	−0.0963988	+	0.995343i	$0.530732\pi$
$278$	262.727	−	409.637i	0.945060	−	1.47351i
$279$			17.5704i			0.0629764i
$280$	277.408	−	38.0113i	0.990742	−	0.135755i
$281$	−1.31393			−0.00467590			−0.00233795	−	0.999997i	$-0.500744\pi$
$281$	−1.31393			−0.00467590			−0.00233795	+	0.999997i	$0.500744\pi$
$282$	−5.41685	−	3.47417i	−0.0192087	−	0.0123198i
$283$	−92.4915	+	345.183i	−0.326825	+	1.21973i	0.585639	+	0.810572i	$0.300844\pi$
$283$	−92.4915	+	345.183i	−0.326825	+	1.21973i	−0.912464	+	0.409156i	$0.865823\pi$
$284$	−73.9582	+	33.9398i	−0.260416	+	0.119507i
$285$	2.67140	+	14.7103i	0.00937334	+	0.0516152i
$286$	−290.735	+	264.783i	−1.01656	+	0.925816i
$287$	71.1091	+	58.5479i	0.247767	+	0.204000i
$288$	−279.358	−	66.4152i	−0.969992	−	0.230608i
$289$	−149.651	−	86.4010i	−0.517823	−	0.298965i
$290$	−149.956	−	359.926i	−0.517090	−	1.24112i
$291$	11.2495	−	6.49487i	0.0386579	−	0.0223192i
$292$	−1.44485	−	8.49679i	−0.00494812	−	0.0290986i
$293$	−102.511	+	102.511i	−0.349867	+	0.349867i	−0.860060	−	0.510193i	$-0.829574\pi$
$293$	−102.511	+	102.511i	−0.349867	+	0.349867i	0.510193	+	0.860060i	$0.329574\pi$
$294$	−12.8666	−	9.55822i	−0.0437639	−	0.0325110i
$295$	31.9861	−	388.454i	0.108427	−	1.31679i
$296$	59.1654	−	7.23942i	0.199883	−	0.0244575i
$297$	−12.8165	+	47.8319i	−0.0431533	+	0.161050i
$298$	118.183	+	228.727i	0.396588	+	0.767542i
$299$	−77.4927	−	44.7404i	−0.259173	−	0.149633i
$300$	−8.23605	−	14.1304i	−0.0274535	−	0.0471014i
$301$	43.1371	+	445.265i	0.143313	+	1.47929i
$302$	−428.500	−	20.0177i	−1.41887	−	0.0662839i
$303$	2.70270	+	10.0866i	0.00891981	+	0.0332892i
$304$	276.078	−	96.6882i	0.908152	−	0.318053i
$305$	−397.188	+	187.688i	−1.30226	+	0.615372i
$306$	−376.774	+	82.3244i	−1.23129	+	0.269034i
$307$	45.7221	−	45.7221i	0.148932	−	0.148932i	−0.628709	−	0.777641i	$-0.716416\pi$
$307$	45.7221	−	45.7221i	0.148932	−	0.148932i	0.777641	+	0.628709i	$0.216416\pi$
$308$	−455.208	+	123.542i	−1.47795	+	0.401111i
$309$		−	28.6224i		−	0.0926290i
$310$	15.5591	+	11.8880i	0.0501906	+	0.0383485i
$311$	−107.982	−	187.030i	−0.347208	−	0.601382i	0.638544	−	0.769585i	$-0.279537\pi$
$311$	−107.982	−	187.030i	−0.347208	−	0.601382i	−0.985752	+	0.168203i	$0.946204\pi$
$312$	14.1623	−	5.71504i	0.0453921	−	0.0183174i
$313$	19.3732	+	72.3017i	0.0618952	+	0.230996i	0.989943	−	0.141464i	$-0.0451810\pi$
$313$	19.3732	+	72.3017i	0.0618952	+	0.230996i	−0.928048	+	0.372460i	$0.878514\pi$
$314$	310.034	−	282.360i	0.987370	−	0.899235i
$315$	76.9025	−	304.503i	0.244135	−	0.966676i
$316$	33.7702	+	3.16211i	0.106868	+	0.0100067i
$317$	−45.2799	−	168.987i	−0.142839	−	0.533082i	−0.999842	−	0.0177709i	$-0.994343\pi$
$317$	−45.2799	−	168.987i	−0.142839	−	0.533082i	0.857003	−	0.515311i	$-0.172324\pi$
$318$	12.6493	+	24.4810i	0.0397777	+	0.0769843i
$319$	328.416	+	568.833i	1.02952	+	1.78317i
$320$	−247.824	+	202.443i	−0.774451	+	0.632634i
$321$		−	18.4701i		−	0.0575394i
$322$	−58.2335	−	90.1571i	−0.180849	−	0.279991i
$323$	277.810	−	277.810i	0.860093	−	0.860093i
$324$	−185.784	+	261.913i	−0.573407	+	0.808374i
$325$	−265.705	−	120.610i	−0.817554	−	0.371108i
$326$	−10.4744	+	32.8707i	−0.0321299	+	0.100830i
$327$	−2.43442	−	9.08538i	−0.00744471	−	0.0277840i
$328$	−104.239	−	14.6944i	−0.317801	−	0.0447999i
$329$	−125.345	−	57.0345i	−0.380988	−	0.173357i
$330$	16.8174	+	21.8236i	0.0509618	+	0.0661321i
$331$	135.954	+	78.4929i	0.410736	+	0.237139i	0.691106	−	0.722753i	$-0.257124\pi$
$331$	135.954	+	78.4929i	0.410736	+	0.237139i	−0.280370	+	0.959892i	$0.590457\pi$
$332$	−160.948	+	433.951i	−0.484785	+	1.30708i
$333$	17.3042	−	64.5801i	0.0519645	−	0.193934i
$334$	−207.978	+	45.4429i	−0.622689	+	0.136057i
$335$	−59.6061	−	70.3030i	−0.177929	−	0.209860i
$336$	18.2437	+	1.64913i	0.0542968	+	0.00490813i
$337$	265.075	−	265.075i	0.786572	−	0.786572i	−0.194358	−	0.980931i	$-0.562262\pi$
$337$	265.075	−	265.075i	0.786572	−	0.786572i	0.980931	+	0.194358i	$0.0622624\pi$
$338$	−35.3791	+	55.1622i	−0.104672	+	0.163202i
$339$	6.91643	−	3.99321i	0.0204025	−	0.0117794i
$340$	−182.022	+	389.344i	−0.535360	+	1.14513i
$341$	−28.5659	−	16.4925i	−0.0837709	−	0.0483652i
$342$	15.3111	−	327.749i	0.0447692	−	0.958330i
$343$	−301.721	−	163.136i	−0.879653	−	0.475615i
$344$	−307.511	−	408.437i	−0.893927	−	1.18732i
$345$	−3.56965	+	5.15384i	−0.0103468	+	0.0149387i
$346$	125.619	−	394.217i	0.363060	−	1.13936i
$347$	−47.0335	+	175.531i	−0.135543	+	0.505854i	0.864452	+	0.502716i	$0.167666\pi$
$347$	−47.0335	+	175.531i	−0.135543	+	0.505854i	−0.999995	+	0.00313870i	$0.999001\pi$
$348$	−4.27633	−	25.1479i	−0.0122883	−	0.0722642i
$349$	−673.331			−1.92931			−0.964657	−	0.263509i	$-0.915120\pi$
$349$	−673.331			−1.92931			−0.964657	+	0.263509i	$0.915120\pi$
$350$	−217.614	−	274.124i	−0.621755	−	0.783212i
$351$		−	34.3109i		−	0.0977518i
$352$	370.197	−	391.837i	1.05170	−	1.11317i
$353$	99.9550	+	26.7829i	0.283159	+	0.0758721i	0.397603	−	0.917558i	$-0.369842\pi$
$353$	99.9550	+	26.7829i	0.283159	+	0.0758721i	−0.114444	+	0.993430i	$0.536509\pi$
$354$	7.74192	−	24.2957i	0.0218698	−	0.0686320i
$355$	83.6192	+	57.9163i	0.235547	+	0.163144i
$356$	−238.518	−	22.3339i	−0.669995	−	0.0627357i
$357$	23.0399	−	8.62965i	0.0645377	−	0.0241727i
$358$	17.5769	−	376.251i	0.0490974	−	1.05098i
$359$	−314.056	+	543.961i	−0.874808	+	1.51521i	−0.0178409	+	0.999841i	$0.505679\pi$
$359$	−314.056	+	543.961i	−0.874808	+	1.51521i	−0.856967	+	0.515371i	$0.827654\pi$
$360$	106.550	+	342.750i	0.295972	+	0.952085i
$361$	−13.3756	−	23.1671i	−0.0370514	−	0.0641749i
$362$	218.779	−	341.115i	0.604363	−	0.942308i
$363$	−18.8247	−	18.8247i	−0.0518586	−	0.0518586i
$364$	282.502	−	164.316i	0.776105	−	0.451417i
$365$	−8.21745	+	6.96712i	−0.0225136	+	0.0190880i
$366$	−28.0775	+	6.13488i	−0.0767144	+	0.0167620i
$367$	390.676	+	104.681i	1.06451	+	0.285235i	0.748236	−	0.663433i	$-0.230901\pi$
$367$	390.676	+	104.681i	1.06451	+	0.285235i	0.316275	+	0.948668i	$0.397568\pi$
$368$	110.529	+	53.1907i	0.300349	+	0.144540i
$369$	−59.0379	+	102.257i	−0.159994	+	0.277118i
$370$	−45.4796	−	59.0179i	−0.122918	−	0.159508i
$371$	342.712	+	479.870i	0.923751	+	1.29345i
$372$	0.817424	+	0.986320i	0.00219738	+	0.00265140i
$373$	12.2910	−	3.29337i	0.0329518	−	0.00882941i	−0.242305	−	0.970200i	$-0.577904\pi$
$373$	12.2910	−	3.29337i	0.0329518	−	0.00882941i	0.275257	+	0.961371i	$0.411237\pi$
$374$	219.817	−	689.830i	0.587746	−	1.84447i
$375$	−9.94957	+	17.8599i	−0.0265322	+	0.0476265i
$376$	156.219	−	19.1148i	0.415476	−	0.0508372i
$377$	−321.808	−	321.808i	−0.853601	−	0.853601i
$378$	18.7740	−	36.6228i	0.0496668	−	0.0968858i
$379$	41.9095			0.110579			0.0552895	−	0.998470i	$-0.482392\pi$
$379$	41.9095			0.110579			0.0552895	+	0.998470i	$0.482392\pi$
$380$	−279.872	−	235.311i	−0.736504	−	0.619241i
$381$	18.3455	−	10.5918i	0.0481509	−	0.0277999i
$382$	234.169	+	453.202i	0.613008	+	1.18639i
$383$	204.079	−	54.6829i	0.532844	−	0.142775i	0.0176429	−	0.999844i	$-0.494384\pi$
$383$	204.079	−	54.6829i	0.532844	−	0.142775i	0.515201	+	0.857069i	$0.327717\pi$
$384$	−18.7716	+	9.26825i	−0.0488844	+	0.0241361i
$385$	422.874	+	410.850i	1.09837	+	1.06714i
$386$	40.1196	−	36.5385i	0.103937	−	0.0946592i
$387$	−553.914	+	148.421i	−1.43130	+	0.383516i
$388$	−110.473	+	297.859i	−0.284724	+	0.767678i
$389$	−156.625	+	90.4277i	−0.402636	+	0.232462i	−0.687621	−	0.726070i	$-0.741345\pi$
$389$	−156.625	+	90.4277i	−0.402636	+	0.232462i	0.284985	+	0.958532i	$0.408011\pi$
$390$	−15.1690	−	11.5900i	−0.0388949	−	0.0297179i
$391$	164.746			0.421346
$392$	391.447	−	20.8096i	0.998590	−	0.0530858i
$393$	−2.44732	−	2.44732i	−0.00622728	−	0.00622728i
$394$	−123.385	+	26.9594i	−0.313159	+	0.0684247i
$395$	−18.1140	−	38.3331i	−0.0458583	−	0.0970458i
$396$	−252.184	−	549.535i	−0.636829	−	1.38771i
$397$	257.955	−	69.1188i	0.649761	−	0.174103i	0.0811400	−	0.996703i	$-0.474144\pi$
$397$	257.955	−	69.1188i	0.649761	−	0.174103i	0.568621	+	0.822600i	$0.307477\pi$
$398$	36.8249	+	1.72031i	0.0925249	+	0.00432237i
$399$	2.01837	+	20.8338i	0.00505856	+	0.0522149i
$400$	375.606	+	137.550i	0.939015	+	0.343876i
$401$	−343.574	+	595.088i	−0.856794	+	1.48401i	0.0181776	+	0.999835i	$0.494214\pi$
$401$	−343.574	+	595.088i	−0.856794	+	1.48401i	−0.874971	+	0.484175i	$0.839120\pi$
$402$	−2.76801	−	5.35711i	−0.00688560	−	0.0133261i
$403$	22.0759	+	5.91522i	0.0547789	+	0.0146780i
$404$	−208.304	−	147.757i	−0.515604	−	0.365735i
$405$	400.038	+	32.9400i	0.987749	+	0.0813333i
$406$	−167.407	−	519.577i	−0.412332	−	1.27975i
$407$	88.7513	+	88.7513i	0.218062	+	0.218062i
$408$	−17.3203	+	22.1498i	−0.0424518	+	0.0542888i
$409$	−95.3652	−	165.177i	−0.233167	−	0.403857i	0.725572	−	0.688147i	$-0.241575\pi$
$409$	−95.3652	−	165.177i	−0.233167	−	0.403857i	−0.958738	+	0.284290i	$0.908242\pi$
$410$	50.6064	+	121.466i	0.123430	+	0.296259i
$411$	2.32599	−	4.02873i	0.00565934	−	0.00980227i
$412$	446.678	+	538.970i	1.08417	+	1.30818i
$413$	89.7476	−	538.245i	0.217307	−	1.30326i
$414$	101.720	−	92.6406i	0.245701	−	0.223770i
$415$	569.236	−	103.373i	1.37165	−	0.249093i
$416$	−177.494	+	328.632i	−0.426667	+	0.789982i
$417$	−38.4408	−	10.3002i	−0.0921843	−	0.0247007i
$418$	518.481	+	332.535i	1.24038	+	0.795538i
$419$		−	665.162i		−	1.58750i	−0.608245	−	0.793749i	$-0.708126\pi$
$419$		−	665.162i		−	1.58750i	0.608245	−	0.793749i	$-0.291874\pi$
$420$	−9.84938	−	20.6711i	−0.0234509	−	0.0492168i
$421$	−347.490			−0.825392			−0.412696	−	0.910869i	$-0.635413\pi$
$421$	−347.490			−0.825392			−0.412696	+	0.910869i	$0.635413\pi$
$422$	−184.823	+	288.172i	−0.437969	+	0.682871i
$423$	45.6895	−	170.516i	0.108013	−	0.403110i
$424$	−620.240	−	263.583i	−1.46283	−	0.621658i
$425$	534.689	−	52.2904i	1.25809	−	0.123036i
$426$	4.48077	+	4.91993i	0.0105182	+	0.0115491i
$427$	−575.947	+	215.722i	−1.34882	+	0.505204i
$428$	288.243	+	347.800i	0.673465	+	0.812616i
$429$	27.8497	+	16.0790i	0.0649177	+	0.0374802i
$430$	−243.344	+	590.927i	−0.565917	+	1.37425i
$431$	185.667	−	107.195i	0.430783	−	0.248712i	−0.268897	−	0.963169i	$-0.586659\pi$
$431$	185.667	−	107.195i	0.430783	−	0.248712i	0.699680	+	0.714456i	$0.253326\pi$
$432$	3.52760	+	46.9013i	0.00816573	+	0.108568i
$433$	132.168	−	132.168i	0.305239	−	0.305239i	−0.537821	−	0.843059i	$-0.680752\pi$
$433$	132.168	−	132.168i	0.305239	−	0.305239i	0.843059	+	0.537821i	$0.180752\pi$
$434$	20.3268	+	18.3932i	0.0468359	+	0.0423806i
$435$	−24.3212	+	20.6206i	−0.0559108	+	0.0474036i
$436$	187.627	+	133.090i	0.430336	+	0.305252i
$437$	−36.2760	+	135.384i	−0.0830114	+	0.309803i
$438$	−0.626172	+	0.323542i	−0.00142962	+	0.000738680i
$439$	−264.946	−	152.967i	−0.603522	−	0.348444i	0.166904	−	0.985973i	$-0.446623\pi$
$439$	−264.946	−	152.967i	−0.603522	−	0.348444i	−0.770426	+	0.637530i	$0.779956\pi$
$440$	−657.255	−	148.496i	−1.49376	−	0.337490i
$441$	142.662	−	415.902i	0.323497	−	0.943087i
$442$	−23.4094	+	501.103i	−0.0529625	+	1.13372i
$443$	−196.349	−	732.784i	−0.443226	−	1.65414i	−0.720579	−	0.693372i	$-0.756124\pi$
$443$	−196.349	−	732.784i	−0.443226	−	1.65414i	0.277354	−	0.960768i	$-0.410543\pi$
$444$	−2.03307	−	4.43026i	−0.00457898	−	0.00997805i
$445$	127.939	+	270.746i	0.287503	+	0.608417i
$446$	−9.13592	−	41.8123i	−0.0204841	−	0.0937496i
$447$	14.8875	−	14.8875i	0.0333053	−	0.0333053i
$448$	−369.273	+	253.656i	−0.824270	+	0.566197i
$449$		−	144.486i		−	0.321795i	−0.986971	−	0.160898i	$-0.948561\pi$
$449$		−	144.486i		−	0.321795i	0.986971	−	0.160898i	$-0.0514389\pi$
$450$	300.732	−	332.954i	0.668294	−	0.739897i
$451$	−110.832	−	191.967i	−0.245748	−	0.425648i
$452$	−67.9215	+	183.131i	−0.150269	+	0.405157i
$453$	9.07932	+	33.8845i	0.0200427	+	0.0748002i
$454$	201.185	+	220.903i	0.443138	+	0.486570i
$455$	−356.695	−	199.135i	−0.783945	−	0.437660i
$456$	−14.3883	−	19.1106i	−0.0315533	−	0.0419092i
$457$	113.698	+	424.328i	0.248793	+	0.928507i	0.971439	+	0.237289i	$0.0762589\pi$
$457$	113.698	+	424.328i	0.248793	+	0.928507i	−0.722646	+	0.691218i	$0.757074\pi$
$458$	−10.2031	+	5.27195i	−0.0222776	+	0.0115108i
$459$	31.5855	+	54.7077i	0.0688137	+	0.119189i
$460$	−13.2124	−	152.756i	−0.0287227	−	0.332079i
$461$		−	19.8637i		−	0.0430883i	−0.999768	−	0.0215441i	$-0.993142\pi$
$461$		−	19.8637i		−	0.0430883i	0.999768	−	0.0215441i	$-0.00685824\pi$
$462$	20.9282	+	32.4011i	0.0452992	+	0.0701323i
$463$	−567.440	+	567.440i	−1.22557	+	1.22557i	−0.259951	+	0.965622i	$0.583706\pi$
$463$	−567.440	+	567.440i	−1.22557	+	1.22557i	−0.965622	+	0.259951i	$0.916294\pi$
$464$	472.981	+	406.809i	1.01936	+	0.876744i
$465$	0.539972	−	1.50748i	0.00116123	−	0.00324190i
$466$	79.0264	+	25.1820i	0.169584	+	0.0540387i
$467$	124.531	+	464.756i	0.266662	+	0.995195i	0.961225	+	0.275764i	$0.0889308\pi$
$467$	124.531	+	464.756i	0.266662	+	0.995195i	−0.694564	+	0.719431i	$0.744403\pi$
$468$	267.328	+	322.563i	0.571213	+	0.689236i
$469$	−74.9946	−	105.009i	−0.159903	−	0.223899i
$470$	−120.083	−	155.829i	−0.255496	−	0.331552i
$471$	−29.6984	−	17.1464i	−0.0630539	−	0.0364042i
$472$	233.373	+	578.317i	0.494435	+	1.22525i
$473$	278.631	−	1039.87i	0.589072	−	2.19845i
$474$	−0.592085	−	2.70979i	−0.00124912	−	0.00571686i
$475$	−74.7639	+	450.906i	−0.157398	+	0.949275i
$476$	−299.178	+	522.059i	−0.628524	+	1.09676i
$477$	−534.510	+	534.510i	−1.12057	+	1.12057i
$478$	296.774	+	190.340i	0.620865	+	0.398201i
$479$	−253.235	+	146.205i	−0.528674	+	0.305230i	−0.740476	−	0.672083i	$-0.765400\pi$
$479$	−253.235	+	146.205i	−0.528674	+	0.305230i	0.211802	+	0.977312i	$0.432067\pi$
$480$	21.9269	+	14.2834i	0.0456810	+	0.0297571i
$481$	−75.3144	−	43.4828i	−0.156579	−	0.0904008i
$482$	141.128	+	6.59293i	0.292798	+	0.0136783i
$483$	−5.57893	+	6.77586i	−0.0115506	+	0.0140287i
$484$	648.251	+	60.6997i	1.33936	+	0.125413i
$485$	390.717	−	70.9543i	0.805602	−	0.146298i
$486$	75.4355	+	24.0378i	0.155217	+	0.0494605i
$487$	154.144	−	575.274i	0.316518	−	1.18126i	−0.606051	−	0.795426i	$-0.707247\pi$
$487$	154.144	−	575.274i	0.316518	−	1.18126i	0.922568	−	0.385834i	$-0.126086\pi$
$488$	432.969	−	553.696i	0.887232	−	1.13462i
$489$	2.82125			0.00576943
$490$	−271.768	−	407.728i	−0.554629	−	0.832098i
$491$		−	511.021i		−	1.04078i	−0.853930	−	0.520388i	$-0.825787\pi$
$491$		−	511.021i		−	1.04078i	0.853930	−	0.520388i	$-0.174213\pi$
$492$	1.44315	+	8.48681i	0.00293324	+	0.0172496i
$493$	809.359	+	216.867i	1.64170	+	0.439893i
$494$	−406.637	−	129.576i	−0.823152	−	0.262300i
$495$	−430.337	+	621.319i	−0.869369	+	1.25519i
$496$	−30.7848	−	5.81613i	−0.0620662	−	0.0117261i
$497$	109.936	+	90.5161i	0.221199	+	0.182125i
$498$	37.8083	+	1.76625i	0.0759204	+	0.00354668i
$499$	103.546	−	179.347i	0.207507	−	0.359413i	−0.743421	−	0.668823i	$-0.766798\pi$
$499$	103.546	−	179.347i	0.207507	−	0.359413i	0.950929	+	0.309410i	$0.100132\pi$
$500$	−91.3661	−	491.581i	−0.182732	−	0.983163i
$501$	8.70458	+	15.0768i	0.0173744	+	0.0300934i
$502$	−543.038	−	348.285i	−1.08175	−	0.693796i
$503$	−581.189	−	581.189i	−1.15544	−	1.15544i	−0.985444	−	0.170001i	$-0.945623\pi$
$503$	−581.189	−	581.189i	−1.15544	−	1.15544i	−0.170001	−	0.985444i	$-0.554377\pi$
$504$	108.843	+	490.573i	0.215958	+	0.973358i
$505$	−26.1977	+	318.157i	−0.0518767	+	0.630014i
$506$	55.1345	+	252.334i	0.108961	+	0.498683i
$507$	5.17649	+	1.38704i	0.0102100	+	0.00273577i
$508$	−180.158	+	485.745i	−0.354643	+	0.956192i
$509$	203.271	−	352.075i	0.399353	−	0.691700i	−0.594293	−	0.804248i	$-0.702568\pi$
$509$	203.271	−	352.075i	0.399353	−	0.691700i	0.993646	+	0.112549i	$0.0359015\pi$
$510$	34.8559	+	4.51580i	0.0683449	+	0.00885451i
$511$	−12.2740	+	8.76583i	−0.0240197	+	0.0171543i
$512$	208.837	−	467.473i	0.407885	−	0.913033i
$513$	−51.9121	+	13.9098i	−0.101193	+	0.0271146i
$514$	−628.050	−	200.131i	−1.22189	−	0.389359i
$515$	295.065	−	823.758i	0.572942	−	1.59953i
$516$	−24.1892	+	34.1013i	−0.0468782	+	0.0660877i
$517$	234.337	+	234.337i	0.453263	+	0.453263i
$518$	−56.5966	−	87.6229i	−0.109260	−	0.169156i
$519$	−33.8352			−0.0651930
$520$	466.511	−	18.4821i	0.897136	−	0.0355425i
$521$	−649.579	+	375.035i	−1.24679	+	0.719836i	−0.970468	−	0.241228i	$-0.922450\pi$
$521$	−649.579	+	375.035i	−1.24679	+	0.719836i	−0.276325	+	0.961064i	$0.589117\pi$
$522$	621.677	−	321.219i	1.19095	−	0.615363i
$523$	−176.706	+	47.3482i	−0.337870	+	0.0905320i	−0.423765	−	0.905772i	$-0.639292\pi$
$523$	−176.706	+	47.3482i	−0.337870	+	0.0905320i	0.0858949	+	0.996304i	$0.472625\pi$
$524$	84.2767	+	7.89133i	0.160833	+	0.0150598i
$525$	−15.9559	+	23.7620i	−0.0303922	+	0.0452609i
$526$	205.966	+	226.153i	0.391571	+	0.429949i
$527$	−40.6447	+	10.8907i	−0.0771247	+	0.0206655i
$528$	−39.7223	−	19.1159i	−0.0752316	−	0.0362044i
$529$	407.229	−	235.114i	0.769809	−	0.444449i
$530$	111.677	+	834.970i	0.210711	+	1.57541i
$531$	699.498			1.31732
$532$	−363.136	−	360.809i	−0.682587	−	0.678213i
$533$	108.602	+	108.602i	0.203756	+	0.203756i
$534$	4.18188	+	19.1392i	0.00783123	+	0.0358412i
$535$	190.407	−	531.574i	0.355901	−	0.993597i
$536$	135.725	+	57.6791i	0.253219	+	0.107610i
$537$	−29.7528	+	7.97223i	−0.0554055	+	0.0148459i
$538$	−38.7843	+	830.219i	−0.0720898	+	1.54316i
$539$	542.260	+	622.326i	1.00605	+	1.15459i
$540$	48.1930	−	33.6742i	0.0892463	−	0.0623597i
$541$	−63.7651	+	110.444i	−0.117865	+	0.204149i	−0.918921	−	0.394440i	$-0.870938\pi$
$541$	−63.7651	+	110.444i	−0.117865	+	0.204149i	0.801056	+	0.598589i	$0.204272\pi$
$542$	606.148	−	313.196i	1.11835	−	0.577852i
$543$	−32.0107	−	8.57724i	−0.0589516	−	0.0157960i
$544$	−19.5202	−	687.389i	−0.0358828	−	1.26358i
$545$	23.5972	−	286.575i	0.0432977	−	0.525826i
$546$	−19.8171	−	17.9320i	−0.0362951	−	0.0328425i
$547$	68.0347	+	68.0347i	0.124378	+	0.124378i	0.766556	−	0.642178i	$-0.221969\pi$
$547$	68.0347	+	68.0347i	0.124378	+	0.124378i	−0.642178	+	0.766556i	$0.721969\pi$
$548$	19.0728	+	112.162i	0.0348043	+	0.204675i
$549$	−394.196	−	682.767i	−0.718025	−	1.24366i
$550$	259.031	+	801.456i	0.470966	+	1.45719i
$551$	−356.430	+	617.355i	−0.646879	+	1.12043i
$552$	1.40020	−	9.93271i	0.00253659	−	0.0179940i
$553$	−20.8196	−	55.5854i	−0.0376484	−	0.100516i
$554$	122.727	+	134.755i	0.221528	+	0.243240i
$555$	−3.46931	+	5.00897i	−0.00625101	+	0.00902516i
$556$	884.600	−	405.948i	1.59101	−	0.730122i
$557$	−785.087	−	210.363i	−1.40949	−	0.377672i	−0.527748	−	0.849401i	$-0.676964\pi$
$557$	−785.087	−	210.363i	−1.40949	−	0.377672i	−0.881744	+	0.471728i	$0.843630\pi$
$558$	−18.9714	+	29.5798i	−0.0339990	+	0.0530104i
$559$			745.918i			1.33438i
$560$	508.058	+	235.535i	0.907247	+	0.420599i
$561$	−59.2073			−0.105539
$562$	−2.21200	−	1.41870i	−0.00393594	−	0.00252437i
$563$	−216.659	+	808.583i	−0.384830	+	1.43621i	0.453605	+	0.891203i	$0.350138\pi$
$563$	−216.659	+	808.583i	−0.384830	+	1.43621i	−0.838435	+	0.545002i	$0.816529\pi$
$564$	−5.36807	−	11.6975i	−0.00951785	−	0.0207403i
$565$	240.222	−	43.6244i	0.425172	−	0.0772114i
$566$	−528.416	+	481.249i	−0.933597	+	0.850263i
$567$	554.297	+	92.4241i	0.977595	+	0.163005i
$568$	−161.155	−	22.7177i	−0.283723	−	0.0399960i
$569$	−768.711	−	443.815i	−1.35099	−	0.779992i	−0.362598	−	0.931946i	$-0.618110\pi$
$569$	−768.711	−	443.815i	−1.35099	−	0.779992i	−0.988388	+	0.151954i	$0.951444\pi$
$570$	−11.3860	+	27.6492i	−0.0199754	+	0.0485074i
$571$	−901.121	+	520.263i	−1.57815	+	0.911143i	−0.583028	+	0.812452i	$0.698132\pi$
$571$	−901.121	+	520.263i	−1.57815	+	0.911143i	−0.995118	+	0.0986909i	$0.968534\pi$
$572$	−775.348	+	131.845i	−1.35550	+	0.230499i
$573$	29.4981	−	29.4981i	0.0514802	−	0.0514802i
$574$	56.4957	+	175.344i	0.0984245	+	0.305478i
$575$	−155.866	+	111.529i	−0.271071	+	0.193964i
$576$	−398.587	−	413.443i	−0.691992	−	0.717782i
$577$	71.0973	−	265.339i	0.123219	−	0.459859i	−0.876551	−	0.481309i	$-0.840161\pi$
$577$	71.0973	−	265.339i	0.123219	−	0.459859i	0.999770	+	0.0214496i	$0.00682815\pi$
$578$	−158.647	−	307.040i	−0.274476	−	0.531210i
$579$	−3.84308	−	2.21881i	−0.00663745	−	0.00383213i
$580$	136.174	−	767.847i	0.234783	−	1.32387i
$581$	806.190	−	78.1034i	1.38759	−	0.134429i
$582$	25.9512	+	1.21233i	0.0445897	+	0.00208304i
$583$	−367.284	−	1370.72i	−0.629989	−	2.35115i
$584$	6.74189	−	15.8644i	0.0115443	−	0.0271651i
$585$	176.591	−	493.002i	0.301864	−	0.842739i
$586$	−283.262	+	61.8923i	−0.483383	+	0.105618i
$587$	−313.797	+	313.797i	−0.534578	+	0.534578i	−0.921931	−	0.387353i	$-0.873389\pi$
$587$	−313.797	+	313.797i	−0.534578	+	0.534578i	0.387353	+	0.921931i	$0.373389\pi$
$588$	−11.3405	−	29.9838i	−0.0192866	−	0.0509928i
$589$		−	35.7987i		−	0.0607788i
$590$	473.276	−	619.425i	0.802164	−	1.04987i
$591$	5.16406	+	8.94442i	0.00873784	+	0.0151344i
$592$	107.422	+	51.6955i	0.181455	+	0.0873235i
$593$	255.961	+	955.259i	0.431637	+	1.61089i	0.748988	+	0.662583i	$0.230540\pi$
$593$	255.961	+	955.259i	0.431637	+	1.61089i	−0.317351	+	0.948308i	$0.602793\pi$
$594$	−73.2225	+	66.6865i	−0.123270	+	0.112267i
$595$	752.057	−	10.8465i	1.26396	−	0.0182294i
$596$	−48.0043	+	512.669i	−0.0805441	+	0.860183i
$597$	−0.780269	−	2.91200i	−0.00130698	−	0.00487773i
$598$	−82.1510	−	158.992i	−0.137376	−	0.265873i
$599$	−233.859	−	405.056i	−0.390416	−	0.676221i	0.602088	−	0.798430i	$-0.294336\pi$
$599$	−233.859	−	405.056i	−0.390416	−	0.676221i	−0.992504	+	0.122209i	$0.961002\pi$
$600$	1.39175	−	32.6813i	0.00231958	−	0.0544689i
$601$		−	261.031i		−	0.434328i	−0.976135	−	0.217164i	$-0.930319\pi$
$601$		−	261.031i		−	0.434328i	0.976135	−	0.217164i	$-0.0696806\pi$
$602$	−408.148	+	796.180i	−0.677986	+	1.32256i
$603$	116.965	−	116.965i	0.193972	−	0.193972i
$604$	−699.765	−	496.367i	−1.15855	−	0.821799i
$605$	−347.716	−	735.839i	−0.574737	−	1.21626i
$606$	−6.34090	+	19.8990i	−0.0104635	+	0.0328367i
$607$	−215.594	−	804.608i	−0.355179	−	1.32555i	−0.880259	−	0.474494i	$-0.842631\pi$
$607$	−215.594	−	804.608i	−0.355179	−	1.32555i	0.525079	−	0.851053i	$-0.324036\pi$
$608$	569.175	+	135.317i	0.936143	+	0.222561i
$609$	−36.3275	+	25.9442i	−0.0596510	+	0.0426013i
$610$	−871.319	−	112.885i	−1.42839	−	0.185057i
$611$	−198.858	−	114.811i	−0.325464	−	0.187906i
$612$	−723.187	−	268.223i	−1.18168	−	0.438273i
$613$	26.0404	−	97.1843i	0.0424803	−	0.158539i	−0.941428	−	0.337215i	$-0.890515\pi$
$613$	26.0404	−	97.1843i	0.0424803	−	0.158539i	0.983908	+	0.178677i	$0.0571816\pi$
$614$	126.341	−	27.6053i	0.205767	−	0.0449598i
$615$	8.20780	−	6.95894i	0.0133460	−	0.0113153i
$616$	−899.735	−	283.521i	−1.46061	−	0.460262i
$617$	338.368	−	338.368i	0.548408	−	0.548408i	−0.377572	−	0.925980i	$-0.623241\pi$
$617$	338.368	−	338.368i	0.548408	−	0.548408i	0.925980	+	0.377572i	$0.123241\pi$
$618$	30.9046	−	48.1857i	0.0500075	−	0.0779704i
$619$	205.472	−	118.630i	0.331943	−	0.191647i	−0.324761	−	0.945796i	$-0.605284\pi$
$619$	205.472	−	118.630i	0.331943	−	0.191647i	0.656703	+	0.754149i	$0.271950\pi$
$620$	13.3578	+	36.8132i	0.0215448	+	0.0593762i
$621$	−19.5168	−	11.2680i	−0.0314280	−	0.0181450i
$622$	20.1558	−	431.456i	0.0324049	−	0.693659i
$623$	147.048	+	392.598i	0.236032	+	0.630173i
$624$	30.0130	+	5.67031i	0.0480978	+	0.00908703i
$625$	−470.467	+	411.443i	−0.752748	+	0.658309i
$626$	−45.4521	+	142.638i	−0.0726072	+	0.227856i
$627$	13.0370	−	48.6549i	0.0207927	−	0.0775995i
$628$	826.816	−	140.597i	1.31659	−	0.223881i
$629$	160.115			0.254555
$630$	458.248	−	429.596i	0.727378	−	0.681898i
$631$		−	397.980i		−	0.630714i	−0.948973	−	0.315357i	$-0.897876\pi$
$631$		−	397.980i		−	0.630714i	0.948973	−	0.315357i	$-0.102124\pi$
$632$	53.4379	+	41.7864i	0.0845537	+	0.0661177i
$633$	27.0424	+	7.24599i	0.0427210	+	0.0114471i
$634$	106.233	−	333.380i	0.167560	−	0.525836i
$635$	637.177	−	115.712i	1.00343	−	0.182223i
$636$	−5.13796	+	54.8717i	−0.00807856	+	0.0862762i
$637$	−474.520	−	319.261i	−0.744930	−	0.501194i
$638$	−61.3020	+	1312.23i	−0.0960846	+	2.05679i
$639$	−91.2737	+	158.091i	−0.142838	+	0.247403i
$640$	−635.797	+	73.2274i	−0.993433	+	0.114418i
$641$	388.662	+	673.182i	0.606336	+	1.05021i	0.991839	+	0.127499i	$0.0406948\pi$
$641$	388.662	+	673.182i	0.606336	+	1.05021i	−0.385502	+	0.922707i	$0.625972\pi$
$642$	19.9429	−	31.0944i	0.0310637	−	0.0484337i
$643$	704.965	+	704.965i	1.09637	+	1.09637i	0.994832	+	0.101537i	$0.0323759\pi$
$643$	704.965	+	704.965i	1.09637	+	1.09637i	0.101537	+	0.994832i	$0.467624\pi$
$644$	−0.690004	−	214.656i	−0.00107143	−	0.333317i
$645$	52.0852	+	4.28881i	0.0807523	+	0.00664931i
$646$	767.655	−	167.731i	1.18832	−	0.259646i
$647$	−488.517	−	130.898i	−0.755049	−	0.202315i	−0.139293	−	0.990251i	$-0.544483\pi$
$647$	−488.517	−	130.898i	−0.755049	−	0.202315i	−0.615757	+	0.787936i	$0.711150\pi$
$648$	−595.564	+	240.333i	−0.919080	+	0.370884i
$649$	−656.586	+	1137.24i	−1.01169	+	1.75230i
$650$	−317.087	−	489.939i	−0.487826	−	0.753752i
$651$	0.928458	−	2.04048i	0.00142620	−	0.00313438i
$652$	−53.1252	+	44.0282i	−0.0814804	+	0.0675279i
$653$	−344.688	+	92.3589i	−0.527853	+	0.141438i	−0.512897	−	0.858450i	$-0.671428\pi$
$653$	−344.688	+	92.3589i	−0.527853	+	0.141438i	−0.0149563	+	0.999888i	$0.504761\pi$
$654$	5.71147	−	17.9238i	0.00873314	−	0.0274064i
$655$	−45.2053	−	95.6637i	−0.0690157	−	0.146051i
$656$	−159.620	−	137.288i	−0.243322	−	0.209281i
$657$	−13.6716	−	13.6716i	−0.0208091	−	0.0208091i
$658$	−149.436	−	231.357i	−0.227107	−	0.351607i
$659$	−247.707			−0.375883			−0.187941	−	0.982180i	$-0.560181\pi$
$659$	−247.707			−0.375883			−0.187941	+	0.982180i	$0.560181\pi$
$660$	4.74835	+	54.8983i	0.00719448	+	0.0831793i
$661$	−692.600	+	399.873i	−1.04781	+	0.604951i	−0.922034	−	0.387108i	$-0.873474\pi$
$661$	−692.600	+	399.873i	−1.04781	+	0.604951i	−0.125771	+	0.992059i	$0.540141\pi$
$662$	144.126	+	278.937i	0.217713	+	0.421355i
$663$	39.6257	−	10.6177i	0.0597673	−	0.0160146i
$664$	−739.510	+	556.774i	−1.11372	+	0.838516i
$665$	−156.684	+	620.407i	−0.235615	+	0.932943i
$666$	98.8611	−	90.0366i	0.148440	−	0.135190i
$667$	−288.736	+	77.3666i	−0.432888	+	0.115992i
$668$	−399.197	−	148.059i	−0.597601	−	0.221645i
$669$	−3.03106	+	1.74999i	−0.00453074	+	0.00261582i
$670$	−24.4380	−	182.714i	−0.0364746	−	0.272707i
$671$	1480.05			2.20574
$672$	28.9327	+	22.4747i	0.0430546	+	0.0334446i
$673$	−627.000	−	627.000i	−0.931650	−	0.931650i	0.0661594	−	0.997809i	$-0.478925\pi$
$673$	−627.000	−	627.000i	−0.931650	−	0.931650i	−0.997809	+	0.0661594i	$0.978925\pi$
$674$	732.464	−	160.042i	1.08674	−	0.237451i
$675$	−66.9187	−	30.3760i	−0.0991388	−	0.0450015i
$676$	−119.121	+	54.6654i	−0.176215	+	0.0808659i
$677$	75.2467	−	20.1623i	0.111147	−	0.0297818i	−0.202817	−	0.979217i	$-0.565010\pi$
$677$	75.2467	−	20.1623i	0.111147	−	0.0297818i	0.313964	+	0.949435i	$0.398343\pi$
$678$	15.9554	+	0.745371i	0.0235331	+	0.00109937i
$679$	553.359	−	53.6092i	0.814962	−	0.0789532i
$680$	−726.823	+	458.924i	−1.06886	+	0.674888i
$681$	12.2170	−	21.1604i	0.0179398	−	0.0310726i
$682$	−30.2831	−	58.6088i	−0.0444033	−	0.0859366i
$683$	1022.15	+	273.883i	1.49655	+	0.401000i	0.911944	−	0.410315i	$-0.134581\pi$
$683$	1022.15	+	273.883i	1.49655	+	0.401000i	0.584609	+	0.811315i	$0.301248\pi$
$684$	379.659	−	535.233i	0.555057	−	0.782505i
$685$	108.474	−	91.9694i	0.158357	−	0.134262i
$686$	−331.803	−	600.419i	−0.483678	−	0.875246i
$687$	0.664104	+	0.664104i	0.000966673	+	0.000966673i
$688$	−76.6899	−	1019.63i	−0.111468	−	1.48203i
$689$	491.624	+	851.518i	0.713533	+	1.23587i
$690$	−11.5743	+	4.82220i	−0.0167743	+	0.00698869i
$691$	−418.319	+	724.549i	−0.605382	+	1.04855i	0.386609	+	0.922244i	$0.373646\pi$
$691$	−418.319	+	724.549i	−0.605382	+	1.04855i	−0.991991	+	0.126308i	$0.959687\pi$
$692$	637.130	−	528.029i	0.920708	−	0.763048i
$693$	−672.565	+	816.860i	−0.970513	+	1.17873i
$694$	−268.709	+	244.723i	−0.387188	+	0.352627i
$695$	−1000.15	−	692.725i	−1.43907	−	0.996727i
$696$	19.9540	−	46.9538i	0.0286695	−	0.0674624i
$697$	−273.139	−	73.1873i	−0.391878	−	0.105003i
$698$	−1133.55	−	727.020i	−1.62400	−	1.04158i
$699$		−	6.78274i		−	0.00970349i
$700$	−70.3712	−	696.454i	−0.100530	−	0.994934i
$701$	664.227			0.947542			0.473771	−	0.880648i	$-0.342892\pi$
$701$	664.227			0.947542			0.473771	+	0.880648i	$0.342892\pi$
$702$	37.0467	−	57.7623i	0.0527731	−	0.0822825i
$703$	−35.2563	+	131.578i	−0.0501512	+	0.187167i
$704$	1046.31	−	259.942i	1.48623	−	0.369236i
$705$	−9.16028	+	13.2256i	−0.0129933	+	0.0187596i
$706$	139.356	+	153.014i	0.197388	+	0.216734i
$707$	−73.5064	+	440.841i	−0.103969	+	0.623538i
$708$	39.2665	−	32.5426i	0.0554611	−	0.0459641i
$709$	699.128	+	403.641i	0.986076	+	0.569311i	0.904099	−	0.427323i	$-0.140543\pi$
$709$	699.128	+	403.641i	0.986076	+	0.569311i	0.0819766	+	0.996634i	$0.473877\pi$
$710$	78.2385	+	187.789i	0.110195	+	0.264491i
$711$	65.8947	−	38.0443i	0.0926788	−	0.0535082i
$712$	−377.431	−	295.136i	−0.530099	−	0.414517i
$713$	10.6146	−	10.6146i	0.0148873	−	0.0148873i
$714$	48.1055	+	10.3491i	0.0673746	+	0.0144945i
$715$	635.763	+	749.858i	0.889179	+	1.04875i
$716$	435.842	−	614.439i	0.608718	−	0.858156i
$717$	7.46228	−	27.8496i	0.0104076	−	0.0388419i
$718$	−1116.05	+	576.660i	−1.55438	+	0.803148i
$719$	−803.403	−	463.845i	−1.11739	−	0.645125i	−0.176656	−	0.984273i	$-0.556528\pi$
$719$	−803.403	−	463.845i	−1.11739	−	0.645125i	−0.940733	+	0.339148i	$0.889861\pi$
$720$	−190.704	+	692.066i	−0.264866	+	0.961202i
$721$	507.352	−	1115.01i	0.703678	−	1.54648i
$722$	2.49668	−	53.4439i	0.00345800	−	0.0740221i
$723$	−2.99032	−	11.1600i	−0.00413598	−	0.0154357i
$724$	736.630	−	338.043i	1.01744	−	0.466911i
$725$	−912.544	+	342.740i	−1.25868	+	0.472745i
$726$	−11.3656	−	52.0170i	−0.0156551	−	0.0716487i
$727$	232.127	−	232.127i	0.319295	−	0.319295i	−0.529201	−	0.848496i	$-0.677508\pi$
$727$	232.127	−	232.127i	0.319295	−	0.319295i	0.848496	+	0.529201i	$0.177508\pi$
$728$	653.010	+	28.4026i	0.896992	+	0.0390145i
$729$			716.032i			0.982211i
$730$	−21.3567	+	2.85646i	−0.0292558	+	0.00391296i
$731$	−686.668	−	1189.34i	−0.939355	−	1.62701i
$732$	−53.8924	−	19.9882i	−0.0736235	−	0.0273063i
$733$	−101.102	−	377.319i	−0.137929	−	0.514759i	−0.999969	−	0.00791790i	$-0.997480\pi$
$733$	−101.102	−	377.319i	−0.137929	−	0.514759i	0.862039	−	0.506841i	$-0.169187\pi$
$734$	544.674	+	598.057i	0.742062	+	0.814792i
$735$	−25.0214	+	31.2987i	−0.0340427	+	0.0425832i
$736$	128.643	+	208.888i	0.174786	+	0.283815i
$737$	80.3716	+	299.951i	0.109052	+	0.406989i
$738$	−209.801	+	108.404i	−0.284283	+	0.146888i
$739$	349.608	+	605.539i	0.473083	+	0.819403i	0.999525	−	0.0308075i	$-0.00980788\pi$
$739$	349.608	+	605.539i	0.473083	+	0.819403i	−0.526443	+	0.850211i	$0.676475\pi$
$740$	−12.8411	−	148.462i	−0.0173528	−	0.200625i
$741$			34.9012i			0.0471001i
$742$	58.8217	+	1177.90i	0.0792745	+	1.58747i
$743$	−201.586	+	201.586i	−0.271314	+	0.271314i	−0.829629	−	0.558315i	$-0.811448\pi$
$743$	−201.586	+	201.586i	−0.271314	+	0.271314i	0.558315	+	0.829629i	$0.311448\pi$
$744$	0.311168	+	2.54307i	0.000418236	+	0.00341811i
$745$	581.938	−	274.991i	0.781125	−	0.369115i
$746$	24.2479	+	7.72668i	0.0325039	+	0.0103575i
$747$	268.729	+	1002.91i	0.359744	+	1.34258i
$748$	1114.90	−	923.984i	1.49050	−	1.23527i
$749$	327.396	−	719.521i	0.437111	−	0.960643i
$750$	−36.0341	+	19.3243i	−0.0480455	+	0.0257657i
$751$	833.759	+	481.371i	1.11020	+	0.640973i	0.938881	−	0.344243i	$-0.111864\pi$
$751$	833.759	+	481.371i	1.11020	+	0.640973i	0.171317	+	0.985216i	$0.445198\pi$
$752$	283.633	+	136.496i	0.377172	+	0.181510i
$753$	−13.6545	+	50.9594i	−0.0181335	+	0.0676752i
$754$	−194.295	−	889.231i	−0.257686	−	1.17935i
$755$	−88.0073	+	1068.80i	−0.116566	+	1.41563i
$756$	71.1491	−	41.3834i	0.0941125	−	0.0547400i
$757$	53.5524	−	53.5524i	0.0707429	−	0.0707429i	−0.670850	−	0.741593i	$-0.734071\pi$
$757$	53.5524	−	53.5524i	0.0707429	−	0.0707429i	0.741593	+	0.670850i	$0.234071\pi$
$758$	70.5545	+	45.2512i	0.0930799	+	0.0596981i
$759$	18.2922	−	10.5610i	0.0241004	−	0.0139144i
$760$	−217.089	−	698.334i	−0.285643	−	0.918861i
$761$	1061.73	+	612.992i	1.39518	+	0.805509i	0.993883	−	0.110438i	$-0.0352254\pi$
$761$	1061.73	+	612.992i	1.39518	+	0.805509i	0.401299	+	0.915947i	$0.368559\pi$
$762$	42.3210	+	1.97706i	0.0555393	+	0.00259456i
$763$	66.2098	−	397.081i	0.0867756	−	0.520421i
$764$	−95.1160	+	1015.81i	−0.124497	+	1.32959i
$765$	172.274	+	948.641i	0.225194	+	1.24005i
$766$	402.610	+	128.293i	0.525601	+	0.167485i
$767$	235.491	−	878.866i	0.307029	−	1.14585i
$768$	−41.6093	−	4.66531i	−0.0541787	−	0.00607463i
$769$	−698.248			−0.907995			−0.453997	−	0.891003i	$-0.650003\pi$
$769$	−698.248			−0.907995			−0.453997	+	0.891003i	$0.650003\pi$
$770$	268.299	+	1148.26i	0.348440	+	1.49124i
$771$			53.9048i			0.0699155i
$772$	106.993	−	18.1939i	0.138592	−	0.0235672i
$773$	592.833	+	158.849i	0.766925	+	0.205497i	0.621013	−	0.783801i	$-0.286722\pi$
$773$	592.833	+	158.849i	0.766925	+	0.205497i	0.145912	+	0.989298i	$0.453388\pi$
$774$	−1092.77	−	348.215i	−1.41185	−	0.449890i
$775$	31.0810	−	37.8192i	0.0401045	−	0.0487989i
$776$	−507.590	+	382.163i	−0.654111	+	0.492478i
$777$	−5.42211	+	6.58539i	−0.00697826	+	0.00847541i
$778$	−361.317	−	16.8792i	−0.464417	−	0.0216956i
$779$	120.286	−	208.342i	0.154411	−	0.267448i
$780$	−13.0229	−	35.8903i	−0.0166960	−	0.0460132i
$781$	−171.349	−	296.784i	−0.219396	−	0.380006i
$782$	277.350	+	177.883i	0.354668	+	0.227471i
$783$	−81.0483	−	81.0483i	−0.103510	−	0.103510i
$784$	681.470	+	387.627i	0.869222	+	0.494422i
$785$	−677.965	−	799.634i	−0.863650	−	1.01864i
$786$	−1.47760	−	6.76253i	−0.00187990	−	0.00860373i
$787$	945.013	+	253.215i	1.20078	+	0.321748i	0.803138	−	0.595793i	$-0.203162\pi$
$787$	945.013	+	253.215i	1.20078	+	0.321748i	0.397641	+	0.917541i	$0.369829\pi$
$788$	−236.827	−	87.8369i	−0.300542	−	0.111468i
$789$	12.5073	−	21.6634i	0.0158521	−	0.0274567i
$790$	10.8947	−	84.0921i	0.0137907	−	0.106446i
$791$	340.219	−	32.9602i	0.430112	−	0.0416691i
$792$	168.800	−	1197.43i	0.213132	−	1.51191i
$793$	−990.553	+	265.418i	−1.24912	+	0.334701i
$794$	508.897	+	162.162i	0.640928	+	0.204234i
$795$	62.2856	−	29.4327i	0.0783467	−	0.0370222i
$796$	60.1372	+	42.6573i	0.0755492	+	0.0535896i
$797$	658.777	+	658.777i	0.826571	+	0.826571i	0.987041	−	0.160470i	$-0.0513010\pi$
$797$	658.777	+	658.777i	0.826571	+	0.826571i	−0.160470	+	0.987041i	$0.551301\pi$
$798$	−19.0970	+	37.2529i	−0.0239311	+	0.0466828i
$799$	422.765			0.529117
$800$	483.814	+	637.121i	0.604768	+	0.796402i
$801$	−465.412	+	268.706i	−0.581039	+	0.335463i
$802$	−1220.95	+	630.860i	−1.52238	+	0.786609i
$803$	35.0601	−	9.39433i	0.0436614	−	0.0116990i
$804$	1.12433	−	12.0074i	0.00139842	−	0.0149346i
$805$	−230.415	+	137.498i	−0.286229	+	0.170805i
$806$	30.7779	+	33.7944i	0.0381859	+	0.0419286i
$807$	65.6512	−	17.5912i	0.0813522	−	0.0217982i
$808$	−191.141	−	473.662i	−0.236560	−	0.586215i
$809$	953.428	−	550.462i	1.17853	−	0.680422i	0.222853	−	0.974852i	$-0.428463\pi$
$809$	953.428	−	550.462i	1.17853	−	0.680422i	0.955673	+	0.294430i	$0.0951297\pi$
$810$	637.898	+	487.391i	0.787528	+	0.601717i
$811$	−620.055			−0.764556			−0.382278	−	0.924047i	$-0.624860\pi$
$811$	−620.055			−0.764556			−0.382278	+	0.924047i	$0.624860\pi$
$812$	279.177	−	1055.46i	0.343814	−	1.29983i
$813$	−39.4531	−	39.4531i	−0.0485278	−	0.0485278i
$814$	53.5847	+	245.241i	0.0658289	+	0.301279i
$815$	81.1962	+	29.0840i	0.0996272	+	0.0356859i
$816$	−53.0747	+	18.5879i	−0.0650426	+	0.0227792i
$817$	1128.57	−	302.399i	1.38136	−	0.370133i
$818$	17.8008	−	381.045i	0.0217614	−	0.465826i
$819$	303.640	−	667.311i	0.370745	−	0.814788i
$820$	−45.9555	+	259.130i	−0.0560432	+	0.316012i
$821$	212.403	−	367.893i	0.258712	−	0.448103i	−0.707185	−	0.707029i	$-0.750035\pi$
$821$	212.403	−	367.893i	0.258712	−	0.448103i	0.965897	+	0.258926i	$0.0833685\pi$
$822$	8.26577	−	4.27091i	0.0100557	−	0.00519576i
$823$	486.314	+	130.307i	0.590904	+	0.158332i	0.541866	−	0.840465i	$-0.317718\pi$
$823$	486.314	+	130.307i	0.590904	+	0.158332i	0.0490374	+	0.998797i	$0.484385\pi$
$824$	170.036	+	1389.65i	0.206355	+	1.68647i
$825$	56.0158	−	40.0820i	0.0678979	−	0.0485842i
$826$	732.253	−	809.231i	0.886505	−	0.979699i
$827$	−512.054	−	512.054i	−0.619171	−	0.619171i	0.326148	−	0.945319i	$-0.394249\pi$
$827$	−512.054	−	512.054i	−0.619171	−	0.619171i	−0.945319	+	0.326148i	$0.894249\pi$
$828$	271.274	−	46.1292i	0.327625	−	0.0557116i
$829$	676.711	+	1172.10i	0.816298	+	1.41387i	0.908392	+	0.418120i	$0.137311\pi$
$829$	676.711	+	1172.10i	0.816298	+	1.41387i	−0.0920935	+	0.995750i	$0.529356\pi$
$830$	1069.92	+	440.596i	1.28907	+	0.530838i
$831$	7.45259	−	12.9083i	0.00896822	−	0.0155334i
$832$	−653.647	+	361.606i	−0.785633	+	0.434623i
$833$	1050.51	+	72.2236i	1.26112	+	0.0867030i
$834$	−53.5936	−	58.8464i	−0.0642610	−	0.0705592i
$835$	95.0946	+	523.648i	0.113886	+	0.627123i
$836$	513.811	+	1119.64i	0.614607	+	1.33929i
$837$	5.55989	+	1.48977i	0.00664264	+	0.00177989i
$838$	718.200	−	1119.80i	0.857040	−	1.33628i
$839$			21.8915i			0.0260923i	0.999915	+	0.0130462i	$0.00415284\pi$
$839$			21.8915i			0.0260923i	−0.999915	+	0.0130462i	$0.995847\pi$
$840$	5.73788	−	45.4344i	0.00683081	−	0.0540886i
$841$	−679.333			−0.807768
$842$	−584.999	−	375.198i	−0.694773	−	0.445603i
$843$	−0.0556200	+	0.207577i	−6.59786e−5	+	0.000246235i
$844$	−622.299	+	285.576i	−0.737321	+	0.338361i
$845$	134.682	+	93.2831i	0.159387	+	0.110394i
$846$	261.030	−	237.730i	0.308546	−	0.281005i
$847$	−399.651	−	1067.01i	−0.471844	−	1.25976i
$848$	−759.573	−	1113.44i	−0.895723	−	1.31302i
$849$	50.6173	+	29.2239i	0.0596200	+	0.0344216i
$850$	956.608	+	489.292i	1.12542	+	0.575638i
$851$	−49.4679	+	28.5603i	−0.0581292	+	0.0335609i
$852$	2.23114	+	13.1208i	0.00261871	+	0.0154000i
$853$	−120.495	+	120.495i	−0.141261	+	0.141261i	−0.774201	−	0.632940i	$-0.781848\pi$
$853$	−120.495	+	120.495i	−0.141261	+	0.141261i	0.632940	+	0.774201i	$0.281848\pi$
$854$	−1202.53	−	258.703i	−1.40811	−	0.302931i
$855$	−817.499	−	67.3146i	−0.956140	−	0.0787305i
$856$	109.725	+	896.747i	0.128183	+	1.04760i
$857$	211.891	−	790.786i	0.247247	−	0.922738i	−0.724994	−	0.688755i	$-0.758157\pi$
$857$	211.891	−	790.786i	0.247247	−	0.922738i	0.972241	−	0.233982i	$-0.0751758\pi$
$858$	29.5238	+	57.1394i	0.0344100	+	0.0665960i
$859$	−834.691	−	481.909i	−0.971700	−	0.561012i	−0.0719462	−	0.997409i	$-0.522921\pi$
$859$	−834.691	−	481.909i	−0.971700	−	0.561012i	−0.899754	+	0.436397i	$0.856254\pi$
$860$	−1047.72	+	732.078i	−1.21827	+	0.851253i
$861$	12.2596	−	8.75553i	0.0142388	−	0.0101690i
$862$	428.313	+	20.0090i	0.496883	+	0.0232123i
$863$	−41.0729	−	153.286i	−0.0475931	−	0.177620i	0.938038	−	0.346533i	$-0.112641\pi$
$863$	−41.0729	−	153.286i	−0.0475931	−	0.177620i	−0.985631	+	0.168913i	$0.945974\pi$
$864$	−44.7023	+	82.7671i	−0.0517388	+	0.0957953i
$865$	−973.784	−	348.804i	−1.12576	−	0.403242i
$866$	365.212	−	79.7982i	0.421723	−	0.0921458i
$867$	−19.9847	+	19.9847i	−0.0230504	+	0.0230504i
$868$	14.3603	+	52.9124i	0.0165441	+	0.0609590i
$869$			142.841i			0.164375i
$870$	−63.2095	+	8.45426i	−0.0726546	+	0.00971754i
$871$	−107.581	−	186.335i	−0.123514	−	0.213932i
$872$	172.167	+	426.644i	0.197440	+	0.489271i
$873$	184.452	+	688.385i	0.211285	+	0.788528i
$874$	−207.249	+	188.750i	−0.237127	+	0.215961i
$875$	−704.175	+	519.387i	−0.804771	+	0.593585i
$876$	−1.40350	−	0.131418i	−0.00160217	−	0.000150021i
$877$	−59.5170	−	222.121i	−0.0678644	−	0.253273i	0.923656	−	0.383222i	$-0.125185\pi$
$877$	−59.5170	−	222.121i	−0.0678644	−	0.253273i	−0.991521	+	0.129948i	$0.958519\pi$
$878$	−280.873	−	543.591i	−0.319901	−	0.619125i
$879$	11.8555	+	20.5343i	0.0134875	+	0.0233610i
$880$	−946.152	−	959.654i	−1.07517	−	1.09052i
$881$		−	1332.64i		−	1.51265i	−0.654198	−	0.756323i	$-0.726994\pi$
$881$		−	1332.64i		−	1.51265i	0.654198	−	0.756323i	$-0.273006\pi$
$882$	689.236	−	546.132i	0.781447	−	0.619198i
$883$	−573.866	+	573.866i	−0.649905	+	0.649905i	−0.952970	−	0.303065i	$-0.901990\pi$
$883$	−573.866	+	573.866i	−0.649905	+	0.649905i	0.303065	+	0.952970i	$0.401990\pi$
$884$	−580.469	+	818.330i	−0.656639	+	0.925712i
$885$	−60.0146	−	21.4969i	−0.0678131	−	0.0242903i
$886$	460.661	−	1445.65i	0.519933	−	1.63166i
$887$	98.9533	+	369.299i	0.111559	+	0.416346i	0.999007	−	0.0445640i	$-0.0141899\pi$
$887$	98.9533	+	369.299i	0.111559	+	0.416346i	−0.887447	+	0.460910i	$0.847523\pi$
$888$	1.36084	−	9.65351i	0.00153248	−	0.0108711i
$889$	902.413	−	87.4254i	1.01509	−	0.0983413i
$890$	−76.9487	+	593.940i	−0.0864592	+	0.667349i
$891$	−1171.15	−	676.166i	−1.31443	−	0.758885i
$892$	29.7660	−	80.2554i	0.0333699	−	0.0899724i
$893$	−93.0898	+	347.416i	−0.104244	+	0.389043i
$894$	41.1376	−	8.98849i	0.0460152	−	0.0100542i
$895$	−938.477	−	77.2761i	−1.04858	−	0.0863420i
$896$	−895.553	+	28.3129i	−0.999501	+	0.0315992i
$897$	−10.3485	+	10.3485i	−0.0115368	+	0.0115368i
$898$	156.007	−	243.242i	0.173727	−	0.270871i
$899$	66.1199	−	38.1744i	0.0735483	−	0.0424631i
$900$	865.785	−	235.816i	0.961983	−	0.262017i
$901$	−1567.76	−	905.146i	−1.74002	−	1.00460i
$902$	20.6879	−	442.846i	0.0229356	−	0.490960i
$903$	72.1698	+	12.0337i	0.0799222	+	0.0133263i
$904$	−312.079	+	234.963i	−0.345220	+	0.259915i
$905$	−832.853	−	576.851i	−0.920280	−	0.637404i
$906$	−21.3013	+	66.8478i	−0.0235114	+	0.0737834i
$907$	−274.001	+	1022.59i	−0.302096	+	1.12744i	0.633321	+	0.773890i	$0.281691\pi$
$907$	−274.001	+	1022.59i	−0.302096	+	1.12744i	−0.935416	+	0.353548i	$0.884975\pi$
$908$	100.177	+	589.117i	0.110328	+	0.648807i
$909$	−572.913			−0.630268
$910$	−385.482	−	720.381i	−0.423606	−	0.791627i
$911$		−	606.894i		−	0.666184i	−0.942894	−	0.333092i	$-0.891908\pi$
$911$		−	606.894i		−	0.666184i	0.942894	−	0.333092i	$-0.108092\pi$
$912$	−3.58829	−	47.7082i	−0.00393453	−	0.0523116i
$913$	−1882.77	−	504.486i	−2.06218	−	0.552558i
$914$	−266.751	+	837.120i	−0.291850	+	0.915886i
$915$	12.8380	+	70.6935i	0.0140306	+	0.0772606i
$916$	−22.8693	−	2.14139i	−0.0249665	−	0.00233776i
$917$	−51.9572	−	138.718i	−0.0566600	−	0.151274i
$918$	−5.89574	+	126.204i	−0.00642237	+	0.137477i
$919$	244.101	−	422.795i	0.265616	−	0.460060i	−0.702109	−	0.712069i	$-0.747758\pi$
$919$	244.101	−	422.795i	0.265616	−	0.460060i	0.967725	+	0.252010i	$0.0810915\pi$
$920$	142.693	−	271.431i	0.155102	−	0.295034i
$921$	−5.28779	−	9.15872i	−0.00574136	−	0.00994433i
$922$	21.4476	−	33.4405i	0.0232620	−	0.0362695i
$923$	167.901	+	167.901i	0.181908	+	0.181908i
$924$	0.247977	+	77.1442i	0.000268373	+	0.0834894i
$925$	−151.484	+	108.394i	−0.163767	+	0.117183i
$926$	−1567.97	+	342.599i	−1.69327	+	0.369977i
$927$	1516.83	+	406.432i	1.63627	+	0.438438i
$928$	357.017	+	1195.56i	0.384716	+	1.28832i
$929$	609.539	−	1055.75i	0.656124	−	1.13644i	−0.325487	−	0.945546i	$-0.605528\pi$
$929$	609.539	−	1055.75i	0.656124	−	1.13644i	0.981611	−	0.190893i	$-0.0611383\pi$
$930$	2.53673	−	1.95482i	0.00272766	−	0.00210196i
$931$	−290.666	+	847.375i	−0.312208	+	0.910178i
$932$	105.851	+	127.722i	0.113574	+	0.137040i
$933$	−34.1183	+	9.14196i	−0.0365683	+	0.00979846i
$934$	−292.166	+	916.877i	−0.312812	+	0.981667i
$935$	−1704.00	−	610.363i	−1.82246	−	0.652795i
$936$	101.763	+	831.677i	0.108721	+	0.888544i
$937$	601.774	+	601.774i	0.642235	+	0.642235i	0.951104	−	0.308869i	$-0.0999506\pi$
$937$	601.774	+	601.774i	0.642235	+	0.642235i	−0.308869	+	0.951104i	$0.599951\pi$
$938$	−12.8718	−	257.756i	−0.0137226	−	0.274793i
$939$	12.2424			0.0130377
$940$	−33.9052	−	391.997i	−0.0360694	−	0.417018i
$941$	−213.349	+	123.177i	−0.226726	+	0.130900i	−0.609061	−	0.793124i	$-0.708453\pi$
$941$	−213.349	+	123.177i	−0.226726	+	0.130900i	0.382335	+	0.924024i	$0.375120\pi$
$942$	−31.4836	−	60.9323i	−0.0334221	−	0.0646840i
$943$	97.4413	−	26.1093i	0.103331	−	0.0276875i
$944$	−231.547	+	1225.58i	−0.245282	+	1.29828i
$945$	−89.8348	−	50.1529i	−0.0950632	−	0.0530718i
$946$	1591.86	−	1449.77i	1.68272	−	1.53252i
$947$	−53.9826	+	14.4646i	−0.0570038	+	0.0152741i	−0.287208	−	0.957868i	$-0.592727\pi$
$947$	−53.9826	+	14.4646i	−0.0570038	+	0.0152741i	0.230204	+	0.973142i	$0.426061\pi$
$948$	1.92909	−	5.20123i	0.00203490	−	0.00548652i
$949$	−21.7800	+	12.5747i	−0.0229505	+	0.0132505i
$950$	−612.724	+	678.374i	−0.644973	+	0.714078i
$951$	−28.6136			−0.0300879
$952$	−1067.35	+	555.853i	−1.12117	+	0.583879i
$953$	356.199	+	356.199i	0.373766	+	0.373766i	0.868847	−	0.495081i	$-0.164862\pi$
$953$	356.199	+	356.199i	0.373766	+	0.373766i	−0.495081	+	0.868847i	$0.664862\pi$
$954$	−1476.98	+	322.717i	−1.54819	+	0.338278i
$955$	1153.06	−	544.869i	1.20739	−	0.570544i
$956$	294.101	+	640.875i	0.307637	+	0.670371i
$957$	103.767	−	27.8044i	0.108430	−	0.0290537i
$958$	−584.183	−	27.2906i	−0.609795	−	0.0284871i
$959$	162.023	−	115.713i	0.168950	−	0.120660i
$960$	21.4916	+	47.7213i	0.0223871	+	0.0497097i
$961$	478.583	−	828.930i	0.498005	−	0.862570i
$962$	−79.8417	−	154.523i	−0.0829956	−	0.160627i
$963$	978.815	+	262.273i	1.01642	+	0.272350i
$964$	230.471	+	163.481i	0.239078	+	0.169586i
$965$	−87.7313	−	103.476i	−0.0909133	−	0.107229i
$966$	−16.7083	+	5.38337i	−0.0172963	+	0.00557285i
$967$	−640.150	−	640.150i	−0.661995	−	0.661995i	0.293855	−	0.955850i	$-0.405062\pi$
$967$	−640.150	−	640.150i	−0.661995	−	0.661995i	−0.955850	+	0.293855i	$0.905062\pi$
$968$	1025.79	+	802.129i	1.05970	+	0.828645i
$969$	−32.1289	−	55.6489i	−0.0331568	−	0.0574292i
$970$	734.383	+	302.420i	0.757096	+	0.311773i
$971$	318.849	−	552.262i	0.328371	−	0.568756i	−0.653817	−	0.756652i	$-0.726834\pi$
$971$	318.849	−	552.262i	0.328371	−	0.568756i	0.982189	+	0.187896i	$0.0601669\pi$
$972$	101.041	+	121.918i	0.103952	+	0.125430i
$973$	−1314.92	−	1082.65i	−1.35141	−	1.11269i
$974$	880.645	−	802.038i	0.904153	−	0.823447i
$975$	−30.3018	+	36.8710i	−0.0310787	+	0.0378164i
$976$	1326.75	−	464.655i	1.35937	−	0.476081i
$977$	−910.282	−	243.909i	−0.931712	−	0.249651i	−0.239127	−	0.970988i	$-0.576861\pi$
$977$	−910.282	−	243.909i	−0.931712	−	0.249651i	−0.692584	+	0.721337i	$0.743528\pi$
$978$	4.74957	+	3.04621i	0.00485641	+	0.00311473i
$979$		−	1008.89i		−	1.03053i
$980$	−17.2823	−	979.848i	−0.0176350	−	0.999844i
$981$	516.043			0.526038
$982$	551.768	−	860.303i	0.561882	−	0.876073i
$983$	−170.561	+	636.543i	−0.173511	+	0.647551i	0.823290	+	0.567622i	$0.192136\pi$
$983$	−170.561	+	636.543i	−0.173511	+	0.647551i	−0.996800	+	0.0799298i	$0.974530\pi$
$984$	−6.73397	+	15.8458i	−0.00684347	+	0.0161034i
$985$	56.4156	+	310.658i	0.0572747	+	0.315389i
$986$	1128.40	+	1238.99i	1.14442	+	1.25658i
$987$	−14.3164	+	17.3879i	−0.0145050	+	0.0176169i
$988$	−544.665	−	657.203i	−0.551280	−	0.665185i
$989$	424.295	+	244.967i	0.429014	+	0.247691i
$990$	−1395.33	+	581.338i	−1.40943	+	0.587210i
$991$	−917.099	+	529.487i	−0.925428	+	0.534296i	−0.885363	−	0.464901i	$-0.846090\pi$
$991$	−917.099	+	529.487i	−0.925428	+	0.534296i	−0.0400650	+	0.999197i	$0.512757\pi$
$992$	−45.5463	−	43.0310i	−0.0459136	−	0.0433780i
$993$	18.1555	−	18.1555i	0.0182835	−	0.0182835i
$994$	87.3433	+	271.086i	0.0878705	+	0.272722i
$995$	7.56327	−	91.8518i	0.00760127	−	0.0923133i
$996$	61.7432	+	43.7965i	0.0619912	+	0.0439724i
$997$	88.3154	−	329.598i	0.0885811	−	0.330589i	−0.907387	−	0.420296i	$-0.861926\pi$
$997$	88.3154	−	329.598i	0.0885811	−	0.330589i	0.995968	+	0.0897066i	$0.0285929\pi$
$998$	367.967	−	190.128i	0.368705	−	0.190509i
$999$	−18.9682	−	10.9513i	−0.0189872	−	0.0109622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.3.x.a.103.37	yes	176
4.3	odd	2	inner	140.3.x.a.103.16	yes	176
5.2	odd	4	inner	140.3.x.a.47.15	yes	176
7.3	odd	6	inner	140.3.x.a.3.8	✓	176
20.7	even	4	inner	140.3.x.a.47.8	yes	176
28.3	even	6	inner	140.3.x.a.3.15	yes	176
35.17	even	12	inner	140.3.x.a.87.16	yes	176
140.87	odd	12	inner	140.3.x.a.87.37	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.x.a.3.8	✓	176	7.3	odd	6	inner
140.3.x.a.3.15	yes	176	28.3	even	6	inner
140.3.x.a.47.8	yes	176	20.7	even	4	inner
140.3.x.a.47.15	yes	176	5.2	odd	4	inner
140.3.x.a.87.16	yes	176	35.17	even	12	inner
140.3.x.a.87.37	yes	176	140.87	odd	12	inner
140.3.x.a.103.16	yes	176	4.3	odd	2	inner
140.3.x.a.103.37	yes	176	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	140.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.68350 + 1.07974i) q^{2} +(0.0423311 - 0.157982i) q^{3} +(1.66834 + 3.63547i) q^{4} +(2.84692 - 4.11036i) q^{5} +(0.241843 - 0.220256i) q^{6} +(4.44939 - 5.40398i) q^{7} +(-1.11671 + 7.92168i) q^{8} +(7.77106 + 4.48662i) q^{9} +O(q^{10})\)	\(q+(1.68350 + 1.07974i) q^{2} +(0.0423311 - 0.157982i) q^{3} +(1.66834 + 3.63547i) q^{4} +(2.84692 - 4.11036i) q^{5} +(0.241843 - 0.220256i) q^{6} +(4.44939 - 5.40398i) q^{7} +(-1.11671 + 7.92168i) q^{8} +(7.77106 + 4.48662i) q^{9} +(9.23089 - 3.84587i) q^{10} +(-14.5887 + 8.42276i) q^{11} +(0.644960 - 0.109673i) q^{12} +(8.25329 - 8.25329i) q^{13} +(13.3254 - 4.29342i) q^{14} +(-0.528849 - 0.623757i) q^{15} +(-10.4333 + 12.1304i) q^{16} +(-5.56191 + 20.7573i) q^{17} +(8.23820 + 15.9439i) q^{18} +(-15.8331 - 9.14124i) q^{19} +(19.6927 + 3.49241i) q^{20} +(-0.665382 - 0.931678i) q^{21} +(-33.6544 - 1.57219i) q^{22} +(-1.98419 - 7.40511i) q^{23} +(1.20421 + 0.511752i) q^{24} +(-8.79013 - 23.4037i) q^{25} +(22.8058 - 4.98303i) q^{26} +(2.07862 - 2.07862i) q^{27} +(27.0691 + 7.15996i) q^{28} -38.9914i q^{29} +(-0.216823 - 1.62111i) q^{30} +(0.979045 + 1.69575i) q^{31} +(-30.6621 + 9.15628i) q^{32} +(0.713089 + 2.66128i) q^{33} +(-31.7759 + 28.9396i) q^{34} +(-9.54526 - 33.6733i) q^{35} +(-3.34624 + 35.7367i) q^{36} +(-1.92842 - 7.19696i) q^{37} +(-16.7849 - 32.4848i) q^{38} +(-0.954498 - 1.65324i) q^{39} +(29.3818 + 27.1424i) q^{40} +13.1587i q^{41} +(-0.114203 - 2.28692i) q^{42} +(-45.1891 + 45.1891i) q^{43} +(-54.9595 - 38.9846i) q^{44} +(40.5652 - 19.1688i) q^{45} +(4.65518 - 14.6089i) q^{46} +(-5.09175 - 19.0027i) q^{47} +(1.47473 + 2.16176i) q^{48} +(-9.40592 - 48.0888i) q^{49} +(10.4717 - 48.8911i) q^{50} +(3.04384 + 1.75736i) q^{51} +(43.7739 + 16.2353i) q^{52} +(-21.8030 + 81.3701i) q^{53} +(5.74371 - 1.25499i) q^{54} +(-6.91209 + 83.9435i) q^{55} +(37.8399 + 41.2813i) q^{56} +(-2.11438 + 2.11438i) q^{57} +(42.1005 - 65.6421i) q^{58} +(67.5099 - 38.9769i) q^{59} +(1.38535 - 2.96325i) q^{60} +(-76.0891 - 43.9301i) q^{61} +(-0.182748 + 3.91191i) q^{62} +(58.8221 - 22.0319i) q^{63} +(-61.5059 - 17.6924i) q^{64} +(-10.4276 - 57.4204i) q^{65} +(-1.67300 + 5.25022i) q^{66} +(4.77110 - 17.8060i) q^{67} +(-84.7419 + 14.4101i) q^{68} -1.25387 q^{69} +(20.2888 - 66.9953i) q^{70} +20.3435i q^{71} +(-44.2196 + 56.5496i) q^{72} +(-2.08127 - 0.557675i) q^{73} +(4.52433 - 14.1983i) q^{74} +(-4.06945 + 0.397976i) q^{75} +(6.81777 - 72.8114i) q^{76} +(-19.3941 + 116.313i) q^{77} +(0.178166 - 3.81383i) q^{78} +(4.23975 - 7.34345i) q^{79} +(20.1575 + 77.4188i) q^{80} +(40.1392 + 69.5232i) q^{81} +(-14.2079 + 22.1526i) q^{82} +(81.8188 + 81.8188i) q^{83} +(2.27701 - 3.97333i) q^{84} +(69.4859 + 81.9559i) q^{85} +(-124.868 + 27.2835i) q^{86} +(-6.15994 - 1.65055i) q^{87} +(-50.4312 - 124.972i) q^{88} +(-29.9452 + 51.8666i) q^{89} +(88.9888 + 11.5291i) q^{90} +(-7.87851 - 81.3227i) q^{91} +(23.6108 - 19.5677i) q^{92} +(0.309342 - 0.0828880i) q^{93} +(11.9459 - 37.4887i) q^{94} +(-82.6493 + 39.0554i) q^{95} +(0.148566 + 5.23164i) q^{96} +(56.1594 + 56.1594i) q^{97} +(36.0883 - 91.1133i) q^{98} -151.159 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more