LMFDB - Embedded newform 384.3.u.a.235.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,3,Mod(19,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 23, 0]))

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

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

chi := DirichletCharacter("384.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	384.u (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:	$10.4632421514$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			235.2
Character	$\chi$	$=$	384.235
Dual form			384.3.u.a.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98371 + 0.254711i) q^{2} +(-1.09880 + 1.33889i) q^{3} +(3.87024 - 1.01055i) q^{4} +(0.233043 + 0.768239i) q^{5} +(1.83868 - 2.93586i) q^{6} +(0.291260 - 1.46426i) q^{7} +(-7.42006 + 2.99044i) q^{8} +(-0.585271 - 2.94236i) q^{9} +O(q^{10})$	\(q+(-1.98371 + 0.254711i) q^{2} +(-1.09880 + 1.33889i) q^{3} +(3.87024 - 1.01055i) q^{4} +(0.233043 + 0.768239i) q^{5} +(1.83868 - 2.93586i) q^{6} +(0.291260 - 1.46426i) q^{7} +(-7.42006 + 2.99044i) q^{8} +(-0.585271 - 2.94236i) q^{9} +(-0.657970 - 1.46461i) q^{10} +(1.24129 + 0.122256i) q^{11} +(-2.89961 + 6.29224i) q^{12} +(14.9500 + 4.53503i) q^{13} +(-0.204812 + 2.97886i) q^{14} +(-1.28466 - 0.532123i) q^{15} +(13.9576 - 7.82214i) q^{16} +(-9.47821 - 22.8824i) q^{17} +(1.91046 + 5.68772i) q^{18} +(-8.43352 + 4.50781i) q^{19} +(1.67828 + 2.73777i) q^{20} +(1.64045 + 1.99890i) q^{21} +(-2.49350 + 0.0736488i) q^{22} +(15.6138 + 10.4328i) q^{23} +(4.14930 - 13.2206i) q^{24} +(20.2509 - 13.5312i) q^{25} +(-30.8116 - 5.18827i) q^{26} +(4.58260 + 2.44945i) q^{27} +(-0.352462 - 5.96138i) q^{28} +(-32.8080 + 3.23131i) q^{29} +(2.68393 + 0.728363i) q^{30} +(19.8175 - 19.8175i) q^{31} +(-25.6955 + 19.0721i) q^{32} +(-1.52762 + 1.52762i) q^{33} +(24.6305 + 42.9780i) q^{34} +(1.19278 - 0.117478i) q^{35} +(-5.23854 - 10.7962i) q^{36} +(14.6893 + 7.85161i) q^{37} +(15.5815 - 11.0903i) q^{38} +(-22.4990 + 15.0333i) q^{39} +(-4.02656 - 5.00348i) q^{40} +(38.1400 + 25.4844i) q^{41} +(-3.76333 - 3.54740i) q^{42} +(10.4203 + 12.6972i) q^{43} +(4.92763 - 0.781221i) q^{44} +(2.12404 - 1.13532i) q^{45} +(-33.6306 - 16.7187i) q^{46} +(17.6180 + 42.5336i) q^{47} +(-4.86359 + 27.2827i) q^{48} +(43.2109 + 17.8985i) q^{49} +(-36.7254 + 32.0001i) q^{50} +(41.0518 + 12.4529i) q^{51} +(62.4430 + 2.44397i) q^{52} +(95.6561 + 9.42130i) q^{53} +(-9.71447 - 3.69177i) q^{54} +(0.195351 + 0.982097i) q^{55} +(2.21761 + 11.7359i) q^{56} +(3.23129 - 16.2448i) q^{57} +(64.2587 - 14.7666i) q^{58} +(15.1039 + 49.7909i) q^{59} +(-5.50968 - 0.761235i) q^{60} +(61.8333 - 75.3440i) q^{61} +(-34.2645 + 44.3599i) q^{62} -4.47884 q^{63} +(46.1146 - 44.3784i) q^{64} +12.5420i q^{65} +(2.64125 - 3.41946i) q^{66} +(71.8329 + 58.9517i) q^{67} +(-59.8068 - 78.9824i) q^{68} +(-31.1249 + 9.44162i) q^{69} +(-2.33621 + 0.536858i) q^{70} +(-101.609 - 20.2113i) q^{71} +(13.1417 + 20.0822i) q^{72} +(-14.9042 + 2.96463i) q^{73} +(-31.1393 - 11.8338i) q^{74} +(-4.13485 + 41.9818i) q^{75} +(-28.0844 + 25.9688i) q^{76} +(0.540552 - 1.78196i) q^{77} +(40.8024 - 35.5526i) q^{78} +(-28.4796 + 68.7559i) q^{79} +(9.26199 + 8.89987i) q^{80} +(-8.31492 + 3.44415i) q^{81} +(-82.1501 - 40.8390i) q^{82} +(32.6268 + 61.0404i) q^{83} +(8.36893 + 6.07846i) q^{84} +(15.3703 - 12.6141i) q^{85} +(-23.9050 - 22.5334i) q^{86} +(31.7231 - 47.4770i) q^{87} +(-9.57603 + 2.80484i) q^{88} +(-44.8198 - 67.0775i) q^{89} +(-3.92431 + 2.79317i) q^{90} +(10.9948 - 20.5698i) q^{91} +(70.9720 + 24.5990i) q^{92} +(4.75802 + 48.3090i) q^{93} +(-45.7829 - 79.8871i) q^{94} +(-5.42845 - 5.42845i) q^{95} +(2.69877 - 55.3599i) q^{96} +(3.45702 + 3.45702i) q^{97} +(-90.2770 - 24.4993i) q^{98} +(-0.366769 - 3.72386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 1248 q^{50} + 1056 q^{52} + 288 q^{54} + 1568 q^{56} + 576 q^{60} + 192 q^{62} - 192 q^{64} - 576 q^{66} - 960 q^{68} - 1344 q^{70} - 2464 q^{74} - 416 q^{76} - 1440 q^{78} - 1632 q^{80}+O(q^{100}) $ 1024 * q + 1248 * q^50 + 1056 * q^52 + 288 * q^54 + 1568 * q^56 + 576 * q^60 + 192 * q^62 - 192 * q^64 - 576 * q^66 - 960 * q^68 - 1344 * q^70 - 2464 * q^74 - 416 * q^76 - 1440 * q^78 - 1632 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{13}{32}\right)$	$1$

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 $

$2$	−1.98371	+	0.254711i	−0.991857	+	0.127356i
$2$	−1.98371	+	0.254711i	−0.991857	+	0.127356i
$3$	−1.09880	+	1.33889i	−0.366267	+	0.446298i
$3$	−1.09880	+	1.33889i	−0.366267	+	0.446298i
$4$	3.87024	−	1.01055i	0.967561	−	0.252637i
$5$	0.233043	+	0.768239i	0.0466086	+	0.153648i	0.977156	−	0.212524i	$-0.0681683\pi$
$5$	0.233043	+	0.768239i	0.0466086	+	0.153648i	−0.930547	+	0.366172i	$0.880668\pi$
$6$	1.83868	−	2.93586i	0.306446	−	0.489310i
$7$	0.291260	−	1.46426i	0.0416085	−	0.209180i	−0.954388	−	0.298568i	$-0.903491\pi$
$7$	0.291260	−	1.46426i	0.0416085	−	0.209180i	0.995997	+	0.0893878i	$0.0284911\pi$
$8$	−7.42006	+	2.99044i	−0.927508	+	0.373804i
$9$	−0.585271	−	2.94236i	−0.0650301	−	0.326928i
$10$	−0.657970	−	1.46461i	−0.0657970	−	0.146461i
$11$	1.24129	+	0.122256i	0.112844	+	0.0111142i	0.154282	−	0.988027i	$-0.450694\pi$
$11$	1.24129	+	0.122256i	0.112844	+	0.0111142i	−0.0414373	+	0.999141i	$0.513194\pi$
$12$	−2.89961	+	6.29224i	−0.241634	+	0.524353i
$13$	14.9500	+	4.53503i	1.15000	+	0.348848i	0.807037	−	0.590501i	$-0.201070\pi$
$13$	14.9500	+	4.53503i	1.15000	+	0.348848i	0.342962	+	0.939349i	$0.388570\pi$
$14$	−0.204812	+	2.97886i	−0.0146294	+	0.212776i
$15$	−1.28466	−	0.532123i	−0.0856439	−	0.0354749i
$16$	13.9576	−	7.82214i	0.872349	−	0.488884i
$17$	−9.47821	−	22.8824i	−0.557542	−	1.34602i	−0.911707	−	0.410842i	$-0.865235\pi$
$17$	−9.47821	−	22.8824i	−0.557542	−	1.34602i	0.354165	−	0.935183i	$-0.384765\pi$
$18$	1.91046	+	5.68772i	0.106137	+	0.315984i
$19$	−8.43352	+	4.50781i	−0.443869	+	0.237253i	−0.678161	−	0.734913i	$-0.737223\pi$
$19$	−8.43352	+	4.50781i	−0.443869	+	0.237253i	0.234292	+	0.972166i	$0.424723\pi$
$20$	1.67828	+	2.73777i	0.0839138	+	0.136889i
$21$	1.64045	+	1.99890i	0.0781168	+	0.0951856i
$22$	−2.49350	+	0.0736488i	−0.113341	+	0.00334767i
$23$	15.6138	+	10.4328i	0.678860	+	0.453600i	0.846599	−	0.532232i	$-0.178646\pi$
$23$	15.6138	+	10.4328i	0.678860	+	0.453600i	−0.167738	+	0.985832i	$0.553646\pi$
$24$	4.14930	−	13.2206i	0.172887	−	0.550857i
$25$	20.2509	−	13.5312i	0.810034	−	0.541248i
$26$	−30.8116	−	5.18827i	−1.18506	−	0.199549i
$27$	4.58260	+	2.44945i	0.169726	+	0.0907203i
$28$	−0.352462	−	5.96138i	−0.0125879	−	0.212906i
$29$	−32.8080	+	3.23131i	−1.13131	+	0.111424i	−0.646300	−	0.763084i	$-0.723684\pi$
$29$	−32.8080	+	3.23131i	−1.13131	+	0.111424i	−0.485011	+	0.874508i	$0.661184\pi$
$30$	2.68393	+	0.728363i	0.0894644	+	0.0242788i
$31$	19.8175	−	19.8175i	0.639273	−	0.639273i	−0.311103	−	0.950376i	$-0.600698\pi$
$31$	19.8175	−	19.8175i	0.639273	−	0.639273i	0.950376	+	0.311103i	$0.100698\pi$
$32$	−25.6955	+	19.0721i	−0.802983	+	0.596002i
$33$	−1.52762	+	1.52762i	−0.0462914	+	0.0462914i
$34$	24.6305	+	42.9780i	0.724426	+	1.26406i
$35$	1.19278	−	0.117478i	0.0340794	−	0.00335653i
$36$	−5.23854	−	10.7962i	−0.145515	−	0.299894i
$37$	14.6893	+	7.85161i	0.397009	+	0.212206i	0.657805	−	0.753188i	$-0.271485\pi$
$37$	14.6893	+	7.85161i	0.397009	+	0.212206i	−0.260796	+	0.965394i	$0.583985\pi$
$38$	15.5815	−	11.0903i	0.410040	−	0.291851i
$39$	−22.4990	+	15.0333i	−0.576897	+	0.385470i
$40$	−4.02656	−	5.00348i	−0.100664	−	0.125087i
$41$	38.1400	+	25.4844i	0.930245	+	0.621570i	0.925634	−	0.378419i	$-0.123532\pi$
$41$	38.1400	+	25.4844i	0.930245	+	0.621570i	0.00461086	+	0.999989i	$0.498532\pi$
$42$	−3.76333	−	3.54740i	−0.0896031	−	0.0844619i
$43$	10.4203	+	12.6972i	0.242333	+	0.295283i	0.879946	−	0.475073i	$-0.157578\pi$
$43$	10.4203	+	12.6972i	0.242333	+	0.295283i	−0.637614	+	0.770356i	$0.720078\pi$
$44$	4.92763	−	0.781221i	0.111992	−	0.0177550i
$45$	2.12404	−	1.13532i	0.0472009	−	0.0252294i
$46$	−33.6306	−	16.7187i	−0.731101	−	0.363450i
$47$	17.6180	+	42.5336i	0.374851	+	0.904971i	0.992913	+	0.118841i	$0.0379180\pi$
$47$	17.6180	+	42.5336i	0.374851	+	0.904971i	−0.618062	+	0.786129i	$0.712082\pi$
$48$	−4.86359	+	27.2827i	−0.101325	+	0.568389i
$49$	43.2109	+	17.8985i	0.881854	+	0.365276i
$50$	−36.7254	+	32.0001i	−0.734507	+	0.640003i
$51$	41.0518	+	12.4529i	0.804937	+	0.244175i
$52$	62.4430	+	2.44397i	1.20083	+	0.0469995i
$53$	95.6561	+	9.42130i	1.80483	+	0.177760i	0.943740	−	0.330689i	$-0.107281\pi$
$53$	95.6561	+	9.42130i	1.80483	+	0.177760i	0.861092	+	0.508449i	$0.169781\pi$
$54$	−9.71447	−	3.69177i	−0.179898	−	0.0683661i
$55$	0.195351	+	0.982097i	0.00355184	+	0.0178563i
$56$	2.21761	+	11.7359i	0.0396002	+	0.209570i
$57$	3.23129	−	16.2448i	0.0566892	−	0.284996i
$58$	64.2587	−	14.7666i	1.10791	−	0.254596i
$59$	15.1039	+	49.7909i	0.255998	+	0.843914i	0.986886	+	0.161416i	$0.0516062\pi$
$59$	15.1039	+	49.7909i	0.255998	+	0.843914i	−0.730888	+	0.682497i	$0.760894\pi$
$60$	−5.50968	−	0.761235i	−0.0918280	−	0.0126873i
$61$	61.8333	−	75.3440i	1.01366	−	1.23515i	0.0419135	−	0.999121i	$-0.486655\pi$
$61$	61.8333	−	75.3440i	1.01366	−	1.23515i	0.971747	−	0.236027i	$-0.0758454\pi$
$62$	−34.2645	+	44.3599i	−0.552653	+	0.715483i
$63$	−4.47884			−0.0710927
$64$	46.1146	−	44.3784i	0.720540	−	0.693413i
$65$			12.5420i			0.192954i
$66$	2.64125	−	3.41946i	0.0400190	−	0.0518100i
$67$	71.8329	+	58.9517i	1.07213	+	0.879877i	0.993132	−	0.116998i	$-0.0373270\pi$
$67$	71.8329	+	58.9517i	1.07213	+	0.879877i	0.0790008	+	0.996875i	$0.474827\pi$
$68$	−59.8068	−	78.9824i	−0.879512	−	1.16151i
$69$	−31.1249	+	9.44162i	−0.451085	+	0.136835i
$70$	−2.33621	+	0.536858i	−0.0333744	+	0.00766940i
$71$	−101.609	−	20.2113i	−1.43112	−	0.284667i	−0.582136	−	0.813092i	$-0.697783\pi$
$71$	−101.609	−	20.2113i	−1.43112	−	0.284667i	−0.848980	+	0.528425i	$0.822783\pi$
$72$	13.1417	+	20.0822i	0.182523	+	0.278920i
$73$	−14.9042	+	2.96463i	−0.204167	+	0.0406114i	−0.296114	−	0.955152i	$-0.595691\pi$
$73$	−14.9042	+	2.96463i	−0.204167	+	0.0406114i	0.0919470	+	0.995764i	$0.470691\pi$
$74$	−31.1393	−	11.8338i	−0.420802	−	0.159916i
$75$	−4.13485	+	41.9818i	−0.0551313	+	0.559758i
$76$	−28.0844	+	25.9688i	−0.369532	+	0.341695i
$77$	0.540552	−	1.78196i	0.00702015	−	0.0231423i
$78$	40.8024	−	35.5526i	0.523108	−	0.455803i
$79$	−28.4796	+	68.7559i	−0.360502	+	0.870328i	0.634725	+	0.772738i	$0.281113\pi$
$79$	−28.4796	+	68.7559i	−0.360502	+	0.870328i	−0.995227	+	0.0975897i	$0.968887\pi$
$80$	9.26199	+	8.89987i	0.115775	+	0.111248i
$81$	−8.31492	+	3.44415i	−0.102653	+	0.0425204i
$82$	−82.1501	−	40.8390i	−1.00183	−	0.498037i
$83$	32.6268	+	61.0404i	0.393094	+	0.735427i	0.998153	−	0.0607537i	$-0.0193504\pi$
$83$	32.6268	+	61.0404i	0.393094	+	0.735427i	−0.605059	+	0.796181i	$0.706850\pi$
$84$	8.36893	+	6.07846i	0.0996302	+	0.0723626i
$85$	15.3703	−	12.6141i	0.180828	−	0.148401i
$86$	−23.9050	−	22.5334i	−0.277966	−	0.262017i
$87$	31.7231	−	47.4770i	0.364633	−	0.545712i
$88$	−9.57603	+	2.80484i	−0.108819	+	0.0318732i
$89$	−44.8198	−	67.0775i	−0.503593	−	0.753680i	0.489374	−	0.872074i	$-0.337225\pi$
$89$	−44.8198	−	67.0775i	−0.503593	−	0.753680i	−0.992967	+	0.118394i	$0.962225\pi$
$90$	−3.92431	+	2.79317i	−0.0436034	+	0.0310353i
$91$	10.9948	−	20.5698i	0.120822	−	0.226042i
$92$	70.9720	+	24.5990i	0.771435	+	0.267380i
$93$	4.75802	+	48.3090i	0.0511615	+	0.519451i
$94$	−45.7829	−	79.8871i	−0.487052	−	0.849862i
$95$	−5.42845	−	5.42845i	−0.0571416	−	0.0571416i
$96$	2.69877	−	55.3599i	0.0281121	−	0.576665i
$97$	3.45702	+	3.45702i	0.0356394	+	0.0356394i	0.724702	−	0.689063i	$-0.241977\pi$
$97$	3.45702	+	3.45702i	0.0356394	+	0.0356394i	−0.689063	+	0.724702i	$0.741977\pi$
$98$	−90.2770	−	24.4993i	−0.921194	−	0.249993i
$99$	−0.366769	−	3.72386i	−0.00370473	−	0.0376148i
$100$	64.7018	−	72.8335i	0.647018	−	0.728335i
$101$	58.8016	−	110.010i	0.582194	−	1.08921i	−0.402582	−	0.915384i	$-0.631887\pi$
$101$	58.8016	−	110.010i	0.582194	−	1.08921i	0.984777	−	0.173825i	$-0.0556127\pi$
$102$	−84.6069	−	14.2467i	−0.829480	−	0.139673i
$103$	10.4529	+	15.6439i	0.101485	+	0.151882i	0.878737	−	0.477307i	$-0.158387\pi$
$103$	10.4529	+	15.6439i	0.101485	+	0.151882i	−0.777252	+	0.629189i	$0.783387\pi$
$104$	−124.492	+	11.0568i	−1.19703	+	0.106315i
$105$	−1.15334	+	1.72609i	−0.0109841	+	0.0164389i
$106$	−192.154	+	5.67552i	−1.81277	+	0.0535427i
$107$	64.6083	−	53.0227i	0.603816	−	0.495539i	−0.282100	−	0.959385i	$-0.591031\pi$
$107$	64.6083	−	53.0227i	0.603816	−	0.495539i	0.885916	+	0.463846i	$0.153531\pi$
$108$	20.2111	+	4.84903i	0.187139	+	0.0448984i
$109$	8.23176	+	15.4005i	0.0755207	+	0.141289i	0.916848	−	0.399237i	$-0.130725\pi$
$109$	8.23176	+	15.4005i	0.0755207	+	0.141289i	−0.841327	+	0.540527i	$0.818225\pi$
$110$	−0.637673	−	1.89844i	−0.00579702	−	0.0172586i
$111$	−26.6531	+	11.0401i	−0.240118	+	0.0994602i
$112$	−7.38838	−	22.7158i	−0.0659677	−	0.202820i
$113$	40.2643	−	97.2066i	0.356321	−	0.860236i	−0.639490	−	0.768800i	$-0.720854\pi$
$113$	40.2643	−	97.2066i	0.356321	−	0.860236i	0.995811	−	0.0914359i	$-0.0291457\pi$
$114$	−2.27222	+	33.0480i	−0.0199318	+	0.289895i
$115$	−4.37621	+	14.4264i	−0.0380540	+	0.125447i
$116$	−123.710	+	45.6600i	−1.06646	+	0.393621i
$117$	4.59388	−	46.6424i	0.0392639	−	0.398653i
$118$	−42.6441	−	94.9238i	−0.361391	−	0.804439i
$119$	−36.2664	+	7.21384i	−0.304760	+	0.0606205i
$120$	11.1235	+	0.106696i	0.0926960	+	0.000889131i
$121$	−117.149	−	23.3024i	−0.968175	−	0.192582i
$122$	−103.469	+	165.211i	−0.848103	+	1.35419i
$123$	−76.0292	+	23.0632i	−0.618123	+	0.187506i
$124$	56.6719	−	96.7250i	0.457032	−	0.780040i
$125$	30.6290	+	25.1366i	0.245032	+	0.201092i
$126$	8.88474	−	1.14081i	0.0705138	−	0.00905406i
$127$		−	11.5753i		−	0.0911443i	−0.998961	−	0.0455721i	$-0.985489\pi$
$127$		−	11.5753i		−	0.0911443i	0.998961	−	0.0455721i	$-0.0145111\pi$
$128$	−80.1745	+	99.7800i	−0.626363	+	0.779531i
$129$	−28.4500			−0.220543
$130$	−3.19460	−	24.8798i	−0.0245738	−	0.191383i
$131$	−44.2760	+	53.9505i	−0.337985	+	0.411836i	−0.914072	−	0.405553i	$-0.867079\pi$
$131$	−44.2760	+	53.9505i	−0.337985	+	0.411836i	0.576087	+	0.817389i	$0.304579\pi$
$132$	−4.36852	+	7.45598i	−0.0330948	+	0.0564847i
$133$	4.14427	+	13.6618i	0.0311599	+	0.102720i
$134$	−157.512	−	98.6468i	−1.17546	−	0.736170i
$135$	−0.813822	+	4.09136i	−0.00602831	+	0.0303064i
$136$	138.757	+	141.445i	1.02027	+	1.04004i
$137$	1.08402	+	5.44974i	0.00791255	+	0.0397791i	0.984540	−	0.175161i	$-0.0560445\pi$
$137$	1.08402	+	5.44974i	0.00791255	+	0.0397791i	−0.976627	+	0.214940i	$0.931044\pi$
$138$	59.3379	−	26.6573i	0.429985	−	0.193169i
$139$	−57.1594	−	5.62971i	−0.411219	−	0.0405015i	−0.109707	−	0.993964i	$-0.534991\pi$
$139$	−57.1594	−	5.62971i	−0.411219	−	0.0405015i	−0.301512	+	0.953462i	$0.597491\pi$
$140$	4.49763	−	1.66003i	0.0321259	−	0.0118574i
$141$	−76.3067	−	23.1474i	−0.541182	−	0.164166i
$142$	206.712	+	14.2125i	1.45572	+	0.100088i
$143$	18.0028	+	7.45701i	0.125894	+	0.0521469i
$144$	−31.1845	−	36.4901i	−0.216559	−	0.253403i
$145$	−10.1281	−	24.4514i	−0.0698489	−	0.168630i
$146$	28.8106	−	9.67726i	0.197333	−	0.0662826i
$147$	−71.4444	+	38.1878i	−0.486016	+	0.259781i
$148$	64.7857	+	15.5434i	0.437741	+	0.105023i
$149$	−131.052	−	159.687i	−0.879543	−	1.07173i	−0.996903	−	0.0786374i	$-0.974943\pi$
$149$	−131.052	−	159.687i	−0.879543	−	1.07173i	0.117360	−	0.993089i	$-0.462557\pi$
$150$	−2.49089	−	84.3331i	−0.0166059	−	0.562221i
$151$	−200.230	−	133.789i	−1.32603	−	0.886022i	−0.327753	−	0.944763i	$-0.606291\pi$
$151$	−200.230	−	133.789i	−1.32603	−	0.886022i	−0.998273	+	0.0587409i	$0.981291\pi$
$152$	49.0969	−	58.6681i	0.323006	−	0.385974i
$153$	−61.7809	+	41.2807i	−0.403797	+	0.269808i
$154$	−0.618415	+	3.67259i	−0.00401568	+	0.0238480i
$155$	19.8429	+	10.6062i	0.128019	+	0.0684274i
$156$	−71.8846	+	80.9190i	−0.460799	+	0.518712i
$157$	−15.8877	+	1.56480i	−0.101195	+	0.00996686i	−0.148488	−	0.988914i	$-0.547441\pi$
$157$	−15.8877	+	1.56480i	−0.101195	+	0.00996686i	0.0472928	+	0.998881i	$0.484941\pi$
$158$	38.9825	−	143.646i	0.246725	−	0.909153i
$159$	−117.721	+	117.721i	−0.740385	+	0.740385i
$160$	−20.6400	−	15.2957i	−0.129000	−	0.0955979i
$161$	19.8240	−	19.8240i	0.123130	−	0.123130i
$162$	15.6172	−	8.95011i	0.0964022	−	0.0552476i
$163$	22.1179	−	2.17842i	0.135693	−	0.0133646i	−0.0299428	−	0.999552i	$-0.509533\pi$
$163$	22.1179	−	2.17842i	0.135693	−	0.0133646i	0.165635	+	0.986187i	$0.447033\pi$
$164$	173.365	+	60.0883i	1.05710	+	0.366392i
$165$	−1.52958	−	0.817575i	−0.00927016	−	0.00495500i
$166$	−80.2699	−	112.776i	−0.483554	−	0.679376i
$167$	242.386	−	161.957i	1.45141	−	0.969803i	0.454544	−	0.890724i	$-0.349802\pi$
$167$	242.386	−	161.957i	1.45141	−	0.969803i	0.996868	−	0.0790780i	$-0.0251976\pi$
$168$	−18.1498	−	9.92627i	−0.108035	−	0.0590849i
$169$	62.4172	+	41.7059i	0.369333	+	0.246780i
$170$	−27.2774	+	28.9378i	−0.160455	+	0.170222i
$171$	18.1995	+	22.1761i	0.106430	+	0.129685i
$172$	53.1603	+	38.6110i	0.309071	+	0.224482i
$173$	−71.3590	+	38.1422i	−0.412480	+	0.220475i	−0.664566	−	0.747230i	$-0.731383\pi$
$173$	−71.3590	+	38.1422i	−0.412480	+	0.220475i	0.252086	+	0.967705i	$0.418883\pi$
$174$	−50.8366	+	102.261i	−0.292165	+	0.587707i
$175$	−13.9149	−	33.5936i	−0.0795139	−	0.191964i
$176$	18.2817	−	8.00313i	0.103873	−	0.0454723i
$177$	−83.2609	−	34.4878i	−0.470401	−	0.194846i
$178$	105.995	+	121.647i	0.595478	+	0.683407i
$179$	197.290	+	59.8473i	1.10218	+	0.334342i	0.788406	−	0.615155i	$-0.210907\pi$
$179$	197.290	+	59.8473i	1.10218	+	0.334342i	0.313774	+	0.949498i	$0.398407\pi$
$180$	7.07326	−	6.54043i	0.0392959	−	0.0363357i
$181$	25.1776	+	2.47978i	0.139103	+	0.0137004i	0.167329	−	0.985901i	$-0.446486\pi$
$181$	25.1776	+	2.47978i	0.139103	+	0.0137004i	−0.0282261	+	0.999602i	$0.508986\pi$
$182$	−16.5712	+	43.6051i	−0.0910503	+	0.239589i
$183$	32.9352	+	165.576i	0.179974	+	0.904788i
$184$	−147.054	−	30.7200i	−0.799206	−	0.166956i
$185$	−2.60867	+	13.1147i	−0.0141009	+	0.0708902i
$186$	−21.7434	−	94.6193i	−0.116900	−	0.508706i
$187$	−8.96767	−	29.5624i	−0.0479554	−	0.158088i
$188$	111.168	+	146.812i	0.591321	+	0.780913i
$189$	4.92136	−	5.99669i	0.0260389	−	0.0317285i
$190$	12.1512	+	9.38580i	0.0639536	+	0.0493990i
$191$	−90.5029			−0.473837			−0.236918	−	0.971530i	$-0.576137\pi$
$191$	−90.5029			−0.473837			−0.236918	+	0.971530i	$0.576137\pi$
$192$	8.74721	+	110.506i	0.0455584	+	0.575550i
$193$		−	59.8776i		−	0.310247i	−0.987895	−	0.155123i	$-0.950422\pi$
$193$		−	59.8776i		−	0.310247i	0.987895	−	0.155123i	$-0.0495775\pi$
$194$	−7.73828	−	5.97719i	−0.0398880	−	0.0308103i
$195$	−16.7924	−	13.7812i	−0.0861151	−	0.0706728i
$196$	185.324	+	25.6050i	0.945530	+	0.130638i
$197$	188.483	−	57.1757i	0.956767	−	0.290232i	0.226974	−	0.973901i	$-0.427117\pi$
$197$	188.483	−	57.1757i	0.956767	−	0.290232i	0.729792	+	0.683669i	$0.239617\pi$
$198$	1.67607	+	7.29366i	0.00846502	+	0.0368367i
$199$	−107.129	−	21.3093i	−0.538338	−	0.107082i	−0.0815693	−	0.996668i	$-0.525993\pi$
$199$	−107.129	−	21.3093i	−0.538338	−	0.107082i	−0.456768	+	0.889586i	$0.650993\pi$
$200$	−109.798	+	160.961i	−0.548992	+	0.804806i
$201$	−157.860	+	31.4003i	−0.785374	+	0.156221i
$202$	−88.6248	+	233.206i	−0.438737	+	1.15449i
$203$	−4.82417	+	48.9806i	−0.0237644	+	0.241284i
$204$	171.465	+	6.71101i	0.840513	+	0.0328971i
$205$	−10.6898	+	35.2396i	−0.0521455	+	0.171901i
$206$	−24.7203	−	28.3705i	−0.120001	−	0.137721i
$207$	21.5587	−	52.0473i	0.104148	−	0.251436i
$208$	244.139	−	53.6429i	1.17375	−	0.257899i
$209$	−11.0195	+	4.56444i	−0.0527250	+	0.0218394i
$210$	1.84823	−	3.71783i	0.00880111	−	0.0177040i
$211$	117.297	+	219.447i	0.555909	+	1.04003i	0.990252	+	0.139285i	$0.0444805\pi$
$211$	117.297	+	219.447i	0.555909	+	1.04003i	−0.434343	+	0.900747i	$0.643020\pi$
$212$	379.733	−	60.2024i	1.79119	−	0.283974i
$213$	138.709	−	113.836i	0.651217	−	0.534440i
$214$	−114.659	+	121.638i	−0.535790	+	0.568403i
$215$	−7.32610	+	10.9643i	−0.0340749	+	0.0509967i
$216$	−41.3281	−	4.47110i	−0.191334	−	0.0206995i
$217$	−23.2459	−	34.7900i	−0.107124	−	0.160322i
$218$	−20.2521	−	28.4535i	−0.0928997	−	0.130521i
$219$	12.4075	−	23.2127i	0.0566550	−	0.105994i
$220$	1.74851	+	3.60354i	0.00794779	+	0.0163797i
$221$	−37.9267	−	385.076i	−0.171614	−	1.74242i
$222$	50.0601	−	28.6892i	0.225496	−	0.129231i
$223$	−1.05610	−	1.05610i	−0.00473589	−	0.00473589i	0.704735	−	0.709471i	$-0.251066\pi$
$223$	−1.05610	−	1.05610i	−0.00473589	−	0.00473589i	−0.709471	+	0.704735i	$0.751066\pi$
$224$	20.4424	+	43.1798i	0.0912607	+	0.192767i
$225$	−51.6658	−	51.6658i	−0.229626	−	0.229626i
$226$	−55.1132	+	203.086i	−0.243864	+	0.898610i
$227$	28.0394	+	284.689i	0.123522	+	1.25414i	0.834534	+	0.550956i	$0.185737\pi$
$227$	28.0394	+	284.689i	0.123522	+	1.25414i	−0.711013	+	0.703179i	$0.751763\pi$
$228$	−3.91027	−	66.1366i	−0.0171503	−	0.290073i
$229$	146.696	−	274.449i	0.640595	−	1.19847i	−0.326776	−	0.945102i	$-0.605962\pi$
$229$	146.696	−	274.449i	0.640595	−	1.19847i	0.967370	−	0.253367i	$-0.0815379\pi$
$230$	5.00657	−	29.7326i	0.0217677	−	0.129272i
$231$	1.79190	+	2.68176i	0.00775713	+	0.0116094i
$232$	233.774	−	122.087i	1.00765	−	0.526236i
$233$	−65.3853	+	97.8560i	−0.280624	+	0.419983i	−0.944827	−	0.327569i	$-0.893771\pi$
$233$	−65.3853	+	97.8560i	−0.280624	+	0.419983i	0.664204	+	0.747552i	$0.268771\pi$
$234$	2.76741	+	93.6953i	0.0118266	+	0.400407i
$235$	−28.5703	+	23.4470i	−0.121576	+	0.0997745i
$236$	108.772	+	177.440i	0.460898	+	0.751863i
$237$	−60.7634	−	113.680i	−0.256385	−	0.479663i
$238$	70.1048	−	23.5477i	0.294558	−	0.0989398i
$239$	−61.1765	+	25.3401i	−0.255969	+	0.106026i	−0.506978	−	0.861959i	$-0.669237\pi$
$239$	−61.1765	+	25.3401i	−0.255969	+	0.106026i	0.251009	+	0.967985i	$0.419237\pi$
$240$	−22.0931	+	2.62163i	−0.0920545	+	0.0109235i
$241$	−178.169	+	430.137i	−0.739289	+	1.78480i	−0.130531	+	0.991444i	$0.541668\pi$
$241$	−178.169	+	430.137i	−0.739289	+	1.78480i	−0.608757	+	0.793356i	$0.708332\pi$
$242$	238.326	+	16.3861i	0.984818	+	0.0677112i
$243$	4.52509	−	14.9172i	0.0186218	−	0.0613878i
$244$	163.171	−	354.085i	0.668733	−	1.45117i
$245$	−3.68037	+	37.3674i	−0.0150219	+	0.152520i
$246$	144.946	−	65.1163i	0.589210	−	0.264700i
$247$	−146.524	+	29.1454i	−0.593215	+	0.117998i
$248$	−87.7840	+	206.310i	−0.353968	+	0.831894i
$249$	−117.577	−	23.3875i	−0.472197	−	0.0939258i
$250$	−67.1617	−	42.0622i	−0.268647	−	0.168249i
$251$	148.766	−	45.1276i	0.592692	−	0.179791i	0.0203316	−	0.999793i	$-0.493528\pi$
$251$	148.766	−	45.1276i	0.592692	−	0.179791i	0.572360	+	0.820002i	$0.306028\pi$
$252$	−17.3342	+	4.52609i	−0.0687865	+	0.0179607i
$253$	18.1057	+	14.8590i	0.0715642	+	0.0587312i
$254$	2.94837	+	22.9621i	0.0116077	+	0.0904021i
$255$			34.4397i			0.135058i
$256$	133.628	−	218.356i	0.521985	−	0.852955i
$257$	−83.2347			−0.323870			−0.161935	−	0.986801i	$-0.551774\pi$
$257$	−83.2347			−0.323870			−0.161935	+	0.986801i	$0.551774\pi$
$258$	56.4368	−	7.24655i	0.218747	−	0.0280874i
$259$	15.7752	−	19.2221i	0.0609081	−	0.0742168i
$260$	12.6743	+	48.5407i	0.0487474	+	0.186695i
$261$	28.7092	+	94.6416i	0.109997	+	0.362612i
$262$	74.0892	−	118.300i	0.282783	−	0.451527i
$263$	63.1253	−	317.352i	0.240020	−	1.20666i	−0.653250	−	0.757143i	$-0.726595\pi$
$263$	63.1253	−	317.352i	0.240020	−	1.20666i	0.893270	−	0.449521i	$-0.148405\pi$
$264$	6.76677	−	15.9033i	0.0256317	−	0.0602396i
$265$	15.0542	+	75.6824i	0.0568081	+	0.285594i
$266$	−11.7009	−	26.0455i	−0.0439882	−	0.0979156i
$267$	139.058	+	13.6960i	0.520815	+	0.0512958i
$268$	337.585	+	155.567i	1.25964	+	0.580474i
$269$	−128.323	−	38.9265i	−0.477038	−	0.144708i	0.0426037	−	0.999092i	$-0.486435\pi$
$269$	−128.323	−	38.9265i	−0.477038	−	0.144708i	−0.519642	+	0.854384i	$0.673935\pi$
$270$	0.572274	−	8.32338i	0.00211953	−	0.0308273i
$271$	−158.675	−	65.7252i	−0.585516	−	0.242529i	0.0702044	−	0.997533i	$-0.477635\pi$
$271$	−158.675	−	65.7252i	−0.585516	−	0.242529i	−0.655720	+	0.755004i	$0.727635\pi$
$272$	−311.282	−	245.243i	−1.14442	−	0.901630i
$273$	15.4597	+	37.3230i	0.0566289	+	0.136714i
$274$	−3.53850	−	10.5346i	−0.0129142	−	0.0384475i
$275$	26.7914	−	14.3203i	0.0974233	−	0.0520739i
$276$	−110.920	+	67.9946i	−0.401883	+	0.246357i
$277$	249.833	+	304.422i	0.901924	+	1.09900i	0.994650	+	0.103306i	$0.0329420\pi$
$277$	249.833	+	304.422i	0.901924	+	1.09900i	−0.0927257	+	0.995692i	$0.529558\pi$
$278$	114.822	−	3.39141i	0.413028	−	0.0121993i
$279$	−69.9087	−	46.7115i	−0.250569	−	0.167425i
$280$	−8.49918	+	4.43863i	−0.0303542	+	0.0158522i
$281$	393.712	−	263.070i	1.40111	−	0.936191i	0.401314	−	0.915941i	$-0.368554\pi$
$281$	393.712	−	263.070i	1.40111	−	0.936191i	0.999795	−	0.0202503i	$-0.00644632\pi$
$282$	157.267	+	26.4816i	0.557683	+	0.0939064i
$283$	−450.719	−	240.914i	−1.59265	−	0.851287i	−0.998912	−	0.0466247i	$-0.985154\pi$
$283$	−450.719	−	240.914i	−1.59265	−	0.851287i	−0.593733	−	0.804662i	$-0.702346\pi$
$284$	−413.677	+	24.4583i	−1.45661	+	0.0861209i
$285$	13.2329	−	1.30333i	0.0464312	−	0.00457308i
$286$	−37.6118	−	10.2070i	−0.131510	−	0.0356890i
$287$	48.4244	−	48.4244i	0.168726	−	0.168726i
$288$	71.1556	+	64.4429i	0.247068	+	0.223760i
$289$	−229.415	+	229.415i	−0.793823	+	0.793823i
$290$	26.3193	+	45.9248i	0.0907561	+	0.158361i
$291$	−8.42715	+	0.830002i	−0.0289593	+	0.00285224i
$292$	−54.6871	+	26.5353i	−0.187284	+	0.0908743i
$293$	58.9134	+	31.4899i	0.201070	+	0.107474i	0.568859	−	0.822435i	$-0.307385\pi$
$293$	58.9134	+	31.4899i	0.201070	+	0.107474i	−0.367789	+	0.929909i	$0.619885\pi$
$294$	131.998	−	93.9514i	0.448974	−	0.319563i
$295$	−34.7315	+	23.2068i	−0.117734	+	0.0786672i
$296$	−132.475	−	14.3319i	−0.447552	−	0.0484186i
$297$	5.38886	+	3.60072i	0.0181443	+	0.0121236i
$298$	300.644	+	283.394i	1.00887	+	0.950985i
$299$	186.113	+	226.779i	0.622451	+	0.758459i
$300$	26.4218	+	166.658i	0.0880727	+	0.555528i
$301$	21.6270	−	11.5599i	0.0718505	−	0.0384049i
$302$	431.277	+	214.399i	1.42807	+	0.709931i
$303$	82.6805	+	199.608i	0.272873	+	0.658773i
$304$	−82.4508	+	128.886i	−0.271220	+	0.423968i
$305$	72.2921	+	29.9444i	0.237023	+	0.0981782i
$306$	112.041	−	97.6254i	0.366147	−	0.319037i
$307$	−282.165	−	85.5938i	−0.919104	−	0.278807i	−0.204931	−	0.978776i	$-0.565697\pi$
$307$	−282.165	−	85.5938i	−0.919104	−	0.278807i	−0.714173	+	0.699969i	$0.753197\pi$
$308$	0.291309	−	7.44288i	0.000945808	−	0.0241652i
$309$	−32.4312	−	3.19419i	−0.104955	−	0.0103372i
$310$	−42.0642	−	15.9856i	−0.135691	−	0.0515663i
$311$	−52.0962	−	261.905i	−0.167512	−	0.842140i	−0.969555	−	0.244873i	$-0.921254\pi$
$311$	−52.0962	−	261.905i	−0.167512	−	0.842140i	0.802043	−	0.597266i	$-0.203746\pi$
$312$	121.988	−	178.830i	0.390986	−	0.573173i
$313$	22.4945	−	113.088i	0.0718674	−	0.361302i	−0.928071	−	0.372403i	$-0.878534\pi$
$313$	22.4945	−	113.088i	0.0718674	−	0.361302i	0.999938	+	0.0111015i	$0.00353378\pi$
$314$	31.1180	−	7.15088i	0.0991019	−	0.0227735i
$315$	−1.04376	−	3.44082i	−0.00331353	−	0.0109232i
$316$	−40.7419	+	294.882i	−0.128930	+	0.933171i
$317$	−14.0716	+	17.1463i	−0.0443900	+	0.0540894i	−0.794732	−	0.606960i	$-0.792389\pi$
$317$	−14.0716	+	17.1463i	−0.0443900	+	0.0540894i	0.750342	+	0.661050i	$0.229889\pi$
$318$	203.540	−	263.510i	0.640064	−	0.828648i
$319$	−41.1192			−0.128900
$320$	44.8399	+	25.0850i	0.140125	+	0.0783905i
$321$			144.765i			0.450982i
$322$	−34.2758	+	44.3746i	−0.106446	+	0.137809i
$323$	183.084	+	150.253i	0.566824	+	0.465181i
$324$	−28.7003	+	21.7323i	−0.0885811	+	0.0670751i
$325$	364.114	−	110.453i	1.12035	−	0.339855i
$326$	−43.3207	+	9.95505i	−0.132886	+	0.0305370i
$327$	−29.6647	−	5.90068i	−0.0907178	−	0.0180449i
$328$	−359.211	−	75.0402i	−1.09515	−	0.228781i
$329$	67.4117	−	13.4090i	0.204899	−	0.0407569i
$330$	3.24249	+	1.23224i	0.00982572	+	0.00373405i
$331$	8.84472	−	89.8020i	0.0267212	−	0.271305i	−0.972535	−	0.232755i	$-0.925226\pi$
$331$	8.84472	−	89.8020i	0.0267212	−	0.271305i	0.999257	−	0.0385503i	$-0.0122740\pi$
$332$	187.958	+	203.270i	0.566139	+	0.612260i
$333$	14.5050	−	47.8165i	0.0435585	−	0.143593i
$334$	−439.572	+	383.015i	−1.31608	+	1.14675i
$335$	−28.5489	+	68.9232i	−0.0852206	+	0.205741i
$336$	38.5324	+	15.0679i	0.114680	+	0.0448450i
$337$	−313.090	+	129.686i	−0.929050	+	0.384825i	−0.795318	−	0.606192i	$-0.792696\pi$
$337$	−313.090	+	129.686i	−0.929050	+	0.384825i	−0.133732	+	0.991018i	$0.542696\pi$
$338$	−134.441	−	66.8341i	−0.397754	−	0.197734i
$339$	85.9068	+	160.720i	0.253412	+	0.474101i
$340$	46.7398	−	64.3522i	0.137470	−	0.189271i
$341$	27.0220	−	22.1764i	0.0792434	−	0.0650334i
$342$	−41.7511	−	39.3555i	−0.122079	−	0.115075i
$343$	79.4361	−	118.885i	0.231592	−	0.346602i
$344$	−115.289	−	63.0526i	−0.335144	−	0.183293i
$345$	−14.5069	−	21.7110i	−0.0420489	−	0.0629306i
$346$	131.841	−	93.8392i	0.381042	−	0.271211i
$347$	−284.932	+	533.071i	−0.821130	+	1.53623i	0.0227787	+	0.999741i	$0.492749\pi$
$347$	−284.932	+	533.071i	−0.821130	+	1.53623i	−0.843909	+	0.536486i	$0.819751\pi$
$348$	74.7983	−	215.805i	0.214938	−	0.620130i
$349$	50.5020	+	512.755i	0.144705	+	1.46921i	0.743729	+	0.668481i	$0.233055\pi$
$349$	50.5020	+	512.755i	0.144705	+	1.46921i	−0.599024	+	0.800731i	$0.704445\pi$
$350$	36.1599	+	63.0958i	0.103314	+	0.180274i
$351$	57.4014	+	57.4014i	0.163537	+	0.163537i
$352$	−34.2271	+	20.5325i	−0.0972362	+	0.0583309i
$353$	342.617	+	342.617i	0.970586	+	0.970586i	0.999580	−	0.0289937i	$-0.00923029\pi$
$353$	342.617	+	342.617i	0.970586	+	0.970586i	−0.0289937	+	0.999580i	$0.509230\pi$
$354$	173.950	+	47.2064i	0.491385	+	0.133352i
$355$	−8.15217	−	82.7703i	−0.0229638	−	0.233156i
$356$	−241.249	−	214.314i	−0.677665	−	0.602005i
$357$	30.1911	−	56.4835i	0.0845688	−	0.158217i
$358$	−406.611	−	68.4679i	−1.13578	−	0.191251i
$359$	−134.485	−	201.271i	−0.374609	−	0.560642i	0.595486	−	0.803365i	$-0.296959\pi$
$359$	−134.485	−	201.271i	−0.374609	−	0.560642i	−0.970096	+	0.242723i	$0.921959\pi$
$360$	−12.3654	+	14.7760i	−0.0343483	+	0.0410444i
$361$	−149.757	+	224.127i	−0.414839	+	0.620851i
$362$	−50.5768	+	1.49385i	−0.139715	+	0.00412666i
$363$	159.923	−	131.246i	0.440560	−	0.361558i
$364$	21.7657	−	90.7209i	0.0597959	−	0.249233i
$365$	−5.75087	−	10.7591i	−0.0157558	−	0.0294771i
$366$	−107.508	−	320.067i	−0.293738	−	0.874500i
$367$	−251.201	+	104.051i	−0.684472	+	0.283518i	−0.697695	−	0.716395i	$-0.745791\pi$
$367$	−251.201	+	104.051i	−0.684472	+	0.283518i	0.0132229	+	0.999913i	$0.495791\pi$
$368$	299.538	+	23.4834i	0.813961	+	0.0638135i
$369$	52.6618	−	127.137i	0.142715	−	0.344544i
$370$	1.83440	−	26.6802i	0.00495784	−	0.0721088i
$371$	41.6560	−	137.321i	0.112280	−	0.370139i
$372$	67.2333	+	182.159i	0.180735	+	0.489675i
$373$	41.7394	−	423.787i	0.111902	−	1.13616i	−0.761165	−	0.648558i	$-0.775372\pi$
$373$	41.7394	−	423.787i	0.111902	−	1.13616i	0.873067	−	0.487600i	$-0.162128\pi$
$374$	25.3192	+	56.3593i	0.0676984	+	0.150693i
$375$	−67.3104	+	13.3889i	−0.179494	+	0.0357036i
$376$	−257.921	−	262.917i	−0.685959	−	0.699246i
$377$	−505.133	−	100.477i	−1.33988	−	0.266518i
$378$	−8.23514	+	13.1492i	−0.0217861	+	0.0347864i
$379$	−386.964	+	117.384i	−1.02101	+	0.309721i	−0.756034	−	0.654532i	$-0.772866\pi$
$379$	−386.964	+	117.384i	−1.02101	+	0.309721i	−0.264981	+	0.964254i	$0.585366\pi$
$380$	−26.4951	−	15.5237i	−0.0697241	−	0.0408519i
$381$	15.4981	+	12.7190i	0.0406775	+	0.0333831i
$382$	179.532	−	23.0521i	0.469979	−	0.0603458i
$383$		−	357.987i		−	0.934691i	−0.884075	−	0.467346i	$-0.845210\pi$
$383$		−	357.987i		−	0.934691i	0.884075	−	0.467346i	$-0.154790\pi$
$384$	−45.4990	−	216.984i	−0.118487	−	0.565061i
$385$	1.49494			0.00388297
$386$	15.2515	+	118.780i	0.0395117	+	0.307721i
$387$	31.2609	−	38.0916i	0.0807776	−	0.0984278i
$388$	16.8730	+	9.88602i	0.0434871	+	0.0254794i
$389$	−118.793	−	391.607i	−0.305380	−	1.00670i	−0.966553	−	0.256469i	$-0.917441\pi$
$389$	−118.793	−	391.607i	−0.305380	−	1.00670i	0.661173	−	0.750234i	$-0.270059\pi$
$390$	36.8216	+	23.0607i	0.0944144	+	0.0591301i
$391$	90.7370	−	456.166i	0.232064	−	1.16666i
$392$	−374.152	−	3.58882i	−0.954469	−	0.00915516i
$393$	−23.5834	−	118.562i	−0.0600086	−	0.301684i
$394$	−359.333	+	161.429i	−0.912013	+	0.409718i
$395$	−59.4580	−	5.85610i	−0.150526	−	0.0148256i
$396$	−5.18263	−	14.0416i	−0.0130875	−	0.0354586i
$397$	−529.607	−	160.654i	−1.33402	−	0.404671i	−0.458863	−	0.888507i	$-0.651743\pi$
$397$	−529.607	−	160.654i	−1.33402	−	0.404671i	−0.875159	+	0.483836i	$0.839243\pi$
$398$	217.941	+	14.9846i	0.547592	+	0.0376497i
$399$	−22.8454	−	9.46289i	−0.0572567	−	0.0237165i
$400$	176.810	−	347.268i	0.442025	−	0.868170i
$401$	30.4325	+	73.4707i	0.0758916	+	0.183219i	0.957272	−	0.289188i	$-0.0933853\pi$
$401$	30.4325	+	73.4707i	0.0758916	+	0.183219i	−0.881381	+	0.472407i	$0.843385\pi$
$402$	305.152	−	102.498i	0.759083	−	0.254970i
$403$	386.144	−	206.398i	0.958173	−	0.512154i
$404$	116.406	−	485.188i	0.288134	−	1.20096i
$405$	−4.58366	−	5.58521i	−0.0113177	−	0.0137906i
$406$	−2.90615	−	98.3923i	−0.00715799	−	0.242346i
$407$	17.2738	+	11.5420i	0.0424417	+	0.0283586i
$408$	−341.846	+	30.3613i	−0.837859	+	0.0744149i
$409$	−567.540	+	379.218i	−1.38763	+	0.927183i	−0.387643	+	0.921810i	$0.626710\pi$
$409$	−567.540	+	379.218i	−1.38763	+	0.927183i	−0.999986	+	0.00537366i	$0.998290\pi$
$410$	12.2296	−	72.6282i	0.0298284	−	0.177142i
$411$	−8.48774	−	4.53679i	−0.0206514	−	0.0110384i
$412$	56.2642	+	49.9825i	0.136564	+	0.121317i
$413$	77.3060	−	7.61398i	0.187182	−	0.0184358i
$414$	−29.5093	+	108.738i	−0.0712785	+	0.262653i
$415$	−39.2902	+	39.2902i	−0.0946753	+	0.0946753i
$416$	−470.639	+	168.597i	−1.13134	+	0.405282i
$417$	70.3444	−	70.3444i	0.168692	−	0.168692i
$418$	20.6970	−	11.8613i	0.0495143	−	0.0283764i
$419$	203.032	−	19.9969i	0.484564	−	0.0477254i	0.147214	−	0.989105i	$-0.452969\pi$
$419$	203.032	−	19.9969i	0.484564	−	0.0477254i	0.337350	+	0.941379i	$0.390469\pi$
$420$	−2.71939	+	7.84589i	−0.00647475	+	0.0186807i
$421$	46.1868	+	24.6874i	0.109707	+	0.0586398i	0.525338	−	0.850894i	$-0.323939\pi$
$421$	46.1868	+	24.6874i	0.109707	+	0.0586398i	−0.415630	+	0.909534i	$0.636439\pi$
$422$	−288.579	−	405.443i	−0.683836	−	0.960765i
$423$	114.838	−	76.7321i	0.271484	−	0.181400i
$424$	−737.948	+	216.147i	−1.74044	+	0.509780i
$425$	−501.568	−	335.137i	−1.18016	−	0.788558i
$426$	−246.164	+	261.148i	−0.577850	+	0.613024i
$427$	−92.3138	−	112.485i	−0.216192	−	0.263430i
$428$	196.468	−	270.501i	0.459037	−	0.632011i
$429$	−29.7656	+	15.9101i	−0.0693838	+	0.0370864i
$430$	11.7402	−	23.6161i	0.0273027	−	0.0549211i
$431$	93.7074	+	226.230i	0.217419	+	0.524895i	0.994528	−	0.104471i	$-0.0333149\pi$
$431$	93.7074	+	226.230i	0.217419	+	0.524895i	−0.777109	+	0.629366i	$0.783315\pi$
$432$	83.1219	−	1.65735i	0.192412	−	0.00383645i
$433$	529.365	+	219.270i	1.22255	+	0.506398i	0.898220	−	0.439545i	$-0.144860\pi$
$433$	529.365	+	219.270i	1.22255	+	0.506398i	0.324332	+	0.945943i	$0.394860\pi$
$434$	54.9747	+	63.0924i	0.126670	+	0.145374i
$435$	43.8665	+	13.3068i	0.100843	+	0.0305903i
$436$	47.4219	+	51.2852i	0.108766	+	0.117627i
$437$	−178.708	−	17.6012i	−0.408943	−	0.0402774i
$438$	−18.7003	+	49.2077i	−0.0426947	+	0.112346i
$439$	40.1397	+	201.796i	0.0914344	+	0.459672i	0.999193	+	0.0401779i	$0.0127925\pi$
$439$	40.1397	+	201.796i	0.0914344	+	0.459672i	−0.907758	+	0.419494i	$0.862208\pi$
$440$	−4.38642	−	6.70304i	−0.00996913	−	0.0152342i
$441$	27.3738	−	137.617i	0.0620720	−	0.312057i
$442$	173.319	+	754.220i	0.392124	+	1.70638i
$443$	−158.631	−	522.936i	−0.358083	−	1.18044i	−0.932284	−	0.361728i	$-0.882187\pi$
$443$	−158.631	−	522.936i	−0.358083	−	1.18044i	0.574200	−	0.818715i	$-0.305313\pi$
$444$	−91.9975	+	69.6621i	−0.207202	+	0.156897i
$445$	41.0867	−	50.0643i	0.0923296	−	0.112504i
$446$	2.36401	+	1.82601i	0.00530047	+	0.00409419i
$447$	357.804			0.800457
$448$	−51.5503	−	80.4494i	−0.115068	−	0.179575i
$449$			430.195i			0.958118i	0.877783	+	0.479059i	$0.159022\pi$
$449$			430.195i			0.958118i	−0.877783	+	0.479059i	$0.840978\pi$
$450$	115.650	+	89.3303i	0.257000	+	0.198512i
$451$	44.2272	+	36.2963i	0.0980647	+	0.0804796i
$452$	57.6006	−	416.902i	0.127435	−	0.922350i
$453$	399.143	−	121.079i	0.881110	−	0.267282i
$454$	−128.136	−	557.599i	−0.282237	−	1.22819i
$455$	18.3648	+	3.65298i	0.0403622	+	0.00802854i
$456$	24.6026	+	130.200i	0.0539531	+	0.285527i
$457$	607.454	−	120.830i	1.32922	−	0.264399i	0.521141	−	0.853471i	$-0.325507\pi$
$457$	607.454	−	120.830i	1.32922	−	0.264399i	0.808081	+	0.589072i	$0.200507\pi$
$458$	−221.098	+	581.794i	−0.482747	+	1.27029i
$459$	12.6145	−	128.077i	0.0274826	−	0.279036i
$460$	−2.35838	+	60.2561i	−0.00512692	+	0.130992i
$461$	−113.907	+	375.502i	−0.247087	+	0.814537i	0.742405	+	0.669951i	$0.233685\pi$
$461$	−113.907	+	375.502i	−0.247087	+	0.814537i	−0.989492	+	0.144586i	$0.953815\pi$
$462$	−4.23769	−	4.86343i	−0.00917248	−	0.0105269i
$463$	23.2992	−	56.2492i	0.0503222	−	0.121489i	−0.896719	−	0.442600i	$-0.854056\pi$
$463$	23.2992	−	56.2492i	0.0503222	−	0.121489i	0.947042	+	0.321111i	$0.104056\pi$
$464$	−432.645	+	301.730i	−0.932424	+	0.650280i
$465$	−36.0040	+	14.9134i	−0.0774280	+	0.0320717i
$466$	104.781	−	210.773i	0.224851	−	0.452302i
$467$	−98.6164	−	184.498i	−0.211170	−	0.395071i	0.753929	−	0.656956i	$-0.228156\pi$
$467$	−98.6164	−	184.498i	−0.211170	−	0.395071i	−0.965099	+	0.261884i	$0.915656\pi$
$468$	−29.3550	−	185.160i	−0.0627244	−	0.395641i
$469$	107.243	−	88.0118i	0.228663	−	0.187659i
$470$	50.7030	−	53.7893i	0.107879	−	0.114445i
$471$	15.3623	−	22.9913i	0.0326163	−	0.0488137i
$472$	−260.968	−	324.284i	−0.552899	−	0.687043i
$473$	11.3823	+	17.0348i	0.0240641	+	0.0360144i
$474$	149.493	+	210.032i	0.315386	+	0.443105i
$475$	−109.790	+	205.403i	−0.231137	+	0.432426i
$476$	−133.070	+	64.5684i	−0.279559	+	0.135648i
$477$	−28.2639	−	286.968i	−0.0592535	−	0.601611i
$478$	114.902	−	65.8499i	0.240381	−	0.137761i
$479$	94.2064	+	94.2064i	0.196673	+	0.196673i	0.798572	−	0.601899i	$-0.205589\pi$
$479$	94.2064	+	94.2064i	0.196673	+	0.196673i	−0.601899	+	0.798572i	$0.705589\pi$
$480$	43.1586	−	10.8279i	0.0899137	−	0.0225582i
$481$	183.998	+	183.998i	0.382532	+	0.382532i
$482$	243.875	−	898.650i	0.505964	−	1.86442i
$483$	4.75958	+	48.3249i	0.00985421	+	0.100051i
$484$	−476.944	+	28.1989i	−0.985422	+	0.0582623i
$485$	−1.85018	+	3.46145i	−0.00381481	+	0.00713701i
$486$	−5.17690	+	30.7441i	−0.0106521	+	0.0632595i
$487$	−287.780	−	430.693i	−0.590924	−	0.884380i	0.408676	−	0.912680i	$-0.365991\pi$
$487$	−287.780	−	430.693i	−0.590924	−	0.884380i	−0.999599	+	0.0282997i	$0.990991\pi$
$488$	−233.495	+	743.966i	−0.478473	+	1.52452i
$489$	−21.3865	+	32.0072i	−0.0437352	+	0.0654543i
$490$	−2.21710	−	75.0637i	−0.00452470	−	0.153191i
$491$	−35.3509	+	29.0118i	−0.0719978	+	0.0590871i	−0.669704	−	0.742628i	$-0.733579\pi$
$491$	−35.3509	+	29.0118i	−0.0719978	+	0.0590871i	0.597706	+	0.801715i	$0.296079\pi$
$492$	−270.945	+	166.091i	−0.550701	+	0.337584i
$493$	384.901	+	720.100i	0.780733	+	1.46065i
$494$	283.238	−	95.1376i	0.573357	−	0.192586i
$495$	2.77535	−	1.14959i	0.00560676	−	0.00232240i
$496$	121.589	−	431.619i	0.245139	−	0.870200i
$497$	−59.1893	+	142.896i	−0.119093	+	0.287516i
$498$	239.196	+	16.4460i	0.480314	+	0.0330240i
$499$	147.682	−	486.842i	0.295956	−	0.975635i	−0.675289	−	0.737553i	$-0.735981\pi$
$499$	147.682	−	486.842i	0.295956	−	0.975635i	0.971245	−	0.238082i	$-0.0765188\pi$
$500$	143.943	+	66.3325i	0.287887	+	0.132665i
$501$	−49.4907	+	502.487i	−0.0987838	+	1.00297i
$502$	−283.614	+	127.413i	−0.564968	+	0.253810i
$503$	366.213	−	72.8442i	0.728057	−	0.144820i	0.182874	−	0.983136i	$-0.441460\pi$
$503$	366.213	−	72.8442i	0.728057	−	0.144820i	0.545183	+	0.838317i	$0.316460\pi$
$504$	33.2333	−	13.3937i	0.0659390	−	0.0265748i
$505$	98.2174	+	19.5367i	0.194490	+	0.0386864i
$506$	−39.7014	−	24.8643i	−0.0784612	−	0.0491388i
$507$	−124.424	+	37.7436i	−0.245412	+	0.0744449i
$508$	−11.6974	−	44.7993i	−0.0230264	−	0.0881876i
$509$	−93.5658	−	76.7875i	−0.183823	−	0.150859i	0.537982	−	0.842957i	$-0.319187\pi$
$509$	−93.5658	−	76.7875i	−0.183823	−	0.150859i	−0.721804	+	0.692097i	$0.756687\pi$
$510$	−8.77218	−	68.3185i	−0.0172003	−	0.133958i
$511$			22.6871i			0.0443975i
$512$	−209.462	+	467.193i	−0.409106	+	0.912487i
$513$	−49.6891			−0.0968598
$514$	165.114	−	21.2008i	0.321233	−	0.0412467i
$515$	−9.58228	+	11.6760i	−0.0186064	+	0.0226719i
$516$	−110.109	+	28.7502i	−0.213389	+	0.0557174i
$517$	16.6690	+	54.9504i	0.0322418	+	0.106287i
$518$	−26.3974	+	42.1494i	−0.0509602	+	0.0813694i
$519$	27.3411	−	137.453i	0.0526803	−	0.264842i
$520$	−37.5061	−	93.0626i	−0.0721272	−	0.178967i
$521$	116.628	+	586.330i	0.223855	+	1.12539i	0.915241	+	0.402908i	$0.132000\pi$
$521$	116.628	+	586.330i	0.223855	+	1.12539i	−0.691386	+	0.722486i	$0.743000\pi$
$522$	−81.0572	−	180.429i	−0.155282	−	0.345650i
$523$	383.679	+	37.7891i	0.733612	+	0.0722545i	0.457922	−	0.888992i	$-0.348594\pi$
$523$	383.679	+	37.7891i	0.733612	+	0.0722545i	0.275690	+	0.961247i	$0.411094\pi$
$524$	−116.839	+	253.545i	−0.222976	+	0.483864i
$525$	60.2680	+	18.2821i	0.114796	+	0.0348231i
$526$	−44.3893	+	645.615i	−0.0843904	+	1.22741i
$527$	−641.306	−	265.638i	−1.21690	−	0.504056i
$528$	−9.37260	+	33.2711i	−0.0177511	+	0.0630134i
$529$	−67.4924	−	162.941i	−0.127585	−	0.308017i
$530$	−49.1403	−	146.298i	−0.0927175	−	0.276033i
$531$	137.663	−	73.5822i	0.259252	−	0.138573i
$532$	29.8453	+	48.6866i	0.0561001	+	0.0915161i
$533$	454.621	+	553.957i	0.852947	+	1.03932i
$534$	−279.339	+	8.25065i	−0.523107	+	0.0154507i
$535$	55.7906	+	37.2781i	0.104282	+	0.0696787i
$536$	−709.296	−	222.614i	−1.32331	−	0.415324i
$537$	−296.912	+	198.390i	−0.552908	+	0.369442i
$538$	264.472	+	44.5336i	0.491583	+	0.0827761i
$539$	51.4489	+	27.5000i	0.0954526	+	0.0510205i
$540$	0.984830	+	16.6570i	0.00182376	+	0.0308462i
$541$	347.416	−	34.2175i	0.642174	−	0.0632486i	0.228312	−	0.973588i	$-0.426679\pi$
$541$	347.416	−	34.2175i	0.642174	−	0.0632486i	0.413862	+	0.910339i	$0.364179\pi$
$542$	331.506	+	89.9638i	0.611635	+	0.165985i
$543$	−30.9854	+	30.9854i	−0.0570633	+	0.0570633i
$544$	679.962	+	407.205i	1.24993	+	0.748540i
$545$	−9.91294	+	9.91294i	−0.0181889	+	0.0181889i
$546$	−40.1742	−	70.1004i	−0.0735791	−	0.128389i
$547$	604.698	−	59.5575i	1.10548	−	0.108880i	0.471232	−	0.882009i	$-0.343810\pi$
$547$	604.698	−	59.5575i	1.10548	−	0.108880i	0.634249	+	0.773129i	$0.281310\pi$
$548$	9.70265	+	19.9964i	0.0177056	+	0.0364897i
$549$	−257.878	−	137.839i	−0.469723	−	0.251072i
$550$	−49.4990	+	35.2315i	−0.0899981	+	0.0640572i
$551$	262.121	−	175.144i	0.475718	−	0.317865i
$552$	202.714	−	163.134i	0.367235	−	0.295533i
$553$	92.3816	+	61.7274i	0.167055	+	0.111623i
$554$	−573.137	−	540.252i	−1.03454	−	0.975183i
$555$	−14.6927	−	17.9032i	−0.0264734	−	0.0322580i
$556$	−226.910	+	35.9740i	−0.408111	+	0.0647015i
$557$	−721.176	+	385.476i	−1.29475	+	0.692058i	−0.967498	−	0.252879i	$-0.918623\pi$
$557$	−721.176	+	385.476i	−1.29475	+	0.692058i	−0.327252	+	0.944937i	$0.606123\pi$
$558$	150.577	+	74.8557i	0.269851	+	0.134150i
$559$	98.2014	+	237.079i	0.175673	+	0.424113i
$560$	15.7294	−	10.9698i	0.0280882	−	0.0195889i
$561$	49.4346	+	20.4765i	0.0881188	+	0.0365000i
$562$	−714.004	+	622.138i	−1.27047	+	1.10701i
$563$	966.011	+	293.036i	1.71583	+	0.520491i	0.986512	−	0.163688i	$-0.0523389\pi$
$563$	966.011	+	293.036i	1.71583	+	0.520491i	0.729315	+	0.684178i	$0.239839\pi$
$564$	−318.717	−	12.4744i	−0.565101	−	0.0221177i
$565$	84.0613	+	8.27931i	0.148781	+	0.0146536i
$566$	955.461	+	363.102i	1.68809	+	0.641522i
$567$	2.62134	+	13.1783i	0.00462317	+	0.0232422i
$568$	814.387	−	153.887i	1.43378	−	0.270927i
$569$	87.2679	−	438.725i	0.153371	−	0.771046i	−0.825153	−	0.564910i	$-0.808911\pi$
$569$	87.2679	−	438.725i	0.153371	−	0.771046i	0.978523	−	0.206136i	$-0.0660891\pi$
$570$	−25.9183	+	5.95600i	−0.0454707	+	0.0104491i
$571$	−273.607	−	901.960i	−0.479171	−	1.57961i	−0.779900	−	0.625905i	$-0.784730\pi$
$571$	−273.607	−	901.960i	−0.479171	−	1.57961i	0.300729	−	0.953710i	$-0.402770\pi$
$572$	77.2109	+	10.6677i	0.134984	+	0.0186499i
$573$	99.4447	−	121.174i	0.173551	−	0.211472i
$574$	−83.7259	+	108.394i	−0.145864	+	0.188840i
$575$	457.361			0.795410
$576$	−157.567	−	109.712i	−0.273553	−	0.190472i
$577$			1027.61i			1.78095i	0.455036	+	0.890473i	$0.349627\pi$
$577$			1027.61i			1.78095i	−0.455036	+	0.890473i	$0.650373\pi$
$578$	396.659	−	513.528i	0.686261	−	0.888457i
$579$	80.1698	+	65.7936i	0.138462	+	0.113633i
$580$	−63.9075	−	84.3978i	−0.110185	−	0.145514i
$581$	98.8820	−	29.9955i	0.170193	−	0.0516274i
$582$	16.5057	−	3.79298i	0.0283602	−	0.00651715i
$583$	117.585	+	23.3891i	0.201689	+	0.0401185i
$584$	101.725	−	66.5679i	0.174186	−	0.113986i
$585$	36.9031	−	7.34048i	0.0630822	−	0.0125478i
$586$	−124.888	−	47.4610i	−0.213120	−	0.0809915i
$587$	−62.4676	+	634.244i	−0.106418	+	1.08048i	0.782573	+	0.622559i	$0.213907\pi$
$587$	−62.4676	+	634.244i	−0.106418	+	1.08048i	−0.888991	+	0.457925i	$0.848593\pi$
$588$	−237.917	+	219.994i	−0.404620	+	0.374140i
$589$	−77.7977	+	256.465i	−0.132084	+	0.435424i
$590$	62.9863	−	54.8822i	0.106756	−	0.0930207i
$591$	−130.553	+	315.183i	−0.220902	+	0.533305i
$592$	266.444	−	5.31256i	0.450074	−	0.00897392i
$593$	12.3493	−	5.11524i	0.0208251	−	0.00862604i	−0.372247	−	0.928134i	$-0.621412\pi$
$593$	12.3493	−	5.11524i	0.0208251	−	0.00862604i	0.393072	+	0.919508i	$0.371412\pi$
$594$	−11.6071	−	5.77020i	−0.0195406	−	0.00971414i
$595$	−13.9936	−	26.1802i	−0.0235186	−	0.0440003i
$596$	−668.575	−	485.594i	−1.12177	−	0.814756i
$597$	146.245	−	120.020i	0.244966	−	0.201038i
$598$	−426.958	−	402.460i	−0.713977	−	0.673010i
$599$	232.150	−	347.436i	0.387562	−	0.580027i	−0.585471	−	0.810693i	$-0.699090\pi$
$599$	232.150	−	347.436i	0.387562	−	0.580027i	0.973033	+	0.230666i	$0.0740904\pi$
$600$	−94.8631	−	323.873i	−0.158105	−	0.539788i
$601$	−297.348	−	445.012i	−0.494755	−	0.740453i	0.497118	−	0.867683i	$-0.334391\pi$
$601$	−297.348	−	445.012i	−0.494755	−	0.740453i	−0.991873	+	0.127230i	$0.959391\pi$
$602$	−39.9574	+	28.4401i	−0.0663744	+	0.0472428i
$603$	131.415	−	245.861i	0.217936	−	0.407729i
$604$	−910.140	−	315.455i	−1.50685	−	0.522277i
$605$	−9.39894	−	95.4291i	−0.0155354	−	0.157734i
$606$	−214.857	−	374.906i	−0.354549	−	0.618657i
$607$	−692.937	−	692.937i	−1.14158	−	1.14158i	−0.988162	−	0.153415i	$-0.950973\pi$
$607$	−692.937	−	692.937i	−1.14158	−	1.14158i	−0.153415	−	0.988162i	$-0.549027\pi$
$608$	130.730	−	276.675i	0.215016	−	0.455057i
$609$	−60.2790	−	60.2790i	−0.0989803	−	0.0989803i
$610$	−151.034	−	40.9874i	−0.247597	−	0.0671925i
$611$	70.4977	+	715.775i	0.115381	+	1.17148i
$612$	−197.391	+	222.199i	−0.322534	+	0.363070i
$613$	−254.794	+	476.686i	−0.415651	+	0.777628i	−0.999412	−	0.0342978i	$-0.989081\pi$
$613$	−254.794	+	476.686i	−0.415651	+	0.777628i	0.583761	+	0.811926i	$0.301581\pi$
$614$	581.536	+	97.9230i	0.947128	+	0.159484i
$615$	−35.4361	−	53.0339i	−0.0576197	−	0.0862340i
$616$	1.31791	+	14.8387i	0.00213947	+	0.0240889i
$617$	95.3641	−	142.723i	0.154561	−	0.231317i	−0.746106	−	0.665828i	$-0.768079\pi$
$617$	95.3641	−	142.723i	0.154561	−	0.231317i	0.900667	+	0.434511i	$0.143079\pi$
$618$	65.1478	−	1.92422i	0.105417	−	0.00311363i
$619$	120.302	−	98.7293i	0.194349	−	0.159498i	−0.532186	−	0.846627i	$-0.678629\pi$
$619$	120.302	−	98.7293i	0.194349	−	0.159498i	0.726535	+	0.687129i	$0.241129\pi$
$620$	87.5150	+	20.9965i	0.141153	+	0.0338654i
$621$	45.9971	+	86.0545i	0.0740694	+	0.138574i
$622$	170.054	+	506.276i	0.273399	+	0.813948i
$623$	−111.273	+	46.0908i	−0.178609	+	0.0739821i
$624$	−196.438	+	385.819i	−0.314805	+	0.618300i
$625$	220.838	−	533.150i	0.353341	−	0.853041i
$626$	−15.8180	+	230.063i	−0.0252684	+	0.367513i
$627$	5.99698	−	19.7694i	0.00956456	−	0.0315301i
$628$	−59.9078	+	22.1114i	−0.0953946	+	0.0352092i
$629$	40.4353	−	410.547i	0.0642851	−	0.652697i
$630$	2.94694	+	6.55975i	0.00467769	+	0.0104123i
$631$	1025.87	−	204.058i	1.62578	−	0.323387i	0.703732	−	0.710466i	$-0.251516\pi$
$631$	1025.87	−	204.058i	1.62578	−	0.323387i	0.922047	+	0.387078i	$0.126516\pi$
$632$	5.71043	−	595.339i	0.00903549	−	0.941993i
$633$	−422.702	−	84.0806i	−0.667775	−	0.132829i
$634$	23.5467	−	37.5976i	0.0371400	−	0.0593023i
$635$	8.89262	−	2.69755i	0.0140041	−	0.00424810i
$636$	−336.647	+	574.573i	−0.529319	+	0.903416i
$637$	564.832	+	463.545i	0.886706	+	0.727701i
$638$	81.5688	−	10.4735i	0.127851	−	0.0164162i
$639$			310.800i			0.486384i
$640$	−95.3390	−	38.3402i	−0.148967	−	0.0599065i
$641$	191.554			0.298837			0.149418	−	0.988774i	$-0.452260\pi$
$641$	191.554			0.298837			0.149418	+	0.988774i	$0.452260\pi$
$642$	−36.8733	−	287.173i	−0.0574351	−	0.447309i
$643$	−302.843	+	369.016i	−0.470985	+	0.573897i	−0.953271	−	0.302117i	$-0.902307\pi$
$643$	−302.843	+	369.016i	−0.470985	+	0.573897i	0.482286	+	0.876014i	$0.339807\pi$
$644$	56.6906	−	96.7569i	0.0880289	−	0.150244i
$645$	−6.63008	−	21.8564i	−0.0102792	−	0.0338860i
$646$	−401.458	−	251.426i	−0.621452	−	0.389205i
$647$	63.6200	−	319.839i	0.0983308	−	0.494342i	−0.899964	−	0.435965i	$-0.856407\pi$
$647$	63.6200	−	319.839i	0.0983308	−	0.494342i	0.998295	−	0.0583775i	$-0.0185927\pi$
$648$	51.3977	−	50.4210i	0.0793174	−	0.0778102i
$649$	12.6611	+	63.6514i	0.0195086	+	0.0980761i
$650$	−694.165	+	311.851i	−1.06795	+	0.479771i
$651$	72.1227	+	7.10347i	0.110788	+	0.0109116i
$652$	83.4002	−	30.7822i	0.127914	−	0.0472120i
$653$	−757.467	−	229.775i	−1.15998	−	0.351876i	−0.349098	−	0.937086i	$-0.613512\pi$
$653$	−757.467	−	229.775i	−1.15998	−	0.351876i	−0.810882	+	0.585210i	$0.801012\pi$
$654$	60.3493	+	4.14932i	0.0922773	+	0.00634453i
$655$	−51.7651	−	21.4418i	−0.0790307	−	0.0327356i
$656$	731.685	+	57.3632i	1.11537	+	0.0874438i
$657$	17.4460	+	42.1184i	0.0265541	+	0.0641072i
$658$	−130.310	+	43.7702i	−0.198040	+	0.0665201i
$659$	−933.399	+	498.912i	−1.41639	+	0.757074i	−0.989128	−	0.147055i	$-0.953020\pi$
$659$	−933.399	+	498.912i	−1.41639	+	0.757074i	−0.427258	+	0.904130i	$0.640520\pi$
$660$	−6.74603	−	1.61850i	−0.0102213	−	0.00245228i
$661$	257.070	+	313.240i	0.388910	+	0.473889i	0.930256	−	0.366912i	$-0.119585\pi$
$661$	257.070	+	313.240i	0.388910	+	0.473889i	−0.541346	+	0.840800i	$0.682085\pi$
$662$	5.32818	+	180.394i	0.00804861	+	0.272499i
$663$	557.249	+	372.342i	0.840497	+	0.561602i
$664$	−424.630	−	355.355i	−0.639504	−	0.535174i
$665$	−9.52975	+	6.36758i	−0.0143305	+	0.00957530i
$666$	−16.5943	+	98.5489i	−0.0249164	+	0.147971i
$667$	−545.969	−	291.826i	−0.818544	−	0.437521i
$668$	774.427	−	871.756i	1.15932	−	1.30502i
$669$	2.57446	−	0.253562i	0.00384822	−	0.000379017i
$670$	39.0774	−	143.996i	0.0583244	−	0.214919i
$671$	85.9642	−	85.9642i	0.128113	−	0.128113i
$672$	−80.2752	−	20.0758i	−0.119457	−	0.0298747i
$673$	−557.121	+	557.121i	−0.827818	+	0.827818i	−0.987215	−	0.159397i	$-0.949045\pi$
$673$	−557.121	+	557.121i	−0.827818	+	0.827818i	0.159397	+	0.987215i	$0.449045\pi$
$674$	588.048	−	337.008i	0.872475	−	0.500011i
$675$	125.945	−	12.4045i	0.186586	−	0.0183771i
$676$	283.716	+	98.3362i	0.419698	+	0.145468i
$677$	−238.726	−	127.602i	−0.352623	−	0.188481i	0.285569	−	0.958358i	$-0.407818\pi$
$677$	−238.726	−	127.602i	−0.352623	−	0.188481i	−0.638192	+	0.769877i	$0.720318\pi$
$678$	−211.352	−	296.942i	−0.311728	−	0.437967i
$679$	6.06886	−	4.05508i	0.00893794	−	0.00597214i
$680$	−76.3272	+	139.562i	−0.112246	+	0.205238i
$681$	−411.978	−	275.275i	−0.604960	−	0.404221i
$682$	−47.9554	+	50.8744i	−0.0703158	+	0.0745959i
$683$	48.7151	+	59.3595i	0.0713252	+	0.0869100i	0.807451	−	0.589935i	$-0.200847\pi$
$683$	48.7151	+	59.3595i	0.0713252	+	0.0869100i	−0.736125	+	0.676845i	$0.763347\pi$
$684$	92.8465	+	67.4356i	0.135740	+	0.0985900i
$685$	−3.93408	+	2.10281i	−0.00574318	+	0.00306979i
$686$	−127.297	+	256.066i	−0.185565	+	0.373274i
$687$	206.268	+	497.976i	0.300245	+	0.724856i
$688$	244.762	+	95.7129i	0.355758	+	0.139118i
$689$	1387.33	+	574.652i	2.01354	+	0.834037i
$690$	34.3075	+	39.3734i	0.0497210	+	0.0570630i
$691$	1176.80	+	356.977i	1.70303	+	0.516610i	0.983970	−	0.178335i	$-0.0570710\pi$
$691$	1176.80	+	356.977i	1.70303	+	0.516610i	0.719064	+	0.694944i	$0.244571\pi$
$692$	−237.632	+	219.731i	−0.343399	+	0.317531i
$693$	−5.55953	−	0.547566i	−0.00802241	−	0.000790139i
$694$	429.445	−	1130.04i	0.618797	−	1.62829i
$695$	−8.99563	−	45.2241i	−0.0129433	−	0.0650706i
$696$	−93.4105	+	447.148i	−0.134210	+	0.642454i
$697$	221.645	−	1114.28i	0.317998	−	1.59868i
$698$	−230.786	−	1004.30i	−0.330639	−	1.43882i
$699$	−59.1733	−	195.068i	−0.0846542	−	0.279068i
$700$	−87.8022	−	115.954i	−0.125432	−	0.165648i
$701$	−120.961	+	147.392i	−0.172555	+	0.210259i	−0.852106	−	0.523370i	$-0.824675\pi$
$701$	−120.961	+	147.392i	−0.172555	+	0.210259i	0.679551	+	0.733628i	$0.262175\pi$
$702$	−128.489	−	99.2473i	−0.183033	−	0.141378i
$703$	−159.276			−0.226567
$704$	62.6670	−	49.4486i	0.0890157	−	0.0702395i
$705$		−	64.0161i		−	0.0908030i
$706$	−766.922	−	592.385i	−1.08629	−	0.839073i
$707$	−143.957	−	118.142i	−0.203617	−	0.167104i
$708$	−357.092	−	49.3370i	−0.504367	−	0.0696850i
$709$	302.276	−	91.6945i	0.426342	−	0.129329i	−0.0698198	−	0.997560i	$-0.522242\pi$
$709$	302.276	−	91.6945i	0.426342	−	0.129329i	0.496161	+	0.868230i	$0.334742\pi$
$710$	37.2541	+	162.116i	0.0524706	+	0.228333i
$711$	218.973	+	43.5564i	0.307978	+	0.0612607i
$712$	533.156	+	363.689i	0.748815	+	0.510799i
$713$	516.178	−	102.674i	0.723952	−	0.144003i
$714$	−45.5034	+	119.737i	−0.0637303	+	0.167699i
$715$	−1.53334	+	15.5683i	−0.00214453	+	0.0217738i
$716$	824.040	+	32.2523i	1.15089	+	0.0450451i
$717$	33.2931	−	109.753i	0.0464339	−	0.153072i
$718$	318.045	+	365.009i	0.442960	+	0.508368i
$719$	−257.228	+	621.003i	−0.357758	+	0.863703i	0.637857	+	0.770155i	$0.279821\pi$
$719$	−257.228	+	621.003i	−0.357758	+	0.863703i	−0.995615	+	0.0935486i	$0.970179\pi$
$720$	20.7658	−	32.4609i	0.0288414	−	0.0450846i
$721$	25.9512	−	10.7494i	0.0359934	−	0.0149090i
$722$	239.987	−	482.749i	0.332392	−	0.668627i
$723$	−380.136	−	711.184i	−0.525775	−	0.983657i
$724$	99.9495	−	15.8459i	0.138052	−	0.0218866i
$725$	−620.667	+	509.368i	−0.856092	+	0.702577i
$726$	−283.812	+	301.088i	−0.390926	+	0.414722i
$727$	−703.205	+	1052.42i	−0.967270	+	1.44762i	−0.0744418	+	0.997225i	$0.523717\pi$
$727$	−703.205	+	1052.42i	−0.967270	+	1.44762i	−0.892828	+	0.450397i	$0.851283\pi$
$728$	−20.0693	+	185.508i	−0.0275677	+	0.254819i
$729$	15.0004	+	22.4497i	0.0205767	+	0.0307952i
$730$	14.1486	+	19.8782i	0.0193816	+	0.0272304i
$731$	191.777	−	358.789i	0.262348	−	0.490819i
$732$	294.790	+	607.538i	0.402719	+	0.829970i
$733$	34.8103	+	353.435i	0.0474902	+	0.482176i	0.989286	+	0.145990i	$0.0466368\pi$
$733$	34.8103	+	353.435i	0.0474902	+	0.482176i	−0.941796	+	0.336185i	$0.890863\pi$
$734$	471.808	−	270.391i	0.642791	−	0.368380i
$735$	−45.9870	−	45.9870i	−0.0625673	−	0.0625673i
$736$	−600.178	+	29.7114i	−0.815460	+	0.0403687i
$737$	81.9581	+	81.9581i	0.111205	+	0.111205i
$738$	−72.0828	+	265.617i	−0.0976731	+	0.359914i
$739$	−102.306	−	1038.73i	−0.138439	−	1.40559i	−0.773826	−	0.633398i	$-0.781659\pi$
$739$	−102.306	−	1038.73i	−0.138439	−	1.40559i	0.635387	−	0.772194i	$-0.280841\pi$
$740$	3.15683	+	53.3932i	0.00426599	+	0.0721530i
$741$	121.978	−	228.205i	0.164613	−	0.307969i
$742$	−47.6563	+	283.017i	−0.0642268	+	0.381424i
$743$	−429.087	−	642.174i	−0.577506	−	0.864299i	0.421591	−	0.906786i	$-0.361472\pi$
$743$	−429.087	−	642.174i	−0.577506	−	0.864299i	−0.999097	+	0.0424874i	$0.986472\pi$
$744$	−179.770	−	344.227i	−0.241626	−	0.462671i
$745$	92.1373	−	137.893i	0.123674	−	0.185092i
$746$	25.1444	+	851.304i	0.0337056	+	1.14116i
$747$	160.507	−	131.725i	0.214869	−	0.176338i
$748$	−64.5814	−	105.352i	−0.0863387	−	0.140844i
$749$	−58.8212	−	110.047i	−0.0785330	−	0.146925i
$750$	130.114	−	43.7044i	0.173486	−	0.0582725i
$751$	−34.3211	+	14.2163i	−0.0457005	+	0.0189298i	−0.405417	−	0.914132i	$-0.632874\pi$
$751$	−34.3211	+	14.2163i	−0.0457005	+	0.0189298i	0.359716	+	0.933062i	$0.382874\pi$
$752$	578.609	+	455.856i	0.769427	+	0.606191i
$753$	−103.043	+	248.768i	−0.136843	+	0.330369i
$754$	1027.63	+	70.6550i	1.36291	+	0.0937069i
$755$	56.1201	−	185.003i	0.0743313	−	0.245037i
$756$	12.9869	−	28.1819i	0.0171784	−	0.0372777i
$757$	−28.7880	+	292.290i	−0.0380291	+	0.386116i	0.957265	+	0.289213i	$0.0933936\pi$
$757$	−28.7880	+	292.290i	−0.0380291	+	0.386116i	−0.995294	+	0.0969028i	$0.969106\pi$
$758$	737.728	−	331.421i	0.973256	−	0.437231i
$759$	−39.7892	+	7.91457i	−0.0524232	+	0.0104276i
$760$	56.5128	+	24.0460i	0.0743590	+	0.0316395i
$761$	−1009.99	−	200.899i	−1.32719	−	0.263994i	−0.519937	−	0.854205i	$-0.674044\pi$
$761$	−1009.99	−	200.899i	−1.32719	−	0.263994i	−0.807249	+	0.590211i	$0.799044\pi$
$762$	−33.9835	−	21.2833i	−0.0445978	−	0.0279308i
$763$	24.9480	−	7.56788i	0.0326972	−	0.00991859i
$764$	−350.268	+	91.4576i	−0.458466	+	0.119709i
$765$	−46.1110	−	37.8424i	−0.0602759	−	0.0494671i
$766$	91.1833	+	710.143i	0.119038	+	0.927080i
$767$			812.870i			1.05980i
$768$	145.525	+	418.844i	0.189486	+	0.545370i
$769$	−161.994			−0.210655			−0.105328	−	0.994438i	$-0.533589\pi$
$769$	−161.994			−0.210655			−0.105328	+	0.994438i	$0.533589\pi$
$770$	−2.96554	+	0.380779i	−0.00385135	+	0.000494519i
$771$	91.4584	−	111.442i	0.118623	−	0.144543i
$772$	−60.5093	−	231.741i	−0.0783799	−	0.300183i
$773$	266.396	+	878.190i	0.344626	+	1.13608i	0.942420	+	0.334430i	$0.108544\pi$
$773$	266.396	+	878.190i	0.344626	+	1.13608i	−0.597794	+	0.801649i	$0.703956\pi$
$774$	−52.3104	+	83.5253i	−0.0675845	+	0.107914i
$775$	133.167	−	669.475i	0.171828	−	0.863839i
$776$	−35.9893	−	15.3133i	−0.0463779	−	0.0197336i
$777$	8.40258	+	42.2426i	0.0108141	+	0.0543663i
$778$	335.398	+	746.579i	0.431102	+	0.959613i
$779$	−436.534	−	42.9948i	−0.560377	−	0.0551923i
$780$	−78.9174	−	36.3670i	−0.101176	−	0.0466244i
$781$	−123.655	−	37.5104i	−0.158330	−	0.0480287i
$782$	−63.8057	+	928.014i	−0.0815929	+	1.18672i
$783$	−158.261	−	65.5538i	−0.202121	−	0.0837213i
$784$	743.124	−	88.1815i	0.947862	−	0.112476i
$785$	−4.90464	−	11.8409i	−0.00624795	−	0.0150839i
$786$	76.9817	+	229.186i	0.0979412	+	0.291585i
$787$	776.558	−	415.079i	0.986732	−	0.527419i	0.102633	−	0.994719i	$-0.467273\pi$
$787$	776.558	−	415.079i	0.986732	−	0.527419i	0.884099	+	0.467300i	$0.154773\pi$
$788$	671.696	−	411.755i	0.852407	−	0.522532i
$789$	355.539	+	433.225i	0.450620	+	0.549082i
$790$	119.439	−	3.52779i	0.151189	−	0.00446556i
$791$	−130.608	−	87.2698i	−0.165118	−	0.110328i
$792$	13.8574	+	26.5345i	0.0174967	+	0.0335032i
$793$	1266.09	−	845.977i	1.59659	−	1.06681i
$794$	1091.51	+	183.796i	1.37470	+	0.231481i
$795$	−117.872	−	63.0040i	−0.148267	−	0.0792503i
$796$	−436.150	+	25.7870i	−0.547928	+	0.0323958i
$797$	−1071.09	+	105.493i	−1.34390	+	0.132362i	−0.744249	−	0.667902i	$-0.767192\pi$
$797$	−1071.09	+	105.493i	−1.34390	+	0.132362i	−0.599647	+	0.800264i	$0.704692\pi$
$798$	47.7291	+	12.9527i	0.0598109	+	0.0162314i
$799$	806.285	−	806.285i	1.00912	−	1.00912i
$800$	−262.288	+	733.916i	−0.327859	+	0.917395i
$801$	−171.134	+	171.134i	−0.213651	+	0.213651i
$802$	−79.0833	−	137.993i	−0.0986076	−	0.172061i
$803$	−18.8629	+	1.85783i	−0.0234905	+	0.00231361i
$804$	−579.226	+	281.053i	−0.720430	+	0.349568i
$805$	19.8494	+	10.6097i	0.0246577	+	0.0131798i
$806$	−713.427	+	507.790i	−0.885145	+	0.630013i
$807$	193.120	−	129.039i	0.239306	−	0.159899i
$808$	−107.333	+	992.124i	−0.132838	+	1.22788i
$809$	1059.03	+	707.620i	1.30906	+	0.874685i	0.997151	−	0.0754272i	$-0.0240321\pi$
$809$	1059.03	+	707.620i	1.30906	+	0.874685i	0.311908	+	0.950112i	$0.399032\pi$
$810$	10.5153	+	9.91195i	0.0129818	+	0.0122370i
$811$	−546.732	−	666.194i	−0.674145	−	0.821448i	0.317795	−	0.948160i	$-0.397058\pi$
$811$	−546.732	−	666.194i	−0.674145	−	0.821448i	−0.991940	+	0.126712i	$0.959558\pi$
$812$	30.8266	+	194.442i	0.0379638	+	0.239461i
$813$	262.351	−	140.230i	0.322695	−	0.172484i
$814$	−37.2061	−	18.4961i	−0.0457077	−	0.0227225i
$815$	6.82797	+	16.4842i	0.00837787	+	0.0202260i
$816$	670.392	−	147.300i	0.821559	−	0.180515i
$817$	−145.116	−	60.1092i	−0.177621	−	0.0735731i
$818$	1029.25	−	896.819i	1.25825	−	1.09636i
$819$	−66.9586	−	20.3117i	−0.0817565	−	0.0248006i
$820$	−5.76086	+	147.189i	−0.00702544	+	0.179498i
$821$	−1498.92	−	147.631i	−1.82572	−	0.179818i	−0.873826	−	0.486239i	$-0.838369\pi$
$821$	−1498.92	−	147.631i	−1.82572	−	0.179818i	−0.951896	+	0.306421i	$0.900869\pi$
$822$	17.9928	+	6.83777i	0.0218891	+	0.00831846i
$823$	306.244	+	1539.59i	0.372107	+	1.87071i	0.481104	+	0.876664i	$0.340236\pi$
$823$	306.244	+	1539.59i	0.372107	+	1.87071i	−0.108997	+	0.994042i	$0.534764\pi$
$824$	−124.343	−	84.8198i	−0.150902	−	0.102937i
$825$	−10.2651	+	51.6060i	−0.0124425	+	0.0625528i
$826$	−151.414	+	34.7947i	−0.183310	+	0.0421243i
$827$	316.245	+	1042.52i	0.382401	+	1.26061i	0.911237	+	0.411883i	$0.135129\pi$
$827$	316.245	+	1042.52i	0.382401	+	1.26061i	−0.528836	+	0.848724i	$0.677371\pi$
$828$	30.8411	−	223.222i	0.0372477	−	0.269592i
$829$	−23.5577	+	28.7051i	−0.0284170	+	0.0346262i	−0.787025	−	0.616921i	$-0.788380\pi$
$829$	−23.5577	+	28.7051i	−0.0284170	+	0.0346262i	0.758608	+	0.651547i	$0.225880\pi$
$830$	67.9329	−	87.9483i	0.0818469	−	0.105962i
$831$	−682.106			−0.820825
$832$	890.670	−	454.326i	1.07052	−	0.546065i
$833$		−	1158.42i		−	1.39065i
$834$	−121.626	+	157.461i	−0.145834	+	0.188802i
$835$	180.908	+	148.467i	0.216656	+	0.177805i
$836$	−38.0357	+	28.8013i	−0.0454972	+	0.0344513i
$837$	139.357	−	42.2736i	0.166496	−	0.0505061i
$838$	−397.665	+	91.3828i	−0.474540	+	0.109049i
$839$	−1231.88	−	245.036i	−1.46827	−	0.292057i	−0.604768	−	0.796401i	$-0.706734\pi$
$839$	−1231.88	−	245.036i	−1.46827	−	0.292057i	−0.863503	+	0.504344i	$0.831734\pi$
$840$	3.39606	−	16.2567i	0.00404293	−	0.0193532i
$841$	241.083	−	47.9544i	0.286663	−	0.0570207i
$842$	−97.9096	−	37.2084i	−0.116282	−	0.0441905i
$843$	−80.3886	+	816.199i	−0.0953601	+	0.968208i
$844$	675.729	+	730.779i	0.800627	+	0.865852i
$845$	−17.4942	+	57.6706i	−0.0207032	+	0.0682493i
$846$	−208.261	+	181.465i	−0.246171	+	0.214498i
$847$	−68.2416	+	164.750i	−0.0805686	+	0.194510i
$848$	1408.82	−	616.737i	1.66135	−	0.727284i
$849$	817.809	−	338.747i	0.963261	−	0.398996i
$850$	1080.33	+	537.061i	1.27098	+	0.631837i
$851$	147.442	+	275.844i	0.173257	+	0.324141i
$852$	421.802	−	580.744i	0.495073	−	0.681625i
$853$	123.171	−	101.084i	0.144397	−	0.118504i	−0.559422	−	0.828883i	$-0.688977\pi$
$853$	123.171	−	101.084i	0.144397	−	0.118504i	0.703819	+	0.710380i	$0.251477\pi$
$854$	211.775	+	199.624i	0.247980	+	0.233752i
$855$	−12.7953	+	19.1495i	−0.0149653	+	0.0223971i
$856$	−320.837	+	586.639i	−0.374809	+	0.685325i
$857$	−289.976	−	433.979i	−0.338361	−	0.506393i	0.622800	−	0.782381i	$-0.285995\pi$
$857$	−289.976	−	433.979i	−0.338361	−	0.506393i	−0.961161	+	0.275988i	$0.910995\pi$
$858$	54.9940	−	39.1427i	0.0640956	−	0.0456208i
$859$	−361.037	+	675.452i	−0.420299	+	0.786324i	−0.999585	−	0.0288004i	$-0.990831\pi$
$859$	−361.037	+	675.452i	−0.420299	+	0.786324i	0.579286	+	0.815124i	$0.303331\pi$
$860$	−17.2739	+	49.8379i	−0.0200859	+	0.0579510i
$861$	11.6263	+	118.044i	0.0135033	+	0.137101i
$862$	−243.512	−	424.907i	−0.282496	−	0.492931i
$863$	633.239	+	633.239i	0.733765	+	0.733765i	0.971363	−	0.237599i	$-0.0763603\pi$
$863$	633.239	+	633.239i	0.733765	+	0.733765i	−0.237599	+	0.971363i	$0.576360\pi$
$864$	−164.468	+	24.4598i	−0.190356	+	0.0283100i
$865$	−45.9320	−	45.9320i	−0.0531006	−	0.0531006i
$866$	−1105.96	−	300.134i	−1.27709	−	0.346575i
$867$	−55.0807	−	559.243i	−0.0635302	−	0.645033i
$868$	−125.124	−	111.155i	−0.144152	−	0.128058i
$869$	−43.7572	+	81.8640i	−0.0503536	+	0.0942049i
$870$	−90.4081	−	15.2235i	−0.103917	−	0.0174983i
$871$	806.553	+	1207.09i	0.926008	+	1.38587i
$872$	−107.134	−	89.6563i	−0.122861	−	0.102817i
$873$	8.14848	−	12.1951i	0.00933389	−	0.0139691i
$874$	358.989	−	10.6032i	0.410743	−	0.0121318i
$875$	45.7275	−	37.5276i	0.0522600	−	0.0428886i
$876$	24.5623	−	102.377i	0.0280391	−	0.116869i
$877$	−303.979	−	568.706i	−0.346613	−	0.648467i	0.646851	−	0.762617i	$-0.276086\pi$
$877$	−303.979	−	568.706i	−0.346613	−	0.648467i	−0.993464	+	0.114150i	$0.963586\pi$
$878$	−131.025	−	390.082i	−0.149232	−	0.444284i
$879$	−106.896	+	44.2777i	−0.121611	+	0.0503728i
$880$	10.4087	+	12.1796i	0.0118281	+	0.0138405i
$881$	284.189	−	686.092i	0.322575	−	0.778765i	−0.676528	−	0.736417i	$-0.736516\pi$
$881$	284.189	−	686.092i	0.322575	−	0.778765i	0.999103	−	0.0423481i	$-0.0134838\pi$
$882$	−19.2491	+	279.966i	−0.0218243	+	0.317421i
$883$	237.395	−	782.587i	0.268851	−	0.886282i	−0.713726	−	0.700425i	$-0.752994\pi$
$883$	237.395	−	782.587i	0.268851	−	0.886282i	0.982577	−	0.185857i	$-0.0595061\pi$
$884$	−535.923	−	1452.01i	−0.606248	−	1.64255i
$885$	7.09152	−	72.0015i	0.00801302	−	0.0813576i
$886$	447.876	+	996.951i	0.505504	+	1.12523i
$887$	60.3820	−	12.0107i	0.0680744	−	0.0135408i	−0.160936	−	0.986965i	$-0.551451\pi$
$887$	60.3820	−	12.0107i	0.0680744	−	0.0135408i	0.229010	+	0.973424i	$0.426451\pi$
$888$	164.753	−	161.623i	0.185533	−	0.182007i
$889$	−16.9493	−	3.37142i	−0.0190656	−	0.00379238i
$890$	−68.7523	+	109.778i	−0.0772498	+	0.123347i
$891$	−10.7423	+	3.25863i	−0.0120564	+	0.00365728i
$892$	−5.15463	−	3.02014i	−0.00577873	−	0.00338580i
$893$	−340.315	−	279.290i	−0.381092	−	0.312754i
$894$	−709.782	+	91.1368i	−0.793939	+	0.101943i
$895$			165.513i			0.184931i
$896$	122.752	+	146.458i	0.137000	+	0.163458i
$897$	−508.134			−0.566482
$898$	−109.576	−	853.384i	−0.122022	−	0.950316i
$899$	−586.136	+	714.208i	−0.651986	+	0.794447i
$900$	−252.170	−	147.748i	−0.280189	−	0.164165i
$901$	−691.066	−	2278.14i	−0.766999	−	2.52846i
$902$	−96.9791	−	60.7363i	−0.107516	−	0.0673352i
$903$	−8.28635	+	41.6583i	−0.00917646	+	0.0461332i
$904$	−8.07337	+	841.687i	−0.00893072	+	0.931069i
$905$	3.96240	+	19.9203i	0.00437834	+	0.0220114i
$906$	−760.945	+	341.852i	−0.839895	+	0.377320i
$907$	−1332.18	−	131.209i	−1.46878	−	0.144662i	−0.668241	−	0.743945i	$-0.732953\pi$
$907$	−1332.18	−	131.209i	−1.46878	−	0.144662i	−0.800538	+	0.599283i	$0.795453\pi$
$908$	396.211	+	1073.48i	0.436356	+	1.18225i
$909$	−358.104	−	108.630i	−0.393953	−	0.119504i
$910$	−37.3610	−	2.56876i	−0.0410560	−	0.00282281i
$911$	−1317.92	−	545.900i	−1.44667	−	0.599232i	−0.485267	−	0.874366i	$-0.661278\pi$
$911$	−1317.92	−	545.900i	−1.44667	−	0.599232i	−0.961406	+	0.275134i	$0.911278\pi$
$912$	−81.9680	−	252.013i	−0.0898772	−	0.276330i
$913$	33.0367	+	79.7576i	0.0361848	+	0.0873577i
$914$	−1174.24	+	394.418i	−1.28473	+	0.431530i
$915$	−119.527	+	63.8885i	−0.130631	+	0.0698235i
$916$	290.406	−	1210.43i	0.317037	−	1.32143i
$917$	66.1018	+	80.5452i	0.0720848	+	0.0878356i
$918$	7.59916	+	257.282i	0.00827795	+	0.280263i
$919$	−752.448	−	502.769i	−0.818768	−	0.547083i	0.0741793	−	0.997245i	$-0.476366\pi$
$919$	−752.448	−	502.769i	−0.818768	−	0.547083i	−0.892947	+	0.450162i	$0.851366\pi$
$920$	−10.6696	−	120.132i	−0.0115974	−	0.130578i
$921$	424.644	−	283.738i	0.461069	−	0.308076i
$922$	130.315	−	773.902i	0.141339	−	0.839373i
$923$	−1427.40	−	762.960i	−1.54648	−	0.826609i
$924$	9.64513	+	8.56828i	0.0104385	+	0.00927303i
$925$	403.713	−	39.7623i	0.436447	−	0.0429862i
$926$	−31.8916	+	117.517i	−0.0344402	+	0.126908i
$927$	39.9121	−	39.9121i	0.0430551	−	0.0430551i
$928$	781.389	−	708.746i	0.842014	−	0.763735i
$929$	138.914	−	138.914i	0.149531	−	0.149531i	−0.628378	−	0.777908i	$-0.716281\pi$
$929$	138.914	−	138.914i	0.149531	−	0.149531i	0.777908	+	0.628378i	$0.216281\pi$
$930$	67.6231	−	38.7545i	0.0727130	−	0.0416715i
$931$	−445.103	+	43.8388i	−0.478091	+	0.0470879i
$932$	−154.169	+	444.802i	−0.165417	+	0.477255i
$933$	407.907	+	218.031i	0.437199	+	0.233688i
$934$	242.621	+	340.873i	0.259765	+	0.364961i
$935$	20.6212	−	13.7786i	0.0220547	−	0.0147365i
$936$	105.394	+	359.827i	0.112601	+	0.384431i
$937$	−1503.85	−	1004.84i	−1.60496	−	1.07240i	−0.947903	−	0.318560i	$-0.896801\pi$
$937$	−1503.85	−	1004.84i	−1.60496	−	1.07240i	−0.657057	−	0.753840i	$-0.728199\pi$
$938$	−190.321	+	201.906i	−0.202901	+	0.215252i
$939$	126.695	+	154.378i	0.134926	+	0.164407i
$940$	−86.8795	+	119.617i	−0.0924250	+	0.127252i
$941$	−701.479	+	374.948i	−0.745462	+	0.398457i	−0.799958	−	0.600057i	$-0.795145\pi$
$941$	−701.479	+	374.948i	−0.745462	+	0.398457i	0.0544961	+	0.998514i	$0.482645\pi$
$942$	−24.6182	+	49.5211i	−0.0261340	+	0.0525701i
$943$	329.637	+	795.815i	0.349562	+	0.843918i
$944$	600.286	+	576.816i	0.635896	+	0.611034i
$945$	5.75378	+	2.38329i	0.00608866	+	0.00252200i
$946$	−26.9182	−	30.8930i	−0.0284548	−	0.0326565i
$947$	−1141.70	−	346.332i	−1.20560	−	0.365715i	−0.377349	−	0.926071i	$-0.623164\pi$
$947$	−1141.70	−	346.332i	−1.20560	−	0.365715i	−0.828252	+	0.560356i	$0.810664\pi$
$948$	−350.048	−	378.566i	−0.369249	−	0.399331i
$949$	−236.263	−	23.2698i	−0.248960	−	0.0245204i
$950$	165.474	−	435.425i	0.174183	−	0.458342i
$951$	−7.49519	−	37.6808i	−0.00788137	−	0.0396223i
$952$	247.527	−	161.980i	0.260007	−	0.170147i
$953$	253.581	−	1274.84i	0.266087	−	1.33771i	−0.584295	−	0.811541i	$-0.698629\pi$
$953$	253.581	−	1274.84i	0.266087	−	1.33771i	0.850382	−	0.526166i	$-0.176371\pi$
$954$	129.162	+	562.064i	0.135390	+	0.589166i
$955$	−21.0910	−	69.5279i	−0.0220849	−	0.0728040i
$956$	−211.161	+	159.894i	−0.220879	+	0.167254i
$957$	45.1819	−	55.0543i	0.0472120	−	0.0575280i
$958$	−210.874	−	162.883i	−0.220119	−	0.170024i
$959$	8.29556			0.00865022
$960$	−82.8563	+	32.4725i	−0.0863086	+	0.0338255i
$961$			175.535i			0.182659i
$962$	−411.866	−	318.133i	−0.428135	−	0.330700i
$963$	−193.825	−	159.068i	−0.201272	−	0.165180i
$964$	−254.881	+	1844.78i	−0.264400	+	1.91368i
$965$	46.0004	−	13.9541i	0.0476688	−	0.0144602i
$966$	−21.7505	−	94.6504i	−0.0225161	−	0.0979818i
$967$	−578.088	−	114.989i	−0.597816	−	0.118913i	−0.113098	−	0.993584i	$-0.536078\pi$
$967$	−578.088	−	114.989i	−0.597816	−	0.118913i	−0.484717	+	0.874671i	$0.661078\pi$
$968$	938.938	−	177.422i	0.969978	−	0.183287i
$969$	−402.346	+	80.0317i	−0.415218	+	0.0825920i
$970$	2.78857	−	7.33779i	0.00287481	−	0.00756473i
$971$	−109.047	+	1107.17i	−0.112304	+	1.14024i	0.759543	+	0.650457i	$0.225423\pi$
$971$	−109.047	+	1107.17i	−0.112304	+	1.14024i	−0.871846	+	0.489780i	$0.837077\pi$
$972$	2.43862	−	62.3061i	0.00250887	−	0.0641010i
$973$	−24.8916	+	82.0565i	−0.0255823	+	0.0843335i
$974$	680.575	+	781.071i	0.698743	+	0.801921i
$975$	−252.205	+	608.876i	−0.258672	+	0.624488i
$976$	273.691	−	1535.29i	0.280421	−	1.57304i
$977$	−36.0692	+	14.9403i	−0.0369183	+	0.0152920i	−0.401066	−	0.916049i	$-0.631360\pi$
$977$	−36.0692	+	14.9403i	−0.0369183	+	0.0152920i	0.364148	+	0.931341i	$0.381360\pi$
$978$	34.2721	−	68.9404i	0.0350431	−	0.0704912i
$979$	−47.4336	−	88.7420i	−0.0484511	−	0.0906456i
$980$	23.5177	+	148.340i	0.0239976	+	0.151368i
$981$	40.4960	−	33.2342i	0.0412804	−	0.0338779i
$982$	62.7365	−	66.5553i	0.0638865	−	0.0677753i
$983$	828.868	−	1240.49i	0.843203	−	1.26194i	−0.119894	−	0.992787i	$-0.538255\pi$
$983$	828.868	−	1240.49i	0.843203	−	1.26194i	0.963097	−	0.269155i	$-0.0867445\pi$
$984$	495.172	−	398.491i	0.503224	−	0.404970i
$985$	87.8493	+	131.476i	0.0891871	+	0.133478i
$986$	−946.952	−	1330.43i	−0.960397	−	1.34932i
$987$	−56.1188	+	104.991i	−0.0568580	+	0.106374i
$988$	−537.631	+	260.870i	−0.544161	+	0.264038i
$989$	30.2333	+	306.964i	0.0305696	+	0.310378i
$990$	−5.21268	+	2.98736i	−0.00526533	+	0.00301754i
$991$	1244.03	+	1244.03i	1.25533	+	1.25533i	0.953297	+	0.302034i	$0.0976655\pi$
$991$	1244.03	+	1244.03i	1.25533	+	1.25533i	0.302034	+	0.953297i	$0.402335\pi$
$992$	−131.259	+	887.179i	−0.132318	+	0.894334i
$993$	110.517	+	110.517i	0.111296	+	0.111296i
$994$	81.0175	−	298.540i	0.0815066	−	0.300342i
$995$	−8.59504	−	87.2669i	−0.00863823	−	0.0877054i
$996$	−478.686	+	28.3019i	−0.480608	+	0.0284156i
$997$	729.140	−	1364.13i	0.731334	−	1.36823i	−0.190904	−	0.981609i	$-0.561142\pi$
$997$	729.140	−	1364.13i	0.731334	−	1.36823i	0.922238	−	0.386621i	$-0.126358\pi$
$998$	−168.955	+	1003.37i	−0.169293	+	1.00538i
$999$	48.0831	+	71.9615i	0.0481313	+	0.0720336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.u.a.235.2	yes	1024
128.67	odd	32	inner	384.3.u.a.67.2	✓	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.3.u.a.67.2	✓	1024	128.67	odd	32	inner
384.3.u.a.235.2	yes	1024	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	384.u (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98371 + 0.254711i) q^{2} +(-1.09880 + 1.33889i) q^{3} +(3.87024 - 1.01055i) q^{4} +(0.233043 + 0.768239i) q^{5} +(1.83868 - 2.93586i) q^{6} +(0.291260 - 1.46426i) q^{7} +(-7.42006 + 2.99044i) q^{8} +(-0.585271 - 2.94236i) q^{9} +O(q^{10})\)	\(q+(-1.98371 + 0.254711i) q^{2} +(-1.09880 + 1.33889i) q^{3} +(3.87024 - 1.01055i) q^{4} +(0.233043 + 0.768239i) q^{5} +(1.83868 - 2.93586i) q^{6} +(0.291260 - 1.46426i) q^{7} +(-7.42006 + 2.99044i) q^{8} +(-0.585271 - 2.94236i) q^{9} +(-0.657970 - 1.46461i) q^{10} +(1.24129 + 0.122256i) q^{11} +(-2.89961 + 6.29224i) q^{12} +(14.9500 + 4.53503i) q^{13} +(-0.204812 + 2.97886i) q^{14} +(-1.28466 - 0.532123i) q^{15} +(13.9576 - 7.82214i) q^{16} +(-9.47821 - 22.8824i) q^{17} +(1.91046 + 5.68772i) q^{18} +(-8.43352 + 4.50781i) q^{19} +(1.67828 + 2.73777i) q^{20} +(1.64045 + 1.99890i) q^{21} +(-2.49350 + 0.0736488i) q^{22} +(15.6138 + 10.4328i) q^{23} +(4.14930 - 13.2206i) q^{24} +(20.2509 - 13.5312i) q^{25} +(-30.8116 - 5.18827i) q^{26} +(4.58260 + 2.44945i) q^{27} +(-0.352462 - 5.96138i) q^{28} +(-32.8080 + 3.23131i) q^{29} +(2.68393 + 0.728363i) q^{30} +(19.8175 - 19.8175i) q^{31} +(-25.6955 + 19.0721i) q^{32} +(-1.52762 + 1.52762i) q^{33} +(24.6305 + 42.9780i) q^{34} +(1.19278 - 0.117478i) q^{35} +(-5.23854 - 10.7962i) q^{36} +(14.6893 + 7.85161i) q^{37} +(15.5815 - 11.0903i) q^{38} +(-22.4990 + 15.0333i) q^{39} +(-4.02656 - 5.00348i) q^{40} +(38.1400 + 25.4844i) q^{41} +(-3.76333 - 3.54740i) q^{42} +(10.4203 + 12.6972i) q^{43} +(4.92763 - 0.781221i) q^{44} +(2.12404 - 1.13532i) q^{45} +(-33.6306 - 16.7187i) q^{46} +(17.6180 + 42.5336i) q^{47} +(-4.86359 + 27.2827i) q^{48} +(43.2109 + 17.8985i) q^{49} +(-36.7254 + 32.0001i) q^{50} +(41.0518 + 12.4529i) q^{51} +(62.4430 + 2.44397i) q^{52} +(95.6561 + 9.42130i) q^{53} +(-9.71447 - 3.69177i) q^{54} +(0.195351 + 0.982097i) q^{55} +(2.21761 + 11.7359i) q^{56} +(3.23129 - 16.2448i) q^{57} +(64.2587 - 14.7666i) q^{58} +(15.1039 + 49.7909i) q^{59} +(-5.50968 - 0.761235i) q^{60} +(61.8333 - 75.3440i) q^{61} +(-34.2645 + 44.3599i) q^{62} -4.47884 q^{63} +(46.1146 - 44.3784i) q^{64} +12.5420i q^{65} +(2.64125 - 3.41946i) q^{66} +(71.8329 + 58.9517i) q^{67} +(-59.8068 - 78.9824i) q^{68} +(-31.1249 + 9.44162i) q^{69} +(-2.33621 + 0.536858i) q^{70} +(-101.609 - 20.2113i) q^{71} +(13.1417 + 20.0822i) q^{72} +(-14.9042 + 2.96463i) q^{73} +(-31.1393 - 11.8338i) q^{74} +(-4.13485 + 41.9818i) q^{75} +(-28.0844 + 25.9688i) q^{76} +(0.540552 - 1.78196i) q^{77} +(40.8024 - 35.5526i) q^{78} +(-28.4796 + 68.7559i) q^{79} +(9.26199 + 8.89987i) q^{80} +(-8.31492 + 3.44415i) q^{81} +(-82.1501 - 40.8390i) q^{82} +(32.6268 + 61.0404i) q^{83} +(8.36893 + 6.07846i) q^{84} +(15.3703 - 12.6141i) q^{85} +(-23.9050 - 22.5334i) q^{86} +(31.7231 - 47.4770i) q^{87} +(-9.57603 + 2.80484i) q^{88} +(-44.8198 - 67.0775i) q^{89} +(-3.92431 + 2.79317i) q^{90} +(10.9948 - 20.5698i) q^{91} +(70.9720 + 24.5990i) q^{92} +(4.75802 + 48.3090i) q^{93} +(-45.7829 - 79.8871i) q^{94} +(-5.42845 - 5.42845i) q^{95} +(2.69877 - 55.3599i) q^{96} +(3.45702 + 3.45702i) q^{97} +(-90.2770 - 24.4993i) q^{98} +(-0.366769 - 3.72386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 1248 q^{50} + 1056 q^{52} + 288 q^{54} + 1568 q^{56} + 576 q^{60} + 192 q^{62} - 192 q^{64} - 576 q^{66} - 960 q^{68} - 1344 q^{70} - 2464 q^{74} - 416 q^{76} - 1440 q^{78} - 1632 q^{80}+O(q^{100}) \) 1024 * q + 1248 * q^50 + 1056 * q^52 + 288 * q^54 + 1568 * q^56 + 576 * q^60 + 192 * q^62 - 192 * q^64 - 576 * q^66 - 960 * q^68 - 1344 * q^70 - 2464 * q^74 - 416 * q^76 - 1440 * q^78 - 1632 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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