LMFDB - Embedded newform 230.4.l.a.217.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.16
Character	$\chi$	$=$	230.217
Dual form			230.4.l.a.53.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.142678 + 1.99490i) q^{2} +(7.65881 - 1.66607i) q^{3} +(-3.95929 - 0.569259i) q^{4} +(-10.5246 - 3.77252i) q^{5} +(2.23091 + 15.5163i) q^{6} +(30.1671 - 16.4725i) q^{7} +(1.70052 - 7.81717i) q^{8} +(31.3215 - 14.3041i) q^{9} +(9.02746 - 20.4574i) q^{10} +(-52.5357 - 45.5225i) q^{11} +(-31.2719 + 2.23661i) q^{12} +(-5.05408 + 9.25586i) q^{13} +(28.5568 + 62.5307i) q^{14} +(-86.8915 - 11.3582i) q^{15} +(15.3519 + 4.50772i) q^{16} +(-26.3381 - 19.7165i) q^{17} +(24.0663 + 64.5244i) q^{18} +(16.0009 - 111.289i) q^{19} +(39.5225 + 20.9277i) q^{20} +(203.600 - 176.420i) q^{21} +(98.3086 - 98.3086i) q^{22} +(41.0776 + 102.370i) q^{23} -62.7035i q^{24} +(96.5362 + 79.4089i) q^{25} +(-17.7434 - 11.4030i) q^{26} +(46.6403 - 34.9145i) q^{27} +(-128.817 + 48.0463i) q^{28} +(42.1443 - 6.05944i) q^{29} +(35.0561 - 171.720i) q^{30} +(177.298 - 113.943i) q^{31} +(-11.1829 + 29.9824i) q^{32} +(-478.205 - 261.120i) q^{33} +(43.0903 - 49.7289i) q^{34} +(-379.640 + 59.5609i) q^{35} +(-132.154 + 38.8038i) q^{36} +(-13.7882 - 5.14274i) q^{37} +(219.728 + 47.7988i) q^{38} +(-23.2873 + 79.3093i) q^{39} +(-47.3879 + 75.8577i) q^{40} +(21.2072 - 46.4373i) q^{41} +(322.892 + 431.333i) q^{42} +(35.1540 + 161.600i) q^{43} +(182.090 + 210.143i) q^{44} +(-383.610 + 32.3840i) q^{45} +(-210.079 + 67.3400i) q^{46} +(298.302 + 298.302i) q^{47} +(125.087 + 8.94643i) q^{48} +(453.270 - 705.302i) q^{49} +(-172.187 + 181.250i) q^{50} +(-234.568 - 107.123i) q^{51} +(25.2795 - 33.7695i) q^{52} +(49.4880 + 90.6305i) q^{53} +(62.9965 + 98.0245i) q^{54} +(381.185 + 677.300i) q^{55} +(-77.4684 - 263.833i) q^{56} +(-62.8673 - 878.999i) q^{57} +(6.07491 + 84.9384i) q^{58} +(175.273 + 596.926i) q^{59} +(337.563 + 94.4343i) q^{60} +(-329.333 - 512.452i) q^{61} +(202.008 + 369.950i) q^{62} +(709.256 - 947.455i) q^{63} +(-58.2164 - 26.5866i) q^{64} +(88.1103 - 78.3480i) q^{65} +(589.138 - 916.717i) q^{66} +(272.829 + 19.5131i) q^{67} +(93.0563 + 93.0563i) q^{68} +(485.162 + 715.595i) q^{69} +(-64.6518 - 765.844i) q^{70} +(-182.495 - 210.610i) q^{71} +(-58.5544 - 269.170i) q^{72} +(420.111 + 561.202i) q^{73} +(12.2266 - 26.7724i) q^{74} +(871.653 + 447.341i) q^{75} +(-126.704 + 431.516i) q^{76} +(-2334.72 - 507.886i) q^{77} +(-154.892 - 57.7717i) q^{78} +(-520.480 + 152.827i) q^{79} +(-144.568 - 105.357i) q^{80} +(-309.783 + 357.508i) q^{81} +(89.6122 + 48.9319i) q^{82} +(57.3391 - 153.732i) q^{83} +(-906.538 + 582.596i) q^{84} +(202.818 + 306.870i) q^{85} +(-327.393 + 47.0720i) q^{86} +(312.680 - 116.624i) q^{87} +(-445.195 + 333.269i) q^{88} +(210.478 + 135.266i) q^{89} +(-9.87005 - 769.887i) q^{90} +362.475i q^{91} +(-104.363 - 428.696i) q^{92} +(1168.06 - 1168.06i) q^{93} +(-637.646 + 552.523i) q^{94} +(-588.244 + 1110.91i) q^{95} +(-35.6945 + 248.261i) q^{96} +(334.909 + 897.926i) q^{97} +(1342.34 + 1004.86i) q^{98} +(-2296.66 - 674.359i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) $ 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	−0.142678	+	1.99490i	−0.0504444	+	0.705305i
$2$	−0.142678	+	1.99490i	−0.0504444	+	0.705305i
$3$	7.65881	−	1.66607i	1.47394	−	0.320636i	0.597391	−	0.801950i	$-0.296204\pi$
$3$	7.65881	−	1.66607i	1.47394	−	0.320636i	0.876548	+	0.481314i	$0.159840\pi$
$4$	−3.95929	−	0.569259i	−0.494911	−	0.0711574i
$5$	−10.5246	−	3.77252i	−0.941353	−	0.337425i
$5$	−10.5246	−	3.77252i	−0.941353	−	0.337425i
$6$	2.23091	+	15.5163i	0.151794	+	1.05575i
$7$	30.1671	−	16.4725i	1.62887	−	0.889430i	0.635805	−	0.771850i	$-0.280668\pi$
$7$	30.1671	−	16.4725i	1.62887	−	0.889430i	0.993063	−	0.117580i	$-0.0375137\pi$
$8$	1.70052	−	7.81717i	0.0751532	−	0.345474i
$9$	31.3215	−	14.3041i	1.16006	−	0.529780i
$10$	9.02746	−	20.4574i	0.285473	−	0.646920i
$11$	−52.5357	−	45.5225i	−1.44001	−	1.24778i	−0.919019	−	0.394214i	$-0.871017\pi$
$11$	−52.5357	−	45.5225i	−1.44001	−	1.24778i	−0.520992	−	0.853562i	$-0.674438\pi$
$12$	−31.2719	+	2.23661i	−0.752284	+	0.0538044i
$13$	−5.05408	+	9.25586i	−0.107827	+	0.197470i	−0.926021	−	0.377472i	$-0.876794\pi$
$13$	−5.05408	+	9.25586i	−0.107827	+	0.197470i	0.818194	+	0.574942i	$0.194975\pi$
$14$	28.5568	+	62.5307i	0.545152	+	1.19372i
$15$	−86.8915	−	11.3582i	−1.49569	−	0.195512i
$16$	15.3519	+	4.50772i	0.239873	+	0.0704331i
$17$	−26.3381	−	19.7165i	−0.375760	−	0.281291i	0.394660	−	0.918827i	$-0.370863\pi$
$17$	−26.3381	−	19.7165i	−0.375760	−	0.281291i	−0.770420	+	0.637537i	$0.779953\pi$
$18$	24.0663	+	64.5244i	0.315138	+	0.844919i
$19$	16.0009	−	111.289i	0.193203	−	1.34376i	−0.630258	−	0.776386i	$-0.717051\pi$
$19$	16.0009	−	111.289i	0.193203	−	1.34376i	0.823461	−	0.567373i	$-0.192040\pi$
$20$	39.5225	+	20.9277i	0.441875	+	0.233979i
$21$	203.600	−	176.420i	2.11567	−	1.83324i
$22$	98.3086	−	98.3086i	0.952703	−	0.952703i
$23$	41.0776	+	102.370i	0.372404	+	0.928071i
$23$	41.0776	+	102.370i	0.372404	+	0.928071i
$24$		−	62.7035i		−	0.533304i
$25$	96.5362	+	79.4089i	0.772289	+	0.635271i
$26$	−17.7434	−	11.4030i	−0.133838	−	0.0860121i
$27$	46.6403	−	34.9145i	0.332442	−	0.248863i
$28$	−128.817	+	48.0463i	−0.869434	+	0.324282i
$29$	42.1443	−	6.05944i	0.269862	−	0.0388003i	−0.00605528	−	0.999982i	$-0.501927\pi$
$29$	42.1443	−	6.05944i	0.269862	−	0.0388003i	0.275917	+	0.961181i	$0.411018\pi$
$30$	35.0561	−	171.720i	0.213345	−	1.04505i
$31$	177.298	−	113.943i	1.02722	−	0.660151i	0.0854222	−	0.996345i	$-0.472776\pi$
$31$	177.298	−	113.943i	1.02722	−	0.660151i	0.941793	+	0.336194i	$0.109140\pi$
$32$	−11.1829	+	29.9824i	−0.0617771	+	0.165631i
$33$	−478.205	−	261.120i	−2.52257	−	1.37743i
$34$	43.0903	−	49.7289i	0.217351	−	0.250836i
$35$	−379.640	+	59.5609i	−1.83346	+	0.287646i
$36$	−132.154	+	38.8038i	−0.611823	+	0.179647i
$37$	−13.7882	−	5.14274i	−0.0612640	−	0.0228503i	0.318645	−	0.947874i	$-0.396772\pi$
$37$	−13.7882	−	5.14274i	−0.0612640	−	0.0228503i	−0.379909	+	0.925024i	$0.624045\pi$
$38$	219.728	+	47.7988i	0.938014	+	0.204052i
$39$	−23.2873	+	79.3093i	−0.0956143	+	0.325632i
$40$	−47.3879	+	75.8577i	−0.187317	+	0.299854i
$41$	21.2072	−	46.4373i	0.0807807	−	0.176885i	−0.864932	−	0.501889i	$-0.832638\pi$
$41$	21.2072	−	46.4373i	0.0807807	−	0.176885i	0.945713	+	0.325004i	$0.105366\pi$
$42$	322.892	+	431.333i	1.18627	+	1.58467i
$43$	35.1540	+	161.600i	0.124673	+	0.573112i	0.996521	+	0.0833367i	$0.0265577\pi$
$43$	35.1540	+	161.600i	0.124673	+	0.573112i	−0.871848	+	0.489776i	$0.837079\pi$
$44$	182.090	+	210.143i	0.623888	+	0.720005i
$45$	−383.610	+	32.3840i	−1.27078	+	0.107278i
$46$	−210.079	+	67.3400i	−0.673359	+	0.215842i
$47$	298.302	+	298.302i	0.925785	+	0.925785i	0.997430	−	0.0716455i	$-0.0228250\pi$
$47$	298.302	+	298.302i	0.925785	+	0.925785i	−0.0716455	+	0.997430i	$0.522825\pi$
$48$	125.087	+	8.94643i	0.376142	+	0.0269022i
$49$	453.270	−	705.302i	1.32149	−	2.05627i
$50$	−172.187	+	181.250i	−0.487018	+	0.512654i
$51$	−234.568	−	107.123i	−0.644040	−	0.294123i
$52$	25.2795	−	33.7695i	0.0674162	−	0.0900575i
$53$	49.4880	+	90.6305i	0.128258	+	0.234888i	0.933915	−	0.357495i	$-0.116369\pi$
$53$	49.4880	+	90.6305i	0.128258	+	0.234888i	−0.805657	+	0.592383i	$0.798187\pi$
$54$	62.9965	+	98.0245i	0.158754	+	0.247027i
$55$	381.185	+	677.300i	0.934527	+	1.66049i
$56$	−77.4684	−	263.833i	−0.184860	−	0.629575i
$57$	−62.8673	−	878.999i	−0.146087	−	2.04257i
$58$	6.07491	+	84.9384i	0.0137530	+	0.192292i
$59$	175.273	+	596.926i	0.386757	+	1.31717i	0.891154	+	0.453700i	$0.149896\pi$
$59$	175.273	+	596.926i	0.386757	+	1.31717i	−0.504398	+	0.863471i	$0.668285\pi$
$60$	337.563	+	94.4343i	0.726319	+	0.203190i
$61$	−329.333	−	512.452i	−0.691258	−	1.07562i	−0.992521	−	0.122077i	$-0.961045\pi$
$61$	−329.333	−	512.452i	−0.691258	−	1.07562i	0.301263	−	0.953541i	$-0.402592\pi$
$62$	202.008	+	369.950i	0.413791	+	0.757801i
$63$	709.256	−	947.455i	1.41838	−	1.89473i
$64$	−58.2164	−	26.5866i	−0.113704	−	0.0519269i
$65$	88.1103	−	78.3480i	0.168134	−	0.149506i
$66$	589.138	−	916.717i	1.09876	−	1.70970i
$67$	272.829	+	19.5131i	0.497484	+	0.0355808i	0.317827	−	0.948149i	$-0.397047\pi$
$67$	272.829	+	19.5131i	0.497484	+	0.0355808i	0.179657	+	0.983729i	$0.442501\pi$
$68$	93.0563	+	93.0563i	0.165952	+	0.165952i
$69$	485.162	+	715.595i	0.846473	+	1.24851i
$70$	−64.6518	−	765.844i	−0.110391	−	1.30766i
$71$	−182.495	−	210.610i	−0.305044	−	0.352040i	0.582444	−	0.812871i	$-0.302097\pi$
$71$	−182.495	−	210.610i	−0.305044	−	0.352040i	−0.887488	+	0.460832i	$0.847551\pi$
$72$	−58.5544	−	269.170i	−0.0958431	−	0.440584i
$73$	420.111	+	561.202i	0.673565	+	0.899778i	0.998950	−	0.0458039i	$-0.0145849\pi$
$73$	420.111	+	561.202i	0.673565	+	0.899778i	−0.325385	+	0.945581i	$0.605494\pi$
$74$	12.2266	−	26.7724i	0.0192069	−	0.0420572i
$75$	871.653	+	447.341i	1.34200	+	0.688727i
$76$	−126.704	+	431.516i	−0.191237	+	0.651293i
$77$	−2334.72	−	507.886i	−3.45540	−	0.751675i
$78$	−154.892	−	57.7717i	−0.224847	−	0.0838636i
$79$	−520.480	+	152.827i	−0.741248	+	0.217650i	−0.630490	−	0.776198i	$-0.717146\pi$
$79$	−520.480	+	152.827i	−0.741248	+	0.217650i	−0.110758	+	0.993847i	$0.535328\pi$
$80$	−144.568	−	105.357i	−0.202039	−	0.147242i
$81$	−309.783	+	357.508i	−0.424942	+	0.490409i
$82$	89.6122	+	48.9319i	0.120683	+	0.0658979i
$83$	57.3391	−	153.732i	0.0758287	−	0.203305i	−0.893505	−	0.449054i	$-0.851761\pi$
$83$	57.3391	−	153.732i	0.0758287	−	0.203305i	0.969333	+	0.245749i	$0.0790339\pi$
$84$	−906.538	+	582.596i	−1.17752	+	0.756744i
$85$	202.818	+	306.870i	0.258809	+	0.391584i
$86$	−327.393	+	47.0720i	−0.410508	+	0.0590222i
$87$	312.680	−	116.624i	0.385320	−	0.143717i
$88$	−445.195	+	333.269i	−0.539295	+	0.403711i
$89$	210.478	+	135.266i	0.250681	+	0.161103i	0.659947	−	0.751312i	$-0.270579\pi$
$89$	210.478	+	135.266i	0.250681	+	0.161103i	−0.409266	+	0.912415i	$0.634215\pi$
$90$	−9.87005	−	769.887i	−0.0115599	−	0.901702i
$91$			362.475i			0.417558i
$92$	−104.363	−	428.696i	−0.118267	−	0.485812i
$93$	1168.06	−	1168.06i	1.30238	−	1.30238i
$94$	−637.646	+	552.523i	−0.699661	+	0.606260i
$95$	−588.244	+	1110.91i	−0.635290	+	1.19976i
$96$	−35.6945	+	248.261i	−0.0379485	+	0.263938i
$97$	334.909	+	897.926i	0.350566	+	0.939903i	0.985851	+	0.167625i	$0.0536098\pi$
$97$	334.909	+	897.926i	0.350566	+	0.939903i	−0.635285	+	0.772278i	$0.719117\pi$
$98$	1342.34	+	1004.86i	1.38364	+	1.03578i
$99$	−2296.66	−	674.359i	−2.33154	−	0.684602i
$100$	−337.010	−	369.357i	−0.337010	−	0.369357i
$101$	−789.173	−	1728.05i	−0.777482	−	1.70245i	−0.709440	−	0.704766i	$-0.751052\pi$
$101$	−789.173	−	1728.05i	−0.777482	−	1.70245i	−0.0680419	−	0.997682i	$-0.521675\pi$
$102$	247.169	−	452.656i	0.239935	−	0.439408i
$103$	−230.566	+	16.4904i	−0.220566	+	0.0157752i	−0.181185	−	0.983449i	$-0.557993\pi$
$103$	−230.566	+	16.4904i	−0.220566	+	0.0157752i	−0.0393814	+	0.999224i	$0.512539\pi$
$104$	63.7601	+	55.2484i	0.0601172	+	0.0520919i
$105$	−2808.36	+	1088.67i	−2.61017	+	1.01184i
$106$	−187.860	+	85.7928i	−0.172138	+	0.0786126i
$107$	−404.251	+	1858.31i	−0.365238	+	1.67897i	0.317461	+	0.948271i	$0.397170\pi$
$107$	−404.251	+	1858.31i	−0.365238	+	1.67897i	−0.682699	+	0.730700i	$0.739194\pi$
$108$	−204.538	+	111.686i	−0.182237	+	0.0995092i
$109$	94.0666	+	654.247i	0.0826600	+	0.574913i	0.988492	+	0.151275i	$0.0483380\pi$
$109$	94.0666	+	654.247i	0.0826600	+	0.574913i	−0.905832	+	0.423638i	$0.860753\pi$
$110$	−1405.53	+	663.792i	−1.21830	+	0.575364i
$111$	−114.170	−	16.4151i	−0.0976261	−	0.0140365i
$112$	537.375	−	116.899i	0.453367	−	0.0986240i
$113$	49.7742	−	695.934i	0.0414368	−	0.579363i	−0.933742	−	0.357946i	$-0.883477\pi$
$113$	49.7742	−	695.934i	0.0414368	−	0.579363i	0.975179	−	0.221417i	$-0.0710682\pi$
$114$	1762.49			1.44800
$115$	−46.1342	−	1232.37i	−0.0374090	−	0.999300i
$116$	−170.311			−0.136319
$117$	−25.9052	+	362.202i	−0.0204695	+	0.286201i
$118$	−1215.82	+	264.485i	−0.948518	+	0.206337i
$119$	−1119.32	−	160.934i	−0.862252	−	0.123973i
$120$	−236.550	+	659.932i	−0.179950	+	0.502027i
$121$	498.286	+	3465.66i	0.374370	+	2.60380i
$122$	1069.28	−	583.871i	0.793509	−	0.433289i
$123$	85.0541	−	390.987i	0.0623502	−	0.286619i
$124$	−766.836	+	350.202i	−0.555354	+	0.253622i
$125$	−716.437	−	1199.93i	−0.512640	−	0.858603i
$126$	1788.89	+	1550.08i	1.26481	+	1.09597i
$127$	42.9732	−	3.07350i	0.0300256	−	0.00214747i	−0.0563183	−	0.998413i	$-0.517936\pi$
$127$	42.9732	−	3.07350i	0.0300256	−	0.00214747i	0.0863439	+	0.996265i	$0.472482\pi$
$128$	61.3439	−	112.343i	0.0423600	−	0.0775766i
$129$	538.476	+	1179.10i	0.367521	+	0.804758i
$130$	143.725	+	186.950i	0.0969657	+	0.126128i
$131$	−1468.29	−	431.128i	−0.979274	−	0.287541i	−0.247349	−	0.968926i	$-0.579559\pi$
$131$	−1468.29	−	431.128i	−0.979274	−	0.287541i	−0.731925	+	0.681386i	$0.761378\pi$
$132$	1744.70	+	1306.07i	1.15043	+	0.861203i
$133$	−1350.50	−	3620.83i	−0.880476	−	2.36065i
$134$	−77.8537	+	541.485i	−0.0501906	+	0.349083i
$135$	−622.588	+	191.511i	−0.396917	+	0.122094i
$136$	−198.915	+	172.361i	−0.125418	+	0.108675i
$137$	764.366	−	764.366i	0.476673	−	0.476673i	−0.427393	−	0.904066i	$-0.640568\pi$
$137$	764.366	−	764.366i	0.476673	−	0.476673i	0.904066	+	0.427393i	$0.140568\pi$
$138$	−1496.76	+	865.752i	−0.923283	+	0.534041i
$139$		−	775.564i		−	0.473255i	−0.971600	−	0.236628i	$-0.923958\pi$
$139$		−	775.564i		−	0.473255i	0.971600	−	0.236628i	$-0.0760421\pi$
$140$	1537.01	−	19.7047i	0.927865	−	0.0118954i
$141$	2781.64	+	1787.65i	1.66139	+	1.06771i
$142$	446.185	−	334.010i	0.263683	−	0.197391i
$143$	686.869	−	256.189i	0.401670	−	0.149815i
$144$	545.324	−	78.4057i	0.315581	−	0.0453737i
$145$	−466.413	−	95.2169i	−0.267128	−	0.0545333i
$146$	−1179.49	+	758.009i	−0.668595	+	0.429680i
$147$	2296.43	−	6156.96i	1.28848	−	3.45454i
$148$	51.6639	+	28.2106i	0.0286943	+	0.0156682i
$149$	2186.15	−	2522.95i	1.20199	−	1.38717i	0.300833	−	0.953677i	$-0.402735\pi$
$149$	2186.15	−	2522.95i	1.20199	−	1.38717i	0.901157	−	0.433494i	$-0.142719\pi$
$150$	−1016.77	+	1675.04i	−0.553459	+	0.911776i
$151$	−530.120	+	155.657i	−0.285699	+	0.0838887i	−0.421442	−	0.906855i	$-0.638476\pi$
$151$	−530.120	+	155.657i	−0.285699	+	0.0838887i	0.135743	+	0.990744i	$0.456658\pi$
$152$	−842.755	−	314.331i	−0.449713	−	0.167734i
$153$	−1106.98	−	240.808i	−0.584926	−	0.127243i
$154$	1346.30	−	4585.07i	0.704466	−	2.39919i
$155$	−2295.85	+	530.343i	−1.18972	+	0.274827i
$156$	137.349	−	300.752i	0.0704917	−	0.154355i
$157$	−563.095	−	752.206i	−0.286241	−	0.382373i	0.634256	−	0.773123i	$-0.281307\pi$
$157$	−563.095	−	752.206i	−0.286241	−	0.382373i	−0.920497	+	0.390750i	$0.872216\pi$
$158$	−230.613	−	1060.11i	−0.116118	−	0.533785i
$159$	530.016	+	611.671i	0.264359	+	0.305086i
$160$	230.805	−	273.366i	0.114042	−	0.135072i
$161$	2925.48	+	2411.55i	1.43205	+	1.18048i
$162$	−668.995	−	668.995i	−0.324452	−	0.324452i
$163$	−526.227	−	37.6365i	−0.252867	−	0.0180854i	−0.0556696	−	0.998449i	$-0.517729\pi$
$163$	−526.227	−	37.6365i	−0.252867	−	0.0180854i	−0.197197	+	0.980364i	$0.563184\pi$
$164$	−110.400	+	171.786i	−0.0525659	+	0.0817942i
$165$	4047.86	+	4552.23i	1.90985	+	2.14782i
$166$	298.500	+	136.320i	0.139567	+	0.0637380i
$167$	−1055.52	+	1410.00i	−0.489092	+	0.653350i	−0.975401	−	0.220437i	$-0.929252\pi$
$167$	−1055.52	+	1410.00i	−0.489092	+	0.653350i	0.486310	+	0.873787i	$0.338343\pi$
$168$	−1032.88	−	1891.58i	−0.474336	−	0.868682i
$169$	1127.66	+	1754.67i	0.513273	+	0.798668i
$170$	−641.113	+	360.819i	−0.289242	+	0.162786i
$171$	−1090.71	−	3714.62i	−0.487770	−	1.66119i
$172$	−47.1923	−	659.834i	−0.0209208	−	0.292511i
$173$	47.8746	+	669.375i	0.0210395	+	0.294171i	0.997068	+	0.0765263i	$0.0243829\pi$
$173$	47.8746	+	669.375i	0.0210395	+	0.294171i	−0.976028	+	0.217645i	$0.930163\pi$
$174$	188.040	+	640.406i	0.0819270	+	0.279018i
$175$	4220.27	+	805.345i	1.82299	+	0.347876i
$176$	−601.320	−	935.672i	−0.257535	−	0.400733i
$177$	2336.91	+	4279.73i	0.992388	+	1.81742i
$178$	−299.873	+	400.584i	−0.126272	+	0.168680i
$179$	3507.69	+	1601.91i	1.46467	+	0.668895i	0.978741	−	0.205101i	$-0.0657523\pi$
$179$	3507.69	+	1601.91i	1.46467	+	0.668895i	0.485934	+	0.873996i	$0.338480\pi$
$180$	1537.26	+	90.1564i	0.636558	+	0.0373325i
$181$	−1450.18	+	2256.53i	−0.595532	+	0.926665i	0.404395	+	0.914584i	$0.367482\pi$
$181$	−1450.18	+	2256.53i	−0.595532	+	0.926665i	−0.999927	+	0.0120812i	$0.996154\pi$
$182$	−723.103	−	51.7174i	−0.294505	−	0.0210634i
$183$	−3376.08	−	3376.08i	−1.36375	−	1.36375i
$184$	870.098	−	147.029i	0.348611	−	0.0589081i
$185$	125.715	+	106.142i	0.0499608	+	0.0421822i
$186$	2163.50	+	2496.82i	0.852880	+	0.984276i
$187$	486.149	+	2234.79i	0.190111	+	0.873926i
$188$	−1011.25	−	1350.88i	−0.392304	−	0.524057i
$189$	831.873	−	1821.55i	0.320158	−	0.701048i
$190$	−2132.23	−	1331.99i	−0.814150	−	0.508594i
$191$	91.7793	−	312.571i	0.0347692	−	0.118413i	−0.940280	−	0.340402i	$-0.889437\pi$
$191$	91.7793	−	312.571i	0.0347692	−	0.118413i	0.975049	+	0.221989i	$0.0712550\pi$
$192$	−490.164	−	106.629i	−0.184242	−	0.0400795i
$193$	1555.57	+	580.196i	0.580166	+	0.216391i	0.622376	−	0.782718i	$-0.286167\pi$
$193$	1555.57	+	580.196i	0.580166	+	0.216391i	−0.0422105	+	0.999109i	$0.513440\pi$
$194$	−1839.06	+	539.997i	−0.680602	+	0.199843i
$195$	544.287	−	746.850i	0.199883	−	0.274272i
$196$	−2196.13	+	2534.46i	−0.800337	+	0.923639i
$197$	−576.970	−	315.050i	−0.208667	−	0.113941i	0.371517	−	0.928426i	$-0.378838\pi$
$197$	−576.970	−	315.050i	−0.208667	−	0.113941i	−0.580184	+	0.814485i	$0.697020\pi$
$198$	1672.96	−	4485.39i	0.600467	−	1.60991i
$199$	301.217	−	193.580i	0.107300	−	0.0689575i	−0.485890	−	0.874020i	$-0.661505\pi$
$199$	301.217	−	193.580i	0.107300	−	0.0689575i	0.593190	+	0.805062i	$0.297868\pi$
$200$	784.915	−	619.603i	0.277509	−	0.219063i
$201$	2122.06	−	305.106i	0.744670	−	0.107067i
$202$	3559.89	−	1327.77i	1.23997	−	0.462483i
$203$	1171.56	−	877.016i	0.405060	−	0.303224i
$204$	867.739	+	557.662i	0.297813	+	0.191393i
$205$	−398.384	+	408.731i	−0.135729	+	0.139254i
$206$		−	462.310i		−	0.156362i
$207$	2750.92	+	2618.81i	0.923683	+	0.879323i
$208$	−119.313	+	119.313i	−0.0397732	+	0.0397732i
$209$	−5906.76	+	5118.24i	−1.95492	+	1.69395i
$210$	−1771.11	−	5757.74i	−0.581991	−	1.89201i
$211$	370.849	−	2579.31i	0.120997	−	0.841549i	−0.835434	−	0.549590i	$-0.814784\pi$
$211$	370.849	−	2579.31i	0.120997	−	0.841549i	0.956431	−	0.291959i	$-0.0943071\pi$
$212$	−144.345	−	387.004i	−0.0467625	−	0.125375i
$213$	−1748.58	−	1308.97i	−0.562493	−	0.421077i
$214$	−3649.48	−	1071.58i	−1.16576	−	0.342299i
$215$	239.658	−	1833.41i	0.0760210	−	0.581569i
$216$	−193.620	−	423.968i	−0.0609915	−	0.133553i
$217$	3471.65	−	6357.85i	1.08604	−	1.98893i
$218$	−1318.58	+	94.3069i	−0.409659	+	0.0292994i
$219$	4152.55	+	3598.21i	1.28129	+	1.11025i
$220$	−1123.66	−	2898.62i	−0.344351	−	0.888294i
$221$	315.608	−	144.133i	0.0960636	−	0.0438708i
$222$	49.0361	−	225.415i	0.0148247	−	0.0681481i
$223$	2888.11	−	1577.03i	0.867273	−	0.473567i	0.0169674	−	0.999856i	$-0.494599\pi$
$223$	2888.11	−	1577.03i	0.867273	−	0.473567i	0.850306	+	0.526289i	$0.176417\pi$
$224$	156.530	+	1088.69i	0.0466902	+	0.324737i
$225$	4159.53	+	1106.35i	1.23245	+	0.327807i
$226$	1381.22	+	198.589i	0.406537	+	0.0584512i
$227$	4327.56	−	941.403i	1.26533	−	0.275256i	0.470670	−	0.882309i	$-0.344012\pi$
$227$	4327.56	−	941.403i	1.26533	−	0.275256i	0.794661	+	0.607053i	$0.207649\pi$
$228$	−251.469	+	3516.00i	−0.0730436	+	1.02128i
$229$	3527.16			1.01782			0.508911	−	0.860819i	$-0.330048\pi$
$229$	3527.16			1.01782			0.508911	+	0.860819i	$0.330048\pi$
$230$	2465.05	+	83.7998i	0.706699	+	0.0240243i
$231$	−18727.3			−5.33406
$232$	24.2997	−	339.754i	0.00687651	−	0.0961462i
$233$	−2486.38	+	540.878i	−0.699090	+	0.152078i	−0.548045	−	0.836449i	$-0.684628\pi$
$233$	−2486.38	+	540.878i	−0.699090	+	0.152078i	−0.151045	+	0.988527i	$0.548264\pi$
$234$	−718.862	−	103.357i	−0.200827	−	0.0288745i
$235$	−2014.17	−	4264.88i	−0.559107	−	1.18387i
$236$	−354.151	−	2463.18i	−0.0976834	−	0.679403i
$237$	−3731.64	+	2037.63i	−1.02277	+	0.558473i
$238$	480.751	−	2209.98i	0.130935	−	0.601897i
$239$	−2640.86	+	1206.04i	−0.714741	+	0.326411i	−0.739383	−	0.673285i	$-0.764883\pi$
$239$	−2640.86	+	1206.04i	−0.714741	+	0.326411i	0.0246421	+	0.999696i	$0.492155\pi$
$240$	−1282.75	−	566.053i	−0.345005	−	0.152244i
$241$	1295.89	+	1122.89i	0.346371	+	0.300132i	0.810620	−	0.585573i	$-0.199130\pi$
$241$	1295.89	+	1122.89i	0.346371	+	0.300132i	−0.464249	+	0.885705i	$0.653676\pi$
$242$	−6984.75	+	499.559i	−1.85536	+	0.132698i
$243$	−2530.81	+	4634.84i	−0.668114	+	1.22356i
$244$	1012.20	+	2216.42i	0.265573	+	0.581523i
$245$	−7431.27	+	5713.08i	−1.93782	+	1.48978i
$246$	767.847	+	225.460i	0.199009	+	0.0584342i
$247$	949.204	+	710.565i	0.244520	+	0.183045i
$248$	−589.209	−	1579.73i	−0.150866	−	0.404488i
$249$	183.021	−	1272.94i	0.0465802	−	0.323972i
$250$	2495.98	−	1258.02i	0.631437	−	0.318256i
$251$	−3363.63	+	2914.60i	−0.845859	+	0.732941i	−0.965647	−	0.259859i	$-0.916324\pi$
$251$	−3363.63	+	2914.60i	−0.845859	+	0.732941i	0.119788	+	0.992800i	$0.461779\pi$
$252$	−3347.49	+	3347.49i	−0.836795	+	0.836795i
$253$	2502.09	−	7248.04i	0.621760	−	1.80111i
$254$			86.1659i			0.0212855i
$255$	2064.61	+	2012.35i	0.507024	+	0.494188i
$256$	215.361	+	138.404i	0.0525783	+	0.0337901i
$257$	3653.86	−	2735.24i	0.886854	−	0.663891i	−0.0555179	−	0.998458i	$-0.517681\pi$
$257$	3653.86	−	2735.24i	0.886854	−	0.663891i	0.942372	+	0.334567i	$0.108590\pi$
$258$	−2429.02	+	905.976i	−0.586139	+	0.218619i
$259$	−500.664	+	71.9846i	−0.120115	+	0.0172699i
$260$	−393.454	+	260.044i	−0.0938500	+	0.0620279i
$261$	1233.35	−	792.626i	0.292500	−	0.187978i
$262$	1069.55	−	2867.58i	0.252203	−	0.676182i
$263$	7181.61	+	3921.46i	1.68379	+	0.919420i	0.977345	+	0.211653i	$0.0678846\pi$
$263$	7181.61	+	3921.46i	1.68379	+	0.919420i	0.706446	+	0.707767i	$0.250297\pi$
$264$	−2854.42	+	3294.17i	−0.665444	+	0.767963i
$265$	−178.938	−	1140.55i	−0.0414795	−	0.264390i
$266$	7415.90	−	2177.51i	1.70939	−	0.501923i
$267$	1837.37	+	685.305i	0.421144	+	0.157079i
$268$	−1069.10	−	232.569i	−0.243678	−	0.0530090i
$269$	1656.69	−	5642.16i	0.375502	−	1.27884i	−0.527628	−	0.849475i	$-0.676919\pi$
$269$	1656.69	−	5642.16i	0.375502	−	1.27884i	0.903130	−	0.429367i	$-0.141263\pi$
$270$	−293.216	−	1269.33i	−0.0660910	−	0.286107i
$271$	913.639	−	2000.59i	0.204796	−	0.448440i	−0.779166	−	0.626817i	$-0.784357\pi$
$271$	913.639	−	2000.59i	0.204796	−	0.448440i	0.983962	+	0.178377i	$0.0570846\pi$
$272$	−315.463	−	421.410i	−0.0703227	−	0.0939401i
$273$	603.910	+	2776.13i	0.133884	+	0.615454i
$274$	1415.78	+	1633.89i	0.312154	+	0.360245i
$275$	−1456.71	−	8566.36i	−0.319428	−	1.87844i
$276$	−1513.54	−	3109.43i	−0.330087	−	0.678136i
$277$	4333.11	+	4333.11i	0.939897	+	0.939897i	0.998293	−	0.0583969i	$-0.0185989\pi$
$277$	4333.11	+	4333.11i	0.939897	+	0.939897i	−0.0583969	+	0.998293i	$0.518599\pi$
$278$	1547.18	+	110.656i	0.333789	+	0.0238731i
$279$	3923.41	−	6104.94i	0.841893	−	1.31001i
$280$	−179.989	+	3069.00i	−0.0384157	+	0.655028i
$281$	621.310	+	283.743i	0.131901	+	0.0602372i	0.480272	−	0.877119i	$-0.340538\pi$
$281$	621.310	+	283.743i	0.131901	+	0.0602372i	−0.348371	+	0.937357i	$0.613265\pi$
$282$	−3963.07	+	5294.04i	−0.836870	+	1.11793i
$283$	1076.86	+	1972.12i	0.226193	+	0.414241i	0.965987	−	0.258592i	$-0.0832587\pi$
$283$	1076.86	+	1972.12i	0.226193	+	0.414241i	−0.739794	+	0.672834i	$0.765077\pi$
$284$	602.657	+	937.752i	0.125919	+	0.195934i
$285$	−2654.39	+	9488.32i	−0.551693	+	1.97207i
$286$	413.071	+	1406.79i	0.0854035	+	0.290858i
$287$	−125.178	−	1750.21i	−0.0257457	−	0.359971i
$288$	78.6060	+	1099.06i	0.0160830	+	0.224870i
$289$	−1079.20	−	3675.40i	−0.219661	−	0.748097i
$290$	256.496	−	916.864i	0.0519377	−	0.185656i
$291$	4061.02	+	6319.06i	0.818079	+	1.27296i
$292$	−1343.87	−	2461.11i	−0.269329	−	0.493239i
$293$	−2276.43	+	3040.95i	−0.453892	+	0.606329i	−0.967863	−	0.251479i	$-0.919083\pi$
$293$	−2276.43	+	3040.95i	−0.453892	+	0.606329i	0.513971	+	0.857808i	$0.328174\pi$
$294$	11954.9	+	5459.61i	2.37151	+	1.08303i
$295$	407.228	−	6943.65i	0.0803720	−	1.37042i
$296$	−63.6489	+	99.0396i	−0.0124984	+	0.0194478i
$297$	−4039.67	−	288.923i	−0.789245	−	0.0564479i
$298$	4721.13	+	4721.13i	0.917745	+	0.917745i
$299$	−1155.13	−	137.178i	−0.223422	−	0.0265324i
$300$	−3196.47	−	2267.35i	−0.615161	−	0.436352i
$301$	3722.45	+	4295.94i	0.712819	+	0.822637i
$302$	−234.885	−	1079.75i	−0.0447552	−	0.205737i
$303$	−8923.19	−	11920.0i	−1.69183	−	2.26002i
$304$	747.304	−	1636.37i	0.140989	−	0.308724i
$305$	1532.87	+	6635.78i	0.287777	+	1.24578i
$306$	638.330	−	2173.95i	0.119251	−	0.406132i
$307$	−3073.00	−	668.491i	−0.571288	−	0.124276i	−0.0823638	−	0.996602i	$-0.526247\pi$
$307$	−3073.00	−	668.491i	−0.571288	−	0.124276i	−0.488924	+	0.872326i	$0.662611\pi$
$308$	8954.69	+	3339.93i	1.65663	+	0.617889i
$309$	−1738.39	+	510.436i	−0.320043	+	0.0939732i
$310$	−730.417	−	4655.67i	−0.133822	−	0.852981i
$311$	5385.68	−	6215.41i	0.981974	−	1.13326i	−0.00910136	−	0.999959i	$-0.502897\pi$
$311$	5385.68	−	6215.41i	0.981974	−	1.13326i	0.991076	−	0.133300i	$-0.0425575\pi$
$312$	580.374	+	316.908i	0.105312	+	0.0575045i
$313$	3357.25	−	9001.13i	0.606271	−	1.62548i	−0.163053	−	0.986617i	$-0.552134\pi$
$313$	3357.25	−	9001.13i	0.606271	−	1.62548i	0.769324	−	0.638859i	$-0.220593\pi$
$314$	1580.92	−	1016.00i	0.284129	−	0.182599i
$315$	−11039.0	+	7295.94i	−1.97452	+	1.30501i
$316$	2147.73	−	308.796i	0.382339	−	0.0549720i
$317$	−1604.30	+	598.374i	−0.284248	+	0.106019i	−0.487544	−	0.873098i	$-0.662107\pi$
$317$	−1604.30	+	598.374i	−0.284248	+	0.106019i	0.203296	+	0.979117i	$0.434835\pi$
$318$	−1295.85	+	970.060i	−0.228514	+	0.171064i
$319$	−2489.92	−	1600.18i	−0.437018	−	0.280855i
$320$	512.409	+	499.437i	0.0895141	+	0.0872480i
$321$			14906.0i			2.59181i
$322$	−5228.22	+	5491.97i	−0.904837	+	0.950484i
$323$	−2615.66	+	2615.66i	−0.450585	+	0.450585i
$324$	1430.03	−	1239.13i	0.245204	−	0.212471i
$325$	−1222.90	+	492.186i	−0.208721	+	0.0840048i
$326$	150.162	−	1044.40i	0.0255114	−	0.177436i
$327$	1810.46	+	4854.04i	0.306174	+	0.820883i
$328$	−326.945	−	244.748i	−0.0550382	−	0.0412011i
$329$	13912.7	+	4085.13i	2.33140	+	0.684561i
$330$	−9658.80	+	7425.58i	−1.61121	+	1.23868i
$331$	−3125.66	−	6844.25i	−0.519039	−	1.13654i	−0.969802	−	0.243894i	$-0.921575\pi$
$331$	−3125.66	−	6844.25i	−0.519039	−	1.13654i	0.450763	−	0.892644i	$-0.351152\pi$
$332$	−314.535	+	576.029i	−0.0519951	+	0.0952219i
$333$	−505.430	+	36.1491i	−0.0831754	+	0.00594882i
$334$	−2662.23	−	2306.83i	−0.436139	−	0.377917i
$335$	−2797.82	−	1234.62i	−0.456302	−	0.201357i
$336$	3920.89	−	1790.61i	0.636613	−	0.290732i
$337$	−1107.97	+	5093.26i	−0.179095	+	0.823286i	0.796661	+	0.604426i	$0.206597\pi$
$337$	−1107.97	+	5093.26i	−0.179095	+	0.823286i	−0.975756	+	0.218860i	$0.929766\pi$
$338$	−3661.30	+	1999.22i	−0.589197	+	0.321726i
$339$	−778.266	−	5412.96i	−0.124689	−	0.867231i
$340$	−628.327	−	1330.44i	−0.100223	−	0.212216i
$341$	−14501.4	−	2084.99i	−2.30292	−	0.331110i
$342$	7565.93	−	1645.87i	1.19625	−	0.260229i
$343$	1214.72	−	16984.0i	0.191221	−	2.67362i
$344$	1323.04			0.207365
$345$	−2406.56	−	9361.66i	−0.375550	−	1.46091i
$346$	−1342.17			−0.208542
$347$	−681.075	+	9522.67i	−0.105366	+	1.47321i	0.619867	+	0.784707i	$0.287186\pi$
$347$	−681.075	+	9522.67i	−0.105366	+	1.47321i	−0.725233	+	0.688503i	$0.758268\pi$
$348$	−1304.38	+	283.750i	−0.200925	+	0.0437086i
$349$	−157.926	−	22.7063i	−0.0242223	−	0.00348264i	0.130193	−	0.991489i	$-0.458440\pi$
$349$	−157.926	−	22.7063i	−0.0242223	−	0.00348264i	−0.154415	+	0.988006i	$0.549349\pi$
$350$	−2208.73	+	8304.14i	−0.337318	+	1.26821i
$351$	87.4397	+	608.157i	0.0132968	+	0.0924815i
$352$	1952.37	−	1066.08i	0.295630	−	0.161426i
$353$	−2426.02	+	11152.2i	−0.365790	+	1.68151i	0.315050	+	0.949075i	$0.397979\pi$
$353$	−2426.02	+	11152.2i	−0.365790	+	1.68151i	−0.680839	+	0.732433i	$0.738385\pi$
$354$	−8871.07	+	4051.28i	−1.33190	+	0.608258i
$355$	1126.16	+	2905.06i	0.168367	+	0.434323i
$356$	−756.341	−	655.373i	−0.112601	−	0.0975695i
$357$	−8840.80	+	632.307i	−1.31066	+	0.0937401i
$358$	−3696.12	+	6768.94i	−0.545659	+	0.999301i
$359$	−121.015	−	264.986i	−0.0177909	−	0.0389567i	0.900528	−	0.434798i	$-0.143180\pi$
$359$	−121.015	−	264.986i	−0.0177909	−	0.0389567i	−0.918319	+	0.395841i	$0.870453\pi$
$360$	−399.187	+	3053.82i	−0.0584416	+	0.447085i
$361$	−5548.02	−	1629.05i	−0.808867	−	0.237505i
$362$	−4294.65	−	3214.93i	−0.623541	−	0.466777i
$363$	9590.32	+	25712.6i	1.38667	+	3.71780i
$364$	206.342	−	1435.14i	0.0297123	−	0.206654i
$365$	−2304.37	−	7491.33i	−0.330455	−	1.07429i
$366$	7216.65	−	6253.26i	1.03066	−	0.893069i
$367$	89.7047	−	89.7047i	0.0127590	−	0.0127590i	−0.700699	−	0.713457i	$-0.747128\pi$
$367$	89.7047	−	89.7047i	0.0127590	−	0.0127590i	0.713457	+	0.700699i	$0.247128\pi$
$368$	169.164	+	1756.74i	0.0239627	+	0.248849i
$369$		−	1757.84i		−	0.247993i
$370$	−229.680	+	235.645i	−0.0322716	+	0.0331097i
$371$	2985.82	+	1918.87i	0.417832	+	0.268525i
$372$	−5289.59	+	3959.74i	−0.737238	+	0.551890i
$373$	9460.60	−	3528.62i	1.31327	−	0.489826i	0.407353	−	0.913271i	$-0.366452\pi$
$373$	9460.60	−	3528.62i	1.31327	−	0.489826i	0.905922	+	0.423445i	$0.139179\pi$
$374$	−4527.56	+	650.965i	−0.625975	+	0.0900016i
$375$	−7486.23	−	7996.44i	−1.03090	−	1.10116i
$376$	2839.15	−	1824.61i	0.389410	−	0.250258i
$377$	−156.915	+	420.707i	−0.0214365	+	0.0574735i
$378$	3515.12	+	1919.40i	0.478303	+	0.261173i
$379$	−1211.62	+	1398.29i	−0.164213	+	0.189512i	−0.831892	−	0.554937i	$-0.812742\pi$
$379$	−1211.62	+	1398.29i	−0.164213	+	0.189512i	0.667679	+	0.744449i	$0.267288\pi$
$380$	2961.42	−	4063.55i	0.399783	−	0.548568i
$381$	324.003	−	95.1358i	0.0435674	−	0.0127925i
$382$	610.455	+	227.688i	0.0817634	+	0.0304962i
$383$	−11060.6	−	2406.09i	−1.47565	−	0.321007i	−0.598458	−	0.801154i	$-0.704220\pi$
$383$	−11060.6	−	2406.09i	−1.47565	−	0.321007i	−0.877188	+	0.480147i	$0.840583\pi$
$384$	282.650	−	962.617i	0.0375623	−	0.127925i
$385$	22656.0	+	14153.1i	2.99911	+	1.87353i
$386$	−1379.38	+	3020.42i	−0.181888	+	0.398278i
$387$	3412.62	+	4558.73i	0.448252	+	0.598794i
$388$	−814.848	−	3745.80i	−0.106618	−	0.490113i
$389$	2592.01	+	2991.34i	0.337841	+	0.389889i	0.899094	−	0.437755i	$-0.144226\pi$
$389$	2592.01	+	2991.34i	0.337841	+	0.389889i	−0.561254	+	0.827644i	$0.689681\pi$
$390$	1412.24	+	1192.36i	0.183363	+	0.154814i
$391$	936.467	−	3506.14i	0.121123	−	0.453486i
$392$	−4742.67	−	4742.67i	−0.611074	−	0.611074i
$393$	−11963.6	−	855.656i	−1.53559	−	0.109827i
$394$	710.815	−	1106.05i	0.0908892	−	0.141426i
$395$	6054.41	+	355.076i	0.771216	+	0.0452299i
$396$	8709.23	+	3977.37i	1.10519	+	0.504724i
$397$	−5372.04	+	7176.21i	−0.679132	+	0.907213i	−0.999192	−	0.0401835i	$-0.987206\pi$
$397$	−5372.04	+	7176.21i	−0.679132	+	0.907213i	0.320061	+	0.947397i	$0.396297\pi$
$398$	343.197	+	628.518i	0.0432234	+	0.0791577i
$399$	−16375.8	−	25481.3i	−2.05468	−	3.19714i
$400$	1124.06	+	1654.23i	0.140507	+	0.206779i
$401$	−291.209	−	991.768i	−0.0362651	−	0.123508i	0.939371	−	0.342902i	$-0.111410\pi$
$401$	−291.209	−	991.768i	−0.0362651	−	0.123508i	−0.975636	+	0.219395i	$0.929592\pi$
$402$	305.886	+	4276.84i	0.0379507	+	0.530620i
$403$	158.557	+	2216.92i	0.0195988	+	0.274026i
$404$	2140.86	+	7291.08i	0.263642	+	0.897883i
$405$	4609.06	−	2593.98i	0.565496	−	0.318262i
$406$	1582.41	+	2462.27i	0.193432	+	0.300987i
$407$	490.264	+	897.851i	0.0597088	+	0.109348i
$408$	−1236.29	+	1651.49i	−0.150013	+	0.200394i
$409$	−11849.2	−	5411.35i	−1.43253	−	0.654215i	−0.460199	−	0.887816i	$-0.652222\pi$
$409$	−11849.2	−	5411.35i	−1.43253	−	0.654215i	−0.972333	+	0.233601i	$0.924949\pi$
$410$	−758.539	−	853.055i	−0.0913697	−	0.102755i
$411$	4580.64	−	7127.62i	0.549748	−	0.855425i
$412$	922.263	+	65.9616i	0.110283	+	0.00788761i
$413$	15120.3	+	15120.3i	1.80151	+	1.80151i
$414$	−5616.77	+	5114.18i	−0.666786	+	0.607122i
$415$	−1183.43	+	1401.66i	−0.139982	+	0.165795i
$416$	−220.994	−	255.040i	−0.0260459	−	0.0300586i
$417$	−1292.15	−	5939.90i	−0.151743	−	0.697549i
$418$	−9367.63	−	12513.7i	−1.09614	−	1.46427i
$419$	1351.59	−	2959.57i	0.157588	−	0.345070i	−0.814325	−	0.580409i	$-0.802893\pi$
$419$	1351.59	−	2959.57i	0.157588	−	0.345070i	0.971913	+	0.235339i	$0.0756200\pi$
$420$	11738.8	−	2711.68i	1.36380	−	0.315040i
$421$	−2148.52	+	7317.18i	−0.248723	+	0.847073i	0.736594	+	0.676336i	$0.236433\pi$
$421$	−2148.52	+	7317.18i	−0.248723	+	0.847073i	−0.985317	+	0.170737i	$0.945385\pi$
$422$	5092.56	+	1107.82i	0.587445	+	0.127791i
$423$	13610.2	+	5076.35i	1.56443	+	0.583501i
$424$	792.630	−	232.737i	0.0907866	−	0.0266573i
$425$	−976.917	−	3994.83i	−0.111500	−	0.455947i
$426$	2860.76	−	3301.49i	0.325362	−	0.375488i
$427$	−18376.3	−	10034.2i	−2.08265	−	1.13722i
$428$	2658.41	−	7127.47i	0.300231	−	0.804952i
$429$	4833.77	−	3106.48i	0.544002	−	0.349609i
$430$	3623.28	+	739.682i	0.406348	+	0.0829549i
$431$	−10496.4	+	1509.16i	−1.17307	+	0.168663i	−0.701175	−	0.712989i	$-0.747341\pi$
$431$	−10496.4	+	1509.16i	−1.17307	+	0.168663i	−0.471900	+	0.881652i	$0.656432\pi$
$432$	873.401	−	325.762i	0.0972721	−	0.0362806i
$433$	−148.976	+	111.522i	−0.0165342	+	0.0123774i	−0.607513	−	0.794310i	$-0.707833\pi$
$433$	−148.976	+	111.522i	−0.0165342	+	0.0123774i	0.590979	+	0.806687i	$0.298742\pi$
$434$	12188.0	+	7832.73i	1.34802	+	0.866321i
$435$	−3730.81	+	47.8295i	−0.411215	+	0.00527183i
$436$		−	2643.90i		−	0.290413i
$437$	12049.9	−	2933.47i	1.31905	−	0.321114i
$438$	−7770.56	+	7770.56i	−0.847698	+	0.847698i
$439$	−9364.37	+	8114.28i	−1.01808	+	0.882171i	−0.993071	−	0.117516i	$-0.962507\pi$
$439$	−9364.37	+	8114.28i	−1.01808	+	0.882171i	−0.0250091	+	0.999687i	$0.507961\pi$
$440$	5942.78	−	1828.03i	0.643889	−	0.198063i
$441$	4108.43	−	28574.8i	0.443627	−	3.08549i
$442$	242.501	+	650.171i	0.0260964	+	0.0699672i
$443$	−2134.70	−	1598.01i	−0.228945	−	0.171386i	0.478647	−	0.878007i	$-0.341127\pi$
$443$	−2134.70	−	1598.01i	−0.228945	−	0.171386i	−0.707592	+	0.706622i	$0.750218\pi$
$444$	442.685	+	129.984i	0.0473174	+	0.0138936i
$445$	−1704.91	−	2217.66i	−0.181619	−	0.236241i
$446$	2733.94	+	5986.50i	0.290260	+	0.635581i
$447$	12539.9	−	22965.1i	1.32688	−	2.43001i
$448$	−2194.17	+	156.930i	−0.231394	+	0.0165496i
$449$	6779.31	+	5874.31i	0.712551	+	0.617429i	0.933803	−	0.357787i	$-0.116469\pi$
$449$	6779.31	+	5874.31i	0.712551	+	0.617429i	−0.221252	+	0.975217i	$0.571014\pi$
$450$	−2800.54	+	8140.02i	−0.293374	+	0.852720i
$451$	−3228.08	+	1474.21i	−0.337038	+	0.153920i
$452$	−593.237	+	2727.07i	−0.0617335	+	0.283784i
$453$	−3800.75	+	2075.37i	−0.394205	+	0.215252i
$454$	1260.56	+	8767.38i	0.130311	+	0.906330i
$455$	1367.45	−	3814.92i	0.140894	−	0.393069i
$456$	−6978.20	−	1003.31i	−0.716632	−	0.103036i
$457$	−4533.55	+	986.213i	−0.464049	+	0.100948i	−0.438510	−	0.898726i	$-0.644494\pi$
$457$	−4533.55	+	986.213i	−0.464049	+	0.100948i	−0.0255386	+	0.999674i	$0.508130\pi$
$458$	−503.250	+	7036.35i	−0.0513435	+	0.717876i
$459$	−1916.81			−0.194921
$460$	−518.882	+	4905.58i	−0.0525935	+	0.497226i
$461$	−14053.9			−1.41986			−0.709931	−	0.704271i	$-0.751274\pi$
$461$	−14053.9			−1.41986			−0.709931	+	0.704271i	$0.751274\pi$
$462$	2671.98	−	37359.2i	0.269073	−	3.76214i
$463$	17.3742	−	3.77954i	0.00174395	−	0.000379373i	−0.211693	−	0.977336i	$-0.567898\pi$
$463$	17.3742	−	3.77954i	0.00174395	−	0.000379373i	0.213437	+	0.976957i	$0.431534\pi$
$464$	674.309	+	96.9510i	0.0674655	+	0.00970008i
$465$	−16699.9	+	7886.85i	−1.66546	+	0.786546i
$466$	−724.248	−	5037.26i	−0.0719960	−	0.500743i
$467$	5338.00	−	2914.77i	0.528936	−	0.288821i	−0.192506	−	0.981296i	$-0.561661\pi$
$467$	5338.00	−	2914.77i	0.528936	−	0.288821i	0.721442	+	0.692475i	$0.243480\pi$
$468$	308.753	−	1419.31i	0.0304959	−	0.140188i
$469$	8551.90	−	3905.52i	0.841983	−	0.384521i
$470$	8795.40	−	3409.58i	0.863195	−	0.334621i
$471$	−5565.87	−	4822.85i	−0.544504	−	0.471816i
$472$	4964.33	−	355.056i	0.484114	−	0.0346245i
$473$	5509.61	−	10090.1i	0.535586	−	0.980852i
$474$	−3532.45	−	7734.98i	−0.342301	−	0.749535i
$475$	10382.0	−	9472.78i	1.00286	−	0.915034i
$476$	4340.10	+	1274.37i	0.417916	+	0.122711i
$477$	2846.43	+	2130.81i	0.273226	+	0.204535i
$478$	−2029.14	−	5440.34i	−0.194165	−	0.520576i
$479$	−866.581	+	6027.20i	−0.0826620	+	0.574926i	0.905829	+	0.423644i	$0.139249\pi$
$479$	−866.581	+	6027.20i	−0.0826620	+	0.574926i	−0.988491	+	0.151282i	$0.951660\pi$
$480$	1312.24	−	2478.20i	0.124782	−	0.235654i
$481$	117.287	−	101.630i	0.0111182	−	0.00963394i
$482$	−2424.95	+	2424.95i	−0.229157	+	0.229157i
$483$	26423.5	+	13595.6i	2.48926	+	1.28079i
$484$		−	14005.2i		−	1.31529i
$485$	−137.352	−	10713.8i	−0.0128595	−	1.00307i
$486$	−8884.96	−	5710.02i	−0.829280	−	0.532946i
$487$	3599.57	−	2694.60i	0.334932	−	0.250727i	−0.418552	−	0.908193i	$-0.637462\pi$
$487$	3599.57	−	2694.60i	0.334932	−	0.250727i	0.753485	+	0.657465i	$0.228371\pi$
$488$	−4565.96	+	1703.02i	−0.423548	+	0.157975i
$489$	−4092.98	+	588.481i	−0.378509	+	0.0544214i
$490$	−10336.8	−	15639.8i	−0.952995	−	1.44191i
$491$	16960.9	−	10900.1i	1.55893	−	1.00186i	0.576088	−	0.817387i	$-0.304578\pi$
$491$	16960.9	−	10900.1i	1.55893	−	1.00186i	0.982838	−	0.184473i	$-0.0590580\pi$
$492$	−559.327	+	1499.61i	−0.0512528	+	0.137414i
$493$	−1229.47	−	671.342i	−0.112318	−	0.0613301i
$494$	−1552.94	+	1792.19i	−0.141437	+	0.163228i
$495$	21627.4	+	15761.6i	1.96380	+	1.43117i
$496$	3235.48	−	950.023i	0.292898	−	0.0860026i
$497$	−8974.59	−	3347.35i	−0.809991	−	0.302111i
$498$	2513.27	+	546.729i	0.226150	+	0.0491958i
$499$	−4589.49	+	15630.4i	−0.411731	+	1.40223i	0.449165	+	0.893449i	$0.351721\pi$
$499$	−4589.49	+	15630.4i	−0.411731	+	1.40223i	−0.860897	+	0.508780i	$0.830097\pi$
$500$	2153.50	+	5158.72i	0.192615	+	0.461410i
$501$	−5734.83	+	12557.5i	−0.511404	+	1.11982i
$502$	−5334.44	−	7125.97i	−0.474278	−	0.633561i
$503$	−3277.88	−	15068.2i	−0.290563	−	1.33570i	−0.858580	−	0.512680i	$-0.828653\pi$
$503$	−3277.88	−	15068.2i	−0.290563	−	1.33570i	0.568016	−	0.823017i	$-0.307711\pi$
$504$	−6200.32	−	7155.55i	−0.547984	−	0.632407i
$505$	1786.67	+	21164.3i	0.157437	+	1.86495i
$506$	14102.1	+	6025.57i	1.23897	+	0.529386i
$507$	11560.0	+	11560.0i	1.01261	+	1.01261i
$508$	−171.893	−	12.2940i	−0.0150128	−	0.00107374i
$509$	4871.73	−	7580.56i	0.424235	−	0.660123i	−0.561683	−	0.827353i	$-0.689846\pi$
$509$	4871.73	−	7580.56i	0.424235	−	0.660123i	0.985918	+	0.167230i	$0.0534822\pi$
$510$	−4309.01	+	3831.59i	−0.374130	+	0.332678i
$511$	21917.9	+	10009.6i	1.89744	+	0.866531i
$512$	−306.830	+	409.877i	−0.0264846	+	0.0353793i
$513$	−3139.31	−	5749.21i	−0.270183	−	0.494803i
$514$	4935.22	+	7679.36i	0.423509	+	0.658992i
$515$	2488.83	+	696.259i	0.212954	+	0.0595745i
$516$	−1460.77	−	4974.92i	−0.124625	−	0.424435i
$517$	−2092.07	−	29251.0i	−0.177968	−	2.48831i
$518$	−72.1684	−	1009.05i	−0.00612143	−	0.0855887i
$519$	1481.89	+	5046.85i	0.125333	+	0.426844i
$520$	−462.626	−	822.006i	−0.0390144	−	0.0693218i
$521$	−4451.90	−	6927.30i	−0.374360	−	0.582515i	0.602045	−	0.798462i	$-0.294353\pi$
$521$	−4451.90	−	6927.30i	−0.374360	−	0.582515i	−0.976405	+	0.215947i	$0.930716\pi$
$522$	1405.24	+	2573.51i	0.117827	+	0.215784i
$523$	1927.70	−	2575.11i	0.161171	−	0.215300i	−0.712685	−	0.701485i	$-0.752521\pi$
$523$	1927.70	−	2575.11i	0.161171	−	0.215300i	0.873856	+	0.486185i	$0.161612\pi$
$524$	5567.95	+	2542.80i	0.464192	+	0.211990i
$525$	33664.0	−	863.297i	2.79851	−	0.0717664i
$526$	−8847.59	+	13767.1i	−0.733409	+	1.14121i
$527$	−6916.23	−	494.659i	−0.571681	−	0.0408874i
$528$	−6164.29	−	6164.29i	−0.508080	−	0.508080i
$529$	−8792.25	+	8410.24i	−0.722631	+	0.691234i
$530$	2300.81	−	194.232i	0.188568	−	0.0159187i
$531$	14028.3	+	16189.5i	1.14647	+	1.32310i
$532$	3285.83	+	15104.7i	0.267779	+	1.23096i
$533$	322.634	+	430.989i	0.0262192	+	0.0350248i
$534$	−1629.27	+	3567.61i	−0.132033	+	0.289111i
$535$	11265.1	−	18033.0i	0.910344	−	1.45726i
$536$	616.490	−	2099.57i	0.0496797	−	0.169194i
$537$	29533.6	+	6424.64i	2.37331	+	0.516283i
$538$	11019.2	+	4109.95i	0.883032	+	0.329354i
$539$	−55919.9	+	16419.6i	−4.46872	+	1.31214i
$540$	2574.02	−	403.832i	0.205127	−	0.0321818i
$541$	4033.05	−	4654.39i	0.320507	−	0.369885i	−0.572518	−	0.819892i	$-0.694033\pi$
$541$	4033.05	−	4654.39i	0.320507	−	0.369885i	0.893025	+	0.450007i	$0.148579\pi$
$542$	3860.63	+	2108.06i	0.305956	+	0.167065i
$543$	−7347.14	+	19698.4i	−0.580655	+	1.55680i
$544$	885.681	−	569.193i	0.0698038	−	0.0448602i
$545$	1478.15	−	7240.59i	0.116178	−	0.569087i
$546$	−5624.28	+	808.649i	−0.440837	+	0.0633828i
$547$	−22413.6	+	8359.85i	−1.75199	+	0.653458i	−0.999984	−	0.00569955i	$-0.998186\pi$
$547$	−22413.6	+	8359.85i	−1.75199	+	0.653458i	−0.752005	+	0.659158i	$0.770913\pi$
$548$	−3461.46	+	2591.22i	−0.269829	+	0.201992i
$549$	−17645.4	−	11340.0i	−1.37174	−	0.881564i
$550$	17296.9	−	1683.76i	1.34099	−	0.130538i
$551$		−	4787.15i		−	0.370126i
$552$	6418.96	−	2575.71i	0.494944	−	0.198604i
$553$	−13183.9	+	13183.9i	−1.01381	+	1.01381i
$554$	−9262.38	+	8025.90i	−0.710326	+	0.615501i
$555$	1139.67	+	603.470i	0.0871643	+	0.0461547i
$556$	−441.497	+	3070.68i	−0.0336756	+	0.234219i
$557$	−4969.77	−	13324.5i	−0.378054	−	1.01360i	−0.977080	−	0.212872i	$-0.931718\pi$
$557$	−4969.77	−	13324.5i	−0.378054	−	1.01360i	0.599026	−	0.800729i	$-0.295554\pi$
$558$	11619.0	+	8697.86i	0.881489	+	0.659874i
$559$	−1673.42	−	491.361i	−0.126616	−	0.0371777i
$560$	−6096.68	−	796.941i	−0.460057	−	0.0601373i
$561$	7446.65	+	16305.9i	0.560424	+	1.22716i
$562$	−654.687	+	1198.97i	−0.0491393	+	0.0899919i
$563$	−5641.99	+	403.523i	−0.422347	+	0.0302069i	−0.280896	−	0.959738i	$-0.590632\pi$
$563$	−5641.99	+	403.523i	−0.422347	+	0.0302069i	−0.141452	+	0.989945i	$0.545177\pi$
$564$	−9995.65	−	8661.28i	−0.746264	−	0.646642i
$565$	−3149.28	+	7136.68i	−0.234498	+	0.531403i
$566$	−4087.83	+	1866.85i	−0.303577	+	0.138639i
$567$	−3456.19	+	15887.9i	−0.255990	+	1.17677i
$568$	−1956.71	+	1068.45i	−0.144545	+	0.0789278i
$569$	−1971.33	−	13710.9i	−0.145242	−	1.01018i	−0.923874	−	0.382697i	$-0.874995\pi$
$569$	−1971.33	−	13710.9i	−0.145242	−	1.01018i	0.778632	−	0.627480i	$-0.215914\pi$
$570$	−18549.6	−	6649.03i	−1.36308	−	0.488592i
$571$	−22402.1	−	3220.93i	−1.64185	−	0.236063i	−0.741415	−	0.671047i	$-0.765845\pi$
$571$	−22402.1	−	3220.93i	−1.64185	−	0.236063i	−0.900438	+	0.434984i	$0.856754\pi$
$572$	−2865.35	+	623.319i	−0.209452	+	0.0455634i
$573$	182.153	−	2546.84i	0.0132802	−	0.185682i
$574$	3509.37			0.255188
$575$	−4163.61	+	13144.3i	−0.301973	+	0.953316i
$576$	−2203.73			−0.159413
$577$	−989.553	+	13835.8i	−0.0713962	+	0.998249i	0.827890	+	0.560890i	$0.189541\pi$
$577$	−989.553	+	13835.8i	−0.0713962	+	0.998249i	−0.899287	+	0.437360i	$0.855914\pi$
$578$	7486.05	−	1628.49i	0.538717	−	0.117191i
$579$	12880.4	+	1851.93i	0.924512	+	0.132925i
$580$	1792.46	+	642.501i	0.128324	+	0.0459972i
$581$	−802.594	−	5582.16i	−0.0573102	−	0.398601i
$582$	−13185.3	+	7199.74i	−0.939090	+	0.512782i
$583$	1525.84	−	7014.15i	0.108394	−	0.498279i
$584$	5101.42	−	2329.74i	0.361470	−	0.165078i
$585$	1639.06	−	3714.32i	0.115840	−	0.262509i
$586$	−5741.61	−	4975.14i	−0.404751	−	0.350718i
$587$	−65.5110	+	4.68544i	−0.00460635	+	0.000329453i	−0.0736422	−	0.997285i	$-0.523462\pi$
$587$	−65.5110	+	4.68544i	−0.00460635	+	0.000329453i	0.0690358	+	0.997614i	$0.478008\pi$
$588$	−12597.1	+	23069.9i	−0.883497	+	1.61800i
$589$	−9843.60	−	21554.5i	−0.688622	−	1.50787i
$590$	13793.8	+	1803.09i	0.962513	+	0.125817i
$591$	−4943.80	−	1451.63i	−0.344096	−	0.101036i
$592$	−188.493	−	141.104i	−0.0130862	−	0.00979619i
$593$	86.2217	+	231.169i	0.00597083	+	0.0160084i	0.939901	−	0.341447i	$-0.110917\pi$
$593$	86.2217	+	231.169i	0.00597083	+	0.0160084i	−0.933930	+	0.357456i	$0.883644\pi$
$594$	1152.75	−	8017.54i	0.0796260	−	0.553811i
$595$	11173.3	+	5916.44i	0.769852	+	0.407648i
$596$	−10091.8	+	8744.61i	−0.693585	+	0.600995i
$597$	1984.44	−	1984.44i	0.136043	−	0.136043i
$598$	438.469	−	2284.81i	0.0299838	−	0.156242i
$599$			1868.53i			0.127456i	0.997967	+	0.0637281i	$0.0202990\pi$
$599$			1868.53i			0.127456i	−0.997967	+	0.0637281i	$0.979701\pi$
$600$	4979.21	−	6053.15i	0.338792	−	0.411865i
$601$	−13961.8	−	8972.72i	−0.947612	−	0.608993i	−0.0270683	−	0.999634i	$-0.508617\pi$
$601$	−13961.8	−	8972.72i	−0.947612	−	0.608993i	−0.920543	+	0.390641i	$0.872254\pi$
$602$	−9101.10	+	6813.00i	−0.616168	+	0.461258i
$603$	8824.56	−	3291.39i	0.595960	−	0.222282i
$604$	2187.50	−	314.516i	0.147365	−	0.0211878i
$605$	7829.98	−	38354.6i	0.526172	−	2.57741i
$606$	25052.4	−	16100.2i	1.67934	−	1.07925i
$607$	2903.37	−	7784.25i	0.194142	−	0.520515i	−0.803007	−	0.595970i	$-0.796768\pi$
$607$	2903.37	−	7784.25i	0.194142	−	0.520515i	0.997149	+	0.0754541i	$0.0240406\pi$
$608$	3157.77	+	1724.27i	0.210632	+	0.115014i
$609$	7511.56	−	8668.80i	0.499809	−	0.576810i
$610$	−13456.5	+	2111.15i	−0.893174	+	0.140128i
$611$	−4268.69	+	1253.40i	−0.282639	+	0.0829904i
$612$	4245.75	+	1583.58i	0.280432	+	0.104596i
$613$	−10481.6	−	2280.12i	−0.690613	−	0.150234i	−0.146456	−	0.989217i	$-0.546787\pi$
$613$	−10481.6	−	2280.12i	−0.690613	−	0.150234i	−0.544157	+	0.838983i	$0.683150\pi$
$614$	1772.03	−	6034.96i	0.116471	−	0.396663i
$615$	−2370.17	+	3794.13i	−0.155406	+	0.248771i
$616$	−7940.47	+	17387.2i	−0.519368	+	1.13726i
$617$	3706.49	+	4951.29i	0.241844	+	0.323065i	0.904997	−	0.425418i	$-0.139873\pi$
$617$	3706.49	+	4951.29i	0.241844	+	0.323065i	−0.663153	+	0.748484i	$0.730782\pi$
$618$	−770.241	−	3540.74i	−0.0501354	−	0.230469i
$619$	14916.0	+	17213.9i	0.968535	+	1.11775i	0.993008	+	0.118049i	$0.0376639\pi$
$619$	14916.0	+	17213.9i	0.968535	+	1.11775i	−0.0244727	+	0.999700i	$0.507791\pi$
$620$	9391.82	−	792.848i	0.608363	−	0.0513573i
$621$	5490.07	+	3340.36i	0.354765	+	0.215852i
$622$	11630.7	+	11630.7i	0.749758	+	0.749758i
$623$	8577.67	+	613.487i	0.551617	+	0.0394524i
$624$	−715.009	+	1112.58i	−0.0458706	+	0.0713761i
$625$	3013.46	+	15331.7i	0.192861	+	0.981226i
$626$	17477.4	+	7981.66i	1.11587	+	0.509602i
$627$	−36711.4	+	49040.7i	−2.33830	+	3.12360i
$628$	1801.25	+	3298.75i	0.114455	+	0.209609i
$629$	261.759	+	407.305i	0.0165930	+	0.0258192i
$630$	−12979.7	−	23062.6i	−0.820830	−	1.45847i
$631$	1319.83	+	4494.94i	0.0832675	+	0.283583i	0.990592	−	0.136848i	$-0.0436971\pi$
$631$	1319.83	+	4494.94i	0.0832675	+	0.283583i	−0.907325	+	0.420431i	$0.861879\pi$
$632$	309.585	+	4328.57i	0.0194852	+	0.272439i
$633$	−1457.06	−	20372.3i	−0.0914894	−	1.27919i
$634$	−964.800	−	3285.81i	−0.0604371	−	0.205830i
$635$	−463.872	−	129.770i	−0.0289893	−	0.00810985i
$636$	−1750.29	−	2723.50i	−0.109125	−	0.169801i
$637$	4237.31	+	7760.06i	0.263561	+	0.482676i
$638$	3547.45	−	4738.84i	0.220133	−	0.294064i
$639$	−8728.59	−	3986.22i	−0.540372	−	0.246780i
$640$	−1069.44	+	950.948i	−0.0660520	+	0.0587336i
$641$	−10112.0	+	15734.6i	−0.623088	+	0.969544i	0.375990	+	0.926624i	$0.377303\pi$
$641$	−10112.0	+	15734.6i	−0.623088	+	0.969544i	−0.999078	+	0.0429205i	$0.986334\pi$
$642$	−29736.0	−	2126.76i	−1.82802	−	0.130742i
$643$	14668.9	+	14668.9i	0.899667	+	0.899667i	0.995406	−	0.0957393i	$-0.0305215\pi$
$643$	14668.9	+	14668.9i	0.899667	+	0.899667i	−0.0957393	+	0.995406i	$0.530522\pi$
$644$	−10210.0	−	11213.4i	−0.624737	−	0.686133i
$645$	−1219.09	−	14441.0i	−0.0744214	−	0.881572i
$646$	−4844.78	−	5591.18i	−0.295070	−	0.340529i
$647$	−3862.06	−	17753.6i	−0.234673	−	1.07877i	−0.932124	−	0.362140i	$-0.882046\pi$
$647$	−3862.06	−	17753.6i	−0.234673	−	1.07877i	0.697451	−	0.716633i	$-0.254318\pi$
$648$	2267.91	+	3029.57i	0.137488	+	0.183662i
$649$	17965.4	−	39338.8i	1.08660	−	2.37933i
$650$	−807.383	−	2509.79i	−0.0487202	−	0.151449i
$651$	15996.1	−	54477.6i	0.963034	−	3.27979i
$652$	2062.06	+	448.573i	0.123860	+	0.0269440i
$653$	−19687.7	−	7343.14i	−1.17985	−	0.440060i	−0.318424	−	0.947948i	$-0.603154\pi$
$653$	−19687.7	−	7343.14i	−1.17985	−	0.440060i	−0.861423	+	0.507888i	$0.830426\pi$
$654$	−9941.65	+	2919.13i	−0.594418	+	0.174537i
$655$	13826.8	+	10076.6i	0.824819	+	0.601108i
$656$	534.897	−	617.304i	0.0318357	−	0.0367404i
$657$	21186.0	+	11568.4i	1.25806	+	0.686952i
$658$	−10134.5	+	27171.6i	−0.600431	+	1.60982i
$659$	−12564.1	+	8074.45i	−0.742682	+	0.477293i	−0.856460	−	0.516213i	$-0.827341\pi$
$659$	−12564.1	+	8074.45i	−0.742682	+	0.477293i	0.113778	+	0.993506i	$0.463705\pi$
$660$	−13435.2	−	20327.9i	−0.792371	−	1.19888i
$661$	−8523.65	+	1225.52i	−0.501560	+	0.0721135i	−0.388452	−	0.921469i	$-0.626990\pi$
$661$	−8523.65	+	1225.52i	−0.501560	+	0.0721135i	−0.113109	+	0.993583i	$0.536081\pi$
$662$	14099.6	−	5258.87i	0.827788	−	0.308749i
$663$	2177.04	−	1629.71i	0.127525	−	0.0954643i
$664$	−1104.24	−	709.655i	−0.0645376	−	0.0414758i
$665$	553.865	+	43202.8i	0.0322977	+	2.51930i
$666$		−	1013.44i		−	0.0589641i
$667$	2351.49	+	4065.41i	0.136507	+	0.236002i
$668$	4981.75	−	4981.75i	0.288547	−	0.288547i
$669$	19492.0	−	16889.9i	1.12647	−	0.976088i
$670$	2862.15	−	5405.23i	0.165036	−	0.311675i
$671$	−6026.33	+	41914.0i	−0.346712	+	2.41144i
$672$	3012.67	+	8077.28i	0.172941	+	0.463673i
$673$	13049.6	+	9768.83i	0.747439	+	0.559526i	0.903688	−	0.428192i	$-0.140849\pi$
$673$	13049.6	+	9768.83i	0.747439	+	0.559526i	−0.156249	+	0.987718i	$0.549940\pi$
$674$	−10002.5	−	2936.99i	−0.571634	−	0.167847i
$675$	7275.00	+	333.143i	0.414837	+	0.0189966i
$676$	−3465.87	−	7589.19i	−0.197193	−	0.431793i
$677$	−5788.26	+	10600.4i	−0.328598	+	0.601782i	−0.988790	−	0.149315i	$-0.952293\pi$
$677$	−5788.26	+	10600.4i	−0.328598	+	0.601782i	0.660192	+	0.751097i	$0.270475\pi$
$678$	10909.4	−	780.254i	0.617953	−	0.0441968i
$679$	24894.3	+	21571.0i	1.40700	+	1.21917i
$680$	2743.75	−	1063.63i	0.154732	−	0.0599827i
$681$	31575.5	−	14420.1i	1.77676	−	0.811421i
$682$	6228.39	−	28631.5i	0.349703	−	1.60756i
$683$	10179.3	−	5558.30i	0.570276	−	0.311394i	−0.168115	−	0.985767i	$-0.553768\pi$
$683$	10179.3	−	5558.30i	0.570276	−	0.311394i	0.738391	+	0.674373i	$0.235586\pi$
$684$	2203.85	+	15328.1i	0.123196	+	0.856850i
$685$	−10928.3	+	5161.09i	−0.609558	+	0.287876i
$686$	33708.2	+	4846.50i	1.87607	+	0.269738i
$687$	27013.9	−	5876.51i	1.50021	−	0.326350i
$688$	−188.769	+	2639.34i	−0.0104604	+	0.146255i
$689$	−1088.98			−0.0602131
$690$	19019.0	−	3465.15i	1.04933	−	0.191182i
$691$	9738.97			0.536162			0.268081	−	0.963396i	$-0.413611\pi$
$691$	9738.97			0.536162			0.268081	+	0.963396i	$0.413611\pi$
$692$	191.499	−	2677.50i	0.0105198	−	0.147086i
$693$	−80391.7	+	17488.2i	−4.40668	+	0.958615i
$694$	−18899.6	−	2717.36i	−1.03375	−	0.148630i
$695$	−2925.83	+	8162.53i	−0.159688	+	0.445500i
$696$	−379.948	−	2642.59i	−0.0206924	−	0.143919i
$697$	−1474.14	+	804.939i	−0.0801103	+	0.0437435i
$698$	67.8295	−	311.807i	0.00367820	−	0.0169084i
$699$	−18141.6	+	8284.97i	−0.981654	+	0.448307i
$700$	−16250.8	−	5591.02i	−0.877462	−	0.301887i
$701$	25094.6	+	21744.6i	1.35208	+	1.17159i	0.968769	+	0.247967i	$0.0797624\pi$
$701$	25094.6	+	21744.6i	1.35208	+	1.17159i	0.383313	+	0.923619i	$0.374783\pi$
$702$	−1225.69	+	87.6631i	−0.0658984	+	0.00471315i
$703$	−792.954	+	1452.19i	−0.0425417	+	0.0779093i
$704$	1848.16	+	4046.90i	0.0989418	+	0.216652i
$705$	−22531.8	−	29308.1i	−1.20368	−	1.56569i
$706$	−21901.5	−	6430.85i	−1.16752	−	0.342816i
$707$	−52272.3	−	39130.5i	−2.78062	−	2.08155i
$708$	−6816.21	−	18275.0i	−0.361820	−	0.970078i
$709$	−1057.73	+	7356.65i	−0.0560279	+	0.389682i	0.942441	+	0.334372i	$0.108524\pi$
$709$	−1057.73	+	7356.65i	−0.0560279	+	0.389682i	−0.998469	+	0.0553108i	$0.982385\pi$
$710$	−5955.99	+	1832.09i	−0.314823	+	0.0968411i
$711$	−14116.2	+	12231.7i	−0.744583	+	0.645185i
$712$	1415.32	−	1415.32i	0.0744963	−	0.0744963i
$713$	18947.3	+	13469.5i	0.995205	+	0.707486i
$714$		−	17726.8i		−	0.929142i
$715$	−8195.53	+	105.068i	−0.428665	+	0.00549554i
$716$	−12976.0	−	8339.19i	−0.677286	−	0.435266i
$717$	−18216.5	+	13636.7i	−0.948825	+	0.710282i
$718$	545.889	−	203.606i	0.0283738	−	0.0105829i
$719$	24204.3	−	3480.05i	1.25545	−	0.180506i	0.517689	−	0.855569i	$-0.326792\pi$
$719$	24204.3	−	3480.05i	1.25545	−	0.180506i	0.737761	+	0.675063i	$0.235883\pi$
$720$	−6035.12	−	1232.05i	−0.312383	−	0.0637721i
$721$	−6683.86	+	4295.45i	−0.345243	+	0.221874i
$722$	4041.37	−	10835.3i	0.208316	−	0.558517i
$723$	11795.8	+	6440.97i	0.606762	+	0.331317i
$724$	7026.24	−	8108.71i	0.360674	−	0.416240i
$725$	4549.62	+	2761.68i	0.233060	+	0.141471i
$726$	−52662.6	+	15463.1i	−2.69214	+	0.790483i
$727$	14932.8	+	5569.64i	0.761796	+	0.284135i	0.700182	−	0.713965i	$-0.253102\pi$
$727$	14932.8	+	5569.64i	0.761796	+	0.284135i	0.0616145	+	0.998100i	$0.480375\pi$
$728$	2833.53	+	616.397i	0.144255	+	0.0313808i
$729$	−8062.65	+	27458.9i	−0.409625	+	1.39505i
$730$	15273.3	−	3528.14i	0.774369	−	0.178880i
$731$	2260.30	−	4949.36i	0.114364	−	0.250422i
$732$	11445.0	+	15288.7i	0.577895	+	0.771977i
$733$	−6993.78	−	32149.9i	−0.352416	−	1.62003i	−0.722734	−	0.691127i	$-0.757115\pi$
$733$	−6993.78	−	32149.9i	−0.352416	−	1.62003i	0.370317	−	0.928905i	$-0.379249\pi$
$734$	166.153	+	191.751i	0.00835535	+	0.00964259i
$735$	−47396.3	+	56136.4i	−2.37856	+	2.81718i
$736$	−3528.66	+	86.8167i	−0.176723	+	0.00434797i
$737$	−13445.0	−	13445.0i	−0.671985	−	0.671985i
$738$	3506.72	+	250.805i	0.174911	+	0.0125099i
$739$	9440.18	−	14689.2i	0.469909	−	0.731193i	−0.522704	−	0.852514i	$-0.675077\pi$
$739$	9440.18	−	14689.2i	0.469909	−	0.731193i	0.992613	+	0.121321i	$0.0387131\pi$
$740$	−437.319	−	491.810i	−0.0217246	−	0.0244315i
$741$	8453.63	+	3860.64i	0.419098	+	0.191396i
$742$	−4253.97	+	5682.64i	−0.210469	+	0.281154i
$743$	2167.79	+	3970.01i	0.107037	+	0.196023i	0.925708	−	0.378240i	$-0.123470\pi$
$743$	2167.79	+	3970.01i	0.107037	+	0.196023i	−0.818671	+	0.574263i	$0.805289\pi$
$744$	−7144.59	−	11117.2i	−0.352061	−	0.547818i
$745$	−32526.4	+	18305.9i	−1.59956	+	0.900235i
$746$	5689.44	+	19376.5i	0.279229	+	0.950968i
$747$	−403.045	−	5635.31i	−0.0197412	−	0.276018i
$748$	−652.628	−	9124.93i	−0.0319016	−	0.446043i
$749$	18415.9	+	62718.9i	0.898402	+	3.05968i
$750$	17020.3	−	13793.4i	0.828656	−	0.671552i
$751$	−6437.66	−	10017.2i	−0.312801	−	0.486728i	0.648883	−	0.760888i	$-0.275236\pi$
$751$	−6437.66	−	10017.2i	−0.312801	−	0.486728i	−0.961684	+	0.274160i	$0.911600\pi$
$752$	3234.84	+	5924.17i	0.156865	+	0.287277i
$753$	−20905.5	+	27926.5i	−1.01174	+	1.35152i
$754$	−816.881	−	373.057i	−0.0394550	−	0.0180185i
$755$	6166.54	+	361.652i	0.297249	+	0.0174329i
$756$	−4330.56	+	6738.48i	−0.208334	+	0.324175i
$757$	−21275.3	−	1521.64i	−1.02149	−	0.0730581i	−0.449466	−	0.893298i	$-0.648386\pi$
$757$	−21275.3	−	1521.64i	−1.02149	−	0.0730581i	−0.572020	+	0.820239i	$0.693840\pi$
$758$	−2616.57	−	2616.57i	−0.125380	−	0.125380i
$759$	7087.30	−	59680.0i	0.338936	−	2.85408i
$760$	7683.87	+	6487.53i	0.366741	+	0.309642i
$761$	−7348.98	−	8481.18i	−0.350066	−	0.403998i	0.553221	−	0.833035i	$-0.313399\pi$
$761$	−7348.98	−	8481.18i	−0.350066	−	0.403998i	−0.903287	+	0.429037i	$0.858853\pi$
$762$	143.559	+	659.928i	0.00682491	+	0.0313736i
$763$	13614.8	+	18187.2i	0.645987	+	0.862938i
$764$	−541.315	+	1185.31i	−0.0256336	+	0.0561298i
$765$	10742.1	+	6710.50i	0.507687	+	0.317149i
$766$	6378.04	−	21721.6i	0.300846	−	1.02459i
$767$	−6410.91	−	1394.61i	−0.301805	−	0.0656537i
$768$	1880.00	+	701.204i	0.0883316	+	0.0329460i
$769$	7486.56	−	2198.25i	0.351069	−	0.103083i	−0.101443	−	0.994841i	$-0.532346\pi$
$769$	7486.56	−	2198.25i	0.351069	−	0.103083i	0.452512	+	0.891758i	$0.350528\pi$
$770$	−31466.6	+	43177.3i	−1.47270	+	2.02078i
$771$	23427.1	−	27036.3i	1.09430	−	1.26289i
$772$	−5828.64	−	3182.68i	−0.271733	−	0.148377i
$773$	−2268.92	+	6083.20i	−0.105572	+	0.283050i	−0.978986	−	0.203930i	$-0.934629\pi$
$773$	−2268.92	+	6083.20i	−0.105572	+	0.283050i	0.873413	+	0.486980i	$0.161901\pi$
$774$	−9581.14	+	6157.42i	−0.444944	+	0.285948i
$775$	26163.7	+	3079.47i	1.21268	+	0.142732i
$776$	7588.77	−	1091.10i	0.351058	−	0.0504745i
$777$	−3714.56	+	1385.46i	−0.171505	+	0.0639679i
$778$	−6337.25	+	4744.01i	−0.292033	+	0.218613i
$779$	−4828.62	−	3103.17i	−0.222084	−	0.142725i
$780$	−2580.14	+	2647.15i	−0.118441	+	0.121517i
$781$			19372.1i			0.887567i
$782$	6860.79	+	2368.41i	0.313736	+	0.108305i
$783$	1754.06	−	1754.06i	0.0800575	−	0.0800575i
$784$	10137.9	−	8784.50i	0.461819	−	0.400169i
$785$	3088.65	+	10041.0i	0.140432	+	0.456533i
$786$	3413.90	−	23744.2i	0.154923	−	1.07752i
$787$	−8454.04	−	22666.2i	−0.382915	−	1.02663i	−0.975282	−	0.220966i	$-0.929079\pi$
$787$	−8454.04	−	22666.2i	−0.382915	−	1.02663i	0.592367	−	0.805668i	$-0.298194\pi$
$788$	2105.05	+	1575.82i	0.0951639	+	0.0712388i
$789$	61536.0	+	18068.6i	2.77660	+	0.815285i
$790$	−1572.17	+	12027.3i	−0.0708044	+	0.541661i
$791$	−9962.21	−	21814.2i	−0.447807	−	0.980561i
$792$	−9177.10	+	16806.6i	−0.411735	+	0.754036i
$793$	6407.65	−	458.284i	0.286939	−	0.0205223i
$794$	−13549.4	−	11740.6i	−0.605604	−	0.524759i
$795$	−3270.69	−	8437.12i	−0.145911	−	0.376395i
$796$	−1302.80	+	594.969i	−0.0580107	+	0.0264926i
$797$	6036.83	−	27750.9i	0.268300	−	1.23336i	−0.623823	−	0.781566i	$-0.714421\pi$
$797$	6036.83	−	27750.9i	0.268300	−	1.23336i	0.892123	−	0.451792i	$-0.149215\pi$
$798$	53169.1	−	29032.5i	2.35861	−	1.28790i
$799$	−1975.25	−	13738.2i	−0.0874586	−	0.608288i
$800$	−3460.42	+	2006.37i	−0.152930	+	0.0886697i
$801$	8527.35	+	1226.05i	0.376154	+	0.0540827i
$802$	2020.03	−	439.431i	0.0889399	−	0.0193477i
$803$	3476.49	−	48607.6i	0.152780	−	2.13615i
$804$	−8575.53			−0.376164
$805$	−21692.0	−	36417.2i	−0.949741	−	1.59446i
$806$	−4445.17			−0.194261
$807$	3288.01	−	45972.4i	0.143424	−	2.00533i
$808$	−14850.5	+	3230.52i	−0.646581	+	0.140655i
$809$	8317.76	+	1195.91i	0.361480	+	0.0519729i	0.320662	−	0.947194i	$-0.396095\pi$
$809$	8317.76	+	1195.91i	0.361480	+	0.0519729i	0.0408176	+	0.999167i	$0.487004\pi$
$810$	4517.13	+	9564.73i	0.195946	+	0.414902i
$811$	180.131	+	1252.84i	0.00779933	+	0.0542455i	0.993349	−	0.115139i	$-0.0367312\pi$
$811$	180.131	+	1252.84i	0.00779933	+	0.0542455i	−0.985550	+	0.169384i	$0.945822\pi$
$812$	−5137.78	+	2805.44i	−0.222045	+	0.121246i
$813$	3664.26	−	16844.3i	0.158070	−	0.726638i
$814$	−1861.08	+	849.925i	−0.0801360	+	0.0365969i
$815$	5396.37	+	2381.31i	0.231934	+	0.102348i
$816$	−3118.17	−	2701.91i	−0.133772	−	0.115914i
$817$	18546.8	−	1326.50i	0.794212	−	0.0568032i
$818$	12485.7	−	22865.9i	0.533685	−	0.977370i
$819$	5184.87	+	11353.3i	0.221214	+	0.484391i
$820$	1809.99	−	1391.50i	0.0770824	−	0.0592601i
$821$	9372.81	+	2752.10i	0.398433	+	0.116990i	0.474809	−	0.880089i	$-0.342517\pi$
$821$	9372.81	+	2752.10i	0.398433	+	0.116990i	−0.0763768	+	0.997079i	$0.524335\pi$
$822$	13565.4	+	10154.9i	0.575604	+	0.430892i
$823$	−5016.30	−	13449.2i	−0.212463	−	0.569636i	0.786379	−	0.617744i	$-0.211953\pi$
$823$	−5016.30	−	13449.2i	−0.212463	−	0.569636i	−0.998842	+	0.0481086i	$0.984681\pi$
$824$	−263.174	+	1830.42i	−0.0111263	+	0.0773854i
$825$	−25428.8	−	63181.2i	−1.07311	−	2.66629i
$826$	−32320.9	+	28006.3i	−1.36149	+	1.17974i
$827$	−2537.83	+	2537.83i	−0.106710	+	0.106710i	−0.758446	−	0.651736i	$-0.774041\pi$
$827$	−2537.83	+	2537.83i	−0.106710	+	0.106710i	0.651736	+	0.758446i	$0.274041\pi$
$828$	−9400.91	−	11934.6i	−0.394570	−	0.500913i
$829$			43329.5i			1.81532i	0.419711	+	0.907658i	$0.362131\pi$
$829$			43329.5i			1.81532i	−0.419711	+	0.907658i	$0.637869\pi$
$830$	−2627.33	−	2560.82i	−0.109875	−	0.107093i
$831$	40405.7	+	25967.2i	1.68671	+	1.08399i
$832$	540.312	−	404.473i	0.0225144	−	0.0168540i
$833$	−25844.3	+	9639.43i	−1.07497	+	0.400944i
$834$	12033.9	−	1730.21i	0.499640	−	0.0718373i
$835$	16428.2	−	10857.8i	0.680864	−	0.450001i
$836$	26300.2	−	16902.1i	1.08805	−	0.699248i
$837$	4290.99	−	11504.6i	0.177202	−	0.475097i
$838$	5711.21	+	3118.56i	0.235430	+	0.128555i
$839$	−25676.9	+	29632.8i	−1.05657	+	1.21935i	−0.0816866	+	0.996658i	$0.526031\pi$
$839$	−25676.9	+	29632.8i	−1.05657	+	1.21935i	−0.974888	+	0.222694i	$0.928515\pi$
$840$	3734.67	+	23804.8i	0.153403	+	0.977789i
$841$	−21661.6	+	6360.43i	−0.888173	+	0.260791i
$842$	−14290.5	−	5330.09i	−0.584898	−	0.218156i
$843$	5231.23	+	1137.98i	0.213728	+	0.0464938i
$844$	−2936.59	+	10001.1i	−0.119765	+	0.407882i
$845$	−5248.68	−	22721.4i	−0.213680	−	0.925019i
$846$	−12068.7	+	26426.8i	−0.490463	+	1.07396i
$847$	72119.7	+	96340.7i	2.92569	+	3.90827i
$848$	351.197	+	1614.43i	0.0142219	+	0.0653770i
$849$	11533.2	+	13310.0i	0.466215	+	0.538041i
$850$	8108.69	−	1378.88i	0.327207	−	0.0556414i
$851$	−39.9250	−	1622.75i	−0.00160824	−	0.0653669i
$852$	6178.00	+	6178.00i	0.248421	+	0.248421i
$853$	−224.728	−	16.0728i	−0.00902055	−	0.000645162i	0.0668282	−	0.997764i	$-0.478712\pi$
$853$	−224.728	−	16.0728i	−0.00902055	−	0.000645162i	−0.0758487	+	0.997119i	$0.524167\pi$
$854$	22639.3	−	35227.4i	0.907142	−	1.41154i
$855$	−2534.14	+	43209.7i	−0.101364	+	1.72835i
$856$	13839.3	+	6320.21i	0.552591	+	0.252360i
$857$	−12032.1	+	16073.1i	−0.479592	+	0.640659i	−0.973455	−	0.228880i	$-0.926494\pi$
$857$	−12032.1	+	16073.1i	−0.479592	+	0.640659i	0.493863	+	0.869540i	$0.335584\pi$
$858$	5507.45	+	10086.1i	0.219139	+	0.401323i
$859$	22500.3	+	35011.2i	0.893714	+	1.39065i	0.920390	+	0.391002i	$0.127872\pi$
$859$	22500.3	+	35011.2i	0.893714	+	1.39065i	−0.0266754	+	0.999644i	$0.508492\pi$
$860$	−1992.56	+	7122.55i	−0.0790065	+	0.282415i
$861$	−3874.69	−	13196.0i	−0.153367	−	0.522321i
$862$	−1513.01	−	21154.7i	−0.0597836	−	0.835884i
$863$	206.388	+	2885.68i	0.00814081	+	0.113823i	0.999898	−	0.0143113i	$-0.00455557\pi$
$863$	206.388	+	2885.68i	0.00814081	+	0.113823i	−0.991757	+	0.128135i	$0.959101\pi$
$864$	525.248	+	1788.83i	0.0206821	+	0.0704367i
$865$	2021.37	−	7225.54i	0.0794550	−	0.284018i
$866$	−201.220	−	313.105i	−0.00789577	−	0.0122861i
$867$	−14388.8	−	26351.2i	−0.563634	−	1.03222i
$868$	−17364.5	+	23196.3i	−0.679021	+	0.907065i
$869$	34300.8	+	15664.7i	1.33898	+	0.611493i
$870$	436.890	−	7449.43i	0.0170253	−	0.290298i
$871$	−1559.51	+	2426.65i	−0.0606683	+	0.0944017i
$872$	5274.33	+	377.227i	0.204829	+	0.0146497i
$873$	23333.9	+	23333.9i	0.904618	+	0.904618i
$874$	4132.73	+	24457.0i	0.159945	+	0.946533i
$875$	−41378.7	−	24397.0i	−1.59869	−	0.942595i
$876$	−14392.8	−	16610.2i	−0.555124	−	0.640647i
$877$	2890.39	+	13286.9i	0.111290	+	0.511593i	0.998717	+	0.0506438i	$0.0161273\pi$
$877$	2890.39	+	13286.9i	0.111290	+	0.511593i	−0.887427	+	0.460949i	$0.847509\pi$
$878$	−14851.1	−	19838.8i	−0.570844	−	0.762558i
$879$	−12368.3	+	27082.8i	−0.474599	+	1.03923i
$880$	2798.83	+	12116.1i	0.107214	+	0.464129i
$881$	11736.8	−	39971.9i	0.448834	−	1.52859i	−0.355653	−	0.934618i	$-0.615741\pi$
$881$	11736.8	−	39971.9i	0.448834	−	1.52859i	0.804487	−	0.593970i	$-0.202440\pi$
$882$	56417.7	+	12272.9i	2.15384	+	0.468538i
$883$	11541.7	+	4304.82i	0.439873	+	0.164064i	0.559636	−	0.828738i	$-0.310941\pi$
$883$	11541.7	+	4304.82i	0.439873	+	0.164064i	−0.119763	+	0.992802i	$0.538214\pi$
$884$	−1331.63	+	391.002i	−0.0506646	+	0.0148765i
$885$	−8449.75	−	53858.6i	−0.320944	−	2.04569i
$886$	3492.46	−	4030.51i	0.132428	−	0.152830i
$887$	−26414.1	−	14423.2i	−0.999885	−	0.545979i	−0.106044	−	0.994361i	$-0.533818\pi$
$887$	−26414.1	−	14423.2i	−0.999885	−	0.545979i	−0.893842	+	0.448383i	$0.852000\pi$
$888$	−322.468	+	864.569i	−0.0121862	+	0.0326723i
$889$	1245.75	−	800.593i	0.0469977	−	0.0302036i
$890$	4667.27	−	3084.72i	0.175784	−	0.116180i
$891$	32549.3	−	4679.88i	1.22384	−	0.175962i
$892$	−12332.6	+	4599.81i	−0.462921	+	0.172660i
$893$	37970.9	−	28424.6i	1.42290	−	1.06517i
$894$	44024.0	+	28292.5i	1.64696	+	1.05844i
$895$	−30873.9	−	30092.3i	−1.15307	−	1.12388i
$896$		−	4399.54i		−	0.164038i
$897$	−9075.49	+	873.917i	−0.337817	+	0.0325298i
$898$	−12685.9	+	12685.9i	−0.471420	+	0.471420i
$899$	6781.68	−	5876.35i	0.251592	−	0.218006i
$900$	−15839.0	−	6748.20i	−0.586629	−	0.249933i
$901$	483.492	−	3362.76i	0.0178773	−	0.124339i
$902$	−2480.34	−	6650.04i	−0.0915590	−	0.245479i
$903$	35666.9	+	26699.9i	1.31442	+	0.983962i
$904$	−5355.60	−	1572.54i	−0.197040	−	0.0578563i
$905$	23775.5	−	18278.3i	0.873285	−	0.671372i
$906$	−3597.87	−	7878.24i	−0.131933	−	0.288893i
$907$	−4976.60	+	9113.96i	−0.182189	+	0.333654i	−0.952773	−	0.303685i	$-0.901783\pi$
$907$	−4976.60	+	9113.96i	−0.182189	+	0.333654i	0.770584	+	0.637339i	$0.219965\pi$
$908$	−17669.9	+	1263.78i	−0.645812	+	0.0461894i
$909$	−49436.3	−	42836.8i	−1.80385	−	1.56304i
$910$	7415.30	+	3272.23i	0.270126	+	0.119202i
$911$	2897.10	−	1323.06i	0.105363	−	0.0481175i	−0.362036	−	0.932164i	$-0.617918\pi$
$911$	2897.10	−	1323.06i	0.105363	−	0.0481175i	0.467399	+	0.884046i	$0.345191\pi$
$912$	2997.15	−	13777.7i	0.108822	−	0.500246i
$913$	−10010.6	+	5466.21i	−0.362873	+	0.198144i
$914$	−1320.56	−	9184.70i	−0.0477902	−	0.332388i
$915$	22795.7	+	48268.3i	0.823609	+	1.74394i
$916$	−13965.0	−	2007.87i	−0.503731	−	0.0724256i
$917$	−51395.7	+	11180.4i	−1.85086	+	0.402629i
$918$	273.487	−	3823.85i	0.00983269	−	0.137479i
$919$	−29862.2			−1.07189			−0.535943	−	0.844254i	$-0.680044\pi$
$919$	−29862.2			−1.07189			−0.535943	+	0.844254i	$0.680044\pi$
$920$	−9712.14	−	1735.04i	−0.348043	−	0.0621767i
$921$	−24649.3			−0.881891
$922$	2005.19	−	28036.2i	0.0716241	−	1.00144i
$923$	2871.72	−	624.704i	0.102409	−	0.0222778i
$924$	74146.8	+	10660.7i	2.63988	+	0.379558i
$925$	−922.682	−	1591.37i	−0.0327974	−	0.0565663i
$926$	5.06088	+	35.1992i	0.000179601	+	0.00124916i
$927$	−6985.80	+	3814.53i	−0.247512	+	0.135152i
$928$	−289.617	+	1331.35i	−0.0102448	+	0.0470945i
$929$	22433.6	−	10245.1i	0.792272	−	0.361819i	0.0221825	−	0.999754i	$-0.492939\pi$
$929$	22433.6	−	10245.1i	0.792272	−	0.361819i	0.770090	+	0.637935i	$0.220211\pi$
$930$	−13350.8	−	34440.0i	−0.470742	−	1.21433i
$931$	−71239.5	−	61729.4i	−2.50782	−	2.17304i
$932$	10152.2	−	726.098i	0.356809	−	0.0255195i
$933$	30892.6	−	56575.6i	1.08401	−	1.98521i
$934$	5053.07	+	11064.7i	0.177025	+	0.387631i
$935$	3314.26	−	25354.4i	0.115923	−	0.886821i
$936$	2787.34	+	818.437i	0.0973367	+	0.0285806i
$937$	29504.3	+	22086.7i	1.02867	+	0.770053i	0.973561	−	0.228427i	$-0.0733583\pi$
$937$	29504.3	+	22086.7i	1.02867	+	0.770053i	0.0551096	+	0.998480i	$0.482449\pi$
$938$	6570.97	+	17617.4i	0.228731	+	0.613252i
$939$	10716.0	−	74531.4i	0.372421	−	2.59025i
$940$	5546.87	+	18032.5i	0.192467	+	0.625696i
$941$	16146.1	−	13990.6i	0.559348	−	0.484678i	−0.328696	−	0.944436i	$-0.606609\pi$
$941$	16146.1	−	13990.6i	0.559348	−	0.484678i	0.888044	+	0.459758i	$0.152064\pi$
$942$	10415.3	−	10415.3i	0.360241	−	0.360241i
$943$	5624.93	+	263.448i	0.194245	+	0.00909760i
$944$			9954.02i			0.343195i
$945$	−15627.0	+	16032.9i	−0.537933	+	0.551905i
$946$	19342.7	+	12430.8i	0.664782	+	0.427230i
$947$	9370.86	−	7014.94i	0.321554	−	0.240713i	−0.426290	−	0.904587i	$-0.640180\pi$
$947$	9370.86	−	7014.94i	0.321554	−	0.240713i	0.747845	+	0.663874i	$0.231089\pi$
$948$	15934.6	−	5943.28i	0.545918	−	0.203617i
$949$	−7317.68	+	1052.12i	−0.250308	+	0.0359888i
$950$	17416.0	+	22062.6i	0.594789	+	0.753481i
$951$	−11290.1	+	7255.72i	−0.384971	+	0.247406i
$952$	−3161.48	+	8476.26i	−0.107630	+	0.288568i
$953$	−25313.2	−	13822.1i	−0.860415	−	0.469822i	−0.0124798	−	0.999922i	$-0.503973\pi$
$953$	−25313.2	−	13822.1i	−0.860415	−	0.469822i	−0.847935	+	0.530100i	$0.822154\pi$
$954$	−4656.88	+	5374.33i	−0.158042	+	0.182390i
$955$	−2145.13	+	2943.46i	−0.0726855	+	0.0997364i
$956$	11142.5	−	3271.72i	0.376959	−	0.110685i
$957$	−21735.9	−	8107.05i	−0.734190	−	0.273839i
$958$	−11900.0	−	2588.70i	−0.401329	−	0.0873037i
$959$	10467.7	−	35649.7i	0.352470	−	1.20040i
$960$	4756.54	+	2971.38i	0.159913	+	0.0998968i
$961$	6076.06	−	13304.7i	0.203956	−	0.446602i
$962$	186.008	+	248.477i	0.00623402	+	0.00832768i
$963$	13919.7	+	63987.7i	0.465789	+	2.14120i
$964$	−4491.56	−	5183.54i	−0.150066	−	0.173185i
$965$	−14183.0	−	11974.8i	−0.473125	−	0.399462i
$966$	−30891.9	+	50772.6i	−1.02892	+	1.69108i
$967$	−1190.51	−	1190.51i	−0.0395908	−	0.0395908i	0.687034	−	0.726625i	$-0.258912\pi$
$967$	−1190.51	−	1190.51i	−0.0395908	−	0.0395908i	−0.726625	+	0.687034i	$0.758912\pi$
$968$	27939.0	+	1998.24i	0.927679	+	0.0663489i
$969$	−15674.9	+	24390.7i	−0.519661	+	0.808609i
$970$	21392.6	+	1254.62i	0.708119	+	0.0415294i
$971$	27315.7	+	12474.6i	0.902782	+	0.412287i	0.812049	−	0.583589i	$-0.198352\pi$
$971$	27315.7	+	12474.6i	0.902782	+	0.412287i	0.0907323	+	0.995875i	$0.471079\pi$
$972$	12658.6	−	16910.0i	0.417722	−	0.558011i
$973$	−12775.4	−	23396.5i	−0.420927	−	0.770870i
$974$	4861.90	+	7565.26i	0.159944	+	0.248877i
$975$	−8545.94	+	5807.00i	−0.280707	+	0.190741i
$976$	−2745.89	−	9351.64i	−0.0900551	−	0.306699i
$977$	991.203	+	13858.8i	0.0324579	+	0.453821i	0.987528	+	0.157442i	$0.0503247\pi$
$977$	991.203	+	13858.8i	0.0324579	+	0.453821i	−0.955070	+	0.296379i	$0.904221\pi$
$978$	−589.985	−	8249.06i	−0.0192900	−	0.269710i
$979$	−4899.97	−	16687.8i	−0.159963	−	0.544784i
$980$	32674.8	−	18389.4i	1.06506	−	0.599416i
$981$	12304.7	+	19146.5i	0.400468	+	0.623140i
$982$	19324.7	+	35390.5i	0.627978	+	1.15006i
$983$	−24840.1	+	33182.5i	−0.805977	+	1.07666i	0.189521	+	0.981877i	$0.439306\pi$
$983$	−24840.1	+	33182.5i	−0.805977	+	1.07666i	−0.995498	+	0.0947825i	$0.969784\pi$
$984$	−2911.78	−	1329.77i	−0.0943335	−	0.0430807i
$985$	4883.87	+	5492.42i	0.157983	+	0.177668i
$986$	1514.68	−	2356.89i	0.0489222	−	0.0761245i
$987$	113361.	+	8107.72i	3.65584	+	0.261471i
$988$	−3353.67	−	3353.67i	−0.107990	−	0.107990i
$989$	−15099.0	+	10236.9i	−0.485460	+	0.329134i
$990$	−34528.6	+	40895.8i	−1.10848	+	1.31288i
$991$	−23978.7	−	27672.9i	−0.768626	−	0.887041i	0.227608	−	0.973753i	$-0.426910\pi$
$991$	−23978.7	−	27672.9i	−0.768626	−	0.887041i	−0.996233	+	0.0867117i	$0.972364\pi$
$992$	1433.57	+	6590.02i	0.0458830	+	0.210921i
$993$	−35341.9	−	47211.2i	−1.12945	−	1.50876i
$994$	7958.12	−	17425.9i	0.253940	−	0.556051i
$995$	−3900.48	+	901.016i	−0.124275	+	0.0287077i
$996$	−1449.26	+	4935.73i	−0.0461060	+	0.157023i
$997$	21889.4	+	4761.74i	0.695330	+	0.151260i	0.546321	−	0.837576i	$-0.316028\pi$
$997$	21889.4	+	4761.74i	0.695330	+	0.151260i	0.149009	+	0.988836i	$0.452392\pi$
$998$	−30526.3	−	11385.7i	−0.968229	−	0.361131i
$999$	−822.643	+	241.550i	−0.0260533	+	0.00764994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.217.16	yes	720
5.3	odd	4	inner	230.4.l.a.33.34	yes	720
23.7	odd	22	inner	230.4.l.a.7.34	✓	720
115.53	even	44	inner	230.4.l.a.53.16	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.34	✓	720	23.7	odd	22	inner
230.4.l.a.33.34	yes	720	5.3	odd	4	inner
230.4.l.a.53.16	yes	720	115.53	even	44	inner
230.4.l.a.217.16	yes	720	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142678 + 1.99490i) q^{2} +(7.65881 - 1.66607i) q^{3} +(-3.95929 - 0.569259i) q^{4} +(-10.5246 - 3.77252i) q^{5} +(2.23091 + 15.5163i) q^{6} +(30.1671 - 16.4725i) q^{7} +(1.70052 - 7.81717i) q^{8} +(31.3215 - 14.3041i) q^{9} +(9.02746 - 20.4574i) q^{10} +(-52.5357 - 45.5225i) q^{11} +(-31.2719 + 2.23661i) q^{12} +(-5.05408 + 9.25586i) q^{13} +(28.5568 + 62.5307i) q^{14} +(-86.8915 - 11.3582i) q^{15} +(15.3519 + 4.50772i) q^{16} +(-26.3381 - 19.7165i) q^{17} +(24.0663 + 64.5244i) q^{18} +(16.0009 - 111.289i) q^{19} +(39.5225 + 20.9277i) q^{20} +(203.600 - 176.420i) q^{21} +(98.3086 - 98.3086i) q^{22} +(41.0776 + 102.370i) q^{23} -62.7035i q^{24} +(96.5362 + 79.4089i) q^{25} +(-17.7434 - 11.4030i) q^{26} +(46.6403 - 34.9145i) q^{27} +(-128.817 + 48.0463i) q^{28} +(42.1443 - 6.05944i) q^{29} +(35.0561 - 171.720i) q^{30} +(177.298 - 113.943i) q^{31} +(-11.1829 + 29.9824i) q^{32} +(-478.205 - 261.120i) q^{33} +(43.0903 - 49.7289i) q^{34} +(-379.640 + 59.5609i) q^{35} +(-132.154 + 38.8038i) q^{36} +(-13.7882 - 5.14274i) q^{37} +(219.728 + 47.7988i) q^{38} +(-23.2873 + 79.3093i) q^{39} +(-47.3879 + 75.8577i) q^{40} +(21.2072 - 46.4373i) q^{41} +(322.892 + 431.333i) q^{42} +(35.1540 + 161.600i) q^{43} +(182.090 + 210.143i) q^{44} +(-383.610 + 32.3840i) q^{45} +(-210.079 + 67.3400i) q^{46} +(298.302 + 298.302i) q^{47} +(125.087 + 8.94643i) q^{48} +(453.270 - 705.302i) q^{49} +(-172.187 + 181.250i) q^{50} +(-234.568 - 107.123i) q^{51} +(25.2795 - 33.7695i) q^{52} +(49.4880 + 90.6305i) q^{53} +(62.9965 + 98.0245i) q^{54} +(381.185 + 677.300i) q^{55} +(-77.4684 - 263.833i) q^{56} +(-62.8673 - 878.999i) q^{57} +(6.07491 + 84.9384i) q^{58} +(175.273 + 596.926i) q^{59} +(337.563 + 94.4343i) q^{60} +(-329.333 - 512.452i) q^{61} +(202.008 + 369.950i) q^{62} +(709.256 - 947.455i) q^{63} +(-58.2164 - 26.5866i) q^{64} +(88.1103 - 78.3480i) q^{65} +(589.138 - 916.717i) q^{66} +(272.829 + 19.5131i) q^{67} +(93.0563 + 93.0563i) q^{68} +(485.162 + 715.595i) q^{69} +(-64.6518 - 765.844i) q^{70} +(-182.495 - 210.610i) q^{71} +(-58.5544 - 269.170i) q^{72} +(420.111 + 561.202i) q^{73} +(12.2266 - 26.7724i) q^{74} +(871.653 + 447.341i) q^{75} +(-126.704 + 431.516i) q^{76} +(-2334.72 - 507.886i) q^{77} +(-154.892 - 57.7717i) q^{78} +(-520.480 + 152.827i) q^{79} +(-144.568 - 105.357i) q^{80} +(-309.783 + 357.508i) q^{81} +(89.6122 + 48.9319i) q^{82} +(57.3391 - 153.732i) q^{83} +(-906.538 + 582.596i) q^{84} +(202.818 + 306.870i) q^{85} +(-327.393 + 47.0720i) q^{86} +(312.680 - 116.624i) q^{87} +(-445.195 + 333.269i) q^{88} +(210.478 + 135.266i) q^{89} +(-9.87005 - 769.887i) q^{90} +362.475i q^{91} +(-104.363 - 428.696i) q^{92} +(1168.06 - 1168.06i) q^{93} +(-637.646 + 552.523i) q^{94} +(-588.244 + 1110.91i) q^{95} +(-35.6945 + 248.261i) q^{96} +(334.909 + 897.926i) q^{97} +(1342.34 + 1004.86i) q^{98} +(-2296.66 - 674.359i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) \) 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more