LMFDB - Embedded newform 120.4.v.a.43.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(43,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("120.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$N$	$=$	$120 = 2^{3} \cdot 3 \cdot 5$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	120.v (of order $4$ , degree $2$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.14
Character	$\chi$	$=$	120.43
Dual form			120.4.v.a.67.14

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05551 + 2.62410i) q^{2} +(2.12132 + 2.12132i) q^{3} +(-5.77179 - 5.53954i) q^{4} +(-4.33793 + 10.3045i) q^{5} +(-7.80563 + 3.32747i) q^{6} +(15.3854 + 15.3854i) q^{7} +(20.6285 - 9.29869i) q^{8} +9.00000i q^{9} +(-22.4612 - 22.2597i) q^{10} -63.8411 q^{11} +(-0.492677 - 23.9949i) q^{12} +(10.5363 - 10.5363i) q^{13} +(-56.6121 + 24.1333i) q^{14} +(-31.0612 + 12.6570i) q^{15} +(2.62706 + 63.9461i) q^{16} +(-58.9296 + 58.9296i) q^{17} +(-23.6169 - 9.49961i) q^{18} -100.850i q^{19} +(82.1197 - 35.4452i) q^{20} +65.2745i q^{21} +(67.3850 - 167.525i) q^{22} +(8.18053 - 8.18053i) q^{23} +(63.4851 + 24.0341i) q^{24} +(-87.3648 - 89.4002i) q^{25} +(16.5270 + 38.7694i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(-3.57325 - 174.029i) q^{28} +16.1242 q^{29} +(-0.427641 - 94.8674i) q^{30} +317.519i q^{31} +(-170.574 - 60.6022i) q^{32} +(-135.427 - 135.427i) q^{33} +(-92.4362 - 216.838i) q^{34} +(-225.279 + 91.7976i) q^{35} +(49.8558 - 51.9461i) q^{36} +(-144.623 - 144.623i) q^{37} +(264.640 + 106.448i) q^{38} +44.7016 q^{39} +(6.33336 + 252.903i) q^{40} +276.422 q^{41} +(-171.287 - 68.8981i) q^{42} +(237.148 + 237.148i) q^{43} +(368.477 + 353.650i) q^{44} +(-92.7404 - 39.0413i) q^{45} +(12.8319 + 30.1012i) q^{46} +(369.925 + 369.925i) q^{47} +(-130.077 + 141.223i) q^{48} +130.418i q^{49} +(326.810 - 134.891i) q^{50} -250.017 q^{51} +(-119.179 + 2.44705i) q^{52} +(-106.168 + 106.168i) q^{53} +(-29.9473 - 70.2507i) q^{54} +(276.938 - 657.849i) q^{55} +(460.440 + 174.313i) q^{56} +(213.935 - 213.935i) q^{57} +(-17.0193 + 42.3116i) q^{58} +611.812i q^{59} +(249.393 + 99.0115i) q^{60} +168.615i q^{61} +(-833.202 - 335.146i) q^{62} +(-138.468 + 138.468i) q^{63} +(339.069 - 383.636i) q^{64} +(62.8652 + 154.276i) q^{65} +(498.320 - 212.429i) q^{66} +(-86.9358 + 86.9358i) q^{67} +(666.572 - 13.6864i) q^{68} +34.7071 q^{69} +(-3.10156 - 688.047i) q^{70} +633.856i q^{71} +(83.6882 + 185.656i) q^{72} +(144.979 + 144.979i) q^{73} +(532.155 - 226.853i) q^{74} +(4.31772 - 374.975i) q^{75} +(-558.662 + 582.084i) q^{76} +(-982.217 - 982.217i) q^{77} +(-47.1831 + 117.301i) q^{78} +974.024 q^{79} +(-670.327 - 250.323i) q^{80} -81.0000 q^{81} +(-291.767 + 725.359i) q^{82} +(-149.672 - 149.672i) q^{83} +(361.591 - 376.751i) q^{84} +(-351.607 - 862.872i) q^{85} +(-872.612 + 371.987i) q^{86} +(34.2047 + 34.2047i) q^{87} +(-1316.94 + 593.638i) q^{88} -770.639i q^{89} +(200.337 - 202.151i) q^{90} +324.208 q^{91} +(-92.5327 + 1.89993i) q^{92} +(-673.560 + 673.560i) q^{93} +(-1361.18 + 580.259i) q^{94} +(1039.21 + 437.479i) q^{95} +(-233.285 - 490.398i) q^{96} +(117.542 - 117.542i) q^{97} +(-342.230 - 137.658i) q^{98} -574.569i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$72 q + 12 q^{6} + 84 q^{8} - 72 q^{10} + 24 q^{12} - 20 q^{16} - 104 q^{17} + 380 q^{20} + 44 q^{22} - 88 q^{25} - 368 q^{26} - 1068 q^{28} + 408 q^{30} + 340 q^{32} + 912 q^{35} - 108 q^{36} - 40 q^{38}+ \cdots + 7576 q^{98}+O(q^{100})$ 72 * q + 12 * q^6 + 84 * q^8 - 72 * q^10 + 24 * q^12 - 20 * q^16 - 104 * q^17 + 380 * q^20 + 44 * q^22 - 88 * q^25 - 368 * q^26 - 1068 * q^28 + 408 * q^30 + 340 * q^32 + 912 * q^35 - 108 * q^36 - 40 * q^38 - 952 * q^40 - 660 * q^42 + 864 * q^43 - 2256 * q^46 + 528 * q^48 - 344 * q^50 - 1488 * q^51 + 2544 * q^52 + 2144 * q^56 + 1004 * q^58 + 420 * q^60 + 2608 * q^62 - 1048 * q^65 + 1368 * q^66 + 3696 * q^67 - 1464 * q^68 + 204 * q^70 - 756 * q^72 + 1480 * q^73 - 4016 * q^76 - 72 * q^78 - 1684 * q^80 - 5832 * q^81 - 6712 * q^82 - 5360 * q^83 - 8416 * q^86 - 404 * q^88 + 108 * q^90 + 3392 * q^91 + 8432 * q^92 + 3828 * q^96 - 328 * q^97 + 7576 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$ .

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.05551	+	2.62410i	−0.373180	+	0.927759i
$2$	−1.05551	+	2.62410i	−0.373180	+	0.927759i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$4$	−5.77179	−	5.53954i	−0.721473	−	0.692442i
$5$	−4.33793	+	10.3045i	−0.387996	+	0.921661i
$5$	−4.33793	+	10.3045i	−0.387996	+	0.921661i
$6$	−7.80563	+	3.32747i	−0.531106	+	0.226406i
$7$	15.3854	+	15.3854i	0.830731	+	0.830731i	0.987617	−	0.156886i	$-0.0501455\pi$
$7$	15.3854	+	15.3854i	0.830731	+	0.830731i	−0.156886	+	0.987617i	$0.550145\pi$
$8$	20.6285	−	9.29869i	0.911659	−	0.410948i
$9$			9.00000i			0.333333i
$10$	−22.4612	−	22.2597i	−0.710287	−	0.703912i
$11$	−63.8411			−1.74989			−0.874946	−	0.484221i	$-0.839103\pi$
$11$	−63.8411			−1.74989			−0.874946	+	0.484221i	$0.839103\pi$
$12$	−0.492677	−	23.9949i	−0.0118520	−	0.577229i
$13$	10.5363	−	10.5363i	0.224787	−	0.224787i	−0.585724	−	0.810511i	$-0.699190\pi$
$13$	10.5363	−	10.5363i	0.224787	−	0.224787i	0.810511	+	0.585724i	$0.199190\pi$
$14$	−56.6121	+	24.1333i	−1.08073	+	0.460706i
$15$	−31.0612	+	12.6570i	−0.534665	+	0.217868i
$16$	2.62706	+	63.9461i	0.0410478	+	0.999157i
$17$	−58.9296	+	58.9296i	−0.840737	+	0.840737i	−0.988955	−	0.148218i	$-0.952646\pi$
$17$	−58.9296	+	58.9296i	−0.840737	+	0.840737i	0.148218	+	0.988955i	$0.452646\pi$
$18$	−23.6169	−	9.49961i	−0.309253	−	0.124393i
$19$		−	100.850i		−	1.21771i	−0.793280	−	0.608857i	$-0.791628\pi$
$19$		−	100.850i		−	1.21771i	0.793280	−	0.608857i	$-0.208372\pi$
$20$	82.1197	−	35.4452i	0.918126	−	0.396289i
$21$			65.2745i			0.678289i
$22$	67.3850	−	167.525i	0.653024	−	1.62348i
$23$	8.18053	−	8.18053i	0.0741634	−	0.0741634i	−0.669052	−	0.743216i	$-0.733300\pi$
$23$	8.18053	−	8.18053i	0.0741634	−	0.0741634i	0.743216	+	0.669052i	$0.233300\pi$
$24$	63.4851	+	24.0341i	0.539952	+	0.204414i
$25$	−87.3648	−	89.4002i	−0.698918	−	0.715201i
$26$	16.5270	+	38.7694i	0.124662	+	0.292434i
$27$	−19.0919	+	19.0919i	−0.136083	+	0.136083i
$28$	−3.57325	−	174.029i	−0.0241172	−	1.17458i
$29$	16.1242			0.103248			0.0516241	−	0.998667i	$-0.483560\pi$
$29$	16.1242			0.103248			0.0516241	+	0.998667i	$0.483560\pi$
$30$	−0.427641	−	94.8674i	−0.00260254	−	0.577344i
$31$			317.519i			1.83962i	0.392366	+	0.919809i	$0.371657\pi$
$31$			317.519i			1.83962i	−0.392366	+	0.919809i	$0.628343\pi$
$32$	−170.574	−	60.6022i	−0.942295	−	0.334783i
$33$	−135.427	−	135.427i	−0.714390	−	0.714390i
$34$	−92.4362	−	216.838i	−0.466255	−	1.09375i
$35$	−225.279	+	91.7976i	−1.08797	+	0.443332i
$36$	49.8558	−	51.9461i	0.230814	−	0.240491i
$37$	−144.623	−	144.623i	−0.642589	−	0.642589i	0.308602	−	0.951191i	$-0.400139\pi$
$37$	−144.623	−	144.623i	−0.642589	−	0.642589i	−0.951191	+	0.308602i	$0.900139\pi$
$38$	264.640	+	106.448i	1.12974	+	0.454426i
$39$	44.7016			0.183538
$40$	6.33336	+	252.903i	0.0250348	+	0.999687i
$41$	276.422			1.05292			0.526462	−	0.850199i	$-0.323518\pi$
$41$	276.422			1.05292			0.526462	+	0.850199i	$0.323518\pi$
$42$	−171.287	−	68.8981i	−0.629289	−	0.253124i
$43$	237.148	+	237.148i	0.841040	+	0.841040i	0.988994	−	0.147955i	$-0.0472689\pi$
$43$	237.148	+	237.148i	0.841040	+	0.841040i	−0.147955	+	0.988994i	$0.547269\pi$
$44$	368.477	+	353.650i	1.26250	+	1.21170i
$45$	−92.7404	−	39.0413i	−0.307220	−	0.129332i
$46$	12.8319	+	30.1012i	0.0411295	+	0.0964821i
$47$	369.925	+	369.925i	1.14807	+	1.14807i	0.986933	+	0.161133i	$0.0515148\pi$
$47$	369.925	+	369.925i	1.14807	+	1.14807i	0.161133	+	0.986933i	$0.448485\pi$
$48$	−130.077	+	141.223i	−0.391147	+	0.424662i
$49$			130.418i			0.380228i
$50$	326.810	−	134.891i	0.924357	−	0.381529i
$51$	−250.017			−0.686459
$52$	−119.179	+	2.44705i	−0.317830	+	0.00652586i
$53$	−106.168	+	106.168i	−0.275157	+	0.275157i	−0.831172	−	0.556015i	$-0.812330\pi$
$53$	−106.168	+	106.168i	−0.275157	+	0.275157i	0.556015	+	0.831172i	$0.312330\pi$
$54$	−29.9473	−	70.2507i	−0.0754686	−	0.177035i
$55$	276.938	−	657.849i	0.678951	−	1.61281i
$56$	460.440	+	174.313i	1.09873	+	0.415956i
$57$	213.935	−	213.935i	0.497129	−	0.497129i
$58$	−17.0193	+	42.3116i	−0.0385302	+	0.0957894i
$59$			611.812i			1.35002i	0.737809	+	0.675009i	$0.235860\pi$
$59$			611.812i			1.35002i	−0.737809	+	0.675009i	$0.764140\pi$
$60$	249.393	+	99.0115i	0.536608	+	0.213039i
$61$			168.615i			0.353916i	0.984218	+	0.176958i	$0.0566257\pi$
$61$			168.615i			0.353916i	−0.984218	+	0.176958i	$0.943374\pi$
$62$	−833.202	−	335.146i	−1.70672	−	0.686509i
$63$	−138.468	+	138.468i	−0.276910	+	0.276910i
$64$	339.069	−	383.636i	0.662244	−	0.749289i
$65$	62.8652	+	154.276i	0.119961	+	0.294394i
$66$	498.320	−	212.429i	0.929378	−	0.396186i
$67$	−86.9358	+	86.9358i	−0.158521	+	0.158521i	−0.781911	−	0.623390i	$-0.785755\pi$
$67$	−86.9358	+	86.9358i	−0.158521	+	0.158521i	0.623390	+	0.781911i	$0.285755\pi$
$68$	666.572	−	13.6864i	1.18873	−	0.0244077i
$69$	34.7071			0.0605542
$70$	−3.10156	−	688.047i	−0.00529583	−	1.17482i
$71$			633.856i			1.05950i	0.848152	+	0.529752i	$0.177715\pi$
$71$			633.856i			1.05950i	−0.848152	+	0.529752i	$0.822285\pi$
$72$	83.6882	+	185.656i	0.136983	+	0.303886i
$73$	144.979	+	144.979i	0.232445	+	0.232445i	0.813712	−	0.581268i	$-0.197443\pi$
$73$	144.979	+	144.979i	0.232445	+	0.232445i	−0.581268	+	0.813712i	$0.697443\pi$
$74$	532.155	−	226.853i	0.835969	−	0.356366i
$75$	4.31772	−	374.975i	0.00664756	−	0.577312i
$76$	−558.662	+	582.084i	−0.843196	+	0.878548i
$77$	−982.217	−	982.217i	−1.45369	−	1.45369i
$78$	−47.1831	+	117.301i	−0.0684927	+	0.170279i
$79$	974.024			1.38717			0.693584	−	0.720376i	$-0.256031\pi$
$79$	974.024			1.38717			0.693584	+	0.720376i	$0.256031\pi$
$80$	−670.327	−	250.323i	−0.936811	−	0.349837i
$81$	−81.0000			−0.111111
$82$	−291.767	+	725.359i	−0.392930	+	0.976859i
$83$	−149.672	−	149.672i	−0.197935	−	0.197935i	0.601179	−	0.799114i	$-0.294698\pi$
$83$	−149.672	−	149.672i	−0.197935	−	0.197935i	−0.799114	+	0.601179i	$0.794698\pi$
$84$	361.591	−	376.751i	0.469676	−	0.489367i
$85$	−351.607	−	862.872i	−0.448672	−	1.10108i
$86$	−872.612	+	371.987i	−1.09414	+	0.466423i
$87$	34.2047	+	34.2047i	0.0421509	+	0.0421509i
$88$	−1316.94	+	593.638i	−1.59530	+	0.719114i
$89$		−	770.639i		−	0.917838i	−0.888478	−	0.458919i	$-0.848237\pi$
$89$		−	770.639i		−	0.917838i	0.888478	−	0.458919i	$-0.151763\pi$
$90$	200.337	−	202.151i	0.234637	−	0.236762i
$91$	324.208			0.373475
$92$	−92.5327	+	1.89993i	−0.104861	+	0.00215306i
$93$	−673.560	+	673.560i	−0.751021	+	0.751021i
$94$	−1361.18	+	580.259i	−1.49356	+	0.636693i
$95$	1039.21	+	437.479i	1.12232	+	0.472468i
$96$	−233.285	−	490.398i	−0.248016	−	0.521365i
$97$	117.542	−	117.542i	0.123037	−	0.123037i	−0.642907	−	0.765944i	$-0.722272\pi$
$97$	117.542	−	117.542i	0.123037	−	0.123037i	0.765944	+	0.642907i	$0.222272\pi$
$98$	−342.230	−	137.658i	−0.352760	−	0.141893i
$99$		−	574.569i		−	0.583297i
$100$	9.01538	+	999.959i	0.00901538	+	0.999959i
$101$		−	546.624i		−	0.538526i	−0.963067	−	0.269263i	$-0.913220\pi$
$101$		−	546.624i		−	0.538526i	0.963067	−	0.269263i	$-0.0867801\pi$
$102$	263.896	−	656.070i	0.256173	−	0.636869i
$103$	80.9163	−	80.9163i	0.0774070	−	0.0774070i	−0.667343	−	0.744750i	$-0.732569\pi$
$103$	80.9163	−	80.9163i	0.0774070	−	0.0774070i	0.744750	+	0.667343i	$0.232569\pi$
$104$	119.374	−	315.321i	0.112553	−	0.297305i
$105$	−672.620	−	283.156i	−0.625153	−	0.263173i
$106$	−166.534	−	390.657i	−0.152596	−	0.357962i
$107$	627.123	−	627.123i	0.566601	−	0.566601i	−0.364574	−	0.931174i	$-0.618785\pi$
$107$	627.123	−	627.123i	0.566601	−	0.566601i	0.931174	+	0.364574i	$0.118785\pi$
$108$	215.954	−	4.43410i	0.192410	−	0.00395066i
$109$	−474.223			−0.416719			−0.208359	−	0.978052i	$-0.566812\pi$
$109$	−474.223			−0.416719			−0.208359	+	0.978052i	$0.566812\pi$
$110$	1433.95	+	1421.08i	1.24292	+	1.23177i
$111$		−	613.581i		−	0.524672i
$112$	−943.414	+	1024.25i	−0.795931	+	0.864130i
$113$	−567.206	−	567.206i	−0.472197	−	0.472197i	0.430428	−	0.902625i	$-0.358363\pi$
$113$	−567.206	−	567.206i	−0.472197	−	0.472197i	−0.902625	+	0.430428i	$0.858363\pi$
$114$	335.575	+	787.197i	0.275698	+	0.646735i
$115$	48.8096	+	119.783i	0.0395784	+	0.0971287i
$116$	−93.0657	−	89.3209i	−0.0744908	−	0.0714934i
$117$	94.8264	+	94.8264i	0.0749291	+	0.0749291i
$118$	−1605.45	−	645.775i	−1.25249	−	0.503800i
$119$	−1813.31			−1.39685
$120$	−523.053	+	549.923i	−0.397900	+	0.418341i
$121$	2744.68			2.06212
$122$	−442.461	−	177.975i	−0.328349	−	0.132074i
$123$	586.380	+	586.380i	0.429854	+	0.429854i
$124$	1758.91	−	1832.65i	1.27383	−	1.32724i
$125$	1300.20	−	512.438i	0.930351	−	0.366671i
$126$	−217.199	−	509.509i	−0.153569	−	0.360243i
$127$	−1056.50	−	1056.50i	−0.738179	−	0.738179i	0.234046	−	0.972225i	$-0.424803\pi$
$127$	−1056.50	−	1056.50i	−0.738179	−	0.738179i	−0.972225	+	0.234046i	$0.924803\pi$
$128$	648.807	+	1294.68i	0.448023	+	0.894022i
$129$			1006.13i			0.686706i
$130$	−471.191	+	2.12403i	−0.317894	+	0.00143300i
$131$	−152.230			−0.101529			−0.0507647	−	0.998711i	$-0.516166\pi$
$131$	−152.230			−0.101529			−0.0507647	+	0.998711i	$0.516166\pi$
$132$	31.4530	+	1531.86i	0.0207397	+	1.01009i
$133$	1551.61	−	1551.61i	1.01159	−	1.01159i
$134$	−136.366	−	319.890i	−0.0879123	−	0.206226i
$135$	−113.913	−	279.551i	−0.0726226	−	0.178222i
$136$	−667.661	+	1763.60i	−0.420966	+	1.11196i
$137$	216.088	−	216.088i	0.134756	−	0.134756i	−0.636511	−	0.771267i	$-0.719623\pi$
$137$	216.088	−	216.088i	0.134756	−	0.134756i	0.771267	+	0.636511i	$0.219623\pi$
$138$	−36.6337	+	91.0748i	−0.0225976	+	0.0561797i
$139$			1918.35i			1.17059i	0.810819	+	0.585297i	$0.199022\pi$
$139$			1918.35i			1.17059i	−0.810819	+	0.585297i	$0.800978\pi$
$140$	1808.78	+	718.103i	1.09193	+	0.433506i
$141$			1569.46i			0.937392i
$142$	−1663.30	−	669.042i	−0.982965	−	0.395386i
$143$	−672.646	+	672.646i	−0.393353	+	0.393353i
$144$	−575.515	+	23.6435i	−0.333052	+	0.0136826i
$145$	−69.9458	+	166.152i	−0.0400599	+	0.0951598i
$146$	−533.465	+	227.411i	−0.302396	+	0.128909i
$147$	−276.659	+	276.659i	−0.155227	+	0.155227i
$148$	33.5886	+	1635.87i	0.0186552	+	0.908567i
$149$	−3524.27			−1.93772			−0.968858	−	0.247617i	$-0.920353\pi$
$149$	−3524.27			−1.93772			−0.968858	+	0.247617i	$0.920353\pi$
$150$	979.414	+	407.121i	0.533126	+	0.221609i
$151$		−	973.526i		−	0.524665i	−0.964978	−	0.262332i	$-0.915508\pi$
$151$		−	973.526i		−	0.524665i	0.964978	−	0.262332i	$-0.0844917\pi$
$152$	−937.772	−	2080.38i	−0.500417	−	1.11014i
$153$	−530.367	−	530.367i	−0.280246	−	0.280246i
$154$	3614.18	−	1540.69i	1.89116	−	0.806185i
$155$	−3271.87	−	1377.38i	−1.69550	−	0.713765i
$156$	−258.008	−	247.626i	−0.132418	−	0.127089i
$157$	2290.78	+	2290.78i	1.16448	+	1.16448i	0.983483	+	0.181001i	$0.0579337\pi$
$157$	2290.78	+	2290.78i	1.16448	+	1.16448i	0.181001	+	0.983483i	$0.442066\pi$
$158$	−1028.09	+	2555.93i	−0.517663	+	1.28696i
$159$	−450.433			−0.224664
$160$	1364.41	−	1494.79i	0.674163	−	0.738582i
$161$	251.721			0.123220
$162$	85.4965	−	212.552i	0.0414644	−	0.103084i
$163$	1044.91	+	1044.91i	0.502110	+	0.502110i	0.912093	−	0.409983i	$-0.134465\pi$
$163$	1044.91	+	1044.91i	0.502110	+	0.502110i	−0.409983	+	0.912093i	$0.634465\pi$
$164$	−1595.45	−	1531.25i	−0.759656	−	0.729089i
$165$	1982.98	−	808.035i	0.935606	−	0.381245i
$166$	550.733	−	234.773i	0.257501	−	0.109771i
$167$	2005.84	+	2005.84i	0.929441	+	0.929441i	0.997670	−	0.0682286i	$-0.0217347\pi$
$167$	2005.84	+	2005.84i	0.929441	+	0.929441i	−0.0682286	+	0.997670i	$0.521735\pi$
$168$	606.968	+	1346.51i	0.278741	+	0.618368i
$169$			1974.97i			0.898941i
$170$	2635.39	−	11.8797i	1.18897	−	0.00535961i
$171$	907.649			0.405904
$172$	−55.0777	−	2682.46i	−0.0244165	−	1.18916i
$173$	2466.13	−	2466.13i	1.08379	−	1.08379i	0.0876398	−	0.996152i	$-0.472068\pi$
$173$	2466.13	−	2466.13i	1.08379	−	1.08379i	0.996152	−	0.0876398i	$-0.0279324\pi$
$174$	−125.860	+	53.6530i	−0.0548357	+	0.0233760i
$175$	31.3152	−	2719.59i	0.0135269	−	1.17475i
$176$	−167.714	−	4082.38i	−0.0718292	−	1.74842i
$177$	−1297.85	+	1297.85i	−0.551143	+	0.551143i
$178$	2022.23	+	813.419i	0.851532	+	0.342519i
$179$		−	998.804i		−	0.417062i	−0.978016	−	0.208531i	$-0.933132\pi$
$179$		−	998.804i		−	0.417062i	0.978016	−	0.208531i	$-0.0668682\pi$
$180$	319.007	+	739.077i	0.132096	+	0.306042i
$181$			2834.05i			1.16383i	0.813250	+	0.581915i	$0.197696\pi$
$181$			2834.05i			1.16383i	−0.813250	+	0.581915i	$0.802304\pi$
$182$	−342.206	+	850.755i	−0.139374	+	0.346495i
$183$	−357.686	+	357.686i	−0.144486	+	0.144486i
$184$	92.6838	−	244.820i	0.0371344	−	0.0980891i
$185$	2117.62	−	862.899i	0.841571	−	0.342927i
$186$	−1056.54	−	2478.44i	−0.416501	−	0.977033i
$187$	3762.13	−	3762.13i	1.47120	−	1.47120i
$188$	−85.9152	−	4184.34i	−0.0333298	−	1.62327i
$189$	−587.471			−0.226096
$190$	−2244.88	+	2265.21i	−0.857163	+	0.864926i
$191$			1571.19i			0.595220i	0.954688	+	0.297610i	$0.0961895\pi$
$191$			1571.19i			0.595220i	−0.954688	+	0.297610i	$0.903810\pi$
$192$	1533.09	−	94.5409i	0.576256	−	0.0355359i
$193$	−3036.38	−	3036.38i	−1.13245	−	1.13245i	−0.989768	−	0.142683i	$-0.954427\pi$
$193$	−3036.38	−	3036.38i	−1.13245	−	1.13245i	−0.142683	−	0.989768i	$-0.545573\pi$
$194$	184.375	+	432.510i	0.0682339	+	0.160064i
$195$	−193.912	+	460.627i	−0.0712120	+	0.169160i
$196$	722.456	−	752.746i	0.263286	−	0.274324i
$197$	1002.52	+	1002.52i	0.362570	+	0.362570i	0.864758	−	0.502188i	$-0.167471\pi$
$197$	1002.52	+	1002.52i	0.362570	+	0.362570i	−0.502188	+	0.864758i	$0.667471\pi$
$198$	1507.73	+	606.465i	0.541159	+	0.217675i
$199$	−1065.88			−0.379691			−0.189845	−	0.981814i	$-0.560799\pi$
$199$	−1065.88			−0.379691			−0.189845	+	0.981814i	$0.560799\pi$
$200$	−2633.51	−	1031.81i	−0.931086	−	0.364801i
$201$	−368.837			−0.129432
$202$	1434.40	+	576.969i	0.499623	+	0.200967i
$203$	248.077	+	248.077i	0.0857715	+	0.0857715i
$204$	1443.05	+	1384.98i	0.495262	+	0.475333i
$205$	−1199.10	+	2848.39i	−0.408530	+	0.970439i
$206$	126.924	+	297.741i	0.0429283	+	0.100702i
$207$	73.6248	+	73.6248i	0.0247211	+	0.0247211i
$208$	701.432	+	646.073i	0.233825	+	0.215371i
$209$			6438.36i			2.13087i
$210$	1452.99	−	1466.15i	0.477456	−	0.481780i
$211$	203.814			0.0664982			0.0332491	−	0.999447i	$-0.489415\pi$
$211$	203.814			0.0664982			0.0332491	+	0.999447i	$0.489415\pi$
$212$	1200.90	−	24.6576i	0.389048	−	0.00798815i
$213$	−1344.61	+	1344.61i	−0.432541	+	0.432541i
$214$	983.697	+	2307.57i	0.314225	+	0.737113i
$215$	−3472.42	+	1414.96i	−1.10147	+	0.448834i
$216$	−216.307	+	571.366i	−0.0681381	+	0.179984i
$217$	−4885.15	+	4885.15i	−1.52823	+	1.52823i
$218$	500.549	−	1244.41i	0.155511	−	0.386615i
$219$			615.092i			0.189790i
$220$	−5242.61	+	2262.86i	−1.60662	+	0.693463i
$221$			1241.80i			0.377974i
$222$	1610.10	+	647.643i	0.486769	+	0.195797i
$223$	135.310	−	135.310i	0.0406323	−	0.0406323i	−0.686499	−	0.727131i	$-0.740853\pi$
$223$	135.310	−	135.310i	0.0406323	−	0.0406323i	0.727131	+	0.686499i	$0.240853\pi$
$224$	−1691.95	−	3556.72i	−0.504679	−	1.06091i
$225$	804.602	−	786.283i	0.238400	−	0.232973i
$226$	2087.10	−	889.712i	0.614300	−	0.261871i
$227$	722.348	−	722.348i	0.211207	−	0.211207i	−0.593573	−	0.804780i	$-0.702283\pi$
$227$	722.348	−	722.348i	0.211207	−	0.211207i	0.804780	+	0.593573i	$0.202283\pi$
$228$	−2419.89	+	49.6865i	−0.702899	+	0.0144323i
$229$	2939.92			0.848363			0.424181	−	0.905577i	$-0.360562\pi$
$229$	2939.92			0.848363			0.424181	+	0.905577i	$0.360562\pi$
$230$	−365.841	+	1.64913i	−0.104882	+	0.000472784i
$231$		−	4167.19i		−	1.18693i
$232$	332.619	−	149.934i	0.0941271	−	0.0424296i
$233$	−3607.24	−	3607.24i	−1.01424	−	1.01424i	−0.999897	−	0.0143435i	$-0.995434\pi$
$233$	−3607.24	−	3607.24i	−1.01424	−	1.01424i	−0.0143435	−	0.999897i	$-0.504566\pi$
$234$	−348.924	+	148.743i	−0.0974782	+	0.0415541i
$235$	−5416.59	+	2207.18i	−1.50357	+	0.612683i
$236$	3389.15	−	3531.25i	0.934810	−	0.974002i
$237$	2066.22	+	2066.22i	0.566309	+	0.566309i
$238$	1913.97	−	4758.29i	0.521278	−	1.29594i
$239$	−1019.91			−0.276035			−0.138018	−	0.990430i	$-0.544073\pi$
$239$	−1019.91			−0.276035			−0.138018	+	0.990430i	$0.544073\pi$
$240$	−890.964	−	1952.99i	−0.239631	−	0.525272i
$241$	−1230.05			−0.328774			−0.164387	−	0.986396i	$-0.552565\pi$
$241$	−1230.05			−0.328774			−0.164387	+	0.986396i	$0.552565\pi$
$242$	−2897.04	+	7202.31i	−0.769541	+	1.91315i
$243$	−171.827	−	171.827i	−0.0453609	−	0.0453609i
$244$	934.047	−	973.208i	0.245067	−	0.255341i
$245$	−1343.89	−	565.744i	−0.350441	−	0.147527i
$246$	−2157.65	+	919.787i	−0.559214	+	0.238388i
$247$	−1062.58	−	1062.58i	−0.273726	−	0.273726i
$248$	2952.51	+	6549.95i	0.755987	+	1.67710i
$249$		−	635.003i		−	0.161613i
$250$	−27.6951	+	3952.75i	−0.00700636	+	0.999975i
$251$	−6991.54			−1.75818			−0.879088	−	0.476660i	$-0.841847\pi$
$251$	−6991.54			−1.75818			−0.879088	+	0.476660i	$0.841847\pi$
$252$	1566.26	−	32.1593i	0.391528	−	0.00803906i
$253$	−522.254	+	522.254i	−0.129778	+	0.129778i
$254$	3887.49	−	1657.20i	0.960326	−	0.409379i
$255$	1084.56	−	2576.30i	0.266343	−	0.632683i
$256$	−4082.20	+	335.980i	−0.996630	+	0.0820264i
$257$	4689.19	−	4689.19i	1.13815	−	1.13815i	0.149363	−	0.988782i	$-0.452278\pi$
$257$	4689.19	−	4689.19i	1.13815	−	1.13815i	0.988782	−	0.149363i	$-0.0477223\pi$
$258$	−2640.19	−	1061.99i	−0.637098	−	0.256265i
$259$		−	4450.14i		−	1.06764i
$260$	491.775	−	1238.69i	0.117302	−	0.295464i
$261$			145.118i			0.0344161i
$262$	160.680	−	399.465i	0.0378888	−	0.0941949i
$263$	907.231	−	907.231i	0.212708	−	0.212708i	−0.592709	−	0.805417i	$-0.701941\pi$
$263$	907.231	−	907.231i	0.212708	−	0.212708i	0.805417	+	0.592709i	$0.201941\pi$
$264$	−4052.96	−	1534.36i	−0.944857	−	0.357703i
$265$	−633.458	−	1554.56i	−0.146842	−	0.360361i
$266$	2433.84	+	5709.33i	0.561008	+	1.31602i
$267$	1634.77	−	1634.77i	0.374706	−	0.374706i
$268$	983.359	−	20.1909i	0.224135	−	0.00460206i
$269$	−2.48444			−0.000563118			−0.000281559	−	1.00000i	$-0.500090\pi$
$269$	−2.48444			−0.000563118			−0.000281559		1.00000i	$0.500090\pi$
$270$	853.806	−	3.84877i	0.192448	−	0.000867514i
$271$			6588.53i			1.47684i	0.674339	+	0.738422i	$0.264429\pi$
$271$			6588.53i			1.47684i	−0.674339	+	0.738422i	$0.735571\pi$
$272$	−3923.13	−	3613.51i	−0.874539	−	0.805518i
$273$	687.750	+	687.750i	0.152471	+	0.152471i
$274$	338.952	+	795.118i	0.0747330	+	0.175310i
$275$	5577.46	+	5707.40i	1.22303	+	1.25152i
$276$	−200.322	−	192.261i	−0.0436882	−	0.0419303i
$277$	−2745.33	−	2745.33i	−0.595490	−	0.595490i	0.343619	−	0.939109i	$-0.388347\pi$
$277$	−2745.33	−	2745.33i	−0.595490	−	0.595490i	−0.939109	+	0.343619i	$0.888347\pi$
$278$	−5033.95	−	2024.84i	−1.08603	−	0.436842i
$279$	−2857.68			−0.613206
$280$	−3793.56	+	3988.44i	−0.809673	+	0.851268i
$281$	2338.73			0.496503			0.248251	−	0.968696i	$-0.420144\pi$
$281$	2338.73			0.496503			0.248251	+	0.968696i	$0.420144\pi$
$282$	−4118.41	−	1656.58i	−0.869674	−	0.349816i
$283$	−2027.74	−	2027.74i	−0.425924	−	0.425924i	0.461313	−	0.887237i	$-0.347379\pi$
$283$	−2027.74	−	2027.74i	−0.425924	−	0.425924i	−0.887237	+	0.461313i	$0.847379\pi$
$284$	3511.27	−	3658.48i	0.733645	−	0.764404i
$285$	1276.46	+	3132.52i	0.265301	+	0.651069i
$286$	−1055.10	−	2475.08i	−0.218145	−	0.511728i
$287$	4252.85	+	4252.85i	0.874696	+	0.874696i
$288$	545.420	−	1535.16i	0.111594	−	0.314098i
$289$		−	2032.40i		−	0.413678i
$290$	−362.171	−	358.920i	−0.0733359	−	0.0726777i
$291$	498.690			0.100460
$292$	−33.6713	−	1639.90i	−0.00674816	−	0.328657i
$293$	5965.14	−	5965.14i	1.18938	−	1.18938i	0.212137	−	0.977240i	$-0.431958\pi$
$293$	5965.14	−	5965.14i	1.18938	−	1.18938i	0.977240	−	0.212137i	$-0.0680423\pi$
$294$	−433.963	−	1018.00i	−0.0860859	−	0.201941i
$295$	−6304.40	−	2653.99i	−1.24426	−	0.523802i
$296$	−4328.14	−	1638.54i	−0.849893	−	0.321751i
$297$	1218.85	−	1218.85i	0.238130	−	0.238130i
$298$	3719.91	−	9248.04i	0.723117	−	1.79773i
$299$		−	172.385i		−	0.0333420i
$300$	−2102.11	+	2140.36i	−0.404551	+	0.411912i
$301$			7297.21i			1.39736i
$302$	2554.63	+	1027.57i	0.486763	+	0.195794i
$303$	1159.57	−	1159.57i	0.219852	−	0.219852i
$304$	6448.95	−	264.939i	1.21669	−	0.0499844i
$305$	−1737.49	−	731.438i	−0.326191	−	0.137318i
$306$	1951.54	−	831.926i	0.364583	−	0.155418i
$307$	−927.744	+	927.744i	−0.172473	+	0.172473i	−0.788065	−	0.615592i	$-0.788917\pi$
$307$	−927.744	+	927.744i	−0.172473	+	0.172473i	0.615592	+	0.788065i	$0.288917\pi$
$308$	228.120	+	11110.2i	0.0422025	+	2.05539i
$309$	343.299			0.0632026
$310$	7067.87	−	7131.88i	1.29493	−	1.30666i
$311$		−	5429.09i		−	0.989888i	−0.868925	−	0.494944i	$-0.835189\pi$
$311$		−	5429.09i		−	0.989888i	0.868925	−	0.494944i	$-0.164811\pi$
$312$	922.126	−	415.666i	0.167324	−	0.0754246i
$313$	293.120	+	293.120i	0.0529333	+	0.0529333i	0.733078	−	0.680145i	$-0.238083\pi$
$313$	293.120	+	293.120i	0.0529333	+	0.0529333i	−0.680145	+	0.733078i	$0.738083\pi$
$314$	−8429.17	+	3593.28i	−1.51492	+	0.645798i
$315$	−826.178	−	2027.51i	−0.147777	−	0.362658i
$316$	−5621.86	−	5395.64i	−1.00080	−	0.960533i
$317$	2409.14	+	2409.14i	0.426848	+	0.426848i	0.887553	−	0.460705i	$-0.152403\pi$
$317$	2409.14	+	2409.14i	0.426848	+	0.426848i	−0.460705	+	0.887553i	$0.652403\pi$
$318$	475.437	−	1181.98i	0.0838403	−	0.208434i
$319$	−1029.39			−0.180673
$320$	2482.31	+	5158.11i	0.433642	+	0.901085i
$321$	2660.66			0.462628
$322$	−265.694	+	660.540i	−0.0459831	+	0.114318i
$323$	5943.05	+	5943.05i	1.02378	+	1.02378i
$324$	467.515	+	448.703i	0.0801637	+	0.0769380i
$325$	−1862.44	−	21.4454i	−0.317876	−	0.00366024i
$326$	−3844.87	+	1639.04i	−0.653214	+	0.278459i
$327$	−1005.98	−	1005.98i	−0.170125	−	0.170125i
$328$	5702.17	−	2570.36i	0.959907	−	0.432697i
$329$			11382.8i			1.90747i
$330$	27.3011	+	6056.43i	0.00455416	+	1.01029i
$331$	10543.9			1.75089			0.875444	−	0.483320i	$-0.160569\pi$
$331$	10543.9			1.75089			0.875444	+	0.483320i	$0.160569\pi$
$332$	34.7613	+	1692.98i	0.00574630	+	0.279863i
$333$	1301.60	−	1301.60i	0.214196	−	0.214196i
$334$	−7380.72	+	3146.34i	−1.20915	+	0.515449i
$335$	−518.707	−	1272.95i	−0.0845971	−	0.207608i
$336$	−4174.05	+	171.480i	−0.677717	+	0.0278423i
$337$	877.859	−	877.859i	0.141899	−	0.141899i	−0.632589	−	0.774488i	$-0.718008\pi$
$337$	877.859	−	877.859i	0.141899	−	0.141899i	0.774488	+	0.632589i	$0.218008\pi$
$338$	−5182.53	−	2084.61i	−0.834001	−	0.335467i
$339$		−	2406.45i		−	0.385547i
$340$	−2750.51	+	6928.05i	−0.438727	+	1.10508i
$341$		−	20270.8i		−	3.21913i
$342$	−958.035	+	2381.76i	−0.151475	+	0.376581i
$343$	3270.65	−	3270.65i	0.514864	−	0.514864i
$344$	7097.16	+	2686.84i	1.11236	+	0.421118i
$345$	−150.557	+	357.638i	−0.0234948	+	0.0558104i
$346$	3868.33	+	9074.38i	0.601048	+	1.40995i
$347$	3484.99	−	3484.99i	0.539147	−	0.539147i	−0.384131	−	0.923278i	$-0.625499\pi$
$347$	3484.99	−	3484.99i	0.539147	−	0.539147i	0.923278	+	0.384131i	$0.125499\pi$
$348$	−7.94405	−	386.900i	−0.00122369	−	0.0595978i
$349$	−3095.32			−0.474753			−0.237377	−	0.971418i	$-0.576288\pi$
$349$	−3095.32			−0.474753			−0.237377	+	0.971418i	$0.576288\pi$
$350$	7103.42	+	2952.74i	1.08484	+	0.450944i
$351$			402.314i			0.0611793i
$352$	10889.6	+	3868.91i	1.64891	+	0.585834i
$353$	2991.09	+	2991.09i	0.450990	+	0.450990i	0.895683	−	0.444693i	$-0.146687\pi$
$353$	2991.09	+	2991.09i	0.450990	+	0.450990i	−0.444693	+	0.895683i	$0.646687\pi$
$354$	−2035.79	−	4775.58i	−0.305652	−	0.717003i
$355$	−6531.55	−	2749.62i	−0.976504	−	0.411083i
$356$	−4268.98	+	4447.96i	−0.635550	+	0.662196i
$357$	−3846.60	−	3846.60i	−0.570263	−	0.570263i
$358$	2620.96	+	1054.25i	0.386933	+	0.155639i
$359$	4985.22			0.732896			0.366448	−	0.930439i	$-0.380574\pi$
$359$	4985.22			0.732896			0.366448	+	0.930439i	$0.380574\pi$
$360$	−2276.13	+	57.0002i	−0.333229	+	0.00834493i
$361$	−3311.70			−0.482826
$362$	−7436.82	−	2991.37i	−1.07975	−	0.434318i
$363$	5822.35	+	5822.35i	0.841856	+	0.841856i
$364$	−1871.26	−	1795.96i	−0.269453	−	0.258610i
$365$	−2122.83	+	865.023i	−0.304423	+	0.124048i
$366$	−561.061	−	1316.14i	−0.0801287	−	0.187967i
$367$	1058.09	+	1058.09i	0.150496	+	0.150496i	0.778339	−	0.627844i	$-0.216062\pi$
$367$	1058.09	+	1058.09i	0.150496	+	0.150496i	−0.627844	+	0.778339i	$0.716062\pi$
$368$	544.604	+	501.622i	0.0771452	+	0.0710567i
$369$			2487.80i			0.350974i
$370$	29.1547	+	6467.65i	0.00409644	+	0.908749i
$371$	−3266.87			−0.457162
$372$	7618.86	−	156.435i	1.06188	−	0.0218031i
$373$	−933.409	+	933.409i	−0.129571	+	0.129571i	−0.768918	−	0.639347i	$-0.779205\pi$
$373$	−933.409	+	933.409i	−0.129571	+	0.129571i	0.639347	+	0.768918i	$0.279205\pi$
$374$	5901.22	+	13843.2i	0.815896	+	1.91394i
$375$	3845.20	+	1671.11i	0.529507	+	0.230121i
$376$	11070.8	+	4191.17i	1.51844	+	0.574849i
$377$	169.889	−	169.889i	0.0232089	−	0.0232089i
$378$	620.083	−	1541.58i	0.0843746	−	0.209763i
$379$		−	5892.18i		−	0.798577i	−0.916825	−	0.399289i	$-0.869257\pi$
$379$		−	5892.18i		−	0.798577i	0.916825	−	0.399289i	$-0.130743\pi$
$380$	−3574.64	−	8281.76i	−0.482567	−	1.11801i
$381$		−	4482.33i		−	0.602721i
$382$	−4122.95	−	1658.41i	−0.552221	−	0.222124i
$383$	−5520.74	+	5520.74i	−0.736545	+	0.736545i	−0.971908	−	0.235363i	$-0.924372\pi$
$383$	−5520.74	+	5520.74i	−0.736545	+	0.736545i	0.235363	+	0.971908i	$0.424372\pi$
$384$	−1370.11	+	4122.76i	−0.182078	+	0.547888i
$385$	14382.0	−	5860.46i	1.90383	−	0.775783i
$386$	11172.7	−	4762.82i	1.47325	−	0.628034i
$387$	−2134.33	+	2134.33i	−0.280347	+	0.280347i
$388$	−1329.56	+	27.2993i	−0.173964	+	0.00357193i
$389$	−6178.13			−0.805254			−0.402627	−	0.915364i	$-0.631903\pi$
$389$	−6178.13			−0.805254			−0.402627	+	0.915364i	$0.631903\pi$
$390$	−1004.05	−	995.042i	−0.130365	−	0.129195i
$391$			964.152i			0.124704i
$392$	1212.72	+	2690.33i	0.156254	+	0.346638i
$393$	−322.928	−	322.928i	−0.0414492	−	0.0414492i
$394$	−3688.87	+	1572.53i	−0.471682	+	0.201074i
$395$	−4225.24	+	10036.8i	−0.538215	+	1.27850i
$396$	−3182.85	+	3316.29i	−0.403899	+	0.420833i
$397$	−3809.27	−	3809.27i	−0.481566	−	0.481566i	0.424065	−	0.905632i	$-0.360603\pi$
$397$	−3809.27	−	3809.27i	−0.481566	−	0.481566i	−0.905632	+	0.424065i	$0.860603\pi$
$398$	1125.05	−	2796.98i	0.141693	−	0.352262i
$399$	6582.93			0.825962
$400$	5487.28	−	5821.49i	0.685910	−	0.727687i
$401$	5417.02			0.674596			0.337298	−	0.941398i	$-0.390487\pi$
$401$	5417.02			0.674596			0.337298	+	0.941398i	$0.390487\pi$
$402$	389.312	−	967.866i	0.0483013	−	0.120081i
$403$	3345.47	+	3345.47i	0.413523	+	0.413523i
$404$	−3028.05	+	3155.00i	−0.372898	+	0.388532i
$405$	351.372	−	834.663i	0.0431107	−	0.102407i
$406$	−912.828	+	389.131i	−0.111583	+	0.0475671i
$407$	9232.85	+	9232.85i	1.12446	+	1.12446i
$408$	−5157.48	+	2324.83i	−0.625817	+	0.282099i
$409$		−	8433.67i		−	1.01960i	−0.860292	−	0.509802i	$-0.829719\pi$
$409$		−	8433.67i		−	1.01960i	0.860292	−	0.509802i	$-0.170281\pi$
$410$	−6208.78	−	6153.06i	−0.747878	−	0.741166i
$411$	916.782			0.110028
$412$	−915.271	+	18.7928i	−0.109447	+	0.00224723i
$413$	−9412.94	+	9412.94i	−1.12150	+	1.12150i
$414$	−270.911	+	115.487i	−0.0321607	+	0.0137098i
$415$	2191.55	−	893.024i	0.259227	−	0.105631i
$416$	−2435.73	+	1158.69i	−0.287071	+	0.136561i
$417$	−4069.44	+	4069.44i	−0.477893	+	0.477893i
$418$	−16894.9	−	6795.77i	−1.97693	−	0.795196i
$419$		−	9602.93i		−	1.11965i	−0.828611	−	0.559825i	$-0.810868\pi$
$419$		−	9602.93i		−	1.11965i	0.828611	−	0.559825i	$-0.189132\pi$
$420$	2313.67	+	5360.32i	0.268799	+	0.622755i
$421$		−	4279.81i		−	0.495451i	−0.968830	−	0.247726i	$-0.920317\pi$
$421$		−	4279.81i		−	0.495451i	0.968830	−	0.247726i	$-0.0796831\pi$
$422$	−215.128	+	534.827i	−0.0248158	+	0.0616943i
$423$	−3329.32	+	3329.32i	−0.382689	+	0.382689i
$424$	−1202.86	+	3177.31i	−0.137774	+	0.363924i
$425$	10416.7	+	119.945i	1.18890	+	0.0136898i
$426$	−2109.14	−	4947.64i	−0.239878	−	0.562709i
$427$	−2594.20	+	2594.20i	−0.294009	+	0.294009i
$428$	−7093.59	+	145.650i	−0.801126	+	0.0164491i
$429$	−2853.80			−0.321172
$430$	−47.8071	−	10605.5i	−0.00536154	−	1.18940i
$431$		−	10309.2i		−	1.15215i	−0.817395	−	0.576077i	$-0.804583\pi$
$431$		−	10309.2i		−	1.15215i	0.817395	−	0.576077i	$-0.195417\pi$
$432$	−1271.01	−	1170.70i	−0.141554	−	0.130382i
$433$	−7545.74	−	7545.74i	−0.837472	−	0.837472i	0.151054	−	0.988526i	$-0.451733\pi$
$433$	−7545.74	−	7545.74i	−0.837472	−	0.837472i	−0.988526	+	0.151054i	$0.951733\pi$
$434$	−7662.78	−	17975.4i	−0.847523	−	1.98813i
$435$	−500.839	+	204.084i	−0.0552032	+	0.0224945i
$436$	2737.12	+	2626.98i	0.300652	+	0.288554i
$437$	−825.006	−	825.006i	−0.0903098	−	0.0903098i
$438$	−1614.06	−	649.237i	−0.176080	−	0.0708259i
$439$	6943.86			0.754926			0.377463	−	0.926025i	$-0.376797\pi$
$439$	6943.86			0.754926			0.377463	+	0.926025i	$0.376797\pi$
$440$	−404.328	−	16145.6i	−0.0438082	−	1.74934i
$441$	−1173.76			−0.126743
$442$	−3258.60	−	1310.73i	−0.350669	−	0.141052i
$443$	−1879.14	−	1879.14i	−0.201537	−	0.201537i	0.599121	−	0.800658i	$-0.295517\pi$
$443$	−1879.14	−	1879.14i	−0.201537	−	0.201537i	−0.800658	+	0.599121i	$0.795517\pi$
$444$	−3398.96	+	3541.46i	−0.363305	+	0.378537i
$445$	7941.04	+	3342.97i	0.845935	+	0.356117i
$446$	212.245	+	497.887i	0.0225338	+	0.0528601i
$447$	−7476.11	−	7476.11i	−0.791069	−	0.791069i
$448$	11119.1	−	685.679i	1.17260	−	0.0723109i
$449$		−	9282.58i		−	0.975661i	−0.872938	−	0.487831i	$-0.837788\pi$
$449$		−	9282.58i		−	0.975661i	0.872938	−	0.487831i	$-0.162212\pi$
$450$	1214.02	+	2941.29i	0.127176	+	0.308119i
$451$	−17647.1			−1.84250
$452$	131.734	+	6415.86i	0.0137085	+	0.667647i
$453$	2065.16	−	2065.16i	0.214194	−	0.214194i
$454$	1133.07	+	2657.96i	0.117131	+	0.274767i
$455$	−1406.39	+	3340.80i	−0.144907	+	0.344218i
$456$	2423.84	−	6402.47i	0.248918	−	0.657507i
$457$	−6379.53	+	6379.53i	−0.653002	+	0.653002i	−0.953715	−	0.300713i	$-0.902776\pi$
$457$	−6379.53	+	6379.53i	−0.653002	+	0.653002i	0.300713	+	0.953715i	$0.402776\pi$
$458$	−3103.12	+	7714.63i	−0.316592	+	0.787076i
$459$		−	2250.16i		−	0.228820i
$460$	381.822	−	961.743i	0.0387012	−	0.0974815i
$461$			13094.5i			1.32293i	0.749975	+	0.661466i	$0.230065\pi$
$461$			13094.5i			1.32293i	−0.749975	+	0.661466i	$0.769935\pi$
$462$	10935.1	+	4398.53i	1.10119	+	0.442939i
$463$	−8019.01	+	8019.01i	−0.804913	+	0.804913i	−0.983859	−	0.178946i	$-0.942731\pi$
$463$	−8019.01	+	8019.01i	−0.804913	+	0.804913i	0.178946	+	0.983859i	$0.442731\pi$
$464$	42.3593	+	1031.08i	0.00423811	+	0.103161i
$465$	−4018.84	−	9862.55i	−0.400794	−	0.983580i
$466$	13273.2	−	5658.26i	1.31947	−	0.562477i
$467$	2753.30	−	2753.30i	0.272822	−	0.272822i	−0.557413	−	0.830235i	$-0.688206\pi$
$467$	2753.30	−	2753.30i	0.272822	−	0.272822i	0.830235	+	0.557413i	$0.188206\pi$
$468$	−22.0235	−	1072.61i	−0.00217529	−	0.105943i
$469$	−2675.08			−0.263376
$470$	−74.5739	−	16543.4i	−0.00731880	−	1.62359i
$471$			9718.95i			0.950797i
$472$	5689.05	+	12620.7i	0.554787	+	1.23076i
$473$	−15139.8	−	15139.8i	−1.47173	−	1.47173i
$474$	−7602.87	+	3241.04i	−0.736733	+	0.314063i
$475$	−9016.00	+	8810.73i	−0.870910	+	0.851082i
$476$	10466.0	+	10044.9i	1.00779	+	0.967240i
$477$	−955.512	−	955.512i	−0.0917189	−	0.0917189i
$478$	1076.53	−	2676.34i	0.103011	−	0.256094i
$479$	18089.0			1.72548			0.862741	−	0.505645i	$-0.168746\pi$
$479$	18089.0			1.72548			0.862741	+	0.505645i	$0.168746\pi$
$480$	6065.27	−	276.568i	0.576751	−	0.0262991i
$481$	−3047.56			−0.288892
$482$	1298.34	−	3227.78i	0.122692	−	0.305023i
$483$	533.980	+	533.980i	0.0503042	+	0.0503042i
$484$	−15841.7	−	15204.3i	−1.48776	−	1.42790i
$485$	701.323	+	1721.10i	0.0656607	+	0.161137i
$486$	632.256	−	269.525i	0.0590118	−	0.0251562i
$487$	10416.7	+	10416.7i	0.969255	+	0.969255i	0.999541	−	0.0302860i	$-0.00964180\pi$
$487$	10416.7	+	10416.7i	0.969255	+	0.969255i	−0.0302860	+	0.999541i	$0.509642\pi$
$488$	1567.90	+	3478.26i	0.145441	+	0.322651i
$489$			4433.19i			0.409971i
$490$	2903.06	−	2929.36i	0.267647	−	0.270071i
$491$	−5176.44			−0.475783			−0.237891	−	0.971292i	$-0.576456\pi$
$491$	−5176.44			−0.475783			−0.237891	+	0.971292i	$0.576456\pi$
$492$	−136.187	−	6632.73i	−0.0124792	−	0.607778i
$493$	−950.196	+	950.196i	−0.0868046	+	0.0868046i
$494$	3909.89	−	1666.75i	0.356101	−	0.151803i
$495$	5920.64	+	2492.44i	0.537602	+	0.226317i
$496$	−20304.1	+	834.142i	−1.83807	+	0.0755123i
$497$	−9752.09	+	9752.09i	−0.880163	+	0.880163i
$498$	1666.31	+	670.253i	0.149938	+	0.0603108i
$499$			11060.6i			0.992261i	0.868248	+	0.496131i	$0.165246\pi$
$499$			11060.6i			0.992261i	−0.868248	+	0.496131i	$0.834754\pi$
$500$	−10343.2	−	4244.85i	−0.925122	−	0.379671i
$501$			8510.06i			0.758885i
$502$	7379.66	−	18346.5i	0.656116	−	1.63116i
$503$	−4839.26	+	4839.26i	−0.428970	+	0.428970i	−0.888277	−	0.459307i	$-0.848098\pi$
$503$	−4839.26	+	4839.26i	−0.428970	+	0.428970i	0.459307	+	0.888277i	$0.348098\pi$
$504$	−1568.82	+	4143.96i	−0.138652	+	0.366243i
$505$	5632.68	+	2371.22i	0.496339	+	0.208946i
$506$	−819.200	−	1921.69i	−0.0719721	−	0.168833i
$507$	−4189.55	+	4189.55i	−0.366991	+	0.366991i
$508$	245.371	+	11950.4i	0.0214303	+	1.04372i
$509$	−4766.43			−0.415066			−0.207533	−	0.978228i	$-0.566543\pi$
$509$	−4766.43			−0.415066			−0.207533	+	0.978228i	$0.566543\pi$
$510$	5615.70	+	5565.30i	0.487583	+	0.483207i
$511$			4461.09i			0.386198i
$512$	3427.16	−	11066.7i	0.295822	−	0.955243i
$513$	1925.41	+	1925.41i	0.165710	+	0.165710i
$514$	7355.39	+	17254.4i	0.631192	+	1.48066i
$515$	482.792	+	1184.81i	0.0413094	+	0.101377i
$516$	5573.51	−	5807.19i	0.475504	−	0.495440i
$517$	−23616.4	−	23616.4i	−2.00899	−	2.00899i
$518$	11677.6	+	4697.17i	0.990510	+	0.398421i
$519$	10462.9			0.884912
$520$	2731.38	+	2597.92i	0.230344	+	0.219089i
$521$	−13373.1			−1.12454			−0.562269	−	0.826955i	$-0.690071\pi$
$521$	−13373.1			−1.12454			−0.562269	+	0.826955i	$0.690071\pi$
$522$	−380.805	−	153.174i	−0.0319298	−	0.0128434i
$523$	13421.7	+	13421.7i	1.12216	+	1.12216i	0.991416	+	0.130749i	$0.0417381\pi$
$523$	13421.7	+	13421.7i	1.12216	+	1.12216i	0.130749	+	0.991416i	$0.458262\pi$
$524$	878.637	+	843.281i	0.0732508	+	0.0703033i
$525$	5835.55	−	5702.70i	0.485113	−	0.474069i
$526$	1423.07	+	3338.26i	0.117963	+	0.276720i
$527$	−18711.3	−	18711.3i	−1.54664	−	1.54664i
$528$	8304.27	−	9015.82i	0.684464	−	0.743112i
$529$			12033.2i			0.989000i
$530$	4747.93	−	21.4026i	0.389126	−	0.00175410i
$531$	−5506.30			−0.450006
$532$	−17550.8	+	360.362i	−1.43031	+	0.0293678i
$533$	2912.46	−	2912.46i	0.236684	−	0.236684i
$534$	2564.28	+	6015.33i	0.207804	+	0.487469i
$535$	3741.77	+	9182.59i	0.302375	+	0.742053i
$536$	−984.965	+	2601.74i	−0.0793731	+	0.209661i
$537$	2118.78	−	2118.78i	0.170265	−	0.170265i
$538$	2.62235	−	6.51940i	0.000210144	−	0.000522438i
$539$		−	8326.03i		−	0.665357i
$540$	−891.104	+	2244.53i	−0.0710129	+	0.178869i
$541$			13168.0i			1.04646i	0.852191	+	0.523232i	$0.175274\pi$
$541$			13168.0i			1.04646i	−0.852191	+	0.523232i	$0.824726\pi$
$542$	−17289.0	−	6954.28i	−1.37016	−	0.551129i
$543$	−6011.92	+	6011.92i	−0.475131	+	0.475131i
$544$	13623.1	−	6480.58i	1.07369	−	0.510758i
$545$	2057.15	−	4886.63i	0.161685	−	0.384074i
$546$	−2530.65	+	1078.79i	−0.198355	+	0.0845571i
$547$	2165.35	−	2165.35i	0.169257	−	0.169257i	−0.617396	−	0.786653i	$-0.711812\pi$
$547$	2165.35	−	2165.35i	0.169257	−	0.169257i	0.786653	+	0.617396i	$0.211812\pi$
$548$	−2444.24	+	50.1864i	−0.190534	+	0.00391215i
$549$	−1517.53			−0.117972
$550$	−20863.9	+	8611.57i	−1.61752	+	0.667634i
$551$		−	1626.13i		−	0.125727i
$552$	715.954	−	322.730i	0.0552048	−	0.0248846i
$553$	14985.7	+	14985.7i	1.15236	+	1.15236i
$554$	10101.7	−	4306.28i	0.774696	−	0.330246i
$555$	6322.64	+	2661.67i	0.483570	+	0.203571i
$556$	10626.8	−	11072.3i	0.810568	−	0.844552i
$557$	13694.8	+	13694.8i	1.04177	+	1.04177i	0.999089	+	0.0426844i	$0.0135910\pi$
$557$	13694.8	+	13694.8i	1.04177	+	1.04177i	0.0426844	+	0.999089i	$0.486409\pi$
$558$	3016.31	−	7498.82i	0.228836	−	0.568908i
$559$	4997.30			0.378110
$560$	−6461.92	−	14164.5i	−0.487617	−	1.06886i
$561$	15961.4			1.20123
$562$	−2468.56	+	6137.07i	−0.185285	+	0.460635i
$563$	−7503.70	−	7503.70i	−0.561711	−	0.561711i	0.368082	−	0.929793i	$-0.380014\pi$
$563$	−7503.70	−	7503.70i	−0.561711	−	0.561711i	−0.929793	+	0.368082i	$0.880014\pi$
$564$	8694.07	−	9058.58i	0.649090	−	0.676303i
$565$	8305.27	−	3384.27i	0.618416	−	0.251995i
$566$	7461.29	−	3180.69i	0.554102	−	0.236209i
$567$	−1246.21	−	1246.21i	−0.0923034	−	0.0923034i
$568$	5894.03	+	13075.5i	0.435401	+	0.965906i
$569$		−	658.014i		−	0.0484805i	−0.999706	−	0.0242402i	$-0.992283\pi$
$569$		−	658.014i		−	0.0484805i	0.999706	−	0.0242402i	$-0.00771666\pi$
$570$	−9567.36	+	43.1276i	−0.703040	+	0.00316915i
$571$	10192.9			0.747042			0.373521	−	0.927622i	$-0.378150\pi$
$571$	10192.9			0.747042			0.373521	+	0.927622i	$0.378150\pi$
$572$	7608.52	−	156.222i	0.556168	−	0.0114195i
$573$	−3332.99	+	3332.99i	−0.242998	+	0.242998i
$574$	−15648.8	+	6670.96i	−1.13793	+	0.485088i
$575$	−1446.03	−	16.6506i	−0.104876	−	0.00120761i
$576$	3452.72	+	3051.62i	0.249763	+	0.220748i
$577$	−9711.43	+	9711.43i	−0.700679	+	0.700679i	−0.964556	−	0.263877i	$-0.914999\pi$
$577$	−9711.43	+	9711.43i	−0.700679	+	0.700679i	0.263877	+	0.964556i	$0.414999\pi$
$578$	5333.22	+	2145.22i	0.383794	+	0.154376i
$579$		−	12882.3i		−	0.924643i
$580$	1324.12	−	571.527i	0.0947948	−	0.0409162i
$581$		−	4605.50i		−	0.328861i
$582$	−526.374	+	1308.61i	−0.0374895	+	0.0932023i
$583$	6777.88	−	6777.88i	0.481494	−	0.481494i
$584$	4338.80	+	1642.58i	0.307433	+	0.116388i
$585$	−1388.49	+	565.787i	−0.0981314	+	0.0399870i
$586$	9356.84	+	21949.4i	0.659603	+	1.54731i
$587$	2374.84	−	2374.84i	0.166985	−	0.166985i	−0.618668	−	0.785653i	$-0.712327\pi$
$587$	2374.84	−	2374.84i	0.166985	−	0.166985i	0.785653	+	0.618668i	$0.212327\pi$
$588$	3129.38	−	64.2541i	0.219478	−	0.00450645i
$589$	32021.8			2.24013
$590$	13618.7	−	13742.1i	0.950294	−	0.958901i
$591$			4253.32i			0.296038i
$592$	8868.11	−	9627.97i	0.615671	−	0.668424i
$593$	−2541.11	−	2541.11i	−0.175971	−	0.175971i	0.613626	−	0.789597i	$-0.289710\pi$
$593$	−2541.11	−	2541.11i	−0.175971	−	0.175971i	−0.789597	+	0.613626i	$0.789710\pi$
$594$	1911.87	+	4484.88i	0.132062	+	0.309793i
$595$	7865.99	−	18685.2i	0.541973	−	1.28743i
$596$	20341.4	+	19522.8i	1.39801	+	1.34176i
$597$	−2261.08	−	2261.08i	−0.155008	−	0.155008i
$598$	452.354	+	181.954i	0.0309333	+	0.0124426i
$599$	−23687.1			−1.61574			−0.807872	−	0.589358i	$-0.799381\pi$
$599$	−23687.1			−1.61574			−0.807872	+	0.589358i	$0.799381\pi$
$600$	−3397.71	−	7775.32i	−0.231185	−	0.529043i
$601$	13631.6			0.925200			0.462600	−	0.886567i	$-0.346917\pi$
$601$	13631.6			0.925200			0.462600	+	0.886567i	$0.346917\pi$
$602$	−19148.6	−	7702.29i	−1.29641	−	0.521465i
$603$	−782.422	−	782.422i	−0.0528403	−	0.0528403i
$604$	−5392.88	+	5618.98i	−0.363300	+	0.378532i
$605$	−11906.2	+	28282.5i	−0.800094	+	1.90057i
$606$	1818.88	+	4266.75i	0.121926	+	0.286015i
$607$	−17002.2	−	17002.2i	−1.13690	−	1.13690i	−0.989003	−	0.147898i	$-0.952749\pi$
$607$	−17002.2	−	17002.2i	−1.13690	−	1.13690i	−0.147898	−	0.989003i	$-0.547251\pi$
$608$	−6111.72	+	17202.3i	−0.407670	+	1.14745i
$609$			1052.50i			0.0700321i
$610$	3753.30	−	3787.30i	0.249126	−	0.251382i
$611$	7795.25			0.516141
$612$	123.178	+	5999.15i	0.00813590	+	0.396244i
$613$	6234.50	−	6234.50i	0.410782	−	0.410782i	−0.471229	−	0.882011i	$-0.656190\pi$
$613$	6234.50	−	6234.50i	0.410782	−	0.410782i	0.882011	+	0.471229i	$0.156190\pi$
$614$	−1455.25	−	3413.74i	−0.0956498	−	0.224377i
$615$	−8586.01	+	3498.67i	−0.562962	+	0.229398i
$616$	−29395.0	−	11128.3i	−1.92266	−	0.727878i
$617$	8184.26	−	8184.26i	0.534013	−	0.534013i	−0.387751	−	0.921764i	$-0.626748\pi$
$617$	8184.26	−	8184.26i	0.534013	−	0.534013i	0.921764	+	0.387751i	$0.126748\pi$
$618$	−362.356	+	900.850i	−0.0235859	+	0.0586367i
$619$		−	11854.7i		−	0.769756i	−0.922967	−	0.384878i	$-0.874243\pi$
$619$		−	11854.7i		−	0.769756i	0.922967	−	0.384878i	$-0.125757\pi$
$620$	11254.5	+	26074.6i	0.729021	+	1.68900i
$621$			312.364i			0.0201847i
$622$	14246.5	+	5730.47i	0.918378	+	0.369406i
$623$	11856.6	−	11856.6i	0.762476	−	0.762476i
$624$	117.434	+	2858.49i	0.00753383	+	0.183383i
$625$	−359.786	+	15620.9i	−0.0230263	+	0.999735i
$626$	−1078.57	+	459.784i	−0.0688630	+	0.0293557i
$627$	−13657.8	+	13657.8i	−0.869922	+	0.869922i
$628$	−532.034	−	25911.7i	−0.0338065	−	1.64648i
$629$	17045.1			1.08050
$630$	6192.42	−	27.9141i	0.391606	−	0.00176528i
$631$		−	19761.4i		−	1.24674i	−0.781929	−	0.623368i	$-0.785764\pi$
$631$		−	19761.4i		−	1.24674i	0.781929	−	0.623368i	$-0.214236\pi$
$632$	20092.6	−	9057.14i	1.26462	−	0.570054i
$633$	432.354	+	432.354i	0.0271478	+	0.0271478i
$634$	−8864.71	+	3778.95i	−0.555304	+	0.236721i
$635$	15469.6	−	6303.64i	0.966762	−	0.393941i
$636$	2599.80	+	2495.19i	0.162089	+	0.155567i
$637$	1374.12	+	1374.12i	0.0854704	+	0.0854704i
$638$	1086.53	−	2701.22i	0.0674236	−	0.167621i
$639$	−5704.70			−0.353168
$640$	−16155.5	+	1069.38i	−0.997816	+	0.0660486i
$641$	−20808.1			−1.28217			−0.641085	−	0.767470i	$-0.721515\pi$
$641$	−20808.1			−1.28217			−0.641085	+	0.767470i	$0.721515\pi$
$642$	−2808.36	+	6981.83i	−0.172643	+	0.429207i
$643$	−5067.56	−	5067.56i	−0.310801	−	0.310801i	0.534419	−	0.845220i	$-0.320530\pi$
$643$	−5067.56	−	5067.56i	−0.310801	−	0.310801i	−0.845220	+	0.534419i	$0.820530\pi$
$644$	−1452.88	−	1394.42i	−0.0888998	−	0.0853225i
$645$	−10367.7	−	4364.53i	−0.632910	−	0.266439i
$646$	−21868.1	+	9322.18i	−1.33187	+	0.567765i
$647$	−5785.51	−	5785.51i	−0.351548	−	0.351548i	0.509137	−	0.860685i	$-0.329965\pi$
$647$	−5785.51	−	5785.51i	−0.351548	−	0.351548i	−0.860685	+	0.509137i	$0.829965\pi$
$648$	−1670.91	+	753.194i	−0.101295	+	0.0456609i
$649$		−	39058.7i		−	2.36239i
$650$	2022.11	−	4864.60i	0.122021	−	0.293546i
$651$	−20725.9			−1.24779
$652$	−242.681	−	11819.3i	−0.0145769	−	0.709941i
$653$	5127.05	−	5127.05i	0.307254	−	0.307254i	−0.536589	−	0.843844i	$-0.680288\pi$
$653$	5127.05	−	5127.05i	0.307254	−	0.307254i	0.843844	+	0.536589i	$0.180288\pi$
$654$	3701.61	−	1577.97i	0.221322	−	0.0943476i
$655$	660.361	−	1568.65i	0.0393930	−	0.0935758i
$656$	726.177	+	17676.1i	0.0432202	+	1.05204i
$657$	−1304.81	+	1304.81i	−0.0774815	+	0.0774815i
$658$	−29869.7	−	12014.7i	−1.76967	−	0.711829i
$659$			18726.0i			1.10692i	0.832875	+	0.553461i	$0.186693\pi$
$659$			18726.0i			1.10692i	−0.832875	+	0.553461i	$0.813307\pi$
$660$	−15921.5	−	6321.00i	−0.939005	−	0.372795i
$661$		−	28985.3i		−	1.70559i	−0.522245	−	0.852795i	$-0.674905\pi$
$661$		−	28985.3i		−	1.70559i	0.522245	−	0.852795i	$-0.325095\pi$
$662$	−11129.2	+	27668.2i	−0.653396	+	1.62440i
$663$	−2634.25	+	2634.25i	−0.154307	+	0.154307i
$664$	−4479.25	−	1695.75i	−0.261790	−	0.0991081i
$665$	9257.78	+	22719.3i	0.539852	+	1.32484i
$666$	2041.68	+	4789.39i	0.118789	+	0.278656i
$667$	131.905	−	131.905i	0.00765724	−	0.00765724i
$668$	−465.857	−	22688.7i	−0.0269829	−	1.31415i
$669$	574.070			0.0331761
$670$	3887.85	−	17.5256i	0.224180	−	0.00101055i
$671$		−	10764.5i		−	0.619315i
$672$	3955.78	−	11134.1i	0.227080	−	0.639149i
$673$	9581.45	+	9581.45i	0.548793	+	0.548793i	0.926092	−	0.377299i	$-0.123147\pi$
$673$	9581.45	+	9581.45i	0.548793	+	0.548793i	−0.377299	+	0.926092i	$0.623147\pi$
$674$	1377.00	+	3230.18i	0.0786943	+	0.184602i
$675$	3374.78	+	38.8594i	0.192437	+	0.00221585i
$676$	10940.4	−	11399.1i	0.622465	−	0.648562i
$677$	679.013	+	679.013i	0.0385474	+	0.0385474i	0.726118	−	0.687570i	$-0.241323\pi$
$677$	679.013	+	679.013i	0.0385474	+	0.0385474i	−0.687570	+	0.726118i	$0.741323\pi$
$678$	6314.77	+	2540.04i	0.357695	+	0.143879i
$679$	3616.86			0.204422
$680$	−15276.7	−	14530.3i	−0.861521	−	0.819426i
$681$	3064.66			0.172450
$682$	53192.5	+	21396.1i	2.98658	+	1.20132i
$683$	17868.6	+	17868.6i	1.00106	+	1.00106i	0.999999	+	0.00105979i	$0.000337342\pi$
$683$	17868.6	+	17868.6i	1.00106	+	1.00106i	0.00105979	+	0.999999i	$0.499663\pi$
$684$	−5238.76	−	5027.96i	−0.292849	−	0.281065i
$685$	1289.30	+	3164.04i	0.0719147	+	0.176484i
$686$	5130.29	+	12034.7i	0.285533	+	0.669806i
$687$	6236.50	+	6236.50i	0.346343	+	0.346343i
$688$	−14541.7	+	15787.7i	−0.805808	+	0.874854i
$689$			2237.23i			0.123703i
$690$	−779.564	−	772.567i	−0.0430109	−	0.0426248i
$691$	33391.7			1.83832			0.919160	−	0.393884i	$-0.128869\pi$
$691$	33391.7			1.83832			0.919160	+	0.393884i	$0.128869\pi$
$692$	−27895.1	+	572.758i	−1.53239	+	0.0314639i
$693$	8839.95	−	8839.95i	0.484563	−	0.484563i
$694$	5466.51	+	12823.4i	0.299000	+	0.701398i
$695$	−19767.6	−	8321.67i	−1.07889	−	0.454186i
$696$	1023.65	+	387.532i	0.0557491	+	0.0211054i
$697$	−16289.4	+	16289.4i	−0.885232	+	0.885232i
$698$	3267.15	−	8122.44i	0.177168	−	0.440457i
$699$		−	15304.2i		−	0.828124i
$700$	−15246.0	+	15523.4i	−0.823208	+	0.838187i
$701$			33926.6i			1.82795i	0.405776	+	0.913973i	$0.367001\pi$
$701$			33926.6i			1.82795i	−0.405776	+	0.913973i	$0.632999\pi$
$702$	−1055.71	−	424.648i	−0.0567597	−	0.0228309i
$703$	−14585.2	+	14585.2i	−0.782489	+	0.782489i
$704$	−21646.5	+	24491.7i	−1.15885	+	1.31117i
$705$	−16172.5	−	6808.19i	−0.863958	−	0.363704i
$706$	−11006.0	+	4691.78i	−0.586711	+	0.250110i
$707$	8410.01	−	8410.01i	0.447370	−	0.447370i
$708$	14680.4	−	301.426i	0.779269	−	0.0160004i
$709$	9411.73			0.498540			0.249270	−	0.968434i	$-0.419809\pi$
$709$	9411.73			0.498540			0.249270	+	0.968434i	$0.419809\pi$
$710$	14109.4	−	14237.2i	0.745798	−	0.752552i
$711$			8766.21i			0.462389i
$712$	−7165.93	−	15897.1i	−0.377184	−	0.836755i
$713$	2597.48	+	2597.48i	0.136432	+	0.136432i
$714$	14154.0	−	6033.73i	0.741877	−	0.316256i
$715$	−4013.38	−	9849.16i	−0.209919	−	0.515158i
$716$	−5532.91	+	5764.88i	−0.288791	+	0.300899i
$717$	−2163.55	−	2163.55i	−0.112691	−	0.112691i
$718$	−5261.96	+	13081.7i	−0.273502	+	0.679951i
$719$	−15044.6			−0.780347			−0.390173	−	0.920741i	$-0.627585\pi$
$719$	−15044.6			−0.780347			−0.390173	+	0.920741i	$0.627585\pi$
$720$	2252.91	−	6032.94i	0.116612	−	0.312270i
$721$	2489.85			0.128609
$722$	3495.54	−	8690.23i	0.180181	−	0.447946i
$723$	−2609.34	−	2609.34i	−0.134222	−	0.134222i
$724$	15699.3	−	16357.5i	0.805884	−	0.839672i
$725$	−1408.69	−	1441.51i	−0.0721621	−	0.0738433i
$726$	−21424.0	+	9132.85i	−1.09520	+	0.466876i
$727$	−5281.26	−	5281.26i	−0.269424	−	0.269424i	0.559444	−	0.828868i	$-0.311015\pi$
$727$	−5281.26	−	5281.26i	−0.269424	−	0.269424i	−0.828868	+	0.559444i	$0.811015\pi$
$728$	6687.93	−	3014.71i	0.340482	−	0.153479i
$729$		−	729.000i		−	0.0370370i
$730$	−29.2265	−	6483.57i	−0.00148181	−	0.328723i
$731$	−27950.1			−1.41419
$732$	4045.90	−	83.0726i	0.204291	−	0.00419461i
$733$	−19953.2	+	19953.2i	−1.00544	+	1.00544i	−0.00545598	+	0.999985i	$0.501737\pi$
$733$	−19953.2	+	19953.2i	−1.00544	+	1.00544i	−0.999985	+	0.00545598i	$0.998263\pi$
$734$	−3893.37	+	1659.71i	−0.195786	+	0.0834618i
$735$	−1650.70	−	4050.95i	−0.0828395	−	0.203295i
$736$	−1891.14	+	899.625i	−0.0947125	+	0.0450552i
$737$	5550.07	−	5550.07i	0.277394	−	0.277394i
$738$	−6528.23	−	2625.90i	−0.325620	−	0.130977i
$739$			37369.4i			1.86016i	0.367362	+	0.930078i	$0.380261\pi$
$739$			37369.4i			1.86016i	−0.367362	+	0.930078i	$0.619739\pi$
$740$	−17002.5	−	6750.18i	−0.844629	−	0.335326i
$741$		−	4508.15i		−	0.223497i
$742$	3448.22	−	8572.58i	0.170604	−	0.424136i
$743$	21880.1	−	21880.1i	1.08035	−	1.08035i	0.0838756	−	0.996476i	$-0.473270\pi$
$743$	21880.1	−	21880.1i	1.08035	−	1.08035i	0.996476	−	0.0838756i	$-0.0267299\pi$
$744$	−7631.30	+	20157.8i	−0.376045	+	0.993306i
$745$	15288.0	−	36315.8i	0.751826	−	1.78592i
$746$	−1464.13	−	3434.58i	−0.0718575	−	0.168564i
$747$	1347.04	−	1347.04i	0.0659783	−	0.0659783i
$748$	−42554.7	+	873.756i	−2.08015	+	0.0427108i
$749$	19297.0			0.941386
$750$	−8443.80	+	8326.30i	−0.411099	+	0.405378i
$751$			10373.1i			0.504021i	0.967724	+	0.252011i	$0.0810918\pi$
$751$			10373.1i			0.504021i	−0.967724	+	0.252011i	$0.918908\pi$
$752$	−22683.4	+	24627.1i	−1.09997	+	1.19422i
$753$	−14831.3	−	14831.3i	−0.717772	−	0.717772i
$754$	266.486	+	625.127i	0.0128712	+	0.0301933i
$755$	10031.7	+	4223.08i	0.483563	+	0.203568i
$756$	3390.76	+	3254.32i	0.163122	+	0.156559i
$757$	7563.48	+	7563.48i	0.363143	+	0.363143i	0.864969	−	0.501826i	$-0.167338\pi$
$757$	7563.48	+	7563.48i	0.363143	+	0.363143i	−0.501826	+	0.864969i	$0.667338\pi$
$758$	15461.7	+	6219.27i	0.740887	+	0.298013i
$759$	−2215.74			−0.105963
$760$	25505.2	−	638.718i	1.21733	−	0.0304852i
$761$	6480.44			0.308694			0.154347	−	0.988017i	$-0.450673\pi$
$761$	6480.44			0.308694			0.154347	+	0.988017i	$0.450673\pi$
$762$	11762.1	+	4731.15i	0.559180	+	0.224923i
$763$	−7296.09	−	7296.09i	−0.346181	−	0.346181i
$764$	8703.64	−	9068.55i	0.412155	−	0.429435i
$765$	7765.85	−	3164.46i	0.367026	−	0.149557i
$766$	−8659.75	−	20314.2i	−0.408472	−	0.958199i
$767$	6446.21	+	6446.21i	0.303467	+	0.303467i
$768$	−9372.37	−	7946.93i	−0.440360	−	0.373385i
$769$			12399.8i			0.581467i	0.956804	+	0.290733i	$0.0938993\pi$
$769$			12399.8i			0.581467i	−0.956804	+	0.290733i	$0.906101\pi$
$770$	198.007	+	43925.6i	0.00926712	+	2.05581i
$771$	19894.5			0.929292
$772$	705.199	+	34345.4i	0.0328765	+	1.60119i
$773$	−1875.45	+	1875.45i	−0.0872641	+	0.0872641i	−0.749391	−	0.662127i	$-0.769654\pi$
$773$	−1875.45	+	1875.45i	−0.0872641	+	0.0872641i	0.662127	+	0.749391i	$0.269654\pi$
$774$	−3347.88	−	7853.51i	−0.155474	−	0.364714i
$775$	28386.3	−	27740.0i	1.31570	−	1.28574i
$776$	1331.73	−	3517.71i	0.0616061	−	0.162730i
$777$	9440.17	−	9440.17i	0.435861	−	0.435861i
$778$	6521.09	−	16212.0i	0.300505	−	0.747081i
$779$		−	27877.1i		−	1.28216i
$780$	3670.88	−	1584.46i	0.168511	−	0.0727341i
$781$		−	40466.0i		−	1.85402i
$782$	−2530.03	−	1017.67i	−0.115695	−	0.0465370i
$783$	−307.842	+	307.842i	−0.0140503	+	0.0140503i
$784$	−8339.73	+	342.616i	−0.379907	+	0.0156075i
$785$	−33542.5	+	13668.1i	−1.52507	+	0.621445i
$786$	1188.25	−	506.540i	0.0539229	−	0.0229869i
$787$	16943.9	−	16943.9i	0.767451	−	0.767451i	−0.210206	−	0.977657i	$-0.567414\pi$
$787$	16943.9	−	16943.9i	0.767451	−	0.767451i	0.977657	+	0.210206i	$0.0674135\pi$
$788$	−232.835	−	11339.8i	−0.0105259	−	0.512644i
$789$	3849.05			0.173675
$790$	−21877.8	−	21681.4i	−0.985287	−	0.976444i
$791$		−	17453.3i		−	0.784538i
$792$	−5342.74	−	11852.5i	−0.239705	−	0.531768i
$793$	1776.57	+	1776.57i	0.0795559	+	0.0795559i
$794$	14016.6	−	5975.17i	0.626488	−	0.267067i
$795$	1953.94	−	4641.48i	0.0871689	−	0.207065i
$796$	6152.05	+	5904.50i	0.273937	+	0.262914i
$797$	16446.8	+	16446.8i	0.730963	+	0.730963i	0.970810	−	0.239848i	$-0.0770976\pi$
$797$	16446.8	+	16446.8i	0.730963	+	0.730963i	−0.239848	+	0.970810i	$0.577098\pi$
$798$	−6948.36	+	17274.3i	−0.308232	+	0.766293i
$799$	−43599.1			−1.93044
$800$	9484.29	+	20543.8i	0.419150	+	0.907917i
$801$	6935.75			0.305946
$802$	−5717.73	+	14214.8i	−0.251746	+	0.625863i
$803$	−9255.58	−	9255.58i	−0.406753	−	0.406753i
$804$	2128.85	+	2043.19i	0.0933816	+	0.0896240i
$805$	−1091.95	+	2593.85i	−0.0478088	+	0.113567i
$806$	−12310.0	+	5247.66i	−0.537968	+	0.229331i
$807$	−5.27028	−	5.27028i	−0.000229892	−	0.000229892i
$808$	−5082.89	−	11276.0i	−0.221306	−	0.490952i
$809$			33508.7i			1.45625i	0.685446	+	0.728123i	$0.259607\pi$
$809$			33508.7i			1.45625i	−0.685446	+	0.728123i	$0.740393\pi$
$810$	1819.36	+	1803.03i	0.0789208	+	0.0782125i
$811$	−29364.1			−1.27141			−0.635706	−	0.771931i	$-0.719291\pi$
$811$	−29364.1			−1.27141			−0.635706	+	0.771931i	$0.719291\pi$
$812$	−57.6160	−	2806.08i	−0.00249006	−	0.121274i
$813$	−13976.4	+	13976.4i	−0.602919	+	0.602919i
$814$	−33973.3	+	14482.5i	−1.46285	+	0.623602i
$815$	−15300.0	+	6234.53i	−0.657591	+	0.267958i
$816$	−656.810	−	15987.6i	−0.0281776	−	0.685881i
$817$	23916.3	−	23916.3i	1.02415	−	1.02415i
$818$	22130.8	+	8901.84i	0.945947	+	0.380496i
$819$			2917.87i			0.124492i
$820$	22699.7	−	9797.83i	0.966716	−	0.417262i
$821$			18018.4i			0.765952i	0.923758	+	0.382976i	$0.125101\pi$
$821$			18018.4i			0.765952i	−0.923758	+	0.382976i	$0.874899\pi$
$822$	−967.675	+	2405.73i	−0.0410603	+	0.102079i
$823$	−11109.1	+	11109.1i	−0.470519	+	0.470519i	−0.902083	−	0.431563i	$-0.857962\pi$
$823$	−11109.1	+	11109.1i	−0.470519	+	0.470519i	0.431563	+	0.902083i	$0.357962\pi$
$824$	916.765	−	2421.60i	0.0387585	−	0.102379i
$825$	−275.648	+	23938.8i	−0.0116325	+	1.01023i
$826$	−14765.0	−	34635.9i	−0.621962	−	1.45901i
$827$	−1016.91	+	1016.91i	−0.0427585	+	0.0427585i	−0.728163	−	0.685404i	$-0.759626\pi$
$827$	−1016.91	+	1016.91i	−0.0427585	+	0.0427585i	0.685404	+	0.728163i	$0.259626\pi$
$828$	−17.0994	−	832.794i	−0.000717687	−	0.0349536i
$829$	−27004.5			−1.13137			−0.565684	−	0.824622i	$-0.691388\pi$
$829$	−27004.5			−1.13137			−0.565684	+	0.824622i	$0.691388\pi$
$830$	30.1726	+	6693.45i	0.00126181	+	0.279919i
$831$		−	11647.4i		−	0.486216i
$832$	−469.570	−	7614.61i	−0.0195666	−	0.317294i
$833$	−7685.49	−	7685.49i	−0.319672	−	0.319672i
$834$	−6383.27	−	14974.0i	−0.265029	−	0.621709i
$835$	−29370.4	+	11968.0i	−1.21725	+	0.496010i
$836$	35665.6	−	37160.9i	1.47550	−	1.53736i
$837$	−6062.04	−	6062.04i	−0.250340	−	0.250340i
$838$	25199.0	+	10136.0i	1.03877	+	0.417831i
$839$	15978.0			0.657477			0.328738	−	0.944421i	$-0.393377\pi$
$839$	15978.0			0.657477			0.328738	+	0.944421i	$0.393377\pi$
$840$	−16508.1	+	413.407i	−0.678076	+	0.0169808i
$841$	−24129.0			−0.989340
$842$	11230.6	+	4517.39i	0.459659	+	0.184892i
$843$	4961.21	+	4961.21i	0.202696	+	0.202696i
$844$	−1176.37	−	1129.03i	−0.0479767	−	0.0460461i
$845$	−20351.1	−	8567.29i	−0.828519	−	0.348786i
$846$	−5222.33	−	12250.6i	−0.212231	−	0.497854i
$847$	42227.9	+	42227.9i	1.71307	+	1.71307i
$848$	−7067.94	−	6510.12i	−0.286219	−	0.263630i
$849$		−	8602.97i		−	0.347766i
$850$	−11309.7	+	27207.8i	−0.456376	+	1.09791i
$851$	−2366.18			−0.0953132
$852$	15209.3	−	312.286i	0.611576	−	0.0125572i
$853$	3121.99	−	3121.99i	0.125316	−	0.125316i	−0.641667	−	0.766983i	$-0.721757\pi$
$853$	3121.99	−	3121.99i	0.125316	−	0.125316i	0.766983	+	0.641667i	$0.221757\pi$
$854$	−4069.22	−	9545.63i	−0.163051	−	0.382488i
$855$	−3937.31	+	9352.86i	−0.157489	+	0.374106i
$856$	7105.18	−	18768.0i	0.283703	−	0.749390i
$857$	6471.91	−	6471.91i	0.257965	−	0.257965i	−0.566261	−	0.824226i	$-0.691610\pi$
$857$	6471.91	−	6471.91i	0.257965	−	0.257965i	0.824226	+	0.566261i	$0.191610\pi$
$858$	3012.22	−	7488.64i	0.119855	−	0.297970i
$859$			16807.5i			0.667593i	0.942645	+	0.333797i	$0.108330\pi$
$859$			16807.5i			0.667593i	−0.942645	+	0.333797i	$0.891670\pi$
$860$	27880.2	+	11068.7i	1.10548	+	0.438885i
$861$			18043.3i			0.714186i
$862$	27052.5	+	10881.5i	1.06892	+	0.429961i
$863$	20367.8	−	20367.8i	0.803393	−	0.803393i	−0.180232	−	0.983624i	$-0.557685\pi$
$863$	20367.8	−	20367.8i	0.803393	−	0.803393i	0.983624	+	0.180232i	$0.0576847\pi$
$864$	4413.58	−	2099.56i	0.173788	−	0.0826719i
$865$	14714.3	+	36110.0i	0.578382	+	1.41940i
$866$	27765.4	−	11836.2i	1.08950	−	0.464444i
$867$	4311.37	−	4311.37i	0.168883	−	0.168883i
$868$	55257.5	−	1134.58i	2.16079	−	0.0443664i
$869$	−62182.7			−2.42739
$870$	−6.89539	−	1529.66i	−0.000268708	−	0.0596098i
$871$			1831.96i			0.0712669i
$872$	−9782.51	+	4409.66i	−0.379905	+	0.171250i
$873$	1057.88	+	1057.88i	0.0410124	+	0.0410124i
$874$	3035.70	−	1294.09i	0.117488	−	0.0500839i
$875$	27888.1	+	12120.1i	1.07748	+	0.468267i
$876$	3407.32	−	3550.18i	0.131419	−	0.136929i
$877$	23645.3	+	23645.3i	0.910429	+	0.910429i	0.996306	−	0.0858766i	$-0.0273691\pi$
$877$	23645.3	+	23645.3i	0.910429	+	0.910429i	−0.0858766	+	0.996306i	$0.527369\pi$
$878$	−7329.33	+	18221.4i	−0.281723	+	0.700389i
$879$	25308.0			0.971122
$880$	42794.4	+	15980.9i	1.63932	+	0.612176i
$881$	35548.9			1.35945			0.679724	−	0.733468i	$-0.262100\pi$
$881$	35548.9			1.35945			0.679724	+	0.733468i	$0.262100\pi$
$882$	1238.92	−	3080.07i	0.0472978	−	0.117587i
$883$	−13927.1	−	13927.1i	−0.530787	−	0.530787i	0.390019	−	0.920807i	$-0.372468\pi$
$883$	−13927.1	−	13927.1i	−0.530787	−	0.530787i	−0.920807	+	0.390019i	$0.872468\pi$
$884$	6878.98	−	7167.38i	0.261725	−	0.272698i
$885$	−7743.69	−	19003.6i	−0.294126	−	0.721808i
$886$	6914.52	−	2947.60i	0.262187	−	0.111768i
$887$	1873.80	+	1873.80i	0.0709311	+	0.0709311i	0.741682	−	0.670751i	$-0.234028\pi$
$887$	1873.80	+	1873.80i	0.0709311	+	0.0709311i	−0.670751	+	0.741682i	$0.734028\pi$
$888$	−5705.50	−	12657.3i	−0.215613	−	0.478322i
$889$		−	32509.1i		−	1.22646i
$890$	−17154.2	+	17309.5i	−0.646077	+	0.651928i
$891$	5171.13			0.194432
$892$	−1530.53	+	31.4257i	−0.0574506	+	0.00117961i
$893$	37306.9	−	37306.9i	1.39801	−	1.39801i
$894$	27509.2	−	11726.9i	1.02913	−	0.438710i
$895$	10292.2	+	4332.74i	0.384390	+	0.161818i
$896$	−9937.02	+	29901.3i	−0.370505	+	1.11488i
$897$	365.683	−	365.683i	0.0136118	−	0.0136118i
$898$	24358.4	+	9797.87i	0.905178	+	0.364097i
$899$			5119.76i			0.189937i
$900$	−8999.63	+	81.1384i	−0.333320	+	0.00300513i
$901$		−	12512.9i		−	0.462669i
$902$	18626.7	−	46307.7i	0.687585	−	1.70940i
$903$	−15479.7	+	15479.7i	−0.570468	+	0.570468i
$904$	−16974.9	−	6426.33i	−0.624531	−	0.236434i
$905$	−29203.4	−	12293.9i	−1.07266	−	0.451561i
$906$	3239.38	+	7598.98i	0.118787	+	0.278653i
$907$	−2917.23	+	2917.23i	−0.106797	+	0.106797i	−0.758486	−	0.651689i	$-0.774061\pi$
$907$	−2917.23	+	2917.23i	−0.106797	+	0.106797i	0.651689	+	0.758486i	$0.274061\pi$
$908$	−8170.72	+	167.766i	−0.298629	+	0.00613160i
$909$	4919.62			0.179509
$910$	−7282.12	−	7216.77i	−0.265275	−	0.262894i
$911$		−	7151.86i		−	0.260101i	−0.991507	−	0.130050i	$-0.958486\pi$
$911$		−	7151.86i		−	0.260101i	0.991507	−	0.130050i	$-0.0415139\pi$
$912$	14242.3	+	13118.3i	0.517116	+	0.476304i
$913$	9555.19	+	9555.19i	0.346364	+	0.346364i
$914$	−10006.8	−	23474.2i	−0.362141	−	0.849516i
$915$	−2134.15	−	5237.38i	−0.0771070	−	0.189227i
$916$	−16968.6	−	16285.8i	−0.612071	−	0.587442i
$917$	−2342.11	−	2342.11i	−0.0843437	−	0.0843437i
$918$	5904.63	+	2375.07i	0.212290	+	0.0853909i
$919$	−10387.5			−0.372853			−0.186427	−	0.982469i	$-0.559691\pi$
$919$	−10387.5			−0.372853			−0.186427	+	0.982469i	$0.559691\pi$
$920$	2120.69	+	2017.07i	0.0759969	+	0.0722835i
$921$	−3936.09			−0.140824
$922$	−34361.2	−	13821.4i	−1.22736	−	0.493692i
$923$	6678.47	+	6678.47i	0.238163	+	0.238163i
$924$	−23084.3	+	24052.2i	−0.821882	+	0.856340i
$925$	−294.363	+	25564.2i	−0.0104634	+	0.908698i
$926$	−12578.5	−	29506.8i	−0.446388	−	1.04714i
$927$	728.247	+	728.247i	0.0258023	+	0.0258023i
$928$	−2750.37	−	977.165i	−0.0972903	−	0.0345657i
$929$			15098.9i			0.533238i	0.963802	+	0.266619i	$0.0859065\pi$
$929$			15098.9i			0.533238i	−0.963802	+	0.266619i	$0.914094\pi$
$930$	30122.2	−	135.784i	1.06209	−	0.00478768i
$931$	13152.7			0.463009
$932$	837.782	+	40802.6i	0.0294447	+	1.43405i
$933$	11516.8	−	11516.8i	0.404120	−	0.404120i
$934$	4318.79	+	10131.1i	0.151301	+	0.354924i
$935$	22447.0	+	55086.6i	0.785127	+	1.92677i
$936$	2837.89	+	1074.36i	0.0991017	+	0.0375178i
$937$	−20599.4	+	20599.4i	−0.718198	+	0.718198i	−0.968236	−	0.250038i	$-0.919557\pi$
$937$	−20599.4	+	20599.4i	−0.718198	+	0.718198i	0.250038	+	0.968236i	$0.419557\pi$
$938$	2823.58	−	7019.66i	0.0982868	−	0.244350i
$939$			1243.60i			0.0432199i
$940$	43490.2	+	17266.0i	1.50903	+	0.599103i
$941$		−	16979.2i		−	0.588210i	−0.955773	−	0.294105i	$-0.904978\pi$
$941$		−	16979.2i		−	0.588210i	0.955773	−	0.294105i	$-0.0950215\pi$
$942$	−25503.5	−	10258.5i	−0.882111	−	0.354818i
$943$	2261.28	−	2261.28i	0.0780884	−	0.0780884i
$944$	−39122.9	+	1607.26i	−1.34888	+	0.0554153i
$945$	2548.40	−	6053.58i	0.0877245	−	0.208384i
$946$	55708.5	−	23748.0i	1.91463	−	0.816189i
$947$	−29996.5	+	29996.5i	−1.02931	+	1.02931i	−0.0297497	+	0.999557i	$0.509471\pi$
$947$	−29996.5	+	29996.5i	−1.02931	+	1.02931i	−0.999557	+	0.0297497i	$0.990529\pi$
$948$	−479.879	−	23371.6i	−0.0164407	−	0.800713i
$949$	3055.06			0.104501
$950$	−13603.7	−	32958.7i	−0.464593	−	1.12560i
$951$			10221.1i			0.348520i
$952$	−37405.8	+	16861.4i	−1.27345	+	0.574034i
$953$	6222.26	+	6222.26i	0.211499	+	0.211499i	0.804904	−	0.593405i	$-0.202217\pi$
$953$	6222.26	+	6222.26i	0.211499	+	0.211499i	−0.593405	+	0.804904i	$0.702217\pi$
$954$	3515.91	−	1498.80i	0.119321	−	0.0508654i
$955$	−16190.3	−	6815.69i	−0.548591	−	0.230943i
$956$	5886.69	+	5649.82i	0.199152	+	0.191138i
$957$	−2183.66	−	2183.66i	−0.0737595	−	0.0737595i
$958$	−19093.1	+	47467.3i	−0.643916	+	1.60083i
$959$	6649.17			0.223892
$960$	−5676.23	+	16207.8i	−0.190833	+	0.544900i
$961$	−71027.6			−2.38420
$962$	3216.74	−	7997.10i	0.107809	−	0.268022i
$963$	5644.11	+	5644.11i	0.188867	+	0.188867i
$964$	7099.60	+	6813.92i	0.237202	+	0.227657i
$965$	44459.9	−	18116.7i	1.48312	−	0.604350i
$966$	−1964.84	+	837.594i	−0.0654428	+	0.0278977i
$967$	−7128.39	−	7128.39i	−0.237057	−	0.237057i	0.578574	−	0.815630i	$-0.303610\pi$
$967$	−7128.39	−	7128.39i	−0.237057	−	0.237057i	−0.815630	+	0.578574i	$0.803610\pi$
$968$	56618.6	−	25521.9i	1.87995	−	0.847423i
$969$			25214.2i			0.835910i
$970$	−5256.60	+	23.6956i	−0.173999	+	0.000784350i
$971$	15133.2			0.500152			0.250076	−	0.968226i	$-0.419544\pi$
$971$	15133.2			0.500152			0.250076	+	0.968226i	$0.419544\pi$
$972$	39.9069	+	1943.59i	0.00131689	+	0.0641365i
$973$	−29514.5	+	29514.5i	−0.972448	+	0.972448i
$974$	−38329.5	+	16339.5i	−1.26094	+	0.537529i
$975$	−3905.34	−	3996.33i	−0.128278	−	0.131267i
$976$	−10782.2	+	442.961i	−0.353618	+	0.0145275i
$977$	33695.6	−	33695.6i	1.10340	−	1.10340i	0.109397	−	0.993998i	$-0.465108\pi$
$977$	33695.6	−	33695.6i	1.10340	−	1.10340i	0.993998	−	0.109397i	$-0.0348921\pi$
$978$	−11633.1	−	4679.29i	−0.380354	−	0.152993i
$979$			49198.4i			1.60612i
$980$	4622.70	+	10709.9i	0.150680	+	0.349097i
$981$		−	4268.01i		−	0.138906i
$982$	5463.79	−	13583.5i	0.177553	−	0.441412i
$983$	−35661.7	+	35661.7i	−1.15710	+	1.15710i	−0.172008	+	0.985096i	$0.555026\pi$
$983$	−35661.7	+	35661.7i	−1.15710	+	1.15710i	−0.985096	+	0.172008i	$0.944974\pi$
$984$	17548.7	+	6643.56i	0.568528	+	0.215233i
$985$	−14679.3	+	5981.58i	−0.474843	+	0.193491i
$986$	−1490.46	−	3496.35i	−0.0481400	−	0.112927i
$987$	−24146.7	+	24146.7i	−0.778720	+	0.778720i
$988$	246.785	+	12019.2i	0.00794663	+	0.387026i
$989$	3879.99			0.124749
$990$	−12789.7	+	12905.5i	−0.410590	+	0.414308i
$991$			29067.1i			0.931733i	0.884855	+	0.465866i	$0.154257\pi$
$991$			29067.1i			0.931733i	−0.884855	+	0.465866i	$0.845743\pi$
$992$	19242.4	−	54160.5i	0.615873	−	1.73346i
$993$	22366.9	+	22366.9i	0.714797	+	0.714797i
$994$	−15297.0	−	35883.9i	−0.488120	−	1.14504i
$995$	4623.72	−	10983.4i	0.147318	−	0.349946i
$996$	−3517.62	+	3665.10i	−0.111908	+	0.116600i
$997$	23766.2	+	23766.2i	0.754948	+	0.754948i	0.975398	−	0.220450i	$-0.0707526\pi$
$997$	23766.2	+	23766.2i	0.754948	+	0.754948i	−0.220450	+	0.975398i	$0.570753\pi$
$998$	−29024.0	−	11674.6i	−0.920579	−	0.370292i
$999$	5522.23			0.174891

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.v.a.43.14	yes	72
4.3	odd	2		480.4.bh.a.463.15		72
5.2	odd	4	inner	120.4.v.a.67.5	yes	72
8.3	odd	2	inner	120.4.v.a.43.5	✓	72
8.5	even	2		480.4.bh.a.463.16		72
20.7	even	4		480.4.bh.a.367.16		72
40.27	even	4	inner	120.4.v.a.67.14	yes	72
40.37	odd	4		480.4.bh.a.367.15		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.v.a.43.5	✓	72	8.3	odd	2	inner
120.4.v.a.43.14	yes	72	1.1	even	1	trivial
120.4.v.a.67.5	yes	72	5.2	odd	4	inner
120.4.v.a.67.14	yes	72	40.27	even	4	inner
480.4.bh.a.367.15		72	40.37	odd	4
480.4.bh.a.367.16		72	20.7	even	4
480.4.bh.a.463.15		72	4.3	odd	2
480.4.bh.a.463.16		72	8.5	even	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	120.4.v.a.43.14

Level	$120$
Weight	$4$
Character	120.43
Analytic conductor	$7.080$
Analytic rank	$0$
Dimension	$72$
Inner twists	$4$