LMFDB - Embedded newform 270.3.n.a.239.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(29,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1, 9]))

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

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

chi := DirichletCharacter("270.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$270 = 2 \cdot 3^{3} \cdot 5$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	270.n (of order $18$ , degree $6$ , 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:	$7.35696713773$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.25
Character	$\chi$	$=$	270.239
Dual form			270.3.n.a.209.25

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32893 + 0.483690i) q^{2} +(-1.34429 + 2.68196i) q^{3} +(1.53209 + 1.28558i) q^{4} +(2.69307 + 4.21276i) q^{5} +(-3.08369 + 2.91390i) q^{6} +(2.97092 + 3.54061i) q^{7} +(1.41421 + 2.44949i) q^{8} +(-5.38578 - 7.21064i) q^{9} +(1.54122 + 6.90106i) q^{10} +(1.05528 - 0.186074i) q^{11} +(-5.50742 + 2.38081i) q^{12} +(1.47894 + 4.06336i) q^{13} +(2.23558 + 6.14221i) q^{14} +(-14.9187 + 1.55953i) q^{15} +(0.694593 + 3.93923i) q^{16} +(-1.77424 + 3.07307i) q^{17} +(-3.66959 - 12.1875i) q^{18} +(-1.99639 - 3.45785i) q^{19} +(-1.28981 + 9.91647i) q^{20} +(-13.4895 + 3.20829i) q^{21} +(1.49239 + 0.263148i) q^{22} +(-19.8908 - 16.6904i) q^{23} +(-8.47053 + 0.500041i) q^{24} +(-10.4948 + 22.6905i) q^{25} +6.11526i q^{26} +(26.5787 - 4.75126i) q^{27} +9.24387i q^{28} +(-2.24324 + 6.16324i) q^{29} +(-20.5802 - 5.14353i) q^{30} +(-11.5358 - 9.67968i) q^{31} +(-0.982302 + 5.57091i) q^{32} +(-0.919555 + 3.08035i) q^{33} +(-3.84424 + 3.22570i) q^{34} +(-6.91485 + 22.0509i) q^{35} +(1.01832 - 17.9712i) q^{36} +(63.7054 + 36.7803i) q^{37} +(-0.980530 - 5.56086i) q^{38} +(-12.8859 - 1.49587i) q^{39} +(-6.51055 + 12.5544i) q^{40} +(6.76713 + 18.5925i) q^{41} +(-19.4784 - 2.26116i) q^{42} +(-4.11607 + 0.725774i) q^{43} +(1.85599 + 1.07156i) q^{44} +(15.8725 - 42.1078i) q^{45} +(-18.3604 - 31.8012i) q^{46} +(18.0082 - 15.1107i) q^{47} +(-11.4986 - 3.43259i) q^{48} +(4.79924 - 27.2179i) q^{49} +(-24.9219 + 25.0778i) q^{50} +(-5.85675 - 8.88951i) q^{51} +(-2.95789 + 8.12672i) q^{52} -20.2797 q^{53} +(37.6192 + 6.54175i) q^{54} +(3.62582 + 3.94453i) q^{55} +(-4.47116 + 12.2844i) q^{56} +(11.9575 - 0.705889i) q^{57} +(-5.96219 + 7.10547i) q^{58} +(55.8827 + 9.85363i) q^{59} +(-24.8617 - 16.7898i) q^{60} +(76.1081 - 63.8623i) q^{61} +(-10.6483 - 18.4433i) q^{62} +(9.52931 - 40.4912i) q^{63} +(-4.00000 + 6.92820i) q^{64} +(-13.1351 + 17.1733i) q^{65} +(-2.71195 + 3.64877i) q^{66} +(-6.06194 - 16.6550i) q^{67} +(-6.66894 + 2.42730i) q^{68} +(71.5018 - 30.9096i) q^{69} +(-19.8551 + 25.9594i) q^{70} +(-26.1941 - 15.1231i) q^{71} +(10.0457 - 23.3898i) q^{72} +(83.2498 - 48.0643i) q^{73} +(66.8695 + 79.6919i) q^{74} +(-46.7470 - 58.6491i) q^{75} +(1.38668 - 7.86425i) q^{76} +(3.79396 + 3.18351i) q^{77} +(-16.4009 - 8.22066i) q^{78} +(132.466 + 48.2137i) q^{79} +(-14.7245 + 13.5348i) q^{80} +(-22.9867 + 77.6699i) q^{81} +27.9813i q^{82} +(-107.784 - 39.2301i) q^{83} +(-24.7916 - 12.4264i) q^{84} +(-17.7242 + 0.801540i) q^{85} +(-5.82100 - 1.02640i) q^{86} +(-13.5140 - 14.3014i) q^{87} +(1.94818 + 2.32174i) q^{88} +(42.0555 - 24.2807i) q^{89} +(41.4604 - 48.2808i) q^{90} +(-9.99294 + 17.3083i) q^{91} +(-9.01775 - 51.1422i) q^{92} +(41.4679 - 17.9262i) q^{93} +(31.2405 - 11.3706i) q^{94} +(9.19069 - 17.7226i) q^{95} +(-13.6205 - 10.1234i) q^{96} +(61.5186 - 10.8474i) q^{97} +(19.5428 - 33.8492i) q^{98} +(-7.02521 - 6.60708i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$216 q - 18 q^{5} + 12 q^{6} + 12 q^{9} - 36 q^{11} + 36 q^{14} + 18 q^{15} - 72 q^{20} + 360 q^{21} + 18 q^{25} - 36 q^{29} + 144 q^{30} + 180 q^{31} + 486 q^{35} - 192 q^{36} + 348 q^{39} - 72 q^{41} + 258 q^{45}+ \cdots - 1008 q^{99}+O(q^{100})$ 216 * q - 18 * q^5 + 12 * q^6 + 12 * q^9 - 36 * q^11 + 36 * q^14 + 18 * q^15 - 72 * q^20 + 360 * q^21 + 18 * q^25 - 36 * q^29 + 144 * q^30 + 180 * q^31 + 486 * q^35 - 192 * q^36 + 348 * q^39 - 72 * q^41 + 258 * q^45 - 72 * q^49 - 288 * q^50 - 312 * q^51 - 360 * q^54 - 72 * q^56 - 612 * q^59 - 36 * q^60 - 144 * q^61 - 864 * q^64 - 234 * q^65 + 336 * q^69 + 288 * q^74 + 642 * q^75 + 72 * q^79 + 636 * q^81 - 216 * q^84 + 432 * q^86 - 1620 * q^89 - 240 * q^90 - 504 * q^94 + 108 * q^95 - 1008 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$ .

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.32893	+	0.483690i	0.664463	+	0.241845i
$2$	1.32893	+	0.483690i	0.664463	+	0.241845i
$3$	−1.34429	+	2.68196i	−0.448096	+	0.893986i
$3$	−1.34429	+	2.68196i	−0.448096	+	0.893986i
$4$	1.53209	+	1.28558i	0.383022	+	0.321394i
$5$	2.69307	+	4.21276i	0.538614	+	0.842553i
$5$	2.69307	+	4.21276i	0.538614	+	0.842553i
$6$	−3.08369	+	2.91390i	−0.513949	+	0.485651i
$7$	2.97092	+	3.54061i	0.424417	+	0.505801i	0.935303	−	0.353848i	$-0.115127\pi$
$7$	2.97092	+	3.54061i	0.424417	+	0.505801i	−0.510886	+	0.859649i	$0.670682\pi$
$8$	1.41421	+	2.44949i	0.176777	+	0.306186i
$9$	−5.38578	−	7.21064i	−0.598420	−	0.801182i
$10$	1.54122	+	6.90106i	0.154122	+	0.690106i
$11$	1.05528	−	0.186074i	0.0959344	−	0.0169158i	−0.125475	−	0.992097i	$-0.540045\pi$
$11$	1.05528	−	0.186074i	0.0959344	−	0.0169158i	0.221409	+	0.975181i	$0.428934\pi$
$12$	−5.50742	+	2.38081i	−0.458952	+	0.198401i
$13$	1.47894	+	4.06336i	0.113765	+	0.312566i	0.983488	−	0.180974i	$-0.0579249\pi$
$13$	1.47894	+	4.06336i	0.113765	+	0.312566i	−0.869723	+	0.493540i	$0.835703\pi$
$14$	2.23558	+	6.14221i	0.159684	+	0.438729i
$15$	−14.9187	+	1.55953i	−0.994581	+	0.103968i
$16$	0.694593	+	3.93923i	0.0434120	+	0.246202i
$17$	−1.77424	+	3.07307i	−0.104367	+	0.180769i	−0.913479	−	0.406885i	$-0.866615\pi$
$17$	−1.77424	+	3.07307i	−0.104367	+	0.180769i	0.809113	+	0.587654i	$0.199948\pi$
$18$	−3.66959	−	12.1875i	−0.203866	−	0.677081i
$19$	−1.99639	−	3.45785i	−0.105073	−	0.181992i	0.808695	−	0.588228i	$-0.200174\pi$
$19$	−1.99639	−	3.45785i	−0.105073	−	0.181992i	−0.913768	+	0.406236i	$0.866841\pi$
$20$	−1.28981	+	9.91647i	−0.0644903	+	0.495824i
$21$	−13.4895	+	3.20829i	−0.642358	+	0.152776i
$22$	1.49239	+	0.263148i	0.0678359	+	0.0119613i
$23$	−19.8908	−	16.6904i	−0.864817	−	0.725668i	0.0981831	−	0.995168i	$-0.468697\pi$
$23$	−19.8908	−	16.6904i	−0.864817	−	0.725668i	−0.963000	+	0.269501i	$0.913141\pi$
$24$	−8.47053	+	0.500041i	−0.352939	+	0.0208350i
$25$	−10.4948	+	22.6905i	−0.419791	+	0.907621i
$26$			6.11526i			0.235202i
$27$	26.5787	−	4.75126i	0.984395	−	0.175973i
$28$			9.24387i			0.330138i
$29$	−2.24324	+	6.16324i	−0.0773530	+	0.212526i	−0.972342	−	0.233563i	$-0.924961\pi$
$29$	−2.24324	+	6.16324i	−0.0773530	+	0.212526i	0.894989	+	0.446089i	$0.147184\pi$
$30$	−20.5802	−	5.14353i	−0.686006	−	0.171451i
$31$	−11.5358	−	9.67968i	−0.372122	−	0.312248i	0.437478	−	0.899229i	$-0.355872\pi$
$31$	−11.5358	−	9.67968i	−0.372122	−	0.312248i	−0.809600	+	0.586981i	$0.800316\pi$
$32$	−0.982302	+	5.57091i	−0.0306970	+	0.174091i
$33$	−0.919555	+	3.08035i	−0.0278653	+	0.0933439i
$34$	−3.84424	+	3.22570i	−0.113066	+	0.0948735i
$35$	−6.91485	+	22.0509i	−0.197567	+	0.630025i
$36$	1.01832	−	17.9712i	0.0282868	−	0.499199i
$37$	63.7054	+	36.7803i	1.72177	+	0.994063i	0.915288	+	0.402799i	$0.131963\pi$
$37$	63.7054	+	36.7803i	1.72177	+	0.994063i	0.806479	+	0.591263i	$0.201371\pi$
$38$	−0.980530	−	5.56086i	−0.0258034	−	0.146338i
$39$	−12.8859	−	1.49587i	−0.330407	−	0.0383555i
$40$	−6.51055	+	12.5544i	−0.162764	+	0.313860i
$41$	6.76713	+	18.5925i	0.165052	+	0.453477i	0.994454	−	0.105176i	$-0.0335406\pi$
$41$	6.76713	+	18.5925i	0.165052	+	0.453477i	−0.829402	+	0.558653i	$0.811318\pi$
$42$	−19.4784	−	2.26116i	−0.463771	−	0.0538372i
$43$	−4.11607	+	0.725774i	−0.0957225	+	0.0168785i	−0.221304	−	0.975205i	$-0.571031\pi$
$43$	−4.11607	+	0.725774i	−0.0957225	+	0.0168785i	0.125582	+	0.992083i	$0.459920\pi$
$44$	1.85599	+	1.07156i	0.0421816	+	0.0243536i
$45$	15.8725	−	42.1078i	0.352721	−	0.935728i
$46$	−18.3604	−	31.8012i	−0.399140	−	0.691331i
$47$	18.0082	−	15.1107i	0.383153	−	0.321504i	−0.430785	−	0.902454i	$-0.641763\pi$
$47$	18.0082	−	15.1107i	0.383153	−	0.321504i	0.813939	+	0.580950i	$0.197319\pi$
$48$	−11.4986	−	3.43259i	−0.239554	−	0.0715123i
$49$	4.79924	−	27.2179i	0.0979437	−	0.555466i
$50$	−24.9219	+	25.0778i	−0.498439	+	0.501556i
$51$	−5.85675	−	8.88951i	−0.114838	−	0.174304i
$52$	−2.95789	+	8.12672i	−0.0568824	+	0.156283i
$53$	−20.2797			−0.382637			−0.191318	−	0.981528i	$-0.561276\pi$
$53$	−20.2797			−0.382637			−0.191318	+	0.981528i	$0.561276\pi$
$54$	37.6192	+	6.54175i	0.696652	+	0.121144i
$55$	3.62582	+	3.94453i	0.0659240	+	0.0717187i
$56$	−4.47116	+	12.2844i	−0.0798422	+	0.219365i
$57$	11.9575	−	0.705889i	0.209781	−	0.0123840i
$58$	−5.96219	+	7.10547i	−0.102796	+	0.122508i
$59$	55.8827	+	9.85363i	0.947164	+	0.167011i	0.625834	−	0.779956i	$-0.284759\pi$
$59$	55.8827	+	9.85363i	0.947164	+	0.167011i	0.321331	+	0.946967i	$0.395870\pi$
$60$	−24.8617	−	16.7898i	−0.414361	−	0.279830i
$61$	76.1081	−	63.8623i	1.24767	−	1.04692i	0.250790	−	0.968042i	$-0.419310\pi$
$61$	76.1081	−	63.8623i	1.24767	−	1.04692i	0.996884	−	0.0788810i	$-0.0251347\pi$
$62$	−10.6483	−	18.4433i	−0.171746	−	0.297473i
$63$	9.52931	−	40.4912i	0.151259	−	0.642717i
$64$	−4.00000	+	6.92820i	−0.0625000	+	0.108253i
$65$	−13.1351	+	17.1733i	−0.202078	+	0.264205i
$66$	−2.71195	+	3.64877i	−0.0410902	+	0.0552845i
$67$	−6.06194	−	16.6550i	−0.0904766	−	0.248583i	0.886198	−	0.463306i	$-0.153337\pi$
$67$	−6.06194	−	16.6550i	−0.0904766	−	0.248583i	−0.976675	+	0.214724i	$0.931115\pi$
$68$	−6.66894	+	2.42730i	−0.0980727	+	0.0356955i
$69$	71.5018	−	30.9096i	1.03626	−	0.447965i
$70$	−19.8551	+	25.9594i	−0.283644	+	0.370848i
$71$	−26.1941	−	15.1231i	−0.368930	−	0.213002i	0.304061	−	0.952653i	$-0.401657\pi$
$71$	−26.1941	−	15.1231i	−0.368930	−	0.213002i	−0.672991	+	0.739651i	$0.734991\pi$
$72$	10.0457	−	23.3898i	0.139524	−	0.324858i
$73$	83.2498	−	48.0643i	1.14041	−	0.658415i	0.193877	−	0.981026i	$-0.437894\pi$
$73$	83.2498	−	48.0643i	1.14041	−	0.658415i	0.946532	+	0.322611i	$0.104561\pi$
$74$	66.8695	+	79.6919i	0.903642	+	1.07692i
$75$	−46.7470	−	58.6491i	−0.623293	−	0.781988i
$76$	1.38668	−	7.86425i	0.0182458	−	0.103477i
$77$	3.79396	+	3.18351i	0.0492723	+	0.0413443i
$78$	−16.4009	−	8.22066i	−0.210267	−	0.105393i
$79$	132.466	+	48.2137i	1.67679	+	0.610300i	0.992864	−	0.119254i	$-0.0380503\pi$
$79$	132.466	+	48.2137i	1.67679	+	0.610300i	0.683923	+	0.729554i	$0.260273\pi$
$80$	−14.7245	+	13.5348i	−0.184056	+	0.169185i
$81$	−22.9867	+	77.6699i	−0.283786	+	0.958888i
$82$			27.9813i			0.341235i
$83$	−107.784	−	39.2301i	−1.29860	−	0.472652i	−0.402060	−	0.915613i	$-0.631706\pi$
$83$	−107.784	−	39.2301i	−1.29860	−	0.472652i	−0.896541	+	0.442961i	$0.853928\pi$
$84$	−24.7916	−	12.4264i	−0.295139	−	0.147933i
$85$	−17.7242	+	0.801540i	−0.208520	+	0.00942988i
$86$	−5.82100	−	1.02640i	−0.0676860	−	0.0119349i
$87$	−13.5140	−	14.3014i	−0.155333	−	0.164384i
$88$	1.94818	+	2.32174i	0.0221384	+	0.0263835i
$89$	42.0555	−	24.2807i	0.472533	−	0.272817i	−0.244766	−	0.969582i	$-0.578711\pi$
$89$	42.0555	−	24.2807i	0.472533	−	0.272817i	0.717300	+	0.696765i	$0.245378\pi$
$90$	41.4604	−	48.2808i	0.460671	−	0.536453i
$91$	−9.99294	+	17.3083i	−0.109813	+	0.190201i
$92$	−9.01775	−	51.1422i	−0.0980191	−	0.555894i
$93$	41.4679	−	17.9262i	0.445891	−	0.192755i
$94$	31.2405	−	11.3706i	0.332345	−	0.120964i
$95$	9.19069	−	17.7226i	0.0967442	−	0.186553i
$96$	−13.6205	−	10.1234i	−0.141880	−	0.105452i
$97$	61.5186	−	10.8474i	0.634213	−	0.111829i	0.152707	−	0.988272i	$-0.451201\pi$
$97$	61.5186	−	10.8474i	0.634213	−	0.111829i	0.481506	+	0.876443i	$0.340090\pi$
$98$	19.5428	−	33.8492i	0.199417	−	0.345400i
$99$	−7.02521	−	6.60708i	−0.0709617	−	0.0667382i
$100$	−45.2493	+	21.2721i	−0.452493	+	0.212721i
$101$	47.4138	+	56.5056i	0.469444	+	0.559461i	0.947866	−	0.318668i	$-0.103236\pi$
$101$	47.4138	+	56.5056i	0.469444	+	0.559461i	−0.478422	+	0.878130i	$0.658791\pi$
$102$	−3.48342	−	14.6463i	−0.0341512	−	0.143592i
$103$	−116.649	−	20.5683i	−1.13251	−	0.199693i	−0.424185	−	0.905576i	$-0.639439\pi$
$103$	−116.649	−	20.5683i	−1.13251	−	0.199693i	−0.708328	+	0.705883i	$0.750550\pi$
$104$	−7.86162	+	9.36912i	−0.0755925	+	0.0900877i
$105$	−49.8440	−	48.1880i	−0.474705	−	0.458934i
$106$	−26.9503	−	9.80910i	−0.254248	−	0.0925387i
$107$	−137.518			−1.28521			−0.642607	−	0.766196i	$-0.722147\pi$
$107$	−137.518			−1.28521			−0.642607	+	0.766196i	$0.722147\pi$
$108$	46.8290	+	26.8895i	0.433602	+	0.248977i
$109$	184.071			1.68872			0.844360	−	0.535776i	$-0.179981\pi$
$109$	184.071			1.68872			0.844360	+	0.535776i	$0.179981\pi$
$110$	2.91052	+	6.99576i	0.0264593	+	0.0635978i
$111$	−184.282	+	121.412i	−1.66019	+	1.09380i
$112$	−11.8837	+	14.1624i	−0.106104	+	0.126450i
$113$	−33.5527	+	190.287i	−0.296927	+	1.68396i	0.362339	+	0.932046i	$0.381978\pi$
$113$	−33.5527	+	190.287i	−0.296927	+	1.68396i	−0.659266	+	0.751910i	$0.729133\pi$
$114$	16.2321	+	4.84566i	0.142387	+	0.0425058i
$115$	16.7453	−	128.744i	0.145611	−	1.11951i
$116$	−11.3602	+	6.55879i	−0.0979324	+	0.0565413i
$117$	21.3342	−	32.5485i	0.182343	−	0.278192i
$118$	69.4979	+	40.1246i	0.588965	+	0.340039i
$119$	−16.1516	+	2.84797i	−0.135728	+	0.0239325i
$120$	−24.9183	−	34.3377i	−0.207652	−	0.286148i
$121$	−112.624	+	40.9917i	−0.930775	+	0.338775i
$122$	132.032	−	48.0556i	1.08223	−	0.393898i
$123$	−58.9614	−	6.84457i	−0.479361	−	0.0556469i
$124$	−5.22990	−	29.6603i	−0.0421766	−	0.239196i
$125$	−123.853	+	16.8951i	−0.990824	+	0.135161i
$126$	32.2489	−	49.2006i	0.255944	−	0.390481i
$127$	113.459	−	65.5058i	0.893381	−	0.515793i	0.0183338	−	0.999832i	$-0.494164\pi$
$127$	113.459	−	65.5058i	0.893381	−	0.515793i	0.875047	+	0.484038i	$0.160831\pi$
$128$	−8.66680	+	7.27231i	−0.0677094	+	0.0568149i
$129$	3.58669	−	12.0148i	0.0278038	−	0.0931377i
$130$	−25.7621	+	16.4688i	−0.198170	+	0.126683i
$131$	17.1461	−	20.4339i	0.130886	−	0.155984i	−0.696621	−	0.717439i	$-0.745314\pi$
$131$	17.1461	−	20.4339i	0.130886	−	0.155984i	0.827507	+	0.561456i	$0.189758\pi$
$132$	−5.36886	+	3.53721i	−0.0406732	+	0.0267970i
$133$	6.31177	−	17.3414i	0.0474569	−	0.130387i
$134$		−	25.0654i		−	0.187055i
$135$	91.5941	+	99.1742i	0.678475	+	0.734624i
$136$	−10.0366			−0.0737985
$137$	−164.163	−	59.7503i	−1.19827	−	0.436134i	−0.335648	−	0.941987i	$-0.608955\pi$
$137$	−164.163	−	59.7503i	−1.19827	−	0.436134i	−0.862619	+	0.505854i	$0.831178\pi$
$138$	109.971	−	6.49193i	0.796893	−	0.0470430i
$139$	7.98939	+	6.70389i	0.0574776	+	0.0482294i	0.671074	−	0.741390i	$-0.265833\pi$
$139$	7.98939	+	6.70389i	0.0574776	+	0.0482294i	−0.613596	+	0.789620i	$0.710278\pi$
$140$	−38.9422	+	24.8944i	−0.278159	+	0.177817i
$141$	16.3180	+	68.6104i	0.115730	+	0.486598i
$142$	−27.4951	−	32.7673i	−0.193627	−	0.230756i
$143$	2.31678	+	4.01278i	0.0162013	+	0.0280614i
$144$	24.6635	−	26.2243i	0.171274	−	0.182113i
$145$	−32.0055	+	7.14781i	−0.220728	+	0.0492952i
$146$	133.881	−	23.6068i	0.916993	−	0.161691i
$147$	66.5455	+	49.4600i	0.452691	+	0.336462i
$148$	50.3184	+	138.249i	0.339989	+	0.934113i
$149$	6.36450	+	17.4863i	0.0427148	+	0.117358i	0.959216	−	0.282674i	$-0.0912214\pi$
$149$	6.36450	+	17.4863i	0.0427148	+	0.117358i	−0.916501	+	0.400032i	$0.868999\pi$
$150$	−33.7554	−	100.551i	−0.225036	−	0.670342i
$151$	−10.0048	−	56.7400i	−0.0662569	−	0.375762i	−0.999848	−	0.0174221i	$-0.994454\pi$
$151$	−10.0048	−	56.7400i	−0.0662569	−	0.375762i	0.933591	−	0.358340i	$-0.116657\pi$
$152$	5.64665	−	9.78028i	0.0371490	−	0.0643439i
$153$	31.7144	−	3.75749i	0.207284	−	0.0245587i
$154$	3.50206	+	6.06575i	0.0227407	+	0.0393880i
$155$	9.71153	−	74.6656i	0.0626550	−	0.481713i
$156$	−17.8193	−	18.8576i	−0.114226	−	0.120882i
$157$	77.2204	+	13.6160i	0.491850	+	0.0867264i	0.414072	−	0.910244i	$-0.364106\pi$
$157$	77.2204	+	13.6160i	0.491850	+	0.0867264i	0.0777782	+	0.996971i	$0.475217\pi$
$158$	152.717	+	128.145i	0.966565	+	0.811044i
$159$	27.2618	−	54.3894i	0.171458	−	0.342072i
$160$	−26.1144	+	10.8646i	−0.163215	+	0.0679040i
$161$		−	120.011i		−	0.745411i
$162$	−68.1157	+	92.0991i	−0.420467	+	0.568513i
$163$		−	116.014i		−	0.711745i	−0.934534	−	0.355873i	$-0.884184\pi$
$163$		−	116.014i		−	0.711745i	0.934534	−	0.355873i	$-0.115816\pi$
$164$	−13.5343	+	37.1851i	−0.0825260	+	0.226738i
$165$	−15.4532	+	4.42172i	−0.0936558	+	0.0267983i
$166$	−124.262	−	104.268i	−0.748564	−	0.628120i
$167$	−15.1628	+	85.9925i	−0.0907952	+	0.514925i	0.905160	+	0.425071i	$0.139751\pi$
$167$	−15.1628	+	85.9925i	−0.0907952	+	0.514925i	−0.995955	+	0.0898536i	$0.971360\pi$
$168$	−26.9357	−	28.5052i	−0.160332	−	0.169674i
$169$	115.138	−	96.6121i	0.681289	−	0.571669i
$170$	−23.9419	−	7.50784i	−0.140835	−	0.0441638i
$171$	−14.1812	+	33.0185i	−0.0829310	+	0.193091i
$172$	−7.23922	−	4.17957i	−0.0420885	−	0.0242998i
$173$	−3.70303	−	21.0010i	−0.0214048	−	0.121393i	0.972233	−	0.234014i	$-0.0751863\pi$
$173$	−3.70303	−	21.0010i	−0.0214048	−	0.121393i	−0.993638	+	0.112622i	$0.964075\pi$
$174$	−11.0416	−	25.5421i	−0.0634578	−	0.146794i
$175$	−111.517	+	30.2539i	−0.637242	+	0.172880i
$176$	1.46598	+	4.02774i	0.00832942	+	0.0228849i
$177$	−101.549	+	136.629i	−0.573725	+	0.771914i
$178$	67.6329	−	11.9255i	0.379960	−	0.0669972i
$179$	−178.291	−	102.937i	−0.996041	−	0.575065i	−0.0889667	−	0.996035i	$-0.528356\pi$
$179$	−178.291	−	102.937i	−0.996041	−	0.575065i	−0.907075	+	0.420970i	$0.861690\pi$
$180$	78.4507	−	44.1076i	0.435837	−	0.245042i
$181$	−76.9019	−	133.198i	−0.424872	−	0.735900i	0.571536	−	0.820577i	$-0.306348\pi$
$181$	−76.9019	−	133.198i	−0.424872	−	0.735900i	−0.996408	+	0.0846766i	$0.973014\pi$
$182$	−21.6517	+	18.1679i	−0.118965	+	0.0998239i
$183$	68.9647	+	289.968i	0.376856	+	1.58452i
$184$	12.7530	−	72.3260i	0.0693099	−	0.393076i
$185$	16.6161	+	367.428i	0.0898168	+	1.98610i
$186$	63.7785	−	3.76503i	0.342895	−	0.0202421i
$187$	−1.30049	+	3.57308i	−0.00695451	+	0.0191074i
$188$	47.0161			0.250086
$189$	95.7855	+	79.9890i	0.506801	+	0.423222i
$190$	20.7860	−	19.1065i	0.109400	−	0.100561i
$191$	9.44838	−	25.9592i	0.0494680	−	0.135912i	−0.912498	−	0.409081i	$-0.865849\pi$
$191$	9.44838	−	25.9592i	0.0494680	−	0.135912i	0.961966	+	0.273169i	$0.0880717\pi$
$192$	−13.2040	−	20.0413i	−0.0687708	−	0.104382i
$193$	−203.216	+	242.184i	−1.05293	+	1.25484i	−0.0869574	+	0.996212i	$0.527714\pi$
$193$	−203.216	+	242.184i	−1.05293	+	1.25484i	−0.965977	+	0.258627i	$0.916730\pi$
$194$	87.0005	+	15.3405i	0.448456	+	0.0790749i
$195$	−28.4008	−	58.3137i	−0.145645	−	0.299044i
$196$	42.3435	−	35.5304i	0.216038	−	0.181277i
$197$	−19.5523	−	33.8655i	−0.0992500	−	0.171906i	0.812124	−	0.583484i	$-0.198311\pi$
$197$	−19.5523	−	33.8655i	−0.0992500	−	0.171906i	−0.911374	+	0.411578i	$0.864978\pi$
$198$	−6.14021	−	12.1783i	−0.0310112	−	0.0615068i
$199$	−130.989	+	226.880i	−0.658238	+	1.14010i	0.322833	+	0.946456i	$0.395365\pi$
$199$	−130.989	+	226.880i	−0.658238	+	1.14010i	−0.981071	+	0.193646i	$0.937969\pi$
$200$	−70.4220	+	6.38242i	−0.352110	+	0.0319121i
$201$	52.8171	+	6.13130i	0.262771	+	0.0305040i
$202$	35.6783	+	98.0253i	0.176625	+	0.485274i
$203$	−28.4861	+	10.3681i	−0.140326	+	0.0510744i
$204$	2.45507	−	21.1488i	0.0120347	−	0.103671i
$205$	−60.1017	+	78.5793i	−0.293179	+	0.383314i
$206$	−145.069	−	83.7556i	−0.704218	−	0.406581i
$207$	−13.2207	+	233.316i	−0.0638681	+	1.12713i
$208$	−14.9793	+	8.64828i	−0.0720157	+	0.0415783i
$209$	−2.75016	−	3.27752i	−0.0131587	−	0.0156819i
$210$	−42.9309	−	88.1474i	−0.204433	−	0.419749i
$211$	−34.7360	+	196.997i	−0.164625	+	0.933637i	0.784824	+	0.619718i	$0.212753\pi$
$211$	−34.7360	+	196.997i	−0.164625	+	0.933637i	−0.949450	+	0.313919i	$0.898358\pi$
$212$	−31.0704	−	26.0711i	−0.146558	−	0.122977i
$213$	75.7720	−	49.9215i	0.355737	−	0.234373i
$214$	−182.751	−	66.5160i	−0.853978	−	0.310822i
$215$	−14.1424	−	15.3855i	−0.0657785	−	0.0715603i
$216$	49.2261	+	58.3849i	0.227898	+	0.270300i
$217$		−	69.6012i		−	0.320743i
$218$	244.616	+	89.0330i	1.12209	+	0.408408i
$219$	16.9947	+	287.885i	0.0776013	+	1.31454i
$220$	0.484094	+	10.7046i	0.00220043	+	0.0486574i
$221$	−15.1110	−	2.66447i	−0.0683754	−	0.0120564i
$222$	−303.622	+	72.2122i	−1.36767	+	0.325280i
$223$	−242.801	−	289.359i	−1.08879	−	1.29757i	−0.951705	−	0.307015i	$-0.900670\pi$
$223$	−242.801	−	289.359i	−1.08879	−	1.29757i	−0.137089	−	0.990559i	$-0.543775\pi$
$224$	−22.6428	+	13.0728i	−0.101084	+	0.0583607i
$225$	220.136	−	46.5322i	0.978381	−	0.206810i
$226$	−136.629	+	236.648i	−0.604553	+	1.04712i
$227$	−61.5697	−	349.179i	−0.271232	−	1.53823i	−0.750681	−	0.660665i	$-0.770274\pi$
$227$	−61.5697	−	349.179i	−0.271232	−	1.53823i	0.479449	−	0.877570i	$-0.340837\pi$
$228$	19.2275	+	14.2908i	0.0843310	+	0.0626790i
$229$	−116.440	+	42.3808i	−0.508473	+	0.185069i	−0.583501	−	0.812112i	$-0.698318\pi$
$229$	−116.440	+	42.3808i	−0.508473	+	0.185069i	0.0750282	+	0.997181i	$0.476095\pi$
$230$	84.5251	−	162.991i	0.367501	−	0.708657i
$231$	−13.6382	+	5.89569i	−0.0590399	+	0.0255225i
$232$	−18.2692	+	3.22136i	−0.0787466	+	0.0138852i
$233$	20.8882	−	36.1794i	0.0896487	−	0.155276i	−0.817714	−	0.575625i	$-0.804759\pi$
$233$	20.8882	−	36.1794i	0.0896487	−	0.155276i	0.907363	+	0.420349i	$0.138092\pi$
$234$	44.0949	−	32.9354i	0.188440	−	0.140750i
$235$	112.155	+	35.1703i	0.477256	+	0.149661i
$236$	72.9497	+	86.9380i	0.309109	+	0.368382i
$237$	−307.380	+	290.455i	−1.29696	+	1.22555i
$238$	−22.8419	−	4.02764i	−0.0959742	−	0.0169228i
$239$	−218.295	+	260.154i	−0.913368	+	1.08851i	0.0823990	+	0.996599i	$0.473742\pi$
$239$	−218.295	+	260.154i	−0.913368	+	1.08851i	−0.995767	+	0.0919105i	$0.970703\pi$
$240$	−16.5058	−	57.6850i	−0.0687740	−	0.240354i
$241$	−36.8119	−	13.3984i	−0.152747	−	0.0555952i	0.264515	−	0.964381i	$-0.414788\pi$
$241$	−36.8119	−	13.3984i	−0.152747	−	0.0555952i	−0.417262	+	0.908786i	$0.637010\pi$
$242$	−169.496			−0.700397
$243$	−177.407	−	166.060i	−0.730068	−	0.683374i
$244$	198.704			0.814361
$245$	127.587	−	53.0815i	0.520764	−	0.216659i
$246$	−75.0446	−	37.6149i	−0.305060	−	0.152906i
$247$	11.0980	−	13.2260i	0.0449310	−	0.0535467i
$248$	7.39620	−	41.9459i	0.0298234	−	0.169137i
$249$	250.106	−	236.335i	1.00444	−	0.949137i
$250$	−172.763	−	37.4540i	−0.691054	−	0.149816i
$251$	209.699	−	121.070i	0.835455	−	0.482350i	−0.0202615	−	0.999795i	$-0.506450\pi$
$251$	209.699	−	121.070i	0.835455	−	0.482350i	0.855717	+	0.517444i	$0.173117\pi$
$252$	66.6542	−	49.7855i	0.264501	−	0.197561i
$253$	−24.0960	−	13.9118i	−0.0952410	−	0.0549874i
$254$	182.464	−	32.1732i	0.718360	−	0.126666i
$255$	21.6768	−	48.6131i	0.0850070	−	0.190640i
$256$	−15.0351	+	5.47232i	−0.0587308	+	0.0213763i
$257$	190.495	−	69.3345i	0.741226	−	0.269784i	0.0563170	−	0.998413i	$-0.482064\pi$
$257$	190.495	−	69.3345i	0.741226	−	0.269784i	0.684909	+	0.728629i	$0.259842\pi$
$258$	10.5779	−	14.2319i	0.0409994	−	0.0551624i
$259$	59.0390	+	334.827i	0.227950	+	1.29277i
$260$	−42.2018	+	9.42495i	−0.162314	+	0.0362498i
$261$	56.5225	−	17.0187i	0.216561	−	0.0652058i
$262$	32.6695	−	18.8617i	0.124693	−	0.0719914i
$263$	226.811	−	190.317i	0.862398	−	0.723638i	−0.100085	−	0.994979i	$-0.531912\pi$
$263$	226.811	−	190.317i	0.862398	−	0.723638i	0.962483	+	0.271341i	$0.0874671\pi$
$264$	−8.84573	+	2.10383i	−0.0335065	+	0.00796905i
$265$	−54.6147	−	85.4338i	−0.206093	−	0.322392i
$266$	16.7757	−	19.9926i	0.0630667	−	0.0751600i
$267$	8.58524	+	145.431i	0.0321544	+	0.544686i
$268$	12.1239	−	33.3101i	0.0452383	−	0.124291i
$269$		−	469.741i		−	1.74625i	−0.487496	−	0.873125i	$-0.662090\pi$
$269$		−	469.741i		−	1.74625i	0.487496	−	0.873125i	$-0.337910\pi$
$270$	73.7523	+	176.098i	0.273157	+	0.652216i
$271$	−392.252			−1.44742			−0.723712	−	0.690102i	$-0.757565\pi$
$271$	−392.252			−1.44742			−0.723712	+	0.690102i	$0.757565\pi$
$272$	−13.3379	−	4.85459i	−0.0490363	−	0.0178478i
$273$	−32.9867	−	50.0679i	−0.120830	−	0.183399i
$274$	−189.259	−	158.808i	−0.690728	−	0.579589i
$275$	−6.85278	+	25.8976i	−0.0249192	+	0.0941732i
$276$	149.284	+	44.5646i	0.540883	+	0.161466i
$277$	−51.0922	−	60.8893i	−0.184448	−	0.219817i	0.665895	−	0.746046i	$-0.268050\pi$
$277$	−51.0922	−	60.8893i	−0.184448	−	0.219817i	−0.850343	+	0.526229i	$0.823606\pi$
$278$	7.37470	+	12.7734i	0.0265277	+	0.0459473i
$279$	−7.66743	+	135.313i	−0.0274818	+	0.484993i
$280$	−63.7925	+	14.2468i	−0.227830	+	0.0508815i
$281$	456.102	−	80.4231i	1.62314	−	0.286203i	0.713205	−	0.700956i	$-0.247243\pi$
$281$	456.102	−	80.4231i	1.62314	−	0.286203i	0.909934	+	0.414753i	$0.136132\pi$
$282$	−11.5007	+	99.0709i	−0.0407827	+	0.351315i
$283$	−33.0319	−	90.7543i	−0.116720	−	0.320687i	0.867551	−	0.497348i	$-0.165693\pi$
$283$	−33.0319	−	90.7543i	−0.116720	−	0.320687i	−0.984272	+	0.176661i	$0.943470\pi$
$284$	−20.6897	−	56.8444i	−0.0728510	−	0.200156i
$285$	35.1762	+	48.4733i	0.123425	+	0.170082i
$286$	1.13789	+	6.45330i	0.00397864	+	0.0225640i
$287$	−45.7243	+	79.1967i	−0.159318	+	0.275947i
$288$	45.4603	−	22.9207i	0.157848	−	0.0795858i
$289$	138.204	+	239.377i	0.478215	+	0.828293i
$290$	−45.9902	−	5.98181i	−0.158587	−	0.0206269i
$291$	−53.6065	+	179.572i	−0.184215	+	0.617087i
$292$	189.336	+	33.3851i	0.648412	+	0.114333i
$293$	−102.665	−	86.1460i	−0.350392	−	0.294014i	0.450556	−	0.892748i	$-0.351226\pi$
$293$	−102.665	−	86.1460i	−0.350392	−	0.294014i	−0.800947	+	0.598735i	$0.795670\pi$
$294$	64.5108	+	97.9160i	0.219425	+	0.333048i
$295$	108.985	+	261.957i	0.369440	+	0.887990i
$296$			208.061i			0.702908i
$297$	27.1638	−	9.95950i	0.0914606	−	0.0335337i
$298$			26.3165i			0.0883103i
$299$	38.4016	−	105.508i	0.128434	−	0.352868i
$300$	3.77725	−	149.952i	0.0125908	−	0.499841i
$301$	−14.7982	−	12.4172i	−0.0491634	−	0.0412530i
$302$	14.1489	−	80.2425i	0.0468507	−	0.265704i
$303$	−215.283	+	51.2021i	−0.710506	+	0.168984i
$304$	12.2346	−	10.2660i	0.0402454	−	0.0337699i
$305$	474.001	+	148.640i	1.55410	+	0.487344i
$306$	43.9636	+	10.3465i	0.143672	+	0.0338121i
$307$	334.151	+	192.922i	1.08844	+	0.628412i	0.933161	−	0.359459i	$-0.117039\pi$
$307$	334.151	+	192.922i	1.08844	+	0.628412i	0.155280	+	0.987871i	$0.450372\pi$
$308$	1.72004	+	9.75485i	0.00558456	+	0.0316716i
$309$	211.973	−	285.197i	0.685997	−	0.922969i
$310$	49.0209	−	94.5277i	0.158132	−	0.304928i
$311$	−130.645	−	358.944i	−0.420080	−	1.15416i	−0.951660	−	0.307152i	$-0.900624\pi$
$311$	−130.645	−	358.944i	−0.420080	−	1.15416i	0.531580	−	0.847008i	$-0.321598\pi$
$312$	−14.5593	−	33.6793i	−0.0466644	−	0.107947i
$313$	−252.243	+	44.4773i	−0.805889	+	0.142100i	−0.561392	−	0.827550i	$-0.689734\pi$
$313$	−252.243	+	44.4773i	−0.805889	+	0.142100i	−0.244497	+	0.969650i	$0.578623\pi$
$314$	96.0343	+	55.4454i	0.305842	+	0.176578i
$315$	196.243	−	68.9008i	0.622993	−	0.218733i
$316$	140.968	+	244.163i	0.446100	+	0.772667i
$317$	384.299	−	322.465i	1.21230	−	1.01724i	0.213108	−	0.977029i	$-0.431641\pi$
$317$	384.299	−	322.465i	1.21230	−	1.01724i	0.999191	−	0.0402109i	$-0.0128030\pi$
$318$	62.5365	−	59.0932i	0.196656	−	0.185828i
$319$	−1.22042	+	6.92135i	−0.00382577	+	0.0216970i
$320$	−39.9592	+	1.80707i	−0.124872	+	0.00564708i
$321$	184.864	−	368.817i	0.575899	−	1.14896i
$322$	58.0482	−	159.486i	0.180274	−	0.495298i
$323$	14.1683			0.0438646
$324$	−135.068	+	89.4460i	−0.416877	+	0.276068i
$325$	−107.721	−	9.08606i	−0.331449	−	0.0279571i
$326$	56.1150	−	154.175i	0.172132	−	0.472928i
$327$	−247.444	+	493.669i	−0.756709	+	1.50969i
$328$	−35.9721	+	42.8698i	−0.109671	+	0.130701i
$329$	107.002	+	18.8673i	0.325234	+	0.0573475i
$330$	−22.6749	−	1.59842i	−0.0687118	−	0.00484369i
$331$	331.751	−	278.372i	1.00227	−	0.841003i	0.0149708	−	0.999888i	$-0.495234\pi$
$331$	331.751	−	278.372i	1.00227	−	0.841003i	0.987297	+	0.158885i	$0.0507900\pi$
$332$	−114.701	−	198.668i	−0.345486	−	0.598399i
$333$	−77.8936	−	657.447i	−0.233915	−	1.97432i
$334$	−61.7439	+	106.944i	−0.184862	+	0.320190i
$335$	53.8385	−	70.3906i	0.160712	−	0.210121i
$336$	−22.0079	−	50.9099i	−0.0654998	−	0.151518i
$337$	−31.8320	−	87.4577i	−0.0944570	−	0.259518i	0.883462	−	0.468503i	$-0.155206\pi$
$337$	−31.8320	−	87.4577i	−0.0944570	−	0.259518i	−0.977919	+	0.208984i	$0.932984\pi$
$338$	199.740	−	72.6994i	0.590947	−	0.215087i
$339$	−465.237	−	345.788i	−1.37238	−	1.02002i
$340$	−28.1855	−	21.5578i	−0.0828987	−	0.0634053i
$341$	−13.9746	−	8.06824i	−0.0409812	−	0.0236605i
$342$	−34.8165	+	37.0198i	−0.101803	+	0.108245i
$343$	306.759	−	177.107i	0.894340	−	0.516348i
$344$	−7.59878	−	9.05587i	−0.0220895	−	0.0263252i
$345$	322.774	+	217.978i	0.935577	+	0.631821i
$346$	5.23688	−	29.6998i	0.0151355	−	0.0858377i
$347$	−436.091	−	365.924i	−1.25675	−	1.05454i	−0.996021	−	0.0891231i	$-0.971594\pi$
$347$	−436.091	−	365.924i	−1.25675	−	1.05454i	−0.260726	−	0.965413i	$-0.583962\pi$
$348$	−2.31907	−	39.2843i	−0.00666400	−	0.112886i
$349$	−462.810	−	168.449i	−1.32610	−	0.482662i	−0.420694	−	0.907203i	$-0.638213\pi$
$349$	−462.810	−	168.449i	−1.32610	−	0.482662i	−0.905409	+	0.424541i	$0.860435\pi$
$350$	−162.832	−	13.7345i	−0.465234	−	0.0392416i
$351$	58.6144	+	100.972i	0.166993	+	0.287669i
$352$			6.06164i			0.0172206i
$353$	224.391	+	81.6716i	0.635668	+	0.231364i	0.639696	−	0.768628i	$-0.279060\pi$
$353$	224.391	+	81.6716i	0.635668	+	0.231364i	−0.00402848	+	0.999992i	$0.501282\pi$
$354$	−201.038	+	132.451i	−0.567903	+	0.374156i
$355$	−6.83213	−	151.077i	−0.0192454	−	0.425569i
$356$	95.6474	+	16.8652i	0.268672	+	0.0473742i
$357$	14.0743	−	47.1465i	0.0394238	−	0.132063i
$358$	−187.147	−	223.033i	−0.522756	−	0.622997i
$359$	−117.184	+	67.6561i	−0.326417	+	0.188457i	−0.654249	−	0.756279i	$-0.727015\pi$
$359$	−117.184	+	67.6561i	−0.326417	+	0.188457i	0.327832	+	0.944736i	$0.393682\pi$
$360$	125.590	−	20.6700i	0.348860	−	0.0574166i
$361$	172.529	−	298.829i	0.477919	−	0.827780i
$362$	−37.7704	−	214.207i	−0.104338	−	0.591732i
$363$	41.4608	−	357.157i	0.114217	−	0.983903i
$364$	−37.5612	+	13.6712i	−0.103190	+	0.0375581i
$365$	426.681	+	221.271i	1.16899	+	0.606223i
$366$	−48.6054	+	418.703i	−0.132802	+	1.14400i
$367$	623.967	−	110.022i	1.70018	−	0.299788i	0.762425	−	0.647076i	$-0.224008\pi$
$367$	623.967	−	110.022i	1.70018	−	0.299788i	0.937759	+	0.347288i	$0.112897\pi$
$368$	51.9312	−	89.9474i	0.141117	−	0.244422i
$369$	97.6179	−	148.931i	0.264547	−	0.403606i
$370$	−155.639	+	496.321i	−0.420647	+	1.34141i
$371$	−60.2495	−	71.8026i	−0.162398	−	0.193538i
$372$	86.5780	+	25.8455i	0.232737	+	0.0694772i
$373$	−452.136	−	79.7237i	−1.21216	−	0.213737i	−0.469212	−	0.883085i	$-0.655462\pi$
$373$	−452.136	−	79.7237i	−1.21216	−	0.213737i	−0.742948	+	0.669349i	$0.766573\pi$
$374$	−3.45652	+	4.11932i	−0.00924203	+	0.0110142i
$375$	121.182	−	354.880i	0.323152	−	0.946347i
$376$	62.4809	+	22.7412i	0.166173	+	0.0604819i
$377$	−28.3611			−0.0752284
$378$	88.6020	+	152.630i	0.234397	+	0.403783i
$379$	−227.796			−0.601044			−0.300522	−	0.953775i	$-0.597161\pi$
$379$	−227.796			−0.601044			−0.300522	+	0.953775i	$0.597161\pi$
$380$	36.8646	−	15.3372i	0.0970122	−	0.0403611i
$381$	23.1617	+	392.352i	0.0607918	+	1.02979i
$382$	25.1124	−	29.9278i	0.0657393	−	0.0783450i
$383$	−37.9240	+	215.078i	−0.0990184	+	0.561561i	0.894423	+	0.447221i	$0.147586\pi$
$383$	−37.9240	+	215.078i	−0.0990184	+	0.561561i	−0.993442	+	0.114340i	$0.963525\pi$
$384$	−7.85335	−	33.0201i	−0.0204514	−	0.0859898i
$385$	−3.19399	+	24.5565i	−0.00829608	+	0.0637831i
$386$	−387.201	+	223.551i	−1.00311	+	0.579147i
$387$	27.4015	+	25.7706i	0.0708050	+	0.0665908i
$388$	108.197	+	62.4677i	0.278859	+	0.160999i
$389$	−511.203	+	90.1389i	−1.31415	+	0.231719i	−0.786418	−	0.617694i	$-0.788067\pi$
$389$	−511.203	+	90.1389i	−1.31415	+	0.231719i	−0.527728	+	0.849414i	$0.676956\pi$
$390$	−9.53690	−	91.2317i	−0.0244536	−	0.233928i
$391$	86.5815	−	31.5131i	0.221436	−	0.0805962i
$392$	73.4570	−	26.7362i	0.187390	−	0.0682045i
$393$	31.7535	+	73.4540i	0.0807978	+	0.186906i
$394$	−9.60312	−	54.4620i	−0.0243734	−	0.138228i
$395$	153.627	+	687.892i	0.388930	+	1.74150i
$396$	−2.26935	−	19.1541i	−0.00573069	−	0.0483689i
$397$	183.568	−	105.983i	0.462388	−	0.266960i	−0.250660	−	0.968075i	$-0.580648\pi$
$397$	183.568	−	105.983i	0.462388	−	0.266960i	0.713048	+	0.701115i	$0.247314\pi$
$398$	−283.815	+	238.149i	−0.713103	+	0.598364i
$399$	38.0242	+	40.2398i	0.0952986	+	0.100852i
$400$	−96.6728	−	25.5806i	−0.241682	−	0.0639516i
$401$	−329.307	+	392.453i	−0.821214	+	0.978685i	−0.999986	−	0.00520541i	$-0.998343\pi$
$401$	−329.307	+	392.453i	−0.821214	+	0.978685i	0.178772	+	0.983891i	$0.442788\pi$
$402$	67.2243	+	33.6951i	0.167225	+	0.0838187i
$403$	22.2713	−	61.1898i	0.0552637	−	0.151836i
$404$			147.526i			0.365163i
$405$	−389.110	+	112.333i	−0.960765	+	0.277365i
$406$	−42.8709			−0.105593
$407$	74.0708	+	26.9595i	0.181992	+	0.0662397i
$408$	13.4921	−	26.9177i	0.0330688	−	0.0659748i
$409$	−173.348	−	145.457i	−0.423835	−	0.355640i	0.405785	−	0.913969i	$-0.366998\pi$
$409$	−173.348	−	145.457i	−0.423835	−	0.355640i	−0.829620	+	0.558329i	$0.811443\pi$
$410$	−117.879	+	75.3556i	−0.287509	+	0.183794i
$411$	380.930	−	359.955i	0.926836	−	0.875804i
$412$	−152.274	−	181.473i	−0.369598	−	0.440469i
$413$	131.135	+	227.133i	0.317519	+	0.549959i
$414$	−130.422	+	303.665i	−0.315029	+	0.733490i
$415$	−125.002	−	559.717i	−0.301210	−	1.34872i
$416$	−24.0894	+	4.24761i	−0.0579072	+	0.0102106i
$417$	−28.7196	+	12.4152i	−0.0688719	+	0.0297727i
$418$	−2.06946	−	5.68581i	−0.00495087	−	0.0136024i
$419$	−48.7527	−	133.947i	−0.116355	−	0.319683i	0.867821	−	0.496877i	$-0.165520\pi$
$419$	−48.7527	−	133.947i	−0.116355	−	0.319683i	−0.984176	+	0.177194i	$0.943298\pi$
$420$	−14.4160	−	137.907i	−0.0343239	−	0.328349i
$421$	−39.3615	−	223.230i	−0.0934952	−	0.530237i	−0.995198	−	0.0978813i	$-0.968793\pi$
$421$	−39.3615	−	223.230i	−0.0934952	−	0.530237i	0.901703	−	0.432356i	$-0.142318\pi$
$422$	−141.447	+	244.994i	−0.335183	+	0.580554i
$423$	−205.946	−	48.4679i	−0.486870	−	0.114581i
$424$	−28.6799	−	49.6750i	−0.0676412	−	0.117158i
$425$	−51.1093	−	72.5094i	−0.120257	−	0.170610i
$426$	124.842	−	29.6918i	0.293056	−	0.0696991i
$427$	452.222	+	79.7390i	1.05907	+	0.186742i
$428$	−210.690	−	176.790i	−0.492266	−	0.413060i
$429$	−13.8765	+	0.819173i	−0.0323462	+	0.00190950i
$430$	−11.3524	−	27.2867i	−0.0264009	−	0.0634574i
$431$			152.951i			0.354875i	0.984132	+	0.177438i	$0.0567808\pi$
$431$			152.951i			0.354875i	−0.984132	+	0.177438i	$0.943219\pi$
$432$	37.1777	+	101.399i	0.0860594	+	0.234721i
$433$			629.659i			1.45418i	0.686544	+	0.727088i	$0.259127\pi$
$433$			629.659i			1.45418i	−0.686544	+	0.727088i	$0.740873\pi$
$434$	33.6654	−	92.4949i	0.0775700	−	0.213122i
$435$	23.8545	−	95.4460i	0.0548379	−	0.219416i
$436$	282.012	+	236.637i	0.646817	+	0.542744i
$437$	−18.0030	+	102.100i	−0.0411967	+	0.233638i
$438$	−116.662	+	390.797i	−0.266352	+	0.892232i
$439$	−148.127	+	124.293i	−0.337418	+	0.283128i	−0.795714	−	0.605672i	$-0.792904\pi$
$439$	−148.127	+	124.293i	−0.337418	+	0.283128i	0.458296	+	0.888800i	$0.348460\pi$
$440$	−4.53440	+	14.4598i	−0.0103054	+	0.0328632i
$441$	−222.106	+	111.984i	−0.503641	+	0.253932i
$442$	−18.7926	−	10.8499i	−0.0425172	−	0.0245473i
$443$	86.3303	+	489.603i	0.194876	+	1.10520i	0.912595	+	0.408865i	$0.134075\pi$
$443$	86.3303	+	489.603i	0.194876	+	1.10520i	−0.717718	+	0.696334i	$0.754813\pi$
$444$	−438.420	−	50.8942i	−0.987432	−	0.114627i
$445$	215.547	+	111.780i	0.484376	+	0.251191i
$446$	−182.705	−	501.977i	−0.409652	−	1.12551i
$447$	−55.4533	−	6.43733i	−0.124057	−	0.0144012i
$448$	−36.4137	+	6.42072i	−0.0812806	+	0.0143320i
$449$	117.872	+	68.0535i	0.262522	+	0.151567i	0.625484	−	0.780237i	$-0.284901\pi$
$449$	117.872	+	68.0535i	0.262522	+	0.151567i	−0.362963	+	0.931804i	$0.618235\pi$
$450$	315.051	+	44.6395i	0.700114	+	0.0991989i
$451$	10.6008	+	18.3611i	0.0235051	+	0.0407120i
$452$	−296.034	+	248.402i	−0.654943	+	0.549562i
$453$	165.624	+	49.4425i	0.365615	+	0.109145i
$454$	87.0727	−	493.814i	0.191790	−	1.08770i
$455$	−99.8274	+	4.51448i	−0.219401	+	0.00992192i
$456$	18.6396	+	28.2916i	0.0408762	+	0.0620429i
$457$	−86.2525	+	236.977i	−0.188736	+	0.518549i	−0.997584	−	0.0694692i	$-0.977869\pi$
$457$	−86.2525	+	236.977i	−0.188736	+	0.518549i	0.808848	+	0.588018i	$0.200092\pi$
$458$	−175.240			−0.382619
$459$	−32.5559	+	90.1078i	−0.0709278	+	0.196313i
$460$	191.165	−	175.719i	0.415575	−	0.381998i
$461$	−207.319	+	569.604i	−0.449716	+	1.23558i	0.483207	+	0.875506i	$0.339472\pi$
$461$	−207.319	+	569.604i	−0.449716	+	1.23558i	−0.932922	+	0.360078i	$0.882750\pi$
$462$	−20.9759	+	1.23827i	−0.0454023	+	0.00268023i
$463$	−244.529	+	291.418i	−0.528140	+	0.629413i	−0.962485	−	0.271334i	$-0.912535\pi$
$463$	−244.529	+	291.418i	−0.528140	+	0.629413i	0.434345	+	0.900746i	$0.356980\pi$
$464$	−25.8366	−	4.55569i	−0.0556823	−	0.00981829i
$465$	187.195	+	126.418i	0.402569	+	0.271867i
$466$	45.2584	−	37.9763i	0.0971210	−	0.0814942i
$467$	−98.5150	−	170.633i	−0.210953	−	0.365381i	0.741060	−	0.671439i	$-0.234323\pi$
$467$	−98.5150	−	170.633i	−0.210953	−	0.365381i	−0.952013	+	0.306058i	$0.900990\pi$
$468$	74.5294	−	22.4405i	0.159251	−	0.0479498i
$469$	40.9594	−	70.9437i	0.0873334	−	0.151266i
$470$	132.034	+	100.987i	0.280924	+	0.214866i
$471$	−140.324	+	188.798i	−0.297928	+	0.400845i
$472$	54.8937	+	150.819i	0.116300	+	0.319532i
$473$	−4.20855	+	1.53179i	−0.00889757	+	0.00323845i
$474$	−548.975	+	237.317i	−1.15818	+	0.500669i
$475$	99.4121	−	9.00982i	0.209289	−	0.0189680i
$476$	−28.4070	−	16.4008i	−0.0596786	−	0.0344554i
$477$	109.222	+	146.230i	0.228978	+	0.306562i
$478$	−415.932	+	240.138i	−0.870150	+	0.502381i
$479$	−373.346	−	444.937i	−0.779429	−	0.928887i	0.219479	−	0.975617i	$-0.429564\pi$
$479$	−373.346	−	444.937i	−0.779429	−	0.928887i	−0.998908	+	0.0467303i	$0.985120\pi$
$480$	5.96670	−	84.6428i	0.0124306	−	0.176339i
$481$	−55.2351	+	313.254i	−0.114834	+	0.651256i
$482$	−42.4397	−	35.6111i	−0.0880491	−	0.0738819i
$483$	321.865	+	161.330i	0.666387	+	0.334016i
$484$	−225.248	−	81.9834i	−0.465388	−	0.169387i
$485$	211.371	+	229.951i	0.435817	+	0.474125i
$486$	−155.439	−	306.491i	−0.319833	−	0.630640i
$487$			60.5966i			0.124428i	0.998063	+	0.0622141i	$0.0198162\pi$
$487$			60.5966i			0.124428i	−0.998063	+	0.0622141i	$0.980184\pi$
$488$	264.063	+	96.1111i	0.541113	+	0.196949i
$489$	311.146	+	155.957i	0.636290	+	0.318930i
$490$	195.229	−	8.82879i	0.398426	−	0.0180179i
$491$	706.057	+	124.497i	1.43800	+	0.253558i	0.837662	−	0.546189i	$-0.183922\pi$
$491$	706.057	+	124.497i	1.43800	+	0.253558i	0.600337	+	0.799747i	$0.295033\pi$
$492$	−81.5348	−	86.2858i	−0.165721	−	0.175378i
$493$	−14.9600	−	17.8287i	−0.0303449	−	0.0361636i
$494$	21.1457	−	12.2084i	0.0428050	−	0.0247135i
$495$	8.91469	−	47.3889i	0.0180095	−	0.0957351i
$496$	30.1178	−	52.1656i	0.0607214	−	0.105173i
$497$	−24.2754	−	137.673i	−0.0488438	−	0.277007i
$498$	446.685	−	193.098i	0.896958	−	0.387747i
$499$	−7.68258	+	2.79623i	−0.0153959	+	0.00560367i	−0.349707	−	0.936859i	$-0.613719\pi$
$499$	−7.68258	+	2.79623i	−0.0153959	+	0.00560367i	0.334311	+	0.942463i	$0.391497\pi$
$500$	−211.474	−	133.337i	−0.422947	−	0.266675i
$501$	−210.245	−	156.265i	−0.419651	−	0.311905i
$502$	337.235	−	59.4637i	0.671783	−	0.118453i
$503$	−98.7718	+	171.078i	−0.196365	+	0.340115i	−0.947347	−	0.320208i	$-0.896247\pi$
$503$	−98.7718	+	171.078i	−0.196365	+	0.340115i	0.750982	+	0.660323i	$0.229581\pi$
$504$	112.659	−	33.9212i	0.223530	−	0.0673041i
$505$	−110.356	+	351.917i	−0.218527	+	0.696865i
$506$	−25.2928	−	30.1427i	−0.0499857	−	0.0595706i
$507$	104.331	+	438.669i	0.205781	+	0.865225i
$508$	258.042	+	45.4998i	0.507957	+	0.0895666i
$509$	−474.663	+	565.681i	−0.932540	+	1.11136i	0.0610294	+	0.998136i	$0.480562\pi$
$509$	−474.663	+	565.681i	−0.932540	+	1.11136i	−0.993570	+	0.113222i	$0.963883\pi$
$510$	52.3205	−	54.1184i	0.102589	−	0.106115i
$511$	417.505	+	151.960i	0.817036	+	0.297377i
$512$	−22.6274			−0.0441942
$513$	−69.4906	−	82.4197i	−0.135459	−	0.160662i
$514$	286.690			0.557763
$515$	−227.494	−	546.806i	−0.441735	−	1.06176i
$516$	20.9410	−	13.7967i	0.0405833	−	0.0267379i
$517$	16.1920	−	19.2968i	0.0313191	−	0.0373246i
$518$	−83.4938	+	473.517i	−0.161185	+	0.914125i
$519$	61.3016	+	18.2999i	0.118115	+	0.0352600i
$520$	−60.6418	−	7.88749i	−0.116619	−	0.0151683i
$521$	−466.322	+	269.231i	−0.895052	+	0.516759i	−0.875592	−	0.483052i	$-0.839528\pi$
$521$	−466.322	+	269.231i	−0.895052	+	0.516759i	−0.0194606	+	0.999811i	$0.506195\pi$
$522$	83.3460	+	4.72275i	0.159667	+	0.00904741i
$523$	172.624	+	99.6647i	0.330066	+	0.190563i	0.655870	−	0.754874i	$-0.272302\pi$
$523$	172.624	+	99.6647i	0.330066	+	0.190563i	−0.325805	+	0.945437i	$0.605635\pi$
$524$	52.5386	−	9.26397i	0.100264	−	0.0176793i
$525$	68.7717	−	339.755i	0.130994	−	0.647152i
$526$	393.469	−	143.211i	0.748040	−	0.272264i
$527$	50.2135	−	18.2762i	0.0952818	−	0.0346797i
$528$	−12.7729	−	1.48275i	−0.0241911	−	0.00280824i
$529$	25.2158	+	143.006i	0.0476668	+	0.270332i
$530$	−31.2555	−	139.952i	−0.0589727	−	0.264060i
$531$	−229.921	−	456.020i	−0.432996	−	0.858794i
$532$	31.9639	−	18.4544i	0.0600825	−	0.0346887i
$533$	−65.5400	+	54.9946i	−0.122964	+	0.103179i
$534$	−58.9344	+	197.420i	−0.110364	+	0.369700i
$535$	−370.345	−	579.331i	−0.692234	−	1.08286i
$536$	32.2235	−	38.4024i	0.0601184	−	0.0716463i
$537$	515.746	−	339.793i	0.960421	−	0.632762i
$538$	227.209	−	624.251i	0.422321	−	1.16032i
$539$		−	29.6154i		−	0.0549451i
$540$	12.8344	+	269.695i	0.0237674	+	0.499435i
$541$	−591.082			−1.09257			−0.546286	−	0.837598i	$-0.683959\pi$
$541$	−591.082			−1.09257			−0.546286	+	0.837598i	$0.683959\pi$
$542$	−521.274	−	189.728i	−0.961759	−	0.350052i
$543$	460.609	−	27.1911i	0.848268	−	0.0500758i
$544$	−15.3769	−	12.9028i	−0.0282665	−	0.0237184i
$545$	495.714	+	775.446i	0.909568	+	1.42284i
$546$	−19.6195	−	82.4919i	−0.0359332	−	0.151084i
$547$	563.089	+	671.063i	1.02941	+	1.22681i	0.973575	+	0.228366i	$0.0733384\pi$
$547$	563.089	+	671.063i	1.02941	+	1.22681i	0.0558374	+	0.998440i	$0.482217\pi$
$548$	−174.698	−	302.586i	−0.318792	−	0.552165i
$549$	−870.390	−	204.840i	−1.58541	−	0.373115i
$550$	−21.6332	+	31.1014i	−0.0393332	+	0.0565480i
$551$	25.7900	−	4.54747i	0.0468057	−	0.00825312i
$552$	176.832	+	131.430i	0.320347	+	0.238098i
$553$	222.841	+	612.250i	0.402967	+	1.10714i
$554$	−38.4462	−	105.630i	−0.0693975	−	0.190668i
$555$	−1007.76	−	449.365i	−1.81579	−	0.809666i
$556$	3.62209	+	20.5419i	0.00651456	+	0.0369459i
$557$	358.559	−	621.042i	0.643732	−	1.11498i	−0.340861	−	0.940114i	$-0.610719\pi$
$557$	358.559	−	621.042i	0.643732	−	1.11498i	0.984593	−	0.174863i	$-0.0559482\pi$
$558$	−75.6390	+	176.112i	−0.135554	+	0.315614i
$559$	−9.03651	−	15.6517i	−0.0161655	−	0.0279995i
$560$	−91.6665	−	11.9228i	−0.163690	−	0.0212907i
$561$	−7.83460	−	8.29111i	−0.0139654	−	0.0147792i
$562$	645.026	+	113.735i	1.14773	+	0.202376i
$563$	−695.355	−	583.472i	−1.23509	−	1.03636i	−0.997892	−	0.0649007i	$-0.979327\pi$
$563$	−695.355	−	583.472i	−1.23509	−	1.03636i	−0.237197	−	0.971462i	$-0.576229\pi$
$564$	−63.2032	+	126.095i	−0.112062	+	0.223573i
$565$	−891.994	+	371.106i	−1.57875	+	0.656825i
$566$		−	136.583i		−	0.241313i
$567$	−343.290	+	149.364i	−0.605450	+	0.263429i
$568$		−	85.5494i		−	0.150615i
$569$	−167.091	+	459.080i	−0.293658	+	0.806818i	0.701866	+	0.712309i	$0.252351\pi$
$569$	−167.091	+	459.080i	−0.293658	+	0.806818i	−0.995524	+	0.0945095i	$0.969872\pi$
$570$	23.3005	+	81.4317i	0.0408782	+	0.142863i
$571$	660.748	+	554.433i	1.15718	+	0.970986i	0.999863	−	0.0165622i	$-0.00527216\pi$
$571$	660.748	+	554.433i	1.15718	+	0.970986i	0.157314	+	0.987549i	$0.449717\pi$
$572$	−1.60922	+	9.12634i	−0.00281332	+	0.0159551i
$573$	56.9201	+	60.2368i	0.0993371	+	0.105125i
$574$	−99.0708	+	83.1303i	−0.172597	+	0.144826i
$575$	587.462	−	276.171i	1.02167	−	0.480298i
$576$	71.4999	−	8.47123i	0.124132	−	0.0147070i
$577$	−548.088	−	316.439i	−0.949893	−	0.548421i	−0.0568452	−	0.998383i	$-0.518104\pi$
$577$	−548.088	−	316.439i	−0.949893	−	0.548421i	−0.893048	+	0.449962i	$0.851437\pi$
$578$	67.8792	+	384.962i	0.117438	+	0.666024i
$579$	−376.345	−	870.582i	−0.649992	−	1.50360i
$580$	−58.2243	−	30.1944i	−0.100387	−	0.0520593i
$581$	−181.319	−	498.170i	−0.312081	−	0.857435i
$582$	−158.096	+	212.709i	−0.271643	+	0.365480i
$583$	−21.4008	+	3.77353i	−0.0367080	+	0.00647261i
$584$	235.466	+	135.946i	0.403195	+	0.232785i
$585$	194.574	+	2.22053i	0.332604	+	0.00379578i
$586$	−94.7660	−	164.140i	−0.161717	−	0.280102i
$587$	−354.795	+	297.708i	−0.604420	+	0.507169i	−0.892863	−	0.450328i	$-0.851307\pi$
$587$	−354.795	+	297.708i	−0.604420	+	0.507169i	0.288443	+	0.957497i	$0.406863\pi$
$588$	38.3692	+	161.326i	0.0652537	+	0.274365i
$589$	−10.4409	+	59.2135i	−0.0177265	+	0.100532i
$590$	18.1270	+	400.836i	0.0307236	+	0.679384i
$591$	117.110	−	6.91333i	0.198155	−	0.0116977i
$592$	−100.637	+	276.498i	−0.169995	+	0.467057i
$593$	445.732			0.751655			0.375828	−	0.926690i	$-0.377358\pi$
$593$	445.732			0.751655			0.375828	+	0.926690i	$0.377358\pi$
$594$	40.9160	−	0.0965927i	0.0688821	−	0.000162614i
$595$	−55.4953	−	60.3732i	−0.0932693	−	0.101468i
$596$	−12.7290	+	34.9726i	−0.0213574	+	0.0586789i
$597$	−432.396	−	656.300i	−0.724281	−	1.09933i
$598$	102.066	−	121.637i	0.170679	−	0.203407i
$599$	216.681	+	38.2067i	0.361738	+	0.0637842i	0.351563	−	0.936164i	$-0.385650\pi$
$599$	216.681	+	38.2067i	0.361738	+	0.0637842i	0.0101746	+	0.999948i	$0.496761\pi$
$600$	77.5501	−	197.449i	0.129250	−	0.329081i
$601$	498.049	−	417.913i	0.828701	−	0.695363i	−0.126291	−	0.991993i	$-0.540307\pi$
$601$	498.049	−	417.913i	0.828701	−	0.695363i	0.954992	+	0.296631i	$0.0958630\pi$
$602$	−13.6597	−	23.6592i	−0.0226905	−	0.0393010i
$603$	−87.4452	+	133.411i	−0.145017	+	0.221245i
$604$	57.6153	−	99.7927i	0.0953896	−	0.165220i
$605$	−475.992	−	364.064i	−0.786764	−	0.601759i
$606$	−310.862	−	36.0866i	−0.512973	−	0.0595488i
$607$	−96.3398	−	264.691i	−0.158715	−	0.436065i	0.834691	−	0.550719i	$-0.185646\pi$
$607$	−96.3398	−	264.691i	−0.158715	−	0.436065i	−0.993406	+	0.114654i	$0.963424\pi$
$608$	21.2245	−	7.72507i	0.0349086	−	0.0127057i
$609$	10.4867	−	90.3362i	0.0172196	−	0.148335i
$610$	558.017	+	426.801i	0.914781	+	0.699674i
$611$	88.0333	+	50.8261i	0.144081	+	0.0831850i
$612$	53.4198	+	35.0145i	0.0872873	+	0.0572132i
$613$	−77.2621	+	44.6073i	−0.126039	+	0.0727688i	−0.561694	−	0.827345i	$-0.689850\pi$
$613$	−77.2621	+	44.6073i	−0.126039	+	0.0727688i	0.435655	+	0.900114i	$0.356517\pi$
$614$	350.748	+	418.005i	0.571251	+	0.680790i
$615$	−129.952	−	266.823i	−0.211305	−	0.433859i
$616$	−2.43251	+	13.7954i	−0.00394888	+	0.0223952i
$617$	−633.227	−	531.341i	−1.02630	−	0.861168i	−0.0358940	−	0.999356i	$-0.511428\pi$
$617$	−633.227	−	531.341i	−1.02630	−	0.861168i	−0.990406	+	0.138188i	$0.955872\pi$
$618$	419.643	−	276.477i	0.679034	−	0.447374i
$619$	444.393	+	161.746i	0.717921	+	0.261302i	0.675043	−	0.737778i	$-0.264125\pi$
$619$	444.393	+	161.746i	0.717921	+	0.261302i	0.0428782	+	0.999080i	$0.486347\pi$
$620$	110.867	−	101.909i	0.178818	−	0.164370i
$621$	−607.971	−	349.101i	−0.979019	−	0.562160i
$622$		−	540.201i		−	0.868491i
$623$	210.912	+	76.7657i	0.338542	+	0.123219i
$624$	−3.05788	−	51.7995i	−0.00490045	−	0.0830120i
$625$	−404.720	−	476.264i	−0.647551	−	0.762022i
$626$	−356.726	−	62.9004i	−0.569850	−	0.100480i
$627$	12.4872	−	2.96989i	0.0199157	−	0.00473667i
$628$	100.804	+	120.134i	0.160516	+	0.191296i
$629$	−226.057	+	130.514i	−0.359391	+	0.207494i
$630$	294.119	+	3.35657i	0.466855	+	0.00532789i
$631$	153.935	−	266.623i	0.243954	−	0.422541i	−0.717883	−	0.696164i	$-0.754889\pi$
$631$	153.935	−	266.623i	0.243954	−	0.422541i	0.961837	+	0.273623i	$0.0882221\pi$
$632$	69.2364	+	392.659i	0.109551	+	0.621296i
$633$	−481.643	−	357.982i	−0.760890	−	0.565532i
$634$	666.678	−	242.651i	1.05154	−	0.382730i
$635$	581.514	+	301.566i	0.915770	+	0.474907i
$636$	111.689	−	48.2823i	0.175612	−	0.0759155i
$637$	117.694	−	20.7526i	0.184763	−	0.0325786i
$638$	−4.96963	+	8.60765i	−0.00778939	+	0.0134916i
$639$	32.0279	+	270.326i	0.0501219	+	0.423045i
$640$	−53.9768	−	16.9264i	−0.0843388	−	0.0264475i
$641$	691.601	+	824.218i	1.07894	+	1.28583i	0.955984	+	0.293420i	$0.0947933\pi$
$641$	691.601	+	824.218i	1.07894	+	1.28583i	0.122957	+	0.992412i	$0.460762\pi$
$642$	424.063	−	400.714i	0.660535	−	0.624165i
$643$	124.519	+	21.9560i	0.193653	+	0.0341462i	0.269633	−	0.962963i	$-0.413098\pi$
$643$	124.519	+	21.9560i	0.193653	+	0.0341462i	−0.0759805	+	0.997109i	$0.524209\pi$
$644$	154.283	−	183.868i	0.239571	−	0.285509i
$645$	60.2746	−	17.2467i	0.0934489	−	0.0267391i
$646$	18.8286	+	6.85304i	0.0291464	+	0.0106084i
$647$	382.577			0.591309			0.295655	−	0.955295i	$-0.404462\pi$
$647$	382.577			0.591309			0.295655	+	0.955295i	$0.404462\pi$
$648$	−222.760	+	53.5361i	−0.343765	+	0.0826175i
$649$	60.8053			0.0936907
$650$	−138.758	−	64.1782i	−0.213474	−	0.0987357i
$651$	186.668	+	93.5641i	0.286740	+	0.143724i
$652$	149.145	−	177.744i	0.228751	−	0.272614i
$653$	−33.0429	+	187.395i	−0.0506016	+	0.286976i	−0.999599	−	0.0283071i	$-0.990988\pi$
$653$	−33.0429	+	187.395i	−0.0506016	+	0.286976i	0.948998	+	0.315283i	$0.102099\pi$
$654$	−567.617	+	536.364i	−0.867916	+	0.820128i
$655$	132.259	+	17.2025i	0.201922	+	0.0262633i
$656$	−68.5399	+	39.5715i	−0.104482	+	0.0603225i
$657$	−794.940	−	341.421i	−1.20995	−	0.519666i
$658$	133.072	+	76.8290i	0.202237	+	0.116761i
$659$	−427.876	+	75.4460i	−0.649280	+	0.114486i	−0.488582	−	0.872518i	$-0.662486\pi$
$659$	−427.876	+	75.4460i	−0.649280	+	0.114486i	−0.160698	+	0.987004i	$0.551375\pi$
$660$	−29.3601	−	13.0918i	−0.0444850	−	0.0198360i
$661$	−181.820	+	66.1771i	−0.275068	+	0.100117i	−0.475871	−	0.879515i	$-0.657867\pi$
$661$	−181.820	+	66.1771i	−0.275068	+	0.100117i	0.200803	+	0.979632i	$0.435645\pi$
$662$	575.518	−	209.471i	0.869362	−	0.316422i
$663$	27.4595	−	36.9452i	0.0414170	−	0.0557242i
$664$	−56.3356	−	319.495i	−0.0848428	−	0.481168i
$665$	90.0534	−	20.1117i	0.135419	−	0.0302431i
$666$	214.486	−	911.375i	0.322050	−	1.36843i
$667$	147.487	−	85.1514i	0.221119	−	0.127663i
$668$	−133.781	+	112.255i	−0.200270	+	0.168047i
$669$	1102.44	−	262.200i	1.64790	−	0.391928i
$670$	105.595	−	67.5028i	0.157604	−	0.100750i
$671$	68.4321	−	81.5542i	0.101985	−	0.121541i
$672$	−4.62231	−	78.3005i	−0.00687844	−	0.116519i
$673$	75.5149	−	207.475i	0.112206	−	0.308284i	−0.870861	−	0.491530i	$-0.836438\pi$
$673$	75.5149	−	207.475i	0.112206	−	0.308284i	0.983067	+	0.183245i	$0.0586602\pi$
$674$		−	131.622i		−	0.195284i
$675$	−171.128	+	652.947i	−0.253524	+	0.967329i
$676$	300.604			0.444680
$677$	−334.532	−	121.760i	−0.494139	−	0.179852i	0.0829172	−	0.996556i	$-0.473576\pi$
$677$	−334.532	−	121.760i	−0.494139	−	0.179852i	−0.577056	+	0.816705i	$0.695799\pi$
$678$	−451.012	−	684.556i	−0.665209	−	1.00967i
$679$	221.173	+	185.587i	0.325734	+	0.273323i
$680$	−27.0292	−	42.2818i	−0.0397489	−	0.0621791i
$681$	1019.25	+	304.270i	1.49670	+	0.446799i
$682$	−14.6687	−	17.4815i	−0.0215083	−	0.0256326i
$683$	−355.821	−	616.301i	−0.520968	−	0.902343i	−0.999703	−	0.0243837i	$-0.992238\pi$
$683$	−355.821	−	616.301i	−0.520968	−	0.902343i	0.478734	−	0.877960i	$-0.341096\pi$
$684$	−64.1746	+	32.3563i	−0.0938225	+	0.0473045i
$685$	−190.387	−	852.490i	−0.277937	−	1.24451i
$686$	493.325	−	86.9864i	0.719132	−	0.126802i
$687$	42.8657	−	369.260i	0.0623956	−	0.537496i
$688$	−5.71798	−	15.7100i	−0.00831102	−	0.0228343i
$689$	−29.9926	−	82.4039i	−0.0435306	−	0.119599i
$690$	323.509	+	445.800i	0.468854	+	0.646086i
$691$	8.39997	+	47.6386i	0.0121563	+	0.0689415i	0.990282	−	0.139071i	$-0.0444116\pi$
$691$	8.39997	+	47.6386i	0.0121563	+	0.0689415i	−0.978126	+	0.208013i	$0.933301\pi$
$692$	21.3249	−	36.9359i	0.0308164	−	0.0533755i
$693$	2.52171	−	44.5026i	0.00363883	−	0.0642173i
$694$	−402.539	−	697.219i	−0.580028	−	1.00464i
$695$	−6.72596	+	51.7115i	−0.00967763	+	0.0744050i
$696$	15.9195	−	53.3277i	0.0228729	−	0.0766202i
$697$	−69.1426	−	12.1917i	−0.0992003	−	0.0174917i
$698$	−533.563	−	447.712i	−0.764417	−	0.641422i
$699$	68.9518	+	104.657i	0.0986434	+	0.149723i
$700$	−209.748	−	97.0122i	−0.299640	−	0.138589i
$701$			1245.33i			1.77650i	0.459356	+	0.888252i	$0.348080\pi$
$701$			1245.33i			1.77650i	−0.459356	+	0.888252i	$0.651920\pi$
$702$	29.0552	+	162.535i	0.0413891	+	0.231532i
$703$		−	293.712i		−	0.417797i
$704$	−2.93195	+	8.05548i	−0.00416471	+	0.0114424i
$705$	−245.094	+	253.516i	−0.347651	+	0.359597i
$706$	258.695	+	217.071i	0.366424	+	0.307466i
$707$	−59.2013	+	335.747i	−0.0837360	+	0.474890i
$708$	−331.229	+	78.7781i	−0.467838	+	0.111269i
$709$	−607.872	+	510.065i	−0.857365	+	0.719414i	−0.961399	−	0.275159i	$-0.911269\pi$
$709$	−607.872	+	510.065i	−0.857365	+	0.719414i	0.104034	+	0.994574i	$0.466825\pi$
$710$	63.9950	−	204.075i	0.0901338	−	0.287429i
$711$	−365.782	−	1214.83i	−0.514461	−	1.70863i
$712$	118.951	+	68.6763i	0.167066	+	0.0964554i
$713$	67.8987	+	385.073i	0.0952297	+	0.540074i
$714$	41.5080	−	55.8466i	0.0581344	−	0.0782165i
$715$	−10.6657	+	20.5668i	−0.0149170	+	0.0287647i
$716$	−140.826	−	386.915i	−0.196684	−	0.540384i
$717$	−404.270	−	935.179i	−0.563836	−	1.30429i
$718$	−188.453	+	33.2294i	−0.262470	+	0.0462805i
$719$	1102.57	+	636.567i	1.53347	+	0.885351i	0.999198	+	0.0400397i	$0.0127484\pi$
$719$	1102.57	+	636.567i	1.53347	+	0.885351i	0.534274	+	0.845311i	$0.320585\pi$
$720$	176.897	+	33.2775i	0.245691	+	0.0462188i
$721$	−273.730	−	474.114i	−0.379653	−	0.657579i
$722$	373.818	−	313.671i	0.517754	−	0.434447i
$723$	85.4199	−	80.7167i	0.118146	−	0.111641i
$724$	53.4155	−	302.934i	0.0737783	−	0.418417i
$725$	−116.305	−	115.582i	−0.160421	−	0.159424i
$726$	227.851	−	454.581i	0.313845	−	0.626144i
$727$	−344.118	+	945.456i	−0.473340	+	1.30049i	0.441713	+	0.897156i	$0.354371\pi$
$727$	−344.118	+	945.456i	−0.473340	+	1.30049i	−0.915053	+	0.403334i	$0.867851\pi$
$728$	−56.5286			−0.0776492
$729$	683.851	−	252.564i	0.938067	−	0.346453i
$730$	460.001	+	500.434i	0.630138	+	0.685527i
$731$	5.07252	−	13.9366i	0.00693916	−	0.0190652i
$732$	−267.115	+	532.916i	−0.364912	+	0.728027i
$733$	643.575	−	766.982i	0.878001	−	1.04636i	−0.120559	−	0.992706i	$-0.538469\pi$
$733$	643.575	−	766.982i	0.878001	−	1.04636i	0.998560	−	0.0536544i	$-0.0170869\pi$
$734$	882.423	+	155.595i	1.20221	+	0.211982i
$735$	−29.1516	+	413.540i	−0.0396620	+	0.562639i
$736$	112.519	−	94.4149i	0.152880	−	0.128281i
$737$	−9.49610	−	16.4477i	−0.0128848	−	0.0223171i
$738$	201.763	−	150.701i	0.273392	−	0.204202i
$739$	296.027	−	512.734i	0.400578	−	0.693822i	−0.593218	−	0.805042i	$-0.702143\pi$
$739$	296.027	−	512.734i	0.400578	−	0.693822i	0.993796	+	0.111220i	$0.0354759\pi$
$740$	−446.899	+	584.293i	−0.603917	+	0.789585i
$741$	20.5528	+	47.5438i	0.0277366	+	0.0641617i
$742$	−45.3370	−	124.562i	−0.0611011	−	0.167874i
$743$	−26.7873	+	9.74979i	−0.0360529	+	0.0131222i	−0.359984	−	0.932959i	$-0.617218\pi$
$743$	−26.7873	+	9.74979i	−0.0360529	+	0.0131222i	0.323931	+	0.946081i	$0.394996\pi$
$744$	102.555	+	76.2237i	0.137842	+	0.102451i
$745$	−56.5257	+	73.9040i	−0.0758735	+	0.0992000i
$746$	−562.294	−	324.640i	−0.753745	−	0.435175i
$747$	297.626	+	988.476i	0.398429	+	1.32326i
$748$	−6.58593	+	3.80239i	−0.00880472	+	0.00508341i
$749$	−408.555	−	486.897i	−0.545467	−	0.650063i
$750$	332.694	−	412.995i	0.443592	−	0.550660i
$751$	−245.498	+	1392.29i	−0.326895	+	1.85391i	0.169115	+	0.985596i	$0.445909\pi$
$751$	−245.498	+	1392.29i	−0.326895	+	1.85391i	−0.496010	+	0.868317i	$0.665202\pi$
$752$	72.0329	+	60.4427i	0.0957884	+	0.0803760i
$753$	42.8082	+	725.157i	0.0568502	+	0.963024i
$754$	−37.6898	−	13.7180i	−0.0499865	−	0.0181936i
$755$	212.089	−	194.953i	0.280912	−	0.258215i
$756$	43.9200	+	245.690i	0.0580952	+	0.324986i
$757$			876.944i			1.15845i	0.815169	+	0.579223i	$0.196644\pi$
$757$			876.944i			1.15845i	−0.815169	+	0.579223i	$0.803356\pi$
$758$	−302.723	−	110.182i	−0.399371	−	0.145359i
$759$	69.7028	−	45.9229i	0.0918350	−	0.0605044i
$760$	56.4088	−	2.55097i	0.0742221	−	0.00335653i
$761$	1192.64	+	210.295i	1.56720	+	0.276340i	0.888781	−	0.458333i	$-0.151553\pi$
$761$	1192.64	+	210.295i	1.56720	+	0.276340i	0.678421	+	0.734673i	$0.262664\pi$
$762$	−158.996	+	532.609i	−0.208656	+	0.698962i
$763$	546.859	+	651.721i	0.716722	+	0.854156i
$764$	47.8483	−	27.6252i	0.0626286	−	0.0361587i
$765$	101.239	+	123.486i	0.132338	+	0.161420i
$766$	−154.429	+	267.479i	−0.201605	+	0.349189i
$767$	42.6085	+	241.645i	0.0555521	+	0.315052i
$768$	5.53494	−	47.6798i	0.00720696	−	0.0620831i
$769$	−353.346	+	128.607i	−0.459487	+	0.167240i	−0.561384	−	0.827555i	$-0.689731\pi$
$769$	−353.346	+	128.607i	−0.459487	+	0.167240i	0.101897	+	0.994795i	$0.467509\pi$
$770$	−16.1223	+	31.0889i	−0.0209380	+	0.0403751i
$771$	−70.1279	+	604.105i	−0.0909571	+	0.783534i
$772$	−622.691	+	109.797i	−0.806595	+	0.142224i
$773$	504.986	−	874.661i	0.653280	−	1.13151i	−0.329042	−	0.944315i	$-0.606726\pi$
$773$	504.986	−	874.661i	0.653280	−	1.13151i	0.982322	−	0.187199i	$-0.0599410\pi$
$774$	23.9496	+	47.5011i	0.0309427	+	0.0613709i
$775$	340.702	−	160.167i	0.439616	−	0.206667i
$776$	113.571	+	135.349i	0.146354	+	0.174418i
$777$	−977.357	−	291.764i	−1.25786	−	0.375500i
$778$	−722.950	−	127.476i	−0.929242	−	0.163850i
$779$	50.7804	−	60.5177i	0.0651867	−	0.0776864i
$780$	31.4540	−	125.853i	0.0403256	−	0.161350i
$781$	−30.4560	−	11.0851i	−0.0389962	−	0.0141935i
$782$	130.303			0.166628
$783$	−30.3391	+	174.469i	−0.0387472	+	0.222821i
$784$	110.551			0.141009
$785$	150.599	+	361.980i	0.191845	+	0.461121i
$786$	6.66918	+	112.974i	0.00848496	+	0.143733i
$787$	143.052	−	170.483i	0.181769	−	0.216624i	−0.667464	−	0.744642i	$-0.732620\pi$
$787$	143.052	−	170.483i	0.181769	−	0.216624i	0.849233	+	0.528018i	$0.177065\pi$
$788$	13.5809	−	77.0209i	0.0172346	−	0.0977422i
$789$	205.523	+	864.137i	0.260485	+	1.09523i
$790$	−128.567	+	988.465i	−0.162743	+	1.25122i
$791$	−773.414	+	446.531i	−0.977768	+	0.564514i
$792$	6.24882	−	26.5520i	0.00788993	−	0.0335253i
$793$	372.055	+	214.806i	0.469174	+	0.270878i
$794$	295.211	−	52.0537i	0.371803	−	0.0655588i
$795$	302.548	−	31.6268i	0.380563	−	0.0397821i
$796$	−492.359	+	179.204i	−0.618542	+	0.225131i
$797$	−434.886	+	158.286i	−0.545654	+	0.198602i	−0.600114	−	0.799914i	$-0.704878\pi$
$797$	−434.886	+	158.286i	−0.545654	+	0.198602i	0.0544606	+	0.998516i	$0.482656\pi$
$798$	31.0677	+	71.8676i	0.0389320	+	0.0900596i
$799$	14.4853	+	82.1503i	0.0181293	+	0.102816i
$800$	−116.098	−	80.7544i	−0.145122	−	0.100943i
$801$	−401.581	−	172.476i	−0.501350	−	0.215326i
$802$	−627.450	+	362.258i	−0.782356	+	0.451694i
$803$	78.9082	−	66.2118i	0.0982667	−	0.0824556i
$804$	73.0382	+	77.2940i	0.0908435	+	0.0961368i
$805$	505.579	−	323.198i	0.628048	−	0.401489i
$806$	59.1937	−	70.5443i	0.0734413	−	0.0875240i
$807$	1259.83	+	631.467i	1.56112	+	0.782487i
$808$	−71.3566	+	196.051i	−0.0883126	+	0.242637i
$809$		−	719.024i		−	0.888781i	−0.895833	−	0.444391i	$-0.853420\pi$
$809$		−	719.024i		−	0.888781i	0.895833	−	0.444391i	$-0.146580\pi$
$810$	−571.432	−	38.9263i	−0.705472	−	0.0480572i
$811$	−1064.31			−1.31234			−0.656169	−	0.754614i	$-0.727824\pi$
$811$	−1064.31			−1.31234			−0.656169	+	0.754614i	$0.727824\pi$
$812$	−56.9722	−	20.7362i	−0.0701628	−	0.0255372i
$813$	527.299	−	1052.00i	0.648584	−	1.29398i
$814$	85.3945	+	71.6545i	0.104907	+	0.0880276i
$815$	488.742	−	312.435i	0.599683	−	0.383356i
$816$	30.9498	−	29.2457i	0.0379286	−	0.0358403i
$817$	10.7269	+	12.7838i	0.0131296	+	0.0156473i
$818$	−160.011	−	277.148i	−0.195613	−	0.338811i
$819$	178.624	−	21.1631i	0.218100	−	0.0258402i
$820$	−193.101	+	43.1253i	−0.235489	+	0.0525918i
$821$	−1020.95	+	180.022i	−1.24355	+	0.219271i	−0.756436	−	0.654068i	$-0.773061\pi$
$821$	−1020.95	+	180.022i	−1.24355	+	0.219271i	−0.487113	+	0.873339i	$0.661950\pi$
$822$	680.334	−	294.103i	0.827657	−	0.357789i
$823$	−304.348	−	836.189i	−0.369803	−	1.01603i	−0.975436	−	0.220282i	$-0.929302\pi$
$823$	−304.348	−	836.189i	−0.369803	−	1.01603i	0.605633	−	0.795744i	$-0.292920\pi$
$824$	−114.584	−	314.818i	−0.139059	−	0.382061i
$825$	−60.2442	−	53.1927i	−0.0730232	−	0.0644760i
$826$	64.4073	+	365.272i	0.0779749	+	0.442218i
$827$	−253.620	+	439.282i	−0.306674	+	0.531176i	−0.977633	−	0.210319i	$-0.932550\pi$
$827$	−253.620	+	439.282i	−0.306674	+	0.531176i	0.670958	+	0.741495i	$0.265883\pi$
$828$	−320.201	+	340.465i	−0.386716	+	0.411189i
$829$	−126.164	−	218.523i	−0.152189	−	0.263598i	0.779843	−	0.625975i	$-0.215299\pi$
$829$	−126.164	−	218.523i	−0.152189	−	0.263598i	−0.932032	+	0.362377i	$0.881965\pi$
$830$	104.611	−	804.285i	0.126037	−	0.969018i
$831$	231.985	−	55.1743i	0.279164	−	0.0663951i
$832$	−34.0676	−	6.00703i	−0.0409466	−	0.00721999i
$833$	75.1273	+	63.0393i	0.0901888	+	0.0756774i
$834$	−44.1713	+	2.60757i	−0.0529632	+	0.00312658i
$835$	−403.101	+	167.706i	−0.482755	+	0.200846i
$836$		−	8.55699i		−	0.0102356i
$837$	−352.597	−	202.463i	−0.421262	−	0.241892i
$838$		−	201.587i		−	0.240557i
$839$	426.305	−	1171.26i	0.508111	−	1.39602i	−0.375072	−	0.926996i	$-0.622382\pi$
$839$	426.305	−	1171.26i	0.508111	−	1.39602i	0.883183	−	0.469028i	$-0.155396\pi$
$840$	47.5461	−	190.240i	0.0566025	−	0.226477i
$841$	611.290	+	512.933i	0.726861	+	0.609909i
$842$	55.6655	−	315.695i	0.0661111	−	0.374934i
$843$	−397.441	+	1331.36i	−0.471460	+	1.57931i
$844$	−306.474	+	257.162i	−0.363120	+	0.304694i
$845$	717.078	+	224.866i	0.848613	+	0.266113i
$846$	−250.244	−	164.024i	−0.295796	−	0.193882i
$847$	−479.732	−	276.973i	−0.566390	−	0.327005i
$848$	−14.0862	−	79.8866i	−0.0166110	−	0.0942059i
$849$	287.803	+	33.4098i	0.338991	+	0.0393520i
$850$	−32.8484	−	121.081i	−0.0386452	−	0.142448i
$851$	−653.274	−	1794.86i	−0.767654	−	2.10911i
$852$	180.267	+	20.9264i	0.211581	+	0.0245615i
$853$	−936.546	+	165.138i	−1.09794	+	0.193597i	−0.693138	−	0.720805i	$-0.743772\pi$
$853$	−936.546	+	165.138i	−1.09794	+	0.193597i	−0.404807	+	0.914402i	$0.632661\pi$
$854$	562.401	+	324.702i	0.658549	+	0.380214i
$855$	−177.290	+	29.1790i	−0.207357	+	0.0341275i
$856$	−194.480	−	336.849i	−0.227196	−	0.393515i
$857$	−242.613	+	203.577i	−0.283096	+	0.237546i	−0.773267	−	0.634081i	$-0.781379\pi$
$857$	−242.613	+	203.577i	−0.283096	+	0.237546i	0.490171	+	0.871626i	$0.336934\pi$
$858$	−18.8371	−	5.62331i	−0.0219547	−	0.00655398i
$859$	−231.550	+	1313.19i	−0.269558	+	1.52874i	0.486177	+	0.873860i	$0.338391\pi$
$859$	−231.550	+	1313.19i	−0.269558	+	1.52874i	−0.755735	+	0.654878i	$0.772720\pi$
$860$	−1.88819	−	41.7530i	−0.00219557	−	0.0485500i
$861$	−150.936	−	229.094i	−0.175303	−	0.266079i
$862$	−73.9810	+	203.261i	−0.0858248	+	0.235802i
$863$	994.926			1.15287			0.576435	−	0.817143i	$-0.304443\pi$
$863$	994.926			1.15287			0.576435	+	0.817143i	$0.304443\pi$
$864$	0.360569	+	152.735i	0.000417325	+	0.176776i
$865$	78.4995	−	72.1570i	0.0907509	−	0.0834185i
$866$	−304.559	+	836.770i	−0.351685	+	0.966247i
$867$	−827.784	+	48.8666i	−0.954768	+	0.0563628i
$868$	89.4776	−	106.635i	0.103085	−	0.122852i
$869$	148.760	+	26.2304i	0.171185	+	0.0301846i
$870$	77.8671	−	115.303i	0.0895024	−	0.132532i
$871$	58.7102	−	49.2637i	0.0674055	−	0.0565599i
$872$	260.315	+	450.879i	0.298526	+	0.517063i
$873$	−409.543	−	385.167i	−0.469121	−	0.441199i
$874$	−73.3093	+	126.975i	−0.0838779	+	0.145281i
$875$	−427.776	−	388.320i	−0.488887	−	0.443795i
$876$	−344.060	+	462.913i	−0.392762	+	0.528439i
$877$	−552.293	−	1517.41i	−0.629753	−	1.73023i	−0.681750	−	0.731585i	$-0.738781\pi$
$877$	−552.293	−	1517.41i	−0.629753	−	1.73023i	0.0519970	−	0.998647i	$-0.483441\pi$
$878$	−256.969	+	93.5289i	−0.292675	+	0.106525i
$879$	369.051	−	159.538i	0.419853	−	0.181499i
$880$	−13.0199	+	17.0228i	−0.0147954	+	0.0193441i
$881$	−1199.21	−	692.365i	−1.36119	−	0.785886i	−0.371411	−	0.928468i	$-0.621126\pi$
$881$	−1199.21	−	692.365i	−1.36119	−	0.785886i	−0.989783	+	0.142583i	$0.954459\pi$
$882$	−349.328	+	41.3879i	−0.396063	+	0.0469251i
$883$	889.386	−	513.487i	1.00723	−	0.581526i	0.0968522	−	0.995299i	$-0.469123\pi$
$883$	889.386	−	513.487i	1.00723	−	0.581526i	0.910380	+	0.413773i	$0.135789\pi$
$884$	−19.7260	−	23.5085i	−0.0223144	−	0.0265933i
$885$	−849.065	−	59.8529i	−0.959395	−	0.0676304i
$886$	−122.089	+	692.403i	−0.137798	+	0.781494i
$887$	219.500	+	184.182i	0.247463	+	0.207646i	0.758079	−	0.652163i	$-0.226138\pi$
$887$	219.500	+	184.182i	0.247463	+	0.207646i	−0.510616	+	0.859809i	$0.670583\pi$
$888$	−558.010	−	279.694i	−0.628390	−	0.314970i
$889$	569.009	+	207.102i	0.640055	+	0.232961i
$890$	232.379	+	252.805i	0.261100	+	0.284051i
$891$	−9.80501	+	86.2406i	−0.0110045	+	0.0967908i
$892$		−	755.462i		−	0.846931i
$893$	−88.2019	−	32.1029i	−0.0987704	−	0.0359495i
$894$	−70.5796	−	35.3769i	−0.0789481	−	0.0395715i
$895$	−46.5033	−	1028.31i	−0.0519590	−	1.14896i
$896$	−51.4968	−	9.08027i	−0.0574741	−	0.0101342i
$897$	231.344	+	244.824i	0.257909	+	0.272936i
$898$	123.727	+	147.452i	0.137780	+	0.164200i
$899$	85.5357	−	49.3841i	0.0951454	−	0.0549322i
$900$	397.088	+	211.710i	0.441209	+	0.235233i
$901$	35.9810	−	62.3210i	0.0399346	−	0.0691687i
$902$	5.20659	+	29.5281i	0.00577228	+	0.0327362i
$903$	53.1953	−	22.9959i	0.0589095	−	0.0254661i
$904$	−513.557	+	186.919i	−0.568094	+	0.206769i
$905$	354.030	−	682.681i	0.391193	−	0.754343i
$906$	196.187	+	145.816i	0.216542	+	0.160945i
$907$	354.616	−	62.5283i	0.390977	−	0.0689397i	0.0252957	−	0.999680i	$-0.491947\pi$
$907$	354.616	−	62.5283i	0.390977	−	0.0689397i	0.365681	+	0.930740i	$0.380836\pi$
$908$	354.566	−	614.126i	0.390491	−	0.676350i
$909$	152.081	−	646.211i	0.167306	−	0.710903i
$910$	−134.847	−	42.2861i	−0.148183	−	0.0464682i
$911$	−27.7420	−	33.0616i	−0.0304523	−	0.0362916i	0.750603	−	0.660753i	$-0.229763\pi$
$911$	−27.7420	−	33.0616i	−0.0304523	−	0.0362916i	−0.781056	+	0.624461i	$0.785318\pi$
$912$	11.0863	+	46.6132i	0.0121560	+	0.0511109i
$913$	−121.042	−	21.3429i	−0.132576	−	0.0233767i
$914$	−229.246	+	273.205i	−0.250817	+	0.298912i
$915$	−1035.84	+	1071.44i	−1.13207	+	1.17097i
$916$	−232.881	−	84.7616i	−0.254236	−	0.0925345i
$917$	123.288			0.134447
$918$	−86.8486	+	104.000i	−0.0946063	+	0.113289i
$919$	939.820			1.02266			0.511328	−	0.859386i	$-0.329154\pi$
$919$	939.820			1.02266			0.511328	+	0.859386i	$0.329154\pi$
$920$	339.037	−	141.053i	0.368519	−	0.153319i
$921$	−966.605	+	636.836i	−1.04952	+	0.691462i
$922$	−551.023	+	656.684i	−0.597639	+	0.712238i
$923$	22.7113	−	128.802i	0.0246060	−	0.139547i
$924$	−28.4743	−	8.50024i	−0.0308164	−	0.00919940i
$925$	−1503.14	+	1059.51i	−1.62501	+	1.14541i
$926$	−465.916	+	268.997i	−0.503150	+	0.290494i
$927$	479.934	+	951.889i	0.517728	+	1.02685i
$928$	−32.1314	−	18.5511i	−0.0346243	−	0.0199904i
$929$	−176.241	+	31.0760i	−0.189710	+	0.0334510i	−0.267696	−	0.963503i	$-0.586262\pi$
$929$	−176.241	+	31.0760i	−0.189710	+	0.0334510i	0.0779857	+	0.996954i	$0.475151\pi$
$930$	187.621	+	258.544i	0.201743	+	0.278005i
$931$	−103.696	+	37.7424i	−0.111382	+	0.0405397i
$932$	78.5138	−	28.5767i	0.0842423	−	0.0306617i
$933$	1138.30	+	132.140i	1.22004	+	0.141629i
$934$	−48.3858	−	274.409i	−0.0518049	−	0.293800i
$935$	−18.5549	+	4.14387i	−0.0198448	+	0.00443194i
$936$	109.898	+	6.22732i	0.117413	+	0.00665312i
$937$	−903.198	+	521.461i	−0.963925	+	0.556522i	−0.897379	−	0.441261i	$-0.854531\pi$
$937$	−903.198	+	521.461i	−0.963925	+	0.556522i	−0.0665461	+	0.997783i	$0.521198\pi$
$938$	88.7467	−	74.4673i	0.0946127	−	0.0793895i
$939$	219.801	−	736.296i	0.234080	−	0.784128i
$940$	126.618	+	198.068i	0.134700	+	0.210710i
$941$	1063.68	−	1267.64i	1.13037	−	1.34712i	0.200305	−	0.979734i	$-0.435807\pi$
$941$	1063.68	−	1267.64i	1.13037	−	1.34712i	0.930067	−	0.367391i	$-0.119749\pi$
$942$	−277.800	+	183.025i	−0.294904	+	0.194294i
$943$	175.713	−	482.766i	0.186334	−	0.511947i
$944$			226.979i			0.240444i
$945$	−79.0179	+	618.937i	−0.0836168	+	0.654960i
$946$	−6.33376			−0.00669531
$947$	1734.49	+	631.302i	1.83156	+	0.666634i	0.992446	+	0.122680i	$0.0391488\pi$
$947$	1734.49	+	631.302i	1.83156	+	0.666634i	0.839115	+	0.543954i	$0.183073\pi$
$948$	−844.335	+	49.8436i	−0.890649	+	0.0525777i
$949$	318.424	+	267.190i	0.335537	+	0.281549i
$950$	136.469	+	36.1112i	0.143652	+	0.0380118i
$951$	348.229	+	1464.16i	0.366171	+	1.53960i
$952$	−29.8179	−	35.5356i	−0.0313213	−	0.0373273i
$953$	607.897	+	1052.91i	0.637878	+	1.10484i	0.985898	+	0.167350i	$0.0535208\pi$
$953$	607.897	+	1052.91i	0.637878	+	1.10484i	−0.348020	+	0.937487i	$0.613146\pi$
$954$	74.4184	+	247.158i	0.0780067	+	0.259076i
$955$	134.805	−	30.1061i	0.141157	−	0.0315247i
$956$	−668.895	+	117.944i	−0.699681	+	0.123373i
$957$	−16.9222	−	12.5774i	−0.0176825	−	0.0131425i
$958$	−280.938	−	771.872i	−0.293255	−	0.805712i
$959$	−276.162	−	758.749i	−0.287969	−	0.791187i
$960$	48.8701	−	109.598i	0.0509064	−	0.114165i
$961$	−127.498	−	723.075i	−0.132672	−	0.752419i
$962$	−224.921	+	389.575i	−0.233806	+	0.404963i
$963$	740.642	+	991.593i	0.769099	+	1.02969i
$964$	−39.1744	−	67.8521i	−0.0406374	−	0.0703860i
$965$	−1567.54	−	203.885i	−1.62439	−	0.211280i
$966$	349.701	+	370.078i	0.362010	+	0.383103i
$967$	−1043.91	−	184.069i	−1.07953	−	0.190351i	−0.394525	−	0.918885i	$-0.629091\pi$
$967$	−1043.91	−	184.069i	−1.07953	−	0.190351i	−0.685009	+	0.728534i	$0.740202\pi$
$968$	−259.683	−	217.900i	−0.268267	−	0.225103i
$969$	−19.0462	+	37.9987i	−0.0196556	+	0.0392143i
$970$	169.672	+	407.826i	0.174920	+	0.420439i
$971$		−	297.361i		−	0.306242i	−0.988207	−	0.153121i	$-0.951068\pi$
$971$		−	297.361i		−	0.306242i	0.988207	−	0.153121i	$-0.0489324\pi$
$972$	−58.3200	−	482.488i	−0.0600000	−	0.496387i
$973$			48.2040i			0.0495416i
$974$	−29.3099	+	80.5284i	−0.0300923	+	0.0826780i
$975$	169.176	−	276.689i	0.173514	−	0.283783i
$976$	304.432	+	255.449i	0.311918	+	0.261731i
$977$	−152.674	+	865.858i	−0.156268	+	0.886242i	0.801349	+	0.598197i	$0.204116\pi$
$977$	−152.674	+	865.858i	−0.156268	+	0.886242i	−0.957617	+	0.288044i	$0.906995\pi$
$978$	338.055	+	357.753i	0.345660	+	0.365801i
$979$	39.8622	−	33.4483i	0.0407173	−	0.0341658i
$980$	263.715	+	82.6973i	0.269097	+	0.0843850i
$981$	−991.364	−	1327.27i	−1.01056	−	1.35297i
$982$	878.080	+	506.960i	0.894175	+	0.516252i
$983$	78.1786	+	443.373i	0.0795307	+	0.451041i	0.998403	+	0.0564867i	$0.0179898\pi$
$983$	78.1786	+	443.373i	0.0795307	+	0.451041i	−0.918873	+	0.394554i	$0.870899\pi$
$984$	−66.6183	−	154.105i	−0.0677015	−	0.156611i
$985$	90.0118	−	173.571i	0.0913826	−	0.176214i
$986$	−11.2572	−	30.9290i	−0.0114171	−	0.0313681i
$987$	−194.443	+	261.612i	−0.197004	+	0.265057i
$988$	34.0061	−	5.99619i	0.0344191	−	0.00606902i
$989$	93.9853	+	54.2624i	0.0950306	+	0.0548660i
$990$	34.7685	−	58.6644i	0.0351197	−	0.0592569i
$991$	−571.988	−	990.712i	−0.577183	−	0.999709i	−0.995801	−	0.0915472i	$-0.970819\pi$
$991$	−571.988	−	990.712i	−0.577183	−	0.999709i	0.418618	−	0.908162i	$-0.362515\pi$
$992$	65.2563	−	54.7565i	0.0657825	−	0.0551981i
$993$	300.613	+	1263.95i	0.302732	+	1.27286i
$994$	34.3306	−	194.698i	0.0345378	−	0.195874i
$995$	−1308.56	+	59.1766i	−1.31513	+	0.0594740i
$996$	687.011	−	40.5563i	0.689770	−	0.0407192i
$997$	385.794	−	1059.96i	0.386955	−	1.06315i	−0.581409	−	0.813611i	$-0.697498\pi$
$997$	385.794	−	1059.96i	0.386955	−	1.06315i	0.968365	−	0.249540i	$-0.0802793\pi$
$998$	−11.5621			−0.0115853
$999$	1867.96	+	674.891i	1.86983	+	0.675567i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.n.a.239.25	yes	216
5.4	even	2	inner	270.3.n.a.239.12	yes	216
27.20	odd	18	inner	270.3.n.a.209.12	✓	216
135.74	odd	18	inner	270.3.n.a.209.25	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.n.a.209.12	✓	216	27.20	odd	18	inner
270.3.n.a.209.25	yes	216	135.74	odd	18	inner
270.3.n.a.239.12	yes	216	5.4	even	2	inner
270.3.n.a.239.25	yes	216	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 $\F_{q}$

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	270.3.n.a.239.25

Level	$270$
Weight	$3$
Character	270.239
Analytic conductor	$7.357$
Analytic rank	$0$
Dimension	$216$
Inner twists	$4$