LMFDB - Embedded newform 270.3.n.a.29.7

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			29.7
Character	$\chi$	$=$	270.29
Dual form			270.3.n.a.149.7

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.245576 + 1.39273i) q^{2} +(-0.936605 + 2.85005i) q^{3} +(-1.87939 - 0.684040i) q^{4} +(-4.96948 + 0.551583i) q^{5} +(-3.73934 - 2.00434i) q^{6} +(1.06409 + 2.92356i) q^{7} +(1.41421 - 2.44949i) q^{8} +(-7.24554 - 5.33874i) q^{9} +(0.452178 - 7.05660i) q^{10} +(-2.53312 + 3.01886i) q^{11} +(3.70979 - 4.71566i) q^{12} +(-2.02480 + 0.357028i) q^{13} +(-4.33305 + 0.764033i) q^{14} +(3.08240 - 14.6799i) q^{15} +(3.06418 + 2.57115i) q^{16} +(-7.57860 - 13.1265i) q^{17} +(9.21474 - 8.78001i) q^{18} +(9.31199 - 16.1288i) q^{19} +(9.71688 + 2.36269i) q^{20} +(-9.32893 + 0.294485i) q^{21} +(-3.58238 - 4.26931i) q^{22} +(-4.12258 - 1.50050i) q^{23} +(5.65660 + 6.32478i) q^{24} +(24.3915 - 5.48217i) q^{25} -2.90768i q^{26} +(22.0019 - 15.6499i) q^{27} -6.22239i q^{28} +(-12.8287 - 2.26205i) q^{29} +(19.6881 + 7.89797i) q^{30} +(9.87851 + 3.59548i) q^{31} +(-4.33340 + 3.63616i) q^{32} +(-6.23135 - 10.0470i) q^{33} +(20.1428 - 7.33138i) q^{34} +(-6.90057 - 13.9417i) q^{35} +(9.96526 + 14.9898i) q^{36} +(-17.1266 + 9.88804i) q^{37} +(20.1763 + 16.9299i) q^{38} +(0.878895 - 6.10518i) q^{39} +(-5.67681 + 12.9528i) q^{40} +(-41.8487 + 7.37905i) q^{41} +(1.88082 - 13.0650i) q^{42} +(-1.64033 + 1.95487i) q^{43} +(6.82573 - 3.94084i) q^{44} +(38.9514 + 22.5342i) q^{45} +(3.10219 - 5.37315i) q^{46} +(3.58455 - 1.30467i) q^{47} +(-10.1978 + 6.32490i) q^{48} +(30.1212 - 25.2747i) q^{49} +(1.64521 + 35.3170i) q^{50} +(44.5094 - 9.30502i) q^{51} +(4.04961 + 0.714055i) q^{52} -72.9202 q^{53} +(16.3929 + 34.4858i) q^{54} +(10.9232 - 16.3994i) q^{55} +(8.66609 + 1.52807i) q^{56} +(37.2463 + 41.6460i) q^{57} +(6.30084 - 17.3114i) q^{58} +(-65.6920 - 78.2886i) q^{59} +(-15.8346 + 25.4807i) q^{60} +(-15.5166 + 5.64757i) q^{61} +(-7.43345 + 12.8751i) q^{62} +(7.89822 - 26.8637i) q^{63} +(-4.00000 - 6.92820i) q^{64} +(9.86530 - 2.89109i) q^{65} +(15.5230 - 6.21129i) q^{66} +(-106.201 + 18.7262i) q^{67} +(5.26404 + 29.8539i) q^{68} +(8.13771 - 10.3442i) q^{69} +(21.1116 - 6.18689i) q^{70} +(-54.4040 + 31.4102i) q^{71} +(-23.3239 + 10.1978i) q^{72} +(-53.9426 - 31.1438i) q^{73} +(-9.56548 - 26.2809i) q^{74} +(-7.22076 + 74.6516i) q^{75} +(-28.5336 + 23.9425i) q^{76} +(-11.5213 - 4.19341i) q^{77} +(8.28703 + 2.72335i) q^{78} +(27.0020 - 153.136i) q^{79} +(-16.6456 - 11.0871i) q^{80} +(23.9958 + 77.3641i) q^{81} -60.0960i q^{82} +(-25.2307 + 143.090i) q^{83} +(17.7341 + 5.82791i) q^{84} +(44.9021 + 61.0518i) q^{85} +(-2.31977 - 2.76460i) q^{86} +(18.4624 - 34.4438i) q^{87} +(3.81228 + 10.4742i) q^{88} +(1.95959 + 1.13137i) q^{89} +(-40.9496 + 48.7148i) q^{90} +(-3.19837 - 5.53974i) q^{91} +(6.72151 + 5.64002i) q^{92} +(-19.4996 + 24.7867i) q^{93} +(0.936773 + 5.31270i) q^{94} +(-37.3794 + 85.2884i) q^{95} +(-6.30453 - 15.7560i) q^{96} +(-63.0205 + 75.1049i) q^{97} +(27.8038 + 48.1576i) q^{98} +(34.4707 - 8.34960i) 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 $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$ .

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

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

)

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

$2$	−0.245576	+	1.39273i	−0.122788	+	0.696364i
$2$	−0.245576	+	1.39273i	−0.122788	+	0.696364i
$3$	−0.936605	+	2.85005i	−0.312202	+	0.950016i
$3$	−0.936605	+	2.85005i	−0.312202	+	0.950016i
$4$	−1.87939	−	0.684040i	−0.469846	−	0.171010i
$5$	−4.96948	+	0.551583i	−0.993896	+	0.110317i
$5$	−4.96948	+	0.551583i	−0.993896	+	0.110317i
$6$	−3.73934	−	2.00434i	−0.623223	−	0.334056i
$7$	1.06409	+	2.92356i	0.152013	+	0.417652i	0.992202	−	0.124642i	$-0.0397782\pi$
$7$	1.06409	+	2.92356i	0.152013	+	0.417652i	−0.840189	+	0.542294i	$0.817556\pi$
$8$	1.41421	−	2.44949i	0.176777	−	0.306186i
$9$	−7.24554	−	5.33874i	−0.805060	−	0.593193i
$10$	0.452178	−	7.05660i	0.0452178	−	0.705660i
$11$	−2.53312	+	3.01886i	−0.230284	+	0.274442i	−0.868796	−	0.495170i	$-0.835106\pi$
$11$	−2.53312	+	3.01886i	−0.230284	+	0.274442i	0.638512	+	0.769612i	$0.279550\pi$
$12$	3.70979	−	4.71566i	0.309149	−	0.392972i
$13$	−2.02480	+	0.357028i	−0.155754	+	0.0274637i	−0.250981	−	0.967992i	$-0.580753\pi$
$13$	−2.02480	+	0.357028i	−0.155754	+	0.0274637i	0.0952273	+	0.995456i	$0.469642\pi$
$14$	−4.33305	+	0.764033i	−0.309503	+	0.0545738i
$15$	3.08240	−	14.6799i	0.205493	−	0.978659i
$16$	3.06418	+	2.57115i	0.191511	+	0.160697i
$17$	−7.57860	−	13.1265i	−0.445800	−	0.772149i	0.552307	−	0.833641i	$-0.313748\pi$
$17$	−7.57860	−	13.1265i	−0.445800	−	0.772149i	−0.998108	+	0.0614919i	$0.980414\pi$
$18$	9.21474	−	8.78001i	0.511930	−	0.487778i
$19$	9.31199	−	16.1288i	0.490105	−	0.848887i	−0.509830	−	0.860275i	$-0.670292\pi$
$19$	9.31199	−	16.1288i	0.490105	−	0.848887i	0.999935	+	0.0113883i	$0.00362510\pi$
$20$	9.71688	+	2.36269i	0.485844	+	0.118134i
$21$	−9.32893	+	0.294485i	−0.444235	+	0.0140231i
$22$	−3.58238	−	4.26931i	−0.162835	−	0.194060i
$23$	−4.12258	−	1.50050i	−0.179243	−	0.0652389i	0.250840	−	0.968029i	$-0.419293\pi$
$23$	−4.12258	−	1.50050i	−0.179243	−	0.0652389i	−0.430082	+	0.902790i	$0.641515\pi$
$24$	5.65660	+	6.32478i	0.235692	+	0.263532i
$25$	24.3915	−	5.48217i	0.975660	−	0.219287i
$26$		−	2.90768i		−	0.111834i
$27$	22.0019	−	15.6499i	0.814884	−	0.579625i
$28$		−	6.22239i		−	0.222228i
$29$	−12.8287	−	2.26205i	−0.442369	−	0.0780017i	−0.0519729	−	0.998648i	$-0.516551\pi$
$29$	−12.8287	−	2.26205i	−0.442369	−	0.0780017i	−0.390396	+	0.920647i	$0.627662\pi$
$30$	19.6881	+	7.89797i	0.656271	+	0.263266i
$31$	9.87851	+	3.59548i	0.318662	+	0.115983i	0.496399	−	0.868095i	$-0.334655\pi$
$31$	9.87851	+	3.59548i	0.318662	+	0.115983i	−0.177737	+	0.984078i	$0.556878\pi$
$32$	−4.33340	+	3.63616i	−0.135419	+	0.113630i
$33$	−6.23135	−	10.0470i	−0.188829	−	0.304454i
$34$	20.1428	−	7.33138i	0.592436	−	0.215629i
$35$	−6.90057	−	13.9417i	−0.197159	−	0.398333i
$36$	9.96526	+	14.9898i	0.276813	+	0.416383i
$37$	−17.1266	+	9.88804i	−0.462881	+	0.267244i	−0.713255	−	0.700905i	$-0.752780\pi$
$37$	−17.1266	+	9.88804i	−0.462881	+	0.267244i	0.250374	+	0.968149i	$0.419446\pi$
$38$	20.1763	+	16.9299i	0.530955	+	0.445525i
$39$	0.878895	−	6.10518i	0.0225358	−	0.156543i
$40$	−5.67681	+	12.9528i	−0.141920	+	0.323819i
$41$	−41.8487	+	7.37905i	−1.02070	+	0.179977i	−0.658862	−	0.752264i	$-0.728962\pi$
$41$	−41.8487	+	7.37905i	−1.02070	+	0.179977i	−0.361838	+	0.932241i	$0.617851\pi$
$42$	1.88082	−	13.0650i	0.0447814	−	0.311071i
$43$	−1.64033	+	1.95487i	−0.0381471	+	0.0454620i	−0.784781	−	0.619774i	$-0.787224\pi$
$43$	−1.64033	+	1.95487i	−0.0381471	+	0.0454620i	0.746634	+	0.665236i	$0.231669\pi$
$44$	6.82573	−	3.94084i	0.155130	−	0.0895645i
$45$	38.9514	+	22.5342i	0.865586	+	0.500761i
$46$	3.10219	−	5.37315i	0.0674389	−	0.116808i
$47$	3.58455	−	1.30467i	0.0762671	−	0.0277590i	−0.303605	−	0.952798i	$-0.598190\pi$
$47$	3.58455	−	1.30467i	0.0762671	−	0.0277590i	0.379872	+	0.925039i	$0.375968\pi$
$48$	−10.1978	+	6.32490i	−0.212455	+	0.131769i
$49$	30.1212	−	25.2747i	0.614719	−	0.515811i
$50$	1.64521	+	35.3170i	0.0329043	+	0.706341i
$51$	44.5094	−	9.30502i	0.872733	−	0.182451i
$52$	4.04961	+	0.714055i	0.0778771	+	0.0137318i
$53$	−72.9202			−1.37585			−0.687927	−	0.725780i	$-0.741479\pi$
$53$	−72.9202			−1.37585			−0.687927	+	0.725780i	$0.741479\pi$
$54$	16.3929	+	34.4858i	0.303572	+	0.638627i
$55$	10.9232	−	16.3994i	0.198603	−	0.298171i
$56$	8.66609	+	1.52807i	0.154752	+	0.0272869i
$57$	37.2463	+	41.6460i	0.653444	+	0.730631i
$58$	6.30084	−	17.3114i	0.108635	−	0.298473i
$59$	−65.6920	−	78.2886i	−1.11342	−	1.32693i	−0.939649	−	0.342141i	$-0.888848\pi$
$59$	−65.6920	−	78.2886i	−1.11342	−	1.32693i	−0.173774	−	0.984785i	$-0.555596\pi$
$60$	−15.8346	+	25.4807i	−0.263911	+	0.424678i
$61$	−15.5166	+	5.64757i	−0.254370	+	0.0925830i	−0.466058	−	0.884754i	$-0.654326\pi$
$61$	−15.5166	+	5.64757i	−0.254370	+	0.0925830i	0.211688	+	0.977337i	$0.432104\pi$
$62$	−7.43345	+	12.8751i	−0.119894	+	0.207663i
$63$	7.89822	−	26.8637i	0.125369	−	0.426408i
$64$	−4.00000	−	6.92820i	−0.0625000	−	0.108253i
$65$	9.86530	−	2.89109i	0.151774	−	0.0444783i
$66$	15.5230	−	6.21129i	0.235197	−	0.0941104i
$67$	−106.201	+	18.7262i	−1.58509	+	0.279495i	−0.895622	−	0.444816i	$-0.853269\pi$
$67$	−106.201	+	18.7262i	−1.58509	+	0.279495i	−0.689473	+	0.724311i	$0.742158\pi$
$68$	5.26404	+	29.8539i	0.0774124	+	0.439028i
$69$	8.13771	−	10.3442i	0.117938	−	0.149916i
$70$	21.1116	−	6.18689i	0.301594	−	0.0883841i
$71$	−54.4040	+	31.4102i	−0.766254	+	0.442397i	−0.831537	−	0.555470i	$-0.812538\pi$
$71$	−54.4040	+	31.4102i	−0.766254	+	0.442397i	0.0652828	+	0.997867i	$0.479205\pi$
$72$	−23.3239	+	10.1978i	−0.323943	+	0.141636i
$73$	−53.9426	−	31.1438i	−0.738940	−	0.426627i	0.0827437	−	0.996571i	$-0.473632\pi$
$73$	−53.9426	−	31.1438i	−0.738940	−	0.426627i	−0.821684	+	0.569944i	$0.806965\pi$
$74$	−9.56548	−	26.2809i	−0.129263	−	0.355148i
$75$	−7.22076	+	74.6516i	−0.0962768	+	0.995355i
$76$	−28.5336	+	23.9425i	−0.375442	+	0.315033i
$77$	−11.5213	−	4.19341i	−0.149627	−	0.0544599i
$78$	8.28703	+	2.72335i	0.106244	+	0.0349147i
$79$	27.0020	−	153.136i	0.341798	−	1.93843i	−0.00364851	−	0.999993i	$-0.501161\pi$
$79$	27.0020	−	153.136i	0.341798	−	1.93843i	0.345446	−	0.938439i	$-0.387728\pi$
$80$	−16.6456	−	11.0871i	−0.208070	−	0.138589i
$81$	23.9958	+	77.3641i	0.296245	+	0.955112i
$82$		−	60.0960i		−	0.732878i
$83$	−25.2307	+	143.090i	−0.303984	+	1.72398i	0.324265	+	0.945966i	$0.394883\pi$
$83$	−25.2307	+	143.090i	−0.303984	+	1.72398i	−0.628249	+	0.778012i	$0.716228\pi$
$84$	17.7341	+	5.82791i	0.211120	+	0.0693799i
$85$	44.9021	+	61.0518i	0.528260	+	0.718257i
$86$	−2.31977	−	2.76460i	−0.0269741	−	0.0321465i
$87$	18.4624	−	34.4438i	0.212211	−	0.395906i
$88$	3.81228	+	10.4742i	0.0433214	+	0.119025i
$89$	1.95959	+	1.13137i	0.0220178	+	0.0127120i	0.510969	−	0.859599i	$-0.329287\pi$
$89$	1.95959	+	1.13137i	0.0220178	+	0.0127120i	−0.488951	+	0.872311i	$0.662620\pi$
$90$	−40.9496	+	48.7148i	−0.454995	+	0.541276i
$91$	−3.19837	−	5.53974i	−0.0351469	−	0.0608762i
$92$	6.72151	+	5.64002i	0.0730599	+	0.0613045i
$93$	−19.4996	+	24.7867i	−0.209673	+	0.266523i
$94$	0.936773	+	5.31270i	0.00996567	+	0.0565181i
$95$	−37.3794	+	85.2884i	−0.393467	+	0.897772i
$96$	−6.30453	−	15.7560i	−0.0656722	−	0.164125i
$97$	−63.0205	+	75.1049i	−0.649695	+	0.774277i	−0.985868	−	0.167524i	$-0.946423\pi$
$97$	−63.0205	+	75.1049i	−0.649695	+	0.774277i	0.336173	+	0.941800i	$0.390867\pi$
$98$	27.8038	+	48.1576i	0.283712	+	0.491404i
$99$	34.4707	−	8.34960i	0.348189	−	0.0843393i
$100$	−49.5911	−	6.38167i	−0.495911	−	0.0638167i
$101$	54.8592	+	150.724i	0.543160	+	1.49232i	0.842778	+	0.538262i	$0.180919\pi$
$101$	54.8592	+	150.724i	0.543160	+	1.49232i	−0.299617	+	0.954059i	$0.596859\pi$
$102$	2.02894	+	64.2746i	0.0198916	+	0.630143i
$103$	3.58900	+	4.27720i	0.0348446	+	0.0415262i	0.783185	−	0.621788i	$-0.213594\pi$
$103$	3.58900	+	4.27720i	0.0348446	+	0.0415262i	−0.748341	+	0.663315i	$0.769149\pi$
$104$	−1.98897	+	5.46465i	−0.0191247	+	0.0525447i
$105$	46.1975	−	6.60912i	0.439976	−	0.0629440i
$106$	17.9074	−	101.558i	0.168938	−	0.958095i
$107$	−115.330			−1.07785			−0.538925	−	0.842354i	$-0.681169\pi$
$107$	−115.330			−1.07785			−0.538925	+	0.842354i	$0.681169\pi$
$108$	−52.0551	+	14.3620i	−0.481992	+	0.132981i
$109$	76.3263			0.700242			0.350121	−	0.936705i	$-0.386141\pi$
$109$	76.3263			0.700242			0.350121	+	0.936705i	$0.386141\pi$
$110$	20.1574	+	19.2403i	0.183249	+	0.174912i
$111$	−12.1405	−	58.0728i	−0.109374	−	0.523178i
$112$	−4.25636	+	11.6943i	−0.0380032	+	0.104413i
$113$	96.3271	−	80.8281i	0.852452	−	0.715293i	−0.107876	−	0.994164i	$-0.534405\pi$
$113$	96.3271	−	80.8281i	0.852452	−	0.715293i	0.960328	+	0.278872i	$0.0899605\pi$
$114$	−67.1483	+	41.6468i	−0.589020	+	0.365323i
$115$	21.3147	+	5.18274i	0.185345	+	0.0450673i
$116$	22.5628	+	13.0266i	0.194507	+	0.112298i
$117$	16.5769	+	8.22304i	0.141683	+	0.0702824i
$118$	125.167	−	72.2653i	1.06074	−	0.612418i
$119$	30.3119	−	36.1244i	0.254722	−	0.303566i
$120$	−31.5990	−	28.3108i	−0.263325	−	0.235923i
$121$	18.3146	+	103.867i	0.151361	+	0.858409i
$122$	−4.05504	−	22.9973i	−0.0332380	−	0.188502i
$123$	18.1650	−	126.182i	0.147683	−	1.02587i
$124$	−16.1061	−	13.5146i	−0.129888	−	0.108989i
$125$	−118.189	+	40.6975i	−0.945515	+	0.325580i
$126$	35.4742	+	17.5972i	0.281542	+	0.139660i
$127$	−84.2556	−	48.6450i	−0.663430	−	0.383031i	0.130153	−	0.991494i	$-0.458453\pi$
$127$	−84.2556	−	48.6450i	−0.663430	−	0.383031i	−0.793583	+	0.608463i	$0.791787\pi$
$128$	10.6314	−	3.86952i	0.0830579	−	0.0302306i
$129$	−4.03512	−	6.50595i	−0.0312800	−	0.0504337i
$130$	1.60383	+	14.4497i	0.0123371	+	0.111151i
$131$	14.1933	−	38.9958i	0.108346	−	0.297678i	−0.873657	−	0.486542i	$-0.838258\pi$
$131$	14.1933	−	38.9958i	0.108346	−	0.297678i	0.982003	+	0.188864i	$0.0604804\pi$
$132$	4.83857	+	23.1447i	0.0366558	+	0.175338i
$133$	57.0625	+	10.0617i	0.429042	+	0.0756516i
$134$		−	152.508i		−	1.13812i
$135$	−100.706	+	89.9076i	−0.745968	+	0.665982i
$136$	−42.8711			−0.315228
$137$	9.42141	−	53.4315i	0.0687694	−	0.390011i	−0.930923	−	0.365215i	$-0.880995\pi$
$137$	9.42141	−	53.4315i	0.0687694	−	0.390011i	0.999693	−	0.0247956i	$-0.00789350\pi$
$138$	12.4082	+	13.8739i	0.0899145	+	0.100535i
$139$	52.8561	+	19.2381i	0.380260	+	0.138403i	0.525076	−	0.851055i	$-0.324037\pi$
$139$	52.8561	+	19.2381i	0.380260	+	0.138403i	−0.144816	+	0.989459i	$0.546259\pi$
$140$	3.43217	+	30.9220i	0.0245155	+	0.220872i
$141$	0.361065	+	11.4381i	0.00256074	+	0.0811213i
$142$	−30.3855	−	83.4836i	−0.213983	−	0.587913i
$143$	4.05126	−	7.01699i	0.0283305	−	0.0490699i
$144$	−8.47494	−	34.9882i	−0.0588538	−	0.242974i
$145$	64.9998	+	4.16510i	0.448274	+	0.0287248i
$146$	56.6218	−	67.4793i	0.387821	−	0.462187i
$147$	43.8225	+	109.519i	0.298112	+	0.745030i
$148$	38.9513	−	6.86816i	0.263184	−	0.0464065i
$149$	51.8469	−	9.14201i	0.347966	−	0.0613557i	0.00306604	−	0.999995i	$-0.499024\pi$
$149$	51.8469	−	9.14201i	0.347966	−	0.0613557i	0.344900	+	0.938640i	$0.387913\pi$
$150$	−102.196	−	28.3892i	−0.681308	−	0.189261i
$151$	−28.6105	−	24.0071i	−0.189474	−	0.158987i	0.543116	−	0.839657i	$-0.317244\pi$
$151$	−28.6105	−	24.0071i	−0.189474	−	0.158987i	−0.732590	+	0.680670i	$0.761689\pi$
$152$	−26.3383	−	45.6193i	−0.173278	−	0.300127i
$153$	−15.1679	+	135.569i	−0.0991369	+	0.886072i
$154$	8.66963	−	15.0162i	0.0562963	−	0.0975080i
$155$	−51.0743	−	12.4189i	−0.329511	−	0.0801217i
$156$	−5.82797	+	10.8728i	−0.0373588	+	0.0696974i
$157$	130.885	+	155.983i	0.833662	+	0.993519i	0.999972	+	0.00744603i	$0.00237017\pi$
$157$	130.885	+	155.983i	0.833662	+	0.993519i	−0.166310	+	0.986073i	$0.553185\pi$
$158$	206.646	+	75.2130i	1.30789	+	0.476032i
$159$	68.2974	−	207.826i	0.429543	−	1.30708i
$160$	19.5291	−	20.4600i	0.122057	−	0.127875i
$161$		−	13.6493i		−	0.0847782i
$162$	−113.640	+	14.4209i	−0.701481	+	0.0890180i
$163$		−	230.167i		−	1.41207i	−0.708179	−	0.706033i	$-0.750483\pi$
$163$		−	230.167i		−	1.41207i	0.708179	−	0.706033i	$-0.249517\pi$
$164$	83.6974	+	14.7581i	0.510350	+	0.0899885i
$165$	36.5084	+	46.4913i	0.221263	+	0.281765i
$166$	−193.090	−	70.2789i	−1.16319	−	0.423367i
$167$	169.866	−	142.535i	1.01716	−	0.853501i	0.0278946	−	0.999611i	$-0.491120\pi$
$167$	169.866	−	142.535i	1.01716	−	0.853501i	0.989268	+	0.146110i	$0.0466753\pi$
$168$	−12.4718	+	23.2676i	−0.0742367	+	0.138498i
$169$	−154.836	+	56.3556i	−0.916188	+	0.333465i
$170$	−96.0555	+	47.5436i	−0.565032	+	0.279668i
$171$	−153.578	+	67.1480i	−0.898118	+	0.392678i
$172$	4.42001	−	2.55190i	0.0256978	−	0.0148366i
$173$	−10.1712	−	8.53468i	−0.0587932	−	0.0493334i	0.612918	−	0.790147i	$-0.289996\pi$
$173$	−10.1712	−	8.53468i	−0.0587932	−	0.0493334i	−0.671711	+	0.740813i	$0.734440\pi$
$174$	43.4369	+	34.1716i	0.249638	+	0.196389i
$175$	41.9823	+	65.4766i	0.239899	+	0.374152i
$176$	−15.5239	+	2.73728i	−0.0882038	+	0.0155527i
$177$	284.654	−	113.900i	1.60821	−	0.643501i
$178$	−2.05691	+	2.45133i	−0.0115557	+	0.0137715i
$179$	−54.9339	+	31.7161i	−0.306894	+	0.177185i	−0.645536	−	0.763730i	$-0.723366\pi$
$179$	−54.9339	+	31.7161i	−0.306894	+	0.177185i	0.338642	+	0.940915i	$0.390032\pi$
$180$	−57.7903	−	68.9948i	−0.321057	−	0.383304i
$181$	−66.4961	+	115.175i	−0.367382	+	0.636324i	−0.989155	−	0.146873i	$-0.953079\pi$
$181$	−66.4961	+	115.175i	−0.367382	+	0.636324i	0.621773	+	0.783197i	$0.286412\pi$
$182$	8.50079	−	3.09404i	0.0467076	−	0.0170002i
$183$	−1.56295	−	49.5125i	−0.00854072	−	0.270560i
$184$	−9.50565	+	7.97619i	−0.0516612	+	0.0433489i
$185$	79.6562	−	58.5852i	0.430574	−	0.316677i
$186$	−29.7325	−	33.2446i	−0.159852	−	0.178734i
$187$	58.8246	+	10.3724i	0.314570	+	0.0554672i
$188$	−7.62920			−0.0405809
$189$	69.1654	+	47.6710i	0.365954	+	0.252227i
$190$	−109.604	−	73.0041i	−0.576864	−	0.384232i
$191$	117.333	+	20.6889i	0.614307	+	0.108319i	0.472140	−	0.881524i	$-0.343482\pi$
$191$	117.333	+	20.6889i	0.614307	+	0.108319i	0.142167	+	0.989843i	$0.454593\pi$
$192$	23.4921	−	4.91120i	0.122355	−	0.0255792i
$193$	−6.12755	+	16.8353i	−0.0317490	+	0.0872296i	−0.954554	−	0.298037i	$-0.903668\pi$
$193$	−6.12755	+	16.8353i	−0.0317490	+	0.0872296i	0.922805	+	0.385266i	$0.125890\pi$
$194$	−89.1244	−	106.214i	−0.459404	−	0.547496i
$195$	−1.00014	+	30.8244i	−0.00512890	+	0.158074i
$196$	−73.8983	+	26.8968i	−0.377032	+	0.137229i
$197$	155.841	−	269.925i	0.791072	−	1.37018i	−0.134232	−	0.990950i	$-0.542857\pi$
$197$	155.841	−	269.925i	0.791072	−	1.37018i	0.925304	−	0.379227i	$-0.123810\pi$
$198$	3.16355	+	50.0588i	0.0159775	+	0.252822i
$199$	−96.0578	−	166.377i	−0.482703	−	0.836065i	0.517100	−	0.855925i	$-0.327011\pi$
$199$	−96.0578	−	166.377i	−0.482703	−	0.836065i	−0.999803	+	0.0198595i	$0.993678\pi$
$200$	21.0663	−	67.4997i	0.105331	−	0.337499i
$201$	46.0982	−	320.218i	0.229344	−	1.59312i
$202$	−223.390	+	39.3897i	−1.10589	+	0.194999i
$203$	−7.03767	−	39.9126i	−0.0346683	−	0.196614i
$204$	−90.0153	−	12.9585i	−0.441251	−	0.0635221i
$205$	203.896	−	59.7531i	0.994616	−	0.291479i
$206$	−6.83835	+	3.94812i	−0.0331959	+	0.0191656i
$207$	21.8596	+	32.8813i	0.105602	+	0.158847i
$208$	−7.12233	−	4.11208i	−0.0342420	−	0.0197696i
$209$	25.1023	+	68.9679i	0.120107	+	0.329990i
$210$	−2.14027	+	65.9637i	−0.0101918	+	0.314113i
$211$	−35.7025	+	29.9580i	−0.169206	+	0.141981i	−0.723459	−	0.690368i	$-0.757449\pi$
$211$	−35.7025	+	29.9580i	−0.169206	+	0.141981i	0.554252	+	0.832349i	$0.313004\pi$
$212$	137.045	+	49.8804i	0.646439	+	0.235285i
$213$	−38.5654	−	184.473i	−0.181058	−	0.866070i
$214$	28.3222	−	160.623i	0.132347	−	0.750576i
$215$	7.07330	−	10.6194i	0.0328991	−	0.0493928i
$216$	−7.21885	−	76.0256i	−0.0334206	−	0.351970i
$217$			32.7064i			0.150721i
$218$	−18.7439	+	106.302i	−0.0859811	+	0.487623i
$219$	139.284	−	124.570i	0.636001	−	0.568811i
$220$	−31.7467	+	23.3489i	−0.144303	+	0.106131i
$221$	20.0317	+	23.8729i	0.0906413	+	0.108022i
$222$	83.8610	−	2.64723i	0.377752	−	0.0119244i
$223$	106.480	+	292.551i	0.477488	+	1.31189i	0.911618	+	0.411038i	$0.134834\pi$
$223$	106.480	+	292.551i	0.477488	+	1.31189i	−0.434130	+	0.900850i	$0.642944\pi$
$224$	−15.2417	−	8.79978i	−0.0680432	−	0.0392847i
$225$	−205.998	−	90.4985i	−0.915545	−	0.402216i
$226$	88.9159	+	154.007i	0.393433	+	0.681447i
$227$	−20.0921	−	16.8592i	−0.0885113	−	0.0742698i	0.597458	−	0.801900i	$-0.296177\pi$
$227$	−20.0921	−	16.8592i	−0.0885113	−	0.0742698i	−0.685970	+	0.727630i	$0.740622\pi$
$228$	−41.5127	−	103.747i	−0.182073	−	0.455030i
$229$	65.3718	+	370.742i	0.285466	+	1.61896i	0.703616	+	0.710581i	$0.251568\pi$
$229$	65.3718	+	370.742i	0.285466	+	1.61896i	−0.418149	+	0.908378i	$0.637321\pi$
$230$	−12.4525	+	28.4129i	−0.0541414	+	0.123534i
$231$	22.7423	−	28.9087i	0.0984516	−	0.125146i
$232$	−23.6834	+	28.2248i	−0.102084	+	0.121659i
$233$	−162.342	−	281.184i	−0.696745	−	1.20680i	−0.969589	−	0.244739i	$-0.921298\pi$
$233$	−162.342	−	281.184i	−0.696745	−	1.20680i	0.272844	−	0.962058i	$-0.412036\pi$
$234$	−15.5233	+	21.0677i	−0.0663390	+	0.0900330i
$235$	−17.0937	+	8.46072i	−0.0727393	+	0.0360031i
$236$	69.9079	+	192.070i	0.296220	+	0.813858i
$237$	411.155	+	220.385i	1.73483	+	0.929895i
$238$	42.8675	+	51.0876i	0.180116	+	0.214654i
$239$	51.0360	−	140.220i	0.213540	−	0.586696i	−0.785961	−	0.618276i	$-0.787832\pi$
$239$	51.0360	−	140.220i	0.213540	−	0.586696i	0.999501	+	0.0315797i	$0.0100538\pi$
$240$	47.1892	−	37.0564i	0.196622	−	0.154402i
$241$	8.91656	−	50.5683i	0.0369982	−	0.209827i	−0.960704	−	0.277573i	$-0.910470\pi$
$241$	8.91656	−	50.5683i	0.0369982	−	0.209827i	0.997703	+	0.0677465i	$0.0215809\pi$
$242$	−149.157			−0.616350
$243$	−242.966	−	4.07034i	−0.999860	−	0.0167504i
$244$	33.0248			0.135347
$245$	−135.746	+	142.217i	−0.554065	+	0.580476i
$246$	171.276	+	56.2862i	0.696246	+	0.228806i
$247$	−13.0965	+	35.9824i	−0.0530224	+	0.145678i
$248$	22.7774	−	19.1125i	0.0918444	−	0.0770666i
$249$	−384.183	−	205.928i	−1.54290	−	0.827018i
$250$	−27.6562	−	174.600i	−0.110625	−	0.698400i
$251$	344.136	+	198.687i	1.37106	+	0.791581i	0.991061	−	0.133407i	$-0.0425918\pi$
$251$	344.136	+	198.687i	1.37106	+	0.791581i	0.379997	+	0.924988i	$0.375925\pi$
$252$	−33.2197	+	45.0846i	−0.131824	+	0.178907i
$253$	14.9728	−	8.64454i	0.0591809	−	0.0341681i
$254$	88.4404	−	105.399i	0.348190	−	0.414957i
$255$	−216.056	+	70.7918i	−0.847279	+	0.277615i
$256$	2.77837	+	15.7569i	0.0108530	+	0.0615505i
$257$	−46.3597	−	262.919i	−0.180388	−	1.02303i	−0.931739	−	0.363128i	$-0.881709\pi$
$257$	−46.3597	−	262.919i	−0.180388	−	1.02303i	0.751351	−	0.659903i	$-0.229403\pi$
$258$	10.0519	−	4.02213i	0.0389610	−	0.0155896i
$259$	−47.1326	−	39.5489i	−0.181979	−	0.152699i
$260$	−20.5183	−	1.31479i	−0.0789166	−	0.00505688i
$261$	80.8745	+	84.8789i	0.309864	+	0.325206i
$262$	50.8251	+	29.3439i	0.193989	+	0.112000i
$263$	−232.412	+	84.5911i	−0.883697	+	0.321639i	−0.743701	−	0.668513i	$-0.766931\pi$
$263$	−232.412	+	84.5911i	−0.883697	+	0.321639i	−0.139996	+	0.990152i	$0.544709\pi$
$264$	−33.4225	+	1.05504i	−0.126600	+	0.00399637i
$265$	362.376	−	40.2216i	1.36746	−	0.151780i
$266$	−28.0263	+	77.0017i	−0.105362	+	0.289480i
$267$	−5.05981	+	4.52527i	−0.0189506	+	0.0169486i
$268$	212.403	+	37.4523i	0.792547	+	0.139747i
$269$			275.726i			1.02500i	0.858686	+	0.512501i	$0.171281\pi$
$269$			275.726i			1.02500i	−0.858686	+	0.512501i	$0.828719\pi$
$270$	−100.486	−	162.335i	−0.372170	−	0.601240i
$271$	−310.742			−1.14665			−0.573324	−	0.819329i	$-0.694346\pi$
$271$	−310.742			−1.14665			−0.573324	+	0.819329i	$0.694346\pi$
$272$	10.5281	−	59.7077i	0.0387062	−	0.219514i
$273$	18.7841	−	3.92696i	0.0688063	−	0.0143845i
$274$	72.1019	+	26.2429i	0.263146	+	0.0957772i
$275$	−45.2368	+	87.5215i	−0.164497	+	0.318260i
$276$	−22.3697	+	13.8742i	−0.0810497	+	0.0502687i
$277$	126.320	+	347.061i	0.456028	+	1.25293i	0.928418	+	0.371537i	$0.121169\pi$
$277$	126.320	+	347.061i	0.456028	+	1.25293i	−0.472390	+	0.881390i	$0.656609\pi$
$278$	−39.7736	+	68.8898i	−0.143070	+	0.247805i
$279$	−52.3798	−	78.7900i	−0.187741	−	0.282401i
$280$	−43.9089	−	2.81362i	−0.156817	−	0.0100487i
$281$	−106.344	+	126.736i	−0.378450	+	0.451019i	−0.921324	−	0.388795i	$-0.872891\pi$
$281$	−106.344	+	126.736i	−0.378450	+	0.451019i	0.542875	+	0.839814i	$0.317336\pi$
$282$	−16.0188	−	2.30606i	−0.0568044	−	0.00817750i
$283$	−327.142	+	57.6839i	−1.15598	+	0.203830i	−0.718584	−	0.695440i	$-0.755210\pi$
$283$	−327.142	+	57.6839i	−1.15598	+	0.203830i	−0.437394	+	0.899270i	$0.644098\pi$
$284$	123.732	−	21.8173i	0.435676	−	0.0768214i
$285$	−208.066	−	186.415i	−0.730057	−	0.654086i
$286$	8.77787	+	7.36551i	0.0306919	+	0.0257535i
$287$	−66.1040	−	114.495i	−0.230327	−	0.398939i
$288$	50.8103	−	3.21104i	0.176425	−	0.0111494i
$289$	29.6295	−	51.3198i	0.102524	−	0.177577i
$290$	−21.7632	+	89.5042i	−0.0750456	+	0.308635i
$291$	−155.027	−	249.955i	−0.532739	−	0.858951i
$292$	80.0754	+	95.4301i	0.274231	+	0.326815i
$293$	−160.495	−	58.4154i	−0.547765	−	0.199370i	0.0532885	−	0.998579i	$-0.483030\pi$
$293$	−160.495	−	58.4154i	−0.547765	−	0.199370i	−0.601053	+	0.799209i	$0.705252\pi$
$294$	−163.292	+	34.1375i	−0.555417	+	0.116114i
$295$	369.638	+	352.819i	1.25301	+	1.19600i
$296$			55.9352i			0.188970i
$297$	−8.48870	+	106.063i	−0.0285815	+	0.357116i
$298$			74.4537i			0.249845i
$299$	8.88313	+	1.56634i	0.0297095	+	0.00523858i
$300$	64.6353	−	135.360i	0.215451	−	0.451199i
$301$	−7.46063	−	2.71545i	−0.0247862	−	0.00902142i
$302$	40.4614	−	33.9512i	0.133978	−	0.112421i
$303$	−480.953	+	15.1822i	−1.58730	+	0.0501062i
$304$	70.0033	−	25.4791i	0.230274	−	0.0838129i
$305$	73.9942	−	36.6242i	0.242604	−	0.120079i
$306$	−185.086	−	54.4173i	−0.604856	−	0.177834i
$307$	−451.996	+	260.960i	−1.47230	+	0.850032i	−0.999515	−	0.0311455i	$-0.990084\pi$
$307$	−451.996	+	260.960i	−1.47230	+	0.850032i	−0.472785	+	0.881178i	$0.656751\pi$
$308$	18.7845	+	15.7621i	0.0609886	+	0.0511755i
$309$	−15.5517	+	6.22277i	−0.0503291	+	0.0201384i
$310$	29.8387	−	68.0828i	0.0962539	−	0.219622i
$311$	−43.8004	+	7.72320i	−0.140837	+	0.0248334i	−0.243622	−	0.969870i	$-0.578336\pi$
$311$	−43.8004	+	7.72320i	−0.140837	+	0.0248334i	0.102785	+	0.994704i	$0.467225\pi$
$312$	−13.7116	−	10.7869i	−0.0439476	−	0.0345733i
$313$	−57.8337	+	68.9236i	−0.184772	+	0.220203i	−0.850477	−	0.526012i	$-0.823687\pi$
$313$	−57.8337	+	68.9236i	−0.184772	+	0.220203i	0.665705	+	0.746215i	$0.268131\pi$
$314$	−249.383	+	143.982i	−0.794215	+	0.458540i
$315$	−24.4325	+	137.855i	−0.0775635	+	0.437636i
$316$	−155.498	+	269.331i	−0.492084	+	0.852314i
$317$	165.062	−	60.0778i	0.520702	−	0.189520i	−0.0682802	−	0.997666i	$-0.521751\pi$
$317$	165.062	−	60.0778i	0.520702	−	0.189520i	0.588982	+	0.808146i	$0.299529\pi$
$318$	272.673	+	146.157i	0.857463	+	0.459612i
$319$	39.3255	−	32.9980i	0.123277	−	0.103442i
$320$	23.6994	+	32.2233i	0.0740607	+	0.100698i
$321$	108.018	−	328.696i	0.336506	−	1.02397i
$322$	19.0097	+	3.35193i	0.0590365	+	0.0104097i
$323$	−282.288			−0.873956
$324$	7.82278	−	161.811i	0.0241444	−	0.499417i
$325$	−47.4308	+	19.8088i	−0.145941	+	0.0609500i
$326$	320.560	+	56.5233i	0.983312	+	0.173384i
$327$	−71.4876	+	217.534i	−0.218617	+	0.665241i
$328$	−41.1081	+	112.944i	−0.125330	+	0.344340i
$329$	7.62858	+	9.09139i	0.0231872	+	0.0276334i
$330$	−73.7153	+	39.4291i	−0.223380	+	0.119482i
$331$	363.633	−	132.352i	1.09859	−	0.399854i	0.271794	−	0.962355i	$-0.412383\pi$
$331$	363.633	−	132.352i	1.09859	−	0.399854i	0.826796	+	0.562501i	$0.190161\pi$
$332$	145.298	−	251.663i	0.437643	−	0.758021i
$333$	176.881	+	19.7901i	0.531174	+	0.0594297i
$334$	156.797	+	271.581i	0.469452	+	0.813115i
$335$	517.437	−	151.638i	1.54459	−	0.452651i
$336$	−29.3427	−	23.0837i	−0.0873294	−	0.0687016i
$337$	−447.042	+	78.8256i	−1.32653	+	0.233904i	−0.791626	−	0.611006i	$-0.790765\pi$
$337$	−447.042	+	78.8256i	−1.32653	+	0.233904i	−0.534909	+	0.844910i	$0.679654\pi$
$338$	−40.4642	−	229.484i	−0.119716	−	0.678946i
$339$	140.143	+	350.241i	0.413402	+	1.03316i
$340$	−42.6265	−	145.455i	−0.125372	−	0.427808i
$341$	−35.8777	+	20.7140i	−0.105213	+	0.0607449i
$342$	−55.8039	−	230.383i	−0.163169	−	0.673633i
$343$	237.968	+	137.391i	0.693785	+	0.400557i
$344$	2.46865	+	6.78256i	0.00717631	+	0.0197167i
$345$	−34.7345	+	55.8938i	−0.100680	+	0.162011i
$346$	14.3843	−	12.0699i	0.0415731	−	0.0348840i
$347$	−239.588	−	87.2029i	−0.690455	−	0.251305i	−0.0271251	−	0.999632i	$-0.508635\pi$
$347$	−239.588	−	87.2029i	−0.690455	−	0.251305i	−0.663330	+	0.748327i	$0.730857\pi$
$348$	−58.2589	+	52.1042i	−0.167411	+	0.149725i
$349$	−80.6595	+	457.443i	−0.231116	+	1.31072i	0.619525	+	0.784977i	$0.287325\pi$
$349$	−80.6595	+	457.443i	−0.231116	+	1.31072i	−0.850641	+	0.525747i	$0.823786\pi$
$350$	−101.501	+	42.3904i	−0.290003	+	0.121115i
$351$	−38.9620	+	39.5432i	−0.111003	+	0.112659i
$352$		−	22.2927i		−	0.0633317i
$353$	−93.3870	+	529.624i	−0.264552	+	1.50035i	0.505755	+	0.862677i	$0.331214\pi$
$353$	−93.3870	+	529.624i	−0.264552	+	1.50035i	−0.770307	+	0.637673i	$0.779897\pi$
$354$	88.7274	+	424.416i	0.250642	+	1.19892i
$355$	253.035	−	186.101i	0.712773	−	0.524227i
$356$	−2.90891	−	3.46671i	−0.00817111	−	0.00973795i
$357$	74.5658	+	120.225i	0.208868	+	0.336764i
$358$	−30.6815	−	84.2968i	−0.0857026	−	0.235466i
$359$	584.753	+	337.607i	1.62884	+	0.940410i	0.984440	+	0.175720i	$0.0562252\pi$
$359$	584.753	+	337.607i	1.62884	+	0.940410i	0.644398	+	0.764690i	$0.277108\pi$
$360$	110.283	−	63.5427i	0.306341	−	0.176508i
$361$	7.07351	+	12.2517i	0.0195942	+	0.0339382i
$362$	−144.077	−	120.895i	−0.398003	−	0.333964i
$363$	−313.181	−	45.0852i	−0.862757	−	0.124202i
$364$	2.22156	+	12.5991i	0.00610320	+	0.0346130i
$365$	285.245	+	125.015i	0.781494	+	0.342506i
$366$	69.3412	+	9.98229i	0.189457	+	0.0272740i
$367$	240.922	−	287.120i	0.656464	−	0.782344i	−0.330409	−	0.943838i	$-0.607187\pi$
$367$	240.922	−	287.120i	0.656464	−	0.782344i	0.986874	+	0.161494i	$0.0516313\pi$
$368$	−8.77431	−	15.1976i	−0.0238432	−	0.0412977i
$369$	342.611	+	169.954i	0.928486	+	0.460580i
$370$	62.0316	+	125.327i	0.167653	+	0.338720i
$371$	−77.5937	−	213.187i	−0.209147	−	0.574628i
$372$	53.6022	−	33.2452i	0.144092	−	0.0893689i
$373$	−314.242	−	374.499i	−0.842471	−	1.00402i	−0.999864	−	0.0164818i	$-0.994753\pi$
$373$	−314.242	−	374.499i	−0.842471	−	1.00402i	0.157393	−	0.987536i	$-0.449691\pi$
$374$	−28.8918	+	79.3796i	−0.0772508	+	0.212245i
$375$	−5.29316	−	374.963i	−0.0141151	−	0.999900i
$376$	1.87355	−	10.6254i	0.00498284	−	0.0282591i
$377$	26.7832			0.0710431
$378$	−83.3781	+	84.6217i	−0.220577	+	0.223867i
$379$	−621.598			−1.64010			−0.820051	−	0.572291i	$-0.806055\pi$
$379$	−621.598			−1.64010			−0.820051	+	0.572291i	$0.806055\pi$
$380$	128.591	−	134.721i	0.338397	−	0.354528i
$381$	217.555	−	194.571i	0.571010	−	0.510686i
$382$	−57.6280	+	158.332i	−0.150859	+	0.414481i
$383$	230.536	−	193.443i	0.601922	−	0.505072i	−0.290141	−	0.956984i	$-0.593702\pi$
$383$	230.536	−	193.443i	0.601922	−	0.505072i	0.892063	+	0.451912i	$0.149258\pi$
$384$	1.07088	+	33.9242i	0.00278875	+	0.0883443i
$385$	59.5679	+	14.4841i	0.154722	+	0.0376211i
$386$	−21.9422	−	12.6684i	−0.0568452	−	0.0328196i
$387$	22.3216	−	5.40679i	0.0576785	−	0.0139710i
$388$	169.814	−	98.0424i	0.437666	−	0.252687i
$389$	−367.718	+	438.229i	−0.945290	+	1.12655i	0.0465310	+	0.998917i	$0.485183\pi$
$389$	−367.718	+	438.229i	−0.945290	+	1.12655i	−0.991821	+	0.127636i	$0.959261\pi$
$390$	−42.6844	−	8.96264i	−0.109447	−	0.0229811i
$391$	11.5471	+	65.4868i	0.0295322	+	0.167485i
$392$	−19.3123	−	109.526i	−0.0492661	−	0.279402i
$393$	97.8465	+	76.9753i	0.248973	+	0.195866i
$394$	337.661	+	283.331i	0.857008	+	0.719115i
$395$	−49.7188	+	775.901i	−0.125870	+	1.96431i
$396$	−70.4952	−	7.88726i	−0.178018	−	0.0199173i
$397$	−211.849	−	122.311i	−0.533624	−	0.308088i	0.208867	−	0.977944i	$-0.433022\pi$
$397$	−211.849	−	122.311i	−0.533624	−	0.308088i	−0.742491	+	0.669856i	$0.766356\pi$
$398$	255.307	−	92.9243i	0.641476	−	0.233478i
$399$	−82.1213	+	153.207i	−0.205818	+	0.383978i
$400$	88.8354	+	45.9159i	0.222089	+	0.114790i
$401$	260.247	−	715.022i	0.648994	−	1.78310i	0.0275724	−	0.999620i	$-0.491222\pi$
$401$	260.247	−	715.022i	0.648994	−	1.78310i	0.621422	−	0.783476i	$-0.286555\pi$
$402$	434.656	+	142.840i	1.08123	+	0.355323i
$403$	−21.2857	−	3.75325i	−0.0528182	−	0.00931327i
$404$		−	320.795i		−	0.794047i
$405$	−161.920	−	371.224i	−0.399801	−	0.916602i
$406$	57.3157			0.141172
$407$	13.5332	−	76.7503i	0.0332510	−	0.188576i
$408$	40.1532	−	122.185i	0.0984148	−	0.299472i
$409$	−16.5164	−	6.01147i	−0.0403823	−	0.0146980i	0.321750	−	0.946825i	$-0.395729\pi$
$409$	−16.5164	−	6.01147i	−0.0403823	−	0.0146980i	−0.362132	+	0.932127i	$0.617951\pi$
$410$	33.1480	+	298.646i	0.0808487	+	0.728405i
$411$	143.458	+	76.8957i	0.349047	+	0.187094i
$412$	−3.81933	−	10.4935i	−0.00927022	−	0.0254697i
$413$	158.980	−	275.361i	0.384939	−	0.666733i
$414$	−51.1628	+	22.3696i	−0.123582	+	0.0540329i
$415$	46.4572	−	725.001i	0.111945	−	1.74699i
$416$	7.47608	−	8.90965i	0.0179714	−	0.0214174i
$417$	−104.335	+	132.624i	−0.250203	+	0.318043i
$418$	−102.218	+	18.0238i	−0.244541	+	0.0431192i
$419$	245.563	−	43.2994i	0.586070	−	0.103340i	0.127252	−	0.991870i	$-0.459384\pi$
$419$	245.563	−	43.2994i	0.586070	−	0.103340i	0.458818	+	0.888531i	$0.348273\pi$
$420$	−91.3439	−	19.1799i	−0.217485	−	0.0456664i
$421$	−222.930	−	187.061i	−0.529525	−	0.444325i	0.338412	−	0.940998i	$-0.390110\pi$
$421$	−222.930	−	187.061i	−0.529525	−	0.444325i	−0.867937	+	0.496673i	$0.834555\pi$
$422$	−32.9556	−	57.0808i	−0.0780939	−	0.135263i
$423$	−32.9373	−	9.68393i	−0.0778660	−	0.0228935i
$424$	−103.125	+	178.617i	−0.243219	+	0.421267i
$425$	−256.815	−	278.629i	−0.604272	−	0.655597i
$426$	266.392	−	8.40914i	0.625332	−	0.0197398i
$427$	−33.0220	−	39.3541i	−0.0773350	−	0.0921643i
$428$	216.749	+	78.8903i	0.506423	+	0.184323i
$429$	16.2043	+	18.1184i	0.0377723	+	0.0422341i
$430$	13.0530	+	12.4591i	0.0303558	+	0.0289746i
$431$		−	634.581i		−	1.47235i	−0.676793	−	0.736173i	$-0.736631\pi$
$431$		−	634.581i		−	1.47235i	0.676793	−	0.736173i	$-0.263369\pi$
$432$	107.656	+	8.61613i	0.249203	+	0.0199448i
$433$			90.2951i			0.208534i	0.994549	+	0.104267i	$0.0332496\pi$
$433$			90.2951i			0.208534i	−0.994549	+	0.104267i	$0.966750\pi$
$434$	−45.5511	−	8.03189i	−0.104956	−	0.0185067i
$435$	−72.7498	+	181.351i	−0.167241	+	0.416900i
$436$	−143.447	−	52.2103i	−0.329006	−	0.119748i
$437$	−62.5907	+	52.5198i	−0.143228	+	0.120183i
$438$	139.287	+	224.576i	0.318007	+	0.512731i
$439$	−175.263	+	63.7904i	−0.399232	+	0.145308i	−0.533830	−	0.845592i	$-0.679248\pi$
$439$	−175.263	+	63.7904i	−0.399232	+	0.145308i	0.134598	+	0.990900i	$0.457026\pi$
$440$	−24.7225	−	49.9484i	−0.0561874	−	0.113519i
$441$	−353.180	+	22.3198i	−0.800861	+	0.0506117i
$442$	−38.1677	+	22.0362i	−0.0863524	+	0.0498556i
$443$	475.568	+	399.049i	1.07352	+	0.900788i	0.995367	−	0.0961534i	$-0.0306539\pi$
$443$	475.568	+	399.049i	1.07352	+	0.900788i	0.0781510	+	0.996942i	$0.475098\pi$
$444$	−16.9074	+	117.446i	−0.0380796	+	0.264517i
$445$	−10.3622	−	4.54143i	−0.0232858	−	0.0102055i
$446$	−433.593	+	76.4542i	−0.972182	+	0.171422i
$447$	−22.5049	+	156.329i	−0.0503465	+	0.349728i
$448$	15.9987	−	19.0665i	0.0357114	−	0.0425591i
$449$	−545.414	+	314.895i	−1.21473	+	0.701325i	−0.963786	−	0.266677i	$-0.914074\pi$
$449$	−545.414	+	314.895i	−1.21473	+	0.701325i	−0.250944	+	0.968002i	$0.580741\pi$
$450$	176.628	−	264.675i	0.392506	−	0.588166i
$451$	83.7316	−	145.027i	0.185658	−	0.321568i
$452$	−236.325	+	86.0154i	−0.522844	+	0.190300i
$453$	95.2181	−	59.0562i	0.210195	−	0.130367i
$454$	28.4145	−	23.8426i	0.0625869	−	0.0525167i
$455$	18.9499	+	25.7655i	0.0416481	+	0.0566274i
$456$	154.686	−	32.3382i	0.339223	−	0.0709171i
$457$	−341.453	−	60.2073i	−0.747161	−	0.131745i	−0.212912	−	0.977071i	$-0.568295\pi$
$457$	−341.453	−	60.2073i	−0.747161	−	0.131745i	−0.534250	+	0.845327i	$0.679406\pi$
$458$	−532.396			−1.16244
$459$	−372.172	−	170.204i	−0.810832	−	0.370815i
$460$	−36.5134	−	24.3205i	−0.0793769	−	0.0528706i
$461$	−798.308	−	140.763i	−1.73169	−	0.305343i	−0.783109	−	0.621885i	$-0.786367\pi$
$461$	−798.308	−	140.763i	−1.73169	−	0.305343i	−0.948579	+	0.316542i	$0.897478\pi$
$462$	34.6770	+	38.7731i	0.0750584	+	0.0839245i
$463$	270.135	−	742.190i	0.583445	−	1.60300i	−0.198806	−	0.980039i	$-0.563707\pi$
$463$	270.135	−	742.190i	0.583445	−	1.60300i	0.782251	−	0.622963i	$-0.214071\pi$
$464$	−33.4934	−	39.9159i	−0.0721840	−	0.0860256i
$465$	83.2308	−	133.933i	0.178991	−	0.288027i
$466$	431.480	−	157.046i	0.925922	−	0.337008i
$467$	142.724	−	247.206i	0.305620	−	0.529349i	−0.671779	−	0.740751i	$-0.734470\pi$
$467$	142.724	−	247.206i	0.305620	−	0.529349i	0.977399	+	0.211402i	$0.0678030\pi$
$468$	−25.5295	−	26.7935i	−0.0545501	−	0.0572511i
$469$	−167.755	−	290.560i	−0.357687	−	0.619531i
$470$	−7.58568	−	25.8847i	−0.0161397	−	0.0550738i
$471$	−567.145	+	226.934i	−1.20413	+	0.481814i
$472$	−284.670	+	50.1949i	−0.603114	+	0.106345i
$473$	−1.74631	−	9.90383i	−0.00369199	−	0.0209383i
$474$	−407.906	+	518.506i	−0.860562	+	1.09389i
$475$	138.713	−	444.457i	0.292026	−	0.935699i
$476$	−81.6783	+	47.1570i	−0.171593	+	0.0990693i
$477$	528.347	+	389.302i	1.10764	+	0.816146i
$478$	182.756	+	105.514i	0.382334	+	0.220741i
$479$	−121.007	−	332.463i	−0.252624	−	0.694078i	−0.999574	−	0.0291975i	$-0.990705\pi$
$479$	−121.007	−	332.463i	−0.252624	−	0.694078i	0.746950	−	0.664880i	$-0.231517\pi$
$480$	40.0210	+	74.8219i	0.0833772	+	0.155879i
$481$	31.1477	−	26.1360i	0.0647561	−	0.0543368i
$482$	68.2382	+	24.8367i	0.141573	+	0.0515284i
$483$	38.9011	+	12.7840i	0.0805406	+	0.0264679i
$484$	36.6293	−	207.735i	0.0756803	−	0.429204i
$485$	271.752	−	407.993i	0.560314	−	0.841223i
$486$	65.3354	−	337.386i	0.134435	−	0.694210i
$487$		−	261.268i		−	0.536485i	−0.963351	−	0.268243i	$-0.913557\pi$
$487$		−	261.268i		−	0.536485i	0.963351	−	0.268243i	$-0.0864429\pi$
$488$	−8.11007	+	45.9945i	−0.0166190	+	0.0942511i
$489$	655.986	+	215.575i	1.34149	+	0.440849i
$490$	−164.733	−	223.982i	−0.336190	−	0.457106i
$491$	−319.477	−	380.738i	−0.650665	−	0.775433i	0.335349	−	0.942094i	$-0.391146\pi$
$491$	−319.477	−	380.738i	−0.650665	−	0.775433i	−0.986014	+	0.166661i	$0.946701\pi$
$492$	−120.453	+	224.719i	−0.244823	+	0.456746i
$493$	67.5309	+	185.540i	0.136980	+	0.376348i
$494$	−46.8975	−	27.0763i	−0.0949343	−	0.0548103i
$495$	−166.696	+	60.5067i	−0.336760	+	0.122236i
$496$	21.0250	+	36.4163i	0.0423891	+	0.0734200i
$497$	−149.721	−	125.630i	−0.301248	−	0.252778i
$498$	381.147	−	484.492i	0.765356	−	0.972875i
$499$	−42.6297	−	241.765i	−0.0854303	−	0.484499i	−0.997263	−	0.0739371i	$-0.976444\pi$
$499$	−42.6297	−	241.765i	−0.0854303	−	0.484499i	0.911833	−	0.410562i	$-0.134668\pi$
$500$	249.962	+	4.35997i	0.499924	+	0.00871995i
$501$	247.133	+	617.625i	0.493280	+	1.23279i
$502$	−361.228	+	430.495i	−0.719578	+	0.857559i
$503$	429.252	+	743.487i	0.853384	+	1.47811i	0.878136	+	0.478411i	$0.158787\pi$
$503$	429.252	+	743.487i	0.853384	+	1.47811i	−0.0247514	+	0.999694i	$0.507879\pi$
$504$	−54.6326	−	57.3376i	−0.108398	−	0.113765i
$505$	−355.759	−	718.763i	−0.704473	−	1.42329i
$506$	8.36254	+	22.9759i	0.0165268	+	0.0454069i
$507$	−15.5963	−	494.072i	−0.0307619	−	0.974501i
$508$	125.074	+	149.057i	0.246208	+	0.293419i
$509$	−46.4191	+	127.535i	−0.0911966	+	0.250561i	−0.976902	−	0.213687i	$-0.931453\pi$
$509$	−46.4191	+	127.535i	−0.0911966	+	0.250561i	0.885706	+	0.464247i	$0.153675\pi$
$510$	−45.5356	−	318.292i	−0.0892855	−	0.624102i
$511$	33.6511	−	190.845i	0.0658533	−	0.373473i
$512$	−22.6274			−0.0441942
$513$	−47.5330	−	500.596i	−0.0926570	−	0.975821i
$514$	377.560			0.734552
$515$	−20.1947	−	19.2758i	−0.0392130	−	0.0374288i
$516$	3.13322	+	14.9874i	0.00607213	+	0.0290453i
$517$	−5.14150	+	14.1261i	−0.00994487	+	0.0273233i
$518$	66.6555	−	55.9306i	0.128679	−	0.107974i
$519$	33.8507	−	20.9949i	0.0652228	−	0.0404526i
$520$	6.86994	−	28.2536i	0.0132114	−	0.0543338i
$521$	640.829	+	369.983i	1.23000	+	0.710140i	0.967029	−	0.254665i	$-0.0819651\pi$
$521$	640.829	+	369.983i	1.23000	+	0.710140i	0.262969	+	0.964804i	$0.415298\pi$
$522$	−138.074	+	91.7921i	−0.264510	+	0.175847i
$523$	533.037	−	307.749i	1.01919	−	0.588430i	0.105321	−	0.994438i	$-0.466413\pi$
$523$	533.037	−	307.749i	1.01919	−	0.588430i	0.913869	+	0.406008i	$0.133080\pi$
$524$	−53.3495	+	63.5794i	−0.101812	+	0.121335i
$525$	−225.932	+	58.3257i	−0.430347	+	0.111097i
$526$	−60.7377	−	344.461i	−0.115471	−	0.654868i
$527$	−27.6691	−	156.919i	−0.0525030	−	0.297759i
$528$	6.73836	−	46.8075i	0.0127620	−	0.0886506i
$529$	−390.493	−	327.663i	−0.738173	−	0.619400i
$530$	−32.9729	+	514.568i	−0.0622130	+	0.970884i
$531$	58.0117	+	917.956i	0.109250	+	1.72873i
$532$	−100.360	−	57.9428i	−0.188646	−	0.108915i
$533$	82.1009	−	29.8823i	0.154035	−	0.0560643i
$534$	−5.05990	−	8.15823i	−0.00947548	−	0.0152776i
$535$	573.130	−	63.6140i	1.07127	−	0.118905i
$536$	−104.322	+	286.622i	−0.194630	+	0.534742i
$537$	−38.9411	−	186.270i	−0.0725160	−	0.346871i
$538$	−384.011	−	67.7115i	−0.713775	−	0.125858i
$539$			154.956i			0.287487i
$540$	250.765	−	100.084i	0.464380	−	0.185341i
$541$	829.643			1.53354			0.766768	−	0.641924i	$-0.221864\pi$
$541$	829.643			1.53354			0.766768	+	0.641924i	$0.221864\pi$
$542$	76.3106	−	432.779i	0.140794	−	0.798485i
$543$	−265.973	−	297.390i	−0.489821	−	0.547680i
$544$	80.5712	+	29.3255i	0.148109	+	0.0539072i
$545$	−379.302	+	42.1003i	−0.695968	+	0.0772483i
$546$	0.856268	+	27.1255i	0.00156826	+	0.0496805i
$547$	−172.050	−	472.705i	−0.314535	−	0.864177i	−0.991726	−	0.128370i	$-0.959025\pi$
$547$	−172.050	−	472.705i	−0.314535	−	0.864177i	0.677192	−	0.735807i	$-0.263197\pi$
$548$	−54.2558	+	93.9737i	−0.0990069	+	0.171485i
$549$	142.577	+	41.9191i	0.259703	+	0.0763554i
$550$	−110.785	−	84.4957i	−0.201427	−	0.153629i
$551$	−155.945	+	185.848i	−0.283022	+	0.337292i
$552$	−13.8295	−	34.5621i	−0.0250534	−	0.0626125i
$553$	476.436	−	84.0085i	0.861548	−	0.151914i
$554$	−514.383	+	90.6995i	−0.928488	+	0.163718i
$555$	92.3642	+	281.895i	0.166422	+	0.507919i
$556$	−86.1774	−	72.3114i	−0.154995	−	0.130057i
$557$	410.682	+	711.322i	0.737311	+	1.27706i	0.953702	+	0.300753i	$0.0972380\pi$
$557$	410.682	+	711.322i	0.737311	+	1.27706i	−0.216391	+	0.976307i	$0.569429\pi$
$558$	122.596	−	53.6020i	0.219707	−	0.0960609i
$559$	2.62340	−	4.54386i	0.00469302	−	0.00812856i
$560$	14.7016	−	60.4622i	0.0262528	−	0.107968i
$561$	−84.6572	+	157.938i	−0.150904	+	0.281530i
$562$	−150.394	−	179.232i	−0.267604	−	0.318918i
$563$	528.511	+	192.362i	0.938741	+	0.341674i	0.765668	−	0.643235i	$-0.222408\pi$
$563$	528.511	+	192.362i	0.938741	+	0.341674i	0.173072	+	0.984909i	$0.444631\pi$
$564$	7.14555	−	21.7436i	0.0126694	−	0.0385525i
$565$	−434.113	+	454.806i	−0.768341	+	0.804966i
$566$		−	469.785i		−	0.830010i
$567$	−200.645	+	152.476i	−0.353872	+	0.268917i
$568$			177.683i			0.312822i
$569$	260.448	+	45.9240i	0.457729	+	0.0807100i	0.397759	−	0.917490i	$-0.369788\pi$
$569$	260.448	+	45.9240i	0.457729	+	0.0807100i	0.0599708	+	0.998200i	$0.480899\pi$
$570$	310.721	−	244.001i	0.545124	−	0.428072i
$571$	−200.873	−	73.1119i	−0.351792	−	0.128042i	0.160079	−	0.987104i	$-0.448825\pi$
$571$	−200.873	−	73.1119i	−0.351792	−	0.128042i	−0.511871	+	0.859062i	$0.671047\pi$
$572$	−12.4138	+	10.4164i	−0.0217024	+	0.0182105i
$573$	−168.859	+	315.026i	−0.294692	+	0.549784i
$574$	175.695	−	63.9476i	0.306088	−	0.111407i
$575$	−108.782	−	13.9987i	−0.189186	−	0.0243455i
$576$	−8.00567	+	71.5535i	−0.0138987	+	0.124225i
$577$	−689.215	+	397.919i	−1.19448	+	0.689633i	−0.959319	−	0.282323i	$-0.908895\pi$
$577$	−689.215	+	397.919i	−1.19448	+	0.689633i	−0.235161	+	0.971956i	$0.575562\pi$
$578$	64.1983	+	53.8687i	0.111070	+	0.0931985i
$579$	−42.2424	−	33.2319i	−0.0729574	−	0.0573953i
$580$	−119.311	−	52.2903i	−0.205708	−	0.0901557i
$581$	−445.181	+	78.4975i	−0.766233	+	0.135108i
$582$	386.190	−	154.528i	0.663557	−	0.265512i
$583$	184.716	−	220.136i	0.316837	−	0.377591i
$584$	−152.573	+	88.0879i	−0.261255	+	0.150836i
$585$	−86.9142	−	31.7207i	−0.148571	−	0.0542234i
$586$	120.770	−	209.181i	0.206093	−	0.356963i
$587$	−166.341	+	60.5432i	−0.283375	+	0.103140i	−0.479797	−	0.877379i	$-0.659290\pi$
$587$	−166.341	+	60.5432i	−0.283375	+	0.103140i	0.196422	+	0.980519i	$0.437068\pi$
$588$	−7.44363	−	235.805i	−0.0126592	−	0.401030i
$589$	149.980	−	125.848i	0.254634	−	0.213664i
$590$	−582.156	+	428.161i	−0.986705	+	0.725697i
$591$	623.337	+	696.968i	1.05472	+	1.17930i
$592$	−77.9025	−	13.7363i	−0.131592	−	0.0232032i
$593$	−551.927			−0.930736			−0.465368	−	0.885117i	$-0.654078\pi$
$593$	−551.927			−0.930736			−0.465368	+	0.885117i	$0.654078\pi$
$594$	−145.633	−	37.8691i	−0.245173	−	0.0637526i
$595$	−130.709	+	196.239i	−0.219679	+	0.329813i
$596$	−103.694	−	18.2840i	−0.173983	−	0.0306779i
$597$	564.151	−	117.940i	0.944976	−	0.197554i
$598$	−4.36296	+	11.9871i	−0.00729592	+	0.0200454i
$599$	575.954	+	686.395i	0.961526	+	1.14590i	0.989242	+	0.146286i	$0.0467319\pi$
$599$	575.954	+	686.395i	0.961526	+	1.14590i	−0.0277166	+	0.999616i	$0.508824\pi$
$600$	172.647	+	123.260i	0.287744	+	0.205434i
$601$	576.622	−	209.873i	0.959437	−	0.349207i	0.185624	−	0.982621i	$-0.440569\pi$
$601$	576.622	−	209.873i	0.959437	−	0.349207i	0.773813	+	0.633414i	$0.218347\pi$
$602$	5.61403	−	9.72379i	0.00932563	−	0.0161525i
$603$	869.461	+	431.300i	1.44189	+	0.715256i
$604$	37.3484	+	64.6893i	0.0618351	+	0.107102i
$605$	−148.306	−	506.066i	−0.245134	−	0.836472i
$606$	96.9657	−	673.566i	0.160009	−	1.11149i
$607$	515.481	−	90.8932i	0.849227	−	0.149742i	0.267935	−	0.963437i	$-0.413659\pi$
$607$	515.481	−	90.8932i	0.849227	−	0.149742i	0.581292	+	0.813695i	$0.302548\pi$
$608$	18.2944	+	103.753i	0.0300895	+	0.170646i
$609$	120.344	+	17.3246i	0.197610	+	0.0284477i
$610$	32.8363	+	112.048i	0.0538301	+	0.183685i
$611$	−6.79222	+	3.92149i	−0.0111166	+	0.00641815i
$612$	121.241	−	244.411i	0.198106	−	0.399364i
$613$	233.519	+	134.822i	0.380945	+	0.219939i	0.678229	−	0.734850i	$-0.262748\pi$
$613$	233.519	+	134.822i	0.380945	+	0.219939i	−0.297284	+	0.954789i	$0.596081\pi$
$614$	−252.447	−	693.593i	−0.411152	−	1.12963i
$615$	−20.6708	+	637.079i	−0.0336111	+	1.03590i
$616$	−26.5653	+	22.2909i	−0.0431255	+	0.0361866i
$617$	−404.492	−	147.223i	−0.655579	−	0.238611i	−0.00725227	−	0.999974i	$-0.502308\pi$
$617$	−404.492	−	147.223i	−0.655579	−	0.238611i	−0.648326	+	0.761363i	$0.724531\pi$
$618$	−4.84751	−	23.1874i	−0.00784387	−	0.0375201i
$619$	−109.106	+	618.771i	−0.176262	+	0.999630i	0.760416	+	0.649437i	$0.224995\pi$
$619$	−109.106	+	618.771i	−0.176262	+	0.999630i	−0.936677	+	0.350193i	$0.886116\pi$
$620$	87.4932	+	58.2767i	0.141118	+	0.0939947i
$621$	−114.187	+	31.5041i	−0.183876	+	0.0507312i
$622$		−	62.8987i		−	0.101123i
$623$	−1.22245	+	6.93285i	−0.00196220	+	0.0111282i
$624$	18.3904	−	16.4476i	0.0294719	−	0.0263583i
$625$	564.892	−	267.437i	0.903827	−	0.427899i
$626$	−81.7893	−	97.4726i	−0.130654	−	0.155707i
$627$	−220.073	+	6.94700i	−0.350993	+	0.0110797i
$628$	−139.285	−	382.682i	−0.221791	−	0.609366i
$629$	259.591	+	149.875i	0.412705	+	0.238275i
$630$	−185.995	−	67.8817i	−0.295230	−	0.107749i
$631$	392.092	+	679.124i	0.621382	+	1.07627i	0.989229	+	0.146379i	$0.0467620\pi$
$631$	392.092	+	679.124i	0.621382	+	1.07627i	−0.367846	+	0.929887i	$0.619905\pi$
$632$	−336.919	−	282.708i	−0.533099	−	0.447323i
$633$	−51.9425	−	129.813i	−0.0820576	−	0.205075i
$634$	43.1368	+	244.641i	0.0680391	+	0.385869i
$635$	445.538	+	195.266i	0.701635	+	0.307506i
$636$	−270.519	+	343.867i	−0.425344	+	0.540672i
$637$	−51.9658	+	61.9305i	−0.0815790	+	0.0972221i
$638$	36.2999	+	62.8732i	0.0568964	+	0.0985474i
$639$	561.877	+	62.8649i	0.879307	+	0.0983801i
$640$	−50.6982	+	25.0936i	−0.0792160	+	0.0392088i
$641$	237.304	+	651.987i	0.370209	+	1.01714i	0.975281	+	0.220970i	$0.0709223\pi$
$641$	237.304	+	651.987i	0.370209	+	1.01714i	−0.605071	+	0.796171i	$0.706855\pi$
$642$	431.257	+	231.160i	0.671740	+	0.360062i
$643$	−303.108	−	361.230i	−0.471396	−	0.561788i	0.476989	−	0.878909i	$-0.341728\pi$
$643$	−303.108	−	361.230i	−0.471396	−	0.561788i	−0.948385	+	0.317121i	$0.897284\pi$
$644$	−9.33666	+	25.6523i	−0.0144979	+	0.0398327i
$645$	23.6410	+	30.1055i	0.0366528	+	0.0466752i
$646$	69.3230	−	393.150i	0.107311	−	0.608592i
$647$	195.799			0.302626			0.151313	−	0.988486i	$-0.451650\pi$
$647$	195.799			0.302626			0.151313	+	0.988486i	$0.451650\pi$
$648$	223.438	+	50.6318i	0.344811	+	0.0781356i
$649$	402.748			0.620567
$650$	−15.9404	−	70.9227i	−0.0245237	−	0.109112i
$651$	−93.2147	−	30.6329i	−0.143187	−	0.0470552i
$652$	−157.443	+	432.572i	−0.241478	+	0.663454i
$653$	−160.861	+	134.978i	−0.246341	+	0.206704i	−0.757595	−	0.652725i	$-0.773626\pi$
$653$	−160.861	+	134.978i	−0.246341	+	0.206704i	0.511254	+	0.859430i	$0.329181\pi$
$654$	−285.410	−	152.984i	−0.436406	−	0.233920i
$655$	−49.0240	+	201.618i	−0.0748458	+	0.307814i
$656$	−147.205	−	84.9886i	−0.224397	−	0.129556i
$657$	224.575	+	513.639i	0.341819	+	0.781795i
$658$	−14.5352	+	8.39192i	−0.0220900	+	0.0127537i
$659$	−179.021	+	213.348i	−0.271655	+	0.323746i	−0.884574	−	0.466400i	$-0.845551\pi$
$659$	−179.021	+	213.348i	−0.271655	+	0.323746i	0.612919	+	0.790146i	$0.289995\pi$
$660$	−36.8114	−	112.348i	−0.0557748	−	0.170224i
$661$	−44.6582	−	253.269i	−0.0675616	−	0.383161i	−0.999774	−	0.0212496i	$-0.993236\pi$
$661$	−44.6582	−	253.269i	−0.0675616	−	0.383161i	0.932213	−	0.361911i	$-0.117876\pi$
$662$	95.0306	+	538.945i	0.143551	+	0.814116i
$663$	−86.8007	+	34.7319i	−0.130921	+	0.0523860i
$664$	314.817	+	264.162i	0.474121	+	0.397835i
$665$	−289.121	−	18.5265i	−0.434769	−	0.0278594i
$666$	−70.9999	+	241.487i	−0.106606	+	0.362594i
$667$	49.4932	+	28.5749i	0.0742027	+	0.0428409i
$668$	−416.744	+	151.682i	−0.623868	+	0.227069i
$669$	−933.514	+	29.4681i	−1.39539	+	0.0440480i
$670$	84.1211	+	757.887i	0.125554	+	1.13118i
$671$	22.2561	−	61.1482i	0.0331686	−	0.0911300i
$672$	39.3552	−	35.1976i	0.0585643	−	0.0523773i
$673$	−653.019	−	115.145i	−0.970310	−	0.171092i	−0.334041	−	0.942559i	$-0.608412\pi$
$673$	−653.019	−	115.145i	−0.970310	−	0.171092i	−0.636270	+	0.771467i	$0.719523\pi$
$674$		−	641.966i		−	0.952472i
$675$	450.863	−	502.342i	0.667946	−	0.744210i
$676$	329.545			0.487493
$677$	79.9812	−	453.596i	0.118141	−	0.670009i	−0.867007	−	0.498297i	$-0.833959\pi$
$677$	79.9812	−	453.596i	0.118141	−	0.670009i	0.985147	−	0.171712i	$-0.0549298\pi$
$678$	−522.206	+	109.171i	−0.770216	+	0.161019i
$679$	−286.633	−	104.326i	−0.422140	−	0.153647i
$680$	213.047	−	23.6470i	0.313304	−	0.0347750i
$681$	66.8680	−	41.4729i	0.0981908	−	0.0609000i
$682$	−20.0383	−	55.0548i	−0.0293817	−	0.0807255i
$683$	29.7154	−	51.4686i	0.0435072	−	0.0753567i	−0.843452	−	0.537205i	$-0.819480\pi$
$683$	29.7154	−	51.4686i	0.0435072	−	0.0753567i	0.886959	+	0.461848i	$0.152814\pi$
$684$	334.564	−	21.1433i	0.489129	−	0.0309113i
$685$	−17.3476	+	270.724i	−0.0253250	+	0.395217i
$686$	−249.788	+	297.685i	−0.364122	+	0.433943i
$687$	−1117.86	−	160.926i	−1.62716	−	0.234244i
$688$	−10.0525	+	1.77253i	−0.0146112	+	0.00257635i
$689$	147.649	−	26.0345i	0.214295	−	0.0377860i
$690$	−69.3149	−	62.1019i	−0.100456	−	0.0900028i
$691$	157.949	+	132.535i	0.228581	+	0.191802i	0.749884	−	0.661570i	$-0.230109\pi$
$691$	157.949	+	132.535i	0.228581	+	0.191802i	−0.521303	+	0.853372i	$0.674554\pi$
$692$	13.2776	+	22.9975i	0.0191873	+	0.0332333i
$693$	61.0906	+	91.8927i	0.0881538	+	0.132601i
$694$	180.287	−	312.266i	0.259779	−	0.449951i
$695$	−273.279	−	66.4486i	−0.393207	−	0.0956095i
$696$	−58.2600	−	93.9343i	−0.0837069	−	0.134963i
$697$	414.016	+	493.405i	0.593997	+	0.707898i
$698$	−617.286	−	224.674i	−0.884363	−	0.321882i
$699$	953.437	−	199.323i	1.36400	−	0.285155i
$700$	−34.1122	−	151.773i	−0.0487317	−	0.216819i
$701$		−	748.973i		−	1.06843i	−0.845347	−	0.534217i	$-0.820606\pi$
$701$		−	748.973i		−	1.06843i	0.845347	−	0.534217i	$-0.179394\pi$
$702$	−45.5048	−	63.9744i	−0.0648216	−	0.0911316i
$703$			368.309i			0.523911i
$704$	31.0477	+	5.47456i	0.0441019	+	0.00777636i
$705$	−8.10338	−	56.6423i	−0.0114942	−	0.0803437i
$706$	−714.689	−	260.125i	−1.01231	−	0.368450i
$707$	−382.277	+	320.769i	−0.540704	+	0.453704i
$708$	−612.886	+	19.3469i	−0.865658	+	0.0273261i
$709$	−1104.89	+	402.148i	−1.55838	+	0.567205i	−0.970365	−	0.241643i	$-0.922314\pi$
$709$	−1104.89	+	402.148i	−1.55838	+	0.567205i	−0.588017	+	0.808848i	$0.700091\pi$
$710$	197.049	+	398.110i	0.277533	+	0.560719i
$711$	−1013.20	+	965.398i	−1.42503	+	1.35780i
$712$	5.54254	−	3.19999i	0.00778447	−	0.00449437i
$713$	−35.3299	−	29.6453i	−0.0495511	−	0.0415783i
$714$	−185.752	+	74.3257i	−0.260157	+	0.104098i
$715$	−16.2622	+	37.1054i	−0.0227444	+	0.0518957i
$716$	124.937	−	22.0298i	0.174493	−	0.0307679i
$717$	351.834	+	276.786i	0.490703	+	0.386034i
$718$	−613.796	+	731.494i	−0.854869	+	1.01879i
$719$	−276.685	+	159.744i	−0.384819	+	0.222175i	−0.679913	−	0.733293i	$-0.737982\pi$
$719$	−276.685	+	159.744i	−0.384819	+	0.222175i	0.295094	+	0.955468i	$0.404649\pi$
$720$	61.4150	+	169.199i	0.0852986	+	0.234998i
$721$	−8.68565	+	15.0440i	−0.0120467	+	0.0208655i
$722$	−18.8003	+	6.84277i	−0.0260393	+	0.00947751i
$723$	135.771	+	72.7751i	0.187788	+	0.100657i
$724$	203.756	−	170.972i	0.281431	−	0.236149i
$725$	−325.313	+	15.1544i	−0.448707	+	0.0209026i
$726$	139.701	−	425.104i	0.192426	−	0.585543i
$727$	−806.354	−	142.182i	−1.10915	−	0.195574i	−0.411079	−	0.911600i	$-0.634848\pi$
$727$	−806.354	−	142.182i	−1.10915	−	0.195574i	−0.698074	+	0.716026i	$0.745959\pi$
$728$	−18.0927			−0.0248526
$729$	239.164	−	688.652i	0.328071	−	0.944653i
$730$	−244.161	+	366.569i	−0.334467	+	0.502149i
$731$	38.0920	+	6.71665i	0.0521094	+	0.00918830i
$732$	−30.9311	+	94.1221i	−0.0422556	+	0.128582i
$733$	−38.1653	+	104.858i	−0.0520672	+	0.143054i	−0.963000	−	0.269501i	$-0.913141\pi$
$733$	−38.1653	+	104.858i	−0.0520672	+	0.143054i	0.910933	+	0.412555i	$0.135363\pi$
$734$	340.716	+	406.049i	0.464190	+	0.553201i
$735$	−278.184	−	520.083i	−0.378482	−	0.707596i
$736$	23.3208	−	8.48808i	0.0316859	−	0.0115327i
$737$	212.489	−	368.042i	0.288317	−	0.499379i
$738$	−320.837	+	435.428i	−0.434738	+	0.590011i
$739$	−150.447	−	260.581i	−0.203581	−	0.352613i	0.746098	−	0.665836i	$-0.231925\pi$
$739$	−150.447	−	260.581i	−0.203581	−	0.352613i	−0.949680	+	0.313222i	$0.898591\pi$
$740$	−189.779	+	55.6161i	−0.256459	+	0.0751569i
$741$	−90.2853	−	71.0270i	−0.121843	−	0.0958529i
$742$	315.967	−	55.7135i	0.425831	−	0.0750855i
$743$	152.080	+	862.488i	0.204684	+	1.16082i	0.897937	+	0.440125i	$0.145066\pi$
$743$	152.080	+	862.488i	0.204684	+	1.16082i	−0.693253	+	0.720694i	$0.743823\pi$
$744$	33.1382	+	82.8176i	0.0445405	+	0.111314i
$745$	−252.610	+	74.0289i	−0.339073	+	0.0993677i
$746$	598.745	−	345.686i	0.802607	−	0.463386i
$747$	946.731	−	902.067i	1.26738	−	1.20759i
$748$	−103.459	−	59.7321i	−0.138314	−	0.0798558i
$749$	−122.721	−	337.174i	−0.163847	−	0.450166i
$750$	523.521	+	84.7097i	0.698028	+	0.112946i
$751$	−343.069	+	287.869i	−0.456817	+	0.383315i	−0.841958	−	0.539543i	$-0.818597\pi$
$751$	−343.069	+	287.869i	−0.456817	+	0.383315i	0.385141	+	0.922858i	$0.374153\pi$
$752$	14.3382	+	5.21868i	0.0190668	+	0.00693974i
$753$	−888.586	+	794.712i	−1.18006	+	1.05539i
$754$	−6.57731	+	37.3018i	−0.00872323	+	0.0494719i
$755$	155.421	+	103.522i	0.205856	+	0.137115i
$756$	−97.3795	−	136.904i	−0.128809	−	0.181090i
$757$			788.512i			1.04163i	0.853670	+	0.520814i	$0.174371\pi$
$757$			788.512i			1.04163i	−0.853670	+	0.520814i	$0.825629\pi$
$758$	152.649	−	865.718i	0.201384	−	1.14211i
$759$	10.6138	+	50.7696i	0.0139839	+	0.0668902i
$760$	156.051	+	212.176i	0.205330	+	0.279179i
$761$	−868.144	−	1034.61i	−1.14079	−	1.35954i	−0.923573	−	0.383422i	$-0.874745\pi$
$761$	−868.144	−	1034.61i	−1.14079	−	1.35954i	−0.217220	−	0.976123i	$-0.569699\pi$
$762$	217.559	+	350.777i	0.285510	+	0.460337i
$763$	81.2181	+	223.145i	0.106446	+	0.292457i
$764$	−206.361	−	119.143i	−0.270106	−	0.155946i
$765$	0.599226	−	682.074i	0.000783302	−	0.891600i
$766$	212.799	+	368.579i	0.277806	+	0.481173i
$767$	160.965	+	135.065i	0.209863	+	0.176096i
$768$	−47.5102	−	6.83952i	−0.0618623	−	0.00890562i
$769$	−20.8679	−	118.348i	−0.0271364	−	0.153898i	0.968229	−	0.250066i	$-0.0804524\pi$
$769$	−20.8679	−	118.348i	−0.0271364	−	0.153898i	−0.995365	+	0.0961682i	$0.969341\pi$
$770$	−34.8009	+	79.4050i	−0.0451959	+	0.103123i
$771$	792.752	+	114.124i	1.02821	+	0.148020i
$772$	23.0321	−	27.4485i	0.0298343	−	0.0355551i
$773$	−75.4440	−	130.673i	−0.0975990	−	0.169046i	0.813091	−	0.582136i	$-0.197783\pi$
$773$	−75.4440	−	130.673i	−0.0975990	−	0.169046i	−0.910690	+	0.413090i	$0.864450\pi$
$774$	2.04856	+	32.4157i	0.00264672	+	0.0418807i
$775$	260.663	+	33.5436i	0.336339	+	0.0432821i
$776$	94.8442	+	260.582i	0.122222	+	0.335802i
$777$	156.861	−	97.2884i	0.201880	−	0.125210i
$778$	−520.032	−	619.750i	−0.668421	−	0.796593i
$779$	−270.679	+	743.685i	−0.347470	+	0.954666i
$780$	22.9648	−	57.2468i	0.0294420	−	0.0733933i
$781$	42.9892	−	243.804i	0.0550438	−	0.312169i
$782$	−94.0410			−0.120257
$783$	−317.656	+	150.998i	−0.405691	+	0.192846i
$784$	157.282			0.200615
$785$	−736.468	−	702.959i	−0.938175	−	0.895489i
$786$	−131.234	+	117.370i	−0.166965	+	0.149326i
$787$	145.714	−	400.347i	0.185152	−	0.508700i	−0.812039	−	0.583603i	$-0.801642\pi$
$787$	145.714	−	400.347i	0.185152	−	0.508700i	0.997191	+	0.0749027i	$0.0238646\pi$
$788$	−477.525	+	400.691i	−0.605996	+	0.508491i
$789$	−23.4104	−	741.614i	−0.0296710	−	0.939942i
$790$	−1068.41	−	259.787i	−1.35242	−	0.328844i
$791$	338.807	+	195.610i	0.428327	+	0.247295i
$792$	28.2967	−	96.2438i	0.0357282	−	0.121520i
$793$	29.4017	−	16.9751i	0.0370765	−	0.0214061i
$794$	222.371	−	265.011i	0.280064	−	0.333767i
$795$	−224.769	+	1070.46i	−0.282729	+	1.34649i
$796$	66.7211	+	378.394i	0.0838204	+	0.475369i
$797$	−30.0946	−	170.675i	−0.0377598	−	0.214146i	0.960090	−	0.279692i	$-0.0902323\pi$
$797$	−30.0946	−	170.675i	−0.0377598	−	0.214146i	−0.997850	+	0.0655456i	$0.979121\pi$
$798$	−193.209	−	151.997i	−0.242117	−	0.190472i
$799$	−44.2917	−	37.1652i	−0.0554339	−	0.0465146i
$800$	−85.7642	+	112.448i	−0.107205	+	0.140560i
$801$	−8.15819	−	18.6591i	−0.0101850	−	0.0232947i
$802$	931.921	+	538.045i	1.16200	+	0.670879i
$803$	230.662	−	83.9541i	0.287250	−	0.104551i
$804$	−305.678	+	570.280i	−0.380197	+	0.709303i
$805$	7.52872	+	67.8299i	0.00935245	+	0.0842607i
$806$	10.4545	−	28.7235i	0.0129709	−	0.0356371i
$807$	−785.831	−	258.246i	−0.973769	−	0.320007i
$808$	446.781	+	78.7795i	0.552946	+	0.0974993i
$809$		−	1039.81i		−	1.28530i	−0.766158	−	0.642652i	$-0.777834\pi$
$809$		−	1039.81i		−	1.28530i	0.766158	−	0.642652i	$-0.222166\pi$
$810$	556.777	−	134.346i	0.687379	−	0.165860i
$811$	1278.12			1.57599			0.787993	−	0.615685i	$-0.211120\pi$
$811$	1278.12			1.57599			0.787993	+	0.615685i	$0.211120\pi$
$812$	−14.0753	+	79.8252i	−0.0173342	+	0.0983069i
$813$	291.042	−	885.628i	0.357985	−	1.08933i
$814$	103.569	+	37.6960i	0.127235	+	0.0463096i
$815$	126.956	+	1143.81i	0.155774	+	1.40345i
$816$	160.309	+	85.9281i	0.196457	+	0.105304i
$817$	16.2550	+	44.6603i	0.0198960	+	0.0546637i
$818$	12.4284	−	21.5265i	0.0151936	−	0.0263161i
$819$	−6.40127	+	57.2137i	−0.00781596	+	0.0698579i
$820$	−424.073	−	27.1741i	−0.517162	−	0.0331391i
$821$	−740.014	+	881.914i	−0.901356	+	1.07419i	0.0955365	+	0.995426i	$0.469543\pi$
$821$	−740.014	+	881.914i	−0.901356	+	1.07419i	−0.996893	+	0.0787688i	$0.974901\pi$
$822$	−142.325	+	180.915i	−0.173144	+	0.220091i
$823$	734.798	−	129.565i	0.892829	−	0.157430i	0.291632	−	0.956531i	$-0.405802\pi$
$823$	734.798	−	129.565i	0.892829	−	0.157430i	0.601197	+	0.799101i	$0.294691\pi$
$824$	15.5526	−	2.74234i	0.0188745	−	0.00332808i
$825$	−207.071	−	210.900i	−0.250996	−	0.255636i
$826$	344.461	+	289.037i	0.417024	+	0.349924i
$827$	329.324	+	570.405i	0.398215	+	0.689728i	0.993506	−	0.113782i	$-0.0362965\pi$
$827$	329.324	+	570.405i	0.398215	+	0.689728i	−0.595291	+	0.803510i	$0.702963\pi$
$828$	−18.5904	−	76.7494i	−0.0224522	−	0.0926925i
$829$	390.112	−	675.694i	0.470581	−	0.815071i	−0.528853	−	0.848714i	$-0.677378\pi$
$829$	390.112	−	675.694i	0.470581	−	0.815071i	0.999434	+	0.0336429i	$0.0107109\pi$
$830$	998.321	+	242.745i	1.20280	+	0.292464i
$831$	−1107.45	+	34.9587i	−1.33267	+	0.0420683i
$832$	10.5728	+	12.6001i	0.0127077	+	0.0151444i
$833$	−560.046	−	203.840i	−0.672324	−	0.244706i
$834$	−159.087	−	177.879i	−0.190752	−	0.213284i
$835$	−765.527	+	802.019i	−0.916799	+	0.960502i
$836$		−	146.788i		−	0.175584i
$837$	273.614	−	75.4900i	0.326899	−	0.0901911i
$838$			352.636i			0.420807i
$839$	1043.86	+	184.060i	1.24417	+	0.219380i	0.756701	−	0.653761i	$-0.226810\pi$
$839$	1043.86	+	184.060i	1.24417	+	0.219380i	0.487467	+	0.873141i	$0.337921\pi$
$840$	49.1442	−	122.507i	0.0585050	−	0.145842i
$841$	−630.823	−	229.601i	−0.750086	−	0.273009i
$842$	315.271	−	264.544i	0.374431	−	0.314185i
$843$	−261.602	−	421.788i	−0.310322	−	0.500342i
$844$	87.5912	−	31.8806i	0.103781	−	0.0377732i
$845$	738.368	−	365.463i	0.873809	−	0.432500i
$846$	21.5757	−	43.4946i	0.0255032	−	0.0514121i
$847$	−284.175	+	164.068i	−0.335507	+	0.193705i
$848$	−223.440	−	187.489i	−0.263491	−	0.221095i
$849$	142.001	−	986.397i	0.167256	−	1.16183i
$850$	451.122	−	289.250i	0.530731	−	0.340294i
$851$	85.4426	−	15.0658i	0.100403	−	0.0177037i
$852$	−53.7076	+	373.076i	−0.0630371	+	0.437883i
$853$	−357.047	+	425.512i	−0.418578	+	0.498841i	−0.933591	−	0.358341i	$-0.883343\pi$
$853$	−357.047	+	425.512i	−0.418578	+	0.498841i	0.515013	+	0.857182i	$0.327787\pi$
$854$	62.9190	−	36.3263i	0.0736757	−	0.0425367i
$855$	726.166	−	418.402i	0.849317	−	0.489359i
$856$	−163.101	+	282.499i	−0.190539	+	0.330023i
$857$	1164.76	−	423.938i	1.35911	−	0.494677i	0.443334	−	0.896357i	$-0.353796\pi$
$857$	1164.76	−	423.938i	1.35911	−	0.494677i	0.915780	+	0.401679i	$0.131573\pi$
$858$	−29.2134	+	18.1188i	−0.0340483	+	0.0211175i
$859$	101.790	−	85.4119i	0.118498	−	0.0994318i	−0.581613	−	0.813466i	$-0.697578\pi$
$859$	101.790	−	85.4119i	0.118498	−	0.0994318i	0.700111	+	0.714034i	$0.253134\pi$
$860$	−20.5576	+	15.1196i	−0.0239042	+	0.0175809i
$861$	388.231	−	81.1625i	0.450907	−	0.0942654i
$862$	883.799	+	155.838i	1.02529	+	0.180786i
$863$	188.473			0.218393			0.109197	−	0.994020i	$-0.465172\pi$
$863$	188.473			0.218393			0.109197	+	0.994020i	$0.465172\pi$
$864$	−38.4376	+	147.819i	−0.0444879	+	0.171087i
$865$	55.2533	+	36.8026i	0.0638767	+	0.0425464i
$866$	−125.757	−	22.1743i	−0.145215	−	0.0256054i
$867$	118.513	+	132.512i	0.136693	+	0.152839i
$868$	22.3725	−	61.4679i	0.0257747	−	0.0708155i
$869$	393.897	+	469.428i	0.453276	+	0.540193i
$870$	−234.708	−	145.856i	−0.269779	−	0.167651i
$871$	208.351	−	75.8336i	0.239209	−	0.0870650i
$872$	107.942	−	186.961i	0.123786	−	0.214404i
$873$	857.582	−	207.726i	0.982340	−	0.237945i
$874$	−57.7751	−	100.069i	−0.0661042	−	0.114496i
$875$	−244.746	−	302.228i	−0.279710	−	0.345404i
$876$	−346.979	+	138.838i	−0.396095	+	0.158491i
$877$	1381.61	−	243.615i	1.57538	−	0.277782i	0.683464	−	0.729984i	$-0.260472\pi$
$877$	1381.61	−	243.615i	1.57538	−	0.277782i	0.891916	+	0.452202i	$0.149361\pi$
$878$	−45.8025	−	259.759i	−0.0521668	−	0.295853i
$879$	316.807	−	402.706i	0.360418	−	0.458141i
$880$	75.6358	−	22.1656i	0.0859497	−	0.0251881i
$881$	686.695	−	396.464i	0.779450	−	0.450015i	−0.0567856	−	0.998386i	$-0.518085\pi$
$881$	686.695	−	396.464i	0.779450	−	0.450015i	0.836235	+	0.548371i	$0.184752\pi$
$882$	55.6470	−	497.365i	0.0630918	−	0.563906i
$883$	405.374	+	234.043i	0.459087	+	0.265054i	0.711660	−	0.702524i	$-0.247943\pi$
$883$	405.374	+	234.043i	0.459087	+	0.265054i	−0.252573	+	0.967578i	$0.581277\pi$
$884$	−21.3173	−	58.5689i	−0.0241146	−	0.0662544i
$885$	−1351.76	+	723.033i	−1.52741	+	0.816987i
$886$	−672.555	+	564.341i	−0.759092	+	0.636953i
$887$	−324.091	−	117.959i	−0.365379	−	0.132987i	0.152805	−	0.988256i	$-0.451169\pi$
$887$	−324.091	−	117.959i	−0.365379	−	0.132987i	−0.518184	+	0.855269i	$0.673392\pi$
$888$	−159.418	−	52.3892i	−0.179525	−	0.0589968i
$889$	52.5612	−	298.089i	0.0591239	−	0.335309i
$890$	8.86968	−	13.3164i	0.00996593	−	0.0149623i
$891$	−294.335	−	123.533i	−0.330343	−	0.138645i
$892$		−	622.653i		−	0.698041i
$893$	12.3365	−	69.9638i	0.0138147	−	0.0783469i
$894$	−212.197	−	69.7337i	−0.237356	−	0.0780019i
$895$	255.499	−	187.913i	0.285474	−	0.209959i
$896$	22.6256	+	26.9641i	0.0252517	+	0.0300939i
$897$	−12.7841	+	23.8503i	−0.0142521	+	0.0265890i
$898$	−304.623	−	836.944i	−0.339223	−	0.932009i
$899$	−118.595	−	68.4711i	−0.131919	−	0.0761636i
$900$	325.244	+	310.992i	0.361382	+	0.345547i
$901$	552.633	+	957.189i	0.613356	+	1.06236i
$902$	181.421	+	152.230i	0.201132	+	0.168770i
$903$	14.7268	−	18.7199i	0.0163088	−	0.0207307i
$904$	−61.7604	−	350.260i	−0.0683190	−	0.387456i
$905$	266.923	−	609.037i	0.294942	−	0.672969i
$906$	58.8661	+	147.116i	0.0649736	+	0.162379i
$907$	523.676	−	624.092i	0.577371	−	0.688084i	−0.395755	−	0.918356i	$-0.629517\pi$
$907$	523.676	−	624.092i	0.577371	−	0.688084i	0.973126	+	0.230272i	$0.0739615\pi$
$908$	26.2283	+	45.4288i	0.0288858	+	0.0500317i
$909$	407.193	−	1384.96i	0.447957	−	1.52361i
$910$	−40.5379	+	20.0646i	−0.0445472	+	0.0220491i
$911$	284.022	+	780.345i	0.311770	+	0.856581i	0.992300	+	0.123860i	$0.0395275\pi$
$911$	284.022	+	780.345i	0.311770	+	0.856581i	−0.680530	+	0.732720i	$0.738250\pi$
$912$	7.05129	+	223.377i	0.00773168	+	0.244930i
$913$	−368.057	−	438.633i	−0.403129	−	0.480430i
$914$	167.705	−	460.765i	0.183485	−	0.504120i
$915$	35.0773	+	245.189i	0.0383359	+	0.267966i
$916$	130.744	−	741.483i	0.142733	−	0.809480i
$917$	129.110			0.140796
$918$	328.444	−	476.536i	0.357782	−	0.519103i
$919$	−1432.39			−1.55864			−0.779320	−	0.626626i	$-0.784435\pi$
$919$	−1432.39			−1.55864			−0.779320	+	0.626626i	$0.784435\pi$
$920$	42.8386	−	44.8807i	0.0465637	−	0.0487834i
$921$	−320.407	−	1532.63i	−0.347890	−	1.66409i
$922$	392.090	−	1077.26i	0.425260	−	1.16839i
$923$	98.9432	−	83.0232i	0.107197	−	0.0899493i
$924$	−62.5163	+	38.7739i	−0.0676583	+	0.0419631i
$925$	−363.535	+	335.075i	−0.393011	+	0.362243i
$926$	967.330	+	558.488i	1.04463	+	0.603119i
$927$	−3.16940	−	50.1513i	−0.00341898	−	0.0541007i
$928$	63.8171	−	36.8448i	0.0687685	−	0.0397035i
$929$	191.050	−	227.685i	0.205652	−	0.245086i	−0.653354	−	0.757053i	$-0.726639\pi$
$929$	191.050	−	227.685i	0.205652	−	0.245086i	0.859005	+	0.511967i	$0.171083\pi$
$930$	166.092	+	148.808i	0.178594	+	0.160009i
$931$	−127.163	−	721.179i	−0.136588	−	0.774628i
$932$	112.761	+	639.501i	0.120988	+	0.686160i
$933$	19.0122	−	132.067i	0.0203775	−	0.141551i
$934$	309.241	+	259.484i	0.331093	+	0.277820i
$935$	−298.049	−	19.0986i	−0.318769	−	0.0204263i
$936$	43.5855	−	28.9758i	0.0465657	−	0.0309570i
$937$	614.632	+	354.858i	0.655957	+	0.378717i	0.790735	−	0.612159i	$-0.209699\pi$
$937$	614.632	+	354.858i	0.655957	+	0.378717i	−0.134778	+	0.990876i	$0.543032\pi$
$938$	445.868	−	162.283i	0.475339	−	0.173009i
$939$	−142.268	−	229.383i	−0.151510	−	0.244284i
$940$	37.9132	−	4.20814i	0.0403332	−	0.00447675i
$941$	−236.391	+	649.478i	−0.251212	+	0.690200i	0.748424	+	0.663221i	$0.230811\pi$
$941$	−236.391	+	649.478i	−0.251212	+	0.690200i	−0.999636	+	0.0269792i	$0.991411\pi$
$942$	−176.781	−	845.609i	−0.187665	−	0.897674i
$943$	183.597	+	32.3731i	0.194694	+	0.0343299i
$944$		−	408.794i		−	0.433045i
$945$	−370.011	−	198.750i	−0.391546	−	0.210317i
$946$	14.2222			0.0150340
$947$	211.352	−	1198.64i	0.223180	−	1.26572i	−0.642953	−	0.765906i	$-0.722291\pi$
$947$	211.352	−	1198.64i	0.223180	−	1.26572i	0.866133	−	0.499813i	$-0.166598\pi$
$948$	−621.966	−	695.435i	−0.656083	−	0.733581i
$949$	120.342	+	43.8011i	0.126810	+	0.0461550i
$950$	584.943	+	302.337i	0.615730	+	0.318249i
$951$	16.6264	+	526.705i	0.0174831	+	0.553843i
$952$	−45.6187	−	125.336i	−0.0479188	−	0.131656i
$953$	459.430	−	795.756i	0.482088	−	0.835001i	−0.517700	−	0.855562i	$-0.673212\pi$
$953$	459.430	−	795.756i	0.482088	−	0.835001i	0.999789	+	0.0205608i	$0.00654517\pi$
$954$	−671.941	+	640.240i	−0.704340	+	0.671111i
$955$	−594.494	−	38.0944i	−0.622507	−	0.0398894i
$956$	−191.833	+	228.617i	−0.200662	+	0.239139i
$957$	57.2135	+	142.986i	0.0597842	+	0.149410i
$958$	492.747	−	86.8846i	0.514350	−	0.0906938i
$959$	166.236	−	29.3118i	0.173343	−	0.0305650i
$960$	−114.035	+	37.3640i	−0.118786	+	0.0389208i
$961$	−651.511	−	546.683i	−0.677951	−	0.568869i
$962$	28.7513	+	49.7986i	0.0298870	+	0.0517657i
$963$	835.628	+	615.716i	0.867734	+	0.639372i
$964$	−51.3484	+	88.9380i	−0.0532660	+	0.0922594i
$965$	21.1647	−	87.0427i	0.0219323	−	0.0901996i
$966$	−27.3578	+	51.0393i	−0.0283207	+	0.0528357i
$967$	−262.230	−	312.514i	−0.271179	−	0.323178i	0.613218	−	0.789914i	$-0.289875\pi$
$967$	−262.230	−	312.514i	−0.271179	−	0.323178i	−0.884397	+	0.466735i	$0.845430\pi$
$968$	280.323	+	102.029i	0.289590	+	0.105402i
$969$	264.392	−	804.533i	0.272850	−	0.830272i
$970$	501.488	+	478.671i	0.516998	+	0.493475i
$971$		−	1887.73i		−	1.94411i	−0.234747	−	0.972056i	$-0.575426\pi$
$971$		−	1887.73i		−	1.94411i	0.234747	−	0.972056i	$-0.424574\pi$
$972$	453.842	+	173.848i	0.466916	+	0.178856i
$973$			174.999i			0.179855i
$974$	363.876	+	64.1611i	0.373589	+	0.0658739i
$975$	−12.0321	−	153.733i	−0.0123406	−	0.157675i
$976$	−62.0662	−	22.5903i	−0.0635925	−	0.0231458i
$977$	−1141.22	+	957.601i	−1.16809	+	0.980144i	−0.999984	−	0.00562513i	$-0.998209\pi$
$977$	−1141.22	+	957.601i	−1.16809	+	0.980144i	−0.168106	+	0.985769i	$0.553765\pi$
$978$	−461.332	+	860.671i	−0.471710	+	0.880031i
$979$	−8.37930	+	3.04982i	−0.00855904	+	0.00311524i
$980$	352.401	−	174.424i	0.359592	−	0.177984i
$981$	−553.026	−	407.486i	−0.563737	−	0.415378i
$982$	608.720	−	351.445i	0.619878	−	0.357886i
$983$	−106.026	−	88.9663i	−0.107860	−	0.0905049i	0.587263	−	0.809396i	$-0.300205\pi$
$983$	−106.026	−	88.9663i	−0.107860	−	0.0905049i	−0.695123	+	0.718891i	$0.744650\pi$
$984$	−283.392	−	222.943i	−0.288000	−	0.226568i
$985$	−625.564	+	1427.35i	−0.635090	+	1.44908i
$986$	−274.990	+	48.4882i	−0.278895	+	0.0491767i
$987$	−33.0558	+	13.2268i	−0.0334912	+	0.0134010i
$988$	49.2268	−	58.6663i	0.0498247	−	0.0593788i
$989$	9.69564	−	5.59778i	0.00980348	−	0.00566004i
$990$	−43.3328	−	247.021i	−0.0437705	−	0.249517i
$991$	−294.159	+	509.498i	−0.296830	+	0.514125i	−0.975409	−	0.220403i	$-0.929263\pi$
$991$	−294.159	+	509.498i	−0.296830	+	0.514125i	0.678579	+	0.734528i	$0.262596\pi$
$992$	−55.8813	+	20.3391i	−0.0563319	+	0.0205031i
$993$	36.6281	+	1160.33i	0.0368863	+	1.16851i
$994$	211.737	−	177.668i	0.213015	−	0.178741i
$995$	569.128	+	773.824i	0.571988	+	0.777712i
$996$	581.165	+	649.814i	0.583499	+	0.652423i
$997$	−173.830	−	30.6510i	−0.174353	−	0.0307432i	0.0857899	−	0.996313i	$-0.472659\pi$
$997$	−173.830	−	30.6510i	−0.174353	−	0.0307432i	−0.260143	+	0.965570i	$0.583770\pi$
$998$	347.182			0.347878
$999$	−222.070	+	485.584i	−0.222293	+	0.486070i

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.29.7	✓	216
5.4	even	2	inner	270.3.n.a.29.30	yes	216
27.14	odd	18	inner	270.3.n.a.149.30	yes	216
135.14	odd	18	inner	270.3.n.a.149.7	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.n.a.29.7	✓	216	1.1	even	1	trivial
270.3.n.a.29.30	yes	216	5.4	even	2	inner
270.3.n.a.149.7	yes	216	135.14	odd	18	inner
270.3.n.a.149.30	yes	216	27.14	odd	18	inner

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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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.29.7

Level	$270$
Weight	$3$
Character	270.29
Analytic conductor	$7.357$
Analytic rank	$0$
Dimension	$216$
Inner twists	$4$