LMFDB - Embedded newform 270.3.o.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,3,Mod(11,270)]

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([13, 0]))

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

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

chi := DirichletCharacter("270.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	270.o (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:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	270.11
Dual form			270.3.o.a.221.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.959500 - 2.84242i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(0.764780 - 2.10122i) q^{5} +(3.95156 + 1.54440i) q^{6} +(-1.57222 + 8.91648i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-7.15872 + 5.45460i) q^{9} +(1.58114 + 2.73861i) q^{10} +(4.64338 + 12.7576i) q^{11} +(-5.26525 + 2.87701i) q^{12} +(6.44056 - 5.40427i) q^{13} +(-8.23047 - 9.80869i) q^{14} +(-6.70635 - 0.157712i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(20.5082 - 11.8404i) q^{17} +(0.598308 - 12.7139i) q^{18} +(9.06954 - 15.7089i) q^{19} +(-4.40419 - 0.776578i) q^{20} +(26.8529 - 4.08646i) q^{21} +(-18.0419 - 6.56673i) q^{22} +(32.2265 - 5.68241i) q^{23} +(1.66951 - 8.31942i) q^{24} +(-3.83022 - 3.21394i) q^{25} +11.8901i q^{26} +(22.3731 + 15.1144i) q^{27} +18.1081 q^{28} +(-12.4808 + 14.8741i) q^{29} +(6.26719 - 7.12196i) q^{30} +(0.179671 + 1.01897i) q^{31} +(1.93476 - 5.31570i) q^{32} +(31.8071 - 25.4393i) q^{33} +(-5.81544 + 32.9810i) q^{34} +(17.5331 + 10.1227i) q^{35} +(13.2297 + 12.2056i) q^{36} +(-20.7478 - 35.9362i) q^{37} +(8.77369 + 24.1055i) q^{38} +(-21.5409 - 13.1214i) q^{39} +(4.84489 - 4.06535i) q^{40} +(34.4924 + 41.1064i) q^{41} +(-19.9833 + 32.8059i) q^{42} +(-28.6233 + 10.4180i) q^{43} +(23.5149 - 13.5763i) q^{44} +(5.98646 + 19.2136i) q^{45} +(-23.1391 + 40.0781i) q^{46} +(87.7702 + 15.4763i) q^{47} +(7.49520 + 9.37134i) q^{48} +(-30.9869 - 11.2783i) q^{49} +(6.96364 - 1.22788i) q^{50} +(-53.3331 - 46.9321i) q^{51} +(-12.8811 - 10.8085i) q^{52} +6.61006i q^{53} +(-36.7122 + 10.4983i) q^{54} +30.3576 q^{55} +(-16.4609 + 19.6174i) q^{56} +(-53.3536 - 10.7068i) q^{57} +(-4.76827 - 27.0422i) q^{58} +(-20.7997 + 57.1467i) q^{59} +(2.01846 + 13.2637i) q^{60} +(-11.1022 + 62.9640i) q^{61} +(-1.26723 - 0.731634i) q^{62} +(-37.3808 - 72.4064i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-6.42993 - 17.6661i) q^{65} +(-1.35418 + 57.5836i) q^{66} +(33.8033 - 28.3643i) q^{67} +(-30.4435 - 36.2812i) q^{68} +(-47.0731 - 86.1491i) q^{69} +(-26.9047 + 9.79251i) q^{70} +(53.2944 - 30.7696i) q^{71} +(-25.2492 + 3.23704i) q^{72} +(-17.0297 + 29.4964i) q^{73} +(57.7920 + 10.1903i) q^{74} +(-5.46027 + 13.9709i) q^{75} +(-34.0903 - 12.4079i) q^{76} +(-121.053 + 21.3449i) q^{77} +(33.7966 - 11.4085i) q^{78} +(62.1935 + 52.1865i) q^{79} +8.94427i q^{80} +(21.4946 - 78.0960i) q^{81} -75.8876 q^{82} +(91.2091 - 108.699i) q^{83} +(-17.3747 - 51.4708i) q^{84} +(-9.19502 - 52.1475i) q^{85} +(14.7333 - 40.4795i) q^{86} +(54.2537 + 21.2041i) q^{87} +(-6.66803 + 37.8163i) q^{88} +(1.86389 + 1.07612i) q^{89} +(-26.2570 - 10.9805i) q^{90} +(38.0611 + 65.9238i) q^{91} +(-22.3843 - 61.5004i) q^{92} +(2.72394 - 1.48840i) q^{93} +(-96.5528 + 81.0174i) q^{94} +(-26.0716 - 31.0709i) q^{95} +(-16.9659 - 0.398982i) q^{96} +(-74.2055 + 27.0086i) q^{97} +(40.3866 - 23.3172i) q^{98} +(-102.828 - 66.0001i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{6} + 12 q^{9} + 24 q^{12} + 36 q^{14} + 96 q^{18} + 96 q^{21} - 72 q^{22} + 216 q^{23} - 12 q^{27} - 252 q^{29} - 516 q^{33} + 144 q^{34} - 48 q^{36} - 144 q^{38} + 48 q^{39} + 108 q^{41}+ \cdots - 444 q^{99}+O(q^{100}) $ 144 * q - 12 * q^6 + 12 * q^9 + 24 * q^12 + 36 * q^14 + 96 * q^18 + 96 * q^21 - 72 * q^22 + 216 * q^23 - 12 * q^27 - 252 * q^29 - 516 * q^33 + 144 * q^34 - 48 * q^36 - 144 * q^38 + 48 * q^39 + 108 * q^41 - 180 * q^43 + 60 * q^45 + 432 * q^47 - 72 * q^49 - 204 * q^51 - 288 * q^54 + 72 * q^56 - 612 * q^57 - 252 * q^59 + 144 * q^61 - 720 * q^63 + 576 * q^64 + 360 * q^65 + 864 * q^66 + 252 * q^67 + 144 * q^68 + 708 * q^69 + 360 * q^70 + 1296 * q^71 - 252 * q^73 + 720 * q^74 + 144 * q^76 + 684 * q^77 + 192 * q^78 + 72 * q^79 - 492 * q^81 - 828 * q^83 - 216 * q^84 - 360 * q^85 - 648 * q^86 - 660 * q^87 - 288 * q^88 + 324 * q^89 - 480 * q^90 + 396 * q^91 - 216 * q^92 - 1548 * q^93 - 504 * q^94 - 720 * q^95 - 192 * q^96 - 180 * q^97 - 1296 * q^98 - 444 * q^99

Character values

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

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	−0.909039	+	1.08335i	−0.454519	+	0.541675i
$2$	−0.909039	+	1.08335i	−0.454519	+	0.541675i
$3$	−0.959500	−	2.84242i	−0.319833	−	0.947474i
$3$	−0.959500	−	2.84242i	−0.319833	−	0.947474i
$4$	−0.347296	−	1.96962i	−0.0868241	−	0.492404i
$5$	0.764780	−	2.10122i	0.152956	−	0.420243i
$5$	0.764780	−	2.10122i	0.152956	−	0.420243i
$6$	3.95156	+	1.54440i	0.658594	+	0.257400i
$7$	−1.57222	+	8.91648i	−0.224602	+	1.27378i	0.638842	+	0.769338i	$0.279414\pi$
$7$	−1.57222	+	8.91648i	−0.224602	+	1.27378i	−0.863444	+	0.504445i	$0.831697\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$	−7.15872	+	5.45460i	−0.795413	+	0.606067i
$10$	1.58114	+	2.73861i	0.158114	+	0.273861i
$11$	4.64338	+	12.7576i	0.422125	+	1.15978i	0.950488	+	0.310761i	$0.100584\pi$
$11$	4.64338	+	12.7576i	0.422125	+	1.15978i	−0.528363	+	0.849019i	$0.677194\pi$
$12$	−5.26525	+	2.87701i	−0.438771	+	0.239751i
$13$	6.44056	−	5.40427i	0.495427	−	0.415713i	−0.360539	−	0.932744i	$-0.617407\pi$
$13$	6.44056	−	5.40427i	0.495427	−	0.415713i	0.855967	+	0.517031i	$0.172963\pi$
$14$	−8.23047	−	9.80869i	−0.587891	−	0.700621i
$15$	−6.70635	−	0.157712i	−0.447090	−	0.0105141i
$16$	−3.75877	+	1.36808i	−0.234923	+	0.0855050i
$17$	20.5082	−	11.8404i	1.20637	−	0.696496i	0.244402	−	0.969674i	$-0.421408\pi$
$17$	20.5082	−	11.8404i	1.20637	−	0.696496i	0.961963	+	0.273178i	$0.0880749\pi$
$18$	0.598308	−	12.7139i	0.0332393	−	0.706325i
$19$	9.06954	−	15.7089i	0.477344	−	0.826785i	−0.522318	−	0.852750i	$-0.674933\pi$
$19$	9.06954	−	15.7089i	0.477344	−	0.826785i	0.999663	+	0.0259658i	$0.00826610\pi$
$20$	−4.40419	−	0.776578i	−0.220210	−	0.0388289i
$21$	26.8529	−	4.08646i	1.27871	−	0.194593i
$22$	−18.0419	−	6.56673i	−0.820088	−	0.298488i
$23$	32.2265	−	5.68241i	1.40115	−	0.247061i	0.578536	−	0.815657i	$-0.303624\pi$
$23$	32.2265	−	5.68241i	1.40115	−	0.247061i	0.822617	+	0.568596i	$0.192513\pi$
$24$	1.66951	−	8.31942i	0.0695628	−	0.346642i
$25$	−3.83022	−	3.21394i	−0.153209	−	0.128558i
$26$			11.8901i			0.457310i
$27$	22.3731	+	15.1144i	0.828632	+	0.559793i
$28$	18.1081			0.646717
$29$	−12.4808	+	14.8741i	−0.430373	+	0.512899i	−0.937030	−	0.349249i	$-0.886437\pi$
$29$	−12.4808	+	14.8741i	−0.430373	+	0.512899i	0.506657	+	0.862148i	$0.330881\pi$
$30$	6.26719	−	7.12196i	0.208906	−	0.237399i
$31$	0.179671	+	1.01897i	0.00579585	+	0.0328699i	0.987569	−	0.157189i	$-0.0502432\pi$
$31$	0.179671	+	1.01897i	0.00579585	+	0.0328699i	−0.981773	+	0.190059i	$0.939132\pi$
$32$	1.93476	−	5.31570i	0.0604612	−	0.166116i
$33$	31.8071	−	25.4393i	0.963851	−	0.770889i
$34$	−5.81544	+	32.9810i	−0.171042	+	0.970029i
$35$	17.5331	+	10.1227i	0.500945	+	0.289221i
$36$	13.2297	+	12.2056i	0.367491	+	0.339043i
$37$	−20.7478	−	35.9362i	−0.560750	−	0.971248i	−0.997431	−	0.0716317i	$-0.977179\pi$
$37$	−20.7478	−	35.9362i	−0.560750	−	0.971248i	0.436681	−	0.899617i	$-0.356154\pi$
$38$	8.77369	+	24.1055i	0.230886	+	0.634355i
$39$	−21.5409	−	13.1214i	−0.552331	−	0.336446i
$40$	4.84489	−	4.06535i	0.121122	−	0.101634i
$41$	34.4924	+	41.1064i	0.841278	+	1.00260i	0.999884	+	0.0152540i	$0.00485569\pi$
$41$	34.4924	+	41.1064i	0.841278	+	1.00260i	−0.158606	+	0.987342i	$0.550700\pi$
$42$	−19.9833	+	32.8059i	−0.475793	+	0.781093i
$43$	−28.6233	+	10.4180i	−0.665659	+	0.242280i	−0.652678	−	0.757636i	$-0.726354\pi$
$43$	−28.6233	+	10.4180i	−0.665659	+	0.242280i	−0.0129814	+	0.999916i	$0.504132\pi$
$44$	23.5149	−	13.5763i	0.534429	−	0.308553i
$45$	5.98646	+	19.2136i	0.133032	+	0.426969i
$46$	−23.1391	+	40.0781i	−0.503025	+	0.871264i
$47$	87.7702	+	15.4763i	1.86745	+	0.329282i	0.988926	−	0.148412i	$-0.0474162\pi$
$47$	87.7702	+	15.4763i	1.86745	+	0.329282i	0.878526	+	0.477694i	$0.158527\pi$
$48$	7.49520	+	9.37134i	0.156150	+	0.195236i
$49$	−30.9869	−	11.2783i	−0.632385	−	0.230169i
$50$	6.96364	−	1.22788i	0.139273	−	0.0245576i
$51$	−53.3331	−	46.9321i	−1.04575	−	0.920238i
$52$	−12.8811	−	10.8085i	−0.247714	−	0.207857i
$53$			6.61006i			0.124718i	0.998054	+	0.0623590i	$0.0198624\pi$
$53$			6.61006i			0.124718i	−0.998054	+	0.0623590i	$0.980138\pi$
$54$	−36.7122	+	10.4983i	−0.679856	+	0.194413i
$55$	30.3576			0.551956
$56$	−16.4609	+	19.6174i	−0.293945	+	0.350310i
$57$	−53.3536	−	10.7068i	−0.936027	−	0.187838i
$58$	−4.76827	−	27.0422i	−0.0822116	−	0.466245i
$59$	−20.7997	+	57.1467i	−0.352537	+	0.968589i	0.629015	+	0.777394i	$0.283459\pi$
$59$	−20.7997	+	57.1467i	−0.352537	+	0.968589i	−0.981552	+	0.191195i	$0.938764\pi$
$60$	2.01846	+	13.2637i	0.0336410	+	0.221062i
$61$	−11.1022	+	62.9640i	−0.182004	+	1.03220i	0.747741	+	0.663991i	$0.231139\pi$
$61$	−11.1022	+	62.9640i	−0.182004	+	1.03220i	−0.929745	+	0.368205i	$0.879972\pi$
$62$	−1.26723	−	0.731634i	−0.0204391	−	0.0118005i
$63$	−37.3808	−	72.4064i	−0.593347	−	1.14931i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−6.42993	−	17.6661i	−0.0989220	−	0.271786i
$66$	−1.35418	+	57.5836i	−0.0205178	+	0.872478i
$67$	33.8033	−	28.3643i	0.504526	−	0.423348i	−0.354672	−	0.934991i	$-0.615407\pi$
$67$	33.8033	−	28.3643i	0.504526	−	0.423348i	0.859198	+	0.511643i	$0.170963\pi$
$68$	−30.4435	−	36.2812i	−0.447699	−	0.533547i
$69$	−47.0731	−	86.1491i	−0.682219	−	1.24854i
$70$	−26.9047	+	9.79251i	−0.384353	+	0.139893i
$71$	53.2944	−	30.7696i	0.750626	−	0.433374i	−0.0752942	−	0.997161i	$-0.523990\pi$
$71$	53.2944	−	30.7696i	0.750626	−	0.433374i	0.825920	+	0.563787i	$0.190656\pi$
$72$	−25.2492	+	3.23704i	−0.350683	+	0.0449589i
$73$	−17.0297	+	29.4964i	−0.233284	+	0.404060i	−0.958773	−	0.284175i	$-0.908280\pi$
$73$	−17.0297	+	29.4964i	−0.233284	+	0.404060i	0.725489	+	0.688234i	$0.241614\pi$
$74$	57.7920	+	10.1903i	0.780973	+	0.137707i
$75$	−5.46027	+	13.9709i	−0.0728036	+	0.186278i
$76$	−34.0903	−	12.4079i	−0.448557	−	0.163261i
$77$	−121.053	+	21.3449i	−1.57212	+	0.277207i
$78$	33.7966	−	11.4085i	0.433290	−	0.146263i
$79$	62.1935	+	52.1865i	0.787259	+	0.660589i	0.945065	−	0.326881i	$-0.105998\pi$
$79$	62.1935	+	52.1865i	0.787259	+	0.660589i	−0.157806	+	0.987470i	$0.550442\pi$
$80$			8.94427i			0.111803i
$81$	21.4946	−	78.0960i	0.265365	−	0.964148i
$82$	−75.8876			−0.925459
$83$	91.2091	−	108.699i	1.09890	−	1.30962i	0.151903	−	0.988395i	$-0.451460\pi$
$83$	91.2091	−	108.699i	1.09890	−	1.30962i	0.947002	−	0.321229i	$-0.104096\pi$
$84$	−17.3747	−	51.4708i	−0.206841	−	0.612747i
$85$	−9.19502	−	52.1475i	−0.108177	−	0.613500i
$86$	14.7333	−	40.4795i	0.171318	−	0.470692i
$87$	54.2537	+	21.2041i	0.623606	+	0.243725i
$88$	−6.66803	+	37.8163i	−0.0757731	+	0.429730i
$89$	1.86389	+	1.07612i	0.0209426	+	0.0120912i	0.510435	−	0.859916i	$-0.329484\pi$
$89$	1.86389	+	1.07612i	0.0209426	+	0.0120912i	−0.489492	+	0.872008i	$0.662818\pi$
$90$	−26.2570	−	10.9805i	−0.291744	−	0.122005i
$91$	38.0611	+	65.9238i	0.418254	+	0.724437i
$92$	−22.3843	−	61.5004i	−0.243308	−	0.668482i
$93$	2.72394	−	1.48840i	0.0292897	−	0.0160043i
$94$	−96.5528	+	81.0174i	−1.02716	+	0.861887i
$95$	−26.0716	−	31.0709i	−0.274438	−	0.327063i
$96$	−16.9659	−	0.398982i	−0.176728	−	0.00415606i
$97$	−74.2055	+	27.0086i	−0.765005	+	0.278439i	−0.694906	−	0.719101i	$-0.744554\pi$
$97$	−74.2055	+	27.0086i	−0.765005	+	0.278439i	−0.0700994	+	0.997540i	$0.522332\pi$
$98$	40.3866	−	23.3172i	0.412108	−	0.237931i
$99$	−102.828	−	66.0001i	−1.03867	−	0.666668i
$100$	−5.00000	+	8.66025i	−0.0500000	+	0.0866025i
$101$	−183.122	−	32.2893i	−1.81308	−	0.319696i	−0.838702	−	0.544591i	$-0.816685\pi$
$101$	−183.122	−	32.2893i	−1.81308	−	0.319696i	−0.974383	+	0.224895i	$0.927796\pi$
$102$	99.3258	−	15.1153i	0.973782	−	0.148189i
$103$	21.9327	+	7.98283i	0.212938	+	0.0775033i	0.446287	−	0.894890i	$-0.352746\pi$
$103$	21.9327	+	7.98283i	0.212938	+	0.0775033i	−0.233349	+	0.972393i	$0.574968\pi$
$104$	23.4189	−	4.12938i	0.225181	−	0.0397056i
$105$	11.9501	−	59.5491i	0.113810	−	0.567134i
$106$	−7.16101	−	6.00880i	−0.0675567	−	0.0566868i
$107$			165.240i			1.54430i	0.635441	+	0.772150i	$0.280818\pi$
$107$			165.240i			1.54430i	−0.635441	+	0.772150i	$0.719182\pi$
$108$	21.9995	−	49.3155i	0.203699	−	0.456625i
$109$	−98.0530			−0.899569			−0.449784	−	0.893137i	$-0.648499\pi$
$109$	−98.0530			−0.899569			−0.449784	+	0.893137i	$0.648499\pi$
$110$	−27.5962	+	32.8879i	−0.250875	+	0.298981i
$111$	−82.2383	+	93.4547i	−0.740886	+	0.841934i
$112$	−6.28887	−	35.6659i	−0.0561506	−	0.318446i
$113$	44.0969	−	121.155i	0.390238	−	1.07217i	−0.576656	−	0.816987i	$-0.695643\pi$
$113$	44.0969	−	121.155i	0.390238	−	1.07217i	0.966893	−	0.255182i	$-0.0821353\pi$
$114$	60.0997	−	48.0677i	0.527190	−	0.421647i
$115$	12.7062	−	72.0607i	0.110489	−	0.626615i
$116$	33.6307	+	19.4167i	0.289920	+	0.167385i
$117$	−16.6280	+	73.8183i	−0.142120	+	0.630926i
$118$	−43.0022	−	74.4820i	−0.364425	−	0.631203i
$119$	73.3316	+	201.477i	0.616232	+	1.69308i
$120$	−16.2041	−	9.87052i	−0.135034	−	0.0822544i
$121$	−48.5034	+	40.6992i	−0.400855	+	0.336357i
$122$	−58.1197	−	69.2643i	−0.476391	−	0.567740i
$123$	83.7464	−	137.484i	0.680865	−	1.11775i
$124$	1.94457	−	0.707767i	0.0156820	−	0.00570780i
$125$	−9.68246	+	5.59017i	−0.0774597	+	0.0447214i
$126$	112.422	+	25.3237i	0.892239	+	0.200982i
$127$	16.3802	−	28.3714i	0.128978	−	0.223397i	−0.794303	−	0.607522i	$-0.792164\pi$
$127$	16.3802	−	28.3714i	0.128978	−	0.223397i	0.923281	+	0.384125i	$0.125497\pi$
$128$	−11.1418	−	1.96460i	−0.0870455	−	0.0153485i
$129$	57.0766	+	71.3635i	0.442454	+	0.553205i
$130$	24.9836	+	9.09329i	0.192182	+	0.0699484i
$131$	−200.023	+	35.2694i	−1.52689	+	0.269232i	−0.873137	−	0.487474i	$-0.837918\pi$
$131$	−200.023	+	35.2694i	−1.52689	+	0.269232i	−0.653755	+	0.756707i	$0.726807\pi$
$132$	−61.1522	−	53.8128i	−0.463274	−	0.407672i
$133$	125.809	+	105.566i	0.945932	+	0.793731i
$134$			62.4050i			0.465709i
$135$	48.8691	−	35.4515i	0.361994	−	0.262604i
$136$	66.9796			0.492497
$137$	25.6568	−	30.5766i	0.187276	−	0.223187i	−0.664235	−	0.747524i	$-0.731242\pi$
$137$	25.6568	−	30.5766i	0.187276	−	0.223187i	0.851511	+	0.524337i	$0.175687\pi$
$138$	136.121	+	27.3162i	0.986384	+	0.197943i
$139$	−34.9069	−	197.967i	−0.251129	−	1.42422i	−0.805818	−	0.592164i	$-0.798274\pi$
$139$	−34.9069	−	197.967i	−0.251129	−	1.42422i	0.554689	−	0.832058i	$-0.312837\pi$
$140$	13.8487	−	38.0490i	0.0989192	−	0.271778i
$141$	−40.2254	−	264.329i	−0.285287	−	1.87468i
$142$	−15.1125	+	85.7073i	−0.106426	+	0.603572i
$143$	98.8513	+	57.0718i	0.691268	+	0.399104i
$144$	19.4457	−	30.2963i	0.135039	−	0.210391i
$145$	21.7085	+	37.6003i	0.149714	+	0.259312i
$146$	−16.4742	−	45.2625i	−0.112837	−	0.310017i
$147$	−2.32579	+	98.8993i	−0.0158217	+	0.672784i
$148$	−63.5748	+	53.3456i	−0.429560	+	0.360443i
$149$	70.8332	+	84.4157i	0.475390	+	0.566548i	0.949439	−	0.313950i	$-0.101652\pi$
$149$	70.8332	+	84.4157i	0.475390	+	0.566548i	−0.474049	+	0.880498i	$0.657208\pi$
$150$	−10.1718	−	18.6155i	−0.0678117	−	0.124103i
$151$	−121.907	+	44.3704i	−0.807328	+	0.293843i	−0.712520	−	0.701652i	$-0.752446\pi$
$151$	−121.907	+	44.3704i	−0.807328	+	0.293843i	−0.0948086	+	0.995496i	$0.530224\pi$
$152$	44.4315	−	25.6525i	0.292313	−	0.168767i
$153$	−82.2278	+	196.627i	−0.537436	+	1.28514i
$154$	86.9179	−	150.546i	0.564402	−	0.977573i
$155$	2.27848	+	0.401757i	0.0146999	+	0.00259198i
$156$	−18.3630	+	46.9843i	−0.117712	+	0.301182i
$157$	167.613	+	61.0060i	1.06760	+	0.388573i	0.815277	−	0.579071i	$-0.196585\pi$
$157$	167.613	+	61.0060i	1.06760	+	0.388573i	0.252319	+	0.967644i	$0.418807\pi$
$158$	−113.073	+	19.9377i	−0.715649	+	0.126188i
$159$	18.7886	−	6.34235i	0.118167	−	0.0398890i
$160$	−9.68978	−	8.13069i	−0.0605611	−	0.0508168i
$161$			296.281i			1.84026i
$162$	65.0659	+	94.2784i	0.401641	+	0.581966i
$163$	−51.7816			−0.317678			−0.158839	−	0.987304i	$-0.550775\pi$
$163$	−51.7816			−0.317678			−0.158839	+	0.987304i	$0.550775\pi$
$164$	68.9848	−	82.2129i	0.420639	−	0.501298i
$165$	−29.1281	−	86.2891i	−0.176534	−	0.522964i
$166$	34.8462	+	197.623i	0.209917	+	1.19050i
$167$	−55.9395	+	153.693i	−0.334967	+	0.920315i	0.651832	+	0.758364i	$0.274001\pi$
$167$	−55.9395	+	153.693i	−0.334967	+	0.920315i	−0.986799	+	0.161951i	$0.948221\pi$
$168$	71.5551	+	27.9661i	0.425923	+	0.166465i
$169$	−17.0719	+	96.8195i	−0.101017	+	0.572896i
$170$	64.8527	+	37.4427i	0.381486	+	0.220251i
$171$	20.7596	+	161.926i	0.121401	+	0.946938i
$172$	30.4603	+	52.7588i	0.177095	+	0.306737i
$173$	−15.7852	−	43.3696i	−0.0912441	−	0.250691i	0.885673	−	0.464309i	$-0.153697\pi$
$173$	−15.7852	−	43.3696i	−0.0912441	−	0.250691i	−0.976917	+	0.213618i	$0.931475\pi$
$174$	−72.2902	+	39.5004i	−0.415461	+	0.227014i
$175$	34.6790	−	29.0991i	0.198165	−	0.166281i
$176$	−34.9068	−	41.6003i	−0.198334	−	0.236365i
$177$	182.392	+	4.28928i	1.03047	+	0.0242332i
$178$	−2.86016	+	1.04101i	−0.0160683	+	0.00584839i
$179$	−23.9078	+	13.8032i	−0.133563	+	0.0771126i	−0.565293	−	0.824890i	$-0.691237\pi$
$179$	−23.9078	+	13.8032i	−0.133563	+	0.0771126i	0.431730	+	0.902003i	$0.357903\pi$
$180$	35.7643	−	18.4638i	0.198691	−	0.102577i
$181$	78.3664	−	135.735i	0.432963	−	0.749915i	−0.564164	−	0.825663i	$-0.690801\pi$
$181$	78.3664	−	135.735i	0.432963	−	0.749915i	0.997127	+	0.0757485i	$0.0241346\pi$
$182$	−106.018	−	18.6938i	−0.582514	−	0.102713i
$183$	189.623	−	28.8566i	1.03619	−	0.157687i
$184$	86.9747	+	31.6562i	0.472688	+	0.172045i
$185$	−91.3772	+	16.1123i	−0.493931	+	0.0870933i
$186$	−0.863708	+	4.30399i	−0.00464359	+	0.0231398i
$187$	246.283	+	206.656i	1.31702	+	1.10511i
$188$		−	178.248i		−	0.948130i
$189$	−169.943	+	175.726i	−0.899168	+	0.929767i
$190$	57.3608			0.301899
$191$	215.139	−	256.393i	1.12638	−	1.34237i	0.193955	−	0.981010i	$-0.437868\pi$
$191$	215.139	−	256.393i	1.12638	−	1.34237i	0.932427	−	0.361359i	$-0.117687\pi$
$192$	15.8549	−	18.0173i	0.0825775	−	0.0938401i
$193$	−53.2860	−	302.200i	−0.276093	−	1.56580i	−0.735467	−	0.677560i	$-0.763037\pi$
$193$	−53.2860	−	302.200i	−0.276093	−	1.56580i	0.459374	−	0.888243i	$-0.348074\pi$
$194$	38.1959	−	104.942i	0.196886	−	0.540940i
$195$	−44.0449	+	35.2272i	−0.225872	+	0.180652i
$196$	−11.4523	+	64.9491i	−0.0584300	+	0.331373i
$197$	−165.958	−	95.8160i	−0.842427	−	0.486375i	0.0156615	−	0.999877i	$-0.495015\pi$
$197$	−165.958	−	95.8160i	−0.842427	−	0.486375i	−0.858088	+	0.513502i	$0.828348\pi$
$198$	164.976	−	51.4023i	0.833213	−	0.259607i
$199$	159.093	+	275.558i	0.799464	+	1.38471i	0.919965	+	0.392000i	$0.128217\pi$
$199$	159.093	+	275.558i	0.799464	+	1.38471i	−0.120501	+	0.992713i	$0.538450\pi$
$200$	−4.83690	−	13.2893i	−0.0241845	−	0.0664463i
$201$	−113.058	−	68.8676i	−0.562475	−	0.342625i
$202$	201.445	−	169.033i	0.997253	−	0.836795i
$203$	−113.002	−	134.670i	−0.556659	−	0.663400i
$204$	−73.9158	+	121.345i	−0.362333	+	0.594829i
$205$	112.753	−	41.0386i	0.550013	−	0.200188i
$206$	−28.5858	+	16.5040i	−0.138766	+	0.0801167i
$207$	−199.705	+	216.462i	−0.964760	+	1.04571i
$208$	−16.8151	+	29.1246i	−0.0808418	+	0.140022i
$209$	242.521	+	42.7630i	1.16039	+	0.204608i
$210$	53.6495	+	67.0786i	0.255474	+	0.319422i
$211$	−327.925	−	119.355i	−1.55415	−	0.565663i	−0.584760	−	0.811206i	$-0.698811\pi$
$211$	−327.925	−	119.355i	−1.55415	−	0.565663i	−0.969386	+	0.245544i	$0.921034\pi$
$212$	13.0193	−	2.29565i	0.0614117	−	0.0108285i
$213$	−138.596	−	121.962i	−0.650686	−	0.572591i
$214$	−179.013	−	150.210i	−0.836509	−	0.701914i
$215$			68.1114i			0.316797i
$216$	33.4276	+	68.6629i	0.154757	+	0.317884i
$217$	−9.36808			−0.0431709
$218$	89.1340	−	106.226i	0.408871	−	0.487274i
$219$	100.181	+	20.1039i	0.457448	+	0.0917987i
$220$	−10.5431	−	59.7928i	−0.0479231	−	0.271785i
$221$	68.0955	−	187.091i	0.308124	−	0.846565i
$222$	−26.4863	−	174.047i	−0.119308	−	0.783995i
$223$	1.82543	−	10.3525i	0.00818577	−	0.0464238i	−0.980441	−	0.196812i	$-0.936941\pi$
$223$	1.82543	−	10.3525i	0.00818577	−	0.0464238i	0.988627	+	0.150388i	$0.0480523\pi$
$224$	44.3555	+	25.6087i	0.198016	+	0.114324i
$225$	44.9503	+	2.11534i	0.199779	+	0.00940150i
$226$	91.1677	+	157.907i	0.403397	+	0.698704i
$227$	48.4178	+	133.027i	0.213294	+	0.586021i	0.999489	−	0.0319576i	$-0.0101742\pi$
$227$	48.4178	+	133.027i	0.213294	+	0.586021i	−0.786195	+	0.617978i	$0.787952\pi$
$228$	−2.55873	+	108.804i	−0.0112225	+	0.477212i
$229$	331.430	−	278.103i	1.44729	−	1.21442i	0.512766	−	0.858528i	$-0.328621\pi$
$229$	331.430	−	278.103i	1.44729	−	1.21442i	0.934526	−	0.355894i	$-0.115824\pi$
$230$	66.5165	+	79.2713i	0.289202	+	0.344658i
$231$	176.822	+	323.604i	0.765462	+	1.40088i
$232$	−51.6067	+	18.7833i	−0.222443	+	0.0809626i
$233$	−118.572	+	68.4575i	−0.508892	+	0.293809i	−0.732378	−	0.680898i	$-0.761590\pi$
$233$	−118.572	+	68.4575i	−0.508892	+	0.293809i	0.223486	+	0.974707i	$0.428256\pi$
$234$	−64.8556	−	85.1177i	−0.277161	−	0.363751i
$235$	99.6439	−	172.588i	0.424017	−	0.734418i
$236$	119.781	+	21.1206i	0.507546	+	0.0894940i
$237$	88.6615	−	226.853i	0.374099	−	0.957185i
$238$	−284.931	−	103.707i	−1.19719	−	0.435742i
$239$	88.9000	−	15.6755i	0.371967	−	0.0655877i	0.0154598	−	0.999880i	$-0.495079\pi$
$239$	88.9000	−	15.6755i	0.371967	−	0.0655877i	0.356507	+	0.934293i	$0.383968\pi$
$240$	25.4234	−	8.58203i	0.105931	−	0.0357584i
$241$	−218.158	−	183.056i	−0.905218	−	0.759568i	0.0659851	−	0.997821i	$-0.478981\pi$
$241$	−218.158	−	183.056i	−0.905218	−	0.759568i	−0.971203	+	0.238252i	$0.923425\pi$
$242$		−	89.5433i		−	0.370014i
$243$	−242.606	+	13.8364i	−0.998378	+	0.0569401i
$244$	127.871			0.524060
$245$	−47.3963	+	56.4847i	−0.193454	+	0.230550i
$246$	72.8141	+	215.705i	0.295992	+	0.876848i
$247$	−26.4823	−	150.188i	−0.107216	−	0.608050i
$248$	−1.00093	+	2.75004i	−0.00403602	+	0.0110889i
$249$	−396.483	−	154.958i	−1.59230	−	0.622323i
$250$	2.74562	−	15.5712i	0.0109825	−	0.0622847i
$251$	−60.3604	−	34.8491i	−0.240480	−	0.138841i	0.374918	−	0.927058i	$-0.377671\pi$
$251$	−60.3604	−	34.8491i	−0.240480	−	0.138841i	−0.615397	+	0.788217i	$0.711004\pi$
$252$	−129.631	+	98.7724i	−0.514407	+	0.391954i
$253$	222.134	+	384.747i	0.877999	+	1.52074i
$254$	15.8459	+	43.5363i	0.0623855	+	0.171403i
$255$	−139.403	+	76.1717i	−0.546677	+	0.298712i
$256$	12.2567	−	10.2846i	0.0478778	−	0.0401742i
$257$	−238.977	−	284.802i	−0.929872	−	1.10818i	−0.993906	−	0.110231i	$-0.964841\pi$
$257$	−238.977	−	284.802i	−0.929872	−	1.10818i	0.0640341	−	0.997948i	$-0.479603\pi$
$258$	−129.196	−	3.03828i	−0.500762	−	0.0117763i
$259$	353.044	−	128.498i	1.36311	−	0.496130i
$260$	−32.5623	+	18.7999i	−0.125240	+	0.0723071i
$261$	8.21458	−	174.557i	0.0314735	−	0.668802i
$262$	143.619	−	248.756i	0.548166	−	0.949451i
$263$	−253.020	−	44.6143i	−0.962054	−	0.169636i	−0.329503	−	0.944155i	$-0.606881\pi$
$263$	−253.020	−	44.6143i	−0.962054	−	0.169636i	−0.632551	+	0.774519i	$0.717992\pi$
$264$	113.888	−	17.3314i	0.431393	−	0.0656491i
$265$	13.8892	+	5.05524i	0.0524119	+	0.0190764i
$266$	−228.730	+	40.3313i	−0.859889	+	0.151622i
$267$	1.27038	−	6.33049i	0.00475797	−	0.0237097i
$268$	−67.6065	−	56.7286i	−0.252263	−	0.211674i
$269$			48.8132i			0.181462i	0.995875	+	0.0907308i	$0.0289203\pi$
$269$			48.8132i			0.181462i	−0.995875	+	0.0907308i	$0.971080\pi$
$270$	−6.01758	+	85.1692i	−0.0222873	+	0.315441i
$271$	220.083			0.812115			0.406057	−	0.913848i	$-0.366903\pi$
$271$	220.083			0.812115			0.406057	+	0.913848i	$0.366903\pi$
$272$	−60.8870	+	72.5623i	−0.223849	+	0.266773i
$273$	150.864	−	171.440i	0.552614	−	0.627984i
$274$	9.80214	+	55.5907i	0.0357742	+	0.202886i
$275$	23.2169	−	63.7879i	0.0844251	−	0.231956i
$276$	−153.332	+	122.635i	−0.555552	+	0.444331i
$277$	−7.86135	+	44.5839i	−0.0283803	+	0.160953i	−0.995704	−	0.0925910i	$-0.970485\pi$
$277$	−7.86135	+	44.5839i	−0.0283803	+	0.160953i	0.967324	+	0.253544i	$0.0815962\pi$
$278$	246.199	+	142.143i	0.885609	+	0.511306i
$279$	−6.84428	−	6.31446i	−0.0245315	−	0.0226325i
$280$	28.6314	+	49.5910i	0.102255	+	0.177111i
$281$	−66.6977	−	183.251i	−0.237359	−	0.652137i	−0.999986	−	0.00529919i	$-0.998313\pi$
$281$	−66.6977	−	183.251i	−0.237359	−	0.652137i	0.762627	−	0.646838i	$-0.223909\pi$
$282$	322.928	+	196.708i	1.14513	+	0.697544i
$283$	−408.300	+	342.604i	−1.44275	+	1.21062i	−0.505093	+	0.863065i	$0.668542\pi$
$283$	−408.300	+	342.604i	−1.44275	+	1.21062i	−0.937661	+	0.347550i	$0.887014\pi$
$284$	−79.1132	−	94.2834i	−0.278567	−	0.331984i
$285$	−63.3010	+	103.919i	−0.222109	+	0.364628i
$286$	−151.688	+	55.2101i	−0.530379	+	0.193042i
$287$	−420.754	+	242.923i	−1.46604	+	0.846420i
$288$	15.1447	+	48.6070i	0.0525857	+	0.168774i
$289$	135.891	−	235.371i	0.470212	−	0.814432i
$290$	−60.4682	−	10.6622i	−0.208511	−	0.0367661i
$291$	147.970	+	185.009i	0.508488	+	0.635768i
$292$	64.0108	+	23.2980i	0.219215	+	0.0797878i
$293$	−235.712	+	41.5624i	−0.804478	+	0.141851i	−0.560742	−	0.827990i	$-0.689484\pi$
$293$	−235.712	+	41.5624i	−0.804478	+	0.141851i	−0.243736	+	0.969842i	$0.578373\pi$
$294$	−105.028	−	92.4229i	−0.357239	−	0.314364i
$295$	104.170	+	87.4094i	0.353120	+	0.296303i
$296$		−	117.367i		−	0.396510i
$297$	−88.9366	+	355.608i	−0.299450	+	1.19733i
$298$	−155.842			−0.522959
$299$	176.848	−	210.759i	0.591463	−	0.704878i
$300$	29.4136	+	5.90260i	0.0980453	+	0.0196753i
$301$	−47.8902	−	271.599i	−0.159104	−	0.902322i
$302$	62.7492	−	172.402i	0.207779	−	0.570867i
$303$	83.9253	+	551.490i	0.276981	+	1.82010i
$304$	−12.5993	+	71.4540i	−0.0414450	+	0.235046i
$305$	123.810	+	71.4818i	0.405935	+	0.234367i
$306$	−138.267	−	267.823i	−0.451854	−	0.875237i
$307$	−222.906	−	386.085i	−0.726079	−	1.25761i	−0.958528	−	0.284997i	$-0.908007\pi$
$307$	−222.906	−	386.085i	−0.726079	−	1.25761i	0.232449	−	0.972609i	$-0.425326\pi$
$308$	84.0826	+	231.015i	0.272995	+	0.750049i
$309$	1.64620	−	70.0014i	0.00532752	−	0.226542i
$310$	−2.50647	+	2.10318i	−0.00808539	+	0.00678445i
$311$	157.581	+	187.798i	0.506691	+	0.603851i	0.957380	−	0.288830i	$-0.0932662\pi$
$311$	157.581	+	187.798i	0.506691	+	0.603851i	−0.450689	+	0.892681i	$0.648822\pi$
$312$	−34.2078	−	62.6042i	−0.109640	−	0.200654i
$313$	−118.024	+	42.9571i	−0.377072	+	0.137243i	−0.523602	−	0.851963i	$-0.675412\pi$
$313$	−118.024	+	42.9571i	−0.377072	+	0.137243i	0.146529	+	0.989206i	$0.453190\pi$
$314$	−218.457	+	126.126i	−0.695724	+	0.401676i
$315$	−180.730	+	23.1702i	−0.573745	+	0.0735562i
$316$	81.1878	−	140.621i	0.256923	−	0.445004i
$317$	−203.649	−	35.9088i	−0.642425	−	0.113277i	−0.157061	−	0.987589i	$-0.550202\pi$
$317$	−203.649	−	35.9088i	−0.642425	−	0.113277i	−0.485364	+	0.874312i	$0.661313\pi$
$318$	−10.2086	+	26.1201i	−0.0321024	+	0.0821385i
$319$	−247.710	−	90.1591i	−0.776521	−	0.282631i
$320$	17.6168	−	3.10631i	0.0550524	−	0.00970723i
$321$	469.682	−	158.548i	1.46318	−	0.493918i
$322$	−320.976	−	269.331i	−0.996821	−	0.836432i
$323$		−	429.549i		−	1.32987i
$324$	−161.284	−	15.2136i	−0.497790	−	0.0469555i
$325$	−42.0378			−0.129347
$326$	47.0715	−	56.0976i	0.144391	−	0.172078i
$327$	94.0818	+	278.708i	0.287712	+	0.852318i
$328$	26.3555	+	149.469i	0.0803521	+	0.455699i
$329$	−275.988	+	758.270i	−0.838868	+	2.30477i
$330$	119.960	+	46.8842i	0.363515	+	0.142073i
$331$	−27.0336	+	153.315i	−0.0816725	+	0.463188i	0.916353	+	0.400372i	$0.131119\pi$
$331$	−27.0336	+	153.315i	−0.0816725	+	0.463188i	−0.998025	+	0.0628158i	$0.979992\pi$
$332$	−245.771	−	141.896i	−0.740275	−	0.427398i
$333$	344.545	+	144.086i	1.03467	+	0.432691i
$334$	−115.652	−	200.315i	−0.346263	−	0.599744i
$335$	−33.7475	−	92.7204i	−0.100739	−	0.276777i
$336$	−95.3435	+	52.0971i	−0.283760	+	0.155051i
$337$	−184.544	+	154.851i	−0.547609	+	0.459499i	−0.874130	−	0.485691i	$-0.838568\pi$
$337$	−184.544	+	154.851i	−0.547609	+	0.459499i	0.326521	+	0.945190i	$0.394123\pi$
$338$	−89.3704	−	106.508i	−0.264410	−	0.315111i
$339$	−386.685	−	9.09357i	−1.14066	−	0.0268247i
$340$	−99.5172	+	36.2213i	−0.292698	+	0.106533i
$341$	−12.1653	+	7.02362i	−0.0356753	+	0.0205971i
$342$	−194.294	−	124.708i	−0.568112	−	0.364642i
$343$	−72.5430	+	125.648i	−0.211496	+	0.366321i
$344$	−84.8459	−	14.9606i	−0.246645	−	0.0434902i
$345$	−217.019	+	33.0257i	−0.629039	+	0.0957267i
$346$	61.3338	+	22.3237i	0.177265	+	0.0645193i
$347$	414.011	−	73.0013i	1.19311	−	0.210378i	0.458395	−	0.888749i	$-0.348425\pi$
$347$	414.011	−	73.0013i	1.19311	−	0.210378i	0.734720	+	0.678371i	$0.237314\pi$
$348$	22.9218	−	114.223i	0.0658673	−	0.328227i
$349$	−62.3979	−	52.3581i	−0.178791	−	0.150023i	0.549000	−	0.835822i	$-0.315009\pi$
$349$	−62.3979	−	52.3581i	−0.178791	−	0.150023i	−0.727791	+	0.685799i	$0.759453\pi$
$350$			64.0217i			0.182919i
$351$	225.777	−	23.5649i	0.643241	−	0.0671365i
$352$	76.7993			0.218180
$353$	288.019	−	343.248i	0.815919	−	0.972374i	−0.184026	−	0.982921i	$-0.558913\pi$
$353$	288.019	−	343.248i	0.815919	−	0.972374i	0.999944	+	0.0105472i	$0.00335735\pi$
$354$	−170.449	+	193.696i	−0.481493	+	0.547163i
$355$	−23.8950	−	135.515i	−0.0673098	−	0.381733i
$356$	1.47221	−	4.04488i	0.00413543	−	0.0113620i
$357$	502.321	−	401.756i	1.40706	−	1.12537i
$358$	6.77944	−	38.4481i	0.0189370	−	0.107397i
$359$	151.936	+	87.7200i	0.423219	+	0.244346i	0.696454	−	0.717602i	$-0.254760\pi$
$359$	151.936	+	87.7200i	0.423219	+	0.244346i	−0.273235	+	0.961947i	$0.588094\pi$
$360$	−12.5084	+	55.5296i	−0.0347455	+	0.154249i
$361$	15.9868	+	27.6899i	0.0442847	+	0.0767034i
$362$	75.8100	+	208.286i	0.209420	+	0.575376i
$363$	162.223	+	98.8163i	0.446896	+	0.272221i
$364$	116.626	−	97.8609i	0.320401	−	0.268849i
$365$	48.9542	+	58.3414i	0.134121	+	0.159839i
$366$	−141.113	+	231.660i	−0.385554	+	0.632950i
$367$	−104.880	+	38.1731i	−0.285776	+	0.104014i	−0.480931	−	0.876758i	$-0.659701\pi$
$367$	−104.880	+	38.1731i	−0.285776	+	0.104014i	0.195155	+	0.980772i	$0.437479\pi$
$368$	−113.358	+	65.4473i	−0.308038	+	0.177846i
$369$	−471.141	−	106.127i	−1.27680	−	0.287607i
$370$	65.6102	−	113.640i	0.177325	−	0.307136i
$371$	−58.9385	−	10.3924i	−0.158864	−	0.0280120i
$372$	−3.87759	−	4.84820i	−0.0104236	−	0.0130328i
$373$	553.129	+	201.322i	1.48292	+	0.539738i	0.951575	−	0.307418i	$-0.0994650\pi$
$373$	553.129	+	201.322i	1.48292	+	0.539738i	0.531344	+	0.847156i	$0.321687\pi$
$374$	−447.761	+	78.9523i	−1.19722	+	0.211102i
$375$	25.1799	+	22.1579i	0.0671465	+	0.0590876i
$376$	193.106	+	162.035i	0.513579	+	0.430944i
$377$			163.247i			0.433016i
$378$	−35.8883	−	343.849i	−0.0949426	−	0.909654i
$379$	168.402			0.444334			0.222167	−	0.975009i	$-0.428687\pi$
$379$	168.402			0.444334			0.222167	+	0.975009i	$0.428687\pi$
$380$	−52.1432	+	62.1419i	−0.137219	+	0.163531i
$381$	−96.3604	−	19.3372i	−0.252914	−	0.0507538i
$382$	82.1934	+	466.142i	0.215166	+	1.22027i
$383$	−23.0713	+	63.3878i	−0.0602383	+	0.165503i	−0.966161	−	0.257940i	$-0.916956\pi$
$383$	−23.0713	+	63.3878i	−0.0602383	+	0.165503i	0.905923	+	0.423443i	$0.139179\pi$
$384$	5.10634	+	33.5548i	0.0132978	+	0.0873823i
$385$	−47.7287	+	270.683i	−0.123971	+	0.703073i
$386$	375.828	+	216.984i	0.973647	+	0.562135i
$387$	148.080	−	230.709i	0.382636	−	0.596147i
$388$	78.9678	+	136.776i	0.203525	+	0.352516i
$389$	−39.1003	−	107.427i	−0.100515	−	0.276163i	0.879235	−	0.476389i	$-0.158055\pi$
$389$	−39.1003	−	107.427i	−0.100515	−	0.276163i	−0.979750	+	0.200226i	$0.935832\pi$
$390$	1.87520	−	79.7390i	0.00480821	−	0.204459i
$391$	593.626	−	498.112i	1.51823	−	1.27394i
$392$	−59.9521	−	71.4481i	−0.152939	−	0.182266i
$393$	292.172	+	534.708i	0.743441	+	1.36058i
$394$	254.665	−	92.6903i	0.646357	−	0.235255i
$395$	157.219	−	90.7707i	0.398024	−	0.229799i
$396$	−94.2830	+	225.454i	−0.238088	+	0.569327i
$397$	270.217	−	468.030i	0.680649	−	1.17892i	−0.294135	−	0.955764i	$-0.595031\pi$
$397$	270.217	−	468.030i	0.680649	−	1.17892i	0.974783	−	0.223154i	$-0.0716353\pi$
$398$	−443.148	−	78.1389i	−1.11344	−	0.196329i
$399$	179.350	−	458.893i	0.449499	−	1.15011i
$400$	18.7939	+	6.84040i	0.0469846	+	0.0171010i
$401$	−201.051	+	35.4507i	−0.501374	+	0.0884058i	−0.418615	−	0.908164i	$-0.637484\pi$
$401$	−201.051	+	35.4507i	−0.501374	+	0.0884058i	−0.0827591	+	0.996570i	$0.526373\pi$
$402$	177.381	−	59.8776i	0.441247	−	0.148949i
$403$	6.66396	+	5.59172i	0.0165359	+	0.0138752i
$404$			371.893i			0.920527i
$405$	−147.658	−	104.891i	−0.364588	−	0.258990i
$406$	248.618			0.612360
$407$	362.119	−	431.556i	0.889727	−	1.06034i
$408$	−64.2669	−	190.384i	−0.157517	−	0.466628i
$409$	57.2047	+	324.424i	0.139865	+	0.793213i	0.971348	+	0.237663i	$0.0763813\pi$
$409$	57.2047	+	324.424i	0.139865	+	0.793213i	−0.831483	+	0.555550i	$0.812508\pi$
$410$	−58.0373	+	159.456i	−0.141555	+	0.388918i
$411$	−111.529	−	43.5893i	−0.271361	−	0.106057i
$412$	8.10598	−	45.9713i	0.0196747	−	0.111581i
$413$	−476.846	−	275.307i	−1.15459	−	0.666604i
$414$	−52.9639	−	413.123i	−0.127932	−	0.997882i
$415$	−158.645	−	274.781i	−0.382277	−	0.662122i
$416$	−16.2666	−	44.6921i	−0.0391023	−	0.107433i
$417$	−529.212	+	289.169i	−1.26909	+	0.693451i
$418$	−266.788	+	223.862i	−0.638249	+	0.535555i
$419$	393.226	+	468.629i	0.938488	+	1.11845i	0.992783	+	0.119921i	$0.0382641\pi$
$419$	393.226	+	468.629i	0.938488	+	1.11845i	−0.0542959	+	0.998525i	$0.517291\pi$
$420$	−121.439	−	2.85585i	−0.289141	−	0.00679964i
$421$	−284.040	+	103.382i	−0.674680	+	0.245563i	−0.656561	−	0.754273i	$-0.727990\pi$
$421$	−284.040	+	103.382i	−0.674680	+	0.245563i	−0.0181182	+	0.999836i	$0.505768\pi$
$422$	427.399	−	246.759i	1.01279	−	0.584737i
$423$	−712.739	+	367.962i	−1.68496	+	0.869886i
$424$	−9.34803	+	16.1913i	−0.0220473	+	0.0381870i
$425$	−116.605	−	20.5607i	−0.274366	−	0.0483781i
$426$	258.117	−	39.2800i	0.605908	−	0.0922065i
$427$	−543.962	−	197.986i	−1.27392	−	0.463667i
$428$	325.459	−	57.3873i	0.760419	−	0.134082i
$429$	67.3744	−	335.738i	0.157050	−	0.782605i
$430$	−73.7885	−	61.9159i	−0.171601	−	0.143990i
$431$		−	547.520i		−	1.27035i	−0.772369	−	0.635175i	$-0.780928\pi$
$431$		−	547.520i		−	1.27035i	0.772369	−	0.635175i	$-0.219072\pi$
$432$	−104.773	−	26.2034i	−0.242530	−	0.0606561i
$433$	−52.4878			−0.121219			−0.0606094	−	0.998162i	$-0.519304\pi$
$433$	−52.4878			−0.121219			−0.0606094	+	0.998162i	$0.519304\pi$
$434$	8.51595	−	10.1489i	0.0196220	−	0.0233846i
$435$	86.0466	−	97.7823i	0.197808	−	0.224787i
$436$	34.0534	+	193.127i	0.0781042	+	0.442951i
$437$	203.015	−	557.780i	0.464566	−	1.27639i
$438$	−112.848	+	90.2560i	−0.257644	+	0.206064i
$439$	112.454	−	637.757i	0.256159	−	1.45275i	−0.536921	−	0.843633i	$-0.680413\pi$
$439$	112.454	−	637.757i	0.256159	−	1.45275i	0.793080	−	0.609118i	$-0.208476\pi$
$440$	74.3606	+	42.9321i	0.169001	+	0.0975730i
$441$	283.345	−	88.2829i	0.642506	−	0.200188i
$442$	140.784	+	243.844i	0.318515	+	0.551684i
$443$	−90.5563	−	248.801i	−0.204416	−	0.561628i	0.794545	−	0.607205i	$-0.207710\pi$
$443$	−90.5563	−	248.801i	−0.204416	−	0.561628i	−0.998961	+	0.0455772i	$0.985487\pi$
$444$	212.631	+	129.521i	0.478898	+	0.291715i
$445$	3.68662	−	3.09344i	0.00828454	−	0.00695155i
$446$	9.55601	+	11.3884i	0.0214260	+	0.0255346i
$447$	171.981	−	282.335i	0.384744	−	0.631621i
$448$	−68.0641	+	24.7733i	−0.151929	+	0.0552975i
$449$	−451.303	+	260.560i	−1.00513	+	0.580312i	−0.909762	−	0.415131i	$-0.863736\pi$
$449$	−451.303	+	260.560i	−1.00513	+	0.580312i	−0.0953673	+	0.995442i	$0.530403\pi$
$450$	−43.1532	+	46.7740i	−0.0958960	+	0.103942i
$451$	−364.257	+	630.912i	−0.807666	+	1.39892i
$452$	−253.944	−	44.7771i	−0.561822	−	0.0990644i
$453$	243.089	+	303.937i	0.536619	+	0.670942i
$454$	−188.128	−	68.4731i	−0.414379	−	0.150822i
$455$	167.629	−	29.5574i	0.368414	−	0.0649614i
$456$	−115.547	−	101.679i	−0.253393	−	0.222981i
$457$	524.687	+	440.265i	1.14811	+	0.963380i	0.999674	−	0.0255414i	$-0.00813095\pi$
$457$	524.687	+	440.265i	1.14811	+	0.963380i	0.148438	+	0.988922i	$0.452575\pi$
$458$			611.861i			1.33594i
$459$	637.793	+	45.0629i	1.38953	+	0.0981763i
$460$	−146.345			−0.318141
$461$	555.244	−	661.714i	1.20443	−	1.43539i	0.334377	−	0.942440i	$-0.391474\pi$
$461$	555.244	−	661.714i	1.20443	−	1.43539i	0.870058	−	0.492949i	$-0.164081\pi$
$462$	−511.314	−	102.608i	−1.10674	−	0.222096i
$463$	−63.9660	−	362.769i	−0.138155	−	0.783519i	−0.972610	−	0.232442i	$-0.925328\pi$
$463$	−63.9660	−	362.769i	−0.138155	−	0.783519i	0.834455	−	0.551076i	$-0.185783\pi$
$464$	26.5636	−	72.9830i	0.0572492	−	0.157291i
$465$	−1.04424	−	6.86188i	−0.00224567	−	0.0147567i
$466$	33.6230	−	190.686i	0.0721524	−	0.409196i
$467$	665.095	+	383.993i	1.42419	+	0.822255i	0.996653	−	0.0817444i	$-0.0260491\pi$
$467$	665.095	+	383.993i	1.42419	+	0.822255i	0.427534	+	0.903999i	$0.359382\pi$
$468$	151.169	+	7.11392i	0.323010	+	0.0152007i
$469$	199.764	+	346.001i	0.425936	+	0.737742i
$470$	96.3934	+	264.839i	0.205092	+	0.563487i
$471$	12.5805	−	534.961i	0.0267103	−	1.13580i
$472$	−131.766	+	110.565i	−0.279166	+	0.234248i
$473$	−265.818	−	316.790i	−0.561983	−	0.669745i
$474$	165.165	+	302.270i	0.348448	+	0.637700i
$475$	−85.2258	+	31.0197i	−0.179423	+	0.0653046i
$476$	371.364	−	214.407i	0.780177	−	0.450435i
$477$	−36.0553	−	47.3196i	−0.0755875	−	0.0992024i
$478$	−63.8315	+	110.559i	−0.133539	+	0.231296i
$479$	286.347	+	50.4908i	0.597802	+	0.105409i	0.464358	−	0.885648i	$-0.346285\pi$
$479$	286.347	+	50.4908i	0.597802	+	0.105409i	0.133444	+	0.991056i	$0.457396\pi$
$480$	−13.8135	+	35.3438i	−0.0287782	+	0.0736330i
$481$	−327.836	−	119.323i	−0.681572	−	0.248072i
$482$	396.628	−	69.9361i	0.822879	−	0.145096i
$483$	842.156	−	284.282i	1.74359	−	0.588575i
$484$	97.0068	+	81.3984i	0.200427	+	0.168178i
$485$			176.577i			0.364077i
$486$	205.548	−	275.405i	0.422939	−	0.566677i
$487$	−779.278			−1.60016			−0.800080	−	0.599893i	$-0.795210\pi$
$487$	−779.278			−1.60016			−0.800080	+	0.599893i	$0.795210\pi$
$488$	−116.239	+	138.529i	−0.238195	+	0.283870i
$489$	49.6844	+	147.185i	0.101604	+	0.300992i
$490$	−18.1076	−	102.694i	−0.0369544	−	0.209579i
$491$	−156.432	+	429.795i	−0.318600	+	0.875345i	0.672244	+	0.740330i	$0.265331\pi$
$491$	−156.432	+	429.795i	−0.318600	+	0.875345i	−0.990843	+	0.135016i	$0.956892\pi$
$492$	−299.875	−	117.201i	−0.609501	−	0.238213i
$493$	−79.8442	+	452.819i	−0.161956	+	0.918497i
$494$	186.780	+	107.838i	0.378097	+	0.218295i
$495$	−217.322	+	165.589i	−0.439033	+	0.334523i
$496$	−2.06937	−	3.58426i	−0.00417212	−	0.00722633i
$497$	190.566	+	523.575i	0.383432	+	1.05347i
$498$	528.293	−	288.667i	1.06083	−	0.579652i
$499$	−581.233	+	487.712i	−1.16480	+	0.977379i	−0.999960	−	0.00894205i	$-0.997154\pi$
$499$	−581.233	+	487.712i	−1.16480	+	0.977379i	−0.164835	+	0.986321i	$0.552709\pi$
$500$	14.3732	+	17.1293i	0.0287463	+	0.0342585i
$501$	490.533	+	11.5357i	0.979108	+	0.0230254i
$502$	92.6237	−	33.7123i	0.184509	−	0.0671559i
$503$	−227.272	+	131.215i	−0.451833	+	0.260866i	−0.708604	−	0.705607i	$-0.750675\pi$
$503$	−227.272	+	131.215i	−0.451833	+	0.260866i	0.256771	+	0.966472i	$0.417341\pi$
$504$	10.8342	−	230.223i	0.0214964	−	0.456792i
$505$	−207.894	+	360.084i	−0.411672	+	0.713037i
$506$	−618.744	−	109.101i	−1.22281	−	0.215615i
$507$	291.582	−	44.3728i	0.575113	−	0.0875202i
$508$	−61.5696	−	22.4095i	−0.121200	−	0.0441132i
$509$	−67.4607	+	11.8951i	−0.132536	+	0.0233696i	−0.239522	−	0.970891i	$-0.576991\pi$
$509$	−67.4607	+	11.8951i	−0.132536	+	0.0233696i	0.106987	+	0.994260i	$0.465880\pi$
$510$	44.2019	−	220.265i	0.0866703	−	0.431892i
$511$	−236.229	−	198.220i	−0.462288	−	0.387906i
$512$			22.6274i			0.0441942i
$513$	440.344	−	214.376i	0.858371	−	0.417887i
$514$	525.780			1.02292
$515$	33.5473	−	39.9802i	0.0651404	−	0.0776314i
$516$	120.736	−	137.203i	0.233985	−	0.265898i
$517$	210.111	+	1191.60i	0.406404	+	2.30483i
$518$	−181.723	+	499.280i	−0.350817	+	0.963861i
$519$	−108.129	+	86.4813i	−0.208340	+	0.166631i
$520$	9.23357	−	52.3662i	0.0177569	−	0.100704i
$521$	−690.456	−	398.635i	−1.32525	−	0.765134i	−0.340690	−	0.940176i	$-0.610661\pi$
$521$	−690.456	−	398.635i	−1.32525	−	0.765134i	−0.984561	+	0.175042i	$0.943994\pi$
$522$	181.639	+	167.579i	0.347968	+	0.321032i
$523$	367.804	+	637.056i	0.703259	+	1.21808i	0.967316	+	0.253573i	$0.0816059\pi$
$523$	367.804	+	637.056i	0.703259	+	1.21808i	−0.264057	+	0.964507i	$0.585061\pi$
$524$	138.934	+	381.719i	0.265142	+	0.728472i
$525$	−115.986	−	70.6517i	−0.220926	−	0.134575i
$526$	278.338	−	233.553i	0.529160	−	0.444018i
$527$	15.7497	+	18.7698i	0.0298857	+	0.0356163i
$528$	−84.7525	+	139.135i	−0.160516	+	0.263514i
$529$	509.162	−	185.320i	0.962498	−	0.350321i
$530$	−18.1024	+	10.4514i	−0.0341555	+	0.0197197i
$531$	−162.814	−	522.552i	−0.306617	−	0.984090i
$532$	164.232	−	284.458i	0.308707	−	0.534695i
$533$	444.300	+	78.3422i	0.833584	+	0.146983i
$534$	5.70332	+	7.13093i	0.0106804	+	0.0133538i
$535$	347.205	+	126.372i	0.648981	+	0.236210i
$536$	122.914	−	21.6730i	0.229317	−	0.0404348i
$537$	62.1739	+	54.7119i	0.115780	+	0.101884i
$538$	−52.8818	−	44.3731i	−0.0982932	−	0.0824778i
$539$		−	447.687i		−	0.830588i
$540$	−86.7978	−	83.9412i	−0.160737	−	0.155447i
$541$	−300.570			−0.555583			−0.277791	−	0.960641i	$-0.589602\pi$
$541$	−300.570			−0.555583			−0.277791	+	0.960641i	$0.589602\pi$
$542$	−200.064	+	238.427i	−0.369122	+	0.439903i
$543$	−461.007	−	92.5130i	−0.849001	−	0.170374i
$544$	−23.2618	−	131.924i	−0.0427606	−	0.242507i
$545$	−74.9890	+	206.031i	−0.137594	+	0.378038i
$546$	48.5883	+	319.283i	0.0889896	+	0.584768i
$547$	−0.869190	+	4.92942i	−0.00158901	+	0.00901174i	−0.985592	−	0.169140i	$-0.945901\pi$
$547$	−0.869190	+	4.92942i	−0.00158901	+	0.00901174i	0.984003	+	0.178152i	$0.0570119\pi$
$548$	−69.1347	−	39.9149i	−0.126158	−	0.0728375i
$549$	−263.966	−	511.300i	−0.480812	−	0.931329i
$550$	47.9996	+	83.1377i	0.0872719	+	0.151159i
$551$	120.460	+	330.961i	0.218621	+	0.600655i
$552$	6.52808	−	277.593i	0.0118262	−	0.502885i
$553$	−563.102	+	472.498i	−1.01827	+	0.854427i
$554$	−41.1538	−	49.0451i	−0.0742848	−	0.0885291i
$555$	133.474	+	244.273i	0.240494	+	0.440131i
$556$	−377.795	+	137.506i	−0.679488	+	0.247314i
$557$	−113.233	+	65.3750i	−0.203290	+	0.117370i	−0.598189	−	0.801355i	$-0.704113\pi$
$557$	−113.233	+	65.3750i	−0.203290	+	0.117370i	0.394899	+	0.918725i	$0.370780\pi$
$558$	13.0625	−	1.67466i	0.0234095	−	0.00300118i
$559$	−128.048	+	221.786i	−0.229067	+	0.396755i
$560$	−79.7514	−	14.0623i	−0.142413	−	0.0251113i
$561$	351.094	−	898.325i	0.625837	−	1.60129i
$562$	259.155	+	94.3249i	0.461131	+	0.167838i
$563$	967.432	−	170.584i	1.71835	−	0.302992i	0.774308	−	0.632809i	$-0.218098\pi$
$563$	967.432	−	170.584i	1.71835	−	0.302992i	0.944045	+	0.329818i	$0.106987\pi$
$564$	−506.657	+	171.029i	−0.898328	+	0.303243i
$565$	−220.849	−	185.314i	−0.390883	−	0.327990i
$566$		−	753.772i		−	1.33175i
$567$	662.547	+	314.440i	1.16851	+	0.554568i
$568$	174.059			0.306442
$569$	3.51593	−	4.19013i	0.00617915	−	0.00736402i	−0.762946	−	0.646462i	$-0.776248\pi$
$569$	3.51593	−	4.19013i	0.00617915	−	0.00736402i	0.769125	+	0.639098i	$0.220692\pi$
$570$	−55.0377	−	163.044i	−0.0965574	−	0.286041i
$571$	−54.3622	−	308.303i	−0.0952052	−	0.539935i	−0.994684	−	0.102972i	$-0.967165\pi$
$571$	−54.3622	−	308.303i	−0.0952052	−	0.539935i	0.899479	−	0.436964i	$-0.143946\pi$
$572$	78.0789	−	214.520i	0.136502	−	0.375035i
$573$	−935.201	−	365.507i	−1.63211	−	0.637883i
$574$	119.312	−	676.651i	0.207860	−	1.17883i
$575$	−141.698	−	81.8092i	−0.246431	−	0.142277i
$576$	−66.4255	−	27.7787i	−0.115322	−	0.0482268i
$577$	−121.599	−	210.616i	−0.210744	−	0.365019i	0.741204	−	0.671280i	$-0.234255\pi$
$577$	−121.599	−	210.616i	−0.210744	−	0.365019i	−0.951948	+	0.306261i	$0.900922\pi$
$578$	131.458	+	361.179i	0.227437	+	0.624877i
$579$	−807.852	+	441.422i	−1.39525	+	0.762387i
$580$	66.5188	−	55.8159i	0.114688	−	0.0962344i
$581$	825.810	+	984.163i	1.42136	+	1.69391i
$582$	−334.940	−	7.87669i	−0.575498	−	0.0135338i
$583$	−84.3283	+	30.6930i	−0.144645	+	0.0526467i
$584$	−83.4283	+	48.1673i	−0.142857	+	0.0824783i
$585$	142.392	+	91.3938i	0.243404	+	0.156229i
$586$	169.245	−	293.141i	0.288814	−	0.500240i
$587$	−959.623	−	169.207i	−1.63479	−	0.288258i	−0.720542	−	0.693411i	$-0.756107\pi$
$587$	−959.623	−	169.207i	−1.63479	−	0.288258i	−0.914249	+	0.405153i	$0.867218\pi$
$588$	195.601	−	29.7664i	0.332655	−	0.0506232i
$589$	17.6364	+	6.41912i	0.0299429	+	0.0108983i
$590$	−189.390	+	33.3946i	−0.321000	+	0.0566010i
$591$	−113.113	+	563.658i	−0.191392	+	0.953736i
$592$	127.150	+	106.691i	0.214780	+	0.180222i
$593$		−	140.671i		−	0.237219i	−0.992941	−	0.118609i	$-0.962156\pi$
$593$		−	140.671i		−	0.237219i	0.992941	−	0.118609i	$-0.0378436\pi$
$594$	−304.401	−	419.611i	−0.512460	−	0.706416i
$595$	479.429			0.805763
$596$	141.666	−	168.831i	0.237695	−	0.283274i
$597$	630.602	−	716.608i	1.05628	−	1.20035i
$598$	67.5642	+	383.176i	0.112984	+	0.640762i
$599$	11.5529	−	31.7413i	0.0192870	−	0.0529905i	−0.929676	−	0.368379i	$-0.879913\pi$
$599$	11.5529	−	31.7413i	0.0192870	−	0.0529905i	0.948963	+	0.315389i	$0.102135\pi$
$600$	−33.1327	+	26.4995i	−0.0552211	+	0.0441659i
$601$	−65.1168	+	369.296i	−0.108347	+	0.614469i	0.881483	+	0.472216i	$0.156546\pi$
$601$	−65.1168	+	369.296i	−0.108347	+	0.614469i	−0.989830	+	0.142253i	$0.954565\pi$
$602$	337.771	+	195.012i	0.561081	+	0.323940i
$603$	−87.2721	+	387.436i	−0.144730	+	0.642513i
$604$	129.730	+	224.699i	0.214785	+	0.372019i
$605$	48.4234	+	133.042i	0.0800386	+	0.219904i
$606$	−673.748	−	410.405i	−1.11180	−	0.677237i
$607$	208.593	−	175.031i	0.343646	−	0.288354i	−0.454586	−	0.890703i	$-0.650213\pi$
$607$	208.593	−	175.031i	0.343646	−	0.288354i	0.798233	+	0.602349i	$0.205768\pi$
$608$	−65.9565	−	78.6039i	−0.108481	−	0.129283i
$609$	−274.365	+	450.415i	−0.450517	+	0.739597i
$610$	−189.988	+	69.1500i	−0.311456	+	0.113361i
$611$	648.927	−	374.658i	1.06207	−	0.613189i
$612$	415.836	+	93.6694i	0.679471	+	0.153055i
$613$	−237.246	+	410.921i	−0.387024	+	0.670345i	−0.992048	−	0.125862i	$-0.959830\pi$
$613$	−237.246	+	410.921i	−0.387024	+	0.670345i	0.605024	+	0.796207i	$0.293164\pi$
$614$	620.896	+	109.481i	1.01123	+	0.178307i
$615$	−224.835	−	281.114i	−0.365586	−	0.457096i
$616$	−326.705	−	118.911i	−0.530365	−	0.193037i
$617$	845.305	−	149.050i	1.37002	−	0.241572i	0.560254	−	0.828321i	$-0.310703\pi$
$617$	845.305	−	149.050i	1.37002	−	0.241572i	0.809769	+	0.586748i	$0.199592\pi$
$618$	74.3396	+	65.4174i	0.120291	+	0.105853i
$619$	−317.118	−	266.094i	−0.512307	−	0.429877i	0.349633	−	0.936887i	$-0.386306\pi$
$619$	−317.118	−	266.094i	−0.512307	−	0.429877i	−0.861940	+	0.507010i	$0.830751\pi$
$620$		−	4.62726i		−	0.00746332i
$621$	806.893	+	359.952i	1.29934	+	0.579633i
$622$	−346.698			−0.557392
$623$	−12.5256	+	14.9274i	−0.0201053	+	0.0239606i
$624$	98.9185	+	19.8506i	0.158523	+	0.0318118i
$625$	4.34120	+	24.6202i	0.00694593	+	0.0393923i
$626$	60.7505	−	166.911i	0.0970455	−	0.266630i
$627$	−111.148	−	730.378i	−0.177270	−	1.16488i
$628$	61.9471	−	351.319i	0.0986419	−	0.559426i
$629$	−850.999	−	491.325i	−1.35294	−	0.781120i
$630$	139.189	−	216.856i	0.220935	−	0.344216i
$631$	−85.7013	−	148.439i	−0.135818	−	0.235244i	0.790091	−	0.612989i	$-0.210033\pi$
$631$	−85.7013	−	148.439i	−0.135818	−	0.235244i	−0.925910	+	0.377745i	$0.876700\pi$
$632$	78.5394	+	215.785i	0.124271	+	0.341432i
$633$	−24.6131	+	1046.62i	−0.0388833	+	1.65343i
$634$	224.027	−	187.981i	0.353354	−	0.296499i
$635$	−47.0872	−	56.1163i	−0.0741531	−	0.0883722i
$636$	−19.0172	−	34.8036i	−0.0299012	−	0.0547226i
$637$	−260.524	+	94.8228i	−0.408985	+	0.148858i
$638$	322.852	−	186.399i	0.506038	−	0.292161i
$639$	−213.684	+	510.971i	−0.334404	+	0.799641i
$640$	−12.6491	+	21.9089i	−0.0197642	+	0.0342327i
$641$	−49.1343	−	8.66370i	−0.0766525	−	0.0135159i	0.135190	−	0.990820i	$-0.456835\pi$
$641$	−49.1343	−	8.66370i	−0.0766525	−	0.0135159i	−0.211843	+	0.977304i	$0.567947\pi$
$642$	−255.196	+	652.956i	−0.397502	+	1.01707i
$643$	−496.508	−	180.714i	−0.772175	−	0.281049i	−0.0742690	−	0.997238i	$-0.523662\pi$
$643$	−496.508	−	180.714i	−0.772175	−	0.281049i	−0.697906	+	0.716190i	$0.745885\pi$
$644$	583.560	−	102.897i	0.906149	−	0.159779i
$645$	193.601	−	65.3528i	0.300157	−	0.101322i
$646$	465.352	+	390.477i	0.720359	+	0.604453i
$647$			832.220i			1.28627i	0.765751	+	0.643137i	$0.222368\pi$
$647$			832.220i			1.28627i	−0.765751	+	0.643137i	$0.777632\pi$
$648$	163.095	−	160.897i	0.251690	−	0.248298i
$649$	−825.635			−1.27216
$650$	38.2140	−	45.5416i	0.0587907	−	0.0700640i
$651$	8.98867	+	26.6280i	0.0138075	+	0.0409033i
$652$	17.9835	+	101.990i	0.0275821	+	0.156426i
$653$	−76.0064	+	208.826i	−0.116396	+	0.319795i	−0.984187	−	0.177135i	$-0.943317\pi$
$653$	−76.0064	+	208.826i	−0.116396	+	0.319795i	0.867791	+	0.496930i	$0.165539\pi$
$654$	−387.462	−	151.433i	−0.592450	−	0.231549i
$655$	−78.8648	+	447.265i	−0.120404	+	0.682847i
$656$	−185.886	−	107.321i	−0.283363	−	0.163600i
$657$	−38.9799	−	304.047i	−0.0593301	−	0.462780i
$658$	−570.588	−	988.288i	−0.867156	−	1.50196i
$659$	265.109	+	728.382i	0.402290	+	1.10528i	0.961151	+	0.276022i	$0.0890163\pi$
$659$	265.109	+	728.382i	0.402290	+	1.10528i	−0.558861	+	0.829261i	$0.688762\pi$
$660$	−159.840	+	87.3390i	−0.242182	+	0.132332i
$661$	−170.834	+	143.347i	−0.258448	+	0.216864i	−0.762800	−	0.646634i	$-0.776176\pi$
$661$	−170.834	+	143.347i	−0.258448	+	0.216864i	0.504352	+	0.863498i	$0.331732\pi$
$662$	−141.520	−	168.656i	−0.213776	−	0.254768i
$663$	−597.129	−	14.0425i	−0.900647	−	0.0211803i
$664$	377.139	−	137.267i	0.567981	−	0.206728i
$665$	318.034	−	183.617i	0.478246	−	0.276116i
$666$	−469.301	+	242.283i	−0.704656	+	0.363788i
$667$	−317.693	+	550.260i	−0.476301	+	0.824978i
$668$	322.143	+	56.8025i	0.482250	+	0.0850336i
$669$	−31.1777	+	4.74460i	−0.0466034	+	0.00709207i
$670$	131.127	+	47.7261i	0.195711	+	0.0712331i
$671$	−854.819	+	150.728i	−1.27395	+	0.224631i
$672$	30.2315	−	150.649i	0.0449874	−	0.224179i
$673$	79.5830	+	66.7780i	0.118251	+	0.0992244i	0.699996	−	0.714147i	$-0.253185\pi$
$673$	79.5830	+	66.7780i	0.118251	+	0.0992244i	−0.581745	+	0.813371i	$0.697630\pi$
$674$		−	340.692i		−	0.505477i
$675$	−37.1171	−	129.797i	−0.0549883	−	0.192292i
$676$	196.626			0.290867
$677$	−199.977	+	238.324i	−0.295387	+	0.352029i	−0.893242	−	0.449575i	$-0.851575\pi$
$677$	−199.977	+	238.324i	−0.295387	+	0.352029i	0.597855	+	0.801604i	$0.296020\pi$
$678$	361.363	−	410.649i	0.532984	−	0.605677i
$679$	−124.155	−	704.115i	−0.182849	−	1.03699i
$680$	51.2246	−	140.739i	0.0753304	−	0.206968i
$681$	331.661	−	265.263i	0.487021	−	0.389519i
$682$	3.44966	−	19.5640i	0.00505815	−	0.0286862i
$683$	−1009.78	−	582.997i	−1.47845	−	0.853583i	−0.478747	−	0.877953i	$-0.658909\pi$
$683$	−1009.78	−	582.997i	−1.47845	−	0.853583i	−0.999703	+	0.0243699i	$0.992242\pi$
$684$	311.723	−	97.1248i	0.455736	−	0.141995i
$685$	−44.6263	−	77.2950i	−0.0651478	−	0.112839i
$686$	−70.1766	−	192.809i	−0.102298	−	0.281062i
$687$	−1108.49	−	675.224i	−1.61353	−	0.982859i
$688$	93.3359	−	78.3181i	0.135663	−	0.113834i
$689$	35.7225	+	42.5725i	0.0518469	+	0.0617888i
$690$	161.500	−	265.129i	0.234058	−	0.384245i
$691$	−411.891	+	149.916i	−0.596080	+	0.216955i	−0.622401	−	0.782698i	$-0.713843\pi$
$691$	−411.891	+	149.916i	−0.596080	+	0.216955i	0.0263216	+	0.999654i	$0.491621\pi$
$692$	−79.9392	+	46.1529i	−0.115519	+	0.0666950i
$693$	750.157	−	813.099i	1.08248	−	1.17330i
$694$	−297.266	+	514.880i	−0.428337	+	0.741902i
$695$	−442.667	−	78.0542i	−0.636931	−	0.112308i
$696$	102.907	+	128.666i	0.147855	+	0.184864i
$697$	1194.10	+	434.615i	1.71319	+	0.623551i
$698$	113.444	−	20.0033i	0.162528	−	0.0286580i
$699$	308.355	+	271.346i	0.441137	+	0.388192i
$700$	−69.3579	−	58.1982i	−0.0990827	−	0.0831403i
$701$			316.030i			0.450827i	0.974263	+	0.225414i	$0.0723733\pi$
$701$			316.030i			0.450827i	−0.974263	+	0.225414i	$0.927627\pi$
$702$	−179.711	+	266.017i	−0.255999	+	0.378942i
$703$	−752.691			−1.07068
$704$	−69.8136	+	83.2006i	−0.0991670	+	0.118183i
$705$	−586.177	−	117.632i	−0.831457	−	0.166853i
$706$	110.037	+	624.052i	0.155860	+	0.883926i
$707$	575.813	−	1582.03i	0.814446	−	2.23767i
$708$	−54.8960	−	360.733i	−0.0775367	−	0.509509i
$709$	140.542	−	797.055i	0.198226	−	1.12420i	−0.709523	−	0.704683i	$-0.751089\pi$
$709$	140.542	−	797.055i	0.198226	−	1.12420i	0.907749	−	0.419514i	$-0.137799\pi$
$710$	168.532	+	97.3019i	0.237369	+	0.137045i
$711$	−729.882	−	34.3479i	−1.02656	−	0.0483093i
$712$	3.04372	+	5.27187i	0.00427489	+	0.00740432i
$713$	11.5804	+	31.8168i	0.0162417	+	0.0446238i
$714$	−21.3862	+	909.401i	−0.0299526	+	1.27367i
$715$	195.520	−	164.061i	0.273454	−	0.229455i
$716$	35.4900	+	42.2953i	0.0495670	+	0.0590717i
$717$	−129.856	−	237.651i	−0.181110	−	0.331451i
$718$	−233.147	+	84.8585i	−0.324717	+	0.118187i
$719$	286.206	−	165.241i	0.398062	−	0.229821i	−0.287586	−	0.957755i	$-0.592853\pi$
$719$	286.206	−	165.241i	0.398062	−	0.229821i	0.685647	+	0.727934i	$0.259519\pi$
$720$	−48.7875	−	64.0295i	−0.0677604	−	0.0889299i
$721$	−105.662	+	183.011i	−0.146549	+	0.253830i
$722$	−44.5305	−	7.85193i	−0.0616766	−	0.0108752i
$723$	−311.000	+	795.738i	−0.430152	+	1.10061i
$724$	−294.561	−	107.212i	−0.406852	−	0.148082i
$725$	95.6086	−	16.8584i	0.131874	−	0.0232529i
$726$	−254.520	+	85.9168i	−0.350578	+	0.118343i
$727$	−1062.25	−	891.333i	−1.46114	−	1.22604i	−0.923912	−	0.382606i	$-0.875027\pi$
$727$	−1062.25	−	891.333i	−1.46114	−	1.22604i	−0.537229	−	0.843437i	$-0.680529\pi$
$728$			215.306i			0.295750i
$729$	272.109	+	676.312i	0.373264	+	0.927725i
$730$	−107.705			−0.147542
$731$	−463.660	+	552.568i	−0.634281	+	0.755907i
$732$	−122.692	−	363.462i	−0.167612	−	0.496533i
$733$	−155.250	−	880.468i	−0.211801	−	1.20118i	−0.886372	−	0.462974i	$-0.846782\pi$
$733$	−155.250	−	880.468i	−0.211801	−	1.20118i	0.674571	−	0.738210i	$-0.264329\pi$
$734$	53.9850	−	148.323i	0.0735490	−	0.202074i
$735$	206.030	+	80.5232i	0.280313	+	0.109555i
$736$	32.1445	−	182.301i	0.0436746	−	0.247691i
$737$	518.821	+	299.542i	0.703964	+	0.406434i
$738$	543.258	−	413.937i	0.736122	−	0.560890i
$739$	−504.138	−	873.193i	−0.682190	−	1.18159i	−0.974311	−	0.225206i	$-0.927694\pi$
$739$	−504.138	−	873.193i	−0.682190	−	1.18159i	0.292121	−	0.956381i	$-0.405639\pi$
$740$	63.4699	+	174.382i	0.0857702	+	0.235652i
$741$	−401.489	+	219.379i	−0.541820	+	0.296059i
$742$	64.8360	−	54.4039i	0.0873801	−	0.0733206i
$743$	−25.8069	−	30.7554i	−0.0347333	−	0.0413936i	0.748398	−	0.663250i	$-0.230823\pi$
$743$	−25.8069	−	30.7554i	−0.0347333	−	0.0413936i	−0.783131	+	0.621856i	$0.786379\pi$
$744$	8.77718	+	0.206411i	0.0117973	+	0.000277434i
$745$	231.547	−	84.2764i	0.310802	−	0.113123i
$746$	−720.918	+	416.222i	−0.966378	+	0.557939i
$747$	−60.0317	+	1275.65i	−0.0803637	+	1.70770i
$748$	321.499	−	556.853i	0.429812	−	0.744455i
$749$	−1473.36	−	259.793i	−1.96710	−	0.346853i
$750$	−46.8943	+	7.13633i	−0.0625257	+	0.00951511i
$751$	583.991	+	212.555i	0.777617	+	0.283030i	0.700179	−	0.713968i	$-0.253104\pi$
$751$	583.991	+	212.555i	0.777617	+	0.283030i	0.0774385	+	0.996997i	$0.475326\pi$
$752$	−351.081	+	61.9050i	−0.466863	+	0.0823205i
$753$	−41.1400	+	205.007i	−0.0546348	+	0.272254i
$754$	−176.854	−	148.398i	−0.234554	−	0.196814i
$755$			290.086i			0.384219i
$756$	405.133	+	273.693i	0.535890	+	0.362028i
$757$	−1401.61			−1.85153			−0.925767	−	0.378094i	$-0.876580\pi$
$757$	−1401.61			−1.85153			−0.925767	+	0.378094i	$0.876580\pi$
$758$	−153.084	+	182.439i	−0.201958	+	0.240684i
$759$	880.475	−	1000.56i	1.16005	−	1.31826i
$760$	−19.9212	−	112.979i	−0.0262121	−	0.148656i
$761$	−227.490	+	625.024i	−0.298936	+	0.821319i	0.695743	+	0.718291i	$0.255075\pi$
$761$	−227.490	+	625.024i	−0.298936	+	0.821319i	−0.994678	+	0.103028i	$0.967147\pi$
$762$	108.544	−	86.8138i	0.142447	−	0.113929i
$763$	154.161	−	874.288i	0.202045	−	1.14586i
$764$	−579.712	−	334.697i	−0.758785	−	0.438085i
$765$	350.269	+	323.154i	0.457868	+	0.422424i
$766$	−47.6985	−	82.6163i	−0.0622696	−	0.107854i
$767$	174.875	+	480.464i	0.227998	+	0.626420i
$768$	−40.9935	−	24.9707i	−0.0533769	−	0.0325139i
$769$	−747.084	+	626.878i	−0.971501	+	0.815186i	−0.982785	−	0.184750i	$-0.940852\pi$
$769$	−747.084	+	626.878i	−0.971501	+	0.815186i	0.0112846	+	0.999936i	$0.496408\pi$
$770$	−249.857	−	297.768i	−0.324490	−	0.386712i
$771$	−580.228	+	952.541i	−0.752566	+	1.23546i
$772$	−576.712	+	209.906i	−0.747036	+	0.271899i
$773$	798.290	−	460.893i	1.03272	−	0.596239i	0.114955	−	0.993371i	$-0.463328\pi$
$773$	798.290	−	460.893i	1.03272	−	0.596239i	0.917762	+	0.397132i	$0.129994\pi$
$774$	115.328	+	370.146i	0.149002	+	0.478225i
$775$	2.58672	−	4.48032i	0.00333770	−	0.00578106i
$776$	−219.962	−	38.7851i	−0.283456	−	0.0499809i
$777$	−703.990	−	880.207i	−0.906037	−	1.13283i
$778$	151.925	+	55.2962i	0.195276	+	0.0710748i
$779$	958.568	−	169.021i	1.23051	−	0.216972i
$780$	84.6806	+	74.5173i	0.108565	+	0.0955350i
$781$	640.011	+	537.033i	0.819476	+	0.687622i
$782$			1095.91i			1.40142i
$783$	−504.047	+	144.138i	−0.643738	+	0.184085i
$784$	131.902			0.168243
$785$	256.374	−	305.534i	0.326591	−	0.389215i
$786$	−844.873	−	169.546i	−1.07490	−	0.215707i
$787$	−75.1934	−	426.443i	−0.0955443	−	0.541859i	−0.994579	−	0.103982i	$-0.966842\pi$
$787$	−75.1934	−	426.443i	−0.0955443	−	0.541859i	0.899035	−	0.437877i	$-0.144269\pi$
$788$	−131.084	+	360.150i	−0.166350	+	0.457043i
$789$	115.960	+	761.998i	0.146971	+	0.965776i
$790$	−44.5821	+	252.838i	−0.0564331	+	0.320048i
$791$	1010.95	+	583.671i	1.27806	+	0.737890i
$792$	−158.538	−	307.088i	−0.200175	−	0.387737i
$793$	268.770	+	465.522i	0.338928	+	0.587040i
$794$	261.403	+	718.198i	0.329223	+	0.904532i
$795$	1.04248	−	44.3294i	0.00131130	−	0.0557602i
$796$	487.491	−	409.053i	0.612425	−	0.513886i
$797$	304.357	+	362.718i	0.381878	+	0.455104i	0.922406	−	0.386222i	$-0.126220\pi$
$797$	304.357	+	362.718i	0.381878	+	0.455104i	−0.540528	+	0.841326i	$0.681776\pi$
$798$	334.105	+	611.450i	0.418679	+	0.766229i
$799$	1983.26	−	721.846i	2.48217	−	0.903437i
$800$	−24.4949	+	14.1421i	−0.0306186	+	0.0176777i
$801$	−19.2129	+	2.46316i	−0.0239861	+	0.00307510i
$802$	144.358	−	250.035i	0.179997	−	0.311764i
$803$	−455.377	−	80.2953i	−0.567095	−	0.0999942i
$804$	−96.3782	+	246.597i	−0.119873	+	0.306713i
$805$	622.551	+	226.590i	0.773355	+	0.281478i
$806$	−12.1156	+	2.13631i	−0.0150317	+	0.00265050i
$807$	138.748	−	46.8362i	0.171930	−	0.0580374i
$808$	−402.890	−	338.065i	−0.498627	−	0.418398i
$809$		−	844.623i		−	1.04403i	−0.852935	−	0.522017i	$-0.825180\pi$
$809$		−	844.623i		−	1.04403i	0.852935	−	0.522017i	$-0.174820\pi$
$810$	247.861	−	64.6153i	0.306001	−	0.0797720i
$811$	−1017.15			−1.25420			−0.627098	−	0.778940i	$-0.715758\pi$
$811$	−1017.15			−1.25420			−0.627098	+	0.778940i	$0.715758\pi$
$812$	−226.004	+	269.341i	−0.278330	+	0.331700i
$813$	−211.170	−	625.569i	−0.259741	−	0.769458i
$814$	138.347	+	784.603i	0.169959	+	0.963886i
$815$	−39.6015	+	108.804i	−0.0485908	+	0.133502i
$816$	264.674	+	103.443i	0.324355	+	0.126768i
$817$	−95.9445	+	544.128i	−0.117435	+	0.666008i
$818$	−403.466	−	232.941i	−0.493235	−	0.284769i
$819$	−632.057	−	264.322i	−0.771743	−	0.322737i
$820$	−119.989	−	207.827i	−0.146328	−	0.253447i
$821$	267.471	+	734.870i	0.325787	+	0.895092i	0.989165	+	0.146808i	$0.0468998\pi$
$821$	267.471	+	734.870i	0.325787	+	0.895092i	−0.663378	+	0.748284i	$0.730878\pi$
$822$	148.607	−	81.2010i	0.180787	−	0.0987847i
$823$	565.424	−	474.447i	0.687028	−	0.576485i	−0.231022	−	0.972948i	$-0.574207\pi$
$823$	565.424	−	474.447i	0.687028	−	0.576485i	0.918051	+	0.396463i	$0.129763\pi$
$824$	42.4344	+	50.5713i	0.0514980	+	0.0613730i
$825$	−203.589	−	4.78774i	−0.246774	−	0.00580332i
$826$	731.726	−	266.327i	0.885867	−	0.322429i
$827$	605.840	−	349.782i	0.732575	−	0.422952i	−0.0867884	−	0.996227i	$-0.527660\pi$
$827$	605.840	−	349.782i	0.732575	−	0.422952i	0.819363	+	0.573274i	$0.194327\pi$
$828$	495.703	+	318.167i	0.598675	+	0.384259i
$829$	556.298	−	963.536i	0.671047	−	1.16229i	−0.306561	−	0.951851i	$-0.599178\pi$
$829$	556.298	−	963.536i	0.671047	−	1.16229i	0.977608	−	0.210436i	$-0.0674883\pi$
$830$	441.898	+	77.9186i	0.532407	+	0.0938778i
$831$	134.269	−	20.4330i	0.161576	−	0.0245884i
$832$	63.2041	+	23.0044i	0.0759665	+	0.0276495i
$833$	−769.025	+	135.600i	−0.923200	+	0.162785i
$834$	167.803	−	836.188i	0.201202	−	1.00262i
$835$	280.160	+	235.082i	0.335521	+	0.281535i
$836$		−	492.524i		−	0.589144i
$837$	−11.3813	+	25.5131i	−0.0135977	+	0.0304815i
$838$	−865.147			−1.03240
$839$	492.701	−	587.178i	0.587248	−	0.699855i	−0.387826	−	0.921732i	$-0.626774\pi$
$839$	492.701	−	587.178i	0.587248	−	0.699855i	0.975075	+	0.221877i	$0.0712184\pi$
$840$	113.487	−	128.965i	0.135103	−	0.153530i
$841$	80.5712	+	456.942i	0.0958041	+	0.543332i
$842$	146.204	−	401.693i	0.173639	−	0.477071i
$843$	−456.879	+	365.412i	−0.541968	+	0.433466i
$844$	−121.196	+	687.337i	−0.143597	+	0.814380i
$845$	190.382	+	109.917i	0.225305	+	0.130080i
$846$	249.276	−	1106.64i	0.294653	−	1.30808i
$847$	−286.636	−	496.468i	−0.338413	−	0.586148i
$848$	−9.04309	−	24.8457i	−0.0106640	−	0.0292992i
$849$	1365.59	+	831.831i	1.60847	+	0.979778i
$850$	128.273	−	107.634i	0.150910	−	0.126628i
$851$	−872.832	−	1040.20i	−1.02565	−	1.22233i
$852$	−192.084	+	315.338i	−0.225451	+	0.370115i
$853$	1385.58	−	504.308i	1.62436	−	0.591217i	0.640151	−	0.768250i	$-0.278872\pi$
$853$	1385.58	−	504.308i	1.62436	−	0.591217i	0.984205	+	0.177032i	$0.0566498\pi$
$854$	708.971	−	409.324i	0.830176	−	0.479303i
$855$	356.119	+	80.2178i	0.416514	+	0.0938220i
$856$	−233.685	+	404.754i	−0.272996	+	0.472843i
$857$	−724.248	−	127.704i	−0.845097	−	0.149013i	−0.265697	−	0.964057i	$-0.585602\pi$
$857$	−724.248	−	127.704i	−0.845097	−	0.149013i	−0.579400	+	0.815043i	$0.696713\pi$
$858$	302.475	+	378.189i	0.352535	+	0.440779i
$859$	259.121	+	94.3124i	0.301654	+	0.109793i	0.488413	−	0.872613i	$-0.337576\pi$
$859$	259.121	+	94.3124i	0.301654	+	0.109793i	−0.186759	+	0.982406i	$0.559798\pi$
$860$	134.153	−	23.6548i	0.155992	−	0.0275056i
$861$	1094.20	+	962.877i	1.27085	+	1.11832i
$862$	593.157	+	497.717i	0.688117	+	0.577398i
$863$		−	914.563i		−	1.05975i	−0.848076	−	0.529874i	$-0.822239\pi$
$863$		−	914.563i		−	1.05975i	0.848076	−	0.529874i	$-0.177761\pi$
$864$	123.630	−	89.6859i	0.143091	−	0.103803i
$865$	−103.201			−0.119308
$866$	47.7134	−	56.8626i	0.0550963	−	0.0656613i
$867$	−799.411	−	160.422i	−0.922042	−	0.185032i
$868$	3.25350	+	18.4515i	0.00374827	+	0.0212575i
$869$	−376.986	+	1035.76i	−0.433815	+	1.19190i
$870$	27.7128	+	182.107i	0.0318538	+	0.209318i
$871$	64.4235	−	365.364i	0.0739650	−	0.419476i
$872$	−240.180	−	138.668i	−0.275436	−	0.159023i
$873$	383.895	−	598.109i	0.439743	−	0.685119i
$874$	419.723	+	726.981i	0.480232	+	0.831786i
$875$	−34.6217	−	95.1224i	−0.0395677	−	0.108711i
$876$	4.80448	−	204.300i	0.00548456	−	0.233219i
$877$	666.447	−	559.215i	0.759917	−	0.637646i	−0.178189	−	0.983996i	$-0.557024\pi$
$877$	666.447	−	559.215i	0.759917	−	0.637646i	0.938105	+	0.346351i	$0.112579\pi$
$878$	588.690	+	701.573i	0.670490	+	0.799058i
$879$	344.304	+	630.114i	0.391699	+	0.716853i
$880$	−114.107	+	41.5316i	−0.129667	+	0.0471950i
$881$	−569.492	+	328.796i	−0.646415	+	0.373208i	−0.787081	−	0.616849i	$-0.788409\pi$
$881$	−569.492	+	328.796i	−0.646415	+	0.373208i	0.140666	+	0.990057i	$0.455076\pi$
$882$	−161.930	+	387.215i	−0.183594	+	0.439019i
$883$	124.361	−	215.400i	0.140840	−	0.243941i	−0.786973	−	0.616987i	$-0.788353\pi$
$883$	124.361	−	215.400i	0.140840	−	0.243941i	0.927813	+	0.373046i	$0.121686\pi$
$884$	−392.146	−	69.1460i	−0.443605	−	0.0782194i
$885$	148.503	−	379.966i	0.167800	−	0.429340i
$886$	351.858	+	128.066i	0.397131	+	0.144544i
$887$	−836.776	+	147.546i	−0.943378	+	0.166343i	−0.624123	−	0.781326i	$-0.714544\pi$
$887$	−836.776	+	147.546i	−0.943378	+	0.166343i	−0.319255	+	0.947669i	$0.603433\pi$
$888$	−333.607	+	112.614i	−0.375683	+	0.126817i
$889$	227.220	+	190.660i	0.255591	+	0.214466i
$890$			6.80596i			0.00764715i
$891$	1096.12	−	88.4106i	1.23022	−	0.0992262i
$892$	−21.0244			−0.0235700
$893$	1039.15	−	1238.41i	1.16366	−	1.38680i
$894$	149.530	+	442.968i	0.167260	+	0.495490i
$895$	10.7192	+	60.7918i	0.0119768	+	0.0679238i
$896$	35.0347	−	96.2571i	0.0391013	−	0.107430i
$897$	−768.750	−	300.452i	−0.857024	−	0.334952i
$898$	127.974	−	725.778i	0.142510	−	0.808217i
$899$	−17.3986	−	10.0451i	−0.0193533	−	0.0111736i
$900$	−11.4447	−	89.2694i	−0.0127163	−	0.0991882i
$901$	78.2659	+	135.561i	0.0868656	+	0.150456i
$902$	−352.375	−	968.142i	−0.390659	−	1.07333i
$903$	−726.048	+	396.723i	−0.804040	+	0.439339i
$904$	279.354	−	234.406i	0.309020	−	0.259298i
$905$	−225.275	−	268.472i	−0.248922	−	0.296654i
$906$	−550.247	−	12.9400i	−0.607336	−	0.0142826i
$907$	278.085	−	101.215i	0.306599	−	0.111593i	−0.184139	−	0.982900i	$-0.558950\pi$
$907$	278.085	−	101.215i	0.306599	−	0.111593i	0.490738	+	0.871307i	$0.336727\pi$
$908$	245.196	−	141.564i	0.270040	−	0.155908i
$909$	1487.04	−	767.706i	1.63591	−	0.844561i
$910$	−120.360	+	208.469i	−0.132264	+	0.229087i
$911$	−173.033	−	30.5103i	−0.189937	−	0.0334910i	0.0778703	−	0.996963i	$-0.475188\pi$
$911$	−173.033	−	30.5103i	−0.189937	−	0.0334910i	−0.267807	+	0.963472i	$0.586299\pi$
$912$	215.192	−	32.7477i	0.235956	−	0.0359075i
$913$	1810.25	+	658.878i	1.98275	+	0.721662i
$914$	−953.922	+	168.202i	−1.04368	+	0.184029i
$915$	84.3857	−	420.507i	0.0922248	−	0.459571i
$916$	−662.860	−	556.205i	−0.723646	−	0.607211i
$917$		−	1838.95i		−	2.00540i
$918$	−628.598	+	649.989i	−0.684747	+	0.708049i
$919$	145.050			0.157835			0.0789174	−	0.996881i	$-0.474854\pi$
$919$	145.050			0.157835			0.0789174	+	0.996881i	$0.474854\pi$
$920$	133.033	−	158.543i	0.144601	−	0.172329i
$921$	−883.538	+	1004.04i	−0.959325	+	1.09017i
$922$	212.130	+	1203.05i	0.230076	+	1.30482i
$923$	176.959	−	486.191i	0.191721	−	0.526750i
$924$	575.965	−	460.657i	0.623339	−	0.498547i
$925$	−36.0281	+	204.326i	−0.0389493	+	0.220893i
$926$	451.154	+	260.474i	0.487207	+	0.281289i
$927$	−200.553	+	62.4871i	−0.216346	+	0.0674079i
$928$	54.9188	+	95.1221i	0.0591797	+	0.102502i
$929$	192.548	+	529.021i	0.207264	+	0.569452i	0.999150	−	0.0412159i	$-0.0131231\pi$
$929$	192.548	+	529.021i	0.207264	+	0.569452i	−0.791887	+	0.610668i	$0.790901\pi$
$930$	8.38308	+	5.10645i	0.00901406	+	0.00549080i
$931$	−458.206	+	384.481i	−0.492166	+	0.412976i
$932$	176.015	+	209.766i	0.188857	+	0.225071i
$933$	382.601	−	628.104i	0.410077	−	0.673208i
$934$	−1020.60	+	371.467i	−1.09272	+	0.397716i
$935$	622.580	−	359.447i	0.665861	−	0.384435i
$936$	−145.125	+	157.302i	−0.155048	+	0.168057i
$937$	−40.8882	+	70.8205i	−0.0436374	+	0.0755821i	−0.887019	−	0.461733i	$-0.847228\pi$
$937$	−40.8882	+	70.8205i	−0.0436374	+	0.0755821i	0.843382	+	0.537315i	$0.180561\pi$
$938$	−556.434	−	98.1142i	−0.593213	−	0.104599i
$939$	235.346	+	294.256i	0.250634	+	0.313371i
$940$	−374.539	−	136.321i	−0.398445	−	0.145022i
$941$	741.861	−	130.810i	0.788375	−	0.139012i	0.235057	−	0.971982i	$-0.424472\pi$
$941$	741.861	−	130.810i	0.788375	−	0.139012i	0.553318	+	0.832970i	$0.313361\pi$
$942$	568.114	+	499.929i	0.603093	+	0.530711i
$943$	1345.15	+	1128.72i	1.42646	+	1.19694i
$944$		−	243.257i		−	0.257688i
$945$	239.270	+	491.478i	0.253195	+	0.520083i
$946$	584.833			0.618217
$947$	−917.522	+	1093.46i	−0.968872	+	1.15466i	0.0190673	+	0.999818i	$0.493930\pi$
$947$	−917.522	+	1093.46i	−0.968872	+	1.15466i	−0.987940	+	0.154839i	$0.950514\pi$
$948$	−477.605	−	95.8438i	−0.503803	−	0.101101i
$949$	49.7253	+	282.006i	0.0523976	+	0.297161i
$950$	43.8684	−	120.528i	0.0461773	−	0.126871i
$951$	93.3331	+	613.310i	0.0981420	+	0.644911i
$952$	−105.306	+	597.222i	−0.110616	+	0.627334i
$953$	−704.738	−	406.881i	−0.739494	−	0.426947i	0.0823912	−	0.996600i	$-0.473744\pi$
$953$	−704.738	−	406.881i	−0.739494	−	0.426947i	−0.821885	+	0.569653i	$0.807078\pi$
$954$	84.0393	+	3.95485i	0.0880915	+	0.00414554i
$955$	−374.202	−	648.137i	−0.391835	−	0.678678i
$956$	−61.7493	−	169.655i	−0.0645913	−	0.177463i
$957$	−18.5924	+	790.604i	−0.0194278	+	0.826128i
$958$	−315.000	+	264.316i	−0.328810	+	0.275904i
$959$	232.298	+	276.842i	0.242229	+	0.288678i
$960$	−25.7327	−	47.0938i	−0.0268049	−	0.0490560i
$961$	902.039	−	328.315i	0.938646	−	0.341639i
$962$	427.284	−	246.692i	0.444162	−	0.256437i
$963$	−901.319	−	1182.91i	−0.935949	−	1.22836i
$964$	−284.785	+	493.261i	−0.295420	+	0.511682i
$965$	−675.740	−	119.151i	−0.700249	−	0.123473i
$966$	−457.576	+	1170.77i	−0.473681	+	1.21198i
$967$	1231.77	+	448.327i	1.27380	+	0.463626i	0.888378	−	0.459113i	$-0.151833\pi$
$967$	1231.77	+	448.327i	1.27380	+	0.463626i	0.385425	+	0.922739i	$0.374055\pi$
$968$	−176.366	+	31.0981i	−0.182196	+	0.0321261i
$969$	−1220.96	+	412.152i	−1.26002	+	0.425338i
$970$	−191.295	−	160.516i	−0.197212	−	0.165480i
$971$			1362.18i			1.40286i	0.712737	+	0.701431i	$0.247455\pi$
$971$			1362.18i			1.40286i	−0.712737	+	0.701431i	$0.752545\pi$
$972$	111.509	+	473.035i	0.114721	+	0.486661i
$973$	1820.05			1.87055
$974$	708.394	−	844.231i	0.727304	−	0.866767i
$975$	40.3352	+	119.489i	0.0413694	+	0.122553i
$976$	−44.4090	−	251.856i	−0.0455010	−	0.258049i
$977$	44.9129	−	123.397i	0.0459702	−	0.126302i	−0.914583	−	0.404398i	$-0.867481\pi$
$977$	44.9129	−	123.397i	0.0459702	−	0.126302i	0.960553	+	0.278096i	$0.0897033\pi$
$978$	−204.618	−	79.9713i	−0.209221	−	0.0817703i
$979$	−5.07390	+	28.7755i	−0.00518274	+	0.0293928i
$980$	127.714	+	73.7355i	0.130320	+	0.0752403i
$981$	701.934	−	534.840i	0.715529	−	0.545199i
$982$	−323.415	−	560.171i	−0.329343	−	0.570439i
$983$	493.739	+	1356.54i	0.502277	+	1.38000i	0.889046	+	0.457819i	$0.151369\pi$
$983$	493.739	+	1356.54i	0.502277	+	1.38000i	−0.386768	+	0.922177i	$0.626409\pi$
$984$	399.567	−	218.329i	0.406064	−	0.221879i
$985$	−328.252	+	275.436i	−0.333250	+	0.279630i
$986$	−417.980	−	498.129i	−0.423915	−	0.505202i
$987$	2420.13	+	56.9136i	2.45201	+	0.0576633i
$988$	−286.616	+	104.320i	−0.290097	+	0.105587i
$989$	−863.231	+	498.387i	−0.872832	+	0.503930i
$990$	18.1632	−	385.962i	0.0183466	−	0.389861i
$991$	−579.512	+	1003.74i	−0.584775	+	1.01286i	0.410128	+	0.912028i	$0.365484\pi$
$991$	−579.512	+	1003.74i	−0.584775	+	1.01286i	−0.994903	+	0.100833i	$0.967849\pi$
$992$	5.76415	+	1.01637i	0.00581063	+	0.00102457i
$993$	461.725	−	70.2650i	0.464980	−	0.0707603i
$994$	−740.447	−	269.501i	−0.744917	−	0.271128i
$995$	700.678	−	123.548i	0.704199	−	0.124169i
$996$	−167.511	+	834.735i	−0.168184	+	0.838088i
$997$	−719.887	−	604.057i	−0.722053	−	0.605875i	0.205899	−	0.978573i	$-0.433988\pi$
$997$	−719.887	−	604.057i	−0.722053	−	0.605875i	−0.927953	+	0.372698i	$0.878433\pi$
$998$		−	1073.03i		−	1.07518i
$999$	78.9629	−	1117.59i	0.0790420	−	1.11871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.o.a.11.6	✓	144
27.5	odd	18	inner	270.3.o.a.221.6	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.o.a.11.6	✓	144	1.1	even	1	trivial
270.3.o.a.221.6	yes	144	27.5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	270.o (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909039 + 1.08335i) q^{2} +(-0.959500 - 2.84242i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(0.764780 - 2.10122i) q^{5} +(3.95156 + 1.54440i) q^{6} +(-1.57222 + 8.91648i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-7.15872 + 5.45460i) q^{9} +(1.58114 + 2.73861i) q^{10} +(4.64338 + 12.7576i) q^{11} +(-5.26525 + 2.87701i) q^{12} +(6.44056 - 5.40427i) q^{13} +(-8.23047 - 9.80869i) q^{14} +(-6.70635 - 0.157712i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(20.5082 - 11.8404i) q^{17} +(0.598308 - 12.7139i) q^{18} +(9.06954 - 15.7089i) q^{19} +(-4.40419 - 0.776578i) q^{20} +(26.8529 - 4.08646i) q^{21} +(-18.0419 - 6.56673i) q^{22} +(32.2265 - 5.68241i) q^{23} +(1.66951 - 8.31942i) q^{24} +(-3.83022 - 3.21394i) q^{25} +11.8901i q^{26} +(22.3731 + 15.1144i) q^{27} +18.1081 q^{28} +(-12.4808 + 14.8741i) q^{29} +(6.26719 - 7.12196i) q^{30} +(0.179671 + 1.01897i) q^{31} +(1.93476 - 5.31570i) q^{32} +(31.8071 - 25.4393i) q^{33} +(-5.81544 + 32.9810i) q^{34} +(17.5331 + 10.1227i) q^{35} +(13.2297 + 12.2056i) q^{36} +(-20.7478 - 35.9362i) q^{37} +(8.77369 + 24.1055i) q^{38} +(-21.5409 - 13.1214i) q^{39} +(4.84489 - 4.06535i) q^{40} +(34.4924 + 41.1064i) q^{41} +(-19.9833 + 32.8059i) q^{42} +(-28.6233 + 10.4180i) q^{43} +(23.5149 - 13.5763i) q^{44} +(5.98646 + 19.2136i) q^{45} +(-23.1391 + 40.0781i) q^{46} +(87.7702 + 15.4763i) q^{47} +(7.49520 + 9.37134i) q^{48} +(-30.9869 - 11.2783i) q^{49} +(6.96364 - 1.22788i) q^{50} +(-53.3331 - 46.9321i) q^{51} +(-12.8811 - 10.8085i) q^{52} +6.61006i q^{53} +(-36.7122 + 10.4983i) q^{54} +30.3576 q^{55} +(-16.4609 + 19.6174i) q^{56} +(-53.3536 - 10.7068i) q^{57} +(-4.76827 - 27.0422i) q^{58} +(-20.7997 + 57.1467i) q^{59} +(2.01846 + 13.2637i) q^{60} +(-11.1022 + 62.9640i) q^{61} +(-1.26723 - 0.731634i) q^{62} +(-37.3808 - 72.4064i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-6.42993 - 17.6661i) q^{65} +(-1.35418 + 57.5836i) q^{66} +(33.8033 - 28.3643i) q^{67} +(-30.4435 - 36.2812i) q^{68} +(-47.0731 - 86.1491i) q^{69} +(-26.9047 + 9.79251i) q^{70} +(53.2944 - 30.7696i) q^{71} +(-25.2492 + 3.23704i) q^{72} +(-17.0297 + 29.4964i) q^{73} +(57.7920 + 10.1903i) q^{74} +(-5.46027 + 13.9709i) q^{75} +(-34.0903 - 12.4079i) q^{76} +(-121.053 + 21.3449i) q^{77} +(33.7966 - 11.4085i) q^{78} +(62.1935 + 52.1865i) q^{79} +8.94427i q^{80} +(21.4946 - 78.0960i) q^{81} -75.8876 q^{82} +(91.2091 - 108.699i) q^{83} +(-17.3747 - 51.4708i) q^{84} +(-9.19502 - 52.1475i) q^{85} +(14.7333 - 40.4795i) q^{86} +(54.2537 + 21.2041i) q^{87} +(-6.66803 + 37.8163i) q^{88} +(1.86389 + 1.07612i) q^{89} +(-26.2570 - 10.9805i) q^{90} +(38.0611 + 65.9238i) q^{91} +(-22.3843 - 61.5004i) q^{92} +(2.72394 - 1.48840i) q^{93} +(-96.5528 + 81.0174i) q^{94} +(-26.0716 - 31.0709i) q^{95} +(-16.9659 - 0.398982i) q^{96} +(-74.2055 + 27.0086i) q^{97} +(40.3866 - 23.3172i) q^{98} +(-102.828 - 66.0001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{6} + 12 q^{9} + 24 q^{12} + 36 q^{14} + 96 q^{18} + 96 q^{21} - 72 q^{22} + 216 q^{23} - 12 q^{27} - 252 q^{29} - 516 q^{33} + 144 q^{34} - 48 q^{36} - 144 q^{38} + 48 q^{39} + 108 q^{41}+ \cdots - 444 q^{99}+O(q^{100}) \) 144 * q - 12 * q^6 + 12 * q^9 + 24 * q^12 + 36 * q^14 + 96 * q^18 + 96 * q^21 - 72 * q^22 + 216 * q^23 - 12 * q^27 - 252 * q^29 - 516 * q^33 + 144 * q^34 - 48 * q^36 - 144 * q^38 + 48 * q^39 + 108 * q^41 - 180 * q^43 + 60 * q^45 + 432 * q^47 - 72 * q^49 - 204 * q^51 - 288 * q^54 + 72 * q^56 - 612 * q^57 - 252 * q^59 + 144 * q^61 - 720 * q^63 + 576 * q^64 + 360 * q^65 + 864 * q^66 + 252 * q^67 + 144 * q^68 + 708 * q^69 + 360 * q^70 + 1296 * q^71 - 252 * q^73 + 720 * q^74 + 144 * q^76 + 684 * q^77 + 192 * q^78 + 72 * q^79 - 492 * q^81 - 828 * q^83 - 216 * q^84 - 360 * q^85 - 648 * q^86 - 660 * q^87 - 288 * q^88 + 324 * q^89 - 480 * q^90 + 396 * q^91 - 216 * q^92 - 1548 * q^93 - 504 * q^94 - 720 * q^95 - 192 * q^96 - 180 * q^97 - 1296 * q^98 - 444 * q^99

Introduction

L-functions

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