LMFDB - Embedded newform 270.3.o.a.221.10

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			221.10
Character	$\chi$	$=$	270.221
Dual form			270.3.o.a.11.10

$q$-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} +(2.46914 + 1.70392i) q^{3} +(-0.347296 + 1.96962i) q^{4} +(-0.764780 - 2.10122i) q^{5} +(-0.398600 - 4.22387i) q^{6} +(0.704886 + 3.99761i) q^{7} +(2.44949 - 1.41421i) q^{8} +(3.19330 + 8.41444i) q^{9} +(-1.58114 + 2.73861i) q^{10} +(0.716831 - 1.96948i) q^{11} +(-4.21359 + 4.27149i) q^{12} +(9.33255 + 7.83094i) q^{13} +(3.69004 - 4.39762i) q^{14} +(1.69196 - 6.49132i) q^{15} +(-3.75877 - 1.36808i) q^{16} +(2.85269 + 1.64700i) q^{17} +(6.21295 - 11.1085i) q^{18} +(6.84331 + 11.8530i) q^{19} +(4.40419 - 0.776578i) q^{20} +(-5.07115 + 11.0717i) q^{21} +(-2.78526 + 1.01375i) q^{22} +(12.4238 + 2.19065i) q^{23} +(8.45784 + 0.681849i) q^{24} +(-3.83022 + 3.21394i) q^{25} -17.2291i q^{26} +(-6.45285 + 26.2176i) q^{27} -8.11855 q^{28} +(10.2201 + 12.1798i) q^{29} +(-8.57043 + 4.06788i) q^{30} +(-4.12158 + 23.3746i) q^{31} +(1.93476 + 5.31570i) q^{32} +(5.12579 - 3.64149i) q^{33} +(-0.808928 - 4.58766i) q^{34} +(7.86075 - 4.53841i) q^{35} +(-17.6822 + 3.36727i) q^{36} +(-6.02054 + 10.4279i) q^{37} +(6.62007 - 18.1885i) q^{38} +(9.70006 + 35.2376i) q^{39} +(-4.84489 - 4.06535i) q^{40} +(21.5629 - 25.6977i) q^{41} +(16.6044 - 4.57079i) q^{42} +(-21.6084 - 7.86482i) q^{43} +(3.63016 + 2.09587i) q^{44} +(15.2384 - 13.1450i) q^{45} +(-8.92048 - 15.4507i) q^{46} +(43.5279 - 7.67515i) q^{47} +(-6.94983 - 9.78263i) q^{48} +(30.5610 - 11.1233i) q^{49} +(6.96364 + 1.22788i) q^{50} +(4.23733 + 8.92745i) q^{51} +(-18.6651 + 15.6619i) q^{52} -78.2835i q^{53} +(34.2687 - 16.8421i) q^{54} -4.68652 q^{55} +(7.38008 + 8.79524i) q^{56} +(-3.29943 + 40.9271i) q^{57} +(3.90455 - 22.1438i) q^{58} +(10.9036 + 29.9575i) q^{59} +(12.1978 + 5.58692i) q^{60} +(-2.59336 - 14.7077i) q^{61} +(29.0696 - 16.7833i) q^{62} +(-31.3867 + 18.6968i) q^{63} +(4.00000 - 6.92820i) q^{64} +(9.31715 - 25.5987i) q^{65} +(-8.60456 - 2.24277i) q^{66} +(8.83180 + 7.41076i) q^{67} +(-4.23469 + 5.04671i) q^{68} +(26.9434 + 26.5782i) q^{69} +(-12.0624 - 4.39036i) q^{70} +(-32.5980 - 18.8205i) q^{71} +(19.7218 + 16.0951i) q^{72} +(-43.9347 - 76.0971i) q^{73} +(16.7699 - 2.95699i) q^{74} +(-14.9337 + 1.40926i) q^{75} +(-25.7224 + 9.36220i) q^{76} +(8.37848 + 1.47735i) q^{77} +(29.3570 - 42.5410i) q^{78} +(-95.3518 + 80.0097i) q^{79} +8.94427i q^{80} +(-60.6057 + 53.7397i) q^{81} -47.4412 q^{82} +(-84.5767 - 100.795i) q^{83} +(-20.0458 - 13.8334i) q^{84} +(1.27903 - 7.25372i) q^{85} +(11.1225 + 30.5589i) q^{86} +(4.48134 + 47.4878i) q^{87} +(-1.02939 - 5.83797i) q^{88} +(-84.3933 + 48.7245i) q^{89} +(-28.0929 - 4.55919i) q^{90} +(-24.7266 + 42.8278i) q^{91} +(-8.62948 + 23.7093i) q^{92} +(-50.0053 + 50.6924i) q^{93} +(-47.8835 - 40.1790i) q^{94} +(19.6720 - 23.4442i) q^{95} +(-4.28036 + 16.4219i) q^{96} +(-170.458 - 62.0418i) q^{97} +(-39.8315 - 22.9967i) q^{98} +(18.8611 - 0.257399i) 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 $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$

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
$3$	2.46914	+	1.70392i	0.823047	+	0.567974i
$3$	2.46914	+	1.70392i	0.823047	+	0.567974i
$4$	−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
$6$	−0.398600	−	4.22387i	−0.0664333	−	0.703979i
$7$	0.704886	+	3.99761i	0.100698	+	0.571087i	0.992852	+	0.119355i	$0.0380825\pi$
$7$	0.704886	+	3.99761i	0.100698	+	0.571087i	−0.892154	+	0.451732i	$0.850806\pi$
$8$	2.44949	−	1.41421i	0.306186	−	0.176777i
$9$	3.19330	+	8.41444i	0.354811	+	0.934938i
$10$	−1.58114	+	2.73861i	−0.158114	+	0.273861i
$11$	0.716831	−	1.96948i	0.0651665	−	0.179043i	−0.902835	−	0.429986i	$-0.858518\pi$
$11$	0.716831	−	1.96948i	0.0651665	−	0.179043i	0.968002	+	0.250943i	$0.0807406\pi$
$12$	−4.21359	+	4.27149i	−0.351133	+	0.355957i
$13$	9.33255	+	7.83094i	0.717889	+	0.602380i	0.926800	−	0.375554i	$-0.122548\pi$
$13$	9.33255	+	7.83094i	0.717889	+	0.602380i	−0.208912	+	0.977935i	$0.566992\pi$
$14$	3.69004	−	4.39762i	0.263574	−	0.314116i
$15$	1.69196	−	6.49132i	0.112797	−	0.432755i
$16$	−3.75877	−	1.36808i	−0.234923	−	0.0855050i
$17$	2.85269	+	1.64700i	0.167805	+	0.0968825i	0.581551	−	0.813510i	$-0.302446\pi$
$17$	2.85269	+	1.64700i	0.167805	+	0.0968825i	−0.413745	+	0.910393i	$0.635780\pi$
$18$	6.21295	−	11.1085i	0.345164	−	0.617140i
$19$	6.84331	+	11.8530i	0.360174	+	0.623840i	0.987989	−	0.154523i	$-0.0493840\pi$
$19$	6.84331	+	11.8530i	0.360174	+	0.623840i	−0.627815	+	0.778362i	$0.716051\pi$
$20$	4.40419	−	0.776578i	0.220210	−	0.0388289i
$21$	−5.07115	+	11.0717i	−0.241483	+	0.527225i
$22$	−2.78526	+	1.01375i	−0.126603	+	0.0460797i
$23$	12.4238	+	2.19065i	0.540165	+	0.0952457i	0.437073	−	0.899426i	$-0.356015\pi$
$23$	12.4238	+	2.19065i	0.540165	+	0.0952457i	0.103092	+	0.994672i	$0.467126\pi$
$24$	8.45784	+	0.681849i	0.352410	+	0.0284104i
$25$	−3.83022	+	3.21394i	−0.153209	+	0.128558i
$26$		−	17.2291i		−	0.662656i
$27$	−6.45285	+	26.2176i	−0.238994	+	0.971021i
$28$	−8.11855			−0.289948
$29$	10.2201	+	12.1798i	0.352416	+	0.419993i	0.912907	−	0.408167i	$-0.133832\pi$
$29$	10.2201	+	12.1798i	0.352416	+	0.419993i	−0.560491	+	0.828160i	$0.689388\pi$
$30$	−8.57043	+	4.06788i	−0.285681	+	0.135596i
$31$	−4.12158	+	23.3746i	−0.132954	+	0.754020i	0.843308	+	0.537430i	$0.180605\pi$
$31$	−4.12158	+	23.3746i	−0.132954	+	0.754020i	−0.976263	+	0.216590i	$0.930506\pi$
$32$	1.93476	+	5.31570i	0.0604612	+	0.166116i
$33$	5.12579	−	3.64149i	0.155327	−	0.110348i
$34$	−0.808928	−	4.58766i	−0.0237920	−	0.134931i
$35$	7.86075	−	4.53841i	0.224593	−	0.129669i
$36$	−17.6822	+	3.36727i	−0.491173	+	0.0935352i
$37$	−6.02054	+	10.4279i	−0.162717	+	0.281834i	−0.935842	−	0.352419i	$-0.885359\pi$
$37$	−6.02054	+	10.4279i	−0.162717	+	0.281834i	0.773125	+	0.634254i	$0.218692\pi$
$38$	6.62007	−	18.1885i	0.174212	−	0.478645i
$39$	9.70006	+	35.2376i	0.248720	+	0.903529i
$40$	−4.84489	−	4.06535i	−0.121122	−	0.101634i
$41$	21.5629	−	25.6977i	0.525925	−	0.626773i	−0.436046	−	0.899924i	$-0.643621\pi$
$41$	21.5629	−	25.6977i	0.525925	−	0.626773i	0.961971	+	0.273151i	$0.0880659\pi$
$42$	16.6044	−	4.57079i	0.395343	−	0.108828i
$43$	−21.6084	−	7.86482i	−0.502521	−	0.182903i	0.0783064	−	0.996929i	$-0.475049\pi$
$43$	−21.6084	−	7.86482i	−0.502521	−	0.182903i	−0.580828	+	0.814027i	$0.697271\pi$
$44$	3.63016	+	2.09587i	0.0825037	+	0.0476335i
$45$	15.2384	−	13.1450i	0.338631	−	0.292111i
$46$	−8.92048	−	15.4507i	−0.193923	−	0.335885i
$47$	43.5279	−	7.67515i	0.926126	−	0.163301i	0.309809	−	0.950799i	$-0.399735\pi$
$47$	43.5279	−	7.67515i	0.926126	−	0.163301i	0.616317	+	0.787498i	$0.288624\pi$
$48$	−6.94983	−	9.78263i	−0.144788	−	0.203805i
$49$	30.5610	−	11.1233i	0.623693	−	0.227006i
$50$	6.96364	+	1.22788i	0.139273	+	0.0245576i
$51$	4.23733	+	8.92745i	0.0830850	+	0.175048i
$52$	−18.6651	+	15.6619i	−0.358944	+	0.301190i
$53$		−	78.2835i		−	1.47705i	−0.674228	−	0.738523i	$-0.735523\pi$
$53$		−	78.2835i		−	1.47705i	0.674228	−	0.738523i	$-0.264477\pi$
$54$	34.2687	−	16.8421i	0.634606	−	0.311891i
$55$	−4.68652			−0.0852094
$56$	7.38008	+	8.79524i	0.131787	+	0.157058i
$57$	−3.29943	+	40.9271i	−0.0578847	+	0.718019i
$58$	3.90455	−	22.1438i	0.0673199	−	0.381790i
$59$	10.9036	+	29.9575i	0.184807	+	0.507754i	0.997152	−	0.0754244i	$-0.0240311\pi$
$59$	10.9036	+	29.9575i	0.184807	+	0.507754i	−0.812344	+	0.583178i	$0.801809\pi$
$60$	12.1978	+	5.58692i	0.203297	+	0.0931154i
$61$	−2.59336	−	14.7077i	−0.0425141	−	0.241109i	0.956144	−	0.292897i	$-0.0946192\pi$
$61$	−2.59336	−	14.7077i	−0.0425141	−	0.241109i	−0.998658	+	0.0517875i	$0.983508\pi$
$62$	29.0696	−	16.7833i	0.468864	−	0.270699i
$63$	−31.3867	+	18.6968i	−0.498202	+	0.296774i
$64$	4.00000	−	6.92820i	0.0625000	−	0.108253i
$65$	9.31715	−	25.5987i	0.143341	−	0.393826i
$66$	−8.60456	−	2.24277i	−0.130372	−	0.0339814i
$67$	8.83180	+	7.41076i	0.131818	+	0.110608i	0.706313	−	0.707900i	$-0.250357\pi$
$67$	8.83180	+	7.41076i	0.131818	+	0.110608i	−0.574495	+	0.818508i	$0.694802\pi$
$68$	−4.23469	+	5.04671i	−0.0622749	+	0.0742163i
$69$	26.9434	+	26.5782i	0.390484	+	0.385192i
$70$	−12.0624	−	4.39036i	−0.172320	−	0.0627194i
$71$	−32.5980	−	18.8205i	−0.459127	−	0.265077i	0.252550	−	0.967584i	$-0.418731\pi$
$71$	−32.5980	−	18.8205i	−0.459127	−	0.265077i	−0.711677	+	0.702507i	$0.752064\pi$
$72$	19.7218	+	16.0951i	0.273914	+	0.223543i
$73$	−43.9347	−	76.0971i	−0.601845	−	1.04243i	−0.992542	−	0.121907i	$-0.961099\pi$
$73$	−43.9347	−	76.0971i	−0.601845	−	1.04243i	0.390696	−	0.920520i	$-0.372234\pi$
$74$	16.7699	−	2.95699i	0.226621	−	0.0399594i
$75$	−14.9337	+	1.40926i	−0.199115	+	0.0187902i
$76$	−25.7224	+	9.36220i	−0.338453	+	0.123187i
$77$	8.37848	+	1.47735i	0.108811	+	0.0191864i
$78$	29.3570	−	42.5410i	0.376371	−	0.545397i
$79$	−95.3518	+	80.0097i	−1.20699	+	1.01278i	−0.207583	+	0.978218i	$0.566560\pi$
$79$	−95.3518	+	80.0097i	−1.20699	+	1.01278i	−0.999403	+	0.0345632i	$0.988996\pi$
$80$			8.94427i			0.111803i
$81$	−60.6057	+	53.7397i	−0.748218	+	0.663453i
$82$	−47.4412			−0.578551
$83$	−84.5767	−	100.795i	−1.01900	−	1.21439i	−0.976549	−	0.215293i	$-0.930929\pi$
$83$	−84.5767	−	100.795i	−1.01900	−	1.21439i	−0.0424467	−	0.999099i	$-0.513515\pi$
$84$	−20.0458	−	13.8334i	−0.238641	−	0.164683i
$85$	1.27903	−	7.25372i	0.0150474	−	0.0853379i
$86$	11.1225	+	30.5589i	0.129332	+	0.355336i
$87$	4.48134	+	47.4878i	0.0515096	+	0.545837i
$88$	−1.02939	−	5.83797i	−0.0116976	−	0.0663405i
$89$	−84.3933	+	48.7245i	−0.948239	+	0.547466i	−0.892533	−	0.450981i	$-0.851074\pi$
$89$	−84.3933	+	48.7245i	−0.948239	+	0.547466i	−0.0557056	+	0.998447i	$0.517741\pi$
$90$	−28.0929	−	4.55919i	−0.312144	−	0.0506576i
$91$	−24.7266	+	42.8278i	−0.271721	+	0.470635i
$92$	−8.62948	+	23.7093i	−0.0937987	+	0.257710i
$93$	−50.0053	+	50.6924i	−0.537691	+	0.545079i
$94$	−47.8835	−	40.1790i	−0.509399	−	0.427436i
$95$	19.6720	−	23.4442i	0.207074	−	0.246781i
$96$	−4.28036	+	16.4219i	−0.0445871	+	0.171061i
$97$	−170.458	−	62.0418i	−1.75730	−	0.639606i	−0.757392	−	0.652961i	$-0.773527\pi$
$97$	−170.458	−	62.0418i	−1.75730	−	0.639606i	−0.999911	+	0.0133547i	$0.995749\pi$
$98$	−39.8315	−	22.9967i	−0.406444	−	0.234660i
$99$	18.8611	−	0.257399i	0.190516	−	0.00259999i
$100$	−5.00000	−	8.66025i	−0.0500000	−	0.0866025i
$101$	3.51045	−	0.618987i	0.0347569	−	0.00612858i	−0.156243	−	0.987719i	$-0.549938\pi$
$101$	3.51045	−	0.618987i	0.0347569	−	0.00612858i	0.191000	+	0.981590i	$0.438827\pi$
$102$	5.81965	−	12.7059i	0.0570554	−	0.124568i
$103$	115.526	−	42.0480i	1.12161	−	0.408233i	0.286371	−	0.958119i	$-0.407551\pi$
$103$	115.526	−	42.0480i	1.12161	−	0.408233i	0.835240	+	0.549886i	$0.185329\pi$
$104$	33.9346	+	5.98359i	0.326294	+	0.0575345i
$105$	27.1424	+	2.18815i	0.258499	+	0.0208395i
$106$	−84.8084	+	71.1627i	−0.800080	+	0.671346i
$107$		−	89.3967i		−	0.835483i	−0.908566	−	0.417742i	$-0.862822\pi$
$107$		−	89.3967i		−	0.835483i	0.908566	−	0.417742i	$-0.137178\pi$
$108$	−49.3975	−	21.8149i	−0.457384	−	0.201990i
$109$	3.04127			0.0279015			0.0139508	−	0.999903i	$-0.495559\pi$
$109$	3.04127			0.0279015			0.0139508	+	0.999903i	$0.495559\pi$
$110$	4.26023	+	5.07714i	0.0387293	+	0.0461558i
$111$	−32.6338	+	15.4894i	−0.293998	+	0.139544i
$112$	2.81954	−	15.9904i	0.0251745	−	0.142772i
$113$	−33.9126	−	93.1740i	−0.300111	−	0.824549i	−0.994480	−	0.104929i	$-0.966538\pi$
$113$	−33.9126	−	93.1740i	−0.300111	−	0.824549i	0.694368	−	0.719620i	$-0.255684\pi$
$114$	47.3377	−	33.6299i	0.415243	−	0.294999i
$115$	−4.89845	−	27.7805i	−0.0425952	−	0.241569i
$116$	−27.5389	+	15.8996i	−0.237404	+	0.137065i
$117$	−36.0914	+	103.535i	−0.308473	+	0.884913i
$118$	22.5426	−	39.0450i	0.191039	−	0.330890i
$119$	−4.57325	+	12.5649i	−0.0384306	+	0.105587i
$120$	−5.03568	−	18.2932i	−0.0419640	−	0.152444i
$121$	89.3264	+	74.9537i	0.738235	+	0.619452i
$122$	−13.5761	+	16.1794i	−0.111279	+	0.132618i
$123$	97.0288	−	26.7097i	0.788852	−	0.217152i
$124$	−44.6076	−	16.2359i	−0.359739	−	0.130934i
$125$	9.68246	+	5.59017i	0.0774597	+	0.0447214i
$126$	48.7869	+	17.0067i	0.387198	+	0.134974i
$127$	−41.8812	−	72.5404i	−0.329773	−	0.571184i	0.652693	−	0.757622i	$-0.273639\pi$
$127$	−41.8812	−	72.5404i	−0.329773	−	0.571184i	−0.982467	+	0.186438i	$0.940306\pi$
$128$	−11.1418	+	1.96460i	−0.0870455	+	0.0153485i
$129$	−39.9531	−	56.2384i	−0.309714	−	0.435956i
$130$	−36.2020	+	13.1764i	−0.278477	+	0.101357i
$131$	164.416	+	28.9910i	1.25508	+	0.221305i	0.761369	−	0.648319i	$-0.224528\pi$
$131$	164.416	+	28.9910i	1.25508	+	0.221305i	0.493714	+	0.869624i	$0.335639\pi$
$132$	5.39217	+	11.3605i	0.0408498	+	0.0860645i
$133$	−42.5597	+	35.7118i	−0.319998	+	0.268510i
$134$		−	16.3046i		−	0.121676i
$135$	60.0238	−	6.49185i	0.444621	−	0.0480878i
$136$	9.31686			0.0685063
$137$	−104.670	−	124.741i	−0.764015	−	0.910517i	0.234080	−	0.972217i	$-0.424792\pi$
$137$	−104.670	−	124.741i	−0.764015	−	0.910517i	−0.998095	+	0.0617003i	$0.980348\pi$
$138$	4.30092	−	53.3498i	0.0311661	−	0.386593i
$139$	15.3390	−	86.9920i	0.110353	−	0.625842i	−0.878594	−	0.477570i	$-0.841518\pi$
$139$	15.3390	−	86.9920i	0.110353	−	0.625842i	0.988947	−	0.148272i	$-0.0473711\pi$
$140$	6.20891	+	17.0588i	0.0443493	+	0.121849i
$141$	120.554	+	55.2172i	0.854996	+	0.391611i
$142$	9.24370	+	52.4237i	0.0650965	+	0.369181i
$143$	22.1127	−	12.7668i	0.154635	−	0.0892783i
$144$	−0.491248	−	35.9966i	−0.00341145	−	0.249977i
$145$	17.7763	−	30.7894i	0.122595	−	0.212341i
$146$	−42.5015	+	116.772i	−0.291106	+	0.799808i
$147$	94.4124	+	24.6086i	0.642262	+	0.167405i
$148$	−18.4480	−	15.4797i	−0.124649	−	0.104593i
$149$	−146.490	+	174.580i	−0.983155	+	1.17168i	0.00199820	+	0.999998i	$0.499364\pi$
$149$	−146.490	+	174.580i	−0.983155	+	1.17168i	−0.985153	+	0.171680i	$0.945080\pi$
$150$	15.1020	+	14.8973i	0.100680	+	0.0993154i
$151$	65.0503	+	23.6764i	0.430797	+	0.156797i	0.548312	−	0.836274i	$-0.315271\pi$
$151$	65.0503	+	23.6764i	0.430797	+	0.156797i	−0.117515	+	0.993071i	$0.537493\pi$
$152$	33.5252	+	19.3558i	0.220561	+	0.127341i
$153$	−4.74911	+	29.2632i	−0.0310399	+	0.191263i
$154$	−6.01587	−	10.4198i	−0.0390641	−	0.0676610i
$155$	52.2673	−	9.21613i	0.337208	−	0.0594589i
$156$	−72.7734	+	6.86749i	−0.466496	+	0.0440224i
$157$	179.295	−	65.2579i	1.14200	−	0.415656i	0.299368	−	0.954138i	$-0.403224\pi$
$157$	179.295	−	65.2579i	1.14200	−	0.415656i	0.842637	+	0.538482i	$0.181002\pi$
$158$	173.357	+	30.5675i	1.09720	+	0.193465i
$159$	133.389	−	193.293i	0.838924	−	1.21568i
$160$	9.68978	−	8.13069i	0.0605611	−	0.0508168i
$161$			51.2096i			0.318072i
$162$	113.312	+	16.8057i	0.699456	+	0.103739i
$163$	279.029			1.71184			0.855918	−	0.517112i	$-0.172993\pi$
$163$	279.029			1.71184			0.855918	+	0.517112i	$0.172993\pi$
$164$	43.1259	+	51.3954i	0.262963	+	0.313387i
$165$	−11.5717	−	7.98546i	−0.0701313	−	0.0483967i
$166$	−32.3123	+	183.252i	−0.194653	+	1.10393i
$167$	47.4930	+	130.486i	0.284389	+	0.781353i	0.996826	+	0.0796164i	$0.0253695\pi$
$167$	47.4930	+	130.486i	0.284389	+	0.781353i	−0.712436	+	0.701737i	$0.752408\pi$
$168$	3.23605	+	34.2917i	0.0192622	+	0.204118i
$169$	−3.57364	−	20.2671i	−0.0211458	−	0.119924i
$170$	−9.02101	+	5.20828i	−0.0530648	+	0.0306370i
$171$	−77.8833	+	95.4327i	−0.455458	+	0.558086i
$172$	22.9952	−	39.8288i	0.133693	−	0.231563i
$173$	40.1577	−	110.332i	0.232126	−	0.637760i	−0.767870	−	0.640605i	$-0.778684\pi$
$173$	40.1577	−	110.332i	0.232126	−	0.637760i	0.999996	+	0.00284552i	$0.000905759\pi$
$174$	47.3722	−	48.0231i	0.272254	−	0.275995i
$175$	−15.5479	−	13.0463i	−0.0888453	−	0.0745501i
$176$	−5.38881	+	6.42213i	−0.0306182	+	0.0364894i
$177$	−24.1226	+	92.5481i	−0.136286	+	0.522871i
$178$	129.502	+	47.1350i	0.727542	+	0.264804i
$179$	−119.278	−	68.8649i	−0.666355	−	0.384720i	0.128339	−	0.991730i	$-0.459035\pi$
$179$	−119.278	−	68.8649i	−0.666355	−	0.384720i	−0.794694	+	0.607010i	$0.792369\pi$
$180$	20.5984	+	34.5790i	0.114435	+	0.192105i
$181$	8.21455	+	14.2280i	0.0453842	+	0.0786078i	0.887825	−	0.460181i	$-0.152215\pi$
$181$	8.21455	+	14.2280i	0.0453842	+	0.0786078i	−0.842441	+	0.538789i	$0.818882\pi$
$182$	68.8750	−	12.1445i	0.378434	−	0.0667281i
$183$	18.6574	−	40.7342i	0.101953	−	0.222591i
$184$	33.5300	−	12.2039i	0.182228	−	0.0663257i
$185$	26.5156	+	4.67542i	0.143328	+	0.0252725i
$186$	100.374	+	8.09191i	0.539647	+	0.0435049i
$187$	5.28864	−	4.43769i	0.0282815	−	0.0237310i
$188$			88.3989i			0.470207i
$189$	−109.356	−	7.31555i	−0.578603	−	0.0387066i
$190$	−43.2809			−0.227794
$191$	−76.5150	−	91.1871i	−0.400602	−	0.477419i	0.527601	−	0.849492i	$-0.323092\pi$
$191$	−76.5150	−	91.1871i	−0.400602	−	0.477419i	−0.928203	+	0.372073i	$0.878647\pi$
$192$	21.6817	−	10.2910i	0.112925	−	0.0535990i
$193$	21.0618	−	119.448i	0.109129	−	0.618899i	−0.880362	−	0.474302i	$-0.842700\pi$
$193$	21.0618	−	119.448i	0.109129	−	0.618899i	0.989491	−	0.144597i	$-0.0461886\pi$
$194$	87.7403	+	241.065i	0.452270	+	1.24260i
$195$	66.6235	−	47.3310i	0.341659	−	0.242723i
$196$	11.2949	+	64.0564i	0.0576269	+	0.326818i
$197$	−168.964	+	97.5512i	−0.857683	+	0.495184i	−0.863236	−	0.504801i	$-0.831566\pi$
$197$	−168.964	+	97.5512i	−0.857683	+	0.495184i	0.00555250	+	0.999985i	$0.498233\pi$
$198$	−17.4243	−	20.1992i	−0.0880017	−	0.102016i
$199$	−21.0963	+	36.5398i	−0.106011	+	0.183617i	−0.914151	−	0.405374i	$-0.867141\pi$
$199$	−21.0963	+	36.5398i	−0.106011	+	0.183617i	0.808140	+	0.588991i	$0.200475\pi$
$200$	−4.83690	+	13.2893i	−0.0241845	+	0.0664463i
$201$	9.17959	+	33.3469i	0.0456696	+	0.165905i
$202$	−3.86171	−	3.24036i	−0.0191174	−	0.0160414i
$203$	−41.4861	+	49.4411i	−0.204365	+	0.243552i
$204$	−19.0552	+	5.24545i	−0.0934081	+	0.0257130i
$205$	−70.4873	−	25.6553i	−0.343841	−	0.125148i
$206$	−150.570	−	86.9318i	−0.730924	−	0.421999i
$207$	21.2398	+	111.535i	0.102608	+	0.538815i
$208$	−24.3656	−	42.2024i	−0.117142	−	0.202896i
$209$	28.2496	−	4.98117i	0.135166	−	0.0238334i
$210$	−22.3030	−	31.3938i	−0.106205	−	0.149494i
$211$	269.954	−	98.2552i	1.27940	−	0.465665i	0.389168	−	0.921167i	$-0.372762\pi$
$211$	269.954	−	98.2552i	1.27940	−	0.465665i	0.890235	+	0.455502i	$0.150540\pi$
$212$	154.188	+	27.1876i	0.727303	+	0.128243i
$213$	−48.4205	−	102.015i	−0.227326	−	0.478943i
$214$	−96.8479	+	81.2651i	−0.452560	+	0.379743i
$215$			51.4188i			0.239157i
$216$	21.2711	+	73.3454i	0.0984771	+	0.339562i
$217$	−96.3478			−0.443999
$218$	−2.76463	−	3.29476i	−0.0126818	−	0.0151136i
$219$	21.1827	−	262.756i	0.0967245	−	1.19980i
$220$	1.62761	−	9.23064i	0.00739823	−	0.0419574i
$221$	13.7253	+	37.7100i	0.0621056	+	0.170634i
$222$	46.4458	+	21.2734i	0.209215	+	0.0958263i
$223$	51.6233	+	292.770i	0.231494	+	1.31287i	0.849872	+	0.526989i	$0.176679\pi$
$223$	51.6233	+	292.770i	0.231494	+	1.31287i	−0.618378	+	0.785881i	$0.712210\pi$
$224$	−19.8863	+	11.4814i	−0.0887782	+	0.0512561i
$225$	−39.2745	−	21.9661i	−0.174554	−	0.0976272i
$226$	−70.1123	+	121.438i	−0.310231	+	0.537336i
$227$	78.7744	−	216.431i	0.347024	−	0.953440i	−0.636278	−	0.771459i	$-0.719527\pi$
$227$	78.7744	−	216.431i	0.347024	−	0.953440i	0.983302	−	0.181980i	$-0.0582507\pi$
$228$	−79.4647	−	20.7124i	−0.348529	−	0.0908440i
$229$	54.6722	+	45.8754i	0.238743	+	0.200329i	0.754307	−	0.656522i	$-0.227973\pi$
$229$	54.6722	+	45.8754i	0.238743	+	0.200329i	−0.515564	+	0.856851i	$0.672418\pi$
$230$	−25.6431	+	30.5603i	−0.111492	+	0.132871i
$231$	18.1703	+	17.9241i	0.0786595	+	0.0775933i
$232$	42.2588	+	15.3809i	0.182150	+	0.0662971i
$233$	−182.832	−	105.558i	−0.784688	−	0.453040i	0.0534011	−	0.998573i	$-0.482994\pi$
$233$	−182.832	−	105.558i	−0.784688	−	0.453040i	−0.838089	+	0.545533i	$0.816327\pi$
$234$	144.973	−	55.0176i	0.619542	−	0.235118i
$235$	−49.4165	−	85.5918i	−0.210283	−	0.364221i
$236$	−62.7915	+	11.0718i	−0.266066	+	0.0469146i
$237$	−371.767	+	35.0830i	−1.56864	+	0.148030i
$238$	17.7694	−	6.46755i	0.0746615	−	0.0271746i
$239$	198.978	+	35.0851i	0.832542	+	0.146800i	0.573644	−	0.819105i	$-0.305529\pi$
$239$	198.978	+	35.0851i	0.832542	+	0.146800i	0.258899	+	0.965905i	$0.416640\pi$
$240$	−15.2403	+	22.0847i	−0.0635014	+	0.0920194i
$241$	215.437	−	180.773i	0.893929	−	0.750096i	−0.0750653	−	0.997179i	$-0.523917\pi$
$241$	215.437	−	180.773i	0.893929	−	0.750096i	0.968994	+	0.247083i	$0.0794721\pi$
$242$		−	164.908i		−	0.681437i
$243$	−241.212	+	29.4234i	−0.992642	+	0.121084i
$244$	29.8691			0.122414
$245$	−46.7448	−	55.7083i	−0.190795	−	0.227381i
$246$	−117.139	−	80.8360i	−0.476174	−	0.328602i
$247$	−28.9543	+	164.208i	−0.117224	+	0.664809i
$248$	22.9610	+	63.0847i	0.0925845	+	0.254374i
$249$	−37.0856	−	392.988i	−0.148938	−	1.57826i
$250$	−2.74562	−	15.5712i	−0.0109825	−	0.0622847i
$251$	−208.167	+	120.185i	−0.829351	+	0.478826i	−0.853630	−	0.520879i	$-0.825604\pi$
$251$	−208.167	+	120.185i	−0.829351	+	0.478826i	0.0242797	+	0.999705i	$0.492271\pi$
$252$	−25.9250	−	68.3131i	−0.102877	−	0.271084i
$253$	13.2202	−	22.8981i	0.0522538	−	0.0905062i
$254$	−40.5150	+	111.314i	−0.159508	+	0.438245i
$255$	15.5179	−	15.7311i	0.0608544	−	0.0616905i
$256$	12.2567	+	10.2846i	0.0478778	+	0.0401742i
$257$	−245.761	+	292.887i	−0.956269	+	1.13964i	0.0338525	+	0.999427i	$0.489222\pi$
$257$	−245.761	+	292.887i	−0.956269	+	1.13964i	−0.990122	+	0.140210i	$0.955222\pi$
$258$	−24.6069	+	94.4061i	−0.0953756	+	0.365915i
$259$	−45.9303	−	16.7173i	−0.177337	−	0.0645454i
$260$	47.1837	+	27.2415i	0.181476	+	0.104775i
$261$	−69.8505	+	124.890i	−0.267626	+	0.478505i
$262$	−118.053	−	204.474i	−0.450584	−	0.780435i
$263$	373.870	−	65.9233i	1.42156	−	0.250659i	0.590587	−	0.806974i	$-0.298896\pi$
$263$	373.870	−	65.9233i	1.42156	−	0.250659i	0.830971	+	0.556315i	$0.187785\pi$
$264$	7.40573	−	16.1688i	0.0280520	−	0.0612453i
$265$	−164.491	+	59.8697i	−0.620719	+	0.225923i
$266$	77.3768	+	13.6436i	0.290890	+	0.0512918i
$267$	−291.402	−	23.4920i	−1.09139	−	0.0879851i
$268$	−17.6636	+	14.8215i	−0.0659090	+	0.0553042i
$269$			314.508i			1.16917i	0.811331	+	0.584586i	$0.198743\pi$
$269$			314.508i			1.16917i	−0.811331	+	0.584586i	$0.801257\pi$
$270$	−61.5969	−	59.1255i	−0.228137	−	0.218983i
$271$	365.083			1.34717			0.673584	−	0.739111i	$-0.264754\pi$
$271$	365.083			1.34717			0.673584	+	0.739111i	$0.264754\pi$
$272$	−8.46939	−	10.0934i	−0.0311374	−	0.0371082i
$273$	−134.029	+	63.6155i	−0.490948	+	0.233024i
$274$	−39.9889	+	226.789i	−0.145945	+	0.827695i
$275$	3.58416	+	9.84739i	0.0130333	+	0.0358087i
$276$	−61.7062	+	43.8376i	−0.223573	+	0.158832i
$277$	25.3016	+	143.492i	0.0913414	+	0.518023i	0.995807	+	0.0914768i	$0.0291587\pi$
$277$	25.3016	+	143.492i	0.0913414	+	0.518023i	−0.904466	+	0.426546i	$0.859730\pi$
$278$	−108.187	+	62.4616i	−0.389160	+	0.224682i
$279$	−209.846	+	39.9614i	−0.752136	+	0.143231i
$280$	12.8366	−	22.2336i	0.0458448	−	0.0794056i
$281$	14.7458	−	40.5136i	0.0524760	−	0.144177i	−0.910685	−	0.413101i	$-0.864446\pi$
$281$	14.7458	−	40.5136i	0.0524760	−	0.144177i	0.963161	+	0.268924i	$0.0866680\pi$
$282$	−49.7691	−	180.797i	−0.176486	−	0.641125i
$283$	409.621	+	343.713i	1.44743	+	1.21453i	0.934432	+	0.356142i	$0.115908\pi$
$283$	409.621	+	343.713i	1.44743	+	1.21453i	0.512994	+	0.858392i	$0.328536\pi$
$284$	48.3903	−	57.6693i	0.170388	−	0.203061i
$285$	88.5200	−	24.3674i	0.310596	−	0.0854996i
$286$	−33.9323	−	12.3503i	−0.118644	−	0.0431830i
$287$	117.929	+	68.0862i	0.410901	+	0.237234i
$288$	−38.5504	+	33.2545i	−0.133856	+	0.115467i
$289$	−139.075	−	240.885i	−0.481228	−	0.833511i
$290$	−49.5151	+	8.73085i	−0.170742	+	0.0301064i
$291$	−315.171	−	443.638i	−1.08306	−	1.52453i
$292$	165.140	−	60.1062i	0.565550	−	0.205843i
$293$	−516.985	−	91.1583i	−1.76445	−	0.311121i	−0.805060	−	0.593194i	$-0.797867\pi$
$293$	−516.985	−	91.1583i	−1.76445	−	0.311121i	−0.959393	+	0.282073i	$0.908978\pi$
$294$	−59.1649	−	124.652i	−0.201241	−	0.423986i
$295$	54.6083	−	45.8218i	0.185113	−	0.155328i
$296$			34.0573i			0.115058i
$297$	47.0093	+	31.5023i	0.158281	+	0.106068i
$298$	322.296			1.08153
$299$	98.7910	+	117.734i	0.330405	+	0.393761i
$300$	2.41070	−	29.9030i	0.00803566	−	0.0996766i
$301$	16.2090	−	91.9257i	0.0538504	−	0.305401i
$302$	−33.4835	−	91.9950i	−0.110872	−	0.304619i
$303$	9.72249	+	4.45317i	0.0320874	+	0.0146969i
$304$	−9.50662	−	53.9147i	−0.0312718	−	0.177351i
$305$	−28.9206	+	16.6973i	−0.0948218	+	0.0547454i
$306$	36.0194	−	21.4564i	0.117711	−	0.0701191i
$307$	−122.609	+	212.365i	−0.399378	+	0.691743i	−0.993649	−	0.112522i	$-0.964107\pi$
$307$	−122.609	+	212.365i	−0.399378	+	0.691743i	0.594271	+	0.804265i	$0.297441\pi$
$308$	−5.81963	+	15.9893i	−0.0188949	+	0.0519133i
$309$	356.896	+	93.0248i	1.15500	+	0.301051i
$310$	−57.4973	−	48.2459i	−0.185475	−	0.155632i
$311$	221.504	−	263.978i	0.712230	−	0.848803i	−0.281621	−	0.959526i	$-0.590872\pi$
$311$	221.504	−	263.978i	0.712230	−	0.848803i	0.993851	+	0.110723i	$0.0353166\pi$
$312$	73.5938	+	72.5963i	0.235877	+	0.232680i
$313$	65.1556	+	23.7147i	0.208165	+	0.0757658i	0.443998	−	0.896028i	$-0.353560\pi$
$313$	65.1556	+	23.7147i	0.208165	+	0.0757658i	−0.235833	+	0.971794i	$0.575782\pi$
$314$	−233.683	−	134.917i	−0.744214	−	0.429672i
$315$	63.2899	+	51.6513i	0.200920	+	0.163973i
$316$	−124.473	−	215.593i	−0.393902	−	0.682258i
$317$	482.778	−	85.1268i	1.52296	−	0.268539i	0.651365	−	0.758765i	$-0.274197\pi$
$317$	482.778	−	85.1268i	1.52296	−	0.268539i	0.871595	+	0.490226i	$0.163086\pi$
$318$	−330.660	+	31.2038i	−1.03981	+	0.0981250i
$319$	31.3139	−	11.3973i	0.0981627	−	0.0357283i
$320$	−17.6168	−	3.10631i	−0.0550524	−	0.00970723i
$321$	152.325	−	220.733i	0.474533	−	0.687641i
$322$	55.4780	−	46.5515i	0.172292	−	0.144570i
$323$			45.0838i			0.139578i
$324$	−84.7984	−	138.033i	−0.261723	−	0.426029i
$325$	−60.9139			−0.187427
$326$	−253.648	−	302.286i	−0.778063	−	0.927259i
$327$	7.50931	+	5.18208i	0.0229643	+	0.0158473i
$328$	16.4761	−	93.4408i	0.0502321	−	0.284881i
$329$	61.3644	+	168.597i	0.186518	+	0.512454i
$330$	1.86804	+	19.7953i	0.00566074	+	0.0599856i
$331$	−56.2994	−	319.290i	−0.170089	−	0.964622i	−0.943661	−	0.330914i	$-0.892643\pi$
$331$	−56.2994	−	319.290i	−0.170089	−	0.964622i	0.773572	−	0.633708i	$-0.218468\pi$
$332$	227.900	−	131.578i	0.686445	−	0.396319i
$333$	−106.970	−	17.3601i	−0.321232	−	0.0521325i
$334$	98.1890	−	170.068i	0.293979	−	0.509187i
$335$	8.81723	−	24.2251i	0.0263201	−	0.0723138i
$336$	34.2083	−	34.6783i	0.101810	−	0.103209i
$337$	347.595	+	291.667i	1.03144	+	0.865480i	0.991021	−	0.133703i	$-0.0426869\pi$
$337$	347.595	+	291.667i	1.03144	+	0.865480i	0.0404170	+	0.999183i	$0.487131\pi$
$338$	−18.7078	+	22.2951i	−0.0553485	+	0.0659618i
$339$	75.0264	−	287.844i	0.221317	−	0.849098i
$340$	13.8428	+	5.03838i	0.0407142	+	0.0148188i
$341$	43.0813	+	24.8730i	0.126338	+	0.0729414i
$342$	174.186	−	2.37713i	0.509316	−	0.00695066i
$343$	165.461	+	286.586i	0.482393	+	0.835529i
$344$	−64.0521	+	11.2941i	−0.186198	+	0.0328317i
$345$	35.2408	−	76.9404i	0.102147	−	0.223016i
$346$	−156.034	+	56.7916i	−0.450964	+	0.164138i
$347$	−262.319	−	46.2540i	−0.755963	−	0.133297i	−0.217633	−	0.976031i	$-0.569834\pi$
$347$	−262.319	−	46.2540i	−0.755963	−	0.133297i	−0.538330	+	0.842734i	$0.680945\pi$
$348$	−95.0891	−	7.66583i	−0.273244	−	0.0220282i
$349$	−414.670	+	347.949i	−1.18817	+	0.996990i	−0.188277	+	0.982116i	$0.560290\pi$
$349$	−414.670	+	347.949i	−1.18817	+	0.996990i	−0.999889	+	0.0148735i	$0.995265\pi$
$350$			28.7034i			0.0820097i
$351$	−265.530	+	194.145i	−0.756495	+	0.553120i
$352$	11.8561			0.0336820
$353$	−270.378	−	322.224i	−0.765944	−	0.912817i	0.232264	−	0.972653i	$-0.425387\pi$
$353$	−270.378	−	322.224i	−0.765944	−	0.912817i	−0.998208	+	0.0598361i	$0.980942\pi$
$354$	122.190	−	57.9966i	0.345171	−	0.163832i
$355$	−14.6156	+	82.8891i	−0.0411706	+	0.233490i
$356$	−66.6590	−	183.144i	−0.187244	−	0.514450i
$357$	−32.7016	+	23.2320i	−0.0916011	+	0.0650757i
$358$	33.8231	+	191.820i	0.0944779	+	0.535811i
$359$	−142.083	+	82.0319i	−0.395775	+	0.228501i	−0.684660	−	0.728863i	$-0.740049\pi$
$359$	−142.083	+	82.0319i	−0.395775	+	0.228501i	0.288884	+	0.957364i	$0.406716\pi$
$360$	18.7364	−	53.7489i	0.0520456	−	0.149303i
$361$	86.8383	−	150.408i	0.240549	−	0.416644i
$362$	7.94658	−	21.8330i	0.0219519	−	0.0603123i
$363$	92.8440	+	337.276i	0.255769	+	0.929136i
$364$	−75.7668	−	63.5759i	−0.208151	−	0.174659i
$365$	−126.296	+	150.514i	−0.346017	+	0.412367i
$366$	−61.0896	+	16.8165i	−0.166912	+	0.0459467i
$367$	1.63295	+	0.594346i	0.00444946	+	0.00161947i	0.344244	−	0.938880i	$-0.388135\pi$
$367$	1.63295	+	0.594346i	0.00444946	+	0.00161947i	−0.339794	+	0.940500i	$0.610358\pi$
$368$	−43.7012	−	25.2309i	−0.118753	−	0.0685623i
$369$	285.089	+	99.3796i	0.772598	+	0.269321i
$370$	−19.0386	−	32.9758i	−0.0514557	−	0.0891239i
$371$	312.946	−	55.1809i	0.843521	−	0.148736i
$372$	−82.4778	−	116.097i	−0.221715	−	0.312087i
$373$	−177.664	+	64.6644i	−0.476311	+	0.173363i	−0.569009	−	0.822331i	$-0.692673\pi$
$373$	−177.664	+	64.6644i	−0.476311	+	0.173363i	0.0926980	+	0.995694i	$0.470451\pi$
$374$	−9.61515	−	1.69541i	−0.0257090	−	0.00453318i
$375$	14.3821	+	30.3011i	0.0383523	+	0.0808028i
$376$	95.7669	−	80.3580i	0.254699	−	0.213718i
$377$			193.701i			0.513797i
$378$	91.4836	+	125.121i	0.242020	+	0.331008i
$379$	−475.958			−1.25583			−0.627913	−	0.778283i	$-0.716091\pi$
$379$	−475.958			−1.25583			−0.627913	+	0.778283i	$0.716091\pi$
$380$	39.3440	+	46.8884i	0.103537	+	0.123390i
$381$	20.1926	−	250.475i	0.0529990	−	0.657414i
$382$	−29.2324	+	165.785i	−0.0765246	+	0.433993i
$383$	−117.918	−	323.977i	−0.307880	−	0.845893i	−0.993070	−	0.117528i	$-0.962503\pi$
$383$	−117.918	−	323.977i	−0.307880	−	0.845893i	0.685190	−	0.728365i	$-0.259719\pi$
$384$	−30.8583	−	14.1339i	−0.0803601	−	0.0368071i
$385$	−3.30346	−	18.7349i	−0.00858041	−	0.0486619i
$386$	−148.550	+	85.7652i	−0.384844	+	0.222190i
$387$	−2.82409	−	206.937i	−0.00729739	−	0.534722i
$388$	181.398	−	314.191i	0.467521	−	0.809769i
$389$	−213.995	+	587.947i	−0.550117	+	1.51143i	0.283435	+	0.958991i	$0.408526\pi$
$389$	−213.995	+	587.947i	−0.550117	+	1.51143i	−0.833552	+	0.552441i	$0.813696\pi$
$390$	−111.839	−	29.1509i	−0.286768	−	0.0747458i
$391$	31.8333	+	26.7113i	0.0814151	+	0.0683154i
$392$	59.1280	−	70.4661i	0.150837	−	0.179760i
$393$	356.567	+	351.735i	0.907296	+	0.894999i
$394$	259.277	+	94.3690i	0.658063	+	0.239515i
$395$	241.041	+	139.165i	0.610230	+	0.352316i
$396$	−6.04342	+	37.2385i	−0.0152612	+	0.0940367i
$397$	−247.708	−	429.043i	−0.623950	−	1.08071i	−0.988743	−	0.149624i	$-0.952194\pi$
$397$	−247.708	−	429.043i	−0.623950	−	1.08071i	0.364793	−	0.931088i	$-0.381140\pi$
$398$	58.7627	−	10.3615i	0.147645	−	0.0260338i
$399$	−165.936	+	15.6591i	−0.415880	+	0.0392458i
$400$	18.7939	−	6.84040i	0.0469846	−	0.0171010i
$401$	−425.871	−	75.0925i	−1.06202	−	0.187263i	−0.384768	−	0.923013i	$-0.625719\pi$
$401$	−425.871	−	75.0925i	−1.06202	−	0.187263i	−0.677253	+	0.735750i	$0.736830\pi$
$402$	27.7818	−	40.2583i	0.0691089	−	0.100145i
$403$	−221.510	+	185.869i	−0.549653	+	0.461214i
$404$			7.12921i			0.0176466i
$405$	159.269	+	86.2466i	0.393256	+	0.212955i
$406$	91.2745			0.224814
$407$	16.2218	+	19.3323i	0.0398569	+	0.0474996i
$408$	23.0046	+	15.8752i	0.0563839	+	0.0389098i
$409$	90.0364	−	510.622i	0.220138	−	1.24846i	−0.651627	−	0.758540i	$-0.725913\pi$
$409$	90.0364	−	510.622i	0.220138	−	1.24846i	0.871765	−	0.489925i	$-0.162976\pi$
$410$	36.2821	+	99.6842i	0.0884928	+	0.243132i
$411$	−45.8962	−	486.352i	−0.111670	−	1.18334i
$412$	42.6967	+	242.145i	0.103633	+	0.587730i
$413$	−112.072	+	64.7050i	−0.271362	+	0.156671i
$414$	101.523	−	124.400i	0.245226	−	0.300482i
$415$	−147.109	+	254.800i	−0.354479	+	0.613975i
$416$	−23.5707	+	64.7601i	−0.0566604	+	0.155673i
$417$	186.102	−	188.659i	0.446287	−	0.452419i
$418$	−31.0764	−	26.0762i	−0.0743454	−	0.0623832i
$419$	7.79797	−	9.29326i	0.0186109	−	0.0221796i	−0.756659	−	0.653810i	$-0.773170\pi$
$419$	7.79797	−	9.29326i	0.0186109	−	0.0221796i	0.775270	+	0.631630i	$0.217614\pi$
$420$	−13.7363	+	52.7001i	−0.0327054	+	0.125477i
$421$	−302.962	−	110.269i	−0.719625	−	0.261922i	−0.0438585	−	0.999038i	$-0.513965\pi$
$421$	−302.962	−	110.269i	−0.719625	−	0.261922i	−0.675767	+	0.737116i	$0.736187\pi$
$422$	−351.844	−	203.137i	−0.833752	−	0.481367i
$423$	203.580	+	341.754i	0.481276	+	0.807930i
$424$	−110.710	−	191.755i	−0.261107	−	0.452251i
$425$	−16.2198	+	2.85999i	−0.0381643	+	0.00672939i
$426$	−66.5018	+	145.192i	−0.156108	+	0.340826i
$427$	56.9674	−	20.7344i	0.133413	−	0.0485584i
$428$	176.077	+	31.0471i	0.411395	+	0.0725401i
$429$	76.3531	+	6.15538i	0.177979	+	0.0143482i
$430$	55.7046	−	46.7417i	0.129546	−	0.108702i
$431$			216.058i			0.501294i	0.968079	+	0.250647i	$0.0806433\pi$
$431$			216.058i			0.501294i	−0.968079	+	0.250647i	$0.919357\pi$
$432$	60.1225	−	89.7178i	0.139172	−	0.207680i
$433$	21.4248			0.0494800			0.0247400	−	0.999694i	$-0.492124\pi$
$433$	21.4248			0.0494800			0.0247400	+	0.999694i	$0.492124\pi$
$434$	87.5839	+	104.378i	0.201806	+	0.240503i
$435$	96.3549	−	45.7340i	0.221506	−	0.105136i
$436$	−1.05622	+	5.99013i	−0.00242253	+	0.0137388i
$437$	59.0542	+	162.250i	0.135135	+	0.371282i
$438$	−303.912	+	215.907i	−0.693864	+	0.492938i
$439$	2.06549	+	11.7140i	0.00470498	+	0.0266833i	0.987070	−	0.160291i	$-0.0512431\pi$
$439$	2.06549	+	11.7140i	0.00470498	+	0.0266833i	−0.982365	+	0.186974i	$0.940132\pi$
$440$	−11.4796	+	6.62774i	−0.0260899	+	0.0150630i
$441$	191.186	+	221.633i	0.433529	+	0.502570i
$442$	28.3763	−	49.1492i	0.0641998	−	0.111197i
$443$	−90.1900	+	247.795i	−0.203589	+	0.559357i	−0.998902	−	0.0468420i	$-0.985084\pi$
$443$	−90.1900	+	247.795i	−0.203589	+	0.559357i	0.795313	+	0.606199i	$0.207306\pi$
$444$	−19.1745	−	69.6555i	−0.0431857	−	0.156882i
$445$	166.923	+	140.065i	0.375108	+	0.314753i
$446$	270.245	−	322.066i	0.605931	−	0.722120i
$447$	−659.175	+	181.455i	−1.47466	+	0.405939i
$448$	30.5158	+	11.1068i	0.0681156	+	0.0247920i
$449$	368.220	+	212.592i	0.820088	+	0.473478i	0.850447	−	0.526061i	$-0.176332\pi$
$449$	368.220	+	212.592i	0.820088	+	0.473478i	−0.0303587	+	0.999539i	$0.509665\pi$
$450$	11.9051	+	62.5161i	0.0264558	+	0.138925i
$451$	−35.1541	−	60.8886i	−0.0779469	−	0.135008i
$452$	195.295	−	34.4357i	0.432068	−	0.0761852i
$453$	120.276	+	169.301i	0.265509	+	0.373733i
$454$	−306.079	+	111.404i	−0.674184	+	0.245383i
$455$	108.901	+	19.2022i	0.239343	+	0.0422026i
$456$	49.7977	+	104.917i	0.109205	+	0.230080i
$457$	355.225	−	298.069i	0.777297	−	0.652230i	−0.165269	−	0.986248i	$-0.552849\pi$
$457$	355.225	−	298.069i	0.777297	−	0.652230i	0.942566	+	0.334019i	$0.108405\pi$
$458$		−	100.932i		−	0.220375i
$459$	−61.5884	+	64.1628i	−0.134180	+	0.139788i
$460$	56.4181			0.122648
$461$	−228.164	−	271.915i	−0.494933	−	0.589838i	0.459532	−	0.888161i	$-0.348017\pi$
$461$	−228.164	−	271.915i	−0.494933	−	0.589838i	−0.954465	+	0.298323i	$0.903573\pi$
$462$	2.90049	−	35.9785i	0.00627812	−	0.0778756i
$463$	−29.8985	+	169.563i	−0.0645757	+	0.366227i	0.935346	+	0.353733i	$0.115088\pi$
$463$	−29.8985	+	169.563i	−0.0645757	+	0.366227i	−0.999922	+	0.0124935i	$0.996023\pi$
$464$	−21.7519	−	59.7629i	−0.0468792	−	0.128799i
$465$	144.759	+	66.3034i	0.311309	+	0.142588i
$466$	51.8451	+	294.028i	0.111256	+	0.630962i
$467$	273.078	−	157.661i	0.584748	−	0.337605i	−0.178270	−	0.983982i	$-0.557050\pi$
$467$	273.078	−	157.661i	0.584748	−	0.337605i	0.763018	+	0.646377i	$0.223717\pi$
$468$	−191.389	−	107.043i	−0.408952	−	0.228725i
$469$	−23.3999	+	40.5298i	−0.0498932	+	0.0864175i
$470$	−47.8045	+	131.342i	−0.101712	+	0.279450i
$471$	553.898	+	144.373i	1.17600	+	0.306525i
$472$	69.0746	+	57.9605i	0.146344	+	0.122798i
$473$	−30.9792	+	36.9195i	−0.0654951	+	0.0780540i
$474$	375.958	+	370.862i	0.793160	+	0.782410i
$475$	−64.3061	−	23.4055i	−0.135381	−	0.0492747i
$476$	−23.1597	−	13.3713i	−0.0486549	−	0.0280909i
$477$	658.712	−	249.983i	1.38095	−	0.524073i
$478$	−142.869	−	247.456i	−0.298889	−	0.517691i
$479$	751.335	−	132.481i	1.56855	−	0.276577i	0.679251	−	0.733906i	$-0.262305\pi$
$479$	751.335	−	132.481i	1.56855	−	0.276577i	0.889298	+	0.457329i	$0.151194\pi$
$480$	37.7795	−	3.56518i	0.0787073	−	0.00742746i
$481$	−137.847	+	50.1722i	−0.286584	+	0.104308i
$482$	−391.681	−	69.0639i	−0.812616	−	0.143286i
$483$	−87.2572	+	126.444i	−0.180657	+	0.261788i
$484$	−178.653	+	149.907i	−0.369117	+	0.309726i
$485$			405.618i			0.836326i
$486$	251.147	+	234.570i	0.516764	+	0.482655i
$487$	−827.829			−1.69985			−0.849927	−	0.526901i	$-0.823354\pi$
$487$	−827.829			−1.69985			−0.849927	+	0.526901i	$0.823354\pi$
$488$	−27.1522	−	32.3587i	−0.0556397	−	0.0663088i
$489$	688.962	+	475.444i	1.40892	+	0.972278i
$490$	−17.8588	+	101.282i	−0.0364464	+	0.206698i
$491$	68.9841	+	189.532i	0.140497	+	0.386013i	0.989907	−	0.141722i	$-0.0452638\pi$
$491$	68.9841	+	189.532i	0.140497	+	0.386013i	−0.849409	+	0.527735i	$0.823042\pi$
$492$	18.9100	+	200.386i	0.0384350	+	0.407288i
$493$	9.09454	+	51.5777i	0.0184473	+	0.104620i
$494$	204.215	−	117.904i	0.413391	−	0.238672i
$495$	−14.9655	−	39.4344i	−0.0302333	−	0.0796655i
$496$	47.4705	−	82.2212i	0.0957066	−	0.165769i
$497$	52.2590	−	143.580i	0.105149	−	0.288894i
$498$	−392.031	+	397.418i	−0.787212	+	0.798028i
$499$	−323.880	−	271.768i	−0.649059	−	0.544625i	0.257726	−	0.966218i	$-0.417027\pi$
$499$	−323.880	−	271.768i	−0.649059	−	0.544625i	−0.906785	+	0.421593i	$0.861471\pi$
$500$	−14.3732	+	17.1293i	−0.0287463	+	0.0342585i
$501$	−105.071	+	403.112i	−0.209723	+	0.804616i
$502$	319.435	+	116.265i	0.636324	+	0.231603i
$503$	−117.882	−	68.0595i	−0.234359	−	0.135307i	0.378222	−	0.925715i	$-0.376535\pi$
$503$	−117.882	−	68.0595i	−0.234359	−	0.135307i	−0.612581	+	0.790408i	$0.709869\pi$
$504$	−50.4402	+	90.1851i	−0.100080	+	0.178939i
$505$	−3.98535	−	6.90282i	−0.00789178	−	0.0136690i
$506$	−36.8243	+	6.49312i	−0.0727754	+	0.0128323i
$507$	25.7097	−	56.1315i	0.0507095	−	0.110713i
$508$	157.422	−	57.2969i	0.309886	−	0.112789i
$509$	319.781	+	56.3861i	0.628254	+	0.110778i	0.478704	−	0.877976i	$-0.341107\pi$
$509$	319.781	+	56.3861i	0.628254	+	0.110778i	0.149549	+	0.988754i	$0.452218\pi$
$510$	−31.1486	−	2.51112i	−0.0610758	−	0.00492376i
$511$	273.237	−	229.273i	0.534711	−	0.448676i
$512$		−	22.6274i		−	0.0441942i
$513$	−354.914	+	102.930i	−0.691841	+	0.200642i
$514$	540.706			1.05196
$515$	−176.704	−	210.588i	−0.343114	−	0.408908i
$516$	124.644	−	59.1610i	0.241557	−	0.114653i
$517$	16.0862	−	91.2291i	0.0311144	−	0.176459i
$518$	23.6418	+	64.9553i	0.0456405	+	0.125396i
$519$	287.153	−	204.001i	0.553281	−	0.393065i
$520$	−13.3797	−	75.8801i	−0.0257302	−	0.145923i
$521$	531.814	−	307.043i	1.02076	−	0.589334i	0.106433	−	0.994320i	$-0.466057\pi$
$521$	531.814	−	307.043i	1.02076	−	0.589334i	0.914323	+	0.404986i	$0.132724\pi$
$522$	198.796	−	37.8572i	0.380836	−	0.0725234i
$523$	−344.609	+	596.880i	−0.658908	+	1.14126i	0.321990	+	0.946743i	$0.395648\pi$
$523$	−344.609	+	596.880i	−0.658908	+	1.14126i	−0.980899	+	0.194520i	$0.937685\pi$
$524$	−114.202	+	313.768i	−0.217943	+	0.598793i
$525$	−16.1602	−	58.7055i	−0.0307813	−	0.111820i
$526$	−411.280	−	345.105i	−0.781902	−	0.656093i
$527$	−50.2557	+	59.8924i	−0.0953619	+	0.113648i
$528$	−24.2485	+	6.67503i	−0.0459252	+	0.0126421i
$529$	−347.545	−	126.496i	−0.656986	−	0.239123i
$530$	214.388	+	123.777i	0.404506	+	0.233542i
$531$	−217.257	+	187.411i	−0.409147	+	0.352940i
$532$	−55.5577	−	96.2288i	−0.104432	−	0.180881i
$533$	402.474	−	70.9671i	0.755112	−	0.133147i
$534$	239.445	+	337.045i	0.448399	+	0.631171i
$535$	−187.842	+	68.3688i	−0.351106	+	0.127792i
$536$	32.1138	+	5.66253i	0.0599138	+	0.0105644i
$537$	−177.172	−	373.277i	−0.329930	−	0.695115i
$538$	340.722	−	285.900i	0.633312	−	0.531412i
$539$		−	68.1626i		−	0.126461i
$540$	−8.05960	+	120.478i	−0.0149252	+	0.223108i
$541$	706.341			1.30562			0.652810	−	0.757521i	$-0.273590\pi$
$541$	706.341			1.30562			0.652810	+	0.757521i	$0.273590\pi$
$542$	−331.874	−	395.512i	−0.612314	−	0.729728i
$543$	−3.96056	+	49.1279i	−0.00729385	+	0.0904749i
$544$	−3.23571	+	18.3506i	−0.00594800	+	0.0337328i
$545$	−2.32590	−	6.39036i	−0.00426771	−	0.0117254i
$546$	190.755	+	87.3711i	0.349369	+	0.160020i
$547$	−114.525	−	649.503i	−0.209369	−	1.18739i	−0.890415	−	0.455151i	$-0.849585\pi$
$547$	−114.525	−	649.503i	−0.209369	−	1.18739i	0.681045	−	0.732241i	$-0.261526\pi$
$548$	282.043	−	162.838i	0.514677	−	0.297149i
$549$	115.475	−	68.7877i	0.210338	−	0.125296i
$550$	7.41004	−	12.8346i	0.0134728	−	0.0233356i
$551$	−74.4276	+	204.488i	−0.135077	+	0.371122i
$552$	103.585	+	26.9993i	0.187654	+	0.0489118i
$553$	−387.059	−	324.781i	−0.699926	−	0.587308i
$554$	132.452	−	157.851i	0.239084	−	0.284929i
$555$	57.5042	+	56.7248i	0.103611	+	0.102207i
$556$	166.014	+	60.4240i	0.298586	+	0.108676i
$557$	396.303	+	228.806i	0.711495	+	0.410782i	0.811614	−	0.584194i	$-0.198589\pi$
$557$	396.303	+	228.806i	0.711495	+	0.410782i	−0.100119	+	0.994975i	$0.531922\pi$
$558$	234.050	+	191.010i	0.419445	+	0.342312i
$559$	−140.073	−	242.613i	−0.250577	−	0.434013i
$560$	−35.7557	+	6.30469i	−0.0638494	+	0.0112584i
$561$	20.6199	−	1.94586i	0.0367555	−	0.00346856i
$562$	−57.2949	+	20.8537i	−0.101948	+	0.0371061i
$563$	435.930	+	76.8661i	0.774298	+	0.136530i	0.546816	−	0.837253i	$-0.315840\pi$
$563$	435.930	+	76.8661i	0.774298	+	0.136530i	0.227482	+	0.973782i	$0.426951\pi$
$564$	−150.625	+	218.269i	−0.267065	+	0.387002i
$565$	−169.843	+	142.515i	−0.300607	+	0.252240i
$566$		−	756.212i		−	1.33606i
$567$	−257.550	−	204.397i	−0.454233	−	0.360489i
$568$	−106.465			−0.187438
$569$	153.046	+	182.393i	0.268974	+	0.320550i	0.883577	−	0.468286i	$-0.155128\pi$
$569$	153.046	+	182.393i	0.268974	+	0.320550i	−0.614603	+	0.788836i	$0.710684\pi$
$570$	−106.867	−	73.7472i	−0.187485	−	0.129381i
$571$	−28.4053	+	161.094i	−0.0497465	+	0.282127i	−0.999526	−	0.0307942i	$-0.990196\pi$
$571$	−28.4053	+	161.094i	−0.0497465	+	0.282127i	0.949779	+	0.312921i	$0.101307\pi$
$572$	17.4660	+	47.9874i	0.0305350	+	0.0838941i
$573$	−33.5507	−	355.529i	−0.0585526	−	0.620470i
$574$	−33.4406	−	189.651i	−0.0582589	−	0.330403i
$575$	−54.6265	+	31.5387i	−0.0950027	+	0.0548498i
$576$	71.0702	+	11.5339i	0.123386	+	0.0200242i
$577$	217.734	−	377.127i	0.377356	−	0.653600i	−0.613321	−	0.789834i	$-0.710167\pi$
$577$	217.734	−	377.127i	0.377356	−	0.653600i	0.990677	+	0.136234i	$0.0435000\pi$
$578$	−134.538	+	369.640i	−0.232765	+	0.639516i
$579$	255.534	−	259.045i	0.441337	−	0.447401i
$580$	54.4697	+	45.7055i	0.0939133	+	0.0788026i
$581$	343.320	−	409.153i	0.590912	−	0.704222i
$582$	−194.112	+	744.725i	−0.333526	+	1.27960i
$583$	−154.178	−	56.1160i	−0.264455	−	0.0962539i
$584$	−215.235	−	124.266i	−0.368553	−	0.212784i
$585$	245.151	−	3.34559i	0.419062	−	0.00571896i
$586$	371.203	+	642.942i	0.633452	+	1.09717i
$587$	203.399	−	35.8647i	0.346506	−	0.0610983i	0.00231299	−	0.999997i	$-0.499264\pi$
$587$	203.399	−	35.8647i	0.346506	−	0.0610983i	0.344193	+	0.938899i	$0.388153\pi$
$588$	−81.2585	+	177.410i	−0.138195	+	0.301717i
$589$	−305.264	+	111.107i	−0.518275	+	0.188637i
$590$	−99.2821	−	17.5061i	−0.168275	−	0.0296714i
$591$	−583.414	−	47.0333i	−0.987165	−	0.0795826i
$592$	36.8960	−	30.9594i	0.0623243	−	0.0522963i
$593$		−	633.457i		−	1.06822i	−0.845414	−	0.534112i	$-0.820646\pi$
$593$		−	633.457i		−	1.06822i	0.845414	−	0.534112i	$-0.179354\pi$
$594$	−8.60525	−	79.5644i	−0.0144870	−	0.133947i
$595$	29.8991			0.0502506
$596$	−292.980	−	349.160i	−0.491577	−	0.585839i
$597$	−114.351	+	54.2755i	−0.191542	+	0.0909137i
$598$	37.7429	−	214.050i	0.0631152	−	0.357944i
$599$	−147.875	−	406.283i	−0.246870	−	0.678269i	−0.999797	−	0.0201651i	$-0.993581\pi$
$599$	−147.875	−	406.283i	−0.246870	−	0.678269i	0.752927	−	0.658104i	$-0.228641\pi$
$600$	−34.5868	+	24.5713i	−0.0576447	+	0.0409522i
$601$	−120.337	−	682.465i	−0.200228	−	1.13555i	−0.904774	−	0.425891i	$-0.859961\pi$
$601$	−120.337	−	682.465i	−0.200228	−	1.13555i	0.704546	−	0.709658i	$-0.251151\pi$
$602$	−114.322	+	66.0040i	−0.189904	+	0.109641i
$603$	−34.1548	+	97.9795i	−0.0566415	+	0.162487i
$604$	−69.2251	+	119.901i	−0.114611	+	0.198512i
$605$	89.1790	−	245.017i	0.147403	−	0.404987i
$606$	−4.01379	−	14.5810i	−0.00662341	−	0.0240610i
$607$	492.621	+	413.358i	0.811566	+	0.680985i	0.950981	−	0.309249i	$-0.100078\pi$
$607$	492.621	+	413.358i	0.811566	+	0.680985i	−0.139415	+	0.990234i	$0.544522\pi$
$608$	−49.7667	+	59.3096i	−0.0818531	+	0.0975487i
$609$	−186.679	+	51.3881i	−0.306533	+	0.0843811i
$610$	44.3791	+	16.1527i	0.0727526	+	0.0264798i
$611$	466.331	+	269.236i	0.763225	+	0.440648i
$612$	−55.9879	−	19.5169i	−0.0914835	−	0.0318904i
$613$	262.564	+	454.773i	0.428325	+	0.741881i	0.996725	−	0.0808715i	$-0.0257704\pi$
$613$	262.564	+	454.773i	0.428325	+	0.741881i	−0.568399	+	0.822753i	$0.692437\pi$
$614$	341.522	−	60.2196i	0.556225	−	0.0980775i
$615$	−130.328	−	183.451i	−0.211916	−	0.298295i
$616$	22.6123	−	8.23020i	0.0367083	−	0.0133607i
$617$	−1152.41	−	203.200i	−1.86776	−	0.329336i	−0.878760	−	0.477263i	$-0.841629\pi$
$617$	−1152.41	−	203.200i	−1.86776	−	0.329336i	−0.988998	+	0.147927i	$0.952740\pi$
$618$	−223.654	−	471.207i	−0.361900	−	0.762471i
$619$	−781.243	+	655.541i	−1.26211	+	1.05903i	−0.266651	+	0.963793i	$0.585917\pi$
$619$	−781.243	+	655.541i	−1.26211	+	1.05903i	−0.995454	+	0.0952390i	$0.969638\pi$
$620$			106.147i			0.171205i
$621$	−137.602	+	311.586i	−0.221582	+	0.501749i
$622$	−487.336			−0.783498
$623$	−254.269	−	303.026i	−0.408136	−	0.486398i
$624$	11.7476	−	145.721i	0.0188263	−	0.233527i
$625$	4.34120	−	24.6202i	0.00694593	−	0.0393923i
$626$	−33.5376	−	92.1439i	−0.0535745	−	0.147195i
$627$	78.2398	+	35.8360i	0.124784	+	0.0571546i
$628$	66.2647	+	375.806i	0.105517	+	0.598416i
$629$	−34.3495	+	19.8317i	−0.0546097	+	0.0315289i
$630$	−1.57648	−	115.518i	−0.00250236	−	0.183362i
$631$	−519.399	+	899.625i	−0.823136	+	1.42571i	0.0802002	+	0.996779i	$0.474444\pi$
$631$	−519.399	+	899.625i	−0.823136	+	1.42571i	−0.903336	+	0.428934i	$0.858889\pi$
$632$	−120.413	+	330.831i	−0.190526	+	0.523466i
$633$	833.973	+	217.375i	1.31749	+	0.343404i
$634$	−531.087	−	445.635i	−0.837676	−	0.702894i
$635$	−120.393	+	143.479i	−0.189596	+	0.225951i
$636$	334.387	+	329.855i	0.525766	+	0.518640i
$637$	372.317	+	135.512i	0.584486	+	0.212735i
$638$	−40.8129	−	23.5633i	−0.0639700	−	0.0369331i
$639$	54.2686	−	334.394i	0.0849273	−	0.523308i
$640$	12.6491	+	21.9089i	0.0197642	+	0.0342327i
$641$	−88.1996	+	15.5520i	−0.137597	+	0.0242620i	−0.242022	−	0.970271i	$-0.577811\pi$
$641$	−88.1996	+	15.5520i	−0.137597	+	0.0242620i	0.104426	+	0.994533i	$0.466700\pi$
$642$	−377.600	+	35.6335i	−0.588163	+	0.0555039i
$643$	−1040.29	+	378.633i	−1.61786	+	0.588854i	−0.982973	−	0.183749i	$-0.941177\pi$
$643$	−1040.29	+	378.633i	−1.61786	+	0.588854i	−0.634890	+	0.772603i	$0.718955\pi$
$644$	−100.863	−	17.7849i	−0.156620	−	0.0276163i
$645$	−87.6136	+	126.960i	−0.135835	+	0.196838i
$646$	48.8416	−	40.9829i	0.0756061	−	0.0634411i
$647$		−	335.682i		−	0.518829i	−0.965766	−	0.259414i	$-0.916470\pi$
$647$		−	335.682i		−	0.518829i	0.965766	−	0.259414i	$-0.0835296\pi$
$648$	−72.4536	+	217.344i	−0.111811	+	0.335408i
$649$	66.8166			0.102953
$650$	55.3731	+	65.9911i	0.0851894	+	0.101525i
$651$	−237.896	−	164.169i	−0.365432	−	0.252180i
$652$	−96.9058	+	549.580i	−0.148629	+	0.842914i
$653$	−205.890	−	565.678i	−0.315298	−	0.866275i	−0.991564	−	0.129617i	$-0.958625\pi$
$653$	−205.890	−	565.678i	−0.315298	−	0.866275i	0.676266	−	0.736658i	$-0.263597\pi$
$654$	−1.21225	−	12.8459i	−0.00185359	−	0.0196421i
$655$	−64.8257	−	367.645i	−0.0989706	−	0.561290i
$656$	−116.207	+	67.0919i	−0.177144	+	0.102274i
$657$	500.018	−	612.687i	0.761063	−	0.932553i
$658$	126.867	−	219.741i	0.192808	−	0.333953i
$659$	−259.923	+	714.132i	−0.394420	+	1.08366i	0.570541	+	0.821269i	$0.306733\pi$
$659$	−259.923	+	714.132i	−0.394420	+	1.08366i	−0.964961	+	0.262392i	$0.915489\pi$
$660$	19.7471	−	20.0184i	0.0299198	−	0.0303309i
$661$	−570.189	−	478.445i	−0.862616	−	0.723821i	0.0999142	−	0.994996i	$-0.468143\pi$
$661$	−570.189	−	478.445i	−0.862616	−	0.723821i	−0.962530	+	0.271176i	$0.912588\pi$
$662$	−294.724	+	351.239i	−0.445203	+	0.530572i
$663$	−30.3652	+	116.498i	−0.0457997	+	0.175714i
$664$	−349.715	−	127.286i	−0.526679	−	0.191695i
$665$	107.587	+	62.1154i	0.161785	+	0.0934067i
$666$	78.4329	+	131.667i	0.117767	+	0.197698i
$667$	100.290	+	173.708i	0.150360	+	0.260432i
$668$	−273.501	+	48.2257i	−0.409433	+	0.0721941i
$669$	−371.392	+	810.852i	−0.555145	+	1.21204i
$670$	−34.2595	+	12.4694i	−0.0511336	+	0.0186111i
$671$	−30.8254	−	5.43535i	−0.0459395	−	0.00810038i
$672$	−68.6654	−	5.53562i	−0.102181	−	0.00823753i
$673$	247.304	−	207.513i	0.367466	−	0.308340i	−0.440292	−	0.897854i	$-0.645125\pi$
$673$	247.304	−	207.513i	0.367466	−	0.308340i	0.807758	+	0.589514i	$0.200681\pi$
$674$		−	641.703i		−	0.952082i
$675$	−59.5458	−	121.158i	−0.0882160	−	0.179494i
$676$	41.1595			0.0608868
$677$	−347.928	−	414.644i	−0.513926	−	0.612473i	0.445208	−	0.895427i	$-0.353130\pi$
$677$	−347.928	−	414.644i	−0.513926	−	0.612473i	−0.959133	+	0.282955i	$0.908685\pi$
$678$	−380.038	+	180.382i	−0.560528	+	0.266050i
$679$	127.865	−	725.158i	0.188313	−	1.06798i
$680$	−7.12535	−	19.5767i	−0.0104785	−	0.0287893i
$681$	563.286	−	400.173i	0.827146	−	0.587625i
$682$	−12.2164	−	69.2827i	−0.0179126	−	0.101588i
$683$	303.467	−	175.207i	0.444315	−	0.256525i	−0.261112	−	0.965309i	$-0.584089\pi$
$683$	303.467	−	175.207i	0.444315	−	0.256525i	0.705426	+	0.708784i	$0.250756\pi$
$684$	−160.917	−	186.544i	−0.235259	−	0.272724i
$685$	−182.058	+	315.334i	−0.265778	+	0.460341i
$686$	160.063	−	439.770i	0.233328	−	0.641064i
$687$	56.8251	+	206.430i	0.0827149	+	0.300480i
$688$	70.4614	+	59.1241i	0.102415	+	0.0859362i
$689$	613.033	−	730.585i	0.889744	−	1.06036i
$690$	−115.389	+	31.7637i	−0.167230	+	0.0460344i
$691$	−280.764	−	102.190i	−0.406315	−	0.147887i	0.130774	−	0.991412i	$-0.458254\pi$
$691$	−280.764	−	102.190i	−0.406315	−	0.147887i	−0.537089	+	0.843526i	$0.680476\pi$
$692$	203.366	+	117.413i	0.293881	+	0.169672i
$693$	14.3239	+	75.2179i	0.0206694	+	0.108539i
$694$	188.349	+	326.230i	0.271397	+	0.470073i
$695$	−194.520	+	34.2991i	−0.279885	+	0.0493513i
$696$	78.1349	+	109.983i	0.112263	+	0.158022i
$697$	103.837	−	37.7934i	0.148977	−	0.0542230i
$698$	753.902	+	132.933i	1.08009	+	0.190449i
$699$	−271.575	−	572.170i	−0.388520	−	0.818555i
$700$	31.0959	−	26.0925i	0.0444226	−	0.0372750i
$701$			722.695i			1.03095i	0.856905	+	0.515475i	$0.172384\pi$
$701$			722.695i			1.03095i	−0.856905	+	0.515475i	$0.827616\pi$
$702$	451.704	+	111.176i	0.643453	+	0.158371i
$703$	−164.802			−0.234426
$704$	−10.7776	−	12.8443i	−0.0153091	−	0.0182447i
$705$	23.8256	−	295.540i	0.0337952	−	0.419206i
$706$	−103.297	+	585.829i	−0.146314	+	0.829786i
$707$	4.94893	+	13.5971i	0.00699990	+	0.0192321i
$708$	−173.907	−	79.6539i	−0.245631	−	0.112506i
$709$	43.6368	+	247.477i	0.0615470	+	0.349050i	0.999993	+	0.00362555i	$0.00115405\pi$
$709$	43.6368	+	247.477i	0.0615470	+	0.349050i	−0.938446	+	0.345425i	$0.887735\pi$
$710$	103.084	−	59.5156i	0.145189	−	0.0838248i
$711$	−977.724	−	546.837i	−1.37514	−	0.769110i
$712$	−137.814	+	238.700i	−0.193559	+	0.335253i
$713$	−102.411	+	281.373i	−0.143634	+	0.394632i
$714$	54.8954	+	14.3085i	0.0768843	+	0.0200399i
$715$	−43.7372	−	36.6999i	−0.0611709	−	0.0513285i
$716$	177.062	−	211.014i	0.247293	−	0.294713i
$717$	431.521	+	425.672i	0.601843	+	0.593685i
$718$	218.029	+	79.3559i	0.303661	+	0.110524i
$719$	−724.990	−	418.573i	−1.00833	−	0.582160i	−0.0976286	−	0.995223i	$-0.531126\pi$
$719$	−724.990	−	418.573i	−1.00833	−	0.582160i	−0.910703	+	0.413063i	$0.864459\pi$
$720$	−75.2611	+	28.5617i	−0.104529	+	0.0396691i
$721$	249.524	+	432.188i	0.346080	+	0.599429i
$722$	−241.884	+	42.6507i	−0.335020	+	0.0590730i
$723$	839.967	−	79.2662i	1.16178	−	0.109635i
$724$	−30.8766	+	11.2382i	−0.0426472	+	0.0155223i
$725$	−78.2902	−	13.8047i	−0.107987	−	0.0190409i
$726$	280.990	−	407.180i	0.387038	−	0.560854i
$727$	550.019	−	461.521i	0.756560	−	0.634829i	−0.180669	−	0.983544i	$-0.557826\pi$
$727$	550.019	−	461.521i	0.756560	−	0.634829i	0.937229	+	0.348715i	$0.113382\pi$
$728$			139.875i			0.192136i
$729$	−645.722	−	338.356i	−0.885763	−	0.464137i
$730$	277.867			0.380640
$731$	−48.6888	−	58.0250i	−0.0666057	−	0.0793776i
$732$	73.7510	+	50.8946i	0.100753	+	0.0695282i
$733$	151.640	−	859.995i	0.206876	−	1.17325i	−0.687583	−	0.726105i	$-0.741328\pi$
$733$	151.640	−	859.995i	0.206876	−	1.17325i	0.894460	−	0.447149i	$-0.147560\pi$
$734$	−0.840532	−	2.30934i	−0.00114514	−	0.00314624i
$735$	−20.4969	−	217.201i	−0.0278869	−	0.295512i
$736$	12.3922	+	70.2796i	0.0168372	+	0.0954887i
$737$	20.9262	−	12.0818i	0.0283938	−	0.0163932i
$738$	−151.494	−	399.191i	−0.205276	−	0.540909i
$739$	−185.208	+	320.790i	−0.250620	+	0.434087i	−0.963697	−	0.266999i	$-0.913968\pi$
$739$	−185.208	+	320.790i	−0.250620	+	0.434087i	0.713076	+	0.701086i	$0.247301\pi$
$740$	−18.4175	+	50.6018i	−0.0248886	+	0.0683808i
$741$	−351.290	+	356.116i	−0.474075	+	0.480589i
$742$	−344.261	−	288.869i	−0.463963	−	0.389311i
$743$	467.528	−	557.178i	0.629243	−	0.749903i	−0.353387	−	0.935477i	$-0.614970\pi$
$743$	467.528	−	557.178i	0.629243	−	0.749903i	0.982630	+	0.185574i	$0.0594145\pi$
$744$	−50.7976	+	194.889i	−0.0682764	+	0.261947i
$745$	478.863	+	174.292i	0.642769	+	0.233949i
$746$	231.558	+	133.690i	0.310399	+	0.179209i
$747$	578.051	−	1033.53i	0.773830	−	1.38358i
$748$	6.90382	+	11.9578i	0.00922971	+	0.0159863i
$749$	357.373	−	63.0144i	0.477133	−	0.0841314i
$750$	19.7528	−	43.1257i	0.0263370	−	0.0575010i
$751$	−639.247	+	232.667i	−0.851195	+	0.309810i	−0.730527	−	0.682883i	$-0.760726\pi$
$751$	−639.247	+	232.667i	−0.851195	+	0.309810i	−0.120668	+	0.992693i	$0.538504\pi$
$752$	−174.112	−	30.7006i	−0.231532	−	0.0408253i
$753$	−718.780	−	57.9461i	−0.954555	−	0.0769536i
$754$	209.846	−	176.082i	0.278311	−	0.233531i
$755$		−	154.792i		−	0.205023i
$756$	52.3878	−	212.849i	0.0692960	−	0.281546i
$757$	0.431389			0.000569866			0.000284933	−	1.00000i	$-0.499909\pi$
$757$	0.431389			0.000569866			0.000284933		1.00000i	$0.499909\pi$
$758$	432.665	+	515.630i	0.570798	+	0.680250i
$759$	71.6591	−	34.0123i	0.0944125	−	0.0448120i
$760$	15.0313	−	85.2467i	0.0197780	−	0.112167i
$761$	16.3396	+	44.8926i	0.0214712	+	0.0589915i	0.949965	−	0.312356i	$-0.101118\pi$
$761$	16.3396	+	44.8926i	0.0214712	+	0.0589915i	−0.928494	+	0.371347i	$0.878896\pi$
$762$	−289.708	+	205.816i	−0.380194	+	0.270099i
$763$	2.14375	+	12.1578i	0.00280963	+	0.0159342i
$764$	206.177	−	119.036i	0.269865	−	0.155807i
$765$	65.1203	−	12.4010i	0.0851246	−	0.0162105i
$766$	−243.788	+	422.254i	−0.318262	+	0.551245i
$767$	−132.837	+	364.965i	−0.173190	+	0.475835i
$768$	12.7394	+	46.2786i	0.0165877	+	0.0602586i
$769$	−693.950	−	582.293i	−0.902406	−	0.757208i	0.0682534	−	0.997668i	$-0.478257\pi$
$769$	−693.950	−	582.293i	−0.902406	−	0.757208i	−0.970659	+	0.240460i	$0.922702\pi$
$770$	−17.2934	+	20.6095i	−0.0224590	+	0.0267656i
$771$	−1105.87	+	304.420i	−1.43434	+	0.394838i
$772$	227.951	+	82.9674i	0.295273	+	0.107471i
$773$	−221.201	−	127.711i	−0.286160	−	0.165214i	0.350049	−	0.936731i	$-0.386165\pi$
$773$	−221.201	−	127.711i	−0.286160	−	0.165214i	−0.636209	+	0.771517i	$0.719498\pi$
$774$	−221.619	+	191.174i	−0.286329	+	0.246994i
$775$	−59.3381	−	102.777i	−0.0765652	−	0.132615i
$776$	−505.276	+	89.0938i	−0.651129	+	0.114812i
$777$	−84.9234	−	119.539i	−0.109297	−	0.153847i
$778$	831.483	−	302.635i	1.06874	−	0.388991i
$779$	452.156	+	79.7272i	0.580431	+	0.102346i
$780$	70.0857	+	147.661i	0.0898535	+	0.189308i
$781$	−60.4338	+	50.7100i	−0.0773801	+	0.0649296i
$782$		−	58.7682i		−	0.0751512i
$783$	−385.273	+	189.351i	−0.492047	+	0.241827i
$784$	−130.089			−0.165930
$785$	−274.242	−	326.829i	−0.349353	−	0.416343i
$786$	56.9181	−	706.028i	0.0724149	−	0.898254i
$787$	−12.8614	+	72.9403i	−0.0163423	+	0.0926815i	−0.991888	−	0.127115i	$-0.959428\pi$
$787$	−12.8614	+	72.9403i	−0.0163423	+	0.0926815i	0.975546	+	0.219797i	$0.0705394\pi$
$788$	−133.458	−	366.673i	−0.169363	−	0.465320i
$789$	1035.46	+	474.271i	1.31238	+	0.601104i
$790$	−68.3511	−	387.638i	−0.0865203	−	0.490681i
$791$	348.569	−	201.246i	0.440668	−	0.254420i
$792$	45.8361	−	27.3041i	0.0578738	−	0.0344749i
$793$	90.9722	−	157.569i	0.114719	−	0.198699i
$794$	−239.627	+	658.371i	−0.301798	+	0.829183i
$795$	−508.163	−	132.452i	−0.639199	−	0.166607i
$796$	−64.6427	−	54.2417i	−0.0812094	−	0.0681428i
$797$	−903.581	+	1076.85i	−1.13373	+	1.35112i	−0.205699	+	0.978615i	$0.565947\pi$
$797$	−903.581	+	1076.85i	−1.13373	+	1.35112i	−0.928029	+	0.372509i	$0.878498\pi$
$798$	167.807	+	165.532i	0.210284	+	0.207434i
$799$	136.813	+	49.7958i	0.171230	+	0.0623227i
$800$	−24.4949	−	14.1421i	−0.0306186	−	0.0176777i
$801$	−679.482	−	554.530i	−0.848293	−	0.692298i
$802$	305.782	+	529.629i	0.381274	+	0.660386i
$803$	−181.365	+	31.9796i	−0.225860	+	0.0398252i
$804$	−68.8686	+	6.49901i	−0.0856575	+	0.00808334i
$805$	107.603	−	39.1641i	0.133668	−	0.0486511i
$806$	402.723	+	71.0109i	0.499656	+	0.0881029i
$807$	−535.896	+	776.563i	−0.664060	+	0.962284i
$808$	7.72343	−	6.48073i	0.00955870	−	0.00802070i
$809$			147.419i			0.182223i	0.995841	+	0.0911117i	$0.0290420\pi$
$809$			147.419i			0.182223i	−0.995841	+	0.0911117i	$0.970958\pi$
$810$	−51.3462	−	250.945i	−0.0633904	−	0.309809i
$811$	518.867			0.639787			0.319894	−	0.947454i	$-0.396353\pi$
$811$	518.867			0.639787			0.319894	+	0.947454i	$0.396353\pi$
$812$	−82.9721	−	98.8823i	−0.102182	−	0.121776i
$813$	901.440	+	622.072i	1.10878	+	0.765157i
$814$	6.19749	−	35.1477i	0.00761362	−	0.0431790i
$815$	−213.396	−	586.301i	−0.261836	−	0.719387i
$816$	−3.71369	−	39.3532i	−0.00455110	−	0.0482270i
$817$	−54.6517	−	309.945i	−0.0668931	−	0.379370i
$818$	−635.029	+	366.634i	−0.776319	+	0.448208i
$819$	−439.332	−	71.2989i	−0.536424	−	0.0870560i
$820$	75.0111	−	129.923i	0.0914769	−	0.158443i
$821$	−492.389	+	1352.83i	−0.599743	+	1.64778i	0.152043	+	0.988374i	$0.451415\pi$
$821$	−492.389	+	1352.83i	−0.599743	+	1.64778i	−0.751786	+	0.659407i	$0.770807\pi$
$822$	−485.168	+	491.835i	−0.590229	+	0.598339i
$823$	491.348	+	412.290i	0.597021	+	0.500960i	0.890486	−	0.455010i	$-0.150364\pi$
$823$	491.348	+	412.290i	0.597021	+	0.500960i	−0.293466	+	0.955970i	$0.594809\pi$
$824$	223.515	−	266.375i	0.271256	−	0.323270i
$825$	−7.92940	+	30.4217i	−0.00961139	+	0.0368748i
$826$	171.976	+	62.5943i	0.208204	+	0.0757800i
$827$	1363.05	+	786.955i	1.64818	+	0.951577i	0.977795	+	0.209565i	$0.0672046\pi$
$827$	1363.05	+	786.955i	1.64818	+	0.951577i	0.670386	+	0.742013i	$0.266129\pi$
$828$	−227.057	+	3.09866i	−0.274224	+	0.00374235i
$829$	664.519	+	1150.98i	0.801591	+	1.38840i	0.918568	+	0.395262i	$0.129346\pi$
$829$	664.519	+	1150.98i	0.801591	+	1.38840i	−0.116977	+	0.993135i	$0.537320\pi$
$830$	409.765	−	72.2526i	0.493692	−	0.0870513i
$831$	−182.027	+	397.415i	−0.219045	+	0.478237i
$832$	91.5846	−	33.3341i	0.110078	−	0.0400650i
$833$	105.501	+	18.6027i	0.126652	+	0.0223322i
$834$	−373.557	−	30.1152i	−0.447911	−	0.0361094i
$835$	237.858	−	199.586i	0.284859	−	0.239025i
$836$			57.3709i			0.0686254i
$837$	−586.230	−	258.891i	−0.700394	−	0.309308i
$838$	−17.1565			−0.0204732
$839$	−495.181	−	590.133i	−0.590203	−	0.703377i	0.385442	−	0.922732i	$-0.374049\pi$
$839$	−495.181	−	590.133i	−0.590203	−	0.703377i	−0.975645	+	0.219355i	$0.929605\pi$
$840$	69.5795	−	33.0253i	0.0828327	−	0.0393158i
$841$	102.140	−	579.267i	0.121451	−	0.688783i
$842$	155.944	+	428.453i	0.185207	+	0.508852i
$843$	105.441	−	74.9082i	0.125079	−	0.0888591i
$844$	99.7710	+	565.829i	0.118212	+	0.670414i
$845$	−39.8525	+	23.0089i	−0.0471627	+	0.0272294i
$846$	185.178	−	531.216i	0.218886	−	0.627915i
$847$	−236.671	+	409.925i	−0.279422	+	0.483973i
$848$	−107.098	+	294.250i	−0.126295	+	0.346992i
$849$	425.752	+	1546.64i	0.501475	+	1.82172i
$850$	17.8428	+	14.9719i	0.0209915	+	0.0176140i
$851$	−97.6418	+	116.365i	−0.114738	+	0.136739i
$852$	217.746	−	59.9403i	0.255571	−	0.0703525i
$853$	−776.870	−	282.757i	−0.910750	−	0.331486i	−0.156198	−	0.987726i	$-0.549924\pi$
$853$	−776.870	−	282.757i	−0.910750	−	0.331486i	−0.754552	+	0.656240i	$0.772146\pi$
$854$	−74.2483	−	42.8673i	−0.0869418	−	0.0501959i
$855$	260.088	+	90.6646i	0.304197	+	0.106040i
$856$	−126.426	−	218.976i	−0.147694	−	0.255813i
$857$	277.851	−	48.9926i	0.324213	−	0.0571676i	−0.00917282	−	0.999958i	$-0.502920\pi$
$857$	277.851	−	48.9926i	0.324213	−	0.0571676i	0.333386	+	0.942790i	$0.391809\pi$
$858$	−62.7395	−	88.3126i	−0.0731229	−	0.102928i
$859$	874.383	−	318.250i	1.01791	−	0.370488i	0.221444	−	0.975173i	$-0.428923\pi$
$859$	874.383	−	318.250i	1.01791	−	0.370488i	0.796465	+	0.604685i	$0.206701\pi$
$860$	−101.275	−	17.8576i	−0.117762	−	0.0207646i
$861$	175.169	+	369.055i	0.203448	+	0.428636i
$862$	234.066	−	196.405i	0.271538	−	0.227848i
$863$		−	891.370i		−	1.03287i	−0.856325	−	0.516437i	$-0.827258\pi$
$863$		−	891.370i		−	1.03287i	0.856325	−	0.516437i	$-0.172742\pi$
$864$	−151.850	+	16.4232i	−0.175752	+	0.0190084i
$865$	−262.544			−0.303519
$866$	−19.4760	−	23.2106i	−0.0224896	−	0.0268021i
$867$	67.0535	−	831.750i	0.0773396	−	0.959343i
$868$	33.4612	−	189.768i	0.0385498	−	0.218627i
$869$	89.2261	+	245.147i	0.102677	+	0.282102i
$870$	−137.136	−	62.8122i	−0.157628	−	0.0721979i
$871$	24.3900	+	138.323i	0.0280023	+	0.158809i
$872$	7.44955	−	4.30100i	0.00854307	−	0.00493234i
$873$	−22.2779	−	1632.43i	−0.0255188	−	1.86991i
$874$	122.091	−	211.468i	0.139692	−	0.241954i
$875$	−15.5223	+	42.6471i	−0.0177397	+	0.0487395i
$876$	510.171	+	132.976i	0.582387	+	0.151799i
$877$	926.115	+	777.103i	1.05600	+	0.886092i	0.993712	−	0.111966i	$-0.0357147\pi$
$877$	926.115	+	777.103i	1.05600	+	0.886092i	0.0622914	+	0.998058i	$0.480159\pi$
$878$	10.8127	−	12.8861i	0.0123152	−	0.0146766i
$879$	−1121.18	−	1105.98i	−1.27552	−	1.25823i
$880$	17.6155	+	6.41153i	0.0200177	+	0.00728583i
$881$	612.796	+	353.798i	0.695569	+	0.401587i	0.805695	−	0.592331i	$-0.201792\pi$
$881$	612.796	+	353.798i	0.695569	+	0.401587i	−0.110126	+	0.993918i	$0.535125\pi$
$882$	66.3107	−	408.595i	0.0751822	−	0.463260i
$883$	512.059	+	886.911i	0.579908	+	1.00443i	0.995489	+	0.0948738i	$0.0302448\pi$
$883$	512.059	+	886.911i	0.579908	+	1.00443i	−0.415582	+	0.909556i	$0.636422\pi$
$884$	−79.0410	+	13.9371i	−0.0894129	+	0.0157659i
$885$	212.912	−	20.0921i	0.240579	−	0.0227030i
$886$	350.435	−	127.548i	0.395525	−	0.143959i
$887$	−371.403	−	65.4884i	−0.418719	−	0.0738314i	−0.0396804	−	0.999212i	$-0.512634\pi$
$887$	−371.403	−	65.4884i	−0.418719	−	0.0738314i	−0.379038	+	0.925381i	$0.623745\pi$
$888$	−58.0310	+	84.0922i	−0.0653502	+	0.0946984i
$889$	260.467	−	218.557i	0.292988	−	0.245846i
$890$		−	308.161i		−	0.346248i
$891$	62.3951	+	157.884i	0.0700281	+	0.177198i
$892$	−594.573			−0.666562
$893$	388.848	+	463.411i	0.435440	+	0.518938i
$894$	795.795	+	549.168i	0.890151	+	0.614282i
$895$	−53.4790	+	303.295i	−0.0597531	+	0.338877i
$896$	−15.7074	−	43.1558i	−0.0175306	−	0.0481650i
$897$	43.3183	+	459.035i	0.0482924	+	0.511745i
$898$	−104.415	−	592.165i	−0.116275	−	0.659427i
$899$	−326.821	+	188.690i	−0.363538	+	0.209889i
$900$	56.9047	−	69.7270i	0.0632274	−	0.0774744i
$901$	128.933	−	223.319i	0.143100	−	0.247857i
$902$	−34.0073	+	93.4343i	−0.0377021	+	0.103586i
$903$	196.656	−	199.359i	0.217781	−	0.220774i
$904$	−214.836	−	180.269i	−0.237651	−	0.199413i
$905$	23.6138	−	28.1418i	0.0260926	−	0.0310960i
$906$	74.0770	−	284.202i	0.0817627	−	0.313689i
$907$	1203.77	+	438.138i	1.32720	+	0.483063i	0.905760	−	0.423791i	$-0.139301\pi$
$907$	1203.77	+	438.138i	1.32720	+	0.483063i	0.421445	+	0.906854i	$0.361523\pi$
$908$	398.927	+	230.321i	0.439347	+	0.253657i
$909$	16.4183	+	27.5619i	0.0180620	+	0.0303211i
$910$	−78.1925	−	135.433i	−0.0859258	−	0.148828i
$911$	−95.6124	+	16.8591i	−0.104953	+	0.0185061i	−0.225878	−	0.974156i	$-0.572525\pi$
$911$	−95.6124	+	16.8591i	−0.104953	+	0.0185061i	0.120925	+	0.992662i	$0.461414\pi$
$912$	68.3933	−	149.322i	0.0749927	−	0.163730i
$913$	−259.140	+	94.3192i	−0.283833	+	0.103307i
$914$	−645.826	−	113.877i	−0.706593	−	0.124591i
$915$	−99.8601	−	8.05045i	−0.109137	−	0.00879831i
$916$	−109.344	+	91.7508i	−0.119372	+	0.100165i
$917$			677.705i			0.739046i
$918$	125.497	+	8.39534i	0.136707	+	0.00914525i
$919$	1106.59			1.20412			0.602062	−	0.798450i	$-0.294346\pi$
$919$	1106.59			1.20412			0.602062	+	0.798450i	$0.294346\pi$
$920$	−51.2862	−	61.1205i	−0.0557459	−	0.0664354i
$921$	−664.592	+	315.443i	−0.721599	+	0.342500i
$922$	−87.1696	+	494.363i	−0.0945440	+	0.536186i
$923$	−156.841	−	430.917i	−0.169925	−	0.466865i
$924$	−41.6140	+	29.5636i	−0.0450368	+	0.0319953i
$925$	−10.4546	−	59.2907i	−0.0113022	−	0.0640981i
$926$	210.875	−	121.749i	0.227727	−	0.131478i
$927$	722.720	+	837.814i	0.779633	+	0.903791i
$928$	−44.9708	+	77.8918i	−0.0484600	+	0.0839351i
$929$	−208.291	+	572.275i	−0.224210	+	0.616012i	−0.999886	−	0.0151197i	$-0.995187\pi$
$929$	−208.291	+	572.275i	−0.224210	+	0.616012i	0.775676	+	0.631132i	$0.217409\pi$
$930$	−59.7615	−	217.097i	−0.0642597	−	0.233437i
$931$	340.982	+	286.118i	0.366253	+	0.307323i
$932$	271.406	−	323.449i	0.291208	−	0.347049i
$933$	996.721	−	274.373i	1.06830	−	0.294076i
$934$	−419.041	−	152.518i	−0.448652	−	0.163296i
$935$	−13.3692	−	7.71871i	−0.0142986	−	0.00825530i
$936$	58.0149	+	304.648i	0.0619817	+	0.325479i
$937$	162.837	+	282.043i	0.173786	+	0.301006i	0.939740	−	0.341889i	$-0.111067\pi$
$937$	162.837	+	282.043i	0.173786	+	0.301006i	−0.765955	+	0.642895i	$0.777733\pi$
$938$	65.1794	−	11.4929i	0.0694876	−	0.0122525i
$939$	120.470	+	169.575i	0.128296	+	0.180591i
$940$	185.745	−	67.6057i	0.197601	−	0.0719210i
$941$	−780.797	−	137.676i	−0.829752	−	0.146308i	−0.257389	−	0.966308i	$-0.582862\pi$
$941$	−780.797	−	137.676i	−0.829752	−	0.146308i	−0.572363	+	0.820000i	$0.693973\pi$
$942$	−347.108	−	731.307i	−0.368480	−	0.776334i
$943$	324.188	−	272.026i	0.343784	−	0.288469i
$944$		−	127.520i		−	0.135085i
$945$	68.2618	+	235.375i	0.0722347	+	0.249075i
$946$	68.1581			0.0720487
$947$	184.240	+	219.569i	0.194551	+	0.231857i	0.854497	−	0.519456i	$-0.173865\pi$
$947$	184.240	+	219.569i	0.194551	+	0.231857i	−0.659946	+	0.751313i	$0.729421\pi$
$948$	60.0134	−	744.423i	0.0633052	−	0.785256i
$949$	185.889	−	1054.23i	0.195879	−	1.11089i
$950$	33.1004	+	90.9425i	0.0348425	+	0.0957289i
$951$	1337.10	+	612.427i	1.40599	+	0.643982i
$952$	6.56732	+	37.2451i	0.00689845	+	0.0391230i
$953$	495.147	−	285.873i	0.519566	−	0.299972i	−0.217191	−	0.976129i	$-0.569689\pi$
$953$	495.147	−	285.873i	0.519566	−	0.299972i	0.736757	+	0.676157i	$0.236356\pi$
$954$	−869.613	−	486.372i	−0.911544	−	0.509824i
$955$	−133.087	+	230.513i	−0.139358	+	0.241375i
$956$	−138.208	+	379.724i	−0.144569	+	0.397201i
$957$	96.7385	+	25.2148i	0.101085	+	0.0263478i
$958$	−826.515	−	693.529i	−0.862751	−	0.723934i
$959$	424.884	−	506.357i	0.443049	−	0.528006i
$960$	−38.2054	−	37.6875i	−0.0397973	−	0.0392578i
$961$	373.659	+	136.001i	0.388823	+	0.141520i
$962$	179.662	+	103.728i	0.186759	+	0.107826i
$963$	752.223	−	285.470i	0.781125	−	0.296439i
$964$	281.233	+	487.110i	0.291735	+	0.505300i
$965$	−267.093	+	47.0957i	−0.276780	+	0.0488038i
$966$	216.303	−	20.4121i	0.223916	−	0.0211306i
$967$	351.727	−	128.018i	0.363730	−	0.132387i	−0.153689	−	0.988119i	$-0.549115\pi$
$967$	351.727	−	128.018i	0.363730	−	0.132387i	0.517418	+	0.855733i	$0.326893\pi$
$968$	324.805	+	57.2718i	0.335542	+	0.0591651i
$969$	−76.8193	+	111.318i	−0.0792769	+	0.114879i
$970$	439.427	−	368.723i	0.453017	−	0.380127i
$971$			1085.93i			1.11836i	0.829046	+	0.559180i	$0.188884\pi$
$971$			1085.93i			1.11836i	−0.829046	+	0.559180i	$0.811116\pi$
$972$	25.8192	−	485.314i	0.0265630	−	0.499294i
$973$	358.572			0.368522
$974$	752.528	+	896.828i	0.772616	+	0.920768i
$975$	−150.405	−	103.793i	−0.154262	−	0.106454i
$976$	−10.3734	+	58.8307i	−0.0106285	+	0.0602773i
$977$	233.624	+	641.877i	0.239124	+	0.656988i	0.999968	+	0.00805242i	$0.00256319\pi$
$977$	233.624	+	641.877i	0.239124	+	0.656988i	−0.760844	+	0.648935i	$0.775215\pi$
$978$	−111.221	−	1178.58i	−0.113723	−	1.20510i
$979$	35.4660	+	201.138i	0.0362268	+	0.205452i
$980$	125.958	−	72.7220i	0.128529	−	0.0742062i
$981$	9.71168	+	25.5906i	0.00989978	+	0.0260862i
$982$	142.621	−	247.026i	0.145235	−	0.251554i
$983$	−573.585	+	1575.91i	−0.583504	+	1.60317i	0.198643	+	0.980072i	$0.436347\pi$
$983$	−573.585	+	1575.91i	−0.583504	+	1.60317i	−0.782147	+	0.623093i	$0.785876\pi$
$984$	199.898	−	202.644i	0.203148	−	0.205939i
$985$	334.196	+	280.424i	0.339285	+	0.284694i
$986$	47.6094	−	56.7387i	0.0482854	−	0.0575443i
$987$	−135.759	+	520.851i	−0.137548	+	0.527711i
$988$	−313.371	−	114.058i	−0.317177	−	0.115443i
$989$	−251.230	−	145.047i	−0.254024	−	0.146661i
$990$	−29.1171	+	52.0603i	−0.0294112	+	0.0525861i
$991$	227.082	+	393.318i	0.229145	+	0.396890i	0.957555	−	0.288251i	$-0.0930738\pi$
$991$	227.082	+	393.318i	0.229145	+	0.396890i	−0.728410	+	0.685141i	$0.759740\pi$
$992$	−132.227	+	23.3152i	−0.133293	+	0.0235032i
$993$	405.034	−	884.301i	0.407889	−	0.890535i
$994$	−203.053	+	73.9054i	−0.204279	+	0.0743515i
$995$	92.9120	+	16.3829i	0.0933789	+	0.0164652i
$996$	786.915	+	63.4390i	0.790075	+	0.0636937i
$997$	435.729	−	365.620i	0.437040	−	0.366720i	−0.397561	−	0.917576i	$-0.630143\pi$
$997$	435.729	−	365.620i	0.437040	−	0.366720i	0.834600	+	0.550856i	$0.185699\pi$
$998$			597.924i			0.599122i
$999$	−234.544	−	225.133i	−0.234779	−	0.225359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.3.o.a.221.10	yes	144
27.11	odd	18	inner	270.3.o.a.11.10	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.3.o.a.11.10	✓	144	27.11	odd	18	inner
270.3.o.a.221.10	yes	144	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(2.46914 + 1.70392i) q^{3} +(-0.347296 + 1.96962i) q^{4} +(-0.764780 - 2.10122i) q^{5} +(-0.398600 - 4.22387i) q^{6} +(0.704886 + 3.99761i) q^{7} +(2.44949 - 1.41421i) q^{8} +(3.19330 + 8.41444i) q^{9} +(-1.58114 + 2.73861i) q^{10} +(0.716831 - 1.96948i) q^{11} +(-4.21359 + 4.27149i) q^{12} +(9.33255 + 7.83094i) q^{13} +(3.69004 - 4.39762i) q^{14} +(1.69196 - 6.49132i) q^{15} +(-3.75877 - 1.36808i) q^{16} +(2.85269 + 1.64700i) q^{17} +(6.21295 - 11.1085i) q^{18} +(6.84331 + 11.8530i) q^{19} +(4.40419 - 0.776578i) q^{20} +(-5.07115 + 11.0717i) q^{21} +(-2.78526 + 1.01375i) q^{22} +(12.4238 + 2.19065i) q^{23} +(8.45784 + 0.681849i) q^{24} +(-3.83022 + 3.21394i) q^{25} -17.2291i q^{26} +(-6.45285 + 26.2176i) q^{27} -8.11855 q^{28} +(10.2201 + 12.1798i) q^{29} +(-8.57043 + 4.06788i) q^{30} +(-4.12158 + 23.3746i) q^{31} +(1.93476 + 5.31570i) q^{32} +(5.12579 - 3.64149i) q^{33} +(-0.808928 - 4.58766i) q^{34} +(7.86075 - 4.53841i) q^{35} +(-17.6822 + 3.36727i) q^{36} +(-6.02054 + 10.4279i) q^{37} +(6.62007 - 18.1885i) q^{38} +(9.70006 + 35.2376i) q^{39} +(-4.84489 - 4.06535i) q^{40} +(21.5629 - 25.6977i) q^{41} +(16.6044 - 4.57079i) q^{42} +(-21.6084 - 7.86482i) q^{43} +(3.63016 + 2.09587i) q^{44} +(15.2384 - 13.1450i) q^{45} +(-8.92048 - 15.4507i) q^{46} +(43.5279 - 7.67515i) q^{47} +(-6.94983 - 9.78263i) q^{48} +(30.5610 - 11.1233i) q^{49} +(6.96364 + 1.22788i) q^{50} +(4.23733 + 8.92745i) q^{51} +(-18.6651 + 15.6619i) q^{52} -78.2835i q^{53} +(34.2687 - 16.8421i) q^{54} -4.68652 q^{55} +(7.38008 + 8.79524i) q^{56} +(-3.29943 + 40.9271i) q^{57} +(3.90455 - 22.1438i) q^{58} +(10.9036 + 29.9575i) q^{59} +(12.1978 + 5.58692i) q^{60} +(-2.59336 - 14.7077i) q^{61} +(29.0696 - 16.7833i) q^{62} +(-31.3867 + 18.6968i) q^{63} +(4.00000 - 6.92820i) q^{64} +(9.31715 - 25.5987i) q^{65} +(-8.60456 - 2.24277i) q^{66} +(8.83180 + 7.41076i) q^{67} +(-4.23469 + 5.04671i) q^{68} +(26.9434 + 26.5782i) q^{69} +(-12.0624 - 4.39036i) q^{70} +(-32.5980 - 18.8205i) q^{71} +(19.7218 + 16.0951i) q^{72} +(-43.9347 - 76.0971i) q^{73} +(16.7699 - 2.95699i) q^{74} +(-14.9337 + 1.40926i) q^{75} +(-25.7224 + 9.36220i) q^{76} +(8.37848 + 1.47735i) q^{77} +(29.3570 - 42.5410i) q^{78} +(-95.3518 + 80.0097i) q^{79} +8.94427i q^{80} +(-60.6057 + 53.7397i) q^{81} -47.4412 q^{82} +(-84.5767 - 100.795i) q^{83} +(-20.0458 - 13.8334i) q^{84} +(1.27903 - 7.25372i) q^{85} +(11.1225 + 30.5589i) q^{86} +(4.48134 + 47.4878i) q^{87} +(-1.02939 - 5.83797i) q^{88} +(-84.3933 + 48.7245i) q^{89} +(-28.0929 - 4.55919i) q^{90} +(-24.7266 + 42.8278i) q^{91} +(-8.62948 + 23.7093i) q^{92} +(-50.0053 + 50.6924i) q^{93} +(-47.8835 - 40.1790i) q^{94} +(19.6720 - 23.4442i) q^{95} +(-4.28036 + 16.4219i) q^{96} +(-170.458 - 62.0418i) q^{97} +(-39.8315 - 22.9967i) q^{98} +(18.8611 - 0.257399i) 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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