LMFDB - Embedded newform 840.2.cf.a.101.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(101,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.cf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$128$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.17
Character	$\chi$	$=$	840.101
Dual form			840.2.cf.a.341.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30091 - 0.554645i) q^{2} +(-1.41157 + 1.00373i) q^{3} +(1.38474 + 1.44309i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(2.39304 - 0.522843i) q^{6} +(2.47291 + 0.940605i) q^{7} +(-1.00102 - 2.64537i) q^{8} +(0.985054 - 2.83367i) q^{9} +(1.40394 - 0.170119i) q^{10} +(-1.85655 + 3.21564i) q^{11} +(-3.40312 - 0.647116i) q^{12} +6.09443 q^{13} +(-2.69533 - 2.59523i) q^{14} +(0.720590 - 1.57504i) q^{15} +(-0.165004 + 3.99660i) q^{16} +(1.02488 - 1.77515i) q^{17} +(-2.85315 + 3.13999i) q^{18} +(-2.22451 - 3.85297i) q^{19} +(-1.92076 - 0.557382i) q^{20} +(-4.43479 + 1.15440i) q^{21} +(4.19875 - 3.15354i) q^{22} +(5.38747 - 3.11046i) q^{23} +(4.06824 + 2.72937i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-7.92831 - 3.38025i) q^{26} +(1.45376 + 4.98864i) q^{27} +(2.06695 + 4.87111i) q^{28} +1.24278 q^{29} +(-1.81101 + 1.64931i) q^{30} +(-6.71818 - 3.87874i) q^{31} +(2.43135 - 5.10769i) q^{32} +(-0.606984 - 6.40258i) q^{33} +(-2.31786 + 1.74086i) q^{34} +(-2.61190 + 0.421865i) q^{35} +(5.45327 - 2.50237i) q^{36} +(0.0470857 - 0.0271850i) q^{37} +(0.756861 + 6.24618i) q^{38} +(-8.60271 + 6.11716i) q^{39} +(2.18959 + 1.79045i) q^{40} +4.69122 q^{41} +(6.40955 + 0.957965i) q^{42} +6.68450i q^{43} +(-7.21129 + 1.77365i) q^{44} +(0.563752 + 2.94655i) q^{45} +(-8.73382 + 1.05829i) q^{46} +(6.22372 + 10.7798i) q^{47} +(-3.77859 - 5.80709i) q^{48} +(5.23052 + 4.65206i) q^{49} +(-1.13079 + 0.849299i) q^{50} +(0.335077 + 3.53445i) q^{51} +(8.43918 + 8.79480i) q^{52} +(-1.35995 + 2.35551i) q^{53} +(0.875710 - 7.29610i) q^{54} -3.71310i q^{55} +(0.0128224 - 7.48330i) q^{56} +(7.00739 + 3.20592i) q^{57} +(-1.61674 - 0.689300i) q^{58} +(6.29130 + 3.63228i) q^{59} +(3.27075 - 1.14114i) q^{60} +(-4.32809 - 7.49648i) q^{61} +(6.58842 + 8.77210i) q^{62} +(5.10131 - 6.08084i) q^{63} +(-5.99593 + 5.29612i) q^{64} +(-5.27793 + 3.04721i) q^{65} +(-2.76153 + 8.66584i) q^{66} +(3.73488 + 2.15633i) q^{67} +(3.98089 - 0.979120i) q^{68} +(-4.48273 + 9.79819i) q^{69} +(3.63184 + 0.899870i) q^{70} +6.67812i q^{71} +(-8.48214 + 0.230724i) q^{72} +(8.02450 + 4.63295i) q^{73} +(-0.0763324 + 0.00924933i) q^{74} +(0.163471 + 1.72432i) q^{75} +(2.47981 - 8.54551i) q^{76} +(-7.61573 + 6.20570i) q^{77} +(14.5842 - 3.18643i) q^{78} +(6.87818 + 11.9134i) q^{79} +(-1.85540 - 3.54366i) q^{80} +(-7.05934 - 5.58263i) q^{81} +(-6.10286 - 2.60196i) q^{82} -13.7830i q^{83} +(-7.80692 - 4.80125i) q^{84} +2.04977i q^{85} +(3.70752 - 8.69593i) q^{86} +(-1.75426 + 1.24741i) q^{87} +(10.3650 + 1.69234i) q^{88} +(3.59457 + 6.22597i) q^{89} +(0.900901 - 4.14589i) q^{90} +(15.0709 + 5.73245i) q^{91} +(11.9489 + 3.46743i) q^{92} +(13.3764 - 1.26812i) q^{93} +(-2.11754 - 17.4755i) q^{94} +(3.85297 + 2.22451i) q^{95} +(1.69473 + 9.65028i) q^{96} -10.4589i q^{97} +(-4.22420 - 8.95299i) q^{98} +(7.28326 + 8.42843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) $ 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.30091	−	0.554645i	−0.919883	−	0.392193i
$2$	−1.30091	−	0.554645i	−0.919883	−	0.392193i
$3$	−1.41157	+	1.00373i	−0.814970	+	0.579504i
$3$	−1.41157	+	1.00373i	−0.814970	+	0.579504i
$4$	1.38474	+	1.44309i	0.692369	+	0.721544i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	2.39304	−	0.522843i	0.976954	−	0.213450i
$7$	2.47291	+	0.940605i	0.934670	+	0.355515i
$7$	2.47291	+	0.940605i	0.934670	+	0.355515i
$8$	−1.00102	−	2.64537i	−0.353913	−	0.935278i
$9$	0.985054	−	2.83367i	0.328351	−	0.944556i
$10$	1.40394	−	0.170119i	0.443966	−	0.0537962i
$11$	−1.85655	+	3.21564i	−0.559772	+	0.969553i	0.437744	+	0.899100i	$0.355778\pi$
$11$	−1.85655	+	3.21564i	−0.559772	+	0.969553i	−0.997515	+	0.0704529i	$0.977556\pi$
$12$	−3.40312	−	0.647116i	−0.982397	−	0.186806i
$13$	6.09443			1.69029			0.845145	−	0.534537i	$-0.179514\pi$
$13$	6.09443			1.69029			0.845145	+	0.534537i	$0.179514\pi$
$14$	−2.69533	−	2.59523i	−0.720356	−	0.693604i
$15$	0.720590	−	1.57504i	0.186055	−	0.406674i
$16$	−0.165004	+	3.99660i	−0.0412511	+	0.999149i
$17$	1.02488	−	1.77515i	0.248571	−	0.430537i	−0.714559	−	0.699575i	$-0.753373\pi$
$17$	1.02488	−	1.77515i	0.248571	−	0.430537i	0.963129	+	0.269038i	$0.0867059\pi$
$18$	−2.85315	+	3.13999i	−0.672493	+	0.740103i
$19$	−2.22451	−	3.85297i	−0.510338	−	0.883931i	−0.999928	−	0.0119787i	$-0.996187\pi$
$19$	−2.22451	−	3.85297i	−0.510338	−	0.883931i	0.489590	−	0.871953i	$-0.337146\pi$
$20$	−1.92076	−	0.557382i	−0.429495	−	0.124634i
$21$	−4.43479	+	1.15440i	−0.967751	+	0.251911i
$22$	4.19875	−	3.15354i	0.895176	−	0.672336i
$23$	5.38747	−	3.11046i	1.12337	−	0.648576i	0.181108	−	0.983463i	$-0.442032\pi$
$23$	5.38747	−	3.11046i	1.12337	−	0.648576i	0.942258	+	0.334888i	$0.108698\pi$
$24$	4.06824	+	2.72937i	0.830426	+	0.557129i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−7.92831	−	3.38025i	−1.55487	−	0.662921i
$27$	1.45376	+	4.98864i	0.279777	+	0.960065i
$28$	2.06695	+	4.87111i	0.390617	+	0.920553i
$29$	1.24278			0.230778			0.115389	−	0.993320i	$-0.463189\pi$
$29$	1.24278			0.230778			0.115389	+	0.993320i	$0.463189\pi$
$30$	−1.81101	+	1.64931i	−0.330644	+	0.301122i
$31$	−6.71818	−	3.87874i	−1.20662	−	0.696643i	−0.244601	−	0.969624i	$-0.578657\pi$
$31$	−6.71818	−	3.87874i	−1.20662	−	0.696643i	−0.962019	+	0.272981i	$0.911990\pi$
$32$	2.43135	−	5.10769i	0.429806	−	0.902921i
$33$	−0.606984	−	6.40258i	−0.105662	−	1.11455i
$34$	−2.31786	+	1.74086i	−0.397510	+	0.298556i
$35$	−2.61190	+	0.421865i	−0.441492	+	0.0713081i
$36$	5.45327	−	2.50237i	0.908878	−	0.417061i
$37$	0.0470857	−	0.0271850i	0.00774085	−	0.00446918i	−0.496125	−	0.868251i	$-0.665244\pi$
$37$	0.0470857	−	0.0271850i	0.00774085	−	0.00446918i	0.503865	+	0.863782i	$0.331911\pi$
$38$	0.756861	+	6.24618i	0.122779	+	1.01326i
$39$	−8.60271	+	6.11716i	−1.37754	+	0.979529i
$40$	2.18959	+	1.79045i	0.346205	+	0.283094i
$41$	4.69122			0.732646			0.366323	−	0.930488i	$-0.380617\pi$
$41$	4.69122			0.732646			0.366323	+	0.930488i	$0.380617\pi$
$42$	6.40955	+	0.957965i	0.989015	+	0.147817i
$43$			6.68450i			1.01938i	0.860359	+	0.509688i	$0.170239\pi$
$43$			6.68450i			1.01938i	−0.860359	+	0.509688i	$0.829761\pi$
$44$	−7.21129	+	1.77365i	−1.08714	+	0.267388i
$45$	0.563752	+	2.94655i	0.0840392	+	0.439246i
$46$	−8.73382	+	1.05829i	−1.28773	+	0.156037i
$47$	6.22372	+	10.7798i	0.907823	+	1.57240i	0.817082	+	0.576521i	$0.195590\pi$
$47$	6.22372	+	10.7798i	0.907823	+	1.57240i	0.0907407	+	0.995875i	$0.471077\pi$
$48$	−3.77859	−	5.80709i	−0.545392	−	0.838181i
$49$	5.23052	+	4.65206i	0.747218	+	0.664579i
$50$	−1.13079	+	0.849299i	−0.159918	+	0.120109i
$51$	0.335077	+	3.53445i	0.0469202	+	0.494922i
$52$	8.43918	+	8.79480i	1.17030	+	1.21962i
$53$	−1.35995	+	2.35551i	−0.186804	+	0.323554i	−0.944183	−	0.329422i	$-0.893146\pi$
$53$	−1.35995	+	2.35551i	−0.186804	+	0.323554i	0.757379	+	0.652976i	$0.226480\pi$
$54$	0.875710	−	7.29610i	0.119169	−	0.992874i
$55$		−	3.71310i		−	0.500675i
$56$	0.0128224	−	7.48330i	0.00171346	−	0.999999i
$57$	7.00739	+	3.20592i	0.928151	+	0.424635i
$58$	−1.61674	−	0.689300i	−0.212289	−	0.0905095i
$59$	6.29130	+	3.63228i	0.819058	+	0.472883i	0.850091	−	0.526635i	$-0.176547\pi$
$59$	6.29130	+	3.63228i	0.819058	+	0.472883i	−0.0310337	+	0.999518i	$0.509880\pi$
$60$	3.27075	−	1.14114i	0.422252	−	0.147321i
$61$	−4.32809	−	7.49648i	−0.554156	−	0.959826i	−0.997969	−	0.0637065i	$-0.979708\pi$
$61$	−4.32809	−	7.49648i	−0.554156	−	0.959826i	0.443813	−	0.896119i	$-0.353625\pi$
$62$	6.58842	+	8.77210i	0.836731	+	1.11406i
$63$	5.10131	−	6.08084i	0.642704	−	0.766114i
$64$	−5.99593	+	5.29612i	−0.749491	+	0.662015i
$65$	−5.27793	+	3.04721i	−0.654647	+	0.377960i
$66$	−2.76153	+	8.66584i	−0.339920	+	1.06669i
$67$	3.73488	+	2.15633i	0.456288	+	0.263438i	0.710482	−	0.703715i	$-0.248477\pi$
$67$	3.73488	+	2.15633i	0.456288	+	0.263438i	−0.254194	+	0.967153i	$0.581810\pi$
$68$	3.98089	−	0.979120i	0.482754	−	0.118736i
$69$	−4.48273	+	9.79819i	−0.539657	+	1.17956i
$70$	3.63184	+	0.899870i	0.434087	+	0.107555i
$71$			6.67812i			0.792547i	0.918133	+	0.396273i	$0.129697\pi$
$71$			6.67812i			0.792547i	−0.918133	+	0.396273i	$0.870303\pi$
$72$	−8.48214	+	0.230724i	−0.999630	+	0.0271911i
$73$	8.02450	+	4.63295i	0.939197	+	0.542246i	0.889708	−	0.456529i	$-0.150908\pi$
$73$	8.02450	+	4.63295i	0.939197	+	0.542246i	0.0494884	+	0.998775i	$0.484241\pi$
$74$	−0.0763324	+	0.00924933i	−0.00887346	+	0.00107521i
$75$	0.163471	+	1.72432i	0.0188760	+	0.199107i
$76$	2.47981	−	8.54551i	0.284453	−	0.980238i
$77$	−7.61573	+	6.20570i	−0.867893	+	0.707205i
$78$	14.5842	−	3.18643i	1.65134	−	0.360792i
$79$	6.87818	+	11.9134i	0.773856	+	1.34036i	0.935435	+	0.353498i	$0.115008\pi$
$79$	6.87818	+	11.9134i	0.773856	+	1.34036i	−0.161579	+	0.986860i	$0.551659\pi$
$80$	−1.85540	−	3.54366i	−0.207440	−	0.396193i
$81$	−7.05934	−	5.58263i	−0.784371	−	0.620292i
$82$	−6.10286	−	2.60196i	−0.673948	−	0.287339i
$83$		−	13.7830i		−	1.51288i	−0.654061	−	0.756442i	$-0.726936\pi$
$83$		−	13.7830i		−	1.51288i	0.654061	−	0.756442i	$-0.273064\pi$
$84$	−7.80692	−	4.80125i	−0.851805	−	0.523859i
$85$			2.04977i			0.222328i
$86$	3.70752	−	8.69593i	0.399793	−	0.937706i
$87$	−1.75426	+	1.24741i	−0.188077	+	0.133737i
$88$	10.3650	+	1.69234i	1.10491	+	0.180404i
$89$	3.59457	+	6.22597i	0.381023	+	0.659952i	0.991209	−	0.132307i	$-0.0422384\pi$
$89$	3.59457	+	6.22597i	0.381023	+	0.659952i	−0.610186	+	0.792259i	$0.708905\pi$
$90$	0.900901	−	4.14589i	0.0949633	−	0.437015i
$91$	15.0709	+	5.73245i	1.57986	+	0.600924i
$92$	11.9489	+	3.46743i	1.24576	+	0.361504i
$93$	13.3764	−	1.26812i	1.38707	−	0.131498i
$94$	−2.11754	−	17.4755i	−0.218408	−	1.80246i
$95$	3.85297	+	2.22451i	0.395306	+	0.228230i
$96$	1.69473	+	9.65028i	0.172968	+	0.984928i
$97$		−	10.4589i		−	1.06194i	−0.847392	−	0.530968i	$-0.821829\pi$
$97$		−	10.4589i		−	1.06194i	0.847392	−	0.530968i	$-0.178171\pi$
$98$	−4.22420	−	8.95299i	−0.426709	−	0.904389i
$99$	7.28326	+	8.42843i	0.731995	+	0.847089i
$100$	1.94212	−	0.477674i	0.194212	−	0.0477674i
$101$	−8.38258	−	4.83969i	−0.834098	−	0.481567i	0.0211557	−	0.999776i	$-0.493265\pi$
$101$	−8.38258	−	4.83969i	−0.834098	−	0.481567i	−0.855254	+	0.518209i	$0.826599\pi$
$102$	1.52446	−	4.78385i	0.150944	−	0.473672i
$103$	−8.88672	+	5.13075i	−0.875634	+	0.505548i	−0.869216	−	0.494432i	$-0.835376\pi$
$103$	−8.88672	+	5.13075i	−0.875634	+	0.505548i	−0.00641768	+	0.999979i	$0.502043\pi$
$104$	−6.10063	−	16.1220i	−0.598216	−	1.58089i
$105$	3.26344	−	3.21713i	0.318479	−	0.313960i
$106$	3.07565	−	2.31001i	0.298733	−	0.224368i
$107$	7.03895	+	12.1918i	0.680481	+	1.17863i	0.974834	+	0.222930i	$0.0715622\pi$
$107$	7.03895	+	12.1918i	0.680481	+	1.17863i	−0.294354	+	0.955696i	$0.595104\pi$
$108$	−5.18597	+	9.00587i	−0.499020	+	0.866590i
$109$	8.58379	+	4.95586i	0.822178	+	0.474685i	0.851167	−	0.524895i	$-0.175895\pi$
$109$	8.58379	+	4.95586i	0.822178	+	0.474685i	−0.0289887	+	0.999580i	$0.509229\pi$
$110$	−2.05946	+	4.83042i	−0.196361	+	0.460562i
$111$	−0.0391784	+	0.0856348i	−0.00371865	+	0.00812810i
$112$	−4.16726	+	9.72800i	−0.393769	+	0.919209i
$113$		−	1.14945i		−	0.108131i	−0.998537	−	0.0540655i	$-0.982782\pi$
$113$		−	1.14945i		−	0.108131i	0.998537	−	0.0540655i	$-0.0172180\pi$
$114$	−7.33784	−	8.05723i	−0.687252	−	0.754629i
$115$	−3.11046	+	5.38747i	−0.290052	+	0.502385i
$116$	1.72092	+	1.79344i	0.159783	+	0.166516i
$117$	6.00334	−	17.2696i	0.555009	−	1.59657i
$118$	−6.16979	−	8.21472i	−0.567975	−	0.756226i
$119$	4.20415	−	3.42577i	0.385394	−	0.314039i
$120$	−4.88788	−	0.329580i	−0.446200	−	0.0300864i
$121$	−1.39357	−	2.41374i	−0.126688	−	0.219431i
$122$	1.47258	+	12.1528i	0.133321	+	1.10026i
$123$	−6.62198	+	4.70872i	−0.597084	+	0.424571i
$124$	−3.70555	−	15.0660i	−0.332768	−	1.35296i
$125$			1.00000i			0.0894427i
$126$	−10.0091	+	5.08122i	−0.891678	+	0.452671i
$127$	−8.96398			−0.795424			−0.397712	−	0.917510i	$-0.630196\pi$
$127$	−8.96398			−0.795424			−0.397712	+	0.917510i	$0.630196\pi$
$128$	10.7376	−	3.56417i	0.949081	−	0.315031i
$129$	−6.70943	−	9.43563i	−0.590732	−	0.830761i
$130$	8.55624	−	1.03678i	0.750432	−	0.0909312i
$131$	−12.9937	+	7.50189i	−1.13526	+	0.655443i	−0.945253	−	0.326340i	$-0.894185\pi$
$131$	−12.9937	+	7.50189i	−1.13526	+	0.655443i	−0.190008	+	0.981783i	$0.560851\pi$
$132$	8.39897	−	9.74182i	0.731036	−	0.847917i
$133$	−1.87689	−	11.6204i	−0.162747	−	1.00762i
$134$	−3.66275	−	4.87673i	−0.316413	−	0.421285i
$135$	−3.75332	−	3.59341i	−0.323034	−	0.309272i
$136$	−5.72185	−	0.934234i	−0.490644	−	0.0801099i
$137$	−9.81061	−	5.66416i	−0.838177	−	0.483922i	0.0184673	−	0.999829i	$-0.494121\pi$
$137$	−9.81061	−	5.66416i	−0.838177	−	0.483922i	−0.856644	+	0.515908i	$0.827455\pi$
$138$	11.2662	−	10.2603i	0.959039	−	0.873411i
$139$	8.35456			0.708625			0.354312	−	0.935127i	$-0.384715\pi$
$139$	8.35456			0.708625			0.354312	+	0.935127i	$0.384715\pi$
$140$	−4.22559	−	3.18503i	−0.357127	−	0.269184i
$141$	−19.6052	−	8.96950i	−1.65106	−	0.755368i
$142$	3.70399	−	8.68764i	0.310832	−	0.729050i
$143$	−11.3146	+	19.5975i	−0.946177	+	1.63883i
$144$	11.1625	+	4.40443i	0.930207	+	0.367036i
$145$	−1.07628	+	0.621388i	−0.0893799	+	0.0516035i
$146$	−7.86952	−	10.4778i	−0.651286	−	0.867149i
$147$	−12.0527	−	1.31667i	−0.994086	−	0.108597i
$148$	0.104432	+	0.0303048i	0.00858423	+	0.00249104i
$149$	4.16644	+	7.21649i	0.341328	+	0.591198i	0.984680	−	0.174373i	$-0.0557899\pi$
$149$	4.16644	+	7.21649i	0.341328	+	0.591198i	−0.643352	+	0.765571i	$0.722457\pi$
$150$	0.743724	−	2.33385i	0.0607248	−	0.190558i
$151$	−9.84977	+	17.0603i	−0.801563	+	1.38835i	0.117024	+	0.993129i	$0.462665\pi$
$151$	−9.84977	+	17.0603i	−0.801563	+	1.38835i	−0.918587	+	0.395219i	$0.870669\pi$
$152$	−7.96573	+	9.74154i	−0.646106	+	0.790143i
$153$	−4.02062	−	4.65279i	−0.325048	−	0.376156i
$154$	13.3493	−	3.84903i	1.07572	−	0.310164i
$155$	7.75748			0.623096
$156$	−20.7401	−	3.94380i	−1.66054	−	0.315757i
$157$	7.84442	−	13.5869i	0.626053	−	1.08436i	−0.362283	−	0.932068i	$-0.618003\pi$
$157$	7.84442	−	13.5869i	0.626053	−	1.08436i	0.988336	−	0.152288i	$-0.0486640\pi$
$158$	−2.34021	−	19.3132i	−0.186177	−	1.53647i
$159$	−0.444626	−	4.68999i	−0.0352611	−	0.371940i
$160$	0.448238	+	5.63907i	0.0354363	+	0.445807i
$161$	16.2484	−	2.62439i	1.28056	−	0.206831i
$162$	6.08719	+	11.1779i	0.478255	+	0.878221i
$163$	15.2175	−	8.78580i	1.19192	−	0.688157i	0.233181	−	0.972433i	$-0.425087\pi$
$163$	15.2175	−	8.78580i	1.19192	−	0.688157i	0.958742	+	0.284276i	$0.0917532\pi$
$164$	6.49611	+	6.76984i	0.507261	+	0.528636i
$165$	3.72695	+	5.24130i	0.290143	+	0.408035i
$166$	−7.64469	+	17.9305i	−0.593343	+	1.39168i
$167$	−13.3735			−1.03487			−0.517437	−	0.855721i	$-0.673114\pi$
$167$	−13.3735			−1.03487			−0.517437	+	0.855721i	$0.673114\pi$
$168$	7.49311	+	10.5761i	0.578106	+	0.815961i
$169$	24.1421			1.85708
$170$	1.13689	−	2.66656i	0.0871957	−	0.204516i
$171$	−13.1093	+	2.50815i	−1.00249	+	0.191803i
$172$	−9.64631	+	9.25627i	−0.735525	+	0.705784i
$173$	−3.62060	+	2.09035i	−0.275269	+	0.158927i	−0.631280	−	0.775555i	$-0.717470\pi$
$173$	−3.62060	+	2.09035i	−0.275269	+	0.158927i	0.356011	+	0.934482i	$0.384137\pi$
$174$	2.97401	−	0.649777i	0.225459	−	0.0492594i
$175$	2.05104	−	1.67130i	0.155044	−	0.126338i
$176$	−12.5453	−	7.95048i	−0.945636	−	0.599290i
$177$	−12.5264	+	1.18755i	−0.941545	+	0.0892614i
$178$	−1.22300	−	10.0931i	−0.0916681	−	0.756513i
$179$	0.440634	−	0.763200i	0.0329345	−	0.0570443i	−0.849088	−	0.528251i	$-0.822848\pi$
$179$	0.440634	−	0.763200i	0.0329345	−	0.0570443i	0.882023	+	0.471207i	$0.156181\pi$
$180$	−3.47149	+	4.89375i	−0.258749	+	0.364758i
$181$	−8.96185			−0.666129			−0.333065	−	0.942904i	$-0.608083\pi$
$181$	−8.96185			−0.666129			−0.333065	+	0.942904i	$0.608083\pi$
$182$	−16.4265	−	15.8164i	−1.21761	−	1.17239i
$183$	13.6338	+	6.23756i	1.00784	+	0.461094i
$184$	−13.6213	−	11.1382i	−1.00417	−	0.821120i
$185$	−0.0271850	+	0.0470857i	−0.00199868	+	0.00346181i
$186$	−18.1048	−	5.76943i	−1.32751	−	0.423035i
$187$	3.80550	+	6.59131i	0.278285	+	0.482005i
$188$	−6.93798	+	23.9086i	−0.506004	+	1.74371i
$189$	−1.09732	+	13.7039i	−0.0798185	+	0.996809i
$190$	−3.77855	−	5.03092i	−0.274125	−	0.364981i
$191$	2.66689	−	1.53973i	0.192969	−	0.111411i	−0.400403	−	0.916339i	$-0.631130\pi$
$191$	2.66689	−	1.53973i	0.192969	−	0.111411i	0.593372	+	0.804929i	$0.297796\pi$
$192$	3.14779	−	13.4941i	0.227172	−	0.973855i
$193$	−7.42255	+	12.8562i	−0.534287	+	0.925412i	0.464911	+	0.885357i	$0.346086\pi$
$193$	−7.42255	+	12.8562i	−0.534287	+	0.925412i	−0.999198	+	0.0400541i	$0.987247\pi$
$194$	−5.80095	+	13.6060i	−0.416484	+	0.976856i
$195$	4.39158	−	9.59897i	0.314488	−	0.687396i
$196$	0.529576	+	13.9900i	0.0378269	+	0.999284i
$197$	14.4448			1.02915			0.514574	−	0.857446i	$-0.327950\pi$
$197$	14.4448			1.02915			0.514574	+	0.857446i	$0.327950\pi$
$198$	−4.80008	−	15.0043i	−0.341127	−	1.06631i
$199$	−15.8345	−	9.14203i	−1.12247	−	0.648061i	−0.180443	−	0.983585i	$-0.557753\pi$
$199$	−15.8345	−	9.14203i	−1.12247	−	0.648061i	−0.942032	+	0.335524i	$0.891087\pi$
$200$	−2.79146	−	0.455776i	−0.197386	−	0.0322282i
$201$	−7.43642	+	0.704996i	−0.524524	+	0.0497266i
$202$	8.22068	+	10.9454i	0.578405	+	0.770113i
$203$	3.07327	+	1.16896i	0.215701	+	0.0820451i
$204$	−4.63653	+	5.37783i	−0.324622	+	0.376524i
$205$	−4.06272	+	2.34561i	−0.283752	+	0.163825i
$206$	14.4066	−	1.74567i	1.00375	−	0.121627i
$207$	−3.50706	−	18.3303i	−0.243757	−	1.27404i
$208$	−1.00561	+	24.3570i	−0.0697264	+	1.68885i
$209$	16.5197			1.14269
$210$	−6.02981	+	2.37515i	−0.416097	+	0.163901i
$211$		−	4.15688i		−	0.286171i	−0.989710	−	0.143086i	$-0.954298\pi$
$211$		−	4.15688i		−	0.286171i	0.989710	−	0.143086i	$-0.0457024\pi$
$212$	−5.28238	+	1.29923i	−0.362796	+	0.0892314i
$213$	−6.70303	−	9.42663i	−0.459284	−	0.645902i
$214$	−2.39491	−	19.7646i	−0.163713	−	1.35108i
$215$	−3.34225	−	5.78894i	−0.227939	−	0.394803i
$216$	11.7415	−	8.83946i	0.798911	−	0.601449i
$217$	−12.9651	−	15.9109i	−0.880125	−	1.08010i
$218$	−8.41801	−	11.2081i	−0.570140	−	0.759107i
$219$	−15.9774	+	1.51470i	−1.07965	+	0.102354i
$220$	5.35834	−	5.14167i	0.361259	−	0.346652i
$221$	6.24608	−	10.8185i	0.420157	−	0.727732i
$222$	0.0984646	−	0.0896731i	0.00660851	−	0.00601847i
$223$		−	23.3392i		−	1.56291i	−0.623962	−	0.781455i	$-0.714478\pi$
$223$		−	23.3392i		−	1.56291i	0.623962	−	0.781455i	$-0.285522\pi$
$224$	10.8168	−	10.3439i	0.722729	−	0.691131i
$225$	−1.96150	−	2.26992i	−0.130767	−	0.151328i
$226$	−0.637536	+	1.49533i	−0.0424082	+	0.0994678i
$227$	9.87389	+	5.70069i	0.655353	+	0.378368i	0.790504	−	0.612457i	$-0.209819\pi$
$227$	9.87389	+	5.70069i	0.655353	+	0.378368i	−0.135151	+	0.990825i	$0.543152\pi$
$228$	5.07697	+	14.5516i	0.336231	+	0.963706i
$229$	−6.03573	−	10.4542i	−0.398852	−	0.690832i	0.594733	−	0.803924i	$-0.297258\pi$
$229$	−6.03573	−	10.4542i	−0.398852	−	0.690832i	−0.993585	+	0.113092i	$0.963925\pi$
$230$	7.03457	−	5.28342i	0.463846	−	0.348378i
$231$	4.52128	−	16.4039i	0.297479	−	1.07930i
$232$	−1.24404	−	3.28760i	−0.0816753	−	0.215841i
$233$	−7.49815	+	4.32906i	−0.491220	+	0.283606i	−0.725080	−	0.688664i	$-0.758197\pi$
$233$	−7.49815	+	4.32906i	−0.491220	+	0.283606i	0.233860	+	0.972270i	$0.424864\pi$
$234$	−17.3883	+	19.1365i	−1.13671	+	1.25099i
$235$	−10.7798	−	6.22372i	−0.703197	−	0.405991i
$236$	3.47010	+	14.1087i	0.225884	+	0.918396i
$237$	−21.6668	−	9.91270i	−1.40741	−	0.643899i
$238$	−7.36931	+	2.12480i	−0.477682	+	0.137730i
$239$		−	6.96486i		−	0.450519i	−0.974299	−	0.225260i	$-0.927677\pi$
$239$		−	6.96486i		−	0.450519i	0.974299	−	0.225260i	$-0.0723230\pi$
$240$	6.17590	+	3.13979i	0.398652	+	0.202673i
$241$	12.7589	+	7.36635i	0.821873	+	0.474509i	0.851062	−	0.525065i	$-0.175959\pi$
$241$	12.7589	+	7.36635i	0.821873	+	0.474509i	−0.0291890	+	0.999574i	$0.509292\pi$
$242$	0.474145	+	3.91299i	0.0304792	+	0.251537i
$243$	15.5682	+	0.794597i	0.998700	+	0.0509734i
$244$	4.82480	−	16.6265i	0.308876	−	1.06440i
$245$	−6.85579	−	1.41354i	−0.438001	−	0.0903076i
$246$	11.2263	−	2.45277i	0.715761	−	0.156383i
$247$	−13.5571	−	23.4816i	−0.862620	−	1.49410i
$248$	−3.53568	+	21.6547i	−0.224516	+	1.37508i
$249$	13.8344	+	19.4557i	0.876722	+	1.23295i
$250$	0.554645	−	1.30091i	0.0350788	−	0.0822768i
$251$		−	18.1064i		−	1.14286i	−0.820650	−	0.571432i	$-0.806388\pi$
$251$		−	18.1064i		−	1.14286i	0.820650	−	0.571432i	$-0.193612\pi$
$252$	15.8392	−	1.05874i	0.997773	−	0.0666943i
$253$			23.0989i			1.45222i
$254$	11.6613	+	4.97183i	0.731697	+	0.311960i
$255$	−2.05741	−	2.89339i	−0.128840	−	0.181191i
$256$	−15.9455	−	1.31891i	−0.996597	−	0.0824320i
$257$	−0.111463	−	0.193060i	−0.00695287	−	0.0120427i	0.862528	−	0.506009i	$-0.168880\pi$
$257$	−0.111463	−	0.193060i	−0.00695287	−	0.0120427i	−0.869481	+	0.493967i	$0.835547\pi$
$258$	3.49494	+	15.9963i	0.217585	+	0.995884i
$259$	0.142009	−	0.0229368i	0.00882401	−	0.00142522i
$260$	−11.7059	−	3.39692i	−0.725972	−	0.210668i
$261$	1.22420	−	3.52161i	0.0757762	−	0.217982i
$262$	21.0645	−	2.55242i	1.30137	−	0.157689i
$263$	2.77290	+	1.60093i	0.170984	+	0.0987178i	0.583050	−	0.812436i	$-0.301859\pi$
$263$	2.77290	+	1.60093i	0.170984	+	0.0987178i	−0.412066	+	0.911154i	$0.635193\pi$
$264$	−16.3296	+	8.01479i	−1.00501	+	0.493276i
$265$		−	2.71991i		−	0.167083i
$266$	−4.00354	+	16.1581i	−0.245473	+	0.990718i
$267$	−11.3232	−	5.18042i	−0.692967	−	0.317036i
$268$	2.06005	+	8.37572i	0.125838	+	0.511628i
$269$	−16.6455	−	9.61028i	−1.01489	−	0.585949i	−0.102273	−	0.994756i	$-0.532612\pi$
$269$	−16.6455	−	9.61028i	−1.01489	−	0.585949i	−0.912621	+	0.408807i	$0.865945\pi$
$270$	2.88967	+	6.75647i	0.175859	+	0.411185i
$271$	1.19595	−	0.690483i	0.0726489	−	0.0419439i	−0.463236	−	0.886235i	$-0.653312\pi$
$271$	1.19595	−	0.690483i	0.0726489	−	0.0419439i	0.535884	+	0.844291i	$0.319978\pi$
$272$	6.92544	+	4.38895i	0.419917	+	0.266119i
$273$	−27.0275	+	7.03540i	−1.63578	+	0.425802i
$274$	9.62113	+	12.8100i	0.581234	+	0.773879i
$275$	1.85655	+	3.21564i	0.111954	+	0.193911i
$276$	−20.3471	+	7.09895i	−1.22475	+	0.427307i
$277$	−6.38282	−	3.68512i	−0.383507	−	0.221418i	0.295836	−	0.955239i	$-0.404402\pi$
$277$	−6.38282	−	3.68512i	−0.383507	−	0.221418i	−0.679343	+	0.733821i	$0.737735\pi$
$278$	−10.8685	−	4.63382i	−0.651852	−	0.277918i
$279$	−17.6088	+	15.2163i	−1.05421	+	0.910977i
$280$	3.73055	+	6.48714i	0.222943	+	0.387681i
$281$		−	4.85308i		−	0.289511i	−0.989467	−	0.144755i	$-0.953761\pi$
$281$		−	4.85308i		−	0.289511i	0.989467	−	0.144755i	$-0.0462395\pi$
$282$	20.5297	+	22.5425i	1.22253	+	1.34238i
$283$	−6.01870	+	10.4247i	−0.357775	+	0.619684i	−0.987589	−	0.157062i	$-0.949798\pi$
$283$	−6.01870	+	10.4247i	−0.357775	+	0.619684i	0.629814	+	0.776746i	$0.283131\pi$
$284$	−9.63711	+	9.24744i	−0.571857	+	0.548735i
$285$	−7.67154	+	0.727286i	−0.454423	+	0.0430807i
$286$	25.5890	−	19.2190i	1.51311	−	1.13644i
$287$	11.6009	+	4.41259i	0.684782	+	0.260467i
$288$	−12.0785	−	11.9210i	−0.711732	−	0.702451i
$289$	6.39923	+	11.0838i	0.376425	+	0.651988i
$290$	1.74479	−	0.211419i	0.102458	−	0.0124150i
$291$	10.4979	+	14.7634i	0.615395	+	0.865445i
$292$	4.42608	+	17.9955i	0.259017	+	1.05311i
$293$		−	23.0767i		−	1.34816i	−0.738660	−	0.674078i	$-0.764541\pi$
$293$		−	23.0767i		−	1.34816i	0.738660	−	0.674078i	$-0.235459\pi$
$294$	14.9491	+	8.39781i	0.871852	+	0.489770i
$295$	−7.26457			−0.422960
$296$	−0.119048	−	0.0973464i	−0.00691952	−	0.00565814i
$297$	−18.7407	−	4.58689i	−1.08744	−	0.266158i
$298$	−1.41758	−	11.6989i	−0.0821181	−	0.677699i
$299$	32.8336	−	18.9565i	1.89881	−	1.09628i
$300$	−2.26198	+	2.62363i	−0.130595	+	0.151475i
$301$	−6.28747	+	16.5301i	−0.362404	+	0.952781i
$302$	22.2761	−	16.7308i	1.28184	−	0.962750i
$303$	16.6903	−	1.58230i	0.958834	−	0.0909005i
$304$	15.7658	−	8.25472i	0.904231	−	0.473440i
$305$	7.49648	+	4.32809i	0.429247	+	0.247826i
$306$	2.64981	+	8.28289i	0.151480	+	0.473501i
$307$	7.15756			0.408503			0.204252	−	0.978918i	$-0.434524\pi$
$307$	7.15756			0.408503			0.204252	+	0.978918i	$0.434524\pi$
$308$	−19.5012	−	2.39690i	−1.11118	−	0.136576i
$309$	7.39433	−	16.1623i	0.420649	−	0.919439i
$310$	−10.0918	−	4.30265i	−0.573175	−	0.244374i
$311$	11.6494	−	20.1774i	0.660579	−	1.14416i	−0.319885	−	0.947456i	$-0.603644\pi$
$311$	11.6494	−	20.1774i	0.660579	−	1.14416i	0.980464	−	0.196699i	$-0.0630223\pi$
$312$	24.7936	+	16.6339i	1.40366	+	0.941710i
$313$	−2.53839	+	1.46554i	−0.143478	+	0.0828371i	−0.570021	−	0.821630i	$-0.693065\pi$
$313$	−2.53839	+	1.46554i	−0.143478	+	0.0828371i	0.426542	+	0.904468i	$0.359731\pi$
$314$	−17.7408	+	13.3245i	−1.00117	+	0.751946i
$315$	−1.37744	+	7.81682i	−0.0776099	+	0.440428i
$316$	−7.66755	+	26.4227i	−0.431333	+	1.48639i
$317$	7.73492	+	13.3973i	0.434436	+	0.752466i	0.997249	−	0.0741183i	$-0.0236142\pi$
$317$	7.73492	+	13.3973i	0.434436	+	0.752466i	−0.562813	+	0.826584i	$0.690281\pi$
$318$	−2.02286	+	6.34786i	−0.113436	+	0.355971i
$319$	−2.30728	+	3.99632i	−0.129183	+	0.223751i
$320$	2.54456	−	7.58454i	0.142245	−	0.423988i
$321$	−22.1732	−	10.1444i	−1.23759	−	0.566204i
$322$	−22.5934	−	5.59802i	−1.25908	−	0.311966i
$323$	−9.11946			−0.507420
$324$	−1.71911	−	17.9177i	−0.0955060	−	0.995429i
$325$	3.04721	−	5.27793i	0.169029	−	0.292767i
$326$	−24.6696	+	2.98926i	−1.36632	+	0.165560i
$327$	−17.0910	+	1.62028i	−0.945132	+	0.0896015i
$328$	−4.69600	−	12.4100i	−0.259293	−	0.685227i
$329$	5.25114	+	32.5115i	0.289504	+	1.79242i
$330$	−1.94137	−	8.88560i	−0.106869	−	0.489136i
$331$	−5.85964	+	3.38307i	−0.322075	+	0.185950i	−0.652317	−	0.757946i	$-0.726203\pi$
$331$	−5.85964	+	3.38307i	−0.322075	+	0.185950i	0.330242	+	0.943896i	$0.392870\pi$
$332$	19.8901	−	19.0859i	1.09161	−	1.04747i
$333$	−0.0306512	−	0.160204i	−0.00167967	−	0.00877912i
$334$	17.3978	+	7.41756i	0.951963	+	0.405871i
$335$	−4.31267			−0.235626
$336$	−3.88191	−	17.9145i	−0.211775	−	0.977318i
$337$	30.5079			1.66187			0.830935	−	0.556369i	$-0.187806\pi$
$337$	30.5079			1.66187			0.830935	+	0.556369i	$0.187806\pi$
$338$	−31.4067	−	13.3903i	−1.70830	−	0.728335i
$339$	1.15373	+	1.62252i	0.0626623	+	0.0881235i
$340$	−2.95799	+	2.83839i	−0.160420	+	0.153933i
$341$	24.9453	−	14.4022i	1.35086	−	0.779921i
$342$	18.4451	+	4.00813i	0.997399	+	0.216735i
$343$	8.55884	+	16.4240i	0.462134	+	0.886810i
$344$	17.6829	−	6.69130i	0.953400	−	0.360771i
$345$	−1.01694	−	10.7269i	−0.0547502	−	0.577514i
$346$	5.86948	−	0.711216i	0.315545	−	0.0382352i
$347$	14.6599	−	25.3916i	0.786983	−	1.36309i	−0.140825	−	0.990035i	$-0.544975\pi$
$347$	14.6599	−	25.3916i	0.786983	−	1.36309i	0.927807	−	0.373059i	$-0.121691\pi$
$348$	−4.22932	−	0.804220i	−0.226715	−	0.0431107i
$349$	−3.82060			−0.204512			−0.102256	−	0.994758i	$-0.532606\pi$
$349$	−3.82060			−0.204512			−0.102256	+	0.994758i	$0.532606\pi$
$350$	−3.59520	+	1.03661i	−0.192171	+	0.0554090i
$351$	8.85986	+	30.4029i	0.472905	+	1.62279i
$352$	11.9106	+	17.3010i	0.634837	+	0.922149i
$353$	−2.49574	+	4.32274i	−0.132835	+	0.230076i	−0.924768	−	0.380531i	$-0.875741\pi$
$353$	−2.49574	+	4.32274i	−0.132835	+	0.230076i	0.791934	+	0.610607i	$0.209075\pi$
$354$	16.9544	+	5.40284i	0.901118	+	0.287158i
$355$	−3.33906	−	5.78342i	−0.177219	−	0.306952i
$356$	−4.00709	+	13.8086i	−0.212375	+	0.731855i
$357$	−2.49591	+	9.05554i	−0.132098	+	0.479270i
$358$	−0.996531	+	0.748460i	−0.0526683	+	0.0395573i
$359$	16.3630	−	9.44720i	0.863608	−	0.498604i	−0.00161106	−	0.999999i	$-0.500513\pi$
$359$	16.3630	−	9.44720i	0.863608	−	0.498604i	0.865219	+	0.501395i	$0.167179\pi$
$360$	7.23039	−	4.44089i	0.381075	−	0.234055i
$361$	−0.396906	+	0.687462i	−0.0208898	+	0.0361822i
$362$	11.6586	+	4.97065i	0.612761	+	0.261251i
$363$	4.38986	+	2.00839i	0.230408	+	0.105413i
$364$	12.5969	+	29.6866i	0.660256	+	1.55600i
$365$	−9.26590			−0.484999
$366$	−14.2768	−	15.6765i	−0.746259	−	0.819421i
$367$	0.575814	+	0.332446i	0.0300572	+	0.0173536i	0.514953	−	0.857218i	$-0.327809\pi$
$367$	0.575814	+	0.332446i	0.0300572	+	0.0173536i	−0.484896	+	0.874572i	$0.661143\pi$
$368$	11.5423	+	22.0448i	0.601683	+	1.14916i
$369$	4.62110	−	13.2934i	0.240565	−	0.692025i
$370$	0.0614811	−	0.0461763i	0.00319625	−	0.00240059i
$371$	−5.57864	+	4.54577i	−0.289629	+	0.236005i
$372$	20.3528	+	17.5473i	1.05524	+	0.909784i
$373$	−11.4621	+	6.61763i	−0.593484	+	0.342648i	−0.766474	−	0.642275i	$-0.777991\pi$
$373$	−11.4621	+	6.61763i	−0.593484	+	0.342648i	0.172990	+	0.984924i	$0.444657\pi$
$374$	−1.29477	−	10.6854i	−0.0669510	−	0.552529i
$375$	−1.00373	−	1.41157i	−0.0518324	−	0.0728931i
$376$	22.2865	−	27.2548i	1.14934	−	1.40556i
$377$	7.57401			0.390082
$378$	9.02830	−	17.2189i	0.464366	−	0.885644i
$379$		−	10.5781i		−	0.543361i	−0.962387	−	0.271681i	$-0.912421\pi$
$379$		−	10.5781i		−	0.543361i	0.962387	−	0.271681i	$-0.0875794\pi$
$380$	2.12518	+	8.64054i	0.109020	+	0.443250i
$381$	12.6533	−	8.99741i	0.648247	−	0.460951i
$382$	−4.32338	+	0.523872i	−0.221204	+	0.0268036i
$383$	17.4867	+	30.2878i	0.893528	+	1.54764i	0.835615	+	0.549315i	$0.185111\pi$
$383$	17.4867	+	30.2878i	0.893528	+	1.54764i	0.0579132	+	0.998322i	$0.481555\pi$
$384$	−11.5794	+	15.8087i	−0.590911	+	0.806737i
$385$	3.49257	−	9.18216i	0.177998	−	0.467966i
$386$	16.7867	−	12.6079i	0.854421	−	0.641726i
$387$	18.9416	+	6.58459i	0.962857	+	0.334713i
$388$	15.0930	−	14.4828i	0.766233	−	0.735251i
$389$	−3.44020	+	5.95861i	−0.174425	+	0.302113i	−0.939962	−	0.341278i	$-0.889140\pi$
$389$	−3.44020	+	5.95861i	−0.174425	+	0.302113i	0.765537	+	0.643392i	$0.222473\pi$
$390$	−11.0371	+	10.0516i	−0.558884	+	0.508984i
$391$		−	12.7514i		−	0.644867i
$392$	7.07054	−	18.4934i	0.357116	−	0.934060i
$393$	10.8116	−	23.6315i	0.545371	−	1.19205i
$394$	−18.7914	−	8.01173i	−0.946696	−	0.403625i
$395$	−11.9134	−	6.87818i	−0.599426	−	0.346079i
$396$	−2.07757	+	22.1815i	−0.104402	+	1.11466i
$397$	15.1708	+	26.2766i	0.761401	+	1.31879i	0.942128	+	0.335252i	$0.108822\pi$
$397$	15.1708	+	26.2766i	0.761401	+	1.31879i	−0.180727	+	0.983533i	$0.557845\pi$
$398$	15.5286	+	20.6755i	0.778380	+	1.03637i
$399$	14.3131	+	14.5191i	0.716552	+	0.726866i
$400$	3.37865	+	2.14120i	0.168933	+	0.107060i
$401$	1.04398	−	0.602741i	0.0521337	−	0.0300994i	−0.473707	−	0.880683i	$-0.657084\pi$
$401$	1.04398	−	0.602741i	0.0521337	−	0.0300994i	0.525840	+	0.850583i	$0.323751\pi$
$402$	10.0651	+	3.20744i	0.502003	+	0.159972i
$403$	−40.9435	−	23.6387i	−2.03954	−	1.17753i
$404$	−4.62358	−	18.7985i	−0.230032	−	0.935260i
$405$	8.90488	+	1.30503i	0.442487	+	0.0648474i
$406$	−3.34969	−	3.22529i	−0.166242	−	0.160068i
$407$			0.201881i			0.0100069i
$408$	9.01450	−	4.42445i	0.446284	−	0.219043i
$409$	15.5248	+	8.96324i	0.767652	+	0.443204i	0.832036	−	0.554721i	$-0.187175\pi$
$409$	15.5248	+	8.96324i	0.767652	+	0.443204i	−0.0643847	+	0.997925i	$0.520508\pi$
$410$	6.58621	−	0.798064i	0.325270	−	0.0394136i
$411$	19.5336	−	1.85185i	0.963523	−	0.0913450i
$412$	−19.7099	−	5.71957i	−0.971036	−	0.281783i
$413$	12.1412	+	14.8999i	0.597432	+	0.733178i
$414$	−5.60443	+	25.7912i	−0.275443	+	1.26757i
$415$	6.89152	+	11.9365i	0.338291	+	0.585938i
$416$	14.8177	−	31.1285i	0.726497	−	1.52620i
$417$	−11.7930	+	8.38572i	−0.577508	+	0.410651i
$418$	−21.4906	−	9.16257i	−1.05114	−	0.448156i
$419$		−	9.97207i		−	0.487167i	−0.969880	−	0.243584i	$-0.921677\pi$
$419$		−	9.97207i		−	0.487167i	0.969880	−	0.243584i	$-0.0783231\pi$
$420$	9.16162	+	0.254546i	0.447041	+	0.0124206i
$421$		−	7.30657i		−	0.356100i	−0.984021	−	0.178050i	$-0.943021\pi$
$421$		−	7.30657i		−	0.356100i	0.984021	−	0.178050i	$-0.0569789\pi$
$422$	−2.30559	+	5.40772i	−0.112234	+	0.263244i
$423$	36.6771	−	7.01727i	1.78330	−	0.341191i
$424$	7.59252	+	1.23967i	0.368725	+	0.0602036i
$425$	−1.02488	−	1.77515i	−0.0497141	−	0.0861074i
$426$	3.49161	+	15.9810i	0.169169	+	0.774282i
$427$	−3.65174	−	22.6091i	−0.176720	−	1.09413i
$428$	−7.84676	+	27.0403i	−0.379288	+	1.30704i
$429$	−3.69922	−	39.0201i	−0.178600	−	1.88391i
$430$	1.13716	+	9.38466i	0.0548386	+	0.452568i
$431$	−10.2397	−	5.91190i	−0.493230	−	0.284766i	0.232684	−	0.972552i	$-0.425249\pi$
$431$	−10.2397	−	5.91190i	−0.493230	−	0.284766i	−0.725913	+	0.687786i	$0.758583\pi$
$432$	−20.1775	+	4.98696i	−0.970789	+	0.239935i
$433$			15.9089i			0.764532i	0.924052	+	0.382266i	$0.124856\pi$
$433$			15.9089i			0.764532i	−0.924052	+	0.382266i	$0.875144\pi$
$434$	8.04147	+	27.8897i	0.386003	+	1.33875i
$435$	0.895532	−	1.95742i	0.0429375	−	0.0938512i
$436$	4.73457	+	19.2497i	0.226745	+	0.921895i
$437$	−23.9690	−	13.8385i	−1.14659	−	0.661986i
$438$	21.6252	+	6.89127i	1.03329	+	0.329278i
$439$	−16.2712	+	9.39420i	−0.776584	+	0.448361i	−0.835218	−	0.549919i	$-0.814659\pi$
$439$	−16.2712	+	9.39420i	−0.776584	+	0.448361i	0.0586346	+	0.998280i	$0.481325\pi$
$440$	−9.82252	+	3.71688i	−0.468270	+	0.177196i
$441$	18.3347	−	10.2390i	0.873082	−	0.487573i
$442$	−14.1260	+	10.6096i	−0.671907	+	0.504646i
$443$	−0.548077	−	0.949297i	−0.0260399	−	0.0451025i	0.852712	−	0.522382i	$-0.174956\pi$
$443$	−0.548077	−	0.949297i	−0.0260399	−	0.0451025i	−0.878752	+	0.477279i	$0.841623\pi$
$444$	−0.177830	+	0.0620438i	−0.00843946	+	0.00294447i
$445$	−6.22597	−	3.59457i	−0.295139	−	0.170399i
$446$	−12.9450	+	30.3622i	−0.612963	+	1.43769i
$447$	−13.1246	−	6.00459i	−0.620773	−	0.284007i
$448$	−19.8089	+	7.45700i	−0.935883	+	0.352310i
$449$		−	14.0937i		−	0.665123i	−0.943082	−	0.332561i	$-0.892087\pi$
$449$		−	14.0937i		−	0.665123i	0.943082	−	0.332561i	$-0.107913\pi$
$450$	1.29274	+	4.04089i	0.0609404	+	0.190490i
$451$	−8.70950	+	15.0853i	−0.410114	+	0.710338i
$452$	1.65875	−	1.59168i	0.0780212	−	0.0748665i
$453$	−3.22030	−	33.9683i	−0.151303	−	1.59597i
$454$	−9.68319	−	12.8926i	−0.454455	−	0.605080i
$455$	−15.9180	+	2.57102i	−0.746250	+	0.120531i
$456$	1.46631	−	21.7463i	0.0686663	−	1.01836i
$457$	−2.79093	−	4.83404i	−0.130554	−	0.226127i	0.793336	−	0.608784i	$-0.208342\pi$
$457$	−2.79093	−	4.83404i	−0.130554	−	0.226127i	−0.923890	+	0.382657i	$0.875009\pi$
$458$	2.05358	+	16.9476i	0.0959574	+	0.791912i
$459$	10.3455	+	2.53213i	0.482888	+	0.118190i
$460$	−12.0818	+	2.97157i	−0.563315	+	0.138550i
$461$			28.8335i			1.34291i	0.741045	+	0.671455i	$0.234330\pi$
$461$			28.8335i			1.34291i	−0.741045	+	0.671455i	$0.765670\pi$
$462$	−14.9801	+	18.8323i	−0.696939	+	0.876158i
$463$	−13.5780			−0.631023			−0.315511	−	0.948922i	$-0.602176\pi$
$463$	−13.5780			−0.631023			−0.315511	+	0.948922i	$0.602176\pi$
$464$	−0.205064	+	4.96687i	−0.00951984	+	0.230581i
$465$	−10.9502	+	7.78642i	−0.507804	+	0.361086i
$466$	12.1555	−	1.47291i	0.563093	−	0.0682310i
$467$	11.1529	−	6.43915i	0.516097	−	0.297968i	−0.219240	−	0.975671i	$-0.570358\pi$
$467$	11.1529	−	6.43915i	0.516097	−	0.297968i	0.735336	+	0.677703i	$0.237024\pi$
$468$	33.2346	−	15.2505i	1.53627	−	0.704954i
$469$	7.20775	+	8.84546i	0.332823	+	0.408445i
$470$	10.5716	+	14.0755i	0.487632	+	0.649253i
$471$	2.56467	+	27.0526i	0.118174	+	1.24652i
$472$	3.31102	−	20.2788i	0.152402	−	0.933406i
$473$	−21.4949	−	12.4101i	−0.988339	−	0.570618i
$474$	22.6886	+	24.9129i	1.04212	+	1.14429i
$475$	−4.44902			−0.204135
$476$	10.7653	+	1.32318i	0.493428	+	0.0606477i
$477$	5.33510	+	6.17396i	0.244277	+	0.282686i
$478$	−3.86303	+	9.06066i	−0.176691	+	0.414425i
$479$	−1.26654	+	2.19372i	−0.0578698	+	0.100233i	−0.893509	−	0.449045i	$-0.851764\pi$
$479$	−1.26654	+	2.19372i	−0.0578698	+	0.100233i	0.835639	+	0.549279i	$0.185097\pi$
$480$	−6.29282	−	7.51002i	−0.287227	−	0.342784i
$481$	0.286961	−	0.165677i	0.0130843	−	0.00755421i
$482$	−12.5125	−	16.6596i	−0.569928	−	0.758825i
$483$	−20.3016	+	20.0135i	−0.923755	+	0.910647i
$484$	1.55350	−	5.35344i	0.0706138	−	0.243338i
$485$	5.22943	+	9.05763i	0.237456	+	0.411286i
$486$	−19.8121	−	9.66852i	−0.898696	−	0.438573i
$487$	14.2873	−	24.7464i	0.647421	−	1.12137i	−0.336315	−	0.941749i	$-0.609181\pi$
$487$	14.2873	−	24.7464i	0.647421	−	1.12137i	0.983737	−	0.179617i	$-0.0574859\pi$
$488$	−15.4984	+	18.9535i	−0.701581	+	0.857985i
$489$	−12.6619	+	27.6760i	−0.572592	+	1.25155i
$490$	8.13476	+	5.64142i	0.367491	+	0.254853i
$491$	−34.4371			−1.55412			−0.777062	−	0.629425i	$-0.783291\pi$
$491$	−34.4371			−1.55412			−0.777062	+	0.629425i	$0.783291\pi$
$492$	−15.9648	−	3.03576i	−0.719749	−	0.136863i
$493$	1.27370	−	2.20611i	0.0573646	−	0.0993584i
$494$	4.61264	+	38.0669i	0.207532	+	1.71271i
$495$	−10.5217	−	3.65761i	−0.472915	−	0.164397i
$496$	16.6103	−	26.2098i	0.745824	−	1.17686i
$497$	−6.28147	+	16.5144i	−0.281763	+	0.740770i
$498$	−7.20636	−	32.9833i	−0.322925	−	1.47802i
$499$	23.2426	−	13.4191i	1.04048	−	0.600722i	0.120512	−	0.992712i	$-0.461546\pi$
$499$	23.2426	−	13.4191i	1.04048	−	0.600722i	0.919970	+	0.391990i	$0.128213\pi$
$500$	−1.44309	+	1.38474i	−0.0645368	+	0.0619273i
$501$	18.8776	−	13.4234i	0.843391	−	0.599713i
$502$	−10.0426	+	23.5548i	−0.448223	+	1.05130i
$503$	27.5107			1.22664			0.613320	−	0.789834i	$-0.289834\pi$
$503$	27.5107			1.22664			0.613320	+	0.789834i	$0.289834\pi$
$504$	−21.1926	−	7.40779i	−0.943992	−	0.329969i
$505$	9.67937			0.430726
$506$	12.8117	−	30.0496i	0.569550	−	1.33587i
$507$	−34.0782	+	24.2321i	−1.51347	+	1.07619i
$508$	−12.4128	−	12.9358i	−0.550727	−	0.573934i
$509$	16.0532	−	9.26830i	0.711544	−	0.410810i	−0.100089	−	0.994979i	$-0.531913\pi$
$509$	16.0532	−	9.26830i	0.711544	−	0.410810i	0.811632	+	0.584169i	$0.198579\pi$
$510$	1.07171	+	4.90517i	0.0474559	+	0.217205i
$511$	15.4861	+	19.0047i	0.685063	+	0.840720i
$512$	20.0122	+	10.5599i	0.884423	+	0.466686i
$513$	15.9872	−	16.6986i	0.705851	−	0.737261i
$514$	0.0379239	+	0.312976i	0.00167275	+	0.0138048i
$515$	5.13075	−	8.88672i	0.226088	−	0.391595i
$516$	4.32564	−	22.7482i	0.190426	−	1.00143i
$517$	−46.2187			−2.03269
$518$	−0.197463	−	0.0489259i	−0.00867601	−	0.00214968i
$519$	3.01258	−	6.58478i	0.132237	−	0.289040i
$520$	13.3443	+	10.9117i	0.585186	+	0.478512i
$521$	−2.43582	+	4.21897i	−0.106715	+	0.184836i	−0.914438	−	0.404727i	$-0.867367\pi$
$521$	−2.43582	+	4.21897i	−0.106715	+	0.184836i	0.807722	+	0.589563i	$0.200700\pi$
$522$	−3.54582	+	3.90231i	−0.155196	+	0.170799i
$523$	−4.29514	−	7.43941i	−0.187813	−	0.325302i	0.756707	−	0.653754i	$-0.226807\pi$
$523$	−4.29514	−	7.43941i	−0.187813	−	0.325302i	−0.944521	+	0.328451i	$0.893473\pi$
$524$	−28.8187	−	8.36283i	−1.25895	−	0.365332i
$525$	−1.21766	+	4.41784i	−0.0531429	+	0.192810i
$526$	−2.71934	−	3.62065i	−0.118569	−	0.157868i
$527$	−13.7707	+	7.95051i	−0.599861	+	0.346330i
$528$	25.6887	−	1.36942i	1.11796	−	0.0595962i
$529$	7.84991	−	13.5965i	0.341301	−	0.591150i
$530$	−1.50858	+	3.53836i	−0.0655287	+	0.153696i
$531$	16.4900	−	14.2495i	0.715603	−	0.618374i
$532$	14.1703	−	18.7997i	0.614360	−	0.815072i
$533$	28.5903			1.23838
$534$	11.8571	+	13.0196i	0.513109	+	0.563413i
$535$	−12.1918	−	7.03895i	−0.527098	−	0.304320i
$536$	1.96561	−	12.0387i	0.0849014	−	0.519991i
$537$	0.144062	+	1.51959i	0.00621672	+	0.0655750i
$538$	16.3240	+	21.7345i	0.703778	+	0.937040i
$539$	−24.6701	+	8.18271i	−1.06262	+	0.352454i
$540$	−0.0117552	−	10.3923i	−0.000505861	−	0.447213i
$541$	−25.8855	+	14.9450i	−1.11290	+	0.642536i	−0.939580	−	0.342329i	$-0.888784\pi$
$541$	−25.8855	+	14.9450i	−1.11290	+	0.642536i	−0.173324	+	0.984865i	$0.555451\pi$
$542$	−1.93880	+	0.234928i	−0.0832786	+	0.0100910i
$543$	12.6503	−	8.99528i	0.542875	−	0.386024i
$544$	−6.57507	−	9.55079i	−0.281904	−	0.409487i
$545$	−9.91171			−0.424571
$546$	39.0625	+	5.83825i	1.67172	+	0.249854i
$547$			13.9138i			0.594909i	0.954736	+	0.297455i	$0.0961377\pi$
$547$			13.9138i			0.594909i	−0.954736	+	0.297455i	$0.903862\pi$
$548$	−5.41124	−	22.0009i	−0.231157	−	0.939834i
$549$	−25.5059	+	4.87994i	−1.08857	+	0.208271i
$550$	−0.631668	−	5.21299i	−0.0269344	−	0.222283i
$551$	−2.76457	−	4.78838i	−0.117775	−	0.203992i
$552$	30.4071	+	2.05029i	1.29421	+	0.0872663i
$553$	5.80332	+	35.9303i	0.246782	+	1.52791i
$554$	6.25955	+	8.33422i	0.265943	+	0.354087i
$555$	−0.00888790	−	0.0937511i	−0.000377270	−	0.00397951i
$556$	11.5689	+	12.0564i	0.490630	+	0.511304i
$557$	10.0246	−	17.3630i	0.424754	−	0.735695i	−0.571643	−	0.820502i	$-0.693694\pi$
$557$	10.0246	−	17.3630i	0.424754	−	0.735695i	0.996397	+	0.0848067i	$0.0270273\pi$
$558$	31.3472	−	10.0284i	1.32703	−	0.424536i
$559$			40.7382i			1.72304i
$560$	−1.25505	−	10.5083i	−0.0530354	−	0.444058i
$561$	−11.9876	−	5.48440i	−0.506118	−	0.231552i
$562$	−2.69174	+	6.31343i	−0.113544	+	0.266316i
$563$	−22.9242	−	13.2353i	−0.966139	−	0.557800i	−0.0680817	−	0.997680i	$-0.521688\pi$
$563$	−22.9242	−	13.2353i	−0.966139	−	0.557800i	−0.898057	+	0.439879i	$0.855021\pi$
$564$	−14.2043	−	40.7124i	−0.598109	−	1.71430i
$565$	0.574724	+	0.995451i	0.0241788	+	0.0418789i
$566$	13.6118	−	10.2234i	0.572147	−	0.429720i
$567$	−12.2060	−	20.4454i	−0.512605	−	0.858625i
$568$	17.6661	−	6.68492i	0.741252	−	0.280493i
$569$	7.62895	−	4.40457i	0.319822	−	0.184649i	−0.331491	−	0.943458i	$-0.607552\pi$
$569$	7.62895	−	4.40457i	0.319822	−	0.184649i	0.651313	+	0.758809i	$0.274218\pi$
$570$	10.3834	+	3.30885i	0.434912	+	0.138592i
$571$	−34.4798	−	19.9069i	−1.44294	−	0.833079i	−0.444891	−	0.895585i	$-0.646757\pi$
$571$	−34.4798	−	19.9069i	−1.44294	−	0.833079i	−0.998045	+	0.0625059i	$0.980091\pi$
$572$	−43.9487	+	10.8094i	−1.83759	+	0.451964i
$573$	−2.21902	+	4.85026i	−0.0927010	+	0.202623i
$574$	−12.6444	−	12.1748i	−0.527766	−	0.508166i
$575$		−	6.22092i		−	0.259430i
$576$	9.10113	+	22.2074i	0.379214	+	0.925309i
$577$	−13.3897	−	7.73055i	−0.557421	−	0.321827i	0.194689	−	0.980865i	$-0.437630\pi$
$577$	−13.3897	−	7.73055i	−0.557421	−	0.321827i	−0.752110	+	0.659038i	$0.770964\pi$
$578$	−2.17726	−	17.9683i	−0.0905619	−	0.747384i
$579$	−2.42674	−	25.5977i	−0.100852	−	1.06380i
$580$	−2.38708	−	0.692701i	−0.0991180	−	0.0287628i
$581$	12.9644	−	34.0841i	0.537854	−	1.41405i
$582$	−5.46833	−	25.0284i	−0.226670	−	1.03746i
$583$	−5.04965	−	8.74625i	−0.209135	−	0.362233i
$584$	4.22317	−	25.8654i	0.174756	−	1.07032i
$585$	3.43575	+	17.9576i	0.142051	+	0.742454i
$586$	−12.7994	+	30.0207i	−0.528738	+	1.24015i
$587$			15.9553i			0.658545i	0.944235	+	0.329273i	$0.106804\pi$
$587$			15.9553i			0.658545i	−0.944235	+	0.329273i	$0.893196\pi$
$588$	−14.7897	−	19.2163i	−0.609917	−	0.792466i
$589$			34.5132i			1.42209i
$590$	9.45056	+	4.02926i	0.389073	+	0.165882i
$591$	−20.3898	+	14.4987i	−0.838725	+	0.596395i
$592$	0.100878	+	0.192668i	0.00414606	+	0.00791862i
$593$	−4.15774	−	7.20142i	−0.170738	−	0.295727i	0.767940	−	0.640522i	$-0.221282\pi$
$593$	−4.15774	−	7.20142i	−0.170738	−	0.295727i	−0.938678	+	0.344795i	$0.887949\pi$
$594$	21.8359	+	16.3616i	0.895936	+	0.671323i
$595$	−1.92802	+	5.06888i	−0.0790411	+	0.207804i
$596$	−4.64460	+	16.0055i	−0.190250	+	0.655610i
$597$	31.5276	−	2.98891i	1.29034	−	0.122328i
$598$	−53.2277	+	6.44970i	−2.17664	+	0.263748i
$599$	−32.0559	−	18.5075i	−1.30977	−	0.756195i	−0.327711	−	0.944778i	$-0.606277\pi$
$599$	−32.0559	−	18.5075i	−1.30977	−	0.756195i	−0.982057	+	0.188583i	$0.939610\pi$
$600$	4.39782	−	2.15852i	0.179540	−	0.0881210i
$601$			1.41835i			0.0578558i	0.999582	+	0.0289279i	$0.00920932\pi$
$601$			1.41835i			0.0578558i	−0.999582	+	0.0289279i	$0.990791\pi$
$602$	17.3478	−	18.0169i	0.707043	−	0.734314i
$603$	9.78939	−	8.45930i	0.398655	−	0.344489i
$604$	−38.2589	+	9.40996i	−1.55673	+	0.382886i
$605$	2.41374	+	1.39357i	0.0981324	+	0.0566568i
$606$	−22.5902	−	7.19878i	−0.917666	−	0.292431i
$607$	0.559732	−	0.323161i	0.0227188	−	0.0131167i	−0.488598	−	0.872509i	$-0.662491\pi$
$607$	0.559732	−	0.323161i	0.0227188	−	0.0131167i	0.511316	+	0.859393i	$0.329158\pi$
$608$	−25.0883	+	1.99422i	−1.01747	+	0.0808763i
$609$	−5.51145	+	1.43466i	−0.223335	+	0.0581354i
$610$	−7.35169	−	9.78835i	−0.297661	−	0.396319i
$611$	37.9300	+	65.6967i	1.53448	+	2.65781i
$612$	1.14689	−	12.2450i	0.0463603	−	0.494975i
$613$	27.9219	+	16.1207i	1.12776	+	0.651110i	0.943369	−	0.331744i	$-0.107637\pi$
$613$	27.9219	+	16.1207i	1.12776	+	0.651110i	0.184386	+	0.982854i	$0.440970\pi$
$614$	−9.31134	−	3.96991i	−0.375775	−	0.160212i
$615$	3.38045	−	7.38886i	0.136313	−	0.297948i
$616$	24.0398	+	13.9344i	0.968592	+	0.561432i
$617$		−	29.0671i		−	1.17020i	−0.810961	−	0.585100i	$-0.801055\pi$
$617$		−	29.0671i		−	1.17020i	0.810961	−	0.585100i	$-0.198945\pi$
$618$	−18.5837	+	16.9244i	−0.747545	+	0.680801i
$619$	8.54194	−	14.7951i	0.343330	−	0.594664i	−0.641719	−	0.766940i	$-0.721779\pi$
$619$	8.54194	−	14.7951i	0.343330	−	0.594664i	0.985049	+	0.172275i	$0.0551118\pi$
$620$	10.7421	+	11.1947i	0.431412	+	0.449591i
$621$	23.3491	+	22.3543i	0.936967	+	0.897048i
$622$	−26.3462	+	19.7877i	−1.05639	+	0.793415i
$623$	3.03284	+	18.7773i	0.121508	+	0.752297i
$624$	−23.0283	−	35.3909i	−0.921871	−	1.41677i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.11507	−	0.498631i	0.164471	−	0.0199293i
$627$	−23.3187	+	16.5813i	−0.931258	+	0.662193i
$628$	30.4696	−	7.49415i	1.21587	−	0.299049i
$629$		−	0.111446i		−	0.00444363i
$630$	6.12749	−	9.40499i	0.244125	−	0.374704i
$631$	−19.4033			−0.772431			−0.386216	−	0.922409i	$-0.626218\pi$
$631$	−19.4033			−0.772431			−0.386216	+	0.922409i	$0.626218\pi$
$632$	24.6300	−	30.1208i	0.979730	−	1.19814i
$633$	4.17238	+	5.86772i	0.165837	+	0.233221i
$634$	−2.63171	−	21.7188i	−0.104518	−	0.862564i
$635$	7.76303	−	4.48199i	0.308067	−	0.177862i
$636$	6.15237	−	7.13603i	0.243957	−	0.282962i
$637$	31.8771	+	28.3516i	1.26301	+	1.12333i
$638$	5.21811	−	3.91914i	0.206587	−	0.155160i
$639$	18.9236	+	6.57831i	0.748605	+	0.260234i
$640$	−7.51698	+	8.45547i	−0.297135	+	0.334232i
$641$	2.54419	+	1.46889i	0.100489	+	0.0580176i	0.549402	−	0.835558i	$-0.314855\pi$
$641$	2.54419	+	1.46889i	0.100489	+	0.0580176i	−0.448913	+	0.893575i	$0.648189\pi$
$642$	23.2189	+	25.4952i	0.916376	+	1.00622i
$643$	45.2268			1.78357			0.891786	−	0.452458i	$-0.149453\pi$
$643$	45.2268			1.78357			0.891786	+	0.452458i	$0.149453\pi$
$644$	26.2870	+	19.8138i	1.03585	+	0.780774i
$645$	10.5283	+	4.81678i	0.414553	+	0.189660i
$646$	11.8636	+	5.05806i	0.466767	+	0.199007i
$647$	−6.85135	+	11.8669i	−0.269354	+	0.466535i	−0.968695	−	0.248253i	$-0.920144\pi$
$647$	−6.85135	+	11.8669i	−0.269354	+	0.466535i	0.699341	+	0.714788i	$0.253477\pi$
$648$	−7.70157	+	24.2628i	−0.302546	+	0.953135i
$649$	−23.3603	+	13.4871i	−0.916970	+	0.529413i
$650$	−6.89153	+	5.17599i	−0.270308	+	0.203019i
$651$	34.2713	+	9.44595i	1.34320	+	0.370216i
$652$	33.7509	+	9.79410i	1.32179	+	0.383566i
$653$	1.21773	+	2.10917i	0.0476534	+	0.0825380i	0.888868	−	0.458163i	$-0.151492\pi$
$653$	1.21773	+	2.10917i	0.0476534	+	0.0825380i	−0.841215	+	0.540701i	$0.818159\pi$
$654$	23.1325	+	7.37158i	0.904552	+	0.288252i
$655$	7.50189	−	12.9937i	0.293123	−	0.507704i
$656$	−0.774072	+	18.7489i	−0.0302224	+	0.732022i
$657$	21.0328	−	18.1751i	0.820568	−	0.709077i
$658$	11.2011	−	45.2071i	0.436664	−	1.76236i
$659$	−35.6881			−1.39021			−0.695106	−	0.718907i	$-0.744643\pi$
$659$	−35.6881			−1.39021			−0.695106	+	0.718907i	$0.744643\pi$
$660$	−2.40281	+	12.6361i	−0.0935292	+	0.491861i
$661$	0.137767	−	0.238619i	0.00535850	−	0.00928120i	−0.863334	−	0.504633i	$-0.831628\pi$
$661$	0.137767	−	0.238619i	0.00535850	−	0.00928120i	0.868692	+	0.495352i	$0.164961\pi$
$662$	9.49927	−	1.15104i	0.369200	−	0.0447366i
$663$	2.04210	+	21.5405i	0.0793087	+	0.836562i
$664$	−36.4612	+	13.7971i	−1.41497	+	0.535430i
$665$	7.43564	+	9.12513i	0.288342	+	0.353857i
$666$	−0.0489819	+	0.225412i	−0.00189801	+	0.00873452i
$667$	6.69543	−	3.86561i	0.259248	−	0.149677i
$668$	−18.5188	−	19.2992i	−0.716514	−	0.746707i
$669$	23.4263	+	32.9449i	0.905711	+	1.27372i
$670$	5.61040	+	2.39200i	0.216749	+	0.0924110i
$671$	32.1413			1.24080
$672$	−4.88620	+	25.4583i	−0.188489	+	0.982075i
$673$	−29.9243			−1.15350			−0.576748	−	0.816922i	$-0.695678\pi$
$673$	−29.9243			−1.15350			−0.576748	+	0.816922i	$0.695678\pi$
$674$	−39.6880	−	16.9210i	−1.52873	−	0.651774i
$675$	5.04717	+	1.23532i	0.194266	+	0.0475477i
$676$	33.4304	+	34.8391i	1.28579	+	1.33997i
$677$	−34.4393	+	19.8835i	−1.32361	+	0.764186i	−0.984302	−	0.176491i	$-0.943525\pi$
$677$	−34.4393	+	19.8835i	−1.32361	+	0.764186i	−0.339306	+	0.940676i	$0.610192\pi$
$678$	−0.600980	−	2.75067i	−0.0230805	−	0.105639i
$679$	9.83765	−	25.8638i	0.377534	−	0.992560i
$680$	5.42238	−	2.05185i	0.207939	−	0.0786850i
$681$	−19.6596	+	1.86380i	−0.753359	+	0.0714208i
$682$	−40.4397	+	4.90015i	−1.54852	+	0.187637i
$683$	−25.5875	+	44.3189i	−0.979079	+	1.69582i	−0.313322	+	0.949647i	$0.601442\pi$
$683$	−25.5875	+	44.3189i	−0.979079	+	1.69582i	−0.665758	+	0.746168i	$0.731892\pi$
$684$	−21.7724	−	15.4447i	−0.832489	−	0.590544i
$685$	11.3283			0.432833
$686$	−2.02482	−	26.1132i	−0.0773080	−	0.997007i
$687$	19.0130	+	8.69857i	0.725392	+	0.331871i
$688$	−26.7152	−	1.10297i	−1.01851	−	0.0420504i
$689$	−8.28814	+	14.3555i	−0.315753	+	0.546900i
$690$	−4.62665	+	14.5187i	−0.176134	+	0.552718i
$691$	−14.3455	−	24.8471i	−0.545727	−	0.945227i	−0.998561	−	0.0536321i	$-0.982920\pi$
$691$	−14.3455	−	24.8471i	−0.545727	−	0.945227i	0.452834	−	0.891595i	$-0.350413\pi$
$692$	−8.03015	−	2.33025i	−0.305260	−	0.0885829i
$693$	10.0830	+	27.6934i	0.383021	+	1.05198i
$694$	−33.1545	+	24.9012i	−1.25853	+	0.945237i
$695$	−7.23526	+	4.17728i	−0.274449	+	0.158453i
$696$	5.05591	+	3.39199i	0.191644	+	0.128573i
$697$	4.80795	−	8.32762i	0.182114	−	0.315431i
$698$	4.97026	+	2.11908i	0.188127	+	0.0802083i
$699$	6.23895	−	13.6369i	0.235979	−	0.515794i
$700$	5.25198	+	0.645525i	0.198506	+	0.0243986i
$701$	−5.54707			−0.209510			−0.104755	−	0.994498i	$-0.533406\pi$
$701$	−5.54707			−0.209510			−0.104755	+	0.994498i	$0.533406\pi$
$702$	5.33695	−	44.4656i	0.201430	−	1.67825i
$703$	−0.209486	−	0.120947i	−0.00790090	−	0.00456159i
$704$	−5.89868	−	29.1133i	−0.222315	−	1.09725i
$705$	21.4634	−	2.03479i	0.808357	−	0.0766348i
$706$	5.64432	−	4.23925i	0.212427	−	0.159546i
$707$	−16.1771	−	19.8528i	−0.608402	−	0.746641i
$708$	−19.0596	−	16.4323i	−0.716302	−	0.617564i
$709$	21.2936	−	12.2939i	0.799699	−	0.461706i	−0.0436669	−	0.999046i	$-0.513904\pi$
$709$	21.2936	−	12.2939i	0.799699	−	0.461706i	0.843366	+	0.537340i	$0.180571\pi$
$710$	1.13607	+	9.37571i	0.0426360	+	0.351864i
$711$	40.5339	−	7.75518i	1.52014	−	0.290842i
$712$	12.8717	−	15.7413i	0.482389	−	0.589929i
$713$	−48.2587			−1.80730
$714$	8.26957	−	10.3961i	0.309481	−	0.389064i
$715$		−	22.6293i		−	0.846286i
$716$	1.71153	−	0.420959i	0.0639628	−	0.0157320i
$717$	6.99083	+	9.83138i	0.261077	+	0.367160i
$718$	−26.5267	+	3.21429i	−0.989967	+	0.119956i
$719$	−13.2217	−	22.9007i	−0.493087	−	0.854051i	0.506882	−	0.862016i	$-0.330798\pi$
$719$	−13.2217	−	22.9007i	−0.493087	−	0.854051i	−0.999968	+	0.00796455i	$0.997465\pi$
$720$	−11.8692	+	1.76689i	−0.442339	+	0.0658483i
$721$	−26.8020	+	4.32896i	−0.998159	+	0.161219i
$722$	0.897637	−	0.674184i	0.0334066	−	0.0250905i
$723$	−25.4039	+	2.40837i	−0.944781	+	0.0895682i
$724$	−12.4098	−	12.9327i	−0.461207	−	0.480641i
$725$	0.621388	−	1.07628i	0.0230778	−	0.0399719i
$726$	−4.59688	−	5.04755i	−0.170606	−	0.187332i
$727$			7.18001i			0.266292i	0.991096	+	0.133146i	$0.0425079\pi$
$727$			7.18001i			0.266292i	−0.991096	+	0.133146i	$0.957492\pi$
$728$	0.0781451	−	45.6065i	0.00289625	−	1.69029i
$729$	−22.7731	+	14.5046i	−0.843450	+	0.537208i
$730$	12.0541	+	5.13928i	0.446142	+	0.190213i
$731$	11.8660	+	6.85082i	0.438879	+	0.253387i
$732$	9.87794	+	28.3122i	0.365099	+	1.04645i
$733$	−17.3916	−	30.1232i	−0.642374	−	1.11263i	−0.984901	−	0.173117i	$-0.944616\pi$
$733$	−17.3916	−	30.1232i	−0.642374	−	1.11263i	0.342527	−	0.939508i	$-0.388717\pi$
$734$	−0.564693	−	0.751855i	−0.0208432	−	0.0277515i
$735$	11.0962	−	4.88606i	0.409291	−	0.180225i
$736$	−2.78845	−	35.0802i	−0.102784	−	1.29307i
$737$	−13.8680	+	8.00669i	−0.510834	+	0.294930i
$738$	−13.3847	+	14.7304i	−0.492699	+	0.542233i
$739$	−34.3522	−	19.8332i	−1.26367	−	0.729577i	−0.289884	−	0.957062i	$-0.593617\pi$
$739$	−34.3522	−	19.8332i	−1.26367	−	0.729577i	−0.973782	+	0.227484i	$0.926950\pi$
$740$	−0.105593	+	0.0259711i	−0.00388167	+	0.000954717i
$741$	42.7060	+	19.5383i	1.56885	+	0.717756i
$742$	9.77860	−	2.81948i	0.358984	−	0.103506i
$743$		−	41.7771i		−	1.53265i	−0.642451	−	0.766327i	$-0.722082\pi$
$743$		−	41.7771i		−	1.53265i	0.642451	−	0.766327i	$-0.277918\pi$
$744$	−16.7446	−	34.1160i	−0.613889	−	1.25075i
$745$	−7.21649	−	4.16644i	−0.264392	−	0.152647i
$746$	18.5816	−	2.25156i	0.680320	−	0.0824356i
$747$	−39.0565	−	13.5770i	−1.42900	−	0.496757i
$748$	−4.24223	+	14.6189i	−0.155111	+	0.534520i
$749$	5.93896	+	36.7701i	0.217005	+	1.34355i
$750$	0.522843	+	2.39304i	0.0190915	+	0.0873814i
$751$	−13.7157	−	23.7564i	−0.500494	−	0.866882i	−1.00000		0.000570880i	$-0.999818\pi$
$751$	−13.7157	−	23.7564i	−0.500494	−	0.866882i	0.499506	−	0.866311i	$-0.333515\pi$
$752$	−44.1094	+	23.0950i	−1.60851	+	0.842187i
$753$	18.1739	+	25.5584i	0.662293	+	0.931399i
$754$	−9.85311	−	4.20089i	−0.358829	−	0.152987i
$755$		−	19.6995i		−	0.716940i
$756$	−21.2954	+	17.3927i	−0.774506	+	0.632567i
$757$			21.1452i			0.768534i	0.923222	+	0.384267i	$0.125546\pi$
$757$			21.1452i			0.768534i	−0.923222	+	0.384267i	$0.874454\pi$
$758$	−5.86710	+	13.7612i	−0.213103	+	0.499829i
$759$	−23.1851	−	32.6057i	−0.841565	−	1.18351i
$760$	2.02776	−	12.4193i	0.0735545	−	0.450495i
$761$	−23.2981	−	40.3535i	−0.844556	−	1.46281i	−0.886006	−	0.463673i	$-0.846531\pi$
$761$	−23.2981	−	40.3535i	−0.844556	−	1.46281i	0.0414503	−	0.999141i	$-0.486802\pi$
$762$	−21.4511	+	4.68675i	−0.777093	+	0.169783i
$763$	16.5654	+	20.3293i	0.599708	+	0.735971i
$764$	5.91490	+	1.71643i	0.213994	+	0.0620983i
$765$	5.80835	+	2.01913i	0.210001	+	0.0730018i
$766$	−5.94962	−	49.1007i	−0.214969	−	1.77408i
$767$	38.3419	+	22.1367i	1.38445	+	0.799310i
$768$	23.8321	−	14.1433i	0.859966	−	0.510352i
$769$		−	32.8936i		−	1.18618i	−0.805138	−	0.593088i	$-0.797909\pi$
$769$		−	32.8936i		−	1.18618i	0.805138	−	0.593088i	$-0.202091\pi$
$770$	−9.63635	+	10.0080i	−0.347270	+	0.360664i
$771$	0.351117	+	0.160638i	0.0126452	+	0.00578525i
$772$	−28.8309	+	7.09111i	−1.03765	+	0.255215i
$773$	−10.0725	−	5.81534i	−0.362281	−	0.209163i	0.307800	−	0.951451i	$-0.400407\pi$
$773$	−10.0725	−	5.81534i	−0.362281	−	0.209163i	−0.670081	+	0.742288i	$0.733741\pi$
$774$	−20.9893	−	19.0718i	−0.754444	−	0.685523i
$775$	−6.71818	+	3.87874i	−0.241324	+	0.139329i
$776$	−27.6675	+	10.4695i	−0.993205	+	0.375833i
$777$	−0.177433	+	0.174915i	−0.00636538	+	0.00627505i
$778$	7.78031	−	5.84353i	0.278938	−	0.209501i
$779$	−10.4357	−	18.0751i	−0.373897	−	0.647608i
$780$	19.9333	−	6.95461i	0.713728	−	0.249015i
$781$	−21.4744	−	12.3983i	−0.768416	−	0.443645i
$782$	−7.07252	+	16.5885i	−0.252913	+	0.593202i
$783$	1.80670	+	6.19977i	0.0645663	+	0.221562i
$784$	−19.4554	+	20.1367i	−0.694837	+	0.719167i
$785$			15.6888i			0.559959i
$786$	−27.1720	+	24.7459i	−0.969193	+	0.882659i
$787$	9.26180	−	16.0419i	0.330147	−	0.571832i	−0.652393	−	0.757881i	$-0.726235\pi$
$787$	9.26180	−	16.0419i	0.330147	−	0.571832i	0.982541	+	0.186049i	$0.0595682\pi$
$788$	20.0022	+	20.8451i	0.712550	+	0.742576i
$789$	−5.52104	+	0.523412i	−0.196554	+	0.0186340i
$790$	11.6833	+	15.5556i	0.415672	+	0.553443i
$791$	1.08118	−	2.84248i	0.0384422	−	0.101067i
$792$	15.0056	−	27.7039i	0.533201	−	0.984415i
$793$	−26.3773	−	45.6868i	−0.936684	−	1.62238i
$794$	−5.16167	−	42.5979i	−0.183181	−	1.51174i
$795$	2.73005	+	3.83934i	0.0968249	+	0.136167i
$796$	−8.73382	−	35.5098i	−0.309562	−	1.25861i
$797$		−	0.954691i		−	0.0338169i	−0.999857	−	0.0169084i	$-0.994618\pi$
$797$		−	0.954691i		−	0.0338169i	0.999857	−	0.0169084i	$-0.00538238\pi$
$798$	−10.5671	−	26.8268i	−0.374072	−	0.949658i
$799$	25.5143			0.902632
$800$	−3.20772	−	4.65946i	−0.113410	−	0.164737i
$801$	21.1832	−	4.05289i	0.748471	−	0.143202i
$802$	−1.69243	+	0.205075i	−0.0597617	+	0.00724144i
$803$	−29.7958	+	17.2026i	−1.05147	+	0.607067i
$804$	−11.3149	−	9.75517i	−0.399044	−	0.344038i
$805$	−12.7594	+	10.3970i	−0.449708	+	0.366446i
$806$	40.1527	+	53.4610i	1.41432	+	1.88308i
$807$	33.1424	−	3.14200i	1.16667	−	0.110604i
$808$	−4.41163	+	27.0196i	−0.155200	+	0.950547i
$809$	46.4968	+	26.8449i	1.63474	+	0.943817i	0.982604	+	0.185715i	$0.0594602\pi$
$809$	46.4968	+	26.8449i	1.63474	+	0.943817i	0.652136	+	0.758102i	$0.273873\pi$
$810$	−10.8606	−	6.63677i	−0.381604	−	0.233193i
$811$	−8.29444			−0.291257			−0.145629	−	0.989339i	$-0.546520\pi$
$811$	−8.29444			−0.291257			−0.145629	+	0.989339i	$0.546520\pi$
$812$	2.56876	+	6.05370i	0.0901456	+	0.212443i
$813$	−0.995111	+	2.17508i	−0.0349001	+	0.0762833i
$814$	0.111972	−	0.262629i	0.00392463	−	0.00920516i
$815$	−8.78580	+	15.2175i	−0.307753	+	0.533044i
$816$	−14.1811	+	0.755967i	−0.496436	+	0.0264641i
$817$	25.7551	−	14.8697i	0.901058	−	0.520226i
$818$	−15.2249	−	20.2711i	−0.532328	−	0.708763i
$819$	31.0896	−	37.0593i	1.08636	−	1.29496i
$820$	−9.01072	−	2.61480i	−0.314668	−	0.0913128i
$821$	2.08024	+	3.60308i	0.0726008	+	0.125748i	0.900040	−	0.435806i	$-0.143537\pi$
$821$	2.08024	+	3.60308i	0.0726008	+	0.125748i	−0.827440	+	0.561555i	$0.810203\pi$
$822$	−26.4386	−	8.42514i	−0.922153	−	0.293861i
$823$	13.8704	−	24.0243i	0.483492	−	0.837433i	−0.516328	−	0.856391i	$-0.672701\pi$
$823$	13.8704	−	24.0243i	0.483492	−	0.837433i	0.999820	+	0.0189578i	$0.00603480\pi$
$824$	22.4685	+	18.3726i	0.782726	+	0.640041i
$825$	−5.84829	−	2.67562i	−0.203611	−	0.0931533i
$826$	−7.53051	−	26.1176i	−0.262020	−	0.908746i
$827$	1.12502			0.0391208			0.0195604	−	0.999809i	$-0.493773\pi$
$827$	1.12502			0.0391208			0.0195604	+	0.999809i	$0.493773\pi$
$828$	21.5958	−	30.4436i	0.750508	−	1.05799i
$829$	−0.00110719	+	0.00191771i	−3.84543e−5	+	6.66048e-5i	−0.866045	−	0.499967i	$-0.833346\pi$
$829$	−0.00110719	+	0.00191771i	−3.84543e−5	+	6.66048e-5i	0.866006	+	0.500033i	$0.166679\pi$
$830$	−2.34475	−	19.3506i	−0.0813874	−	0.671670i
$831$	12.7087	−	1.20482i	0.440859	−	0.0417948i
$832$	−36.5417	+	32.2768i	−1.26686	+	1.11900i
$833$	13.6188	−	4.51715i	0.471862	−	0.156510i
$834$	19.9928	−	4.36812i	0.692294	−	0.151256i
$835$	11.5818	−	6.68676i	0.400805	−	0.231405i
$836$	22.8754	+	23.8394i	0.791163	+	0.824502i
$837$	9.58301	−	39.1534i	0.331237	−	1.35334i
$838$	−5.53096	+	12.9728i	−0.191064	+	0.448137i
$839$	−31.8724			−1.10036			−0.550178	−	0.835047i	$-0.685440\pi$
$839$	−31.8724			−1.10036			−0.550178	+	0.835047i	$0.685440\pi$
$840$	−11.7773	−	5.41259i	−0.406354	−	0.186752i
$841$	−27.4555			−0.946742
$842$	−4.05255	+	9.50519i	−0.139660	+	0.327571i
$843$	4.87118	+	6.85046i	0.167772	+	0.235942i
$844$	5.99874	−	5.75618i	0.206485	−	0.198136i
$845$	−20.9076	+	12.0710i	−0.719245	+	0.415256i
$846$	−51.6057	−	11.2139i	−1.77424	−	0.385542i
$847$	−1.17580	−	7.27975i	−0.0404009	−	0.250135i
$848$	−9.18961	−	5.82385i	−0.315573	−	0.199992i
$849$	−1.96776	−	20.7563i	−0.0675335	−	0.712355i
$850$	0.348703	+	2.87776i	0.0119604	+	0.0987062i
$851$	0.169115	−	0.292917i	0.00579720	−	0.0100411i
$852$	4.32152	−	22.7265i	0.148053	−	0.778596i
$853$	−19.0335			−0.651696			−0.325848	−	0.945422i	$-0.605650\pi$
$853$	−19.0335			−0.651696			−0.325848	+	0.945422i	$0.605650\pi$
$854$	−7.78945	+	31.4379i	−0.266549	+	1.07578i
$855$	10.0989	−	8.72676i	0.345375	−	0.298449i
$856$	25.2057	−	30.8248i	0.861513	−	1.05357i
$857$	17.5296	−	30.3621i	0.598799	−	1.03715i	−0.394199	−	0.919025i	$-0.628978\pi$
$857$	17.5296	−	30.3621i	0.598799	−	1.03715i	0.992999	−	0.118126i	$-0.0376886\pi$
$858$	−16.8299	+	52.8134i	−0.574564	+	1.80302i
$859$	14.4471	+	25.0231i	0.492928	+	0.853776i	0.999967	−	0.00814729i	$-0.00259339\pi$
$859$	14.4471	+	25.0231i	0.492928	+	0.853776i	−0.507039	+	0.861923i	$0.669260\pi$
$860$	3.72582	−	12.8393i	0.127049	−	0.437817i
$861$	−20.8046	+	5.41554i	−0.709018	+	0.184561i
$862$	10.0419	+	13.3703i	0.342030	+	0.455393i
$863$	−13.8732	+	8.00968i	−0.472248	+	0.272653i	−0.717180	−	0.696888i	$-0.754568\pi$
$863$	−13.8732	+	8.00968i	−0.472248	+	0.272653i	0.244932	+	0.969540i	$0.421234\pi$
$864$	29.0151	+	4.70375i	0.987113	+	0.160025i
$865$	2.09035	−	3.62060i	0.0710742	−	0.123104i
$866$	8.82378	−	20.6960i	0.299844	−	0.703280i
$867$	−20.1581	−	9.22244i	−0.684604	−	0.313210i
$868$	5.00765	−	40.7422i	0.169971	−	1.38288i
$869$	−51.0788			−1.73273
$870$	−2.25068	+	2.04973i	−0.0763053	+	0.0694923i
$871$	22.7620	+	13.1416i	0.771260	+	0.445287i
$872$	4.51752	−	27.6682i	0.152983	−	0.936963i
$873$	−29.6369	−	10.3025i	−1.00306	−	0.348688i
$874$	23.5061	+	31.2970i	0.795105	+	1.05864i
$875$	−0.940605	+	2.47291i	−0.0317983	+	0.0835995i
$876$	−24.3103	−	20.9593i	−0.821369	−	0.708148i
$877$	22.6522	−	13.0782i	0.764910	−	0.441621i	−0.0661458	−	0.997810i	$-0.521070\pi$
$877$	22.6522	−	13.0782i	0.764910	−	0.441621i	0.831056	+	0.556189i	$0.187737\pi$
$878$	26.3779	−	3.19626i	0.890210	−	0.107868i
$879$	23.1628	+	32.5744i	0.781261	+	1.09871i
$880$	14.8398	+	0.612679i	0.500249	+	0.0206534i
$881$	25.2590			0.850998			0.425499	−	0.904959i	$-0.360099\pi$
$881$	25.2590			0.850998			0.425499	+	0.904959i	$0.360099\pi$
$882$	−29.5309	+	3.15081i	−0.994356	+	0.106093i
$883$			53.2980i			1.79362i	0.442416	+	0.896810i	$0.354122\pi$
$883$			53.2980i			1.79362i	−0.442416	+	0.896810i	$0.645878\pi$
$884$	24.2612	−	5.96717i	0.815994	−	0.200698i
$885$	10.2544	−	7.29166i	0.344699	−	0.245107i
$886$	0.186476	+	1.53894i	0.00626479	+	0.0517017i
$887$	−29.4551	−	51.0177i	−0.989005	−	1.71301i	−0.622572	−	0.782562i	$-0.713912\pi$
$887$	−29.4551	−	51.0177i	−0.989005	−	1.71301i	−0.366433	−	0.930445i	$-0.619421\pi$
$888$	0.265754	+	0.0179193i	0.00891811	+	0.000601331i
$889$	−22.1671	−	8.43157i	−0.743460	−	0.282786i
$890$	6.10572	+	8.12942i	0.204664	+	0.272499i
$891$	31.0578	−	12.3359i	1.04047	−	0.413267i
$892$	33.6805	−	32.3187i	1.12771	−	1.08211i
$893$	27.6895	−	47.9596i	0.926593	−	1.60491i
$894$	13.7435	+	15.0909i	0.459653	+	0.504717i
$895$			0.881268i			0.0294575i
$896$	29.9056	+	1.28602i	0.999077	+	0.0429631i
$897$	−27.3197	+	59.7144i	−0.912178	+	1.99381i
$898$	−7.81700	+	18.3346i	−0.260857	+	0.611835i
$899$	−8.34919	−	4.82041i	−0.278461	−	0.160770i
$900$	0.559523	−	5.97385i	0.0186508	−	0.199128i
$901$	2.78759	+	4.82824i	0.0928679	+	0.160852i
$902$	19.6973	−	14.7939i	0.655847	−	0.492584i
$903$	−7.71658	−	29.6443i	−0.256792	−	0.986502i
$904$	−3.04071	+	1.15062i	−0.101133	+	0.0382690i
$905$	7.76119	−	4.48093i	0.257991	−	0.148951i
$906$	−14.6510	+	45.9759i	−0.486748	+	1.52745i
$907$	−12.6965	−	7.33031i	−0.421580	−	0.243399i	0.274173	−	0.961680i	$-0.411596\pi$
$907$	−12.6965	−	7.33031i	−0.421580	−	0.243399i	−0.695753	+	0.718281i	$0.744929\pi$
$908$	5.44615	+	22.1429i	0.180737	+	0.734837i
$909$	−21.9714	+	18.9861i	−0.728744	+	0.629729i
$910$	22.1340	+	5.48420i	0.733734	+	0.181799i
$911$			40.0568i			1.32714i	0.748114	+	0.663571i	$0.230960\pi$
$911$			40.0568i			1.32714i	−0.748114	+	0.663571i	$0.769040\pi$
$912$	−13.9690	+	27.4767i	−0.462560	+	0.909845i
$913$	44.3213	+	25.5889i	1.46682	+	0.846870i
$914$	0.949579	+	7.83663i	0.0314093	+	0.259213i
$915$	−14.9260	+	1.41504i	−0.493440	+	0.0467796i
$916$	6.72841	−	23.1864i	0.222313	−	0.766100i
$917$	−39.1884	+	6.32956i	−1.29411	+	0.209021i
$918$	−12.0542	−	9.03217i	−0.397847	−	0.298106i
$919$	−3.35888	−	5.81776i	−0.110799	−	0.191910i	0.805293	−	0.592876i	$-0.202008\pi$
$919$	−3.35888	−	5.81776i	−0.110799	−	0.191910i	−0.916093	+	0.400966i	$0.868674\pi$
$920$	17.3655	+	2.83535i	0.572523	+	0.0934786i
$921$	−10.1034	+	7.18425i	−0.332918	+	0.236729i
$922$	15.9924	−	37.5098i	0.526680	−	1.23532i
$923$			40.6993i			1.33963i
$924$	29.9331	−	16.1905i	0.984725	−	0.532628i
$925$		−	0.0543699i		−	0.00178767i
$926$	17.6638	+	7.53097i	0.580467	+	0.247483i
$927$	5.78494	+	30.2361i	0.190002	+	0.993082i
$928$	3.02162	−	6.34772i	0.0991896	−	0.208374i
$929$	22.3117	+	38.6450i	0.732022	+	1.26790i	0.956018	+	0.293310i	$0.0947567\pi$
$929$	22.3117	+	38.6450i	0.732022	+	1.26790i	−0.223995	+	0.974590i	$0.571910\pi$
$930$	18.5640	−	4.05594i	0.608736	−	0.133000i
$931$	6.28886	−	30.5016i	0.206109	−	0.999649i
$932$	−16.6302	−	4.82588i	−0.544739	−	0.158077i
$933$	3.80869	+	40.1747i	0.124691	+	1.31526i
$934$	−18.0804	+	2.19084i	−0.591610	+	0.0716864i
$935$	−6.59131	−	3.80550i	−0.215559	−	0.124453i
$936$	−51.6938	+	1.40613i	−1.68967	+	0.0459609i
$937$			6.28708i			0.205390i	0.994713	+	0.102695i	$0.0327466\pi$
$937$			6.28708i			0.205390i	−0.994713	+	0.102695i	$0.967253\pi$
$938$	−4.47054	−	15.5049i	−0.145968	−	0.506253i
$939$	2.11210	−	4.61656i	0.0689259	−	0.150656i
$940$	−5.94582	−	24.1744i	−0.193931	−	0.788483i
$941$	40.2732	+	23.2517i	1.31287	+	0.757985i	0.982570	−	0.185892i	$-0.0595175\pi$
$941$	40.2732	+	23.2517i	1.31287	+	0.757985i	0.330298	+	0.943877i	$0.392851\pi$
$942$	11.6682	−	36.6155i	0.380170	−	1.19300i
$943$	25.2738	−	14.5919i	0.823029	−	0.475176i
$944$	−15.5549	+	24.5444i	−0.506268	+	0.798854i
$945$	−5.90162	−	12.4166i	−0.191980	−	0.403911i
$946$	21.0798	+	28.0665i	0.685363	+	0.912521i
$947$	−1.78889	−	3.09844i	−0.0581310	−	0.100686i	0.835495	−	0.549497i	$-0.185181\pi$
$947$	−1.78889	−	3.09844i	−0.0581310	−	0.100686i	−0.893626	+	0.448812i	$0.851847\pi$
$948$	−15.6980	−	44.9936i	−0.509846	−	1.46132i
$949$	48.9048	+	28.2352i	1.58752	+	0.916552i
$950$	5.78778	+	2.46763i	0.187780	+	0.0800605i
$951$	−24.3656	−	11.1474i	−0.790109	−	0.361480i
$952$	−13.2708	−	7.69227i	−0.430110	−	0.249308i
$953$			27.3490i			0.885921i	0.896541	+	0.442960i	$0.146072\pi$
$953$			27.3490i			0.885921i	−0.896541	+	0.442960i	$0.853928\pi$
$954$	−3.51613	−	10.9909i	−0.113839	−	0.355842i
$955$	−1.53973	+	2.66689i	−0.0498244	+	0.0862984i
$956$	10.0509	−	9.64450i	0.325069	−	0.311925i
$957$	−0.754346	−	7.95697i	−0.0243845	−	0.257212i
$958$	2.86439	−	2.15135i	0.0925443	−	0.0695068i
$959$	−18.9330	−	23.2348i	−0.611377	−	0.750292i
$960$	4.02100	+	13.2602i	0.129777	+	0.427970i
$961$	14.5893	+	25.2694i	0.470622	+	0.815141i
$962$	−0.465202	+	0.0563694i	−0.0149987	+	0.00181742i
$963$	41.4813	−	7.93644i	1.33672	−	0.255748i
$964$	7.03743	+	28.6127i	0.226660	+	0.921552i
$965$		−	14.8451i		−	0.477880i
$966$	37.5110	−	14.7756i	1.20690	−	0.475398i
$967$	−23.5270			−0.756577			−0.378288	−	0.925688i	$-0.623487\pi$
$967$	−23.5270			−0.756577			−0.378288	+	0.925688i	$0.623487\pi$
$968$	−4.99023	+	6.10270i	−0.160392	+	0.196148i
$969$	12.8727	−	9.15347i	0.413532	−	0.294052i
$970$	−1.77924	−	14.6836i	−0.0571281	−	0.471463i
$971$	39.1004	−	22.5746i	1.25479	−	0.724454i	0.282734	−	0.959198i	$-0.408759\pi$
$971$	39.1004	−	22.5746i	1.25479	−	0.724454i	0.972057	+	0.234744i	$0.0754253\pi$
$972$	20.4112	+	23.5666i	0.654689	+	0.755898i
$973$	20.6600	+	7.85835i	0.662331	+	0.251927i
$974$	−32.3120	+	24.2685i	−1.03534	+	0.777612i
$975$	0.996262	+	10.5087i	0.0319059	+	0.336549i
$976$	30.6746	−	16.0607i	0.981868	−	0.514090i
$977$	−1.31173	−	0.757327i	−0.0419659	−	0.0242290i	0.478870	−	0.877886i	$-0.341046\pi$
$977$	−1.31173	−	0.757327i	−0.0419659	−	0.0242290i	−0.520836	+	0.853657i	$0.674380\pi$
$978$	31.8224	−	28.9811i	1.01757	−	0.926714i
$979$	−26.6940			−0.853144
$980$	−7.45362	−	11.8509i	−0.238097	−	0.378563i
$981$	22.4987	−	19.4418i	0.718330	−	0.620730i
$982$	44.7996	+	19.1004i	1.42961	+	0.609517i
$983$	−19.5897	+	33.9303i	−0.624814	+	1.08221i	0.363763	+	0.931492i	$0.381492\pi$
$983$	−19.5897	+	33.9303i	−0.624814	+	1.08221i	−0.988577	+	0.150718i	$0.951841\pi$
$984$	19.0850	+	12.8041i	0.608408	+	0.408178i
$985$	−12.5096	+	7.22239i	−0.398587	+	0.230125i
$986$	−2.88058	+	2.16350i	−0.0917364	+	0.0689000i
$987$	−40.0451	−	40.6215i	−1.27465	−	1.29300i
$988$	15.1130	−	52.0800i	0.480809	−	1.65689i
$989$	20.7919	+	36.0125i	0.661142	+	1.14513i
$990$	11.6591	+	10.5940i	0.370551	+	0.336700i
$991$	20.2495	−	35.0732i	0.643247	−	1.11414i	−0.341456	−	0.939898i	$-0.610920\pi$
$991$	20.2495	−	35.0732i	0.643247	−	1.11414i	0.984703	−	0.174239i	$-0.0557467\pi$
$992$	−36.1457	+	24.8838i	−1.14763	+	0.790062i
$993$	4.87561	−	10.6569i	0.154723	−	0.338187i
$994$	17.3312	−	17.9997i	0.549714	−	0.570916i
$995$	18.2841			0.579644
$996$	−8.91922	+	46.9053i	−0.282616	+	1.48625i
$997$	−7.76394	+	13.4475i	−0.245886	+	0.425888i	−0.962380	−	0.271705i	$-0.912412\pi$
$997$	−7.76394	+	13.4475i	−0.245886	+	0.425888i	0.716494	+	0.697593i	$0.245746\pi$
$998$	−37.6794	+	4.56568i	−1.19272	+	0.144524i
$999$	0.204068	+	0.195373i	0.00645642	+	0.00618134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.cf.a.101.17	✓	256
3.2	odd	2	inner	840.2.cf.a.101.112	yes	256
7.5	odd	6	inner	840.2.cf.a.341.69	yes	256
8.5	even	2	inner	840.2.cf.a.101.60	yes	256
21.5	even	6	inner	840.2.cf.a.341.60	yes	256
24.5	odd	2	inner	840.2.cf.a.101.69	yes	256
56.5	odd	6	inner	840.2.cf.a.341.112	yes	256
168.5	even	6	inner	840.2.cf.a.341.17	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.cf.a.101.17	✓	256	1.1	even	1	trivial
840.2.cf.a.101.60	yes	256	8.5	even	2	inner
840.2.cf.a.101.69	yes	256	24.5	odd	2	inner
840.2.cf.a.101.112	yes	256	3.2	odd	2	inner
840.2.cf.a.341.17	yes	256	168.5	even	6	inner
840.2.cf.a.341.60	yes	256	21.5	even	6	inner
840.2.cf.a.341.69	yes	256	7.5	odd	6	inner
840.2.cf.a.341.112	yes	256	56.5	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.cf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30091 - 0.554645i) q^{2} +(-1.41157 + 1.00373i) q^{3} +(1.38474 + 1.44309i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(2.39304 - 0.522843i) q^{6} +(2.47291 + 0.940605i) q^{7} +(-1.00102 - 2.64537i) q^{8} +(0.985054 - 2.83367i) q^{9} +(1.40394 - 0.170119i) q^{10} +(-1.85655 + 3.21564i) q^{11} +(-3.40312 - 0.647116i) q^{12} +6.09443 q^{13} +(-2.69533 - 2.59523i) q^{14} +(0.720590 - 1.57504i) q^{15} +(-0.165004 + 3.99660i) q^{16} +(1.02488 - 1.77515i) q^{17} +(-2.85315 + 3.13999i) q^{18} +(-2.22451 - 3.85297i) q^{19} +(-1.92076 - 0.557382i) q^{20} +(-4.43479 + 1.15440i) q^{21} +(4.19875 - 3.15354i) q^{22} +(5.38747 - 3.11046i) q^{23} +(4.06824 + 2.72937i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-7.92831 - 3.38025i) q^{26} +(1.45376 + 4.98864i) q^{27} +(2.06695 + 4.87111i) q^{28} +1.24278 q^{29} +(-1.81101 + 1.64931i) q^{30} +(-6.71818 - 3.87874i) q^{31} +(2.43135 - 5.10769i) q^{32} +(-0.606984 - 6.40258i) q^{33} +(-2.31786 + 1.74086i) q^{34} +(-2.61190 + 0.421865i) q^{35} +(5.45327 - 2.50237i) q^{36} +(0.0470857 - 0.0271850i) q^{37} +(0.756861 + 6.24618i) q^{38} +(-8.60271 + 6.11716i) q^{39} +(2.18959 + 1.79045i) q^{40} +4.69122 q^{41} +(6.40955 + 0.957965i) q^{42} +6.68450i q^{43} +(-7.21129 + 1.77365i) q^{44} +(0.563752 + 2.94655i) q^{45} +(-8.73382 + 1.05829i) q^{46} +(6.22372 + 10.7798i) q^{47} +(-3.77859 - 5.80709i) q^{48} +(5.23052 + 4.65206i) q^{49} +(-1.13079 + 0.849299i) q^{50} +(0.335077 + 3.53445i) q^{51} +(8.43918 + 8.79480i) q^{52} +(-1.35995 + 2.35551i) q^{53} +(0.875710 - 7.29610i) q^{54} -3.71310i q^{55} +(0.0128224 - 7.48330i) q^{56} +(7.00739 + 3.20592i) q^{57} +(-1.61674 - 0.689300i) q^{58} +(6.29130 + 3.63228i) q^{59} +(3.27075 - 1.14114i) q^{60} +(-4.32809 - 7.49648i) q^{61} +(6.58842 + 8.77210i) q^{62} +(5.10131 - 6.08084i) q^{63} +(-5.99593 + 5.29612i) q^{64} +(-5.27793 + 3.04721i) q^{65} +(-2.76153 + 8.66584i) q^{66} +(3.73488 + 2.15633i) q^{67} +(3.98089 - 0.979120i) q^{68} +(-4.48273 + 9.79819i) q^{69} +(3.63184 + 0.899870i) q^{70} +6.67812i q^{71} +(-8.48214 + 0.230724i) q^{72} +(8.02450 + 4.63295i) q^{73} +(-0.0763324 + 0.00924933i) q^{74} +(0.163471 + 1.72432i) q^{75} +(2.47981 - 8.54551i) q^{76} +(-7.61573 + 6.20570i) q^{77} +(14.5842 - 3.18643i) q^{78} +(6.87818 + 11.9134i) q^{79} +(-1.85540 - 3.54366i) q^{80} +(-7.05934 - 5.58263i) q^{81} +(-6.10286 - 2.60196i) q^{82} -13.7830i q^{83} +(-7.80692 - 4.80125i) q^{84} +2.04977i q^{85} +(3.70752 - 8.69593i) q^{86} +(-1.75426 + 1.24741i) q^{87} +(10.3650 + 1.69234i) q^{88} +(3.59457 + 6.22597i) q^{89} +(0.900901 - 4.14589i) q^{90} +(15.0709 + 5.73245i) q^{91} +(11.9489 + 3.46743i) q^{92} +(13.3764 - 1.26812i) q^{93} +(-2.11754 - 17.4755i) q^{94} +(3.85297 + 2.22451i) q^{95} +(1.69473 + 9.65028i) q^{96} -10.4589i q^{97} +(-4.22420 - 8.95299i) q^{98} +(7.28326 + 8.42843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 30 q^{12} + 16 q^{16} - 10 q^{18} + 8 q^{22} + 128 q^{25} + 12 q^{28} - 40 q^{36} - 54 q^{42} + 16 q^{46} + 16 q^{49} + 36 q^{52} - 72 q^{54} - 16 q^{58} - 14 q^{60} + 80 q^{63} - 48 q^{64} - 60 q^{66}+ \cdots - 144 q^{96}+O(q^{100}) \) 256 * q + 30 * q^12 + 16 * q^16 - 10 * q^18 + 8 * q^22 + 128 * q^25 + 12 * q^28 - 40 * q^36 - 54 * q^42 + 16 * q^46 + 16 * q^49 + 36 * q^52 - 72 * q^54 - 16 * q^58 - 14 * q^60 + 80 * q^63 - 48 * q^64 - 60 * q^66 - 12 * q^70 - 50 * q^72 + 48 * q^73 - 16 * q^78 + 64 * q^79 - 8 * q^81 - 72 * q^82 - 56 * q^84 - 8 * q^88 - 72 * q^94 - 144 * q^96

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