LMFDB - Embedded newform 230.2.j.a.209.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(9,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, degree $10$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			209.6
Character	$\chi$	$=$	230.209
Dual form			230.2.j.a.219.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.540641 + 0.841254i) q^{2} +(2.56448 - 0.368717i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(2.23602 + 0.0141641i) q^{5} +(-1.07628 + 2.35672i) q^{6} +(-1.82575 - 1.58202i) q^{7} +(0.989821 + 0.142315i) q^{8} +(3.56212 - 1.04593i) q^{9} +(-1.22080 + 1.87340i) q^{10} +(1.25768 - 0.808265i) q^{11} +(-1.40072 - 2.17956i) q^{12} +(-3.06511 + 2.65594i) q^{13} +(2.31795 - 0.680612i) q^{14} +(5.73946 - 0.788135i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-5.62426 - 2.56851i) q^{17} +(-1.04593 + 3.56212i) q^{18} +(0.291448 + 0.638182i) q^{19} +(-0.915993 - 2.03984i) q^{20} +(-5.26540 - 3.38387i) q^{21} +1.49501i q^{22} +(3.56194 + 3.21132i) q^{23} +2.59085 q^{24} +(4.99960 + 0.0633425i) q^{25} +(-0.577190 - 4.01445i) q^{26} +(1.67918 - 0.766856i) q^{27} +(-0.680612 + 2.31795i) q^{28} +(-2.53349 + 5.54757i) q^{29} +(-2.43996 + 5.25444i) q^{30} +(-0.649873 + 4.51997i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(2.92729 - 2.53651i) q^{33} +(5.20148 - 3.34279i) q^{34} +(-4.06000 - 3.56329i) q^{35} +(-2.43118 - 2.80573i) q^{36} +(1.60042 + 5.45053i) q^{37} +(-0.694442 - 0.0998457i) q^{38} +(-6.88114 + 7.94125i) q^{39} +(2.21125 + 0.332239i) q^{40} +(-4.89061 - 1.43601i) q^{41} +(5.69338 - 2.60008i) q^{42} +(4.99509 - 0.718186i) q^{43} +(-1.25768 - 0.808265i) q^{44} +(7.97981 - 2.28828i) q^{45} +(-4.62726 + 1.26033i) q^{46} -4.52400i q^{47} +(-1.40072 + 2.17956i) q^{48} +(-0.165637 - 1.15203i) q^{49} +(-2.75627 + 4.17168i) q^{50} +(-15.3704 - 4.51315i) q^{51} +(3.68922 + 1.68481i) q^{52} +(-4.01724 - 3.48096i) q^{53} +(-0.262713 + 1.82721i) q^{54} +(2.82366 - 1.78948i) q^{55} +(-1.58202 - 1.82575i) q^{56} +(0.982721 + 1.52914i) q^{57} +(-3.29720 - 5.13055i) q^{58} +(-9.64692 - 11.1331i) q^{59} +(-3.10117 - 4.89339i) q^{60} +(2.04923 - 14.2527i) q^{61} +(-3.45109 - 2.99039i) q^{62} +(-8.15822 - 3.72573i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-6.89129 + 5.89532i) q^{65} +(0.551236 + 3.83393i) q^{66} +(-1.77215 + 2.75752i) q^{67} +6.18301i q^{68} +(10.3186 + 6.92201i) q^{69} +(5.19263 - 1.48903i) q^{70} +(9.51232 + 6.11320i) q^{71} +(3.67472 - 0.528345i) q^{72} +(3.05196 - 1.39378i) q^{73} +(-5.45053 - 1.60042i) q^{74} +(12.8447 - 1.68099i) q^{75} +(0.459439 - 0.530221i) q^{76} +(-3.57490 - 0.513993i) q^{77} +(-2.96039 - 10.0821i) q^{78} +(1.54077 + 1.77814i) q^{79} +(-1.47499 + 1.68060i) q^{80} +(-5.34601 + 3.43567i) q^{81} +(3.85212 - 3.33788i) q^{82} +(-0.823140 - 2.80336i) q^{83} +(-0.890748 + 6.19529i) q^{84} +(-12.5396 - 5.82292i) q^{85} +(-2.09637 + 4.59042i) q^{86} +(-4.45160 + 15.1608i) q^{87} +(1.35991 - 0.621051i) q^{88} +(-0.515328 - 3.58419i) q^{89} +(-2.38919 + 7.95018i) q^{90} +9.79786 q^{91} +(1.44143 - 4.57409i) q^{92} +11.8310i q^{93} +(3.80583 + 2.44586i) q^{94} +(0.642645 + 1.43112i) q^{95} +(-1.07628 - 2.35672i) q^{96} +(-3.34235 + 11.3830i) q^{97} +(1.05870 + 0.483491i) q^{98} +(3.63464 - 4.19460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$3$	2.56448	−	0.368717i	1.48060	−	0.212879i	0.645834	−	0.763478i	$-0.276510\pi$
$3$	2.56448	−	0.368717i	1.48060	−	0.212879i	0.834769	+	0.550600i	$0.185601\pi$
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	2.23602	+	0.0141641i	0.999980	+	0.00633437i
$5$	2.23602	+	0.0141641i	0.999980	+	0.00633437i
$6$	−1.07628	+	2.35672i	−0.439389	+	0.962127i
$7$	−1.82575	−	1.58202i	−0.690067	−	0.597946i	0.237596	−	0.971364i	$-0.423640\pi$
$7$	−1.82575	−	1.58202i	−0.690067	−	0.597946i	−0.927663	+	0.373418i	$0.878186\pi$
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	3.56212	−	1.04593i	1.18737	−	0.348645i
$10$	−1.22080	+	1.87340i	−0.386051	+	0.592423i
$11$	1.25768	−	0.808265i	0.379206	−	0.243701i	−0.337127	−	0.941459i	$-0.609455\pi$
$11$	1.25768	−	0.808265i	0.379206	−	0.243701i	0.716333	+	0.697758i	$0.245819\pi$
$12$	−1.40072	−	2.17956i	−0.404353	−	0.629185i
$13$	−3.06511	+	2.65594i	−0.850110	+	0.736624i	−0.966524	−	0.256576i	$-0.917405\pi$
$13$	−3.06511	+	2.65594i	−0.850110	+	0.736624i	0.116414	+	0.993201i	$0.462860\pi$
$14$	2.31795	−	0.680612i	0.619498	−	0.181901i
$15$	5.73946	−	0.788135i	1.48192	−	0.203496i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−5.62426	−	2.56851i	−1.36408	−	0.622956i	−0.407177	−	0.913349i	$-0.633487\pi$
$17$	−5.62426	−	2.56851i	−1.36408	−	0.622956i	−0.956907	+	0.290393i	$0.906214\pi$
$18$	−1.04593	+	3.56212i	−0.246529	+	0.839601i
$19$	0.291448	+	0.638182i	0.0668628	+	0.146409i	0.940113	−	0.340863i	$-0.110719\pi$
$19$	0.291448	+	0.638182i	0.0668628	+	0.146409i	−0.873250	+	0.487272i	$0.837992\pi$
$20$	−0.915993	−	2.03984i	−0.204822	−	0.456123i
$21$	−5.26540	−	3.38387i	−1.14901	−	0.738421i
$22$			1.49501i			0.318738i
$23$	3.56194	+	3.21132i	0.742716	+	0.669606i
$23$	3.56194	+	3.21132i	0.742716	+	0.669606i
$24$	2.59085			0.528855
$25$	4.99960	+	0.0633425i	0.999920	+	0.0126685i
$26$	−0.577190	−	4.01445i	−0.113196	−	0.787298i
$27$	1.67918	−	0.766856i	0.323159	−	0.147582i
$28$	−0.680612	+	2.31795i	−0.128623	+	0.438051i
$29$	−2.53349	+	5.54757i	−0.470457	+	1.03016i	0.514521	+	0.857478i	$0.327970\pi$
$29$	−2.53349	+	5.54757i	−0.470457	+	1.03016i	−0.984978	+	0.172679i	$0.944758\pi$
$30$	−2.43996	+	5.25444i	−0.445474	+	0.959325i
$31$	−0.649873	+	4.51997i	−0.116721	+	0.811810i	0.844406	+	0.535703i	$0.179953\pi$
$31$	−0.649873	+	4.51997i	−0.116721	+	0.811810i	−0.961127	+	0.276107i	$0.910956\pi$
$32$	−0.281733	−	0.959493i	−0.0498038	−	0.169616i
$33$	2.92729	−	2.53651i	0.509575	−	0.441549i
$34$	5.20148	−	3.34279i	0.892046	−	0.573283i
$35$	−4.06000	−	3.56329i	−0.686265	−	0.602305i
$36$	−2.43118	−	2.80573i	−0.405196	−	0.467621i
$37$	1.60042	+	5.45053i	0.263108	+	0.896062i	0.980020	+	0.198899i	$0.0637366\pi$
$37$	1.60042	+	5.45053i	0.263108	+	0.896062i	−0.716912	+	0.697163i	$0.754445\pi$
$38$	−0.694442	−	0.0998457i	−0.112653	−	0.0161971i
$39$	−6.88114	+	7.94125i	−1.10186	+	1.27162i
$40$	2.21125	+	0.332239i	0.349629	+	0.0525316i
$41$	−4.89061	−	1.43601i	−0.763785	−	0.224268i	−0.123437	−	0.992352i	$-0.539392\pi$
$41$	−4.89061	−	1.43601i	−0.763785	−	0.224268i	−0.640348	+	0.768085i	$0.721210\pi$
$42$	5.69338	−	2.60008i	0.878508	−	0.401201i
$43$	4.99509	−	0.718186i	0.761744	−	0.109522i	0.249515	−	0.968371i	$-0.419729\pi$
$43$	4.99509	−	0.718186i	0.761744	−	0.109522i	0.512229	+	0.858849i	$0.328820\pi$
$44$	−1.25768	−	0.808265i	−0.189603	−	0.121850i
$45$	7.97981	−	2.28828i	1.18956	−	0.341116i
$46$	−4.62726	+	1.26033i	−0.682253	+	0.185825i
$47$		−	4.52400i		−	0.659893i	−0.944000	−	0.329947i	$-0.892969\pi$
$47$		−	4.52400i		−	0.659893i	0.944000	−	0.329947i	$-0.107031\pi$
$48$	−1.40072	+	2.17956i	−0.202176	+	0.314593i
$49$	−0.165637	−	1.15203i	−0.0236624	−	0.164576i
$50$	−2.75627	+	4.17168i	−0.389796	+	0.589965i
$51$	−15.3704	−	4.51315i	−2.15228	−	0.631967i
$52$	3.68922	+	1.68481i	0.511603	+	0.233641i
$53$	−4.01724	−	3.48096i	−0.551811	−	0.478147i	0.333756	−	0.942660i	$-0.391684\pi$
$53$	−4.01724	−	3.48096i	−0.551811	−	0.478147i	−0.885566	+	0.464513i	$0.846229\pi$
$54$	−0.262713	+	1.82721i	−0.0357508	+	0.248652i
$55$	2.82366	−	1.78948i	0.380742	−	0.241294i
$56$	−1.58202	−	1.82575i	−0.211406	−	0.243975i
$57$	0.982721	+	1.52914i	0.130165	+	0.202540i
$58$	−3.29720	−	5.13055i	−0.432944	−	0.673674i
$59$	−9.64692	−	11.1331i	−1.25592	−	1.44941i	−0.842342	−	0.538943i	$-0.818824\pi$
$59$	−9.64692	−	11.1331i	−1.25592	−	1.44941i	−0.413580	−	0.910468i	$-0.635722\pi$
$60$	−3.10117	−	4.89339i	−0.400359	−	0.631734i
$61$	2.04923	−	14.2527i	0.262377	−	1.82487i	−0.252486	−	0.967600i	$-0.581248\pi$
$61$	2.04923	−	14.2527i	0.262377	−	1.82487i	0.514864	−	0.857272i	$-0.327843\pi$
$62$	−3.45109	−	2.99039i	−0.438289	−	0.379779i
$63$	−8.15822	−	3.72573i	−1.02784	−	0.469398i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−6.89129	+	5.89532i	−0.854759	+	0.731225i
$66$	0.551236	+	3.83393i	0.0678524	+	0.471924i
$67$	−1.77215	+	2.75752i	−0.216503	+	0.336885i	−0.932469	−	0.361250i	$-0.882350\pi$
$67$	−1.77215	+	2.75752i	−0.216503	+	0.336885i	0.715966	+	0.698135i	$0.245986\pi$
$68$			6.18301i			0.749800i
$69$	10.3186	+	6.92201i	1.24221	+	0.833312i
$70$	5.19263	−	1.48903i	0.620638	−	0.177973i
$71$	9.51232	+	6.11320i	1.12891	+	0.725503i	0.965331	−	0.261028i	$-0.0840614\pi$
$71$	9.51232	+	6.11320i	1.12891	+	0.725503i	0.163574	+	0.986531i	$0.447698\pi$
$72$	3.67472	−	0.528345i	0.433070	−	0.0622660i
$73$	3.05196	−	1.39378i	0.357205	−	0.163130i	−0.228726	−	0.973491i	$-0.573456\pi$
$73$	3.05196	−	1.39378i	0.357205	−	0.163130i	0.585931	+	0.810361i	$0.300729\pi$
$74$	−5.45053	−	1.60042i	−0.633612	−	0.186045i
$75$	12.8447	−	1.68099i	1.48318	−	0.194104i
$76$	0.459439	−	0.530221i	0.0527013	−	0.0608205i
$77$	−3.57490	−	0.513993i	−0.407398	−	0.0585749i
$78$	−2.96039	−	10.0821i	−0.335198	−	1.14158i
$79$	1.54077	+	1.77814i	0.173350	+	0.200057i	0.835776	−	0.549071i	$-0.185018\pi$
$79$	1.54077	+	1.77814i	0.173350	+	0.200057i	−0.662425	+	0.749128i	$0.730473\pi$
$80$	−1.47499	+	1.68060i	−0.164909	+	0.187897i
$81$	−5.34601	+	3.43567i	−0.594001	+	0.381741i
$82$	3.85212	−	3.33788i	0.425395	−	0.368607i
$83$	−0.823140	−	2.80336i	−0.0903513	−	0.307708i	0.901902	−	0.431941i	$-0.142171\pi$
$83$	−0.823140	−	2.80336i	−0.0903513	−	0.307708i	−0.992253	+	0.124233i	$0.960353\pi$
$84$	−0.890748	+	6.19529i	−0.0971886	+	0.675961i
$85$	−12.5396	−	5.82292i	−1.36011	−	0.631584i
$86$	−2.09637	+	4.59042i	−0.226058	+	0.494998i
$87$	−4.45160	+	15.1608i	−0.477262	+	1.62540i
$88$	1.35991	−	0.621051i	0.144967	−	0.0662042i
$89$	−0.515328	−	3.58419i	−0.0546247	−	0.379923i	−0.998735	−	0.0502921i	$-0.983985\pi$
$89$	−0.515328	−	3.58419i	−0.0546247	−	0.379923i	0.944110	−	0.329631i	$-0.106924\pi$
$90$	−2.38919	+	7.95018i	−0.251842	+	0.838022i
$91$	9.79786			1.02709
$92$	1.44143	−	4.57409i	0.150280	−	0.476882i
$93$			11.8310i			1.22682i
$94$	3.80583	+	2.44586i	0.392541	+	0.252271i
$95$	0.642645	+	1.43112i	0.0659340	+	0.146830i
$96$	−1.07628	−	2.35672i	−0.109847	−	0.240532i
$97$	−3.34235	+	11.3830i	−0.339364	+	1.15577i	0.596267	+	0.802786i	$0.296650\pi$
$97$	−3.34235	+	11.3830i	−0.339364	+	1.15577i	−0.935631	+	0.352981i	$0.885168\pi$
$98$	1.05870	+	0.483491i	0.106945	+	0.0488400i
$99$	3.63464	−	4.19460i	0.365295	−	0.421573i
$100$	−2.01929	−	4.57411i	−0.201929	−	0.457411i
$101$	−18.3614	+	5.39140i	−1.82703	+	0.536464i	−0.999682	−	0.0252253i	$-0.991970\pi$
$101$	−18.3614	+	5.39140i	−1.82703	+	0.536464i	−0.827348	+	0.561690i	$0.810151\pi$
$102$	12.1065	−	10.4904i	1.19873	−	1.03870i
$103$	2.68750	+	4.18183i	0.264807	+	0.412048i	0.948039	−	0.318153i	$-0.103063\pi$
$103$	2.68750	+	4.18183i	0.264807	+	0.412048i	−0.683232	+	0.730201i	$0.739426\pi$
$104$	−3.41190	+	2.19269i	−0.334564	+	0.215011i
$105$	−11.7256	−	7.64099i	−1.14430	−	0.745684i
$106$	5.10026	−	1.49757i	0.495381	−	0.145457i
$107$	17.3483	+	2.49431i	1.67712	+	0.241134i	0.914173	−	0.405325i	$-0.132841\pi$
$107$	17.3483	+	2.49431i	1.67712	+	0.241134i	0.762949	+	0.646458i	$0.223751\pi$
$108$	−1.39511	−	1.20887i	−0.134245	−	0.116324i
$109$	6.21222	−	13.6029i	0.595022	−	1.30292i	−0.337337	−	0.941384i	$-0.609526\pi$
$109$	6.21222	−	13.6029i	0.595022	−	1.30292i	0.932359	−	0.361533i	$-0.117747\pi$
$110$	−0.0211755	+	3.34288i	−0.00201900	+	0.318731i
$111$	6.11395	+	13.3877i	0.580310	+	1.27070i
$112$	2.39122	−	0.343805i	0.225949	−	0.0324865i
$113$	10.2744	−	15.9873i	0.966535	−	1.50396i	0.106127	−	0.994353i	$-0.466155\pi$
$113$	10.2744	−	15.9873i	0.966535	−	1.50396i	0.860408	−	0.509606i	$-0.170209\pi$
$114$	−1.81770			−0.170243
$115$	7.91910	+	7.23103i	0.738460	+	0.674297i
$116$	6.09869			0.566249
$117$	−8.14039	+	12.6667i	−0.752579	+	1.17104i
$118$	14.5813	−	2.09648i	1.34232	−	0.192996i
$119$	6.20504	+	13.5871i	0.568815	+	1.24553i
$120$	5.79320	+	0.0366970i	0.528845	+	0.00334997i
$121$	−3.64109	+	7.97287i	−0.331008	+	0.724806i
$122$	10.8822	+	9.42952i	0.985232	+	0.853709i
$123$	−13.0714	−	1.87938i	−1.17860	−	0.169458i
$124$	4.38147	−	1.28652i	0.393468	−	0.115533i
$125$	11.1783	+	0.212450i	0.999819	+	0.0190021i
$126$	7.54495	−	4.84885i	0.672158	−	0.431970i
$127$	7.18318	+	11.1772i	0.637404	+	0.991820i	0.998247	+	0.0591930i	$0.0188527\pi$
$127$	7.18318	+	11.1772i	0.637404	+	0.991820i	−0.360843	+	0.932627i	$0.617511\pi$
$128$	−0.755750	+	0.654861i	−0.0667995	+	0.0578821i
$129$	12.5450	−	3.68355i	1.10453	−	0.324318i
$130$	−1.23375	−	8.98457i	−0.108207	−	0.787999i
$131$	9.11394	−	10.5181i	0.796289	−	0.918966i	−0.201883	−	0.979410i	$-0.564706\pi$
$131$	9.11394	−	10.5181i	0.796289	−	0.918966i	0.998172	+	0.0604434i	$0.0192515\pi$
$132$	−3.52333	−	1.60905i	−0.306666	−	0.140050i
$133$	0.477505	−	1.62623i	0.0414050	−	0.141012i
$134$	−1.36168	−	2.98166i	−0.117631	−	0.257576i
$135$	3.76555	−	1.69092i	0.324087	−	0.145532i
$136$	−5.20148	−	3.34279i	−0.446023	−	0.286642i
$137$		−	16.9150i		−	1.44514i	−0.691297	−	0.722571i	$-0.742960\pi$
$137$		−	16.9150i		−	1.44514i	0.691297	−	0.722571i	$-0.257040\pi$
$138$	−11.4018	+	4.93823i	−0.970588	+	0.420370i
$139$	17.9369			1.52139			0.760696	−	0.649109i	$-0.224858\pi$
$139$	17.9369			1.52139			0.760696	+	0.649109i	$0.224858\pi$
$140$	−1.55469	+	5.17335i	−0.131396	+	0.437228i
$141$	−1.66807	−	11.6017i	−0.140477	−	0.977040i
$142$	−10.2855	+	4.69723i	−0.863140	+	0.394183i
$143$	−1.70825	+	5.81775i	−0.142851	+	0.486505i
$144$	−1.54223	+	3.37702i	−0.128519	+	0.281418i
$145$	−5.74351	+	12.3686i	−0.476973	+	1.02716i
$146$	−0.477489	+	3.32101i	−0.0395173	+	0.274849i
$147$	−0.849544	−	2.89328i	−0.0700692	−	0.238634i
$148$	4.29314	−	3.72003i	0.352894	−	0.305784i
$149$	−13.3485	+	8.57858i	−1.09355	+	0.702784i	−0.957649	−	0.287937i	$-0.907030\pi$
$149$	−13.3485	+	8.57858i	−1.09355	+	0.702784i	−0.135905	+	0.990722i	$0.543394\pi$
$150$	−5.53024	+	11.7145i	−0.451542	+	0.956484i
$151$	7.06380	+	8.15206i	0.574844	+	0.663405i	0.966488	−	0.256711i	$-0.0826390\pi$
$151$	7.06380	+	8.15206i	0.574844	+	0.663405i	−0.391644	+	0.920117i	$0.628094\pi$
$152$	0.197659	+	0.673164i	0.0160322	+	0.0546008i
$153$	−22.7208	−	3.26676i	−1.83687	−	0.264102i
$154$	2.36514	−	2.72951i	0.190588	−	0.219950i
$155$	−1.51715	+	10.0975i	−0.121861	+	0.811054i
$156$	10.0821	+	2.96039i	0.807218	+	0.237020i
$157$	−2.78637	+	1.27249i	−0.222377	+	0.101556i	−0.523488	−	0.852033i	$-0.675370\pi$
$157$	−2.78637	+	1.27249i	−0.222377	+	0.101556i	0.301112	+	0.953589i	$0.402642\pi$
$158$	−2.32887	+	0.334842i	−0.185275	+	0.0266386i
$159$	−11.5856	−	7.44563i	−0.918800	−	0.590477i
$160$	−0.616370	−	2.14944i	−0.0487283	−	0.169928i
$161$	−1.42284	−	11.4981i	−0.112135	−	0.906178i
$162$		−	6.35481i		−	0.499281i
$163$	−1.59230	+	2.47766i	−0.124718	+	0.194065i	−0.897998	−	0.440000i	$-0.854979\pi$
$163$	−1.59230	+	2.47766i	−0.124718	+	0.194065i	0.773280	+	0.634065i	$0.218615\pi$
$164$	0.725390	+	5.04520i	0.0566435	+	0.393964i
$165$	6.58141	−	5.63023i	0.512362	−	0.438313i
$166$	2.80336	+	0.823140i	0.217583	+	0.0638880i
$167$	−14.0597	−	6.42086i	−1.08797	−	0.496861i	−0.211043	−	0.977477i	$-0.567686\pi$
$167$	−14.0597	−	6.42086i	−1.08797	−	0.496861i	−0.876931	+	0.480615i	$0.840413\pi$
$168$	−4.73023	−	4.09877i	−0.364945	−	0.316227i
$169$	0.490833	−	3.41382i	0.0377564	−	0.262602i
$170$	11.6780	−	7.40087i	0.895660	−	0.567621i
$171$	1.70567	+	1.96845i	0.130436	+	0.150531i
$172$	−2.72832	−	4.24535i	−0.208033	−	0.323705i
$173$	7.00534	+	10.9005i	0.532606	+	0.828751i	0.998423	−	0.0561299i	$-0.0178761\pi$
$173$	7.00534	+	10.9005i	0.532606	+	0.828751i	−0.465818	+	0.884881i	$0.654240\pi$
$174$	−10.3473	−	11.9414i	−0.784429	−	0.905279i
$175$	−9.02779	−	8.02510i	−0.682436	−	0.606640i
$176$	−0.212762	+	1.47980i	−0.0160376	+	0.111544i
$177$	−28.8443	−	24.9937i	−2.16807	−	1.87864i
$178$	3.29382	+	1.50424i	0.246882	+	0.112747i
$179$	−10.6510	−	3.12741i	−0.796092	−	0.233754i	−0.141701	−	0.989910i	$-0.545257\pi$
$179$	−10.6510	−	3.12741i	−0.796092	−	0.233754i	−0.654392	+	0.756156i	$0.727075\pi$
$180$	−5.39642	−	6.30810i	−0.402226	−	0.470178i
$181$	0.716678	+	4.98460i	0.0532702	+	0.370503i	0.998967	+	0.0454512i	$0.0144725\pi$
$181$	0.716678	+	4.98460i	0.0532702	+	0.370503i	−0.945696	+	0.325051i	$0.894618\pi$
$182$	−5.29712	+	8.24248i	−0.392649	+	0.610973i
$183$		−	37.3064i		−	2.75777i
$184$	3.06867	+	3.68555i	0.226225	+	0.271702i
$185$	3.50138	+	12.2102i	0.257426	+	0.897711i
$186$	−9.95285	−	6.39631i	−0.729779	−	0.469000i
$187$	−9.14959	+	1.31551i	−0.669084	+	0.0961998i
$188$	−4.11517	+	1.87934i	−0.300130	+	0.137065i
$189$	−4.27894	−	1.25641i	−0.311247	−	0.0913903i
$190$	−1.55137	−	0.233093i	−0.112548	−	0.0169104i
$191$	4.85692	−	5.60518i	0.351434	−	0.405577i	−0.552317	−	0.833634i	$-0.686256\pi$
$191$	4.85692	−	5.60518i	0.351434	−	0.405577i	0.903752	+	0.428057i	$0.140802\pi$
$192$	2.56448	+	0.368717i	0.185075	+	0.0266098i
$193$	3.79451	+	12.9229i	0.273135	+	0.930212i	0.975795	+	0.218686i	$0.0701771\pi$
$193$	3.79451	+	12.9229i	0.273135	+	0.930212i	−0.702660	+	0.711525i	$0.748005\pi$
$194$	−7.76897	−	8.96587i	−0.557779	−	0.643712i
$195$	−15.4989	+	17.6594i	−1.10990	+	1.26461i
$196$	−0.979114	+	0.629238i	−0.0699367	+	0.0449456i
$197$	−1.13562	+	0.984024i	−0.0809099	+	0.0701088i	−0.694377	−	0.719612i	$-0.744320\pi$
$197$	−1.13562	+	0.984024i	−0.0809099	+	0.0701088i	0.613467	+	0.789720i	$0.289774\pi$
$198$	1.56368	+	5.32542i	0.111126	+	0.378461i
$199$	0.172134	−	1.19722i	0.0122022	−	0.0848684i	−0.982810	−	0.184618i	$-0.940895\pi$
$199$	0.172134	−	1.19722i	0.0122022	−	0.0848684i	0.995013	+	0.0997498i	$0.0318042\pi$
$200$	4.93970	+	0.774215i	0.349289	+	0.0547453i
$201$	−3.52790	+	7.72503i	−0.248839	+	0.544882i
$202$	5.39140	−	18.3614i	0.379338	−	1.29191i
$203$	13.4018	−	6.12042i	0.940625	−	0.429569i
$204$	2.27978	+	15.8562i	0.159616	+	1.11016i
$205$	−10.9152	−	3.28023i	−0.762350	−	0.229101i
$206$	−4.97095			−0.346343
$207$	16.0469	+	7.71356i	1.11534	+	0.536129i
$208$		−	4.05573i		−	0.281214i
$209$	0.882370	+	0.567065i	0.0610348	+	0.0392247i
$210$	12.7674	−	5.73320i	0.881032	−	0.395628i
$211$	−2.24700	−	4.92025i	−0.154690	−	0.338724i	0.816381	−	0.577513i	$-0.195977\pi$
$211$	−2.24700	−	4.92025i	−0.154690	−	0.338724i	−0.971071	+	0.238789i	$0.923250\pi$
$212$	−1.49757	+	5.10026i	−0.102854	+	0.350287i
$213$	26.6482	+	12.1698i	1.82590	+	0.833863i
$214$	−11.4775	+	13.2458i	−0.784588	+	0.905463i
$215$	11.1793	−	1.53513i	0.762423	−	0.104695i
$216$	1.77122	−	0.520079i	0.120517	−	0.0353869i
$217$	8.33717	−	7.22420i	0.565964	−	0.490410i
$218$	8.08487	+	12.5803i	0.547577	+	0.852046i
$219$	7.31279	−	4.69964i	0.494152	−	0.317572i
$220$	−2.80076	−	1.82511i	−0.188827	−	0.123049i
$221$	24.0608	−	7.06489i	1.61851	−	0.475236i
$222$	−14.5679	−	2.09455i	−0.977732	−	0.140577i
$223$	4.15604	+	3.60123i	0.278309	+	0.241156i	0.782819	−	0.622250i	$-0.213781\pi$
$223$	4.15604	+	3.60123i	0.278309	+	0.241156i	−0.504510	+	0.863406i	$0.668327\pi$
$224$	−1.00356	+	2.19750i	−0.0670533	+	0.146826i
$225$	17.8754	−	5.00362i	1.19170	−	0.333575i
$226$	7.89460	+	17.2868i	0.525141	+	1.14990i
$227$	−2.10956	+	0.303310i	−0.140017	+	0.0201314i	−0.211967	−	0.977277i	$-0.567987\pi$
$227$	−2.10956	+	0.303310i	−0.140017	+	0.0201314i	0.0719501	+	0.997408i	$0.477078\pi$
$228$	0.982721	−	1.52914i	0.0650823	−	0.101270i
$229$	−18.6710			−1.23381			−0.616906	−	0.787037i	$-0.711614\pi$
$229$	−18.6710			−1.23381			−0.616906	+	0.787037i	$0.711614\pi$
$230$	−10.3645	+	2.75258i	−0.683416	+	0.181500i
$231$	−9.35728			−0.615664
$232$	−3.29720	+	5.13055i	−0.216472	+	0.336837i
$233$	12.0965	−	1.73922i	0.792469	−	0.113940i	0.265820	−	0.964023i	$-0.414357\pi$
$233$	12.0965	−	1.73922i	0.792469	−	0.113940i	0.526649	+	0.850083i	$0.323448\pi$
$234$	−6.25487	−	13.6963i	−0.408894	−	0.895352i
$235$	0.0640783	−	10.1158i	0.00418001	−	0.659880i
$236$	−6.11958	+	13.4000i	−0.398351	+	0.872267i
$237$	4.60691	+	3.99191i	0.299251	+	0.259302i
$238$	−14.7849	−	2.12575i	−0.958364	−	0.137792i
$239$	−0.676711	+	0.198700i	−0.0437728	+	0.0128529i	−0.303546	−	0.952817i	$-0.598170\pi$
$239$	−0.676711	+	0.198700i	−0.0437728	+	0.0128529i	0.259773	+	0.965670i	$0.416352\pi$
$240$	−3.16291	+	4.85371i	−0.204165	+	0.313306i
$241$	7.17710	−	4.61244i	0.462318	−	0.297114i	−0.288671	−	0.957428i	$-0.593213\pi$
$241$	7.17710	−	4.61244i	0.462318	−	0.297114i	0.750989	+	0.660315i	$0.229577\pi$
$242$	−4.73868	−	7.37354i	−0.304614	−	0.473989i
$243$	−16.6283	+	14.4085i	−1.06670	+	0.924305i
$244$	−13.8160	+	4.05674i	−0.884479	+	0.259706i
$245$	−0.354050	−	2.57831i	−0.0226194	−	0.164722i
$246$	8.64794	−	9.98026i	0.551373	−	0.636318i
$247$	−2.58829	−	1.18203i	−0.164689	−	0.0752110i
$248$	−1.28652	+	4.38147i	−0.0816939	+	0.278224i
$249$	−3.14457	−	6.88565i	−0.199279	−	0.436360i
$250$	−6.22218	+	9.28894i	−0.393525	+	0.587484i
$251$	21.2403	+	13.6503i	1.34067	+	0.861599i	0.996993	−	0.0774875i	$-0.0246898\pi$
$251$	21.2403	+	13.6503i	1.34067	+	0.861599i	0.343681	+	0.939086i	$0.388326\pi$
$252$			8.96870i			0.564975i
$253$	7.07539	+	1.15983i	0.444826	+	0.0729181i
$254$	−13.2864			−0.833664
$255$	−34.3046	−	10.3092i	−2.14823	−	0.645587i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−5.11793	+	2.33728i	−0.319247	+	0.145795i	−0.568593	−	0.822619i	$-0.692512\pi$
$257$	−5.11793	+	2.33728i	−0.319247	+	0.145795i	0.249345	+	0.968415i	$0.419785\pi$
$258$	−3.68355	+	12.5450i	−0.229328	+	0.781018i
$259$	5.70088	−	12.4832i	0.354235	−	0.775667i
$260$	8.22532	+	3.81953i	0.510112	+	0.236877i
$261$	−3.22221	+	22.4110i	−0.199450	+	1.38721i
$262$	3.92098	+	13.3536i	0.242239	+	0.824990i
$263$	16.8925	−	14.6374i	1.04163	−	0.902581i	0.0462863	−	0.998928i	$-0.485261\pi$
$263$	16.8925	−	14.6374i	1.04163	−	0.902581i	0.995348	+	0.0963471i	$0.0307159\pi$
$264$	3.25847	−	2.09409i	0.200545	−	0.128883i
$265$	−8.93334	−	7.84041i	−0.548771	−	0.481633i
$266$	1.10992	+	1.28091i	0.0680533	+	0.0785377i
$267$	−2.64310	−	9.00157i	−0.161755	−	0.550887i
$268$	3.24451	+	0.466490i	0.198190	+	0.0284954i
$269$	−1.26262	+	1.45714i	−0.0769830	+	0.0888432i	−0.792934	−	0.609307i	$-0.791448\pi$
$269$	−1.26262	+	1.45714i	−0.0769830	+	0.0888432i	0.715951	+	0.698150i	$0.245993\pi$
$270$	−0.613314	+	4.08197i	−0.0373251	+	0.248421i
$271$	−1.10040	−	0.323107i	−0.0668445	−	0.0196273i	0.248139	−	0.968724i	$-0.420181\pi$
$271$	−1.10040	−	0.323107i	−0.0668445	−	0.0196273i	−0.314984	+	0.949097i	$0.601999\pi$
$272$	5.62426	−	2.56851i	0.341021	−	0.155739i
$273$	25.1264	−	3.61263i	1.52072	−	0.218646i
$274$	14.2298	+	9.14492i	0.859652	+	0.552465i
$275$	6.33911	−	3.96133i	0.382263	−	0.238877i
$276$	2.00999	−	12.2616i	0.120987	−	0.738064i
$277$		−	15.5372i		−	0.933538i	−0.884379	−	0.466769i	$-0.845418\pi$
$277$		−	15.5372i		−	0.933538i	0.884379	−	0.466769i	$-0.154582\pi$
$278$	−9.69744	+	15.0895i	−0.581614	+	0.905009i
$279$	2.41266	+	16.7804i	0.144442	+	1.00462i
$280$	−3.51157	−	4.10482i	−0.209856	−	0.245310i
$281$	−3.71420	−	1.09059i	−0.221570	−	0.0650589i	0.169063	−	0.985605i	$-0.445926\pi$
$281$	−3.71420	−	1.09059i	−0.221570	−	0.0650589i	−0.390633	+	0.920546i	$0.627744\pi$
$282$	10.6618	+	4.86908i	0.634901	+	0.289950i
$283$	−15.8360	−	13.7220i	−0.941354	−	0.815688i	0.0416763	−	0.999131i	$-0.486730\pi$
$283$	−15.8360	−	13.7220i	−0.941354	−	0.815688i	−0.983030	+	0.183443i	$0.941276\pi$
$284$	1.60920	−	11.1922i	0.0954884	−	0.664137i
$285$	2.17573	+	3.43312i	0.128879	+	0.203360i
$286$	−3.97066	−	4.58238i	−0.234790	−	0.270962i
$287$	6.65722	+	10.3588i	0.392963	+	0.611462i
$288$	−2.00713	−	3.12316i	−0.118271	−	0.184034i
$289$	13.9024	+	16.0443i	0.817790	+	0.943780i
$290$	−7.29995	−	11.5187i	−0.428668	−	0.676403i
$291$	−4.37428	+	30.4238i	−0.256425	+	1.78348i
$292$	−2.53566	−	2.19716i	−0.148388	−	0.128579i
$293$	−5.42971	−	2.47966i	−0.317207	−	0.144864i	0.250448	−	0.968130i	$-0.419422\pi$
$293$	−5.42971	−	2.47966i	−0.317207	−	0.144864i	−0.567655	+	0.823266i	$0.692149\pi$
$294$	2.89328	+	0.849544i	0.168740	+	0.0495464i
$295$	−21.4130	−	25.0306i	−1.24672	−	1.45734i
$296$	0.808439	+	5.62282i	0.0469896	+	0.326820i
$297$	1.49206	−	2.32169i	0.0865779	−	0.134718i
$298$		−	15.8674i		−	0.919175i
$299$	−19.4468	−	0.382764i	−1.12464	−	0.0221358i
$300$	−6.86498	−	10.9857i	−0.396350	−	0.634258i
$301$	−10.2559	−	6.59110i	−0.591143	−	0.379905i
$302$	−10.6769	+	1.53511i	−0.614388	+	0.0883357i
$303$	−45.0996	+	20.5963i	−2.59090	+	1.18323i
$304$	−0.673164	−	0.197659i	−0.0386086	−	0.0113365i
$305$	4.78400	−	31.8404i	0.273931	−	1.82317i
$306$	15.0320	−	17.3478i	0.859321	−	0.991709i
$307$	13.6163	+	1.95773i	0.777123	+	0.111733i	0.519452	−	0.854499i	$-0.326136\pi$
$307$	13.6163	+	1.95773i	0.777123	+	0.111733i	0.257671	+	0.966233i	$0.417045\pi$
$308$	1.01752	+	3.46536i	0.0579787	+	0.197457i
$309$	8.43395	+	9.73329i	0.479790	+	0.553708i
$310$	−7.67436	−	6.73545i	−0.435874	−	0.382548i
$311$	23.6829	−	15.2201i	1.34293	−	0.863050i	0.345769	−	0.938320i	$-0.387618\pi$
$311$	23.6829	−	15.2201i	1.34293	−	0.863050i	0.997163	+	0.0752698i	$0.0239818\pi$
$312$	−7.94125	+	6.88114i	−0.449585	+	0.389568i
$313$	−0.813212	−	2.76955i	−0.0459655	−	0.156544i	0.933312	−	0.359066i	$-0.116905\pi$
$313$	−0.813212	−	2.76955i	−0.0459655	−	0.156544i	−0.979278	+	0.202522i	$0.935086\pi$
$314$	0.435937	−	3.03201i	0.0246013	−	0.171106i
$315$	−18.1892	−	8.44638i	−1.02485	−	0.475900i
$316$	0.977398	−	2.14020i	0.0549829	−	0.120396i
$317$	−4.75833	+	16.2054i	−0.267254	+	0.910185i	0.711073	+	0.703119i	$0.248210\pi$
$317$	−4.75833	+	16.2054i	−0.267254	+	0.910185i	−0.978327	+	0.207066i	$0.933608\pi$
$318$	12.5273	−	5.72104i	0.702497	−	0.320820i
$319$	1.29757	+	9.02482i	0.0726501	+	0.505293i
$320$	2.14146	+	0.643551i	0.119711	+	0.0359756i
$321$	45.4090			2.53448
$322$	10.4421	+	5.01938i	0.581914	+	0.279719i
$323$		−	4.33789i		−	0.241367i
$324$	5.34601	+	3.43567i	0.297000	+	0.190871i
$325$	−15.4926	+	13.0845i	−0.859373	+	0.725796i
$326$	−1.22348	−	2.67905i	−0.0677623	−	0.148379i
$327$	10.9155	−	37.1748i	0.603629	−	2.05577i
$328$	−4.63647	−	2.11740i	−0.256006	−	0.116914i
$329$	−7.15704	+	8.25967i	−0.394581	+	0.455370i
$330$	1.17827	+	8.58056i	0.0648617	+	0.472344i
$331$	−22.3968	+	6.57628i	−1.23104	+	0.361465i	−0.831641	−	0.555313i	$-0.812598\pi$
$331$	−22.3968	+	6.57628i	−1.23104	+	0.361465i	−0.399396	+	0.916778i	$0.630780\pi$
$332$	−2.20808	+	1.91331i	−0.121184	+	0.105007i
$333$	11.4018	+	17.7415i	0.624815	+	0.972231i
$334$	13.0028	−	8.35642i	0.711484	−	0.457243i
$335$	−4.00163	+	6.14078i	−0.218633	+	0.335507i
$336$	6.00546	−	1.76336i	0.327625	−	0.0961993i
$337$	10.5303	+	1.51402i	0.573620	+	0.0824741i	0.423020	−	0.906121i	$-0.360970\pi$
$337$	10.5303	+	1.51402i	0.573620	+	0.0824741i	0.150601	+	0.988595i	$0.451879\pi$
$338$	2.60652	+	2.25857i	0.141776	+	0.122850i
$339$	20.4537	−	44.7874i	1.11089	−	2.43252i
$340$	−0.0875767	+	13.8254i	−0.00474951	+	0.749785i
$341$	2.83599	+	6.20996i	0.153578	+	0.336288i
$342$	−2.57812	+	0.370678i	−0.139409	+	0.0200440i
$343$	−10.6627	+	16.5915i	−0.575732	+	0.895857i
$344$	5.04646			0.272087
$345$	22.9746	+	15.6239i	1.23691	+	0.841164i
$346$	−12.9575			−0.696598
$347$	−7.02594	+	10.9326i	−0.377172	+	0.586892i	−0.977000	−	0.213237i	$-0.931599\pi$
$347$	−7.02594	+	10.9326i	−0.377172	+	0.586892i	0.599828	+	0.800129i	$0.295236\pi$
$348$	15.6400	−	2.24869i	0.838390	−	0.120542i
$349$	2.69252	+	5.89579i	0.144127	+	0.315594i	0.967904	−	0.251320i	$-0.0808645\pi$
$349$	2.69252	+	5.89579i	0.144127	+	0.315594i	−0.823777	+	0.566914i	$0.808137\pi$
$350$	11.6319	−	3.25596i	0.621753	−	0.174038i
$351$	−3.11016	+	6.81030i	−0.166008	+	0.363507i
$352$	−1.12985	−	0.979025i	−0.0602215	−	0.0521822i
$353$	−17.7999	−	2.55923i	−0.947391	−	0.136214i	−0.348736	−	0.937221i	$-0.613389\pi$
$353$	−17.7999	−	2.55923i	−0.947391	−	0.136214i	−0.598655	+	0.801007i	$0.704298\pi$
$354$	36.6205	−	10.7527i	1.94636	−	0.571502i
$355$	21.1832	+	13.8040i	1.12429	+	0.732640i
$356$	−3.04622	+	1.95768i	−0.161449	+	0.103757i
$357$	20.9225	+	32.5560i	1.10734	+	1.72305i
$358$	8.38931	−	7.26938i	0.443389	−	0.384198i
$359$	−20.4195	+	5.99571i	−1.07770	+	0.316441i	−0.771959	−	0.635673i	$-0.780723\pi$
$359$	−20.4195	+	5.99571i	−1.07770	+	0.316441i	−0.305742	+	0.952114i	$0.598905\pi$
$360$	8.22424	−	1.12934i	0.433456	−	0.0595216i
$361$	12.1200	−	13.9872i	0.637896	−	0.736171i
$362$	−4.58078	−	2.09197i	−0.240760	−	0.109952i
$363$	−6.39777	+	21.7888i	−0.335796	+	1.14361i
$364$	−4.07018	−	8.91244i	−0.213335	−	0.467139i
$365$	6.84400	−	3.07331i	0.358231	−	0.160864i
$366$	31.3841	+	20.1693i	1.64047	+	1.05427i
$367$		−	12.7296i		−	0.664479i	−0.943195	−	0.332239i	$-0.892196\pi$
$367$		−	12.7296i		−	0.664479i	0.943195	−	0.332239i	$-0.107804\pi$
$368$	−4.75953	+	0.588970i	−0.248108	+	0.0307022i
$369$	−18.9230			−0.985090
$370$	−12.1649	−	3.65578i	−0.632420	−	0.190055i
$371$	1.82752	+	12.7107i	0.0948802	+	0.659906i
$372$	10.7618	−	4.91477i	0.557975	−	0.254819i
$373$	−6.44841	+	21.9613i	−0.333886	+	1.13711i	0.605955	+	0.795499i	$0.292791\pi$
$373$	−6.44841	+	21.9613i	−0.333886	+	1.13711i	−0.939841	+	0.341612i	$0.889027\pi$
$374$	3.83996	−	8.40834i	0.198560	−	0.434785i
$375$	28.7449	−	3.57681i	1.48438	−	0.184706i
$376$	0.643832	−	4.47795i	0.0332031	−	0.230933i
$377$	−6.96855	−	23.7327i	−0.358899	−	1.22230i
$378$	3.37033	−	2.92041i	0.173351	−	0.150209i
$379$	−17.2762	+	11.1027i	−0.887417	+	0.570308i	−0.903034	−	0.429570i	$-0.858665\pi$
$379$	−17.2762	+	11.1027i	−0.887417	+	0.570308i	0.0156170	+	0.999878i	$0.495029\pi$
$380$	1.03483	−	1.17908i	0.0530855	−	0.0604855i
$381$	22.5423	+	26.0152i	1.15488	+	1.33280i
$382$	2.08953	+	7.11629i	0.106910	+	0.364101i
$383$	−10.6314	−	1.52857i	−0.543240	−	0.0781062i	−0.134769	−	0.990877i	$-0.543029\pi$
$383$	−10.6314	−	1.52857i	−0.543240	−	0.0781062i	−0.408472	+	0.912771i	$0.633938\pi$
$384$	−1.69665	+	1.95803i	−0.0865816	+	0.0999205i
$385$	−7.98628	−	1.19994i	−0.407018	−	0.0611544i
$386$	−12.9229	−	3.79451i	−0.657759	−	0.193135i
$387$	17.0420	−	7.78280i	0.866292	−	0.395622i
$388$	11.7428	−	1.68836i	0.596150	−	0.0857134i
$389$	−11.6149	−	7.46445i	−0.588900	−	0.378463i	0.211993	−	0.977271i	$-0.432005\pi$
$389$	−11.6149	−	7.46445i	−0.588900	−	0.378463i	−0.800892	+	0.598808i	$0.795641\pi$
$390$	−6.47668	−	22.5858i	−0.327960	−	1.14368i
$391$	−11.7850	−	27.2102i	−0.595992	−	1.37608i
$392$		−	1.16388i		−	0.0587846i
$393$	19.4943	−	30.3338i	0.983359	−	1.53014i
$394$	−0.213849	−	1.48735i	−0.0107736	−	0.0749317i
$395$	3.42001	+	3.99780i	0.172080	+	0.201151i
$396$	−5.32542	−	1.56368i	−0.267612	−	0.0785781i
$397$	28.8570	+	13.1786i	1.44829	+	0.661413i	0.975548	−	0.219787i	$-0.0705362\pi$
$397$	28.8570	+	13.1786i	1.44829	+	0.661413i	0.472744	+	0.881200i	$0.343263\pi$
$398$	0.914100	+	0.792072i	0.0458197	+	0.0397030i
$399$	0.624934	−	4.34651i	0.0312858	−	0.217598i
$400$	−3.32191	+	3.73696i	−0.166096	+	0.186848i
$401$	−8.35448	−	9.64158i	−0.417203	−	0.481478i	0.507780	−	0.861487i	$-0.330466\pi$
$401$	−8.35448	−	9.64158i	−0.417203	−	0.481478i	−0.924983	+	0.380009i	$0.875921\pi$
$402$	−4.59138	−	7.14433i	−0.228997	−	0.356327i
$403$	−10.0128	−	15.5802i	−0.498774	−	0.776107i
$404$	12.5318	+	14.4625i	0.623480	+	0.719535i
$405$	−12.0025	+	7.60652i	−0.596407	+	0.377971i
$406$	−2.09676	+	14.5833i	−0.104061	+	0.723757i
$407$	6.41830	+	5.56149i	0.318143	+	0.275673i
$408$	−14.5716	−	6.65464i	−0.721403	−	0.329454i
$409$	−10.7737	−	3.16344i	−0.532725	−	0.156422i	0.00429653	−	0.999991i	$-0.498632\pi$
$409$	−10.7737	−	3.16344i	−0.532725	−	0.156422i	−0.537021	+	0.843569i	$0.680451\pi$
$410$	8.66070	−	7.40901i	0.427721	−	0.365905i
$411$	−6.23682	−	43.3781i	−0.307640	−	2.13968i
$412$	2.68750	−	4.18183i	0.132404	−	0.206024i
$413$			35.5879i			1.75116i
$414$	−15.1647	+	9.32926i	−0.745303	+	0.458508i
$415$	−1.80085	−	6.28003i	−0.0884004	−	0.308275i
$416$	3.41190	+	2.19269i	0.167282	+	0.107506i
$417$	45.9989	−	6.61364i	2.25258	−	0.323872i
$418$	−0.954090	+	0.435719i	−0.0466661	+	0.0213117i
$419$	11.9348	+	3.50437i	0.583053	+	0.171200i	0.559940	−	0.828533i	$-0.310824\pi$
$419$	11.9348	+	3.50437i	0.583053	+	0.171200i	0.0231127	+	0.999733i	$0.492642\pi$
$420$	−2.07948	+	13.8402i	−0.101468	+	0.675332i
$421$	−5.76463	+	6.65273i	−0.280951	+	0.324234i	−0.878632	−	0.477499i	$-0.841543\pi$
$421$	−5.76463	+	6.65273i	−0.280951	+	0.324234i	0.597681	+	0.801734i	$0.296089\pi$
$422$	5.35400	+	0.769790i	0.260629	+	0.0374728i
$423$	−4.73181	−	16.1151i	−0.230068	−	0.783541i
$424$	−3.48096	−	4.01724i	−0.169050	−	0.195095i
$425$	−27.9564	−	13.1978i	−1.35608	−	0.640187i
$426$	−24.6450	+	15.8384i	−1.19405	+	0.767372i
$427$	−26.2894	+	22.7799i	−1.27223	+	1.10240i
$428$	−4.93784	−	16.8167i	−0.238679	−	0.812867i
$429$	−2.23566	+	15.5494i	−0.107939	+	0.750731i
$430$	−4.75256	+	10.2346i	−0.229189	+	0.493556i
$431$	11.4845	−	25.1475i	0.553188	−	1.21131i	−0.402089	−	0.915601i	$-0.631716\pi$
$431$	11.4845	−	25.1475i	0.553188	−	1.21131i	0.955277	−	0.295713i	$-0.0955571\pi$
$432$	−0.520079	+	1.77122i	−0.0250223	+	0.0852181i
$433$	−9.46083	+	4.32062i	−0.454659	+	0.207636i	−0.629562	−	0.776950i	$-0.716766\pi$
$433$	−9.46083	+	4.32062i	−0.454659	+	0.207636i	0.174904	+	0.984586i	$0.444039\pi$
$434$	1.56997	+	10.9194i	0.0753609	+	0.524146i
$435$	−10.1686	+	33.8368i	−0.487548	+	1.62235i
$436$	−14.9542			−0.716178
$437$	−1.01129	+	3.20910i	−0.0483763	+	0.153512i
$438$			8.69273i			0.415354i
$439$	8.17338	+	5.25271i	0.390094	+	0.250698i	0.720956	−	0.692981i	$-0.243703\pi$
$439$	8.17338	+	5.25271i	0.390094	+	0.250698i	−0.330862	+	0.943679i	$0.607339\pi$
$440$	3.04959	−	1.36942i	0.145383	−	0.0652846i
$441$	−1.79496	−	3.93043i	−0.0854745	−	0.187163i
$442$	−7.06489	+	24.0608i	−0.336043	+	1.14446i
$443$	−8.65078	−	3.95068i	−0.411011	−	0.187702i	0.199169	−	0.979965i	$-0.436176\pi$
$443$	−8.65078	−	3.95068i	−0.411011	−	0.187702i	−0.610180	+	0.792263i	$0.708903\pi$
$444$	9.63804	−	11.1229i	0.457401	−	0.527869i
$445$	−1.10152	−	8.02163i	−0.0522170	−	0.380262i
$446$	−5.27647	+	1.54931i	−0.249848	+	0.0733620i
$447$	−31.0690	+	26.9214i	−1.46951	+	1.27334i
$448$	−1.30608	−	2.03231i	−0.0617067	−	0.0960175i
$449$	13.4491	−	8.64324i	0.634704	−	0.407900i	−0.183344	−	0.983049i	$-0.558692\pi$
$449$	13.4491	−	8.64324i	0.634704	−	0.407900i	0.818049	+	0.575149i	$0.195056\pi$
$450$	−5.45489	+	17.7429i	−0.257146	+	0.836410i
$451$	−7.31153	+	2.14686i	−0.344286	+	0.101092i
$452$	−18.8107	−	2.70457i	−0.884781	−	0.127212i
$453$	21.1208	+	18.3013i	0.992341	+	0.859868i
$454$	0.885356	−	1.93866i	0.0415518	−	0.0909858i
$455$	21.9082	+	0.138778i	1.02707	+	0.00650600i
$456$	0.755099	+	1.65344i	0.0353607	+	0.0774292i
$457$	0.0670682	−	0.00964295i	0.00313732	−	0.000451078i	−0.140746	−	0.990046i	$-0.544950\pi$
$457$	0.0670682	−	0.00964295i	0.00313732	−	0.000451078i	0.143883	+	0.989595i	$0.454041\pi$
$458$	10.0943	−	15.7070i	0.471675	−	0.733940i
$459$	−11.4138			−0.532752
$460$	3.28787	−	10.2073i	0.153298	−	0.475920i
$461$	−10.2698			−0.478315			−0.239157	−	0.970981i	$-0.576871\pi$
$461$	−10.2698			−0.478315			−0.239157	+	0.970981i	$0.576871\pi$
$462$	5.05893	−	7.87184i	0.235363	−	0.366231i
$463$	−31.4603	+	4.52330i	−1.46208	+	0.210216i	−0.826988	−	0.562219i	$-0.809948\pi$
$463$	−31.4603	+	4.52330i	−1.46208	+	0.210216i	−0.635094	+	0.772435i	$0.719039\pi$
$464$	−2.53349	−	5.54757i	−0.117614	−	0.257539i
$465$	−0.167575	+	26.4543i	−0.00777111	+	1.22679i
$466$	−5.07675	+	11.1165i	−0.235176	+	0.514963i
$467$	3.00482	+	2.60369i	0.139046	+	0.120484i	0.721607	−	0.692303i	$-0.243404\pi$
$467$	3.00482	+	2.60369i	0.139046	+	0.120484i	−0.582561	+	0.812787i	$0.697949\pi$
$468$	14.9037	+	2.14282i	0.688922	+	0.0990520i
$469$	7.59795	−	2.23096i	0.350841	−	0.103016i
$470$	8.47528	+	5.52290i	0.390936	+	0.254752i
$471$	−6.67640	+	4.29066i	−0.307633	+	0.197703i
$472$	−7.96432	−	12.3927i	−0.366587	−	0.570421i
$473$	5.70176	−	4.94061i	0.262167	−	0.227169i
$474$	−5.84889	+	1.71739i	−0.268648	+	0.0788823i
$475$	1.41670	+	3.20912i	0.0650026	+	0.147244i
$476$	9.78163	−	11.2886i	0.448340	−	0.517412i
$477$	−17.9508	−	8.19785i	−0.821910	−	0.375354i
$478$	0.198700	−	0.676711i	0.00908834	−	0.0309521i
$479$	−1.46663	−	3.21147i	−0.0670120	−	0.146736i	0.873162	−	0.487429i	$-0.162065\pi$
$479$	−1.46663	−	3.21147i	−0.0670120	−	0.146736i	−0.940174	+	0.340694i	$0.889338\pi$
$480$	−2.37320	−	5.28493i	−0.108321	−	0.241223i
$481$	−19.3817	−	12.4559i	−0.883732	−	0.567940i
$482$			8.53144i			0.388596i
$483$	−7.88838	−	28.9620i	−0.358934	−	1.31782i
$484$	8.76494			0.398406
$485$	−7.63479	+	25.4053i	−0.346678	+	1.15359i
$486$	−3.13126	−	21.7784i	−0.142037	−	0.987889i
$487$	−3.53050	+	1.61232i	−0.159982	+	0.0730614i	−0.493797	−	0.869577i	$-0.664391\pi$
$487$	−3.53050	+	1.61232i	−0.159982	+	0.0730614i	0.333815	+	0.942639i	$0.391664\pi$
$488$	4.05674	−	13.8160i	0.183640	−	0.625421i
$489$	−3.16986	+	6.94102i	−0.143346	+	0.313884i
$490$	2.36043	+	1.09609i	0.106633	+	0.0495164i
$491$	−3.74182	+	26.0250i	−0.168866	+	1.17449i	0.712367	+	0.701807i	$0.247623\pi$
$491$	−3.74182	+	26.0250i	−0.168866	+	1.17449i	−0.881233	+	0.472682i	$0.843286\pi$
$492$	3.72050	+	12.6708i	0.167733	+	0.571246i
$493$	28.4980	−	24.6937i	1.28349	−	1.11215i
$494$	2.39373	−	1.53836i	0.107699	−	0.0692139i
$495$	8.18655	−	9.32773i	0.367958	−	0.419250i
$496$	−2.99039	−	3.45109i	−0.134272	−	0.154958i
$497$	−7.69589	−	26.2098i	−0.345208	−	1.17567i
$498$	7.49266	+	1.07728i	0.335754	+	0.0482741i
$499$	11.6560	−	13.4517i	0.521793	−	0.602181i	−0.432286	−	0.901737i	$-0.642293\pi$
$499$	11.6560	−	13.4517i	0.521793	−	0.602181i	0.954079	+	0.299555i	$0.0968383\pi$
$500$	−4.45039	−	10.2564i	−0.199028	−	0.458681i
$501$	−38.4234	−	11.2821i	−1.71663	−	0.504048i
$502$	−22.9667	+	10.4885i	−1.02505	+	0.468127i
$503$	12.5167	−	1.79963i	0.558094	−	0.0802417i	0.142504	−	0.989794i	$-0.454484\pi$
$503$	12.5167	−	1.79963i	0.558094	−	0.0802417i	0.415589	+	0.909552i	$0.363575\pi$
$504$	−7.54495	−	4.84885i	−0.336079	−	0.215985i
$505$	−41.1329	+	11.7952i	−1.83039	+	0.524880i
$506$	−4.80096	+	5.32515i	−0.213429	+	0.236732i
$507$		−	8.93565i		−	0.396846i
$508$	7.18318	−	11.1772i	0.318702	−	0.495910i
$509$	0.724478	+	5.03886i	0.0321119	+	0.223343i	0.999558	−	0.0297345i	$-0.00946618\pi$
$509$	0.724478	+	5.03886i	0.0321119	+	0.223343i	−0.967446	+	0.253078i	$0.918557\pi$
$510$	27.2191	−	23.2853i	1.20528	−	1.03109i
$511$	−7.77710	−	2.28356i	−0.344039	−	0.101019i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	0.978788	+	0.848125i	0.0432146	+	0.0374456i
$514$	0.800716	−	5.56910i	0.0353181	−	0.245643i
$515$	5.95008	+	9.38873i	0.262192	+	0.413717i
$516$	−8.56205	−	9.88114i	−0.376923	−	0.434993i
$517$	−3.65659	−	5.68976i	−0.160817	−	0.250235i
$518$	7.41939	+	11.5448i	0.325989	+	0.507249i
$519$	21.9842	+	25.3712i	0.965001	+	1.11367i
$520$	−7.66013	+	4.85458i	−0.335919	+	0.212888i
$521$	−0.479945	+	3.33809i	−0.0210268	+	0.146244i	−0.997630	−	0.0688037i	$-0.978082\pi$
$521$	−0.479945	+	3.33809i	−0.0210268	+	0.146244i	0.976603	+	0.215048i	$0.0689909\pi$
$522$	−17.1113	−	14.8270i	−0.748939	−	0.648960i
$523$	11.6173	+	5.30545i	0.507990	+	0.231991i	0.652887	−	0.757456i	$-0.273558\pi$
$523$	11.6173	+	5.30545i	0.507990	+	0.231991i	−0.144897	+	0.989447i	$0.546285\pi$
$524$	−13.3536	−	3.92098i	−0.583356	−	0.171289i
$525$	−26.1106	−	17.2515i	−1.13956	−	0.752918i
$526$	3.18101	+	22.1244i	0.138699	+	0.964671i
$527$	15.2647	−	23.7523i	0.664939	−	1.03467i
$528$			3.87335i			0.168566i
$529$	2.37487	+	22.8771i	0.103255	+	0.994655i
$530$	11.4255	−	3.27636i	0.496292	−	0.142316i
$531$	−46.0081	−	29.5676i	−1.99658	−	1.28312i
$532$	−1.67764	+	0.241208i	−0.0727348	+	0.0104577i
$533$	18.8043	−	8.58761i	0.814502	−	0.371971i
$534$	9.00157	+	2.64310i	0.389536	+	0.114378i
$535$	38.7558	+	5.82305i	1.67556	+	0.251752i
$536$	−2.14655	+	2.47725i	−0.0927169	+	0.107001i
$537$	−28.4674	−	4.09299i	−1.22846	−	0.176626i
$538$	−0.543199	−	1.84997i	−0.0234190	−	0.0797577i
$539$	−1.13946	−	1.31501i	−0.0490801	−	0.0566415i
$540$	−3.10239	−	2.72283i	−0.133505	−	0.117172i
$541$	11.6836	−	7.50856i	0.502315	−	0.322818i	−0.264826	−	0.964296i	$-0.585315\pi$
$541$	11.6836	−	7.50856i	0.502315	−	0.322818i	0.767142	+	0.641478i	$0.221678\pi$
$542$	0.866736	−	0.751031i	0.0372295	−	0.0322595i
$543$	3.67581	+	12.5187i	0.157744	+	0.537227i
$544$	−0.879934	+	6.12007i	−0.0377269	+	0.262396i
$545$	14.0833	−	30.3283i	0.603264	−	1.29912i
$546$	−10.5452	+	23.0908i	−0.451294	+	0.988195i
$547$	5.65506	−	19.2594i	0.241793	−	0.823471i	−0.745764	−	0.666210i	$-0.767915\pi$
$547$	5.65506	−	19.2594i	0.241793	−	0.823471i	0.987557	−	0.157261i	$-0.0502664\pi$
$548$	−15.3864	+	7.02673i	−0.657274	+	0.300167i
$549$	−7.60778	−	52.9133i	−0.324692	−	2.25828i
$550$	−0.0946977	+	7.47446i	−0.00403793	+	0.318712i
$551$	−4.27874			−0.182280
$552$	9.22846	+	8.32005i	0.392789	+	0.354125i
$553$		−	5.68397i		−	0.241707i
$554$	13.0707	+	8.40003i	0.555321	+	0.356883i
$555$	13.4813	+	30.0218i	0.572250	+	1.27435i
$556$	−7.45127	−	16.3160i	−0.316004	−	0.691953i
$557$	−10.4569	+	35.6128i	−0.443071	+	1.50896i	0.371242	+	0.928536i	$0.378932\pi$
$557$	−10.4569	+	35.6128i	−0.443071	+	1.50896i	−0.814313	+	0.580425i	$0.802886\pi$
$558$	−15.4210	−	7.04252i	−0.652821	−	0.298133i
$559$	−13.4031	+	15.4680i	−0.566889	+	0.654225i
$560$	5.35169	−	0.734887i	0.226150	−	0.0310546i
$561$	−22.9789	+	6.74721i	−0.970169	+	0.284867i
$562$	2.92551	−	2.53496i	0.123405	−	0.106931i
$563$	−10.5256	−	16.3781i	−0.443601	−	0.690257i	0.545398	−	0.838177i	$-0.316378\pi$
$563$	−10.5256	−	16.3781i	−0.443601	−	0.690257i	−0.988999	+	0.147920i	$0.952742\pi$
$564$	−9.86034	+	6.33685i	−0.415195	+	0.266830i
$565$	23.2003	−	35.6024i	0.976043	−	1.49781i
$566$	20.1053	−	5.90344i	0.845088	−	0.248140i
$567$	15.1957	+	2.18482i	0.638161	+	0.0917537i
$568$	8.54550	+	7.40472i	0.358561	+	0.310695i
$569$	−1.96027	+	4.29239i	−0.0821787	+	0.179946i	−0.946261	−	0.323405i	$-0.895172\pi$
$569$	−1.96027	+	4.29239i	−0.0821787	+	0.179946i	0.864082	+	0.503351i	$0.167900\pi$
$570$	−4.06441	−	0.0257460i	−0.170239	−	0.00107838i
$571$	15.2898	+	33.4800i	0.639858	+	1.40109i	0.900157	+	0.435566i	$0.143452\pi$
$571$	15.2898	+	33.4800i	0.639858	+	1.40109i	−0.260299	+	0.965528i	$0.583821\pi$
$572$	6.00165	−	0.862906i	0.250941	−	0.0360799i
$573$	10.3887	−	16.1652i	0.433996	−	0.675311i
$574$	−12.3136			−0.513958
$575$	17.6049	+	16.2809i	0.734174	+	0.678962i
$576$	3.71251			0.154688
$577$	23.0160	−	35.8136i	0.958168	−	1.49094i	0.0892342	−	0.996011i	$-0.471558\pi$
$577$	23.0160	−	35.8136i	0.958168	−	1.49094i	0.868934	−	0.494928i	$-0.164806\pi$
$578$	−21.0135	+	3.02129i	−0.874047	+	0.125669i
$579$	14.4958	+	31.7414i	0.602426	+	1.31913i
$580$	13.6368	+	0.0863824i	0.566238	+	0.00358683i
$581$	−2.93212	+	6.42044i	−0.121645	+	0.266365i
$582$	−23.2292	−	20.1282i	−0.962882	−	0.834342i
$583$	−7.86596	−	1.13095i	−0.325775	−	0.0468394i
$584$	3.21925	−	0.945259i	0.133214	−	0.0391151i
$585$	−18.3815	+	28.2077i	−0.759982	+	1.16624i
$586$	5.02155	−	3.22715i	0.207438	−	0.133312i
$587$	−16.0681	−	25.0024i	−0.663201	−	1.03196i	−0.996034	−	0.0889750i	$-0.971641\pi$
$587$	−16.0681	−	25.0024i	−0.663201	−	1.03196i	0.332833	−	0.942986i	$-0.391995\pi$
$588$	−2.27891	+	1.97468i	−0.0939806	+	0.0814346i
$589$	−3.07397	+	0.902598i	−0.126661	+	0.0371909i
$590$	32.6338	−	4.48124i	1.34351	−	0.184490i
$591$	−2.54946	+	2.94223i	−0.104871	+	0.121027i
$592$	−5.16729	−	2.35982i	−0.212374	−	0.0969881i
$593$	−12.1010	+	41.2121i	−0.496927	+	1.69238i	0.203854	+	0.979001i	$0.434653\pi$
$593$	−12.1010	+	41.2121i	−0.496927	+	1.69238i	−0.700781	+	0.713377i	$0.747165\pi$
$594$	1.14646	+	2.51040i	0.0470398	+	0.103003i
$595$	13.6822	+	30.4690i	0.560914	+	1.24911i
$596$	13.3485	+	8.57858i	0.546777	+	0.351392i
$597$		−	3.13371i		−	0.128254i
$598$	10.8357	−	16.1528i	0.443107	−	0.660536i
$599$	−41.0730			−1.67820			−0.839099	−	0.543979i	$-0.816917\pi$
$599$	−41.0730			−1.67820			−0.839099	+	0.543979i	$0.816917\pi$
$600$	12.9532	+	0.164111i	0.528813	+	0.00669980i
$601$	4.05076	+	28.1736i	0.165234	+	1.14923i	0.888574	+	0.458734i	$0.151697\pi$
$601$	4.05076	+	28.1736i	0.165234	+	1.14923i	−0.723340	+	0.690492i	$0.757394\pi$
$602$	11.0896	−	5.06444i	0.451977	−	0.206411i
$603$	−3.42844	+	11.6762i	−0.139617	+	0.475492i
$604$	4.48097	−	9.81195i	0.182328	−	0.399243i
$605$	−8.25448	+	17.7759i	−0.335592	+	0.722695i
$606$	7.05598	−	49.0754i	0.286629	−	1.99355i
$607$	−2.04027	−	6.94851i	−0.0828119	−	0.282031i	0.907668	−	0.419689i	$-0.137861\pi$
$607$	−2.04027	−	6.94851i	−0.0828119	−	0.282031i	−0.990480	+	0.137658i	$0.956043\pi$
$608$	0.530221	−	0.459439i	0.0215033	−	0.0186327i
$609$	32.1121	−	20.6372i	1.30125	−	0.836260i
$610$	24.1994	+	21.2388i	0.979805	+	0.859932i
$611$	12.0155	+	13.8666i	0.486093	+	0.560982i
$612$	6.46702	+	22.0247i	0.261414	+	0.890294i
$613$	−26.7135	−	3.84083i	−1.07895	−	0.155130i	−0.420155	−	0.907452i	$-0.638024\pi$
$613$	−26.7135	−	3.84083i	−1.07895	−	0.155130i	−0.658795	+	0.752323i	$0.728933\pi$
$614$	−9.00847	+	10.3963i	−0.363552	+	0.419562i
$615$	−29.2012	−	4.38748i	−1.17751	−	0.176920i
$616$	−3.46536	−	1.01752i	−0.139623	−	0.0409972i
$617$	−14.4775	+	6.61165i	−0.582842	+	0.266175i	−0.684940	−	0.728599i	$-0.740172\pi$
$617$	−14.4775	+	6.61165i	−0.582842	+	0.266175i	0.102098	+	0.994774i	$0.467444\pi$
$618$	−12.7479	+	1.83287i	−0.512796	+	0.0737289i
$619$	−11.6323	−	7.47565i	−0.467543	−	0.300472i	0.285576	−	0.958356i	$-0.407815\pi$
$619$	−11.6323	−	7.47565i	−0.467543	−	0.300472i	−0.753119	+	0.657884i	$0.771452\pi$
$620$	9.81530	−	2.81462i	0.394192	−	0.113038i
$621$	8.44377	+	2.66089i	0.338837	+	0.106778i
$622$			28.1519i			1.12879i
$623$	−4.72939	+	7.35907i	−0.189479	+	0.294835i
$624$	−1.49541	−	10.4008i	−0.0598645	−	0.416366i
$625$	24.9920	+	0.633374i	0.999679	+	0.0253349i
$626$	2.76955	+	0.813212i	0.110693	+	0.0325025i
$627$	2.47191	+	1.12888i	0.0987184	+	0.0450832i
$628$	2.31500	+	2.00596i	0.0923786	+	0.0800465i
$629$	4.99859	−	34.7659i	0.199307	−	1.38621i
$630$	16.9394	−	10.7353i	0.674881	−	0.427703i
$631$	−23.8670	−	27.5440i	−0.950131	−	1.09651i	−0.995233	−	0.0975273i	$-0.968907\pi$
$631$	−23.8670	−	27.5440i	−0.950131	−	1.09651i	0.0451017	−	0.998982i	$-0.485639\pi$
$632$	1.27203	+	1.97932i	0.0505987	+	0.0787331i
$633$	−7.57658	−	11.7894i	−0.301142	−	0.468586i
$634$	−11.0603	−	12.7643i	−0.439260	−	0.506933i
$635$	15.9034	+	25.0943i	0.631108	+	0.995837i
$636$	−1.95994	+	13.6317i	−0.0777167	+	0.540531i
$637$	3.56741	+	3.09118i	0.141346	+	0.122477i
$638$	−8.29368	−	3.78760i	−0.328350	−	0.149952i
$639$	40.2781	+	11.8267i	1.59338	+	0.467858i
$640$	−1.69915	+	1.45358i	−0.0671648	+	0.0574578i
$641$	0.564030	+	3.92292i	0.0222779	+	0.154946i	0.997924	−	0.0644053i	$-0.0205150\pi$
$641$	0.564030	+	3.92292i	0.0222779	+	0.154946i	−0.975646	+	0.219351i	$0.929606\pi$
$642$	−24.5500	+	38.2005i	−0.968910	+	1.50765i
$643$			24.8411i			0.979637i	0.871824	+	0.489818i	$0.162937\pi$
$643$			24.8411i			0.979637i	−0.871824	+	0.489818i	$0.837063\pi$
$644$	−9.86797	+	6.07074i	−0.388853	+	0.239221i
$645$	28.1031	−	8.05880i	1.10656	−	0.317315i
$646$	3.64927	+	2.34524i	0.143579	+	0.0922723i
$647$	25.4353	−	3.65704i	0.999963	−	0.143773i	0.377157	−	0.926149i	$-0.376902\pi$
$647$	25.4353	−	3.65704i	0.999963	−	0.143773i	0.622806	+	0.782376i	$0.285993\pi$
$648$	−5.78054	+	2.63988i	−0.227081	+	0.103704i
$649$	−21.1313	−	6.20471i	−0.829476	−	0.243556i
$650$	−2.63143	−	20.1072i	−0.103213	−	0.788668i
$651$	18.7168	−	21.6004i	0.733570	−	0.846585i
$652$	2.91522	+	0.419146i	0.114169	+	0.0164150i
$653$	−12.7330	−	43.3646i	−0.498280	−	1.69699i	−0.697120	−	0.716955i	$-0.745535\pi$
$653$	−12.7330	−	43.3646i	−0.498280	−	1.69699i	0.198839	−	0.980032i	$-0.436283\pi$
$654$	25.3721	+	29.2809i	0.992126	+	1.14497i
$655$	20.5280	−	23.3895i	0.802094	−	0.913904i
$656$	4.28794	−	2.75569i	0.167416	−	0.107592i
$657$	9.41367	−	8.15699i	0.367262	−	0.318234i
$658$	−3.07909	−	10.4864i	−0.120035	−	0.408803i
$659$	−1.30081	+	9.04735i	−0.0506724	+	0.352435i	0.948673	+	0.316259i	$0.102427\pi$
$659$	−1.30081	+	9.04735i	−0.0506724	+	0.352435i	−0.999345	+	0.0361759i	$0.988482\pi$
$660$	−7.85545	−	3.64778i	−0.305773	−	0.141989i
$661$	−14.8571	+	32.5326i	−0.577875	+	1.26537i	0.364622	+	0.931156i	$0.381198\pi$
$661$	−14.8571	+	32.5326i	−0.577875	+	1.26537i	−0.942497	+	0.334214i	$0.891529\pi$
$662$	6.57628	−	22.3968i	0.255595	−	0.870475i
$663$	59.0985	−	26.9894i	2.29520	−	1.04818i
$664$	−0.415802	−	2.89197i	−0.0161363	−	0.112230i
$665$	1.09075	−	3.62953i	0.0422974	−	0.140747i
$666$	−21.0894			−0.817198
$667$	−26.8391	+	11.6243i	−1.03922	+	0.450094i
$668$			15.4565i			0.598030i
$669$	11.9859	+	7.70287i	0.463402	+	0.297810i
$670$	−3.00251	−	6.68635i	−0.115997	−	0.258316i
$671$	−8.94268	−	19.5817i	−0.345228	−	0.755944i
$672$	−1.76336	+	6.00546i	−0.0680232	+	0.231666i
$673$	8.30660	+	3.79350i	0.320196	+	0.146229i	0.569028	−	0.822318i	$-0.307320\pi$
$673$	8.30660	+	3.79350i	0.320196	+	0.146229i	−0.248832	+	0.968547i	$0.580047\pi$
$674$	−6.96677	+	8.04008i	−0.268350	+	0.309692i
$675$	8.44381	−	3.72761i	0.325002	−	0.143476i
$676$	−3.30922	+	0.971675i	−0.127278	+	0.0373721i
$677$	−10.2257	+	8.86062i	−0.393006	+	0.340541i	−0.828840	−	0.559485i	$-0.810999\pi$
$677$	−10.2257	+	8.86062i	−0.393006	+	0.340541i	0.435834	+	0.900027i	$0.356453\pi$
$678$	26.6195	+	41.4207i	1.02231	+	1.59075i
$679$	24.1103	−	15.4948i	0.925270	−	0.594635i
$680$	−11.5833	−	7.54822i	−0.444198	−	0.289461i
$681$	−5.29810	+	1.55566i	−0.203024	+	0.0596131i
$682$	−6.75740	−	0.971568i	−0.258754	−	0.0372033i
$683$	0.226706	+	0.196442i	0.00867466	+	0.00751664i	0.659187	−	0.751979i	$-0.270900\pi$
$683$	0.226706	+	0.196442i	0.00867466	+	0.00751664i	−0.650513	+	0.759495i	$0.725446\pi$
$684$	1.08200	−	2.36926i	0.0413714	−	0.0905908i
$685$	0.239585	−	37.8222i	0.00915407	−	1.44511i
$686$	−8.19296	−	17.9401i	−0.312809	−	0.684955i
$687$	−47.8813	+	6.88429i	−1.82678	+	0.262652i
$688$	−2.72832	+	4.24535i	−0.104016	+	0.161852i
$689$	21.5585			0.821314
$690$	−25.5647	+	10.8805i	−0.973231	+	0.414214i
$691$	0.587233			0.0223394			0.0111697	−	0.999938i	$-0.496445\pi$
$691$	0.587233			0.0223394			0.0111697	+	0.999938i	$0.496445\pi$
$692$	7.00534	−	10.9005i	0.266303	−	0.414375i
$693$	−13.2718	+	1.90820i	−0.504156	+	0.0724866i
$694$	−5.39856	−	11.8212i	−0.204927	−	0.448727i
$695$	40.1074	+	0.254060i	1.52136	+	0.00963706i
$696$	−6.56389	+	14.3729i	−0.248804	+	0.544804i
$697$	23.8177	+	20.6381i	0.902159	+	0.781725i
$698$	−6.41553	−	0.922415i	−0.242832	−	0.0349139i
$699$	30.3800	−	8.92037i	1.14908	−	0.337399i
$700$	−3.54961	+	11.5457i	−0.134163	+	0.436387i
$701$	38.7268	−	24.8882i	1.46269	−	0.940016i	0.464166	−	0.885748i	$-0.346354\pi$
$701$	38.7268	−	24.8882i	1.46269	−	0.940016i	0.998526	−	0.0542674i	$-0.0172823\pi$
$702$	−4.04771	−	6.29836i	−0.152771	−	0.237716i
$703$	−3.01199	+	2.60991i	−0.113600	+	0.0984345i
$704$	1.43445	−	0.421194i	0.0540630	−	0.0158743i
$705$	−3.56552	−	25.9653i	−0.134285	−	0.977910i
$706$	11.7763	−	13.5906i	0.443207	−	0.511488i
$707$	42.0526	+	19.2048i	1.58155	+	0.722270i
$708$	−10.7527	+	36.6205i	−0.404113	+	1.37628i
$709$	20.8063	+	45.5594i	0.781396	+	1.71102i	0.699785	+	0.714354i	$0.253279\pi$
$709$	20.8063	+	45.5594i	0.781396	+	1.71102i	0.0816110	+	0.996664i	$0.473993\pi$
$710$	−23.0652	+	10.3574i	−0.865620	+	0.388708i
$711$	7.34824	+	4.72243i	0.275581	+	0.177105i
$712$		−	3.62104i		−	0.135704i
$713$	−16.8299	+	14.0129i	−0.630283	+	0.524788i
$714$	−38.6994			−1.44829
$715$	−3.90208	+	12.9844i	−0.145930	+	0.485590i
$716$	1.57979	+	10.9877i	0.0590394	+	0.410628i
$717$	−1.66215	+	0.759078i	−0.0620741	+	0.0283483i
$718$	5.99571	−	20.4195i	0.223758	−	0.762049i
$719$	12.7313	−	27.8776i	0.474797	−	1.03966i	−0.509065	−	0.860728i	$-0.670009\pi$
$719$	12.7313	−	27.8776i	0.474797	−	1.03966i	0.983862	−	0.178931i	$-0.0572640\pi$
$720$	−3.49630	+	7.52924i	−0.130299	+	0.280598i
$721$	1.70904	−	11.8866i	0.0636479	−	0.442681i
$722$	5.21424	+	17.7581i	0.194054	+	0.660888i
$723$	16.7048	−	14.4748i	0.621260	−	0.538325i
$724$	4.23644	−	2.72259i	0.157446	−	0.101184i
$725$	−13.0178	+	27.5751i	−0.483470	+	1.02411i
$726$	−14.8710	−	17.1620i	−0.551915	−	0.636943i
$727$	−2.77362	−	9.44608i	−0.102868	−	0.350336i	0.891934	−	0.452166i	$-0.149348\pi$
$727$	−2.77362	−	9.44608i	−0.102868	−	0.350336i	−0.994802	+	0.101830i	$0.967530\pi$
$728$	9.69813	+	1.39438i	0.359437	+	0.0516792i
$729$	−24.8457	+	28.6735i	−0.920211	+	1.06198i
$730$	−1.11472	+	7.41910i	−0.0412575	+	0.274593i
$731$	−29.9384	−	8.79070i	−1.10731	−	0.325136i
$732$	−33.9351	+	15.4976i	−1.25428	+	0.572809i
$733$	−29.2600	+	4.20696i	−1.08074	+	0.155388i	−0.659608	−	0.751610i	$-0.729278\pi$
$733$	−29.2600	+	4.20696i	−1.08074	+	0.155388i	−0.421136	+	0.906997i	$0.638369\pi$
$734$	10.7088	+	6.88213i	0.395269	+	0.254024i
$735$	−1.85862	−	6.48148i	−0.0685562	−	0.239073i
$736$	2.07772	−	4.32239i	0.0765859	−	0.159325i
$737$			4.90046i			0.180511i
$738$	10.2305	−	15.9190i	0.376591	−	0.585986i
$739$	2.37446	+	16.5148i	0.0873460	+	0.607505i	0.985735	+	0.168304i	$0.0538292\pi$
$739$	2.37446	+	16.5148i	0.0873460	+	0.607505i	−0.898389	+	0.439201i	$0.855262\pi$
$740$	9.65225	−	8.25726i	0.354824	−	0.303543i
$741$	−7.07346	−	2.07696i	−0.259850	−	0.0762989i
$742$	−11.6810	−	5.33451i	−0.428821	−	0.195836i
$743$	−2.29186	−	1.98591i	−0.0840803	−	0.0728560i	0.611807	−	0.791007i	$-0.290443\pi$
$743$	−2.29186	−	1.98591i	−0.0840803	−	0.0728560i	−0.695887	+	0.718151i	$0.744989\pi$
$744$	−1.68372	+	11.7106i	−0.0617283	+	0.429330i
$745$	−29.9691	+	18.9928i	−1.09798	+	0.695843i
$746$	−14.9887	−	17.2979i	−0.548776	−	0.633321i
$747$	−5.86425	−	9.12496i	−0.214562	−	0.333865i
$748$	4.99751	+	7.77627i	0.182727	+	0.284329i
$749$	−27.7275	−	31.9993i	−1.01314	−	1.16923i
$750$	−12.5317	+	26.1155i	−0.457592	+	0.953604i
$751$	5.44047	−	37.8393i	0.198526	−	1.38078i	−0.610040	−	0.792371i	$-0.708847\pi$
$751$	5.44047	−	37.8393i	0.198526	−	1.38078i	0.808566	−	0.588406i	$-0.200244\pi$
$752$	3.41901	+	2.96259i	0.124678	+	0.108035i
$753$	59.5033	+	27.1743i	2.16842	+	0.990285i
$754$	23.7327	+	6.96855i	0.864294	+	0.253780i
$755$	15.6794	+	18.3283i	0.570630	+	0.667033i
$756$	0.634665	+	4.41419i	0.0230825	+	0.160543i
$757$	4.34433	−	6.75990i	0.157897	−	0.245693i	−0.753287	−	0.657692i	$-0.771533\pi$
$757$	4.34433	−	6.75990i	0.157897	−	0.245693i	0.911184	+	0.411999i	$0.135169\pi$
$758$		−	20.5362i		−	0.745909i
$759$	18.5724	+	0.365552i	0.674134	+	0.0132687i
$760$	0.432435	+	1.50801i	0.0156861	+	0.0547013i
$761$	36.9682	+	23.7580i	1.34010	+	0.861228i	0.996949	−	0.0780539i	$-0.0248706\pi$
$761$	36.9682	+	23.7580i	1.34010	+	0.861228i	0.343147	+	0.939282i	$0.388507\pi$
$762$	−34.0727	+	4.89892i	−1.23432	+	0.177469i
$763$	−32.8619	+	15.0075i	−1.18968	+	0.543309i
$764$	−7.11629	−	2.08953i	−0.257458	−	0.0755966i
$765$	−50.7580	−	7.62637i	−1.83516	−	0.275732i
$766$	7.03369	−	8.11732i	0.254138	−	0.293291i
$767$	59.1378	+	8.50274i	2.13534	+	0.307016i
$768$	−0.729927	−	2.48590i	−0.0263390	−	0.0897023i
$769$	10.6393	+	12.2784i	0.383663	+	0.442771i	0.914428	−	0.404748i	$-0.132641\pi$
$769$	10.6393	+	12.2784i	0.383663	+	0.442771i	−0.530765	+	0.847519i	$0.678095\pi$
$770$	5.32716	−	6.06975i	0.191977	−	0.218739i
$771$	−12.2630	+	7.88097i	−0.441642	+	0.283826i
$772$	10.1788	−	8.81998i	0.366343	−	0.317438i
$773$	−10.0254	−	34.1434i	−0.360589	−	1.22805i	−0.917586	−	0.397538i	$-0.869865\pi$
$773$	−10.0254	−	34.1434i	−0.360589	−	1.22805i	0.556997	−	0.830515i	$-0.311954\pi$
$774$	−2.66627	+	18.5443i	−0.0958371	+	0.666562i
$775$	−3.53541	+	22.5569i	−0.126996	+	0.810266i
$776$	−4.92829	+	10.7915i	−0.176915	+	0.387391i
$777$	10.0170	−	34.1149i	0.359359	−	1.22386i
$778$	12.5590	−	5.73550i	0.450262	−	0.205628i
$779$	−0.508921	−	3.53963i	−0.0182340	−	0.126820i
$780$	22.5020	+	6.76229i	0.805700	+	0.242129i
$781$	16.9046			0.604894
$782$	29.2621	+	4.79679i	1.04641	+	0.171533i
$783$			11.2582i			0.402335i
$784$	0.979114	+	0.629238i	0.0349684	+	0.0224728i
$785$	−6.24842	+	2.80586i	−0.223016	+	0.100145i
$786$	14.9790	+	32.7994i	0.534282	+	1.16991i
$787$	13.2613	−	45.1638i	0.472714	−	1.60992i	−0.285820	−	0.958283i	$-0.592266\pi$
$787$	13.2613	−	45.1638i	0.472714	−	1.60992i	0.758534	−	0.651633i	$-0.225916\pi$
$788$	1.36686	+	0.624222i	0.0486922	+	0.0222370i
$789$	37.9233	−	43.7659i	1.35011	−	1.55811i
$790$	−5.21216	+	0.715727i	−0.185440	+	0.0254644i
$791$	−44.0506	+	12.9344i	−1.56626	+	0.459896i
$792$	4.19460	−	3.63464i	0.149048	−	0.129151i
$793$	31.5732	+	49.1288i	1.12120	+	1.74462i
$794$	−26.6878	+	17.1512i	−0.947114	+	0.608673i
$795$	−25.8003	−	16.8127i	−0.915041	−	0.596285i
$796$	−1.16053	+	0.340763i	−0.0411340	+	0.0120780i
$797$	33.9932	+	4.88748i	1.20410	+	0.173124i	0.715013	−	0.699111i	$-0.246421\pi$
$797$	33.9932	+	4.88748i	1.20410	+	0.173124i	0.489088	+	0.872235i	$0.337330\pi$
$798$	3.31865	+	2.87563i	0.117479	+	0.101796i
$799$	−11.6200	+	25.4442i	−0.411085	+	0.900150i
$800$	−1.34777	−	4.81493i	−0.0476510	−	0.170233i
$801$	−5.58449	−	12.2283i	−0.197318	−	0.432067i
$802$	12.6278	−	1.81560i	0.445903	−	0.0641111i
$803$	2.71186	−	4.21974i	0.0956994	−	0.148911i
$804$	8.49248			0.299507
$805$	−3.01864	−	25.7302i	−0.106393	−	0.906870i
$806$	18.5203			0.652348
$807$	−2.70068	+	4.20234i	−0.0950685	+	0.147929i
$808$	−18.9418	+	2.72342i	−0.666370	+	0.0958096i
$809$	4.28637	+	9.38585i	0.150701	+	0.329989i	0.969893	−	0.243530i	$-0.0783053\pi$
$809$	4.28637	+	9.38585i	0.150701	+	0.329989i	−0.819193	+	0.573519i	$0.805578\pi$
$810$	0.0900101	−	14.2095i	0.00316263	−	0.499271i
$811$	−2.70172	+	5.91594i	−0.0948703	+	0.207737i	−0.951117	−	0.308829i	$-0.900063\pi$
$811$	−2.70172	+	5.91594i	−0.0948703	+	0.207737i	0.856247	+	0.516566i	$0.172790\pi$
$812$	−11.1347	−	9.64824i	−0.390750	−	0.338587i
$813$	−2.94109	−	0.422865i	−0.103148	−	0.0148305i
$814$	−8.14861	+	2.39265i	−0.285609	+	0.0838623i
$815$	−3.59550	+	5.51755i	−0.125945	+	0.193271i
$816$	13.4763	−	8.66066i	0.471763	−	0.303184i
$817$	1.91414	+	2.97847i	0.0669674	+	0.104203i
$818$	8.48595	−	7.35312i	0.296704	−	0.257096i
$819$	34.9012	−	10.2479i	1.21955	−	0.358091i
$820$	1.55053	+	11.2915i	0.0541468	+	0.394315i
$821$	−24.1404	+	27.8595i	−0.842504	+	0.972302i	−0.999884	−	0.0152365i	$-0.995150\pi$
$821$	−24.1404	+	27.8595i	−0.842504	+	0.972302i	0.157380	+	0.987538i	$0.449695\pi$
$822$	39.8638	+	18.2052i	1.39041	+	0.634979i
$823$	−1.55967	+	5.31173i	−0.0543665	+	0.185155i	−0.982200	−	0.187840i	$-0.939851\pi$
$823$	−1.55967	+	5.31173i	−0.0543665	+	0.185155i	0.927833	+	0.372996i	$0.121669\pi$
$824$	2.06501	+	4.52174i	0.0719379	+	0.157522i
$825$	14.7959	−	12.4961i	0.515128	−	0.435058i
$826$	−29.9384	−	19.2403i	−1.04169	−	0.669454i
$827$			34.5351i			1.20090i	0.799661	+	0.600452i	$0.205013\pi$
$827$			34.5351i			1.20090i	−0.799661	+	0.600452i	$0.794987\pi$
$828$	0.350372	−	17.8011i	0.0121763	−	0.618631i
$829$	44.1739			1.53422			0.767112	−	0.641514i	$-0.221693\pi$
$829$	44.1739			1.53422			0.767112	+	0.641514i	$0.221693\pi$
$830$	6.25671	+	1.88027i	0.217174	+	0.0652650i
$831$	−5.72881	−	39.8448i	−0.198730	−	1.38220i
$832$	−3.68922	+	1.68481i	−0.127901	+	0.0584103i
$833$	−2.02742	+	6.90475i	−0.0702459	+	0.239235i
$834$	−19.3051	+	42.2724i	−0.668482	+	1.46377i
$835$	−31.3469	−	14.5563i	−1.08481	−	0.503743i
$836$	0.149271	−	1.03820i	0.00516263	−	0.0359069i
$837$	2.37491	+	8.08820i	0.0820889	+	0.279569i
$838$	−9.40050	+	8.14558i	−0.324735	+	0.281384i
$839$	−28.4148	+	18.2611i	−0.980988	+	0.630443i	−0.929730	−	0.368243i	$-0.879960\pi$
$839$	−28.4148	+	18.2611i	−0.980988	+	0.630443i	−0.0512585	+	0.998685i	$0.516323\pi$
$840$	−10.5189	−	9.23195i	−0.362935	−	0.318532i
$841$	−5.36596	−	6.19265i	−0.185033	−	0.213540i
$842$	−2.48004	−	8.44625i	−0.0854679	−	0.291077i
$843$	−9.92710	−	1.42730i	−0.341907	−	0.0491589i
$844$	−3.54218	+	4.08790i	−0.121927	+	0.140711i
$845$	1.14587	−	7.62643i	0.0394191	−	0.262357i
$846$	16.1151	+	4.73181i	0.554047	+	0.162683i
$847$	19.2609	−	8.79616i	0.661813	−	0.302240i
$848$	5.26147	−	0.756485i	0.180680	−	0.0259778i
$849$	−45.6707	−	29.3508i	−1.56741	−	1.00732i
$850$	26.2170	−	16.3831i	0.899237	−	0.561936i
$851$	−11.8028	+	24.5539i	−0.404594	+	0.841699i
$852$		−	29.2956i		−	1.00365i
$853$	2.39038	−	3.71950i	0.0818450	−	0.127353i	−0.797918	−	0.602767i	$-0.794065\pi$
$853$	2.39038	−	3.71950i	0.0818450	−	0.127353i	0.879763	+	0.475413i	$0.157701\pi$
$854$	−4.95055	−	34.4318i	−0.169404	−	1.17823i
$855$	3.78604	+	4.42566i	0.129480	+	0.151354i
$856$	16.8167	+	4.93784i	0.574784	+	0.168772i
$857$	−53.1672	−	24.2807i	−1.81616	−	0.829411i	−0.932345	−	0.361571i	$-0.882241\pi$
$857$	−53.1672	−	24.2807i	−1.81616	−	0.829411i	−0.883813	−	0.467841i	$-0.845032\pi$
$858$	−11.8723	−	10.2874i	−0.405313	−	0.351205i
$859$	5.70704	−	39.6933i	0.194722	−	1.35432i	−0.624582	−	0.780959i	$-0.714731\pi$
$859$	5.70704	−	39.6933i	0.194722	−	1.35432i	0.819304	−	0.573360i	$-0.194360\pi$
$860$	−6.04046	−	9.53134i	−0.205978	−	0.325016i
$861$	20.8918	+	24.1104i	0.711989	+	0.821680i
$862$	14.9465	+	23.2571i	0.509078	+	0.792141i
$863$	−14.6706	−	22.8279i	−0.499392	−	0.777070i	0.496459	−	0.868060i	$-0.334633\pi$
$863$	−14.6706	−	22.8279i	−0.499392	−	0.777070i	−0.995852	+	0.0909901i	$0.970997\pi$
$864$	−1.20887	−	1.39511i	−0.0411267	−	0.0474628i
$865$	15.5097	+	24.4730i	0.527346	+	0.832108i
$866$	1.48018	−	10.2949i	0.0502985	−	0.349834i
$867$	41.5683	+	36.0191i	1.41173	+	1.22327i
$868$	−10.0347	−	4.58271i	−0.340601	−	0.155547i
$869$	3.37502	+	0.990994i	0.114490	+	0.0336172i
$870$	−22.9677	−	26.8479i	−0.778679	−	0.910230i
$871$	−1.89196	−	13.1588i	−0.0641065	−	0.445871i
$872$	8.08487	−	12.5803i	0.273788	−	0.426023i
$873$			44.0435i			1.49065i
$874$	−2.15293	−	2.58572i	−0.0728238	−	0.0874632i
$875$	−20.0727	−	18.0722i	−0.678580	−	0.610951i
$876$	−7.31279	−	4.69964i	−0.247076	−	0.158786i
$877$	10.3992	−	1.49519i	0.351157	−	0.0504888i	0.0355208	−	0.999369i	$-0.488691\pi$
$877$	10.3992	−	1.49519i	0.351157	−	0.0504888i	0.315637	+	0.948880i	$0.397782\pi$
$878$	−8.83772	+	4.03605i	−0.298259	+	0.136210i
$879$	−14.8387	−	4.35703i	−0.500496	−	0.146959i
$880$	−0.496702	+	3.30584i	−0.0167438	+	0.111440i
$881$	−6.23389	+	7.19429i	−0.210025	+	0.242382i	−0.850982	−	0.525195i	$-0.823992\pi$
$881$	−6.23389	+	7.19429i	−0.210025	+	0.242382i	0.640957	+	0.767577i	$0.278538\pi$
$882$	4.27692	+	0.614928i	0.144011	+	0.0207057i
$883$	−7.52758	−	25.6366i	−0.253323	−	0.862739i	−0.983719	−	0.179715i	$-0.942482\pi$
$883$	−7.52758	−	25.6366i	−0.253323	−	0.862739i	0.730396	−	0.683024i	$-0.239336\pi$
$884$	−16.4217	−	18.9516i	−0.552321	−	0.637412i
$885$	−64.1425	−	56.2951i	−2.15613	−	1.89234i
$886$	8.00049	−	5.14160i	0.268782	−	0.172735i
$887$	−14.6556	+	12.6992i	−0.492088	+	0.426396i	−0.865228	−	0.501379i	$-0.832826\pi$
$887$	−14.6556	+	12.6992i	−0.492088	+	0.426396i	0.373140	+	0.927775i	$0.378281\pi$
$888$	4.14645	+	14.1215i	0.139146	+	0.473887i
$889$	4.56794	−	31.7707i	0.153204	−	1.06556i
$890$	7.34375	+	3.41016i	0.246163	+	0.114309i
$891$	−3.94666	+	8.64198i	−0.132218	+	0.289517i
$892$	1.54931	−	5.27647i	0.0518747	−	0.176669i
$893$	2.88714	−	1.31851i	0.0966143	−	0.0441223i
$894$	−5.85058	−	40.6917i	−0.195673	−	1.36093i
$895$	−23.7716	−	7.14383i	−0.794596	−	0.238792i
$896$	2.41581			0.0807065
$897$	−50.0121	+	6.18877i	−1.66986	+	0.206637i
$898$			15.9870i			0.533494i
$899$	−23.4284	−	15.0565i	−0.781380	−	0.502162i
$900$	−11.9772	−	14.1815i	−0.399239	−	0.472717i
$901$	13.6531	+	29.8962i	0.454852	+	0.995986i
$902$	2.14686	−	7.31153i	0.0714826	−	0.243447i
$903$	−28.7314	−	13.1212i	−0.956122	−	0.436646i
$904$	12.4451	−	14.3624i	0.413917	−	0.477685i
$905$	1.53191	+	11.1558i	0.0509223	+	0.370833i
$906$	−26.8147	+	7.87352i	−0.890860	+	0.261580i
$907$	−21.5552	+	18.6777i	−0.715728	+	0.620182i	−0.934654	−	0.355559i	$-0.884290\pi$
$907$	−21.5552	+	18.6777i	−0.715728	+	0.620182i	0.218925	+	0.975742i	$0.429745\pi$
$908$	1.15224	+	1.79293i	0.0382386	+	0.0595004i
$909$	−59.7666	+	38.4097i	−1.98233	+	1.27397i
$910$	−11.9612	+	18.3553i	−0.396511	+	0.608474i
$911$	−33.3300	+	9.78657i	−1.10427	+	0.324244i	−0.782548	−	0.622590i	$-0.786080\pi$
$911$	−33.3300	+	9.78657i	−1.10427	+	0.324244i	−0.321724	+	0.946834i	$0.604262\pi$
$912$	−1.79920	−	0.258685i	−0.0595773	−	0.00856592i
$913$	−3.30110	−	2.86042i	−0.109251	−	0.0946662i
$914$	−0.0281476	+	0.0616347i	−0.000931041	+	0.00203870i
$915$	0.528411	−	83.4179i	0.0174687	−	2.75771i
$916$	7.75619	+	16.9837i	0.256272	+	0.561157i
$917$	−33.2795	+	4.78487i	−1.09899	+	0.158010i
$918$	6.17079	−	9.60193i	0.203666	−	0.316911i
$919$	−13.5686			−0.447586			−0.223793	−	0.974637i	$-0.571844\pi$
$919$	−13.5686			−0.447586			−0.223793	+	0.974637i	$0.571844\pi$
$920$	6.80941	+	8.28444i	0.224500	+	0.273130i
$921$	35.6406			1.17440
$922$	5.55230	−	8.63955i	0.182855	−	0.284528i
$923$	−45.3926	+	6.52648i	−1.49412	+	0.214822i
$924$	3.88715	+	8.51168i	0.127878	+	0.280014i
$925$	7.65621	+	27.3519i	0.251735	+	0.899323i
$926$	13.2035	−	28.9115i	0.433892	−	0.950092i
$927$	13.9471	+	12.0853i	0.458084	+	0.396932i
$928$	6.03662	+	0.867934i	0.198162	+	0.0284913i
$929$	−17.5627	+	5.15687i	−0.576213	+	0.169192i	−0.556839	−	0.830621i	$-0.687986\pi$
$929$	−17.5627	+	5.15687i	−0.576213	+	0.169192i	−0.0193749	+	0.999812i	$0.506168\pi$
$930$	−22.1642	−	14.4433i	−0.726793	−	0.473614i
$931$	0.686930	−	0.441463i	0.0225132	−	0.0144684i
$932$	−6.60712	−	10.2809i	−0.216423	−	0.336761i
$933$	55.1223	−	47.7638i	1.80462	−	1.56372i
$934$	−3.81489	+	1.12015i	−0.124827	+	0.0366525i
$935$	−20.4773	+	2.81192i	−0.669680	+	0.0919596i
$936$	−9.86019	+	11.3793i	−0.322290	+	0.371943i
$937$	−15.8248	−	7.22695i	−0.516974	−	0.236094i	0.139803	−	0.990179i	$-0.455353\pi$
$937$	−15.8248	−	7.22695i	−0.516974	−	0.236094i	−0.656776	+	0.754085i	$0.728080\pi$
$938$	−2.23096	+	7.59795i	−0.0728434	+	0.248082i
$939$	−3.10664	−	6.80260i	−0.101382	−	0.221995i
$940$	−9.22824	+	4.14395i	−0.300992	+	0.135161i
$941$	−0.870322	−	0.559322i	−0.0283717	−	0.0182334i	0.526378	−	0.850251i	$-0.323550\pi$
$941$	−0.870322	−	0.559322i	−0.0283717	−	0.0182334i	−0.554750	+	0.832017i	$0.687186\pi$
$942$		−	7.93626i		−	0.258577i
$943$	−12.8086	−	20.8203i	−0.417105	−	0.678003i
$944$	14.7313			0.479461
$945$	−9.55001	−	2.86997i	−0.310662	−	0.0933601i
$946$	1.07370	+	7.46772i	0.0349089	+	0.242797i
$947$	38.1652	−	17.4295i	1.24020	−	0.566381i	0.316172	−	0.948702i	$-0.397602\pi$
$947$	38.1652	−	17.4295i	1.24020	−	0.566381i	0.924030	+	0.382321i	$0.124875\pi$
$948$	1.71739	−	5.84889i	0.0557782	−	0.189963i
$949$	−5.65281	+	12.3779i	−0.183498	+	0.401805i
$950$	−3.46561	−	0.543176i	−0.112439	−	0.0176230i
$951$	−6.22745	+	43.3128i	−0.201939	+	1.40452i
$952$	4.20823	+	14.3319i	0.136389	+	0.464500i
$953$	−17.6476	+	15.2917i	−0.571662	+	0.495348i	−0.892049	−	0.451939i	$-0.850733\pi$
$953$	−17.6476	+	15.2917i	−0.571662	+	0.495348i	0.320387	+	0.947287i	$0.396187\pi$
$954$	16.6014	−	10.6691i	0.537490	−	0.345424i
$955$	10.9396	−	12.4645i	0.353996	−	0.403343i
$956$	0.461860	+	0.533015i	0.0149376	+	0.0172389i
$957$	6.65520	+	22.6655i	0.215132	+	0.732672i
$958$	3.49458	+	0.502445i	0.112905	+	0.0162332i
$959$	−26.7598	+	30.8824i	−0.864118	+	0.997245i
$960$	5.72901	+	0.860782i	0.184903	+	0.0277816i
$961$	9.73652	+	2.85890i	0.314081	+	0.0922226i
$962$	20.9571	−	9.57080i	0.675685	−	0.308575i
$963$	64.4056	−	9.26013i	2.07544	−	0.298404i
$964$	−7.17710	−	4.61244i	−0.231159	−	0.148557i
$965$	8.30157	+	28.9497i	0.267237	+	0.931923i
$966$	28.6292	+	9.02193i	0.921129	+	0.290276i
$967$			16.0285i			0.515442i	0.966219	+	0.257721i	$0.0829716\pi$
$967$			16.0285i			0.515442i	−0.966219	+	0.257721i	$0.917028\pi$
$968$	−4.73868	+	7.37354i	−0.152307	+	0.236994i
$969$	−1.59945	−	11.1244i	−0.0513818	−	0.357368i
$970$	−17.2446	−	20.1579i	−0.553691	−	0.647232i
$971$	21.5331	+	6.32268i	0.691029	+	0.202904i	0.608347	−	0.793671i	$-0.291833\pi$
$971$	21.5331	+	6.32268i	0.691029	+	0.202904i	0.0826826	+	0.996576i	$0.473651\pi$
$972$	20.0141	+	9.14011i	0.641951	+	0.293169i
$973$	−32.7483	−	28.3765i	−1.04986	−	0.909710i
$974$	0.552358	−	3.84173i	0.0176987	−	0.123097i
$975$	−34.9059	+	39.2672i	−1.11788	+	1.25756i
$976$	9.42952	+	10.8822i	0.301832	+	0.348332i
$977$	−8.22441	−	12.7974i	−0.263122	−	0.409426i	0.684405	−	0.729102i	$-0.260062\pi$
$977$	−8.22441	−	12.7974i	−0.263122	−	0.409426i	−0.947527	+	0.319676i	$0.896426\pi$
$978$	−4.12540	−	6.41925i	−0.131916	−	0.205265i
$979$	−3.54509	−	4.09126i	−0.113302	−	0.130757i
$980$	−2.19823	+	1.39312i	−0.0702200	+	0.0445017i
$981$	7.90100	−	54.9526i	0.252259	−	1.75450i
$982$	−19.8706	−	17.2180i	−0.634096	−	0.549448i
$983$	40.3851	+	18.4433i	1.28809	+	0.588249i	0.937403	−	0.348245i	$-0.113222\pi$
$983$	40.3851	+	18.4433i	1.28809	+	0.588249i	0.350682	+	0.936494i	$0.385950\pi$
$984$	−12.6708	−	3.72050i	−0.403932	−	0.118605i
$985$	−2.55322	+	2.18422i	−0.0813524	+	0.0695949i
$986$	5.36645	+	37.3245i	0.170902	+	1.18865i
$987$	−15.3086	+	23.8207i	−0.487279	+	0.758220i
$988$			2.84543i			0.0905252i
$989$	20.0986	+	13.4827i	0.639097	+	0.428725i
$990$	3.42101	+	11.9299i	0.108727	+	0.379157i
$991$	30.3739	+	19.5201i	0.964860	+	0.620078i	0.925339	−	0.379141i	$-0.123780\pi$
$991$	30.3739	+	19.5201i	0.964860	+	0.620078i	0.0395211	+	0.999219i	$0.487417\pi$
$992$	4.51997	−	0.649873i	0.143509	−	0.0206335i
$993$	−55.0113	+	25.1228i	−1.74573	+	0.797248i
$994$	26.2098	+	7.69589i	0.831325	+	0.244099i
$995$	0.401853	−	2.67457i	0.0127396	−	0.0847894i
$996$	−4.95710	+	5.72080i	−0.157072	+	0.181271i
$997$	−27.8175	−	3.99955i	−0.880988	−	0.126667i	−0.313048	−	0.949737i	$-0.601350\pi$
$997$	−27.8175	−	3.99955i	−0.880988	−	0.126667i	−0.567939	+	0.823070i	$0.692259\pi$
$998$	5.01461	+	17.0782i	0.158735	+	0.540600i
$999$	6.86717	+	7.92514i	0.217268	+	0.250740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.j.a.209.6	✓	120
5.4	even	2	inner	230.2.j.a.209.7	yes	120
23.12	even	11	inner	230.2.j.a.219.7	yes	120
115.104	even	22	inner	230.2.j.a.219.6	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.209.6	✓	120	1.1	even	1	trivial
230.2.j.a.209.7	yes	120	5.4	even	2	inner
230.2.j.a.219.6	yes	120	115.104	even	22	inner
230.2.j.a.219.7	yes	120	23.12	even	11	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 + 0.841254i) q^{2} +(2.56448 - 0.368717i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(2.23602 + 0.0141641i) q^{5} +(-1.07628 + 2.35672i) q^{6} +(-1.82575 - 1.58202i) q^{7} +(0.989821 + 0.142315i) q^{8} +(3.56212 - 1.04593i) q^{9} +(-1.22080 + 1.87340i) q^{10} +(1.25768 - 0.808265i) q^{11} +(-1.40072 - 2.17956i) q^{12} +(-3.06511 + 2.65594i) q^{13} +(2.31795 - 0.680612i) q^{14} +(5.73946 - 0.788135i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-5.62426 - 2.56851i) q^{17} +(-1.04593 + 3.56212i) q^{18} +(0.291448 + 0.638182i) q^{19} +(-0.915993 - 2.03984i) q^{20} +(-5.26540 - 3.38387i) q^{21} +1.49501i q^{22} +(3.56194 + 3.21132i) q^{23} +2.59085 q^{24} +(4.99960 + 0.0633425i) q^{25} +(-0.577190 - 4.01445i) q^{26} +(1.67918 - 0.766856i) q^{27} +(-0.680612 + 2.31795i) q^{28} +(-2.53349 + 5.54757i) q^{29} +(-2.43996 + 5.25444i) q^{30} +(-0.649873 + 4.51997i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(2.92729 - 2.53651i) q^{33} +(5.20148 - 3.34279i) q^{34} +(-4.06000 - 3.56329i) q^{35} +(-2.43118 - 2.80573i) q^{36} +(1.60042 + 5.45053i) q^{37} +(-0.694442 - 0.0998457i) q^{38} +(-6.88114 + 7.94125i) q^{39} +(2.21125 + 0.332239i) q^{40} +(-4.89061 - 1.43601i) q^{41} +(5.69338 - 2.60008i) q^{42} +(4.99509 - 0.718186i) q^{43} +(-1.25768 - 0.808265i) q^{44} +(7.97981 - 2.28828i) q^{45} +(-4.62726 + 1.26033i) q^{46} -4.52400i q^{47} +(-1.40072 + 2.17956i) q^{48} +(-0.165637 - 1.15203i) q^{49} +(-2.75627 + 4.17168i) q^{50} +(-15.3704 - 4.51315i) q^{51} +(3.68922 + 1.68481i) q^{52} +(-4.01724 - 3.48096i) q^{53} +(-0.262713 + 1.82721i) q^{54} +(2.82366 - 1.78948i) q^{55} +(-1.58202 - 1.82575i) q^{56} +(0.982721 + 1.52914i) q^{57} +(-3.29720 - 5.13055i) q^{58} +(-9.64692 - 11.1331i) q^{59} +(-3.10117 - 4.89339i) q^{60} +(2.04923 - 14.2527i) q^{61} +(-3.45109 - 2.99039i) q^{62} +(-8.15822 - 3.72573i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-6.89129 + 5.89532i) q^{65} +(0.551236 + 3.83393i) q^{66} +(-1.77215 + 2.75752i) q^{67} +6.18301i q^{68} +(10.3186 + 6.92201i) q^{69} +(5.19263 - 1.48903i) q^{70} +(9.51232 + 6.11320i) q^{71} +(3.67472 - 0.528345i) q^{72} +(3.05196 - 1.39378i) q^{73} +(-5.45053 - 1.60042i) q^{74} +(12.8447 - 1.68099i) q^{75} +(0.459439 - 0.530221i) q^{76} +(-3.57490 - 0.513993i) q^{77} +(-2.96039 - 10.0821i) q^{78} +(1.54077 + 1.77814i) q^{79} +(-1.47499 + 1.68060i) q^{80} +(-5.34601 + 3.43567i) q^{81} +(3.85212 - 3.33788i) q^{82} +(-0.823140 - 2.80336i) q^{83} +(-0.890748 + 6.19529i) q^{84} +(-12.5396 - 5.82292i) q^{85} +(-2.09637 + 4.59042i) q^{86} +(-4.45160 + 15.1608i) q^{87} +(1.35991 - 0.621051i) q^{88} +(-0.515328 - 3.58419i) q^{89} +(-2.38919 + 7.95018i) q^{90} +9.79786 q^{91} +(1.44143 - 4.57409i) q^{92} +11.8310i q^{93} +(3.80583 + 2.44586i) q^{94} +(0.642645 + 1.43112i) q^{95} +(-1.07628 - 2.35672i) q^{96} +(-3.34235 + 11.3830i) q^{97} +(1.05870 + 0.483491i) q^{98} +(3.63464 - 4.19460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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