LMFDB - Embedded newform 228.2.w.a.211.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(67,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.w (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			211.8
Character	$\chi$	$=$	228.211
Dual form			228.2.w.a.67.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866706 + 1.11751i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.497640 + 1.93710i) q^{4} +(-2.00728 + 0.730589i) q^{5} +(0.0543836 - 1.41317i) q^{6} +(-3.36529 + 1.94295i) q^{7} +(-2.59603 + 1.12278i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-2.55616 - 1.60994i) q^{10} +(1.03222 + 0.595952i) q^{11} +(1.62636 - 1.16403i) q^{12} +(2.69633 + 3.21336i) q^{13} +(-5.08798 - 2.07676i) q^{14} +(2.00728 + 0.730589i) q^{15} +(-3.50471 - 1.92796i) q^{16} +(-0.0991862 + 0.562513i) q^{17} +(-0.950027 + 1.04759i) q^{18} +(4.29922 - 0.718796i) q^{19} +(-0.416321 - 4.25186i) q^{20} +(3.82687 + 0.674780i) q^{21} +(0.228651 + 1.67003i) q^{22} +(1.97361 - 5.42244i) q^{23} +(2.71038 + 0.808596i) q^{24} +(-0.334824 + 0.280951i) q^{25} +(-1.25403 + 5.79821i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-2.08899 - 7.48579i) q^{28} +(-7.06698 + 1.24610i) q^{29} +(0.923281 + 2.87635i) q^{30} +(3.19007 + 5.52537i) q^{31} +(-0.883048 - 5.58751i) q^{32} +(-0.407655 - 1.12002i) q^{33} +(-0.714577 + 0.376692i) q^{34} +(5.33557 - 6.35868i) q^{35} +(-1.99408 - 0.153706i) q^{36} +5.16918i q^{37} +(4.52942 + 4.18143i) q^{38} -4.19475i q^{39} +(4.39066 - 4.15036i) q^{40} +(6.98473 - 8.32408i) q^{41} +(2.56270 + 4.86138i) q^{42} +(0.969597 + 2.66394i) q^{43} +(-1.66809 + 1.70294i) q^{44} +(-1.06805 - 1.84992i) q^{45} +(7.77015 - 2.49415i) q^{46} +(-5.84871 + 1.03129i) q^{47} +(1.44549 + 3.72968i) q^{48} +(4.05012 - 7.01501i) q^{49} +(-0.604159 - 0.130666i) q^{50} +(0.437558 - 0.367154i) q^{51} +(-7.56641 + 3.62397i) q^{52} +(-3.23383 + 8.88487i) q^{53} +(1.40114 - 0.191837i) q^{54} +(-2.50734 - 0.442113i) q^{55} +(6.55488 - 8.82244i) q^{56} +(-3.75543 - 2.21286i) q^{57} +(-7.51752 - 6.81739i) q^{58} +(-1.18557 + 6.72368i) q^{59} +(-2.41412 + 3.52472i) q^{60} +(13.1163 + 4.77393i) q^{61} +(-3.40978 + 8.35380i) q^{62} +(-2.49781 - 2.97677i) q^{63} +(5.47873 - 5.82954i) q^{64} +(-7.75993 - 4.48020i) q^{65} +(0.898316 - 1.42629i) q^{66} +(1.03100 + 5.84710i) q^{67} +(-1.04028 - 0.472063i) q^{68} +(-4.99735 + 2.88522i) q^{69} +(11.7302 + 0.451421i) q^{70} +(6.26466 - 2.28015i) q^{71} +(-1.55652 - 2.36162i) q^{72} +(1.05767 + 0.887487i) q^{73} +(-5.77659 + 4.48016i) q^{74} +0.437082 q^{75} +(-0.747089 + 8.68573i) q^{76} -4.63162 q^{77} +(4.68766 - 3.63562i) q^{78} +(-5.51482 - 4.62748i) q^{79} +(8.44346 + 1.30944i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(15.3559 + 0.590949i) q^{82} +(-6.34481 + 3.66318i) q^{83} +(-3.21152 + 7.07722i) q^{84} +(-0.211872 - 1.20158i) q^{85} +(-2.13662 + 3.39239i) q^{86} +(6.21460 + 3.58800i) q^{87} +(-3.34879 - 0.388153i) q^{88} +(4.42805 + 5.27715i) q^{89} +(1.14161 - 2.79689i) q^{90} +(-15.3174 - 5.57506i) q^{91} +(9.52166 + 6.52150i) q^{92} +(1.10790 - 6.28322i) q^{93} +(-6.22158 - 5.64215i) q^{94} +(-8.10459 + 4.58379i) q^{95} +(-2.91513 + 4.84789i) q^{96} +(0.159517 + 0.0281271i) q^{97} +(11.3496 - 1.55392i) q^{98} +(-0.407655 + 1.12002i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{2} - 3 q^{4} + 3 q^{6} + 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} - 27 q^{16} - 18 q^{19} + 30 q^{20} - 6 q^{21} + 12 q^{22} + 18 q^{24} + 30 q^{27} - 18 q^{28} + 12 q^{31} - 63 q^{32} - 39 q^{34}+ \cdots + 117 q^{98}+O(q^{100}) $ 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^6 + 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 - 27 * q^16 - 18 * q^19 + 30 * q^20 - 6 * q^21 + 12 * q^22 + 18 * q^24 + 30 * q^27 - 18 * q^28 + 12 * q^31 - 63 * q^32 - 39 * q^34 - 3 * q^36 - 48 * q^38 + 33 * q^40 - 12 * q^41 - 9 * q^42 + 18 * q^43 - 9 * q^44 - 69 * q^46 + 6 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 - 42 * q^56 - 36 * q^58 - 3 * q^60 + 27 * q^62 + 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 - 42 * q^67 + 93 * q^68 - 72 * q^69 + 132 * q^70 - 24 * q^71 + 18 * q^72 + 18 * q^73 + 27 * q^74 - 60 * q^75 + 66 * q^76 - 72 * q^77 - 33 * q^78 - 12 * q^79 + 6 * q^80 - 9 * q^82 + 69 * q^84 - 60 * q^85 + 123 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 + 84 * q^91 - 99 * q^92 - 12 * q^93 + 24 * q^95 + 12 * q^97 + 117 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{1}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866706	+	1.11751i	0.612854	+	0.790196i
$2$	0.866706	+	1.11751i	0.612854	+	0.790196i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$4$	−0.497640	+	1.93710i	−0.248820	+	0.968550i
$5$	−2.00728	+	0.730589i	−0.897681	+	0.326729i	−0.749323	−	0.662204i	$-0.769621\pi$
$5$	−2.00728	+	0.730589i	−0.897681	+	0.326729i	−0.148358	+	0.988934i	$0.547399\pi$
$6$	0.0543836	−	1.41317i	0.0222020	−	0.576923i
$7$	−3.36529	+	1.94295i	−1.27196	+	0.734367i	−0.975357	−	0.220634i	$-0.929187\pi$
$7$	−3.36529	+	1.94295i	−1.27196	+	0.734367i	−0.296604	+	0.955001i	$0.595854\pi$
$8$	−2.59603	+	1.12278i	−0.917835	+	0.396963i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	−2.55616	−	1.60994i	−0.808328	−	0.509107i
$11$	1.03222	+	0.595952i	0.311226	+	0.179686i	0.647475	−	0.762087i	$-0.275825\pi$
$11$	1.03222	+	0.595952i	0.311226	+	0.179686i	−0.336249	+	0.941773i	$0.609158\pi$
$12$	1.62636	−	1.16403i	0.469489	−	0.336026i
$13$	2.69633	+	3.21336i	0.747828	+	0.891227i	0.997013	−	0.0772288i	$-0.0246072\pi$
$13$	2.69633	+	3.21336i	0.747828	+	0.891227i	−0.249185	+	0.968456i	$0.580163\pi$
$14$	−5.08798	−	2.07676i	−1.35982	−	0.555039i
$15$	2.00728	+	0.730589i	0.518276	+	0.188637i
$16$	−3.50471	−	1.92796i	−0.876177	−	0.481989i
$17$	−0.0991862	+	0.562513i	−0.0240562	+	0.136429i	−0.994470	−	0.105016i	$-0.966511\pi$
$17$	−0.0991862	+	0.562513i	−0.0240562	+	0.136429i	0.970414	+	0.241446i	$0.0776216\pi$
$18$	−0.950027	+	1.04759i	−0.223923	+	0.246920i
$19$	4.29922	−	0.718796i	0.986310	−	0.164903i
$19$	4.29922	−	0.718796i	0.986310	−	0.164903i
$20$	−0.416321	−	4.25186i	−0.0930923	−	0.950746i
$21$	3.82687	+	0.674780i	0.835091	+	0.147249i
$22$	0.228651	+	1.67003i	0.0487485	+	0.356051i
$23$	1.97361	−	5.42244i	0.411526	−	1.13066i	−0.544854	−	0.838531i	$-0.683415\pi$
$23$	1.97361	−	5.42244i	0.411526	−	1.13066i	0.956380	−	0.292127i	$-0.0943628\pi$
$24$	2.71038	+	0.808596i	0.553255	+	0.165054i
$25$	−0.334824	+	0.280951i	−0.0669649	+	0.0561902i
$26$	−1.25403	+	5.79821i	−0.245935	+	1.13712i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	−2.08899	−	7.48579i	−0.394781	−	1.41468i
$29$	−7.06698	+	1.24610i	−1.31231	+	0.231395i	−0.785643	−	0.618680i	$-0.787668\pi$
$29$	−7.06698	+	1.24610i	−1.31231	+	0.231395i	−0.526662	+	0.850075i	$0.676557\pi$
$30$	0.923281	+	2.87635i	0.168567	+	0.525147i
$31$	3.19007	+	5.52537i	0.572954	+	0.992386i	0.996261	+	0.0863992i	$0.0275361\pi$
$31$	3.19007	+	5.52537i	0.572954	+	0.992386i	−0.423306	+	0.905987i	$0.639131\pi$
$32$	−0.883048	−	5.58751i	−0.156102	−	0.987741i
$33$	−0.407655	−	1.12002i	−0.0709637	−	0.194971i
$34$	−0.714577	+	0.376692i	−0.122549	+	0.0646022i
$35$	5.33557	−	6.35868i	0.901876	−	1.07481i
$36$	−1.99408	−	0.153706i	−0.332347	−	0.0256177i
$37$			5.16918i			0.849808i	0.905238	+	0.424904i	$0.139692\pi$
$37$			5.16918i			0.849808i	−0.905238	+	0.424904i	$0.860308\pi$
$38$	4.52942	+	4.18143i	0.734770	+	0.678317i
$39$		−	4.19475i		−	0.671698i
$40$	4.39066	−	4.15036i	0.694224	−	0.656229i
$41$	6.98473	−	8.32408i	1.09083	−	1.30000i	0.140049	−	0.990145i	$-0.455274\pi$
$41$	6.98473	−	8.32408i	1.09083	−	1.30000i	0.950783	−	0.309858i	$-0.100282\pi$
$42$	2.56270	+	4.86138i	0.395433	+	0.750128i
$43$	0.969597	+	2.66394i	0.147862	+	0.406248i	0.991407	−	0.130810i	$-0.0417578\pi$
$43$	0.969597	+	2.66394i	0.147862	+	0.406248i	−0.843545	+	0.537058i	$0.819536\pi$
$44$	−1.66809	+	1.70294i	−0.251474	+	0.256728i
$45$	−1.06805	−	1.84992i	−0.159215	−	0.275769i
$46$	7.77015	−	2.49415i	1.14565	−	0.367742i
$47$	−5.84871	+	1.03129i	−0.853122	+	0.150428i	−0.583075	−	0.812419i	$-0.698150\pi$
$47$	−5.84871	+	1.03129i	−0.853122	+	0.150428i	−0.270047	+	0.962847i	$0.587039\pi$
$48$	1.44549	+	3.72968i	0.208639	+	0.538334i
$49$	4.05012	−	7.01501i	0.578588	−	1.00214i
$50$	−0.604159	−	0.130666i	−0.0854410	−	0.0184790i
$51$	0.437558	−	0.367154i	0.0612703	−	0.0514119i
$52$	−7.56641	+	3.62397i	−1.04927	+	0.502554i
$53$	−3.23383	+	8.88487i	−0.444200	+	1.22043i	0.492504	+	0.870310i	$0.336082\pi$
$53$	−3.23383	+	8.88487i	−0.444200	+	1.22043i	−0.936705	+	0.350120i	$0.886141\pi$
$54$	1.40114	−	0.191837i	0.190671	−	0.0261056i
$55$	−2.50734	−	0.442113i	−0.338090	−	0.0596144i
$56$	6.55488	−	8.82244i	0.875933	−	1.17895i
$57$	−3.75543	−	2.21286i	−0.497419	−	0.293100i
$58$	−7.51752	−	6.81739i	−0.987099	−	0.895167i
$59$	−1.18557	+	6.72368i	−0.154348	+	0.875348i	0.805032	+	0.593231i	$0.202148\pi$
$59$	−1.18557	+	6.72368i	−0.154348	+	0.875348i	−0.959380	+	0.282117i	$0.908963\pi$
$60$	−2.41412	+	3.52472i	−0.311662	+	0.455040i
$61$	13.1163	+	4.77393i	1.67937	+	0.611239i	0.993223	−	0.116228i	$-0.0370804\pi$
$61$	13.1163	+	4.77393i	1.67937	+	0.611239i	0.686143	+	0.727467i	$0.259303\pi$
$62$	−3.40978	+	8.35380i	−0.433042	+	1.06093i
$63$	−2.49781	−	2.97677i	−0.314694	−	0.375038i
$64$	5.47873	−	5.82954i	0.684841	−	0.728692i
$65$	−7.75993	−	4.48020i	−0.962501	−	0.555700i
$66$	0.898316	−	1.42629i	0.110575	−	0.175564i
$67$	1.03100	+	5.84710i	0.125957	+	0.714337i	0.980735	+	0.195343i	$0.0625822\pi$
$67$	1.03100	+	5.84710i	0.125957	+	0.714337i	−0.854778	+	0.518994i	$0.826307\pi$
$68$	−1.04028	−	0.472063i	−0.126153	−	0.0572460i
$69$	−4.99735	+	2.88522i	−0.601610	+	0.347340i
$70$	11.7302	+	0.451421i	1.40203	+	0.0539551i
$71$	6.26466	−	2.28015i	0.743478	−	0.270604i	0.0576193	−	0.998339i	$-0.481649\pi$
$71$	6.26466	−	2.28015i	0.743478	−	0.270604i	0.685859	+	0.727735i	$0.259427\pi$
$72$	−1.55652	−	2.36162i	−0.183437	−	0.278320i
$73$	1.05767	+	0.887487i	0.123790	+	0.103873i	0.702581	−	0.711604i	$-0.252031\pi$
$73$	1.05767	+	0.887487i	0.123790	+	0.103873i	−0.578791	+	0.815476i	$0.696475\pi$
$74$	−5.77659	+	4.48016i	−0.671515	+	0.520808i
$75$	0.437082			0.0504699
$76$	−0.747089	+	8.68573i	−0.0856970	+	0.996321i
$77$	−4.63162			−0.527822
$78$	4.68766	−	3.63562i	0.530773	−	0.411652i
$79$	−5.51482	−	4.62748i	−0.620465	−	0.520632i	0.277484	−	0.960730i	$-0.410499\pi$
$79$	−5.51482	−	4.62748i	−0.620465	−	0.520632i	−0.897950	+	0.440098i	$0.854944\pi$
$80$	8.44346	+	1.30944i	0.944008	+	0.146400i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	15.3559	+	0.590949i	1.69578	+	0.0652594i
$83$	−6.34481	+	3.66318i	−0.696434	+	0.402086i	−0.806018	−	0.591891i	$-0.798381\pi$
$83$	−6.34481	+	3.66318i	−0.696434	+	0.402086i	0.109584	+	0.993978i	$0.465048\pi$
$84$	−3.21152	+	7.07722i	−0.350405	+	0.772188i
$85$	−0.211872	−	1.20158i	−0.0229807	−	0.130330i
$86$	−2.13662	+	3.39239i	−0.230398	+	0.365811i
$87$	6.21460	+	3.58800i	0.666275	+	0.384674i
$88$	−3.34879	−	0.388153i	−0.356983	−	0.0413773i
$89$	4.42805	+	5.27715i	0.469373	+	0.559377i	0.947847	−	0.318725i	$-0.103255\pi$
$89$	4.42805	+	5.27715i	0.469373	+	0.559377i	−0.478474	+	0.878101i	$0.658810\pi$
$90$	1.14161	−	2.79689i	0.120336	−	0.294818i
$91$	−15.3174	−	5.57506i	−1.60570	−	0.584425i
$92$	9.52166	+	6.52150i	0.992702	+	0.679913i
$93$	1.10790	−	6.28322i	0.114884	−	0.651540i
$94$	−6.22158	−	5.64215i	−0.641707	−	0.581943i
$95$	−8.10459	+	4.58379i	−0.831513	+	0.470287i
$96$	−2.91513	+	4.84789i	−0.297524	+	0.494786i
$97$	0.159517	+	0.0281271i	0.0161965	+	0.00285588i	0.181741	−	0.983347i	$-0.441827\pi$
$97$	0.159517	+	0.0281271i	0.0161965	+	0.00285588i	−0.165544	+	0.986202i	$0.552938\pi$
$98$	11.3496	−	1.55392i	1.14648	−	0.156970i
$99$	−0.407655	+	1.12002i	−0.0409709	+	0.112567i
$100$	−0.377608	−	0.788401i	−0.0377608	−	0.0788401i
$101$	−2.57417	+	2.15998i	−0.256139	+	0.214926i	−0.761811	−	0.647800i	$-0.775689\pi$
$101$	−2.57417	+	2.15998i	−0.256139	+	0.214926i	0.505671	+	0.862726i	$0.331245\pi$
$102$	0.789531	+	0.170758i	0.0781752	+	0.0169076i
$103$	5.37262	−	9.30565i	0.529380	−	0.916913i	−0.470033	−	0.882649i	$-0.655758\pi$
$103$	5.37262	−	9.30565i	0.529380	−	0.916913i	0.999413	−	0.0342642i	$-0.0109088\pi$
$104$	−10.6077	−	5.31460i	−1.04017	−	0.521139i
$105$	−8.17457	+	1.44140i	−0.797756	+	0.140666i
$106$	−12.7317	+	4.08675i	−1.23661	+	0.396940i
$107$	−1.35395	−	2.34511i	−0.130891	−	0.226710i	0.793129	−	0.609054i	$-0.208451\pi$
$107$	−1.35395	−	2.34511i	−0.130891	−	0.226710i	−0.924020	+	0.382343i	$0.875117\pi$
$108$	1.42876	+	1.39952i	0.137482	+	0.134669i
$109$	−5.13775	−	14.1159i	−0.492107	−	1.35205i	−0.898748	−	0.438466i	$-0.855522\pi$
$109$	−5.13775	−	14.1159i	−0.492107	−	1.35205i	0.406640	−	0.913588i	$-0.366700\pi$
$110$	−1.67907	−	3.18515i	−0.160093	−	0.303693i
$111$	3.32268	−	3.95982i	0.315375	−	0.375850i
$112$	15.5403	−	0.321340i	1.46842	−	0.0303637i
$113$		−	20.6286i		−	1.94057i	−0.241960	−	0.970286i	$-0.577790\pi$
$113$		−	20.6286i		−	1.94057i	0.241960	−	0.970286i	$-0.422210\pi$
$114$	−0.781971	−	6.11462i	−0.0732383	−	0.572686i
$115$			12.3262i			1.14943i
$116$	1.10300	−	14.3096i	0.102411	−	1.32861i
$117$	−2.69633	+	3.21336i	−0.249276	+	0.297076i
$118$	−8.54129	+	4.50258i	−0.786289	+	0.414496i
$119$	−0.759145	−	2.08573i	−0.0695907	−	0.191199i
$120$	−6.03124	+	0.357100i	−0.550574	+	0.0325986i
$121$	−4.78968	−	8.29597i	−0.435426	−	0.754179i
$122$	6.03305	+	18.7951i	0.546207	+	1.70163i
$123$	−10.7012	+	1.88692i	−0.964897	+	0.170137i
$124$	−12.2907	+	3.42984i	−1.10374	+	0.308009i
$125$	5.80707	−	10.0581i	0.519400	−	0.899628i
$126$	1.16170	−	5.37131i	0.103492	−	0.478514i
$127$	−14.9489	+	12.5436i	−1.32650	+	1.11307i	−0.341620	+	0.939838i	$0.610976\pi$
$127$	−14.9489	+	12.5436i	−1.32650	+	1.11307i	−0.984882	+	0.173229i	$0.944580\pi$
$128$	11.2630	+	1.07002i	0.995518	+	0.0945771i
$129$	0.969597	−	2.66394i	0.0853682	−	0.234547i
$130$	−1.71893	−	12.5548i	−0.150760	−	1.10113i
$131$	8.51495	+	1.50142i	0.743955	+	0.131179i	0.532762	−	0.846265i	$-0.321154\pi$
$131$	8.51495	+	1.50142i	0.743955	+	0.131179i	0.211193	+	0.977444i	$0.432265\pi$
$132$	2.37246	−	0.232300i	0.206496	−	0.0202191i
$133$	−13.0716	+	10.7721i	−1.13345	+	0.934063i
$134$	−5.64060	+	6.21987i	−0.487273	+	0.537315i
$135$	−0.370930	+	2.10365i	−0.0319245	+	0.181053i
$136$	−0.374088	−	1.57166i	−0.0320778	−	0.134769i
$137$	3.39707	+	1.23643i	0.290231	+	0.105635i	0.483033	−	0.875602i	$-0.339535\pi$
$137$	3.39707	+	1.23643i	0.290231	+	0.105635i	−0.192802	+	0.981238i	$0.561757\pi$
$138$	−7.55549	−	3.08393i	−0.643166	−	0.262522i
$139$	4.92442	+	5.86869i	0.417684	+	0.497776i	0.933327	−	0.359027i	$-0.116892\pi$
$139$	4.92442	+	5.86869i	0.417684	+	0.497776i	−0.515643	+	0.856803i	$0.672447\pi$
$140$	9.66221	+	13.4999i	0.816606	+	1.14095i
$141$	5.14327	+	2.96947i	0.433141	+	0.250074i
$142$	7.97770	+	5.02457i	0.669474	+	0.421653i
$143$	0.868196	+	4.92378i	0.0726022	+	0.411747i
$144$	1.29008	−	3.78625i	0.107507	−	0.315521i
$145$	13.2750	−	7.66432i	1.10243	−	0.636487i
$146$	−0.0750867	+	1.95114i	−0.00621422	+	0.161477i
$147$	−7.61173	+	2.77044i	−0.627805	+	0.228502i
$148$	−10.0132	−	2.57239i	−0.823081	−	0.211449i
$149$	3.39876	+	2.85190i	0.278437	+	0.233637i	0.771302	−	0.636469i	$-0.219606\pi$
$149$	3.39876	+	2.85190i	0.278437	+	0.233637i	−0.492865	+	0.870106i	$0.664050\pi$
$150$	0.378822	+	0.488442i	0.0309307	+	0.0398811i
$151$	0.263103			0.0214110			0.0107055	−	0.999943i	$-0.496592\pi$
$151$	0.263103			0.0214110			0.0107055	+	0.999943i	$0.496592\pi$
$152$	−10.3539	+	6.69310i	−0.839809	+	0.542882i
$153$	−0.571191			−0.0461780
$154$	−4.01426	−	5.17587i	−0.323478	−	0.417083i
$155$	−10.4401	−	8.76031i	−0.838572	−	0.703645i
$156$	8.12565	+	2.08748i	0.650572	+	0.167132i
$157$	3.18440	−	1.15903i	0.254143	−	0.0925004i	−0.211807	−	0.977311i	$-0.567935\pi$
$157$	3.18440	−	1.15903i	0.254143	−	0.0925004i	0.465950	+	0.884811i	$0.345713\pi$
$158$	0.391512	−	10.1735i	0.0311470	−	0.809361i
$159$	8.18834	−	4.72754i	0.649377	−	0.374918i
$160$	5.85469	+	10.5705i	0.462854	+	0.835673i
$161$	3.89378	+	22.0827i	0.306873	+	1.74036i
$162$	−1.19665	−	0.753681i	−0.0940175	−	0.0592148i
$163$	8.58258	+	4.95516i	0.672240	+	0.388118i	0.796925	−	0.604079i	$-0.206459\pi$
$163$	8.58258	+	4.95516i	0.672240	+	0.388118i	−0.124685	+	0.992196i	$0.539792\pi$
$164$	12.6487	+	17.6725i	0.987696	+	1.37999i
$165$	1.63655	+	1.95037i	0.127405	+	0.151836i
$166$	−9.59272	−	3.91547i	−0.744539	−	0.303899i
$167$	−0.837907	−	0.304973i	−0.0648392	−	0.0235995i	0.309397	−	0.950933i	$-0.399873\pi$
$167$	−0.837907	−	0.304973i	−0.0648392	−	0.0235995i	−0.374236	+	0.927333i	$0.622095\pi$
$168$	−10.6923	+	2.54498i	−0.824928	+	0.196350i
$169$	−0.798074	+	4.52610i	−0.0613903	+	0.348162i
$170$	1.15915	−	1.27819i	0.0889025	−	0.0980325i
$171$	1.45443	+	4.10909i	0.111223	+	0.314230i
$172$	−5.64284	+	0.552519i	−0.430262	+	0.0421291i
$173$	19.5404	+	3.44549i	1.48563	+	0.261956i	0.856824	−	0.515609i	$-0.172434\pi$
$173$	19.5404	+	3.44549i	1.48563	+	0.261956i	0.628802	+	0.777565i	$0.283545\pi$
$174$	1.37662	+	10.0546i	0.104361	+	0.762237i
$175$	0.580907	−	1.59603i	0.0439125	−	0.120648i
$176$	−2.46866	−	4.07871i	−0.186082	−	0.307445i
$177$	5.23009	−	4.38857i	0.393118	−	0.329865i
$178$	−2.05943	+	9.52212i	−0.154360	+	0.713713i
$179$	4.71596	−	8.16828i	0.352487	−	0.610526i	−0.634197	−	0.773171i	$-0.718669\pi$
$179$	4.71596	−	8.16828i	0.352487	−	0.610526i	0.986685	+	0.162645i	$0.0520026\pi$
$180$	4.11498	−	1.14833i	0.306712	−	0.0855911i
$181$	−16.8723	+	2.97504i	−1.25411	+	0.221133i	−0.760952	−	0.648808i	$-0.775268\pi$
$181$	−16.8723	+	2.97504i	−1.25411	+	0.221133i	−0.493155	+	0.869941i	$0.664157\pi$
$182$	−7.04548	−	21.9492i	−0.522246	−	1.62698i
$183$	−6.97902	−	12.0880i	−0.515904	−	0.893572i
$184$	0.964668	+	16.2927i	0.0711163	+	1.20112i
$185$	−3.77654	−	10.3760i	−0.277657	−	0.762857i
$186$	7.98176	−	4.20762i	0.585251	−	0.308518i
$187$	−0.437613	+	0.521527i	−0.0320014	+	0.0381378i
$188$	0.912852	−	11.8427i	0.0665766	−	0.863721i
$189$			3.88590i			0.282658i
$190$	−12.1467	−	5.08413i	−0.881215	−	0.368842i
$191$			10.2517i			0.741786i	0.928676	+	0.370893i	$0.120948\pi$
$191$			10.2517i			0.741786i	−0.928676	+	0.370893i	$0.879052\pi$
$192$	−7.94411	+	0.944026i	−0.573316	+	0.0681292i
$193$	−15.2492	+	18.1733i	−1.09766	+	1.30815i	−0.150069	+	0.988676i	$0.547949\pi$
$193$	−15.2492	+	18.1733i	−1.09766	+	1.30815i	−0.947596	+	0.319470i	$0.896495\pi$
$194$	0.106822	+	0.202639i	0.00766938	+	0.0145486i
$195$	3.06464	+	8.42002i	0.219463	+	0.602970i
$196$	11.5733	+	11.3364i	0.826662	+	0.809745i
$197$	3.70130	+	6.41084i	0.263707	+	0.456753i	0.967224	−	0.253925i	$-0.0817216\pi$
$197$	3.70130	+	6.41084i	0.263707	+	0.456753i	−0.703517	+	0.710678i	$0.748388\pi$
$198$	−1.60495	+	0.515174i	−0.114059	+	0.0366118i
$199$	12.0670	−	2.12774i	0.855409	−	0.150832i	0.271288	−	0.962498i	$-0.412550\pi$
$199$	12.0670	−	2.12774i	0.855409	−	0.150832i	0.584121	+	0.811666i	$0.301439\pi$
$200$	0.553768	−	1.10529i	0.0391573	−	0.0781559i
$201$	2.96865	−	5.14186i	0.209393	−	0.362679i
$202$	−4.64484	−	1.00458i	−0.326810	−	0.0706818i
$203$	21.3613	−	17.9243i	1.49927	−	1.25804i
$204$	0.493468	+	1.03030i	0.0345497	+	0.0721357i
$205$	−7.93881	+	21.8117i	−0.554470	+	1.52339i
$206$	15.0556	−	2.06133i	1.04897	−	0.143620i
$207$	5.68278	+	1.00203i	0.394980	+	0.0696457i
$208$	−3.25463	−	16.4603i	−0.225668	−	1.14132i
$209$	4.86611	+	1.82018i	0.336596	+	0.125904i
$210$	−8.69572	−	7.88586i	−0.600061	−	0.544176i
$211$	4.12301	−	23.3828i	0.283840	−	1.60974i	−0.425560	−	0.904930i	$-0.639923\pi$
$211$	4.12301	−	23.3828i	0.283840	−	1.60974i	0.709400	−	0.704807i	$-0.248966\pi$
$212$	−15.6016	−	10.6857i	−1.07152	−	0.733898i
$213$	−6.26466	−	2.28015i	−0.429247	−	0.156233i
$214$	1.44720	−	3.54557i	0.0989285	−	0.242370i
$215$	−3.89250	−	4.63890i	−0.265466	−	0.316370i
$216$	−0.325658	+	2.80962i	−0.0221582	+	0.191170i
$217$	−21.4711	−	12.3963i	−1.45755	−	0.841517i
$218$	11.3216	−	17.9758i	0.766798	−	1.21747i
$219$	−0.239753	−	1.35971i	−0.0162010	−	0.0918807i
$220$	2.10417	−	4.63696i	0.141863	−	0.312624i
$221$	−2.07500	+	1.19800i	−0.139580	+	0.0805863i
$222$	7.30492	+	0.281119i	0.490274	+	0.0188674i
$223$	19.8399	−	7.22114i	1.32858	−	0.483563i	0.422382	−	0.906418i	$-0.361194\pi$
$223$	19.8399	−	7.22114i	1.32858	−	0.483563i	0.906198	+	0.422854i	$0.138972\pi$
$224$	13.8280	+	17.0879i	0.923920	+	1.14173i
$225$	−0.334824	−	0.280951i	−0.0223216	−	0.0187301i
$226$	23.0526	−	17.8789i	1.53343	−	1.18929i
$227$	−7.07156			−0.469356			−0.234678	−	0.972073i	$-0.575404\pi$
$227$	−7.07156			−0.469356			−0.234678	+	0.972073i	$0.575404\pi$
$228$	6.15538	−	6.17343i	0.407650	−	0.408846i
$229$	26.5681			1.75567			0.877835	−	0.478963i	$-0.158987\pi$
$229$	26.5681			1.75567			0.877835	+	0.478963i	$0.158987\pi$
$230$	−13.7746	+	10.6832i	−0.908273	+	0.704431i
$231$	3.54803	+	2.97715i	0.233443	+	0.195882i
$232$	16.9470	−	11.1696i	1.11262	−	0.733318i
$233$	20.5728	−	7.48788i	1.34777	−	0.490547i	0.435517	−	0.900180i	$-0.356565\pi$
$233$	20.5728	−	7.48788i	1.34777	−	0.490547i	0.912250	+	0.409633i	$0.134343\pi$
$234$	−5.92788	−	0.228126i	−0.387518	−	0.0149130i
$235$	10.9865	−	6.34308i	0.716682	−	0.413777i
$236$	−12.4344	−	5.64253i	−0.809414	−	0.367298i
$237$	1.25011	+	7.08971i	0.0812032	+	0.460526i
$238$	1.67287	−	2.65607i	0.108436	−	0.172167i
$239$	16.0962	+	9.29314i	1.04118	+	0.601123i	0.920166	−	0.391528i	$-0.128054\pi$
$239$	16.0962	+	9.29314i	1.04118	+	0.601123i	0.121009	+	0.992651i	$0.461387\pi$
$240$	−5.62637	−	6.43044i	−0.363181	−	0.415083i
$241$	−0.561724	−	0.669437i	−0.0361839	−	0.0431222i	0.747649	−	0.664094i	$-0.231183\pi$
$241$	−0.561724	−	0.669437i	−0.0361839	−	0.0431222i	−0.783833	+	0.620972i	$0.786738\pi$
$242$	5.11955	−	12.5427i	0.329097	−	0.806274i
$243$	0.939693	+	0.342020i	0.0602813	+	0.0219406i
$244$	−15.7748	+	23.0318i	−1.00988	+	1.47446i
$245$	−3.00462	+	17.0400i	−0.191958	+	1.08865i
$246$	−11.3835	−	10.3233i	−0.725783	−	0.658189i
$247$	13.9019	+	11.8769i	0.884556	+	0.755707i
$248$	−14.4853	−	10.7623i	−0.919817	−	0.683405i
$249$	7.21506	+	1.27221i	0.457236	+	0.0806230i
$250$	16.2731	−	2.22802i	1.02920	−	0.140912i
$251$	0.167210	−	0.459405i	0.0105542	−	0.0289974i	−0.934304	−	0.356478i	$-0.883977\pi$
$251$	0.167210	−	0.459405i	0.0105542	−	0.0289974i	0.944858	+	0.327481i	$0.106200\pi$
$252$	7.00932	−	3.35714i	0.441546	−	0.211480i
$253$	5.26871	−	4.42097i	0.331241	−	0.277944i
$254$	−26.9739	−	5.83386i	−1.69249	−	0.366049i
$255$	−0.610060	+	1.05665i	−0.0382034	+	0.0661703i
$256$	8.56596	+	13.5139i	0.535372	+	0.844616i
$257$	−12.4419	+	2.19385i	−0.776106	+	0.136848i	−0.547652	−	0.836706i	$-0.684478\pi$
$257$	−12.4419	+	2.19385i	−0.776106	+	0.136848i	−0.228454	+	0.973555i	$0.573367\pi$
$258$	3.81733	−	1.22533i	0.237657	−	0.0762856i
$259$	−10.0435	−	17.3958i	−0.624070	−	1.08092i
$260$	12.5402	−	12.8022i	0.777713	−	0.793961i
$261$	−2.45434	−	6.74323i	−0.151920	−	0.417396i
$262$	5.70212	+	10.8168i	0.352278	+	0.668264i
$263$	−14.4841	+	17.2615i	−0.893127	+	1.06439i	0.104430	+	0.994532i	$0.466698\pi$
$263$	−14.4841	+	17.2615i	−0.893127	+	1.06439i	−0.997557	+	0.0698553i	$0.977746\pi$
$264$	2.31582	+	2.44991i	0.142529	+	0.150781i
$265$		−	20.1970i		−	1.24069i
$266$	−23.3671	−	5.27126i	−1.43273	−	0.323202i
$267$		−	6.88883i		−	0.421590i
$268$	−11.8395	−	0.912601i	−0.723212	−	0.0557460i
$269$	−5.15241	+	6.14040i	−0.314148	+	0.374387i	−0.899895	−	0.436107i	$-0.856357\pi$
$269$	−5.15241	+	6.14040i	−0.314148	+	0.374387i	0.585747	+	0.810494i	$0.300801\pi$
$270$	−2.67233	+	1.40873i	−0.162633	+	0.0857324i
$271$	−9.53494	−	26.1970i	−0.579207	−	1.59136i	−0.789521	−	0.613723i	$-0.789671\pi$
$271$	−9.53494	−	26.1970i	−0.579207	−	1.59136i	0.210315	−	0.977634i	$-0.432551\pi$
$272$	1.43212	−	1.78022i	0.0868351	−	0.107942i
$273$	8.15019	+	14.1166i	0.493272	+	0.854372i
$274$	1.56254	+	4.86786i	0.0943964	+	0.294078i
$275$	−0.513045	+	0.0904638i	−0.0309378	+	0.00545517i
$276$	−3.10208	−	11.1162i	−0.186723	−	0.669115i
$277$	0.813301	−	1.40868i	0.0488665	−	0.0846393i	−0.840558	−	0.541722i	$-0.817772\pi$
$277$	0.813301	−	1.40868i	0.0488665	−	0.0846393i	0.889424	+	0.457083i	$0.151106\pi$
$278$	−2.29028	+	10.5895i	−0.137362	+	0.635116i
$279$	−4.88748	+	4.10108i	−0.292606	+	0.245525i
$280$	−6.71189	+	22.4980i	−0.401112	+	1.34451i
$281$	−2.95883	+	8.12931i	−0.176509	+	0.484954i	−0.996124	−	0.0879605i	$-0.971965\pi$
$281$	−2.95883	+	8.12931i	−0.176509	+	0.484954i	0.819615	+	0.572915i	$0.194187\pi$
$282$	1.13930	+	8.32129i	0.0678446	+	0.495526i
$283$	−24.3476	−	4.29314i	−1.44731	−	0.255201i	−0.605879	−	0.795557i	$-0.707178\pi$
$283$	−24.3476	−	4.29314i	−1.44731	−	0.255201i	−0.841436	+	0.540357i	$0.818289\pi$
$284$	1.29933	+	13.2700i	0.0771010	+	0.787427i
$285$	9.15488	+	1.69814i	0.542288	+	0.100589i
$286$	−4.74989	+	5.23769i	−0.280867	+	0.309711i
$287$	−7.33237	+	41.5839i	−0.432816	+	2.45462i
$288$	5.34928	−	1.83989i	0.315209	−	0.108417i
$289$	15.6682	+	5.70276i	0.921658	+	0.335456i
$290$	20.0704	+	8.19217i	1.17858	+	0.481061i
$291$	−0.104117	−	0.124082i	−0.00610346	−	0.00727382i
$292$	−2.24549	+	1.60716i	−0.131407	+	0.0940516i
$293$	7.77772	+	4.49047i	0.454379	+	0.262336i	0.709678	−	0.704526i	$-0.248841\pi$
$293$	7.77772	+	4.49047i	0.454379	+	0.262336i	−0.255299	+	0.966862i	$0.582174\pi$
$294$	−9.69313	−	6.10500i	−0.565315	−	0.356051i
$295$	−2.53249	−	14.3624i	−0.147447	−	0.836214i
$296$	−5.80385	−	13.4193i	−0.337342	−	0.779983i
$297$	1.03222	−	0.595952i	0.0598954	−	0.0345806i
$298$	−0.241287	+	6.26989i	−0.0139774	+	0.363205i
$299$	22.7458	−	8.27879i	1.31542	−	0.478775i
$300$	−0.217510	+	0.846672i	−0.0125579	+	0.0488826i
$301$	−8.43889	−	7.08107i	−0.486409	−	0.408146i
$302$	0.228033	+	0.294020i	0.0131218	+	0.0169189i
$303$	3.36034			0.193046
$304$	−16.4533	−	5.76955i	−0.943664	−	0.330907i
$305$	−29.8157			−1.70724
$306$	−0.495055	−	0.638309i	−0.0283004	−	0.0364897i
$307$	13.5022	+	11.3297i	0.770611	+	0.646619i	0.940865	−	0.338781i	$-0.110014\pi$
$307$	13.5022	+	11.3297i	0.770611	+	0.646619i	−0.170254	+	0.985400i	$0.554459\pi$
$308$	2.30488	−	8.97191i	0.131333	−	0.511222i
$309$	−10.0972	+	3.67509i	−0.574411	+	0.209069i
$310$	0.741174	−	19.2595i	0.0420959	−	1.09387i
$311$	−6.03453	+	3.48404i	−0.342187	+	0.197562i	−0.661239	−	0.750176i	$-0.729969\pi$
$311$	−6.03453	+	3.48404i	−0.342187	+	0.197562i	0.319052	+	0.947737i	$0.396636\pi$
$312$	4.70978	+	10.8897i	0.266639	+	0.616507i
$313$	0.0923910	+	0.523975i	0.00522225	+	0.0296168i	0.987308	−	0.158820i	$-0.0507690\pi$
$313$	0.0923910	+	0.523975i	0.00522225	+	0.0296168i	−0.982085	+	0.188437i	$0.939658\pi$
$314$	4.05516	+	2.55405i	0.228846	+	0.144133i
$315$	7.18859	+	4.15034i	0.405031	+	0.233845i
$316$	11.7083	−	8.37993i	0.658642	−	0.471408i
$317$	−6.14785	−	7.32672i	−0.345298	−	0.411510i	0.565246	−	0.824922i	$-0.308781\pi$
$317$	−6.14785	−	7.32672i	−0.345298	−	0.411510i	−0.910544	+	0.413412i	$0.864337\pi$
$318$	12.3799	+	5.05313i	0.694233	+	0.283366i
$319$	−8.03729	−	2.92533i	−0.450002	−	0.163787i
$320$	−6.73833	+	15.7042i	−0.376684	+	0.877891i
$321$	−0.470222	+	2.66676i	−0.0262452	+	0.148844i
$322$	−21.3028	+	23.4906i	−1.18716	+	1.30908i
$323$	−0.0220919	+	2.48967i	−0.00122923	+	0.138529i
$324$	−0.194898	−	1.99048i	−0.0108277	−	0.110582i
$325$	−1.80560	−	0.318375i	−0.100156	−	0.0176603i
$326$	1.90116	+	13.8858i	0.105296	+	0.769061i
$327$	−5.13775	+	14.1159i	−0.284118	+	0.780609i
$328$	−8.78645	+	29.4519i	−0.485151	+	1.62621i
$329$	17.6789	−	14.8343i	0.974667	−	0.817843i
$330$	−0.761138	+	3.51925i	−0.0418992	+	0.193729i
$331$	5.92951	−	10.2702i	0.325915	−	0.564502i	−0.655782	−	0.754950i	$-0.727661\pi$
$331$	5.92951	−	10.2702i	0.325915	−	0.564502i	0.981697	+	0.190448i	$0.0609942\pi$
$332$	−3.93851	−	14.1135i	−0.216154	−	0.774578i
$333$	−5.09065	+	0.897619i	−0.278966	+	0.0491892i
$334$	−0.385410	−	1.20069i	−0.0210887	−	0.0656987i
$335$	−6.34133	−	10.9835i	−0.346464	−	0.600093i
$336$	−12.1111	−	9.74294i	−0.660715	−	0.531521i
$337$	−4.64291	−	12.7563i	−0.252915	−	0.694879i	−0.999560	−	0.0296564i	$-0.990559\pi$
$337$	−4.64291	−	12.7563i	−0.252915	−	0.694879i	0.746645	−	0.665223i	$-0.231664\pi$
$338$	−5.74964	+	3.03095i	−0.312739	+	0.164862i
$339$	−13.2598	+	15.8024i	−0.720173	+	0.858268i
$340$	2.43302	+	0.187540i	0.131949	+	0.0101708i
$341$			7.60452i			0.411808i
$342$	−3.33137	+	5.18671i	−0.180140	+	0.280465i
$343$			4.27542i			0.230851i
$344$	−5.50812	−	5.82703i	−0.296978	−	0.314173i
$345$	7.92315	−	9.44244i	0.426568	−	0.508364i
$346$	13.0854	+	24.8227i	0.703475	+	1.33448i
$347$	6.88372	+	18.9129i	0.369538	+	1.01530i	0.975538	+	0.219832i	$0.0705509\pi$
$347$	6.88372	+	18.9129i	0.369538	+	1.01530i	−0.606000	+	0.795465i	$0.707227\pi$
$348$	−10.0429	+	10.2528i	−0.538358	+	0.549606i
$349$	6.93698	+	12.0152i	0.371328	+	0.643159i	0.989770	−	0.142672i	$-0.0455693\pi$
$349$	6.93698	+	12.0152i	0.371328	+	0.643159i	−0.618442	+	0.785830i	$0.712236\pi$
$350$	2.28705	−	0.734121i	0.122248	−	0.0392404i
$351$	4.13102	−	0.728411i	0.220498	−	0.0388797i
$352$	2.41839	−	6.29378i	0.128900	−	0.335460i
$353$	0.720446	−	1.24785i	0.0383454	−	0.0664163i	−0.846216	−	0.532840i	$-0.821125\pi$
$353$	0.720446	−	1.24785i	0.0383454	−	0.0664163i	0.884561	+	0.466424i	$0.154458\pi$
$354$	9.43721	+	2.04106i	0.501582	+	0.108481i
$355$	−10.9090	+	9.15378i	−0.578992	+	0.485832i
$356$	−12.4259	+	5.95146i	−0.658574	+	0.315427i
$357$	−0.759145	+	2.08573i	−0.0401782	+	0.110389i
$358$	13.2155	−	1.80939i	0.698459	−	0.0956291i
$359$	−25.7374	−	4.53820i	−1.35837	−	0.239517i	−0.553440	−	0.832889i	$-0.686685\pi$
$359$	−25.7374	−	4.53820i	−1.35837	−	0.239517i	−0.804929	+	0.593372i	$0.797796\pi$
$360$	4.84974	+	3.60325i	0.255603	+	0.189908i
$361$	17.9667	−	6.18053i	0.945614	−	0.325291i
$362$	−17.9479	−	16.2764i	−0.943323	−	0.855469i
$363$	−1.66344	+	9.43383i	−0.0873079	+	0.495148i
$364$	18.4220	−	26.8969i	0.965574	−	1.40978i
$365$	−2.77142	−	1.00871i	−0.145063	−	0.0527985i
$366$	7.45967	−	18.2759i	0.389923	−	0.955294i
$367$	14.0629	+	16.7596i	0.734079	+	0.874842i	0.995917	−	0.0902701i	$-0.0287730\pi$
$367$	14.0629	+	16.7596i	0.734079	+	0.874842i	−0.261838	+	0.965112i	$0.584329\pi$
$368$	−17.3712	+	15.1990i	−0.905534	+	0.792305i
$369$	9.41050	+	5.43316i	0.489891	+	0.282839i
$370$	8.32206	−	13.2132i	0.432643	−	0.686923i
$371$	−6.38010	−	36.1833i	−0.331238	−	1.87854i
$372$	11.6199	+	5.27290i	0.602463	+	0.273387i
$373$	−30.3346	+	17.5137i	−1.57067	+	0.906826i	−0.574581	+	0.818447i	$0.694835\pi$
$373$	−30.3346	+	17.5137i	−1.57067	+	0.906826i	−0.996087	+	0.0883784i	$0.971832\pi$
$374$	−0.962091	−	0.0370246i	−0.0497485	−	0.00191450i
$375$	−10.9137	+	3.97227i	−0.563582	+	0.205127i
$376$	14.0255	−	9.24406i	0.723310	−	0.476726i
$377$	−23.0591	−	19.3489i	−1.18760	−	0.996518i
$378$	−4.34252	+	3.36794i	−0.223355	+	0.173228i
$379$	−2.69677			−0.138524			−0.0692619	−	0.997599i	$-0.522064\pi$
$379$	−2.69677			−0.138524			−0.0692619	+	0.997599i	$0.522064\pi$
$380$	−4.84608	−	17.9805i	−0.248599	−	0.922379i
$381$	19.5144			0.999754
$382$	−11.4563	+	8.88520i	−0.586156	+	0.454606i
$383$	−24.2834	−	20.3762i	−1.24082	−	1.04117i	−0.997459	−	0.0712394i	$-0.977305\pi$
$383$	−24.2834	−	20.3762i	−1.24082	−	1.04117i	−0.243364	−	0.969935i	$-0.578251\pi$
$384$	−7.94016	−	8.05939i	−0.405195	−	0.411279i
$385$	9.29695	−	3.38381i	0.473816	−	0.172455i
$386$	−33.5254	−	1.29018i	−1.70640	−	0.0656682i
$387$	−2.45510	+	1.41746i	−0.124800	+	0.0720533i
$388$	−0.133867	+	0.295003i	−0.00679607	+	0.0149765i
$389$	1.99661	+	11.3233i	0.101232	+	0.574116i	0.992659	+	0.120950i	$0.0385942\pi$
$389$	1.99661	+	11.3233i	0.101232	+	0.574116i	−0.891426	+	0.453165i	$0.850295\pi$
$390$	−6.75329	+	10.7224i	−0.341966	+	0.542952i
$391$	2.85444	+	1.64801i	0.144355	+	0.0833436i
$392$	−2.63791	+	22.7586i	−0.133235	+	1.14948i
$393$	−5.55774	−	6.62346i	−0.280351	−	0.334109i
$394$	−3.95621	+	9.69254i	−0.199311	+	0.488303i
$395$	14.4505	+	5.25957i	0.727086	+	0.264638i
$396$	−1.96673	−	1.34704i	−0.0988319	−	0.0676912i
$397$	4.69292	−	26.6149i	0.235531	−	1.33576i	−0.605962	−	0.795494i	$-0.707212\pi$
$397$	4.69292	−	26.6149i	0.235531	−	1.33576i	0.841493	−	0.540268i	$-0.181677\pi$
$398$	12.8363	+	11.6409i	0.643428	+	0.583503i
$399$	16.9376	+	0.150295i	0.847940	+	0.00752415i
$400$	1.71512	−	0.339124i	0.0857562	−	0.0169562i
$401$	−11.7859	−	2.07818i	−0.588561	−	0.103779i	−0.128567	−	0.991701i	$-0.541038\pi$
$401$	−11.7859	−	2.07818i	−0.588561	−	0.103779i	−0.459995	+	0.887922i	$0.652149\pi$
$402$	8.31901	−	1.13899i	0.414914	−	0.0568078i
$403$	−9.15353	+	25.1491i	−0.455970	+	1.25277i
$404$	−2.90309	−	6.06132i	−0.144434	−	0.301562i
$405$	1.63635	−	1.37306i	0.0813107	−	0.0682278i
$406$	38.5445	+	8.33633i	1.91293	+	0.413725i
$407$	−3.08058	+	5.33573i	−0.152699	+	0.264482i
$408$	−0.723678	+	1.44442i	−0.0358274	+	0.0715097i
$409$	18.3731	−	3.23967i	0.908490	−	0.160191i	0.300172	−	0.953885i	$-0.402956\pi$
$409$	18.3731	−	3.23967i	0.908490	−	0.160191i	0.608317	+	0.793694i	$0.291845\pi$
$410$	−31.2553	+	10.0327i	−1.54359	+	0.495478i
$411$	−1.80754	−	3.13075i	−0.0891594	−	0.154429i
$412$	15.3523	+	15.0382i	0.756356	+	0.740877i
$413$	−9.07401	−	24.9306i	−0.446503	−	1.22676i
$414$	3.80553	+	7.21900i	0.187031	+	0.354795i
$415$	10.0595	−	11.9885i	0.493802	−	0.588491i
$416$	15.5737	−	17.9033i	0.763564	−	0.877783i
$417$		−	7.66103i		−	0.375162i
$418$	2.18343	+	7.01547i	0.106795	+	0.343138i
$419$			32.8066i			1.60271i	0.598190	+	0.801355i	$0.295887\pi$
$419$			32.8066i			1.60271i	−0.598190	+	0.801355i	$0.704113\pi$
$420$	1.27587	−	16.5522i	0.0622559	−	0.807667i
$421$	−9.94197	+	11.8484i	−0.484542	+	0.577455i	−0.951821	−	0.306655i	$-0.900790\pi$
$421$	−9.94197	+	11.8484i	−0.484542	+	0.577455i	0.467278	+	0.884110i	$0.345235\pi$
$422$	29.7038	−	15.6585i	1.44596	−	0.762244i
$423$	−2.03124	−	5.58077i	−0.0987620	−	0.271346i
$424$	−1.58064	−	26.6962i	−0.0767628	−	1.29648i
$425$	−0.124829	−	0.216210i	−0.00605508	−	0.0104877i
$426$	−2.88154	−	8.97701i	−0.139611	−	0.434938i
$427$	−53.4155	+	9.41860i	−2.58496	+	0.455798i
$428$	5.21649	−	1.45572i	0.252149	−	0.0703646i
$429$	2.49987	−	4.32990i	0.120695	−	0.209050i
$430$	1.81034	−	8.37045i	0.0873026	−	0.403659i
$431$	−3.93064	+	3.29820i	−0.189332	+	0.158869i	−0.732527	−	0.680738i	$-0.761659\pi$
$431$	−3.93064	+	3.29820i	−0.189332	+	0.158869i	0.543194	+	0.839607i	$0.317215\pi$
$432$	−3.42201	+	2.07119i	−0.164642	+	0.0996501i
$433$	−8.28201	+	22.7546i	−0.398008	+	1.09352i	0.565245	+	0.824923i	$0.308782\pi$
$433$	−8.28201	+	22.7546i	−0.398008	+	1.09352i	−0.963253	+	0.268595i	$0.913441\pi$
$434$	−4.75613	−	34.7380i	−0.228302	−	1.66748i
$435$	−15.0958	−	2.66179i	−0.723787	−	0.127623i
$436$	29.9006	−	2.92772i	1.43198	−	0.140212i
$437$	4.58735	−	24.7309i	0.219443	−	1.18304i
$438$	1.31169	−	1.44639i	0.0626749	−	0.0691114i
$439$	2.04427	−	11.5936i	0.0975676	−	0.553334i	−0.896363	−	0.443322i	$-0.853800\pi$
$439$	2.04427	−	11.5936i	0.0975676	−	0.553334i	0.993930	−	0.110012i	$-0.0350889\pi$
$440$	7.00553	−	1.66746i	0.333976	−	0.0794930i
$441$	7.61173	+	2.77044i	0.362464	+	0.131926i
$442$	−3.13719	−	1.28051i	−0.149221	−	0.0609076i
$443$	−1.75292	−	2.08905i	−0.0832837	−	0.0992537i	0.722793	−	0.691064i	$-0.242858\pi$
$443$	−1.75292	−	2.08905i	−0.0832837	−	0.0992537i	−0.806077	+	0.591810i	$0.798413\pi$
$444$	6.01707	+	8.40694i	0.285557	+	0.398976i
$445$	−12.7438	−	7.35761i	−0.604112	−	0.348784i
$446$	25.2651	+	15.9126i	1.19634	+	0.753485i
$447$	−0.770436	−	4.36936i	−0.0364404	−	0.206664i
$448$	−7.11101	+	30.2630i	−0.335964	+	1.42979i
$449$	7.09301	−	4.09515i	0.334740	−	0.193262i	−0.323204	−	0.946329i	$-0.604760\pi$
$449$	7.09301	−	4.09515i	0.334740	−	0.193262i	0.657944	+	0.753067i	$0.271427\pi$
$450$	0.0237701	−	0.617670i	0.00112053	−	0.0291173i
$451$	12.1705	−	4.42971i	0.573088	−	0.208587i
$452$	39.9596	+	10.2656i	1.87954	+	0.482854i
$453$	−0.201549	−	0.169120i	−0.00946959	−	0.00794593i
$454$	−6.12896	−	7.90251i	−0.287647	−	0.370883i
$455$	34.8192			1.63235
$456$	12.2338	+	1.52812i	0.572898	+	0.0715609i
$457$	−0.995054			−0.0465466			−0.0232733	−	0.999729i	$-0.507409\pi$
$457$	−0.995054			−0.0465466			−0.0232733	+	0.999729i	$0.507409\pi$
$458$	23.0267	+	29.6900i	1.07597	+	1.38732i
$459$	0.437558	+	0.367154i	0.0204234	+	0.0171373i
$460$	−23.8771	−	6.13403i	−1.11328	−	0.286001i
$461$	−9.98005	+	3.63244i	−0.464817	+	0.169180i	−0.563803	−	0.825909i	$-0.690662\pi$
$461$	−9.98005	+	3.63244i	−0.464817	+	0.169180i	0.0989860	+	0.995089i	$0.468440\pi$
$462$	−0.251884	+	6.54526i	−0.0117187	+	0.304513i
$463$	26.6080	−	15.3621i	1.23658	−	0.713938i	0.268185	−	0.963368i	$-0.413576\pi$
$463$	26.6080	−	15.3621i	1.23658	−	0.713938i	0.968393	+	0.249429i	$0.0802429\pi$
$464$	27.1701	+	9.25762i	1.26134	+	0.429774i
$465$	2.36659	+	13.4216i	0.109748	+	0.622411i
$466$	26.1983	+	16.5004i	1.21361	+	0.764367i
$467$	−27.2647	−	15.7413i	−1.26166	−	0.728420i	−0.288265	−	0.957551i	$-0.593079\pi$
$467$	−27.2647	−	15.7413i	−1.26166	−	0.728420i	−0.973396	+	0.229130i	$0.926412\pi$
$468$	−4.88280	−	6.82217i	−0.225708	−	0.315355i
$469$	−14.8303	−	17.6740i	−0.684798	−	0.816110i
$470$	16.6105	+	6.77993i	0.766186	+	0.312735i
$471$	−3.18440	−	1.15903i	−0.146729	−	0.0534051i
$472$	−4.47145	−	18.7860i	−0.205815	−	0.864695i
$473$	−0.586747	+	3.32761i	−0.0269787	+	0.153004i
$474$	−6.83932	+	7.54170i	−0.314140	+	0.346402i
$475$	−1.23754	+	1.44854i	−0.0567822	+	0.0664637i
$476$	4.41806	−	0.432594i	0.202501	−	0.0198279i
$477$	−9.31143	−	1.64186i	−0.426341	−	0.0751755i
$478$	3.56553	+	26.0420i	0.163083	+	1.19113i
$479$	6.05970	−	16.6489i	0.276875	−	0.760707i	−0.720838	−	0.693104i	$-0.756243\pi$
$479$	6.05970	−	16.6489i	0.276875	−	0.760707i	0.997712	−	0.0676031i	$-0.0215352\pi$
$480$	2.30965	−	11.8608i	0.105421	−	0.541370i
$481$	−16.6105	+	13.9378i	−0.757372	+	0.635510i
$482$	0.261250	−	1.20794i	0.0118996	−	0.0550200i
$483$	11.2117	−	19.4192i	0.510150	−	0.883605i
$484$	18.4537	−	5.14968i	0.838803	−	0.234076i
$485$	−0.340744	+	0.0600823i	−0.0154724	+	0.00272820i
$486$	0.432228	+	1.34654i	0.0196063	+	0.0610804i
$487$	2.34081	+	4.05441i	0.106072	+	0.183723i	0.914176	−	0.405318i	$-0.132839\pi$
$487$	2.34081	+	4.05441i	0.106072	+	0.183723i	−0.808103	+	0.589041i	$0.799506\pi$
$488$	−39.4103	+	2.33342i	−1.78402	+	0.105629i
$489$	−3.38953	−	9.31265i	−0.153280	−	0.421133i
$490$	−21.6465	+	11.4110i	−0.977888	+	0.515498i
$491$	27.2395	−	32.4627i	1.22930	−	1.46502i	0.390482	−	0.920610i	$-0.372308\pi$
$491$	27.2395	−	32.4627i	1.22930	−	1.46502i	0.838818	−	0.544412i	$-0.183247\pi$
$492$	1.67022	−	21.6684i	0.0752994	−	0.976885i
$493$		−	4.09887i		−	0.184604i
$494$	−1.22361	+	25.8292i	−0.0550528	+	1.16211i
$495$		−	2.54602i		−	0.114435i
$496$	−0.527598	−	25.5151i	−0.0236898	−	1.14566i
$497$	−16.6522	+	19.8453i	−0.746952	+	0.890183i
$498$	4.83163	+	9.16550i	0.216511	+	0.410716i
$499$	1.44456	+	3.96890i	0.0646674	+	0.177672i	0.967818	−	0.251652i	$-0.0809739\pi$
$499$	1.44456	+	3.96890i	0.0646674	+	0.177672i	−0.903150	+	0.429324i	$0.858752\pi$
$500$	16.5938	+	16.2542i	0.742097	+	0.726911i
$501$	0.445841	+	0.772219i	0.0199187	+	0.0345002i
$502$	0.658310	−	0.211311i	0.0293818	−	0.00943129i
$503$	−2.57848	+	0.454655i	−0.114969	+	0.0202721i	−0.230836	−	0.972993i	$-0.574146\pi$
$503$	−2.57848	+	0.454655i	−0.114969	+	0.0202721i	0.115868	+	0.993265i	$0.463035\pi$
$504$	9.82665	+	4.92330i	0.437714	+	0.219301i
$505$	3.58901	−	6.21634i	0.159709	−	0.276624i
$506$	9.50689	+	2.05613i	0.422633	+	0.0914062i
$507$	3.52068	−	2.95420i	0.156359	−	0.131201i
$508$	−16.8591	−	35.1998i	−0.748001	−	1.56174i
$509$	4.30234	−	11.8206i	0.190698	−	0.523938i	−0.807089	−	0.590429i	$-0.798958\pi$
$509$	4.30234	−	11.8206i	0.190698	−	0.523938i	0.997787	+	0.0664917i	$0.0211806\pi$
$510$	−1.70956	+	0.234064i	−0.0757006	+	0.0103645i
$511$	−5.28370	−	0.931659i	−0.233737	−	0.0412142i
$512$	−7.67765	+	21.2851i	−0.339307	+	0.940676i
$513$	1.52712	−	4.08264i	0.0674239	−	0.180253i
$514$	−13.2351	−	12.0025i	−0.583777	−	0.529408i
$515$	−3.98573	+	22.6042i	−0.175632	+	0.996060i
$516$	4.67782	+	3.20389i	0.205929	+	0.141043i
$517$	−6.65175	−	2.42104i	−0.292543	−	0.106477i
$518$	10.7352	−	26.3007i	0.471676	−	1.15559i
$519$	−12.7541	−	15.1997i	−0.559841	−	0.667193i
$520$	25.1753	+	2.91803i	1.10401	+	0.127964i
$521$	−8.84073	−	5.10420i	−0.387319	−	0.223619i	0.293679	−	0.955904i	$-0.405120\pi$
$521$	−8.84073	−	5.10420i	−0.387319	−	0.223619i	−0.680998	+	0.732285i	$0.738454\pi$
$522$	5.40842	−	8.58714i	0.236720	−	0.375849i
$523$	0.604315	+	3.42724i	0.0264249	+	0.149863i	0.995165	−	0.0982134i	$-0.0313128\pi$
$523$	0.604315	+	3.42724i	0.0264249	+	0.149863i	−0.968741	+	0.248076i	$0.920202\pi$
$524$	−7.14578	+	15.7471i	−0.312165	+	0.687917i
$525$	−1.47091	+	0.849229i	−0.0641957	+	0.0370634i
$526$	−31.8432	−	1.22544i	−1.38843	−	0.0534317i
$527$	−3.42451	+	1.24642i	−0.149174	+	0.0542948i
$528$	−0.730645	+	4.71130i	−0.0317973	+	0.205033i
$529$	−7.88874	−	6.61944i	−0.342989	−	0.287802i
$530$	22.5703	−	17.5049i	0.980389	−	0.760362i
$531$	−6.82740			−0.296284
$532$	−14.3618	−	30.6816i	−0.622662	−	1.33021i
$533$	45.5815			1.97435
$534$	7.69831	−	5.97059i	0.333138	−	0.258373i
$535$	4.43107	+	3.71811i	0.191572	+	0.160748i
$536$	−9.24152	−	14.0217i	−0.399173	−	0.605643i
$537$	−8.86310	+	3.22591i	−0.382471	+	0.139208i
$538$	−11.3276	−	0.435924i	−0.488366	−	0.0187940i
$539$	8.36122	−	4.82735i	0.360143	−	0.207929i
$540$	−3.89038	−	1.76539i	−0.167415	−	0.0759702i
$541$	−6.42230	−	36.4227i	−0.276116	−	1.56593i	−0.735393	−	0.677641i	$-0.763002\pi$
$541$	−6.42230	−	36.4227i	−0.276116	−	1.56593i	0.459277	−	0.888293i	$-0.348109\pi$
$542$	21.0114	−	33.3605i	0.902515	−	1.43296i
$543$	14.8372	+	8.56629i	0.636727	+	0.367614i
$544$	3.23063	+	0.0574778i	0.138512	+	0.00246434i
$545$	20.6258	+	24.5808i	0.883511	+	1.05293i
$546$	−8.71151	+	21.3428i	−0.372818	+	0.913387i
$547$	3.09359	+	1.12598i	0.132272	+	0.0481432i	0.407308	−	0.913291i	$-0.366467\pi$
$547$	3.09359	+	1.12598i	0.132272	+	0.0481432i	−0.275036	+	0.961434i	$0.588690\pi$
$548$	−4.08561	+	5.96516i	−0.174528	+	0.254819i
$549$	−2.42379	+	13.7460i	−0.103445	+	0.586664i
$550$	−0.545754	−	0.494926i	−0.0232710	−	0.0211037i
$551$	−29.4868	+	10.4370i	−1.25618	+	0.444630i
$552$	9.73380	−	13.1010i	0.414298	−	0.557617i
$553$	27.5499	+	4.85780i	1.17154	+	0.206574i
$554$	2.27910	−	0.312042i	0.0968297	−	0.0132574i
$555$	−3.77654	+	10.3760i	−0.160305	+	0.440435i
$556$	−13.8188	+	6.61859i	−0.586049	+	0.280691i
$557$	−1.48823	+	1.24877i	−0.0630583	+	0.0529122i	−0.673772	−	0.738939i	$-0.735327\pi$
$557$	−1.48823	+	1.24877i	−0.0630583	+	0.0529122i	0.610714	+	0.791851i	$0.290883\pi$
$558$	−8.81899	−	1.90735i	−0.373338	−	0.0807447i
$559$	−5.94587	+	10.2986i	−0.251484	+	0.435582i
$560$	−30.9589	+	11.9986i	−1.30825	+	0.507032i
$561$	0.670462	−	0.118220i	0.0283069	−	0.00499127i
$562$	−11.6490	+	3.73922i	−0.491383	+	0.157729i
$563$	21.5529	+	37.3307i	0.908347	+	1.57330i	0.816361	+	0.577542i	$0.195988\pi$
$563$	21.5529	+	37.3307i	0.908347	+	1.57330i	0.0919857	+	0.995760i	$0.470679\pi$
$564$	−8.31165	+	8.48530i	−0.349984	+	0.357295i
$565$	15.0710	+	41.4072i	0.634042	+	1.74202i
$566$	−16.3046	−	30.9295i	−0.685334	−	1.30006i
$567$	2.49781	−	2.97677i	0.104898	−	0.125013i
$568$	−13.7031	+	12.9532i	−0.574970	+	0.543503i
$569$			36.2239i			1.51859i	0.650749	+	0.759293i	$0.274455\pi$
$569$			36.2239i			1.51859i	−0.650749	+	0.759293i	$0.725545\pi$
$570$	6.03690	+	11.7024i	0.252858	+	0.490161i
$571$			18.7318i			0.783902i	0.919986	+	0.391951i	$0.128200\pi$
$571$			18.7318i			0.783902i	−0.919986	+	0.391951i	$0.871800\pi$
$572$	−9.96990	−	0.768491i	−0.416863	−	0.0321322i
$573$	6.58965	−	7.85324i	0.275287	−	0.328074i
$574$	−52.8253	+	27.8471i	−2.20489	+	1.16232i
$575$	0.862629	+	2.37005i	0.0359741	+	0.0988381i
$576$	6.69235	+	4.38321i	0.278848	+	0.182634i
$577$	−9.87936	−	17.1116i	−0.411283	−	0.712363i	0.583747	−	0.811935i	$-0.301586\pi$
$577$	−9.87936	−	17.1116i	−0.411283	−	0.712363i	−0.995030	+	0.0995722i	$0.968253\pi$
$578$	7.20686	+	22.4519i	0.299766	+	0.933877i
$579$	23.3632	−	4.11956i	0.970942	−	0.171203i
$580$	8.24038	+	29.5291i	0.342163	+	1.22613i
$581$	14.2348	−	24.6553i	0.590557	−	1.02288i
$582$	0.0484235	−	0.223895i	0.00200722	−	0.00928073i
$583$	−8.63297	+	7.24392i	−0.357541	+	0.300013i
$584$	−3.74219	−	1.11642i	−0.154853	−	0.0461976i
$585$	3.06464	−	8.42002i	0.126707	−	0.348125i
$586$	1.72287	+	12.5836i	0.0711711	+	0.519822i
$587$	14.4585	+	2.54942i	0.596765	+	0.105226i	0.463868	−	0.885904i	$-0.346461\pi$
$587$	14.4585	+	2.54942i	0.596765	+	0.105226i	0.132897	+	0.991130i	$0.457572\pi$
$588$	−1.57872	−	16.1234i	−0.0651053	−	0.664917i
$589$	17.6865	+	21.4618i	0.728758	+	0.884318i
$590$	13.8552	−	15.2781i	0.570409	−	0.628989i
$591$	1.28545	−	7.29014i	0.0528763	−	0.299876i
$592$	9.96596	−	18.1165i	0.409598	−	0.744582i
$593$	17.4962	+	6.36809i	0.718482	+	0.261506i	0.675281	−	0.737560i	$-0.264022\pi$
$593$	17.4962	+	6.36809i	0.718482	+	0.261506i	0.0432006	+	0.999066i	$0.486245\pi$
$594$	1.56061	+	0.636996i	0.0640326	+	0.0261363i
$595$	3.04763	+	3.63202i	0.124941	+	0.148898i
$596$	−7.21577	+	5.16452i	−0.295569	+	0.211547i
$597$	−10.6116	−	6.12659i	−0.434303	−	0.250745i
$598$	28.9655	+	18.2433i	1.18449	+	0.746023i
$599$	4.28499	+	24.3014i	0.175080	+	0.992928i	0.938052	+	0.346496i	$0.112628\pi$
$599$	4.28499	+	24.3014i	0.175080	+	0.992928i	−0.762972	+	0.646432i	$0.776260\pi$
$600$	−1.13468	+	0.490747i	−0.0463230	+	0.0200347i
$601$	−12.1480	+	7.01366i	−0.495528	+	0.286093i	−0.726865	−	0.686780i	$-0.759023\pi$
$601$	−12.1480	+	7.01366i	−0.495528	+	0.286093i	0.231337	+	0.972874i	$0.425690\pi$
$602$	0.599100	−	15.5677i	0.0244175	−	0.634493i
$603$	−5.57924	+	2.03068i	−0.227204	+	0.0826956i
$604$	−0.130931	+	0.509657i	−0.00532750	+	0.0207377i
$605$	15.6752	+	13.1530i	0.637286	+	0.534746i
$606$	2.91243	+	3.75520i	0.118309	+	0.152545i
$607$	13.9495			0.566192			0.283096	−	0.959092i	$-0.408638\pi$
$607$	13.9495			0.566192			0.283096	+	0.959092i	$0.408638\pi$
$608$	−7.81270	−	23.3872i	−0.316847	−	0.948477i
$609$	−27.8852			−1.12997
$610$	−25.8415	−	33.3193i	−1.04629	−	1.34906i
$611$	−19.0840	−	16.0133i	−0.772055	−	0.647831i
$612$	0.284248	−	1.10645i	0.0114900	−	0.0447257i
$613$	32.4841	−	11.8232i	1.31202	−	0.477536i	0.411127	−	0.911578i	$-0.365135\pi$
$613$	32.4841	−	11.8232i	1.31202	−	0.477536i	0.900893	+	0.434042i	$0.142913\pi$
$614$	−0.958558	+	24.9083i	−0.0386843	+	1.00522i
$615$	20.1018	−	11.6058i	0.810581	−	0.467989i
$616$	12.0238	−	5.20029i	0.484454	−	0.209526i
$617$	1.57454	+	8.92965i	0.0633885	+	0.359494i	0.999959	+	0.00901587i	$0.00286988\pi$
$617$	1.57454	+	8.92965i	0.0633885	+	0.359494i	−0.936571	+	0.350478i	$0.886019\pi$
$618$	−12.8583	−	8.09849i	−0.517235	−	0.325769i
$619$	−11.8156	−	6.82174i	−0.474909	−	0.274189i	0.243383	−	0.969930i	$-0.421743\pi$
$619$	−11.8156	−	6.82174i	−0.474909	−	0.274189i	−0.718292	+	0.695741i	$0.755076\pi$
$620$	22.1650	−	15.8641i	0.890169	−	0.637117i
$621$	−3.70917	−	4.42042i	−0.148844	−	0.177385i
$622$	−9.12360	−	3.72399i	−0.365823	−	0.149318i
$623$	−25.1549	−	9.15565i	−1.00781	−	0.366813i
$624$	−8.08730	+	14.7014i	−0.323751	+	0.588526i
$625$	−3.92854	+	22.2798i	−0.157142	+	0.891194i
$626$	−0.505470	+	0.557380i	−0.0202026	+	0.0222774i
$627$	−2.55767	−	4.52221i	−0.102143	−	0.180600i
$628$	0.660464	+	6.74528i	0.0263554	+	0.269166i
$629$	−2.90773	−	0.512712i	−0.115939	−	0.0204431i
$630$	1.59237	+	11.6304i	0.0634416	+	0.463367i
$631$	7.63883	−	20.9875i	0.304097	−	0.835500i	−0.689680	−	0.724114i	$-0.742249\pi$
$631$	7.63883	−	20.9875i	0.304097	−	0.835500i	0.993777	−	0.111386i	$-0.0355290\pi$
$632$	19.5123	+	5.82115i	0.776156	+	0.231553i
$633$	−18.1886	+	15.2620i	−0.722931	+	0.606611i
$634$	2.85928	−	13.2204i	0.113556	−	0.525048i
$635$	20.8424	−	36.1000i	0.827104	−	1.43259i
$636$	5.08287	+	18.2142i	0.201549	+	0.722242i
$637$	33.4623	−	5.90030i	1.32582	−	0.233778i
$638$	−3.69689	−	11.5171i	−0.146361	−	0.455967i
$639$	3.33335	+	5.77354i	0.131865	+	0.228398i
$640$	−23.3897	+	6.08080i	−0.924558	+	0.240365i
$641$	4.06155	+	11.1590i	0.160422	+	0.440755i	0.993696	−	0.112104i	$-0.0357590\pi$
$641$	4.06155	+	11.1590i	0.160422	+	0.440755i	−0.833275	+	0.552859i	$0.813537\pi$
$642$	−3.38767	+	1.78582i	−0.133701	+	0.0704808i
$643$	6.35401	−	7.57242i	0.250578	−	0.298627i	−0.626063	−	0.779773i	$-0.715335\pi$
$643$	6.35401	−	7.57242i	0.250578	−	0.298627i	0.876641	+	0.481146i	$0.159779\pi$
$644$	−44.7141	−	3.44662i	−1.76198	−	0.135816i
$645$			6.05565i			0.238441i
$646$	−2.80136	+	2.13312i	−0.110218	+	0.0839265i
$647$		−	15.0664i		−	0.592321i	−0.955138	−	0.296160i	$-0.904294\pi$
$647$		−	15.0664i		−	0.592321i	0.955138	−	0.296160i	$-0.0957063\pi$
$648$	2.05546	−	1.94296i	0.0807459	−	0.0763268i
$649$	−5.23075	+	6.23377i	−0.205325	+	0.244697i
$650$	−1.20914	−	2.29370i	−0.0474262	−	0.0899664i
$651$	8.47958	+	23.2975i	0.332341	+	0.913099i
$652$	−13.8697	+	14.1594i	−0.543178	+	0.554526i
$653$	−12.4217	−	21.5150i	−0.486097	−	0.841945i	0.513775	−	0.857925i	$-0.328247\pi$
$653$	−12.4217	−	21.5150i	−0.486097	−	0.841945i	−0.999872	+	0.0159796i	$0.994913\pi$
$654$	−20.2275	+	6.49283i	−0.790957	+	0.253890i
$655$	−18.1888	+	3.20717i	−0.710695	+	0.125315i
$656$	−40.5279	+	15.7072i	−1.58235	+	0.613263i
$657$	−0.690343	+	1.19571i	−0.0269328	+	0.0466490i
$658$	31.8998	+	6.89924i	1.24359	+	0.268960i
$659$	11.7295	−	9.84220i	0.456915	−	0.383398i	−0.385079	−	0.922884i	$-0.625826\pi$
$659$	11.7295	−	9.84220i	0.456915	−	0.383398i	0.841995	+	0.539486i	$0.181381\pi$
$660$	−4.59247	+	2.19958i	−0.178762	+	0.0856187i
$661$	1.08753	−	2.98796i	0.0423000	−	0.116218i	−0.916744	−	0.399475i	$-0.869193\pi$
$661$	1.08753	−	2.98796i	0.0423000	−	0.116218i	0.959044	+	0.283256i	$0.0914148\pi$
$662$	16.6162	−	2.27499i	0.645806	−	0.0884201i
$663$	2.35960	+	0.416061i	0.0916393	+	0.0161585i
$664$	12.3584	−	16.6336i	0.479598	−	0.645507i
$665$	18.3682	−	31.1726i	0.712289	−	1.20882i
$666$	−5.41519	−	4.91086i	−0.209834	−	0.190292i
$667$	−7.19054	+	40.7796i	−0.278419	+	1.57899i
$668$	1.00774	−	1.47134i	0.0389906	−	0.0569279i
$669$	−19.8399	−	7.22114i	−0.767056	−	0.279186i
$670$	6.77807	−	16.6060i	0.261860	−	0.641544i
$671$	10.6938	+	12.7444i	0.412830	+	0.491992i
$672$	0.391030	−	21.9785i	0.0150843	−	0.847839i
$673$	−22.7000	−	13.1058i	−0.875020	−	0.505193i	−0.00600653	−	0.999982i	$-0.501912\pi$
$673$	−22.7000	−	13.1058i	−0.875020	−	0.505193i	−0.869013	+	0.494789i	$0.835245\pi$
$674$	10.2312	−	16.2444i	0.394091	−	0.625712i
$675$	0.0758985	+	0.430442i	0.00292134	+	0.0165677i
$676$	−8.37036	−	3.79832i	−0.321937	−	0.146089i
$677$	−44.7079	+	25.8121i	−1.71827	+	0.992041i	−0.796175	+	0.605066i	$0.793147\pi$
$677$	−44.7079	+	25.8121i	−1.71827	+	0.992041i	−0.922090	+	0.386975i	$0.873520\pi$
$678$	−29.1516	−	1.12186i	−1.11956	−	0.0430846i
$679$	−0.591470	+	0.215278i	−0.0226986	+	0.00826160i
$680$	1.89914	+	2.88146i	0.0728287	+	0.110499i
$681$	5.41713	+	4.54551i	0.207585	+	0.174184i
$682$	−8.49810	+	6.59089i	−0.325409	+	0.252378i
$683$	1.69049			0.0646847			0.0323423	−	0.999477i	$-0.489703\pi$
$683$	1.69049			0.0646847			0.0323423	+	0.999477i	$0.489703\pi$
$684$	−8.68350	+	0.772522i	−0.332022	+	0.0295381i
$685$	−7.72217			−0.295049
$686$	−4.77781	+	3.70553i	−0.182417	+	0.141478i
$687$	−20.3524	−	17.0777i	−0.776491	−	0.651553i
$688$	1.73782	−	11.2057i	0.0662538	−	0.427213i
$689$	−37.2698	+	13.5651i	−1.41987	+	0.516789i
$690$	17.4190	+	0.670345i	0.663131	+	0.0255196i
$691$	−3.88032	+	2.24031i	−0.147614	+	0.0852253i	−0.571988	−	0.820262i	$-0.693828\pi$
$691$	−3.88032	+	2.24031i	−0.147614	+	0.0852253i	0.424374	+	0.905487i	$0.360494\pi$
$692$	−16.3983	+	36.1370i	−0.623371	+	1.37372i
$693$	−0.804273	−	4.56126i	−0.0305518	−	0.173268i
$694$	−15.1691	+	24.0845i	−0.575811	+	0.914236i
$695$	−14.1723	−	8.18236i	−0.537585	−	0.310375i
$696$	−20.1618	−	2.33692i	−0.764231	−	0.0885809i
$697$	3.98961	+	4.75464i	0.151117	+	0.180095i
$698$	−7.41473	+	18.1658i	−0.280652	+	0.687584i
$699$	−20.5728	−	7.48788i	−0.778134	−	0.283218i
$700$	2.80258	+	1.91952i	0.105928	+	0.0725512i
$701$	0.716351	−	4.06263i	0.0270562	−	0.153443i	−0.968287	−	0.249842i	$-0.919621\pi$
$701$	0.716351	−	4.06263i	0.0270562	−	0.153443i	0.995343	+	0.0963988i	$0.0307324\pi$
$702$	4.39439	+	3.98512i	0.165855	+	0.150409i
$703$	3.71558	+	22.2235i	0.140136	+	0.838174i
$704$	9.12937	−	2.75230i	0.344076	−	0.103731i
$705$	−12.4934	−	2.20293i	−0.470529	−	0.0829670i
$706$	2.01889	−	0.276416i	0.0759820	−	0.0104030i
$707$	4.46608	−	12.2705i	0.167964	−	0.461478i
$708$	5.89839	+	12.3151i	0.221675	+	0.462831i
$709$	0.556412	−	0.466885i	0.0208965	−	0.0175342i	−0.632280	−	0.774740i	$-0.717881\pi$
$709$	0.556412	−	0.466885i	0.0208965	−	0.0175342i	0.653176	+	0.757206i	$0.273436\pi$
$710$	−19.6843	−	4.25729i	−0.738740	−	0.159773i
$711$	3.59954	−	6.23459i	0.134993	−	0.233815i
$712$	−17.4204	−	8.72790i	−0.652858	−	0.327092i
$713$	36.2570	−	6.39308i	1.35783	−	0.239423i
$714$	−2.98878	+	0.959369i	−0.111852	+	0.0359035i
$715$	−5.33997	−	9.24910i	−0.199703	−	0.345897i
$716$	13.4759	+	13.2001i	0.503619	+	0.493313i
$717$	−6.35688	−	17.4654i	−0.237402	−	0.652257i
$718$	−17.2353	−	32.6950i	−0.643216	−	1.22017i
$719$	3.57291	−	4.25803i	0.133247	−	0.158798i	−0.695295	−	0.718725i	$-0.744726\pi$
$719$	3.57291	−	4.25803i	0.133247	−	0.158798i	0.828542	+	0.559927i	$0.189171\pi$
$720$	0.176642	+	8.54257i	0.00658305	+	0.318363i
$721$			41.7550i			1.55504i
$722$	22.4786	+	14.7212i	0.836567	+	0.547865i
$723$			0.873888i			0.0325003i
$724$	2.63338	−	34.1638i	0.0978690	−	1.26969i
$725$	2.01610	−	2.40270i	0.0748762	−	0.0892340i
$726$	−11.9841	+	6.31746i	−0.444771	+	0.234463i
$727$	−9.05610	−	24.8814i	−0.335872	−	0.922801i	−0.986552	−	0.163449i	$-0.947738\pi$
$727$	−9.05610	−	24.8814i	−0.335872	−	0.922801i	0.650680	−	0.759352i	$-0.274484\pi$
$728$	46.0239	−	2.72500i	1.70576	−	0.100995i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−1.27476	−	3.97133i	−0.0471810	−	0.146986i
$731$	−1.59467	+	0.281184i	−0.0589812	+	0.0104000i
$732$	26.8887	−	7.50357i	0.993836	−	0.277340i
$733$	17.4860	−	30.2867i	0.645861	−	1.11866i	−0.338241	−	0.941060i	$-0.609832\pi$
$733$	17.4860	−	30.2867i	0.645861	−	1.11866i	0.984102	−	0.177605i	$-0.0568349\pi$
$734$	−6.54047	+	30.2410i	−0.241413	+	1.11622i
$735$	13.2548	−	11.1221i	0.488911	−	0.410245i
$736$	−32.0407	−	6.23927i	−1.18104	−	0.229983i
$737$	−2.42037	+	6.64992i	−0.0891556	+	0.244953i
$738$	2.08456	+	15.2252i	0.0767336	+	0.560449i
$739$	−0.464568	−	0.0819158i	−0.0170894	−	0.00301332i	0.165097	−	0.986277i	$-0.447206\pi$
$739$	−0.464568	−	0.0819158i	−0.0170894	−	0.00301332i	−0.182186	+	0.983264i	$0.558317\pi$
$740$	21.9786	−	2.15204i	0.807951	−	0.0791106i
$741$	−3.01517	−	18.0342i	−0.110765	−	0.662502i
$742$	34.9054	−	38.4901i	1.28142	−	1.41302i
$743$	1.20606	−	6.83991i	0.0442461	−	0.250932i	−0.954660	−	0.297699i	$-0.903781\pi$
$743$	1.20606	−	6.83991i	0.0442461	−	0.250932i	0.998906	+	0.0467671i	$0.0148919\pi$
$744$	4.17853	+	17.5553i	0.153192	+	0.643610i
$745$	−8.90581	−	3.24145i	−0.326284	−	0.118758i
$746$	−45.8629	−	18.7199i	−1.67916	−	0.685385i
$747$	−4.70929	−	5.61232i	−0.172304	−	0.205344i
$748$	−0.792475	−	1.10723i	−0.0289758	−	0.0404844i
$749$	9.11287	+	5.26132i	0.332977	+	0.192244i
$750$	−13.8980	−	8.75336i	−0.507484	−	0.319628i
$751$	−1.52015	−	8.62120i	−0.0554711	−	0.314592i	0.944429	−	0.328715i	$-0.106616\pi$
$751$	−1.52015	−	8.62120i	−0.0554711	−	0.314592i	−0.999900	+	0.0141228i	$0.995504\pi$
$752$	22.4863	+	7.66171i	0.819991	+	0.279394i
$753$	−0.423390	+	0.244445i	−0.0154292	+	0.00890805i
$754$	1.63703	−	42.5385i	0.0596171	−	1.54916i
$755$	−0.528121	+	0.192220i	−0.0192203	+	0.00699561i
$756$	−7.52738	−	1.93378i	−0.273768	−	0.0703310i
$757$	28.6471	+	24.0378i	1.04120	+	0.873667i	0.992140	−	0.125129i	$-0.0399345\pi$
$757$	28.6471	+	24.0378i	1.04120	+	0.873667i	0.0490552	+	0.998796i	$0.484379\pi$
$758$	−2.33731	−	3.01366i	−0.0848948	−	0.109461i
$759$	−6.87781			−0.249649
$760$	15.8932	−	20.9993i	0.576505	−	0.761725i
$761$	33.3267			1.20809			0.604047	−	0.796949i	$-0.293554\pi$
$761$	33.3267			1.20809			0.604047	+	0.796949i	$0.293554\pi$
$762$	16.9133	+	21.8075i	0.612703	+	0.790002i
$763$	44.7165	+	37.5216i	1.61884	+	1.35837i
$764$	−19.8585	−	5.10165i	−0.718456	−	0.184571i
$765$	1.14654	−	0.417306i	0.0414532	−	0.0150877i
$766$	1.72395	−	44.7970i	0.0622887	−	1.61858i
$767$	−24.8023	+	14.3196i	−0.895559	+	0.517052i
$768$	2.12464	−	15.8583i	0.0766662	−	0.572237i
$769$	9.10794	+	51.6537i	0.328441	+	1.86268i	0.484301	+	0.874901i	$0.339074\pi$
$769$	9.10794	+	51.6537i	0.328441	+	1.86268i	−0.155861	+	0.987779i	$0.549815\pi$
$770$	11.8392	+	7.45662i	0.426653	+	0.268718i
$771$	10.9412	+	6.31693i	0.394039	+	0.227499i
$772$	−27.6149	−	38.5831i	−0.993883	−	1.38864i
$773$	7.20015	+	8.58081i	0.258972	+	0.308630i	0.879826	−	0.475295i	$-0.157659\pi$
$773$	7.20015	+	8.58081i	0.258972	+	0.308630i	−0.620855	+	0.783926i	$0.713214\pi$
$774$	−3.71187	−	1.51508i	−0.133420	−	0.0544583i
$775$	−2.62047	−	0.953774i	−0.0941302	−	0.0342606i
$776$	−0.445691	+	0.106084i	−0.0159994	+	0.00380818i
$777$	−3.48806	+	19.7818i	−0.125133	+	0.709667i
$778$	−10.9234	+	12.0452i	−0.391624	+	0.431842i
$779$	24.0456	−	40.8077i	0.861524	−	1.46209i
$780$	−17.8355	+	1.74636i	−0.638614	+	0.0625299i
$781$	7.82536	+	1.37982i	0.280013	+	0.0493739i
$782$	0.632298	+	4.61820i	0.0226109	+	0.165146i
$783$	−2.45434	+	6.74323i	−0.0877108	+	0.240984i
$784$	−27.7191	+	16.7771i	−0.989969	+	0.599183i
$785$	−5.54520	+	4.65297i	−0.197917	+	0.166072i
$786$	2.58483	−	11.9514i	0.0921977	−	0.426292i
$787$	−5.87013	+	10.1674i	−0.209247	+	0.362427i	−0.951478	−	0.307718i	$-0.900435\pi$
$787$	−5.87013	+	10.1674i	−0.209247	+	0.362427i	0.742230	+	0.670145i	$0.233768\pi$
$788$	−14.2604	+	3.97949i	−0.508004	+	0.141764i
$789$	22.1909	−	3.91286i	0.790017	−	0.139301i
$790$	6.64678	+	20.7071i	0.236482	+	0.736725i
$791$	40.0803	+	69.4211i	1.42509	+	2.46833i
$792$	−0.199255	−	3.36532i	−0.00708023	−	0.119581i
$793$	20.0254	+	55.0194i	0.711124	+	1.95380i
$794$	33.8097	−	17.8229i	1.19986	−	0.632511i
$795$	−12.9824	+	15.4718i	−0.460437	+	0.548728i
$796$	−1.88339	+	24.4339i	−0.0667551	+	0.866036i
$797$		−	33.9185i		−	1.20145i	−0.799454	−	0.600727i	$-0.794878\pi$
$797$		−	33.9185i		−	1.20145i	0.799454	−	0.600727i	$-0.205122\pi$
$798$	14.5120	+	19.0581i	0.513718	+	0.674650i
$799$		−	3.39227i		−	0.120010i
$800$	1.86548	+	1.62274i	0.0659547	+	0.0573725i
$801$	−4.42805	+	5.27715i	−0.156458	+	0.186459i
$802$	−7.89257	−	14.9720i	−0.278696	−	0.528681i
$803$	0.562843	+	1.54640i	0.0198623	+	0.0545713i
$804$	8.48297	+	8.30937i	0.299171	+	0.293049i
$805$	−23.9493	−	41.4814i	−0.844101	−	1.46203i
$806$	−36.0377	+	11.5678i	−1.26937	+	0.407457i
$807$	7.89395	−	1.39192i	0.277880	−	0.0489978i
$808$	4.25743	−	8.49761i	0.149776	−	0.298945i
$809$	−13.7251	+	23.7726i	−0.482549	+	0.835799i	−0.999799	−	0.0200352i	$-0.993622\pi$
$809$	−13.7251	+	23.7726i	−0.482549	+	0.835799i	0.517251	+	0.855834i	$0.326956\pi$
$810$	2.95263	+	0.638590i	0.103745	+	0.0224378i
$811$	−9.78481	+	8.21043i	−0.343591	+	0.288307i	−0.798210	−	0.602379i	$-0.794220\pi$
$811$	−9.78481	+	8.21043i	−0.343591	+	0.288307i	0.454619	+	0.890686i	$0.349775\pi$
$812$	24.0909	+	50.2989i	0.845423	+	1.76514i
$813$	−9.53494	+	26.1970i	−0.334405	+	0.918770i
$814$	−8.63267	+	1.18194i	−0.302575	+	0.0414269i
$815$	−20.8478	−	3.67603i	−0.730267	−	0.128766i
$816$	−2.24137	+	0.443176i	−0.0784636	+	0.0155143i
$817$	6.08335	+	10.7560i	0.212829	+	0.376303i
$818$	19.5444	+	17.7242i	0.683354	+	0.619711i
$819$	2.83053	−	16.0527i	0.0989068	−	0.560928i
$820$	−38.3007	−	26.2326i	−1.33752	−	0.916083i
$821$	−48.1262	−	17.5165i	−1.67962	−	0.611330i	−0.686359	−	0.727262i	$-0.740792\pi$
$821$	−48.1262	−	17.5165i	−1.67962	−	0.611330i	−0.993257	+	0.115932i	$0.963015\pi$
$822$	1.93203	−	4.73338i	0.0673872	−	0.165096i
$823$	−0.362807	−	0.432377i	−0.0126467	−	0.0150717i	0.759684	−	0.650292i	$-0.225354\pi$
$823$	−0.362807	−	0.432377i	−0.0126467	−	0.0150717i	−0.772331	+	0.635221i	$0.780909\pi$
$824$	−3.49928	+	30.1900i	−0.121903	+	1.05172i
$825$	0.451165	+	0.260480i	0.0157075	+	0.00906875i
$826$	19.9956	−	31.7478i	0.695737	−	1.10465i
$827$	−6.34529	−	35.9859i	−0.220647	−	1.25135i	−0.870833	−	0.491578i	$-0.836420\pi$
$827$	−6.34529	−	35.9859i	−0.220647	−	1.25135i	0.650186	−	0.759775i	$-0.274691\pi$
$828$	−4.76901	+	10.5095i	−0.165734	+	0.365229i
$829$	27.8720	−	16.0919i	0.968035	−	0.558896i	0.0693987	−	0.997589i	$-0.477892\pi$
$829$	27.8720	−	16.0919i	0.968035	−	0.558896i	0.898637	+	0.438693i	$0.144559\pi$
$830$	22.1158	+	0.851094i	0.767652	+	0.0295419i
$831$	−1.52851	+	0.556331i	−0.0530233	+	0.0192989i
$832$	33.5049	+	1.88678i	1.16157	+	0.0654123i
$833$	3.54432	+	2.97404i	0.122803	+	0.103044i
$834$	8.56125	−	6.63987i	0.296452	−	0.229920i
$835$	1.90472			0.0659156
$836$	−5.94744	+	8.52034i	−0.205696	+	0.294682i
$837$	6.38015			0.220530
$838$	−36.6616	+	28.4337i	−1.26645	+	0.982227i
$839$	−17.0142	−	14.2766i	−0.587395	−	0.492883i	0.299971	−	0.953948i	$-0.403023\pi$
$839$	−17.0142	−	14.2766i	−0.587395	−	0.492883i	−0.887366	+	0.461066i	$0.847467\pi$
$840$	19.6030	−	12.9201i	0.676369	−	0.445787i
$841$	21.1384	−	7.69373i	0.728909	−	0.265301i
$842$	−21.8574	−	0.841150i	−0.753256	−	0.0289879i
$843$	7.49201	−	4.32552i	0.258039	−	0.148979i
$844$	43.2430	+	19.6229i	1.48849	+	0.675448i
$845$	−1.70476	−	9.66820i	−0.0586457	−	0.332596i
$846$	4.47606	−	7.10681i	0.153890	−	0.244337i
$847$	32.2373	+	18.6122i	1.10769	+	0.639524i
$848$	28.4633	−	24.9042i	0.977433	−	0.855213i
$849$	15.8918	+	18.9391i	0.545404	+	0.649987i
$850$	0.133426	−	0.326887i	0.00457647	−	0.0112121i
$851$	28.0296	+	10.2019i	0.960842	+	0.349718i
$852$	7.53442	−	11.0006i	0.258125	−	0.376873i
$853$	3.58621	−	20.3384i	0.122790	−	0.696374i	−0.859807	−	0.510620i	$-0.829416\pi$
$853$	3.58621	−	20.3384i	0.122790	−	0.696374i	0.982596	−	0.185755i	$-0.0594729\pi$
$854$	−56.8209	−	51.5290i	−1.94437	−	1.76329i
$855$	−5.92150	−	7.18549i	−0.202511	−	0.245739i
$856$	6.14794	+	4.56779i	0.210132	+	0.156124i
$857$	−45.4976	−	8.02246i	−1.55417	−	0.274042i	−0.670412	−	0.741989i	$-0.733883\pi$
$857$	−45.4976	−	8.02246i	−1.55417	−	0.274042i	−0.883757	+	0.467947i	$0.844994\pi$
$858$	7.00534	−	0.959133i	0.239158	−	0.0327442i
$859$	11.5378	−	31.6998i	0.393664	−	1.08158i	−0.571652	−	0.820496i	$-0.693697\pi$
$859$	11.5378	−	31.6998i	0.393664	−	1.08158i	0.965316	−	0.261086i	$-0.0840806\pi$
$860$	10.9231	−	5.23165i	0.372474	−	0.178398i
$861$	32.3466	−	27.1420i	1.10237	−	0.924996i
$862$	−7.09248	−	1.53395i	−0.241571	−	0.0522464i
$863$	6.54436	−	11.3352i	0.222772	−	0.385853i	−0.732876	−	0.680362i	$-0.761823\pi$
$863$	6.54436	−	11.3352i	0.222772	−	0.385853i	0.955649	+	0.294509i	$0.0951560\pi$
$864$	−5.28045	−	2.02901i	−0.179644	−	0.0690284i
$865$	−41.7401	+	7.35991i	−1.41921	+	0.250245i
$866$	−32.6065	+	10.4664i	−1.10801	+	0.355662i
$867$	−8.33687	−	14.4399i	−0.283135	−	0.490404i
$868$	34.6978	−	35.4227i	1.17772	−	1.20232i
$869$	−2.93474	−	8.06314i	−0.0995543	−	0.273523i
$870$	−10.1090	−	19.1766i	−0.342728	−	0.650148i
$871$	−16.0090	+	19.0787i	−0.542443	+	0.646458i
$872$	29.1868	+	30.8766i	0.988388	+	1.04561i
$873$			0.161978i			0.00548212i
$874$	31.6128	−	16.3080i	1.06932	−	0.551628i
$875$			45.1314i			1.52572i
$876$	2.75320	+	0.212220i	0.0930221	+	0.00717025i
$877$	−6.19938	+	7.38813i	−0.209338	+	0.249480i	−0.860489	−	0.509469i	$-0.829842\pi$
$877$	−6.19938	+	7.38813i	−0.209338	+	0.249480i	0.651151	+	0.758948i	$0.274286\pi$
$878$	14.7277	−	7.76379i	0.497037	−	0.262015i
$879$	−3.07166	−	8.43932i	−0.103605	−	0.284651i
$880$	7.93514	+	6.38353i	0.267493	+	0.215189i
$881$	15.1001	+	26.1541i	0.508735	+	0.881155i	0.999949	+	0.0101158i	$0.00322001\pi$
$881$	15.1001	+	26.1541i	0.508735	+	0.881155i	−0.491214	+	0.871039i	$0.663447\pi$
$882$	3.50115	+	10.9073i	0.117890	+	0.367269i
$883$	−22.1580	+	3.90705i	−0.745676	+	0.131483i	−0.533561	−	0.845762i	$-0.679146\pi$
$883$	−22.1580	+	3.90705i	−0.745676	+	0.131483i	−0.212115	+	0.977245i	$0.568035\pi$
$884$	−1.28804	−	4.61565i	−0.0433216	−	0.155241i
$885$	−7.29200	+	12.6301i	−0.245118	+	0.424557i
$886$	0.815258	−	3.76949i	0.0273891	−	0.126639i
$887$	30.1632	−	25.3099i	1.01278	−	0.849824i	0.0240777	−	0.999710i	$-0.492335\pi$
$887$	30.1632	−	25.3099i	1.01278	−	0.849824i	0.988703	+	0.149886i	$0.0478906\pi$
$888$	−4.17978	+	14.0105i	−0.140264	+	0.470160i
$889$	25.9358	−	71.2580i	0.869858	−	2.38992i
$890$	−2.82292	−	20.6181i	−0.0946244	−	0.691121i
$891$	−1.17380	−	0.206972i	−0.0393237	−	0.00693382i
$892$	4.11492	+	42.0254i	0.137778	+	1.40712i
$893$	−24.4036	+	8.63775i	−0.816636	+	0.289051i
$894$	4.21505	−	4.64792i	0.140972	−	0.155450i
$895$	−3.49858	+	19.8414i	−0.116945	+	0.663226i
$896$	−39.9822	+	18.2825i	−1.33571	+	0.610777i
$897$	−22.7458	−	8.27879i	−0.759460	−	0.276421i
$898$	10.7239	+	4.37719i	0.357862	+	0.146069i
$899$	−29.4293	−	35.0725i	−0.981524	−	1.16973i
$900$	0.710852	−	0.508776i	0.0236951	−	0.0169592i
$901$	−4.67710	−	2.70033i	−0.155817	−	0.0899609i
$902$	15.4985	+	9.76138i	0.516044	+	0.325018i
$903$	1.91294	+	10.8488i	0.0636587	+	0.361026i
$904$	23.1613	+	53.5523i	0.770335	+	1.78112i
$905$	31.6938	−	18.2984i	1.05354	−	0.608260i
$906$	0.0143085	−	0.371809i	0.000475368	−	0.0123525i
$907$	−18.2222	+	6.63234i	−0.605059	+	0.220223i	−0.626340	−	0.779550i	$-0.715448\pi$
$907$	−18.2222	+	6.63234i	−0.605059	+	0.220223i	0.0212810	+	0.999774i	$0.493226\pi$
$908$	3.51909	−	13.6983i	0.116785	−	0.454594i
$909$	−2.57417	−	2.15998i	−0.0853798	−	0.0716421i
$910$	30.1781	+	38.9107i	1.00039	+	1.28988i
$911$	−28.3645			−0.939757			−0.469879	−	0.882731i	$-0.655702\pi$
$911$	−28.3645			−0.939757			−0.469879	+	0.882731i	$0.655702\pi$
$912$	8.89539	+	14.9957i	0.294556	+	0.496558i
$913$	−8.73232			−0.288998
$914$	−0.862419	−	1.11198i	−0.0285263	−	0.0367810i
$915$	22.8402	+	19.1652i	0.755073	+	0.633582i
$916$	−13.2214	+	51.4651i	−0.436846	+	1.70045i
$917$	−31.5725	+	11.4914i	−1.04261	+	0.379481i
$918$	−0.0310634	+	0.807188i	−0.00102525	+	0.0266412i
$919$	−22.5273	+	13.0061i	−0.743106	+	0.429033i	−0.823198	−	0.567755i	$-0.807812\pi$
$919$	−22.5273	+	13.0061i	−0.743106	+	0.429033i	0.0800915	+	0.996788i	$0.474479\pi$
$920$	−13.8397	−	31.9993i	−0.456280	−	1.05498i
$921$	−3.06070	−	17.3581i	−0.100853	−	0.571968i
$922$	−12.7090	−	8.00451i	−0.418550	−	0.263614i
$923$	24.2186	+	13.9826i	0.797163	+	0.460242i
$924$	−7.53268	+	5.39133i	−0.247807	+	0.177362i
$925$	−1.45229	−	1.73077i	−0.0477509	−	0.0569073i
$926$	40.2286	+	16.4201i	1.32199	+	0.539599i
$927$	10.0972	+	3.67509i	0.331636	+	0.120706i
$928$	13.2031	+	38.3864i	0.433412	+	1.26010i
$929$	1.46097	−	8.28559i	0.0479330	−	0.271842i	−0.951416	−	0.307907i	$-0.900371\pi$
$929$	1.46097	−	8.28559i	0.0479330	−	0.271842i	0.999349	+	0.0360656i	$0.0114825\pi$
$930$	−12.9476	+	14.2772i	−0.424567	+	0.468169i
$931$	12.3700	−	33.0703i	0.405411	−	1.08384i
$932$	4.26692	+	43.5778i	0.139768	+	1.42744i
$933$	6.86222	+	1.20999i	0.224659	+	0.0396134i
$934$	−6.03951	−	44.1116i	−0.197619	−	1.44338i
$935$	0.497388	−	1.36656i	0.0162663	−	0.0446914i
$936$	3.39186	−	11.3694i	0.110866	−	0.371620i
$937$	−2.79982	+	2.34932i	−0.0914660	+	0.0767491i	−0.687374	−	0.726304i	$-0.741237\pi$
$937$	−2.79982	+	2.34932i	−0.0914660	+	0.0767491i	0.595908	+	0.803053i	$0.296792\pi$
$938$	6.89734	−	31.8911i	0.225206	−	1.04128i
$939$	0.266029	−	0.460776i	0.00868154	−	0.0150369i
$940$	6.81983	+	24.4386i	0.222438	+	0.797098i
$941$	−19.3662	+	3.41478i	−0.631319	+	0.111319i	−0.480146	−	0.877189i	$-0.659416\pi$
$941$	−19.3662	+	3.41478i	−0.631319	+	0.111319i	−0.151173	+	0.988507i	$0.548305\pi$
$942$	−1.46472	−	4.56312i	−0.0477232	−	0.148675i
$943$	−31.3517	−	54.3028i	−1.02095	−	1.76834i
$944$	17.1180	−	21.2788i	0.557144	−	0.692566i
$945$	−2.83900	−	7.80008i	−0.0923526	−	0.253737i
$946$	−4.22716	+	2.22837i	−0.137437	+	0.0724504i
$947$	−3.85181	+	4.59041i	−0.125167	+	0.149168i	−0.824988	−	0.565150i	$-0.808818\pi$
$947$	−3.85181	+	4.59041i	−0.125167	+	0.149168i	0.699821	+	0.714318i	$0.253263\pi$
$948$	−14.3556	−	1.10654i	−0.466248	−	0.0359389i
$949$			5.79163i			0.188004i
$950$	−2.69134	−	0.127497i	−0.0873185	−	0.00413655i
$951$			9.56436i			0.310146i
$952$	4.31258	+	4.56227i	0.139772	+	0.147864i
$953$	19.1739	−	22.8506i	0.621103	−	0.740202i	−0.360156	−	0.932892i	$-0.617277\pi$
$953$	19.1739	−	22.8506i	0.621103	−	0.740202i	0.981260	+	0.192690i	$0.0617211\pi$
$954$	−6.23549	−	11.8286i	−0.201882	−	0.382965i
$955$	−7.48976	−	20.5780i	−0.242363	−	0.665887i
$956$	−26.0118	+	26.5553i	−0.841283	+	0.858859i
$957$	4.27655	+	7.40720i	0.138241	+	0.239441i
$958$	23.8572	−	7.65795i	0.770792	−	0.247417i
$959$	−13.8344	+	2.43938i	−0.446737	+	0.0787718i
$960$	15.2563	−	7.69879i	0.492396	−	0.248478i
$961$	−4.85315	+	8.40590i	−0.156553	+	0.271158i
$962$	−29.9720	−	6.48229i	−0.966336	−	0.208997i
$963$	2.07437	−	1.74061i	0.0668457	−	0.0560902i
$964$	1.57630	−	0.754977i	0.0507693	−	0.0243162i
$965$	17.3322	−	47.6199i	0.557944	−	1.53294i
$966$	31.4183	−	4.30162i	1.01087	−	0.138402i
$967$	59.8422	+	10.5518i	1.92440	+	0.339323i	0.999194	−	0.0401503i	$-0.0127837\pi$
$967$	59.8422	+	10.5518i	1.92440	+	0.339323i	0.925203	+	0.379473i	$0.123895\pi$
$968$	21.7487	+	16.1588i	0.699030	+	0.519364i
$969$	1.61725	−	1.89299i	0.0519535	−	0.0608117i
$970$	−0.362467	−	0.328710i	−0.0116381	−	0.0105542i
$971$	1.52802	−	8.66581i	0.0490364	−	0.278099i	−0.950424	−	0.310958i	$-0.899350\pi$
$971$	1.52802	−	8.66581i	0.0490364	−	0.278099i	0.999460	+	0.0328590i	$0.0104612\pi$
$972$	−1.13016	+	1.65007i	−0.0362498	+	0.0529262i
$973$	−27.9747	−	10.1819i	−0.896827	−	0.326418i
$974$	−2.50203	+	6.12985i	−0.0801701	+	0.196413i
$975$	1.17852	+	1.40450i	0.0377428	+	0.0449801i
$976$	−36.7647	−	42.0188i	−1.17681	−	1.34499i
$977$	5.31094	+	3.06627i	0.169912	+	0.0980988i	0.582544	−	0.812799i	$-0.302057\pi$
$977$	5.31094	+	3.06627i	0.169912	+	0.0980988i	−0.412632	+	0.910898i	$0.635391\pi$
$978$	7.46922	−	11.8591i	0.238839	−	0.379214i
$979$	1.42579	+	8.08608i	0.0455686	+	0.258432i
$980$	−31.5130	−	14.3001i	−1.00665	−	0.456799i
$981$	13.0092	−	7.51089i	0.415353	−	0.239804i
$982$	59.8859	+	2.30462i	1.91104	+	0.0735434i
$983$	45.7442	−	16.6495i	1.45901	−	0.531037i	0.513920	−	0.857838i	$-0.328193\pi$
$983$	45.7442	−	16.6495i	1.45901	−	0.531037i	0.945093	+	0.326801i	$0.105971\pi$
$984$	25.6621	−	16.9136i	0.818078	−	0.539186i
$985$	−12.1132	−	10.1642i	−0.385959	−	0.323858i
$986$	4.58051	−	3.55251i	0.145873	−	0.113135i
$987$	−23.0781			−0.734585
$988$	−29.9248	+	21.0189i	−0.952035	+	0.668702i
$989$	16.3587			0.520176
$990$	2.84520	−	2.20666i	0.0904263	−	0.0701321i
$991$	−5.14706	−	4.31890i	−0.163502	−	0.137194i	0.557366	−	0.830267i	$-0.311812\pi$
$991$	−5.14706	−	4.31890i	−0.163502	−	0.137194i	−0.720868	+	0.693073i	$0.756257\pi$
$992$	28.0561	−	22.7037i	0.890781	−	0.720844i
$993$	−11.1438	+	4.05602i	−0.353639	+	0.128714i
$994$	−36.6098	−	1.40887i	−1.16119	−	0.0446867i
$995$	−22.6674	+	13.0870i	−0.718604	+	0.414886i
$996$	−6.05490	+	13.3432i	−0.191857	+	0.422795i
$997$	−5.12623	−	29.0723i	−0.162349	−	0.920728i	−0.951756	−	0.306857i	$-0.900723\pi$
$997$	−5.12623	−	29.0723i	−0.162349	−	0.920728i	0.789406	−	0.613871i	$-0.210389\pi$
$998$	−3.18326	+	5.05417i	−0.100764	+	0.159987i
$999$	4.47664	+	2.58459i	0.141635	+	0.0817728i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.w.a.211.8	yes	60
3.2	odd	2		684.2.cf.c.667.3		60
4.3	odd	2		228.2.w.b.211.9	yes	60
12.11	even	2		684.2.cf.b.667.2		60
19.10	odd	18		228.2.w.b.67.9	yes	60
57.29	even	18		684.2.cf.b.523.2		60
76.67	even	18	inner	228.2.w.a.67.8	✓	60
228.143	odd	18		684.2.cf.c.523.3		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.67.8	✓	60	76.67	even	18	inner
228.2.w.a.211.8	yes	60	1.1	even	1	trivial
228.2.w.b.67.9	yes	60	19.10	odd	18
228.2.w.b.211.9	yes	60	4.3	odd	2
684.2.cf.b.523.2		60	57.29	even	18
684.2.cf.b.667.2		60	12.11	even	2
684.2.cf.c.523.3		60	228.143	odd	18
684.2.cf.c.667.3		60	3.2	odd	2

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:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.w (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866706 + 1.11751i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.497640 + 1.93710i) q^{4} +(-2.00728 + 0.730589i) q^{5} +(0.0543836 - 1.41317i) q^{6} +(-3.36529 + 1.94295i) q^{7} +(-2.59603 + 1.12278i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-2.55616 - 1.60994i) q^{10} +(1.03222 + 0.595952i) q^{11} +(1.62636 - 1.16403i) q^{12} +(2.69633 + 3.21336i) q^{13} +(-5.08798 - 2.07676i) q^{14} +(2.00728 + 0.730589i) q^{15} +(-3.50471 - 1.92796i) q^{16} +(-0.0991862 + 0.562513i) q^{17} +(-0.950027 + 1.04759i) q^{18} +(4.29922 - 0.718796i) q^{19} +(-0.416321 - 4.25186i) q^{20} +(3.82687 + 0.674780i) q^{21} +(0.228651 + 1.67003i) q^{22} +(1.97361 - 5.42244i) q^{23} +(2.71038 + 0.808596i) q^{24} +(-0.334824 + 0.280951i) q^{25} +(-1.25403 + 5.79821i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-2.08899 - 7.48579i) q^{28} +(-7.06698 + 1.24610i) q^{29} +(0.923281 + 2.87635i) q^{30} +(3.19007 + 5.52537i) q^{31} +(-0.883048 - 5.58751i) q^{32} +(-0.407655 - 1.12002i) q^{33} +(-0.714577 + 0.376692i) q^{34} +(5.33557 - 6.35868i) q^{35} +(-1.99408 - 0.153706i) q^{36} +5.16918i q^{37} +(4.52942 + 4.18143i) q^{38} -4.19475i q^{39} +(4.39066 - 4.15036i) q^{40} +(6.98473 - 8.32408i) q^{41} +(2.56270 + 4.86138i) q^{42} +(0.969597 + 2.66394i) q^{43} +(-1.66809 + 1.70294i) q^{44} +(-1.06805 - 1.84992i) q^{45} +(7.77015 - 2.49415i) q^{46} +(-5.84871 + 1.03129i) q^{47} +(1.44549 + 3.72968i) q^{48} +(4.05012 - 7.01501i) q^{49} +(-0.604159 - 0.130666i) q^{50} +(0.437558 - 0.367154i) q^{51} +(-7.56641 + 3.62397i) q^{52} +(-3.23383 + 8.88487i) q^{53} +(1.40114 - 0.191837i) q^{54} +(-2.50734 - 0.442113i) q^{55} +(6.55488 - 8.82244i) q^{56} +(-3.75543 - 2.21286i) q^{57} +(-7.51752 - 6.81739i) q^{58} +(-1.18557 + 6.72368i) q^{59} +(-2.41412 + 3.52472i) q^{60} +(13.1163 + 4.77393i) q^{61} +(-3.40978 + 8.35380i) q^{62} +(-2.49781 - 2.97677i) q^{63} +(5.47873 - 5.82954i) q^{64} +(-7.75993 - 4.48020i) q^{65} +(0.898316 - 1.42629i) q^{66} +(1.03100 + 5.84710i) q^{67} +(-1.04028 - 0.472063i) q^{68} +(-4.99735 + 2.88522i) q^{69} +(11.7302 + 0.451421i) q^{70} +(6.26466 - 2.28015i) q^{71} +(-1.55652 - 2.36162i) q^{72} +(1.05767 + 0.887487i) q^{73} +(-5.77659 + 4.48016i) q^{74} +0.437082 q^{75} +(-0.747089 + 8.68573i) q^{76} -4.63162 q^{77} +(4.68766 - 3.63562i) q^{78} +(-5.51482 - 4.62748i) q^{79} +(8.44346 + 1.30944i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(15.3559 + 0.590949i) q^{82} +(-6.34481 + 3.66318i) q^{83} +(-3.21152 + 7.07722i) q^{84} +(-0.211872 - 1.20158i) q^{85} +(-2.13662 + 3.39239i) q^{86} +(6.21460 + 3.58800i) q^{87} +(-3.34879 - 0.388153i) q^{88} +(4.42805 + 5.27715i) q^{89} +(1.14161 - 2.79689i) q^{90} +(-15.3174 - 5.57506i) q^{91} +(9.52166 + 6.52150i) q^{92} +(1.10790 - 6.28322i) q^{93} +(-6.22158 - 5.64215i) q^{94} +(-8.10459 + 4.58379i) q^{95} +(-2.91513 + 4.84789i) q^{96} +(0.159517 + 0.0281271i) q^{97} +(11.3496 - 1.55392i) q^{98} +(-0.407655 + 1.12002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{6} + 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} - 27 q^{16} - 18 q^{19} + 30 q^{20} - 6 q^{21} + 12 q^{22} + 18 q^{24} + 30 q^{27} - 18 q^{28} + 12 q^{31} - 63 q^{32} - 39 q^{34}+ \cdots + 117 q^{98}+O(q^{100}) \) 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^6 + 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 - 27 * q^16 - 18 * q^19 + 30 * q^20 - 6 * q^21 + 12 * q^22 + 18 * q^24 + 30 * q^27 - 18 * q^28 + 12 * q^31 - 63 * q^32 - 39 * q^34 - 3 * q^36 - 48 * q^38 + 33 * q^40 - 12 * q^41 - 9 * q^42 + 18 * q^43 - 9 * q^44 - 69 * q^46 + 6 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 - 42 * q^56 - 36 * q^58 - 3 * q^60 + 27 * q^62 + 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 - 42 * q^67 + 93 * q^68 - 72 * q^69 + 132 * q^70 - 24 * q^71 + 18 * q^72 + 18 * q^73 + 27 * q^74 - 60 * q^75 + 66 * q^76 - 72 * q^77 - 33 * q^78 - 12 * q^79 + 6 * q^80 - 9 * q^82 + 69 * q^84 - 60 * q^85 + 123 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 + 84 * q^91 - 99 * q^92 - 12 * q^93 + 24 * q^95 + 12 * q^97 + 117 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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