LMFDB - Embedded newform 378.2.ba.a.185.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,2,Mod(47,378)] 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("378.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.ba (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			185.15
Character	$\chi$	$=$	378.185
Dual form			378.2.ba.a.47.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.984808 - 0.173648i) q^{2} +(-1.49340 + 0.877362i) q^{3} +(0.939693 - 0.342020i) q^{4} +(3.97042 - 1.44511i) q^{5} +(-1.31836 + 1.12336i) q^{6} +(-1.73420 - 1.99814i) q^{7} +(0.866025 - 0.500000i) q^{8} +(1.46047 - 2.62050i) q^{9} +(3.65916 - 2.11262i) q^{10} +(-0.506876 + 1.39263i) q^{11} +(-1.10326 + 1.33522i) q^{12} +(0.0656487 + 0.180368i) q^{13} +(-2.05482 - 1.66664i) q^{14} +(-4.66153 + 5.64163i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.01012 - 1.74957i) q^{17} +(0.983240 - 2.83430i) q^{18} +(-2.40015 - 1.38573i) q^{19} +(3.23672 - 2.71593i) q^{20} +(4.34294 + 1.46250i) q^{21} +(-0.257348 + 1.45949i) q^{22} +(9.15708 + 1.61464i) q^{23} +(-0.854639 + 1.50652i) q^{24} +(9.84566 - 8.26149i) q^{25} +(0.0959719 + 0.166228i) q^{26} +(0.118059 + 5.19481i) q^{27} +(-2.31302 - 1.28451i) q^{28} +(-1.08284 + 2.97507i) q^{29} +(-3.61105 + 6.36538i) q^{30} +(2.98656 + 8.20552i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-0.464873 - 2.52447i) q^{33} +(-1.29858 - 1.54759i) q^{34} +(-9.77303 - 5.42734i) q^{35} +(0.476132 - 2.96198i) q^{36} -1.76011 q^{37} +(-2.60431 - 0.947892i) q^{38} +(-0.256288 - 0.211764i) q^{39} +(2.71593 - 3.23672i) q^{40} +(-8.23124 + 2.99593i) q^{41} +(4.53092 + 0.686135i) q^{42} +(0.731893 + 4.15077i) q^{43} +1.48201i q^{44} +(2.01177 - 12.5150i) q^{45} +9.29834 q^{46} +(-9.65595 - 3.51448i) q^{47} +(-0.580052 + 1.63204i) q^{48} +(-0.985115 + 6.93034i) q^{49} +(8.26149 - 9.84566i) q^{50} +(3.04352 + 1.72657i) q^{51} +(0.123379 + 0.147038i) q^{52} +(-0.697789 - 0.402869i) q^{53} +(1.01833 + 5.09539i) q^{54} +6.26182i q^{55} +(-2.50093 - 0.863340i) q^{56} +(4.80016 - 0.0363577i) q^{57} +(-0.549771 + 3.11790i) q^{58} +(-9.93729 - 8.33837i) q^{59} +(-2.45085 + 6.89573i) q^{60} +(0.253965 - 0.697764i) q^{61} +(4.36607 + 7.56225i) q^{62} +(-7.76887 + 1.62624i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.521306 + 0.621268i) q^{65} +(-0.896180 - 2.40539i) q^{66} +(0.524394 - 2.97399i) q^{67} +(-1.54759 - 1.29858i) q^{68} +(-15.0918 + 5.62277i) q^{69} +(-10.5670 - 3.64781i) q^{70} +(-1.21869 - 0.703610i) q^{71} +(-0.0454431 - 2.99966i) q^{72} +5.22639i q^{73} +(-1.73337 + 0.305639i) q^{74} +(-7.45517 + 20.9759i) q^{75} +(-2.72935 - 0.481257i) q^{76} +(3.66169 - 1.40229i) q^{77} +(-0.289167 - 0.164043i) q^{78} +(1.27291 + 7.21904i) q^{79} +(2.11262 - 3.65916i) q^{80} +(-4.73404 - 7.65434i) q^{81} +(-7.58595 + 4.37975i) q^{82} +(-3.70712 - 1.34928i) q^{83} +(4.58123 - 0.111075i) q^{84} +(-6.53893 - 5.48681i) q^{85} +(1.44155 + 3.96062i) q^{86} +(-0.993106 - 5.39300i) q^{87} +(0.257348 + 1.45949i) q^{88} +(-5.61778 + 9.73028i) q^{89} +(-0.192008 - 12.6742i) q^{90} +(0.246553 - 0.443969i) q^{91} +(9.15708 - 1.61464i) q^{92} +(-11.6593 - 9.63381i) q^{93} +(-10.1195 - 1.78435i) q^{94} +(-11.5321 - 2.03342i) q^{95} +(-0.287839 + 1.70797i) q^{96} +(11.9147 - 2.10087i) q^{97} +(0.233291 + 6.99611i) q^{98} +(2.90911 + 3.36217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) $ 144 * q - 18 * q^6 + 24 * q^9 - 24 * q^11 + 6 * q^14 + 12 * q^15 - 30 * q^21 - 42 * q^23 - 6 * q^29 - 18 * q^30 + 6 * q^36 + 48 * q^39 - 48 * q^42 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 12 * q^50 - 36 * q^51 - 90 * q^53 + 6 * q^56 - 6 * q^57 + 18 * q^60 + 54 * q^61 - 24 * q^63 + 72 * q^64 + 78 * q^65 - 72 * q^66 - 54 * q^68 + 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 - 36 * q^74 - 6 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 36 * q^91 - 42 * q^92 + 96 * q^93 - 66 * q^95 - 108 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	−1.49340	+	0.877362i	−0.862214	+	0.506545i
$3$	−1.49340	+	0.877362i	−0.862214	+	0.506545i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	3.97042	−	1.44511i	1.77563	−	0.646275i	0.775742	−	0.631050i	$-0.217376\pi$
$5$	3.97042	−	1.44511i	1.77563	−	0.646275i	0.999884	−	0.0152248i	$-0.00484641\pi$
$6$	−1.31836	+	1.12336i	−0.538217	+	0.458609i
$7$	−1.73420	−	1.99814i	−0.655465	−	0.755225i
$7$	−1.73420	−	1.99814i	−0.655465	−	0.755225i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	1.46047	−	2.62050i	0.486824	−	0.873500i
$10$	3.65916	−	2.11262i	1.15713	−	0.668068i
$11$	−0.506876	+	1.39263i	−0.152829	+	0.419894i	−0.992354	−	0.123428i	$-0.960611\pi$
$11$	−0.506876	+	1.39263i	−0.152829	+	0.419894i	0.839525	+	0.543322i	$0.182834\pi$
$12$	−1.10326	+	1.33522i	−0.318484	+	0.385445i
$13$	0.0656487	+	0.180368i	0.0182077	+	0.0500252i	0.948464	−	0.316886i	$-0.102637\pi$
$13$	0.0656487	+	0.180368i	0.0182077	+	0.0500252i	−0.930256	+	0.366912i	$0.880415\pi$
$14$	−2.05482	−	1.66664i	−0.549175	−	0.445429i
$15$	−4.66153	+	5.64163i	−1.20360	+	1.45666i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−1.01012	−	1.74957i	−0.244989	−	0.424334i	0.717139	−	0.696930i	$-0.245451\pi$
$17$	−1.01012	−	1.74957i	−0.244989	−	0.424334i	−0.962129	+	0.272596i	$0.912118\pi$
$18$	0.983240	−	2.83430i	0.231752	−	0.668050i
$19$	−2.40015	−	1.38573i	−0.550631	−	0.317907i	0.198745	−	0.980051i	$-0.436313\pi$
$19$	−2.40015	−	1.38573i	−0.550631	−	0.317907i	−0.749377	+	0.662144i	$0.769647\pi$
$20$	3.23672	−	2.71593i	0.723752	−	0.607300i
$21$	4.34294	+	1.46250i	0.947707	+	0.319143i
$22$	−0.257348	+	1.45949i	−0.0548667	+	0.311165i
$23$	9.15708	+	1.61464i	1.90938	+	0.336676i	0.997307	−	0.0733444i	$-0.0233672\pi$
$23$	9.15708	+	1.61464i	1.90938	+	0.336676i	0.912076	+	0.410020i	$0.134478\pi$
$24$	−0.854639	+	1.50652i	−0.174453	+	0.307516i
$25$	9.84566	−	8.26149i	1.96913	−	1.65230i
$26$	0.0959719	+	0.166228i	0.0188216	+	0.0326001i
$27$	0.118059	+	5.19481i	0.0227205	+	0.999742i
$28$	−2.31302	−	1.28451i	−0.437119	−	0.242749i
$29$	−1.08284	+	2.97507i	−0.201078	+	0.552457i	−0.998715	−	0.0506810i	$-0.983861\pi$
$29$	−1.08284	+	2.97507i	−0.201078	+	0.552457i	0.797637	+	0.603138i	$0.206083\pi$
$30$	−3.61105	+	6.36538i	−0.659285	+	1.16215i
$31$	2.98656	+	8.20552i	0.536403	+	1.47375i	0.851326	+	0.524637i	$0.175799\pi$
$31$	2.98656	+	8.20552i	0.536403	+	1.47375i	−0.314923	+	0.949117i	$0.601979\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	−0.464873	−	2.52447i	−0.0809240	−	0.439453i
$34$	−1.29858	−	1.54759i	−0.222705	−	0.265409i
$35$	−9.77303	−	5.42734i	−1.65194	−	0.917387i
$36$	0.476132	−	2.96198i	0.0793553	−	0.493663i
$37$	−1.76011			−0.289360			−0.144680	−	0.989479i	$-0.546215\pi$
$37$	−1.76011			−0.289360			−0.144680	+	0.989479i	$0.546215\pi$
$38$	−2.60431	−	0.947892i	−0.422475	−	0.153768i
$39$	−0.256288	−	0.211764i	−0.0410389	−	0.0339094i
$40$	2.71593	−	3.23672i	0.429426	−	0.511770i
$41$	−8.23124	+	2.99593i	−1.28550	+	0.467885i	−0.892249	−	0.451544i	$-0.850873\pi$
$41$	−8.23124	+	2.99593i	−1.28550	+	0.467885i	−0.393255	+	0.919429i	$0.628651\pi$
$42$	4.53092	+	0.686135i	0.699136	+	0.105873i
$43$	0.731893	+	4.15077i	0.111613	+	0.632987i	0.988372	+	0.152057i	$0.0485898\pi$
$43$	0.731893	+	4.15077i	0.111613	+	0.632987i	−0.876759	+	0.480930i	$0.840299\pi$
$44$			1.48201i			0.223421i
$45$	2.01177	−	12.5150i	0.299897	−	1.86563i
$46$	9.29834			1.37097
$47$	−9.65595	−	3.51448i	−1.40846	−	0.512639i	−0.477786	−	0.878476i	$-0.658560\pi$
$47$	−9.65595	−	3.51448i	−1.40846	−	0.512639i	−0.930679	+	0.365837i	$0.880783\pi$
$48$	−0.580052	+	1.63204i	−0.0837233	+	0.235564i
$49$	−0.985115	+	6.93034i	−0.140731	+	0.990048i
$50$	8.26149	−	9.84566i	1.16835	−	1.39239i
$51$	3.04352	+	1.72657i	0.426178	+	0.241768i
$52$	0.123379	+	0.147038i	0.0171096	+	0.0203904i
$53$	−0.697789	−	0.402869i	−0.0958487	−	0.0553383i	0.451309	−	0.892368i	$-0.350957\pi$
$53$	−0.697789	−	0.402869i	−0.0958487	−	0.0553383i	−0.547158	+	0.837029i	$0.684290\pi$
$54$	1.01833	+	5.09539i	0.138578	+	0.693395i
$55$			6.26182i			0.844344i
$56$	−2.50093	−	0.863340i	−0.334201	−	0.115369i
$57$	4.80016	−	0.0363577i	0.635796	−	0.00481570i
$58$	−0.549771	+	3.11790i	−0.0721884	+	0.409401i
$59$	−9.93729	−	8.33837i	−1.29372	−	1.08556i	−0.991193	−	0.132424i	$-0.957724\pi$
$59$	−9.93729	−	8.33837i	−1.29372	−	1.08556i	−0.302531	−	0.953139i	$-0.597832\pi$
$60$	−2.45085	+	6.89573i	−0.316404	+	0.890235i
$61$	0.253965	−	0.697764i	0.0325169	−	0.0893395i	−0.922372	−	0.386303i	$-0.873752\pi$
$61$	0.253965	−	0.697764i	0.0325169	−	0.0893395i	0.954889	+	0.296964i	$0.0959741\pi$
$62$	4.36607	+	7.56225i	0.554491	+	0.960406i
$63$	−7.76887	+	1.62624i	−0.978786	+	0.204887i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	0.521306	+	0.621268i	0.0646600	+	0.0770588i
$66$	−0.896180	−	2.40539i	−0.110312	−	0.296083i
$67$	0.524394	−	2.97399i	0.0640649	−	0.363330i	−0.935875	−	0.352333i	$-0.885388\pi$
$67$	0.524394	−	2.97399i	0.0640649	−	0.363330i	0.999940	−	0.0109970i	$-0.00350052\pi$
$68$	−1.54759	−	1.29858i	−0.187673	−	0.157476i
$69$	−15.0918	+	5.62277i	−1.81684	+	0.676902i
$70$	−10.5670	−	3.64781i	−1.26300	−	0.435997i
$71$	−1.21869	−	0.703610i	−0.144632	−	0.0835032i	0.425938	−	0.904752i	$-0.359944\pi$
$71$	−1.21869	−	0.703610i	−0.144632	−	0.0835032i	−0.570570	+	0.821249i	$0.693278\pi$
$72$	−0.0454431	−	2.99966i	−0.00535552	−	0.353513i
$73$			5.22639i			0.611703i	0.952079	+	0.305851i	$0.0989411\pi$
$73$			5.22639i			0.611703i	−0.952079	+	0.305851i	$0.901059\pi$
$74$	−1.73337	+	0.305639i	−0.201500	+	0.0355298i
$75$	−7.45517	+	20.9759i	−0.860849	+	2.42209i
$76$	−2.72935	−	0.481257i	−0.313077	−	0.0552040i
$77$	3.66169	−	1.40229i	0.417289	−	0.159806i
$78$	−0.289167	−	0.164043i	−0.0327417	−	0.0185742i
$79$	1.27291	+	7.21904i	0.143214	+	0.812206i	0.968784	+	0.247906i	$0.0797425\pi$
$79$	1.27291	+	7.21904i	0.143214	+	0.812206i	−0.825570	+	0.564299i	$0.809146\pi$
$80$	2.11262	−	3.65916i	0.236198	−	0.409106i
$81$	−4.73404	−	7.65434i	−0.526004	−	0.850482i
$82$	−7.58595	+	4.37975i	−0.837728	+	0.483663i
$83$	−3.70712	−	1.34928i	−0.406909	−	0.148103i	0.130453	−	0.991455i	$-0.458357\pi$
$83$	−3.70712	−	1.34928i	−0.406909	−	0.148103i	−0.537362	+	0.843352i	$0.680579\pi$
$84$	4.58123	−	0.111075i	0.499853	−	0.0121192i
$85$	−6.53893	−	5.48681i	−0.709246	−	0.595128i
$86$	1.44155	+	3.96062i	0.155446	+	0.427085i
$87$	−0.993106	−	5.39300i	−0.106472	−	0.578191i
$88$	0.257348	+	1.45949i	0.0274334	+	0.155582i
$89$	−5.61778	+	9.73028i	−0.595483	+	1.03141i	0.397995	+	0.917387i	$0.369706\pi$
$89$	−5.61778	+	9.73028i	−0.595483	+	1.03141i	−0.993478	+	0.114020i	$0.963627\pi$
$90$	−0.192008	−	12.6742i	−0.0202394	−	1.33598i
$91$	0.246553	−	0.443969i	0.0258458	−	0.0465406i
$92$	9.15708	−	1.61464i	0.954692	−	0.168338i
$93$	−11.6593	−	9.63381i	−1.20902	−	0.998979i
$94$	−10.1195	−	1.78435i	−1.04375	−	0.184041i
$95$	−11.5321	−	2.03342i	−1.18317	−	0.208625i
$96$	−0.287839	+	1.70797i	−0.0293775	+	0.174319i
$97$	11.9147	−	2.10087i	1.20975	−	0.213311i	0.467841	−	0.883813i	$-0.345032\pi$
$97$	11.9147	−	2.10087i	1.20975	−	0.213311i	0.741908	+	0.670501i	$0.233921\pi$
$98$	0.233291	+	6.99611i	0.0235659	+	0.706714i
$99$	2.90911	+	3.36217i	0.292377	+	0.337911i
$100$	6.42630	−	11.1307i	0.642630	−	1.11307i
$101$	2.51752	+	14.2776i	0.250503	+	1.42067i	0.807358	+	0.590062i	$0.200897\pi$
$101$	2.51752	+	14.2776i	0.250503	+	1.42067i	−0.556855	+	0.830610i	$0.687992\pi$
$102$	3.29709	+	1.17184i	0.326461	+	0.116030i
$103$	−0.0991553	−	0.272427i	−0.00977006	−	0.0268430i	0.934712	−	0.355407i	$-0.115658\pi$
$103$	−0.0991553	−	0.272427i	−0.00977006	−	0.0268430i	−0.944482	+	0.328564i	$0.893435\pi$
$104$	0.147038	+	0.123379i	0.0144182	+	0.0120983i
$105$	19.3568	−	0.469317i	1.88903	−	0.0458006i
$106$	−0.757146	−	0.275578i	−0.0735405	−	0.0267665i
$107$	5.30878	−	3.06502i	0.513219	−	0.296307i	−0.220937	−	0.975288i	$-0.570912\pi$
$107$	5.30878	−	3.06502i	0.513219	−	0.296307i	0.734156	+	0.678981i	$0.237578\pi$
$108$	1.88767	+	4.84115i	0.181641	+	0.465840i
$109$	−2.96141	+	5.12932i	−0.283652	+	0.491300i	−0.972281	−	0.233814i	$-0.924879\pi$
$109$	−2.96141	+	5.12932i	−0.283652	+	0.491300i	0.688629	+	0.725114i	$0.258213\pi$
$110$	1.08735	+	6.16669i	0.103675	+	0.587971i
$111$	2.62854	−	1.54425i	0.249490	−	0.146574i
$112$	−2.61285	−	0.415942i	−0.246891	−	0.0393028i
$113$	6.06834	+	1.07001i	0.570862	+	0.100658i	0.451625	−	0.892208i	$-0.350844\pi$
$113$	6.06834	+	1.07001i	0.570862	+	0.100658i	0.119236	+	0.992866i	$0.461955\pi$
$114$	4.72092	−	0.869344i	0.442154	−	0.0814215i
$115$	38.6908	−	6.82223i	3.60794	−	0.636176i
$116$			3.16600i			0.293956i
$117$	0.568533	+	0.0913906i	0.0525609	+	0.00844907i
$118$	−11.2343	−	6.48610i	−1.03420	−	0.597094i
$119$	−1.74415	+	5.05246i	−0.159886	+	0.463159i
$120$	−1.21619	+	7.21656i	−0.111022	+	0.658778i
$121$	6.74399	+	5.65888i	0.613090	+	0.514444i
$122$	0.128942	−	0.731264i	0.0116738	−	0.0662055i
$123$	9.66401	−	11.6959i	0.871374	−	1.05458i
$124$	5.61291	+	6.68920i	0.504054	+	0.600708i
$125$	16.5895	−	28.7339i	1.48381	−	2.57004i
$126$	−7.36845	+	2.95058i	−0.656434	+	0.262859i
$127$	−5.08797	−	8.81262i	−0.451484	−	0.781993i	0.546994	−	0.837136i	$-0.315772\pi$
$127$	−5.08797	−	8.81262i	−0.451484	−	0.781993i	−0.998478	+	0.0551430i	$0.982439\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	−4.73474	−	5.55662i	−0.416870	−	0.489233i
$130$	0.621268	+	0.521306i	0.0544888	+	0.0457215i
$131$	2.54308	−	14.4225i	0.222190	−	1.26010i	−0.645795	−	0.763511i	$-0.723474\pi$
$131$	2.54308	−	14.4225i	0.222190	−	1.26010i	0.867985	−	0.496591i	$-0.165415\pi$
$132$	−1.30026	−	2.21323i	−0.113173	−	0.192637i
$133$	1.39346	+	7.19895i	0.120828	+	0.624228i
$134$		−	3.01986i		−	0.260877i
$135$	7.97584	+	20.4550i	0.686451	+	1.76048i
$136$	−1.74957	−	1.01012i	−0.150025	−	0.0866169i
$137$	−2.46829	−	2.94159i	−0.210880	−	0.251317i	0.650228	−	0.759739i	$-0.274673\pi$
$137$	−2.46829	−	2.94159i	−0.210880	−	0.251317i	−0.861108	+	0.508422i	$0.830229\pi$
$138$	−13.8861	+	8.15801i	−1.18207	+	0.694456i
$139$	−3.42887	+	4.08637i	−0.290833	+	0.346602i	−0.891601	−	0.452822i	$-0.850417\pi$
$139$	−3.42887	+	4.08637i	−0.290833	+	0.346602i	0.600768	+	0.799424i	$0.294862\pi$
$140$	−11.0399	−	1.75745i	−0.933042	−	0.148532i
$141$	17.5036	−	3.22325i	1.47407	−	0.271446i
$142$	−1.32235	−	0.481298i	−0.110970	−	0.0403896i
$143$	−0.284462			−0.0237879
$144$	−0.565637	−	2.94619i	−0.0471365	−	0.245516i
$145$			13.3771i			1.11091i
$146$	0.907553	+	5.14699i	0.0751097	+	0.425968i
$147$	−4.60924	−	11.2140i	−0.380164	−	0.924919i
$148$	−1.65396	+	0.601992i	−0.135955	+	0.0494834i
$149$	−8.87642	+	10.5785i	−0.727185	+	0.866625i	−0.995308	−	0.0967595i	$-0.969152\pi$
$149$	−8.87642	+	10.5785i	−0.727185	+	0.866625i	0.268123	+	0.963385i	$0.413597\pi$
$150$	−3.69948	+	21.9518i	−0.302062	+	1.79236i
$151$	−0.996307	−	0.362626i	−0.0810783	−	0.0295101i	0.301163	−	0.953573i	$-0.402625\pi$
$151$	−0.996307	−	0.362626i	−0.0810783	−	0.0295101i	−0.382241	+	0.924063i	$0.624848\pi$
$152$	−2.77145			−0.224794
$153$	−6.06001	+	0.0918057i	−0.489923	+	0.00742205i
$154$	3.36256	−	2.01683i	0.270963	−	0.162521i
$155$	23.7158	+	28.2634i	1.90490	+	2.27017i
$156$	−0.313259	−	0.111337i	−0.0250808	−	0.00891413i
$157$	1.10214	−	1.31348i	0.0879602	−	0.104827i	−0.720269	−	0.693695i	$-0.755982\pi$
$157$	1.10214	−	1.31348i	0.0879602	−	0.104827i	0.808229	+	0.588868i	$0.200426\pi$
$158$	2.50715	+	6.88833i	0.199458	+	0.548006i
$159$	1.39554	−	0.0105702i	0.110673	−	0.000838272i
$160$	1.44511	−	3.97042i	0.114246	−	0.313889i
$161$	−12.6539	−	21.0972i	−0.997268	−	1.66269i
$162$	−5.99128	−	6.71599i	−0.470719	−	0.527658i
$163$	−7.02330	−	12.1647i	−0.550108	−	0.952814i	−0.998266	−	0.0588602i	$-0.981253\pi$
$163$	−7.02330	−	12.1647i	−0.550108	−	0.952814i	0.448159	−	0.893954i	$-0.352080\pi$
$164$	−6.71017	+	5.63050i	−0.523976	+	0.439668i
$165$	−5.49388	−	9.35139i	−0.427698	−	0.728005i
$166$	−3.88510	−	0.685048i	−0.301542	−	0.0531700i
$167$	4.12751	−	23.4083i	0.319396	−	1.81139i	−0.227041	−	0.973885i	$-0.572905\pi$
$167$	4.12751	−	23.4083i	0.319396	−	1.81139i	0.546437	−	0.837500i	$-0.315984\pi$
$168$	4.49234	−	0.904909i	0.346592	−	0.0698153i
$169$	9.93035	−	8.33256i	0.763873	−	0.640966i
$170$	−7.39236	−	4.26798i	−0.566968	−	0.327339i
$171$	−7.13664	+	4.26577i	−0.545753	+	0.326212i
$172$	2.10740	+	3.65013i	0.160688	+	0.278320i
$173$	−9.04875	+	7.59280i	−0.687964	+	0.577270i	−0.918321	−	0.395836i	$-0.870455\pi$
$173$	−9.04875	+	7.59280i	−0.687964	+	0.577270i	0.230358	+	0.973106i	$0.426010\pi$
$174$	−1.91450	−	5.13862i	−0.145138	−	0.389558i
$175$	−33.5819	−	5.34594i	−2.53856	−	0.404115i
$176$	0.506876	+	1.39263i	0.0382072	+	0.104973i
$177$	22.1561	+	3.73391i	1.66535	+	0.280658i
$178$	−3.84279	+	10.5580i	−0.288029	+	0.791353i
$179$	−14.0893	+	8.13448i	−1.05309	+	0.608000i	−0.923512	−	0.383570i	$-0.874695\pi$
$179$	−14.0893	+	8.13448i	−1.05309	+	0.608000i	−0.129575	+	0.991570i	$0.541361\pi$
$180$	−2.38995	−	12.4484i	−0.178136	−	0.927846i
$181$	−9.64937	+	5.57107i	−0.717232	+	0.414094i	−0.813733	−	0.581239i	$-0.802568\pi$
$181$	−9.64937	+	5.57107i	−0.717232	+	0.414094i	0.0965009	+	0.995333i	$0.469235\pi$
$182$	0.165713	−	0.480038i	0.0122835	−	0.0355828i
$183$	0.232920	+	1.26486i	0.0172179	+	0.0935010i
$184$	8.73758	−	3.18022i	0.644143	−	0.234449i
$185$	−6.98836	+	2.54355i	−0.513794	+	0.187006i
$186$	−13.1551	−	7.46282i	−0.964579	−	0.547201i
$187$	2.94852	−	0.519903i	0.215617	−	0.0380191i
$188$	−10.2756			−0.749428
$189$	10.1752	−	9.24473i	0.740138	−	0.672455i
$190$	−11.7100			−0.849535
$191$	11.3711	−	2.00504i	0.822785	−	0.145079i	0.253622	−	0.967303i	$-0.418378\pi$
$191$	11.3711	−	2.00504i	0.822785	−	0.145079i	0.569164	+	0.822224i	$0.307267\pi$
$192$	0.0131187	+	1.73200i	0.000946758	+	0.124996i
$193$	11.0195	−	4.01078i	0.793204	−	0.288703i	0.0865365	−	0.996249i	$-0.472420\pi$
$193$	11.0195	−	4.01078i	0.793204	−	0.288703i	0.706667	+	0.707546i	$0.250198\pi$
$194$	11.3688	−	4.13791i	0.816234	−	0.297085i
$195$	−1.32359	−	0.470426i	−0.0947845	−	0.0336879i
$196$	1.44461	+	6.84931i	0.103186	+	0.489237i
$197$	−14.6216	+	8.44177i	−1.04174	+	0.601451i	−0.920327	−	0.391150i	$-0.872077\pi$
$197$	−14.6216	+	8.44177i	−1.04174	+	0.601451i	−0.121417	+	0.992602i	$0.538744\pi$
$198$	3.44875	+	2.80593i	0.245092	+	0.199409i
$199$	15.3443	−	8.85905i	1.08773	−	0.628001i	0.154759	−	0.987952i	$-0.450540\pi$
$199$	15.3443	−	8.85905i	1.08773	−	0.628001i	0.932971	+	0.359951i	$0.117207\pi$
$200$	4.39585	−	12.0775i	0.310833	−	0.854008i
$201$	1.82613	+	4.90143i	0.128805	+	0.345720i
$202$	4.95855	+	13.6235i	0.348882	+	0.958546i
$203$	7.82246	−	2.99570i	0.549029	−	0.210257i
$204$	3.45049	+	0.581503i	0.241583	+	0.0407134i
$205$	−28.3520	+	23.7902i	−1.98019	+	1.66158i
$206$	−0.144955	−	0.251070i	−0.0100995	−	0.0174929i
$207$	17.6048	−	21.6380i	1.22362	−	1.50394i
$208$	0.166228	+	0.0959719i	0.0115259	+	0.00665446i
$209$	3.14638	−	2.64013i	0.217640	−	0.182621i
$210$	18.9812	−	3.82345i	1.30983	−	0.263843i
$211$	−3.30791	+	18.7601i	−0.227726	+	1.29150i	0.629680	+	0.776855i	$0.283186\pi$
$211$	−3.30791	+	18.7601i	−0.227726	+	1.29150i	−0.857406	+	0.514641i	$0.827925\pi$
$212$	−0.793497	−	0.139915i	−0.0544976	−	0.00960939i
$213$	2.43731	−	0.0184609i	0.167002	−	0.00126492i
$214$	4.69589	−	3.94032i	0.321004	−	0.269355i
$215$	8.90427	+	15.4226i	0.607266	+	1.05182i
$216$	2.69965	+	4.43981i	0.183688	+	0.302091i
$217$	11.2165	−	20.1976i	0.761424	−	1.37110i
$218$	−2.02573	+	5.56564i	−0.137200	+	0.376953i
$219$	−4.58544	−	7.80508i	−0.309855	−	0.527418i
$220$	2.14167	+	5.88419i	0.144391	+	0.396712i
$221$	0.249255	−	0.297050i	0.0167667	−	0.0199818i
$222$	2.32045	−	1.97723i	0.155738	−	0.132703i
$223$	9.50125	+	11.3231i	0.636251	+	0.758254i	0.983773	−	0.179418i	$-0.0574213\pi$
$223$	9.50125	+	11.3231i	0.636251	+	0.758254i	−0.347522	+	0.937672i	$0.612977\pi$
$224$	−2.64538	+	0.0440940i	−0.176752	+	0.00294615i
$225$	−7.26991	−	37.8662i	−0.484661	−	2.52442i
$226$	6.16196			0.409887
$227$	19.1781	+	6.98025i	1.27289	+	0.463295i	0.888076	−	0.459697i	$-0.152042\pi$
$227$	19.1781	+	6.98025i	1.27289	+	0.463295i	0.384818	+	0.922993i	$0.374264\pi$
$228$	4.49824	−	1.67592i	0.297903	−	0.110990i
$229$	12.1966	−	14.5354i	0.805976	−	0.960525i	−0.193814	−	0.981038i	$-0.562086\pi$
$229$	12.1966	−	14.5354i	0.805976	−	0.960525i	0.999790	+	0.0205136i	$0.00653013\pi$
$230$	36.9183	−	13.4372i	2.43432	−	0.886021i
$231$	−4.23805	+	5.30680i	−0.278843	+	0.349162i
$232$	0.549771	+	3.11790i	0.0360942	+	0.204700i
$233$		−	2.34180i		−	0.153416i	−0.997054	−	0.0767082i	$-0.975559\pi$
$233$		−	2.34180i		−	0.153416i	0.997054	−	0.0767082i	$-0.0244410\pi$
$234$	0.575766	−	0.00872252i	0.0376390	−	0.000570209i
$235$	−43.4170			−2.83221
$236$	−12.1899	−	4.43676i	−0.793494	−	0.288808i
$237$	−8.23468	−	9.66410i	−0.534900	−	0.627751i
$238$	−0.840301	+	5.27857i	−0.0544686	+	0.342159i
$239$	−6.44557	+	7.68153i	−0.416929	+	0.496877i	−0.933104	−	0.359606i	$-0.882911\pi$
$239$	−6.44557	+	7.68153i	−0.416929	+	0.496877i	0.516175	+	0.856483i	$0.327355\pi$
$240$	0.0554294	+	7.31811i	0.00357795	+	0.472382i
$241$	−10.2698	−	12.2391i	−0.661536	−	0.788388i	0.326069	−	0.945346i	$-0.394276\pi$
$241$	−10.2698	−	12.2391i	−0.661536	−	0.788388i	−0.987605	+	0.156958i	$0.949831\pi$
$242$	7.62419	+	4.40183i	0.490101	+	0.282960i
$243$	13.7854	+	7.27751i	0.884335	+	0.466852i
$244$		−	0.742545i		−	0.0475365i
$245$	6.10381	+	28.9400i	0.389958	+	1.84891i
$246$	7.48622	−	13.1963i	0.477304	−	0.841368i
$247$	0.0923744	−	0.523881i	0.00587764	−	0.0333338i
$248$	6.68920	+	5.61291i	0.424765	+	0.356420i
$249$	6.72001	−	1.23747i	0.425863	−	0.0784215i
$250$	11.3479	−	31.1781i	0.717705	−	1.97188i
$251$	7.40412	+	12.8243i	0.467344	+	0.809464i	0.999304	−	0.0373059i	$-0.0118776\pi$
$251$	7.40412	+	12.8243i	0.467344	+	0.809464i	−0.531960	+	0.846770i	$0.678544\pi$
$252$	−6.74414	+	4.18527i	−0.424841	+	0.263647i
$253$	−6.89010	+	11.9340i	−0.433177	+	0.750285i
$254$	−6.54096	−	7.79522i	−0.410417	−	0.489115i
$255$	14.5791	+	2.45699i	0.912981	+	0.153863i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−7.47860	−	6.27529i	−0.466503	−	0.391442i	0.379014	−	0.925391i	$-0.376263\pi$
$257$	−7.47860	−	6.27529i	−0.466503	−	0.391442i	−0.845517	+	0.533949i	$0.820708\pi$
$258$	−5.62770	−	4.65002i	−0.350366	−	0.289498i
$259$	3.05237	+	3.51693i	0.189665	+	0.218532i
$260$	0.702353	+	0.405504i	0.0435581	+	0.0251483i
$261$	6.21472	+	7.18258i	0.384681	+	0.444591i
$262$		−	14.6450i		−	0.904772i
$263$	2.87434	−	0.506825i	0.177240	−	0.0312521i	−0.0843238	−	0.996438i	$-0.526873\pi$
$263$	2.87434	−	0.506825i	0.177240	−	0.0312521i	0.261564	+	0.965186i	$0.415762\pi$
$264$	−1.66482	−	1.95381i	−0.102463	−	0.120249i
$265$	−3.35271	−	0.591173i	−0.205955	−	0.0363155i
$266$	2.62237	+	6.84761i	0.160788	+	0.419854i
$267$	−0.147396	−	19.4600i	−0.00902046	−	1.19093i
$268$	−0.524394	−	2.97399i	−0.0320325	−	0.181665i
$269$	1.69834	−	2.94161i	0.103550	−	0.179353i	−0.809595	−	0.586989i	$-0.800313\pi$
$269$	1.69834	−	2.94161i	0.103550	−	0.179353i	0.913145	+	0.407636i	$0.133647\pi$
$270$	11.4066	+	18.7592i	0.694186	+	1.14165i
$271$	−0.721049	+	0.416298i	−0.0438006	+	0.0252883i	−0.521740	−	0.853104i	$-0.674717\pi$
$271$	−0.721049	+	0.416298i	−0.0438006	+	0.0252883i	0.477940	+	0.878393i	$0.341384\pi$
$272$	−1.89840	−	0.690961i	−0.115107	−	0.0418957i
$273$	0.0213201	+	0.879339i	0.00129035	+	0.0532200i
$274$	−2.94159	−	2.46829i	−0.177708	−	0.149115i
$275$	6.51468	+	17.8989i	0.392850	+	1.07935i
$276$	−12.2585	+	10.4454i	−0.737877	+	0.628737i
$277$	1.75307	+	9.94215i	0.105332	+	0.597366i	0.991087	+	0.133214i	$0.0425297\pi$
$277$	1.75307	+	9.94215i	0.105332	+	0.597366i	−0.885756	+	0.464152i	$0.846359\pi$
$278$	−2.66719	+	4.61971i	−0.159967	+	0.277072i
$279$	25.8644	+	4.15765i	1.54846	+	0.248912i
$280$	−11.1774	+	0.186307i	−0.667975	+	0.0111340i
$281$	−3.30648	+	0.583022i	−0.197248	+	0.0347802i	−0.271399	−	0.962467i	$-0.587486\pi$
$281$	−3.30648	+	0.583022i	−0.197248	+	0.0347802i	0.0741512	+	0.997247i	$0.476375\pi$
$282$	16.6780	−	6.21375i	0.993161	−	0.370024i
$283$	−27.5864	−	4.86423i	−1.63984	−	0.289148i	−0.723733	−	0.690080i	$-0.757575\pi$
$283$	−27.5864	−	4.86423i	−1.63984	−	0.289148i	−0.916108	+	0.400931i	$0.868687\pi$
$284$	−1.38584	−	0.244361i	−0.0822346	−	0.0145002i
$285$	19.0061	−	7.08113i	1.12582	−	0.419450i
$286$	−0.280141	+	0.0493963i	−0.0165651	+	0.00292087i
$287$	20.2609	+	11.2516i	1.19596	+	0.664163i
$288$	−1.06865	−	2.80321i	−0.0629705	−	0.165181i
$289$	6.45933	−	11.1879i	0.379960	−	0.658111i
$290$	2.32291	+	13.1739i	0.136406	+	0.773597i
$291$	−15.9501	+	13.5909i	−0.935010	+	0.796713i
$292$	1.78753	+	4.91120i	0.104607	+	0.287406i
$293$	13.5604	+	11.3785i	0.792204	+	0.664738i	0.946290	−	0.323319i	$-0.104799\pi$
$293$	13.5604	+	11.3785i	0.792204	+	0.664738i	−0.154086	+	0.988058i	$0.549243\pi$
$294$	−6.48652	−	10.2433i	−0.378301	−	0.597401i
$295$	−51.5051	−	18.7463i	−2.99874	−	1.09145i
$296$	−1.52430	+	0.880053i	−0.0885979	+	0.0511520i
$297$	−7.29430	−	2.46871i	−0.423258	−	0.143249i
$298$	−6.90463	+	11.9592i	−0.399975	+	0.692776i
$299$	0.309920	+	1.75765i	0.0179232	+	0.101647i
$300$	0.168609	+	22.2607i	0.00973464	+	1.28522i
$301$	7.02457	−	8.66069i	0.404890	−	0.499194i
$302$	−1.04414	−	0.184110i	−0.0600835	−	0.0105943i
$303$	−16.2863	−	19.1133i	−0.935621	−	1.09803i
$304$	−2.72935	+	0.481257i	−0.156539	+	0.0276020i
$305$		−	3.13742i		−	0.179648i
$306$	−5.95200	+	1.14272i	−0.340253	+	0.0653250i
$307$	17.4229	+	10.0591i	0.994379	+	0.574105i	0.906580	−	0.422034i	$-0.138684\pi$
$307$	17.4229	+	10.0591i	0.994379	+	0.574105i	0.0877984	+	0.996138i	$0.472017\pi$
$308$	2.96125	−	2.57009i	0.168733	−	0.146445i
$309$	0.387095	+	0.319847i	0.0220211	+	0.0181954i
$310$	28.2634	+	23.7158i	1.60526	+	1.34697i
$311$	1.28644	−	7.29577i	0.0729474	−	0.413705i	−0.926365	−	0.376627i	$-0.877084\pi$
$311$	1.28644	−	7.29577i	0.0729474	−	0.413705i	0.999312	−	0.0370782i	$-0.0118051\pi$
$312$	−0.327834	−	0.0552490i	−0.0185599	−	0.00312786i
$313$	−4.38479	−	5.22559i	−0.247843	−	0.295368i	0.627752	−	0.778413i	$-0.283975\pi$
$313$	−4.38479	−	5.22559i	−0.247843	−	0.295368i	−0.875595	+	0.483045i	$0.839531\pi$
$314$	0.857312	−	1.48491i	0.0483809	−	0.0837982i
$315$	−28.4956	+	17.6838i	−1.60554	+	0.996367i
$316$	3.66520	+	6.34832i	0.206184	+	0.357121i
$317$	8.66695	−	23.8123i	0.486785	−	1.33743i	−0.416792	−	0.909002i	$-0.636846\pi$
$317$	8.66695	−	23.8123i	0.486785	−	1.33743i	0.903576	−	0.428428i	$-0.140932\pi$
$318$	1.37250	−	0.252742i	0.0769661	−	0.0141731i
$319$	−3.59431	−	3.01598i	−0.201243	−	0.168863i
$320$	0.733704	−	4.16104i	0.0410153	−	0.232609i
$321$	−5.23898	+	9.23501i	−0.292411	+	0.515448i
$322$	−16.1252	−	18.5794i	−0.898620	−	1.03539i
$323$			5.59898i			0.311536i
$324$	−7.06648	−	5.57359i	−0.392582	−	0.309644i
$325$	2.13647	+	1.23349i	0.118510	+	0.0684216i
$326$	−9.02898	−	10.7603i	−0.500069	−	0.595959i
$327$	−0.0776996	−	10.2583i	−0.00429680	−	0.567288i
$328$	−5.63050	+	6.71017i	−0.310892	+	0.370507i
$329$	9.72291	+	25.3887i	0.536041	+	1.39973i
$330$	−7.03427	−	8.25532i	−0.387224	−	0.454441i
$331$	10.9317	+	3.97883i	0.600863	+	0.218696i	0.624501	−	0.781024i	$-0.285302\pi$
$331$	10.9317	+	3.97883i	0.600863	+	0.218696i	−0.0236374	+	0.999721i	$0.507525\pi$
$332$	−3.94503			−0.216512
$333$	−2.57059	+	4.61236i	−0.140867	+	0.252756i
$334$		−	23.7694i		−	1.30060i
$335$	−2.21569	−	12.5658i	−0.121056	−	0.686542i
$336$	4.26696	−	1.67125i	0.232782	−	0.0911741i
$337$	17.7791	−	6.47105i	0.968487	−	0.352500i	0.191133	−	0.981564i	$-0.438784\pi$
$337$	17.7791	−	6.47105i	0.968487	−	0.352500i	0.777354	+	0.629064i	$0.216562\pi$
$338$	8.33256	−	9.93035i	0.453231	−	0.540140i
$339$	−10.0012	+	3.72618i	−0.543192	+	0.202378i
$340$	−8.02118	−	2.91947i	−0.435010	−	0.158331i
$341$	−12.9411			−0.700799
$342$	−6.28748	+	5.44023i	−0.339988	+	0.294174i
$343$	15.5562	−	10.0502i	0.839953	−	0.542659i
$344$	2.70923	+	3.22873i	0.146072	+	0.174081i
$345$	−51.7952	+	44.1341i	−2.78856	+	2.37610i
$346$	−7.59280	+	9.04875i	−0.408192	+	0.486464i
$347$	−1.65116	−	4.53653i	−0.0886389	−	0.243534i	0.887450	−	0.460903i	$-0.152474\pi$
$347$	−1.65116	−	4.53653i	−0.0886389	−	0.243534i	−0.976089	+	0.217370i	$0.930252\pi$
$348$	−2.77773	−	4.72810i	−0.148902	−	0.253453i
$349$	1.22982	−	3.37891i	0.0658310	−	0.180869i	−0.902415	−	0.430867i	$-0.858208\pi$
$349$	1.22982	−	3.37891i	0.0658310	−	0.180869i	0.968246	+	0.249998i	$0.0804300\pi$
$350$	−34.0001	+	0.566722i	−1.81738	+	0.0302926i
$351$	−0.929229	+	0.362327i	−0.0495986	+	0.0193396i
$352$	0.741003	+	1.28346i	0.0394956	+	0.0684084i
$353$	19.6477	−	16.4864i	1.04574	−	0.877482i	0.0531029	−	0.998589i	$-0.483089\pi$
$353$	19.6477	−	16.4864i	1.04574	−	0.877482i	0.992639	+	0.121107i	$0.0386444\pi$
$354$	22.4679	−	0.170178i	1.19415	−	0.00904486i
$355$	−5.85550	−	1.03248i	−0.310778	−	0.0547985i
$356$	−1.95103	+	11.0649i	−0.103405	+	0.586436i
$357$	−1.82813	−	9.07559i	−0.0967549	−	0.480331i
$358$	−12.4628	+	10.4575i	−0.658677	+	0.552696i
$359$	−25.6480	−	14.8079i	−1.35365	−	0.781531i	−0.364893	−	0.931050i	$-0.618894\pi$
$359$	−25.6480	−	14.8079i	−1.35365	−	0.781531i	−0.988759	+	0.149518i	$0.952228\pi$
$360$	−4.51528	−	11.8442i	−0.237976	−	0.624245i
$361$	−5.65953	−	9.80259i	−0.297870	−	0.515926i
$362$	−8.53537	+	7.16203i	−0.448609	+	0.376428i
$363$	−15.0363	−	2.53404i	−0.789204	−	0.133003i
$364$	0.0798375	−	0.501521i	0.00418462	−	0.0262868i
$365$	7.55274	+	20.7510i	0.395328	+	1.08616i
$366$	0.449022	+	1.20520i	0.0234707	+	0.0629966i
$367$	3.29045	−	9.04043i	0.171760	−	0.471907i	−0.823707	−	0.567016i	$-0.808098\pi$
$367$	3.29045	−	9.04043i	0.171760	−	0.471907i	0.995467	+	0.0951092i	$0.0303200\pi$
$368$	8.05260	−	4.64917i	0.419771	−	0.242355i
$369$	−4.17068	+	25.9454i	−0.217117	+	1.35067i
$370$	−6.44051	+	3.71843i	−0.334826	+	0.193312i
$371$	0.405117	+	2.09293i	0.0210326	+	0.108660i
$372$	−14.2511	−	5.06509i	−0.738888	−	0.262613i
$373$	−9.29174	+	3.38192i	−0.481108	+	0.175109i	−0.571178	−	0.820826i	$-0.693513\pi$
$373$	−9.29174	+	3.38192i	−0.481108	+	0.175109i	0.0900695	+	0.995935i	$0.471291\pi$
$374$	2.81344	−	1.02401i	0.145480	−	0.0529502i
$375$	0.435265	+	57.4662i	0.0224770	+	2.96754i
$376$	−10.1195	+	1.78435i	−0.521875	+	0.0920207i
$377$	−0.607695			−0.0312979
$378$	8.41530	−	10.8712i	0.432836	−	0.559154i
$379$	7.39121			0.379661			0.189831	−	0.981817i	$-0.439206\pi$
$379$	7.39121			0.379661			0.189831	+	0.981817i	$0.439206\pi$
$380$	−11.5321	+	2.03342i	−0.591585	+	0.104312i
$381$	15.3302	+	8.69675i	0.785390	+	0.445548i
$382$	10.8502	−	3.94915i	0.555144	−	0.202056i
$383$	−0.000181964	0	6.62293e-5i	−9.29790e−6	0	3.38416e-6i	−0.342025	−	0.939691i	$-0.611113\pi$
$383$	−0.000181964	0	6.62293e-5i	−9.29790e−6	0	3.38416e-6i	0.342015	+	0.939694i	$0.388890\pi$
$384$	0.313678	+	1.70341i	0.0160073	+	0.0869268i
$385$	12.5120	−	10.8592i	0.637670	−	0.553438i
$386$	10.1557	−	5.86337i	0.516909	−	0.298438i
$387$	11.9460	+	4.14417i	0.607250	+	0.210660i
$388$	10.4776	−	6.04923i	0.531918	−	0.307103i
$389$	8.01770	−	22.0285i	0.406514	−	1.11689i	−0.552497	−	0.833515i	$-0.686325\pi$
$389$	8.01770	−	22.0285i	0.406514	−	1.11689i	0.959010	−	0.283372i	$-0.0914530\pi$
$390$	−1.38517	−	0.233440i	−0.0701410	−	0.0118207i
$391$	−6.42479	−	17.6520i	−0.324916	−	0.892699i
$392$	2.61203	+	6.49440i	0.131928	+	0.328017i
$393$	8.85594	+	23.7698i	0.446723	+	1.19903i
$394$	−12.9335	+	10.8525i	−0.651582	+	0.546742i
$395$	15.4863	+	26.8231i	0.779203	+	1.34962i
$396$	3.88360	+	2.16443i	0.195158	+	0.108767i
$397$	−3.16688	−	1.82840i	−0.158941	−	0.0917647i	0.418420	−	0.908254i	$-0.362584\pi$
$397$	−3.16688	−	1.82840i	−0.158941	−	0.0917647i	−0.577361	+	0.816489i	$0.695917\pi$
$398$	13.5728	−	11.3890i	0.680345	−	0.570878i
$399$	−8.39707	−	9.52832i	−0.420379	−	0.477013i
$400$	2.23183	−	12.6573i	0.111592	−	0.632867i
$401$	−15.8400	−	2.79302i	−0.791012	−	0.139477i	−0.236477	−	0.971637i	$-0.575993\pi$
$401$	−15.8400	−	2.79302i	−0.791012	−	0.139477i	−0.554535	+	0.832160i	$0.687104\pi$
$402$	2.64951	+	4.50986i	0.132146	+	0.224931i
$403$	−1.28395	+	1.07736i	−0.0639582	+	0.0536673i
$404$	7.24892	+	12.5555i	0.360647	+	0.624659i
$405$	−29.8575	−	23.5497i	−1.48363	−	1.17019i
$406$	7.18342	−	4.30855i	0.356507	−	0.213830i
$407$	0.892155	−	2.45118i	0.0442225	−	0.121500i
$408$	3.49905	−	0.0265028i	0.173229	−	0.00131208i
$409$	2.16648	+	5.95235i	0.107125	+	0.294325i	0.981660	−	0.190638i	$-0.0610555\pi$
$409$	2.16648	+	5.95235i	0.107125	+	0.294325i	−0.874535	+	0.484962i	$0.838833\pi$
$410$	−23.7902	+	28.3520i	−1.17491	+	1.40021i
$411$	6.26698	+	2.22738i	0.309127	+	0.109869i
$412$	−0.186351	−	0.222084i	−0.00918085	−	0.0109413i
$413$	0.571996	+	34.3165i	0.0281461	+	1.68860i
$414$	13.5800	−	24.3663i	0.667420	−	1.19754i
$415$	−16.6687			−0.818233
$416$	0.180368	+	0.0656487i	0.00884328	+	0.00321869i
$417$	1.53545	−	9.11094i	0.0751911	−	0.446165i
$418$	2.64013	−	3.14638i	0.129133	−	0.153895i
$419$	−6.48313	+	2.35967i	−0.316722	+	0.115277i	−0.495489	−	0.868614i	$-0.665011\pi$
$419$	−6.48313	+	2.35967i	−0.316722	+	0.115277i	0.178768	+	0.983891i	$0.442789\pi$
$420$	18.0289	−	7.06142i	0.879720	−	0.344562i
$421$	0.923275	+	5.23615i	0.0449977	+	0.255194i	0.999005	−	0.0445873i	$-0.0141973\pi$
$421$	0.923275	+	5.23615i	0.0449977	+	0.255194i	−0.954008	+	0.299782i	$0.903086\pi$
$422$			19.0495i			0.927314i
$423$	−23.3119	+	20.1706i	−1.13347	+	0.980729i
$424$	−0.805738			−0.0391301
$425$	−24.3994	−	8.88064i	−1.18354	−	0.430774i
$426$	2.39707	−	0.441414i	0.116139	−	0.0213866i
$427$	−1.83465	+	0.702603i	−0.0887851	+	0.0340013i
$428$	3.94032	−	4.69589i	0.190462	−	0.226984i
$429$	0.424815	−	0.249576i	0.0205103	−	0.0120497i
$430$	11.4471	+	13.6421i	0.552029	+	0.657882i
$431$	−14.1802	−	8.18697i	−0.683038	−	0.394352i	0.117961	−	0.993018i	$-0.462364\pi$
$431$	−14.1802	−	8.18697i	−0.683038	−	0.394352i	−0.800999	+	0.598666i	$0.795698\pi$
$432$	3.42960	+	3.90357i	0.165007	+	0.187811i
$433$			38.7574i			1.86256i	0.364302	+	0.931281i	$0.381308\pi$
$433$			38.7574i			1.86256i	−0.364302	+	0.931281i	$0.618692\pi$
$434$	7.53880	−	21.8384i	0.361874	−	1.04828i
$435$	−11.7366	−	19.9773i	−0.562725	−	0.957840i
$436$	−1.02849	+	5.83285i	−0.0492557	+	0.279343i
$437$	−19.7409	−	16.5646i	−0.944335	−	0.792391i
$438$	−5.87111	−	6.89025i	−0.280533	−	0.329229i
$439$	−9.44073	+	25.9382i	−0.450582	+	1.23796i	0.481734	+	0.876317i	$0.340007\pi$
$439$	−9.44073	+	25.9382i	−0.450582	+	1.23796i	−0.932316	+	0.361645i	$0.882215\pi$
$440$	3.13091	+	5.42290i	0.149260	+	0.258527i
$441$	16.7222	+	12.7031i	0.796296	+	0.604908i
$442$	0.193886	−	0.335820i	0.00922221	−	0.0159733i
$443$	0.680787	+	0.811330i	0.0323452	+	0.0385475i	0.781975	−	0.623310i	$-0.214213\pi$
$443$	0.680787	+	0.811330i	0.0323452	+	0.0385475i	−0.749629	+	0.661858i	$0.769768\pi$
$444$	1.94185	−	2.35013i	0.0921563	−	0.111532i
$445$	−8.24357	+	46.7516i	−0.390783	+	2.21624i
$446$	11.3231	+	9.50125i	0.536167	+	0.449897i
$447$	3.97485	−	23.5858i	0.188004	−	1.11557i
$448$	−2.59754	+	0.502790i	−0.122722	+	0.0237546i
$449$	−35.4815	−	20.4852i	−1.67447	−	0.966758i	−0.965083	−	0.261943i	$-0.915637\pi$
$449$	−35.4815	−	20.4852i	−1.67447	−	0.966758i	−0.709391	−	0.704815i	$-0.751030\pi$
$450$	−13.7349	−	36.0286i	−0.647468	−	1.69840i
$451$		−	12.9816i		−	0.611282i
$452$	6.06834	−	1.07001i	0.285431	−	0.0503291i
$453$	1.80604	−	0.332576i	0.0848550	−	0.0156258i
$454$	20.0988	+	3.54396i	0.943284	+	0.166326i
$455$	0.337332	−	2.11904i	0.0158144	−	0.0993423i
$456$	4.13888	−	2.43156i	0.193821	−	0.113868i
$457$	−3.16049	−	17.9240i	−0.147842	−	0.838451i	−0.965042	−	0.262097i	$-0.915586\pi$
$457$	−3.16049	−	17.9240i	−0.147842	−	0.838451i	0.817200	−	0.576354i	$-0.195525\pi$
$458$	9.48729	−	16.4325i	0.443312	−	0.767839i
$459$	8.96946	−	5.45392i	0.418658	−	0.254567i
$460$	34.0241	−	19.6438i	1.58638	−	0.915898i
$461$	−20.2961	−	7.38716i	−0.945282	−	0.344054i	−0.177032	−	0.984205i	$-0.556650\pi$
$461$	−20.2961	−	7.38716i	−0.945282	−	0.344054i	−0.768249	+	0.640151i	$0.778872\pi$
$462$	−3.25215	+	5.96211i	−0.151304	+	0.277382i
$463$	6.16101	+	5.16970i	0.286326	+	0.240256i	0.774626	−	0.632420i	$-0.217938\pi$
$463$	6.16101	+	5.16970i	0.286326	+	0.240256i	−0.488300	+	0.872676i	$0.662383\pi$
$464$	1.08284	+	2.97507i	0.0502694	+	0.138114i
$465$	−60.2144	−	21.4012i	−2.79238	−	0.992456i
$466$	−0.406649	−	2.30622i	−0.0188377	−	0.106834i
$467$	0.602665	−	1.04385i	0.0278880	−	0.0483034i	−0.851745	−	0.523957i	$-0.824455\pi$
$467$	0.602665	−	1.04385i	0.0278880	−	0.0483034i	0.879633	+	0.475654i	$0.157788\pi$
$468$	0.565504	−	0.108571i	0.0261404	−	0.00501868i
$469$	−6.85184	+	4.10967i	−0.316389	+	0.189767i
$470$	−42.7574	+	7.53928i	−1.97225	+	0.347761i
$471$	−0.493536	+	2.92852i	−0.0227409	+	0.134939i
$472$	−12.7751	−	2.25260i	−0.588023	−	0.103684i
$473$	−6.15147	−	1.08467i	−0.282845	−	0.0498732i
$474$	−9.78773	−	8.08734i	−0.449565	−	0.371464i
$475$	−35.0792	+	6.18541i	−1.60954	+	0.283806i
$476$	0.0890802	+	5.34430i	0.00408298	+	0.244955i
$477$	−2.07482	+	1.24018i	−0.0949995	+	0.0567838i
$478$	−5.01377	+	8.68410i	−0.229324	+	0.397201i
$479$	−4.21195	−	23.8871i	−0.192449	−	1.09143i	−0.916005	−	0.401166i	$-0.868605\pi$
$479$	−4.21195	−	23.8871i	−0.192449	−	1.09143i	0.723557	−	0.690265i	$-0.242506\pi$
$480$	1.32536	+	7.19731i	0.0604943	+	0.328511i
$481$	−0.115549	−	0.317467i	−0.00526856	−	0.0144753i
$482$	−12.2391	−	10.2698i	−0.557475	−	0.467777i
$483$	37.4072	+	20.4045i	1.70209	+	0.928436i
$484$	8.27273	+	3.01103i	0.376033	+	0.136865i
$485$	44.2702	−	25.5594i	2.01020	−	1.16059i
$486$	14.8397	+	4.77313i	0.673143	+	0.216514i
$487$	14.7237	−	25.5022i	0.667196	−	1.15562i	−0.311490	−	0.950250i	$-0.600828\pi$
$487$	14.7237	−	25.5022i	0.667196	−	1.15562i	0.978685	−	0.205367i	$-0.0658388\pi$
$488$	−0.128942	−	0.731264i	−0.00583691	−	0.0331027i
$489$	21.1614	+	12.0048i	0.956953	+	0.542875i
$490$	11.0364	+	27.4404i	0.498576	+	1.23963i
$491$	29.4534	+	5.19343i	1.32921	+	0.234376i	0.792750	−	0.609547i	$-0.208649\pi$
$491$	29.4534	+	5.19343i	1.32921	+	0.234376i	0.536464	+	0.843923i	$0.319760\pi$
$492$	5.08097	−	14.2958i	0.229068	−	0.644506i
$493$	6.29890	−	1.11067i	0.283688	−	0.0500219i
$494$		−	0.531963i		−	0.0239341i
$495$	16.4091	+	9.14523i	0.737535	+	0.411047i
$496$	7.56225	+	4.36607i	0.339555	+	0.196042i
$497$	0.707536	+	3.65531i	0.0317373	+	0.163963i
$498$	6.40303	−	2.38559i	0.286927	−	0.106901i
$499$	8.00532	+	6.71726i	0.358367	+	0.300706i	0.804140	−	0.594440i	$-0.202626\pi$
$499$	8.00532	+	6.71726i	0.358367	+	0.300706i	−0.445772	+	0.895146i	$0.647071\pi$
$500$	5.76148	−	32.6750i	0.257661	−	1.46127i
$501$	14.3735	+	38.5792i	0.642161	+	1.72359i
$502$	9.51856	+	11.3438i	0.424834	+	0.506297i
$503$	16.2725	−	28.1848i	0.725554	−	1.25670i	−0.233192	−	0.972431i	$-0.574917\pi$
$503$	16.2725	−	28.1848i	0.725554	−	1.25670i	0.958746	−	0.284265i	$-0.0917497\pi$
$504$	−5.91492	+	5.29280i	−0.263472	+	0.235760i
$505$	30.6284	+	53.0499i	1.36294	+	2.36069i
$506$	−4.71311	+	12.9492i	−0.209523	+	0.575660i
$507$	−7.51930	+	21.1563i	−0.333944	+	0.939586i
$508$	−7.79522	−	6.54096i	−0.345857	−	0.290208i
$509$	1.22155	−	6.92778i	0.0541445	−	0.307069i	−0.945694	−	0.325059i	$-0.894616\pi$
$509$	1.22155	−	6.92778i	0.0541445	−	0.307069i	0.999838	+	0.0179906i	$0.00572690\pi$
$510$	14.7843	−	0.111980i	0.654660	−	0.00495858i
$511$	10.4431	−	9.06360i	0.461974	−	0.400950i
$512$		−	1.00000i		−	0.0441942i
$513$	6.91522	−	12.6319i	0.305315	−	0.557712i
$514$	−8.45468	−	4.88131i	−0.372920	−	0.215305i
$515$	−0.787376	−	0.938358i	−0.0346959	−	0.0413490i
$516$	−6.34967	−	3.60214i	−0.279529	−	0.158575i
$517$	9.78874	−	11.6658i	0.430508	−	0.513060i
$518$	3.61671	+	2.93347i	0.158909	+	0.128889i
$519$	6.85175	−	19.2781i	0.300758	−	0.846215i
$520$	0.762098	+	0.277381i	0.0334202	+	0.0121640i
$521$	−22.3426			−0.978847			−0.489424	−	0.872046i	$-0.662793\pi$
$521$	−22.3426			−0.978847			−0.489424	+	0.872046i	$0.662793\pi$
$522$	7.36754	+	5.99429i	0.322469	+	0.262363i
$523$		−	20.3935i		−	0.891745i	−0.895096	−	0.445873i	$-0.852893\pi$
$523$		−	20.3935i		−	0.891745i	0.895096	−	0.445873i	$-0.147107\pi$
$524$	−2.54308	−	14.4225i	−0.111095	−	0.630051i
$525$	54.8415	−	21.4799i	2.39348	−	0.937459i
$526$	2.74267	−	0.998249i	0.119586	−	0.0435257i
$527$	11.3394	−	13.5138i	0.493951	−	0.588668i
$528$	−1.97881	−	1.63504i	−0.0861166	−	0.0711559i
$529$	59.6321	+	21.7043i	2.59270	+	0.943666i
$530$	−3.40443			−0.147879
$531$	−36.3638	+	13.8627i	−1.57806	+	0.601589i
$532$	3.77161	+	6.28821i	0.163520	+	0.272628i
$533$	−1.08074	−	1.28798i	−0.0468121	−	0.0557884i
$534$	−3.52435	−	19.1388i	−0.152513	−	0.828215i
$535$	16.6488	−	19.8412i	0.719789	−	0.857811i
$536$	−1.03285	−	2.83774i	−0.0446125	−	0.122572i
$537$	13.9041	−	24.5095i	0.600006	−	1.05766i
$538$	1.16173	−	3.19184i	0.0500859	−	0.137610i
$539$	−9.15207	−	4.88472i	−0.394207	−	0.210400i
$540$	14.4909	+	16.4935i	0.623587	+	0.709767i
$541$	−8.68856	−	15.0490i	−0.373550	−	0.647008i	0.616559	−	0.787309i	$-0.288526\pi$
$541$	−8.68856	−	15.0490i	−0.373550	−	0.647008i	−0.990109	+	0.140301i	$0.955193\pi$
$542$	−0.637805	+	0.535182i	−0.0273961	+	0.0229880i
$543$	9.52251	−	16.7858i	0.408650	−	0.720348i
$544$	−1.98954	−	0.350810i	−0.0853009	−	0.0150409i
$545$	−4.34560	+	24.6451i	−0.186145	+	1.05568i
$546$	0.173692	+	0.862278i	0.00743332	+	0.0369021i
$547$	−23.2533	+	19.5118i	−0.994239	+	0.834266i	−0.986176	−	0.165702i	$-0.947011\pi$
$547$	−23.2533	+	19.5118i	−0.994239	+	0.834266i	−0.00806345	+	0.999967i	$0.502567\pi$
$548$	−3.32552	−	1.91999i	−0.142059	−	0.0820178i
$549$	−1.45758	−	1.68458i	−0.0622080	−	0.0718962i
$550$	9.52382	+	16.4957i	0.406097	+	0.703381i
$551$	6.72160	−	5.64009i	0.286350	−	0.240276i
$552$	−10.2585	+	12.4154i	−0.436630	+	0.528433i
$553$	12.2172	−	15.0627i	0.519527	−	0.640531i
$554$	3.45287	+	9.48668i	0.146698	+	0.403051i
$555$	8.20478	−	9.92986i	0.348274	−	0.421499i
$556$	−1.82447	+	5.01268i	−0.0773746	+	0.212585i
$557$	−0.882347	+	0.509423i	−0.0373862	+	0.0215850i	−0.518577	−	0.855031i	$-0.673538\pi$
$557$	−0.882347	+	0.509423i	−0.0373862	+	0.0215850i	0.481190	+	0.876616i	$0.340205\pi$
$558$	26.1934	−	0.396815i	1.10885	−	0.0167985i
$559$	−0.700620	+	0.404503i	−0.0296331	+	0.0171087i
$560$	−10.9752	+	2.12441i	−0.463787	+	0.0897725i
$561$	−3.94716	+	3.36334i	−0.166649	+	0.142000i
$562$	−3.15501	+	1.14833i	−0.133086	+	0.0484393i
$563$	−19.3067	+	7.02706i	−0.813680	+	0.296155i	−0.715143	−	0.698978i	$-0.753638\pi$
$563$	−19.3067	+	7.02706i	−0.813680	+	0.296155i	−0.0985368	+	0.995133i	$0.531416\pi$
$564$	15.3456	−	9.01546i	0.646167	−	0.379619i
$565$	25.6402	−	4.52105i	1.07869	−	0.190202i
$566$	−28.0120			−1.17743
$567$	−7.08467	+	22.7334i	−0.297528	+	0.954713i
$568$	−1.40722			−0.0590456
$569$	−13.4461	+	2.37091i	−0.563690	+	0.0993937i	−0.448230	−	0.893918i	$-0.647945\pi$
$569$	−13.4461	+	2.37091i	−0.563690	+	0.0993937i	−0.115460	+	0.993312i	$0.536834\pi$
$570$	17.4877	−	10.2739i	0.732480	−	0.430327i
$571$	5.44928	−	1.98337i	0.228045	−	0.0830016i	−0.225470	−	0.974250i	$-0.572392\pi$
$571$	5.44928	−	1.98337i	0.228045	−	0.0830016i	0.453516	+	0.891248i	$0.350170\pi$
$572$	−0.267307	+	0.0972918i	−0.0111767	+	0.00406797i
$573$	−15.2225	+	12.9709i	−0.635927	+	0.541867i
$574$	21.9069	+	7.56243i	0.914376	+	0.315650i
$575$	103.497	−	59.7539i	4.31612	−	2.49191i
$576$	−1.53918	−	2.57506i	−0.0641326	−	0.107294i
$577$	−14.6741	+	8.47208i	−0.610890	+	0.352697i	−0.773314	−	0.634024i	$-0.781402\pi$
$577$	−14.6741	+	8.47208i	−0.610890	+	0.352697i	0.162424	+	0.986721i	$0.448069\pi$
$578$	4.41844	−	12.1396i	0.183783	−	0.504939i
$579$	−12.9376	+	15.6578i	−0.537670	+	0.650717i
$580$	4.57524	+	12.5704i	0.189976	+	0.521956i
$581$	3.73283	+	9.74725i	0.154864	+	0.404384i
$582$	−13.3477	+	16.1541i	−0.553281	+	0.669610i
$583$	0.914740	−	0.767558i	0.0378847	−	0.0317890i
$584$	2.61320	+	4.52619i	0.108135	+	0.187295i
$585$	2.38939	−	0.458736i	0.0987889	−	0.0189664i
$586$	15.3302	+	8.85089i	0.633285	+	0.365627i
$587$	−6.70387	+	5.62522i	−0.276698	+	0.232178i	−0.770567	−	0.637359i	$-0.780027\pi$
$587$	−6.70387	+	5.62522i	−0.276698	+	0.232178i	0.493869	+	0.869537i	$0.335582\pi$
$588$	−8.16670	−	8.96131i	−0.336789	−	0.369558i
$589$	4.20240	−	23.8330i	0.173157	−	0.982022i
$590$	−53.9779	−	9.51776i	−2.22224	−	0.391840i
$591$	14.4293	−	25.4353i	0.593544	−	1.04627i
$592$	−1.34832	+	1.13137i	−0.0554156	+	0.0464992i
$593$	−22.5781	−	39.1064i	−0.927172	−	1.60591i	−0.788030	−	0.615637i	$-0.788899\pi$
$593$	−22.5781	−	39.1064i	−0.927172	−	1.60591i	−0.139142	−	0.990272i	$-0.544434\pi$
$594$	−7.61217	−	1.16457i	−0.312331	−	0.0477828i
$595$	0.376384	+	22.5809i	0.0154303	+	0.925727i
$596$	−4.72305	+	12.9765i	−0.193463	+	0.531537i
$597$	−15.1426	+	26.6926i	−0.619745	+	1.09246i
$598$	0.610424	+	1.67713i	0.0249621	+	0.0685828i
$599$	−8.70535	+	10.3746i	−0.355691	+	0.423896i	−0.913985	−	0.405747i	$-0.867011\pi$
$599$	−8.70535	+	10.3746i	−0.355691	+	0.423896i	0.558295	+	0.829643i	$0.311456\pi$
$600$	4.03158	+	21.8932i	0.164589	+	0.893788i
$601$	18.2122	+	21.7044i	0.742891	+	0.885343i	0.996638	−	0.0819276i	$-0.0261076\pi$
$601$	18.2122	+	21.7044i	0.742891	+	0.885343i	−0.253747	+	0.967271i	$0.581663\pi$
$602$	5.41394	−	9.74892i	0.220656	−	0.397336i
$603$	−7.02747	−	5.71760i	−0.286181	−	0.232839i
$604$	−1.06025			−0.0431409
$605$	34.9542	+	12.7223i	1.42109	+	0.517235i
$606$	−19.3578	−	15.9949i	−0.786358	−	0.649747i
$607$	13.0035	−	15.4969i	0.527795	−	0.629001i	−0.434611	−	0.900618i	$-0.643114\pi$
$607$	13.0035	−	15.4969i	0.527795	−	0.629001i	0.962405	+	0.271617i	$0.0875584\pi$
$608$	−2.60431	+	0.947892i	−0.105619	+	0.0384421i
$609$	−9.05372	+	11.3369i	−0.366875	+	0.459394i
$610$	−0.544808	−	3.08976i	−0.0220586	−	0.125101i
$611$		−	1.97235i		−	0.0797926i
$612$	−5.66315	+	2.15891i	−0.228919	+	0.0872689i
$613$	−20.5005			−0.828007			−0.414003	−	0.910275i	$-0.635870\pi$
$613$	−20.5005			−0.828007			−0.414003	+	0.910275i	$0.635870\pi$
$614$	18.9050	+	6.88085i	0.762943	+	0.277688i
$615$	21.4683	−	60.4032i	0.865684	−	2.43569i
$616$	2.46997	−	3.04526i	0.0995181	−	0.122697i
$617$	−30.2178	+	36.0122i	−1.21652	+	1.44980i	−0.360579	+	0.932729i	$0.617421\pi$
$617$	−30.2178	+	36.0122i	−1.21652	+	1.44980i	−0.855945	+	0.517067i	$0.827024\pi$
$618$	0.436755	+	0.247769i	0.0175689	+	0.00996673i
$619$	8.90410	+	10.6115i	0.357886	+	0.426512i	0.914705	−	0.404122i	$-0.132423\pi$
$619$	8.90410	+	10.6115i	0.357886	+	0.426512i	−0.556819	+	0.830634i	$0.687978\pi$
$620$	31.9523	+	18.4476i	1.28323	+	0.740875i
$621$	−7.30668	+	47.7599i	−0.293207	+	1.91654i
$622$		−	7.40832i		−	0.297047i
$623$	29.1848	−	5.64913i	1.16926	−	0.226327i
$624$	−0.332447	+	0.00251805i	−0.0133085	+	0.000100803i
$625$	13.1845	−	74.7728i	0.527378	−	2.99091i
$626$	−5.22559	−	4.38479i	−0.208857	−	0.175251i
$627$	−2.38245	+	6.70327i	−0.0951459	+	0.267703i
$628$	0.586436	−	1.61122i	0.0234013	−	0.0642946i
$629$	1.77791	+	3.07944i	0.0708900	+	0.122785i
$630$	−24.9919	+	22.3633i	−0.995702	+	0.890976i
$631$	−7.38376	+	12.7890i	−0.293943	+	0.509124i	−0.974738	−	0.223350i	$-0.928301\pi$
$631$	−7.38376	+	12.7890i	−0.293943	+	0.509124i	0.680796	+	0.732473i	$0.261634\pi$
$632$	4.71190	+	5.61542i	0.187429	+	0.223369i
$633$	−11.5193	−	30.9185i	−0.457853	−	1.22890i
$634$	4.40033	−	24.9555i	0.174759	−	0.991109i
$635$	−32.9366	−	27.6371i	−1.30705	−	1.09674i
$636$	1.30776	−	0.487235i	0.0518561	−	0.0193201i
$637$	−1.31468	+	0.277284i	−0.0520897	+	0.0109864i
$638$	−4.06342	−	2.34602i	−0.160873	−	0.0928798i
$639$	−3.62367	+	2.16597i	−0.143350	+	0.0856844i
$640$		−	4.22523i		−	0.167017i
$641$	−24.5076	+	4.32135i	−0.967993	+	0.170683i	−0.635226	−	0.772326i	$-0.719093\pi$
$641$	−24.5076	+	4.32135i	−0.967993	+	0.170683i	−0.332766	+	0.943009i	$0.607982\pi$
$642$	−3.55574	+	10.0045i	−0.140334	+	0.394844i
$643$	1.86065	+	0.328082i	0.0733767	+	0.0129383i	0.210216	−	0.977655i	$-0.432583\pi$
$643$	1.86065	+	0.328082i	0.0733767	+	0.0129383i	−0.136839	+	0.990593i	$0.543694\pi$
$644$	−19.1065	−	15.4970i	−0.752900	−	0.610668i
$645$	−26.8289	−	15.2199i	−1.05639	−	0.599282i
$646$	0.972253	+	5.51392i	0.0382528	+	0.216942i
$647$	−12.9150	+	22.3694i	−0.507740	+	0.879431i	0.492220	+	0.870471i	$0.336185\pi$
$647$	−12.9150	+	22.3694i	−0.507740	+	0.879431i	−0.999960	+	0.00896015i	$0.997148\pi$
$648$	−7.92697	−	4.26183i	−0.311401	−	0.167421i
$649$	16.6492	−	9.61245i	0.653540	−	0.377322i
$650$	2.31820	+	0.843756i	0.0909273	+	0.0330948i
$651$	0.969919	+	40.0039i	0.0380141	+	1.56788i
$652$	−10.7603	−	9.02898i	−0.421407	−	0.353602i
$653$	−12.3181	−	33.8437i	−0.482045	−	1.32441i	−0.907737	−	0.419540i	$-0.862192\pi$
$653$	−12.3181	−	33.8437i	−0.482045	−	1.32441i	0.425692	−	0.904868i	$-0.360031\pi$
$654$	−1.85786	−	10.0890i	−0.0726482	−	0.394511i
$655$	−10.7451	−	60.9386i	−0.419846	−	2.38107i
$656$	−4.37975	+	7.58595i	−0.171001	+	0.296182i
$657$	13.6958	+	7.63300i	0.534322	+	0.297792i
$658$	13.9839	+	23.3146i	0.545149	+	0.908899i
$659$	5.93475	−	1.04646i	0.231185	−	0.0407642i	−0.0568553	−	0.998382i	$-0.518107\pi$
$659$	5.93475	−	1.04646i	0.231185	−	0.0407642i	0.288040	+	0.957618i	$0.406996\pi$
$660$	−8.36093	−	6.90842i	−0.325449	−	0.268910i
$661$	14.8408	+	2.61683i	0.577239	+	0.101783i	0.454643	−	0.890674i	$-0.349767\pi$
$661$	14.8408	+	2.61683i	0.577239	+	0.101783i	0.122596	+	0.992457i	$0.460878\pi$
$662$	11.4566	+	2.02011i	0.445273	+	0.0785136i
$663$	−0.111616	+	0.662301i	−0.00433481	+	0.0257216i
$664$	−3.88510	+	0.685048i	−0.150771	+	0.0265850i
$665$	15.9359	+	26.5691i	0.617969	+	1.03031i
$666$	−1.73061	+	4.98866i	−0.0670596	+	0.193307i
$667$	−14.7193	+	25.4946i	−0.569933	+	0.987153i
$668$	−4.12751	−	23.4083i	−0.159698	−	0.905693i
$669$	−24.1236	−	8.57393i	−0.932674	−	0.331487i
$670$	−4.36405	−	11.9901i	−0.168598	−	0.463219i
$671$	0.842998	+	0.707359i	0.0325436	+	0.0273073i
$672$	3.91192	−	2.38681i	0.150906	−	0.0920731i
$673$	−24.9408	−	9.07770i	−0.961396	−	0.349919i	−0.186815	−	0.982395i	$-0.559817\pi$
$673$	−24.9408	−	9.07770i	−0.961396	−	0.349919i	−0.774580	+	0.632476i	$0.782039\pi$
$674$	16.3853	−	9.46004i	0.631137	−	0.364387i
$675$	44.0792	+	50.1710i	1.69661	+	1.93108i
$676$	6.48158	−	11.2264i	0.249291	−	0.431786i
$677$	−7.07883	−	40.1461i	−0.272062	−	1.54294i	−0.748143	−	0.663537i	$-0.769054\pi$
$677$	−7.07883	−	40.1461i	−0.272062	−	1.54294i	0.476082	−	0.879401i	$-0.342057\pi$
$678$	−9.20225	+	5.40626i	−0.353410	+	0.207626i
$679$	−24.8602	−	20.1638i	−0.954047	−	0.773815i
$680$	−8.40628	−	1.48225i	−0.322366	−	0.0568419i
$681$	−34.7647	+	6.40182i	−1.33219	+	0.245318i
$682$	−12.7445	+	2.24719i	−0.488011	+	0.0860495i
$683$			10.9155i			0.417669i	0.977951	+	0.208835i	$0.0669671\pi$
$683$			10.9155i			0.417669i	−0.977951	+	0.208835i	$0.933033\pi$
$684$	−5.24727	+	6.44939i	−0.200634	+	0.246598i
$685$	−14.0511	−	8.11240i	−0.536864	−	0.309959i
$686$	13.5746	−	12.5988i	0.518282	−	0.481024i
$687$	−5.46164	+	32.4080i	−0.208374	+	1.23644i
$688$	3.22873	+	2.70923i	0.123094	+	0.103288i
$689$	0.0268558	−	0.152307i	0.00102312	−	0.00580243i
$690$	−43.3445	+	52.4578i	−1.65010	+	1.99703i
$691$	−29.3006	−	34.9191i	−1.11465	−	1.32838i	−0.938995	−	0.343931i	$-0.888241\pi$
$691$	−29.3006	−	34.9191i	−1.11465	−	1.32838i	−0.175652	−	0.984452i	$-0.556203\pi$
$692$	−5.90615	+	10.2298i	−0.224518	+	0.388877i
$693$	1.67311	−	11.6435i	0.0635561	−	0.442299i
$694$	−2.41384	−	4.18089i	−0.0916279	−	0.158704i
$695$	−7.70880	+	21.1797i	−0.292411	+	0.803393i
$696$	−3.55656	−	4.17392i	−0.134811	−	0.158212i
$697$	13.5561	+	11.3749i	0.513475	+	0.430856i
$698$	0.624398	−	3.54114i	0.0236338	−	0.134034i
$699$	2.05460	+	3.49724i	0.0777123	+	0.132278i
$700$	−33.3851	+	6.46216i	−1.26184	+	0.244247i
$701$			29.1414i			1.10066i	0.834948	+	0.550329i	$0.185498\pi$
$701$			29.1414i			1.10066i	−0.834948	+	0.550329i	$0.814502\pi$
$702$	−0.852194	+	0.518181i	−0.0321640	+	0.0195575i
$703$	4.22451	+	2.43902i	0.159330	+	0.0919895i
$704$	0.952616	+	1.13528i	0.0359030	+	0.0427876i
$705$	64.8388	−	38.0924i	2.44197	−	1.43464i
$706$	16.4864	−	19.6477i	0.620473	−	0.739451i
$707$	24.1627	−	29.7905i	0.908732	−	1.12039i
$708$	22.0970	−	4.06910i	0.830456	−	0.152926i
$709$	15.3404	+	5.58343i	0.576119	+	0.209690i	0.613613	−	0.789607i	$-0.289715\pi$
$709$	15.3404	+	5.58343i	0.576119	+	0.209690i	−0.0374942	+	0.999297i	$0.511938\pi$
$710$	−5.94583			−0.223143
$711$	20.7766	+	7.20755i	0.779182	+	0.270304i
$712$			11.2356i			0.421070i
$713$	14.0993	+	79.9608i	0.528021	+	2.99456i
$714$	−3.37631	−	8.62026i	−0.126355	−	0.322605i
$715$	−1.12943	+	0.411080i	−0.0422385	+	0.0153735i
$716$	−10.4575	+	12.4628i	−0.390815	+	0.465755i
$717$	2.88632	−	17.1267i	0.107792	−	0.639608i
$718$	−27.8298	−	10.1292i	−1.03860	−	0.378018i
$719$	25.0564			0.934446			0.467223	−	0.884139i	$-0.345254\pi$
$719$	25.0564			0.934446			0.467223	+	0.884139i	$0.345254\pi$
$720$	−6.50341	−	10.8802i	−0.242368	−	0.405482i
$721$	−0.372392	+	0.670568i	−0.0138686	+	0.0249733i
$722$	−7.27575	−	8.67090i	−0.270775	−	0.322698i
$723$	26.0750	+	9.26747i	0.969739	+	0.344661i
$724$	−7.16203	+	8.53537i	−0.266175	+	0.317215i
$725$	13.9173	+	38.2374i	0.516874	+	1.42010i
$726$	−15.2479	+	0.115492i	−0.565904	+	0.00428632i
$727$	6.29728	−	17.3016i	0.233553	−	0.641682i	−0.766447	−	0.642308i	$-0.777977\pi$
$727$	6.29728	−	17.3016i	0.233553	−	0.641682i	1.00000		0.000625865i	$0.000199219\pi$
$728$	−0.00846357	−	0.507765i	−0.000313681	−	0.0188190i
$729$	−26.9721	+	1.22659i	−0.998968	+	0.0454292i
$730$	11.0414	+	19.1242i	0.408659	+	0.707818i
$731$	6.52279	−	5.47327i	0.241254	−	0.202436i
$732$	0.651480	+	1.10891i	0.0240794	+	0.0409867i
$733$	−23.4263	−	4.13069i	−0.865270	−	0.152570i	−0.276641	−	0.960973i	$-0.589221\pi$
$733$	−23.4263	−	4.13069i	−0.865270	−	0.152570i	−0.588630	+	0.808403i	$0.700332\pi$
$734$	1.67060	−	9.47447i	0.0616631	−	0.349709i
$735$	−34.5062	−	37.8636i	−1.27278	−	1.39662i
$736$	7.12294	−	5.97686i	0.262555	−	0.220310i
$737$	3.87586	+	2.23773i	0.142769	+	0.0824278i
$738$	0.398059	+	26.2755i	0.0146528	+	0.967215i
$739$	−14.7812	−	25.6019i	−0.543737	−	0.941780i	−0.998685	−	0.0512620i	$-0.983676\pi$
$739$	−14.7812	−	25.6019i	−0.543737	−	0.941780i	0.454948	−	0.890518i	$-0.349658\pi$
$740$	−5.69696	+	4.78032i	−0.209425	+	0.175728i
$741$	0.321682	+	0.863409i	0.0118173	+	0.0317181i
$742$	0.762396	+	1.99079i	0.0279885	+	0.0730842i
$743$	6.04653	+	16.6127i	0.221826	+	0.609461i	0.999823	−	0.0188063i	$-0.00598660\pi$
$743$	6.04653	+	16.6127i	0.221826	+	0.609461i	−0.777997	+	0.628267i	$0.783764\pi$
$744$	−14.9142	−	2.51345i	−0.546781	−	0.0921476i
$745$	−19.9560	+	54.8286i	−0.731130	+	2.00876i
$746$	−8.56332	+	4.94403i	−0.313525	+	0.181014i
$747$	−8.94993	+	7.74391i	−0.327461	+	0.283335i
$748$	2.59288	−	1.49700i	0.0948051	−	0.0547358i
$749$	−15.3308	−	5.29231i	−0.560176	−	0.193377i
$750$	10.4075	+	56.5175i	0.380030	+	2.06373i
$751$	26.1938	−	9.53375i	0.955824	−	0.347891i	0.183428	−	0.983033i	$-0.441281\pi$
$751$	26.1938	−	9.53375i	0.955824	−	0.347891i	0.772396	+	0.635142i	$0.219058\pi$
$752$	−9.65595	+	3.51448i	−0.352116	+	0.128160i
$753$	−22.3089	−	12.6557i	−0.812980	−	0.461200i
$754$	−0.598463	+	0.105525i	−0.0217947	+	0.00384300i
$755$	−4.47979			−0.163036
$756$	6.39969	−	12.1673i	0.232755	−	0.442522i
$757$	−38.8826			−1.41321			−0.706607	−	0.707606i	$-0.749775\pi$
$757$	−38.8826			−1.41321			−0.706607	+	0.707606i	$0.749775\pi$
$758$	7.27892	−	1.28347i	0.264382	−	0.0466177i
$759$	−0.180778	−	23.8673i	−0.00656182	−	0.866329i
$760$	−11.0038	+	4.00506i	−0.399151	+	0.145279i
$761$	18.2437	−	6.64017i	0.661334	−	0.240706i	0.0105218	−	0.999945i	$-0.496651\pi$
$761$	18.2437	−	6.64017i	0.661334	−	0.240706i	0.650812	+	0.759239i	$0.274429\pi$
$762$	16.6075	+	5.90257i	0.601626	+	0.213827i
$763$	15.3848	−	2.97794i	0.556966	−	0.107809i
$764$	9.99959	−	5.77327i	0.361773	−	0.208870i
$765$	−23.9281	+	9.12192i	−0.865123	+	0.329804i
$766$	−0.000167699	0	9.68208e-5i	−6.05919e−6	0	3.49828e-6i
$767$	0.851608	−	2.33977i	0.0307498	−	0.0844844i
$768$	0.604707	+	1.62306i	0.0218205	+	0.0585672i
$769$	7.44636	+	20.4587i	0.268523	+	0.737760i	0.998524	+	0.0543139i	$0.0172972\pi$
$769$	7.44636	+	20.4587i	0.268523	+	0.737760i	−0.730001	+	0.683446i	$0.760481\pi$
$770$	10.4362	−	12.8670i	0.376095	−	0.463693i
$771$	16.6742	+	2.81007i	0.600508	+	0.101202i
$772$	8.98321	−	7.53781i	0.323313	−	0.271292i
$773$	4.76252	+	8.24893i	0.171296	+	0.296693i	0.938873	−	0.344263i	$-0.111871\pi$
$773$	4.76252	+	8.24893i	0.171296	+	0.296693i	−0.767577	+	0.640956i	$0.778538\pi$
$774$	12.4842	+	2.00680i	0.448734	+	0.0721331i
$775$	97.1945	+	56.1153i	3.49133	+	2.01572i
$776$	9.26795	−	7.77674i	0.332700	−	0.279169i
$777$	−7.64403	−	2.57415i	−0.274228	−	0.0923471i
$778$	4.07069	−	23.0860i	0.145941	−	0.827675i
$779$	23.9077	+	4.21558i	0.856583	+	0.151039i
$780$	−1.40467	+	0.0106393i	−0.0502951	+	0.000380950i
$781$	1.59759	−	1.34054i	0.0571664	−	0.0479683i
$782$	−9.39242	−	16.2681i	−0.335872	−	0.581748i
$783$	−15.5828	−	5.27390i	−0.556883	−	0.188474i
$784$	3.70009	+	5.94216i	0.132146	+	0.212220i
$785$	2.47783	−	6.80778i	0.0884375	−	0.242980i
$786$	12.8490	+	21.8708i	0.458308	+	0.780107i
$787$	16.5672	+	45.5179i	0.590556	+	1.62254i	0.769477	+	0.638675i	$0.220517\pi$
$787$	16.5672	+	45.5179i	0.590556	+	1.62254i	−0.178921	+	0.983863i	$0.557261\pi$
$788$	−10.8525	+	12.9335i	−0.386605	+	0.460738i
$789$	−3.84787	+	3.27873i	−0.136988	+	0.116726i
$790$	19.9089	+	23.7265i	0.708325	+	0.844149i
$791$	−8.38567	−	13.9810i	−0.298160	−	0.497107i
$792$	4.20045	+	1.45717i	0.149256	+	0.0517782i
$793$	0.142527			0.00506128
$794$	−3.43626	−	1.25070i	−0.121948	−	0.0443856i
$795$	5.52560	−	2.05868i	0.195973	−	0.0730139i
$796$	11.3890	−	13.5728i	0.403671	−	0.481077i
$797$	3.46019	−	1.25941i	0.122566	−	0.0446105i	−0.280009	−	0.959997i	$-0.590337\pi$
$797$	3.46019	−	1.25941i	0.122566	−	0.0446105i	0.402575	+	0.915387i	$0.368115\pi$
$798$	−9.92407	−	7.92543i	−0.351308	−	0.280557i
$799$	3.60480	+	20.4438i	0.127529	+	0.723251i
$800$		−	12.8526i		−	0.454408i
$801$	17.2936	+	28.9322i	0.611038	+	1.02227i
$802$	−16.0844			−0.567959
$803$	−7.27843	−	2.64913i	−0.256850	−	0.0934859i
$804$	3.39239	+	3.98126i	0.119640	+	0.140408i
$805$	−80.7293	−	65.4785i	−2.84533	−	2.30781i
$806$	−1.07736	+	1.28395i	−0.0379485	+	0.0452253i
$807$	0.0445599	+	5.88305i	0.00156858	+	0.207093i
$808$	9.31903	+	11.1060i	0.327842	+	0.390707i
$809$	40.2522	+	23.2396i	1.41519	+	0.817061i	0.995871	−	0.0907769i	$-0.0289350\pi$
$809$	40.2522	+	23.2396i	1.41519	+	0.817061i	0.419321	+	0.907838i	$0.362268\pi$
$810$	−33.4933	−	18.0072i	−1.17683	−	0.632710i
$811$			32.7012i			1.14830i	0.818752	+	0.574148i	$0.194666\pi$
$811$			32.7012i			1.14830i	−0.818752	+	0.574148i	$0.805334\pi$
$812$	6.32611	−	5.49048i	0.222003	−	0.192678i
$813$	0.711569	−	1.25432i	0.0249558	−	0.0439909i
$814$	0.452959	−	2.56886i	0.0158762	−	0.0900385i
$815$	−45.4649	−	38.1496i	−1.59257	−	1.33632i
$816$	3.44129	−	0.633704i	0.120469	−	0.0221841i
$817$	3.99518	−	10.9767i	0.139774	−	0.384025i
$818$	3.16718	+	5.48572i	0.110738	+	0.191804i
$819$	−0.803338	−	1.29450i	−0.0280709	−	0.0452334i
$820$	−18.5055	+	32.0524i	−0.646239	+	1.11932i
$821$	−6.51230	−	7.76106i	−0.227281	−	0.270863i	0.640337	−	0.768094i	$-0.278795\pi$
$821$	−6.51230	−	7.76106i	−0.227281	−	0.270863i	−0.867618	+	0.497231i	$0.834350\pi$
$822$	6.55855	+	1.10530i	0.228756	+	0.0385516i
$823$	1.69425	−	9.60855i	0.0590577	−	0.334933i	−0.940936	−	0.338586i	$-0.890052\pi$
$823$	1.69425	−	9.60855i	0.0590577	−	0.334933i	0.999993	+	0.00365252i	$0.00116263\pi$
$824$	−0.222084	−	0.186351i	−0.00773668	−	0.00649184i
$825$	−25.4328	−	21.0145i	−0.885457	−	0.731630i
$826$	6.52230	+	33.6958i	0.226940	+	1.17243i
$827$	−23.3228	−	13.4654i	−0.811014	−	0.468239i	0.0362936	−	0.999341i	$-0.488445\pi$
$827$	−23.3228	−	13.4654i	−0.811014	−	0.468239i	−0.847308	+	0.531102i	$0.821778\pi$
$828$	9.14250	−	26.3543i	0.317724	−	0.915874i
$829$			9.83872i			0.341713i	0.985296	+	0.170856i	$0.0546535\pi$
$829$			9.83872i			0.341713i	−0.985296	+	0.170856i	$0.945347\pi$
$830$	−16.4154	+	2.89449i	−0.569788	+	0.100469i
$831$	−11.3409	−	13.3095i	−0.393411	−	0.461701i
$832$	0.189028	+	0.0333307i	0.00655336	+	0.00115553i
$833$	13.1202	−	5.27692i	0.454589	−	0.182834i
$834$	−0.0699800	−	9.23916i	−0.00242321	−	0.319926i
$835$	−17.4397	−	98.9054i	−0.603525	−	3.42276i
$836$	2.05365	−	3.55703i	0.0710271	−	0.123023i
$837$	−42.2735	+	16.4834i	−1.46119	+	0.569749i
$838$	−5.97489	+	3.44960i	−0.206399	+	0.119165i
$839$	2.27935	+	0.829616i	0.0786920	+	0.0286415i	0.381066	−	0.924548i	$-0.375557\pi$
$839$	2.27935	+	0.829616i	0.0786920	+	0.0286415i	−0.302374	+	0.953189i	$0.597779\pi$
$840$	16.5288	−	10.0848i	0.570297	−	0.347959i
$841$	14.5368	+	12.1978i	0.501268	+	0.420614i
$842$	1.81850	+	4.99628i	0.0626695	+	0.172183i
$843$	4.42637	−	3.77166i	0.152452	−	0.129903i
$844$	3.30791	+	18.7601i	0.113863	+	0.645748i
$845$	27.3862	−	47.4343i	0.942113	−	1.63179i
$846$	−19.4552	+	23.9122i	−0.668883	+	0.822120i
$847$	−0.388188	−	23.2890i	−0.0133383	−	0.800221i
$848$	−0.793497	+	0.139915i	−0.0272488	+	0.00480470i
$849$	45.4652	−	16.9390i	1.56036	−	0.581346i
$850$	−25.5708	−	4.50882i	−0.877071	−	0.154651i
$851$	−16.1174	−	2.84194i	−0.552498	−	0.0974203i
$852$	2.28401	−	0.850956i	0.0782487	−	0.0291533i
$853$	14.7314	−	2.59755i	0.504394	−	0.0889383i	0.0843394	−	0.996437i	$-0.473122\pi$
$853$	14.7314	−	2.59755i	0.504394	−	0.0889383i	0.420055	+	0.907499i	$0.362011\pi$
$854$	−1.68478	+	1.01051i	−0.0576519	+	0.0345790i
$855$	−22.1709	+	27.2502i	−0.758230	+	0.931936i
$856$	3.06502	−	5.30878i	0.104760	−	0.181450i
$857$	−5.74647	−	32.5898i	−0.196296	−	1.11325i	−0.910562	−	0.413373i	$-0.864351\pi$
$857$	−5.74647	−	32.5898i	−0.196296	−	1.11325i	0.714266	−	0.699874i	$-0.246761\pi$
$858$	0.375023	−	0.319553i	0.0128031	−	0.0109094i
$859$	18.8372	+	51.7547i	0.642716	+	1.76585i	0.643023	+	0.765847i	$0.277680\pi$
$859$	18.8372	+	51.7547i	0.642716	+	1.76585i	−0.000307456		1.00000i	$0.500098\pi$
$860$	13.6421	+	11.4471i	0.465193	+	0.390343i
$861$	−40.1293	+	0.972959i	−1.36760	+	0.0331584i
$862$	−15.3865	−	5.60021i	−0.524065	−	0.190744i
$863$	41.9339	−	24.2106i	1.42745	−	0.824137i	0.430529	−	0.902577i	$-0.358327\pi$
$863$	41.9339	−	24.2106i	1.42745	−	0.824137i	0.996919	+	0.0784397i	$0.0249938\pi$
$864$	4.05534	+	3.24872i	0.137966	+	0.110524i
$865$	−24.9549	+	43.2231i	−0.848491	+	1.46963i
$866$	6.73015	+	38.1686i	0.228700	+	1.29702i
$867$	0.169475	+	22.3751i	0.00575569	+	0.759899i
$868$	3.63206	−	22.8158i	0.123280	−	0.774417i
$869$	−10.6987	−	1.88646i	−0.362928	−	0.0639939i
$870$	−15.0273	−	17.6358i	−0.509473	−	0.597910i
$871$	0.570838	−	0.100654i	0.0193421	−	0.00341054i
$872$			5.92283i			0.200572i
$873$	11.8957	−	34.2906i	0.402608	−	1.16056i
$874$	−22.3174	−	12.8849i	−0.754897	−	0.435840i
$875$	−86.1838	+	16.6821i	−2.91355	+	0.563958i
$876$	−6.97839	−	5.76607i	−0.235778	−	0.194817i
$877$	6.47415	+	5.43246i	0.218616	+	0.183441i	0.745518	−	0.666485i	$-0.232202\pi$
$877$	6.47415	+	5.43246i	0.218616	+	0.183441i	−0.526902	+	0.849926i	$0.676646\pi$
$878$	−4.79319	+	27.1835i	−0.161762	+	0.917399i
$879$	−30.2341	−	5.09527i	−1.01977	−	0.171859i
$880$	4.02502	+	4.79684i	0.135684	+	0.161701i
$881$	−2.95687	+	5.12145i	−0.0996194	+	0.172546i	−0.911527	−	0.411240i	$-0.865096\pi$
$881$	−2.95687	+	5.12145i	−0.0996194	+	0.172546i	0.811908	+	0.583786i	$0.198429\pi$
$882$	18.6740	+	9.60629i	0.628787	+	0.323461i
$883$	−16.4041	−	28.4128i	−0.552043	−	0.956166i	−0.998127	−	0.0611754i	$-0.980515\pi$
$883$	−16.4041	−	28.4128i	−0.552043	−	0.956166i	0.446084	−	0.894991i	$-0.352818\pi$
$884$	0.132626	−	0.364386i	0.00446069	−	0.0122556i
$885$	93.3649	−	17.1929i	3.13843	−	0.577933i
$886$	0.811330	+	0.680787i	0.0272572	+	0.0228715i
$887$	−4.06207	+	23.0371i	−0.136391	+	0.773512i	0.837490	+	0.546453i	$0.184022\pi$
$887$	−4.06207	+	23.0371i	−0.136391	+	0.773512i	−0.973881	+	0.227059i	$0.927089\pi$
$888$	1.50426	−	2.65163i	0.0504795	−	0.0889828i
$889$	−8.78529	+	25.4493i	−0.294649	+	0.853541i
$890$			47.4728i			1.59129i
$891$	13.0592	−	2.71296i	0.437501	−	0.0908877i
$892$	12.8010	+	7.39066i	0.428609	+	0.247458i
$893$	18.3056	+	21.8158i	0.612573	+	0.730036i
$894$	−0.181159	−	23.9177i	−0.00605887	−	0.799926i
$895$	−44.1853	+	52.6580i	−1.47695	+	1.76016i
$896$	−2.47077	+	0.946209i	−0.0825425	+	0.0316106i
$897$	−2.00493	−	2.35295i	−0.0669425	−	0.0785628i
$898$	−38.4997	−	14.0127i	−1.28475	−	0.467611i
$899$	−27.6460			−0.922044
$900$	−19.7825	−	33.0962i	−0.659417	−	1.10321i
$901$			1.62778i			0.0542292i
$902$	−2.25424	−	12.7844i	−0.0750580	−	0.425675i
$903$	−2.89193	+	19.0969i	−0.0962373	+	0.635506i
$904$	5.79034	−	2.10751i	0.192584	−	0.0700948i
$905$	−30.2612	+	36.0639i	−1.00592	+	1.19881i
$906$	1.72085	−	0.641139i	0.0571713	−	0.0213004i
$907$	18.3701	+	6.68617i	0.609969	+	0.222011i	0.628490	−	0.777818i	$-0.283673\pi$
$907$	18.3701	+	6.68617i	0.609969	+	0.222011i	−0.0185206	+	0.999828i	$0.505896\pi$
$908$	20.4089			0.677292
$909$	41.0912	+	14.2548i	1.36291	+	0.472804i
$910$	−0.0357605	−	2.14543i	−0.00118545	−	0.0711202i
$911$	−21.0797	−	25.1218i	−0.698401	−	0.832322i	0.293943	−	0.955823i	$-0.405032\pi$
$911$	−21.0797	−	25.1218i	−0.698401	−	0.832322i	−0.992344	+	0.123501i	$0.960588\pi$
$912$	3.65376	−	3.11333i	0.120988	−	0.103093i
$913$	3.75810	−	4.47873i	0.124375	−	0.148224i
$914$	−6.22495	−	17.1029i	−0.205903	−	0.565714i
$915$	2.75266	+	4.68542i	0.0910000	+	0.154895i
$916$	6.48969	−	17.8303i	0.214425	−	0.589129i
$917$	−33.2284	+	19.9301i	−1.09730	+	0.658150i
$918$	7.88613	−	6.92859i	0.260281	−	0.228678i
$919$	15.1520	+	26.2440i	0.499817	+	0.865708i	1.00000		0.000211285i	$-6.72541e-5\pi$
$919$	15.1520	+	26.2440i	0.499817	+	0.865708i	−0.500183	+	0.865920i	$0.666734\pi$
$920$	30.0961	−	25.2536i	0.992239	−	0.832587i
$921$	−34.8448	+	0.263925i	−1.14818	+	0.00869661i
$922$	−21.2705	−	3.75056i	−0.700506	−	0.123518i
$923$	0.0469036	−	0.266004i	0.00154385	−	0.00875562i
$924$	−2.16743	+	6.43626i	−0.0713032	+	0.211737i
$925$	−17.3294	+	14.5411i	−0.569787	+	0.478108i
$926$	6.96512	+	4.02131i	0.228888	+	0.132149i
$927$	−0.858708	−	0.138036i	−0.0282037	−	0.00453369i
$928$	1.58300	+	2.74184i	0.0519646	+	0.0900053i
$929$	6.81394	−	5.71757i	0.223558	−	0.187587i	−0.524129	−	0.851639i	$-0.675609\pi$
$929$	6.81394	−	5.71757i	0.223558	−	0.187587i	0.747687	+	0.664052i	$0.231164\pi$
$930$	−63.0159	−	10.6199i	−2.06637	−	0.348241i
$931$	11.9680	−	15.2687i	0.392234	−	0.500412i
$932$	−0.800942	−	2.20057i	−0.0262357	−	0.0720821i
$933$	4.47986	+	12.0242i	0.146664	+	0.393653i
$934$	0.412247	−	1.13264i	0.0134891	−	0.0370611i
$935$	10.9555	−	6.32518i	0.358284	−	0.206855i
$936$	0.538059	−	0.205120i	0.0175870	−	0.00670455i
$937$	48.4864	−	27.9936i	1.58398	−	0.914511i	0.589710	−	0.807615i	$-0.299242\pi$
$937$	48.4864	−	27.9936i	1.58398	−	0.914511i	0.994270	−	0.106896i	$-0.0340913\pi$
$938$	−6.03411	+	5.23704i	−0.197021	+	0.170996i
$939$	11.1330	+	3.95684i	0.363311	+	0.129126i
$940$	−40.7986	+	14.8495i	−1.33070	+	0.484337i
$941$	22.5029	−	8.19037i	0.733572	−	0.266999i	0.0518962	−	0.998652i	$-0.483474\pi$
$941$	22.5029	−	8.19037i	0.733572	−	0.266999i	0.681676	+	0.731654i	$0.261251\pi$
$942$	0.0224936	+	2.96973i	0.000732880	+	0.0967590i
$943$	−80.2115	+	14.1434i	−2.61205	+	0.460574i
$944$	−12.9722			−0.422209
$945$	27.0402	−	51.4098i	0.879617	−	1.67236i
$946$	−6.24637			−0.203087
$947$	−36.0148	+	6.35038i	−1.17032	+	0.206360i	−0.724831	−	0.688926i	$-0.758082\pi$
$947$	−36.0148	+	6.35038i	−1.17032	+	0.206360i	−0.445492	+	0.895286i	$0.646971\pi$
$948$	−11.0434	−	6.26486i	−0.358672	−	0.203473i
$949$	−0.942675	+	0.343106i	−0.0306005	+	0.0111377i
$950$	−33.4722	+	12.1829i	−1.08598	+	0.395265i
$951$	7.94875	+	43.1652i	0.257756	+	1.39973i
$952$	1.01575	+	5.24764i	0.0329208	+	0.170077i
$953$	−12.4873	+	7.20957i	−0.404505	+	0.233541i	−0.688426	−	0.725307i	$-0.741698\pi$
$953$	−12.4873	+	7.20957i	−0.404505	+	0.233541i	0.283921	+	0.958848i	$0.408365\pi$
$954$	−1.82794	+	1.58163i	−0.0591819	+	0.0512070i
$955$	42.2506	−	24.3934i	1.36720	−	0.789352i
$956$	−3.42962	+	9.42280i	−0.110922	+	0.304755i
$957$	8.01384	+	1.35055i	0.259051	+	0.0436572i
$958$	−8.29591	−	22.7928i	−0.268029	−	0.736403i
$959$	−1.59721	+	10.0333i	−0.0515765	+	0.323992i
$960$	2.55503	+	6.85782i	0.0824632	+	0.221335i
$961$	−34.6636	+	29.0862i	−1.11818	+	0.938265i
$962$	−0.168921	−	0.292579i	−0.00544622	−	0.00943314i
$963$	−0.278568	−	18.3880i	−0.00897674	−	0.592546i
$964$	−13.8365	−	7.98849i	−0.445643	−	0.257292i
$965$	37.9562	−	31.8490i	1.22185	−	1.02526i
$966$	40.3821	+	13.5988i	1.29927	+	0.437534i
$967$	9.54019	−	54.1051i	0.306792	−	1.73990i	−0.308156	−	0.951336i	$-0.599712\pi$
$967$	9.54019	−	54.1051i	0.306792	−	1.73990i	0.614948	−	0.788568i	$-0.289177\pi$
$968$	8.66991	+	1.52874i	0.278661	+	0.0491355i
$969$	−4.91233	−	8.36150i	−0.157807	−	0.268610i
$970$	39.1593	−	32.8585i	1.25733	−	1.05502i
$971$	8.64777	+	14.9784i	0.277520	+	0.480679i	0.970768	−	0.240020i	$-0.0771541\pi$
$971$	8.64777	+	14.9784i	0.277520	+	0.480679i	−0.693248	+	0.720700i	$0.743821\pi$
$972$	15.4431	+	2.12373i	0.495338	+	0.0681186i
$973$	14.1115	−	0.235214i	0.452394	−	0.00754062i
$974$	10.0716	−	27.6715i	0.322715	−	0.886654i
$975$	−4.27281	+	0.0323635i	−0.136839	+	0.00103646i
$976$	−0.253965	−	0.697764i	−0.00812923	−	0.0223349i
$977$	0.938795	−	1.11881i	0.0300347	−	0.0357940i	−0.750818	−	0.660509i	$-0.770340\pi$
$977$	0.938795	−	1.11881i	0.0300347	−	0.0357940i	0.780853	+	0.624715i	$0.214785\pi$
$978$	22.9246	+	8.14776i	0.733047	+	0.260537i
$979$	−10.7032	−	12.7555i	−0.342075	−	0.407669i
$980$	15.6338	+	25.1070i	0.499402	+	0.802015i
$981$	9.11632	+	15.2516i	0.291062	+	0.486947i
$982$	29.9078			0.954396
$983$	−47.7239	−	17.3701i	−1.52216	−	0.554020i	−0.560471	−	0.828174i	$-0.689380\pi$
$983$	−47.7239	−	17.3701i	−1.52216	−	0.554020i	−0.961686	+	0.274155i	$0.911602\pi$
$984$	2.52133	−	14.9609i	0.0803771	−	0.476937i
$985$	−45.8545	+	54.6472i	−1.46104	+	1.74121i
$986$	6.01034	−	2.18758i	0.191408	−	0.0696669i
$987$	−36.7953	−	29.3849i	−1.17121	−	0.935333i
$988$	−0.0923744	−	0.523881i	−0.00293882	−	0.0166669i
$989$			39.1907i			1.24619i
$990$	17.7479	+	6.15688i	0.564064	+	0.195678i
$991$	12.4321			0.394920			0.197460	−	0.980311i	$-0.436731\pi$
$991$	12.4321			0.394920			0.197460	+	0.980311i	$0.436731\pi$
$992$	8.20552	+	2.98656i	0.260525	+	0.0948235i
$993$	−19.8163	+	3.64912i	−0.628852	+	0.115801i
$994$	1.33152	+	3.47691i	0.0422334	+	0.110281i
$995$	48.1211	−	57.3484i	1.52554	−	1.81807i
$996$	5.89150	−	3.46122i	0.186679	−	0.109673i
$997$	15.1347	+	18.0369i	0.479322	+	0.571234i	0.950468	−	0.310821i	$-0.100604\pi$
$997$	15.1347	+	18.0369i	0.479322	+	0.571234i	−0.471146	+	0.882055i	$0.656160\pi$
$998$	9.05014	+	5.22510i	0.286477	+	0.165398i
$999$	−0.207796	−	9.14342i	−0.00657438	−	0.289285i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.ba.a.185.15	yes	144
7.5	odd	6		378.2.bf.a.131.8	yes	144
27.20	odd	18		378.2.bf.a.101.8	yes	144
189.47	even	18	inner	378.2.ba.a.47.15	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.15	✓	144	189.47	even	18	inner
378.2.ba.a.185.15	yes	144	1.1	even	1	trivial
378.2.bf.a.101.8	yes	144	27.20	odd	18
378.2.bf.a.131.8	yes	144	7.5	odd	6

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(-1.49340 + 0.877362i) q^{3} +(0.939693 - 0.342020i) q^{4} +(3.97042 - 1.44511i) q^{5} +(-1.31836 + 1.12336i) q^{6} +(-1.73420 - 1.99814i) q^{7} +(0.866025 - 0.500000i) q^{8} +(1.46047 - 2.62050i) q^{9} +(3.65916 - 2.11262i) q^{10} +(-0.506876 + 1.39263i) q^{11} +(-1.10326 + 1.33522i) q^{12} +(0.0656487 + 0.180368i) q^{13} +(-2.05482 - 1.66664i) q^{14} +(-4.66153 + 5.64163i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-1.01012 - 1.74957i) q^{17} +(0.983240 - 2.83430i) q^{18} +(-2.40015 - 1.38573i) q^{19} +(3.23672 - 2.71593i) q^{20} +(4.34294 + 1.46250i) q^{21} +(-0.257348 + 1.45949i) q^{22} +(9.15708 + 1.61464i) q^{23} +(-0.854639 + 1.50652i) q^{24} +(9.84566 - 8.26149i) q^{25} +(0.0959719 + 0.166228i) q^{26} +(0.118059 + 5.19481i) q^{27} +(-2.31302 - 1.28451i) q^{28} +(-1.08284 + 2.97507i) q^{29} +(-3.61105 + 6.36538i) q^{30} +(2.98656 + 8.20552i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-0.464873 - 2.52447i) q^{33} +(-1.29858 - 1.54759i) q^{34} +(-9.77303 - 5.42734i) q^{35} +(0.476132 - 2.96198i) q^{36} -1.76011 q^{37} +(-2.60431 - 0.947892i) q^{38} +(-0.256288 - 0.211764i) q^{39} +(2.71593 - 3.23672i) q^{40} +(-8.23124 + 2.99593i) q^{41} +(4.53092 + 0.686135i) q^{42} +(0.731893 + 4.15077i) q^{43} +1.48201i q^{44} +(2.01177 - 12.5150i) q^{45} +9.29834 q^{46} +(-9.65595 - 3.51448i) q^{47} +(-0.580052 + 1.63204i) q^{48} +(-0.985115 + 6.93034i) q^{49} +(8.26149 - 9.84566i) q^{50} +(3.04352 + 1.72657i) q^{51} +(0.123379 + 0.147038i) q^{52} +(-0.697789 - 0.402869i) q^{53} +(1.01833 + 5.09539i) q^{54} +6.26182i q^{55} +(-2.50093 - 0.863340i) q^{56} +(4.80016 - 0.0363577i) q^{57} +(-0.549771 + 3.11790i) q^{58} +(-9.93729 - 8.33837i) q^{59} +(-2.45085 + 6.89573i) q^{60} +(0.253965 - 0.697764i) q^{61} +(4.36607 + 7.56225i) q^{62} +(-7.76887 + 1.62624i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.521306 + 0.621268i) q^{65} +(-0.896180 - 2.40539i) q^{66} +(0.524394 - 2.97399i) q^{67} +(-1.54759 - 1.29858i) q^{68} +(-15.0918 + 5.62277i) q^{69} +(-10.5670 - 3.64781i) q^{70} +(-1.21869 - 0.703610i) q^{71} +(-0.0454431 - 2.99966i) q^{72} +5.22639i q^{73} +(-1.73337 + 0.305639i) q^{74} +(-7.45517 + 20.9759i) q^{75} +(-2.72935 - 0.481257i) q^{76} +(3.66169 - 1.40229i) q^{77} +(-0.289167 - 0.164043i) q^{78} +(1.27291 + 7.21904i) q^{79} +(2.11262 - 3.65916i) q^{80} +(-4.73404 - 7.65434i) q^{81} +(-7.58595 + 4.37975i) q^{82} +(-3.70712 - 1.34928i) q^{83} +(4.58123 - 0.111075i) q^{84} +(-6.53893 - 5.48681i) q^{85} +(1.44155 + 3.96062i) q^{86} +(-0.993106 - 5.39300i) q^{87} +(0.257348 + 1.45949i) q^{88} +(-5.61778 + 9.73028i) q^{89} +(-0.192008 - 12.6742i) q^{90} +(0.246553 - 0.443969i) q^{91} +(9.15708 - 1.61464i) q^{92} +(-11.6593 - 9.63381i) q^{93} +(-10.1195 - 1.78435i) q^{94} +(-11.5321 - 2.03342i) q^{95} +(-0.287839 + 1.70797i) q^{96} +(11.9147 - 2.10087i) q^{97} +(0.233291 + 6.99611i) q^{98} +(2.90911 + 3.36217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) \) 144 * q - 18 * q^6 + 24 * q^9 - 24 * q^11 + 6 * q^14 + 12 * q^15 - 30 * q^21 - 42 * q^23 - 6 * q^29 - 18 * q^30 + 6 * q^36 + 48 * q^39 - 48 * q^42 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 12 * q^50 - 36 * q^51 - 90 * q^53 + 6 * q^56 - 6 * q^57 + 18 * q^60 + 54 * q^61 - 24 * q^63 + 72 * q^64 + 78 * q^65 - 72 * q^66 - 54 * q^68 + 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 - 36 * q^74 - 6 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 36 * q^91 - 42 * q^92 + 96 * q^93 - 66 * q^95 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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