LMFDB - Embedded newform 350.2.r.a.223.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(13,350)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("350.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.r (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.15
Character	$\chi$	$=$	350.223
Dual form			350.2.r.a.237.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 - 0.987688i) q^{2} +(-0.217631 - 0.427124i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-0.542612 + 2.16923i) q^{5} +(-0.455911 + 0.148134i) q^{6} +(0.295851 + 2.62916i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(1.62828 - 2.24114i) q^{9} +O(q^{10})$	\(q+(0.156434 - 0.987688i) q^{2} +(-0.217631 - 0.427124i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-0.542612 + 2.16923i) q^{5} +(-0.455911 + 0.148134i) q^{6} +(0.295851 + 2.62916i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(1.62828 - 2.24114i) q^{9} +(2.05764 + 0.875274i) q^{10} +(2.41720 - 1.75620i) q^{11} +(0.0749905 + 0.473471i) q^{12} +(5.43857 - 0.861384i) q^{13} +(2.64307 + 0.119083i) q^{14} +(1.04462 - 0.240329i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-0.545507 + 1.07062i) q^{17} +(-1.95883 - 1.95883i) q^{18} +(1.35998 + 4.18559i) q^{19} +(1.18638 - 1.89539i) q^{20} +(1.05859 - 0.698551i) q^{21} +(-1.35645 - 2.66217i) q^{22} +(6.66780 + 1.05608i) q^{23} +0.479373 q^{24} +(-4.41115 - 2.35410i) q^{25} -5.50636i q^{26} +(-2.73202 - 0.432710i) q^{27} +(0.531084 - 2.59190i) q^{28} +(-6.53744 - 2.12414i) q^{29} +(-0.0739556 - 1.06936i) q^{30} +(-4.79869 + 1.55919i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.27617 - 0.650243i) q^{33} +(0.972101 + 0.706273i) q^{34} +(-5.86379 - 0.784842i) q^{35} +(-2.24114 + 1.62828i) q^{36} +(1.83940 - 0.291332i) q^{37} +(4.34680 - 0.688466i) q^{38} +(-1.55152 - 2.13548i) q^{39} +(-1.68646 - 1.46828i) q^{40} +(1.02842 - 1.41550i) q^{41} +(-0.524350 - 1.15484i) q^{42} +(8.57562 + 8.57562i) q^{43} +(-2.84159 + 0.923290i) q^{44} +(3.97803 + 4.74820i) q^{45} +(2.08615 - 6.42050i) q^{46} +(1.72716 - 0.880034i) q^{47} +(0.0749905 - 0.473471i) q^{48} +(-6.82494 + 1.55568i) q^{49} +(-3.01517 + 3.98857i) q^{50} +0.576007 q^{51} +(-5.43857 - 0.861384i) q^{52} +(0.640698 - 0.326452i) q^{53} +(-0.854765 + 2.63070i) q^{54} +(2.49801 + 6.19641i) q^{55} +(-2.47691 - 0.930008i) q^{56} +(1.49179 - 1.49179i) q^{57} +(-3.12067 + 6.12466i) q^{58} +(-6.62540 - 4.81364i) q^{59} +(-1.06776 - 0.0942391i) q^{60} +(-2.31240 - 3.18274i) q^{61} +(0.789312 + 4.98352i) q^{62} +(6.37404 + 3.61797i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-1.08249 + 12.2649i) q^{65} +(-0.841875 + 1.15874i) q^{66} +(-6.97503 - 3.55395i) q^{67} +(0.849648 - 0.849648i) q^{68} +(-1.00004 - 3.07781i) q^{69} +(-1.69248 + 5.66882i) q^{70} +(-0.129512 + 0.398597i) q^{71} +(1.25765 + 2.46827i) q^{72} +(1.46695 - 9.26194i) q^{73} -1.86233i q^{74} +(-0.0454936 + 2.39643i) q^{75} -4.40099i q^{76} +(5.33246 + 5.83564i) q^{77} +(-2.35190 + 1.19835i) q^{78} +(8.47346 + 2.75319i) q^{79} +(-1.71403 + 1.43601i) q^{80} +(-2.15837 - 6.64277i) q^{81} +(-1.23719 - 1.23719i) q^{82} +(-8.69411 - 4.42987i) q^{83} +(-1.22264 + 0.337239i) q^{84} +(-2.02642 - 1.76426i) q^{85} +(9.81156 - 7.12851i) q^{86} +(0.515475 + 3.25458i) q^{87} +(0.467399 + 2.95104i) q^{88} +(-6.48207 + 4.70950i) q^{89} +(5.31204 - 3.18627i) q^{90} +(3.87372 + 14.0440i) q^{91} +(-6.01511 - 3.06485i) q^{92} +(1.71031 + 1.71031i) q^{93} +(-0.599011 - 1.84357i) q^{94} +(-9.81746 + 0.678965i) q^{95} +(-0.455911 - 0.148134i) q^{96} +(-14.6967 + 7.48832i) q^{97} +(0.468867 + 6.98428i) q^{98} -8.27689i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{7}+O(q^{10}) $ 160 * q + 8 * q^7	$ 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) $ 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$3$	−0.217631	−	0.427124i	−0.125649	−	0.246600i	0.819609	−	0.572923i	$-0.194191\pi$
$3$	−0.217631	−	0.427124i	−0.125649	−	0.246600i	−0.945259	+	0.326322i	$0.894191\pi$
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	−0.542612	+	2.16923i	−0.242663	+	0.970111i
$5$	−0.542612	+	2.16923i	−0.242663	+	0.970111i
$6$	−0.455911	+	0.148134i	−0.186125	+	0.0604756i
$7$	0.295851	+	2.62916i	0.111821	+	0.993728i
$7$	0.295851	+	2.62916i	0.111821	+	0.993728i
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	1.62828	−	2.24114i	0.542761	−	0.747047i
$10$	2.05764	+	0.875274i	0.650684	+	0.276786i
$11$	2.41720	−	1.75620i	0.728814	−	0.529515i	−0.160374	−	0.987056i	$-0.551270\pi$
$11$	2.41720	−	1.75620i	0.728814	−	0.529515i	0.889188	+	0.457542i	$0.151270\pi$
$12$	0.0749905	+	0.473471i	0.0216479	+	0.136679i
$13$	5.43857	−	0.861384i	1.50839	−	0.238905i	0.653184	−	0.757199i	$-0.273433\pi$
$13$	5.43857	−	0.861384i	1.50839	−	0.238905i	0.855202	+	0.518294i	$0.173433\pi$
$14$	2.64307	+	0.119083i	0.706390	+	0.0318262i
$15$	1.04462	−	0.240329i	0.269720	−	0.0620528i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−0.545507	+	1.07062i	−0.132305	+	0.259663i	−0.947649	−	0.319313i	$-0.896548\pi$
$17$	−0.545507	+	1.07062i	−0.132305	+	0.259663i	0.815344	+	0.578977i	$0.196548\pi$
$18$	−1.95883	−	1.95883i	−0.461700	−	0.461700i
$19$	1.35998	+	4.18559i	0.312001	+	0.960240i	0.976971	+	0.213370i	$0.0684440\pi$
$19$	1.35998	+	4.18559i	0.312001	+	0.960240i	−0.664971	+	0.746869i	$0.731556\pi$
$20$	1.18638	−	1.89539i	0.265284	−	0.423821i
$21$	1.05859	−	0.698551i	0.231004	−	0.152436i
$22$	−1.35645	−	2.66217i	−0.289195	−	0.567577i
$23$	6.66780	+	1.05608i	1.39033	+	0.220207i	0.806292	−	0.591518i	$-0.201471\pi$
$23$	6.66780	+	1.05608i	1.39033	+	0.220207i	0.584040	+	0.811725i	$0.301471\pi$
$24$	0.479373			0.0978516
$25$	−4.41115	−	2.35410i	−0.882229	−	0.470820i
$26$		−	5.50636i		−	1.07989i
$27$	−2.73202	−	0.432710i	−0.525778	−	0.0832751i
$28$	0.531084	−	2.59190i	0.100365	−	0.489823i
$29$	−6.53744	−	2.12414i	−1.21397	−	0.394443i	−0.369088	−	0.929394i	$-0.620330\pi$
$29$	−6.53744	−	2.12414i	−1.21397	−	0.394443i	−0.844883	+	0.534951i	$0.820330\pi$
$30$	−0.0739556	−	1.06936i	−0.0135024	−	0.195237i
$31$	−4.79869	+	1.55919i	−0.861870	+	0.280039i	−0.706409	−	0.707804i	$-0.749686\pi$
$31$	−4.79869	+	1.55919i	−0.861870	+	0.280039i	−0.155461	+	0.987842i	$0.549686\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.27617	−	0.650243i	−0.222153	−	0.113193i
$34$	0.972101	+	0.706273i	0.166714	+	0.121125i
$35$	−5.86379	−	0.784842i	−0.991161	−	0.132663i
$36$	−2.24114	+	1.62828i	−0.373523	+	0.271381i
$37$	1.83940	−	0.291332i	0.302395	−	0.0478947i	−0.00339293	−	0.999994i	$-0.501080\pi$
$37$	1.83940	−	0.291332i	0.302395	−	0.0478947i	0.305788	+	0.952100i	$0.401080\pi$
$38$	4.34680	−	0.688466i	0.705145	−	0.111684i
$39$	−1.55152	−	2.13548i	−0.248442	−	0.341951i
$40$	−1.68646	−	1.46828i	−0.266653	−	0.232156i
$41$	1.02842	−	1.41550i	0.160613	−	0.221064i	−0.721124	−	0.692806i	$-0.756374\pi$
$41$	1.02842	−	1.41550i	0.160613	−	0.221064i	0.881737	+	0.471741i	$0.156374\pi$
$42$	−0.524350	−	1.15484i	−0.0809090	−	0.178195i
$43$	8.57562	+	8.57562i	1.30777	+	1.30777i	0.923022	+	0.384747i	$0.125711\pi$
$43$	8.57562	+	8.57562i	1.30777	+	1.30777i	0.384747	+	0.923022i	$0.374289\pi$
$44$	−2.84159	+	0.923290i	−0.428386	+	0.139191i
$45$	3.97803	+	4.74820i	0.593010	+	0.707819i
$46$	2.08615	−	6.42050i	0.307585	−	0.946651i
$47$	1.72716	−	0.880034i	0.251933	−	0.128366i	−0.323464	−	0.946240i	$-0.604848\pi$
$47$	1.72716	−	0.880034i	0.251933	−	0.128366i	0.575397	+	0.817874i	$0.304848\pi$
$48$	0.0749905	−	0.473471i	0.0108239	−	0.0683397i
$49$	−6.82494	+	1.55568i	−0.974992	+	0.222240i
$50$	−3.01517	+	3.98857i	−0.426410	+	0.564070i
$51$	0.576007			0.0806571
$52$	−5.43857	−	0.861384i	−0.754193	−	0.119452i
$53$	0.640698	−	0.326452i	0.0880066	−	0.0448416i	−0.409433	−	0.912340i	$-0.634274\pi$
$53$	0.640698	−	0.326452i	0.0880066	−	0.0448416i	0.497440	+	0.867498i	$0.334274\pi$
$54$	−0.854765	+	2.63070i	−0.116319	+	0.357993i
$55$	2.49801	+	6.19641i	0.336831	+	0.835524i
$56$	−2.47691	−	0.930008i	−0.330991	−	0.124278i
$57$	1.49179	−	1.49179i	0.197593	−	0.197593i
$58$	−3.12067	+	6.12466i	−0.409764	+	0.804207i
$59$	−6.62540	−	4.81364i	−0.862554	−	0.626682i	0.0660246	−	0.997818i	$-0.478968\pi$
$59$	−6.62540	−	4.81364i	−0.862554	−	0.626682i	−0.928579	+	0.371136i	$0.878968\pi$
$60$	−1.06776	−	0.0942391i	−0.137847	−	0.0121662i
$61$	−2.31240	−	3.18274i	−0.296072	−	0.407508i	0.634903	−	0.772592i	$-0.281040\pi$
$61$	−2.31240	−	3.18274i	−0.296072	−	0.407508i	−0.930975	+	0.365084i	$0.881040\pi$
$62$	0.789312	+	4.98352i	0.100243	+	0.632908i
$63$	6.37404	+	3.61797i	0.803054	+	0.455822i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−1.08249	+	12.2649i	−0.134266	+	1.52128i
$66$	−0.841875	+	1.15874i	−0.103628	+	0.142631i
$67$	−6.97503	−	3.55395i	−0.852135	−	0.434185i	−0.0273469	−	0.999626i	$-0.508706\pi$
$67$	−6.97503	−	3.55395i	−0.852135	−	0.434185i	−0.824789	+	0.565441i	$0.808706\pi$
$68$	0.849648	−	0.849648i	0.103035	−	0.103035i
$69$	−1.00004	−	3.07781i	−0.120391	−	0.370525i
$70$	−1.69248	+	5.66882i	−0.202290	+	0.677554i
$71$	−0.129512	+	0.398597i	−0.0153702	+	0.0473047i	−0.958447	−	0.285269i	$-0.907917\pi$
$71$	−0.129512	+	0.398597i	−0.0153702	+	0.0473047i	0.943077	+	0.332574i	$0.107917\pi$
$72$	1.25765	+	2.46827i	0.148215	+	0.290888i
$73$	1.46695	−	9.26194i	0.171693	−	1.08403i	−0.739834	−	0.672789i	$-0.765096\pi$
$73$	1.46695	−	9.26194i	0.171693	−	1.08403i	0.911527	−	0.411239i	$-0.134904\pi$
$74$		−	1.86233i		−	0.216491i
$75$	−0.0454936	+	2.39643i	−0.00525314	+	0.276716i
$76$		−	4.40099i		−	0.504828i
$77$	5.33246	+	5.83564i	0.607690	+	0.665033i
$78$	−2.35190	+	1.19835i	−0.266300	+	0.135687i
$79$	8.47346	+	2.75319i	0.953338	+	0.309758i	0.744071	−	0.668100i	$-0.232892\pi$
$79$	8.47346	+	2.75319i	0.953338	+	0.309758i	0.209267	+	0.977859i	$0.432892\pi$
$80$	−1.71403	+	1.43601i	−0.191634	+	0.160551i
$81$	−2.15837	−	6.64277i	−0.239819	−	0.738085i
$82$	−1.23719	−	1.23719i	−0.136625	−	0.136625i
$83$	−8.69411	−	4.42987i	−0.954302	−	0.486241i	−0.0937456	−	0.995596i	$-0.529884\pi$
$83$	−8.69411	−	4.42987i	−0.954302	−	0.486241i	−0.860557	+	0.509355i	$0.829884\pi$
$84$	−1.22264	+	0.337239i	−0.133401	+	0.0367957i
$85$	−2.02642	−	1.76426i	−0.219796	−	0.191361i
$86$	9.81156	−	7.12851i	1.05801	−	0.768687i
$87$	0.515475	+	3.25458i	0.0552647	+	0.348927i
$88$	0.467399	+	2.95104i	0.0498249	+	0.314582i
$89$	−6.48207	+	4.70950i	−0.687098	+	0.499206i	−0.875705	−	0.482847i	$-0.839603\pi$
$89$	−6.48207	+	4.70950i	−0.687098	+	0.499206i	0.188607	+	0.982053i	$0.439603\pi$
$90$	5.31204	−	3.18627i	0.559938	−	0.335863i
$91$	3.87372	+	14.0440i	0.406076	+	1.47221i
$92$	−6.01511	−	3.06485i	−0.627118	−	0.319533i
$93$	1.71031	+	1.71031i	0.177351	+	0.177351i
$94$	−0.599011	−	1.84357i	−0.0617833	−	0.190149i
$95$	−9.81746	+	0.678965i	−1.00725	+	0.0696604i
$96$	−0.455911	−	0.148134i	−0.0465312	−	0.0151189i
$97$	−14.6967	+	7.48832i	−1.49222	+	0.760324i	−0.994272	−	0.106882i	$-0.965913\pi$
$97$	−14.6967	+	7.48832i	−1.49222	+	0.760324i	−0.497949	+	0.867207i	$0.665913\pi$
$98$	0.468867	+	6.98428i	0.0473627	+	0.705519i
$99$		−	8.27689i		−	0.831858i
$100$	3.46779	+	3.60200i	0.346779	+	0.360200i
$101$		−	12.3951i		−	1.23336i	−0.787216	−	0.616678i	$-0.788478\pi$
$101$		−	12.3951i		−	1.23336i	0.787216	−	0.616678i	$-0.211522\pi$
$102$	0.0901073	−	0.568915i	0.00892195	−	0.0563310i
$103$	4.55049	+	8.93084i	0.448373	+	0.879981i	0.998977	+	0.0452151i	$0.0143973\pi$
$103$	4.55049	+	8.93084i	0.448373	+	0.879981i	−0.550604	+	0.834766i	$0.685603\pi$
$104$	−1.70156	+	5.23686i	−0.166852	+	0.513516i
$105$	0.940916	+	2.67537i	0.0918240	+	0.261090i
$106$	−0.222205	−	0.683878i	−0.0215825	−	0.0664241i
$107$	−2.08190	+	2.08190i	−0.201265	+	0.201265i	−0.800542	−	0.599277i	$-0.795455\pi$
$107$	−2.08190	+	2.08190i	−0.201265	+	0.201265i	0.599277	+	0.800542i	$0.295455\pi$
$108$	2.46459	+	1.25577i	0.237156	+	0.120837i
$109$	7.32588	−	10.0832i	0.701692	−	0.965796i	−0.298244	−	0.954490i	$-0.596401\pi$
$109$	7.32588	−	10.0832i	0.701692	−	0.965796i	0.999936	−	0.0113064i	$-0.00359903\pi$
$110$	6.51090	−	1.49792i	0.620790	−	0.142821i
$111$	−0.524745	−	0.722250i	−0.0498066	−	0.0685529i
$112$	−1.30603	+	2.30093i	−0.123408	+	0.217417i
$113$	−2.07787	−	13.1192i	−0.195470	−	1.23415i	−0.868934	−	0.494929i	$-0.835194\pi$
$113$	−2.07787	−	13.1192i	−0.195470	−	1.23415i	0.673464	−	0.739220i	$-0.264806\pi$
$114$	−1.24006	−	1.70679i	−0.116142	−	0.159856i
$115$	−5.90890	+	13.8910i	−0.551007	+	1.29534i
$116$	5.56108	+	4.04036i	0.516333	+	0.375138i
$117$	6.92504	−	13.5912i	0.640221	−	1.25650i
$118$	−5.79081	+	5.79081i	−0.533088	+	0.533088i
$119$	−2.97621	−	1.11748i	−0.272829	−	0.102439i
$120$	−0.260113	+	1.03987i	−0.0237450	+	0.0949269i
$121$	−0.640557	+	1.97143i	−0.0582324	+	0.179221i
$122$	−3.50529	+	1.78604i	−0.317354	+	0.161700i
$123$	−0.828412	−	0.131208i	−0.0746954	−	0.0118306i
$124$	5.04564			0.453112
$125$	7.50013	−	8.29144i	0.670832	−	0.741609i
$126$	4.57055	−	5.72959i	0.407177	−	0.510432i
$127$	−1.56938	+	9.90868i	−0.139260	+	0.879253i	0.814823	+	0.579710i	$0.196834\pi$
$127$	−1.56938	+	9.90868i	−0.139260	+	0.879253i	−0.954083	+	0.299543i	$0.903166\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$	1.79654	−	5.52917i	0.158176	−	0.486817i
$130$	11.9446	+	2.98781i	1.04761	+	0.262049i
$131$	0.464917	−	0.151061i	0.0406200	−	0.0131982i	−0.288637	−	0.957439i	$-0.593202\pi$
$131$	0.464917	−	0.151061i	0.0406200	−	0.0131982i	0.329257	+	0.944241i	$0.393202\pi$
$132$	1.01278	+	1.01278i	0.0881510	+	0.0881510i
$133$	−10.6022	+	4.81391i	−0.919329	+	0.417419i
$134$	−4.60133	+	6.33319i	−0.397495	+	0.547105i
$135$	2.42108	−	5.69160i	0.208373	−	0.489855i
$136$	−0.706273	−	0.972101i	−0.0605624	−	0.0833570i
$137$	−10.2918	+	1.63006i	−0.879287	+	0.139265i	−0.579726	−	0.814812i	$-0.696840\pi$
$137$	−10.2918	+	1.63006i	−0.879287	+	0.139265i	−0.299561	+	0.954077i	$0.596840\pi$
$138$	−3.19636	+	0.506254i	−0.272092	+	0.0430952i
$139$	−4.76514	+	3.46208i	−0.404174	+	0.293650i	−0.771239	−	0.636546i	$-0.780363\pi$
$139$	−4.76514	+	3.46208i	−0.404174	+	0.293650i	0.367065	+	0.930195i	$0.380363\pi$
$140$	5.33427	+	2.55844i	0.450828	+	0.216228i
$141$	−0.751768	−	0.546191i	−0.0633103	−	0.0459976i
$142$	0.373429	+	0.190272i	0.0313375	+	0.0159672i
$143$	11.6334	−	11.6334i	0.972830	−	0.972830i
$144$	2.63462	−	0.856039i	0.219552	−	0.0713366i
$145$	8.15505	−	13.0286i	0.677240	−	1.08197i
$146$	−8.91843	−	2.89777i	−0.738095	−	0.239821i
$147$	2.14979	+	2.57654i	0.177311	+	0.212509i
$148$	−1.83940	−	0.291332i	−0.151198	−	0.0239474i
$149$		−	12.9491i		−	1.06083i	−0.847737	−	0.530417i	$-0.822035\pi$
$149$		−	12.9491i		−	1.06083i	0.847737	−	0.530417i	$-0.177965\pi$
$150$	2.35981	+	0.419818i	0.192678	+	0.0342780i
$151$	−18.6207			−1.51533			−0.757666	−	0.652642i	$-0.773661\pi$
$151$	−18.6207			−1.51533			−0.757666	+	0.652642i	$0.773661\pi$
$152$	−4.34680	−	0.688466i	−0.352572	−	0.0558420i
$153$	1.51117	+	2.96583i	0.122170	+	0.239773i
$154$	6.59797	−	4.35392i	0.531680	−	0.350849i
$155$	−0.778419	−	11.2555i	−0.0625242	−	0.904064i
$156$	0.815681	+	2.51041i	0.0653068	+	0.200994i
$157$	15.9654	+	15.9654i	1.27418	+	1.27418i	0.943876	+	0.330300i	$0.107150\pi$
$157$	15.9654	+	15.9654i	1.27418	+	1.27418i	0.330300	+	0.943876i	$0.392850\pi$
$158$	4.04484	−	7.93844i	0.321790	−	0.631548i
$159$	−0.278871	−	0.202612i	−0.0221159	−	0.0160682i
$160$	1.15020	+	1.91756i	0.0909309	+	0.151597i
$161$	−0.803916	+	17.8431i	−0.0633575	+	1.40624i
$162$	−6.89863	+	1.09264i	−0.542007	+	0.0858455i
$163$	−0.0338154	−	0.213502i	−0.00264863	−	0.0167228i	0.986329	−	0.164790i	$-0.0526947\pi$
$163$	−0.0338154	−	0.213502i	−0.00264863	−	0.0167228i	−0.988977	+	0.148067i	$0.952695\pi$
$164$	−1.41550	+	1.02842i	−0.110532	+	0.0803063i
$165$	2.10300	−	2.41549i	0.163718	−	0.188046i
$166$	−5.73539	+	7.89408i	−0.445152	+	0.612700i
$167$	3.09960	−	6.08331i	0.239854	−	0.470741i	−0.739429	−	0.673234i	$-0.764905\pi$
$167$	3.09960	−	6.08331i	0.239854	−	0.470741i	0.979284	+	0.202494i	$0.0649045\pi$
$168$	0.141823	+	1.26035i	0.0109419	+	0.0972379i
$169$	16.4723	−	5.35217i	1.26710	−	0.411705i
$170$	−2.05954	+	1.72548i	−0.157960	+	0.132338i
$171$	11.5949	+	3.76742i	0.886686	+	0.288102i
$172$	−5.50588	−	10.8059i	−0.419820	−	0.823943i
$173$	2.03679	−	12.8598i	0.154854	−	0.977711i	−0.780797	−	0.624785i	$-0.785187\pi$
$173$	2.03679	−	12.8598i	0.154854	−	0.977711i	0.935651	−	0.352926i	$-0.114813\pi$
$174$	3.29515			0.249804
$175$	4.88427	−	12.2941i	0.369216	−	0.929344i
$176$	2.98783			0.225216
$177$	−0.614130	+	3.87747i	−0.0461609	+	0.291448i
$178$	3.63750	+	7.13899i	0.272642	+	0.535090i
$179$	−16.9492	−	5.50713i	−1.26684	−	0.411622i	−0.402914	−	0.915238i	$-0.632003\pi$
$179$	−16.9492	−	5.50713i	−1.26684	−	0.411622i	−0.863928	+	0.503616i	$0.832003\pi$
$180$	−2.31606	−	5.74508i	−0.172629	−	0.428213i
$181$	21.9652	−	7.13692i	1.63266	−	0.530483i	0.657779	−	0.753211i	$-0.271496\pi$
$181$	21.9652	−	7.13692i	1.63266	−	0.530483i	0.974881	+	0.222727i	$0.0714959\pi$
$182$	14.4771	−	1.62906i	1.07311	−	0.120754i
$183$	−0.856177	+	1.68034i	−0.0632905	+	0.124215i
$184$	−3.96809	+	5.46160i	−0.292531	+	0.402635i
$185$	−0.366112	+	4.14817i	−0.0269171	+	0.304979i
$186$	1.95680	−	1.42170i	0.143480	−	0.104244i
$187$	0.561619	+	3.54592i	0.0410697	+	0.259304i
$188$	−1.91458	+	0.303239i	−0.139635	+	0.0221160i
$189$	0.329392	−	7.31094i	0.0239597	−	0.531793i
$190$	−0.865183	+	9.80280i	−0.0627669	+	0.711170i
$191$	6.24991	+	4.54082i	0.452227	+	0.328562i	0.790475	−	0.612495i	$-0.209834\pi$
$191$	6.24991	+	4.54082i	0.452227	+	0.328562i	−0.338247	+	0.941057i	$0.609834\pi$
$192$	−0.217631	+	0.427124i	−0.0157062	+	0.0308251i
$193$	−2.67420	−	2.67420i	−0.192493	−	0.192493i	0.604280	−	0.796772i	$-0.293461\pi$
$193$	−2.67420	−	2.67420i	−0.192493	−	0.192493i	−0.796772	+	0.604280i	$0.793461\pi$
$194$	5.09707	+	15.6872i	0.365948	+	1.12627i
$195$	5.47423	−	2.20687i	0.392018	−	0.158037i
$196$	6.97164	+	0.629487i	0.497974	+	0.0449634i
$197$	−3.73471	−	7.32979i	−0.266087	−	0.522226i	0.718844	−	0.695171i	$-0.244672\pi$
$197$	−3.73471	−	7.32979i	−0.266087	−	0.522226i	−0.984931	+	0.172946i	$0.944672\pi$
$198$	−8.17498	−	1.29479i	−0.580971	−	0.0920167i
$199$	−19.0415			−1.34982			−0.674910	−	0.737900i	$-0.735817\pi$
$199$	−19.0415			−1.34982			−0.674910	+	0.737900i	$0.735817\pi$
$200$	4.10014	−	2.86162i	0.289924	−	0.202347i
$201$			3.75266i			0.264692i
$202$	−12.2425	−	1.93902i	−0.861377	−	0.136429i
$203$	3.65060	−	17.8164i	0.256222	−	1.25047i
$204$	−0.547815	−	0.177996i	−0.0383547	−	0.0124622i
$205$	2.51252	+	2.99896i	0.175482	+	0.209456i
$206$	9.53274	−	3.09737i	0.664177	−	0.215804i
$207$	13.2239	−	13.2239i	0.919123	−	0.919123i
$208$	4.90620	+	2.49983i	0.340184	+	0.173332i
$209$	10.6381	+	7.72902i	0.735851	+	0.534627i
$210$	2.78963	−	0.510811i	0.192503	−	0.0352493i
$211$	16.1031	−	11.6996i	1.10858	−	0.805433i	0.126144	−	0.992012i	$-0.459740\pi$
$211$	16.1031	−	11.6996i	1.10858	−	0.805433i	0.982440	+	0.186579i	$0.0597400\pi$
$212$	−0.710219	+	0.112488i	−0.0487780	+	0.00772568i
$213$	0.198436	−	0.0314292i	0.0135966	−	0.00215349i
$214$	1.73059	+	2.38195i	0.118300	+	0.162827i
$215$	−23.2557	+	13.9493i	−1.58603	+	0.951333i
$216$	1.62586	−	2.23780i	0.110626	−	0.152263i
$217$	−5.51905	−	12.1552i	−0.374657	−	0.825150i
$218$	−8.81305	−	8.81305i	−0.596895	−	0.596895i
$219$	−4.27526	+	1.38911i	−0.288895	+	0.0938677i
$220$	−0.460949	−	6.66507i	−0.0310772	−	0.449359i
$221$	−2.04456	+	6.29252i	−0.137532	+	0.423281i
$222$	−0.795446	+	0.405300i	−0.0533868	+	0.0272019i
$223$	−2.90877	+	18.3652i	−0.194786	+	1.22983i	0.675530	+	0.737333i	$0.263915\pi$
$223$	−2.90877	+	18.3652i	−0.194786	+	1.22983i	−0.870315	+	0.492495i	$0.836085\pi$
$224$	2.06829	+	1.64990i	0.138194	+	0.110238i
$225$	−12.4585	+	6.05285i	−0.830565	+	0.403523i
$226$	−13.2827			−0.883553
$227$	2.81827	+	0.446370i	0.187055	+	0.0296266i	0.249259	−	0.968437i	$-0.419813\pi$
$227$	2.81827	+	0.446370i	0.187055	+	0.0296266i	−0.0622040	+	0.998063i	$0.519813\pi$
$228$	−1.87977	+	0.957790i	−0.124491	+	0.0634312i
$229$	4.45918	−	13.7239i	0.294671	−	0.906903i	−0.688661	−	0.725083i	$-0.741801\pi$
$229$	4.45918	−	13.7239i	0.294671	−	0.906903i	0.983332	−	0.181820i	$-0.0581988\pi$
$230$	12.7956	+	8.00917i	0.843716	+	0.528109i
$231$	1.33204	−	3.54764i	0.0876415	−	0.233418i
$232$	4.86056	−	4.86056i	0.319111	−	0.319111i
$233$	1.86797	−	3.66609i	0.122375	−	0.240174i	−0.821690	−	0.569935i	$-0.806968\pi$
$233$	1.86797	−	3.66609i	0.122375	−	0.240174i	0.944064	+	0.329761i	$0.106968\pi$
$234$	−12.3405	−	8.96591i	−0.806725	−	0.586120i
$235$	0.971820	+	4.22414i	0.0633945	+	0.275552i
$236$	4.81364	+	6.62540i	0.313341	+	0.431277i
$237$	−0.668129	−	4.21840i	−0.0433996	−	0.274015i
$238$	−1.56931	+	2.76476i	−0.101723	+	0.179213i
$239$	6.41457	+	8.82890i	0.414924	+	0.571094i	0.964411	−	0.264408i	$-0.0851767\pi$
$239$	6.41457	+	8.82890i	0.414924	+	0.571094i	−0.549487	+	0.835503i	$0.685177\pi$
$240$	0.986379	+	0.419583i	0.0636705	+	0.0270839i
$241$	−10.1319	+	13.9453i	−0.652651	+	0.898297i	−0.999210	−	0.0397307i	$-0.987350\pi$
$241$	−10.1319	+	13.9453i	−0.652651	+	0.898297i	0.346559	+	0.938028i	$0.387350\pi$
$242$	1.84695	+	0.941070i	0.118727	+	0.0604943i
$243$	−8.23530	+	8.23530i	−0.528295	+	0.528295i
$244$	1.21570	+	3.74153i	0.0778271	+	0.239527i
$245$	0.328668	−	15.6490i	0.0209978	−	0.999780i
$246$	−0.259184	+	0.797688i	−0.0165250	+	0.0508587i
$247$	11.0017	+	21.5921i	0.700024	+	1.37387i
$248$	0.789312	−	4.98352i	0.0501214	−	0.316454i
$249$			4.67754i			0.296427i
$250$	−7.01608	−	8.70486i	−0.443736	−	0.550544i
$251$		−	23.2298i		−	1.46625i	−0.680092	−	0.733127i	$-0.738060\pi$
$251$		−	23.2298i		−	1.46625i	0.680092	−	0.733127i	$-0.261940\pi$
$252$	−4.94406	−	5.41058i	−0.311446	−	0.340835i
$253$	17.9721	−	9.15724i	1.12990	−	0.575711i
$254$	9.54118	+	3.10012i	0.598667	+	0.194519i
$255$	−0.312548	+	1.24949i	−0.0195725	+	0.0782463i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	7.84871	+	7.84871i	0.489589	+	0.489589i	0.908176	−	0.418588i	$-0.137475\pi$
$257$	7.84871	+	7.84871i	0.489589	+	0.489589i	−0.418588	+	0.908176i	$0.637475\pi$
$258$	−5.18006	−	2.63937i	−0.322496	−	0.164320i
$259$	1.31015	+	4.74988i	0.0814085	+	0.295143i
$260$	4.81957	−	11.3301i	0.298897	−	0.702664i
$261$	−15.4053	+	11.1926i	−0.953564	+	0.692805i
$262$	−0.0764719	−	0.482825i	−0.00472445	−	0.0298290i
$263$	0.672747	+	4.24756i	0.0414833	+	0.261916i	0.999710	−	0.0240955i	$-0.00767059\pi$
$263$	0.672747	+	4.24756i	0.0414833	+	0.261916i	−0.958226	+	0.286011i	$0.907671\pi$
$264$	1.15874	−	0.841875i	0.0713157	−	0.0518139i
$265$	0.360500	+	1.56696i	0.0221453	+	0.0962575i
$266$	3.09609	+	11.2248i	0.189834	+	0.688234i
$267$	3.42224	+	1.74372i	0.209438	+	0.106714i
$268$	5.53541	+	5.53541i	0.338129	+	0.338129i
$269$	−5.97341	−	18.3843i	−0.364205	−	1.12091i	−0.950477	−	0.310794i	$-0.899405\pi$
$269$	−5.97341	−	18.3843i	−0.364205	−	1.12091i	0.586272	−	0.810114i	$-0.300595\pi$
$270$	−5.24279	−	3.28163i	−0.319066	−	0.199714i
$271$	−13.5960	−	4.41762i	−0.825900	−	0.268351i	−0.134583	−	0.990902i	$-0.542969\pi$
$271$	−13.5960	−	4.41762i	−0.825900	−	0.268351i	−0.691318	+	0.722551i	$0.742969\pi$
$272$	−1.07062	+	0.545507i	−0.0649158	+	0.0330762i
$273$	5.15550	−	4.71097i	0.312025	−	0.285121i
$274$			10.4201i			0.629500i
$275$	−14.7969	+	2.05651i	−0.892287	+	0.124013i
$276$			3.23620i			0.194797i
$277$	−1.59681	+	10.0818i	−0.0959428	+	0.605759i	0.892131	+	0.451777i	$0.149210\pi$
$277$	−1.59681	+	10.0818i	−0.0959428	+	0.605759i	−0.988074	+	0.153982i	$0.950790\pi$
$278$	2.67402	+	5.24807i	0.160377	+	0.314758i
$279$	−4.31927	+	13.2933i	−0.258588	+	0.795851i
$280$	3.36140	−	4.86836i	0.200882	−	0.290940i
$281$	5.27314	+	16.2291i	0.314569	+	0.968144i	0.975931	+	0.218078i	$0.0699786\pi$
$281$	5.27314	+	16.2291i	0.314569	+	0.968144i	−0.661362	+	0.750067i	$0.730021\pi$
$282$	−0.657069	+	0.657069i	−0.0391279	+	0.0391279i
$283$	25.0182	+	12.7474i	1.48717	+	0.757753i	0.993707	−	0.112011i	$-0.0357291\pi$
$283$	25.0182	+	12.7474i	1.48717	+	0.757753i	0.493468	+	0.869764i	$0.335729\pi$
$284$	0.246346	−	0.339066i	0.0146180	−	0.0201199i
$285$	2.42658	+	4.04551i	0.143738	+	0.239635i
$286$	−9.67027	−	13.3100i	−0.571815	−	0.787036i
$287$	4.02584	+	2.28511i	0.237638	+	0.134886i
$288$	−0.433355	−	2.73610i	−0.0255357	−	0.161226i
$289$	9.14370	+	12.5852i	0.537865	+	0.740308i
$290$	−11.5925	−	10.0928i	−0.680735	−	0.592668i
$291$	6.39689	+	4.64762i	0.374993	+	0.272448i
$292$	−4.25725	+	8.35532i	−0.249137	+	0.488958i
$293$	−18.8183	+	18.8183i	−1.09938	+	1.09938i	−0.104894	+	0.994483i	$0.533450\pi$
$293$	−18.8183	+	18.8183i	−1.09938	+	1.09938i	−0.994483	+	0.104894i	$0.966550\pi$
$294$	2.88112	−	1.72026i	0.168030	−	0.100328i
$295$	14.0369	−	11.7601i	0.817261	−	0.684700i
$296$	−0.575491	+	1.77118i	−0.0334497	+	0.102948i
$297$	−7.36378	+	3.75204i	−0.427290	+	0.217715i
$298$	−12.7897	−	2.02569i	−0.740888	−	0.117345i
$299$	37.1729			2.14977
$300$	0.783806	−	2.26509i	0.0452530	−	0.130775i
$301$	−20.0095	+	25.0838i	−1.15333	+	1.44580i
$302$	−2.91292	+	18.3915i	−0.167620	+	1.05831i
$303$	−5.29424	+	2.69755i	−0.304146	+	0.154970i
$304$	−1.35998	+	4.18559i	−0.0780002	+	0.240060i
$305$	8.15884	−	3.28913i	0.467174	−	0.188335i
$306$	3.16571	−	1.02860i	0.180972	−	0.0588013i
$307$	−11.6783	−	11.6783i	−0.666515	−	0.666515i	0.290392	−	0.956908i	$-0.406214\pi$
$307$	−11.6783	−	11.6783i	−0.666515	−	0.666515i	−0.956908	+	0.290392i	$0.906214\pi$
$308$	−3.26816	−	7.19784i	−0.186221	−	0.410135i
$309$	2.82425	−	3.88725i	0.160666	−	0.221138i
$310$	−11.2387	−	0.991914i	−0.638316	−	0.0563369i
$311$	3.89268	+	5.35781i	0.220734	+	0.303814i	0.904994	−	0.425424i	$-0.139875\pi$
$311$	3.89268	+	5.35781i	0.220734	+	0.303814i	−0.684261	+	0.729238i	$0.739875\pi$
$312$	2.60710	−	0.412924i	0.147598	−	0.0233772i
$313$	−31.3141	+	4.95967i	−1.76998	+	0.280337i	−0.954449	−	0.298375i	$-0.903555\pi$
$313$	−31.3141	+	4.95967i	−1.76998	+	0.280337i	−0.815532	+	0.578713i	$0.803555\pi$
$314$	18.2664	−	13.2713i	1.03083	−	0.748942i
$315$	−11.3069	+	11.8636i	−0.637069	+	0.668440i
$316$	−7.20795	−	5.23688i	−0.405479	−	0.294598i
$317$	−23.4292	−	11.9378i	−1.31592	−	0.670493i	−0.351825	−	0.936066i	$-0.614439\pi$
$317$	−23.4292	−	11.9378i	−1.31592	−	0.670493i	−0.964091	+	0.265573i	$0.914439\pi$
$318$	−0.243742	+	0.243742i	−0.0136684	+	0.0136684i
$319$	−19.5327	+	6.34657i	−1.09362	+	0.355340i
$320$	2.07389	−	0.836061i	0.115934	−	0.0467372i
$321$	1.34231	+	0.436144i	0.0749207	+	0.0243432i
$322$	17.4977	+	3.58530i	0.975108	+	0.199801i
$323$	−5.22305	−	0.827249i	−0.290618	−	0.0460294i
$324$			6.98462i			0.388034i
$325$	−26.0181	−	9.00325i	−1.44322	−	0.499410i
$326$	−0.216164			−0.0119722
$327$	−5.90112	−	0.934646i	−0.326333	−	0.0516860i
$328$	0.794328	+	1.55896i	0.0438594	+	0.0860789i
$329$	2.82473	+	4.28063i	0.155732	+	0.235999i
$330$	−2.05677	−	2.45497i	−0.113221	−	0.135142i
$331$	−4.87600	−	15.0068i	−0.268009	−	0.824847i	−0.990985	−	0.133974i	$-0.957226\pi$
$331$	−4.87600	−	15.0068i	−0.268009	−	0.824847i	0.722976	−	0.690873i	$-0.242774\pi$
$332$	6.89968	+	6.89968i	0.378669	+	0.378669i
$333$	2.34215	−	4.59672i	0.128349	−	0.251899i
$334$	−5.52353	−	4.01308i	−0.302234	−	0.219586i
$335$	11.4941	−	13.2020i	0.627989	−	0.721305i
$336$	1.26702	+	0.0570850i	0.0691214	+	0.00311424i
$337$	26.5718	−	4.20857i	1.44746	−	0.229255i	0.617277	−	0.786746i	$-0.288236\pi$
$337$	26.5718	−	4.20857i	1.44746	−	0.229255i	0.830183	+	0.557491i	$0.188236\pi$
$338$	−2.70944	−	17.1067i	−0.147374	−	0.930484i
$339$	−5.15132	+	3.74265i	−0.279781	+	0.203273i
$340$	1.38206	+	2.30411i	0.0749525	+	0.124958i
$341$	−8.86116	+	12.1963i	−0.479859	+	0.660469i
$342$	5.53488	−	10.8628i	0.299292	−	0.587394i
$343$	−6.10929	−	17.4836i	−0.329870	−	0.944026i
$344$	−11.5342	+	3.74768i	−0.621881	+	0.202061i
$345$	7.21913	−	0.499268i	0.388665	−	0.0268797i
$346$	−12.3828	−	4.02343i	−0.665705	−	0.216301i
$347$	15.8893	+	31.1845i	0.852982	+	1.67407i	0.731882	+	0.681431i	$0.238642\pi$
$347$	15.8893	+	31.1845i	0.852982	+	1.67407i	0.121100	+	0.992640i	$0.461358\pi$
$348$	0.515475	−	3.25458i	0.0276323	−	0.174464i
$349$	−6.31517			−0.338043			−0.169022	−	0.985612i	$-0.554061\pi$
$349$	−6.31517			−0.338043			−0.169022	+	0.985612i	$0.554061\pi$
$350$	−11.3786	−	6.74735i	−0.608214	−	0.360661i
$351$	−15.2310			−0.812972
$352$	0.467399	−	2.95104i	0.0249125	−	0.157291i
$353$	−3.32320	−	6.52214i	−0.176876	−	0.347138i	0.785499	−	0.618862i	$-0.212406\pi$
$353$	−3.32320	−	6.52214i	−0.176876	−	0.347138i	−0.962375	+	0.271724i	$0.912406\pi$
$354$	3.73366	+	1.21314i	0.198442	+	0.0644776i
$355$	−0.794374	−	0.497225i	−0.0421610	−	0.0263899i
$356$	7.62013	−	2.47593i	0.403866	−	0.131224i
$357$	0.170412	+	1.51441i	0.00901916	+	0.0801512i
$358$	−8.09076	+	15.8790i	−0.427610	+	0.839232i
$359$	0.174783	−	0.240569i	0.00922472	−	0.0126967i	−0.804380	−	0.594116i	$-0.797502\pi$
$359$	0.174783	−	0.240569i	0.00922472	−	0.0126967i	0.813604	+	0.581419i	$0.197502\pi$
$360$	−6.03666	+	1.38882i	−0.318160	+	0.0731970i
$361$	−0.298275	+	0.216709i	−0.0156987	+	0.0114058i
$362$	−3.61294	−	22.8112i	−0.189892	−	1.19893i
$363$	0.981451	−	0.155447i	0.0515128	−	0.00815883i
$364$	0.655711	−	14.5537i	0.0343686	−	0.762821i
$365$	19.2953	+	8.20779i	1.00996	+	0.429615i
$366$	1.52572	+	1.10850i	0.0797506	+	0.0579422i
$367$	13.9499	−	27.3783i	0.728180	−	1.42913i	−0.168156	−	0.985760i	$-0.553781\pi$
$367$	13.9499	−	27.3783i	0.728180	−	1.42913i	0.896337	−	0.443374i	$-0.146219\pi$
$368$	4.77361	+	4.77361i	0.248842	+	0.248842i
$369$	−1.49778	−	4.60968i	−0.0779711	−	0.239970i
$370$	4.03982	+	1.01052i	0.210020	+	0.0525345i
$371$	1.04784	+	1.58791i	0.0544013	+	0.0824404i
$372$	−1.09809	−	2.15512i	−0.0569331	−	0.111738i
$373$	−35.7071	−	5.65545i	−1.84884	−	0.292828i	−0.869334	−	0.494226i	$-0.835452\pi$
$373$	−35.7071	−	5.65545i	−1.84884	−	0.292828i	−0.979510	+	0.201398i	$0.935452\pi$
$374$	3.59012			0.185641
$375$	−5.17374	−	1.39902i	−0.267171	−	0.0722450i
$376$			1.93844i			0.0999675i
$377$	−37.3840	−	5.92104i	−1.92537	−	0.304949i
$378$	−7.16940	−	1.46902i	−0.368754	−	0.0755582i
$379$	−0.163478	−	0.0531172i	−0.00839730	−	0.00272845i	0.304815	−	0.952411i	$-0.401405\pi$
$379$	−0.163478	−	0.0531172i	−0.00839730	−	0.00272845i	−0.313213	+	0.949683i	$0.601405\pi$
$380$	9.54677	+	2.38803i	0.489739	+	0.122503i
$381$	4.57379	−	1.48611i	0.234322	−	0.0761359i
$382$	5.46262	−	5.46262i	0.279492	−	0.279492i
$383$	−20.0500	−	10.2160i	−1.02451	−	0.522012i	−0.140792	−	0.990039i	$-0.544965\pi$
$383$	−20.0500	−	10.2160i	−1.02451	−	0.522012i	−0.883714	+	0.468027i	$0.844965\pi$
$384$	0.387821	+	0.281768i	0.0197909	+	0.0143789i
$385$	−15.5523	+	8.40087i	−0.792619	+	0.428148i
$386$	−3.05961	+	2.22294i	−0.155730	+	0.113144i
$387$	33.1827	−	5.25562i	1.68677	−	0.267158i
$388$	16.2914	−	2.58030i	0.827069	−	0.130995i
$389$	18.3356	+	25.2368i	0.929653	+	1.27956i	0.959995	+	0.280018i	$0.0903405\pi$
$389$	18.3356	+	25.2368i	0.929653	+	1.27956i	−0.0303415	+	0.999540i	$0.509659\pi$
$390$	−1.32334	−	5.75206i	−0.0670099	−	0.291267i
$391$	−4.76798	+	6.56257i	−0.241127	+	0.331883i
$392$	1.71234	−	6.78733i	0.0864863	−	0.342812i
$393$	−0.165702	−	0.165702i	−0.00835856	−	0.00835856i
$394$	−7.82379	+	2.54210i	−0.394157	+	0.128069i
$395$	−10.5701	+	16.8870i	−0.531840	+	0.849677i
$396$	−2.55770	+	7.87179i	−0.128529	+	0.395572i
$397$	8.85530	−	4.51200i	0.444435	−	0.226451i	−0.217427	−	0.976077i	$-0.569766\pi$
$397$	8.85530	−	4.51200i	0.444435	−	0.226451i	0.661862	+	0.749626i	$0.269766\pi$
$398$	−2.97875	+	18.8071i	−0.149311	+	0.942715i
$399$	4.36351	+	3.48081i	0.218449	+	0.174259i
$400$	−2.18499	−	4.49731i	−0.109249	−	0.224866i
$401$	4.02433			0.200965			0.100483	−	0.994939i	$-0.467961\pi$
$401$	4.02433			0.200965			0.100483	+	0.994939i	$0.467961\pi$
$402$	3.70645	+	0.587045i	0.184861	+	0.0292791i
$403$	−24.7549	+	12.6133i	−1.23313	+	0.628311i
$404$	−3.83029	+	11.7884i	−0.190564	+	0.586495i
$405$	15.5809	−	1.07756i	0.774220	−	0.0535442i
$406$	−17.0260	−	6.39275i	−0.844984	−	0.317267i
$407$	3.93456	−	3.93456i	0.195029	−	0.195029i
$408$	−0.261502	+	0.513226i	−0.0129463	+	0.0254085i
$409$	0.503937	+	0.366132i	0.0249181	+	0.0181041i	0.600175	−	0.799869i	$-0.295098\pi$
$409$	0.503937	+	0.366132i	0.0249181	+	0.0181041i	−0.575256	+	0.817973i	$0.695098\pi$
$410$	3.35508	−	2.01245i	0.165696	−	0.0993877i
$411$	2.93605	+	4.04112i	0.144825	+	0.199334i
$412$	−1.56799	−	9.89991i	−0.0772494	−	0.487733i
$413$	10.6957	−	18.8433i	0.526300	−	0.927221i
$414$	−10.9924	−	15.1297i	−0.540247	−	0.743586i
$415$	14.3269	−	16.4558i	0.703282	−	0.807786i
$416$	3.23656	−	4.45474i	0.158685	−	0.218411i
$417$	2.51578	+	1.28185i	0.123198	+	0.0627727i
$418$	9.29802	−	9.29802i	0.454781	−	0.454781i
$419$	9.19163	+	28.2889i	0.449041	+	1.38200i	0.877991	+	0.478677i	$0.158883\pi$
$419$	9.19163	+	28.2889i	0.449041	+	1.38200i	−0.428951	+	0.903328i	$0.641117\pi$
$420$	−0.0681281	−	2.83519i	−0.00332431	−	0.138343i
$421$	−4.18469	+	12.8791i	−0.203949	+	0.627691i	0.795806	+	0.605552i	$0.207048\pi$
$421$	−4.18469	+	12.8791i	−0.203949	+	0.627691i	−0.999755	+	0.0221390i	$0.992952\pi$
$422$	−9.03647	−	17.7351i	−0.439888	−	0.863330i
$423$	0.840033	−	5.30376i	0.0408438	−	0.257878i
$424$			0.719072i			0.0349212i
$425$	4.92666	−	3.43847i	0.238978	−	0.166790i
$426$		−	0.200910i		−	0.00973410i
$427$	7.68380	−	7.02127i	0.371845	−	0.339783i
$428$	2.62334	−	1.33666i	0.126804	−	0.0646099i
$429$	−7.50067	−	2.43711i	−0.362136	−	0.117665i
$430$	10.1395	+	25.1516i	0.488972	+	1.21292i
$431$	0.763269	+	2.34910i	0.0367654	+	0.113152i	0.967755	−	0.251894i	$-0.0810533\pi$
$431$	0.763269	+	2.34910i	0.0367654	+	0.113152i	−0.930990	+	0.365046i	$0.881053\pi$
$432$	−1.95591	−	1.95591i	−0.0941039	−	0.0941039i
$433$	11.3593	+	5.78787i	0.545895	+	0.278147i	0.705112	−	0.709096i	$-0.250897\pi$
$433$	11.3593	+	5.78787i	0.545895	+	0.278147i	−0.159217	+	0.987244i	$0.550897\pi$
$434$	−12.8689	+	3.54960i	−0.617729	+	0.170386i
$435$	−7.33964	−	0.647787i	−0.351909	−	0.0310590i
$436$	−10.0832	+	7.32588i	−0.482898	+	0.350846i
$437$	4.64777	+	29.3449i	0.222333	+	1.40376i
$438$	0.703215	+	4.43993i	0.0336009	+	0.212148i
$439$	8.12979	−	5.90664i	0.388014	−	0.281909i	−0.376627	−	0.926365i	$-0.622916\pi$
$439$	8.12979	−	5.90664i	0.388014	−	0.281909i	0.764641	+	0.644456i	$0.222916\pi$
$440$	−6.65512	−	0.587372i	−0.317270	−	0.0280019i
$441$	−7.62646	+	17.8287i	−0.363165	+	0.848988i
$442$	5.89521	+	3.00376i	0.280406	+	0.142874i
$443$	10.9709	+	10.9709i	0.521242	+	0.521242i	0.917946	−	0.396705i	$-0.129846\pi$
$443$	10.9709	+	10.9709i	0.521242	+	0.521242i	−0.396705	+	0.917946i	$0.629846\pi$
$444$	0.275875	+	0.849055i	0.0130924	+	0.0402944i
$445$	−6.69875	−	16.6165i	−0.317551	−	0.787700i
$446$	17.6841	+	5.74591i	0.837367	+	0.272077i
$447$	−5.53089	+	2.81813i	−0.261602	+	0.133293i
$448$	1.95314	−	1.78473i	0.0922770	−	0.0843205i
$449$			36.7120i			1.73255i	0.499569	+	0.866274i	$0.333492\pi$
$449$			36.7120i			1.73255i	−0.499569	+	0.866274i	$0.666508\pi$
$450$	4.02939	+	13.2520i	0.189947	+	0.624703i
$451$		−	5.22767i		−	0.246162i
$452$	−2.07787	+	13.1192i	−0.0977350	+	0.617075i
$453$	4.05244	+	7.95337i	0.190400	+	0.373682i
$454$	0.881749	−	2.71374i	0.0413825	−	0.127362i
$455$	−32.5667	+	0.782559i	−1.52675	+	0.0366869i
$456$	0.651938	+	2.00646i	0.0305298	+	0.0939610i
$457$	7.59216	−	7.59216i	0.355146	−	0.355146i	−0.506874	−	0.862020i	$-0.669199\pi$
$457$	7.59216	−	7.59216i	0.355146	−	0.355146i	0.862020	+	0.506874i	$0.169199\pi$
$458$	−12.8574	−	6.55117i	−0.600787	−	0.306116i
$459$	1.95361	−	2.68891i	0.0911865	−	0.125508i
$460$	9.91224	−	11.3851i	0.462160	−	0.530835i
$461$	1.14005	+	1.56915i	0.0530975	+	0.0730824i	0.834740	−	0.550644i	$-0.185618\pi$
$461$	1.14005	+	1.56915i	0.0530975	+	0.0730824i	−0.781643	+	0.623727i	$0.785618\pi$
$462$	−3.29559	−	1.87061i	−0.153325	−	0.0870286i
$463$	2.97360	+	18.7746i	0.138195	+	0.872528i	0.955214	+	0.295917i	$0.0956251\pi$
$463$	2.97360	+	18.7746i	0.138195	+	0.872528i	−0.817019	+	0.576611i	$0.804375\pi$
$464$	−4.04036	−	5.56108i	−0.187569	−	0.258166i
$465$	−4.63810	+	2.78203i	−0.215087	+	0.129013i
$466$	−3.32874	−	2.41847i	−0.154201	−	0.112034i
$467$	17.8957	−	35.1223i	0.828114	−	1.62527i	0.0486528	−	0.998816i	$-0.484507\pi$
$467$	17.8957	−	35.1223i	0.828114	−	1.62527i	0.779462	−	0.626450i	$-0.215493\pi$
$468$	−10.7860	+	10.7860i	−0.498583	+	0.498583i
$469$	7.28034	−	19.3899i	0.336175	−	0.895342i
$470$	4.32416	−	0.299054i	0.199458	−	0.0137943i
$471$	3.34465	−	10.2938i	0.154113	−	0.474312i
$472$	7.29685	−	3.71793i	0.335865	−	0.171132i
$473$	35.7895	+	5.66850i	1.64560	+	0.260638i
$474$	−4.27098			−0.196173
$475$	3.85423	−	21.6648i	0.176844	−	0.994048i
$476$	2.48523	+	1.98249i	0.113910	+	0.0908672i
$477$	0.311613	−	1.96745i	0.0142678	−	0.0900833i
$478$	9.72366	−	4.95445i	0.444750	−	0.226611i
$479$	5.94451	−	18.2953i	0.271612	−	0.835934i	−0.718485	−	0.695543i	$-0.755164\pi$
$479$	5.94451	−	18.2953i	0.271612	−	0.835934i	0.990096	−	0.140391i	$-0.0448361\pi$
$480$	0.568721	−	0.908597i	0.0259584	−	0.0414716i
$481$	9.75275	−	3.16886i	0.444687	−	0.144488i
$482$	12.1887	+	12.1887i	0.555178	+	0.555178i
$483$	7.79619	−	3.53984i	0.354739	−	0.161068i
$484$	1.21841	−	1.67700i	0.0553823	−	0.0762272i
$485$	−8.26934	−	35.9437i	−0.375491	−	1.63212i
$486$	6.84563	+	9.42220i	0.310524	+	0.427400i
$487$	7.63489	−	1.20925i	0.345970	−	0.0547962i	0.0189684	−	0.999820i	$-0.493962\pi$
$487$	7.63489	−	1.20925i	0.345970	−	0.0547962i	0.327001	+	0.945024i	$0.393962\pi$
$488$	3.88565	−	0.615426i	0.175895	−	0.0278590i
$489$	−0.0838328	+	0.0609081i	−0.00379105	+	0.00275436i
$490$	−15.4049	−	2.77267i	−0.695924	−	0.125256i
$491$	−20.1767	−	14.6592i	−0.910560	−	0.661561i	0.0305963	−	0.999532i	$-0.490259\pi$
$491$	−20.1767	−	14.6592i	−0.910560	−	0.661561i	−0.941156	+	0.337971i	$0.890259\pi$
$492$	0.747321	+	0.380779i	0.0336918	+	0.0171669i
$493$	5.84037	−	5.84037i	0.263037	−	0.263037i
$494$	23.0473	−	7.48854i	1.03695	−	0.336925i
$495$	17.9545	+	4.49113i	0.806994	+	0.201861i
$496$	−4.79869	−	1.55919i	−0.215468	−	0.0700096i
$497$	−1.08629	−	0.222582i	−0.0487267	−	0.00998417i
$498$	4.61995	+	0.731729i	0.207025	+	0.0327895i
$499$		−	13.7546i		−	0.615742i	−0.951428	−	0.307871i	$-0.900383\pi$
$499$		−	13.7546i		−	0.615742i	0.951428	−	0.307871i	$-0.0996166\pi$
$500$	−9.69525	+	5.56796i	−0.433585	+	0.249007i
$501$	−3.27290			−0.146222
$502$	−22.9438	−	3.63395i	−1.02403	−	0.162191i
$503$	0.374500	+	0.734997i	0.0166981	+	0.0327719i	0.899205	−	0.437528i	$-0.144146\pi$
$503$	0.374500	+	0.734997i	0.0166981	+	0.0327719i	−0.882507	+	0.470300i	$0.844146\pi$
$504$	−6.11739	+	4.03679i	−0.272490	+	0.179813i
$505$	26.8878	+	6.72571i	1.19649	+	0.299290i
$506$	−6.23305	−	19.1833i	−0.277093	−	0.852804i
$507$	−5.87092	−	5.87092i	−0.260737	−	0.260737i
$508$	4.55452	−	8.93875i	0.202074	−	0.396593i
$509$	24.2054	+	17.5863i	1.07289	+	0.779498i	0.976429	−	0.215839i	$-0.0692486\pi$
$509$	24.2054	+	17.5863i	1.07289	+	0.779498i	0.0964582	+	0.995337i	$0.469249\pi$
$510$	1.18522	+	0.504164i	0.0524822	+	0.0223247i
$511$	24.7851	+	1.11668i	1.09643	+	0.0493992i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	−1.90435	−	12.0236i	−0.0840792	−	0.530855i
$514$	8.97989	−	6.52427i	0.396086	−	0.287773i
$515$	−21.8422	+	5.02510i	−0.962483	+	0.221432i
$516$	−3.41722	+	4.70340i	−0.150435	+	0.207055i
$517$	2.62939	−	5.16047i	0.115640	−	0.226957i
$518$	4.89635	−	0.550971i	0.215133	−	0.0242083i
$519$	−5.93600	+	1.92872i	−0.260561	+	0.0846615i
$520$	−10.4367	−	6.53266i	−0.457679	−	0.286476i
$521$	−0.189421	−	0.0615468i	−0.00829871	−	0.00269641i	0.304865	−	0.952396i	$-0.401389\pi$
$521$	−0.189421	−	0.0615468i	−0.00829871	−	0.00269641i	−0.313163	+	0.949699i	$0.601389\pi$
$522$	8.64489	+	16.9665i	0.378376	+	0.742606i
$523$	−4.05276	+	25.5881i	−0.177215	+	1.11889i	0.725364	+	0.688366i	$0.241672\pi$
$523$	−4.05276	+	25.5881i	−0.177215	+	1.11889i	−0.902579	+	0.430525i	$0.858328\pi$
$524$	−0.488843			−0.0213552
$525$	−6.31406	+	0.589377i	−0.275568	+	0.0257225i
$526$	4.30050			0.187511
$527$	0.948424	−	5.98811i	0.0413140	−	0.260846i
$528$	−0.650243	−	1.27617i	−0.0282982	−	0.0555384i
$529$	21.4699	+	6.97599i	0.933474	+	0.303304i
$530$	1.60406	−	0.110935i	0.0696760	−	0.00481872i
$531$	−21.5761	+	7.01049i	−0.936322	+	0.304229i
$532$	11.5709	−	1.30204i	0.501662	−	0.0564504i
$533$	4.37385	−	8.58417i	0.189453	−	0.371822i
$534$	2.25761	−	3.10733i	0.0976962	−	0.134467i
$535$	−3.38646	−	5.64578i	−0.146409	−	0.244088i
$536$	6.33319	−	4.60133i	0.273552	−	0.198747i
$537$	1.33644	+	8.43794i	0.0576715	+	0.364124i
$538$	−19.0924	+	3.02393i	−0.823131	+	0.130371i
$539$	−13.7652	+	15.7464i	−0.592909	+	0.678244i
$540$	−4.06138	+	4.66488i	−0.174774	+	0.200745i
$541$	−2.36711	−	1.71981i	−0.101770	−	0.0739403i	0.535736	−	0.844385i	$-0.320034\pi$
$541$	−2.36711	−	1.71981i	−0.101770	−	0.0739403i	−0.637506	+	0.770445i	$0.720034\pi$
$542$	−6.49012	+	12.7376i	−0.278775	+	0.547126i
$543$	−7.82866	−	7.82866i	−0.335960	−	0.335960i
$544$	0.371310	+	1.14277i	0.0159198	+	0.0489960i
$545$	17.8977	+	21.3628i	0.766654	+	0.915082i
$546$	−3.84647	−	5.82898i	−0.164614	−	0.249457i
$547$	−10.5132	−	20.6333i	−0.449511	−	0.882214i	−0.998911	−	0.0466551i	$-0.985144\pi$
$547$	−10.5132	−	20.6333i	−0.449511	−	0.882214i	0.549400	−	0.835559i	$-0.314856\pi$
$548$	10.2918	+	1.63006i	0.439643	+	0.0696327i
$549$	−10.8982			−0.465124
$550$	−0.283551	+	14.9364i	−0.0120907	+	0.636892i
$551$		−	30.2518i		−	1.28877i
$552$	3.19636	+	0.506254i	0.136046	+	0.0215476i
$553$	−4.73170	+	23.0926i	−0.201212	+	0.981997i
$554$	9.70792	+	3.15429i	0.412450	+	0.134013i
$555$	1.85146	−	0.746394i	0.0785901	−	0.0316826i
$556$	5.60176	−	1.82012i	0.237568	−	0.0771904i
$557$	7.28548	−	7.28548i	0.308696	−	0.308696i	−0.535708	−	0.844403i	$-0.679955\pi$
$557$	7.28548	−	7.28548i	0.308696	−	0.308696i	0.844403	+	0.535708i	$0.179955\pi$
$558$	12.4540	+	6.34563i	0.527219	+	0.268632i
$559$	54.0259	+	39.2521i	2.28505	+	1.66019i
$560$	−4.28259	−	4.08160i	−0.180972	−	0.172479i
$561$	1.39233	−	1.01158i	0.0587840	−	0.0427091i
$562$	16.8542	−	2.66944i	0.710950	−	0.112603i
$563$	8.79041	−	1.39226i	0.370472	−	0.0586769i	0.0315771	−	0.999501i	$-0.489947\pi$
$563$	8.79041	−	1.39226i	0.370472	−	0.0586769i	0.338894	+	0.940824i	$0.389947\pi$
$564$	0.546191	+	0.751768i	0.0229988	+	0.0316551i
$565$	29.5861	+	2.61123i	1.24469	+	0.109855i
$566$	16.5041	−	22.7160i	0.693721	−	0.954825i
$567$	16.8263	−	7.63996i	0.706640	−	0.320848i
$568$	−0.296355	−	0.296355i	−0.0124348	−	0.0124348i
$569$	−36.5499	+	11.8758i	−1.53225	+	0.497859i	−0.949226	−	0.314594i	$-0.898132\pi$
$569$	−36.5499	+	11.8758i	−1.53225	+	0.497859i	−0.583026	+	0.812453i	$0.698132\pi$
$570$	4.37531	−	1.76385i	0.183261	−	0.0738796i
$571$	0.730626	−	2.24864i	0.0305757	−	0.0941025i	−0.934604	−	0.355690i	$-0.884246\pi$
$571$	0.730626	−	2.24864i	0.0305757	−	0.0941025i	0.965180	+	0.261587i	$0.0842460\pi$
$572$	−14.6589	+	7.46907i	−0.612919	+	0.312298i
$573$	0.579324	−	3.65771i	0.0242016	−	0.152803i
$574$	2.88675	−	3.61880i	0.120491	−	0.151046i
$575$	−26.9265	−	20.3552i	−1.12291	−	0.848869i
$576$	−2.77020			−0.115425
$577$	−1.47394	−	0.233449i	−0.0613610	−	0.00971863i	0.125678	−	0.992071i	$-0.459889\pi$
$577$	−1.47394	−	0.233449i	−0.0613610	−	0.00971863i	−0.187039	+	0.982352i	$0.559889\pi$
$578$	13.8607	−	7.06237i	0.576528	−	0.293756i
$579$	−0.560227	+	1.72420i	−0.0232823	+	0.0716554i
$580$	−11.7820	+	9.87093i	−0.489220	+	0.409868i
$581$	9.07467	−	24.1688i	0.376481	−	1.00269i
$582$	5.59109	−	5.59109i	0.231758	−	0.231758i
$583$	0.975381	−	1.91429i	0.0403962	−	0.0792820i
$584$	7.58647	+	5.51189i	0.313930	+	0.228084i
$585$	25.7248	+	22.3968i	1.06359	+	0.925992i
$586$	15.6428	+	21.5305i	0.646198	+	0.889415i
$587$	−1.13163	−	7.14482i	−0.0467073	−	0.294898i	0.953267	−	0.302131i	$-0.0976979\pi$
$587$	−1.13163	−	7.14482i	−0.0467073	−	0.294898i	−0.999974	+	0.00723222i	$0.997698\pi$
$588$	−1.24837	−	3.11475i	−0.0514821	−	0.128450i
$589$	−13.0522	−	17.9649i	−0.537808	−	0.740229i
$590$	−9.41946	−	15.7038i	−0.387793	−	0.646515i
$591$	−2.31794	+	3.19038i	−0.0953475	+	0.131235i
$592$	1.65935	+	0.845479i	0.0681987	+	0.0347490i
$593$	−25.7853	+	25.7853i	−1.05887	+	1.05887i	−0.0607188	+	0.998155i	$0.519339\pi$
$593$	−25.7853	+	25.7853i	−1.05887	+	1.05887i	−0.998155	+	0.0607188i	$0.980661\pi$
$594$	2.55389	+	7.86007i	0.104787	+	0.322503i
$595$	4.03901	−	5.84974i	0.165583	−	0.239816i
$596$	−4.00150	+	12.3154i	−0.163908	+	0.504457i
$597$	4.14403	+	8.13311i	0.169604	+	0.332866i
$598$	5.81513	−	36.7153i	0.237798	−	1.50140i
$599$			38.0831i			1.55603i	0.628244	+	0.778016i	$0.283774\pi$
$599$			38.0831i			1.55603i	−0.628244	+	0.778016i	$0.716226\pi$
$600$	−2.11458	−	1.12849i	−0.0863275	−	0.0460705i
$601$		−	46.5239i		−	1.89775i	−0.315651	−	0.948875i	$-0.602223\pi$
$601$		−	46.5239i		−	1.89775i	0.315651	−	0.948875i	$-0.397777\pi$
$602$	21.6447	+	23.6872i	0.882174	+	0.965417i
$603$	−19.3222	+	9.84517i	−0.786862	+	0.400926i
$604$	17.7094	+	5.75412i	0.720584	+	0.234132i
$605$	−3.92892	−	2.45924i	−0.159733	−	0.0999822i
$606$	1.83614	+	5.65105i	0.0745880	+	0.229558i
$607$	15.6486	+	15.6486i	0.635156	+	0.635156i	0.949357	−	0.314200i	$-0.101736\pi$
$607$	15.6486	+	15.6486i	0.635156	+	0.635156i	−0.314200	+	0.949357i	$0.601736\pi$
$608$	3.92131	+	1.99801i	0.159030	+	0.0810299i
$609$	−8.40430	+	2.31813i	−0.340559	+	0.0939355i
$610$	−1.97232	−	8.57292i	−0.0798567	−	0.347107i
$611$	8.63525	−	6.27387i	0.349345	−	0.253814i
$612$	−0.520712	−	3.28765i	−0.0210485	−	0.132895i
$613$	−0.619279	−	3.90997i	−0.0250124	−	0.157922i	0.972021	−	0.234895i	$-0.0754746\pi$
$613$	−0.619279	−	3.90997i	−0.0250124	−	0.157922i	−0.997033	+	0.0769726i	$0.975475\pi$
$614$	−13.3614	+	9.70763i	−0.539222	+	0.391768i
$615$	0.734126	−	1.72582i	0.0296028	−	0.0695919i
$616$	−7.62048	+	2.10193i	−0.307038	+	0.0846894i
$617$	−8.22498	−	4.19083i	−0.331125	−	0.168717i	0.280522	−	0.959848i	$-0.409493\pi$
$617$	−8.22498	−	4.19083i	−0.331125	−	0.168717i	−0.611647	+	0.791131i	$0.709493\pi$
$618$	−3.39758	−	3.39758i	−0.136671	−	0.136671i
$619$	−11.9280	−	36.7107i	−0.479428	−	1.47553i	−0.839891	−	0.542755i	$-0.817381\pi$
$619$	−11.9280	−	36.7107i	−0.479428	−	1.47553i	0.360463	−	0.932774i	$-0.382619\pi$
$620$	−2.73782	+	10.9452i	−0.109954	+	0.439569i
$621$	−17.7596	−	5.77044i	−0.712668	−	0.231560i
$622$	5.90080	−	3.00661i	0.236601	−	0.120554i
$623$	−14.2997	−	15.6491i	−0.572907	−	0.626967i
$624$		−	2.63960i		−	0.105669i
$625$	13.9164	+	20.7686i	0.556656	+	0.830743i
$626$			31.7045i			1.26717i
$627$	0.986079	−	6.22586i	0.0393802	−	0.248637i
$628$	−10.2504	−	20.1176i	−0.409036	−	0.802778i
$629$	−0.691500	+	2.12822i	−0.0275719	+	0.0848576i
$630$	9.94878	+	13.0235i	0.396369	+	0.518870i
$631$	−1.08114	−	3.32740i	−0.0430394	−	0.132462i	0.927228	−	0.374498i	$-0.122185\pi$
$631$	−1.08114	−	3.32740i	−0.0430394	−	0.132462i	−0.970267	+	0.242036i	$0.922185\pi$
$632$	−6.29998	+	6.29998i	−0.250600	+	0.250600i
$633$	−8.50171	−	4.33184i	−0.337913	−	0.172175i
$634$	−15.4560	+	21.2733i	−0.613834	+	0.844870i
$635$	−20.6427	−	8.78092i	−0.819180	−	0.348460i
$636$	0.202612	+	0.278871i	0.00803408	+	0.0110580i
$637$	−35.7779	+	14.3395i	−1.41757	+	0.568154i
$638$	3.21284	+	20.2851i	0.127198	+	0.803094i
$639$	0.682429	+	0.939282i	0.0269965	+	0.0371574i
$640$	−0.501341	−	2.17914i	−0.0198172	−	0.0861381i
$641$	26.4901	+	19.2462i	1.04630	+	0.760180i	0.971505	−	0.237019i	$-0.0761704\pi$
$641$	26.4901	+	19.2462i	1.04630	+	0.760180i	0.0747929	+	0.997199i	$0.476170\pi$
$642$	0.640759	−	1.25756i	0.0252887	−	0.0496319i
$643$	17.3144	−	17.3144i	0.682814	−	0.682814i	−0.277819	−	0.960633i	$-0.589612\pi$
$643$	17.3144	−	17.3144i	0.682814	−	0.682814i	0.960633	+	0.277819i	$0.0896116\pi$
$644$	6.27840	−	16.7214i	0.247404	−	0.658915i
$645$	11.0192	+	6.89730i	0.433882	+	0.271581i
$646$	−1.63413	+	5.02933i	−0.0642939	+	0.197876i
$647$	−8.22753	+	4.19213i	−0.323457	+	0.164810i	−0.608178	−	0.793801i	$-0.708099\pi$
$647$	−8.22753	+	4.19213i	−0.323457	+	0.164810i	0.284720	+	0.958611i	$0.408099\pi$
$648$	6.89863	+	1.09264i	0.271004	+	0.0429228i
$649$	−24.4687			−0.960479
$650$	−12.9625	+	24.2893i	−0.508432	+	0.952707i
$651$	−3.99068	+	5.00267i	−0.156407	+	0.196070i
$652$	−0.0338154	+	0.213502i	−0.00132431	+	0.00836139i
$653$	19.0131	−	9.68767i	0.744041	−	0.379108i	−0.0405042	−	0.999179i	$-0.512896\pi$
$653$	19.0131	−	9.68767i	0.744041	−	0.379108i	0.784545	+	0.620071i	$0.212896\pi$
$654$	−1.84628	+	5.68226i	−0.0721952	+	0.222194i
$655$	0.0754166	+	1.09048i	0.00294677	+	0.0426086i
$656$	1.66402	−	0.540674i	0.0649692	−	0.0211098i
$657$	−18.3687	−	18.3687i	−0.716631	−	0.716631i
$658$	4.66981	−	2.12032i	0.182048	−	0.0826585i
$659$	−8.13593	+	11.1981i	−0.316931	+	0.436218i	−0.937527	−	0.347912i	$-0.886891\pi$
$659$	−8.13593	+	11.1981i	−0.316931	+	0.436218i	0.620596	+	0.784130i	$0.286891\pi$
$660$	−2.74650	+	1.64741i	−0.106907	+	0.0641252i
$661$	21.8692	+	30.1004i	0.850615	+	1.17077i	0.983727	+	0.179670i	$0.0575030\pi$
$661$	21.8692	+	30.1004i	0.850615	+	1.17077i	−0.133112	+	0.991101i	$0.542497\pi$
$662$	−15.5848	+	2.46839i	−0.605720	+	0.0959367i
$663$	3.13265	−	0.496163i	0.121662	−	0.0192694i
$664$	7.89408	−	5.73539i	0.306350	−	0.222576i
$665$	−4.68961	−	25.6108i	−0.181855	−	0.993143i
$666$	−4.17374	−	3.03240i	−0.161729	−	0.117503i
$667$	−41.3470	−	21.0674i	−1.60096	−	0.815732i
$668$	−4.82774	+	4.82774i	−0.186791	+	0.186791i
$669$	8.47728	−	2.75444i	0.327751	−	0.106493i
$670$	−11.2414	−	13.4178i	−0.434295	−	0.518376i
$671$	−11.1791	−	3.63230i	−0.431563	−	0.140223i
$672$	0.254587	−	1.24249i	0.00982092	−	0.0479300i
$673$	−16.2283	−	2.57032i	−0.625556	−	0.0990784i	−0.164395	−	0.986395i	$-0.552567\pi$
$673$	−16.2283	−	2.57032i	−0.625556	−	0.0990784i	−0.461161	+	0.887316i	$0.652567\pi$
$674$		−	26.9031i		−	1.03627i
$675$	11.0327	+	8.34021i	0.424649	+	0.321015i
$676$	−17.3200			−0.666153
$677$	−9.63477	−	1.52600i	−0.370294	−	0.0586488i	−0.0314857	−	0.999504i	$-0.510024\pi$
$677$	−9.63477	−	1.52600i	−0.370294	−	0.0586488i	−0.338808	+	0.940855i	$0.610024\pi$
$678$	2.89073	+	5.67337i	0.111018	+	0.217885i
$679$	−24.0360	−	36.4244i	−0.922417	−	1.39784i
$680$	2.49195	−	1.00460i	0.0955618	−	0.0385245i
$681$	−0.422687	−	1.30090i	−0.0161974	−	0.0498504i
$682$	10.6600	+	10.6600i	0.408192	+	0.408192i
$683$	−6.58638	+	12.9265i	−0.252021	+	0.494619i	−0.982007	−	0.188843i	$-0.939526\pi$
$683$	−6.58638	+	12.9265i	−0.252021	+	0.494619i	0.729987	+	0.683462i	$0.239526\pi$
$684$	−9.86323	−	7.16606i	−0.377130	−	0.274001i
$685$	2.04846	−	23.2098i	0.0782678	−	0.886800i
$686$	−18.2241	+	3.29903i	−0.695798	+	0.125958i
$687$	−6.83228	+	1.08213i	−0.260668	+	0.0412857i
$688$	1.89720	+	11.9784i	0.0723300	+	0.456674i
$689$	3.20328	−	2.32732i	0.122035	−	0.0886637i
$690$	0.636200	−	7.20835i	0.0242197	−	0.274417i
$691$	17.5325	−	24.1315i	0.666969	−	0.918005i	−0.332718	−	0.943027i	$-0.607966\pi$
$691$	17.5325	−	24.1315i	0.666969	−	0.918005i	0.999687	+	0.0250220i	$0.00796557\pi$
$692$	−5.91099	+	11.6010i	−0.224702	+	0.441003i
$693$	21.7612	−	2.44872i	0.826641	−	0.0930193i
$694$	33.2862	−	10.8153i	1.26353	−	0.410545i
$695$	−4.92444	−	12.2153i	−0.186794	−	0.463352i
$696$	−3.13387	−	1.01826i	−0.118789	−	0.0385969i
$697$	0.954451	+	1.87321i	0.0361524	+	0.0709531i
$698$	−0.987909	+	6.23741i	−0.0373929	+	0.236090i
$699$	−1.97240			−0.0746032
$700$	−8.44429	+	10.1830i	−0.319164	+	0.384882i
$701$	16.3017			0.615705			0.307852	−	0.951434i	$-0.400390\pi$
$701$	16.3017			0.615705			0.307852	+	0.951434i	$0.400390\pi$
$702$	−2.38266	+	15.0435i	−0.0899276	+	0.567780i
$703$	3.72094	+	7.30276i	0.140338	+	0.275429i
$704$	−2.84159	−	0.923290i	−0.107097	−	0.0347978i
$705$	1.59273	−	1.33439i	0.0599859	−	0.0502560i
$706$	−6.96170	+	2.26199i	−0.262007	+	0.0851313i
$707$	32.5886	−	3.66709i	1.22562	−	0.137915i
$708$	1.78228	−	3.49791i	0.0669820	−	0.131460i
$709$	15.0726	−	20.7456i	0.566062	−	0.779118i	−0.426019	−	0.904714i	$-0.640084\pi$
$709$	15.0726	−	20.7456i	0.566062	−	0.779118i	0.992081	+	0.125596i	$0.0400844\pi$
$710$	−0.615370	+	0.706811i	−0.0230944	+	0.0265261i
$711$	19.9675	−	14.5072i	0.748839	−	0.544063i
$712$	−1.25340	−	7.91363i	−0.0469730	−	0.296576i
$713$	−33.6433	+	5.32857i	−1.25995	+	0.199557i
$714$	1.52243	+	0.0685924i	0.0569754	+	0.00256700i
$715$	18.9231	+	31.5479i	0.707683	+	1.17982i
$716$	14.4178	+	10.4752i	0.538820	+	0.391476i
$717$	2.37503	−	4.66126i	0.0886972	−	0.174078i
$718$	−0.210265	−	0.210265i	−0.00784701	−	0.00784701i
$719$	−3.75149	−	11.5459i	−0.139907	−	0.430589i	0.856414	−	0.516290i	$-0.172687\pi$
$719$	−3.75149	−	11.5459i	−0.139907	−	0.430589i	−0.996321	+	0.0857003i	$0.972687\pi$
$720$	0.427375	+	6.17960i	0.0159273	+	0.230300i
$721$	−22.1343	+	14.6061i	−0.824325	+	0.543961i
$722$	0.167381	+	0.328503i	0.00622927	+	0.0122256i
$723$	8.16140	+	1.29264i	0.303526	+	0.0480737i
$724$	−23.0956			−0.858340
$725$	23.8371	+	24.7597i	0.885289	+	0.919552i
$726$		−	0.993685i		−	0.0368791i
$727$	−25.3791	−	4.01966i	−0.941260	−	0.149081i	−0.333097	−	0.942893i	$-0.608094\pi$
$727$	−25.3791	−	4.01966i	−0.941260	−	0.149081i	−0.608164	+	0.793812i	$0.708094\pi$
$728$	−14.2719	−	2.92434i	−0.528953	−	0.108383i
$729$	−14.6186	−	4.74986i	−0.541428	−	0.175921i
$730$	11.1252	−	17.7738i	0.411762	−	0.657838i
$731$	−13.8593	+	4.50315i	−0.512604	+	0.166555i
$732$	1.33353	−	1.33353i	0.0492886	−	0.0492886i
$733$	−15.9827	−	8.14358i	−0.590334	−	0.300790i	0.133189	−	0.991091i	$-0.457478\pi$
$733$	−15.9827	−	8.14358i	−0.590334	−	0.300790i	−0.723523	+	0.690301i	$0.757478\pi$
$734$	−24.8590	−	18.0611i	−0.917561	−	0.666647i
$735$	−6.75561	+	3.26533i	−0.249184	+	0.120443i
$736$	5.46160	−	3.96809i	0.201317	−	0.146266i
$737$	−23.1015	+	3.65892i	−0.850956	+	0.134778i
$738$	−4.78723	+	0.758222i	−0.176220	+	0.0279106i
$739$	−22.7415	−	31.3011i	−0.836561	−	1.15143i	−0.986666	−	0.162758i	$-0.947961\pi$
$739$	−22.7415	−	31.3011i	−0.836561	−	1.15143i	0.150105	−	0.988670i	$-0.452039\pi$
$740$	1.63005	−	3.83201i	0.0599217	−	0.140867i
$741$	6.82821	−	9.39822i	0.250841	−	0.345252i
$742$	1.73228	−	0.786539i	0.0635941	−	0.0288747i
$743$	−8.75490	−	8.75490i	−0.321186	−	0.321186i	0.528036	−	0.849222i	$-0.322929\pi$
$743$	−8.75490	−	8.75490i	−0.321186	−	0.321186i	−0.849222	+	0.528036i	$0.822929\pi$
$744$	−2.30036	+	0.747433i	−0.0843354	+	0.0274022i
$745$	28.0897	+	7.02635i	1.02913	+	0.257425i
$746$	−11.1716	+	34.3828i	−0.409023	+	1.25884i
$747$	−24.0844	+	12.2716i	−0.881203	+	0.448995i
$748$	0.561619	−	3.54592i	0.0205348	−	0.129652i
$749$	−6.08957	−	4.85771i	−0.222508	−	0.177497i
$750$	−2.19115	+	4.89119i	−0.0800093	+	0.178601i
$751$	32.1289			1.17240			0.586199	−	0.810167i	$-0.300623\pi$
$751$	32.1289			1.17240			0.586199	+	0.810167i	$0.300623\pi$
$752$	1.91458	+	0.303239i	0.0698174	+	0.0110580i
$753$	−9.92203	+	5.05553i	−0.361579	+	0.184234i
$754$	−11.6963	+	35.9975i	−0.425954	+	1.31095i
$755$	10.1038	−	40.3927i	0.367716	−	1.47004i
$756$	−2.57248	+	6.85133i	−0.0935600	+	0.249180i
$757$	−29.2360	+	29.2360i	−1.06260	+	1.06260i	−0.0646959	+	0.997905i	$0.520608\pi$
$757$	−29.2360	+	29.2360i	−1.06260	+	1.06260i	−0.997905	+	0.0646959i	$0.979392\pi$
$758$	−0.0780368	+	0.153156i	−0.00283442	+	0.00556287i
$759$	−7.82256	−	5.68343i	−0.283941	−	0.206295i
$760$	3.85207	−	9.05566i	0.139729	−	0.328483i
$761$	−16.4585	−	22.6532i	−0.596621	−	0.821178i	0.398773	−	0.917050i	$-0.369436\pi$
$761$	−16.4585	−	22.6532i	−0.596621	−	0.821178i	−0.995394	+	0.0958719i	$0.969436\pi$
$762$	−0.752319	−	4.74995i	−0.0272536	−	0.172073i
$763$	28.6777	+	16.2778i	1.03820	+	0.589295i
$764$	−4.54082	−	6.24991i	−0.164281	−	0.226114i
$765$	−7.25355	+	1.66878i	−0.262253	+	0.0603348i
$766$	−13.2267	+	18.2050i	−0.477900	+	0.657773i
$767$	−40.1791	−	20.4723i	−1.45078	−	0.739211i
$768$	0.338968	−	0.338968i	0.0122315	−	0.0122315i
$769$	8.92914	+	27.4811i	0.321993	+	0.990993i	0.972780	+	0.231732i	$0.0744392\pi$
$769$	8.92914	+	27.4811i	0.321993	+	0.990993i	−0.650787	+	0.759261i	$0.725561\pi$
$770$	5.86452	+	16.6750i	0.211343	+	0.600926i
$771$	1.64425	−	5.06050i	0.0592164	−	0.182249i
$772$	1.71694	+	3.36968i	0.0617940	+	0.121278i
$773$	2.53973	−	16.0352i	0.0913477	−	0.576747i	−0.898979	−	0.437992i	$-0.855690\pi$
$773$	2.53973	−	16.0352i	0.0913477	−	0.576747i	0.990327	−	0.138755i	$-0.0443101\pi$
$774$		−	33.5963i		−	1.20759i
$775$	24.8382	+	4.41880i	0.892215	+	0.158728i
$776$		−	16.4945i		−	0.592116i
$777$	1.74366	−	1.59332i	0.0625535	−	0.0571599i
$778$	27.7944	−	14.1620i	0.996479	−	0.507731i
$779$	7.32334	+	2.37950i	0.262386	+	0.0852544i
$780$	−5.88826	+	0.407226i	−0.210833	+	0.0145810i
$781$	0.386959	+	1.19094i	0.0138465	+	0.0426151i
$782$	5.73589	+	5.73589i	0.205115	+	0.205115i
$783$	16.9413	+	8.63202i	0.605433	+	0.308483i
$784$	−6.43590	−	2.75303i	−0.229854	−	0.0983226i
$785$	−43.2956	+	25.9696i	−1.54529	+	0.926896i
$786$	−0.189584	+	0.137741i	−0.00676222	+	0.00491304i
$787$	0.177076	+	1.11801i	0.00631207	+	0.0398528i	0.990643	−	0.136476i	$-0.0435777\pi$
$787$	0.177076	+	1.11801i	0.00631207	+	0.0398528i	−0.984331	+	0.176329i	$0.943578\pi$
$788$	1.28689	+	8.12513i	0.0458437	+	0.289446i
$789$	1.66782	−	1.21175i	0.0593761	−	0.0431393i
$790$	15.0256	+	13.0817i	0.534585	+	0.465425i
$791$	33.8777	−	9.34438i	1.20455	−	0.332248i
$792$	7.37476	+	3.75763i	0.262051	+	0.133521i
$793$	−15.3177	−	15.3177i	−0.543947	−	0.543947i
$794$	−3.07118	−	9.45211i	−0.108992	−	0.335443i
$795$	0.590831	−	0.494997i	0.0209546	−	0.0175557i
$796$	18.1096	+	5.88416i	0.641877	+	0.208559i
$797$	−41.6460	+	21.2197i	−1.47518	+	0.751641i	−0.992278	−	0.124035i	$-0.960417\pi$
$797$	−41.6460	+	21.2197i	−1.47518	+	0.751641i	−0.482900	+	0.875675i	$0.660417\pi$
$798$	4.12056	−	3.76527i	0.145866	−	0.133289i
$799$			2.32920i			0.0824011i
$800$	−4.78375	+	1.45455i	−0.169131	+	0.0514261i
$801$			22.1956i			0.784243i
$802$	0.629543	−	3.97478i	0.0222299	−	0.140354i
$803$	−12.7199	−	24.9643i	−0.448876	−	0.880969i
$804$	1.15963	−	3.56899i	0.0408971	−	0.125868i
$805$	−38.2697	−	11.4258i	−1.34883	−	0.402705i
$806$	8.58545	+	26.4233i	0.302410	+	0.930721i
$807$	−6.55237	+	6.55237i	−0.230654	+	0.230654i
$808$	11.0441	+	5.62724i	0.388530	+	0.197966i
$809$	4.90329	−	6.74880i	0.172391	−	0.237275i	−0.714076	−	0.700069i	$-0.753153\pi$
$809$	4.90329	−	6.74880i	0.172391	−	0.237275i	0.886466	+	0.462793i	$0.153153\pi$
$810$	1.37309	−	15.5576i	0.0482456	−	0.546639i
$811$	−1.26944	−	1.74723i	−0.0445759	−	0.0613535i	0.786147	−	0.618039i	$-0.212073\pi$
$811$	−1.26944	−	1.74723i	−0.0445759	−	0.0613535i	−0.830723	+	0.556686i	$0.812073\pi$
$812$	−8.97749	+	15.8163i	−0.315048	+	0.555043i
$813$	1.07204	+	6.76861i	0.0375982	+	0.237386i
$814$	−3.27062	−	4.50163i	−0.114635	−	0.157782i
$815$	0.481485	+	0.0424952i	0.0168657	+	0.00148854i
$816$	0.465999	+	0.338568i	0.0163132	+	0.0118523i
$817$	−24.2313	+	47.5567i	−0.847747	+	1.66380i
$818$	0.440457	−	0.440457i	0.0154002	−	0.0154002i
$819$	37.7821	+	14.1861i	1.32021	+	0.495702i
$820$	−1.46282	−	3.62859i	−0.0510839	−	0.126716i
$821$	−1.82956	+	5.63082i	−0.0638522	+	0.196517i	−0.977893	−	0.209105i	$-0.932945\pi$
$821$	−1.82956	+	5.63082i	−0.0638522	+	0.196517i	0.914041	+	0.405622i	$0.132945\pi$
$822$	4.45067	−	2.26773i	0.155235	−	0.0790961i
$823$	21.9721	+	3.48005i	0.765901	+	0.121307i	0.527148	−	0.849774i	$-0.323261\pi$
$823$	21.9721	+	3.48005i	0.765901	+	0.121307i	0.238753	+	0.971080i	$0.423261\pi$
$824$	−10.0233			−0.349179
$825$	4.09865	+	5.87256i	0.142697	+	0.204456i
$826$	−16.9382	−	13.5117i	−0.589355	−	0.470134i
$827$	−5.53610	+	34.9536i	−0.192509	+	1.21545i	0.682331	+	0.731043i	$0.260966\pi$
$827$	−5.53610	+	34.9536i	−0.192509	+	1.21545i	−0.874840	+	0.484411i	$0.839034\pi$
$828$	−16.6631	+	8.49025i	−0.579081	+	0.295057i
$829$	2.01698	−	6.20764i	0.0700528	−	0.215600i	−0.909901	−	0.414826i	$-0.863843\pi$
$829$	2.01698	−	6.20764i	0.0700528	−	0.215600i	0.979954	+	0.199225i	$0.0638426\pi$
$830$	−14.0120	−	16.7248i	−0.486364	−	0.580527i
$831$	4.65371	−	1.51208i	0.161436	−	0.0524536i
$832$	−3.89358	−	3.89358i	−0.134986	−	0.134986i
$833$	2.05752	−	8.15554i	0.0712889	−	0.282573i
$834$	1.65963	−	2.28428i	0.0574682	−	0.0790982i
$835$	11.5142	+	10.0246i	0.398467	+	0.346917i
$836$	−7.72902	−	10.6381i	−0.267314	−	0.367926i
$837$	13.7848	−	2.18330i	0.476473	−	0.0754659i
$838$	29.3785	−	4.65310i	1.01486	−	0.160739i
$839$	−40.9357	+	29.7415i	−1.41326	+	1.02679i	−0.420418	+	0.907330i	$0.638117\pi$
$839$	−40.9357	+	29.7415i	−1.41326	+	1.02679i	−0.992839	+	0.119461i	$0.961883\pi$
$840$	−2.81094	−	0.376232i	−0.0969867	−	0.0129812i
$841$	14.7646	+	10.7271i	0.509124	+	0.369901i
$842$	12.0660	+	6.14791i	0.415820	+	0.211871i
$843$	5.78423	−	5.78423i	0.199219	−	0.199219i
$844$	−18.9303	+	6.15084i	−0.651609	+	0.211721i
$845$	2.67205	+	38.6364i	0.0919213	+	1.32913i
$846$	−5.10705	−	1.65938i	−0.175584	−	0.0570507i
$847$	−5.37271	−	1.10088i	−0.184609	−	0.0378265i
$848$	0.710219	+	0.112488i	0.0243890	+	0.00386284i
$849$		−	13.4601i		−	0.461949i
$850$	−2.62544	−	5.40390i	−0.0900519	−	0.185352i
$851$	12.5724			0.430977
$852$	−0.198436	−	0.0314292i	−0.00679831	−	0.00107675i
$853$	11.3837	+	22.3418i	0.389770	+	0.764968i	0.999620	−	0.0275493i	$-0.00877032\pi$
$853$	11.3837	+	22.3418i	0.389770	+	0.764968i	−0.609850	+	0.792517i	$0.708770\pi$
$854$	−5.73281	−	8.68757i	−0.196173	−	0.297283i
$855$	−14.4639	+	23.1078i	−0.494657	+	0.790272i
$856$	−0.909823	−	2.80015i	−0.0310971	−	0.0957070i
$857$	16.7993	+	16.7993i	0.573854	+	0.573854i	0.933203	−	0.359349i	$-0.117001\pi$
$857$	16.7993	+	16.7993i	0.573854	+	0.573854i	−0.359349	+	0.933203i	$0.617001\pi$
$858$	−3.58047	+	7.02707i	−0.122235	+	0.239900i
$859$	−12.8117	−	9.30821i	−0.437128	−	0.317592i	0.347365	−	0.937730i	$-0.387077\pi$
$859$	−12.8117	−	9.30821i	−0.437128	−	0.317592i	−0.784493	+	0.620138i	$0.787077\pi$
$860$	26.4281	−	6.08014i	0.901190	−	0.207331i
$861$	0.0998791	−	2.21684i	0.00340387	−	0.0755498i
$862$	2.43958	−	0.386391i	0.0830924	−	0.0131605i
$863$	0.925513	+	5.84346i	0.0315048	+	0.198914i	0.998421	−	0.0561825i	$-0.0178929\pi$
$863$	0.925513	+	5.84346i	0.0315048	+	0.198914i	−0.966916	+	0.255096i	$0.917893\pi$
$864$	−2.23780	+	1.62586i	−0.0761317	+	0.0553129i
$865$	26.7907	+	11.3961i	0.910911	+	0.387480i
$866$	7.49361	−	10.3141i	0.254643	−	0.350486i
$867$	3.38551	−	6.64443i	0.114978	−	0.225657i
$868$	1.49276	+	13.2658i	0.0506675	+	0.450270i
$869$	25.3172	−	8.22607i	0.858828	−	0.279050i
$870$	−1.78798	+	7.14794i	−0.0606184	+	0.242338i
$871$	−40.9955	−	13.3202i	−1.38908	−	0.451339i
$872$	5.65832	+	11.1051i	0.191615	+	0.376066i
$873$	−7.14795	+	45.1304i	−0.241922	+	1.52743i
$874$	29.7107			1.00498
$875$	24.0184	+	17.2660i	0.811971	+	0.583698i
$876$	4.49527			0.151881
$877$	4.90769	−	30.9859i	0.165721	−	1.04632i	−0.754893	−	0.655848i	$-0.772311\pi$
$877$	4.90769	−	30.9859i	0.165721	−	1.04632i	0.920614	−	0.390473i	$-0.127689\pi$
$878$	−4.56214	−	8.95370i	−0.153965	−	0.302173i
$879$	12.1332	+	3.94232i	0.409243	+	0.132971i
$880$	−1.62123	+	6.48130i	−0.0546517	+	0.218484i
$881$	25.5535	−	8.30283i	0.860919	−	0.279729i	0.154906	−	0.987929i	$-0.450492\pi$
$881$	25.5535	−	8.30283i	0.860919	−	0.279729i	0.706012	+	0.708200i	$0.250492\pi$
$882$	16.4162	+	10.3216i	0.552762	+	0.347546i
$883$	0.578060	−	1.13451i	0.0194533	−	0.0381792i	−0.881075	−	0.472976i	$-0.843180\pi$
$883$	0.578060	−	1.13451i	0.0194533	−	0.0381792i	0.900529	+	0.434797i	$0.143180\pi$
$884$	3.88899	−	5.35274i	0.130801	−	0.180032i
$885$	−8.07790	−	3.43615i	−0.271536	−	0.115505i
$886$	12.5520	−	9.11958i	0.421693	−	0.306378i
$887$	2.46071	+	15.5363i	0.0826224	+	0.521657i	0.993937	+	0.109948i	$0.0350683\pi$
$887$	2.46071	+	15.5363i	0.0826224	+	0.521657i	−0.911315	+	0.411710i	$0.864932\pi$
$888$	0.881759	−	0.139657i	0.0295899	−	0.00468658i
$889$	−26.5158	−	1.19466i	−0.889311	−	0.0400676i
$890$	−17.4599	+	4.01688i	−0.585256	+	0.134646i
$891$	−16.8832	−	12.2664i	−0.565610	−	0.410940i
$892$	8.44158	−	16.5675i	0.282645	−	0.554722i
$893$	6.03237	+	6.03237i	0.201865	+	0.201865i
$894$	1.91821	+	5.90365i	0.0641546	+	0.197448i
$895$	21.1431	−	33.7785i	0.706735	−	1.12909i
$896$	−1.45722	−	2.20828i	−0.0486822	−	0.0737736i
$897$	−8.08997	−	15.8775i	−0.270116	−	0.530133i
$898$	36.2601	+	5.74303i	1.21001	+	0.191647i
$899$	34.6831			1.15674
$900$	13.7191	−	1.90672i	0.457305	−	0.0635574i
$901$			0.864024i			0.0287848i
$902$	−5.16331	−	0.817788i	−0.171919	−	0.0272294i
$903$	15.0686	+	3.08757i	0.501451	+	0.102748i
$904$	12.6326	+	4.10459i	0.420155	+	0.136516i
$905$	3.56308	+	51.5202i	0.118441	+	1.71259i
$906$	8.48939	−	2.75837i	0.282041	−	0.0916407i
$907$	−16.2703	+	16.2703i	−0.540248	+	0.540248i	−0.923602	−	0.383354i	$-0.874769\pi$
$907$	−16.2703	+	16.2703i	−0.540248	+	0.540248i	0.383354	+	0.923602i	$0.374769\pi$
$908$	−2.54240	−	1.29542i	−0.0843724	−	0.0429899i
$909$	−27.7791	−	20.1827i	−0.921374	−	0.669418i
$910$	−4.32162	+	32.2881i	−0.143260	+	1.07034i
$911$	1.56995	−	1.14064i	0.0520148	−	0.0377909i	−0.561474	−	0.827494i	$-0.689766\pi$
$911$	1.56995	−	1.14064i	0.0520148	−	0.0377909i	0.613489	+	0.789703i	$0.289766\pi$
$912$	2.08374	−	0.330032i	0.0689995	−	0.0109285i
$913$	−28.7952	+	4.56071i	−0.952981	+	0.150937i
$914$	−6.31101	−	8.68637i	−0.208750	−	0.287319i
$915$	−3.18048	−	2.76902i	−0.105144	−	0.0915410i
$916$	−8.48186	+	11.6743i	−0.280249	+	0.385729i
$917$	0.534709	+	1.17765i	0.0176576	+	0.0388894i
$918$	−2.35019	−	2.35019i	−0.0775679	−	0.0775679i
$919$	−19.5140	+	6.34049i	−0.643709	+	0.209154i	−0.612638	−	0.790364i	$-0.709892\pi$
$919$	−19.5140	+	6.34049i	−0.643709	+	0.209154i	−0.0310705	+	0.999517i	$0.509892\pi$
$920$	−9.69436	−	11.5712i	−0.319614	−	0.381492i
$921$	−2.44653	+	7.52964i	−0.0806159	+	0.248110i
$922$	1.72817	−	0.880547i	0.0569143	−	0.0289993i
$923$	−0.361014	+	2.27935i	−0.0118829	+	0.0750258i
$924$	−2.36312	+	2.96238i	−0.0777410	+	0.0974553i
$925$	−8.79968	−	3.04503i	−0.289332	−	0.100120i
$926$	19.0086			0.624661
$927$	27.4247	+	4.34365i	0.900747	+	0.142664i
$928$	−6.12466	+	3.12067i	−0.201052	+	0.102441i
$929$	14.3101	−	44.0419i	0.469498	−	1.44497i	−0.383738	−	0.923442i	$-0.625363\pi$
$929$	14.3101	−	44.0419i	0.469498	−	1.44497i	0.853236	−	0.521525i	$-0.174637\pi$
$930$	2.02222	+	5.01620i	0.0663111	+	0.164488i
$931$	−15.7932	−	26.4507i	−0.517601	−	0.866887i
$932$	−2.90943	+	2.90943i	−0.0953014	+	0.0953014i
$933$	1.44129	−	2.82868i	0.0471856	−	0.0926070i
$934$	−31.8904	−	23.1697i	−1.04348	−	0.758136i
$935$	−7.99668	−	0.705776i	−0.261519	−	0.0230814i
$936$	8.96591	+	12.3405i	0.293060	+	0.403362i
$937$	2.64428	+	16.6953i	0.0863849	+	0.545413i	0.992487	+	0.122353i	$0.0390440\pi$
$937$	2.64428	+	16.6953i	0.0863849	+	0.545413i	−0.906102	+	0.423060i	$0.860956\pi$
$938$	−18.0123	−	10.2240i	−0.588122	−	0.333824i
$939$	8.93332	+	12.2957i	0.291528	+	0.401254i
$940$	0.381075	−	4.31770i	0.0124293	−	0.140828i
$941$	−5.82772	+	8.02117i	−0.189978	+	0.261483i	−0.893372	−	0.449318i	$-0.851667\pi$
$941$	−5.82772	+	8.02117i	−0.189978	+	0.261483i	0.703394	+	0.710800i	$0.251667\pi$
$942$	−9.64381	−	4.91377i	−0.314212	−	0.160099i
$943$	8.35219	−	8.35219i	0.271985	−	0.271985i
$944$	−2.53068	−	7.78863i	−0.0823666	−	0.253498i
$945$	15.6804	+	4.68153i	0.510084	+	0.152290i
$946$	11.1974	−	34.4621i	0.364060	−	1.12046i
$947$	−0.486184	−	0.954191i	−0.0157989	−	0.0310070i	0.882972	−	0.469425i	$-0.155539\pi$
$947$	−0.486184	−	0.954191i	−0.0157989	−	0.0310070i	−0.898771	+	0.438418i	$0.855539\pi$
$948$	−0.668129	+	4.21840i	−0.0216998	+	0.137007i
$949$		−	51.6353i		−	1.67615i
$950$	−20.7951	−	7.19590i	−0.674682	−	0.233466i
$951$			12.6052i			0.408752i
$952$	2.34686	−	2.14450i	0.0760621	−	0.0695036i
$953$	−12.2464	+	6.23986i	−0.396700	+	0.202129i	−0.640949	−	0.767584i	$-0.721459\pi$
$953$	−12.2464	+	6.23986i	−0.396700	+	0.202129i	0.244248	+	0.969713i	$0.421459\pi$
$954$	−1.89448	−	0.615554i	−0.0613360	−	0.0199293i
$955$	−13.2414	+	11.0936i	−0.428481	+	0.358980i
$956$	−3.37234	−	10.3790i	−0.109069	−	0.335681i
$957$	6.96170	+	6.96170i	0.225040	+	0.225040i
$958$	−17.1401	−	8.73334i	−0.553773	−	0.282161i
$959$	−7.33051	−	26.5765i	−0.236715	−	0.858199i
$960$	−0.808444	−	0.703855i	−0.0260924	−	0.0227168i
$961$	−4.48318	+	3.25722i	−0.144619	+	0.105072i
$962$	−1.60418	−	10.1284i	−0.0517208	−	0.326552i
$963$	1.27590	+	8.05574i	0.0411154	+	0.259593i
$964$	13.9453	−	10.1319i	0.449149	−	0.326326i
$965$	7.25201	−	4.34991i	0.233450	−	0.140028i
$966$	−2.27667	−	8.25396i	−0.0732506	−	0.265567i
$967$	33.3905	+	17.0133i	1.07377	+	0.547111i	0.899202	−	0.437534i	$-0.144148\pi$
$967$	33.3905	+	17.0133i	1.07377	+	0.547111i	0.174565	+	0.984646i	$0.444148\pi$
$968$	−1.46575	−	1.46575i	−0.0471110	−	0.0471110i
$969$	0.783357	+	2.41093i	0.0251651	+	0.0774501i
$970$	−36.7948	+	2.54469i	−1.18141	+	0.0817052i
$971$	−33.9855	−	11.0426i	−1.09065	−	0.354373i	−0.292151	−	0.956372i	$-0.594371\pi$
$971$	−33.9855	−	11.0426i	−1.09065	−	0.354373i	−0.798496	+	0.601999i	$0.794371\pi$
$972$	10.3771	−	5.28739i	0.332845	−	0.169593i
$973$	−10.5121	−	11.5041i	−0.337003	−	0.368803i
$974$		−	7.73006i		−	0.247687i
$975$	1.81683	+	13.0723i	0.0581851	+	0.418650i
$976$		−	3.93408i		−	0.125927i
$977$	7.84011	−	49.5005i	0.250827	−	1.58366i	−0.464953	−	0.885335i	$-0.653929\pi$
$977$	7.84011	−	49.5005i	0.250827	−	1.58366i	0.715780	−	0.698326i	$-0.246071\pi$
$978$	0.0470439	+	0.0923288i	0.00150430	+	0.00295235i
$979$	−7.39765	+	22.7676i	−0.236430	+	0.727656i
$980$	−5.14840	+	14.7815i	−0.164459	+	0.472179i
$981$	−10.6693	−	32.8366i	−0.340644	−	1.04839i
$982$	−17.6351	+	17.6351i	−0.562757	+	0.562757i
$983$	21.2968	+	10.8513i	0.679263	+	0.346102i	0.759347	−	0.650686i	$-0.225519\pi$
$983$	21.2968	+	10.8513i	0.679263	+	0.346102i	−0.0800835	+	0.996788i	$0.525519\pi$
$984$	0.492998	−	0.678554i	0.0157162	−	0.0216315i
$985$	17.9265	−	4.12424i	0.571187	−	0.131409i
$986$	−4.85483	−	6.68210i	−0.154609	−	0.212801i
$987$	1.21361	−	2.13811i	0.0386297	−	0.0680567i
$988$	−3.79094	−	23.9351i	−0.120606	−	0.761476i
$989$	48.1240	+	66.2369i	1.53025	+	2.10621i
$990$	7.24454	−	17.0309i	0.230247	−	0.541277i
$991$	−44.0284	−	31.9885i	−1.39861	−	1.01615i	−0.994858	−	0.101281i	$-0.967706\pi$
$991$	−44.0284	−	31.9885i	−1.39861	−	1.01615i	−0.403752	−	0.914868i	$-0.632294\pi$
$992$	−2.29067	+	4.49570i	−0.0727289	+	0.142739i
$993$	−5.34860	+	5.34860i	−0.169733	+	0.169733i
$994$	−0.389775	+	1.03810i	−0.0123629	+	0.0329264i
$995$	10.3322	−	41.3056i	0.327552	−	1.30947i
$996$	1.44544	−	4.44861i	0.0458005	−	0.140959i
$997$	37.0116	−	18.8584i	1.17217	−	0.597250i	0.244134	−	0.969741i	$-0.421496\pi$
$997$	37.0116	−	18.8584i	1.17217	−	0.597250i	0.928036	+	0.372491i	$0.121496\pi$
$998$	−13.5853	−	2.15170i	−0.430035	−	0.0681109i
$999$	−5.15135			−0.162981

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.r.a.223.15	✓	160
7.6	odd	2	inner	350.2.r.a.223.16	yes	160
25.12	odd	20	inner	350.2.r.a.237.16	yes	160
175.62	even	20	inner	350.2.r.a.237.15	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.223.15	✓	160	1.1	even	1	trivial
350.2.r.a.223.16	yes	160	7.6	odd	2	inner
350.2.r.a.237.15	yes	160	175.62	even	20	inner
350.2.r.a.237.16	yes	160	25.12	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(-0.217631 - 0.427124i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-0.542612 + 2.16923i) q^{5} +(-0.455911 + 0.148134i) q^{6} +(0.295851 + 2.62916i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(1.62828 - 2.24114i) q^{9} +O(q^{10})\)	\(q+(0.156434 - 0.987688i) q^{2} +(-0.217631 - 0.427124i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-0.542612 + 2.16923i) q^{5} +(-0.455911 + 0.148134i) q^{6} +(0.295851 + 2.62916i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(1.62828 - 2.24114i) q^{9} +(2.05764 + 0.875274i) q^{10} +(2.41720 - 1.75620i) q^{11} +(0.0749905 + 0.473471i) q^{12} +(5.43857 - 0.861384i) q^{13} +(2.64307 + 0.119083i) q^{14} +(1.04462 - 0.240329i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-0.545507 + 1.07062i) q^{17} +(-1.95883 - 1.95883i) q^{18} +(1.35998 + 4.18559i) q^{19} +(1.18638 - 1.89539i) q^{20} +(1.05859 - 0.698551i) q^{21} +(-1.35645 - 2.66217i) q^{22} +(6.66780 + 1.05608i) q^{23} +0.479373 q^{24} +(-4.41115 - 2.35410i) q^{25} -5.50636i q^{26} +(-2.73202 - 0.432710i) q^{27} +(0.531084 - 2.59190i) q^{28} +(-6.53744 - 2.12414i) q^{29} +(-0.0739556 - 1.06936i) q^{30} +(-4.79869 + 1.55919i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.27617 - 0.650243i) q^{33} +(0.972101 + 0.706273i) q^{34} +(-5.86379 - 0.784842i) q^{35} +(-2.24114 + 1.62828i) q^{36} +(1.83940 - 0.291332i) q^{37} +(4.34680 - 0.688466i) q^{38} +(-1.55152 - 2.13548i) q^{39} +(-1.68646 - 1.46828i) q^{40} +(1.02842 - 1.41550i) q^{41} +(-0.524350 - 1.15484i) q^{42} +(8.57562 + 8.57562i) q^{43} +(-2.84159 + 0.923290i) q^{44} +(3.97803 + 4.74820i) q^{45} +(2.08615 - 6.42050i) q^{46} +(1.72716 - 0.880034i) q^{47} +(0.0749905 - 0.473471i) q^{48} +(-6.82494 + 1.55568i) q^{49} +(-3.01517 + 3.98857i) q^{50} +0.576007 q^{51} +(-5.43857 - 0.861384i) q^{52} +(0.640698 - 0.326452i) q^{53} +(-0.854765 + 2.63070i) q^{54} +(2.49801 + 6.19641i) q^{55} +(-2.47691 - 0.930008i) q^{56} +(1.49179 - 1.49179i) q^{57} +(-3.12067 + 6.12466i) q^{58} +(-6.62540 - 4.81364i) q^{59} +(-1.06776 - 0.0942391i) q^{60} +(-2.31240 - 3.18274i) q^{61} +(0.789312 + 4.98352i) q^{62} +(6.37404 + 3.61797i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-1.08249 + 12.2649i) q^{65} +(-0.841875 + 1.15874i) q^{66} +(-6.97503 - 3.55395i) q^{67} +(0.849648 - 0.849648i) q^{68} +(-1.00004 - 3.07781i) q^{69} +(-1.69248 + 5.66882i) q^{70} +(-0.129512 + 0.398597i) q^{71} +(1.25765 + 2.46827i) q^{72} +(1.46695 - 9.26194i) q^{73} -1.86233i q^{74} +(-0.0454936 + 2.39643i) q^{75} -4.40099i q^{76} +(5.33246 + 5.83564i) q^{77} +(-2.35190 + 1.19835i) q^{78} +(8.47346 + 2.75319i) q^{79} +(-1.71403 + 1.43601i) q^{80} +(-2.15837 - 6.64277i) q^{81} +(-1.23719 - 1.23719i) q^{82} +(-8.69411 - 4.42987i) q^{83} +(-1.22264 + 0.337239i) q^{84} +(-2.02642 - 1.76426i) q^{85} +(9.81156 - 7.12851i) q^{86} +(0.515475 + 3.25458i) q^{87} +(0.467399 + 2.95104i) q^{88} +(-6.48207 + 4.70950i) q^{89} +(5.31204 - 3.18627i) q^{90} +(3.87372 + 14.0440i) q^{91} +(-6.01511 - 3.06485i) q^{92} +(1.71031 + 1.71031i) q^{93} +(-0.599011 - 1.84357i) q^{94} +(-9.81746 + 0.678965i) q^{95} +(-0.455911 - 0.148134i) q^{96} +(-14.6967 + 7.48832i) q^{97} +(0.468867 + 6.98428i) q^{98} -8.27689i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{7}+O(q^{10}) \) 160 * q + 8 * q^7	\( 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) \) 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

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Database

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