LMFDB - Embedded newform 168.2.t.a.115.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(19,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("168.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.t (of order $6$, degree $2$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.9
Character	$\chi$	$=$	168.115
Dual form			168.2.t.a.19.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.297109 + 1.38265i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.82345 - 0.821596i) q^{4} +(-1.44142 - 2.49662i) q^{5} +(0.948630 - 1.04886i) q^{6} +(2.63862 + 0.194181i) q^{7} +(1.67775 - 2.27710i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.297109 + 1.38265i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.82345 - 0.821596i) q^{4} +(-1.44142 - 2.49662i) q^{5} +(0.948630 - 1.04886i) q^{6} +(2.63862 + 0.194181i) q^{7} +(1.67775 - 2.27710i) q^{8} +(0.500000 + 0.866025i) q^{9} +(3.88021 - 1.25122i) q^{10} +(2.91340 - 5.04616i) q^{11} +(1.16836 + 1.62325i) q^{12} -1.04841 q^{13} +(-1.05244 + 3.59059i) q^{14} +2.88284i q^{15} +(2.64996 + 2.99628i) q^{16} +(-5.91062 - 3.41250i) q^{17} +(-1.34597 + 0.434022i) q^{18} +(-0.589961 + 0.340614i) q^{19} +(0.577155 + 5.73673i) q^{20} +(-2.18802 - 1.48747i) q^{21} +(6.11148 + 5.52748i) q^{22} +(1.85937 - 1.07351i) q^{23} +(-2.59152 + 1.13315i) q^{24} +(-1.65540 + 2.86723i) q^{25} +(0.311491 - 1.44958i) q^{26} -1.00000i q^{27} +(-4.65185 - 2.52196i) q^{28} +6.61515i q^{29} +(-3.98597 - 0.856518i) q^{30} +(1.91558 - 3.31788i) q^{31} +(-4.93014 + 2.77375i) q^{32} +(-5.04616 + 2.91340i) q^{33} +(6.47439 - 7.15845i) q^{34} +(-3.31857 - 6.86751i) q^{35} +(-0.200203 - 1.98995i) q^{36} +(2.06185 - 1.19041i) q^{37} +(-0.295668 - 0.916911i) q^{38} +(0.907949 + 0.524204i) q^{39} +(-8.10338 - 0.906428i) q^{40} +1.19919i q^{41} +(2.70674 - 2.58333i) q^{42} +1.34319 q^{43} +(-9.45835 + 6.80779i) q^{44} +(1.44142 - 2.49662i) q^{45} +(0.931851 + 2.88980i) q^{46} +(5.52670 + 9.57253i) q^{47} +(-0.796791 - 3.91984i) q^{48} +(6.92459 + 1.02474i) q^{49} +(-3.47255 - 3.14072i) q^{50} +(3.41250 + 5.91062i) q^{51} +(1.91172 + 0.861368i) q^{52} +(-6.99615 - 4.03923i) q^{53} +(1.38265 + 0.297109i) q^{54} -16.7978 q^{55} +(4.86909 - 5.68260i) q^{56} +0.681229 q^{57} +(-9.14645 - 1.96542i) q^{58} +(6.81625 + 3.93537i) q^{59} +(2.36853 - 5.25673i) q^{60} +(-1.63471 - 2.83140i) q^{61} +(4.01834 + 3.63435i) q^{62} +(1.15114 + 2.38220i) q^{63} +(-2.37034 - 7.64078i) q^{64} +(1.51120 + 2.61747i) q^{65} +(-2.52896 - 7.84268i) q^{66} +(-6.65629 + 11.5290i) q^{67} +(7.97404 + 11.0787i) q^{68} -2.14701 q^{69} +(10.4813 - 2.54802i) q^{70} +1.08533i q^{71} +(2.81090 + 0.314421i) q^{72} +(4.88878 + 2.82254i) q^{73} +(1.03333 + 3.20450i) q^{74} +(2.86723 - 1.65540i) q^{75} +(1.35561 - 0.136384i) q^{76} +(8.66721 - 12.7491i) q^{77} +(-0.994552 + 1.09963i) q^{78} +(10.9630 - 6.32946i) q^{79} +(3.66086 - 10.9348i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.65806 - 0.356289i) q^{82} -0.482042i q^{83} +(2.76765 + 4.51000i) q^{84} +19.6754i q^{85} +(-0.399075 + 1.85717i) q^{86} +(3.30757 - 5.72889i) q^{87} +(-6.60265 - 15.1003i) q^{88} +(10.7308 - 6.19543i) q^{89} +(3.02369 + 2.73475i) q^{90} +(-2.76635 - 0.203581i) q^{91} +(-4.27246 + 0.429839i) q^{92} +(-3.31788 + 1.91558i) q^{93} +(-14.8775 + 4.79742i) q^{94} +(1.70077 + 0.981939i) q^{95} +(5.65650 + 0.0629331i) q^{96} +3.63532i q^{97} +(-3.47421 + 9.26984i) q^{98} +5.82680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36} - 18 q^{38} - 30 q^{40} + 4 q^{42} - 16 q^{43} + 24 q^{44} + 8 q^{46} + 8 q^{49} + 76 q^{50} + 36 q^{52} + 16 q^{56} + 16 q^{57} - 6 q^{58} - 96 q^{59} - 2 q^{60} + 76 q^{64} - 36 q^{66} - 32 q^{67} + 96 q^{68} + 6 q^{70} + 8 q^{72} - 24 q^{73} - 34 q^{74} - 12 q^{78} + 36 q^{80} - 16 q^{81} - 36 q^{82} + 16 q^{84} + 50 q^{86} - 14 q^{88} + 56 q^{91} - 128 q^{92} + 36 q^{94} + 30 q^{96} + 60 q^{98} + 16 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.297109	+	1.38265i	−0.210088	+	0.977683i
$2$	−0.297109	+	1.38265i	−0.210088	+	0.977683i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−1.82345	−	0.821596i	−0.911726	−	0.410798i
$5$	−1.44142	−	2.49662i	−0.644624	−	1.11652i	−0.984388	−	0.176010i	$-0.943681\pi$
$5$	−1.44142	−	2.49662i	−0.644624	−	1.11652i	0.339765	−	0.940511i	$-0.389653\pi$
$6$	0.948630	−	1.04886i	0.387276	−	0.428194i
$7$	2.63862	+	0.194181i	0.997303	+	0.0733933i
$7$	2.63862	+	0.194181i	0.997303	+	0.0733933i
$8$	1.67775	−	2.27710i	0.593172	−	0.805075i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	3.88021	−	1.25122i	1.22703	−	0.395670i
$11$	2.91340	−	5.04616i	0.878423	−	1.52147i	0.0253527	−	0.999679i	$-0.491929\pi$
$11$	2.91340	−	5.04616i	0.878423	−	1.52147i	0.853071	−	0.521795i	$-0.174738\pi$
$12$	1.16836	+	1.62325i	0.337276	+	0.468592i
$13$	−1.04841			−0.290776			−0.145388	−	0.989375i	$-0.546443\pi$
$13$	−1.04841			−0.290776			−0.145388	+	0.989375i	$0.546443\pi$
$14$	−1.05244	+	3.59059i	−0.281276	+	0.959627i
$15$			2.88284i			0.744347i
$16$	2.64996	+	2.99628i	0.662490	+	0.749071i
$17$	−5.91062	−	3.41250i	−1.43354	−	0.827652i	−0.436147	−	0.899875i	$-0.643657\pi$
$17$	−5.91062	−	3.41250i	−1.43354	−	0.827652i	−0.997388	+	0.0722232i	$0.976991\pi$
$18$	−1.34597	+	0.434022i	−0.317247	+	0.102300i
$19$	−0.589961	+	0.340614i	−0.135346	+	0.0781423i	−0.566144	−	0.824306i	$-0.691566\pi$
$19$	−0.589961	+	0.340614i	−0.135346	+	0.0781423i	0.430798	+	0.902448i	$0.358232\pi$
$20$	0.577155	+	5.73673i	0.129056	+	1.28277i
$21$	−2.18802	−	1.48747i	−0.477465	−	0.324593i
$22$	6.11148	+	5.52748i	1.30297	+	1.17846i
$23$	1.85937	−	1.07351i	0.387705	−	0.223841i	−0.293460	−	0.955971i	$-0.594807\pi$
$23$	1.85937	−	1.07351i	0.387705	−	0.223841i	0.681165	+	0.732130i	$0.261474\pi$
$24$	−2.59152	+	1.13315i	−0.528991	+	0.231304i
$25$	−1.65540	+	2.86723i	−0.331079	+	0.573446i
$26$	0.311491	−	1.44958i	0.0610885	−	0.284287i
$27$		−	1.00000i		−	0.192450i
$28$	−4.65185	−	2.52196i	−0.879118	−	0.476605i
$29$			6.61515i			1.22840i	0.789149	+	0.614201i	$0.210522\pi$
$29$			6.61515i			1.22840i	−0.789149	+	0.614201i	$0.789478\pi$
$30$	−3.98597	−	0.856518i	−0.727735	−	0.156378i
$31$	1.91558	−	3.31788i	0.344048	−	0.595909i	−0.641132	−	0.767430i	$-0.721535\pi$
$31$	1.91558	−	3.31788i	0.344048	−	0.595909i	0.985180	+	0.171522i	$0.0548684\pi$
$32$	−4.93014	+	2.77375i	−0.871534	+	0.490334i
$33$	−5.04616	+	2.91340i	−0.878423	+	0.507158i
$34$	6.47439	−	7.15845i	1.11035	−	1.22766i
$35$	−3.31857	−	6.86751i	−0.560940	−	1.16082i
$36$	−0.200203	−	1.98995i	−0.0333672	−	0.331659i
$37$	2.06185	−	1.19041i	0.338966	−	0.195702i	−0.320849	−	0.947130i	$-0.603968\pi$
$37$	2.06185	−	1.19041i	0.338966	−	0.195702i	0.659814	+	0.751429i	$0.270635\pi$
$38$	−0.295668	−	0.916911i	−0.0479638	−	0.148743i
$39$	0.907949	+	0.524204i	0.145388	+	0.0839399i
$40$	−8.10338	−	0.906428i	−1.28126	−	0.143319i
$41$			1.19919i			0.187281i	0.995606	+	0.0936407i	$0.0298505\pi$
$41$			1.19919i			0.187281i	−0.995606	+	0.0936407i	$0.970149\pi$
$42$	2.70674	−	2.58333i	0.417659	−	0.398616i
$43$	1.34319			0.204835			0.102418	−	0.994741i	$-0.467342\pi$
$43$	1.34319			0.204835			0.102418	+	0.994741i	$0.467342\pi$
$44$	−9.45835	+	6.80779i	−1.42590	+	1.02631i
$45$	1.44142	−	2.49662i	0.214875	−	0.372174i
$46$	0.931851	+	2.88980i	0.137394	+	0.426078i
$47$	5.52670	+	9.57253i	0.806152	+	1.39630i	0.915511	+	0.402294i	$0.131787\pi$
$47$	5.52670	+	9.57253i	0.806152	+	1.39630i	−0.109359	+	0.994002i	$0.534880\pi$
$48$	−0.796791	−	3.91984i	−0.115007	−	0.565780i
$49$	6.92459	+	1.02474i	0.989227	+	0.146391i
$50$	−3.47255	−	3.14072i	−0.491093	−	0.444165i
$51$	3.41250	+	5.91062i	0.477845	+	0.827652i
$52$	1.91172	+	0.861368i	0.265108	+	0.119450i
$53$	−6.99615	−	4.03923i	−0.960995	−	0.554830i	−0.0645156	−	0.997917i	$-0.520550\pi$
$53$	−6.99615	−	4.03923i	−0.960995	−	0.554830i	−0.896479	+	0.443086i	$0.853884\pi$
$54$	1.38265	+	0.297109i	0.188155	+	0.0404314i
$55$	−16.7978			−2.26501
$56$	4.86909	−	5.68260i	0.650660	−	0.759369i
$57$	0.681229			0.0902310
$58$	−9.14645	−	1.96542i	−1.20099	−	0.258072i
$59$	6.81625	+	3.93537i	0.887400	+	0.512341i	0.873091	−	0.487557i	$-0.162112\pi$
$59$	6.81625	+	3.93537i	0.887400	+	0.512341i	0.0143092	+	0.999898i	$0.495445\pi$
$60$	2.36853	−	5.25673i	0.305776	−	0.678641i
$61$	−1.63471	−	2.83140i	−0.209303	−	0.362524i	0.742192	−	0.670187i	$-0.233786\pi$
$61$	−1.63471	−	2.83140i	−0.209303	−	0.362524i	−0.951495	+	0.307663i	$0.900453\pi$
$62$	4.01834	+	3.63435i	0.510329	+	0.461563i
$63$	1.15114	+	2.38220i	0.145030	+	0.300129i
$64$	−2.37034	−	7.64078i	−0.296293	−	0.955097i
$65$	1.51120	+	2.61747i	0.187441	+	0.324658i
$66$	−2.52896	−	7.84268i	−0.311294	−	0.965367i
$67$	−6.65629	+	11.5290i	−0.813195	+	1.40850i	0.0974214	+	0.995243i	$0.468941\pi$
$67$	−6.65629	+	11.5290i	−0.813195	+	1.40850i	−0.910617	+	0.413252i	$0.864393\pi$
$68$	7.97404	+	11.0787i	0.966994	+	1.34349i
$69$	−2.14701			−0.258470
$70$	10.4813	−	2.54802i	1.25276	−	0.304547i
$71$			1.08533i			0.128805i	0.997924	+	0.0644027i	$0.0205142\pi$
$71$			1.08533i			0.128805i	−0.997924	+	0.0644027i	$0.979486\pi$
$72$	2.81090	+	0.314421i	0.331267	+	0.0370549i
$73$	4.88878	+	2.82254i	0.572188	+	0.330353i	0.758023	−	0.652228i	$-0.226166\pi$
$73$	4.88878	+	2.82254i	0.572188	+	0.330353i	−0.185835	+	0.982581i	$0.559499\pi$
$74$	1.03333	+	3.20450i	0.120122	+	0.372515i
$75$	2.86723	−	1.65540i	0.331079	−	0.191149i
$76$	1.35561	−	0.136384i	0.155500	−	0.0156444i
$77$	8.66721	−	12.7491i	0.987720	−	1.45290i
$78$	−0.994552	+	1.09963i	−0.112611	+	0.124509i
$79$	10.9630	−	6.32946i	1.23343	−	0.712120i	0.265686	−	0.964060i	$-0.414402\pi$
$79$	10.9630	−	6.32946i	1.23343	−	0.712120i	0.967743	+	0.251939i	$0.0810684\pi$
$80$	3.66086	−	10.9348i	0.409296	−	1.22255i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.65806	−	0.356289i	−0.183102	−	0.0393455i
$83$		−	0.482042i		−	0.0529110i	−0.999650	−	0.0264555i	$-0.991578\pi$
$83$		−	0.482042i		−	0.0529110i	0.999650	−	0.0264555i	$-0.00842203\pi$
$84$	2.76765	+	4.51000i	0.301975	+	0.492082i
$85$			19.6754i			2.13410i
$86$	−0.399075	+	1.85717i	−0.0430333	+	0.200264i
$87$	3.30757	−	5.72889i	0.354609	−	0.614201i
$88$	−6.60265	−	15.1003i	−0.703845	−	1.60969i
$89$	10.7308	−	6.19543i	1.13746	−	0.656714i	0.191661	−	0.981461i	$-0.438612\pi$
$89$	10.7308	−	6.19543i	1.13746	−	0.656714i	0.945801	+	0.324747i	$0.105279\pi$
$90$	3.02369	+	2.73475i	0.318725	+	0.288268i
$91$	−2.76635	−	0.203581i	−0.289992	−	0.0213410i
$92$	−4.27246	+	0.429839i	−0.445434	+	0.0448138i
$93$	−3.31788	+	1.91558i	−0.344048	+	0.198636i
$94$	−14.8775	+	4.79742i	−1.53450	+	0.494816i
$95$	1.70077	+	0.981939i	0.174495	+	0.100745i
$96$	5.65650	+	0.0629331i	0.577315	+	0.00642308i
$97$			3.63532i			0.369111i	0.982822	+	0.184556i	$0.0590846\pi$
$97$			3.63532i			0.369111i	−0.982822	+	0.184556i	$0.940915\pi$
$98$	−3.47421	+	9.26984i	−0.350948	+	0.936395i
$99$	5.82680			0.585616
$100$	5.37424	−	3.86819i	0.537424	−	0.386819i
$101$	1.25234	−	2.16911i	0.124612	−	0.215835i	−0.796969	−	0.604020i	$-0.793565\pi$
$101$	1.25234	−	2.16911i	0.124612	−	0.215835i	0.921581	+	0.388185i	$0.126898\pi$
$102$	−9.18621	+	2.96220i	−0.909570	+	0.293301i
$103$	−2.31322	−	4.00661i	−0.227928	−	0.394783i	0.729266	−	0.684231i	$-0.239862\pi$
$103$	−2.31322	−	4.00661i	−0.227928	−	0.394783i	−0.957194	+	0.289447i	$0.906529\pi$
$104$	−1.75896	+	2.38733i	−0.172480	+	0.234097i
$105$	−0.559792	+	7.60672i	−0.0546301	+	0.742340i
$106$	7.66346	−	8.47315i	0.744341	−	0.822985i
$107$	3.03473	+	5.25631i	0.293378	+	0.508146i	0.974606	−	0.223925i	$-0.0718871\pi$
$107$	3.03473	+	5.25631i	0.293378	+	0.508146i	−0.681228	+	0.732071i	$0.738554\pi$
$108$	−0.821596	+	1.82345i	−0.0790581	+	0.175462i
$109$	12.6132	+	7.28224i	1.20813	+	0.697513i	0.962350	−	0.271814i	$-0.0876235\pi$
$109$	12.6132	+	7.28224i	1.20813	+	0.697513i	0.245777	+	0.969326i	$0.420957\pi$
$110$	4.99076	−	23.2255i	0.475851	−	2.21446i
$111$	−2.38082			−0.225977
$112$	6.41041	+	8.42061i	0.605727	+	0.795673i
$113$	−3.82875			−0.360179			−0.180089	−	0.983650i	$-0.557639\pi$
$113$	−3.82875			−0.360179			−0.180089	+	0.983650i	$0.557639\pi$
$114$	−0.202399	+	0.941902i	−0.0189564	+	0.0882172i
$115$	−5.36027	−	3.09475i	−0.499847	−	0.288587i
$116$	5.43498	−	12.0624i	0.504625	−	1.11997i
$117$	−0.524204	−	0.907949i	−0.0484627	−	0.0839399i
$118$	−7.46641	+	8.25527i	−0.687339	+	0.759959i
$119$	−14.9332	−	10.1520i	−1.36893	−	0.930632i
$120$	6.56452	+	4.83668i	0.599256	+	0.441526i
$121$	−11.4758	−	19.8767i	−1.04326	−	1.80697i
$122$	4.40053	−	1.41900i	0.398405	−	0.128470i
$123$	0.599593	−	1.03853i	0.0540635	−	0.0936407i
$124$	−6.21892	+	4.47616i	−0.558476	+	0.401971i
$125$	−4.86972			−0.435561
$126$	−3.63577	+	0.883858i	−0.323900	+	0.0787403i
$127$			0.550415i			0.0488415i	0.999702	+	0.0244207i	$0.00777413\pi$
$127$			0.550415i			0.0488415i	−0.999702	+	0.0244207i	$0.992226\pi$
$128$	11.2688	−	1.00722i	0.996029	−	0.0890263i
$129$	−1.16324	−	0.671597i	−0.102418	−	0.0591308i
$130$	−4.06805	+	1.31179i	−0.356791	+	0.115051i
$131$	−2.42818	+	1.40191i	−0.212151	+	0.122486i	−0.602311	−	0.798262i	$-0.705753\pi$
$131$	−2.42818	+	1.40191i	−0.212151	+	0.122486i	0.390159	+	0.920747i	$0.372420\pi$
$132$	11.5951	−	1.16655i	1.00922	−	0.101535i
$133$	−1.62282	+	0.784192i	−0.140717	+	0.0679980i
$134$	−13.9630	−	12.6287i	−1.20622	−	1.09095i
$135$	−2.49662	+	1.44142i	−0.214875	+	0.124058i
$136$	−17.6871	+	7.73375i	−1.51666	+	0.663164i
$137$	−6.38148	+	11.0530i	−0.545206	+	0.944325i	0.453387	+	0.891314i	$0.350215\pi$
$137$	−6.38148	+	11.0530i	−0.545206	+	0.944325i	−0.998594	+	0.0530118i	$0.983118\pi$
$138$	0.637896	−	2.96857i	0.0543013	−	0.252701i
$139$		−	6.11761i		−	0.518889i	−0.965758	−	0.259444i	$-0.916461\pi$
$139$		−	6.11761i		−	0.518889i	0.965758	−	0.259444i	$-0.0835394\pi$
$140$	0.408930	+	15.2491i	0.0345609	+	1.28878i
$141$		−	11.0534i		−	0.930864i
$142$	−1.50064	−	0.322462i	−0.125931	−	0.0270604i
$143$	−3.05443	+	5.29044i	−0.255425	+	0.442408i
$144$	−1.26988	+	3.79307i	−0.105823	+	0.316090i
$145$	16.5155	−	9.53522i	1.37154	−	0.791857i
$146$	−5.35508	+	5.92087i	−0.443190	+	0.490015i
$147$	−5.48450	−	4.34974i	−0.452354	−	0.358761i
$148$	−4.73771	+	0.476647i	−0.389438	+	0.0391802i
$149$	−1.75163	+	1.01130i	−0.143499	+	0.0828491i	−0.570030	−	0.821624i	$-0.693069\pi$
$149$	−1.75163	+	1.01130i	−0.143499	+	0.0828491i	0.426532	+	0.904473i	$0.359735\pi$
$150$	1.43696	+	4.45622i	0.117327	+	0.363849i
$151$	−12.1833	−	7.03404i	−0.991464	−	0.572422i	−0.0857523	−	0.996316i	$-0.527329\pi$
$151$	−12.1833	−	7.03404i	−0.991464	−	0.572422i	−0.905712	+	0.423895i	$0.860663\pi$
$152$	−0.214193	+	1.91486i	−0.0173733	+	0.155316i
$153$		−	6.82499i		−	0.551768i
$154$	15.0525	+	15.7716i	1.21297	+	1.27091i
$155$	−11.0446			−0.887126
$156$	−1.22492	−	1.70183i	−0.0980719	−	0.136255i
$157$	−2.61739	+	4.53344i	−0.208890	+	0.361808i	−0.951365	−	0.308065i	$-0.900318\pi$
$157$	−2.61739	+	4.53344i	−0.208890	+	0.361808i	0.742475	+	0.669874i	$0.233652\pi$
$158$	5.49426	+	17.0385i	0.437100	+	1.35551i
$159$	4.03923	+	6.99615i	0.320332	+	0.554830i
$160$	14.0314	+	8.31053i	1.10928	+	0.657005i
$161$	5.11461	−	2.47152i	0.403088	−	0.194783i
$162$	−1.04886	−	0.948630i	−0.0824060	−	0.0745314i
$163$	−0.488212	−	0.845609i	−0.0382397	−	0.0662332i	0.846272	−	0.532751i	$-0.178842\pi$
$163$	−0.488212	−	0.845609i	−0.0382397	−	0.0662332i	−0.884512	+	0.466518i	$0.845508\pi$
$164$	0.985247	−	2.18666i	0.0769349	−	0.170749i
$165$	14.5473	+	8.39888i	1.13251	+	0.653852i
$166$	0.666497	+	0.143219i	0.0517302	+	0.0111160i
$167$	2.08267			0.161162			0.0805808	−	0.996748i	$-0.474322\pi$
$167$	2.08267			0.161162			0.0805808	+	0.996748i	$0.474322\pi$
$168$	−7.05806	+	2.48673i	−0.544541	+	0.191855i
$169$	−11.9008			−0.915449
$170$	−27.2042	−	5.84573i	−2.08647	−	0.448347i
$171$	−0.589961	−	0.340614i	−0.0451155	−	0.0260474i
$172$	−2.44925	−	1.10356i	−0.186754	−	0.0841459i
$173$	10.6732	+	18.4864i	0.811465	+	1.40550i	0.911839	+	0.410548i	$0.134663\pi$
$173$	10.6732	+	18.4864i	0.811465	+	1.40550i	−0.100374	+	0.994950i	$0.532004\pi$
$174$	6.93835	+	6.27533i	0.525995	+	0.475731i
$175$	−4.92472	+	7.24408i	−0.372274	+	0.547601i
$176$	22.8401	−	4.64274i	1.72164	−	0.349960i
$177$	−3.93537	−	6.81625i	−0.295800	−	0.512341i
$178$	5.37791	+	16.6777i	0.403091	+	1.25004i
$179$	3.47487	−	6.01865i	0.259724	−	0.449855i	−0.706444	−	0.707769i	$-0.749702\pi$
$179$	3.47487	−	6.01865i	0.259724	−	0.449855i	0.966168	+	0.257914i	$0.0830351\pi$
$180$	−4.67958	+	3.36820i	−0.348795	+	0.251051i
$181$	7.67619			0.570566			0.285283	−	0.958443i	$-0.407912\pi$
$181$	7.67619			0.570566			0.285283	+	0.958443i	$0.407912\pi$
$182$	1.10339	−	3.76441i	0.0817885	−	0.279037i
$183$			3.26942i			0.241683i
$184$	0.675066	−	6.03503i	0.0497665	−	0.444908i
$185$	−5.94398	−	3.43176i	−0.437010	−	0.252308i
$186$	−1.66281	−	5.15661i	−0.121923	−	0.378101i
$187$	−34.4400	+	19.8839i	−2.51850	+	1.45406i
$188$	−2.21293	−	21.9958i	−0.161394	−	1.60421i
$189$	0.194181	−	2.63862i	0.0141246	−	0.191931i
$190$	−1.86299	+	2.05983i	−0.135156	+	0.149436i
$191$	15.4238	−	8.90495i	1.11603	−	0.644340i	0.175645	−	0.984454i	$-0.443799\pi$
$191$	15.4238	−	8.90495i	1.11603	−	0.644340i	0.940384	+	0.340114i	$0.110466\pi$
$192$	−1.76761	+	7.80228i	−0.127566	+	0.563081i
$193$	6.89797	−	11.9476i	0.496527	−	0.860010i	−0.503465	−	0.864016i	$-0.667942\pi$
$193$	6.89797	−	11.9476i	0.496527	−	0.860010i	0.999992	+	0.00400574i	$0.00127507\pi$
$194$	−5.02639	−	1.08009i	−0.360874	−	0.0775457i
$195$		−	3.02240i		−	0.216439i
$196$	−11.7847	−	7.55777i	−0.841767	−	0.539841i
$197$			1.13180i			0.0806374i	0.999187	+	0.0403187i	$0.0128373\pi$
$197$			1.13180i			0.0806374i	−0.999187	+	0.0403187i	$0.987163\pi$
$198$	−1.73119	+	8.05644i	−0.123031	+	0.572546i
$199$	4.26593	−	7.38881i	0.302404	−	0.523779i	−0.674276	−	0.738479i	$-0.735544\pi$
$199$	4.26593	−	7.38881i	0.302404	−	0.523779i	0.976680	+	0.214701i	$0.0688776\pi$
$200$	3.75163	+	8.57998i	0.265280	+	0.606696i
$201$	11.5290	−	6.65629i	0.813195	−	0.469498i
$202$	2.62705	+	2.37601i	0.184838	+	0.167175i
$203$	−1.28453	+	17.4548i	−0.0901566	+	1.22509i
$204$	−1.36639	−	13.5814i	−0.0956662	−	0.950890i
$205$	2.99391	−	1.72853i	0.209104	−	0.120726i
$206$	6.22703	−	2.00798i	0.433858	−	0.139902i
$207$	1.85937	+	1.07351i	0.129235	+	0.0746138i
$208$	−2.77824	−	3.14133i	−0.192636	−	0.217812i
$209$			3.96939i			0.274568i
$210$	−10.3511	−	3.03402i	−0.714296	−	0.209367i
$211$	21.2436			1.46247			0.731237	−	0.682124i	$-0.238944\pi$
$211$	21.2436			1.46247			0.731237	+	0.682124i	$0.238944\pi$
$212$	9.43853	+	13.1133i	0.648241	+	0.900628i
$213$	0.542667	−	0.939926i	0.0371829	−	0.0644027i
$214$	−8.16929	+	2.63428i	−0.558441	+	0.180076i
$215$	−1.93611	−	3.35344i	−0.132042	−	0.228703i
$216$	−2.27710	−	1.67775i	−0.154937	−	0.114156i
$217$	5.69874	−	8.38264i	0.386856	−	0.569051i
$218$	−13.8163	+	15.2761i	−0.935758	+	1.03463i
$219$	−2.82254	−	4.88878i	−0.190729	−	0.330353i
$220$	30.6299	+	13.8010i	2.06507	+	0.930462i
$221$	6.19674	+	3.57769i	0.416838	+	0.240662i
$222$	0.707361	−	3.29184i	0.0474750	−	0.220934i
$223$	−3.12207			−0.209069			−0.104535	−	0.994521i	$-0.533335\pi$
$223$	−3.12207			−0.209069			−0.104535	+	0.994521i	$0.533335\pi$
$224$	−13.5474	+	6.36152i	−0.905171	+	0.425047i
$225$	−3.31079			−0.220720
$226$	1.13756	−	5.29383i	0.0756691	−	0.352140i
$227$	4.52649	+	2.61337i	0.300434	+	0.173456i	0.642638	−	0.766170i	$-0.277840\pi$
$227$	4.52649	+	2.61337i	0.300434	+	0.173456i	−0.342204	+	0.939626i	$0.611173\pi$
$228$	−1.24219	−	0.559695i	−0.0822660	−	0.0370667i
$229$	−14.2129	−	24.6175i	−0.939215	−	1.62677i	−0.766939	−	0.641720i	$-0.778221\pi$
$229$	−14.2129	−	24.6175i	−0.939215	−	1.62677i	−0.172276	−	0.985049i	$-0.555112\pi$
$230$	5.87154	−	6.49190i	0.387158	−	0.428063i
$231$	−13.8806	+	6.70748i	−0.913276	+	0.441320i
$232$	15.0633	+	11.0985i	0.988957	+	0.728655i
$233$	−3.05971	−	5.29957i	−0.200448	−	0.347186i	0.748225	−	0.663445i	$-0.230906\pi$
$233$	−3.05971	−	5.29957i	−0.200448	−	0.347186i	−0.948673	+	0.316259i	$0.897573\pi$
$234$	1.41112	−	0.455033i	0.0922480	−	0.0297464i
$235$	15.9326	−	27.5961i	1.03933	−	1.80017i
$236$	−9.19583	−	12.7762i	−0.598598	−	0.831657i
$237$	−12.6589			−0.822286
$238$	18.4735	−	17.6312i	1.19746	−	1.14286i
$239$			8.83528i			0.571507i	0.958303	+	0.285753i	$0.0922439\pi$
$239$			8.83528i			0.571507i	−0.958303	+	0.285753i	$0.907756\pi$
$240$	−8.63782	+	7.63942i	−0.557569	+	0.493123i
$241$	5.15757	+	2.97772i	0.332228	+	0.191812i	0.656830	−	0.754039i	$-0.271897\pi$
$241$	5.15757	+	2.97772i	0.332228	+	0.191812i	−0.324602	+	0.945851i	$0.605230\pi$
$242$	30.8921	−	9.96151i	1.98582	−	0.640350i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	0.654550	+	6.50600i	0.0419032	+	0.416504i
$245$	−7.42288	−	18.7651i	−0.474231	−	1.19886i
$246$	1.25778	+	1.13758i	0.0801928	+	0.0725297i
$247$	0.618521	−	0.357103i	0.0393555	−	0.0227219i
$248$	−4.34128	−	9.92851i	−0.275672	−	0.630461i
$249$	−0.241021	+	0.417461i	−0.0152741	+	0.0264555i
$250$	1.44684	−	6.73313i	0.0915059	−	0.425840i
$251$			2.13955i			0.135047i	0.997718	+	0.0675235i	$0.0215098\pi$
$251$			2.13955i			0.135047i	−0.997718	+	0.0675235i	$0.978490\pi$
$252$	−0.141849	−	5.28960i	−0.00893567	−	0.333214i
$253$		−	12.5102i		−	0.786510i
$254$	−0.761033	−	0.163533i	−0.0477514	−	0.0102610i
$255$	9.83770	−	17.0394i	0.616061	−	1.06705i
$256$	−1.95542	+	15.8801i	−0.122214	+	0.992504i
$257$	−16.7030	+	9.64346i	−1.04190	+	0.601543i	−0.920372	−	0.391045i	$-0.872114\pi$
$257$	−16.7030	+	9.64346i	−1.04190	+	0.601543i	−0.121531	+	0.992588i	$0.538780\pi$
$258$	1.27419	−	1.40882i	0.0793278	−	0.0877092i
$259$	5.67158	−	2.74066i	0.352415	−	0.170296i
$260$	−0.605095	−	6.01444i	−0.0375264	−	0.373000i
$261$	−5.72889	+	3.30757i	−0.354609	+	0.204734i
$262$	−1.21692	−	3.77385i	−0.0751817	−	0.233150i
$263$	−21.0740	−	12.1671i	−1.29948	−	0.750254i	−0.319164	−	0.947699i	$-0.603402\pi$
$263$	−21.0740	−	12.1671i	−1.29948	−	0.750254i	−0.980314	+	0.197446i	$0.936735\pi$
$264$	−1.83207	+	16.3785i	−0.112756	+	1.00803i
$265$			23.2889i			1.43063i
$266$	−0.602109	−	2.47679i	−0.0369177	−	0.151862i
$267$	−12.3909			−0.758308
$268$	21.6096	−	15.5539i	1.32002	−	0.950103i
$269$	−10.4505	+	18.1007i	−0.637176	+	1.10362i	0.348873	+	0.937170i	$0.386564\pi$
$269$	−10.4505	+	18.1007i	−0.637176	+	1.10362i	−0.986050	+	0.166452i	$0.946769\pi$
$270$	−1.25122	−	3.88021i	−0.0761467	−	0.236142i
$271$	9.99697	+	17.3153i	0.607273	+	1.05183i	0.991688	+	0.128667i	$0.0410698\pi$
$271$	9.99697	+	17.3153i	0.607273	+	1.05183i	−0.384415	+	0.923160i	$0.625597\pi$
$272$	−5.43810	−	26.7529i	−0.329733	−	1.62213i
$273$	2.29394	+	1.55948i	0.138835	+	0.0943840i
$274$	−13.3865	−	12.1073i	−0.808709	−	0.731430i
$275$	9.64567	+	16.7068i	0.581656	+	1.00746i
$276$	3.91497	+	1.76398i	0.235654	+	0.106179i
$277$	13.2433	+	7.64600i	0.795710	+	0.459404i	0.841969	−	0.539526i	$-0.181396\pi$
$277$	13.2433	+	7.64600i	0.795710	+	0.459404i	−0.0462586	+	0.998929i	$0.514730\pi$
$278$	8.45852	+	1.81760i	0.507309	+	0.109012i
$279$	3.83116			0.229365
$280$	−21.2057	−	3.96523i	−1.26728	−	0.236968i
$281$	5.59802			0.333950			0.166975	−	0.985961i	$-0.446600\pi$
$281$	5.59802			0.333950			0.166975	+	0.985961i	$0.446600\pi$
$282$	15.2830	+	3.28406i	0.910090	+	0.195563i
$283$	9.72911	+	5.61710i	0.578335	+	0.333902i	0.760472	−	0.649371i	$-0.224968\pi$
$283$	9.72911	+	5.61710i	0.578335	+	0.333902i	−0.182136	+	0.983273i	$0.558301\pi$
$284$	0.891706	−	1.97905i	0.0529130	−	0.117435i
$285$	−0.981939	−	1.70077i	−0.0581650	−	0.100745i
$286$	−6.40733	−	5.79505i	−0.378874	−	0.342669i
$287$	−0.232859	+	3.16419i	−0.0137452	+	0.186776i
$288$	−4.86721	−	2.88275i	−0.286803	−	0.169868i
$289$	14.7903	+	25.6175i	0.870016	+	1.50691i
$290$	8.27700	+	25.6682i	0.486042	+	1.50729i
$291$	1.81766	−	3.14828i	0.106553	−	0.184556i
$292$	−6.59547	−	9.16336i	−0.385971	−	0.536245i
$293$	17.7212			1.03528			0.517642	−	0.855598i	$-0.326810\pi$
$293$	17.7212			1.03528			0.517642	+	0.855598i	$0.326810\pi$
$294$	7.64367	−	6.29081i	0.445788	−	0.366887i
$295$		−	22.6901i		−	1.32107i
$296$	0.748579	−	6.69223i	0.0435103	−	0.388978i
$297$	−5.04616	−	2.91340i	−0.292808	−	0.169053i
$298$	−0.877855	−	2.72236i	−0.0508528	−	0.157702i
$299$	−1.94938	+	1.12547i	−0.112735	+	0.0650878i
$300$	−6.58833	+	0.662832i	−0.380377	+	0.0382686i
$301$	3.54417	+	0.260822i	0.204283	+	0.0150335i
$302$	13.3454	−	14.7554i	0.767941	−	0.849078i
$303$	−2.16911	+	1.25234i	−0.124612	+	0.0719449i
$304$	−2.58395	−	0.865077i	−0.148200	−	0.0496156i
$305$	−4.71262	+	8.16250i	−0.269844	+	0.467383i
$306$	9.43659	+	2.02777i	0.539454	+	0.115920i
$307$		−	20.3724i		−	1.16271i	−0.813649	−	0.581357i	$-0.802522\pi$
$307$		−	20.3724i		−	1.16271i	0.813649	−	0.581357i	$-0.197478\pi$
$308$	−26.2789	+	16.1265i	−1.49738	+	0.918894i
$309$			4.62644i			0.263189i
$310$	3.28146	−	15.2709i	0.186374	−	0.867328i
$311$	−14.4363	+	25.0045i	−0.818610	+	1.41787i	0.0880964	+	0.996112i	$0.471922\pi$
$311$	−14.4363	+	25.0045i	−0.818610	+	1.41787i	−0.906706	+	0.421762i	$0.861412\pi$
$312$	2.71697	−	1.18801i	0.153818	−	0.0672576i
$313$	−4.08718	+	2.35974i	−0.231021	+	0.133380i	−0.611043	−	0.791597i	$-0.709250\pi$
$313$	−4.08718	+	2.35974i	−0.231021	+	0.133380i	0.380022	+	0.924978i	$0.375916\pi$
$314$	−5.49053	−	4.96586i	−0.309848	−	0.280240i
$315$	4.28815	−	6.30772i	0.241610	−	0.355400i
$316$	−25.1907	+	2.53436i	−1.41709	+	0.142569i
$317$	−22.0349	+	12.7218i	−1.23760	+	0.714529i	−0.968603	−	0.248612i	$-0.920026\pi$
$317$	−22.0349	+	12.7218i	−1.23760	+	0.714529i	−0.268998	+	0.963141i	$0.586692\pi$
$318$	−10.8733	+	3.50623i	−0.609746	+	0.196620i
$319$	33.3811	+	19.2726i	1.86898	+	1.07906i
$320$	−15.6594	+	16.9314i	−0.875389	+	0.946495i
$321$		−	6.06946i		−	0.338764i
$322$	1.89765	+	7.80603i	0.105752	+	0.435013i
$323$	4.64938			0.258699
$324$	1.62325	−	1.16836i	0.0901805	−	0.0649088i
$325$	1.73553	−	3.00603i	0.0962700	−	0.166745i
$326$	1.31423	−	0.423790i	0.0727887	−	0.0234716i
$327$	−7.28224	−	12.6132i	−0.402709	−	0.697513i
$328$	2.73066	+	2.01193i	0.150776	+	0.111090i
$329$	12.7240	+	26.3314i	0.701499	+	1.45170i
$330$	−15.9349	+	17.6185i	−0.877185	+	0.969864i
$331$	9.85929	+	17.0768i	0.541916	+	0.938625i	0.998794	+	0.0490963i	$0.0156341\pi$
$331$	9.85929	+	17.0768i	0.541916	+	0.938625i	−0.456878	+	0.889529i	$0.651033\pi$
$332$	−0.396044	+	0.878981i	−0.0217357	+	0.0482404i
$333$	2.06185	+	1.19041i	0.112989	+	0.0652339i
$334$	−0.618778	+	2.87960i	−0.0338581	+	0.157565i
$335$	38.3781			2.09682
$336$	−1.34127	−	10.4977i	−0.0731723	−	0.572695i
$337$	−24.7720			−1.34942			−0.674709	−	0.738084i	$-0.735731\pi$
$337$	−24.7720			−1.34942			−0.674709	+	0.738084i	$0.735731\pi$
$338$	3.53584	−	16.4547i	0.192325	−	0.895019i
$339$	3.31580	+	1.91438i	0.180089	+	0.103975i
$340$	16.1652	−	35.8772i	0.876683	−	1.94571i
$341$	−11.1617	−	19.3326i	−0.604440	−	1.04692i
$342$	0.646234	−	0.714512i	0.0349443	−	0.0386364i
$343$	18.0723	+	4.04850i	0.975815	+	0.218599i
$344$	2.25354	−	3.05858i	0.121503	−	0.164908i
$345$	3.09475	+	5.36027i	0.166616	+	0.288587i
$346$	−28.7314	+	9.26477i	−1.54461	+	0.498077i
$347$	7.49413	−	12.9802i	0.402306	−	0.696815i	−0.591698	−	0.806160i	$-0.701542\pi$
$347$	7.49413	−	12.9802i	0.402306	−	0.696815i	0.994004	+	0.109345i	$0.0348754\pi$
$348$	−10.7380	+	7.72887i	−0.575619	+	0.414311i
$349$	−27.4546			−1.46961			−0.734806	−	0.678278i	$-0.762727\pi$
$349$	−27.4546			−1.46961			−0.734806	+	0.678278i	$0.762727\pi$
$350$	−8.55286	−	8.96145i	−0.457170	−	0.479010i
$351$			1.04841i			0.0559599i
$352$	−0.366699	+	32.9593i	−0.0195451	+	1.75674i
$353$	20.7884	+	12.0022i	1.10645	+	0.638811i	0.937908	−	0.346883i	$-0.112760\pi$
$353$	20.7884	+	12.0022i	1.10645	+	0.638811i	0.168544	+	0.985694i	$0.446093\pi$
$354$	10.5937	−	3.41607i	0.563051	−	0.181562i
$355$	2.70966	−	1.56442i	0.143814	−	0.0830310i
$356$	−24.6572	+	2.48069i	−1.30683	+	0.131476i
$357$	7.85654	+	16.2585i	0.415812	+	0.860491i
$358$	7.28928	+	6.59273i	0.385251	+	0.348437i
$359$	11.8249	−	6.82714i	0.624097	−	0.360322i	−0.154366	−	0.988014i	$-0.549333\pi$
$359$	11.8249	−	6.82714i	0.624097	−	0.360322i	0.778462	+	0.627691i	$0.216000\pi$
$360$	−3.26670	−	7.47095i	−0.172170	−	0.393753i
$361$	−9.26796	+	16.0526i	−0.487788	+	0.844873i
$362$	−2.28066	+	10.6135i	−0.119869	+	0.557833i
$363$			22.9516i			1.20465i
$364$	4.87704	+	2.64404i	0.255627	+	0.138585i
$365$		−	16.2739i		−	0.851813i
$366$	−4.52047	−	0.971374i	−0.236289	−	0.0507745i
$367$	−17.3424	+	30.0379i	−0.905264	+	1.56796i	−0.0847016	+	0.996406i	$0.526994\pi$
$367$	−17.3424	+	30.0379i	−0.905264	+	1.56796i	−0.820562	+	0.571557i	$0.806340\pi$
$368$	8.14377	+	2.72644i	0.424524	+	0.142126i
$369$	−1.03853	+	0.599593i	−0.0540635	+	0.0312136i
$370$	6.51094	−	7.19885i	0.338488	−	0.374251i
$371$	−17.6758	−	12.0165i	−0.917682	−	0.623865i
$372$	7.62383	−	0.767011i	0.395277	−	0.0397676i
$373$	−5.26744	+	3.04116i	−0.272738	+	0.157465i	−0.630131	−	0.776489i	$-0.716999\pi$
$373$	−5.26744	+	3.04116i	−0.272738	+	0.157465i	0.357393	+	0.933954i	$0.383666\pi$
$374$	−17.2601	−	53.5262i	−0.892501	−	2.76778i
$375$	4.21730	+	2.43486i	0.217780	+	0.125736i
$376$	31.0700	+	3.47542i	1.60231	+	0.179231i
$377$		−	6.93538i		−	0.357190i
$378$	3.59059	+	1.05244i	0.184680	+	0.0541317i
$379$	19.0628			0.979189			0.489594	−	0.871950i	$-0.337145\pi$
$379$	19.0628			0.979189			0.489594	+	0.871950i	$0.337145\pi$
$380$	−2.29451	−	3.18786i	−0.117706	−	0.163534i
$381$	0.275208	−	0.476674i	0.0140993	−	0.0244207i
$382$	7.72989	+	23.9715i	0.395496	+	1.22649i
$383$	4.12501	+	7.14473i	0.210778	+	0.365079i	0.951958	−	0.306228i	$-0.0990668\pi$
$383$	4.12501	+	7.14473i	0.210778	+	0.365079i	−0.741180	+	0.671306i	$0.765733\pi$
$384$	−10.2627	−	4.76212i	−0.523714	−	0.243016i
$385$	−44.3228	−	3.26180i	−2.25890	−	0.166237i
$386$	14.4700	+	13.0872i	0.736502	+	0.666123i
$387$	0.671597	+	1.16324i	0.0341392	+	0.0591308i
$388$	2.98677	−	6.62884i	0.151630	−	0.336528i
$389$	−16.9926	−	9.81070i	−0.861560	−	0.497422i	0.00297421	−	0.999996i	$-0.499053\pi$
$389$	−16.9926	−	9.81070i	−0.861560	−	0.497422i	−0.864534	+	0.502574i	$0.832387\pi$
$390$	4.17893	+	0.897981i	0.211608	+	0.0454711i
$391$	−14.6533			−0.741051
$392$	13.9511	−	14.0487i	0.704638	−	0.709567i
$393$	2.80383			0.141434
$394$	−1.56488	−	0.336268i	−0.0788378	−	0.0169409i
$395$	−31.6045	−	18.2469i	−1.59019	−	0.918099i
$396$	−10.6249	−	4.78728i	−0.533921	−	0.240570i
$397$	−15.6816	−	27.1613i	−0.787035	−	1.36318i	−0.927776	−	0.373138i	$-0.878282\pi$
$397$	−15.6816	−	27.1613i	−0.787035	−	1.36318i	0.140741	−	0.990047i	$-0.455052\pi$
$398$	8.94870	+	8.09358i	0.448558	+	0.405694i
$399$	1.79750	+	0.132281i	0.0899876	+	0.00662235i
$400$	−12.9778	+	2.63801i	−0.648889	+	0.131901i
$401$	−17.4562	−	30.2350i	−0.871722	−	1.50987i	−0.860215	−	0.509932i	$-0.829670\pi$
$401$	−17.4562	−	30.2350i	−0.871722	−	1.50987i	−0.0115069	−	0.999934i	$-0.503663\pi$
$402$	5.77796	+	17.9183i	0.288178	+	0.893683i
$403$	−2.00831	+	3.47849i	−0.100041	+	0.173276i
$404$	−4.06571	+	2.92636i	−0.202277	+	0.145592i
$405$	2.88284			0.143250
$406$	−23.7523	−	6.96205i	−1.17881	−	0.345521i
$407$		−	13.8725i		−	0.687636i
$408$	19.1844	+	2.14592i	0.949767	+	0.106239i
$409$	11.8182	+	6.82325i	0.584373	+	0.337388i	0.762869	−	0.646553i	$-0.223790\pi$
$409$	11.8182	+	6.82325i	0.584373	+	0.337388i	−0.178496	+	0.983941i	$0.557123\pi$
$410$	1.50044	+	4.65310i	0.0741017	+	0.229800i
$411$	11.0530	−	6.38148i	0.545206	−	0.314775i
$412$	0.926229	+	9.20640i	0.0456320	+	0.453567i
$413$	17.2213	+	11.7075i	0.847405	+	0.576088i
$414$	−2.03672	+	2.25191i	−0.100099	+	0.110675i
$415$	−1.20348	+	0.694827i	−0.0590763	+	0.0341077i
$416$	5.16880	−	2.90802i	0.253421	−	0.142578i
$417$	−3.05880	+	5.29800i	−0.149790	+	0.259444i
$418$	−5.48828	−	1.17934i	−0.268440	−	0.0576834i
$419$			4.22322i			0.206318i	0.994665	+	0.103159i	$0.0328950\pi$
$419$			4.22322i			0.206318i	−0.994665	+	0.103159i	$0.967105\pi$
$420$	7.27041	−	13.4106i	0.354759	−	0.654369i
$421$			11.6892i			0.569697i	0.958573	+	0.284849i	$0.0919433\pi$
$421$			11.6892i			0.569697i	−0.958573	+	0.284849i	$0.908057\pi$
$422$	−6.31167	+	29.3726i	−0.307247	+	1.42983i
$423$	−5.52670	+	9.57253i	−0.268717	+	0.465432i
$424$	−20.9355	+	9.15411i	−1.01672	+	0.444563i
$425$	19.5688	−	11.2981i	0.949228	−	0.548037i
$426$	1.13836	+	1.02958i	0.0551537	+	0.0498833i
$427$	−3.76357	−	7.78842i	−0.182132	−	0.376908i
$428$	−1.21513	−	12.0779i	−0.0587354	−	0.583810i
$429$	5.29044	−	3.05443i	0.255425	−	0.147469i
$430$	5.21188	−	1.68063i	0.251339	−	0.0810472i
$431$	−29.7064	−	17.1510i	−1.43091	−	0.826136i	−0.433719	−	0.901048i	$-0.642799\pi$
$431$	−29.7064	−	17.1510i	−1.43091	−	0.826136i	−0.997190	+	0.0749129i	$0.976132\pi$
$432$	2.99628	−	2.64996i	0.144159	−	0.127496i
$433$		−	14.1884i		−	0.681853i	−0.940090	−	0.340926i	$-0.889259\pi$
$433$		−	14.1884i		−	0.681853i	0.940090	−	0.340926i	$-0.110741\pi$
$434$	9.89713	+	10.3699i	0.475077	+	0.497773i
$435$	−19.0704			−0.914358
$436$	−17.0165	−	23.6418i	−0.814945	−	1.13224i
$437$	−0.731303	+	1.26665i	−0.0349830	+	0.0605923i
$438$	7.59807	−	2.45009i	0.363050	−	0.117070i
$439$	14.0252	+	24.2923i	0.669386	+	1.15941i	0.978076	+	0.208247i	$0.0667759\pi$
$439$	14.0252	+	24.2923i	0.669386	+	1.15941i	−0.308691	+	0.951163i	$0.599891\pi$
$440$	−28.1824	+	38.2501i	−1.34354	+	1.82350i
$441$	2.57485	+	6.50924i	0.122612	+	0.309964i
$442$	−6.78781	+	7.50498i	−0.322863	+	0.356975i
$443$	−5.51040	−	9.54430i	−0.261807	−	0.453463i	0.704915	−	0.709292i	$-0.250985\pi$
$443$	−5.51040	−	9.54430i	−0.261807	−	0.453463i	−0.966722	+	0.255828i	$0.917652\pi$
$444$	4.34130	+	1.95607i	0.206029	+	0.0928309i
$445$	−30.9352	−	17.8605i	−1.46647	−	0.846667i
$446$	0.927595	−	4.31674i	0.0439229	−	0.204403i
$447$	2.02260			0.0956659
$448$	−4.77073	−	20.6214i	−0.225396	−	0.974267i
$449$	30.2270			1.42650			0.713250	−	0.700910i	$-0.247222\pi$
$449$	30.2270			1.42650			0.713250	+	0.700910i	$0.247222\pi$
$450$	0.983666	−	4.57768i	0.0463705	−	0.215794i
$451$	6.05128	+	3.49371i	0.284944	+	0.164512i
$452$	6.98155	+	3.14569i	0.328384	+	0.147961i
$453$	7.03404	+	12.1833i	0.330488	+	0.572422i
$454$	−4.95825	+	5.48211i	−0.232702	+	0.257288i
$455$	3.47921	+	7.19996i	0.163108	+	0.337539i
$456$	1.14293	−	1.55122i	0.0535225	−	0.0726427i
$457$	−12.7386	−	22.0639i	−0.595887	−	1.03211i	−0.993421	−	0.114519i	$-0.963467\pi$
$457$	−12.7386	−	22.0639i	−0.595887	−	1.03211i	0.397534	−	0.917587i	$-0.369866\pi$
$458$	38.2602	−	12.3374i	1.78778	−	0.576490i
$459$	−3.41250	+	5.91062i	−0.159282	+	0.275884i
$460$	7.23156	+	10.0471i	0.337173	+	0.468449i
$461$	27.9292			1.30079			0.650395	−	0.759596i	$-0.274603\pi$
$461$	27.9292			1.30079			0.650395	+	0.759596i	$0.274603\pi$
$462$	−5.15006	−	21.1849i	−0.239603	−	0.985610i
$463$		−	19.4232i		−	0.902674i	−0.892354	−	0.451337i	$-0.850947\pi$
$463$		−	19.4232i		−	0.902674i	0.892354	−	0.451337i	$-0.149053\pi$
$464$	−19.8209	+	17.5299i	−0.920160	+	0.813804i
$465$	9.56493	+	5.52232i	0.443563	+	0.256091i
$466$	8.23652	−	2.65596i	0.381550	−	0.123035i
$467$	−1.30760	+	0.754943i	−0.0605085	+	0.0349346i	−0.529949	−	0.848029i	$-0.677789\pi$
$467$	−1.30760	+	0.754943i	−0.0605085	+	0.0349346i	0.469441	+	0.882964i	$0.344456\pi$
$468$	0.209895	+	2.08629i	0.00970240	+	0.0964386i
$469$	−19.8021	+	29.1282i	−0.914376	+	1.34501i
$470$	33.4221	+	30.2283i	1.54165	+	1.39433i
$471$	4.53344	−	2.61739i	0.208890	−	0.120603i
$472$	20.3971	−	8.91873i	0.938855	−	0.410518i
$473$	3.91326	−	6.77797i	0.179932	−	0.311651i
$474$	3.76108	−	17.5029i	0.172752	−	0.803934i
$475$		−	2.25541i		−	0.103485i
$476$	18.8892	+	30.7808i	0.865784	+	1.41083i
$477$		−	8.07845i		−	0.369887i
$478$	−12.2161	−	2.62504i	−0.558752	−	0.120067i
$479$	7.12030	−	12.3327i	0.325335	−	0.563496i	−0.656245	−	0.754548i	$-0.727856\pi$
$479$	7.12030	−	12.3327i	0.325335	−	0.563496i	0.981580	+	0.191051i	$0.0611897\pi$
$480$	−7.99629	−	14.2128i	−0.364979	−	0.648724i
$481$	−2.16166	+	1.24803i	−0.0985631	+	0.0569054i
$482$	−5.64951	+	6.24641i	−0.257328	+	0.284516i
$483$	−5.66514	−	0.416908i	−0.257773	−	0.0189700i
$484$	4.59499	+	45.6727i	0.208863	+	2.07603i
$485$	9.07601	−	5.24004i	0.412120	−	0.237938i
$486$	0.434022	+	1.34597i	0.0196876	+	0.0610543i
$487$	−6.40076	−	3.69548i	−0.290046	−	0.167458i	0.347916	−	0.937526i	$-0.386889\pi$
$487$	−6.40076	−	3.69548i	−0.290046	−	0.167458i	−0.637963	+	0.770067i	$0.720223\pi$
$488$	−9.19001	−	1.02798i	−0.416012	−	0.0465343i
$489$			0.976425i			0.0441555i
$490$	28.1510	−	4.68798i	1.27173	−	0.211781i
$491$	14.0578			0.634420			0.317210	−	0.948355i	$-0.397254\pi$
$491$	14.0578			0.634420			0.317210	+	0.948355i	$0.397254\pi$
$492$	−1.94658	+	1.40108i	−0.0877585	+	0.0631655i
$493$	22.5742	−	39.0996i	1.01669	−	1.76096i
$494$	0.309981	+	0.961297i	0.0139467	+	0.0432508i
$495$	−8.39888	−	14.5473i	−0.377502	−	0.653852i
$496$	15.0175	−	3.05263i	0.674306	−	0.137067i
$497$	−0.210751	+	2.86378i	−0.00945346	+	0.128458i
$498$	−0.505594	−	0.457280i	−0.0226562	−	0.0204912i
$499$	−13.4960	−	23.3757i	−0.604162	−	1.04644i	−0.992183	−	0.124789i	$-0.960175\pi$
$499$	−13.4960	−	23.3757i	−0.604162	−	1.04644i	0.388021	−	0.921651i	$-0.373159\pi$
$500$	8.87970	+	4.00094i	0.397112	+	0.178928i
$501$	−1.80364	−	1.04133i	−0.0805808	−	0.0465233i
$502$	−2.95825	−	0.635678i	−0.132033	−	0.0283717i
$503$	3.15505			0.140677			0.0703384	−	0.997523i	$-0.477592\pi$
$503$	3.15505			0.140677			0.0703384	+	0.997523i	$0.477592\pi$
$504$	7.35582	+	1.37546i	0.327654	+	0.0612678i
$505$	−7.22059			−0.321312
$506$	17.2973	+	3.71689i	0.768957	+	0.165236i
$507$	10.3064	+	5.95042i	0.457725	+	0.264267i
$508$	0.452219	−	1.00366i	0.0200640	−	0.0445301i
$509$	10.8815	+	18.8473i	0.482315	+	0.835394i	0.999794	−	0.0203019i	$-0.00646275\pi$
$509$	10.8815	+	18.8473i	0.482315	+	0.835394i	−0.517479	+	0.855696i	$0.673129\pi$
$510$	20.6367	+	18.6647i	0.913808	+	0.826485i
$511$	12.3515	+	8.39689i	0.546399	+	0.371457i
$512$	−21.3756	−	7.42178i	−0.944678	−	0.327999i
$513$	0.340614	+	0.589961i	0.0150385	+	0.0260474i
$514$	−8.37095	−	25.9595i	−0.369227	−	1.14503i
$515$	−6.66865	+	11.5504i	−0.293856	+	0.508973i
$516$	1.56933	+	2.18034i	0.0690860	+	0.0959841i
$517$	64.4060			2.83257
$518$	2.10430	+	8.65609i	0.0924577	+	0.380327i
$519$		−	21.3463i		−	0.936999i
$520$	8.49565	+	0.950307i	0.372559	+	0.0416737i
$521$	−34.9828	−	20.1973i	−1.53262	−	0.884860i	−0.999240	−	0.0389867i	$-0.987587\pi$
$521$	−34.9828	−	20.1973i	−1.53262	−	0.884860i	−0.533383	−	0.845874i	$-0.679080\pi$
$522$	−2.87112	−	8.90377i	−0.125666	−	0.389707i
$523$	25.4468	−	14.6917i	1.11271	−	0.642424i	0.173181	−	0.984890i	$-0.444595\pi$
$523$	25.4468	−	14.6917i	1.11271	−	0.642424i	0.939530	+	0.342466i	$0.111262\pi$
$524$	5.57949	−	0.561335i	0.243741	−	0.0245221i
$525$	7.88697	−	3.81120i	0.344216	−	0.166334i
$526$	23.0841	−	25.5230i	1.00651	−	1.11286i
$527$	−22.6445	+	13.0738i	−0.986410	+	0.569504i
$528$	−22.1015	−	7.39932i	−0.961844	−	0.322014i
$529$	−9.19517	+	15.9265i	−0.399790	+	0.692457i
$530$	−32.2005	−	6.91934i	−1.39870	−	0.300557i
$531$			7.87073i			0.341561i
$532$	3.60343	−	0.0966319i	0.156228	−	0.00418952i
$533$		−	1.25724i		−	0.0544570i
$534$	3.68143	−	17.1322i	0.159311	−	0.741385i
$535$	8.74866	−	15.1531i	0.378237	−	0.655126i
$536$	15.0852	+	34.4998i	0.651580	+	1.49016i
$537$	−6.01865	+	3.47487i	−0.259724	+	0.149952i
$538$	−21.9221	−	19.8272i	−0.945129	−	0.854813i
$539$	25.3451	−	31.9571i	1.09169	−	1.37649i
$540$	5.73673	−	0.577155i	0.246870	−	0.0248368i
$541$	−26.5848	+	15.3487i	−1.14297	+	0.659893i	−0.947164	−	0.320749i	$-0.896065\pi$
$541$	−26.5848	+	15.3487i	−1.14297	+	0.659893i	−0.195805	+	0.980643i	$0.562732\pi$
$542$	−26.9112	+	8.67782i	−1.15593	+	0.372744i
$543$	−6.64777	−	3.83809i	−0.285283	−	0.164708i
$544$	38.6056	+	0.429518i	1.65520	+	0.0184154i
$545$		−	41.9872i		−	1.79853i
$546$	−2.83777	+	2.70838i	−0.121445	+	0.115908i
$547$	−15.7691			−0.674240			−0.337120	−	0.941462i	$-0.609453\pi$
$547$	−15.7691			−0.674240			−0.337120	+	0.941462i	$0.609453\pi$
$548$	20.7175	−	14.9117i	0.885006	−	0.636997i
$549$	1.63471	−	2.83140i	0.0697678	−	0.120841i
$550$	−25.9655	+	8.37287i	−1.10717	+	0.357020i
$551$	−2.25322	−	3.90268i	−0.0959902	−	0.166260i
$552$	−3.60214	+	4.88895i	−0.153317	+	0.208088i
$553$	30.1561	−	14.5722i	1.28237	−	0.619674i
$554$	−14.5064	+	16.0391i	−0.616320	+	0.681437i
$555$	3.43176	+	5.94398i	0.145670	+	0.252308i
$556$	−5.02620	+	11.1552i	−0.213158	+	0.473085i
$557$	19.2427	+	11.1098i	0.815340	+	0.470737i	0.848807	−	0.528703i	$-0.177321\pi$
$557$	19.2427	+	11.1098i	0.815340	+	0.470737i	−0.0334668	+	0.999440i	$0.510655\pi$
$558$	−1.13827	+	5.29716i	−0.0481868	+	0.224247i
$559$	−1.40822			−0.0595612
$560$	11.7829	−	28.1420i	0.497920	−	1.18922i
$561$	39.7679			1.67900
$562$	−1.66322	+	7.74012i	−0.0701588	+	0.326497i
$563$	20.7809	+	11.9978i	0.875809	+	0.505648i	0.869274	−	0.494330i	$-0.164587\pi$
$563$	20.7809	+	11.9978i	0.875809	+	0.505648i	0.00653450	+	0.999979i	$0.497920\pi$
$564$	−9.08143	+	20.1554i	−0.382397	+	0.848693i
$565$	5.51885	+	9.55893i	0.232180	+	0.402147i
$566$	−10.6571	+	11.7831i	−0.447951	+	0.495280i
$567$	−1.48747	+	2.18802i	−0.0624680	+	0.0918881i
$568$	2.47141	+	1.82091i	0.103698	+	0.0764038i
$569$	−0.631897	−	1.09448i	−0.0264905	−	0.0458829i	0.852476	−	0.522766i	$-0.175100\pi$
$569$	−0.631897	−	1.09448i	−0.0264905	−	0.0458829i	−0.878967	+	0.476883i	$0.841767\pi$
$570$	2.64331	−	0.852366i	0.110716	−	0.0357017i
$571$	−10.3555	+	17.9363i	−0.433365	+	0.750611i	−0.997161	−	0.0753037i	$-0.976007\pi$
$571$	−10.3555	+	17.9363i	−0.433365	+	0.750611i	0.563795	+	0.825915i	$0.309341\pi$
$572$	9.91622	−	7.13735i	0.414618	−	0.298428i
$573$	−17.8099			−0.744019
$574$	−4.30579	−	1.26207i	−0.179720	−	0.0526779i
$575$			7.10831i			0.296437i
$576$	5.43194	−	5.87317i	0.226331	−	0.244715i
$577$	−27.2402	−	15.7271i	−1.13402	−	0.654728i	−0.189079	−	0.981962i	$-0.560550\pi$
$577$	−27.2402	−	15.7271i	−1.13402	−	0.654728i	−0.944943	+	0.327234i	$0.893884\pi$
$578$	−39.8144	+	12.8386i	−1.65606	+	0.534016i
$579$	−11.9476	+	6.89797i	−0.496527	+	0.286670i
$580$	−37.9493	+	3.81797i	−1.57576	+	0.158533i
$581$	0.0936032	−	1.27192i	0.00388332	−	0.0527683i
$582$	3.81294	+	3.44858i	0.158051	+	0.142948i
$583$	−40.7652	+	23.5358i	−1.68832	+	0.974752i
$584$	14.6293	−	6.39672i	0.605365	−	0.264698i
$585$	−1.51120	+	2.61747i	−0.0624804	+	0.108219i
$586$	−5.26512	+	24.5022i	−0.217500	+	1.01218i
$587$			5.93391i			0.244919i	0.992474	+	0.122459i	$0.0390781\pi$
$587$			5.93391i			0.244919i	−0.992474	+	0.122459i	$0.960922\pi$
$588$	6.42700	+	12.4376i	0.265045	+	0.512918i
$589$			2.60989i			0.107539i
$590$	31.3725	+	6.74143i	1.29159	+	0.277540i
$591$	0.565900	−	0.980167i	0.0232780	−	0.0403187i
$592$	9.03061	+	3.02334i	0.371156	+	0.124259i
$593$	−13.6001	+	7.85199i	−0.558487	+	0.322443i	−0.752538	−	0.658549i	$-0.771171\pi$
$593$	−13.6001	+	7.85199i	−0.558487	+	0.322443i	0.194051	+	0.980991i	$0.437837\pi$
$594$	5.52748	−	6.11148i	0.226795	−	0.250757i
$595$	−3.82058	+	51.9158i	−0.156628	+	2.12834i
$596$	4.02489	−	0.404932i	0.164866	−	0.0165867i
$597$	−7.38881	+	4.26593i	−0.302404	+	0.174593i
$598$	−0.976960	−	3.02970i	−0.0399509	−	0.123894i
$599$	−15.0452	−	8.68632i	−0.614728	−	0.354914i	0.160085	−	0.987103i	$-0.448823\pi$
$599$	−15.0452	−	8.68632i	−0.614728	−	0.354914i	−0.774814	+	0.632190i	$0.782156\pi$
$600$	1.04098	−	9.30630i	0.0424980	−	0.379928i
$601$			43.6846i			1.78193i	0.454069	+	0.890966i	$0.349972\pi$
$601$			43.6846i			1.78193i	−0.454069	+	0.890966i	$0.650028\pi$
$602$	−1.41363	+	4.82287i	−0.0576153	+	0.196565i
$603$	−13.3126			−0.542130
$604$	16.4366	+	22.8360i	0.668794	+	0.929184i
$605$	−33.0830	+	57.3014i	−1.34501	+	2.32963i
$606$	−1.08708	−	3.37121i	−0.0441598	−	0.136946i
$607$	−9.60046	−	16.6285i	−0.389671	−	0.674929i	0.602734	−	0.797942i	$-0.294078\pi$
$607$	−9.60046	−	16.6285i	−0.389671	−	0.674929i	−0.992405	+	0.123012i	$0.960745\pi$
$608$	1.96382	−	3.31568i	0.0796432	−	0.134469i
$609$	9.83986	−	14.4741i	0.398731	−	0.586519i
$610$	−9.88573	−	8.94106i	−0.400262	−	0.362013i
$611$	−5.79424	−	10.0359i	−0.234410	−	0.406010i
$612$	−5.60739	+	12.4451i	−0.226665	+	0.503062i
$613$	−14.8672	−	8.58358i	−0.600480	−	0.346688i	0.168750	−	0.985659i	$-0.446027\pi$
$613$	−14.8672	−	8.58358i	−0.600480	−	0.346688i	−0.769231	+	0.638971i	$0.779360\pi$
$614$	28.1679	+	6.05282i	1.13676	+	0.244272i
$615$	−3.45707			−0.139402
$616$	−14.4897	−	41.1259i	−0.583806	−	1.65701i
$617$	−16.8150			−0.676946			−0.338473	−	0.940976i	$-0.609910\pi$
$617$	−16.8150			−0.676946			−0.338473	+	0.940976i	$0.609910\pi$
$618$	−6.39676	−	1.37456i	−0.257315	−	0.0552927i
$619$	−30.1572	−	17.4113i	−1.21212	−	0.699818i	−0.248899	−	0.968529i	$-0.580069\pi$
$619$	−30.1572	−	17.4113i	−1.21212	−	0.699818i	−0.963221	+	0.268712i	$0.913402\pi$
$620$	20.1394	+	9.07422i	0.808816	+	0.364430i
$621$	−1.07351	−	1.85937i	−0.0430783	−	0.0746138i
$622$	−30.2833	−	27.3895i	−1.21425	−	1.09822i
$623$	29.5175	−	14.2636i	1.18259	−	0.571461i
$624$	0.835363	+	4.10959i	0.0334413	+	0.164515i
$625$	15.2963	+	26.4940i	0.611852	+	1.05976i
$626$	−2.04836	−	6.35225i	−0.0818688	−	0.253887i
$627$	1.98469	−	3.43759i	0.0792610	−	0.137284i
$628$	8.49734	−	6.11609i	0.339081	−	0.244059i
$629$	−16.2491			−0.647892
$630$	7.44733	+	7.80310i	0.296709	+	0.310883i
$631$			11.8869i			0.473210i	0.971606	+	0.236605i	$0.0760346\pi$
$631$			11.8869i			0.473210i	−0.971606	+	0.236605i	$0.923965\pi$
$632$	3.98024	−	35.5829i	0.158325	−	1.41541i
$633$	−18.3975	−	10.6218i	−0.731237	−	0.422180i
$634$	−11.0431	−	34.2463i	−0.438578	−	1.36009i
$635$	1.37418	−	0.793381i	0.0545325	−	0.0314844i
$636$	−1.61733	−	16.0758i	−0.0641315	−	0.637445i
$637$	−7.25980	−	1.07434i	−0.287644	−	0.0425670i
$638$	−36.5651	+	40.4284i	−1.44763	+	1.60057i
$639$	−0.939926	+	0.542667i	−0.0371829	+	0.0214676i
$640$	−18.7577	−	26.6820i	−0.741464	−	1.05470i
$641$	18.4447	−	31.9472i	0.728523	−	1.26184i	−0.228984	−	0.973430i	$-0.573540\pi$
$641$	18.4447	−	31.9472i	0.728523	−	1.26184i	0.957507	−	0.288409i	$-0.0931263\pi$
$642$	8.39195	+	1.80329i	0.331204	+	0.0711702i
$643$		−	10.0475i		−	0.396235i	−0.980178	−	0.198117i	$-0.936517\pi$
$643$		−	10.0475i		−	0.396235i	0.980178	−	0.198117i	$-0.0634827\pi$
$644$	−11.3568	+	0.304552i	−0.447522	+	0.0120010i
$645$			3.87222i			0.152469i
$646$	−1.38137	+	6.42848i	−0.0543494	+	0.252925i
$647$	19.5824	−	33.9177i	0.769862	−	1.33344i	−0.167775	−	0.985825i	$-0.553658\pi$
$647$	19.5824	−	33.9177i	0.769862	−	1.33344i	0.937637	−	0.347615i	$-0.113008\pi$
$648$	1.13315	+	2.59152i	0.0445144	+	0.101804i
$649$	39.7169	−	22.9306i	1.55903	−	0.900104i
$650$	3.64065	+	3.29276i	0.142798	+	0.129153i
$651$	−9.12658	+	4.41021i	−0.357699	+	0.172850i
$652$	0.195484	+	1.94304i	0.00765573	+	0.0760954i
$653$	35.9422	−	20.7512i	1.40653	−	0.812058i	0.411475	−	0.911421i	$-0.365014\pi$
$653$	35.9422	−	20.7512i	1.40653	−	0.812058i	0.995051	+	0.0993632i	$0.0316806\pi$
$654$	19.6033	−	6.32131i	0.766550	−	0.247183i
$655$	7.00008	+	4.04150i	0.273516	+	0.157914i
$656$	−3.59310	+	3.17780i	−0.140287	+	0.124072i
$657$			5.64507i			0.220235i
$658$	−40.1876	+	9.76963i	−1.56667	+	0.380860i
$659$	−35.4347			−1.38034			−0.690170	−	0.723647i	$-0.742464\pi$
$659$	−35.4347			−1.38034			−0.690170	+	0.723647i	$0.742464\pi$
$660$	−19.6258	−	27.2670i	−0.763934	−	1.06137i
$661$	11.8165	−	20.4668i	0.459610	−	0.796067i	−0.539330	−	0.842094i	$-0.681323\pi$
$661$	11.8165	−	20.4668i	0.459610	−	0.796067i	0.998940	+	0.0460268i	$0.0146560\pi$
$662$	−26.5405	+	8.55830i	−1.03153	+	0.332628i
$663$	−3.57769	−	6.19674i	−0.138946	−	0.240662i
$664$	−1.09766	−	0.808744i	−0.0425974	−	0.0313854i
$665$	4.29700	+	2.92121i	0.166630	+	0.113280i
$666$	−2.25851	+	2.49714i	−0.0875156	+	0.0967620i
$667$	7.10140	+	12.3000i	0.274967	+	0.476257i
$668$	−3.79764	−	1.71111i	−0.146935	−	0.0662049i
$669$	2.70379	+	1.56104i	0.104535	+	0.0603531i
$670$	−11.4025	+	53.0636i	−0.440516	+	2.05002i
$671$	−19.0503			−0.735428
$672$	14.9131	+	1.26444i	0.575286	+	0.0487768i
$673$	8.69720			0.335253			0.167626	−	0.985851i	$-0.446390\pi$
$673$	8.69720			0.335253			0.167626	+	0.985851i	$0.446390\pi$
$674$	7.35999	−	34.2511i	0.283496	−	1.31930i
$675$	2.86723	+	1.65540i	0.110360	+	0.0637163i
$676$	21.7006	+	9.77768i	0.834639	+	0.376065i
$677$	−5.45947	−	9.45608i	−0.209825	−	0.363427i	0.741835	−	0.670583i	$-0.233956\pi$
$677$	−5.45947	−	9.45608i	−0.209825	−	0.363427i	−0.951659	+	0.307156i	$0.900623\pi$
$678$	−3.63207	+	4.01581i	−0.139489	+	0.154226i
$679$	−0.705909	+	9.59223i	−0.0270903	+	0.368116i
$680$	44.8028	+	33.0103i	1.71811	+	1.26589i
$681$	−2.61337	−	4.52649i	−0.100145	−	0.173456i
$682$	30.0465	−	9.68885i	1.15054	−	0.371005i
$683$	−18.2758	+	31.6547i	−0.699305	+	1.21123i	0.269402	+	0.963028i	$0.413174\pi$
$683$	−18.2758	+	31.6547i	−0.699305	+	1.21123i	−0.968708	+	0.248204i	$0.920160\pi$
$684$	0.795919	+	1.10580i	0.0304327	+	0.0422815i
$685$	36.7936			1.40581
$686$	−10.9671	+	23.7849i	−0.418727	+	0.908112i
$687$			28.4258i			1.08451i
$688$	3.55941	+	4.02459i	0.135701	+	0.153436i
$689$	7.33482	+	4.23476i	0.279434	+	0.161332i
$690$	−8.33086	+	2.68638i	−0.317150	+	0.102269i
$691$	−4.59821	+	2.65478i	−0.174924	+	0.100993i	−0.584906	−	0.811101i	$-0.698869\pi$
$691$	−4.59821	+	2.65478i	−0.174924	+	0.100993i	0.409981	+	0.912094i	$0.365535\pi$
$692$	−4.27360	−	42.4782i	−0.162458	−	1.61478i
$693$	15.3747	+	1.13145i	0.584036	+	0.0429803i
$694$	15.7206	+	14.2183i	0.596744	+	0.539720i
$695$	−15.2733	+	8.81806i	−0.579350	+	0.334488i
$696$	−7.49597	−	17.1433i	−0.284134	−	0.649814i
$697$	4.09222	−	7.08793i	0.155004	−	0.268475i
$698$	8.15700	−	37.9602i	0.308747	−	1.43681i
$699$			6.11941i			0.231457i
$700$	14.9317	−	9.16311i	0.564365	−	0.346333i
$701$			6.16681i			0.232917i	0.993196	+	0.116459i	$0.0371542\pi$
$701$			6.16681i			0.232917i	−0.993196	+	0.116459i	$0.962846\pi$
$702$	−1.44958	−	0.311491i	−0.0547110	−	0.0117565i
$703$	−0.810940	+	1.40459i	−0.0305852	+	0.0529751i
$704$	−45.4623	−	10.2995i	−1.71343	−	0.388178i
$705$	−27.5961	+	15.9326i	−1.03933	+	0.600057i
$706$	−22.7712	+	25.1771i	−0.857006	+	0.947553i
$707$	3.72564	−	5.48028i	0.140117	−	0.206107i
$708$	1.57575	+	15.6624i	0.0592202	+	0.588629i
$709$	−1.73062	+	0.999172i	−0.0649947	+	0.0375247i	−0.532145	−	0.846653i	$-0.678614\pi$
$709$	−1.73062	+	0.999172i	−0.0649947	+	0.0375247i	0.467151	+	0.884178i	$0.345281\pi$
$710$	1.35799	+	4.21132i	0.0509644	+	0.158048i
$711$	10.9630	+	6.32946i	0.411143	+	0.237373i
$712$	3.89595	−	34.8294i	0.146007	−	1.30529i
$713$		−	8.22554i		−	0.308049i
$714$	−24.8141	+	6.03232i	−0.928644	+	0.225754i
$715$	17.6109			0.658611
$716$	−11.2812	+	8.11979i	−0.421597	+	0.303451i
$717$	4.41764	−	7.65158i	0.164980	−	0.285753i
$718$	5.92626	+	18.3782i	0.221166	+	0.685868i
$719$	−6.72446	−	11.6471i	−0.250780	−	0.434364i	0.712961	−	0.701204i	$-0.247354\pi$
$719$	−6.72446	−	11.6471i	−0.250780	−	0.434364i	−0.963741	+	0.266840i	$0.914020\pi$
$720$	11.3003	−	2.29703i	0.421137	−	0.0856051i
$721$	−5.32569	−	11.0211i	−0.198339	−	0.410447i
$722$	−19.4415	−	17.5837i	−0.723539	−	0.654399i
$723$	−2.97772	−	5.15757i	−0.110743	−	0.191812i
$724$	−13.9972	−	6.30672i	−0.520201	−	0.234388i
$725$	−18.9672	−	10.9507i	−0.704423	−	0.406699i
$726$	−31.7341	−	6.81913i	−1.17776	−	0.253082i
$727$	19.6532			0.728897			0.364448	−	0.931224i	$-0.381258\pi$
$727$	19.6532			0.728897			0.364448	+	0.931224i	$0.381258\pi$
$728$	−5.10480	+	5.95769i	−0.189196	+	0.220807i
$729$	−1.00000			−0.0370370
$730$	22.5011	+	4.83511i	0.832803	+	0.178955i
$731$	−7.93911	−	4.58365i	−0.293639	−	0.169532i
$732$	2.68614	−	5.96164i	0.0992828	−	0.220349i
$733$	12.6139	+	21.8480i	0.465907	+	0.806974i	0.999242	−	0.0389298i	$-0.0123949\pi$
$733$	12.6139	+	21.8480i	0.465907	+	0.806974i	−0.533335	+	0.845904i	$0.679062\pi$
$734$	−36.3793	−	32.9030i	−1.34279	−	1.21447i
$735$	−2.95415	+	19.9625i	−0.108966	+	0.736328i
$736$	−6.18931	+	10.4500i	−0.228141	+	0.385190i
$737$	38.7849	+	67.1774i	1.42866	+	2.47451i
$738$	−0.520474	−	1.61406i	−0.0191589	−	0.0594145i
$739$	−3.35478	+	5.81064i	−0.123407	+	0.213748i	−0.921109	−	0.389304i	$-0.872716\pi$
$739$	−3.35478	+	5.81064i	−0.123407	+	0.213748i	0.797702	+	0.603052i	$0.206049\pi$
$740$	8.01905	+	11.1412i	0.294786	+	0.409559i
$741$	−0.714206			−0.0262370
$742$	21.8662	−	20.8693i	0.802735	−	0.766135i
$743$			26.0661i			0.956273i	0.878286	+	0.478137i	$0.158688\pi$
$743$			26.0661i			0.956273i	−0.878286	+	0.478137i	$0.841312\pi$
$744$	−1.20460	+	10.7690i	−0.0441627	+	0.394810i
$745$	5.04967	+	2.91543i	0.185005	+	0.106813i
$746$	−2.63986	−	8.18660i	−0.0966522	−	0.299733i
$747$	0.417461	−	0.241021i	0.0152741	−	0.00881850i
$748$	79.1363	−	7.96167i	2.89351	−	0.291107i
$749$	6.98682	+	14.4587i	0.255293	+	0.528308i
$750$	−4.61956	+	5.10764i	−0.168682	+	0.186505i
$751$	−4.94762	+	2.85651i	−0.180541	+	0.104236i	−0.587547	−	0.809190i	$-0.699906\pi$
$751$	−4.94762	+	2.85651i	−0.180541	+	0.104236i	0.407006	+	0.913426i	$0.366573\pi$
$752$	−14.0365	+	41.9264i	−0.511857	+	1.52890i
$753$	1.06977	−	1.85290i	0.0389847	−	0.0675235i
$754$	9.58922	+	2.06056i	0.349219	+	0.0750412i
$755$			40.5561i			1.47599i
$756$	−2.52196	+	4.65185i	−0.0917226	+	0.169186i
$757$			4.75364i			0.172774i	0.996262	+	0.0863869i	$0.0275321\pi$
$757$			4.75364i			0.172774i	−0.996262	+	0.0863869i	$0.972468\pi$
$758$	−5.66371	+	26.3572i	−0.205715	+	0.957336i
$759$	−6.25511	+	10.8342i	−0.227046	+	0.393255i
$760$	5.08942	−	2.22537i	0.184613	−	0.0807227i
$761$	−23.6671	+	13.6642i	−0.857931	+	0.495327i	−0.863319	−	0.504659i	$-0.831618\pi$
$761$	−23.6671	+	13.6642i	−0.857931	+	0.495327i	0.00538774	+	0.999985i	$0.498285\pi$
$762$	0.577307	+	0.522140i	0.0209136	+	0.0189151i
$763$	31.8674	+	21.6643i	1.15368	+	0.784300i
$764$	−35.4409	+	3.56560i	−1.28221	+	0.128999i
$765$	−17.0394	+	9.83770i	−0.616061	+	0.355683i
$766$	−11.1043	+	3.58070i	−0.401213	+	0.129376i
$767$	−7.14622	−	4.12587i	−0.258035	−	0.148977i
$768$	9.63348	−	12.7748i	0.347618	−	0.460972i
$769$			22.7151i			0.819127i	0.912282	+	0.409564i	$0.134319\pi$
$769$			22.7151i			0.819127i	−0.912282	+	0.409564i	$0.865681\pi$
$770$	17.6786	−	60.3140i	0.637094	−	2.17356i
$771$	19.2869			0.694602
$772$	−22.3943	+	16.1186i	−0.805987	+	0.580121i
$773$	9.05937	−	15.6913i	0.325843	−	0.564376i	−0.655840	−	0.754900i	$-0.727685\pi$
$773$	9.05937	−	15.6913i	0.325843	−	0.564376i	0.981683	+	0.190524i	$0.0610187\pi$
$774$	−1.80789	+	0.582976i	−0.0649834	+	0.0209546i
$775$	6.34209	+	10.9848i	0.227814	+	0.394586i
$776$	8.27799	+	6.09915i	0.297162	+	0.218947i
$777$	−6.28206	−	0.462308i	−0.225368	−	0.0165852i
$778$	18.6134	−	20.5800i	0.667324	−	0.737830i
$779$	−0.408460	−	0.707474i	−0.0146346	−	0.0253479i
$780$	−2.48319	+	5.51120i	−0.0889125	+	0.197333i
$781$	5.47676	+	3.16201i	0.195974	+	0.113146i
$782$	4.35364	−	20.2605i	0.155686	−	0.724513i
$783$	6.61515			0.236406
$784$	15.2795	+	23.4635i	0.545696	+	0.837983i
$785$	15.0910			0.538622
$786$	−0.833041	+	3.87672i	−0.0297136	+	0.138278i
$787$	4.25358	+	2.45581i	0.151624	+	0.0875400i	0.573892	−	0.818931i	$-0.305433\pi$
$787$	4.25358	+	2.45581i	0.151624	+	0.0875400i	−0.422269	+	0.906471i	$0.638766\pi$
$788$	0.929882	−	2.06378i	0.0331257	−	0.0735192i
$789$	12.1671	+	21.0740i	0.433159	+	0.750254i
$790$	34.6190	−	38.2767i	1.23169	−	1.36182i
$791$	−10.1026	−	0.743469i	−0.359207	−	0.0264347i
$792$	9.77589	−	13.2682i	0.347371	−	0.471465i
$793$	1.71385	+	2.96847i	0.0608604	+	0.105413i
$794$	42.2137	−	13.6123i	1.49811	−	0.483082i
$795$	11.6445	−	20.1688i	0.412987	−	0.715314i
$796$	−13.8493	+	9.96827i	−0.490877	+	0.353316i
$797$	−23.8384			−0.844398			−0.422199	−	0.906503i	$-0.638742\pi$
$797$	−23.8384			−0.844398			−0.422199	+	0.906503i	$0.638742\pi$
$798$	−0.716952	+	2.44602i	−0.0253798	+	0.0865881i
$799$		−	75.4394i		−	2.66885i
$800$	0.208358	−	18.7275i	0.00736658	−	0.662118i
$801$	10.7308	+	6.19543i	0.379154	+	0.218905i
$802$	46.9909	−	15.1528i	1.65931	−	0.535063i
$803$	28.4859	−	16.4464i	1.00525	−	0.580379i
$804$	−26.4914	+	2.66522i	−0.934281	+	0.0939952i
$805$	−13.5427	−	9.20672i	−0.477319	−	0.324494i
$806$	−4.21286	−	3.81028i	−0.148392	−	0.134211i
$807$	18.1007	−	10.4505i	0.637176	−	0.367874i
$808$	−2.83818	−	6.49091i	−0.0998467	−	0.228350i
$809$	0.597915	−	1.03562i	0.0210216	−	0.0364104i	−0.855323	−	0.518095i	$-0.826641\pi$
$809$	0.597915	−	1.03562i	0.0210216	−	0.0364104i	0.876345	+	0.481684i	$0.159975\pi$
$810$	−0.856518	+	3.98597i	−0.0300950	+	0.140053i
$811$			6.44559i			0.226335i	0.993576	+	0.113168i	$0.0360997\pi$
$811$			6.44559i			0.226335i	−0.993576	+	0.113168i	$0.963900\pi$
$812$	16.6831	−	30.7727i	0.585462	−	1.07991i
$813$		−	19.9939i		−	0.701218i
$814$	19.1809	+	4.12165i	0.672290	+	0.144464i
$815$	−1.40744	+	2.43776i	−0.0493005	+	0.0853910i
$816$	−8.66691	+	25.8877i	−0.303402	+	0.906251i
$817$	−0.792433	+	0.457511i	−0.0277237	+	0.0160063i
$818$	−12.9455	+	14.3132i	−0.452628	+	0.500450i
$819$	−1.20687	−	2.49752i	−0.0421714	−	0.0872703i
$820$	−6.87941	+	0.692117i	−0.240239	+	0.0241698i
$821$	1.87701	−	1.08369i	0.0655079	−	0.0378210i	−0.466888	−	0.884316i	$-0.654625\pi$
$821$	1.87701	−	1.08369i	0.0655079	−	0.0378210i	0.532396	+	0.846495i	$0.321292\pi$
$822$	5.53941	+	17.1785i	0.193209	+	0.599169i
$823$	−5.19529	−	2.99950i	−0.181096	−	0.104556i	0.406711	−	0.913557i	$-0.366675\pi$
$823$	−5.19529	−	2.99950i	−0.181096	−	0.104556i	−0.587808	+	0.809001i	$0.700009\pi$
$824$	−13.0044	−	1.45465i	−0.453031	−	0.0506752i
$825$		−	19.2913i		−	0.671638i
$826$	−21.3040	+	20.3327i	−0.741261	+	0.707464i
$827$	21.0143			0.730738			0.365369	−	0.930863i	$-0.380943\pi$
$827$	21.0143			0.730738			0.365369	+	0.930863i	$0.380943\pi$
$828$	−2.50848	−	3.48514i	−0.0871757	−	0.121117i
$829$	−6.59891	+	11.4296i	−0.229190	+	0.396968i	−0.957568	−	0.288207i	$-0.906941\pi$
$829$	−6.59891	+	11.4296i	−0.229190	+	0.396968i	0.728379	+	0.685175i	$0.240274\pi$
$830$	−0.603140	−	1.87043i	−0.0209353	−	0.0649234i
$831$	−7.64600	−	13.2433i	−0.265237	−	0.459404i
$832$	2.48509	+	8.01066i	0.0861549	+	0.277720i
$833$	−37.4317	−	29.6870i	−1.29693	−	1.02859i
$834$	−6.41650	−	5.80335i	−0.222185	−	0.200953i
$835$	−3.00200	−	5.19962i	−0.103889	−	0.179940i
$836$	3.26123	−	7.23799i	0.112792	−	0.250331i
$837$	−3.31788	−	1.91558i	−0.114683	−	0.0662121i
$838$	−5.83924	−	1.25475i	−0.201713	−	0.0433448i
$839$	33.8661			1.16919			0.584594	−	0.811326i	$-0.301254\pi$
$839$	33.8661			1.16919			0.584594	+	0.811326i	$0.301254\pi$
$840$	16.3821	+	14.0368i	0.565234	+	0.484317i
$841$	−14.7602			−0.508973
$842$	−16.1621	−	3.47297i	−0.556983	−	0.119686i
$843$	−4.84803	−	2.79901i	−0.166975	−	0.0964031i
$844$	−38.7368	−	17.4537i	−1.33338	−	0.600781i
$845$	17.1541	+	29.7118i	0.590120	+	1.02212i
$846$	−11.5934	−	10.4856i	−0.398591	−	0.360502i
$847$	−26.4206	−	54.6753i	−0.907822	−	1.87867i
$848$	−6.43684	−	31.6662i	−0.221042	−	1.08742i
$849$	−5.61710	−	9.72911i	−0.192778	−	0.333902i
$850$	9.80723	+	30.4137i	0.336385	+	1.04318i
$851$	2.55582	−	4.42681i	0.0876124	−	0.151749i
$852$	−1.76177	+	1.26806i	−0.0603571	+	0.0434430i
$853$	−50.0832			−1.71482			−0.857408	−	0.514638i	$-0.827926\pi$
$853$	−50.0832			−1.71482			−0.857408	+	0.514638i	$0.827926\pi$
$854$	11.8869	−	2.88970i	0.406760	−	0.0988836i
$855$			1.96388i			0.0671632i
$856$	17.0606	+	1.90837i	0.583120	+	0.0652267i
$857$	42.6628	+	24.6314i	1.45734	+	0.841393i	0.998880	−	0.0473246i	$-0.0150695\pi$
$857$	42.6628	+	24.6314i	1.45734	+	0.841393i	0.458455	+	0.888717i	$0.348403\pi$
$858$	2.65139	+	8.22233i	0.0905168	+	0.280706i
$859$	−3.38667	+	1.95530i	−0.115552	+	0.0667139i	−0.556662	−	0.830739i	$-0.687918\pi$
$859$	−3.38667	+	1.95530i	−0.115552	+	0.0667139i	0.441110	+	0.897453i	$0.354585\pi$
$860$	0.775232	+	7.70554i	0.0264352	+	0.262757i
$861$	1.78376	−	2.62384i	0.0607903	−	0.0894203i
$862$	32.5399	−	35.9779i	1.10831	−	1.22541i
$863$	−37.4230	+	21.6062i	−1.27390	+	0.735484i	−0.975719	−	0.219027i	$-0.929712\pi$
$863$	−37.4230	+	21.6062i	−1.27390	+	0.735484i	−0.298176	+	0.954511i	$0.596378\pi$
$864$	2.77375	+	4.93014i	0.0943649	+	0.167727i
$865$	30.7690	−	53.2935i	1.04618	−	1.81203i
$866$	19.6177	+	4.21551i	0.666636	+	0.143249i
$867$		−	29.5806i		−	1.00461i
$868$	−17.2785	+	10.6033i	−0.586472	+	0.359899i
$869$		−	73.7611i		−	2.50217i
$870$	5.66600	−	26.3678i	0.192095	−	0.893952i
$871$	6.97851	−	12.0871i	0.236458	−	0.409557i
$872$	37.7441	−	16.5038i	1.27818	−	0.558888i
$873$	−3.14828	+	1.81766i	−0.106553	+	0.0615185i
$874$	−1.53407	−	1.38747i	−0.0518905	−	0.0469319i
$875$	−12.8493	−	0.945604i	−0.434386	−	0.0319673i
$876$	1.13016	+	11.2334i	0.0381846	+	0.379543i
$877$	18.3069	−	10.5695i	0.618182	−	0.356907i	−0.157979	−	0.987442i	$-0.550498\pi$
$877$	18.3069	−	10.5695i	0.618182	−	0.356907i	0.776161	+	0.630535i	$0.217165\pi$
$878$	−37.7549	+	12.1745i	−1.27416	+	0.410869i
$879$	−15.3470	−	8.86060i	−0.517642	−	0.298860i
$880$	−44.5134	−	50.3309i	−1.50055	−	1.69665i
$881$			49.1167i			1.65478i	0.561625	+	0.827392i	$0.310177\pi$
$881$			49.1167i			1.65478i	−0.561625	+	0.827392i	$0.689823\pi$
$882$	−9.76502	+	1.62617i	−0.328805	+	0.0547558i
$883$	37.8457			1.27361			0.636804	−	0.771025i	$-0.280256\pi$
$883$	37.8457			1.27361			0.636804	+	0.771025i	$0.280256\pi$
$884$	−8.36005	−	11.6150i	−0.281179	−	0.390654i
$885$	−11.3450	+	19.6502i	−0.381360	+	0.660534i
$886$	14.8336	−	4.78328i	0.498346	−	0.160697i
$887$	−8.97039	−	15.5372i	−0.301196	−	0.521687i	0.675211	−	0.737625i	$-0.264053\pi$
$887$	−8.97039	−	15.5372i	−0.301196	−	0.521687i	−0.976407	+	0.215937i	$0.930719\pi$
$888$	−3.99440	+	5.42135i	−0.134043	+	0.181929i
$889$	−0.106880	+	1.45233i	−0.00358464	+	0.0487097i
$890$	33.8859	−	37.4662i	1.13586	−	1.25587i
$891$	2.91340	+	5.04616i	0.0976026	+	0.169053i
$892$	5.69295	+	2.56508i	0.190614	+	0.0858853i
$893$	−6.52108	−	3.76495i	−0.218220	−	0.125989i
$894$	−0.600933	+	2.79656i	−0.0200982	+	0.0935309i
$895$	−20.0350			−0.669697
$896$	29.9296	−	0.469481i	0.999877	−	0.0156843i
$897$	2.25095			0.0751569
$898$	−8.98070	+	41.7934i	−0.299690	+	1.39466i
$899$	21.9483	+	12.6718i	0.732016	+	0.422629i
$900$	6.03708	+	2.72014i	0.201236	+	0.0906712i
$901$	27.5677	+	47.7487i	0.918413	+	1.59074i
$902$	−6.62848	+	7.32881i	−0.220704	+	0.244023i
$903$	−2.93893	−	1.99797i	−0.0978016	−	0.0664881i
$904$	−6.42367	+	8.71844i	−0.213648	+	0.289971i
$905$	−11.0646	−	19.1645i	−0.367801	−	0.637049i
$906$	−18.9352	+	6.10586i	−0.629078	+	0.202854i
$907$	−11.0887	+	19.2062i	−0.368194	+	0.637730i	−0.989283	−	0.146009i	$-0.953357\pi$
$907$	−11.0887	+	19.2062i	−0.368194	+	0.637730i	0.621089	+	0.783740i	$0.286690\pi$
$908$	−6.10671	−	8.48431i	−0.202658	−	0.281562i
$909$	2.50468			0.0830748
$910$	−10.9887	+	2.67137i	−0.364273	+	0.0885551i
$911$			35.2495i			1.16787i	0.811801	+	0.583934i	$0.198487\pi$
$911$			35.2495i			1.16787i	−0.811801	+	0.583934i	$0.801513\pi$
$912$	1.80523	+	2.04115i	0.0597771	+	0.0675894i
$913$	−2.43246	−	1.40438i	−0.0805027	−	0.0464783i
$914$	34.2915	−	11.0577i	1.13426	−	0.365756i
$915$	8.16250	−	4.71262i	0.269844	−	0.155794i
$916$	5.69094	+	56.5661i	0.188034	+	1.86900i
$917$	−6.67927	+	3.22760i	−0.220569	+	0.106585i
$918$	−7.15845	−	6.47439i	−0.236264	−	0.213687i
$919$	15.1837	−	8.76632i	0.500864	−	0.289174i	−0.228206	−	0.973613i	$-0.573286\pi$
$919$	15.1837	−	8.76632i	0.500864	−	0.289174i	0.729070	+	0.684439i	$0.239953\pi$
$920$	−16.0402	+	7.01364i	−0.528830	+	0.231233i
$921$	−10.1862	+	17.6430i	−0.335647	+	0.581357i
$922$	−8.29800	+	38.6163i	−0.273280	+	1.27176i
$923$		−	1.13787i		−	0.0374535i
$924$	30.8215	−	0.826528i	1.01395	−	0.0271908i
$925$			7.88239i			0.259171i
$926$	26.8556	+	5.77081i	0.882529	+	0.189641i
$927$	2.31322	−	4.00661i	0.0759761	−	0.131594i
$928$	−18.3488	−	32.6136i	−0.602328	−	1.07059i
$929$	−44.9106	+	25.9292i	−1.47347	+	0.850708i	−0.999554	−	0.0298619i	$-0.990493\pi$
$929$	−44.9106	+	25.9292i	−1.47347	+	0.850708i	−0.473916	+	0.880570i	$0.657160\pi$
$930$	−10.4773	+	11.5842i	−0.343563	+	0.379862i
$931$	−4.43428	+	1.75406i	−0.145328	+	0.0574870i
$932$	1.22513	+	12.1774i	0.0401304	+	0.398882i
$933$	25.0045	−	14.4363i	0.818610	−	0.472625i
$934$	−0.655324	−	2.03225i	−0.0214428	−	0.0664974i
$935$	99.2852	+	57.3223i	3.24697	+	1.87464i
$936$	−2.94697	−	0.329642i	−0.0963247	−	0.0107747i
$937$		−	36.9665i		−	1.20764i	−0.797120	−	0.603821i	$-0.793644\pi$
$937$		−	36.9665i		−	1.20764i	0.797120	−	0.603821i	$-0.206356\pi$
$938$	−34.3907	−	36.0337i	−1.12290	−	1.17654i
$939$	4.71947			0.154014
$940$	−51.7252	+	37.2300i	−1.68709	+	1.21431i
$941$	26.2751	−	45.5098i	0.856544	−	1.48358i	−0.0186621	−	0.999826i	$-0.505941\pi$
$941$	26.2751	−	45.5098i	0.856544	−	1.48358i	0.875206	−	0.483751i	$-0.160726\pi$
$942$	2.27201	+	7.04582i	0.0740260	+	0.229565i
$943$	1.28733	+	2.22973i	0.0419214	+	0.0726099i
$944$	6.27133	+	30.8520i	0.204114	+	1.00415i
$945$	−6.86751	+	3.31857i	−0.223400	+	0.107953i
$946$	8.20891	+	7.42448i	0.266895	+	0.241391i
$947$	−13.4671	−	23.3256i	−0.437621	−	0.757982i	0.559885	−	0.828571i	$-0.310845\pi$
$947$	−13.4671	−	23.3256i	−0.437621	−	0.757982i	−0.997505	+	0.0705889i	$0.977512\pi$
$948$	23.0830	+	10.4005i	0.749700	+	0.337793i
$949$	−5.12543	−	2.95917i	−0.166379	−	0.0960588i
$950$	3.11844	+	0.670102i	0.101176	+	0.0217410i
$951$	25.4437			0.825067
$952$	−48.1712	+	16.9719i	−1.56124	+	0.550063i
$953$	−31.5488			−1.02196			−0.510982	−	0.859591i	$-0.670718\pi$
$953$	−31.5488			−1.02196			−0.510982	+	0.859591i	$0.670718\pi$
$954$	11.1697	+	2.40018i	0.361632	+	0.0777087i
$955$	−44.4645	−	25.6716i	−1.43884	−	0.830713i
$956$	7.25903	−	16.1107i	0.234774	−	0.521058i
$957$	−19.2726	−	33.3811i	−0.622994	−	1.07906i
$958$	14.9364	+	13.5091i	0.482572	+	0.436458i
$959$	−18.9846	+	27.9256i	−0.613043	+	0.901764i
$960$	22.0272	−	6.83333i	0.710924	−	0.220545i
$961$	8.16112	+	14.1355i	0.263262	+	0.455983i
$962$	−1.08335	−	3.35962i	−0.0349286	−	0.108319i
$963$	−3.03473	+	5.25631i	−0.0977928	+	0.169382i
$964$	−6.95810	−	9.66717i	−0.224105	−	0.311359i
$965$	−39.7716			−1.28029
$966$	2.25960	−	7.70905i	0.0727015	−	0.248035i
$967$			60.7635i			1.95402i	0.213187	+	0.977011i	$0.431616\pi$
$967$			60.7635i			1.95402i	−0.213187	+	0.977011i	$0.568384\pi$
$968$	−64.5146	−	7.21648i	−2.07358	−	0.231946i
$969$	−4.02648	−	2.32469i	−0.129349	−	0.0746799i
$970$	4.54859	+	14.1058i	0.146046	+	0.452911i
$971$	−13.9382	+	8.04723i	−0.447299	+	0.258248i	−0.706689	−	0.707525i	$-0.749812\pi$
$971$	−13.9382	+	8.04723i	−0.447299	+	0.258248i	0.259390	+	0.965773i	$0.416479\pi$
$972$	−1.98995	+	0.200203i	−0.0638278	+	0.00642153i
$973$	1.18792	−	16.1420i	0.0380830	−	0.517489i
$974$	7.01129	−	7.75207i	0.224656	−	0.248392i
$975$	−3.00603	+	1.73553i	−0.0962700	+	0.0555815i
$976$	4.15177	−	12.4012i	0.132895	−	0.396952i
$977$	16.3583	−	28.3334i	0.523349	−	0.906467i	−0.476282	−	0.879293i	$-0.658016\pi$
$977$	16.3583	−	28.3334i	0.523349	−	0.906467i	0.999631	−	0.0271741i	$-0.00865086\pi$
$978$	−1.35006	−	0.290104i	−0.0431700	−	0.00927652i
$979$		−	72.1991i		−	2.30749i
$980$	−1.88207	+	40.3159i	−0.0601205	+	1.28784i
$981$			14.5645i			0.465008i
$982$	−4.17670	+	19.4371i	−0.133284	+	0.620261i
$983$	−18.5785	+	32.1789i	−0.592561	+	1.02635i	0.401325	+	0.915936i	$0.368550\pi$
$983$	−18.5785	+	32.1789i	−0.592561	+	1.02635i	−0.993886	+	0.110410i	$0.964783\pi$
$984$	−1.35886	−	3.10771i	−0.0433189	−	0.0990703i
$985$	2.82567	−	1.63140i	0.0900333	−	0.0519808i
$986$	47.3542	+	42.8291i	1.50806	+	1.36396i
$987$	2.14636	−	29.1657i	0.0683192	−	0.928354i
$988$	−1.42124	+	0.142987i	−0.0452156	+	0.00454901i
$989$	2.49749	−	1.44193i	0.0794156	−	0.0458506i
$990$	22.6092	−	7.29060i	0.718568	−	0.231711i
$991$	38.2912	+	22.1074i	1.21636	+	0.702266i	0.964137	−	0.265403i	$-0.0855051\pi$
$991$	38.2912	+	22.1074i	1.21636	+	0.702266i	0.252223	+	0.967669i	$0.418838\pi$
$992$	−0.241107	+	21.6710i	−0.00765514	+	0.688053i
$993$		−	19.7186i		−	0.625750i
$994$	−3.89699	−	1.14225i	−0.123605	−	0.0362299i
$995$	−24.5960			−0.779747
$996$	0.782475	−	0.563198i	0.0247937	−	0.0178456i
$997$	−13.3432	+	23.1110i	−0.422582	+	0.731934i	−0.996191	−	0.0871953i	$-0.972210\pi$
$997$	−13.3432	+	23.1110i	−0.422582	+	0.731934i	0.573609	+	0.819129i	$0.305543\pi$
$998$	36.3302	−	11.7151i	1.15001	−	0.370835i
$999$	−1.19041	−	2.06185i	−0.0376628	−	0.0652339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.t.a.115.9	yes	32
3.2	odd	2		504.2.bk.c.451.8		32
4.3	odd	2		672.2.bb.a.367.10		32
7.3	odd	6		1176.2.p.a.979.6		32
7.4	even	3		1176.2.p.a.979.5		32
7.5	odd	6	inner	168.2.t.a.19.14	yes	32
8.3	odd	2	inner	168.2.t.a.115.14	yes	32
8.5	even	2		672.2.bb.a.367.15		32
12.11	even	2		2016.2.bs.c.1711.14		32
21.5	even	6		504.2.bk.c.19.3		32
24.5	odd	2		2016.2.bs.c.1711.3		32
24.11	even	2		504.2.bk.c.451.3		32
28.3	even	6		4704.2.p.a.3919.26		32
28.11	odd	6		4704.2.p.a.3919.29		32
28.19	even	6		672.2.bb.a.271.15		32
56.3	even	6		1176.2.p.a.979.7		32
56.5	odd	6		672.2.bb.a.271.10		32
56.11	odd	6		1176.2.p.a.979.8		32
56.19	even	6	inner	168.2.t.a.19.9	✓	32
56.45	odd	6		4704.2.p.a.3919.30		32
56.53	even	6		4704.2.p.a.3919.25		32
84.47	odd	6		2016.2.bs.c.271.3		32
168.5	even	6		2016.2.bs.c.271.14		32
168.131	odd	6		504.2.bk.c.19.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.9	✓	32	56.19	even	6	inner
168.2.t.a.19.14	yes	32	7.5	odd	6	inner
168.2.t.a.115.9	yes	32	1.1	even	1	trivial
168.2.t.a.115.14	yes	32	8.3	odd	2	inner
504.2.bk.c.19.3		32	21.5	even	6
504.2.bk.c.19.8		32	168.131	odd	6
504.2.bk.c.451.3		32	24.11	even	2
504.2.bk.c.451.8		32	3.2	odd	2
672.2.bb.a.271.10		32	56.5	odd	6
672.2.bb.a.271.15		32	28.19	even	6
672.2.bb.a.367.10		32	4.3	odd	2
672.2.bb.a.367.15		32	8.5	even	2
1176.2.p.a.979.5		32	7.4	even	3
1176.2.p.a.979.6		32	7.3	odd	6
1176.2.p.a.979.7		32	56.3	even	6
1176.2.p.a.979.8		32	56.11	odd	6
2016.2.bs.c.271.3		32	84.47	odd	6
2016.2.bs.c.271.14		32	168.5	even	6
2016.2.bs.c.1711.3		32	24.5	odd	2
2016.2.bs.c.1711.14		32	12.11	even	2
4704.2.p.a.3919.25		32	56.53	even	6
4704.2.p.a.3919.26		32	28.3	even	6
4704.2.p.a.3919.29		32	28.11	odd	6
4704.2.p.a.3919.30		32	56.45	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.297109 + 1.38265i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.82345 - 0.821596i) q^{4} +(-1.44142 - 2.49662i) q^{5} +(0.948630 - 1.04886i) q^{6} +(2.63862 + 0.194181i) q^{7} +(1.67775 - 2.27710i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.297109 + 1.38265i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.82345 - 0.821596i) q^{4} +(-1.44142 - 2.49662i) q^{5} +(0.948630 - 1.04886i) q^{6} +(2.63862 + 0.194181i) q^{7} +(1.67775 - 2.27710i) q^{8} +(0.500000 + 0.866025i) q^{9} +(3.88021 - 1.25122i) q^{10} +(2.91340 - 5.04616i) q^{11} +(1.16836 + 1.62325i) q^{12} -1.04841 q^{13} +(-1.05244 + 3.59059i) q^{14} +2.88284i q^{15} +(2.64996 + 2.99628i) q^{16} +(-5.91062 - 3.41250i) q^{17} +(-1.34597 + 0.434022i) q^{18} +(-0.589961 + 0.340614i) q^{19} +(0.577155 + 5.73673i) q^{20} +(-2.18802 - 1.48747i) q^{21} +(6.11148 + 5.52748i) q^{22} +(1.85937 - 1.07351i) q^{23} +(-2.59152 + 1.13315i) q^{24} +(-1.65540 + 2.86723i) q^{25} +(0.311491 - 1.44958i) q^{26} -1.00000i q^{27} +(-4.65185 - 2.52196i) q^{28} +6.61515i q^{29} +(-3.98597 - 0.856518i) q^{30} +(1.91558 - 3.31788i) q^{31} +(-4.93014 + 2.77375i) q^{32} +(-5.04616 + 2.91340i) q^{33} +(6.47439 - 7.15845i) q^{34} +(-3.31857 - 6.86751i) q^{35} +(-0.200203 - 1.98995i) q^{36} +(2.06185 - 1.19041i) q^{37} +(-0.295668 - 0.916911i) q^{38} +(0.907949 + 0.524204i) q^{39} +(-8.10338 - 0.906428i) q^{40} +1.19919i q^{41} +(2.70674 - 2.58333i) q^{42} +1.34319 q^{43} +(-9.45835 + 6.80779i) q^{44} +(1.44142 - 2.49662i) q^{45} +(0.931851 + 2.88980i) q^{46} +(5.52670 + 9.57253i) q^{47} +(-0.796791 - 3.91984i) q^{48} +(6.92459 + 1.02474i) q^{49} +(-3.47255 - 3.14072i) q^{50} +(3.41250 + 5.91062i) q^{51} +(1.91172 + 0.861368i) q^{52} +(-6.99615 - 4.03923i) q^{53} +(1.38265 + 0.297109i) q^{54} -16.7978 q^{55} +(4.86909 - 5.68260i) q^{56} +0.681229 q^{57} +(-9.14645 - 1.96542i) q^{58} +(6.81625 + 3.93537i) q^{59} +(2.36853 - 5.25673i) q^{60} +(-1.63471 - 2.83140i) q^{61} +(4.01834 + 3.63435i) q^{62} +(1.15114 + 2.38220i) q^{63} +(-2.37034 - 7.64078i) q^{64} +(1.51120 + 2.61747i) q^{65} +(-2.52896 - 7.84268i) q^{66} +(-6.65629 + 11.5290i) q^{67} +(7.97404 + 11.0787i) q^{68} -2.14701 q^{69} +(10.4813 - 2.54802i) q^{70} +1.08533i q^{71} +(2.81090 + 0.314421i) q^{72} +(4.88878 + 2.82254i) q^{73} +(1.03333 + 3.20450i) q^{74} +(2.86723 - 1.65540i) q^{75} +(1.35561 - 0.136384i) q^{76} +(8.66721 - 12.7491i) q^{77} +(-0.994552 + 1.09963i) q^{78} +(10.9630 - 6.32946i) q^{79} +(3.66086 - 10.9348i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.65806 - 0.356289i) q^{82} -0.482042i q^{83} +(2.76765 + 4.51000i) q^{84} +19.6754i q^{85} +(-0.399075 + 1.85717i) q^{86} +(3.30757 - 5.72889i) q^{87} +(-6.60265 - 15.1003i) q^{88} +(10.7308 - 6.19543i) q^{89} +(3.02369 + 2.73475i) q^{90} +(-2.76635 - 0.203581i) q^{91} +(-4.27246 + 0.429839i) q^{92} +(-3.31788 + 1.91558i) q^{93} +(-14.8775 + 4.79742i) q^{94} +(1.70077 + 0.981939i) q^{95} +(5.65650 + 0.0629331i) q^{96} +3.63532i q^{97} +(-3.47421 + 9.26984i) q^{98} +5.82680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36} - 18 q^{38} - 30 q^{40} + 4 q^{42} - 16 q^{43} + 24 q^{44} + 8 q^{46} + 8 q^{49} + 76 q^{50} + 36 q^{52} + 16 q^{56} + 16 q^{57} - 6 q^{58} - 96 q^{59} - 2 q^{60} + 76 q^{64} - 36 q^{66} - 32 q^{67} + 96 q^{68} + 6 q^{70} + 8 q^{72} - 24 q^{73} - 34 q^{74} - 12 q^{78} + 36 q^{80} - 16 q^{81} - 36 q^{82} + 16 q^{84} + 50 q^{86} - 14 q^{88} + 56 q^{91} - 128 q^{92} + 36 q^{94} + 30 q^{96} + 60 q^{98} + 16 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

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