LMFDB - Embedded newform 666.2.k.a.175.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.16
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.35

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(1.47450 - 0.908769i) q^{3} -1.00000 q^{4} +3.44654i q^{5} +(-0.908769 - 1.47450i) q^{6} +(0.240097 - 0.415860i) q^{7} +1.00000i q^{8} +(1.34828 - 2.67995i) q^{9} +3.44654 q^{10} +(1.57883 + 2.73461i) q^{11} +(-1.47450 + 0.908769i) q^{12} -1.35094i q^{13} +(-0.415860 - 0.240097i) q^{14} +(3.13211 + 5.08191i) q^{15} +1.00000 q^{16} +(0.944880 + 0.545527i) q^{17} +(-2.67995 - 1.34828i) q^{18} +(0.333391 - 0.192483i) q^{19} -3.44654i q^{20} +(-0.0238987 - 0.831377i) q^{21} +(2.73461 - 1.57883i) q^{22} +(6.91907 + 3.99473i) q^{23} +(0.908769 + 1.47450i) q^{24} -6.87863 q^{25} -1.35094 q^{26} +(-0.447426 - 5.17685i) q^{27} +(-0.240097 + 0.415860i) q^{28} +(5.40267 - 3.11923i) q^{29} +(5.08191 - 3.13211i) q^{30} +(3.60235 + 2.07982i) q^{31} -1.00000i q^{32} +(4.81311 + 2.59739i) q^{33} +(0.545527 - 0.944880i) q^{34} +(1.43328 + 0.827504i) q^{35} +(-1.34828 + 2.67995i) q^{36} +(5.65702 + 2.23564i) q^{37} +(-0.192483 - 0.333391i) q^{38} +(-1.22769 - 1.99195i) q^{39} -3.44654 q^{40} -3.30060 q^{41} +(-0.831377 + 0.0238987i) q^{42} +(-7.47606 + 4.31631i) q^{43} +(-1.57883 - 2.73461i) q^{44} +(9.23656 + 4.64689i) q^{45} +(3.99473 - 6.91907i) q^{46} +(-5.93648 - 10.2823i) q^{47} +(1.47450 - 0.908769i) q^{48} +(3.38471 + 5.86248i) q^{49} +6.87863i q^{50} +(1.88898 - 0.0543004i) q^{51} +1.35094i q^{52} +(1.47126 - 2.54830i) q^{53} +(-5.17685 + 0.447426i) q^{54} +(-9.42495 + 5.44150i) q^{55} +(0.415860 + 0.240097i) q^{56} +(0.316661 - 0.586791i) q^{57} +(-3.11923 - 5.40267i) q^{58} +(-0.294868 + 0.170242i) q^{59} +(-3.13211 - 5.08191i) q^{60} +(-12.3122 - 7.10847i) q^{61} +(2.07982 - 3.60235i) q^{62} +(-0.790768 - 1.20414i) q^{63} -1.00000 q^{64} +4.65605 q^{65} +(2.59739 - 4.81311i) q^{66} -8.89333 q^{67} +(-0.944880 - 0.545527i) q^{68} +(13.8324 - 0.397625i) q^{69} +(0.827504 - 1.43328i) q^{70} +(1.04493 + 1.80988i) q^{71} +(2.67995 + 1.34828i) q^{72} -7.32053 q^{73} +(2.23564 - 5.65702i) q^{74} +(-10.1425 + 6.25109i) q^{75} +(-0.333391 + 0.192483i) q^{76} +1.51629 q^{77} +(-1.99195 + 1.22769i) q^{78} +(-14.1139 - 8.14864i) q^{79} +3.44654i q^{80} +(-5.36429 - 7.22664i) q^{81} +3.30060i q^{82} -10.7584 q^{83} +(0.0238987 + 0.831377i) q^{84} +(-1.88018 + 3.25657i) q^{85} +(4.31631 + 7.47606i) q^{86} +(5.13156 - 9.50908i) q^{87} +(-2.73461 + 1.57883i) q^{88} +(2.15753 + 1.24565i) q^{89} +(4.64689 - 9.23656i) q^{90} +(-0.561801 - 0.324356i) q^{91} +(-6.91907 - 3.99473i) q^{92} +(7.20172 - 0.207020i) q^{93} +(-10.2823 + 5.93648i) q^{94} +(0.663401 + 1.14904i) q^{95} +(-0.908769 - 1.47450i) q^{96} +(10.9363 - 6.31410i) q^{97} +(5.86248 - 3.38471i) q^{98} +(9.45734 - 0.544169i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.47450	−	0.908769i	0.851301	−	0.524678i
$3$	1.47450	−	0.908769i	0.851301	−	0.524678i
$4$	−1.00000			−0.500000
$5$			3.44654i			1.54134i	0.637235	+	0.770670i	$0.280078\pi$
$5$			3.44654i			1.54134i	−0.637235	+	0.770670i	$0.719922\pi$
$6$	−0.908769	−	1.47450i	−0.371003	−	0.601961i
$7$	0.240097	−	0.415860i	0.0907482	−	0.157180i	−0.817078	−	0.576527i	$-0.804407\pi$
$7$	0.240097	−	0.415860i	0.0907482	−	0.157180i	0.907826	+	0.419347i	$0.137741\pi$
$8$			1.00000i			0.353553i
$9$	1.34828	−	2.67995i	0.449426	−	0.893317i
$10$	3.44654			1.08989
$11$	1.57883	+	2.73461i	0.476035	+	0.824517i	0.999623	−	0.0274546i	$-0.00874017\pi$
$11$	1.57883	+	2.73461i	0.476035	+	0.824517i	−0.523588	+	0.851972i	$0.675407\pi$
$12$	−1.47450	+	0.908769i	−0.425650	+	0.262339i
$13$		−	1.35094i		−	0.374682i	−0.982295	−	0.187341i	$-0.940013\pi$
$13$		−	1.35094i		−	0.374682i	0.982295	−	0.187341i	$-0.0599870\pi$
$14$	−0.415860	−	0.240097i	−0.111143	−	0.0641687i
$15$	3.13211	+	5.08191i	0.808707	+	1.31214i
$16$	1.00000			0.250000
$17$	0.944880	+	0.545527i	0.229167	+	0.132310i	0.610188	−	0.792257i	$-0.291094\pi$
$17$	0.944880	+	0.545527i	0.229167	+	0.132310i	−0.381021	+	0.924567i	$0.624427\pi$
$18$	−2.67995	−	1.34828i	−0.631671	−	0.317792i
$19$	0.333391	−	0.192483i	0.0764851	−	0.0441587i	−0.461270	−	0.887260i	$-0.652606\pi$
$19$	0.333391	−	0.192483i	0.0764851	−	0.0441587i	0.537755	+	0.843101i	$0.319273\pi$
$20$		−	3.44654i		−	0.770670i
$21$	−0.0238987	−	0.831377i	−0.00521512	−	0.181421i
$22$	2.73461	−	1.57883i	0.583022	−	0.336608i
$23$	6.91907	+	3.99473i	1.44273	+	0.832958i	0.998031	−	0.0627234i	$-0.0199786\pi$
$23$	6.91907	+	3.99473i	1.44273	+	0.832958i	0.444695	+	0.895682i	$0.353312\pi$
$24$	0.908769	+	1.47450i	0.185502	+	0.300980i
$25$	−6.87863			−1.37573
$26$	−1.35094			−0.264940
$27$	−0.447426	−	5.17685i	−0.0861071	−	0.996286i
$28$	−0.240097	+	0.415860i	−0.0453741	+	0.0785902i
$29$	5.40267	−	3.11923i	1.00325	−	0.579227i	0.0940423	−	0.995568i	$-0.470021\pi$
$29$	5.40267	−	3.11923i	1.00325	−	0.579227i	0.909209	+	0.416341i	$0.136688\pi$
$30$	5.08191	−	3.13211i	0.927825	−	0.571842i
$31$	3.60235	+	2.07982i	0.647001	+	0.373546i	0.787306	−	0.616562i	$-0.211475\pi$
$31$	3.60235	+	2.07982i	0.647001	+	0.373546i	−0.140305	+	0.990108i	$0.544808\pi$
$32$		−	1.00000i		−	0.176777i
$33$	4.81311	+	2.59739i	0.837855	+	0.452147i
$34$	0.545527	−	0.944880i	0.0935571	−	0.162046i
$35$	1.43328	+	0.827504i	0.242268	+	0.139874i
$36$	−1.34828	+	2.67995i	−0.224713	+	0.446659i
$37$	5.65702	+	2.23564i	0.930009	+	0.367538i
$37$	5.65702	+	2.23564i	0.930009	+	0.367538i
$38$	−0.192483	−	0.333391i	−0.0312249	−	0.0540831i
$39$	−1.22769	−	1.99195i	−0.196588	−	0.318967i
$40$	−3.44654			−0.544946
$41$	−3.30060			−0.515466			−0.257733	−	0.966216i	$-0.582976\pi$
$41$	−3.30060			−0.515466			−0.257733	+	0.966216i	$0.582976\pi$
$42$	−0.831377	+	0.0238987i	−0.128284	+	0.00368765i
$43$	−7.47606	+	4.31631i	−1.14009	+	0.658231i	−0.946453	−	0.322843i	$-0.895362\pi$
$43$	−7.47606	+	4.31631i	−1.14009	+	0.658231i	−0.193636	+	0.981073i	$0.562028\pi$
$44$	−1.57883	−	2.73461i	−0.238018	−	0.412259i
$45$	9.23656	+	4.64689i	1.37691	+	0.692718i
$46$	3.99473	−	6.91907i	0.588991	−	1.02016i
$47$	−5.93648	−	10.2823i	−0.865925	−	1.49983i	−0.866126	−	0.499826i	$-0.833397\pi$
$47$	−5.93648	−	10.2823i	−0.865925	−	1.49983i	0.000200737	−	1.00000i	$-0.499936\pi$
$48$	1.47450	−	0.908769i	0.212825	−	0.131169i
$49$	3.38471	+	5.86248i	0.483530	+	0.837498i
$50$			6.87863i			0.972785i
$51$	1.88898	−	0.0543004i	0.264510	−	0.00760358i
$52$			1.35094i			0.187341i
$53$	1.47126	−	2.54830i	0.202094	−	0.350037i	−0.747109	−	0.664701i	$-0.768559\pi$
$53$	1.47126	−	2.54830i	0.202094	−	0.350037i	0.949203	+	0.314665i	$0.101892\pi$
$54$	−5.17685	+	0.447426i	−0.704481	+	0.0608869i
$55$	−9.42495	+	5.44150i	−1.27086	+	0.733732i
$56$	0.415860	+	0.240097i	0.0555717	+	0.0320843i
$57$	0.316661	−	0.586791i	0.0419427	−	0.0777223i
$58$	−3.11923	−	5.40267i	−0.409575	−	0.709405i
$59$	−0.294868	+	0.170242i	−0.0383886	+	0.0221636i	−0.519071	−	0.854731i	$-0.673722\pi$
$59$	−0.294868	+	0.170242i	−0.0383886	+	0.0221636i	0.480683	+	0.876894i	$0.340389\pi$
$60$	−3.13211	−	5.08191i	−0.404353	−	0.656072i
$61$	−12.3122	−	7.10847i	−1.57642	−	0.910147i	−0.995353	−	0.0962916i	$-0.969302\pi$
$61$	−12.3122	−	7.10847i	−1.57642	−	0.910147i	−0.581068	−	0.813855i	$-0.697365\pi$
$62$	2.07982	−	3.60235i	0.264137	−	0.457499i
$63$	−0.790768	−	1.20414i	−0.0996275	−	0.151708i
$64$	−1.00000			−0.125000
$65$	4.65605			0.577512
$66$	2.59739	−	4.81311i	0.319716	−	0.592453i
$67$	−8.89333			−1.08649			−0.543247	−	0.839573i	$-0.682805\pi$
$67$	−8.89333			−1.08649			−0.543247	+	0.839573i	$0.682805\pi$
$68$	−0.944880	−	0.545527i	−0.114584	−	0.0661549i
$69$	13.8324	−	0.397625i	1.66523	−	0.0478685i
$70$	0.827504	−	1.43328i	0.0989057	−	0.171310i
$71$	1.04493	+	1.80988i	0.124011	+	0.214793i	0.921346	−	0.388744i	$-0.127091\pi$
$71$	1.04493	+	1.80988i	0.124011	+	0.214793i	−0.797335	+	0.603537i	$0.793758\pi$
$72$	2.67995	+	1.34828i	0.315835	+	0.158896i
$73$	−7.32053			−0.856803			−0.428402	−	0.903588i	$-0.640923\pi$
$73$	−7.32053			−0.856803			−0.428402	+	0.903588i	$0.640923\pi$
$74$	2.23564	−	5.65702i	0.259888	−	0.657615i
$75$	−10.1425	+	6.25109i	−1.17116	+	0.721813i
$76$	−0.333391	+	0.192483i	−0.0382425	+	0.0220793i
$77$	1.51629			0.172797
$78$	−1.99195	+	1.22769i	−0.225544	+	0.139008i
$79$	−14.1139	−	8.14864i	−1.58793	−	0.916794i	−0.993647	−	0.112541i	$-0.964101\pi$
$79$	−14.1139	−	8.14864i	−1.58793	−	0.916794i	−0.594287	−	0.804253i	$-0.702566\pi$
$80$			3.44654i			0.385335i
$81$	−5.36429	−	7.22664i	−0.596032	−	0.802960i
$82$			3.30060i			0.364490i
$83$	−10.7584			−1.18088			−0.590442	−	0.807080i	$-0.701047\pi$
$83$	−10.7584			−1.18088			−0.590442	+	0.807080i	$0.701047\pi$
$84$	0.0238987	+	0.831377i	0.00260756	+	0.0907107i
$85$	−1.88018	+	3.25657i	−0.203934	+	0.353224i
$86$	4.31631	+	7.47606i	0.465439	+	0.806165i
$87$	5.13156	−	9.50908i	0.550161	−	1.01948i
$88$	−2.73461	+	1.57883i	−0.291511	+	0.168304i
$89$	2.15753	+	1.24565i	0.228697	+	0.132038i	0.609971	−	0.792424i	$-0.291181\pi$
$89$	2.15753	+	1.24565i	0.228697	+	0.132038i	−0.381274	+	0.924462i	$0.624514\pi$
$90$	4.64689	−	9.23656i	0.489826	−	0.973619i
$91$	−0.561801	−	0.324356i	−0.0588927	−	0.0340017i
$92$	−6.91907	−	3.99473i	−0.721363	−	0.416479i
$93$	7.20172	−	0.207020i	0.746784	−	0.0214670i
$94$	−10.2823	+	5.93648i	−1.06054	+	0.612301i
$95$	0.663401	+	1.14904i	0.0680635	+	0.117889i
$96$	−0.908769	−	1.47450i	−0.0927508	−	0.150490i
$97$	10.9363	−	6.31410i	1.11042	−	0.641100i	0.171480	−	0.985188i	$-0.445145\pi$
$97$	10.9363	−	6.31410i	1.11042	−	0.641100i	0.938938	+	0.344088i	$0.111812\pi$
$98$	5.86248	−	3.38471i	0.592200	−	0.341907i
$99$	9.45734	−	0.544169i	0.950498	−	0.0546910i
$100$	6.87863			0.687863
$101$	0.492396	+	0.852854i	0.0489952	+	0.0848622i	0.889483	−	0.456968i	$-0.151065\pi$
$101$	0.492396	+	0.852854i	0.0489952	+	0.0848622i	−0.840488	+	0.541831i	$0.817731\pi$
$102$	−0.0543004	−	1.88898i	−0.00537654	−	0.187037i
$103$	1.04404	+	0.602776i	0.102872	+	0.0593933i	0.550553	−	0.834800i	$-0.314417\pi$
$103$	1.04404	+	0.602776i	0.102872	+	0.0593933i	−0.447681	+	0.894193i	$0.647750\pi$
$104$	1.35094			0.132470
$105$	2.86537	−	0.0823677i	0.279632	−	0.00803827i
$106$	−2.54830	−	1.47126i	−0.247513	−	0.142902i
$107$	7.88782	+	13.6621i	0.762544	+	1.32077i	0.941535	+	0.336915i	$0.109383\pi$
$107$	7.88782	+	13.6621i	0.762544	+	1.32077i	−0.178991	+	0.983851i	$0.557283\pi$
$108$	0.447426	+	5.17685i	0.0430536	+	0.498143i
$109$	4.39231	+	2.53590i	0.420707	+	0.242895i	0.695380	−	0.718643i	$-0.255236\pi$
$109$	4.39231	+	2.53590i	0.420707	+	0.242895i	−0.274673	+	0.961538i	$0.588570\pi$
$110$	5.44150	+	9.42495i	0.518827	+	0.898634i
$111$	10.3729	−	1.84448i	0.984556	−	0.175070i
$112$	0.240097	−	0.415860i	0.0226870	−	0.0392951i
$113$	0.515396	−	0.297564i	0.0484844	−	0.0279925i	−0.475562	−	0.879682i	$-0.657755\pi$
$113$	0.515396	−	0.297564i	0.0484844	−	0.0279925i	0.524046	+	0.851690i	$0.324422\pi$
$114$	−0.586791	−	0.316661i	−0.0549580	−	0.0296580i
$115$	−13.7680	+	23.8469i	−1.28387	+	2.22373i
$116$	−5.40267	+	3.11923i	−0.501625	+	0.289614i
$117$	−3.62044	−	1.82144i	−0.334710	−	0.168392i
$118$	0.170242	+	0.294868i	0.0156721	+	0.0271448i
$119$	0.453726	−	0.261959i	0.0415930	−	0.0240137i
$120$	−5.08191	+	3.13211i	−0.463913	+	0.285921i
$121$	0.514592	−	0.891300i	0.0467811	−	0.0810272i
$122$	−7.10847	+	12.3122i	−0.643571	+	1.11470i
$123$	−4.86672	+	2.99948i	−0.438817	+	0.270454i
$124$	−3.60235	−	2.07982i	−0.323501	−	0.186773i
$125$		−	6.47477i		−	0.579121i
$126$	−1.20414	+	0.790768i	−0.107274	+	0.0704473i
$127$	3.39075	−	5.87296i	0.300881	−	0.521141i	−0.675455	−	0.737401i	$-0.736053\pi$
$127$	3.39075	−	5.87296i	0.300881	−	0.521141i	0.976336	+	0.216261i	$0.0693861\pi$
$128$			1.00000i			0.0883883i
$129$	−7.10090	+	13.1584i	−0.625200	+	1.15853i
$130$		−	4.65605i		−	0.408363i
$131$	6.98950	−	4.03539i	0.610676	−	0.352574i	−0.162554	−	0.986700i	$-0.551973\pi$
$131$	6.98950	−	4.03539i	0.610676	−	0.352574i	0.773230	+	0.634126i	$0.218640\pi$
$132$	−4.81311	−	2.59739i	−0.418927	−	0.226073i
$133$		−	0.184859i		−	0.0160293i
$134$			8.89333i			0.768267i
$135$	17.8422	−	1.54207i	1.53561	−	0.132720i
$136$	−0.545527	+	0.944880i	−0.0467785	+	0.0810228i
$137$	0.0848084	+	0.146893i	0.00724567	+	0.0125499i	0.869626	−	0.493712i	$-0.164360\pi$
$137$	0.0848084	+	0.146893i	0.00724567	+	0.0125499i	−0.862380	+	0.506262i	$0.831027\pi$
$138$	−0.397625	−	13.8324i	−0.0338481	−	1.17749i
$139$	−4.32699	−	7.49457i	−0.367011	−	0.635681i	0.622086	−	0.782949i	$-0.286285\pi$
$139$	−4.32699	−	7.49457i	−0.367011	−	0.635681i	−0.989097	+	0.147268i	$0.952952\pi$
$140$	−1.43328	−	0.827504i	−0.121134	−	0.0699369i
$141$	−18.0975	−	9.76631i	−1.52409	−	0.822471i
$142$	1.80988	−	1.04493i	0.151881	−	0.0876888i
$143$	3.69429	−	2.13290i	0.308932	−	0.178362i
$144$	1.34828	−	2.67995i	0.112357	−	0.223329i
$145$	10.7506	+	18.6205i	0.892785	+	1.54635i
$146$			7.32053i			0.605851i
$147$	10.3184	+	5.56829i	0.851046	+	0.459265i
$148$	−5.65702	−	2.23564i	−0.465004	−	0.183769i
$149$	−2.53720	+	4.39456i	−0.207855	+	0.360016i	−0.951039	−	0.309072i	$-0.899982\pi$
$149$	−2.53720	+	4.39456i	−0.207855	+	0.360016i	0.743183	+	0.669088i	$0.233315\pi$
$150$	6.25109	+	10.1425i	0.510399	+	0.828133i
$151$	−2.46576	+	4.27082i	−0.200661	+	0.347555i	−0.948741	−	0.316053i	$-0.897642\pi$
$151$	−2.46576	+	4.27082i	−0.200661	+	0.347555i	0.748081	+	0.663608i	$0.230976\pi$
$152$	0.192483	+	0.333391i	0.0156125	+	0.0270416i
$153$	2.73595	−	1.79671i	0.221188	−	0.145256i
$154$		−	1.51629i		−	0.122186i
$155$	−7.16817	+	12.4156i	−0.575761	+	0.997248i
$156$	1.22769	+	1.99195i	0.0982938	+	0.159484i
$157$	−3.53659	−	6.12555i	−0.282251	−	0.488872i	0.689688	−	0.724107i	$-0.257748\pi$
$157$	−3.53659	−	6.12555i	−0.282251	−	0.488872i	−0.971939	+	0.235234i	$0.924414\pi$
$158$	−8.14864	+	14.1139i	−0.648271	+	1.12284i
$159$	−0.146446	−	5.09450i	−0.0116139	−	0.404020i
$160$	3.44654			0.272473
$161$	3.32250	−	1.91825i	0.261850	−	0.151179i
$162$	−7.22664	+	5.36429i	−0.567779	+	0.421458i
$163$	−16.5023	−	9.52761i	−1.29256	−	0.746260i	−0.313452	−	0.949604i	$-0.601486\pi$
$163$	−16.5023	−	9.52761i	−1.29256	−	0.746260i	−0.979107	+	0.203344i	$0.934819\pi$
$164$	3.30060			0.257733
$165$	−8.95199	+	16.5886i	−0.696912	+	1.29142i
$166$			10.7584i			0.835012i
$167$		−	10.3512i		−	0.801003i	−0.916296	−	0.400501i	$-0.868836\pi$
$167$		−	10.3512i		−	0.801003i	0.916296	−	0.400501i	$-0.131164\pi$
$168$	0.831377	−	0.0238987i	0.0641422	−	0.00184382i
$169$	11.1750			0.859613
$170$	3.25657	+	1.88018i	0.249767	+	0.144203i
$171$	−0.0663424	−	1.15299i	−0.00507333	−	0.0881715i
$172$	7.47606	−	4.31631i	0.570044	−	0.329115i
$173$	−3.86787			−0.294069			−0.147034	−	0.989131i	$-0.546973\pi$
$173$	−3.86787			−0.294069			−0.147034	+	0.989131i	$0.546973\pi$
$174$	−9.50908	−	5.13156i	−0.720881	−	0.389022i
$175$	−1.65154	+	2.86055i	−0.124845	+	0.216237i
$176$	1.57883	+	2.73461i	0.119009	+	0.206129i
$177$	−0.280071	+	0.518988i	−0.0210514	+	0.0390096i
$178$	1.24565	−	2.15753i	0.0933653	−	0.161713i
$179$		−	2.26842i		−	0.169550i	−0.996400	−	0.0847748i	$-0.972983\pi$
$179$		−	2.26842i		−	0.169550i	0.996400	−	0.0847748i	$-0.0270171\pi$
$180$	−9.23656	−	4.64689i	−0.688453	−	0.346359i
$181$	−1.66515	−	2.88412i	−0.123769	−	0.214375i	0.797482	−	0.603343i	$-0.206165\pi$
$181$	−1.66515	−	2.88412i	−0.123769	−	0.214375i	−0.921251	+	0.388968i	$0.872832\pi$
$182$	−0.324356	+	0.561801i	−0.0240429	+	0.0416435i
$183$	−24.6143	+	0.707560i	−1.81954	+	0.0523043i
$184$	−3.99473	+	6.91907i	−0.294495	+	0.510081i
$185$	−7.70523	+	19.4971i	−0.566500	+	1.43346i
$186$	−0.207020	−	7.20172i	−0.0151794	−	0.528056i
$187$			3.44518i			0.251936i
$188$	5.93648	+	10.2823i	0.432963	+	0.749913i
$189$	−2.26027	−	1.05688i	−0.164411	−	0.0768768i
$190$	1.14904	−	0.663401i	0.0833604	−	0.0481282i
$191$	4.54498	−	2.62405i	0.328863	−	0.189869i	−0.326473	−	0.945207i	$-0.605860\pi$
$191$	4.54498	−	2.62405i	0.328863	−	0.189869i	0.655336	+	0.755337i	$0.272527\pi$
$192$	−1.47450	+	0.908769i	−0.106413	+	0.0655847i
$193$	5.51469	+	3.18391i	0.396956	+	0.229183i	0.685170	−	0.728384i	$-0.259728\pi$
$193$	5.51469	+	3.18391i	0.396956	+	0.229183i	−0.288214	+	0.957566i	$0.593061\pi$
$194$	−6.31410	−	10.9363i	−0.453326	−	0.785184i
$195$	6.86533	−	4.23128i	0.491637	−	0.303008i
$196$	−3.38471	−	5.86248i	−0.241765	−	0.418749i
$197$	−3.14271	+	5.44333i	−0.223909	+	0.387821i	−0.955991	−	0.293394i	$-0.905215\pi$
$197$	−3.14271	+	5.44333i	−0.223909	+	0.387821i	0.732083	+	0.681216i	$0.238548\pi$
$198$	−0.544169	−	9.45734i	−0.0386724	−	0.672104i
$199$		−	13.2707i		−	0.940735i	−0.882471	−	0.470368i	$-0.844121\pi$
$199$		−	13.2707i		−	0.940735i	0.882471	−	0.470368i	$-0.155879\pi$
$200$		−	6.87863i		−	0.486393i
$201$	−13.1132	+	8.08198i	−0.924933	+	0.570059i
$202$	0.852854	−	0.492396i	0.0600066	−	0.0346448i
$203$		−	2.99568i		−	0.210255i
$204$	−1.88898	+	0.0543004i	−0.132255	+	0.00380179i
$205$		−	11.3756i		−	0.794509i
$206$	0.602776	−	1.04404i	0.0419974	−	0.0727417i
$207$	20.0345	−	13.1568i	1.39250	−	0.914459i
$208$		−	1.35094i		−	0.0936706i
$209$	1.05273	+	0.607797i	0.0728192	+	0.0420422i
$210$	−0.0823677	−	2.86537i	−0.00568391	−	0.197730i
$211$	−8.29561	+	14.3684i	−0.571093	+	0.989163i	0.425361	+	0.905024i	$0.360147\pi$
$211$	−8.29561	+	14.3684i	−0.571093	+	0.989163i	−0.996454	+	0.0841389i	$0.973186\pi$
$212$	−1.47126	+	2.54830i	−0.101047	+	0.175018i
$213$	3.18551	+	1.71905i	0.218267	+	0.117788i
$214$	13.6621	−	7.88782i	0.933922	−	0.539200i
$215$	−14.8763	−	25.7665i	−1.01456	−	1.75726i
$216$	5.17685	−	0.447426i	0.352240	−	0.0304435i
$217$	1.72983	−	0.998716i	0.117428	−	0.0677973i
$218$	2.53590	−	4.39231i	0.171753	−	0.297484i
$219$	−10.7941	+	6.65267i	−0.729397	+	0.449546i
$220$	9.42495	−	5.44150i	0.635430	−	0.366866i
$221$	0.736972	−	1.27647i	0.0495741	−	0.0858649i
$222$	−1.84448	−	10.3729i	−0.123793	−	0.696186i
$223$	−9.16344	−	15.8715i	−0.613629	−	1.06284i	−0.990623	−	0.136621i	$-0.956376\pi$
$223$	−9.16344	−	15.8715i	−0.613629	−	1.06284i	0.376994	−	0.926216i	$-0.376958\pi$
$224$	−0.415860	−	0.240097i	−0.0277858	−	0.0160422i
$225$	−9.27431	+	18.4344i	−0.618287	+	1.22896i
$226$	−0.297564	−	0.515396i	−0.0197937	−	0.0342837i
$227$	−1.61764	−	0.933947i	−0.107367	−	0.0619883i	0.445355	−	0.895354i	$-0.353077\pi$
$227$	−1.61764	−	0.933947i	−0.107367	−	0.0619883i	−0.552722	+	0.833366i	$0.686411\pi$
$228$	−0.316661	+	0.586791i	−0.0209714	+	0.0388612i
$229$	6.81939			0.450638			0.225319	−	0.974285i	$-0.427658\pi$
$229$	6.81939			0.450638			0.225319	+	0.974285i	$0.427658\pi$
$230$	23.8469	+	13.7680i	1.57241	+	0.907834i
$231$	2.23576	−	1.37796i	0.147102	−	0.0906629i
$232$	3.11923	+	5.40267i	0.204788	+	0.354703i
$233$	−28.3171			−1.85512			−0.927559	−	0.373678i	$-0.878097\pi$
$233$	−28.3171			−1.85512			−0.927559	+	0.373678i	$0.878097\pi$
$234$	−1.82144	+	3.62044i	−0.119071	+	0.236676i
$235$	35.4383	−	20.4603i	2.31174	−	1.33468i
$236$	0.294868	−	0.170242i	0.0191943	−	0.0110818i
$237$	−28.2161	+	0.811096i	−1.83283	+	0.0526863i
$238$	−0.261959	−	0.453726i	−0.0169803	−	0.0294107i
$239$	16.8722	−	9.74117i	1.09137	−	0.630104i	0.157430	−	0.987530i	$-0.449679\pi$
$239$	16.8722	−	9.74117i	1.09137	−	0.630104i	0.933941	+	0.357426i	$0.116346\pi$
$240$	3.13211	+	5.08191i	0.202177	+	0.328036i
$241$	20.6711	+	11.9345i	1.33154	+	0.768766i	0.985536	−	0.169466i	$-0.0542044\pi$
$241$	20.6711	+	11.9345i	1.33154	+	0.768766i	0.346006	+	0.938232i	$0.387538\pi$
$242$	−0.891300	−	0.514592i	−0.0572949	−	0.0330792i
$243$	−14.4770	−	5.78076i	−0.928698	−	0.370836i
$244$	12.3122	+	7.10847i	0.788210	+	0.455073i
$245$	−20.2053	+	11.6655i	−1.29087	+	0.745283i
$246$	2.99948	+	4.86672i	0.191240	+	0.310290i
$247$	−0.260033	−	0.450390i	−0.0165455	−	0.0286576i
$248$	−2.07982	+	3.60235i	−0.132069	+	0.228749i
$249$	−15.8632	+	9.77687i	−1.00529	+	0.619584i
$250$	−6.47477			−0.409501
$251$			15.8983i			1.00349i	0.865016	+	0.501745i	$0.167308\pi$
$251$			15.8983i			1.00349i	−0.865016	+	0.501745i	$0.832692\pi$
$252$	0.790768	+	1.20414i	0.0498137	+	0.0758540i
$253$			25.2280i			1.58607i
$254$	−5.87296	−	3.39075i	−0.368502	−	0.212755i
$255$	0.187148	+	6.51044i	0.0117197	+	0.407700i
$256$	1.00000			0.0625000
$257$	14.6449	−	8.45521i	0.913521	−	0.527421i	0.0319585	−	0.999489i	$-0.489826\pi$
$257$	14.6449	−	8.45521i	0.913521	−	0.527421i	0.881562	+	0.472068i	$0.156492\pi$
$258$	13.1584	+	7.10090i	0.819206	+	0.442083i
$259$	2.28795	−	1.81576i	0.142166	−	0.112826i
$260$	−4.65605			−0.288756
$261$	−1.07509	−	18.6845i	−0.0665466	−	1.15654i
$262$	−4.03539	−	6.98950i	−0.249307	−	0.431813i
$263$	−11.4568	+	19.8437i	−0.706455	+	1.22362i	0.259708	+	0.965687i	$0.416374\pi$
$263$	−11.4568	+	19.8437i	−0.706455	+	1.22362i	−0.966164	+	0.257930i	$0.916960\pi$
$264$	−2.59739	+	4.81311i	−0.159858	+	0.296226i
$265$	8.78283	+	5.07077i	0.539525	+	0.311495i
$266$	−0.184859			−0.0113344
$267$	4.31327	−	0.123989i	0.263968	−	0.00758799i
$268$	8.89333			0.543247
$269$	−18.9536			−1.15562			−0.577812	−	0.816170i	$-0.696093\pi$
$269$	−18.9536			−1.15562			−0.577812	+	0.816170i	$0.696093\pi$
$270$	−1.54207	−	17.8422i	−0.0938474	−	1.08584i
$271$	2.10857	−	3.65215i	0.128086	−	0.221852i	−0.794849	−	0.606808i	$-0.792450\pi$
$271$	2.10857	−	3.65215i	0.128086	−	0.221852i	0.922935	+	0.384955i	$0.125783\pi$
$272$	0.944880	+	0.545527i	0.0572918	+	0.0330774i
$273$	−1.12314	+	0.0322856i	−0.0679754	+	0.00195401i
$274$	0.146893	−	0.0848084i	0.00887410	−	0.00512347i
$275$	−10.8602	−	18.8104i	−0.654894	−	1.13431i
$276$	−13.8324	+	0.397625i	−0.832615	+	0.0239342i
$277$	−26.7507	−	15.4445i	−1.60729	−	0.927971i	−0.989973	−	0.141258i	$-0.954885\pi$
$277$	−26.7507	−	15.4445i	−1.60729	−	0.927971i	−0.617319	−	0.786713i	$-0.711781\pi$
$278$	−7.49457	+	4.32699i	−0.449494	+	0.259516i
$279$	10.4308	−	6.84995i	0.624475	−	0.410096i
$280$	−0.827504	+	1.43328i	−0.0494528	+	0.0856548i
$281$			32.3624i			1.93058i	0.261181	+	0.965290i	$0.415888\pi$
$281$			32.3624i			1.93058i	−0.261181	+	0.965290i	$0.584112\pi$
$282$	−9.76631	+	18.0975i	−0.581575	+	1.07769i
$283$			16.3590i			0.972440i	0.873836	+	0.486220i	$0.161625\pi$
$283$			16.3590i			0.972440i	−0.873836	+	0.486220i	$0.838375\pi$
$284$	−1.04493	−	1.80988i	−0.0620053	−	0.107396i
$285$	2.02240	+	1.09138i	0.119796	+	0.0646480i
$286$	−2.13290	−	3.69429i	−0.126121	−	0.218448i
$287$	−0.792464	+	1.37259i	−0.0467776	+	0.0810213i
$288$	−2.67995	−	1.34828i	−0.157918	−	0.0794481i
$289$	−7.90480	−	13.6915i	−0.464988	−	0.805383i
$290$	18.6205	−	10.7506i	1.09343	−	0.631295i
$291$	10.3875	−	19.2487i	0.608929	−	1.12838i
$292$	7.32053			0.428402
$293$	17.9908			1.05103			0.525516	−	0.850784i	$-0.323872\pi$
$293$	17.9908			1.05103			0.525516	+	0.850784i	$0.323872\pi$
$294$	5.56829	−	10.3184i	0.324750	−	0.601780i
$295$	−0.586746	−	1.01627i	−0.0341617	−	0.0591698i
$296$	−2.23564	+	5.65702i	−0.129944	+	0.328808i
$297$	13.4503	−	9.39691i	0.780465	−	0.545264i
$298$	4.39456	+	2.53720i	0.254570	+	0.146976i
$299$	5.39662	−	9.34723i	0.312095	−	0.540564i
$300$	10.1425	−	6.25109i	0.585578	−	0.360907i
$301$			4.14533i			0.238933i
$302$	4.27082	+	2.46576i	0.245758	+	0.141889i
$303$	1.50108	+	0.810057i	0.0862350	+	0.0465365i
$304$	0.333391	−	0.192483i	0.0191213	−	0.0110397i
$305$	24.4996	−	42.4346i	1.40285	−	2.42980i
$306$	−1.79671	−	2.73595i	−0.102711	−	0.156404i
$307$	−8.71513			−0.497399			−0.248699	−	0.968581i	$-0.580003\pi$
$307$	−8.71513			−0.497399			−0.248699	+	0.968581i	$0.580003\pi$
$308$	−1.51629			−0.0863987
$309$	2.08722	−	0.0599989i	0.118738	−	0.00341322i
$310$	12.4156	+	7.16817i	0.705161	+	0.407125i
$311$	21.3032	−	12.2994i	1.20800	−	0.697437i	0.245675	−	0.969352i	$-0.420990\pi$
$311$	21.3032	−	12.2994i	1.20800	−	0.697437i	0.962321	+	0.271915i	$0.0876571\pi$
$312$	1.99195	−	1.22769i	0.112772	−	0.0695042i
$313$		−	10.3660i		−	0.585918i	−0.956125	−	0.292959i	$-0.905360\pi$
$313$		−	10.3660i		−	0.585918i	0.956125	−	0.292959i	$-0.0946400\pi$
$314$	−6.12555	+	3.53659i	−0.345685	+	0.199581i
$315$	4.15013	−	2.72541i	0.233833	−	0.153560i
$316$	14.1139	+	8.14864i	0.793967	+	0.458397i
$317$	29.8730			1.67784			0.838918	−	0.544257i	$-0.183189\pi$
$317$	29.8730			1.67784			0.838918	+	0.544257i	$0.183189\pi$
$318$	−5.09450	+	0.146446i	−0.285686	+	0.00821228i
$319$	17.0598	+	9.84948i	0.955165	+	0.551465i
$320$		−	3.44654i		−	0.192667i
$321$	24.0463	+	12.9765i	1.34213	+	0.724278i
$322$	−1.91825	−	3.32250i	−0.106900	−	0.185156i
$323$	0.420019			0.0233705
$324$	5.36429	+	7.22664i	0.298016	+	0.401480i
$325$			9.29259i			0.515460i
$326$	−9.52761	+	16.5023i	−0.527685	+	0.913978i
$327$	8.78098	−	0.252417i	0.485590	−	0.0139587i
$328$		−	3.30060i		−	0.182245i
$329$	−5.70133			−0.314325
$330$	16.5886	+	8.95199i	0.913171	+	0.492791i
$331$		−	23.5213i		−	1.29285i	−0.762979	−	0.646423i	$-0.776264\pi$
$331$		−	23.5213i		−	1.29285i	0.762979	−	0.646423i	$-0.223736\pi$
$332$	10.7584			0.590442
$333$	13.6187	−	12.1463i	0.746298	−	0.665612i
$334$	−10.3512			−0.566395
$335$		−	30.6512i		−	1.67466i
$336$	−0.0238987	−	0.831377i	−0.00130378	−	0.0453554i
$337$	−4.22458			−0.230127			−0.115064	−	0.993358i	$-0.536707\pi$
$337$	−4.22458			−0.230127			−0.115064	+	0.993358i	$0.536707\pi$
$338$		−	11.1750i		−	0.607838i
$339$	0.489533	−	0.907133i	0.0265878	−	0.0492687i
$340$	1.88018	−	3.25657i	0.101967	−	0.176612i
$341$			13.1347i			0.711285i
$342$	−1.15299	+	0.0663424i	−0.0623467	+	0.00358738i
$343$	6.61199			0.357014
$344$	−4.31631	−	7.47606i	−0.232720	−	0.403082i
$345$	1.37043	+	47.6740i	0.0737815	+	2.56668i
$346$			3.86787i			0.207938i
$347$	−22.1211	−	12.7716i	−1.18752	−	0.685616i	−0.229779	−	0.973243i	$-0.573800\pi$
$347$	−22.1211	−	12.7716i	−1.18752	−	0.685616i	−0.957743	+	0.287627i	$0.907134\pi$
$348$	−5.13156	+	9.50908i	−0.275080	+	0.509740i
$349$	25.6560			1.37333			0.686667	−	0.726972i	$-0.259073\pi$
$349$	25.6560			1.37333			0.686667	+	0.726972i	$0.259073\pi$
$350$	2.86055	+	1.65154i	0.152903	+	0.0882785i
$351$	−6.99360	+	0.604444i	−0.373291	+	0.0322628i
$352$	2.73461	−	1.57883i	0.145755	−	0.0841519i
$353$		−	18.1520i		−	0.966132i	−0.875584	−	0.483066i	$-0.839523\pi$
$353$		−	18.1520i		−	0.966132i	0.875584	−	0.483066i	$-0.160477\pi$
$354$	0.518988	+	0.280071i	0.0275839	+	0.0148856i
$355$	−6.23781	+	3.60140i	−0.331068	+	0.191142i
$356$	−2.15753	−	1.24565i	−0.114349	−	0.0660192i
$357$	0.430957	−	0.798590i	0.0228087	−	0.0422658i
$358$	−2.26842			−0.119890
$359$	3.62838			0.191499			0.0957493	−	0.995405i	$-0.469475\pi$
$359$	3.62838			0.191499			0.0957493	+	0.995405i	$0.469475\pi$
$360$	−4.64689	+	9.23656i	−0.244913	+	0.486809i
$361$	−9.42590	+	16.3261i	−0.496100	+	0.859270i
$362$	−2.88412	+	1.66515i	−0.151586	+	0.0875182i
$363$	−0.0512212	−	1.78186i	−0.00268842	−	0.0935236i
$364$	0.561801	+	0.324356i	0.0294464	+	0.0170009i
$365$		−	25.2305i		−	1.32062i
$366$	0.707560	+	24.6143i	0.0369848	+	1.28661i
$367$	11.3379	−	19.6379i	0.591835	−	1.02509i	−0.402151	−	0.915574i	$-0.631737\pi$
$367$	11.3379	−	19.6379i	0.591835	−	1.02509i	0.993985	−	0.109514i	$-0.0349295\pi$
$368$	6.91907	+	3.99473i	0.360682	+	0.208240i
$369$	−4.45012	+	8.84544i	−0.231664	+	0.460475i
$370$	19.4971	+	7.70523i	1.01361	+	0.400576i
$371$	−0.706493	−	1.22368i	−0.0366793	−	0.0635304i
$372$	−7.20172	+	0.207020i	−0.373392	+	0.0107335i
$373$	−26.6954			−1.38223			−0.691117	−	0.722743i	$-0.742881\pi$
$373$	−26.6954			−1.38223			−0.691117	+	0.722743i	$0.742881\pi$
$374$	3.44518			0.178146
$375$	−5.88407	−	9.54703i	−0.303852	−	0.493007i
$376$	10.2823	−	5.93648i	0.530269	−	0.306151i
$377$	−4.21389	−	7.29866i	−0.217026	−	0.375900i
$378$	−1.05688	+	2.26027i	−0.0543601	+	0.116256i
$379$	−11.6509	+	20.1799i	−0.598466	+	1.03657i	0.394582	+	0.918861i	$0.370889\pi$
$379$	−11.6509	+	20.1799i	−0.598466	+	1.03657i	−0.993048	+	0.117712i	$0.962444\pi$
$380$	−0.663401	−	1.14904i	−0.0340317	−	0.0589447i
$381$	−0.337507	−	11.7411i	−0.0172910	−	0.601513i
$382$	−2.62405	−	4.54498i	−0.134258	−	0.232542i
$383$		−	14.3137i		−	0.731394i	−0.930734	−	0.365697i	$-0.880831\pi$
$383$		−	14.3137i		−	0.731394i	0.930734	−	0.365697i	$-0.119169\pi$
$384$	0.908769	+	1.47450i	0.0463754	+	0.0752451i
$385$			5.22595i			0.266339i
$386$	3.18391	−	5.51469i	0.162057	−	0.280690i
$387$	1.48768	+	25.8551i	0.0756232	+	1.31429i
$388$	−10.9363	+	6.31410i	−0.555209	+	0.320550i
$389$	16.2561	+	9.38545i	0.824216	+	0.475861i	0.851868	−	0.523756i	$-0.175470\pi$
$389$	16.2561	+	9.38545i	0.824216	+	0.475861i	−0.0276524	+	0.999618i	$0.508803\pi$
$390$	−4.23128	−	6.86533i	−0.214259	−	0.347640i
$391$	4.35846	+	7.54908i	0.220417	+	0.381773i
$392$	−5.86248	+	3.38471i	−0.296100	+	0.170954i
$393$	6.63876	−	12.3020i	0.334881	−	0.620554i
$394$	5.44333	+	3.14271i	0.274231	+	0.158327i
$395$	28.0846	−	48.6440i	1.41309	−	2.44754i
$396$	−9.45734	+	0.544169i	−0.475249	+	0.0273455i
$397$	39.5953			1.98723			0.993616	−	0.112812i	$-0.0359857\pi$
$397$	39.5953			1.98723			0.993616	+	0.112812i	$0.0359857\pi$
$398$	−13.2707			−0.665200
$399$	−0.167994	−	0.272573i	−0.00841021	−	0.0136457i
$400$	−6.87863			−0.343932
$401$	−24.0748	−	13.8996i	−1.20224	−	0.694111i	−0.241184	−	0.970479i	$-0.577536\pi$
$401$	−24.0748	−	13.8996i	−1.20224	−	0.694111i	−0.961052	+	0.276368i	$0.910869\pi$
$402$	8.08198	+	13.1132i	0.403093	+	0.654026i
$403$	2.80970	−	4.86654i	0.139961	−	0.242420i
$404$	−0.492396	−	0.852854i	−0.0244976	−	0.0424311i
$405$	24.9069	−	18.4882i	1.23763	−	0.918688i
$406$	−2.99568			−0.148673
$407$	2.81785	+	18.9995i	0.139676	+	0.941769i
$408$	0.0543004	+	1.88898i	0.00268827	+	0.0935185i
$409$	12.7414	−	7.35625i	0.630021	−	0.363743i	−0.150739	−	0.988574i	$-0.548165\pi$
$409$	12.7414	−	7.35625i	0.630021	−	0.363743i	0.780760	+	0.624831i	$0.214832\pi$
$410$	−11.3756			−0.561802
$411$	0.258541	+	0.139521i	0.0127529	+	0.00688207i
$412$	−1.04404	−	0.602776i	−0.0514361	−	0.0296967i
$413$			0.163499i			0.00804524i
$414$	−13.1568	−	20.0345i	−0.646620	−	0.984643i
$415$		−	37.0792i		−	1.82014i
$416$	−1.35094			−0.0662351
$417$	−13.1910	−	7.11848i	−0.645964	−	0.348593i
$418$	0.607797	−	1.05273i	0.0297283	−	0.0514909i
$419$	0.330848	+	0.573045i	0.0161630	+	0.0279951i	0.873994	−	0.485937i	$-0.161522\pi$
$419$	0.330848	+	0.573045i	0.0161630	+	0.0279951i	−0.857831	+	0.513932i	$0.828188\pi$
$420$	−2.86537	+	0.0823677i	−0.139816	+	0.00401913i
$421$	19.0635	−	11.0063i	0.929098	−	0.536415i	0.0425721	−	0.999093i	$-0.486445\pi$
$421$	19.0635	−	11.0063i	0.929098	−	0.536415i	0.886526	+	0.462678i	$0.153111\pi$
$422$	14.3684	+	8.29561i	0.699444	+	0.403824i
$423$	−35.5601	+	2.04610i	−1.72899	+	0.0994849i
$424$	2.54830	+	1.47126i	0.123757	+	0.0714509i
$425$	−6.49948	−	3.75248i	−0.315271	−	0.182022i
$426$	1.71905	−	3.18551i	0.0832884	−	0.154338i
$427$	−5.91227	+	3.41345i	−0.286115	+	0.165188i
$428$	−7.88782	−	13.6621i	−0.381272	−	0.660383i
$429$	3.50890	−	6.50221i	0.169411	−	0.313929i
$430$	−25.7665	+	14.8763i	−1.24257	+	0.717400i
$431$	−5.70464	+	3.29357i	−0.274783	+	0.158646i	−0.631059	−	0.775735i	$-0.717379\pi$
$431$	−5.70464	+	3.29357i	−0.274783	+	0.158646i	0.356276	+	0.934381i	$0.384046\pi$
$432$	−0.447426	−	5.17685i	−0.0215268	−	0.249071i
$433$	−12.7700			−0.613686			−0.306843	−	0.951760i	$-0.599273\pi$
$433$	−12.7700			−0.613686			−0.306843	+	0.951760i	$0.599273\pi$
$434$	−0.998716	−	1.72983i	−0.0479399	−	0.0830344i
$435$	32.7734	+	17.6861i	1.57136	+	0.847984i
$436$	−4.39231	−	2.53590i	−0.210353	−	0.121448i
$437$	3.07567			0.147129
$438$	6.65267	+	10.7941i	0.317877	+	0.515762i
$439$	−31.1553	−	17.9875i	−1.48696	−	0.858497i	−0.487071	−	0.873363i	$-0.661935\pi$
$439$	−31.1553	−	17.9875i	−1.48696	−	0.858497i	−0.999890	+	0.0148656i	$0.995268\pi$
$440$	−5.44150	−	9.42495i	−0.259413	−	0.449317i
$441$	20.2747	−	1.16659i	0.965462	−	0.0555520i
$442$	−1.27647	−	0.736972i	−0.0607156	−	0.0350542i
$443$	−7.80056	−	13.5110i	−0.370616	−	0.641925i	0.619045	−	0.785356i	$-0.287520\pi$
$443$	−7.80056	−	13.5110i	−0.370616	−	0.641925i	−0.989660	+	0.143430i	$0.954187\pi$
$444$	−10.3729	+	1.84448i	−0.492278	+	0.0875350i
$445$	−4.29318	+	7.43600i	−0.203516	+	0.352500i
$446$	−15.8715	+	9.16344i	−0.751539	+	0.433901i
$447$	0.252546	+	8.78548i	0.0119450	+	0.415539i
$448$	−0.240097	+	0.415860i	−0.0113435	+	0.0196476i
$449$	−7.19308	+	4.15293i	−0.339462	+	0.195989i	−0.660034	−	0.751235i	$-0.729458\pi$
$449$	−7.19308	+	4.15293i	−0.339462	+	0.195989i	0.320572	+	0.947224i	$0.396125\pi$
$450$	18.4344	+	9.27431i	0.869006	+	0.437195i
$451$	−5.21108	−	9.02585i	−0.245380	−	0.425011i
$452$	−0.515396	+	0.297564i	−0.0242422	+	0.0139962i
$453$	0.245436	+	8.53812i	0.0115316	+	0.401156i
$454$	−0.933947	+	1.61764i	−0.0438323	+	0.0759198i
$455$	1.11791	−	1.93627i	0.0524082	−	0.0907737i
$456$	0.586791	+	0.316661i	0.0274790	+	0.0148290i
$457$	−2.84257	−	1.64116i	−0.132970	−	0.0767700i	0.432040	−	0.901855i	$-0.357794\pi$
$457$	−2.84257	−	1.64116i	−0.132970	−	0.0767700i	−0.565009	+	0.825085i	$0.691127\pi$
$458$		−	6.81939i		−	0.318649i
$459$	2.40135	−	5.13559i	0.112085	−	0.239709i
$460$	13.7680	−	23.8469i	0.641936	−	1.11187i
$461$			32.0126i			1.49097i	0.666520	+	0.745487i	$0.267783\pi$
$461$			32.0126i			1.49097i	−0.666520	+	0.745487i	$0.732217\pi$
$462$	−1.37796	−	2.23576i	−0.0641084	−	0.104017i
$463$			21.1009i			0.980643i	0.871542	+	0.490321i	$0.163121\pi$
$463$			21.1009i			0.980643i	−0.871542	+	0.490321i	$0.836879\pi$
$464$	5.40267	−	3.11923i	0.250813	−	0.144807i
$465$	0.713502	+	24.8210i	0.0330879	+	1.15105i
$466$			28.3171i			1.31177i
$467$		−	26.7437i		−	1.23755i	−0.785568	−	0.618776i	$-0.787629\pi$
$467$		−	26.7437i		−	1.23755i	0.785568	−	0.618776i	$-0.212371\pi$
$468$	3.62044	+	1.82144i	0.167355	+	0.0841960i
$469$	−2.13526	+	3.69839i	−0.0985973	+	0.170776i
$470$	−20.4603	−	35.4383i	−0.943764	−	1.63465i
$471$	−10.7814	−	5.81816i	−0.496781	−	0.268087i
$472$	−0.170242	−	0.294868i	−0.00783603	−	0.0135724i
$473$	−23.6069	−	13.6294i	−1.08544	−	0.626682i
$474$	0.811096	+	28.2161i	0.0372549	+	1.29601i
$475$	−2.29327	+	1.32402i	−0.105223	+	0.0607502i
$476$	−0.453726	+	0.261959i	−0.0207965	+	0.0120069i
$477$	−4.84566	−	7.37874i	−0.221868	−	0.337849i
$478$	−9.74117	−	16.8722i	−0.445551	−	0.771716i
$479$		−	7.16000i		−	0.327149i	−0.986531	−	0.163574i	$-0.947698\pi$
$479$		−	7.16000i		−	0.327149i	0.986531	−	0.163574i	$-0.0523024\pi$
$480$	5.08191	−	3.13211i	0.231956	−	0.142960i
$481$	3.02021	−	7.64228i	0.137710	−	0.348458i
$482$	11.9345	−	20.6711i	0.543600	−	0.941542i
$483$	3.15577	−	5.84783i	0.143593	−	0.266085i
$484$	−0.514592	+	0.891300i	−0.0233905	+	0.0405136i
$485$	21.7618	+	37.6925i	0.988153	+	1.71153i
$486$	−5.78076	+	14.4770i	−0.262221	+	0.656689i
$487$			24.2615i			1.09939i	0.835364	+	0.549697i	$0.185257\pi$
$487$			24.2615i			1.09939i	−0.835364	+	0.549697i	$0.814743\pi$
$488$	7.10847	−	12.3122i	0.321786	−	0.557349i
$489$	−32.9910	+	0.948354i	−1.49190	+	0.0428861i
$490$	11.6655	+	20.2053i	0.526995	+	0.912781i
$491$	−16.1023	+	27.8901i	−0.726688	+	1.25866i	0.231587	+	0.972814i	$0.425608\pi$
$491$	−16.1023	+	27.8901i	−0.726688	+	1.25866i	−0.958275	+	0.285847i	$0.907725\pi$
$492$	4.86672	−	2.99948i	0.219408	−	0.135227i
$493$	6.80650			0.306549
$494$	−0.450390	+	0.260033i	−0.0202640	+	0.0116994i
$495$	1.87550	+	32.5951i	0.0842974	+	1.46504i
$496$	3.60235	+	2.07982i	0.161750	+	0.0933866i
$497$	1.00354			0.0450150
$498$	9.77687	+	15.8632i	0.438112	+	0.710846i
$499$			18.4340i			0.825219i	0.910908	+	0.412610i	$0.135383\pi$
$499$			18.4340i			0.825219i	−0.910908	+	0.412610i	$0.864617\pi$
$500$			6.47477i			0.289561i
$501$	−9.40688	−	15.2629i	−0.420269	−	0.681894i
$502$	15.8983			0.709574
$503$	−28.9751	−	16.7288i	−1.29193	−	0.745898i	−0.312937	−	0.949774i	$-0.601313\pi$
$503$	−28.9751	−	16.7288i	−1.29193	−	0.745898i	−0.978997	+	0.203876i	$0.934646\pi$
$504$	1.20414	−	0.790768i	0.0536369	−	0.0352236i
$505$	−2.93940	+	1.69706i	−0.130801	+	0.0755182i
$506$	25.2280			1.12152
$507$	16.4775	−	10.1555i	0.731789	−	0.451020i
$508$	−3.39075	+	5.87296i	−0.150440	+	0.260570i
$509$	9.58637	+	16.6041i	0.424908	+	0.735963i	0.996412	−	0.0846366i	$-0.0269729\pi$
$509$	9.58637	+	16.6041i	0.424908	+	0.735963i	−0.571503	+	0.820600i	$0.693640\pi$
$510$	6.51044	−	0.187148i	0.288287	−	0.00828707i
$511$	−1.75764	+	3.04432i	−0.0777533	+	0.134673i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.14562	−	1.63979i	−0.0505806	−	0.0723986i
$514$	−8.45521	−	14.6449i	−0.372943	−	0.645957i
$515$	−2.07749	+	3.59832i	−0.0915453	+	0.158561i
$516$	7.10090	−	13.1584i	0.312600	−	0.579266i
$517$	18.7454	−	32.4680i	0.824421	−	1.42794i
$518$	−1.81576	−	2.28795i	−0.0797799	−	0.100527i
$519$	−5.70316	+	3.51500i	−0.250341	+	0.154291i
$520$			4.65605i			0.204181i
$521$	18.7964	+	32.5563i	0.823485	+	1.42632i	0.903072	+	0.429489i	$0.141306\pi$
$521$	18.7964	+	32.5563i	0.823485	+	1.42632i	−0.0795871	+	0.996828i	$0.525360\pi$
$522$	−18.6845	+	1.07509i	−0.817798	+	0.0470555i
$523$	−5.51977	+	3.18684i	−0.241363	+	0.139351i	−0.615803	−	0.787900i	$-0.711168\pi$
$523$	−5.51977	+	3.18684i	−0.241363	+	0.139351i	0.374440	+	0.927251i	$0.377835\pi$
$524$	−6.98950	+	4.03539i	−0.305338	+	0.176287i
$525$	0.164390	+	5.71874i	0.00717458	+	0.249586i
$526$	19.8437	+	11.4568i	0.865228	+	0.499539i
$527$	2.26919	+	3.93036i	0.0988476	+	0.171209i
$528$	4.81311	+	2.59739i	0.209464	+	0.113037i
$529$	20.4157	+	35.3610i	0.887640	+	1.53744i
$530$	5.07077	−	8.78283i	0.220260	−	0.381502i
$531$	0.0586766	+	1.01977i	0.00254635	+	0.0442541i
$532$			0.184859i			0.00801464i
$533$			4.45889i			0.193136i
$534$	−0.123989	−	4.31327i	−0.00536552	−	0.186653i
$535$	−47.0870	+	27.1857i	−2.03575	+	1.17534i
$536$		−	8.89333i		−	0.384134i
$537$	−2.06147	−	3.34478i	−0.0889590	−	0.144338i
$538$			18.9536i			0.817149i
$539$	−10.6878	+	18.5117i	−0.460354	+	0.797357i
$540$	−17.8422	+	1.54207i	−0.767807	+	0.0663601i
$541$		−	8.62312i		−	0.370737i	−0.982669	−	0.185369i	$-0.940652\pi$
$541$		−	8.62312i		−	0.370737i	0.982669	−	0.185369i	$-0.0593479\pi$
$542$	−3.65215	−	2.10857i	−0.156873	−	0.0905708i
$543$	−5.07625	−	2.73939i	−0.217843	−	0.117558i
$544$	0.545527	−	0.944880i	0.0233893	−	0.0405114i
$545$	−8.74007	+	15.1383i	−0.374384	+	0.648452i
$546$	0.0322856	+	1.12314i	0.00138170	+	0.0480659i
$547$	−7.56083	+	4.36525i	−0.323278	+	0.186644i	−0.652853	−	0.757485i	$-0.726428\pi$
$547$	−7.56083	+	4.36525i	−0.323278	+	0.186644i	0.329575	+	0.944129i	$0.393095\pi$
$548$	−0.0848084	−	0.146893i	−0.00362284	−	0.00627494i
$549$	−35.6507	+	23.4120i	−1.52153	+	0.999200i
$550$	−18.8104	+	10.8602i	−0.802078	+	0.463080i
$551$	1.20080	−	2.07985i	0.0511558	−	0.0886045i
$552$	0.397625	+	13.8324i	0.0169241	+	0.588747i
$553$	−6.77740	+	3.91293i	−0.288204	+	0.166395i
$554$	−15.4445	+	26.7507i	−0.656174	+	1.13653i
$555$	6.35706	+	35.7507i	0.269842	+	1.51753i
$556$	4.32699	+	7.49457i	0.183505	+	0.317841i
$557$	24.9911	+	14.4286i	1.05891	+	0.611361i	0.925130	−	0.379651i	$-0.123956\pi$
$557$	24.9911	+	14.4286i	1.05891	+	0.611361i	0.133778	+	0.991011i	$0.457289\pi$
$558$	−6.84995	−	10.4308i	−0.289982	−	0.441570i
$559$	5.83106	+	10.0997i	0.246627	+	0.427171i
$560$	1.43328	+	0.827504i	0.0605671	+	0.0349684i
$561$	3.13087	+	5.07990i	0.132185	+	0.214474i
$562$	32.3624			1.36513
$563$	39.2375	+	22.6538i	1.65366	+	0.954742i	0.975548	+	0.219785i	$0.0705357\pi$
$563$	39.2375	+	22.6538i	1.65366	+	0.954742i	0.678114	+	0.734957i	$0.262798\pi$
$564$	18.0975	+	9.76631i	0.762044	+	0.411236i
$565$	1.02557	+	1.77633i	0.0431459	+	0.0747309i
$566$	16.3590			0.687619
$567$	−4.29323	+	0.495700i	−0.180299	+	0.0208174i
$568$	−1.80988	+	1.04493i	−0.0759407	+	0.0438444i
$569$	−7.70454	+	4.44822i	−0.322991	+	0.186479i	−0.652725	−	0.757595i	$-0.726374\pi$
$569$	−7.70454	+	4.44822i	−0.322991	+	0.186479i	0.329734	+	0.944074i	$0.393041\pi$
$570$	1.09138	−	2.02240i	0.0457130	−	0.0847089i
$571$	−16.0879	−	27.8651i	−0.673259	−	1.16612i	−0.976974	−	0.213357i	$-0.931560\pi$
$571$	−16.0879	−	27.8651i	−0.673259	−	1.16612i	0.303715	−	0.952763i	$-0.401773\pi$
$572$	−3.69429	+	2.13290i	−0.154466	+	0.0891810i
$573$	4.31691	−	7.99948i	0.180341	−	0.334183i
$574$	1.37259	+	0.792464i	0.0572907	+	0.0330768i
$575$	−47.5937	−	27.4783i	−1.98480	−	1.14592i
$576$	−1.34828	+	2.67995i	−0.0561783	+	0.111665i
$577$	25.1077	+	14.4959i	1.04525	+	0.603474i	0.921315	−	0.388817i	$-0.127116\pi$
$577$	25.1077	+	14.4959i	1.04525	+	0.603474i	0.123933	+	0.992291i	$0.460449\pi$
$578$	−13.6915	+	7.90480i	−0.569492	+	0.328796i
$579$	11.0248	−	0.316918i	0.458176	−	0.0131707i
$580$	−10.7506	−	18.6205i	−0.446393	−	0.773175i
$581$	−2.58305	+	4.47398i	−0.107163	+	0.185612i
$582$	−19.2487	−	10.3875i	−0.797886	−	0.430577i
$583$	9.29150			0.384815
$584$		−	7.32053i		−	0.302926i
$585$	6.27766	−	12.4780i	0.259549	−	0.515902i
$586$		−	17.9908i		−	0.743192i
$587$	4.54399	+	2.62347i	0.187551	+	0.108282i	0.590835	−	0.806792i	$-0.298798\pi$
$587$	4.54399	+	2.62347i	0.187551	+	0.108282i	−0.403285	+	0.915075i	$0.632132\pi$
$588$	−10.3184	−	5.56829i	−0.425523	−	0.229633i
$589$	1.60132			0.0659812
$590$	−1.01627	+	0.586746i	−0.0418393	+	0.0241560i
$591$	0.312817	+	10.8822i	0.0128676	+	0.447633i
$592$	5.65702	+	2.23564i	0.232502	+	0.0918844i
$593$	−8.42504			−0.345975			−0.172987	−	0.984924i	$-0.555342\pi$
$593$	−8.42504			−0.345975			−0.172987	+	0.984924i	$0.555342\pi$
$594$	−9.39691	−	13.4503i	−0.385560	−	0.551872i
$595$	0.902852	+	1.56378i	0.0370133	+	0.0641089i
$596$	2.53720	−	4.39456i	0.103928	−	0.180008i
$597$	−12.0600	−	19.5676i	−0.493583	−	0.800849i
$598$	−9.34723	−	5.39662i	−0.382236	−	0.220684i
$599$	−32.0998			−1.31156			−0.655781	−	0.754951i	$-0.727661\pi$
$599$	−32.0998			−1.31156			−0.655781	+	0.754951i	$0.727661\pi$
$600$	−6.25109	−	10.1425i	−0.255199	−	0.414066i
$601$	−2.43777			−0.0994385			−0.0497193	−	0.998763i	$-0.515833\pi$
$601$	−2.43777			−0.0994385			−0.0497193	+	0.998763i	$0.515833\pi$
$602$	4.14533			0.168951
$603$	−11.9907	+	23.8337i	−0.488299	+	0.970584i
$604$	2.46576	−	4.27082i	0.100330	−	0.173777i
$605$	3.07190	+	1.77356i	0.124890	+	0.0721055i
$606$	0.810057	−	1.50108i	0.0329063	−	0.0609773i
$607$	1.48613	−	0.858019i	0.0603203	−	0.0348259i	−0.469537	−	0.882913i	$-0.655579\pi$
$607$	1.48613	−	0.858019i	0.0603203	−	0.0348259i	0.529857	+	0.848087i	$0.322246\pi$
$608$	−0.192483	−	0.333391i	−0.00780623	−	0.0135208i
$609$	−2.72238	−	4.41711i	−0.110316	−	0.178990i
$610$	−42.4346	−	24.4996i	−1.71813	−	0.991961i
$611$	−13.8907	+	8.01981i	−0.561958	+	0.324447i
$612$	−2.73595	+	1.79671i	−0.110594	+	0.0726278i
$613$	17.8592	−	30.9331i	0.721327	−	1.24938i	−0.239141	−	0.970985i	$-0.576866\pi$
$613$	17.8592	−	30.9331i	0.721327	−	1.24938i	0.960468	−	0.278390i	$-0.0898009\pi$
$614$			8.71513i			0.351714i
$615$	−10.3378	−	16.7733i	−0.416861	−	0.676366i
$616$			1.51629i			0.0610931i
$617$	−23.5236	−	40.7441i	−0.947025	−	1.64030i	−0.751644	−	0.659568i	$-0.770739\pi$
$617$	−23.5236	−	40.7441i	−0.947025	−	1.64030i	−0.195381	−	0.980727i	$-0.562594\pi$
$618$	−0.0599989	−	2.08722i	−0.00241351	−	0.0839602i
$619$	17.1311	+	29.6720i	0.688558	+	1.19262i	0.972304	+	0.233718i	$0.0750892\pi$
$619$	17.1311	+	29.6720i	0.688558	+	1.19262i	−0.283747	+	0.958899i	$0.591578\pi$
$620$	7.16817	−	12.4156i	0.287881	−	0.498624i
$621$	17.5844	−	37.6064i	0.705636	−	1.50909i
$622$	−12.2994	−	21.3032i	−0.493162	−	0.854182i
$623$	1.03603	−	0.598153i	0.0415077	−	0.0239645i
$624$	−1.22769	−	1.99195i	−0.0491469	−	0.0797418i
$625$	−12.0776			−0.483104
$626$	−10.3660			−0.414307
$627$	2.10460	−	0.0604986i	0.0840496	−	0.00241608i
$628$	3.53659	+	6.12555i	0.141125	+	0.244436i
$629$	4.12560	+	5.19847i	0.164499	+	0.207277i
$630$	−2.72541	−	4.15013i	−0.108583	−	0.165345i
$631$	8.67244	+	5.00704i	0.345244	+	0.199327i	0.662589	−	0.748983i	$-0.269458\pi$
$631$	8.67244	+	5.00704i	0.345244	+	0.199327i	−0.317344	+	0.948310i	$0.602791\pi$
$632$	8.14864	−	14.1139i	0.324136	−	0.561419i
$633$	0.825725	+	28.7250i	0.0328196	+	1.14172i
$634$		−	29.8730i		−	1.18641i
$635$	20.2414	+	11.6864i	0.803254	+	0.463759i
$636$	0.146446	+	5.09450i	0.00580696	+	0.202010i
$637$	7.91984	−	4.57252i	0.313796	−	0.181170i
$638$	9.84948	−	17.0598i	0.389945	−	0.675404i
$639$	6.25924	−	0.360152i	0.247612	−	0.0142474i
$640$	−3.44654			−0.136236
$641$	5.28022			0.208556			0.104278	−	0.994548i	$-0.466747\pi$
$641$	5.28022			0.208556			0.104278	+	0.994548i	$0.466747\pi$
$642$	12.9765	−	24.0463i	0.512142	−	0.949030i
$643$	2.93253	+	1.69309i	0.115648	+	0.0667691i	0.556708	−	0.830708i	$-0.312064\pi$
$643$	2.93253	+	1.69309i	0.115648	+	0.0667691i	−0.441060	+	0.897477i	$0.645398\pi$
$644$	−3.32250	+	1.91825i	−0.130925	+	0.0755895i
$645$	−45.3509	−	24.4735i	−1.78569	−	0.963645i
$646$		−	0.420019i		−	0.0165254i
$647$	15.0995	−	8.71769i	0.593622	−	0.342728i	−0.172907	−	0.984938i	$-0.555316\pi$
$647$	15.0995	−	8.71769i	0.593622	−	0.342728i	0.766528	+	0.642211i	$0.221983\pi$
$648$	7.22664	−	5.36429i	0.283889	−	0.210729i
$649$	−0.931093	−	0.537567i	−0.0365486	−	0.0211013i
$650$	9.29259			0.364485
$651$	1.64302	−	3.04462i	0.0643951	−	0.119328i
$652$	16.5023	+	9.52761i	0.646280	+	0.373130i
$653$			47.6415i			1.86436i	0.362001	+	0.932178i	$0.382094\pi$
$653$			47.6415i			1.86436i	−0.362001	+	0.932178i	$0.617906\pi$
$654$	−0.252417	−	8.78098i	−0.00987029	−	0.343364i
$655$	13.9081	+	24.0896i	0.543436	+	0.941258i
$656$	−3.30060			−0.128867
$657$	−9.87011	+	19.6187i	−0.385070	+	0.765397i
$658$			5.70133i			0.222261i
$659$	1.98601	−	3.43986i	0.0773638	−	0.133998i	−0.824748	−	0.565501i	$-0.808683\pi$
$659$	1.98601	−	3.43986i	0.0773638	−	0.133998i	0.902112	+	0.431502i	$0.142016\pi$
$660$	8.95199	−	16.5886i	0.348456	−	0.645709i
$661$		−	21.3576i		−	0.830715i	−0.909658	−	0.415357i	$-0.863657\pi$
$661$		−	21.3576i		−	0.830715i	0.909658	−	0.415357i	$-0.136343\pi$
$662$	−23.5213			−0.914181
$663$	−0.0733564	−	2.55189i	−0.00284893	−	0.0991073i
$664$		−	10.7584i		−	0.417506i
$665$	0.637123			0.0247066
$666$	−12.1463	−	13.6187i	−0.470659	−	0.527712i
$667$	49.8420			1.92989
$668$			10.3512i			0.400501i
$669$	−27.9350	−	15.0751i	−1.08003	−	0.582836i
$670$	−30.6512			−1.18416
$671$		−	44.8923i		−	1.73305i
$672$	−0.831377	+	0.0238987i	−0.0320711	+	0.000921911i
$673$	11.4122	−	19.7665i	0.439908	−	0.761943i	−0.557774	−	0.829993i	$-0.688344\pi$
$673$	11.4122	−	19.7665i	0.439908	−	0.761943i	0.997682	+	0.0680500i	$0.0216777\pi$
$674$			4.22458i			0.162725i
$675$	3.07768	+	35.6097i	0.118460	+	1.37062i
$676$	−11.1750			−0.429807
$677$	−6.16271	−	10.6741i	−0.236852	−	0.410240i	0.722957	−	0.690893i	$-0.242782\pi$
$677$	−6.16271	−	10.6741i	−0.236852	−	0.410240i	−0.959809	+	0.280653i	$0.909449\pi$
$678$	−0.907133	−	0.489533i	−0.0348382	−	0.0188004i
$679$		−	6.06399i		−	0.232715i
$680$	−3.25657	−	1.88018i	−0.124884	−	0.0721016i
$681$	−3.23395	+	0.0929628i	−0.123925	+	0.00356234i
$682$	13.1347			0.502954
$683$	2.66192	+	1.53686i	0.101855	+	0.0588063i	0.550062	−	0.835124i	$-0.314604\pi$
$683$	2.66192	+	1.53686i	0.101855	+	0.0588063i	−0.448207	+	0.893930i	$0.647937\pi$
$684$	0.0663424	+	1.15299i	0.00253666	+	0.0440858i
$685$	−0.506271	+	0.292296i	−0.0193436	+	0.0111680i
$686$		−	6.61199i		−	0.252447i
$687$	10.0552	−	6.19725i	0.383629	−	0.236440i
$688$	−7.47606	+	4.31631i	−0.285022	+	0.164558i
$689$	−3.44260	−	1.98758i	−0.131152	−	0.0757209i
$690$	47.6740	−	1.37043i	1.81492	−	0.0521714i
$691$	−16.1966			−0.616148			−0.308074	−	0.951362i	$-0.599684\pi$
$691$	−16.1966			−0.616148			−0.308074	+	0.951362i	$0.599684\pi$
$692$	3.86787			0.147034
$693$	2.04438	−	4.06359i	0.0776596	−	0.154363i
$694$	−12.7716	+	22.1211i	−0.484804	+	0.839705i
$695$	25.8303	−	14.9131i	0.979800	−	0.565688i
$696$	9.50908	+	5.13156i	0.360441	+	0.194511i
$697$	−3.11867	−	1.80056i	−0.118128	−	0.0682012i
$698$		−	25.6560i		−	0.971094i
$699$	−41.7535	+	25.7337i	−1.57926	+	0.973339i
$700$	1.65154	−	2.86055i	0.0624223	−	0.108119i
$701$	−3.84777	−	2.22151i	−0.145328	−	0.0839052i	0.425573	−	0.904924i	$-0.360073\pi$
$701$	−3.84777	−	2.22151i	−0.145328	−	0.0839052i	−0.570901	+	0.821019i	$0.693406\pi$
$702$	0.604444	+	6.99360i	0.0228133	+	0.263956i
$703$	2.31632	−	0.343539i	0.0873618	−	0.0129568i
$704$	−1.57883	−	2.73461i	−0.0595044	−	0.103065i
$705$	33.6600	−	62.3739i	1.26771	−	2.34914i
$706$	−18.1520			−0.683158
$707$	0.472891			0.0177849
$708$	0.280071	−	0.518988i	0.0105257	−	0.0195048i
$709$	−26.3142	+	15.1925i	−0.988252	+	0.570567i	−0.904751	−	0.425940i	$-0.859943\pi$
$709$	−26.3142	+	15.1925i	−0.988252	+	0.570567i	−0.0835004	+	0.996508i	$0.526610\pi$
$710$	3.60140	+	6.23781i	0.135158	+	0.234101i
$711$	−40.8674	+	26.8378i	−1.53265	+	1.00650i
$712$	−1.24565	+	2.15753i	−0.0466826	+	0.0808567i
$713$	16.6166	+	28.7808i	0.622297	+	1.07785i
$714$	−0.798590	−	0.430957i	−0.0298865	−	0.0161282i
$715$	7.35112	+	12.7325i	0.274916	+	0.476169i
$716$			2.26842i			0.0847748i
$717$	16.0255	−	29.6962i	0.598484	−	1.10903i
$718$		−	3.62838i		−	0.135410i
$719$	−20.5554	+	35.6030i	−0.766588	+	1.32777i	0.172816	+	0.984954i	$0.444714\pi$
$719$	−20.5554	+	35.6030i	−0.766588	+	1.32777i	−0.939403	+	0.342814i	$0.888620\pi$
$720$	9.23656	+	4.64689i	0.344226	+	0.173180i
$721$	0.501342	−	0.289450i	0.0186709	−	0.0107797i
$722$	16.3261	+	9.42590i	0.607596	+	0.350796i
$723$	41.3251	−	1.18793i	1.53690	−	0.0441795i
$724$	1.66515	+	2.88412i	0.0618847	+	0.107187i
$725$	−37.1630	+	21.4561i	−1.38020	+	0.796858i
$726$	−1.78186	+	0.0512212i	−0.0661311	+	0.00190100i
$727$	6.34411	+	3.66277i	0.235290	+	0.135845i	0.613010	−	0.790075i	$-0.289958\pi$
$727$	6.34411	+	3.66277i	0.235290	+	0.135845i	−0.377720	+	0.925920i	$0.623292\pi$
$728$	0.324356	−	0.561801i	0.0120214	−	0.0208217i
$729$	−26.5996	+	4.63252i	−0.985171	+	0.171575i
$730$	−25.2305			−0.933822
$731$	−9.41865			−0.348361
$732$	24.6143	−	0.707560i	0.909771	−	0.0261522i
$733$	−12.9640			−0.478837			−0.239418	−	0.970917i	$-0.576957\pi$
$733$	−12.9640			−0.478837			−0.239418	+	0.970917i	$0.576957\pi$
$734$	−19.6379	−	11.3379i	−0.724846	−	0.418490i
$735$	−19.1913	+	35.5627i	−0.707883	+	1.31175i
$736$	3.99473	−	6.91907i	0.147248	−	0.255040i
$737$	−14.0411	−	24.3198i	−0.517209	−	0.895833i
$738$	8.84544	+	4.45012i	0.325605	+	0.163811i
$739$	23.1115			0.850172			0.425086	−	0.905153i	$-0.360244\pi$
$739$	23.1115			0.850172			0.425086	+	0.905153i	$0.360244\pi$
$740$	7.70523	−	19.4971i	0.283250	−	0.716729i
$741$	−0.792717	−	0.427788i	−0.0291212	−	0.0157152i
$742$	−1.22368	+	0.706493i	−0.0449227	+	0.0259362i
$743$	39.8458			1.46180			0.730901	−	0.682484i	$-0.239100\pi$
$743$	39.8458			1.46180			0.730901	+	0.682484i	$0.239100\pi$
$744$	0.207020	+	7.20172i	0.00758972	+	0.264028i
$745$	−15.1460	−	8.74455i	−0.554907	−	0.320376i
$746$			26.6954i			0.977387i
$747$	−14.5053	+	28.8319i	−0.530721	+	1.05491i
$748$		−	3.44518i		−	0.125968i
$749$	7.57537			0.276798
$750$	−9.54703	+	5.88407i	−0.348608	+	0.214856i
$751$	−0.276749	+	0.479344i	−0.0100987	+	0.0174915i	−0.871031	−	0.491229i	$-0.836548\pi$
$751$	−0.276749	+	0.479344i	−0.0100987	+	0.0174915i	0.860932	+	0.508720i	$0.169881\pi$
$752$	−5.93648	−	10.2823i	−0.216481	−	0.374957i
$753$	14.4478	+	23.4419i	0.526509	+	0.854271i
$754$	−7.29866	+	4.21389i	−0.265802	+	0.153461i
$755$	−14.7196	−	8.49834i	−0.535699	−	0.309286i
$756$	2.26027	+	1.05688i	0.0822054	+	0.0384384i
$757$	−4.11305	−	2.37467i	−0.149491	−	0.0863088i	0.423389	−	0.905948i	$-0.360841\pi$
$757$	−4.11305	−	2.37467i	−0.149491	−	0.0863088i	−0.572880	+	0.819639i	$0.694174\pi$
$758$	20.1799	+	11.6509i	0.732968	+	0.423179i
$759$	22.9264	+	37.1986i	0.832176	+	1.35022i
$760$	−1.14904	+	0.663401i	−0.0416802	+	0.0240641i
$761$	−3.55972	−	6.16562i	−0.129040	−	0.223504i	0.794265	−	0.607572i	$-0.207856\pi$
$761$	−3.55972	−	6.16562i	−0.129040	−	0.223504i	−0.923305	+	0.384068i	$0.874523\pi$
$762$	−11.7411	+	0.337507i	−0.425334	+	0.0122266i
$763$	2.10916	−	1.21772i	0.0763567	−	0.0440846i
$764$	−4.54498	+	2.62405i	−0.164432	+	0.0949347i
$765$	6.19244	+	9.42955i	0.223888	+	0.340926i
$766$	−14.3137			−0.517174
$767$	0.229986	+	0.398348i	0.00830432	+	0.0143835i
$768$	1.47450	−	0.908769i	0.0532063	−	0.0327924i
$769$	31.9973	+	18.4736i	1.15385	+	0.666177i	0.949823	−	0.312788i	$-0.101263\pi$
$769$	31.9973	+	18.4736i	1.15385	+	0.666177i	0.204029	+	0.978965i	$0.434596\pi$
$770$	5.22595			0.188330
$771$	13.9099	−	25.7760i	0.500955	−	0.928298i
$772$	−5.51469	−	3.18391i	−0.198478	−	0.114591i
$773$	9.49564	+	16.4469i	0.341534	+	0.591555i	0.984718	−	0.174157i	$-0.0557201\pi$
$773$	9.49564	+	16.4469i	0.341534	+	0.591555i	−0.643184	+	0.765712i	$0.722387\pi$
$774$	25.8551	−	1.48768i	0.929342	−	0.0534737i
$775$	−24.7792	−	14.3063i	−0.890096	−	0.513897i
$776$	6.31410	+	10.9363i	0.226663	+	0.392592i
$777$	1.72347	−	4.75655i	0.0618291	−	0.170640i
$778$	9.38545	−	16.2561i	0.336485	−	0.582808i
$779$	−1.10039	+	0.635309i	−0.0394255	+	0.0227623i
$780$	−6.86533	+	4.23128i	−0.245818	+	0.151504i
$781$	−3.29954	+	5.71497i	−0.118067	+	0.204498i
$782$	7.54908	−	4.35846i	0.269955	−	0.155858i
$783$	−18.5651	−	26.5732i	−0.663463	−	0.949649i
$784$	3.38471	+	5.86248i	0.120882	+	0.209374i
$785$	21.1120	−	12.1890i	0.753518	−	0.435044i
$786$	−12.3020	−	6.63876i	−0.438798	−	0.236797i
$787$	26.4114	−	45.7459i	0.941465	−	1.63067i	0.178787	−	0.983888i	$-0.442783\pi$
$787$	26.4114	−	45.7459i	0.941465	−	1.63067i	0.762678	−	0.646778i	$-0.223884\pi$
$788$	3.14271	−	5.44333i	0.111954	−	0.193911i
$789$	1.14038	+	39.6711i	0.0405986	+	1.41233i
$790$	−48.6440	−	28.0846i	−1.73068	−	0.999206i
$791$		−	0.285777i		−	0.0101611i
$792$	0.544169	+	9.45734i	0.0193362	+	0.336052i
$793$	−9.60310	+	16.6331i	−0.341016	+	0.590657i
$794$		−	39.5953i		−	1.40519i
$795$	17.5584	−	0.504732i	0.622733	−	0.0179010i
$796$			13.2707i			0.470368i
$797$	0.504789	−	0.291440i	0.0178806	−	0.0103233i	−0.491033	−	0.871141i	$-0.663381\pi$
$797$	0.504789	−	0.291440i	0.0178806	−	0.0103233i	0.508914	+	0.860818i	$0.330047\pi$
$798$	−0.272573	+	0.167994i	−0.00964899	+	0.00594692i
$799$		−	12.9540i		−	0.458281i
$800$			6.87863i			0.243196i
$801$	6.24722	−	4.10259i	0.220735	−	0.144958i
$802$	−13.8996	+	24.0748i	−0.490811	+	0.850109i
$803$	−11.5579	−	20.0188i	−0.407868	−	0.706449i
$804$	13.1132	−	8.08198i	0.462466	−	0.285030i
$805$	6.61131	+	11.4511i	0.233018	+	0.403599i
$806$	−4.86654	−	2.80970i	−0.171417	−	0.0989675i
$807$	−27.9471	+	17.2245i	−0.983783	+	0.606330i
$808$	−0.852854	+	0.492396i	−0.0300033	+	0.0173224i
$809$	−0.932228	+	0.538222i	−0.0327754	+	0.0189229i	−0.516298	−	0.856409i	$-0.672690\pi$
$809$	−0.932228	+	0.538222i	−0.0327754	+	0.0189229i	0.483523	+	0.875332i	$0.339357\pi$
$810$	−18.4882	−	24.9069i	−0.649610	−	0.875140i
$811$	−9.15259	−	15.8527i	−0.321391	−	0.556665i	0.659384	−	0.751806i	$-0.270817\pi$
$811$	−9.15259	−	15.8527i	−0.321391	−	0.556665i	−0.980775	+	0.195141i	$0.937484\pi$
$812$			2.99568i			0.105128i
$813$	−0.209882	−	7.30128i	−0.00736087	−	0.256067i
$814$	18.9995	−	2.81785i	0.665931	−	0.0987657i
$815$	32.8373	−	56.8758i	1.15024	−	1.99227i
$816$	1.88898	−	0.0543004i	0.0661275	−	0.00190089i
$817$	−1.66163	+	2.87803i	−0.0581332	+	0.100690i
$818$	−7.35625	−	12.7414i	−0.257205	−	0.445492i
$819$	−1.62672	+	1.06828i	−0.0568423	+	0.0373286i
$820$			11.3756i			0.397254i
$821$	−18.2447	+	31.6007i	−0.636744	+	1.10287i	0.349399	+	0.936974i	$0.386386\pi$
$821$	−18.2447	+	31.6007i	−0.636744	+	1.10287i	−0.986143	+	0.165899i	$0.946947\pi$
$822$	0.139521	−	0.258541i	0.00486636	−	0.00901766i
$823$	24.2164	+	41.9440i	0.844130	+	1.46208i	0.886375	+	0.462968i	$0.153216\pi$
$823$	24.2164	+	41.9440i	0.844130	+	1.46208i	−0.0422453	+	0.999107i	$0.513451\pi$
$824$	−0.602776	+	1.04404i	−0.0209987	+	0.0363708i
$825$	−33.1076	−	17.8665i	−1.15266	−	0.622030i
$826$	0.163499			0.00568884
$827$	−41.2844	+	23.8356i	−1.43560	+	0.828845i	−0.997540	−	0.0701008i	$-0.977668\pi$
$827$	−41.2844	+	23.8356i	−1.43560	+	0.828845i	−0.438061	+	0.898945i	$0.644335\pi$
$828$	−20.0345	+	13.1568i	−0.696248	+	0.457230i
$829$	−2.70886	−	1.56396i	−0.0940825	−	0.0543186i	0.452221	−	0.891906i	$-0.350632\pi$
$829$	−2.70886	−	1.56396i	−0.0940825	−	0.0543186i	−0.546303	+	0.837588i	$0.683965\pi$
$830$	−37.0792			−1.28704
$831$	−53.4793	+	1.53731i	−1.85517	+	0.0533286i
$832$			1.35094i			0.0468353i
$833$			7.38579i			0.255903i
$834$	−7.11848	+	13.1910i	−0.246493	+	0.456766i
$835$	35.6760			1.23462
$836$	−1.05273	−	0.607797i	−0.0364096	−	0.0210211i
$837$	9.15513	−	19.5794i	0.316447	−	0.676763i
$838$	0.573045	−	0.330848i	0.0197955	−	0.0114289i
$839$	−49.8670			−1.72160			−0.860800	−	0.508944i	$-0.830036\pi$
$839$	−49.8670			−1.72160			−0.860800	+	0.508944i	$0.830036\pi$
$840$	0.0823677	+	2.86537i	0.00284196	+	0.0988648i
$841$	4.95924	−	8.58965i	0.171008	−	0.296195i
$842$	−11.0063	−	19.0635i	−0.379303	−	0.656972i
$843$	29.4100	+	47.7183i	1.01293	+	1.64350i
$844$	8.29561	−	14.3684i	0.285547	−	0.494581i
$845$			38.5150i			1.32496i
$846$	2.04610	+	35.5601i	0.0703464	+	1.22258i
$847$	−0.247104	−	0.427997i	−0.00849060	−	0.0147061i
$848$	1.47126	−	2.54830i	0.0505234	−	0.0875091i
$849$	14.8665	+	24.1212i	0.510218	+	0.827839i
$850$	−3.75248	+	6.49948i	−0.128709	+	0.222930i
$851$	30.2106	+	38.0668i	1.03560	+	1.30491i
$852$	−3.18551	−	1.71905i	−0.109134	−	0.0588938i
$853$		−	2.38208i		−	0.0815608i	−0.999168	−	0.0407804i	$-0.987016\pi$
$853$		−	2.38208i		−	0.0815608i	0.999168	−	0.0407804i	$-0.0129844\pi$
$854$	3.41345	+	5.91227i	0.116806	+	0.202314i
$855$	3.97383	−	0.228652i	0.135902	−	0.00781972i
$856$	−13.6621	+	7.88782i	−0.466961	+	0.269600i
$857$	36.0471	−	20.8118i	1.23135	−	0.710918i	0.264036	−	0.964513i	$-0.414946\pi$
$857$	36.0471	−	20.8118i	1.23135	−	0.710918i	0.967311	+	0.253595i	$0.0816129\pi$
$858$	−6.50221	−	3.50890i	−0.221982	−	0.119792i
$859$	18.8119	+	10.8611i	0.641854	+	0.370574i	0.785328	−	0.619080i	$-0.212494\pi$
$859$	18.8119	+	10.8611i	0.641854	+	0.370574i	−0.143475	+	0.989654i	$0.545828\pi$
$860$	14.8763	+	25.7665i	0.507278	+	0.878632i
$861$	0.0788799	+	2.74404i	0.00268822	+	0.0935167i
$862$	3.29357	+	5.70464i	0.112180	+	0.194301i
$863$	−7.13935	+	12.3657i	−0.243026	+	0.420934i	−0.961575	−	0.274543i	$-0.911473\pi$
$863$	−7.13935	+	12.3657i	−0.243026	+	0.420934i	0.718549	+	0.695477i	$0.244807\pi$
$864$	−5.17685	+	0.447426i	−0.176120	+	0.0152217i
$865$		−	13.3308i		−	0.453260i
$866$			12.7700i			0.433942i
$867$	−24.0980	−	13.0045i	−0.818412	−	0.441654i
$868$	−1.72983	+	0.998716i	−0.0587142	+	0.0338986i
$869$		−	51.4613i		−	1.74570i
$870$	17.6861	−	32.7734i	0.599615	−	1.11112i
$871$			12.0143i			0.407090i
$872$	−2.53590	+	4.39231i	−0.0858764	+	0.148742i
$873$	−2.17625	−	37.8221i	−0.0736551	−	1.28008i
$874$		−	3.07567i		−	0.104036i
$875$	−2.69260	−	1.55457i	−0.0910266	−	0.0525542i
$876$	10.7941	−	6.65267i	0.364699	−	0.224773i
$877$	8.18576	−	14.1781i	0.276413	−	0.478762i	−0.694077	−	0.719900i	$-0.744187\pi$
$877$	8.18576	−	14.1781i	0.276413	−	0.478762i	0.970491	+	0.241138i	$0.0775208\pi$
$878$	−17.9875	+	31.1553i	−0.607049	+	1.05144i
$879$	26.5273	−	16.3495i	0.894745	−	0.551453i
$880$	−9.42495	+	5.44150i	−0.317715	+	0.183433i
$881$	12.4391	+	21.5451i	0.419082	+	0.725872i	0.995847	−	0.0910380i	$-0.0290185\pi$
$881$	12.4391	+	21.5451i	0.419082	+	0.725872i	−0.576765	+	0.816910i	$0.695685\pi$
$882$	−1.16659	−	20.2747i	−0.0392812	−	0.682685i
$883$	−38.8179	+	22.4115i	−1.30633	+	0.754208i	−0.981481	−	0.191559i	$-0.938646\pi$
$883$	−38.8179	+	22.4115i	−1.30633	+	0.754208i	−0.324845	+	0.945767i	$0.605312\pi$
$884$	−0.736972	+	1.27647i	−0.0247871	+	0.0429324i
$885$	−1.78871	−	0.965276i	−0.0601269	−	0.0324474i
$886$	−13.5110	+	7.80056i	−0.453910	+	0.262065i
$887$	−16.8558	+	29.1951i	−0.565962	+	0.980275i	0.430997	+	0.902353i	$0.358162\pi$
$887$	−16.8558	+	29.1951i	−0.565962	+	0.980275i	−0.996959	+	0.0779220i	$0.975172\pi$
$888$	1.84448	+	10.3729i	0.0618966	+	0.348093i
$889$	−1.62822	−	2.82016i	−0.0546088	−	0.0945851i
$890$	7.43600	+	4.29318i	0.249255	+	0.143908i
$891$	11.2928	−	26.0789i	0.378322	−	0.873676i
$892$	9.16344	+	15.8715i	0.306815	+	0.531419i
$893$	−3.95834	−	2.28535i	−0.132461	−	0.0764762i
$894$	8.78548	−	0.252546i	0.293830	−	0.00844641i
$895$	7.81820			0.261334
$896$	0.415860	+	0.240097i	0.0138929	+	0.00802108i
$897$	−0.537167	−	18.6867i	−0.0179355	−	0.623932i
$898$	4.15293	+	7.19308i	0.138585	+	0.240036i
$899$	25.9497			0.865472
$900$	9.27431	−	18.4344i	0.309144	−	0.614480i
$901$	2.78034	−	1.60523i	0.0926265	−	0.0534779i
$902$	−9.02585	+	5.21108i	−0.300528	+	0.173510i
$903$	3.76715	+	6.11228i	0.125363	+	0.203404i
$904$	0.297564	+	0.515396i	0.00989684	+	0.0171418i
$905$	9.94023	−	5.73900i	0.330424	−	0.190771i
$906$	8.53812	−	0.245436i	0.283660	−	0.00815405i
$907$	22.3092	+	12.8802i	0.740763	+	0.427680i	0.822347	−	0.568987i	$-0.192664\pi$
$907$	22.3092	+	12.8802i	0.740763	+	0.427680i	−0.0815835	+	0.996667i	$0.525998\pi$
$908$	1.61764	+	0.933947i	0.0536834	+	0.0309941i
$909$	2.94950	−	0.169712i	0.0978286	−	0.00562899i
$910$	−1.93627	−	1.11791i	−0.0641867	−	0.0370582i
$911$	45.3764	−	26.1981i	1.50339	−	0.867982i	0.503396	−	0.864056i	$-0.332084\pi$
$911$	45.3764	−	26.1981i	1.50339	−	0.867982i	0.999992	−	0.00392616i	$-0.00124974\pi$
$912$	0.316661	−	0.586791i	0.0104857	−	0.0194306i
$913$	−16.9856	−	29.4200i	−0.562143	−	0.973660i
$914$	−1.64116	+	2.84257i	−0.0542846	+	0.0940237i
$915$	−2.43863	−	84.8342i	−0.0806187	−	2.80453i
$916$	−6.81939			−0.225319
$917$		−	3.87554i		−	0.127982i
$918$	−5.13559	−	2.40135i	−0.169500	−	0.0792563i
$919$		−	20.5345i		−	0.677371i	−0.940900	−	0.338686i	$-0.890018\pi$
$919$		−	20.5345i		−	0.677371i	0.940900	−	0.338686i	$-0.109982\pi$
$920$	−23.8469	−	13.7680i	−0.786207	−	0.453917i
$921$	−12.8504	+	7.92004i	−0.423436	+	0.260974i
$922$	32.0126			1.05428
$923$	2.44503	−	1.41164i	0.0804790	−	0.0464646i
$924$	−2.23576	+	1.37796i	−0.0735512	+	0.0453315i
$925$	−38.9126	−	15.3782i	−1.27944	−	0.505631i
$926$	21.1009			0.693419
$927$	3.02307	−	1.98527i	0.0992906	−	0.0652047i
$928$	−3.11923	−	5.40267i	−0.102394	−	0.177351i
$929$	−21.3238	+	36.9339i	−0.699610	+	1.21176i	0.268991	+	0.963143i	$0.413310\pi$
$929$	−21.3238	+	36.9339i	−0.699610	+	1.21176i	−0.968602	+	0.248618i	$0.920024\pi$
$930$	24.8210	−	0.713502i	0.813913	−	0.0233967i
$931$	2.25686	+	1.30300i	0.0739656	+	0.0427040i
$932$	28.3171			0.927559
$933$	20.2342	−	37.4952i	0.662438	−	1.22754i
$934$	−26.7437			−0.875081
$935$	−11.8739			−0.388319
$936$	1.82144	−	3.62044i	0.0595356	−	0.118338i
$937$	4.08392	−	7.07356i	0.133416	−	0.231083i	−0.791575	−	0.611072i	$-0.790739\pi$
$937$	4.08392	−	7.07356i	0.133416	−	0.231083i	0.924991	+	0.379989i	$0.124072\pi$
$938$	3.69839	+	2.13526i	0.120757	+	0.0697188i
$939$	−9.42026	−	15.2846i	−0.307418	−	0.498793i
$940$	−35.4383	+	20.4603i	−1.15587	+	0.667342i
$941$	27.3976	+	47.4540i	0.893136	+	1.54696i	0.836095	+	0.548585i	$0.184833\pi$
$941$	27.3976	+	47.4540i	0.893136	+	1.54696i	0.0570412	+	0.998372i	$0.481833\pi$
$942$	−5.81816	+	10.7814i	−0.189566	+	0.351277i
$943$	−22.8371	−	13.1850i	−0.743677	−	0.429362i
$944$	−0.294868	+	0.170242i	−0.00959714	+	0.00554091i
$945$	3.64258	−	7.79012i	0.118493	−	0.253413i
$946$	−13.6294	+	23.6069i	−0.443131	+	0.767525i
$947$			41.2720i			1.34116i	0.741837	+	0.670580i	$0.233955\pi$
$947$			41.2720i			1.34116i	−0.741837	+	0.670580i	$0.766045\pi$
$948$	28.2161	−	0.811096i	0.916415	−	0.0263432i
$949$			9.88957i			0.321029i
$950$	1.32402	+	2.29327i	0.0429569	+	0.0744036i
$951$	44.0477	−	27.1477i	1.42834	−	0.880324i
$952$	0.261959	+	0.453726i	0.00849014	+	0.0147053i
$953$	−0.885286	+	1.53336i	−0.0286772	+	0.0496704i	−0.880008	−	0.474959i	$-0.842463\pi$
$953$	−0.885286	+	1.53336i	−0.0286772	+	0.0496704i	0.851331	+	0.524630i	$0.175796\pi$
$954$	−7.37874	+	4.84566i	−0.238896	+	0.156884i
$955$	9.04388	+	15.6645i	0.292653	+	0.506890i
$956$	−16.8722	+	9.74117i	−0.545686	+	0.315052i
$957$	34.1055	−	0.980393i	1.10247	−	0.0316916i
$958$	−7.16000			−0.231329
$959$	0.0814491			0.00263013
$960$	−3.13211	−	5.08191i	−0.101088	−	0.164018i
$961$	−6.84872	−	11.8623i	−0.220926	−	0.382656i
$962$	−7.64228	−	3.02021i	−0.246397	−	0.0973756i
$963$	47.2488	−	2.71866i	1.52257	−	0.0876076i
$964$	−20.6711	−	11.9345i	−0.665771	−	0.384383i
$965$	−10.9735	+	19.0066i	−0.353248	+	0.611843i
$966$	−5.84783	−	3.15577i	−0.188151	−	0.101535i
$967$		−	58.5476i		−	1.88276i	−0.337343	−	0.941382i	$-0.609528\pi$
$967$		−	58.5476i		−	1.88276i	0.337343	−	0.941382i	$-0.390472\pi$
$968$	0.891300	+	0.514592i	0.0286475	+	0.0165396i
$969$	0.619317	−	0.381700i	0.0198953	−	0.0122620i
$970$	37.6925	−	21.7618i	1.21023	−	0.698729i
$971$	−0.0438050	+	0.0758725i	−0.00140577	+	0.00243486i	−0.866727	−	0.498782i	$-0.833781\pi$
$971$	−0.0438050	+	0.0758725i	−0.00140577	+	0.00243486i	0.865322	+	0.501217i	$0.167114\pi$
$972$	14.4770	+	5.78076i	0.464349	+	0.185418i
$973$	−4.15559			−0.133222
$974$	24.2615			0.777388
$975$	8.44482	+	13.7019i	0.270451	+	0.438812i
$976$	−12.3122	−	7.10847i	−0.394105	−	0.227537i
$977$	49.9112	−	28.8162i	1.59680	−	0.921913i	0.604702	−	0.796452i	$-0.293292\pi$
$977$	49.9112	−	28.8162i	1.59680	−	0.921913i	0.992098	−	0.125462i	$-0.0400413\pi$
$978$	0.948354	+	32.9910i	0.0303250	+	1.05493i
$979$			7.86667i			0.251420i
$980$	20.2053	−	11.6655i	0.645434	−	0.372641i
$981$	12.7181	−	8.35207i	0.406059	−	0.266661i
$982$	27.8901	+	16.1023i	0.890008	+	0.513846i
$983$	39.6479			1.26457			0.632286	−	0.774735i	$-0.282117\pi$
$983$	39.6479			1.26457			0.632286	+	0.774735i	$0.282117\pi$
$984$	−2.99948	−	4.86672i	−0.0956199	−	0.155145i
$985$	−18.7607	−	10.8315i	−0.597764	−	0.345119i
$986$		−	6.80650i		−	0.216763i
$987$	−8.40659	+	5.18119i	−0.267585	+	0.164919i
$988$	0.260033	+	0.450390i	0.00827274	+	0.0143288i
$989$	−68.9699			−2.19312
$990$	32.5951	−	1.87550i	1.03594	−	0.0596072i
$991$			18.8014i			0.597247i	0.954371	+	0.298624i	$0.0965275\pi$
$991$			18.8014i			0.597247i	−0.954371	+	0.298624i	$0.903472\pi$
$992$	2.07982	−	3.60235i	0.0660343	−	0.114375i
$993$	−21.3754	−	34.6820i	−0.678328	−	1.10060i
$994$		−	1.00354i		−	0.0318304i
$995$	45.7380			1.44999
$996$	15.8632	−	9.77687i	0.502644	−	0.309792i
$997$		−	31.2936i		−	0.991079i	−0.868585	−	0.495540i	$-0.834970\pi$
$997$		−	31.2936i		−	0.991079i	0.868585	−	0.495540i	$-0.165030\pi$
$998$	18.4340			0.583518
$999$	9.04250	−	30.2859i	0.286092	−	0.958202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.16	✓	76
3.2	odd	2		1998.2.k.a.1063.37		76
9.2	odd	6		1998.2.t.a.397.37		76
9.7	even	3		666.2.t.a.619.3	yes	76
37.11	even	6		666.2.t.a.85.3	yes	76
111.11	odd	6		1998.2.t.a.307.37		76
333.11	odd	6		1998.2.k.a.1639.2		76
333.196	even	6	inner	666.2.k.a.529.35	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.16	✓	76	1.1	even	1	trivial
666.2.k.a.529.35	yes	76	333.196	even	6	inner
666.2.t.a.85.3	yes	76	37.11	even	6
666.2.t.a.619.3	yes	76	9.7	even	3
1998.2.k.a.1063.37		76	3.2	odd	2
1998.2.k.a.1639.2		76	333.11	odd	6
1998.2.t.a.307.37		76	111.11	odd	6
1998.2.t.a.397.37		76	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.47450 - 0.908769i) q^{3} -1.00000 q^{4} +3.44654i q^{5} +(-0.908769 - 1.47450i) q^{6} +(0.240097 - 0.415860i) q^{7} +1.00000i q^{8} +(1.34828 - 2.67995i) q^{9} +3.44654 q^{10} +(1.57883 + 2.73461i) q^{11} +(-1.47450 + 0.908769i) q^{12} -1.35094i q^{13} +(-0.415860 - 0.240097i) q^{14} +(3.13211 + 5.08191i) q^{15} +1.00000 q^{16} +(0.944880 + 0.545527i) q^{17} +(-2.67995 - 1.34828i) q^{18} +(0.333391 - 0.192483i) q^{19} -3.44654i q^{20} +(-0.0238987 - 0.831377i) q^{21} +(2.73461 - 1.57883i) q^{22} +(6.91907 + 3.99473i) q^{23} +(0.908769 + 1.47450i) q^{24} -6.87863 q^{25} -1.35094 q^{26} +(-0.447426 - 5.17685i) q^{27} +(-0.240097 + 0.415860i) q^{28} +(5.40267 - 3.11923i) q^{29} +(5.08191 - 3.13211i) q^{30} +(3.60235 + 2.07982i) q^{31} -1.00000i q^{32} +(4.81311 + 2.59739i) q^{33} +(0.545527 - 0.944880i) q^{34} +(1.43328 + 0.827504i) q^{35} +(-1.34828 + 2.67995i) q^{36} +(5.65702 + 2.23564i) q^{37} +(-0.192483 - 0.333391i) q^{38} +(-1.22769 - 1.99195i) q^{39} -3.44654 q^{40} -3.30060 q^{41} +(-0.831377 + 0.0238987i) q^{42} +(-7.47606 + 4.31631i) q^{43} +(-1.57883 - 2.73461i) q^{44} +(9.23656 + 4.64689i) q^{45} +(3.99473 - 6.91907i) q^{46} +(-5.93648 - 10.2823i) q^{47} +(1.47450 - 0.908769i) q^{48} +(3.38471 + 5.86248i) q^{49} +6.87863i q^{50} +(1.88898 - 0.0543004i) q^{51} +1.35094i q^{52} +(1.47126 - 2.54830i) q^{53} +(-5.17685 + 0.447426i) q^{54} +(-9.42495 + 5.44150i) q^{55} +(0.415860 + 0.240097i) q^{56} +(0.316661 - 0.586791i) q^{57} +(-3.11923 - 5.40267i) q^{58} +(-0.294868 + 0.170242i) q^{59} +(-3.13211 - 5.08191i) q^{60} +(-12.3122 - 7.10847i) q^{61} +(2.07982 - 3.60235i) q^{62} +(-0.790768 - 1.20414i) q^{63} -1.00000 q^{64} +4.65605 q^{65} +(2.59739 - 4.81311i) q^{66} -8.89333 q^{67} +(-0.944880 - 0.545527i) q^{68} +(13.8324 - 0.397625i) q^{69} +(0.827504 - 1.43328i) q^{70} +(1.04493 + 1.80988i) q^{71} +(2.67995 + 1.34828i) q^{72} -7.32053 q^{73} +(2.23564 - 5.65702i) q^{74} +(-10.1425 + 6.25109i) q^{75} +(-0.333391 + 0.192483i) q^{76} +1.51629 q^{77} +(-1.99195 + 1.22769i) q^{78} +(-14.1139 - 8.14864i) q^{79} +3.44654i q^{80} +(-5.36429 - 7.22664i) q^{81} +3.30060i q^{82} -10.7584 q^{83} +(0.0238987 + 0.831377i) q^{84} +(-1.88018 + 3.25657i) q^{85} +(4.31631 + 7.47606i) q^{86} +(5.13156 - 9.50908i) q^{87} +(-2.73461 + 1.57883i) q^{88} +(2.15753 + 1.24565i) q^{89} +(4.64689 - 9.23656i) q^{90} +(-0.561801 - 0.324356i) q^{91} +(-6.91907 - 3.99473i) q^{92} +(7.20172 - 0.207020i) q^{93} +(-10.2823 + 5.93648i) q^{94} +(0.663401 + 1.14904i) q^{95} +(-0.908769 - 1.47450i) q^{96} +(10.9363 - 6.31410i) q^{97} +(5.86248 - 3.38471i) q^{98} +(9.45734 - 0.544169i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

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