LMFDB - Embedded newform 672.2.bs.b.155.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(155,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))

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

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

chi := DirichletCharacter("672.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bs (of order $8$, degree $4$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.3
Character	$\chi$	$=$	672.155
Dual form			672.2.bs.b.659.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41064 + 0.100442i) q^{2} +(-1.73160 - 0.0395123i) q^{3} +(1.97982 - 0.283377i) q^{4} +(1.24365 - 3.00244i) q^{5} +(2.44664 - 0.118189i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.76436 + 0.598602i) q^{8} +(2.99688 + 0.136839i) q^{9} +O(q^{10})$	\(q+(-1.41064 + 0.100442i) q^{2} +(-1.73160 - 0.0395123i) q^{3} +(1.97982 - 0.283377i) q^{4} +(1.24365 - 3.00244i) q^{5} +(2.44664 - 0.118189i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.76436 + 0.598602i) q^{8} +(2.99688 + 0.136839i) q^{9} +(-1.45278 + 4.36029i) q^{10} +(2.49601 - 6.02591i) q^{11} +(-3.43946 + 0.412468i) q^{12} +(-0.615837 + 0.255088i) q^{13} +(-0.926451 + 1.06850i) q^{14} +(-2.27214 + 5.14989i) q^{15} +(3.83940 - 1.12207i) q^{16} +4.86140 q^{17} +(-4.24127 + 0.107983i) q^{18} +(0.0951292 + 0.229662i) q^{19} +(1.61139 - 6.29673i) q^{20} +(-1.25237 + 1.19649i) q^{21} +(-2.91572 + 8.75111i) q^{22} +(-4.71335 + 4.71335i) q^{23} +(4.81041 - 0.927313i) q^{24} +(-3.93246 - 3.93246i) q^{25} +(0.843103 - 0.421694i) q^{26} +(-5.18399 - 0.355364i) q^{27} +(1.19957 - 1.60032i) q^{28} +(5.53112 - 2.29107i) q^{29} +(2.68791 - 7.49288i) q^{30} +5.29455i q^{31} +(-5.30331 + 1.96848i) q^{32} +(-4.56019 + 10.3358i) q^{33} +(-6.85770 + 0.488291i) q^{34} +(-1.24365 - 3.00244i) q^{35} +(5.97206 - 0.578329i) q^{36} +(3.09343 + 1.28134i) q^{37} +(-0.157261 - 0.314416i) q^{38} +(1.07646 - 0.417377i) q^{39} +(-1.64063 + 9.04428i) q^{40} +(-4.39563 - 4.39563i) q^{41} +(1.64646 - 1.81361i) q^{42} +(-1.99911 - 0.828058i) q^{43} +(3.23406 - 12.6375i) q^{44} +(4.13793 - 8.82778i) q^{45} +(6.17543 - 7.12227i) q^{46} -7.55093i q^{47} +(-6.69263 + 1.79128i) q^{48} -1.00000i q^{49} +(5.94228 + 5.15231i) q^{50} +(-8.41800 - 0.192085i) q^{51} +(-1.14696 + 0.679543i) q^{52} +(5.56266 + 2.30413i) q^{53} +(7.34844 - 0.0194018i) q^{54} +(-14.9883 - 14.9883i) q^{55} +(-1.53142 + 2.37797i) q^{56} +(-0.155651 - 0.401442i) q^{57} +(-7.57231 + 3.78743i) q^{58} +(-4.29080 - 1.77731i) q^{59} +(-3.03908 + 10.8397i) q^{60} +(-2.72403 - 6.57639i) q^{61} +(-0.531797 - 7.46871i) q^{62} +(2.21587 - 2.02235i) q^{63} +(7.28335 - 3.30950i) q^{64} +2.16626i q^{65} +(5.39464 - 15.0382i) q^{66} +(5.57909 - 2.31093i) q^{67} +(9.62471 - 1.37761i) q^{68} +(8.34787 - 7.97540i) q^{69} +(2.05592 + 4.11046i) q^{70} +(-7.66663 - 7.66663i) q^{71} +(-8.36635 + 1.41566i) q^{72} +(4.05842 - 4.05842i) q^{73} +(-4.49243 - 1.49680i) q^{74} +(6.65407 + 6.96483i) q^{75} +(0.253420 + 0.427733i) q^{76} +(-2.49601 - 6.02591i) q^{77} +(-1.47658 + 0.696892i) q^{78} +14.6996 q^{79} +(1.40592 - 12.9230i) q^{80} +(8.96255 + 0.820178i) q^{81} +(6.64217 + 5.75915i) q^{82} +(-15.2899 + 6.33330i) q^{83} +(-2.14040 + 2.72372i) q^{84} +(6.04589 - 14.5961i) q^{85} +(2.90320 + 0.967298i) q^{86} +(-9.66822 + 3.74866i) q^{87} +(-3.29276 + 18.1519i) q^{88} +(-7.64598 + 7.64598i) q^{89} +(-4.95045 + 12.8685i) q^{90} +(-0.255088 + 0.615837i) q^{91} +(-7.99594 + 10.6672i) q^{92} +(0.209199 - 9.16804i) q^{93} +(0.758434 + 10.6517i) q^{94} +0.807856 q^{95} +(9.26099 - 3.19907i) q^{96} +0.220128 q^{97} +(0.100442 + 1.41064i) q^{98} +(8.30482 - 17.7174i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{4}+O(q^{10}) $ 192 * q + 16 * q^4	$ 192 q + 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} + 44 q^{30} - 104 q^{36} - 32 q^{37} + 24 q^{39} + 32 q^{46} - 32 q^{48} - 80 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} + 80 q^{61} + 64 q^{64} + 76 q^{66} - 32 q^{67} - 56 q^{69} - 24 q^{70} + 60 q^{72} - 80 q^{75} - 56 q^{76} - 76 q^{78} - 32 q^{79} + 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} + 80 q^{93} - 120 q^{94} - 32 q^{96} - 64 q^{99}+O(q^{100}) $ 192 * q + 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 + 44 * q^30 - 104 * q^36 - 32 * q^37 + 24 * q^39 + 32 * q^46 - 32 * q^48 - 80 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 + 80 * q^61 + 64 * q^64 + 76 * q^66 - 32 * q^67 - 56 * q^69 - 24 * q^70 + 60 * q^72 - 80 * q^75 - 56 * q^76 - 76 * q^78 - 32 * q^79 + 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 + 80 * q^93 - 120 * q^94 - 32 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$	$1$

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 $

$2$	−1.41064	+	0.100442i	−0.997475	+	0.0710236i
$2$	−1.41064	+	0.100442i	−0.997475	+	0.0710236i
$3$	−1.73160	−	0.0395123i	−0.999740	−	0.0228124i
$3$	−1.73160	−	0.0395123i	−0.999740	−	0.0228124i
$4$	1.97982	−	0.283377i	0.989911	−	0.141688i
$5$	1.24365	−	3.00244i	0.556179	−	1.34273i	−0.356592	−	0.934260i	$-0.616061\pi$
$5$	1.24365	−	3.00244i	0.556179	−	1.34273i	0.912770	−	0.408473i	$-0.133939\pi$
$6$	2.44664	−	0.118189i	0.998835	−	0.0482503i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−2.76436	+	0.598602i	−0.977348	+	0.211638i
$9$	2.99688	+	0.136839i	0.998959	+	0.0456129i
$10$	−1.45278	+	4.36029i	−0.459408	+	1.37884i
$11$	2.49601	−	6.02591i	0.752576	−	1.81688i	0.208091	−	0.978110i	$-0.433275\pi$
$11$	2.49601	−	6.02591i	0.752576	−	1.81688i	0.544486	−	0.838770i	$-0.316725\pi$
$12$	−3.43946	+	0.412468i	−0.992886	+	0.119069i
$13$	−0.615837	+	0.255088i	−0.170802	+	0.0707486i	−0.466446	−	0.884550i	$-0.654466\pi$
$13$	−0.615837	+	0.255088i	−0.170802	+	0.0707486i	0.295644	+	0.955298i	$0.404466\pi$
$14$	−0.926451	+	1.06850i	−0.247604	+	0.285568i
$15$	−2.27214	+	5.14989i	−0.586665	+	1.32970i
$16$	3.83940	−	1.12207i	0.959849	−	0.280518i
$17$	4.86140			1.17906			0.589531	−	0.807746i	$-0.299312\pi$
$17$	4.86140			1.17906			0.589531	+	0.807746i	$0.299312\pi$
$18$	−4.24127	+	0.107983i	−0.999676	+	0.0254519i
$19$	0.0951292	+	0.229662i	0.0218241	+	0.0526881i	0.934416	−	0.356184i	$-0.115922\pi$
$19$	0.0951292	+	0.229662i	0.0218241	+	0.0526881i	−0.912592	+	0.408872i	$0.865922\pi$
$20$	1.61139	−	6.29673i	0.360318	−	1.40799i
$21$	−1.25237	+	1.19649i	−0.273289	+	0.261095i
$22$	−2.91572	+	8.75111i	−0.621634	+	1.86574i
$23$	−4.71335	+	4.71335i	−0.982801	+	0.982801i	−0.999855	−	0.0170536i	$-0.994571\pi$
$23$	−4.71335	+	4.71335i	−0.982801	+	0.982801i	0.0170536	+	0.999855i	$0.494571\pi$
$24$	4.81041	−	0.927313i	0.981922	−	0.189287i
$25$	−3.93246	−	3.93246i	−0.786493	−	0.786493i
$26$	0.843103	−	0.421694i	0.165346	−	0.0827010i
$27$	−5.18399	−	0.355364i	−0.997659	−	0.0683897i
$28$	1.19957	−	1.60032i	0.226697	−	0.302433i
$29$	5.53112	−	2.29107i	1.02710	−	0.425440i	0.195438	−	0.980716i	$-0.437387\pi$
$29$	5.53112	−	2.29107i	1.02710	−	0.425440i	0.831666	+	0.555276i	$0.187387\pi$
$30$	2.68791	−	7.49288i	0.490743	−	1.36801i
$31$			5.29455i			0.950928i	0.879735	+	0.475464i	$0.157720\pi$
$31$			5.29455i			0.950928i	−0.879735	+	0.475464i	$0.842280\pi$
$32$	−5.30331	+	1.96848i	−0.937501	+	0.347981i
$33$	−4.56019	+	10.3358i	−0.793828	+	1.79924i
$34$	−6.85770	+	0.488291i	−1.17609	+	0.0837412i
$35$	−1.24365	−	3.00244i	−0.210216	−	0.507506i
$36$	5.97206	−	0.578329i	0.995344	−	0.0963882i
$37$	3.09343	+	1.28134i	0.508558	+	0.210651i	0.622182	−	0.782872i	$-0.286246\pi$
$37$	3.09343	+	1.28134i	0.508558	+	0.210651i	−0.113625	+	0.993524i	$0.536246\pi$
$38$	−0.157261	−	0.314416i	−0.0255111	−	0.0510051i
$39$	1.07646	−	0.417377i	0.172372	−	0.0668338i
$40$	−1.64063	+	9.04428i	−0.259407	+	1.43003i
$41$	−4.39563	−	4.39563i	−0.686482	−	0.686482i	0.274971	−	0.961453i	$-0.411332\pi$
$41$	−4.39563	−	4.39563i	−0.686482	−	0.686482i	−0.961453	+	0.274971i	$0.911332\pi$
$42$	1.64646	−	1.81361i	0.254055	−	0.279845i
$43$	−1.99911	−	0.828058i	−0.304861	−	0.126278i	0.225008	−	0.974357i	$-0.427759\pi$
$43$	−1.99911	−	0.828058i	−0.304861	−	0.126278i	−0.529869	+	0.848079i	$0.677759\pi$
$44$	3.23406	−	12.6375i	0.487553	−	1.90518i
$45$	4.13793	−	8.82778i	0.616846	−	1.31597i
$46$	6.17543	−	7.12227i	0.910517	−	1.05012i
$47$		−	7.55093i		−	1.10142i	−0.834698	−	0.550708i	$-0.814358\pi$
$47$		−	7.55093i		−	1.10142i	0.834698	−	0.550708i	$-0.185642\pi$
$48$	−6.69263	+	1.79128i	−0.965998	+	0.258548i
$49$		−	1.00000i		−	0.142857i
$50$	5.94228	+	5.15231i	0.840366	+	0.728647i
$51$	−8.41800	−	0.192085i	−1.17876	−	0.0268973i
$52$	−1.14696	+	0.679543i	−0.159055	+	0.0942356i
$53$	5.56266	+	2.30413i	0.764090	+	0.316497i	0.730476	−	0.682938i	$-0.239298\pi$
$53$	5.56266	+	2.30413i	0.764090	+	0.316497i	0.0336142	+	0.999435i	$0.489298\pi$
$54$	7.34844	−	0.0194018i	0.999997	−	0.00264025i
$55$	−14.9883	−	14.9883i	−2.02102	−	2.02102i
$56$	−1.53142	+	2.37797i	−0.204645	+	0.317770i
$57$	−0.155651	−	0.401442i	−0.0206165	−	0.0531723i
$58$	−7.57231	+	3.78743i	−0.994294	+	0.497314i
$59$	−4.29080	−	1.77731i	−0.558615	−	0.231386i	0.0854688	−	0.996341i	$-0.472761\pi$
$59$	−4.29080	−	1.77731i	−0.558615	−	0.231386i	−0.644084	+	0.764955i	$0.722761\pi$
$60$	−3.03908	+	10.8397i	−0.392344	+	1.39941i
$61$	−2.72403	−	6.57639i	−0.348776	−	0.842021i	−0.996765	−	0.0803706i	$-0.974390\pi$
$61$	−2.72403	−	6.57639i	−0.348776	−	0.842021i	0.647989	−	0.761650i	$-0.275610\pi$
$62$	−0.531797	−	7.46871i	−0.0675383	−	0.948527i
$63$	2.21587	−	2.02235i	0.279174	−	0.254793i
$64$	7.28335	−	3.30950i	0.910419	−	0.413687i
$65$			2.16626i			0.268691i
$66$	5.39464	−	15.0382i	0.664035	−	1.85108i
$67$	5.57909	−	2.31093i	0.681594	−	0.282325i	−0.0148992	−	0.999889i	$-0.504743\pi$
$67$	5.57909	−	2.31093i	0.681594	−	0.282325i	0.696493	+	0.717564i	$0.254743\pi$
$68$	9.62471	−	1.37761i	1.16717	−	0.167060i
$69$	8.34787	−	7.97540i	1.00497	−	0.960125i
$70$	2.05592	+	4.11046i	0.245730	+	0.491294i
$71$	−7.66663	−	7.66663i	−0.909861	−	0.909861i	0.0863995	−	0.996261i	$-0.472464\pi$
$71$	−7.66663	−	7.66663i	−0.909861	−	0.909861i	−0.996261	+	0.0863995i	$0.972464\pi$
$72$	−8.36635	+	1.41566i	−0.985984	+	0.166838i
$73$	4.05842	−	4.05842i	0.475003	−	0.475003i	−0.428527	−	0.903529i	$-0.640967\pi$
$73$	4.05842	−	4.05842i	0.475003	−	0.475003i	0.903529	+	0.428527i	$0.140967\pi$
$74$	−4.49243	−	1.49680i	−0.522234	−	0.174000i
$75$	6.65407	+	6.96483i	0.768346	+	0.804230i
$76$	0.253420	+	0.427733i	0.0290693	+	0.0490644i
$77$	−2.49601	−	6.02591i	−0.284447	−	0.686716i
$78$	−1.47658	+	0.696892i	−0.167190	+	0.0789075i
$79$	14.6996			1.65383			0.826916	−	0.562326i	$-0.190093\pi$
$79$	14.6996			1.65383			0.826916	+	0.562326i	$0.190093\pi$
$80$	1.40592	−	12.9230i	0.157186	−	1.44484i
$81$	8.96255	+	0.820178i	0.995839	+	0.0911309i
$82$	6.64217	+	5.75915i	0.733505	+	0.635992i
$83$	−15.2899	+	6.33330i	−1.67829	+	0.695170i	−0.999242	−	0.0389240i	$-0.987607\pi$
$83$	−15.2899	+	6.33330i	−1.67829	+	0.695170i	−0.679047	+	0.734094i	$0.737607\pi$
$84$	−2.14040	+	2.72372i	−0.233537	+	0.297183i
$85$	6.04589	−	14.5961i	0.655769	−	1.58317i
$86$	2.90320	+	0.967298i	0.313060	+	0.104306i
$87$	−9.66822	+	3.74866i	−1.03654	+	0.401899i
$88$	−3.29276	+	18.1519i	−0.351009	+	1.93500i
$89$	−7.64598	+	7.64598i	−0.810472	+	0.810472i	−0.984705	−	0.174232i	$-0.944256\pi$
$89$	−7.64598	+	7.64598i	−0.810472	+	0.810472i	0.174232	+	0.984705i	$0.444256\pi$
$90$	−4.95045	+	12.8685i	−0.521823	+	1.35645i
$91$	−0.255088	+	0.615837i	−0.0267405	+	0.0645572i
$92$	−7.99594	+	10.6672i	−0.833634	+	1.11214i
$93$	0.209199	−	9.16804i	0.0216930	−	0.950681i
$94$	0.758434	+	10.6517i	0.0782265	+	1.09864i
$95$	0.807856			0.0828843
$96$	9.26099	−	3.19907i	0.945196	−	0.326504i
$97$	0.220128			0.0223507			0.0111753	−	0.999938i	$-0.496443\pi$
$97$	0.220128			0.0223507			0.0111753	+	0.999938i	$0.496443\pi$
$98$	0.100442	+	1.41064i	0.0101462	+	0.142496i
$99$	8.30482	−	17.7174i	0.834666	−	1.78066i
$100$	−8.89995	−	6.67121i	−0.889995	−	0.667121i
$101$	−3.58820	+	8.66268i	−0.357039	+	0.861969i	0.638674	+	0.769477i	$0.279483\pi$
$101$	−3.58820	+	8.66268i	−0.357039	+	0.861969i	−0.995713	+	0.0924916i	$0.970517\pi$
$102$	11.8941	−	0.574562i	1.17769	−	0.0568901i
$103$	−2.17786	+	2.17786i	−0.214591	+	0.214591i	−0.806215	−	0.591623i	$-0.798487\pi$
$103$	−2.17786	+	2.17786i	−0.214591	+	0.214591i	0.591623	+	0.806215i	$0.298487\pi$
$104$	1.54970	−	1.07379i	0.151960	−	0.105294i
$105$	2.03488	+	5.24817i	0.198584	+	0.512169i
$106$	−8.07836	−	2.69157i	−0.784639	−	0.261429i
$107$	0.176771	−	0.426763i	0.0170891	−	0.0412567i	−0.915105	−	0.403216i	$-0.867892\pi$
$107$	0.176771	−	0.426763i	0.0170891	−	0.0412567i	0.932194	+	0.361960i	$0.117892\pi$
$108$	−10.3641	+	0.765465i	−0.997284	+	0.0736569i
$109$	−0.148358	+	0.0614521i	−0.0142102	+	0.00588604i	−0.389777	−	0.920909i	$-0.627448\pi$
$109$	−0.148358	+	0.0614521i	−0.0142102	+	0.00588604i	0.375567	+	0.926795i	$0.377448\pi$
$110$	22.6486	+	19.6376i	2.15946	+	1.87238i
$111$	−5.30596	−	2.34100i	−0.503620	−	0.222198i
$112$	1.92144	−	3.50829i	0.181559	−	0.331502i
$113$	−10.6348			−1.00044			−0.500220	−	0.865898i	$-0.666747\pi$
$113$	−10.6348			−1.00044			−0.500220	+	0.865898i	$0.666747\pi$
$114$	0.259890	+	0.550657i	0.0243409	+	0.0515738i
$115$	8.28979	+	20.0133i	0.773027	+	1.86625i
$116$	10.3014	−	6.10330i	0.956462	−	0.566677i
$117$	−1.88049	+	0.680197i	−0.173852	+	0.0628842i
$118$	6.23131	+	2.07617i	0.573638	+	0.191127i
$119$	3.43753	−	3.43753i	0.315118	−	0.315118i
$120$	3.19828	−	15.5963i	0.291962	−	1.42374i
$121$	−22.3033	−	22.3033i	−2.02757	−	2.02757i
$122$	4.50318	+	9.00333i	0.407699	+	0.815123i
$123$	7.43779	+	7.78515i	0.670643	+	0.701964i
$124$	1.50035	+	10.4823i	0.134736	+	0.941335i
$125$	−1.68540	+	0.698116i	−0.150747	+	0.0624414i
$126$	−2.92267	+	3.07538i	−0.260372	+	0.273977i
$127$			15.1194i			1.34163i	0.741624	+	0.670815i	$0.234056\pi$
$127$			15.1194i			1.34163i	−0.741624	+	0.670815i	$0.765944\pi$
$128$	−9.94179	+	5.40008i	−0.878738	+	0.477304i
$129$	3.42894	+	1.51285i	0.301901	+	0.133199i
$130$	−0.217584	−	3.05581i	−0.0190834	−	0.268012i
$131$	4.26197	+	10.2893i	0.372370	+	0.898982i	0.993348	+	0.115153i	$0.0367359\pi$
$131$	4.26197	+	10.2893i	0.372370	+	0.898982i	−0.620977	+	0.783829i	$0.713264\pi$
$132$	−6.09944	+	21.7554i	−0.530888	+	1.89356i
$133$	0.229662	+	0.0951292i	0.0199142	+	0.00824875i
$134$	−7.63798	+	3.82028i	−0.659821	+	0.330022i
$135$	−7.51404	+	15.1227i	−0.646706	+	1.30155i
$136$	−13.4387	+	2.91004i	−1.15235	+	0.249534i
$137$	1.07269	+	1.07269i	0.0916458	+	0.0916458i	0.751443	−	0.659798i	$-0.229358\pi$
$137$	1.07269	+	1.07269i	0.0916458	+	0.0916458i	−0.659798	+	0.751443i	$0.729358\pi$
$138$	−10.9748	+	12.0889i	−0.934236	+	1.02908i
$139$	−20.4535	−	8.47210i	−1.73484	−	0.718594i	−0.999148	−	0.0412786i	$-0.986857\pi$
$139$	−20.4535	−	8.47210i	−1.73484	−	0.718594i	−0.735692	−	0.677316i	$-0.763143\pi$
$140$	−3.31304	−	5.59188i	−0.280003	−	0.472600i
$141$	−0.298354	+	13.0752i	−0.0251260	+	1.10113i
$142$	11.5849	+	10.0448i	0.972185	+	0.842942i
$143$			4.34768i			0.363571i
$144$	11.6597	−	2.83733i	0.971645	−	0.236444i
$145$		−	19.4562i		−	1.61575i
$146$	−5.31735	+	6.13262i	−0.440067	+	0.507539i
$147$	−0.0395123	+	1.73160i	−0.00325892	+	0.142820i
$148$	6.48756	+	1.66022i	0.533274	+	0.136470i
$149$	10.0294	+	4.15430i	0.821638	+	0.340333i	0.753587	−	0.657348i	$-0.228322\pi$
$149$	10.0294	+	4.15430i	0.821638	+	0.340333i	0.0680509	+	0.997682i	$0.478322\pi$
$150$	−10.0861	−	9.15654i	−0.823525	−	0.747628i
$151$	17.0139	+	17.0139i	1.38457	+	1.38457i	0.836307	+	0.548261i	$0.184710\pi$
$151$	17.0139	+	17.0139i	1.38457	+	1.38457i	0.548261	+	0.836307i	$0.315290\pi$
$152$	−0.400447	−	0.577924i	−0.0324806	−	0.0468759i
$153$	14.5690	+	0.665228i	1.17784	+	0.0537805i
$154$	4.12624	+	8.24969i	0.332502	+	0.664779i
$155$	15.8966	+	6.58458i	1.27684	+	0.528886i
$156$	2.01293	−	1.13138i	0.161163	−	0.0905826i
$157$	3.22702	+	7.79073i	0.257545	+	0.621768i	0.998775	−	0.0494831i	$-0.0157574\pi$
$157$	3.22702	+	7.79073i	0.257545	+	0.621768i	−0.741230	+	0.671251i	$0.765757\pi$
$158$	−20.7358	+	1.47646i	−1.64966	+	0.117461i
$159$	−9.54126	−	4.20962i	−0.756671	−	0.333845i
$160$	−0.685225	+	18.3710i	−0.0541718	+	1.45235i
$161$			6.66568i			0.525329i
$162$	−12.7253	−	0.256757i	−0.999797	−	0.0201728i
$163$	13.6163	−	5.64004i	1.06651	−	0.441762i	0.220751	−	0.975330i	$-0.429149\pi$
$163$	13.6163	−	5.64004i	1.06651	−	0.441762i	0.845757	+	0.533568i	$0.179149\pi$
$164$	−9.94819	−	7.45695i	−0.776823	−	0.582290i
$165$	25.3615	+	26.5459i	1.97439	+	2.06660i
$166$	20.9325	−	10.4698i	1.62468	−	0.812613i
$167$	−0.999991	−	0.999991i	−0.0773816	−	0.0773816i	0.667357	−	0.744738i	$-0.267426\pi$
$167$	−0.999991	−	0.999991i	−0.0773816	−	0.0773816i	−0.744738	+	0.667357i	$0.767426\pi$
$168$	2.74577	−	4.05719i	0.211841	−	0.313019i
$169$	−8.87820	+	8.87820i	−0.682939	+	0.682939i
$170$	−7.06253	+	21.1971i	−0.541671	+	1.62574i
$171$	0.253664	+	0.701287i	0.0193982	+	0.0536288i
$172$	−4.19253	−	1.07291i	−0.319678	−	0.0818083i
$173$	−3.21698	−	7.76649i	−0.244583	−	0.590475i	0.753145	−	0.657855i	$-0.228536\pi$
$173$	−3.21698	−	7.76649i	−0.244583	−	0.590475i	−0.997727	+	0.0673799i	$0.978536\pi$
$174$	13.2619	−	6.25912i	1.00538	−	0.474503i
$175$	−5.56134			−0.420398
$176$	2.82168	−	25.9365i	0.212692	−	1.95504i
$177$	7.35973	+	3.24713i	0.553191	+	0.244069i
$178$	10.0178	−	11.5537i	0.750863	−	0.865988i
$179$	7.53055	−	3.11925i	0.562859	−	0.233144i	−0.0830666	−	0.996544i	$-0.526471\pi$
$179$	7.53055	−	3.11925i	0.562859	−	0.233144i	0.645926	+	0.763400i	$0.276471\pi$
$180$	5.69077	−	18.6500i	0.424165	−	1.39009i
$181$	2.87093	−	6.93104i	0.213395	−	0.515180i	−0.780546	−	0.625098i	$-0.785059\pi$
$181$	2.87093	−	6.93104i	0.213395	−	0.515180i	0.993941	+	0.109918i	$0.0350589\pi$
$182$	0.297982	−	0.894347i	0.0220879	−	0.0662934i
$183$	4.45708	+	11.4953i	0.329477	+	0.849758i
$184$	10.2080	−	15.8508i	0.752541	−	1.16854i
$185$	7.69432	−	7.69432i	0.565698	−	0.565698i
$186$	0.625755	+	12.9538i	0.0458826	+	0.949821i
$187$	12.1341	−	29.2944i	0.887335	−	2.14222i
$188$	−2.13976	−	14.9495i	−0.156058	−	1.09030i
$189$	−3.91691	+	3.41435i	−0.284913	+	0.248358i
$190$	−1.13960	+	0.0811431i	−0.0826750	+	0.00588674i
$191$	6.25312			0.452460			0.226230	−	0.974074i	$-0.427360\pi$
$191$	6.25312			0.452460			0.226230	+	0.974074i	$0.427360\pi$
$192$	−12.7426	+	5.44295i	−0.919619	+	0.392811i
$193$	−6.80764			−0.490025			−0.245012	−	0.969520i	$-0.578792\pi$
$193$	−6.80764			−0.490025			−0.245012	+	0.969520i	$0.578792\pi$
$194$	−0.310522	+	0.0221102i	−0.0222942	+	0.00158742i
$195$	0.0855936	−	3.75109i	0.00612949	−	0.268621i
$196$	−0.283377	−	1.97982i	−0.0202412	−	0.141416i
$197$	4.67801	−	11.2937i	0.333294	−	0.804644i	−0.665032	−	0.746815i	$-0.731582\pi$
$197$	4.67801	−	11.2937i	0.333294	−	0.804644i	0.998326	−	0.0578292i	$-0.0184179\pi$
$198$	−9.93556	+	25.8270i	−0.706089	+	1.83545i
$199$	−2.63103	+	2.63103i	−0.186509	+	0.186509i	−0.794185	−	0.607676i	$-0.792102\pi$
$199$	−2.63103	+	2.63103i	−0.186509	+	0.186509i	0.607676	+	0.794185i	$0.292102\pi$
$200$	13.2247	+	8.51676i	0.935129	+	0.602226i
$201$	−9.75205	+	3.78117i	−0.687857	+	0.266703i
$202$	4.19156	−	12.5803i	0.294917	−	0.885150i
$203$	2.29107	−	5.53112i	0.160801	−	0.388209i
$204$	−16.7206	+	2.00517i	−1.17067	+	0.140390i
$205$	−18.6643	+	7.73099i	−1.30357	+	0.539956i
$206$	2.85344	−	3.29094i	0.198808	−	0.229291i
$207$	−14.7703	+	13.4804i	−1.02661	+	0.936950i
$208$	−2.07821	+	1.67040i	−0.144098	+	0.115821i
$209$	1.62137			0.112152
$210$	−3.39762	−	7.19890i	−0.234458	−	0.496772i
$211$	0.333835	+	0.805950i	0.0229822	+	0.0554839i	0.934954	−	0.354769i	$-0.115440\pi$
$211$	0.333835	+	0.805950i	0.0229822	+	0.0554839i	−0.911972	+	0.410253i	$0.865440\pi$
$212$	11.6660	+	2.98544i	0.801225	+	0.205041i
$213$	12.9726	+	13.5785i	0.888868	+	0.930380i
$214$	−0.206495	+	0.619765i	−0.0141157	+	0.0423662i
$215$	−4.97239	+	4.97239i	−0.339114	+	0.339114i
$216$	14.5431	−	2.12079i	0.989534	−	0.144302i
$217$	3.74381	+	3.74381i	0.254146	+	0.254146i
$218$	0.203108	−	0.101588i	0.0137562	−	0.00688044i
$219$	−7.18793	+	6.86721i	−0.485715	+	0.464043i
$220$	−33.9215	−	25.4268i	−2.28698	−	1.71427i
$221$	−2.99383	+	1.24008i	−0.201387	+	0.0834171i
$222$	7.71995	+	2.76937i	0.518129	+	0.185868i
$223$		−	8.24324i		−	0.552008i	−0.961156	−	0.276004i	$-0.910990\pi$
$223$		−	8.24324i		−	0.552008i	0.961156	−	0.276004i	$-0.0890103\pi$
$224$	−2.35808	+	5.14193i	−0.157556	+	0.343560i
$225$	−11.2470	−	12.3232i	−0.749800	−	0.821548i
$226$	15.0019	−	1.06819i	0.997913	−	0.0710548i
$227$	−5.65275	−	13.6470i	−0.375186	−	0.905780i	−0.992853	−	0.119340i	$-0.961922\pi$
$227$	−5.65275	−	13.6470i	−0.375186	−	0.905780i	0.617667	−	0.786440i	$-0.288078\pi$
$228$	−0.421921	−	0.750676i	−0.0279424	−	0.0497147i
$229$	9.26295	+	3.83684i	0.612113	+	0.253545i	0.667132	−	0.744940i	$-0.267522\pi$
$229$	9.26295	+	3.83684i	0.612113	+	0.253545i	−0.0550188	+	0.998485i	$0.517522\pi$
$230$	−13.7041	−	27.3990i	−0.903623	−	1.80664i
$231$	4.08400	+	10.5331i	0.268707	+	0.693026i
$232$	−13.9186	+	9.64427i	−0.913799	+	0.633177i
$233$	−3.46899	−	3.46899i	−0.227261	−	0.227261i	0.584287	−	0.811547i	$-0.301374\pi$
$233$	−3.46899	−	3.46899i	−0.227261	−	0.227261i	−0.811547	+	0.584287i	$0.801374\pi$
$234$	2.58438	−	1.14840i	0.168946	−	0.0750730i
$235$	−22.6713	−	9.39074i	−1.47891	−	0.612584i
$236$	−8.99868	−	2.30284i	−0.585764	−	0.149902i
$237$	−25.4538	−	0.580813i	−1.65340	−	0.0377279i
$238$	−4.50385	+	5.19440i	−0.291941	+	0.336703i
$239$		−	9.00449i		−	0.582452i	−0.956654	−	0.291226i	$-0.905937\pi$
$239$		−	9.00449i		−	0.582452i	0.956654	−	0.291226i	$-0.0940632\pi$
$240$	−2.94511	+	22.3220i	−0.190106	+	1.44088i
$241$			6.30783i			0.406323i	0.979145	+	0.203161i	$0.0651216\pi$
$241$			6.30783i			0.406323i	−0.979145	+	0.203161i	$0.934878\pi$
$242$	33.7022	+	29.2218i	2.16646	+	1.87845i
$243$	−15.4871	−	1.77435i	−0.993501	−	0.113825i
$244$	−7.25669	−	12.2482i	−0.464562	−	0.784108i
$245$	−3.00244	−	1.24365i	−0.191819	−	0.0794541i
$246$	−11.2740	−	10.2350i	−0.718805	−	0.652559i
$247$	−0.117168	−	0.117168i	−0.00745523	−	0.00745523i
$248$	−3.16932	−	14.6360i	−0.201252	−	0.929388i
$249$	26.7263	−	10.3626i	1.69371	−	0.656704i
$250$	2.30738	−	1.15408i	0.145931	−	0.0729903i
$251$	24.6376	+	10.2052i	1.55511	+	0.644150i	0.984232	−	0.176882i	$-0.0566011\pi$
$251$	24.6376	+	10.2052i	1.55511	+	0.644150i	0.570883	+	0.821032i	$0.306601\pi$
$252$	3.81395	−	4.63183i	0.240256	−	0.291778i
$253$	16.6376	+	40.1668i	1.04600	+	2.52526i
$254$	−1.51863	−	21.3281i	−0.0952874	−	1.33824i
$255$	−11.0458	+	25.0357i	−0.691715	+	1.56780i
$256$	13.4819	−	8.61615i	0.842619	−	0.538510i
$257$			29.9728i			1.86965i	0.355103	+	0.934827i	$0.384446\pi$
$257$			29.9728i			1.86965i	−0.355103	+	0.934827i	$0.615554\pi$
$258$	−4.98896	−	1.78968i	−0.310599	−	0.111421i
$259$	3.09343	−	1.28134i	0.192217	−	0.0796188i
$260$	0.613867	+	4.28880i	0.0380704	+	0.265980i
$261$	16.8896	−	6.10917i	1.04544	−	0.378148i
$262$	−7.04561	−	14.0865i	−0.435279	−	0.870264i
$263$	10.6888	+	10.6888i	0.659099	+	0.659099i	0.955167	−	0.296068i	$-0.0956753\pi$
$263$	10.6888	+	10.6888i	0.659099	+	0.659099i	−0.296068	+	0.955167i	$0.595675\pi$
$264$	6.41896	−	31.3017i	0.395060	−	1.92649i
$265$	13.8360	−	13.8360i	0.849941	−	0.849941i
$266$	−0.333526	−	0.111125i	−0.0204498	−	0.00681354i
$267$	13.5419	−	12.9377i	0.828750	−	0.791773i
$268$	10.3907	−	6.15622i	0.634715	−	0.376051i
$269$	−5.49124	−	13.2570i	−0.334807	−	0.808296i	−0.998197	−	0.0600220i	$-0.980883\pi$
$269$	−5.49124	−	13.2570i	−0.334807	−	0.808296i	0.663390	−	0.748274i	$-0.269117\pi$
$270$	9.08066	−	22.0874i	0.552631	−	1.34420i
$271$	−16.3331			−0.992168			−0.496084	−	0.868275i	$-0.665229\pi$
$271$	−16.3331			−0.992168			−0.496084	+	0.868275i	$0.665229\pi$
$272$	18.6648	−	5.45484i	1.13172	−	0.330748i
$273$	0.466043	−	1.05630i	0.0282062	−	0.0639304i
$274$	−1.62092	−	1.40543i	−0.0979234	−	0.0849054i
$275$	−33.5121	+	13.8812i	−2.02086	+	0.837067i
$276$	14.2673	−	18.1555i	0.858788	−	1.09283i
$277$	−9.29263	+	22.4344i	−0.558340	+	1.34795i	0.352739	+	0.935722i	$0.385250\pi$
$277$	−9.29263	+	22.4344i	−0.558340	+	1.34795i	−0.911079	+	0.412231i	$0.864750\pi$
$278$	29.7035	+	9.89671i	1.78150	+	0.593565i
$279$	−0.724499	+	15.8671i	−0.0433746	+	0.949939i
$280$	5.23517	+	7.55538i	0.312861	+	0.451520i
$281$	−4.41496	+	4.41496i	−0.263374	+	0.263374i	−0.826423	−	0.563049i	$-0.809628\pi$
$281$	−4.41496	+	4.41496i	−0.263374	+	0.263374i	0.563049	+	0.826423i	$0.309628\pi$
$282$	−0.892434	−	18.4744i	−0.0531437	−	1.10013i
$283$	10.2764	−	24.8094i	0.610867	−	1.47476i	−0.251182	−	0.967940i	$-0.580819\pi$
$283$	10.2764	−	24.8094i	0.610867	−	1.47476i	0.862049	−	0.506824i	$-0.169181\pi$
$284$	−17.3511	−	13.0060i	−1.02960	−	0.771765i
$285$	−1.39888	−	0.0319202i	−0.0828627	−	0.00189079i
$286$	−0.436692	−	6.13302i	−0.0258221	−	0.362653i
$287$	−6.21636			−0.366940
$288$	−16.1627	+	5.17359i	−0.952398	+	0.304857i
$289$	6.63321			0.390189
$290$	1.95423	+	27.4457i	0.114756	+	1.61167i
$291$	−0.381174	−	0.00869777i	−0.0223448	−	0.000509872i
$292$	6.88490	−	9.18502i	0.402908	−	0.537513i
$293$	−9.42534	+	22.7548i	−0.550634	+	1.32935i	0.366370	+	0.930469i	$0.380601\pi$
$293$	−9.42534	+	22.7548i	−0.550634	+	1.32935i	−0.917004	+	0.398879i	$0.869399\pi$
$294$	−0.118189	−	2.44664i	−0.00689290	−	0.142691i
$295$	−10.6725	+	10.6725i	−0.621379	+	0.621379i
$296$	−9.31838	−	1.69036i	−0.541620	−	0.0982499i
$297$	−15.0807	+	30.3512i	−0.875070	+	1.76116i
$298$	−14.5651	−	4.85286i	−0.843734	−	0.281118i
$299$	1.70033	−	4.10497i	0.0983329	−	0.237397i
$300$	15.1476	+	11.9035i	0.874545	+	0.687250i
$301$	−1.99911	+	0.828058i	−0.115227	+	0.0477285i
$302$	−25.7094	−	22.2916i	−1.47941	−	1.28273i
$303$	6.55561	−	14.8585i	0.376610	−	0.853600i
$304$	0.622936	+	0.775022i	0.0357278	+	0.0444506i
$305$	−23.1330			−1.32459
$306$	−20.6185	+	0.524950i	−1.17868	+	0.0300094i
$307$	−1.06927	−	2.58144i	−0.0610262	−	0.147330i	0.890425	−	0.455130i	$-0.150407\pi$
$307$	−1.06927	−	2.58144i	−0.0610262	−	0.147330i	−0.951451	+	0.307800i	$0.900407\pi$
$308$	−6.64927	−	11.2229i	−0.378877	−	0.639485i
$309$	3.85724	−	3.68514i	0.219431	−	0.209640i
$310$	−23.0858	−	7.69179i	−1.31118	−	0.436864i
$311$	6.24082	−	6.24082i	0.353884	−	0.353884i	−0.507668	−	0.861553i	$-0.669492\pi$
$311$	6.24082	−	6.24082i	0.353884	−	0.353884i	0.861553	+	0.507668i	$0.169492\pi$
$312$	−2.72588	+	1.79815i	−0.154323	+	0.101800i
$313$	2.14870	+	2.14870i	0.121452	+	0.121452i	0.765220	−	0.643769i	$-0.222630\pi$
$313$	2.14870	+	2.14870i	0.121452	+	0.121452i	−0.643769	+	0.765220i	$0.722630\pi$
$314$	−5.33470	−	10.6658i	−0.301054	−	0.601906i
$315$	−3.31622	−	9.16814i	−0.186848	−	0.516566i
$316$	29.1026	−	4.16552i	1.63715	−	0.234329i
$317$	5.05675	−	2.09457i	0.284015	−	0.117643i	−0.236128	−	0.971722i	$-0.575879\pi$
$317$	5.05675	−	2.09457i	0.284015	−	0.117643i	0.520143	+	0.854079i	$0.325879\pi$
$318$	13.8821	+	4.97993i	0.778471	+	0.279260i
$319$		−	39.0486i		−	2.18630i
$320$	−0.878621	−	25.9837i	−0.0491164	−	1.45253i
$321$	−0.322959	+	0.731997i	−0.0180258	+	0.0408561i
$322$	−0.669518	−	9.40289i	−0.0373108	−	0.524003i
$323$	0.462461	+	1.11648i	0.0257320	+	0.0621226i
$324$	17.9767	−	0.915971i	0.998704	−	0.0508873i
$325$	3.42488	+	1.41863i	0.189978	+	0.0786915i
$326$	−18.6412	+	9.32374i	−1.03244	+	0.516394i
$327$	0.259326	−	0.100548i	0.0143407	−	0.00556034i
$328$	14.7823	+	9.51986i	0.816217	+	0.525647i
$329$	−5.33932	−	5.33932i	−0.294366	−	0.294366i
$330$	−38.4423	−	34.8994i	−2.11618	−	1.92115i
$331$	9.49727	+	3.93390i	0.522017	+	0.216227i	0.628103	−	0.778130i	$-0.283832\pi$
$331$	9.49727	+	3.93390i	0.522017	+	0.216227i	−0.106085	+	0.994357i	$0.533832\pi$
$332$	−28.4767	+	16.8716i	−1.56286	+	0.925951i
$333$	9.09531	+	4.26333i	0.498420	+	0.233629i
$334$	1.51107	+	1.31019i	0.0826821	+	0.0716903i
$335$		−	19.6249i		−	1.07222i
$336$	−3.46578	+	5.99903i	−0.189074	+	0.327274i
$337$		−	2.27097i		−	0.123708i	−0.998085	−	0.0618538i	$-0.980299\pi$
$337$		−	2.27097i		−	0.123708i	0.998085	−	0.0618538i	$-0.0197013\pi$
$338$	11.6322	−	13.4157i	0.632709	−	0.729719i
$339$	18.4153	+	0.420206i	1.00018	+	0.0228224i
$340$	7.83361	−	30.6109i	0.424837	−	1.66011i
$341$	31.9044	+	13.2153i	1.72772	+	0.715646i
$342$	−0.428268	−	0.963787i	−0.0231581	−	0.0521156i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	6.02193	+	1.09238i	0.324681	+	0.0588971i
$345$	−13.5638	−	34.9826i	−0.730252	−	1.88340i
$346$	5.31810	+	10.6326i	0.285903	+	0.571613i
$347$	−0.649937	−	0.269213i	−0.0348905	−	0.0144521i	0.365170	−	0.930941i	$-0.381011\pi$
$347$	−0.649937	−	0.269213i	−0.0348905	−	0.0144521i	−0.400060	+	0.916489i	$0.631011\pi$
$348$	−18.0791	+	10.1614i	−0.969140	+	0.544710i
$349$	−0.424519	−	1.02488i	−0.0227240	−	0.0548606i	0.912110	−	0.409945i	$-0.134452\pi$
$349$	−0.424519	−	1.02488i	−0.0227240	−	0.0548606i	−0.934834	+	0.355084i	$0.884452\pi$
$350$	7.84506	−	0.558595i	0.419336	−	0.0298582i
$351$	3.28314	−	1.10353i	0.175241	−	0.0589019i
$352$	−1.37525	+	36.8706i	−0.0733010	+	1.96521i
$353$		−	29.4845i		−	1.56930i	−0.619939	−	0.784650i	$-0.712843\pi$
$353$		−	29.4845i		−	1.56930i	0.619939	−	0.784650i	$-0.287157\pi$
$354$	−10.7081	−	3.84131i	−0.569129	−	0.204163i
$355$	−32.5532	+	13.4840i	−1.72775	+	0.715656i
$356$	−12.9710	+	17.3044i	−0.687461	+	0.917130i
$357$	−6.08825	+	5.81660i	−0.322224	+	0.307847i
$358$	−10.3096	+	5.15654i	−0.544879	+	0.272532i
$359$	24.2350	+	24.2350i	1.27907	+	1.27907i	0.941187	+	0.337885i	$0.109711\pi$
$359$	24.2350	+	24.2350i	1.27907	+	1.27907i	0.337885	+	0.941187i	$0.390289\pi$
$360$	−6.15439	+	26.8801i	−0.324365	+	1.41671i
$361$	13.3913	−	13.3913i	0.704807	−	0.704807i
$362$	−3.35368	+	10.0656i	−0.176266	+	0.529035i
$363$	37.7392	+	39.5017i	1.98079	+	2.07330i
$364$	−0.330515	+	1.29153i	−0.0173237	+	0.0676947i
$365$	−7.13792	−	17.2325i	−0.373616	−	0.901988i
$366$	−7.44197	−	15.7681i	−0.388998	−	0.824211i
$367$	−1.91450			−0.0999363			−0.0499681	−	0.998751i	$-0.515912\pi$
$367$	−1.91450			−0.0999363			−0.0499681	+	0.998751i	$0.515912\pi$
$368$	−12.8077	+	23.3851i	−0.667647	+	1.21903i
$369$	−12.5717	−	13.7747i	−0.654455	−	0.717080i
$370$	−10.0811	+	11.6268i	−0.524091	+	0.604447i
$371$	5.56266	−	2.30413i	0.288799	−	0.119624i
$372$	−2.18383	−	18.2104i	−0.113226	−	0.944164i
$373$	−0.616798	+	1.48908i	−0.0319366	+	0.0771018i	−0.939043	−	0.343799i	$-0.888286\pi$
$373$	−0.616798	+	1.48908i	−0.0319366	+	0.0771018i	0.907107	+	0.420901i	$0.138286\pi$
$374$	−14.1745	+	42.5426i	−0.732946	+	2.19983i
$375$	2.94602	−	1.14226i	0.152132	−	0.0589862i
$376$	4.52000	+	20.8735i	0.233101	+	1.07647i
$377$	−2.82184	+	2.82184i	−0.145332	+	0.145332i
$378$	5.18242	−	5.20985i	0.266555	−	0.267966i
$379$	9.00316	−	21.7356i	0.462461	−	1.11648i	−0.504922	−	0.863165i	$-0.668479\pi$
$379$	9.00316	−	21.7356i	0.462461	−	1.11648i	0.967384	−	0.253316i	$-0.0815212\pi$
$380$	1.59941	−	0.228928i	0.0820481	−	0.0117437i
$381$	0.597402	−	26.1808i	0.0306058	−	1.34128i
$382$	−8.82092	+	0.628079i	−0.451318	+	0.0321353i
$383$	31.3827			1.60358			0.801791	−	0.597605i	$-0.203881\pi$
$383$	31.3827			1.60358			0.801791	+	0.597605i	$0.203881\pi$
$384$	17.4286	−	8.95795i	0.889398	−	0.457133i
$385$	−21.1966			−1.08028
$386$	9.60314	−	0.683776i	0.488787	−	0.0348033i
$387$	−5.87777	−	2.75514i	−0.298784	−	0.140052i
$388$	0.435815	−	0.0623793i	0.0221252	−	0.00316683i
$389$	−7.35326	+	17.7523i	−0.372825	+	0.900079i	0.620444	+	0.784251i	$0.286952\pi$
$389$	−7.35326	+	17.7523i	−0.372825	+	0.900079i	−0.993269	+	0.115828i	$0.963048\pi$
$390$	0.256027	+	5.30004i	0.0129644	+	0.268378i
$391$	−22.9135	+	22.9135i	−1.15878	+	1.15878i
$392$	0.598602	+	2.76436i	0.0302339	+	0.139621i
$393$	−6.97348	−	17.9854i	−0.351766	−	0.907242i
$394$	−5.46463	+	16.4013i	−0.275304	+	0.826284i
$395$	18.2812	−	44.1347i	0.919826	−	2.22066i
$396$	11.4214	−	37.4306i	0.573946	−	1.88096i
$397$	11.5559	−	4.78663i	0.579976	−	0.240234i	−0.0733557	−	0.997306i	$-0.523371\pi$
$397$	11.5559	−	4.78663i	0.579976	−	0.240234i	0.653331	+	0.757072i	$0.273371\pi$
$398$	3.44718	−	3.97571i	0.172791	−	0.199284i
$399$	−0.393924	−	0.173800i	−0.0197209	−	0.00870090i
$400$	−19.5108	−	10.6858i	−0.975539	−	0.534289i
$401$	10.5898			0.528828			0.264414	−	0.964409i	$-0.414821\pi$
$401$	10.5898			0.528828			0.264414	+	0.964409i	$0.414821\pi$
$402$	13.3769	−	6.31340i	0.667178	−	0.314884i
$403$	−1.35057	−	3.26057i	−0.0672769	−	0.162421i
$404$	−4.64920	+	18.1674i	−0.231306	+	0.903861i
$405$	13.6088	−	25.8895i	0.676229	−	1.28646i
$406$	−2.67631	+	8.03256i	−0.132823	+	0.398649i
$407$	15.4425	−	15.4425i	0.765457	−	0.765457i
$408$	23.3854	−	4.50804i	1.15775	−	0.223181i
$409$	−11.1734	−	11.1734i	−0.552488	−	0.552488i	0.374670	−	0.927158i	$-0.377756\pi$
$409$	−11.1734	−	11.1734i	−0.552488	−	0.552488i	−0.927158	+	0.374670i	$0.877756\pi$
$410$	25.5521	−	12.7804i	1.26193	−	0.631177i
$411$	−1.81508	−	1.89985i	−0.0895313	−	0.0937126i
$412$	−3.69463	+	4.92894i	−0.182021	+	0.242832i
$413$	−4.29080	+	1.77731i	−0.211137	+	0.0874557i
$414$	19.4816	−	20.4995i	0.957468	−	1.00750i
$415$			53.7836i			2.64014i
$416$	2.76384	−	2.56507i	0.135508	−	0.125763i
$417$	35.0825	+	15.4785i	1.71800	+	0.757983i
$418$	−2.28717	+	0.162854i	−0.111869	+	0.00796546i
$419$	4.05059	+	9.77898i	0.197884	+	0.477734i	0.991408	−	0.130804i	$-0.0417560\pi$
$419$	4.05059	+	9.77898i	0.197884	+	0.477734i	−0.793524	+	0.608539i	$0.791756\pi$
$420$	5.51590	+	9.81381i	0.269149	+	0.478865i
$421$	4.65223	+	1.92701i	0.226736	+	0.0939170i	0.493159	−	0.869939i	$-0.335842\pi$
$421$	4.65223	+	1.92701i	0.226736	+	0.0939170i	−0.266424	+	0.963856i	$0.585842\pi$
$422$	−0.551874	−	1.10338i	−0.0268648	−	0.0537115i
$423$	1.03326	−	22.6292i	0.0502389	−	1.10027i
$424$	−16.7564	−	3.03962i	−0.813765	−	0.147617i
$425$	−19.1173	−	19.1173i	−0.927324	−	0.927324i
$426$	−19.6636	−	17.8513i	−0.952702	−	0.864900i
$427$	−6.57639	−	2.72403i	−0.318254	−	0.131825i
$428$	0.229040	−	0.895007i	0.0110711	−	0.0432618i
$429$	0.171787	−	7.52844i	0.00829393	−	0.363476i
$430$	6.51483	−	7.51371i	0.314173	−	0.362343i
$431$		−	12.3214i		−	0.593501i	−0.954955	−	0.296751i	$-0.904097\pi$
$431$		−	12.3214i		−	0.593501i	0.954955	−	0.296751i	$-0.0959030\pi$
$432$	−20.3021	+	4.45242i	−0.976786	+	0.214217i
$433$			18.3568i			0.882172i	0.897465	+	0.441086i	$0.145407\pi$
$433$			18.3568i			0.882172i	−0.897465	+	0.441086i	$0.854593\pi$
$434$	−5.65721	−	4.90514i	−0.271555	−	0.235454i
$435$	−0.768757	+	33.6903i	−0.0368591	+	1.61533i
$436$	−0.276309	+	0.163706i	−0.0132328	+	0.00784008i
$437$	−1.53086	−	0.634101i	−0.0732308	−	0.0303332i
$438$	9.44983	−	10.4092i	0.451530	−	0.497368i
$439$	18.1055	+	18.1055i	0.864127	+	0.864127i	0.991814	−	0.127688i	$-0.0407556\pi$
$439$	18.1055	+	18.1055i	0.864127	+	0.864127i	−0.127688	+	0.991814i	$0.540756\pi$
$440$	50.4050	+	32.4610i	2.40296	+	1.54752i
$441$	0.136839	−	2.99688i	0.00651613	−	0.142708i
$442$	4.09866	−	2.05002i	0.194953	−	0.0975096i
$443$	−25.8953	−	10.7262i	−1.23032	−	0.509617i	−0.329646	−	0.944105i	$-0.606929\pi$
$443$	−25.8953	−	10.7262i	−1.23032	−	0.509617i	−0.900678	+	0.434488i	$0.856929\pi$
$444$	−11.1683	−	3.13118i	−0.530022	−	0.148599i
$445$	13.4477	+	32.4656i	0.637481	+	1.53902i
$446$	0.827971	+	11.6283i	0.0392056	+	0.550614i
$447$	−17.2027	−	7.58987i	−0.813660	−	0.358988i
$448$	2.80994	−	7.49028i	0.132757	−	0.353882i
$449$			24.5079i			1.15660i	0.815824	+	0.578300i	$0.196284\pi$
$449$			24.5079i			1.15660i	−0.815824	+	0.578300i	$0.803716\pi$
$450$	17.1033	+	16.2540i	0.806256	+	0.766220i
$451$	−37.4592	+	15.5161i	−1.76389	+	0.730625i
$452$	−21.0551	+	3.01366i	−0.990347	+	0.141751i
$453$	−28.7889	−	30.1335i	−1.35262	−	1.41579i
$454$	9.34474	+	18.6832i	0.438571	+	0.876845i
$455$	1.53177	+	1.53177i	0.0718107	+	0.0718107i
$456$	0.670580	+	1.01656i	0.0314028	+	0.0476046i
$457$	6.44946	−	6.44946i	0.301693	−	0.301693i	−0.539983	−	0.841676i	$-0.681569\pi$
$457$	6.44946	−	6.44946i	0.301693	−	0.301693i	0.841676	+	0.539983i	$0.181569\pi$
$458$	−13.4521	−	4.48201i	−0.628575	−	0.209431i
$459$	−25.2014	−	1.72756i	−1.17630	−	0.0806358i
$460$	22.0836	+	37.2737i	1.02965	+	1.73790i
$461$	1.77042	+	4.27416i	0.0824565	+	0.199068i	0.959731	−	0.280922i	$-0.0906403\pi$
$461$	1.77042	+	4.27416i	0.0824565	+	0.199068i	−0.877274	+	0.479990i	$0.840640\pi$
$462$	−6.81903	−	14.4482i	−0.317250	−	0.672192i
$463$	5.58393			0.259507			0.129754	−	0.991546i	$-0.458581\pi$
$463$	5.58393			0.259507			0.129754	+	0.991546i	$0.458581\pi$
$464$	18.6654	−	15.0026i	0.866521	−	0.696479i
$465$	−27.2663	−	12.0300i	−1.26445	−	0.557876i
$466$	5.24193	+	4.54507i	0.242828	+	0.210546i
$467$	8.76502	−	3.63059i	0.405597	−	0.168004i	−0.170552	−	0.985349i	$-0.554555\pi$
$467$	8.76502	−	3.63059i	0.405597	−	0.168004i	0.576148	+	0.817345i	$0.304555\pi$
$468$	−3.53029	+	1.87956i	−0.163188	+	0.0868825i
$469$	2.31093	−	5.57909i	0.106709	−	0.257618i
$470$	32.9243	+	10.9698i	1.51868	+	0.506000i
$471$	−5.28009	−	13.6179i	−0.243294	−	0.627481i
$472$	12.9252	+	2.34464i	0.594931	+	0.107921i
$473$	−9.97960	+	9.97960i	−0.458862	+	0.458862i
$474$	35.9645	−	1.73732i	1.65191	−	0.0797978i
$475$	0.529046	−	1.27723i	0.0242743	−	0.0586034i
$476$	5.83158	−	7.77981i	0.267290	−	0.356587i
$477$	16.3553	+	7.66638i	0.748859	+	0.351020i
$478$	0.904433	+	12.7021i	0.0413678	+	0.580981i
$479$	31.7707			1.45164			0.725820	−	0.687885i	$-0.241461\pi$
$479$	31.7707			1.45164			0.725820	+	0.687885i	$0.241461\pi$
$480$	1.91242	−	31.7841i	0.0872894	−	1.45074i
$481$	−2.23191			−0.101766
$482$	−0.633574	−	8.89808i	−0.0288585	−	0.405297i
$483$	0.263376	−	11.5423i	0.0119840	−	0.525193i
$484$	−50.4769	−	37.8364i	−2.29440	−	1.71983i
$485$	0.273763	−	0.660923i	0.0124310	−	0.0300110i
$486$	22.0250	+	0.947408i	0.999076	+	0.0429753i
$487$	19.3228	−	19.3228i	0.875598	−	0.875598i	−0.117478	−	0.993076i	$-0.537481\pi$
$487$	19.3228	−	19.3228i	0.875598	−	0.875598i	0.993076	+	0.117478i	$0.0374808\pi$
$488$	11.4668	+	16.5489i	0.519079	+	0.749133i
$489$	−23.8008	+	9.22829i	−1.07631	+	0.417318i
$490$	4.36029	+	1.45278i	0.196978	+	0.0656297i
$491$	−12.1745	+	29.3918i	−0.549427	+	1.32643i	0.368479	+	0.929636i	$0.379879\pi$
$491$	−12.1745	+	29.3918i	−0.549427	+	1.32643i	−0.917906	+	0.396798i	$0.870121\pi$
$492$	16.9316	+	13.3055i	0.763337	+	0.599859i
$493$	26.8890	−	11.1378i	1.21102	−	0.501621i
$494$	0.177051	+	0.153514i	0.00796590	+	0.00690691i
$495$	−42.8671	−	46.9690i	−1.92673	−	2.11110i
$496$	5.94086	+	20.3279i	0.266752	+	0.912748i
$497$	−10.8422			−0.486341
$498$	−36.6604	+	17.3024i	−1.64279	+	0.775339i
$499$	−7.20738	−	17.4002i	−0.322647	−	0.778938i	−0.999099	−	0.0424510i	$-0.986483\pi$
$499$	−7.20738	−	17.4002i	−0.322647	−	0.778938i	0.676452	−	0.736487i	$-0.263517\pi$
$500$	−3.13896	+	1.85975i	−0.140379	+	0.0831705i
$501$	1.69207	+	1.77110i	0.0755962	+	0.0791268i
$502$	−35.7799	−	11.9213i	−1.59694	−	0.532073i
$503$	−18.3771	+	18.3771i	−0.819392	+	0.819392i	−0.986020	−	0.166627i	$-0.946712\pi$
$503$	−18.3771	+	18.3771i	−0.819392	+	0.819392i	0.166627	+	0.986020i	$0.446712\pi$
$504$	−4.91488	+	6.91693i	−0.218926	+	0.308105i
$505$	21.5467	+	21.5467i	0.958817	+	0.958817i
$506$	−27.5042	−	54.9898i	−1.22271	−	2.44460i
$507$	15.7243	−	15.0227i	0.698340	−	0.667182i
$508$	4.28449	+	29.9338i	0.190094	+	1.32810i
$509$	14.6351	−	6.06207i	0.648690	−	0.268696i	−0.0339804	−	0.999422i	$-0.510818\pi$
$509$	14.6351	−	6.06207i	0.648690	−	0.268696i	0.682671	+	0.730726i	$0.260818\pi$
$510$	13.0670	−	36.4259i	0.578617	−	1.61296i
$511$		−	5.73948i		−	0.253900i
$512$	−18.1527	+	13.5085i	−0.802245	+	0.596995i
$513$	−0.411535	−	1.22437i	−0.0181697	−	0.0540573i
$514$	−3.01055	−	42.2809i	−0.132790	−	1.86493i
$515$	3.83041	+	9.24743i	0.168788	+	0.407490i
$516$	7.21740	+	2.02350i	0.317728	+	0.0890797i
$517$	−45.5012	−	18.8472i	−2.00114	−	0.828900i
$518$	−4.23503	+	2.11823i	−0.186076	+	0.0930696i
$519$	5.26366	+	13.5756i	0.231049	+	0.595901i
$520$	−1.29672	−	5.98831i	−0.0568651	−	0.262605i
$521$	20.9822	+	20.9822i	0.919247	+	0.919247i	0.996975	−	0.0777280i	$-0.0247666\pi$
$521$	20.9822	+	20.9822i	0.919247	+	0.919247i	−0.0777280	+	0.996975i	$0.524767\pi$
$522$	−23.2116	+	10.3143i	−1.01594	+	0.451444i
$523$	6.01798	+	2.49273i	0.263148	+	0.108999i	0.510357	−	0.859963i	$-0.329513\pi$
$523$	6.01798	+	2.49273i	0.263148	+	0.108999i	−0.247209	+	0.968962i	$0.579513\pi$
$524$	11.3537	+	19.1633i	0.495989	+	0.837152i
$525$	9.63002	+	0.219741i	0.420289	+	0.00959029i
$526$	−16.1517	−	14.0045i	−0.704247	−	0.610623i
$527$			25.7389i			1.12120i
$528$	−5.91083	+	44.8002i	−0.257236	+	1.94968i
$529$		−	21.4313i		−	0.931796i
$530$	−18.1280	+	20.9074i	−0.787429	+	0.908161i
$531$	−12.6158	−	5.91353i	−0.547479	−	0.256625i
$532$	0.481648	+	0.123258i	0.0208821	+	0.00534391i
$533$	3.82826	+	1.58572i	0.165820	+	0.0686851i
$534$	−17.8033	+	19.6106i	−0.770423	+	0.848634i
$535$	−1.06149	−	1.06149i	−0.0458922	−	0.0458922i
$536$	−14.0393	+	9.72790i	−0.606404	+	0.420181i
$537$	−13.1631	+	5.10375i	−0.568031	+	0.220243i
$538$	9.07775	+	18.1494i	0.391370	+	0.782475i
$539$	−6.02591	−	2.49601i	−0.259554	−	0.107511i
$540$	−10.5910	+	32.0695i	−0.455766	+	1.38005i
$541$	2.03386	+	4.91018i	0.0874426	+	0.211105i	0.961551	−	0.274625i	$-0.0885538\pi$
$541$	2.03386	+	4.91018i	0.0874426	+	0.211105i	−0.874109	+	0.485730i	$0.838554\pi$
$542$	23.0402	−	1.64054i	0.989662	−	0.0704673i
$543$	−5.24516	+	11.8883i	−0.225092	+	0.510178i
$544$	−25.7815	+	9.56957i	−1.10537	+	0.410292i
$545$			0.521863i			0.0223542i
$546$	−0.551322	+	1.53688i	−0.0235944	+	0.0657723i
$547$	4.93971	−	2.04609i	0.211207	−	0.0874847i	−0.274572	−	0.961567i	$-0.588536\pi$
$547$	4.93971	−	2.04609i	0.211207	−	0.0874847i	0.485779	+	0.874082i	$0.338536\pi$
$548$	2.42770	+	1.81975i	0.103706	+	0.0777361i
$549$	−7.26368	−	20.0814i	−0.310006	−	0.857053i
$550$	45.8794	−	22.9474i	1.95630	−	0.978482i
$551$	1.05234	+	1.05234i	0.0448313	+	0.0448313i
$552$	−18.3024	+	27.0439i	−0.779002	+	1.15107i
$553$	10.3942	−	10.3942i	0.442005	−	0.442005i
$554$	10.8552	−	32.5803i	0.461194	−	1.38420i
$555$	−13.6275	+	13.0195i	−0.578455	+	0.552645i
$556$	−42.8950	−	10.9772i	−1.81915	−	0.465538i
$557$	−8.90629	−	21.5017i	−0.377372	−	0.911056i	−0.992457	−	0.122595i	$-0.960878\pi$
$557$	−8.90629	−	21.5017i	−0.377372	−	0.911056i	0.615085	−	0.788461i	$-0.289122\pi$
$558$	−0.571722	−	22.4556i	−0.0242029	−	0.950620i
$559$	1.44235			0.0610050
$560$	−8.14383	−	10.1321i	−0.344140	−	0.428159i
$561$	−22.1689	+	50.2467i	−0.935973	+	2.12142i
$562$	5.78448	−	6.67138i	0.244003	−	0.281415i
$563$	−24.7931	+	10.2696i	−1.04490	+	0.432813i	−0.838070	−	0.545563i	$-0.816316\pi$
$563$	−24.7931	+	10.2696i	−1.04490	+	0.432813i	−0.206833	+	0.978376i	$0.566316\pi$
$564$	3.11452	+	25.9711i	0.131145	+	1.09358i
$565$	−13.2260	+	31.9305i	−0.556423	+	1.34332i
$566$	−12.0044	+	36.0293i	−0.504582	+	1.51443i
$567$	6.91743	−	5.75753i	0.290505	−	0.241793i
$568$	25.7826	+	16.6040i	1.08181	+	0.696690i
$569$	11.3040	−	11.3040i	0.473888	−	0.473888i	−0.429282	−	0.903170i	$-0.641233\pi$
$569$	11.3040	−	11.3040i	0.473888	−	0.473888i	0.903170	+	0.429282i	$0.141233\pi$
$570$	1.97653	−	0.0954793i	0.0827877	−	0.00399919i
$571$	−11.2145	+	27.0742i	−0.469313	+	1.13302i	0.495152	+	0.868807i	$0.335113\pi$
$571$	−11.2145	+	27.0742i	−0.469313	+	1.13302i	−0.964464	+	0.264214i	$0.914887\pi$
$572$	1.23203	+	8.60763i	0.0515138	+	0.359903i
$573$	−10.8279	−	0.247075i	−0.452342	−	0.0103217i
$574$	8.76906	−	0.624387i	0.366013	−	0.0260614i
$575$	37.0701			1.54593
$576$	22.2802	−	8.92152i	0.928341	−	0.371730i
$577$	45.2713			1.88467			0.942335	−	0.334671i	$-0.108625\pi$
$577$	45.2713			1.88467			0.942335	+	0.334671i	$0.108625\pi$
$578$	−9.35708	+	0.666256i	−0.389203	+	0.0277126i
$579$	11.7881	+	0.268985i	0.489897	+	0.0111786i
$580$	−5.51343	−	38.5198i	−0.228933	−	1.59945i
$581$	−6.33330	+	15.2899i	−0.262750	+	0.634334i
$582$	0.538574	−	0.0260167i	0.0223246	−	0.00107843i
$583$	27.7689	−	27.7689i	1.15007	−	1.15007i
$584$	−8.78956	+	13.6483i	−0.363715	+	0.564771i
$585$	−0.296428	+	6.49200i	−0.0122558	+	0.268411i
$586$	11.0102	−	33.0456i	0.454828	−	1.36510i
$587$	14.9635	−	36.1250i	0.617608	−	1.49104i	−0.236864	−	0.971543i	$-0.576120\pi$
$587$	14.9635	−	36.1250i	0.617608	−	1.49104i	0.854473	−	0.519496i	$-0.173880\pi$
$588$	0.412468	+	3.43946i	0.0170099	+	0.141841i
$589$	−1.21596	+	0.503666i	−0.0501027	+	0.0207532i
$590$	13.9832	−	16.1271i	0.575678	−	0.663943i
$591$	−8.54668	+	19.3714i	−0.351564	+	0.796831i
$592$	13.3147	+	1.44853i	0.547230	+	0.0595340i
$593$	−27.0888			−1.11240			−0.556201	−	0.831048i	$-0.687742\pi$
$593$	−27.0888			−1.11240			−0.556201	+	0.831048i	$0.687742\pi$
$594$	18.2249	−	44.3295i	0.747777	−	1.81886i
$595$	−6.04589	−	14.5961i	−0.247858	−	0.598381i
$596$	21.0336	+	5.38269i	0.861570	+	0.220483i
$597$	4.65985	−	4.45193i	0.190715	−	0.182206i
$598$	−1.98625	+	5.96143i	−0.0812238	+	0.243781i
$599$	26.1378	−	26.1378i	1.06796	−	1.06796i	0.0704466	−	0.997516i	$-0.477558\pi$
$599$	26.1378	−	26.1378i	1.06796	−	1.06796i	0.997516	−	0.0704466i	$-0.0224424\pi$
$600$	−22.5634	−	15.2702i	−0.921147	−	0.623402i
$601$	−5.52678	−	5.52678i	−0.225442	−	0.225442i	0.585343	−	0.810785i	$-0.300960\pi$
$601$	−5.52678	−	5.52678i	−0.225442	−	0.225442i	−0.810785	+	0.585343i	$0.800960\pi$
$602$	2.73685	−	1.36889i	0.111546	−	0.0557917i
$603$	17.0361	−	6.16215i	0.693762	−	0.250942i
$604$	38.5058	+	28.8631i	1.56678	+	1.17442i
$605$	−94.7020	+	39.2269i	−3.85019	+	1.59480i
$606$	−7.75519	+	21.6185i	−0.315033	+	0.878192i
$607$			0.284544i			0.0115493i	0.999983	+	0.00577463i	$0.00183813\pi$
$607$			0.284544i			0.0115493i	−0.999983	+	0.00577463i	$0.998162\pi$
$608$	−0.956585	−	1.03071i	−0.0387947	−	0.0418008i
$609$	−4.18576	+	9.48717i	−0.169615	+	0.384439i
$610$	32.6324	−	2.32354i	1.32125	−	0.0940772i
$611$	1.92615	+	4.65014i	0.0779237	+	0.188125i
$612$	29.0326	−	2.81149i	1.17357	−	0.113648i
$613$	−38.5933	−	15.9859i	−1.55877	−	0.645663i	−0.573893	−	0.818931i	$-0.694567\pi$
$613$	−38.5933	−	15.9859i	−1.55877	−	0.645663i	−0.984875	+	0.173268i	$0.944567\pi$
$614$	1.76764	+	3.53408i	0.0713360	+	0.142624i
$615$	32.6245	−	12.6495i	1.31555	−	0.510078i
$616$	10.5070	+	15.1637i	0.423339	+	0.610961i
$617$	34.1497	+	34.1497i	1.37482	+	1.37482i	0.853148	+	0.521668i	$0.174690\pi$
$617$	34.1497	+	34.1497i	1.37482	+	1.37482i	0.521668	+	0.853148i	$0.325310\pi$
$618$	−5.07105	+	5.58584i	−0.203987	+	0.224696i
$619$	40.9440	+	16.9596i	1.64568	+	0.681662i	0.996853	−	0.0792758i	$-0.0252608\pi$
$619$	40.9440	+	16.9596i	1.64568	+	0.681662i	0.648825	+	0.760938i	$0.275261\pi$
$620$	33.3383	+	8.53157i	1.33890	+	0.342636i
$621$	26.1089	−	22.7590i	1.04771	−	0.913286i
$622$	−8.17672	+	9.43040i	−0.327856	+	0.378125i
$623$			10.8130i			0.433216i
$624$	3.66463	−	2.81034i	0.146703	−	0.112504i
$625$		−	21.8782i		−	0.875127i
$626$	−3.24687	−	2.81523i	−0.129771	−	0.112519i
$627$	−2.80756	−	0.0640639i	−0.112123	−	0.00255847i
$628$	8.59665	+	14.5098i	0.343044	+	0.579004i
$629$	15.0384	+	6.22912i	0.599621	+	0.248371i
$630$	5.59888	+	12.5999i	0.223065	+	0.501991i
$631$	11.4730	+	11.4730i	0.456733	+	0.456733i	0.897582	−	0.440848i	$-0.145322\pi$
$631$	11.4730	+	11.4730i	0.456733	+	0.456733i	−0.440848	+	0.897582i	$0.645322\pi$
$632$	−40.6349	+	8.79919i	−1.61637	+	0.350013i
$633$	−0.546224	−	1.40877i	−0.0217105	−	0.0559937i
$634$	−6.92288	+	3.46261i	−0.274943	+	0.137518i
$635$	45.3952	+	18.8033i	1.80145	+	0.746186i
$636$	−20.0829	−	5.63054i	−0.796339	−	0.223265i
$637$	0.255088	+	0.615837i	0.0101069	+	0.0244003i
$638$	3.92214	+	55.0836i	0.155279	+	2.18078i
$639$	−21.9268	−	24.0250i	−0.867413	−	0.950415i
$640$	3.84929	+	36.5655i	0.152157	+	1.44538i
$641$			22.7737i			0.899507i	0.893153	+	0.449753i	$0.148488\pi$
$641$			22.7737i			0.899507i	−0.893153	+	0.449753i	$0.851512\pi$
$642$	0.382056	−	1.06503i	0.0150785	−	0.0420332i
$643$	13.4889	−	5.58730i	0.531952	−	0.220342i	−0.100506	−	0.994936i	$-0.532046\pi$
$643$	13.4889	−	5.58730i	0.531952	−	0.220342i	0.632458	+	0.774595i	$0.282046\pi$
$644$	1.88890	+	13.1969i	0.0744331	+	0.520029i
$645$	8.80667	−	8.41373i	0.346762	−	0.331290i
$646$	−0.764509	−	1.52850i	−0.0300792	−	0.0601382i
$647$	13.4351	+	13.4351i	0.528189	+	0.528189i	0.920032	−	0.391843i	$-0.128162\pi$
$647$	13.4351	+	13.4351i	0.528189	+	0.528189i	−0.391843	+	0.920032i	$0.628162\pi$
$648$	−25.2667	+	3.09773i	−0.992568	+	0.121690i
$649$	−21.4198	+	21.4198i	−0.840801	+	0.840801i
$650$	−4.97377	−	1.65718i	−0.195087	−	0.0649998i
$651$	−6.33485	−	6.63071i	−0.248282	−	0.259878i
$652$	25.3595	−	15.0248i	0.993156	−	0.588417i
$653$	−18.6845	−	45.1084i	−0.731182	−	1.76523i	−0.638619	−	0.769523i	$-0.720494\pi$
$653$	−18.6845	−	45.1084i	−0.731182	−	1.76523i	−0.0925630	−	0.995707i	$-0.529506\pi$
$654$	−0.355716	+	0.167885i	−0.0139096	+	0.00656483i
$655$	36.1935			1.41420
$656$	−21.8088	−	11.9443i	−0.851489	−	0.466348i
$657$	12.7180	−	11.6073i	0.496175	−	0.452842i
$658$	8.06816	+	6.99557i	0.314530	+	0.272716i
$659$	−31.4487	+	13.0265i	−1.22507	+	0.507440i	−0.899018	−	0.437912i	$-0.855718\pi$
$659$	−31.4487	+	13.0265i	−1.22507	+	0.507440i	−0.326051	+	0.945352i	$0.605718\pi$
$660$	57.7337	+	45.3694i	2.24728	+	1.76600i
$661$	−14.3225	+	34.5775i	−0.557079	+	1.34491i	0.354989	+	0.934871i	$0.384485\pi$
$661$	−14.3225	+	34.5775i	−0.557079	+	1.34491i	−0.912068	+	0.410038i	$0.865515\pi$
$662$	−13.7924	−	4.59539i	−0.536056	−	0.178605i
$663$	5.23311	−	2.02904i	0.203237	−	0.0788013i
$664$	38.4758	−	26.6601i	1.49315	−	1.03461i
$665$	0.571240	−	0.571240i	0.0221518	−	0.0221518i
$666$	−13.2584	−	5.10048i	−0.513754	−	0.197639i
$667$	−15.2715	+	36.8687i	−0.591315	+	1.42756i
$668$	−2.26318	−	1.69643i	−0.0875650	−	0.0656369i
$669$	−0.325709	+	14.2740i	−0.0125926	+	0.551864i
$670$	1.97117	+	27.6837i	0.0761530	+	1.06951i
$671$	−46.4279			−1.79233
$672$	4.28642	−	8.81060i	0.165352	−	0.339876i
$673$	−1.19148			−0.0459281			−0.0229641	−	0.999736i	$-0.507310\pi$
$673$	−1.19148			−0.0459281			−0.0229641	+	0.999736i	$0.507310\pi$
$674$	0.228102	+	3.20353i	0.00878615	+	0.123395i
$675$	18.9884	+	21.7833i	0.730863	+	0.838439i
$676$	−15.0614	+	20.0931i	−0.579284	+	0.772813i
$677$	−8.75045	+	21.1255i	−0.336307	+	0.811918i	0.661757	+	0.749719i	$0.269811\pi$
$677$	−8.75045	+	21.1255i	−0.336307	+	0.811918i	−0.998064	+	0.0621988i	$0.980189\pi$
$678$	−26.0195	+	1.25691i	−0.999275	+	0.0482715i
$679$	0.155654	−	0.155654i	0.00597346	−	0.00597346i
$680$	−7.97578	+	43.9679i	−0.305857	+	1.68609i
$681$	9.24908	+	23.8544i	0.354426	+	0.914103i
$682$	−46.3331	−	15.4374i	−1.77419	−	0.591130i
$683$	12.4132	−	29.9681i	0.474978	−	1.14670i	−0.486958	−	0.873425i	$-0.661894\pi$
$683$	12.4132	−	29.9681i	0.474978	−	1.14670i	0.961936	−	0.273273i	$-0.0881064\pi$
$684$	0.700938	+	1.31654i	0.0268010	+	0.0503392i
$685$	4.55473	−	1.88663i	0.174027	−	0.0720845i
$686$	1.06850	+	0.926451i	0.0407955	+	0.0353721i
$687$	−15.8881	−	7.00987i	−0.606169	−	0.267443i
$688$	−8.60451	−	0.936098i	−0.328044	−	0.0356884i
$689$	−4.01345			−0.152900
$690$	22.6475	+	47.9856i	0.862174	+	1.82678i
$691$	−8.72257	−	21.0582i	−0.331822	−	0.801090i	−0.998448	−	0.0556969i	$-0.982262\pi$
$691$	−8.72257	−	21.0582i	−0.331822	−	0.801090i	0.666625	−	0.745393i	$-0.267738\pi$
$692$	−8.56990	−	14.4646i	−0.325779	−	0.549863i
$693$	−6.65567	−	18.4005i	−0.252828	−	0.698976i
$694$	0.943869	+	0.314482i	0.0358288	+	0.0119376i
$695$	−50.8740	+	50.8740i	−1.92976	+	1.92976i
$696$	24.4825	−	16.1501i	0.928005	−	0.612166i
$697$	−21.3689	−	21.3689i	−0.809405	−	0.809405i
$698$	0.701786	+	1.40310i	0.0265630	+	0.0531081i
$699$	5.86983	+	6.14397i	0.222017	+	0.232386i
$700$	−11.0105	+	1.57596i	−0.416157	+	0.0595655i
$701$	−28.2171	+	11.6879i	−1.06574	+	0.441446i	−0.845487	−	0.533996i	$-0.820690\pi$
$701$	−28.2171	+	11.6879i	−1.06574	+	0.441446i	−0.220257	+	0.975442i	$0.570690\pi$
$702$	−4.52049	+	1.88645i	−0.170615	+	0.0711994i
$703$			0.832339i			0.0313922i
$704$	−1.76339	−	52.1494i	−0.0664604	−	1.96545i
$705$	38.8865	+	17.1568i	1.46455	+	0.646162i
$706$	2.96149	+	41.5920i	0.111457	+	1.56534i
$707$	3.58820	+	8.66268i	0.134948	+	0.325794i
$708$	15.4911	+	4.34316i	0.582192	+	0.163226i
$709$	31.9480	+	13.2333i	1.19983	+	0.496986i	0.890944	−	0.454113i	$-0.150044\pi$
$709$	31.9480	+	13.2333i	1.19983	+	0.496986i	0.308886	+	0.951099i	$0.400044\pi$
$710$	44.5666	−	22.2908i	1.67255	−	0.836559i
$711$	44.0528	+	2.01147i	1.65211	+	0.0754361i
$712$	16.5593	−	25.7131i	0.620587	−	0.963640i
$713$	−24.9550	−	24.9550i	−0.934573	−	0.934573i
$714$	8.00411	−	8.81666i	0.299546	−	0.329955i
$715$	13.0537	+	5.40700i	0.488179	+	0.202210i
$716$	14.0252	−	8.30955i	0.524147	−	0.310543i
$717$	−0.355788	+	15.5922i	−0.0132871	+	0.582300i
$718$	−36.6211	−	31.7526i	−1.36669	−	1.18500i
$719$		−	16.3447i		−	0.609554i	−0.952424	−	0.304777i	$-0.901418\pi$
$719$		−	16.3447i		−	0.609554i	0.952424	−	0.304777i	$-0.0985820\pi$
$720$	5.98174	−	38.5364i	0.222926	−	1.43617i
$721$			3.07997i			0.114704i
$722$	−17.5453	+	20.2354i	−0.652969	+	0.753085i
$723$	0.249236	−	10.9226i	0.00926920	−	0.406217i
$724$	3.71984	−	14.5358i	0.138247	−	0.540218i
$725$	−30.7605	−	12.7414i	−1.14242	−	0.473204i
$726$	−57.2041	−	51.9321i	−2.12304	−	1.92738i
$727$	18.7110	+	18.7110i	0.693953	+	0.693953i	0.963099	−	0.269146i	$-0.0867414\pi$
$727$	18.7110	+	18.7110i	0.693953	+	0.693953i	−0.269146	+	0.963099i	$0.586741\pi$
$728$	0.336513	−	1.85509i	0.0124720	−	0.0687542i
$729$	26.7474	+	3.68440i	0.990646	+	0.136459i
$730$	11.7999	+	23.5919i	0.436735	+	0.873175i
$731$	−9.71846	−	4.02552i	−0.359450	−	0.148889i
$732$	12.0817	+	21.4956i	0.446554	+	0.794502i
$733$	−0.274462	−	0.662610i	−0.0101375	−	0.0244741i	0.918730	−	0.394887i	$-0.129216\pi$
$733$	−0.274462	−	0.662610i	−0.0101375	−	0.0244741i	−0.928867	+	0.370413i	$0.879216\pi$
$734$	2.70068	−	0.192298i	0.0996839	−	0.00709783i
$735$	5.14989	+	2.27214i	0.189957	+	0.0838093i
$736$	15.7182	−	34.2745i	0.579381	−	1.26337i
$737$		−	39.3872i		−	1.45085i
$738$	19.1177	+	18.1684i	0.703732	+	0.668787i
$739$	4.72742	−	1.95816i	0.173901	−	0.0720321i	−0.294034	−	0.955795i	$-0.594998\pi$
$739$	4.72742	−	1.95816i	0.173901	−	0.0720321i	0.467935	+	0.883763i	$0.344998\pi$
$740$	13.0530	−	17.4138i	0.479838	−	0.640143i
$741$	0.198259	+	0.207518i	0.00728322	+	0.00762336i
$742$	−7.61549	+	3.80903i	−0.279573	+	0.139834i
$743$	19.2519	+	19.2519i	0.706284	+	0.706284i	0.965752	−	0.259468i	$-0.0835473\pi$
$743$	19.2519	+	19.2519i	0.706284	+	0.706284i	−0.259468	+	0.965752i	$0.583547\pi$
$744$	4.90970	+	25.4690i	0.179998	+	0.933737i
$745$	24.9461	−	24.9461i	0.913955	−	0.913955i
$746$	0.720515	−	2.16252i	0.0263799	−	0.0791753i
$747$	−46.6887	+	16.8879i	−1.70825	+	0.617895i
$748$	15.7221	−	61.4361i	0.574855	−	2.24633i
$749$	−0.176771	−	0.426763i	−0.00645907	−	0.0155936i
$750$	−4.04105	+	1.90723i	−0.147558	+	0.0696422i
$751$	1.01430			0.0370122			0.0185061	−	0.999829i	$-0.494109\pi$
$751$	1.01430			0.0370122			0.0185061	+	0.999829i	$0.494109\pi$
$752$	−8.47269	−	28.9910i	−0.308967	−	1.05719i
$753$	−42.2593	−	18.6449i	−1.54002	−	0.679458i
$754$	3.69718	−	4.26405i	0.134643	−	0.155287i
$755$	72.2425	−	29.9238i	2.62917	−	1.08904i
$756$	−6.78724	+	7.86977i	−0.246850	+	0.286221i
$757$	5.77112	−	13.9327i	0.209755	−	0.506393i	−0.783630	−	0.621228i	$-0.786634\pi$
$757$	5.77112	−	13.9327i	0.209755	−	0.506393i	0.993385	+	0.114835i	$0.0366340\pi$
$758$	−10.5171	+	31.5654i	−0.381997	+	1.14651i
$759$	−27.2226	−	70.2102i	−0.988119	−	2.54847i
$760$	−2.23320	+	0.483584i	−0.0810068	+	0.0175414i
$761$	−13.1483	+	13.1483i	−0.476624	+	0.476624i	−0.904050	−	0.427426i	$-0.859420\pi$
$761$	−13.1483	+	13.1483i	−0.476624	+	0.476624i	0.427426	+	0.904050i	$0.359420\pi$
$762$	1.78694	+	36.9917i	0.0647341	+	1.34007i
$763$	−0.0614521	+	0.148358i	−0.00222472	+	0.00537094i
$764$	12.3801	−	1.77199i	0.447895	−	0.0641084i
$765$	20.1161	−	42.9154i	0.727300	−	1.55161i
$766$	−44.2698	+	3.15216i	−1.59953	+	0.113892i
$767$	3.09580			0.111783
$768$	−23.6857	+	14.3870i	−0.854685	+	0.519147i
$769$	−11.6013			−0.418352			−0.209176	−	0.977878i	$-0.567078\pi$
$769$	−11.6013			−0.418352			−0.209176	+	0.977878i	$0.567078\pi$
$770$	29.9009	−	2.12904i	1.07755	−	0.0767253i
$771$	1.18429	−	51.9010i	0.0426513	−	1.86917i
$772$	−13.4779	+	1.92913i	−0.485081	+	0.0694308i
$773$	−9.84562	+	23.7694i	−0.354122	+	0.854927i	0.641980	+	0.766721i	$0.278113\pi$
$773$	−9.84562	+	23.7694i	−0.354122	+	0.854927i	−0.996102	+	0.0882054i	$0.971887\pi$
$774$	8.56817	+	3.29614i	0.307976	+	0.118477i
$775$	20.8206	−	20.8206i	0.747898	−	0.747898i
$776$	−0.608514	+	0.131769i	−0.0218444	+	0.00473024i
$777$	−5.40722	+	2.09654i	−0.193983	+	0.0752131i
$778$	8.58973	−	25.7808i	0.307957	−	0.924285i
$779$	0.591357	−	1.42766i	0.0211876	−	0.0511513i
$780$	−0.893511	−	7.45074i	−0.0319928	−	0.266779i
$781$	−65.3344	+	27.0624i	−2.33785	+	0.968368i
$782$	30.0212	−	34.6242i	1.07356	−	1.23816i
$783$	−29.4874	+	9.91130i	−1.05379	+	0.354201i
$784$	−1.12207	−	3.83940i	−0.0400740	−	0.137121i
$785$	27.4045			0.978109
$786$	11.6436	+	24.6705i	0.415313	+	0.879968i
$787$	−3.27447	−	7.90527i	−0.116722	−	0.281792i	0.854712	−	0.519103i	$-0.173734\pi$
$787$	−3.27447	−	7.90527i	−0.116722	−	0.281792i	−0.971434	+	0.237311i	$0.923734\pi$
$788$	6.06125	−	23.6852i	0.215923	−	0.843750i
$789$	−18.0864	−	18.9311i	−0.643892	−	0.673964i
$790$	−21.3552	+	64.0944i	−0.759784	+	2.28038i
$791$	−7.51995	+	7.51995i	−0.267379	+	0.267379i
$792$	−12.3519	+	53.9484i	−0.438905	+	1.91697i
$793$	3.35512	+	3.35512i	0.119144	+	0.119144i
$794$	−15.8205	+	7.91292i	−0.561449	+	0.280819i
$795$	−24.5052	+	23.4118i	−0.869109	+	0.830331i
$796$	−4.46340	+	5.95455i	−0.158201	+	0.211053i
$797$	−2.58831	+	1.07211i	−0.0916827	+	0.0379762i	−0.428053	−	0.903753i	$-0.640800\pi$
$797$	−2.58831	+	1.07211i	−0.0916827	+	0.0379762i	0.336371	+	0.941730i	$0.390800\pi$
$798$	0.573143	+	0.205603i	0.0202891	+	0.00727828i
$799$		−	36.7081i		−	1.29864i
$800$	28.5960	+	13.1141i	1.01102	+	0.463653i
$801$	−23.9603	+	21.8678i	−0.846597	+	0.772661i
$802$	−14.9384	+	1.06366i	−0.527493	+	0.0375593i
$803$	−14.3258	−	34.5856i	−0.505547	−	1.22050i
$804$	−18.2358	+	10.2496i	−0.643129	+	0.361474i
$805$	20.0133	+	8.28979i	0.705377	+	0.292177i
$806$	2.23268	+	4.46385i	0.0786427	+	0.157232i
$807$	8.98482	+	23.1729i	0.316281	+	0.815723i
$808$	4.73357	−	26.0946i	0.166527	−	0.918007i
$809$	−2.51714	−	2.51714i	−0.0884979	−	0.0884979i	0.661472	−	0.749970i	$-0.269932\pi$
$809$	−2.51714	−	2.51714i	−0.0884979	−	0.0884979i	−0.749970	+	0.661472i	$0.769932\pi$
$810$	−16.5968	+	37.8878i	−0.583152	+	1.33124i
$811$	−28.5171	−	11.8122i	−1.00137	−	0.414782i	−0.179072	−	0.983836i	$-0.557309\pi$
$811$	−28.5171	−	11.8122i	−1.00137	−	0.414782i	−0.822300	+	0.569054i	$0.807309\pi$
$812$	2.96851	−	11.5999i	0.104174	−	0.407076i
$813$	28.2825	+	0.645359i	0.991910	+	0.0226337i
$814$	−20.2328	+	23.3349i	−0.709158	+	0.817889i
$815$		−	47.8963i		−	1.67774i
$816$	−32.5356	+	8.70811i	−1.13897	+	0.304845i
$817$		−	0.537892i		−	0.0188185i
$818$	16.8839	+	14.6394i	0.590333	+	0.511853i
$819$	−0.848737	+	1.81068i	−0.0296573	+	0.0632703i
$820$	−34.7612	+	20.5950i	−1.21391	+	0.719209i
$821$	6.79764	+	2.81568i	0.237239	+	0.0982678i	0.498136	−	0.867099i	$-0.334018\pi$
$821$	6.79764	+	2.81568i	0.237239	+	0.0982678i	−0.260896	+	0.965367i	$0.584018\pi$
$822$	2.75125	+	2.49770i	0.0959610	+	0.0871171i
$823$	4.74340	+	4.74340i	0.165344	+	0.165344i	0.784929	−	0.619585i	$-0.212699\pi$
$823$	4.74340	+	4.74340i	0.165344	+	0.165344i	−0.619585	+	0.784929i	$0.712699\pi$
$824$	4.71673	−	7.32407i	0.164315	−	0.255146i
$825$	58.5781	−	22.7125i	2.03943	−	0.790748i
$826$	5.87427	−	2.93813i	0.204392	−	0.102230i
$827$	19.1847	+	7.94655i	0.667116	+	0.276329i	0.690430	−	0.723400i	$-0.257421\pi$
$827$	19.1847	+	7.94655i	0.667116	+	0.276329i	−0.0233132	+	0.999728i	$0.507421\pi$
$828$	−25.4225	+	30.8743i	−0.883495	+	1.07296i
$829$	−13.3958	−	32.3403i	−0.465255	−	1.12323i	−0.966211	−	0.257753i	$-0.917018\pi$
$829$	−13.3958	−	32.3403i	−0.465255	−	1.12323i	0.500956	−	0.865473i	$-0.332982\pi$
$830$	−5.40216	−	75.8695i	−0.187512	−	2.63347i
$831$	16.9776	−	38.4802i	0.588945	−	1.33486i
$832$	−3.64114	+	3.89600i	−0.126234	+	0.135070i
$833$		−	4.86140i		−	0.168438i
$834$	−51.0435	−	18.3108i	−1.76749	−	0.634051i
$835$	−4.24606	+	1.75878i	−0.146941	+	0.0608649i
$836$	3.21002	−	0.459458i	0.111021	−	0.0158907i
$837$	1.88149	−	27.4469i	0.0650338	−	0.948702i
$838$	−6.69615	−	13.3878i	−0.231315	−	0.462474i
$839$	5.07708	+	5.07708i	0.175280	+	0.175280i	0.789295	−	0.614014i	$-0.210446\pi$
$839$	5.07708	+	5.07708i	0.175280	+	0.175280i	−0.614014	+	0.789295i	$0.710446\pi$
$840$	−8.76669	−	13.2897i	−0.302480	−	0.458540i
$841$	4.83824	−	4.83824i	0.166836	−	0.166836i
$842$	−6.75618	−	2.25105i	−0.232833	−	0.0775762i
$843$	7.81939	−	7.47050i	0.269314	−	0.257298i
$844$	0.889322	+	1.50104i	0.0306117	+	0.0516678i
$845$	15.6149	+	37.6977i	0.537169	+	1.29684i
$846$	0.815374	+	32.0255i	0.0280331	+	1.10106i
$847$	−31.5417			−1.08378
$848$	23.9427	+	2.60476i	0.822194	+	0.0894478i
$849$	−18.7749	+	42.5539i	−0.644351	+	1.46045i
$850$	28.8878	+	25.0474i	0.990844	+	0.859120i
$851$	−20.6198	+	8.54102i	−0.706839	+	0.292782i
$852$	29.5313	+	23.2068i	1.01172	+	0.795052i
$853$	9.74139	−	23.5178i	0.333539	−	0.805234i	−0.664767	−	0.747051i	$-0.731469\pi$
$853$	9.74139	−	23.5178i	0.333539	−	0.805234i	0.998306	−	0.0581835i	$-0.0185309\pi$
$854$	9.55054	+	3.18208i	0.326813	+	0.108889i
$855$	2.42105	+	0.110546i	0.0827980	+	0.00378060i
$856$	−0.233197	+	1.28554i	−0.00797051	+	0.0439388i
$857$	−7.62957	+	7.62957i	−0.260621	+	0.260621i	−0.825306	−	0.564685i	$-0.808998\pi$
$857$	−7.62957	+	7.62957i	−0.260621	+	0.260621i	0.564685	+	0.825306i	$0.308998\pi$
$858$	0.513846	+	10.6372i	0.0175424	+	0.363148i
$859$	2.05531	−	4.96195i	0.0701261	−	0.169299i	−0.884930	−	0.465723i	$-0.845794\pi$
$859$	2.05531	−	4.96195i	0.0701261	−	0.169299i	0.955056	+	0.296424i	$0.0957942\pi$
$860$	−8.43540	+	11.2535i	−0.287645	+	0.383742i
$861$	10.7642	+	0.245622i	0.366845	+	0.00837079i
$862$	1.23759	+	17.3811i	0.0421526	+	0.592003i
$863$	−32.3277			−1.10045			−0.550224	−	0.835017i	$-0.685458\pi$
$863$	−32.3277			−1.10045			−0.550224	+	0.835017i	$0.685458\pi$
$864$	28.1918	−	8.31997i	0.959105	−	0.283051i
$865$	−27.3193			−0.928883
$866$	−1.84380	−	25.8949i	−0.0626550	−	0.879944i
$867$	−11.4861	−	0.262093i	−0.390087	−	0.00890115i
$868$	8.47299	+	6.35117i	0.287592	+	0.215573i
$869$	36.6903	−	88.5783i	1.24463	−	3.00481i
$870$	−2.29950	−	47.6022i	−0.0779603	−	1.61387i
$871$	−2.84631	+	2.84631i	−0.0964437	+	0.0964437i
$872$	0.373331	−	0.258683i	0.0126426	−	0.00876012i
$873$	0.659698	+	0.0301221i	0.0223274	+	0.00101948i
$874$	2.22318	+	0.740727i	0.0752002	+	0.0250555i
$875$	−0.698116	+	1.68540i	−0.0236006	+	0.0569769i
$876$	−12.2848	+	15.6328i	−0.415065	+	0.528182i
$877$	9.45154	−	3.91496i	0.319156	−	0.132199i	−0.217354	−	0.976093i	$-0.569743\pi$
$877$	9.45154	−	3.91496i	0.319156	−	0.132199i	0.536510	+	0.843894i	$0.319743\pi$
$878$	−27.3589	−	23.7218i	−0.923318	−	0.800571i
$879$	17.2200	−	39.0298i	0.580816	−	1.31644i
$880$	−74.3638	−	40.7280i	−2.50680	−	1.37294i
$881$	27.6612			0.931929			0.465964	−	0.884803i	$-0.345707\pi$
$881$	27.6612			0.931929			0.465964	+	0.884803i	$0.345707\pi$
$882$	0.107983	+	4.24127i	0.00363598	+	0.142811i
$883$	−6.51736	−	15.7343i	−0.219327	−	0.529501i	0.775470	−	0.631385i	$-0.217513\pi$
$883$	−6.51736	−	15.7343i	−0.219327	−	0.529501i	−0.994796	+	0.101883i	$0.967513\pi$
$884$	−5.57584	+	3.30353i	−0.187536	+	0.111110i
$885$	18.9023	−	18.0589i	0.635393	−	0.607043i
$886$	37.6064	+	12.5298i	1.26341	+	0.420948i
$887$	−29.8243	+	29.8243i	−1.00140	+	1.00140i	−0.00140254	+	0.999999i	$0.500446\pi$
$887$	−29.8243	+	29.8243i	−1.00140	+	1.00140i	−0.999999	+	0.00140254i	$0.999554\pi$
$888$	16.0689	+	3.29521i	0.539237	+	0.110580i
$889$	10.6910	+	10.6910i	0.358566	+	0.358566i
$890$	−22.2308	−	44.4466i	−0.745178	−	1.48985i
$891$	27.3130	−	51.9603i	0.915019	−	1.74074i
$892$	−2.33594	−	16.3201i	−0.0782131	−	0.546439i
$893$	1.73416	−	0.718314i	0.0580316	−	0.0240375i
$894$	25.0292	+	8.97871i	0.837102	+	0.300293i
$895$		−	26.4893i		−	0.885440i
$896$	−3.21148	+	10.8483i	−0.107288	+	0.362418i
$897$	−3.10650	+	7.04098i	−0.103723	+	0.235092i
$898$	−2.46164	−	34.5719i	−0.0821458	−	1.15368i
$899$	12.1302	+	29.2848i	0.404563	+	0.976702i
$900$	−25.7592	−	21.2107i	−0.858639	−	0.707022i
$901$	27.0423	+	11.2013i	0.900910	+	0.373169i
$902$	51.2831	−	25.6502i	1.70754	−	0.854058i
$903$	3.49437	−	1.35488i	0.116285	−	0.0450874i
$904$	29.3985	−	6.36602i	0.977778	−	0.211731i
$905$	−17.2396	−	17.2396i	−0.573064	−	0.573064i
$906$	43.6376	+	39.6159i	1.44976	+	1.31615i
$907$	−21.0117	−	8.70334i	−0.697683	−	0.288990i	0.00551419	−	0.999985i	$-0.498245\pi$
$907$	−21.0117	−	8.70334i	−0.697683	−	0.288990i	−0.703197	+	0.710995i	$0.748245\pi$
$908$	−15.0587	−	25.4167i	−0.499740	−	0.843482i
$909$	−11.9388	+	25.4700i	−0.395984	+	0.844786i
$910$	−2.31464	−	2.00693i	−0.0767296	−	0.0665291i
$911$			36.6059i			1.21281i	0.795157	+	0.606403i	$0.207388\pi$
$911$			36.6059i			1.21281i	−0.795157	+	0.606403i	$0.792612\pi$
$912$	−1.04805	−	1.36664i	−0.0347045	−	0.0452541i
$913$			107.944i			3.57242i
$914$	−8.45008	+	9.74568i	−0.279504	+	0.322358i
$915$	40.0571	+	0.914037i	1.32425	+	0.0302171i
$916$	19.4263	+	4.97135i	0.641862	+	0.164258i
$917$	10.2893	+	4.26197i	0.339783	+	0.140743i
$918$	35.7237	−	0.0943197i	1.17906	−	0.00311302i
$919$	−19.4782	−	19.4782i	−0.642526	−	0.642526i	0.308650	−	0.951176i	$-0.400123\pi$
$919$	−19.4782	−	19.4782i	−0.642526	−	0.642526i	−0.951176	+	0.308650i	$0.900123\pi$
$920$	−34.8960	−	50.3617i	−1.15049	−	1.66038i
$921$	1.74954	+	4.51226i	0.0576494	+	0.148684i
$922$	−2.92673	−	5.85149i	−0.0963868	−	0.192709i
$923$	6.67705	+	2.76573i	0.219778	+	0.0910350i
$924$	11.0704	+	19.6963i	0.364190	+	0.647962i
$925$	−7.12599	−	17.2037i	−0.234301	−	0.565653i
$926$	−7.87693	+	0.560864i	−0.258852	+	0.0184311i
$927$	−6.82481	+	6.22878i	−0.224156	+	0.204580i
$928$	−24.8233	+	23.0381i	−0.814866	+	0.756264i
$929$		−	33.1826i		−	1.08869i	−0.838863	−	0.544343i	$-0.816779\pi$
$929$		−	33.1826i		−	1.08869i	0.838863	−	0.544343i	$-0.183221\pi$
$930$	39.6714	+	14.2313i	1.30088	+	0.466662i
$931$	0.229662	−	0.0951292i	0.00752688	−	0.00311773i
$932$	−7.85101	−	5.88495i	−0.257168	−	0.192768i
$933$	−11.0532	+	10.5600i	−0.361865	+	0.345719i
$934$	−11.9996	+	6.00184i	−0.392640	+	0.196386i
$935$	−72.8640	−	72.8640i	−2.38291	−	2.38291i
$936$	4.79119	−	3.00597i	0.156605	−	0.0982533i
$937$	−14.2544	+	14.2544i	−0.465671	+	0.465671i	−0.900509	−	0.434838i	$-0.856806\pi$
$937$	−14.2544	+	14.2544i	−0.465671	+	0.465671i	0.434838	+	0.900509i	$0.356806\pi$
$938$	−2.69952	+	8.10221i	−0.0881425	+	0.264546i
$939$	−3.63579	−	3.80559i	−0.118649	−	0.124191i
$940$	−47.5462	−	12.1675i	−1.55079	−	0.396860i
$941$	−0.610301	−	1.47340i	−0.0198952	−	0.0480314i	0.913620	−	0.406570i	$-0.133275\pi$
$941$	−0.610301	−	1.47340i	−0.0198952	−	0.0480314i	−0.933515	+	0.358538i	$0.883275\pi$
$942$	8.81613	+	18.6797i	0.287245	+	0.608617i
$943$	41.4363			1.34935
$944$	−18.4684	−	2.00920i	−0.601094	−	0.0653940i
$945$	5.38012	+	16.0066i	0.175015	+	0.520694i
$946$	13.0753	−	15.0800i	0.425114	−	0.490294i
$947$	24.1463	−	10.0017i	0.784651	−	0.325013i	0.0458600	−	0.998948i	$-0.485397\pi$
$947$	24.1463	−	10.0017i	0.784651	−	0.325013i	0.738791	+	0.673935i	$0.235397\pi$
$948$	−50.5586	+	6.06311i	−1.64207	+	0.196921i
$949$	−1.46407	+	3.53458i	−0.0475258	+	0.114737i
$950$	−0.618007	+	1.85485i	−0.0200508	+	0.0601794i
$951$	−8.83902	+	3.42716i	−0.286625	+	0.111133i
$952$	−7.44485	+	11.5603i	−0.241289	+	0.374671i
$953$	36.2147	−	36.2147i	1.17311	−	1.17311i	0.191643	−	0.981465i	$-0.438618\pi$
$953$	36.2147	−	36.2147i	1.17311	−	1.17311i	0.981465	−	0.191643i	$-0.0613816\pi$
$954$	−23.8415	−	9.17175i	−0.771898	−	0.296946i
$955$	7.77672	−	18.7747i	0.251649	−	0.607534i
$956$	−2.55166	−	17.8273i	−0.0825267	−	0.576576i
$957$	−1.54290	+	67.6165i	−0.0498748	+	2.18573i
$958$	−44.8170	+	3.19113i	−1.44797	+	0.103101i
$959$	1.51701			0.0489867
$960$	0.494744	+	45.0281i	0.0159678	+	1.45328i
$961$	2.96779			0.0957350
$962$	3.14842	−	0.224178i	0.101509	−	0.00722779i
$963$	0.588158	−	1.25477i	0.0189531	−	0.0404343i
$964$	1.78749	+	12.4884i	0.0575712	+	0.402223i
$965$	−8.46634	+	20.4396i	−0.272541	+	0.657973i
$966$	0.787807	+	16.3085i	0.0253473	+	0.524717i
$967$	−28.0445	+	28.0445i	−0.901851	+	0.901851i	−0.995596	−	0.0937453i	$-0.970116\pi$
$967$	−28.0445	+	28.0445i	−0.901851	+	0.901851i	0.0937453	+	0.995596i	$0.470116\pi$
$968$	75.0052	+	48.3036i	2.41076	+	1.55254i
$969$	−0.756683	−	1.95157i	−0.0243082	−	0.0626935i
$970$	−0.319797	+	0.959824i	−0.0102681	+	0.0308181i
$971$	−0.560281	+	1.35264i	−0.0179803	+	0.0434082i	−0.932615	−	0.360874i	$-0.882479\pi$
$971$	−0.560281	+	1.35264i	−0.0179803	+	0.0434082i	0.914634	+	0.404282i	$0.132479\pi$
$972$	−31.1646	+	0.875797i	−0.999605	+	0.0280912i
$973$	−20.4535	+	8.47210i	−0.655708	+	0.271603i
$974$	−25.3167	+	29.1983i	−0.811199	+	0.935575i
$975$	−5.87447	−	2.59183i	−0.188133	−	0.0830049i
$976$	−17.8378	−	22.1928i	−0.570974	−	0.710374i
$977$	−35.4992			−1.13572			−0.567859	−	0.823126i	$-0.692228\pi$
$977$	−35.4992			−1.13572			−0.567859	+	0.823126i	$0.692228\pi$
$978$	32.6475	−	15.4084i	1.04395	−	0.492707i
$979$	26.9895	+	65.1584i	0.862589	+	2.08247i
$980$	−6.29673	−	1.61139i	−0.201142	−	0.0514739i
$981$	−0.453021	+	0.163863i	−0.0144639	+	0.00523175i
$982$	14.2217	−	42.6842i	0.453831	−	1.36211i
$983$	−9.13478	+	9.13478i	−0.291354	+	0.291354i	−0.837615	−	0.546261i	$-0.816051\pi$
$983$	−9.13478	+	9.13478i	−0.291354	+	0.291354i	0.546261	+	0.837615i	$0.316051\pi$
$984$	−25.2209	−	17.0687i	−0.804014	−	0.544130i
$985$	−28.0909	−	28.0909i	−0.895051	−	0.895051i
$986$	−36.8121	+	18.4122i	−1.17233	+	0.586365i
$987$	9.03459	+	9.45653i	0.287574	+	0.301005i
$988$	−0.265175	−	0.198769i	−0.00843634	−	0.00632370i
$989$	13.3254	−	5.51957i	0.423724	−	0.175512i
$990$	65.1878	+	61.9508i	2.07180	+	1.96893i
$991$			11.7665i			0.373774i	0.982381	+	0.186887i	$0.0598399\pi$
$991$			11.7665i			0.373774i	−0.982381	+	0.186887i	$0.940160\pi$
$992$	−10.4222	−	28.0786i	−0.330905	−	0.891497i
$993$	−16.2900	−	7.18720i	−0.516949	−	0.228079i
$994$	15.2945	−	1.08902i	0.485113	−	0.0345417i
$995$	4.62743	+	11.1716i	0.146699	+	0.354164i
$996$	49.9768	−	28.0897i	1.58358	−	0.890058i
$997$	39.6568	+	16.4264i	1.25594	+	0.520229i	0.908662	−	0.417532i	$-0.137105\pi$
$997$	39.6568	+	16.4264i	1.25594	+	0.520229i	0.347282	+	0.937761i	$0.387105\pi$
$998$	11.9147	+	23.8215i	0.377155	+	0.754055i
$999$	−15.5810	−	7.74176i	−0.492960	−	0.244938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bs.b.155.3	✓	192
3.2	odd	2	inner	672.2.bs.b.155.46	yes	192
32.19	odd	8	inner	672.2.bs.b.659.46	yes	192
96.83	even	8	inner	672.2.bs.b.659.3	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bs.b.155.3	✓	192	1.1	even	1	trivial
672.2.bs.b.155.46	yes	192	3.2	odd	2	inner
672.2.bs.b.659.3	yes	192	96.83	even	8	inner
672.2.bs.b.659.46	yes	192	32.19	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bs (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41064 + 0.100442i) q^{2} +(-1.73160 - 0.0395123i) q^{3} +(1.97982 - 0.283377i) q^{4} +(1.24365 - 3.00244i) q^{5} +(2.44664 - 0.118189i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.76436 + 0.598602i) q^{8} +(2.99688 + 0.136839i) q^{9} +O(q^{10})\)	\(q+(-1.41064 + 0.100442i) q^{2} +(-1.73160 - 0.0395123i) q^{3} +(1.97982 - 0.283377i) q^{4} +(1.24365 - 3.00244i) q^{5} +(2.44664 - 0.118189i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.76436 + 0.598602i) q^{8} +(2.99688 + 0.136839i) q^{9} +(-1.45278 + 4.36029i) q^{10} +(2.49601 - 6.02591i) q^{11} +(-3.43946 + 0.412468i) q^{12} +(-0.615837 + 0.255088i) q^{13} +(-0.926451 + 1.06850i) q^{14} +(-2.27214 + 5.14989i) q^{15} +(3.83940 - 1.12207i) q^{16} +4.86140 q^{17} +(-4.24127 + 0.107983i) q^{18} +(0.0951292 + 0.229662i) q^{19} +(1.61139 - 6.29673i) q^{20} +(-1.25237 + 1.19649i) q^{21} +(-2.91572 + 8.75111i) q^{22} +(-4.71335 + 4.71335i) q^{23} +(4.81041 - 0.927313i) q^{24} +(-3.93246 - 3.93246i) q^{25} +(0.843103 - 0.421694i) q^{26} +(-5.18399 - 0.355364i) q^{27} +(1.19957 - 1.60032i) q^{28} +(5.53112 - 2.29107i) q^{29} +(2.68791 - 7.49288i) q^{30} +5.29455i q^{31} +(-5.30331 + 1.96848i) q^{32} +(-4.56019 + 10.3358i) q^{33} +(-6.85770 + 0.488291i) q^{34} +(-1.24365 - 3.00244i) q^{35} +(5.97206 - 0.578329i) q^{36} +(3.09343 + 1.28134i) q^{37} +(-0.157261 - 0.314416i) q^{38} +(1.07646 - 0.417377i) q^{39} +(-1.64063 + 9.04428i) q^{40} +(-4.39563 - 4.39563i) q^{41} +(1.64646 - 1.81361i) q^{42} +(-1.99911 - 0.828058i) q^{43} +(3.23406 - 12.6375i) q^{44} +(4.13793 - 8.82778i) q^{45} +(6.17543 - 7.12227i) q^{46} -7.55093i q^{47} +(-6.69263 + 1.79128i) q^{48} -1.00000i q^{49} +(5.94228 + 5.15231i) q^{50} +(-8.41800 - 0.192085i) q^{51} +(-1.14696 + 0.679543i) q^{52} +(5.56266 + 2.30413i) q^{53} +(7.34844 - 0.0194018i) q^{54} +(-14.9883 - 14.9883i) q^{55} +(-1.53142 + 2.37797i) q^{56} +(-0.155651 - 0.401442i) q^{57} +(-7.57231 + 3.78743i) q^{58} +(-4.29080 - 1.77731i) q^{59} +(-3.03908 + 10.8397i) q^{60} +(-2.72403 - 6.57639i) q^{61} +(-0.531797 - 7.46871i) q^{62} +(2.21587 - 2.02235i) q^{63} +(7.28335 - 3.30950i) q^{64} +2.16626i q^{65} +(5.39464 - 15.0382i) q^{66} +(5.57909 - 2.31093i) q^{67} +(9.62471 - 1.37761i) q^{68} +(8.34787 - 7.97540i) q^{69} +(2.05592 + 4.11046i) q^{70} +(-7.66663 - 7.66663i) q^{71} +(-8.36635 + 1.41566i) q^{72} +(4.05842 - 4.05842i) q^{73} +(-4.49243 - 1.49680i) q^{74} +(6.65407 + 6.96483i) q^{75} +(0.253420 + 0.427733i) q^{76} +(-2.49601 - 6.02591i) q^{77} +(-1.47658 + 0.696892i) q^{78} +14.6996 q^{79} +(1.40592 - 12.9230i) q^{80} +(8.96255 + 0.820178i) q^{81} +(6.64217 + 5.75915i) q^{82} +(-15.2899 + 6.33330i) q^{83} +(-2.14040 + 2.72372i) q^{84} +(6.04589 - 14.5961i) q^{85} +(2.90320 + 0.967298i) q^{86} +(-9.66822 + 3.74866i) q^{87} +(-3.29276 + 18.1519i) q^{88} +(-7.64598 + 7.64598i) q^{89} +(-4.95045 + 12.8685i) q^{90} +(-0.255088 + 0.615837i) q^{91} +(-7.99594 + 10.6672i) q^{92} +(0.209199 - 9.16804i) q^{93} +(0.758434 + 10.6517i) q^{94} +0.807856 q^{95} +(9.26099 - 3.19907i) q^{96} +0.220128 q^{97} +(0.100442 + 1.41064i) q^{98} +(8.30482 - 17.7174i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{4}+O(q^{10}) \) 192 * q + 16 * q^4	\( 192 q + 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} + 44 q^{30} - 104 q^{36} - 32 q^{37} + 24 q^{39} + 32 q^{46} - 32 q^{48} - 80 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} + 80 q^{61} + 64 q^{64} + 76 q^{66} - 32 q^{67} - 56 q^{69} - 24 q^{70} + 60 q^{72} - 80 q^{75} - 56 q^{76} - 76 q^{78} - 32 q^{79} + 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} + 80 q^{93} - 120 q^{94} - 32 q^{96} - 64 q^{99}+O(q^{100}) \) 192 * q + 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 + 44 * q^30 - 104 * q^36 - 32 * q^37 + 24 * q^39 + 32 * q^46 - 32 * q^48 - 80 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 + 80 * q^61 + 64 * q^64 + 76 * q^66 - 32 * q^67 - 56 * q^69 - 24 * q^70 + 60 * q^72 - 80 * q^75 - 56 * q^76 - 76 * q^78 - 32 * q^79 + 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 + 80 * q^93 - 120 * q^94 - 32 * q^96 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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