LMFDB - Embedded newform 370.2.h.e.253.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 103x^16 - 394x^15 + 760x^14 + 278x^13 + 2009x^12 - 7362x^11 + 13826x^10 + 4848x^9 + 13544x^8 - 44248x^7 + 76384x^6 + 24512x^5 + 28432x^4 - 61952x^3 + 61952x^2 - 5632*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.8
Root			$1.29397 + 1.29397i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.e.117.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(1.29397 - 1.29397i) q^{3} +1.00000 q^{4} +(-2.20164 + 0.390851i) q^{5} +(-1.29397 + 1.29397i) q^{6} +(-2.67087 + 2.67087i) q^{7} -1.00000 q^{8} -0.348729i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(1.29397 - 1.29397i) q^{3} +1.00000 q^{4} +(-2.20164 + 0.390851i) q^{5} +(-1.29397 + 1.29397i) q^{6} +(-2.67087 + 2.67087i) q^{7} -1.00000 q^{8} -0.348729i q^{9} +(2.20164 - 0.390851i) q^{10} +1.29587i q^{11} +(1.29397 - 1.29397i) q^{12} -6.92612 q^{13} +(2.67087 - 2.67087i) q^{14} +(-2.34312 + 3.35462i) q^{15} +1.00000 q^{16} +4.85071i q^{17} +0.348729i q^{18} +(-4.69555 - 4.69555i) q^{19} +(-2.20164 + 0.390851i) q^{20} +6.91207i q^{21} -1.29587i q^{22} +3.33959 q^{23} +(-1.29397 + 1.29397i) q^{24} +(4.69447 - 1.72103i) q^{25} +6.92612 q^{26} +(3.43067 + 3.43067i) q^{27} +(-2.67087 + 2.67087i) q^{28} +(3.73955 - 3.73955i) q^{29} +(2.34312 - 3.35462i) q^{30} +(-0.146916 - 0.146916i) q^{31} -1.00000 q^{32} +(1.67682 + 1.67682i) q^{33} -4.85071i q^{34} +(4.83640 - 6.92422i) q^{35} -0.348729i q^{36} +(-6.03371 + 0.770943i) q^{37} +(4.69555 + 4.69555i) q^{38} +(-8.96221 + 8.96221i) q^{39} +(2.20164 - 0.390851i) q^{40} +6.38351i q^{41} -6.91207i q^{42} -2.51195 q^{43} +1.29587i q^{44} +(0.136301 + 0.767778i) q^{45} -3.33959 q^{46} +(-2.93686 + 2.93686i) q^{47} +(1.29397 - 1.29397i) q^{48} -7.26713i q^{49} +(-4.69447 + 1.72103i) q^{50} +(6.27669 + 6.27669i) q^{51} -6.92612 q^{52} +(-1.30971 - 1.30971i) q^{53} +(-3.43067 - 3.43067i) q^{54} +(-0.506490 - 2.85304i) q^{55} +(2.67087 - 2.67087i) q^{56} -12.1518 q^{57} +(-3.73955 + 3.73955i) q^{58} +(4.70039 + 4.70039i) q^{59} +(-2.34312 + 3.35462i) q^{60} +(-7.81965 - 7.81965i) q^{61} +(0.146916 + 0.146916i) q^{62} +(0.931412 + 0.931412i) q^{63} +1.00000 q^{64} +(15.2488 - 2.70708i) q^{65} +(-1.67682 - 1.67682i) q^{66} +(3.10789 + 3.10789i) q^{67} +4.85071i q^{68} +(4.32133 - 4.32133i) q^{69} +(-4.83640 + 6.92422i) q^{70} -5.59124 q^{71} +0.348729i q^{72} +(0.134980 - 0.134980i) q^{73} +(6.03371 - 0.770943i) q^{74} +(3.84755 - 8.30148i) q^{75} +(-4.69555 - 4.69555i) q^{76} +(-3.46110 - 3.46110i) q^{77} +(8.96221 - 8.96221i) q^{78} +(10.8080 + 10.8080i) q^{79} +(-2.20164 + 0.390851i) q^{80} +9.92458 q^{81} -6.38351i q^{82} +(-8.74652 - 8.74652i) q^{83} +6.91207i q^{84} +(-1.89590 - 10.6795i) q^{85} +2.51195 q^{86} -9.67775i q^{87} -1.29587i q^{88} +(3.83829 - 3.83829i) q^{89} +(-0.136301 - 0.767778i) q^{90} +(18.4988 - 18.4988i) q^{91} +3.33959 q^{92} -0.380211 q^{93} +(2.93686 - 2.93686i) q^{94} +(12.1732 + 8.50267i) q^{95} +(-1.29397 + 1.29397i) q^{96} -13.2514i q^{97} +7.26713i q^{98} +0.451907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	$ 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) $ 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	1.29397	−	1.29397i	0.747075	−	0.747075i	−0.226854	−	0.973929i	$-0.572844\pi$
$3$	1.29397	−	1.29397i	0.747075	−	0.747075i	0.973929	+	0.226854i	$0.0728439\pi$
$4$	1.00000			0.500000
$5$	−2.20164	+	0.390851i	−0.984605	+	0.174794i
$5$	−2.20164	+	0.390851i	−0.984605	+	0.174794i
$6$	−1.29397	+	1.29397i	−0.528262	+	0.528262i
$7$	−2.67087	+	2.67087i	−1.00950	+	1.00950i	−0.00954076	+	0.999954i	$0.503037\pi$
$7$	−2.67087	+	2.67087i	−1.00950	+	1.00950i	−0.999954	+	0.00954076i	$0.996963\pi$
$8$	−1.00000			−0.353553
$9$		−	0.348729i		−	0.116243i
$10$	2.20164	−	0.390851i	0.696221	−	0.123598i
$11$			1.29587i			0.390719i	0.980732	+	0.195359i	$0.0625873\pi$
$11$			1.29587i			0.390719i	−0.980732	+	0.195359i	$0.937413\pi$
$12$	1.29397	−	1.29397i	0.373538	−	0.373538i
$13$	−6.92612			−1.92096			−0.960480	−	0.278349i	$-0.910213\pi$
$13$	−6.92612			−1.92096			−0.960480	+	0.278349i	$0.910213\pi$
$14$	2.67087	−	2.67087i	0.713821	−	0.713821i
$15$	−2.34312	+	3.35462i	−0.604990	+	0.866158i
$16$	1.00000			0.250000
$17$			4.85071i			1.17647i	0.808690	+	0.588235i	$0.200177\pi$
$17$			4.85071i			1.17647i	−0.808690	+	0.588235i	$0.799823\pi$
$18$			0.348729i			0.0821963i
$19$	−4.69555	−	4.69555i	−1.07723	−	1.07723i	−0.996756	−	0.0804769i	$-0.974356\pi$
$19$	−4.69555	−	4.69555i	−1.07723	−	1.07723i	−0.0804769	−	0.996756i	$-0.525644\pi$
$20$	−2.20164	+	0.390851i	−0.492303	+	0.0873969i
$21$			6.91207i			1.50834i
$22$		−	1.29587i		−	0.276280i
$23$	3.33959			0.696352			0.348176	−	0.937429i	$-0.386801\pi$
$23$	3.33959			0.696352			0.348176	+	0.937429i	$0.386801\pi$
$24$	−1.29397	+	1.29397i	−0.264131	+	0.264131i
$25$	4.69447	−	1.72103i	0.938894	−	0.344206i
$26$	6.92612			1.35832
$27$	3.43067	+	3.43067i	0.660233	+	0.660233i
$28$	−2.67087	+	2.67087i	−0.504748	+	0.504748i
$29$	3.73955	−	3.73955i	0.694417	−	0.694417i	−0.268783	−	0.963201i	$-0.586622\pi$
$29$	3.73955	−	3.73955i	0.694417	−	0.694417i	0.963201	+	0.268783i	$0.0866216\pi$
$30$	2.34312	−	3.35462i	0.427793	−	0.612466i
$31$	−0.146916	−	0.146916i	−0.0263869	−	0.0263869i	0.693790	−	0.720177i	$-0.255939\pi$
$31$	−0.146916	−	0.146916i	−0.0263869	−	0.0263869i	−0.720177	+	0.693790i	$0.755939\pi$
$32$	−1.00000			−0.176777
$33$	1.67682	+	1.67682i	0.291896	+	0.291896i
$34$		−	4.85071i		−	0.831890i
$35$	4.83640	−	6.92422i	0.817501	−	1.17041i
$36$		−	0.348729i		−	0.0581216i
$37$	−6.03371	+	0.770943i	−0.991936	+	0.126742i
$37$	−6.03371	+	0.770943i	−0.991936	+	0.126742i
$38$	4.69555	+	4.69555i	0.761719	+	0.761719i
$39$	−8.96221	+	8.96221i	−1.43510	+	1.43510i
$40$	2.20164	−	0.390851i	0.348110	−	0.0617989i
$41$			6.38351i			0.996937i	0.866908	+	0.498469i	$0.166104\pi$
$41$			6.38351i			0.996937i	−0.866908	+	0.498469i	$0.833896\pi$
$42$		−	6.91207i		−	1.06656i
$43$	−2.51195			−0.383069			−0.191535	−	0.981486i	$-0.561346\pi$
$43$	−2.51195			−0.383069			−0.191535	+	0.981486i	$0.561346\pi$
$44$			1.29587i			0.195359i
$45$	0.136301	+	0.767778i	0.0203186	+	0.114454i
$46$	−3.33959			−0.492395
$47$	−2.93686	+	2.93686i	−0.428385	+	0.428385i	−0.888078	−	0.459693i	$-0.847960\pi$
$47$	−2.93686	+	2.93686i	−0.428385	+	0.428385i	0.459693	+	0.888078i	$0.347960\pi$
$48$	1.29397	−	1.29397i	0.186769	−	0.186769i
$49$		−	7.26713i		−	1.03816i
$50$	−4.69447	+	1.72103i	−0.663899	+	0.243390i
$51$	6.27669	+	6.27669i	0.878912	+	0.878912i
$52$	−6.92612			−0.960480
$53$	−1.30971	−	1.30971i	−0.179902	−	0.179902i	0.611411	−	0.791313i	$-0.290602\pi$
$53$	−1.30971	−	1.30971i	−0.179902	−	0.179902i	−0.791313	+	0.611411i	$0.790602\pi$
$54$	−3.43067	−	3.43067i	−0.466855	−	0.466855i
$55$	−0.506490	−	2.85304i	−0.0682952	−	0.384704i
$56$	2.67087	−	2.67087i	0.356910	−	0.356910i
$57$	−12.1518			−1.60955
$58$	−3.73955	+	3.73955i	−0.491027	+	0.491027i
$59$	4.70039	+	4.70039i	0.611938	+	0.611938i	0.943451	−	0.331512i	$-0.107559\pi$
$59$	4.70039	+	4.70039i	0.611938	+	0.611938i	−0.331512	+	0.943451i	$0.607559\pi$
$60$	−2.34312	+	3.35462i	−0.302495	+	0.433079i
$61$	−7.81965	−	7.81965i	−1.00120	−	1.00120i	−0.999999	−	0.00120494i	$-0.999616\pi$
$61$	−7.81965	−	7.81965i	−1.00120	−	1.00120i	−0.00120494	−	0.999999i	$-0.500384\pi$
$62$	0.146916	+	0.146916i	0.0186584	+	0.0186584i
$63$	0.931412	+	0.931412i	0.117347	+	0.117347i
$64$	1.00000			0.125000
$65$	15.2488	−	2.70708i	1.89139	−	0.335772i
$66$	−1.67682	−	1.67682i	−0.206402	−	0.206402i
$67$	3.10789	+	3.10789i	0.379690	+	0.379690i	0.870990	−	0.491301i	$-0.163478\pi$
$67$	3.10789	+	3.10789i	0.379690	+	0.379690i	−0.491301	+	0.870990i	$0.663478\pi$
$68$			4.85071i			0.588235i
$69$	4.32133	−	4.32133i	0.520227	−	0.520227i
$70$	−4.83640	+	6.92422i	−0.578060	+	0.827603i
$71$	−5.59124			−0.663558			−0.331779	−	0.943357i	$-0.607649\pi$
$71$	−5.59124			−0.663558			−0.331779	+	0.943357i	$0.607649\pi$
$72$			0.348729i			0.0410982i
$73$	0.134980	−	0.134980i	0.0157983	−	0.0157983i	−0.699164	−	0.714962i	$-0.746444\pi$
$73$	0.134980	−	0.134980i	0.0157983	−	0.0157983i	0.714962	+	0.699164i	$0.246444\pi$
$74$	6.03371	−	0.770943i	0.701404	−	0.0896204i
$75$	3.84755	−	8.30148i	0.444277	−	0.958572i
$76$	−4.69555	−	4.69555i	−0.538617	−	0.538617i
$77$	−3.46110	−	3.46110i	−0.394429	−	0.394429i
$78$	8.96221	−	8.96221i	1.01477	−	1.01477i
$79$	10.8080	+	10.8080i	1.21600	+	1.21600i	0.969021	+	0.246978i	$0.0794376\pi$
$79$	10.8080	+	10.8080i	1.21600	+	1.21600i	0.246978	+	0.969021i	$0.420562\pi$
$80$	−2.20164	+	0.390851i	−0.246151	+	0.0436984i
$81$	9.92458			1.10273
$82$		−	6.38351i		−	0.704941i
$83$	−8.74652	−	8.74652i	−0.960055	−	0.960055i	0.0391772	−	0.999232i	$-0.487526\pi$
$83$	−8.74652	−	8.74652i	−0.960055	−	0.960055i	−0.999232	+	0.0391772i	$0.987526\pi$
$84$			6.91207i			0.754169i
$85$	−1.89590	−	10.6795i	−0.205640	−	1.15836i
$86$	2.51195			0.270871
$87$		−	9.67775i		−	1.03756i
$88$		−	1.29587i		−	0.138140i
$89$	3.83829	−	3.83829i	0.406858	−	0.406858i	−0.473783	−	0.880642i	$-0.657112\pi$
$89$	3.83829	−	3.83829i	0.406858	−	0.406858i	0.880642	+	0.473783i	$0.157112\pi$
$90$	−0.136301	−	0.767778i	−0.0143674	−	0.0809309i
$91$	18.4988	−	18.4988i	1.93920	−	1.93920i
$92$	3.33959			0.348176
$93$	−0.380211			−0.0394261
$94$	2.93686	−	2.93686i	0.302914	−	0.302914i
$95$	12.1732	+	8.50267i	1.24894	+	0.872356i
$96$	−1.29397	+	1.29397i	−0.132066	+	0.132066i
$97$		−	13.2514i		−	1.34547i	−0.739882	−	0.672737i	$-0.765119\pi$
$97$		−	13.2514i		−	1.34547i	0.739882	−	0.672737i	$-0.234881\pi$
$98$			7.26713i			0.734091i
$99$	0.451907			0.0454184
$100$	4.69447	−	1.72103i	0.469447	−	0.172103i
$101$			13.7890i			1.37205i	0.727577	+	0.686026i	$0.240646\pi$
$101$			13.7890i			1.37205i	−0.727577	+	0.686026i	$0.759354\pi$
$102$	−6.27669	−	6.27669i	−0.621485	−	0.621485i
$103$			10.6833i			1.05265i	0.850283	+	0.526327i	$0.176431\pi$
$103$			10.6833i			1.05265i	−0.850283	+	0.526327i	$0.823569\pi$
$104$	6.92612			0.679162
$105$	−2.70159	−	15.2179i	−0.263648	−	1.48512i
$106$	1.30971	+	1.30971i	0.127210	+	0.127210i
$107$	−7.62669	+	7.62669i	−0.737300	+	0.737300i	−0.972055	−	0.234755i	$-0.924571\pi$
$107$	−7.62669	+	7.62669i	−0.737300	+	0.737300i	0.234755	+	0.972055i	$0.424571\pi$
$108$	3.43067	+	3.43067i	0.330116	+	0.330116i
$109$	−3.39395	−	3.39395i	−0.325081	−	0.325081i	0.525631	−	0.850713i	$-0.323829\pi$
$109$	−3.39395	−	3.39395i	−0.325081	−	0.325081i	−0.850713	+	0.525631i	$0.823829\pi$
$110$	0.506490	+	2.85304i	0.0482920	+	0.272027i
$111$	−6.80987	+	8.80503i	−0.646365	+	0.835737i
$112$	−2.67087	+	2.67087i	−0.252374	+	0.252374i
$113$		−	4.28955i		−	0.403527i	−0.979434	−	0.201764i	$-0.935333\pi$
$113$		−	4.28955i		−	0.403527i	0.979434	−	0.201764i	$-0.0646673\pi$
$114$	12.1518			1.13812
$115$	−7.35258	+	1.30528i	−0.685632	+	0.121718i
$116$	3.73955	−	3.73955i	0.347209	−	0.347209i
$117$			2.41534i			0.223298i
$118$	−4.70039	−	4.70039i	−0.432706	−	0.432706i
$119$	−12.9556	−	12.9556i	−1.18764	−	1.18764i
$120$	2.34312	−	3.35462i	0.213896	−	0.306233i
$121$	9.32073			0.847339
$122$	7.81965	+	7.81965i	0.707958	+	0.707958i
$123$	8.26009	+	8.26009i	0.744787	+	0.744787i
$124$	−0.146916	−	0.146916i	−0.0131935	−	0.0131935i
$125$	−9.66289	+	5.62393i	−0.864275	+	0.503019i
$126$	−0.931412	−	0.931412i	−0.0829768	−	0.0829768i
$127$	0.938326	−	0.938326i	0.0832629	−	0.0832629i	−0.664249	−	0.747512i	$-0.731248\pi$
$127$	0.938326	−	0.938326i	0.0832629	−	0.0832629i	0.747512	+	0.664249i	$0.231248\pi$
$128$	−1.00000			−0.0883883
$129$	−3.25040	+	3.25040i	−0.286182	+	0.286182i
$130$	−15.2488	+	2.70708i	−1.33741	+	0.237426i
$131$	2.47395	+	2.47395i	0.216150	+	0.216150i	0.806874	−	0.590724i	$-0.201158\pi$
$131$	2.47395	+	2.47395i	0.216150	+	0.216150i	−0.590724	+	0.806874i	$0.701158\pi$
$132$	1.67682	+	1.67682i	0.145948	+	0.145948i
$133$	25.0824			2.17492
$134$	−3.10789	−	3.10789i	−0.268481	−	0.268481i
$135$	−8.89400	−	6.21224i	−0.765473	−	0.534664i
$136$		−	4.85071i		−	0.415945i
$137$	14.6348	−	14.6348i	1.25034	−	1.25034i	0.294767	−	0.955569i	$-0.404758\pi$
$137$	14.6348	−	14.6348i	1.25034	−	1.25034i	0.955569	−	0.294767i	$-0.0952420\pi$
$138$	−4.32133	+	4.32133i	−0.367856	+	0.367856i
$139$	−14.2080			−1.20511			−0.602554	−	0.798078i	$-0.705850\pi$
$139$	−14.2080			−1.20511			−0.602554	+	0.798078i	$0.705850\pi$
$140$	4.83640	−	6.92422i	0.408750	−	0.585204i
$141$			7.60043i			0.640072i
$142$	5.59124			0.469207
$143$		−	8.97533i		−	0.750555i
$144$		−	0.348729i		−	0.0290608i
$145$	−6.77155	+	9.69476i	−0.562347	+	0.805106i
$146$	−0.134980	+	0.134980i	−0.0111711	+	0.0111711i
$147$	−9.40346	−	9.40346i	−0.775585	−	0.775585i
$148$	−6.03371	+	0.770943i	−0.495968	+	0.0633712i
$149$			7.52248i			0.616266i	0.951343	+	0.308133i	$0.0997041\pi$
$149$			7.52248i			0.616266i	−0.951343	+	0.308133i	$0.900296\pi$
$150$	−3.84755	+	8.30148i	−0.314152	+	0.677813i
$151$			4.35018i			0.354012i	0.984210	+	0.177006i	$0.0566412\pi$
$151$			4.35018i			0.354012i	−0.984210	+	0.177006i	$0.943359\pi$
$152$	4.69555	+	4.69555i	0.380860	+	0.380860i
$153$	1.69159			0.136757
$154$	3.46110	+	3.46110i	0.278903	+	0.278903i
$155$	0.380880	+	0.266035i	0.0305930	+	0.0213684i
$156$	−8.96221	+	8.96221i	−0.717551	+	0.717551i
$157$	−13.0961	+	13.0961i	−1.04518	+	1.04518i	−0.0462518	+	0.998930i	$0.514728\pi$
$157$	−13.0961	+	13.0961i	−1.04518	+	1.04518i	−0.998930	+	0.0462518i	$0.985272\pi$
$158$	−10.8080	−	10.8080i	−0.859841	−	0.859841i
$159$	−3.38945			−0.268801
$160$	2.20164	−	0.390851i	0.174055	−	0.0308995i
$161$	−8.91961	+	8.91961i	−0.702964	+	0.702964i
$162$	−9.92458			−0.779748
$163$			14.8033i			1.15948i	0.814801	+	0.579741i	$0.196846\pi$
$163$			14.8033i			1.15948i	−0.814801	+	0.579741i	$0.803154\pi$
$164$			6.38351i			0.498469i
$165$	−4.34714	−	3.03637i	−0.338424	−	0.236381i
$166$	8.74652	+	8.74652i	0.678861	+	0.678861i
$167$			1.13442i			0.0877842i	0.999036	+	0.0438921i	$0.0139758\pi$
$167$			1.13442i			0.0877842i	−0.999036	+	0.0438921i	$0.986024\pi$
$168$		−	6.91207i		−	0.533278i
$169$	34.9711			2.69009
$170$	1.89590	+	10.6795i	0.145409	+	0.819083i
$171$	−1.63748	+	1.63748i	−0.125221	+	0.125221i
$172$	−2.51195			−0.191535
$173$	7.57033	−	7.57033i	0.575562	−	0.575562i	−0.358116	−	0.933677i	$-0.616581\pi$
$173$	7.57033	−	7.57033i	0.575562	−	0.575562i	0.933677	+	0.358116i	$0.116581\pi$
$174$			9.67775i			0.733668i
$175$	−7.94169	+	17.1350i	−0.600335	+	1.29528i
$176$			1.29587i			0.0976797i
$177$	12.1643			0.914328
$178$	−3.83829	+	3.83829i	−0.287692	+	0.287692i
$179$	−5.64137	+	5.64137i	−0.421656	+	0.421656i	−0.885773	−	0.464118i	$-0.846371\pi$
$179$	−5.64137	+	5.64137i	−0.421656	+	0.421656i	0.464118	+	0.885773i	$0.346371\pi$
$180$	0.136301	+	0.767778i	0.0101593	+	0.0572268i
$181$	−5.21779			−0.387835			−0.193918	−	0.981018i	$-0.562119\pi$
$181$	−5.21779			−0.387835			−0.193918	+	0.981018i	$0.562119\pi$
$182$	−18.4988	+	18.4988i	−1.37122	+	1.37122i
$183$	−20.2368			−1.49595
$184$	−3.33959			−0.246198
$185$	12.9828	−	4.05562i	0.954511	−	0.298175i
$186$	0.380211			0.0278784
$187$	−6.28588			−0.459669
$188$	−2.93686	+	2.93686i	−0.214193	+	0.214193i
$189$	−18.3258			−1.33300
$190$	−12.1732	−	8.50267i	−0.883136	−	0.616849i
$191$	−6.11582	+	6.11582i	−0.442525	+	0.442525i	−0.892860	−	0.450335i	$-0.851305\pi$
$191$	−6.11582	+	6.11582i	−0.442525	+	0.442525i	0.450335	+	0.892860i	$0.351305\pi$
$192$	1.29397	−	1.29397i	0.0933844	−	0.0933844i
$193$	−15.9965			−1.15145			−0.575725	−	0.817643i	$-0.695280\pi$
$193$	−15.9965			−1.15145			−0.575725	+	0.817643i	$0.695280\pi$
$194$			13.2514i			0.951394i
$195$	16.2287	−	23.2345i	1.16216	−	1.66386i
$196$		−	7.26713i		−	0.519081i
$197$	17.7621	−	17.7621i	1.26550	−	1.26550i	0.317109	−	0.948389i	$-0.397288\pi$
$197$	17.7621	−	17.7621i	1.26550	−	1.26550i	0.948389	−	0.317109i	$-0.102712\pi$
$198$	−0.451907			−0.0321156
$199$	−15.7905	+	15.7905i	−1.11936	+	1.11936i	−0.127524	+	0.991835i	$0.540703\pi$
$199$	−15.7905	+	15.7905i	−1.11936	+	1.11936i	−0.991835	+	0.127524i	$0.959297\pi$
$200$	−4.69447	+	1.72103i	−0.331949	+	0.121695i
$201$	8.04306			0.567314
$202$		−	13.7890i		−	0.970188i
$203$			19.9757i			1.40202i
$204$	6.27669	+	6.27669i	0.439456	+	0.439456i
$205$	−2.49500	−	14.0542i	−0.174258	−	0.981590i
$206$		−	10.6833i		−	0.744338i
$207$		−	1.16461i		−	0.0809462i
$208$	−6.92612			−0.480240
$209$	6.08481	−	6.08481i	0.420895	−	0.420895i
$210$	2.70159	+	15.2179i	0.186427	+	1.05014i
$211$	−24.3785			−1.67829			−0.839144	−	0.543909i	$-0.816944\pi$
$211$	−24.3785			−1.67829			−0.839144	+	0.543909i	$0.816944\pi$
$212$	−1.30971	−	1.30971i	−0.0899510	−	0.0899510i
$213$	−7.23491	+	7.23491i	−0.495728	+	0.495728i
$214$	7.62669	−	7.62669i	0.521350	−	0.521350i
$215$	5.53043	−	0.981798i	0.377172	−	0.0669581i
$216$	−3.43067	−	3.43067i	−0.233428	−	0.233428i
$217$	0.784789			0.0532750
$218$	3.39395	+	3.39395i	0.229867	+	0.229867i
$219$		−	0.349322i		−	0.0236050i
$220$	−0.506490	−	2.85304i	−0.0341476	−	0.192352i
$221$		−	33.5966i		−	2.25995i
$222$	6.80987	−	8.80503i	0.457049	−	0.590955i
$223$	11.0916	+	11.0916i	0.742750	+	0.742750i	0.973106	−	0.230356i	$-0.0739892\pi$
$223$	11.0916	+	11.0916i	0.742750	+	0.742750i	−0.230356	+	0.973106i	$0.573989\pi$
$224$	2.67087	−	2.67087i	0.178455	−	0.178455i
$225$	−0.600173	−	1.63710i	−0.0400115	−	0.109140i
$226$			4.28955i			0.285337i
$227$			13.1902i			0.875463i	0.899106	+	0.437732i	$0.144218\pi$
$227$			13.1902i			0.875463i	−0.899106	+	0.437732i	$0.855782\pi$
$228$	−12.1518			−0.804775
$229$		−	6.06268i		−	0.400633i	−0.979731	−	0.200317i	$-0.935803\pi$
$229$		−	6.06268i		−	0.400633i	0.979731	−	0.200317i	$-0.0641971\pi$
$230$	7.35258	−	1.30528i	0.484815	−	0.0860676i
$231$	−8.95713			−0.589336
$232$	−3.73955	+	3.73955i	−0.245514	+	0.245514i
$233$	−11.6145	+	11.6145i	−0.760893	+	0.760893i	−0.976484	−	0.215590i	$-0.930832\pi$
$233$	−11.6145	+	11.6145i	−0.760893	+	0.760893i	0.215590	+	0.976484i	$0.430832\pi$
$234$		−	2.41534i		−	0.157896i
$235$	5.31805	−	7.61379i	0.346911	−	0.496669i
$236$	4.70039	+	4.70039i	0.305969	+	0.305969i
$237$	27.9706			1.81689
$238$	12.9556	+	12.9556i	0.839789	+	0.839789i
$239$	−0.628920	−	0.628920i	−0.0406815	−	0.0406815i	0.686473	−	0.727155i	$-0.259158\pi$
$239$	−0.628920	−	0.628920i	−0.0406815	−	0.0406815i	−0.727155	+	0.686473i	$0.759158\pi$
$240$	−2.34312	+	3.35462i	−0.151248	+	0.216540i
$241$	14.1376	−	14.1376i	0.910686	−	0.910686i	−0.0856405	−	0.996326i	$-0.527294\pi$
$241$	14.1376	−	14.1376i	0.910686	−	0.910686i	0.996326	+	0.0856405i	$0.0272937\pi$
$242$	−9.32073			−0.599159
$243$	2.55012	−	2.55012i	0.163590	−	0.163590i
$244$	−7.81965	−	7.81965i	−0.500602	−	0.500602i
$245$	2.84036	+	15.9996i	0.181464	+	1.02218i
$246$	−8.26009	−	8.26009i	−0.526644	−	0.526644i
$247$	32.5219	+	32.5219i	2.06932	+	2.06932i
$248$	0.146916	+	0.146916i	0.00932919	+	0.00932919i
$249$	−22.6355			−1.43447
$250$	9.66289	−	5.62393i	0.611135	−	0.355688i
$251$	14.7200	+	14.7200i	0.929119	+	0.929119i	0.997649	−	0.0685304i	$-0.0218310\pi$
$251$	14.7200	+	14.7200i	0.929119	+	0.929119i	−0.0685304	+	0.997649i	$0.521831\pi$
$252$	0.931412	+	0.931412i	0.0586735	+	0.0586735i
$253$			4.32766i			0.272078i
$254$	−0.938326	+	0.938326i	−0.0588758	+	0.0588758i
$255$	−16.2723	−	11.3658i	−1.01901	−	0.711753i
$256$	1.00000			0.0625000
$257$			23.6607i			1.47591i	0.674848	+	0.737957i	$0.264209\pi$
$257$			23.6607i			1.47591i	−0.674848	+	0.737957i	$0.735791\pi$
$258$	3.25040	−	3.25040i	0.202361	−	0.202361i
$259$	14.0562	−	18.1744i	0.873409	−	1.12930i
$260$	15.2488	−	2.70708i	0.945693	−	0.167886i
$261$	−1.30409	−	1.30409i	−0.0807212	−	0.0807212i
$262$	−2.47395	−	2.47395i	−0.152841	−	0.152841i
$263$	17.6417	−	17.6417i	1.08783	−	1.08783i	0.0920831	−	0.995751i	$-0.470647\pi$
$263$	17.6417	−	17.6417i	1.08783	−	1.08783i	0.995751	−	0.0920831i	$-0.0293525\pi$
$264$	−1.67682	−	1.67682i	−0.103201	−	0.103201i
$265$	3.39541	+	2.37161i	0.208578	+	0.145687i
$266$	−25.0824			−1.53790
$267$		−	9.93329i		−	0.607908i
$268$	3.10789	+	3.10789i	0.189845	+	0.189845i
$269$		−	2.23989i		−	0.136568i	−0.997666	−	0.0682841i	$-0.978248\pi$
$269$		−	2.23989i		−	0.136568i	0.997666	−	0.0682841i	$-0.0217524\pi$
$270$	8.89400	+	6.21224i	0.541271	+	0.378065i
$271$	0.860850			0.0522929			0.0261465	−	0.999658i	$-0.491676\pi$
$271$	0.860850			0.0522929			0.0261465	+	0.999658i	$0.491676\pi$
$272$			4.85071i			0.294118i
$273$		−	47.8738i		−	2.89746i
$274$	−14.6348	+	14.6348i	−0.884121	+	0.884121i
$275$	2.23022	+	6.08341i	0.134488	+	0.366844i
$276$	4.32133	−	4.32133i	0.260114	−	0.260114i
$277$	1.08776			0.0653573			0.0326787	−	0.999466i	$-0.489596\pi$
$277$	1.08776			0.0653573			0.0326787	+	0.999466i	$0.489596\pi$
$278$	14.2080			0.852140
$279$	−0.0512340	+	0.0512340i	−0.00306730	+	0.00306730i
$280$	−4.83640	+	6.92422i	−0.289030	+	0.413802i
$281$	−12.3965	+	12.3965i	−0.739516	+	0.739516i	−0.972484	−	0.232969i	$-0.925156\pi$
$281$	−12.3965	+	12.3965i	−0.739516	+	0.739516i	0.232969	+	0.972484i	$0.425156\pi$
$282$		−	7.60043i		−	0.452599i
$283$		−	2.50115i		−	0.148678i	−0.997233	−	0.0743390i	$-0.976315\pi$
$283$		−	2.50115i		−	0.148678i	0.997233	−	0.0743390i	$-0.0236847\pi$
$284$	−5.59124			−0.331779
$285$	26.7540	−	4.74955i	1.58477	−	0.281339i
$286$			8.97533i			0.530722i
$287$	−17.0496	−	17.0496i	−1.00640	−	1.00640i
$288$			0.348729i			0.0205491i
$289$	−6.52939			−0.384082
$290$	6.77155	−	9.69476i	0.397639	−	0.569296i
$291$	−17.1469	−	17.1469i	−1.00517	−	1.00517i
$292$	0.134980	−	0.134980i	0.00789913	−	0.00789913i
$293$	7.08204	+	7.08204i	0.413737	+	0.413737i	0.883038	−	0.469301i	$-0.155494\pi$
$293$	7.08204	+	7.08204i	0.413737	+	0.413737i	−0.469301	+	0.883038i	$0.655494\pi$
$294$	9.40346	+	9.40346i	0.548421	+	0.548421i
$295$	−12.1857	−	8.51143i	−0.709481	−	0.495555i
$296$	6.03371	−	0.770943i	0.350702	−	0.0448102i
$297$	−4.44569	+	4.44569i	−0.257965	+	0.257965i
$298$		−	7.52248i		−	0.435766i
$299$	−23.1304			−1.33766
$300$	3.84755	−	8.30148i	0.222139	−	0.479286i
$301$	6.70911	−	6.70911i	0.386707	−	0.386707i
$302$		−	4.35018i		−	0.250324i
$303$	17.8425	+	17.8425i	1.02503	+	1.02503i
$304$	−4.69555	−	4.69555i	−0.269308	−	0.269308i
$305$	20.2724	+	14.1598i	1.16079	+	0.810787i
$306$	−1.69159			−0.0967015
$307$	18.8346	+	18.8346i	1.07495	+	1.07495i	0.996954	+	0.0779923i	$0.0248510\pi$
$307$	18.8346	+	18.8346i	1.07495	+	1.07495i	0.0779923	+	0.996954i	$0.475149\pi$
$308$	−3.46110	−	3.46110i	−0.197214	−	0.197214i
$309$	13.8238	+	13.8238i	0.786411	+	0.786411i
$310$	−0.380880	−	0.266035i	−0.0216325	−	0.0151098i
$311$	−15.1202	−	15.1202i	−0.857389	−	0.857389i	0.133641	−	0.991030i	$-0.457333\pi$
$311$	−15.1202	−	15.1202i	−0.857389	−	0.857389i	−0.991030	+	0.133641i	$0.957333\pi$
$312$	8.96221	−	8.96221i	0.507385	−	0.507385i
$313$	−8.77570			−0.496032			−0.248016	−	0.968756i	$-0.579779\pi$
$313$	−8.77570			−0.496032			−0.248016	+	0.968756i	$0.579779\pi$
$314$	13.0961	−	13.0961i	0.739055	−	0.739055i
$315$	−2.41468	−	1.68660i	−0.136052	−	0.0950289i
$316$	10.8080	+	10.8080i	0.608000	+	0.608000i
$317$	13.7979	+	13.7979i	0.774970	+	0.774970i	0.978971	−	0.204001i	$-0.0653946\pi$
$317$	13.7979	+	13.7979i	0.774970	+	0.774970i	−0.204001	+	0.978971i	$0.565395\pi$
$318$	3.38945			0.190071
$319$	4.84596	+	4.84596i	0.271322	+	0.271322i
$320$	−2.20164	+	0.390851i	−0.123076	+	0.0218492i
$321$			19.7374i			1.10164i
$322$	8.91961	−	8.91961i	0.497071	−	0.497071i
$323$	22.7768	−	22.7768i	1.26733	−	1.26733i
$324$	9.92458			0.551365
$325$	−32.5145	+	11.9200i	−1.80358	+	0.661205i
$326$		−	14.8033i		−	0.819877i
$327$	−8.78335			−0.485721
$328$		−	6.38351i		−	0.352471i
$329$		−	15.6880i		−	0.864905i
$330$	4.34714	+	3.03637i	0.239302	+	0.167147i
$331$	0.223075	−	0.223075i	0.0122613	−	0.0122613i	−0.700950	−	0.713211i	$-0.747240\pi$
$331$	0.223075	−	0.223075i	0.0122613	−	0.0122613i	0.713211	+	0.700950i	$0.247240\pi$
$332$	−8.74652	−	8.74652i	−0.480028	−	0.480028i
$333$	0.268851	+	2.10413i	0.0147329	+	0.115306i
$334$		−	1.13442i		−	0.0620728i
$335$	−8.05720	−	5.62775i	−0.440212	−	0.307477i
$336$			6.91207i			0.377085i
$337$	−12.6737	−	12.6737i	−0.690381	−	0.690381i	0.271935	−	0.962316i	$-0.412336\pi$
$337$	−12.6737	−	12.6737i	−0.690381	−	0.690381i	−0.962316	+	0.271935i	$0.912336\pi$
$338$	−34.9711			−1.90218
$339$	−5.55057	−	5.55057i	−0.301465	−	0.301465i
$340$	−1.89590	−	10.6795i	−0.102820	−	0.579179i
$341$	0.190384	−	0.190384i	0.0103099	−	0.0103099i
$342$	1.63748	−	1.63748i	0.0885446	−	0.0885446i
$343$	0.713468	+	0.713468i	0.0385236	+	0.0385236i
$344$	2.51195			0.135435
$345$	−7.82504	+	11.2030i	−0.421286	+	0.603151i
$346$	−7.57033	+	7.57033i	−0.406983	+	0.406983i
$347$	9.68557			0.519948			0.259974	−	0.965616i	$-0.416286\pi$
$347$	9.68557			0.519948			0.259974	+	0.965616i	$0.416286\pi$
$348$		−	9.67775i		−	0.518782i
$349$		−	9.40675i		−	0.503532i	−0.967788	−	0.251766i	$-0.918989\pi$
$349$		−	9.40675i		−	0.503532i	0.967788	−	0.251766i	$-0.0810113\pi$
$350$	7.94169	−	17.1350i	0.424501	−	0.915904i
$351$	−23.7612	−	23.7612i	−1.26828	−	1.26828i
$352$		−	1.29587i		−	0.0690700i
$353$			8.93094i			0.475346i	0.971345	+	0.237673i	$0.0763846\pi$
$353$			8.93094i			0.475346i	−0.971345	+	0.237673i	$0.923615\pi$
$354$	−12.1643			−0.646528
$355$	12.3099	−	2.18534i	0.653343	−	0.115986i
$356$	3.83829	−	3.83829i	0.203429	−	0.203429i
$357$	−33.5285			−1.77451
$358$	5.64137	−	5.64137i	0.298156	−	0.298156i
$359$			14.7945i			0.780823i	0.920640	+	0.390412i	$0.127667\pi$
$359$			14.7945i			0.780823i	−0.920640	+	0.390412i	$0.872333\pi$
$360$	−0.136301	−	0.767778i	−0.00718370	−	0.0404655i
$361$			25.0964i			1.32086i
$362$	5.21779			0.274241
$363$	12.0608	−	12.0608i	0.633026	−	0.633026i
$364$	18.4988	−	18.4988i	0.969600	−	0.969600i
$365$	−0.244421	+	0.349936i	−0.0127936	+	0.0183165i
$366$	20.2368			1.05780
$367$	19.5831	−	19.5831i	1.02223	−	1.02223i	0.0224808	−	0.999747i	$-0.492844\pi$
$367$	19.5831	−	19.5831i	1.02223	−	1.02223i	0.999747	−	0.0224808i	$-0.00715646\pi$
$368$	3.33959			0.174088
$369$	2.22612			0.115887
$370$	−12.9828	+	4.05562i	−0.674941	+	0.210842i
$371$	6.99612			0.363221
$372$	−0.380211			−0.0197130
$373$	7.70109	−	7.70109i	0.398747	−	0.398747i	−0.479044	−	0.877791i	$-0.659016\pi$
$373$	7.70109	−	7.70109i	0.398747	−	0.398747i	0.877791	+	0.479044i	$0.159016\pi$
$374$	6.28588			0.325035
$375$	−5.22631	+	19.7807i	−0.269885	+	1.02147i
$376$	2.93686	−	2.93686i	0.151457	−	0.151457i
$377$	−25.9006	+	25.9006i	−1.33395	+	1.33395i
$378$	18.3258			0.942576
$379$			19.2451i			0.988556i	0.869304	+	0.494278i	$0.164567\pi$
$379$			19.2451i			0.988556i	−0.869304	+	0.494278i	$0.835433\pi$
$380$	12.1732	+	8.50267i	0.624472	+	0.436178i
$381$		−	2.42834i		−	0.124407i
$382$	6.11582	−	6.11582i	0.312913	−	0.312913i
$383$	−8.69427			−0.444257			−0.222128	−	0.975017i	$-0.571300\pi$
$383$	−8.69427			−0.444257			−0.222128	+	0.975017i	$0.571300\pi$
$384$	−1.29397	+	1.29397i	−0.0660328	+	0.0660328i
$385$	8.97288	+	6.26733i	0.457300	+	0.319413i
$386$	15.9965			0.814198
$387$			0.875992i			0.0445292i
$388$		−	13.2514i		−	0.672737i
$389$	−14.2389	−	14.2389i	−0.721941	−	0.721941i	0.247059	−	0.969000i	$-0.420536\pi$
$389$	−14.2389	−	14.2389i	−0.721941	−	0.721941i	−0.969000	+	0.247059i	$0.920536\pi$
$390$	−16.2287	+	23.2345i	−0.821772	+	1.17652i
$391$			16.1994i			0.819237i
$392$			7.26713i			0.367045i
$393$	6.40246			0.322961
$394$	−17.7621	+	17.7621i	−0.894842	+	0.894842i
$395$	−28.0198	−	19.5711i	−1.40983	−	0.984730i
$396$	0.451907			0.0227092
$397$	10.2910	+	10.2910i	0.516489	+	0.516489i	0.916507	−	0.400018i	$-0.130996\pi$
$397$	10.2910	+	10.2910i	0.516489	+	0.516489i	−0.400018	+	0.916507i	$0.630996\pi$
$398$	15.7905	−	15.7905i	0.791507	−	0.791507i
$399$	32.4560	−	32.4560i	1.62483	−	1.62483i
$400$	4.69447	−	1.72103i	0.234724	−	0.0860514i
$401$	−13.7676	−	13.7676i	−0.687523	−	0.687523i	0.274161	−	0.961684i	$-0.411600\pi$
$401$	−13.7676	−	13.7676i	−0.687523	−	0.687523i	−0.961684	+	0.274161i	$0.911600\pi$
$402$	−8.04306			−0.401151
$403$	1.01756	+	1.01756i	0.0506883	+	0.0506883i
$404$			13.7890i			0.686026i
$405$	−21.8504	+	3.87903i	−1.08575	+	0.192750i
$406$		−	19.9757i		−	0.991379i
$407$	−0.999040	−	7.81889i	−0.0495206	−	0.387568i
$408$	−6.27669	−	6.27669i	−0.310742	−	0.310742i
$409$	−14.5393	+	14.5393i	−0.718920	+	0.718920i	−0.968384	−	0.249464i	$-0.919745\pi$
$409$	−14.5393	+	14.5393i	−0.718920	+	0.718920i	0.249464	+	0.968384i	$0.419745\pi$
$410$	2.49500	+	14.0542i	0.123219	+	0.694089i
$411$		−	37.8741i		−	1.86819i
$412$			10.6833i			0.526327i
$413$	−25.1083			−1.23550
$414$			1.16461i			0.0572376i
$415$	22.6753	+	15.8381i	1.11309	+	0.777463i
$416$	6.92612			0.339581
$417$	−18.3848	+	18.3848i	−0.900307	+	0.900307i
$418$	−6.08481	+	6.08481i	−0.297618	+	0.297618i
$419$		−	8.30494i		−	0.405723i	−0.979207	−	0.202861i	$-0.934976\pi$
$419$		−	8.30494i		−	0.405723i	0.979207	−	0.202861i	$-0.0650241\pi$
$420$	−2.70159	−	15.2179i	−0.131824	−	0.742559i
$421$	−5.43095	−	5.43095i	−0.264688	−	0.264688i	0.562267	−	0.826956i	$-0.309929\pi$
$421$	−5.43095	−	5.43095i	−0.264688	−	0.264688i	−0.826956	+	0.562267i	$0.809929\pi$
$422$	24.3785			1.18673
$423$	1.02417	+	1.02417i	0.0497968	+	0.0497968i
$424$	1.30971	+	1.30971i	0.0636050	+	0.0636050i
$425$	8.34821	+	22.7715i	0.404948	+	1.10458i
$426$	7.23491	−	7.23491i	0.350533	−	0.350533i
$427$	41.7706			2.02142
$428$	−7.62669	+	7.62669i	−0.368650	+	0.368650i
$429$	−11.6138	−	11.6138i	−0.560721	−	0.560721i
$430$	−5.53043	+	0.981798i	−0.266701	+	0.0473465i
$431$	16.0000	+	16.0000i	0.770693	+	0.770693i	0.978228	−	0.207535i	$-0.0665439\pi$
$431$	16.0000	+	16.0000i	0.770693	+	0.770693i	−0.207535	+	0.978228i	$0.566544\pi$
$432$	3.43067	+	3.43067i	0.165058	+	0.165058i
$433$	−21.6988	−	21.6988i	−1.04278	−	1.04278i	−0.999043	−	0.0437350i	$-0.986074\pi$
$433$	−21.6988	−	21.6988i	−1.04278	−	1.04278i	−0.0437350	−	0.999043i	$-0.513926\pi$
$434$	−0.784789			−0.0376711
$435$	3.78256	+	21.3070i	0.181360	+	1.02159i
$436$	−3.39395	−	3.39395i	−0.162541	−	0.162541i
$437$	−15.6812	−	15.6812i	−0.750134	−	0.750134i
$438$			0.349322i			0.0166912i
$439$	5.60815	−	5.60815i	0.267662	−	0.267662i	−0.560495	−	0.828158i	$-0.689389\pi$
$439$	5.60815	−	5.60815i	0.267662	−	0.267662i	0.828158	+	0.560495i	$0.189389\pi$
$440$	0.506490	+	2.85304i	0.0241460	+	0.136013i
$441$	−2.53426			−0.120679
$442$			33.5966i			1.59803i
$443$	17.9895	−	17.9895i	0.854708	−	0.854708i	−0.136001	−	0.990709i	$-0.543425\pi$
$443$	17.9895	−	17.9895i	0.854708	−	0.854708i	0.990709	+	0.136001i	$0.0434250\pi$
$444$	−6.80987	+	8.80503i	−0.323182	+	0.417868i
$445$	−6.95036	+	9.95076i	−0.329479	+	0.471711i
$446$	−11.0916	−	11.0916i	−0.525203	−	0.525203i
$447$	9.73388	+	9.73388i	0.460397	+	0.460397i
$448$	−2.67087	+	2.67087i	−0.126187	+	0.126187i
$449$	6.18967	+	6.18967i	0.292109	+	0.292109i	0.837913	−	0.545804i	$-0.183776\pi$
$449$	6.18967	+	6.18967i	0.292109	+	0.292109i	−0.545804	+	0.837913i	$0.683776\pi$
$450$	0.600173	+	1.63710i	0.0282924	+	0.0771737i
$451$	−8.27219			−0.389522
$452$		−	4.28955i		−	0.201764i
$453$	5.62901	+	5.62901i	0.264474	+	0.264474i
$454$		−	13.1902i		−	0.619046i
$455$	−33.4975	+	47.9580i	−1.57039	+	2.24831i
$456$	12.1518			0.569062
$457$		−	31.9423i		−	1.49420i	−0.664712	−	0.747100i	$-0.731446\pi$
$457$		−	31.9423i		−	1.49420i	0.664712	−	0.747100i	$-0.268554\pi$
$458$			6.06268i			0.283291i
$459$	−16.6412	+	16.6412i	−0.776744	+	0.776744i
$460$	−7.35258	+	1.30528i	−0.342816	+	0.0608590i
$461$	2.73403	−	2.73403i	0.127336	−	0.127336i	−0.640566	−	0.767903i	$-0.721300\pi$
$461$	2.73403	−	2.73403i	0.127336	−	0.127336i	0.767903	+	0.640566i	$0.221300\pi$
$462$	8.95713			0.416723
$463$	−4.32970			−0.201218			−0.100609	−	0.994926i	$-0.532079\pi$
$463$	−4.32970			−0.201218			−0.100609	+	0.994926i	$0.532079\pi$
$464$	3.73955	−	3.73955i	0.173604	−	0.173604i
$465$	0.837090	−	0.148606i	0.0388191	−	0.00689143i
$466$	11.6145	−	11.6145i	0.538033	−	0.538033i
$467$		−	0.826696i		−	0.0382549i	−0.999817	−	0.0191275i	$-0.993911\pi$
$467$		−	0.826696i		−	0.0382549i	0.999817	−	0.0191275i	$-0.00608884\pi$
$468$			2.41534i			0.111649i
$469$	−16.6016			−0.766590
$470$	−5.31805	+	7.61379i	−0.245303	+	0.351198i
$471$			33.8920i			1.56166i
$472$	−4.70039	−	4.70039i	−0.216353	−	0.216353i
$473$		−	3.25516i		−	0.149672i
$474$	−27.9706			−1.28473
$475$	−30.1243	−	13.9620i	−1.38220	−	0.640619i
$476$	−12.9556	−	12.9556i	−0.593821	−	0.593821i
$477$	−0.456733	+	0.456733i	−0.0209124	+	0.0209124i
$478$	0.628920	+	0.628920i	0.0287661	+	0.0287661i
$479$	19.7849	+	19.7849i	0.903997	+	0.903997i	0.995779	−	0.0917818i	$-0.0292562\pi$
$479$	19.7849	+	19.7849i	0.903997	+	0.903997i	−0.0917818	+	0.995779i	$0.529256\pi$
$480$	2.34312	−	3.35462i	0.106948	−	0.153117i
$481$	41.7902	−	5.33965i	1.90547	−	0.243467i
$482$	−14.1376	+	14.1376i	−0.643952	+	0.643952i
$483$			23.0835i			1.05033i
$484$	9.32073			0.423669
$485$	5.17931	+	29.1748i	0.235180	+	1.32476i
$486$	−2.55012	+	2.55012i	−0.115676	+	0.115676i
$487$			28.2154i			1.27856i	0.768973	+	0.639282i	$0.220768\pi$
$487$			28.2154i			1.27856i	−0.768973	+	0.639282i	$0.779232\pi$
$488$	7.81965	+	7.81965i	0.353979	+	0.353979i
$489$	19.1550	+	19.1550i	0.866220	+	0.866220i
$490$	−2.84036	−	15.9996i	−0.128314	−	0.722790i
$491$	2.48442			0.112121			0.0560603	−	0.998427i	$-0.482146\pi$
$491$	2.48442			0.112121			0.0560603	+	0.998427i	$0.482146\pi$
$492$	8.26009	+	8.26009i	0.372394	+	0.372394i
$493$	18.1395	+	18.1395i	0.816961	+	0.816961i
$494$	−32.5219	−	32.5219i	−1.46323	−	1.46323i
$495$	−0.994939	+	0.176628i	−0.0447192	+	0.00793885i
$496$	−0.146916	−	0.146916i	−0.00659674	−	0.00659674i
$497$	14.9335	−	14.9335i	0.669859	−	0.669859i
$498$	22.6355			1.01432
$499$	1.49326	−	1.49326i	0.0668473	−	0.0668473i	−0.672893	−	0.739740i	$-0.734948\pi$
$499$	1.49326	−	1.49326i	0.0668473	−	0.0668473i	0.739740	+	0.672893i	$0.234948\pi$
$500$	−9.66289	+	5.62393i	−0.432138	+	0.251510i
$501$	1.46791	+	1.46791i	0.0655814	+	0.0655814i
$502$	−14.7200	−	14.7200i	−0.656986	−	0.656986i
$503$	3.35307			0.149506			0.0747531	−	0.997202i	$-0.476183\pi$
$503$	3.35307			0.149506			0.0747531	+	0.997202i	$0.476183\pi$
$504$	−0.931412	−	0.931412i	−0.0414884	−	0.0414884i
$505$	−5.38942	−	30.3584i	−0.239826	−	1.35093i
$506$		−	4.32766i		−	0.192388i
$507$	45.2517	−	45.2517i	2.00970	−	2.00970i
$508$	0.938326	−	0.938326i	0.0416315	−	0.0416315i
$509$	9.46119			0.419360			0.209680	−	0.977770i	$-0.432758\pi$
$509$	9.46119			0.419360			0.209680	+	0.977770i	$0.432758\pi$
$510$	16.2723	+	11.3658i	0.720548	+	0.503285i
$511$			0.721031i			0.0318965i
$512$	−1.00000			−0.0441942
$513$		−	32.2178i		−	1.42245i
$514$		−	23.6607i		−	1.04363i
$515$	−4.17556	−	23.5207i	−0.183997	−	1.03645i
$516$	−3.25040	+	3.25040i	−0.143091	+	0.143091i
$517$	−3.80578	−	3.80578i	−0.167378	−	0.167378i
$518$	−14.0562	+	18.1744i	−0.617593	+	0.798536i
$519$		−	19.5916i		−	0.859976i
$520$	−15.2488	+	2.70708i	−0.668706	+	0.118713i
$521$			28.0496i			1.22887i	0.788966	+	0.614437i	$0.210617\pi$
$521$			28.0496i			1.22887i	−0.788966	+	0.614437i	$0.789383\pi$
$522$	1.30409	+	1.30409i	0.0570785	+	0.0570785i
$523$	−10.2294			−0.447300			−0.223650	−	0.974669i	$-0.571797\pi$
$523$	−10.2294			−0.447300			−0.223650	+	0.974669i	$0.571797\pi$
$524$	2.47395	+	2.47395i	0.108075	+	0.108075i
$525$	11.8959	+	32.4485i	0.519178	+	1.41617i
$526$	−17.6417	+	17.6417i	−0.769215	+	0.769215i
$527$	0.712648	−	0.712648i	0.0310434	−	0.0310434i
$528$	1.67682	+	1.67682i	0.0729741	+	0.0729741i
$529$	−11.8472			−0.515094
$530$	−3.39541	−	2.37161i	−0.147487	−	0.103016i
$531$	1.63916	−	1.63916i	0.0711337	−	0.0711337i
$532$	25.0824			1.08746
$533$		−	44.2130i		−	1.91508i
$534$			9.93329i			0.429856i
$535$	13.8104	−	19.7721i	0.597074	−	0.854824i
$536$	−3.10789	−	3.10789i	−0.134241	−	0.134241i
$537$			14.5995i			0.630017i
$538$			2.23989i			0.0965683i
$539$	9.41723			0.405629
$540$	−8.89400	−	6.21224i	−0.382737	−	0.267332i
$541$	11.2603	−	11.2603i	0.484116	−	0.484116i	−0.422327	−	0.906443i	$-0.638787\pi$
$541$	11.2603	−	11.2603i	0.484116	−	0.484116i	0.906443	+	0.422327i	$0.138787\pi$
$542$	−0.860850			−0.0369767
$543$	−6.75168	+	6.75168i	−0.289742	+	0.289742i
$544$		−	4.85071i		−	0.207973i
$545$	8.79879	+	6.14574i	0.376899	+	0.263255i
$546$			47.8738i			2.04881i
$547$	25.5984			1.09451			0.547254	−	0.836966i	$-0.315673\pi$
$547$	25.5984			1.09451			0.547254	+	0.836966i	$0.315673\pi$
$548$	14.6348	−	14.6348i	0.625168	−	0.625168i
$549$	−2.72694	+	2.72694i	−0.116383	+	0.116383i
$550$	−2.23022	−	6.08341i	−0.0950970	−	0.259398i
$551$	−35.1185			−1.49610
$552$	−4.32133	+	4.32133i	−0.183928	+	0.183928i
$553$	−57.7338			−2.45509
$554$	−1.08776			−0.0462146
$555$	11.5515	−	22.0472i	0.490332	−	0.935851i
$556$	−14.2080			−0.602554
$557$	14.7290			0.624089			0.312045	−	0.950067i	$-0.398986\pi$
$557$	14.7290			0.624089			0.312045	+	0.950067i	$0.398986\pi$
$558$	0.0512340	−	0.0512340i	0.00216891	−	0.00216891i
$559$	17.3981			0.735861
$560$	4.83640	−	6.92422i	0.204375	−	0.292602i
$561$	−8.13375	+	8.13375i	−0.343407	+	0.343407i
$562$	12.3965	−	12.3965i	0.522917	−	0.522917i
$563$	−30.0223			−1.26529			−0.632645	−	0.774442i	$-0.718031\pi$
$563$	−30.0223			−1.26529			−0.632645	+	0.774442i	$0.718031\pi$
$564$			7.60043i			0.320036i
$565$	1.67658	+	9.44407i	0.0705341	+	0.397315i
$566$			2.50115i			0.105131i
$567$	−26.5073	+	26.5073i	−1.11320	+	1.11320i
$568$	5.59124			0.234603
$569$	−5.23109	+	5.23109i	−0.219298	+	0.219298i	−0.808203	−	0.588904i	$-0.799559\pi$
$569$	−5.23109	+	5.23109i	−0.219298	+	0.219298i	0.588904	+	0.808203i	$0.299559\pi$
$570$	−26.7540	+	4.74955i	−1.12060	+	0.198937i
$571$	−13.0995			−0.548196			−0.274098	−	0.961702i	$-0.588379\pi$
$571$	−13.0995			−0.548196			−0.274098	+	0.961702i	$0.588379\pi$
$572$		−	8.97533i		−	0.375277i
$573$			15.8274i			0.661199i
$574$	17.0496	+	17.0496i	0.711635	+	0.711635i
$575$	15.6776	−	5.74752i	0.653801	−	0.239688i
$576$		−	0.348729i		−	0.0145304i
$577$		−	21.6061i		−	0.899475i	−0.893161	−	0.449737i	$-0.851518\pi$
$577$		−	21.6061i		−	0.899475i	0.893161	−	0.449737i	$-0.148482\pi$
$578$	6.52939			0.271587
$579$	−20.6990	+	20.6990i	−0.860220	+	0.860220i
$580$	−6.77155	+	9.69476i	−0.281173	+	0.402553i
$581$	46.7217			1.93834
$582$	17.1469	+	17.1469i	0.710763	+	0.710763i
$583$	1.69721	−	1.69721i	0.0702911	−	0.0702911i
$584$	−0.134980	+	0.134980i	−0.00558553	+	0.00558553i
$585$	−0.944038	−	5.31772i	−0.0390312	−	0.219861i
$586$	−7.08204	−	7.08204i	−0.292556	−	0.292556i
$587$	−37.7655			−1.55875			−0.779375	−	0.626557i	$-0.784463\pi$
$587$	−37.7655			−1.55875			−0.779375	+	0.626557i	$0.784463\pi$
$588$	−9.40346	−	9.40346i	−0.387792	−	0.387792i
$589$			1.37971i			0.0568498i
$590$	12.1857	+	8.51143i	0.501679	+	0.350410i
$591$		−	45.9674i		−	1.89084i
$592$	−6.03371	+	0.770943i	−0.247984	+	0.0316856i
$593$	−5.60150	−	5.60150i	−0.230026	−	0.230026i	0.582678	−	0.812703i	$-0.302005\pi$
$593$	−5.60150	−	5.60150i	−0.230026	−	0.230026i	−0.812703	+	0.582678i	$0.802005\pi$
$594$	4.44569	−	4.44569i	0.182409	−	0.182409i
$595$	33.5874	+	23.4600i	1.37695	+	0.961765i
$596$			7.52248i			0.308133i
$597$			40.8650i			1.67249i
$598$	23.1304			0.945871
$599$			3.81331i			0.155808i	0.996961	+	0.0779039i	$0.0248227\pi$
$599$			3.81331i			0.155808i	−0.996961	+	0.0779039i	$0.975177\pi$
$600$	−3.84755	+	8.30148i	−0.157076	+	0.338906i
$601$	15.0394			0.613469			0.306734	−	0.951795i	$-0.400764\pi$
$601$	15.0394			0.613469			0.306734	+	0.951795i	$0.400764\pi$
$602$	−6.70911	+	6.70911i	−0.273443	+	0.273443i
$603$	1.08381	−	1.08381i	0.0441363	−	0.0441363i
$604$			4.35018i			0.177006i
$605$	−20.5209	+	3.64301i	−0.834294	+	0.148110i
$606$	−17.8425	−	17.8425i	−0.724803	−	0.724803i
$607$	28.5167			1.15746			0.578729	−	0.815520i	$-0.303549\pi$
$607$	28.5167			1.15746			0.578729	+	0.815520i	$0.303549\pi$
$608$	4.69555	+	4.69555i	0.190430	+	0.190430i
$609$	25.8480	+	25.8480i	1.04742	+	1.04742i
$610$	−20.2724	−	14.1598i	−0.820806	−	0.573313i
$611$	20.3410	−	20.3410i	0.822911	−	0.822911i
$612$	1.69159			0.0683783
$613$	−11.7097	+	11.7097i	−0.472948	+	0.472948i	−0.902867	−	0.429919i	$-0.858542\pi$
$613$	−11.7097	+	11.7097i	−0.472948	+	0.472948i	0.429919	+	0.902867i	$0.358542\pi$
$614$	−18.8346	−	18.8346i	−0.760102	−	0.760102i
$615$	−21.4142	−	14.9573i	−0.863506	−	0.603137i
$616$	3.46110	+	3.46110i	0.139452	+	0.139452i
$617$	−31.2569	−	31.2569i	−1.25836	−	1.25836i	−0.951878	−	0.306477i	$-0.900850\pi$
$617$	−31.2569	−	31.2569i	−1.25836	−	1.25836i	−0.306477	−	0.951878i	$-0.599150\pi$
$618$	−13.8238	−	13.8238i	−0.556077	−	0.556077i
$619$	−3.97357			−0.159711			−0.0798556	−	0.996806i	$-0.525446\pi$
$619$	−3.97357			−0.159711			−0.0798556	+	0.996806i	$0.525446\pi$
$620$	0.380880	+	0.266035i	0.0152965	+	0.0106842i
$621$	11.4570	+	11.4570i	0.459755	+	0.459755i
$622$	15.1202	+	15.1202i	0.606265	+	0.606265i
$623$			20.5032i			0.821443i
$624$	−8.96221	+	8.96221i	−0.358775	+	0.358775i
$625$	19.0761	−	16.1586i	0.763045	−	0.646345i
$626$	8.77570			0.350748
$627$		−	15.7472i		−	0.628881i
$628$	−13.0961	+	13.0961i	−0.522591	+	0.522591i
$629$	−3.73962	−	29.2678i	−0.149109	−	1.16698i
$630$	2.41468	+	1.68660i	0.0962032	+	0.0671956i
$631$	−31.7078	−	31.7078i	−1.26227	−	1.26227i	−0.949991	−	0.312278i	$-0.898908\pi$
$631$	−31.7078	−	31.7078i	−1.26227	−	1.26227i	−0.312278	−	0.949991i	$-0.601092\pi$
$632$	−10.8080	−	10.8080i	−0.429921	−	0.429921i
$633$	−31.5452	+	31.5452i	−1.25381	+	1.25381i
$634$	−13.7979	−	13.7979i	−0.547986	−	0.547986i
$635$	−1.69911	+	2.43260i	−0.0674273	+	0.0965350i
$636$	−3.38945			−0.134400
$637$			50.3330i			1.99427i
$638$	−4.84596	−	4.84596i	−0.191853	−	0.191853i
$639$			1.94983i			0.0771341i
$640$	2.20164	−	0.390851i	0.0870276	−	0.0154497i
$641$	−3.77934			−0.149275			−0.0746374	−	0.997211i	$-0.523780\pi$
$641$	−3.77934			−0.149275			−0.0746374	+	0.997211i	$0.523780\pi$
$642$		−	19.7374i		−	0.778975i
$643$			28.5420i			1.12558i	0.826598	+	0.562792i	$0.190273\pi$
$643$			28.5420i			1.12558i	−0.826598	+	0.562792i	$0.809727\pi$
$644$	−8.91961	+	8.91961i	−0.351482	+	0.351482i
$645$	5.88580	−	8.42664i	0.231753	−	0.331799i
$646$	−22.7768	+	22.7768i	−0.896140	+	0.896140i
$647$	−22.3386			−0.878222			−0.439111	−	0.898433i	$-0.644707\pi$
$647$	−22.3386			−0.878222			−0.439111	+	0.898433i	$0.644707\pi$
$648$	−9.92458			−0.389874
$649$	−6.09108	+	6.09108i	−0.239096	+	0.239096i
$650$	32.5145	−	11.9200i	1.27532	−	0.467543i
$651$	1.01550	−	1.01550i	0.0398004	−	0.0398004i
$652$			14.8033i			0.579741i
$653$		−	19.9863i		−	0.782125i	−0.920364	−	0.391063i	$-0.872108\pi$
$653$		−	19.9863i		−	0.782125i	0.920364	−	0.391063i	$-0.127892\pi$
$654$	8.78335			0.343456
$655$	−6.41371	−	4.47982i	−0.250605	−	0.175041i
$656$			6.38351i			0.249234i
$657$	−0.0470716	−	0.0470716i	−0.00183644	−	0.00183644i
$658$			15.6880i			0.611581i
$659$	−30.3524			−1.18236			−0.591182	−	0.806538i	$-0.701338\pi$
$659$	−30.3524			−1.18236			−0.591182	+	0.806538i	$0.701338\pi$
$660$	−4.34714	−	3.03637i	−0.169212	−	0.118190i
$661$	10.1177	+	10.1177i	0.393535	+	0.393535i	0.875945	−	0.482411i	$-0.160239\pi$
$661$	10.1177	+	10.1177i	0.393535	+	0.393535i	−0.482411	+	0.875945i	$0.660239\pi$
$662$	−0.223075	+	0.223075i	−0.00867004	+	0.00867004i
$663$	−43.4731	−	43.4731i	−1.68835	−	1.68835i
$664$	8.74652	+	8.74652i	0.339431	+	0.339431i
$665$	−55.2226	+	9.80349i	−2.14144	+	0.380163i
$666$	−0.268851	−	2.10413i	−0.0104178	−	0.0815335i
$667$	12.4886	−	12.4886i	0.483559	−	0.483559i
$668$			1.13442i			0.0438921i
$669$	28.7045			1.10978
$670$	8.05720	+	5.62775i	0.311277	+	0.217419i
$671$	10.1332	−	10.1332i	0.391189	−	0.391189i
$672$		−	6.91207i		−	0.266639i
$673$	−13.7492	−	13.7492i	−0.529992	−	0.529992i	0.390578	−	0.920570i	$-0.372275\pi$
$673$	−13.7492	−	13.7492i	−0.529992	−	0.529992i	−0.920570	+	0.390578i	$0.872275\pi$
$674$	12.6737	+	12.6737i	0.488173	+	0.488173i
$675$	22.0095	+	10.2009i	0.847145	+	0.392633i
$676$	34.9711			1.34504
$677$	−24.9315	−	24.9315i	−0.958197	−	0.958197i	0.0409634	−	0.999161i	$-0.486957\pi$
$677$	−24.9315	−	24.9315i	−0.958197	−	0.958197i	−0.999161	+	0.0409634i	$0.986957\pi$
$678$	5.55057	+	5.55057i	0.213168	+	0.213168i
$679$	35.3928	+	35.3928i	1.35825	+	1.35825i
$680$	1.89590	+	10.6795i	0.0727046	+	0.409542i
$681$	17.0677	+	17.0677i	0.654037	+	0.654037i
$682$	−0.190384	+	0.190384i	−0.00729018	+	0.00729018i
$683$	37.2952			1.42706			0.713531	−	0.700624i	$-0.247095\pi$
$683$	37.2952			1.42706			0.713531	+	0.700624i	$0.247095\pi$
$684$	−1.63748	+	1.63748i	−0.0626105	+	0.0626105i
$685$	−26.5006	+	37.9407i	−1.01254	+	1.44964i
$686$	−0.713468	−	0.713468i	−0.0272403	−	0.0272403i
$687$	−7.84495	−	7.84495i	−0.299303	−	0.299303i
$688$	−2.51195			−0.0957673
$689$	9.07118	+	9.07118i	0.345585	+	0.345585i
$690$	7.82504	−	11.2030i	0.297894	−	0.426492i
$691$		−	5.06456i		−	0.192665i	−0.995349	−	0.0963324i	$-0.969289\pi$
$691$		−	5.06456i		−	0.192665i	0.995349	−	0.0963324i	$-0.0307112\pi$
$692$	7.57033	−	7.57033i	0.287781	−	0.287781i
$693$	−1.20699	+	1.20699i	−0.0458496	+	0.0458496i
$694$	−9.68557			−0.367659
$695$	31.2810	−	5.55321i	1.18656	−	0.210645i
$696$			9.67775i			0.366834i
$697$	−30.9646			−1.17287
$698$			9.40675i			0.356051i
$699$			30.0578i			1.13689i
$700$	−7.94169	+	17.1350i	−0.300168	+	0.647642i
$701$	−18.0567	+	18.0567i	−0.681993	+	0.681993i	−0.960449	−	0.278456i	$-0.910177\pi$
$701$	−18.0567	+	18.0567i	−0.681993	+	0.681993i	0.278456	+	0.960449i	$0.410177\pi$
$702$	23.7612	+	23.7612i	0.896810	+	0.896810i
$703$	31.9516	+	24.7116i	1.20508	+	0.932015i
$704$			1.29587i			0.0488398i
$705$	−2.97063	−	16.7334i	−0.111881	−	0.630218i
$706$		−	8.93094i		−	0.336120i
$707$	−36.8286	−	36.8286i	−1.38508	−	1.38508i
$708$	12.1643			0.457164
$709$	20.2886	+	20.2886i	0.761953	+	0.761953i	0.976675	−	0.214722i	$-0.0688845\pi$
$709$	20.2886	+	20.2886i	0.761953	+	0.761953i	−0.214722	+	0.976675i	$0.568885\pi$
$710$	−12.3099	+	2.18534i	−0.461983	+	0.0820144i
$711$	3.76908	−	3.76908i	0.141352	−	0.141352i
$712$	−3.83829	+	3.83829i	−0.143846	+	0.143846i
$713$	−0.490640	−	0.490640i	−0.0183746	−	0.0183746i
$714$	33.5285			1.25477
$715$	3.50801	+	19.7605i	0.131192	+	0.739000i
$716$	−5.64137	+	5.64137i	−0.210828	+	0.210828i
$717$	−1.62761			−0.0607842
$718$		−	14.7945i		−	0.552125i
$719$		−	37.3366i		−	1.39242i	−0.717838	−	0.696210i	$-0.754868\pi$
$719$		−	37.3366i		−	1.39242i	0.717838	−	0.696210i	$-0.245132\pi$
$720$	0.136301	+	0.767778i	0.00507964	+	0.0286134i
$721$	−28.5336	−	28.5336i	−1.06265	−	1.06265i
$722$		−	25.0964i		−	0.933992i
$723$		−	36.5874i		−	1.36070i
$724$	−5.21779			−0.193918
$725$	11.1193	−	23.9911i	0.412962	−	0.891007i
$726$	−12.0608	+	12.0608i	−0.447617	+	0.447617i
$727$	6.83943			0.253660			0.126830	−	0.991924i	$-0.459520\pi$
$727$	6.83943			0.253660			0.126830	+	0.991924i	$0.459520\pi$
$728$	−18.4988	+	18.4988i	−0.685611	+	0.685611i
$729$			23.1742i			0.858303i
$730$	0.244421	−	0.349936i	0.00904644	−	0.0129517i
$731$		−	12.1848i		−	0.450669i
$732$	−20.2368			−0.747975
$733$	−10.1492	+	10.1492i	−0.374870	+	0.374870i	−0.869247	−	0.494378i	$-0.835396\pi$
$733$	−10.1492	+	10.1492i	−0.374870	+	0.374870i	0.494378	+	0.869247i	$0.335396\pi$
$734$	−19.5831	+	19.5831i	−0.722824	+	0.722824i
$735$	24.3784	+	17.0277i	0.899212	+	0.628077i
$736$	−3.33959			−0.123099
$737$	−4.02742	+	4.02742i	−0.148352	+	0.148352i
$738$	−2.22612			−0.0819446
$739$	32.3194			1.18889			0.594445	−	0.804136i	$-0.297372\pi$
$739$	32.3194			1.18889			0.594445	+	0.804136i	$0.297372\pi$
$740$	12.9828	−	4.05562i	0.477256	−	0.149088i
$741$	84.1650			3.09188
$742$	−6.99612			−0.256836
$743$	−17.4266	+	17.4266i	−0.639319	+	0.639319i	−0.950387	−	0.311069i	$-0.899313\pi$
$743$	−17.4266	+	17.4266i	−0.639319	+	0.639319i	0.311069	+	0.950387i	$0.399313\pi$
$744$	0.380211			0.0139392
$745$	−2.94017	−	16.5618i	−0.107719	−	0.606778i
$746$	−7.70109	+	7.70109i	−0.281957	+	0.281957i
$747$	−3.05017	+	3.05017i	−0.111600	+	0.111600i
$748$	−6.28588			−0.229834
$749$		−	40.7398i		−	1.48860i
$750$	5.22631	−	19.7807i	0.190838	−	0.722290i
$751$		−	9.29027i		−	0.339007i	−0.985530	−	0.169503i	$-0.945784\pi$
$751$		−	9.29027i		−	0.339007i	0.985530	−	0.169503i	$-0.0542164\pi$
$752$	−2.93686	+	2.93686i	−0.107096	+	0.107096i
$753$	38.0946			1.38824
$754$	25.9006	−	25.9006i	0.943243	−	0.943243i
$755$	−1.70027	−	9.57754i	−0.0618791	−	0.348562i
$756$	−18.3258			−0.666502
$757$		−	27.5608i		−	1.00171i	−0.865530	−	0.500857i	$-0.833018\pi$
$757$		−	27.5608i		−	1.00171i	0.865530	−	0.500857i	$-0.166982\pi$
$758$		−	19.2451i		−	0.699015i
$759$	5.59987	+	5.59987i	0.203263	+	0.203263i
$760$	−12.1732	−	8.50267i	−0.441568	−	0.308424i
$761$		−	14.9003i		−	0.540137i	−0.962841	−	0.270069i	$-0.912954\pi$
$761$		−	14.9003i		−	0.540137i	0.962841	−	0.270069i	$-0.0870464\pi$
$762$			2.42834i			0.0879693i
$763$	18.1296			0.656336
$764$	−6.11582	+	6.11582i	−0.221263	+	0.221263i
$765$	−3.72427	+	0.661157i	−0.134651	+	0.0239042i
$766$	8.69427			0.314137
$767$	−32.5554	−	32.5554i	−1.17551	−	1.17551i
$768$	1.29397	−	1.29397i	0.0466922	−	0.0466922i
$769$	−19.2793	+	19.2793i	−0.695229	+	0.695229i	−0.963378	−	0.268148i	$-0.913588\pi$
$769$	−19.2793	+	19.2793i	−0.695229	+	0.695229i	0.268148	+	0.963378i	$0.413588\pi$
$770$	−8.97288	−	6.26733i	−0.323360	−	0.225859i
$771$	30.6163	+	30.6163i	1.10262	+	1.10262i
$772$	−15.9965			−0.575725
$773$	12.1435	+	12.1435i	0.436770	+	0.436770i	0.890923	−	0.454153i	$-0.150058\pi$
$773$	12.1435	+	12.1435i	0.436770	+	0.436770i	−0.454153	+	0.890923i	$0.650058\pi$
$774$		−	0.875992i		−	0.0314869i
$775$	−0.942541	−	0.436847i	−0.0338571	−	0.0156920i
$776$			13.2514i			0.475697i
$777$	−5.32882	−	41.7054i	−0.191170	−	1.49617i
$778$	14.2389	+	14.2389i	0.510490	+	0.510490i
$779$	29.9741	−	29.9741i	1.07393	−	1.07393i
$780$	16.2287	−	23.2345i	0.581081	−	0.831928i
$781$		−	7.24551i		−	0.259265i
$782$		−	16.1994i		−	0.579288i
$783$	25.6583			0.916954
$784$		−	7.26713i		−	0.259540i
$785$	23.7143	−	33.9515i	0.846400	−	1.21178i
$786$	−6.40246			−0.228368
$787$	26.4221	−	26.4221i	0.941846	−	0.941846i	−0.0565540	−	0.998400i	$-0.518011\pi$
$787$	26.4221	−	26.4221i	0.941846	−	0.941846i	0.998400	+	0.0565540i	$0.0180113\pi$
$788$	17.7621	−	17.7621i	0.632749	−	0.632749i
$789$		−	45.6558i		−	1.62539i
$790$	28.0198	+	19.5711i	0.996899	+	0.696309i
$791$	11.4569	+	11.4569i	0.407359	+	0.407359i
$792$	−0.451907			−0.0160578
$793$	54.1599	+	54.1599i	1.92327	+	1.92327i
$794$	−10.2910	−	10.2910i	−0.365213	−	0.365213i
$795$	7.46236	−	1.32477i	0.264663	−	0.0469847i
$796$	−15.7905	+	15.7905i	−0.559680	+	0.559680i
$797$	48.7252			1.72593			0.862967	−	0.505261i	$-0.168604\pi$
$797$	48.7252			1.72593			0.862967	+	0.505261i	$0.168604\pi$
$798$	−32.4560	+	32.4560i	−1.14893	+	1.14893i
$799$	−14.2459	−	14.2459i	−0.503982	−	0.503982i
$800$	−4.69447	+	1.72103i	−0.165975	+	0.0608475i
$801$	−1.33853	−	1.33853i	−0.0472945	−	0.0472945i
$802$	13.7676	+	13.7676i	0.486152	+	0.486152i
$803$	0.174917	+	0.174917i	0.00617267	+	0.00617267i
$804$	8.04306			0.283657
$805$	16.1516	−	23.1240i	0.569268	−	0.815016i
$806$	−1.01756	−	1.01756i	−0.0358420	−	0.0358420i
$807$	−2.89835	−	2.89835i	−0.102027	−	0.102027i
$808$		−	13.7890i		−	0.485094i
$809$	−31.4838	+	31.4838i	−1.10691	+	1.10691i	−0.113356	+	0.993554i	$0.536160\pi$
$809$	−31.4838	+	31.4838i	−1.10691	+	1.10691i	−0.993554	+	0.113356i	$0.963840\pi$
$810$	21.8504	−	3.87903i	0.767744	−	0.136295i
$811$	−17.7803			−0.624352			−0.312176	−	0.950024i	$-0.601058\pi$
$811$	−17.7803			−0.624352			−0.312176	+	0.950024i	$0.601058\pi$
$812$			19.9757i			0.701011i
$813$	1.11392	−	1.11392i	0.0390667	−	0.0390667i
$814$	0.999040	+	7.81889i	0.0350163	+	0.274052i
$815$	−5.78587	−	32.5915i	−0.202670	−	1.14163i
$816$	6.27669	+	6.27669i	0.219728	+	0.219728i
$817$	11.7950	+	11.7950i	0.412655	+	0.412655i
$818$	14.5393	−	14.5393i	0.508353	−	0.508353i
$819$	−6.45107	−	6.45107i	−0.225419	−	0.225419i
$820$	−2.49500	−	14.0542i	−0.0871292	−	0.490795i
$821$	−23.5885			−0.823243			−0.411622	−	0.911355i	$-0.635038\pi$
$821$	−23.5885			−0.823243			−0.411622	+	0.911355i	$0.635038\pi$
$822$			37.8741i			1.32101i
$823$	−34.7320	−	34.7320i	−1.21068	−	1.21068i	−0.970803	−	0.239878i	$-0.922892\pi$
$823$	−34.7320	−	34.7320i	−1.21068	−	1.21068i	−0.239878	−	0.970803i	$-0.577108\pi$
$824$		−	10.6833i		−	0.372169i
$825$	10.7576	+	4.98592i	0.374532	+	0.173587i
$826$	25.1083			0.873629
$827$			33.9081i			1.17910i	0.807732	+	0.589549i	$0.200695\pi$
$827$			33.9081i			1.17910i	−0.807732	+	0.589549i	$0.799305\pi$
$828$		−	1.16461i		−	0.0404731i
$829$	16.2123	−	16.2123i	0.563075	−	0.563075i	−0.367105	−	0.930180i	$-0.619651\pi$
$829$	16.2123	−	16.2123i	0.563075	−	0.563075i	0.930180	+	0.367105i	$0.119651\pi$
$830$	−22.6753	−	15.8381i	−0.787071	−	0.549750i
$831$	1.40753	−	1.40753i	0.0488268	−	0.0488268i
$832$	−6.92612			−0.240120
$833$	35.2507			1.22137
$834$	18.3848	−	18.3848i	0.636613	−	0.636613i
$835$	−0.443390	−	2.49759i	−0.0153441	−	0.0864328i
$836$	6.08481	−	6.08481i	0.210448	−	0.210448i
$837$		−	1.00804i		−	0.0348431i
$838$			8.30494i			0.286889i
$839$	11.5043			0.397174			0.198587	−	0.980083i	$-0.436365\pi$
$839$	11.5043			0.397174			0.198587	+	0.980083i	$0.436365\pi$
$840$	2.70159	+	15.2179i	0.0932136	+	0.525068i
$841$			1.03152i			0.0355697i
$842$	5.43095	+	5.43095i	0.187163	+	0.187163i
$843$			32.0816i			1.10495i
$844$	−24.3785			−0.839144
$845$	−76.9940	+	13.6685i	−2.64867	+	0.470210i
$846$	−1.02417	−	1.02417i	−0.0352117	−	0.0352117i
$847$	−24.8945	+	24.8945i	−0.855385	+	0.855385i
$848$	−1.30971	−	1.30971i	−0.0449755	−	0.0449755i
$849$	−3.23642	−	3.23642i	−0.111074	−	0.111074i
$850$	−8.34821	−	22.7715i	−0.286341	−	0.781057i
$851$	−20.1501	+	2.57463i	−0.690736	+	0.0882573i
$852$	−7.23491	+	7.23491i	−0.247864	+	0.247864i
$853$		−	9.19244i		−	0.314743i	−0.987539	−	0.157372i	$-0.949698\pi$
$853$		−	9.19244i		−	0.314743i	0.987539	−	0.157372i	$-0.0503021\pi$
$854$	−41.7706			−1.42936
$855$	2.96513	−	4.24515i	0.101405	−	0.145181i
$856$	7.62669	−	7.62669i	0.260675	−	0.260675i
$857$			22.7340i			0.776579i	0.921538	+	0.388289i	$0.126934\pi$
$857$			22.7340i			0.776579i	−0.921538	+	0.388289i	$0.873066\pi$
$858$	11.6138	+	11.6138i	0.396490	+	0.396490i
$859$	−8.40939	−	8.40939i	−0.286925	−	0.286925i	0.548938	−	0.835863i	$-0.315032\pi$
$859$	−8.40939	−	8.40939i	−0.286925	−	0.286925i	−0.835863	+	0.548938i	$0.815032\pi$
$860$	5.53043	−	0.981798i	0.188586	−	0.0334790i
$861$	−44.1233			−1.50372
$862$	−16.0000	−	16.0000i	−0.544962	−	0.544962i
$863$	−12.6007	−	12.6007i	−0.428932	−	0.428932i	0.459333	−	0.888264i	$-0.348089\pi$
$863$	−12.6007	−	12.6007i	−0.428932	−	0.428932i	−0.888264	+	0.459333i	$0.848089\pi$
$864$	−3.43067	−	3.43067i	−0.116714	−	0.116714i
$865$	−13.7083	+	19.6260i	−0.466096	+	0.667305i
$866$	21.6988	+	21.6988i	0.737356	+	0.737356i
$867$	−8.44886	+	8.44886i	−0.286938	+	0.286938i
$868$	0.784789			0.0266375
$869$	−14.0058	+	14.0058i	−0.475114	+	0.475114i
$870$	−3.78256	−	21.3070i	−0.128241	−	0.722374i
$871$	−21.5256	−	21.5256i	−0.729369	−	0.729369i
$872$	3.39395	+	3.39395i	0.114934	+	0.114934i
$873$	−4.62115			−0.156402
$874$	15.6812	+	15.6812i	0.530425	+	0.530425i
$875$	10.7876	−	40.8292i	0.364686	−	1.38028i
$876$		−	0.349322i		−	0.0118025i
$877$	7.77308	−	7.77308i	0.262478	−	0.262478i	−0.563582	−	0.826060i	$-0.690577\pi$
$877$	7.77308	−	7.77308i	0.262478	−	0.262478i	0.826060	+	0.563582i	$0.190577\pi$
$878$	−5.60815	+	5.60815i	−0.189266	+	0.189266i
$879$	18.3279			0.618186
$880$	−0.506490	−	2.85304i	−0.0170738	−	0.0961759i
$881$		−	17.5111i		−	0.589963i	−0.955503	−	0.294982i	$-0.904686\pi$
$881$		−	17.5111i		−	0.589963i	0.955503	−	0.294982i	$-0.0953136\pi$
$882$	2.53426			0.0853330
$883$		−	13.3235i		−	0.448372i	−0.974546	−	0.224186i	$-0.928028\pi$
$883$		−	13.3235i		−	0.448372i	0.974546	−	0.224186i	$-0.0719723\pi$
$884$		−	33.5966i		−	1.12998i
$885$	−26.7816	+	4.75444i	−0.900252	+	0.159819i
$886$	−17.9895	+	17.9895i	−0.604370	+	0.604370i
$887$	11.6899	+	11.6899i	0.392508	+	0.392508i	0.875580	−	0.483072i	$-0.160479\pi$
$887$	11.6899	+	11.6899i	0.392508	+	0.392508i	−0.483072	+	0.875580i	$0.660479\pi$
$888$	6.80987	−	8.80503i	0.228524	−	0.295478i
$889$			5.01230i			0.168107i
$890$	6.95036	−	9.95076i	0.232977	−	0.333550i
$891$			12.8609i			0.430857i
$892$	11.0916	+	11.0916i	0.371375	+	0.371375i
$893$	27.5804			0.922942
$894$	−9.73388	−	9.73388i	−0.325550	−	0.325550i
$895$	10.2154	−	14.6252i	0.341462	−	0.488867i
$896$	2.67087	−	2.67087i	0.0892276	−	0.0892276i
$897$	−29.9301	+	29.9301i	−0.999336	+	0.999336i
$898$	−6.18967	−	6.18967i	−0.206552	−	0.206552i
$899$	−1.09880			−0.0366471
$900$	−0.600173	−	1.63710i	−0.0200058	−	0.0545700i
$901$	6.35301	−	6.35301i	0.211649	−	0.211649i
$902$	8.27219			0.275434
$903$		−	17.3628i		−	0.577798i
$904$			4.28955i			0.142668i
$905$	11.4877	−	2.03938i	0.381865	−	0.0677912i
$906$	−5.62901	−	5.62901i	−0.187011	−	0.187011i
$907$		−	32.4447i		−	1.07731i	−0.842527	−	0.538654i	$-0.818933\pi$
$907$		−	32.4447i		−	1.07731i	0.842527	−	0.538654i	$-0.181067\pi$
$908$			13.1902i			0.437732i
$909$	4.80862			0.159492
$910$	33.4975	−	47.9580i	1.11043	−	1.58979i
$911$	−30.7018	+	30.7018i	−1.01719	+	1.01719i	−0.0173451	+	0.999850i	$0.505521\pi$
$911$	−30.7018	+	30.7018i	−1.01719	+	1.01719i	−0.999850	+	0.0173451i	$0.994479\pi$
$912$	−12.1518			−0.402387
$913$	11.3343	−	11.3343i	0.375111	−	0.375111i
$914$			31.9423i			1.05656i
$915$	44.5543	−	7.90958i	1.47292	−	0.261483i
$916$		−	6.06268i		−	0.200317i
$917$	−13.2152			−0.436406
$918$	16.6412	−	16.6412i	0.549241	−	0.549241i
$919$	31.2648	−	31.2648i	1.03133	−	1.03133i	0.0318365	−	0.999493i	$-0.489864\pi$
$919$	31.2648	−	31.2648i	1.03133	−	1.03133i	0.999493	−	0.0318365i	$-0.0101356\pi$
$920$	7.35258	−	1.30528i	0.242407	−	0.0430338i
$921$	48.7429			1.60613
$922$	−2.73403	+	2.73403i	−0.0900405	+	0.0900405i
$923$	38.7256			1.27467
$924$	−8.95713			−0.294668
$925$	−26.9983	+	14.0034i	−0.887697	+	0.460427i
$926$	4.32970			0.142283
$927$	3.72557			0.122364
$928$	−3.73955	+	3.73955i	−0.122757	+	0.122757i
$929$	−6.27539			−0.205889			−0.102944	−	0.994687i	$-0.532826\pi$
$929$	−6.27539			−0.205889			−0.102944	+	0.994687i	$0.532826\pi$
$930$	−0.837090	+	0.148606i	−0.0274493	+	0.00487298i
$931$	−34.1232	+	34.1232i	−1.11834	+	1.11834i
$932$	−11.6145	+	11.6145i	−0.380447	+	0.380447i
$933$	−39.1303			−1.28107
$934$			0.826696i			0.0270503i
$935$	13.8393	−	2.45684i	0.452592	−	0.0803472i
$936$		−	2.41534i		−	0.0789479i
$937$	−37.4173	+	37.4173i	−1.22237	+	1.22237i	−0.255585	+	0.966787i	$0.582268\pi$
$937$	−37.4173	+	37.4173i	−1.22237	+	1.22237i	−0.966787	+	0.255585i	$0.917732\pi$
$938$	16.6016			0.542061
$939$	−11.3555	+	11.3555i	−0.370573	+	0.370573i
$940$	5.31805	−	7.61379i	0.173456	−	0.248335i
$941$	−17.9677			−0.585730			−0.292865	−	0.956154i	$-0.594609\pi$
$941$	−17.9677			−0.585730			−0.292865	+	0.956154i	$0.594609\pi$
$942$		−	33.8920i		−	1.10426i
$943$			21.3183i			0.694219i
$944$	4.70039	+	4.70039i	0.152985	+	0.152985i
$945$	40.3468	−	7.16264i	1.31248	−	0.233001i
$946$			3.25516i			0.105834i
$947$			36.1480i			1.17465i	0.809351	+	0.587326i	$0.199819\pi$
$947$			36.1480i			1.17465i	−0.809351	+	0.587326i	$0.800181\pi$
$948$	27.9706			0.908443
$949$	−0.934890	+	0.934890i	−0.0303478	+	0.0303478i
$950$	30.1243	+	13.9620i	0.977362	+	0.452986i
$951$	35.7083			1.15792
$952$	12.9556	+	12.9556i	0.419895	+	0.419895i
$953$	−25.3431	+	25.3431i	−0.820945	+	0.820945i	−0.986244	−	0.165299i	$-0.947141\pi$
$953$	−25.3431	+	25.3431i	−0.820945	+	0.820945i	0.165299	+	0.986244i	$0.447141\pi$
$954$	0.456733	−	0.456733i	0.0147873	−	0.0147873i
$955$	11.0745	−	15.8552i	0.358362	−	0.513063i
$956$	−0.628920	−	0.628920i	−0.0203407	−	0.0203407i
$957$	12.5411			0.405396
$958$	−19.7849	−	19.7849i	−0.639223	−	0.639223i
$959$			78.1754i			2.52442i
$960$	−2.34312	+	3.35462i	−0.0756238	+	0.108270i
$961$		−	30.9568i		−	0.998607i
$962$	−41.7902	+	5.33965i	−1.34737	+	0.172157i
$963$	2.65965	+	2.65965i	0.0857061	+	0.0857061i
$964$	14.1376	−	14.1376i	0.455343	−	0.455343i
$965$	35.2185	−	6.25223i	1.13372	−	0.201266i
$966$		−	23.0835i		−	0.742698i
$967$			20.8936i			0.671892i	0.941881	+	0.335946i	$0.109056\pi$
$967$			20.8936i			0.671892i	−0.941881	+	0.335946i	$0.890944\pi$
$968$	−9.32073			−0.299580
$969$		−	58.9450i		−	1.89359i
$970$	−5.17931	−	29.1748i	−0.166298	−	0.936747i
$971$	−28.1995			−0.904966			−0.452483	−	0.891773i	$-0.649462\pi$
$971$	−28.1995			−0.904966			−0.452483	+	0.891773i	$0.649462\pi$
$972$	2.55012	−	2.55012i	0.0817950	−	0.0817950i
$973$	37.9478	−	37.9478i	1.21655	−	1.21655i
$974$		−	28.2154i		−	0.904081i
$975$	−26.6486	+	57.4970i	−0.853439	+	1.84138i
$976$	−7.81965	−	7.81965i	−0.250301	−	0.250301i
$977$	21.6547			0.692796			0.346398	−	0.938088i	$-0.387405\pi$
$977$	21.6547			0.692796			0.346398	+	0.938088i	$0.387405\pi$
$978$	−19.1550	−	19.1550i	−0.612510	−	0.612510i
$979$	4.97392	+	4.97392i	0.158967	+	0.158967i
$980$	2.84036	+	15.9996i	0.0907320	+	0.511089i
$981$	−1.18357	+	1.18357i	−0.0377885	+	0.0377885i
$982$	−2.48442			−0.0792812
$983$	−30.3949	+	30.3949i	−0.969448	+	0.969448i	−0.999547	−	0.0300989i	$-0.990418\pi$
$983$	−30.3949	+	30.3949i	−0.969448	+	0.969448i	0.0300989	+	0.999547i	$0.490418\pi$
$984$	−8.26009	−	8.26009i	−0.263322	−	0.263322i
$985$	−32.1635	+	46.0482i	−1.02481	+	1.46722i
$986$	−18.1395	−	18.1395i	−0.577679	−	0.577679i
$987$	−20.2998	−	20.2998i	−0.646150	−	0.646150i
$988$	32.5219	+	32.5219i	1.03466	+	1.03466i
$989$	−8.38888			−0.266751
$990$	0.994939	−	0.176628i	0.0316212	−	0.00561361i
$991$	−9.25603	−	9.25603i	−0.294027	−	0.294027i	0.544642	−	0.838669i	$-0.316666\pi$
$991$	−9.25603	−	9.25603i	−0.294027	−	0.294027i	−0.838669	+	0.544642i	$0.816666\pi$
$992$	0.146916	+	0.146916i	0.00466460	+	0.00466460i
$993$		−	0.577305i		−	0.0183202i
$994$	−14.9335	+	14.9335i	−0.473662	+	0.473662i
$995$	28.5934	−	40.9368i	0.906470	−	1.29778i
$996$	−22.6355			−0.717233
$997$			4.98797i			0.157971i	0.996876	+	0.0789854i	$0.0251680\pi$
$997$			4.98797i			0.157971i	−0.996876	+	0.0789854i	$0.974832\pi$
$998$	−1.49326	+	1.49326i	−0.0472682	+	0.0472682i
$999$	−23.3445	−	18.0548i	−0.738588	−	0.571229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.e.253.8	yes	20
5.2	odd	4		370.2.g.e.327.3	yes	20
37.6	odd	4		370.2.g.e.43.3	✓	20
185.117	even	4	inner	370.2.h.e.117.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.3	✓	20	37.6	odd	4
370.2.g.e.327.3	yes	20	5.2	odd	4
370.2.h.e.117.8	yes	20	185.117	even	4	inner
370.2.h.e.253.8	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(1.29397 - 1.29397i) q^{3} +1.00000 q^{4} +(-2.20164 + 0.390851i) q^{5} +(-1.29397 + 1.29397i) q^{6} +(-2.67087 + 2.67087i) q^{7} -1.00000 q^{8} -0.348729i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(1.29397 - 1.29397i) q^{3} +1.00000 q^{4} +(-2.20164 + 0.390851i) q^{5} +(-1.29397 + 1.29397i) q^{6} +(-2.67087 + 2.67087i) q^{7} -1.00000 q^{8} -0.348729i q^{9} +(2.20164 - 0.390851i) q^{10} +1.29587i q^{11} +(1.29397 - 1.29397i) q^{12} -6.92612 q^{13} +(2.67087 - 2.67087i) q^{14} +(-2.34312 + 3.35462i) q^{15} +1.00000 q^{16} +4.85071i q^{17} +0.348729i q^{18} +(-4.69555 - 4.69555i) q^{19} +(-2.20164 + 0.390851i) q^{20} +6.91207i q^{21} -1.29587i q^{22} +3.33959 q^{23} +(-1.29397 + 1.29397i) q^{24} +(4.69447 - 1.72103i) q^{25} +6.92612 q^{26} +(3.43067 + 3.43067i) q^{27} +(-2.67087 + 2.67087i) q^{28} +(3.73955 - 3.73955i) q^{29} +(2.34312 - 3.35462i) q^{30} +(-0.146916 - 0.146916i) q^{31} -1.00000 q^{32} +(1.67682 + 1.67682i) q^{33} -4.85071i q^{34} +(4.83640 - 6.92422i) q^{35} -0.348729i q^{36} +(-6.03371 + 0.770943i) q^{37} +(4.69555 + 4.69555i) q^{38} +(-8.96221 + 8.96221i) q^{39} +(2.20164 - 0.390851i) q^{40} +6.38351i q^{41} -6.91207i q^{42} -2.51195 q^{43} +1.29587i q^{44} +(0.136301 + 0.767778i) q^{45} -3.33959 q^{46} +(-2.93686 + 2.93686i) q^{47} +(1.29397 - 1.29397i) q^{48} -7.26713i q^{49} +(-4.69447 + 1.72103i) q^{50} +(6.27669 + 6.27669i) q^{51} -6.92612 q^{52} +(-1.30971 - 1.30971i) q^{53} +(-3.43067 - 3.43067i) q^{54} +(-0.506490 - 2.85304i) q^{55} +(2.67087 - 2.67087i) q^{56} -12.1518 q^{57} +(-3.73955 + 3.73955i) q^{58} +(4.70039 + 4.70039i) q^{59} +(-2.34312 + 3.35462i) q^{60} +(-7.81965 - 7.81965i) q^{61} +(0.146916 + 0.146916i) q^{62} +(0.931412 + 0.931412i) q^{63} +1.00000 q^{64} +(15.2488 - 2.70708i) q^{65} +(-1.67682 - 1.67682i) q^{66} +(3.10789 + 3.10789i) q^{67} +4.85071i q^{68} +(4.32133 - 4.32133i) q^{69} +(-4.83640 + 6.92422i) q^{70} -5.59124 q^{71} +0.348729i q^{72} +(0.134980 - 0.134980i) q^{73} +(6.03371 - 0.770943i) q^{74} +(3.84755 - 8.30148i) q^{75} +(-4.69555 - 4.69555i) q^{76} +(-3.46110 - 3.46110i) q^{77} +(8.96221 - 8.96221i) q^{78} +(10.8080 + 10.8080i) q^{79} +(-2.20164 + 0.390851i) q^{80} +9.92458 q^{81} -6.38351i q^{82} +(-8.74652 - 8.74652i) q^{83} +6.91207i q^{84} +(-1.89590 - 10.6795i) q^{85} +2.51195 q^{86} -9.67775i q^{87} -1.29587i q^{88} +(3.83829 - 3.83829i) q^{89} +(-0.136301 - 0.767778i) q^{90} +(18.4988 - 18.4988i) q^{91} +3.33959 q^{92} -0.380211 q^{93} +(2.93686 - 2.93686i) q^{94} +(12.1732 + 8.50267i) q^{95} +(-1.29397 + 1.29397i) q^{96} -13.2514i q^{97} +7.26713i q^{98} +0.451907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8}+O(q^{10}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27} - 2 q^{28} + 18 q^{29} + 4 q^{30} + 12 q^{31} - 20 q^{32} + 4 q^{33} - 12 q^{35} - 32 q^{37} - 6 q^{38} + 6 q^{39} + 4 q^{40} + 16 q^{43} + 22 q^{45} + 4 q^{46} - 22 q^{47} + 4 q^{48} - 10 q^{50} + 8 q^{51} - 4 q^{53} + 20 q^{54} + 16 q^{55} + 2 q^{56} + 24 q^{57} - 18 q^{58} - 10 q^{59} - 4 q^{60} + 10 q^{61} - 12 q^{62} - 2 q^{63} + 20 q^{64} + 20 q^{65} - 4 q^{66} + 8 q^{67} - 34 q^{69} + 12 q^{70} + 16 q^{71} - 6 q^{73} + 32 q^{74} - 26 q^{75} + 6 q^{76} - 4 q^{77} - 6 q^{78} + 12 q^{79} - 4 q^{80} - 28 q^{81} + 6 q^{83} + 10 q^{85} - 16 q^{86} - 44 q^{89} - 22 q^{90} - 40 q^{91} - 4 q^{92} - 40 q^{93} + 22 q^{94} + 50 q^{95} - 4 q^{96} - 20 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 4 * q^3 + 20 * q^4 - 4 * q^5 - 4 * q^6 - 2 * q^7 - 20 * q^8 + 4 * q^10 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 6 * q^19 - 4 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 - 20 * q^27 - 2 * q^28 + 18 * q^29 + 4 * q^30 + 12 * q^31 - 20 * q^32 + 4 * q^33 - 12 * q^35 - 32 * q^37 - 6 * q^38 + 6 * q^39 + 4 * q^40 + 16 * q^43 + 22 * q^45 + 4 * q^46 - 22 * q^47 + 4 * q^48 - 10 * q^50 + 8 * q^51 - 4 * q^53 + 20 * q^54 + 16 * q^55 + 2 * q^56 + 24 * q^57 - 18 * q^58 - 10 * q^59 - 4 * q^60 + 10 * q^61 - 12 * q^62 - 2 * q^63 + 20 * q^64 + 20 * q^65 - 4 * q^66 + 8 * q^67 - 34 * q^69 + 12 * q^70 + 16 * q^71 - 6 * q^73 + 32 * q^74 - 26 * q^75 + 6 * q^76 - 4 * q^77 - 6 * q^78 + 12 * q^79 - 4 * q^80 - 28 * q^81 + 6 * q^83 + 10 * q^85 - 16 * q^86 - 44 * q^89 - 22 * q^90 - 40 * q^91 - 4 * q^92 - 40 * q^93 + 22 * q^94 + 50 * q^95 - 4 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

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Database

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