LMFDB - Embedded newform 403.2.k.e.66.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			66.10
Character	$\chi$	$=$	403.66
Dual form			403.2.k.e.287.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.165656 + 0.509838i) q^{2} +(0.987660 - 3.03970i) q^{3} +(1.38554 - 1.00665i) q^{4} -3.75225 q^{5} +1.71337 q^{6} +(1.77021 - 1.28613i) q^{7} +(1.61014 + 1.16984i) q^{8} +(-5.83728 - 4.24103i) q^{9} +O(q^{10})$	\(q+(0.165656 + 0.509838i) q^{2} +(0.987660 - 3.03970i) q^{3} +(1.38554 - 1.00665i) q^{4} -3.75225 q^{5} +1.71337 q^{6} +(1.77021 - 1.28613i) q^{7} +(1.61014 + 1.16984i) q^{8} +(-5.83728 - 4.24103i) q^{9} +(-0.621584 - 1.91304i) q^{10} +(-1.96727 + 1.42931i) q^{11} +(-1.69149 - 5.20587i) q^{12} +(0.309017 - 0.951057i) q^{13} +(0.948968 + 0.689465i) q^{14} +(-3.70595 + 11.4057i) q^{15} +(0.728762 - 2.24290i) q^{16} +(2.91030 + 2.11446i) q^{17} +(1.19526 - 3.67862i) q^{18} +(0.603093 + 1.85613i) q^{19} +(-5.19890 + 3.77722i) q^{20} +(-2.16110 - 6.65119i) q^{21} +(-1.05461 - 0.766217i) q^{22} +(-0.657174 - 0.477465i) q^{23} +(5.14623 - 3.73896i) q^{24} +9.07937 q^{25} +0.536075 q^{26} +(-10.8995 + 7.91898i) q^{27} +(1.15801 - 3.56399i) q^{28} +(-2.17818 - 6.70376i) q^{29} -6.42899 q^{30} +(4.95384 + 2.54154i) q^{31} +5.24473 q^{32} +(2.40168 + 7.39160i) q^{33} +(-0.595920 + 1.83405i) q^{34} +(-6.64228 + 4.82590i) q^{35} -12.3570 q^{36} -1.77861 q^{37} +(-0.846419 + 0.614960i) q^{38} +(-2.58573 - 1.87864i) q^{39} +(-6.04166 - 4.38952i) q^{40} +(-0.899707 - 2.76901i) q^{41} +(3.03303 - 2.20362i) q^{42} +(-2.92136 - 8.99102i) q^{43} +(-1.28692 + 3.96073i) q^{44} +(21.9029 + 15.9134i) q^{45} +(0.134565 - 0.414147i) q^{46} +(-0.272966 + 0.840101i) q^{47} +(-6.09798 - 4.43044i) q^{48} +(-0.683609 + 2.10393i) q^{49} +(1.50406 + 4.62901i) q^{50} +(9.30171 - 6.75808i) q^{51} +(-0.529230 - 1.62880i) q^{52} +(10.8857 + 7.90892i) q^{53} +(-5.84298 - 4.24517i) q^{54} +(7.38170 - 5.36312i) q^{55} +4.35486 q^{56} +6.23774 q^{57} +(3.05700 - 2.22104i) q^{58} +(4.40280 - 13.5504i) q^{59} +(6.34689 + 19.5337i) q^{60} +14.8865 q^{61} +(-0.475140 + 2.94668i) q^{62} -15.7878 q^{63} +(-0.588701 - 1.81184i) q^{64} +(-1.15951 + 3.56860i) q^{65} +(-3.37067 + 2.44893i) q^{66} -2.30645 q^{67} +6.16087 q^{68} +(-2.10042 + 1.52604i) q^{69} +(-3.56076 - 2.58705i) q^{70} +(3.13269 + 2.27604i) q^{71} +(-4.43754 - 13.6573i) q^{72} +(0.864488 - 0.628087i) q^{73} +(-0.294638 - 0.906802i) q^{74} +(8.96733 - 27.5986i) q^{75} +(2.70409 + 1.96464i) q^{76} +(-1.64421 + 5.06036i) q^{77} +(0.529460 - 1.62951i) q^{78} +(-2.27427 - 1.65236i) q^{79} +(-2.73450 + 8.41592i) q^{80} +(6.61740 + 20.3663i) q^{81} +(1.26271 - 0.917410i) q^{82} +(4.46980 + 13.7566i) q^{83} +(-9.68974 - 7.04001i) q^{84} +(-10.9202 - 7.93396i) q^{85} +(4.10002 - 2.97884i) q^{86} -22.5287 q^{87} -4.83965 q^{88} +(-5.84766 + 4.24857i) q^{89} +(-4.48490 + 13.8031i) q^{90} +(-0.676161 - 2.08101i) q^{91} -1.39118 q^{92} +(12.6183 - 12.5480i) q^{93} -0.473534 q^{94} +(-2.26296 - 6.96466i) q^{95} +(5.18001 - 15.9424i) q^{96} +(-6.99394 + 5.08139i) q^{97} -1.18591 q^{98} +17.5453 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.165656	+	0.509838i	0.117137	+	0.360510i	0.992387	−	0.123161i	$-0.0393032\pi$
$2$	0.165656	+	0.509838i	0.117137	+	0.360510i	−0.875250	+	0.483671i	$0.839303\pi$
$3$	0.987660	−	3.03970i	0.570226	−	1.75497i	−0.0816637	−	0.996660i	$-0.526023\pi$
$3$	0.987660	−	3.03970i	0.570226	−	1.75497i	0.651889	−	0.758314i	$-0.273977\pi$
$4$	1.38554	−	1.00665i	0.692771	−	0.503327i
$5$	−3.75225			−1.67806			−0.839028	−	0.544088i	$-0.816876\pi$
$5$	−3.75225			−1.67806			−0.839028	+	0.544088i	$0.816876\pi$
$6$	1.71337			0.699480
$7$	1.77021	−	1.28613i	0.669078	−	0.486113i	−0.200639	−	0.979665i	$-0.564302\pi$
$7$	1.77021	−	1.28613i	0.669078	−	0.486113i	0.869716	+	0.493552i	$0.164302\pi$
$8$	1.61014	+	1.16984i	0.569271	+	0.413600i
$9$	−5.83728	−	4.24103i	−1.94576	−	1.41368i
$10$	−0.621584	−	1.91304i	−0.196562	−	0.604956i
$11$	−1.96727	+	1.42931i	−0.593155	+	0.430953i	−0.843443	−	0.537219i	$-0.819475\pi$
$11$	−1.96727	+	1.42931i	−0.593155	+	0.430953i	0.250287	+	0.968172i	$0.419475\pi$
$12$	−1.69149	−	5.20587i	−0.488291	−	1.50280i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	0.948968	+	0.689465i	0.253622	+	0.184267i
$15$	−3.70595	+	11.4057i	−0.956871	+	2.94495i
$16$	0.728762	−	2.24290i	0.182191	−	0.560725i
$17$	2.91030	+	2.11446i	0.705851	+	0.512831i	0.881833	−	0.471563i	$-0.156310\pi$
$17$	2.91030	+	2.11446i	0.705851	+	0.512831i	−0.175981	+	0.984393i	$0.556310\pi$
$18$	1.19526	−	3.67862i	0.281725	−	0.867059i
$19$	0.603093	+	1.85613i	0.138359	+	0.425825i	0.996097	−	0.0882612i	$-0.0281310\pi$
$19$	0.603093	+	1.85613i	0.138359	+	0.425825i	−0.857738	+	0.514087i	$0.828131\pi$
$20$	−5.19890	+	3.77722i	−1.16251	+	0.844612i
$21$	−2.16110	−	6.65119i	−0.471591	−	1.45141i
$22$	−1.05461	−	0.766217i	−0.224843	−	0.163358i
$23$	−0.657174	−	0.477465i	−0.137030	−	0.0995583i	0.517158	−	0.855890i	$-0.326990\pi$
$23$	−0.657174	−	0.477465i	−0.137030	−	0.0995583i	−0.654189	+	0.756331i	$0.726990\pi$
$24$	5.14623	−	3.73896i	1.05047	−	0.763211i
$25$	9.07937			1.81587
$26$	0.536075			0.105133
$27$	−10.8995	+	7.91898i	−2.09762	+	1.52401i
$28$	1.15801	−	3.56399i	0.218843	−	0.673530i
$29$	−2.17818	−	6.70376i	−0.404478	−	1.24486i	−0.921330	−	0.388781i	$-0.872896\pi$
$29$	−2.17818	−	6.70376i	−0.404478	−	1.24486i	0.516852	−	0.856075i	$-0.327104\pi$
$30$	−6.42899			−1.17377
$31$	4.95384	+	2.54154i	0.889736	+	0.456475i
$31$	4.95384	+	2.54154i	0.889736	+	0.456475i
$32$	5.24473			0.927146
$33$	2.40168	+	7.39160i	0.418078	+	1.28671i
$34$	−0.595920	+	1.83405i	−0.102199	+	0.314538i
$35$	−6.64228	+	4.82590i	−1.12275	+	0.815726i
$36$	−12.3570			−2.05951
$37$	−1.77861			−0.292401			−0.146201	−	0.989255i	$-0.546705\pi$
$37$	−1.77861			−0.292401			−0.146201	+	0.989255i	$0.546705\pi$
$38$	−0.846419	+	0.614960i	−0.137307	+	0.0997596i
$39$	−2.58573	−	1.87864i	−0.414048	−	0.300823i
$40$	−6.04166	−	4.38952i	−0.955270	−	0.694044i
$41$	−0.899707	−	2.76901i	−0.140511	−	0.432447i	0.855896	−	0.517148i	$-0.173006\pi$
$41$	−0.899707	−	2.76901i	−0.140511	−	0.432447i	−0.996406	+	0.0847011i	$0.973006\pi$
$42$	3.03303	−	2.20362i	0.468006	−	0.340026i
$43$	−2.92136	−	8.99102i	−0.445503	−	1.37112i	−0.881931	−	0.471379i	$-0.843756\pi$
$43$	−2.92136	−	8.99102i	−0.445503	−	1.37112i	0.436428	−	0.899739i	$-0.356244\pi$
$44$	−1.28692	+	3.96073i	−0.194010	+	0.597103i
$45$	21.9029	+	15.9134i	3.26510	+	2.37223i
$46$	0.134565	−	0.414147i	0.0198405	−	0.0610627i
$47$	−0.272966	+	0.840101i	−0.0398161	+	0.122541i	−0.968989	−	0.247104i	$-0.920521\pi$
$47$	−0.272966	+	0.840101i	−0.0398161	+	0.122541i	0.929173	+	0.369646i	$0.120521\pi$
$48$	−6.09798	−	4.43044i	−0.880168	−	0.639479i
$49$	−0.683609	+	2.10393i	−0.0976584	+	0.300562i
$50$	1.50406	+	4.62901i	0.212706	+	0.654641i
$51$	9.30171	−	6.75808i	1.30250	−	0.946321i
$52$	−0.529230	−	1.62880i	−0.0733909	−	0.225874i
$53$	10.8857	+	7.90892i	1.49527	+	1.08637i	0.972220	+	0.234070i	$0.0752044\pi$
$53$	10.8857	+	7.90892i	1.49527	+	1.08637i	0.523046	+	0.852305i	$0.324796\pi$
$54$	−5.84298	−	4.24517i	−0.795129	−	0.577695i
$55$	7.38170	−	5.36312i	0.995349	−	0.723163i
$56$	4.35486			0.581943
$57$	6.23774			0.826208
$58$	3.05700	−	2.22104i	0.401404	−	0.291637i
$59$	4.40280	−	13.5504i	0.573196	−	1.76412i	−0.0690449	−	0.997614i	$-0.521995\pi$
$59$	4.40280	−	13.5504i	0.573196	−	1.76412i	0.642241	−	0.766503i	$-0.278005\pi$
$60$	6.34689	+	19.5337i	0.819380	+	2.52179i
$61$	14.8865			1.90602			0.953010	−	0.302939i	$-0.0979678\pi$
$61$	14.8865			1.90602			0.953010	+	0.302939i	$0.0979678\pi$
$62$	−0.475140	+	2.94668i	−0.0603428	+	0.374229i
$63$	−15.7878			−1.98907
$64$	−0.588701	−	1.81184i	−0.0735876	−	0.226479i
$65$	−1.15951	+	3.56860i	−0.143819	+	0.442630i
$66$	−3.37067	+	2.44893i	−0.414900	+	0.301443i
$67$	−2.30645			−0.281777			−0.140889	−	0.990025i	$-0.544996\pi$
$67$	−2.30645			−0.281777			−0.140889	+	0.990025i	$0.544996\pi$
$68$	6.16087			0.747115
$69$	−2.10042	+	1.52604i	−0.252860	+	0.183714i
$70$	−3.56076	−	2.58705i	−0.425592	−	0.309211i
$71$	3.13269	+	2.27604i	0.371782	+	0.270116i	0.757950	−	0.652313i	$-0.226201\pi$
$71$	3.13269	+	2.27604i	0.371782	+	0.270116i	−0.386167	+	0.922429i	$0.626201\pi$
$72$	−4.43754	−	13.6573i	−0.522969	−	1.60953i
$73$	0.864488	−	0.628087i	0.101181	−	0.0735121i	−0.536045	−	0.844190i	$-0.680082\pi$
$73$	0.864488	−	0.628087i	0.101181	−	0.0735121i	0.637225	+	0.770678i	$0.280082\pi$
$74$	−0.294638	−	0.906802i	−0.0342510	−	0.105414i
$75$	8.96733	−	27.5986i	1.03546	−	3.18681i
$76$	2.70409	+	1.96464i	0.310181	+	0.225359i
$77$	−1.64421	+	5.06036i	−0.187375	+	0.576682i
$78$	0.529460	−	1.62951i	0.0599496	−	0.184506i
$79$	−2.27427	−	1.65236i	−0.255876	−	0.185904i	0.452451	−	0.891789i	$-0.350550\pi$
$79$	−2.27427	−	1.65236i	−0.255876	−	0.185904i	−0.708327	+	0.705885i	$0.750550\pi$
$80$	−2.73450	+	8.41592i	−0.305726	+	0.940928i
$81$	6.61740	+	20.3663i	0.735267	+	2.26292i
$82$	1.26271	−	0.917410i	0.139443	−	0.101311i
$83$	4.46980	+	13.7566i	0.490625	+	1.50999i	0.823666	+	0.567075i	$0.191925\pi$
$83$	4.46980	+	13.7566i	0.490625	+	1.50999i	−0.333041	+	0.942912i	$0.608075\pi$
$84$	−9.68974	−	7.04001i	−1.05724	−	0.768128i
$85$	−10.9202	−	7.93396i	−1.18446	−	0.860559i
$86$	4.10002	−	2.97884i	0.442117	−	0.321217i
$87$	−22.5287			−2.41533
$88$	−4.83965			−0.515908
$89$	−5.84766	+	4.24857i	−0.619851	+	0.450348i	−0.852869	−	0.522124i	$-0.825140\pi$
$89$	−5.84766	+	4.24857i	−0.619851	+	0.450348i	0.233019	+	0.972472i	$0.425140\pi$
$90$	−4.48490	+	13.8031i	−0.472750	+	1.45497i
$91$	−0.676161	−	2.08101i	−0.0708809	−	0.218149i
$92$	−1.39118			−0.145041
$93$	12.6183	−	12.5480i	1.30845	−	1.30117i
$94$	−0.473534			−0.0488413
$95$	−2.26296	−	6.96466i	−0.232174	−	0.714559i
$96$	5.18001	−	15.9424i	0.528683	−	1.62712i
$97$	−6.99394	+	5.08139i	−0.710127	+	0.515937i	−0.883214	−	0.468969i	$-0.844626\pi$
$97$	−6.99394	+	5.08139i	−0.710127	+	0.515937i	0.173088	+	0.984906i	$0.444626\pi$
$98$	−1.18591			−0.119795
$99$	17.5453			1.76337
$100$	12.5798	−	9.13979i	1.25798	−	0.913979i
$101$	1.36483	+	0.991609i	0.135806	+	0.0986688i	0.653614	−	0.756828i	$-0.273252\pi$
$101$	1.36483	+	0.991609i	0.135806	+	0.0986688i	−0.517808	+	0.855497i	$0.673252\pi$
$102$	4.98642	+	3.62284i	0.493729	+	0.358715i
$103$	5.55699	+	17.1026i	0.547546	+	1.68517i	0.714858	+	0.699270i	$0.246491\pi$
$103$	5.55699	+	17.1026i	0.547546	+	1.68517i	−0.167312	+	0.985904i	$0.553509\pi$
$104$	1.61014	−	1.16984i	0.157887	−	0.114712i
$105$	8.10899	+	24.9569i	0.791356	+	2.43554i
$106$	−2.22898	+	6.86011i	−0.216498	+	0.666312i
$107$	−7.46837	−	5.42609i	−0.721994	−	0.524560i	0.165026	−	0.986289i	$-0.447229\pi$
$107$	−7.46837	−	5.42609i	−0.721994	−	0.524560i	−0.887021	+	0.461729i	$0.847229\pi$
$108$	−7.13009	+	21.9442i	−0.686093	+	2.11158i
$109$	−1.49225	+	4.59267i	−0.142932	+	0.439898i	−0.996739	−	0.0806905i	$-0.974287\pi$
$109$	−1.49225	+	4.59267i	−0.142932	+	0.439898i	0.853808	+	0.520589i	$0.174287\pi$
$110$	3.95715	+	2.87504i	0.377299	+	0.274124i
$111$	−1.75666	+	5.40644i	−0.166735	+	0.513157i
$112$	−1.59461	−	4.90770i	−0.150676	−	0.463734i
$113$	7.17438	−	5.21249i	0.674909	−	0.490350i	−0.196756	−	0.980452i	$-0.563041\pi$
$113$	7.17438	−	5.21249i	0.674909	−	0.490350i	0.871665	+	0.490103i	$0.163041\pi$
$114$	1.03332	+	3.18024i	0.0967794	+	0.297856i
$115$	2.46588	+	1.79157i	0.229944	+	0.167064i
$116$	−9.76633	−	7.09565i	−0.906781	−	0.658815i
$117$	−5.83728	+	4.24103i	−0.539657	+	0.392084i
$118$	7.63788			0.703124
$119$	7.87132			0.721563
$120$	−19.3099	+	14.0295i	−1.76275	+	1.28071i
$121$	−1.57194	+	4.83794i	−0.142904	+	0.439813i
$122$	2.46604	+	7.58970i	0.223265	+	0.687139i
$123$	−9.30559			−0.839057
$124$	9.42221	−	1.46539i	0.846139	−	0.131596i
$125$	−15.3068			−1.36908
$126$	−2.61534	−	8.04920i	−0.232993	−	0.717080i
$127$	−3.66691	+	11.2856i	−0.325385	+	1.00143i	0.645881	+	0.763438i	$0.276490\pi$
$127$	−3.66691	+	11.2856i	−0.325385	+	1.00143i	−0.971266	+	0.237995i	$0.923510\pi$
$128$	9.31237	−	6.76584i	0.823105	−	0.598021i
$129$	−30.2154			−2.66031
$130$	−2.01149			−0.176419
$131$	−16.7654	+	12.1808i	−1.46480	+	1.06424i	−0.482717	+	0.875776i	$0.660350\pi$
$131$	−16.7654	+	12.1808i	−1.46480	+	1.06424i	−0.982081	+	0.188461i	$0.939650\pi$
$132$	10.7684	+	7.82371i	0.937270	+	0.680967i
$133$	3.45484	+	2.51009i	0.299572	+	0.217652i
$134$	−0.382078	−	1.17591i	−0.0330065	−	0.101584i
$135$	40.8978	−	29.7140i	3.51992	−	2.55737i
$136$	2.21243	+	6.80915i	0.189714	+	0.583880i
$137$	3.62276	−	11.1497i	0.309513	−	0.952584i	−0.668441	−	0.743765i	$-0.733038\pi$
$137$	3.62276	−	11.1497i	0.309513	−	0.952584i	0.977954	−	0.208819i	$-0.0669618\pi$
$138$	−1.12598	−	0.818073i	−0.0958499	−	0.0696390i
$139$	−2.37166	+	7.29922i	−0.201162	+	0.619112i	0.798688	+	0.601746i	$0.205528\pi$
$139$	−2.37166	+	7.29922i	−0.201162	+	0.619112i	−0.999849	+	0.0173658i	$0.994472\pi$
$140$	−4.34514	+	13.3730i	−0.367231	+	1.13022i
$141$	2.28406	+	1.65947i	0.192353	+	0.139752i
$142$	−0.641459	+	1.97421i	−0.0538300	+	0.165672i
$143$	0.751432	+	2.31267i	0.0628379	+	0.193395i
$144$	−13.7662	+	10.0017i	−1.14718	+	0.833477i
$145$	8.17308	+	25.1542i	0.678738	+	2.08894i
$146$	0.463431	+	0.336702i	0.0383538	+	0.0278657i
$147$	5.72016	+	4.15594i	0.471791	+	0.342776i
$148$	−2.46434	+	1.79044i	−0.202567	+	0.147174i
$149$	12.9281			1.05911			0.529557	−	0.848274i	$-0.322358\pi$
$149$	12.9281			1.05911			0.529557	+	0.848274i	$0.322358\pi$
$150$	15.5563			1.27017
$151$	4.13994	−	3.00784i	0.336904	−	0.244775i	−0.406451	−	0.913673i	$-0.633234\pi$
$151$	4.13994	−	3.00784i	0.336904	−	0.244775i	0.743354	+	0.668898i	$0.233234\pi$
$152$	−1.20030	+	3.69415i	−0.0973575	+	0.299636i
$153$	−8.02075	−	24.6853i	−0.648439	−	1.99569i
$154$	−2.85234			−0.229848
$155$	−18.5880	−	9.53650i	−1.49303	−	0.765990i
$156$	−5.47377			−0.438253
$157$	−2.13612	−	6.57430i	−0.170481	−	0.524686i	0.828917	−	0.559371i	$-0.188957\pi$
$157$	−2.13612	−	6.57430i	−0.170481	−	0.524686i	−0.999398	+	0.0346848i	$0.988957\pi$
$158$	0.465686	−	1.43323i	0.0370480	−	0.114022i
$159$	34.7922	−	25.2780i	2.75920	−	2.00467i
$160$	−19.6795			−1.55580
$161$	−1.77742			−0.140080
$162$	−9.28728	+	6.74760i	−0.729678	+	0.530142i
$163$	−20.0374	−	14.5580i	−1.56945	−	1.14027i	−0.927682	−	0.373371i	$-0.878202\pi$
$163$	−20.0374	−	14.5580i	−1.56945	−	1.14027i	−0.641766	−	0.766900i	$-0.721798\pi$
$164$	−4.03402	−	2.93089i	−0.315004	−	0.228864i
$165$	−9.01169	−	27.7351i	−0.701559	−	2.15918i
$166$	−6.27321	+	4.55775i	−0.486895	+	0.353750i
$167$	2.89145	+	8.89898i	0.223747	+	0.688624i	0.998416	+	0.0562568i	$0.0179166\pi$
$167$	2.89145	+	8.89898i	0.223747	+	0.688624i	−0.774669	+	0.632367i	$0.782083\pi$
$168$	4.30112	−	13.2375i	0.331839	−	1.02130i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	2.23604	−	6.88183i	0.171497	−	0.527812i
$171$	4.35148	−	13.3925i	0.332766	−	1.02415i
$172$	−13.0985	−	9.51663i	−0.998753	−	0.725636i
$173$	2.40908	−	7.41438i	0.183159	−	0.563705i	−0.816753	−	0.576988i	$-0.804228\pi$
$173$	2.40908	−	7.41438i	0.183159	−	0.563705i	0.999912	+	0.0132826i	$0.00422810\pi$
$174$	−3.73203	−	11.4860i	−0.282924	−	0.870752i
$175$	16.0724	−	11.6773i	1.21496	−	0.882721i
$176$	1.77212	+	5.45402i	0.133579	+	0.411113i
$177$	−36.8408	−	26.7664i	−2.76913	−	2.01189i
$178$	−3.13479	−	2.27756i	−0.234962	−	0.170710i
$179$	1.81988	−	1.32222i	0.136024	−	0.0988275i	−0.517692	−	0.855567i	$-0.673209\pi$
$179$	1.81988	−	1.32222i	0.136024	−	0.0988275i	0.653717	+	0.756739i	$0.273209\pi$
$180$	46.3667			3.45597
$181$	−7.43335			−0.552516			−0.276258	−	0.961083i	$-0.589094\pi$
$181$	−7.43335			−0.552516			−0.276258	+	0.961083i	$0.589094\pi$
$182$	0.948968	−	0.689465i	0.0703422	−	0.0511066i
$183$	14.7028	−	45.2505i	1.08686	−	3.34502i
$184$	−0.499588	−	1.53757i	−0.0368301	−	0.113351i
$185$	6.67378			0.490666
$186$	8.48776	+	4.35460i	0.622353	+	0.319295i
$187$	−8.74756			−0.639685
$188$	0.467487	+	1.43878i	0.0340950	+	0.104934i
$189$	−9.10964	+	28.0366i	−0.662628	+	2.03936i
$190$	3.17598	−	2.30748i	0.230409	−	0.167402i
$191$	4.47355			0.323695			0.161847	−	0.986816i	$-0.448255\pi$
$191$	4.47355			0.323695			0.161847	+	0.986816i	$0.448255\pi$
$192$	−6.08888			−0.439427
$193$	3.33841	−	2.42549i	0.240304	−	0.174591i	−0.461115	−	0.887340i	$-0.652550\pi$
$193$	3.33841	−	2.42549i	0.240304	−	0.174591i	0.701419	+	0.712750i	$0.252550\pi$
$194$	−3.74928	−	2.72401i	−0.269182	−	0.195572i
$195$	9.70229	+	7.04913i	0.694795	+	0.504798i
$196$	1.17076	+	3.60324i	0.0836260	+	0.257374i
$197$	−17.5453	+	12.7474i	−1.25005	+	0.908214i	−0.998225	−	0.0595592i	$-0.981030\pi$
$197$	−17.5453	+	12.7474i	−1.25005	+	0.908214i	−0.251824	+	0.967773i	$0.581030\pi$
$198$	2.90649	+	8.94525i	0.206555	+	0.635711i
$199$	−5.31284	+	16.3512i	−0.376617	+	1.15911i	0.565764	+	0.824567i	$0.308581\pi$
$199$	−5.31284	+	16.3512i	−0.376617	+	1.15911i	−0.942381	+	0.334541i	$0.891419\pi$
$200$	14.6191	+	10.6214i	1.03373	+	0.751045i
$201$	−2.27799	+	7.01092i	−0.160677	+	0.494512i
$202$	−0.279467	+	0.860110i	−0.0196632	+	0.0605171i
$203$	−12.4778	−	9.06564i	−0.875768	−	0.636283i
$204$	6.08484	−	18.7272i	0.426024	−	1.31117i
$205$	3.37592	+	10.3900i	0.235785	+	0.725671i
$206$	−7.79903	+	5.66633i	−0.543384	+	0.394792i
$207$	1.81116	+	5.57419i	0.125885	+	0.387433i
$208$	−1.90792	−	1.38619i	−0.132291	−	0.0961149i
$209$	−3.83943	−	2.78951i	−0.265579	−	0.192954i
$210$	−11.3807	+	8.26854i	−0.785341	+	0.570584i
$211$	15.4297			1.06222			0.531111	−	0.847302i	$-0.321775\pi$
$211$	15.4297			1.06222			0.531111	+	0.847302i	$0.321775\pi$
$212$	23.0441			1.58268
$213$	10.0125	−	7.27452i	0.686046	−	0.498442i
$214$	1.52924	−	4.70652i	0.104537	−	0.321731i
$215$	10.9617	+	33.7366i	0.747580	+	2.30081i
$216$	−26.8138			−1.82444
$217$	12.0381	−	1.87224i	0.817201	−	0.127096i
$218$	−2.58872			−0.175330
$219$	−1.05538	−	3.24812i	−0.0713160	−	0.219488i
$220$	4.82884	−	14.8616i	0.325561	−	1.00197i
$221$	2.91030	−	2.11446i	0.195768	−	0.142234i
$222$	−3.04741			−0.204529
$223$	9.73481			0.651891			0.325945	−	0.945389i	$-0.394317\pi$
$223$	9.73481			0.651891			0.325945	+	0.945389i	$0.394317\pi$
$224$	9.28429	−	6.74543i	0.620333	−	0.450698i
$225$	−52.9988	−	38.5059i	−3.53325	−	2.56706i
$226$	3.84601	+	2.79429i	0.255833	+	0.185873i
$227$	−6.18219	−	19.0268i	−0.410326	−	1.26285i	−0.916365	−	0.400344i	$-0.868891\pi$
$227$	−6.18219	−	19.0268i	−0.410326	−	1.26285i	0.506039	−	0.862511i	$-0.331109\pi$
$228$	8.64264	−	6.27925i	0.572373	−	0.415853i
$229$	7.92757	+	24.3985i	0.523868	+	1.61230i	0.766543	+	0.642193i	$0.221975\pi$
$229$	7.92757	+	24.3985i	0.523868	+	1.61230i	−0.242674	+	0.970108i	$0.578025\pi$
$230$	−0.504920	+	1.55398i	−0.0332934	+	0.102467i
$231$	13.7581	+	9.99583i	0.905215	+	0.657677i
$232$	4.33512	−	13.3421i	0.284614	−	0.875953i
$233$	−2.25671	+	6.94545i	−0.147842	+	0.455011i	−0.997366	−	0.0725396i	$-0.976890\pi$
$233$	−2.25671	+	6.94545i	−0.147842	+	0.455011i	0.849523	+	0.527551i	$0.176890\pi$
$234$	−3.12922	−	2.27351i	−0.204564	−	0.148624i
$235$	1.02423	−	3.15227i	0.0668137	−	0.205631i
$236$	−7.54034	−	23.2068i	−0.490834	−	1.51063i
$237$	−7.26888	+	5.28115i	−0.472164	+	0.343047i
$238$	1.30394	+	4.01310i	0.0845216	+	0.260131i
$239$	1.75903	+	1.27801i	0.113782	+	0.0826678i	0.643221	−	0.765680i	$-0.277598\pi$
$239$	1.75903	+	1.27801i	0.113782	+	0.0826678i	−0.529439	+	0.848348i	$0.677598\pi$
$240$	22.8811	+	16.6241i	1.47697	+	1.07308i
$241$	−11.3115	+	8.21832i	−0.728641	+	0.529388i	−0.889133	−	0.457649i	$-0.848692\pi$
$241$	−11.3115	+	8.21832i	−0.728641	+	0.529388i	0.160493	+	0.987037i	$0.448692\pi$
$242$	−2.72697			−0.175296
$243$	28.0254			1.79783
$244$	20.6258	−	14.9856i	1.32043	−	0.959352i
$245$	2.56507	−	7.89447i	0.163876	−	0.504359i
$246$	−1.54153	−	4.74434i	−0.0982844	−	0.302488i
$247$	1.95165			0.124181
$248$	5.00320	+	9.88744i	0.317704	+	0.627853i
$249$	46.2308			2.92976
$250$	−2.53567	−	7.80400i	−0.160370	−	0.493568i
$251$	0.812527	−	2.50070i	0.0512863	−	0.157843i	−0.922133	−	0.386873i	$-0.873555\pi$
$251$	0.812527	−	2.50070i	0.0512863	−	0.157843i	0.973419	+	0.229030i	$0.0735553\pi$
$252$	−21.8746	+	15.8928i	−1.37797	+	1.00115i
$253$	1.97529			0.124185
$254$	−6.36126			−0.399141
$255$	−34.9023	+	25.3580i	−2.18567	+	1.58798i
$256$	1.90966	+	1.38745i	0.119353	+	0.0867154i
$257$	−4.76760	−	3.46386i	−0.297395	−	0.216070i	0.429074	−	0.903269i	$-0.358840\pi$
$257$	−4.76760	−	3.46386i	−0.297395	−	0.216070i	−0.726469	+	0.687199i	$0.758840\pi$
$258$	−5.00537	−	15.4049i	−0.311621	−	0.959070i
$259$	−3.14851	+	2.28753i	−0.195639	+	0.142140i
$260$	1.98580	+	6.11167i	0.123154	+	0.379030i
$261$	−15.7162	+	48.3694i	−0.972807	+	2.99399i
$262$	−8.98751	−	6.52981i	−0.555250	−	0.403413i
$263$	2.52635	−	7.77531i	0.155781	−	0.479446i	−0.842458	−	0.538762i	$-0.818892\pi$
$263$	2.52635	−	7.77531i	0.155781	−	0.479446i	0.998239	+	0.0593163i	$0.0188921\pi$
$264$	−4.77993	+	14.7111i	−0.294184	+	0.905406i
$265$	−40.8458	−	29.6762i	−2.50914	−	1.82300i
$266$	−0.707421	+	2.17722i	−0.0433748	+	0.133494i
$267$	7.13891	+	21.9713i	0.436894	+	1.34462i
$268$	−3.19568	+	2.32180i	−0.195207	+	0.141826i
$269$	6.55274	+	20.1673i	0.399528	+	1.22962i	0.925379	+	0.379043i	$0.123747\pi$
$269$	6.55274	+	20.1673i	0.399528	+	1.22962i	−0.525851	+	0.850577i	$0.676253\pi$
$270$	21.9243	+	15.9289i	1.33427	+	0.969405i
$271$	1.96897	+	1.43054i	0.119607	+	0.0868993i	0.645980	−	0.763354i	$-0.276449\pi$
$271$	1.96897	+	1.43054i	0.119607	+	0.0868993i	−0.526374	+	0.850253i	$0.676449\pi$
$272$	6.86343	−	4.98657i	0.416156	−	0.302355i
$273$	−6.99347			−0.423264
$274$	6.28468			0.379671
$275$	−17.8616	+	12.9772i	−1.07710	+	0.782556i
$276$	−1.37402	+	4.22879i	−0.0827060	+	0.254543i
$277$	−4.22164	−	12.9929i	−0.253654	−	0.780666i	−0.994092	−	0.108541i	$-0.965382\pi$
$277$	−4.22164	−	12.9929i	−0.253654	−	0.780666i	0.740438	−	0.672124i	$-0.234618\pi$
$278$	−4.11430			−0.246759
$279$	−18.1382	−	35.8451i	−1.08591	−	2.14599i
$280$	−16.3405			−0.976534
$281$	3.79580	+	11.6823i	0.226438	+	0.696906i	0.998142	+	0.0609240i	$0.0194047\pi$
$281$	3.79580	+	11.6823i	0.226438	+	0.696906i	−0.771704	+	0.635982i	$0.780595\pi$
$282$	−0.467691	+	1.43940i	−0.0278506	+	0.0857152i
$283$	3.66249	−	2.66096i	0.217713	−	0.158177i	−0.473584	−	0.880749i	$-0.657040\pi$
$283$	3.66249	−	2.66096i	0.217713	−	0.158177i	0.691296	+	0.722571i	$0.257040\pi$
$284$	6.63166			0.393517
$285$	−23.4055			−1.38642
$286$	−1.05461	+	0.766217i	−0.0623602	+	0.0453074i
$287$	−5.15400	−	3.74460i	−0.304231	−	0.221037i
$288$	−30.6150	−	22.2431i	−1.80400	−	1.31069i
$289$	−1.25437	−	3.86057i	−0.0737867	−	0.227092i
$290$	−11.4706	+	8.33390i	−0.673578	+	0.489383i
$291$	8.53830	+	26.2782i	0.500524	+	1.54045i
$292$	0.565517	−	1.74048i	0.0330944	−	0.101854i
$293$	−20.4424	−	14.8523i	−1.19426	−	0.867679i	−0.200550	−	0.979684i	$-0.564273\pi$
$293$	−20.4424	−	14.8523i	−1.19426	−	0.867679i	−0.993708	+	0.112005i	$0.964273\pi$
$294$	−1.17127	+	3.60481i	−0.0683101	+	0.210237i
$295$	−16.5204	+	50.8446i	−0.961856	+	2.96029i
$296$	−2.86381	−	2.08068i	−0.166456	−	0.120937i
$297$	10.1237	−	31.1576i	0.587438	−	1.80795i
$298$	2.14163	+	6.59126i	0.124061	+	0.381821i
$299$	−0.657174	+	0.477465i	−0.0380053	+	0.0276125i
$300$	−15.3577	−	47.2660i	−0.886675	−	2.72890i
$301$	−16.7351	−	12.1588i	−0.964595	−	0.700819i
$302$	2.21932	+	1.61243i	0.127708	+	0.0927850i
$303$	4.36219	−	3.16932i	0.250601	−	0.182072i
$304$	4.60262			0.263979
$305$	−55.8578			−3.19841
$306$	11.2568	−	8.17857i	0.643510	−	0.467538i
$307$	−1.21259	+	3.73196i	−0.0692060	+	0.212994i	−0.979678	−	0.200576i	$-0.935719\pi$
$307$	−1.21259	+	3.73196i	−0.0692060	+	0.212994i	0.910472	+	0.413571i	$0.135719\pi$
$308$	2.81591	+	8.66649i	0.160452	+	0.493819i
$309$	57.4754			3.26966
$310$	1.78284	−	11.0567i	0.101259	−	0.627977i
$311$	10.0567			0.570263			0.285132	−	0.958488i	$-0.407963\pi$
$311$	10.0567			0.570263			0.285132	+	0.958488i	$0.407963\pi$
$312$	−1.96569	−	6.04976i	−0.111285	−	0.342500i
$313$	6.71620	−	20.6703i	0.379622	−	1.16836i	−0.560685	−	0.828029i	$-0.689462\pi$
$313$	6.71620	−	20.6703i	0.379622	−	1.16836i	0.940307	−	0.340328i	$-0.110538\pi$
$314$	2.99797	−	2.17815i	0.169185	−	0.122920i
$315$	59.2396			3.33777
$316$	−4.81445			−0.270834
$317$	1.24983	−	0.908052i	0.0701972	−	0.0510013i	−0.552133	−	0.833756i	$-0.686186\pi$
$317$	1.24983	−	0.908052i	0.0701972	−	0.0510013i	0.622330	+	0.782755i	$0.286186\pi$
$318$	18.6512	+	13.5509i	1.04591	+	0.759897i
$319$	13.8668	+	10.0748i	0.776393	+	0.564082i
$320$	2.20895	+	6.79846i	0.123484	+	0.380045i
$321$	−23.8699	+	17.3425i	−1.33229	+	0.967964i
$322$	−0.294441	−	0.906197i	−0.0164086	−	0.0505004i
$323$	−2.16952	+	6.67711i	−0.120715	+	0.371524i
$324$	29.6705	+	21.5569i	1.64836	+	1.19760i
$325$	2.80568	−	8.63499i	0.155631	−	0.478983i
$326$	4.10291	−	12.6274i	0.227239	−	0.699369i
$327$	12.4865	+	9.07199i	0.690506	+	0.501682i
$328$	1.79064	−	5.51102i	0.0988715	−	0.304295i
$329$	0.597277	+	1.83823i	0.0329289	+	0.101345i
$330$	12.6476	−	9.18900i	0.696226	−	0.505838i
$331$	−8.07917	−	24.8651i	−0.444071	−	1.36671i	−0.883499	−	0.468433i	$-0.844819\pi$
$331$	−8.07917	−	24.8651i	−0.444071	−	1.36671i	0.439427	−	0.898278i	$-0.355181\pi$
$332$	20.0413	+	14.5608i	1.09991	+	0.799130i
$333$	10.3822	+	7.54313i	0.568943	+	0.413361i
$334$	−4.05805	+	2.94835i	−0.222047	+	0.161326i
$335$	8.65436			0.472838
$336$	−16.4929			−0.899760
$337$	−16.5708	+	12.0394i	−0.902670	+	0.655828i	−0.939150	−	0.343506i	$-0.888385\pi$
$337$	−16.5708	+	12.0394i	−0.902670	+	0.655828i	0.0364805	+	0.999334i	$0.488385\pi$
$338$	0.165656	−	0.509838i	0.00901052	−	0.0277315i
$339$	−8.75858	−	26.9562i	−0.475701	−	1.46406i
$340$	−23.1171			−1.25370
$341$	−13.3782	+	2.08066i	−0.724471	+	0.112674i
$342$	7.54885			0.408195
$343$	6.22893	+	19.1707i	0.336331	+	1.03512i
$344$	5.81423	−	17.8943i	0.313482	−	0.964799i
$345$	7.88128	−	5.72609i	0.424314	−	0.308282i
$346$	4.17921			0.224676
$347$	−25.4216			−1.36470			−0.682351	−	0.731025i	$-0.739042\pi$
$347$	−25.4216			−1.36470			−0.682351	+	0.731025i	$0.739042\pi$
$348$	−31.2145	+	22.6787i	−1.67327	+	1.21570i
$349$	−8.52965	−	6.19715i	−0.456582	−	0.331726i	0.335607	−	0.942002i	$-0.391059\pi$
$349$	−8.52965	−	6.19715i	−0.456582	−	0.331726i	−0.792189	+	0.610276i	$0.791059\pi$
$350$	8.61603	+	6.25991i	0.460546	+	0.334606i
$351$	4.16326	+	12.8132i	0.222218	+	0.683917i
$352$	−10.3178	+	7.49634i	−0.549942	+	0.399556i
$353$	8.36046	+	25.7308i	0.444982	+	1.36951i	0.882503	+	0.470306i	$0.155857\pi$
$353$	8.36046	+	25.7308i	0.444982	+	1.36951i	−0.437521	+	0.899208i	$0.644143\pi$
$354$	7.54363	−	23.2169i	0.400939	−	1.23396i
$355$	−11.7546	−	8.54025i	−0.623872	−	0.453270i
$356$	−3.82533	+	11.7731i	−0.202742	+	0.623976i
$357$	7.77419	−	23.9265i	0.411454	−	1.26632i
$358$	0.975594	+	0.708811i	0.0515618	+	0.0374618i
$359$	2.24432	−	6.90731i	0.118451	−	0.364554i	−0.874200	−	0.485565i	$-0.838614\pi$
$359$	2.24432	−	6.90731i	0.118451	−	0.364554i	0.992651	+	0.121012i	$0.0386138\pi$
$360$	16.6507	+	51.2457i	0.877571	+	2.70089i
$361$	12.2898	−	8.92908i	0.646833	−	0.469952i
$362$	−1.23138	−	3.78980i	−0.0647200	−	0.199188i
$363$	13.1534	+	9.55647i	0.690372	+	0.501585i
$364$	−3.03171	−	2.20266i	−0.158905	−	0.115451i
$365$	−3.24377	+	2.35674i	−0.169787	+	0.123357i
$366$	25.5061			1.33322
$367$	17.2969			0.902890			0.451445	−	0.892299i	$-0.350909\pi$
$367$	17.2969			0.902890			0.451445	+	0.892299i	$0.350909\pi$
$368$	−1.54983	+	1.12602i	−0.0807904	+	0.0586977i
$369$	−6.49163	+	19.9792i	−0.337941	+	1.04008i
$370$	1.10555	+	3.40255i	0.0574750	+	0.176890i
$371$	29.4419			1.52855
$372$	4.85157	−	30.0880i	0.251542	−	1.55999i
$373$	8.66586			0.448701			0.224350	−	0.974509i	$-0.427974\pi$
$373$	8.66586			0.448701			0.224350	+	0.974509i	$0.427974\pi$
$374$	−1.44909	−	4.45984i	−0.0749307	−	0.230613i
$375$	−15.1179	+	46.5282i	−0.780686	+	2.40271i
$376$	−1.42230	+	1.03336i	−0.0733493	+	0.0532914i
$377$	−7.04875			−0.363029
$378$	−15.8032			−0.812828
$379$	−4.78624	+	3.47740i	−0.245852	+	0.178622i	−0.703887	−	0.710312i	$-0.748554\pi$
$379$	−4.78624	+	3.47740i	−0.245852	+	0.178622i	0.458034	+	0.888935i	$0.348554\pi$
$380$	−10.1464	−	7.37181i	−0.520501	−	0.378166i
$381$	30.6832	+	22.2926i	1.57195	+	1.14209i
$382$	0.741072	+	2.28078i	0.0379165	+	0.116695i
$383$	−18.7446	+	13.6187i	−0.957803	+	0.695884i	−0.952639	−	0.304102i	$-0.901644\pi$
$383$	−18.7446	+	13.6187i	−0.957803	+	0.695884i	−0.00516319	+	0.999987i	$0.501644\pi$
$384$	−11.3687	−	34.9892i	−0.580156	−	1.78554i
$385$	6.16949	−	18.9877i	0.314426	−	0.967704i
$386$	1.78964	+	1.30025i	0.0910901	+	0.0661809i
$387$	−21.0784	+	64.8727i	−1.07148	+	3.29766i
$388$	−4.57518	+	14.0810i	−0.232270	+	0.714852i
$389$	16.0543	+	11.6641i	0.813985	+	0.591395i	0.914983	−	0.403492i	$-0.132204\pi$
$389$	16.0543	+	11.6641i	0.813985	+	0.591395i	−0.100998	+	0.994887i	$0.532204\pi$
$390$	−1.98667	+	6.11433i	−0.100599	+	0.309611i
$391$	−0.902994	−	2.77913i	−0.0456664	−	0.140547i
$392$	−3.56196	+	2.58792i	−0.179906	+	0.130710i
$393$	20.4674	+	62.9922i	1.03244	+	3.17754i
$394$	−9.40559	−	6.83356i	−0.473847	−	0.344270i
$395$	8.53363	+	6.20005i	0.429374	+	0.311958i
$396$	24.3097	−	17.6620i	1.22161	−	0.887550i
$397$	−22.5623			−1.13237			−0.566183	−	0.824279i	$-0.691581\pi$
$397$	−22.5623			−1.13237			−0.566183	+	0.824279i	$0.691581\pi$
$398$	−9.21658			−0.461986
$399$	11.0421	−	8.02257i	0.552797	−	0.401631i
$400$	6.61670	−	20.3641i	0.330835	−	1.01821i
$401$	1.41617	+	4.35851i	0.0707200	+	0.217654i	0.980170	−	0.198160i	$-0.0634967\pi$
$401$	1.41617	+	4.35851i	0.0707200	+	0.217654i	−0.909450	+	0.415814i	$0.863497\pi$
$402$	−3.95180			−0.197098
$403$	3.94797	−	3.92600i	0.196663	−	0.195568i
$404$	2.88924			0.143745
$405$	−24.8301	−	76.4193i	−1.23382	−	3.79731i
$406$	2.55498	−	7.86343i	0.126802	−	0.390255i
$407$	3.49901	−	2.54218i	0.173439	−	0.126011i
$408$	22.8829			1.13287
$409$	−26.4715			−1.30893			−0.654465	−	0.756092i	$-0.727106\pi$
$409$	−26.4715			−1.30893			−0.654465	+	0.756092i	$0.727106\pi$
$410$	−4.73799	+	3.44235i	−0.233993	+	0.170006i
$411$	−30.3138	−	22.0242i	−1.49527	−	1.08638i
$412$	24.9159	+	18.1025i	1.22752	+	0.891844i
$413$	−9.63379	−	29.6497i	−0.474048	−	1.45897i
$414$	−2.54190	+	1.84680i	−0.124928	+	0.0907653i
$415$	−16.7718	−	51.6183i	−0.823296	−	2.53384i
$416$	1.62071	−	4.98804i	0.0794619	−	0.244559i
$417$	19.8451	+	14.4183i	0.971817	+	0.706067i
$418$	0.786172	−	2.41959i	0.0384529	−	0.118346i
$419$	−2.88703	+	8.88536i	−0.141041	+	0.434078i	−0.996481	−	0.0838236i	$-0.973287\pi$
$419$	−2.88703	+	8.88536i	−0.141041	+	0.434078i	0.855440	+	0.517902i	$0.173287\pi$
$420$	36.3583	+	26.4159i	1.77410	+	1.28896i
$421$	−0.821418	+	2.52806i	−0.0400335	+	0.123210i	−0.969076	−	0.246763i	$-0.920633\pi$
$421$	−0.821418	+	2.52806i	−0.0400335	+	0.123210i	0.929042	+	0.369973i	$0.120633\pi$
$422$	2.55602	+	7.86663i	0.124425	+	0.382941i
$423$	5.15627	−	3.74625i	0.250707	−	0.182149i
$424$	8.27538	+	25.4690i	0.401888	+	1.23688i
$425$	26.4237	+	19.1979i	1.28174	+	0.931236i
$426$	5.36746	+	3.89969i	0.260054	+	0.188941i
$427$	26.3523	−	19.1460i	1.27528	−	0.926542i
$428$	−15.8099			−0.764202
$429$	7.77199			0.375235
$430$	−15.3843	+	11.1774i	−0.741897	+	0.539020i
$431$	2.07264	−	6.37892i	0.0998354	−	0.307262i	−0.888648	−	0.458589i	$-0.848355\pi$
$431$	2.07264	−	6.37892i	0.0998354	−	0.307262i	0.988484	+	0.151328i	$0.0483549\pi$
$432$	9.81831	+	30.2176i	0.472384	+	1.45385i
$433$	−5.30344			−0.254867			−0.127434	−	0.991847i	$-0.540674\pi$
$433$	−5.30344			−0.254867			−0.127434	+	0.991847i	$0.540674\pi$
$434$	2.94873	+	5.82734i	0.141544	+	0.279721i
$435$	84.5334			4.05307
$436$	2.55566	+	7.86551i	0.122394	+	0.376690i
$437$	0.489899	−	1.50776i	0.0234351	−	0.0721257i
$438$	1.48119	−	1.07615i	0.0707739	−	0.0514202i
$439$	6.71803			0.320634			0.160317	−	0.987066i	$-0.448748\pi$
$439$	6.71803			0.320634			0.160317	+	0.987066i	$0.448748\pi$
$440$	18.1596			0.865724
$441$	12.9133	−	9.38203i	0.614917	−	0.446763i
$442$	1.56014	+	1.13351i	0.0742083	+	0.0539155i
$443$	−24.3917	−	17.7216i	−1.15889	−	0.841979i	−0.169249	−	0.985573i	$-0.554134\pi$
$443$	−24.3917	−	17.7216i	−1.15889	−	0.841979i	−0.989637	+	0.143594i	$0.954134\pi$
$444$	3.00850	+	9.25920i	0.142777	+	0.439422i
$445$	21.9419	−	15.9417i	1.04014	−	0.755709i
$446$	1.61263	+	4.96317i	0.0763604	+	0.235013i
$447$	12.7686	−	39.2977i	0.603934	−	1.85872i
$448$	−3.37239	−	2.45019i	−0.159331	−	0.115760i
$449$	−4.89536	+	15.0664i	−0.231026	+	0.711026i	0.766597	+	0.642128i	$0.221948\pi$
$449$	−4.89536	+	15.0664i	−0.231026	+	0.711026i	−0.997624	+	0.0688980i	$0.978052\pi$
$450$	10.8522	−	33.3996i	0.511576	−	1.57447i
$451$	5.72774	+	4.16145i	0.269709	+	0.195955i
$452$	4.69322	−	14.4442i	0.220750	−	0.679400i
$453$	−5.05410	−	15.5549i	−0.237462	−	0.730834i
$454$	8.67648	−	6.30383i	0.407207	−	0.295853i
$455$	2.53712	+	7.80847i	0.118942	+	0.366067i
$456$	10.0436	+	7.29714i	0.470337	+	0.341720i
$457$	−3.89794	−	2.83202i	−0.182338	−	0.132476i	0.492872	−	0.870102i	$-0.335947\pi$
$457$	−3.89794	−	2.83202i	−0.182338	−	0.132476i	−0.675210	+	0.737626i	$0.735947\pi$
$458$	−11.1261	+	8.08355i	−0.519886	+	0.377720i
$459$	−48.4653			−2.26217
$460$	5.22007			0.243387
$461$	17.5818	−	12.7739i	0.818866	−	0.594941i	−0.0975214	−	0.995233i	$-0.531091\pi$
$461$	17.5818	−	12.7739i	0.818866	−	0.594941i	0.916387	+	0.400292i	$0.131091\pi$
$462$	−2.81714	+	8.67026i	−0.131065	+	0.403377i
$463$	−3.05268	−	9.39518i	−0.141870	−	0.436631i	0.854725	−	0.519081i	$-0.173726\pi$
$463$	−3.05268	−	9.39518i	−0.141870	−	0.436631i	−0.996595	+	0.0824498i	$0.973726\pi$
$464$	−16.6232			−0.771714
$465$	−47.3468	+	47.0834i	−2.19566	+	2.18344i
$466$	−3.91489			−0.181354
$467$	4.44121	+	13.6686i	0.205515	+	0.632509i	0.999692	+	0.0248226i	$0.00790210\pi$
$467$	4.44121	+	13.6686i	0.205515	+	0.632509i	−0.794177	+	0.607686i	$0.792098\pi$
$468$	−3.81854	+	11.7522i	−0.176512	+	0.543248i
$469$	−4.08290	+	2.96640i	−0.188531	+	0.136976i
$470$	1.77682			0.0819585
$471$	−22.0937			−1.01802
$472$	22.9409	−	16.6676i	1.05594	−	0.767187i
$473$	18.5981	+	13.5123i	0.855140	+	0.621295i
$474$	−3.89667	−	2.83109i	−0.178980	−	0.130036i
$475$	5.47571	+	16.8525i	0.251243	+	0.773245i
$476$	10.9060	−	7.92370i	0.499878	−	0.363182i
$477$	−30.0009	−	92.3332i	−1.37365	−	4.22765i
$478$	−0.360184	+	1.10853i	−0.0164745	+	0.0507031i
$479$	−18.9387	−	13.7598i	−0.865333	−	0.628701i	0.0639974	−	0.997950i	$-0.479615\pi$
$479$	−18.9387	−	13.7598i	−0.865333	−	0.628701i	−0.929331	+	0.369249i	$0.879615\pi$
$480$	−19.4367	+	59.8200i	−0.887159	+	2.73040i
$481$	−0.549620	+	1.69156i	−0.0250605	+	0.0771284i
$482$	−6.06384	−	4.40564i	−0.276200	−	0.200671i
$483$	−1.75549	+	5.40284i	−0.0798775	+	0.245838i
$484$	2.69214	+	8.28557i	0.122370	+	0.376617i
$485$	26.2430	−	19.0666i	1.19163	−	0.865772i
$486$	4.64259	+	14.2884i	0.210592	+	0.648136i
$487$	4.03909	+	2.93457i	0.183029	+	0.132978i	0.675527	−	0.737335i	$-0.263916\pi$
$487$	4.03909	+	2.93457i	0.183029	+	0.132978i	−0.492498	+	0.870313i	$0.663916\pi$
$488$	23.9694	+	17.4148i	1.08504	+	0.788330i
$489$	−64.0421	+	46.5293i	−2.89609	+	2.10413i
$490$	4.44982			0.201023
$491$	25.8099			1.16478			0.582392	−	0.812908i	$-0.302117\pi$
$491$	25.8099			1.16478			0.582392	+	0.812908i	$0.302117\pi$
$492$	−12.8933	+	9.36751i	−0.581274	+	0.422320i
$493$	7.83563	−	24.1156i	0.352899	−	1.08611i
$494$	0.323303	+	0.995026i	0.0145461	+	0.0447683i
$495$	−65.8342			−2.95903
$496$	9.31060	−	9.25879i	0.418058	−	0.415732i
$497$	8.47282			0.380058
$498$	7.65842	+	23.5702i	0.343182	+	1.05621i
$499$	4.38946	−	13.5094i	0.196499	−	0.604762i	−0.803457	−	0.595363i	$-0.797008\pi$
$499$	4.38946	−	13.5094i	0.196499	−	0.604762i	0.999956	−	0.00939903i	$-0.00299185\pi$
$500$	−21.2082	+	15.4087i	−0.948461	+	0.689097i
$501$	29.9060			1.33610
$502$	1.40955			0.0629114
$503$	−3.52032	+	2.55767i	−0.156963	+	0.114041i	−0.663495	−	0.748181i	$-0.730927\pi$
$503$	−3.52032	+	2.55767i	−0.156963	+	0.114041i	0.506531	+	0.862222i	$0.330927\pi$
$504$	−25.4206	−	18.4691i	−1.13232	−	0.822680i
$505$	−5.12119	−	3.72076i	−0.227890	−	0.165572i
$506$	0.327219	+	1.00708i	0.0145466	+	0.0447700i
$507$	−2.58573	+	1.87864i	−0.114836	+	0.0834334i
$508$	6.28003	+	19.3279i	0.278631	+	0.857539i
$509$	−2.27022	+	6.98701i	−0.100626	+	0.309694i	−0.988679	−	0.150047i	$-0.952058\pi$
$509$	−2.27022	+	6.98701i	−0.100626	+	0.309694i	0.888053	+	0.459741i	$0.152058\pi$
$510$	−18.7103	−	13.5938i	−0.828505	−	0.601944i
$511$	0.722523	−	2.22370i	0.0319625	−	0.0983705i
$512$	6.72300	−	20.6913i	0.297117	−	0.914433i
$513$	−21.2721	−	15.4551i	−0.939186	−	0.682359i
$514$	0.976226	−	3.00452i	0.0430595	−	0.132523i
$515$	−20.8512	−	64.1734i	−0.918813	−	2.82782i
$516$	−41.8646	+	30.4164i	−1.84299	+	1.33901i
$517$	−0.663766	−	2.04286i	−0.0291924	−	0.0898450i
$518$	−1.68784	−	1.22629i	−0.0741595	−	0.0538800i
$519$	−20.1582	−	14.6458i	−0.884846	−	0.642878i
$520$	−6.04166	+	4.38952i	−0.264944	+	0.192493i
$521$	43.2596			1.89524			0.947620	−	0.319401i	$-0.103482\pi$
$521$	43.2596			1.89524			0.947620	+	0.319401i	$0.103482\pi$
$522$	−27.2641			−1.19332
$523$	8.90690	−	6.47124i	0.389471	−	0.282968i	−0.375767	−	0.926714i	$-0.622621\pi$
$523$	8.90690	−	6.47124i	0.389471	−	0.282968i	0.765239	+	0.643746i	$0.222621\pi$
$524$	−10.9673	+	33.7539i	−0.479109	+	1.47455i
$525$	−19.6214	−	60.3886i	−0.856350	−	2.63557i
$526$	4.38265			0.191093
$527$	9.04318	+	17.8713i	0.393927	+	0.778487i
$528$	18.3289			0.797662
$529$	−6.90349	−	21.2467i	−0.300152	−	0.923772i
$530$	8.36370	−	25.7408i	0.363296	−	1.11811i
$531$	−83.1682	+	60.4252i	−3.60919	+	2.62223i
$532$	7.31361			0.317085
$533$	−2.91151			−0.126112
$534$	−10.0192	+	7.27938i	−0.433573	+	0.315009i
$535$	28.0232	+	20.3600i	1.21155	+	0.880241i
$536$	−3.71371	−	2.69817i	−0.160408	−	0.116543i
$537$	−2.22174	−	6.83781i	−0.0958751	−	0.295073i
$538$	−9.19653	+	6.68167i	−0.396491	+	0.288067i
$539$	−1.66232	−	5.11610i	−0.0716012	−	0.220366i
$540$	26.7539	−	82.3399i	1.15130	−	3.54335i
$541$	22.9176	+	16.6506i	0.985304	+	0.715865i	0.958888	−	0.283786i	$-0.0915904\pi$
$541$	22.9176	+	16.6506i	0.985304	+	0.715865i	0.0264165	+	0.999651i	$0.491590\pi$
$542$	−0.403172	+	1.24084i	−0.0173177	+	0.0532985i
$543$	−7.34162	+	22.5952i	−0.315059	+	0.969652i
$544$	15.2637	+	11.0898i	0.654427	+	0.475469i
$545$	5.59929	−	17.2328i	0.239847	−	0.738174i
$546$	−1.15851	−	3.56554i	−0.0495798	−	0.152591i
$547$	−1.50421	+	1.09287i	−0.0643152	+	0.0467277i	−0.619478	−	0.785014i	$-0.712656\pi$
$547$	−1.50421	+	1.09287i	−0.0643152	+	0.0467277i	0.555163	+	0.831741i	$0.312656\pi$
$548$	−6.20442	−	19.0952i	−0.265040	−	0.815708i
$549$	−86.8966	−	63.1341i	−3.70866	−	2.69450i
$550$	−9.57517	−	6.95677i	−0.408287	−	0.296638i
$551$	11.1294	−	8.08598i	0.474128	−	0.344474i
$552$	−5.16719			−0.219930
$553$	−6.15110			−0.261571
$554$	5.92492	−	4.30470i	0.251726	−	0.182889i
$555$	6.59142	−	20.2863i	0.279790	−	0.861106i
$556$	4.06176	+	12.5008i	0.172257	+	0.530152i
$557$	1.65370			0.0700696			0.0350348	−	0.999386i	$-0.488846\pi$
$557$	1.65370			0.0700696			0.0350348	+	0.999386i	$0.488846\pi$
$558$	15.2705	−	15.1855i	0.646451	−	0.642854i
$559$	−9.45372			−0.399850
$560$	5.98336	+	18.4149i	0.252843	+	0.778171i
$561$	−8.63962	+	26.5900i	−0.364765	+	1.12263i
$562$	−5.32727	+	3.87049i	−0.224717	+	0.163267i
$563$	1.15378			0.0486259			0.0243130	−	0.999704i	$-0.492260\pi$
$563$	1.15378			0.0486259			0.0243130	+	0.999704i	$0.492260\pi$
$564$	4.83518			0.203598
$565$	−26.9200	+	19.5586i	−1.13253	+	0.822835i
$566$	1.96337	+	1.42647i	0.0825267	+	0.0599592i
$567$	37.9080	+	27.5418i	1.59198	+	1.15664i
$568$	2.38149	+	7.32949i	0.0999253	+	0.307538i
$569$	−20.1474	+	14.6379i	−0.844623	+	0.613654i	−0.923658	−	0.383218i	$-0.874816\pi$
$569$	−20.1474	+	14.6379i	−0.844623	+	0.613654i	0.0790355	+	0.996872i	$0.474816\pi$
$570$	−3.87728	−	11.9330i	−0.162401	−	0.499820i
$571$	−4.47743	+	13.7801i	−0.187374	+	0.576679i	−0.999981	−	0.00613315i	$-0.998048\pi$
$571$	−4.47743	+	13.7801i	−0.187374	+	0.576679i	0.812607	+	0.582812i	$0.198048\pi$
$572$	3.36920	+	2.44787i	0.140873	+	0.102350i
$573$	4.41834	−	13.5983i	0.184579	−	0.568076i
$574$	1.05535	−	3.24802i	0.0440493	−	0.135570i
$575$	−5.96672	−	4.33508i	−0.248830	−	0.180785i
$576$	−4.24764	+	13.0729i	−0.176985	+	0.544704i
$577$	11.4887	+	35.3587i	0.478282	+	1.47200i	0.841480	+	0.540289i	$0.181685\pi$
$577$	11.4887	+	35.3587i	0.478282	+	1.47200i	−0.363198	+	0.931712i	$0.618315\pi$
$578$	1.76047	−	1.27905i	0.0732258	−	0.0532017i
$579$	−4.07557	−	12.5433i	−0.169375	−	0.521283i
$580$	36.6457	+	26.6247i	1.52163	+	1.10553i
$581$	25.6054	+	18.6034i	1.06229	+	0.771800i
$582$	−11.9832	+	8.70630i	−0.496719	+	0.360888i
$583$	−32.7194			−1.35510
$584$	2.12671			0.0880039
$585$	21.9029	−	15.9134i	0.905574	−	0.657938i
$586$	4.18584	−	12.8827i	0.172915	−	0.532179i
$587$	−5.32455	−	16.3873i	−0.219768	−	0.676376i	−0.998781	−	0.0493680i	$-0.984279\pi$
$587$	−5.32455	−	16.3873i	−0.219768	−	0.676376i	0.779013	−	0.627008i	$-0.215721\pi$
$588$	12.1091			0.499371
$589$	−1.72981	+	10.7278i	−0.0712754	+	0.442030i
$590$	−28.6592			−1.17988
$591$	21.4195	+	65.9225i	0.881082	+	2.71169i
$592$	−1.29618	+	3.98924i	−0.0532728	+	0.163957i
$593$	−21.0360	+	15.2835i	−0.863844	+	0.627619i	−0.928928	−	0.370261i	$-0.879268\pi$
$593$	−21.0360	+	15.2835i	−0.863844	+	0.627619i	0.0650843	+	0.997880i	$0.479268\pi$
$594$	17.5624			0.720594
$595$	−29.5352			−1.21082
$596$	17.9125	−	13.0142i	0.733723	−	0.533081i
$597$	44.4556	+	32.2989i	1.81945	+	1.32191i
$598$	−0.352295	−	0.255957i	−0.0144064	−	0.0104669i
$599$	−3.10151	−	9.54546i	−0.126724	−	0.390017i	0.867487	−	0.497460i	$-0.165734\pi$
$599$	−3.10151	−	9.54546i	−0.126724	−	0.390017i	−0.994211	+	0.107443i	$0.965734\pi$
$600$	46.7246	−	33.9474i	1.90752	−	1.38590i
$601$	13.7032	+	42.1740i	0.558963	+	1.72031i	0.685240	+	0.728317i	$0.259697\pi$
$601$	13.7032	+	42.1740i	0.558963	+	1.72031i	−0.126277	+	0.991995i	$0.540303\pi$
$602$	3.42672	−	10.5464i	0.139663	−	0.429838i
$603$	13.4634	+	9.78172i	0.548271	+	0.398342i
$604$	2.70820	−	8.33499i	0.110195	−	0.339146i
$605$	5.89832	−	18.1531i	0.239801	−	0.738030i
$606$	2.33846	+	1.69899i	0.0949935	+	0.0690168i
$607$	7.01882	−	21.6017i	0.284885	−	0.876787i	−0.701548	−	0.712622i	$-0.747507\pi$
$607$	7.01882	−	21.6017i	0.284885	−	0.876787i	0.986433	−	0.164164i	$-0.0524927\pi$
$608$	3.16306	+	9.73490i	0.128279	+	0.394802i
$609$	−39.8807	+	28.9750i	−1.61605	+	1.17413i
$610$	−9.25321	−	28.4784i	−0.374651	−	1.15306i
$611$	0.714633	+	0.519211i	0.0289110	+	0.0210050i
$612$	−35.9627	−	26.1284i	−1.45371	−	1.05618i
$613$	4.53168	−	3.29246i	0.183033	−	0.132981i	−0.492496	−	0.870315i	$-0.663915\pi$
$613$	4.53168	−	3.29246i	0.183033	−	0.132981i	0.675529	+	0.737334i	$0.263915\pi$
$614$	−2.10357			−0.0848931
$615$	34.9169			1.40798
$616$	−8.56721	+	6.22444i	−0.345183	+	0.250790i
$617$	12.9979	−	40.0035i	0.523277	−	1.61048i	−0.244421	−	0.969669i	$-0.578598\pi$
$617$	12.9979	−	40.0035i	0.523277	−	1.61048i	0.767698	−	0.640811i	$-0.221402\pi$
$618$	9.52117	+	29.3031i	0.382998	+	1.17875i
$619$	5.10997			0.205387			0.102693	−	0.994713i	$-0.467254\pi$
$619$	5.10997			0.205387			0.102693	+	0.994713i	$0.467254\pi$
$620$	−35.3545	+	5.49853i	−1.41987	+	0.220826i
$621$	10.9439			0.439165
$622$	1.66596	+	5.12729i	0.0667988	+	0.205586i
$623$	−4.88736	+	15.0418i	−0.195808	+	0.602635i
$624$	−6.09798	+	4.43044i	−0.244115	+	0.177360i
$625$	12.0381			0.481525
$626$	11.6511			0.465672
$627$	−12.2713	+	8.91565i	−0.490070	+	0.356057i
$628$	−9.57773	−	6.95863i	−0.382193	−	0.277679i
$629$	−5.17628	−	3.76079i	−0.206392	−	0.149952i
$630$	9.81342	+	30.2026i	0.390976	+	1.20330i
$631$	−1.43275	+	1.04096i	−0.0570370	+	0.0414398i	−0.615938	−	0.787794i	$-0.711223\pi$
$631$	−1.43275	+	1.04096i	−0.0570370	+	0.0414398i	0.558901	+	0.829234i	$0.311223\pi$
$632$	−1.72892	−	5.32106i	−0.0687726	−	0.211660i
$633$	15.2393	−	46.9016i	0.605706	−	1.86417i
$634$	0.670001	+	0.486784i	0.0266091	+	0.0193327i
$635$	13.7591	−	42.3463i	0.546015	−	1.68046i
$636$	22.7598	−	70.0474i	0.902484	−	2.77756i
$637$	1.78971	+	1.30030i	0.0709109	+	0.0515198i
$638$	−2.83941	+	8.73879i	−0.112413	+	0.345972i
$639$	−8.63367	−	26.5717i	−0.341543	−	1.05116i
$640$	−34.9423	+	25.3871i	−1.38122	+	1.00351i
$641$	5.65014	+	17.3893i	0.223167	+	0.686838i	0.998472	+	0.0552512i	$0.0175959\pi$
$641$	5.65014	+	17.3893i	0.223167	+	0.686838i	−0.775305	+	0.631587i	$0.782404\pi$
$642$	−12.7961	−	9.29689i	−0.505021	−	0.366919i
$643$	9.65496	+	7.01474i	0.380754	+	0.276634i	0.761656	−	0.647981i	$-0.224386\pi$
$643$	9.65496	+	7.01474i	0.380754	+	0.276634i	−0.380902	+	0.924615i	$0.624386\pi$
$644$	−2.46269	+	1.78925i	−0.0970436	+	0.0705063i
$645$	113.376			4.46416
$646$	−3.76364			−0.148078
$647$	17.5564	−	12.7555i	0.690213	−	0.501469i	−0.186517	−	0.982452i	$-0.559720\pi$
$647$	17.5564	−	12.7555i	0.690213	−	0.501469i	0.876730	+	0.480983i	$0.159720\pi$
$648$	−13.1703	+	40.5339i	−0.517376	+	1.59232i
$649$	10.7062	+	32.9504i	0.420256	+	1.29342i
$650$	4.86723			0.190908
$651$	6.19852	−	38.4415i	0.242939	−	1.50664i
$652$	−42.4175			−1.66120
$653$	−2.28154	−	7.02185i	−0.0892834	−	0.274786i	0.896438	−	0.443168i	$-0.146146\pi$
$653$	−2.28154	−	7.02185i	−0.0892834	−	0.274786i	−0.985722	+	0.168382i	$0.946146\pi$
$654$	−2.55677	+	7.86894i	−0.0999778	+	0.307700i
$655$	62.9079	−	45.7052i	2.45801	−	1.78585i
$656$	−6.86629			−0.268084
$657$	−7.71000			−0.300796
$658$	−0.838256	+	0.609029i	−0.0326786	+	0.0237424i
$659$	2.19197	+	1.59256i	0.0853870	+	0.0620373i	0.629660	−	0.776871i	$-0.283194\pi$
$659$	2.19197	+	1.59256i	0.0853870	+	0.0620373i	−0.544273	+	0.838908i	$0.683194\pi$
$660$	−40.4058	−	29.3565i	−1.57279	−	1.14270i
$661$	−10.2345	−	31.4985i	−0.398075	−	1.22515i	−0.926541	−	0.376194i	$-0.877233\pi$
$661$	−10.2345	−	31.4985i	−0.398075	−	1.22515i	0.528466	−	0.848954i	$-0.322767\pi$
$662$	11.3388	−	8.23814i	0.440696	−	0.320184i
$663$	−3.55294	−	10.9348i	−0.137985	−	0.424673i
$664$	−8.89601	+	27.3791i	−0.345232	+	1.06252i
$665$	−12.9634	−	9.41846i	−0.502699	−	0.365232i
$666$	−2.12589	+	6.54283i	−0.0823767	+	0.253529i
$667$	−1.76936	+	5.44554i	−0.0685100	+	0.210852i
$668$	12.9644	+	9.41921i	0.501609	+	0.364440i
$669$	9.61468	−	29.5909i	0.371725	−	1.14405i
$670$	1.43365	+	4.41232i	0.0553868	+	0.170463i
$671$	−29.2858	+	21.2774i	−1.13057	+	0.821404i
$672$	−11.3344	−	34.8837i	−0.437234	−	1.34567i
$673$	14.2376	+	10.3442i	0.548819	+	0.398740i	0.827350	−	0.561687i	$-0.189848\pi$
$673$	14.2376	+	10.3442i	0.548819	+	0.398740i	−0.278531	+	0.960427i	$0.589848\pi$
$674$	−8.88321	−	6.45403i	−0.342168	−	0.248600i
$675$	−98.9610	+	71.8994i	−3.80901	+	2.76741i
$676$	−1.71262			−0.0658701
$677$	−6.57737			−0.252789			−0.126394	−	0.991980i	$-0.540341\pi$
$677$	−6.57737			−0.252789			−0.126394	+	0.991980i	$0.540341\pi$
$678$	12.2924	−	8.93092i	0.472085	−	0.342990i
$679$	−5.84540	+	17.9903i	−0.224326	+	0.690404i
$680$	−8.30158	−	25.5496i	−0.318351	−	0.979784i
$681$	−63.9418			−2.45026
$682$	−3.27698	−	6.47605i	−0.125482	−	0.247981i
$683$	−10.7317			−0.410639			−0.205319	−	0.978695i	$-0.565823\pi$
$683$	−10.7317			−0.410639			−0.205319	+	0.978695i	$0.565823\pi$
$684$	−7.45245	−	22.9363i	−0.284952	−	0.876991i
$685$	−13.5935	+	41.8365i	−0.519381	+	1.59849i
$686$	−8.74208	+	6.35149i	−0.333774	+	0.242501i
$687$	81.9941			3.12827
$688$	−22.2949			−0.849987
$689$	10.8857	−	7.90892i	0.414712	−	0.301306i
$690$	4.22496	+	3.06961i	0.160842	+	0.116858i
$691$	32.4434	+	23.5715i	1.23421	+	0.896704i	0.997198	−	0.0748038i	$-0.0238331\pi$
$691$	32.4434	+	23.5715i	1.23421	+	0.896704i	0.237009	+	0.971508i	$0.423833\pi$
$692$	−4.12584	−	12.6980i	−0.156841	−	0.482707i
$693$	31.0589	−	22.5656i	1.17983	−	0.857196i
$694$	−4.21125	−	12.9609i	−0.159857	−	0.491988i
$695$	8.89906	−	27.3885i	0.337560	−	1.03890i
$696$	−36.2745	−	26.3550i	−1.37498	−	0.998982i
$697$	3.23654	−	9.96105i	0.122593	−	0.377302i
$698$	1.74655	−	5.37534i	0.0661080	−	0.203460i
$699$	18.8832	+	13.7195i	0.714230	+	0.518918i
$700$	10.5140	−	32.3587i	0.397392	−	1.22305i
$701$	−11.7403	−	36.1329i	−0.443424	−	1.36472i	−0.884202	−	0.467104i	$-0.845297\pi$
$701$	−11.7403	−	36.1329i	−0.443424	−	1.36472i	0.440778	−	0.897616i	$-0.354703\pi$
$702$	−5.84298	+	4.24517i	−0.220529	+	0.160224i
$703$	−1.07267	−	3.30133i	−0.0404564	−	0.124512i
$704$	3.74781	+	2.72294i	0.141251	+	0.102625i
$705$	−8.57037	−	6.22674i	−0.322779	−	0.234513i
$706$	−11.7336	+	8.52496i	−0.441600	+	0.320841i
$707$	3.69139			0.138829
$708$	−77.9891			−2.93101
$709$	−27.4154	+	19.9185i	−1.02961	+	0.748053i	−0.968230	−	0.250061i	$-0.919549\pi$
$709$	−27.4154	+	19.9185i	−1.02961	+	0.748053i	−0.0613773	+	0.998115i	$0.519549\pi$
$710$	2.40691	−	7.40771i	0.0903298	−	0.278007i
$711$	6.26787	+	19.2905i	0.235063	+	0.723451i
$712$	−14.3857			−0.539127
$713$	−2.04204	−	4.03552i	−0.0764749	−	0.151131i
$714$	13.4865			0.504719
$715$	−2.81956	−	8.67771i	−0.105446	−	0.324528i
$716$	1.19050	−	3.66399i	0.0444911	−	0.136930i
$717$	5.62211	−	4.08470i	0.209962	−	0.152546i
$718$	3.89339			0.145300
$719$	42.2779			1.57670			0.788351	−	0.615226i	$-0.210935\pi$
$719$	42.2779			1.57670			0.788351	+	0.615226i	$0.210935\pi$
$720$	51.6542	−	37.5290i	1.92504	−	1.39862i
$721$	31.8334	+	23.1283i	1.18554	+	0.861342i
$722$	6.58827	+	4.78666i	0.245190	+	0.178141i
$723$	13.8093	+	42.5006i	0.513573	+	1.58062i
$724$	−10.2992	+	7.48281i	−0.382767	+	0.278097i
$725$	−19.7765	−	60.8659i	−0.734482	−	2.26050i
$726$	−2.69332	+	8.28917i	−0.0999583	+	0.307640i
$727$	28.1492	+	20.4516i	1.04400	+	0.758509i	0.971062	−	0.238828i	$-0.0767631\pi$
$727$	28.1492	+	20.4516i	1.04400	+	0.758509i	0.0729359	+	0.997337i	$0.476763\pi$
$728$	1.34573	−	4.14172i	0.0498760	−	0.153502i
$729$	7.82738	−	24.0902i	0.289903	−	0.892229i
$730$	−1.73891	−	1.26339i	−0.0643599	−	0.0467602i
$731$	10.5091	−	32.3437i	0.388693	−	1.19627i
$732$	−25.1803	−	77.4971i	−0.930692	−	2.86438i
$733$	−24.1487	+	17.5450i	−0.891952	+	0.648041i	−0.936386	−	0.350971i	$-0.885851\pi$
$733$	−24.1487	+	17.5450i	−0.891952	+	0.648041i	0.0444344	+	0.999012i	$0.485851\pi$
$734$	2.86534	+	8.81860i	0.105762	+	0.325501i
$735$	−21.4634	−	15.5941i	−0.791691	−	0.575197i
$736$	−3.44670	−	2.50417i	−0.127047	−	0.0923051i
$737$	4.53741	−	3.29662i	0.167138	−	0.121433i
$738$	−11.2615			−0.414543
$739$	37.9707			1.39677			0.698387	−	0.715720i	$-0.253902\pi$
$739$	37.9707			1.39677			0.698387	+	0.715720i	$0.253902\pi$
$740$	9.24680	−	6.71819i	0.339919	−	0.246966i
$741$	1.92757	−	5.93244i	0.0708109	−	0.217934i
$742$	4.87725	+	15.0106i	0.179049	+	0.551057i
$743$	−14.4900			−0.531586			−0.265793	−	0.964030i	$-0.585634\pi$
$743$	−14.4900			−0.531586			−0.265793	+	0.964030i	$0.585634\pi$
$744$	34.9963	−	5.44283i	1.28303	−	0.199544i
$745$	−48.5096			−1.77725
$746$	1.43555	+	4.41818i	0.0525594	+	0.161761i
$747$	32.2509	−	99.2579i	1.18000	−	3.63166i
$748$	−12.1201	+	8.80578i	−0.443155	+	0.321971i
$749$	−20.1993			−0.738066
$750$	−26.2262			−0.957646
$751$	31.2066	−	22.6729i	1.13874	−	0.827346i	0.151800	−	0.988411i	$-0.451493\pi$
$751$	31.2066	−	22.6729i	1.13874	−	0.827346i	0.986944	+	0.161065i	$0.0514929\pi$
$752$	1.68534	+	1.22447i	0.0614579	+	0.0446518i
$753$	−6.79889	−	4.93968i	−0.247765	−	0.180012i
$754$	−1.16767	−	3.59372i	−0.0425240	−	0.130876i
$755$	−15.5341	+	11.2862i	−0.565344	+	0.410746i
$756$	15.6014	+	48.0161i	0.567416	+	1.74633i
$757$	−14.5435	+	44.7604i	−0.528593	+	1.62684i	0.228505	+	0.973543i	$0.426616\pi$
$757$	−14.5435	+	44.7604i	−0.528593	+	1.62684i	−0.757099	+	0.653301i	$0.773384\pi$
$758$	−2.56578	−	1.86415i	−0.0931935	−	0.0677090i
$759$	1.95091	−	6.00428i	0.0708135	−	0.217942i
$760$	4.50384	−	13.8614i	0.163371	−	0.502805i
$761$	−26.9685	−	19.5938i	−0.977609	−	0.710274i	−0.0204357	−	0.999791i	$-0.506505\pi$
$761$	−26.9685	−	19.5938i	−0.977609	−	0.710274i	−0.957173	+	0.289517i	$0.906505\pi$
$762$	−6.28276	+	19.3364i	−0.227600	+	0.700482i
$763$	3.26520	+	10.0492i	0.118208	+	0.363807i
$764$	6.19828	−	4.50332i	0.224246	−	0.162924i
$765$	30.0959	+	92.6255i	1.08812	+	3.34888i
$766$	−10.0485	−	7.30066i	−0.363067	−	0.263784i
$767$	−11.5267	−	8.37463i	−0.416205	−	0.302390i
$768$	6.10352	−	4.43446i	0.220242	−	0.160015i
$769$	32.7062			1.17942			0.589709	−	0.807616i	$-0.299243\pi$
$769$	32.7062			1.17942			0.589709	+	0.807616i	$0.299243\pi$
$770$	10.7027			0.385698
$771$	−15.2379	+	11.0710i	−0.548779	+	0.398711i
$772$	2.18386	−	6.72124i	0.0785990	−	0.241903i
$773$	9.76676	+	30.0590i	0.351286	+	1.08115i	0.958132	+	0.286327i	$0.0924345\pi$
$773$	9.76676	+	30.0590i	0.351286	+	1.08115i	−0.606846	+	0.794819i	$0.707566\pi$
$774$	−36.5663			−1.31435
$775$	44.9778	+	23.0756i	1.61565	+	0.828901i
$776$	−17.2056			−0.617646
$777$	3.84375	+	11.8299i	0.137894	+	0.424394i
$778$	−3.28732	+	10.1173i	−0.117856	+	0.362724i
$779$	4.59704	−	3.33995i	0.164706	−	0.119666i
$780$	20.5390			0.735413
$781$	−9.41603			−0.336932
$782$	1.26732	−	0.920761i	0.0453192	−	0.0329264i
$783$	76.8281	+	55.8189i	2.74561	+	1.99481i
$784$	4.22072	+	3.06653i	0.150740	+	0.109519i
$785$	8.01525	+	24.6684i	0.286077	+	0.880453i
$786$	−28.7253	+	20.8701i	−1.02460	+	0.744413i
$787$	−1.88022	−	5.78673i	−0.0670227	−	0.206275i	0.911936	−	0.410332i	$-0.134587\pi$
$787$	−1.88022	−	5.78673i	−0.0670227	−	0.206275i	−0.978959	+	0.204057i	$0.934587\pi$
$788$	−11.4775	+	35.3241i	−0.408868	+	1.25837i
$789$	−21.1395	−	15.3587i	−0.752585	−	0.546785i
$790$	−1.74737	+	5.37785i	−0.0621686	+	0.191335i
$791$	5.99621	−	18.4544i	0.213201	−	0.656164i
$792$	28.2504	+	20.5251i	1.00383	+	0.729328i
$793$	4.60018	−	14.1579i	0.163357	−	0.502762i
$794$	−3.73758	−	11.5031i	−0.132642	−	0.408229i
$795$	−130.549	+	94.8493i	−4.63009	+	3.36396i
$796$	9.09889	+	28.0035i	0.322502	+	0.992558i
$797$	17.2114	+	12.5048i	0.609658	+	0.442942i	0.849294	−	0.527920i	$-0.177028\pi$
$797$	17.2114	+	12.5048i	0.609658	+	0.442942i	−0.239636	+	0.970863i	$0.577028\pi$
$798$	5.91941	+	4.30070i	0.209545	+	0.152243i
$799$	−2.57077	+	1.86777i	−0.0909473	+	0.0660770i
$800$	47.6189			1.68358
$801$	52.1528			1.84273
$802$	−1.98754	+	1.44403i	−0.0701824	+	0.0509905i
$803$	−0.802955	+	2.47124i	−0.0283357	+	0.0872082i
$804$	3.90133	+	12.0071i	0.137589	+	0.423456i
$805$	6.66933			0.235063
$806$	2.65563	+	1.36246i	0.0935407	+	0.0479906i
$807$	67.7744			2.38577
$808$	1.03755	+	3.19326i	0.0365010	+	0.112339i
$809$	−1.81959	+	5.60013i	−0.0639735	+	0.196890i	−0.977934	−	0.208912i	$-0.933008\pi$
$809$	−1.81959	+	5.60013i	−0.0639735	+	0.196890i	0.913961	+	0.405802i	$0.133008\pi$
$810$	34.8482	−	25.3187i	1.22444	−	0.889608i
$811$	−40.9894			−1.43933			−0.719667	−	0.694320i	$-0.755705\pi$
$811$	−40.9894			−1.43933			−0.719667	+	0.694320i	$0.755705\pi$
$812$	−26.4144			−0.926965
$813$	6.29310	−	4.57221i	0.220709	−	0.160354i
$814$	1.87573	+	1.36280i	0.0657444	+	0.0477661i
$815$	75.1852	+	54.6253i	2.63362	+	1.91344i
$816$	−8.37897	−	25.7878i	−0.293323	−	0.902755i
$817$	14.9267	−	10.8448i	0.522218	−	0.379413i
$818$	−4.38517	−	13.4962i	−0.153324	−	0.471882i
$819$	−4.87869	+	15.0151i	−0.170475	+	0.524669i
$820$	15.1367	+	10.9974i	0.528595	+	0.384047i
$821$	−5.14150	+	15.8239i	−0.179440	+	0.552258i	−0.999808	−	0.0195767i	$-0.993768\pi$
$821$	−5.14150	+	15.8239i	−0.179440	+	0.552258i	0.820369	+	0.571835i	$0.193768\pi$
$822$	6.20712	−	19.1036i	0.216498	−	0.666313i
$823$	−18.0750	−	13.1322i	−0.630053	−	0.457761i	0.226365	−	0.974042i	$-0.427316\pi$
$823$	−18.0750	−	13.1322i	−0.630053	−	0.457761i	−0.856419	+	0.516282i	$0.827316\pi$
$824$	−11.0598	+	34.0385i	−0.385285	+	1.18579i
$825$	21.8057	+	67.1111i	0.759178	+	2.33651i
$826$	13.5207	−	9.82334i	0.470444	−	0.341798i
$827$	−11.2832	−	34.7261i	−0.392355	−	1.20755i	−0.931002	−	0.365014i	$-0.881064\pi$
$827$	−11.2832	−	34.7261i	−0.392355	−	1.20755i	0.538647	−	0.842532i	$-0.318936\pi$
$828$	8.12073	+	5.90005i	0.282215	+	0.205041i
$829$	−38.4624	−	27.9446i	−1.33585	−	0.970555i	−0.999585	−	0.0287896i	$-0.990835\pi$
$829$	−38.4624	−	27.9446i	−1.33585	−	0.970555i	−0.336269	−	0.941766i	$-0.609165\pi$
$830$	23.5386	−	17.1018i	0.817038	−	0.593613i
$831$	−43.6640			−1.51469
$832$	−1.90508			−0.0660467
$833$	−6.43818	+	4.67761i	−0.223070	+	0.162070i
$834$	−4.06353	+	12.5063i	−0.140708	+	0.433056i
$835$	−10.8495	−	33.3912i	−0.375461	−	1.15555i
$836$	−8.12776			−0.281105
$837$	−74.1211	+	11.5277i	−2.56200	+	0.398457i
$838$	−5.00835			−0.173011
$839$	−15.1692	−	46.6860i	−0.523699	−	1.61178i	−0.766874	−	0.641797i	$-0.778189\pi$
$839$	−15.1692	−	46.6860i	−0.523699	−	1.61178i	0.243175	−	0.969982i	$-0.421811\pi$
$840$	−16.1389	+	49.6704i	−0.556844	+	1.71379i
$841$	−16.7344	+	12.1582i	−0.577047	+	0.419249i
$842$	−1.42498			−0.0491079
$843$	39.2596			1.35217
$844$	21.3784	−	15.5323i	0.735876	−	0.534645i
$845$	3.03563	+	2.20552i	0.104429	+	0.0758721i
$846$	2.76415	+	2.00827i	0.0950335	+	0.0690459i
$847$	3.43957	+	10.5859i	0.118185	+	0.363736i
$848$	25.6720	−	18.6518i	0.881580	−	0.640506i
$849$	−4.47123	−	13.7610i	−0.153452	−	0.472277i
$850$	−5.41058	+	16.6521i	−0.185581	+	0.571161i
$851$	1.16885	+	0.849223i	0.0400678	+	0.0291110i
$852$	6.54982	−	20.1583i	0.224393	−	0.690611i
$853$	−0.518035	+	1.59435i	−0.0177372	+	0.0545894i	−0.959533	−	0.281595i	$-0.909137\pi$
$853$	−0.518035	+	1.59435i	−0.0177372	+	0.0545894i	0.941796	+	0.336184i	$0.109137\pi$
$854$	14.1268	+	10.2637i	0.483409	+	0.351217i
$855$	−16.3278	+	50.2519i	−0.558400	+	1.71858i
$856$	−5.67750	−	17.4736i	−0.194053	−	0.597234i
$857$	15.9468	−	11.5860i	0.544732	−	0.395771i	−0.281108	−	0.959676i	$-0.590702\pi$
$857$	15.9468	−	11.5860i	0.544732	−	0.395771i	0.825839	+	0.563906i	$0.190702\pi$
$858$	1.28748	+	3.96246i	0.0439538	+	0.135276i
$859$	22.9891	+	16.7026i	0.784378	+	0.569884i	0.906290	−	0.422657i	$-0.138902\pi$
$859$	22.9891	+	16.7026i	0.784378	+	0.569884i	−0.121912	+	0.992541i	$0.538902\pi$
$860$	49.1489	+	35.7088i	1.67596	+	1.21766i
$861$	−16.4729	+	11.9682i	−0.561394	+	0.407877i
$862$	3.59556			0.122465
$863$	−47.3328			−1.61123			−0.805614	−	0.592441i	$-0.798165\pi$
$863$	−47.3328			−1.61123			−0.805614	+	0.592441i	$0.798165\pi$
$864$	−57.1652	+	41.5330i	−1.94480	+	1.41298i
$865$	−9.03946	+	27.8206i	−0.307351	+	0.945929i
$866$	−0.878549	−	2.70390i	−0.0298543	−	0.0918821i
$867$	−12.9739			−0.440616
$868$	14.7946	−	14.7123i	0.502162	−	0.499368i
$869$	6.83584			0.231890
$870$	14.0035	+	43.0984i	0.474763	+	1.46117i
$871$	−0.712731	+	2.19356i	−0.0241500	+	0.0743260i
$872$	−7.77541	+	5.64917i	−0.263309	+	0.191305i
$873$	62.3759			2.11110
$874$	0.849866			0.0287471
$875$	−27.0963	+	19.6866i	−0.916023	+	0.665529i
$876$	−4.73201	−	3.43801i	−0.159880	−	0.116160i
$877$	6.12007	+	4.44649i	0.206660	+	0.150147i	0.686301	−	0.727317i	$-0.259233\pi$
$877$	6.12007	+	4.44649i	0.206660	+	0.150147i	−0.479641	+	0.877465i	$0.659233\pi$
$878$	1.11288	+	3.42511i	0.0375580	+	0.115592i
$879$	−65.3366	+	47.4698i	−2.20375	+	1.60112i
$880$	−6.64944	−	20.4649i	−0.224152	−	0.689870i
$881$	5.40938	−	16.6484i	0.182247	−	0.560898i	−0.817643	−	0.575725i	$-0.804720\pi$
$881$	5.40938	−	16.6484i	0.182247	−	0.560898i	0.999890	+	0.0148275i	$0.00471990\pi$
$882$	6.92248	+	5.02947i	0.233092	+	0.169351i
$883$	6.68461	−	20.5731i	0.224955	−	0.692341i	−0.773341	−	0.633990i	$-0.781416\pi$
$883$	6.68461	−	20.5731i	0.224955	−	0.692341i	0.998296	−	0.0583505i	$-0.0185841\pi$
$884$	1.90381	−	5.85933i	0.0640321	−	0.197071i
$885$	138.236	+	100.434i	4.64675	+	3.37606i
$886$	4.99451	−	15.3715i	0.167794	−	0.516416i
$887$	−13.4292	−	41.3309i	−0.450910	−	1.38776i	−0.875871	−	0.482546i	$-0.839712\pi$
$887$	−13.4292	−	41.3309i	−0.450910	−	1.38776i	0.424961	−	0.905212i	$-0.360288\pi$
$888$	−9.15313	+	6.65014i	−0.307159	+	0.223164i
$889$	8.02357	+	24.6940i	0.269102	+	0.828210i
$890$	11.7625	+	8.54596i	0.394280	+	0.286461i
$891$	−42.1279	−	30.6077i	−1.41134	−	1.02540i
$892$	13.4880	−	9.79959i	0.451611	−	0.328115i
$893$	−1.72396			−0.0576902
$894$	22.1507			0.740829
$895$	−6.82865	+	4.96131i	−0.228257	+	0.165838i
$896$	7.78311	−	23.9539i	0.260015	−	0.800245i
$897$	0.802287	+	2.46919i	0.0267876	+	0.0824437i
$898$	−8.49236			−0.283394
$899$	6.24752	−	38.7453i	0.208366	−	1.29223i
$900$	−112.194			−3.73981
$901$	14.9576	+	46.0347i	0.498309	+	1.53364i
$902$	−1.17283	+	3.60959i	−0.0390509	+	0.120186i
$903$	−53.4876	+	38.8610i	−1.77996	+	1.29321i
$904$	17.6495			0.587015
$905$	27.8918			0.927154
$906$	7.09325	−	5.15355i	0.235657	−	0.171215i
$907$	−36.9150	−	26.8203i	−1.22574	−	0.890555i	−0.229180	−	0.973384i	$-0.573604\pi$
$907$	−36.9150	−	26.8203i	−1.22574	−	0.890555i	−0.996564	+	0.0828291i	$0.973604\pi$
$908$	−27.7191	−	20.1391i	−0.919891	−	0.668340i
$909$	−3.76146	−	11.5766i	−0.124760	−	0.383971i
$910$	−3.56076	+	2.58705i	−0.118038	+	0.0857597i
$911$	−0.346516	−	1.06647i	−0.0114806	−	0.0353336i	0.945152	−	0.326630i	$-0.105913\pi$
$911$	−0.346516	−	1.06647i	−0.0114806	−	0.0353336i	−0.956633	+	0.291297i	$0.905913\pi$
$912$	4.54583	−	13.9906i	0.150527	−	0.463276i
$913$	−28.4558	−	20.6744i	−0.941750	−	0.684221i
$914$	0.798151	−	2.45646i	0.0264005	−	0.0812524i
$915$	−55.1685	+	169.791i	−1.82382	+	5.61313i
$916$	35.5449	+	25.8249i	1.17444	+	0.853278i
$917$	−14.0122	+	43.1251i	−0.462723	+	1.42412i
$918$	−8.02858	−	24.7094i	−0.264983	−	0.815533i
$919$	−9.47684	+	6.88533i	−0.312612	+	0.227126i	−0.733017	−	0.680211i	$-0.761888\pi$
$919$	−9.47684	+	6.88533i	−0.312612	+	0.227126i	0.420404	+	0.907337i	$0.361888\pi$
$920$	1.87458	+	5.76936i	0.0618030	+	0.190210i
$921$	10.1464	+	7.37182i	0.334336	+	0.242910i
$922$	9.42517	+	6.84779i	0.310401	+	0.225520i
$923$	3.13269	−	2.27604i	0.103114	−	0.0749166i
$924$	29.1247			0.958133
$925$	−16.1486			−0.530964
$926$	4.28432	−	3.11274i	0.140792	−	0.102291i
$927$	40.0952	−	123.400i	1.31690	−	4.05300i
$928$	−11.4240	−	35.1594i	−0.375011	−	1.15416i
$929$	−2.57692			−0.0845460			−0.0422730	−	0.999106i	$-0.513460\pi$
$929$	−2.57692			−0.0845460			−0.0422730	+	0.999106i	$0.513460\pi$
$930$	−31.8482	−	16.3396i	−1.04434	−	0.535795i
$931$	−4.31745			−0.141499
$932$	3.86490	+	11.8949i	0.126599	+	0.389632i
$933$	9.93260	−	30.5694i	0.325179	−	1.00080i
$934$	−6.23307	+	4.52859i	−0.203952	+	0.148180i
$935$	32.8230			1.07343
$936$	−14.3602			−0.469377
$937$	−8.36037	+	6.07416i	−0.273121	+	0.198434i	−0.715912	−	0.698191i	$-0.753989\pi$
$937$	−8.36037	+	6.07416i	−0.273121	+	0.198434i	0.442790	+	0.896625i	$0.353989\pi$
$938$	−2.18874	−	1.59022i	−0.0714650	−	0.0519224i
$939$	−56.1984	−	40.8305i	−1.83397	−	1.33245i
$940$	−1.75413	−	5.39865i	−0.0572133	−	0.176085i
$941$	27.7000	−	20.1252i	0.902995	−	0.656064i	−0.0362384	−	0.999343i	$-0.511538\pi$
$941$	27.7000	−	20.1252i	0.902995	−	0.656064i	0.939234	+	0.343279i	$0.111538\pi$
$942$	−3.65996	−	11.2642i	−0.119248	−	0.367007i
$943$	−0.730842	+	2.24930i	−0.0237995	+	0.0732473i
$944$	−27.1837	−	19.7501i	−0.884753	−	0.642811i
$945$	34.1816	−	105.200i	1.11193	−	3.42216i
$946$	−3.80819	+	11.7204i	−0.123815	+	0.381063i
$947$	−21.3237	−	15.4926i	−0.692928	−	0.503442i	0.184693	−	0.982796i	$-0.440871\pi$
$947$	−21.3237	−	15.4926i	−0.692928	−	0.503442i	−0.877621	+	0.479355i	$0.840871\pi$
$948$	−4.75504	+	14.6345i	−0.154436	+	0.475306i
$949$	−0.330205	−	1.01627i	−0.0107189	−	0.0329894i
$950$	−7.68495	+	5.58345i	−0.249333	+	0.181151i
$951$	−1.52581	−	4.69595i	−0.0494776	−	0.152277i
$952$	12.6740	+	9.20817i	0.410765	+	0.298438i
$953$	36.4246	+	26.4640i	1.17991	+	0.857255i	0.992161	−	0.124963i	$-0.0398811\pi$
$953$	36.4246	+	26.4640i	1.17991	+	0.857255i	0.187748	+	0.982217i	$0.439881\pi$
$954$	42.1051	−	30.5912i	1.36320	−	0.990426i
$955$	−16.7859			−0.543178
$956$	3.72373			0.120434
$957$	44.3202	−	32.2005i	1.43267	−	1.04089i
$958$	3.87795	−	11.9351i	0.125291	−	0.385605i
$959$	−7.92697	−	24.3967i	−0.255975	−	0.787811i
$960$	22.8470			0.737384
$961$	18.0811	+	25.1808i	0.583262	+	0.812284i
$962$	−0.953468			−0.0307410
$963$	20.5827	+	63.3472i	0.663270	+	2.04133i
$964$	−7.39960	+	22.7736i	−0.238325	+	0.733489i
$965$	−12.5265	+	9.10106i	−0.403243	+	0.292973i
$966$	−3.04538			−0.0979835
$967$	47.5817			1.53012			0.765062	−	0.643956i	$-0.222708\pi$
$967$	47.5817			1.53012			0.765062	+	0.643956i	$0.222708\pi$
$968$	−8.19065	+	5.95086i	−0.263257	+	0.191268i
$969$	18.1537	+	13.1894i	0.583180	+	0.423705i
$970$	14.0682	+	10.2212i	0.451703	+	0.328182i
$971$	6.44777	+	19.8442i	0.206919	+	0.636830i	0.999629	+	0.0272320i	$0.00866928\pi$
$971$	6.44777	+	19.8442i	0.206919	+	0.636830i	−0.792710	+	0.609598i	$0.791331\pi$
$972$	38.8304	−	28.2119i	1.24548	−	0.904898i
$973$	5.18944	+	15.9714i	0.166366	+	0.512021i
$974$	−0.827055	+	2.54541i	−0.0265005	+	0.0815603i
$975$	−23.4768	−	17.0569i	−0.751858	−	0.546257i
$976$	10.8487	−	33.3889i	0.347259	−	1.06875i
$977$	−1.60299	+	4.93348i	−0.0512840	+	0.157836i	−0.973419	−	0.229033i	$-0.926444\pi$
$977$	−1.60299	+	4.93348i	−0.0512840	+	0.157836i	0.922135	+	0.386869i	$0.126444\pi$
$978$	−34.3314	−	24.9432i	−1.09780	−	0.797597i
$979$	5.43143	−	16.7162i	0.173589	−	0.534253i
$980$	−4.39300	−	13.5203i	−0.140329	−	0.431889i
$981$	28.1883	−	20.4800i	0.899984	−	0.653877i
$982$	4.27557	+	13.1589i	0.136439	+	0.419916i
$983$	−33.7171	−	24.4969i	−1.07541	−	0.781330i	−0.0985323	−	0.995134i	$-0.531415\pi$
$983$	−33.7171	−	24.4969i	−1.07541	−	0.781330i	−0.976877	+	0.213803i	$0.931415\pi$
$984$	−14.9833	−	10.8860i	−0.477651	−	0.347034i
$985$	65.8342	−	47.8314i	2.09765	−	1.52403i
$986$	13.5931			0.432892
$987$	6.17758			0.196634
$988$	2.70409	−	1.96464i	0.0860286	−	0.0625035i
$989$	−2.37305	+	7.30351i	−0.0754588	+	0.232238i
$990$	−10.9059	−	33.5648i	−0.346611	−	1.06676i
$991$	−16.7951			−0.533515			−0.266757	−	0.963764i	$-0.585952\pi$
$991$	−16.7951			−0.533515			−0.266757	+	0.963764i	$0.585952\pi$
$992$	25.9816	+	13.3297i	0.824916	+	0.423219i
$993$	−83.5621			−2.65176
$994$	1.40358	+	4.31977i	0.0445188	+	0.137015i
$995$	19.9351	−	61.3539i	0.631985	−	1.94505i
$996$	64.0546	−	46.5384i	2.02965	−	1.47463i
$997$	−39.1716			−1.24058			−0.620289	−	0.784373i	$-0.712985\pi$
$997$	−39.1716			−1.24058			−0.620289	+	0.784373i	$0.712985\pi$
$998$	7.61473			0.241040
$999$	19.3860	−	14.0848i	0.613347	−	0.445622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.66.10	✓	68
31.8	even	5	inner	403.2.k.e.287.10	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.10	✓	68	1.1	even	1	trivial
403.2.k.e.287.10	yes	68	31.8	even	5	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.165656 + 0.509838i) q^{2} +(0.987660 - 3.03970i) q^{3} +(1.38554 - 1.00665i) q^{4} -3.75225 q^{5} +1.71337 q^{6} +(1.77021 - 1.28613i) q^{7} +(1.61014 + 1.16984i) q^{8} +(-5.83728 - 4.24103i) q^{9} +O(q^{10})\)	\(q+(0.165656 + 0.509838i) q^{2} +(0.987660 - 3.03970i) q^{3} +(1.38554 - 1.00665i) q^{4} -3.75225 q^{5} +1.71337 q^{6} +(1.77021 - 1.28613i) q^{7} +(1.61014 + 1.16984i) q^{8} +(-5.83728 - 4.24103i) q^{9} +(-0.621584 - 1.91304i) q^{10} +(-1.96727 + 1.42931i) q^{11} +(-1.69149 - 5.20587i) q^{12} +(0.309017 - 0.951057i) q^{13} +(0.948968 + 0.689465i) q^{14} +(-3.70595 + 11.4057i) q^{15} +(0.728762 - 2.24290i) q^{16} +(2.91030 + 2.11446i) q^{17} +(1.19526 - 3.67862i) q^{18} +(0.603093 + 1.85613i) q^{19} +(-5.19890 + 3.77722i) q^{20} +(-2.16110 - 6.65119i) q^{21} +(-1.05461 - 0.766217i) q^{22} +(-0.657174 - 0.477465i) q^{23} +(5.14623 - 3.73896i) q^{24} +9.07937 q^{25} +0.536075 q^{26} +(-10.8995 + 7.91898i) q^{27} +(1.15801 - 3.56399i) q^{28} +(-2.17818 - 6.70376i) q^{29} -6.42899 q^{30} +(4.95384 + 2.54154i) q^{31} +5.24473 q^{32} +(2.40168 + 7.39160i) q^{33} +(-0.595920 + 1.83405i) q^{34} +(-6.64228 + 4.82590i) q^{35} -12.3570 q^{36} -1.77861 q^{37} +(-0.846419 + 0.614960i) q^{38} +(-2.58573 - 1.87864i) q^{39} +(-6.04166 - 4.38952i) q^{40} +(-0.899707 - 2.76901i) q^{41} +(3.03303 - 2.20362i) q^{42} +(-2.92136 - 8.99102i) q^{43} +(-1.28692 + 3.96073i) q^{44} +(21.9029 + 15.9134i) q^{45} +(0.134565 - 0.414147i) q^{46} +(-0.272966 + 0.840101i) q^{47} +(-6.09798 - 4.43044i) q^{48} +(-0.683609 + 2.10393i) q^{49} +(1.50406 + 4.62901i) q^{50} +(9.30171 - 6.75808i) q^{51} +(-0.529230 - 1.62880i) q^{52} +(10.8857 + 7.90892i) q^{53} +(-5.84298 - 4.24517i) q^{54} +(7.38170 - 5.36312i) q^{55} +4.35486 q^{56} +6.23774 q^{57} +(3.05700 - 2.22104i) q^{58} +(4.40280 - 13.5504i) q^{59} +(6.34689 + 19.5337i) q^{60} +14.8865 q^{61} +(-0.475140 + 2.94668i) q^{62} -15.7878 q^{63} +(-0.588701 - 1.81184i) q^{64} +(-1.15951 + 3.56860i) q^{65} +(-3.37067 + 2.44893i) q^{66} -2.30645 q^{67} +6.16087 q^{68} +(-2.10042 + 1.52604i) q^{69} +(-3.56076 - 2.58705i) q^{70} +(3.13269 + 2.27604i) q^{71} +(-4.43754 - 13.6573i) q^{72} +(0.864488 - 0.628087i) q^{73} +(-0.294638 - 0.906802i) q^{74} +(8.96733 - 27.5986i) q^{75} +(2.70409 + 1.96464i) q^{76} +(-1.64421 + 5.06036i) q^{77} +(0.529460 - 1.62951i) q^{78} +(-2.27427 - 1.65236i) q^{79} +(-2.73450 + 8.41592i) q^{80} +(6.61740 + 20.3663i) q^{81} +(1.26271 - 0.917410i) q^{82} +(4.46980 + 13.7566i) q^{83} +(-9.68974 - 7.04001i) q^{84} +(-10.9202 - 7.93396i) q^{85} +(4.10002 - 2.97884i) q^{86} -22.5287 q^{87} -4.83965 q^{88} +(-5.84766 + 4.24857i) q^{89} +(-4.48490 + 13.8031i) q^{90} +(-0.676161 - 2.08101i) q^{91} -1.39118 q^{92} +(12.6183 - 12.5480i) q^{93} -0.473534 q^{94} +(-2.26296 - 6.96466i) q^{95} +(5.18001 - 15.9424i) q^{96} +(-6.99394 + 5.08139i) q^{97} -1.18591 q^{98} +17.5453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

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