LMFDB - Embedded newform 403.2.k.e.287.10

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			287.10
Character	$\chi$	$=$	403.287
Dual form			403.2.k.e.66.10

$q$-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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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	−0.875250	−	0.483671i	$-0.839303\pi$
$2$	0.165656	−	0.509838i	0.117137	−	0.360510i	0.992387	+	0.123161i	$0.0393032\pi$
$3$	0.987660	+	3.03970i	0.570226	+	1.75497i	0.651889	+	0.758314i	$0.273977\pi$
$3$	0.987660	+	3.03970i	0.570226	+	1.75497i	−0.0816637	+	0.996660i	$0.526023\pi$
$4$	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	0.869716	−	0.493552i	$-0.164302\pi$
$7$	1.77021	+	1.28613i	0.669078	+	0.486113i	−0.200639	+	0.979665i	$0.564302\pi$
$8$	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	0.250287	−	0.968172i	$-0.419475\pi$
$11$	−1.96727	−	1.42931i	−0.593155	−	0.430953i	−0.843443	+	0.537219i	$0.819475\pi$
$12$	−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	−0.175981	−	0.984393i	$-0.556310\pi$
$17$	2.91030	−	2.11446i	0.705851	−	0.512831i	0.881833	+	0.471563i	$0.156310\pi$
$18$	1.19526	+	3.67862i	0.281725	+	0.867059i
$19$	0.603093	−	1.85613i	0.138359	−	0.425825i	−0.857738	−	0.514087i	$-0.828131\pi$
$19$	0.603093	−	1.85613i	0.138359	−	0.425825i	0.996097	+	0.0882612i	$0.0281310\pi$
$20$	−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	−0.654189	−	0.756331i	$-0.726990\pi$
$23$	−0.657174	+	0.477465i	−0.137030	+	0.0995583i	0.517158	+	0.855890i	$0.326990\pi$
$24$	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	0.516852	+	0.856075i	$0.327104\pi$
$29$	−2.17818	+	6.70376i	−0.404478	+	1.24486i	−0.921330	+	0.388781i	$0.872896\pi$
$30$	−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	−0.996406	−	0.0847011i	$-0.973006\pi$
$41$	−0.899707	+	2.76901i	−0.140511	+	0.432447i	0.855896	+	0.517148i	$0.173006\pi$
$42$	3.03303	+	2.20362i	0.468006	+	0.340026i
$43$	−2.92136	+	8.99102i	−0.445503	+	1.37112i	0.436428	+	0.899739i	$0.356244\pi$
$43$	−2.92136	+	8.99102i	−0.445503	+	1.37112i	−0.881931	+	0.471379i	$0.843756\pi$
$44$	−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	0.929173	−	0.369646i	$-0.120521\pi$
$47$	−0.272966	−	0.840101i	−0.0398161	−	0.122541i	−0.968989	+	0.247104i	$0.920521\pi$
$48$	−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	0.523046	−	0.852305i	$-0.324796\pi$
$53$	10.8857	−	7.90892i	1.49527	−	1.08637i	0.972220	−	0.234070i	$-0.0752044\pi$
$54$	−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	0.642241	+	0.766503i	$0.278005\pi$
$59$	4.40280	+	13.5504i	0.573196	+	1.76412i	−0.0690449	+	0.997614i	$0.521995\pi$
$60$	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	−0.386167	−	0.922429i	$-0.626201\pi$
$71$	3.13269	−	2.27604i	0.371782	−	0.270116i	0.757950	+	0.652313i	$0.226201\pi$
$72$	−4.43754	+	13.6573i	−0.522969	+	1.60953i
$73$	0.864488	+	0.628087i	0.101181	+	0.0735121i	0.637225	−	0.770678i	$-0.280082\pi$
$73$	0.864488	+	0.628087i	0.101181	+	0.0735121i	−0.536045	+	0.844190i	$0.680082\pi$
$74$	−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	−0.708327	−	0.705885i	$-0.750550\pi$
$79$	−2.27427	+	1.65236i	−0.255876	+	0.185904i	0.452451	+	0.891789i	$0.350550\pi$
$80$	−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	−0.333041	−	0.942912i	$-0.608075\pi$
$83$	4.46980	−	13.7566i	0.490625	−	1.50999i	0.823666	−	0.567075i	$-0.191925\pi$
$84$	−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	0.233019	−	0.972472i	$-0.425140\pi$
$89$	−5.84766	−	4.24857i	−0.619851	−	0.450348i	−0.852869	+	0.522124i	$0.825140\pi$
$90$	−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	0.173088	−	0.984906i	$-0.444626\pi$
$97$	−6.99394	−	5.08139i	−0.710127	−	0.515937i	−0.883214	+	0.468969i	$0.844626\pi$
$98$	−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	−0.517808	−	0.855497i	$-0.673252\pi$
$101$	1.36483	−	0.991609i	0.135806	−	0.0986688i	0.653614	+	0.756828i	$0.273252\pi$
$102$	4.98642	−	3.62284i	0.493729	−	0.358715i
$103$	5.55699	−	17.1026i	0.547546	−	1.68517i	−0.167312	−	0.985904i	$-0.553509\pi$
$103$	5.55699	−	17.1026i	0.547546	−	1.68517i	0.714858	−	0.699270i	$-0.246491\pi$
$104$	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	−0.887021	−	0.461729i	$-0.847229\pi$
$107$	−7.46837	+	5.42609i	−0.721994	+	0.524560i	0.165026	+	0.986289i	$0.447229\pi$
$108$	−7.13009	−	21.9442i	−0.686093	−	2.11158i
$109$	−1.49225	−	4.59267i	−0.142932	−	0.439898i	0.853808	−	0.520589i	$-0.174287\pi$
$109$	−1.49225	−	4.59267i	−0.142932	−	0.439898i	−0.996739	+	0.0806905i	$0.974287\pi$
$110$	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	0.871665	−	0.490103i	$-0.163041\pi$
$113$	7.17438	+	5.21249i	0.674909	+	0.490350i	−0.196756	+	0.980452i	$0.563041\pi$
$114$	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	−0.971266	−	0.237995i	$-0.923510\pi$
$127$	−3.66691	−	11.2856i	−0.325385	−	1.00143i	0.645881	−	0.763438i	$-0.276490\pi$
$128$	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	−0.982081	−	0.188461i	$-0.939650\pi$
$131$	−16.7654	−	12.1808i	−1.46480	−	1.06424i	−0.482717	−	0.875776i	$-0.660350\pi$
$132$	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	0.977954	+	0.208819i	$0.0669618\pi$
$137$	3.62276	+	11.1497i	0.309513	+	0.952584i	−0.668441	+	0.743765i	$0.733038\pi$
$138$	−1.12598	+	0.818073i	−0.0958499	+	0.0696390i
$139$	−2.37166	−	7.29922i	−0.201162	−	0.619112i	−0.999849	−	0.0173658i	$-0.994472\pi$
$139$	−2.37166	−	7.29922i	−0.201162	−	0.619112i	0.798688	−	0.601746i	$-0.205528\pi$
$140$	−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	0.743354	−	0.668898i	$-0.233234\pi$
$151$	4.13994	+	3.00784i	0.336904	+	0.244775i	−0.406451	+	0.913673i	$0.633234\pi$
$152$	−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	−0.999398	−	0.0346848i	$-0.988957\pi$
$157$	−2.13612	+	6.57430i	−0.170481	+	0.524686i	0.828917	+	0.559371i	$0.188957\pi$
$158$	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	−0.641766	+	0.766900i	$0.721798\pi$
$163$	−20.0374	+	14.5580i	−1.56945	+	1.14027i	−0.927682	+	0.373371i	$0.878202\pi$
$164$	−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	−0.774669	−	0.632367i	$-0.782083\pi$
$167$	2.89145	−	8.89898i	0.223747	−	0.688624i	0.998416	−	0.0562568i	$-0.0179166\pi$
$168$	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	0.999912	−	0.0132826i	$-0.00422810\pi$
$173$	2.40908	+	7.41438i	0.183159	+	0.563705i	−0.816753	+	0.576988i	$0.804228\pi$
$174$	−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	0.653717	−	0.756739i	$-0.273209\pi$
$179$	1.81988	+	1.32222i	0.136024	+	0.0988275i	−0.517692	+	0.855567i	$0.673209\pi$
$180$	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	0.701419	−	0.712750i	$-0.252550\pi$
$193$	3.33841	+	2.42549i	0.240304	+	0.174591i	−0.461115	+	0.887340i	$0.652550\pi$
$194$	−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	−0.251824	−	0.967773i	$-0.581030\pi$
$197$	−17.5453	−	12.7474i	−1.25005	−	0.908214i	−0.998225	+	0.0595592i	$0.981030\pi$
$198$	2.90649	−	8.94525i	0.206555	−	0.635711i
$199$	−5.31284	−	16.3512i	−0.376617	−	1.15911i	−0.942381	−	0.334541i	$-0.891419\pi$
$199$	−5.31284	−	16.3512i	−0.376617	−	1.15911i	0.565764	−	0.824567i	$-0.308581\pi$
$200$	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	0.506039	+	0.862511i	$0.331109\pi$
$227$	−6.18219	+	19.0268i	−0.410326	+	1.26285i	−0.916365	+	0.400344i	$0.868891\pi$
$228$	8.64264	+	6.27925i	0.572373	+	0.415853i
$229$	7.92757	−	24.3985i	0.523868	−	1.61230i	−0.242674	−	0.970108i	$-0.578025\pi$
$229$	7.92757	−	24.3985i	0.523868	−	1.61230i	0.766543	−	0.642193i	$-0.221975\pi$
$230$	−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	0.849523	−	0.527551i	$-0.176890\pi$
$233$	−2.25671	−	6.94545i	−0.147842	−	0.455011i	−0.997366	+	0.0725396i	$0.976890\pi$
$234$	−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	−0.529439	−	0.848348i	$-0.677598\pi$
$239$	1.75903	−	1.27801i	0.113782	−	0.0826678i	0.643221	+	0.765680i	$0.277598\pi$
$240$	22.8811	−	16.6241i	1.47697	−	1.07308i
$241$	−11.3115	−	8.21832i	−0.728641	−	0.529388i	0.160493	−	0.987037i	$-0.448692\pi$
$241$	−11.3115	−	8.21832i	−0.728641	−	0.529388i	−0.889133	+	0.457649i	$0.848692\pi$
$242$	−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	0.973419	−	0.229030i	$-0.0735553\pi$
$251$	0.812527	+	2.50070i	0.0512863	+	0.157843i	−0.922133	+	0.386873i	$0.873555\pi$
$252$	−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	−0.726469	−	0.687199i	$-0.758840\pi$
$257$	−4.76760	+	3.46386i	−0.297395	+	0.216070i	0.429074	+	0.903269i	$0.358840\pi$
$258$	−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	0.998239	−	0.0593163i	$-0.0188921\pi$
$263$	2.52635	+	7.77531i	0.155781	+	0.479446i	−0.842458	+	0.538762i	$0.818892\pi$
$264$	−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	−0.525851	−	0.850577i	$-0.676253\pi$
$269$	6.55274	−	20.1673i	0.399528	−	1.22962i	0.925379	−	0.379043i	$-0.123747\pi$
$270$	21.9243	−	15.9289i	1.33427	−	0.969405i
$271$	1.96897	−	1.43054i	0.119607	−	0.0868993i	−0.526374	−	0.850253i	$-0.676449\pi$
$271$	1.96897	−	1.43054i	0.119607	−	0.0868993i	0.645980	+	0.763354i	$0.276449\pi$
$272$	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	0.740438	+	0.672124i	$0.234618\pi$
$277$	−4.22164	+	12.9929i	−0.253654	+	0.780666i	−0.994092	+	0.108541i	$0.965382\pi$
$278$	−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	−0.771704	−	0.635982i	$-0.780595\pi$
$281$	3.79580	−	11.6823i	0.226438	−	0.696906i	0.998142	−	0.0609240i	$-0.0194047\pi$
$282$	−0.467691	−	1.43940i	−0.0278506	−	0.0857152i
$283$	3.66249	+	2.66096i	0.217713	+	0.158177i	0.691296	−	0.722571i	$-0.257040\pi$
$283$	3.66249	+	2.66096i	0.217713	+	0.158177i	−0.473584	+	0.880749i	$0.657040\pi$
$284$	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	−0.993708	−	0.112005i	$-0.964273\pi$
$293$	−20.4424	+	14.8523i	−1.19426	+	0.867679i	−0.200550	+	0.979684i	$0.564273\pi$
$294$	−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	0.910472	−	0.413571i	$-0.135719\pi$
$307$	−1.21259	−	3.73196i	−0.0692060	−	0.212994i	−0.979678	+	0.200576i	$0.935719\pi$
$308$	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	0.940307	+	0.340328i	$0.110538\pi$
$313$	6.71620	+	20.6703i	0.379622	+	1.16836i	−0.560685	+	0.828029i	$0.689462\pi$
$314$	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	0.622330	−	0.782755i	$-0.286186\pi$
$317$	1.24983	+	0.908052i	0.0701972	+	0.0510013i	−0.552133	+	0.833756i	$0.686186\pi$
$318$	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	0.439427	+	0.898278i	$0.355181\pi$
$331$	−8.07917	+	24.8651i	−0.444071	+	1.36671i	−0.883499	+	0.468433i	$0.844819\pi$
$332$	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	0.0364805	−	0.999334i	$-0.488385\pi$
$337$	−16.5708	−	12.0394i	−0.902670	−	0.655828i	−0.939150	+	0.343506i	$0.888385\pi$
$338$	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	−0.792189	−	0.610276i	$-0.791059\pi$
$349$	−8.52965	+	6.19715i	−0.456582	+	0.331726i	0.335607	+	0.942002i	$0.391059\pi$
$350$	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	−0.437521	−	0.899208i	$-0.644143\pi$
$353$	8.36046	−	25.7308i	0.444982	−	1.36951i	0.882503	−	0.470306i	$-0.155857\pi$
$354$	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	0.992651	−	0.121012i	$-0.0386138\pi$
$359$	2.24432	+	6.90731i	0.118451	+	0.364554i	−0.874200	+	0.485565i	$0.838614\pi$
$360$	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	0.458034	−	0.888935i	$-0.348554\pi$
$379$	−4.78624	−	3.47740i	−0.245852	−	0.178622i	−0.703887	+	0.710312i	$0.748554\pi$
$380$	−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	−0.00516319	−	0.999987i	$-0.501644\pi$
$383$	−18.7446	−	13.6187i	−0.957803	−	0.695884i	−0.952639	+	0.304102i	$0.901644\pi$
$384$	−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	−0.100998	−	0.994887i	$-0.532204\pi$
$389$	16.0543	−	11.6641i	0.813985	−	0.591395i	0.914983	+	0.403492i	$0.132204\pi$
$390$	−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	−0.909450	−	0.415814i	$-0.863497\pi$
$401$	1.41617	−	4.35851i	0.0707200	−	0.217654i	0.980170	+	0.198160i	$0.0634967\pi$
$402$	−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	0.855440	−	0.517902i	$-0.173287\pi$
$419$	−2.88703	−	8.88536i	−0.141041	−	0.434078i	−0.996481	+	0.0838236i	$0.973287\pi$
$420$	36.3583	−	26.4159i	1.77410	−	1.28896i
$421$	−0.821418	−	2.52806i	−0.0400335	−	0.123210i	0.929042	−	0.369973i	$-0.120633\pi$
$421$	−0.821418	−	2.52806i	−0.0400335	−	0.123210i	−0.969076	+	0.246763i	$0.920633\pi$
$422$	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	0.988484	−	0.151328i	$-0.0483549\pi$
$431$	2.07264	+	6.37892i	0.0998354	+	0.307262i	−0.888648	+	0.458589i	$0.848355\pi$
$432$	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	−0.989637	−	0.143594i	$-0.954134\pi$
$443$	−24.3917	+	17.7216i	−1.15889	+	0.841979i	−0.169249	+	0.985573i	$0.554134\pi$
$444$	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	−0.997624	−	0.0688980i	$-0.978052\pi$
$449$	−4.89536	−	15.0664i	−0.231026	−	0.711026i	0.766597	−	0.642128i	$-0.221948\pi$
$450$	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	−0.675210	−	0.737626i	$-0.735947\pi$
$457$	−3.89794	+	2.83202i	−0.182338	+	0.132476i	0.492872	+	0.870102i	$0.335947\pi$
$458$	−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	0.916387	−	0.400292i	$-0.131091\pi$
$461$	17.5818	+	12.7739i	0.818866	+	0.594941i	−0.0975214	+	0.995233i	$0.531091\pi$
$462$	−2.81714	−	8.67026i	−0.131065	−	0.403377i
$463$	−3.05268	+	9.39518i	−0.141870	+	0.436631i	−0.996595	−	0.0824498i	$-0.973726\pi$
$463$	−3.05268	+	9.39518i	−0.141870	+	0.436631i	0.854725	+	0.519081i	$0.173726\pi$
$464$	−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	−0.794177	−	0.607686i	$-0.792098\pi$
$467$	4.44121	−	13.6686i	0.205515	−	0.632509i	0.999692	−	0.0248226i	$-0.00790210\pi$
$468$	−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	−0.929331	−	0.369249i	$-0.879615\pi$
$479$	−18.9387	+	13.7598i	−0.865333	+	0.628701i	0.0639974	+	0.997950i	$0.479615\pi$
$480$	−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	−0.492498	−	0.870313i	$-0.663916\pi$
$487$	4.03909	−	2.93457i	0.183029	−	0.132978i	0.675527	+	0.737335i	$0.263916\pi$
$488$	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	0.999956	+	0.00939903i	$0.00299185\pi$
$499$	4.38946	+	13.5094i	0.196499	+	0.604762i	−0.803457	+	0.595363i	$0.797008\pi$
$500$	−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	0.506531	−	0.862222i	$-0.330927\pi$
$503$	−3.52032	−	2.55767i	−0.156963	−	0.114041i	−0.663495	+	0.748181i	$0.730927\pi$
$504$	−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	0.888053	−	0.459741i	$-0.152058\pi$
$509$	−2.27022	−	6.98701i	−0.100626	−	0.309694i	−0.988679	+	0.150047i	$0.952058\pi$
$510$	−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	0.765239	−	0.643746i	$-0.222621\pi$
$523$	8.90690	+	6.47124i	0.389471	+	0.282968i	−0.375767	+	0.926714i	$0.622621\pi$
$524$	−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	0.0264165	−	0.999651i	$-0.491590\pi$
$541$	22.9176	−	16.6506i	0.985304	−	0.715865i	0.958888	+	0.283786i	$0.0915904\pi$
$542$	−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	0.555163	−	0.831741i	$-0.312656\pi$
$547$	−1.50421	−	1.09287i	−0.0643152	−	0.0467277i	−0.619478	+	0.785014i	$0.712656\pi$
$548$	−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	0.0790355	−	0.996872i	$-0.474816\pi$
$569$	−20.1474	−	14.6379i	−0.844623	−	0.613654i	−0.923658	+	0.383218i	$0.874816\pi$
$570$	−3.87728	+	11.9330i	−0.162401	+	0.499820i
$571$	−4.47743	−	13.7801i	−0.187374	−	0.576679i	0.812607	−	0.582812i	$-0.198048\pi$
$571$	−4.47743	−	13.7801i	−0.187374	−	0.576679i	−0.999981	+	0.00613315i	$0.998048\pi$
$572$	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	−0.363198	−	0.931712i	$-0.618315\pi$
$577$	11.4887	−	35.3587i	0.478282	−	1.47200i	0.841480	−	0.540289i	$-0.181685\pi$
$578$	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	0.779013	+	0.627008i	$0.215721\pi$
$587$	−5.32455	+	16.3873i	−0.219768	+	0.676376i	−0.998781	+	0.0493680i	$0.984279\pi$
$588$	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	0.0650843	−	0.997880i	$-0.479268\pi$
$593$	−21.0360	−	15.2835i	−0.863844	−	0.627619i	−0.928928	+	0.370261i	$0.879268\pi$
$594$	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	−0.994211	−	0.107443i	$-0.965734\pi$
$599$	−3.10151	+	9.54546i	−0.126724	+	0.390017i	0.867487	+	0.497460i	$0.165734\pi$
$600$	46.7246	+	33.9474i	1.90752	+	1.38590i
$601$	13.7032	−	42.1740i	0.558963	−	1.72031i	−0.126277	−	0.991995i	$-0.540303\pi$
$601$	13.7032	−	42.1740i	0.558963	−	1.72031i	0.685240	−	0.728317i	$-0.259697\pi$
$602$	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	0.986433	+	0.164164i	$0.0524927\pi$
$607$	7.01882	+	21.6017i	0.284885	+	0.876787i	−0.701548	+	0.712622i	$0.747507\pi$
$608$	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	0.675529	−	0.737334i	$-0.263915\pi$
$613$	4.53168	+	3.29246i	0.183033	+	0.132981i	−0.492496	+	0.870315i	$0.663915\pi$
$614$	−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	0.767698	+	0.640811i	$0.221402\pi$
$617$	12.9979	+	40.0035i	0.523277	+	1.61048i	−0.244421	+	0.969669i	$0.578598\pi$
$618$	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	0.558901	−	0.829234i	$-0.311223\pi$
$631$	−1.43275	−	1.04096i	−0.0570370	−	0.0414398i	−0.615938	+	0.787794i	$0.711223\pi$
$632$	−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	−0.775305	−	0.631587i	$-0.782404\pi$
$641$	5.65014	−	17.3893i	0.223167	−	0.686838i	0.998472	−	0.0552512i	$-0.0175959\pi$
$642$	−12.7961	+	9.29689i	−0.505021	+	0.366919i
$643$	9.65496	−	7.01474i	0.380754	−	0.276634i	−0.380902	−	0.924615i	$-0.624386\pi$
$643$	9.65496	−	7.01474i	0.380754	−	0.276634i	0.761656	+	0.647981i	$0.224386\pi$
$644$	−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	0.876730	−	0.480983i	$-0.159720\pi$
$647$	17.5564	+	12.7555i	0.690213	+	0.501469i	−0.186517	+	0.982452i	$0.559720\pi$
$648$	−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	−0.985722	−	0.168382i	$-0.946146\pi$
$653$	−2.28154	+	7.02185i	−0.0892834	+	0.274786i	0.896438	+	0.443168i	$0.146146\pi$
$654$	−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	−0.544273	−	0.838908i	$-0.683194\pi$
$659$	2.19197	−	1.59256i	0.0853870	−	0.0620373i	0.629660	+	0.776871i	$0.283194\pi$
$660$	−40.4058	+	29.3565i	−1.57279	+	1.14270i
$661$	−10.2345	+	31.4985i	−0.398075	+	1.22515i	0.528466	+	0.848954i	$0.322767\pi$
$661$	−10.2345	+	31.4985i	−0.398075	+	1.22515i	−0.926541	+	0.376194i	$0.877233\pi$
$662$	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	−0.278531	−	0.960427i	$-0.589848\pi$
$673$	14.2376	−	10.3442i	0.548819	−	0.398740i	0.827350	+	0.561687i	$0.189848\pi$
$674$	−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	0.237009	−	0.971508i	$-0.423833\pi$
$691$	32.4434	−	23.5715i	1.23421	−	0.896704i	0.997198	+	0.0748038i	$0.0238331\pi$
$692$	−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	0.440778	+	0.897616i	$0.354703\pi$
$701$	−11.7403	+	36.1329i	−0.443424	+	1.36472i	−0.884202	+	0.467104i	$0.845297\pi$
$702$	−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	−0.0613773	−	0.998115i	$-0.519549\pi$
$709$	−27.4154	−	19.9185i	−1.02961	−	0.748053i	−0.968230	+	0.250061i	$0.919549\pi$
$710$	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	0.0729359	−	0.997337i	$-0.476763\pi$
$727$	28.1492	−	20.4516i	1.04400	−	0.758509i	0.971062	+	0.238828i	$0.0767631\pi$
$728$	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	0.0444344	−	0.999012i	$-0.485851\pi$
$733$	−24.1487	−	17.5450i	−0.891952	−	0.648041i	−0.936386	+	0.350971i	$0.885851\pi$
$734$	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	0.986944	−	0.161065i	$-0.0514929\pi$
$751$	31.2066	+	22.6729i	1.13874	+	0.827346i	0.151800	+	0.988411i	$0.451493\pi$
$752$	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	−0.757099	−	0.653301i	$-0.773384\pi$
$757$	−14.5435	−	44.7604i	−0.528593	−	1.62684i	0.228505	−	0.973543i	$-0.426616\pi$
$758$	−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	−0.957173	−	0.289517i	$-0.906505\pi$
$761$	−26.9685	+	19.5938i	−0.977609	+	0.710274i	−0.0204357	+	0.999791i	$0.506505\pi$
$762$	−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	−0.606846	−	0.794819i	$-0.707566\pi$
$773$	9.76676	−	30.0590i	0.351286	−	1.08115i	0.958132	−	0.286327i	$-0.0924345\pi$
$774$	−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	−0.978959	−	0.204057i	$-0.934587\pi$
$787$	−1.88022	+	5.78673i	−0.0670227	+	0.206275i	0.911936	+	0.410332i	$0.134587\pi$
$788$	−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	−0.239636	−	0.970863i	$-0.577028\pi$
$797$	17.2114	−	12.5048i	0.609658	−	0.442942i	0.849294	+	0.527920i	$0.177028\pi$
$798$	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	0.913961	−	0.405802i	$-0.133008\pi$
$809$	−1.81959	−	5.60013i	−0.0639735	−	0.196890i	−0.977934	+	0.208912i	$0.933008\pi$
$810$	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	0.820369	−	0.571835i	$-0.193768\pi$
$821$	−5.14150	−	15.8239i	−0.179440	−	0.552258i	−0.999808	+	0.0195767i	$0.993768\pi$
$822$	6.20712	+	19.1036i	0.216498	+	0.666313i
$823$	−18.0750	+	13.1322i	−0.630053	+	0.457761i	−0.856419	−	0.516282i	$-0.827316\pi$
$823$	−18.0750	+	13.1322i	−0.630053	+	0.457761i	0.226365	+	0.974042i	$0.427316\pi$
$824$	−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	0.538647	+	0.842532i	$0.318936\pi$
$827$	−11.2832	+	34.7261i	−0.392355	+	1.20755i	−0.931002	+	0.365014i	$0.881064\pi$
$828$	8.12073	−	5.90005i	0.282215	−	0.205041i
$829$	−38.4624	+	27.9446i	−1.33585	+	0.970555i	−0.336269	+	0.941766i	$0.609165\pi$
$829$	−38.4624	+	27.9446i	−1.33585	+	0.970555i	−0.999585	+	0.0287896i	$0.990835\pi$
$830$	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	0.243175	+	0.969982i	$0.421811\pi$
$839$	−15.1692	+	46.6860i	−0.523699	+	1.61178i	−0.766874	+	0.641797i	$0.778189\pi$
$840$	−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	0.941796	−	0.336184i	$-0.109137\pi$
$853$	−0.518035	−	1.59435i	−0.0177372	−	0.0545894i	−0.959533	+	0.281595i	$0.909137\pi$
$854$	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	0.825839	−	0.563906i	$-0.190702\pi$
$857$	15.9468	+	11.5860i	0.544732	+	0.395771i	−0.281108	+	0.959676i	$0.590702\pi$
$858$	1.28748	−	3.96246i	0.0439538	−	0.135276i
$859$	22.9891	−	16.7026i	0.784378	−	0.569884i	−0.121912	−	0.992541i	$-0.538902\pi$
$859$	22.9891	−	16.7026i	0.784378	−	0.569884i	0.906290	+	0.422657i	$0.138902\pi$
$860$	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	−0.479641	−	0.877465i	$-0.659233\pi$
$877$	6.12007	−	4.44649i	0.206660	−	0.150147i	0.686301	+	0.727317i	$0.259233\pi$
$878$	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	0.999890	−	0.0148275i	$-0.00471990\pi$
$881$	5.40938	+	16.6484i	0.182247	+	0.560898i	−0.817643	+	0.575725i	$0.804720\pi$
$882$	6.92248	−	5.02947i	0.233092	−	0.169351i
$883$	6.68461	+	20.5731i	0.224955	+	0.692341i	0.998296	+	0.0583505i	$0.0185841\pi$
$883$	6.68461	+	20.5731i	0.224955	+	0.692341i	−0.773341	+	0.633990i	$0.781416\pi$
$884$	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	0.424961	+	0.905212i	$0.360288\pi$
$887$	−13.4292	+	41.3309i	−0.450910	+	1.38776i	−0.875871	+	0.482546i	$0.839712\pi$
$888$	−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	−0.996564	−	0.0828291i	$-0.973604\pi$
$907$	−36.9150	+	26.8203i	−1.22574	+	0.890555i	−0.229180	+	0.973384i	$0.573604\pi$
$908$	−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	−0.956633	−	0.291297i	$-0.905913\pi$
$911$	−0.346516	+	1.06647i	−0.0114806	+	0.0353336i	0.945152	+	0.326630i	$0.105913\pi$
$912$	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	0.420404	−	0.907337i	$-0.361888\pi$
$919$	−9.47684	−	6.88533i	−0.312612	−	0.227126i	−0.733017	+	0.680211i	$0.761888\pi$
$920$	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	0.442790	−	0.896625i	$-0.353989\pi$
$937$	−8.36037	−	6.07416i	−0.273121	−	0.198434i	−0.715912	+	0.698191i	$0.753989\pi$
$938$	−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	0.939234	−	0.343279i	$-0.111538\pi$
$941$	27.7000	+	20.1252i	0.902995	+	0.656064i	−0.0362384	+	0.999343i	$0.511538\pi$
$942$	−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	−0.877621	−	0.479355i	$-0.840871\pi$
$947$	−21.3237	+	15.4926i	−0.692928	+	0.503442i	0.184693	+	0.982796i	$0.440871\pi$
$948$	−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	0.187748	−	0.982217i	$-0.439881\pi$
$953$	36.4246	−	26.4640i	1.17991	−	0.857255i	0.992161	+	0.124963i	$0.0398811\pi$
$954$	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	−0.792710	−	0.609598i	$-0.791331\pi$
$971$	6.44777	−	19.8442i	0.206919	−	0.636830i	0.999629	−	0.0272320i	$-0.00866928\pi$
$972$	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	0.922135	−	0.386869i	$-0.126444\pi$
$977$	−1.60299	−	4.93348i	−0.0512840	−	0.157836i	−0.973419	+	0.229033i	$0.926444\pi$
$978$	−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	−0.976877	−	0.213803i	$-0.931415\pi$
$983$	−33.7171	+	24.4969i	−1.07541	+	0.781330i	−0.0985323	+	0.995134i	$0.531415\pi$
$984$	−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.287.10	yes	68
31.4	even	5	inner	403.2.k.e.66.10	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.10	✓	68	31.4	even	5	inner
403.2.k.e.287.10	yes	68	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
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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