LMFDB - Embedded newform 670.2.e.f.171.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			171.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.f.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -1.44949 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.724745 + 1.25529i) q^{6} +(0.224745 - 0.389270i) q^{7} +1.00000 q^{8} -0.898979 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -1.44949 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.724745 + 1.25529i) q^{6} +(0.224745 - 0.389270i) q^{7} +1.00000 q^{8} -0.898979 q^{9} +(0.500000 + 0.866025i) q^{10} +(0.724745 - 1.25529i) q^{12} +(2.00000 + 3.46410i) q^{13} -0.449490 q^{14} +1.44949 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.224745 + 0.389270i) q^{17} +(0.449490 + 0.778539i) q^{18} +(-1.44949 - 2.51059i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.325765 + 0.564242i) q^{21} +(1.22474 + 2.12132i) q^{23} -1.44949 q^{24} +1.00000 q^{25} +(2.00000 - 3.46410i) q^{26} +5.65153 q^{27} +(0.224745 + 0.389270i) q^{28} +(3.00000 - 5.19615i) q^{29} +(-0.724745 - 1.25529i) q^{30} +(2.72474 - 4.71940i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.224745 - 0.389270i) q^{34} +(-0.224745 + 0.389270i) q^{35} +(0.449490 - 0.778539i) q^{36} +(1.94949 + 3.37662i) q^{37} +(-1.44949 + 2.51059i) q^{38} +(-2.89898 - 5.02118i) q^{39} -1.00000 q^{40} +(5.94949 - 10.3048i) q^{41} +0.651531 q^{42} +4.00000 q^{43} +0.898979 q^{45} +(1.22474 - 2.12132i) q^{46} +(3.67423 - 6.36396i) q^{47} +(0.724745 + 1.25529i) q^{48} +(3.39898 + 5.88721i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.325765 - 0.564242i) q^{51} -4.00000 q^{52} -7.00000 q^{53} +(-2.82577 - 4.89437i) q^{54} +(0.224745 - 0.389270i) q^{56} +(2.10102 + 3.63907i) q^{57} -6.00000 q^{58} +2.89898 q^{59} +(-0.724745 + 1.25529i) q^{60} +(0.224745 + 0.389270i) q^{61} -5.44949 q^{62} +(-0.202041 + 0.349945i) q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(7.17423 - 3.94086i) q^{67} -0.449490 q^{68} +(-1.77526 - 3.07483i) q^{69} +0.449490 q^{70} +(7.17423 - 12.4261i) q^{71} -0.898979 q^{72} +(1.77526 + 3.07483i) q^{73} +(1.94949 - 3.37662i) q^{74} -1.44949 q^{75} +2.89898 q^{76} +(-2.89898 + 5.02118i) q^{78} +(-1.00000 + 1.73205i) q^{79} +(0.500000 + 0.866025i) q^{80} -5.49490 q^{81} -11.8990 q^{82} +(1.17423 + 2.03383i) q^{83} +(-0.325765 - 0.564242i) q^{84} +(-0.224745 - 0.389270i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-4.34847 + 7.53177i) q^{87} -11.8990 q^{89} +(-0.449490 - 0.778539i) q^{90} +1.79796 q^{91} -2.44949 q^{92} +(-3.94949 + 6.84072i) q^{93} -7.34847 q^{94} +(1.44949 + 2.51059i) q^{95} +(0.724745 - 1.25529i) q^{96} +(1.89898 + 3.28913i) q^{97} +(3.39898 - 5.88721i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} + 16 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 + 16 * q^9	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} + 16 q^{9} + 2 q^{10} - 2 q^{12} + 8 q^{13} + 8 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 8 q^{18} + 4 q^{19} + 2 q^{20} - 16 q^{21} + 4 q^{24} + 4 q^{25} + 8 q^{26} + 52 q^{27} - 4 q^{28} + 12 q^{29} + 2 q^{30} + 6 q^{31} - 2 q^{32} - 4 q^{34} + 4 q^{35} - 8 q^{36} - 2 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} + 14 q^{41} + 32 q^{42} + 16 q^{43} - 16 q^{45} - 2 q^{48} - 6 q^{49} - 2 q^{50} - 16 q^{51} - 16 q^{52} - 28 q^{53} - 26 q^{54} - 4 q^{56} + 28 q^{57} - 24 q^{58} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 12 q^{62} - 40 q^{63} + 4 q^{64} - 8 q^{65} + 14 q^{67} + 8 q^{68} - 12 q^{69} - 8 q^{70} + 14 q^{71} + 16 q^{72} + 12 q^{73} - 2 q^{74} + 4 q^{75} - 8 q^{76} + 8 q^{78} - 4 q^{79} + 2 q^{80} + 76 q^{81} - 28 q^{82} - 10 q^{83} - 16 q^{84} + 4 q^{85} - 8 q^{86} + 12 q^{87} - 28 q^{89} + 8 q^{90} - 32 q^{91} - 6 q^{93} - 4 q^{95} - 2 q^{96} - 12 q^{97} - 6 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 + 16 * q^9 + 2 * q^10 - 2 * q^12 + 8 * q^13 + 8 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 8 * q^18 + 4 * q^19 + 2 * q^20 - 16 * q^21 + 4 * q^24 + 4 * q^25 + 8 * q^26 + 52 * q^27 - 4 * q^28 + 12 * q^29 + 2 * q^30 + 6 * q^31 - 2 * q^32 - 4 * q^34 + 4 * q^35 - 8 * q^36 - 2 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 + 14 * q^41 + 32 * q^42 + 16 * q^43 - 16 * q^45 - 2 * q^48 - 6 * q^49 - 2 * q^50 - 16 * q^51 - 16 * q^52 - 28 * q^53 - 26 * q^54 - 4 * q^56 + 28 * q^57 - 24 * q^58 - 8 * q^59 + 2 * q^60 - 4 * q^61 - 12 * q^62 - 40 * q^63 + 4 * q^64 - 8 * q^65 + 14 * q^67 + 8 * q^68 - 12 * q^69 - 8 * q^70 + 14 * q^71 + 16 * q^72 + 12 * q^73 - 2 * q^74 + 4 * q^75 - 8 * q^76 + 8 * q^78 - 4 * q^79 + 2 * q^80 + 76 * q^81 - 28 * q^82 - 10 * q^83 - 16 * q^84 + 4 * q^85 - 8 * q^86 + 12 * q^87 - 28 * q^89 + 8 * q^90 - 32 * q^91 - 6 * q^93 - 4 * q^95 - 2 * q^96 - 12 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.44949			−0.836863			−0.418432	−	0.908248i	$-0.637420\pi$
$3$	−1.44949			−0.836863			−0.418432	+	0.908248i	$0.637420\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.724745	+	1.25529i	0.295876	+	0.512472i
$7$	0.224745	−	0.389270i	0.0849456	−	0.147130i	−0.820422	−	0.571758i	$-0.806262\pi$
$7$	0.224745	−	0.389270i	0.0849456	−	0.147130i	0.905368	+	0.424628i	$0.139595\pi$
$8$	1.00000			0.353553
$9$	−0.898979			−0.299660
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	0.724745	−	1.25529i	0.209216	−	0.362372i
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	0.997927	+	0.0643593i	$0.0205004\pi$
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−0.449490			−0.120131
$15$	1.44949			0.374257
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.224745	+	0.389270i	0.0545086	+	0.0944117i	0.891992	−	0.452051i	$-0.149307\pi$
$17$	0.224745	+	0.389270i	0.0545086	+	0.0944117i	−0.837484	+	0.546463i	$0.815974\pi$
$18$	0.449490	+	0.778539i	0.105946	+	0.183503i
$19$	−1.44949	−	2.51059i	−0.332536	−	0.575969i	0.650473	−	0.759530i	$-0.274571\pi$
$19$	−1.44949	−	2.51059i	−0.332536	−	0.575969i	−0.983008	+	0.183561i	$0.941238\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−0.325765	+	0.564242i	−0.0710878	+	0.123128i
$22$		0			0
$23$	1.22474	+	2.12132i	0.255377	+	0.442326i	0.964998	−	0.262258i	$-0.0844671\pi$
$23$	1.22474	+	2.12132i	0.255377	+	0.442326i	−0.709621	+	0.704584i	$0.751134\pi$
$24$	−1.44949			−0.295876
$25$	1.00000			0.200000
$26$	2.00000	−	3.46410i	0.392232	−	0.679366i
$27$	5.65153			1.08764
$28$	0.224745	+	0.389270i	0.0424728	+	0.0735650i
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$	−0.724745	−	1.25529i	−0.132320	−	0.229184i
$31$	2.72474	−	4.71940i	0.489379	−	0.847629i	−0.510547	−	0.859850i	$-0.670557\pi$
$31$	2.72474	−	4.71940i	0.489379	−	0.847629i	0.999925	+	0.0122214i	$0.00389029\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	0.224745	−	0.389270i	0.0385434	−	0.0667592i
$35$	−0.224745	+	0.389270i	−0.0379888	+	0.0657986i
$36$	0.449490	−	0.778539i	0.0749150	−	0.129757i
$37$	1.94949	+	3.37662i	0.320494	+	0.555112i	0.980590	−	0.196069i	$-0.0628177\pi$
$37$	1.94949	+	3.37662i	0.320494	+	0.555112i	−0.660096	+	0.751181i	$0.729484\pi$
$38$	−1.44949	+	2.51059i	−0.235138	+	0.407271i
$39$	−2.89898	−	5.02118i	−0.464208	−	0.804032i
$40$	−1.00000			−0.158114
$41$	5.94949	−	10.3048i	0.929154	−	1.60934i	0.144414	−	0.989517i	$-0.453870\pi$
$41$	5.94949	−	10.3048i	0.929154	−	1.60934i	0.784740	−	0.619825i	$-0.212796\pi$
$42$	0.651531			0.100533
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	0.898979			0.134012
$46$	1.22474	−	2.12132i	0.180579	−	0.312772i
$47$	3.67423	−	6.36396i	0.535942	−	0.928279i	−0.463175	−	0.886267i	$-0.653290\pi$
$47$	3.67423	−	6.36396i	0.535942	−	0.928279i	0.999117	−	0.0420122i	$-0.0133768\pi$
$48$	0.724745	+	1.25529i	0.104608	+	0.181186i
$49$	3.39898	+	5.88721i	0.485568	+	0.841029i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−0.325765	−	0.564242i	−0.0456163	−	0.0790097i
$52$	−4.00000			−0.554700
$53$	−7.00000			−0.961524			−0.480762	−	0.876851i	$-0.659640\pi$
$53$	−7.00000			−0.961524			−0.480762	+	0.876851i	$0.659640\pi$
$54$	−2.82577	−	4.89437i	−0.384538	−	0.666039i
$55$		0			0
$56$	0.224745	−	0.389270i	0.0300328	−	0.0520183i
$57$	2.10102	+	3.63907i	0.278287	+	0.482007i
$58$	−6.00000			−0.787839
$59$	2.89898			0.377415			0.188707	−	0.982033i	$-0.439570\pi$
$59$	2.89898			0.377415			0.188707	+	0.982033i	$0.439570\pi$
$60$	−0.724745	+	1.25529i	−0.0935642	+	0.162058i
$61$	0.224745	+	0.389270i	0.0287756	+	0.0498409i	0.880055	−	0.474873i	$-0.157506\pi$
$61$	0.224745	+	0.389270i	0.0287756	+	0.0498409i	−0.851279	+	0.524713i	$0.824173\pi$
$62$	−5.44949			−0.692086
$63$	−0.202041	+	0.349945i	−0.0254548	+	0.0440890i
$64$	1.00000			0.125000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	7.17423	−	3.94086i	0.876472	−	0.481452i
$67$	7.17423	−	3.94086i	0.876472	−	0.481452i
$68$	−0.449490			−0.0545086
$69$	−1.77526	−	3.07483i	−0.213716	−	0.370166i
$70$	0.449490			0.0537243
$71$	7.17423	−	12.4261i	0.851425	−	1.47471i	−0.0284974	−	0.999594i	$-0.509072\pi$
$71$	7.17423	−	12.4261i	0.851425	−	1.47471i	0.879922	−	0.475117i	$-0.157594\pi$
$72$	−0.898979			−0.105946
$73$	1.77526	+	3.07483i	0.207778	+	0.359882i	0.951014	−	0.309147i	$-0.100044\pi$
$73$	1.77526	+	3.07483i	0.207778	+	0.359882i	−0.743236	+	0.669029i	$0.766710\pi$
$74$	1.94949	−	3.37662i	0.226624	−	0.392524i
$75$	−1.44949			−0.167373
$76$	2.89898			0.332536
$77$		0			0
$78$	−2.89898	+	5.02118i	−0.328245	+	0.568537i
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−5.49490			−0.610544
$82$	−11.8990			−1.31402
$83$	1.17423	+	2.03383i	0.128889	+	0.223242i	0.923246	−	0.384208i	$-0.125526\pi$
$83$	1.17423	+	2.03383i	0.128889	+	0.223242i	−0.794357	+	0.607451i	$0.792192\pi$
$84$	−0.325765	−	0.564242i	−0.0355439	−	0.0615639i
$85$	−0.224745	−	0.389270i	−0.0243770	−	0.0422222i
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$	−4.34847	+	7.53177i	−0.466205	+	0.807490i
$88$		0			0
$89$	−11.8990			−1.26129			−0.630645	−	0.776072i	$-0.717209\pi$
$89$	−11.8990			−1.26129			−0.630645	+	0.776072i	$0.717209\pi$
$90$	−0.449490	−	0.778539i	−0.0473804	−	0.0820652i
$91$	1.79796			0.188477
$92$	−2.44949			−0.255377
$93$	−3.94949	+	6.84072i	−0.409543	+	0.709349i
$94$	−7.34847			−0.757937
$95$	1.44949	+	2.51059i	0.148715	+	0.257581i
$96$	0.724745	−	1.25529i	0.0739690	−	0.128118i
$97$	1.89898	+	3.28913i	0.192812	+	0.333960i	0.946181	−	0.323638i	$-0.104906\pi$
$97$	1.89898	+	3.28913i	0.192812	+	0.333960i	−0.753369	+	0.657598i	$0.771573\pi$
$98$	3.39898	−	5.88721i	0.343349	−	0.594698i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−6.12372	+	10.6066i	−0.609333	+	1.05540i	0.382017	+	0.924155i	$0.375230\pi$
$101$	−6.12372	+	10.6066i	−0.609333	+	1.05540i	−0.991350	+	0.131241i	$0.958104\pi$
$102$	−0.325765	+	0.564242i	−0.0322556	+	0.0558683i
$103$	−5.22474	+	9.04952i	−0.514809	+	0.891676i	0.485043	+	0.874490i	$0.338804\pi$
$103$	−5.22474	+	9.04952i	−0.514809	+	0.891676i	−0.999852	+	0.0171857i	$0.994529\pi$
$104$	2.00000	+	3.46410i	0.196116	+	0.339683i
$105$	0.325765	−	0.564242i	0.0317914	−	0.0550644i
$106$	3.50000	+	6.06218i	0.339950	+	0.588811i
$107$	10.5505			1.01996			0.509978	−	0.860187i	$-0.329653\pi$
$107$	10.5505			1.01996			0.509978	+	0.860187i	$0.329653\pi$
$108$	−2.82577	+	4.89437i	−0.271909	+	0.470961i
$109$	5.55051			0.531642			0.265821	−	0.964022i	$-0.414357\pi$
$109$	5.55051			0.531642			0.265821	+	0.964022i	$0.414357\pi$
$110$		0			0
$111$	−2.82577	−	4.89437i	−0.268210	−	0.464553i
$112$	−0.449490			−0.0424728
$113$	−2.00000	+	3.46410i	−0.188144	+	0.325875i	−0.944632	−	0.328133i	$-0.893581\pi$
$113$	−2.00000	+	3.46410i	−0.188144	+	0.325875i	0.756487	+	0.654008i	$0.226914\pi$
$114$	2.10102	−	3.63907i	0.196779	−	0.340831i
$115$	−1.22474	−	2.12132i	−0.114208	−	0.197814i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	−1.79796	−	3.11416i	−0.166221	−	0.287904i
$118$	−1.44949	−	2.51059i	−0.133436	−	0.231119i
$119$	0.202041			0.0185211
$120$	1.44949			0.132320
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	0.224745	−	0.389270i	0.0203474	−	0.0352428i
$123$	−8.62372	+	14.9367i	−0.777575	+	1.34680i
$124$	2.72474	+	4.71940i	0.244689	+	0.423814i
$125$	−1.00000			−0.0894427
$126$	0.404082			0.0359985
$127$	1.44949	−	2.51059i	0.128621	−	0.222779i	−0.794521	−	0.607236i	$-0.792278\pi$
$127$	1.44949	−	2.51059i	0.128621	−	0.222779i	0.923143	+	0.384457i	$0.125611\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−5.79796			−0.510482
$130$	−2.00000	+	3.46410i	−0.175412	+	0.303822i
$131$	14.2474			1.24481			0.622403	−	0.782697i	$-0.286157\pi$
$131$	14.2474			1.24481			0.622403	+	0.782697i	$0.286157\pi$
$132$		0			0
$133$	−1.30306			−0.112990
$134$	−7.00000	−	4.24264i	−0.604708	−	0.366508i
$135$	−5.65153			−0.486406
$136$	0.224745	+	0.389270i	0.0192717	+	0.0333796i
$137$	4.44949			0.380146			0.190073	−	0.981770i	$-0.439128\pi$
$137$	4.44949			0.380146			0.190073	+	0.981770i	$0.439128\pi$
$138$	−1.77526	+	3.07483i	−0.151120	+	0.261747i
$139$	9.79796			0.831052			0.415526	−	0.909581i	$-0.363598\pi$
$139$	9.79796			0.831052			0.415526	+	0.909581i	$0.363598\pi$
$140$	−0.224745	−	0.389270i	−0.0189944	−	0.0328993i
$141$	−5.32577	+	9.22450i	−0.448510	+	0.776843i
$142$	−14.3485			−1.20410
$143$		0			0
$144$	0.449490	+	0.778539i	0.0374575	+	0.0648783i
$145$	−3.00000	+	5.19615i	−0.249136	+	0.431517i
$146$	1.77526	−	3.07483i	0.146921	−	0.254475i
$147$	−4.92679	−	8.53344i	−0.406354	−	0.703827i
$148$	−3.89898			−0.320494
$149$	−6.24745			−0.511811			−0.255905	−	0.966702i	$-0.582374\pi$
$149$	−6.24745			−0.511811			−0.255905	+	0.966702i	$0.582374\pi$
$150$	0.724745	+	1.25529i	0.0591752	+	0.102494i
$151$	−5.72474	−	9.91555i	−0.465873	−	0.806916i	0.533367	−	0.845884i	$-0.320926\pi$
$151$	−5.72474	−	9.91555i	−0.465873	−	0.806916i	−0.999240	+	0.0389678i	$0.987593\pi$
$152$	−1.44949	−	2.51059i	−0.117569	−	0.203636i
$153$	−0.202041	−	0.349945i	−0.0163340	−	0.0282914i
$154$		0			0
$155$	−2.72474	+	4.71940i	−0.218857	+	0.379071i
$156$	5.79796			0.464208
$157$	8.79796	+	15.2385i	0.702154	+	1.21617i	0.967709	+	0.252070i	$0.0811113\pi$
$157$	8.79796	+	15.2385i	0.702154	+	1.21617i	−0.265555	+	0.964096i	$0.585555\pi$
$158$	2.00000			0.159111
$159$	10.1464			0.804664
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	1.10102			0.0867726
$162$	2.74745	+	4.75872i	0.215860	+	0.373880i
$163$	1.27526	−	2.20881i	0.0998857	−	0.173007i	−0.811751	−	0.584003i	$-0.801486\pi$
$163$	1.27526	−	2.20881i	0.0998857	−	0.173007i	0.911637	+	0.410996i	$0.134819\pi$
$164$	5.94949	+	10.3048i	0.464577	+	0.804671i
$165$		0			0
$166$	1.17423	−	2.03383i	0.0911383	−	0.157856i
$167$	5.12372	−	8.87455i	0.396486	−	0.686733i	−0.596804	−	0.802387i	$-0.703563\pi$
$167$	5.12372	−	8.87455i	0.396486	−	0.686733i	0.993290	+	0.115654i	$0.0368963\pi$
$168$	−0.325765	+	0.564242i	−0.0251333	+	0.0435322i
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	−0.224745	+	0.389270i	−0.0172371	+	0.0298556i
$171$	1.30306	+	2.25697i	0.0996476	+	0.172595i
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$	8.69694			0.659313
$175$	0.224745	−	0.389270i	0.0169891	−	0.0294260i
$176$		0			0
$177$	−4.20204			−0.315845
$178$	5.94949	+	10.3048i	0.445933	+	0.772379i
$179$	−12.2474			−0.915417			−0.457709	−	0.889102i	$-0.651330\pi$
$179$	−12.2474			−0.915417			−0.457709	+	0.889102i	$0.651330\pi$
$180$	−0.449490	+	0.778539i	−0.0335030	+	0.0580289i
$181$	−5.67423	+	9.82806i	−0.421763	+	0.730514i	−0.996112	−	0.0880961i	$-0.971922\pi$
$181$	−5.67423	+	9.82806i	−0.421763	+	0.730514i	0.574349	+	0.818610i	$0.305255\pi$
$182$	−0.898979	−	1.55708i	−0.0666368	−	0.115418i
$183$	−0.325765	−	0.564242i	−0.0240813	−	0.0417100i
$184$	1.22474	+	2.12132i	0.0902894	+	0.156386i
$185$	−1.94949	−	3.37662i	−0.143329	−	0.248254i
$186$	7.89898			0.579181
$187$		0			0
$188$	3.67423	+	6.36396i	0.267971	+	0.464140i
$189$	1.27015	−	2.19997i	0.0923900	−	0.160024i
$190$	1.44949	−	2.51059i	0.105157	−	0.182137i
$191$	−7.27526	−	12.6011i	−0.526419	−	0.911784i	−0.999526	−	0.0307796i	$-0.990201\pi$
$191$	−7.27526	−	12.6011i	−0.526419	−	0.911784i	0.473107	−	0.881005i	$-0.343132\pi$
$192$	−1.44949			−0.104608
$193$	−15.5505			−1.11935			−0.559675	−	0.828712i	$-0.689074\pi$
$193$	−15.5505			−1.11935			−0.559675	+	0.828712i	$0.689074\pi$
$194$	1.89898	−	3.28913i	0.136339	−	0.236146i
$195$	2.89898	+	5.02118i	0.207600	+	0.359574i
$196$	−6.79796			−0.485568
$197$	4.44949	−	7.70674i	0.317013	−	0.549083i	−0.662850	−	0.748752i	$-0.730653\pi$
$197$	4.44949	−	7.70674i	0.317013	−	0.549083i	0.979863	+	0.199669i	$0.0639868\pi$
$198$		0			0
$199$	−1.17423	−	2.03383i	−0.0832393	−	0.144175i	0.821400	−	0.570352i	$-0.193193\pi$
$199$	−1.17423	−	2.03383i	−0.0832393	−	0.144175i	−0.904640	+	0.426177i	$0.859860\pi$
$200$	1.00000			0.0707107
$201$	−10.3990	+	5.71223i	−0.733487	+	0.402910i
$202$	12.2474			0.861727
$203$	−1.34847	−	2.33562i	−0.0946440	−	0.163928i
$204$	0.651531			0.0456163
$205$	−5.94949	+	10.3048i	−0.415530	+	0.719720i
$206$	10.4495			0.728050
$207$	−1.10102	−	1.90702i	−0.0765262	−	0.132547i
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$		0			0
$210$	−0.651531			−0.0449599
$211$	0.325765	+	0.564242i	0.0224266	+	0.0388440i	0.877021	−	0.480452i	$-0.159527\pi$
$211$	0.325765	+	0.564242i	0.0224266	+	0.0388440i	−0.854594	+	0.519296i	$0.826194\pi$
$212$	3.50000	−	6.06218i	0.240381	−	0.416352i
$213$	−10.3990	+	18.0116i	−0.712526	+	1.23413i
$214$	−5.27526	−	9.13701i	−0.360609	−	0.624593i
$215$	−4.00000			−0.272798
$216$	5.65153			0.384538
$217$	−1.22474	−	2.12132i	−0.0831411	−	0.144005i
$218$	−2.77526	−	4.80688i	−0.187964	−	0.325563i
$219$	−2.57321	−	4.45694i	−0.173882	−	0.301172i
$220$		0			0
$221$	−0.898979	+	1.55708i	−0.0604719	+	0.104740i
$222$	−2.82577	+	4.89437i	−0.189653	+	0.328489i
$223$	18.8990			1.26557			0.632785	−	0.774328i	$-0.281912\pi$
$223$	18.8990			1.26557			0.632785	+	0.774328i	$0.281912\pi$
$224$	0.224745	+	0.389270i	0.0150164	+	0.0260092i
$225$	−0.898979			−0.0599320
$226$	4.00000			0.266076
$227$	−3.82577	+	6.62642i	−0.253925	+	0.439811i	−0.964603	−	0.263706i	$-0.915055\pi$
$227$	−3.82577	+	6.62642i	−0.253925	+	0.439811i	0.710678	+	0.703517i	$0.248388\pi$
$228$	−4.20204			−0.278287
$229$	11.1237	+	19.2669i	0.735076	+	1.27319i	0.954690	+	0.297603i	$0.0961871\pi$
$229$	11.1237	+	19.2669i	0.735076	+	1.27319i	−0.219613	+	0.975587i	$0.570480\pi$
$230$	−1.22474	+	2.12132i	−0.0807573	+	0.139876i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	4.22474	−	7.31747i	0.276772	−	0.479384i	−0.693808	−	0.720160i	$-0.744069\pi$
$233$	4.22474	−	7.31747i	0.276772	−	0.479384i	0.970581	+	0.240776i	$0.0774019\pi$
$234$	−1.79796	+	3.11416i	−0.117536	+	0.203579i
$235$	−3.67423	+	6.36396i	−0.239681	+	0.415139i
$236$	−1.44949	+	2.51059i	−0.0943537	+	0.163425i
$237$	1.44949	−	2.51059i	0.0941545	−	0.163080i
$238$	−0.101021	−	0.174973i	−0.00654819	−	0.0113418i
$239$	3.10102	−	5.37113i	0.200588	−	0.347429i	−0.748130	−	0.663552i	$-0.769048\pi$
$239$	3.10102	−	5.37113i	0.200588	−	0.347429i	0.948718	+	0.316123i	$0.102381\pi$
$240$	−0.724745	−	1.25529i	−0.0467821	−	0.0810289i
$241$	−18.1010			−1.16599			−0.582995	−	0.812476i	$-0.698119\pi$
$241$	−18.1010			−1.16599			−0.582995	+	0.812476i	$0.698119\pi$
$242$	5.50000	−	9.52628i	0.353553	−	0.612372i
$243$	−8.98979			−0.576696
$244$	−0.449490			−0.0287756
$245$	−3.39898	−	5.88721i	−0.217153	−	0.376120i
$246$	17.2474			1.09966
$247$	5.79796	−	10.0424i	0.368915	−	0.638980i
$248$	2.72474	−	4.71940i	0.173021	−	0.299682i
$249$	−1.70204	−	2.94802i	−0.107862	−	0.186823i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−13.6742	−	23.6845i	−0.863110	−	1.49495i	−0.868912	−	0.494967i	$-0.835180\pi$
$251$	−13.6742	−	23.6845i	−0.863110	−	1.49495i	0.00580159	−	0.999983i	$-0.498153\pi$
$252$	−0.202041	−	0.349945i	−0.0127274	−	0.0220445i
$253$		0			0
$254$	−2.89898			−0.181898
$255$	0.325765	+	0.564242i	0.0204002	+	0.0353342i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.89898	−	13.6814i	0.492725	−	0.853424i	−0.507240	−	0.861805i	$-0.669334\pi$
$257$	7.89898	−	13.6814i	0.492725	−	0.853424i	0.999965	+	0.00838040i	$0.00266760\pi$
$258$	2.89898	+	5.02118i	0.180483	+	0.312605i
$259$	1.75255			0.108898
$260$	4.00000			0.248069
$261$	−2.69694	+	4.67123i	−0.166936	+	0.289142i
$262$	−7.12372	−	12.3387i	−0.440105	−	0.762284i
$263$	−5.10102			−0.314542			−0.157271	−	0.987555i	$-0.550270\pi$
$263$	−5.10102			−0.314542			−0.157271	+	0.987555i	$0.550270\pi$
$264$		0			0
$265$	7.00000			0.430007
$266$	0.651531	+	1.12848i	0.0399479	+	0.0691918i
$267$	17.2474			1.05553
$268$	−0.174235	+	8.18350i	−0.0106431	+	0.499887i
$269$	31.5959			1.92644			0.963219	−	0.268719i	$-0.0866004\pi$
$269$	31.5959			1.92644			0.963219	+	0.268719i	$0.0866004\pi$
$270$	2.82577	+	4.89437i	0.171971	+	0.297862i
$271$	−2.14643			−0.130386			−0.0651931	−	0.997873i	$-0.520766\pi$
$271$	−2.14643			−0.130386			−0.0651931	+	0.997873i	$0.520766\pi$
$272$	0.224745	−	0.389270i	0.0136272	−	0.0236029i
$273$	−2.60612			−0.157730
$274$	−2.22474	−	3.85337i	−0.134402	−	0.232791i
$275$		0			0
$276$	3.55051			0.213716
$277$	−25.8990			−1.55612			−0.778059	−	0.628191i	$-0.783796\pi$
$277$	−25.8990			−1.55612			−0.778059	+	0.628191i	$0.783796\pi$
$278$	−4.89898	−	8.48528i	−0.293821	−	0.508913i
$279$	−2.44949	+	4.24264i	−0.146647	+	0.254000i
$280$	−0.224745	+	0.389270i	−0.0134311	+	0.0232633i
$281$	−15.7474	−	27.2754i	−0.939414	−	1.62711i	−0.766567	−	0.642164i	$-0.778037\pi$
$281$	−15.7474	−	27.2754i	−0.939414	−	1.62711i	−0.172847	−	0.984949i	$-0.555297\pi$
$282$	10.6515			0.634289
$283$	−7.79796			−0.463541			−0.231770	−	0.972771i	$-0.574452\pi$
$283$	−7.79796			−0.463541			−0.231770	+	0.972771i	$0.574452\pi$
$284$	7.17423	+	12.4261i	0.425713	+	0.737356i
$285$	−2.10102	−	3.63907i	−0.124454	−	0.215560i
$286$		0			0
$287$	−2.67423	−	4.63191i	−0.157855	−	0.273413i
$288$	0.449490	−	0.778539i	0.0264864	−	0.0458759i
$289$	8.39898	−	14.5475i	0.494058	−	0.855733i
$290$	6.00000			0.352332
$291$	−2.75255	−	4.76756i	−0.161357	−	0.279479i
$292$	−3.55051			−0.207778
$293$	4.79796			0.280300			0.140150	−	0.990130i	$-0.455242\pi$
$293$	4.79796			0.280300			0.140150	+	0.990130i	$0.455242\pi$
$294$	−4.92679	+	8.53344i	−0.287336	+	0.497681i
$295$	−2.89898			−0.168785
$296$	1.94949	+	3.37662i	0.113312	+	0.196262i
$297$		0			0
$298$	3.12372	+	5.41045i	0.180952	+	0.313419i
$299$	−4.89898	+	8.48528i	−0.283315	+	0.490716i
$300$	0.724745	−	1.25529i	0.0418432	−	0.0724745i
$301$	0.898979	−	1.55708i	0.0518163	−	0.0897485i
$302$	−5.72474	+	9.91555i	−0.329422	+	0.570576i
$303$	8.87628	−	15.3742i	0.509929	−	0.883222i
$304$	−1.44949	+	2.51059i	−0.0831339	+	0.143992i
$305$	−0.224745	−	0.389270i	−0.0128689	−	0.0222895i
$306$	−0.202041	+	0.349945i	−0.0115499	+	0.0200050i
$307$	5.17423	+	8.96204i	0.295309	+	0.511490i	0.975057	−	0.221956i	$-0.0712440\pi$
$307$	5.17423	+	8.96204i	0.295309	+	0.511490i	−0.679748	+	0.733446i	$0.737911\pi$
$308$		0			0
$309$	7.57321	−	13.1172i	0.430825	−	0.746211i
$310$	5.44949			0.309510
$311$	11.4495			0.649241			0.324620	−	0.945844i	$-0.394763\pi$
$311$	11.4495			0.649241			0.324620	+	0.945844i	$0.394763\pi$
$312$	−2.89898	−	5.02118i	−0.164122	−	0.284268i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	8.79796	−	15.2385i	0.496498	−	0.859959i
$315$	0.202041	−	0.349945i	0.0113837	−	0.0197172i
$316$	−1.00000	−	1.73205i	−0.0562544	−	0.0974355i
$317$	−0.848469	−	1.46959i	−0.0476548	−	0.0825405i	0.841214	−	0.540702i	$-0.181841\pi$
$317$	−0.848469	−	1.46959i	−0.0476548	−	0.0825405i	−0.888869	+	0.458162i	$0.848508\pi$
$318$	−5.07321	−	8.78706i	−0.284492	−	0.492754i
$319$		0			0
$320$	−1.00000			−0.0559017
$321$	−15.2929			−0.853564
$322$	−0.550510	−	0.953512i	−0.0306787	−	0.0531371i
$323$	0.651531	−	1.12848i	0.0362521	−	0.0627906i
$324$	2.74745	−	4.75872i	0.152636	−	0.264373i
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$	−2.55051			−0.141260
$327$	−8.04541			−0.444912
$328$	5.94949	−	10.3048i	0.328506	−	0.568988i
$329$	−1.65153	−	2.86054i	−0.0910518	−	0.157706i
$330$		0			0
$331$	3.44949	−	5.97469i	0.189601	−	0.328399i	−0.755516	−	0.655130i	$-0.772614\pi$
$331$	3.44949	−	5.97469i	0.189601	−	0.328399i	0.945117	+	0.326731i	$0.105947\pi$
$332$	−2.34847			−0.128889
$333$	−1.75255	−	3.03551i	−0.0960392	−	0.166345i
$334$	−10.2474			−0.560715
$335$	−7.17423	+	3.94086i	−0.391970	+	0.215312i
$336$	0.651531			0.0355439
$337$	2.22474	+	3.85337i	0.121190	+	0.209907i	0.920237	−	0.391361i	$-0.127996\pi$
$337$	2.22474	+	3.85337i	0.121190	+	0.209907i	−0.799047	+	0.601268i	$0.794662\pi$
$338$	3.00000			0.163178
$339$	2.89898	−	5.02118i	0.157451	−	0.272713i
$340$	0.449490			0.0243770
$341$		0			0
$342$	1.30306	−	2.25697i	0.0704615	−	0.122043i
$343$	6.20204			0.334879
$344$	4.00000			0.215666
$345$	1.77526	+	3.07483i	0.0955765	+	0.165543i
$346$	4.50000	−	7.79423i	0.241921	−	0.419020i
$347$	5.34847	−	9.26382i	0.287121	−	0.497308i	−0.686000	−	0.727601i	$-0.740635\pi$
$347$	5.34847	−	9.26382i	0.287121	−	0.497308i	0.973121	+	0.230293i	$0.0739685\pi$
$348$	−4.34847	−	7.53177i	−0.233102	−	0.403745i
$349$	−13.7980			−0.738588			−0.369294	−	0.929313i	$-0.620400\pi$
$349$	−13.7980			−0.738588			−0.369294	+	0.929313i	$0.620400\pi$
$350$	−0.449490			−0.0240262
$351$	11.3031	+	19.5775i	0.603313	+	1.04497i
$352$		0			0
$353$	2.22474	+	3.85337i	0.118411	+	0.205094i	0.919138	−	0.393935i	$-0.128887\pi$
$353$	2.22474	+	3.85337i	0.118411	+	0.205094i	−0.800727	+	0.599029i	$0.795553\pi$
$354$	2.10102	+	3.63907i	0.111668	+	0.193415i
$355$	−7.17423	+	12.4261i	−0.380769	+	0.659511i
$356$	5.94949	−	10.3048i	0.315322	−	0.546154i
$357$	−0.292856			−0.0154996
$358$	6.12372	+	10.6066i	0.323649	+	0.560576i
$359$	−20.1464			−1.06329			−0.531644	−	0.846968i	$-0.678426\pi$
$359$	−20.1464			−1.06329			−0.531644	+	0.846968i	$0.678426\pi$
$360$	0.898979			0.0473804
$361$	5.29796	−	9.17633i	0.278840	−	0.482965i
$362$	11.3485			0.596462
$363$	−7.97219	−	13.8082i	−0.418432	−	0.724745i
$364$	−0.898979	+	1.55708i	−0.0471193	+	0.0816131i
$365$	−1.77526	−	3.07483i	−0.0929211	−	0.160944i
$366$	−0.325765	+	0.564242i	−0.0170280	+	0.0294934i
$367$	9.12372	−	15.8028i	0.476255	−	0.824897i	−0.523375	−	0.852102i	$-0.675327\pi$
$367$	9.12372	−	15.8028i	0.476255	−	0.824897i	0.999630	+	0.0272052i	$0.00866075\pi$
$368$	1.22474	−	2.12132i	0.0638442	−	0.110581i
$369$	−5.34847	+	9.26382i	−0.278430	+	0.482255i
$370$	−1.94949	+	3.37662i	−0.101349	+	0.175542i
$371$	−1.57321	+	2.72489i	−0.0816772	+	0.141469i
$372$	−3.94949	−	6.84072i	−0.204772	−	0.354675i
$373$	7.50000	−	12.9904i	0.388335	−	0.672616i	−0.603890	−	0.797067i	$-0.706384\pi$
$373$	7.50000	−	12.9904i	0.388335	−	0.672616i	0.992226	+	0.124451i	$0.0397169\pi$
$374$		0			0
$375$	1.44949			0.0748513
$376$	3.67423	−	6.36396i	0.189484	−	0.328196i
$377$	24.0000			1.23606
$378$	−2.54031			−0.130659
$379$	2.89898	+	5.02118i	0.148911	+	0.257921i	0.930825	−	0.365465i	$-0.119090\pi$
$379$	2.89898	+	5.02118i	0.148911	+	0.257921i	−0.781915	+	0.623386i	$0.785757\pi$
$380$	−2.89898			−0.148715
$381$	−2.10102	+	3.63907i	−0.107639	+	0.186435i
$382$	−7.27526	+	12.6011i	−0.372234	+	0.644729i
$383$	−10.3485	−	17.9241i	−0.528782	−	0.915877i	−0.999437	−	0.0335599i	$-0.989316\pi$
$383$	−10.3485	−	17.9241i	−0.528782	−	0.915877i	0.470655	−	0.882318i	$-0.344018\pi$
$384$	0.724745	+	1.25529i	0.0369845	+	0.0640590i
$385$		0			0
$386$	7.77526	+	13.4671i	0.395750	+	0.685459i
$387$	−3.59592			−0.182791
$388$	−3.79796			−0.192812
$389$	6.77526	+	11.7351i	0.343519	+	0.594992i	0.985084	−	0.172077i	$-0.0550477\pi$
$389$	6.77526	+	11.7351i	0.343519	+	0.594992i	−0.641564	+	0.767069i	$0.721714\pi$
$390$	2.89898	−	5.02118i	0.146796	−	0.254257i
$391$	−0.550510	+	0.953512i	−0.0278405	+	0.0482212i
$392$	3.39898	+	5.88721i	0.171674	+	0.297349i
$393$	−20.6515			−1.04173
$394$	−8.89898			−0.448324
$395$	1.00000	−	1.73205i	0.0503155	−	0.0871489i
$396$		0			0
$397$	−7.00000			−0.351320			−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000			−0.351320			−0.175660	+	0.984451i	$0.556206\pi$
$398$	−1.17423	+	2.03383i	−0.0588591	+	0.101947i
$399$	1.88877			0.0945570
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−4.89898			−0.244643			−0.122322	−	0.992491i	$-0.539034\pi$
$401$	−4.89898			−0.244643			−0.122322	+	0.992491i	$0.539034\pi$
$402$	10.1464	+	6.14966i	0.506058	+	0.306717i
$403$	21.7980			1.08583
$404$	−6.12372	−	10.6066i	−0.304667	−	0.527698i
$405$	5.49490			0.273044
$406$	−1.34847	+	2.33562i	−0.0669234	+	0.115915i
$407$		0			0
$408$	−0.325765	−	0.564242i	−0.0161278	−	0.0279342i
$409$	14.0505	−	24.3362i	0.694753	−	1.20335i	−0.275511	−	0.961298i	$-0.588847\pi$
$409$	14.0505	−	24.3362i	0.694753	−	1.20335i	0.970264	−	0.242050i	$-0.0778197\pi$
$410$	11.8990			0.587649
$411$	−6.44949			−0.318130
$412$	−5.22474	−	9.04952i	−0.257405	−	0.445838i
$413$	0.651531	−	1.12848i	0.0320597	−	0.0555291i
$414$	−1.10102	+	1.90702i	−0.0541122	+	0.0937251i
$415$	−1.17423	−	2.03383i	−0.0576409	−	0.0998370i
$416$	−4.00000			−0.196116
$417$	−14.2020			−0.695477
$418$		0			0
$419$	13.7980	+	23.8988i	0.674074	+	1.16753i	0.976739	+	0.214434i	$0.0687906\pi$
$419$	13.7980	+	23.8988i	0.674074	+	1.16753i	−0.302664	+	0.953097i	$0.597876\pi$
$420$	0.325765	+	0.564242i	0.0158957	+	0.0275322i
$421$	5.89898	+	10.2173i	0.287499	+	0.497962i	0.973212	−	0.229909i	$-0.0738430\pi$
$421$	5.89898	+	10.2173i	0.287499	+	0.497962i	−0.685713	+	0.727872i	$0.740510\pi$
$422$	0.325765	−	0.564242i	0.0158580	−	0.0274669i
$423$	−3.30306	+	5.72107i	−0.160600	+	0.278168i
$424$	−7.00000			−0.339950
$425$	0.224745	+	0.389270i	0.0109017	+	0.0188823i
$426$	20.7980			1.00766
$427$	0.202041			0.00977745
$428$	−5.27526	+	9.13701i	−0.254989	+	0.441654i
$429$		0			0
$430$	2.00000	+	3.46410i	0.0964486	+	0.167054i
$431$	−0.825765	+	1.43027i	−0.0397757	+	0.0688936i	−0.885228	−	0.465158i	$-0.845998\pi$
$431$	−0.825765	+	1.43027i	−0.0397757	+	0.0688936i	0.845452	+	0.534051i	$0.179331\pi$
$432$	−2.82577	−	4.89437i	−0.135955	−	0.235480i
$433$	13.0227	−	22.5560i	0.625831	−	1.08397i	−0.362548	−	0.931965i	$-0.618093\pi$
$433$	13.0227	−	22.5560i	0.625831	−	1.08397i	0.988379	−	0.152006i	$-0.0485735\pi$
$434$	−1.22474	+	2.12132i	−0.0587896	+	0.101827i
$435$	4.34847	−	7.53177i	0.208493	−	0.361121i
$436$	−2.77526	+	4.80688i	−0.132911	+	0.230208i
$437$	3.55051	−	6.14966i	0.169844	−	0.294178i
$438$	−2.57321	+	4.45694i	−0.122953	+	0.212961i
$439$	2.72474	+	4.71940i	0.130045	+	0.225245i	0.923694	−	0.383132i	$-0.125154\pi$
$439$	2.72474	+	4.71940i	0.130045	+	0.225245i	−0.793649	+	0.608376i	$0.791821\pi$
$440$		0			0
$441$	−3.05561	−	5.29248i	−0.145505	−	0.252023i
$442$	1.79796			0.0855202
$443$	6.62372	−	11.4726i	0.314703	−	0.545081i	−0.664672	−	0.747136i	$-0.731429\pi$
$443$	6.62372	−	11.4726i	0.314703	−	0.545081i	0.979374	+	0.202055i	$0.0647619\pi$
$444$	5.65153			0.268210
$445$	11.8990			0.564066
$446$	−9.44949	−	16.3670i	−0.447446	−	0.775000i
$447$	9.05561			0.428316
$448$	0.224745	−	0.389270i	0.0106182	−	0.0183913i
$449$	−6.94949	+	12.0369i	−0.327967	+	0.568055i	−0.982108	−	0.188317i	$-0.939697\pi$
$449$	−6.94949	+	12.0369i	−0.327967	+	0.568055i	0.654142	+	0.756372i	$0.273030\pi$
$450$	0.449490	+	0.778539i	0.0211891	+	0.0367007i
$451$		0			0
$452$	−2.00000	−	3.46410i	−0.0940721	−	0.162938i
$453$	8.29796	+	14.3725i	0.389872	+	0.675278i
$454$	7.65153			0.359104
$455$	−1.79796			−0.0842896
$456$	2.10102	+	3.63907i	0.0983893	+	0.170415i
$457$	−18.2247	+	31.5662i	−0.852518	+	1.47660i	0.0264114	+	0.999651i	$0.491592\pi$
$457$	−18.2247	+	31.5662i	−0.852518	+	1.47660i	−0.878929	+	0.476953i	$0.841741\pi$
$458$	11.1237	−	19.2669i	0.519778	−	0.900281i
$459$	1.27015	+	2.19997i	0.0592856	+	0.102686i
$460$	2.44949			0.114208
$461$	34.7423			1.61811			0.809056	−	0.587731i	$-0.199979\pi$
$461$	34.7423			1.61811			0.809056	+	0.587731i	$0.199979\pi$
$462$		0			0
$463$	−2.67423	−	4.63191i	−0.124282	−	0.215263i	0.797170	−	0.603755i	$-0.206329\pi$
$463$	−2.67423	−	4.63191i	−0.124282	−	0.215263i	−0.921452	+	0.388492i	$0.872996\pi$
$464$	−6.00000			−0.278543
$465$	3.94949	−	6.84072i	0.183153	−	0.317231i
$466$	−8.44949			−0.391415
$467$	15.9722	+	27.6647i	0.739105	+	1.28017i	0.952899	+	0.303289i	$0.0980846\pi$
$467$	15.9722	+	27.6647i	0.739105	+	1.28017i	−0.213794	+	0.976879i	$0.568582\pi$
$468$	3.59592			0.166221
$469$	0.0783167	−	3.67840i	0.00361633	−	0.169853i
$470$	7.34847			0.338960
$471$	−12.7526	−	22.0881i	−0.587607	−	1.01776i
$472$	2.89898			0.133436
$473$		0			0
$474$	−2.89898			−0.133155
$475$	−1.44949	−	2.51059i	−0.0665072	−	0.115194i
$476$	−0.101021	+	0.174973i	−0.00463027	+	0.00801986i
$477$	6.29286			0.288130
$478$	−6.20204			−0.283675
$479$	19.3485	+	33.5125i	0.884054	+	1.53123i	0.846794	+	0.531921i	$0.178530\pi$
$479$	19.3485	+	33.5125i	0.884054	+	1.53123i	0.0372602	+	0.999306i	$0.488137\pi$
$480$	−0.724745	+	1.25529i	−0.0330799	+	0.0572961i
$481$	−7.79796	+	13.5065i	−0.355556	+	0.615842i
$482$	9.05051	+	15.6759i	0.412239	+	0.714020i
$483$	−1.59592			−0.0726168
$484$	−11.0000			−0.500000
$485$	−1.89898	−	3.28913i	−0.0862282	−	0.149352i
$486$	4.49490	+	7.78539i	0.203893	+	0.353152i
$487$	−10.1237	−	17.5348i	−0.458750	−	0.794578i	0.540145	−	0.841572i	$-0.318369\pi$
$487$	−10.1237	−	17.5348i	−0.458750	−	0.794578i	−0.998895	+	0.0469938i	$0.985036\pi$
$488$	0.224745	+	0.389270i	0.0101737	+	0.0176214i
$489$	−1.84847	+	3.20164i	−0.0835907	+	0.144783i
$490$	−3.39898	+	5.88721i	−0.153550	+	0.265957i
$491$	−1.34847			−0.0608556			−0.0304278	−	0.999537i	$-0.509687\pi$
$491$	−1.34847			−0.0608556			−0.0304278	+	0.999537i	$0.509687\pi$
$492$	−8.62372	−	14.9367i	−0.388788	−	0.673400i
$493$	2.69694			0.121464
$494$	−11.5959			−0.521725
$495$		0			0
$496$	−5.44949			−0.244689
$497$	−3.22474	−	5.58542i	−0.144650	−	0.250540i
$498$	−1.70204	+	2.94802i	−0.0762703	+	0.132104i
$499$	−6.89898	−	11.9494i	−0.308841	−	0.534928i	0.669268	−	0.743021i	$-0.266608\pi$
$499$	−6.89898	−	11.9494i	−0.308841	−	0.534928i	−0.978109	+	0.208093i	$0.933274\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−7.42679	+	12.8636i	−0.331804	+	0.574702i
$502$	−13.6742	+	23.6845i	−0.610311	+	1.05709i
$503$	−11.7980	+	20.4347i	−0.526045	+	0.911137i	0.473495	+	0.880797i	$0.342992\pi$
$503$	−11.7980	+	20.4347i	−0.526045	+	0.911137i	−0.999540	+	0.0303400i	$0.990341\pi$
$504$	−0.202041	+	0.349945i	−0.00899962	+	0.0155878i
$505$	6.12372	−	10.6066i	0.272502	−	0.471988i
$506$		0			0
$507$	2.17423	−	3.76588i	0.0965611	−	0.167249i
$508$	1.44949	+	2.51059i	0.0643107	+	0.111389i
$509$	14.4495			0.640462			0.320231	−	0.947339i	$-0.396239\pi$
$509$	14.4495			0.640462			0.320231	+	0.947339i	$0.396239\pi$
$510$	0.325765	−	0.564242i	0.0144251	−	0.0249851i
$511$	1.59592			0.0705993
$512$	1.00000			0.0441942
$513$	−8.19184	−	14.1887i	−0.361678	−	0.626445i
$514$	−15.7980			−0.696818
$515$	5.22474	−	9.04952i	0.230230	−	0.398770i
$516$	2.89898	−	5.02118i	0.127620	−	0.221045i
$517$		0			0
$518$	−0.876276	−	1.51775i	−0.0385013	−	0.0666863i
$519$	−6.52270	−	11.2977i	−0.286315	−	0.495912i
$520$	−2.00000	−	3.46410i	−0.0877058	−	0.151911i
$521$	−24.0000			−1.05146			−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000			−1.05146			−0.525730	+	0.850652i	$0.676208\pi$
$522$	5.39388			0.236084
$523$	−4.97219	−	8.61209i	−0.217419	−	0.376580i	0.736599	−	0.676329i	$-0.236430\pi$
$523$	−4.97219	−	8.61209i	−0.217419	−	0.376580i	−0.954018	+	0.299749i	$0.903097\pi$
$524$	−7.12372	+	12.3387i	−0.311201	+	0.539017i
$525$	−0.325765	+	0.564242i	−0.0142176	+	0.0246255i
$526$	2.55051	+	4.41761i	0.111208	+	0.192617i
$527$	2.44949			0.106701
$528$		0			0
$529$	8.50000	−	14.7224i	0.369565	−	0.640106i
$530$	−3.50000	−	6.06218i	−0.152030	−	0.263324i
$531$	−2.60612			−0.113096
$532$	0.651531	−	1.12848i	0.0282474	−	0.0489260i
$533$	47.5959			2.06161
$534$	−8.62372	−	14.9367i	−0.373185	−	0.646375i
$535$	−10.5505			−0.456138
$536$	7.17423	−	3.94086i	0.309880	−	0.170219i
$537$	17.7526			0.766079
$538$	−15.7980	−	27.3629i	−0.681098	−	1.17970i
$539$		0			0
$540$	2.82577	−	4.89437i	0.121602	−	0.210620i
$541$	−5.59592			−0.240587			−0.120294	−	0.992738i	$-0.538384\pi$
$541$	−5.59592			−0.240587			−0.120294	+	0.992738i	$0.538384\pi$
$542$	1.07321	+	1.85886i	0.0460985	+	0.0798449i
$543$	8.22474	−	14.2457i	0.352958	−	0.611340i
$544$	−0.449490			−0.0192717
$545$	−5.55051			−0.237758
$546$	1.30306	+	2.25697i	0.0557659	+	0.0965893i
$547$	−19.3207	+	33.4644i	−0.826092	+	1.43083i	0.0749901	+	0.997184i	$0.476107\pi$
$547$	−19.3207	+	33.4644i	−0.826092	+	1.43083i	−0.901082	+	0.433649i	$0.857226\pi$
$548$	−2.22474	+	3.85337i	−0.0950364	+	0.164608i
$549$	−0.202041	−	0.349945i	−0.00862290	−	0.0149353i
$550$		0			0
$551$	−17.3939			−0.741004
$552$	−1.77526	−	3.07483i	−0.0755599	−	0.130874i
$553$	0.449490	+	0.778539i	0.0191142	+	0.0331068i
$554$	12.9495	+	22.4292i	0.550171	+	0.952924i
$555$	2.82577	+	4.89437i	0.119947	+	0.207754i
$556$	−4.89898	+	8.48528i	−0.207763	+	0.359856i
$557$	−10.1969	+	17.6616i	−0.432058	+	0.748347i	−0.997050	−	0.0767495i	$-0.975546\pi$
$557$	−10.1969	+	17.6616i	−0.432058	+	0.748347i	0.564992	+	0.825096i	$0.308879\pi$
$558$	4.89898			0.207390
$559$	8.00000	+	13.8564i	0.338364	+	0.586064i
$560$	0.449490			0.0189944
$561$		0			0
$562$	−15.7474	+	27.2754i	−0.664266	+	1.15054i
$563$	−22.5505			−0.950391			−0.475195	−	0.879880i	$-0.657623\pi$
$563$	−22.5505			−0.950391			−0.475195	+	0.879880i	$0.657623\pi$
$564$	−5.32577	−	9.22450i	−0.224255	−	0.388421i
$565$	2.00000	−	3.46410i	0.0841406	−	0.145736i
$566$	3.89898	+	6.75323i	0.163886	+	0.283859i
$567$	−1.23495	+	2.13900i	−0.0518630	+	0.0898294i
$568$	7.17423	−	12.4261i	0.301024	−	0.521389i
$569$	−3.94949	+	6.84072i	−0.165571	+	0.286778i	−0.936858	−	0.349710i	$-0.886280\pi$
$569$	−3.94949	+	6.84072i	−0.165571	+	0.286778i	0.771287	+	0.636488i	$0.219613\pi$
$570$	−2.10102	+	3.63907i	−0.0880021	+	0.152424i
$571$	−0.348469	+	0.603566i	−0.0145830	+	0.0252585i	−0.873225	−	0.487318i	$-0.837975\pi$
$571$	−0.348469	+	0.603566i	−0.0145830	+	0.0252585i	0.858642	+	0.512576i	$0.171309\pi$
$572$		0			0
$573$	10.5454	+	18.2652i	0.440541	+	0.763039i
$574$	−2.67423	+	4.63191i	−0.111620	+	0.193332i
$575$	1.22474	+	2.12132i	0.0510754	+	0.0884652i
$576$	−0.898979			−0.0374575
$577$	7.77526	−	13.4671i	0.323688	−	0.560644i	−0.657558	−	0.753404i	$-0.728410\pi$
$577$	7.77526	−	13.4671i	0.323688	−	0.560644i	0.981246	+	0.192760i	$0.0617438\pi$
$578$	−16.7980			−0.698703
$579$	22.5403			0.936743
$580$	−3.00000	−	5.19615i	−0.124568	−	0.215758i
$581$	1.05561			0.0437942
$582$	−2.75255	+	4.76756i	−0.114097	+	0.197622i
$583$		0			0
$584$	1.77526	+	3.07483i	0.0734606	+	0.127237i
$585$	1.79796	+	3.11416i	0.0743365	+	0.128755i
$586$	−2.39898	−	4.15515i	−0.0991009	−	0.171648i
$587$	3.27526	+	5.67291i	0.135184	+	0.234146i	0.925668	−	0.378337i	$-0.123504\pi$
$587$	3.27526	+	5.67291i	0.135184	+	0.234146i	−0.790484	+	0.612483i	$0.790171\pi$
$588$	9.85357			0.406354
$589$	−15.7980			−0.650944
$590$	1.44949	+	2.51059i	0.0596745	+	0.103359i
$591$	−6.44949	+	11.1708i	−0.265297	+	0.459507i
$592$	1.94949	−	3.37662i	0.0801235	−	0.138778i
$593$	−14.6969	−	25.4558i	−0.603531	−	1.04535i	−0.992282	−	0.124003i	$-0.960427\pi$
$593$	−14.6969	−	25.4558i	−0.603531	−	1.04535i	0.388751	−	0.921343i	$-0.372907\pi$
$594$		0			0
$595$	−0.202041			−0.00828287
$596$	3.12372	−	5.41045i	0.127953	−	0.221621i
$597$	1.70204	+	2.94802i	0.0696599	+	0.120654i
$598$	9.79796			0.400668
$599$	−19.1464	+	33.1626i	−0.782302	+	1.35499i	0.148296	+	0.988943i	$0.452621\pi$
$599$	−19.1464	+	33.1626i	−0.782302	+	1.35499i	−0.930598	+	0.366044i	$0.880712\pi$
$600$	−1.44949			−0.0591752
$601$	7.34847	+	12.7279i	0.299750	+	0.519183i	0.976079	−	0.217417i	$-0.0697633\pi$
$601$	7.34847	+	12.7279i	0.299750	+	0.519183i	−0.676328	+	0.736600i	$0.736430\pi$
$602$	−1.79796			−0.0732793
$603$	−6.44949	+	3.54275i	−0.262644	+	0.144272i
$604$	11.4495			0.465873
$605$	−5.50000	−	9.52628i	−0.223607	−	0.387298i
$606$	−17.7526			−0.721148
$607$	−6.34847	+	10.9959i	−0.257676	+	0.446309i	−0.965619	−	0.259961i	$-0.916290\pi$
$607$	−6.34847	+	10.9959i	−0.257676	+	0.446309i	0.707943	+	0.706270i	$0.249624\pi$
$608$	2.89898			0.117569
$609$	1.95459	+	3.38545i	0.0792041	+	0.137185i
$610$	−0.224745	+	0.389270i	−0.00909965	+	0.0157611i
$611$	29.3939			1.18915
$612$	0.404082			0.0163340
$613$	14.5000	+	25.1147i	0.585649	+	1.01437i	0.994794	+	0.101905i	$0.0324938\pi$
$613$	14.5000	+	25.1147i	0.585649	+	1.01437i	−0.409145	+	0.912470i	$0.634173\pi$
$614$	5.17423	−	8.96204i	0.208815	−	0.361678i
$615$	8.62372	−	14.9367i	0.347742	−	0.602307i
$616$		0			0
$617$	−16.6515			−0.670365			−0.335183	−	0.942153i	$-0.608798\pi$
$617$	−16.6515			−0.670365			−0.335183	+	0.942153i	$0.608798\pi$
$618$	−15.1464			−0.609279
$619$	12.2247	+	21.1739i	0.491354	+	0.851050i	0.999950	−	0.00995495i	$-0.00316881\pi$
$619$	12.2247	+	21.1739i	0.491354	+	0.851050i	−0.508596	+	0.861005i	$0.669835\pi$
$620$	−2.72474	−	4.71940i	−0.109428	−	0.189536i
$621$	6.92168	+	11.9887i	0.277758	+	0.481090i
$622$	−5.72474	−	9.91555i	−0.229541	−	0.397577i
$623$	−2.67423	+	4.63191i	−0.107141	+	0.185574i
$624$	−2.89898	+	5.02118i	−0.116052	+	0.201008i
$625$	1.00000			0.0400000
$626$	3.00000	+	5.19615i	0.119904	+	0.207680i
$627$		0			0
$628$	−17.5959			−0.702154
$629$	−0.876276	+	1.51775i	−0.0349394	+	0.0605168i
$630$	−0.404082			−0.0160990
$631$	4.89898	+	8.48528i	0.195025	+	0.337794i	0.946909	−	0.321502i	$-0.104188\pi$
$631$	4.89898	+	8.48528i	0.195025	+	0.337794i	−0.751884	+	0.659296i	$0.770854\pi$
$632$	−1.00000	+	1.73205i	−0.0397779	+	0.0688973i
$633$	−0.472194	−	0.817863i	−0.0187680	−	0.0325071i
$634$	−0.848469	+	1.46959i	−0.0336970	+	0.0583649i
$635$	−1.44949	+	2.51059i	−0.0575212	+	0.0996297i
$636$	−5.07321	+	8.78706i	−0.201166	+	0.348430i
$637$	−13.5959	+	23.5488i	−0.538690	+	0.933038i
$638$		0			0
$639$	−6.44949	+	11.1708i	−0.255138	+	0.441912i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−0.651531	+	1.12848i	−0.0257339	+	0.0445725i	−0.878606	−	0.477548i	$-0.841526\pi$
$641$	−0.651531	+	1.12848i	−0.0257339	+	0.0445725i	0.852872	+	0.522121i	$0.174859\pi$
$642$	7.64643	+	13.2440i	0.301780	+	0.522699i
$643$	43.0454			1.69755			0.848773	−	0.528758i	$-0.177342\pi$
$643$	43.0454			1.69755			0.848773	+	0.528758i	$0.177342\pi$
$644$	−0.550510	+	0.953512i	−0.0216931	+	0.0375736i
$645$	5.79796			0.228294
$646$	−1.30306			−0.0512683
$647$	−1.65153	−	2.86054i	−0.0649284	−	0.112459i	0.831734	−	0.555175i	$-0.187349\pi$
$647$	−1.65153	−	2.86054i	−0.0649284	−	0.112459i	−0.896662	+	0.442715i	$0.854015\pi$
$648$	−5.49490			−0.215860
$649$		0			0
$650$	2.00000	−	3.46410i	0.0784465	−	0.135873i
$651$	1.77526	+	3.07483i	0.0695777	+	0.120512i
$652$	1.27526	+	2.20881i	0.0499428	+	0.0865035i
$653$	−3.74745	−	6.49077i	−0.146649	−	0.254004i	0.783338	−	0.621596i	$-0.213515\pi$
$653$	−3.74745	−	6.49077i	−0.146649	−	0.254004i	−0.929987	+	0.367593i	$0.880182\pi$
$654$	4.02270	+	6.96753i	0.157300	+	0.272452i
$655$	−14.2474			−0.556694
$656$	−11.8990			−0.464577
$657$	−1.59592	−	2.76421i	−0.0622627	−	0.107842i
$658$	−1.65153	+	2.86054i	−0.0643834	+	0.111515i
$659$	−7.10102	+	12.2993i	−0.276616	+	0.479114i	−0.970542	−	0.240933i	$-0.922546\pi$
$659$	−7.10102	+	12.2993i	−0.276616	+	0.479114i	0.693925	+	0.720047i	$0.255880\pi$
$660$		0			0
$661$	−8.85357			−0.344364			−0.172182	−	0.985065i	$-0.555082\pi$
$661$	−8.85357			−0.344364			−0.172182	+	0.985065i	$0.555082\pi$
$662$	−6.89898			−0.268136
$663$	1.30306	−	2.25697i	0.0506067	−	0.0876534i
$664$	1.17423	+	2.03383i	0.0455691	+	0.0789281i
$665$	1.30306			0.0505306
$666$	−1.75255	+	3.03551i	−0.0679100	+	0.117624i
$667$	14.6969			0.569068
$668$	5.12372	+	8.87455i	0.198243	+	0.343367i
$669$	−27.3939			−1.05911
$670$	7.00000	+	4.24264i	0.270434	+	0.163908i
$671$		0			0
$672$	−0.325765	−	0.564242i	−0.0125667	−	0.0217661i
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	2.22474	−	3.85337i	0.0856940	−	0.148426i
$675$	5.65153			0.217528
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	−18.9495	+	32.8215i	−0.728288	+	1.26143i	0.229318	+	0.973352i	$0.426350\pi$
$677$	−18.9495	+	32.8215i	−0.728288	+	1.26143i	−0.957606	+	0.288080i	$0.906983\pi$
$678$	−5.79796			−0.222669
$679$	1.70714			0.0655142
$680$	−0.224745	−	0.389270i	−0.00861857	−	0.0149278i
$681$	5.54541	−	9.60493i	0.212500	−	0.368062i
$682$		0			0
$683$	−23.0732	−	39.9640i	−0.882872	−	1.52918i	−0.848133	−	0.529783i	$-0.822273\pi$
$683$	−23.0732	−	39.9640i	−0.882872	−	1.52918i	−0.0347386	−	0.999396i	$-0.511060\pi$
$684$	−2.60612			−0.0996476
$685$	−4.44949			−0.170006
$686$	−3.10102	−	5.37113i	−0.118398	−	0.205071i
$687$	−16.1237	−	27.9271i	−0.615158	−	1.06549i
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	−14.0000	−	24.2487i	−0.533358	−	0.923802i
$690$	1.77526	−	3.07483i	0.0675828	−	0.117057i
$691$	−21.2474	+	36.8017i	−0.808291	+	1.40000i	0.105756	+	0.994392i	$0.466274\pi$
$691$	−21.2474	+	36.8017i	−0.808291	+	1.40000i	−0.914047	+	0.405609i	$0.867059\pi$
$692$	−9.00000			−0.342129
$693$		0			0
$694$	−10.6969			−0.406050
$695$	−9.79796			−0.371658
$696$	−4.34847	+	7.53177i	−0.164828	+	0.285491i
$697$	5.34847			0.202588
$698$	6.89898	+	11.9494i	0.261130	+	0.452291i
$699$	−6.12372	+	10.6066i	−0.231621	+	0.401179i
$700$	0.224745	+	0.389270i	0.00849456	+	0.0147130i
$701$	−7.79796	+	13.5065i	−0.294525	+	0.510132i	−0.974874	−	0.222756i	$-0.928495\pi$
$701$	−7.79796	+	13.5065i	−0.294525	+	0.510132i	0.680349	+	0.732888i	$0.261828\pi$
$702$	11.3031	−	19.5775i	0.426607	−	0.738904i
$703$	5.65153	−	9.78874i	0.213152	−	0.369189i
$704$		0			0
$705$	5.32577	−	9.22450i	0.200580	−	0.347415i
$706$	2.22474	−	3.85337i	0.0837294	−	0.145024i
$707$	2.75255	+	4.76756i	0.103520	+	0.179302i
$708$	2.10102	−	3.63907i	0.0789612	−	0.136765i
$709$	−5.79796	−	10.0424i	−0.217747	−	0.377149i	0.736372	−	0.676577i	$-0.236537\pi$
$709$	−5.79796	−	10.0424i	−0.217747	−	0.377149i	−0.954119	+	0.299428i	$0.903204\pi$
$710$	14.3485			0.538488
$711$	0.898979	−	1.55708i	0.0337144	−	0.0583950i
$712$	−11.8990			−0.445933
$713$	13.3485			0.499904
$714$	0.146428	+	0.253621i	0.00547994	+	0.00949153i
$715$		0			0
$716$	6.12372	−	10.6066i	0.228854	−	0.396387i
$717$	−4.49490	+	7.78539i	−0.167865	+	0.290751i
$718$	10.0732	+	17.4473i	0.375929	+	0.651128i
$719$	−15.1742	−	26.2825i	−0.565903	−	0.980174i	−0.996965	−	0.0778510i	$-0.975194\pi$
$719$	−15.1742	−	26.2825i	−0.565903	−	0.980174i	0.431062	−	0.902323i	$-0.358139\pi$
$720$	−0.449490	−	0.778539i	−0.0167515	−	0.0290144i
$721$	2.34847	+	4.06767i	0.0874616	+	0.151488i
$722$	−10.5959			−0.394339
$723$	26.2372			0.975774
$724$	−5.67423	−	9.82806i	−0.210881	−	0.365257i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	−7.97219	+	13.8082i	−0.295876	+	0.512472i
$727$	9.24745	+	16.0171i	0.342969	+	0.594040i	0.984983	−	0.172654i	$-0.0552341\pi$
$727$	9.24745	+	16.0171i	0.342969	+	0.594040i	−0.642014	+	0.766693i	$0.721901\pi$
$728$	1.79796			0.0666368
$729$	29.5153			1.09316
$730$	−1.77526	+	3.07483i	−0.0657051	+	0.113805i
$731$	0.898979	+	1.55708i	0.0332500	+	0.0575906i
$732$	0.651531			0.0240813
$733$	10.7474	−	18.6151i	0.396966	−	0.687565i	−0.596384	−	0.802699i	$-0.703396\pi$
$733$	10.7474	−	18.6151i	0.396966	−	0.687565i	0.993350	+	0.115134i	$0.0367297\pi$
$734$	−18.2474			−0.673526
$735$	4.92679	+	8.53344i	0.181727	+	0.314761i
$736$	−2.44949			−0.0902894
$737$		0			0
$738$	10.6969			0.393760
$739$	−21.0454	−	36.4517i	−0.774168	−	1.34090i	−0.935261	−	0.353959i	$-0.884835\pi$
$739$	−21.0454	−	36.4517i	−0.774168	−	1.34090i	0.161093	−	0.986939i	$-0.448498\pi$
$740$	3.89898			0.143329
$741$	−8.40408	+	14.5563i	−0.308732	+	0.534739i
$742$	3.14643			0.115509
$743$	14.8990	+	25.8058i	0.546591	+	0.946723i	0.998505	+	0.0546613i	$0.0174079\pi$
$743$	14.8990	+	25.8058i	0.546591	+	0.946723i	−0.451914	+	0.892061i	$0.649259\pi$
$744$	−3.94949	+	6.84072i	−0.144795	+	0.250793i
$745$	6.24745			0.228889
$746$	−15.0000			−0.549189
$747$	−1.05561	−	1.82838i	−0.0386229	−	0.0668967i
$748$		0			0
$749$	2.37117	−	4.10699i	0.0866408	−	0.150066i
$750$	−0.724745	−	1.25529i	−0.0264639	−	0.0458369i
$751$	−0.348469			−0.0127158			−0.00635791	−	0.999980i	$-0.502024\pi$
$751$	−0.348469			−0.0127158			−0.00635791	+	0.999980i	$0.502024\pi$
$752$	−7.34847			−0.267971
$753$	19.8207	+	34.3304i	0.722305	+	1.25107i
$754$	−12.0000	−	20.7846i	−0.437014	−	0.756931i
$755$	5.72474	+	9.91555i	0.208345	+	0.360864i
$756$	1.27015	+	2.19997i	0.0461950	+	0.0800121i
$757$	−26.9495	+	46.6779i	−0.979496	+	1.69654i	−0.315275	+	0.949000i	$0.602097\pi$
$757$	−26.9495	+	46.6779i	−0.979496	+	1.69654i	−0.664221	+	0.747536i	$0.731237\pi$
$758$	2.89898	−	5.02118i	0.105296	−	0.182377i
$759$		0			0
$760$	1.44949	+	2.51059i	0.0525785	+	0.0910687i
$761$	−23.4949			−0.851689			−0.425845	−	0.904796i	$-0.640023\pi$
$761$	−23.4949			−0.851689			−0.425845	+	0.904796i	$0.640023\pi$
$762$	4.20204			0.152224
$763$	1.24745	−	2.16064i	0.0451607	−	0.0782206i
$764$	14.5505			0.526419
$765$	0.202041	+	0.349945i	0.00730481	+	0.0126523i
$766$	−10.3485	+	17.9241i	−0.373905	+	0.647623i
$767$	5.79796	+	10.0424i	0.209352	+	0.362609i
$768$	0.724745	−	1.25529i	0.0261520	−	0.0452966i
$769$	25.1464	−	43.5549i	0.906803	−	1.57063i	0.0883254	−	0.996092i	$-0.471848\pi$
$769$	25.1464	−	43.5549i	0.906803	−	1.57063i	0.818478	−	0.574538i	$-0.194818\pi$
$770$		0			0
$771$	−11.4495	+	19.8311i	−0.412343	+	0.714200i
$772$	7.77526	−	13.4671i	0.279838	−	0.484693i
$773$	−5.84847	+	10.1298i	−0.210355	+	0.364345i	−0.951826	−	0.306640i	$-0.900795\pi$
$773$	−5.84847	+	10.1298i	−0.210355	+	0.364345i	0.741471	+	0.670985i	$0.234129\pi$
$774$	1.79796	+	3.11416i	0.0646263	+	0.111936i
$775$	2.72474	−	4.71940i	0.0978757	−	0.169526i
$776$	1.89898	+	3.28913i	0.0681694	+	0.118073i
$777$	−2.54031			−0.0911329
$778$	6.77526	−	11.7351i	0.242905	−	0.420723i
$779$	−34.4949			−1.23591
$780$	−5.79796			−0.207600
$781$		0			0
$782$	1.10102			0.0393724
$783$	16.9546	−	29.3662i	0.605908	−	1.04946i
$784$	3.39898	−	5.88721i	0.121392	−	0.210257i
$785$	−8.79796	−	15.2385i	−0.314013	−	0.543886i
$786$	10.3258	+	17.8848i	0.368308	+	0.637928i
$787$	−13.4217	−	23.2470i	−0.478431	−	0.828667i	0.521263	−	0.853396i	$-0.325461\pi$
$787$	−13.4217	−	23.2470i	−0.478431	−	0.828667i	−0.999694	+	0.0247288i	$0.992128\pi$
$788$	4.44949	+	7.70674i	0.158507	+	0.274541i
$789$	7.39388			0.263229
$790$	−2.00000			−0.0711568
$791$	0.898979	+	1.55708i	0.0319640	+	0.0553633i
$792$		0			0
$793$	−0.898979	+	1.55708i	−0.0319237	+	0.0552935i
$794$	3.50000	+	6.06218i	0.124210	+	0.215139i
$795$	−10.1464			−0.359857
$796$	2.34847			0.0832393
$797$	14.1969	−	24.5898i	0.502881	−	0.871016i	−0.497113	−	0.867686i	$-0.665607\pi$
$797$	14.1969	−	24.5898i	0.502881	−	0.871016i	0.999994	−	0.00333031i	$-0.00106007\pi$
$798$	−0.944387	−	1.63573i	−0.0334309	−	0.0579041i
$799$	3.30306			0.116854
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	10.6969			0.377958
$802$	2.44949	+	4.24264i	0.0864945	+	0.149813i
$803$		0			0
$804$	0.252551	−	11.8619i	0.00890680	−	0.418337i
$805$	−1.10102			−0.0388059
$806$	−10.8990	−	18.8776i	−0.383900	−	0.664935i
$807$	−45.7980			−1.61216
$808$	−6.12372	+	10.6066i	−0.215432	+	0.373139i
$809$	6.69694			0.235452			0.117726	−	0.993046i	$-0.462440\pi$
$809$	6.69694			0.235452			0.117726	+	0.993046i	$0.462440\pi$
$810$	−2.74745	−	4.75872i	−0.0965355	−	0.167204i
$811$	25.3712	−	43.9442i	0.890902	−	1.54309i	0.0521069	−	0.998642i	$-0.483406\pi$
$811$	25.3712	−	43.9442i	0.890902	−	1.54309i	0.838795	−	0.544447i	$-0.183260\pi$
$812$	2.69694			0.0946440
$813$	3.11123			0.109115
$814$		0			0
$815$	−1.27526	+	2.20881i	−0.0446702	+	0.0773711i
$816$	−0.325765	+	0.564242i	−0.0114041	+	0.0197524i
$817$	−5.79796	−	10.0424i	−0.202845	−	0.351338i
$818$	−28.1010			−0.982529
$819$	−1.61633			−0.0564791
$820$	−5.94949	−	10.3048i	−0.207765	−	0.359860i
$821$	−2.87628	−	4.98186i	−0.100383	−	0.173868i	0.811460	−	0.584408i	$-0.198673\pi$
$821$	−2.87628	−	4.98186i	−0.100383	−	0.173868i	−0.911842	+	0.410540i	$0.865340\pi$
$822$	3.22474	+	5.58542i	0.112476	+	0.194814i
$823$	−22.1464	−	38.3587i	−0.771976	−	1.33710i	−0.936479	−	0.350725i	$-0.885935\pi$
$823$	−22.1464	−	38.3587i	−0.771976	−	1.33710i	0.164503	−	0.986377i	$-0.447398\pi$
$824$	−5.22474	+	9.04952i	−0.182013	+	0.315255i
$825$		0			0
$826$	−1.30306			−0.0453393
$827$	−19.1464	−	33.1626i	−0.665787	−	1.15318i	−0.979071	−	0.203517i	$-0.934763\pi$
$827$	−19.1464	−	33.1626i	−0.665787	−	1.15318i	0.313285	−	0.949659i	$-0.398571\pi$
$828$	2.20204			0.0765262
$829$	43.8434			1.52274			0.761372	−	0.648316i	$-0.224526\pi$
$829$	43.8434			1.52274			0.761372	+	0.648316i	$0.224526\pi$
$830$	−1.17423	+	2.03383i	−0.0407583	+	0.0705954i
$831$	37.5403			1.30226
$832$	2.00000	+	3.46410i	0.0693375	+	0.120096i
$833$	−1.52781	+	2.64624i	−0.0529354	+	0.0916867i
$834$	7.10102	+	12.2993i	0.245888	+	0.425891i
$835$	−5.12372	+	8.87455i	−0.177314	+	0.307116i
$836$		0			0
$837$	15.3990	−	26.6718i	0.532267	−	0.921913i
$838$	13.7980	−	23.8988i	0.476643	−	0.825569i
$839$	2.07321	−	3.59091i	0.0715753	−	0.123972i	−0.828017	−	0.560704i	$-0.810531\pi$
$839$	2.07321	−	3.59091i	0.0715753	−	0.123972i	0.899592	+	0.436732i	$0.143864\pi$
$840$	0.325765	−	0.564242i	0.0112400	−	0.0194682i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	5.89898	−	10.2173i	0.203292	−	0.352113i
$843$	22.8258	+	39.5354i	0.786161	+	1.36167i
$844$	−0.651531			−0.0224266
$845$	1.50000	−	2.59808i	0.0516016	−	0.0893765i
$846$	6.60612			0.227123
$847$	4.94439			0.169891
$848$	3.50000	+	6.06218i	0.120190	+	0.208176i
$849$	11.3031			0.387920
$850$	0.224745	−	0.389270i	0.00770869	−	0.0133518i
$851$	−4.77526	+	8.27098i	−0.163694	+	0.283526i
$852$	−10.3990	−	18.0116i	−0.356263	−	0.617066i
$853$	−8.94949	−	15.5010i	−0.306425	−	0.530743i	0.671153	−	0.741319i	$-0.265799\pi$
$853$	−8.94949	−	15.5010i	−0.306425	−	0.530743i	−0.977578	+	0.210576i	$0.932466\pi$
$854$	−0.101021	−	0.174973i	−0.00345685	−	0.00598744i
$855$	−1.30306	−	2.25697i	−0.0445638	−	0.0771867i
$856$	10.5505			0.360609
$857$	29.6413			1.01253			0.506264	−	0.862378i	$-0.331026\pi$
$857$	29.6413			1.01253			0.506264	+	0.862378i	$0.331026\pi$
$858$		0			0
$859$	−0.550510	+	0.953512i	−0.0187832	+	0.0325334i	−0.875264	−	0.483645i	$-0.839313\pi$
$859$	−0.550510	+	0.953512i	−0.0187832	+	0.0325334i	0.856481	+	0.516178i	$0.172646\pi$
$860$	2.00000	−	3.46410i	0.0681994	−	0.118125i
$861$	3.87628	+	6.71391i	0.132103	+	0.228809i
$862$	1.65153			0.0562514
$863$	52.2474			1.77852			0.889262	−	0.457398i	$-0.151219\pi$
$863$	52.2474			1.77852			0.889262	+	0.457398i	$0.151219\pi$
$864$	−2.82577	+	4.89437i	−0.0961345	+	0.166510i
$865$	−4.50000	−	7.79423i	−0.153005	−	0.265012i
$866$	−26.0454			−0.885059
$867$	−12.1742	+	21.0864i	−0.413459	+	0.716131i
$868$	2.44949			0.0831411
$869$		0			0
$870$	−8.69694			−0.294854
$871$	28.0000	+	16.9706i	0.948744	+	0.575026i
$872$	5.55051			0.187964
$873$	−1.70714	−	2.95686i	−0.0577781	−	0.100075i
$874$	−7.10102			−0.240196
$875$	−0.224745	+	0.389270i	−0.00759776	+	0.0131597i
$876$	5.14643			0.173882
$877$	−20.0000	−	34.6410i	−0.675352	−	1.16974i	−0.976366	−	0.216124i	$-0.930658\pi$
$877$	−20.0000	−	34.6410i	−0.675352	−	1.16974i	0.301014	−	0.953620i	$-0.402675\pi$
$878$	2.72474	−	4.71940i	0.0919557	−	0.159272i
$879$	−6.95459			−0.234573
$880$		0			0
$881$	0.601021	+	1.04100i	0.0202489	+	0.0350721i	0.875972	−	0.482361i	$-0.160221\pi$
$881$	0.601021	+	1.04100i	0.0202489	+	0.0350721i	−0.855723	+	0.517434i	$0.826887\pi$
$882$	−3.05561	+	5.29248i	−0.102888	+	0.178207i
$883$	6.89898	−	11.9494i	0.232169	−	0.402129i	−0.726277	−	0.687402i	$-0.758751\pi$
$883$	6.89898	−	11.9494i	0.232169	−	0.402129i	0.958446	+	0.285273i	$0.0920844\pi$
$884$	−0.898979	−	1.55708i	−0.0302360	−	0.0523702i
$885$	4.20204			0.141250
$886$	−13.2474			−0.445057
$887$	5.77526	+	10.0030i	0.193914	+	0.335869i	0.946544	−	0.322575i	$-0.104548\pi$
$887$	5.77526	+	10.0030i	0.193914	+	0.335869i	−0.752630	+	0.658444i	$0.771215\pi$
$888$	−2.82577	−	4.89437i	−0.0948265	−	0.164244i
$889$	−0.651531	−	1.12848i	−0.0218516	−	0.0378482i
$890$	−5.94949	−	10.3048i	−0.199427	−	0.345418i
$891$		0			0
$892$	−9.44949	+	16.3670i	−0.316392	+	0.548008i
$893$	−21.3031			−0.712880
$894$	−4.52781	−	7.84239i	−0.151432	−	0.262289i
$895$	12.2474			0.409387
$896$	−0.449490			−0.0150164
$897$	7.10102	−	12.2993i	0.237096	−	0.410663i
$898$	13.8990			0.463815
$899$	−16.3485	−	28.3164i	−0.545252	−	0.944404i
$900$	0.449490	−	0.778539i	0.0149830	−	0.0259513i
$901$	−1.57321	−	2.72489i	−0.0524114	−	0.0907791i
$902$		0			0
$903$	−1.30306	+	2.25697i	−0.0433632	+	0.0751072i
$904$	−2.00000	+	3.46410i	−0.0665190	+	0.115214i
$905$	5.67423	−	9.82806i	0.188618	−	0.326696i
$906$	8.29796	−	14.3725i	0.275681	−	0.477494i
$907$	−26.8712	+	46.5422i	−0.892243	+	1.54541i	−0.0550622	+	0.998483i	$0.517536\pi$
$907$	−26.8712	+	46.5422i	−0.892243	+	1.54541i	−0.837181	+	0.546927i	$0.815798\pi$
$908$	−3.82577	−	6.62642i	−0.126962	−	0.219905i
$909$	5.50510	−	9.53512i	0.182593	−	0.316260i
$910$	0.898979	+	1.55708i	0.0298009	+	0.0516166i
$911$	−22.8434			−0.756835			−0.378417	−	0.925635i	$-0.623532\pi$
$911$	−22.8434			−0.756835			−0.378417	+	0.925635i	$0.623532\pi$
$912$	2.10102	−	3.63907i	0.0695717	−	0.120502i
$913$		0			0
$914$	36.4495			1.20564
$915$	0.325765	+	0.564242i	0.0107695	+	0.0186533i
$916$	−22.2474			−0.735076
$917$	3.20204	−	5.54610i	0.105741	−	0.183148i
$918$	1.27015	−	2.19997i	0.0419213	−	0.0726098i
$919$	0.174235	+	0.301783i	0.00574747	+	0.00995491i	0.868885	−	0.495014i	$-0.164837\pi$
$919$	0.174235	+	0.301783i	0.00574747	+	0.00995491i	−0.863137	+	0.504969i	$0.831504\pi$
$920$	−1.22474	−	2.12132i	−0.0403786	−	0.0699379i
$921$	−7.50000	−	12.9904i	−0.247133	−	0.428048i
$922$	−17.3712	−	30.0878i	−0.572089	−	0.990887i
$923$	57.3939			1.88914
$924$		0			0
$925$	1.94949	+	3.37662i	0.0640988	+	0.111022i
$926$	−2.67423	+	4.63191i	−0.0878808	+	0.152214i
$927$	4.69694	−	8.13534i	0.154268	−	0.267199i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	−19.1010			−0.626684			−0.313342	−	0.949640i	$-0.601449\pi$
$929$	−19.1010			−0.626684			−0.313342	+	0.949640i	$0.601449\pi$
$930$	−7.89898			−0.259018
$931$	9.85357	−	17.0669i	0.322938	−	0.559345i
$932$	4.22474	+	7.31747i	0.138386	+	0.239692i
$933$	−16.5959			−0.543326
$934$	15.9722	−	27.6647i	0.522626	−	0.905215i
$935$		0			0
$936$	−1.79796	−	3.11416i	−0.0587681	−	0.101789i
$937$	5.34847			0.174727			0.0873634	−	0.996177i	$-0.472156\pi$
$937$	5.34847			0.174727			0.0873634	+	0.996177i	$0.472156\pi$
$938$	−3.22474	+	1.77138i	−0.105292	+	0.0578374i
$939$	8.69694			0.283814
$940$	−3.67423	−	6.36396i	−0.119840	−	0.207570i
$941$	−8.40408			−0.273965			−0.136983	−	0.990573i	$-0.543740\pi$
$941$	−8.40408			−0.273965			−0.136983	+	0.990573i	$0.543740\pi$
$942$	−12.7526	+	22.0881i	−0.415501	+	0.719668i
$943$	29.1464			0.949138
$944$	−1.44949	−	2.51059i	−0.0471769	−	0.0817127i
$945$	−1.27015	+	2.19997i	−0.0413181	+	0.0715650i
$946$		0			0
$947$	24.4949			0.795977			0.397989	−	0.917390i	$-0.369708\pi$
$947$	24.4949			0.795977			0.397989	+	0.917390i	$0.369708\pi$
$948$	1.44949	+	2.51059i	0.0470772	+	0.0815402i
$949$	−7.10102	+	12.2993i	−0.230509	+	0.399253i
$950$	−1.44949	+	2.51059i	−0.0470277	+	0.0814543i
$951$	1.22985	+	2.13016i	0.0398805	+	0.0690751i
$952$	0.202041			0.00654819
$953$	19.7980			0.641319			0.320659	−	0.947195i	$-0.396096\pi$
$953$	19.7980			0.641319			0.320659	+	0.947195i	$0.396096\pi$
$954$	−3.14643	−	5.44977i	−0.101869	−	0.176443i
$955$	7.27526	+	12.6011i	0.235422	+	0.407762i
$956$	3.10102	+	5.37113i	0.100294	+	0.173715i
$957$		0			0
$958$	19.3485	−	33.5125i	0.625121	−	1.08274i
$959$	1.00000	−	1.73205i	0.0322917	−	0.0559308i
$960$	1.44949			0.0467821
$961$	0.651531	+	1.12848i	0.0210171	+	0.0364027i
$962$	15.5959			0.502833
$963$	−9.48469			−0.305640
$964$	9.05051	−	15.6759i	0.291497	−	0.504888i
$965$	15.5505			0.500589
$966$	0.797959	+	1.38211i	0.0256739	+	0.0444685i
$967$	18.4722	−	31.9948i	0.594026	−	1.02888i	−0.399658	−	0.916664i	$-0.630871\pi$
$967$	18.4722	−	31.9948i	0.594026	−	1.02888i	0.993684	−	0.112218i	$-0.0357956\pi$
$968$	5.50000	+	9.52628i	0.176777	+	0.306186i
$969$	−0.944387	+	1.63573i	−0.0303381	+	0.0525471i
$970$	−1.89898	+	3.28913i	−0.0609726	+	0.105608i
$971$	−15.7980	+	27.3629i	−0.506981	+	0.878116i	0.492987	+	0.870037i	$0.335905\pi$
$971$	−15.7980	+	27.3629i	−0.506981	+	0.878116i	−0.999967	+	0.00807938i	$0.997428\pi$
$972$	4.49490	−	7.78539i	0.144174	−	0.249717i
$973$	2.20204	−	3.81405i	0.0705942	−	0.122273i
$974$	−10.1237	+	17.5348i	−0.324385	+	0.561851i
$975$	−2.89898	−	5.02118i	−0.0928416	−	0.160806i
$976$	0.224745	−	0.389270i	0.00719391	−	0.0124602i
$977$	22.2702	+	38.5730i	0.712485	+	1.23406i	0.963921	+	0.266187i	$0.0857638\pi$
$977$	22.2702	+	38.5730i	0.712485	+	1.23406i	−0.251436	+	0.967874i	$0.580903\pi$
$978$	3.69694			0.118215
$979$		0			0
$980$	6.79796			0.217153
$981$	−4.98979			−0.159312
$982$	0.674235	+	1.16781i	0.0215157	+	0.0372663i
$983$	7.14643			0.227936			0.113968	−	0.993484i	$-0.463644\pi$
$983$	7.14643			0.227936			0.113968	+	0.993484i	$0.463644\pi$
$984$	−8.62372	+	14.9367i	−0.274914	+	0.476166i
$985$	−4.44949	+	7.70674i	−0.141773	+	0.245557i
$986$	−1.34847	−	2.33562i	−0.0429440	−	0.0743812i
$987$	2.39388	+	4.14632i	0.0761979	+	0.131979i
$988$	5.79796	+	10.0424i	0.184458	+	0.319490i
$989$	4.89898	+	8.48528i	0.155778	+	0.269816i
$990$		0			0
$991$	23.7423			0.754200			0.377100	−	0.926172i	$-0.376921\pi$
$991$	23.7423			0.754200			0.377100	+	0.926172i	$0.376921\pi$
$992$	2.72474	+	4.71940i	0.0865107	+	0.149841i
$993$	−5.00000	+	8.66025i	−0.158670	+	0.274825i
$994$	−3.22474	+	5.58542i	−0.102283	+	0.177159i
$995$	1.17423	+	2.03383i	0.0372257	+	0.0644769i
$996$	3.40408			0.107862
$997$	42.3939			1.34263			0.671314	−	0.741173i	$-0.265730\pi$
$997$	42.3939			1.34263			0.671314	+	0.741173i	$0.265730\pi$
$998$	−6.89898	+	11.9494i	−0.218383	+	0.378251i
$999$	11.0176	+	19.0830i	0.348581	+	0.603761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.f.171.1	✓	4
67.29	even	3	inner	670.2.e.f.431.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.f.171.1	✓	4	1.1	even	1	trivial
670.2.e.f.431.1	yes	4	67.29	even	3	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.44949 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.724745 + 1.25529i) q^{6} +(0.224745 - 0.389270i) q^{7} +1.00000 q^{8} -0.898979 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.44949 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.724745 + 1.25529i) q^{6} +(0.224745 - 0.389270i) q^{7} +1.00000 q^{8} -0.898979 q^{9} +(0.500000 + 0.866025i) q^{10} +(0.724745 - 1.25529i) q^{12} +(2.00000 + 3.46410i) q^{13} -0.449490 q^{14} +1.44949 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.224745 + 0.389270i) q^{17} +(0.449490 + 0.778539i) q^{18} +(-1.44949 - 2.51059i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.325765 + 0.564242i) q^{21} +(1.22474 + 2.12132i) q^{23} -1.44949 q^{24} +1.00000 q^{25} +(2.00000 - 3.46410i) q^{26} +5.65153 q^{27} +(0.224745 + 0.389270i) q^{28} +(3.00000 - 5.19615i) q^{29} +(-0.724745 - 1.25529i) q^{30} +(2.72474 - 4.71940i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.224745 - 0.389270i) q^{34} +(-0.224745 + 0.389270i) q^{35} +(0.449490 - 0.778539i) q^{36} +(1.94949 + 3.37662i) q^{37} +(-1.44949 + 2.51059i) q^{38} +(-2.89898 - 5.02118i) q^{39} -1.00000 q^{40} +(5.94949 - 10.3048i) q^{41} +0.651531 q^{42} +4.00000 q^{43} +0.898979 q^{45} +(1.22474 - 2.12132i) q^{46} +(3.67423 - 6.36396i) q^{47} +(0.724745 + 1.25529i) q^{48} +(3.39898 + 5.88721i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.325765 - 0.564242i) q^{51} -4.00000 q^{52} -7.00000 q^{53} +(-2.82577 - 4.89437i) q^{54} +(0.224745 - 0.389270i) q^{56} +(2.10102 + 3.63907i) q^{57} -6.00000 q^{58} +2.89898 q^{59} +(-0.724745 + 1.25529i) q^{60} +(0.224745 + 0.389270i) q^{61} -5.44949 q^{62} +(-0.202041 + 0.349945i) q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(7.17423 - 3.94086i) q^{67} -0.449490 q^{68} +(-1.77526 - 3.07483i) q^{69} +0.449490 q^{70} +(7.17423 - 12.4261i) q^{71} -0.898979 q^{72} +(1.77526 + 3.07483i) q^{73} +(1.94949 - 3.37662i) q^{74} -1.44949 q^{75} +2.89898 q^{76} +(-2.89898 + 5.02118i) q^{78} +(-1.00000 + 1.73205i) q^{79} +(0.500000 + 0.866025i) q^{80} -5.49490 q^{81} -11.8990 q^{82} +(1.17423 + 2.03383i) q^{83} +(-0.325765 - 0.564242i) q^{84} +(-0.224745 - 0.389270i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-4.34847 + 7.53177i) q^{87} -11.8990 q^{89} +(-0.449490 - 0.778539i) q^{90} +1.79796 q^{91} -2.44949 q^{92} +(-3.94949 + 6.84072i) q^{93} -7.34847 q^{94} +(1.44949 + 2.51059i) q^{95} +(0.724745 - 1.25529i) q^{96} +(1.89898 + 3.28913i) q^{97} +(3.39898 - 5.88721i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} + 16 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 + 16 * q^9	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} - 4 q^{7} + 4 q^{8} + 16 q^{9} + 2 q^{10} - 2 q^{12} + 8 q^{13} + 8 q^{14} - 4 q^{15} - 2 q^{16} - 4 q^{17} - 8 q^{18} + 4 q^{19} + 2 q^{20} - 16 q^{21} + 4 q^{24} + 4 q^{25} + 8 q^{26} + 52 q^{27} - 4 q^{28} + 12 q^{29} + 2 q^{30} + 6 q^{31} - 2 q^{32} - 4 q^{34} + 4 q^{35} - 8 q^{36} - 2 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} + 14 q^{41} + 32 q^{42} + 16 q^{43} - 16 q^{45} - 2 q^{48} - 6 q^{49} - 2 q^{50} - 16 q^{51} - 16 q^{52} - 28 q^{53} - 26 q^{54} - 4 q^{56} + 28 q^{57} - 24 q^{58} - 8 q^{59} + 2 q^{60} - 4 q^{61} - 12 q^{62} - 40 q^{63} + 4 q^{64} - 8 q^{65} + 14 q^{67} + 8 q^{68} - 12 q^{69} - 8 q^{70} + 14 q^{71} + 16 q^{72} + 12 q^{73} - 2 q^{74} + 4 q^{75} - 8 q^{76} + 8 q^{78} - 4 q^{79} + 2 q^{80} + 76 q^{81} - 28 q^{82} - 10 q^{83} - 16 q^{84} + 4 q^{85} - 8 q^{86} + 12 q^{87} - 28 q^{89} + 8 q^{90} - 32 q^{91} - 6 q^{93} - 4 q^{95} - 2 q^{96} - 12 q^{97} - 6 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 - 4 * q^7 + 4 * q^8 + 16 * q^9 + 2 * q^10 - 2 * q^12 + 8 * q^13 + 8 * q^14 - 4 * q^15 - 2 * q^16 - 4 * q^17 - 8 * q^18 + 4 * q^19 + 2 * q^20 - 16 * q^21 + 4 * q^24 + 4 * q^25 + 8 * q^26 + 52 * q^27 - 4 * q^28 + 12 * q^29 + 2 * q^30 + 6 * q^31 - 2 * q^32 - 4 * q^34 + 4 * q^35 - 8 * q^36 - 2 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 + 14 * q^41 + 32 * q^42 + 16 * q^43 - 16 * q^45 - 2 * q^48 - 6 * q^49 - 2 * q^50 - 16 * q^51 - 16 * q^52 - 28 * q^53 - 26 * q^54 - 4 * q^56 + 28 * q^57 - 24 * q^58 - 8 * q^59 + 2 * q^60 - 4 * q^61 - 12 * q^62 - 40 * q^63 + 4 * q^64 - 8 * q^65 + 14 * q^67 + 8 * q^68 - 12 * q^69 - 8 * q^70 + 14 * q^71 + 16 * q^72 + 12 * q^73 - 2 * q^74 + 4 * q^75 - 8 * q^76 + 8 * q^78 - 4 * q^79 + 2 * q^80 + 76 * q^81 - 28 * q^82 - 10 * q^83 - 16 * q^84 + 4 * q^85 - 8 * q^86 + 12 * q^87 - 28 * q^89 + 8 * q^90 - 32 * q^91 - 6 * q^93 - 4 * q^95 - 2 * q^96 - 12 * q^97 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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