LMFDB - Embedded newform 816.2.r.a.395.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [816,2,Mod(395,816)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(816, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 3]))

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

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

chi := DirichletCharacter("816.395");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 816 = 2^{4} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	816.r (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			395.1
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	816.395
Dual form			816.2.r.a.659.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-0.618034 - 1.61803i) q^{3} +2.00000i q^{4} -1.23607i q^{5} +(-1.00000 + 2.23607i) q^{6} +(2.23607 + 2.23607i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.618034 - 1.61803i) q^{3} +2.00000i q^{4} -1.23607i q^{5} +(-1.00000 + 2.23607i) q^{6} +(2.23607 + 2.23607i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.23607 + 2.00000i) q^{9} +(-1.23607 + 1.23607i) q^{10} +0.763932i q^{11} +(3.23607 - 1.23607i) q^{12} +(-1.00000 + 1.00000i) q^{13} -4.47214i q^{14} +(-2.00000 + 0.763932i) q^{15} -4.00000 q^{16} +(-1.00000 - 4.00000i) q^{17} +(4.23607 + 0.236068i) q^{18} +(4.23607 - 4.23607i) q^{19} +2.47214 q^{20} +(2.23607 - 5.00000i) q^{21} +(0.763932 - 0.763932i) q^{22} +(2.23607 - 2.23607i) q^{23} +(-4.47214 - 2.00000i) q^{24} +3.47214 q^{25} +2.00000 q^{26} +(4.61803 + 2.38197i) q^{27} +(-4.47214 + 4.47214i) q^{28} +3.23607 q^{29} +(2.76393 + 1.23607i) q^{30} +(-5.47214 - 5.47214i) q^{31} +(4.00000 + 4.00000i) q^{32} +(1.23607 - 0.472136i) q^{33} +(-3.00000 + 5.00000i) q^{34} +(2.76393 - 2.76393i) q^{35} +(-4.00000 - 4.47214i) q^{36} +9.70820 q^{37} -8.47214 q^{38} +(2.23607 + 1.00000i) q^{39} +(-2.47214 - 2.47214i) q^{40} +(-3.76393 - 3.76393i) q^{41} +(-7.23607 + 2.76393i) q^{42} +(-6.70820 - 6.70820i) q^{43} -1.52786 q^{44} +(2.47214 + 2.76393i) q^{45} -4.47214 q^{46} -8.00000 q^{47} +(2.47214 + 6.47214i) q^{48} +3.00000i q^{49} +(-3.47214 - 3.47214i) q^{50} +(-5.85410 + 4.09017i) q^{51} +(-2.00000 - 2.00000i) q^{52} +(5.00000 + 5.00000i) q^{53} +(-2.23607 - 7.00000i) q^{54} +0.944272 q^{55} +8.94427 q^{56} +(-9.47214 - 4.23607i) q^{57} +(-3.23607 - 3.23607i) q^{58} +(7.47214 - 7.47214i) q^{59} +(-1.52786 - 4.00000i) q^{60} +1.70820 q^{61} +10.9443i q^{62} +(-9.47214 - 0.527864i) q^{63} -8.00000i q^{64} +(1.23607 + 1.23607i) q^{65} +(-1.70820 - 0.763932i) q^{66} +(-1.47214 - 1.47214i) q^{67} +(8.00000 - 2.00000i) q^{68} +(-5.00000 - 2.23607i) q^{69} -5.52786 q^{70} +(-6.23607 - 6.23607i) q^{71} +(-0.472136 + 8.47214i) q^{72} +(3.76393 + 3.76393i) q^{73} +(-9.70820 - 9.70820i) q^{74} +(-2.14590 - 5.61803i) q^{75} +(8.47214 + 8.47214i) q^{76} +(-1.70820 + 1.70820i) q^{77} +(-1.23607 - 3.23607i) q^{78} +(-11.4721 + 11.4721i) q^{79} +4.94427i q^{80} +(1.00000 - 8.94427i) q^{81} +7.52786i q^{82} +(0.527864 + 0.527864i) q^{83} +(10.0000 + 4.47214i) q^{84} +(-4.94427 + 1.23607i) q^{85} +13.4164i q^{86} +(-2.00000 - 5.23607i) q^{87} +(1.52786 + 1.52786i) q^{88} -4.47214 q^{89} +(0.291796 - 5.23607i) q^{90} -4.47214 q^{91} +(4.47214 + 4.47214i) q^{92} +(-5.47214 + 12.2361i) q^{93} +(8.00000 + 8.00000i) q^{94} +(-5.23607 - 5.23607i) q^{95} +(4.00000 - 8.94427i) q^{96} +(-1.47214 + 1.47214i) q^{97} +(3.00000 - 3.00000i) q^{98} +(-1.52786 - 1.70820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 2 q^{3} - 4 q^{6} + 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 2 * q^3 - 4 * q^6 + 8 * q^8	$ 4 q - 4 q^{2} + 2 q^{3} - 4 q^{6} + 8 q^{8} + 4 q^{10} + 4 q^{12} - 4 q^{13} - 8 q^{15} - 16 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{19} - 8 q^{20} + 12 q^{22} - 4 q^{25} + 8 q^{26} + 14 q^{27} + 4 q^{29} + 20 q^{30} - 4 q^{31} + 16 q^{32} - 4 q^{33} - 12 q^{34} + 20 q^{35} - 16 q^{36} + 12 q^{37} - 16 q^{38} + 8 q^{40} - 24 q^{41} - 20 q^{42} - 24 q^{44} - 8 q^{45} - 32 q^{47} - 8 q^{48} + 4 q^{50} - 10 q^{51} - 8 q^{52} + 20 q^{53} - 32 q^{55} - 20 q^{57} - 4 q^{58} + 12 q^{59} - 24 q^{60} - 20 q^{61} - 20 q^{63} - 4 q^{65} + 20 q^{66} + 12 q^{67} + 32 q^{68} - 20 q^{69} - 40 q^{70} - 16 q^{71} + 16 q^{72} + 24 q^{73} - 12 q^{74} - 22 q^{75} + 16 q^{76} + 20 q^{77} + 4 q^{78} - 28 q^{79} + 4 q^{81} + 20 q^{83} + 40 q^{84} + 16 q^{85} - 8 q^{87} + 24 q^{88} + 28 q^{90} - 4 q^{93} + 32 q^{94} - 12 q^{95} + 16 q^{96} + 12 q^{97} + 12 q^{98} - 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 2 * q^3 - 4 * q^6 + 8 * q^8 + 4 * q^10 + 4 * q^12 - 4 * q^13 - 8 * q^15 - 16 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^19 - 8 * q^20 + 12 * q^22 - 4 * q^25 + 8 * q^26 + 14 * q^27 + 4 * q^29 + 20 * q^30 - 4 * q^31 + 16 * q^32 - 4 * q^33 - 12 * q^34 + 20 * q^35 - 16 * q^36 + 12 * q^37 - 16 * q^38 + 8 * q^40 - 24 * q^41 - 20 * q^42 - 24 * q^44 - 8 * q^45 - 32 * q^47 - 8 * q^48 + 4 * q^50 - 10 * q^51 - 8 * q^52 + 20 * q^53 - 32 * q^55 - 20 * q^57 - 4 * q^58 + 12 * q^59 - 24 * q^60 - 20 * q^61 - 20 * q^63 - 4 * q^65 + 20 * q^66 + 12 * q^67 + 32 * q^68 - 20 * q^69 - 40 * q^70 - 16 * q^71 + 16 * q^72 + 24 * q^73 - 12 * q^74 - 22 * q^75 + 16 * q^76 + 20 * q^77 + 4 * q^78 - 28 * q^79 + 4 * q^81 + 20 * q^83 + 40 * q^84 + 16 * q^85 - 8 * q^87 + 24 * q^88 + 28 * q^90 - 4 * q^93 + 32 * q^94 - 12 * q^95 + 16 * q^96 + 12 * q^97 + 12 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/816\mathbb{Z}\right)^\times$.

$n$	$241$	$511$	$545$	$613$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	−0.618034	−	1.61803i	−0.356822	−	0.934172i
$3$	−0.618034	−	1.61803i	−0.356822	−	0.934172i
$4$			2.00000i			1.00000i
$5$		−	1.23607i		−	0.552786i	−0.961045	−	0.276393i	$-0.910861\pi$
$5$		−	1.23607i		−	0.552786i	0.961045	−	0.276393i	$-0.0891392\pi$
$6$	−1.00000	+	2.23607i	−0.408248	+	0.912871i
$7$	2.23607	+	2.23607i	0.845154	+	0.845154i	0.989524	−	0.144370i	$-0.0461154\pi$
$7$	2.23607	+	2.23607i	0.845154	+	0.845154i	−0.144370	+	0.989524i	$0.546115\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	−2.23607	+	2.00000i	−0.745356	+	0.666667i
$10$	−1.23607	+	1.23607i	−0.390879	+	0.390879i
$11$			0.763932i			0.230334i	0.993346	+	0.115167i	$0.0367403\pi$
$11$			0.763932i			0.230334i	−0.993346	+	0.115167i	$0.963260\pi$
$12$	3.23607	−	1.23607i	0.934172	−	0.356822i
$13$	−1.00000	+	1.00000i	−0.277350	+	0.277350i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−1.00000	+	1.00000i	−0.277350	+	0.277350i	0.554700	+	0.832050i	$0.312833\pi$
$14$		−	4.47214i		−	1.19523i
$15$	−2.00000	+	0.763932i	−0.516398	+	0.197246i
$16$	−4.00000			−1.00000
$17$	−1.00000	−	4.00000i	−0.242536	−	0.970143i
$17$	−1.00000	−	4.00000i	−0.242536	−	0.970143i
$18$	4.23607	+	0.236068i	0.998451	+	0.0556418i
$19$	4.23607	−	4.23607i	0.971821	−	0.971821i	−0.0277931	−	0.999614i	$-0.508848\pi$
$19$	4.23607	−	4.23607i	0.971821	−	0.971821i	0.999614	+	0.0277931i	$0.00884794\pi$
$20$	2.47214			0.552786
$21$	2.23607	−	5.00000i	0.487950	−	1.09109i
$22$	0.763932	−	0.763932i	0.162871	−	0.162871i
$23$	2.23607	−	2.23607i	0.466252	−	0.466252i	−0.434446	−	0.900698i	$-0.643056\pi$
$23$	2.23607	−	2.23607i	0.466252	−	0.466252i	0.900698	+	0.434446i	$0.143056\pi$
$24$	−4.47214	−	2.00000i	−0.912871	−	0.408248i
$25$	3.47214			0.694427
$26$	2.00000			0.392232
$27$	4.61803	+	2.38197i	0.888741	+	0.458410i
$28$	−4.47214	+	4.47214i	−0.845154	+	0.845154i
$29$	3.23607			0.600923			0.300461	−	0.953794i	$-0.402859\pi$
$29$	3.23607			0.600923			0.300461	+	0.953794i	$0.402859\pi$
$30$	2.76393	+	1.23607i	0.504623	+	0.225674i
$31$	−5.47214	−	5.47214i	−0.982825	−	0.982825i	0.0170303	−	0.999855i	$-0.494579\pi$
$31$	−5.47214	−	5.47214i	−0.982825	−	0.982825i	−0.999855	+	0.0170303i	$0.994579\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	1.23607	−	0.472136i	0.215172	−	0.0821883i
$34$	−3.00000	+	5.00000i	−0.514496	+	0.857493i
$35$	2.76393	−	2.76393i	0.467190	−	0.467190i
$36$	−4.00000	−	4.47214i	−0.666667	−	0.745356i
$37$	9.70820			1.59602			0.798009	−	0.602645i	$-0.205886\pi$
$37$	9.70820			1.59602			0.798009	+	0.602645i	$0.205886\pi$
$38$	−8.47214			−1.37436
$39$	2.23607	+	1.00000i	0.358057	+	0.160128i
$40$	−2.47214	−	2.47214i	−0.390879	−	0.390879i
$41$	−3.76393	−	3.76393i	−0.587827	−	0.587827i	0.349215	−	0.937043i	$-0.386448\pi$
$41$	−3.76393	−	3.76393i	−0.587827	−	0.587827i	−0.937043	+	0.349215i	$0.886448\pi$
$42$	−7.23607	+	2.76393i	−1.11655	+	0.426484i
$43$	−6.70820	−	6.70820i	−1.02299	−	1.02299i	−0.999729	−	0.0232621i	$-0.992595\pi$
$43$	−6.70820	−	6.70820i	−1.02299	−	1.02299i	−0.0232621	−	0.999729i	$-0.507405\pi$
$44$	−1.52786			−0.230334
$45$	2.47214	+	2.76393i	0.368524	+	0.412023i
$46$	−4.47214			−0.659380
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	2.47214	+	6.47214i	0.356822	+	0.934172i
$49$			3.00000i			0.428571i
$50$	−3.47214	−	3.47214i	−0.491034	−	0.491034i
$51$	−5.85410	+	4.09017i	−0.819738	+	0.572738i
$52$	−2.00000	−	2.00000i	−0.277350	−	0.277350i
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	−0.274721	+	0.961524i	$0.588586\pi$
$54$	−2.23607	−	7.00000i	−0.304290	−	0.952579i
$55$	0.944272			0.127326
$56$	8.94427			1.19523
$57$	−9.47214	−	4.23607i	−1.25462	−	0.561081i
$58$	−3.23607	−	3.23607i	−0.424917	−	0.424917i
$59$	7.47214	−	7.47214i	0.972789	−	0.972789i	−0.0268502	−	0.999639i	$-0.508548\pi$
$59$	7.47214	−	7.47214i	0.972789	−	0.972789i	0.999639	+	0.0268502i	$0.00854772\pi$
$60$	−1.52786	−	4.00000i	−0.197246	−	0.516398i
$61$	1.70820			0.218713			0.109357	−	0.994003i	$-0.465121\pi$
$61$	1.70820			0.218713			0.109357	+	0.994003i	$0.465121\pi$
$62$			10.9443i			1.38992i
$63$	−9.47214	−	0.527864i	−1.19338	−	0.0665046i
$64$		−	8.00000i		−	1.00000i
$65$	1.23607	+	1.23607i	0.153315	+	0.153315i
$66$	−1.70820	−	0.763932i	−0.210265	−	0.0940335i
$67$	−1.47214	−	1.47214i	−0.179850	−	0.179850i	0.611440	−	0.791290i	$-0.290590\pi$
$67$	−1.47214	−	1.47214i	−0.179850	−	0.179850i	−0.791290	+	0.611440i	$0.790590\pi$
$68$	8.00000	−	2.00000i	0.970143	−	0.242536i
$69$	−5.00000	−	2.23607i	−0.601929	−	0.269191i
$70$	−5.52786			−0.660706
$71$	−6.23607	−	6.23607i	−0.740085	−	0.740085i	0.232509	−	0.972594i	$-0.425306\pi$
$71$	−6.23607	−	6.23607i	−0.740085	−	0.740085i	−0.972594	+	0.232509i	$0.925306\pi$
$72$	−0.472136	+	8.47214i	−0.0556418	+	0.998451i
$73$	3.76393	+	3.76393i	0.440535	+	0.440535i	0.892192	−	0.451657i	$-0.149167\pi$
$73$	3.76393	+	3.76393i	0.440535	+	0.440535i	−0.451657	+	0.892192i	$0.649167\pi$
$74$	−9.70820	−	9.70820i	−1.12856	−	1.12856i
$75$	−2.14590	−	5.61803i	−0.247787	−	0.648715i
$76$	8.47214	+	8.47214i	0.971821	+	0.971821i
$77$	−1.70820	+	1.70820i	−0.194668	+	0.194668i
$78$	−1.23607	−	3.23607i	−0.139957	−	0.366413i
$79$	−11.4721	+	11.4721i	−1.29072	+	1.29072i	−0.356372	+	0.934344i	$0.615986\pi$
$79$	−11.4721	+	11.4721i	−1.29072	+	1.29072i	−0.934344	+	0.356372i	$0.884014\pi$
$80$			4.94427i			0.552786i
$81$	1.00000	−	8.94427i	0.111111	−	0.993808i
$82$			7.52786i			0.831314i
$83$	0.527864	+	0.527864i	0.0579406	+	0.0579406i	0.735483	−	0.677543i	$-0.236955\pi$
$83$	0.527864	+	0.527864i	0.0579406	+	0.0579406i	−0.677543	+	0.735483i	$0.736955\pi$
$84$	10.0000	+	4.47214i	1.09109	+	0.487950i
$85$	−4.94427	+	1.23607i	−0.536282	+	0.134070i
$86$			13.4164i			1.44673i
$87$	−2.00000	−	5.23607i	−0.214423	−	0.561365i
$88$	1.52786	+	1.52786i	0.162871	+	0.162871i
$89$	−4.47214			−0.474045			−0.237023	−	0.971504i	$-0.576172\pi$
$89$	−4.47214			−0.474045			−0.237023	+	0.971504i	$0.576172\pi$
$90$	0.291796	−	5.23607i	0.0307580	−	0.551930i
$91$	−4.47214			−0.468807
$92$	4.47214	+	4.47214i	0.466252	+	0.466252i
$93$	−5.47214	+	12.2361i	−0.567434	+	1.26882i
$94$	8.00000	+	8.00000i	0.825137	+	0.825137i
$95$	−5.23607	−	5.23607i	−0.537209	−	0.537209i
$96$	4.00000	−	8.94427i	0.408248	−	0.912871i
$97$	−1.47214	+	1.47214i	−0.149473	+	0.149473i	−0.777883	−	0.628410i	$-0.783706\pi$
$97$	−1.47214	+	1.47214i	−0.149473	+	0.149473i	0.628410	+	0.777883i	$0.283706\pi$
$98$	3.00000	−	3.00000i	0.303046	−	0.303046i
$99$	−1.52786	−	1.70820i	−0.153556	−	0.171681i
$100$			6.94427i			0.694427i
$101$	6.23607	−	6.23607i	0.620512	−	0.620512i	−0.325150	−	0.945662i	$-0.605415\pi$
$101$	6.23607	−	6.23607i	0.620512	−	0.620512i	0.945662	+	0.325150i	$0.105415\pi$
$102$	9.94427	+	1.76393i	0.984630	+	0.174655i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$			4.00000i			0.392232i
$105$	−6.18034	−	2.76393i	−0.603139	−	0.269732i
$106$		−	10.0000i		−	0.971286i
$107$	−5.23607			−0.506190			−0.253095	−	0.967441i	$-0.581448\pi$
$107$	−5.23607			−0.506190			−0.253095	+	0.967441i	$0.581448\pi$
$108$	−4.76393	+	9.23607i	−0.458410	+	0.888741i
$109$	17.7082			1.69614			0.848069	−	0.529886i	$-0.177765\pi$
$109$	17.7082			1.69614			0.848069	+	0.529886i	$0.177765\pi$
$110$	−0.944272	−	0.944272i	−0.0900328	−	0.0900328i
$111$	−6.00000	−	15.7082i	−0.569495	−	1.49096i
$112$	−8.94427	−	8.94427i	−0.845154	−	0.845154i
$113$	0.527864	−	0.527864i	0.0496573	−	0.0496573i	−0.681842	−	0.731499i	$-0.738821\pi$
$113$	0.527864	−	0.527864i	0.0496573	−	0.0496573i	0.731499	+	0.681842i	$0.238821\pi$
$114$	5.23607	+	13.7082i	0.490403	+	1.28389i
$115$	−2.76393	−	2.76393i	−0.257738	−	0.257738i
$116$			6.47214i			0.600923i
$117$	0.236068	−	4.23607i	0.0218245	−	0.391625i
$118$	−14.9443			−1.37573
$119$	6.70820	−	11.1803i	0.614940	−	1.02490i
$120$	−2.47214	+	5.52786i	−0.225674	+	0.504623i
$121$	10.4164			0.946946
$122$	−1.70820	−	1.70820i	−0.154654	−	0.154654i
$123$	−3.76393	+	8.41641i	−0.339382	+	0.758882i
$124$	10.9443	−	10.9443i	0.982825	−	0.982825i
$125$		−	10.4721i		−	0.936656i
$126$	8.94427	+	10.0000i	0.796819	+	0.890871i
$127$	3.05573			0.271152			0.135576	−	0.990767i	$-0.456712\pi$
$127$	3.05573			0.271152			0.135576	+	0.990767i	$0.456712\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$	−6.70820	+	15.0000i	−0.590624	+	1.32068i
$130$		−	2.47214i		−	0.216821i
$131$			13.7082i			1.19769i	0.800864	+	0.598846i	$0.204374\pi$
$131$			13.7082i			1.19769i	−0.800864	+	0.598846i	$0.795626\pi$
$132$	0.944272	+	2.47214i	0.0821883	+	0.215172i
$133$	18.9443			1.64268
$134$			2.94427i			0.254346i
$135$	2.94427	−	5.70820i	0.253403	−	0.491284i
$136$	−10.0000	−	6.00000i	−0.857493	−	0.514496i
$137$	−12.4721			−1.06557			−0.532783	−	0.846252i	$-0.678854\pi$
$137$	−12.4721			−1.06557			−0.532783	+	0.846252i	$0.678854\pi$
$138$	2.76393	+	7.23607i	0.235282	+	0.615975i
$139$		−	21.7082i		−	1.84127i	−0.390429	−	0.920633i	$-0.627673\pi$
$139$		−	21.7082i		−	1.84127i	0.390429	−	0.920633i	$-0.372327\pi$
$140$	5.52786	+	5.52786i	0.467190	+	0.467190i
$141$	4.94427	+	12.9443i	0.416383	+	1.09010i
$142$			12.4721i			1.04664i
$143$	−0.763932	−	0.763932i	−0.0638832	−	0.0638832i
$144$	8.94427	−	8.00000i	0.745356	−	0.666667i
$145$		−	4.00000i		−	0.332182i
$146$		−	7.52786i		−	0.623010i
$147$	4.85410	−	1.85410i	0.400360	−	0.152924i
$148$			19.4164i			1.59602i
$149$	14.2361	−	14.2361i	1.16626	−	1.16626i	0.183186	−	0.983078i	$-0.441359\pi$
$149$	14.2361	−	14.2361i	1.16626	−	1.16626i	0.983078	−	0.183186i	$-0.0586410\pi$
$150$	−3.47214	+	7.76393i	−0.283499	+	0.633922i
$151$			13.4164i			1.09181i	0.837846	+	0.545906i	$0.183814\pi$
$151$			13.4164i			1.09181i	−0.837846	+	0.545906i	$0.816186\pi$
$152$		−	16.9443i		−	1.37436i
$153$	10.2361	+	6.94427i	0.827537	+	0.561411i
$154$	3.41641			0.275302
$155$	−6.76393	+	6.76393i	−0.543292	+	0.543292i
$156$	−2.00000	+	4.47214i	−0.160128	+	0.358057i
$157$	−5.00000	+	5.00000i	−0.399043	+	0.399043i	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−5.00000	+	5.00000i	−0.399043	+	0.399043i	0.478852	+	0.877896i	$0.341053\pi$
$158$	22.9443			1.82535
$159$	5.00000	−	11.1803i	0.396526	−	0.886659i
$160$	4.94427	−	4.94427i	0.390879	−	0.390879i
$161$	10.0000			0.788110
$162$	−9.94427	+	7.94427i	−0.781296	+	0.624161i
$163$			11.2361i			0.880077i	0.897979	+	0.440038i	$0.145035\pi$
$163$			11.2361i			0.880077i	−0.897979	+	0.440038i	$0.854965\pi$
$164$	7.52786	−	7.52786i	0.587827	−	0.587827i
$165$	−0.583592	−	1.52786i	−0.0454326	−	0.118944i
$166$		−	1.05573i		−	0.0819404i
$167$	−2.23607	−	2.23607i	−0.173032	−	0.173032i	0.615278	−	0.788310i	$-0.289044\pi$
$167$	−2.23607	−	2.23607i	−0.173032	−	0.173032i	−0.788310	+	0.615278i	$0.789044\pi$
$168$	−5.52786	−	14.4721i	−0.426484	−	1.11655i
$169$			11.0000i			0.846154i
$170$	6.18034	+	3.70820i	0.474010	+	0.284406i
$171$	−1.00000	+	17.9443i	−0.0764719	+	1.37223i
$172$	13.4164	−	13.4164i	1.02299	−	1.02299i
$173$	−6.65248			−0.505778			−0.252889	−	0.967495i	$-0.581381\pi$
$173$	−6.65248			−0.505778			−0.252889	+	0.967495i	$0.581381\pi$
$174$	−3.23607	+	7.23607i	−0.245326	+	0.548565i
$175$	7.76393	+	7.76393i	0.586898	+	0.586898i
$176$		−	3.05573i		−	0.230334i
$177$	−16.7082	−	7.47214i	−1.25587	−	0.561640i
$178$	4.47214	+	4.47214i	0.335201	+	0.335201i
$179$	−1.94427	−	1.94427i	−0.145322	−	0.145322i	0.630703	−	0.776024i	$-0.282767\pi$
$179$	−1.94427	−	1.94427i	−0.145322	−	0.145322i	−0.776024	+	0.630703i	$0.782767\pi$
$180$	−5.52786	+	4.94427i	−0.412023	+	0.368524i
$181$		−	1.81966i		−	0.135254i	−0.997711	−	0.0676271i	$-0.978457\pi$
$181$		−	1.81966i		−	0.135254i	0.997711	−	0.0676271i	$-0.0215428\pi$
$182$	4.47214	+	4.47214i	0.331497	+	0.331497i
$183$	−1.05573	−	2.76393i	−0.0780417	−	0.204316i
$184$		−	8.94427i		−	0.659380i
$185$		−	12.0000i		−	0.882258i
$186$	17.7082	−	6.76393i	1.29843	−	0.495956i
$187$	3.05573	−	0.763932i	0.223457	−	0.0558642i
$188$		−	16.0000i		−	1.16692i
$189$	5.00000	+	15.6525i	0.363696	+	1.13855i
$190$			10.4721i			0.759729i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$	−12.9443	+	4.94427i	−0.934172	+	0.356822i
$193$	3.47214	+	3.47214i	0.249930	+	0.249930i	0.820942	−	0.571012i	$-0.193449\pi$
$193$	3.47214	+	3.47214i	0.249930	+	0.249930i	−0.571012	+	0.820942i	$0.693449\pi$
$194$	2.94427			0.211386
$195$	1.23607	−	2.76393i	0.0885167	−	0.197929i
$196$	−6.00000			−0.428571
$197$	13.1246			0.935090			0.467545	−	0.883969i	$-0.345139\pi$
$197$	13.1246			0.935090			0.467545	+	0.883969i	$0.345139\pi$
$198$	−0.180340	+	3.23607i	−0.0128162	+	0.229977i
$199$	18.7082	−	18.7082i	1.32619	−	1.32619i	0.417523	−	0.908666i	$-0.362898\pi$
$199$	18.7082	−	18.7082i	1.32619	−	1.32619i	0.908666	−	0.417523i	$-0.137102\pi$
$200$	6.94427	−	6.94427i	0.491034	−	0.491034i
$201$	−1.47214	+	3.29180i	−0.103836	+	0.232185i
$202$	−12.4721			−0.877536
$203$	7.23607	+	7.23607i	0.507872	+	0.507872i
$204$	−8.18034	−	11.7082i	−0.572738	−	0.819738i
$205$	−4.65248	+	4.65248i	−0.324943	+	0.324943i
$206$	−4.00000	−	4.00000i	−0.278693	−	0.278693i
$207$	−0.527864	+	9.47214i	−0.0366891	+	0.658359i
$208$	4.00000	−	4.00000i	0.277350	−	0.277350i
$209$	3.23607	+	3.23607i	0.223844	+	0.223844i
$210$	3.41641	+	8.94427i	0.235755	+	0.617213i
$211$		−	18.6525i		−	1.28409i	−0.766667	−	0.642045i	$-0.778086\pi$
$211$		−	18.6525i		−	1.28409i	0.766667	−	0.642045i	$-0.221914\pi$
$212$	−10.0000	+	10.0000i	−0.686803	+	0.686803i
$213$	−6.23607	+	13.9443i	−0.427288	+	0.955446i
$214$	5.23607	+	5.23607i	0.357930	+	0.357930i
$215$	−8.29180	+	8.29180i	−0.565496	+	0.565496i
$216$	14.0000	−	4.47214i	0.952579	−	0.304290i
$217$		−	24.4721i		−	1.66128i
$218$	−17.7082	−	17.7082i	−1.19935	−	1.19935i
$219$	3.76393	−	8.41641i	0.254343	−	0.568728i
$220$			1.88854i			0.127326i
$221$	5.00000	+	3.00000i	0.336336	+	0.201802i
$222$	−9.70820	+	21.7082i	−0.651572	+	1.45696i
$223$	4.94427			0.331093			0.165546	−	0.986202i	$-0.447061\pi$
$223$	4.94427			0.331093			0.165546	+	0.986202i	$0.447061\pi$
$224$			17.8885i			1.19523i
$225$	−7.76393	+	6.94427i	−0.517595	+	0.462951i
$226$	−1.05573			−0.0702260
$227$	−14.7639			−0.979917			−0.489958	−	0.871746i	$-0.662988\pi$
$227$	−14.7639			−0.979917			−0.489958	+	0.871746i	$0.662988\pi$
$228$	8.47214	−	18.9443i	0.561081	−	1.25462i
$229$	−1.29180	+	1.29180i	−0.0853643	+	0.0853643i	−0.748500	−	0.663135i	$-0.769225\pi$
$229$	−1.29180	+	1.29180i	−0.0853643	+	0.0853643i	0.663135	+	0.748500i	$0.269225\pi$
$230$			5.52786i			0.364497i
$231$	3.81966	+	1.70820i	0.251315	+	0.112392i
$232$	6.47214	−	6.47214i	0.424917	−	0.424917i
$233$	−11.1803	+	11.1803i	−0.732448	+	0.732448i	−0.971104	−	0.238656i	$-0.923293\pi$
$233$	−11.1803	+	11.1803i	−0.732448	+	0.732448i	0.238656	+	0.971104i	$0.423293\pi$
$234$	−4.47214	+	4.00000i	−0.292353	+	0.261488i
$235$			9.88854i			0.645057i
$236$	14.9443	+	14.9443i	0.972789	+	0.972789i
$237$	25.6525	+	11.4721i	1.66631	+	0.745195i
$238$	−17.8885	+	4.47214i	−1.15954	+	0.289886i
$239$	28.9443			1.87225			0.936125	−	0.351668i	$-0.114386\pi$
$239$	28.9443			1.87225			0.936125	+	0.351668i	$0.114386\pi$
$240$	8.00000	−	3.05573i	0.516398	−	0.197246i
$241$	−13.4721	+	13.4721i	−0.867817	+	0.867817i	−0.992230	−	0.124414i	$-0.960295\pi$
$241$	−13.4721	+	13.4721i	−0.867817	+	0.867817i	0.124414	+	0.992230i	$0.460295\pi$
$242$	−10.4164	−	10.4164i	−0.669592	−	0.669592i
$243$	−15.0902	+	3.90983i	−0.968035	+	0.250816i
$244$			3.41641i			0.218713i
$245$	3.70820			0.236908
$246$	12.1803	−	4.65248i	0.776590	−	0.296631i
$247$			8.47214i			0.539069i
$248$	−21.8885			−1.38992
$249$	0.527864	−	1.18034i	0.0334520	−	0.0748010i
$250$	−10.4721	+	10.4721i	−0.662316	+	0.662316i
$251$	19.6525	+	19.6525i	1.24045	+	1.24045i	0.959813	+	0.280640i	$0.0905468\pi$
$251$	19.6525	+	19.6525i	1.24045	+	1.24045i	0.280640	+	0.959813i	$0.409453\pi$
$252$	1.05573	−	18.9443i	0.0665046	−	1.19338i
$253$	1.70820	+	1.70820i	0.107394	+	0.107394i
$254$	−3.05573	−	3.05573i	−0.191733	−	0.191733i
$255$	5.05573	+	7.23607i	0.316602	+	0.453140i
$256$	16.0000			1.00000
$257$	9.05573			0.564881			0.282440	−	0.959285i	$-0.408856\pi$
$257$	9.05573			0.564881			0.282440	+	0.959285i	$0.408856\pi$
$258$	21.7082	−	8.29180i	1.35149	−	0.516225i
$259$	21.7082	+	21.7082i	1.34888	+	1.34888i
$260$	−2.47214	+	2.47214i	−0.153315	+	0.153315i
$261$	−7.23607	+	6.47214i	−0.447901	+	0.400615i
$262$	13.7082	−	13.7082i	0.846896	−	0.846896i
$263$	4.00000			0.246651			0.123325	−	0.992366i	$-0.460644\pi$
$263$	4.00000			0.246651			0.123325	+	0.992366i	$0.460644\pi$
$264$	1.52786	−	3.41641i	0.0940335	−	0.210265i
$265$	6.18034	−	6.18034i	0.379655	−	0.379655i
$266$	−18.9443	−	18.9443i	−1.16155	−	1.16155i
$267$	2.76393	+	7.23607i	0.169150	+	0.442840i
$268$	2.94427	−	2.94427i	0.179850	−	0.179850i
$269$	−25.7082			−1.56746			−0.783728	−	0.621104i	$-0.786685\pi$
$269$	−25.7082			−1.56746			−0.783728	+	0.621104i	$0.786685\pi$
$270$	−8.65248	+	2.76393i	−0.526573	+	0.168208i
$271$		−	7.88854i		−	0.479195i	−0.970872	−	0.239597i	$-0.922985\pi$
$271$		−	7.88854i		−	0.479195i	0.970872	−	0.239597i	$-0.0770155\pi$
$272$	4.00000	+	16.0000i	0.242536	+	0.970143i
$273$	2.76393	+	7.23607i	0.167281	+	0.437947i
$274$	12.4721	+	12.4721i	0.753469	+	0.753469i
$275$			2.65248i			0.159950i
$276$	4.47214	−	10.0000i	0.269191	−	0.601929i
$277$	9.70820			0.583309			0.291655	−	0.956524i	$-0.405794\pi$
$277$	9.70820			0.583309			0.291655	+	0.956524i	$0.405794\pi$
$278$	−21.7082	+	21.7082i	−1.30197	+	1.30197i
$279$	23.1803	+	1.29180i	1.38777	+	0.0773378i
$280$		−	11.0557i		−	0.660706i
$281$			17.8885i			1.06714i	0.845756	+	0.533571i	$0.179150\pi$
$281$			17.8885i			1.06714i	−0.845756	+	0.533571i	$0.820850\pi$
$282$	8.00000	−	17.8885i	0.476393	−	1.06525i
$283$	−7.70820			−0.458205			−0.229103	−	0.973402i	$-0.573579\pi$
$283$	−7.70820			−0.458205			−0.229103	+	0.973402i	$0.573579\pi$
$284$	12.4721	−	12.4721i	0.740085	−	0.740085i
$285$	−5.23607	+	11.7082i	−0.310158	+	0.693534i
$286$			1.52786i			0.0903445i
$287$		−	16.8328i		−	0.993610i
$288$	−16.9443	−	0.944272i	−0.998451	−	0.0556418i
$289$	−15.0000	+	8.00000i	−0.882353	+	0.470588i
$290$	−4.00000	+	4.00000i	−0.234888	+	0.234888i
$291$	3.29180	+	1.47214i	0.192969	+	0.0862981i
$292$	−7.52786	+	7.52786i	−0.440535	+	0.440535i
$293$	−10.7082	+	10.7082i	−0.625580	+	0.625580i	−0.946953	−	0.321373i	$-0.895856\pi$
$293$	−10.7082	+	10.7082i	−0.625580	+	0.625580i	0.321373	+	0.946953i	$0.395856\pi$
$294$	−6.70820	−	3.00000i	−0.391230	−	0.174964i
$295$	−9.23607	−	9.23607i	−0.537745	−	0.537745i
$296$	19.4164	−	19.4164i	1.12856	−	1.12856i
$297$	−1.81966	+	3.52786i	−0.105587	+	0.204707i
$298$	−28.4721			−1.64935
$299$			4.47214i			0.258630i
$300$	11.2361	−	4.29180i	0.648715	−	0.247787i
$301$		−	30.0000i		−	1.72917i
$302$	13.4164	−	13.4164i	0.772028	−	0.772028i
$303$	−13.9443	−	6.23607i	−0.801077	−	0.358253i
$304$	−16.9443	+	16.9443i	−0.971821	+	0.971821i
$305$		−	2.11146i		−	0.120902i
$306$	−3.29180	−	17.1803i	−0.188179	−	0.982135i
$307$	−15.9443	−	15.9443i	−0.909988	−	0.909988i	0.0862830	−	0.996271i	$-0.472501\pi$
$307$	−15.9443	−	15.9443i	−0.909988	−	0.909988i	−0.996271	+	0.0862830i	$0.972501\pi$
$308$	−3.41641	−	3.41641i	−0.194668	−	0.194668i
$309$	−2.47214	−	6.47214i	−0.140635	−	0.368187i
$310$	13.5279			0.768331
$311$	−6.23607	−	6.23607i	−0.353615	−	0.353615i	0.507838	−	0.861453i	$-0.330445\pi$
$311$	−6.23607	−	6.23607i	−0.353615	−	0.353615i	−0.861453	+	0.507838i	$0.830445\pi$
$312$	6.47214	−	2.47214i	0.366413	−	0.139957i
$313$	−6.70820	+	6.70820i	−0.379170	+	0.379170i	−0.870803	−	0.491633i	$-0.836400\pi$
$313$	−6.70820	+	6.70820i	−0.379170	+	0.379170i	0.491633	+	0.870803i	$0.336400\pi$
$314$	10.0000			0.564333
$315$	−0.652476	+	11.7082i	−0.0367628	+	0.659683i
$316$	−22.9443	−	22.9443i	−1.29072	−	1.29072i
$317$		−	1.81966i		−	0.102202i	−0.998693	−	0.0511011i	$-0.983727\pi$
$317$		−	1.81966i		−	0.102202i	0.998693	−	0.0511011i	$-0.0162731\pi$
$318$	−16.1803	+	6.18034i	−0.907348	+	0.346576i
$319$			2.47214i			0.138413i
$320$	−9.88854			−0.552786
$321$	3.23607	+	8.47214i	0.180620	+	0.472869i
$322$	−10.0000	−	10.0000i	−0.557278	−	0.557278i
$323$	−21.1803	−	12.7082i	−1.17851	−	0.707103i
$324$	17.8885	+	2.00000i	0.993808	+	0.111111i
$325$	−3.47214	+	3.47214i	−0.192599	+	0.192599i
$326$	11.2361	−	11.2361i	0.622308	−	0.622308i
$327$	−10.9443	−	28.6525i	−0.605220	−	1.58449i
$328$	−15.0557			−0.831314
$329$	−17.8885	−	17.8885i	−0.986227	−	0.986227i
$330$	−0.944272	+	2.11146i	−0.0519805	+	0.116232i
$331$	−13.7639	−	13.7639i	−0.756534	−	0.756534i	0.219156	−	0.975690i	$-0.429670\pi$
$331$	−13.7639	−	13.7639i	−0.756534	−	0.756534i	−0.975690	+	0.219156i	$0.929670\pi$
$332$	−1.05573	+	1.05573i	−0.0579406	+	0.0579406i
$333$	−21.7082	+	19.4164i	−1.18960	+	1.06401i
$334$			4.47214i			0.244704i
$335$	−1.81966	+	1.81966i	−0.0994187	+	0.0994187i
$336$	−8.94427	+	20.0000i	−0.487950	+	1.09109i
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	−0.257992	−	0.966147i	$-0.583061\pi$
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	0.966147	+	0.257992i	$0.0830608\pi$
$338$	11.0000	−	11.0000i	0.598321	−	0.598321i
$339$	−1.18034	−	0.527864i	−0.0641073	−	0.0286696i
$340$	−2.47214	−	9.88854i	−0.134070	−	0.536282i
$341$	4.18034	−	4.18034i	0.226378	−	0.226378i
$342$	18.9443	−	16.9443i	1.02439	−	0.916241i
$343$	8.94427	−	8.94427i	0.482945	−	0.482945i
$344$	−26.8328			−1.44673
$345$	−2.76393	+	6.18034i	−0.148805	+	0.332738i
$346$	6.65248	+	6.65248i	0.357639	+	0.357639i
$347$			22.6525i			1.21605i	0.793918	+	0.608024i	$0.208038\pi$
$347$			22.6525i			1.21605i	−0.793918	+	0.608024i	$0.791962\pi$
$348$	10.4721	−	4.00000i	0.561365	−	0.214423i
$349$	−3.18034	−	3.18034i	−0.170240	−	0.170240i	0.616845	−	0.787085i	$-0.288411\pi$
$349$	−3.18034	−	3.18034i	−0.170240	−	0.170240i	−0.787085	+	0.616845i	$0.788411\pi$
$350$		−	15.5279i		−	0.829999i
$351$	−7.00000	+	2.23607i	−0.373632	+	0.119352i
$352$	−3.05573	+	3.05573i	−0.162871	+	0.162871i
$353$			32.9443i			1.75345i	0.480995	+	0.876723i	$0.340276\pi$
$353$			32.9443i			1.75345i	−0.480995	+	0.876723i	$0.659724\pi$
$354$	9.23607	+	24.1803i	0.490891	+	1.28517i
$355$	−7.70820	+	7.70820i	−0.409109	+	0.409109i
$356$		−	8.94427i		−	0.474045i
$357$	−22.2361	−	3.94427i	−1.17686	−	0.208753i
$358$			3.88854i			0.205516i
$359$	−8.94427			−0.472061			−0.236030	−	0.971746i	$-0.575846\pi$
$359$	−8.94427			−0.472061			−0.236030	+	0.971746i	$0.575846\pi$
$360$	10.4721	+	0.583592i	0.551930	+	0.0307580i
$361$		−	16.8885i		−	0.888871i
$362$	−1.81966	+	1.81966i	−0.0956392	+	0.0956392i
$363$	−6.43769	−	16.8541i	−0.337891	−	0.884611i
$364$		−	8.94427i		−	0.468807i
$365$	4.65248	−	4.65248i	0.243522	−	0.243522i
$366$	−1.70820	+	3.81966i	−0.0892892	+	0.199657i
$367$	12.5279	−	12.5279i	0.653949	−	0.653949i	−0.299992	−	0.953942i	$-0.596984\pi$
$367$	12.5279	−	12.5279i	0.653949	−	0.653949i	0.953942	+	0.299992i	$0.0969842\pi$
$368$	−8.94427	+	8.94427i	−0.466252	+	0.466252i
$369$	15.9443	+	0.888544i	0.830026	+	0.0462557i
$370$	−12.0000	+	12.0000i	−0.623850	+	0.623850i
$371$			22.3607i			1.16091i
$372$	−24.4721	−	10.9443i	−1.26882	−	0.567434i
$373$	23.9443	+	23.9443i	1.23979	+	1.23979i	0.960087	+	0.279700i	$0.0902350\pi$
$373$	23.9443	+	23.9443i	1.23979	+	1.23979i	0.279700	+	0.960087i	$0.409765\pi$
$374$	−3.81966	−	2.29180i	−0.197510	−	0.118506i
$375$	−16.9443	+	6.47214i	−0.874998	+	0.334220i
$376$	−16.0000	+	16.0000i	−0.825137	+	0.825137i
$377$	−3.23607	+	3.23607i	−0.166666	+	0.166666i
$378$	10.6525	−	20.6525i	0.547904	−	1.06225i
$379$			5.12461i			0.263234i	0.991301	+	0.131617i	$0.0420168\pi$
$379$			5.12461i			0.263234i	−0.991301	+	0.131617i	$0.957983\pi$
$380$	10.4721	−	10.4721i	0.537209	−	0.537209i
$381$	−1.88854	−	4.94427i	−0.0967530	−	0.253303i
$382$	−8.00000	−	8.00000i	−0.409316	−	0.409316i
$383$			23.8885i			1.22065i	0.792152	+	0.610324i	$0.208961\pi$
$383$			23.8885i			1.22065i	−0.792152	+	0.610324i	$0.791039\pi$
$384$	17.8885	+	8.00000i	0.912871	+	0.408248i
$385$	2.11146	+	2.11146i	0.107610	+	0.107610i
$386$		−	6.94427i		−	0.353454i
$387$	28.4164	+	1.58359i	1.44449	+	0.0804985i
$388$	−2.94427	−	2.94427i	−0.149473	−	0.149473i
$389$	−3.00000	−	3.00000i	−0.152106	−	0.152106i	0.626952	−	0.779058i	$-0.284302\pi$
$389$	−3.00000	−	3.00000i	−0.152106	−	0.152106i	−0.779058	+	0.626952i	$0.784302\pi$
$390$	−4.00000	+	1.52786i	−0.202548	+	0.0773664i
$391$	−11.1803	−	6.70820i	−0.565414	−	0.339248i
$392$	6.00000	+	6.00000i	0.303046	+	0.303046i
$393$	22.1803	−	8.47214i	1.11885	−	0.427363i
$394$	−13.1246	−	13.1246i	−0.661208	−	0.661208i
$395$	14.1803	+	14.1803i	0.713490	+	0.713490i
$396$	3.41641	−	3.05573i	0.171681	−	0.153556i
$397$	−13.1246			−0.658705			−0.329353	−	0.944207i	$-0.606831\pi$
$397$	−13.1246			−0.658705			−0.329353	+	0.944207i	$0.606831\pi$
$398$	−37.4164			−1.87552
$399$	−11.7082	−	30.6525i	−0.586143	−	1.53454i
$400$	−13.8885			−0.694427
$401$	−9.00000	+	9.00000i	−0.449439	+	0.449439i	−0.895168	−	0.445729i	$-0.852944\pi$
$401$	−9.00000	+	9.00000i	−0.449439	+	0.449439i	0.445729	+	0.895168i	$0.352944\pi$
$402$	4.76393	−	1.81966i	0.237603	−	0.0907564i
$403$	10.9443			0.545173
$404$	12.4721	+	12.4721i	0.620512	+	0.620512i
$405$	−11.0557	−	1.23607i	−0.549364	−	0.0614207i
$406$		−	14.4721i		−	0.718240i
$407$			7.41641i			0.367618i
$408$	−3.52786	+	19.8885i	−0.174655	+	0.984630i
$409$			4.00000i			0.197787i	0.995098	+	0.0988936i	$0.0315304\pi$
$409$			4.00000i			0.197787i	−0.995098	+	0.0988936i	$0.968470\pi$
$410$	9.30495			0.459539
$411$	7.70820	+	20.1803i	0.380218	+	0.995423i
$412$			8.00000i			0.394132i
$413$	33.4164			1.64431
$414$	10.0000	−	8.94427i	0.491473	−	0.439587i
$415$	0.652476	−	0.652476i	0.0320288	−	0.0320288i
$416$	−8.00000			−0.392232
$417$	−35.1246	+	13.4164i	−1.72006	+	0.657004i
$418$		−	6.47214i		−	0.316563i
$419$	−9.81966			−0.479722			−0.239861	−	0.970807i	$-0.577102\pi$
$419$	−9.81966			−0.479722			−0.239861	+	0.970807i	$0.577102\pi$
$420$	5.52786	−	12.3607i	0.269732	−	0.603139i
$421$	2.05573	+	2.05573i	0.100190	+	0.100190i	0.755425	−	0.655235i	$-0.227430\pi$
$421$	2.05573	+	2.05573i	0.100190	+	0.100190i	−0.655235	+	0.755425i	$0.727430\pi$
$422$	−18.6525	+	18.6525i	−0.907988	+	0.907988i
$423$	17.8885	−	16.0000i	0.869771	−	0.777947i
$424$	20.0000			0.971286
$425$	−3.47214	−	13.8885i	−0.168423	−	0.673693i
$426$	20.1803	−	7.70820i	0.977741	−	0.373464i
$427$	3.81966	+	3.81966i	0.184846	+	0.184846i
$428$		−	10.4721i		−	0.506190i
$429$	−0.763932	+	1.70820i	−0.0368830	+	0.0824729i
$430$	16.5836			0.799732
$431$	−4.41641	−	4.41641i	−0.212731	−	0.212731i	0.592696	−	0.805427i	$-0.298064\pi$
$431$	−4.41641	−	4.41641i	−0.212731	−	0.212731i	−0.805427	+	0.592696i	$0.798064\pi$
$432$	−18.4721	−	9.52786i	−0.888741	−	0.458410i
$433$		−	33.8885i		−	1.62858i	−0.580459	−	0.814290i	$-0.697127\pi$
$433$		−	33.8885i		−	1.62858i	0.580459	−	0.814290i	$-0.302873\pi$
$434$	−24.4721	+	24.4721i	−1.17470	+	1.17470i
$435$	−6.47214	+	2.47214i	−0.310315	+	0.118530i
$436$			35.4164i			1.69614i
$437$		−	18.9443i		−	0.906227i
$438$	−12.1803	+	4.65248i	−0.581999	+	0.222304i
$439$	−1.29180	+	1.29180i	−0.0616541	+	0.0616541i	−0.737262	−	0.675607i	$-0.763881\pi$
$439$	−1.29180	+	1.29180i	−0.0616541	+	0.0616541i	0.675607	+	0.737262i	$0.263881\pi$
$440$	1.88854	−	1.88854i	0.0900328	−	0.0900328i
$441$	−6.00000	−	6.70820i	−0.285714	−	0.319438i
$442$	−2.00000	−	8.00000i	−0.0951303	−	0.380521i
$443$	17.7639	+	17.7639i	0.843990	+	0.843990i	0.989375	−	0.145385i	$-0.0464422\pi$
$443$	17.7639	+	17.7639i	0.843990	+	0.843990i	−0.145385	+	0.989375i	$0.546442\pi$
$444$	31.4164	−	12.0000i	1.49096	−	0.569495i
$445$			5.52786i			0.262046i
$446$	−4.94427	−	4.94427i	−0.234118	−	0.234118i
$447$	−31.8328	−	14.2361i	−1.50564	−	0.673343i
$448$	17.8885	−	17.8885i	0.845154	−	0.845154i
$449$	−1.94427	+	1.94427i	−0.0917559	+	0.0917559i	−0.751495	−	0.659739i	$-0.770667\pi$
$449$	−1.94427	+	1.94427i	−0.0917559	+	0.0917559i	0.659739	+	0.751495i	$0.270667\pi$
$450$	14.7082	+	0.819660i	0.693351	+	0.0386391i
$451$	2.87539	−	2.87539i	0.135397	−	0.135397i
$452$	1.05573	+	1.05573i	0.0496573	+	0.0496573i
$453$	21.7082	−	8.29180i	1.01994	−	0.389583i
$454$	14.7639	+	14.7639i	0.692906	+	0.692906i
$455$			5.52786i			0.259150i
$456$	−27.4164	+	10.4721i	−1.28389	+	0.490403i
$457$	−1.41641			−0.0662568			−0.0331284	−	0.999451i	$-0.510547\pi$
$457$	−1.41641			−0.0662568			−0.0331284	+	0.999451i	$0.510547\pi$
$458$	2.58359			0.120723
$459$	4.90983	−	20.8541i	0.229171	−	0.973386i
$460$	5.52786	−	5.52786i	0.257738	−	0.257738i
$461$	18.8885	−	18.8885i	0.879727	−	0.879727i	−0.113779	−	0.993506i	$-0.536296\pi$
$461$	18.8885	−	18.8885i	0.879727	−	0.879727i	0.993506	+	0.113779i	$0.0362956\pi$
$462$	−2.11146	−	5.52786i	−0.0982338	−	0.257180i
$463$			26.0000i			1.20832i	0.796862	+	0.604161i	$0.206492\pi$
$463$			26.0000i			1.20832i	−0.796862	+	0.604161i	$0.793508\pi$
$464$	−12.9443			−0.600923
$465$	15.1246	+	6.76393i	0.701387	+	0.313670i
$466$	22.3607			1.03584
$467$	−25.9443	−	25.9443i	−1.20056	−	1.20056i	−0.973997	−	0.226561i	$-0.927252\pi$
$467$	−25.9443	−	25.9443i	−1.20056	−	1.20056i	−0.226561	−	0.973997i	$-0.572748\pi$
$468$	8.47214	+	0.472136i	0.391625	+	0.0218245i
$469$		−	6.58359i		−	0.304002i
$470$	9.88854	−	9.88854i	0.456125	−	0.456125i
$471$	11.1803	+	5.00000i	0.515163	+	0.230388i
$472$		−	29.8885i		−	1.37573i
$473$	5.12461	−	5.12461i	0.235630	−	0.235630i
$474$	−14.1803	−	37.1246i	−0.651325	−	1.70519i
$475$	14.7082	−	14.7082i	0.674859	−	0.674859i
$476$	22.3607	+	13.4164i	1.02490	+	0.614940i
$477$	−21.1803	−	1.18034i	−0.969781	−	0.0540441i
$478$	−28.9443	−	28.9443i	−1.32388	−	1.32388i
$479$	−30.4164	+	30.4164i	−1.38976	+	1.38976i	−0.563957	+	0.825804i	$0.690722\pi$
$479$	−30.4164	+	30.4164i	−1.38976	+	1.38976i	−0.825804	+	0.563957i	$0.809278\pi$
$480$	−11.0557	−	4.94427i	−0.504623	−	0.225674i
$481$	−9.70820	+	9.70820i	−0.442656	+	0.442656i
$482$	26.9443			1.22728
$483$	−6.18034	−	16.1803i	−0.281215	−	0.736231i
$484$			20.8328i			0.946946i
$485$	1.81966	+	1.81966i	0.0826265	+	0.0826265i
$486$	19.0000	+	11.1803i	0.861858	+	0.507151i
$487$	−6.70820	−	6.70820i	−0.303978	−	0.303978i	0.538590	−	0.842568i	$-0.318957\pi$
$487$	−6.70820	−	6.70820i	−0.303978	−	0.303978i	−0.842568	+	0.538590i	$0.818957\pi$
$488$	3.41641	−	3.41641i	0.154654	−	0.154654i
$489$	18.1803	−	6.94427i	0.822143	−	0.314031i
$490$	−3.70820	−	3.70820i	−0.167520	−	0.167520i
$491$	1.00000	−	1.00000i	0.0451294	−	0.0451294i	−0.684182	−	0.729311i	$-0.739841\pi$
$491$	1.00000	−	1.00000i	0.0451294	−	0.0451294i	0.729311	+	0.684182i	$0.239841\pi$
$492$	−16.8328	−	7.52786i	−0.758882	−	0.339382i
$493$	−3.23607	−	12.9443i	−0.145745	−	0.582981i
$494$	8.47214	−	8.47214i	0.381179	−	0.381179i
$495$	−2.11146	+	1.88854i	−0.0949029	+	0.0848837i
$496$	21.8885	+	21.8885i	0.982825	+	0.982825i
$497$		−	27.8885i		−	1.25097i
$498$	−1.70820	+	0.652476i	−0.0765464	+	0.0292381i
$499$			18.2918i			0.818853i	0.912343	+	0.409427i	$0.134271\pi$
$499$			18.2918i			0.818853i	−0.912343	+	0.409427i	$0.865729\pi$
$500$	20.9443			0.936656
$501$	−2.23607	+	5.00000i	−0.0999001	+	0.223384i
$502$		−	39.3050i		−	1.75427i
$503$	2.23607	−	2.23607i	0.0997013	−	0.0997013i	−0.655497	−	0.755198i	$-0.727541\pi$
$503$	2.23607	−	2.23607i	0.0997013	−	0.0997013i	0.755198	+	0.655497i	$0.227541\pi$
$504$	−20.0000	+	17.8885i	−0.890871	+	0.796819i
$505$	−7.70820	−	7.70820i	−0.343011	−	0.343011i
$506$		−	3.41641i		−	0.151878i
$507$	17.7984	−	6.79837i	0.790454	−	0.301926i
$508$			6.11146i			0.271152i
$509$	19.1803	+	19.1803i	0.850154	+	0.850154i	0.990152	−	0.139998i	$-0.0447097\pi$
$509$	19.1803	+	19.1803i	0.850154	+	0.850154i	−0.139998	+	0.990152i	$0.544710\pi$
$510$	2.18034	−	12.2918i	0.0965471	−	0.544290i
$511$			16.8328i			0.744640i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	29.6525	−	9.47214i	1.30919	−	0.418205i
$514$	−9.05573	−	9.05573i	−0.399431	−	0.399431i
$515$		−	4.94427i		−	0.217871i
$516$	−30.0000	−	13.4164i	−1.32068	−	0.590624i
$517$		−	6.11146i		−	0.268782i
$518$		−	43.4164i		−	1.90761i
$519$	4.11146	+	10.7639i	0.180473	+	0.472484i
$520$	4.94427			0.216821
$521$	16.2361	+	16.2361i	0.711315	+	0.711315i	0.966810	−	0.255495i	$-0.0822385\pi$
$521$	16.2361	+	16.2361i	0.711315	+	0.711315i	−0.255495	+	0.966810i	$0.582239\pi$
$522$	13.7082	+	0.763932i	0.599992	+	0.0334364i
$523$	−13.3607	+	13.3607i	−0.584222	+	0.584222i	−0.936061	−	0.351839i	$-0.885557\pi$
$523$	−13.3607	+	13.3607i	−0.584222	+	0.584222i	0.351839	+	0.936061i	$0.385557\pi$
$524$	−27.4164			−1.19769
$525$	7.76393	−	17.3607i	0.338846	−	0.757682i
$526$	−4.00000	−	4.00000i	−0.174408	−	0.174408i
$527$	−16.4164	+	27.3607i	−0.715110	+	1.19185i
$528$	−4.94427	+	1.88854i	−0.215172	+	0.0821883i
$529$			13.0000i			0.565217i
$530$	−12.3607			−0.536914
$531$	−1.76393	+	31.6525i	−0.0765481	+	1.37360i
$532$			37.8885i			1.64268i
$533$	7.52786			0.326068
$534$	4.47214	−	10.0000i	0.193528	−	0.432742i
$535$			6.47214i			0.279815i
$536$	−5.88854			−0.254346
$537$	−1.94427	+	4.34752i	−0.0839015	+	0.187610i
$538$	25.7082	+	25.7082i	1.10836	+	1.10836i
$539$	−2.29180			−0.0987146
$540$	11.4164	+	5.88854i	0.491284	+	0.253403i
$541$			1.81966i			0.0782333i	0.999235	+	0.0391166i	$0.0124544\pi$
$541$			1.81966i			0.0782333i	−0.999235	+	0.0391166i	$0.987546\pi$
$542$	−7.88854	+	7.88854i	−0.338842	+	0.338842i
$543$	−2.94427	+	1.12461i	−0.126351	+	0.0482617i
$544$	12.0000	−	20.0000i	0.514496	−	0.857493i
$545$		−	21.8885i		−	0.937602i
$546$	4.47214	−	10.0000i	0.191390	−	0.427960i
$547$	−29.2361			−1.25004			−0.625022	−	0.780607i	$-0.714910\pi$
$547$	−29.2361			−1.25004			−0.625022	+	0.780607i	$0.714910\pi$
$548$		−	24.9443i		−	1.06557i
$549$	−3.81966	+	3.41641i	−0.163019	+	0.145809i
$550$	2.65248	−	2.65248i	0.113102	−	0.113102i
$551$	13.7082	−	13.7082i	0.583989	−	0.583989i
$552$	−14.4721	+	5.52786i	−0.615975	+	0.235282i
$553$	−51.3050			−2.18171
$554$	−9.70820	−	9.70820i	−0.412462	−	0.412462i
$555$	−19.4164	+	7.41641i	−0.824181	+	0.314809i
$556$	43.4164			1.84127
$557$	3.18034	+	3.18034i	0.134755	+	0.134755i	0.771267	−	0.636512i	$-0.219623\pi$
$557$	3.18034	+	3.18034i	0.134755	+	0.134755i	−0.636512	+	0.771267i	$0.719623\pi$
$558$	−21.8885	−	24.4721i	−0.926616	−	1.03599i
$559$	13.4164			0.567454
$560$	−11.0557	+	11.0557i	−0.467190	+	0.467190i
$561$	−3.12461	−	4.47214i	−0.131921	−	0.188814i
$562$	17.8885	−	17.8885i	0.754583	−	0.754583i
$563$	18.4164	+	18.4164i	0.776159	+	0.776159i	0.979175	−	0.203016i	$-0.0650744\pi$
$563$	18.4164	+	18.4164i	0.776159	+	0.776159i	−0.203016	+	0.979175i	$0.565074\pi$
$564$	−25.8885	+	9.88854i	−1.09010	+	0.416383i
$565$	−0.652476	−	0.652476i	−0.0274499	−	0.0274499i
$566$	7.70820	+	7.70820i	0.324000	+	0.324000i
$567$	22.2361	−	17.7639i	0.933827	−	0.746015i
$568$	−24.9443			−1.04664
$569$			30.8328i			1.29258i	0.763092	+	0.646289i	$0.223680\pi$
$569$			30.8328i			1.29258i	−0.763092	+	0.646289i	$0.776320\pi$
$570$	16.9443	−	6.47214i	0.709717	−	0.271088i
$571$	−4.87539			−0.204029			−0.102014	−	0.994783i	$-0.532529\pi$
$571$	−4.87539			−0.204029			−0.102014	+	0.994783i	$0.532529\pi$
$572$	1.52786	−	1.52786i	0.0638832	−	0.0638832i
$573$	−4.94427	−	12.9443i	−0.206550	−	0.540755i
$574$	−16.8328	+	16.8328i	−0.702588	+	0.702588i
$575$	7.76393	−	7.76393i	0.323778	−	0.323778i
$576$	16.0000	+	17.8885i	0.666667	+	0.745356i
$577$	−39.8885			−1.66058			−0.830291	−	0.557330i	$-0.811826\pi$
$577$	−39.8885			−1.66058			−0.830291	+	0.557330i	$0.811826\pi$
$578$	23.0000	+	7.00000i	0.956674	+	0.291162i
$579$	3.47214	−	7.76393i	0.144297	−	0.322658i
$580$	8.00000			0.332182
$581$			2.36068i			0.0979375i
$582$	−1.81966	−	4.76393i	−0.0754273	−	0.197471i
$583$	−3.81966	+	3.81966i	−0.158194	+	0.158194i
$584$	15.0557			0.623010
$585$	−5.23607	−	0.291796i	−0.216485	−	0.0120643i
$586$	21.4164			0.884704
$587$	−23.9443	+	23.9443i	−0.988286	+	0.988286i	−0.999932	−	0.0116463i	$-0.996293\pi$
$587$	−23.9443	+	23.9443i	−0.988286	+	0.988286i	0.0116463	+	0.999932i	$0.496293\pi$
$588$	3.70820	+	9.70820i	0.152924	+	0.400360i
$589$	−46.3607			−1.91026
$590$			18.4721i			0.760486i
$591$	−8.11146	−	21.2361i	−0.333661	−	0.873535i
$592$	−38.8328			−1.59602
$593$	2.94427			0.120907			0.0604534	−	0.998171i	$-0.480745\pi$
$593$	2.94427			0.120907			0.0604534	+	0.998171i	$0.480745\pi$
$594$	5.34752	−	1.70820i	0.219412	−	0.0700885i
$595$	−13.8197	−	8.29180i	−0.566551	−	0.339930i
$596$	28.4721	+	28.4721i	1.16626	+	1.16626i
$597$	−41.8328	−	18.7082i	−1.71210	−	0.765676i
$598$	4.47214	−	4.47214i	0.182879	−	0.182879i
$599$			38.3607i			1.56737i	0.621155	+	0.783687i	$0.286664\pi$
$599$			38.3607i			1.56737i	−0.621155	+	0.783687i	$0.713336\pi$
$600$	−15.5279	−	6.94427i	−0.633922	−	0.283499i
$601$	20.7082	−	20.7082i	0.844705	−	0.844705i	−0.144761	−	0.989467i	$-0.546241\pi$
$601$	20.7082	−	20.7082i	0.844705	−	0.844705i	0.989467	+	0.144761i	$0.0462414\pi$
$602$	−30.0000	+	30.0000i	−1.22271	+	1.22271i
$603$	6.23607	+	0.347524i	0.253952	+	0.0141523i
$604$	−26.8328			−1.09181
$605$		−	12.8754i		−	0.523459i
$606$	7.70820	+	20.1803i	0.313124	+	0.819770i
$607$	8.41641	+	8.41641i	0.341611	+	0.341611i	0.856973	−	0.515361i	$-0.172342\pi$
$607$	8.41641	+	8.41641i	0.341611	+	0.341611i	−0.515361	+	0.856973i	$0.672342\pi$
$608$	33.8885			1.37436
$609$	7.23607	−	16.1803i	0.293220	−	0.655660i
$610$	−2.11146	+	2.11146i	−0.0854904	+	0.0854904i
$611$	8.00000	−	8.00000i	0.323645	−	0.323645i
$612$	−13.8885	+	20.4721i	−0.561411	+	0.827537i
$613$	32.8885	+	32.8885i	1.32836	+	1.32836i	0.906805	+	0.421551i	$0.138514\pi$
$613$	32.8885	+	32.8885i	1.32836	+	1.32836i	0.421551	+	0.906805i	$0.361486\pi$
$614$			31.8885i			1.28692i
$615$	10.4033	+	4.65248i	0.419500	+	0.187606i
$616$			6.83282i			0.275302i
$617$	27.6525	−	27.6525i	1.11325	−	1.11325i	0.120538	−	0.992709i	$-0.461538\pi$
$617$	27.6525	−	27.6525i	1.11325	−	1.11325i	0.992709	−	0.120538i	$-0.0384620\pi$
$618$	−4.00000	+	8.94427i	−0.160904	+	0.359791i
$619$	40.0689			1.61050			0.805252	−	0.592932i	$-0.202030\pi$
$619$	40.0689			1.61050			0.805252	+	0.592932i	$0.202030\pi$
$620$	−13.5279	−	13.5279i	−0.543292	−	0.543292i
$621$	15.6525	−	5.00000i	0.628112	−	0.200643i
$622$			12.4721i			0.500087i
$623$	−10.0000	−	10.0000i	−0.400642	−	0.400642i
$624$	−8.94427	−	4.00000i	−0.358057	−	0.160128i
$625$	4.41641			0.176656
$626$	13.4164			0.536228
$627$	3.23607	−	7.23607i	0.129236	−	0.288981i
$628$	−10.0000	−	10.0000i	−0.399043	−	0.399043i
$629$	−9.70820	−	38.8328i	−0.387091	−	1.54837i
$630$	12.3607	−	11.0557i	0.492461	−	0.440471i
$631$			42.3607i			1.68635i	0.537638	+	0.843176i	$0.319317\pi$
$631$			42.3607i			1.68635i	−0.537638	+	0.843176i	$0.680683\pi$
$632$			45.8885i			1.82535i
$633$	−30.1803	+	11.5279i	−1.19956	+	0.458191i
$634$	−1.81966	+	1.81966i	−0.0722679	+	0.0722679i
$635$		−	3.77709i		−	0.149889i
$636$	22.3607	+	10.0000i	0.886659	+	0.396526i
$637$	−3.00000	−	3.00000i	−0.118864	−	0.118864i
$638$	2.47214	−	2.47214i	0.0978728	−	0.0978728i
$639$	26.4164	+	1.47214i	1.04502	+	0.0582368i
$640$	9.88854	+	9.88854i	0.390879	+	0.390879i
$641$	−9.00000	−	9.00000i	−0.355479	−	0.355479i	0.506665	−	0.862143i	$-0.330878\pi$
$641$	−9.00000	−	9.00000i	−0.355479	−	0.355479i	−0.862143	+	0.506665i	$0.830878\pi$
$642$	5.23607	−	11.7082i	0.206651	−	0.462086i
$643$	−30.1803			−1.19020			−0.595098	−	0.803653i	$-0.702887\pi$
$643$	−30.1803			−1.19020			−0.595098	+	0.803653i	$0.702887\pi$
$644$			20.0000i			0.788110i
$645$	18.5410	+	8.29180i	0.730052	+	0.326489i
$646$	8.47214	+	33.8885i	0.333332	+	1.33333i
$647$		−	21.4164i		−	0.841966i	−0.907069	−	0.420983i	$-0.861685\pi$
$647$		−	21.4164i		−	0.841966i	0.907069	−	0.420983i	$-0.138315\pi$
$648$	−15.8885	−	19.8885i	−0.624161	−	0.781296i
$649$	5.70820	+	5.70820i	0.224067	+	0.224067i
$650$	6.94427			0.272377
$651$	−39.5967	+	15.1246i	−1.55192	+	0.592780i
$652$	−22.4721			−0.880077
$653$		−	6.76393i		−	0.264693i	−0.991204	−	0.132347i	$-0.957749\pi$
$653$		−	6.76393i		−	0.264693i	0.991204	−	0.132347i	$-0.0422512\pi$
$654$	−17.7082	+	39.5967i	−0.692446	+	1.54836i
$655$	16.9443			0.662067
$656$	15.0557	+	15.0557i	0.587827	+	0.587827i
$657$	−15.9443	−	0.888544i	−0.622045	−	0.0346654i
$658$			35.7771i			1.39474i
$659$	−20.2361	+	20.2361i	−0.788285	+	0.788285i	−0.981213	−	0.192928i	$-0.938202\pi$
$659$	−20.2361	+	20.2361i	−0.788285	+	0.788285i	0.192928	+	0.981213i	$0.438202\pi$
$660$	3.05573	−	1.16718i	0.118944	−	0.0454326i
$661$	1.76393	−	1.76393i	0.0686090	−	0.0686090i	−0.671970	−	0.740579i	$-0.734551\pi$
$661$	1.76393	−	1.76393i	0.0686090	−	0.0686090i	0.740579	+	0.671970i	$0.234551\pi$
$662$			27.5279i			1.06990i
$663$	1.76393	−	9.94427i	0.0685054	−	0.386204i
$664$	2.11146			0.0819404
$665$		−	23.4164i		−	0.908049i
$666$	41.1246	+	2.29180i	1.59355	+	0.0888053i
$667$	7.23607	−	7.23607i	0.280182	−	0.280182i
$668$	4.47214	−	4.47214i	0.173032	−	0.173032i
$669$	−3.05573	−	8.00000i	−0.118141	−	0.309298i
$670$	3.63932			0.140599
$671$			1.30495i			0.0503771i
$672$	28.9443	−	11.0557i	1.11655	−	0.426484i
$673$	21.3607	+	21.3607i	0.823394	+	0.823394i	0.986593	−	0.163199i	$-0.0521814\pi$
$673$	21.3607	+	21.3607i	0.823394	+	0.823394i	−0.163199	+	0.986593i	$0.552181\pi$
$674$	−26.0000			−1.00148
$675$	16.0344	+	8.27051i	0.617166	+	0.318332i
$676$	−22.0000			−0.846154
$677$			37.5967i			1.44496i	0.691392	+	0.722480i	$0.256998\pi$
$677$			37.5967i			1.44496i	−0.691392	+	0.722480i	$0.743002\pi$
$678$	0.652476	+	1.70820i	0.0250582	+	0.0656032i
$679$	−6.58359			−0.252655
$680$	−7.41641	+	12.3607i	−0.284406	+	0.474010i
$681$	9.12461	+	23.8885i	0.349656	+	0.915411i
$682$	−8.36068			−0.320147
$683$	−11.1246			−0.425671			−0.212836	−	0.977088i	$-0.568270\pi$
$683$	−11.1246			−0.425671			−0.212836	+	0.977088i	$0.568270\pi$
$684$	−35.8885	−	2.00000i	−1.37223	−	0.0764719i
$685$			15.4164i			0.589031i
$686$	−17.8885			−0.682988
$687$	2.88854	+	1.29180i	0.110205	+	0.0492851i
$688$	26.8328	+	26.8328i	1.02299	+	1.02299i
$689$	−10.0000			−0.380970
$690$	8.94427	−	3.41641i	0.340503	−	0.130060i
$691$			17.1246i			0.651451i	0.945464	+	0.325725i	$0.105609\pi$
$691$			17.1246i			0.651451i	−0.945464	+	0.325725i	$0.894391\pi$
$692$		−	13.3050i		−	0.505778i
$693$	0.403252	−	7.23607i	0.0153183	−	0.274875i
$694$	22.6525	−	22.6525i	0.859876	−	0.859876i
$695$	−26.8328			−1.01783
$696$	−14.4721	−	6.47214i	−0.548565	−	0.245326i
$697$	−11.2918	+	18.8197i	−0.427707	+	0.712845i
$698$			6.36068i			0.240755i
$699$	25.0000	+	11.1803i	0.945587	+	0.422879i
$700$	−15.5279	+	15.5279i	−0.586898	+	0.586898i
$701$	−2.70820	−	2.70820i	−0.102287	−	0.102287i	0.654111	−	0.756399i	$-0.273043\pi$
$701$	−2.70820	−	2.70820i	−0.102287	−	0.102287i	−0.756399	+	0.654111i	$0.773043\pi$
$702$	9.23607	+	4.76393i	0.348593	+	0.179803i
$703$	41.1246	−	41.1246i	1.55104	−	1.55104i
$704$	6.11146			0.230334
$705$	16.0000	−	6.11146i	0.602595	−	0.230171i
$706$	32.9443	−	32.9443i	1.23987	−	1.23987i
$707$	27.8885			1.04886
$708$	14.9443	−	33.4164i	0.561640	−	1.25587i
$709$	−3.23607			−0.121533			−0.0607665	−	0.998152i	$-0.519355\pi$
$709$	−3.23607			−0.121533			−0.0607665	+	0.998152i	$0.519355\pi$
$710$	15.4164			0.578567
$711$	2.70820	−	48.5967i	0.101566	−	1.82252i
$712$	−8.94427	+	8.94427i	−0.335201	+	0.335201i
$713$	−24.4721			−0.916489
$714$	18.2918	+	26.1803i	0.684553	+	0.979775i
$715$	−0.944272	+	0.944272i	−0.0353138	+	0.0353138i
$716$	3.88854	−	3.88854i	0.145322	−	0.145322i
$717$	−17.8885	−	46.8328i	−0.668060	−	1.74900i
$718$	8.94427	+	8.94427i	0.333797	+	0.333797i
$719$	18.5279	−	18.5279i	0.690973	−	0.690973i	−0.271473	−	0.962446i	$-0.587511\pi$
$719$	18.5279	−	18.5279i	0.690973	−	0.690973i	0.962446	+	0.271473i	$0.0875108\pi$
$720$	−9.88854	−	11.0557i	−0.368524	−	0.412023i
$721$	8.94427	+	8.94427i	0.333102	+	0.333102i
$722$	−16.8885	+	16.8885i	−0.628527	+	0.628527i
$723$	30.1246	+	13.4721i	1.12035	+	0.501034i
$724$	3.63932			0.135254
$725$	11.2361			0.417297
$726$	−10.4164	+	23.2918i	−0.386589	+	0.864440i
$727$	−0.944272			−0.0350211			−0.0175106	−	0.999847i	$-0.505574\pi$
$727$	−0.944272			−0.0350211			−0.0175106	+	0.999847i	$0.505574\pi$
$728$	−8.94427	+	8.94427i	−0.331497	+	0.331497i
$729$	15.6525	+	22.0000i	0.579721	+	0.814815i
$730$	−9.30495			−0.344392
$731$	−20.1246	+	33.5410i	−0.744336	+	1.24056i
$732$	5.52786	−	2.11146i	0.204316	−	0.0780417i
$733$	24.5967	+	24.5967i	0.908502	+	0.908502i	0.996151	−	0.0876497i	$-0.0279356\pi$
$733$	24.5967	+	24.5967i	0.908502	+	0.908502i	−0.0876497	+	0.996151i	$0.527936\pi$
$734$	−25.0557			−0.924824
$735$	−2.29180	−	6.00000i	−0.0845342	−	0.221313i
$736$	17.8885			0.659380
$737$	1.12461	−	1.12461i	0.0414256	−	0.0414256i
$738$	−15.0557	−	16.8328i	−0.554209	−	0.619625i
$739$	22.1246	−	22.1246i	0.813867	−	0.813867i	−0.171344	−	0.985211i	$-0.554811\pi$
$739$	22.1246	−	22.1246i	0.813867	−	0.813867i	0.985211	+	0.171344i	$0.0548110\pi$
$740$	24.0000			0.882258
$741$	13.7082	−	5.23607i	0.503583	−	0.192352i
$742$	22.3607	−	22.3607i	0.820886	−	0.820886i
$743$	−27.1803	−	27.1803i	−0.997150	−	0.997150i	0.00284599	−	0.999996i	$-0.499094\pi$
$743$	−27.1803	−	27.1803i	−0.997150	−	0.997150i	−0.999996	+	0.00284599i	$0.999094\pi$
$744$	13.5279	+	35.4164i	0.495956	+	1.29843i
$745$	−17.5967	−	17.5967i	−0.644695	−	0.644695i
$746$		−	47.8885i		−	1.75332i
$747$	−2.23607	−	0.124612i	−0.0818134	−	0.00455931i
$748$	1.52786	+	6.11146i	0.0558642	+	0.223457i
$749$	−11.7082	−	11.7082i	−0.427808	−	0.427808i
$750$	23.4164	+	10.4721i	0.855046	+	0.382388i
$751$	23.4721	+	23.4721i	0.856510	+	0.856510i	0.990925	−	0.134415i	$-0.0429154\pi$
$751$	23.4721	+	23.4721i	0.856510	+	0.856510i	−0.134415	+	0.990925i	$0.542915\pi$
$752$	32.0000			1.16692
$753$	19.6525	−	43.9443i	0.716176	−	1.60142i
$754$	6.47214			0.235701
$755$	16.5836			0.603539
$756$	−31.3050	+	10.0000i	−1.13855	+	0.363696i
$757$	6.70820	−	6.70820i	0.243814	−	0.243814i	−0.574612	−	0.818426i	$-0.694847\pi$
$757$	6.70820	−	6.70820i	0.243814	−	0.243814i	0.818426	+	0.574612i	$0.194847\pi$
$758$	5.12461	−	5.12461i	0.186134	−	0.186134i
$759$	1.70820	−	3.81966i	0.0620039	−	0.138645i
$760$	−20.9443			−0.759729
$761$	3.52786			0.127885			0.0639425	−	0.997954i	$-0.479633\pi$
$761$	3.52786			0.127885			0.0639425	+	0.997954i	$0.479633\pi$
$762$	−3.05573	+	6.83282i	−0.110697	+	0.247527i
$763$	39.5967	+	39.5967i	1.43350	+	1.43350i
$764$			16.0000i			0.578860i
$765$	8.58359	−	12.6525i	0.310340	−	0.457451i
$766$	23.8885	−	23.8885i	0.863128	−	0.863128i
$767$			14.9443i			0.539606i
$768$	−9.88854	−	25.8885i	−0.356822	−	0.934172i
$769$	25.7771			0.929546			0.464773	−	0.885430i	$-0.346136\pi$
$769$	25.7771			0.929546			0.464773	+	0.885430i	$0.346136\pi$
$770$		−	4.22291i		−	0.152183i
$771$	−5.59675	−	14.6525i	−0.201562	−	0.527696i
$772$	−6.94427	+	6.94427i	−0.249930	+	0.249930i
$773$	16.0557	+	16.0557i	0.577484	+	0.577484i	0.934209	−	0.356725i	$-0.116107\pi$
$773$	16.0557	+	16.0557i	0.577484	+	0.577484i	−0.356725	+	0.934209i	$0.616107\pi$
$774$	−26.8328	−	30.0000i	−0.964486	−	1.07833i
$775$	−19.0000	−	19.0000i	−0.682500	−	0.682500i
$776$			5.88854i			0.211386i
$777$	21.7082	−	48.5410i	0.778777	−	1.74140i
$778$			6.00000i			0.215110i
$779$	−31.8885			−1.14253
$780$	5.52786	+	2.47214i	0.197929	+	0.0885167i
$781$	4.76393	−	4.76393i	0.170467	−	0.170467i
$782$	4.47214	+	17.8885i	0.159923	+	0.639693i
$783$	14.9443	+	7.70820i	0.534065	+	0.275469i
$784$		−	12.0000i		−	0.428571i
$785$	6.18034	+	6.18034i	0.220586	+	0.220586i
$786$	−30.6525	−	13.7082i	−1.09334	−	0.488955i
$787$	−7.12461			−0.253965			−0.126982	−	0.991905i	$-0.540529\pi$
$787$	−7.12461			−0.253965			−0.126982	+	0.991905i	$0.540529\pi$
$788$			26.2492i			0.935090i
$789$	−2.47214	−	6.47214i	−0.0880104	−	0.230414i
$790$		−	28.3607i		−	1.00903i
$791$	2.36068			0.0839361
$792$	−6.47214	−	0.360680i	−0.229977	−	0.0128162i
$793$	−1.70820	+	1.70820i	−0.0606601	+	0.0606601i
$794$	13.1246	+	13.1246i	0.465775	+	0.465775i
$795$	−13.8197	−	6.18034i	−0.490133	−	0.219194i
$796$	37.4164	+	37.4164i	1.32619	+	1.32619i
$797$	−12.8885	+	12.8885i	−0.456536	+	0.456536i	−0.897517	−	0.440981i	$-0.854631\pi$
$797$	−12.8885	+	12.8885i	−0.456536	+	0.456536i	0.440981	+	0.897517i	$0.354631\pi$
$798$	−18.9443	+	42.3607i	−0.670620	+	1.49955i
$799$	8.00000	+	32.0000i	0.283020	+	1.13208i
$800$	13.8885	+	13.8885i	0.491034	+	0.491034i
$801$	10.0000	−	8.94427i	0.353333	−	0.316030i
$802$	18.0000			0.635602
$803$	−2.87539	+	2.87539i	−0.101470	+	0.101470i
$804$	−6.58359	−	2.94427i	−0.232185	−	0.103836i
$805$		−	12.3607i		−	0.435657i
$806$	−10.9443	−	10.9443i	−0.385496	−	0.385496i
$807$	15.8885	+	41.5967i	0.559303	+	1.46427i
$808$		−	24.9443i		−	0.877536i
$809$	−24.7082	−	24.7082i	−0.868694	−	0.868694i	0.123634	−	0.992328i	$-0.460545\pi$
$809$	−24.7082	−	24.7082i	−0.868694	−	0.868694i	−0.992328	+	0.123634i	$0.960545\pi$
$810$	9.81966	+	12.2918i	0.345028	+	0.431890i
$811$		−	40.5410i		−	1.42359i	−0.702388	−	0.711794i	$-0.747883\pi$
$811$		−	40.5410i		−	1.42359i	0.702388	−	0.711794i	$-0.252117\pi$
$812$	−14.4721	+	14.4721i	−0.507872	+	0.507872i
$813$	−12.7639	+	4.87539i	−0.447651	+	0.170987i
$814$	7.41641	−	7.41641i	0.259945	−	0.259945i
$815$	13.8885			0.486494
$816$	23.4164	−	16.3607i	0.819738	−	0.572738i
$817$	−56.8328			−1.98833
$818$	4.00000	−	4.00000i	0.139857	−	0.139857i
$819$	10.0000	−	8.94427i	0.349428	−	0.312538i
$820$	−9.30495	−	9.30495i	−0.324943	−	0.324943i
$821$		−	3.12461i		−	0.109050i	−0.998512	−	0.0545249i	$-0.982636\pi$
$821$		−	3.12461i		−	0.109050i	0.998512	−	0.0545249i	$-0.0173644\pi$
$822$	12.4721	−	27.8885i	0.435016	−	0.972725i
$823$	−2.70820	−	2.70820i	−0.0944021	−	0.0944021i	0.658329	−	0.752731i	$-0.271264\pi$
$823$	−2.70820	−	2.70820i	−0.0944021	−	0.0944021i	−0.752731	+	0.658329i	$0.771264\pi$
$824$	8.00000	−	8.00000i	0.278693	−	0.278693i
$825$	4.29180	−	1.63932i	0.149421	−	0.0570738i
$826$	−33.4164	−	33.4164i	−1.16271	−	1.16271i
$827$		−	51.0132i		−	1.77390i	−0.461864	−	0.886951i	$-0.652819\pi$
$827$		−	51.0132i		−	1.77390i	0.461864	−	0.886951i	$-0.347181\pi$
$828$	−18.9443	−	1.05573i	−0.658359	−	0.0366891i
$829$	11.9443	−	11.9443i	0.414842	−	0.414842i	−0.468580	−	0.883421i	$-0.655234\pi$
$829$	11.9443	−	11.9443i	0.414842	−	0.414842i	0.883421	+	0.468580i	$0.155234\pi$
$830$	−1.30495			−0.0452955
$831$	−6.00000	−	15.7082i	−0.208138	−	0.544912i
$832$	8.00000	+	8.00000i	0.277350	+	0.277350i
$833$	12.0000	−	3.00000i	0.415775	−	0.103944i
$834$	48.5410	+	21.7082i	1.68084	+	0.751694i
$835$	−2.76393	+	2.76393i	−0.0956498	+	0.0956498i
$836$	−6.47214	+	6.47214i	−0.223844	+	0.223844i
$837$	−12.2361	−	38.3050i	−0.422940	−	1.32401i
$838$	9.81966	+	9.81966i	0.339215	+	0.339215i
$839$	−5.76393	+	5.76393i	−0.198993	+	0.198993i	−0.799568	−	0.600575i	$-0.794938\pi$
$839$	−5.76393	+	5.76393i	−0.198993	+	0.198993i	0.600575	+	0.799568i	$0.294938\pi$
$840$	−17.8885	+	6.83282i	−0.617213	+	0.235755i
$841$	−18.5279			−0.638892
$842$		−	4.11146i		−	0.141690i
$843$	28.9443	−	11.0557i	0.996894	−	0.380780i
$844$	37.3050			1.28409
$845$	13.5967			0.467742
$846$	−33.8885	−	1.88854i	−1.16511	−	0.0649295i
$847$	23.2918	+	23.2918i	0.800316	+	0.800316i
$848$	−20.0000	−	20.0000i	−0.686803	−	0.686803i
$849$	4.76393	+	12.4721i	0.163498	+	0.428043i
$850$	−10.4164	+	17.3607i	−0.357280	+	0.595466i
$851$	21.7082	−	21.7082i	0.744148	−	0.744148i
$852$	−27.8885	−	12.4721i	−0.955446	−	0.427288i
$853$	−29.1246			−0.997208			−0.498604	−	0.866830i	$-0.666154\pi$
$853$	−29.1246			−0.997208			−0.498604	+	0.866830i	$0.666154\pi$
$854$		−	7.63932i		−	0.261412i
$855$	22.1803	+	1.23607i	0.758552	+	0.0422726i
$856$	−10.4721	+	10.4721i	−0.357930	+	0.357930i
$857$	21.1803	+	21.1803i	0.723507	+	0.723507i	0.969318	−	0.245811i	$-0.0790543\pi$
$857$	21.1803	+	21.1803i	0.723507	+	0.723507i	−0.245811	+	0.969318i	$0.579054\pi$
$858$	2.47214	−	0.944272i	0.0843973	−	0.0322369i
$859$	17.0689	+	17.0689i	0.582383	+	0.582383i	0.935557	−	0.353175i	$-0.114898\pi$
$859$	17.0689	+	17.0689i	0.582383	+	0.582383i	−0.353175	+	0.935557i	$0.614898\pi$
$860$	−16.5836	−	16.5836i	−0.565496	−	0.565496i
$861$	−27.2361	+	10.4033i	−0.928203	+	0.354542i
$862$			8.83282i			0.300847i
$863$	−1.88854			−0.0642868			−0.0321434	−	0.999483i	$-0.510233\pi$
$863$	−1.88854			−0.0642868			−0.0321434	+	0.999483i	$0.510233\pi$
$864$	8.94427	+	28.0000i	0.304290	+	0.952579i
$865$			8.22291i			0.279587i
$866$	−33.8885	+	33.8885i	−1.15158	+	1.15158i
$867$	22.2148	+	19.3262i	0.754454	+	0.656353i
$868$	48.9443			1.66128
$869$	−8.76393	−	8.76393i	−0.297296	−	0.297296i
$870$	8.94427	+	4.00000i	0.303239	+	0.135613i
$871$	2.94427			0.0997628
$872$	35.4164	−	35.4164i	1.19935	−	1.19935i
$873$	0.347524	−	6.23607i	0.0117619	−	0.211059i
$874$	−18.9443	+	18.9443i	−0.640800	+	0.640800i
$875$	23.4164	−	23.4164i	0.791619	−	0.791619i
$876$	16.8328	+	7.52786i	0.568728	+	0.254343i
$877$	−17.3475			−0.585784			−0.292892	−	0.956145i	$-0.594618\pi$
$877$	−17.3475			−0.585784			−0.292892	+	0.956145i	$0.594618\pi$
$878$	2.58359			0.0871920
$879$	23.9443	+	10.7082i	0.807620	+	0.361179i
$880$	−3.77709			−0.127326
$881$	25.4721	+	25.4721i	0.858178	+	0.858178i	0.991123	−	0.132945i	$-0.0424435\pi$
$881$	25.4721	+	25.4721i	0.858178	+	0.858178i	−0.132945	+	0.991123i	$0.542443\pi$
$882$	−0.708204	+	12.7082i	−0.0238465	+	0.427907i
$883$	8.41641	+	8.41641i	0.283235	+	0.283235i	0.834398	−	0.551163i	$-0.185816\pi$
$883$	8.41641	+	8.41641i	0.283235	+	0.283235i	−0.551163	+	0.834398i	$0.685816\pi$
$884$	−6.00000	+	10.0000i	−0.201802	+	0.336336i
$885$	−9.23607	+	20.6525i	−0.310467	+	0.694225i
$886$		−	35.5279i		−	1.19358i
$887$	−2.23607	−	2.23607i	−0.0750798	−	0.0750798i	0.668570	−	0.743649i	$-0.266907\pi$
$887$	−2.23607	−	2.23607i	−0.0750798	−	0.0750798i	−0.743649	+	0.668570i	$0.766907\pi$
$888$	−43.4164	−	19.4164i	−1.45696	−	0.651572i
$889$	6.83282	+	6.83282i	0.229165	+	0.229165i
$890$	5.52786	−	5.52786i	0.185294	−	0.185294i
$891$	6.83282	+	0.763932i	0.228908	+	0.0255927i
$892$			9.88854i			0.331093i
$893$	−33.8885	+	33.8885i	−1.13404	+	1.13404i
$894$	17.5967	+	46.0689i	0.588523	+	1.54077i
$895$	−2.40325	+	2.40325i	−0.0803319	+	0.0803319i
$896$	−35.7771			−1.19523
$897$	7.23607	−	2.76393i	0.241605	−	0.0922850i
$898$	3.88854			0.129762
$899$	−17.7082	−	17.7082i	−0.590602	−	0.590602i
$900$	−13.8885	−	15.5279i	−0.462951	−	0.517595i
$901$	15.0000	−	25.0000i	0.499722	−	0.832871i
$902$	−5.75078			−0.191480
$903$	−48.5410	+	18.5410i	−1.61534	+	0.617007i
$904$		−	2.11146i		−	0.0702260i
$905$	−2.24922			−0.0747667
$906$	−30.0000	−	13.4164i	−0.996683	−	0.445730i
$907$	18.1803			0.603668			0.301834	−	0.953360i	$-0.402401\pi$
$907$	18.1803			0.603668			0.301834	+	0.953360i	$0.402401\pi$
$908$		−	29.5279i		−	0.979917i
$909$	−1.47214	+	26.4164i	−0.0488277	+	0.876177i
$910$	5.52786	−	5.52786i	0.183247	−	0.183247i
$911$	−4.41641	−	4.41641i	−0.146322	−	0.146322i	0.630151	−	0.776473i	$-0.282993\pi$
$911$	−4.41641	−	4.41641i	−0.146322	−	0.146322i	−0.776473	+	0.630151i	$0.782993\pi$
$912$	37.8885	+	16.9443i	1.25462	+	0.561081i
$913$	−0.403252	+	0.403252i	−0.0133457	+	0.0133457i
$914$	1.41641	+	1.41641i	0.0468506	+	0.0468506i
$915$	−3.41641	+	1.30495i	−0.112943	+	0.0431404i
$916$	−2.58359	−	2.58359i	−0.0853643	−	0.0853643i
$917$	−30.6525	+	30.6525i	−1.01223	+	1.01223i
$918$	−25.7639	+	15.9443i	−0.850336	+	0.526239i
$919$	−26.8328			−0.885133			−0.442566	−	0.896736i	$-0.645932\pi$
$919$	−26.8328			−0.885133			−0.442566	+	0.896736i	$0.645932\pi$
$920$	−11.0557			−0.364497
$921$	−15.9443	+	35.6525i	−0.525382	+	1.17479i
$922$	−37.7771			−1.24412
$923$	12.4721			0.410525
$924$	−3.41641	+	7.63932i	−0.112392	+	0.251315i
$925$	33.7082			1.10832
$926$	26.0000	−	26.0000i	0.854413	−	0.854413i
$927$	−8.94427	+	8.00000i	−0.293768	+	0.262754i
$928$	12.9443	+	12.9443i	0.424917	+	0.424917i
$929$	15.9443	−	15.9443i	0.523115	−	0.523115i	−0.395396	−	0.918511i	$-0.629393\pi$
$929$	15.9443	−	15.9443i	0.523115	−	0.523115i	0.918511	+	0.395396i	$0.129393\pi$
$930$	−8.36068	−	21.8885i	−0.274157	−	0.717754i
$931$	12.7082	+	12.7082i	0.416495	+	0.416495i
$932$	−22.3607	−	22.3607i	−0.732448	−	0.732448i
$933$	−6.23607	+	13.9443i	−0.204160	+	0.456515i
$934$			51.8885i			1.69785i
$935$	−0.944272	−	3.77709i	−0.0308810	−	0.123524i
$936$	−8.00000	−	8.94427i	−0.261488	−	0.292353i
$937$	−3.52786			−0.115250			−0.0576251	−	0.998338i	$-0.518353\pi$
$937$	−3.52786			−0.115250			−0.0576251	+	0.998338i	$0.518353\pi$
$938$	−6.58359	+	6.58359i	−0.214962	+	0.214962i
$939$	15.0000	+	6.70820i	0.489506	+	0.218914i
$940$	−19.7771			−0.645057
$941$		−	50.5410i		−	1.64759i	−0.566888	−	0.823795i	$-0.691853\pi$
$941$		−	50.5410i		−	1.64759i	0.566888	−	0.823795i	$-0.308147\pi$
$942$	−6.18034	−	16.1803i	−0.201366	−	0.527184i
$943$	−16.8328			−0.548152
$944$	−29.8885	+	29.8885i	−0.972789	+	0.972789i
$945$	19.3475	−	6.18034i	0.629375	−	0.201046i
$946$	−10.2492			−0.333231
$947$			40.7639i			1.32465i	0.749217	+	0.662325i	$0.230430\pi$
$947$			40.7639i			1.32465i	−0.749217	+	0.662325i	$0.769570\pi$
$948$	−22.9443	+	51.3050i	−0.745195	+	1.66631i
$949$	−7.52786			−0.244365
$950$	−29.4164			−0.954394
$951$	−2.94427	+	1.12461i	−0.0954746	+	0.0364680i
$952$	−8.94427	−	35.7771i	−0.289886	−	1.15954i
$953$	−37.4164			−1.21204			−0.606018	−	0.795451i	$-0.707234\pi$
$953$	−37.4164			−1.21204			−0.606018	+	0.795451i	$0.707234\pi$
$954$	20.0000	+	22.3607i	0.647524	+	0.723954i
$955$		−	9.88854i		−	0.319986i
$956$			57.8885i			1.87225i
$957$	4.00000	−	1.52786i	0.129302	−	0.0493888i
$958$	60.8328			1.96542
$959$	−27.8885	−	27.8885i	−0.900568	−	0.900568i
$960$	6.11146	+	16.0000i	0.197246	+	0.516398i
$961$			28.8885i			0.931889i
$962$	19.4164			0.626010
$963$	11.7082	−	10.4721i	0.377292	−	0.337460i
$964$	−26.9443	−	26.9443i	−0.867817	−	0.867817i
$965$	4.29180	−	4.29180i	0.138158	−	0.138158i
$966$	−10.0000	+	22.3607i	−0.321745	+	0.719443i
$967$		−	1.41641i		−	0.0455486i	−0.999741	−	0.0227743i	$-0.992750\pi$
$967$		−	1.41641i		−	0.0455486i	0.999741	−	0.0227743i	$-0.00724991\pi$
$968$	20.8328	−	20.8328i	0.669592	−	0.669592i
$969$	−7.47214	+	42.1246i	−0.240040	+	1.35324i
$970$		−	3.63932i		−	0.116852i
$971$	−11.3607	+	11.3607i	−0.364582	+	0.364582i	−0.865497	−	0.500915i	$-0.832997\pi$
$971$	−11.3607	+	11.3607i	−0.364582	+	0.364582i	0.500915	+	0.865497i	$0.332997\pi$
$972$	−7.81966	−	30.1803i	−0.250816	−	0.968035i
$973$	48.5410	−	48.5410i	1.55615	−	1.55615i
$974$			13.4164i			0.429889i
$975$	7.76393	+	3.47214i	0.248645	+	0.111197i
$976$	−6.83282			−0.218713
$977$	−4.11146			−0.131537			−0.0657686	−	0.997835i	$-0.520950\pi$
$977$	−4.11146			−0.131537			−0.0657686	+	0.997835i	$0.520950\pi$
$978$	−25.1246	−	11.2361i	−0.803396	−	0.359290i
$979$		−	3.41641i		−	0.109189i
$980$			7.41641i			0.236908i
$981$	−39.5967	+	35.4164i	−1.26423	+	1.13076i
$982$	−2.00000			−0.0638226
$983$	28.5967	+	28.5967i	0.912095	+	0.912095i	0.996437	−	0.0843422i	$-0.0268789\pi$
$983$	28.5967	+	28.5967i	0.912095	+	0.912095i	−0.0843422	+	0.996437i	$0.526879\pi$
$984$	9.30495	+	24.3607i	0.296631	+	0.776590i
$985$		−	16.2229i		−	0.516905i
$986$	−9.70820	+	16.1803i	−0.309172	+	0.515287i
$987$	−17.8885	+	40.0000i	−0.569399	+	1.27321i
$988$	−16.9443			−0.539069
$989$	−30.0000			−0.953945
$990$	4.00000	+	0.222912i	0.127128	+	0.00708462i
$991$	−23.3607	−	23.3607i	−0.742076	−	0.742076i	0.230901	−	0.972977i	$-0.425833\pi$
$991$	−23.3607	−	23.3607i	−0.742076	−	0.742076i	−0.972977	+	0.230901i	$0.925833\pi$
$992$		−	43.7771i		−	1.38992i
$993$	−13.7639	+	30.7771i	−0.436785	+	0.976681i
$994$	−27.8885	+	27.8885i	−0.884571	+	0.884571i
$995$	−23.1246	−	23.1246i	−0.733099	−	0.733099i
$996$	2.36068	+	1.05573i	0.0748010	+	0.0334520i
$997$		−	21.5967i		−	0.683976i	−0.939704	−	0.341988i	$-0.888900\pi$
$997$		−	21.5967i		−	0.683976i	0.939704	−	0.341988i	$-0.111100\pi$
$998$	18.2918	−	18.2918i	0.579017	−	0.579017i
$999$	44.8328	+	23.1246i	1.41845	+	0.731630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	816.2.r.a.395.1	✓	4
3.2	odd	2		816.2.r.b.395.1	yes	4
16.3	odd	4		816.2.bm.a.803.1	yes	4
17.13	even	4		816.2.bm.b.251.2	yes	4
48.35	even	4		816.2.bm.b.803.2	yes	4
51.47	odd	4		816.2.bm.a.251.1	yes	4
272.115	odd	4		816.2.r.b.659.1	yes	4
816.659	even	4	inner	816.2.r.a.659.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
816.2.r.a.395.1	✓	4	1.1	even	1	trivial
816.2.r.a.659.1	yes	4	816.659	even	4	inner
816.2.r.b.395.1	yes	4	3.2	odd	2
816.2.r.b.659.1	yes	4	272.115	odd	4
816.2.bm.a.251.1	yes	4	51.47	odd	4
816.2.bm.a.803.1	yes	4	16.3	odd	4
816.2.bm.b.251.2	yes	4	17.13	even	4
816.2.bm.b.803.2	yes	4	48.35	even	4

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:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.618034 - 1.61803i) q^{3} +2.00000i q^{4} -1.23607i q^{5} +(-1.00000 + 2.23607i) q^{6} +(2.23607 + 2.23607i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.23607 + 2.00000i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-0.618034 - 1.61803i) q^{3} +2.00000i q^{4} -1.23607i q^{5} +(-1.00000 + 2.23607i) q^{6} +(2.23607 + 2.23607i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.23607 + 2.00000i) q^{9} +(-1.23607 + 1.23607i) q^{10} +0.763932i q^{11} +(3.23607 - 1.23607i) q^{12} +(-1.00000 + 1.00000i) q^{13} -4.47214i q^{14} +(-2.00000 + 0.763932i) q^{15} -4.00000 q^{16} +(-1.00000 - 4.00000i) q^{17} +(4.23607 + 0.236068i) q^{18} +(4.23607 - 4.23607i) q^{19} +2.47214 q^{20} +(2.23607 - 5.00000i) q^{21} +(0.763932 - 0.763932i) q^{22} +(2.23607 - 2.23607i) q^{23} +(-4.47214 - 2.00000i) q^{24} +3.47214 q^{25} +2.00000 q^{26} +(4.61803 + 2.38197i) q^{27} +(-4.47214 + 4.47214i) q^{28} +3.23607 q^{29} +(2.76393 + 1.23607i) q^{30} +(-5.47214 - 5.47214i) q^{31} +(4.00000 + 4.00000i) q^{32} +(1.23607 - 0.472136i) q^{33} +(-3.00000 + 5.00000i) q^{34} +(2.76393 - 2.76393i) q^{35} +(-4.00000 - 4.47214i) q^{36} +9.70820 q^{37} -8.47214 q^{38} +(2.23607 + 1.00000i) q^{39} +(-2.47214 - 2.47214i) q^{40} +(-3.76393 - 3.76393i) q^{41} +(-7.23607 + 2.76393i) q^{42} +(-6.70820 - 6.70820i) q^{43} -1.52786 q^{44} +(2.47214 + 2.76393i) q^{45} -4.47214 q^{46} -8.00000 q^{47} +(2.47214 + 6.47214i) q^{48} +3.00000i q^{49} +(-3.47214 - 3.47214i) q^{50} +(-5.85410 + 4.09017i) q^{51} +(-2.00000 - 2.00000i) q^{52} +(5.00000 + 5.00000i) q^{53} +(-2.23607 - 7.00000i) q^{54} +0.944272 q^{55} +8.94427 q^{56} +(-9.47214 - 4.23607i) q^{57} +(-3.23607 - 3.23607i) q^{58} +(7.47214 - 7.47214i) q^{59} +(-1.52786 - 4.00000i) q^{60} +1.70820 q^{61} +10.9443i q^{62} +(-9.47214 - 0.527864i) q^{63} -8.00000i q^{64} +(1.23607 + 1.23607i) q^{65} +(-1.70820 - 0.763932i) q^{66} +(-1.47214 - 1.47214i) q^{67} +(8.00000 - 2.00000i) q^{68} +(-5.00000 - 2.23607i) q^{69} -5.52786 q^{70} +(-6.23607 - 6.23607i) q^{71} +(-0.472136 + 8.47214i) q^{72} +(3.76393 + 3.76393i) q^{73} +(-9.70820 - 9.70820i) q^{74} +(-2.14590 - 5.61803i) q^{75} +(8.47214 + 8.47214i) q^{76} +(-1.70820 + 1.70820i) q^{77} +(-1.23607 - 3.23607i) q^{78} +(-11.4721 + 11.4721i) q^{79} +4.94427i q^{80} +(1.00000 - 8.94427i) q^{81} +7.52786i q^{82} +(0.527864 + 0.527864i) q^{83} +(10.0000 + 4.47214i) q^{84} +(-4.94427 + 1.23607i) q^{85} +13.4164i q^{86} +(-2.00000 - 5.23607i) q^{87} +(1.52786 + 1.52786i) q^{88} -4.47214 q^{89} +(0.291796 - 5.23607i) q^{90} -4.47214 q^{91} +(4.47214 + 4.47214i) q^{92} +(-5.47214 + 12.2361i) q^{93} +(8.00000 + 8.00000i) q^{94} +(-5.23607 - 5.23607i) q^{95} +(4.00000 - 8.94427i) q^{96} +(-1.47214 + 1.47214i) q^{97} +(3.00000 - 3.00000i) q^{98} +(-1.52786 - 1.70820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 2 q^{3} - 4 q^{6} + 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 2 * q^3 - 4 * q^6 + 8 * q^8	\( 4 q - 4 q^{2} + 2 q^{3} - 4 q^{6} + 8 q^{8} + 4 q^{10} + 4 q^{12} - 4 q^{13} - 8 q^{15} - 16 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{19} - 8 q^{20} + 12 q^{22} - 4 q^{25} + 8 q^{26} + 14 q^{27} + 4 q^{29} + 20 q^{30} - 4 q^{31} + 16 q^{32} - 4 q^{33} - 12 q^{34} + 20 q^{35} - 16 q^{36} + 12 q^{37} - 16 q^{38} + 8 q^{40} - 24 q^{41} - 20 q^{42} - 24 q^{44} - 8 q^{45} - 32 q^{47} - 8 q^{48} + 4 q^{50} - 10 q^{51} - 8 q^{52} + 20 q^{53} - 32 q^{55} - 20 q^{57} - 4 q^{58} + 12 q^{59} - 24 q^{60} - 20 q^{61} - 20 q^{63} - 4 q^{65} + 20 q^{66} + 12 q^{67} + 32 q^{68} - 20 q^{69} - 40 q^{70} - 16 q^{71} + 16 q^{72} + 24 q^{73} - 12 q^{74} - 22 q^{75} + 16 q^{76} + 20 q^{77} + 4 q^{78} - 28 q^{79} + 4 q^{81} + 20 q^{83} + 40 q^{84} + 16 q^{85} - 8 q^{87} + 24 q^{88} + 28 q^{90} - 4 q^{93} + 32 q^{94} - 12 q^{95} + 16 q^{96} + 12 q^{97} + 12 q^{98} - 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 2 * q^3 - 4 * q^6 + 8 * q^8 + 4 * q^10 + 4 * q^12 - 4 * q^13 - 8 * q^15 - 16 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^19 - 8 * q^20 + 12 * q^22 - 4 * q^25 + 8 * q^26 + 14 * q^27 + 4 * q^29 + 20 * q^30 - 4 * q^31 + 16 * q^32 - 4 * q^33 - 12 * q^34 + 20 * q^35 - 16 * q^36 + 12 * q^37 - 16 * q^38 + 8 * q^40 - 24 * q^41 - 20 * q^42 - 24 * q^44 - 8 * q^45 - 32 * q^47 - 8 * q^48 + 4 * q^50 - 10 * q^51 - 8 * q^52 + 20 * q^53 - 32 * q^55 - 20 * q^57 - 4 * q^58 + 12 * q^59 - 24 * q^60 - 20 * q^61 - 20 * q^63 - 4 * q^65 + 20 * q^66 + 12 * q^67 + 32 * q^68 - 20 * q^69 - 40 * q^70 - 16 * q^71 + 16 * q^72 + 24 * q^73 - 12 * q^74 - 22 * q^75 + 16 * q^76 + 20 * q^77 + 4 * q^78 - 28 * q^79 + 4 * q^81 + 20 * q^83 + 40 * q^84 + 16 * q^85 - 8 * q^87 + 24 * q^88 + 28 * q^90 - 4 * q^93 + 32 * q^94 - 12 * q^95 + 16 * q^96 + 12 * q^97 + 12 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more