LMFDB - Embedded newform 546.2.p.c.281.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(239,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("546.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.p (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 $ x^20 - 4x^19 + 8x^18 - 20x^17 + 56x^16 - 140x^15 + 288x^14 - 532x^13 + 1065x^12 - 2080x^11 + 3712x^10 - 6240x^9 + 9585x^8 - 14364x^7 + 23328x^6 - 34020x^5 + 40824x^4 - 43740x^3 + 52488x^2 - 78732*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			281.5
Root			$0.813276 + 1.52924i$ of defining polynomial
Character	$\chi$	$=$	546.281
Dual form			546.2.p.c.239.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.65641 + 0.506265i) q^{3} -1.00000i q^{4} +(-0.645532 + 0.645532i) q^{5} +(-1.52924 + 0.813276i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.48739 + 1.67717i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.65641 + 0.506265i) q^{3} -1.00000i q^{4} +(-0.645532 + 0.645532i) q^{5} +(-1.52924 + 0.813276i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.48739 + 1.67717i) q^{9} -0.912921i q^{10} +(-0.346115 - 0.346115i) q^{11} +(0.506265 - 1.65641i) q^{12} +(0.964947 + 3.47403i) q^{13} +1.00000i q^{14} +(-1.39608 + 0.742456i) q^{15} -1.00000 q^{16} +3.74401 q^{17} +(-2.94479 + 0.572916i) q^{18} +(-0.564337 - 0.564337i) q^{19} +(0.645532 + 0.645532i) q^{20} +(1.52924 - 0.813276i) q^{21} +0.489480 q^{22} +2.93468 q^{23} +(0.813276 + 1.52924i) q^{24} +4.16658i q^{25} +(-3.13883 - 1.77419i) q^{26} +(3.27105 + 4.03735i) q^{27} +(-0.707107 - 0.707107i) q^{28} +4.18850i q^{29} +(0.462180 - 1.51217i) q^{30} +(-1.21118 - 1.21118i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.398082 - 0.748534i) q^{33} +(-2.64741 + 2.64741i) q^{34} +0.912921i q^{35} +(1.67717 - 2.48739i) q^{36} +(2.17001 - 2.17001i) q^{37} +0.798093 q^{38} +(-0.160431 + 6.24294i) q^{39} -0.912921 q^{40} +(2.35038 - 2.35038i) q^{41} +(-0.506265 + 1.65641i) q^{42} +2.44891i q^{43} +(-0.346115 + 0.346115i) q^{44} +(-2.68836 + 0.523027i) q^{45} +(-2.07513 + 2.07513i) q^{46} +(-7.22377 - 7.22377i) q^{47} +(-1.65641 - 0.506265i) q^{48} -1.00000i q^{49} +(-2.94621 - 2.94621i) q^{50} +(6.20161 + 1.89546i) q^{51} +(3.47403 - 0.964947i) q^{52} -5.03273i q^{53} +(-5.16782 - 0.541858i) q^{54} +0.446857 q^{55} +1.00000 q^{56} +(-0.649069 - 1.22048i) q^{57} +(-2.96172 - 2.96172i) q^{58} +(2.23605 + 2.23605i) q^{59} +(0.742456 + 1.39608i) q^{60} -4.58319 q^{61} +1.71287 q^{62} +(2.94479 - 0.572916i) q^{63} +1.00000i q^{64} +(-2.86550 - 1.61969i) q^{65} +(0.810780 + 0.247807i) q^{66} +(1.55654 + 1.55654i) q^{67} -3.74401i q^{68} +(4.86103 + 1.48572i) q^{69} +(-0.645532 - 0.645532i) q^{70} +(-1.98965 + 1.98965i) q^{71} +(0.572916 + 2.94479i) q^{72} +(-2.94861 + 2.94861i) q^{73} +3.06885i q^{74} +(-2.10939 + 6.90156i) q^{75} +(-0.564337 + 0.564337i) q^{76} -0.489480 q^{77} +(-4.30098 - 4.52787i) q^{78} -5.80866 q^{79} +(0.645532 - 0.645532i) q^{80} +(3.37423 + 8.34353i) q^{81} +3.32394i q^{82} +(1.45281 - 1.45281i) q^{83} +(-0.813276 - 1.52924i) q^{84} +(-2.41688 + 2.41688i) q^{85} +(-1.73164 - 1.73164i) q^{86} +(-2.12049 + 6.93788i) q^{87} -0.489480i q^{88} +(-12.0210 - 12.0210i) q^{89} +(1.53112 - 2.27079i) q^{90} +(3.13883 + 1.77419i) q^{91} -2.93468i q^{92} +(-1.39303 - 2.61939i) q^{93} +10.2160 q^{94} +0.728595 q^{95} +(1.52924 - 0.813276i) q^{96} +(6.69250 + 6.69250i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-0.280431 - 1.44142i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9}+O(q^{10}) $ 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9	$ 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9 - 16 * q^11 - 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 + 12 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 24 * q^27 + 12 * q^30 - 8 * q^31 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * q^54 + 28 * q^55 + 20 * q^56 + 36 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 48 * q^62 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * q^78 - 64 * q^79 + 4 * q^80 + 32 * q^81 - 24 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^89 - 8 * q^90 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.65641	+	0.506265i	0.956329	+	0.292292i
$3$	1.65641	+	0.506265i	0.956329	+	0.292292i
$4$		−	1.00000i		−	0.500000i
$5$	−0.645532	+	0.645532i	−0.288691	+	0.288691i	−0.836562	−	0.547872i	$-0.815438\pi$
$5$	−0.645532	+	0.645532i	−0.288691	+	0.288691i	0.547872	+	0.836562i	$0.315438\pi$
$6$	−1.52924	+	0.813276i	−0.624311	+	0.332018i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.48739	+	1.67717i	0.829130	+	0.559055i
$10$		−	0.912921i		−	0.288691i
$11$	−0.346115	−	0.346115i	−0.104358	−	0.104358i	0.653000	−	0.757358i	$-0.273510\pi$
$11$	−0.346115	−	0.346115i	−0.104358	−	0.104358i	−0.757358	+	0.653000i	$0.773510\pi$
$12$	0.506265	−	1.65641i	0.146146	−	0.478165i
$13$	0.964947	+	3.47403i	0.267628	+	0.963522i
$13$	0.964947	+	3.47403i	0.267628	+	0.963522i
$14$			1.00000i			0.267261i
$15$	−1.39608	+	0.742456i	−0.360466	+	0.191701i
$16$	−1.00000			−0.250000
$17$	3.74401			0.908055			0.454028	−	0.890988i	$-0.349987\pi$
$17$	3.74401			0.908055			0.454028	+	0.890988i	$0.349987\pi$
$18$	−2.94479	+	0.572916i	−0.694093	+	0.135038i
$19$	−0.564337	−	0.564337i	−0.129468	−	0.129468i	0.639404	−	0.768871i	$-0.279181\pi$
$19$	−0.564337	−	0.564337i	−0.129468	−	0.129468i	−0.768871	+	0.639404i	$0.779181\pi$
$20$	0.645532	+	0.645532i	0.144345	+	0.144345i
$21$	1.52924	−	0.813276i	0.333708	−	0.177471i
$22$	0.489480			0.104358
$23$	2.93468			0.611922			0.305961	−	0.952044i	$-0.401022\pi$
$23$	2.93468			0.611922			0.305961	+	0.952044i	$0.401022\pi$
$24$	0.813276	+	1.52924i	0.166009	+	0.312155i
$25$			4.16658i			0.833315i
$26$	−3.13883	−	1.77419i	−0.615575	−	0.347947i
$27$	3.27105	+	4.03735i	0.629514	+	0.776989i
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$			4.18850i			0.777785i	0.921283	+	0.388893i	$0.127142\pi$
$29$			4.18850i			0.777785i	−0.921283	+	0.388893i	$0.872858\pi$
$30$	0.462180	−	1.51217i	0.0843821	−	0.276083i
$31$	−1.21118	−	1.21118i	−0.217534	−	0.217534i	0.589924	−	0.807459i	$-0.299158\pi$
$31$	−1.21118	−	1.21118i	−0.217534	−	0.217534i	−0.807459	+	0.589924i	$0.799158\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.398082	−	0.748534i	−0.0692973	−	0.130303i
$34$	−2.64741	+	2.64741i	−0.454028	+	0.454028i
$35$			0.912921i			0.154312i
$36$	1.67717	−	2.48739i	0.279528	−	0.414565i
$37$	2.17001	−	2.17001i	0.356747	−	0.356747i	−0.505866	−	0.862612i	$-0.668827\pi$
$37$	2.17001	−	2.17001i	0.356747	−	0.356747i	0.862612	+	0.505866i	$0.168827\pi$
$38$	0.798093			0.129468
$39$	−0.160431	+	6.24294i	−0.0256896	+	0.999670i
$40$	−0.912921			−0.144345
$41$	2.35038	−	2.35038i	0.367068	−	0.367068i	−0.499339	−	0.866407i	$-0.666424\pi$
$41$	2.35038	−	2.35038i	0.367068	−	0.367068i	0.866407	+	0.499339i	$0.166424\pi$
$42$	−0.506265	+	1.65641i	−0.0781184	+	0.255590i
$43$			2.44891i			0.373455i	0.982412	+	0.186727i	$0.0597881\pi$
$43$			2.44891i			0.373455i	−0.982412	+	0.186727i	$0.940212\pi$
$44$	−0.346115	+	0.346115i	−0.0521788	+	0.0521788i
$45$	−2.68836	+	0.523027i	−0.400757	+	0.0779683i
$46$	−2.07513	+	2.07513i	−0.305961	+	0.305961i
$47$	−7.22377	−	7.22377i	−1.05370	−	1.05370i	−0.998474	−	0.0552213i	$-0.982414\pi$
$47$	−7.22377	−	7.22377i	−1.05370	−	1.05370i	−0.0552213	−	0.998474i	$-0.517586\pi$
$48$	−1.65641	−	0.506265i	−0.239082	−	0.0730731i
$49$		−	1.00000i		−	0.142857i
$50$	−2.94621	−	2.94621i	−0.416658	−	0.416658i
$51$	6.20161	+	1.89546i	0.868400	+	0.265418i
$52$	3.47403	−	0.964947i	0.481761	−	0.133814i
$53$		−	5.03273i		−	0.691298i	−0.938364	−	0.345649i	$-0.887659\pi$
$53$		−	5.03273i		−	0.691298i	0.938364	−	0.345649i	$-0.112341\pi$
$54$	−5.16782	−	0.541858i	−0.703252	−	0.0737376i
$55$	0.446857			0.0602542
$56$	1.00000			0.133631
$57$	−0.649069	−	1.22048i	−0.0859713	−	0.161656i
$58$	−2.96172	−	2.96172i	−0.388893	−	0.388893i
$59$	2.23605	+	2.23605i	0.291109	+	0.291109i	0.837518	−	0.546409i	$-0.184006\pi$
$59$	2.23605	+	2.23605i	0.291109	+	0.291109i	−0.546409	+	0.837518i	$0.684006\pi$
$60$	0.742456	+	1.39608i	0.0958507	+	0.180233i
$61$	−4.58319			−0.586818			−0.293409	−	0.955987i	$-0.594790\pi$
$61$	−4.58319			−0.586818			−0.293409	+	0.955987i	$0.594790\pi$
$62$	1.71287			0.217534
$63$	2.94479	−	0.572916i	0.371008	−	0.0721806i
$64$			1.00000i			0.125000i
$65$	−2.86550	−	1.61969i	−0.355422	−	0.200898i
$66$	0.810780	+	0.247807i	0.0998002	+	0.0305029i
$67$	1.55654	+	1.55654i	0.190162	+	0.190162i	0.795766	−	0.605604i	$-0.207069\pi$
$67$	1.55654	+	1.55654i	0.190162	+	0.190162i	−0.605604	+	0.795766i	$0.707069\pi$
$68$		−	3.74401i		−	0.454028i
$69$	4.86103	+	1.48572i	0.585199	+	0.178860i
$70$	−0.645532	−	0.645532i	−0.0771559	−	0.0771559i
$71$	−1.98965	+	1.98965i	−0.236128	+	0.236128i	−0.815245	−	0.579117i	$-0.803398\pi$
$71$	−1.98965	+	1.98965i	−0.236128	+	0.236128i	0.579117	+	0.815245i	$0.303398\pi$
$72$	0.572916	+	2.94479i	0.0675188	+	0.347046i
$73$	−2.94861	+	2.94861i	−0.345108	+	0.345108i	−0.858284	−	0.513175i	$-0.828469\pi$
$73$	−2.94861	+	2.94861i	−0.345108	+	0.345108i	0.513175	+	0.858284i	$0.328469\pi$
$74$			3.06885i			0.356747i
$75$	−2.10939	+	6.90156i	−0.243572	+	0.796923i
$76$	−0.564337	+	0.564337i	−0.0647339	+	0.0647339i
$77$	−0.489480			−0.0557815
$78$	−4.30098	−	4.52787i	−0.486990	−	0.512680i
$79$	−5.80866			−0.653525			−0.326762	−	0.945106i	$-0.605958\pi$
$79$	−5.80866			−0.653525			−0.326762	+	0.945106i	$0.605958\pi$
$80$	0.645532	−	0.645532i	0.0721727	−	0.0721727i
$81$	3.37423	+	8.34353i	0.374915	+	0.927059i
$82$			3.32394i			0.367068i
$83$	1.45281	−	1.45281i	0.159467	−	0.159467i	−0.622864	−	0.782330i	$-0.714031\pi$
$83$	1.45281	−	1.45281i	0.159467	−	0.159467i	0.782330	+	0.622864i	$0.214031\pi$
$84$	−0.813276	−	1.52924i	−0.0887356	−	0.166854i
$85$	−2.41688	+	2.41688i	−0.262147	+	0.262147i
$86$	−1.73164	−	1.73164i	−0.186727	−	0.186727i
$87$	−2.12049	+	6.93788i	−0.227341	+	0.743819i
$88$		−	0.489480i		−	0.0521788i
$89$	−12.0210	−	12.0210i	−1.27423	−	1.27423i	−0.943848	−	0.330380i	$-0.892823\pi$
$89$	−12.0210	−	12.0210i	−1.27423	−	1.27423i	−0.330380	−	0.943848i	$-0.607177\pi$
$90$	1.53112	−	2.27079i	0.161394	−	0.239362i
$91$	3.13883	+	1.77419i	0.329039	+	0.185986i
$92$		−	2.93468i		−	0.305961i
$93$	−1.39303	−	2.61939i	−0.144451	−	0.271618i
$94$	10.2160			1.05370
$95$	0.728595			0.0747523
$96$	1.52924	−	0.813276i	0.156078	−	0.0830046i
$97$	6.69250	+	6.69250i	0.679520	+	0.679520i	0.959892	−	0.280371i	$-0.0904576\pi$
$97$	6.69250	+	6.69250i	0.679520	+	0.679520i	−0.280371	+	0.959892i	$0.590458\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$	−0.280431	−	1.44142i	−0.0281844	−	0.144868i
$100$	4.16658			0.416658
$101$	13.4516			1.33848			0.669241	−	0.743045i	$-0.266619\pi$
$101$	13.4516			1.33848			0.669241	+	0.743045i	$0.266619\pi$
$102$	−5.72550	+	3.04491i	−0.566909	+	0.301491i
$103$		−	6.61463i		−	0.651759i	−0.945411	−	0.325879i	$-0.894340\pi$
$103$		−	6.61463i		−	0.651759i	0.945411	−	0.325879i	$-0.105660\pi$
$104$	−1.77419	+	3.13883i	−0.173974	+	0.307788i
$105$	−0.462180	+	1.51217i	−0.0451041	+	0.147573i
$106$	3.55868	+	3.55868i	0.345649	+	0.345649i
$107$			0.232092i			0.0224372i	0.999937	+	0.0112186i	$0.00357107\pi$
$107$			0.232092i			0.0224372i	−0.999937	+	0.0112186i	$0.996429\pi$
$108$	4.03735	−	3.27105i	0.388495	−	0.314757i
$109$	−8.15828	−	8.15828i	−0.781422	−	0.781422i	0.198649	−	0.980071i	$-0.436345\pi$
$109$	−8.15828	−	8.15828i	−0.781422	−	0.781422i	−0.980071	+	0.198649i	$0.936345\pi$
$110$	−0.315975	+	0.315975i	−0.0301271	+	0.0301271i
$111$	4.69302	−	2.49582i	0.445441	−	0.236893i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$		−	9.58107i		−	0.901311i	−0.892698	−	0.450656i	$-0.851190\pi$
$113$		−	9.58107i		−	0.901311i	0.892698	−	0.450656i	$-0.148810\pi$
$114$	1.32197	+	0.404047i	0.123814	+	0.0378424i
$115$	−1.89443	+	1.89443i	−0.176656	+	0.176656i
$116$	4.18850			0.388893
$117$	−3.42632	+	10.2596i	−0.316764	+	0.948505i
$118$	−3.16225			−0.291109
$119$	2.64741	−	2.64741i	0.242688	−	0.242688i
$120$	−1.51217	−	0.462180i	−0.138042	−	0.0421911i
$121$		−	10.7604i		−	0.978219i
$122$	3.24081	−	3.24081i	0.293409	−	0.293409i
$123$	5.08311	−	2.70328i	0.458329	−	0.243747i
$124$	−1.21118	+	1.21118i	−0.108767	+	0.108767i
$125$	−5.91732	−	5.91732i	−0.529261	−	0.529261i
$126$	−1.67717	+	2.48739i	−0.149414	+	0.221594i
$127$		−	16.8593i		−	1.49602i	−0.663686	−	0.748012i	$-0.731009\pi$
$127$		−	16.8593i		−	1.49602i	0.663686	−	0.748012i	$-0.268991\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−1.23980	+	4.05640i	−0.109158	+	0.357146i
$130$	3.17151	−	0.880920i	0.278160	−	0.0772618i
$131$		−	21.4186i		−	1.87135i	−0.352862	−	0.935676i	$-0.614791\pi$
$131$		−	21.4186i		−	1.87135i	0.352862	−	0.935676i	$-0.385209\pi$
$132$	−0.748534	+	0.398082i	−0.0651515	+	0.0346486i
$133$	−0.798093			−0.0692034
$134$	−2.20128			−0.190162
$135$	−4.71781	−	0.494674i	−0.406045	−	0.0425747i
$136$	2.64741	+	2.64741i	0.227014	+	0.227014i
$137$	4.89961	+	4.89961i	0.418602	+	0.418602i	0.884722	−	0.466120i	$-0.154348\pi$
$137$	4.89961	+	4.89961i	0.418602	+	0.418602i	−0.466120	+	0.884722i	$0.654348\pi$
$138$	−4.48783	+	2.38670i	−0.382030	+	0.203169i
$139$	4.43061			0.375799			0.187900	−	0.982188i	$-0.439832\pi$
$139$	4.43061			0.375799			0.187900	+	0.982188i	$0.439832\pi$
$140$	0.912921			0.0771559
$141$	−8.30839	−	15.6227i	−0.699692	−	1.31567i
$142$		−	2.81379i		−	0.236128i
$143$	0.868431	−	1.53640i	0.0726218	−	0.128480i
$144$	−2.48739	−	1.67717i	−0.207283	−	0.139764i
$145$	−2.70381	−	2.70381i	−0.224540	−	0.224540i
$146$		−	4.16996i		−	0.345108i
$147$	0.506265	−	1.65641i	0.0417560	−	0.136618i
$148$	−2.17001	−	2.17001i	−0.178373	−	0.178373i
$149$	−7.00938	+	7.00938i	−0.574231	+	0.574231i	−0.933308	−	0.359077i	$-0.883091\pi$
$149$	−7.00938	+	7.00938i	−0.574231	+	0.574231i	0.359077	+	0.933308i	$0.383091\pi$
$150$	−3.38857	−	6.37171i	−0.276676	−	0.520248i
$151$	6.30515	−	6.30515i	0.513105	−	0.513105i	−0.402371	−	0.915477i	$-0.631814\pi$
$151$	6.30515	−	6.30515i	0.513105	−	0.513105i	0.915477	+	0.402371i	$0.131814\pi$
$152$		−	0.798093i		−	0.0647339i
$153$	9.31281	+	6.27932i	0.752896	+	0.507653i
$154$	0.346115	−	0.346115i	0.0278907	−	0.0278907i
$155$	1.56371			0.125600
$156$	6.24294	+	0.160431i	0.499835	+	0.0128448i
$157$	−19.2209			−1.53400			−0.766998	−	0.641649i	$-0.778250\pi$
$157$	−19.2209			−1.53400			−0.766998	+	0.641649i	$0.778250\pi$
$158$	4.10734	−	4.10734i	0.326762	−	0.326762i
$159$	2.54789	−	8.33626i	0.202061	−	0.661109i
$160$			0.912921i			0.0721727i
$161$	2.07513	−	2.07513i	0.163543	−	0.163543i
$162$	−8.28571	−	3.51383i	−0.650987	−	0.276072i
$163$	9.47285	−	9.47285i	0.741971	−	0.741971i	−0.230986	−	0.972957i	$-0.574195\pi$
$163$	9.47285	−	9.47285i	0.741971	−	0.741971i	0.972957	+	0.230986i	$0.0741953\pi$
$164$	−2.35038	−	2.35038i	−0.183534	−	0.183534i
$165$	0.740178	+	0.226228i	0.0576228	+	0.0176118i
$166$			2.05459i			0.159467i
$167$	−17.0105	−	17.0105i	−1.31631	−	1.31631i	−0.916674	−	0.399636i	$-0.869137\pi$
$167$	−17.0105	−	17.0105i	−1.31631	−	1.31631i	−0.399636	−	0.916674i	$-0.630863\pi$
$168$	1.65641	+	0.506265i	0.127795	+	0.0390592i
$169$	−11.1378	+	6.70451i	−0.856750	+	0.515731i
$170$		−	3.41798i		−	0.262147i
$171$	−0.457240	−	2.35021i	−0.0349660	−	0.179725i
$172$	2.44891			0.186727
$173$	−0.945226			−0.0718642			−0.0359321	−	0.999354i	$-0.511440\pi$
$173$	−0.945226			−0.0718642			−0.0359321	+	0.999354i	$0.511440\pi$
$174$	−3.40641	−	6.40524i	−0.258239	−	0.485580i
$175$	2.94621	+	2.94621i	0.222713	+	0.222713i
$176$	0.346115	+	0.346115i	0.0260894	+	0.0260894i
$177$	2.57178	+	4.83585i	0.193307	+	0.363485i
$178$	17.0003			1.27423
$179$	18.1644			1.35767			0.678834	−	0.734292i	$-0.262485\pi$
$179$	18.1644			1.35767			0.678834	+	0.734292i	$0.262485\pi$
$180$	0.523027	+	2.68836i	0.0389841	+	0.200378i
$181$			18.4772i			1.37340i	0.726940	+	0.686701i	$0.240942\pi$
$181$			18.4772i			1.37340i	−0.726940	+	0.686701i	$0.759058\pi$
$182$	−3.47403	+	0.964947i	−0.257512	+	0.0715266i
$183$	−7.59165	−	2.32031i	−0.561191	−	0.171522i
$184$	2.07513	+	2.07513i	0.152981	+	0.152981i
$185$			2.80162i			0.205979i
$186$	2.83721	+	0.867164i	0.208034	+	0.0635836i
$187$	−1.29586	−	1.29586i	−0.0947625	−	0.0947625i
$188$	−7.22377	+	7.22377i	−0.526848	+	0.526848i
$189$	5.16782	+	0.541858i	0.375904	+	0.0394144i
$190$	−0.515195	+	0.515195i	−0.0373762	+	0.0373762i
$191$			14.1792i			1.02597i	0.858398	+	0.512984i	$0.171460\pi$
$191$			14.1792i			1.02597i	−0.858398	+	0.512984i	$0.828540\pi$
$192$	−0.506265	+	1.65641i	−0.0365365	+	0.119541i
$193$	3.37846	−	3.37846i	0.243187	−	0.243187i	−0.574980	−	0.818167i	$-0.694990\pi$
$193$	3.37846	−	3.37846i	0.243187	−	0.243187i	0.818167	+	0.574980i	$0.194990\pi$
$194$	−9.46462			−0.679520
$195$	−3.92645	−	4.13358i	−0.281179	−	0.296012i
$196$	−1.00000			−0.0714286
$197$	1.50781	−	1.50781i	0.107427	−	0.107427i	−0.651350	−	0.758777i	$-0.725797\pi$
$197$	1.50781	−	1.50781i	0.107427	−	0.107427i	0.758777	+	0.651350i	$0.225797\pi$
$198$	1.21753	+	0.820940i	0.0865260	+	0.0583416i
$199$		−	11.1999i		−	0.793937i	−0.917832	−	0.396968i	$-0.870062\pi$
$199$		−	11.1999i		−	0.793937i	0.917832	−	0.396968i	$-0.129938\pi$
$200$	−2.94621	+	2.94621i	−0.208329	+	0.208329i
$201$	1.79025	+	3.36629i	0.126274	+	0.237440i
$202$	−9.51170	+	9.51170i	−0.669241	+	0.669241i
$203$	2.96172	+	2.96172i	0.207872	+	0.207872i
$204$	1.89546	−	6.20161i	0.132709	−	0.434200i
$205$			3.03449i			0.211938i
$206$	4.67725	+	4.67725i	0.325879	+	0.325879i
$207$	7.29969	+	4.92194i	0.507364	+	0.342098i
$208$	−0.964947	−	3.47403i	−0.0669070	−	0.240881i
$209$			0.390651i			0.0270219i
$210$	−0.742456	−	1.39608i	−0.0512343	−	0.0963385i
$211$	16.7046			1.14999			0.574997	−	0.818156i	$-0.305003\pi$
$211$	16.7046			1.14999			0.574997	+	0.818156i	$0.305003\pi$
$212$	−5.03273			−0.345649
$213$	−4.30297	+	2.28839i	−0.294834	+	0.156798i
$214$	−0.164114	−	0.164114i	−0.0112186	−	0.0112186i
$215$	−1.58085	−	1.58085i	−0.107813	−	0.107813i
$216$	−0.541858	+	5.16782i	−0.0368688	+	0.351626i
$217$	−1.71287			−0.116277
$218$	11.5376			0.781422
$219$	−6.37688	+	3.39133i	−0.430910	+	0.229165i
$220$		−	0.446857i		−	0.0301271i
$221$	3.61277	+	13.0068i	0.243021	+	0.874932i
$222$	−1.55365	+	5.08328i	−0.104274	+	0.341167i
$223$	−16.2269	−	16.2269i	−1.08663	−	1.08663i	−0.995873	−	0.0907580i	$-0.971071\pi$
$223$	−16.2269	−	16.2269i	−1.08663	−	1.08663i	−0.0907580	−	0.995873i	$-0.528929\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−6.98804	+	10.3639i	−0.465869	+	0.690927i
$226$	6.77484	+	6.77484i	0.450656	+	0.450656i
$227$	−18.5844	+	18.5844i	−1.23349	+	1.23349i	−0.270871	+	0.962616i	$0.587312\pi$
$227$	−18.5844	+	18.5844i	−1.23349	+	1.23349i	−0.962616	+	0.270871i	$0.912688\pi$
$228$	−1.22048	+	0.649069i	−0.0808281	+	0.0429857i
$229$	−10.3015	+	10.3015i	−0.680741	+	0.680741i	−0.960167	−	0.279426i	$-0.909856\pi$
$229$	−10.3015	+	10.3015i	−0.680741	+	0.680741i	0.279426	+	0.960167i	$0.409856\pi$
$230$		−	2.67913i		−	0.176656i
$231$	−0.810780	−	0.247807i	−0.0533454	−	0.0163045i
$232$	−2.96172	+	2.96172i	−0.194446	+	0.194446i
$233$	29.5763			1.93761			0.968803	−	0.247830i	$-0.0797176\pi$
$233$	29.5763			1.93761			0.968803	+	0.247830i	$0.0797176\pi$
$234$	−4.83189	−	9.67744i	−0.315871	−	0.632634i
$235$	9.32636			0.608384
$236$	2.23605	−	2.23605i	0.145555	−	0.145555i
$237$	−9.62152	−	2.94072i	−0.624985	−	0.191020i
$238$			3.74401i			0.242688i
$239$	−4.42519	+	4.42519i	−0.286242	+	0.286242i	−0.835592	−	0.549350i	$-0.814875\pi$
$239$	−4.42519	+	4.42519i	−0.286242	+	0.286242i	0.549350	+	0.835592i	$0.314875\pi$
$240$	1.39608	−	0.742456i	0.0901164	−	0.0479253i
$241$	−11.6682	+	11.6682i	−0.751615	+	0.751615i	−0.974781	−	0.223165i	$-0.928361\pi$
$241$	−11.6682	+	11.6682i	−0.751615	+	0.751615i	0.223165	+	0.974781i	$0.428361\pi$
$242$	7.60876	+	7.60876i	0.489109	+	0.489109i
$243$	1.36507	+	15.5286i	0.0875694	+	0.996158i
$244$			4.58319i			0.293409i
$245$	0.645532	+	0.645532i	0.0412416	+	0.0412416i
$246$	−1.68280	+	5.50581i	−0.107291	+	0.351038i
$247$	1.41597	−	2.50508i	0.0900958	−	0.159394i
$248$		−	1.71287i		−	0.108767i
$249$	3.14196	−	1.67094i	0.199114	−	0.105892i
$250$	8.36836			0.529261
$251$	−14.2635			−0.900304			−0.450152	−	0.892952i	$-0.648630\pi$
$251$	−14.2635			−0.900304			−0.450152	+	0.892952i	$0.648630\pi$
$252$	−0.572916	−	2.94479i	−0.0360903	−	0.185504i
$253$	−1.01574	−	1.01574i	−0.0638587	−	0.0638587i
$254$	11.9213	+	11.9213i	0.748012	+	0.748012i
$255$	−5.22692	+	2.77976i	−0.327323	+	0.174075i
$256$	1.00000			0.0625000
$257$	−14.5921			−0.910229			−0.455114	−	0.890433i	$-0.650402\pi$
$257$	−14.5921			−0.910229			−0.455114	+	0.890433i	$0.650402\pi$
$258$	−1.99164	−	3.74497i	−0.123994	−	0.233152i
$259$		−	3.06885i		−	0.190689i
$260$	−1.61969	+	2.86550i	−0.100449	+	0.177711i
$261$	−7.02481	+	10.4184i	−0.434825	+	0.644886i
$262$	15.1452	+	15.1452i	0.935676	+	0.935676i
$263$			26.6102i			1.64086i	0.571749	+	0.820429i	$0.306265\pi$
$263$			26.6102i			1.64086i	−0.571749	+	0.820429i	$0.693735\pi$
$264$	0.247807	−	0.810780i	0.0152515	−	0.0499001i
$265$	3.24879	+	3.24879i	0.199571	+	0.199571i
$266$	0.564337	−	0.564337i	0.0346017	−	0.0346017i
$267$	−13.8259	−	25.9976i	−0.846134	−	1.59103i
$268$	1.55654	−	1.55654i	0.0950808	−	0.0950808i
$269$			27.5224i			1.67807i	0.544078	+	0.839035i	$0.316880\pi$
$269$			27.5224i			1.67807i	−0.544078	+	0.839035i	$0.683120\pi$
$270$	3.68578	−	2.98621i	0.224310	−	0.181735i
$271$	11.2423	−	11.2423i	0.682924	−	0.682924i	−0.277734	−	0.960658i	$-0.589583\pi$
$271$	11.2423	−	11.2423i	0.682924	−	0.682924i	0.960658	+	0.277734i	$0.0895834\pi$
$272$	−3.74401			−0.227014
$273$	4.30098	+	4.52787i	0.260307	+	0.274039i
$274$	−6.92909			−0.418602
$275$	1.44211	−	1.44211i	0.0869627	−	0.0869627i
$276$	1.48572	−	4.86103i	0.0894301	−	0.292600i
$277$		−	24.6439i		−	1.48071i	−0.672216	−	0.740355i	$-0.734657\pi$
$277$		−	24.6439i		−	1.48071i	0.672216	−	0.740355i	$-0.265343\pi$
$278$	−3.13291	+	3.13291i	−0.187900	+	0.187900i
$279$	−0.981329	−	5.04402i	−0.0587506	−	0.301978i
$280$	−0.645532	+	0.645532i	−0.0385779	+	0.0385779i
$281$	23.3880	+	23.3880i	1.39521	+	1.39521i	0.813126	+	0.582087i	$0.197764\pi$
$281$	23.3880	+	23.3880i	1.39521	+	1.39521i	0.582087	+	0.813126i	$0.302236\pi$
$282$	16.9218	+	5.17198i	1.00768	+	0.307987i
$283$		−	9.52921i		−	0.566453i	−0.959053	−	0.283226i	$-0.908595\pi$
$283$		−	9.52921i		−	0.566453i	0.959053	−	0.283226i	$-0.0914048\pi$
$284$	1.98965	+	1.98965i	0.118064	+	0.118064i
$285$	1.20685	+	0.368862i	0.0714878	+	0.0218495i
$286$	0.472323	+	1.70047i	0.0279290	+	0.100551i
$287$		−	3.32394i		−	0.196206i
$288$	2.94479	−	0.572916i	0.173523	−	0.0337594i
$289$	−2.98240			−0.175435
$290$	3.82377			0.224540
$291$	7.69735	+	14.4737i	0.451227	+	0.848464i
$292$	2.94861	+	2.94861i	0.172554	+	0.172554i
$293$	6.68662	+	6.68662i	0.390636	+	0.390636i	0.874914	−	0.484278i	$-0.160918\pi$
$293$	6.68662	+	6.68662i	0.390636	+	0.390636i	−0.484278	+	0.874914i	$0.660918\pi$
$294$	0.813276	+	1.52924i	0.0474312	+	0.0891872i
$295$	−2.88689			−0.168081
$296$	3.06885			0.178373
$297$	0.265229	−	2.52955i	0.0153901	−	0.146779i
$298$		−	9.91276i		−	0.574231i
$299$	2.83181	+	10.1952i	0.163768	+	0.589601i
$300$	6.90156	+	2.10939i	0.398462	+	0.121786i
$301$	1.73164	+	1.73164i	0.0998100	+	0.0998100i
$302$			8.91682i			0.513105i
$303$	22.2813	+	6.81006i	1.28003	+	0.391228i
$304$	0.564337	+	0.564337i	0.0323669	+	0.0323669i
$305$	2.95860	−	2.95860i	0.169409	−	0.169409i
$306$	−11.0253	+	2.14500i	−0.630275	+	0.122622i
$307$	17.6200	−	17.6200i	1.00563	−	1.00563i	0.00564240	−	0.999984i	$-0.498204\pi$
$307$	17.6200	−	17.6200i	1.00563	−	1.00563i	0.999984	−	0.00564240i	$-0.00179604\pi$
$308$			0.489480i			0.0278907i
$309$	3.34876	−	10.9565i	0.190504	−	0.623296i
$310$	−1.10571	+	1.10571i	−0.0628001	+	0.0628001i
$311$	4.11610			0.233403			0.116701	−	0.993167i	$-0.462768\pi$
$311$	4.11610			0.233403			0.116701	+	0.993167i	$0.462768\pi$
$312$	−4.52787	+	4.30098i	−0.256340	+	0.243495i
$313$	−15.1426			−0.855910			−0.427955	−	0.903800i	$-0.640766\pi$
$313$	−15.1426			−0.855910			−0.427955	+	0.903800i	$0.640766\pi$
$314$	13.5912	−	13.5912i	0.766998	−	0.766998i
$315$	−1.53112	+	2.27079i	−0.0862688	+	0.127945i
$316$			5.80866i			0.326762i
$317$	−15.8113	+	15.8113i	−0.888053	+	0.888053i	−0.994336	−	0.106283i	$-0.966105\pi$
$317$	−15.8113	+	15.8113i	−0.888053	+	0.888053i	0.106283	+	0.994336i	$0.466105\pi$
$318$	4.09299	+	7.69626i	0.229524	+	0.431585i
$319$	1.44970	−	1.44970i	0.0811678	−	0.0811678i
$320$	−0.645532	−	0.645532i	−0.0360864	−	0.0360864i
$321$	−0.117500	+	0.384440i	−0.00655823	+	0.0214574i
$322$			2.93468i			0.163543i
$323$	−2.11288	−	2.11288i	−0.117564	−	0.117564i
$324$	8.34353	−	3.37423i	0.463530	−	0.187457i
$325$	−14.4748	+	4.02052i	−0.802918	+	0.223019i
$326$			13.3966i			0.741971i
$327$	−9.38321	−	17.6437i	−0.518893	−	0.975700i
$328$	3.32394			0.183534
$329$	−10.2160			−0.563224
$330$	−0.683352	+	0.363418i	−0.0376173	+	0.0200055i
$331$	11.5195	+	11.5195i	0.633169	+	0.633169i	0.948861	−	0.315693i	$-0.102237\pi$
$331$	11.5195	+	11.5195i	0.633169	+	0.633169i	−0.315693	+	0.948861i	$0.602237\pi$
$332$	−1.45281	−	1.45281i	−0.0797334	−	0.0797334i
$333$	9.03711	−	1.75819i	0.495231	−	0.0963484i
$334$	24.0564			1.31631
$335$	−2.00959			−0.109796
$336$	−1.52924	+	0.813276i	−0.0834270	+	0.0443678i
$337$			29.3517i			1.59889i	0.600740	+	0.799444i	$0.294873\pi$
$337$			29.3517i			1.59889i	−0.600740	+	0.799444i	$0.705127\pi$
$338$	3.13478	−	12.6164i	0.170510	−	0.686241i
$339$	4.85056	−	15.8702i	0.263446	−	0.861950i
$340$	2.41688	+	2.41688i	0.131074	+	0.131074i
$341$			0.838414i			0.0454027i
$342$	1.98517	+	1.33853i	0.107346	+	0.0723796i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−1.73164	+	1.73164i	−0.0933637	+	0.0933637i
$345$	−4.09704	+	2.17887i	−0.220577	+	0.117306i
$346$	0.668376	−	0.668376i	0.0359321	−	0.0359321i
$347$			11.4483i			0.614575i	0.951617	+	0.307287i	$0.0994212\pi$
$347$			11.4483i			0.614575i	−0.951617	+	0.307287i	$0.900579\pi$
$348$	6.93788	+	2.12049i	0.371909	+	0.113670i
$349$	−3.56656	+	3.56656i	−0.190914	+	0.190914i	−0.796091	−	0.605177i	$-0.793102\pi$
$349$	−3.56656	+	3.56656i	−0.190914	+	0.190914i	0.605177	+	0.796091i	$0.293102\pi$
$350$	−4.16658			−0.222713
$351$	−10.8695	+	15.2596i	−0.580171	+	0.814495i
$352$	−0.489480			−0.0260894
$353$	3.64816	−	3.64816i	0.194172	−	0.194172i	−0.603324	−	0.797496i	$-0.706157\pi$
$353$	3.64816	−	3.64816i	0.194172	−	0.194172i	0.797496	+	0.603324i	$0.206157\pi$
$354$	−5.23799	−	1.60094i	−0.278396	−	0.0850889i
$355$		−	2.56877i		−	0.136336i
$356$	−12.0210	+	12.0210i	−0.637114	+	0.637114i
$357$	5.72550	−	3.04491i	0.303025	−	0.161154i
$358$	−12.8441	+	12.8441i	−0.678834	+	0.678834i
$359$	−0.169016	−	0.169016i	−0.00892035	−	0.00892035i	0.702633	−	0.711553i	$-0.252008\pi$
$359$	−0.169016	−	0.169016i	−0.00892035	−	0.00892035i	−0.711553	+	0.702633i	$0.752008\pi$
$360$	−2.27079	−	1.53112i	−0.119681	−	0.0806971i
$361$		−	18.3630i		−	0.966476i
$362$	−13.0654	−	13.0654i	−0.686701	−	0.686701i
$363$	5.44762	−	17.8237i	0.285926	−	0.935499i
$364$	1.77419	−	3.13883i	0.0929928	−	0.164519i
$365$		−	3.80684i		−	0.199259i
$366$	7.00881	−	3.72740i	0.366357	−	0.194834i
$367$	−19.5827			−1.02221			−0.511104	−	0.859519i	$-0.670763\pi$
$367$	−19.5827			−1.02221			−0.511104	+	0.859519i	$0.670763\pi$
$368$	−2.93468			−0.152981
$369$	9.78830	−	1.90434i	0.509558	−	0.0991359i
$370$	−1.98104	−	1.98104i	−0.102989	−	0.102989i
$371$	−3.55868	−	3.55868i	−0.184757	−	0.184757i
$372$	−2.61939	+	1.39303i	−0.135809	+	0.0722254i
$373$	−26.8148			−1.38842			−0.694210	−	0.719773i	$-0.744246\pi$
$373$	−26.8148			−1.38842			−0.694210	+	0.719773i	$0.744246\pi$
$374$	1.83262			0.0947625
$375$	−6.80578	−	12.7972i	−0.351449	−	0.660847i
$376$		−	10.2160i		−	0.526848i
$377$	−14.5510	+	4.04168i	−0.749414	+	0.208157i
$378$	−4.03735	+	3.27105i	−0.207659	+	0.168245i
$379$	0.249109	+	0.249109i	0.0127959	+	0.0127959i	0.713476	−	0.700680i	$-0.247120\pi$
$379$	0.249109	+	0.249109i	0.0127959	+	0.0127959i	−0.700680	+	0.713476i	$0.747120\pi$
$380$		−	0.728595i		−	0.0373762i
$381$	8.53529	−	27.9260i	0.437276	−	1.43069i
$382$	−10.0262	−	10.0262i	−0.512984	−	0.512984i
$383$	−2.01331	+	2.01331i	−0.102875	+	0.102875i	−0.756671	−	0.653796i	$-0.773176\pi$
$383$	−2.01331	+	2.01331i	−0.102875	+	0.102875i	0.653796	+	0.756671i	$0.273176\pi$
$384$	−0.813276	−	1.52924i	−0.0415023	−	0.0780388i
$385$	0.315975	−	0.315975i	0.0161036	−	0.0161036i
$386$			4.77786i			0.243187i
$387$	−4.10722	+	6.09139i	−0.208782	+	0.309643i
$388$	6.69250	−	6.69250i	0.339760	−	0.339760i
$389$	−6.62477			−0.335889			−0.167945	−	0.985796i	$-0.553713\pi$
$389$	−6.62477			−0.335889			−0.167945	+	0.985796i	$0.553713\pi$
$390$	5.69931	+	0.146461i	0.288596	+	0.00741635i
$391$	10.9875			0.555659
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	10.8435	−	35.4780i	0.546981	−	1.78963i
$394$			2.13237i			0.107427i
$395$	3.74968	−	3.74968i	0.188667	−	0.188667i
$396$	−1.44142	+	0.280431i	−0.0724338	+	0.0140922i
$397$	−16.9697	+	16.9697i	−0.851684	+	0.851684i	−0.990341	−	0.138657i	$-0.955722\pi$
$397$	−16.9697	+	16.9697i	−0.851684	+	0.851684i	0.138657	+	0.990341i	$0.455722\pi$
$398$	7.91950	+	7.91950i	0.396968	+	0.396968i
$399$	−1.32197	−	0.404047i	−0.0661812	−	0.0202276i
$400$		−	4.16658i		−	0.208329i
$401$	−19.1843	−	19.1843i	−0.958019	−	0.958019i	0.0411346	−	0.999154i	$-0.486903\pi$
$401$	−19.1843	−	19.1843i	−0.958019	−	0.958019i	−0.999154	+	0.0411346i	$0.986903\pi$
$402$	−3.64622	−	1.11443i	−0.181857	−	0.0555828i
$403$	3.03895	−	5.37640i	0.151381	−	0.267817i
$404$		−	13.4516i		−	0.669241i
$405$	−7.56420	−	3.20785i	−0.375868	−	0.159399i
$406$	−4.18850			−0.207872
$407$	−1.50214			−0.0744584
$408$	3.04491	+	5.72550i	0.150746	+	0.283454i
$409$	6.18510	+	6.18510i	0.305834	+	0.305834i	0.843291	−	0.537457i	$-0.180615\pi$
$409$	6.18510	+	6.18510i	0.305834	+	0.305834i	−0.537457	+	0.843291i	$0.680615\pi$
$410$	−2.14571	−	2.14571i	−0.105969	−	0.105969i
$411$	5.63526	+	10.5963i	0.277967	+	0.522675i
$412$	−6.61463			−0.325879
$413$	3.16225			0.155604
$414$	−8.64200	+	1.68132i	−0.424731	+	0.0826325i
$415$			1.87567i			0.0920732i
$416$	3.13883	+	1.77419i	0.153894	+	0.0869868i
$417$	7.33891	+	2.24306i	0.359388	+	0.109843i
$418$	−0.276232	−	0.276232i	−0.0135109	−	0.0135109i
$419$		−	21.7419i		−	1.06216i	−0.847321	−	0.531080i	$-0.821786\pi$
$419$		−	21.7419i		−	1.06216i	0.847321	−	0.531080i	$-0.178214\pi$
$420$	1.51217	+	0.462180i	0.0737864	+	0.0225521i
$421$	20.0060	+	20.0060i	0.975035	+	0.975035i	0.999696	−	0.0246608i	$-0.00785059\pi$
$421$	20.0060	+	20.0060i	0.975035	+	0.975035i	−0.0246608	+	0.999696i	$0.507851\pi$
$422$	−11.8119	+	11.8119i	−0.574997	+	0.574997i
$423$	−5.85289	−	30.0838i	−0.284577	−	1.46272i
$424$	3.55868	−	3.55868i	0.172825	−	0.172825i
$425$			15.5997i			0.756696i
$426$	1.42452	−	4.66079i	0.0690184	−	0.225816i
$427$	−3.24081	+	3.24081i	−0.156834	+	0.156834i
$428$	0.232092			0.0112186
$429$	2.21630	−	2.10525i	0.107004	−	0.101642i
$430$	2.23566			0.107813
$431$	19.5706	−	19.5706i	0.942682	−	0.942682i	−0.0557616	−	0.998444i	$-0.517759\pi$
$431$	19.5706	−	19.5706i	0.942682	−	0.942682i	0.998444	+	0.0557616i	$0.0177587\pi$
$432$	−3.27105	−	4.03735i	−0.157378	−	0.194247i
$433$		−	1.51276i		−	0.0726985i	−0.999339	−	0.0363493i	$-0.988427\pi$
$433$		−	1.51276i		−	0.0726985i	0.999339	−	0.0363493i	$-0.0115729\pi$
$434$	1.21118	−	1.21118i	0.0581385	−	0.0581385i
$435$	−3.10978	−	5.84747i	−0.149102	−	0.280365i
$436$	−8.15828	+	8.15828i	−0.390711	+	0.390711i
$437$	−1.65615	−	1.65615i	−0.0792242	−	0.0792242i
$438$	2.11111	−	6.90717i	0.100873	−	0.330037i
$439$			3.57755i			0.170747i	0.996349	+	0.0853737i	$0.0272084\pi$
$439$			3.57755i			0.170747i	−0.996349	+	0.0853737i	$0.972792\pi$
$440$	0.315975	+	0.315975i	0.0150635	+	0.0150635i
$441$	1.67717	−	2.48739i	0.0798650	−	0.118447i
$442$	−11.7518	−	6.64258i	−0.558976	−	0.315955i
$443$		−	2.53190i		−	0.120294i	−0.998190	−	0.0601472i	$-0.980843\pi$
$443$		−	2.53190i		−	0.120294i	0.998190	−	0.0601472i	$-0.0191570\pi$
$444$	−2.49582	−	4.69302i	−0.118446	−	0.222721i
$445$	15.5199			0.735716
$446$	22.9482			1.08663
$447$	−15.1590	+	8.06181i	−0.716997	+	0.381310i
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	12.5933	+	12.5933i	0.594314	+	0.594314i	0.938794	−	0.344480i	$-0.111945\pi$
$449$	12.5933	+	12.5933i	0.594314	+	0.594314i	−0.344480	+	0.938794i	$0.611945\pi$
$450$	−2.38710	−	12.2697i	−0.112529	−	0.578398i
$451$	−1.62700			−0.0766126
$452$	−9.58107			−0.450656
$453$	13.6360	−	7.25183i	0.640674	−	0.340721i
$454$		−	26.2822i		−	1.23349i
$455$	−3.17151	+	0.880920i	−0.148683	+	0.0412982i
$456$	0.404047	−	1.32197i	0.0189212	−	0.0619069i
$457$	2.80065	+	2.80065i	0.131009	+	0.131009i	0.769571	−	0.638562i	$-0.220470\pi$
$457$	2.80065	+	2.80065i	0.131009	+	0.131009i	−0.638562	+	0.769571i	$0.720470\pi$
$458$		−	14.5685i		−	0.680741i
$459$	12.2468	+	15.1159i	0.571634	+	0.705549i
$460$	1.89443	+	1.89443i	0.0883282	+	0.0883282i
$461$	1.30086	−	1.30086i	0.0605872	−	0.0605872i	−0.676164	−	0.736751i	$-0.736359\pi$
$461$	1.30086	−	1.30086i	0.0605872	−	0.0605872i	0.736751	+	0.676164i	$0.236359\pi$
$462$	0.748534	−	0.398082i	0.0348250	−	0.0185205i
$463$	8.21976	−	8.21976i	0.382005	−	0.382005i	−0.489819	−	0.871824i	$-0.662937\pi$
$463$	8.21976	−	8.21976i	0.382005	−	0.382005i	0.871824	+	0.489819i	$0.162937\pi$
$464$		−	4.18850i		−	0.194446i
$465$	2.59015	+	0.791652i	0.120115	+	0.0367120i
$466$	−20.9136	+	20.9136i	−0.968803	+	0.968803i
$467$	−32.5141			−1.50457			−0.752286	−	0.658837i	$-0.771049\pi$
$467$	−32.5141			−1.50457			−0.752286	+	0.658837i	$0.771049\pi$
$468$	10.2596	+	3.42632i	0.474252	+	0.158382i
$469$	2.20128			0.101646
$470$	−6.59473	+	6.59473i	−0.304192	+	0.304192i
$471$	−31.8377	−	9.73088i	−1.46701	−	0.448375i
$472$			3.16225i			0.145555i
$473$	0.847603	−	0.847603i	0.0389728	−	0.0389728i
$474$	8.88285	−	4.72404i	0.408003	−	0.216982i
$475$	2.35135	−	2.35135i	0.107887	−	0.107887i
$476$	−2.64741	−	2.64741i	−0.121344	−	0.121344i
$477$	8.44072	−	12.5184i	0.386474	−	0.573176i
$478$		−	6.25816i		−	0.286242i
$479$	22.3153	+	22.3153i	1.01961	+	1.01961i	0.999804	+	0.0198079i	$0.00630546\pi$
$479$	22.3153	+	22.3153i	1.01961	+	1.01961i	0.0198079	+	0.999804i	$0.493695\pi$
$480$	−0.462180	+	1.51217i	−0.0210955	+	0.0690209i
$481$	9.63260	+	5.44472i	0.439209	+	0.248258i
$482$		−	16.5013i		−	0.751615i
$483$	4.48783	−	2.38670i	0.204203	−	0.108599i
$484$	−10.7604			−0.489109
$485$	−8.64045			−0.392343
$486$	−11.9456	−	10.0151i	−0.541864	−	0.454295i
$487$	−7.39827	−	7.39827i	−0.335247	−	0.335247i	0.519328	−	0.854575i	$-0.326182\pi$
$487$	−7.39827	−	7.39827i	−0.335247	−	0.335247i	−0.854575	+	0.519328i	$0.826182\pi$
$488$	−3.24081	−	3.24081i	−0.146704	−	0.146704i
$489$	20.4867	−	10.8952i	0.926440	−	0.492696i
$490$	−0.912921			−0.0412416
$491$	22.4035			1.01106			0.505528	−	0.862810i	$-0.331298\pi$
$491$	22.4035			1.01106			0.505528	+	0.862810i	$0.331298\pi$
$492$	−2.70328	−	5.08311i	−0.121873	−	0.229164i
$493$			15.6818i			0.706272i
$494$	0.770117	+	2.77260i	0.0346492	+	0.124745i
$495$	1.11151	+	0.749453i	0.0499586	+	0.0336854i
$496$	1.21118	+	1.21118i	0.0543836	+	0.0543836i
$497$			2.81379i			0.126216i
$498$	−1.04017	+	3.40324i	−0.0466109	+	0.152503i
$499$	25.8150	+	25.8150i	1.15564	+	1.15564i	0.985404	+	0.170232i	$0.0544517\pi$
$499$	25.8150	+	25.8150i	1.15564	+	1.15564i	0.170232	+	0.985404i	$0.445548\pi$
$500$	−5.91732	+	5.91732i	−0.264631	+	0.264631i
$501$	−19.5645	−	36.7881i	−0.874078	−	1.64357i
$502$	10.0858	−	10.0858i	0.450152	−	0.450152i
$503$			2.80539i			0.125086i	0.998042	+	0.0625430i	$0.0199211\pi$
$503$			2.80539i			0.125086i	−0.998042	+	0.0625430i	$0.980079\pi$
$504$	2.48739	+	1.67717i	0.110797	+	0.0747069i
$505$	−8.68343	+	8.68343i	−0.386408	+	0.386408i
$506$	1.43647			0.0638587
$507$	−21.8430	+	5.46676i	−0.970080	+	0.242787i
$508$	−16.8593			−0.748012
$509$	14.7980	−	14.7980i	0.655912	−	0.655912i	−0.298499	−	0.954410i	$-0.596486\pi$
$509$	14.7980	−	14.7980i	0.655912	−	0.655912i	0.954410	+	0.298499i	$0.0964858\pi$
$510$	1.73041	−	5.66158i	0.0766236	−	0.250699i
$511$			4.16996i			0.184468i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.432453	−	4.12440i	0.0190933	−	0.182097i
$514$	10.3182	−	10.3182i	0.455114	−	0.455114i
$515$	4.26996	+	4.26996i	0.188157	+	0.188157i
$516$	4.05640	+	1.23980i	0.178573	+	0.0545790i
$517$			5.00051i			0.219922i
$518$	2.17001	+	2.17001i	0.0953446	+	0.0953446i
$519$	−1.56568	−	0.478535i	−0.0687258	−	0.0210054i
$520$	−0.880920	−	3.17151i	−0.0386309	−	0.139080i
$521$		−	41.1077i		−	1.80096i	−0.434896	−	0.900481i	$-0.643215\pi$
$521$		−	41.1077i		−	1.80096i	0.434896	−	0.900481i	$-0.356785\pi$
$522$	−2.39966	−	12.3342i	−0.105030	−	0.539855i
$523$	−10.5444			−0.461074			−0.230537	−	0.973064i	$-0.574048\pi$
$523$	−10.5444			−0.461074			−0.230537	+	0.973064i	$0.574048\pi$
$524$	−21.4186			−0.935676
$525$	3.38857	+	6.37171i	0.147890	+	0.278084i
$526$	−18.8163	−	18.8163i	−0.820429	−	0.820429i
$527$	−4.53467	−	4.53467i	−0.197533	−	0.197533i
$528$	0.398082	+	0.748534i	0.0173243	+	0.0325758i
$529$	−14.3877			−0.625551
$530$	−4.59448			−0.199571
$531$	1.81171	+	9.31216i	0.0786214	+	0.404113i
$532$			0.798093i			0.0346017i
$533$	10.4333	+	5.89730i	0.451916	+	0.255440i
$534$	28.1595	+	8.60667i	1.21858	+	0.372447i
$535$	−0.149823	−	0.149823i	−0.00647742	−	0.00647742i
$536$			2.20128i			0.0950808i
$537$	30.0876	+	9.19598i	1.29838	+	0.396836i
$538$	−19.4613	−	19.4613i	−0.839035	−	0.839035i
$539$	−0.346115	+	0.346115i	−0.0149082	+	0.0149082i
$540$	−0.494674	+	4.71781i	−0.0212874	+	0.203022i
$541$	9.48820	−	9.48820i	0.407930	−	0.407930i	−0.473086	−	0.881016i	$-0.656860\pi$
$541$	9.48820	−	9.48820i	0.407930	−	0.407930i	0.881016	+	0.473086i	$0.156860\pi$
$542$			15.8991i			0.682924i
$543$	−9.35438	+	30.6059i	−0.401435	+	1.31342i
$544$	2.64741	−	2.64741i	0.113507	−	0.113507i
$545$	10.5329			0.451179
$546$	−6.24294	−	0.160431i	−0.267173	−	0.00686583i
$547$	34.3778			1.46989			0.734945	−	0.678127i	$-0.237208\pi$
$547$	34.3778			1.46989			0.734945	+	0.678127i	$0.237208\pi$
$548$	4.89961	−	4.89961i	0.209301	−	0.209301i
$549$	−11.4002	−	7.68677i	−0.486549	−	0.328064i
$550$			2.03946i			0.0869627i
$551$	2.36373	−	2.36373i	0.100698	−	0.100698i
$552$	2.38670	+	4.48783i	0.101585	+	0.191015i
$553$	−4.10734	+	4.10734i	−0.174662	+	0.174662i
$554$	17.4259	+	17.4259i	0.740355	+	0.740355i
$555$	−1.41836	+	4.64063i	−0.0602061	+	0.196984i
$556$		−	4.43061i		−	0.187900i
$557$	−23.0785	−	23.0785i	−0.977867	−	0.977867i	0.0218937	−	0.999760i	$-0.493030\pi$
$557$	−23.0785	−	23.0785i	−0.977867	−	0.977867i	−0.999760	+	0.0218937i	$0.993030\pi$
$558$	4.26057	+	2.87276i	0.180364	+	0.121614i
$559$	−8.50757	+	2.36307i	−0.359832	+	0.0999470i
$560$		−	0.912921i		−	0.0385779i
$561$	−1.49042	−	2.80252i	−0.0629258	−	0.118322i
$562$	−33.0757			−1.39521
$563$	19.8382			0.836082			0.418041	−	0.908428i	$-0.362717\pi$
$563$	19.8382			0.836082			0.418041	+	0.908428i	$0.362717\pi$
$564$	−15.6227	+	8.30839i	−0.657833	+	0.349846i
$565$	6.18489	+	6.18489i	0.260200	+	0.260200i
$566$	6.73817	+	6.73817i	0.283226	+	0.283226i
$567$	8.28571	+	3.51383i	0.347967	+	0.147567i
$568$	−2.81379			−0.118064
$569$	6.55300			0.274716			0.137358	−	0.990521i	$-0.456139\pi$
$569$	6.55300			0.274716			0.137358	+	0.990521i	$0.456139\pi$
$570$	−1.11420	+	0.592549i	−0.0466687	+	0.0248191i
$571$			30.9170i			1.29384i	0.762559	+	0.646919i	$0.223943\pi$
$571$			30.9170i			1.29384i	−0.762559	+	0.646919i	$0.776057\pi$
$572$	−1.53640	−	0.868431i	−0.0642399	−	0.0363109i
$573$	−7.17841	+	23.4865i	−0.299882	+	0.981163i
$574$	2.35038	+	2.35038i	0.0981030	+	0.0981030i
$575$			12.2276i			0.509924i
$576$	−1.67717	+	2.48739i	−0.0698819	+	0.103641i
$577$	10.8612	+	10.8612i	0.452158	+	0.452158i	0.896070	−	0.443912i	$-0.146410\pi$
$577$	10.8612	+	10.8612i	0.452158	+	0.452158i	−0.443912	+	0.896070i	$0.646410\pi$
$578$	2.10888	−	2.10888i	0.0877177	−	0.0877177i
$579$	7.30651	−	3.88572i	0.303648	−	0.161485i
$580$	−2.70381	+	2.70381i	−0.112270	+	0.112270i
$581$		−	2.05459i		−	0.0852386i
$582$	−15.6773	−	4.79161i	−0.649845	−	0.198619i
$583$	−1.74190	+	1.74190i	−0.0721422	+	0.0721422i
$584$	−4.16996			−0.172554
$585$	−4.41113	−	8.83473i	−0.182378	−	0.365271i
$586$	−9.45631			−0.390636
$587$	−4.36741	+	4.36741i	−0.180262	+	0.180262i	−0.791470	−	0.611208i	$-0.790684\pi$
$587$	−4.36741	+	4.36741i	−0.180262	+	0.180262i	0.611208	+	0.791470i	$0.290684\pi$
$588$	−1.65641	−	0.506265i	−0.0683092	−	0.0208780i
$589$			1.36703i			0.0563273i
$590$	2.04134	−	2.04134i	0.0840405	−	0.0840405i
$591$	3.26091	−	1.73421i	0.134136	−	0.0713357i
$592$	−2.17001	+	2.17001i	−0.0891867	+	0.0891867i
$593$	6.15560	+	6.15560i	0.252780	+	0.252780i	0.822109	−	0.569329i	$-0.192797\pi$
$593$	6.15560	+	6.15560i	0.252780	+	0.252780i	−0.569329	+	0.822109i	$0.692797\pi$
$594$	1.60112	+	1.97621i	0.0656945	+	0.0810847i
$595$			3.41798i			0.140124i
$596$	7.00938	+	7.00938i	0.287115	+	0.287115i
$597$	5.67010	−	18.5516i	0.232062	−	0.759265i
$598$	−9.21145	−	5.20667i	−0.376684	−	0.212917i
$599$		−	31.1615i		−	1.27323i	−0.771184	−	0.636613i	$-0.780335\pi$
$599$		−	31.1615i		−	1.27323i	0.771184	−	0.636613i	$-0.219665\pi$
$600$	−6.37171	+	3.38857i	−0.260124	+	0.138338i
$601$	10.3915			0.423878			0.211939	−	0.977283i	$-0.432022\pi$
$601$	10.3915			0.423878			0.211939	+	0.977283i	$0.432022\pi$
$602$	−2.44891			−0.0998100
$603$	1.26115	+	6.48230i	0.0513579	+	0.263980i
$604$	−6.30515	−	6.30515i	−0.256553	−	0.256553i
$605$	6.94619	+	6.94619i	0.282403	+	0.282403i
$606$	−20.5707	+	10.9398i	−0.835629	+	0.444401i
$607$	−19.5779			−0.794643			−0.397322	−	0.917679i	$-0.630060\pi$
$607$	−19.5779			−0.794643			−0.397322	+	0.917679i	$0.630060\pi$
$608$	−0.798093			−0.0323669
$609$	3.40641	+	6.40524i	0.138035	+	0.259553i
$610$			4.18409i			0.169409i
$611$	18.1250	−	32.0661i	0.733260	−	1.29726i
$612$	6.27932	−	9.31281i	0.253827	−	0.376448i
$613$	6.71448	+	6.71448i	0.271195	+	0.271195i	0.829581	−	0.558386i	$-0.188579\pi$
$613$	6.71448	+	6.71448i	0.271195	+	0.271195i	−0.558386	+	0.829581i	$0.688579\pi$
$614$			24.9184i			1.00563i
$615$	−1.53626	+	5.02637i	−0.0619479	+	0.202683i
$616$	−0.346115	−	0.346115i	−0.0139454	−	0.0139454i
$617$	−10.3723	+	10.3723i	−0.417575	+	0.417575i	−0.884367	−	0.466792i	$-0.845410\pi$
$617$	−10.3723	+	10.3723i	−0.417575	+	0.417575i	0.466792	+	0.884367i	$0.345410\pi$
$618$	5.37952	+	10.1154i	0.216396	+	0.406900i
$619$	−17.7776	+	17.7776i	−0.714542	+	0.714542i	−0.967482	−	0.252940i	$-0.918602\pi$
$619$	−17.7776	+	17.7776i	−0.714542	+	0.714542i	0.252940	+	0.967482i	$0.418602\pi$
$620$		−	1.56371i		−	0.0628001i
$621$	9.59948	+	11.8483i	0.385214	+	0.475457i
$622$	−2.91052	+	2.91052i	−0.116701	+	0.116701i
$623$	−17.0003			−0.681104
$624$	0.160431	−	6.24294i	0.00642240	−	0.249917i
$625$	−13.1932			−0.527729
$626$	10.7074	−	10.7074i	0.427955	−	0.427955i
$627$	−0.197773	+	0.647078i	−0.00789829	+	0.0258418i
$628$			19.2209i			0.766998i
$629$	8.12452	−	8.12452i	0.323946	−	0.323946i
$630$	−0.523027	−	2.68836i	−0.0208379	−	0.107107i
$631$	33.4192	−	33.4192i	1.33040	−	1.33040i	0.425388	−	0.905011i	$-0.360138\pi$
$631$	33.4192	−	33.4192i	1.33040	−	1.33040i	0.905011	−	0.425388i	$-0.139862\pi$
$632$	−4.10734	−	4.10734i	−0.163381	−	0.163381i
$633$	27.6697	+	8.45697i	1.09977	+	0.336134i
$634$		−	22.3606i		−	0.888053i
$635$	10.8832	+	10.8832i	0.431888	+	0.431888i
$636$	−8.33626	−	2.54789i	−0.330554	−	0.101031i
$637$	3.47403	−	0.964947i	0.137646	−	0.0382326i
$638$			2.05019i			0.0811678i
$639$	−8.28601	+	1.61206i	−0.327789	+	0.0637723i
$640$	0.912921			0.0360864
$641$	−33.1552			−1.30955			−0.654775	−	0.755823i	$-0.727237\pi$
$641$	−33.1552			−1.30955			−0.654775	+	0.755823i	$0.727237\pi$
$642$	−0.188755	−	0.354926i	−0.00744957	−	0.0140078i
$643$	12.7533	+	12.7533i	0.502941	+	0.502941i	0.912351	−	0.409410i	$-0.134265\pi$
$643$	12.7533	+	12.7533i	0.502941	+	0.502941i	−0.409410	+	0.912351i	$0.634265\pi$
$644$	−2.07513	−	2.07513i	−0.0817716	−	0.0817716i
$645$	−1.81821	−	3.41886i	−0.0715918	−	0.134618i
$646$	2.98807			0.117564
$647$	−25.5626			−1.00497			−0.502484	−	0.864586i	$-0.667580\pi$
$647$	−25.5626			−1.00497			−0.502484	+	0.864586i	$0.667580\pi$
$648$	−3.51383	+	8.28571i	−0.138036	+	0.325493i
$649$		−	1.54786i		−	0.0607589i
$650$	7.39229	−	13.0782i	0.289950	−	0.512968i
$651$	−2.83721	−	0.867164i	−0.111199	−	0.0339868i
$652$	−9.47285	−	9.47285i	−0.370985	−	0.370985i
$653$		−	37.4482i		−	1.46546i	−0.680520	−	0.732730i	$-0.738246\pi$
$653$		−	37.4482i		−	1.46546i	0.680520	−	0.732730i	$-0.261754\pi$
$654$	19.1109	+	5.84106i	0.747296	+	0.228404i
$655$	13.8264	+	13.8264i	0.540242	+	0.540242i
$656$	−2.35038	+	2.35038i	−0.0917670	+	0.0917670i
$657$	−12.2796	+	2.38904i	−0.479075	+	0.0932052i
$658$	7.22377	−	7.22377i	0.281612	−	0.281612i
$659$			9.60599i			0.374196i	0.982341	+	0.187098i	$0.0599082\pi$
$659$			9.60599i			0.374196i	−0.982341	+	0.187098i	$0.940092\pi$
$660$	0.226228	−	0.740178i	0.00880591	−	0.0288114i
$661$	6.14906	−	6.14906i	0.239171	−	0.239171i	−0.577336	−	0.816507i	$-0.695908\pi$
$661$	6.14906	−	6.14906i	0.239171	−	0.239171i	0.816507	+	0.577336i	$0.195908\pi$
$662$	−16.2910			−0.633169
$663$	−0.600657	+	23.3736i	−0.0233276	+	0.907756i
$664$	2.05459			0.0797334
$665$	0.515195	−	0.515195i	0.0199784	−	0.0199784i
$666$	−5.14697	+	7.63343i	−0.199441	+	0.295790i
$667$			12.2919i			0.475944i
$668$	−17.0105	+	17.0105i	−0.658155	+	0.658155i
$669$	−18.6632	−	35.0934i	−0.721563	−	1.35679i
$670$	1.42100	−	1.42100i	0.0548979	−	0.0548979i
$671$	1.58631	+	1.58631i	0.0612389	+	0.0612389i
$672$	0.506265	−	1.65641i	0.0195296	−	0.0638974i
$673$		−	6.96650i		−	0.268539i	−0.990945	−	0.134269i	$-0.957131\pi$
$673$		−	6.96650i		−	0.268539i	0.990945	−	0.134269i	$-0.0428688\pi$
$674$	−20.7548	−	20.7548i	−0.799444	−	0.799444i
$675$	−16.8219	+	13.6291i	−0.647477	+	0.524584i
$676$	6.70451	+	11.1378i	0.257866	+	0.428375i
$677$		−	5.13417i		−	0.197322i	−0.995121	−	0.0986611i	$-0.968544\pi$
$677$		−	5.13417i		−	0.197322i	0.995121	−	0.0986611i	$-0.0314560\pi$
$678$	7.79205	+	14.6518i	0.299252	+	0.562698i
$679$	9.46462			0.363219
$680$	−3.41798			−0.131074
$681$	−40.1919	+	21.3747i	−1.54016	+	0.819081i
$682$	−0.592848	−	0.592848i	−0.0227013	−	0.0227013i
$683$	−15.1739	−	15.1739i	−0.580615	−	0.580615i	0.354457	−	0.935072i	$-0.384666\pi$
$683$	−15.1739	−	15.1739i	−0.580615	−	0.580615i	−0.935072	+	0.354457i	$0.884666\pi$
$684$	−2.35021	+	0.457240i	−0.0898626	+	0.0174830i
$685$	−6.32571			−0.241693
$686$	1.00000			0.0381802
$687$	−22.2788	+	11.8482i	−0.849988	+	0.452037i
$688$		−	2.44891i		−	0.0933637i
$689$	17.4838	−	4.85631i	0.666081	−	0.185011i
$690$	1.35635	−	4.43773i	0.0516353	−	0.168942i
$691$	−19.4188	−	19.4188i	−0.738725	−	0.738725i	0.233607	−	0.972331i	$-0.424947\pi$
$691$	−19.4188	−	19.4188i	−0.738725	−	0.738725i	−0.972331	+	0.233607i	$0.924947\pi$
$692$			0.945226i			0.0359321i
$693$	−1.21753	−	0.820940i	−0.0462501	−	0.0311849i
$694$	−8.09514	−	8.09514i	−0.307287	−	0.307287i
$695$	−2.86010	+	2.86010i	−0.108490	+	0.108490i
$696$	−6.40524	+	3.40641i	−0.242790	+	0.129120i
$697$	8.79985	−	8.79985i	0.333318	−	0.333318i
$698$		−	5.04388i		−	0.190914i
$699$	48.9905	+	14.9734i	1.85299	+	0.566348i
$700$	2.94621	−	2.94621i	0.111356	−	0.111356i
$701$	24.6973			0.932803			0.466402	−	0.884573i	$-0.345550\pi$
$701$	24.6973			0.932803			0.466402	+	0.884573i	$0.345550\pi$
$702$	−3.10424	−	18.4760i	−0.117162	−	0.697333i
$703$	−2.44923			−0.0923744
$704$	0.346115	−	0.346115i	0.0130447	−	0.0130447i
$705$	15.4483	+	4.72161i	0.581816	+	0.177826i
$706$			5.15928i			0.194172i
$707$	9.51170	−	9.51170i	0.357724	−	0.357724i
$708$	4.83585	−	2.57178i	0.181743	−	0.0966536i
$709$	15.9540	−	15.9540i	0.599167	−	0.599167i	−0.340924	−	0.940091i	$-0.610740\pi$
$709$	15.9540	−	15.9540i	0.599167	−	0.599167i	0.940091	+	0.340924i	$0.110740\pi$
$710$	1.81639	+	1.81639i	0.0681680	+	0.0681680i
$711$	−14.4484	−	9.74208i	−0.541857	−	0.365357i
$712$		−	17.0003i		−	0.637114i
$713$	−3.55442	−	3.55442i	−0.133114	−	0.133114i
$714$	−1.89546	+	6.20161i	−0.0709358	+	0.232090i
$715$	0.431193	+	1.55239i	0.0161257	+	0.0580562i
$716$		−	18.1644i		−	0.678834i
$717$	−9.57025	+	5.08961i	−0.357407	+	0.190075i
$718$	0.239025			0.00892035
$719$	10.8293			0.403865			0.201933	−	0.979399i	$-0.435278\pi$
$719$	10.8293			0.403865			0.201933	+	0.979399i	$0.435278\pi$
$720$	2.68836	−	0.523027i	0.100189	−	0.0194921i
$721$	−4.67725	−	4.67725i	−0.174190	−	0.174190i
$722$	12.9846	+	12.9846i	0.483238	+	0.483238i
$723$	−25.2345	+	13.4201i	−0.938483	+	0.499100i
$724$	18.4772			0.686701
$725$	−17.4517			−0.648140
$726$	8.75118	+	16.4553i	0.324787	+	0.610713i
$727$		−	33.1488i		−	1.22942i	−0.788753	−	0.614710i	$-0.789273\pi$
$727$		−	33.1488i		−	1.22942i	0.788753	−	0.614710i	$-0.210727\pi$
$728$	0.964947	+	3.47403i	0.0357633	+	0.128756i
$729$	−5.60046	+	26.4128i	−0.207424	+	0.978251i
$730$	2.69185	+	2.69185i	0.0996297	+	0.0996297i
$731$			9.16873i			0.339118i
$732$	−2.32031	+	7.59165i	−0.0857612	+	0.280595i
$733$	16.6460	+	16.6460i	0.614835	+	0.614835i	0.944202	−	0.329367i	$-0.106835\pi$
$733$	16.6460	+	16.6460i	0.614835	+	0.614835i	−0.329367	+	0.944202i	$0.606835\pi$
$734$	13.8470	−	13.8470i	0.511104	−	0.511104i
$735$	0.742456	+	1.39608i	0.0273859	+	0.0514951i
$736$	2.07513	−	2.07513i	0.0764903	−	0.0764903i
$737$		−	1.07748i		−	0.0396896i
$738$	−5.57480	+	8.26794i	−0.205211	+	0.304347i
$739$	−31.1450	+	31.1450i	−1.14569	+	1.14569i	−0.158294	+	0.987392i	$0.550599\pi$
$739$	−31.1450	+	31.1450i	−1.14569	+	1.14569i	−0.987392	+	0.158294i	$0.949401\pi$
$740$	2.80162			0.102989
$741$	3.61366	−	3.43258i	0.132751	−	0.126099i
$742$	5.03273			0.184757
$743$	20.0711	−	20.0711i	0.736339	−	0.736339i	−0.235529	−	0.971867i	$-0.575682\pi$
$743$	20.0711	−	20.0711i	0.736339	−	0.736339i	0.971867	+	0.235529i	$0.0756822\pi$
$744$	0.867164	−	2.83721i	0.0317918	−	0.104017i
$745$		−	9.04956i		−	0.331550i
$746$	18.9610	−	18.9610i	0.694210	−	0.694210i
$747$	6.05032	−	1.17711i	0.221369	−	0.0430680i
$748$	−1.29586	+	1.29586i	−0.0473812	+	0.0473812i
$749$	0.164114	+	0.164114i	0.00599660	+	0.00599660i
$750$	13.8614	+	4.23661i	0.506148	+	0.154699i
$751$			5.53789i			0.202080i	0.994882	+	0.101040i	$0.0322171\pi$
$751$			5.53789i			0.202080i	−0.994882	+	0.101040i	$0.967783\pi$
$752$	7.22377	+	7.22377i	0.263424	+	0.263424i
$753$	−23.6262	−	7.22111i	−0.860987	−	0.263152i
$754$	7.43119	−	13.1470i	0.270628	−	0.478785i
$755$			8.14035i			0.296258i
$756$	0.541858	−	5.16782i	0.0197072	−	0.187952i
$757$	37.7422			1.37176			0.685882	−	0.727713i	$-0.259417\pi$
$757$	37.7422			1.37176			0.685882	+	0.727713i	$0.259417\pi$
$758$	−0.352294			−0.0127959
$759$	−1.16824	−	2.19671i	−0.0424045	−	0.0797354i
$760$	0.515195	+	0.515195i	0.0186881	+	0.0186881i
$761$	13.0324	+	13.0324i	0.472423	+	0.472423i	0.902698	−	0.430275i	$-0.141583\pi$
$761$	13.0324	+	13.0324i	0.472423	+	0.472423i	−0.430275	+	0.902698i	$0.641583\pi$
$762$	13.7113	+	25.7820i	0.496707	+	0.933983i
$763$	−11.5376			−0.417687
$764$	14.1792			0.512984
$765$	−10.0652	+	1.95822i	−0.363909	+	0.0707995i
$766$		−	2.84725i		−	0.102875i
$767$	−5.61044	+	9.92578i	−0.202581	+	0.358399i
$768$	1.65641	+	0.506265i	0.0597706	+	0.0182683i
$769$	−8.01862	−	8.01862i	−0.289159	−	0.289159i	0.547589	−	0.836748i	$-0.315546\pi$
$769$	−8.01862	−	8.01862i	−0.289159	−	0.289159i	−0.836748	+	0.547589i	$0.815546\pi$
$770$			0.446857i			0.0161036i
$771$	−24.1705	−	7.38746i	−0.870478	−	0.266053i
$772$	−3.37846	−	3.37846i	−0.121593	−	0.121593i
$773$	−27.9230	+	27.9230i	−1.00432	+	1.00432i	−0.00433086	+	0.999991i	$0.501379\pi$
$773$	−27.9230	+	27.9230i	−1.00432	+	1.00432i	−0.999991	+	0.00433086i	$0.998621\pi$
$774$	−1.40302	−	7.21151i	−0.0504304	−	0.259212i
$775$	5.04647	−	5.04647i	0.181275	−	0.181275i
$776$			9.46462i			0.339760i
$777$	1.55365	−	5.08328i	0.0557370	−	0.182362i
$778$	4.68442	−	4.68442i	0.167945	−	0.167945i
$779$	−2.65281			−0.0950469
$780$	−4.13358	+	3.92645i	−0.148006	+	0.140590i
$781$	1.37729			0.0492835
$782$	−7.76930	+	7.76930i	−0.277830	+	0.277830i
$783$	−16.9105	+	13.7008i	−0.604331	+	0.489627i
$784$			1.00000i			0.0357143i
$785$	12.4077	−	12.4077i	0.442851	−	0.442851i
$786$	17.4192	+	32.7542i	0.621323	+	1.16830i
$787$	10.8587	−	10.8587i	0.387072	−	0.387072i	−0.486570	−	0.873642i	$-0.661752\pi$
$787$	10.8587	−	10.8587i	0.387072	−	0.387072i	0.873642	+	0.486570i	$0.161752\pi$
$788$	−1.50781	−	1.50781i	−0.0537137	−	0.0537137i
$789$	−13.4718	+	44.0775i	−0.479610	+	1.56920i
$790$			5.30284i			0.188667i
$791$	−6.77484	−	6.77484i	−0.240886	−	0.240886i
$792$	0.820940	−	1.21753i	0.0291708	−	0.0432630i
$793$	−4.42254	−	15.9221i	−0.157049	−	0.565412i
$794$		−	23.9988i		−	0.851684i
$795$	3.73658	+	7.02608i	0.132523	+	0.249189i
$796$	−11.1999			−0.396968
$797$	−20.7467			−0.734884			−0.367442	−	0.930046i	$-0.619766\pi$
$797$	−20.7467			−0.734884			−0.367442	+	0.930046i	$0.619766\pi$
$798$	1.22048	−	0.649069i	0.0432044	−	0.0229768i
$799$	−27.0459	−	27.0459i	−0.956814	−	0.956814i
$800$	2.94621	+	2.94621i	0.104164	+	0.104164i
$801$	−9.73976	−	50.0623i	−0.344137	−	1.76887i
$802$	27.1307			0.958019
$803$	2.04111			0.0720294
$804$	3.36629	−	1.79025i	0.118720	−	0.0631371i
$805$			2.67913i			0.0944268i
$806$	1.65282	+	5.95055i	0.0582183	+	0.209599i
$807$	−13.9336	+	45.5884i	−0.490487	+	1.60479i
$808$	9.51170	+	9.51170i	0.334621	+	0.334621i
$809$			8.50252i			0.298933i	0.988767	+	0.149466i	$0.0477556\pi$
$809$			8.50252i			0.298933i	−0.988767	+	0.149466i	$0.952244\pi$
$810$	7.61698	−	3.08041i	0.267634	−	0.108234i
$811$	30.5279	+	30.5279i	1.07198	+	1.07198i	0.997200	+	0.0747808i	$0.0238257\pi$
$811$	30.5279	+	30.5279i	1.07198	+	1.07198i	0.0747808	+	0.997200i	$0.476174\pi$
$812$	2.96172	−	2.96172i	0.103936	−	0.103936i
$813$	24.3135	−	12.9303i	0.852713	−	0.453487i
$814$	1.06217	−	1.06217i	0.0372292	−	0.0372292i
$815$			12.2301i			0.428400i
$816$	−6.20161	−	1.89546i	−0.217100	−	0.0663544i
$817$	1.38201	−	1.38201i	0.0483504	−	0.0483504i
$818$	−8.74706			−0.305834
$819$	4.83189	+	9.67744i	0.168840	+	0.338157i
$820$	3.03449			0.105969
$821$	−19.1767	+	19.1767i	−0.669270	+	0.669270i	−0.957547	−	0.288277i	$-0.906918\pi$
$821$	−19.1767	+	19.1767i	−0.669270	+	0.669270i	0.288277	+	0.957547i	$0.406918\pi$
$822$	−11.4774	−	3.50796i	−0.400321	−	0.122354i
$823$			15.6058i			0.543984i	0.962300	+	0.271992i	$0.0876824\pi$
$823$			15.6058i			0.543984i	−0.962300	+	0.271992i	$0.912318\pi$
$824$	4.67725	−	4.67725i	0.162940	−	0.162940i
$825$	3.11882	−	1.65864i	0.108584	−	0.0577465i
$826$	−2.23605	+	2.23605i	−0.0778022	+	0.0778022i
$827$	10.6978	+	10.6978i	0.371999	+	0.371999i	0.868205	−	0.496206i	$-0.165274\pi$
$827$	10.6978	+	10.6978i	0.371999	+	0.371999i	−0.496206	+	0.868205i	$0.665274\pi$
$828$	4.92194	−	7.29969i	0.171049	−	0.253682i
$829$		−	28.2914i		−	0.982601i	−0.870990	−	0.491301i	$-0.836522\pi$
$829$		−	28.2914i		−	0.982601i	0.870990	−	0.491301i	$-0.163478\pi$
$830$	−1.32630	−	1.32630i	−0.0460366	−	0.0460366i
$831$	12.4764	−	40.8205i	0.432800	−	1.41605i
$832$	−3.47403	+	0.964947i	−0.120440	+	0.0334535i
$833$		−	3.74401i		−	0.129722i
$834$	−6.77548	+	3.60331i	−0.234616	+	0.124772i
$835$	21.9616			0.760013
$836$	0.390651			0.0135109
$837$	0.928131	−	8.85179i	0.0320809	−	0.305963i
$838$	15.3738	+	15.3738i	0.531080	+	0.531080i
$839$	39.8387	+	39.8387i	1.37539	+	1.37539i	0.852249	+	0.523137i	$0.175238\pi$
$839$	39.8387	+	39.8387i	1.37539	+	1.37539i	0.523137	+	0.852249i	$0.324762\pi$
$840$	−1.39608	+	0.742456i	−0.0481692	+	0.0256172i
$841$	11.4564			0.395050
$842$	−28.2928			−0.975035
$843$	26.8996	+	50.5807i	0.926473	+	1.74209i
$844$		−	16.7046i		−	0.574997i
$845$	2.86181	−	11.5178i	0.0984491	−	0.396223i
$846$	25.4111	+	17.1339i	0.873651	+	0.589074i
$847$	−7.60876	−	7.60876i	−0.261440	−	0.261440i
$848$			5.03273i			0.172825i
$849$	4.82431	−	15.7843i	0.165570	−	0.541715i
$850$	−11.0307	−	11.0307i	−0.378348	−	0.378348i
$851$	6.36826	−	6.36826i	0.218301	−	0.218301i
$852$	2.28839	+	4.30297i	0.0783988	+	0.147417i
$853$	33.9837	−	33.9837i	1.16358	−	1.16358i	0.179894	−	0.983686i	$-0.442424\pi$
$853$	33.9837	−	33.9837i	1.16358	−	1.16358i	0.983686	−	0.179894i	$-0.0575756\pi$
$854$		−	4.58319i		−	0.156834i
$855$	1.81230	+	1.22198i	0.0619794	+	0.0417907i
$856$	−0.164114	+	0.164114i	−0.00560930	+	0.00560930i
$857$	−36.2526			−1.23836			−0.619182	−	0.785247i	$-0.712536\pi$
$857$	−36.2526			−1.23836			−0.619182	+	0.785247i	$0.712536\pi$
$858$	−0.0785280	+	3.05580i	−0.00268090	+	0.104323i
$859$	23.8722			0.814510			0.407255	−	0.913314i	$-0.366486\pi$
$859$	23.8722			0.814510			0.407255	+	0.913314i	$0.366486\pi$
$860$	−1.58085	+	1.58085i	−0.0539065	+	0.0539065i
$861$	1.68280	−	5.50581i	0.0573495	−	0.187638i
$862$			27.6770i			0.942682i
$863$	−9.11408	+	9.11408i	−0.310247	+	0.310247i	−0.845005	−	0.534758i	$-0.820403\pi$
$863$	−9.11408	+	9.11408i	−0.310247	+	0.310247i	0.534758	+	0.845005i	$0.320403\pi$
$864$	5.16782	+	0.541858i	0.175813	+	0.0184344i
$865$	0.610174	−	0.610174i	0.0207465	−	0.0207465i
$866$	1.06968	+	1.06968i	0.0363493	+	0.0363493i
$867$	−4.94008	−	1.50989i	−0.167774	−	0.0512784i
$868$			1.71287i			0.0581385i
$869$	2.01046	+	2.01046i	0.0682003	+	0.0682003i
$870$	6.33373	+	1.93584i	0.214734	+	0.0656312i
$871$	−3.90549	+	6.90944i	−0.132332	+	0.234118i
$872$		−	11.5376i		−	0.390711i
$873$	5.42244	+	27.8713i	0.183522	+	0.943300i
$874$	2.34214			0.0792242
$875$	−8.36836			−0.282902
$876$	3.39133	+	6.37688i	0.114582	+	0.215455i
$877$	34.8819	+	34.8819i	1.17788	+	1.17788i	0.980284	+	0.197594i	$0.0633129\pi$
$877$	34.8819	+	34.8819i	1.17788	+	1.17788i	0.197594	+	0.980284i	$0.436687\pi$
$878$	−2.52971	−	2.52971i	−0.0853737	−	0.0853737i
$879$	7.69058	+	14.4610i	0.259397	+	0.487757i
$880$	−0.446857			−0.0150635
$881$	5.86477			0.197589			0.0987946	−	0.995108i	$-0.468501\pi$
$881$	5.86477			0.197589			0.0987946	+	0.995108i	$0.468501\pi$
$882$	0.572916	+	2.94479i	0.0192911	+	0.0991561i
$883$		−	29.2851i		−	0.985523i	−0.870165	−	0.492761i	$-0.835988\pi$
$883$		−	29.2851i		−	0.985523i	0.870165	−	0.492761i	$-0.164012\pi$
$884$	13.0068	−	3.61277i	0.437466	−	0.121511i
$885$	−4.78187	−	1.46153i	−0.160741	−	0.0491288i
$886$	1.79033	+	1.79033i	0.0601472	+	0.0601472i
$887$			31.3717i			1.05336i	0.850064	+	0.526680i	$0.176563\pi$
$887$			31.3717i			1.05336i	−0.850064	+	0.526680i	$0.823437\pi$
$888$	5.08328	+	1.55365i	0.170584	+	0.0521371i
$889$	−11.9213	−	11.9213i	−0.399829	−	0.399829i
$890$	−10.9743	+	10.9743i	−0.367858	+	0.367858i
$891$	1.71995	−	4.05569i	0.0576205	−	0.135871i
$892$	−16.2269	+	16.2269i	−0.543315	+	0.543315i
$893$			8.15328i			0.272839i
$894$	5.01848	−	16.4196i	0.167843	−	0.549154i
$895$	−11.7257	+	11.7257i	−0.391946	+	0.391946i
$896$	−1.00000			−0.0334077
$897$	−0.470814	+	18.3210i	−0.0157200	+	0.611720i
$898$	−17.8096			−0.594314
$899$	5.07303	−	5.07303i	0.169195	−	0.169195i
$900$	10.3639	+	6.98804i	0.345463	+	0.232935i
$901$		−	18.8426i		−	0.627737i
$902$	1.15047	−	1.15047i	0.0383063	−	0.0383063i
$903$	1.99164	+	3.74497i	0.0662775	+	0.124625i
$904$	6.77484	−	6.77484i	0.225328	−	0.225328i
$905$	−11.9276	−	11.9276i	−0.396488	−	0.396488i
$906$	−4.51428	+	14.7699i	−0.149977	+	0.490698i
$907$			50.4013i			1.67355i	0.547548	+	0.836775i	$0.315562\pi$
$907$			50.4013i			1.67355i	−0.547548	+	0.836775i	$0.684438\pi$
$908$	18.5844	+	18.5844i	0.616743	+	0.616743i
$909$	33.4593	+	22.5605i	1.10978	+	0.748285i
$910$	1.61969	−	2.86550i	0.0536923	−	0.0949905i
$911$			31.2810i			1.03639i	0.855264	+	0.518193i	$0.173395\pi$
$911$			31.2810i			1.03639i	−0.855264	+	0.518193i	$0.826605\pi$
$912$	0.649069	+	1.22048i	0.0214928	+	0.0404140i
$913$	−1.00568			−0.0332831
$914$	−3.96071			−0.131009
$915$	6.39849	−	3.40282i	0.211528	−	0.112494i
$916$	10.3015	+	10.3015i	0.340371	+	0.340371i
$917$	−15.1452	−	15.1452i	−0.500140	−	0.500140i
$918$	−19.3484	−	2.02872i	−0.638591	−	0.0669578i
$919$	−22.5225			−0.742948			−0.371474	−	0.928443i	$-0.621148\pi$
$919$	−22.5225			−0.742948			−0.371474	+	0.928443i	$0.621148\pi$
$920$	−2.67913			−0.0883282
$921$	38.1063	−	20.2656i	1.25565	−	0.667773i
$922$			1.83970i			0.0605872i
$923$	−8.83200	−	4.99219i	−0.290709	−	0.164320i
$924$	−0.247807	+	0.810780i	−0.00815225	+	0.0266727i
$925$	9.04149	+	9.04149i	0.297282	+	0.297282i
$926$			11.6245i			0.382005i
$927$	11.0938	−	16.4532i	0.364369	−	0.540393i
$928$	2.96172	+	2.96172i	0.0972232	+	0.0972232i
$929$	5.35331	−	5.35331i	0.175636	−	0.175636i	−0.613814	−	0.789451i	$-0.710366\pi$
$929$	5.35331	−	5.35331i	0.175636	−	0.175636i	0.789451	+	0.613814i	$0.210366\pi$
$930$	−2.39129	+	1.27173i	−0.0784136	+	0.0417016i
$931$	−0.564337	+	0.564337i	−0.0184954	+	0.0184954i
$932$		−	29.5763i		−	0.968803i
$933$	6.81795	+	2.08384i	0.223210	+	0.0682218i
$934$	22.9909	−	22.9909i	0.752286	−	0.752286i
$935$	1.67304			0.0547141
$936$	−9.67744	+	4.83189i	−0.316317	+	0.157935i
$937$	16.9581			0.553998			0.276999	−	0.960870i	$-0.410660\pi$
$937$	16.9581			0.553998			0.276999	+	0.960870i	$0.410660\pi$
$938$	−1.55654	+	1.55654i	−0.0508228	+	0.0508228i
$939$	−25.0823	−	7.66616i	−0.818531	−	0.250176i
$940$		−	9.32636i		−	0.304192i
$941$	29.5920	−	29.5920i	0.964672	−	0.964672i	−0.0347252	−	0.999397i	$-0.511056\pi$
$941$	29.5920	−	29.5920i	0.964672	−	0.964672i	0.999397	+	0.0347252i	$0.0110556\pi$
$942$	29.3934	−	15.6319i	0.957690	−	0.509315i
$943$	6.89761	−	6.89761i	0.224617	−	0.224617i
$944$	−2.23605	−	2.23605i	−0.0727773	−	0.0727773i
$945$	−3.68578	+	2.98621i	−0.119899	+	0.0971414i
$946$			1.19869i			0.0389728i
$947$	−21.1614	−	21.1614i	−0.687653	−	0.687653i	0.274060	−	0.961713i	$-0.411633\pi$
$947$	−21.1614	−	21.1614i	−0.687653	−	0.687653i	−0.961713	+	0.274060i	$0.911633\pi$
$948$	−2.94072	+	9.62152i	−0.0955101	+	0.312492i
$949$	−13.0888	−	7.39830i	−0.424880	−	0.240159i
$950$			3.32531i			0.107887i
$951$	−34.1948	+	18.1853i	−1.10884	+	0.589700i
$952$	3.74401			0.121344
$953$	−5.31495			−0.172168			−0.0860841	−	0.996288i	$-0.527435\pi$
$953$	−5.31495			−0.172168			−0.0860841	+	0.996288i	$0.527435\pi$
$954$	2.88333	+	14.8203i	0.0933513	+	0.479825i
$955$	−9.15310	−	9.15310i	−0.296187	−	0.296187i
$956$	4.42519	+	4.42519i	0.143121	+	0.143121i
$957$	3.13524	−	1.66737i	0.101348	−	0.0538984i
$958$	−31.5586			−1.01961
$959$	6.92909			0.223752
$960$	−0.742456	−	1.39608i	−0.0239627	−	0.0450582i
$961$		−	28.0661i		−	0.905358i
$962$	−10.6613	+	2.96128i	−0.343733	+	0.0954754i
$963$	−0.389257	+	0.577305i	−0.0125436	+	0.0186034i
$964$	11.6682	+	11.6682i	0.375808	+	0.375808i
$965$			4.36181i			0.140412i
$966$	−1.48572	+	4.86103i	−0.0478024	+	0.156401i
$967$	−25.6241	−	25.6241i	−0.824017	−	0.824017i	0.162665	−	0.986681i	$-0.447991\pi$
$967$	−25.6241	−	25.6241i	−0.824017	−	0.824017i	−0.986681	+	0.162665i	$0.947991\pi$
$968$	7.60876	−	7.60876i	0.244555	−	0.244555i
$969$	−2.43012	−	4.56948i	−0.0780667	−	0.146793i
$970$	6.10972	−	6.10972i	0.196171	−	0.196171i
$971$		−	7.76748i		−	0.249270i	−0.992203	−	0.124635i	$-0.960224\pi$
$971$		−	7.76748i		−	0.249270i	0.992203	−	0.124635i	$-0.0397760\pi$
$972$	15.5286	−	1.36507i	0.498079	−	0.0437847i
$973$	3.13291	−	3.13291i	0.100437	−	0.100437i
$974$	10.4627			0.335247
$975$	−26.0117	−	0.668450i	−0.833040	−	0.0214075i
$976$	4.58319			0.146704
$977$	−4.94323	+	4.94323i	−0.158148	+	0.158148i	−0.781746	−	0.623598i	$-0.785670\pi$
$977$	−4.94323	+	4.94323i	−0.158148	+	0.158148i	0.623598	+	0.781746i	$0.285670\pi$
$978$	−6.78225	+	22.1903i	−0.216872	+	0.709568i
$979$			8.32133i			0.265951i
$980$	0.645532	−	0.645532i	0.0206208	−	0.0206208i
$981$	−6.61005	−	33.9756i	−0.211043	−	1.08476i
$982$	−15.8417	+	15.8417i	−0.505528	+	0.505528i
$983$	−30.0897	−	30.0897i	−0.959713	−	0.959713i	0.0395061	−	0.999219i	$-0.487422\pi$
$983$	−30.0897	−	30.0897i	−0.959713	−	0.959713i	−0.999219	+	0.0395061i	$0.987422\pi$
$984$	5.50581	+	1.68280i	0.175519	+	0.0536456i
$985$			1.94669i			0.0620266i
$986$	−11.0887	−	11.0887i	−0.353136	−	0.353136i
$987$	−16.9218	−	5.17198i	−0.538627	−	0.164626i
$988$	−2.50508	−	1.41597i	−0.0796971	−	0.0450479i
$989$			7.18675i			0.228525i
$990$	−1.31590	+	0.256011i	−0.0418220	+	0.00813658i
$991$	−21.8501			−0.694092			−0.347046	−	0.937848i	$-0.612815\pi$
$991$	−21.8501			−0.694092			−0.347046	+	0.937848i	$0.612815\pi$
$992$	−1.71287			−0.0543836
$993$	13.2491	+	24.9129i	0.420447	+	0.790588i
$994$	−1.98965	−	1.98965i	−0.0631078	−	0.0631078i
$995$	7.22987	+	7.22987i	0.229202	+	0.229202i
$996$	−1.67094	−	3.14196i	−0.0529459	−	0.0995568i
$997$	7.97068			0.252434			0.126217	−	0.992003i	$-0.459716\pi$
$997$	7.97068			0.252434			0.126217	+	0.992003i	$0.459716\pi$
$998$	−36.5079			−1.15564
$999$	15.8593	+	1.66288i	0.501765	+	0.0526113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.c.281.5	yes	20
3.2	odd	2		546.2.p.d.281.10	yes	20
13.5	odd	4		546.2.p.d.239.10	yes	20
39.5	even	4	inner	546.2.p.c.239.5	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.5	✓	20	39.5	even	4	inner
546.2.p.c.281.5	yes	20	1.1	even	1	trivial
546.2.p.d.239.10	yes	20	13.5	odd	4
546.2.p.d.281.10	yes	20	3.2	odd	2

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.65641 + 0.506265i) q^{3} -1.00000i q^{4} +(-0.645532 + 0.645532i) q^{5} +(-1.52924 + 0.813276i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.48739 + 1.67717i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.65641 + 0.506265i) q^{3} -1.00000i q^{4} +(-0.645532 + 0.645532i) q^{5} +(-1.52924 + 0.813276i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.48739 + 1.67717i) q^{9} -0.912921i q^{10} +(-0.346115 - 0.346115i) q^{11} +(0.506265 - 1.65641i) q^{12} +(0.964947 + 3.47403i) q^{13} +1.00000i q^{14} +(-1.39608 + 0.742456i) q^{15} -1.00000 q^{16} +3.74401 q^{17} +(-2.94479 + 0.572916i) q^{18} +(-0.564337 - 0.564337i) q^{19} +(0.645532 + 0.645532i) q^{20} +(1.52924 - 0.813276i) q^{21} +0.489480 q^{22} +2.93468 q^{23} +(0.813276 + 1.52924i) q^{24} +4.16658i q^{25} +(-3.13883 - 1.77419i) q^{26} +(3.27105 + 4.03735i) q^{27} +(-0.707107 - 0.707107i) q^{28} +4.18850i q^{29} +(0.462180 - 1.51217i) q^{30} +(-1.21118 - 1.21118i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.398082 - 0.748534i) q^{33} +(-2.64741 + 2.64741i) q^{34} +0.912921i q^{35} +(1.67717 - 2.48739i) q^{36} +(2.17001 - 2.17001i) q^{37} +0.798093 q^{38} +(-0.160431 + 6.24294i) q^{39} -0.912921 q^{40} +(2.35038 - 2.35038i) q^{41} +(-0.506265 + 1.65641i) q^{42} +2.44891i q^{43} +(-0.346115 + 0.346115i) q^{44} +(-2.68836 + 0.523027i) q^{45} +(-2.07513 + 2.07513i) q^{46} +(-7.22377 - 7.22377i) q^{47} +(-1.65641 - 0.506265i) q^{48} -1.00000i q^{49} +(-2.94621 - 2.94621i) q^{50} +(6.20161 + 1.89546i) q^{51} +(3.47403 - 0.964947i) q^{52} -5.03273i q^{53} +(-5.16782 - 0.541858i) q^{54} +0.446857 q^{55} +1.00000 q^{56} +(-0.649069 - 1.22048i) q^{57} +(-2.96172 - 2.96172i) q^{58} +(2.23605 + 2.23605i) q^{59} +(0.742456 + 1.39608i) q^{60} -4.58319 q^{61} +1.71287 q^{62} +(2.94479 - 0.572916i) q^{63} +1.00000i q^{64} +(-2.86550 - 1.61969i) q^{65} +(0.810780 + 0.247807i) q^{66} +(1.55654 + 1.55654i) q^{67} -3.74401i q^{68} +(4.86103 + 1.48572i) q^{69} +(-0.645532 - 0.645532i) q^{70} +(-1.98965 + 1.98965i) q^{71} +(0.572916 + 2.94479i) q^{72} +(-2.94861 + 2.94861i) q^{73} +3.06885i q^{74} +(-2.10939 + 6.90156i) q^{75} +(-0.564337 + 0.564337i) q^{76} -0.489480 q^{77} +(-4.30098 - 4.52787i) q^{78} -5.80866 q^{79} +(0.645532 - 0.645532i) q^{80} +(3.37423 + 8.34353i) q^{81} +3.32394i q^{82} +(1.45281 - 1.45281i) q^{83} +(-0.813276 - 1.52924i) q^{84} +(-2.41688 + 2.41688i) q^{85} +(-1.73164 - 1.73164i) q^{86} +(-2.12049 + 6.93788i) q^{87} -0.489480i q^{88} +(-12.0210 - 12.0210i) q^{89} +(1.53112 - 2.27079i) q^{90} +(3.13883 + 1.77419i) q^{91} -2.93468i q^{92} +(-1.39303 - 2.61939i) q^{93} +10.2160 q^{94} +0.728595 q^{95} +(1.52924 - 0.813276i) q^{96} +(6.69250 + 6.69250i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-0.280431 - 1.44142i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9}+O(q^{10}) \) 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9 - 16 * q^11 - 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 + 12 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 24 * q^27 + 12 * q^30 - 8 * q^31 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * q^54 + 28 * q^55 + 20 * q^56 + 36 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 48 * q^62 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * q^78 - 64 * q^79 + 4 * q^80 + 32 * q^81 - 24 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^89 - 8 * q^90 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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