LMFDB - Embedded newform 546.2.o.d.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(265,546)]

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([0, 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("546.265");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.o (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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.7442857984.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 $ x^8 + 26x^6 + 205x^4 + 540*x^2 + 324
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			307.3
Root			$1.91681i$ of defining polynomial
Character	$\chi$	$=$	546.307
Dual form			546.2.o.d.265.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(-2.27220 + 2.27220i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.27220 - 1.35539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(-2.27220 + 2.27220i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.27220 - 1.35539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -3.21338 q^{10} +(0.355392 - 0.355392i) q^{11} -1.00000 q^{12} +(-2.00000 - 3.00000i) q^{13} +(-0.648285 - 2.56510i) q^{14} +(-2.27220 - 2.27220i) q^{15} -1.00000 q^{16} +4.32583 q^{17} +(-0.707107 - 0.707107i) q^{18} +(-5.98299 + 5.98299i) q^{19} +(-2.27220 - 2.27220i) q^{20} +(1.35539 - 2.27220i) q^{21} +0.502600 q^{22} -2.38496i q^{23} +(-0.707107 - 0.707107i) q^{24} -5.32583i q^{25} +(0.707107 - 3.53553i) q^{26} -1.00000i q^{27} +(1.35539 - 2.27220i) q^{28} +1.09574 q^{29} -3.21338i q^{30} +(-1.08319 + 1.08319i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.355392 + 0.355392i) q^{33} +(3.05882 + 3.05882i) q^{34} +(8.24264 - 2.08319i) q^{35} -1.00000i q^{36} +(-5.18902 + 5.18902i) q^{37} -8.46122 q^{38} +(3.00000 - 2.00000i) q^{39} -3.21338i q^{40} +(-3.53186 + 3.53186i) q^{41} +(2.56510 - 0.648285i) q^{42} +7.44867i q^{43} +(0.355392 + 0.355392i) q^{44} +(2.27220 - 2.27220i) q^{45} +(1.68642 - 1.68642i) q^{46} +(4.71078 + 4.71078i) q^{47} -1.00000i q^{48} +(3.32583 + 6.15945i) q^{49} +(3.76593 - 3.76593i) q^{50} +4.32583i q^{51} +(3.00000 - 2.00000i) q^{52} -11.2552 q^{53} +(0.707107 - 0.707107i) q^{54} +1.61504i q^{55} +(2.56510 - 0.648285i) q^{56} +(-5.98299 - 5.98299i) q^{57} +(0.774804 + 0.774804i) q^{58} +(-3.61504 - 3.61504i) q^{59} +(2.27220 - 2.27220i) q^{60} -4.32583i q^{61} -1.53186 q^{62} +(2.27220 + 1.35539i) q^{63} -1.00000i q^{64} +(11.3610 + 2.27220i) q^{65} +0.502600i q^{66} +(-0.531858 - 0.531858i) q^{67} +4.32583i q^{68} +2.38496 q^{69} +(7.30146 + 4.35539i) q^{70} +(6.38496 + 6.38496i) q^{71} +(0.707107 - 0.707107i) q^{72} +(5.18902 + 5.18902i) q^{73} -7.33838 q^{74} +5.32583 q^{75} +(-5.98299 - 5.98299i) q^{76} +(-1.28922 + 0.325828i) q^{77} +(3.53553 + 0.707107i) q^{78} -11.3143 q^{79} +(2.27220 - 2.27220i) q^{80} +1.00000 q^{81} -4.99480 q^{82} +(-6.71078 + 6.71078i) q^{83} +(2.27220 + 1.35539i) q^{84} +(-9.82917 + 9.82917i) q^{85} +(-5.26701 + 5.26701i) q^{86} +1.09574i q^{87} +0.502600i q^{88} +(3.75044 + 3.75044i) q^{89} +3.21338 q^{90} +(0.478235 + 9.52740i) q^{91} +2.38496 q^{92} +(-1.08319 - 1.08319i) q^{93} +6.66205i q^{94} -27.1891i q^{95} +(0.707107 - 0.707107i) q^{96} +(12.9931 - 12.9931i) q^{97} +(-2.00368 + 6.70711i) q^{98} +(-0.355392 + 0.355392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^5 + 4 * q^7 - 8 * q^9	$ 8 q + 4 q^{5} + 4 q^{7} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 8 q^{12} - 16 q^{13} + 4 q^{15} - 8 q^{16} + 12 q^{17} - 4 q^{19} + 4 q^{20} + 4 q^{22} - 12 q^{29} - 20 q^{31} - 8 q^{33} + 24 q^{34} + 32 q^{35} - 8 q^{37} - 12 q^{38} + 24 q^{39} - 16 q^{41} + 4 q^{42} - 8 q^{44} - 4 q^{45} - 20 q^{46} + 16 q^{47} + 4 q^{49} + 24 q^{50} + 24 q^{52} - 24 q^{53} + 4 q^{56} - 4 q^{57} - 16 q^{58} - 28 q^{59} - 4 q^{60} - 4 q^{63} - 20 q^{65} + 8 q^{67} + 20 q^{69} + 24 q^{70} + 52 q^{71} + 8 q^{73} - 4 q^{74} + 20 q^{75} - 4 q^{76} - 32 q^{77} - 48 q^{79} - 4 q^{80} + 8 q^{81} - 40 q^{82} - 32 q^{83} - 4 q^{84} + 20 q^{85} - 20 q^{86} - 4 q^{89} + 4 q^{90} - 8 q^{91} + 20 q^{92} - 20 q^{93} + 36 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^5 + 4 * q^7 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 8 * q^12 - 16 * q^13 + 4 * q^15 - 8 * q^16 + 12 * q^17 - 4 * q^19 + 4 * q^20 + 4 * q^22 - 12 * q^29 - 20 * q^31 - 8 * q^33 + 24 * q^34 + 32 * q^35 - 8 * q^37 - 12 * q^38 + 24 * q^39 - 16 * q^41 + 4 * q^42 - 8 * q^44 - 4 * q^45 - 20 * q^46 + 16 * q^47 + 4 * q^49 + 24 * q^50 + 24 * q^52 - 24 * q^53 + 4 * q^56 - 4 * q^57 - 16 * q^58 - 28 * q^59 - 4 * q^60 - 4 * q^63 - 20 * q^65 + 8 * q^67 + 20 * q^69 + 24 * q^70 + 52 * q^71 + 8 * q^73 - 4 * q^74 + 20 * q^75 - 4 * q^76 - 32 * q^77 - 48 * q^79 - 4 * q^80 + 8 * q^81 - 40 * q^82 - 32 * q^83 - 4 * q^84 + 20 * q^85 - 20 * q^86 - 4 * q^89 + 4 * q^90 - 8 * q^91 + 20 * q^92 - 20 * q^93 + 36 * q^97 + 8 * 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
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$			1.00000i			0.500000i
$5$	−2.27220	+	2.27220i	−1.01616	+	1.01616i	−0.0162935	+	0.999867i	$0.505187\pi$
$5$	−2.27220	+	2.27220i	−1.01616	+	1.01616i	−0.999867	+	0.0162935i	$0.994813\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−2.27220	−	1.35539i	−0.858813	−	0.512290i
$7$	−2.27220	−	1.35539i	−0.858813	−	0.512290i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	−3.21338			−1.01616
$11$	0.355392	−	0.355392i	0.107155	−	0.107155i	−0.651497	−	0.758651i	$-0.725859\pi$
$11$	0.355392	−	0.355392i	0.107155	−	0.107155i	0.758651	+	0.651497i	$0.225859\pi$
$12$	−1.00000			−0.288675
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$14$	−0.648285	−	2.56510i	−0.173261	−	0.685551i
$15$	−2.27220	−	2.27220i	−0.586681	−	0.586681i
$16$	−1.00000			−0.250000
$17$	4.32583			1.04917			0.524584	−	0.851359i	$-0.324221\pi$
$17$	4.32583			1.04917			0.524584	+	0.851359i	$0.324221\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−5.98299	+	5.98299i	−1.37259	+	1.37259i	−0.516007	+	0.856584i	$0.672582\pi$
$19$	−5.98299	+	5.98299i	−1.37259	+	1.37259i	−0.856584	+	0.516007i	$0.827418\pi$
$20$	−2.27220	−	2.27220i	−0.508080	−	0.508080i
$21$	1.35539	−	2.27220i	0.295771	−	0.495836i
$22$	0.502600			0.107155
$23$		−	2.38496i		−	0.497298i	−0.968594	−	0.248649i	$-0.920014\pi$
$23$		−	2.38496i		−	0.497298i	0.968594	−	0.248649i	$-0.0799865\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$		−	5.32583i		−	1.06517i
$26$	0.707107	−	3.53553i	0.138675	−	0.693375i
$27$		−	1.00000i		−	0.192450i
$28$	1.35539	−	2.27220i	0.256145	−	0.429406i
$29$	1.09574			0.203474			0.101737	−	0.994811i	$-0.467560\pi$
$29$	1.09574			0.203474			0.101737	+	0.994811i	$0.467560\pi$
$30$		−	3.21338i		−	0.586681i
$31$	−1.08319	+	1.08319i	−0.194546	+	0.194546i	−0.797657	−	0.603111i	$-0.793928\pi$
$31$	−1.08319	+	1.08319i	−0.194546	+	0.194546i	0.603111	+	0.797657i	$0.293928\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.355392	+	0.355392i	0.0618657	+	0.0618657i
$34$	3.05882	+	3.05882i	0.524584	+	0.524584i
$35$	8.24264	−	2.08319i	1.39326	−	0.352123i
$36$		−	1.00000i		−	0.166667i
$37$	−5.18902	+	5.18902i	−0.853069	+	0.853069i	−0.990510	−	0.137441i	$-0.956112\pi$
$37$	−5.18902	+	5.18902i	−0.853069	+	0.853069i	0.137441	+	0.990510i	$0.456112\pi$
$38$	−8.46122			−1.37259
$39$	3.00000	−	2.00000i	0.480384	−	0.320256i
$40$		−	3.21338i		−	0.508080i
$41$	−3.53186	+	3.53186i	−0.551583	+	0.551583i	−0.926898	−	0.375314i	$-0.877535\pi$
$41$	−3.53186	+	3.53186i	−0.551583	+	0.551583i	0.375314	+	0.926898i	$0.377535\pi$
$42$	2.56510	−	0.648285i	0.395803	−	0.100033i
$43$			7.44867i			1.13591i	0.823059	+	0.567956i	$0.192266\pi$
$43$			7.44867i			1.13591i	−0.823059	+	0.567956i	$0.807734\pi$
$44$	0.355392	+	0.355392i	0.0535773	+	0.0535773i
$45$	2.27220	−	2.27220i	0.338720	−	0.338720i
$46$	1.68642	−	1.68642i	0.248649	−	0.248649i
$47$	4.71078	+	4.71078i	0.687138	+	0.687138i	0.961598	−	0.274460i	$-0.0884991\pi$
$47$	4.71078	+	4.71078i	0.687138	+	0.687138i	−0.274460	+	0.961598i	$0.588499\pi$
$48$		−	1.00000i		−	0.144338i
$49$	3.32583	+	6.15945i	0.475118	+	0.879922i
$50$	3.76593	−	3.76593i	0.532583	−	0.532583i
$51$			4.32583i			0.605737i
$52$	3.00000	−	2.00000i	0.416025	−	0.277350i
$53$	−11.2552			−1.54602			−0.773010	−	0.634394i	$-0.781250\pi$
$53$	−11.2552			−1.54602			−0.773010	+	0.634394i	$0.781250\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$			1.61504i			0.217773i
$56$	2.56510	−	0.648285i	0.342776	−	0.0866307i
$57$	−5.98299	−	5.98299i	−0.792466	−	0.792466i
$58$	0.774804	+	0.774804i	0.101737	+	0.101737i
$59$	−3.61504	−	3.61504i	−0.470639	−	0.470639i	0.431483	−	0.902121i	$-0.357991\pi$
$59$	−3.61504	−	3.61504i	−0.470639	−	0.470639i	−0.902121	+	0.431483i	$0.857991\pi$
$60$	2.27220	−	2.27220i	0.293340	−	0.293340i
$61$		−	4.32583i		−	0.553865i	−0.960889	−	0.276933i	$-0.910682\pi$
$61$		−	4.32583i		−	0.553865i	0.960889	−	0.276933i	$-0.0893179\pi$
$62$	−1.53186			−0.194546
$63$	2.27220	+	1.35539i	0.286271	+	0.170763i
$64$		−	1.00000i		−	0.125000i
$65$	11.3610	+	2.27220i	1.40916	+	0.281832i
$66$			0.502600i			0.0618657i
$67$	−0.531858	−	0.531858i	−0.0649768	−	0.0649768i	0.673872	−	0.738848i	$-0.264630\pi$
$67$	−0.531858	−	0.531858i	−0.0649768	−	0.0649768i	−0.738848	+	0.673872i	$0.764630\pi$
$68$			4.32583i			0.524584i
$69$	2.38496			0.287115
$70$	7.30146	+	4.35539i	0.872692	+	0.520569i
$71$	6.38496	+	6.38496i	0.757755	+	0.757755i	0.975913	−	0.218159i	$-0.0700050\pi$
$71$	6.38496	+	6.38496i	0.757755	+	0.757755i	−0.218159	+	0.975913i	$0.570005\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	5.18902	+	5.18902i	0.607329	+	0.607329i	0.942247	−	0.334919i	$-0.108709\pi$
$73$	5.18902	+	5.18902i	0.607329	+	0.607329i	−0.334919	+	0.942247i	$0.608709\pi$
$74$	−7.33838			−0.853069
$75$	5.32583			0.614974
$76$	−5.98299	−	5.98299i	−0.686296	−	0.686296i
$77$	−1.28922	+	0.325828i	−0.146920	+	0.0371315i
$78$	3.53553	+	0.707107i	0.400320	+	0.0800641i
$79$	−11.3143			−1.27296			−0.636480	−	0.771293i	$-0.719610\pi$
$79$	−11.3143			−1.27296			−0.636480	+	0.771293i	$0.719610\pi$
$80$	2.27220	−	2.27220i	0.254040	−	0.254040i
$81$	1.00000			0.111111
$82$	−4.99480			−0.551583
$83$	−6.71078	+	6.71078i	−0.736604	+	0.736604i	−0.971919	−	0.235315i	$-0.924388\pi$
$83$	−6.71078	+	6.71078i	−0.736604	+	0.736604i	0.235315	+	0.971919i	$0.424388\pi$
$84$	2.27220	+	1.35539i	0.247918	+	0.147885i
$85$	−9.82917	+	9.82917i	−1.06612	+	1.06612i
$86$	−5.26701	+	5.26701i	−0.567956	+	0.567956i
$87$			1.09574i			0.117475i
$88$			0.502600i			0.0535773i
$89$	3.75044	+	3.75044i	0.397546	+	0.397546i	0.877367	−	0.479821i	$-0.159298\pi$
$89$	3.75044	+	3.75044i	0.397546	+	0.397546i	−0.479821	+	0.877367i	$0.659298\pi$
$90$	3.21338			0.338720
$91$	0.478235	+	9.52740i	0.0501326	+	0.998743i
$92$	2.38496			0.248649
$93$	−1.08319	−	1.08319i	−0.112321	−	0.112321i
$94$			6.66205i			0.687138i
$95$		−	27.1891i		−	2.78955i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	12.9931	−	12.9931i	1.31925	−	1.31925i	0.404876	−	0.914372i	$-0.367315\pi$
$97$	12.9931	−	12.9931i	1.31925	−	1.31925i	0.914372	−	0.404876i	$-0.132685\pi$
$98$	−2.00368	+	6.70711i	−0.202402	+	0.677520i
$99$	−0.355392	+	0.355392i	−0.0357182	+	0.0357182i
$100$	5.32583			0.532583
$101$	19.7996			1.97013			0.985067	−	0.172171i	$-0.0550783\pi$
$101$	19.7996			1.97013			0.985067	+	0.172171i	$0.0550783\pi$
$102$	−3.05882	+	3.05882i	−0.302869	+	0.302869i
$103$	−2.70386			−0.266420			−0.133210	−	0.991088i	$-0.542528\pi$
$103$	−2.70386			−0.266420			−0.133210	+	0.991088i	$0.542528\pi$
$104$	3.53553	+	0.707107i	0.346688	+	0.0693375i
$105$	2.08319	+	8.24264i	0.203298	+	0.804399i
$106$	−7.95862	−	7.95862i	−0.773010	−	0.773010i
$107$	−11.6673			−1.12792			−0.563958	−	0.825804i	$-0.690722\pi$
$107$	−11.6673			−1.12792			−0.563958	+	0.825804i	$0.690722\pi$
$108$	1.00000			0.0962250
$109$	−5.29626	−	5.29626i	−0.507290	−	0.507290i	0.406404	−	0.913694i	$-0.366783\pi$
$109$	−5.29626	−	5.29626i	−0.507290	−	0.507290i	−0.913694	+	0.406404i	$0.866783\pi$
$110$	−1.14201	+	1.14201i	−0.108886	+	0.108886i
$111$	−5.18902	−	5.18902i	−0.492520	−	0.492520i
$112$	2.27220	+	1.35539i	0.214703	+	0.128072i
$113$	20.3440			1.91380			0.956902	−	0.290412i	$-0.0937923\pi$
$113$	20.3440			1.91380			0.956902	+	0.290412i	$0.0937923\pi$
$114$		−	8.46122i		−	0.792466i
$115$	5.41911	+	5.41911i	0.505334	+	0.505334i
$116$			1.09574i			0.101737i
$117$	2.00000	+	3.00000i	0.184900	+	0.277350i
$118$		−	5.11245i		−	0.470639i
$119$	−9.82917	−	5.86319i	−0.901038	−	0.537478i
$120$	3.21338			0.293340
$121$			10.7474i			0.977036i
$122$	3.05882	−	3.05882i	0.276933	−	0.276933i
$123$	−3.53186	−	3.53186i	−0.318457	−	0.318457i
$124$	−1.08319	−	1.08319i	−0.0972731	−	0.0972731i
$125$	0.740347	+	0.740347i	0.0662186	+	0.0662186i
$126$	0.648285	+	2.56510i	0.0577538	+	0.228517i
$127$		−	7.60812i		−	0.675112i	−0.941305	−	0.337556i	$-0.890400\pi$
$127$		−	7.60812i		−	0.675112i	0.941305	−	0.337556i	$-0.109600\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−7.44867			−0.655819
$130$	6.42677	+	9.64015i	0.563665	+	0.845497i
$131$		−	6.87024i		−	0.600255i	−0.953899	−	0.300128i	$-0.902971\pi$
$131$		−	6.87024i		−	0.600255i	0.953899	−	0.300128i	$-0.0970293\pi$
$132$	−0.355392	+	0.355392i	−0.0309329	+	0.0309329i
$133$	21.7039	−	5.48528i	1.88196	−	0.475634i
$134$		−	0.752160i		−	0.0649768i
$135$	2.27220	+	2.27220i	0.195560	+	0.195560i
$136$	−3.05882	+	3.05882i	−0.262292	+	0.262292i
$137$	−0.272205	+	0.272205i	−0.0232560	+	0.0232560i	−0.718639	−	0.695383i	$-0.755235\pi$
$137$	−0.272205	+	0.272205i	−0.0232560	+	0.0232560i	0.695383	+	0.718639i	$0.255235\pi$
$138$	1.68642	+	1.68642i	0.143557	+	0.143557i
$139$			20.3440i			1.72556i	0.505583	+	0.862778i	$0.331278\pi$
$139$			20.3440i			1.72556i	−0.505583	+	0.862778i	$0.668722\pi$
$140$	2.08319	+	8.24264i	0.176061	+	0.696630i
$141$	−4.71078	+	4.71078i	−0.396720	+	0.396720i
$142$			9.02969i			0.757755i
$143$	−1.77696	−	0.355392i	−0.148597	−	0.0297193i
$144$	1.00000			0.0833333
$145$	−2.48974	+	2.48974i	−0.206762	+	0.206762i
$146$			7.33838i			0.607329i
$147$	−6.15945	+	3.32583i	−0.508023	+	0.274310i
$148$	−5.18902	−	5.18902i	−0.426535	−	0.426535i
$149$	10.5685	+	10.5685i	0.865803	+	0.865803i	0.992005	−	0.126202i	$-0.0402787\pi$
$149$	10.5685	+	10.5685i	0.865803	+	0.865803i	−0.126202	+	0.992005i	$0.540279\pi$
$150$	3.76593	+	3.76593i	0.307487	+	0.307487i
$151$	−0.149362	+	0.149362i	−0.0121549	+	0.0121549i	−0.713158	−	0.701003i	$-0.752736\pi$
$151$	−0.149362	+	0.149362i	−0.0121549	+	0.0121549i	0.701003	+	0.713158i	$0.252736\pi$
$152$		−	8.46122i		−	0.686296i
$153$	−4.32583			−0.349722
$154$	−1.14201	−	0.681219i	−0.0920257	−	0.0548942i
$155$		−	4.92244i		−	0.395380i
$156$	2.00000	+	3.00000i	0.160128	+	0.240192i
$157$		−	10.7630i		−	0.858980i	−0.903072	−	0.429490i	$-0.858693\pi$
$157$		−	10.7630i		−	0.858980i	0.903072	−	0.429490i	$-0.141307\pi$
$158$	−8.00043	−	8.00043i	−0.636480	−	0.636480i
$159$		−	11.2552i		−	0.892595i
$160$	3.21338			0.254040
$161$	−3.23255	+	5.41911i	−0.254761	+	0.427085i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−3.40901	+	3.40901i	−0.267015	+	0.267015i	−0.827896	−	0.560881i	$-0.810462\pi$
$163$	−3.40901	+	3.40901i	−0.267015	+	0.267015i	0.560881	+	0.827896i	$0.310462\pi$
$164$	−3.53186	−	3.53186i	−0.275792	−	0.275792i
$165$	−1.61504			−0.125731
$166$	−9.49048			−0.736604
$167$	10.0226	+	10.0226i	0.775575	+	0.775575i	0.979075	−	0.203500i	$-0.0652316\pi$
$167$	10.0226	+	10.0226i	0.775575	+	0.775575i	−0.203500	+	0.979075i	$0.565232\pi$
$168$	0.648285	+	2.56510i	0.0500163	+	0.197902i
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	−13.9005			−1.06612
$171$	5.98299	−	5.98299i	0.457531	−	0.457531i
$172$	−7.44867			−0.567956
$173$	19.7405			1.50084			0.750420	−	0.660961i	$-0.229851\pi$
$173$	19.7405			1.50084			0.750420	+	0.660961i	$0.229851\pi$
$174$	−0.774804	+	0.774804i	−0.0587377	+	0.0587377i
$175$	−7.21858	+	12.1014i	−0.545673	+	0.914778i
$176$	−0.355392	+	0.355392i	−0.0267886	+	0.0267886i
$177$	3.61504	−	3.61504i	0.271723	−	0.271723i
$178$			5.30392i			0.397546i
$179$		−	9.79960i		−	0.732457i	−0.930525	−	0.366228i	$-0.880649\pi$
$179$		−	9.79960i		−	0.732457i	0.930525	−	0.366228i	$-0.119351\pi$
$180$	2.27220	+	2.27220i	0.169360	+	0.169360i
$181$	−10.4372			−0.775788			−0.387894	−	0.921704i	$-0.626797\pi$
$181$	−10.4372			−0.775788			−0.387894	+	0.921704i	$0.626797\pi$
$182$	−6.39872	+	7.07505i	−0.474305	+	0.524438i
$183$	4.32583			0.319774
$184$	1.68642	+	1.68642i	0.124324	+	0.124324i
$185$		−	23.5810i		−	1.73371i
$186$		−	1.53186i		−	0.112321i
$187$	1.53736	−	1.53736i	0.112423	−	0.112423i
$188$	−4.71078	+	4.71078i	−0.343569	+	0.343569i
$189$	−1.35539	+	2.27220i	−0.0985902	+	0.165279i
$190$	19.2256	−	19.2256i	1.39477	−	1.39477i
$191$	11.1410			0.806136			0.403068	−	0.915170i	$-0.367944\pi$
$191$	11.1410			0.806136			0.403068	+	0.915170i	$0.367944\pi$
$192$	1.00000			0.0721688
$193$	4.03661	−	4.03661i	0.290562	−	0.290562i	−0.546741	−	0.837302i	$-0.684132\pi$
$193$	4.03661	−	4.03661i	0.290562	−	0.290562i	0.837302	+	0.546741i	$0.184132\pi$
$194$	18.3750			1.31925
$195$	−2.27220	+	11.3610i	−0.162716	+	0.813580i
$196$	−6.15945	+	3.32583i	−0.439961	+	0.237559i
$197$	0.627596	+	0.627596i	0.0447144	+	0.0447144i	0.729110	−	0.684396i	$-0.239934\pi$
$197$	0.627596	+	0.627596i	0.0447144	+	0.0447144i	−0.684396	+	0.729110i	$0.739934\pi$
$198$	−0.502600			−0.0357182
$199$	−16.5375			−1.17231			−0.586156	−	0.810198i	$-0.699359\pi$
$199$	−16.5375			−1.17231			−0.586156	+	0.810198i	$0.699359\pi$
$200$	3.76593	+	3.76593i	0.266291	+	0.266291i
$201$	0.531858	−	0.531858i	0.0375143	−	0.0375143i
$202$	14.0004	+	14.0004i	0.985067	+	0.985067i
$203$	−2.48974	−	1.48515i	−0.174746	−	0.104237i
$204$	−4.32583			−0.302869
$205$		−	16.0502i		−	1.12100i
$206$	−1.91192	−	1.91192i	−0.133210	−	0.133210i
$207$			2.38496i			0.165766i
$208$	2.00000	+	3.00000i	0.138675	+	0.208013i
$209$			4.25261i			0.294159i
$210$	−4.35539	+	7.30146i	−0.300551	+	0.503849i
$211$	−0.551329			−0.0379551			−0.0189775	−	0.999820i	$-0.506041\pi$
$211$	−0.551329			−0.0379551			−0.0189775	+	0.999820i	$0.506041\pi$
$212$		−	11.2552i		−	0.773010i
$213$	−6.38496	+	6.38496i	−0.437490	+	0.437490i
$214$	−8.24999	−	8.24999i	−0.563958	−	0.563958i
$215$	−16.9249	−	16.9249i	−1.15427	−	1.15427i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	3.92936	−	0.993080i	0.266743	−	0.0674147i
$218$		−	7.49005i		−	0.507290i
$219$	−5.18902	+	5.18902i	−0.350641	+	0.350641i
$220$	−1.61504			−0.108886
$221$	−8.65166	−	12.9775i	−0.581973	−	0.872960i
$222$		−	7.33838i		−	0.492520i
$223$	9.89430	−	9.89430i	0.662571	−	0.662571i	−0.293414	−	0.955985i	$-0.594792\pi$
$223$	9.89430	−	9.89430i	0.662571	−	0.662571i	0.955985	+	0.293414i	$0.0947915\pi$
$224$	0.648285	+	2.56510i	0.0433153	+	0.171388i
$225$			5.32583i			0.355055i
$226$	14.3854	+	14.3854i	0.956902	+	0.956902i
$227$	1.67417	−	1.67417i	0.111119	−	0.111119i	−0.649361	−	0.760480i	$-0.724964\pi$
$227$	1.67417	−	1.67417i	0.111119	−	0.111119i	0.760480	+	0.649361i	$0.224964\pi$
$228$	5.98299	−	5.98299i	0.396233	−	0.396233i
$229$	−1.32583	−	1.32583i	−0.0876132	−	0.0876132i	0.661942	−	0.749555i	$-0.269733\pi$
$229$	−1.32583	−	1.32583i	−0.0876132	−	0.0876132i	−0.749555	+	0.661942i	$0.769733\pi$
$230$			7.66377i			0.505334i
$231$	−0.325828	−	1.28922i	−0.0214379	−	0.0848242i
$232$	−0.774804	+	0.774804i	−0.0508684	+	0.0508684i
$233$			10.2117i			0.668988i	0.942398	+	0.334494i	$0.108565\pi$
$233$			10.2117i			0.668988i	−0.942398	+	0.334494i	$0.891435\pi$
$234$	−0.707107	+	3.53553i	−0.0462250	+	0.231125i
$235$	−21.4077			−1.39649
$236$	3.61504	−	3.61504i	0.235319	−	0.235319i
$237$		−	11.3143i		−	0.734944i
$238$	−2.80437	−	11.0962i	−0.181780	−	0.719258i
$239$	−15.2212	−	15.2212i	−0.984575	−	0.984575i	0.0153074	−	0.999883i	$-0.495127\pi$
$239$	−15.2212	−	15.2212i	−0.984575	−	0.984575i	−0.999883	+	0.0153074i	$0.995127\pi$
$240$	2.27220	+	2.27220i	0.146670	+	0.146670i
$241$	3.38496	+	3.38496i	0.218044	+	0.218044i	0.807674	−	0.589630i	$-0.200726\pi$
$241$	3.38496	+	3.38496i	0.218044	+	0.218044i	−0.589630	+	0.807674i	$0.700726\pi$
$242$	−7.59955	+	7.59955i	−0.488518	+	0.488518i
$243$			1.00000i			0.0641500i
$244$	4.32583			0.276933
$245$	−21.5525	−	6.43858i	−1.37694	−	0.411346i
$246$		−	4.99480i		−	0.318457i
$247$	29.9149	+	5.98299i	1.90344	+	0.380688i
$248$		−	1.53186i		−	0.0972731i
$249$	−6.71078	−	6.71078i	−0.425279	−	0.425279i
$250$			1.04701i			0.0662186i
$251$	−17.2281			−1.08743			−0.543714	−	0.839271i	$-0.682982\pi$
$251$	−17.2281			−1.08743			−0.543714	+	0.839271i	$0.682982\pi$
$252$	−1.35539	+	2.27220i	−0.0853816	+	0.143135i
$253$	−0.847593	−	0.847593i	−0.0532877	−	0.0532877i
$254$	5.37976	−	5.37976i	0.337556	−	0.337556i
$255$	−9.82917	−	9.82917i	−0.615526	−	0.615526i
$256$	1.00000			0.0625000
$257$	−3.32324			−0.207298			−0.103649	−	0.994614i	$-0.533052\pi$
$257$	−3.32324			−0.207298			−0.103649	+	0.994614i	$0.533052\pi$
$258$	−5.26701	−	5.26701i	−0.327909	−	0.327909i
$259$	18.8237	−	4.75736i	1.16965	−	0.295608i
$260$	−2.27220	+	11.3610i	−0.140916	+	0.704581i
$261$	−1.09574			−0.0678245
$262$	4.85799	−	4.85799i	0.300128	−	0.300128i
$263$	−0.818029			−0.0504418			−0.0252209	−	0.999682i	$-0.508029\pi$
$263$	−0.818029			−0.0504418			−0.0252209	+	0.999682i	$0.508029\pi$
$264$	−0.502600			−0.0309329
$265$	25.5741	−	25.5741i	1.57100	−	1.57100i
$266$	19.2256	+	11.4683i	1.17880	+	0.703165i
$267$	−3.75044	+	3.75044i	−0.229523	+	0.229523i
$268$	0.531858	−	0.531858i	0.0324884	−	0.0324884i
$269$			21.6081i			1.31747i	0.752375	+	0.658735i	$0.228908\pi$
$269$			21.6081i			1.31747i	−0.752375	+	0.658735i	$0.771092\pi$
$270$			3.21338i			0.195560i
$271$	−15.0422	−	15.0422i	−0.913751	−	0.913751i	0.0828139	−	0.996565i	$-0.473609\pi$
$271$	−15.0422	−	15.0422i	−0.913751	−	0.913751i	−0.996565	+	0.0828139i	$0.973609\pi$
$272$	−4.32583			−0.262292
$273$	−9.52740	+	0.478235i	−0.576624	+	0.0289441i
$274$	−0.384955			−0.0232560
$275$	−1.89275	−	1.89275i	−0.114137	−	0.114137i
$276$			2.38496i			0.143557i
$277$		−	17.7996i		−	1.06947i	−0.845018	−	0.534737i	$-0.820411\pi$
$277$		−	17.7996i		−	1.06947i	0.845018	−	0.534737i	$-0.179589\pi$
$278$	−14.3854	+	14.3854i	−0.862778	+	0.862778i
$279$	1.08319	−	1.08319i	0.0648487	−	0.0648487i
$280$	−4.35539	+	7.30146i	−0.260284	+	0.436346i
$281$	6.20862	−	6.20862i	0.370375	−	0.370375i	−0.497239	−	0.867614i	$-0.665653\pi$
$281$	6.20862	−	6.20862i	0.370375	−	0.370375i	0.867614	+	0.497239i	$0.165653\pi$
$282$	−6.66205			−0.396720
$283$	−25.1090			−1.49258			−0.746288	−	0.665624i	$-0.768166\pi$
$283$	−25.1090			−1.49258			−0.746288	+	0.665624i	$0.768166\pi$
$284$	−6.38496	+	6.38496i	−0.378877	+	0.378877i
$285$	27.1891			1.61055
$286$	−1.00520	−	1.50780i	−0.0594387	−	0.0891580i
$287$	12.8122	−	3.23805i	0.756277	−	0.191136i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	1.71278			0.100752
$290$	−3.52103			−0.206762
$291$	12.9931	+	12.9931i	0.761668	+	0.761668i
$292$	−5.18902	+	5.18902i	−0.303664	+	0.303664i
$293$	−8.51343	−	8.51343i	−0.497360	−	0.497360i	0.413255	−	0.910615i	$-0.364392\pi$
$293$	−8.51343	−	8.51343i	−0.497360	−	0.497360i	−0.910615	+	0.413255i	$0.864392\pi$
$294$	−6.70711	−	2.00368i	−0.391166	−	0.116857i
$295$	16.4282			0.956489
$296$		−	7.33838i		−	0.426535i
$297$	−0.355392	−	0.355392i	−0.0206219	−	0.0206219i
$298$			14.9461i			0.865803i
$299$	−7.15487	+	4.76991i	−0.413777	+	0.275851i
$300$			5.32583i			0.307487i
$301$	10.0959	−	16.9249i	0.581916	−	0.975535i
$302$	−0.211229			−0.0121549
$303$			19.7996i			1.13746i
$304$	5.98299	−	5.98299i	0.343148	−	0.343148i
$305$	9.82917	+	9.82917i	0.562816	+	0.562816i
$306$	−3.05882	−	3.05882i	−0.174861	−	0.174861i
$307$	−10.0397	−	10.0397i	−0.572993	−	0.572993i	0.359970	−	0.932964i	$-0.382787\pi$
$307$	−10.0397	−	10.0397i	−0.572993	−	0.572993i	−0.932964	+	0.359970i	$0.882787\pi$
$308$	−0.325828	−	1.28922i	−0.0185658	−	0.0734600i
$309$		−	2.70386i		−	0.153817i
$310$	3.48069	−	3.48069i	0.197690	−	0.197690i
$311$	−15.7064			−0.890631			−0.445316	−	0.895374i	$-0.646908\pi$
$311$	−15.7064			−0.890631			−0.445316	+	0.895374i	$0.646908\pi$
$312$	−0.707107	+	3.53553i	−0.0400320	+	0.200160i
$313$			20.7702i			1.17400i	0.809587	+	0.587000i	$0.199691\pi$
$313$			20.7702i			1.17400i	−0.809587	+	0.587000i	$0.800309\pi$
$314$	7.61058	−	7.61058i	0.429490	−	0.429490i
$315$	−8.24264	+	2.08319i	−0.464420	+	0.117374i
$316$		−	11.3143i		−	0.636480i
$317$	19.0126	+	19.0126i	1.06785	+	1.06785i	0.997524	+	0.0703273i	$0.0224044\pi$
$317$	19.0126	+	19.0126i	1.06785	+	1.06785i	0.0703273	+	0.997524i	$0.477596\pi$
$318$	7.95862	−	7.95862i	0.446297	−	0.446297i
$319$	0.389416	−	0.389416i	0.0218031	−	0.0218031i
$320$	2.27220	+	2.27220i	0.127020	+	0.127020i
$321$		−	11.6673i		−	0.651203i
$322$	−6.11764	+	1.54613i	−0.340923	+	0.0861625i
$323$	−25.8814	+	25.8814i	−1.44008	+	1.44008i
$324$			1.00000i			0.0555556i
$325$	−15.9775	+	10.6517i	−0.886271	+	0.590848i
$326$	−4.82107			−0.267015
$327$	5.29626	−	5.29626i	0.292884	−	0.292884i
$328$		−	4.99480i		−	0.275792i
$329$	−4.31891	−	17.0888i	−0.238109	−	0.942137i
$330$	−1.14201	−	1.14201i	−0.0628655	−	0.0628655i
$331$	−13.9785	−	13.9785i	−0.768329	−	0.768329i	0.209483	−	0.977812i	$-0.432822\pi$
$331$	−13.9785	−	13.9785i	−0.768329	−	0.768329i	−0.977812	+	0.209483i	$0.932822\pi$
$332$	−6.71078	−	6.71078i	−0.368302	−	0.368302i
$333$	5.18902	−	5.18902i	0.284356	−	0.284356i
$334$			14.1742i			0.775575i
$335$	2.41698			0.132054
$336$	−1.35539	+	2.27220i	−0.0739427	+	0.123959i
$337$		−	1.09574i		−	0.0596887i	−0.999555	−	0.0298443i	$-0.990499\pi$
$337$		−	1.09574i		−	0.0596887i	0.999555	−	0.0298443i	$-0.00950116\pi$
$338$	−12.0208	+	4.94975i	−0.653846	+	0.269231i
$339$			20.3440i			1.10493i
$340$	−9.82917	−	9.82917i	−0.533061	−	0.533061i
$341$			0.769911i			0.0416930i
$342$	8.46122			0.457531
$343$	0.791511	−	18.5033i	0.0427376	−	0.999086i
$344$	−5.26701	−	5.26701i	−0.283978	−	0.283978i
$345$	−5.41911	+	5.41911i	−0.291755	+	0.291755i
$346$	13.9586	+	13.9586i	0.750420	+	0.750420i
$347$	32.0983			1.72313			0.861564	−	0.507649i	$-0.169485\pi$
$347$	32.0983			1.72313			0.861564	+	0.507649i	$0.169485\pi$
$348$	−1.09574			−0.0587377
$349$	−18.9660	−	18.9660i	−1.01523	−	1.01523i	−0.999882	−	0.0153431i	$-0.995116\pi$
$349$	−18.9660	−	18.9660i	−1.01523	−	1.01523i	−0.0153431	−	0.999882i	$-0.504884\pi$
$350$	−13.6613	+	3.45265i	−0.730226	+	0.184552i
$351$	−3.00000	+	2.00000i	−0.160128	+	0.106752i
$352$	−0.502600			−0.0267886
$353$	−15.5500	+	15.5500i	−0.827645	+	0.827645i	−0.987191	−	0.159545i	$-0.948997\pi$
$353$	−15.5500	+	15.5500i	−0.827645	+	0.827645i	0.159545	+	0.987191i	$0.448997\pi$
$354$	5.11245			0.271723
$355$	−29.0159			−1.54000
$356$	−3.75044	+	3.75044i	−0.198773	+	0.198773i
$357$	5.86319	−	9.82917i	0.310313	−	0.520215i
$358$	6.92936	−	6.92936i	0.366228	−	0.366228i
$359$	−14.1846	+	14.1846i	−0.748632	+	0.748632i	−0.974222	−	0.225590i	$-0.927569\pi$
$359$	−14.1846	+	14.1846i	−0.748632	+	0.748632i	0.225590	+	0.974222i	$0.427569\pi$
$360$			3.21338i			0.169360i
$361$		−	52.5923i		−	2.76801i
$362$	−7.38019	−	7.38019i	−0.387894	−	0.387894i
$363$	−10.7474			−0.564092
$364$	−9.52740	+	0.478235i	−0.499371	+	0.0250663i
$365$	−23.5810			−1.23429
$366$	3.05882	+	3.05882i	0.159887	+	0.159887i
$367$			11.2552i			0.587516i	0.955880	+	0.293758i	$0.0949060\pi$
$367$			11.2552i			0.587516i	−0.955880	+	0.293758i	$0.905094\pi$
$368$			2.38496i			0.124324i
$369$	3.53186	−	3.53186i	0.183861	−	0.183861i
$370$	16.6743	−	16.6743i	0.866856	−	0.866856i
$371$	25.5741	+	15.2552i	1.32774	+	0.792010i
$372$	1.08319	−	1.08319i	0.0561606	−	0.0561606i
$373$	17.1479			0.887887			0.443944	−	0.896055i	$-0.353579\pi$
$373$	17.1479			0.887887			0.443944	+	0.896055i	$0.353579\pi$
$374$	2.17416			0.112423
$375$	−0.740347	+	0.740347i	−0.0382314	+	0.0382314i
$376$	−6.66205			−0.343569
$377$	−2.19148	−	3.28722i	−0.112867	−	0.169300i
$378$	−2.56510	+	0.648285i	−0.131934	+	0.0333442i
$379$	11.5685	+	11.5685i	0.594232	+	0.594232i	0.938772	−	0.344540i	$-0.111965\pi$
$379$	11.5685	+	11.5685i	0.594232	+	0.594232i	−0.344540	+	0.938772i	$0.611965\pi$
$380$	27.1891			1.39477
$381$	7.60812			0.389776
$382$	7.87790	+	7.87790i	0.403068	+	0.403068i
$383$	−1.26657	+	1.26657i	−0.0647189	+	0.0647189i	−0.738725	−	0.674007i	$-0.764572\pi$
$383$	−1.26657	+	1.26657i	−0.0647189	+	0.0647189i	0.674007	+	0.738725i	$0.264572\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	2.18902	−	3.66971i	0.111563	−	0.187026i
$386$	5.70863			0.290562
$387$		−	7.44867i		−	0.378637i
$388$	12.9931	+	12.9931i	0.659624	+	0.659624i
$389$			7.90685i			0.400893i	0.979705	+	0.200447i	$0.0642393\pi$
$389$			7.90685i			0.400893i	−0.979705	+	0.200447i	$0.935761\pi$
$390$	−9.64015	+	6.42677i	−0.488148	+	0.325432i
$391$		−	10.3169i		−	0.521748i
$392$	−6.70711	−	2.00368i	−0.338760	−	0.101201i
$393$	6.87024			0.346558
$394$			0.887555i			0.0447144i
$395$	25.7085	−	25.7085i	1.29353	−	1.29353i
$396$	−0.355392	−	0.355392i	−0.0178591	−	0.0178591i
$397$	16.4467	+	16.4467i	0.825435	+	0.825435i	0.986881	−	0.161447i	$-0.0516160\pi$
$397$	16.4467	+	16.4467i	0.825435	+	0.825435i	−0.161447	+	0.986881i	$0.551616\pi$
$398$	−11.6938	−	11.6938i	−0.586156	−	0.586156i
$399$	5.48528	+	21.7039i	0.274608	+	1.08655i
$400$			5.32583i			0.266291i
$401$	15.0126	−	15.0126i	0.749691	−	0.749691i	−0.224730	−	0.974421i	$-0.572150\pi$
$401$	15.0126	−	15.0126i	0.749691	−	0.749691i	0.974421	+	0.224730i	$0.0721500\pi$
$402$	0.752160			0.0375143
$403$	5.41593	+	1.08319i	0.269787	+	0.0539574i
$404$			19.7996i			0.985067i
$405$	−2.27220	+	2.27220i	−0.112907	+	0.112907i
$406$	−0.710351	−	2.81068i	−0.0352541	−	0.139492i
$407$			3.68827i			0.182821i
$408$	−3.05882	−	3.05882i	−0.151434	−	0.151434i
$409$	−19.0477	+	19.0477i	−0.941850	+	0.941850i	−0.998400	−	0.0565493i	$-0.981990\pi$
$409$	−19.0477	+	19.0477i	−0.941850	+	0.941850i	0.0565493	+	0.998400i	$0.481990\pi$
$410$	11.3492	−	11.3492i	0.560498	−	0.560498i
$411$	−0.272205	−	0.272205i	−0.0134269	−	0.0134269i
$412$		−	2.70386i		−	0.133210i
$413$	3.31432	+	13.1139i	0.163087	+	0.645294i
$414$	−1.68642	+	1.68642i	−0.0828829	+	0.0828829i
$415$		−	30.4965i		−	1.49702i
$416$	−0.707107	+	3.53553i	−0.0346688	+	0.173344i
$417$	−20.3440			−0.996250
$418$	−3.00705	+	3.00705i	−0.147079	+	0.147079i
$419$			38.8022i			1.89561i	0.318849	+	0.947805i	$0.396704\pi$
$419$			38.8022i			1.89561i	−0.318849	+	0.947805i	$0.603296\pi$
$420$	−8.24264	+	2.08319i	−0.402200	+	0.101649i
$421$	−19.5375	−	19.5375i	−0.952199	−	0.952199i	0.0467096	−	0.998909i	$-0.485126\pi$
$421$	−19.5375	−	19.5375i	−0.952199	−	0.952199i	−0.998909	+	0.0467096i	$0.985126\pi$
$422$	−0.389849	−	0.389849i	−0.0189775	−	0.0189775i
$423$	−4.71078	−	4.71078i	−0.229046	−	0.229046i
$424$	7.95862	−	7.95862i	0.386505	−	0.386505i
$425$		−	23.0386i		−	1.11754i
$426$	−9.02969			−0.437490
$427$	−5.86319	+	9.82917i	−0.283740	+	0.475667i
$428$		−	11.6673i		−	0.563958i
$429$	0.355392	−	1.77696i	0.0171585	−	0.0857923i
$430$		−	23.9354i		−	1.15427i
$431$	1.45559	+	1.45559i	0.0701133	+	0.0701133i	0.741294	−	0.671181i	$-0.234212\pi$
$431$	1.45559	+	1.45559i	0.0701133	+	0.0701133i	−0.671181	+	0.741294i	$0.734212\pi$
$432$			1.00000i			0.0481125i
$433$	35.8137			1.72110			0.860548	−	0.509369i	$-0.170121\pi$
$433$	35.8137			1.72110			0.860548	+	0.509369i	$0.170121\pi$
$434$	3.48069	+	2.07627i	0.167079	+	0.0996640i
$435$	−2.48974	−	2.48974i	−0.119374	−	0.119374i
$436$	5.29626	−	5.29626i	0.253645	−	0.253645i
$437$	14.2692	+	14.2692i	0.682586	+	0.682586i
$438$	−7.33838			−0.350641
$439$	−14.2667			−0.680912			−0.340456	−	0.940260i	$-0.610582\pi$
$439$	−14.2667			−0.680912			−0.340456	+	0.940260i	$0.610582\pi$
$440$	−1.14201	−	1.14201i	−0.0544431	−	0.0544431i
$441$	−3.32583	−	6.15945i	−0.158373	−	0.293307i
$442$	3.05882	−	15.2941i	0.145493	−	0.727467i
$443$	−20.7019			−0.983575			−0.491788	−	0.870715i	$-0.663656\pi$
$443$	−20.7019			−0.983575			−0.491788	+	0.870715i	$0.663656\pi$
$444$	5.18902	−	5.18902i	0.246260	−	0.246260i
$445$	−17.0435			−0.807941
$446$	13.9926			0.662571
$447$	−10.5685	+	10.5685i	−0.499871	+	0.499871i
$448$	−1.35539	+	2.27220i	−0.0640362	+	0.107352i
$449$	−20.2382	+	20.2382i	−0.955099	+	0.955099i	−0.999034	−	0.0439356i	$-0.986010\pi$
$449$	−20.2382	+	20.2382i	−0.955099	+	0.955099i	0.0439356	+	0.999034i	$0.486010\pi$
$450$	−3.76593	+	3.76593i	−0.177528	+	0.177528i
$451$			2.51038i			0.118209i
$452$			20.3440i			0.956902i
$453$	−0.149362	−	0.149362i	−0.00701762	−	0.00701762i
$454$	2.36764			0.111119
$455$	−22.7348	−	20.5615i	−1.06583	−	0.963940i
$456$	8.46122			0.396233
$457$	−18.1891	−	18.1891i	−0.850852	−	0.850852i	0.139386	−	0.990238i	$-0.455487\pi$
$457$	−18.1891	−	18.1891i	−0.850852	−	0.850852i	−0.990238	+	0.139386i	$0.955487\pi$
$458$		−	1.87500i		−	0.0876132i
$459$		−	4.32583i		−	0.201912i
$460$	−5.41911	+	5.41911i	−0.252667	+	0.252667i
$461$	1.18339	−	1.18339i	0.0551158	−	0.0551158i	−0.679012	−	0.734127i	$-0.737591\pi$
$461$	1.18339	−	1.18339i	0.0551158	−	0.0551158i	0.734127	+	0.679012i	$0.237591\pi$
$462$	0.681219	−	1.14201i	0.0316932	−	0.0531311i
$463$	4.93946	−	4.93946i	0.229556	−	0.229556i	−0.582951	−	0.812507i	$-0.698102\pi$
$463$	4.93946	−	4.93946i	0.229556	−	0.229556i	0.812507	+	0.582951i	$0.198102\pi$
$464$	−1.09574			−0.0508684
$465$	4.92244			0.228273
$466$	−7.22074	+	7.22074i	−0.334494	+	0.334494i
$467$	26.6900			1.23507			0.617533	−	0.786545i	$-0.288132\pi$
$467$	26.6900			1.23507			0.617533	+	0.786545i	$0.288132\pi$
$468$	−3.00000	+	2.00000i	−0.138675	+	0.0924500i
$469$	0.487614	+	1.92936i	0.0225159	+	0.0890898i
$470$	−15.1375	−	15.1375i	−0.698243	−	0.698243i
$471$	10.7630			0.495932
$472$	5.11245			0.235319
$473$	2.64719	+	2.64719i	0.121718	+	0.121718i
$474$	8.00043	−	8.00043i	0.367472	−	0.367472i
$475$	31.8644	+	31.8644i	1.46204	+	1.46204i
$476$	5.86319	−	9.82917i	0.268739	−	0.450519i
$477$	11.2552			0.515340
$478$		−	21.5260i		−	0.984575i
$479$	7.35998	+	7.35998i	0.336286	+	0.336286i	0.854968	−	0.518682i	$-0.173577\pi$
$479$	7.35998	+	7.35998i	0.336286	+	0.336286i	−0.518682	+	0.854968i	$0.673577\pi$
$480$			3.21338i			0.146670i
$481$	25.9451	+	5.18902i	1.18299	+	0.236599i
$482$			4.78705i			0.218044i
$483$	−5.41911	−	3.23255i	−0.246578	−	0.147086i
$484$	−10.7474			−0.488518
$485$			59.0459i			2.68113i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	25.1766	+	25.1766i	1.14086	+	1.14086i	0.988293	+	0.152567i	$0.0487541\pi$
$487$	25.1766	+	25.1766i	1.14086	+	1.14086i	0.152567	+	0.988293i	$0.451246\pi$
$488$	3.05882	+	3.05882i	0.138466	+	0.138466i
$489$	−3.40901	−	3.40901i	−0.154161	−	0.154161i
$490$	−10.6872	−	19.7927i	−0.482797	−	0.894142i
$491$			7.77450i			0.350858i	0.984492	+	0.175429i	$0.0561313\pi$
$491$			7.77450i			0.350858i	−0.984492	+	0.175429i	$0.943869\pi$
$492$	3.53186	−	3.53186i	0.159228	−	0.159228i
$493$	4.73998			0.213478
$494$	16.9224	+	25.3837i	0.761377	+	1.14207i
$495$		−	1.61504i		−	0.0725909i
$496$	1.08319	−	1.08319i	0.0486365	−	0.0486365i
$497$	−5.85381	−	23.1620i	−0.262579	−	1.03896i
$498$		−	9.49048i		−	0.425279i
$499$	23.4592	+	23.4592i	1.05018	+	1.05018i	0.998673	+	0.0515063i	$0.0164022\pi$
$499$	23.4592	+	23.4592i	1.05018	+	1.05018i	0.0515063	+	0.998673i	$0.483598\pi$
$500$	−0.740347	+	0.740347i	−0.0331093	+	0.0331093i
$501$	−10.0226	+	10.0226i	−0.447779	+	0.447779i
$502$	−12.1821	−	12.1821i	−0.543714	−	0.543714i
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$	−2.56510	+	0.648285i	−0.114259	+	0.0288769i
$505$	−44.9887	+	44.9887i	−2.00197	+	2.00197i
$506$		−	1.19868i		−	0.0532877i
$507$	−12.0000	−	5.00000i	−0.532939	−	0.222058i
$508$	7.60812			0.337556
$509$	−11.0283	+	11.0283i	−0.488820	+	0.488820i	−0.907934	−	0.419114i	$-0.862341\pi$
$509$	−11.0283	+	11.0283i	−0.488820	+	0.488820i	0.419114	+	0.907934i	$0.362341\pi$
$510$		−	13.9005i		−	0.615526i
$511$	−4.75736	−	18.8237i	−0.210453	−	0.832710i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	5.98299	+	5.98299i	0.264155	+	0.264155i
$514$	−2.34989	−	2.34989i	−0.103649	−	0.103649i
$515$	6.14373	−	6.14373i	0.270725	−	0.270725i
$516$		−	7.44867i		−	0.327909i
$517$	3.34834			0.147260
$518$	16.6743	+	9.94638i	0.732627	+	0.437019i
$519$			19.7405i			0.866511i
$520$	−9.64015	+	6.42677i	−0.422748	+	0.281832i
$521$		−	18.5654i		−	0.813366i	−0.913569	−	0.406683i	$-0.866685\pi$
$521$		−	18.5654i		−	0.813366i	0.913569	−	0.406683i	$-0.133315\pi$
$522$	−0.774804	−	0.774804i	−0.0339123	−	0.0339123i
$523$			27.5741i			1.20573i	0.797843	+	0.602866i	$0.205974\pi$
$523$			27.5741i			1.20573i	−0.797843	+	0.602866i	$0.794026\pi$
$524$	6.87024			0.300128
$525$	−12.1014	−	7.21858i	−0.528147	−	0.315045i
$526$	−0.578434	−	0.578434i	−0.0252209	−	0.0252209i
$527$	−4.68568	+	4.68568i	−0.204111	+	0.204111i
$528$	−0.355392	−	0.355392i	−0.0154664	−	0.0154664i
$529$	17.3120			0.752695
$530$	36.1672			1.57100
$531$	3.61504	+	3.61504i	0.156880	+	0.156880i
$532$	5.48528	+	21.7039i	0.237817	+	0.940982i
$533$	17.6593	+	3.53186i	0.764909	+	0.152982i
$534$	−5.30392			−0.229523
$535$	26.5104	−	26.5104i	1.14614	−	1.14614i
$536$	0.752160			0.0324884
$537$	9.79960			0.422884
$538$	−15.2793	+	15.2793i	−0.658735	+	0.658735i
$539$	3.37099	+	1.00705i	0.145199	+	0.0433766i
$540$	−2.27220	+	2.27220i	−0.0977801	+	0.0977801i
$541$	−25.5330	+	25.5330i	−1.09775	+	1.09775i	−0.103077	+	0.994673i	$0.532869\pi$
$541$	−25.5330	+	25.5330i	−1.09775	+	1.09775i	−0.994673	+	0.103077i	$0.967131\pi$
$542$		−	21.2729i		−	0.913751i
$543$		−	10.4372i		−	0.447902i
$544$	−3.05882	−	3.05882i	−0.131146	−	0.131146i
$545$	24.0684			1.03098
$546$	−7.07505	−	6.39872i	−0.302784	−	0.273840i
$547$	44.1966			1.88971			0.944856	−	0.327486i	$-0.106201\pi$
$547$	44.1966			1.88971			0.944856	+	0.327486i	$0.106201\pi$
$548$	−0.272205	−	0.272205i	−0.0116280	−	0.0116280i
$549$			4.32583i			0.184622i
$550$		−	2.67676i		−	0.114137i
$551$	−6.55579	+	6.55579i	−0.279286	+	0.279286i
$552$	−1.68642	+	1.68642i	−0.0717787	+	0.0717787i
$553$	25.7085	+	15.3353i	1.09323	+	0.652125i
$554$	12.5862	−	12.5862i	0.534737	−	0.534737i
$555$	23.5810			1.00096
$556$	−20.3440			−0.862778
$557$	−11.7755	+	11.7755i	−0.498946	+	0.498946i	−0.911110	−	0.412164i	$-0.864773\pi$
$557$	−11.7755	+	11.7755i	−0.498946	+	0.498946i	0.412164	+	0.911110i	$0.364773\pi$
$558$	1.53186			0.0648487
$559$	22.3460	−	14.8973i	0.945136	−	0.630090i
$560$	−8.24264	+	2.08319i	−0.348315	+	0.0880307i
$561$	1.53736	+	1.53736i	0.0649075	+	0.0649075i
$562$	8.78031			0.370375
$563$	45.7636			1.92870			0.964352	−	0.264621i	$-0.0852470\pi$
$563$	45.7636			1.92870			0.964352	+	0.264621i	$0.0852470\pi$
$564$	−4.71078	−	4.71078i	−0.198360	−	0.198360i
$565$	−46.2258	+	46.2258i	−1.94473	+	1.94473i
$566$	−17.7547	−	17.7547i	−0.746288	−	0.746288i
$567$	−2.27220	−	1.35539i	−0.0954236	−	0.0569211i
$568$	−9.02969			−0.378877
$569$		−	39.5061i		−	1.65618i	−0.560595	−	0.828090i	$-0.689428\pi$
$569$		−	39.5061i		−	1.65618i	0.560595	−	0.828090i	$-0.310572\pi$
$570$	19.2256	+	19.2256i	0.805273	+	0.805273i
$571$		−	19.1620i		−	0.801906i	−0.916099	−	0.400953i	$-0.868679\pi$
$571$		−	19.1620i		−	0.801906i	0.916099	−	0.400953i	$-0.131321\pi$
$572$	0.355392	−	1.77696i	0.0148597	−	0.0742983i
$573$			11.1410i			0.465423i
$574$	11.3492	+	6.76991i	0.473707	+	0.282571i
$575$	−12.7019			−0.529704
$576$			1.00000i			0.0416667i
$577$	3.53749	−	3.53749i	0.147268	−	0.147268i	−0.629629	−	0.776896i	$-0.716793\pi$
$577$	3.53749	−	3.53749i	0.147268	−	0.147268i	0.776896	+	0.629629i	$0.216793\pi$
$578$	1.21112	+	1.21112i	0.0503760	+	0.0503760i
$579$	4.03661	+	4.03661i	0.167756	+	0.167756i
$580$	−2.48974	−	2.48974i	−0.103381	−	0.103381i
$581$	24.3440	−	6.15253i	1.00996	−	0.255250i
$582$			18.3750i			0.761668i
$583$	−4.00000	+	4.00000i	−0.165663	+	0.165663i
$584$	−7.33838			−0.303664
$585$	−11.3610	−	2.27220i	−0.469720	−	0.0939441i
$586$		−	12.0398i		−	0.497360i
$587$	4.98849	−	4.98849i	0.205897	−	0.205897i	−0.596624	−	0.802521i	$-0.703492\pi$
$587$	4.98849	−	4.98849i	0.205897	−	0.205897i	0.802521	+	0.596624i	$0.203492\pi$
$588$	−3.32583	−	6.15945i	−0.137155	−	0.254012i
$589$		−	12.9614i		−	0.534065i
$590$	11.6165	+	11.6165i	0.478245	+	0.478245i
$591$	−0.627596	+	0.627596i	−0.0258159	+	0.0258159i
$592$	5.18902	−	5.18902i	0.213267	−	0.213267i
$593$	3.14690	+	3.14690i	0.129228	+	0.129228i	0.768762	−	0.639535i	$-0.220873\pi$
$593$	3.14690	+	3.14690i	0.129228	+	0.129228i	−0.639535	+	0.768762i	$0.720873\pi$
$594$		−	0.502600i		−	0.0206219i
$595$	35.6562	−	9.01151i	1.46176	−	0.369436i
$596$	−10.5685	+	10.5685i	−0.432901	+	0.432901i
$597$		−	16.5375i		−	0.676834i
$598$	−8.43209	−	1.68642i	−0.344814	−	0.0689628i
$599$	14.9244			0.609796			0.304898	−	0.952385i	$-0.401378\pi$
$599$	14.9244			0.609796			0.304898	+	0.952385i	$0.401378\pi$
$600$	−3.76593	+	3.76593i	−0.153743	+	0.153743i
$601$			14.3189i			0.584080i	0.956406	+	0.292040i	$0.0943341\pi$
$601$			14.3189i			0.584080i	−0.956406	+	0.292040i	$0.905666\pi$
$602$	19.1066	−	4.82886i	0.778726	−	0.196810i
$603$	0.531858	+	0.531858i	0.0216589	+	0.0216589i
$604$	−0.149362	−	0.149362i	−0.00607743	−	0.00607743i
$605$	−24.4203	−	24.4203i	−0.992825	−	0.992825i
$606$	−14.0004	+	14.0004i	−0.568729	+	0.568729i
$607$		−	17.3212i		−	0.703047i	−0.936179	−	0.351524i	$-0.885664\pi$
$607$		−	17.3212i		−	0.703047i	0.936179	−	0.351524i	$-0.114336\pi$
$608$	8.46122			0.343148
$609$	1.48515	−	2.48974i	0.0601815	−	0.100889i
$610$			13.9005i			0.562816i
$611$	4.71078	−	23.5539i	0.190578	−	0.952889i
$612$		−	4.32583i		−	0.174861i
$613$	28.6700	+	28.6700i	1.15797	+	1.15797i	0.984912	+	0.173057i	$0.0553646\pi$
$613$	28.6700	+	28.6700i	1.15797	+	1.15797i	0.173057	+	0.984912i	$0.444635\pi$
$614$		−	14.1982i		−	0.572993i
$615$	16.0502			0.647207
$616$	0.681219	−	1.14201i	0.0274471	−	0.0460129i
$617$	−9.91435	−	9.91435i	−0.399137	−	0.399137i	0.478792	−	0.877929i	$-0.341075\pi$
$617$	−9.91435	−	9.91435i	−0.399137	−	0.399137i	−0.877929	+	0.478792i	$0.841075\pi$
$618$	1.91192	−	1.91192i	0.0769087	−	0.0769087i
$619$	3.87574	+	3.87574i	0.155779	+	0.155779i	0.780693	−	0.624914i	$-0.214866\pi$
$619$	3.87574	+	3.87574i	0.155779	+	0.155779i	−0.624914	+	0.780693i	$0.714866\pi$
$620$	4.92244			0.197690
$621$	−2.38496			−0.0957050
$622$	−11.1061	−	11.1061i	−0.445316	−	0.445316i
$623$	−3.43845	−	13.6051i	−0.137759	−	0.545076i
$624$	−3.00000	+	2.00000i	−0.120096	+	0.0800641i
$625$	23.2647			0.930588
$626$	−14.6867	+	14.6867i	−0.587000	+	0.587000i
$627$	−4.25261			−0.169833
$628$	10.7630			0.429490
$629$	−22.4468	+	22.4468i	−0.895012	+	0.895012i
$630$	−7.30146	−	4.35539i	−0.290897	−	0.173523i
$631$	−21.5709	+	21.5709i	−0.858725	+	0.858725i	−0.991188	−	0.132463i	$-0.957711\pi$
$631$	−21.5709	+	21.5709i	−0.858725	+	0.858725i	0.132463	+	0.991188i	$0.457711\pi$
$632$	8.00043	−	8.00043i	0.318240	−	0.318240i
$633$		−	0.551329i		−	0.0219134i
$634$			26.8878i			1.06785i
$635$	17.2872	+	17.2872i	0.686022	+	0.686022i
$636$	11.2552			0.446297
$637$	11.8267	−	22.2964i	0.468591	−	0.883415i
$638$	0.550718			0.0218031
$639$	−6.38496	−	6.38496i	−0.252585	−	0.252585i
$640$			3.21338i			0.127020i
$641$			25.8728i			1.02192i	0.859606	+	0.510958i	$0.170709\pi$
$641$			25.8728i			1.02192i	−0.859606	+	0.510958i	$0.829291\pi$
$642$	8.24999	−	8.24999i	0.325601	−	0.325601i
$643$	3.32032	−	3.32032i	0.130941	−	0.130941i	−0.638599	−	0.769540i	$-0.720486\pi$
$643$	3.32032	−	3.32032i	0.130941	−	0.130941i	0.769540	+	0.638599i	$0.220486\pi$
$644$	−5.41911	−	3.23255i	−0.213543	−	0.127380i
$645$	16.9249	−	16.9249i	0.666417	−	0.666417i
$646$	−36.6018			−1.44008
$647$	28.6969			1.12819			0.564097	−	0.825709i	$-0.309225\pi$
$647$	28.6969			1.12819			0.564097	+	0.825709i	$0.309225\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	−2.56951			−0.100862
$650$	−18.8296	−	3.76593i	−0.738559	−	0.147712i
$651$	0.993080	+	3.92936i	0.0389219	+	0.154004i
$652$	−3.40901	−	3.40901i	−0.133507	−	0.133507i
$653$	−27.9250			−1.09279			−0.546395	−	0.837527i	$-0.684000\pi$
$653$	−27.9250			−1.09279			−0.546395	+	0.837527i	$0.684000\pi$
$654$	7.49005			0.292884
$655$	15.6106	+	15.6106i	0.609956	+	0.609956i
$656$	3.53186	−	3.53186i	0.137896	−	0.137896i
$657$	−5.18902	−	5.18902i	−0.202443	−	0.202443i
$658$	9.02969	−	15.1375i	0.352014	−	0.590123i
$659$	−38.2258			−1.48906			−0.744532	−	0.667587i	$-0.767327\pi$
$659$	−38.2258			−1.48906			−0.744532	+	0.667587i	$0.767327\pi$
$660$		−	1.61504i		−	0.0628655i
$661$	4.52189	+	4.52189i	0.175881	+	0.175881i	0.789558	−	0.613676i	$-0.210310\pi$
$661$	4.52189	+	4.52189i	0.175881	+	0.175881i	−0.613676	+	0.789558i	$0.710310\pi$
$662$		−	19.7686i		−	0.768329i
$663$	12.9775	−	8.65166i	0.504004	−	0.336002i
$664$		−	9.49048i		−	0.368302i
$665$	−36.8519	+	61.7793i	−1.42906	+	2.39570i
$666$	7.33838			0.284356
$667$		−	2.61329i		−	0.101187i
$668$	−10.0226	+	10.0226i	−0.387788	+	0.387788i
$669$	9.89430	+	9.89430i	0.382536	+	0.382536i
$670$	1.70906	+	1.70906i	0.0660268	+	0.0660268i
$671$	−1.53736	−	1.53736i	−0.0593492	−	0.0593492i
$672$	−2.56510	+	0.648285i	−0.0989508	+	0.0250081i
$673$		−	16.7180i		−	0.644430i	−0.946667	−	0.322215i	$-0.895573\pi$
$673$		−	16.7180i		−	0.644430i	0.946667	−	0.322215i	$-0.104427\pi$
$674$	0.774804	−	0.774804i	0.0298443	−	0.0298443i
$675$	−5.32583			−0.204991
$676$	−12.0000	−	5.00000i	−0.461538	−	0.192308i
$677$		−	37.8247i		−	1.45372i	−0.686785	−	0.726861i	$-0.740979\pi$
$677$		−	37.8247i		−	1.45372i	0.686785	−	0.726861i	$-0.259021\pi$
$678$	−14.3854	+	14.3854i	−0.552467	+	0.552467i
$679$	−47.1336	+	11.9122i	−1.80882	+	0.457149i
$680$		−	13.9005i		−	0.533061i
$681$	1.67417	+	1.67417i	0.0641544	+	0.0641544i
$682$	−0.544409	+	0.544409i	−0.0208465	+	0.0208465i
$683$	3.10020	−	3.10020i	0.118626	−	0.118626i	−0.645302	−	0.763928i	$-0.723268\pi$
$683$	3.10020	−	3.10020i	0.118626	−	0.118626i	0.763928	+	0.645302i	$0.223268\pi$
$684$	5.98299	+	5.98299i	0.228765	+	0.228765i
$685$		−	1.23701i		−	0.0472637i
$686$	13.6435	−	12.5242i	0.520912	−	0.478174i
$687$	1.32583	−	1.32583i	0.0505835	−	0.0505835i
$688$		−	7.44867i		−	0.283978i
$689$	22.5104	+	33.7656i	0.857577	+	1.28637i
$690$	−7.66377			−0.291755
$691$	11.1083	−	11.1083i	0.422579	−	0.422579i	−0.463512	−	0.886091i	$-0.653411\pi$
$691$	11.1083	−	11.1083i	0.422579	−	0.422579i	0.886091	+	0.463512i	$0.153411\pi$
$692$			19.7405i			0.750420i
$693$	1.28922	−	0.325828i	0.0489733	−	0.0123772i
$694$	22.6969	+	22.6969i	0.861564	+	0.861564i
$695$	−46.2258	−	46.2258i	−1.75344	−	1.75344i
$696$	−0.774804	−	0.774804i	−0.0293689	−	0.0293689i
$697$	−15.2782	+	15.2782i	−0.578703	+	0.578703i
$698$		−	26.8219i		−	1.01523i
$699$	−10.2117			−0.386241
$700$	−12.1014	−	7.21858i	−0.457389	−	0.272837i
$701$		−	2.49912i		−	0.0943905i	−0.998886	−	0.0471953i	$-0.984972\pi$
$701$		−	2.49912i		−	0.0943905i	0.998886	−	0.0471953i	$-0.0150283\pi$
$702$	−3.53553	−	0.707107i	−0.133440	−	0.0266880i
$703$		−	62.0917i		−	2.34183i
$704$	−0.355392	−	0.355392i	−0.0133943	−	0.0133943i
$705$		−	21.4077i		−	0.806262i
$706$	−21.9911			−0.827645
$707$	−44.9887	−	26.8362i	−1.69198	−	1.00928i
$708$	3.61504	+	3.61504i	0.135862	+	0.135862i
$709$	25.3601	−	25.3601i	0.952419	−	0.952419i	−0.0464996	−	0.998918i	$-0.514807\pi$
$709$	25.3601	−	25.3601i	0.952419	−	0.952419i	0.998918	+	0.0464996i	$0.0148066\pi$
$710$	−20.5173	−	20.5173i	−0.770001	−	0.770001i
$711$	11.3143			0.424320
$712$	−5.30392			−0.198773
$713$	2.58335	+	2.58335i	0.0967473	+	0.0967473i
$714$	11.0962	−	2.80437i	0.415264	−	0.104951i
$715$	4.84513	−	3.23009i	0.181198	−	0.120798i
$716$	9.79960			0.366228
$717$	15.2212	−	15.2212i	0.568445	−	0.568445i
$718$	−20.0600			−0.748632
$719$	−41.5150			−1.54825			−0.774124	−	0.633034i	$-0.781809\pi$
$719$	−41.5150			−1.54825			−0.774124	+	0.633034i	$0.781809\pi$
$720$	−2.27220	+	2.27220i	−0.0846801	+	0.0846801i
$721$	6.14373	+	3.66479i	0.228804	+	0.136484i
$722$	37.1884	−	37.1884i	1.38401	−	1.38401i
$723$	−3.38496	+	3.38496i	−0.125888	+	0.125888i
$724$		−	10.4372i		−	0.387894i
$725$		−	5.83571i		−	0.216733i
$726$	−7.59955	−	7.59955i	−0.282046	−	0.282046i
$727$	−48.1505			−1.78580			−0.892902	−	0.450251i	$-0.851335\pi$
$727$	−48.1505			−1.78580			−0.892902	+	0.450251i	$0.851335\pi$
$728$	−7.07505	−	6.39872i	−0.262219	−	0.237152i
$729$	−1.00000			−0.0370370
$730$	−16.6743	−	16.6743i	−0.617143	−	0.617143i
$731$			32.2217i			1.19176i
$732$			4.32583i			0.159887i
$733$	−7.58561	+	7.58561i	−0.280181	+	0.280181i	−0.833181	−	0.553000i	$-0.813483\pi$
$733$	−7.58561	+	7.58561i	−0.280181	+	0.280181i	0.553000	+	0.833181i	$0.313483\pi$
$734$	−7.95862	+	7.95862i	−0.293758	+	0.293758i
$735$	6.43858	−	21.5525i	0.237491	−	0.794976i
$736$	−1.68642	+	1.68642i	−0.0621622	+	0.0621622i
$737$	−0.378035			−0.0139251
$738$	4.99480			0.183861
$739$	0.923733	−	0.923733i	0.0339801	−	0.0339801i	−0.689913	−	0.723893i	$-0.742351\pi$
$739$	0.923733	−	0.923733i	0.0339801	−	0.0339801i	0.723893	+	0.689913i	$0.242351\pi$
$740$	23.5810			0.866856
$741$	−5.98299	+	29.9149i	−0.219791	+	1.09895i
$742$	7.29657	+	28.8707i	0.267865	+	1.05988i
$743$	−7.95906	−	7.95906i	−0.291989	−	0.291989i	0.545876	−	0.837866i	$-0.316197\pi$
$743$	−7.95906	−	7.95906i	−0.291989	−	0.291989i	−0.837866	+	0.545876i	$0.816197\pi$
$744$	1.53186			0.0561606
$745$	−48.0274			−1.75959
$746$	12.1254	+	12.1254i	0.443944	+	0.443944i
$747$	6.71078	−	6.71078i	0.245535	−	0.245535i
$748$	1.53736	+	1.53736i	0.0562115	+	0.0562115i
$749$	26.5104	+	15.8137i	0.968668	+	0.577820i
$750$	−1.04701			−0.0382314
$751$			48.2119i			1.75928i	0.475642	+	0.879639i	$0.342216\pi$
$751$			48.2119i			1.75928i	−0.475642	+	0.879639i	$0.657784\pi$
$752$	−4.71078	−	4.71078i	−0.171785	−	0.171785i
$753$		−	17.2281i		−	0.627826i
$754$	0.774804	−	3.87402i	0.0282167	−	0.141084i
$755$		−	0.678760i		−	0.0247026i
$756$	−2.27220	−	1.35539i	−0.0826393	−	0.0492951i
$757$	47.8137			1.73782			0.868909	−	0.494972i	$-0.164822\pi$
$757$	47.8137			1.73782			0.868909	+	0.494972i	$0.164822\pi$
$758$			16.3603i			0.594232i
$759$	0.847593	−	0.847593i	0.0307657	−	0.0307657i
$760$	19.2256	+	19.2256i	0.697387	+	0.697387i
$761$	−14.6867	−	14.6867i	−0.532393	−	0.532393i	0.388891	−	0.921284i	$-0.372858\pi$
$761$	−14.6867	−	14.6867i	−0.532393	−	0.532393i	−0.921284	+	0.388891i	$0.872858\pi$
$762$	5.37976	+	5.37976i	0.194888	+	0.194888i
$763$	4.85568	+	19.2127i	0.175788	+	0.695547i
$764$			11.1410i			0.403068i
$765$	9.82917	−	9.82917i	0.355374	−	0.355374i
$766$	−1.79120			−0.0647189
$767$	−3.61504	+	18.0752i	−0.130532	+	0.652658i
$768$			1.00000i			0.0360844i
$769$	−34.5766	+	34.5766i	−1.24686	+	1.24686i	−0.289765	+	0.957098i	$0.593577\pi$
$769$	−34.5766	+	34.5766i	−1.24686	+	1.24686i	−0.957098	+	0.289765i	$0.906423\pi$
$770$	4.14275	−	1.04701i	0.149294	−	0.0377316i
$771$		−	3.32324i		−	0.119684i
$772$	4.03661	+	4.03661i	0.145281	+	0.145281i
$773$	3.88033	−	3.88033i	0.139566	−	0.139566i	−0.633872	−	0.773438i	$-0.718535\pi$
$773$	3.88033	−	3.88033i	0.139566	−	0.139566i	0.773438	+	0.633872i	$0.218535\pi$
$774$	5.26701	−	5.26701i	0.189319	−	0.189319i
$775$	5.76887	+	5.76887i	0.207224	+	0.207224i
$776$			18.3750i			0.659624i
$777$	4.75736	+	18.8237i	0.170669	+	0.675295i
$778$	−5.59099	+	5.59099i	−0.200447	+	0.200447i
$779$		−	42.2621i		−	1.51420i
$780$	−11.3610	−	2.27220i	−0.406790	−	0.0813580i
$781$	4.53832			0.162394
$782$	7.29515	−	7.29515i	0.260874	−	0.260874i
$783$		−	1.09574i		−	0.0391585i
$784$	−3.32583	−	6.15945i	−0.118780	−	0.219980i
$785$	24.4557	+	24.4557i	0.872862	+	0.872862i
$786$	4.85799	+	4.85799i	0.173279	+	0.173279i
$787$	−7.06054	−	7.06054i	−0.251681	−	0.251681i	0.569978	−	0.821660i	$-0.306952\pi$
$787$	−7.06054	−	7.06054i	−0.251681	−	0.251681i	−0.821660	+	0.569978i	$0.806952\pi$
$788$	−0.627596	+	0.627596i	−0.0223572	+	0.0223572i
$789$		−	0.818029i		−	0.0291226i
$790$	36.3572			1.29353
$791$	−46.2258	−	27.5741i	−1.64360	−	0.980422i
$792$		−	0.502600i		−	0.0178591i
$793$	−12.9775	+	8.65166i	−0.460844	+	0.307229i
$794$			23.2591i			0.825435i
$795$	25.5741	+	25.5741i	0.907020	+	0.907020i
$796$		−	16.5375i		−	0.586156i
$797$	−31.7376			−1.12421			−0.562103	−	0.827068i	$-0.690007\pi$
$797$	−31.7376			−1.12421			−0.562103	+	0.827068i	$0.690007\pi$
$798$	−11.4683	+	19.2256i	−0.405972	+	0.680580i
$799$	20.3780	+	20.3780i	0.720923	+	0.720923i
$800$	−3.76593	+	3.76593i	−0.133146	+	0.133146i
$801$	−3.75044	−	3.75044i	−0.132515	−	0.132515i
$802$	21.2310			0.749691
$803$	3.68827			0.130156
$804$	0.531858	+	0.531858i	0.0187572	+	0.0187572i
$805$	−4.96831	−	19.6583i	−0.175110	−	0.692865i
$806$	3.06372	+	4.59557i	0.107915	+	0.161872i
$807$	−21.6081			−0.760642
$808$	−14.0004	+	14.0004i	−0.492533	+	0.492533i
$809$	5.38754			0.189416			0.0947079	−	0.995505i	$-0.469808\pi$
$809$	5.38754			0.189416			0.0947079	+	0.995505i	$0.469808\pi$
$810$	−3.21338			−0.112907
$811$	24.4934	−	24.4934i	0.860079	−	0.860079i	−0.131268	−	0.991347i	$-0.541905\pi$
$811$	24.4934	−	24.4934i	0.860079	−	0.860079i	0.991347	+	0.131268i	$0.0419049\pi$
$812$	1.48515	−	2.48974i	0.0521187	−	0.0873728i
$813$	15.0422	−	15.0422i	0.527554	−	0.527554i
$814$	−2.60800	+	2.60800i	−0.0914103	+	0.0914103i
$815$		−	15.4920i		−	0.542660i
$816$		−	4.32583i		−	0.151434i
$817$	−44.5653	−	44.5653i	−1.55914	−	1.55914i
$818$	−26.9376			−0.941850
$819$	−0.478235	−	9.52740i	−0.0167109	−	0.332914i
$820$	16.0502			0.560498
$821$	−14.8664	−	14.8664i	−0.518840	−	0.518840i	0.398381	−	0.917220i	$-0.369572\pi$
$821$	−14.8664	−	14.8664i	−0.518840	−	0.518840i	−0.917220	+	0.398381i	$0.869572\pi$
$822$		−	0.384955i		−	0.0134269i
$823$			46.5078i			1.62116i	0.585628	+	0.810580i	$0.300848\pi$
$823$			46.5078i			1.62116i	−0.585628	+	0.810580i	$0.699152\pi$
$824$	1.91192	−	1.91192i	0.0666049	−	0.0666049i
$825$	1.89275	−	1.89275i	0.0658972	−	0.0658972i
$826$	−6.92936	+	11.6165i	−0.241103	+	0.404190i
$827$	−2.43470	+	2.43470i	−0.0846630	+	0.0846630i	−0.748170	−	0.663507i	$-0.769067\pi$
$827$	−2.43470	+	2.43470i	−0.0846630	+	0.0846630i	0.663507	+	0.748170i	$0.269067\pi$
$828$	−2.38496			−0.0828829
$829$	5.61013			0.194848			0.0974239	−	0.995243i	$-0.468940\pi$
$829$	5.61013			0.194848			0.0974239	+	0.995243i	$0.468940\pi$
$830$	21.5643	−	21.5643i	0.748508	−	0.748508i
$831$	17.7996			0.617461
$832$	−3.00000	+	2.00000i	−0.104006	+	0.0693375i
$833$	14.3870	+	26.6447i	0.498479	+	0.923185i
$834$	−14.3854	−	14.3854i	−0.498125	−	0.498125i
$835$	−45.5470			−1.57622
$836$	−4.25261			−0.147079
$837$	1.08319	+	1.08319i	0.0374404	+	0.0374404i
$838$	−27.4373	+	27.4373i	−0.947805	+	0.947805i
$839$	−35.6724	−	35.6724i	−1.23155	−	1.23155i	−0.963369	−	0.268180i	$-0.913578\pi$
$839$	−35.6724	−	35.6724i	−1.23155	−	1.23155i	−0.268180	−	0.963369i	$-0.586422\pi$
$840$	−7.30146	−	4.35539i	−0.251924	−	0.150275i
$841$	−27.7994			−0.958599
$842$		−	27.6302i		−	0.952199i
$843$	6.20862	+	6.20862i	0.213836	+	0.213836i
$844$		−	0.551329i		−	0.0189775i
$845$	−15.9054	−	38.6275i	−0.547164	−	1.32883i
$846$		−	6.66205i		−	0.229046i
$847$	14.5669	−	24.4203i	0.500526	−	0.839091i
$848$	11.2552			0.386505
$849$		−	25.1090i		−	0.861739i
$850$	16.2908	−	16.2908i	0.558768	−	0.558768i
$851$	12.3756	+	12.3756i	0.424229	+	0.424229i
$852$	−6.38496	−	6.38496i	−0.218745	−	0.218745i
$853$	−9.68368	−	9.68368i	−0.331563	−	0.331563i	0.521617	−	0.853180i	$-0.325329\pi$
$853$	−9.68368	−	9.68368i	−0.331563	−	0.331563i	−0.853180	+	0.521617i	$0.825329\pi$
$854$	−11.0962	+	2.80437i	−0.379703	+	0.0959635i
$855$			27.1891i			0.929849i
$856$	8.24999	−	8.24999i	0.281979	−	0.281979i
$857$	−10.6859			−0.365025			−0.182512	−	0.983204i	$-0.558423\pi$
$857$	−10.6859			−0.365025			−0.182512	+	0.983204i	$0.558423\pi$
$858$	1.50780	−	1.00520i	0.0514754	−	0.0343169i
$859$			15.4218i			0.526186i	0.964771	+	0.263093i	$0.0847426\pi$
$859$			15.4218i			0.526186i	−0.964771	+	0.263093i	$0.915257\pi$
$860$	16.9249	−	16.9249i	0.577134	−	0.577134i
$861$	3.23805	+	12.8122i	0.110353	+	0.436637i
$862$			2.05852i			0.0701133i
$863$	−13.8546	−	13.8546i	−0.471617	−	0.471617i	0.430820	−	0.902438i	$-0.358224\pi$
$863$	−13.8546	−	13.8546i	−0.471617	−	0.471617i	−0.902438	+	0.430820i	$0.858224\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	−44.8544	+	44.8544i	−1.52510	+	1.52510i
$866$	25.3241	+	25.3241i	0.860548	+	0.860548i
$867$			1.71278i			0.0581692i
$868$	0.993080	+	3.92936i	0.0337073	+	0.133371i
$869$	−4.02101	+	4.02101i	−0.136404	+	0.136404i
$870$		−	3.52103i		−	0.119374i
$871$	−0.531858	+	2.65929i	−0.0180213	+	0.0901065i
$872$	7.49005			0.253645
$873$	−12.9931	+	12.9931i	−0.439749	+	0.439749i
$874$			20.1796i			0.682586i
$875$	−0.678760	−	2.68568i	−0.0229463	−	0.0907926i
$876$	−5.18902	−	5.18902i	−0.175321	−	0.175321i
$877$	6.59203	+	6.59203i	0.222597	+	0.222597i	0.809591	−	0.586994i	$-0.199689\pi$
$877$	6.59203	+	6.59203i	0.222597	+	0.222597i	−0.586994	+	0.809591i	$0.699689\pi$
$878$	−10.0881	−	10.0881i	−0.340456	−	0.340456i
$879$	8.51343	−	8.51343i	0.287151	−	0.287151i
$880$		−	1.61504i		−	0.0544431i
$881$	4.21366			0.141962			0.0709810	−	0.997478i	$-0.477387\pi$
$881$	4.21366			0.141962			0.0709810	+	0.997478i	$0.477387\pi$
$882$	2.00368	−	6.70711i	0.0674673	−	0.225840i
$883$		−	22.3169i		−	0.751024i	−0.926818	−	0.375512i	$-0.877467\pi$
$883$		−	22.3169i		−	0.751024i	0.926818	−	0.375512i	$-0.122533\pi$
$884$	12.9775	−	8.65166i	0.436480	−	0.290987i
$885$			16.4282i			0.552229i
$886$	−14.6384	−	14.6384i	−0.491788	−	0.491788i
$887$		−	22.4573i		−	0.754044i	−0.926204	−	0.377022i	$-0.876948\pi$
$887$		−	22.4573i		−	0.754044i	0.926204	−	0.377022i	$-0.123052\pi$
$888$	7.33838			0.246260
$889$	−10.3120	+	17.2872i	−0.345853	+	0.579795i
$890$	−12.0516	−	12.0516i	−0.403970	−	0.403970i
$891$	0.355392	−	0.355392i	0.0119061	−	0.0119061i
$892$	9.89430	+	9.89430i	0.331286	+	0.331286i
$893$	−56.3691			−1.88632
$894$	−14.9461			−0.499871
$895$	22.2667	+	22.2667i	0.744294	+	0.744294i
$896$	−2.56510	+	0.648285i	−0.0856939	+	0.0216577i
$897$	−4.76991	−	7.15487i	−0.159263	−	0.238894i
$898$	−28.6211			−0.955099
$899$	−1.18689	+	1.18689i	−0.0395850	+	0.0395850i
$900$	−5.32583			−0.177528
$901$	−48.6880			−1.62203
$902$	−1.77511	+	1.77511i	−0.0591047	+	0.0591047i
$903$	16.9249	+	10.0959i	0.563226	+	0.335969i
$904$	−14.3854	+	14.3854i	−0.478451	+	0.478451i
$905$	23.7154	−	23.7154i	0.788326	−	0.788326i
$906$		−	0.211229i		−	0.00701762i
$907$			27.5490i			0.914749i	0.889274	+	0.457375i	$0.151210\pi$
$907$			27.5490i			0.914749i	−0.889274	+	0.457375i	$0.848790\pi$
$908$	1.67417	+	1.67417i	0.0555594	+	0.0555594i
$909$	−19.7996			−0.656711
$910$	−1.53675	−	30.6152i	−0.0509428	−	1.01488i
$911$	50.9409			1.68775			0.843873	−	0.536542i	$-0.180270\pi$
$911$	50.9409			1.68775			0.843873	+	0.536542i	$0.180270\pi$
$912$	5.98299	+	5.98299i	0.198117	+	0.198117i
$913$			4.76991i			0.157861i
$914$		−	25.7233i		−	0.850852i
$915$	−9.82917	+	9.82917i	−0.324942	+	0.324942i
$916$	1.32583	−	1.32583i	0.0438066	−	0.0438066i
$917$	−9.31186	+	15.6106i	−0.307505	+	0.515507i
$918$	3.05882	−	3.05882i	0.100956	−	0.100956i
$919$	−7.00433			−0.231052			−0.115526	−	0.993304i	$-0.536855\pi$
$919$	−7.00433			−0.231052			−0.115526	+	0.993304i	$0.536855\pi$
$920$	−7.66377			−0.252667
$921$	10.0397	−	10.0397i	0.330818	−	0.330818i
$922$	1.67356			0.0551158
$923$	6.38496	−	31.9248i	0.210163	−	1.05082i
$924$	1.28922	−	0.325828i	0.0424121	−	0.0107189i
$925$	27.6358	+	27.6358i	0.908660	+	0.908660i
$926$	6.98545			0.229556
$927$	2.70386			0.0888065
$928$	−0.774804	−	0.774804i	−0.0254342	−	0.0254342i
$929$	7.38650	−	7.38650i	0.242343	−	0.242343i	−0.575476	−	0.817819i	$-0.695183\pi$
$929$	7.38650	−	7.38650i	0.242343	−	0.242343i	0.817819	+	0.575476i	$0.195183\pi$
$930$	3.48069	+	3.48069i	0.114136	+	0.114136i
$931$	−56.7503	−	16.9536i	−1.85992	−	0.555630i
$932$	−10.2117			−0.334494
$933$		−	15.7064i		−	0.514206i
$934$	18.8727	+	18.8727i	0.617533	+	0.617533i
$935$			6.98640i			0.228480i
$936$	−3.53553	−	0.707107i	−0.115563	−	0.0231125i
$937$		−	47.1203i		−	1.53935i	−0.638435	−	0.769676i	$-0.720418\pi$
$937$		−	47.1203i		−	1.53935i	0.638435	−	0.769676i	$-0.279582\pi$
$938$	−1.01947	+	1.70906i	−0.0332869	+	0.0558029i
$939$	−20.7702			−0.677809
$940$		−	21.4077i		−	0.698243i
$941$	18.1495	−	18.1495i	0.591656	−	0.591656i	−0.346422	−	0.938079i	$-0.612604\pi$
$941$	18.1495	−	18.1495i	0.591656	−	0.591656i	0.938079	+	0.346422i	$0.112604\pi$
$942$	7.61058	+	7.61058i	0.247966	+	0.247966i
$943$	8.42332	+	8.42332i	0.274301	+	0.274301i
$944$	3.61504	+	3.61504i	0.117660	+	0.117660i
$945$	−2.08319	−	8.24264i	−0.0677661	−	0.268133i
$946$			3.74370i			0.121718i
$947$	−2.89980	+	2.89980i	−0.0942309	+	0.0942309i	−0.752651	−	0.658420i	$-0.771225\pi$
$947$	−2.89980	+	2.89980i	−0.0942309	+	0.0942309i	0.658420	+	0.752651i	$0.271225\pi$
$948$	11.3143			0.367472
$949$	5.18902	−	25.9451i	0.168443	−	0.842213i
$950$			45.0630i			1.46204i
$951$	−19.0126	+	19.0126i	−0.616524	+	0.616524i
$952$	11.0962	−	2.80437i	0.359629	−	0.0908901i
$953$			39.8477i			1.29079i	0.763847	+	0.645397i	$0.223308\pi$
$953$			39.8477i			1.29079i	−0.763847	+	0.645397i	$0.776692\pi$
$954$	7.95862	+	7.95862i	0.257670	+	0.257670i
$955$	−25.3147	+	25.3147i	−0.819164	+	0.819164i
$956$	15.2212	−	15.2212i	0.492288	−	0.492288i
$957$	0.389416	+	0.389416i	0.0125880	+	0.0125880i
$958$			10.4086i			0.336286i
$959$	0.987448	−	0.249561i	0.0318864	−	0.00805874i
$960$	−2.27220	+	2.27220i	−0.0733351	+	0.0733351i
$961$			28.6534i			0.924304i
$962$	14.6768	+	22.0151i	0.473198	+	0.709797i
$963$	11.6673			0.375972
$964$	−3.38496	+	3.38496i	−0.109022	+	0.109022i
$965$			18.3440i			0.590515i
$966$	−1.54613	−	6.11764i	−0.0497459	−	0.196832i
$967$	−19.7373	−	19.7373i	−0.634709	−	0.634709i	0.314537	−	0.949245i	$-0.398151\pi$
$967$	−19.7373	−	19.7373i	−0.634709	−	0.634709i	−0.949245	+	0.314537i	$0.898151\pi$
$968$	−7.59955	−	7.59955i	−0.244259	−	0.244259i
$969$	−25.8814	−	25.8814i	−0.831429	−	0.831429i
$970$	−41.7517	+	41.7517i	−1.34057	+	1.34057i
$971$			12.5416i			0.402478i	0.979542	+	0.201239i	$0.0644969\pi$
$971$			12.5416i			0.402478i	−0.979542	+	0.201239i	$0.935503\pi$
$972$	−1.00000			−0.0320750
$973$	27.5741	−	46.2258i	0.883985	−	1.48193i
$974$			35.6051i			1.14086i
$975$	−10.6517	−	15.9775i	−0.341126	−	0.511689i
$976$			4.32583i			0.138466i
$977$	13.8123	+	13.8123i	0.441894	+	0.441894i	0.892648	−	0.450754i	$-0.148845\pi$
$977$	13.8123	+	13.8123i	0.441894	+	0.441894i	−0.450754	+	0.892648i	$0.648845\pi$
$978$		−	4.82107i		−	0.154161i
$979$	2.66575			0.0851977
$980$	6.43858	−	21.5525i	0.205673	−	0.688469i
$981$	5.29626	+	5.29626i	0.169097	+	0.169097i
$982$	−5.49740	+	5.49740i	−0.175429	+	0.175429i
$983$	26.1069	+	26.1069i	0.832680	+	0.832680i	0.987883	−	0.155203i	$-0.0496031\pi$
$983$	26.1069	+	26.1069i	0.832680	+	0.832680i	−0.155203	+	0.987883i	$0.549603\pi$
$984$	4.99480			0.159228
$985$	−2.85205			−0.0908740
$986$	3.35167	+	3.35167i	0.106739	+	0.106739i
$987$	17.0888	−	4.31891i	0.543943	−	0.137472i
$988$	−5.98299	+	29.9149i	−0.190344	+	0.951721i
$989$	17.7647			0.564886
$990$	1.14201	−	1.14201i	0.0362954	−	0.0362954i
$991$	7.35727			0.233711			0.116856	−	0.993149i	$-0.462719\pi$
$991$	7.35727			0.233711			0.116856	+	0.993149i	$0.462719\pi$
$992$	1.53186			0.0486365
$993$	13.9785	−	13.9785i	0.443595	−	0.443595i
$994$	12.2388	−	20.5173i	0.388190	−	0.650769i
$995$	37.5766	−	37.5766i	1.19126	−	1.19126i
$996$	6.71078	−	6.71078i	0.212639	−	0.212639i
$997$			14.1274i			0.447420i	0.974656	+	0.223710i	$0.0718169\pi$
$997$			14.1274i			0.447420i	−0.974656	+	0.223710i	$0.928183\pi$
$998$			33.1763i			1.05018i
$999$	5.18902	+	5.18902i	0.164173	+	0.164173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.o.d.307.3	yes	8
3.2	odd	2		1638.2.x.b.307.2		8
7.6	odd	2		546.2.o.a.307.4	yes	8
13.5	odd	4		546.2.o.a.265.4	✓	8
21.20	even	2		1638.2.x.d.307.1		8
39.5	even	4		1638.2.x.d.811.1		8
91.83	even	4	inner	546.2.o.d.265.3	yes	8
273.83	odd	4		1638.2.x.b.811.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.a.265.4	✓	8	13.5	odd	4
546.2.o.a.307.4	yes	8	7.6	odd	2
546.2.o.d.265.3	yes	8	91.83	even	4	inner
546.2.o.d.307.3	yes	8	1.1	even	1	trivial
1638.2.x.b.307.2		8	3.2	odd	2
1638.2.x.b.811.2		8	273.83	odd	4
1638.2.x.d.307.1		8	21.20	even	2
1638.2.x.d.811.1		8	39.5	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(-2.27220 + 2.27220i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.27220 - 1.35539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(-2.27220 + 2.27220i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.27220 - 1.35539i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -3.21338 q^{10} +(0.355392 - 0.355392i) q^{11} -1.00000 q^{12} +(-2.00000 - 3.00000i) q^{13} +(-0.648285 - 2.56510i) q^{14} +(-2.27220 - 2.27220i) q^{15} -1.00000 q^{16} +4.32583 q^{17} +(-0.707107 - 0.707107i) q^{18} +(-5.98299 + 5.98299i) q^{19} +(-2.27220 - 2.27220i) q^{20} +(1.35539 - 2.27220i) q^{21} +0.502600 q^{22} -2.38496i q^{23} +(-0.707107 - 0.707107i) q^{24} -5.32583i q^{25} +(0.707107 - 3.53553i) q^{26} -1.00000i q^{27} +(1.35539 - 2.27220i) q^{28} +1.09574 q^{29} -3.21338i q^{30} +(-1.08319 + 1.08319i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.355392 + 0.355392i) q^{33} +(3.05882 + 3.05882i) q^{34} +(8.24264 - 2.08319i) q^{35} -1.00000i q^{36} +(-5.18902 + 5.18902i) q^{37} -8.46122 q^{38} +(3.00000 - 2.00000i) q^{39} -3.21338i q^{40} +(-3.53186 + 3.53186i) q^{41} +(2.56510 - 0.648285i) q^{42} +7.44867i q^{43} +(0.355392 + 0.355392i) q^{44} +(2.27220 - 2.27220i) q^{45} +(1.68642 - 1.68642i) q^{46} +(4.71078 + 4.71078i) q^{47} -1.00000i q^{48} +(3.32583 + 6.15945i) q^{49} +(3.76593 - 3.76593i) q^{50} +4.32583i q^{51} +(3.00000 - 2.00000i) q^{52} -11.2552 q^{53} +(0.707107 - 0.707107i) q^{54} +1.61504i q^{55} +(2.56510 - 0.648285i) q^{56} +(-5.98299 - 5.98299i) q^{57} +(0.774804 + 0.774804i) q^{58} +(-3.61504 - 3.61504i) q^{59} +(2.27220 - 2.27220i) q^{60} -4.32583i q^{61} -1.53186 q^{62} +(2.27220 + 1.35539i) q^{63} -1.00000i q^{64} +(11.3610 + 2.27220i) q^{65} +0.502600i q^{66} +(-0.531858 - 0.531858i) q^{67} +4.32583i q^{68} +2.38496 q^{69} +(7.30146 + 4.35539i) q^{70} +(6.38496 + 6.38496i) q^{71} +(0.707107 - 0.707107i) q^{72} +(5.18902 + 5.18902i) q^{73} -7.33838 q^{74} +5.32583 q^{75} +(-5.98299 - 5.98299i) q^{76} +(-1.28922 + 0.325828i) q^{77} +(3.53553 + 0.707107i) q^{78} -11.3143 q^{79} +(2.27220 - 2.27220i) q^{80} +1.00000 q^{81} -4.99480 q^{82} +(-6.71078 + 6.71078i) q^{83} +(2.27220 + 1.35539i) q^{84} +(-9.82917 + 9.82917i) q^{85} +(-5.26701 + 5.26701i) q^{86} +1.09574i q^{87} +0.502600i q^{88} +(3.75044 + 3.75044i) q^{89} +3.21338 q^{90} +(0.478235 + 9.52740i) q^{91} +2.38496 q^{92} +(-1.08319 - 1.08319i) q^{93} +6.66205i q^{94} -27.1891i q^{95} +(0.707107 - 0.707107i) q^{96} +(12.9931 - 12.9931i) q^{97} +(-2.00368 + 6.70711i) q^{98} +(-0.355392 + 0.355392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^5 + 4 * q^7 - 8 * q^9	\( 8 q + 4 q^{5} + 4 q^{7} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 8 q^{12} - 16 q^{13} + 4 q^{15} - 8 q^{16} + 12 q^{17} - 4 q^{19} + 4 q^{20} + 4 q^{22} - 12 q^{29} - 20 q^{31} - 8 q^{33} + 24 q^{34} + 32 q^{35} - 8 q^{37} - 12 q^{38} + 24 q^{39} - 16 q^{41} + 4 q^{42} - 8 q^{44} - 4 q^{45} - 20 q^{46} + 16 q^{47} + 4 q^{49} + 24 q^{50} + 24 q^{52} - 24 q^{53} + 4 q^{56} - 4 q^{57} - 16 q^{58} - 28 q^{59} - 4 q^{60} - 4 q^{63} - 20 q^{65} + 8 q^{67} + 20 q^{69} + 24 q^{70} + 52 q^{71} + 8 q^{73} - 4 q^{74} + 20 q^{75} - 4 q^{76} - 32 q^{77} - 48 q^{79} - 4 q^{80} + 8 q^{81} - 40 q^{82} - 32 q^{83} - 4 q^{84} + 20 q^{85} - 20 q^{86} - 4 q^{89} + 4 q^{90} - 8 q^{91} + 20 q^{92} - 20 q^{93} + 36 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^5 + 4 * q^7 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 8 * q^12 - 16 * q^13 + 4 * q^15 - 8 * q^16 + 12 * q^17 - 4 * q^19 + 4 * q^20 + 4 * q^22 - 12 * q^29 - 20 * q^31 - 8 * q^33 + 24 * q^34 + 32 * q^35 - 8 * q^37 - 12 * q^38 + 24 * q^39 - 16 * q^41 + 4 * q^42 - 8 * q^44 - 4 * q^45 - 20 * q^46 + 16 * q^47 + 4 * q^49 + 24 * q^50 + 24 * q^52 - 24 * q^53 + 4 * q^56 - 4 * q^57 - 16 * q^58 - 28 * q^59 - 4 * q^60 - 4 * q^63 - 20 * q^65 + 8 * q^67 + 20 * q^69 + 24 * q^70 + 52 * q^71 + 8 * q^73 - 4 * q^74 + 20 * q^75 - 4 * q^76 - 32 * q^77 - 48 * q^79 - 4 * q^80 + 8 * q^81 - 40 * q^82 - 32 * q^83 - 4 * q^84 + 20 * q^85 - 20 * q^86 - 4 * q^89 + 4 * q^90 - 8 * q^91 + 20 * q^92 - 20 * q^93 + 36 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more