LMFDB - Embedded newform 390.2.s.a.233.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(77,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("390.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.s (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.40960000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7x^{4} + 1 $ x^8 + 7*x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			233.3
Root			$1.14412 - 1.14412i$ of defining polynomial
Character	$\chi$	$=$	390.233
Dual form			390.2.s.a.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(0.707107 + 1.58114i) q^{6} +(-3.16228 - 3.16228i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(0.707107 + 1.58114i) q^{6} +(-3.16228 - 3.16228i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.23607 - 2.00000i) q^{9} +(-1.00000 - 2.00000i) q^{10} -5.65685 q^{11} +(1.61803 + 0.618034i) q^{12} +(3.58114 + 0.418861i) q^{13} -4.47214 q^{14} +(2.99535 + 2.45517i) q^{15} -1.00000 q^{16} +(-2.23607 - 2.23607i) q^{17} +(-2.99535 + 0.166925i) q^{18} +6.32456 q^{19} +(-2.12132 - 0.707107i) q^{20} +(7.07107 - 3.16228i) q^{21} +(-4.00000 + 4.00000i) q^{22} +(1.58114 - 0.707107i) q^{24} +(-4.00000 - 3.00000i) q^{25} +(2.82843 - 2.23607i) q^{26} +(4.61803 - 2.38197i) q^{27} +(-3.16228 + 3.16228i) q^{28} +4.47214 q^{29} +(3.85410 - 0.381966i) q^{30} +3.16228i q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.49613 - 9.15298i) q^{33} -3.16228 q^{34} +(-8.94427 + 4.47214i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(-3.16228 - 3.16228i) q^{37} +(4.47214 - 4.47214i) q^{38} +(-2.89100 + 5.53553i) q^{39} +(-2.00000 + 1.00000i) q^{40} +5.65685 q^{41} +(2.76393 - 7.23607i) q^{42} +(-5.00000 - 5.00000i) q^{43} +5.65685i q^{44} +(-5.82378 + 3.32920i) q^{45} +(1.41421 - 1.41421i) q^{47} +(0.618034 - 1.61803i) q^{48} +13.0000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(5.00000 - 2.23607i) q^{51} +(0.418861 - 3.58114i) q^{52} +(4.47214 - 4.47214i) q^{53} +(1.58114 - 4.94975i) q^{54} +(-4.00000 + 12.0000i) q^{55} +4.47214i q^{56} +(-3.90879 + 10.2333i) q^{57} +(3.16228 - 3.16228i) q^{58} +2.82843i q^{59} +(2.45517 - 2.99535i) q^{60} +10.0000 q^{61} +(2.23607 + 2.23607i) q^{62} +(0.746512 + 13.3956i) q^{63} +1.00000i q^{64} +(3.42079 - 7.30056i) q^{65} +(-4.00000 - 8.94427i) q^{66} +(-2.23607 + 2.23607i) q^{68} +(-3.16228 + 9.48683i) q^{70} -1.41421 q^{71} +(0.166925 + 2.99535i) q^{72} +(-3.16228 + 3.16228i) q^{73} -4.47214 q^{74} +(7.32624 - 4.61803i) q^{75} -6.32456i q^{76} +(17.8885 + 17.8885i) q^{77} +(1.86997 + 5.95846i) q^{78} +(-0.707107 + 2.12132i) q^{80} +(1.00000 + 8.94427i) q^{81} +(4.00000 - 4.00000i) q^{82} +(-2.82843 - 2.82843i) q^{83} +(-3.16228 - 7.07107i) q^{84} +(-6.32456 + 3.16228i) q^{85} -7.07107 q^{86} +(-2.76393 + 7.23607i) q^{87} +(4.00000 + 4.00000i) q^{88} -2.82843i q^{89} +(-1.76393 + 6.47214i) q^{90} +(-10.0000 - 12.6491i) q^{91} +(-5.11667 - 1.95440i) q^{93} -2.00000i q^{94} +(4.47214 - 13.4164i) q^{95} +(-0.707107 - 1.58114i) q^{96} +(-9.48683 - 9.48683i) q^{97} +(9.19239 + 9.19239i) q^{98} +(12.6491 + 11.3137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3}+O(q^{10}) $ 8 * q + 4 * q^3	$ 8 q + 4 q^{3} - 8 q^{10} + 4 q^{12} + 16 q^{13} - 8 q^{16} - 32 q^{22} - 32 q^{25} + 28 q^{27} + 4 q^{30} - 16 q^{36} - 16 q^{40} + 40 q^{42} - 40 q^{43} - 4 q^{48} + 40 q^{51} + 16 q^{52} - 32 q^{55} + 80 q^{61} - 32 q^{66} - 4 q^{75} + 20 q^{78} + 8 q^{81} + 32 q^{82} - 40 q^{87} + 32 q^{88} - 32 q^{90} - 80 q^{91}+O(q^{100}) $ 8 * q + 4 * q^3 - 8 * q^10 + 4 * q^12 + 16 * q^13 - 8 * q^16 - 32 * q^22 - 32 * q^25 + 28 * q^27 + 4 * q^30 - 16 * q^36 - 16 * q^40 + 40 * q^42 - 40 * q^43 - 4 * q^48 + 40 * q^51 + 16 * q^52 - 32 * q^55 + 80 * q^61 - 32 * q^66 - 4 * q^75 + 20 * q^78 + 8 * q^81 + 32 * q^82 - 40 * q^87 + 32 * q^88 - 32 * q^90 - 80 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	−0.618034	+	1.61803i	−0.356822	+	0.934172i
$3$	−0.618034	+	1.61803i	−0.356822	+	0.934172i
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$5$	0.707107	−	2.12132i	0.316228	−	0.948683i
$6$	0.707107	+	1.58114i	0.288675	+	0.645497i
$7$	−3.16228	−	3.16228i	−1.19523	−	1.19523i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−3.16228	−	3.16228i	−1.19523	−	1.19523i	−0.219650	−	0.975579i	$-0.570491\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.23607	−	2.00000i	−0.745356	−	0.666667i
$10$	−1.00000	−	2.00000i	−0.316228	−	0.632456i
$11$	−5.65685			−1.70561			−0.852803	−	0.522233i	$-0.825099\pi$
$11$	−5.65685			−1.70561			−0.852803	+	0.522233i	$0.825099\pi$
$12$	1.61803	+	0.618034i	0.467086	+	0.178411i
$13$	3.58114	+	0.418861i	0.993229	+	0.116171i
$13$	3.58114	+	0.418861i	0.993229	+	0.116171i
$14$	−4.47214			−1.19523
$15$	2.99535	+	2.45517i	0.773397	+	0.633922i
$16$	−1.00000			−0.250000
$17$	−2.23607	−	2.23607i	−0.542326	−	0.542326i	0.381884	−	0.924210i	$-0.375275\pi$
$17$	−2.23607	−	2.23607i	−0.542326	−	0.542326i	−0.924210	+	0.381884i	$0.875275\pi$
$18$	−2.99535	+	0.166925i	−0.706011	+	0.0393447i
$19$	6.32456			1.45095			0.725476	−	0.688247i	$-0.241620\pi$
$19$	6.32456			1.45095			0.725476	+	0.688247i	$0.241620\pi$
$20$	−2.12132	−	0.707107i	−0.474342	−	0.158114i
$21$	7.07107	−	3.16228i	1.54303	−	0.690066i
$22$	−4.00000	+	4.00000i	−0.852803	+	0.852803i
$23$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$23$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$24$	1.58114	−	0.707107i	0.322749	−	0.144338i
$25$	−4.00000	−	3.00000i	−0.800000	−	0.600000i
$26$	2.82843	−	2.23607i	0.554700	−	0.438529i
$27$	4.61803	−	2.38197i	0.888741	−	0.458410i
$28$	−3.16228	+	3.16228i	−0.597614	+	0.597614i
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$	3.85410	−	0.381966i	0.703660	−	0.0697371i
$31$			3.16228i			0.567962i	0.958830	+	0.283981i	$0.0916552\pi$
$31$			3.16228i			0.567962i	−0.958830	+	0.283981i	$0.908345\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.49613	−	9.15298i	0.608598	−	1.59333i
$34$	−3.16228			−0.542326
$35$	−8.94427	+	4.47214i	−1.51186	+	0.755929i
$36$	−2.00000	+	2.23607i	−0.333333	+	0.372678i
$37$	−3.16228	−	3.16228i	−0.519875	−	0.519875i	0.397658	−	0.917534i	$-0.369823\pi$
$37$	−3.16228	−	3.16228i	−0.519875	−	0.519875i	−0.917534	+	0.397658i	$0.869823\pi$
$38$	4.47214	−	4.47214i	0.725476	−	0.725476i
$39$	−2.89100	+	5.53553i	−0.462930	+	0.886395i
$40$	−2.00000	+	1.00000i	−0.316228	+	0.158114i
$41$	5.65685			0.883452			0.441726	−	0.897150i	$-0.354366\pi$
$41$	5.65685			0.883452			0.441726	+	0.897150i	$0.354366\pi$
$42$	2.76393	−	7.23607i	0.426484	−	1.11655i
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	0.214280	−	0.976772i	$-0.431260\pi$
$43$	−5.00000	−	5.00000i	−0.762493	−	0.762493i	−0.976772	+	0.214280i	$0.931260\pi$
$44$			5.65685i			0.852803i
$45$	−5.82378	+	3.32920i	−0.868158	+	0.496288i
$46$		0			0
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	−0.596402	−	0.802686i	$-0.703403\pi$
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	0.802686	+	0.596402i	$0.203403\pi$
$48$	0.618034	−	1.61803i	0.0892055	−	0.233543i
$49$			13.0000i			1.85714i
$50$	−4.94975	+	0.707107i	−0.700000	+	0.100000i
$51$	5.00000	−	2.23607i	0.700140	−	0.313112i
$52$	0.418861	−	3.58114i	0.0580856	−	0.496615i
$53$	4.47214	−	4.47214i	0.614295	−	0.614295i	−0.329767	−	0.944062i	$-0.606970\pi$
$53$	4.47214	−	4.47214i	0.614295	−	0.614295i	0.944062	+	0.329767i	$0.106970\pi$
$54$	1.58114	−	4.94975i	0.215166	−	0.673575i
$55$	−4.00000	+	12.0000i	−0.539360	+	1.61808i
$56$			4.47214i			0.597614i
$57$	−3.90879	+	10.2333i	−0.517732	+	1.35544i
$58$	3.16228	−	3.16228i	0.415227	−	0.415227i
$59$			2.82843i			0.368230i	0.982905	+	0.184115i	$0.0589419\pi$
$59$			2.82843i			0.368230i	−0.982905	+	0.184115i	$0.941058\pi$
$60$	2.45517	−	2.99535i	0.316961	−	0.386698i
$61$	10.0000			1.28037			0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000			1.28037			0.640184	+	0.768221i	$0.278858\pi$
$62$	2.23607	+	2.23607i	0.283981	+	0.283981i
$63$	0.746512	+	13.3956i	0.0940517	+	1.68769i
$64$			1.00000i			0.125000i
$65$	3.42079	−	7.30056i	0.424296	−	0.905523i
$66$	−4.00000	−	8.94427i	−0.492366	−	1.10096i
$67$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$67$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$68$	−2.23607	+	2.23607i	−0.271163	+	0.271163i
$69$		0			0
$70$	−3.16228	+	9.48683i	−0.377964	+	1.13389i
$71$	−1.41421			−0.167836			−0.0839181	−	0.996473i	$-0.526743\pi$
$71$	−1.41421			−0.167836			−0.0839181	+	0.996473i	$0.526743\pi$
$72$	0.166925	+	2.99535i	0.0196723	+	0.353006i
$73$	−3.16228	+	3.16228i	−0.370117	+	0.370117i	−0.867520	−	0.497403i	$-0.834287\pi$
$73$	−3.16228	+	3.16228i	−0.370117	+	0.370117i	0.497403	+	0.867520i	$0.334287\pi$
$74$	−4.47214			−0.519875
$75$	7.32624	−	4.61803i	0.845961	−	0.533245i
$76$		−	6.32456i		−	0.725476i
$77$	17.8885	+	17.8885i	2.03859	+	2.03859i
$78$	1.86997	+	5.95846i	0.211732	+	0.674662i
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	−0.707107	+	2.12132i	−0.0790569	+	0.237171i
$81$	1.00000	+	8.94427i	0.111111	+	0.993808i
$82$	4.00000	−	4.00000i	0.441726	−	0.441726i
$83$	−2.82843	−	2.82843i	−0.310460	−	0.310460i	0.534628	−	0.845088i	$-0.320452\pi$
$83$	−2.82843	−	2.82843i	−0.310460	−	0.310460i	−0.845088	+	0.534628i	$0.820452\pi$
$84$	−3.16228	−	7.07107i	−0.345033	−	0.771517i
$85$	−6.32456	+	3.16228i	−0.685994	+	0.342997i
$86$	−7.07107			−0.762493
$87$	−2.76393	+	7.23607i	−0.296325	+	0.775788i
$88$	4.00000	+	4.00000i	0.426401	+	0.426401i
$89$		−	2.82843i		−	0.299813i	−0.988700	−	0.149906i	$-0.952103\pi$
$89$		−	2.82843i		−	0.299813i	0.988700	−	0.149906i	$-0.0478972\pi$
$90$	−1.76393	+	6.47214i	−0.185935	+	0.682223i
$91$	−10.0000	−	12.6491i	−1.04828	−	1.32599i
$92$		0			0
$93$	−5.11667	−	1.95440i	−0.530574	−	0.202661i
$94$		−	2.00000i		−	0.206284i
$95$	4.47214	−	13.4164i	0.458831	−	1.37649i
$96$	−0.707107	−	1.58114i	−0.0721688	−	0.161374i
$97$	−9.48683	−	9.48683i	−0.963242	−	0.963242i	0.0361060	−	0.999348i	$-0.488505\pi$
$97$	−9.48683	−	9.48683i	−0.963242	−	0.963242i	−0.999348	+	0.0361060i	$0.988505\pi$
$98$	9.19239	+	9.19239i	0.928571	+	0.928571i
$99$	12.6491	+	11.3137i	1.27128	+	1.13707i
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$			4.47214i			0.444994i	0.974933	+	0.222497i	$0.0714208\pi$
$101$			4.47214i			0.444994i	−0.974933	+	0.222497i	$0.928579\pi$
$102$	1.95440	−	5.11667i	0.193514	−	0.506626i
$103$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$103$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$104$	−2.23607	−	2.82843i	−0.219265	−	0.277350i
$105$	−1.70820	−	17.2361i	−0.166704	−	1.68207i
$106$		−	6.32456i		−	0.614295i
$107$	2.23607	+	2.23607i	0.216169	+	0.216169i	0.806882	−	0.590713i	$-0.201153\pi$
$107$	2.23607	+	2.23607i	0.216169	+	0.216169i	−0.590713	+	0.806882i	$0.701153\pi$
$108$	−2.38197	−	4.61803i	−0.229205	−	0.444371i
$109$	−3.16228			−0.302891			−0.151446	−	0.988466i	$-0.548393\pi$
$109$	−3.16228			−0.302891			−0.151446	+	0.988466i	$0.548393\pi$
$110$	5.65685	+	11.3137i	0.539360	+	1.07872i
$111$	7.07107	−	3.16228i	0.671156	−	0.300150i
$112$	3.16228	+	3.16228i	0.298807	+	0.298807i
$113$	6.70820	−	6.70820i	0.631055	−	0.631055i	−0.317278	−	0.948333i	$-0.602769\pi$
$113$	6.70820	−	6.70820i	0.631055	−	0.631055i	0.948333	+	0.317278i	$0.102769\pi$
$114$	4.47214	+	10.0000i	0.418854	+	0.936586i
$115$		0			0
$116$		−	4.47214i		−	0.415227i
$117$	−7.16995	−	8.09888i	−0.662862	−	0.748742i
$118$	2.00000	+	2.00000i	0.184115	+	0.184115i
$119$			14.1421i			1.29641i
$120$	−0.381966	−	3.85410i	−0.0348686	−	0.351830i
$121$	21.0000			1.90909
$122$	7.07107	−	7.07107i	0.640184	−	0.640184i
$123$	−3.49613	+	9.15298i	−0.315235	+	0.825297i
$124$	3.16228			0.283981
$125$	−9.19239	+	6.36396i	−0.822192	+	0.569210i
$126$	10.0000	+	8.94427i	0.890871	+	0.796819i
$127$	−2.00000	+	2.00000i	−0.177471	+	0.177471i	−0.790253	−	0.612781i	$-0.790051\pi$
$127$	−2.00000	+	2.00000i	−0.177471	+	0.177471i	0.612781	+	0.790253i	$0.290051\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	11.1803	−	5.00000i	0.984374	−	0.440225i
$130$	−2.74342	−	7.58114i	−0.240614	−	0.664910i
$131$		−	17.8885i		−	1.56293i	−0.623949	−	0.781465i	$-0.714473\pi$
$131$		−	17.8885i		−	1.56293i	0.623949	−	0.781465i	$-0.285527\pi$
$132$	−9.15298	−	3.49613i	−0.796665	−	0.304299i
$133$	−20.0000	−	20.0000i	−1.73422	−	1.73422i
$134$		0			0
$135$	−1.78747	−	11.4806i	−0.153841	−	0.988096i
$136$			3.16228i			0.271163i
$137$	12.7279	−	12.7279i	1.08742	−	1.08742i	0.0916263	−	0.995793i	$-0.470793\pi$
$137$	12.7279	−	12.7279i	1.08742	−	1.08742i	0.995793	−	0.0916263i	$-0.0292065\pi$
$138$		0			0
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$	4.47214	+	8.94427i	0.377964	+	0.755929i
$141$	1.41421	+	3.16228i	0.119098	+	0.266312i
$142$	−1.00000	+	1.00000i	−0.0839181	+	0.0839181i
$143$	−20.2580	−	2.36944i	−1.69406	−	0.198142i
$144$	2.23607	+	2.00000i	0.186339	+	0.166667i
$145$	3.16228	−	9.48683i	0.262613	−	0.787839i
$146$			4.47214i			0.370117i
$147$	−21.0344	−	8.03444i	−1.73489	−	0.662670i
$148$	−3.16228	+	3.16228i	−0.259938	+	0.259938i
$149$		−	4.24264i		−	0.347571i	−0.984784	−	0.173785i	$-0.944400\pi$
$149$		−	4.24264i		−	0.347571i	0.984784	−	0.173785i	$-0.0555999\pi$
$150$	1.91499	−	8.44588i	0.156358	−	0.689603i
$151$			22.1359i			1.80140i	0.434444	+	0.900699i	$0.356945\pi$
$151$			22.1359i			1.80140i	−0.434444	+	0.900699i	$0.643055\pi$
$152$	−4.47214	−	4.47214i	−0.362738	−	0.362738i
$153$	0.527864	+	9.47214i	0.0426753	+	0.765777i
$154$	25.2982			2.03859
$155$	6.70820	+	2.23607i	0.538816	+	0.179605i
$156$	5.53553	+	2.89100i	0.443197	+	0.231465i
$157$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$157$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$158$		0			0
$159$	4.47214	+	10.0000i	0.354663	+	0.793052i
$160$	1.00000	+	2.00000i	0.0790569	+	0.158114i
$161$		0			0
$162$	7.03166	+	5.61745i	0.552460	+	0.441348i
$163$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$163$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$164$		−	5.65685i		−	0.441726i
$165$	−16.9443	−	13.8885i	−1.31911	−	1.08122i
$166$	−4.00000			−0.310460
$167$	12.7279	−	12.7279i	0.984916	−	0.984916i	−0.0149717	−	0.999888i	$-0.504766\pi$
$167$	12.7279	−	12.7279i	0.984916	−	0.984916i	0.999888	+	0.0149717i	$0.00476583\pi$
$168$	−7.23607	−	2.76393i	−0.558275	−	0.213242i
$169$	12.6491	+	3.00000i	0.973009	+	0.230769i
$170$	−2.23607	+	6.70820i	−0.171499	+	0.514496i
$171$	−14.1421	−	12.6491i	−1.08148	−	0.967302i
$172$	−5.00000	+	5.00000i	−0.381246	+	0.381246i
$173$	−13.4164	+	13.4164i	−1.02003	+	1.02003i	−0.0202354	+	0.999795i	$0.506442\pi$
$173$	−13.4164	+	13.4164i	−1.02003	+	1.02003i	−0.999795	+	0.0202354i	$0.993558\pi$
$174$	3.16228	+	7.07107i	0.239732	+	0.536056i
$175$	3.16228	+	22.1359i	0.239046	+	1.67332i
$176$	5.65685			0.426401
$177$	−4.57649	−	1.74806i	−0.343990	−	0.131393i
$178$	−2.00000	−	2.00000i	−0.149906	−	0.149906i
$179$	17.8885			1.33705			0.668526	−	0.743689i	$-0.266925\pi$
$179$	17.8885			1.33705			0.668526	+	0.743689i	$0.266925\pi$
$180$	3.32920	+	5.82378i	0.248144	+	0.434079i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	−16.0153	−	1.87320i	−1.18714	−	0.138851i
$183$	−6.18034	+	16.1803i	−0.456864	+	1.19609i
$184$		0			0
$185$	−8.94427	+	4.47214i	−0.657596	+	0.328798i
$186$	−5.00000	+	2.23607i	−0.366618	+	0.163956i
$187$	12.6491	+	12.6491i	0.924995	+	0.924995i
$188$	−1.41421	−	1.41421i	−0.103142	−	0.103142i
$189$	−22.1359	−	7.07107i	−1.61015	−	0.514344i
$190$	−6.32456	−	12.6491i	−0.458831	−	0.917663i
$191$			8.94427i			0.647185i	0.946197	+	0.323592i	$0.104891\pi$
$191$			8.94427i			0.647185i	−0.946197	+	0.323592i	$0.895109\pi$
$192$	−1.61803	−	0.618034i	−0.116772	−	0.0446028i
$193$	−9.48683	+	9.48683i	−0.682877	+	0.682877i	−0.960648	−	0.277770i	$-0.910405\pi$
$193$	−9.48683	+	9.48683i	−0.682877	+	0.682877i	0.277770	+	0.960648i	$0.410405\pi$
$194$	−13.4164			−0.963242
$195$	9.69840	+	10.0469i	0.694517	+	0.719477i
$196$	13.0000			0.928571
$197$	1.41421	−	1.41421i	0.100759	−	0.100759i	−0.654931	−	0.755689i	$-0.727302\pi$
$197$	1.41421	−	1.41421i	0.100759	−	0.100759i	0.755689	+	0.654931i	$0.227302\pi$
$198$	16.9443	−	0.944272i	1.20418	−	0.0671065i
$199$		−	20.0000i		−	1.41776i	−0.705328	−	0.708881i	$-0.749200\pi$
$199$		−	20.0000i		−	1.41776i	0.705328	−	0.708881i	$-0.250800\pi$
$200$	0.707107	+	4.94975i	0.0500000	+	0.350000i
$201$		0			0
$202$	3.16228	+	3.16228i	0.222497	+	0.222497i
$203$	−14.1421	−	14.1421i	−0.992583	−	0.992583i
$204$	−2.23607	−	5.00000i	−0.156556	−	0.350070i
$205$	4.00000	−	12.0000i	0.279372	−	0.838116i
$206$		0			0
$207$		0			0
$208$	−3.58114	−	0.418861i	−0.248307	−	0.0290428i
$209$	−35.7771			−2.47475
$210$	−13.3956	−	10.9799i	−0.924386	−	0.757682i
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	−4.47214	−	4.47214i	−0.307148	−	0.307148i
$213$	0.874032	−	2.28825i	0.0598877	−	0.156788i
$214$	3.16228			0.216169
$215$	−14.1421	+	7.07107i	−0.964486	+	0.482243i
$216$	−4.94975	−	1.58114i	−0.336788	−	0.107583i
$217$	10.0000	−	10.0000i	0.678844	−	0.678844i
$218$	−2.23607	+	2.23607i	−0.151446	+	0.151446i
$219$	−3.16228	−	7.07107i	−0.213687	−	0.477818i
$220$	12.0000	+	4.00000i	0.809040	+	0.269680i
$221$	−7.07107	−	8.94427i	−0.475651	−	0.601657i
$222$	2.76393	−	7.23607i	0.185503	−	0.485653i
$223$	18.9737	−	18.9737i	1.27057	−	1.27057i	0.324782	−	0.945789i	$-0.394709\pi$
$223$	18.9737	−	18.9737i	1.27057	−	1.27057i	0.945789	−	0.324782i	$-0.105291\pi$
$224$	4.47214			0.298807
$225$	2.94427	+	14.7082i	0.196285	+	0.980547i
$226$		−	9.48683i		−	0.631055i
$227$	−8.48528	+	8.48528i	−0.563188	+	0.563188i	−0.930212	−	0.367024i	$-0.880377\pi$
$227$	−8.48528	+	8.48528i	−0.563188	+	0.563188i	0.367024	+	0.930212i	$0.380377\pi$
$228$	10.2333	+	3.90879i	0.677720	+	0.258866i
$229$	−9.48683			−0.626908			−0.313454	−	0.949603i	$-0.601486\pi$
$229$	−9.48683			−0.626908			−0.313454	+	0.949603i	$0.601486\pi$
$230$		0			0
$231$	−40.0000	+	17.8885i	−2.63181	+	1.17698i
$232$	−3.16228	−	3.16228i	−0.207614	−	0.207614i
$233$	−2.23607	+	2.23607i	−0.146490	+	0.146490i	−0.776548	−	0.630058i	$-0.783031\pi$
$233$	−2.23607	+	2.23607i	−0.146490	+	0.146490i	0.630058	+	0.776548i	$0.283031\pi$
$234$	−10.7967	−	0.656854i	−0.705802	−	0.0429399i
$235$	−2.00000	−	4.00000i	−0.130466	−	0.260931i
$236$	2.82843			0.184115
$237$		0			0
$238$	10.0000	+	10.0000i	0.648204	+	0.648204i
$239$		−	4.24264i		−	0.274434i	−0.990541	−	0.137217i	$-0.956184\pi$
$239$		−	4.24264i		−	0.274434i	0.990541	−	0.137217i	$-0.0438157\pi$
$240$	−2.99535	−	2.45517i	−0.193349	−	0.158481i
$241$		−	12.6491i		−	0.814801i	−0.913250	−	0.407400i	$-0.866435\pi$
$241$		−	12.6491i		−	0.814801i	0.913250	−	0.407400i	$-0.133565\pi$
$242$	14.8492	−	14.8492i	0.954545	−	0.954545i
$243$	−15.0902	−	3.90983i	−0.968035	−	0.250816i
$244$		−	10.0000i		−	0.640184i
$245$	27.5772	+	9.19239i	1.76184	+	0.587280i
$246$	4.00000	+	8.94427i	0.255031	+	0.570266i
$247$	22.6491	+	2.64911i	1.44113	+	0.168559i
$248$	2.23607	−	2.23607i	0.141990	−	0.141990i
$249$	6.32456	−	2.82843i	0.400802	−	0.179244i
$250$	−2.00000	+	11.0000i	−0.126491	+	0.695701i
$251$		−	17.8885i		−	1.12911i	−0.825394	−	0.564557i	$-0.809047\pi$
$251$		−	17.8885i		−	1.12911i	0.825394	−	0.564557i	$-0.190953\pi$
$252$	13.3956	−	0.746512i	0.843845	−	0.0470259i
$253$		0			0
$254$			2.82843i			0.177471i
$255$	−1.20788	−	12.1877i	−0.0756405	−	0.763226i
$256$	1.00000			0.0625000
$257$	20.1246	+	20.1246i	1.25534	+	1.25534i	0.953294	+	0.302045i	$0.0976694\pi$
$257$	20.1246	+	20.1246i	1.25534	+	1.25534i	0.302045	+	0.953294i	$0.402331\pi$
$258$	4.37016	−	11.4412i	0.272074	−	0.712300i
$259$			20.0000i			1.24274i
$260$	−7.30056	−	3.42079i	−0.452762	−	0.212148i
$261$	−10.0000	−	8.94427i	−0.618984	−	0.553637i
$262$	−12.6491	−	12.6491i	−0.781465	−	0.781465i
$263$	8.94427	−	8.94427i	0.551527	−	0.551527i	−0.375354	−	0.926882i	$-0.622479\pi$
$263$	8.94427	−	8.94427i	0.551527	−	0.551527i	0.926882	+	0.375354i	$0.122479\pi$
$264$	−8.94427	+	4.00000i	−0.550482	+	0.246183i
$265$	−6.32456	−	12.6491i	−0.388514	−	0.777029i
$266$	−28.2843			−1.73422
$267$	4.57649	+	1.74806i	0.280077	+	0.106980i
$268$		0			0
$269$	22.3607			1.36335			0.681677	−	0.731653i	$-0.261251\pi$
$269$	22.3607			1.36335			0.681677	+	0.731653i	$0.261251\pi$
$270$	−9.38197	−	6.85410i	−0.570968	−	0.417127i
$271$			9.48683i			0.576284i	0.957588	+	0.288142i	$0.0930375\pi$
$271$			9.48683i			0.576284i	−0.957588	+	0.288142i	$0.906962\pi$
$272$	2.23607	+	2.23607i	0.135582	+	0.135582i
$273$	26.6470	−	8.36276i	1.61275	−	0.506137i
$274$		−	18.0000i		−	1.08742i
$275$	22.6274	+	16.9706i	1.36448	+	1.02336i
$276$		0			0
$277$	10.0000	−	10.0000i	0.600842	−	0.600842i	−0.339694	−	0.940536i	$-0.610324\pi$
$277$	10.0000	−	10.0000i	0.600842	−	0.600842i	0.940536	+	0.339694i	$0.110324\pi$
$278$	2.82843	+	2.82843i	0.169638	+	0.169638i
$279$	6.32456	−	7.07107i	0.378641	−	0.423334i
$280$	9.48683	+	3.16228i	0.566947	+	0.188982i
$281$	8.48528			0.506189			0.253095	−	0.967442i	$-0.418552\pi$
$281$	8.48528			0.506189			0.253095	+	0.967442i	$0.418552\pi$
$282$	3.23607	+	1.23607i	0.192705	+	0.0736068i
$283$	9.00000	+	9.00000i	0.534994	+	0.534994i	0.922055	−	0.387060i	$-0.126509\pi$
$283$	9.00000	+	9.00000i	0.534994	+	0.534994i	−0.387060	+	0.922055i	$0.626509\pi$
$284$			1.41421i			0.0839181i
$285$	18.9443	+	15.5279i	1.12216	+	0.919791i
$286$	−16.0000	+	12.6491i	−0.946100	+	0.747958i
$287$	−17.8885	−	17.8885i	−1.05593	−	1.05593i
$288$	2.99535	−	0.166925i	0.176503	−	0.00983617i
$289$		−	7.00000i		−	0.411765i
$290$	−4.47214	−	8.94427i	−0.262613	−	0.525226i
$291$	21.2132	−	9.48683i	1.24354	−	0.556128i
$292$	3.16228	+	3.16228i	0.185058	+	0.185058i
$293$	−11.3137	−	11.3137i	−0.660954	−	0.660954i	0.294651	−	0.955605i	$-0.404797\pi$
$293$	−11.3137	−	11.3137i	−0.660954	−	0.660954i	−0.955605	+	0.294651i	$0.904797\pi$
$294$	−20.5548	+	9.19239i	−1.19878	+	0.536111i
$295$	6.00000	+	2.00000i	0.349334	+	0.116445i
$296$			4.47214i			0.259938i
$297$	−26.1235	+	13.4744i	−1.51584	+	0.781866i
$298$	−3.00000	−	3.00000i	−0.173785	−	0.173785i
$299$		0			0
$300$	−4.61803	−	7.32624i	−0.266622	−	0.422981i
$301$			31.6228i			1.82271i
$302$	15.6525	+	15.6525i	0.900699	+	0.900699i
$303$	−7.23607	−	2.76393i	−0.415701	−	0.158784i
$304$	−6.32456			−0.362738
$305$	7.07107	−	21.2132i	0.404888	−	1.21466i
$306$	7.07107	+	6.32456i	0.404226	+	0.361551i
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$	17.8885	−	17.8885i	1.01929	−	1.01929i
$309$		0			0
$310$	6.32456	−	3.16228i	0.359211	−	0.179605i
$311$			8.94427i			0.507183i	0.967311	+	0.253592i	$0.0816119\pi$
$311$			8.94427i			0.507183i	−0.967311	+	0.253592i	$0.918388\pi$
$312$	5.95846	−	1.86997i	0.337331	−	0.105866i
$313$	−1.00000	−	1.00000i	−0.0565233	−	0.0565233i	0.678280	−	0.734803i	$-0.262726\pi$
$313$	−1.00000	−	1.00000i	−0.0565233	−	0.0565233i	−0.734803	+	0.678280i	$0.762726\pi$
$314$		0			0
$315$	28.9443	+	7.88854i	1.63082	+	0.444469i
$316$		0			0
$317$	−19.7990	+	19.7990i	−1.11202	+	1.11202i	−0.119145	+	0.992877i	$0.538015\pi$
$317$	−19.7990	+	19.7990i	−1.11202	+	1.11202i	−0.992877	+	0.119145i	$0.961985\pi$
$318$	10.2333	+	3.90879i	0.573858	+	0.219194i
$319$	−25.2982			−1.41643
$320$	2.12132	+	0.707107i	0.118585	+	0.0395285i
$321$	−5.00000	+	2.23607i	−0.279073	+	0.124805i
$322$		0			0
$323$	−14.1421	−	14.1421i	−0.786889	−	0.786889i
$324$	8.94427	−	1.00000i	0.496904	−	0.0555556i
$325$	−13.0680	−	12.4189i	−0.724881	−	0.688874i
$326$		0			0
$327$	1.95440	−	5.11667i	0.108078	−	0.282953i
$328$	−4.00000	−	4.00000i	−0.220863	−	0.220863i
$329$	−8.94427			−0.493114
$330$	−21.8021	+	2.16073i	−1.20017	+	0.118944i
$331$		−	12.6491i		−	0.695258i	−0.937632	−	0.347629i	$-0.886987\pi$
$331$		−	12.6491i		−	0.695258i	0.937632	−	0.347629i	$-0.113013\pi$
$332$	−2.82843	+	2.82843i	−0.155230	+	0.155230i
$333$	0.746512	+	13.3956i	0.0409086	+	0.734076i
$334$		−	18.0000i		−	0.984916i
$335$		0			0
$336$	−7.07107	+	3.16228i	−0.385758	+	0.172516i
$337$	−13.0000	+	13.0000i	−0.708155	+	0.708155i	−0.966147	−	0.257992i	$-0.916939\pi$
$337$	−13.0000	+	13.0000i	−0.708155	+	0.708155i	0.257992	+	0.966147i	$0.416939\pi$
$338$	11.0656	−	6.82295i	0.601889	−	0.371120i
$339$	6.70820	+	15.0000i	0.364340	+	0.814688i
$340$	3.16228	+	6.32456i	0.171499	+	0.342997i
$341$		−	17.8885i		−	0.968719i
$342$	−18.9443	+	1.05573i	−1.02439	+	0.0570872i
$343$	18.9737	−	18.9737i	1.02448	−	1.02448i
$344$			7.07107i			0.381246i
$345$		0			0
$346$			18.9737i			1.02003i
$347$	−20.1246	−	20.1246i	−1.08035	−	1.08035i	−0.996477	−	0.0838690i	$-0.973272\pi$
$347$	−20.1246	−	20.1246i	−1.08035	−	1.08035i	−0.0838690	−	0.996477i	$-0.526728\pi$
$348$	7.23607	+	2.76393i	0.387894	+	0.148162i
$349$	−3.16228			−0.169273			−0.0846364	−	0.996412i	$-0.526973\pi$
$349$	−3.16228			−0.169273			−0.0846364	+	0.996412i	$0.526973\pi$
$350$	17.8885	+	13.4164i	0.956183	+	0.717137i
$351$	17.5355	−	6.59584i	0.935978	−	0.352060i
$352$	4.00000	−	4.00000i	0.213201	−	0.213201i
$353$	9.89949	+	9.89949i	0.526897	+	0.526897i	0.919646	−	0.392749i	$-0.128476\pi$
$353$	9.89949	+	9.89949i	0.526897	+	0.526897i	−0.392749	+	0.919646i	$0.628476\pi$
$354$	−4.47214	+	2.00000i	−0.237691	+	0.106299i
$355$	−1.00000	+	3.00000i	−0.0530745	+	0.159223i
$356$	−2.82843			−0.149906
$357$	−22.8825	−	8.74032i	−1.21107	−	0.462587i
$358$	12.6491	−	12.6491i	0.668526	−	0.668526i
$359$			32.5269i			1.71670i	0.513061	+	0.858352i	$0.328512\pi$
$359$			32.5269i			1.71670i	−0.513061	+	0.858352i	$0.671488\pi$
$360$	6.47214	+	1.76393i	0.341112	+	0.0929674i
$361$	21.0000			1.10526
$362$	−15.5563	+	15.5563i	−0.817624	+	0.817624i
$363$	−12.9787	+	33.9787i	−0.681206	+	1.78342i
$364$	−12.6491	+	10.0000i	−0.662994	+	0.524142i
$365$	4.47214	+	8.94427i	0.234082	+	0.468165i
$366$	7.07107	+	15.8114i	0.369611	+	0.826475i
$367$	−20.0000	+	20.0000i	−1.04399	+	1.04399i	−0.0450047	+	0.998987i	$0.514330\pi$
$367$	−20.0000	+	20.0000i	−1.04399	+	1.04399i	−0.998987	+	0.0450047i	$0.985670\pi$
$368$		0			0
$369$	−12.6491	−	11.3137i	−0.658486	−	0.588968i
$370$	−3.16228	+	9.48683i	−0.164399	+	0.493197i
$371$	−28.2843			−1.46845
$372$	−1.95440	+	5.11667i	−0.101331	+	0.265287i
$373$	16.0000	+	16.0000i	0.828449	+	0.828449i	0.987302	−	0.158854i	$-0.0507798\pi$
$373$	16.0000	+	16.0000i	0.828449	+	0.828449i	−0.158854	+	0.987302i	$0.550780\pi$
$374$	17.8885			0.924995
$375$	−4.61590	−	18.8067i	−0.238364	−	0.971176i
$376$	−2.00000			−0.103142
$377$	16.0153	+	1.87320i	0.824832	+	0.0964749i
$378$	−20.6525	+	10.6525i	−1.06225	+	0.547904i
$379$	−6.32456			−0.324871			−0.162435	−	0.986719i	$-0.551935\pi$
$379$	−6.32456			−0.324871			−0.162435	+	0.986719i	$0.551935\pi$
$380$	−13.4164	−	4.47214i	−0.688247	−	0.229416i
$381$	−2.00000	−	4.47214i	−0.102463	−	0.229114i
$382$	6.32456	+	6.32456i	0.323592	+	0.323592i
$383$	11.3137	+	11.3137i	0.578103	+	0.578103i	0.934380	−	0.356277i	$-0.115954\pi$
$383$	11.3137	+	11.3137i	0.578103	+	0.578103i	−0.356277	+	0.934380i	$0.615954\pi$
$384$	−1.58114	+	0.707107i	−0.0806872	+	0.0360844i
$385$	50.5964	−	25.2982i	2.57863	−	1.28932i
$386$			13.4164i			0.682877i
$387$	1.18034	+	21.1803i	0.0600000	+	1.07666i
$388$	−9.48683	+	9.48683i	−0.481621	+	0.481621i
$389$	−13.4164			−0.680239			−0.340119	−	0.940382i	$-0.610468\pi$
$389$	−13.4164			−0.680239			−0.340119	+	0.940382i	$0.610468\pi$
$390$	13.9621	+	0.246460i	0.706997	+	0.0124800i
$391$		0			0
$392$	9.19239	−	9.19239i	0.464286	−	0.464286i
$393$	28.9443	+	11.0557i	1.46005	+	0.557688i
$394$		−	2.00000i		−	0.100759i
$395$		0			0
$396$	11.3137	−	12.6491i	0.568535	−	0.635642i
$397$	25.2982	+	25.2982i	1.26968	+	1.26968i	0.946252	+	0.323429i	$0.104836\pi$
$397$	25.2982	+	25.2982i	1.26968	+	1.26968i	0.323429	+	0.946252i	$0.395164\pi$
$398$	−14.1421	−	14.1421i	−0.708881	−	0.708881i
$399$	44.7214	−	20.0000i	2.23887	−	1.00125i
$400$	4.00000	+	3.00000i	0.200000	+	0.150000i
$401$	−8.48528			−0.423735			−0.211867	−	0.977298i	$-0.567954\pi$
$401$	−8.48528			−0.423735			−0.211867	+	0.977298i	$0.567954\pi$
$402$		0			0
$403$	−1.32456	+	11.3246i	−0.0659808	+	0.564116i
$404$	4.47214			0.222497
$405$	19.6808	+	4.20323i	0.977945	+	0.208860i
$406$	−20.0000			−0.992583
$407$	17.8885	+	17.8885i	0.886702	+	0.886702i
$408$	−5.11667	−	1.95440i	−0.253313	−	0.0967570i
$409$	−18.9737			−0.938187			−0.469094	−	0.883148i	$-0.655419\pi$
$409$	−18.9737			−0.938187			−0.469094	+	0.883148i	$0.655419\pi$
$410$	−5.65685	−	11.3137i	−0.279372	−	0.558744i
$411$	12.7279	+	28.4605i	0.627822	+	1.40385i
$412$		0			0
$413$	8.94427	−	8.94427i	0.440119	−	0.440119i
$414$		0			0
$415$	−8.00000	+	4.00000i	−0.392705	+	0.196352i
$416$	−2.82843	+	2.23607i	−0.138675	+	0.109632i
$417$	−6.47214	−	2.47214i	−0.316942	−	0.121061i
$418$	−25.2982	+	25.2982i	−1.23738	+	1.23738i
$419$	13.4164			0.655434			0.327717	−	0.944776i	$-0.393721\pi$
$419$	13.4164			0.655434			0.327717	+	0.944776i	$0.393721\pi$
$420$	−17.2361	+	1.70820i	−0.841034	+	0.0833518i
$421$			3.16228i			0.154120i	0.997026	+	0.0770600i	$0.0245533\pi$
$421$			3.16228i			0.154120i	−0.997026	+	0.0770600i	$0.975447\pi$
$422$	14.1421	−	14.1421i	0.688428	−	0.688428i
$423$	−5.99070	+	0.333851i	−0.291278	+	0.0162324i
$424$	−6.32456			−0.307148
$425$	2.23607	+	15.6525i	0.108465	+	0.759257i
$426$	−1.00000	−	2.23607i	−0.0484502	−	0.108338i
$427$	−31.6228	−	31.6228i	−1.53033	−	1.53033i
$428$	2.23607	−	2.23607i	0.108084	−	0.108084i
$429$	16.3539	−	31.3137i	0.789576	−	1.51184i
$430$	−5.00000	+	15.0000i	−0.241121	+	0.723364i
$431$	1.41421			0.0681203			0.0340601	−	0.999420i	$-0.489156\pi$
$431$	1.41421			0.0681203			0.0340601	+	0.999420i	$0.489156\pi$
$432$	−4.61803	+	2.38197i	−0.222185	+	0.114602i
$433$	21.0000	+	21.0000i	1.00920	+	1.00920i	0.999957	+	0.00923827i	$0.00294067\pi$
$433$	21.0000	+	21.0000i	1.00920	+	1.00920i	0.00923827	+	0.999957i	$0.497059\pi$
$434$		−	14.1421i		−	0.678844i
$435$	13.3956	+	10.9799i	0.642271	+	0.526444i
$436$			3.16228i			0.151446i
$437$		0			0
$438$	−7.23607	−	2.76393i	−0.345753	−	0.132066i
$439$		−	16.0000i		−	0.763638i	−0.924237	−	0.381819i	$-0.875298\pi$
$439$		−	16.0000i		−	0.763638i	0.924237	−	0.381819i	$-0.124702\pi$
$440$	11.3137	−	5.65685i	0.539360	−	0.269680i
$441$	26.0000	−	29.0689i	1.23810	−	1.38423i
$442$	−11.3246	−	1.32456i	−0.538654	−	0.0630027i
$443$	11.1803	−	11.1803i	0.531194	−	0.531194i	−0.389734	−	0.920928i	$-0.627433\pi$
$443$	11.1803	−	11.1803i	0.531194	−	0.531194i	0.920928	+	0.389734i	$0.127433\pi$
$444$	−3.16228	−	7.07107i	−0.150075	−	0.335578i
$445$	−6.00000	−	2.00000i	−0.284427	−	0.0948091i
$446$		−	26.8328i		−	1.27057i
$447$	6.86474	+	2.62210i	0.324691	+	0.124021i
$448$	3.16228	−	3.16228i	0.149404	−	0.149404i
$449$			31.1127i			1.46830i	0.678988	+	0.734150i	$0.262419\pi$
$449$			31.1127i			1.46830i	−0.678988	+	0.734150i	$0.737581\pi$
$450$	12.4822	+	8.31836i	0.588416	+	0.392131i
$451$	−32.0000			−1.50682
$452$	−6.70820	−	6.70820i	−0.315527	−	0.315527i
$453$	−35.8167	−	13.6808i	−1.68282	−	0.642778i
$454$			12.0000i			0.563188i
$455$	−33.9039	+	12.2689i	−1.58944	+	0.575176i
$456$	10.0000	−	4.47214i	0.468293	−	0.209427i
$457$	22.1359	+	22.1359i	1.03548	+	1.03548i	0.999347	+	0.0361286i	$0.0115026\pi$
$457$	22.1359	+	22.1359i	1.03548	+	1.03548i	0.0361286	+	0.999347i	$0.488497\pi$
$458$	−6.70820	+	6.70820i	−0.313454	+	0.313454i
$459$	−15.6525	−	5.00000i	−0.730595	−	0.233380i
$460$		0			0
$461$	1.41421			0.0658665			0.0329332	−	0.999458i	$-0.489515\pi$
$461$	1.41421			0.0658665			0.0329332	+	0.999458i	$0.489515\pi$
$462$	−15.6352	+	40.9334i	−0.727414	+	1.90439i
$463$	18.9737	−	18.9737i	0.881781	−	0.881781i	−0.111935	−	0.993716i	$-0.535705\pi$
$463$	18.9737	−	18.9737i	0.881781	−	0.881781i	0.993716	+	0.111935i	$0.0357047\pi$
$464$	−4.47214			−0.207614
$465$	−7.76393	+	9.47214i	−0.360044	+	0.439260i
$466$			3.16228i			0.146490i
$467$	−6.70820	−	6.70820i	−0.310419	−	0.310419i	0.534653	−	0.845072i	$-0.320442\pi$
$467$	−6.70820	−	6.70820i	−0.310419	−	0.310419i	−0.845072	+	0.534653i	$0.820442\pi$
$468$	−8.09888	+	7.16995i	−0.374371	+	0.331431i
$469$		0			0
$470$	−4.24264	−	1.41421i	−0.195698	−	0.0652328i
$471$		0			0
$472$	2.00000	−	2.00000i	0.0920575	−	0.0920575i
$473$	28.2843	+	28.2843i	1.30051	+	1.30051i
$474$		0			0
$475$	−25.2982	−	18.9737i	−1.16076	−	0.870572i
$476$	14.1421			0.648204
$477$	−18.9443	+	1.05573i	−0.867399	+	0.0483385i
$478$	−3.00000	−	3.00000i	−0.137217	−	0.137217i
$479$			18.3848i			0.840022i	0.907519	+	0.420011i	$0.137974\pi$
$479$			18.3848i			0.840022i	−0.907519	+	0.420011i	$0.862026\pi$
$480$	−3.85410	+	0.381966i	−0.175915	+	0.0174343i
$481$	−10.0000	−	12.6491i	−0.455961	−	0.576750i
$482$	−8.94427	−	8.94427i	−0.407400	−	0.407400i
$483$		0			0
$484$		−	21.0000i		−	0.954545i
$485$	−26.8328	+	13.4164i	−1.21842	+	0.609208i
$486$	−13.4350	+	7.90569i	−0.609425	+	0.358610i
$487$	3.16228	+	3.16228i	0.143296	+	0.143296i	0.775116	−	0.631819i	$-0.217692\pi$
$487$	3.16228	+	3.16228i	0.143296	+	0.143296i	−0.631819	+	0.775116i	$0.717692\pi$
$488$	−7.07107	−	7.07107i	−0.320092	−	0.320092i
$489$		0			0
$490$	26.0000	−	13.0000i	1.17456	−	0.587280i
$491$			22.3607i			1.00912i	0.863376	+	0.504562i	$0.168346\pi$
$491$			22.3607i			1.00912i	−0.863376	+	0.504562i	$0.831654\pi$
$492$	9.15298	+	3.49613i	0.412648	+	0.157618i
$493$	−10.0000	−	10.0000i	−0.450377	−	0.450377i
$494$	17.8885	−	14.1421i	0.804844	−	0.636285i
$495$	32.9443	−	18.8328i	1.48073	−	0.846472i
$496$		−	3.16228i		−	0.141990i
$497$	4.47214	+	4.47214i	0.200603	+	0.200603i
$498$	2.47214	−	6.47214i	0.110779	−	0.290023i
$499$	−12.6491			−0.566252			−0.283126	−	0.959083i	$-0.591371\pi$
$499$	−12.6491			−0.566252			−0.283126	+	0.959083i	$0.591371\pi$
$500$	6.36396	+	9.19239i	0.284605	+	0.411096i
$501$	12.7279	+	28.4605i	0.568642	+	1.27152i
$502$	−12.6491	−	12.6491i	−0.564557	−	0.564557i
$503$	4.47214	−	4.47214i	0.199403	−	0.199403i	−0.600341	−	0.799744i	$-0.704969\pi$
$503$	4.47214	−	4.47214i	0.199403	−	0.199403i	0.799744	+	0.600341i	$0.204969\pi$
$504$	8.94427	−	10.0000i	0.398410	−	0.445435i
$505$	9.48683	+	3.16228i	0.422159	+	0.140720i
$506$		0			0
$507$	−12.6717	+	18.6126i	−0.562769	+	0.826614i
$508$	2.00000	+	2.00000i	0.0887357	+	0.0887357i
$509$		−	24.0416i		−	1.06563i	−0.846233	−	0.532813i	$-0.821135\pi$
$509$		−	24.0416i		−	1.06563i	0.846233	−	0.532813i	$-0.178865\pi$
$510$	−9.47214	−	7.76393i	−0.419433	−	0.343793i
$511$	20.0000			0.884748
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	29.2070	−	15.0649i	1.28952	−	0.665131i
$514$	28.4605			1.25534
$515$		0			0
$516$	−5.00000	−	11.1803i	−0.220113	−	0.492187i
$517$	−8.00000	+	8.00000i	−0.351840	+	0.351840i
$518$	14.1421	+	14.1421i	0.621370	+	0.621370i
$519$	−13.4164	−	30.0000i	−0.588915	−	1.31685i
$520$	−7.58114	+	2.74342i	−0.332455	+	0.120307i
$521$			26.8328i			1.17557i	0.809018	+	0.587784i	$0.199999\pi$
$521$			26.8328i			1.17557i	−0.809018	+	0.587784i	$0.800001\pi$
$522$	−13.3956	+	0.746512i	−0.586310	+	0.0326740i
$523$	−15.0000	−	15.0000i	−0.655904	−	0.655904i	0.298504	−	0.954408i	$-0.403512\pi$
$523$	−15.0000	−	15.0000i	−0.655904	−	0.655904i	−0.954408	+	0.298504i	$0.903512\pi$
$524$	−17.8885			−0.781465
$525$	−37.7711	−	8.56409i	−1.64847	−	0.373768i
$526$		−	12.6491i		−	0.551527i
$527$	7.07107	−	7.07107i	0.308021	−	0.308021i
$528$	−3.49613	+	9.15298i	−0.152149	+	0.398332i
$529$			23.0000i			1.00000i
$530$	−13.4164	−	4.47214i	−0.582772	−	0.194257i
$531$	5.65685	−	6.32456i	0.245487	−	0.274462i
$532$	−20.0000	+	20.0000i	−0.867110	+	0.867110i
$533$	20.2580	+	2.36944i	0.877471	+	0.102632i
$534$	4.47214	−	2.00000i	0.193528	−	0.0865485i
$535$	6.32456	−	3.16228i	0.273434	−	0.136717i
$536$		0			0
$537$	−11.0557	+	28.9443i	−0.477090	+	1.24904i
$538$	15.8114	−	15.8114i	0.681677	−	0.681677i
$539$		−	73.5391i		−	3.16755i
$540$	−11.4806	+	1.78747i	−0.494048	+	0.0769205i
$541$		−	41.1096i		−	1.76744i	−0.468016	−	0.883720i	$-0.655031\pi$
$541$		−	41.1096i		−	1.76744i	0.468016	−	0.883720i	$-0.344969\pi$
$542$	6.70820	+	6.70820i	0.288142	+	0.288142i
$543$	13.5967	−	35.5967i	0.583492	−	1.52760i
$544$	3.16228			0.135582
$545$	−2.23607	+	6.70820i	−0.0957826	+	0.287348i
$546$	12.9289	−	24.7557i	0.553307	−	1.05944i
$547$	5.00000	−	5.00000i	0.213785	−	0.213785i	−0.592088	−	0.805873i	$-0.701696\pi$
$547$	5.00000	−	5.00000i	0.213785	−	0.213785i	0.805873	+	0.592088i	$0.201696\pi$
$548$	−12.7279	−	12.7279i	−0.543710	−	0.543710i
$549$	−22.3607	−	20.0000i	−0.954331	−	0.853579i
$550$	28.0000	−	4.00000i	1.19392	−	0.170561i
$551$	28.2843			1.20495
$552$		0			0
$553$		0			0
$554$		−	14.1421i		−	0.600842i
$555$	−1.70820	−	17.2361i	−0.0725092	−	0.731630i
$556$	4.00000			0.169638
$557$	12.7279	−	12.7279i	0.539299	−	0.539299i	−0.384024	−	0.923323i	$-0.625462\pi$
$557$	12.7279	−	12.7279i	0.539299	−	0.539299i	0.923323	+	0.384024i	$0.125462\pi$
$558$	−0.527864	−	9.47214i	−0.0223463	−	0.400987i
$559$	−15.8114	−	20.0000i	−0.668750	−	0.845910i
$560$	8.94427	−	4.47214i	0.377964	−	0.188982i
$561$	−28.2843	+	12.6491i	−1.19416	+	0.534046i
$562$	6.00000	−	6.00000i	0.253095	−	0.253095i
$563$	−20.1246	+	20.1246i	−0.848151	+	0.848151i	−0.989902	−	0.141751i	$-0.954727\pi$
$563$	−20.1246	+	20.1246i	−0.848151	+	0.848151i	0.141751	+	0.989902i	$0.454727\pi$
$564$	3.16228	−	1.41421i	0.133156	−	0.0595491i
$565$	−9.48683	−	18.9737i	−0.399114	−	0.798228i
$566$	12.7279			0.534994
$567$	25.1220	−	31.4465i	1.05502	−	1.32063i
$568$	1.00000	+	1.00000i	0.0419591	+	0.0419591i
$569$	−8.94427			−0.374963			−0.187482	−	0.982268i	$-0.560033\pi$
$569$	−8.94427			−0.374963			−0.187482	+	0.982268i	$0.560033\pi$
$570$	24.3755	−	2.41577i	1.02098	−	0.101185i
$571$	−10.0000			−0.418487			−0.209243	−	0.977864i	$-0.567100\pi$
$571$	−10.0000			−0.418487			−0.209243	+	0.977864i	$0.567100\pi$
$572$	−2.36944	+	20.2580i	−0.0990711	+	0.847029i
$573$	−14.4721	−	5.52786i	−0.604582	−	0.230930i
$574$	−25.2982			−1.05593
$575$		0			0
$576$	2.00000	−	2.23607i	0.0833333	−	0.0931695i
$577$	9.48683	+	9.48683i	0.394942	+	0.394942i	0.876445	−	0.481503i	$-0.159909\pi$
$577$	9.48683	+	9.48683i	0.394942	+	0.394942i	−0.481503	+	0.876445i	$0.659909\pi$
$578$	−4.94975	−	4.94975i	−0.205882	−	0.205882i
$579$	−9.48683	−	21.2132i	−0.394259	−	0.881591i
$580$	−9.48683	−	3.16228i	−0.393919	−	0.131306i
$581$			17.8885i			0.742142i
$582$	8.29180	−	21.7082i	0.343706	−	0.899834i
$583$	−25.2982	+	25.2982i	−1.04775	+	1.04775i
$584$	4.47214			0.185058
$585$	−22.2502	+	9.48298i	−0.919934	+	0.392073i
$586$	−16.0000			−0.660954
$587$	−8.48528	+	8.48528i	−0.350225	+	0.350225i	−0.860193	−	0.509968i	$-0.829657\pi$
$587$	−8.48528	+	8.48528i	−0.350225	+	0.350225i	0.509968	+	0.860193i	$0.329657\pi$
$588$	−8.03444	+	21.0344i	−0.331335	+	0.867446i
$589$			20.0000i			0.824086i
$590$	5.65685	−	2.82843i	0.232889	−	0.116445i
$591$	1.41421	+	3.16228i	0.0581730	+	0.130079i
$592$	3.16228	+	3.16228i	0.129969	+	0.129969i
$593$	4.24264	+	4.24264i	0.174224	+	0.174224i	0.788833	−	0.614608i	$-0.210686\pi$
$593$	4.24264	+	4.24264i	0.174224	+	0.174224i	−0.614608	+	0.788833i	$0.710686\pi$
$594$	−8.94427	+	28.0000i	−0.366988	+	1.14885i
$595$	30.0000	+	10.0000i	1.22988	+	0.409960i
$596$	−4.24264			−0.173785
$597$	32.3607	+	12.3607i	1.32443	+	0.505889i
$598$		0			0
$599$	−8.94427			−0.365453			−0.182727	−	0.983164i	$-0.558492\pi$
$599$	−8.94427			−0.365453			−0.182727	+	0.983164i	$0.558492\pi$
$600$	−8.44588	−	1.91499i	−0.344801	−	0.0781791i
$601$	−40.0000			−1.63163			−0.815817	−	0.578310i	$-0.803712\pi$
$601$	−40.0000			−1.63163			−0.815817	+	0.578310i	$0.803712\pi$
$602$	22.3607	+	22.3607i	0.911353	+	0.911353i
$603$		0			0
$604$	22.1359			0.900699
$605$	14.8492	−	44.5477i	0.603708	−	1.81112i
$606$	−7.07107	+	3.16228i	−0.287242	+	0.128459i
$607$	30.0000	−	30.0000i	1.21766	−	1.21766i	0.249214	−	0.968448i	$-0.419828\pi$
$607$	30.0000	−	30.0000i	1.21766	−	1.21766i	0.968448	−	0.249214i	$-0.0801723\pi$
$608$	−4.47214	+	4.47214i	−0.181369	+	0.181369i
$609$	31.6228	−	14.1421i	1.28142	−	0.573068i
$610$	−10.0000	−	20.0000i	−0.404888	−	0.809776i
$611$	5.65685	−	4.47214i	0.228852	−	0.180923i
$612$	9.47214	−	0.527864i	0.382888	−	0.0213376i
$613$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$613$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$614$		0			0
$615$	16.9443	+	13.8885i	0.683259	+	0.560040i
$616$		−	25.2982i		−	1.01929i
$617$	−12.7279	+	12.7279i	−0.512407	+	0.512407i	−0.915263	−	0.402856i	$-0.868017\pi$
$617$	−12.7279	+	12.7279i	−0.512407	+	0.512407i	0.402856	+	0.915263i	$0.368017\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$	2.23607	−	6.70820i	0.0898027	−	0.269408i
$621$		0			0
$622$	6.32456	+	6.32456i	0.253592	+	0.253592i
$623$	−8.94427	+	8.94427i	−0.358345	+	0.358345i
$624$	2.89100	−	5.53553i	0.115733	−	0.221599i
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$	−1.41421			−0.0565233
$627$	22.1115	−	57.8885i	0.883047	−	2.31185i
$628$		0			0
$629$			14.1421i			0.563884i
$630$	26.0447	−	14.8886i	1.03765	−	0.593178i
$631$			15.8114i			0.629441i	0.949184	+	0.314721i	$0.101911\pi$
$631$			15.8114i			0.629441i	−0.949184	+	0.314721i	$0.898089\pi$
$632$		0			0
$633$	−12.3607	+	32.3607i	−0.491293	+	1.28622i
$634$			28.0000i			1.11202i
$635$	2.82843	+	5.65685i	0.112243	+	0.224485i
$636$	10.0000	−	4.47214i	0.396526	−	0.177332i
$637$	−5.44520	+	46.5548i	−0.215746	+	1.84457i
$638$	−17.8885	+	17.8885i	−0.708214	+	0.708214i
$639$	3.16228	+	2.82843i	0.125098	+	0.111891i
$640$	2.00000	−	1.00000i	0.0790569	−	0.0395285i
$641$		−	49.1935i		−	1.94303i	−0.236986	−	0.971513i	$-0.576159\pi$
$641$		−	49.1935i		−	1.94303i	0.236986	−	0.971513i	$-0.423841\pi$
$642$	−1.95440	+	5.11667i	−0.0771338	+	0.201939i
$643$	−18.9737	+	18.9737i	−0.748248	+	0.748248i	−0.974150	−	0.225902i	$-0.927467\pi$
$643$	−18.9737	+	18.9737i	−0.748248	+	0.748248i	0.225902	+	0.974150i	$0.427467\pi$
$644$		0			0
$645$	−2.70091	−	27.2526i	−0.106348	−	1.07307i
$646$	−20.0000			−0.786889
$647$	−22.3607	−	22.3607i	−0.879089	−	0.879089i	0.114351	−	0.993440i	$-0.463521\pi$
$647$	−22.3607	−	22.3607i	−0.879089	−	0.879089i	−0.993440	+	0.114351i	$0.963521\pi$
$648$	5.61745	−	7.03166i	0.220674	−	0.276230i
$649$		−	16.0000i		−	0.628055i
$650$	−18.0219	+	0.458991i	−0.706878	+	0.0180031i
$651$	10.0000	+	22.3607i	0.391931	+	0.876384i
$652$		0			0
$653$	−17.8885	+	17.8885i	−0.700033	+	0.700033i	−0.964417	−	0.264385i	$-0.914831\pi$
$653$	−17.8885	+	17.8885i	−0.700033	+	0.700033i	0.264385	+	0.964417i	$0.414831\pi$
$654$	−2.23607	−	5.00000i	−0.0874372	−	0.195515i
$655$	−37.9473	−	12.6491i	−1.48272	−	0.494242i
$656$	−5.65685			−0.220863
$657$	13.3956	−	0.746512i	0.522613	−	0.0291242i
$658$	−6.32456	+	6.32456i	−0.246557	+	0.246557i
$659$	−31.3050			−1.21947			−0.609734	−	0.792606i	$-0.708724\pi$
$659$	−31.3050			−1.21947			−0.609734	+	0.792606i	$0.708724\pi$
$660$	−13.8885	+	16.9443i	−0.540611	+	0.659555i
$661$			41.1096i			1.59898i	0.600680	+	0.799489i	$0.294896\pi$
$661$			41.1096i			1.59898i	−0.600680	+	0.799489i	$0.705104\pi$
$662$	−8.94427	−	8.94427i	−0.347629	−	0.347629i
$663$	18.8423	−	5.91336i	0.731774	−	0.229656i
$664$			4.00000i			0.155230i
$665$	−56.5685	+	28.2843i	−2.19363	+	1.09682i
$666$	10.0000	+	8.94427i	0.387492	+	0.346583i
$667$		0			0
$668$	−12.7279	−	12.7279i	−0.492458	−	0.492458i
$669$	18.9737	+	42.4264i	0.733564	+	1.64030i
$670$		0			0
$671$	−56.5685			−2.18380
$672$	−2.76393	+	7.23607i	−0.106621	+	0.279137i
$673$	−15.0000	−	15.0000i	−0.578208	−	0.578208i	0.356202	−	0.934409i	$-0.384072\pi$
$673$	−15.0000	−	15.0000i	−0.578208	−	0.578208i	−0.934409	+	0.356202i	$0.884072\pi$
$674$			18.3848i			0.708155i
$675$	−25.6180	−	4.32624i	−0.986039	−	0.166517i
$676$	3.00000	−	12.6491i	0.115385	−	0.486504i
$677$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$677$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$678$	15.3500	+	5.86319i	0.589514	+	0.225174i
$679$			60.0000i			2.30259i
$680$	6.70820	+	2.23607i	0.257248	+	0.0857493i
$681$	−8.48528	−	18.9737i	−0.325157	−	0.727072i
$682$	−12.6491	−	12.6491i	−0.484359	−	0.484359i
$683$	16.9706	+	16.9706i	0.649361	+	0.649361i	0.952838	−	0.303478i	$-0.0981479\pi$
$683$	16.9706	+	16.9706i	0.649361	+	0.649361i	−0.303478	+	0.952838i	$0.598148\pi$
$684$	−12.6491	+	14.1421i	−0.483651	+	0.540738i
$685$	−18.0000	−	36.0000i	−0.687745	−	1.37549i
$686$		−	26.8328i		−	1.02448i
$687$	5.86319	−	15.3500i	0.223694	−	0.585640i
$688$	5.00000	+	5.00000i	0.190623	+	0.190623i
$689$	17.8885	−	14.1421i	0.681499	−	0.538772i
$690$		0			0
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$	13.4164	+	13.4164i	0.510015	+	0.510015i
$693$	−4.22291	−	75.7771i	−0.160415	−	2.87853i
$694$	−28.4605			−1.08035
$695$	8.48528	+	2.82843i	0.321865	+	0.107288i
$696$	7.07107	−	3.16228i	0.268028	−	0.119866i
$697$	−12.6491	−	12.6491i	−0.479119	−	0.479119i
$698$	−2.23607	+	2.23607i	−0.0846364	+	0.0846364i
$699$	−2.23607	−	5.00000i	−0.0845759	−	0.189117i
$700$	22.1359	−	3.16228i	0.836660	−	0.119523i
$701$		−	49.1935i		−	1.85801i	−0.370064	−	0.929006i	$-0.620664\pi$
$701$		−	49.1935i		−	1.85801i	0.370064	−	0.929006i	$-0.379336\pi$
$702$	7.73553	−	17.0635i	0.291959	−	0.644019i
$703$	−20.0000	−	20.0000i	−0.754314	−	0.754314i
$704$		−	5.65685i		−	0.213201i
$705$	7.70820	−	0.763932i	0.290308	−	0.0287713i
$706$	14.0000			0.526897
$707$	14.1421	−	14.1421i	0.531870	−	0.531870i
$708$	−1.74806	+	4.57649i	−0.0656963	+	0.171995i
$709$	−47.4342			−1.78143			−0.890714	−	0.454565i	$-0.849795\pi$
$709$	−47.4342			−1.78143			−0.890714	+	0.454565i	$0.849795\pi$
$710$	1.41421	+	2.82843i	0.0530745	+	0.106149i
$711$		0			0
$712$	−2.00000	+	2.00000i	−0.0749532	+	0.0749532i
$713$		0			0
$714$	−22.3607	+	10.0000i	−0.836827	+	0.374241i
$715$	−19.3509	+	41.2982i	−0.723682	+	1.54447i
$716$		−	17.8885i		−	0.668526i
$717$	6.86474	+	2.62210i	0.256368	+	0.0979240i
$718$	23.0000	+	23.0000i	0.858352	+	0.858352i
$719$	17.8885			0.667130			0.333565	−	0.942727i	$-0.391748\pi$
$719$	17.8885			0.667130			0.333565	+	0.942727i	$0.391748\pi$
$720$	5.82378	−	3.32920i	0.217039	−	0.124072i
$721$		0			0
$722$	14.8492	−	14.8492i	0.552632	−	0.552632i
$723$	20.4667	+	7.81758i	0.761164	+	0.290739i
$724$			22.0000i			0.817624i
$725$	−17.8885	−	13.4164i	−0.664364	−	0.498273i
$726$	14.8492	+	33.2039i	0.551107	+	1.23231i
$727$	18.0000	−	18.0000i	0.667583	−	0.667583i	−0.289573	−	0.957156i	$-0.593513\pi$
$727$	18.0000	−	18.0000i	0.667583	−	0.667583i	0.957156	+	0.289573i	$0.0935133\pi$
$728$	−1.87320	+	16.0153i	−0.0694256	+	0.593568i
$729$	15.6525	−	22.0000i	0.579721	−	0.814815i
$730$	9.48683	+	3.16228i	0.351123	+	0.117041i
$731$			22.3607i			0.827040i
$732$	16.1803	+	6.18034i	0.598043	+	0.228432i
$733$	−9.48683	+	9.48683i	−0.350404	+	0.350404i	−0.860260	−	0.509856i	$-0.829699\pi$
$733$	−9.48683	+	9.48683i	−0.350404	+	0.350404i	0.509856	+	0.860260i	$0.329699\pi$
$734$			28.2843i			1.04399i
$735$	−31.9172	+	38.9396i	−1.17728	+	1.43631i
$736$		0			0
$737$		0			0
$738$	−16.9443	+	0.944272i	−0.623727	+	0.0347591i
$739$	44.2719			1.62857			0.814284	−	0.580467i	$-0.197130\pi$
$739$	44.2719			1.62857			0.814284	+	0.580467i	$0.197130\pi$
$740$	4.47214	+	8.94427i	0.164399	+	0.328798i
$741$	−18.2843	+	35.0098i	−0.671689	+	1.28612i
$742$	−20.0000	+	20.0000i	−0.734223	+	0.734223i
$743$	−16.9706	−	16.9706i	−0.622590	−	0.622590i	0.323603	−	0.946193i	$-0.395106\pi$
$743$	−16.9706	−	16.9706i	−0.622590	−	0.622590i	−0.946193	+	0.323603i	$0.895106\pi$
$744$	2.23607	+	5.00000i	0.0819782	+	0.183309i
$745$	−9.00000	−	3.00000i	−0.329734	−	0.109911i
$746$	22.6274			0.828449
$747$	0.667701	+	11.9814i	0.0244299	+	0.438377i
$748$	12.6491	−	12.6491i	0.462497	−	0.462497i
$749$		−	14.1421i		−	0.516742i
$750$	−16.5623	−	10.0344i	−0.604770	−	0.366406i
$751$	48.0000			1.75154			0.875772	−	0.482724i	$-0.160353\pi$
$751$	48.0000			1.75154			0.875772	+	0.482724i	$0.160353\pi$
$752$	−1.41421	+	1.41421i	−0.0515711	+	0.0515711i
$753$	28.9443	+	11.0557i	1.05479	+	0.402893i
$754$	12.6491	−	10.0000i	0.460653	−	0.364179i
$755$	46.9574	+	15.6525i	1.70896	+	0.569652i
$756$	−7.07107	+	22.1359i	−0.257172	+	0.805076i
$757$	−18.0000	+	18.0000i	−0.654221	+	0.654221i	−0.954007	−	0.299786i	$-0.903085\pi$
$757$	−18.0000	+	18.0000i	−0.654221	+	0.654221i	0.299786	+	0.954007i	$0.403085\pi$
$758$	−4.47214	+	4.47214i	−0.162435	+	0.162435i
$759$		0			0
$760$	−12.6491	+	6.32456i	−0.458831	+	0.229416i
$761$	36.7696			1.33290			0.666448	−	0.745552i	$-0.267814\pi$
$761$	36.7696			1.33290			0.666448	+	0.745552i	$0.267814\pi$
$762$	−4.57649	−	1.74806i	−0.165789	−	0.0633257i
$763$	10.0000	+	10.0000i	0.362024	+	0.362024i
$764$	8.94427			0.323592
$765$	20.4667	+	5.57804i	0.739975	+	0.201675i
$766$	16.0000			0.578103
$767$	−1.18472	+	10.1290i	−0.0427777	+	0.365737i
$768$	−0.618034	+	1.61803i	−0.0223014	+	0.0583858i
$769$	50.5964			1.82455			0.912277	−	0.409573i	$-0.134322\pi$
$769$	50.5964			1.82455			0.912277	+	0.409573i	$0.134322\pi$
$770$	17.8885	−	53.6656i	0.644658	−	1.93398i
$771$	−45.0000	+	20.1246i	−1.62064	+	0.724770i
$772$	9.48683	+	9.48683i	0.341439	+	0.341439i
$773$	4.24264	+	4.24264i	0.152597	+	0.152597i	0.779277	−	0.626680i	$-0.215587\pi$
$773$	4.24264	+	4.24264i	0.152597	+	0.152597i	−0.626680	+	0.779277i	$0.715587\pi$
$774$	15.8114	+	14.1421i	0.568329	+	0.508329i
$775$	9.48683	−	12.6491i	0.340777	−	0.454369i
$776$			13.4164i			0.481621i
$777$	−32.3607	−	12.3607i	−1.16093	−	0.443437i
$778$	−9.48683	+	9.48683i	−0.340119	+	0.340119i
$779$	35.7771			1.28185
$780$	10.0469	−	9.69840i	0.359738	−	0.347258i
$781$	8.00000			0.286263
$782$		0			0
$783$	20.6525	−	10.6525i	0.738059	−	0.380688i
$784$		−	13.0000i		−	0.464286i
$785$		0			0
$786$	28.2843	−	12.6491i	1.00887	−	0.451179i
$787$	12.6491	+	12.6491i	0.450892	+	0.450892i	0.895651	−	0.444758i	$-0.146710\pi$
$787$	12.6491	+	12.6491i	0.450892	+	0.450892i	−0.444758	+	0.895651i	$0.646710\pi$
$788$	−1.41421	−	1.41421i	−0.0503793	−	0.0503793i
$789$	8.94427	+	20.0000i	0.318425	+	0.712019i
$790$		0			0
$791$	−42.4264			−1.50851
$792$	−0.944272	−	16.9443i	−0.0335532	−	0.602088i
$793$	35.8114	+	4.18861i	1.27170	+	0.148742i
$794$	35.7771			1.26968
$795$	24.3755	−	2.41577i	0.864509	−	0.0856784i
$796$	−20.0000			−0.708881
$797$	13.4164	+	13.4164i	0.475234	+	0.475234i	0.903603	−	0.428370i	$-0.140912\pi$
$797$	13.4164	+	13.4164i	0.475234	+	0.475234i	−0.428370	+	0.903603i	$0.640912\pi$
$798$	17.4806	−	45.7649i	0.618808	−	1.62006i
$799$	−6.32456			−0.223747
$800$	4.94975	−	0.707107i	0.175000	−	0.0250000i
$801$	−5.65685	+	6.32456i	−0.199875	+	0.223467i
$802$	−6.00000	+	6.00000i	−0.211867	+	0.211867i
$803$	17.8885	−	17.8885i	0.631273	−	0.631273i
$804$		0			0
$805$		0			0
$806$	7.07107	+	8.94427i	0.249068	+	0.315049i
$807$	−13.8197	+	36.1803i	−0.486475	+	1.27361i
$808$	3.16228	−	3.16228i	0.111249	−	0.111249i
$809$	−17.8885			−0.628928			−0.314464	−	0.949269i	$-0.601825\pi$
$809$	−17.8885			−0.628928			−0.314464	+	0.949269i	$0.601825\pi$
$810$	16.8885	−	10.9443i	0.593403	−	0.384543i
$811$		−	44.2719i		−	1.55460i	−0.629132	−	0.777298i	$-0.716590\pi$
$811$		−	44.2719i		−	1.55460i	0.629132	−	0.777298i	$-0.283410\pi$
$812$	−14.1421	+	14.1421i	−0.496292	+	0.496292i
$813$	−15.3500	−	5.86319i	−0.538349	−	0.205631i
$814$	25.2982			0.886702
$815$		0			0
$816$	−5.00000	+	2.23607i	−0.175035	+	0.0782780i
$817$	−31.6228	−	31.6228i	−1.10634	−	1.10634i
$818$	−13.4164	+	13.4164i	−0.469094	+	0.469094i
$819$	−2.93754	+	48.2843i	−0.102646	+	1.68719i
$820$	−12.0000	−	4.00000i	−0.419058	−	0.139686i
$821$	15.5563			0.542920			0.271460	−	0.962450i	$-0.412493\pi$
$821$	15.5563			0.542920			0.271460	+	0.962450i	$0.412493\pi$
$822$	29.1246	+	11.1246i	1.01584	+	0.388015i
$823$	10.0000	+	10.0000i	0.348578	+	0.348578i	0.859580	−	0.511002i	$-0.170725\pi$
$823$	10.0000	+	10.0000i	0.348578	+	0.348578i	−0.511002	+	0.859580i	$0.670725\pi$
$824$		0			0
$825$	−41.4435	+	26.1235i	−1.44288	+	0.909505i
$826$		−	12.6491i		−	0.440119i
$827$	−5.65685	+	5.65685i	−0.196708	+	0.196708i	−0.798587	−	0.601879i	$-0.794419\pi$
$827$	−5.65685	+	5.65685i	−0.196708	+	0.196708i	0.601879	+	0.798587i	$0.294419\pi$
$828$		0			0
$829$			10.0000i			0.347314i	0.984806	+	0.173657i	$0.0555585\pi$
$829$			10.0000i			0.347314i	−0.984806	+	0.173657i	$0.944442\pi$
$830$	−2.82843	+	8.48528i	−0.0981761	+	0.294528i
$831$	10.0000	+	22.3607i	0.346896	+	0.775683i
$832$	−0.418861	+	3.58114i	−0.0145214	+	0.124154i
$833$	29.0689	−	29.0689i	1.00718	−	1.00718i
$834$	−6.32456	+	2.82843i	−0.219001	+	0.0979404i
$835$	−18.0000	−	36.0000i	−0.622916	−	1.24583i
$836$			35.7771i			1.23738i
$837$	7.53244	+	14.6035i	0.260359	+	0.504771i
$838$	9.48683	−	9.48683i	0.327717	−	0.327717i
$839$			18.3848i			0.634713i	0.948306	+	0.317356i	$0.102795\pi$
$839$			18.3848i			0.634713i	−0.948306	+	0.317356i	$0.897205\pi$
$840$	−10.9799	+	13.3956i	−0.378841	+	0.462193i
$841$	−9.00000			−0.310345
$842$	2.23607	+	2.23607i	0.0770600	+	0.0770600i
$843$	−5.24419	+	13.7295i	−0.180620	+	0.472868i
$844$		−	20.0000i		−	0.688428i
$845$	15.3082	−	24.7115i	0.526619	−	0.850101i
$846$	−4.00000	+	4.47214i	−0.137523	+	0.153755i
$847$	−66.4078	−	66.4078i	−2.28180	−	2.28180i
$848$	−4.47214	+	4.47214i	−0.153574	+	0.153574i
$849$	−20.1246	+	9.00000i	−0.690675	+	0.308879i
$850$	12.6491	+	9.48683i	0.433861	+	0.325396i
$851$		0			0
$852$	−2.28825	−	0.874032i	−0.0783940	−	0.0299438i
$853$	−37.9473	+	37.9473i	−1.29929	+	1.29929i	−0.370433	+	0.928859i	$0.620791\pi$
$853$	−37.9473	+	37.9473i	−1.29929	+	1.29929i	−0.928859	+	0.370433i	$0.879209\pi$
$854$	−44.7214			−1.53033
$855$	−36.8328	+	21.0557i	−1.25966	+	0.720091i
$856$		−	3.16228i		−	0.108084i
$857$	−20.1246	−	20.1246i	−0.687444	−	0.687444i	0.274223	−	0.961666i	$-0.411579\pi$
$857$	−20.1246	−	20.1246i	−0.687444	−	0.687444i	−0.961666	+	0.274223i	$0.911579\pi$
$858$	−10.5781	−	33.7061i	−0.361132	−	1.15071i
$859$		−	50.0000i		−	1.70598i	−0.521929	−	0.852989i	$-0.674787\pi$
$859$		−	50.0000i		−	1.70598i	0.521929	−	0.852989i	$-0.325213\pi$
$860$	7.07107	+	14.1421i	0.241121	+	0.482243i
$861$	40.0000	−	17.8885i	1.36320	−	0.609640i
$862$	1.00000	−	1.00000i	0.0340601	−	0.0340601i
$863$	9.89949	+	9.89949i	0.336983	+	0.336983i	0.855231	−	0.518248i	$-0.173415\pi$
$863$	9.89949	+	9.89949i	0.336983	+	0.336983i	−0.518248	+	0.855231i	$0.673415\pi$
$864$	−1.58114	+	4.94975i	−0.0537914	+	0.168394i
$865$	18.9737	+	37.9473i	0.645124	+	1.29025i
$866$	29.6985			1.00920
$867$	11.3262	+	4.32624i	0.384659	+	0.146927i
$868$	−10.0000	−	10.0000i	−0.339422	−	0.339422i
$869$		0			0
$870$	17.2361	−	1.70820i	0.584357	−	0.0579135i
$871$		0			0
$872$	2.23607	+	2.23607i	0.0757228	+	0.0757228i
$873$	2.23954	+	40.1869i	0.0757969	+	1.36012i
$874$		0			0
$875$	49.1935	+	8.94427i	1.66304	+	0.302372i
$876$	−7.07107	+	3.16228i	−0.238909	+	0.106843i
$877$	−6.32456	−	6.32456i	−0.213565	−	0.213565i	0.592215	−	0.805780i	$-0.298254\pi$
$877$	−6.32456	−	6.32456i	−0.213565	−	0.213565i	−0.805780	+	0.592215i	$0.798254\pi$
$878$	−11.3137	−	11.3137i	−0.381819	−	0.381819i
$879$	25.2982	−	11.3137i	0.853288	−	0.381602i
$880$	4.00000	−	12.0000i	0.134840	−	0.404520i
$881$			31.3050i			1.05469i	0.849651	+	0.527345i	$0.176813\pi$
$881$			31.3050i			1.05469i	−0.849651	+	0.527345i	$0.823187\pi$
$882$	−2.17003	−	38.9396i	−0.0730687	−	1.31116i
$883$	−21.0000	−	21.0000i	−0.706706	−	0.706706i	0.259135	−	0.965841i	$-0.416563\pi$
$883$	−21.0000	−	21.0000i	−0.706706	−	0.706706i	−0.965841	+	0.259135i	$0.916563\pi$
$884$	−8.94427	+	7.07107i	−0.300828	+	0.237826i
$885$	−6.94427	+	8.47214i	−0.233429	+	0.284788i
$886$		−	15.8114i		−	0.531194i
$887$	−35.7771	−	35.7771i	−1.20128	−	1.20128i	−0.973778	−	0.227499i	$-0.926945\pi$
$887$	−35.7771	−	35.7771i	−1.20128	−	1.20128i	−0.227499	−	0.973778i	$-0.573055\pi$
$888$	−7.23607	−	2.76393i	−0.242827	−	0.0927515i
$889$	12.6491			0.424238
$890$	−5.65685	+	2.82843i	−0.189618	+	0.0948091i
$891$	−5.65685	−	50.5964i	−0.189512	−	1.69504i
$892$	−18.9737	−	18.9737i	−0.635285	−	0.635285i
$893$	8.94427	−	8.94427i	0.299309	−	0.299309i
$894$	6.70820	−	3.00000i	0.224356	−	0.100335i
$895$	12.6491	−	37.9473i	0.422813	−	1.26844i
$896$		−	4.47214i		−	0.149404i
$897$		0			0
$898$	22.0000	+	22.0000i	0.734150	+	0.734150i
$899$			14.1421i			0.471667i
$900$	14.7082	−	2.94427i	0.490273	−	0.0981424i
$901$	−20.0000			−0.666297
$902$	−22.6274	+	22.6274i	−0.753411	+	0.753411i
$903$	−51.1667	−	19.5440i	−1.70272	−	0.650382i
$904$	−9.48683			−0.315527
$905$	−15.5563	+	46.6690i	−0.517111	+	1.55133i
$906$	−35.0000	+	15.6525i	−1.16280	+	0.520019i
$907$	33.0000	−	33.0000i	1.09575	−	1.09575i	0.100845	−	0.994902i	$-0.467845\pi$
$907$	33.0000	−	33.0000i	1.09575	−	1.09575i	0.994902	−	0.100845i	$-0.0321546\pi$
$908$	8.48528	+	8.48528i	0.281594	+	0.281594i
$909$	8.94427	−	10.0000i	0.296663	−	0.331679i
$910$	−15.2982	+	32.6491i	−0.507131	+	1.08231i
$911$			44.7214i			1.48168i	0.671679	+	0.740842i	$0.265573\pi$
$911$			44.7214i			1.48168i	−0.671679	+	0.740842i	$0.734427\pi$
$912$	3.90879	−	10.2333i	0.129433	−	0.338860i
$913$	16.0000	+	16.0000i	0.529523	+	0.529523i
$914$	31.3050			1.03548
$915$	29.9535	+	24.5517i	0.990233	+	0.811654i
$916$			9.48683i			0.313454i
$917$	−56.5685	+	56.5685i	−1.86806	+	1.86806i
$918$	−14.6035	+	7.53244i	−0.481988	+	0.248607i
$919$			40.0000i			1.31948i	0.751495	+	0.659739i	$0.229333\pi$
$919$			40.0000i			1.31948i	−0.751495	+	0.659739i	$0.770667\pi$
$920$		0			0
$921$		0			0
$922$	1.00000	−	1.00000i	0.0329332	−	0.0329332i
$923$	−5.06450	−	0.592359i	−0.166700	−	0.0194977i
$924$	17.8885	+	40.0000i	0.588490	+	1.31590i
$925$	3.16228	+	22.1359i	0.103975	+	0.727825i
$926$		−	26.8328i		−	0.881781i
$927$		0			0
$928$	−3.16228	+	3.16228i	−0.103807	+	0.103807i
$929$		−	2.82843i		−	0.0927977i	−0.998923	−	0.0463988i	$-0.985225\pi$
$929$		−	2.82843i		−	0.0927977i	0.998923	−	0.0463988i	$-0.0147745\pi$
$930$	1.20788	+	12.1877i	0.0396080	+	0.399652i
$931$			82.2192i			2.69463i
$932$	2.23607	+	2.23607i	0.0732448	+	0.0732448i
$933$	−14.4721	−	5.52786i	−0.473796	−	0.180974i
$934$	−9.48683			−0.310419
$935$	35.7771	−	17.8885i	1.17004	−	0.585018i
$936$	−0.656854	+	10.7967i	−0.0214700	+	0.352901i
$937$	3.00000	−	3.00000i	0.0980057	−	0.0980057i	−0.656404	−	0.754410i	$-0.727923\pi$
$937$	3.00000	−	3.00000i	0.0980057	−	0.0980057i	0.754410	+	0.656404i	$0.227923\pi$
$938$		0			0
$939$	2.23607	−	1.00000i	0.0729713	−	0.0326338i
$940$	−4.00000	+	2.00000i	−0.130466	+	0.0652328i
$941$	−1.41421			−0.0461020			−0.0230510	−	0.999734i	$-0.507338\pi$
$941$	−1.41421			−0.0461020			−0.0230510	+	0.999734i	$0.507338\pi$
$942$		0			0
$943$		0			0
$944$		−	2.82843i		−	0.0920575i
$945$	−30.6525	+	41.9574i	−0.997125	+	1.36488i
$946$	40.0000			1.30051
$947$	36.7696	−	36.7696i	1.19485	−	1.19485i	0.219161	−	0.975689i	$-0.429668\pi$
$947$	36.7696	−	36.7696i	1.19485	−	1.19485i	0.975689	−	0.219161i	$-0.0703321\pi$
$948$		0			0
$949$	−12.6491	+	10.0000i	−0.410608	+	0.324614i
$950$	−31.3050	+	4.47214i	−1.01567	+	0.145095i
$951$	−19.7990	−	44.2719i	−0.642026	−	1.43561i
$952$	10.0000	−	10.0000i	0.324102	−	0.324102i
$953$	6.70820	−	6.70820i	0.217300	−	0.217300i	−0.590060	−	0.807360i	$-0.700896\pi$
$953$	6.70820	−	6.70820i	0.217300	−	0.217300i	0.807360	+	0.590060i	$0.200896\pi$
$954$	−12.6491	+	14.1421i	−0.409530	+	0.457869i
$955$	18.9737	+	6.32456i	0.613973	+	0.204658i
$956$	−4.24264			−0.137217
$957$	15.6352	−	40.9334i	0.505413	−	1.32319i
$958$	13.0000	+	13.0000i	0.420011	+	0.420011i
$959$	−80.4984			−2.59943
$960$	−2.45517	+	2.99535i	−0.0792403	+	0.0966746i
$961$	21.0000			0.677419
$962$	−16.0153	−	1.87320i	−0.516355	−	0.0603945i
$963$	−0.527864	−	9.47214i	−0.0170102	−	0.305235i
$964$	−12.6491			−0.407400
$965$	13.4164	+	26.8328i	0.431889	+	0.863779i
$966$		0			0
$967$	31.6228	+	31.6228i	1.01692	+	1.01692i	0.999854	+	0.0170656i	$0.00543240\pi$
$967$	31.6228	+	31.6228i	1.01692	+	1.01692i	0.0170656	+	0.999854i	$0.494568\pi$
$968$	−14.8492	−	14.8492i	−0.477273	−	0.477273i
$969$	31.6228	−	14.1421i	1.01587	−	0.454311i
$970$	−9.48683	+	28.4605i	−0.304604	+	0.913812i
$971$		−	31.3050i		−	1.00462i	−0.864687	−	0.502312i	$-0.832483\pi$
$971$		−	31.3050i		−	1.00462i	0.864687	−	0.502312i	$-0.167517\pi$
$972$	−3.90983	+	15.0902i	−0.125408	+	0.484017i
$973$	12.6491	−	12.6491i	0.405512	−	0.405512i
$974$	4.47214			0.143296
$975$	28.1706	−	13.4691i	0.902181	−	0.431358i
$976$	−10.0000			−0.320092
$977$	29.6985	−	29.6985i	0.950139	−	0.950139i	−0.0486759	−	0.998815i	$-0.515500\pi$
$977$	29.6985	−	29.6985i	0.950139	−	0.950139i	0.998815	+	0.0486759i	$0.0155002\pi$
$978$		0			0
$979$			16.0000i			0.511362i
$980$	9.19239	−	27.5772i	0.293640	−	0.880920i
$981$	7.07107	+	6.32456i	0.225762	+	0.201928i
$982$	15.8114	+	15.8114i	0.504562	+	0.504562i
$983$	−18.3848	−	18.3848i	−0.586383	−	0.586383i	0.350267	−	0.936650i	$-0.386091\pi$
$983$	−18.3848	−	18.3848i	−0.586383	−	0.586383i	−0.936650	+	0.350267i	$0.886091\pi$
$984$	8.94427	−	4.00000i	0.285133	−	0.127515i
$985$	−2.00000	−	4.00000i	−0.0637253	−	0.127451i
$986$	−14.1421			−0.450377
$987$	5.52786	−	14.4721i	0.175954	−	0.460653i
$988$	2.64911	−	22.6491i	0.0842794	−	0.720564i
$989$		0			0
$990$	9.97831	−	36.6119i	0.317131	−	1.16360i
$991$	−28.0000			−0.889449			−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000			−0.889449			−0.444725	+	0.895667i	$0.646698\pi$
$992$	−2.23607	−	2.23607i	−0.0709952	−	0.0709952i
$993$	20.4667	+	7.81758i	0.649491	+	0.248083i
$994$	6.32456			0.200603
$995$	−42.4264	−	14.1421i	−1.34501	−	0.448336i
$996$	−2.82843	−	6.32456i	−0.0896221	−	0.200401i
$997$	20.0000	−	20.0000i	0.633406	−	0.633406i	−0.315514	−	0.948921i	$-0.602177\pi$
$997$	20.0000	−	20.0000i	0.633406	−	0.633406i	0.948921	+	0.315514i	$0.102177\pi$
$998$	−8.94427	+	8.94427i	−0.283126	+	0.283126i
$999$	−22.1359	−	7.07107i	−0.700350	−	0.223719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.s.a.233.3	yes	8
3.2	odd	2	inner	390.2.s.a.233.2	yes	8
5.2	odd	4	inner	390.2.s.a.77.4	yes	8
13.12	even	2	inner	390.2.s.a.233.1	yes	8
15.2	even	4	inner	390.2.s.a.77.1	✓	8
39.38	odd	2	inner	390.2.s.a.233.4	yes	8
65.12	odd	4	inner	390.2.s.a.77.2	yes	8
195.77	even	4	inner	390.2.s.a.77.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.s.a.77.1	✓	8	15.2	even	4	inner
390.2.s.a.77.2	yes	8	65.12	odd	4	inner
390.2.s.a.77.3	yes	8	195.77	even	4	inner
390.2.s.a.77.4	yes	8	5.2	odd	4	inner
390.2.s.a.233.1	yes	8	13.12	even	2	inner
390.2.s.a.233.2	yes	8	3.2	odd	2	inner
390.2.s.a.233.3	yes	8	1.1	even	1	trivial
390.2.s.a.233.4	yes	8	39.38	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(0.707107 + 1.58114i) q^{6} +(-3.16228 - 3.16228i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.23607 - 2.00000i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.618034 + 1.61803i) q^{3} -1.00000i q^{4} +(0.707107 - 2.12132i) q^{5} +(0.707107 + 1.58114i) q^{6} +(-3.16228 - 3.16228i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.23607 - 2.00000i) q^{9} +(-1.00000 - 2.00000i) q^{10} -5.65685 q^{11} +(1.61803 + 0.618034i) q^{12} +(3.58114 + 0.418861i) q^{13} -4.47214 q^{14} +(2.99535 + 2.45517i) q^{15} -1.00000 q^{16} +(-2.23607 - 2.23607i) q^{17} +(-2.99535 + 0.166925i) q^{18} +6.32456 q^{19} +(-2.12132 - 0.707107i) q^{20} +(7.07107 - 3.16228i) q^{21} +(-4.00000 + 4.00000i) q^{22} +(1.58114 - 0.707107i) q^{24} +(-4.00000 - 3.00000i) q^{25} +(2.82843 - 2.23607i) q^{26} +(4.61803 - 2.38197i) q^{27} +(-3.16228 + 3.16228i) q^{28} +4.47214 q^{29} +(3.85410 - 0.381966i) q^{30} +3.16228i q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.49613 - 9.15298i) q^{33} -3.16228 q^{34} +(-8.94427 + 4.47214i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(-3.16228 - 3.16228i) q^{37} +(4.47214 - 4.47214i) q^{38} +(-2.89100 + 5.53553i) q^{39} +(-2.00000 + 1.00000i) q^{40} +5.65685 q^{41} +(2.76393 - 7.23607i) q^{42} +(-5.00000 - 5.00000i) q^{43} +5.65685i q^{44} +(-5.82378 + 3.32920i) q^{45} +(1.41421 - 1.41421i) q^{47} +(0.618034 - 1.61803i) q^{48} +13.0000i q^{49} +(-4.94975 + 0.707107i) q^{50} +(5.00000 - 2.23607i) q^{51} +(0.418861 - 3.58114i) q^{52} +(4.47214 - 4.47214i) q^{53} +(1.58114 - 4.94975i) q^{54} +(-4.00000 + 12.0000i) q^{55} +4.47214i q^{56} +(-3.90879 + 10.2333i) q^{57} +(3.16228 - 3.16228i) q^{58} +2.82843i q^{59} +(2.45517 - 2.99535i) q^{60} +10.0000 q^{61} +(2.23607 + 2.23607i) q^{62} +(0.746512 + 13.3956i) q^{63} +1.00000i q^{64} +(3.42079 - 7.30056i) q^{65} +(-4.00000 - 8.94427i) q^{66} +(-2.23607 + 2.23607i) q^{68} +(-3.16228 + 9.48683i) q^{70} -1.41421 q^{71} +(0.166925 + 2.99535i) q^{72} +(-3.16228 + 3.16228i) q^{73} -4.47214 q^{74} +(7.32624 - 4.61803i) q^{75} -6.32456i q^{76} +(17.8885 + 17.8885i) q^{77} +(1.86997 + 5.95846i) q^{78} +(-0.707107 + 2.12132i) q^{80} +(1.00000 + 8.94427i) q^{81} +(4.00000 - 4.00000i) q^{82} +(-2.82843 - 2.82843i) q^{83} +(-3.16228 - 7.07107i) q^{84} +(-6.32456 + 3.16228i) q^{85} -7.07107 q^{86} +(-2.76393 + 7.23607i) q^{87} +(4.00000 + 4.00000i) q^{88} -2.82843i q^{89} +(-1.76393 + 6.47214i) q^{90} +(-10.0000 - 12.6491i) q^{91} +(-5.11667 - 1.95440i) q^{93} -2.00000i q^{94} +(4.47214 - 13.4164i) q^{95} +(-0.707107 - 1.58114i) q^{96} +(-9.48683 - 9.48683i) q^{97} +(9.19239 + 9.19239i) q^{98} +(12.6491 + 11.3137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3}+O(q^{10}) \) 8 * q + 4 * q^3	\( 8 q + 4 q^{3} - 8 q^{10} + 4 q^{12} + 16 q^{13} - 8 q^{16} - 32 q^{22} - 32 q^{25} + 28 q^{27} + 4 q^{30} - 16 q^{36} - 16 q^{40} + 40 q^{42} - 40 q^{43} - 4 q^{48} + 40 q^{51} + 16 q^{52} - 32 q^{55} + 80 q^{61} - 32 q^{66} - 4 q^{75} + 20 q^{78} + 8 q^{81} + 32 q^{82} - 40 q^{87} + 32 q^{88} - 32 q^{90} - 80 q^{91}+O(q^{100}) \) 8 * q + 4 * q^3 - 8 * q^10 + 4 * q^12 + 16 * q^13 - 8 * q^16 - 32 * q^22 - 32 * q^25 + 28 * q^27 + 4 * q^30 - 16 * q^36 - 16 * q^40 + 40 * q^42 - 40 * q^43 - 4 * q^48 + 40 * q^51 + 16 * q^52 - 32 * q^55 + 80 * q^61 - 32 * q^66 - 4 * q^75 + 20 * q^78 + 8 * q^81 + 32 * q^82 - 40 * q^87 + 32 * q^88 - 32 * q^90 - 80 * q^91

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