LMFDB - Embedded newform 385.2.b.a.309.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(309,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

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

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

chi := DirichletCharacter("385.309");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.b (of order $2$, degree $1$, 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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			309.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	385.309
Dual form			385.2.b.a.309.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -2.00000i q^{3} +1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} +2.00000 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -2.00000i q^{3} +1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} +2.00000 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +(-2.00000 + 1.00000i) q^{10} +1.00000 q^{11} -2.00000i q^{12} +6.00000i q^{13} +1.00000 q^{14} +(4.00000 - 2.00000i) q^{15} -1.00000 q^{16} -6.00000i q^{17} -1.00000i q^{18} +(1.00000 + 2.00000i) q^{20} -2.00000 q^{21} +1.00000i q^{22} -6.00000i q^{23} +6.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -6.00000 q^{26} -4.00000i q^{27} -1.00000i q^{28} +6.00000 q^{29} +(2.00000 + 4.00000i) q^{30} +5.00000i q^{32} -2.00000i q^{33} +6.00000 q^{34} +(2.00000 - 1.00000i) q^{35} -1.00000 q^{36} +4.00000i q^{37} +12.0000 q^{39} +(-6.00000 + 3.00000i) q^{40} -6.00000 q^{41} -2.00000i q^{42} +8.00000i q^{43} +1.00000 q^{44} +(-1.00000 - 2.00000i) q^{45} +6.00000 q^{46} -10.0000i q^{47} +2.00000i q^{48} -1.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -12.0000 q^{51} +6.00000i q^{52} -4.00000i q^{53} +4.00000 q^{54} +(1.00000 + 2.00000i) q^{55} +3.00000 q^{56} +6.00000i q^{58} -12.0000 q^{59} +(4.00000 - 2.00000i) q^{60} -10.0000 q^{61} +1.00000i q^{63} -7.00000 q^{64} +(-12.0000 + 6.00000i) q^{65} +2.00000 q^{66} -2.00000i q^{67} -6.00000i q^{68} -12.0000 q^{69} +(1.00000 + 2.00000i) q^{70} +8.00000 q^{71} -3.00000i q^{72} -2.00000i q^{73} -4.00000 q^{74} +(8.00000 + 6.00000i) q^{75} -1.00000i q^{77} +12.0000i q^{78} -8.00000 q^{79} +(-1.00000 - 2.00000i) q^{80} -11.0000 q^{81} -6.00000i q^{82} -2.00000 q^{84} +(12.0000 - 6.00000i) q^{85} -8.00000 q^{86} -12.0000i q^{87} +3.00000i q^{88} +6.00000 q^{89} +(2.00000 - 1.00000i) q^{90} +6.00000 q^{91} -6.00000i q^{92} +10.0000 q^{94} +10.0000 q^{96} -1.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^4 + 2 * q^5 + 4 * q^6 - 2 * q^9	$ 2 q + 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{9} - 4 q^{10} + 2 q^{11} + 2 q^{14} + 8 q^{15} - 2 q^{16} + 2 q^{20} - 4 q^{21} + 12 q^{24} - 6 q^{25} - 12 q^{26} + 12 q^{29} + 4 q^{30} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 24 q^{39} - 12 q^{40} - 12 q^{41} + 2 q^{44} - 2 q^{45} + 12 q^{46} - 2 q^{49} - 8 q^{50} - 24 q^{51} + 8 q^{54} + 2 q^{55} + 6 q^{56} - 24 q^{59} + 8 q^{60} - 20 q^{61} - 14 q^{64} - 24 q^{65} + 4 q^{66} - 24 q^{69} + 2 q^{70} + 16 q^{71} - 8 q^{74} + 16 q^{75} - 16 q^{79} - 2 q^{80} - 22 q^{81} - 4 q^{84} + 24 q^{85} - 16 q^{86} + 12 q^{89} + 4 q^{90} + 12 q^{91} + 20 q^{94} + 20 q^{96} - 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^4 + 2 * q^5 + 4 * q^6 - 2 * q^9 - 4 * q^10 + 2 * q^11 + 2 * q^14 + 8 * q^15 - 2 * q^16 + 2 * q^20 - 4 * q^21 + 12 * q^24 - 6 * q^25 - 12 * q^26 + 12 * q^29 + 4 * q^30 + 12 * q^34 + 4 * q^35 - 2 * q^36 + 24 * q^39 - 12 * q^40 - 12 * q^41 + 2 * q^44 - 2 * q^45 + 12 * q^46 - 2 * q^49 - 8 * q^50 - 24 * q^51 + 8 * q^54 + 2 * q^55 + 6 * q^56 - 24 * q^59 + 8 * q^60 - 20 * q^61 - 14 * q^64 - 24 * q^65 + 4 * q^66 - 24 * q^69 + 2 * q^70 + 16 * q^71 - 8 * q^74 + 16 * q^75 - 16 * q^79 - 2 * q^80 - 22 * q^81 - 4 * q^84 + 24 * q^85 - 16 * q^86 + 12 * q^89 + 4 * q^90 + 12 * q^91 + 20 * q^94 + 20 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$		−	2.00000i		−	1.15470i	−0.816497	−	0.577350i	$-0.804087\pi$
$3$		−	2.00000i		−	1.15470i	0.816497	−	0.577350i	$-0.195913\pi$
$4$	1.00000			0.500000
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$	2.00000			0.816497
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			3.00000i			1.06066i
$9$	−1.00000			−0.333333
$10$	−2.00000	+	1.00000i	−0.632456	+	0.316228i
$11$	1.00000			0.301511
$11$	1.00000			0.301511
$12$		−	2.00000i		−	0.577350i
$13$			6.00000i			1.66410i	0.554700	+	0.832050i	$0.312833\pi$
$13$			6.00000i			1.66410i	−0.554700	+	0.832050i	$0.687167\pi$
$14$	1.00000			0.267261
$15$	4.00000	−	2.00000i	1.03280	−	0.516398i
$16$	−1.00000			−0.250000
$17$		−	6.00000i		−	1.45521i	−0.685994	−	0.727607i	$-0.740633\pi$
$17$		−	6.00000i		−	1.45521i	0.685994	−	0.727607i	$-0.259367\pi$
$18$		−	1.00000i		−	0.235702i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	1.00000	+	2.00000i	0.223607	+	0.447214i
$21$	−2.00000			−0.436436
$22$			1.00000i			0.213201i
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$	6.00000			1.22474
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	−6.00000			−1.17670
$27$		−	4.00000i		−	0.769800i
$28$		−	1.00000i		−	0.188982i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	2.00000	+	4.00000i	0.365148	+	0.730297i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$			5.00000i			0.883883i
$33$		−	2.00000i		−	0.348155i
$34$	6.00000			1.02899
$35$	2.00000	−	1.00000i	0.338062	−	0.169031i
$36$	−1.00000			−0.166667
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$		0			0
$39$	12.0000			1.92154
$40$	−6.00000	+	3.00000i	−0.948683	+	0.474342i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		−	2.00000i		−	0.308607i
$43$			8.00000i			1.21999i	0.792406	+	0.609994i	$0.208828\pi$
$43$			8.00000i			1.21999i	−0.792406	+	0.609994i	$0.791172\pi$
$44$	1.00000			0.150756
$45$	−1.00000	−	2.00000i	−0.149071	−	0.298142i
$46$	6.00000			0.884652
$47$		−	10.0000i		−	1.45865i	−0.684167	−	0.729325i	$-0.739834\pi$
$47$		−	10.0000i		−	1.45865i	0.684167	−	0.729325i	$-0.260166\pi$
$48$			2.00000i			0.288675i
$49$	−1.00000			−0.142857
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$	−12.0000			−1.68034
$52$			6.00000i			0.832050i
$53$		−	4.00000i		−	0.549442i	−0.961524	−	0.274721i	$-0.911414\pi$
$53$		−	4.00000i		−	0.549442i	0.961524	−	0.274721i	$-0.0885855\pi$
$54$	4.00000			0.544331
$55$	1.00000	+	2.00000i	0.134840	+	0.269680i
$56$	3.00000			0.400892
$57$		0			0
$58$			6.00000i			0.787839i
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$	4.00000	−	2.00000i	0.516398	−	0.258199i
$61$	−10.0000			−1.28037			−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000			−1.28037			−0.640184	+	0.768221i	$0.721142\pi$
$62$		0			0
$63$			1.00000i			0.125988i
$64$	−7.00000			−0.875000
$65$	−12.0000	+	6.00000i	−1.48842	+	0.744208i
$66$	2.00000			0.246183
$67$		−	2.00000i		−	0.244339i	−0.992509	−	0.122169i	$-0.961015\pi$
$67$		−	2.00000i		−	0.244339i	0.992509	−	0.122169i	$-0.0389851\pi$
$68$		−	6.00000i		−	0.727607i
$69$	−12.0000			−1.44463
$70$	1.00000	+	2.00000i	0.119523	+	0.239046i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		−	3.00000i		−	0.353553i
$73$		−	2.00000i		−	0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$		−	2.00000i		−	0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$	−4.00000			−0.464991
$75$	8.00000	+	6.00000i	0.923760	+	0.692820i
$76$		0			0
$77$		−	1.00000i		−	0.113961i
$78$			12.0000i			1.35873i
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$	−1.00000	−	2.00000i	−0.111803	−	0.223607i
$81$	−11.0000			−1.22222
$82$		−	6.00000i		−	0.662589i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	−2.00000			−0.218218
$85$	12.0000	−	6.00000i	1.30158	−	0.650791i
$86$	−8.00000			−0.862662
$87$		−	12.0000i		−	1.28654i
$88$			3.00000i			0.319801i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	2.00000	−	1.00000i	0.210819	−	0.105409i
$91$	6.00000			0.628971
$92$		−	6.00000i		−	0.625543i
$93$		0			0
$94$	10.0000			1.03142
$95$		0			0
$96$	10.0000			1.02062
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$		−	1.00000i		−	0.101015i
$99$	−1.00000			−0.100504
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	−14.0000			−1.39305			−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000			−1.39305			−0.696526	+	0.717532i	$0.745272\pi$
$102$		−	12.0000i		−	1.18818i
$103$		−	14.0000i		−	1.37946i	−0.724066	−	0.689730i	$-0.757729\pi$
$103$		−	14.0000i		−	1.37946i	0.724066	−	0.689730i	$-0.242271\pi$
$104$	−18.0000			−1.76505
$105$	−2.00000	−	4.00000i	−0.195180	−	0.390360i
$106$	4.00000			0.388514
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$		−	4.00000i		−	0.384900i
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$	−2.00000	+	1.00000i	−0.190693	+	0.0953463i
$111$	8.00000			0.759326
$112$			1.00000i			0.0944911i
$113$			12.0000i			1.12887i	0.825479	+	0.564433i	$0.190905\pi$
$113$			12.0000i			1.12887i	−0.825479	+	0.564433i	$0.809095\pi$
$114$		0			0
$115$	12.0000	−	6.00000i	1.11901	−	0.559503i
$116$	6.00000			0.557086
$117$		−	6.00000i		−	0.554700i
$118$		−	12.0000i		−	1.10469i
$119$	−6.00000			−0.550019
$120$	6.00000	+	12.0000i	0.547723	+	1.09545i
$121$	1.00000			0.0909091
$122$		−	10.0000i		−	0.905357i
$123$			12.0000i			1.08200i
$124$		0			0
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	−1.00000			−0.0890871
$127$		−	12.0000i		−	1.06483i	−0.846484	−	0.532414i	$-0.821285\pi$
$127$		−	12.0000i		−	1.06483i	0.846484	−	0.532414i	$-0.178715\pi$
$128$			3.00000i			0.265165i
$129$	16.0000			1.40872
$130$	−6.00000	−	12.0000i	−0.526235	−	1.05247i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		−	2.00000i		−	0.174078i
$133$		0			0
$134$	2.00000			0.172774
$135$	8.00000	−	4.00000i	0.688530	−	0.344265i
$136$	18.0000			1.54349
$137$		−	20.0000i		−	1.70872i	−0.519685	−	0.854358i	$-0.673951\pi$
$137$		−	20.0000i		−	1.70872i	0.519685	−	0.854358i	$-0.326049\pi$
$138$		−	12.0000i		−	1.02151i
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$	2.00000	−	1.00000i	0.169031	−	0.0845154i
$141$	−20.0000			−1.68430
$142$			8.00000i			0.671345i
$143$			6.00000i			0.501745i
$144$	1.00000			0.0833333
$145$	6.00000	+	12.0000i	0.498273	+	0.996546i
$146$	2.00000			0.165521
$147$			2.00000i			0.164957i
$148$			4.00000i			0.328798i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$	−6.00000	+	8.00000i	−0.489898	+	0.653197i
$151$	4.00000			0.325515			0.162758	−	0.986666i	$-0.447961\pi$
$151$	4.00000			0.325515			0.162758	+	0.986666i	$0.447961\pi$
$152$		0			0
$153$			6.00000i			0.485071i
$154$	1.00000			0.0805823
$155$		0			0
$156$	12.0000			0.960769
$157$			4.00000i			0.319235i	0.987179	+	0.159617i	$0.0510260\pi$
$157$			4.00000i			0.319235i	−0.987179	+	0.159617i	$0.948974\pi$
$158$		−	8.00000i		−	0.636446i
$159$	−8.00000			−0.634441
$160$	−10.0000	+	5.00000i	−0.790569	+	0.395285i
$161$	−6.00000			−0.472866
$162$		−	11.0000i		−	0.864242i
$163$			18.0000i			1.40987i	0.709273	+	0.704934i	$0.249024\pi$
$163$			18.0000i			1.40987i	−0.709273	+	0.704934i	$0.750976\pi$
$164$	−6.00000			−0.468521
$165$	4.00000	−	2.00000i	0.311400	−	0.155700i
$166$		0			0
$167$			20.0000i			1.54765i	0.633402	+	0.773823i	$0.281658\pi$
$167$			20.0000i			1.54765i	−0.633402	+	0.773823i	$0.718342\pi$
$168$		−	6.00000i		−	0.462910i
$169$	−23.0000			−1.76923
$170$	6.00000	+	12.0000i	0.460179	+	0.920358i
$171$		0			0
$172$			8.00000i			0.609994i
$173$			18.0000i			1.36851i	0.729241	+	0.684257i	$0.239873\pi$
$173$			18.0000i			1.36851i	−0.729241	+	0.684257i	$0.760127\pi$
$174$	12.0000			0.909718
$175$	4.00000	+	3.00000i	0.302372	+	0.226779i
$176$	−1.00000			−0.0753778
$177$			24.0000i			1.80395i
$178$			6.00000i			0.449719i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	−1.00000	−	2.00000i	−0.0745356	−	0.149071i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$			6.00000i			0.444750i
$183$			20.0000i			1.47844i
$184$	18.0000			1.32698
$185$	−8.00000	+	4.00000i	−0.588172	+	0.294086i
$186$		0			0
$187$		−	6.00000i		−	0.438763i
$188$		−	10.0000i		−	0.729325i
$189$	−4.00000			−0.290957
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$			14.0000i			1.01036i
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$		0			0
$195$	12.0000	+	24.0000i	0.859338	+	1.71868i
$196$	−1.00000			−0.0714286
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		−	1.00000i		−	0.0710669i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−12.0000	−	9.00000i	−0.848528	−	0.636396i
$201$	−4.00000			−0.282138
$202$		−	14.0000i		−	0.985037i
$203$		−	6.00000i		−	0.421117i
$204$	−12.0000			−0.840168
$205$	−6.00000	−	12.0000i	−0.419058	−	0.838116i
$206$	14.0000			0.975426
$207$			6.00000i			0.417029i
$208$		−	6.00000i		−	0.416025i
$209$		0			0
$210$	4.00000	−	2.00000i	0.276026	−	0.138013i
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$		−	4.00000i		−	0.274721i
$213$		−	16.0000i		−	1.09630i
$214$	−12.0000			−0.820303
$215$	−16.0000	+	8.00000i	−1.09119	+	0.545595i
$216$	12.0000			0.816497
$217$		0			0
$218$		−	6.00000i		−	0.406371i
$219$	−4.00000			−0.270295
$220$	1.00000	+	2.00000i	0.0674200	+	0.134840i
$221$	36.0000			2.42162
$222$			8.00000i			0.536925i
$223$		−	2.00000i		−	0.133930i	−0.997755	−	0.0669650i	$-0.978668\pi$
$223$		−	2.00000i		−	0.133930i	0.997755	−	0.0669650i	$-0.0213316\pi$
$224$	5.00000			0.334077
$225$	3.00000	−	4.00000i	0.200000	−	0.266667i
$226$	−12.0000			−0.798228
$227$		−	8.00000i		−	0.530979i	−0.964114	−	0.265489i	$-0.914466\pi$
$227$		−	8.00000i		−	0.530979i	0.964114	−	0.265489i	$-0.0855335\pi$
$228$		0			0
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$	6.00000	+	12.0000i	0.395628	+	0.791257i
$231$	−2.00000			−0.131590
$232$			18.0000i			1.18176i
$233$		−	22.0000i		−	1.44127i	−0.693316	−	0.720634i	$-0.743851\pi$
$233$		−	22.0000i		−	1.44127i	0.693316	−	0.720634i	$-0.256149\pi$
$234$	6.00000			0.392232
$235$	20.0000	−	10.0000i	1.30466	−	0.652328i
$236$	−12.0000			−0.781133
$237$			16.0000i			1.03931i
$238$		−	6.00000i		−	0.388922i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−4.00000	+	2.00000i	−0.258199	+	0.129099i
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$			1.00000i			0.0642824i
$243$			10.0000i			0.641500i
$244$	−10.0000			−0.640184
$245$	−1.00000	−	2.00000i	−0.0638877	−	0.127775i
$246$	−12.0000			−0.765092
$247$		0			0
$248$		0			0
$249$		0			0
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$			1.00000i			0.0629941i
$253$		−	6.00000i		−	0.377217i
$254$	12.0000			0.752947
$255$	−12.0000	−	24.0000i	−0.751469	−	1.50294i
$256$	−17.0000			−1.06250
$257$		−	4.00000i		−	0.249513i	−0.992187	−	0.124757i	$-0.960185\pi$
$257$		−	4.00000i		−	0.249513i	0.992187	−	0.124757i	$-0.0398150\pi$
$258$			16.0000i			0.996116i
$259$	4.00000			0.248548
$260$	−12.0000	+	6.00000i	−0.744208	+	0.372104i
$261$	−6.00000			−0.371391
$262$			12.0000i			0.741362i
$263$		−	28.0000i		−	1.72655i	−0.504730	−	0.863277i	$-0.668408\pi$
$263$		−	28.0000i		−	1.72655i	0.504730	−	0.863277i	$-0.331592\pi$
$264$	6.00000			0.369274
$265$	8.00000	−	4.00000i	0.491436	−	0.245718i
$266$		0			0
$267$		−	12.0000i		−	0.734388i
$268$		−	2.00000i		−	0.122169i
$269$	30.0000			1.82913			0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000			1.82913			0.914566	+	0.404436i	$0.132532\pi$
$270$	4.00000	+	8.00000i	0.243432	+	0.486864i
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$			6.00000i			0.363803i
$273$		−	12.0000i		−	0.726273i
$274$	20.0000			1.20824
$275$	−3.00000	+	4.00000i	−0.180907	+	0.241209i
$276$	−12.0000			−0.722315
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$		−	12.0000i		−	0.719712i
$279$		0			0
$280$	3.00000	+	6.00000i	0.179284	+	0.358569i
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		−	20.0000i		−	1.19098i
$283$			16.0000i			0.951101i	0.879688	+	0.475551i	$0.157751\pi$
$283$			16.0000i			0.951101i	−0.879688	+	0.475551i	$0.842249\pi$
$284$	8.00000			0.474713
$285$		0			0
$286$	−6.00000			−0.354787
$287$			6.00000i			0.354169i
$288$		−	5.00000i		−	0.294628i
$289$	−19.0000			−1.11765
$290$	−12.0000	+	6.00000i	−0.704664	+	0.352332i
$291$		0			0
$292$		−	2.00000i		−	0.117041i
$293$		−	26.0000i		−	1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$		−	26.0000i		−	1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$	−2.00000			−0.116642
$295$	−12.0000	−	24.0000i	−0.698667	−	1.39733i
$296$	−12.0000			−0.697486
$297$		−	4.00000i		−	0.232104i
$298$			10.0000i			0.579284i
$299$	36.0000			2.08193
$300$	8.00000	+	6.00000i	0.461880	+	0.346410i
$301$	8.00000			0.461112
$302$			4.00000i			0.230174i
$303$			28.0000i			1.60856i
$304$		0			0
$305$	−10.0000	−	20.0000i	−0.572598	−	1.14520i
$306$	−6.00000			−0.342997
$307$		−	20.0000i		−	1.14146i	−0.821138	−	0.570730i	$-0.806660\pi$
$307$		−	20.0000i		−	1.14146i	0.821138	−	0.570730i	$-0.193340\pi$
$308$		−	1.00000i		−	0.0569803i
$309$	−28.0000			−1.59286
$310$		0			0
$311$	−8.00000			−0.453638			−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000			−0.453638			−0.226819	+	0.973937i	$0.572833\pi$
$312$			36.0000i			2.03810i
$313$			28.0000i			1.58265i	0.611393	+	0.791327i	$0.290609\pi$
$313$			28.0000i			1.58265i	−0.611393	+	0.791327i	$0.709391\pi$
$314$	−4.00000			−0.225733
$315$	−2.00000	+	1.00000i	−0.112687	+	0.0563436i
$316$	−8.00000			−0.450035
$317$			8.00000i			0.449325i	0.974437	+	0.224662i	$0.0721279\pi$
$317$			8.00000i			0.449325i	−0.974437	+	0.224662i	$0.927872\pi$
$318$		−	8.00000i		−	0.448618i
$319$	6.00000			0.335936
$320$	−7.00000	−	14.0000i	−0.391312	−	0.782624i
$321$	24.0000			1.33955
$322$		−	6.00000i		−	0.334367i
$323$		0			0
$324$	−11.0000			−0.611111
$325$	−24.0000	−	18.0000i	−1.33128	−	0.998460i
$326$	−18.0000			−0.996928
$327$			12.0000i			0.663602i
$328$		−	18.0000i		−	0.993884i
$329$	−10.0000			−0.551318
$330$	2.00000	+	4.00000i	0.110096	+	0.220193i
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$		0			0
$333$		−	4.00000i		−	0.219199i
$334$	−20.0000			−1.09435
$335$	4.00000	−	2.00000i	0.218543	−	0.109272i
$336$	2.00000			0.109109
$337$		−	6.00000i		−	0.326841i	−0.986557	−	0.163420i	$-0.947747\pi$
$337$		−	6.00000i		−	0.326841i	0.986557	−	0.163420i	$-0.0522527\pi$
$338$		−	23.0000i		−	1.25104i
$339$	24.0000			1.30350
$340$	12.0000	−	6.00000i	0.650791	−	0.325396i
$341$		0			0
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	−24.0000			−1.29399
$345$	−12.0000	−	24.0000i	−0.646058	−	1.29212i
$346$	−18.0000			−0.967686
$347$			4.00000i			0.214731i	0.994220	+	0.107366i	$0.0342415\pi$
$347$			4.00000i			0.214731i	−0.994220	+	0.107366i	$0.965758\pi$
$348$		−	12.0000i		−	0.643268i
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$	−3.00000	+	4.00000i	−0.160357	+	0.213809i
$351$	24.0000			1.28103
$352$			5.00000i			0.266501i
$353$			20.0000i			1.06449i	0.846590	+	0.532246i	$0.178652\pi$
$353$			20.0000i			1.06449i	−0.846590	+	0.532246i	$0.821348\pi$
$354$	−24.0000			−1.27559
$355$	8.00000	+	16.0000i	0.424596	+	0.849192i
$356$	6.00000			0.317999
$357$			12.0000i			0.635107i
$358$		−	12.0000i		−	0.634220i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	6.00000	−	3.00000i	0.316228	−	0.158114i
$361$	−19.0000			−1.00000
$362$			10.0000i			0.525588i
$363$		−	2.00000i		−	0.104973i
$364$	6.00000			0.314485
$365$	4.00000	−	2.00000i	0.209370	−	0.104685i
$366$	−20.0000			−1.04542
$367$			22.0000i			1.14839i	0.818718	+	0.574195i	$0.194685\pi$
$367$			22.0000i			1.14839i	−0.818718	+	0.574195i	$0.805315\pi$
$368$			6.00000i			0.312772i
$369$	6.00000			0.312348
$370$	−4.00000	−	8.00000i	−0.207950	−	0.415900i
$371$	−4.00000			−0.207670
$372$		0			0
$373$		−	14.0000i		−	0.724893i	−0.932005	−	0.362446i	$-0.881942\pi$
$373$		−	14.0000i		−	0.724893i	0.932005	−	0.362446i	$-0.118058\pi$
$374$	6.00000			0.310253
$375$	−4.00000	+	22.0000i	−0.206559	+	1.13608i
$376$	30.0000			1.54713
$377$			36.0000i			1.85409i
$378$		−	4.00000i		−	0.205738i
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$		0			0
$381$	−24.0000			−1.22956
$382$			8.00000i			0.409316i
$383$			18.0000i			0.919757i	0.887982	+	0.459879i	$0.152107\pi$
$383$			18.0000i			0.919757i	−0.887982	+	0.459879i	$0.847893\pi$
$384$	6.00000			0.306186
$385$	2.00000	−	1.00000i	0.101929	−	0.0509647i
$386$	−14.0000			−0.712581
$387$		−	8.00000i		−	0.406663i
$388$		0			0
$389$	−26.0000			−1.31825			−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000			−1.31825			−0.659126	+	0.752032i	$0.729074\pi$
$390$	−24.0000	+	12.0000i	−1.21529	+	0.607644i
$391$	−36.0000			−1.82060
$392$		−	3.00000i		−	0.151523i
$393$		−	24.0000i		−	1.21064i
$394$	18.0000			0.906827
$395$	−8.00000	−	16.0000i	−0.402524	−	0.805047i
$396$	−1.00000			−0.0502519
$397$		−	28.0000i		−	1.40528i	−0.711546	−	0.702640i	$-0.752005\pi$
$397$		−	28.0000i		−	1.40528i	0.711546	−	0.702640i	$-0.247995\pi$
$398$			8.00000i			0.401004i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$	−2.00000			−0.0998752			−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−2.00000			−0.0998752			−0.0499376	+	0.998752i	$0.515902\pi$
$402$		−	4.00000i		−	0.199502i
$403$		0			0
$404$	−14.0000			−0.696526
$405$	−11.0000	−	22.0000i	−0.546594	−	1.09319i
$406$	6.00000			0.297775
$407$			4.00000i			0.198273i
$408$		−	36.0000i		−	1.78227i
$409$	−14.0000			−0.692255			−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000			−0.692255			−0.346128	+	0.938187i	$0.612504\pi$
$410$	12.0000	−	6.00000i	0.592638	−	0.296319i
$411$	−40.0000			−1.97305
$412$		−	14.0000i		−	0.689730i
$413$			12.0000i			0.590481i
$414$	−6.00000			−0.294884
$415$		0			0
$416$	−30.0000			−1.47087
$417$			24.0000i			1.17529i
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$	−2.00000	−	4.00000i	−0.0975900	−	0.195180i
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$			8.00000i			0.389434i
$423$			10.0000i			0.486217i
$424$	12.0000			0.582772
$425$	24.0000	+	18.0000i	1.16417	+	0.873128i
$426$	16.0000			0.775203
$427$			10.0000i			0.483934i
$428$			12.0000i			0.580042i
$429$	12.0000			0.579365
$430$	−8.00000	−	16.0000i	−0.385794	−	0.771589i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$			4.00000i			0.192450i
$433$			16.0000i			0.768911i	0.923144	+	0.384455i	$0.125611\pi$
$433$			16.0000i			0.768911i	−0.923144	+	0.384455i	$0.874389\pi$
$434$		0			0
$435$	24.0000	−	12.0000i	1.15071	−	0.575356i
$436$	−6.00000			−0.287348
$437$		0			0
$438$		−	4.00000i		−	0.191127i
$439$	−40.0000			−1.90910			−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000			−1.90910			−0.954548	+	0.298057i	$0.903661\pi$
$440$	−6.00000	+	3.00000i	−0.286039	+	0.143019i
$441$	1.00000			0.0476190
$442$			36.0000i			1.71235i
$443$			26.0000i			1.23530i	0.786454	+	0.617649i	$0.211915\pi$
$443$			26.0000i			1.23530i	−0.786454	+	0.617649i	$0.788085\pi$
$444$	8.00000			0.379663
$445$	6.00000	+	12.0000i	0.284427	+	0.568855i
$446$	2.00000			0.0947027
$447$		−	20.0000i		−	0.945968i
$448$			7.00000i			0.330719i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	4.00000	+	3.00000i	0.188562	+	0.141421i
$451$	−6.00000			−0.282529
$452$			12.0000i			0.564433i
$453$		−	8.00000i		−	0.375873i
$454$	8.00000			0.375459
$455$	6.00000	+	12.0000i	0.281284	+	0.562569i
$456$		0			0
$457$		−	2.00000i		−	0.0935561i	−0.998905	−	0.0467780i	$-0.985105\pi$
$457$		−	2.00000i		−	0.0935561i	0.998905	−	0.0467780i	$-0.0148953\pi$
$458$			22.0000i			1.02799i
$459$	−24.0000			−1.12022
$460$	12.0000	−	6.00000i	0.559503	−	0.279751i
$461$	10.0000			0.465746			0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000			0.465746			0.232873	+	0.972507i	$0.425187\pi$
$462$		−	2.00000i		−	0.0930484i
$463$			26.0000i			1.20832i	0.796862	+	0.604161i	$0.206492\pi$
$463$			26.0000i			1.20832i	−0.796862	+	0.604161i	$0.793508\pi$
$464$	−6.00000			−0.278543
$465$		0			0
$466$	22.0000			1.01913
$467$		−	30.0000i		−	1.38823i	−0.719862	−	0.694117i	$-0.755795\pi$
$467$		−	30.0000i		−	1.38823i	0.719862	−	0.694117i	$-0.244205\pi$
$468$		−	6.00000i		−	0.277350i
$469$	−2.00000			−0.0923514
$470$	10.0000	+	20.0000i	0.461266	+	0.922531i
$471$	8.00000			0.368621
$472$		−	36.0000i		−	1.65703i
$473$			8.00000i			0.367840i
$474$	−16.0000			−0.734904
$475$		0			0
$476$	−6.00000			−0.275010
$477$			4.00000i			0.183147i
$478$		0			0
$479$	4.00000			0.182765			0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000			0.182765			0.0913823	+	0.995816i	$0.470871\pi$
$480$	10.0000	+	20.0000i	0.456435	+	0.912871i
$481$	−24.0000			−1.09431
$482$			10.0000i			0.455488i
$483$			12.0000i			0.546019i
$484$	1.00000			0.0454545
$485$		0			0
$486$	−10.0000			−0.453609
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$		−	30.0000i		−	1.35804i
$489$	36.0000			1.62798
$490$	2.00000	−	1.00000i	0.0903508	−	0.0451754i
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$			12.0000i			0.541002i
$493$		−	36.0000i		−	1.62136i
$494$		0			0
$495$	−1.00000	−	2.00000i	−0.0449467	−	0.0898933i
$496$		0			0
$497$		−	8.00000i		−	0.358849i
$498$		0			0
$499$	36.0000			1.61158			0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000			1.61158			0.805791	+	0.592200i	$0.201741\pi$
$500$	−11.0000	−	2.00000i	−0.491935	−	0.0894427i
$501$	40.0000			1.78707
$502$		−	12.0000i		−	0.535586i
$503$		−	24.0000i		−	1.07011i	−0.844818	−	0.535054i	$-0.820291\pi$
$503$		−	24.0000i		−	1.07011i	0.844818	−	0.535054i	$-0.179709\pi$
$504$	−3.00000			−0.133631
$505$	−14.0000	−	28.0000i	−0.622992	−	1.24598i
$506$	6.00000			0.266733
$507$			46.0000i			2.04293i
$508$		−	12.0000i		−	0.532414i
$509$	−18.0000			−0.797836			−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000			−0.797836			−0.398918	+	0.916987i	$0.630614\pi$
$510$	24.0000	−	12.0000i	1.06274	−	0.531369i
$511$	−2.00000			−0.0884748
$512$		−	11.0000i		−	0.486136i
$513$		0			0
$514$	4.00000			0.176432
$515$	28.0000	−	14.0000i	1.23383	−	0.616914i
$516$	16.0000			0.704361
$517$		−	10.0000i		−	0.439799i
$518$			4.00000i			0.175750i
$519$	36.0000			1.58022
$520$	−18.0000	−	36.0000i	−0.789352	−	1.57870i
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		−	6.00000i		−	0.262613i
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	12.0000			0.524222
$525$	6.00000	−	8.00000i	0.261861	−	0.349149i
$526$	28.0000			1.22086
$527$		0			0
$528$			2.00000i			0.0870388i
$529$	−13.0000			−0.565217
$530$	4.00000	+	8.00000i	0.173749	+	0.347498i
$531$	12.0000			0.520756
$532$		0			0
$533$		−	36.0000i		−	1.55933i
$534$	12.0000			0.519291
$535$	−24.0000	+	12.0000i	−1.03761	+	0.518805i
$536$	6.00000			0.259161
$537$			24.0000i			1.03568i
$538$			30.0000i			1.29339i
$539$	−1.00000			−0.0430730
$540$	8.00000	−	4.00000i	0.344265	−	0.172133i
$541$	−26.0000			−1.11783			−0.558914	−	0.829226i	$-0.688782\pi$
$541$	−26.0000			−1.11783			−0.558914	+	0.829226i	$0.688782\pi$
$542$			16.0000i			0.687259i
$543$		−	20.0000i		−	0.858282i
$544$	30.0000			1.28624
$545$	−6.00000	−	12.0000i	−0.257012	−	0.514024i
$546$	12.0000			0.513553
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$		−	20.0000i		−	0.854358i
$549$	10.0000			0.426790
$550$	−4.00000	−	3.00000i	−0.170561	−	0.127920i
$551$		0			0
$552$		−	36.0000i		−	1.53226i
$553$			8.00000i			0.340195i
$554$	−2.00000			−0.0849719
$555$	8.00000	+	16.0000i	0.339581	+	0.679162i
$556$	−12.0000			−0.508913
$557$		−	18.0000i		−	0.762684i	−0.924434	−	0.381342i	$-0.875462\pi$
$557$		−	18.0000i		−	0.762684i	0.924434	−	0.381342i	$-0.124538\pi$
$558$		0			0
$559$	−48.0000			−2.03018
$560$	−2.00000	+	1.00000i	−0.0845154	+	0.0422577i
$561$	−12.0000			−0.506640
$562$			6.00000i			0.253095i
$563$			12.0000i			0.505740i	0.967500	+	0.252870i	$0.0813744\pi$
$563$			12.0000i			0.505740i	−0.967500	+	0.252870i	$0.918626\pi$
$564$	−20.0000			−0.842152
$565$	−24.0000	+	12.0000i	−1.00969	+	0.504844i
$566$	−16.0000			−0.672530
$567$			11.0000i			0.461957i
$568$			24.0000i			1.00702i
$569$	−10.0000			−0.419222			−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000			−0.419222			−0.209611	+	0.977785i	$0.567220\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$			6.00000i			0.250873i
$573$		−	16.0000i		−	0.668410i
$574$	−6.00000			−0.250435
$575$	24.0000	+	18.0000i	1.00087	+	0.750652i
$576$	7.00000			0.291667
$577$		−	8.00000i		−	0.333044i	−0.986038	−	0.166522i	$-0.946746\pi$
$577$		−	8.00000i		−	0.333044i	0.986038	−	0.166522i	$-0.0532537\pi$
$578$		−	19.0000i		−	0.790296i
$579$	28.0000			1.16364
$580$	6.00000	+	12.0000i	0.249136	+	0.498273i
$581$		0			0
$582$		0			0
$583$		−	4.00000i		−	0.165663i
$584$	6.00000			0.248282
$585$	12.0000	−	6.00000i	0.496139	−	0.248069i
$586$	26.0000			1.07405
$587$			18.0000i			0.742940i	0.928445	+	0.371470i	$0.121146\pi$
$587$			18.0000i			0.742940i	−0.928445	+	0.371470i	$0.878854\pi$
$588$			2.00000i			0.0824786i
$589$		0			0
$590$	24.0000	−	12.0000i	0.988064	−	0.494032i
$591$	−36.0000			−1.48084
$592$		−	4.00000i		−	0.164399i
$593$			38.0000i			1.56047i	0.625485	+	0.780236i	$0.284901\pi$
$593$			38.0000i			1.56047i	−0.625485	+	0.780236i	$0.715099\pi$
$594$	4.00000			0.164122
$595$	−6.00000	−	12.0000i	−0.245976	−	0.491952i
$596$	10.0000			0.409616
$597$		−	16.0000i		−	0.654836i
$598$			36.0000i			1.47215i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−18.0000	+	24.0000i	−0.734847	+	0.979796i
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$			8.00000i			0.326056i
$603$			2.00000i			0.0814463i
$604$	4.00000			0.162758
$605$	1.00000	+	2.00000i	0.0406558	+	0.0813116i
$606$	−28.0000			−1.13742
$607$			20.0000i			0.811775i	0.913923	+	0.405887i	$0.133038\pi$
$607$			20.0000i			0.811775i	−0.913923	+	0.405887i	$0.866962\pi$
$608$		0			0
$609$	−12.0000			−0.486265
$610$	20.0000	−	10.0000i	0.809776	−	0.404888i
$611$	60.0000			2.42734
$612$			6.00000i			0.242536i
$613$			34.0000i			1.37325i	0.727013	+	0.686624i	$0.240908\pi$
$613$			34.0000i			1.37325i	−0.727013	+	0.686624i	$0.759092\pi$
$614$	20.0000			0.807134
$615$	−24.0000	+	12.0000i	−0.967773	+	0.483887i
$616$	3.00000			0.120873
$617$			36.0000i			1.44931i	0.689114	+	0.724653i	$0.258000\pi$
$617$			36.0000i			1.44931i	−0.689114	+	0.724653i	$0.742000\pi$
$618$		−	28.0000i		−	1.12633i
$619$	36.0000			1.44696			0.723481	−	0.690344i	$-0.242541\pi$
$619$	36.0000			1.44696			0.723481	+	0.690344i	$0.242541\pi$
$620$		0			0
$621$	−24.0000			−0.963087
$622$		−	8.00000i		−	0.320771i
$623$		−	6.00000i		−	0.240385i
$624$	−12.0000			−0.480384
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−28.0000			−1.11911
$627$		0			0
$628$			4.00000i			0.159617i
$629$	24.0000			0.956943
$630$	−1.00000	−	2.00000i	−0.0398410	−	0.0796819i
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		−	24.0000i		−	0.954669i
$633$		−	16.0000i		−	0.635943i
$634$	−8.00000			−0.317721
$635$	24.0000	−	12.0000i	0.952411	−	0.476205i
$636$	−8.00000			−0.317221
$637$		−	6.00000i		−	0.237729i
$638$			6.00000i			0.237542i
$639$	−8.00000			−0.316475
$640$	−6.00000	+	3.00000i	−0.237171	+	0.118585i
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$			24.0000i			0.947204i
$643$			6.00000i			0.236617i	0.992977	+	0.118308i	$0.0377472\pi$
$643$			6.00000i			0.236617i	−0.992977	+	0.118308i	$0.962253\pi$
$644$	−6.00000			−0.236433
$645$	16.0000	+	32.0000i	0.629999	+	1.26000i
$646$		0			0
$647$			18.0000i			0.707653i	0.935311	+	0.353827i	$0.115120\pi$
$647$			18.0000i			0.707653i	−0.935311	+	0.353827i	$0.884880\pi$
$648$		−	33.0000i		−	1.29636i
$649$	−12.0000			−0.471041
$650$	18.0000	−	24.0000i	0.706018	−	0.941357i
$651$		0			0
$652$			18.0000i			0.704934i
$653$			36.0000i			1.40879i	0.709809	+	0.704394i	$0.248781\pi$
$653$			36.0000i			1.40879i	−0.709809	+	0.704394i	$0.751219\pi$
$654$	−12.0000			−0.469237
$655$	12.0000	+	24.0000i	0.468879	+	0.937758i
$656$	6.00000			0.234261
$657$			2.00000i			0.0780274i
$658$		−	10.0000i		−	0.389841i
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$	4.00000	−	2.00000i	0.155700	−	0.0778499i
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$			20.0000i			0.777322i
$663$		−	72.0000i		−	2.79625i
$664$		0			0
$665$		0			0
$666$	4.00000			0.154997
$667$		−	36.0000i		−	1.39393i
$668$			20.0000i			0.773823i
$669$	−4.00000			−0.154649
$670$	2.00000	+	4.00000i	0.0772667	+	0.154533i
$671$	−10.0000			−0.386046
$672$		−	10.0000i		−	0.385758i
$673$		−	26.0000i		−	1.00223i	−0.865382	−	0.501113i	$-0.832924\pi$
$673$		−	26.0000i		−	1.00223i	0.865382	−	0.501113i	$-0.167076\pi$
$674$	6.00000			0.231111
$675$	16.0000	+	12.0000i	0.615840	+	0.461880i
$676$	−23.0000			−0.884615
$677$			18.0000i			0.691796i	0.938272	+	0.345898i	$0.112426\pi$
$677$			18.0000i			0.691796i	−0.938272	+	0.345898i	$0.887574\pi$
$678$			24.0000i			0.921714i
$679$		0			0
$680$	18.0000	+	36.0000i	0.690268	+	1.38054i
$681$	−16.0000			−0.613121
$682$		0			0
$683$		−	26.0000i		−	0.994862i	−0.867503	−	0.497431i	$-0.834277\pi$
$683$		−	26.0000i		−	0.994862i	0.867503	−	0.497431i	$-0.165723\pi$
$684$		0			0
$685$	40.0000	−	20.0000i	1.52832	−	0.764161i
$686$	−1.00000			−0.0381802
$687$		−	44.0000i		−	1.67870i
$688$		−	8.00000i		−	0.304997i
$689$	24.0000			0.914327
$690$	24.0000	−	12.0000i	0.913664	−	0.456832i
$691$	4.00000			0.152167			0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000			0.152167			0.0760836	+	0.997101i	$0.475758\pi$
$692$			18.0000i			0.684257i
$693$			1.00000i			0.0379869i
$694$	−4.00000			−0.151838
$695$	−12.0000	−	24.0000i	−0.455186	−	0.910372i
$696$	36.0000			1.36458
$697$			36.0000i			1.36360i
$698$			10.0000i			0.378506i
$699$	−44.0000			−1.66423
$700$	4.00000	+	3.00000i	0.151186	+	0.113389i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$			24.0000i			0.905822i
$703$		0			0
$704$	−7.00000			−0.263822
$705$	−20.0000	−	40.0000i	−0.753244	−	1.50649i
$706$	−20.0000			−0.752710
$707$			14.0000i			0.526524i
$708$			24.0000i			0.901975i
$709$	−46.0000			−1.72757			−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000			−1.72757			−0.863783	+	0.503864i	$0.831911\pi$
$710$	−16.0000	+	8.00000i	−0.600469	+	0.300235i
$711$	8.00000			0.300023
$712$			18.0000i			0.674579i
$713$		0			0
$714$	−12.0000			−0.449089
$715$	−12.0000	+	6.00000i	−0.448775	+	0.224387i
$716$	−12.0000			−0.448461
$717$		0			0
$718$			24.0000i			0.895672i
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$	1.00000	+	2.00000i	0.0372678	+	0.0745356i
$721$	−14.0000			−0.521387
$722$		−	19.0000i		−	0.707107i
$723$		−	20.0000i		−	0.743808i
$724$	10.0000			0.371647
$725$	−18.0000	+	24.0000i	−0.668503	+	0.891338i
$726$	2.00000			0.0742270
$727$		−	22.0000i		−	0.815935i	−0.912996	−	0.407967i	$-0.866238\pi$
$727$		−	22.0000i		−	0.815935i	0.912996	−	0.407967i	$-0.133762\pi$
$728$			18.0000i			0.667124i
$729$	−13.0000			−0.481481
$730$	2.00000	+	4.00000i	0.0740233	+	0.148047i
$731$	48.0000			1.77534
$732$			20.0000i			0.739221i
$733$			50.0000i			1.84679i	0.383849	+	0.923396i	$0.374598\pi$
$733$			50.0000i			1.84679i	−0.383849	+	0.923396i	$0.625402\pi$
$734$	−22.0000			−0.812035
$735$	−4.00000	+	2.00000i	−0.147542	+	0.0737711i
$736$	30.0000			1.10581
$737$		−	2.00000i		−	0.0736709i
$738$			6.00000i			0.220863i
$739$	−16.0000			−0.588570			−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000			−0.588570			−0.294285	+	0.955718i	$0.595081\pi$
$740$	−8.00000	+	4.00000i	−0.294086	+	0.147043i
$741$		0			0
$742$		−	4.00000i		−	0.146845i
$743$		−	12.0000i		−	0.440237i	−0.975473	−	0.220119i	$-0.929356\pi$
$743$		−	12.0000i		−	0.440237i	0.975473	−	0.220119i	$-0.0706445\pi$
$744$		0			0
$745$	10.0000	+	20.0000i	0.366372	+	0.732743i
$746$	14.0000			0.512576
$747$		0			0
$748$		−	6.00000i		−	0.219382i
$749$	12.0000			0.438470
$750$	−22.0000	−	4.00000i	−0.803326	−	0.146059i
$751$	40.0000			1.45962			0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000			1.45962			0.729810	+	0.683650i	$0.239608\pi$
$752$			10.0000i			0.364662i
$753$			24.0000i			0.874609i
$754$	−36.0000			−1.31104
$755$	4.00000	+	8.00000i	0.145575	+	0.291150i
$756$	−4.00000			−0.145479
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		−	12.0000i		−	0.435860i
$759$	−12.0000			−0.435572
$760$		0			0
$761$	−42.0000			−1.52250			−0.761249	−	0.648459i	$-0.775414\pi$
$761$	−42.0000			−1.52250			−0.761249	+	0.648459i	$0.775414\pi$
$762$		−	24.0000i		−	0.869428i
$763$			6.00000i			0.217215i
$764$	8.00000			0.289430
$765$	−12.0000	+	6.00000i	−0.433861	+	0.216930i
$766$	−18.0000			−0.650366
$767$		−	72.0000i		−	2.59977i
$768$			34.0000i			1.22687i
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$	1.00000	+	2.00000i	0.0360375	+	0.0720750i
$771$	−8.00000			−0.288113
$772$			14.0000i			0.503871i
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$	8.00000			0.287554
$775$		0			0
$776$		0			0
$777$		−	8.00000i		−	0.286998i
$778$		−	26.0000i		−	0.932145i
$779$		0			0
$780$	12.0000	+	24.0000i	0.429669	+	0.859338i
$781$	8.00000			0.286263
$782$		−	36.0000i		−	1.28736i
$783$		−	24.0000i		−	0.857690i
$784$	1.00000			0.0357143
$785$	−8.00000	+	4.00000i	−0.285532	+	0.142766i
$786$	24.0000			0.856052
$787$		−	4.00000i		−	0.142585i	−0.997455	−	0.0712923i	$-0.977288\pi$
$787$		−	4.00000i		−	0.142585i	0.997455	−	0.0712923i	$-0.0227123\pi$
$788$		−	18.0000i		−	0.641223i
$789$	−56.0000			−1.99365
$790$	16.0000	−	8.00000i	0.569254	−	0.284627i
$791$	12.0000			0.426671
$792$		−	3.00000i		−	0.106600i
$793$		−	60.0000i		−	2.13066i
$794$	28.0000			0.993683
$795$	−8.00000	−	16.0000i	−0.283731	−	0.567462i
$796$	8.00000			0.283552
$797$			44.0000i			1.55856i	0.626676	+	0.779280i	$0.284415\pi$
$797$			44.0000i			1.55856i	−0.626676	+	0.779280i	$0.715585\pi$
$798$		0			0
$799$	−60.0000			−2.12265
$800$	−20.0000	−	15.0000i	−0.707107	−	0.530330i
$801$	−6.00000			−0.212000
$802$		−	2.00000i		−	0.0706225i
$803$		−	2.00000i		−	0.0705785i
$804$	−4.00000			−0.141069
$805$	−6.00000	−	12.0000i	−0.211472	−	0.422944i
$806$		0			0
$807$		−	60.0000i		−	2.11210i
$808$		−	42.0000i		−	1.47755i
$809$	50.0000			1.75791			0.878953	−	0.476908i	$-0.158243\pi$
$809$	50.0000			1.75791			0.878953	+	0.476908i	$0.158243\pi$
$810$	22.0000	−	11.0000i	0.773001	−	0.386501i
$811$	−32.0000			−1.12367			−0.561836	−	0.827249i	$-0.689905\pi$
$811$	−32.0000			−1.12367			−0.561836	+	0.827249i	$0.689905\pi$
$812$		−	6.00000i		−	0.210559i
$813$		−	32.0000i		−	1.12229i
$814$	−4.00000			−0.140200
$815$	−36.0000	+	18.0000i	−1.26102	+	0.630512i
$816$	12.0000			0.420084
$817$		0			0
$818$		−	14.0000i		−	0.489499i
$819$	−6.00000			−0.209657
$820$	−6.00000	−	12.0000i	−0.209529	−	0.419058i
$821$	26.0000			0.907406			0.453703	−	0.891153i	$-0.350103\pi$
$821$	26.0000			0.907406			0.453703	+	0.891153i	$0.350103\pi$
$822$		−	40.0000i		−	1.39516i
$823$			46.0000i			1.60346i	0.597687	+	0.801730i	$0.296087\pi$
$823$			46.0000i			1.60346i	−0.597687	+	0.801730i	$0.703913\pi$
$824$	42.0000			1.46314
$825$	8.00000	+	6.00000i	0.278524	+	0.208893i
$826$	−12.0000			−0.417533
$827$			12.0000i			0.417281i	0.977992	+	0.208640i	$0.0669038\pi$
$827$			12.0000i			0.417281i	−0.977992	+	0.208640i	$0.933096\pi$
$828$			6.00000i			0.208514i
$829$	42.0000			1.45872			0.729360	−	0.684130i	$-0.239818\pi$
$829$	42.0000			1.45872			0.729360	+	0.684130i	$0.239818\pi$
$830$		0			0
$831$	4.00000			0.138758
$832$		−	42.0000i		−	1.45609i
$833$			6.00000i			0.207888i
$834$	−24.0000			−0.831052
$835$	−40.0000	+	20.0000i	−1.38426	+	0.692129i
$836$		0			0
$837$		0			0
$838$		−	12.0000i		−	0.414533i
$839$	16.0000			0.552381			0.276191	−	0.961103i	$-0.410928\pi$
$839$	16.0000			0.552381			0.276191	+	0.961103i	$0.410928\pi$
$840$	12.0000	−	6.00000i	0.414039	−	0.207020i
$841$	7.00000			0.241379
$842$			26.0000i			0.896019i
$843$		−	12.0000i		−	0.413302i
$844$	8.00000			0.275371
$845$	−23.0000	−	46.0000i	−0.791224	−	1.58245i
$846$	−10.0000			−0.343807
$847$		−	1.00000i		−	0.0343604i
$848$			4.00000i			0.137361i
$849$	32.0000			1.09824
$850$	−18.0000	+	24.0000i	−0.617395	+	0.823193i
$851$	24.0000			0.822709
$852$		−	16.0000i		−	0.548151i
$853$			26.0000i			0.890223i	0.895475	+	0.445112i	$0.146836\pi$
$853$			26.0000i			0.890223i	−0.895475	+	0.445112i	$0.853164\pi$
$854$	−10.0000			−0.342193
$855$		0			0
$856$	−36.0000			−1.23045
$857$			26.0000i			0.888143i	0.895991	+	0.444072i	$0.146466\pi$
$857$			26.0000i			0.888143i	−0.895991	+	0.444072i	$0.853534\pi$
$858$			12.0000i			0.409673i
$859$	44.0000			1.50126			0.750630	−	0.660722i	$-0.229750\pi$
$859$	44.0000			1.50126			0.750630	+	0.660722i	$0.229750\pi$
$860$	−16.0000	+	8.00000i	−0.545595	+	0.272798i
$861$	12.0000			0.408959
$862$		0			0
$863$			6.00000i			0.204242i	0.994772	+	0.102121i	$0.0325630\pi$
$863$			6.00000i			0.204242i	−0.994772	+	0.102121i	$0.967437\pi$
$864$	20.0000			0.680414
$865$	−36.0000	+	18.0000i	−1.22404	+	0.612018i
$866$	−16.0000			−0.543702
$867$			38.0000i			1.29055i
$868$		0			0
$869$	−8.00000			−0.271381
$870$	12.0000	+	24.0000i	0.406838	+	0.813676i
$871$	12.0000			0.406604
$872$		−	18.0000i		−	0.609557i
$873$		0			0
$874$		0			0
$875$	−2.00000	+	11.0000i	−0.0676123	+	0.371868i
$876$	−4.00000			−0.135147
$877$			22.0000i			0.742887i	0.928456	+	0.371444i	$0.121137\pi$
$877$			22.0000i			0.742887i	−0.928456	+	0.371444i	$0.878863\pi$
$878$		−	40.0000i		−	1.34993i
$879$	−52.0000			−1.75392
$880$	−1.00000	−	2.00000i	−0.0337100	−	0.0674200i
$881$	−14.0000			−0.471672			−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000			−0.471672			−0.235836	+	0.971793i	$0.575783\pi$
$882$			1.00000i			0.0336718i
$883$			2.00000i			0.0673054i	0.999434	+	0.0336527i	$0.0107140\pi$
$883$			2.00000i			0.0673054i	−0.999434	+	0.0336527i	$0.989286\pi$
$884$	36.0000			1.21081
$885$	−48.0000	+	24.0000i	−1.61350	+	0.806751i
$886$	−26.0000			−0.873487
$887$		−	28.0000i		−	0.940148i	−0.882627	−	0.470074i	$-0.844227\pi$
$887$		−	28.0000i		−	0.940148i	0.882627	−	0.470074i	$-0.155773\pi$
$888$			24.0000i			0.805387i
$889$	−12.0000			−0.402467
$890$	−12.0000	+	6.00000i	−0.402241	+	0.201120i
$891$	−11.0000			−0.368514
$892$		−	2.00000i		−	0.0669650i
$893$		0			0
$894$	20.0000			0.668900
$895$	−12.0000	−	24.0000i	−0.401116	−	0.802232i
$896$	3.00000			0.100223
$897$		−	72.0000i		−	2.40401i
$898$			30.0000i			1.00111i
$899$		0			0
$900$	3.00000	−	4.00000i	0.100000	−	0.133333i
$901$	−24.0000			−0.799556
$902$		−	6.00000i		−	0.199778i
$903$		−	16.0000i		−	0.532447i
$904$	−36.0000			−1.19734
$905$	10.0000	+	20.0000i	0.332411	+	0.664822i
$906$	8.00000			0.265782
$907$		−	50.0000i		−	1.66022i	−0.557598	−	0.830111i	$-0.688277\pi$
$907$		−	50.0000i		−	1.66022i	0.557598	−	0.830111i	$-0.311723\pi$
$908$		−	8.00000i		−	0.265489i
$909$	14.0000			0.464351
$910$	−12.0000	+	6.00000i	−0.397796	+	0.198898i
$911$	16.0000			0.530104			0.265052	−	0.964234i	$-0.414611\pi$
$911$	16.0000			0.530104			0.265052	+	0.964234i	$0.414611\pi$
$912$		0			0
$913$		0			0
$914$	2.00000			0.0661541
$915$	−40.0000	+	20.0000i	−1.32236	+	0.661180i
$916$	22.0000			0.726900
$917$		−	12.0000i		−	0.396275i
$918$		−	24.0000i		−	0.792118i
$919$	−20.0000			−0.659739			−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000			−0.659739			−0.329870	+	0.944027i	$0.607005\pi$
$920$	18.0000	+	36.0000i	0.593442	+	1.18688i
$921$	−40.0000			−1.31804
$922$			10.0000i			0.329332i
$923$			48.0000i			1.57994i
$924$	−2.00000			−0.0657952
$925$	−16.0000	−	12.0000i	−0.526077	−	0.394558i
$926$	−26.0000			−0.854413
$927$			14.0000i			0.459820i
$928$			30.0000i			0.984798i
$929$	34.0000			1.11550			0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000			1.11550			0.557752	+	0.830008i	$0.311664\pi$
$930$		0			0
$931$		0			0
$932$		−	22.0000i		−	0.720634i
$933$			16.0000i			0.523816i
$934$	30.0000			0.981630
$935$	12.0000	−	6.00000i	0.392442	−	0.196221i
$936$	18.0000			0.588348
$937$		−	26.0000i		−	0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$		−	26.0000i		−	0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$		−	2.00000i		−	0.0653023i
$939$	56.0000			1.82749
$940$	20.0000	−	10.0000i	0.652328	−	0.326164i
$941$	26.0000			0.847576			0.423788	−	0.905761i	$-0.360700\pi$
$941$	26.0000			0.847576			0.423788	+	0.905761i	$0.360700\pi$
$942$			8.00000i			0.260654i
$943$			36.0000i			1.17232i
$944$	12.0000			0.390567
$945$	−4.00000	−	8.00000i	−0.130120	−	0.260240i
$946$	−8.00000			−0.260102
$947$		−	26.0000i		−	0.844886i	−0.906389	−	0.422443i	$-0.861173\pi$
$947$		−	26.0000i		−	0.844886i	0.906389	−	0.422443i	$-0.138827\pi$
$948$			16.0000i			0.519656i
$949$	12.0000			0.389536
$950$		0			0
$951$	16.0000			0.518836
$952$		−	18.0000i		−	0.583383i
$953$			26.0000i			0.842223i	0.907009	+	0.421111i	$0.138360\pi$
$953$			26.0000i			0.842223i	−0.907009	+	0.421111i	$0.861640\pi$
$954$	−4.00000			−0.129505
$955$	8.00000	+	16.0000i	0.258874	+	0.517748i
$956$		0			0
$957$		−	12.0000i		−	0.387905i
$958$			4.00000i			0.129234i
$959$	−20.0000			−0.645834
$960$	−28.0000	+	14.0000i	−0.903696	+	0.451848i
$961$	−31.0000			−1.00000
$962$		−	24.0000i		−	0.773791i
$963$		−	12.0000i		−	0.386695i
$964$	10.0000			0.322078
$965$	−28.0000	+	14.0000i	−0.901352	+	0.450676i
$966$	−12.0000			−0.386094
$967$		−	20.0000i		−	0.643157i	−0.946883	−	0.321578i	$-0.895787\pi$
$967$		−	20.0000i		−	0.643157i	0.946883	−	0.321578i	$-0.104213\pi$
$968$			3.00000i			0.0964237i
$969$		0			0
$970$		0			0
$971$	−36.0000			−1.15529			−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000			−1.15529			−0.577647	+	0.816286i	$0.696029\pi$
$972$			10.0000i			0.320750i
$973$			12.0000i			0.384702i
$974$	−2.00000			−0.0640841
$975$	−36.0000	+	48.0000i	−1.15292	+	1.53723i
$976$	10.0000			0.320092
$977$			52.0000i			1.66363i	0.555055	+	0.831814i	$0.312697\pi$
$977$			52.0000i			1.66363i	−0.555055	+	0.831814i	$0.687303\pi$
$978$			36.0000i			1.15115i
$979$	6.00000			0.191761
$980$	−1.00000	−	2.00000i	−0.0319438	−	0.0638877i
$981$	6.00000			0.191565
$982$		−	12.0000i		−	0.382935i
$983$		−	54.0000i		−	1.72233i	−0.508323	−	0.861166i	$-0.669735\pi$
$983$		−	54.0000i		−	1.72233i	0.508323	−	0.861166i	$-0.330265\pi$
$984$	−36.0000			−1.14764
$985$	36.0000	−	18.0000i	1.14706	−	0.573528i
$986$	36.0000			1.14647
$987$			20.0000i			0.636607i
$988$		0			0
$989$	48.0000			1.52631
$990$	2.00000	−	1.00000i	0.0635642	−	0.0317821i
$991$	−48.0000			−1.52477			−0.762385	−	0.647124i	$-0.775972\pi$
$991$	−48.0000			−1.52477			−0.762385	+	0.647124i	$0.775972\pi$
$992$		0			0
$993$		−	40.0000i		−	1.26936i
$994$	8.00000			0.253745
$995$	8.00000	+	16.0000i	0.253617	+	0.507234i
$996$		0			0
$997$		−	10.0000i		−	0.316703i	−0.987383	−	0.158352i	$-0.949382\pi$
$997$		−	10.0000i		−	0.316703i	0.987383	−	0.158352i	$-0.0506179\pi$
$998$			36.0000i			1.13956i
$999$	16.0000			0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.b.a.309.2	yes	2
5.2	odd	4		1925.2.a.d.1.1		1
5.3	odd	4		1925.2.a.k.1.1		1
5.4	even	2	inner	385.2.b.a.309.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.b.a.309.1	✓	2	5.4	even	2	inner
385.2.b.a.309.2	yes	2	1.1	even	1	trivial
1925.2.a.d.1.1		1	5.2	odd	4
1925.2.a.k.1.1		1	5.3	odd	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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.00000i q^{3} +1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} +2.00000 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -2.00000i q^{3} +1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} +2.00000 q^{6} -1.00000i q^{7} +3.00000i q^{8} -1.00000 q^{9} +(-2.00000 + 1.00000i) q^{10} +1.00000 q^{11} -2.00000i q^{12} +6.00000i q^{13} +1.00000 q^{14} +(4.00000 - 2.00000i) q^{15} -1.00000 q^{16} -6.00000i q^{17} -1.00000i q^{18} +(1.00000 + 2.00000i) q^{20} -2.00000 q^{21} +1.00000i q^{22} -6.00000i q^{23} +6.00000 q^{24} +(-3.00000 + 4.00000i) q^{25} -6.00000 q^{26} -4.00000i q^{27} -1.00000i q^{28} +6.00000 q^{29} +(2.00000 + 4.00000i) q^{30} +5.00000i q^{32} -2.00000i q^{33} +6.00000 q^{34} +(2.00000 - 1.00000i) q^{35} -1.00000 q^{36} +4.00000i q^{37} +12.0000 q^{39} +(-6.00000 + 3.00000i) q^{40} -6.00000 q^{41} -2.00000i q^{42} +8.00000i q^{43} +1.00000 q^{44} +(-1.00000 - 2.00000i) q^{45} +6.00000 q^{46} -10.0000i q^{47} +2.00000i q^{48} -1.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -12.0000 q^{51} +6.00000i q^{52} -4.00000i q^{53} +4.00000 q^{54} +(1.00000 + 2.00000i) q^{55} +3.00000 q^{56} +6.00000i q^{58} -12.0000 q^{59} +(4.00000 - 2.00000i) q^{60} -10.0000 q^{61} +1.00000i q^{63} -7.00000 q^{64} +(-12.0000 + 6.00000i) q^{65} +2.00000 q^{66} -2.00000i q^{67} -6.00000i q^{68} -12.0000 q^{69} +(1.00000 + 2.00000i) q^{70} +8.00000 q^{71} -3.00000i q^{72} -2.00000i q^{73} -4.00000 q^{74} +(8.00000 + 6.00000i) q^{75} -1.00000i q^{77} +12.0000i q^{78} -8.00000 q^{79} +(-1.00000 - 2.00000i) q^{80} -11.0000 q^{81} -6.00000i q^{82} -2.00000 q^{84} +(12.0000 - 6.00000i) q^{85} -8.00000 q^{86} -12.0000i q^{87} +3.00000i q^{88} +6.00000 q^{89} +(2.00000 - 1.00000i) q^{90} +6.00000 q^{91} -6.00000i q^{92} +10.0000 q^{94} +10.0000 q^{96} -1.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^4 + 2 * q^5 + 4 * q^6 - 2 * q^9	\( 2 q + 2 q^{4} + 2 q^{5} + 4 q^{6} - 2 q^{9} - 4 q^{10} + 2 q^{11} + 2 q^{14} + 8 q^{15} - 2 q^{16} + 2 q^{20} - 4 q^{21} + 12 q^{24} - 6 q^{25} - 12 q^{26} + 12 q^{29} + 4 q^{30} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 24 q^{39} - 12 q^{40} - 12 q^{41} + 2 q^{44} - 2 q^{45} + 12 q^{46} - 2 q^{49} - 8 q^{50} - 24 q^{51} + 8 q^{54} + 2 q^{55} + 6 q^{56} - 24 q^{59} + 8 q^{60} - 20 q^{61} - 14 q^{64} - 24 q^{65} + 4 q^{66} - 24 q^{69} + 2 q^{70} + 16 q^{71} - 8 q^{74} + 16 q^{75} - 16 q^{79} - 2 q^{80} - 22 q^{81} - 4 q^{84} + 24 q^{85} - 16 q^{86} + 12 q^{89} + 4 q^{90} + 12 q^{91} + 20 q^{94} + 20 q^{96} - 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^4 + 2 * q^5 + 4 * q^6 - 2 * q^9 - 4 * q^10 + 2 * q^11 + 2 * q^14 + 8 * q^15 - 2 * q^16 + 2 * q^20 - 4 * q^21 + 12 * q^24 - 6 * q^25 - 12 * q^26 + 12 * q^29 + 4 * q^30 + 12 * q^34 + 4 * q^35 - 2 * q^36 + 24 * q^39 - 12 * q^40 - 12 * q^41 + 2 * q^44 - 2 * q^45 + 12 * q^46 - 2 * q^49 - 8 * q^50 - 24 * q^51 + 8 * q^54 + 2 * q^55 + 6 * q^56 - 24 * q^59 + 8 * q^60 - 20 * q^61 - 14 * q^64 - 24 * q^65 + 4 * q^66 - 24 * q^69 + 2 * q^70 + 16 * q^71 - 8 * q^74 + 16 * q^75 - 16 * q^79 - 2 * q^80 - 22 * q^81 - 4 * q^84 + 24 * q^85 - 16 * q^86 + 12 * q^89 + 4 * q^90 + 12 * q^91 + 20 * q^94 + 20 * q^96 - 2 * q^99

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