LMFDB - Embedded newform 1170.2.s.c.1061.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(161,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,12,0,0,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1061.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1170.1061
Dual form			1170.2.s.c.161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(3.00000 - 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{10} +(2.82843 + 2.82843i) q^{11} +(-2.00000 - 3.00000i) q^{13} +4.24264i q^{14} -1.00000 q^{16} -2.82843 q^{17} +(5.00000 + 5.00000i) q^{19} +(-0.707107 - 0.707107i) q^{20} -4.00000 q^{22} +7.07107 q^{23} -1.00000i q^{25} +(3.53553 + 0.707107i) q^{26} +(-3.00000 - 3.00000i) q^{28} -2.82843i q^{29} +(-6.00000 - 6.00000i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.00000 - 2.00000i) q^{34} -4.24264i q^{35} +(-1.00000 + 1.00000i) q^{37} -7.07107 q^{38} +1.00000 q^{40} +(-5.65685 + 5.65685i) q^{41} -12.0000i q^{43} +(2.82843 - 2.82843i) q^{44} +(-5.00000 + 5.00000i) q^{46} +(5.65685 + 5.65685i) q^{47} -11.0000i q^{49} +(0.707107 + 0.707107i) q^{50} +(-3.00000 + 2.00000i) q^{52} +1.41421i q^{53} +4.00000 q^{55} +4.24264 q^{56} +(2.00000 + 2.00000i) q^{58} +(-8.48528 - 8.48528i) q^{59} +6.00000 q^{61} +8.48528 q^{62} +1.00000i q^{64} +(-3.53553 - 0.707107i) q^{65} +(6.00000 + 6.00000i) q^{67} +2.82843i q^{68} +(3.00000 + 3.00000i) q^{70} +(2.82843 - 2.82843i) q^{71} +(8.00000 - 8.00000i) q^{73} -1.41421i q^{74} +(5.00000 - 5.00000i) q^{76} +16.9706 q^{77} -4.00000 q^{79} +(-0.707107 + 0.707107i) q^{80} -8.00000i q^{82} +(2.82843 - 2.82843i) q^{83} +(-2.00000 + 2.00000i) q^{85} +(8.48528 + 8.48528i) q^{86} +4.00000i q^{88} +(5.65685 + 5.65685i) q^{89} +(-15.0000 - 3.00000i) q^{91} -7.07107i q^{92} -8.00000 q^{94} +7.07107 q^{95} +(7.77817 + 7.77817i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{7} - 8 q^{13} - 4 q^{16} + 20 q^{19} - 16 q^{22} - 12 q^{28} - 24 q^{31} + 8 q^{34} - 4 q^{37} + 4 q^{40} - 20 q^{46} - 12 q^{52} + 16 q^{55} + 8 q^{58} + 24 q^{61} + 24 q^{67} + 12 q^{70} + 32 q^{73}+ \cdots - 32 q^{94}+O(q^{100}) $ 4 * q + 12 * q^7 - 8 * q^13 - 4 * q^16 + 20 * q^19 - 16 * q^22 - 12 * q^28 - 24 * q^31 + 8 * q^34 - 4 * q^37 + 4 * q^40 - 20 * q^46 - 12 * q^52 + 16 * q^55 + 8 * q^58 + 24 * q^61 + 24 * q^67 + 12 * q^70 + 32 * q^73 + 20 * q^76 - 16 * q^79 - 8 * q^85 - 60 * q^91 - 32 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$	3.00000	−	3.00000i	1.13389	−	1.13389i	0.144370	−	0.989524i	$-0.453885\pi$
$7$	3.00000	−	3.00000i	1.13389	−	1.13389i	0.989524	−	0.144370i	$-0.0461154\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$			1.00000i			0.316228i
$11$	2.82843	+	2.82843i	0.852803	+	0.852803i	0.990478	−	0.137675i	$-0.0439628\pi$
$11$	2.82843	+	2.82843i	0.852803	+	0.852803i	−0.137675	+	0.990478i	$0.543963\pi$
$12$		0			0
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$14$			4.24264i			1.13389i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.82843			−0.685994			−0.342997	−	0.939336i	$-0.611442\pi$
$17$	−2.82843			−0.685994			−0.342997	+	0.939336i	$0.611442\pi$
$18$		0			0
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.987124	+	0.159954i	$0.0511347\pi$
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.159954	+	0.987124i	$0.448865\pi$
$20$	−0.707107	−	0.707107i	−0.158114	−	0.158114i
$21$		0			0
$22$	−4.00000			−0.852803
$23$	7.07107			1.47442			0.737210	−	0.675664i	$-0.236143\pi$
$23$	7.07107			1.47442			0.737210	+	0.675664i	$0.236143\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	3.53553	+	0.707107i	0.693375	+	0.138675i
$27$		0			0
$28$	−3.00000	−	3.00000i	−0.566947	−	0.566947i
$29$		−	2.82843i		−	0.525226i	−0.964901	−	0.262613i	$-0.915416\pi$
$29$		−	2.82843i		−	0.525226i	0.964901	−	0.262613i	$-0.0845842\pi$
$30$		0			0
$31$	−6.00000	−	6.00000i	−1.07763	−	1.07763i	−0.996721	−	0.0809104i	$-0.974217\pi$
$31$	−6.00000	−	6.00000i	−1.07763	−	1.07763i	−0.0809104	−	0.996721i	$-0.525783\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	2.00000	−	2.00000i	0.342997	−	0.342997i
$35$		−	4.24264i		−	0.717137i
$36$		0			0
$37$	−1.00000	+	1.00000i	−0.164399	+	0.164399i	−0.784512	−	0.620113i	$-0.787087\pi$
$37$	−1.00000	+	1.00000i	−0.164399	+	0.164399i	0.620113	+	0.784512i	$0.287087\pi$
$38$	−7.07107			−1.14708
$39$		0			0
$40$	1.00000			0.158114
$41$	−5.65685	+	5.65685i	−0.883452	+	0.883452i	−0.993884	−	0.110432i	$-0.964777\pi$
$41$	−5.65685	+	5.65685i	−0.883452	+	0.883452i	0.110432	+	0.993884i	$0.464777\pi$
$42$		0			0
$43$		−	12.0000i		−	1.82998i	−0.403473	−	0.914991i	$-0.632197\pi$
$43$		−	12.0000i		−	1.82998i	0.403473	−	0.914991i	$-0.367803\pi$
$44$	2.82843	−	2.82843i	0.426401	−	0.426401i
$45$		0			0
$46$	−5.00000	+	5.00000i	−0.737210	+	0.737210i
$47$	5.65685	+	5.65685i	0.825137	+	0.825137i	0.986840	−	0.161703i	$-0.0516985\pi$
$47$	5.65685	+	5.65685i	0.825137	+	0.825137i	−0.161703	+	0.986840i	$0.551699\pi$
$48$		0			0
$49$		−	11.0000i		−	1.57143i
$50$	0.707107	+	0.707107i	0.100000	+	0.100000i
$51$		0			0
$52$	−3.00000	+	2.00000i	−0.416025	+	0.277350i
$53$			1.41421i			0.194257i	0.995272	+	0.0971286i	$0.0309658\pi$
$53$			1.41421i			0.194257i	−0.995272	+	0.0971286i	$0.969034\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$	4.24264			0.566947
$57$		0			0
$58$	2.00000	+	2.00000i	0.262613	+	0.262613i
$59$	−8.48528	−	8.48528i	−1.10469	−	1.10469i	−0.993837	−	0.110853i	$-0.964642\pi$
$59$	−8.48528	−	8.48528i	−1.10469	−	1.10469i	−0.110853	−	0.993837i	$-0.535358\pi$
$60$		0			0
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$	8.48528			1.07763
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−3.53553	−	0.707107i	−0.438529	−	0.0877058i
$66$		0			0
$67$	6.00000	+	6.00000i	0.733017	+	0.733017i	0.971216	−	0.238200i	$-0.0765572\pi$
$67$	6.00000	+	6.00000i	0.733017	+	0.733017i	−0.238200	+	0.971216i	$0.576557\pi$
$68$			2.82843i			0.342997i
$69$		0			0
$70$	3.00000	+	3.00000i	0.358569	+	0.358569i
$71$	2.82843	−	2.82843i	0.335673	−	0.335673i	−0.519063	−	0.854736i	$-0.673719\pi$
$71$	2.82843	−	2.82843i	0.335673	−	0.335673i	0.854736	+	0.519063i	$0.173719\pi$
$72$		0			0
$73$	8.00000	−	8.00000i	0.936329	−	0.936329i	−0.0617617	−	0.998091i	$-0.519672\pi$
$73$	8.00000	−	8.00000i	0.936329	−	0.936329i	0.998091	+	0.0617617i	$0.0196719\pi$
$74$		−	1.41421i		−	0.164399i
$75$		0			0
$76$	5.00000	−	5.00000i	0.573539	−	0.573539i
$77$	16.9706			1.93398
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−0.707107	+	0.707107i	−0.0790569	+	0.0790569i
$81$		0			0
$82$		−	8.00000i		−	0.883452i
$83$	2.82843	−	2.82843i	0.310460	−	0.310460i	−0.534628	−	0.845088i	$-0.679548\pi$
$83$	2.82843	−	2.82843i	0.310460	−	0.310460i	0.845088	+	0.534628i	$0.179548\pi$
$84$		0			0
$85$	−2.00000	+	2.00000i	−0.216930	+	0.216930i
$86$	8.48528	+	8.48528i	0.914991	+	0.914991i
$87$		0			0
$88$			4.00000i			0.426401i
$89$	5.65685	+	5.65685i	0.599625	+	0.599625i	0.940213	−	0.340587i	$-0.110626\pi$
$89$	5.65685	+	5.65685i	0.599625	+	0.599625i	−0.340587	+	0.940213i	$0.610626\pi$
$90$		0			0
$91$	−15.0000	−	3.00000i	−1.57243	−	0.314485i
$92$		−	7.07107i		−	0.737210i
$93$		0			0
$94$	−8.00000			−0.825137
$95$	7.07107			0.725476
$96$		0			0
$97$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$97$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$98$	7.77817	+	7.77817i	0.785714	+	0.785714i
$99$		0			0
$100$	−1.00000			−0.100000
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$			2.00000i			0.197066i	0.995134	+	0.0985329i	$0.0314150\pi$
$103$			2.00000i			0.197066i	−0.995134	+	0.0985329i	$0.968585\pi$
$104$	0.707107	−	3.53553i	0.0693375	−	0.346688i
$105$		0			0
$106$	−1.00000	−	1.00000i	−0.0971286	−	0.0971286i
$107$			16.9706i			1.64061i	0.571929	+	0.820303i	$0.306195\pi$
$107$			16.9706i			1.64061i	−0.571929	+	0.820303i	$0.693805\pi$
$108$		0			0
$109$	12.0000	+	12.0000i	1.14939	+	1.14939i	0.986672	+	0.162719i	$0.0520264\pi$
$109$	12.0000	+	12.0000i	1.14939	+	1.14939i	0.162719	+	0.986672i	$0.447974\pi$
$110$	−2.82843	+	2.82843i	−0.269680	+	0.269680i
$111$		0			0
$112$	−3.00000	+	3.00000i	−0.283473	+	0.283473i
$113$		−	11.3137i		−	1.06430i	−0.846649	−	0.532152i	$-0.821383\pi$
$113$		−	11.3137i		−	1.06430i	0.846649	−	0.532152i	$-0.178617\pi$
$114$		0			0
$115$	5.00000	−	5.00000i	0.466252	−	0.466252i
$116$	−2.82843			−0.262613
$117$		0			0
$118$	12.0000			1.10469
$119$	−8.48528	+	8.48528i	−0.777844	+	0.777844i
$120$		0			0
$121$			5.00000i			0.454545i
$122$	−4.24264	+	4.24264i	−0.384111	+	0.384111i
$123$		0			0
$124$	−6.00000	+	6.00000i	−0.538816	+	0.538816i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$			14.0000i			1.24230i	0.783692	+	0.621150i	$0.213334\pi$
$127$			14.0000i			1.24230i	−0.783692	+	0.621150i	$0.786666\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	3.00000	−	2.00000i	0.263117	−	0.175412i
$131$		−	7.07107i		−	0.617802i	−0.951094	−	0.308901i	$-0.900039\pi$
$131$		−	7.07107i		−	0.617802i	0.951094	−	0.308901i	$-0.0999612\pi$
$132$		0			0
$133$	30.0000			2.60133
$134$	−8.48528			−0.733017
$135$		0			0
$136$	−2.00000	−	2.00000i	−0.171499	−	0.171499i
$137$	−12.7279	−	12.7279i	−1.08742	−	1.08742i	−0.995793	−	0.0916263i	$-0.970793\pi$
$137$	−12.7279	−	12.7279i	−1.08742	−	1.08742i	−0.0916263	−	0.995793i	$-0.529207\pi$
$138$		0			0
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$	−4.24264			−0.358569
$141$		0			0
$142$			4.00000i			0.335673i
$143$	2.82843	−	14.1421i	0.236525	−	1.18262i
$144$		0			0
$145$	−2.00000	−	2.00000i	−0.166091	−	0.166091i
$146$			11.3137i			0.936329i
$147$		0			0
$148$	1.00000	+	1.00000i	0.0821995	+	0.0821995i
$149$	4.24264	−	4.24264i	0.347571	−	0.347571i	−0.511633	−	0.859204i	$-0.670959\pi$
$149$	4.24264	−	4.24264i	0.347571	−	0.347571i	0.859204	+	0.511633i	$0.170959\pi$
$150$		0			0
$151$	−6.00000	+	6.00000i	−0.488273	+	0.488273i	−0.907761	−	0.419488i	$-0.862210\pi$
$151$	−6.00000	+	6.00000i	−0.488273	+	0.488273i	0.419488	+	0.907761i	$0.362210\pi$
$152$			7.07107i			0.573539i
$153$		0			0
$154$	−12.0000	+	12.0000i	−0.966988	+	0.966988i
$155$	−8.48528			−0.681554
$156$		0			0
$157$	16.0000			1.27694			0.638470	−	0.769647i	$-0.279568\pi$
$157$	16.0000			1.27694			0.638470	+	0.769647i	$0.279568\pi$
$158$	2.82843	−	2.82843i	0.225018	−	0.225018i
$159$		0			0
$160$		−	1.00000i		−	0.0790569i
$161$	21.2132	−	21.2132i	1.67183	−	1.67183i
$162$		0			0
$163$	12.0000	−	12.0000i	0.939913	−	0.939913i	−0.0583818	−	0.998294i	$-0.518594\pi$
$163$	12.0000	−	12.0000i	0.939913	−	0.939913i	0.998294	+	0.0583818i	$0.0185941\pi$
$164$	5.65685	+	5.65685i	0.441726	+	0.441726i
$165$		0			0
$166$			4.00000i			0.310460i
$167$	−12.7279	−	12.7279i	−0.984916	−	0.984916i	0.0149717	−	0.999888i	$-0.495234\pi$
$167$	−12.7279	−	12.7279i	−0.984916	−	0.984916i	−0.999888	+	0.0149717i	$0.995234\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$		−	2.82843i		−	0.216930i
$171$		0			0
$172$	−12.0000			−0.914991
$173$	−7.07107			−0.537603			−0.268802	−	0.963196i	$-0.586628\pi$
$173$	−7.07107			−0.537603			−0.268802	+	0.963196i	$0.586628\pi$
$174$		0			0
$175$	−3.00000	−	3.00000i	−0.226779	−	0.226779i
$176$	−2.82843	−	2.82843i	−0.213201	−	0.213201i
$177$		0			0
$178$	−8.00000			−0.599625
$179$	−24.0416			−1.79696			−0.898478	−	0.439019i	$-0.855326\pi$
$179$	−24.0416			−1.79696			−0.898478	+	0.439019i	$0.855326\pi$
$180$		0			0
$181$			14.0000i			1.04061i	0.853980	+	0.520306i	$0.174182\pi$
$181$			14.0000i			1.04061i	−0.853980	+	0.520306i	$0.825818\pi$
$182$	12.7279	−	8.48528i	0.943456	−	0.628971i
$183$		0			0
$184$	5.00000	+	5.00000i	0.368605	+	0.368605i
$185$			1.41421i			0.103975i
$186$		0			0
$187$	−8.00000	−	8.00000i	−0.585018	−	0.585018i
$188$	5.65685	−	5.65685i	0.412568	−	0.412568i
$189$		0			0
$190$	−5.00000	+	5.00000i	−0.362738	+	0.362738i
$191$			22.6274i			1.63726i	0.574320	+	0.818631i	$0.305267\pi$
$191$			22.6274i			1.63726i	−0.574320	+	0.818631i	$0.694733\pi$
$192$		0			0
$193$	6.00000	−	6.00000i	0.431889	−	0.431889i	−0.457381	−	0.889271i	$-0.651213\pi$
$193$	6.00000	−	6.00000i	0.431889	−	0.431889i	0.889271	+	0.457381i	$0.151213\pi$
$194$		0			0
$195$		0			0
$196$	−11.0000			−0.785714
$197$	2.82843	−	2.82843i	0.201517	−	0.201517i	−0.599133	−	0.800650i	$-0.704488\pi$
$197$	2.82843	−	2.82843i	0.201517	−	0.201517i	0.800650	+	0.599133i	$0.204488\pi$
$198$		0			0
$199$		−	8.00000i		−	0.567105i	−0.958957	−	0.283552i	$-0.908487\pi$
$199$		−	8.00000i		−	0.567105i	0.958957	−	0.283552i	$-0.0915130\pi$
$200$	0.707107	−	0.707107i	0.0500000	−	0.0500000i
$201$		0			0
$202$		0			0
$203$	−8.48528	−	8.48528i	−0.595550	−	0.595550i
$204$		0			0
$205$			8.00000i			0.558744i
$206$	−1.41421	−	1.41421i	−0.0985329	−	0.0985329i
$207$		0			0
$208$	2.00000	+	3.00000i	0.138675	+	0.208013i
$209$			28.2843i			1.95646i
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	1.41421			0.0971286
$213$		0			0
$214$	−12.0000	−	12.0000i	−0.820303	−	0.820303i
$215$	−8.48528	−	8.48528i	−0.578691	−	0.578691i
$216$		0			0
$217$	−36.0000			−2.44384
$218$	−16.9706			−1.14939
$219$		0			0
$220$		−	4.00000i		−	0.269680i
$221$	5.65685	+	8.48528i	0.380521	+	0.570782i
$222$		0			0
$223$	3.00000	+	3.00000i	0.200895	+	0.200895i	0.800383	−	0.599489i	$-0.204629\pi$
$223$	3.00000	+	3.00000i	0.200895	+	0.200895i	−0.599489	+	0.800383i	$0.704629\pi$
$224$		−	4.24264i		−	0.283473i
$225$		0			0
$226$	8.00000	+	8.00000i	0.532152	+	0.532152i
$227$	−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	$0.380377\pi$
$228$		0			0
$229$	4.00000	−	4.00000i	0.264327	−	0.264327i	−0.562482	−	0.826809i	$-0.690153\pi$
$229$	4.00000	−	4.00000i	0.264327	−	0.264327i	0.826809	+	0.562482i	$0.190153\pi$
$230$			7.07107i			0.466252i
$231$		0			0
$232$	2.00000	−	2.00000i	0.131306	−	0.131306i
$233$	2.82843			0.185296			0.0926482	−	0.995699i	$-0.470467\pi$
$233$	2.82843			0.185296			0.0926482	+	0.995699i	$0.470467\pi$
$234$		0			0
$235$	8.00000			0.521862
$236$	−8.48528	+	8.48528i	−0.552345	+	0.552345i
$237$		0			0
$238$		−	12.0000i		−	0.777844i
$239$	2.82843	−	2.82843i	0.182956	−	0.182956i	−0.609687	−	0.792642i	$-0.708705\pi$
$239$	2.82843	−	2.82843i	0.182956	−	0.182956i	0.792642	+	0.609687i	$0.208705\pi$
$240$		0			0
$241$	−15.0000	+	15.0000i	−0.966235	+	0.966235i	−0.999448	−	0.0332133i	$-0.989426\pi$
$241$	−15.0000	+	15.0000i	−0.966235	+	0.966235i	0.0332133	+	0.999448i	$0.489426\pi$
$242$	−3.53553	−	3.53553i	−0.227273	−	0.227273i
$243$		0			0
$244$		−	6.00000i		−	0.384111i
$245$	−7.77817	−	7.77817i	−0.496929	−	0.496929i
$246$		0			0
$247$	5.00000	−	25.0000i	0.318142	−	1.59071i
$248$		−	8.48528i		−	0.538816i
$249$		0			0
$250$	1.00000			0.0632456
$251$	−1.41421			−0.0892644			−0.0446322	−	0.999003i	$-0.514212\pi$
$251$	−1.41421			−0.0892644			−0.0446322	+	0.999003i	$0.514212\pi$
$252$		0			0
$253$	20.0000	+	20.0000i	1.25739	+	1.25739i
$254$	−9.89949	−	9.89949i	−0.621150	−	0.621150i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−16.9706			−1.05859			−0.529297	−	0.848436i	$-0.677544\pi$
$257$	−16.9706			−1.05859			−0.529297	+	0.848436i	$0.677544\pi$
$258$		0			0
$259$			6.00000i			0.372822i
$260$	−0.707107	+	3.53553i	−0.0438529	+	0.219265i
$261$		0			0
$262$	5.00000	+	5.00000i	0.308901	+	0.308901i
$263$		−	1.41421i		−	0.0872041i	−0.999049	−	0.0436021i	$-0.986117\pi$
$263$		−	1.41421i		−	0.0872041i	0.999049	−	0.0436021i	$-0.0138834\pi$
$264$		0			0
$265$	1.00000	+	1.00000i	0.0614295	+	0.0614295i
$266$	−21.2132	+	21.2132i	−1.30066	+	1.30066i
$267$		0			0
$268$	6.00000	−	6.00000i	0.366508	−	0.366508i
$269$			5.65685i			0.344904i	0.985018	+	0.172452i	$0.0551690\pi$
$269$			5.65685i			0.344904i	−0.985018	+	0.172452i	$0.944831\pi$
$270$		0			0
$271$	−14.0000	+	14.0000i	−0.850439	+	0.850439i	−0.990187	−	0.139748i	$-0.955371\pi$
$271$	−14.0000	+	14.0000i	−0.850439	+	0.850439i	0.139748	+	0.990187i	$0.455371\pi$
$272$	2.82843			0.171499
$273$		0			0
$274$	18.0000			1.08742
$275$	2.82843	−	2.82843i	0.170561	−	0.170561i
$276$		0			0
$277$			22.0000i			1.32185i	0.750451	+	0.660926i	$0.229836\pi$
$277$			22.0000i			1.32185i	−0.750451	+	0.660926i	$0.770164\pi$
$278$	9.89949	−	9.89949i	0.593732	−	0.593732i
$279$		0			0
$280$	3.00000	−	3.00000i	0.179284	−	0.179284i
$281$	1.41421	+	1.41421i	0.0843649	+	0.0843649i	0.748030	−	0.663665i	$-0.231000\pi$
$281$	1.41421	+	1.41421i	0.0843649	+	0.0843649i	−0.663665	+	0.748030i	$0.731000\pi$
$282$		0			0
$283$		−	16.0000i		−	0.951101i	−0.879688	−	0.475551i	$-0.842249\pi$
$283$		−	16.0000i		−	0.951101i	0.879688	−	0.475551i	$-0.157751\pi$
$284$	−2.82843	−	2.82843i	−0.167836	−	0.167836i
$285$		0			0
$286$	8.00000	+	12.0000i	0.473050	+	0.709575i
$287$			33.9411i			2.00348i
$288$		0			0
$289$	−9.00000			−0.529412
$290$	2.82843			0.166091
$291$		0			0
$292$	−8.00000	−	8.00000i	−0.468165	−	0.468165i
$293$	−1.41421	−	1.41421i	−0.0826192	−	0.0826192i	0.664589	−	0.747209i	$-0.268606\pi$
$293$	−1.41421	−	1.41421i	−0.0826192	−	0.0826192i	−0.747209	+	0.664589i	$0.768606\pi$
$294$		0			0
$295$	−12.0000			−0.698667
$296$	−1.41421			−0.0821995
$297$		0			0
$298$			6.00000i			0.347571i
$299$	−14.1421	−	21.2132i	−0.817861	−	1.22679i
$300$		0			0
$301$	−36.0000	−	36.0000i	−2.07501	−	2.07501i
$302$		−	8.48528i		−	0.488273i
$303$		0			0
$304$	−5.00000	−	5.00000i	−0.286770	−	0.286770i
$305$	4.24264	−	4.24264i	0.242933	−	0.242933i
$306$		0			0
$307$	6.00000	−	6.00000i	0.342438	−	0.342438i	−0.514845	−	0.857283i	$-0.672151\pi$
$307$	6.00000	−	6.00000i	0.342438	−	0.342438i	0.857283	+	0.514845i	$0.172151\pi$
$308$		−	16.9706i		−	0.966988i
$309$		0			0
$310$	6.00000	−	6.00000i	0.340777	−	0.340777i
$311$	−5.65685			−0.320771			−0.160385	−	0.987054i	$-0.551274\pi$
$311$	−5.65685			−0.320771			−0.160385	+	0.987054i	$0.551274\pi$
$312$		0			0
$313$	−26.0000			−1.46961			−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000			−1.46961			−0.734803	+	0.678280i	$0.762726\pi$
$314$	−11.3137	+	11.3137i	−0.638470	+	0.638470i
$315$		0			0
$316$			4.00000i			0.225018i
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	−0.666276	−	0.745706i	$-0.732113\pi$
$317$	1.41421	−	1.41421i	0.0794301	−	0.0794301i	0.745706	+	0.666276i	$0.232113\pi$
$318$		0			0
$319$	8.00000	−	8.00000i	0.447914	−	0.447914i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$		0			0
$322$			30.0000i			1.67183i
$323$	−14.1421	−	14.1421i	−0.786889	−	0.786889i
$324$		0			0
$325$	−3.00000	+	2.00000i	−0.166410	+	0.110940i
$326$			16.9706i			0.939913i
$327$		0			0
$328$	−8.00000			−0.441726
$329$	33.9411			1.87123
$330$		0			0
$331$	−9.00000	−	9.00000i	−0.494685	−	0.494685i	0.415094	−	0.909779i	$-0.363749\pi$
$331$	−9.00000	−	9.00000i	−0.494685	−	0.494685i	−0.909779	+	0.415094i	$0.863749\pi$
$332$	−2.82843	−	2.82843i	−0.155230	−	0.155230i
$333$		0			0
$334$	18.0000			0.984916
$335$	8.48528			0.463600
$336$		0			0
$337$			14.0000i			0.762629i	0.924445	+	0.381314i	$0.124528\pi$
$337$			14.0000i			0.762629i	−0.924445	+	0.381314i	$0.875472\pi$
$338$	−4.94975	−	12.0208i	−0.269231	−	0.653846i
$339$		0			0
$340$	2.00000	+	2.00000i	0.108465	+	0.108465i
$341$		−	33.9411i		−	1.83801i
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	8.48528	−	8.48528i	0.457496	−	0.457496i
$345$		0			0
$346$	5.00000	−	5.00000i	0.268802	−	0.268802i
$347$			25.4558i			1.36654i	0.730165	+	0.683271i	$0.239443\pi$
$347$			25.4558i			1.36654i	−0.730165	+	0.683271i	$0.760557\pi$
$348$		0			0
$349$	−20.0000	+	20.0000i	−1.07058	+	1.07058i	−0.0732628	+	0.997313i	$0.523341\pi$
$349$	−20.0000	+	20.0000i	−1.07058	+	1.07058i	−0.997313	+	0.0732628i	$0.976659\pi$
$350$	4.24264			0.226779
$351$		0			0
$352$	4.00000			0.213201
$353$	−4.24264	+	4.24264i	−0.225813	+	0.225813i	−0.810941	−	0.585128i	$-0.801044\pi$
$353$	−4.24264	+	4.24264i	−0.225813	+	0.225813i	0.585128	+	0.810941i	$0.301044\pi$
$354$		0			0
$355$		−	4.00000i		−	0.212298i
$356$	5.65685	−	5.65685i	0.299813	−	0.299813i
$357$		0			0
$358$	17.0000	−	17.0000i	0.898478	−	0.898478i
$359$	−22.6274	−	22.6274i	−1.19423	−	1.19423i	−0.975868	−	0.218361i	$-0.929929\pi$
$359$	−22.6274	−	22.6274i	−1.19423	−	1.19423i	−0.218361	−	0.975868i	$-0.570071\pi$
$360$		0			0
$361$			31.0000i			1.63158i
$362$	−9.89949	−	9.89949i	−0.520306	−	0.520306i
$363$		0			0
$364$	−3.00000	+	15.0000i	−0.157243	+	0.786214i
$365$		−	11.3137i		−	0.592187i
$366$		0			0
$367$	−10.0000			−0.521996			−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000			−0.521996			−0.260998	+	0.965339i	$0.584052\pi$
$368$	−7.07107			−0.368605
$369$		0			0
$370$	−1.00000	−	1.00000i	−0.0519875	−	0.0519875i
$371$	4.24264	+	4.24264i	0.220267	+	0.220267i
$372$		0			0
$373$	32.0000			1.65690			0.828449	−	0.560065i	$-0.189224\pi$
$373$	32.0000			1.65690			0.828449	+	0.560065i	$0.189224\pi$
$374$	11.3137			0.585018
$375$		0			0
$376$			8.00000i			0.412568i
$377$	−8.48528	+	5.65685i	−0.437014	+	0.291343i
$378$		0			0
$379$	−3.00000	−	3.00000i	−0.154100	−	0.154100i	0.625847	−	0.779946i	$-0.284754\pi$
$379$	−3.00000	−	3.00000i	−0.154100	−	0.154100i	−0.779946	+	0.625847i	$0.784754\pi$
$380$		−	7.07107i		−	0.362738i
$381$		0			0
$382$	−16.0000	−	16.0000i	−0.818631	−	0.818631i
$383$	−21.2132	+	21.2132i	−1.08394	+	1.08394i	−0.0878065	+	0.996138i	$0.527986\pi$
$383$	−21.2132	+	21.2132i	−1.08394	+	1.08394i	−0.996138	+	0.0878065i	$0.972014\pi$
$384$		0			0
$385$	12.0000	−	12.0000i	0.611577	−	0.611577i
$386$			8.48528i			0.431889i
$387$		0			0
$388$		0			0
$389$	−11.3137			−0.573628			−0.286814	−	0.957986i	$-0.592596\pi$
$389$	−11.3137			−0.573628			−0.286814	+	0.957986i	$0.592596\pi$
$390$		0			0
$391$	−20.0000			−1.01144
$392$	7.77817	−	7.77817i	0.392857	−	0.392857i
$393$		0			0
$394$			4.00000i			0.201517i
$395$	−2.82843	+	2.82843i	−0.142314	+	0.142314i
$396$		0			0
$397$	1.00000	−	1.00000i	0.0501886	−	0.0501886i	−0.681567	−	0.731756i	$-0.738701\pi$
$397$	1.00000	−	1.00000i	0.0501886	−	0.0501886i	0.731756	+	0.681567i	$0.238701\pi$
$398$	5.65685	+	5.65685i	0.283552	+	0.283552i
$399$		0			0
$400$			1.00000i			0.0500000i
$401$	12.7279	+	12.7279i	0.635602	+	0.635602i	0.949467	−	0.313865i	$-0.101624\pi$
$401$	12.7279	+	12.7279i	0.635602	+	0.635602i	−0.313865	+	0.949467i	$0.601624\pi$
$402$		0			0
$403$	−6.00000	+	30.0000i	−0.298881	+	1.49441i
$404$		0			0
$405$		0			0
$406$	12.0000			0.595550
$407$	−5.65685			−0.280400
$408$		0			0
$409$	19.0000	+	19.0000i	0.939490	+	0.939490i	0.998271	−	0.0587813i	$-0.0187215\pi$
$409$	19.0000	+	19.0000i	0.939490	+	0.939490i	−0.0587813	+	0.998271i	$0.518721\pi$
$410$	−5.65685	−	5.65685i	−0.279372	−	0.279372i
$411$		0			0
$412$	2.00000			0.0985329
$413$	−50.9117			−2.50520
$414$		0			0
$415$		−	4.00000i		−	0.196352i
$416$	−3.53553	−	0.707107i	−0.173344	−	0.0346688i
$417$		0			0
$418$	−20.0000	−	20.0000i	−0.978232	−	0.978232i
$419$			4.24264i			0.207267i	0.994616	+	0.103633i	$0.0330468\pi$
$419$			4.24264i			0.207267i	−0.994616	+	0.103633i	$0.966953\pi$
$420$		0			0
$421$	−14.0000	−	14.0000i	−0.682318	−	0.682318i	0.278204	−	0.960522i	$-0.410261\pi$
$421$	−14.0000	−	14.0000i	−0.682318	−	0.682318i	−0.960522	+	0.278204i	$0.910261\pi$
$422$	−14.1421	+	14.1421i	−0.688428	+	0.688428i
$423$		0			0
$424$	−1.00000	+	1.00000i	−0.0485643	+	0.0485643i
$425$			2.82843i			0.137199i
$426$		0			0
$427$	18.0000	−	18.0000i	0.871081	−	0.871081i
$428$	16.9706			0.820303
$429$		0			0
$430$	12.0000			0.578691
$431$	16.9706	−	16.9706i	0.817443	−	0.817443i	−0.168294	−	0.985737i	$-0.553826\pi$
$431$	16.9706	−	16.9706i	0.817443	−	0.817443i	0.985737	+	0.168294i	$0.0538257\pi$
$432$		0			0
$433$			18.0000i			0.865025i	0.901628	+	0.432512i	$0.142373\pi$
$433$			18.0000i			0.865025i	−0.901628	+	0.432512i	$0.857627\pi$
$434$	25.4558	−	25.4558i	1.22192	−	1.22192i
$435$		0			0
$436$	12.0000	−	12.0000i	0.574696	−	0.574696i
$437$	35.3553	+	35.3553i	1.69128	+	1.69128i
$438$		0			0
$439$			8.00000i			0.381819i	0.981608	+	0.190910i	$0.0611437\pi$
$439$			8.00000i			0.381819i	−0.981608	+	0.190910i	$0.938856\pi$
$440$	2.82843	+	2.82843i	0.134840	+	0.134840i
$441$		0			0
$442$	−10.0000	−	2.00000i	−0.475651	−	0.0951303i
$443$			19.7990i			0.940678i	0.882486	+	0.470339i	$0.155868\pi$
$443$			19.7990i			0.940678i	−0.882486	+	0.470339i	$0.844132\pi$
$444$		0			0
$445$	8.00000			0.379236
$446$	−4.24264			−0.200895
$447$		0			0
$448$	3.00000	+	3.00000i	0.141737	+	0.141737i
$449$	22.6274	+	22.6274i	1.06785	+	1.06785i	0.997524	+	0.0703301i	$0.0224052\pi$
$449$	22.6274	+	22.6274i	1.06785	+	1.06785i	0.0703301	+	0.997524i	$0.477595\pi$
$450$		0			0
$451$	−32.0000			−1.50682
$452$	−11.3137			−0.532152
$453$		0			0
$454$		−	12.0000i		−	0.563188i
$455$	−12.7279	+	8.48528i	−0.596694	+	0.397796i
$456$		0			0
$457$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$457$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$458$			5.65685i			0.264327i
$459$		0			0
$460$	−5.00000	−	5.00000i	−0.233126	−	0.233126i
$461$	7.07107	−	7.07107i	0.329332	−	0.329332i	−0.523000	−	0.852333i	$-0.675187\pi$
$461$	7.07107	−	7.07107i	0.329332	−	0.329332i	0.852333	+	0.523000i	$0.175187\pi$
$462$		0			0
$463$	21.0000	−	21.0000i	0.975953	−	0.975953i	−0.0237648	−	0.999718i	$-0.507565\pi$
$463$	21.0000	−	21.0000i	0.975953	−	0.975953i	0.999718	+	0.0237648i	$0.00756529\pi$
$464$			2.82843i			0.131306i
$465$		0			0
$466$	−2.00000	+	2.00000i	−0.0926482	+	0.0926482i
$467$	28.2843			1.30884			0.654420	−	0.756131i	$-0.272913\pi$
$467$	28.2843			1.30884			0.654420	+	0.756131i	$0.272913\pi$
$468$		0			0
$469$	36.0000			1.66233
$470$	−5.65685	+	5.65685i	−0.260931	+	0.260931i
$471$		0			0
$472$		−	12.0000i		−	0.552345i
$473$	33.9411	−	33.9411i	1.56061	−	1.56061i
$474$		0			0
$475$	5.00000	−	5.00000i	0.229416	−	0.229416i
$476$	8.48528	+	8.48528i	0.388922	+	0.388922i
$477$		0			0
$478$			4.00000i			0.182956i
$479$	25.4558	+	25.4558i	1.16311	+	1.16311i	0.983792	+	0.179316i	$0.0573883\pi$
$479$	25.4558	+	25.4558i	1.16311	+	1.16311i	0.179316	+	0.983792i	$0.442612\pi$
$480$		0			0
$481$	5.00000	+	1.00000i	0.227980	+	0.0455961i
$482$		−	21.2132i		−	0.966235i
$483$		0			0
$484$	5.00000			0.227273
$485$		0			0
$486$		0			0
$487$	3.00000	+	3.00000i	0.135943	+	0.135943i	0.771804	−	0.635861i	$-0.219355\pi$
$487$	3.00000	+	3.00000i	0.135943	+	0.135943i	−0.635861	+	0.771804i	$0.719355\pi$
$488$	4.24264	+	4.24264i	0.192055	+	0.192055i
$489$		0			0
$490$	11.0000			0.496929
$491$	−18.3848			−0.829693			−0.414847	−	0.909891i	$-0.636165\pi$
$491$	−18.3848			−0.829693			−0.414847	+	0.909891i	$0.636165\pi$
$492$		0			0
$493$			8.00000i			0.360302i
$494$	14.1421	+	21.2132i	0.636285	+	0.954427i
$495$		0			0
$496$	6.00000	+	6.00000i	0.269408	+	0.269408i
$497$		−	16.9706i		−	0.761234i
$498$		0			0
$499$	5.00000	+	5.00000i	0.223831	+	0.223831i	0.810109	−	0.586279i	$-0.199408\pi$
$499$	5.00000	+	5.00000i	0.223831	+	0.223831i	−0.586279	+	0.810109i	$0.699408\pi$
$500$	−0.707107	+	0.707107i	−0.0316228	+	0.0316228i
$501$		0			0
$502$	1.00000	−	1.00000i	0.0446322	−	0.0446322i
$503$			38.1838i			1.70253i	0.524736	+	0.851265i	$0.324164\pi$
$503$			38.1838i			1.70253i	−0.524736	+	0.851265i	$0.675836\pi$
$504$		0			0
$505$		0			0
$506$	−28.2843			−1.25739
$507$		0			0
$508$	14.0000			0.621150
$509$	12.7279	−	12.7279i	0.564155	−	0.564155i	−0.366330	−	0.930485i	$-0.619386\pi$
$509$	12.7279	−	12.7279i	0.564155	−	0.564155i	0.930485	+	0.366330i	$0.119386\pi$
$510$		0			0
$511$		−	48.0000i		−	2.12339i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	12.0000	−	12.0000i	0.529297	−	0.529297i
$515$	1.41421	+	1.41421i	0.0623177	+	0.0623177i
$516$		0			0
$517$			32.0000i			1.40736i
$518$	−4.24264	−	4.24264i	−0.186411	−	0.186411i
$519$		0			0
$520$	−2.00000	−	3.00000i	−0.0877058	−	0.131559i
$521$			32.5269i			1.42503i	0.701657	+	0.712515i	$0.252444\pi$
$521$			32.5269i			1.42503i	−0.701657	+	0.712515i	$0.747556\pi$
$522$		0			0
$523$	−12.0000			−0.524723			−0.262362	−	0.964970i	$-0.584501\pi$
$523$	−12.0000			−0.524723			−0.262362	+	0.964970i	$0.584501\pi$
$524$	−7.07107			−0.308901
$525$		0			0
$526$	1.00000	+	1.00000i	0.0436021	+	0.0436021i
$527$	16.9706	+	16.9706i	0.739249	+	0.739249i
$528$		0			0
$529$	27.0000			1.17391
$530$	−1.41421			−0.0614295
$531$		0			0
$532$		−	30.0000i		−	1.30066i
$533$	28.2843	+	5.65685i	1.22513	+	0.245026i
$534$		0			0
$535$	12.0000	+	12.0000i	0.518805	+	0.518805i
$536$			8.48528i			0.366508i
$537$		0			0
$538$	−4.00000	−	4.00000i	−0.172452	−	0.172452i
$539$	31.1127	−	31.1127i	1.34012	−	1.34012i
$540$		0			0
$541$	−6.00000	+	6.00000i	−0.257960	+	0.257960i	−0.824224	−	0.566264i	$-0.808388\pi$
$541$	−6.00000	+	6.00000i	−0.257960	+	0.257960i	0.566264	+	0.824224i	$0.308388\pi$
$542$		−	19.7990i		−	0.850439i
$543$		0			0
$544$	−2.00000	+	2.00000i	−0.0857493	+	0.0857493i
$545$	16.9706			0.726939
$546$		0			0
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$	−12.7279	+	12.7279i	−0.543710	+	0.543710i
$549$		0			0
$550$			4.00000i			0.170561i
$551$	14.1421	−	14.1421i	0.602475	−	0.602475i
$552$		0			0
$553$	−12.0000	+	12.0000i	−0.510292	+	0.510292i
$554$	−15.5563	−	15.5563i	−0.660926	−	0.660926i
$555$		0			0
$556$			14.0000i			0.593732i
$557$	−16.9706	−	16.9706i	−0.719066	−	0.719066i	0.249348	−	0.968414i	$-0.419784\pi$
$557$	−16.9706	−	16.9706i	−0.719066	−	0.719066i	−0.968414	+	0.249348i	$0.919784\pi$
$558$		0			0
$559$	−36.0000	+	24.0000i	−1.52264	+	1.01509i
$560$			4.24264i			0.179284i
$561$		0			0
$562$	−2.00000			−0.0843649
$563$	−14.1421			−0.596020			−0.298010	−	0.954563i	$-0.596323\pi$
$563$	−14.1421			−0.596020			−0.298010	+	0.954563i	$0.596323\pi$
$564$		0			0
$565$	−8.00000	−	8.00000i	−0.336563	−	0.336563i
$566$	11.3137	+	11.3137i	0.475551	+	0.475551i
$567$		0			0
$568$	4.00000			0.167836
$569$	−1.41421			−0.0592869			−0.0296435	−	0.999561i	$-0.509437\pi$
$569$	−1.41421			−0.0592869			−0.0296435	+	0.999561i	$0.509437\pi$
$570$		0			0
$571$			6.00000i			0.251092i	0.992088	+	0.125546i	$0.0400683\pi$
$571$			6.00000i			0.251092i	−0.992088	+	0.125546i	$0.959932\pi$
$572$	−14.1421	−	2.82843i	−0.591312	−	0.118262i
$573$		0			0
$574$	−24.0000	−	24.0000i	−1.00174	−	1.00174i
$575$		−	7.07107i		−	0.294884i
$576$		0			0
$577$	10.0000	+	10.0000i	0.416305	+	0.416305i	0.883928	−	0.467623i	$-0.154889\pi$
$577$	10.0000	+	10.0000i	0.416305	+	0.416305i	−0.467623	+	0.883928i	$0.654889\pi$
$578$	6.36396	−	6.36396i	0.264706	−	0.264706i
$579$		0			0
$580$	−2.00000	+	2.00000i	−0.0830455	+	0.0830455i
$581$		−	16.9706i		−	0.704058i
$582$		0			0
$583$	−4.00000	+	4.00000i	−0.165663	+	0.165663i
$584$	11.3137			0.468165
$585$		0			0
$586$	2.00000			0.0826192
$587$	28.2843	−	28.2843i	1.16742	−	1.16742i	0.184604	−	0.982813i	$-0.440900\pi$
$587$	28.2843	−	28.2843i	1.16742	−	1.16742i	0.982813	−	0.184604i	$-0.0591002\pi$
$588$		0			0
$589$		−	60.0000i		−	2.47226i
$590$	8.48528	−	8.48528i	0.349334	−	0.349334i
$591$		0			0
$592$	1.00000	−	1.00000i	0.0410997	−	0.0410997i
$593$	−4.24264	−	4.24264i	−0.174224	−	0.174224i	0.614608	−	0.788833i	$-0.289314\pi$
$593$	−4.24264	−	4.24264i	−0.174224	−	0.174224i	−0.788833	+	0.614608i	$0.789314\pi$
$594$		0			0
$595$			12.0000i			0.491952i
$596$	−4.24264	−	4.24264i	−0.173785	−	0.173785i
$597$		0			0
$598$	25.0000	+	5.00000i	1.02233	+	0.204465i
$599$			39.5980i			1.61793i	0.587857	+	0.808965i	$0.299972\pi$
$599$			39.5980i			1.61793i	−0.587857	+	0.808965i	$0.700028\pi$
$600$		0			0
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$	50.9117			2.07501
$603$		0			0
$604$	6.00000	+	6.00000i	0.244137	+	0.244137i
$605$	3.53553	+	3.53553i	0.143740	+	0.143740i
$606$		0			0
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$	7.07107			0.286770
$609$		0			0
$610$			6.00000i			0.242933i
$611$	5.65685	−	28.2843i	0.228852	−	1.14426i
$612$		0			0
$613$	1.00000	+	1.00000i	0.0403896	+	0.0403896i	0.727013	−	0.686624i	$-0.240908\pi$
$613$	1.00000	+	1.00000i	0.0403896	+	0.0403896i	−0.686624	+	0.727013i	$0.740908\pi$
$614$			8.48528i			0.342438i
$615$		0			0
$616$	12.0000	+	12.0000i	0.483494	+	0.483494i
$617$	−18.3848	+	18.3848i	−0.740143	+	0.740143i	−0.972605	−	0.232462i	$-0.925322\pi$
$617$	−18.3848	+	18.3848i	−0.740143	+	0.740143i	0.232462	+	0.972605i	$0.425322\pi$
$618$		0			0
$619$	29.0000	−	29.0000i	1.16561	−	1.16561i	0.182380	−	0.983228i	$-0.441620\pi$
$619$	29.0000	−	29.0000i	1.16561	−	1.16561i	0.983228	−	0.182380i	$-0.0583802\pi$
$620$			8.48528i			0.340777i
$621$		0			0
$622$	4.00000	−	4.00000i	0.160385	−	0.160385i
$623$	33.9411			1.35982
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	18.3848	−	18.3848i	0.734803	−	0.734803i
$627$		0			0
$628$		−	16.0000i		−	0.638470i
$629$	2.82843	−	2.82843i	0.112777	−	0.112777i
$630$		0			0
$631$	−16.0000	+	16.0000i	−0.636950	+	0.636950i	−0.949802	−	0.312852i	$-0.898716\pi$
$631$	−16.0000	+	16.0000i	−0.636950	+	0.636950i	0.312852	+	0.949802i	$0.398716\pi$
$632$	−2.82843	−	2.82843i	−0.112509	−	0.112509i
$633$		0			0
$634$			2.00000i			0.0794301i
$635$	9.89949	+	9.89949i	0.392849	+	0.392849i
$636$		0			0
$637$	−33.0000	+	22.0000i	−1.30751	+	0.871672i
$638$			11.3137i			0.447914i
$639$		0			0
$640$	−1.00000			−0.0395285
$641$	−15.5563			−0.614439			−0.307219	−	0.951639i	$-0.599399\pi$
$641$	−15.5563			−0.614439			−0.307219	+	0.951639i	$0.599399\pi$
$642$		0			0
$643$	−26.0000	−	26.0000i	−1.02534	−	1.02534i	−0.999670	−	0.0256694i	$-0.991828\pi$
$643$	−26.0000	−	26.0000i	−1.02534	−	1.02534i	−0.0256694	−	0.999670i	$-0.508172\pi$
$644$	−21.2132	−	21.2132i	−0.835917	−	0.835917i
$645$		0			0
$646$	20.0000			0.786889
$647$	−15.5563			−0.611583			−0.305792	−	0.952098i	$-0.598921\pi$
$647$	−15.5563			−0.611583			−0.305792	+	0.952098i	$0.598921\pi$
$648$		0			0
$649$		−	48.0000i		−	1.88416i
$650$	0.707107	−	3.53553i	0.0277350	−	0.138675i
$651$		0			0
$652$	−12.0000	−	12.0000i	−0.469956	−	0.469956i
$653$			4.24264i			0.166027i	0.996548	+	0.0830137i	$0.0264545\pi$
$653$			4.24264i			0.166027i	−0.996548	+	0.0830137i	$0.973545\pi$
$654$		0			0
$655$	−5.00000	−	5.00000i	−0.195366	−	0.195366i
$656$	5.65685	−	5.65685i	0.220863	−	0.220863i
$657$		0			0
$658$	−24.0000	+	24.0000i	−0.935617	+	0.935617i
$659$			26.8701i			1.04671i	0.852115	+	0.523354i	$0.175320\pi$
$659$			26.8701i			1.04671i	−0.852115	+	0.523354i	$0.824680\pi$
$660$		0			0
$661$	−6.00000	+	6.00000i	−0.233373	+	0.233373i	−0.814099	−	0.580726i	$-0.802769\pi$
$661$	−6.00000	+	6.00000i	−0.233373	+	0.233373i	0.580726	+	0.814099i	$0.302769\pi$
$662$	12.7279			0.494685
$663$		0			0
$664$	4.00000			0.155230
$665$	21.2132	−	21.2132i	0.822613	−	0.822613i
$666$		0			0
$667$		−	20.0000i		−	0.774403i
$668$	−12.7279	+	12.7279i	−0.492458	+	0.492458i
$669$		0			0
$670$	−6.00000	+	6.00000i	−0.231800	+	0.231800i
$671$	16.9706	+	16.9706i	0.655141	+	0.655141i
$672$		0			0
$673$			10.0000i			0.385472i	0.981251	+	0.192736i	$0.0617360\pi$
$673$			10.0000i			0.385472i	−0.981251	+	0.192736i	$0.938264\pi$
$674$	−9.89949	−	9.89949i	−0.381314	−	0.381314i
$675$		0			0
$676$	12.0000	+	5.00000i	0.461538	+	0.192308i
$677$		−	24.0416i		−	0.923995i	−0.886881	−	0.461997i	$-0.847133\pi$
$677$		−	24.0416i		−	0.923995i	0.886881	−	0.461997i	$-0.152867\pi$
$678$		0			0
$679$		0			0
$680$	−2.82843			−0.108465
$681$		0			0
$682$	24.0000	+	24.0000i	0.919007	+	0.919007i
$683$	−16.9706	−	16.9706i	−0.649361	−	0.649361i	0.303478	−	0.952838i	$-0.401852\pi$
$683$	−16.9706	−	16.9706i	−0.649361	−	0.649361i	−0.952838	+	0.303478i	$0.901852\pi$
$684$		0			0
$685$	−18.0000			−0.687745
$686$	16.9706			0.647939
$687$		0			0
$688$			12.0000i			0.457496i
$689$	4.24264	−	2.82843i	0.161632	−	0.107754i
$690$		0			0
$691$	33.0000	+	33.0000i	1.25538	+	1.25538i	0.953275	+	0.302104i	$0.0976891\pi$
$691$	33.0000	+	33.0000i	1.25538	+	1.25538i	0.302104	+	0.953275i	$0.402311\pi$
$692$			7.07107i			0.268802i
$693$		0			0
$694$	−18.0000	−	18.0000i	−0.683271	−	0.683271i
$695$	−9.89949	+	9.89949i	−0.375509	+	0.375509i
$696$		0			0
$697$	16.0000	−	16.0000i	0.606043	−	0.606043i
$698$		−	28.2843i		−	1.07058i
$699$		0			0
$700$	−3.00000	+	3.00000i	−0.113389	+	0.113389i
$701$	28.2843			1.06828			0.534141	−	0.845395i	$-0.320635\pi$
$701$	28.2843			1.06828			0.534141	+	0.845395i	$0.320635\pi$
$702$		0			0
$703$	−10.0000			−0.377157
$704$	−2.82843	+	2.82843i	−0.106600	+	0.106600i
$705$		0			0
$706$		−	6.00000i		−	0.225813i
$707$		0			0
$708$		0			0
$709$	−12.0000	+	12.0000i	−0.450669	+	0.450669i	−0.895577	−	0.444907i	$-0.853237\pi$
$709$	−12.0000	+	12.0000i	−0.450669	+	0.450669i	0.444907	+	0.895577i	$0.353237\pi$
$710$	2.82843	+	2.82843i	0.106149	+	0.106149i
$711$		0			0
$712$			8.00000i			0.299813i
$713$	−42.4264	−	42.4264i	−1.58888	−	1.58888i
$714$		0			0
$715$	−8.00000	−	12.0000i	−0.299183	−	0.448775i
$716$			24.0416i			0.898478i
$717$		0			0
$718$	32.0000			1.19423
$719$	19.7990			0.738378			0.369189	−	0.929354i	$-0.379636\pi$
$719$	19.7990			0.738378			0.369189	+	0.929354i	$0.379636\pi$
$720$		0			0
$721$	6.00000	+	6.00000i	0.223452	+	0.223452i
$722$	−21.9203	−	21.9203i	−0.815789	−	0.815789i
$723$		0			0
$724$	14.0000			0.520306
$725$	−2.82843			−0.105045
$726$		0			0
$727$			32.0000i			1.18681i	0.804902	+	0.593407i	$0.202218\pi$
$727$			32.0000i			1.18681i	−0.804902	+	0.593407i	$0.797782\pi$
$728$	−8.48528	−	12.7279i	−0.314485	−	0.471728i
$729$		0			0
$730$	8.00000	+	8.00000i	0.296093	+	0.296093i
$731$			33.9411i			1.25536i
$732$		0			0
$733$	−15.0000	−	15.0000i	−0.554038	−	0.554038i	0.373566	−	0.927604i	$-0.378135\pi$
$733$	−15.0000	−	15.0000i	−0.554038	−	0.554038i	−0.927604	+	0.373566i	$0.878135\pi$
$734$	7.07107	−	7.07107i	0.260998	−	0.260998i
$735$		0			0
$736$	5.00000	−	5.00000i	0.184302	−	0.184302i
$737$			33.9411i			1.25024i
$738$		0			0
$739$	−35.0000	+	35.0000i	−1.28750	+	1.28750i	−0.351193	+	0.936303i	$0.614224\pi$
$739$	−35.0000	+	35.0000i	−1.28750	+	1.28750i	−0.936303	+	0.351193i	$0.885776\pi$
$740$	1.41421			0.0519875
$741$		0			0
$742$	−6.00000			−0.220267
$743$	7.07107	−	7.07107i	0.259412	−	0.259412i	−0.565403	−	0.824815i	$-0.691279\pi$
$743$	7.07107	−	7.07107i	0.259412	−	0.259412i	0.824815	+	0.565403i	$0.191279\pi$
$744$		0			0
$745$		−	6.00000i		−	0.219823i
$746$	−22.6274	+	22.6274i	−0.828449	+	0.828449i
$747$		0			0
$748$	−8.00000	+	8.00000i	−0.292509	+	0.292509i
$749$	50.9117	+	50.9117i	1.86027	+	1.86027i
$750$		0			0
$751$		−	4.00000i		−	0.145962i	−0.997333	−	0.0729810i	$-0.976749\pi$
$751$		−	4.00000i		−	0.145962i	0.997333	−	0.0729810i	$-0.0232513\pi$
$752$	−5.65685	−	5.65685i	−0.206284	−	0.206284i
$753$		0			0
$754$	2.00000	−	10.0000i	0.0728357	−	0.364179i
$755$			8.48528i			0.308811i
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	4.24264			0.154100
$759$		0			0
$760$	5.00000	+	5.00000i	0.181369	+	0.181369i
$761$	−8.48528	−	8.48528i	−0.307591	−	0.307591i	0.536383	−	0.843975i	$-0.319790\pi$
$761$	−8.48528	−	8.48528i	−0.307591	−	0.307591i	−0.843975	+	0.536383i	$0.819790\pi$
$762$		0			0
$763$	72.0000			2.60658
$764$	22.6274			0.818631
$765$		0			0
$766$		−	30.0000i		−	1.08394i
$767$	−8.48528	+	42.4264i	−0.306386	+	1.53193i
$768$		0			0
$769$	−25.0000	−	25.0000i	−0.901523	−	0.901523i	0.0940449	−	0.995568i	$-0.470020\pi$
$769$	−25.0000	−	25.0000i	−0.901523	−	0.901523i	−0.995568	+	0.0940449i	$0.970020\pi$
$770$			16.9706i			0.611577i
$771$		0			0
$772$	−6.00000	−	6.00000i	−0.215945	−	0.215945i
$773$	4.24264	−	4.24264i	0.152597	−	0.152597i	−0.626680	−	0.779277i	$-0.715587\pi$
$773$	4.24264	−	4.24264i	0.152597	−	0.152597i	0.779277	+	0.626680i	$0.215587\pi$
$774$		0			0
$775$	−6.00000	+	6.00000i	−0.215526	+	0.215526i
$776$		0			0
$777$		0			0
$778$	8.00000	−	8.00000i	0.286814	−	0.286814i
$779$	−56.5685			−2.02678
$780$		0			0
$781$	16.0000			0.572525
$782$	14.1421	−	14.1421i	0.505722	−	0.505722i
$783$		0			0
$784$			11.0000i			0.392857i
$785$	11.3137	−	11.3137i	0.403804	−	0.403804i
$786$		0			0
$787$	−24.0000	+	24.0000i	−0.855508	+	0.855508i	−0.990805	−	0.135297i	$-0.956801\pi$
$787$	−24.0000	+	24.0000i	−0.855508	+	0.855508i	0.135297	+	0.990805i	$0.456801\pi$
$788$	−2.82843	−	2.82843i	−0.100759	−	0.100759i
$789$		0			0
$790$		−	4.00000i		−	0.142314i
$791$	−33.9411	−	33.9411i	−1.20681	−	1.20681i
$792$		0			0
$793$	−12.0000	−	18.0000i	−0.426132	−	0.639199i
$794$			1.41421i			0.0501886i
$795$		0			0
$796$	−8.00000			−0.283552
$797$	26.8701			0.951786			0.475893	−	0.879503i	$-0.342125\pi$
$797$	26.8701			0.951786			0.475893	+	0.879503i	$0.342125\pi$
$798$		0			0
$799$	−16.0000	−	16.0000i	−0.566039	−	0.566039i
$800$	−0.707107	−	0.707107i	−0.0250000	−	0.0250000i
$801$		0			0
$802$	−18.0000			−0.635602
$803$	45.2548			1.59701
$804$		0			0
$805$		−	30.0000i		−	1.05736i
$806$	−16.9706	−	25.4558i	−0.597763	−	0.896644i
$807$		0			0
$808$		0			0
$809$			35.3553i			1.24303i	0.783403	+	0.621514i	$0.213482\pi$
$809$			35.3553i			1.24303i	−0.783403	+	0.621514i	$0.786518\pi$
$810$		0			0
$811$	−5.00000	−	5.00000i	−0.175574	−	0.175574i	0.613849	−	0.789423i	$-0.289620\pi$
$811$	−5.00000	−	5.00000i	−0.175574	−	0.175574i	−0.789423	+	0.613849i	$0.789620\pi$
$812$	−8.48528	+	8.48528i	−0.297775	+	0.297775i
$813$		0			0
$814$	4.00000	−	4.00000i	0.140200	−	0.140200i
$815$		−	16.9706i		−	0.594453i
$816$		0			0
$817$	60.0000	−	60.0000i	2.09913	−	2.09913i
$818$	−26.8701			−0.939490
$819$		0			0
$820$	8.00000			0.279372
$821$	4.24264	−	4.24264i	0.148069	−	0.148069i	−0.629186	−	0.777255i	$-0.716612\pi$
$821$	4.24264	−	4.24264i	0.148069	−	0.148069i	0.777255	+	0.629186i	$0.216612\pi$
$822$		0			0
$823$		−	14.0000i		−	0.488009i	−0.969774	−	0.244005i	$-0.921539\pi$
$823$		−	14.0000i		−	0.488009i	0.969774	−	0.244005i	$-0.0784612\pi$
$824$	−1.41421	+	1.41421i	−0.0492665	+	0.0492665i
$825$		0			0
$826$	36.0000	−	36.0000i	1.25260	−	1.25260i
$827$	−16.9706	−	16.9706i	−0.590124	−	0.590124i	0.347541	−	0.937665i	$-0.387017\pi$
$827$	−16.9706	−	16.9706i	−0.590124	−	0.590124i	−0.937665	+	0.347541i	$0.887017\pi$
$828$		0			0
$829$		−	34.0000i		−	1.18087i	−0.807086	−	0.590434i	$-0.798956\pi$
$829$		−	34.0000i		−	1.18087i	0.807086	−	0.590434i	$-0.201044\pi$
$830$	2.82843	+	2.82843i	0.0981761	+	0.0981761i
$831$		0			0
$832$	3.00000	−	2.00000i	0.104006	−	0.0693375i
$833$			31.1127i			1.07799i
$834$		0			0
$835$	−18.0000			−0.622916
$836$	28.2843			0.978232
$837$		0			0
$838$	−3.00000	−	3.00000i	−0.103633	−	0.103633i
$839$	2.82843	+	2.82843i	0.0976481	+	0.0976481i	0.754243	−	0.656595i	$-0.228004\pi$
$839$	2.82843	+	2.82843i	0.0976481	+	0.0976481i	−0.656595	+	0.754243i	$0.728004\pi$
$840$		0			0
$841$	21.0000			0.724138
$842$	19.7990			0.682318
$843$		0			0
$844$		−	20.0000i		−	0.688428i
$845$	4.94975	+	12.0208i	0.170276	+	0.413529i
$846$		0			0
$847$	15.0000	+	15.0000i	0.515406	+	0.515406i
$848$		−	1.41421i		−	0.0485643i
$849$		0			0
$850$	−2.00000	−	2.00000i	−0.0685994	−	0.0685994i
$851$	−7.07107	+	7.07107i	−0.242393	+	0.242393i
$852$		0			0
$853$	−35.0000	+	35.0000i	−1.19838	+	1.19838i	−0.223725	+	0.974652i	$0.571822\pi$
$853$	−35.0000	+	35.0000i	−1.19838	+	1.19838i	−0.974652	+	0.223725i	$0.928178\pi$
$854$			25.4558i			0.871081i
$855$		0			0
$856$	−12.0000	+	12.0000i	−0.410152	+	0.410152i
$857$	−11.3137			−0.386469			−0.193234	−	0.981153i	$-0.561898\pi$
$857$	−11.3137			−0.386469			−0.193234	+	0.981153i	$0.561898\pi$
$858$		0			0
$859$	−20.0000			−0.682391			−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000			−0.682391			−0.341196	+	0.939992i	$0.610832\pi$
$860$	−8.48528	+	8.48528i	−0.289346	+	0.289346i
$861$		0			0
$862$			24.0000i			0.817443i
$863$	26.8701	−	26.8701i	0.914667	−	0.914667i	−0.0819676	−	0.996635i	$-0.526120\pi$
$863$	26.8701	−	26.8701i	0.914667	−	0.914667i	0.996635	+	0.0819676i	$0.0261204\pi$
$864$		0			0
$865$	−5.00000	+	5.00000i	−0.170005	+	0.170005i
$866$	−12.7279	−	12.7279i	−0.432512	−	0.432512i
$867$		0			0
$868$			36.0000i			1.22192i
$869$	−11.3137	−	11.3137i	−0.383791	−	0.383791i
$870$		0			0
$871$	6.00000	−	30.0000i	0.203302	−	1.01651i
$872$			16.9706i			0.574696i
$873$		0			0
$874$	−50.0000			−1.69128
$875$	−4.24264			−0.143427
$876$		0			0
$877$	17.0000	+	17.0000i	0.574049	+	0.574049i	0.933257	−	0.359208i	$-0.116953\pi$
$877$	17.0000	+	17.0000i	0.574049	+	0.574049i	−0.359208	+	0.933257i	$0.616953\pi$
$878$	−5.65685	−	5.65685i	−0.190910	−	0.190910i
$879$		0			0
$880$	−4.00000			−0.134840
$881$	−55.1543			−1.85820			−0.929098	−	0.369833i	$-0.879415\pi$
$881$	−55.1543			−1.85820			−0.929098	+	0.369833i	$0.879415\pi$
$882$		0			0
$883$		−	8.00000i		−	0.269221i	−0.990899	−	0.134611i	$-0.957022\pi$
$883$		−	8.00000i		−	0.269221i	0.990899	−	0.134611i	$-0.0429784\pi$
$884$	8.48528	−	5.65685i	0.285391	−	0.190261i
$885$		0			0
$886$	−14.0000	−	14.0000i	−0.470339	−	0.470339i
$887$			7.07107i			0.237423i	0.992929	+	0.118712i	$0.0378764\pi$
$887$			7.07107i			0.237423i	−0.992929	+	0.118712i	$0.962124\pi$
$888$		0			0
$889$	42.0000	+	42.0000i	1.40863	+	1.40863i
$890$	−5.65685	+	5.65685i	−0.189618	+	0.189618i
$891$		0			0
$892$	3.00000	−	3.00000i	0.100447	−	0.100447i
$893$			56.5685i			1.89299i
$894$		0			0
$895$	−17.0000	+	17.0000i	−0.568247	+	0.568247i
$896$	−4.24264			−0.141737
$897$		0			0
$898$	−32.0000			−1.06785
$899$	−16.9706	+	16.9706i	−0.566000	+	0.566000i
$900$		0			0
$901$		−	4.00000i		−	0.133259i
$902$	22.6274	−	22.6274i	0.753411	−	0.753411i
$903$		0			0
$904$	8.00000	−	8.00000i	0.266076	−	0.266076i
$905$	9.89949	+	9.89949i	0.329070	+	0.329070i
$906$		0			0
$907$		−	44.0000i		−	1.46100i	−0.682915	−	0.730498i	$-0.739288\pi$
$907$		−	44.0000i		−	1.46100i	0.682915	−	0.730498i	$-0.260712\pi$
$908$	8.48528	+	8.48528i	0.281594	+	0.281594i
$909$		0			0
$910$	3.00000	−	15.0000i	0.0994490	−	0.497245i
$911$		−	8.48528i		−	0.281130i	−0.990071	−	0.140565i	$-0.955108\pi$
$911$		−	8.48528i		−	0.281130i	0.990071	−	0.140565i	$-0.0448919\pi$
$912$		0			0
$913$	16.0000			0.529523
$914$		0			0
$915$		0			0
$916$	−4.00000	−	4.00000i	−0.132164	−	0.132164i
$917$	−21.2132	−	21.2132i	−0.700522	−	0.700522i
$918$		0			0
$919$	4.00000			0.131948			0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000			0.131948			0.0659739	+	0.997821i	$0.478985\pi$
$920$	7.07107			0.233126
$921$		0			0
$922$			10.0000i			0.329332i
$923$	−14.1421	−	2.82843i	−0.465494	−	0.0930988i
$924$		0			0
$925$	1.00000	+	1.00000i	0.0328798	+	0.0328798i
$926$			29.6985i			0.975953i
$927$		0			0
$928$	−2.00000	−	2.00000i	−0.0656532	−	0.0656532i
$929$	−9.89949	+	9.89949i	−0.324792	+	0.324792i	−0.850602	−	0.525810i	$-0.823762\pi$
$929$	−9.89949	+	9.89949i	−0.324792	+	0.324792i	0.525810	+	0.850602i	$0.323762\pi$
$930$		0			0
$931$	55.0000	−	55.0000i	1.80255	−	1.80255i
$932$		−	2.82843i		−	0.0926482i
$933$		0			0
$934$	−20.0000	+	20.0000i	−0.654420	+	0.654420i
$935$	−11.3137			−0.369998
$936$		0			0
$937$	30.0000			0.980057			0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000			0.980057			0.490029	+	0.871706i	$0.336986\pi$
$938$	−25.4558	+	25.4558i	−0.831163	+	0.831163i
$939$		0			0
$940$		−	8.00000i		−	0.260931i
$941$	−12.7279	+	12.7279i	−0.414918	+	0.414918i	−0.883448	−	0.468529i	$-0.844784\pi$
$941$	−12.7279	+	12.7279i	−0.414918	+	0.414918i	0.468529	+	0.883448i	$0.344784\pi$
$942$		0			0
$943$	−40.0000	+	40.0000i	−1.30258	+	1.30258i
$944$	8.48528	+	8.48528i	0.276172	+	0.276172i
$945$		0			0
$946$			48.0000i			1.56061i
$947$	−22.6274	−	22.6274i	−0.735292	−	0.735292i	0.236371	−	0.971663i	$-0.424042\pi$
$947$	−22.6274	−	22.6274i	−0.735292	−	0.735292i	−0.971663	+	0.236371i	$0.924042\pi$
$948$		0			0
$949$	−40.0000	−	8.00000i	−1.29845	−	0.259691i
$950$			7.07107i			0.229416i
$951$		0			0
$952$	−12.0000			−0.388922
$953$	19.7990			0.641352			0.320676	−	0.947189i	$-0.396090\pi$
$953$	19.7990			0.641352			0.320676	+	0.947189i	$0.396090\pi$
$954$		0			0
$955$	16.0000	+	16.0000i	0.517748	+	0.517748i
$956$	−2.82843	−	2.82843i	−0.0914779	−	0.0914779i
$957$		0			0
$958$	−36.0000			−1.16311
$959$	−76.3675			−2.46604
$960$		0			0
$961$			41.0000i			1.32258i
$962$	−4.24264	+	2.82843i	−0.136788	+	0.0911922i
$963$		0			0
$964$	15.0000	+	15.0000i	0.483117	+	0.483117i
$965$		−	8.48528i		−	0.273151i
$966$		0			0
$967$	−19.0000	−	19.0000i	−0.610999	−	0.610999i	0.332208	−	0.943206i	$-0.392207\pi$
$967$	−19.0000	−	19.0000i	−0.610999	−	0.610999i	−0.943206	+	0.332208i	$0.892207\pi$
$968$	−3.53553	+	3.53553i	−0.113636	+	0.113636i
$969$		0			0
$970$		0			0
$971$		−	29.6985i		−	0.953070i	−0.879156	−	0.476535i	$-0.841893\pi$
$971$		−	29.6985i		−	0.953070i	0.879156	−	0.476535i	$-0.158107\pi$
$972$		0			0
$973$	−42.0000	+	42.0000i	−1.34646	+	1.34646i
$974$	−4.24264			−0.135943
$975$		0			0
$976$	−6.00000			−0.192055
$977$	−35.3553	+	35.3553i	−1.13112	+	1.13112i	−0.141126	+	0.989992i	$0.545072\pi$
$977$	−35.3553	+	35.3553i	−1.13112	+	1.13112i	−0.989992	+	0.141126i	$0.954928\pi$
$978$		0			0
$979$			32.0000i			1.02272i
$980$	−7.77817	+	7.77817i	−0.248465	+	0.248465i
$981$		0			0
$982$	13.0000	−	13.0000i	0.414847	−	0.414847i
$983$	7.07107	+	7.07107i	0.225532	+	0.225532i	0.810823	−	0.585291i	$-0.199020\pi$
$983$	7.07107	+	7.07107i	0.225532	+	0.225532i	−0.585291	+	0.810823i	$0.699020\pi$
$984$		0			0
$985$		−	4.00000i		−	0.127451i
$986$	−5.65685	−	5.65685i	−0.180151	−	0.180151i
$987$		0			0
$988$	−25.0000	−	5.00000i	−0.795356	−	0.159071i
$989$		−	84.8528i		−	2.69816i
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$	−8.48528			−0.269408
$993$		0			0
$994$	12.0000	+	12.0000i	0.380617	+	0.380617i
$995$	−5.65685	−	5.65685i	−0.179334	−	0.179334i
$996$		0			0
$997$	−26.0000			−0.823428			−0.411714	−	0.911313i	$-0.635070\pi$
$997$	−26.0000			−0.823428			−0.411714	+	0.911313i	$0.635070\pi$
$998$	−7.07107			−0.223831
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.s.c.1061.1	yes	4
3.2	odd	2	inner	1170.2.s.c.1061.2	yes	4
13.5	odd	4	inner	1170.2.s.c.161.2	yes	4
39.5	even	4	inner	1170.2.s.c.161.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.s.c.161.1	✓	4	39.5	even	4	inner
1170.2.s.c.161.2	yes	4	13.5	odd	4	inner
1170.2.s.c.1061.1	yes	4	1.1	even	1	trivial
1170.2.s.c.1061.2	yes	4	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 - 0.707107i) q^{5} +(3.00000 - 3.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{10} +(2.82843 + 2.82843i) q^{11} +(-2.00000 - 3.00000i) q^{13} +4.24264i q^{14} -1.00000 q^{16} -2.82843 q^{17} +(5.00000 + 5.00000i) q^{19} +(-0.707107 - 0.707107i) q^{20} -4.00000 q^{22} +7.07107 q^{23} -1.00000i q^{25} +(3.53553 + 0.707107i) q^{26} +(-3.00000 - 3.00000i) q^{28} -2.82843i q^{29} +(-6.00000 - 6.00000i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.00000 - 2.00000i) q^{34} -4.24264i q^{35} +(-1.00000 + 1.00000i) q^{37} -7.07107 q^{38} +1.00000 q^{40} +(-5.65685 + 5.65685i) q^{41} -12.0000i q^{43} +(2.82843 - 2.82843i) q^{44} +(-5.00000 + 5.00000i) q^{46} +(5.65685 + 5.65685i) q^{47} -11.0000i q^{49} +(0.707107 + 0.707107i) q^{50} +(-3.00000 + 2.00000i) q^{52} +1.41421i q^{53} +4.00000 q^{55} +4.24264 q^{56} +(2.00000 + 2.00000i) q^{58} +(-8.48528 - 8.48528i) q^{59} +6.00000 q^{61} +8.48528 q^{62} +1.00000i q^{64} +(-3.53553 - 0.707107i) q^{65} +(6.00000 + 6.00000i) q^{67} +2.82843i q^{68} +(3.00000 + 3.00000i) q^{70} +(2.82843 - 2.82843i) q^{71} +(8.00000 - 8.00000i) q^{73} -1.41421i q^{74} +(5.00000 - 5.00000i) q^{76} +16.9706 q^{77} -4.00000 q^{79} +(-0.707107 + 0.707107i) q^{80} -8.00000i q^{82} +(2.82843 - 2.82843i) q^{83} +(-2.00000 + 2.00000i) q^{85} +(8.48528 + 8.48528i) q^{86} +4.00000i q^{88} +(5.65685 + 5.65685i) q^{89} +(-15.0000 - 3.00000i) q^{91} -7.07107i q^{92} -8.00000 q^{94} +7.07107 q^{95} +(7.77817 + 7.77817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{7} - 8 q^{13} - 4 q^{16} + 20 q^{19} - 16 q^{22} - 12 q^{28} - 24 q^{31} + 8 q^{34} - 4 q^{37} + 4 q^{40} - 20 q^{46} - 12 q^{52} + 16 q^{55} + 8 q^{58} + 24 q^{61} + 24 q^{67} + 12 q^{70} + 32 q^{73}+ \cdots - 32 q^{94}+O(q^{100}) \) 4 * q + 12 * q^7 - 8 * q^13 - 4 * q^16 + 20 * q^19 - 16 * q^22 - 12 * q^28 - 24 * q^31 + 8 * q^34 - 4 * q^37 + 4 * q^40 - 20 * q^46 - 12 * q^52 + 16 * q^55 + 8 * q^58 + 24 * q^61 + 24 * q^67 + 12 * q^70 + 32 * q^73 + 20 * q^76 - 16 * q^79 - 8 * q^85 - 60 * q^91 - 32 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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