LMFDB - Embedded newform 170.2.b.b.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(101,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("170.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.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:	$1.35745683436$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	170.101
Dual form			170.2.b.b.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.00000i q^{3} +1.00000 q^{4} -1.00000i q^{5} -3.00000i q^{6} +4.00000i q^{7} +1.00000 q^{8} -6.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.00000i q^{3} +1.00000 q^{4} -1.00000i q^{5} -3.00000i q^{6} +4.00000i q^{7} +1.00000 q^{8} -6.00000 q^{9} -1.00000i q^{10} -2.00000i q^{11} -3.00000i q^{12} +1.00000 q^{13} +4.00000i q^{14} -3.00000 q^{15} +1.00000 q^{16} +(-4.00000 + 1.00000i) q^{17} -6.00000 q^{18} +7.00000 q^{19} -1.00000i q^{20} +12.0000 q^{21} -2.00000i q^{22} +6.00000i q^{23} -3.00000i q^{24} -1.00000 q^{25} +1.00000 q^{26} +9.00000i q^{27} +4.00000i q^{28} -3.00000i q^{29} -3.00000 q^{30} +7.00000i q^{31} +1.00000 q^{32} -6.00000 q^{33} +(-4.00000 + 1.00000i) q^{34} +4.00000 q^{35} -6.00000 q^{36} -2.00000i q^{37} +7.00000 q^{38} -3.00000i q^{39} -1.00000i q^{40} -8.00000i q^{41} +12.0000 q^{42} -8.00000 q^{43} -2.00000i q^{44} +6.00000i q^{45} +6.00000i q^{46} +9.00000 q^{47} -3.00000i q^{48} -9.00000 q^{49} -1.00000 q^{50} +(3.00000 + 12.0000i) q^{51} +1.00000 q^{52} -11.0000 q^{53} +9.00000i q^{54} -2.00000 q^{55} +4.00000i q^{56} -21.0000i q^{57} -3.00000i q^{58} -5.00000 q^{59} -3.00000 q^{60} +1.00000i q^{61} +7.00000i q^{62} -24.0000i q^{63} +1.00000 q^{64} -1.00000i q^{65} -6.00000 q^{66} -10.0000 q^{67} +(-4.00000 + 1.00000i) q^{68} +18.0000 q^{69} +4.00000 q^{70} -1.00000i q^{71} -6.00000 q^{72} +9.00000i q^{73} -2.00000i q^{74} +3.00000i q^{75} +7.00000 q^{76} +8.00000 q^{77} -3.00000i q^{78} -1.00000i q^{80} +9.00000 q^{81} -8.00000i q^{82} +6.00000 q^{83} +12.0000 q^{84} +(1.00000 + 4.00000i) q^{85} -8.00000 q^{86} -9.00000 q^{87} -2.00000i q^{88} -1.00000 q^{89} +6.00000i q^{90} +4.00000i q^{91} +6.00000i q^{92} +21.0000 q^{93} +9.00000 q^{94} -7.00000i q^{95} -3.00000i q^{96} -1.00000i q^{97} -9.00000 q^{98} +12.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 12 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 12 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 12 q^{9} + 2 q^{13} - 6 q^{15} + 2 q^{16} - 8 q^{17} - 12 q^{18} + 14 q^{19} + 24 q^{21} - 2 q^{25} + 2 q^{26} - 6 q^{30} + 2 q^{32} - 12 q^{33} - 8 q^{34} + 8 q^{35} - 12 q^{36} + 14 q^{38} + 24 q^{42} - 16 q^{43} + 18 q^{47} - 18 q^{49} - 2 q^{50} + 6 q^{51} + 2 q^{52} - 22 q^{53} - 4 q^{55} - 10 q^{59} - 6 q^{60} + 2 q^{64} - 12 q^{66} - 20 q^{67} - 8 q^{68} + 36 q^{69} + 8 q^{70} - 12 q^{72} + 14 q^{76} + 16 q^{77} + 18 q^{81} + 12 q^{83} + 24 q^{84} + 2 q^{85} - 16 q^{86} - 18 q^{87} - 2 q^{89} + 42 q^{93} + 18 q^{94} - 18 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 12 * q^9 + 2 * q^13 - 6 * q^15 + 2 * q^16 - 8 * q^17 - 12 * q^18 + 14 * q^19 + 24 * q^21 - 2 * q^25 + 2 * q^26 - 6 * q^30 + 2 * q^32 - 12 * q^33 - 8 * q^34 + 8 * q^35 - 12 * q^36 + 14 * q^38 + 24 * q^42 - 16 * q^43 + 18 * q^47 - 18 * q^49 - 2 * q^50 + 6 * q^51 + 2 * q^52 - 22 * q^53 - 4 * q^55 - 10 * q^59 - 6 * q^60 + 2 * q^64 - 12 * q^66 - 20 * q^67 - 8 * q^68 + 36 * q^69 + 8 * q^70 - 12 * q^72 + 14 * q^76 + 16 * q^77 + 18 * q^81 + 12 * q^83 + 24 * q^84 + 2 * q^85 - 16 * q^86 - 18 * q^87 - 2 * q^89 + 42 * q^93 + 18 * q^94 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	3.00000i		−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$		−	3.00000i		−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$4$	1.00000			0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		−	3.00000i		−	1.22474i
$7$			4.00000i			1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$			4.00000i			1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$	1.00000			0.353553
$9$	−6.00000			−2.00000
$10$		−	1.00000i		−	0.316228i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$		−	3.00000i		−	0.866025i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$			4.00000i			1.06904i
$15$	−3.00000			−0.774597
$16$	1.00000			0.250000
$17$	−4.00000	+	1.00000i	−0.970143	+	0.242536i
$17$	−4.00000	+	1.00000i	−0.970143	+	0.242536i
$18$	−6.00000			−1.41421
$19$	7.00000			1.60591			0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000			1.60591			0.802955	+	0.596040i	$0.203260\pi$
$20$		−	1.00000i		−	0.223607i
$21$	12.0000			2.61861
$22$		−	2.00000i		−	0.426401i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$		−	3.00000i		−	0.612372i
$25$	−1.00000			−0.200000
$26$	1.00000			0.196116
$27$			9.00000i			1.73205i
$28$			4.00000i			0.755929i
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$	−3.00000			−0.547723
$31$			7.00000i			1.25724i	0.777714	+	0.628619i	$0.216379\pi$
$31$			7.00000i			1.25724i	−0.777714	+	0.628619i	$0.783621\pi$
$32$	1.00000			0.176777
$33$	−6.00000			−1.04447
$34$	−4.00000	+	1.00000i	−0.685994	+	0.171499i
$35$	4.00000			0.676123
$36$	−6.00000			−1.00000
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$	7.00000			1.13555
$39$		−	3.00000i		−	0.480384i
$40$		−	1.00000i		−	0.158114i
$41$		−	8.00000i		−	1.24939i	−0.780869	−	0.624695i	$-0.785223\pi$
$41$		−	8.00000i		−	1.24939i	0.780869	−	0.624695i	$-0.214777\pi$
$42$	12.0000			1.85164
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		−	2.00000i		−	0.301511i
$45$			6.00000i			0.894427i
$46$			6.00000i			0.884652i
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$		−	3.00000i		−	0.433013i
$49$	−9.00000			−1.28571
$50$	−1.00000			−0.141421
$51$	3.00000	+	12.0000i	0.420084	+	1.68034i
$52$	1.00000			0.138675
$53$	−11.0000			−1.51097			−0.755483	−	0.655168i	$-0.772598\pi$
$53$	−11.0000			−1.51097			−0.755483	+	0.655168i	$0.772598\pi$
$54$			9.00000i			1.22474i
$55$	−2.00000			−0.269680
$56$			4.00000i			0.534522i
$57$		−	21.0000i		−	2.78152i
$58$		−	3.00000i		−	0.393919i
$59$	−5.00000			−0.650945			−0.325472	−	0.945552i	$-0.605523\pi$
$59$	−5.00000			−0.650945			−0.325472	+	0.945552i	$0.605523\pi$
$60$	−3.00000			−0.387298
$61$			1.00000i			0.128037i	0.997949	+	0.0640184i	$0.0203916\pi$
$61$			1.00000i			0.128037i	−0.997949	+	0.0640184i	$0.979608\pi$
$62$			7.00000i			0.889001i
$63$		−	24.0000i		−	3.02372i
$64$	1.00000			0.125000
$65$		−	1.00000i		−	0.124035i
$66$	−6.00000			−0.738549
$67$	−10.0000			−1.22169			−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000			−1.22169			−0.610847	+	0.791748i	$0.709171\pi$
$68$	−4.00000	+	1.00000i	−0.485071	+	0.121268i
$69$	18.0000			2.16695
$70$	4.00000			0.478091
$71$		−	1.00000i		−	0.118678i	−0.998238	−	0.0593391i	$-0.981101\pi$
$71$		−	1.00000i		−	0.118678i	0.998238	−	0.0593391i	$-0.0188993\pi$
$72$	−6.00000			−0.707107
$73$			9.00000i			1.05337i	0.850060	+	0.526685i	$0.176565\pi$
$73$			9.00000i			1.05337i	−0.850060	+	0.526685i	$0.823435\pi$
$74$		−	2.00000i		−	0.232495i
$75$			3.00000i			0.346410i
$76$	7.00000			0.802955
$77$	8.00000			0.911685
$78$		−	3.00000i		−	0.339683i
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		−	1.00000i		−	0.111803i
$81$	9.00000			1.00000
$82$		−	8.00000i		−	0.883452i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	12.0000			1.30931
$85$	1.00000	+	4.00000i	0.108465	+	0.433861i
$86$	−8.00000			−0.862662
$87$	−9.00000			−0.964901
$88$		−	2.00000i		−	0.213201i
$89$	−1.00000			−0.106000			−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000			−0.106000			−0.0529999	+	0.998595i	$0.516878\pi$
$90$			6.00000i			0.632456i
$91$			4.00000i			0.419314i
$92$			6.00000i			0.625543i
$93$	21.0000			2.17760
$94$	9.00000			0.928279
$95$		−	7.00000i		−	0.718185i
$96$		−	3.00000i		−	0.306186i
$97$		−	1.00000i		−	0.101535i	−0.998711	−	0.0507673i	$-0.983833\pi$
$97$		−	1.00000i		−	0.101535i	0.998711	−	0.0507673i	$-0.0161667\pi$
$98$	−9.00000			−0.909137
$99$			12.0000i			1.20605i
$100$	−1.00000			−0.100000
$101$	−2.00000			−0.199007			−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000			−0.199007			−0.0995037	+	0.995037i	$0.531726\pi$
$102$	3.00000	+	12.0000i	0.297044	+	1.18818i
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	1.00000			0.0980581
$105$		−	12.0000i		−	1.17108i
$106$	−11.0000			−1.06841
$107$		−	16.0000i		−	1.54678i	−0.633932	−	0.773389i	$-0.718560\pi$
$107$		−	16.0000i		−	1.54678i	0.633932	−	0.773389i	$-0.281440\pi$
$108$			9.00000i			0.866025i
$109$		−	19.0000i		−	1.81987i	−0.414751	−	0.909935i	$-0.636131\pi$
$109$		−	19.0000i		−	1.81987i	0.414751	−	0.909935i	$-0.363869\pi$
$110$	−2.00000			−0.190693
$111$	−6.00000			−0.569495
$112$			4.00000i			0.377964i
$113$			1.00000i			0.0940721i	0.998893	+	0.0470360i	$0.0149776\pi$
$113$			1.00000i			0.0940721i	−0.998893	+	0.0470360i	$0.985022\pi$
$114$		−	21.0000i		−	1.96683i
$115$	6.00000			0.559503
$116$		−	3.00000i		−	0.278543i
$117$	−6.00000			−0.554700
$118$	−5.00000			−0.460287
$119$	−4.00000	−	16.0000i	−0.366679	−	1.46672i
$120$	−3.00000			−0.273861
$121$	7.00000			0.636364
$122$			1.00000i			0.0905357i
$123$	−24.0000			−2.16401
$124$			7.00000i			0.628619i
$125$			1.00000i			0.0894427i
$126$		−	24.0000i		−	2.13809i
$127$	−15.0000			−1.33103			−0.665517	−	0.746382i	$-0.731789\pi$
$127$	−15.0000			−1.33103			−0.665517	+	0.746382i	$0.731789\pi$
$128$	1.00000			0.0883883
$129$			24.0000i			2.11308i
$130$		−	1.00000i		−	0.0877058i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	−6.00000			−0.522233
$133$			28.0000i			2.42791i
$134$	−10.0000			−0.863868
$135$	9.00000			0.774597
$136$	−4.00000	+	1.00000i	−0.342997	+	0.0857493i
$137$	8.00000			0.683486			0.341743	−	0.939793i	$-0.388983\pi$
$137$	8.00000			0.683486			0.341743	+	0.939793i	$0.388983\pi$
$138$	18.0000			1.53226
$139$			14.0000i			1.18746i	0.804663	+	0.593732i	$0.202346\pi$
$139$			14.0000i			1.18746i	−0.804663	+	0.593732i	$0.797654\pi$
$140$	4.00000			0.338062
$141$		−	27.0000i		−	2.27381i
$142$		−	1.00000i		−	0.0839181i
$143$		−	2.00000i		−	0.167248i
$144$	−6.00000			−0.500000
$145$	−3.00000			−0.249136
$146$			9.00000i			0.744845i
$147$			27.0000i			2.22692i
$148$		−	2.00000i		−	0.164399i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$			3.00000i			0.244949i
$151$	22.0000			1.79033			0.895167	−	0.445730i	$-0.147056\pi$
$151$	22.0000			1.79033			0.895167	+	0.445730i	$0.147056\pi$
$152$	7.00000			0.567775
$153$	24.0000	−	6.00000i	1.94029	−	0.485071i
$154$	8.00000			0.644658
$155$	7.00000			0.562254
$156$		−	3.00000i		−	0.240192i
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$		0			0
$159$			33.0000i			2.61707i
$160$		−	1.00000i		−	0.0790569i
$161$	−24.0000			−1.89146
$162$	9.00000			0.707107
$163$			4.00000i			0.313304i	0.987654	+	0.156652i	$0.0500701\pi$
$163$			4.00000i			0.313304i	−0.987654	+	0.156652i	$0.949930\pi$
$164$		−	8.00000i		−	0.624695i
$165$			6.00000i			0.467099i
$166$	6.00000			0.465690
$167$		−	2.00000i		−	0.154765i	−0.997001	−	0.0773823i	$-0.975344\pi$
$167$		−	2.00000i		−	0.154765i	0.997001	−	0.0773823i	$-0.0246562\pi$
$168$	12.0000			0.925820
$169$	−12.0000			−0.923077
$170$	1.00000	+	4.00000i	0.0766965	+	0.306786i
$171$	−42.0000			−3.21182
$172$	−8.00000			−0.609994
$173$			2.00000i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$	−9.00000			−0.682288
$175$		−	4.00000i		−	0.302372i
$176$		−	2.00000i		−	0.150756i
$177$			15.0000i			1.12747i
$178$	−1.00000			−0.0749532
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$			6.00000i			0.447214i
$181$		−	10.0000i		−	0.743294i	−0.928374	−	0.371647i	$-0.878793\pi$
$181$		−	10.0000i		−	0.743294i	0.928374	−	0.371647i	$-0.121207\pi$
$182$			4.00000i			0.296500i
$183$	3.00000			0.221766
$184$			6.00000i			0.442326i
$185$	−2.00000			−0.147043
$186$	21.0000			1.53979
$187$	2.00000	+	8.00000i	0.146254	+	0.585018i
$188$	9.00000			0.656392
$189$	−36.0000			−2.61861
$190$		−	7.00000i		−	0.507833i
$191$	10.0000			0.723575			0.361787	−	0.932261i	$-0.382167\pi$
$191$	10.0000			0.723575			0.361787	+	0.932261i	$0.382167\pi$
$192$		−	3.00000i		−	0.216506i
$193$		−	2.00000i		−	0.143963i	−0.997406	−	0.0719816i	$-0.977068\pi$
$193$		−	2.00000i		−	0.143963i	0.997406	−	0.0719816i	$-0.0229323\pi$
$194$		−	1.00000i		−	0.0717958i
$195$	−3.00000			−0.214834
$196$	−9.00000			−0.642857
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$			12.0000i			0.852803i
$199$		−	11.0000i		−	0.779769i	−0.920864	−	0.389885i	$-0.872515\pi$
$199$		−	11.0000i		−	0.779769i	0.920864	−	0.389885i	$-0.127485\pi$
$200$	−1.00000			−0.0707107
$201$			30.0000i			2.11604i
$202$	−2.00000			−0.140720
$203$	12.0000			0.842235
$204$	3.00000	+	12.0000i	0.210042	+	0.840168i
$205$	−8.00000			−0.558744
$206$		0			0
$207$		−	36.0000i		−	2.50217i
$208$	1.00000			0.0693375
$209$		−	14.0000i		−	0.968400i
$210$		−	12.0000i		−	0.828079i
$211$			10.0000i			0.688428i	0.938891	+	0.344214i	$0.111855\pi$
$211$			10.0000i			0.688428i	−0.938891	+	0.344214i	$0.888145\pi$
$212$	−11.0000			−0.755483
$213$	−3.00000			−0.205557
$214$		−	16.0000i		−	1.09374i
$215$			8.00000i			0.545595i
$216$			9.00000i			0.612372i
$217$	−28.0000			−1.90076
$218$		−	19.0000i		−	1.28684i
$219$	27.0000			1.82449
$220$	−2.00000			−0.134840
$221$	−4.00000	+	1.00000i	−0.269069	+	0.0672673i
$222$	−6.00000			−0.402694
$223$	29.0000			1.94198			0.970992	−	0.239113i	$-0.0768565\pi$
$223$	29.0000			1.94198			0.970992	+	0.239113i	$0.0768565\pi$
$224$			4.00000i			0.267261i
$225$	6.00000			0.400000
$226$			1.00000i			0.0665190i
$227$		−	27.0000i		−	1.79205i	−0.444001	−	0.896026i	$-0.646441\pi$
$227$		−	27.0000i		−	1.79205i	0.444001	−	0.896026i	$-0.353559\pi$
$228$		−	21.0000i		−	1.39076i
$229$	−4.00000			−0.264327			−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000			−0.264327			−0.132164	+	0.991228i	$0.542192\pi$
$230$	6.00000			0.395628
$231$		−	24.0000i		−	1.57908i
$232$		−	3.00000i		−	0.196960i
$233$			3.00000i			0.196537i	0.995160	+	0.0982683i	$0.0313303\pi$
$233$			3.00000i			0.196537i	−0.995160	+	0.0982683i	$0.968670\pi$
$234$	−6.00000			−0.392232
$235$		−	9.00000i		−	0.587095i
$236$	−5.00000			−0.325472
$237$		0			0
$238$	−4.00000	−	16.0000i	−0.259281	−	1.03713i
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$	−3.00000			−0.193649
$241$			4.00000i			0.257663i	0.991667	+	0.128831i	$0.0411226\pi$
$241$			4.00000i			0.257663i	−0.991667	+	0.128831i	$0.958877\pi$
$242$	7.00000			0.449977
$243$		0			0
$244$			1.00000i			0.0640184i
$245$			9.00000i			0.574989i
$246$	−24.0000			−1.53018
$247$	7.00000			0.445399
$248$			7.00000i			0.444500i
$249$		−	18.0000i		−	1.14070i
$250$			1.00000i			0.0632456i
$251$	−8.00000			−0.504956			−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000			−0.504956			−0.252478	+	0.967603i	$0.581245\pi$
$252$		−	24.0000i		−	1.51186i
$253$	12.0000			0.754434
$254$	−15.0000			−0.941184
$255$	12.0000	−	3.00000i	0.751469	−	0.187867i
$256$	1.00000			0.0625000
$257$	24.0000			1.49708			0.748539	−	0.663090i	$-0.230755\pi$
$257$	24.0000			1.49708			0.748539	+	0.663090i	$0.230755\pi$
$258$			24.0000i			1.49417i
$259$	8.00000			0.497096
$260$		−	1.00000i		−	0.0620174i
$261$			18.0000i			1.11417i
$262$		0			0
$263$	−9.00000			−0.554964			−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000			−0.554964			−0.277482	+	0.960731i	$0.589500\pi$
$264$	−6.00000			−0.369274
$265$			11.0000i			0.675725i
$266$			28.0000i			1.71679i
$267$			3.00000i			0.183597i
$268$	−10.0000			−0.610847
$269$		−	25.0000i		−	1.52428i	−0.647414	−	0.762138i	$-0.724150\pi$
$269$		−	25.0000i		−	1.52428i	0.647414	−	0.762138i	$-0.275850\pi$
$270$	9.00000			0.547723
$271$	12.0000			0.728948			0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000			0.728948			0.364474	+	0.931214i	$0.381249\pi$
$272$	−4.00000	+	1.00000i	−0.242536	+	0.0606339i
$273$	12.0000			0.726273
$274$	8.00000			0.483298
$275$			2.00000i			0.120605i
$276$	18.0000			1.08347
$277$			2.00000i			0.120168i	0.998193	+	0.0600842i	$0.0191369\pi$
$277$			2.00000i			0.120168i	−0.998193	+	0.0600842i	$0.980863\pi$
$278$			14.0000i			0.839664i
$279$		−	42.0000i		−	2.51447i
$280$	4.00000			0.239046
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$		−	27.0000i		−	1.60783i
$283$		−	7.00000i		−	0.416107i	−0.978117	−	0.208053i	$-0.933287\pi$
$283$		−	7.00000i		−	0.416107i	0.978117	−	0.208053i	$-0.0667128\pi$
$284$		−	1.00000i		−	0.0593391i
$285$	−21.0000			−1.24393
$286$		−	2.00000i		−	0.118262i
$287$	32.0000			1.88890
$288$	−6.00000			−0.353553
$289$	15.0000	−	8.00000i	0.882353	−	0.470588i
$290$	−3.00000			−0.176166
$291$	−3.00000			−0.175863
$292$			9.00000i			0.526685i
$293$	−5.00000			−0.292103			−0.146052	−	0.989277i	$-0.546657\pi$
$293$	−5.00000			−0.292103			−0.146052	+	0.989277i	$0.546657\pi$
$294$			27.0000i			1.57467i
$295$			5.00000i			0.291111i
$296$		−	2.00000i		−	0.116248i
$297$	18.0000			1.04447
$298$	−6.00000			−0.347571
$299$			6.00000i			0.346989i
$300$			3.00000i			0.173205i
$301$		−	32.0000i		−	1.84445i
$302$	22.0000			1.26596
$303$			6.00000i			0.344691i
$304$	7.00000			0.401478
$305$	1.00000			0.0572598
$306$	24.0000	−	6.00000i	1.37199	−	0.342997i
$307$	22.0000			1.25561			0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000			1.25561			0.627803	+	0.778372i	$0.283954\pi$
$308$	8.00000			0.455842
$309$		0			0
$310$	7.00000			0.397573
$311$			16.0000i			0.907277i	0.891186	+	0.453638i	$0.149874\pi$
$311$			16.0000i			0.907277i	−0.891186	+	0.453638i	$0.850126\pi$
$312$		−	3.00000i		−	0.169842i
$313$		−	26.0000i		−	1.46961i	−0.678280	−	0.734803i	$-0.737274\pi$
$313$		−	26.0000i		−	1.46961i	0.678280	−	0.734803i	$-0.262726\pi$
$314$	2.00000			0.112867
$315$	−24.0000			−1.35225
$316$		0			0
$317$			20.0000i			1.12331i	0.827371	+	0.561656i	$0.189836\pi$
$317$			20.0000i			1.12331i	−0.827371	+	0.561656i	$0.810164\pi$
$318$			33.0000i			1.85055i
$319$	−6.00000			−0.335936
$320$		−	1.00000i		−	0.0559017i
$321$	−48.0000			−2.67910
$322$	−24.0000			−1.33747
$323$	−28.0000	+	7.00000i	−1.55796	+	0.389490i
$324$	9.00000			0.500000
$325$	−1.00000			−0.0554700
$326$			4.00000i			0.221540i
$327$	−57.0000			−3.15211
$328$		−	8.00000i		−	0.441726i
$329$			36.0000i			1.98474i
$330$			6.00000i			0.330289i
$331$	−19.0000			−1.04433			−0.522167	−	0.852843i	$-0.674876\pi$
$331$	−19.0000			−1.04433			−0.522167	+	0.852843i	$0.674876\pi$
$332$	6.00000			0.329293
$333$			12.0000i			0.657596i
$334$		−	2.00000i		−	0.109435i
$335$			10.0000i			0.546358i
$336$	12.0000			0.654654
$337$		−	23.0000i		−	1.25289i	−0.779466	−	0.626445i	$-0.784509\pi$
$337$		−	23.0000i		−	1.25289i	0.779466	−	0.626445i	$-0.215491\pi$
$338$	−12.0000			−0.652714
$339$	3.00000			0.162938
$340$	1.00000	+	4.00000i	0.0542326	+	0.216930i
$341$	14.0000			0.758143
$342$	−42.0000			−2.27110
$343$		−	8.00000i		−	0.431959i
$344$	−8.00000			−0.431331
$345$		−	18.0000i		−	0.969087i
$346$			2.00000i			0.107521i
$347$			27.0000i			1.44944i	0.689046	+	0.724718i	$0.258030\pi$
$347$			27.0000i			1.44944i	−0.689046	+	0.724718i	$0.741970\pi$
$348$	−9.00000			−0.482451
$349$	12.0000			0.642345			0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000			0.642345			0.321173	+	0.947021i	$0.395923\pi$
$350$		−	4.00000i		−	0.213809i
$351$			9.00000i			0.480384i
$352$		−	2.00000i		−	0.106600i
$353$	−10.0000			−0.532246			−0.266123	−	0.963939i	$-0.585743\pi$
$353$	−10.0000			−0.532246			−0.266123	+	0.963939i	$0.585743\pi$
$354$			15.0000i			0.797241i
$355$	−1.00000			−0.0530745
$356$	−1.00000			−0.0529999
$357$	−48.0000	+	12.0000i	−2.54043	+	0.635107i
$358$	24.0000			1.26844
$359$	−4.00000			−0.211112			−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000			−0.211112			−0.105556	+	0.994413i	$0.533662\pi$
$360$			6.00000i			0.316228i
$361$	30.0000			1.57895
$362$		−	10.0000i		−	0.525588i
$363$		−	21.0000i		−	1.10221i
$364$			4.00000i			0.209657i
$365$	9.00000			0.471082
$366$	3.00000			0.156813
$367$			10.0000i			0.521996i	0.965339	+	0.260998i	$0.0840516\pi$
$367$			10.0000i			0.521996i	−0.965339	+	0.260998i	$0.915948\pi$
$368$			6.00000i			0.312772i
$369$			48.0000i			2.49878i
$370$	−2.00000			−0.103975
$371$		−	44.0000i		−	2.28437i
$372$	21.0000			1.08880
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	2.00000	+	8.00000i	0.103418	+	0.413670i
$375$	3.00000			0.154919
$376$	9.00000			0.464140
$377$		−	3.00000i		−	0.154508i
$378$	−36.0000			−1.85164
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$		−	7.00000i		−	0.359092i
$381$			45.0000i			2.30542i
$382$	10.0000			0.511645
$383$	−19.0000			−0.970855			−0.485427	−	0.874277i	$-0.661336\pi$
$383$	−19.0000			−0.970855			−0.485427	+	0.874277i	$0.661336\pi$
$384$		−	3.00000i		−	0.153093i
$385$		−	8.00000i		−	0.407718i
$386$		−	2.00000i		−	0.101797i
$387$	48.0000			2.43998
$388$		−	1.00000i		−	0.0507673i
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$	−3.00000			−0.151911
$391$	−6.00000	−	24.0000i	−0.303433	−	1.21373i
$392$	−9.00000			−0.454569
$393$		0			0
$394$			18.0000i			0.906827i
$395$		0			0
$396$			12.0000i			0.603023i
$397$			4.00000i			0.200754i	0.994949	+	0.100377i	$0.0320049\pi$
$397$			4.00000i			0.200754i	−0.994949	+	0.100377i	$0.967995\pi$
$398$		−	11.0000i		−	0.551380i
$399$	84.0000			4.20526
$400$	−1.00000			−0.0500000
$401$			24.0000i			1.19850i	0.800561	+	0.599251i	$0.204535\pi$
$401$			24.0000i			1.19850i	−0.800561	+	0.599251i	$0.795465\pi$
$402$			30.0000i			1.49626i
$403$			7.00000i			0.348695i
$404$	−2.00000			−0.0995037
$405$		−	9.00000i		−	0.447214i
$406$	12.0000			0.595550
$407$	−4.00000			−0.198273
$408$	3.00000	+	12.0000i	0.148522	+	0.594089i
$409$	−19.0000			−0.939490			−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000			−0.939490			−0.469745	+	0.882802i	$0.655654\pi$
$410$	−8.00000			−0.395092
$411$		−	24.0000i		−	1.18383i
$412$		0			0
$413$		−	20.0000i		−	0.984136i
$414$		−	36.0000i		−	1.76930i
$415$		−	6.00000i		−	0.294528i
$416$	1.00000			0.0490290
$417$	42.0000			2.05675
$418$		−	14.0000i		−	0.684762i
$419$			10.0000i			0.488532i	0.969708	+	0.244266i	$0.0785470\pi$
$419$			10.0000i			0.488532i	−0.969708	+	0.244266i	$0.921453\pi$
$420$		−	12.0000i		−	0.585540i
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$			10.0000i			0.486792i
$423$	−54.0000			−2.62557
$424$	−11.0000			−0.534207
$425$	4.00000	−	1.00000i	0.194029	−	0.0485071i
$426$	−3.00000			−0.145350
$427$	−4.00000			−0.193574
$428$		−	16.0000i		−	0.773389i
$429$	−6.00000			−0.289683
$430$			8.00000i			0.385794i
$431$		−	8.00000i		−	0.385346i	−0.981263	−	0.192673i	$-0.938284\pi$
$431$		−	8.00000i		−	0.385346i	0.981263	−	0.192673i	$-0.0617157\pi$
$432$			9.00000i			0.433013i
$433$	−8.00000			−0.384455			−0.192228	−	0.981350i	$-0.561571\pi$
$433$	−8.00000			−0.384455			−0.192228	+	0.981350i	$0.561571\pi$
$434$	−28.0000			−1.34404
$435$			9.00000i			0.431517i
$436$		−	19.0000i		−	0.909935i
$437$			42.0000i			2.00913i
$438$	27.0000			1.29011
$439$			32.0000i			1.52728i	0.645644	+	0.763638i	$0.276589\pi$
$439$			32.0000i			1.52728i	−0.645644	+	0.763638i	$0.723411\pi$
$440$	−2.00000			−0.0953463
$441$	54.0000			2.57143
$442$	−4.00000	+	1.00000i	−0.190261	+	0.0475651i
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$	−6.00000			−0.284747
$445$			1.00000i			0.0474045i
$446$	29.0000			1.37319
$447$			18.0000i			0.851371i
$448$			4.00000i			0.188982i
$449$			30.0000i			1.41579i	0.706319	+	0.707894i	$0.250354\pi$
$449$			30.0000i			1.41579i	−0.706319	+	0.707894i	$0.749646\pi$
$450$	6.00000			0.282843
$451$	−16.0000			−0.753411
$452$			1.00000i			0.0470360i
$453$		−	66.0000i		−	3.10095i
$454$		−	27.0000i		−	1.26717i
$455$	4.00000			0.187523
$456$		−	21.0000i		−	0.983415i
$457$	−36.0000			−1.68401			−0.842004	−	0.539471i	$-0.818624\pi$
$457$	−36.0000			−1.68401			−0.842004	+	0.539471i	$0.818624\pi$
$458$	−4.00000			−0.186908
$459$	−9.00000	−	36.0000i	−0.420084	−	1.68034i
$460$	6.00000			0.279751
$461$	−6.00000			−0.279448			−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000			−0.279448			−0.139724	+	0.990190i	$0.544622\pi$
$462$		−	24.0000i		−	1.11658i
$463$	9.00000			0.418265			0.209133	−	0.977887i	$-0.432936\pi$
$463$	9.00000			0.418265			0.209133	+	0.977887i	$0.432936\pi$
$464$		−	3.00000i		−	0.139272i
$465$		−	21.0000i		−	0.973852i
$466$			3.00000i			0.138972i
$467$	26.0000			1.20314			0.601568	−	0.798821i	$-0.294543\pi$
$467$	26.0000			1.20314			0.601568	+	0.798821i	$0.294543\pi$
$468$	−6.00000			−0.277350
$469$		−	40.0000i		−	1.84703i
$470$		−	9.00000i		−	0.415139i
$471$		−	6.00000i		−	0.276465i
$472$	−5.00000			−0.230144
$473$			16.0000i			0.735681i
$474$		0			0
$475$	−7.00000			−0.321182
$476$	−4.00000	−	16.0000i	−0.183340	−	0.733359i
$477$	66.0000			3.02193
$478$	−20.0000			−0.914779
$479$		−	15.0000i		−	0.685367i	−0.939451	−	0.342684i	$-0.888664\pi$
$479$		−	15.0000i		−	0.685367i	0.939451	−	0.342684i	$-0.111336\pi$
$480$	−3.00000			−0.136931
$481$		−	2.00000i		−	0.0911922i
$482$			4.00000i			0.182195i
$483$			72.0000i			3.27611i
$484$	7.00000			0.318182
$485$	−1.00000			−0.0454077
$486$		0			0
$487$		−	40.0000i		−	1.81257i	−0.422664	−	0.906287i	$-0.638905\pi$
$487$		−	40.0000i		−	1.81257i	0.422664	−	0.906287i	$-0.361095\pi$
$488$			1.00000i			0.0452679i
$489$	12.0000			0.542659
$490$			9.00000i			0.406579i
$491$	−15.0000			−0.676941			−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000			−0.676941			−0.338470	+	0.940977i	$0.609909\pi$
$492$	−24.0000			−1.08200
$493$	3.00000	+	12.0000i	0.135113	+	0.540453i
$494$	7.00000			0.314945
$495$	12.0000			0.539360
$496$			7.00000i			0.314309i
$497$	4.00000			0.179425
$498$		−	18.0000i		−	0.806599i
$499$			20.0000i			0.895323i	0.894203	+	0.447661i	$0.147743\pi$
$499$			20.0000i			0.895323i	−0.894203	+	0.447661i	$0.852257\pi$
$500$			1.00000i			0.0447214i
$501$	−6.00000			−0.268060
$502$	−8.00000			−0.357057
$503$		−	12.0000i		−	0.535054i	−0.963550	−	0.267527i	$-0.913794\pi$
$503$		−	12.0000i		−	0.535054i	0.963550	−	0.267527i	$-0.0862064\pi$
$504$		−	24.0000i		−	1.06904i
$505$			2.00000i			0.0889988i
$506$	12.0000			0.533465
$507$			36.0000i			1.59882i
$508$	−15.0000			−0.665517
$509$	−36.0000			−1.59567			−0.797836	−	0.602875i	$-0.794022\pi$
$509$	−36.0000			−1.59567			−0.797836	+	0.602875i	$0.794022\pi$
$510$	12.0000	−	3.00000i	0.531369	−	0.132842i
$511$	−36.0000			−1.59255
$512$	1.00000			0.0441942
$513$			63.0000i			2.78152i
$514$	24.0000			1.05859
$515$		0			0
$516$			24.0000i			1.05654i
$517$		−	18.0000i		−	0.791639i
$518$	8.00000			0.351500
$519$	6.00000			0.263371
$520$		−	1.00000i		−	0.0438529i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$			18.0000i			0.787839i
$523$	−22.0000			−0.961993			−0.480996	−	0.876723i	$-0.659725\pi$
$523$	−22.0000			−0.961993			−0.480996	+	0.876723i	$0.659725\pi$
$524$		0			0
$525$	−12.0000			−0.523723
$526$	−9.00000			−0.392419
$527$	−7.00000	−	28.0000i	−0.304925	−	1.21970i
$528$	−6.00000			−0.261116
$529$	−13.0000			−0.565217
$530$			11.0000i			0.477809i
$531$	30.0000			1.30189
$532$			28.0000i			1.21395i
$533$		−	8.00000i		−	0.346518i
$534$			3.00000i			0.129823i
$535$	−16.0000			−0.691740
$536$	−10.0000			−0.431934
$537$		−	72.0000i		−	3.10703i
$538$		−	25.0000i		−	1.07783i
$539$			18.0000i			0.775315i
$540$	9.00000			0.387298
$541$			22.0000i			0.945854i	0.881102	+	0.472927i	$0.156803\pi$
$541$			22.0000i			0.945854i	−0.881102	+	0.472927i	$0.843197\pi$
$542$	12.0000			0.515444
$543$	−30.0000			−1.28742
$544$	−4.00000	+	1.00000i	−0.171499	+	0.0428746i
$545$	−19.0000			−0.813871
$546$	12.0000			0.513553
$547$		−	39.0000i		−	1.66752i	−0.552127	−	0.833760i	$-0.686184\pi$
$547$		−	39.0000i		−	1.66752i	0.552127	−	0.833760i	$-0.313816\pi$
$548$	8.00000			0.341743
$549$		−	6.00000i		−	0.256074i
$550$			2.00000i			0.0852803i
$551$		−	21.0000i		−	0.894630i
$552$	18.0000			0.766131
$553$		0			0
$554$			2.00000i			0.0849719i
$555$			6.00000i			0.254686i
$556$			14.0000i			0.593732i
$557$	−27.0000			−1.14403			−0.572013	−	0.820244i	$-0.693837\pi$
$557$	−27.0000			−1.14403			−0.572013	+	0.820244i	$0.693837\pi$
$558$		−	42.0000i		−	1.77800i
$559$	−8.00000			−0.338364
$560$	4.00000			0.169031
$561$	24.0000	−	6.00000i	1.01328	−	0.253320i
$562$	9.00000			0.379642
$563$	18.0000			0.758610			0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000			0.758610			0.379305	+	0.925272i	$0.376163\pi$
$564$		−	27.0000i		−	1.13691i
$565$	1.00000			0.0420703
$566$		−	7.00000i		−	0.294232i
$567$			36.0000i			1.51186i
$568$		−	1.00000i		−	0.0419591i
$569$	−15.0000			−0.628833			−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000			−0.628833			−0.314416	+	0.949285i	$0.601809\pi$
$570$	−21.0000			−0.879593
$571$			16.0000i			0.669579i	0.942293	+	0.334790i	$0.108665\pi$
$571$			16.0000i			0.669579i	−0.942293	+	0.334790i	$0.891335\pi$
$572$		−	2.00000i		−	0.0836242i
$573$		−	30.0000i		−	1.25327i
$574$	32.0000			1.33565
$575$		−	6.00000i		−	0.250217i
$576$	−6.00000			−0.250000
$577$	32.0000			1.33218			0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000			1.33218			0.666089	+	0.745873i	$0.267967\pi$
$578$	15.0000	−	8.00000i	0.623918	−	0.332756i
$579$	−6.00000			−0.249351
$580$	−3.00000			−0.124568
$581$			24.0000i			0.995688i
$582$	−3.00000			−0.124354
$583$			22.0000i			0.911147i
$584$			9.00000i			0.372423i
$585$			6.00000i			0.248069i
$586$	−5.00000			−0.206548
$587$	−10.0000			−0.412744			−0.206372	−	0.978474i	$-0.566166\pi$
$587$	−10.0000			−0.412744			−0.206372	+	0.978474i	$0.566166\pi$
$588$			27.0000i			1.11346i
$589$			49.0000i			2.01901i
$590$			5.00000i			0.205847i
$591$	54.0000			2.22126
$592$		−	2.00000i		−	0.0821995i
$593$	22.0000			0.903432			0.451716	−	0.892162i	$-0.350812\pi$
$593$	22.0000			0.903432			0.451716	+	0.892162i	$0.350812\pi$
$594$	18.0000			0.738549
$595$	−16.0000	+	4.00000i	−0.655936	+	0.163984i
$596$	−6.00000			−0.245770
$597$	−33.0000			−1.35060
$598$			6.00000i			0.245358i
$599$	2.00000			0.0817178			0.0408589	−	0.999165i	$-0.486991\pi$
$599$	2.00000			0.0817178			0.0408589	+	0.999165i	$0.486991\pi$
$600$			3.00000i			0.122474i
$601$		−	16.0000i		−	0.652654i	−0.945257	−	0.326327i	$-0.894189\pi$
$601$		−	16.0000i		−	0.652654i	0.945257	−	0.326327i	$-0.105811\pi$
$602$		−	32.0000i		−	1.30422i
$603$	60.0000			2.44339
$604$	22.0000			0.895167
$605$		−	7.00000i		−	0.284590i
$606$			6.00000i			0.243733i
$607$		−	12.0000i		−	0.487065i	−0.969893	−	0.243532i	$-0.921694\pi$
$607$		−	12.0000i		−	0.487065i	0.969893	−	0.243532i	$-0.0783062\pi$
$608$	7.00000			0.283887
$609$		−	36.0000i		−	1.45879i
$610$	1.00000			0.0404888
$611$	9.00000			0.364101
$612$	24.0000	−	6.00000i	0.970143	−	0.242536i
$613$	29.0000			1.17130			0.585649	−	0.810564i	$-0.300840\pi$
$613$	29.0000			1.17130			0.585649	+	0.810564i	$0.300840\pi$
$614$	22.0000			0.887848
$615$			24.0000i			0.967773i
$616$	8.00000			0.322329
$617$		−	1.00000i		−	0.0402585i	−0.999797	−	0.0201292i	$-0.993592\pi$
$617$		−	1.00000i		−	0.0402585i	0.999797	−	0.0201292i	$-0.00640777\pi$
$618$		0			0
$619$			22.0000i			0.884255i	0.896952	+	0.442127i	$0.145776\pi$
$619$			22.0000i			0.884255i	−0.896952	+	0.442127i	$0.854224\pi$
$620$	7.00000			0.281127
$621$	−54.0000			−2.16695
$622$			16.0000i			0.641542i
$623$		−	4.00000i		−	0.160257i
$624$		−	3.00000i		−	0.120096i
$625$	1.00000			0.0400000
$626$		−	26.0000i		−	1.03917i
$627$	−42.0000			−1.67732
$628$	2.00000			0.0798087
$629$	2.00000	+	8.00000i	0.0797452	+	0.318981i
$630$	−24.0000			−0.956183
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$	30.0000			1.19239
$634$			20.0000i			0.794301i
$635$			15.0000i			0.595257i
$636$			33.0000i			1.30854i
$637$	−9.00000			−0.356593
$638$	−6.00000			−0.237542
$639$			6.00000i			0.237356i
$640$		−	1.00000i		−	0.0395285i
$641$			2.00000i			0.0789953i	0.999220	+	0.0394976i	$0.0125758\pi$
$641$			2.00000i			0.0789953i	−0.999220	+	0.0394976i	$0.987424\pi$
$642$	−48.0000			−1.89441
$643$			12.0000i			0.473234i	0.971603	+	0.236617i	$0.0760386\pi$
$643$			12.0000i			0.473234i	−0.971603	+	0.236617i	$0.923961\pi$
$644$	−24.0000			−0.945732
$645$	24.0000			0.944999
$646$	−28.0000	+	7.00000i	−1.10165	+	0.275411i
$647$	11.0000			0.432455			0.216227	−	0.976343i	$-0.430625\pi$
$647$	11.0000			0.432455			0.216227	+	0.976343i	$0.430625\pi$
$648$	9.00000			0.353553
$649$			10.0000i			0.392534i
$650$	−1.00000			−0.0392232
$651$			84.0000i			3.29222i
$652$			4.00000i			0.156652i
$653$		−	16.0000i		−	0.626128i	−0.949732	−	0.313064i	$-0.898644\pi$
$653$		−	16.0000i		−	0.626128i	0.949732	−	0.313064i	$-0.101356\pi$
$654$	−57.0000			−2.22888
$655$		0			0
$656$		−	8.00000i		−	0.312348i
$657$		−	54.0000i		−	2.10674i
$658$			36.0000i			1.40343i
$659$	−29.0000			−1.12968			−0.564840	−	0.825201i	$-0.691062\pi$
$659$	−29.0000			−1.12968			−0.564840	+	0.825201i	$0.691062\pi$
$660$			6.00000i			0.233550i
$661$	12.0000			0.466746			0.233373	−	0.972387i	$-0.425024\pi$
$661$	12.0000			0.466746			0.233373	+	0.972387i	$0.425024\pi$
$662$	−19.0000			−0.738456
$663$	3.00000	+	12.0000i	0.116510	+	0.466041i
$664$	6.00000			0.232845
$665$	28.0000			1.08579
$666$			12.0000i			0.464991i
$667$	18.0000			0.696963
$668$		−	2.00000i		−	0.0773823i
$669$		−	87.0000i		−	3.36361i
$670$			10.0000i			0.386334i
$671$	2.00000			0.0772091
$672$	12.0000			0.462910
$673$		−	33.0000i		−	1.27206i	−0.771666	−	0.636028i	$-0.780576\pi$
$673$		−	33.0000i		−	1.27206i	0.771666	−	0.636028i	$-0.219424\pi$
$674$		−	23.0000i		−	0.885927i
$675$		−	9.00000i		−	0.346410i
$676$	−12.0000			−0.461538
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$	3.00000			0.115214
$679$	4.00000			0.153506
$680$	1.00000	+	4.00000i	0.0383482	+	0.153393i
$681$	−81.0000			−3.10393
$682$	14.0000			0.536088
$683$		−	35.0000i		−	1.33924i	−0.742705	−	0.669619i	$-0.766457\pi$
$683$		−	35.0000i		−	1.33924i	0.742705	−	0.669619i	$-0.233543\pi$
$684$	−42.0000			−1.60591
$685$		−	8.00000i		−	0.305664i
$686$		−	8.00000i		−	0.305441i
$687$			12.0000i			0.457829i
$688$	−8.00000			−0.304997
$689$	−11.0000			−0.419067
$690$		−	18.0000i		−	0.685248i
$691$			18.0000i			0.684752i	0.939563	+	0.342376i	$0.111232\pi$
$691$			18.0000i			0.684752i	−0.939563	+	0.342376i	$0.888768\pi$
$692$			2.00000i			0.0760286i
$693$	−48.0000			−1.82337
$694$			27.0000i			1.02491i
$695$	14.0000			0.531050
$696$	−9.00000			−0.341144
$697$	8.00000	+	32.0000i	0.303022	+	1.21209i
$698$	12.0000			0.454207
$699$	9.00000			0.340411
$700$		−	4.00000i		−	0.151186i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$			9.00000i			0.339683i
$703$		−	14.0000i		−	0.528020i
$704$		−	2.00000i		−	0.0753778i
$705$	−27.0000			−1.01688
$706$	−10.0000			−0.376355
$707$		−	8.00000i		−	0.300871i
$708$			15.0000i			0.563735i
$709$			17.0000i			0.638448i	0.947679	+	0.319224i	$0.103422\pi$
$709$			17.0000i			0.638448i	−0.947679	+	0.319224i	$0.896578\pi$
$710$	−1.00000			−0.0375293
$711$		0			0
$712$	−1.00000			−0.0374766
$713$	−42.0000			−1.57291
$714$	−48.0000	+	12.0000i	−1.79635	+	0.449089i
$715$	−2.00000			−0.0747958
$716$	24.0000			0.896922
$717$			60.0000i			2.24074i
$718$	−4.00000			−0.149279
$719$			15.0000i			0.559406i	0.960087	+	0.279703i	$0.0902359\pi$
$719$			15.0000i			0.559406i	−0.960087	+	0.279703i	$0.909764\pi$
$720$			6.00000i			0.223607i
$721$		0			0
$722$	30.0000			1.11648
$723$	12.0000			0.446285
$724$		−	10.0000i		−	0.371647i
$725$			3.00000i			0.111417i
$726$		−	21.0000i		−	0.779383i
$727$	13.0000			0.482143			0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000			0.482143			0.241072	+	0.970507i	$0.422501\pi$
$728$			4.00000i			0.148250i
$729$	27.0000			1.00000
$730$	9.00000			0.333105
$731$	32.0000	−	8.00000i	1.18356	−	0.295891i
$732$	3.00000			0.110883
$733$	6.00000			0.221615			0.110808	−	0.993842i	$-0.464656\pi$
$733$	6.00000			0.221615			0.110808	+	0.993842i	$0.464656\pi$
$734$			10.0000i			0.369107i
$735$	27.0000			0.995910
$736$			6.00000i			0.221163i
$737$			20.0000i			0.736709i
$738$			48.0000i			1.76690i
$739$	−27.0000			−0.993211			−0.496606	−	0.867976i	$-0.665420\pi$
$739$	−27.0000			−0.993211			−0.496606	+	0.867976i	$0.665420\pi$
$740$	−2.00000			−0.0735215
$741$		−	21.0000i		−	0.771454i
$742$		−	44.0000i		−	1.61529i
$743$			44.0000i			1.61420i	0.590412	+	0.807102i	$0.298965\pi$
$743$			44.0000i			1.61420i	−0.590412	+	0.807102i	$0.701035\pi$
$744$	21.0000			0.769897
$745$			6.00000i			0.219823i
$746$	10.0000			0.366126
$747$	−36.0000			−1.31717
$748$	2.00000	+	8.00000i	0.0731272	+	0.292509i
$749$	64.0000			2.33851
$750$	3.00000			0.109545
$751$			45.0000i			1.64207i	0.570875	+	0.821037i	$0.306604\pi$
$751$			45.0000i			1.64207i	−0.570875	+	0.821037i	$0.693396\pi$
$752$	9.00000			0.328196
$753$			24.0000i			0.874609i
$754$		−	3.00000i		−	0.109254i
$755$		−	22.0000i		−	0.800662i
$756$	−36.0000			−1.30931
$757$	43.0000			1.56286			0.781431	−	0.623992i	$-0.214490\pi$
$757$	43.0000			1.56286			0.781431	+	0.623992i	$0.214490\pi$
$758$		−	8.00000i		−	0.290573i
$759$		−	36.0000i		−	1.30672i
$760$		−	7.00000i		−	0.253917i
$761$	−18.0000			−0.652499			−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000			−0.652499			−0.326250	+	0.945284i	$0.605785\pi$
$762$			45.0000i			1.63018i
$763$	76.0000			2.75138
$764$	10.0000			0.361787
$765$	−6.00000	−	24.0000i	−0.216930	−	0.867722i
$766$	−19.0000			−0.686498
$767$	−5.00000			−0.180540
$768$		−	3.00000i		−	0.108253i
$769$	−23.0000			−0.829401			−0.414701	−	0.909958i	$-0.636114\pi$
$769$	−23.0000			−0.829401			−0.414701	+	0.909958i	$0.636114\pi$
$770$		−	8.00000i		−	0.288300i
$771$		−	72.0000i		−	2.59302i
$772$		−	2.00000i		−	0.0719816i
$773$	−6.00000			−0.215805			−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000			−0.215805			−0.107903	+	0.994161i	$0.534413\pi$
$774$	48.0000			1.72532
$775$		−	7.00000i		−	0.251447i
$776$		−	1.00000i		−	0.0358979i
$777$		−	24.0000i		−	0.860995i
$778$		0			0
$779$		−	56.0000i		−	2.00641i
$780$	−3.00000			−0.107417
$781$	−2.00000			−0.0715656
$782$	−6.00000	−	24.0000i	−0.214560	−	0.858238i
$783$	27.0000			0.964901
$784$	−9.00000			−0.321429
$785$		−	2.00000i		−	0.0713831i
$786$		0			0
$787$			17.0000i			0.605985i	0.952993	+	0.302992i	$0.0979856\pi$
$787$			17.0000i			0.605985i	−0.952993	+	0.302992i	$0.902014\pi$
$788$			18.0000i			0.641223i
$789$			27.0000i			0.961225i
$790$		0			0
$791$	−4.00000			−0.142224
$792$			12.0000i			0.426401i
$793$			1.00000i			0.0355110i
$794$			4.00000i			0.141955i
$795$	33.0000			1.17039
$796$		−	11.0000i		−	0.389885i
$797$	18.0000			0.637593			0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$	84.0000			2.97357
$799$	−36.0000	+	9.00000i	−1.27359	+	0.318397i
$800$	−1.00000			−0.0353553
$801$	6.00000			0.212000
$802$			24.0000i			0.847469i
$803$	18.0000			0.635206
$804$			30.0000i			1.05802i
$805$			24.0000i			0.845889i
$806$			7.00000i			0.246564i
$807$	−75.0000			−2.64013
$808$	−2.00000			−0.0703598
$809$		−	16.0000i		−	0.562530i	−0.959630	−	0.281265i	$-0.909246\pi$
$809$		−	16.0000i		−	0.562530i	0.959630	−	0.281265i	$-0.0907540\pi$
$810$		−	9.00000i		−	0.316228i
$811$		−	32.0000i		−	1.12367i	−0.827249	−	0.561836i	$-0.810095\pi$
$811$		−	32.0000i		−	1.12367i	0.827249	−	0.561836i	$-0.189905\pi$
$812$	12.0000			0.421117
$813$		−	36.0000i		−	1.26258i
$814$	−4.00000			−0.140200
$815$	4.00000			0.140114
$816$	3.00000	+	12.0000i	0.105021	+	0.420084i
$817$	−56.0000			−1.95919
$818$	−19.0000			−0.664319
$819$		−	24.0000i		−	0.838628i
$820$	−8.00000			−0.279372
$821$		−	21.0000i		−	0.732905i	−0.930437	−	0.366453i	$-0.880572\pi$
$821$		−	21.0000i		−	0.732905i	0.930437	−	0.366453i	$-0.119428\pi$
$822$		−	24.0000i		−	0.837096i
$823$			2.00000i			0.0697156i	0.999392	+	0.0348578i	$0.0110978\pi$
$823$			2.00000i			0.0697156i	−0.999392	+	0.0348578i	$0.988902\pi$
$824$		0			0
$825$	6.00000			0.208893
$826$		−	20.0000i		−	0.695889i
$827$		−	4.00000i		−	0.139094i	−0.997579	−	0.0695468i	$-0.977845\pi$
$827$		−	4.00000i		−	0.139094i	0.997579	−	0.0695468i	$-0.0221553\pi$
$828$		−	36.0000i		−	1.25109i
$829$	24.0000			0.833554			0.416777	−	0.909009i	$-0.363160\pi$
$829$	24.0000			0.833554			0.416777	+	0.909009i	$0.363160\pi$
$830$		−	6.00000i		−	0.208263i
$831$	6.00000			0.208138
$832$	1.00000			0.0346688
$833$	36.0000	−	9.00000i	1.24733	−	0.311832i
$834$	42.0000			1.45434
$835$	−2.00000			−0.0692129
$836$		−	14.0000i		−	0.484200i
$837$	−63.0000			−2.17760
$838$			10.0000i			0.345444i
$839$			43.0000i			1.48452i	0.670109	+	0.742262i	$0.266247\pi$
$839$			43.0000i			1.48452i	−0.670109	+	0.742262i	$0.733753\pi$
$840$		−	12.0000i		−	0.414039i
$841$	20.0000			0.689655
$842$	6.00000			0.206774
$843$		−	27.0000i		−	0.929929i
$844$			10.0000i			0.344214i
$845$			12.0000i			0.412813i
$846$	−54.0000			−1.85656
$847$			28.0000i			0.962091i
$848$	−11.0000			−0.377742
$849$	−21.0000			−0.720718
$850$	4.00000	−	1.00000i	0.137199	−	0.0342997i
$851$	12.0000			0.411355
$852$	−3.00000			−0.102778
$853$		−	4.00000i		−	0.136957i	−0.997653	−	0.0684787i	$-0.978185\pi$
$853$		−	4.00000i		−	0.136957i	0.997653	−	0.0684787i	$-0.0218145\pi$
$854$	−4.00000			−0.136877
$855$			42.0000i			1.43637i
$856$		−	16.0000i		−	0.546869i
$857$		−	23.0000i		−	0.785665i	−0.919610	−	0.392833i	$-0.871495\pi$
$857$		−	23.0000i		−	0.785665i	0.919610	−	0.392833i	$-0.128505\pi$
$858$	−6.00000			−0.204837
$859$	15.0000			0.511793			0.255897	−	0.966704i	$-0.417629\pi$
$859$	15.0000			0.511793			0.255897	+	0.966704i	$0.417629\pi$
$860$			8.00000i			0.272798i
$861$		−	96.0000i		−	3.27167i
$862$		−	8.00000i		−	0.272481i
$863$	−20.0000			−0.680808			−0.340404	−	0.940279i	$-0.610564\pi$
$863$	−20.0000			−0.680808			−0.340404	+	0.940279i	$0.610564\pi$
$864$			9.00000i			0.306186i
$865$	2.00000			0.0680020
$866$	−8.00000			−0.271851
$867$	−24.0000	−	45.0000i	−0.815083	−	1.52828i
$868$	−28.0000			−0.950382
$869$		0			0
$870$			9.00000i			0.305129i
$871$	−10.0000			−0.338837
$872$		−	19.0000i		−	0.643421i
$873$			6.00000i			0.203069i
$874$			42.0000i			1.42067i
$875$	−4.00000			−0.135225
$876$	27.0000			0.912245
$877$			38.0000i			1.28317i	0.767052	+	0.641584i	$0.221723\pi$
$877$			38.0000i			1.28317i	−0.767052	+	0.641584i	$0.778277\pi$
$878$			32.0000i			1.07995i
$879$			15.0000i			0.505937i
$880$	−2.00000			−0.0674200
$881$			6.00000i			0.202145i	0.994879	+	0.101073i	$0.0322274\pi$
$881$			6.00000i			0.202145i	−0.994879	+	0.101073i	$0.967773\pi$
$882$	54.0000			1.81827
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$	−4.00000	+	1.00000i	−0.134535	+	0.0336336i
$885$	15.0000			0.504219
$886$	−24.0000			−0.806296
$887$			36.0000i			1.20876i	0.796696	+	0.604381i	$0.206579\pi$
$887$			36.0000i			1.20876i	−0.796696	+	0.604381i	$0.793421\pi$
$888$	−6.00000			−0.201347
$889$		−	60.0000i		−	2.01234i
$890$			1.00000i			0.0335201i
$891$		−	18.0000i		−	0.603023i
$892$	29.0000			0.970992
$893$	63.0000			2.10821
$894$			18.0000i			0.602010i
$895$		−	24.0000i		−	0.802232i
$896$			4.00000i			0.133631i
$897$	18.0000			0.601003
$898$			30.0000i			1.00111i
$899$	21.0000			0.700389
$900$	6.00000			0.200000
$901$	44.0000	−	11.0000i	1.46585	−	0.366463i
$902$	−16.0000			−0.532742
$903$	−96.0000			−3.19468
$904$			1.00000i			0.0332595i
$905$	−10.0000			−0.332411
$906$		−	66.0000i		−	2.19270i
$907$			45.0000i			1.49420i	0.664711	+	0.747100i	$0.268555\pi$
$907$			45.0000i			1.49420i	−0.664711	+	0.747100i	$0.731445\pi$
$908$		−	27.0000i		−	0.896026i
$909$	12.0000			0.398015
$910$	4.00000			0.132599
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		−	21.0000i		−	0.695379i
$913$		−	12.0000i		−	0.397142i
$914$	−36.0000			−1.19077
$915$		−	3.00000i		−	0.0991769i
$916$	−4.00000			−0.132164
$917$		0			0
$918$	−9.00000	−	36.0000i	−0.297044	−	1.18818i
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$	6.00000			0.197814
$921$		−	66.0000i		−	2.17477i
$922$	−6.00000			−0.197599
$923$		−	1.00000i		−	0.0329154i
$924$		−	24.0000i		−	0.789542i
$925$			2.00000i			0.0657596i
$926$	9.00000			0.295758
$927$		0			0
$928$		−	3.00000i		−	0.0984798i
$929$			12.0000i			0.393707i	0.980433	+	0.196854i	$0.0630724\pi$
$929$			12.0000i			0.393707i	−0.980433	+	0.196854i	$0.936928\pi$
$930$		−	21.0000i		−	0.688617i
$931$	−63.0000			−2.06474
$932$			3.00000i			0.0982683i
$933$	48.0000			1.57145
$934$	26.0000			0.850746
$935$	8.00000	−	2.00000i	0.261628	−	0.0654070i
$936$	−6.00000			−0.196116
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		−	40.0000i		−	1.30605i
$939$	−78.0000			−2.54543
$940$		−	9.00000i		−	0.293548i
$941$			7.00000i			0.228193i	0.993470	+	0.114097i	$0.0363974\pi$
$941$			7.00000i			0.228193i	−0.993470	+	0.114097i	$0.963603\pi$
$942$		−	6.00000i		−	0.195491i
$943$	48.0000			1.56310
$944$	−5.00000			−0.162736
$945$			36.0000i			1.17108i
$946$			16.0000i			0.520205i
$947$		−	41.0000i		−	1.33232i	−0.745808	−	0.666160i	$-0.767937\pi$
$947$		−	41.0000i		−	1.33232i	0.745808	−	0.666160i	$-0.232063\pi$
$948$		0			0
$949$			9.00000i			0.292152i
$950$	−7.00000			−0.227110
$951$	60.0000			1.94563
$952$	−4.00000	−	16.0000i	−0.129641	−	0.518563i
$953$	−34.0000			−1.10137			−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000			−1.10137			−0.550684	+	0.834714i	$0.685633\pi$
$954$	66.0000			2.13683
$955$		−	10.0000i		−	0.323592i
$956$	−20.0000			−0.646846
$957$			18.0000i			0.581857i
$958$		−	15.0000i		−	0.484628i
$959$			32.0000i			1.03333i
$960$	−3.00000			−0.0968246
$961$	−18.0000			−0.580645
$962$		−	2.00000i		−	0.0644826i
$963$			96.0000i			3.09356i
$964$			4.00000i			0.128831i
$965$	−2.00000			−0.0643823
$966$			72.0000i			2.31656i
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	7.00000			0.224989
$969$	21.0000	+	84.0000i	0.674617	+	2.69847i
$970$	−1.00000			−0.0321081
$971$	−29.0000			−0.930654			−0.465327	−	0.885139i	$-0.654063\pi$
$971$	−29.0000			−0.930654			−0.465327	+	0.885139i	$0.654063\pi$
$972$		0			0
$973$	−56.0000			−1.79528
$974$		−	40.0000i		−	1.28168i
$975$			3.00000i			0.0960769i
$976$			1.00000i			0.0320092i
$977$	−10.0000			−0.319928			−0.159964	−	0.987123i	$-0.551138\pi$
$977$	−10.0000			−0.319928			−0.159964	+	0.987123i	$0.551138\pi$
$978$	12.0000			0.383718
$979$			2.00000i			0.0639203i
$980$			9.00000i			0.287494i
$981$			114.000i			3.63974i
$982$	−15.0000			−0.478669
$983$		−	4.00000i		−	0.127580i	−0.997963	−	0.0637901i	$-0.979681\pi$
$983$		−	4.00000i		−	0.127580i	0.997963	−	0.0637901i	$-0.0203188\pi$
$984$	−24.0000			−0.765092
$985$	18.0000			0.573528
$986$	3.00000	+	12.0000i	0.0955395	+	0.382158i
$987$	108.000			3.43768
$988$	7.00000			0.222700
$989$		−	48.0000i		−	1.52631i
$990$	12.0000			0.381385
$991$			23.0000i			0.730619i	0.930886	+	0.365310i	$0.119037\pi$
$991$			23.0000i			0.730619i	−0.930886	+	0.365310i	$0.880963\pi$
$992$			7.00000i			0.222250i
$993$			57.0000i			1.80884i
$994$	4.00000			0.126872
$995$	−11.0000			−0.348723
$996$		−	18.0000i		−	0.570352i
$997$		−	12.0000i		−	0.380044i	−0.981780	−	0.190022i	$-0.939144\pi$
$997$		−	12.0000i		−	0.380044i	0.981780	−	0.190022i	$-0.0608559\pi$
$998$			20.0000i			0.633089i
$999$	18.0000			0.569495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.b.b.101.1	✓	2
3.2	odd	2		1530.2.c.b.271.2		2
4.3	odd	2		1360.2.c.a.1121.2		2
5.2	odd	4		850.2.d.a.849.2		2
5.3	odd	4		850.2.d.h.849.1		2
5.4	even	2		850.2.b.a.101.2		2
17.4	even	4		2890.2.a.a.1.1		1
17.13	even	4		2890.2.a.l.1.1		1
17.16	even	2	inner	170.2.b.b.101.2	yes	2
51.50	odd	2		1530.2.c.b.271.1		2
68.67	odd	2		1360.2.c.a.1121.1		2
85.33	odd	4		850.2.d.a.849.1		2
85.67	odd	4		850.2.d.h.849.2		2
85.84	even	2		850.2.b.a.101.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.b.b.101.1	✓	2	1.1	even	1	trivial
170.2.b.b.101.2	yes	2	17.16	even	2	inner
850.2.b.a.101.1		2	85.84	even	2
850.2.b.a.101.2		2	5.4	even	2
850.2.d.a.849.1		2	85.33	odd	4
850.2.d.a.849.2		2	5.2	odd	4
850.2.d.h.849.1		2	5.3	odd	4
850.2.d.h.849.2		2	85.67	odd	4
1360.2.c.a.1121.1		2	68.67	odd	2
1360.2.c.a.1121.2		2	4.3	odd	2
1530.2.c.b.271.1		2	51.50	odd	2
1530.2.c.b.271.2		2	3.2	odd	2
2890.2.a.a.1.1		1	17.4	even	4
2890.2.a.l.1.1		1	17.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.00000i q^{3} +1.00000 q^{4} -1.00000i q^{5} -3.00000i q^{6} +4.00000i q^{7} +1.00000 q^{8} -6.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.00000i q^{3} +1.00000 q^{4} -1.00000i q^{5} -3.00000i q^{6} +4.00000i q^{7} +1.00000 q^{8} -6.00000 q^{9} -1.00000i q^{10} -2.00000i q^{11} -3.00000i q^{12} +1.00000 q^{13} +4.00000i q^{14} -3.00000 q^{15} +1.00000 q^{16} +(-4.00000 + 1.00000i) q^{17} -6.00000 q^{18} +7.00000 q^{19} -1.00000i q^{20} +12.0000 q^{21} -2.00000i q^{22} +6.00000i q^{23} -3.00000i q^{24} -1.00000 q^{25} +1.00000 q^{26} +9.00000i q^{27} +4.00000i q^{28} -3.00000i q^{29} -3.00000 q^{30} +7.00000i q^{31} +1.00000 q^{32} -6.00000 q^{33} +(-4.00000 + 1.00000i) q^{34} +4.00000 q^{35} -6.00000 q^{36} -2.00000i q^{37} +7.00000 q^{38} -3.00000i q^{39} -1.00000i q^{40} -8.00000i q^{41} +12.0000 q^{42} -8.00000 q^{43} -2.00000i q^{44} +6.00000i q^{45} +6.00000i q^{46} +9.00000 q^{47} -3.00000i q^{48} -9.00000 q^{49} -1.00000 q^{50} +(3.00000 + 12.0000i) q^{51} +1.00000 q^{52} -11.0000 q^{53} +9.00000i q^{54} -2.00000 q^{55} +4.00000i q^{56} -21.0000i q^{57} -3.00000i q^{58} -5.00000 q^{59} -3.00000 q^{60} +1.00000i q^{61} +7.00000i q^{62} -24.0000i q^{63} +1.00000 q^{64} -1.00000i q^{65} -6.00000 q^{66} -10.0000 q^{67} +(-4.00000 + 1.00000i) q^{68} +18.0000 q^{69} +4.00000 q^{70} -1.00000i q^{71} -6.00000 q^{72} +9.00000i q^{73} -2.00000i q^{74} +3.00000i q^{75} +7.00000 q^{76} +8.00000 q^{77} -3.00000i q^{78} -1.00000i q^{80} +9.00000 q^{81} -8.00000i q^{82} +6.00000 q^{83} +12.0000 q^{84} +(1.00000 + 4.00000i) q^{85} -8.00000 q^{86} -9.00000 q^{87} -2.00000i q^{88} -1.00000 q^{89} +6.00000i q^{90} +4.00000i q^{91} +6.00000i q^{92} +21.0000 q^{93} +9.00000 q^{94} -7.00000i q^{95} -3.00000i q^{96} -1.00000i q^{97} -9.00000 q^{98} +12.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 12 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 12 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 12 q^{9} + 2 q^{13} - 6 q^{15} + 2 q^{16} - 8 q^{17} - 12 q^{18} + 14 q^{19} + 24 q^{21} - 2 q^{25} + 2 q^{26} - 6 q^{30} + 2 q^{32} - 12 q^{33} - 8 q^{34} + 8 q^{35} - 12 q^{36} + 14 q^{38} + 24 q^{42} - 16 q^{43} + 18 q^{47} - 18 q^{49} - 2 q^{50} + 6 q^{51} + 2 q^{52} - 22 q^{53} - 4 q^{55} - 10 q^{59} - 6 q^{60} + 2 q^{64} - 12 q^{66} - 20 q^{67} - 8 q^{68} + 36 q^{69} + 8 q^{70} - 12 q^{72} + 14 q^{76} + 16 q^{77} + 18 q^{81} + 12 q^{83} + 24 q^{84} + 2 q^{85} - 16 q^{86} - 18 q^{87} - 2 q^{89} + 42 q^{93} + 18 q^{94} - 18 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 12 * q^9 + 2 * q^13 - 6 * q^15 + 2 * q^16 - 8 * q^17 - 12 * q^18 + 14 * q^19 + 24 * q^21 - 2 * q^25 + 2 * q^26 - 6 * q^30 + 2 * q^32 - 12 * q^33 - 8 * q^34 + 8 * q^35 - 12 * q^36 + 14 * q^38 + 24 * q^42 - 16 * q^43 + 18 * q^47 - 18 * q^49 - 2 * q^50 + 6 * q^51 + 2 * q^52 - 22 * q^53 - 4 * q^55 - 10 * q^59 - 6 * q^60 + 2 * q^64 - 12 * q^66 - 20 * q^67 - 8 * q^68 + 36 * q^69 + 8 * q^70 - 12 * q^72 + 14 * q^76 + 16 * q^77 + 18 * q^81 + 12 * q^83 + 24 * q^84 + 2 * q^85 - 16 * q^86 - 18 * q^87 - 2 * q^89 + 42 * q^93 + 18 * q^94 - 18 * q^98

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