LMFDB - Embedded newform 170.3.j.b.123.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,3,Mod(47,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("170.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	170.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.63216449413$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 80 x^{14} + 2532 x^{12} + 40532 x^{10} + 346464 x^{8} + 1518752 x^{6} + 2895224 x^{4} + \cdots + 148996 $ x^16 + 80x^14 + 2532x^12 + 40532x^10 + 346464x^8 + 1518752x^6 + 2895224x^4 + 1253728*x^2 + 148996
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			123.7
Root			$3.64449i$ of defining polynomial
Character	$\chi$	$=$	170.123
Dual form			170.3.j.b.47.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +3.64449 q^{3} +2.00000i q^{4} +(4.23872 - 2.65202i) q^{5} +(-3.64449 - 3.64449i) q^{6} +2.51762 q^{7} +(2.00000 - 2.00000i) q^{8} +4.28231 q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +3.64449 q^{3} +2.00000i q^{4} +(4.23872 - 2.65202i) q^{5} +(-3.64449 - 3.64449i) q^{6} +2.51762 q^{7} +(2.00000 - 2.00000i) q^{8} +4.28231 q^{9} +(-6.89075 - 1.58670i) q^{10} +(1.84002 + 1.84002i) q^{11} +7.28898i q^{12} +(-1.57608 - 1.57608i) q^{13} +(-2.51762 - 2.51762i) q^{14} +(15.4480 - 9.66527i) q^{15} -4.00000 q^{16} +(13.6177 + 10.1763i) q^{17} +(-4.28231 - 4.28231i) q^{18} -10.4683 q^{19} +(5.30404 + 8.47745i) q^{20} +9.17545 q^{21} -3.68003i q^{22} -2.86447i q^{23} +(7.28898 - 7.28898i) q^{24} +(10.9336 - 22.4824i) q^{25} +3.15217i q^{26} -17.1936 q^{27} +5.03524i q^{28} +(-16.7455 - 16.7455i) q^{29} +(-25.1133 - 5.78272i) q^{30} +(19.3791 - 19.3791i) q^{31} +(4.00000 + 4.00000i) q^{32} +(6.70592 + 6.70592i) q^{33} +(-3.44145 - 23.7940i) q^{34} +(10.6715 - 6.67679i) q^{35} +8.56461i q^{36} -14.1464i q^{37} +(10.4683 + 10.4683i) q^{38} +(-5.74402 - 5.74402i) q^{39} +(3.17340 - 13.7815i) q^{40} +(35.8985 + 35.8985i) q^{41} +(-9.17545 - 9.17545i) q^{42} +(-10.5842 + 10.5842i) q^{43} +(-3.68003 + 3.68003i) q^{44} +(18.1515 - 11.3568i) q^{45} +(-2.86447 + 2.86447i) q^{46} +(-60.3631 + 60.3631i) q^{47} -14.5780 q^{48} -42.6616 q^{49} +(-33.4159 + 11.5488i) q^{50} +(49.6297 + 37.0874i) q^{51} +(3.15217 - 3.15217i) q^{52} +(-47.7065 + 47.7065i) q^{53} +(17.1936 + 17.1936i) q^{54} +(12.6791 + 2.91956i) q^{55} +(5.03524 - 5.03524i) q^{56} -38.1517 q^{57} +33.4909i q^{58} +24.3243 q^{59} +(19.3305 + 30.8960i) q^{60} +(39.3536 + 39.3536i) q^{61} -38.7582 q^{62} +10.7812 q^{63} -8.00000i q^{64} +(-10.8604 - 2.50078i) q^{65} -13.4118i q^{66} +(-64.8353 + 64.8353i) q^{67} +(-20.3526 + 27.2355i) q^{68} -10.4395i q^{69} +(-17.3483 - 3.99471i) q^{70} +(-10.0191 + 10.0191i) q^{71} +(8.56461 - 8.56461i) q^{72} -54.0001 q^{73} +(-14.1464 + 14.1464i) q^{74} +(39.8472 - 81.9368i) q^{75} -20.9367i q^{76} +(4.63247 + 4.63247i) q^{77} +11.4880i q^{78} +(47.7062 - 47.7062i) q^{79} +(-16.9549 + 10.6081i) q^{80} -101.203 q^{81} -71.7969i q^{82} +(-33.3253 + 33.3253i) q^{83} +18.3509i q^{84} +(84.7096 + 7.01995i) q^{85} +21.1685 q^{86} +(-61.0287 - 61.0287i) q^{87} +7.36007 q^{88} +36.1413i q^{89} +(-29.5083 - 6.79474i) q^{90} +(-3.96798 - 3.96798i) q^{91} +5.72894 q^{92} +(70.6269 - 70.6269i) q^{93} +120.726 q^{94} +(-44.3724 + 27.7622i) q^{95} +(14.5780 + 14.5780i) q^{96} -143.564i q^{97} +(42.6616 + 42.6616i) q^{98} +(7.87951 + 7.87951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 2 q^{5} - 12 q^{7} + 32 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 + 2 * q^5 - 12 * q^7 + 32 * q^8 + 16 * q^9	$ 16 q - 16 q^{2} + 2 q^{5} - 12 q^{7} + 32 q^{8} + 16 q^{9} + 20 q^{11} + 4 q^{13} + 12 q^{14} - 12 q^{15} - 64 q^{16} - 12 q^{17} - 16 q^{18} + 16 q^{19} - 4 q^{20} - 44 q^{25} + 108 q^{27} + 20 q^{29} + 12 q^{30} + 92 q^{31} + 64 q^{32} - 60 q^{33} - 24 q^{34} - 124 q^{35} - 16 q^{38} + 140 q^{39} + 8 q^{40} - 60 q^{41} - 52 q^{43} - 40 q^{44} + 62 q^{45} + 16 q^{46} + 112 q^{47} - 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} - 48 q^{53} - 108 q^{54} + 40 q^{55} - 24 q^{56} + 88 q^{57} + 76 q^{61} - 184 q^{62} - 8 q^{63} + 4 q^{65} + 116 q^{67} + 72 q^{68} + 124 q^{70} - 268 q^{71} + 32 q^{72} - 148 q^{73} - 32 q^{74} - 76 q^{75} + 116 q^{77} + 88 q^{79} - 8 q^{80} - 352 q^{81} + 160 q^{83} + 142 q^{85} + 104 q^{86} - 236 q^{87} + 80 q^{88} + 136 q^{90} - 168 q^{91} - 32 q^{92} - 48 q^{93} - 224 q^{94} - 388 q^{95} + 136 q^{98} + 348 q^{99}+O(q^{100}) $ 16 * q - 16 * q^2 + 2 * q^5 - 12 * q^7 + 32 * q^8 + 16 * q^9 + 20 * q^11 + 4 * q^13 + 12 * q^14 - 12 * q^15 - 64 * q^16 - 12 * q^17 - 16 * q^18 + 16 * q^19 - 4 * q^20 - 44 * q^25 + 108 * q^27 + 20 * q^29 + 12 * q^30 + 92 * q^31 + 64 * q^32 - 60 * q^33 - 24 * q^34 - 124 * q^35 - 16 * q^38 + 140 * q^39 + 8 * q^40 - 60 * q^41 - 52 * q^43 - 40 * q^44 + 62 * q^45 + 16 * q^46 + 112 * q^47 - 136 * q^49 - 4 * q^50 - 140 * q^51 - 8 * q^52 - 48 * q^53 - 108 * q^54 + 40 * q^55 - 24 * q^56 + 88 * q^57 + 76 * q^61 - 184 * q^62 - 8 * q^63 + 4 * q^65 + 116 * q^67 + 72 * q^68 + 124 * q^70 - 268 * q^71 + 32 * q^72 - 148 * q^73 - 32 * q^74 - 76 * q^75 + 116 * q^77 + 88 * q^79 - 8 * q^80 - 352 * q^81 + 160 * q^83 + 142 * q^85 + 104 * q^86 - 236 * q^87 + 80 * q^88 + 136 * q^90 - 168 * q^91 - 32 * q^92 - 48 * q^93 - 224 * q^94 - 388 * q^95 + 136 * q^98 + 348 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	3.64449			1.21483			0.607415	−	0.794385i	$-0.292207\pi$
$3$	3.64449			1.21483			0.607415	+	0.794385i	$0.292207\pi$
$4$			2.00000i			0.500000i
$5$	4.23872	−	2.65202i	0.847745	−	0.530404i
$5$	4.23872	−	2.65202i	0.847745	−	0.530404i
$6$	−3.64449	−	3.64449i	−0.607415	−	0.607415i
$7$	2.51762			0.359660			0.179830	−	0.983698i	$-0.442445\pi$
$7$	2.51762			0.359660			0.179830	+	0.983698i	$0.442445\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	4.28231			0.475812
$10$	−6.89075	−	1.58670i	−0.689075	−	0.158670i
$11$	1.84002	+	1.84002i	0.167274	+	0.167274i	0.785780	−	0.618506i	$-0.212262\pi$
$11$	1.84002	+	1.84002i	0.167274	+	0.167274i	−0.618506	+	0.785780i	$0.712262\pi$
$12$			7.28898i			0.607415i
$13$	−1.57608	−	1.57608i	−0.121237	−	0.121237i	0.643885	−	0.765122i	$-0.277322\pi$
$13$	−1.57608	−	1.57608i	−0.121237	−	0.121237i	−0.765122	+	0.643885i	$0.777322\pi$
$14$	−2.51762	−	2.51762i	−0.179830	−	0.179830i
$15$	15.4480	−	9.66527i	1.02987	−	0.644351i
$16$	−4.00000			−0.250000
$17$	13.6177	+	10.1763i	0.801044	+	0.598606i
$17$	13.6177	+	10.1763i	0.801044	+	0.598606i
$18$	−4.28231	−	4.28231i	−0.237906	−	0.237906i
$19$	−10.4683			−0.550965			−0.275482	−	0.961306i	$-0.588838\pi$
$19$	−10.4683			−0.550965			−0.275482	+	0.961306i	$0.588838\pi$
$20$	5.30404	+	8.47745i	0.265202	+	0.423872i
$21$	9.17545			0.436926
$22$		−	3.68003i		−	0.167274i
$23$		−	2.86447i		−	0.124542i	−0.998059	−	0.0622711i	$-0.980166\pi$
$23$		−	2.86447i		−	0.124542i	0.998059	−	0.0622711i	$-0.0198343\pi$
$24$	7.28898	−	7.28898i	0.303707	−	0.303707i
$25$	10.9336	−	22.4824i	0.437342	−	0.899295i
$26$			3.15217i			0.121237i
$27$	−17.1936			−0.636800
$28$			5.03524i			0.179830i
$29$	−16.7455	−	16.7455i	−0.577430	−	0.577430i	0.356765	−	0.934194i	$-0.383880\pi$
$29$	−16.7455	−	16.7455i	−0.577430	−	0.577430i	−0.934194	+	0.356765i	$0.883880\pi$
$30$	−25.1133	−	5.78272i	−0.837108	−	0.192757i
$31$	19.3791	−	19.3791i	0.625132	−	0.625132i	−0.321707	−	0.946839i	$-0.604257\pi$
$31$	19.3791	−	19.3791i	0.625132	−	0.625132i	0.946839	+	0.321707i	$0.104257\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	6.70592	+	6.70592i	0.203210	+	0.203210i
$34$	−3.44145	−	23.7940i	−0.101219	−	0.699825i
$35$	10.6715	−	6.67679i	0.304900	−	0.190765i
$36$			8.56461i			0.237906i
$37$		−	14.1464i		−	0.382335i	−0.981557	−	0.191167i	$-0.938773\pi$
$37$		−	14.1464i		−	0.382335i	0.981557	−	0.191167i	$-0.0612273\pi$
$38$	10.4683	+	10.4683i	0.275482	+	0.275482i
$39$	−5.74402	−	5.74402i	−0.147283	−	0.147283i
$40$	3.17340	−	13.7815i	0.0793351	−	0.344537i
$41$	35.8985	+	35.8985i	0.875573	+	0.875573i	0.993073	−	0.117500i	$-0.0374881\pi$
$41$	35.8985	+	35.8985i	0.875573	+	0.875573i	−0.117500	+	0.993073i	$0.537488\pi$
$42$	−9.17545	−	9.17545i	−0.218463	−	0.218463i
$43$	−10.5842	+	10.5842i	−0.246145	+	0.246145i	−0.819387	−	0.573241i	$-0.805686\pi$
$43$	−10.5842	+	10.5842i	−0.246145	+	0.246145i	0.573241	+	0.819387i	$0.305686\pi$
$44$	−3.68003	+	3.68003i	−0.0836371	+	0.0836371i
$45$	18.1515	−	11.3568i	0.403367	−	0.252373i
$46$	−2.86447	+	2.86447i	−0.0622711	+	0.0622711i
$47$	−60.3631	+	60.3631i	−1.28432	+	1.28432i	−0.346138	+	0.938184i	$0.612507\pi$
$47$	−60.3631	+	60.3631i	−1.28432	+	1.28432i	−0.938184	+	0.346138i	$0.887493\pi$
$48$	−14.5780			−0.303707
$49$	−42.6616			−0.870645
$50$	−33.4159	+	11.5488i	−0.668319	+	0.230976i
$51$	49.6297	+	37.0874i	0.973132	+	0.727204i
$52$	3.15217	−	3.15217i	0.0606186	−	0.0606186i
$53$	−47.7065	+	47.7065i	−0.900122	+	0.900122i	−0.995446	−	0.0953242i	$-0.969611\pi$
$53$	−47.7065	+	47.7065i	−0.900122	+	0.900122i	0.0953242	+	0.995446i	$0.469611\pi$
$54$	17.1936	+	17.1936i	0.318400	+	0.318400i
$55$	12.6791	+	2.91956i	0.230529	+	0.0530829i
$56$	5.03524	−	5.03524i	0.0899151	−	0.0899151i
$57$	−38.1517			−0.669328
$58$			33.4909i			0.577430i
$59$	24.3243			0.412276			0.206138	−	0.978523i	$-0.433910\pi$
$59$	24.3243			0.412276			0.206138	+	0.978523i	$0.433910\pi$
$60$	19.3305	+	30.8960i	0.322176	+	0.514933i
$61$	39.3536	+	39.3536i	0.645141	+	0.645141i	0.951815	−	0.306673i	$-0.0992159\pi$
$61$	39.3536	+	39.3536i	0.645141	+	0.645141i	−0.306673	+	0.951815i	$0.599216\pi$
$62$	−38.7582			−0.625132
$63$	10.7812			0.171131
$64$		−	8.00000i		−	0.125000i
$65$	−10.8604	−	2.50078i	−0.167083	−	0.0384735i
$66$		−	13.4118i		−	0.203210i
$67$	−64.8353	+	64.8353i	−0.967692	+	0.967692i	−0.999494	−	0.0318024i	$-0.989875\pi$
$67$	−64.8353	+	64.8353i	−0.967692	+	0.967692i	0.0318024	+	0.999494i	$0.489875\pi$
$68$	−20.3526	+	27.2355i	−0.299303	+	0.400522i
$69$		−	10.4395i		−	0.151298i
$70$	−17.3483	−	3.99471i	−0.247833	−	0.0570673i
$71$	−10.0191	+	10.0191i	−0.141115	+	0.141115i	−0.774135	−	0.633020i	$-0.781815\pi$
$71$	−10.0191	+	10.0191i	−0.141115	+	0.141115i	0.633020	+	0.774135i	$0.281815\pi$
$72$	8.56461	−	8.56461i	0.118953	−	0.118953i
$73$	−54.0001			−0.739728			−0.369864	−	0.929086i	$-0.620596\pi$
$73$	−54.0001			−0.739728			−0.369864	+	0.929086i	$0.620596\pi$
$74$	−14.1464	+	14.1464i	−0.191167	+	0.191167i
$75$	39.8472	−	81.9368i	0.531297	−	1.09249i
$76$		−	20.9367i		−	0.275482i
$77$	4.63247	+	4.63247i	0.0601619	+	0.0601619i
$78$			11.4880i			0.147283i
$79$	47.7062	−	47.7062i	0.603876	−	0.603876i	−0.337463	−	0.941339i	$-0.609569\pi$
$79$	47.7062	−	47.7062i	0.603876	−	0.603876i	0.941339	+	0.337463i	$0.109569\pi$
$80$	−16.9549	+	10.6081i	−0.211936	+	0.132601i
$81$	−101.203			−1.24941
$82$		−	71.7969i		−	0.875573i
$83$	−33.3253	+	33.3253i	−0.401509	+	0.401509i	−0.878765	−	0.477255i	$-0.841632\pi$
$83$	−33.3253	+	33.3253i	−0.401509	+	0.401509i	0.477255	+	0.878765i	$0.341632\pi$
$84$			18.3509i			0.218463i
$85$	84.7096	+	7.01995i	0.996584	+	0.0825876i
$86$	21.1685			0.246145
$87$	−61.0287	−	61.0287i	−0.701479	−	0.701479i
$88$	7.36007			0.0836371
$89$			36.1413i			0.406082i	0.979170	+	0.203041i	$0.0650825\pi$
$89$			36.1413i			0.406082i	−0.979170	+	0.203041i	$0.934917\pi$
$90$	−29.5083	−	6.79474i	−0.327870	−	0.0754971i
$91$	−3.96798	−	3.96798i	−0.0436042	−	0.0436042i
$92$	5.72894			0.0622711
$93$	70.6269	−	70.6269i	0.759429	−	0.759429i
$94$	120.726			1.28432
$95$	−44.3724	+	27.7622i	−0.467077	+	0.292234i
$96$	14.5780	+	14.5780i	0.151854	+	0.151854i
$97$		−	143.564i		−	1.48004i	−0.672584	−	0.740021i	$-0.734816\pi$
$97$		−	143.564i		−	1.48004i	0.672584	−	0.740021i	$-0.265184\pi$
$98$	42.6616	+	42.6616i	0.435322	+	0.435322i
$99$	7.87951	+	7.87951i	0.0795911	+	0.0795911i
$100$	44.9648	+	21.8671i	0.449648	+	0.218671i
$101$	−36.3606			−0.360006			−0.180003	−	0.983666i	$-0.557611\pi$
$101$	−36.3606			−0.360006			−0.180003	+	0.983666i	$0.557611\pi$
$102$	−12.5423	−	86.7171i	−0.122964	−	0.850168i
$103$	55.7838	+	55.7838i	0.541591	+	0.541591i	0.923995	−	0.382404i	$-0.124904\pi$
$103$	55.7838	+	55.7838i	0.541591	+	0.541591i	−0.382404	+	0.923995i	$0.624904\pi$
$104$	−6.30434			−0.0606186
$105$	38.8922	−	24.3335i	0.370402	−	0.231747i
$106$	95.4129			0.900122
$107$			102.118i			0.954370i	0.878803	+	0.477185i	$0.158343\pi$
$107$			102.118i			0.954370i	−0.878803	+	0.477185i	$0.841657\pi$
$108$		−	34.3872i		−	0.318400i
$109$	135.242	−	135.242i	1.24075	−	1.24075i	0.281057	−	0.959691i	$-0.409315\pi$
$109$	135.242	−	135.242i	1.24075	−	1.24075i	0.959691	−	0.281057i	$-0.0906849\pi$
$110$	−9.75953	−	15.5986i	−0.0887230	−	0.141806i
$111$		−	51.5563i		−	0.464472i
$112$	−10.0705			−0.0899151
$113$		−	171.052i		−	1.51374i	−0.653567	−	0.756869i	$-0.726728\pi$
$113$		−	171.052i		−	1.51374i	0.653567	−	0.756869i	$-0.273272\pi$
$114$	38.1517	+	38.1517i	0.334664	+	0.334664i
$115$	−7.59663	−	12.1417i	−0.0660577	−	0.105580i
$116$	33.4909	−	33.4909i	0.288715	−	0.288715i
$117$	−6.74928	−	6.74928i	−0.0576861	−	0.0576861i
$118$	−24.3243	−	24.3243i	−0.206138	−	0.206138i
$119$	34.2843	+	25.6201i	0.288104	+	0.215295i
$120$	11.5654	−	50.2265i	0.0963786	−	0.418554i
$121$		−	114.229i		−	0.944039i
$122$		−	78.7073i		−	0.645141i
$123$	130.832	+	130.832i	1.06367	+	1.06367i
$124$	38.7582	+	38.7582i	0.312566	+	0.312566i
$125$	−13.2794	−	124.293i	−0.106235	−	0.994341i
$126$	−10.7812	−	10.7812i	−0.0855653	−	0.0855653i
$127$	35.7971	+	35.7971i	0.281867	+	0.281867i	0.833853	−	0.551986i	$-0.186130\pi$
$127$	35.7971	+	35.7971i	0.281867	+	0.281867i	−0.551986	+	0.833853i	$0.686130\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$	−38.5742	+	38.5742i	−0.299025	+	0.299025i
$130$	8.35962	+	13.3612i	0.0643048	+	0.102778i
$131$	−42.2809	+	42.2809i	−0.322755	+	0.322755i	−0.849823	−	0.527068i	$-0.823291\pi$
$131$	−42.2809	+	42.2809i	−0.322755	+	0.322755i	0.527068	+	0.849823i	$0.323291\pi$
$132$	−13.4118	+	13.4118i	−0.101605	+	0.101605i
$133$	−26.3553			−0.198160
$134$	129.671			0.967692
$135$	−72.8789	+	45.5978i	−0.539843	+	0.337761i
$136$	47.5881	−	6.88290i	0.349912	−	0.0506095i
$137$	−126.790	+	126.790i	−0.925473	+	0.925473i	−0.997409	−	0.0719358i	$-0.977082\pi$
$137$	−126.790	+	126.790i	−0.925473	+	0.925473i	0.0719358	+	0.997409i	$0.477082\pi$
$138$	−10.4395	+	10.4395i	−0.0756488	+	0.0756488i
$139$	−23.0228	−	23.0228i	−0.165632	−	0.165632i	0.619424	−	0.785056i	$-0.287366\pi$
$139$	−23.0228	−	23.0228i	−0.165632	−	0.165632i	−0.785056	+	0.619424i	$0.787366\pi$
$140$	13.3536	+	21.3430i	0.0953827	+	0.152450i
$141$	−219.993	+	219.993i	−1.56023	+	1.56023i
$142$	20.0383			0.141115
$143$		−	5.80004i		−	0.0405597i
$144$	−17.1292			−0.118953
$145$	−115.389	−	26.5701i	−0.795784	−	0.183242i
$146$	54.0001	+	54.0001i	0.369864	+	0.369864i
$147$	−155.480			−1.05769
$148$	28.2928			0.191167
$149$		−	107.972i		−	0.724647i	−0.932052	−	0.362323i	$-0.881984\pi$
$149$		−	107.972i		−	0.724647i	0.932052	−	0.362323i	$-0.118016\pi$
$150$	−121.784	+	42.0896i	−0.811894	+	0.280597i
$151$			75.4687i			0.499793i	0.968273	+	0.249896i	$0.0803966\pi$
$151$			75.4687i			0.499793i	−0.968273	+	0.249896i	$0.919603\pi$
$152$	−20.9367	+	20.9367i	−0.137741	+	0.137741i
$153$	58.3154	+	43.5780i	0.381146	+	0.284824i
$154$		−	9.26493i		−	0.0601619i
$155$	30.7488	−	133.536i	0.198380	−	0.861525i
$156$	11.4880	−	11.4880i	0.0736413	−	0.0736413i
$157$	150.157	−	150.157i	0.956416	−	0.956416i	−0.0426732	−	0.999089i	$-0.513587\pi$
$157$	150.157	−	150.157i	0.956416	−	0.956416i	0.999089	+	0.0426732i	$0.0135874\pi$
$158$	−95.4124			−0.603876
$159$	−173.866	+	173.866i	−1.09350	+	1.09350i
$160$	27.5630	+	6.34681i	0.172269	+	0.0396675i
$161$		−	7.21165i		−	0.0447928i
$162$	101.203	+	101.203i	0.624707	+	0.624707i
$163$			182.657i			1.12060i	0.828291	+	0.560299i	$0.189314\pi$
$163$			182.657i			1.12060i	−0.828291	+	0.560299i	$0.810686\pi$
$164$	−71.7969	+	71.7969i	−0.437786	+	0.437786i
$165$	46.2088	+	10.6403i	0.280053	+	0.0644866i
$166$	66.6506			0.401509
$167$			195.792i			1.17241i	0.810164	+	0.586204i	$0.199378\pi$
$167$			195.792i			1.17241i	−0.810164	+	0.586204i	$0.800622\pi$
$168$	18.3509	−	18.3509i	0.109231	−	0.109231i
$169$		−	164.032i		−	0.970603i
$170$	−77.6897	−	91.7296i	−0.456998	−	0.539586i
$171$	−44.8286			−0.262155
$172$	−21.1685	−	21.1685i	−0.123073	−	0.123073i
$173$	76.6493			0.443060			0.221530	−	0.975154i	$-0.428895\pi$
$173$	76.6493			0.443060			0.221530	+	0.975154i	$0.428895\pi$
$174$			122.057i			0.701479i
$175$	27.5266	−	56.6021i	0.157295	−	0.323441i
$176$	−7.36007	−	7.36007i	−0.0418186	−	0.0418186i
$177$	88.6496			0.500845
$178$	36.1413	−	36.1413i	0.203041	−	0.203041i
$179$	20.8905			0.116706			0.0583532	−	0.998296i	$-0.481415\pi$
$179$	20.8905			0.116706			0.0583532	+	0.998296i	$0.481415\pi$
$180$	22.7135	+	36.3030i	0.126186	+	0.201683i
$181$	−25.6431	−	25.6431i	−0.141674	−	0.141674i	0.632712	−	0.774387i	$-0.281942\pi$
$181$	−25.6431	−	25.6431i	−0.141674	−	0.141674i	−0.774387	+	0.632712i	$0.781942\pi$
$182$			7.93597i			0.0436042i
$183$	143.424	+	143.424i	0.783737	+	0.783737i
$184$	−5.72894	−	5.72894i	−0.0311355	−	0.0311355i
$185$	−37.5165	−	59.9626i	−0.202792	−	0.324122i
$186$	−141.254			−0.759429
$187$	6.33232	+	43.7814i	0.0338627	+	0.234125i
$188$	−120.726	−	120.726i	−0.642161	−	0.642161i
$189$	−43.2869			−0.229031
$190$	72.1346	+	16.6101i	0.379656	+	0.0874217i
$191$	343.538			1.79863			0.899315	−	0.437302i	$-0.144066\pi$
$191$	343.538			1.79863			0.899315	+	0.437302i	$0.144066\pi$
$192$		−	29.1559i		−	0.151854i
$193$		−	200.723i		−	1.04002i	−0.854161	−	0.520009i	$-0.825929\pi$
$193$		−	200.723i		−	1.04002i	0.854161	−	0.520009i	$-0.174071\pi$
$194$	−143.564	+	143.564i	−0.740021	+	0.740021i
$195$	−39.5806	−	9.11405i	−0.202977	−	0.0467387i
$196$		−	85.3232i		−	0.435322i
$197$	367.945			1.86774			0.933871	−	0.357611i	$-0.116409\pi$
$197$	367.945			1.86774			0.933871	+	0.357611i	$0.116409\pi$
$198$		−	15.7590i		−	0.0795911i
$199$	−264.121	−	264.121i	−1.32724	−	1.32724i	−0.907765	−	0.419478i	$-0.862213\pi$
$199$	−264.121	−	264.121i	−1.32724	−	1.32724i	−0.419478	−	0.907765i	$-0.637787\pi$
$200$	−23.0976	−	66.8319i	−0.115488	−	0.334159i
$201$	−236.292	+	236.292i	−1.17558	+	1.17558i
$202$	36.3606	+	36.3606i	0.180003	+	0.180003i
$203$	−42.1587	−	42.1587i	−0.207679	−	0.207679i
$204$	−74.1748	+	99.2595i	−0.363602	+	0.486566i
$205$	247.367	+	56.9602i	1.20667	+	0.277854i
$206$		−	111.568i		−	0.541591i
$207$		−	12.2665i		−	0.0592586i
$208$	6.30434	+	6.30434i	0.0303093	+	0.0303093i
$209$	−19.2619	−	19.2619i	−0.0921622	−	0.0921622i
$210$	−63.2257	−	14.5587i	−0.301075	−	0.0693271i
$211$	71.8600	+	71.8600i	0.340569	+	0.340569i	0.856581	−	0.516013i	$-0.172584\pi$
$211$	71.8600	+	71.8600i	0.340569	+	0.340569i	−0.516013	+	0.856581i	$0.672584\pi$
$212$	−95.4129	−	95.4129i	−0.450061	−	0.450061i
$213$	−36.5147	+	36.5147i	−0.171430	+	0.171430i
$214$	102.118	−	102.118i	0.477185	−	0.477185i
$215$	−16.7940	+	72.9334i	−0.0781118	+	0.339225i
$216$	−34.3872	+	34.3872i	−0.159200	+	0.159200i
$217$	48.7892	−	48.7892i	0.224835	−	0.224835i
$218$	−270.483			−1.24075
$219$	−196.803			−0.898643
$220$	−5.83911	+	25.3582i	−0.0265414	+	0.115264i
$221$	−5.42401	−	37.5014i	−0.0245431	−	0.169690i
$222$	−51.5563	+	51.5563i	−0.232236	+	0.232236i
$223$	−18.1765	+	18.1765i	−0.0815089	+	0.0815089i	−0.746686	−	0.665177i	$-0.768356\pi$
$223$	−18.1765	+	18.1765i	−0.0815089	+	0.0815089i	0.665177	+	0.746686i	$0.268356\pi$
$224$	10.0705	+	10.0705i	0.0449575	+	0.0449575i
$225$	46.8208	−	96.2764i	0.208093	−	0.427895i
$226$	−171.052	+	171.052i	−0.756869	+	0.756869i
$227$	239.348			1.05439			0.527197	−	0.849743i	$-0.323243\pi$
$227$	239.348			1.05439			0.527197	+	0.849743i	$0.323243\pi$
$228$		−	76.3034i		−	0.334664i
$229$	−167.835			−0.732904			−0.366452	−	0.930437i	$-0.619428\pi$
$229$	−167.835			−0.732904			−0.366452	+	0.930437i	$0.619428\pi$
$230$	−4.54506	+	19.7383i	−0.0197611	+	0.0858188i
$231$	16.8830	+	16.8830i	0.0730865	+	0.0730865i
$232$	−66.9819			−0.288715
$233$	92.4647			0.396844			0.198422	−	0.980117i	$-0.436418\pi$
$233$	92.4647			0.396844			0.198422	+	0.980117i	$0.436418\pi$
$234$			13.4986i			0.0576861i
$235$	−95.7782	+	415.947i	−0.407567	+	1.76999i
$236$			48.6486i			0.206138i
$237$	173.865	−	173.865i	0.733607	−	0.733607i
$238$	−8.66427	−	59.9044i	−0.0364045	−	0.251699i
$239$			1.73597i			0.00726346i	0.999993	+	0.00363173i	$0.00115602\pi$
$239$			1.73597i			0.00726346i	−0.999993	+	0.00363173i	$0.998844\pi$
$240$	−61.7919	+	38.6611i	−0.257466	+	0.161088i
$241$	−27.9790	+	27.9790i	−0.116096	+	0.116096i	−0.762768	−	0.646672i	$-0.776160\pi$
$241$	−27.9790	+	27.9790i	−0.116096	+	0.116096i	0.646672	+	0.762768i	$0.276160\pi$
$242$	−114.229	+	114.229i	−0.472019	+	0.472019i
$243$	−214.090			−0.881027
$244$	−78.7073	+	78.7073i	−0.322571	+	0.322571i
$245$	−180.831	+	113.139i	−0.738084	+	0.461794i
$246$		−	261.663i		−	1.06367i
$247$	16.4990	+	16.4990i	0.0667974	+	0.0667974i
$248$		−	77.5163i		−	0.312566i
$249$	−121.454	+	121.454i	−0.487766	+	0.487766i
$250$	−111.013	+	137.572i	−0.444053	+	0.550288i
$251$	−237.556			−0.946439			−0.473219	−	0.880945i	$-0.656908\pi$
$251$	−237.556			−0.946439			−0.473219	+	0.880945i	$0.656908\pi$
$252$			21.5625i			0.0855653i
$253$	5.27067	−	5.27067i	0.0208327	−	0.0208327i
$254$		−	71.5943i		−	0.281867i
$255$	308.723	+	25.5841i	1.21068	+	0.100330i
$256$	16.0000			0.0625000
$257$	93.1226	+	93.1226i	0.362345	+	0.362345i	0.864676	−	0.502331i	$-0.167524\pi$
$257$	93.1226	+	93.1226i	0.362345	+	0.362345i	−0.502331	+	0.864676i	$0.667524\pi$
$258$	77.1484			0.299025
$259$		−	35.6152i		−	0.137511i
$260$	5.00155	−	21.7208i	0.0192367	−	0.0835415i
$261$	−71.7092	−	71.7092i	−0.274748	−	0.274748i
$262$	84.5618			0.322755
$263$	320.642	−	320.642i	1.21917	−	1.21917i	0.251249	−	0.967922i	$-0.419159\pi$
$263$	320.642	−	320.642i	1.21917	−	1.21917i	0.967922	−	0.251249i	$-0.0808414\pi$
$264$	26.8237			0.101605
$265$	−75.6959	+	328.733i	−0.285645	+	1.24050i
$266$	26.3553	+	26.3553i	0.0990800	+	0.0990800i
$267$			131.717i			0.493321i
$268$	−129.671	−	129.671i	−0.483846	−	0.483846i
$269$	194.466	+	194.466i	0.722921	+	0.722921i	0.969199	−	0.246279i	$-0.0792078\pi$
$269$	194.466	+	194.466i	0.722921	+	0.722921i	−0.246279	+	0.969199i	$0.579208\pi$
$270$	118.477	+	27.2811i	0.438802	+	0.101041i
$271$	140.688			0.519143			0.259571	−	0.965724i	$-0.416419\pi$
$271$	140.688			0.519143			0.259571	+	0.965724i	$0.416419\pi$
$272$	−54.4710	−	40.7052i	−0.200261	−	0.149651i
$273$	−14.4613	−	14.4613i	−0.0529717	−	0.0529717i
$274$	253.580			0.925473
$275$	61.4859	−	21.2500i	0.223585	−	0.0772728i
$276$	20.8791			0.0756488
$277$		−	191.172i		−	0.690153i	−0.938575	−	0.345076i	$-0.887853\pi$
$277$		−	191.172i		−	0.690153i	0.938575	−	0.345076i	$-0.112147\pi$
$278$			46.0457i			0.165632i
$279$	82.9872	−	82.9872i	0.297445	−	0.297445i
$280$	7.98943	−	34.6966i	0.0285337	−	0.123916i
$281$		−	541.518i		−	1.92711i	−0.267508	−	0.963556i	$-0.586200\pi$
$281$		−	541.518i		−	1.92711i	0.267508	−	0.963556i	$-0.413800\pi$
$282$	439.985			1.56023
$283$		−	493.314i		−	1.74316i	−0.490256	−	0.871579i	$-0.663097\pi$
$283$		−	493.314i		−	1.74316i	0.490256	−	0.871579i	$-0.336903\pi$
$284$	−20.0383	−	20.0383i	−0.0705574	−	0.0705574i
$285$	−161.715	+	101.179i	−0.567420	+	0.355015i
$286$	−5.80004	+	5.80004i	−0.0202799	+	0.0202799i
$287$	90.3788	+	90.3788i	0.314909	+	0.314909i
$288$	17.1292	+	17.1292i	0.0594765	+	0.0594765i
$289$	81.8860	+	277.156i	0.283342	+	0.959019i
$290$	88.8187	+	141.959i	0.306271	+	0.489513i
$291$		−	523.218i		−	1.79800i
$292$		−	108.000i		−	0.369864i
$293$	64.7582	+	64.7582i	0.221018	+	0.221018i	0.808927	−	0.587909i	$-0.200049\pi$
$293$	64.7582	+	64.7582i	0.221018	+	0.221018i	−0.587909	+	0.808927i	$0.700049\pi$
$294$	155.480	+	155.480i	0.528843	+	0.528843i
$295$	103.104	−	64.5085i	0.349505	−	0.218673i
$296$	−28.2928	−	28.2928i	−0.0955836	−	0.0955836i
$297$	−31.6365	−	31.6365i	−0.106520	−	0.106520i
$298$	−107.972	+	107.972i	−0.362323	+	0.362323i
$299$	−4.51465	+	4.51465i	−0.0150991	+	0.0150991i
$300$	163.874	+	79.6945i	0.546245	+	0.265648i
$301$	−26.6471	+	26.6471i	−0.0885287	+	0.0885287i
$302$	75.4687	−	75.4687i	0.249896	−	0.249896i
$303$	−132.516			−0.437346
$304$	41.8733			0.137741
$305$	271.176	+	62.4425i	0.889101	+	0.204729i
$306$	−14.7373	−	101.893i	−0.0481612	−	0.332985i
$307$	−410.438	+	410.438i	−1.33693	+	1.33693i	−0.437916	+	0.899016i	$0.644283\pi$
$307$	−410.438	+	410.438i	−1.33693	+	1.33693i	−0.899016	+	0.437916i	$0.855717\pi$
$308$	−9.26493	+	9.26493i	−0.0300809	+	0.0300809i
$309$	203.304	+	203.304i	0.657941	+	0.657941i
$310$	−164.285	+	102.788i	−0.529952	+	0.331573i
$311$	323.185	−	323.185i	1.03918	−	1.03918i	0.0399809	−	0.999200i	$-0.487270\pi$
$311$	323.185	−	323.185i	1.03918	−	1.03918i	0.999200	−	0.0399809i	$-0.0127297\pi$
$312$	−22.9761			−0.0736413
$313$			320.505i			1.02398i	0.858993	+	0.511988i	$0.171091\pi$
$313$			320.505i			1.02398i	−0.858993	+	0.511988i	$0.828909\pi$
$314$	−300.315			−0.956416
$315$	45.6986	−	28.5921i	0.145075	−	0.0907684i
$316$	95.4124	+	95.4124i	0.301938	+	0.301938i
$317$	−259.019			−0.817096			−0.408548	−	0.912737i	$-0.633965\pi$
$317$	−259.019			−0.817096			−0.408548	+	0.912737i	$0.633965\pi$
$318$	347.731			1.09350
$319$		−	61.6239i		−	0.193178i
$320$	−21.2162	−	33.9098i	−0.0663006	−	0.105968i
$321$			372.166i			1.15940i
$322$	−7.21165	+	7.21165i	−0.0223964	+	0.0223964i
$323$	−142.555	−	106.529i	−0.441347	−	0.329811i
$324$		−	202.405i		−	0.624707i
$325$	−52.6663	+	18.2019i	−0.162050	+	0.0560059i
$326$	182.657	−	182.657i	0.560299	−	0.560299i
$327$	492.886	−	492.886i	1.50730	−	1.50730i
$328$	143.594			0.437786
$329$	−151.971	+	151.971i	−0.461919	+	0.461919i
$330$	−35.5685	−	56.8491i	−0.107783	−	0.172270i
$331$		−	621.830i		−	1.87864i	−0.343043	−	0.939320i	$-0.611458\pi$
$331$		−	621.830i		−	1.87864i	0.343043	−	0.939320i	$-0.388542\pi$
$332$	−66.6506	−	66.6506i	−0.200755	−	0.200755i
$333$		−	60.5791i		−	0.181919i
$334$	195.792	−	195.792i	0.586204	−	0.586204i
$335$	−102.874	+	446.764i	−0.307088	+	1.33362i
$336$	−36.7018			−0.109231
$337$			159.768i			0.474089i	0.971499	+	0.237045i	$0.0761788\pi$
$337$			159.768i			0.474089i	−0.971499	+	0.237045i	$0.923821\pi$
$338$	−164.032	+	164.032i	−0.485302	+	0.485302i
$339$		−	623.399i		−	1.83893i
$340$	−14.0399	+	169.419i	−0.0412938	+	0.498292i
$341$	71.3157			0.209137
$342$	44.8286	+	44.8286i	0.131078	+	0.131078i
$343$	−230.769			−0.672796
$344$			42.3370i			0.123073i
$345$	−27.6859	−	44.2503i	−0.0802489	−	0.128262i
$346$	−76.6493	−	76.6493i	−0.221530	−	0.221530i
$347$	−283.689			−0.817549			−0.408774	−	0.912635i	$-0.634044\pi$
$347$	−283.689			−0.817549			−0.408774	+	0.912635i	$0.634044\pi$
$348$	122.057	−	122.057i	0.350740	−	0.350740i
$349$	−95.7372			−0.274318			−0.137159	−	0.990549i	$-0.543797\pi$
$349$	−95.7372			−0.274318			−0.137159	+	0.990549i	$0.543797\pi$
$350$	−84.1287	+	29.0756i	−0.240368	+	0.0830730i
$351$	27.0985	+	27.0985i	0.0772038	+	0.0772038i
$352$			14.7201i			0.0418186i
$353$	−379.043	−	379.043i	−1.07378	−	1.07378i	−0.997052	−	0.0767229i	$-0.975554\pi$
$353$	−379.043	−	379.043i	−1.07378	−	1.07378i	−0.0767229	−	0.997052i	$-0.524446\pi$
$354$	−88.6496	−	88.6496i	−0.250423	−	0.250423i
$355$	−15.8974	+	69.0394i	−0.0447814	+	0.194477i
$356$	−72.2827			−0.203041
$357$	124.949	+	93.3721i	0.349997	+	0.261546i
$358$	−20.8905	−	20.8905i	−0.0583532	−	0.0583532i
$359$	527.313			1.46884			0.734419	−	0.678696i	$-0.237455\pi$
$359$	527.313			1.46884			0.734419	+	0.678696i	$0.237455\pi$
$360$	13.5895	−	59.0166i	0.0377486	−	0.163935i
$361$	−251.414			−0.696438
$362$			51.2861i			0.141674i
$363$		−	416.305i		−	1.14685i
$364$	7.93597	−	7.93597i	0.0218021	−	0.0218021i
$365$	−228.892	+	143.210i	−0.627100	+	0.392355i
$366$		−	286.848i		−	0.783737i
$367$	269.563			0.734505			0.367253	−	0.930121i	$-0.380298\pi$
$367$	269.563			0.734505			0.367253	+	0.930121i	$0.380298\pi$
$368$			11.4579i			0.0311355i
$369$	153.728	+	153.728i	0.416608	+	0.416608i
$370$	−22.4461	+	97.4791i	−0.0606651	+	0.263457i
$371$	−120.107	+	120.107i	−0.323738	+	0.323738i
$372$	141.254	+	141.254i	0.379714	+	0.379714i
$373$	403.169	+	403.169i	1.08088	+	1.08088i	0.996427	+	0.0844542i	$0.0269147\pi$
$373$	403.169	+	403.169i	1.08088	+	1.08088i	0.0844542	+	0.996427i	$0.473085\pi$
$374$	37.4491	−	50.1138i	0.100131	−	0.133994i
$375$	−48.3968	−	452.983i	−0.129058	−	1.20796i
$376$			241.452i			0.642161i
$377$			52.7845i			0.140012i
$378$	43.2869	+	43.2869i	0.114516	+	0.114516i
$379$	−29.0227	−	29.0227i	−0.0765771	−	0.0765771i	0.667781	−	0.744358i	$-0.267244\pi$
$379$	−29.0227	−	29.0227i	−0.0765771	−	0.0765771i	−0.744358	+	0.667781i	$0.767244\pi$
$380$	−55.5245	−	88.7447i	−0.146117	−	0.233539i
$381$	130.462	+	130.462i	0.342421	+	0.342421i
$382$	−343.538	−	343.538i	−0.899315	−	0.899315i
$383$	−393.130	+	393.130i	−1.02645	+	1.02645i	−0.0268076	+	0.999641i	$0.508534\pi$
$383$	−393.130	+	393.130i	−1.02645	+	1.02645i	−0.999641	+	0.0268076i	$0.991466\pi$
$384$	−29.1559	+	29.1559i	−0.0759269	+	0.0759269i
$385$	31.9211	+	7.35034i	0.0829121	+	0.0190918i
$386$	−200.723	+	200.723i	−0.520009	+	0.520009i
$387$	−45.3250	+	45.3250i	−0.117119	+	0.117119i
$388$	287.128			0.740021
$389$	326.044			0.838159			0.419080	−	0.907950i	$-0.362353\pi$
$389$	326.044			0.838159			0.419080	+	0.907950i	$0.362353\pi$
$390$	30.4666	+	48.6947i	0.0781194	+	0.124858i
$391$	29.1497	−	39.0076i	0.0745516	−	0.0997637i
$392$	−85.3232	+	85.3232i	−0.217661	+	0.217661i
$393$	−154.092	+	154.092i	−0.392092	+	0.392092i
$394$	−367.945	−	367.945i	−0.933871	−	0.933871i
$395$	75.6955	−	328.731i	0.191634	−	0.832231i
$396$	−15.7590	+	15.7590i	−0.0397955	+	0.0397955i
$397$	−222.136			−0.559536			−0.279768	−	0.960068i	$-0.590258\pi$
$397$	−222.136			−0.559536			−0.279768	+	0.960068i	$0.590258\pi$
$398$			528.243i			1.32724i
$399$	−96.0516			−0.240731
$400$	−43.7342	+	89.9295i	−0.109336	+	0.224824i
$401$	168.413	+	168.413i	0.419982	+	0.419982i	0.885197	−	0.465215i	$-0.154023\pi$
$401$	168.413	+	168.413i	0.419982	+	0.419982i	−0.465215	+	0.885197i	$0.654023\pi$
$402$	472.584			1.17558
$403$	−61.0862			−0.151579
$404$		−	72.7211i		−	0.180003i
$405$	−428.970	+	268.392i	−1.05918	+	0.662695i
$406$			84.3175i			0.207679i
$407$	26.0296	−	26.0296i	0.0639547	−	0.0639547i
$408$	173.434	−	25.0847i	0.425084	−	0.0614820i
$409$			213.459i			0.521905i	0.965352	+	0.260952i	$0.0840365\pi$
$409$			213.459i			0.521905i	−0.965352	+	0.260952i	$0.915963\pi$
$410$	−190.407	−	304.327i	−0.464408	−	0.742262i
$411$	−462.084	+	462.084i	−1.12429	+	1.12429i
$412$	−111.568	+	111.568i	−0.270795	+	0.270795i
$413$	61.2393			0.148279
$414$	−12.2665	+	12.2665i	−0.0296293	+	0.0296293i
$415$	−52.8773	+	229.636i	−0.127415	+	0.553340i
$416$		−	12.6087i		−	0.0303093i
$417$	−83.9065	−	83.9065i	−0.201215	−	0.201215i
$418$			38.5238i			0.0921622i
$419$	−374.883	+	374.883i	−0.894710	+	0.894710i	−0.994962	−	0.100252i	$-0.968035\pi$
$419$	−374.883	+	374.883i	−0.894710	+	0.894710i	0.100252	+	0.994962i	$0.468035\pi$
$420$	48.6670	+	77.7844i	0.115874	+	0.185201i
$421$	−605.275			−1.43771			−0.718854	−	0.695161i	$-0.755333\pi$
$421$	−605.275			−1.43771			−0.718854	+	0.695161i	$0.755333\pi$
$422$		−	143.720i		−	0.340569i
$423$	−258.493	+	258.493i	−0.611095	+	0.611095i
$424$			190.826i			0.450061i
$425$	377.678	−	194.896i	0.888654	−	0.458579i
$426$	73.0294			0.171430
$427$	99.0775	+	99.0775i	0.232032	+	0.232032i
$428$	−204.235			−0.477185
$429$		−	21.1382i		−	0.0492732i
$430$	89.7274	−	56.1393i	0.208668	−	0.130557i
$431$	481.785	+	481.785i	1.11783	+	1.11783i	0.992059	+	0.125771i	$0.0401405\pi$
$431$	481.785	+	481.785i	1.11783	+	1.11783i	0.125771	+	0.992059i	$0.459859\pi$
$432$	68.7743			0.159200
$433$	245.936	−	245.936i	0.567982	−	0.567982i	−0.363581	−	0.931563i	$-0.618446\pi$
$433$	245.936	−	245.936i	0.567982	−	0.567982i	0.931563	+	0.363581i	$0.118446\pi$
$434$	−97.5784			−0.224835
$435$	−420.533	−	96.8343i	−0.966743	−	0.222608i
$436$	270.483	+	270.483i	0.620374	+	0.620374i
$437$			29.9862i			0.0686183i
$438$	196.803	+	196.803i	0.449322	+	0.449322i
$439$	100.177	+	100.177i	0.228193	+	0.228193i	0.811937	−	0.583745i	$-0.198413\pi$
$439$	100.177	+	100.177i	0.228193	+	0.228193i	−0.583745	+	0.811937i	$0.698413\pi$
$440$	31.1973	−	19.5191i	0.0709029	−	0.0443615i
$441$	−182.690			−0.414263
$442$	−32.0774	+	42.9254i	−0.0725733	+	0.0971164i
$443$	−533.095	−	533.095i	−1.20338	−	1.20338i	−0.973133	−	0.230242i	$-0.926048\pi$
$443$	−533.095	−	533.095i	−1.20338	−	1.20338i	−0.230242	−	0.973133i	$-0.573952\pi$
$444$	103.113			0.232236
$445$	95.8476	+	153.193i	0.215388	+	0.344254i
$446$	36.3530			0.0815089
$447$		−	393.504i		−	0.880323i
$448$		−	20.1410i		−	0.0449575i
$449$	−88.8706	+	88.8706i	−0.197930	+	0.197930i	−0.799112	−	0.601182i	$-0.794697\pi$
$449$	−88.8706	+	88.8706i	−0.197930	+	0.197930i	0.601182	+	0.799112i	$0.294697\pi$
$450$	−143.097	+	49.4556i	−0.317994	+	0.109901i
$451$			132.108i			0.292921i
$452$	342.105			0.756869
$453$			275.045i			0.607163i
$454$	−239.348	−	239.348i	−0.527197	−	0.527197i
$455$	−27.3424	−	6.29601i	−0.0600931	−	0.0138374i
$456$	−76.3034	+	76.3034i	−0.167332	+	0.167332i
$457$	−241.878	−	241.878i	−0.529274	−	0.529274i	0.391082	−	0.920356i	$-0.372101\pi$
$457$	−241.878	−	241.878i	−0.529274	−	0.529274i	−0.920356	+	0.391082i	$0.872101\pi$
$458$	167.835	+	167.835i	0.366452	+	0.366452i
$459$	−234.138	−	174.967i	−0.510104	−	0.381192i
$460$	24.2834	−	15.1933i	0.0527900	−	0.0330288i
$461$		−	487.235i		−	1.05691i	−0.848961	−	0.528455i	$-0.822772\pi$
$461$		−	487.235i		−	1.05691i	0.848961	−	0.528455i	$-0.177228\pi$
$462$		−	33.7659i		−	0.0730865i
$463$	394.406	+	394.406i	0.851849	+	0.851849i	0.990361	−	0.138512i	$-0.0442320\pi$
$463$	394.406	+	394.406i	0.851849	+	0.851849i	−0.138512	+	0.990361i	$0.544232\pi$
$464$	66.9819	+	66.9819i	0.144357	+	0.144357i
$465$	112.064	−	486.672i	0.240997	−	1.04661i
$466$	−92.4647	−	92.4647i	−0.198422	−	0.198422i
$467$	147.754	+	147.754i	0.316390	+	0.316390i	0.847379	−	0.530989i	$-0.178179\pi$
$467$	147.754	+	147.754i	0.316390	+	0.316390i	−0.530989	+	0.847379i	$0.678179\pi$
$468$	13.4986	−	13.4986i	0.0288431	−	0.0288431i
$469$	−163.231	+	163.231i	−0.348040	+	0.348040i
$470$	511.725	−	320.169i	1.08878	−	0.681210i
$471$	547.247	−	547.247i	1.16188	−	1.16188i
$472$	48.6486	−	48.6486i	0.103069	−	0.103069i
$473$	−38.9504			−0.0823475
$474$	−347.730			−0.733607
$475$	−114.456	+	235.353i	−0.240960	+	0.495480i
$476$	−51.2401	+	68.5687i	−0.107647	+	0.144052i
$477$	−204.294	+	204.294i	−0.428289	+	0.428289i
$478$	1.73597	−	1.73597i	0.00363173	−	0.00363173i
$479$	−45.1285	−	45.1285i	−0.0942140	−	0.0942140i	0.658429	−	0.752643i	$-0.271221\pi$
$479$	−45.1285	−	45.1285i	−0.0942140	−	0.0942140i	−0.752643	+	0.658429i	$0.771221\pi$
$480$	100.453	+	23.1309i	0.209277	+	0.0481893i
$481$	−22.2959	+	22.2959i	−0.0463532	+	0.0463532i
$482$	55.9580			0.116096
$483$		−	26.2828i		−	0.0544157i
$484$	228.457			0.472019
$485$	−380.735	−	608.528i	−0.785020	−	1.25470i
$486$	214.090	+	214.090i	0.440514	+	0.440514i
$487$	−810.637			−1.66455			−0.832276	−	0.554361i	$-0.812963\pi$
$487$	−810.637			−1.66455			−0.832276	+	0.554361i	$0.812963\pi$
$488$	157.415			0.322571
$489$			665.693i			1.36134i
$490$	293.970	+	67.6912i	0.599939	+	0.138145i
$491$			313.136i			0.637752i	0.947796	+	0.318876i	$0.103305\pi$
$491$			313.136i			0.637752i	−0.947796	+	0.318876i	$0.896695\pi$
$492$	−261.663	+	261.663i	−0.531836	+	0.531836i
$493$	−57.6287	−	398.442i	−0.116894	−	0.808199i
$494$		−	32.9979i		−	0.0667974i
$495$	54.2957	+	12.5024i	0.109688	+	0.0252575i
$496$	−77.5163	+	77.5163i	−0.156283	+	0.156283i
$497$	−25.2244	+	25.2244i	−0.0507534	+	0.0507534i
$498$	242.907			0.487766
$499$	−230.154	+	230.154i	−0.461231	+	0.461231i	−0.899059	−	0.437828i	$-0.855748\pi$
$499$	−230.154	+	230.154i	−0.461231	+	0.461231i	0.437828	+	0.899059i	$0.355748\pi$
$500$	248.585	−	26.5589i	0.497171	−	0.0531177i
$501$			713.562i			1.42428i
$502$	237.556	+	237.556i	0.473219	+	0.473219i
$503$		−	230.360i		−	0.457972i	−0.973430	−	0.228986i	$-0.926459\pi$
$503$		−	230.360i		−	0.457972i	0.973430	−	0.228986i	$-0.0735410\pi$
$504$	21.5625	−	21.5625i	0.0427826	−	0.0427826i
$505$	−154.122	+	96.4290i	−0.305193	+	0.190949i
$506$	−10.5413			−0.0208327
$507$		−	597.813i		−	1.17912i
$508$	−71.5943	+	71.5943i	−0.140934	+	0.140934i
$509$		−	176.293i		−	0.346352i	−0.984891	−	0.173176i	$-0.944597\pi$
$509$		−	176.293i		−	0.346352i	0.984891	−	0.173176i	$-0.0554030\pi$
$510$	−283.139	−	334.307i	−0.555175	−	0.655505i
$511$	−135.952			−0.266051
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	179.988			0.350854
$514$		−	186.245i		−	0.362345i
$515$	384.392	+	88.5123i	0.746393	+	0.171869i
$516$	−77.1484	−	77.1484i	−0.149512	−	0.149512i
$517$	−222.138			−0.429668
$518$	−35.6152	+	35.6152i	−0.0687553	+	0.0687553i
$519$	279.348			0.538242
$520$	−26.7223	+	16.7192i	−0.0513891	+	0.0321524i
$521$	454.583	+	454.583i	0.872519	+	0.872519i	0.992746	−	0.120227i	$-0.0383623\pi$
$521$	454.583	+	454.583i	0.872519	+	0.872519i	−0.120227	+	0.992746i	$0.538362\pi$
$522$			143.418i			0.274748i
$523$	283.667	+	283.667i	0.542384	+	0.542384i	0.924227	−	0.381843i	$-0.124710\pi$
$523$	283.667	+	283.667i	0.542384	+	0.542384i	−0.381843	+	0.924227i	$0.624710\pi$
$524$	−84.5618	−	84.5618i	−0.161377	−	0.161377i
$525$	100.320	−	206.286i	0.191086	−	0.392925i
$526$	−641.284			−1.21917
$527$	461.107	−	66.6921i	0.874965	−	0.126551i
$528$	−26.8237	−	26.8237i	−0.0508024	−	0.0508024i
$529$	520.795			0.984489
$530$	404.429	−	253.037i	0.763074	−	0.477429i
$531$	104.164			0.196166
$532$		−	52.7106i		−	0.0990800i
$533$		−	113.158i		−	0.212304i
$534$	131.717	−	131.717i	0.246660	−	0.246660i
$535$	270.818	+	432.848i	0.506202	+	0.809062i
$536$			259.341i			0.483846i
$537$	76.1351			0.141779
$538$		−	388.931i		−	0.722921i
$539$	−78.4980	−	78.4980i	−0.145636	−	0.145636i
$540$	−91.1955	−	145.758i	−0.168881	−	0.269922i
$541$	−120.760	+	120.760i	−0.223216	+	0.223216i	−0.809851	−	0.586635i	$-0.800452\pi$
$541$	−120.760	+	120.760i	−0.223216	+	0.223216i	0.586635	+	0.809851i	$0.300452\pi$
$542$	−140.688	−	140.688i	−0.259571	−	0.259571i
$543$	−93.4559	−	93.4559i	−0.172110	−	0.172110i
$544$	13.7658	+	95.1762i	0.0253048	+	0.174956i
$545$	214.588	−	931.915i	0.393739	−	1.70994i
$546$			28.9226i			0.0529717i
$547$			392.045i			0.716718i	0.933584	+	0.358359i	$0.116664\pi$
$547$			392.045i			0.716718i	−0.933584	+	0.358359i	$0.883336\pi$
$548$	−253.580	−	253.580i	−0.462737	−	0.462737i
$549$	168.524	+	168.524i	0.306966	+	0.306966i
$550$	−82.7359	−	40.2359i	−0.150429	−	0.0731561i
$551$	175.297	+	175.297i	0.318143	+	0.318143i
$552$	−20.8791	−	20.8791i	−0.0378244	−	0.0378244i
$553$	120.106	−	120.106i	0.217190	−	0.217190i
$554$	−191.172	+	191.172i	−0.345076	+	0.345076i
$555$	−136.729	−	218.533i	−0.246358	−	0.393753i
$556$	46.0457	−	46.0457i	0.0828160	−	0.0828160i
$557$	−91.4718	+	91.4718i	−0.164222	+	0.164222i	−0.784434	−	0.620212i	$-0.787047\pi$
$557$	−91.4718	+	91.4718i	−0.164222	+	0.164222i	0.620212	+	0.784434i	$0.287047\pi$
$558$	−165.974			−0.297445
$559$	33.3633			0.0596840
$560$	−42.6860	+	26.7072i	−0.0762250	+	0.0476913i
$561$	23.0781	+	159.561i	0.0411374	+	0.284422i
$562$	−541.518	+	541.518i	−0.963556	+	0.963556i
$563$	−672.399	+	672.399i	−1.19431	+	1.19431i	−0.218470	+	0.975844i	$0.570107\pi$
$563$	−672.399	+	672.399i	−1.19431	+	1.19431i	−0.975844	+	0.218470i	$0.929893\pi$
$564$	−439.985	−	439.985i	−0.780116	−	0.780116i
$565$	−453.635	−	725.044i	−0.802893	−	1.28326i
$566$	−493.314	+	493.314i	−0.871579	+	0.871579i
$567$	−254.790			−0.449365
$568$			40.0766i			0.0705574i
$569$	1000.49			1.75833			0.879164	−	0.476520i	$-0.158102\pi$
$569$	1000.49			1.75833			0.879164	+	0.476520i	$0.158102\pi$
$570$	262.894	+	60.5354i	0.461217	+	0.106202i
$571$	−522.562	−	522.562i	−0.915170	−	0.915170i	0.0815027	−	0.996673i	$-0.474028\pi$
$571$	−522.562	−	522.562i	−0.915170	−	0.915170i	−0.996673	+	0.0815027i	$0.974028\pi$
$572$	11.6001			0.0202799
$573$	1252.02			2.18503
$574$		−	180.758i		−	0.314909i
$575$	−64.4001	−	31.3188i	−0.112000	−	0.0544675i
$576$		−	34.2585i		−	0.0594765i
$577$	277.369	−	277.369i	0.480710	−	0.480710i	−0.424649	−	0.905358i	$-0.639602\pi$
$577$	277.369	−	277.369i	0.480710	−	0.480710i	0.905358	+	0.424649i	$0.139602\pi$
$578$	195.270	−	359.042i	0.337838	−	0.621181i
$579$		−	731.535i		−	1.26344i
$580$	53.1401	−	230.777i	0.0916209	−	0.397892i
$581$	−83.9005	+	83.9005i	−0.144407	+	0.144407i
$582$	−523.218	+	523.218i	−0.898999	+	0.898999i
$583$	−175.561			−0.301134
$584$	−108.000	+	108.000i	−0.184932	+	0.184932i
$585$	−46.5075	−	10.7091i	−0.0795001	−	0.0183061i
$586$		−	129.516i		−	0.221018i
$587$	511.397	+	511.397i	0.871205	+	0.871205i	0.992604	−	0.121399i	$-0.0387381\pi$
$587$	511.397	+	511.397i	0.871205	+	0.871205i	−0.121399	+	0.992604i	$0.538738\pi$
$588$		−	310.959i		−	0.528843i
$589$	−202.867	+	202.867i	−0.344426	+	0.344426i
$590$	−167.612	−	38.5954i	−0.284089	−	0.0654159i
$591$	1340.97			2.26899
$592$			56.5855i			0.0955836i
$593$	485.752	−	485.752i	0.819143	−	0.819143i	−0.166841	−	0.985984i	$-0.553357\pi$
$593$	485.752	−	485.752i	0.819143	−	0.819143i	0.985984	+	0.166841i	$0.0533567\pi$
$594$			63.2730i			0.106520i
$595$	213.267	+	17.6736i	0.358432	+	0.0297035i
$596$	215.945			0.362323
$597$	−962.588	−	962.588i	−1.61238	−	1.61238i
$598$	9.02929			0.0150991
$599$		−	240.970i		−	0.402287i	−0.979562	−	0.201144i	$-0.935534\pi$
$599$		−	240.970i		−	0.402287i	0.979562	−	0.201144i	$-0.0644658\pi$
$600$	−84.1791	−	243.568i	−0.140299	−	0.405947i
$601$	273.824	+	273.824i	0.455614	+	0.455614i	0.897213	−	0.441599i	$-0.145589\pi$
$601$	273.824	+	273.824i	0.455614	+	0.455614i	−0.441599	+	0.897213i	$0.645589\pi$
$602$	53.2943			0.0885287
$603$	−277.645	+	277.645i	−0.460439	+	0.460439i
$604$	−150.937			−0.249896
$605$	−302.937	−	484.184i	−0.500722	−	0.800304i
$606$	132.516	+	132.516i	0.218673	+	0.218673i
$607$		−	774.909i		−	1.27662i	−0.769779	−	0.638311i	$-0.779634\pi$
$607$		−	774.909i		−	1.27662i	0.769779	−	0.638311i	$-0.220366\pi$
$608$	−41.8733	−	41.8733i	−0.0688706	−	0.0688706i
$609$	−153.647	−	153.647i	−0.252294	−	0.252294i
$610$	−208.733	−	333.618i	−0.342186	−	0.546915i
$611$	190.275			0.311415
$612$	−87.1560	+	116.631i	−0.142412	+	0.190573i
$613$	415.326	+	415.326i	0.677530	+	0.677530i	0.959441	−	0.281911i	$-0.0909682\pi$
$613$	415.326	+	415.326i	0.677530	+	0.677530i	−0.281911	+	0.959441i	$0.590968\pi$
$614$	820.876			1.33693
$615$	901.527	+	207.591i	1.46590	+	0.337546i
$616$	18.5299			0.0300809
$617$			422.398i			0.684599i	0.939591	+	0.342300i	$0.111206\pi$
$617$			422.398i			0.684599i	−0.939591	+	0.342300i	$0.888794\pi$
$618$		−	406.607i		−	0.657941i
$619$	532.726	−	532.726i	0.860624	−	0.860624i	−0.130786	−	0.991411i	$-0.541750\pi$
$619$	532.726	−	532.726i	0.860624	−	0.860624i	0.991411	+	0.130786i	$0.0417501\pi$
$620$	267.073	+	61.4977i	0.430762	+	0.0991898i
$621$			49.2505i			0.0793084i
$622$	−646.371			−1.03918
$623$			90.9902i			0.146052i
$624$	22.9761	+	22.9761i	0.0368207	+	0.0368207i
$625$	−385.915	−	491.625i	−0.617463	−	0.786600i
$626$	320.505	−	320.505i	0.511988	−	0.511988i
$627$	−70.1998	−	70.1998i	−0.111961	−	0.111961i
$628$	300.315	+	300.315i	0.478208	+	0.478208i
$629$	143.958	−	192.642i	0.228868	−	0.306267i
$630$	−74.2907	−	17.1066i	−0.117922	−	0.0271533i
$631$		−	838.893i		−	1.32947i	−0.747081	−	0.664733i	$-0.768545\pi$
$631$		−	838.893i		−	1.32947i	0.747081	−	0.664733i	$-0.231455\pi$
$632$		−	190.825i		−	0.301938i
$633$	261.893	+	261.893i	0.413733	+	0.413733i
$634$	259.019	+	259.019i	0.408548	+	0.408548i
$635$	246.669	+	56.7994i	0.388455	+	0.0894478i
$636$	−347.731	−	347.731i	−0.546748	−	0.546748i
$637$	67.2383	+	67.2383i	0.105555	+	0.105555i
$638$	−61.6239	+	61.6239i	−0.0965891	+	0.0965891i
$639$	−42.9051	+	42.9051i	−0.0671441	+	0.0671441i
$640$	−12.6936	+	55.1260i	−0.0198338	+	0.0861343i
$641$	498.102	−	498.102i	0.777070	−	0.777070i	−0.202261	−	0.979332i	$-0.564829\pi$
$641$	498.102	−	498.102i	0.777070	−	0.777070i	0.979332	+	0.202261i	$0.0648290\pi$
$642$	372.166	−	372.166i	0.579699	−	0.579699i
$643$	368.397			0.572935			0.286467	−	0.958090i	$-0.407519\pi$
$643$	368.397			0.572935			0.286467	+	0.958090i	$0.407519\pi$
$644$	14.4233			0.0223964
$645$	−61.2057	+	265.805i	−0.0948926	+	0.412101i
$646$	36.0262	+	249.084i	0.0557681	+	0.385579i
$647$	211.121	−	211.121i	0.326308	−	0.326308i	−0.524873	−	0.851181i	$-0.675887\pi$
$647$	211.121	−	211.121i	0.326308	−	0.326308i	0.851181	+	0.524873i	$0.175887\pi$
$648$	−202.405	+	202.405i	−0.312354	+	0.312354i
$649$	44.7571	+	44.7571i	0.0689631	+	0.0689631i
$650$	70.8683	+	34.4644i	0.109028	+	0.0530222i
$651$	177.812	−	177.812i	0.273136	−	0.273136i
$652$	−365.315			−0.560299
$653$			1012.81i			1.55101i	0.631339	+	0.775507i	$0.282506\pi$
$653$			1012.81i			1.55101i	−0.631339	+	0.775507i	$0.717494\pi$
$654$	−985.773			−1.50730
$655$	−67.0872	+	291.347i	−0.102423	+	0.444804i
$656$	−143.594	−	143.594i	−0.218893	−	0.218893i
$657$	−231.245			−0.351971
$658$	303.943			0.461919
$659$			747.453i			1.13422i	0.823641	+	0.567112i	$0.191939\pi$
$659$			747.453i			1.13422i	−0.823641	+	0.567112i	$0.808061\pi$
$660$	−21.2806	+	92.4176i	−0.0322433	+	0.140027i
$661$			151.853i			0.229732i	0.993381	+	0.114866i	$0.0366438\pi$
$661$			151.853i			0.229732i	−0.993381	+	0.114866i	$0.963356\pi$
$662$	−621.830	+	621.830i	−0.939320	+	0.939320i
$663$	−19.7678	−	136.674i	−0.0298156	−	0.206144i
$664$			133.301i			0.200755i
$665$	−111.713	+	69.8948i	−0.167989	+	0.105105i
$666$	−60.5791	+	60.5791i	−0.0909597	+	0.0909597i
$667$	−47.9669	+	47.9669i	−0.0719143	+	0.0719143i
$668$	−391.584			−0.586204
$669$	−66.2440	+	66.2440i	−0.0990195	+	0.0990195i
$670$	549.638	−	343.890i	0.820356	−	0.513268i
$671$			144.823i			0.215831i
$672$	36.7018	+	36.7018i	0.0546157	+	0.0546157i
$673$			698.260i			1.03753i	0.854916	+	0.518767i	$0.173609\pi$
$673$			698.260i			1.03753i	−0.854916	+	0.518767i	$0.826391\pi$
$674$	159.768	−	159.768i	0.237045	−	0.237045i
$675$	−187.987	+	386.553i	−0.278499	+	0.572671i
$676$	328.064			0.485302
$677$		−	890.337i		−	1.31512i	−0.753402	−	0.657560i	$-0.771588\pi$
$677$		−	890.337i		−	1.31512i	0.753402	−	0.657560i	$-0.228412\pi$
$678$	−623.399	+	623.399i	−0.919467	+	0.919467i
$679$		−	361.440i		−	0.532312i
$680$	183.459	−	155.379i	0.269793	−	0.228499i
$681$	872.300			1.28091
$682$	−71.3157	−	71.3157i	−0.104568	−	0.104568i
$683$	−534.965			−0.783258			−0.391629	−	0.920123i	$-0.628088\pi$
$683$	−534.965			−0.783258			−0.391629	+	0.920123i	$0.628088\pi$
$684$		−	89.6572i		−	0.131078i
$685$	−201.178	+	873.677i	−0.293690	+	1.27544i
$686$	230.769	+	230.769i	0.336398	+	0.336398i
$687$	−611.673			−0.890354
$688$	42.3370	−	42.3370i	0.0615363	−	0.0615363i
$689$	150.379			0.218257
$690$	−16.5644	+	71.9361i	−0.0240064	+	0.104255i
$691$	−582.534	−	582.534i	−0.843030	−	0.843030i	0.146222	−	0.989252i	$-0.453289\pi$
$691$	−582.534	−	582.534i	−0.843030	−	0.843030i	−0.989252	+	0.146222i	$0.953289\pi$
$692$			153.299i			0.221530i
$693$	19.8376	+	19.8376i	0.0286257	+	0.0286257i
$694$	283.689	+	283.689i	0.408774	+	0.408774i
$695$	−158.645	−	36.5304i	−0.228266	−	0.0525617i
$696$	−244.115			−0.350740
$697$	123.543	+	854.170i	0.177249	+	1.22549i
$698$	95.7372	+	95.7372i	0.137159	+	0.137159i
$699$	336.987			0.482098
$700$	113.204	+	55.0531i	0.161720	+	0.0786473i
$701$	−975.816			−1.39203			−0.696017	−	0.718025i	$-0.745046\pi$
$701$	−975.816			−1.39203			−0.696017	+	0.718025i	$0.745046\pi$
$702$		−	54.1971i		−	0.0772038i
$703$			148.089i			0.210653i
$704$	14.7201	−	14.7201i	0.0209093	−	0.0209093i
$705$	−349.063	+	1515.91i	−0.495125	+	2.15023i
$706$			758.085i			1.07378i
$707$	−91.5422			−0.129480
$708$			177.299i			0.250423i
$709$	−701.131	−	701.131i	−0.988901	−	0.988901i	0.0110383	−	0.999939i	$-0.496486\pi$
$709$	−701.131	−	701.131i	−0.988901	−	0.988901i	−0.999939	+	0.0110383i	$0.996486\pi$
$710$	84.9368	−	53.1420i	0.119629	−	0.0748479i
$711$	204.293	−	204.293i	0.287331	−	0.287331i
$712$	72.2827	+	72.2827i	0.101521	+	0.101521i
$713$	−55.5108	−	55.5108i	−0.0778552	−	0.0778552i
$714$	−31.5768	−	218.321i	−0.0442252	−	0.305772i
$715$	−15.3818	−	24.5848i	−0.0215131	−	0.0343843i
$716$			41.7809i			0.0583532i
$717$			6.32671i			0.00882387i
$718$	−527.313	−	527.313i	−0.734419	−	0.734419i
$719$	765.138	+	765.138i	1.06417	+	1.06417i	0.997795	+	0.0663752i	$0.0211434\pi$
$719$	765.138	+	765.138i	1.06417	+	1.06417i	0.0663752	+	0.997795i	$0.478857\pi$
$720$	−72.6061	+	45.4271i	−0.100842	+	0.0630932i
$721$	140.443	+	140.443i	0.194789	+	0.194789i
$722$	251.414	+	251.414i	0.348219	+	0.348219i
$723$	−101.969	+	101.969i	−0.141036	+	0.141036i
$724$	51.2861	−	51.2861i	0.0708372	−	0.0708372i
$725$	−559.565	+	193.390i	−0.771814	+	0.266745i
$726$	−416.305	+	416.305i	−0.573423	+	0.573423i
$727$	427.059	−	427.059i	0.587426	−	0.587426i	−0.349508	−	0.936933i	$-0.613651\pi$
$727$	427.059	−	427.059i	0.587426	−	0.587426i	0.936933	+	0.349508i	$0.113651\pi$
$728$	−15.8719			−0.0218021
$729$	130.576			0.179117
$730$	372.101	+	85.6821i	0.509728	+	0.117373i
$731$	−251.842	+	36.4252i	−0.344517	+	0.0498292i
$732$	−286.848	+	286.848i	−0.391869	+	0.391869i
$733$	−835.348	+	835.348i	−1.13963	+	1.13963i	−0.151112	+	0.988517i	$0.548285\pi$
$733$	−835.348	+	835.348i	−1.13963	+	1.13963i	−0.988517	+	0.151112i	$0.951715\pi$
$734$	−269.563	−	269.563i	−0.367253	−	0.367253i
$735$	−659.036	+	412.336i	−0.896647	+	0.561001i
$736$	11.4579	−	11.4579i	0.0155678	−	0.0155678i
$737$	−238.596			−0.323740
$738$		−	307.457i		−	0.416608i
$739$	334.577			0.452743			0.226372	−	0.974041i	$-0.427314\pi$
$739$	334.577			0.452743			0.226372	+	0.974041i	$0.427314\pi$
$740$	119.925	−	75.0330i	0.162061	−	0.101396i
$741$	60.1303	+	60.1303i	0.0811475	+	0.0811475i
$742$	240.214			0.323738
$743$	−1352.66			−1.82054			−0.910270	−	0.414015i	$-0.864126\pi$
$743$	−1352.66			−1.82054			−0.910270	+	0.414015i	$0.864126\pi$
$744$		−	282.508i		−	0.379714i
$745$	−286.345	−	457.665i	−0.384356	−	0.614315i
$746$		−	806.338i		−	1.08088i
$747$	−142.709	+	142.709i	−0.191043	+	0.191043i
$748$	−87.5629	+	12.6646i	−0.117063	+	0.0169313i
$749$			257.093i			0.343249i
$750$	−404.586	+	501.380i	−0.539449	+	0.668507i
$751$	−481.112	+	481.112i	−0.640629	+	0.640629i	−0.950710	−	0.310081i	$-0.899644\pi$
$751$	−481.112	+	481.112i	−0.640629	+	0.640629i	0.310081	+	0.950710i	$0.399644\pi$
$752$	241.452	−	241.452i	0.321080	−	0.321080i
$753$	−865.771			−1.14976
$754$	52.7845	−	52.7845i	0.0700060	−	0.0700060i
$755$	200.145	+	319.891i	0.265092	+	0.423697i
$756$		−	86.5739i		−	0.114516i
$757$	295.942	+	295.942i	0.390940	+	0.390940i	0.875022	−	0.484082i	$-0.160846\pi$
$757$	295.942	+	295.942i	0.390940	+	0.390940i	−0.484082	+	0.875022i	$0.660846\pi$
$758$			58.0454i			0.0765771i
$759$	19.2089	−	19.2089i	0.0253082	−	0.0253082i
$760$	−33.2202	+	144.269i	−0.0437108	+	0.189828i
$761$	−384.390			−0.505111			−0.252556	−	0.967582i	$-0.581271\pi$
$761$	−384.390			−0.505111			−0.252556	+	0.967582i	$0.581271\pi$
$762$		−	260.925i		−	0.342421i
$763$	340.487	−	340.487i	0.446248	−	0.446248i
$764$			687.076i			0.899315i
$765$	362.753	+	30.0616i	0.474186	+	0.0392962i
$766$	786.259			1.02645
$767$	−38.3371	−	38.3371i	−0.0499832	−	0.0499832i
$768$	58.3118			0.0759269
$769$			396.785i			0.515975i	0.966148	+	0.257987i	$0.0830593\pi$
$769$			396.785i			0.515975i	−0.966148	+	0.257987i	$0.916941\pi$
$770$	−24.5708	−	39.2715i	−0.0319101	−	0.0510019i
$771$	339.384	+	339.384i	0.440187	+	0.440187i
$772$	401.447			0.520009
$773$	−456.510	+	456.510i	−0.590570	+	0.590570i	−0.937785	−	0.347216i	$-0.887127\pi$
$773$	−456.510	+	456.510i	−0.590570	+	0.590570i	0.347216	+	0.937785i	$0.387127\pi$
$774$	90.6500			0.117119
$775$	−223.806	−	647.570i	−0.288781	−	0.835575i
$776$	−287.128	−	287.128i	−0.370010	−	0.370010i
$777$		−	129.799i		−	0.167052i
$778$	−326.044	−	326.044i	−0.419080	−	0.419080i
$779$	−375.797	−	375.797i	−0.482410	−	0.482410i
$780$	18.2281	−	79.1612i	0.0233694	−	0.101489i
$781$	−36.8708			−0.0472097
$782$	−68.1573	+	9.85792i	−0.0871577	+	0.0126060i
$783$	287.915	+	287.915i	0.367707	+	0.367707i
$784$	170.646			0.217661
$785$	238.255	−	1034.70i	0.303509	−	1.31808i
$786$	308.185			0.392092
$787$		−	977.913i		−	1.24258i	−0.783579	−	0.621292i	$-0.786608\pi$
$787$		−	977.913i		−	1.24258i	0.783579	−	0.621292i	$-0.213392\pi$
$788$			735.890i			0.933871i
$789$	1168.58	−	1168.58i	1.48109	−	1.48109i
$790$	−404.427	+	253.036i	−0.511933	+	0.320299i
$791$		−	430.645i		−	0.544431i
$792$	31.5181			0.0397955
$793$		−	124.049i		−	0.156430i
$794$	222.136	+	222.136i	0.279768	+	0.279768i
$795$	−275.873	+	1198.06i	−0.347010	+	1.50700i
$796$	528.243	−	528.243i	0.663622	−	0.663622i
$797$	−447.266	−	447.266i	−0.561187	−	0.561187i	0.368458	−	0.929644i	$-0.379886\pi$
$797$	−447.266	−	447.266i	−0.561187	−	0.561187i	−0.929644	+	0.368458i	$0.879886\pi$
$798$	96.0516	+	96.0516i	0.120365	+	0.120365i
$799$	−1436.28	+	207.737i	−1.79760	+	0.259996i
$800$	133.664	−	46.1953i	0.167080	−	0.0577441i
$801$			154.768i			0.193219i
$802$		−	336.826i		−	0.419982i
$803$	−99.3611	−	99.3611i	−0.123737	−	0.123737i
$804$	−472.584	−	472.584i	−0.587790	−	0.587790i
$805$	−19.1255	−	30.5682i	−0.0237583	−	0.0379729i
$806$	61.0862	+	61.0862i	0.0757893	+	0.0757893i
$807$	708.728	+	708.728i	0.878226	+	0.878226i
$808$	−72.7211	+	72.7211i	−0.0900014	+	0.0900014i
$809$	−638.195	+	638.195i	−0.788869	+	0.788869i	−0.981309	−	0.192440i	$-0.938360\pi$
$809$	−638.195	+	638.195i	−0.788869	+	0.788869i	0.192440	+	0.981309i	$0.438360\pi$
$810$	697.361	+	160.578i	0.860940	+	0.198245i
$811$	−234.284	+	234.284i	−0.288882	+	0.288882i	−0.836638	−	0.547756i	$-0.815482\pi$
$811$	−234.284	+	234.284i	−0.288882	+	0.288882i	0.547756	+	0.836638i	$0.315482\pi$
$812$	84.3175	−	84.3175i	0.103839	−	0.103839i
$813$	512.735			0.630670
$814$	−52.0591			−0.0639547
$815$	484.411	+	774.234i	0.594370	+	0.949981i
$816$	−198.519	−	148.350i	−0.243283	−	0.181801i
$817$	110.799	−	110.799i	0.135617	−	0.135617i
$818$	213.459	−	213.459i	0.260952	−	0.260952i
$819$	−16.9921	−	16.9921i	−0.0207474	−	0.0207474i
$820$	−113.920	+	494.735i	−0.138927	+	0.603335i
$821$	351.453	−	351.453i	0.428079	−	0.428079i	−0.459894	−	0.887974i	$-0.652113\pi$
$821$	351.453	−	351.453i	0.428079	−	0.428079i	0.887974	+	0.459894i	$0.152113\pi$
$822$	924.169			1.12429
$823$		−	354.346i		−	0.430554i	−0.976553	−	0.215277i	$-0.930935\pi$
$823$		−	354.346i		−	0.430554i	0.976553	−	0.215277i	$-0.0690654\pi$
$824$	223.135			0.270795
$825$	224.085	−	77.4455i	0.271618	−	0.0938733i
$826$	−61.2393	−	61.2393i	−0.0741396	−	0.0741396i
$827$	−382.794			−0.462871			−0.231436	−	0.972850i	$-0.574342\pi$
$827$	−382.794			−0.462871			−0.231436	+	0.972850i	$0.574342\pi$
$828$	24.5331			0.0296293
$829$			84.7448i			0.102225i	0.998693	+	0.0511126i	$0.0162768\pi$
$829$			84.7448i			0.102225i	−0.998693	+	0.0511126i	$0.983723\pi$
$830$	282.513	−	176.759i	0.340378	−	0.212962i
$831$		−	696.726i		−	0.838418i
$832$	−12.6087	+	12.6087i	−0.0151547	+	0.0151547i
$833$	−580.955	−	434.137i	−0.697424	−	0.521173i
$834$			167.813i			0.201215i
$835$	519.245	+	829.909i	0.621850	+	0.993903i
$836$	38.5238	−	38.5238i	0.0460811	−	0.0460811i
$837$	−333.196	+	333.196i	−0.398084	+	0.398084i
$838$	749.767			0.894710
$839$	−277.619	+	277.619i	−0.330892	+	0.330892i	−0.852925	−	0.522033i	$-0.825174\pi$
$839$	−277.619	+	277.619i	−0.330892	+	0.330892i	0.522033	+	0.852925i	$0.325174\pi$
$840$	29.1174	−	126.451i	0.0346636	−	0.150537i
$841$		−	280.179i		−	0.333150i
$842$	605.275	+	605.275i	0.718854	+	0.718854i
$843$		−	1973.56i		−	2.34111i
$844$	−143.720	+	143.720i	−0.170284	+	0.170284i
$845$	−435.016	−	695.286i	−0.514812	−	0.822824i
$846$	516.987			0.611095
$847$		−	287.585i		−	0.339533i
$848$	190.826	−	190.826i	0.225031	−	0.225031i
$849$		−	1797.88i		−	2.11764i
$850$	−572.574	−	182.782i	−0.673616	−	0.215037i
$851$	−40.5219			−0.0476168
$852$	−73.0294	−	73.0294i	−0.0857152	−	0.0857152i
$853$	628.367			0.736655			0.368328	−	0.929696i	$-0.379930\pi$
$853$	628.367			0.736655			0.368328	+	0.929696i	$0.379930\pi$
$854$		−	198.155i		−	0.232032i
$855$	−190.016	+	118.886i	−0.222241	+	0.139048i
$856$	204.235	+	204.235i	0.238592	+	0.238592i
$857$	−1006.94			−1.17496			−0.587478	−	0.809240i	$-0.699879\pi$
$857$	−1006.94			−1.17496			−0.587478	+	0.809240i	$0.699879\pi$
$858$	−21.1382	+	21.1382i	−0.0246366	+	0.0246366i
$859$	−421.287			−0.490439			−0.245219	−	0.969468i	$-0.578860\pi$
$859$	−421.287			−0.490439			−0.245219	+	0.969468i	$0.578860\pi$
$860$	−145.867	−	33.5881i	−0.169612	−	0.0390559i
$861$	329.384	+	329.384i	0.382560	+	0.382560i
$862$		−	963.570i		−	1.11783i
$863$	−222.829	−	222.829i	−0.258203	−	0.258203i	0.566120	−	0.824323i	$-0.308444\pi$
$863$	−222.829	−	222.829i	−0.258203	−	0.258203i	−0.824323	+	0.566120i	$0.808444\pi$
$864$	−68.7743	−	68.7743i	−0.0795999	−	0.0795999i
$865$	324.895	−	203.276i	0.375602	−	0.235001i
$866$	−491.872			−0.567982
$867$	298.433	+	1010.09i	0.344213	+	1.16504i
$868$	97.5784	+	97.5784i	0.112418	+	0.112418i
$869$	175.560			0.202026
$870$	323.699	+	517.367i	0.372068	+	0.594675i
$871$	204.372			0.234641
$872$		−	540.966i		−	0.620374i
$873$		−	614.785i		−	0.704221i
$874$	29.9862	−	29.9862i	0.0343092	−	0.0343092i
$875$	−33.4326	−	312.922i	−0.0382087	−	0.357625i
$876$		−	393.606i		−	0.449322i
$877$	1500.39			1.71082			0.855411	−	0.517950i	$-0.173305\pi$
$877$	1500.39			1.71082			0.855411	+	0.517950i	$0.173305\pi$
$878$		−	200.353i		−	0.228193i
$879$	236.010	+	236.010i	0.268499	+	0.268499i
$880$	−50.7163	−	11.6782i	−0.0576322	−	0.0132707i
$881$	606.925	−	606.925i	0.688905	−	0.688905i	−0.273085	−	0.961990i	$-0.588044\pi$
$881$	606.925	−	606.925i	0.688905	−	0.688905i	0.961990	+	0.273085i	$0.0880440\pi$
$882$	182.690	+	182.690i	0.207131	+	0.207131i
$883$	108.618	+	108.618i	0.123011	+	0.123011i	0.765932	−	0.642921i	$-0.222278\pi$
$883$	108.618	+	108.618i	0.123011	+	0.123011i	−0.642921	+	0.765932i	$0.722278\pi$
$884$	75.0028	−	10.8480i	0.0848448	−	0.0122715i
$885$	375.761	−	235.101i	0.424589	−	0.265650i
$886$			1066.19i			1.20338i
$887$			904.123i			1.01930i	0.860381	+	0.509652i	$0.170226\pi$
$887$			904.123i			1.01930i	−0.860381	+	0.509652i	$0.829774\pi$
$888$	−103.113	−	103.113i	−0.116118	−	0.116118i
$889$	90.1236	+	90.1236i	0.101376	+	0.101376i
$890$	57.3455	−	249.041i	0.0644332	−	0.279821i
$891$	−186.214	−	186.214i	−0.208995	−	0.208995i
$892$	−36.3530	−	36.3530i	−0.0407545	−	0.0407545i
$893$	631.901	−	631.901i	0.707616	−	0.707616i
$894$	−393.504	+	393.504i	−0.440161	+	0.440161i
$895$	88.5489	−	55.4020i	0.0989373	−	0.0619016i
$896$	−20.1410	+	20.1410i	−0.0224788	+	0.0224788i
$897$	−16.4536	+	16.4536i	−0.0183429	+	0.0183429i
$898$	177.741			0.197930
$899$	−649.024			−0.721939
$900$	192.553	+	93.6417i	0.213948	+	0.104046i
$901$	−1135.13	+	164.179i	−1.25986	+	0.182219i
$902$	132.108	−	132.108i	0.146461	−	0.146461i
$903$	−97.1152	+	97.1152i	−0.107547	+	0.107547i
$904$	−342.105	−	342.105i	−0.378434	−	0.378434i
$905$	−176.700	−	40.6879i	−0.195248	−	0.0449590i
$906$	275.045	−	275.045i	0.303582	−	0.303582i
$907$	813.684			0.897116			0.448558	−	0.893754i	$-0.351938\pi$
$907$	813.684			0.897116			0.448558	+	0.893754i	$0.351938\pi$
$908$			478.695i			0.527197i
$909$	−155.707			−0.171295
$910$	21.0464	+	33.6384i	0.0231279	+	0.0369652i
$911$	−948.907	−	948.907i	−1.04161	−	1.04161i	−0.999096	−	0.0425140i	$-0.986463\pi$
$911$	−948.907	−	948.907i	−1.04161	−	1.04161i	−0.0425140	−	0.999096i	$-0.513537\pi$
$912$	152.607			0.167332
$913$	−122.638			−0.134324
$914$			483.756i			0.529274i
$915$	988.298	+	227.571i	1.08011	+	0.248711i
$916$		−	335.670i		−	0.366452i
$917$	−106.447	+	106.447i	−0.116082	+	0.116082i
$918$	59.1709	+	409.105i	0.0644563	+	0.445648i
$919$			781.247i			0.850105i	0.905169	+	0.425053i	$0.139744\pi$
$919$			781.247i			0.850105i	−0.905169	+	0.425053i	$0.860256\pi$
$920$	−39.4767	−	9.09012i	−0.0429094	−	0.00988056i
$921$	−1495.84	+	1495.84i	−1.62415	+	1.62415i
$922$	−487.235	+	487.235i	−0.528455	+	0.528455i
$923$	31.5820			0.0342167
$924$	−33.7659	+	33.7659i	−0.0365432	+	0.0365432i
$925$	−318.044	−	154.670i	−0.343832	−	0.167211i
$926$		−	788.812i		−	0.851849i
$927$	238.884	+	238.884i	0.257695	+	0.257695i
$928$		−	133.964i		−	0.144357i
$929$	133.019	−	133.019i	0.143185	−	0.143185i	−0.631881	−	0.775066i	$-0.717717\pi$
$929$	133.019	−	133.019i	0.143185	−	0.143185i	0.775066	+	0.631881i	$0.217717\pi$
$930$	−598.736	+	374.608i	−0.643802	+	0.402804i
$931$	446.595			0.479694
$932$			184.929i			0.198422i
$933$	1177.85	−	1177.85i	1.26243	−	1.26243i
$934$		−	295.508i		−	0.316390i
$935$	142.950	+	168.784i	0.152888	+	0.180518i
$936$	−26.9971			−0.0288431
$937$	560.333	+	560.333i	0.598008	+	0.598008i	0.939782	−	0.341774i	$-0.111028\pi$
$937$	560.333	+	560.333i	0.598008	+	0.598008i	−0.341774	+	0.939782i	$0.611028\pi$
$938$	326.462			0.348040
$939$			1168.08i			1.24396i
$940$	−831.894	−	191.556i	−0.884993	−	0.203783i
$941$	424.440	+	424.440i	0.451052	+	0.451052i	0.895704	−	0.444652i	$-0.146672\pi$
$941$	424.440	+	424.440i	0.451052	+	0.451052i	−0.444652	+	0.895704i	$0.646672\pi$
$942$	−1094.49			−1.16188
$943$	102.830	−	102.830i	0.109046	−	0.109046i
$944$	−97.2971			−0.103069
$945$	−183.481	+	114.798i	−0.194160	+	0.121479i
$946$	38.9504	+	38.9504i	0.0411738	+	0.0411738i
$947$			1480.38i			1.56324i	0.623757	+	0.781618i	$0.285605\pi$
$947$			1480.38i			1.56324i	−0.623757	+	0.781618i	$0.714395\pi$
$948$	347.730	+	347.730i	0.366803	+	0.366803i
$949$	85.1088	+	85.1088i	0.0896826	+	0.0896826i
$950$	349.809	−	120.897i	0.368220	−	0.127260i
$951$	−943.994			−0.992633
$952$	119.809	−	17.3285i	0.125850	−	0.0182022i
$953$	195.573	+	195.573i	0.205218	+	0.205218i	0.802231	−	0.597013i	$-0.203646\pi$
$953$	195.573	+	195.573i	0.205218	+	0.205218i	−0.597013	+	0.802231i	$0.703646\pi$
$954$	408.587			0.428289
$955$	1456.16	−	911.071i	1.52478	−	0.954001i
$956$	−3.47193			−0.00363173
$957$		−	224.588i		−	0.234679i
$958$			90.2570i			0.0942140i
$959$	−319.209	+	319.209i	−0.332856	+	0.332856i
$960$	−77.3221	−	123.584i	−0.0805439	−	0.128733i
$961$			209.902i			0.218420i
$962$	44.5918			0.0463532
$963$			437.299i			0.454100i
$964$	−55.9580	−	55.9580i	−0.0580478	−	0.0580478i
$965$	−532.323	−	850.811i	−0.551630	−	0.881670i
$966$	−26.2828	+	26.2828i	−0.0272078	+	0.0272078i
$967$	−4.45430	−	4.45430i	−0.00460631	−	0.00460631i	0.704800	−	0.709406i	$-0.251037\pi$
$967$	−4.45430	−	4.45430i	−0.00460631	−	0.00460631i	−0.709406	+	0.704800i	$0.751037\pi$
$968$	−228.457	−	228.457i	−0.236010	−	0.236010i
$969$	−519.540	−	388.243i	−0.536161	−	0.400664i
$970$	−227.793	+	989.263i	−0.234838	+	1.01986i
$971$			648.849i			0.668227i	0.942533	+	0.334114i	$0.108437\pi$
$971$			648.849i			0.668227i	−0.942533	+	0.334114i	$0.891563\pi$
$972$		−	428.179i		−	0.440514i
$973$	−57.9628	−	57.9628i	−0.0595712	−	0.0595712i
$974$	810.637	+	810.637i	0.832276	+	0.832276i
$975$	−191.942	+	66.3367i	−0.196864	+	0.0680376i
$976$	−157.415	−	157.415i	−0.161285	−	0.161285i
$977$	−8.60532	−	8.60532i	−0.00880790	−	0.00880790i	0.702689	−	0.711497i	$-0.251982\pi$
$977$	−8.60532	−	8.60532i	−0.00880790	−	0.00880790i	−0.711497	+	0.702689i	$0.751982\pi$
$978$	665.693	−	665.693i	0.680668	−	0.680668i
$979$	−66.5006	+	66.5006i	−0.0679271	+	0.0679271i
$980$	−226.279	−	361.661i	−0.230897	−	0.369042i
$981$	579.146	−	579.146i	0.590363	−	0.590363i
$982$	313.136	−	313.136i	0.318876	−	0.318876i
$983$	715.161			0.727529			0.363765	−	0.931491i	$-0.381491\pi$
$983$	715.161			0.727529			0.363765	+	0.931491i	$0.381491\pi$
$984$	523.326			0.531836
$985$	1559.62	−	975.798i	1.58337	−	0.990658i
$986$	−340.814	+	456.071i	−0.345653	+	0.462547i
$987$	−553.858	+	553.858i	−0.561153	+	0.561153i
$988$	−32.9979	+	32.9979i	−0.0333987	+	0.0333987i
$989$	30.3183	+	30.3183i	0.0306555	+	0.0306555i
$990$	−41.7933	−	66.7982i	−0.0422154	−	0.0674729i
$991$	831.390	−	831.390i	0.838941	−	0.838941i	−0.149779	−	0.988720i	$-0.547856\pi$
$991$	831.390	−	831.390i	0.838941	−	0.838941i	0.988720	+	0.149779i	$0.0478561\pi$
$992$	155.033			0.156283
$993$		−	2266.25i		−	2.28223i
$994$	50.4488			0.0507534
$995$	−1819.99	−	419.082i	−1.82914	−	0.421188i
$996$	−242.907	−	242.907i	−0.243883	−	0.243883i
$997$	1365.27			1.36937			0.684687	−	0.728837i	$-0.259939\pi$
$997$	1365.27			1.36937			0.684687	+	0.728837i	$0.259939\pi$
$998$	460.309			0.461231
$999$			243.227i			0.243470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.3.j.b.123.7	yes	16
5.2	odd	4		170.3.e.b.157.2	yes	16
17.13	even	4		170.3.e.b.13.7	✓	16
85.47	odd	4	inner	170.3.j.b.47.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.3.e.b.13.7	✓	16	17.13	even	4
170.3.e.b.157.2	yes	16	5.2	odd	4
170.3.j.b.47.7	yes	16	85.47	odd	4	inner
170.3.j.b.123.7	yes	16	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	170.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +3.64449 q^{3} +2.00000i q^{4} +(4.23872 - 2.65202i) q^{5} +(-3.64449 - 3.64449i) q^{6} +2.51762 q^{7} +(2.00000 - 2.00000i) q^{8} +4.28231 q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +3.64449 q^{3} +2.00000i q^{4} +(4.23872 - 2.65202i) q^{5} +(-3.64449 - 3.64449i) q^{6} +2.51762 q^{7} +(2.00000 - 2.00000i) q^{8} +4.28231 q^{9} +(-6.89075 - 1.58670i) q^{10} +(1.84002 + 1.84002i) q^{11} +7.28898i q^{12} +(-1.57608 - 1.57608i) q^{13} +(-2.51762 - 2.51762i) q^{14} +(15.4480 - 9.66527i) q^{15} -4.00000 q^{16} +(13.6177 + 10.1763i) q^{17} +(-4.28231 - 4.28231i) q^{18} -10.4683 q^{19} +(5.30404 + 8.47745i) q^{20} +9.17545 q^{21} -3.68003i q^{22} -2.86447i q^{23} +(7.28898 - 7.28898i) q^{24} +(10.9336 - 22.4824i) q^{25} +3.15217i q^{26} -17.1936 q^{27} +5.03524i q^{28} +(-16.7455 - 16.7455i) q^{29} +(-25.1133 - 5.78272i) q^{30} +(19.3791 - 19.3791i) q^{31} +(4.00000 + 4.00000i) q^{32} +(6.70592 + 6.70592i) q^{33} +(-3.44145 - 23.7940i) q^{34} +(10.6715 - 6.67679i) q^{35} +8.56461i q^{36} -14.1464i q^{37} +(10.4683 + 10.4683i) q^{38} +(-5.74402 - 5.74402i) q^{39} +(3.17340 - 13.7815i) q^{40} +(35.8985 + 35.8985i) q^{41} +(-9.17545 - 9.17545i) q^{42} +(-10.5842 + 10.5842i) q^{43} +(-3.68003 + 3.68003i) q^{44} +(18.1515 - 11.3568i) q^{45} +(-2.86447 + 2.86447i) q^{46} +(-60.3631 + 60.3631i) q^{47} -14.5780 q^{48} -42.6616 q^{49} +(-33.4159 + 11.5488i) q^{50} +(49.6297 + 37.0874i) q^{51} +(3.15217 - 3.15217i) q^{52} +(-47.7065 + 47.7065i) q^{53} +(17.1936 + 17.1936i) q^{54} +(12.6791 + 2.91956i) q^{55} +(5.03524 - 5.03524i) q^{56} -38.1517 q^{57} +33.4909i q^{58} +24.3243 q^{59} +(19.3305 + 30.8960i) q^{60} +(39.3536 + 39.3536i) q^{61} -38.7582 q^{62} +10.7812 q^{63} -8.00000i q^{64} +(-10.8604 - 2.50078i) q^{65} -13.4118i q^{66} +(-64.8353 + 64.8353i) q^{67} +(-20.3526 + 27.2355i) q^{68} -10.4395i q^{69} +(-17.3483 - 3.99471i) q^{70} +(-10.0191 + 10.0191i) q^{71} +(8.56461 - 8.56461i) q^{72} -54.0001 q^{73} +(-14.1464 + 14.1464i) q^{74} +(39.8472 - 81.9368i) q^{75} -20.9367i q^{76} +(4.63247 + 4.63247i) q^{77} +11.4880i q^{78} +(47.7062 - 47.7062i) q^{79} +(-16.9549 + 10.6081i) q^{80} -101.203 q^{81} -71.7969i q^{82} +(-33.3253 + 33.3253i) q^{83} +18.3509i q^{84} +(84.7096 + 7.01995i) q^{85} +21.1685 q^{86} +(-61.0287 - 61.0287i) q^{87} +7.36007 q^{88} +36.1413i q^{89} +(-29.5083 - 6.79474i) q^{90} +(-3.96798 - 3.96798i) q^{91} +5.72894 q^{92} +(70.6269 - 70.6269i) q^{93} +120.726 q^{94} +(-44.3724 + 27.7622i) q^{95} +(14.5780 + 14.5780i) q^{96} -143.564i q^{97} +(42.6616 + 42.6616i) q^{98} +(7.87951 + 7.87951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 2 q^{5} - 12 q^{7} + 32 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 + 2 * q^5 - 12 * q^7 + 32 * q^8 + 16 * q^9	\( 16 q - 16 q^{2} + 2 q^{5} - 12 q^{7} + 32 q^{8} + 16 q^{9} + 20 q^{11} + 4 q^{13} + 12 q^{14} - 12 q^{15} - 64 q^{16} - 12 q^{17} - 16 q^{18} + 16 q^{19} - 4 q^{20} - 44 q^{25} + 108 q^{27} + 20 q^{29} + 12 q^{30} + 92 q^{31} + 64 q^{32} - 60 q^{33} - 24 q^{34} - 124 q^{35} - 16 q^{38} + 140 q^{39} + 8 q^{40} - 60 q^{41} - 52 q^{43} - 40 q^{44} + 62 q^{45} + 16 q^{46} + 112 q^{47} - 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} - 48 q^{53} - 108 q^{54} + 40 q^{55} - 24 q^{56} + 88 q^{57} + 76 q^{61} - 184 q^{62} - 8 q^{63} + 4 q^{65} + 116 q^{67} + 72 q^{68} + 124 q^{70} - 268 q^{71} + 32 q^{72} - 148 q^{73} - 32 q^{74} - 76 q^{75} + 116 q^{77} + 88 q^{79} - 8 q^{80} - 352 q^{81} + 160 q^{83} + 142 q^{85} + 104 q^{86} - 236 q^{87} + 80 q^{88} + 136 q^{90} - 168 q^{91} - 32 q^{92} - 48 q^{93} - 224 q^{94} - 388 q^{95} + 136 q^{98} + 348 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^5 - 12 * q^7 + 32 * q^8 + 16 * q^9 + 20 * q^11 + 4 * q^13 + 12 * q^14 - 12 * q^15 - 64 * q^16 - 12 * q^17 - 16 * q^18 + 16 * q^19 - 4 * q^20 - 44 * q^25 + 108 * q^27 + 20 * q^29 + 12 * q^30 + 92 * q^31 + 64 * q^32 - 60 * q^33 - 24 * q^34 - 124 * q^35 - 16 * q^38 + 140 * q^39 + 8 * q^40 - 60 * q^41 - 52 * q^43 - 40 * q^44 + 62 * q^45 + 16 * q^46 + 112 * q^47 - 136 * q^49 - 4 * q^50 - 140 * q^51 - 8 * q^52 - 48 * q^53 - 108 * q^54 + 40 * q^55 - 24 * q^56 + 88 * q^57 + 76 * q^61 - 184 * q^62 - 8 * q^63 + 4 * q^65 + 116 * q^67 + 72 * q^68 + 124 * q^70 - 268 * q^71 + 32 * q^72 - 148 * q^73 - 32 * q^74 - 76 * q^75 + 116 * q^77 + 88 * q^79 - 8 * q^80 - 352 * q^81 + 160 * q^83 + 142 * q^85 + 104 * q^86 - 236 * q^87 + 80 * q^88 + 136 * q^90 - 168 * q^91 - 32 * q^92 - 48 * q^93 - 224 * q^94 - 388 * q^95 + 136 * q^98 + 348 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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