LMFDB - Embedded newform 170.3.e.b.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,3,Mod(13,170)]

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([3, 1]))

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

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

chi := DirichletCharacter("170.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	170.e (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			13.7
Root			$-3.64449i$ of defining polynomial
Character	$\chi$	$=$	170.13
Dual form			170.3.e.b.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +3.64449i q^{3} +2.00000i q^{4} +(2.65202 + 4.23872i) q^{5} +(-3.64449 + 3.64449i) q^{6} -2.51762i q^{7} +(-2.00000 + 2.00000i) q^{8} -4.28231 q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +3.64449i q^{3} +2.00000i q^{4} +(2.65202 + 4.23872i) q^{5} +(-3.64449 + 3.64449i) q^{6} -2.51762i q^{7} +(-2.00000 + 2.00000i) q^{8} -4.28231 q^{9} +(-1.58670 + 6.89075i) q^{10} +(1.84002 - 1.84002i) q^{11} -7.28898 q^{12} +(-1.57608 - 1.57608i) q^{13} +(2.51762 - 2.51762i) q^{14} +(-15.4480 + 9.66527i) q^{15} -4.00000 q^{16} +(-10.1763 - 13.6177i) q^{17} +(-4.28231 - 4.28231i) q^{18} +10.4683 q^{19} +(-8.47745 + 5.30404i) q^{20} +9.17545 q^{21} +3.68003 q^{22} -2.86447 q^{23} +(-7.28898 - 7.28898i) q^{24} +(-10.9336 + 22.4824i) q^{25} -3.15217i q^{26} +17.1936i q^{27} +5.03524 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} +14.1464 q^{37} +(10.4683 + 10.4683i) q^{38} +(5.74402 - 5.74402i) q^{39} +(-13.7815 - 3.17340i) 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} +(-11.3568 - 18.1515i) q^{45} +(-2.86447 - 2.86447i) q^{46} +(-60.3631 + 60.3631i) q^{47} -14.5780i 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} +38.1517i q^{57} +33.4909 q^{58} -24.3243 q^{59} +(-19.3305 - 30.8960i) q^{60} +(39.3536 - 39.3536i) q^{61} +38.7582i q^{62} +10.7812i q^{63} -8.00000i q^{64} +(2.50078 - 10.8604i) q^{65} +13.4118i q^{66} +(-64.8353 + 64.8353i) q^{67} +(27.2355 - 20.3526i) q^{68} -10.4395i q^{69} +(17.3483 + 3.99471i) q^{70} +(-10.0191 - 10.0191i) q^{71} +(8.56461 - 8.56461i) q^{72} -54.0001i q^{73} +(14.1464 + 14.1464i) q^{74} +(-81.9368 - 39.8472i) q^{75} +20.9367i q^{76} +(-4.63247 - 4.63247i) q^{77} +11.4880 q^{78} +(-47.7062 - 47.7062i) q^{79} +(-10.6081 - 16.9549i) q^{80} -101.203 q^{81} +71.7969 q^{82} +(33.3253 - 33.3253i) q^{83} +18.3509i q^{84} +(30.7341 - 79.2491i) q^{85} +21.1685 q^{86} +(61.0287 + 61.0287i) q^{87} +7.36007i q^{88} +36.1413i q^{89} +(6.79474 - 29.5083i) q^{90} +(-3.96798 + 3.96798i) q^{91} -5.72894i q^{92} +(-70.6269 + 70.6269i) q^{93} -120.726 q^{94} +(27.7622 + 44.3724i) q^{95} +(14.5780 - 14.5780i) q^{96} +143.564 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} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9	$ 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9} - 4 q^{10} + 20 q^{11} + 4 q^{13} - 12 q^{14} + 12 q^{15} - 64 q^{16} + 36 q^{17} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 40 q^{22} + 16 q^{23} + 44 q^{25} - 24 q^{28} - 20 q^{29} + 12 q^{30} + 92 q^{31} - 64 q^{32} - 60 q^{33} + 24 q^{34} - 124 q^{35} + 32 q^{37} - 16 q^{38} - 140 q^{39} - 60 q^{41} + 52 q^{43} + 40 q^{44} + 198 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} - 40 q^{58} + 76 q^{61} - 40 q^{65} + 116 q^{67} - 24 q^{68} - 124 q^{70} - 268 q^{71} + 32 q^{72} + 32 q^{74} + 136 q^{75} - 116 q^{77} - 280 q^{78} - 88 q^{79} + 8 q^{80} - 352 q^{81} - 120 q^{82} - 160 q^{83} + 310 q^{85} + 104 q^{86} + 236 q^{87} + 260 q^{90} - 168 q^{91} + 48 q^{93} + 224 q^{94} + 264 q^{95} - 256 q^{97} + 136 q^{98} - 348 q^{99}+O(q^{100}) $ 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9 - 4 * q^10 + 20 * q^11 + 4 * q^13 - 12 * q^14 + 12 * q^15 - 64 * q^16 + 36 * q^17 - 16 * q^18 - 16 * q^19 - 4 * q^20 + 40 * q^22 + 16 * q^23 + 44 * q^25 - 24 * q^28 - 20 * q^29 + 12 * q^30 + 92 * q^31 - 64 * q^32 - 60 * q^33 + 24 * q^34 - 124 * q^35 + 32 * q^37 - 16 * q^38 - 140 * q^39 - 60 * q^41 + 52 * q^43 + 40 * q^44 + 198 * 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 - 40 * q^58 + 76 * q^61 - 40 * q^65 + 116 * q^67 - 24 * q^68 - 124 * q^70 - 268 * q^71 + 32 * q^72 + 32 * q^74 + 136 * q^75 - 116 * q^77 - 280 * q^78 - 88 * q^79 + 8 * q^80 - 352 * q^81 - 120 * q^82 - 160 * q^83 + 310 * q^85 + 104 * q^86 + 236 * q^87 + 260 * q^90 - 168 * q^91 + 48 * q^93 + 224 * q^94 + 264 * q^95 - 256 * q^97 + 136 * q^98 - 348 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$			3.64449i			1.21483i	0.794385	+	0.607415i	$0.207793\pi$
$3$			3.64449i			1.21483i	−0.794385	+	0.607415i	$0.792207\pi$
$4$			2.00000i			0.500000i
$5$	2.65202	+	4.23872i	0.530404	+	0.847745i
$5$	2.65202	+	4.23872i	0.530404	+	0.847745i
$6$	−3.64449	+	3.64449i	−0.607415	+	0.607415i
$7$		−	2.51762i		−	0.359660i	−0.983698	−	0.179830i	$-0.942445\pi$
$7$		−	2.51762i		−	0.359660i	0.983698	−	0.179830i	$-0.0575548\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−4.28231			−0.475812
$10$	−1.58670	+	6.89075i	−0.158670	+	0.689075i
$11$	1.84002	−	1.84002i	0.167274	−	0.167274i	−0.618506	−	0.785780i	$-0.712262\pi$
$11$	1.84002	−	1.84002i	0.167274	−	0.167274i	0.785780	+	0.618506i	$0.212262\pi$
$12$	−7.28898			−0.607415
$13$	−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
$17$	−10.1763	−	13.6177i	−0.598606	−	0.801044i
$17$	−10.1763	−	13.6177i	−0.598606	−	0.801044i
$18$	−4.28231	−	4.28231i	−0.237906	−	0.237906i
$19$	10.4683			0.550965			0.275482	−	0.961306i	$-0.411162\pi$
$19$	10.4683			0.550965			0.275482	+	0.961306i	$0.411162\pi$
$20$	−8.47745	+	5.30404i	−0.423872	+	0.265202i
$21$	9.17545			0.436926
$22$	3.68003			0.167274
$23$	−2.86447			−0.124542			−0.0622711	−	0.998059i	$-0.519834\pi$
$23$	−2.86447			−0.124542			−0.0622711	+	0.998059i	$0.519834\pi$
$24$	−7.28898	−	7.28898i	−0.303707	−	0.303707i
$25$	−10.9336	+	22.4824i	−0.437342	+	0.899295i
$26$		−	3.15217i		−	0.121237i
$27$			17.1936i			0.636800i
$28$	5.03524			0.179830
$29$	16.7455	−	16.7455i	0.577430	−	0.577430i	−0.356765	−	0.934194i	$-0.616120\pi$
$29$	16.7455	−	16.7455i	0.577430	−	0.577430i	0.934194	+	0.356765i	$0.116120\pi$
$30$	−25.1133	−	5.78272i	−0.837108	−	0.192757i
$31$	19.3791	+	19.3791i	0.625132	+	0.625132i	0.946839	−	0.321707i	$-0.104257\pi$
$31$	19.3791	+	19.3791i	0.625132	+	0.625132i	−0.321707	+	0.946839i	$0.604257\pi$
$32$	−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
$37$	14.1464			0.382335			0.191167	−	0.981557i	$-0.438773\pi$
$37$	14.1464			0.382335			0.191167	+	0.981557i	$0.438773\pi$
$38$	10.4683	+	10.4683i	0.275482	+	0.275482i
$39$	5.74402	−	5.74402i	0.147283	−	0.147283i
$40$	−13.7815	−	3.17340i	−0.344537	−	0.0793351i
$41$	35.8985	−	35.8985i	0.875573	−	0.875573i	−0.117500	−	0.993073i	$-0.537488\pi$
$41$	35.8985	−	35.8985i	0.875573	−	0.875573i	0.993073	+	0.117500i	$0.0374881\pi$
$42$	9.17545	+	9.17545i	0.218463	+	0.218463i
$43$	10.5842	−	10.5842i	0.246145	−	0.246145i	−0.573241	−	0.819387i	$-0.694314\pi$
$43$	10.5842	−	10.5842i	0.246145	−	0.246145i	0.819387	+	0.573241i	$0.194314\pi$
$44$	3.68003	+	3.68003i	0.0836371	+	0.0836371i
$45$	−11.3568	−	18.1515i	−0.252373	−	0.403367i
$46$	−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	$0.887493\pi$
$48$		−	14.5780i		−	0.303707i
$49$	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	−0.0953242	−	0.995446i	$-0.530389\pi$
$53$	47.7065	−	47.7065i	0.900122	−	0.900122i	0.995446	+	0.0953242i	$0.0303888\pi$
$54$	−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
$57$			38.1517i			0.669328i
$58$	33.4909			0.577430
$59$	−24.3243			−0.412276			−0.206138	−	0.978523i	$-0.566090\pi$
$59$	−24.3243			−0.412276			−0.206138	+	0.978523i	$0.566090\pi$
$60$	−19.3305	−	30.8960i	−0.322176	−	0.514933i
$61$	39.3536	−	39.3536i	0.645141	−	0.645141i	−0.306673	−	0.951815i	$-0.599216\pi$
$61$	39.3536	−	39.3536i	0.645141	−	0.645141i	0.951815	+	0.306673i	$0.0992159\pi$
$62$			38.7582i			0.625132i
$63$			10.7812i			0.171131i
$64$		−	8.00000i		−	0.125000i
$65$	2.50078	−	10.8604i	0.0384735	−	0.167083i
$66$			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	$0.489875\pi$
$68$	27.2355	−	20.3526i	0.400522	−	0.299303i
$69$		−	10.4395i		−	0.151298i
$70$	17.3483	+	3.99471i	0.247833	+	0.0570673i
$71$	−10.0191	−	10.0191i	−0.141115	−	0.141115i	0.633020	−	0.774135i	$-0.281815\pi$
$71$	−10.0191	−	10.0191i	−0.141115	−	0.141115i	−0.774135	+	0.633020i	$0.781815\pi$
$72$	8.56461	−	8.56461i	0.118953	−	0.118953i
$73$		−	54.0001i		−	0.739728i	−0.929086	−	0.369864i	$-0.879404\pi$
$73$		−	54.0001i		−	0.739728i	0.929086	−	0.369864i	$-0.120596\pi$
$74$	14.1464	+	14.1464i	0.191167	+	0.191167i
$75$	−81.9368	−	39.8472i	−1.09249	−	0.531297i
$76$			20.9367i			0.275482i
$77$	−4.63247	−	4.63247i	−0.0601619	−	0.0601619i
$78$	11.4880			0.147283
$79$	−47.7062	−	47.7062i	−0.603876	−	0.603876i	0.337463	−	0.941339i	$-0.390431\pi$
$79$	−47.7062	−	47.7062i	−0.603876	−	0.603876i	−0.941339	+	0.337463i	$0.890431\pi$
$80$	−10.6081	−	16.9549i	−0.132601	−	0.211936i
$81$	−101.203			−1.24941
$82$	71.7969			0.875573
$83$	33.3253	−	33.3253i	0.401509	−	0.401509i	−0.477255	−	0.878765i	$-0.658368\pi$
$83$	33.3253	−	33.3253i	0.401509	−	0.401509i	0.878765	+	0.477255i	$0.158368\pi$
$84$			18.3509i			0.218463i
$85$	30.7341	−	79.2491i	0.361578	−	0.932342i
$86$	21.1685			0.246145
$87$	61.0287	+	61.0287i	0.701479	+	0.701479i
$88$			7.36007i			0.0836371i
$89$			36.1413i			0.406082i	0.979170	+	0.203041i	$0.0650825\pi$
$89$			36.1413i			0.406082i	−0.979170	+	0.203041i	$0.934917\pi$
$90$	6.79474	−	29.5083i	0.0754971	−	0.327870i
$91$	−3.96798	+	3.96798i	−0.0436042	+	0.0436042i
$92$		−	5.72894i		−	0.0622711i
$93$	−70.6269	+	70.6269i	−0.759429	+	0.759429i
$94$	−120.726			−1.28432
$95$	27.7622	+	44.3724i	0.292234	+	0.467077i
$96$	14.5780	−	14.5780i	0.151854	−	0.151854i
$97$	143.564			1.48004			0.740021	−	0.672584i	$-0.234816\pi$
$97$	143.564			1.48004			0.740021	+	0.672584i	$0.234816\pi$
$98$	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	$0.557611\pi$
$102$	86.7171	+	12.5423i	0.850168	+	0.122964i
$103$	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
$105$	24.3335	+	38.8922i	0.231747	+	0.370402i
$106$	95.4129			0.900122
$107$	−102.118			−0.954370			−0.477185	−	0.878803i	$-0.658343\pi$
$107$	−102.118			−0.954370			−0.477185	+	0.878803i	$0.658343\pi$
$108$	−34.3872			−0.318400
$109$	−135.242	−	135.242i	−1.24075	−	1.24075i	−0.959691	−	0.281057i	$-0.909315\pi$
$109$	−135.242	−	135.242i	−1.24075	−	1.24075i	−0.281057	−	0.959691i	$-0.590685\pi$
$110$	9.75953	+	15.5986i	0.0887230	+	0.141806i
$111$			51.5563i			0.464472i
$112$			10.0705i			0.0899151i
$113$	−171.052			−1.51374			−0.756869	−	0.653567i	$-0.773272\pi$
$113$	−171.052			−1.51374			−0.756869	+	0.653567i	$0.773272\pi$
$114$	−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
$122$	78.7073			0.645141
$123$	130.832	+	130.832i	1.06367	+	1.06367i
$124$	−38.7582	+	38.7582i	−0.312566	+	0.312566i
$125$	−124.293	+	13.2794i	−0.994341	+	0.106235i
$126$	−10.7812	+	10.7812i	−0.0855653	+	0.0855653i
$127$	−35.7971	−	35.7971i	−0.281867	−	0.281867i	0.551986	−	0.833853i	$-0.313870\pi$
$127$	−35.7971	−	35.7971i	−0.281867	−	0.281867i	−0.833853	+	0.551986i	$0.813870\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	38.5742	+	38.5742i	0.299025	+	0.299025i
$130$	13.3612	−	8.35962i	0.102778	−	0.0643048i
$131$	−42.2809	−	42.2809i	−0.322755	−	0.322755i	0.527068	−	0.849823i	$-0.323291\pi$
$131$	−42.2809	−	42.2809i	−0.322755	−	0.322755i	−0.849823	+	0.527068i	$0.823291\pi$
$132$	−13.4118	+	13.4118i	−0.101605	+	0.101605i
$133$		−	26.3553i		−	0.198160i
$134$	−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	$-0.712634\pi$
$139$	23.0228	−	23.0228i	0.165632	−	0.165632i	0.785056	+	0.619424i	$0.212634\pi$
$140$	13.3536	+	21.3430i	0.0953827	+	0.152450i
$141$	−219.993	−	219.993i	−1.56023	−	1.56023i
$142$		−	20.0383i		−	0.141115i
$143$	−5.80004			−0.0405597
$144$	17.1292			0.118953
$145$	115.389	+	26.5701i	0.795784	+	0.183242i
$146$	54.0001	−	54.0001i	0.369864	−	0.369864i
$147$			155.480i			1.05769i
$148$			28.2928i			0.191167i
$149$		−	107.972i		−	0.724647i	−0.932052	−	0.362323i	$-0.881984\pi$
$149$		−	107.972i		−	0.724647i	0.932052	−	0.362323i	$-0.118016\pi$
$150$	−42.0896	−	121.784i	−0.280597	−	0.811894i
$151$		−	75.4687i		−	0.499793i	−0.968273	−	0.249896i	$-0.919603\pi$
$151$		−	75.4687i		−	0.499793i	0.968273	−	0.249896i	$-0.0803966\pi$
$152$	−20.9367	+	20.9367i	−0.137741	+	0.137741i
$153$	43.5780	+	58.3154i	0.284824	+	0.381146i
$154$		−	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	$0.0135874\pi$
$158$		−	95.4124i		−	0.603876i
$159$	173.866	+	173.866i	1.09350	+	1.09350i
$160$	6.34681	−	27.5630i	0.0396675	−	0.172269i
$161$			7.21165i			0.0447928i
$162$	−101.203	−	101.203i	−0.624707	−	0.624707i
$163$	182.657			1.12060			0.560299	−	0.828291i	$-0.310686\pi$
$163$	182.657			1.12060			0.560299	+	0.828291i	$0.310686\pi$
$164$	71.7969	+	71.7969i	0.437786	+	0.437786i
$165$	−10.6403	+	46.2088i	−0.0644866	+	0.280053i
$166$	66.6506			0.401509
$167$	−195.792			−1.17241			−0.586204	−	0.810164i	$-0.699378\pi$
$167$	−195.792			−1.17241			−0.586204	+	0.810164i	$0.699378\pi$
$168$	−18.3509	+	18.3509i	−0.109231	+	0.109231i
$169$		−	164.032i		−	0.970603i
$170$	109.983	−	48.5150i	0.646960	−	0.285382i
$171$	−44.8286			−0.262155
$172$	21.1685	+	21.1685i	0.123073	+	0.123073i
$173$			76.6493i			0.443060i	0.975154	+	0.221530i	$0.0711050\pi$
$173$			76.6493i			0.443060i	−0.975154	+	0.221530i	$0.928895\pi$
$174$			122.057i			0.701479i
$175$	56.6021	+	27.5266i	0.323441	+	0.157295i
$176$	−7.36007	+	7.36007i	−0.0418186	+	0.0418186i
$177$		−	88.6496i		−	0.500845i
$178$	−36.1413	+	36.1413i	−0.203041	+	0.203041i
$179$	−20.8905			−0.116706			−0.0583532	−	0.998296i	$-0.518585\pi$
$179$	−20.8905			−0.116706			−0.0583532	+	0.998296i	$0.518585\pi$
$180$	36.3030	−	22.7135i	0.201683	−	0.126186i
$181$	−25.6431	+	25.6431i	−0.141674	+	0.141674i	−0.774387	−	0.632712i	$-0.781942\pi$
$181$	−25.6431	+	25.6431i	−0.141674	+	0.141674i	0.632712	+	0.774387i	$0.281942\pi$
$182$	−7.93597			−0.0436042
$183$	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
$187$	−43.7814	−	6.33232i	−0.234125	−	0.0338627i
$188$	−120.726	−	120.726i	−0.642161	−	0.642161i
$189$	43.2869			0.229031
$190$	−16.6101	+	72.1346i	−0.0874217	+	0.379656i
$191$	343.538			1.79863			0.899315	−	0.437302i	$-0.144066\pi$
$191$	343.538			1.79863			0.899315	+	0.437302i	$0.144066\pi$
$192$	29.1559			0.151854
$193$	−200.723			−1.04002			−0.520009	−	0.854161i	$-0.674071\pi$
$193$	−200.723			−1.04002			−0.520009	+	0.854161i	$0.674071\pi$
$194$	143.564	+	143.564i	0.740021	+	0.740021i
$195$	39.5806	+	9.11405i	0.202977	+	0.0467387i
$196$			85.3232i			0.435322i
$197$		−	367.945i		−	1.86774i	−0.357611	−	0.933871i	$-0.616409\pi$
$197$		−	367.945i		−	1.86774i	0.357611	−	0.933871i	$-0.383591\pi$
$198$	−15.7590			−0.0795911
$199$	264.121	−	264.121i	1.32724	−	1.32724i	0.419478	−	0.907765i	$-0.362213\pi$
$199$	264.121	−	264.121i	1.32724	−	1.32724i	0.907765	−	0.419478i	$-0.137787\pi$
$200$	−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
$207$	12.2665			0.0592586
$208$	6.30434	+	6.30434i	0.0303093	+	0.0303093i
$209$	19.2619	−	19.2619i	0.0921622	−	0.0921622i
$210$	−14.5587	+	63.2257i	−0.0693271	+	0.301075i
$211$	71.8600	−	71.8600i	0.340569	−	0.340569i	−0.516013	−	0.856581i	$-0.672584\pi$
$211$	71.8600	−	71.8600i	0.340569	−	0.340569i	0.856581	+	0.516013i	$0.172584\pi$
$212$	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
$215$	72.9334	+	16.7940i	0.339225	+	0.0781118i
$216$	−34.3872	−	34.3872i	−0.159200	−	0.159200i
$217$	48.7892	−	48.7892i	0.224835	−	0.224835i
$218$		−	270.483i		−	1.24075i
$219$	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	−0.665177	−	0.746686i	$-0.731644\pi$
$223$	18.1765	−	18.1765i	0.0815089	−	0.0815089i	0.746686	+	0.665177i	$0.231644\pi$
$224$	−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
$227$		−	239.348i		−	1.05439i	−0.849743	−	0.527197i	$-0.823243\pi$
$227$		−	239.348i		−	1.05439i	0.849743	−	0.527197i	$-0.176757\pi$
$228$	−76.3034			−0.334664
$229$	167.835			0.732904			0.366452	−	0.930437i	$-0.380572\pi$
$229$	167.835			0.732904			0.366452	+	0.930437i	$0.380572\pi$
$230$	4.54506	−	19.7383i	0.0197611	−	0.0858188i
$231$	16.8830	−	16.8830i	0.0730865	−	0.0730865i
$232$			66.9819i			0.288715i
$233$			92.4647i			0.396844i	0.980117	+	0.198422i	$0.0635817\pi$
$233$			92.4647i			0.396844i	−0.980117	+	0.198422i	$0.936418\pi$
$234$			13.4986i			0.0576861i
$235$	−415.947	−	95.7782i	−1.76999	−	0.407567i
$236$		−	48.6486i		−	0.206138i
$237$	173.865	−	173.865i	0.733607	−	0.733607i
$238$	−59.9044	−	8.66427i	−0.251699	−	0.0364045i
$239$			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	0.646672	−	0.762768i	$-0.276160\pi$
$241$	−27.9790	−	27.9790i	−0.116096	−	0.116096i	−0.762768	+	0.646672i	$0.776160\pi$
$242$	−114.229	+	114.229i	−0.472019	+	0.472019i
$243$		−	214.090i		−	0.881027i
$244$	78.7073	+	78.7073i	0.322571	+	0.322571i
$245$	113.139	+	180.831i	0.461794	+	0.738084i
$246$			261.663i			1.06367i
$247$	−16.4990	−	16.4990i	−0.0667974	−	0.0667974i
$248$	−77.5163			−0.312566
$249$	121.454	+	121.454i	0.487766	+	0.487766i
$250$	−137.572	−	111.013i	−0.550288	−	0.444053i
$251$	−237.556			−0.946439			−0.473219	−	0.880945i	$-0.656908\pi$
$251$	−237.556			−0.946439			−0.473219	+	0.880945i	$0.656908\pi$
$252$	−21.5625			−0.0855653
$253$	−5.27067	+	5.27067i	−0.0208327	+	0.0208327i
$254$		−	71.5943i		−	0.281867i
$255$	288.822	+	112.010i	1.13264	+	0.439255i
$256$	16.0000			0.0625000
$257$	−93.1226	−	93.1226i	−0.362345	−	0.362345i	0.502331	−	0.864676i	$-0.332476\pi$
$257$	−93.1226	−	93.1226i	−0.362345	−	0.362345i	−0.864676	+	0.502331i	$0.832476\pi$
$258$			77.1484i			0.299025i
$259$		−	35.6152i		−	0.137511i
$260$	21.7208	+	5.00155i	0.0835415	+	0.0192367i
$261$	−71.7092	+	71.7092i	−0.274748	+	0.274748i
$262$		−	84.5618i		−	0.322755i
$263$	−320.642	+	320.642i	−1.21917	+	1.21917i	−0.251249	+	0.967922i	$0.580841\pi$
$263$	−320.642	+	320.642i	−1.21917	+	1.21917i	−0.967922	+	0.251249i	$0.919159\pi$
$264$	−26.8237			−0.101605
$265$	328.733	+	75.6959i	1.24050	+	0.285645i
$266$	26.3553	−	26.3553i	0.0990800	−	0.0990800i
$267$	−131.717			−0.493321
$268$	−129.671	−	129.671i	−0.483846	−	0.483846i
$269$	−194.466	+	194.466i	−0.722921	+	0.722921i	−0.969199	−	0.246279i	$-0.920792\pi$
$269$	−194.466	+	194.466i	−0.722921	+	0.722921i	0.246279	+	0.969199i	$0.420792\pi$
$270$	−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	$0.416419\pi$
$272$	40.7052	+	54.4710i	0.149651	+	0.200261i
$273$	−14.4613	−	14.4613i	−0.0529717	−	0.0529717i
$274$	−253.580			−0.925473
$275$	21.2500	+	61.4859i	0.0772728	+	0.223585i
$276$	20.8791			0.0756488
$277$	191.172			0.690153			0.345076	−	0.938575i	$-0.387853\pi$
$277$	191.172			0.690153			0.345076	+	0.938575i	$0.387853\pi$
$278$	46.0457			0.165632
$279$	−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	$0.413800\pi$
$281$			541.518i			1.92711i	−0.267508	+	0.963556i	$0.586200\pi$
$282$		−	439.985i		−	1.56023i
$283$	−493.314			−1.74316			−0.871579	−	0.490256i	$-0.836903\pi$
$283$	−493.314			−1.74316			−0.871579	+	0.490256i	$0.836903\pi$
$284$	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
$292$	108.000			0.369864
$293$	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
$295$	−64.5085	−	103.104i	−0.218673	−	0.349505i
$296$	−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
$300$	79.6945	−	163.874i	0.265648	−	0.546245i
$301$	−26.6471	−	26.6471i	−0.0885287	−	0.0885287i
$302$	75.4687	−	75.4687i	0.249896	−	0.249896i
$303$		−	132.516i		−	0.437346i
$304$	−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	0.999200	+	0.0399809i	$0.0127297\pi$
$311$	323.185	+	323.185i	1.03918	+	1.03918i	0.0399809	+	0.999200i	$0.487270\pi$
$312$			22.9761i			0.0736413i
$313$	320.505			1.02398			0.511988	−	0.858993i	$-0.328909\pi$
$313$	320.505			1.02398			0.511988	+	0.858993i	$0.328909\pi$
$314$	300.315			0.956416
$315$	−45.6986	+	28.5921i	−0.145075	+	0.0907684i
$316$	95.4124	−	95.4124i	0.301938	−	0.301938i
$317$			259.019i			0.817096i	0.912737	+	0.408548i	$0.133965\pi$
$317$			259.019i			0.817096i	−0.912737	+	0.408548i	$0.866035\pi$
$318$			347.731i			1.09350i
$319$		−	61.6239i		−	0.193178i
$320$	33.9098	−	21.2162i	0.105968	−	0.0663006i
$321$		−	372.166i		−	1.15940i
$322$	−7.21165	+	7.21165i	−0.0223964	+	0.0223964i
$323$	−106.529	−	142.555i	−0.329811	−	0.441347i
$324$		−	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
$328$			143.594i			0.437786i
$329$	151.971	+	151.971i	0.461919	+	0.461919i
$330$	−56.8491	+	35.5685i	−0.172270	+	0.107783i
$331$			621.830i			1.87864i	0.343043	+	0.939320i	$0.388542\pi$
$331$			621.830i			1.87864i	−0.343043	+	0.939320i	$0.611458\pi$
$332$	66.6506	+	66.6506i	0.200755	+	0.200755i
$333$	−60.5791			−0.181919
$334$	−195.792	−	195.792i	−0.586204	−	0.586204i
$335$	−446.764	−	102.874i	−1.33362	−	0.307088i
$336$	−36.7018			−0.109231
$337$	−159.768			−0.474089			−0.237045	−	0.971499i	$-0.576179\pi$
$337$	−159.768			−0.474089			−0.237045	+	0.971499i	$0.576179\pi$
$338$	164.032	−	164.032i	0.485302	−	0.485302i
$339$		−	623.399i		−	1.83893i
$340$	158.498	+	61.4682i	0.466171	+	0.180789i
$341$	71.3157			0.209137
$342$	−44.8286	−	44.8286i	−0.131078	−	0.131078i
$343$		−	230.769i		−	0.672796i
$344$			42.3370i			0.123073i
$345$	44.2503	−	27.6859i	0.128262	−	0.0802489i
$346$	−76.6493	+	76.6493i	−0.221530	+	0.221530i
$347$			283.689i			0.817549i	0.912635	+	0.408774i	$0.134044\pi$
$347$			283.689i			0.817549i	−0.912635	+	0.408774i	$0.865956\pi$
$348$	−122.057	+	122.057i	−0.350740	+	0.350740i
$349$	95.7372			0.274318			0.137159	−	0.990549i	$-0.456203\pi$
$349$	95.7372			0.274318			0.137159	+	0.990549i	$0.456203\pi$
$350$	29.0756	+	84.1287i	0.0830730	+	0.240368i
$351$	27.0985	−	27.0985i	0.0772038	−	0.0772038i
$352$	−14.7201			−0.0418186
$353$	−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
$357$	−93.3721	−	124.949i	−0.261546	−	0.349997i
$358$	−20.8905	−	20.8905i	−0.0583532	−	0.0583532i
$359$	−527.313			−1.46884			−0.734419	−	0.678696i	$-0.762545\pi$
$359$	−527.313			−1.46884			−0.734419	+	0.678696i	$0.762545\pi$
$360$	59.0166	+	13.5895i	0.163935	+	0.0377486i
$361$	−251.414			−0.696438
$362$	−51.2861			−0.141674
$363$	−416.305			−1.14685
$364$	−7.93597	−	7.93597i	−0.0218021	−	0.0218021i
$365$	228.892	−	143.210i	0.627100	−	0.392355i
$366$			286.848i			0.783737i
$367$		−	269.563i		−	0.734505i	−0.930121	−	0.367253i	$-0.880298\pi$
$367$		−	269.563i		−	0.734505i	0.930121	−	0.367253i	$-0.119702\pi$
$368$	11.4579			0.0311355
$369$	−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
$377$	−52.7845			−0.140012
$378$	43.2869	+	43.2869i	0.114516	+	0.114516i
$379$	29.0227	−	29.0227i	0.0765771	−	0.0765771i	−0.667781	−	0.744358i	$-0.732756\pi$
$379$	29.0227	−	29.0227i	0.0765771	−	0.0765771i	0.744358	+	0.667781i	$0.232756\pi$
$380$	−88.7447	+	55.5245i	−0.233539	+	0.146117i
$381$	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	$-0.491466\pi$
$383$	393.130	−	393.130i	1.02645	−	1.02645i	0.999641	−	0.0268076i	$-0.00853416\pi$
$384$	29.1559	+	29.1559i	0.0759269	+	0.0759269i
$385$	7.35034	−	31.9211i	0.0190918	−	0.0829121i
$386$	−200.723	−	200.723i	−0.520009	−	0.520009i
$387$	−45.3250	+	45.3250i	−0.117119	+	0.117119i
$388$			287.128i			0.740021i
$389$	−326.044			−0.838159			−0.419080	−	0.907950i	$-0.637647\pi$
$389$	−326.044			−0.838159			−0.419080	+	0.907950i	$0.637647\pi$
$390$	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
$397$			222.136i			0.559536i	0.960068	+	0.279768i	$0.0902576\pi$
$397$			222.136i			0.559536i	−0.960068	+	0.279768i	$0.909742\pi$
$398$	528.243			1.32724
$399$	96.0516			0.240731
$400$	43.7342	−	89.9295i	0.109336	−	0.224824i
$401$	168.413	−	168.413i	0.419982	−	0.419982i	−0.465215	−	0.885197i	$-0.654023\pi$
$401$	168.413	−	168.413i	0.419982	−	0.419982i	0.885197	+	0.465215i	$0.154023\pi$
$402$		−	472.584i		−	1.17558i
$403$		−	61.0862i		−	0.151579i
$404$		−	72.7211i		−	0.180003i
$405$	−268.392	−	428.970i	−0.662695	−	1.05918i
$406$		−	84.3175i		−	0.207679i
$407$	26.0296	−	26.0296i	0.0639547	−	0.0639547i
$408$	−25.0847	+	173.434i	−0.0614820	+	0.425084i
$409$			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
$413$			61.2393i			0.148279i
$414$	12.2665	+	12.2665i	0.0296293	+	0.0296293i
$415$	229.636	+	52.8773i	0.553340	+	0.127415i
$416$			12.6087i			0.0303093i
$417$	83.9065	+	83.9065i	0.201215	+	0.201215i
$418$	38.5238			0.0921622
$419$	374.883	+	374.883i	0.894710	+	0.894710i	0.994962	−	0.100252i	$-0.0319650\pi$
$419$	374.883	+	374.883i	0.894710	+	0.894710i	−0.100252	+	0.994962i	$0.531965\pi$
$420$	−77.7844	+	48.6670i	−0.185201	+	0.115874i
$421$	−605.275			−1.43771			−0.718854	−	0.695161i	$-0.755333\pi$
$421$	−605.275			−1.43771			−0.718854	+	0.695161i	$0.755333\pi$
$422$	143.720			0.340569
$423$	258.493	−	258.493i	0.611095	−	0.611095i
$424$			190.826i			0.450061i
$425$	417.422	−	79.8969i	0.982170	−	0.187993i
$426$	73.0294			0.171430
$427$	−99.0775	−	99.0775i	−0.232032	−	0.232032i
$428$		−	204.235i		−	0.477185i
$429$		−	21.1382i		−	0.0492732i
$430$	56.1393	+	89.7274i	0.130557	+	0.208668i
$431$	481.785	−	481.785i	1.11783	−	1.11783i	0.125771	−	0.992059i	$-0.459859\pi$
$431$	481.785	−	481.785i	1.11783	−	1.11783i	0.992059	−	0.125771i	$-0.0401405\pi$
$432$		−	68.7743i		−	0.159200i
$433$	−245.936	+	245.936i	−0.567982	+	0.567982i	−0.931563	−	0.363581i	$-0.881554\pi$
$433$	−245.936	+	245.936i	−0.567982	+	0.567982i	0.363581	+	0.931563i	$0.381554\pi$
$434$	97.5784			0.224835
$435$	−96.8343	+	420.533i	−0.222608	+	0.966743i
$436$	270.483	−	270.483i	0.620374	−	0.620374i
$437$	−29.9862			−0.0686183
$438$	196.803	+	196.803i	0.449322	+	0.449322i
$439$	−100.177	+	100.177i	−0.228193	+	0.228193i	−0.811937	−	0.583745i	$-0.801587\pi$
$439$	−100.177	+	100.177i	−0.228193	+	0.228193i	0.583745	+	0.811937i	$0.301587\pi$
$440$	−31.1973	+	19.5191i	−0.0709029	+	0.0443615i
$441$	−182.690			−0.414263
$442$	−42.9254	+	32.0774i	−0.0971164	+	0.0725733i
$443$	−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
$445$	−153.193	+	95.8476i	−0.344254	+	0.215388i
$446$	36.3530			0.0815089
$447$	393.504			0.880323
$448$	−20.1410			−0.0449575
$449$	88.8706	+	88.8706i	0.197930	+	0.197930i	0.799112	−	0.601182i	$-0.205303\pi$
$449$	88.8706	+	88.8706i	0.197930	+	0.197930i	−0.601182	+	0.799112i	$0.705303\pi$
$450$	143.097	−	49.4556i	0.317994	−	0.109901i
$451$		−	132.108i		−	0.292921i
$452$		−	342.105i		−	0.756869i
$453$	275.045			0.607163
$454$	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	0.920356	−	0.391082i	$-0.127899\pi$
$457$	241.878	+	241.878i	0.529274	+	0.529274i	−0.391082	+	0.920356i	$0.627899\pi$
$458$	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	$0.177228\pi$
$461$			487.235i			1.05691i	−0.848961	+	0.528455i	$0.822772\pi$
$462$	33.7659			0.0730865
$463$	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
$465$	−486.672	−	112.064i	−1.04661	−	0.240997i
$466$	−92.4647	+	92.4647i	−0.198422	+	0.198422i
$467$	−147.754	−	147.754i	−0.316390	−	0.316390i	0.530989	−	0.847379i	$-0.321821\pi$
$467$	−147.754	−	147.754i	−0.316390	−	0.316390i	−0.847379	+	0.530989i	$0.821821\pi$
$468$	−13.4986	+	13.4986i	−0.0288431	+	0.0288431i
$469$	163.231	+	163.231i	0.348040	+	0.348040i
$470$	−320.169	−	511.725i	−0.681210	−	1.08878i
$471$	547.247	+	547.247i	1.16188	+	1.16188i
$472$	48.6486	−	48.6486i	0.103069	−	0.103069i
$473$		−	38.9504i		−	0.0823475i
$474$	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	$-0.728779\pi$
$479$	45.1285	−	45.1285i	0.0942140	−	0.0942140i	0.752643	+	0.658429i	$0.228779\pi$
$480$	100.453	+	23.1309i	0.209277	+	0.0481893i
$481$	−22.2959	−	22.2959i	−0.0463532	−	0.0463532i
$482$		−	55.9580i		−	0.116096i
$483$	−26.2828			−0.0544157
$484$	−228.457			−0.472019
$485$	380.735	+	608.528i	0.785020	+	1.25470i
$486$	214.090	−	214.090i	0.440514	−	0.440514i
$487$			810.637i			1.66455i	0.554361	+	0.832276i	$0.312963\pi$
$487$			810.637i			1.66455i	−0.554361	+	0.832276i	$0.687037\pi$
$488$			157.415i			0.322571i
$489$			665.693i			1.36134i
$490$	−67.6912	+	293.970i	−0.138145	+	0.599939i
$491$		−	313.136i		−	0.637752i	−0.947796	−	0.318876i	$-0.896695\pi$
$491$		−	313.136i		−	0.637752i	0.947796	−	0.318876i	$-0.103305\pi$
$492$	−261.663	+	261.663i	−0.531836	+	0.531836i
$493$	−398.442	−	57.6287i	−0.808199	−	0.116894i
$494$		−	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
$498$			242.907i			0.487766i
$499$	230.154	+	230.154i	0.461231	+	0.461231i	0.899059	−	0.437828i	$-0.144252\pi$
$499$	230.154	+	230.154i	0.461231	+	0.461231i	−0.437828	+	0.899059i	$0.644252\pi$
$500$	−26.5589	−	248.585i	−0.0531177	−	0.497171i
$501$		−	713.562i		−	1.42428i
$502$	−237.556	−	237.556i	−0.473219	−	0.473219i
$503$	−230.360			−0.457972			−0.228986	−	0.973430i	$-0.573541\pi$
$503$	−230.360			−0.457972			−0.228986	+	0.973430i	$0.573541\pi$
$504$	−21.5625	−	21.5625i	−0.0427826	−	0.0427826i
$505$	−96.4290	−	154.122i	−0.190949	−	0.305193i
$506$	−10.5413			−0.0208327
$507$	597.813			1.17912
$508$	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	$-0.0554030\pi$
$510$	176.812	+	400.833i	0.346691	+	0.785946i
$511$	−135.952			−0.266051
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$			179.988i			0.350854i
$514$		−	186.245i		−	0.362345i
$515$	−88.5123	+	384.392i	−0.171869	+	0.746393i
$516$	−77.1484	+	77.1484i	−0.149512	+	0.149512i
$517$			222.138i			0.429668i
$518$	35.6152	−	35.6152i	0.0687553	−	0.0687553i
$519$	−279.348			−0.538242
$520$	16.7192	+	26.7223i	0.0321524	+	0.0513891i
$521$	454.583	−	454.583i	0.872519	−	0.872519i	−0.120227	−	0.992746i	$-0.538362\pi$
$521$	454.583	−	454.583i	0.872519	−	0.872519i	0.992746	+	0.120227i	$0.0383623\pi$
$522$	−143.418			−0.274748
$523$	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
$527$	66.6921	−	461.107i	0.126551	−	0.874965i
$528$	−26.8237	−	26.8237i	−0.0508024	−	0.0508024i
$529$	−520.795			−0.984489
$530$	253.037	+	404.429i	0.477429	+	0.763074i
$531$	104.164			0.196166
$532$	52.7106			0.0990800
$533$	−113.158			−0.212304
$534$	−131.717	−	131.717i	−0.246660	−	0.246660i
$535$	−270.818	−	432.848i	−0.506202	−	0.809062i
$536$		−	259.341i		−	0.483846i
$537$		−	76.1351i		−	0.141779i
$538$	−388.931			−0.722921
$539$	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	0.586635	−	0.809851i	$-0.300452\pi$
$541$	−120.760	−	120.760i	−0.223216	−	0.223216i	−0.809851	+	0.586635i	$0.800452\pi$
$542$	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
$547$	−392.045			−0.716718			−0.358359	−	0.933584i	$-0.616664\pi$
$547$	−392.045			−0.716718			−0.358359	+	0.933584i	$0.616664\pi$
$548$	−253.580	−	253.580i	−0.462737	−	0.462737i
$549$	−168.524	+	168.524i	−0.306966	+	0.306966i
$550$	−40.2359	+	82.7359i	−0.0731561	+	0.150429i
$551$	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
$555$	−218.533	+	136.729i	−0.393753	+	0.246358i
$556$	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	$0.287047\pi$
$558$		−	165.974i		−	0.297445i
$559$	−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	$-0.429893\pi$
$563$	672.399	−	672.399i	1.19431	−	1.19431i	0.975844	−	0.218470i	$-0.0701066\pi$
$564$	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
$567$			254.790i			0.449365i
$568$	40.0766			0.0705574
$569$	−1000.49			−1.75833			−0.879164	−	0.476520i	$-0.841898\pi$
$569$	−1000.49			−1.75833			−0.879164	+	0.476520i	$0.841898\pi$
$570$	−262.894	−	60.5354i	−0.461217	−	0.106202i
$571$	−522.562	+	522.562i	−0.915170	+	0.915170i	−0.996673	−	0.0815027i	$-0.974028\pi$
$571$	−522.562	+	522.562i	−0.915170	+	0.915170i	0.0815027	+	0.996673i	$0.474028\pi$
$572$		−	11.6001i		−	0.0202799i
$573$			1252.02i			2.18503i
$574$		−	180.758i		−	0.314909i
$575$	31.3188	−	64.4001i	0.0544675	−	0.112000i
$576$			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	$0.139602\pi$
$578$	−359.042	+	195.270i	−0.621181	+	0.337838i
$579$		−	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
$583$		−	175.561i		−	0.301134i
$584$	108.000	+	108.000i	0.184932	+	0.184932i
$585$	−10.7091	+	46.5075i	−0.0183061	+	0.0795001i
$586$			129.516i			0.221018i
$587$	−511.397	−	511.397i	−0.871205	−	0.871205i	0.121399	−	0.992604i	$-0.461262\pi$
$587$	−511.397	−	511.397i	−0.871205	−	0.871205i	−0.992604	+	0.121399i	$0.961262\pi$
$588$	−310.959			−0.528843
$589$	202.867	+	202.867i	0.344426	+	0.344426i
$590$	38.5954	−	167.612i	0.0654159	−	0.284089i
$591$	1340.97			2.26899
$592$	−56.5855			−0.0955836
$593$	−485.752	+	485.752i	−0.819143	+	0.819143i	−0.985984	−	0.166841i	$-0.946643\pi$
$593$	−485.752	+	485.752i	−0.819143	+	0.819143i	0.166841	+	0.985984i	$0.446643\pi$
$594$			63.2730i			0.106520i
$595$	−199.519	−	77.3768i	−0.335326	−	0.130045i
$596$	215.945			0.362323
$597$	962.588	+	962.588i	1.61238	+	1.61238i
$598$			9.02929i			0.0150991i
$599$		−	240.970i		−	0.402287i	−0.979562	−	0.201144i	$-0.935534\pi$
$599$		−	240.970i		−	0.402287i	0.979562	−	0.201144i	$-0.0644658\pi$
$600$	243.568	−	84.1791i	0.405947	−	0.140299i
$601$	273.824	−	273.824i	0.455614	−	0.455614i	−0.441599	−	0.897213i	$-0.645589\pi$
$601$	273.824	−	273.824i	0.455614	−	0.455614i	0.897213	+	0.441599i	$0.145589\pi$
$602$		−	53.2943i		−	0.0885287i
$603$	277.645	−	277.645i	0.460439	−	0.460439i
$604$	150.937			0.249896
$605$	−484.184	+	302.937i	−0.800304	+	0.500722i
$606$	132.516	−	132.516i	0.218673	−	0.218673i
$607$	774.909			1.27662			0.638311	−	0.769779i	$-0.279634\pi$
$607$	774.909			1.27662			0.638311	+	0.769779i	$0.279634\pi$
$608$	−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
$612$	−116.631	+	87.1560i	−0.190573	+	0.142412i
$613$	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
$615$	−207.591	+	901.527i	−0.337546	+	1.46590i
$616$	18.5299			0.0300809
$617$	−422.398			−0.684599			−0.342300	−	0.939591i	$-0.611206\pi$
$617$	−422.398			−0.684599			−0.342300	+	0.939591i	$0.611206\pi$
$618$	−406.607			−0.657941
$619$	−532.726	−	532.726i	−0.860624	−	0.860624i	0.130786	−	0.991411i	$-0.458250\pi$
$619$	−532.726	−	532.726i	−0.860624	−	0.860624i	−0.991411	+	0.130786i	$0.958250\pi$
$620$	−267.073	−	61.4977i	−0.430762	−	0.0991898i
$621$		−	49.2505i		−	0.0793084i
$622$			646.371i			1.03918i
$623$	90.9902			0.146052
$624$	−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	$0.231455\pi$
$631$			838.893i			1.32947i	−0.747081	+	0.664733i	$0.768545\pi$
$632$	190.825			0.301938
$633$	261.893	+	261.893i	0.413733	+	0.413733i
$634$	−259.019	+	259.019i	−0.408548	+	0.408548i
$635$	56.7994	−	246.669i	0.0894478	−	0.388455i
$636$	−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
$640$	55.1260	+	12.6936i	0.0861343	+	0.0198338i
$641$	498.102	+	498.102i	0.777070	+	0.777070i	0.979332	−	0.202261i	$-0.0648290\pi$
$641$	498.102	+	498.102i	0.777070	+	0.777070i	−0.202261	+	0.979332i	$0.564829\pi$
$642$	372.166	−	372.166i	0.579699	−	0.579699i
$643$			368.397i			0.572935i	0.958090	+	0.286467i	$0.0924810\pi$
$643$			368.397i			0.572935i	−0.958090	+	0.286467i	$0.907519\pi$
$644$	−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
$652$			365.315i			0.560299i
$653$	1012.81			1.55101			0.775507	−	0.631339i	$-0.217494\pi$
$653$	1012.81			1.55101			0.775507	+	0.631339i	$0.217494\pi$
$654$	985.773			1.50730
$655$	67.0872	−	291.347i	0.102423	−	0.444804i
$656$	−143.594	+	143.594i	−0.218893	+	0.218893i
$657$			231.245i			0.351971i
$658$			303.943i			0.461919i
$659$			747.453i			1.13422i	0.823641	+	0.567112i	$0.191939\pi$
$659$			747.453i			1.13422i	−0.823641	+	0.567112i	$0.808061\pi$
$660$	−92.4176	−	21.2806i	−0.140027	−	0.0322433i
$661$		−	151.853i		−	0.229732i	−0.993381	−	0.114866i	$-0.963356\pi$
$661$		−	151.853i		−	0.229732i	0.993381	−	0.114866i	$-0.0366438\pi$
$662$	−621.830	+	621.830i	−0.939320	+	0.939320i
$663$	−136.674	−	19.7678i	−0.206144	−	0.0298156i
$664$			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
$668$		−	391.584i		−	0.586204i
$669$	66.2440	+	66.2440i	0.0990195	+	0.0990195i
$670$	−343.890	−	549.638i	−0.513268	−	0.820356i
$671$		−	144.823i		−	0.215831i
$672$	−36.7018	−	36.7018i	−0.0546157	−	0.0546157i
$673$	698.260			1.03753			0.518767	−	0.854916i	$-0.326391\pi$
$673$	698.260			1.03753			0.518767	+	0.854916i	$0.326391\pi$
$674$	−159.768	−	159.768i	−0.237045	−	0.237045i
$675$	−386.553	−	187.987i	−0.572671	−	0.278499i
$676$	328.064			0.485302
$677$	890.337			1.31512			0.657560	−	0.753402i	$-0.271588\pi$
$677$	890.337			1.31512			0.657560	+	0.753402i	$0.271588\pi$
$678$	623.399	−	623.399i	0.919467	−	0.919467i
$679$		−	361.440i		−	0.532312i
$680$	97.0299	+	219.966i	0.142691	+	0.323480i
$681$	872.300			1.28091
$682$	71.3157	+	71.3157i	0.104568	+	0.104568i
$683$		−	534.965i		−	0.783258i	−0.920123	−	0.391629i	$-0.871912\pi$
$683$		−	534.965i		−	0.783258i	0.920123	−	0.391629i	$-0.128088\pi$
$684$		−	89.6572i		−	0.131078i
$685$	−873.677	−	201.178i	−1.27544	−	0.293690i
$686$	230.769	−	230.769i	0.336398	−	0.336398i
$687$			611.673i			0.890354i
$688$	−42.3370	+	42.3370i	−0.0615363	+	0.0615363i
$689$	−150.379			−0.218257
$690$	71.9361	+	16.5644i	0.104255	+	0.0240064i
$691$	−582.534	+	582.534i	−0.843030	+	0.843030i	−0.989252	−	0.146222i	$-0.953289\pi$
$691$	−582.534	+	582.534i	−0.843030	+	0.843030i	0.146222	+	0.989252i	$0.453289\pi$
$692$	−153.299			−0.221530
$693$	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
$697$	−854.170	−	123.543i	−1.22549	−	0.177249i
$698$	95.7372	+	95.7372i	0.137159	+	0.137159i
$699$	−336.987			−0.482098
$700$	−55.0531	+	113.204i	−0.0786473	+	0.161720i
$701$	−975.816			−1.39203			−0.696017	−	0.718025i	$-0.745046\pi$
$701$	−975.816			−1.39203			−0.696017	+	0.718025i	$0.745046\pi$
$702$	54.1971			0.0772038
$703$	148.089			0.210653
$704$	−14.7201	−	14.7201i	−0.0209093	−	0.0209093i
$705$	349.063	−	1515.91i	0.495125	−	2.15023i
$706$		−	758.085i		−	1.07378i
$707$			91.5422i			0.129480i
$708$	177.299			0.250423
$709$	701.131	−	701.131i	0.988901	−	0.988901i	−0.0110383	−	0.999939i	$-0.503514\pi$
$709$	701.131	−	701.131i	0.988901	−	0.988901i	0.999939	+	0.0110383i	$0.00351368\pi$
$710$	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
$717$	−6.32671			−0.00882387
$718$	−527.313	−	527.313i	−0.734419	−	0.734419i
$719$	−765.138	+	765.138i	−1.06417	+	1.06417i	−0.0663752	+	0.997795i	$0.521143\pi$
$719$	−765.138	+	765.138i	−1.06417	+	1.06417i	−0.997795	+	0.0663752i	$0.978857\pi$
$720$	45.4271	+	72.6061i	0.0630932	+	0.100842i
$721$	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
$725$	193.390	+	559.565i	0.266745	+	0.771814i
$726$	−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	$0.113651\pi$
$728$		−	15.8719i		−	0.0218021i
$729$	−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	$-0.451715\pi$
$733$	835.348	−	835.348i	1.13963	−	1.13963i	0.988517	−	0.151112i	$-0.0482853\pi$
$734$	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
$737$			238.596i			0.323740i
$738$	−307.457			−0.416608
$739$	−334.577			−0.452743			−0.226372	−	0.974041i	$-0.572686\pi$
$739$	−334.577			−0.452743			−0.226372	+	0.974041i	$0.572686\pi$
$740$	−119.925	+	75.0330i	−0.162061	+	0.101396i
$741$	60.1303	−	60.1303i	0.0811475	−	0.0811475i
$742$		−	240.214i		−	0.323738i
$743$		−	1352.66i		−	1.82054i	−0.414015	−	0.910270i	$-0.635874\pi$
$743$		−	1352.66i		−	1.82054i	0.414015	−	0.910270i	$-0.364126\pi$
$744$		−	282.508i		−	0.379714i
$745$	457.665	−	286.345i	0.614315	−	0.384356i
$746$			806.338i			1.08088i
$747$	−142.709	+	142.709i	−0.191043	+	0.191043i
$748$	12.6646	−	87.5629i	0.0169313	−	0.117063i
$749$			257.093i			0.343249i
$750$	404.586	−	501.380i	0.539449	−	0.668507i
$751$	−481.112	−	481.112i	−0.640629	−	0.640629i	0.310081	−	0.950710i	$-0.399644\pi$
$751$	−481.112	−	481.112i	−0.640629	−	0.640629i	−0.950710	+	0.310081i	$0.899644\pi$
$752$	241.452	−	241.452i	0.321080	−	0.321080i
$753$		−	865.771i		−	1.14976i
$754$	−52.7845	−	52.7845i	−0.0700060	−	0.0700060i
$755$	319.891	−	200.145i	0.423697	−	0.265092i
$756$			86.5739i			0.114516i
$757$	−295.942	−	295.942i	−0.390940	−	0.390940i	0.484082	−	0.875022i	$-0.339154\pi$
$757$	−295.942	−	295.942i	−0.390940	−	0.390940i	−0.875022	+	0.484082i	$0.839154\pi$
$758$	58.0454			0.0765771
$759$	−19.2089	−	19.2089i	−0.0253082	−	0.0253082i
$760$	−144.269	−	33.2202i	−0.189828	−	0.0437108i
$761$	−384.390			−0.505111			−0.252556	−	0.967582i	$-0.581271\pi$
$761$	−384.390			−0.505111			−0.252556	+	0.967582i	$0.581271\pi$
$762$	260.925			0.342421
$763$	−340.487	+	340.487i	−0.446248	+	0.446248i
$764$			687.076i			0.899315i
$765$	−131.613	+	339.369i	−0.172043	+	0.443619i
$766$	786.259			1.02645
$767$	38.3371	+	38.3371i	0.0499832	+	0.0499832i
$768$			58.3118i			0.0759269i
$769$			396.785i			0.515975i	0.966148	+	0.257987i	$0.0830593\pi$
$769$			396.785i			0.515975i	−0.966148	+	0.257987i	$0.916941\pi$
$770$	39.2715	−	24.5708i	0.0510019	−	0.0319101i
$771$	339.384	−	339.384i	0.440187	−	0.440187i
$772$		−	401.447i		−	0.520009i
$773$	456.510	−	456.510i	0.590570	−	0.590570i	−0.347216	−	0.937785i	$-0.612873\pi$
$773$	456.510	−	456.510i	0.590570	−	0.590570i	0.937785	+	0.347216i	$0.112873\pi$
$774$	−90.6500			−0.117119
$775$	−647.570	+	223.806i	−0.835575	+	0.288781i
$776$	−287.128	+	287.128i	−0.370010	+	0.370010i
$777$	129.799			0.167052
$778$	−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
$782$	−9.85792	+	68.1573i	−0.0126060	+	0.0871577i
$783$	287.915	+	287.915i	0.367707	+	0.367707i
$784$	−170.646			−0.217661
$785$	1034.70	+	238.255i	1.31808	+	0.303509i
$786$	308.185			0.392092
$787$	977.913			1.24258			0.621292	−	0.783579i	$-0.286608\pi$
$787$	977.913			1.24258			0.621292	+	0.783579i	$0.286608\pi$
$788$	735.890			0.933871
$789$	−1168.58	−	1168.58i	−1.48109	−	1.48109i
$790$	404.427	−	253.036i	0.511933	−	0.320299i
$791$			430.645i			0.544431i
$792$		−	31.5181i		−	0.0397955i
$793$	−124.049			−0.156430
$794$	−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	0.929644	−	0.368458i	$-0.120114\pi$
$797$	447.266	+	447.266i	0.561187	+	0.561187i	−0.368458	+	0.929644i	$0.620114\pi$
$798$	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
$802$	336.826			0.419982
$803$	−99.3611	−	99.3611i	−0.123737	−	0.123737i
$804$	472.584	−	472.584i	0.587790	−	0.587790i
$805$	−30.5682	+	19.1255i	−0.0379729	+	0.0237583i
$806$	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	$-0.0616400\pi$
$809$	638.195	+	638.195i	0.788869	+	0.788869i	−0.192440	+	0.981309i	$0.561640\pi$
$810$	160.578	−	697.361i	0.198245	−	0.860940i
$811$	−234.284	−	234.284i	−0.288882	−	0.288882i	0.547756	−	0.836638i	$-0.315482\pi$
$811$	−234.284	−	234.284i	−0.288882	−	0.288882i	−0.836638	+	0.547756i	$0.815482\pi$
$812$	84.3175	−	84.3175i	0.103839	−	0.103839i
$813$			512.735i			0.630670i
$814$	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	0.887974	−	0.459894i	$-0.152113\pi$
$821$	351.453	+	351.453i	0.428079	+	0.428079i	−0.459894	+	0.887974i	$0.652113\pi$
$822$		−	924.169i		−	1.12429i
$823$	−354.346			−0.430554			−0.215277	−	0.976553i	$-0.569065\pi$
$823$	−354.346			−0.430554			−0.215277	+	0.976553i	$0.569065\pi$
$824$	−223.135			−0.270795
$825$	−224.085	+	77.4455i	−0.271618	+	0.0938733i
$826$	−61.2393	+	61.2393i	−0.0741396	+	0.0741396i
$827$			382.794i			0.462871i	0.972850	+	0.231436i	$0.0743422\pi$
$827$			382.794i			0.462871i	−0.972850	+	0.231436i	$0.925658\pi$
$828$			24.5331i			0.0296293i
$829$			84.7448i			0.102225i	0.998693	+	0.0511126i	$0.0162768\pi$
$829$			84.7448i			0.102225i	−0.998693	+	0.0511126i	$0.983723\pi$
$830$	176.759	+	282.513i	0.212962	+	0.340378i
$831$			696.726i			0.838418i
$832$	−12.6087	+	12.6087i	−0.0151547	+	0.0151547i
$833$	−434.137	−	580.955i	−0.521173	−	0.697424i
$834$			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
$838$			749.767i			0.894710i
$839$	277.619	+	277.619i	0.330892	+	0.330892i	0.852925	−	0.522033i	$-0.174826\pi$
$839$	277.619	+	277.619i	0.330892	+	0.330892i	−0.522033	+	0.852925i	$0.674826\pi$
$840$	−126.451	−	29.1174i	−0.150537	−	0.0346636i
$841$			280.179i			0.333150i
$842$	−605.275	−	605.275i	−0.718854	−	0.718854i
$843$	−1973.56			−2.34111
$844$	143.720	+	143.720i	0.170284	+	0.170284i
$845$	695.286	−	435.016i	0.822824	−	0.514812i
$846$	516.987			0.611095
$847$	287.585			0.339533
$848$	−190.826	+	190.826i	−0.225031	+	0.225031i
$849$		−	1797.88i		−	2.11764i
$850$	497.319	+	337.525i	0.585082	+	0.397089i
$851$	−40.5219			−0.0476168
$852$	73.0294	+	73.0294i	0.0857152	+	0.0857152i
$853$			628.367i			0.736655i	0.929696	+	0.368328i	$0.120070\pi$
$853$			628.367i			0.736655i	−0.929696	+	0.368328i	$0.879930\pi$
$854$		−	198.155i		−	0.232032i
$855$	−118.886	−	190.016i	−0.139048	−	0.222241i
$856$	204.235	−	204.235i	0.238592	−	0.238592i
$857$			1006.94i			1.17496i	0.809240	+	0.587478i	$0.199879\pi$
$857$			1006.94i			1.17496i	−0.809240	+	0.587478i	$0.800121\pi$
$858$	21.1382	−	21.1382i	0.0246366	−	0.0246366i
$859$	421.287			0.490439			0.245219	−	0.969468i	$-0.421140\pi$
$859$	421.287			0.490439			0.245219	+	0.969468i	$0.421140\pi$
$860$	−33.5881	+	145.867i	−0.0390559	+	0.169612i
$861$	329.384	−	329.384i	0.382560	−	0.382560i
$862$	963.570			1.11783
$863$	−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
$867$	−1010.09	−	298.433i	−1.16504	−	0.344213i
$868$	97.5784	+	97.5784i	0.112418	+	0.112418i
$869$	−175.560			−0.202026
$870$	−517.367	+	323.699i	−0.594675	+	0.372068i
$871$	204.372			0.234641
$872$	540.966			0.620374
$873$	−614.785			−0.704221
$874$	−29.9862	−	29.9862i	−0.0343092	−	0.0343092i
$875$	33.4326	+	312.922i	0.0382087	+	0.357625i
$876$			393.606i			0.449322i
$877$		−	1500.39i		−	1.71082i	−0.517950	−	0.855411i	$-0.673305\pi$
$877$		−	1500.39i		−	1.71082i	0.517950	−	0.855411i	$-0.326695\pi$
$878$	−200.353			−0.228193
$879$	−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	0.961990	−	0.273085i	$-0.0880440\pi$
$881$	606.925	+	606.925i	0.688905	+	0.688905i	−0.273085	+	0.961990i	$0.588044\pi$
$882$	−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
$887$	−904.123			−1.01930			−0.509652	−	0.860381i	$-0.670226\pi$
$887$	−904.123			−1.01930			−0.509652	+	0.860381i	$0.670226\pi$
$888$	−103.113	−	103.113i	−0.116118	−	0.116118i
$889$	−90.1236	+	90.1236i	−0.101376	+	0.101376i
$890$	−249.041	−	57.3455i	−0.279821	−	0.0644332i
$891$	−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
$895$	−55.4020	−	88.5489i	−0.0619016	−	0.0989373i
$896$	−20.1410	−	20.1410i	−0.0224788	−	0.0224788i
$897$	−16.4536	+	16.4536i	−0.0183429	+	0.0183429i
$898$			177.741i			0.197930i
$899$	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
$907$		−	813.684i		−	0.897116i	−0.893754	−	0.448558i	$-0.851938\pi$
$907$		−	813.684i		−	0.897116i	0.893754	−	0.448558i	$-0.148062\pi$
$908$	478.695			0.527197
$909$	155.707			0.171295
$910$	−21.0464	−	33.6384i	−0.0231279	−	0.0369652i
$911$	−948.907	+	948.907i	−1.04161	+	1.04161i	−0.0425140	+	0.999096i	$0.513537\pi$
$911$	−948.907	+	948.907i	−1.04161	+	1.04161i	−0.999096	+	0.0425140i	$0.986463\pi$
$912$		−	152.607i		−	0.167332i
$913$		−	122.638i		−	0.134324i
$914$			483.756i			0.529274i
$915$	−227.571	+	988.298i	−0.248711	+	1.08011i
$916$			335.670i			0.366452i
$917$	−106.447	+	106.447i	−0.116082	+	0.116082i
$918$	409.105	+	59.1709i	0.445648	+	0.0644563i
$919$			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
$923$			31.5820i			0.0342167i
$924$	33.7659	+	33.7659i	0.0365432	+	0.0365432i
$925$	−154.670	+	318.044i	−0.167211	+	0.343832i
$926$			788.812i			0.851849i
$927$	−238.884	−	238.884i	−0.257695	−	0.257695i
$928$	−133.964			−0.144357
$929$	−133.019	−	133.019i	−0.143185	−	0.143185i	0.631881	−	0.775066i	$-0.282283\pi$
$929$	−133.019	−	133.019i	−0.143185	−	0.143185i	−0.775066	+	0.631881i	$0.782283\pi$
$930$	−374.608	−	598.736i	−0.402804	−	0.643802i
$931$	446.595			0.479694
$932$	−184.929			−0.198422
$933$	−1177.85	+	1177.85i	−1.26243	+	1.26243i
$934$		−	295.508i		−	0.316390i
$935$	−89.2684	−	202.371i	−0.0954742	−	0.216439i
$936$	−26.9971			−0.0288431
$937$	−560.333	−	560.333i	−0.598008	−	0.598008i	0.341774	−	0.939782i	$-0.388972\pi$
$937$	−560.333	−	560.333i	−0.598008	−	0.598008i	−0.939782	+	0.341774i	$0.888972\pi$
$938$			326.462i			0.348040i
$939$			1168.08i			1.24396i
$940$	191.556	−	831.894i	0.203783	−	0.884993i
$941$	424.440	−	424.440i	0.451052	−	0.451052i	−0.444652	−	0.895704i	$-0.646672\pi$
$941$	424.440	−	424.440i	0.451052	−	0.451052i	0.895704	+	0.444652i	$0.146672\pi$
$942$			1094.49i			1.16188i
$943$	−102.830	+	102.830i	−0.109046	+	0.109046i
$944$	97.2971			0.103069
$945$	114.798	+	183.481i	0.121479	+	0.194160i
$946$	38.9504	−	38.9504i	0.0411738	−	0.0411738i
$947$	−1480.38			−1.56324			−0.781618	−	0.623757i	$-0.785605\pi$
$947$	−1480.38			−1.56324			−0.781618	+	0.623757i	$0.785605\pi$
$948$	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
$952$	17.3285	−	119.809i	0.0182022	−	0.125850i
$953$	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
$955$	911.071	+	1456.16i	0.954001	+	1.52478i
$956$	−3.47193			−0.00363173
$957$	224.588			0.234679
$958$	90.2570			0.0942140
$959$	319.209	+	319.209i	0.332856	+	0.332856i
$960$	77.3221	+	123.584i	0.0805439	+	0.128733i
$961$		−	209.902i		−	0.218420i
$962$		−	44.5918i		−	0.0463532i
$963$	437.299			0.454100
$964$	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	0.709406	−	0.704800i	$-0.248963\pi$
$967$	4.45430	+	4.45430i	0.00460631	+	0.00460631i	−0.704800	+	0.709406i	$0.748963\pi$
$968$	−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	$-0.891563\pi$
$971$		−	648.849i		−	0.668227i	0.942533	−	0.334114i	$-0.108437\pi$
$972$	428.179			0.440514
$973$	−57.9628	−	57.9628i	−0.0595712	−	0.0595712i
$974$	−810.637	+	810.637i	−0.832276	+	0.832276i
$975$	66.3367	+	191.942i	0.0680376	+	0.196864i
$976$	−157.415	+	157.415i	−0.161285	+	0.161285i
$977$	8.60532	+	8.60532i	0.00880790	+	0.00880790i	0.711497	−	0.702689i	$-0.248018\pi$
$977$	8.60532	+	8.60532i	0.00880790	+	0.00880790i	−0.702689	+	0.711497i	$0.748018\pi$
$978$	−665.693	+	665.693i	−0.680668	+	0.680668i
$979$	66.5006	+	66.5006i	0.0679271	+	0.0679271i
$980$	−361.661	+	226.279i	−0.369042	+	0.230897i
$981$	579.146	+	579.146i	0.590363	+	0.590363i
$982$	313.136	−	313.136i	0.318876	−	0.318876i
$983$			715.161i			0.727529i	0.931491	+	0.363765i	$0.118509\pi$
$983$			715.161i			0.727529i	−0.931491	+	0.363765i	$0.881491\pi$
$984$	−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	0.988720	−	0.149779i	$-0.0478561\pi$
$991$	831.390	+	831.390i	0.838941	+	0.838941i	−0.149779	+	0.988720i	$0.547856\pi$
$992$		−	155.033i		−	0.156283i
$993$	−2266.25			−2.28223
$994$	−50.4488			−0.0507534
$995$	1819.99	+	419.082i	1.82914	+	0.421188i
$996$	−242.907	+	242.907i	−0.243883	+	0.243883i
$997$		−	1365.27i		−	1.36937i	−0.728837	−	0.684687i	$-0.759939\pi$
$997$		−	1365.27i		−	1.36937i	0.728837	−	0.684687i	$-0.240061\pi$
$998$			460.309i			0.461231i
$999$			243.227i			0.243470i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.3.e.b.13.7	✓	16	1.1	even	1	trivial
170.3.e.b.157.2	yes	16	85.72	odd	4	inner
170.3.j.b.47.7	yes	16	5.2	odd	4
170.3.j.b.123.7	yes	16	17.4	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	170.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +3.64449i q^{3} +2.00000i q^{4} +(2.65202 + 4.23872i) q^{5} +(-3.64449 + 3.64449i) q^{6} -2.51762i q^{7} +(-2.00000 + 2.00000i) q^{8} -4.28231 q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +3.64449i q^{3} +2.00000i q^{4} +(2.65202 + 4.23872i) q^{5} +(-3.64449 + 3.64449i) q^{6} -2.51762i q^{7} +(-2.00000 + 2.00000i) q^{8} -4.28231 q^{9} +(-1.58670 + 6.89075i) q^{10} +(1.84002 - 1.84002i) q^{11} -7.28898 q^{12} +(-1.57608 - 1.57608i) q^{13} +(2.51762 - 2.51762i) q^{14} +(-15.4480 + 9.66527i) q^{15} -4.00000 q^{16} +(-10.1763 - 13.6177i) q^{17} +(-4.28231 - 4.28231i) q^{18} +10.4683 q^{19} +(-8.47745 + 5.30404i) q^{20} +9.17545 q^{21} +3.68003 q^{22} -2.86447 q^{23} +(-7.28898 - 7.28898i) q^{24} +(-10.9336 + 22.4824i) q^{25} -3.15217i q^{26} +17.1936i q^{27} +5.03524 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} +14.1464 q^{37} +(10.4683 + 10.4683i) q^{38} +(5.74402 - 5.74402i) q^{39} +(-13.7815 - 3.17340i) 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} +(-11.3568 - 18.1515i) q^{45} +(-2.86447 - 2.86447i) q^{46} +(-60.3631 + 60.3631i) q^{47} -14.5780i 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} +38.1517i q^{57} +33.4909 q^{58} -24.3243 q^{59} +(-19.3305 - 30.8960i) q^{60} +(39.3536 - 39.3536i) q^{61} +38.7582i q^{62} +10.7812i q^{63} -8.00000i q^{64} +(2.50078 - 10.8604i) q^{65} +13.4118i q^{66} +(-64.8353 + 64.8353i) q^{67} +(27.2355 - 20.3526i) q^{68} -10.4395i q^{69} +(17.3483 + 3.99471i) q^{70} +(-10.0191 - 10.0191i) q^{71} +(8.56461 - 8.56461i) q^{72} -54.0001i q^{73} +(14.1464 + 14.1464i) q^{74} +(-81.9368 - 39.8472i) q^{75} +20.9367i q^{76} +(-4.63247 - 4.63247i) q^{77} +11.4880 q^{78} +(-47.7062 - 47.7062i) q^{79} +(-10.6081 - 16.9549i) q^{80} -101.203 q^{81} +71.7969 q^{82} +(33.3253 - 33.3253i) q^{83} +18.3509i q^{84} +(30.7341 - 79.2491i) q^{85} +21.1685 q^{86} +(61.0287 + 61.0287i) q^{87} +7.36007i q^{88} +36.1413i q^{89} +(6.79474 - 29.5083i) q^{90} +(-3.96798 + 3.96798i) q^{91} -5.72894i q^{92} +(-70.6269 + 70.6269i) q^{93} -120.726 q^{94} +(27.7622 + 44.3724i) q^{95} +(14.5780 - 14.5780i) q^{96} +143.564 q^{97} +(42.6616 + 42.6616i) q^{98} +(-7.87951 + 7.87951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9	\( 16 q + 16 q^{2} - 2 q^{5} - 32 q^{8} - 16 q^{9} - 4 q^{10} + 20 q^{11} + 4 q^{13} - 12 q^{14} + 12 q^{15} - 64 q^{16} + 36 q^{17} - 16 q^{18} - 16 q^{19} - 4 q^{20} + 40 q^{22} + 16 q^{23} + 44 q^{25} - 24 q^{28} - 20 q^{29} + 12 q^{30} + 92 q^{31} - 64 q^{32} - 60 q^{33} + 24 q^{34} - 124 q^{35} + 32 q^{37} - 16 q^{38} - 140 q^{39} - 60 q^{41} + 52 q^{43} + 40 q^{44} + 198 q^{45} + 16 q^{46} + 112 q^{47} + 136 q^{49} - 4 q^{50} - 140 q^{51} - 8 q^{52} + 48 q^{53} + 108 q^{54} + 40 q^{55} - 24 q^{56} - 40 q^{58} + 76 q^{61} - 40 q^{65} + 116 q^{67} - 24 q^{68} - 124 q^{70} - 268 q^{71} + 32 q^{72} + 32 q^{74} + 136 q^{75} - 116 q^{77} - 280 q^{78} - 88 q^{79} + 8 q^{80} - 352 q^{81} - 120 q^{82} - 160 q^{83} + 310 q^{85} + 104 q^{86} + 236 q^{87} + 260 q^{90} - 168 q^{91} + 48 q^{93} + 224 q^{94} + 264 q^{95} - 256 q^{97} + 136 q^{98} - 348 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 2 * q^5 - 32 * q^8 - 16 * q^9 - 4 * q^10 + 20 * q^11 + 4 * q^13 - 12 * q^14 + 12 * q^15 - 64 * q^16 + 36 * q^17 - 16 * q^18 - 16 * q^19 - 4 * q^20 + 40 * q^22 + 16 * q^23 + 44 * q^25 - 24 * q^28 - 20 * q^29 + 12 * q^30 + 92 * q^31 - 64 * q^32 - 60 * q^33 + 24 * q^34 - 124 * q^35 + 32 * q^37 - 16 * q^38 - 140 * q^39 - 60 * q^41 + 52 * q^43 + 40 * q^44 + 198 * 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 - 40 * q^58 + 76 * q^61 - 40 * q^65 + 116 * q^67 - 24 * q^68 - 124 * q^70 - 268 * q^71 + 32 * q^72 + 32 * q^74 + 136 * q^75 - 116 * q^77 - 280 * q^78 - 88 * q^79 + 8 * q^80 - 352 * q^81 - 120 * q^82 - 160 * q^83 + 310 * q^85 + 104 * q^86 + 236 * q^87 + 260 * q^90 - 168 * q^91 + 48 * q^93 + 224 * q^94 + 264 * q^95 - 256 * q^97 + 136 * q^98 - 348 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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