LMFDB - Embedded newform 144.3.w.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(5,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("144.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.w (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	144.5
Dual form			144.3.w.a.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99959 + 0.0402970i) q^{2} +(0.538615 + 2.95125i) q^{3} +(3.99675 - 0.161155i) q^{4} +(-2.08673 - 7.78777i) q^{5} +(-1.19594 - 5.87960i) q^{6} +(-2.60739 + 1.50538i) q^{7} +(-7.98539 + 0.483303i) q^{8} +(-8.41979 + 3.17918i) q^{9} +O(q^{10})$	\(q+(-1.99959 + 0.0402970i) q^{2} +(0.538615 + 2.95125i) q^{3} +(3.99675 - 0.161155i) q^{4} +(-2.08673 - 7.78777i) q^{5} +(-1.19594 - 5.87960i) q^{6} +(-2.60739 + 1.50538i) q^{7} +(-7.98539 + 0.483303i) q^{8} +(-8.41979 + 3.17918i) q^{9} +(4.48643 + 15.4883i) q^{10} +(-5.77989 - 1.54872i) q^{11} +(2.62832 + 11.7086i) q^{12} +(-3.94343 - 14.7171i) q^{13} +(5.15305 - 3.11521i) q^{14} +(21.8597 - 10.3531i) q^{15} +(15.9481 - 1.28820i) q^{16} -23.3509i q^{17} +(16.7080 - 6.69636i) q^{18} +(-8.30523 + 8.30523i) q^{19} +(-9.59517 - 30.7895i) q^{20} +(-5.84712 - 6.88424i) q^{21} +(11.6198 + 2.86389i) q^{22} +(2.08290 - 3.60768i) q^{23} +(-5.72740 - 23.3066i) q^{24} +(-34.6443 + 20.0019i) q^{25} +(8.47832 + 29.2693i) q^{26} +(-13.9176 - 23.1366i) q^{27} +(-10.1785 + 6.43681i) q^{28} +(6.59225 - 24.6026i) q^{29} +(-43.2934 + 21.5828i) q^{30} +(11.4094 - 19.7616i) q^{31} +(-31.8377 + 3.21853i) q^{32} +(1.45752 - 17.8921i) q^{33} +(0.940971 + 46.6922i) q^{34} +(17.1644 + 17.1644i) q^{35} +(-33.1395 + 14.0633i) q^{36} +(27.8343 + 27.8343i) q^{37} +(16.2724 - 16.9418i) q^{38} +(41.3099 - 19.5649i) q^{39} +(20.4272 + 61.1798i) q^{40} +(-36.7431 + 63.6409i) q^{41} +(11.9693 + 13.5301i) q^{42} +(19.0166 - 70.9710i) q^{43} +(-23.3504 - 5.25838i) q^{44} +(42.3285 + 58.9373i) q^{45} +(-4.01957 + 7.29783i) q^{46} +(-39.5925 + 22.8588i) q^{47} +(12.3917 + 46.3729i) q^{48} +(-19.9677 + 34.5851i) q^{49} +(68.4684 - 41.3917i) q^{50} +(68.9143 - 12.5771i) q^{51} +(-18.1327 - 58.1850i) q^{52} +(21.0485 - 21.0485i) q^{53} +(28.7619 + 45.7029i) q^{54} +48.2442i q^{55} +(20.0934 - 13.2812i) q^{56} +(-28.9842 - 20.0375i) q^{57} +(-12.1904 + 49.4609i) q^{58} +(20.6648 + 77.1219i) q^{59} +(85.6995 - 44.9014i) q^{60} +(-51.0660 - 13.6831i) q^{61} +(-22.0177 + 39.9749i) q^{62} +(17.1678 - 20.9643i) q^{63} +(63.5328 - 7.71872i) q^{64} +(-106.384 + 61.4211i) q^{65} +(-2.19345 + 35.8356i) q^{66} +(-12.0068 - 44.8100i) q^{67} +(-3.76312 - 93.3276i) q^{68} +(11.7691 + 4.20400i) q^{69} +(-35.0135 - 33.6302i) q^{70} -82.1279 q^{71} +(65.6988 - 29.4563i) q^{72} -25.3786i q^{73} +(-56.7789 - 54.5356i) q^{74} +(-77.6905 - 91.4707i) q^{75} +(-31.8555 + 34.5324i) q^{76} +(17.4018 - 4.66280i) q^{77} +(-81.8145 + 40.7865i) q^{78} +(45.7098 + 79.1717i) q^{79} +(-43.3114 - 121.512i) q^{80} +(60.7857 - 53.5360i) q^{81} +(70.9068 - 128.737i) q^{82} +(-12.1468 + 45.3324i) q^{83} +(-24.4789 - 26.5723i) q^{84} +(-181.851 + 48.7268i) q^{85} +(-35.1656 + 142.679i) q^{86} +(76.1592 + 6.20406i) q^{87} +(46.9032 + 9.57367i) q^{88} +79.4644 q^{89} +(-87.0148 - 116.145i) q^{90} +(32.4368 + 32.4368i) q^{91} +(7.74342 - 14.7547i) q^{92} +(64.4667 + 23.0280i) q^{93} +(78.2479 - 47.3037i) q^{94} +(82.0099 + 47.3485i) q^{95} +(-26.6470 - 92.2276i) q^{96} +(-57.7693 - 100.059i) q^{97} +(38.5336 - 69.9607i) q^{98} +(53.5891 - 5.33544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.99959	+	0.0402970i	−0.999797	+	0.0201485i
$2$	−1.99959	+	0.0402970i	−0.999797	+	0.0201485i
$3$	0.538615	+	2.95125i	0.179538	+	0.983751i
$3$	0.538615	+	2.95125i	0.179538	+	0.983751i
$4$	3.99675	−	0.161155i	0.999188	−	0.0402889i
$5$	−2.08673	−	7.78777i	−0.417345	−	1.55755i	−0.780091	−	0.625665i	$-0.784828\pi$
$5$	−2.08673	−	7.78777i	−0.417345	−	1.55755i	0.362746	−	0.931888i	$-0.381839\pi$
$6$	−1.19594	−	5.87960i	−0.199323	−	0.979934i
$7$	−2.60739	+	1.50538i	−0.372484	+	0.215054i	−0.674543	−	0.738236i	$-0.735659\pi$
$7$	−2.60739	+	1.50538i	−0.372484	+	0.215054i	0.302059	+	0.953289i	$0.402326\pi$
$8$	−7.98539	+	0.483303i	−0.998173	+	0.0604128i
$9$	−8.41979	+	3.17918i	−0.935532	+	0.353242i
$10$	4.48643	+	15.4883i	0.448643	+	1.54883i
$11$	−5.77989	−	1.54872i	−0.525445	−	0.140793i	−0.0136608	−	0.999907i	$-0.504349\pi$
$11$	−5.77989	−	1.54872i	−0.525445	−	0.140793i	−0.511784	+	0.859114i	$0.671015\pi$
$12$	2.62832	+	11.7086i	0.219027	+	0.975719i
$13$	−3.94343	−	14.7171i	−0.303341	−	1.13208i	−0.934364	−	0.356320i	$-0.884031\pi$
$13$	−3.94343	−	14.7171i	−0.303341	−	1.13208i	0.631023	−	0.775764i	$-0.282635\pi$
$14$	5.15305	−	3.11521i	0.368075	−	0.222515i
$15$	21.8597	−	10.3531i	1.45732	−	0.690204i
$16$	15.9481	−	1.28820i	0.996754	−	0.0805123i
$17$		−	23.3509i		−	1.37358i	−0.726856	−	0.686790i	$-0.759019\pi$
$17$		−	23.3509i		−	1.37358i	0.726856	−	0.686790i	$-0.240981\pi$
$18$	16.7080	−	6.69636i	0.928225	−	0.372020i
$19$	−8.30523	+	8.30523i	−0.437117	+	0.437117i	−0.891041	−	0.453923i	$-0.850024\pi$
$19$	−8.30523	+	8.30523i	−0.437117	+	0.437117i	0.453923	+	0.891041i	$0.350024\pi$
$20$	−9.59517	−	30.7895i	−0.479758	−	1.53947i
$21$	−5.84712	−	6.88424i	−0.278434	−	0.327821i
$22$	11.6198	+	2.86389i	0.528175	+	0.130177i
$23$	2.08290	−	3.60768i	0.0905607	−	0.156856i	−0.817187	−	0.576373i	$-0.804467\pi$
$23$	2.08290	−	3.60768i	0.0905607	−	0.156856i	0.907747	+	0.419518i	$0.137801\pi$
$24$	−5.72740	−	23.3066i	−0.238642	−	0.971108i
$25$	−34.6443	+	20.0019i	−1.38577	+	0.800075i
$26$	8.47832	+	29.2693i	0.326089	+	1.12574i
$27$	−13.9176	−	23.1366i	−0.515466	−	0.856910i
$28$	−10.1785	+	6.43681i	−0.363517	+	0.229886i
$29$	6.59225	−	24.6026i	0.227319	−	0.848365i	−0.754143	−	0.656710i	$-0.771948\pi$
$29$	6.59225	−	24.6026i	0.227319	−	0.848365i	0.981462	−	0.191656i	$-0.0613857\pi$
$30$	−43.2934	+	21.5828i	−1.44311	+	0.719427i
$31$	11.4094	−	19.7616i	0.368044	−	0.637470i	−0.621216	−	0.783639i	$-0.713361\pi$
$31$	11.4094	−	19.7616i	0.368044	−	0.637470i	0.989260	+	0.146169i	$0.0466943\pi$
$32$	−31.8377	+	3.21853i	−0.994929	+	0.100579i
$33$	1.45752	−	17.8921i	0.0441673	−	0.542184i
$34$	0.940971	+	46.6922i	0.0276756	+	1.37330i
$35$	17.1644	+	17.1644i	0.490412	+	0.490412i
$36$	−33.1395	+	14.0633i	−0.920541	+	0.390647i
$37$	27.8343	+	27.8343i	0.752277	+	0.752277i	0.974904	−	0.222626i	$-0.0714630\pi$
$37$	27.8343	+	27.8343i	0.752277	+	0.752277i	−0.222626	+	0.974904i	$0.571463\pi$
$38$	16.2724	−	16.9418i	0.428221	−	0.445836i
$39$	41.3099	−	19.5649i	1.05923	−	0.501664i
$40$	20.4272	+	61.1798i	0.510679	+	1.52950i
$41$	−36.7431	+	63.6409i	−0.896173	+	1.55222i	−0.0638280	+	0.997961i	$0.520331\pi$
$41$	−36.7431	+	63.6409i	−0.896173	+	1.55222i	−0.832346	+	0.554257i	$0.813002\pi$
$42$	11.9693	+	13.5301i	0.284983	+	0.322144i
$43$	19.0166	−	70.9710i	0.442247	−	1.65049i	−0.280858	−	0.959749i	$-0.590619\pi$
$43$	19.0166	−	70.9710i	0.442247	−	1.65049i	0.723105	−	0.690738i	$-0.242714\pi$
$44$	−23.3504	−	5.25838i	−0.530691	−	0.119509i
$45$	42.3285	+	58.9373i	0.940633	+	1.30972i
$46$	−4.01957	+	7.29783i	−0.0873819	+	0.158648i
$47$	−39.5925	+	22.8588i	−0.842395	+	0.486357i	−0.858077	−	0.513520i	$-0.828341\pi$
$47$	−39.5925	+	22.8588i	−0.842395	+	0.486357i	0.0156829	+	0.999877i	$0.495008\pi$
$48$	12.3917	+	46.3729i	0.258160	+	0.966102i
$49$	−19.9677	+	34.5851i	−0.407504	+	0.705817i
$50$	68.4684	−	41.3917i	1.36937	−	0.827834i
$51$	68.9143	−	12.5771i	1.35126	−	0.246610i
$52$	−18.1327	−	58.1850i	−0.348705	−	1.11894i
$53$	21.0485	−	21.0485i	0.397142	−	0.397142i	−0.480082	−	0.877224i	$-0.659393\pi$
$53$	21.0485	−	21.0485i	0.397142	−	0.397142i	0.877224	+	0.480082i	$0.159393\pi$
$54$	28.7619	+	45.7029i	0.532627	+	0.846350i
$55$			48.2442i			0.877167i
$56$	20.0934	−	13.2812i	0.358811	−	0.237164i
$57$	−28.9842	−	20.0375i	−0.508494	−	0.351535i
$58$	−12.1904	+	49.4609i	−0.210179	+	0.852773i
$59$	20.6648	+	77.1219i	0.350250	+	1.30715i	0.886358	+	0.463001i	$0.153227\pi$
$59$	20.6648	+	77.1219i	0.350250	+	1.30715i	−0.536108	+	0.844150i	$0.680106\pi$
$60$	85.6995	−	44.9014i	1.42832	−	0.748357i
$61$	−51.0660	−	13.6831i	−0.837147	−	0.224313i	−0.185318	−	0.982679i	$-0.559331\pi$
$61$	−51.0660	−	13.6831i	−0.837147	−	0.224313i	−0.651829	+	0.758366i	$0.725998\pi$
$62$	−22.0177	+	39.9749i	−0.355125	+	0.644757i
$63$	17.1678	−	20.9643i	0.272504	−	0.332766i
$64$	63.5328	−	7.71872i	0.992701	−	0.120605i
$65$	−106.384	+	61.4211i	−1.63668	+	0.944939i
$66$	−2.19345	+	35.8356i	−0.0332341	+	0.542964i
$67$	−12.0068	−	44.8100i	−0.179206	−	0.668806i	−0.995797	−	0.0915891i	$-0.970805\pi$
$67$	−12.0068	−	44.8100i	−0.179206	−	0.668806i	0.816591	−	0.577217i	$-0.195861\pi$
$68$	−3.76312	−	93.3276i	−0.0553400	−	1.37246i
$69$	11.7691	+	4.20400i	0.170566	+	0.0609275i
$70$	−35.0135	−	33.6302i	−0.500193	−	0.480431i
$71$	−82.1279			−1.15673			−0.578366	−	0.815778i	$-0.696309\pi$
$71$	−82.1279			−1.15673			−0.578366	+	0.815778i	$0.696309\pi$
$72$	65.6988	−	29.4563i	0.912483	−	0.409115i
$73$		−	25.3786i		−	0.347652i	−0.984776	−	0.173826i	$-0.944387\pi$
$73$		−	25.3786i		−	0.347652i	0.984776	−	0.173826i	$-0.0556130\pi$
$74$	−56.7789	−	54.5356i	−0.767282	−	0.736967i
$75$	−77.6905	−	91.4707i	−1.03587	−	1.21961i
$76$	−31.8555	+	34.5324i	−0.419152	+	0.454373i
$77$	17.4018	−	4.66280i	0.225998	−	0.0605559i
$78$	−81.8145	+	40.7865i	−1.04890	+	0.522904i
$79$	45.7098	+	79.1717i	0.578605	+	1.00217i	0.995640	+	0.0932826i	$0.0297360\pi$
$79$	45.7098	+	79.1717i	0.578605	+	1.00217i	−0.417035	+	0.908891i	$0.636931\pi$
$80$	−43.3114	−	121.512i	−0.541393	−	1.51890i
$81$	60.7857	−	53.5360i	0.750440	−	0.660938i
$82$	70.9068	−	128.737i	0.864717	−	1.56996i
$83$	−12.1468	+	45.3324i	−0.146347	+	0.546173i	0.853345	+	0.521346i	$0.174570\pi$
$83$	−12.1468	+	45.3324i	−0.146347	+	0.546173i	−0.999692	+	0.0248266i	$0.992097\pi$
$84$	−24.4789	−	26.5723i	−0.291416	−	0.316337i
$85$	−181.851	+	48.7268i	−2.13942	+	0.573257i
$86$	−35.1656	+	142.679i	−0.408902	+	1.65906i
$87$	76.1592	+	6.20406i	0.875393	+	0.0713110i
$88$	46.9032	+	9.57367i	0.532991	+	0.108792i
$89$	79.4644			0.892858			0.446429	−	0.894819i	$-0.352695\pi$
$89$	79.4644			0.892858			0.446429	+	0.894819i	$0.352695\pi$
$90$	−87.0148	−	116.145i	−0.966831	−	1.29050i
$91$	32.4368	+	32.4368i	0.356448	+	0.356448i
$92$	7.74342	−	14.7547i	0.0841676	−	0.160377i
$93$	64.4667	+	23.0280i	0.693190	+	0.247613i
$94$	78.2479	−	47.3037i	0.832424	−	0.503231i
$95$	82.0099	+	47.3485i	0.863263	+	0.498405i
$96$	−26.6470	−	92.2276i	−0.277573	−	0.960705i
$97$	−57.7693	−	100.059i	−0.595560	−	1.03154i	−0.993468	−	0.114114i	$-0.963597\pi$
$97$	−57.7693	−	100.059i	−0.595560	−	1.03154i	0.397908	−	0.917425i	$-0.369736\pi$
$98$	38.5336	−	69.9607i	0.393200	−	0.713885i
$99$	53.5891	−	5.33544i	0.541304	−	0.0538933i
$100$	−135.241	+	85.5256i	−1.35241	+	0.855256i
$101$	73.2561	+	19.6289i	0.725308	+	0.194346i	0.602539	−	0.798090i	$-0.294156\pi$
$101$	73.2561	+	19.6289i	0.725308	+	0.194346i	0.122769	+	0.992435i	$0.460823\pi$
$102$	−137.294	+	27.9262i	−1.34602	+	0.273786i
$103$	−47.2845	−	27.2997i	−0.459072	−	0.265046i	0.252582	−	0.967576i	$-0.418720\pi$
$103$	−47.2845	−	27.2997i	−0.459072	−	0.265046i	−0.711654	+	0.702530i	$0.752054\pi$
$104$	38.6026	+	115.616i	0.371179	+	1.11169i
$105$	−41.4115	+	59.9015i	−0.394395	+	0.570491i
$106$	−41.2403	+	42.9367i	−0.389059	+	0.405063i
$107$	137.095	−	137.095i	1.28126	−	1.28126i	0.341307	−	0.939952i	$-0.389131\pi$
$107$	137.095	−	137.095i	1.28126	−	1.28126i	0.939952	−	0.341307i	$-0.110869\pi$
$108$	−59.3537	−	90.2282i	−0.549571	−	0.835447i
$109$	113.630	−	113.630i	1.04247	−	1.04247i	0.0434170	−	0.999057i	$-0.486176\pi$
$109$	113.630	−	113.630i	1.04247	−	1.04247i	0.999057	−	0.0434170i	$-0.0138244\pi$
$110$	−1.94410	−	96.4688i	−0.0176736	−	0.876989i
$111$	−67.1540	+	97.1379i	−0.604991	+	0.875116i
$112$	−39.6435	+	27.3666i	−0.353960	+	0.244345i
$113$	−11.3738	−	6.56666i	−0.100653	−	0.0581121i	0.448829	−	0.893618i	$-0.351841\pi$
$113$	−11.3738	−	6.56666i	−0.100653	−	0.0581121i	−0.549482	+	0.835506i	$0.685175\pi$
$114$	58.7640	+	38.8989i	0.515474	+	0.341219i
$115$	−32.4422	−	8.69286i	−0.282106	−	0.0755901i
$116$	22.3827	−	99.3929i	0.192955	−	0.856835i
$117$	79.9911	+	111.378i	0.683685	+	0.951948i
$118$	−44.4289	−	153.380i	−0.376516	−	1.29983i
$119$	35.1518	+	60.8847i	0.295393	+	0.511636i
$120$	−169.555	+	93.2381i	−1.41296	+	0.776984i
$121$	−73.7804	−	42.5972i	−0.609756	−	0.352043i
$122$	102.663	+	25.3028i	0.841497	+	0.207400i
$123$	−207.611	−	74.1603i	−1.68789	−	0.602929i
$124$	42.4157	−	80.8208i	0.342062	−	0.651781i
$125$	85.5369	+	85.5369i	0.684296	+	0.684296i
$126$	−33.4838	+	42.6119i	−0.265744	+	0.338189i
$127$	90.5005			0.712602			0.356301	−	0.934371i	$-0.384038\pi$
$127$	90.5005			0.712602			0.356301	+	0.934371i	$0.384038\pi$
$128$	−126.729	+	17.9945i	−0.990069	+	0.140582i
$129$	219.696	+	17.8968i	1.70307	+	0.138735i
$130$	210.250	−	127.104i	1.61731	−	0.977724i
$131$	−61.2946	+	16.4238i	−0.467897	+	0.125373i	−0.485062	−	0.874480i	$-0.661203\pi$
$131$	−61.2946	+	16.4238i	−0.467897	+	0.125373i	0.0171642	+	0.999853i	$0.494536\pi$
$132$	2.94194	−	71.7451i	0.0222874	−	0.543524i
$133$	9.15246	−	34.1574i	0.0688155	−	0.256823i
$134$	25.8144	+	89.1180i	0.192645	+	0.665060i
$135$	−151.140	+	156.667i	−1.11956	+	1.16049i
$136$	11.2855	+	186.466i	0.0829819	+	1.37107i
$137$	73.8486	+	127.909i	0.539041	+	0.933646i	0.998956	+	0.0456831i	$0.0145465\pi$
$137$	73.8486	+	127.909i	0.539041	+	0.933646i	−0.459915	+	0.887963i	$0.652120\pi$
$138$	−23.7027	−	7.93203i	−0.171759	−	0.0574785i
$139$	85.7706	−	22.9822i	0.617055	−	0.165339i	0.0632661	−	0.997997i	$-0.479848\pi$
$139$	85.7706	−	22.9822i	0.617055	−	0.165339i	0.553788	+	0.832657i	$0.313182\pi$
$140$	71.3680	+	65.8358i	0.509772	+	0.470255i
$141$	−88.7871	−	104.536i	−0.629696	−	0.741387i
$142$	164.223	−	3.30951i	1.15650	−	0.0233064i
$143$			91.1704i			0.637556i
$144$	−130.184	+	61.5481i	−0.904055	+	0.427417i
$145$	−205.356			−1.41624
$146$	1.02268	+	50.7469i	0.00700467	+	0.347581i
$147$	−112.824	−	40.3017i	−0.767511	−	0.274161i
$148$	115.732	+	106.761i	0.781975	+	0.721358i
$149$	−64.5889	−	241.049i	−0.433482	−	1.61778i	−0.744672	−	0.667431i	$-0.767394\pi$
$149$	−64.5889	−	241.049i	−0.433482	−	1.61778i	0.311190	−	0.950348i	$-0.399273\pi$
$150$	159.035	+	179.773i	1.06024	+	1.19849i
$151$	199.871	−	115.396i	1.32365	−	0.764210i	0.339342	−	0.940663i	$-0.389796\pi$
$151$	199.871	−	115.396i	1.32365	−	0.764210i	0.984309	+	0.176453i	$0.0564624\pi$
$152$	62.3065	−	70.3344i	0.409911	−	0.462726i
$153$	74.2365	+	196.609i	0.485206	+	1.28503i
$154$	−34.6087	+	10.0250i	−0.224732	+	0.0650971i
$155$	−177.707	−	47.6164i	−1.14650	−	0.307203i
$156$	161.952	−	84.8534i	1.03816	−	0.543932i
$157$	−1.58942	−	5.93179i	−0.0101237	−	0.0377821i	0.960679	−	0.277661i	$-0.0895591\pi$
$157$	−1.58942	−	5.93179i	−0.0101237	−	0.0377821i	−0.970803	+	0.239878i	$0.922892\pi$
$158$	−94.5914	−	156.469i	−0.598680	−	0.990312i
$159$	73.4566	+	50.7825i	0.461991	+	0.319387i
$160$	91.5018	+	241.229i	0.571886	+	1.50768i
$161$			12.5422i			0.0779016i
$162$	−119.389	+	109.500i	−0.736971	+	0.675925i
$163$	−129.554	+	129.554i	−0.794811	+	0.794811i	−0.982272	−	0.187461i	$-0.939974\pi$
$163$	−129.554	+	129.554i	−0.794811	+	0.794811i	0.187461	+	0.982272i	$0.439974\pi$
$164$	−136.597	+	260.278i	−0.832909	+	1.58706i
$165$	−142.381	+	25.9851i	−0.862914	+	0.157485i
$166$	22.4618	−	91.1358i	0.135312	−	0.549011i
$167$	−141.391	+	244.897i	−0.846653	+	1.46645i	0.0375246	+	0.999296i	$0.488053\pi$
$167$	−141.391	+	244.897i	−0.846653	+	1.46645i	−0.884178	+	0.467151i	$0.845281\pi$
$168$	50.0187	+	52.1474i	0.297730	+	0.310401i
$169$	−54.6837	+	31.5717i	−0.323572	+	0.186815i
$170$	361.665	−	104.762i	2.12744	−	0.616247i
$171$	43.5245	−	96.3321i	0.254529	−	0.563346i
$172$	64.5673	−	286.718i	0.375391	−	1.66697i
$173$	58.4155	−	218.009i	0.337662	−	1.26017i	−0.563293	−	0.826257i	$-0.690466\pi$
$173$	58.4155	−	218.009i	0.337662	−	1.26017i	0.900955	−	0.433913i	$-0.142868\pi$
$174$	−152.537	−	9.33661i	−0.876652	−	0.0536587i
$175$	60.2206	−	104.305i	0.344118	−	0.596030i
$176$	−94.1731	−	17.2534i	−0.535074	−	0.0980307i
$177$	−216.476	+	102.526i	−1.22303	+	0.579242i
$178$	−158.897	+	3.20218i	−0.892677	+	0.0179898i
$179$	38.3604	+	38.3604i	0.214304	+	0.214304i	0.806093	−	0.591789i	$-0.201578\pi$
$179$	38.3604	+	38.3604i	0.214304	+	0.214304i	−0.591789	+	0.806093i	$0.701578\pi$
$180$	178.675	+	228.736i	0.992636	+	1.27076i
$181$	20.4423	+	20.4423i	0.112941	+	0.112941i	0.761319	−	0.648378i	$-0.224552\pi$
$181$	20.4423	+	20.4423i	0.112941	+	0.112941i	−0.648378	+	0.761319i	$0.724552\pi$
$182$	−66.1675	−	63.5533i	−0.363558	−	0.349194i
$183$	12.8773	−	158.079i	0.0703680	−	0.863817i
$184$	−14.8891	+	29.8154i	−0.0809191	+	0.162040i
$185$	158.684	−	274.849i	0.857753	−	1.48567i
$186$	−129.835	−	43.4489i	−0.698039	−	0.233596i
$187$	−36.1639	+	134.965i	−0.193390	+	0.721740i
$188$	−154.558	+	97.7414i	−0.822116	+	0.519901i
$189$	71.1177	+	39.3748i	0.376284	+	0.208332i
$190$	−165.895	−	91.3729i	−0.873129	−	0.480910i
$191$	68.3229	−	39.4463i	0.357712	−	0.206525i	−0.310365	−	0.950618i	$-0.600451\pi$
$191$	68.3229	−	39.4463i	0.357712	−	0.206525i	0.668077	+	0.744093i	$0.267118\pi$
$192$	56.9996	+	183.344i	0.296873	+	0.954917i
$193$	25.8209	−	44.7231i	0.133787	−	0.231726i	−0.791346	−	0.611368i	$-0.790620\pi$
$193$	25.8209	−	44.7231i	0.133787	−	0.231726i	0.925133	+	0.379642i	$0.123953\pi$
$194$	119.547	+	197.750i	0.616223	+	1.01933i
$195$	−238.569	−	280.885i	−1.22343	−	1.44044i
$196$	−74.2323	+	141.446i	−0.378736	+	0.721662i
$197$	121.764	−	121.764i	0.618089	−	0.618089i	−0.326952	−	0.945041i	$-0.606021\pi$
$197$	121.764	−	121.764i	0.618089	−	0.618089i	0.945041	+	0.326952i	$0.106021\pi$
$198$	−106.941	+	12.8282i	−0.540108	+	0.0647888i
$199$			14.7523i			0.0741321i	0.999313	+	0.0370661i	$0.0118012\pi$
$199$			14.7523i			0.0741321i	−0.999313	+	0.0370661i	$0.988199\pi$
$200$	266.981	−	176.466i	1.33490	−	0.882332i
$201$	125.779	−	59.5705i	0.625764	−	0.296370i
$202$	−147.273	−	36.2978i	−0.729076	−	0.179692i
$203$	19.8476	+	74.0723i	0.0977715	+	0.364888i
$204$	273.406	−	61.3736i	1.34023	−	0.300851i
$205$	572.294	+	153.346i	2.79168	+	0.748027i
$206$	95.6498	+	52.6829i	0.464319	+	0.255742i
$207$	−6.06808	+	36.9978i	−0.0293144	+	0.178733i
$208$	−81.8486	−	229.629i	−0.393503	−	1.10399i
$209$	60.8658	−	35.1409i	0.291224	−	0.168138i
$210$	80.3924	−	121.448i	0.382821	−	0.578321i
$211$	−2.34783	−	8.76223i	−0.0111272	−	0.0415272i	0.960139	−	0.279523i	$-0.0901763\pi$
$211$	−2.34783	−	8.76223i	−0.0111272	−	0.0415272i	−0.971266	+	0.237996i	$0.923510\pi$
$212$	80.7336	−	87.5178i	0.380819	−	0.412820i
$213$	−44.2353	−	242.380i	−0.207678	−	1.13794i
$214$	−268.609	+	279.658i	−1.25518	+	1.30681i
$215$	−592.388			−2.75529
$216$	122.319	+	178.028i	0.566293	+	0.824204i
$217$			68.7014i			0.316597i
$218$	−222.634	+	231.792i	−1.02126	+	1.06327i
$219$	74.8987	−	13.6693i	0.342003	−	0.0624169i
$220$	7.77482	+	192.820i	0.0353401	+	0.876455i
$221$	−343.657	+	92.0825i	−1.55501	+	0.416663i
$222$	130.366	−	196.942i	0.587236	−	0.887128i
$223$	−204.189	−	353.666i	−0.915646	−	1.58594i	−0.805953	−	0.591979i	$-0.798347\pi$
$223$	−204.189	−	353.666i	−0.915646	−	1.58594i	−0.109692	−	0.993966i	$-0.534987\pi$
$224$	78.1682	−	56.3197i	0.348965	−	0.251427i
$225$	228.108	−	278.552i	1.01381	−	1.23801i
$226$	23.0076	+	12.6723i	0.101803	+	0.0560723i
$227$	10.6696	−	39.8196i	0.0470028	−	0.175417i	−0.938434	−	0.345458i	$-0.887724\pi$
$227$	10.6696	−	39.8196i	0.0470028	−	0.175417i	0.985437	+	0.170042i	$0.0543902\pi$
$228$	−119.072	−	75.4140i	−0.522244	−	0.330763i
$229$	−21.1498	+	5.66706i	−0.0923570	+	0.0247470i	−0.304702	−	0.952448i	$-0.598557\pi$
$229$	−21.1498	+	5.66706i	−0.0923570	+	0.0247470i	0.212345	+	0.977195i	$0.431890\pi$
$230$	65.2215	+	16.0749i	0.283572	+	0.0698907i
$231$	23.1340	+	48.8457i	0.100147	+	0.211453i
$232$	−40.7511	+	199.647i	−0.175651	+	0.860549i
$233$	39.8502			0.171031			0.0855155	−	0.996337i	$-0.472746\pi$
$233$	39.8502			0.171031			0.0855155	+	0.996337i	$0.472746\pi$
$234$	−164.438	−	219.487i	−0.702726	−	0.937979i
$235$	260.638	+	260.638i	1.10910	+	1.10910i
$236$	95.0205	+	304.907i	0.402629	+	1.29198i
$237$	−209.036	+	177.544i	−0.882007	+	0.749132i
$238$	−72.7428	−	120.328i	−0.305642	−	0.505581i
$239$	191.059	+	110.308i	0.799409	+	0.461539i	0.843264	−	0.537499i	$-0.180631\pi$
$239$	191.059	+	110.308i	0.799409	+	0.461539i	−0.0438555	+	0.999038i	$0.513964\pi$
$240$	335.283	−	193.271i	1.39701	−	0.805295i
$241$	−4.52961	−	7.84552i	−0.0187951	−	0.0325540i	0.856475	−	0.516189i	$-0.172650\pi$
$241$	−4.52961	−	7.84552i	−0.0187951	−	0.0325540i	−0.875270	+	0.483635i	$0.839316\pi$
$242$	149.247	+	82.2039i	0.616725	+	0.339685i
$243$	190.738	+	150.559i	0.784932	+	0.619582i
$244$	−206.303	−	46.4583i	−0.845505	−	0.190403i
$245$	311.007	+	83.3342i	1.26942	+	0.340140i
$246$	418.126	+	139.924i	1.69970	+	0.568798i
$247$	154.980	+	89.4777i	0.627449	+	0.362258i
$248$	−81.5573	+	163.318i	−0.328860	+	0.658541i
$249$	−140.330	−	11.4315i	−0.563573	−	0.0459096i
$250$	−174.486	−	167.592i	−0.697944	−	0.670369i
$251$	−14.8880	+	14.8880i	−0.0593147	+	0.0593147i	−0.736142	−	0.676827i	$-0.763354\pi$
$251$	−14.8880	+	14.8880i	−0.0593147	+	0.0593147i	0.676827	+	0.736142i	$0.263354\pi$
$252$	65.2369	−	86.5557i	0.258876	−	0.343475i
$253$	−17.6262	+	17.6262i	−0.0696687	+	0.0696687i
$254$	−180.964	+	3.64690i	−0.712458	+	0.0143579i
$255$	−241.753	−	510.443i	−0.948051	−	2.00174i
$256$	252.681	−	41.0885i	0.987036	−	0.160502i
$257$	159.082	+	91.8461i	0.618997	+	0.357378i	0.776478	−	0.630144i	$-0.217004\pi$
$257$	159.082	+	91.8461i	0.618997	+	0.357378i	−0.157481	+	0.987522i	$0.550337\pi$
$258$	−440.024	−	26.9333i	−1.70552	−	0.104392i
$259$	−114.476	−	30.6737i	−0.441991	−	0.118431i
$260$	−415.294	+	262.629i	−1.59728	+	1.01011i
$261$	22.7107	+	228.107i	0.0870143	+	0.873972i
$262$	121.902	−	35.3110i	0.465276	−	0.134775i
$263$	−136.494	−	236.415i	−0.518989	−	0.898915i	−0.999756	−	0.0220670i	$-0.992975\pi$
$263$	−136.494	−	236.415i	−0.518989	−	0.898915i	0.480768	−	0.876848i	$-0.340358\pi$
$264$	−2.99157	+	143.580i	−0.0113317	+	0.543862i
$265$	−207.843	−	119.998i	−0.784315	−	0.452825i
$266$	−16.9248	+	68.6698i	−0.0636269	+	0.258157i
$267$	42.8007	+	234.519i	0.160302	+	0.878350i
$268$	−55.2096	−	177.160i	−0.206006	−	0.661043i
$269$	−183.737	−	183.737i	−0.683036	−	0.683036i	0.277647	−	0.960683i	$-0.410445\pi$
$269$	−183.737	−	183.737i	−0.683036	−	0.683036i	−0.960683	+	0.277647i	$0.910445\pi$
$270$	295.906	−	319.360i	1.09595	−	1.18281i
$271$	−274.391			−1.01251			−0.506256	−	0.862383i	$-0.668971\pi$
$271$	−274.391			−1.01251			−0.506256	+	0.862383i	$0.668971\pi$
$272$	−30.0805	−	372.401i	−0.110590	−	1.36912i
$273$	−78.2582	+	113.200i	−0.286660	+	0.414652i
$274$	−152.822	−	252.791i	−0.557743	−	0.922596i
$275$	231.217	−	61.9545i	0.840790	−	0.225289i
$276$	47.7155	+	14.9057i	0.172882	+	0.0540062i
$277$	−42.3116	+	157.909i	−0.152749	+	0.570068i	0.846538	+	0.532328i	$0.178683\pi$
$277$	−42.3116	+	157.909i	−0.152749	+	0.570068i	−0.999288	+	0.0377403i	$0.987984\pi$
$278$	−170.580	+	49.4113i	−0.613598	+	0.177738i
$279$	−33.2388	+	202.661i	−0.119135	+	0.726383i
$280$	−145.360	−	128.769i	−0.519143	−	0.459889i
$281$	−265.130	−	459.219i	−0.943524	−	1.63423i	−0.758681	−	0.651463i	$-0.774156\pi$
$281$	−265.130	−	459.219i	−0.943524	−	1.63423i	−0.184843	−	0.982768i	$-0.559178\pi$
$282$	181.751	+	205.451i	0.644506	+	0.728549i
$283$	−223.598	+	59.9128i	−0.790098	+	0.211706i	−0.631232	−	0.775594i	$-0.717450\pi$
$283$	−223.598	+	59.9128i	−0.790098	+	0.211706i	−0.158866	+	0.987300i	$0.550784\pi$
$284$	−328.245	+	13.2354i	−1.15579	+	0.0466034i
$285$	−95.5655	+	267.535i	−0.335318	+	0.938718i
$286$	−3.67390	−	182.304i	−0.0128458	−	0.637426i
$287$		−	221.249i		−	0.770901i
$288$	257.835	−	128.317i	0.895259	−	0.445546i
$289$	−256.263			−0.886722
$290$	410.628	−	8.27522i	1.41596	−	0.0285352i
$291$	264.185	−	224.385i	0.907852	−	0.771083i
$292$	−4.08990	−	101.432i	−0.0140065	−	0.347370i
$293$	−58.0169	−	216.522i	−0.198010	−	0.738983i	−0.991467	−	0.130357i	$-0.958388\pi$
$293$	−58.0169	−	216.522i	−0.198010	−	0.738983i	0.793457	−	0.608626i	$-0.208279\pi$
$294$	227.227	+	76.0405i	0.772879	+	0.258641i
$295$	557.486	−	321.865i	1.88978	−	1.09107i
$296$	−235.720	−	208.815i	−0.796351	−	0.705456i
$297$	44.6101	+	155.281i	0.150202	+	0.522833i
$298$	138.865	+	479.397i	0.465990	+	1.60872i
$299$	−61.3083	−	16.4275i	−0.205044	−	0.0549415i
$300$	−325.251	−	353.065i	−1.08417	−	1.17688i
$301$	57.2543	+	213.676i	0.190214	+	0.709887i
$302$	−395.011	+	238.799i	−1.30798	+	0.790724i
$303$	−18.4730	+	226.770i	−0.0609671	+	0.748414i
$304$	−121.754	+	143.151i	−0.400505	+	0.470892i
$305$			426.243i			1.39752i
$306$	−156.366	−	390.147i	−0.510999	−	1.27499i
$307$	57.4022	−	57.4022i	0.186978	−	0.186978i	−0.607410	−	0.794388i	$-0.707792\pi$
$307$	57.4022	−	57.4022i	0.186978	−	0.186978i	0.794388	+	0.607410i	$0.207792\pi$
$308$	68.7993	−	21.4405i	0.223374	−	0.0696119i
$309$	55.1002	−	154.252i	0.178318	−	0.499199i
$310$	357.260	+	88.0524i	1.15245	+	0.284040i
$311$	188.714	−	326.862i	0.606797	−	1.05100i	−0.384968	−	0.922930i	$-0.625787\pi$
$311$	188.714	−	326.862i	0.606797	−	1.05100i	0.991765	−	0.128073i	$-0.0408792\pi$
$312$	−320.419	+	176.199i	−1.02699	+	0.564739i
$313$	224.605	−	129.676i	0.717588	−	0.414300i	−0.0962760	−	0.995355i	$-0.530693\pi$
$313$	224.605	−	129.676i	0.717588	−	0.414300i	0.813864	+	0.581055i	$0.197360\pi$
$314$	3.41723	+	11.7971i	0.0108829	+	0.0375705i
$315$	−199.089	−	89.9520i	−0.632030	−	0.285562i
$316$	195.450	+	309.063i	0.618512	+	0.978048i
$317$	37.8333	−	141.196i	0.119348	−	0.445413i	−0.880227	−	0.474552i	$-0.842610\pi$
$317$	37.8333	−	141.196i	0.119348	−	0.445413i	0.999575	+	0.0291393i	$0.00927665\pi$
$318$	−148.930	−	98.5842i	−0.468332	−	0.310013i
$319$	−76.2050	+	131.991i	−0.238887	+	0.413764i
$320$	−192.687	−	478.672i	−0.602148	−	1.49585i
$321$	478.442	+	330.760i	1.49047	+	1.03040i
$322$	−0.505412	−	25.0792i	−0.00156960	−	0.0778858i
$323$	193.934	+	193.934i	0.600416	+	0.600416i
$324$	234.318	−	223.766i	0.723202	−	0.690636i
$325$	430.987	+	430.987i	1.32611	+	1.32611i
$326$	253.835	−	264.276i	0.778635	−	0.810664i
$327$	396.553	+	274.147i	1.21270	+	0.838371i
$328$	262.650	−	525.956i	0.800763	−	1.60352i
$329$	68.8220	−	119.203i	0.209186	−	0.362320i
$330$	283.657	−	57.6971i	0.859566	−	0.174840i
$331$	−96.7332	+	361.013i	−0.292245	+	1.09067i	0.651135	+	0.758962i	$0.274293\pi$
$331$	−96.7332	+	361.013i	−0.292245	+	1.09067i	−0.943381	+	0.331712i	$0.892374\pi$
$332$	−41.2421	+	183.140i	−0.124223	+	0.551626i
$333$	−322.849	−	145.869i	−0.969516	−	0.438044i
$334$	272.856	−	495.391i	0.816935	−	1.48321i
$335$	−323.915	+	187.012i	−0.966910	+	0.558246i
$336$	−102.118	−	102.258i	−0.303924	−	0.304339i
$337$	19.0170	−	32.9383i	0.0564301	−	0.0977399i	−0.836430	−	0.548073i	$-0.815362\pi$
$337$	19.0170	−	32.9383i	0.0564301	−	0.0977399i	0.892861	+	0.450333i	$0.148695\pi$
$338$	108.073	−	65.3341i	0.319743	−	0.193296i
$339$	13.2538	−	37.1038i	0.0390967	−	0.109451i
$340$	−718.961	+	224.055i	−2.11459	+	0.658986i
$341$	−96.5500	+	96.5500i	−0.283138	+	0.283138i
$342$	−83.1494	+	194.379i	−0.243127	+	0.568360i
$343$		−	267.762i		−	0.780648i
$344$	−117.555	+	575.921i	−0.341728	+	1.67419i
$345$	8.18098	−	100.427i	0.0237130	−	0.291093i
$346$	−108.022	+	438.284i	−0.312203	+	1.26672i
$347$	40.7606	+	152.120i	0.117466	+	0.438388i	0.999460	−	0.0328732i	$-0.0104658\pi$
$347$	40.7606	+	152.120i	0.117466	+	0.438388i	−0.881994	+	0.471261i	$0.843799\pi$
$348$	305.389	+	12.5226i	0.877555	+	0.0359845i
$349$	−201.972	−	54.1182i	−0.578716	−	0.155067i	−0.0424253	−	0.999100i	$-0.513508\pi$
$349$	−201.972	−	54.1182i	−0.578716	−	0.155067i	−0.536291	+	0.844033i	$0.680175\pi$
$350$	−116.214	+	210.995i	−0.332039	+	0.602842i
$351$	−285.620	+	296.064i	−0.813732	+	0.843487i
$352$	189.003	+	30.7049i	0.536941	+	0.0872298i
$353$	−99.4507	+	57.4179i	−0.281730	+	0.162657i	−0.634206	−	0.773164i	$-0.718673\pi$
$353$	−99.4507	+	57.4179i	−0.281730	+	0.162657i	0.352476	+	0.935821i	$0.385340\pi$
$354$	428.732	−	213.734i	1.21111	−	0.603767i
$355$	171.378	+	639.593i	0.482756	+	1.80167i
$356$	317.599	−	12.8061i	0.892133	−	0.0359722i
$357$	−160.753	+	136.535i	−0.450288	+	0.382452i
$358$	−78.2511	−	75.1595i	−0.218578	−	0.209943i
$359$	202.626			0.564419			0.282209	−	0.959353i	$-0.408933\pi$
$359$	202.626			0.564419			0.282209	+	0.959353i	$0.408933\pi$
$360$	−366.494	−	450.179i	−1.01804	−	1.25050i
$361$			223.046i			0.617857i
$362$	−41.7000	−	40.0525i	−0.115193	−	0.110642i
$363$	85.9757	−	240.688i	0.236848	−	0.663053i
$364$	134.869	+	124.414i	0.370520	+	0.341798i
$365$	−197.643	+	52.9582i	−0.541487	+	0.145091i
$366$	−19.3794	+	316.612i	−0.0529491	+	0.865060i
$367$	198.330	+	343.518i	0.540409	+	0.936016i	0.998880	+	0.0473067i	$0.0150638\pi$
$367$	198.330	+	343.518i	0.540409	+	0.936016i	−0.458471	+	0.888709i	$0.651603\pi$
$368$	28.5707	−	60.2187i	0.0776379	−	0.163638i
$369$	107.043	−	652.656i	0.290090	−	1.76872i
$370$	−306.229	+	555.981i	−0.827645	+	1.50265i
$371$	−23.1957	+	86.5676i	−0.0625221	+	0.233336i
$372$	261.368	+	81.6481i	0.702603	+	0.219484i
$373$	−352.304	+	94.3996i	−0.944515	+	0.253082i	−0.698033	−	0.716065i	$-0.745941\pi$
$373$	−352.304	+	94.3996i	−0.944515	+	0.253082i	−0.246482	+	0.969147i	$0.579275\pi$
$374$	66.8744	−	271.333i	0.178808	−	0.725490i
$375$	−206.370	+	298.513i	−0.550319	+	0.796034i
$376$	305.114	−	201.671i	0.811474	−	0.536360i
$377$	−388.075			−1.02938
$378$	−143.793	−	75.8678i	−0.380406	−	0.200708i
$379$	291.312	+	291.312i	0.768633	+	0.768633i	0.977866	−	0.209232i	$-0.0670965\pi$
$379$	291.312	+	291.312i	0.768633	+	0.768633i	−0.209232	+	0.977866i	$0.567097\pi$
$380$	335.404	+	176.024i	0.882642	+	0.463220i
$381$	48.7449	+	267.090i	0.127939	+	0.701023i
$382$	−135.029	+	81.6297i	−0.353478	+	0.213690i
$383$	−16.9453	−	9.78336i	−0.0442435	−	0.0255440i	0.477715	−	0.878515i	$-0.341465\pi$
$383$	−16.9453	−	9.78336i	−0.0442435	−	0.0255440i	−0.521959	+	0.852971i	$0.674798\pi$
$384$	−121.364	−	364.317i	−0.316053	−	0.948742i
$385$	−72.6256	−	125.791i	−0.188638	−	0.326731i
$386$	−49.8291	+	90.4686i	−0.129091	+	0.234375i
$387$	65.5135	+	658.018i	0.169286	+	1.70030i
$388$	−247.015	−	390.603i	−0.636636	−	1.00671i
$389$	−142.929	−	38.2977i	−0.367427	−	0.0984518i	0.0703812	−	0.997520i	$-0.477578\pi$
$389$	−142.929	−	38.2977i	−0.367427	−	0.0984518i	−0.437808	+	0.899068i	$0.644245\pi$
$390$	488.361	+	552.042i	1.25221	+	1.41549i
$391$	−84.2424	−	48.6374i	−0.215454	−	0.124392i
$392$	142.735	−	285.826i	0.364119	−	0.729147i
$393$	−81.4850	−	172.050i	−0.207341	−	0.437785i
$394$	−238.571	+	248.385i	−0.605510	+	0.630418i
$395$	521.187	−	521.187i	1.31946	−	1.31946i
$396$	213.323	−	29.9606i	0.538693	−	0.0756581i
$397$	−91.7365	+	91.7365i	−0.231074	+	0.231074i	−0.813141	−	0.582067i	$-0.802244\pi$
$397$	−91.7365	+	91.7365i	−0.231074	+	0.231074i	0.582067	+	0.813141i	$0.302244\pi$
$398$	−0.594474	−	29.4986i	−0.00149365	−	0.0741171i
$399$	105.737	+	8.61351i	0.265005	+	0.0215877i
$400$	−526.742	+	363.620i	−1.31686	+	0.909049i
$401$	213.356	+	123.181i	0.532060	+	0.307185i	0.741855	−	0.670560i	$-0.233946\pi$
$401$	213.356	+	123.181i	0.532060	+	0.307185i	−0.209795	+	0.977745i	$0.567280\pi$
$402$	−249.106	+	124.185i	−0.619666	+	0.308919i
$403$	−335.825	−	89.9840i	−0.833313	−	0.223285i
$404$	295.950	+	66.6462i	0.732549	+	0.164966i
$405$	−543.769	−	361.670i	−1.34264	−	0.893011i
$406$	−42.6721	−	147.315i	−0.105104	−	0.362844i
$407$	−117.772	−	203.986i	−0.289365	−	0.501195i
$408$	−544.229	+	133.740i	−1.33389	+	0.327793i
$409$	551.068	+	318.159i	1.34735	+	0.777896i	0.987874	−	0.155257i	$-0.0496206\pi$
$409$	551.068	+	318.159i	1.34735	+	0.777896i	0.359480	+	0.933153i	$0.382954\pi$
$410$	−1150.53	−	283.567i	−2.80618	−	0.691627i
$411$	−337.717	+	286.840i	−0.821697	+	0.697907i
$412$	−193.384	−	101.490i	−0.469378	−	0.246335i
$413$	−169.978	−	169.978i	−0.411570	−	0.411570i
$414$	10.6428	−	74.2251i	0.0257072	−	0.179288i
$415$	378.385			0.911771
$416$	172.917	+	455.867i	0.415667	+	1.09583i
$417$	114.023	+	240.752i	0.273438	+	0.577343i
$418$	−120.291	+	72.7202i	−0.287777	+	0.173972i
$419$	60.8647	−	16.3087i	0.145262	−	0.0389228i	−0.185455	−	0.982653i	$-0.559376\pi$
$419$	60.8647	−	16.3087i	0.145262	−	0.0389228i	0.330717	+	0.943730i	$0.392709\pi$
$420$	−155.858	+	246.085i	−0.371091	+	0.585917i
$421$	113.002	−	421.729i	0.268413	−	1.00173i	−0.691715	−	0.722171i	$-0.743144\pi$
$421$	113.002	−	421.729i	0.268413	−	1.00173i	0.960128	−	0.279561i	$-0.0901890\pi$
$422$	5.04781	+	17.4263i	0.0119616	+	0.0412946i
$423$	260.689	−	318.338i	0.616285	−	0.752571i
$424$	−157.908	+	178.253i	−0.372424	+	0.420409i
$425$	467.061	+	808.973i	1.09897	+	1.90347i
$426$	98.2199	+	482.880i	0.230563	+	1.13352i
$427$	153.747	−	41.1964i	0.360063	−	0.0964786i
$428$	525.840	−	570.027i	1.22860	−	1.33184i
$429$	−269.067	+	49.1058i	−0.627196	+	0.114466i
$430$	1184.54	−	23.8715i	2.75473	−	0.0555151i
$431$		−	513.207i		−	1.19074i	−0.803453	−	0.595368i	$-0.797006\pi$
$431$		−	513.207i		−	1.19074i	0.803453	−	0.595368i	$-0.202994\pi$
$432$	−251.763	−	351.055i	−0.582784	−	0.812627i
$433$	−292.020			−0.674411			−0.337205	−	0.941431i	$-0.609482\pi$
$433$	−292.020			−0.674411			−0.337205	+	0.941431i	$0.609482\pi$
$434$	−2.76847	−	137.375i	−0.00637895	−	0.316532i
$435$	−110.608	−	606.056i	−0.254270	−	1.39323i
$436$	435.838	−	472.462i	0.999628	−	1.08363i
$437$	12.6637	+	47.2615i	0.0289787	+	0.108150i
$438$	−149.216	+	30.3512i	−0.340676	+	0.0692950i
$439$	121.141	−	69.9406i	0.275947	−	0.159318i	−0.355640	−	0.934623i	$-0.615737\pi$
$439$	121.141	−	69.9406i	0.275947	−	0.159318i	0.631587	+	0.775305i	$0.282404\pi$
$440$	−23.3166	−	385.249i	−0.0529922	−	0.875565i
$441$	58.1717	−	354.680i	0.131909	−	0.804262i
$442$	683.463	−	197.976i	1.54630	−	0.447909i
$443$	506.463	+	135.706i	1.14326	+	0.306335i	0.780260	−	0.625456i	$-0.215087\pi$
$443$	506.463	+	135.706i	1.14326	+	0.306335i	0.362997	+	0.931790i	$0.381754\pi$
$444$	−252.744	+	399.058i	−0.569242	+	0.898780i
$445$	−165.820	−	618.850i	−0.372630	−	1.39067i
$446$	422.547	+	698.960i	0.947414	+	1.56717i
$447$	676.608	−	320.451i	1.51366	−	0.716892i
$448$	−154.035	+	115.766i	−0.343828	+	0.258407i
$449$			843.172i			1.87789i	0.344069	+	0.938944i	$0.388195\pi$
$449$			843.172i			1.87789i	−0.344069	+	0.938944i	$0.611805\pi$
$450$	−444.898	+	566.183i	−0.988662	+	1.25818i
$451$	310.933	−	310.933i	0.689430	−	0.689430i
$452$	−46.5165	−	24.4124i	−0.102913	−	0.0540097i
$453$	448.216	+	527.717i	0.989438	+	1.16494i
$454$	−19.7303	+	80.0530i	−0.0434588	+	0.176328i
$455$	184.923	−	320.297i	0.406425	−	0.703949i
$456$	241.134	+	145.999i	0.528802	+	0.320174i
$457$	142.799	−	82.4450i	0.312470	−	0.180405i	−0.335561	−	0.942018i	$-0.608926\pi$
$457$	142.799	−	82.4450i	0.312470	−	0.180405i	0.648031	+	0.761614i	$0.275593\pi$
$458$	42.0626	−	12.1841i	0.0918396	−	0.0266028i
$459$	−540.259	+	324.988i	−1.17703	+	0.708034i
$460$	−131.064	−	29.5150i	−0.284923	−	0.0641630i
$461$	118.024	−	440.470i	0.256017	−	0.955467i	−0.711506	−	0.702680i	$-0.751986\pi$
$461$	118.024	−	440.470i	0.256017	−	0.955467i	0.967522	−	0.252786i	$-0.0813469\pi$
$462$	−48.2269	−	96.7393i	−0.104387	−	0.209392i
$463$	−110.082	+	190.668i	−0.237759	+	0.411810i	−0.960071	−	0.279757i	$-0.909746\pi$
$463$	−110.082	+	190.668i	−0.237759	+	0.411810i	0.722312	+	0.691567i	$0.243079\pi$
$464$	73.4405	−	400.856i	0.158277	−	0.863913i
$465$	44.8125	−	550.105i	0.0963709	−	1.18302i
$466$	−79.6842	+	1.60585i	−0.170996	+	0.00344602i
$467$	−281.438	−	281.438i	−0.602651	−	0.602651i	0.338364	−	0.941015i	$-0.390126\pi$
$467$	−281.438	−	281.438i	−0.602651	−	0.602651i	−0.941015	+	0.338364i	$0.890126\pi$
$468$	337.654	+	432.259i	0.721482	+	0.923630i
$469$	98.7623	+	98.7623i	0.210581	+	0.210581i
$470$	−531.672	−	510.666i	−1.13122	−	1.08652i
$471$	16.6501	−	7.88573i	0.0353506	−	0.0167425i
$472$	−202.289	−	605.861i	−0.428579	−	1.28360i
$473$	−219.828	+	380.753i	−0.464753	+	0.804975i
$474$	410.832	−	363.440i	0.866734	−	0.766751i
$475$	121.608	−	453.849i	0.256018	−	0.955471i
$476$	150.305	+	237.676i	0.315767	+	0.499320i
$477$	−110.307	+	244.141i	−0.231252	+	0.511826i
$478$	−386.485	−	212.872i	−0.808546	−	0.445338i
$479$	−321.243	+	185.470i	−0.670653	+	0.387202i	−0.796324	−	0.604870i	$-0.793225\pi$
$479$	−321.243	+	185.470i	−0.670653	+	0.387202i	0.125671	+	0.992072i	$0.459892\pi$
$480$	−662.642	+	399.974i	−1.38051	+	0.833280i
$481$	299.877	−	519.402i	0.623444	−	1.07984i
$482$	9.37354	+	15.5053i	0.0194472	+	0.0321687i
$483$	−37.0151	+	6.75539i	−0.0766358	+	0.0139863i
$484$	−301.747	−	158.360i	−0.623444	−	0.327190i
$485$	−658.690	+	658.690i	−1.35812	+	1.35812i
$486$	−387.466	−	293.370i	−0.797256	−	0.603641i
$487$		−	144.495i		−	0.296705i	−0.988935	−	0.148352i	$-0.952603\pi$
$487$		−	144.495i		−	0.296705i	0.988935	−	0.148352i	$-0.0473970\pi$
$488$	414.395	+	84.5844i	0.849169	+	0.173329i
$489$	−452.127	−	312.567i	−0.924595	−	0.639197i
$490$	−625.247	−	154.102i	−1.27601	−	0.314494i
$491$	7.70017	+	28.7374i	0.0156826	+	0.0585284i	0.973324	−	0.229436i	$-0.0736882\pi$
$491$	7.70017	+	28.7374i	0.0156826	+	0.0585284i	−0.957641	+	0.287964i	$0.907022\pi$
$492$	−841.721	−	262.943i	−1.71081	−	0.534436i
$493$	−574.492	−	153.935i	−1.16530	−	0.312241i
$494$	−313.503	−	172.674i	−0.634621	−	0.349542i
$495$	−153.377	−	406.206i	−0.309852	−	0.820618i
$496$	156.500	−	329.856i	0.315525	−	0.665033i
$497$	214.139	−	123.633i	0.430864	−	0.248759i
$498$	281.063	+	17.2035i	0.564384	+	0.0345452i
$499$	−116.925	−	436.369i	−0.234318	−	0.874487i	−0.978455	−	0.206460i	$-0.933806\pi$
$499$	−116.925	−	436.369i	−0.234318	−	0.874487i	0.744137	−	0.668027i	$-0.232861\pi$
$500$	355.655	+	328.085i	0.711309	+	0.656170i
$501$	−798.907	−	285.376i	−1.59462	−	0.569613i
$502$	29.1700	−	30.3699i	0.0581076	−	0.0604978i
$503$	94.4911			0.187855			0.0939275	−	0.995579i	$-0.470058\pi$
$503$	94.4911			0.187855			0.0939275	+	0.995579i	$0.470058\pi$
$504$	−126.959	+	175.705i	−0.251903	+	0.348621i
$505$		−	611.461i		−	1.21081i
$506$	34.5349	−	35.9555i	0.0682509	−	0.0710583i
$507$	−122.629	−	144.380i	−0.241873	−	0.284774i
$508$	361.708	−	14.5847i	0.712024	−	0.0287099i
$509$	−314.639	+	84.3073i	−0.618152	+	0.165633i	−0.554287	−	0.832325i	$-0.687009\pi$
$509$	−314.639	+	84.3073i	−0.618152	+	0.165633i	−0.0638642	+	0.997959i	$0.520342\pi$
$510$	503.977	+	1010.94i	0.988190	+	1.98223i
$511$	38.2043	+	66.1718i	0.0747638	+	0.129495i
$512$	−503.604	+	92.3426i	−0.983601	+	0.180357i
$513$	307.743	+	76.5658i	0.599889	+	0.149251i
$514$	−321.801	−	177.244i	−0.626072	−	0.344834i
$515$	−113.934	+	425.207i	−0.221231	+	0.825645i
$516$	880.954	+	36.1239i	1.70728	+	0.0700076i
$517$	264.242	−	70.8035i	0.511107	−	0.136951i
$518$	230.141	+	56.7219i	0.444288	+	0.109502i
$519$	674.865	+	54.9756i	1.30032	+	0.105926i
$520$	819.836	−	541.887i	1.57661	−	1.04209i
$521$	325.511			0.624781			0.312391	−	0.949954i	$-0.398870\pi$
$521$	325.511			0.624781			0.312391	+	0.949954i	$0.398870\pi$
$522$	−54.6043	−	455.205i	−0.104606	−	0.872041i
$523$	−539.325	−	539.325i	−1.03121	−	1.03121i	−0.999497	−	0.0317170i	$-0.989902\pi$
$523$	−539.325	−	539.325i	−1.03121	−	1.03121i	−0.0317170	−	0.999497i	$-0.510098\pi$
$524$	−242.332	+	75.5199i	−0.462466	+	0.144122i
$525$	340.267	+	121.546i	0.648127	+	0.231516i
$526$	282.460	+	467.233i	0.536995	+	0.888276i
$527$	−461.450	−	266.418i	−0.875617	−	0.505538i
$528$	0.196087	−	287.222i	0.000371378	−	0.543980i
$529$	255.823	+	443.099i	0.483598	+	0.837616i
$530$	420.438	+	231.573i	0.793280	+	0.436930i
$531$	−419.177	−	583.653i	−0.789411	−	1.09916i
$532$	31.0754	−	137.994i	0.0584125	−	0.259387i
$533$	1081.50	+	289.788i	2.02909	+	0.543692i
$534$	−95.0345	−	467.219i	−0.177967	−	0.874942i
$535$	−1353.74	−	781.582i	−2.53036	−	1.46090i
$536$	117.536	+	352.022i	0.219283	+	0.656758i
$537$	−92.5498	+	133.873i	−0.172346	+	0.249298i
$538$	374.803	+	359.995i	0.696659	+	0.669135i
$539$	168.974	−	168.974i	0.313495	−	0.313495i
$540$	−578.822	+	650.515i	−1.07189	+	1.20466i
$541$	−114.321	+	114.321i	−0.211315	+	0.211315i	−0.804826	−	0.593511i	$-0.797741\pi$
$541$	−114.321	+	114.321i	−0.211315	+	0.211315i	0.593511	+	0.804826i	$0.297741\pi$
$542$	548.670	−	11.0571i	1.01231	−	0.0204006i
$543$	−49.3198	+	71.3408i	−0.0908283	+	0.131383i
$544$	75.1554	+	743.438i	0.138153	+	1.36661i
$545$	−1122.04	−	647.807i	−2.05878	−	1.18864i
$546$	151.923	−	229.508i	0.278247	−	0.420344i
$547$	−753.518	−	201.904i	−1.37755	−	0.369112i	−0.507317	−	0.861760i	$-0.669363\pi$
$547$	−753.518	−	201.904i	−1.37755	−	0.369112i	−0.870229	+	0.492647i	$0.836029\pi$
$548$	315.768	+	499.321i	0.576219	+	0.911171i
$549$	473.466	−	47.1392i	0.862415	−	0.0858637i
$550$	−459.844	+	133.201i	−0.836080	+	0.242184i
$551$	149.580	+	259.080i	0.271470	+	0.470200i
$552$	−96.0123	−	27.8825i	−0.173935	−	0.0505119i
$553$	−238.366	−	137.621i	−0.431042	−	0.248862i
$554$	78.2427	−	317.459i	0.141232	−	0.573030i
$555$	896.619	+	320.280i	1.61553	+	0.577080i
$556$	339.100	−	105.676i	0.609892	−	0.190065i
$557$	102.575	+	102.575i	0.184157	+	0.184157i	0.793164	−	0.609008i	$-0.208432\pi$
$557$	102.575	+	102.575i	0.184157	+	0.184157i	−0.609008	+	0.793164i	$0.708432\pi$
$558$	58.2974	−	406.579i	0.104476	−	0.728635i
$559$	−1119.48			−2.00264
$560$	295.850	+	251.628i	0.528304	+	0.449336i
$561$	−417.796	−	34.0344i	−0.744734	−	0.0606673i
$562$	548.658	+	907.567i	0.976259	+	1.61489i
$563$	579.897	−	155.383i	1.03001	−	0.275991i	0.296044	−	0.955174i	$-0.404332\pi$
$563$	579.897	−	155.383i	1.03001	−	0.275991i	0.733969	+	0.679183i	$0.237666\pi$
$564$	−371.707	−	403.494i	−0.659054	−	0.715415i
$565$	−27.4057	+	102.279i	−0.0485056	+	0.181025i
$566$	444.690	−	128.812i	0.785672	−	0.227582i
$567$	−77.8999	+	231.094i	−0.137390	+	0.407574i
$568$	655.823	−	39.6927i	1.15462	−	0.0698814i
$569$	−138.669	−	240.182i	−0.243707	−	0.422113i	0.718060	−	0.695981i	$-0.245030\pi$
$569$	−138.669	−	240.182i	−0.243707	−	0.422113i	−0.961767	+	0.273868i	$0.911697\pi$
$570$	180.311	−	538.812i	0.316336	−	0.945284i
$571$	−739.455	+	198.136i	−1.29502	+	0.346999i	−0.839564	−	0.543260i	$-0.817190\pi$
$571$	−739.455	+	198.136i	−1.29502	+	0.346999i	−0.455454	+	0.890259i	$0.650523\pi$
$572$	14.6926	+	364.386i	0.0256864	+	0.637038i
$573$	153.216	+	180.392i	0.267392	+	0.314820i
$574$	8.91567	+	442.408i	0.0155325	+	0.770745i
$575$			166.647i			0.289821i
$576$	−510.394	+	266.972i	−0.886100	+	0.463493i
$577$	283.334			0.491048			0.245524	−	0.969391i	$-0.421040\pi$
$577$	283.334			0.491048			0.245524	+	0.969391i	$0.421040\pi$
$578$	512.421	−	10.3266i	0.886542	−	0.0178661i
$579$	145.897	+	52.1155i	0.251981	+	0.0900094i
$580$	−820.755	+	33.0942i	−1.41510	+	0.0570589i
$581$	−36.5709	−	136.484i	−0.0629447	−	0.234913i
$582$	−519.221	+	459.325i	−0.892132	+	0.789219i
$583$	−154.256	+	89.0600i	−0.264591	+	0.152762i
$584$	12.2655	+	202.658i	0.0210026	+	0.347017i
$585$	700.465	−	855.367i	1.19738	−	1.46217i
$586$	124.735	+	430.618i	0.212859	+	0.734843i
$587$	720.218	+	192.982i	1.22695	+	0.328759i	0.813390	−	0.581719i	$-0.197620\pi$
$587$	720.218	+	192.982i	1.22695	+	0.328759i	0.413557	+	0.910478i	$0.364286\pi$
$588$	−457.425	−	142.894i	−0.777934	−	0.243016i
$589$	69.3672	+	258.882i	0.117771	+	0.439528i
$590$	−1101.77	+	666.063i	−1.86742	+	1.12892i
$591$	424.939	+	293.772i	0.719017	+	0.497075i
$592$	479.759	+	408.046i	0.810403	+	0.689268i
$593$			496.014i			0.836449i	0.908344	+	0.418224i	$0.137347\pi$
$593$			496.014i			0.836449i	−0.908344	+	0.418224i	$0.862653\pi$
$594$	−95.4595	−	308.702i	−0.160706	−	0.519700i
$595$	400.804	−	400.804i	0.673620	−	0.673620i
$596$	−296.992	−	953.004i	−0.498309	−	1.59900i
$597$	−43.5377	+	7.94581i	−0.0729275	+	0.0133096i
$598$	123.254	+	30.3778i	0.206110	+	0.0507990i
$599$	−485.209	+	840.406i	−0.810032	+	1.40302i	0.102810	+	0.994701i	$0.467217\pi$
$599$	−485.209	+	840.406i	−0.810032	+	1.40302i	−0.912841	+	0.408315i	$0.866117\pi$
$600$	664.597	+	692.881i	1.10766	+	1.15480i
$601$	−313.781	+	181.162i	−0.522099	+	0.301434i	−0.737793	−	0.675027i	$-0.764132\pi$
$601$	−313.781	+	181.162i	−0.522099	+	0.301434i	0.215694	+	0.976461i	$0.430799\pi$
$602$	−123.096	−	424.958i	−0.204478	−	0.705910i
$603$	243.554	+	339.119i	0.403903	+	0.562386i
$604$	780.239	−	493.418i	1.29179	−	0.816918i
$605$	−177.777	+	663.474i	−0.293847	+	1.09665i
$606$	27.8004	−	454.191i	0.0458753	−	0.749491i
$607$	252.276	−	436.954i	0.415611	−	0.719859i	−0.579882	−	0.814701i	$-0.696901\pi$
$607$	252.276	−	436.954i	0.415611	−	0.719859i	0.995492	+	0.0948420i	$0.0302346\pi$
$608$	237.689	−	291.150i	0.390936	−	0.478866i
$609$	−207.916	+	98.4718i	−0.341405	+	0.161694i
$610$	−17.1763	−	852.312i	−0.0281579	−	1.39723i
$611$	492.545	+	492.545i	0.806129	+	0.806129i
$612$	328.390	+	773.835i	0.536585	+	1.26444i
$613$	423.437	+	423.437i	0.690762	+	0.690762i	0.962400	−	0.271637i	$-0.0875651\pi$
$613$	423.437	+	423.437i	0.690762	+	0.690762i	−0.271637	+	0.962400i	$0.587565\pi$
$614$	−112.468	+	117.094i	−0.183172	+	0.190707i
$615$	−144.316	+	1771.58i	−0.234660	+	2.88061i
$616$	−136.707	+	45.6446i	−0.221926	+	0.0740984i
$617$	−209.043	+	362.074i	−0.338806	+	0.586829i	−0.984208	−	0.177013i	$-0.943356\pi$
$617$	−209.043	+	362.074i	−0.338806	+	0.586829i	0.645402	+	0.763843i	$0.276690\pi$
$618$	−103.962	+	310.663i	−0.168223	+	0.502690i
$619$	−198.588	+	741.141i	−0.320821	+	1.19732i	0.597626	+	0.801775i	$0.296111\pi$
$619$	−198.588	+	741.141i	−0.320821	+	1.19732i	−0.918447	+	0.395544i	$0.870556\pi$
$620$	−717.924	−	161.673i	−1.15794	−	0.260762i
$621$	−112.458	+	2.01914i	−0.181092	+	0.00325143i
$622$	−364.180	+	661.196i	−0.585498	+	1.06302i
$623$	−207.194	+	119.624i	−0.332575	+	0.192012i
$624$	633.609	−	365.238i	1.01540	−	0.585317i
$625$	−12.3971	+	21.4724i	−0.0198354	+	0.0343559i
$626$	−443.894	+	268.350i	−0.709095	+	0.428674i
$627$	136.493	+	160.703i	0.217692	+	0.256305i
$628$	−7.30846	−	23.4518i	−0.0116377	−	0.0373436i
$629$	649.954	−	649.954i	1.03331	−	1.03331i
$630$	401.723	+	171.845i	0.637655	+	0.272769i
$631$			371.144i			0.588184i	0.955777	+	0.294092i	$0.0950172\pi$
$631$			371.144i			0.588184i	−0.955777	+	0.294092i	$0.904983\pi$
$632$	−403.274	−	610.125i	−0.638092	−	0.965387i
$633$	24.5950	−	11.6485i	0.0388546	−	0.0184021i
$634$	−69.9615	+	283.859i	−0.110349	+	0.447727i
$635$	−188.850	−	704.797i	−0.297401	−	1.10992i
$636$	301.772	+	191.127i	0.474484	+	0.300514i
$637$	587.732	+	157.482i	0.922657	+	0.247225i
$638$	147.060	−	266.999i	0.230502	−	0.418494i
$639$	691.500	−	261.099i	1.08216	−	0.408606i
$640$	404.585	+	949.385i	0.632164	+	1.48341i
$641$	816.691	−	471.517i	1.27409	−	0.735596i	0.298334	−	0.954462i	$-0.403569\pi$
$641$	816.691	−	471.517i	1.27409	−	0.735596i	0.975755	+	0.218866i	$0.0702357\pi$
$642$	−970.019	−	642.106i	−1.51093	−	1.00016i
$643$	161.607	+	603.124i	0.251332	+	0.937984i	0.970094	+	0.242728i	$0.0780423\pi$
$643$	161.607	+	603.124i	0.251332	+	0.937984i	−0.718762	+	0.695256i	$0.755291\pi$
$644$	2.02124	+	50.1279i	0.00313857	+	0.0778383i
$645$	−319.069	−	1748.29i	−0.494681	−	2.71052i
$646$	−395.605	−	379.975i	−0.612391	−	0.588196i
$647$	842.116			1.30157			0.650785	−	0.759262i	$-0.274440\pi$
$647$	842.116			1.30157			0.650785	+	0.759262i	$0.274440\pi$
$648$	−459.523	+	456.884i	−0.709140	+	0.705067i
$649$		−	477.760i		−	0.736148i
$650$	−879.166	−	844.431i	−1.35256	−	1.29912i
$651$	−202.755	+	37.0036i	−0.311452	+	0.0568412i
$652$	−496.918	+	538.674i	−0.762144	+	0.826188i
$653$	976.873	−	261.752i	1.49598	−	0.400846i	0.584226	−	0.811591i	$-0.301398\pi$
$653$	976.873	−	261.752i	1.49598	−	0.400846i	0.911750	+	0.410745i	$0.134731\pi$
$654$	−803.991	−	532.203i	−1.22934	−	0.813767i
$655$	255.810	+	443.076i	0.390549	+	0.676452i
$656$	−503.999	+	1062.28i	−0.768292	+	1.61933i
$657$	80.6831	+	213.682i	0.122805	+	0.325240i
$658$	−132.813	+	241.131i	−0.201843	+	0.366461i
$659$	−217.660	+	812.320i	−0.330289	+	1.23266i	0.578598	+	0.815613i	$0.303600\pi$
$659$	−217.660	+	812.320i	−0.330289	+	1.23266i	−0.908887	+	0.417042i	$0.863067\pi$
$660$	−564.873	+	126.801i	−0.855869	+	0.192123i
$661$	−98.6689	+	26.4383i	−0.149272	+	0.0399974i	−0.332681	−	0.943039i	$-0.607953\pi$
$661$	−98.6689	+	26.4383i	−0.149272	+	0.0399974i	0.183409	+	0.983037i	$0.441287\pi$
$662$	178.879	−	725.778i	0.270210	−	1.09634i
$663$	−456.857	−	964.621i	−0.689076	−	1.45493i
$664$	75.0874	−	367.867i	0.113083	−	0.554017i
$665$	−285.109			−0.428735
$666$	651.444	+	278.668i	0.978145	+	0.418420i
$667$	−75.0273	−	75.0273i	−0.112485	−	0.112485i
$668$	−525.639	+	1001.58i	−0.786884	+	1.49937i
$669$	933.778	−	793.103i	1.39578	−	1.18551i
$670$	640.162	−	387.002i	0.955466	−	0.577614i
$671$	273.965	+	158.174i	0.408293	+	0.235728i
$672$	208.316	+	200.359i	0.309994	+	0.298154i
$673$	−345.603	−	598.603i	−0.513527	−	0.889454i	−0.999877	−	0.0156903i	$-0.995005\pi$
$673$	−345.603	−	598.603i	−0.513527	−	0.889454i	0.486350	−	0.873764i	$-0.338328\pi$
$674$	−36.6989	+	66.6296i	−0.0544494	+	0.0988570i
$675$	944.939	+	523.172i	1.39991	+	0.775069i
$676$	−213.469	+	134.997i	−0.315783	+	0.199699i
$677$	−788.942	−	211.396i	−1.16535	−	0.312255i	−0.376250	−	0.926518i	$-0.622787\pi$
$677$	−788.942	−	211.396i	−1.16535	−	0.312255i	−0.789101	+	0.614264i	$0.789453\pi$
$678$	−25.0070	+	74.7267i	−0.0368835	+	0.110216i
$679$	301.254	+	173.929i	0.443673	+	0.256155i
$680$	1428.60	−	476.992i	2.10088	−	0.701459i
$681$	123.264	+	10.0413i	0.181005	+	0.0147450i
$682$	189.170	−	196.951i	0.277375	−	0.288785i
$683$	−722.723	+	722.723i	−1.05816	+	1.05816i	−0.0599580	+	0.998201i	$0.519097\pi$
$683$	−722.723	+	722.723i	−1.05816	+	1.05816i	−0.998201	+	0.0599580i	$0.980903\pi$
$684$	158.432	−	392.030i	0.231626	−	0.573143i
$685$	842.028	−	842.028i	1.22924	−	1.22924i
$686$	10.7900	+	535.416i	0.0157289	+	0.780489i
$687$	−28.1165	−	59.3659i	−0.0409265	−	0.0864133i
$688$	211.853	−	1156.35i	0.307927	−	1.68074i
$689$	−392.776	−	226.770i	−0.570067	−	0.329128i
$690$	−12.3117	+	201.143i	−0.0178431	+	0.291512i
$691$	−1030.30	−	276.067i	−1.49102	−	0.399518i	−0.580939	−	0.813947i	$-0.697315\pi$
$691$	−1030.30	−	276.067i	−1.49102	−	0.399518i	−0.910082	+	0.414429i	$0.863981\pi$
$692$	198.339	−	880.744i	0.286617	−	1.27275i
$693$	−131.696	+	94.5833i	−0.190037	+	0.136484i
$694$	−87.6346	−	302.537i	−0.126275	−	0.435932i
$695$	−357.959	−	620.004i	−0.515049	−	0.892092i
$696$	−611.159	−	12.7339i	−0.878102	−	0.0182958i
$697$	1486.07	+	857.983i	2.13210	+	1.23097i
$698$	406.043	+	100.076i	0.581723	+	0.143375i
$699$	21.4639	+	117.608i	0.0307066	+	0.168252i
$700$	223.878	−	426.587i	0.319825	−	0.609410i
$701$	55.9778	+	55.9778i	0.0798542	+	0.0798542i	0.745906	−	0.666052i	$-0.232017\pi$
$701$	55.9778	+	55.9778i	0.0798542	+	0.0798542i	−0.666052	+	0.745906i	$0.732017\pi$
$702$	559.193	−	603.517i	0.796572	−	0.859711i
$703$	−462.340			−0.657667
$704$	−379.167	−	53.7810i	−0.538590	−	0.0763935i
$705$	−628.824	+	909.591i	−0.891949	+	1.29020i
$706$	196.547	−	118.820i	0.278395	−	0.168300i
$707$	−220.556	+	59.0977i	−0.311960	+	0.0835894i
$708$	−848.678	+	444.657i	−1.19870	+	0.628047i
$709$	152.692	−	569.856i	0.215363	−	0.803746i	−0.770675	−	0.637228i	$-0.780081\pi$
$709$	152.692	−	569.856i	0.215363	−	0.803746i	0.986038	−	0.166518i	$-0.0532524\pi$
$710$	−368.461	−	1272.02i	−0.518959	−	1.79158i
$711$	−636.568	−	521.289i	−0.895313	−	0.733177i
$712$	−634.554	+	38.4054i	−0.891227	+	0.0539401i
$713$	−47.5290	−	82.3226i	−0.0666606	−	0.115459i
$714$	315.939	−	279.493i	0.442491	−	0.391447i
$715$	710.014	−	190.248i	0.993027	−	0.266081i
$716$	159.499	+	147.135i	0.222764	+	0.205496i
$717$	−222.639	+	623.276i	−0.310515	+	0.869283i
$718$	−405.170	+	8.16524i	−0.564304	+	0.0113722i
$719$			43.5371i			0.0605523i	0.999542	+	0.0302762i	$0.00963868\pi$
$719$			43.5371i			0.0605523i	−0.999542	+	0.0302762i	$0.990361\pi$
$720$	750.980	+	885.408i	1.04303	+	1.22973i
$721$	164.385			0.227996
$722$	−8.98811	−	446.002i	−0.0124489	−	0.617731i
$723$	20.7144	−	17.5938i	0.0286506	−	0.0243344i
$724$	84.9971	+	78.4083i	0.117399	+	0.108299i
$725$	263.715	+	984.196i	0.363744	+	1.35751i
$726$	−162.218	+	484.743i	−0.223440	+	0.667690i
$727$	−182.291	+	105.246i	−0.250745	+	0.144768i	−0.620105	−	0.784519i	$-0.712910\pi$
$727$	−182.291	+	105.246i	−0.250745	+	0.144768i	0.369360	+	0.929286i	$0.379577\pi$
$728$	−274.697	−	243.344i	−0.377331	−	0.334263i
$729$	−341.602	+	644.010i	−0.468590	+	0.883416i
$730$	393.071	−	113.859i	0.538453	−	0.155972i
$731$	−1657.23	−	444.054i	−2.26708	−	0.607461i
$732$	25.9924	−	633.876i	0.0355087	−	0.865951i
$733$	214.507	+	800.550i	0.292642	+	1.09216i	0.943072	+	0.332589i	$0.107922\pi$
$733$	214.507	+	800.550i	0.292642	+	1.09216i	−0.650429	+	0.759567i	$0.725411\pi$
$734$	−410.422	−	678.904i	−0.559159	−	0.924937i
$735$	−78.4270	+	962.747i	−0.106703	+	1.30986i
$736$	−54.7032	+	121.564i	−0.0743250	+	0.165169i
$737$			277.592i			0.376652i
$738$	−187.743	+	1309.36i	−0.254394	+	1.77420i
$739$	−423.799	+	423.799i	−0.573476	+	0.573476i	−0.933098	−	0.359622i	$-0.882906\pi$
$739$	−423.799	+	423.799i	−0.573476	+	0.573476i	0.359622	+	0.933098i	$0.382906\pi$
$740$	589.928	−	1124.08i	0.797201	−	1.51902i
$741$	−180.597	+	505.579i	−0.243720	+	0.682293i
$742$	42.8936	−	174.035i	0.0578081	−	0.234548i
$743$	−270.936	+	469.275i	−0.364652	+	0.631596i	−0.988720	−	0.149774i	$-0.952145\pi$
$743$	−270.936	+	469.275i	−0.364652	+	0.631596i	0.624068	+	0.781370i	$0.285479\pi$
$744$	−525.921	−	152.731i	−0.706883	−	0.205283i
$745$	−1742.45	+	1006.01i	−2.33886	+	1.35034i
$746$	700.661	−	202.958i	0.939224	−	0.272061i
$747$	−41.8464	−	420.306i	−0.0560193	−	0.562658i
$748$	−122.788	+	545.251i	−0.164155	+	0.728946i
$749$	−151.080	+	563.838i	−0.201709	+	0.752787i
$750$	400.626	−	605.220i	0.534169	−	0.806960i
$751$	615.386	−	1065.88i	0.819422	−	1.41928i	−0.0866868	−	0.996236i	$-0.527628\pi$
$751$	615.386	−	1065.88i	0.819422	−	1.41928i	0.906109	−	0.423045i	$-0.139039\pi$
$752$	−601.978	+	415.556i	−0.800502	+	0.552601i
$753$	−51.9571	−	35.9193i	−0.0690002	−	0.0477016i
$754$	775.992	−	15.6383i	1.02917	−	0.0207404i
$755$	−1315.75	−	1315.75i	−1.74272	−	1.74272i
$756$	290.585	+	145.910i	0.384372	+	0.193003i
$757$	−41.7353	−	41.7353i	−0.0551326	−	0.0551326i	0.679003	−	0.734136i	$-0.262412\pi$
$757$	−41.7353	−	41.7353i	−0.0551326	−	0.0551326i	−0.734136	+	0.679003i	$0.762412\pi$
$758$	−594.245	−	570.767i	−0.783964	−	0.752991i
$759$	−61.5131	−	42.5256i	−0.0810449	−	0.0560285i
$760$	−677.765	−	338.460i	−0.891796	−	0.445342i
$761$	56.7643	−	98.3187i	0.0745917	−	0.129197i	−0.826317	−	0.563205i	$-0.809568\pi$
$761$	56.7643	−	98.3187i	0.0745917	−	0.129197i	0.900909	+	0.434009i	$0.142901\pi$
$762$	−108.233	−	532.107i	−0.142038	−	0.698303i
$763$	−125.221	+	467.332i	−0.164117	+	0.612492i
$764$	266.713	−	168.668i	0.349101	−	0.220769i
$765$	1376.24	−	988.407i	1.79900	−	1.29203i
$766$	34.2779	+	18.8799i	0.0447492	+	0.0246474i
$767$	1053.52	−	608.250i	1.37356	−	0.793025i
$768$	257.360	+	723.595i	0.335105	+	0.942181i
$769$	348.676	−	603.925i	0.453415	−	0.785338i	−0.545180	−	0.838319i	$-0.683539\pi$
$769$	348.676	−	603.925i	0.453415	−	0.785338i	0.998596	+	0.0529807i	$0.0168722\pi$
$770$	150.291	+	248.605i	0.195183	+	0.322863i
$771$	−185.377	+	518.961i	−0.240437	+	0.673102i
$772$	95.9924	−	182.908i	0.124342	−	0.236928i
$773$	−380.830	+	380.830i	−0.492665	+	0.492665i	−0.909145	−	0.416480i	$-0.863264\pi$
$773$	−380.830	+	380.830i	−0.492665	+	0.492665i	0.416480	+	0.909145i	$0.363264\pi$
$774$	−157.517	−	1313.13i	−0.203510	−	1.69655i
$775$			912.834i			1.17785i
$776$	509.669	+	771.093i	0.656790	+	0.993676i
$777$	28.8674	−	354.368i	0.0371524	−	0.456072i
$778$	287.343	+	70.8203i	0.369336	+	0.0910287i
$779$	−223.393	−	833.713i	−0.286768	−	1.07023i
$780$	−998.769	−	1084.18i	−1.28047	−	1.38998i
$781$	474.691	+	127.193i	0.607799	+	0.162859i
$782$	170.411	+	93.8603i	0.217916	+	0.120026i
$783$	−660.968	+	189.887i	−0.844148	+	0.242512i
$784$	−273.894	+	577.287i	−0.349354	+	0.736335i
$785$	−42.8788	+	24.7561i	−0.0546226	+	0.0315364i
$786$	169.870	+	340.746i	0.216120	+	0.433519i
$787$	40.4632	+	151.011i	0.0514145	+	0.191882i	0.986857	−	0.161598i	$-0.0516649\pi$
$787$	40.4632	+	151.011i	0.0514145	+	0.191882i	−0.935442	+	0.353480i	$0.884998\pi$
$788$	467.036	−	506.282i	0.592685	−	0.642490i
$789$	624.202	−	530.165i	0.791130	−	0.671945i
$790$	−1021.16	+	1063.16i	−1.29261	+	1.34578i
$791$	39.5412			0.0499888
$792$	−425.351	+	68.5053i	−0.537060	+	0.0864966i
$793$			805.501i			1.01576i
$794$	179.739	−	187.132i	0.226372	−	0.235683i
$795$	242.198	−	678.032i	0.304652	−	0.852870i
$796$	2.37741	+	58.9613i	0.00298670	+	0.0740719i
$797$	40.7309	−	10.9138i	0.0511052	−	0.0136936i	−0.233176	−	0.972435i	$-0.574912\pi$
$797$	40.7309	−	10.9138i	0.0511052	−	0.0136936i	0.284281	+	0.958741i	$0.408245\pi$
$798$	−211.778	−	12.9626i	−0.265386	−	0.0162439i
$799$	533.772	+	924.520i	0.668050	+	1.15710i
$800$	1038.62	−	748.318i	1.29827	−	0.935397i
$801$	−669.073	+	252.631i	−0.835297	+	0.315395i
$802$	−431.589	−	237.715i	−0.538141	−	0.296402i
$803$	−39.3043	+	146.686i	−0.0489468	+	0.182672i
$804$	493.106	−	258.358i	0.613316	−	0.321341i
$805$	97.6754	−	26.1720i	0.121336	−	0.0325118i
$806$	675.140	+	166.399i	0.837642	+	0.206450i
$807$	443.290	−	641.216i	0.549306	−	0.794568i
$808$	−594.465	−	121.340i	−0.735724	−	0.150173i
$809$	−478.319			−0.591248			−0.295624	−	0.955304i	$-0.595528\pi$
$809$	−478.319			−0.591248			−0.295624	+	0.955304i	$0.595528\pi$
$810$	1101.89	+	701.280i	1.36036	+	0.865778i
$811$	−677.084	−	677.084i	−0.834876	−	0.834876i	0.153304	−	0.988179i	$-0.451009\pi$
$811$	−677.084	−	677.084i	−0.834876	−	0.834876i	−0.988179	+	0.153304i	$0.951009\pi$
$812$	91.2631	+	292.850i	0.112393	+	0.360653i
$813$	−147.791	−	809.797i	−0.181785	−	0.996060i
$814$	243.716	+	403.144i	0.299405	+	0.495263i
$815$	1279.28	+	738.594i	1.56967	+	0.906250i
$816$	1082.85	−	289.356i	1.32702	−	0.354603i
$817$	431.493	+	747.368i	0.528143	+	0.914771i
$818$	−1114.73	−	613.983i	−1.36275	−	0.750590i
$819$	−376.233	−	169.989i	−0.459381	−	0.207556i
$820$	2312.03	+	520.656i	2.81955	+	0.634947i
$821$	−1056.63	−	283.124i	−1.28701	−	0.344852i	−0.450484	−	0.892784i	$-0.648749\pi$
$821$	−1056.63	−	283.124i	−1.28701	−	0.344852i	−0.836523	+	0.547932i	$0.815415\pi$
$822$	663.739	−	587.172i	0.807468	−	0.714321i
$823$	−242.222	−	139.847i	−0.294316	−	0.169924i	0.345571	−	0.938393i	$-0.387685\pi$
$823$	−242.222	−	139.847i	−0.294316	−	0.169924i	−0.639887	+	0.768469i	$0.721019\pi$
$824$	390.779	+	195.146i	0.474246	+	0.236828i
$825$	307.380	+	649.011i	0.372582	+	0.786680i
$826$	346.737	+	333.038i	0.419779	+	0.403194i
$827$	569.091	−	569.091i	0.688139	−	0.688139i	−0.273681	−	0.961820i	$-0.588241\pi$
$827$	569.091	−	569.091i	0.688139	−	0.688139i	0.961820	+	0.273681i	$0.0882414\pi$
$828$	−18.2902	+	148.849i	−0.0220896	+	0.179769i
$829$	−80.7363	+	80.7363i	−0.0973900	+	0.0973900i	−0.754123	−	0.656733i	$-0.771938\pi$
$829$	−80.7363	+	80.7363i	−0.0973900	+	0.0973900i	0.656733	+	0.754123i	$0.271938\pi$
$830$	−756.616	+	15.2478i	−0.911586	+	0.0183708i
$831$	−488.819	−	39.8200i	−0.588229	−	0.0479182i
$832$	−364.134	−	904.580i	−0.437662	−	1.08724i
$833$	807.591	+	466.263i	0.969497	+	0.559739i
$834$	−237.702	−	476.812i	−0.285015	−	0.571717i
$835$	2202.24	+	590.089i	2.63741	+	0.706693i
$836$	237.602	−	150.258i	0.284213	−	0.179735i
$837$	−616.006	+	11.0601i	−0.735969	+	0.0132140i
$838$	−121.048	+	35.0634i	−0.144448	+	0.0418417i
$839$	289.410	+	501.274i	0.344947	+	0.597465i	0.985344	−	0.170578i	$-0.0545636\pi$
$839$	289.410	+	501.274i	0.344947	+	0.597465i	−0.640397	+	0.768044i	$0.721230\pi$
$840$	301.736	−	498.351i	0.359210	−	0.593275i
$841$	166.497	+	96.1272i	0.197975	+	0.114301i
$842$	−208.964	+	847.841i	−0.248175	+	1.00694i
$843$	1212.47	−	1029.81i	1.43828	−	1.22160i
$844$	−10.7958	−	34.6421i	−0.0127912	−	0.0410452i
$845$	359.983	+	359.983i	0.426015	+	0.426015i
$846$	−508.444	+	647.051i	−0.600997	+	0.764836i
$847$	256.499			0.302832
$848$	308.568	−	362.798i	0.363878	−	0.427827i
$849$	−297.251	−	627.624i	−0.350119	−	0.739250i
$850$	−966.531	−	1598.80i	−1.13710	−	1.88094i
$851$	158.393	−	42.4413i	0.186126	−	0.0498722i
$852$	−215.859	−	961.605i	−0.253355	−	1.12864i
$853$	272.983	−	1018.79i	0.320027	−	1.19436i	−0.599191	−	0.800606i	$-0.704511\pi$
$853$	272.983	−	1018.79i	0.320027	−	1.19436i	0.919218	−	0.393750i	$-0.128822\pi$
$854$	−305.771	+	88.5715i	−0.358046	+	0.103714i
$855$	−841.035	−	137.940i	−0.983667	−	0.161333i
$856$	−1028.50	+	1161.01i	−1.20151	+	1.35632i
$857$	−217.412	−	376.568i	−0.253689	−	0.439403i	0.710849	−	0.703344i	$-0.248311\pi$
$857$	−217.412	−	376.568i	−0.253689	−	0.439403i	−0.964539	+	0.263942i	$0.914977\pi$
$858$	536.046	−	109.034i	0.624762	−	0.127079i
$859$	−494.627	+	132.535i	−0.575817	+	0.154290i	−0.534963	−	0.844875i	$-0.679675\pi$
$859$	−494.627	+	132.535i	−0.575817	+	0.154290i	−0.0408540	+	0.999165i	$0.513008\pi$
$860$	−2367.63	+	95.4665i	−2.75306	+	0.111008i
$861$	652.961	−	119.168i	0.758375	−	0.138406i
$862$	20.6807	+	1026.21i	0.0239916	+	1.19049i
$863$		−	793.043i		−	0.918938i	−0.888194	−	0.459469i	$-0.848040\pi$
$863$		−	793.043i		−	0.918938i	0.888194	−	0.459469i	$-0.151960\pi$
$864$	517.570	+	691.822i	0.599039	+	0.800720i
$865$	−1819.70			−2.10370
$866$	583.921	−	11.7675i	0.674274	−	0.0135884i
$867$	−138.027	−	756.296i	−0.159201	−	0.872313i
$868$	11.0716	+	274.583i	0.0127553	+	0.316339i
$869$	−141.583	−	528.395i	−0.162926	−	0.608050i
$870$	245.592	+	1207.41i	0.282290	+	1.38783i
$871$	−612.125	+	353.410i	−0.702784	+	0.405752i
$872$	−852.459	+	962.295i	−0.977591	+	1.10355i
$873$	804.512	+	658.820i	0.921548	+	0.754662i
$874$	−27.2267	−	93.9936i	−0.0311519	−	0.107544i
$875$	−351.793	−	94.2627i	−0.402049	−	0.107729i
$876$	297.148	−	66.7031i	0.339211	−	0.0761451i
$877$	136.381	+	508.981i	0.155509	+	0.580366i	0.999061	+	0.0433195i	$0.0137933\pi$
$877$	136.381	+	508.981i	0.155509	+	0.580366i	−0.843553	+	0.537046i	$0.819540\pi$
$878$	−239.414	+	144.734i	−0.272681	+	0.164846i
$879$	607.762	−	287.845i	0.691425	−	0.327468i
$880$	62.1480	+	769.401i	0.0706228	+	0.874320i
$881$		−	526.136i		−	0.597204i	−0.954378	−	0.298602i	$-0.903480\pi$
$881$		−	526.136i		−	0.597204i	0.954378	−	0.298602i	$-0.0965202\pi$
$882$	−102.027	+	711.559i	−0.115677	+	0.806757i
$883$	525.594	−	525.594i	0.595237	−	0.595237i	−0.343804	−	0.939041i	$-0.611716\pi$
$883$	525.594	−	525.594i	0.595237	−	0.595237i	0.939041	+	0.343804i	$0.111716\pi$
$884$	−1358.67	+	423.413i	−1.53696	+	0.478974i
$885$	1250.17	+	1471.92i	1.41263	+	1.66319i
$886$	−1018.19	−	250.949i	−1.14920	−	0.283238i
$887$	−103.642	+	179.513i	−0.116846	+	0.202383i	−0.918516	−	0.395384i	$-0.870612\pi$
$887$	−103.642	+	179.513i	−0.116846	+	0.202383i	0.801670	+	0.597766i	$0.203945\pi$
$888$	489.304	−	808.140i	0.551018	−	0.910067i
$889$	−235.970	+	136.237i	−0.265433	+	0.153248i
$890$	356.511	+	1230.77i	0.400574	+	1.38288i
$891$	−434.247	+	215.293i	−0.487370	+	0.241630i
$892$	−873.088	−	1380.61i	−0.978798	−	1.54777i
$893$	138.978	−	518.672i	0.155630	−	0.580820i
$894$	−1340.03	+	668.037i	−1.49891	+	0.747245i
$895$	218.694	−	378.790i	0.244351	−	0.423229i
$896$	303.343	−	237.693i	0.338552	−	0.265282i
$897$	15.4602	−	189.784i	0.0172354	−	0.211577i
$898$	−33.9773	−	1686.00i	−0.0378367	−	1.87751i
$899$	−410.973	−	410.973i	−0.457145	−	0.457145i
$900$	866.800	−	1150.06i	0.963111	−	1.27785i
$901$	−491.501	−	491.501i	−0.545506	−	0.545506i
$902$	−609.210	+	634.270i	−0.675399	+	0.703181i
$903$	−599.774	+	284.061i	−0.664201	+	0.314575i
$904$	93.9978	+	46.9404i	0.103980	+	0.0519252i
$905$	116.542	−	201.857i	0.128776	−	0.223046i
$906$	−917.515	−	1037.16i	−1.01271	−	1.14477i
$907$	67.3421	−	251.324i	0.0742470	−	0.277094i	−0.918814	−	0.394690i	$-0.870852\pi$
$907$	67.3421	−	251.324i	0.0742470	−	0.277094i	0.993062	+	0.117596i	$0.0375188\pi$
$908$	36.2267	−	160.868i	0.0398973	−	0.177168i
$909$	−679.204	+	67.6229i	−0.747199	+	0.0743926i
$910$	−356.865	+	647.915i	−0.392159	+	0.711995i
$911$	−713.768	+	412.094i	−0.783500	+	0.452354i	−0.837669	−	0.546178i	$-0.816082\pi$
$911$	−713.768	+	412.094i	−0.783500	+	0.452354i	0.0541694	+	0.998532i	$0.482749\pi$
$912$	−488.053	−	282.222i	−0.535146	−	0.309454i
$913$	140.414	−	243.204i	0.153794	−	0.266379i
$914$	−282.217	+	170.611i	−0.308772	+	0.186664i
$915$	−1257.95	+	229.581i	−1.37481	+	0.250908i
$916$	−83.6170	+	26.0582i	−0.0912850	+	0.0284478i
$917$	135.095	−	135.095i	0.147322	−	0.147322i
$918$	1067.20	−	671.614i	1.16253	−	0.731606i
$919$			443.203i			0.482267i	0.970492	+	0.241133i	$0.0775191\pi$
$919$			443.203i			0.482267i	−0.970492	+	0.241133i	$0.922481\pi$
$920$	263.265	+	53.7365i	0.286157	+	0.0584092i
$921$	200.326	+	138.491i	0.217509	+	0.150370i
$922$	−218.250	+	885.517i	−0.236713	+	0.960431i
$923$	323.866	+	1208.68i	0.350884	+	1.30952i
$924$	100.333	+	191.496i	0.108585	+	0.207247i
$925$	−1521.03	−	407.560i	−1.64436	−	0.440605i
$926$	212.436	−	385.695i	0.229413	−	0.416517i
$927$	484.916	+	79.5319i	0.523102	+	0.0857949i
$928$	−130.698	+	804.508i	−0.140838	+	0.866927i
$929$	45.8533	−	26.4734i	0.0493577	−	0.0284967i	−0.475118	−	0.879922i	$-0.657595\pi$
$929$	45.8533	−	26.4734i	0.0493577	−	0.0284967i	0.524476	+	0.851425i	$0.324261\pi$
$930$	−67.4392	+	1101.79i	−0.0725152	+	1.18472i
$931$	−121.401	−	453.073i	−0.130398	−	0.486652i
$932$	159.271	−	6.42208i	0.170892	−	0.00689064i
$933$	1066.30	+	380.890i	1.14287	+	0.408242i
$934$	574.103	+	551.420i	0.614671	+	0.590386i
$935$	1126.54			1.20486
$936$	−692.589	−	850.736i	−0.739946	−	0.908906i
$937$		−	1456.88i		−	1.55484i	−0.628983	−	0.777419i	$-0.716529\pi$
$937$		−	1456.88i		−	1.55484i	0.628983	−	0.777419i	$-0.283471\pi$
$938$	−201.464	−	193.505i	−0.214781	−	0.206295i
$939$	503.682	+	593.021i	0.536403	+	0.631546i
$940$	1083.71	+	999.700i	1.15288	+	1.06351i
$941$	46.6568	−	12.5017i	0.0495822	−	0.0132855i	−0.233943	−	0.972250i	$-0.575163\pi$
$941$	46.6568	−	12.5017i	0.0495822	−	0.0132855i	0.283525	+	0.958965i	$0.408496\pi$
$942$	−32.9758	+	16.4392i	−0.0350061	+	0.0174514i
$943$	153.064	+	265.115i	0.162316	+	0.281140i
$944$	428.911	+	1203.32i	0.454355	+	1.27471i
$945$	158.238	−	636.013i	0.167448	−	0.673029i
$946$	424.223	−	770.210i	0.448439	−	0.814176i
$947$	447.800	−	1671.21i	0.472861	−	1.76474i	−0.156549	−	0.987670i	$-0.550037\pi$
$947$	447.800	−	1671.21i	0.472861	−	1.76474i	0.629411	−	0.777073i	$-0.283296\pi$
$948$	−806.852	+	743.287i	−0.851109	+	0.784058i
$949$	−373.499	+	100.079i	−0.393571	+	0.105457i
$950$	−224.879	+	912.414i	−0.236714	+	0.960435i
$951$	437.082	+	35.6055i	0.459603	+	0.0374401i
$952$	−310.127	−	469.199i	−0.325763	−	0.492856i
$953$	314.313			0.329814			0.164907	−	0.986309i	$-0.447268\pi$
$953$	314.313			0.329814			0.164907	+	0.986309i	$0.447268\pi$
$954$	210.731	−	492.628i	0.220892	−	0.516382i
$955$	−449.770	−	449.770i	−0.470963	−	0.470963i
$956$	781.391	+	410.083i	0.817355	+	0.428957i
$957$	−430.584	−	153.808i	−0.449931	−	0.160719i
$958$	634.881	−	383.809i	0.662715	−	0.400636i
$959$	−385.104	−	222.340i	−0.401568	−	0.231845i
$960$	1308.90	−	826.489i	1.36344	−	0.860926i
$961$	220.153	+	381.316i	0.229088	+	0.396791i
$962$	−578.701	+	1050.68i	−0.601561	+	1.09218i
$963$	−718.460	+	1590.16i	−0.746064	+	1.65125i
$964$	−19.3681	−	30.6266i	−0.0200914	−	0.0317704i
$965$	−402.174	−	107.762i	−0.416761	−	0.111671i
$966$	73.7429	−	14.9996i	0.0763384	−	0.0155276i
$967$	1491.50	+	861.116i	1.54240	+	0.890503i	0.998687	+	0.0512290i	$0.0163138\pi$
$967$	1491.50	+	861.116i	1.54240	+	0.890503i	0.543709	+	0.839274i	$0.317019\pi$
$968$	609.753	+	304.497i	0.629910	+	0.314563i
$969$	−467.893	+	676.805i	−0.482862	+	0.698457i
$970$	1290.57	−	1343.66i	1.33048	−	1.38521i
$971$	695.679	−	695.679i	0.716456	−	0.716456i	−0.251422	−	0.967878i	$-0.580898\pi$
$971$	695.679	−	695.679i	0.716456	−	0.716456i	0.967878	+	0.251422i	$0.0808981\pi$
$972$	786.597	+	571.007i	0.809257	+	0.587455i
$973$	−189.040	+	189.040i	−0.194286	+	0.194286i
$974$	5.82273	+	288.932i	0.00597816	+	0.296644i
$975$	−1039.81	+	1504.09i	−1.06648	+	1.54265i
$976$	−832.030	−	152.436i	−0.852489	−	0.156184i
$977$	−360.870	−	208.348i	−0.369365	−	0.213253i	0.303816	−	0.952731i	$-0.401739\pi$
$977$	−360.870	−	208.348i	−0.369365	−	0.213253i	−0.673181	+	0.739478i	$0.735073\pi$
$978$	916.666	+	606.788i	0.937286	+	0.620438i
$979$	−459.296	−	123.068i	−0.469148	−	0.125708i
$980$	1256.45	+	282.946i	1.28209	+	0.288720i
$981$	−595.489	+	1317.99i	−0.607022	+	1.34351i
$982$	−16.5552	−	57.1529i	−0.0168587	−	0.0582005i
$983$	−205.834	−	356.515i	−0.209394	−	0.362680i	0.742130	−	0.670256i	$-0.233816\pi$
$983$	−205.834	−	356.515i	−0.209394	−	0.362680i	−0.951524	+	0.307576i	$0.900482\pi$
$984$	1693.70	+	491.859i	1.72124	+	0.499857i
$985$	−1202.35	−	694.179i	−1.22066	−	0.704751i
$986$	1154.95	+	284.656i	1.17135	+	0.288698i
$987$	388.868	+	138.907i	0.393989	+	0.140736i
$988$	633.836	+	332.644i	0.641535	+	0.336685i
$989$	−216.431	−	216.431i	−0.218838	−	0.218838i
$990$	323.060	+	806.066i	0.326324	+	0.814208i
$991$	556.918			0.561976			0.280988	−	0.959711i	$-0.409338\pi$
$991$	556.918			0.561976			0.280988	+	0.959711i	$0.409338\pi$
$992$	−299.645	+	665.885i	−0.302061	+	0.671255i
$993$	−1117.54	−	91.0370i	−1.12542	−	0.0916787i
$994$	−423.210	+	255.846i	−0.425764	+	0.257390i
$995$	114.887	−	30.7840i	0.115465	−	0.0309387i
$996$	−562.705	−	23.0740i	−0.564965	−	0.0231666i
$997$	−165.464	+	617.519i	−0.165962	+	0.619377i	0.831954	+	0.554845i	$0.187222\pi$
$997$	−165.464	+	617.519i	−0.165962	+	0.619377i	−0.997916	+	0.0645326i	$0.979444\pi$
$998$	251.386	+	867.849i	0.251890	+	0.869589i
$999$	256.604	−	1031.38i	0.256861	−	1.03241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.w.a.5.1	✓	184
3.2	odd	2		432.3.x.a.341.46		184
9.2	odd	6	inner	144.3.w.a.101.16	yes	184
9.7	even	3		432.3.x.a.197.31		184
16.13	even	4	inner	144.3.w.a.77.16	yes	184
48.29	odd	4		432.3.x.a.125.31		184
144.29	odd	12	inner	144.3.w.a.29.1	yes	184
144.61	even	12		432.3.x.a.413.46		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.1	✓	184	1.1	even	1	trivial
144.3.w.a.29.1	yes	184	144.29	odd	12	inner
144.3.w.a.77.16	yes	184	16.13	even	4	inner
144.3.w.a.101.16	yes	184	9.2	odd	6	inner
432.3.x.a.125.31		184	48.29	odd	4
432.3.x.a.197.31		184	9.7	even	3
432.3.x.a.341.46		184	3.2	odd	2
432.3.x.a.413.46		184	144.61	even	12

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99959 + 0.0402970i) q^{2} +(0.538615 + 2.95125i) q^{3} +(3.99675 - 0.161155i) q^{4} +(-2.08673 - 7.78777i) q^{5} +(-1.19594 - 5.87960i) q^{6} +(-2.60739 + 1.50538i) q^{7} +(-7.98539 + 0.483303i) q^{8} +(-8.41979 + 3.17918i) q^{9} +O(q^{10})\)	\(q+(-1.99959 + 0.0402970i) q^{2} +(0.538615 + 2.95125i) q^{3} +(3.99675 - 0.161155i) q^{4} +(-2.08673 - 7.78777i) q^{5} +(-1.19594 - 5.87960i) q^{6} +(-2.60739 + 1.50538i) q^{7} +(-7.98539 + 0.483303i) q^{8} +(-8.41979 + 3.17918i) q^{9} +(4.48643 + 15.4883i) q^{10} +(-5.77989 - 1.54872i) q^{11} +(2.62832 + 11.7086i) q^{12} +(-3.94343 - 14.7171i) q^{13} +(5.15305 - 3.11521i) q^{14} +(21.8597 - 10.3531i) q^{15} +(15.9481 - 1.28820i) q^{16} -23.3509i q^{17} +(16.7080 - 6.69636i) q^{18} +(-8.30523 + 8.30523i) q^{19} +(-9.59517 - 30.7895i) q^{20} +(-5.84712 - 6.88424i) q^{21} +(11.6198 + 2.86389i) q^{22} +(2.08290 - 3.60768i) q^{23} +(-5.72740 - 23.3066i) q^{24} +(-34.6443 + 20.0019i) q^{25} +(8.47832 + 29.2693i) q^{26} +(-13.9176 - 23.1366i) q^{27} +(-10.1785 + 6.43681i) q^{28} +(6.59225 - 24.6026i) q^{29} +(-43.2934 + 21.5828i) q^{30} +(11.4094 - 19.7616i) q^{31} +(-31.8377 + 3.21853i) q^{32} +(1.45752 - 17.8921i) q^{33} +(0.940971 + 46.6922i) q^{34} +(17.1644 + 17.1644i) q^{35} +(-33.1395 + 14.0633i) q^{36} +(27.8343 + 27.8343i) q^{37} +(16.2724 - 16.9418i) q^{38} +(41.3099 - 19.5649i) q^{39} +(20.4272 + 61.1798i) q^{40} +(-36.7431 + 63.6409i) q^{41} +(11.9693 + 13.5301i) q^{42} +(19.0166 - 70.9710i) q^{43} +(-23.3504 - 5.25838i) q^{44} +(42.3285 + 58.9373i) q^{45} +(-4.01957 + 7.29783i) q^{46} +(-39.5925 + 22.8588i) q^{47} +(12.3917 + 46.3729i) q^{48} +(-19.9677 + 34.5851i) q^{49} +(68.4684 - 41.3917i) q^{50} +(68.9143 - 12.5771i) q^{51} +(-18.1327 - 58.1850i) q^{52} +(21.0485 - 21.0485i) q^{53} +(28.7619 + 45.7029i) q^{54} +48.2442i q^{55} +(20.0934 - 13.2812i) q^{56} +(-28.9842 - 20.0375i) q^{57} +(-12.1904 + 49.4609i) q^{58} +(20.6648 + 77.1219i) q^{59} +(85.6995 - 44.9014i) q^{60} +(-51.0660 - 13.6831i) q^{61} +(-22.0177 + 39.9749i) q^{62} +(17.1678 - 20.9643i) q^{63} +(63.5328 - 7.71872i) q^{64} +(-106.384 + 61.4211i) q^{65} +(-2.19345 + 35.8356i) q^{66} +(-12.0068 - 44.8100i) q^{67} +(-3.76312 - 93.3276i) q^{68} +(11.7691 + 4.20400i) q^{69} +(-35.0135 - 33.6302i) q^{70} -82.1279 q^{71} +(65.6988 - 29.4563i) q^{72} -25.3786i q^{73} +(-56.7789 - 54.5356i) q^{74} +(-77.6905 - 91.4707i) q^{75} +(-31.8555 + 34.5324i) q^{76} +(17.4018 - 4.66280i) q^{77} +(-81.8145 + 40.7865i) q^{78} +(45.7098 + 79.1717i) q^{79} +(-43.3114 - 121.512i) q^{80} +(60.7857 - 53.5360i) q^{81} +(70.9068 - 128.737i) q^{82} +(-12.1468 + 45.3324i) q^{83} +(-24.4789 - 26.5723i) q^{84} +(-181.851 + 48.7268i) q^{85} +(-35.1656 + 142.679i) q^{86} +(76.1592 + 6.20406i) q^{87} +(46.9032 + 9.57367i) q^{88} +79.4644 q^{89} +(-87.0148 - 116.145i) q^{90} +(32.4368 + 32.4368i) q^{91} +(7.74342 - 14.7547i) q^{92} +(64.4667 + 23.0280i) q^{93} +(78.2479 - 47.3037i) q^{94} +(82.0099 + 47.3485i) q^{95} +(-26.6470 - 92.2276i) q^{96} +(-57.7693 - 100.059i) q^{97} +(38.5336 - 69.9607i) q^{98} +(53.5891 - 5.33544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

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