LMFDB - Embedded newform 144.3.w.a.5.16

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			5.16
Character	$\chi$	$=$	144.5
Dual form			144.3.w.a.29.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08605 - 1.67944i) q^{2} +(1.99667 - 2.23905i) q^{3} +(-1.64101 + 3.64789i) q^{4} +(1.20857 + 4.51043i) q^{5} +(-5.92880 - 0.921569i) q^{6} +(7.69955 - 4.44534i) q^{7} +(7.90861 - 1.20579i) q^{8} +(-1.02665 - 8.94125i) q^{9} +O(q^{10})$	\(q+(-1.08605 - 1.67944i) q^{2} +(1.99667 - 2.23905i) q^{3} +(-1.64101 + 3.64789i) q^{4} +(1.20857 + 4.51043i) q^{5} +(-5.92880 - 0.921569i) q^{6} +(7.69955 - 4.44534i) q^{7} +(7.90861 - 1.20579i) q^{8} +(-1.02665 - 8.94125i) q^{9} +(6.26242 - 6.92824i) q^{10} +(9.59821 + 2.57183i) q^{11} +(4.89123 + 10.9579i) q^{12} +(-5.52790 - 20.6304i) q^{13} +(-15.8277 - 8.10307i) q^{14} +(12.5122 + 6.29978i) q^{15} +(-10.6142 - 11.9725i) q^{16} +16.2606i q^{17} +(-13.9013 + 11.4348i) q^{18} +(-12.7191 + 12.7191i) q^{19} +(-18.4368 - 2.99296i) q^{20} +(5.42012 - 26.1155i) q^{21} +(-6.10486 - 18.9127i) q^{22} +(-3.20182 + 5.54571i) q^{23} +(13.0910 - 20.1153i) q^{24} +(2.76731 - 1.59771i) q^{25} +(-28.6439 + 31.6893i) q^{26} +(-22.0697 - 15.5540i) q^{27} +(3.58103 + 35.3819i) q^{28} +(3.23789 - 12.0840i) q^{29} +(-3.00868 - 27.8552i) q^{30} +(22.0027 - 38.1098i) q^{31} +(-8.57952 + 30.8284i) q^{32} +(24.9229 - 16.3557i) q^{33} +(27.3086 - 17.6597i) q^{34} +(29.3558 + 29.3558i) q^{35} +(34.3014 + 10.9276i) q^{36} +(29.7857 + 29.7857i) q^{37} +(35.1745 + 7.54742i) q^{38} +(-57.2298 - 28.8148i) q^{39} +(14.9967 + 34.2139i) q^{40} +(-0.584432 + 1.01227i) q^{41} +(-49.7458 + 19.2599i) q^{42} +(-9.91228 + 36.9931i) q^{43} +(-25.1325 + 30.7928i) q^{44} +(39.0881 - 15.4367i) q^{45} +(12.7910 - 0.645643i) q^{46} +(-54.6786 + 31.5687i) q^{47} +(-47.9998 - 0.139414i) q^{48} +(15.0221 - 26.0190i) q^{49} +(-5.68868 - 2.91234i) q^{50} +(36.4081 + 32.4669i) q^{51} +(84.3288 + 13.6896i) q^{52} +(-12.4936 + 12.4936i) q^{53} +(-2.15318 + 53.9571i) q^{54} +46.4003i q^{55} +(55.5326 - 44.4405i) q^{56} +(3.08285 + 53.8745i) q^{57} +(-23.8108 + 7.68591i) q^{58} +(7.14507 + 26.6658i) q^{59} +(-43.5135 + 35.3049i) q^{60} +(-105.639 - 28.3060i) q^{61} +(-87.8989 + 4.43682i) q^{62} +(-47.6516 - 64.2798i) q^{63} +(61.0921 - 19.0723i) q^{64} +(86.3711 - 49.8664i) q^{65} +(-54.5358 - 24.0933i) q^{66} +(34.4781 + 128.674i) q^{67} +(-59.3167 - 26.6838i) q^{68} +(6.02413 + 18.2419i) q^{69} +(17.4195 - 81.1829i) q^{70} +16.9880 q^{71} +(-18.9007 - 69.4749i) q^{72} -12.4974i q^{73} +(17.6746 - 82.3718i) q^{74} +(1.94806 - 9.38623i) q^{75} +(-25.5257 - 67.2702i) q^{76} +(85.3346 - 22.8653i) q^{77} +(13.7615 + 127.408i) q^{78} +(13.6564 + 23.6535i) q^{79} +(41.1730 - 62.3439i) q^{80} +(-78.8920 + 18.3591i) q^{81} +(2.33476 - 0.117850i) q^{82} +(-20.0789 + 74.9354i) q^{83} +(86.3719 + 62.6278i) q^{84} +(-73.3421 + 19.6519i) q^{85} +(72.8928 - 23.5292i) q^{86} +(-20.5916 - 31.3775i) q^{87} +(79.0096 + 8.76615i) q^{88} +158.598 q^{89} +(-68.3764 - 48.8810i) q^{90} +(-134.272 - 134.272i) q^{91} +(-14.9759 - 20.7804i) q^{92} +(-41.3975 - 125.358i) q^{93} +(112.401 + 57.5442i) q^{94} +(-72.7406 - 41.9968i) q^{95} +(51.8958 + 80.7640i) q^{96} +(-56.3634 - 97.6244i) q^{97} +(-60.0119 + 3.02918i) q^{98} +(13.1414 - 88.4604i) 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 $

$2$	−1.08605	−	1.67944i	−0.543023	−	0.839718i
$2$	−1.08605	−	1.67944i	−0.543023	−	0.839718i
$3$	1.99667	−	2.23905i	0.665555	−	0.746348i
$3$	1.99667	−	2.23905i	0.665555	−	0.746348i
$4$	−1.64101	+	3.64789i	−0.410253	+	0.911972i
$5$	1.20857	+	4.51043i	0.241713	+	0.902085i	0.975007	+	0.222174i	$0.0713152\pi$
$5$	1.20857	+	4.51043i	0.241713	+	0.902085i	−0.733294	+	0.679912i	$0.762018\pi$
$6$	−5.92880	−	0.921569i	−0.988134	−	0.153595i
$7$	7.69955	−	4.44534i	1.09994	−	0.635048i	0.163732	−	0.986505i	$-0.447647\pi$
$7$	7.69955	−	4.44534i	1.09994	−	0.635048i	0.936204	+	0.351457i	$0.114313\pi$
$8$	7.90861	−	1.20579i	0.988576	−	0.150724i
$9$	−1.02665	−	8.94125i	−0.114072	−	0.993472i
$10$	6.26242	−	6.92824i	0.626242	−	0.692824i
$11$	9.59821	+	2.57183i	0.872565	+	0.233803i	0.667196	−	0.744882i	$-0.267494\pi$
$11$	9.59821	+	2.57183i	0.872565	+	0.233803i	0.205368	+	0.978685i	$0.434161\pi$
$12$	4.89123	+	10.9579i	0.407603	+	0.913159i
$13$	−5.52790	−	20.6304i	−0.425223	−	1.58695i	−0.763435	−	0.645885i	$-0.776489\pi$
$13$	−5.52790	−	20.6304i	−0.425223	−	1.58695i	0.338212	−	0.941070i	$-0.390178\pi$
$14$	−15.8277	−	8.10307i	−1.13055	−	0.578791i
$15$	12.5122	+	6.29978i	0.834144	+	0.419986i
$16$	−10.6142	−	11.9725i	−0.663385	−	0.748278i
$17$			16.2606i			0.956504i	0.878223	+	0.478252i	$0.158729\pi$
$17$			16.2606i			0.956504i	−0.878223	+	0.478252i	$0.841271\pi$
$18$	−13.9013	+	11.4348i	−0.772293	+	0.635266i
$19$	−12.7191	+	12.7191i	−0.669428	+	0.669428i	−0.957584	−	0.288156i	$-0.906958\pi$
$19$	−12.7191	+	12.7191i	−0.669428	+	0.669428i	0.288156	+	0.957584i	$0.406958\pi$
$20$	−18.4368	−	2.99296i	−0.921840	−	0.149648i
$21$	5.42012	−	26.1155i	0.258101	−	1.24360i
$22$	−6.10486	−	18.9127i	−0.277494	−	0.859669i
$23$	−3.20182	+	5.54571i	−0.139209	+	0.241118i	−0.927198	−	0.374573i	$-0.877789\pi$
$23$	−3.20182	+	5.54571i	−0.139209	+	0.241118i	0.787988	+	0.615690i	$0.211123\pi$
$24$	13.0910	−	20.1153i	0.545459	−	0.838137i
$25$	2.76731	−	1.59771i	0.110692	−	0.0639083i
$26$	−28.6439	+	31.6893i	−1.10169	+	1.21882i
$27$	−22.0697	−	15.5540i	−0.817398	−	0.576073i
$28$	3.58103	+	35.3819i	0.127894	+	1.26364i
$29$	3.23789	−	12.0840i	0.111651	−	0.416689i	−0.887363	−	0.461071i	$-0.847465\pi$
$29$	3.23789	−	12.0840i	0.111651	−	0.416689i	0.999015	+	0.0443823i	$0.0141320\pi$
$30$	−3.00868	−	27.8552i	−0.100289	−	0.928507i
$31$	22.0027	−	38.1098i	0.709765	−	1.22935i	−0.255180	−	0.966894i	$-0.582135\pi$
$31$	22.0027	−	38.1098i	0.709765	−	1.22935i	0.964944	−	0.262455i	$-0.0845320\pi$
$32$	−8.57952	+	30.8284i	−0.268110	+	0.963388i
$33$	24.9229	−	16.3557i	0.755239	−	0.495628i
$34$	27.3086	−	17.6597i	0.803193	−	0.519403i
$35$	29.3558	+	29.3558i	0.838737	+	0.838737i
$36$	34.3014	+	10.9276i	0.952817	+	0.303545i
$37$	29.7857	+	29.7857i	0.805019	+	0.805019i	0.983875	−	0.178856i	$-0.0572396\pi$
$37$	29.7857	+	29.7857i	0.805019	+	0.805019i	−0.178856	+	0.983875i	$0.557240\pi$
$38$	35.1745	+	7.54742i	0.925645	+	0.198616i
$39$	−57.2298	−	28.8148i	−1.46743	−	0.738841i
$40$	14.9967	+	34.2139i	0.374918	+	0.855348i
$41$	−0.584432	+	1.01227i	−0.0142544	+	0.0246894i	−0.873065	−	0.487604i	$-0.837871\pi$
$41$	−0.584432	+	1.01227i	−0.0142544	+	0.0246894i	0.858810	+	0.512294i	$0.171204\pi$
$42$	−49.7458	+	19.2599i	−1.18442	+	0.458568i
$43$	−9.91228	+	36.9931i	−0.230518	+	0.860306i	0.749600	+	0.661891i	$0.230246\pi$
$43$	−9.91228	+	36.9931i	−0.230518	+	0.860306i	−0.980118	+	0.198415i	$0.936421\pi$
$44$	−25.1325	+	30.7928i	−0.571194	+	0.699836i
$45$	39.0881	−	15.4367i	0.868624	−	0.343038i
$46$	12.7910	−	0.645643i	0.278065	−	0.0140357i
$47$	−54.6786	+	31.5687i	−1.16337	+	0.671675i	−0.952110	−	0.305754i	$-0.901091\pi$
$47$	−54.6786	+	31.5687i	−1.16337	+	0.671675i	−0.211264	+	0.977429i	$0.567758\pi$
$48$	−47.9998	−	0.139414i	−0.999996	−	0.00290446i
$49$	15.0221	−	26.0190i	0.306573	−	0.531000i
$50$	−5.68868	−	2.91234i	−0.113774	−	0.0582468i
$51$	36.4081	+	32.4669i	0.713885	+	0.636606i
$52$	84.3288	+	13.6896i	1.62171	+	0.263261i
$53$	−12.4936	+	12.4936i	−0.235729	+	0.235729i	−0.815079	−	0.579350i	$-0.803307\pi$
$53$	−12.4936	+	12.4936i	−0.235729	+	0.235729i	0.579350	+	0.815079i	$0.303307\pi$
$54$	−2.15318	+	53.9571i	−0.0398738	+	0.999205i
$55$			46.4003i			0.843641i
$56$	55.5326	−	44.4405i	0.991653	−	0.793580i
$57$	3.08285	+	53.8745i	0.0540851	+	0.945168i
$58$	−23.8108	+	7.68591i	−0.410530	+	0.132516i
$59$	7.14507	+	26.6658i	0.121103	+	0.451962i	0.999671	−	0.0256553i	$-0.00816724\pi$
$59$	7.14507	+	26.6658i	0.121103	+	0.451962i	−0.878568	+	0.477617i	$0.841501\pi$
$60$	−43.5135	+	35.3049i	−0.725225	+	0.588415i
$61$	−105.639	−	28.3060i	−1.73179	−	0.464032i	−0.751197	−	0.660078i	$-0.770523\pi$
$61$	−105.639	−	28.3060i	−1.73179	−	0.464032i	−0.980595	+	0.196046i	$0.937190\pi$
$62$	−87.8989	+	4.43682i	−1.41772	+	0.0715616i
$63$	−47.6516	−	64.2798i	−0.756375	−	1.02031i
$64$	61.0921	−	19.0723i	0.954564	−	0.298005i
$65$	86.3711	−	49.8664i	1.32879	−	0.767175i
$66$	−54.5358	−	24.0933i	−0.826300	−	0.365050i
$67$	34.4781	+	128.674i	0.514599	+	1.92051i	0.361815	+	0.932250i	$0.382157\pi$
$67$	34.4781	+	128.674i	0.514599	+	1.92051i	0.152784	+	0.988260i	$0.451176\pi$
$68$	−59.3167	−	26.6838i	−0.872304	−	0.392409i
$69$	6.02413	+	18.2419i	0.0873063	+	0.264376i
$70$	17.4195	−	81.1829i	0.248850	−	1.15976i
$71$	16.9880			0.239268			0.119634	−	0.992818i	$-0.461828\pi$
$71$	16.9880			0.239268			0.119634	+	0.992818i	$0.461828\pi$
$72$	−18.9007	−	69.4749i	−0.262509	−	0.964929i
$73$		−	12.4974i		−	0.171198i	−0.996330	−	0.0855989i	$-0.972720\pi$
$73$		−	12.4974i		−	0.171198i	0.996330	−	0.0855989i	$-0.0272804\pi$
$74$	17.6746	−	82.3718i	0.238846	−	1.11313i
$75$	1.94806	−	9.38623i	0.0259741	−	0.125150i
$76$	−25.5257	−	67.2702i	−0.335864	−	0.885134i
$77$	85.3346	−	22.8653i	1.10824	−	0.296952i
$78$	13.7615	+	127.408i	0.176429	+	1.63344i
$79$	13.6564	+	23.6535i	0.172866	+	0.299412i	0.939421	−	0.342767i	$-0.111364\pi$
$79$	13.6564	+	23.6535i	0.172866	+	0.299412i	−0.766555	+	0.642179i	$0.778031\pi$
$80$	41.1730	−	62.3439i	0.514662	−	0.779298i
$81$	−78.8920	+	18.3591i	−0.973975	+	0.226655i
$82$	2.33476	−	0.117850i	0.0284726	−	0.00143720i
$83$	−20.0789	+	74.9354i	−0.241914	+	0.902836i	0.732995	+	0.680234i	$0.238122\pi$
$83$	−20.0789	+	74.9354i	−0.241914	+	0.902836i	−0.974909	+	0.222602i	$0.928545\pi$
$84$	86.3719	+	62.6278i	1.02824	+	0.745570i
$85$	−73.3421	+	19.6519i	−0.862848	+	0.231199i
$86$	72.8928	−	23.5292i	0.847591	−	0.273595i
$87$	−20.5916	−	31.3775i	−0.236685	−	0.360660i
$88$	79.0096	+	8.76615i	0.897836	+	0.0996154i
$89$	158.598			1.78200			0.891000	−	0.454004i	$-0.150005\pi$
$89$	158.598			1.78200			0.891000	+	0.454004i	$0.150005\pi$
$90$	−68.3764	−	48.8810i	−0.759738	−	0.543122i
$91$	−134.272	−	134.272i	−1.47551	−	1.47551i
$92$	−14.9759	−	20.7804i	−0.162781	−	0.225874i
$93$	−41.3975	−	125.358i	−0.445135	−	1.34793i
$94$	112.401	+	57.5442i	1.19576	+	0.612172i
$95$	−72.7406	−	41.9968i	−0.765690	−	0.442072i
$96$	51.8958	+	80.7640i	0.540581	+	0.841292i
$97$	−56.3634	−	97.6244i	−0.581066	−	1.00644i	−0.995353	−	0.0962903i	$-0.969302\pi$
$97$	−56.3634	−	97.6244i	−0.581066	−	1.00644i	0.414287	−	0.910146i	$-0.364031\pi$
$98$	−60.0119	+	3.02918i	−0.612366	+	0.0309100i
$99$	13.1414	−	88.4604i	0.132742	−	0.893539i
$100$	1.28707	+	12.7167i	0.0128707	+	0.127167i
$101$	−104.739	−	28.0647i	−1.03702	−	0.277868i	−0.300142	−	0.953895i	$-0.597034\pi$
$101$	−104.739	−	28.0647i	−1.03702	−	0.277868i	−0.736878	+	0.676026i	$0.763701\pi$
$102$	14.9852	−	96.4057i	0.146914	−	0.945154i
$103$	−18.2870	−	10.5580i	−0.177544	−	0.102505i	0.408594	−	0.912716i	$-0.366019\pi$
$103$	−18.2870	−	10.5580i	−0.177544	−	0.102505i	−0.586138	+	0.810211i	$0.699352\pi$
$104$	−68.5940	−	156.492i	−0.659558	−	1.50473i
$105$	124.343	−	7.11524i	1.18422	−	0.0677641i
$106$	34.5509	+	7.41362i	0.325952	+	0.0699398i
$107$	−107.994	+	107.994i	−1.00929	+	1.00929i	−0.00933781	+	0.999956i	$0.502972\pi$
$107$	−107.994	+	107.994i	−1.00929	+	1.00929i	−0.999956	+	0.00933781i	$0.997028\pi$
$108$	92.9559	−	54.9837i	0.860703	−	0.509108i
$109$	−93.8919	+	93.8919i	−0.861393	+	0.861393i	−0.991500	−	0.130107i	$-0.958468\pi$
$109$	−93.8919	+	93.8919i	−0.861393	+	0.861393i	0.130107	+	0.991500i	$0.458468\pi$
$110$	77.9263	−	50.3928i	0.708421	−	0.458116i
$111$	126.164	−	7.21944i	1.13661	−	0.0650400i
$112$	−134.946	−	44.9990i	−1.20487	−	0.401777i
$113$	−96.8308	−	55.9053i	−0.856910	−	0.494737i	0.00606644	−	0.999982i	$-0.498069\pi$
$113$	−96.8308	−	55.9053i	−0.856910	−	0.494737i	−0.862976	+	0.505244i	$0.831402\pi$
$114$	87.1308	−	63.6876i	0.764305	−	0.558664i
$115$	−28.8831	−	7.73921i	−0.251158	−	0.0672975i
$116$	38.7676	+	31.6414i	0.334203	+	0.272771i
$117$	−178.786	+	70.6065i	−1.52809	+	0.603475i
$118$	37.0236	−	40.9599i	0.313759	−	0.347118i
$119$	72.2837	+	125.199i	0.607426	+	1.05209i
$120$	106.550	+	34.7354i	0.887916	+	0.289462i
$121$	−19.2777	−	11.1300i	−0.159320	−	0.0919835i
$122$	67.1910	+	208.156i	0.550746	+	1.70620i
$123$	1.09959	+	3.32973i	0.00893979	+	0.0270710i
$124$	102.914	+	142.802i	0.829948	+	1.15163i
$125$	93.0974	+	93.0974i	0.744779	+	0.744779i
$126$	−56.2021	+	149.839i	−0.446048	+	1.18920i
$127$	90.1123			0.709546			0.354773	−	0.934952i	$-0.384558\pi$
$127$	90.1123			0.709546			0.354773	+	0.934952i	$0.384558\pi$
$128$	−98.3795	−	81.8869i	−0.768590	−	0.639742i
$129$	63.0378	+	96.0570i	0.488665	+	0.744628i
$130$	−177.550	−	90.8977i	−1.36577	−	0.699213i
$131$	−95.6847	+	25.6386i	−0.730418	+	0.195715i	−0.604815	−	0.796366i	$-0.706753\pi$
$131$	−95.6847	+	25.6386i	−0.730418	+	0.195715i	−0.125602	+	0.992081i	$0.540086\pi$
$132$	18.7651	+	117.756i	0.142160	+	0.892089i
$133$	−41.3908	+	154.472i	−0.311209	+	1.16145i
$134$	178.655	−	197.650i	1.33325	−	1.47500i
$135$	43.4824	−	118.342i	0.322092	−	0.876607i
$136$	19.6069	+	128.598i	0.144168	+	0.945576i
$137$	−13.0908	−	22.6739i	−0.0955533	−	0.165503i	0.814286	−	0.580464i	$-0.197129\pi$
$137$	−13.0908	−	22.6739i	−0.0955533	−	0.165503i	−0.909839	+	0.414961i	$0.863795\pi$
$138$	24.0937	−	29.9287i	0.174592	−	0.216875i
$139$	83.3543	−	22.3347i	0.599671	−	0.160681i	0.0538016	−	0.998552i	$-0.482866\pi$
$139$	83.3543	−	22.3347i	0.599671	−	0.160681i	0.545869	+	0.837870i	$0.316199\pi$
$140$	−155.260	+	58.9134i	−1.10900	+	0.420810i
$141$	−38.4911	+	185.460i	−0.272987	+	1.31532i
$142$	−18.4498	−	28.5303i	−0.129928	−	0.200918i
$143$		−	212.232i		−	1.48414i
$144$	−96.1517	+	107.195i	−0.667720	+	0.744412i
$145$	58.4171			0.402877
$146$	−20.9887	+	13.5728i	−0.143758	+	0.0929643i
$147$	−28.2636	−	85.5863i	−0.192270	−	0.582220i
$148$	−157.534	+	59.7762i	−1.06442	+	0.403893i
$149$	−30.6516	−	114.393i	−0.205715	−	0.767739i	−0.989230	−	0.146367i	$-0.953242\pi$
$149$	−30.6516	−	114.393i	−0.205715	−	0.767739i	0.783515	−	0.621373i	$-0.213425\pi$
$150$	−17.8792	+	6.92223i	−0.119195	+	0.0461482i
$151$	89.2008	−	51.5001i	0.590734	−	0.341060i	−0.174654	−	0.984630i	$-0.555881\pi$
$151$	89.2008	−	51.5001i	0.590734	−	0.341060i	0.765388	+	0.643569i	$0.222547\pi$
$152$	−85.2539	+	115.927i	−0.560881	+	0.762679i
$153$	145.390	−	16.6939i	0.950260	−	0.109110i
$154$	−131.078	−	118.481i	−0.851156	−	0.769359i
$155$	198.483	+	53.1834i	1.28054	+	0.343119i
$156$	199.028	−	161.482i	1.27582	−	1.03514i
$157$	16.6183	+	62.0202i	0.105849	+	0.395033i	0.998440	−	0.0558335i	$-0.0177816\pi$
$157$	16.6183	+	62.0202i	0.105849	+	0.395033i	−0.892591	+	0.450867i	$0.851115\pi$
$158$	24.8932	−	48.6238i	0.157552	−	0.307746i
$159$	3.02820	+	52.9195i	0.0190453	+	0.332827i
$160$	−149.418	−	1.43914i	−0.933864	−	0.00899463i
$161$			56.9326i			0.353619i
$162$	116.513	+	112.555i	0.719217	+	0.694786i
$163$	99.9028	−	99.9028i	0.612901	−	0.612901i	−0.330800	−	0.943701i	$-0.607319\pi$
$163$	99.9028	−	99.9028i	0.612901	−	0.612901i	0.943701	+	0.330800i	$0.107319\pi$
$164$	−2.73357	−	3.79308i	−0.0166681	−	0.0231286i
$165$	103.892	+	92.6458i	0.629650	+	0.561490i
$166$	147.656	−	47.6620i	0.889493	−	0.287121i
$167$	10.8859	−	18.8549i	0.0651848	−	0.112903i	−0.831591	−	0.555388i	$-0.812570\pi$
$167$	10.8859	−	18.8549i	0.0651848	−	0.112903i	0.896776	+	0.442485i	$0.145903\pi$
$168$	11.3757	−	213.073i	0.0677124	−	1.26829i
$169$	−248.698	+	143.586i	−1.47158	+	0.849620i
$170$	112.657	+	101.830i	0.662688	+	0.599003i
$171$	126.783	+	100.667i	0.741421	+	0.588695i
$172$	−118.681	−	96.8651i	−0.690004	−	0.563169i
$173$	65.2154	−	243.387i	0.376968	−	1.40686i	−0.473481	−	0.880804i	$-0.657003\pi$
$173$	65.2154	−	243.387i	0.376968	−	1.40686i	0.850449	−	0.526058i	$-0.176331\pi$
$174$	−30.3330	+	68.6596i	−0.174328	+	0.394595i
$175$	14.2047	−	24.6033i	0.0811698	−	0.140590i
$176$	−71.0858	−	142.212i	−0.403896	−	0.808023i
$177$	73.9721	+	37.2445i	0.417922	+	0.210421i
$178$	−172.245	−	266.355i	−0.967666	−	1.49638i
$179$	67.5246	+	67.5246i	0.377232	+	0.377232i	0.870103	−	0.492870i	$-0.164052\pi$
$179$	67.5246	+	67.5246i	0.377232	+	0.377232i	−0.492870	+	0.870103i	$0.664052\pi$
$180$	−7.83267	+	167.921i	−0.0435148	+	0.932893i
$181$	−113.951	−	113.951i	−0.629565	−	0.629565i	0.318393	−	0.947959i	$-0.396857\pi$
$181$	−113.951	−	113.951i	−0.629565	−	0.629565i	−0.947959	+	0.318393i	$0.896857\pi$
$182$	−79.6755	+	371.325i	−0.437778	+	2.04025i
$183$	−274.305	+	180.014i	−1.49893	+	0.983681i
$184$	−18.6349	+	47.7196i	−0.101277	+	0.259345i
$185$	−98.3483	+	170.344i	−0.531612	+	0.920780i
$186$	−165.571	+	205.668i	−0.890164	+	1.10574i
$187$	−41.8194	+	156.072i	−0.223633	+	0.834611i
$188$	−25.4308	−	251.266i	−0.135270	−	1.33652i
$189$	−239.070	−	21.6512i	−1.26492	−	0.114557i
$190$	8.46861	+	167.774i	0.0445716	+	0.883019i
$191$	213.217	−	123.101i	1.11632	−	0.644508i	0.175861	−	0.984415i	$-0.443729\pi$
$191$	213.217	−	123.101i	1.11632	−	0.644508i	0.940459	+	0.339907i	$0.110396\pi$
$192$	79.2768	−	174.869i	0.412900	−	0.910776i
$193$	28.2180	−	48.8751i	0.146207	−	0.253239i	−0.783615	−	0.621246i	$-0.786627\pi$
$193$	28.2180	−	48.8751i	0.146207	−	0.253239i	0.929823	+	0.368008i	$0.119960\pi$
$194$	−102.741	+	200.683i	−0.529591	+	1.03445i
$195$	60.8012	−	292.955i	0.311801	−	1.50234i
$196$	70.2629	+	97.4963i	0.358484	+	0.497430i
$197$	36.9038	−	36.9038i	0.187329	−	0.187329i	−0.607211	−	0.794540i	$-0.707712\pi$
$197$	36.9038	−	36.9038i	0.187329	−	0.187329i	0.794540	+	0.607211i	$0.207712\pi$
$198$	−162.836	+	74.0018i	−0.822403	+	0.373747i
$199$		−	62.7806i		−	0.315480i	−0.987481	−	0.157740i	$-0.949579\pi$
$199$		−	62.7806i		−	0.315480i	0.987481	−	0.157740i	$-0.0504208\pi$
$200$	19.9591	−	15.9725i	0.0997954	−	0.0798623i
$201$	356.949	+	179.721i	1.77586	+	0.894135i
$202$	66.6183	+	206.382i	0.329794	+	1.02169i
$203$	−28.7870	−	107.435i	−0.141808	−	0.529235i
$204$	−178.182	+	79.5342i	−0.873440	+	0.389873i
$205$	−5.27208	−	1.41265i	−0.0257175	−	0.00689097i
$206$	2.12901	+	42.1783i	0.0103350	+	0.204749i
$207$	52.8727	+	22.9347i	0.255424	+	0.110796i
$208$	−188.323	+	285.157i	−0.905397	+	1.37095i
$209$	−154.792	+	89.3694i	−0.740633	+	0.427605i
$210$	−146.991	−	201.098i	−0.699959	−	0.957610i
$211$	22.5178	+	84.0376i	0.106719	+	0.398283i	0.998535	−	0.0541176i	$-0.0172346\pi$
$211$	22.5178	+	84.0376i	0.106719	+	0.398283i	−0.891815	+	0.452400i	$0.850568\pi$
$212$	−25.0732	−	66.0776i	−0.118270	−	0.311687i
$213$	33.9194	−	38.0370i	0.159246	−	0.178577i
$214$	298.657	+	64.0830i	1.39559	+	0.299453i
$215$	−178.835			−0.831789
$216$	−193.296	−	96.3988i	−0.894888	−	0.446291i
$217$		−	391.238i		−	1.80294i
$218$	259.656	+	55.7146i	1.19108	+	0.255572i
$219$	−27.9823	−	24.9532i	−0.127773	−	0.113942i
$220$	−169.263	−	76.1434i	−0.769377	−	0.346106i
$221$	335.462	−	89.8868i	1.51793	−	0.406728i
$222$	−149.144	−	204.043i	−0.671820	−	0.919114i
$223$	−11.5556	−	20.0149i	−0.0518190	−	0.0897531i	0.838952	−	0.544205i	$-0.183169\pi$
$223$	−11.5556	−	20.0149i	−0.0518190	−	0.0897531i	−0.890771	+	0.454452i	$0.849835\pi$
$224$	70.9843	+	275.504i	0.316894	+	1.22993i
$225$	−17.1266	−	23.1030i	−0.0761181	−	0.102680i
$226$	11.2732	+	223.337i	0.0498816	+	0.988216i
$227$	23.5744	−	87.9808i	0.103852	−	0.387581i	−0.894360	−	0.447347i	$-0.852369\pi$
$227$	23.5744	−	87.9808i	0.103852	−	0.387581i	0.998212	+	0.0597663i	$0.0190356\pi$
$228$	−201.587	−	77.1629i	−0.884155	−	0.338434i
$229$	304.617	−	81.6219i	1.33021	−	0.356427i	0.477414	−	0.878679i	$-0.341574\pi$
$229$	304.617	−	81.6219i	1.33021	−	0.356427i	0.852792	+	0.522251i	$0.174908\pi$
$230$	18.3709	+	56.9125i	0.0798733	+	0.247446i
$231$	119.188	−	236.722i	0.515966	−	1.02477i
$232$	11.0364	−	99.4716i	0.0475708	−	0.428757i
$233$	−248.144			−1.06500			−0.532498	−	0.846431i	$-0.678747\pi$
$233$	−248.144			−1.06500			−0.532498	+	0.846431i	$0.678747\pi$
$234$	312.749	+	223.579i	1.33654	+	0.955464i
$235$	−208.471	−	208.471i	−0.887111	−	0.887111i
$236$	−108.999	−	17.6944i	−0.461859	−	0.0749764i
$237$	80.2286	+	16.6510i	0.338517	+	0.0702573i
$238$	131.760	−	257.368i	0.553615	−	1.08138i
$239$	−258.238	−	149.094i	−1.08050	−	0.623824i	−0.149465	−	0.988767i	$-0.547755\pi$
$239$	−258.238	−	149.094i	−1.08050	−	0.623824i	−0.931030	+	0.364943i	$0.881089\pi$
$240$	−57.3821	−	216.668i	−0.239092	−	0.902784i
$241$	105.364	+	182.495i	0.437194	+	0.757241i	0.997472	−	0.0710630i	$-0.0226391\pi$
$241$	105.364	+	182.495i	0.437194	+	0.757241i	−0.560278	+	0.828304i	$0.689306\pi$
$242$	2.24435	+	44.4634i	0.00927419	+	0.183733i
$243$	−116.414	+	213.300i	−0.479071	+	0.877776i
$244$	276.612	−	338.910i	1.13366	−	1.38897i
$245$	135.512	+	36.3103i	0.553110	+	0.148205i
$246$	4.39786	−	5.46293i	0.0178775	−	0.0222070i
$247$	332.711	+	192.091i	1.34701	+	0.777695i
$248$	128.058	−	327.926i	0.516364	−	1.32228i
$249$	127.693	+	194.579i	0.512823	+	0.781440i
$250$	55.2432	−	257.459i	0.220973	−	1.02984i
$251$	−278.376	+	278.376i	−1.10907	+	1.10907i	−0.115792	+	0.993273i	$0.536941\pi$
$251$	−278.376	+	278.376i	−1.10907	+	1.10907i	−0.993273	+	0.115792i	$0.963059\pi$
$252$	312.682	−	68.3437i	1.24080	−	0.271205i
$253$	−44.9943	+	44.9943i	−0.177843	+	0.177843i
$254$	−97.8661	−	151.338i	−0.385299	−	0.595819i
$255$	−102.438	+	203.455i	−0.401718	+	0.797861i
$256$	−30.6793	+	254.155i	−0.119841	+	0.992793i
$257$	165.293	+	95.4322i	0.643165	+	0.371332i	0.785833	−	0.618439i	$-0.212235\pi$
$257$	165.293	+	95.4322i	0.643165	+	0.371332i	−0.142668	+	0.989771i	$0.545568\pi$
$258$	92.8597	−	210.190i	0.359921	−	0.814691i
$259$	361.744	+	96.9291i	1.39670	+	0.374244i
$260$	40.1709	+	396.903i	0.154503	+	1.52655i
$261$	−111.370	−	16.5448i	−0.426705	−	0.0633901i
$262$	146.976	+	132.852i	0.560979	+	0.507067i
$263$	−124.627	−	215.860i	−0.473866	−	0.820759i	0.525687	−	0.850678i	$-0.323808\pi$
$263$	−124.627	−	215.860i	−0.473866	−	0.820759i	−0.999552	+	0.0299188i	$0.990475\pi$
$264$	177.384	−	159.403i	0.671907	−	0.603799i
$265$	−71.4511	−	41.2523i	−0.269627	−	0.155669i
$266$	304.379	−	98.2508i	1.14428	−	0.369364i
$267$	316.667	−	355.108i	1.18602	−	1.32999i
$268$	−525.968	−	85.3835i	−1.96257	−	0.318595i
$269$	−6.17571	−	6.17571i	−0.0229580	−	0.0229580i	0.695535	−	0.718493i	$-0.255168\pi$
$269$	−6.17571	−	6.17571i	−0.0229580	−	0.0229580i	−0.718493	+	0.695535i	$0.755168\pi$
$270$	−245.972	+	55.4988i	−0.911006	+	0.205551i
$271$	469.985			1.73426			0.867131	−	0.498080i	$-0.165962\pi$
$271$	469.985			1.73426			0.867131	+	0.498080i	$0.165962\pi$
$272$	194.679	−	172.592i	0.715731	−	0.634530i
$273$	−568.735	+	32.5446i	−2.08328	+	0.119211i
$274$	−23.8622	+	46.6101i	−0.0870884	+	0.170110i
$275$	30.6703	−	8.21808i	0.111528	−	0.0298839i
$276$	−76.4302	−	7.95988i	−0.276921	−	0.0288402i
$277$	7.91698	−	29.5466i	0.0285811	−	0.106666i	−0.950162	−	0.311757i	$-0.899082\pi$
$277$	7.91698	−	29.5466i	0.0285811	−	0.106666i	0.978743	+	0.205091i	$0.0657491\pi$
$278$	−128.036	−	115.732i	−0.460562	−	0.416301i
$279$	−363.338	−	157.606i	−1.30229	−	0.564897i
$280$	267.560	+	196.766i	0.955573	+	0.702737i
$281$	−265.967	−	460.669i	−0.946503	−	1.63939i	−0.752713	−	0.658349i	$-0.771255\pi$
$281$	−265.967	−	460.669i	−0.946503	−	1.63939i	−0.193790	−	0.981043i	$-0.562078\pi$
$282$	353.271	−	136.775i	1.25274	−	0.485016i
$283$	159.323	−	42.6905i	0.562980	−	0.150850i	0.0339048	−	0.999425i	$-0.489206\pi$
$283$	159.323	−	42.6905i	0.562980	−	0.150850i	0.529075	+	0.848575i	$0.322539\pi$
$284$	−27.8776	+	61.9704i	−0.0981605	+	0.218206i
$285$	−239.271	+	79.0159i	−0.839549	+	0.277249i
$286$	−356.430	+	230.493i	−1.24626	+	0.805921i
$287$			10.3920i			0.0362090i
$288$	284.453	+	45.0617i	0.987684	+	0.156464i
$289$	24.5942			0.0851009
$290$	−63.4436	−	98.1078i	−0.218771	−	0.338303i
$291$	−331.124	−	68.7229i	−1.13788	−	0.236161i
$292$	45.5893	+	20.5085i	0.156128	+	0.0702345i
$293$	55.5680	+	207.382i	0.189652	+	0.707790i	0.993587	+	0.113073i	$0.0360693\pi$
$293$	55.5680	+	207.382i	0.189652	+	0.707790i	−0.803935	+	0.594717i	$0.797264\pi$
$294$	−113.041	+	140.418i	−0.384494	+	0.477611i
$295$	−111.639	+	64.4546i	−0.378436	+	0.218490i
$296$	271.479	+	199.648i	0.917159	+	0.674487i
$297$	−171.828	−	206.050i	−0.578545	−	0.693771i
$298$	−158.827	+	175.713i	−0.532977	+	0.589642i
$299$	132.110	+	35.3986i	0.441838	+	0.118390i
$300$	31.0431	+	22.5092i	0.103477	+	0.0750307i
$301$	88.1269	+	328.894i	0.292780	+	1.09267i
$302$	−183.367	−	93.8757i	−0.607177	−	0.310847i
$303$	−271.967	+	178.479i	−0.897580	+	0.589041i
$304$	287.282	+	17.2764i	0.945006	+	0.0568301i
$305$		−	510.688i		−	1.67439i
$306$	−185.936	−	226.043i	−0.607635	−	0.738701i
$307$	−23.4220	+	23.4220i	−0.0762931	+	0.0762931i	−0.744224	−	0.667931i	$-0.767180\pi$
$307$	−23.4220	+	23.4220i	−0.0762931	+	0.0762931i	0.667931	+	0.744224i	$0.267180\pi$
$308$	−56.6250	+	348.813i	−0.183847	+	1.13251i
$309$	−60.1529	+	19.8646i	−0.194670	+	0.0642868i
$310$	−126.244	−	391.099i	−0.407237	−	1.26161i
$311$	28.1457	−	48.7497i	0.0905005	−	0.156752i	−0.817221	−	0.576324i	$-0.804487\pi$
$311$	28.1457	−	48.7497i	0.0905005	−	0.156752i	0.907722	+	0.419572i	$0.137820\pi$
$312$	−487.353	−	158.878i	−1.56203	−	0.509223i
$313$	327.449	−	189.053i	1.04616	−	0.604003i	0.124591	−	0.992208i	$-0.460238\pi$
$313$	327.449	−	189.053i	1.04616	−	0.604003i	0.921573	+	0.388205i	$0.126905\pi$
$314$	86.1108	−	95.2661i	0.274238	−	0.303395i
$315$	232.339	−	292.616i	0.737585	−	0.928938i
$316$	−108.696	+	11.0012i	−0.343974	+	0.0348138i
$317$	−105.022	+	391.947i	−0.331299	+	1.23643i	0.576527	+	0.817078i	$0.304408\pi$
$317$	−105.022	+	391.947i	−0.331299	+	1.23643i	−0.907826	+	0.419347i	$0.862259\pi$
$318$	85.5861	−	62.5586i	0.269139	−	0.196725i
$319$	62.1559	−	107.657i	0.194846	−	0.337484i
$320$	159.858	+	252.501i	0.499556	+	0.789067i
$321$	26.1756	+	457.433i	0.0815440	+	1.42503i
$322$	95.6147	−	61.8314i	0.296940	−	0.192023i
$323$	−206.820	−	206.820i	−0.640310	−	0.640310i
$324$	62.4910	−	317.916i	0.192873	−	0.981224i
$325$	−48.2588	−	48.2588i	−0.148489	−	0.148489i
$326$	−276.279	−	59.2814i	−0.847483	−	0.181845i
$327$	22.7574	+	397.699i	0.0695946	+	1.21620i
$328$	−3.40146	+	8.71032i	−0.0103703	+	0.0265559i
$329$	−280.667	+	486.130i	−0.853092	+	1.47760i
$330$	42.7611	−	275.098i	0.129579	−	0.833630i
$331$	52.4111	−	195.601i	0.158342	−	0.590939i	−0.840454	−	0.541882i	$-0.817712\pi$
$331$	52.4111	−	195.601i	0.158342	−	0.590939i	0.998796	−	0.0490567i	$-0.0156215\pi$
$332$	−240.406	−	196.215i	−0.724115	−	0.591010i
$333$	235.742	−	296.901i	0.707934	−	0.891595i
$334$	−43.4880	+	2.19512i	−0.130204	+	0.00657222i
$335$	−538.706	+	311.022i	−1.60808	+	0.928424i
$336$	−370.197	+	212.302i	−1.10178	+	0.631851i
$337$	105.669	−	183.024i	0.313557	−	0.543097i	−0.665573	−	0.746333i	$-0.731813\pi$
$337$	105.669	−	183.024i	0.313557	−	0.543097i	0.979130	+	0.203236i	$0.0651460\pi$
$338$	511.240	+	261.732i	1.51254	+	0.774354i
$339$	−318.513	+	105.184i	−0.939567	+	0.310278i
$340$	48.6672	−	299.793i	0.143139	−	0.881743i
$341$	309.199	−	309.199i	0.906741	−	0.906741i
$342$	31.3715	−	322.253i	0.0917295	−	0.942259i
$343$			168.530i			0.491342i
$344$	−33.7862	+	304.516i	−0.0982158	+	0.885222i
$345$	−74.9984	+	49.2180i	−0.217387	+	0.142661i
$346$	−479.580	+	154.804i	−1.38607	+	0.447411i
$347$	169.114	+	631.141i	0.487359	+	1.81885i	0.569194	+	0.822203i	$0.307255\pi$
$347$	169.114	+	631.141i	0.487359	+	1.81885i	−0.0818345	+	0.996646i	$0.526078\pi$
$348$	148.252	−	23.6250i	0.426013	−	0.0678879i
$349$	−404.054	−	108.266i	−1.15775	−	0.310218i	−0.371682	−	0.928360i	$-0.621219\pi$
$349$	−404.054	−	108.266i	−1.15775	−	0.310218i	−0.786066	+	0.618142i	$0.787886\pi$
$350$	−56.7466	+	2.86436i	−0.162133	+	0.00818390i
$351$	−198.886	+	541.289i	−0.566626	+	1.54213i
$352$	−161.634	+	273.833i	−0.459186	+	0.777934i
$353$	−104.140	+	60.1252i	−0.295014	+	0.170326i	−0.640201	−	0.768208i	$-0.721149\pi$
$353$	−104.140	+	60.1252i	−0.295014	+	0.170326i	0.345187	+	0.938534i	$0.387815\pi$
$354$	−17.7874	−	164.681i	−0.0502468	−	0.465200i
$355$	20.5311	+	76.6233i	0.0578342	+	0.215840i
$356$	−260.261	+	578.547i	−0.731071	+	1.62513i
$357$	424.653	+	88.1342i	1.18950	+	0.246874i
$358$	40.0685	−	186.738i	0.111923	−	0.521614i
$359$	230.419			0.641836			0.320918	−	0.947107i	$-0.396009\pi$
$359$	230.419			0.641836			0.320918	+	0.947107i	$0.396009\pi$
$360$	290.519	−	169.215i	0.806997	−	0.470042i
$361$			37.4477i			0.103733i
$362$	−67.6177	+	315.130i	−0.186789	+	0.870525i
$363$	−63.4118	+	20.9408i	−0.174688	+	0.0576882i
$364$	710.149	−	269.466i	1.95096	−	0.740291i
$365$	56.3688	−	15.1040i	0.154435	−	0.0413808i
$366$	600.229	+	265.174i	1.63997	+	0.724520i
$367$	133.404	+	231.062i	0.363499	+	0.629598i	0.988534	−	0.150998i	$-0.0482488\pi$
$367$	133.404	+	231.062i	0.363499	+	0.629598i	−0.625035	+	0.780596i	$0.714915\pi$
$368$	100.380	−	20.5294i	0.272773	−	0.0557865i
$369$	9.65093	+	4.18631i	0.0261543	+	0.0113450i
$370$	392.893	−	19.8318i	1.06187	−	0.0535995i
$371$	−40.6570	+	151.734i	−0.109588	+	0.408986i
$372$	525.224	+	54.6999i	1.41189	+	0.147043i
$373$	307.403	−	82.3684i	0.824137	−	0.220827i	0.177983	−	0.984034i	$-0.443043\pi$
$373$	307.403	−	82.3684i	0.824137	−	0.220827i	0.646154	+	0.763207i	$0.276376\pi$
$374$	307.531	−	99.2685i	0.822276	−	0.265424i
$375$	394.334	−	22.5649i	1.05156	−	0.0601730i
$376$	−394.366	+	315.596i	−1.04885	+	0.839350i
$377$	−267.196			−0.708743
$378$	223.279	+	425.017i	0.590685	+	1.12438i
$379$	−225.622	−	225.622i	−0.595310	−	0.595310i	0.343751	−	0.939061i	$-0.388302\pi$
$379$	−225.622	−	225.622i	−0.595310	−	0.595310i	−0.939061	+	0.343751i	$0.888302\pi$
$380$	272.568	−	196.432i	0.717284	−	0.516927i
$381$	179.924	−	201.766i	0.472242	−	0.529569i
$382$	−438.304	−	224.391i	−1.14739	−	0.587412i
$383$	−166.640	−	96.2096i	−0.435091	−	0.251200i	0.266422	−	0.963856i	$-0.414159\pi$
$383$	−166.640	−	96.2096i	−0.435091	−	0.251200i	−0.701513	+	0.712657i	$0.747492\pi$
$384$	−379.780	+	56.7753i	−0.989009	+	0.147852i
$385$	206.265	+	357.261i	0.535753	+	0.927951i
$386$	−112.729	+	5.69014i	−0.292043	+	0.0147413i
$387$	340.942	+	50.6493i	0.880986	+	0.130877i
$388$	448.616	−	45.4047i	1.15623	−	0.117022i
$389$	−440.463	−	118.022i	−1.13230	−	0.303398i	−0.356446	−	0.934316i	$-0.616012\pi$
$389$	−440.463	−	118.022i	−1.13230	−	0.303398i	−0.775849	+	0.630918i	$0.782678\pi$
$390$	−558.033	+	216.051i	−1.43085	+	0.553977i
$391$	−90.1763	−	52.0633i	−0.230630	−	0.133154i
$392$	87.4301	−	223.887i	0.223036	−	0.571141i
$393$	−133.644	+	265.434i	−0.340062	+	0.675405i
$394$	−102.057	−	21.8984i	−0.259028	−	0.0555797i
$395$	−90.1830	+	90.1830i	−0.228311	+	0.228311i
$396$	301.128	+	193.103i	0.760425	+	0.487634i
$397$	235.247	−	235.247i	0.592561	−	0.592561i	−0.345762	−	0.938322i	$-0.612379\pi$
$397$	235.247	−	235.247i	0.592561	−	0.592561i	0.938322	+	0.345762i	$0.112379\pi$
$398$	−105.436	+	68.1825i	−0.264914	+	0.171313i
$399$	263.227	+	401.106i	0.659717	+	1.00528i
$400$	−48.5012	−	16.1732i	−0.121253	−	0.0404330i
$401$	−13.6229	−	7.86516i	−0.0339722	−	0.0196139i	0.482918	−	0.875666i	$-0.339577\pi$
$401$	−13.6229	−	7.86516i	−0.0339722	−	0.0196139i	−0.516890	+	0.856052i	$0.672910\pi$
$402$	−85.8319	−	794.658i	−0.213512	−	1.97676i
$403$	−907.849	−	243.258i	−2.25273	−	0.603617i
$404$	274.255	−	336.021i	0.678849	−	0.831736i
$405$	−178.153	−	333.648i	−0.439885	−	0.823823i
$406$	−149.166	+	165.025i	−0.367403	+	0.406465i
$407$	209.286	+	362.493i	0.514215	+	0.890647i
$408$	327.086	+	212.867i	0.801681	+	0.521734i
$409$	−538.004	−	310.617i	−1.31541	−	0.759454i	−0.332426	−	0.943129i	$-0.607867\pi$
$409$	−538.004	−	310.617i	−1.31541	−	0.759454i	−0.982987	+	0.183675i	$0.941200\pi$
$410$	3.35326	+	10.3883i	0.00817868	+	0.0253374i
$411$	−76.9060	−	15.9614i	−0.187119	−	0.0388355i
$412$	68.5236	−	49.3831i	0.166319	−	0.119862i
$413$	173.552	+	173.552i	0.420223	+	0.420223i
$414$	−18.9047	−	113.705i	−0.0456635	−	0.274649i
$415$	−362.257			−0.872909
$416$	683.430	+	6.58254i	1.64286	+	0.0158234i
$417$	116.422	−	231.229i	0.279190	−	0.554506i
$418$	318.202	+	162.905i	0.761248	+	0.389724i
$419$	626.017	−	167.741i	1.49407	−	0.400336i	0.582964	−	0.812498i	$-0.301893\pi$
$419$	626.017	−	167.741i	1.49407	−	0.400336i	0.911111	+	0.412162i	$0.135226\pi$
$420$	−178.092	+	465.264i	−0.424029	+	1.10777i
$421$	27.8013	−	103.756i	0.0660364	−	0.246451i	−0.925015	−	0.379930i	$-0.875948\pi$
$421$	27.8013	−	103.756i	0.0660364	−	0.246451i	0.991052	+	0.133479i	$0.0426148\pi$
$422$	116.680	−	129.086i	0.276494	−	0.305891i
$423$	338.399	+	456.485i	0.799999	+	1.07916i
$424$	−83.7426	+	113.872i	−0.197506	+	0.268566i
$425$	25.9796	+	44.9980i	0.0611286	+	0.105878i
$426$	−100.719	−	15.6556i	−0.236429	−	0.0367503i
$427$	−939.205	+	251.659i	−2.19954	+	0.589366i
$428$	−216.731	−	571.172i	−0.506382	−	1.33451i
$429$	−475.197	−	423.756i	−1.10768	−	0.987777i
$430$	194.222	+	300.341i	0.451680	+	0.698468i
$431$			62.8664i			0.145862i	0.997337	+	0.0729309i	$0.0232353\pi$
$431$			62.8664i			0.145862i	−0.997337	+	0.0729309i	$0.976765\pi$
$432$	48.0324	+	429.321i	0.111186	+	0.993800i
$433$	−246.671			−0.569679			−0.284840	−	0.958575i	$-0.591940\pi$
$433$	−246.671			−0.569679			−0.284840	+	0.958575i	$0.591940\pi$
$434$	−657.059	+	424.902i	−1.51396	+	0.979037i
$435$	116.639	−	130.799i	0.268137	−	0.300686i
$436$	−188.429	−	496.585i	−0.432177	−	1.13896i
$437$	−29.8123	−	111.261i	−0.0682203	−	0.254601i
$438$	−11.5173	+	74.0949i	−0.0262951	+	0.169166i
$439$	273.335	−	157.810i	0.622632	−	0.359477i	−0.155261	−	0.987873i	$-0.549622\pi$
$439$	273.335	−	157.810i	0.622632	−	0.359477i	0.777893	+	0.628397i	$0.216289\pi$
$440$	55.9492	+	366.961i	0.127157	+	0.834003i
$441$	−248.065	−	107.604i	−0.562505	−	0.243999i
$442$	−515.286	−	465.766i	−1.16581	−	1.05377i
$443$	452.814	+	121.331i	1.02215	+	0.273885i	0.730699	−	0.682699i	$-0.239194\pi$
$443$	452.814	+	121.331i	1.02215	+	0.273885i	0.291455	+	0.956585i	$0.405861\pi$
$444$	−180.700	+	472.078i	−0.406983	+	1.06324i
$445$	191.676	+	715.344i	0.430733	+	1.60752i
$446$	−21.0639	+	41.1441i	−0.0472284	+	0.0922513i
$447$	−317.332	−	159.775i	−0.709916	−	0.357438i
$448$	385.599	−	418.423i	0.860712	−	0.933981i
$449$			227.625i			0.506959i	0.967341	+	0.253480i	$0.0815751\pi$
$449$			227.625i			0.506959i	−0.967341	+	0.253480i	$0.918425\pi$
$450$	−20.1997	+	53.8538i	−0.0448882	+	0.119675i
$451$	−8.21288	+	8.21288i	−0.0182104	+	0.0182104i
$452$	362.837	−	261.487i	0.802736	−	0.578510i
$453$	62.7932	−	302.553i	0.138616	−	0.667888i
$454$	−173.361	+	55.9595i	−0.381853	+	0.123259i
$455$	443.346	−	767.898i	0.974387	−	1.68769i
$456$	89.3427	+	422.355i	0.195927	+	0.926218i
$457$	113.790	−	65.6968i	0.248994	−	0.143757i	−0.370310	−	0.928908i	$-0.620748\pi$
$457$	113.790	−	65.6968i	0.248994	−	0.143757i	0.619303	+	0.785152i	$0.287415\pi$
$458$	−467.907	−	422.940i	−1.02163	−	0.923449i
$459$	252.916	−	358.866i	0.551016	−	0.781844i
$460$	75.6293	−	92.6622i	0.164412	−	0.201440i
$461$	156.559	−	584.287i	0.339608	−	1.26743i	−0.559179	−	0.829047i	$-0.688883\pi$
$461$	156.559	−	584.287i	0.339608	−	1.26743i	0.898787	−	0.438386i	$-0.144450\pi$
$462$	−527.004	+	56.9223i	−1.14070	+	0.123209i
$463$	−150.505	+	260.683i	−0.325066	+	0.563030i	−0.981526	−	0.191331i	$-0.938720\pi$
$463$	−150.505	+	260.683i	−0.325066	+	0.563030i	0.656460	+	0.754361i	$0.272053\pi$
$464$	−179.042	+	89.4957i	−0.385867	+	0.192879i
$465$	515.385	−	338.223i	1.10835	−	0.727362i
$466$	269.496	+	416.742i	0.578317	+	0.894296i
$467$	−604.827	−	604.827i	−1.29513	−	1.29513i	−0.931570	−	0.363563i	$-0.881560\pi$
$467$	−604.827	−	604.827i	−1.29513	−	1.29513i	−0.363563	−	0.931570i	$-0.618440\pi$
$468$	35.8261	−	768.059i	0.0765515	−	1.64115i
$469$	837.466	+	837.466i	1.78564	+	1.78564i
$470$	−123.705	+	576.523i	−0.263202	+	1.22664i
$471$	172.047	+	86.6246i	0.365281	+	0.183916i
$472$	88.6609	+	202.273i	0.187841	+	0.428545i
$473$	−190.280	+	329.575i	−0.402284	+	0.696777i
$474$	−59.1676	−	152.823i	−0.124826	−	0.322410i
$475$	−14.8763	+	55.5192i	−0.0313186	+	0.116883i
$476$	−575.330	+	58.2296i	−1.20868	+	0.122331i
$477$	124.535	+	98.8823i	0.261081	+	0.207300i
$478$	30.0646	+	595.618i	0.0628967	+	1.24606i
$479$	−303.519	+	175.237i	−0.633652	+	0.365839i	−0.782165	−	0.623071i	$-0.785885\pi$
$479$	−303.519	+	175.237i	−0.633652	+	0.365839i	0.148513	+	0.988910i	$0.452551\pi$
$480$	−301.561	+	331.681i	−0.628251	+	0.691002i
$481$	449.839	−	779.144i	0.935216	−	1.61984i
$482$	192.059	−	375.150i	0.398463	−	0.778318i
$483$	127.475	+	113.675i	0.263923	+	0.235353i
$484$	72.2360	−	52.0585i	0.149248	−	0.107559i
$485$	372.209	−	372.209i	0.767440	−	0.767440i
$486$	484.654	−	36.1428i	0.997231	−	0.0743679i
$487$			276.365i			0.567485i	0.958901	+	0.283742i	$0.0915760\pi$
$487$			276.365i			0.567485i	−0.958901	+	0.283742i	$0.908424\pi$
$488$	−869.591	−	96.4815i	−1.78195	−	0.197708i
$489$	−24.2144	−	423.159i	−0.0495181	−	0.865357i
$490$	−86.1912	−	267.018i	−0.175900	−	0.544935i
$491$	−236.459	−	882.478i	−0.481587	−	1.79731i	−0.594960	−	0.803755i	$-0.702832\pi$
$491$	−236.459	−	882.478i	−0.481587	−	1.79731i	0.113373	−	0.993553i	$-0.463835\pi$
$492$	−13.9509	−	1.45293i	−0.0283555	−	0.00295311i
$493$	196.492	+	52.6499i	0.398564	+	0.106795i
$494$	−38.7349	−	767.386i	−0.0784107	−	1.55341i
$495$	414.876	−	47.6368i	0.838134	−	0.0962359i
$496$	−689.808	+	141.077i	−1.39074	+	0.284429i
$497$	130.800	−	75.5176i	0.263180	−	0.151947i
$498$	188.102	−	425.773i	0.377715	−	0.854966i
$499$	−59.0884	−	220.521i	−0.118414	−	0.441926i	0.881106	−	0.472919i	$-0.156800\pi$
$499$	−59.0884	−	220.521i	−0.118414	−	0.441926i	−0.999520	+	0.0309932i	$0.990133\pi$
$500$	−492.383	+	186.835i	−0.984765	+	0.373669i
$501$	−20.4815	−	62.0208i	−0.0408811	−	0.123794i
$502$	769.842	+	165.186i	1.53355	+	0.329055i
$503$	−270.076			−0.536931			−0.268465	−	0.963289i	$-0.586517\pi$
$503$	−270.076			−0.536931			−0.268465	+	0.963289i	$0.586517\pi$
$504$	−454.366	−	450.906i	−0.901520	−	0.894655i
$505$		−	506.335i		−	1.00264i
$506$	124.431	+	26.6992i	0.245911	+	0.0527653i
$507$	−175.071	+	843.539i	−0.345309	+	1.66378i
$508$	−147.875	+	328.720i	−0.291093	+	0.647086i
$509$	−291.942	+	78.2256i	−0.573560	+	0.153685i	−0.533929	−	0.845530i	$-0.679285\pi$
$509$	−291.942	+	78.2256i	−0.573560	+	0.153685i	−0.0396309	+	0.999214i	$0.512618\pi$
$510$	452.941	−	48.9227i	0.888120	−	0.0959269i
$511$	−55.5554	−	96.2247i	−0.108719	−	0.188307i
$512$	460.156	−	224.500i	0.898743	−	0.438476i
$513$	478.541	−	82.8748i	0.932828	−	0.161549i
$514$	−19.2438	−	381.243i	−0.0374393	−	0.741719i
$515$	25.5201	−	95.2422i	0.0495535	−	0.184936i
$516$	−453.851	+	72.3241i	−0.879556	+	0.140163i
$517$	−606.006	+	162.379i	−1.17216	+	0.314079i
$518$	−230.084	−	712.796i	−0.444178	−	1.37605i
$519$	−414.742	−	631.983i	−0.799117	−	1.21769i
$520$	622.947	−	498.519i	1.19797	−	0.958691i
$521$	919.602			1.76507			0.882536	−	0.470245i	$-0.155835\pi$
$521$	919.602			1.76507			0.882536	+	0.470245i	$0.155835\pi$
$522$	93.1670	+	205.007i	0.178481	+	0.392734i
$523$	−14.6806	−	14.6806i	−0.0280699	−	0.0280699i	0.692933	−	0.721002i	$-0.256318\pi$
$523$	−14.6806	−	14.6806i	−0.0280699	−	0.0280699i	−0.721002	+	0.692933i	$0.756318\pi$
$524$	63.4929	−	391.120i	0.121170	−	0.746413i
$525$	−26.7258	−	80.9295i	−0.0509063	−	0.154151i
$526$	−227.172	+	443.736i	−0.431887	+	0.843605i
$527$	619.687	+	357.776i	1.17588	+	0.678892i
$528$	−460.354	−	124.786i	−0.871882	−	0.236336i
$529$	243.997	+	422.615i	0.461241	+	0.798894i
$530$	8.31848	+	164.799i	0.0156952	+	0.310942i
$531$	231.090	−	91.2622i	0.435197	−	0.171869i
$532$	−495.575	−	404.480i	−0.931532	−	0.760301i
$533$	24.1142	+	6.46137i	0.0452423	+	0.0121226i
$534$	−940.296	−	146.159i	−1.76085	−	0.273706i
$535$	−617.620	−	356.583i	−1.15443	−	0.666510i
$536$	427.828	+	976.060i	0.798187	+	1.82101i
$537$	286.015	−	16.3666i	0.532616	−	0.0304778i
$538$	−3.66461	+	17.0788i	−0.00681155	+	0.0317450i
$539$	211.101	−	211.101i	0.391654	−	0.391654i
$540$	360.343	+	352.819i	0.667302	+	0.653369i
$541$	−72.9591	+	72.9591i	−0.134860	+	0.134860i	−0.771314	−	0.636455i	$-0.780400\pi$
$541$	−72.9591	+	72.9591i	−0.134860	+	0.134860i	0.636455	+	0.771314i	$0.280400\pi$
$542$	−510.425	−	789.310i	−0.941743	−	1.45629i
$543$	−482.665	+	27.6194i	−0.888885	+	0.0508645i
$544$	−501.287	−	139.508i	−0.921484	−	0.256448i
$545$	−536.967	−	310.018i	−0.985260	−	0.568840i
$546$	672.329	+	919.810i	1.23137	+	1.68463i
$547$	−494.391	−	132.472i	−0.903823	−	0.242179i	−0.223166	−	0.974781i	$-0.571639\pi$
$547$	−494.391	−	132.472i	−0.903823	−	0.242179i	−0.680657	+	0.732602i	$0.738306\pi$
$548$	104.194	−	10.5456i	0.190135	−	0.0192437i
$549$	−144.636	+	973.608i	−0.263454	+	1.77342i
$550$	−47.1111	−	42.5836i	−0.0856565	−	0.0774247i
$551$	112.514	+	194.881i	0.204200	+	0.353686i
$552$	69.6385	+	137.004i	0.126157	+	0.248196i
$553$	210.296	+	121.414i	0.380282	+	0.219556i
$554$	−58.2198	+	18.7928i	−0.105090	+	0.0339221i
$555$	185.040	+	560.327i	0.333405	+	1.00960i
$556$	−55.3109	+	340.718i	−0.0994800	+	0.612803i
$557$	318.126	+	318.126i	0.571142	+	0.571142i	0.932448	−	0.361305i	$-0.117669\pi$
$557$	318.126	+	318.126i	0.571142	+	0.571142i	−0.361305	+	0.932448i	$0.617669\pi$
$558$	129.912	+	781.371i	0.232817	+	1.40031i
$559$	817.978			1.46329
$560$	39.8739	−	663.048i	0.0712034	−	1.18401i
$561$	265.954	+	405.260i	0.474070	+	0.722388i
$562$	−484.812	+	946.983i	−0.862654	+	1.68502i
$563$	891.989	−	239.008i	1.58435	−	0.424525i	0.644080	−	0.764958i	$-0.277240\pi$
$563$	891.989	−	239.008i	1.58435	−	0.424525i	0.940269	+	0.340433i	$0.110574\pi$
$564$	−613.373	−	444.754i	−1.08754	−	0.788570i
$565$	135.130	−	504.314i	0.239169	−	0.892590i
$566$	−244.728	−	221.209i	−0.432382	−	0.390829i
$567$	−525.821	+	492.058i	−0.927373	+	0.867827i
$568$	134.352	−	20.4841i	0.236535	−	0.0360635i
$569$	490.590	+	849.727i	0.862197	+	1.49337i	0.869803	+	0.493399i	$0.164246\pi$
$569$	490.590	+	849.727i	0.862197	+	1.49337i	−0.00760600	+	0.999971i	$0.502421\pi$
$570$	392.562	+	316.026i	0.688705	+	0.554432i
$571$	830.286	−	222.475i	1.45409	−	0.389623i	0.556647	−	0.830749i	$-0.312088\pi$
$571$	830.286	−	222.475i	1.45409	−	0.389623i	0.897445	+	0.441127i	$0.145421\pi$
$572$	774.198	+	348.275i	1.35349	+	0.608873i
$573$	150.095	−	723.195i	0.261946	−	1.26212i
$574$	17.4527	−	11.2862i	0.0304054	−	0.0196623i
$575$			20.4623i			0.0355866i
$576$	−233.250	−	526.660i	−0.404949	−	0.914339i
$577$	−944.713			−1.63728			−0.818642	−	0.574304i	$-0.805273\pi$
$577$	−944.713			−1.63728			−0.818642	+	0.574304i	$0.805273\pi$
$578$	−26.7104	−	41.3043i	−0.0462117	−	0.0714608i
$579$	−53.0915	−	160.769i	−0.0916952	−	0.277666i
$580$	−95.8632	+	213.099i	−0.165281	+	0.367412i
$581$	178.515	+	666.227i	0.307255	+	1.14669i
$582$	244.200	+	630.738i	0.419588	+	1.08374i
$583$	−152.048	+	87.7851i	−0.260803	+	0.150575i
$584$	−15.0693	−	98.8374i	−0.0258037	−	0.169242i
$585$	−534.541	−	721.071i	−0.913745	−	1.23260i
$586$	287.936	−	318.550i	0.491359	−	0.543600i
$587$	−527.453	−	141.331i	−0.898557	−	0.240768i	−0.220161	−	0.975464i	$-0.570658\pi$
$587$	−527.453	−	141.331i	−0.898557	−	0.240768i	−0.678396	+	0.734696i	$0.737325\pi$
$588$	358.590	+	37.3457i	0.609847	+	0.0635130i
$589$	204.868	+	764.578i	0.347824	+	1.29810i
$590$	229.492	+	117.489i	0.388970	+	0.199135i
$591$	−8.94473	−	156.314i	−0.0151349	−	0.264491i
$592$	40.4579	−	672.758i	0.0683410	−	1.13642i
$593$		−	500.144i		−	0.843413i	−0.906732	−	0.421707i	$-0.861431\pi$
$593$		−	500.144i		−	0.843413i	0.906732	−	0.421707i	$-0.138569\pi$
$594$	−159.435	+	512.354i	−0.268410	+	0.862548i
$595$	−477.342	+	477.342i	−0.802255	+	0.802255i
$596$	467.593	+	75.9072i	0.784552	+	0.127361i
$597$	−140.569	−	125.352i	−0.235458	−	0.209970i
$598$	−84.0271	−	260.314i	−0.140514	−	0.435308i
$599$	184.227	−	319.090i	0.307557	−	0.532704i	−0.670270	−	0.742117i	$-0.733822\pi$
$599$	184.227	−	319.090i	0.307557	−	0.532704i	0.977827	+	0.209413i	$0.0671552\pi$
$600$	4.08856	−	76.5809i	0.00681426	−	0.127635i
$601$	144.684	−	83.5331i	0.240738	−	0.138990i	−0.374778	−	0.927115i	$-0.622281\pi$
$601$	144.684	−	83.5331i	0.240738	−	0.138990i	0.615516	+	0.788124i	$0.288948\pi$
$602$	456.647	−	505.197i	0.758550	−	0.839198i
$603$	1115.11	−	440.381i	1.84927	−	0.730316i
$604$	41.4870	+	409.907i	0.0686870	+	0.678654i
$605$	26.9027	−	100.402i	0.0444672	−	0.165954i
$606$	595.113	+	262.914i	0.982035	+	0.433852i
$607$	267.871	−	463.966i	0.441303	−	0.764359i	−0.556484	−	0.830859i	$-0.687850\pi$
$607$	267.871	−	463.966i	0.441303	−	0.764359i	0.997786	+	0.0664995i	$0.0211831\pi$
$608$	−282.987	−	501.235i	−0.465438	−	0.824399i
$609$	−298.029	−	150.056i	−0.489375	−	0.246397i
$610$	−857.668	+	554.630i	−1.40601	+	0.909230i
$611$	953.533	+	953.533i	1.56061	+	1.56061i
$612$	−177.689	+	557.760i	−0.290342	+	0.911373i
$613$	−438.390	−	438.390i	−0.715155	−	0.715155i	0.252454	−	0.967609i	$-0.418762\pi$
$613$	−438.390	−	438.390i	−0.715155	−	0.715155i	−0.967609	+	0.252454i	$0.918762\pi$
$614$	64.7731	+	13.8984i	0.105494	+	0.0226358i
$615$	−13.6896	+	8.98383i	−0.0222595	+	0.0146079i
$616$	647.307	−	283.729i	1.05082	−	0.460599i
$617$	−290.931	+	503.907i	−0.471525	+	0.816706i	−0.999469	−	0.0325735i	$-0.989630\pi$
$617$	−290.931	+	503.907i	−0.471525	+	0.816706i	0.527944	+	0.849279i	$0.322963\pi$
$618$	98.6901	+	79.4491i	0.159693	+	0.128558i
$619$	−90.7444	+	338.663i	−0.146598	+	0.547113i	0.853081	+	0.521779i	$0.174731\pi$
$619$	−90.7444	+	338.663i	−0.146598	+	0.547113i	−0.999679	+	0.0253336i	$0.991935\pi$
$620$	−519.720	+	636.770i	−0.838259	+	1.02705i
$621$	156.921	−	72.5914i	0.252691	−	0.116894i
$622$	−112.440	+	5.67554i	−0.180771	+	0.00912467i
$623$	1221.13	−	705.022i	1.96009	−	1.13166i
$624$	262.462	+	991.026i	0.420612	+	1.58818i
$625$	−267.452	+	463.240i	−0.427923	+	0.741185i
$626$	−673.127	−	344.610i	−1.07528	−	0.550496i
$627$	−108.966	+	525.028i	−0.173790	+	0.837365i
$628$	−253.514	−	41.1544i	−0.403684	−	0.0655325i
$629$	−484.332	+	484.332i	−0.770004	+	0.770004i
$630$	−743.760	−	72.4055i	−1.18057	−	0.114929i
$631$			1149.26i			1.82134i	0.413140	+	0.910668i	$0.364432\pi$
$631$			1149.26i			1.82134i	−0.413140	+	0.910668i	$0.635568\pi$
$632$	136.524	+	170.600i	0.216019	+	0.269936i
$633$	233.125	+	117.377i	0.368285	+	0.185429i
$634$	772.308	−	249.294i	1.21815	−	0.393209i
$635$	108.907	+	406.445i	0.171507	+	0.640071i
$636$	−198.014	−	75.7950i	−0.311342	−	0.119175i
$637$	−619.823	−	166.081i	−0.973034	−	0.260724i
$638$	−248.308	+	12.5337i	−0.389197	+	0.0196453i
$639$	−17.4407	−	151.894i	−0.0272938	−	0.237706i
$640$	250.447	−	542.699i	0.391324	−	0.847968i
$641$	−680.483	+	392.877i	−1.06160	+	0.612912i	−0.925873	−	0.377835i	$-0.876669\pi$
$641$	−680.483	+	392.877i	−1.06160	+	0.612912i	−0.135722	+	0.990747i	$0.543335\pi$
$642$	739.802	−	540.754i	1.15234	−	0.842295i
$643$	−55.1072	−	205.663i	−0.0857033	−	0.319849i	0.909743	−	0.415172i	$-0.136278\pi$
$643$	−55.1072	−	205.663i	−0.0857033	−	0.319849i	−0.995446	+	0.0953224i	$0.969612\pi$
$644$	−207.684	−	93.4271i	−0.322490	−	0.145073i
$645$	−357.073	+	400.419i	−0.553601	+	0.620804i
$646$	−122.725	+	571.957i	−0.189977	+	0.885383i
$647$	36.6439			0.0566366			0.0283183	−	0.999599i	$-0.490985\pi$
$647$	36.6439			0.0566366			0.0283183	+	0.999599i	$0.490985\pi$
$648$	−601.788	+	240.322i	−0.928686	+	0.370867i
$649$			274.319i			0.422680i
$650$	−28.6364	+	133.459i	−0.0440559	+	0.205321i
$651$	−875.999	−	781.171i	−1.34562	−	1.19996i
$652$	200.492	+	528.376i	0.307504	+	0.810392i
$653$	−729.681	+	195.517i	−1.11743	+	0.299414i	−0.769842	−	0.638234i	$-0.779665\pi$
$653$	−729.681	+	195.517i	−1.11743	+	0.299414i	−0.347586	+	0.937648i	$0.612999\pi$
$654$	643.194	−	470.139i	0.983478	−	0.718866i
$655$	−231.282	−	400.593i	−0.353103	−	0.611592i
$656$	18.3226	−	3.74727i	0.0279307	−	0.00571229i
$657$	−111.743	+	12.8305i	−0.170080	+	0.0195289i
$658$	1121.24	−	56.5962i	1.70401	−	0.0860125i
$659$	−3.19047	+	11.9070i	−0.00484138	+	0.0180683i	−0.968304	−	0.249774i	$-0.919644\pi$
$659$	−3.19047	+	11.9070i	−0.00484138	+	0.0180683i	0.963463	+	0.267842i	$0.0863105\pi$
$660$	−508.450	+	226.954i	−0.770379	+	0.343870i
$661$	−669.383	+	179.361i	−1.01268	+	0.271347i	−0.726750	−	0.686902i	$-0.758970\pi$
$661$	−669.383	+	179.361i	−1.01268	+	0.271347i	−0.285933	+	0.958250i	$0.592303\pi$
$662$	−385.420	+	124.410i	−0.582205	+	0.187931i
$663$	468.545	−	930.589i	0.706705	−	1.40360i
$664$	−68.4393	+	616.846i	−0.103071	+	0.928985i
$665$	−746.760			−1.12295
$666$	−754.653	−	73.4659i	−1.13311	−	0.110309i
$667$	56.6471	+	56.6471i	0.0849281	+	0.0849281i
$668$	50.9165	+	70.6514i	0.0762224	+	0.105766i
$669$	−67.8871	−	14.0896i	−0.101475	−	0.0210606i
$670$	1107.40	+	566.939i	1.65284	+	0.846177i
$671$	−941.150	−	543.373i	−1.40261	−	0.809796i
$672$	758.598	+	391.152i	1.12887	+	0.582072i
$673$	300.181	+	519.928i	0.446034	+	0.772553i	0.998124	−	0.0612314i	$-0.0195028\pi$
$673$	300.181	+	519.928i	0.446034	+	0.772553i	−0.552090	+	0.833785i	$0.686169\pi$
$674$	−422.137	+	21.3080i	−0.626317	+	0.0316142i
$675$	−85.9246	−	7.78171i	−0.127296	−	0.0115285i
$676$	−115.668	−	1142.85i	−0.171107	−	1.69060i
$677$	−307.335	−	82.3501i	−0.453966	−	0.121640i	0.0245887	−	0.999698i	$-0.492172\pi$
$677$	−307.335	−	82.3501i	−0.453966	−	0.121640i	−0.478554	+	0.878058i	$0.658839\pi$
$678$	522.570	+	420.688i	0.770753	+	0.620483i
$679$	−867.947	−	501.109i	−1.27827	−	0.738011i
$680$	−556.337	+	243.855i	−0.818143	+	0.358610i
$681$	−149.923	−	228.452i	−0.220151	−	0.335466i
$682$	−855.083	−	183.476i	−1.25379	−	0.269026i
$683$	−160.877	+	160.877i	−0.235545	+	0.235545i	−0.815003	−	0.579457i	$-0.803265\pi$
$683$	−160.877	+	160.877i	−0.235545	+	0.235545i	0.579457	+	0.815003i	$0.303265\pi$
$684$	−575.274	+	297.294i	−0.841043	+	0.434641i
$685$	86.4481	−	86.4481i	0.126202	−	0.126202i
$686$	283.036	−	183.032i	0.412589	−	0.266810i
$687$	425.463	−	845.023i	0.619306	−	1.23002i
$688$	548.109	−	273.977i	0.796671	−	0.398222i
$689$	326.813	+	188.685i	0.474329	+	0.273854i
$690$	164.110	+	72.5020i	0.237841	+	0.105075i
$691$	285.527	+	76.5069i	0.413209	+	0.110719i	0.459434	−	0.888212i	$-0.348052\pi$
$691$	285.527	+	76.5069i	0.413209	+	0.110719i	−0.0462247	+	0.998931i	$0.514719\pi$
$692$	780.830	+	637.300i	1.12837	+	0.920953i
$693$	−292.053	−	739.523i	−0.421433	−	1.06713i
$694$	876.296	−	969.463i	1.26267	−	1.39692i
$695$	201.478	+	348.970i	0.289897	+	0.502116i
$696$	−200.685	−	223.323i	−0.288341	−	0.320866i
$697$	−16.4600	−	9.50320i	−0.0236155	−	0.0136344i
$698$	256.995	+	796.165i	0.368188	+	1.14064i
$699$	−495.461	+	555.606i	−0.708814	+	0.794858i
$700$	66.4399	+	92.1915i	0.0949141	+	0.131702i
$701$	397.627	+	397.627i	0.567228	+	0.567228i	0.931351	−	0.364123i	$-0.118631\pi$
$701$	397.627	+	397.627i	0.567228	+	0.567228i	−0.364123	+	0.931351i	$0.618631\pi$
$702$	1125.06	−	253.848i	1.60265	−	0.361607i
$703$	−757.696			−1.07780
$704$	635.426	−	25.9412i	0.902594	−	0.0368483i
$705$	−883.023	+	50.5291i	−1.25251	+	0.0716724i
$706$	214.077	+	109.598i	0.303225	+	0.155237i
$707$	−931.200	+	249.514i	−1.31711	+	0.352920i
$708$	−257.253	+	208.723i	−0.363351	+	0.294807i
$709$	238.924	−	891.677i	0.336987	−	1.25765i	−0.564711	−	0.825289i	$-0.691012\pi$
$709$	238.924	−	891.677i	0.336987	−	1.25765i	0.901698	−	0.432366i	$-0.142321\pi$
$710$	106.386	−	117.697i	0.149840	−	0.165771i
$711$	197.472	−	146.389i	0.277738	−	0.205892i
$712$	1254.29	−	191.236i	1.76164	−	0.268590i
$713$	140.897	+	244.041i	0.197612	+	0.342274i
$714$	−313.176	−	808.895i	−0.438622	−	1.13291i
$715$	957.256	−	256.496i	1.33882	−	0.358736i
$716$	−357.131	+	135.513i	−0.498786	+	0.189264i
$717$	−849.444	+	280.516i	−1.18472	+	0.391236i
$718$	−250.246	−	386.974i	−0.348532	−	0.538962i
$719$			22.8952i			0.0318431i	0.999873	+	0.0159215i	$0.00506820\pi$
$719$			22.8952i			0.0318431i	−0.999873	+	0.0159215i	$0.994932\pi$
$720$	−599.703	−	304.133i	−0.832920	−	0.422407i
$721$	−187.736			−0.260382
$722$	62.8910	−	40.6699i	0.0871066	−	0.0563295i
$723$	618.991	+	128.468i	0.856142	+	0.177687i
$724$	602.677	−	228.686i	0.832427	−	0.315865i
$725$	−10.3464	−	38.6133i	−0.0142709	−	0.0532598i
$726$	104.037	+	83.7534i	0.143301	+	0.115363i
$727$	−799.813	+	461.772i	−1.10015	+	0.635175i	−0.936262	−	0.351303i	$-0.885739\pi$
$727$	−799.813	+	461.772i	−1.10015	+	0.635175i	−0.163893	+	0.986478i	$0.552405\pi$
$728$	−1223.80	−	899.997i	−1.68105	−	1.23626i
$729$	245.147	+	686.545i	0.336279	+	0.941762i
$730$	−86.5852	−	78.2642i	−0.118610	−	0.107211i
$731$	−601.529	−	161.179i	−0.822886	−	0.220492i
$732$	−206.532	−	1296.04i	−0.282147	−	1.77054i
$733$	−177.694	−	663.162i	−0.242420	−	0.904724i	−0.974663	−	0.223680i	$-0.928193\pi$
$733$	−177.694	−	663.162i	−0.242420	−	0.904724i	0.732243	−	0.681044i	$-0.238474\pi$
$734$	243.172	−	474.988i	0.331297	−	0.647122i
$735$	351.872	−	230.918i	0.478738	−	0.314174i
$736$	−143.495	−	146.286i	−0.194967	−	0.198759i
$737$			1323.71i			1.79608i
$738$	−3.45070	−	20.7547i	−0.00467575	−	0.0281228i
$739$	608.238	−	608.238i	0.823055	−	0.823055i	−0.163490	−	0.986545i	$-0.552275\pi$
$739$	608.238	−	608.238i	0.823055	−	0.823055i	0.986545	+	0.163490i	$0.0522751\pi$
$740$	−460.006	−	638.301i	−0.621630	−	0.862568i
$741$	1094.41	−	361.414i	1.47694	−	0.487738i
$742$	298.983	−	96.5091i	0.402942	−	0.130066i
$743$	328.331	−	568.686i	0.441899	−	0.765392i	−0.555931	−	0.831228i	$-0.687638\pi$
$743$	328.331	−	568.686i	0.441899	−	0.765392i	0.997830	+	0.0658362i	$0.0209715\pi$
$744$	−478.552	−	941.487i	−0.643215	−	1.26544i
$745$	478.918	−	276.503i	0.642842	−	0.371145i
$746$	−472.186	−	426.808i	−0.632957	−	0.572129i
$747$	690.630	+	102.598i	0.924539	+	0.137347i
$748$	−500.708	−	408.669i	−0.669396	−	0.546349i
$749$	−351.437	+	1311.58i	−0.469208	+	1.75111i
$750$	−466.160	−	637.752i	−0.621547	−	0.850336i
$751$	151.781	−	262.893i	0.202106	−	0.350057i	−0.747101	−	0.664710i	$-0.768555\pi$
$751$	151.781	−	262.893i	0.202106	−	0.350057i	0.949207	+	0.314653i	$0.101888\pi$
$752$	958.322	+	319.562i	1.27436	+	0.424949i
$753$	67.4725	+	1179.12i	0.0896049	+	1.56589i
$754$	290.187	+	448.739i	0.384863	+	0.595144i
$755$	340.093	+	340.093i	0.450454	+	0.450454i
$756$	471.298	−	836.570i	0.623410	−	1.10657i
$757$	465.613	+	465.613i	0.615077	+	0.615077i	0.944264	−	0.329188i	$-0.106775\pi$
$757$	465.613	+	465.613i	0.615077	+	0.615077i	−0.329188	+	0.944264i	$0.606775\pi$
$758$	−133.882	+	623.954i	−0.176626	+	0.823159i
$759$	10.9057	+	190.583i	0.0143685	+	0.251098i
$760$	−625.916	−	244.426i	−0.823574	−	0.321613i
$761$	624.864	−	1082.30i	0.821109	−	1.42220i	−0.0837482	−	0.996487i	$-0.526689\pi$
$761$	624.864	−	1082.30i	0.821109	−	1.42220i	0.904857	−	0.425715i	$-0.139978\pi$
$762$	−534.258	−	83.0448i	−0.701126	−	0.108983i
$763$	−305.544	+	1140.31i	−0.400451	+	1.49450i
$764$	99.1665	+	979.802i	0.129799	+	1.28246i
$765$	251.010	+	635.594i	0.328117	+	0.830842i
$766$	19.4006	+	384.349i	0.0253271	+	0.501761i
$767$	510.628	−	294.811i	0.665747	−	0.384369i
$768$	507.808	+	576.155i	0.661209	+	0.750202i
$769$	254.390	−	440.616i	0.330806	−	0.572973i	−0.651864	−	0.758336i	$-0.726013\pi$
$769$	254.390	−	440.616i	0.330806	−	0.572973i	0.982670	+	0.185363i	$0.0593460\pi$
$770$	375.985	−	734.410i	0.488292	−	0.953780i
$771$	543.713	−	179.553i	0.705205	−	0.232884i
$772$	131.985	+	183.141i	0.170964	+	0.237229i
$773$	448.856	−	448.856i	0.580667	−	0.580667i	−0.354419	−	0.935087i	$-0.615321\pi$
$773$	448.856	−	448.856i	0.580667	−	0.580667i	0.935087	+	0.354419i	$0.115321\pi$
$774$	−285.216	−	627.597i	−0.368496	−	0.810849i
$775$		−	140.616i		−	0.181439i
$776$	−563.471	−	704.110i	−0.726123	−	0.907358i
$777$	939.311	−	616.427i	1.20889	−	0.793342i
$778$	280.153	+	867.906i	0.360093	+	1.11556i
$779$	−5.44168	−	20.3086i	−0.00698546	−	0.0260701i
$780$	968.893	+	702.539i	1.24217	+	0.900691i
$781$	163.055	+	43.6904i	0.208777	+	0.0559416i
$782$	10.4985	+	207.988i	0.0134252	+	0.265970i
$783$	−259.413	+	216.328i	−0.331307	+	0.276281i
$784$	−470.958	+	96.3186i	−0.600711	+	0.122855i
$785$	−259.653	+	149.911i	−0.330769	+	0.190969i
$786$	590.924	−	63.8264i	0.751811	−	0.0812040i
$787$	98.1139	+	366.166i	0.124668	+	0.465268i	0.999828	−	0.0185664i	$-0.00591022\pi$
$787$	98.1139	+	366.166i	0.124668	+	0.465268i	−0.875159	+	0.483835i	$0.839244\pi$
$788$	74.0614	+	195.181i	0.0939865	+	0.247691i
$789$	−732.158	−	151.955i	−0.927956	−	0.192592i
$790$	249.399	+	53.5138i	0.315695	+	0.0677390i
$791$	−994.072			−1.25673
$792$	−2.73472	−	715.444i	−0.00345293	−	0.903339i
$793$			2335.85i			2.94559i
$794$	−650.570	−	139.593i	−0.819358	−	0.175810i
$795$	−235.030	+	77.6151i	−0.295635	+	0.0976291i
$796$	229.016	+	103.024i	0.287709	+	0.129427i
$797$	−187.895	+	50.3464i	−0.235753	+	0.0631698i	−0.374761	−	0.927121i	$-0.622275\pi$
$797$	−187.895	+	50.3464i	−0.235753	+	0.0631698i	0.139008	+	0.990291i	$0.455609\pi$
$798$	387.755	−	877.692i	0.485908	−	1.09986i
$799$	−513.325	−	889.105i	−0.642459	−	1.11277i
$800$	25.5126	+	99.0195i	0.0318908	+	0.123774i
$801$	−162.824	−	1418.06i	−0.203276	−	1.77037i
$802$	1.58600	+	31.4207i	0.00197756	+	0.0391779i
$803$	32.1413	−	119.953i	0.0400266	−	0.149381i
$804$	−1241.36	+	1007.18i	−1.54398	+	1.25272i
$805$	−256.790	+	68.8068i	−0.318994	+	0.0854743i
$806$	577.430	+	1788.86i	0.716414	+	2.21943i
$807$	−26.1585	+	1.49686i	−0.0324145	+	0.00185485i
$808$	−862.179	−	95.6592i	−1.06705	−	0.118390i
$809$	303.139			0.374708			0.187354	−	0.982292i	$-0.440009\pi$
$809$	303.139			0.374708			0.187354	+	0.982292i	$0.440009\pi$
$810$	−366.859	+	661.554i	−0.452912	+	0.816734i
$811$	−650.267	−	650.267i	−0.801809	−	0.801809i	0.181569	−	0.983378i	$-0.441882\pi$
$811$	−650.267	−	650.267i	−0.801809	−	0.801809i	−0.983378	+	0.181569i	$0.941882\pi$
$812$	439.150	+	71.2898i	0.540825	+	0.0877953i
$813$	938.403	−	1052.32i	1.15425	−	1.29436i
$814$	381.491	−	745.166i	0.468662	−	0.915438i
$815$	571.343	+	329.865i	0.701035	+	0.404743i
$816$	2.26695	−	780.504i	0.00277813	−	0.956500i
$817$	−344.445	−	596.596i	−0.421597	−	0.730228i
$818$	62.6355	+	1240.89i	0.0765715	+	1.51698i
$819$	−1062.71	+	1338.41i	−1.29757	+	1.63419i
$820$	13.8047	−	16.9138i	0.0168350	−	0.0206265i
$821$	−269.096	−	72.1042i	−0.327767	−	0.0878248i	0.0911834	−	0.995834i	$-0.470935\pi$
$821$	−269.096	−	72.1042i	−0.327767	−	0.0878248i	−0.418950	+	0.908009i	$0.637602\pi$
$822$	56.7172	+	146.493i	0.0689990	+	0.178216i
$823$	−205.861	−	118.854i	−0.250135	−	0.144416i	0.369691	−	0.929155i	$-0.379464\pi$
$823$	−205.861	−	118.854i	−0.250135	−	0.144416i	−0.619826	+	0.784739i	$0.712797\pi$
$824$	−157.355	−	61.4488i	−0.190965	−	0.0745737i
$825$	42.8377	−	85.0809i	0.0519244	−	0.103128i
$826$	102.984	−	479.955i	0.124678	−	0.581059i
$827$	130.553	−	130.553i	0.157864	−	0.157864i	−0.623756	−	0.781619i	$-0.714394\pi$
$827$	130.553	−	130.553i	0.157864	−	0.157864i	0.781619	+	0.623756i	$0.214394\pi$
$828$	−170.428	+	155.237i	−0.205831	+	0.187485i
$829$	964.034	−	964.034i	1.16289	−	1.16289i	0.179047	−	0.983841i	$-0.442699\pi$
$829$	964.034	−	964.034i	1.16289	−	1.16289i	0.983841	−	0.179047i	$-0.0573014\pi$
$830$	393.428	+	608.388i	0.474009	+	0.732998i
$831$	−50.3485	−	76.7211i	−0.0605879	−	0.0923238i
$832$	−731.181	−	1154.93i	−0.878823	−	1.38813i
$833$	423.083	+	244.267i	0.507903	+	0.293238i
$834$	−514.774	+	55.6014i	−0.617235	+	0.0666683i
$835$	98.1997	+	26.3125i	0.117604	+	0.0315120i
$836$	−71.9933	−	711.321i	−0.0861164	−	0.850863i
$837$	−1078.35	+	498.844i	−1.28835	+	0.595990i
$838$	−961.593	−	869.182i	−1.14749	−	1.03721i
$839$	−502.563	−	870.464i	−0.599002	−	1.03750i	−0.992969	−	0.118377i	$-0.962231\pi$
$839$	−502.563	−	870.464i	−0.599002	−	1.03750i	0.393966	−	0.919125i	$-0.371103\pi$
$840$	974.798	−	206.203i	1.16047	−	0.245480i
$841$	592.789	+	342.247i	0.704862	+	0.406952i
$842$	−204.445	+	65.9931i	−0.242809	+	0.0783766i
$843$	−1562.51	−	324.289i	−1.85351	−	0.384685i
$844$	−343.512	−	55.7643i	−0.407004	−	0.0660715i
$845$	−948.201	−	948.201i	−1.12213	−	1.12213i
$846$	399.121	−	1064.08i	0.471774	−	1.25778i
$847$	−197.907			−0.233656
$848$	282.189	+	16.9701i	0.332770	+	0.0200119i
$849$	222.529	−	441.971i	0.262108	−	0.520578i
$850$	47.3563	−	92.5010i	0.0557133	−	0.108825i
$851$	−260.551	+	69.8145i	−0.306171	+	0.0820382i
$852$	83.0924	+	186.153i	0.0975263	+	0.218490i
$853$	−272.744	+	1017.90i	−0.319747	+	1.19331i	0.599740	+	0.800195i	$0.295271\pi$
$853$	−272.744	+	1017.90i	−0.319747	+	1.19331i	−0.919488	+	0.393119i	$0.871396\pi$
$854$	1442.66	+	1304.02i	1.68930	+	1.52696i
$855$	−300.825	+	693.508i	−0.351842	+	0.811120i
$856$	−723.867	+	984.305i	−0.845639	+	1.14989i
$857$	−434.700	−	752.922i	−0.507234	−	0.878556i	−0.999965	−	0.00837381i	$-0.997335\pi$
$857$	−434.700	−	752.922i	−0.507234	−	0.878556i	0.492731	−	0.870182i	$-0.335999\pi$
$858$	−195.586	+	1258.28i	−0.227956	+	1.46653i
$859$	−145.253	+	38.9204i	−0.169095	+	0.0453090i	−0.342373	−	0.939564i	$-0.611231\pi$
$859$	−145.253	+	38.9204i	−0.169095	+	0.0453090i	0.173278	+	0.984873i	$0.444564\pi$
$860$	293.470	−	652.368i	0.341244	−	0.758568i
$861$	23.2682	+	20.7493i	0.0270246	+	0.0240991i
$862$	105.580	−	68.2758i	0.122483	−	0.0792063i
$863$			1029.95i			1.19345i	0.802445	+	0.596726i	$0.203532\pi$
$863$			1029.95i			1.19345i	−0.802445	+	0.596726i	$0.796468\pi$
$864$	668.853	−	546.930i	0.774135	−	0.633021i
$865$	1176.60			1.36023
$866$	267.896	+	414.268i	0.309349	+	0.478370i
$867$	49.1063	−	55.0674i	0.0566394	−	0.0635149i
$868$	1427.19	+	642.026i	1.64423	+	0.739661i
$869$	70.2439	+	262.154i	0.0808330	+	0.301673i
$870$	−346.343	−	53.8354i	−0.398096	−	0.0618798i
$871$	2464.01	−	1422.60i	2.82894	−	1.63329i
$872$	−629.340	+	855.768i	−0.721720	+	0.981385i
$873$	−815.019	+	604.186i	−0.933584	+	0.692080i
$874$	−154.478	+	170.902i	−0.176748	+	0.195540i
$875$	1130.66	+	302.959i	1.29218	+	0.346239i
$876$	136.946	−	61.1279i	0.156331	−	0.0697807i
$877$	0.476631	+	1.77881i	0.000543479	+	0.00202829i	0.966197	−	0.257805i	$-0.0829991\pi$
$877$	0.476631	+	1.77881i	0.000543479	+	0.00202829i	−0.965654	+	0.259833i	$0.916332\pi$
$878$	−561.887	−	287.660i	−0.639962	−	0.327631i
$879$	575.289	+	289.654i	0.654482	+	0.329527i
$880$	555.525	−	492.500i	0.631278	−	0.559659i
$881$		−	1270.97i		−	1.44264i	−0.692601	−	0.721321i	$-0.743535\pi$
$881$		−	1270.97i		−	1.44264i	0.692601	−	0.721321i	$-0.256465\pi$
$882$	88.6958	+	533.471i	0.100562	+	0.604843i
$883$	191.436	−	191.436i	0.216801	−	0.216801i	−0.590348	−	0.807149i	$-0.701009\pi$
$883$	191.436	−	191.436i	0.216801	−	0.216801i	0.807149	+	0.590348i	$0.201009\pi$
$884$	−222.601	+	1371.23i	−0.251811	+	1.55117i
$885$	−78.5883	+	378.658i	−0.0888004	+	0.427863i
$886$	−288.009	−	892.244i	−0.325066	−	1.00705i
$887$	−551.253	+	954.798i	−0.621480	+	1.07644i	0.367730	+	0.929933i	$0.380135\pi$
$887$	−551.253	+	954.798i	−0.621480	+	1.07644i	−0.989210	+	0.146503i	$0.953198\pi$
$888$	989.074	−	209.223i	1.11382	−	0.235612i
$889$	693.825	−	400.580i	0.780455	−	0.450596i
$890$	993.207	−	1098.80i	1.11596	−	1.23461i
$891$	−804.438	−	26.6829i	−0.902849	−	0.0299472i
$892$	91.9752	−	9.30887i	0.103111	−	0.0104360i
$893$	293.938	−	1096.99i	0.329158	−	1.22843i
$894$	76.3058	+	706.462i	0.0853533	+	0.790226i
$895$	−222.957	+	386.173i	−0.249114	+	0.431478i
$896$	−1121.49	−	193.163i	−1.25167	−	0.215583i
$897$	343.038	−	225.120i	0.382428	−	0.250970i
$898$	382.281	−	247.211i	0.425703	−	0.275290i
$899$	−389.276	−	389.276i	−0.433009	−	0.433009i
$900$	112.382	−	24.5636i	0.124869	−	0.0272929i
$901$	−203.154	−	203.154i	−0.225476	−	0.225476i
$902$	22.7126	+	4.87345i	0.0251802	+	0.00540294i
$903$	912.369	+	459.372i	1.01038	+	0.508717i
$904$	−833.207	−	325.375i	−0.921689	−	0.359928i
$905$	376.251	−	651.687i	0.415747	−	0.720096i
$906$	−576.315	+	223.129i	−0.636110	+	0.246280i
$907$	45.9065	−	171.325i	0.0506135	−	0.188892i	−0.935991	−	0.352025i	$-0.885493\pi$
$907$	45.9065	−	171.325i	0.0506135	−	0.188892i	0.986604	+	0.163133i	$0.0521599\pi$
$908$	282.258	+	230.374i	0.310857	+	0.253716i
$909$	−143.404	+	965.310i	−0.157760	+	1.06195i
$910$	−1771.13	+	89.4003i	−1.94630	+	0.0982420i
$911$	273.677	−	158.007i	0.300414	−	0.173444i	−0.342215	−	0.939622i	$-0.611177\pi$
$911$	273.677	−	158.007i	0.300414	−	0.173444i	0.642629	+	0.766178i	$0.277844\pi$
$912$	612.289	−	608.742i	0.671369	−	0.667481i
$913$	−385.443	+	667.606i	−0.422172	+	0.731223i
$914$	−233.915	−	119.754i	−0.255924	−	0.131022i
$915$	−1143.45	−	1019.67i	−1.24968	−	1.11440i
$916$	−202.133	+	1245.15i	−0.220669	+	1.35934i
$917$	−622.757	+	622.757i	−0.679124	+	0.679124i
$918$	−877.372	−	35.0120i	−0.955743	−	0.0381394i
$919$		−	565.893i		−	0.615770i	−0.951424	−	0.307885i	$-0.900379\pi$
$919$		−	565.893i		−	0.615770i	0.951424	−	0.307885i	$-0.0996212\pi$
$920$	−237.757	−	26.3793i	−0.258432	−	0.0286731i
$921$	5.67701	+	99.2088i	0.00616396	+	0.107719i
$922$	−1151.30	+	371.631i	−1.24870	+	0.403070i
$923$	−93.9082	−	350.470i	−0.101742	−	0.379708i
$924$	667.948	+	823.249i	0.722887	+	0.890963i
$925$	130.015	+	34.8375i	0.140557	+	0.0376621i
$926$	601.256	−	30.3493i	0.649305	−	0.0327746i
$927$	−75.6275	+	174.348i	−0.0815830	+	0.188078i
$928$	344.750	+	203.494i	0.371498	+	0.219282i
$929$	1303.37	−	752.499i	1.40298	−	0.810009i	0.408280	−	0.912857i	$-0.366129\pi$
$929$	1303.37	−	752.499i	1.40298	−	0.810009i	0.994697	+	0.102847i	$0.0327954\pi$
$930$	−1127.76	−	498.230i	−1.21264	−	0.535731i
$931$	139.871	+	522.006i	0.150238	+	0.560694i
$932$	407.207	−	905.201i	0.436918	−	0.971246i
$933$	−52.9553	−	160.356i	−0.0567581	−	0.171872i
$934$	−358.899	+	1672.64i	−0.384260	+	1.79083i
$935$	−754.494			−0.806946
$936$	−1328.82	+	773.979i	−1.41967	+	0.826901i
$937$			397.758i			0.424501i	0.977215	+	0.212251i	$0.0680794\pi$
$937$			397.758i			0.424501i	−0.977215	+	0.212251i	$0.931921\pi$
$938$	496.945	−	2316.00i	0.529792	−	2.46908i
$939$	230.509	−	1110.65i	0.245483	−	1.18280i
$940$	1102.58	−	418.375i	1.17296	−	0.445080i
$941$	−1568.88	+	420.379i	−1.66724	+	0.446736i	−0.964365	−	0.264575i	$-0.914768\pi$
$941$	−1568.88	+	420.379i	−1.66724	+	0.446736i	−0.702877	+	0.711311i	$0.748102\pi$
$942$	−41.3705	−	383.021i	−0.0439177	−	0.406604i
$943$	−3.74249	−	6.48218i	−0.00396870	−	0.00687400i
$944$	243.416	−	368.578i	0.257856	−	0.390443i
$945$	−191.275	−	1104.47i	−0.202408	−	1.16876i
$946$	760.154	−	38.3698i	0.803545	−	0.0405601i
$947$	−317.120	+	1183.51i	−0.334868	+	1.24974i	0.569145	+	0.822237i	$0.307274\pi$
$947$	−317.120	+	1183.51i	−0.334868	+	1.24974i	−0.904012	+	0.427506i	$0.859392\pi$
$948$	−192.397	+	265.340i	−0.202950	+	0.279895i
$949$	−257.827	+	69.0846i	−0.271683	+	0.0727973i
$950$	109.397	−	35.3125i	0.115155	−	0.0371711i
$951$	667.893	+	1017.74i	0.702306	+	1.07017i
$952$	722.628	+	902.991i	0.759063	+	0.948520i
$953$	1482.94			1.55608			0.778038	−	0.628217i	$-0.216215\pi$
$953$	1482.94			1.55608			0.778038	+	0.628217i	$0.216215\pi$
$954$	30.8154	−	316.540i	0.0323012	−	0.331803i
$955$	812.925	+	812.925i	0.851230	+	0.851230i
$956$	967.650	−	697.359i	1.01219	−	0.729455i
$957$	−116.945	−	354.126i	−0.122199	−	0.370037i
$958$	623.935	+	319.426i	0.651289	+	0.333430i
$959$	−201.587	−	116.386i	−0.210205	−	0.121362i
$960$	884.545	+	146.232i	0.921401	+	0.152325i
$961$	−487.738	−	844.787i	−0.507531	−	0.879070i
$962$	−1797.07	+	90.7096i	−1.86805	+	0.0942927i
$963$	1076.48	+	854.733i	1.11784	+	0.887574i
$964$	−838.625	+	84.8778i	−0.869943	+	0.0880475i
$965$	254.551	+	68.2067i	0.263783	+	0.0706805i
$966$	52.4674	−	337.542i	0.0543140	−	0.349423i
$967$	40.5376	+	23.4044i	0.0419210	+	0.0242031i	0.520814	−	0.853670i	$-0.325629\pi$
$967$	40.5376	+	23.4044i	0.0419210	+	0.0242031i	−0.478893	+	0.877873i	$0.658962\pi$
$968$	−165.881	−	64.7779i	−0.171364	−	0.0669193i
$969$	−876.030	+	50.1289i	−0.904056	+	0.0517326i
$970$	−1029.34	−	220.865i	−1.06117	−	0.227696i
$971$	53.4939	−	53.4939i	0.0550916	−	0.0550916i	−0.679024	−	0.734116i	$-0.737597\pi$
$971$	53.4939	−	53.4939i	0.0550916	−	0.0550916i	0.734116	+	0.679024i	$0.237597\pi$
$972$	−587.056	−	774.693i	−0.603967	−	0.797009i
$973$	542.505	−	542.505i	0.557559	−	0.557559i
$974$	464.138	−	300.145i	0.476527	−	0.308157i
$975$	−204.410	+	11.6969i	−0.209652	+	0.0119969i
$976$	782.380	+	1565.21i	0.801619	+	1.60369i
$977$	488.068	+	281.786i	0.499558	+	0.288420i	0.728531	−	0.685013i	$-0.240203\pi$
$977$	488.068	+	281.786i	0.499558	+	0.288420i	−0.228973	+	0.973433i	$0.573537\pi$
$978$	−684.371	+	500.237i	−0.699766	+	0.511490i
$979$	1522.26	+	407.887i	1.55491	+	0.416637i
$980$	−354.833	+	434.746i	−0.362074	+	0.443619i
$981$	935.905	+	743.117i	0.954032	+	0.757510i
$982$	−1225.26	+	1355.53i	−1.24772	+	1.38038i
$983$	206.735	+	358.076i	0.210311	+	0.364269i	0.951812	−	0.306683i	$-0.0992191\pi$
$983$	206.735	+	358.076i	0.210311	+	0.364269i	−0.741501	+	0.670952i	$0.765886\pi$
$984$	12.7112	+	25.0076i	0.0129179	+	0.0254143i
$985$	211.053	+	121.851i	0.214267	+	0.123707i
$986$	−124.977	−	387.176i	−0.126752	−	0.392674i
$987$	528.068	+	1599.07i	0.535023	+	1.62013i
$988$	−1246.71	+	898.468i	−1.26185	+	0.909381i
$989$	−173.416	−	173.416i	−0.175345	−	0.175345i
$990$	−530.577	−	645.023i	−0.535937	−	0.651538i
$991$	53.2364			0.0537198			0.0268599	−	0.999639i	$-0.491449\pi$
$991$	53.2364			0.0537198			0.0268599	+	0.999639i	$0.491449\pi$
$992$	986.092	+	1005.27i	0.994045	+	1.01338i
$993$	−333.312	−	507.900i	−0.335661	−	0.511481i
$994$	−268.882	−	137.655i	−0.270505	−	0.138486i
$995$	283.167	−	75.8744i	0.284590	−	0.0762557i
$996$	−919.346	+	146.504i	−0.923038	+	0.147092i
$997$	−4.98276	+	18.5959i	−0.00499776	+	0.0186519i	−0.968380	−	0.249481i	$-0.919740\pi$
$997$	−4.98276	+	18.5959i	−0.00499776	+	0.0186519i	0.963382	+	0.268133i	$0.0864066\pi$
$998$	−306.178	+	338.731i	−0.306792	+	0.339410i
$999$	−194.077	−	1120.65i	−0.194271	−	1.12177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.w.a.5.16	✓	184
3.2	odd	2		432.3.x.a.341.31		184
9.2	odd	6	inner	144.3.w.a.101.31	yes	184
9.7	even	3		432.3.x.a.197.16		184
16.13	even	4	inner	144.3.w.a.77.31	yes	184
48.29	odd	4		432.3.x.a.125.16		184
144.29	odd	12	inner	144.3.w.a.29.16	yes	184
144.61	even	12		432.3.x.a.413.31		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.16	✓	184	1.1	even	1	trivial
144.3.w.a.29.16	yes	184	144.29	odd	12	inner
144.3.w.a.77.31	yes	184	16.13	even	4	inner
144.3.w.a.101.31	yes	184	9.2	odd	6	inner
432.3.x.a.125.16		184	48.29	odd	4
432.3.x.a.197.16		184	9.7	even	3
432.3.x.a.341.31		184	3.2	odd	2
432.3.x.a.413.31		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)

\(f(q)\)	\(=\)	\(q+(-1.08605 - 1.67944i) q^{2} +(1.99667 - 2.23905i) q^{3} +(-1.64101 + 3.64789i) q^{4} +(1.20857 + 4.51043i) q^{5} +(-5.92880 - 0.921569i) q^{6} +(7.69955 - 4.44534i) q^{7} +(7.90861 - 1.20579i) q^{8} +(-1.02665 - 8.94125i) q^{9} +O(q^{10})\)	\(q+(-1.08605 - 1.67944i) q^{2} +(1.99667 - 2.23905i) q^{3} +(-1.64101 + 3.64789i) q^{4} +(1.20857 + 4.51043i) q^{5} +(-5.92880 - 0.921569i) q^{6} +(7.69955 - 4.44534i) q^{7} +(7.90861 - 1.20579i) q^{8} +(-1.02665 - 8.94125i) q^{9} +(6.26242 - 6.92824i) q^{10} +(9.59821 + 2.57183i) q^{11} +(4.89123 + 10.9579i) q^{12} +(-5.52790 - 20.6304i) q^{13} +(-15.8277 - 8.10307i) q^{14} +(12.5122 + 6.29978i) q^{15} +(-10.6142 - 11.9725i) q^{16} +16.2606i q^{17} +(-13.9013 + 11.4348i) q^{18} +(-12.7191 + 12.7191i) q^{19} +(-18.4368 - 2.99296i) q^{20} +(5.42012 - 26.1155i) q^{21} +(-6.10486 - 18.9127i) q^{22} +(-3.20182 + 5.54571i) q^{23} +(13.0910 - 20.1153i) q^{24} +(2.76731 - 1.59771i) q^{25} +(-28.6439 + 31.6893i) q^{26} +(-22.0697 - 15.5540i) q^{27} +(3.58103 + 35.3819i) q^{28} +(3.23789 - 12.0840i) q^{29} +(-3.00868 - 27.8552i) q^{30} +(22.0027 - 38.1098i) q^{31} +(-8.57952 + 30.8284i) q^{32} +(24.9229 - 16.3557i) q^{33} +(27.3086 - 17.6597i) q^{34} +(29.3558 + 29.3558i) q^{35} +(34.3014 + 10.9276i) q^{36} +(29.7857 + 29.7857i) q^{37} +(35.1745 + 7.54742i) q^{38} +(-57.2298 - 28.8148i) q^{39} +(14.9967 + 34.2139i) q^{40} +(-0.584432 + 1.01227i) q^{41} +(-49.7458 + 19.2599i) q^{42} +(-9.91228 + 36.9931i) q^{43} +(-25.1325 + 30.7928i) q^{44} +(39.0881 - 15.4367i) q^{45} +(12.7910 - 0.645643i) q^{46} +(-54.6786 + 31.5687i) q^{47} +(-47.9998 - 0.139414i) q^{48} +(15.0221 - 26.0190i) q^{49} +(-5.68868 - 2.91234i) q^{50} +(36.4081 + 32.4669i) q^{51} +(84.3288 + 13.6896i) q^{52} +(-12.4936 + 12.4936i) q^{53} +(-2.15318 + 53.9571i) q^{54} +46.4003i q^{55} +(55.5326 - 44.4405i) q^{56} +(3.08285 + 53.8745i) q^{57} +(-23.8108 + 7.68591i) q^{58} +(7.14507 + 26.6658i) q^{59} +(-43.5135 + 35.3049i) q^{60} +(-105.639 - 28.3060i) q^{61} +(-87.8989 + 4.43682i) q^{62} +(-47.6516 - 64.2798i) q^{63} +(61.0921 - 19.0723i) q^{64} +(86.3711 - 49.8664i) q^{65} +(-54.5358 - 24.0933i) q^{66} +(34.4781 + 128.674i) q^{67} +(-59.3167 - 26.6838i) q^{68} +(6.02413 + 18.2419i) q^{69} +(17.4195 - 81.1829i) q^{70} +16.9880 q^{71} +(-18.9007 - 69.4749i) q^{72} -12.4974i q^{73} +(17.6746 - 82.3718i) q^{74} +(1.94806 - 9.38623i) q^{75} +(-25.5257 - 67.2702i) q^{76} +(85.3346 - 22.8653i) q^{77} +(13.7615 + 127.408i) q^{78} +(13.6564 + 23.6535i) q^{79} +(41.1730 - 62.3439i) q^{80} +(-78.8920 + 18.3591i) q^{81} +(2.33476 - 0.117850i) q^{82} +(-20.0789 + 74.9354i) q^{83} +(86.3719 + 62.6278i) q^{84} +(-73.3421 + 19.6519i) q^{85} +(72.8928 - 23.5292i) q^{86} +(-20.5916 - 31.3775i) q^{87} +(79.0096 + 8.76615i) q^{88} +158.598 q^{89} +(-68.3764 - 48.8810i) q^{90} +(-134.272 - 134.272i) q^{91} +(-14.9759 - 20.7804i) q^{92} +(-41.3975 - 125.358i) q^{93} +(112.401 + 57.5442i) q^{94} +(-72.7406 - 41.9968i) q^{95} +(51.8958 + 80.7640i) q^{96} +(-56.3634 - 97.6244i) q^{97} +(-60.0119 + 3.02918i) q^{98} +(13.1414 - 88.4604i) 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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