LMFDB - Embedded newform 361.3.f.d.262.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,3,Mod(116,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("361.116");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	361.f (of order $18$, degree $6$, not 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:	$9.83653754341$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	12.0.7659539263855005696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2197x^{6} + 4826809 $ x^12 - 2197*x^6 + 4826809
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			262.2
Root			$1.23317 - 3.38811i$ of defining polynomial
Character	$\chi$	$=$	361.262
Dual form			361.3.f.d.299.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23317 - 3.38811i) q^{2} +(3.55077 - 0.626097i) q^{3} +(-6.89440 - 5.78509i) q^{4} +(3.06418 - 2.57115i) q^{5} +(2.25743 - 12.8025i) q^{6} +(2.50000 - 4.33013i) q^{7} +(-15.6125 + 9.01388i) q^{8} +(3.75877 - 1.36808i) q^{9} +O(q^{10})$	\(q+(1.23317 - 3.38811i) q^{2} +(3.55077 - 0.626097i) q^{3} +(-6.89440 - 5.78509i) q^{4} +(3.06418 - 2.57115i) q^{5} +(2.25743 - 12.8025i) q^{6} +(2.50000 - 4.33013i) q^{7} +(-15.6125 + 9.01388i) q^{8} +(3.75877 - 1.36808i) q^{9} +(-4.93268 - 13.5524i) q^{10} +(5.00000 + 8.66025i) q^{11} +(-28.1025 - 16.2250i) q^{12} +(3.55077 + 0.626097i) q^{13} +(-11.5880 - 13.8101i) q^{14} +(9.27041 - 11.0481i) q^{15} +(5.03580 + 28.5594i) q^{16} +(-14.0954 - 5.13030i) q^{17} -14.4222i q^{18} -36.0000 q^{20} +(6.16586 - 16.9405i) q^{21} +(35.5077 - 6.26097i) q^{22} +(26.8116 + 22.4976i) q^{23} +(-49.7929 + 41.7812i) q^{24} +(-1.56283 + 8.86327i) q^{25} +(6.50000 - 11.2583i) q^{26} +(-15.6125 + 9.01388i) q^{27} +(-42.2862 + 15.3909i) q^{28} +(-6.16586 - 16.9405i) q^{29} +(-26.0000 - 45.0333i) q^{30} +(31.2250 + 18.0278i) q^{31} +(31.9570 + 5.63488i) q^{32} +(23.1760 + 27.6201i) q^{33} +(-34.7641 + 41.4302i) q^{34} +(-3.47296 - 19.6962i) q^{35} +(-33.8289 - 12.3127i) q^{36} -21.6333i q^{37} +13.0000 q^{39} +(-24.6634 + 67.7622i) q^{40} +(-35.5077 + 6.26097i) q^{41} +(-49.7929 - 41.7812i) q^{42} +(-15.3209 + 12.8558i) q^{43} +(15.6283 - 88.6327i) q^{44} +(8.00000 - 13.8564i) q^{45} +(109.287 - 63.0971i) q^{46} +(-9.39693 + 3.42020i) q^{47} +(35.7620 + 98.2552i) q^{48} +(12.0000 + 20.7846i) q^{49} +(28.1025 + 16.2250i) q^{50} +(-53.2616 - 9.39146i) q^{51} +(-20.8584 - 24.8581i) q^{52} +(48.6697 - 58.0023i) q^{53} +(11.2871 + 64.0125i) q^{54} +(37.5877 + 13.6808i) q^{55} +90.1388i q^{56} -65.0000 q^{58} +(6.16586 - 16.9405i) q^{59} +(-127.828 + 22.5395i) q^{60} +(-30.6418 - 25.7115i) q^{61} +(99.5858 - 83.5624i) q^{62} +(3.47296 - 19.6962i) q^{63} +(0.500000 - 0.866025i) q^{64} +(12.4900 - 7.21110i) q^{65} +(122.160 - 44.4626i) q^{66} +(-13.5649 - 37.2692i) q^{67} +(67.5000 + 116.913i) q^{68} +(109.287 + 63.0971i) q^{69} +(-71.0155 - 12.5219i) q^{70} +(69.5281 + 82.8604i) q^{71} +(-46.3521 + 55.2403i) q^{72} +(18.2331 + 103.405i) q^{73} +(-73.2960 - 26.6776i) q^{74} +32.4500i q^{75} +50.0000 q^{77} +(16.0312 - 44.0454i) q^{78} +(35.5077 - 6.26097i) q^{79} +(88.8612 + 74.5634i) q^{80} +(-77.3705 + 64.9215i) q^{81} +(-22.5743 + 128.025i) q^{82} +(20.0000 - 34.6410i) q^{83} +(-140.512 + 81.1249i) q^{84} +(-56.3816 + 20.5212i) q^{85} +(24.6634 + 67.7622i) q^{86} +(-32.5000 - 56.2917i) q^{87} +(-156.125 - 90.1388i) q^{88} +(-37.0817 - 44.1922i) q^{90} +(11.5880 - 13.8101i) q^{91} +(-54.6992 - 310.214i) q^{92} +(122.160 + 44.4626i) q^{93} +36.0555i q^{94} +117.000 q^{96} +(41.9278 - 115.196i) q^{97} +(85.2186 - 15.0263i) q^{98} +(30.6418 + 25.7115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 30 q^{7}+O(q^{10}) $ 12 * q + 30 * q^7	$ 12 q + 30 q^{7} + 60 q^{11} - 432 q^{20} + 78 q^{26} - 312 q^{30} + 156 q^{39} + 96 q^{45} + 144 q^{49} - 780 q^{58} + 6 q^{64} + 810 q^{68} + 600 q^{77} + 240 q^{83} - 390 q^{87} + 1404 q^{96}+O(q^{100}) $ 12 * q + 30 * q^7 + 60 * q^11 - 432 * q^20 + 78 * q^26 - 312 * q^30 + 156 * q^39 + 96 * q^45 + 144 * q^49 - 780 * q^58 + 6 * q^64 + 810 * q^68 + 600 * q^77 + 240 * q^83 - 390 * q^87 + 1404 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	1.23317	−	3.38811i	0.616586	−	1.69405i	−0.0986060	−	0.995127i	$-0.531438\pi$
$2$	1.23317	−	3.38811i	0.616586	−	1.69405i	0.715192	−	0.698928i	$-0.246339\pi$
$3$	3.55077	−	0.626097i	1.18359	−	0.208699i	0.452998	−	0.891512i	$-0.350355\pi$
$3$	3.55077	−	0.626097i	1.18359	−	0.208699i	0.730594	+	0.682812i	$0.239243\pi$
$4$	−6.89440	−	5.78509i	−1.72360	−	1.44627i
$5$	3.06418	−	2.57115i	0.612836	−	0.514230i	−0.282707	−	0.959206i	$-0.591232\pi$
$5$	3.06418	−	2.57115i	0.612836	−	0.514230i	0.895542	+	0.444976i	$0.146788\pi$
$6$	2.25743	−	12.8025i	0.376238	−	2.13375i
$7$	2.50000	−	4.33013i	0.357143	−	0.618590i	−0.630339	−	0.776320i	$-0.717084\pi$
$7$	2.50000	−	4.33013i	0.357143	−	0.618590i	0.987482	+	0.157730i	$0.0504176\pi$
$8$	−15.6125	+	9.01388i	−1.95156	+	1.12673i
$9$	3.75877	−	1.36808i	0.417641	−	0.152009i
$10$	−4.93268	−	13.5524i	−0.493268	−	1.35524i
$11$	5.00000	+	8.66025i	0.454545	+	0.787296i	0.998662	−	0.0517139i	$-0.0164684\pi$
$11$	5.00000	+	8.66025i	0.454545	+	0.787296i	−0.544116	+	0.839010i	$0.683135\pi$
$12$	−28.1025	−	16.2250i	−2.34187	−	1.35208i
$13$	3.55077	+	0.626097i	0.273137	+	0.0481613i	0.308539	−	0.951212i	$-0.400160\pi$
$13$	3.55077	+	0.626097i	0.273137	+	0.0481613i	−0.0354021	+	0.999373i	$0.511271\pi$
$14$	−11.5880	−	13.8101i	−0.827716	−	0.986433i
$15$	9.27041	−	11.0481i	0.618028	−	0.736537i
$16$	5.03580	+	28.5594i	0.314737	+	1.78496i
$17$	−14.0954	−	5.13030i	−0.829141	−	0.301782i	−0.107634	−	0.994191i	$-0.534328\pi$
$17$	−14.0954	−	5.13030i	−0.829141	−	0.301782i	−0.721506	+	0.692408i	$0.756550\pi$
$18$		−	14.4222i		−	0.801234i
$19$		0			0
$19$		0			0
$20$	−36.0000			−1.80000
$21$	6.16586	−	16.9405i	0.293612	−	0.806693i
$22$	35.5077	−	6.26097i	1.61399	−	0.284590i
$23$	26.8116	+	22.4976i	1.16572	+	0.978155i	0.999968	−	0.00801243i	$-0.00255046\pi$
$23$	26.8116	+	22.4976i	1.16572	+	0.978155i	0.165752	+	0.986167i	$0.446995\pi$
$24$	−49.7929	+	41.7812i	−2.07470	+	1.74088i
$25$	−1.56283	+	8.86327i	−0.0625133	+	0.354531i
$26$	6.50000	−	11.2583i	0.250000	−	0.433013i
$27$	−15.6125	+	9.01388i	−0.578241	+	0.333847i
$28$	−42.2862	+	15.3909i	−1.51022	+	0.549675i
$29$	−6.16586	−	16.9405i	−0.212616	−	0.584157i	0.786840	−	0.617158i	$-0.211716\pi$
$29$	−6.16586	−	16.9405i	−0.212616	−	0.584157i	−0.999455	+	0.0330007i	$0.989494\pi$
$30$	−26.0000	−	45.0333i	−0.866667	−	1.50111i
$31$	31.2250	+	18.0278i	1.00726	+	0.581541i	0.910388	−	0.413756i	$-0.135784\pi$
$31$	31.2250	+	18.0278i	1.00726	+	0.581541i	0.0968702	+	0.995297i	$0.469117\pi$
$32$	31.9570	+	5.63488i	0.998655	+	0.176090i
$33$	23.1760	+	27.6201i	0.702304	+	0.836973i
$34$	−34.7641	+	41.4302i	−1.02247	+	1.21853i
$35$	−3.47296	−	19.6962i	−0.0992275	−	0.562747i
$36$	−33.8289	−	12.3127i	−0.939693	−	0.342020i
$37$		−	21.6333i		−	0.584684i	−0.956314	−	0.292342i	$-0.905565\pi$
$37$		−	21.6333i		−	0.584684i	0.956314	−	0.292342i	$-0.0944346\pi$
$38$		0			0
$39$	13.0000			0.333333
$40$	−24.6634	+	67.7622i	−0.616586	+	1.69405i
$41$	−35.5077	+	6.26097i	−0.866043	+	0.152707i	−0.588982	−	0.808146i	$-0.700471\pi$
$41$	−35.5077	+	6.26097i	−0.866043	+	0.152707i	−0.277060	+	0.960853i	$0.589360\pi$
$42$	−49.7929	−	41.7812i	−1.18554	−	0.994790i
$43$	−15.3209	+	12.8558i	−0.356300	+	0.298971i	−0.803314	−	0.595556i	$-0.796932\pi$
$43$	−15.3209	+	12.8558i	−0.356300	+	0.298971i	0.447014	+	0.894527i	$0.352487\pi$
$44$	15.6283	−	88.6327i	0.355189	−	2.01438i
$45$	8.00000	−	13.8564i	0.177778	−	0.307920i
$46$	109.287	−	63.0971i	2.37581	−	1.37168i
$47$	−9.39693	+	3.42020i	−0.199935	+	0.0727702i	−0.440047	−	0.897975i	$-0.645038\pi$
$47$	−9.39693	+	3.42020i	−0.199935	+	0.0727702i	0.240112	+	0.970745i	$0.422816\pi$
$48$	35.7620	+	98.2552i	0.745041	+	2.04698i
$49$	12.0000	+	20.7846i	0.244898	+	0.424176i
$50$	28.1025	+	16.2250i	0.562050	+	0.324500i
$51$	−53.2616	−	9.39146i	−1.04435	−	0.184146i
$52$	−20.8584	−	24.8581i	−0.401124	−	0.478041i
$53$	48.6697	−	58.0023i	0.918296	−	1.09438i	−0.0769546	−	0.997035i	$-0.524520\pi$
$53$	48.6697	−	58.0023i	0.918296	−	1.09438i	0.995250	−	0.0973477i	$-0.0310359\pi$
$54$	11.2871	+	64.0125i	0.209021	+	1.18542i
$55$	37.5877	+	13.6808i	0.683413	+	0.248742i
$56$			90.1388i			1.60962i
$57$		0			0
$58$	−65.0000			−1.12069
$59$	6.16586	−	16.9405i	0.104506	−	0.287128i	−0.876408	−	0.481569i	$-0.840067\pi$
$59$	6.16586	−	16.9405i	0.104506	−	0.287128i	0.980914	+	0.194441i	$0.0622893\pi$
$60$	−127.828	+	22.5395i	−2.13046	+	0.375658i
$61$	−30.6418	−	25.7115i	−0.502324	−	0.421500i	0.356094	−	0.934450i	$-0.384108\pi$
$61$	−30.6418	−	25.7115i	−0.502324	−	0.421500i	−0.858419	+	0.512950i	$0.828553\pi$
$62$	99.5858	−	83.5624i	1.60622	−	1.34778i
$63$	3.47296	−	19.6962i	0.0551264	−	0.312637i
$64$	0.500000	−	0.866025i	0.00781250	−	0.0135316i
$65$	12.4900	−	7.21110i	0.192154	−	0.110940i
$66$	122.160	−	44.4626i	1.85091	−	0.673676i
$67$	−13.5649	−	37.2692i	−0.202461	−	0.556257i	0.796359	−	0.604824i	$-0.206757\pi$
$67$	−13.5649	−	37.2692i	−0.202461	−	0.556257i	−0.998820	+	0.0485674i	$0.984534\pi$
$68$	67.5000	+	116.913i	0.992647	+	1.71932i
$69$	109.287	+	63.0971i	1.58388	+	0.914451i
$70$	−71.0155	−	12.5219i	−1.01451	−	0.178885i
$71$	69.5281	+	82.8604i	0.979269	+	1.16705i	0.985945	+	0.167070i	$0.0534305\pi$
$71$	69.5281	+	82.8604i	0.979269	+	1.16705i	−0.00667590	+	0.999978i	$0.502125\pi$
$72$	−46.3521	+	55.2403i	−0.643779	+	0.767226i
$73$	18.2331	+	103.405i	0.249768	+	1.41650i	0.809154	+	0.587597i	$0.199926\pi$
$73$	18.2331	+	103.405i	0.249768	+	1.41650i	−0.559386	+	0.828907i	$0.688963\pi$
$74$	−73.2960	−	26.6776i	−0.990487	−	0.360508i
$75$			32.4500i			0.432666i
$76$		0			0
$77$	50.0000			0.649351
$78$	16.0312	−	44.0454i	0.205529	−	0.564685i
$79$	35.5077	−	6.26097i	0.449465	−	0.0792528i	0.0556662	−	0.998449i	$-0.482272\pi$
$79$	35.5077	−	6.26097i	0.449465	−	0.0792528i	0.393799	+	0.919197i	$0.371161\pi$
$80$	88.8612	+	74.5634i	1.11076	+	0.932042i
$81$	−77.3705	+	64.9215i	−0.955191	+	0.801501i
$82$	−22.5743	+	128.025i	−0.275296	+	1.56128i
$83$	20.0000	−	34.6410i	0.240964	−	0.417362i	−0.720025	−	0.693948i	$-0.755870\pi$
$83$	20.0000	−	34.6410i	0.240964	−	0.417362i	0.960989	+	0.276586i	$0.0892031\pi$
$84$	−140.512	+	81.1249i	−1.67277	+	0.965773i
$85$	−56.3816	+	20.5212i	−0.663312	+	0.241426i
$86$	24.6634	+	67.7622i	0.286784	+	0.787933i
$87$	−32.5000	−	56.2917i	−0.373563	−	0.647030i
$88$	−156.125	−	90.1388i	−1.77415	−	1.02430i
$89$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$89$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$90$	−37.0817	−	44.1922i	−0.412018	−	0.491024i
$91$	11.5880	−	13.8101i	0.127341	−	0.151759i
$92$	−54.6992	−	310.214i	−0.594556	−	3.37190i
$93$	122.160	+	44.4626i	1.31355	+	0.478093i
$94$			36.0555i			0.383569i
$95$		0			0
$96$	117.000			1.21875
$97$	41.9278	−	115.196i	0.432246	−	1.18758i	−0.512185	−	0.858875i	$-0.671164\pi$
$97$	41.9278	−	115.196i	0.432246	−	1.18758i	0.944431	−	0.328710i	$-0.106614\pi$
$98$	85.2186	−	15.0263i	0.869578	−	0.153330i
$99$	30.6418	+	25.7115i	0.309513	+	0.259712i
$100$	62.0496	−	52.0658i	0.620496	−	0.520658i
$101$	−8.68241	+	49.2404i	−0.0859644	+	0.487529i	0.911180	+	0.412009i	$0.135173\pi$
$101$	−8.68241	+	49.2404i	−0.0859644	+	0.487529i	−0.997144	+	0.0755198i	$0.975938\pi$
$102$	−97.5000	+	168.875i	−0.955882	+	1.65564i
$103$	49.9600	−	28.8444i	0.485048	−	0.280043i	−0.237470	−	0.971395i	$-0.576318\pi$
$103$	49.9600	−	28.8444i	0.485048	−	0.280043i	0.722518	+	0.691352i	$0.242985\pi$
$104$	−61.0800	+	22.2313i	−0.587308	+	0.213763i
$105$	−24.6634	−	67.7622i	−0.234890	−	0.645354i
$106$	−136.500	−	236.425i	−1.28774	−	2.23042i
$107$	−65.5725	−	37.8583i	−0.612827	−	0.353816i	0.161244	−	0.986915i	$-0.448449\pi$
$107$	−65.5725	−	37.8583i	−0.612827	−	0.353816i	−0.774071	+	0.633099i	$0.781783\pi$
$108$	159.785	+	28.1744i	1.47949	+	0.260874i
$109$	−127.468	−	151.911i	−1.16943	−	1.39368i	−0.902900	−	0.429850i	$-0.858566\pi$
$109$	−127.468	−	151.911i	−1.16943	−	1.39368i	−0.266533	−	0.963826i	$-0.585878\pi$
$110$	92.7041	−	110.481i	0.842765	−	1.00437i
$111$	−13.5446	−	76.8150i	−0.122023	−	0.692027i
$112$	136.255	+	49.5929i	1.21657	+	0.442794i
$113$		−	122.589i		−	1.08486i	−0.840102	−	0.542428i	$-0.817505\pi$
$113$		−	122.589i		−	1.08486i	0.840102	−	0.542428i	$-0.182495\pi$
$114$		0			0
$115$	140.000			1.21739
$116$	−55.4927	+	152.465i	−0.478385	+	1.31435i
$117$	14.2031	−	2.50439i	0.121394	−	0.0214050i
$118$	−49.7929	−	41.7812i	−0.421974	−	0.354078i
$119$	−57.4533	+	48.2091i	−0.482801	+	0.405118i
$120$	−45.1485	+	256.050i	−0.376238	+	2.13375i
$121$	10.5000	−	18.1865i	0.0867769	−	0.150302i
$122$	−124.900	+	72.1110i	−1.02377	+	0.591074i
$123$	−122.160	+	44.4626i	−0.993171	+	0.361485i
$124$	−110.985	−	304.930i	−0.895044	−	2.45911i
$125$	68.0000	+	117.779i	0.544000	+	0.942236i
$126$	−62.4500	−	36.0555i	−0.495635	−	0.286155i
$127$	−127.828	−	22.5395i	−1.00652	−	0.177476i	−0.353997	−	0.935246i	$-0.615178\pi$
$127$	−127.828	−	22.5395i	−1.00652	−	0.177476i	−0.652522	+	0.757770i	$0.726289\pi$
$128$	81.1161	+	96.6704i	0.633720	+	0.755238i
$129$	−46.3521	+	55.2403i	−0.359318	+	0.428219i
$130$	−9.02971	−	51.2100i	−0.0694593	−	0.393923i
$131$	−105.246	−	38.3063i	−0.803401	−	0.292414i	−0.0925061	−	0.995712i	$-0.529488\pi$
$131$	−105.246	−	38.3063i	−0.803401	−	0.292414i	−0.710895	+	0.703298i	$0.751710\pi$
$132$		−	324.500i		−	2.45833i
$133$		0			0
$134$	−143.000			−1.06716
$135$	−24.6634	+	67.7622i	−0.182692	+	0.501942i
$136$	266.308	−	46.9573i	1.95815	−	0.345274i
$137$	95.7556	+	80.3485i	0.698946	+	0.586485i	0.921473	−	0.388441i	$-0.126986\pi$
$137$	95.7556	+	80.3485i	0.698946	+	0.586485i	−0.222528	+	0.974926i	$0.571431\pi$
$138$	348.550	−	292.468i	2.52573	−	2.11934i
$139$	8.68241	−	49.2404i	0.0624634	−	0.354247i	−0.937517	−	0.347940i	$-0.886881\pi$
$139$	8.68241	−	49.2404i	0.0624634	−	0.354247i	0.999980	−	0.00630721i	$-0.00200766\pi$
$140$	−90.0000	+	155.885i	−0.642857	+	1.11346i
$141$	−31.2250	+	18.0278i	−0.221454	+	0.127856i
$142$	366.480	−	133.388i	2.58085	−	0.939351i
$143$	12.3317	+	33.8811i	0.0862357	+	0.236931i
$144$	58.0000	+	100.459i	0.402778	+	0.697632i
$145$	−62.4500	−	36.0555i	−0.430690	−	0.248659i
$146$	372.831	+	65.7402i	2.55364	+	0.450276i
$147$	55.6225	+	66.2883i	0.378384	+	0.450941i
$148$	−125.151	+	149.149i	−0.845612	+	1.00776i
$149$	12.1554	+	68.9365i	0.0815797	+	0.462661i	0.998042	+	0.0625412i	$0.0199205\pi$
$149$	12.1554	+	68.9365i	0.0815797	+	0.462661i	−0.916463	+	0.400120i	$0.868968\pi$
$150$	109.944	+	40.0164i	0.732960	+	0.266776i
$151$			36.0555i			0.238778i	0.992848	+	0.119389i	$0.0380936\pi$
$151$			36.0555i			0.238778i	−0.992848	+	0.119389i	$0.961906\pi$
$152$		0			0
$153$	−60.0000			−0.392157
$154$	61.6586	−	169.405i	0.400380	−	1.10004i
$155$	142.031	−	25.0439i	0.916329	−	0.161574i
$156$	−89.6272	−	75.2062i	−0.574533	−	0.482091i
$157$	7.66044	−	6.42788i	0.0487926	−	0.0409419i	−0.618065	−	0.786127i	$-0.712083\pi$
$157$	7.66044	−	6.42788i	0.0487926	−	0.0409419i	0.666858	+	0.745185i	$0.267639\pi$
$158$	22.5743	−	128.025i	0.142875	−	0.810285i
$159$	136.500	−	236.425i	0.858491	−	1.48695i
$160$	112.410	−	64.8999i	0.702562	−	0.405625i
$161$	164.446	−	59.8535i	1.02141	−	0.371761i
$162$	124.550	+	342.199i	0.768829	+	2.11234i
$163$	135.000	+	233.827i	0.828221	+	1.43452i	0.899433	+	0.437059i	$0.143980\pi$
$163$	135.000	+	233.827i	0.828221	+	1.43452i	−0.0712118	+	0.997461i	$0.522687\pi$
$164$	281.025	+	162.250i	1.71357	+	0.989328i
$165$	142.031	+	25.0439i	0.860794	+	0.151781i
$166$	−92.7041	−	110.481i	−0.558459	−	0.665545i
$167$	−78.7985	+	93.9084i	−0.471847	+	0.562326i	−0.948505	−	0.316763i	$-0.897404\pi$
$167$	−78.7985	+	93.9084i	−0.471847	+	0.562326i	0.476657	+	0.879089i	$0.341848\pi$
$168$	56.4357	+	320.063i	0.335927	+	1.90513i
$169$	−146.592	−	53.3551i	−0.867409	−	0.315711i
$170$			216.333i			1.27255i
$171$		0			0
$172$	180.000			1.04651
$173$	−41.9278	+	115.196i	−0.242357	+	0.665871i	0.757557	+	0.652769i	$0.226393\pi$
$173$	−41.9278	+	115.196i	−0.242357	+	0.665871i	−0.999914	+	0.0131021i	$0.995829\pi$
$174$	−230.800	+	40.6963i	−1.32644	+	0.233887i
$175$	34.4720	+	28.9254i	0.196983	+	0.165288i
$176$	−222.153	+	186.408i	−1.26223	+	1.05914i
$177$	11.2871	−	64.0125i	0.0637691	−	0.361653i
$178$		0			0
$179$	31.2250	−	18.0278i	0.174441	−	0.100714i	−0.410237	−	0.911979i	$-0.634554\pi$
$179$	31.2250	−	18.0278i	0.174441	−	0.100714i	0.584678	+	0.811265i	$0.301221\pi$
$180$	−135.316	+	49.2509i	−0.751754	+	0.273616i
$181$	−36.9951	−	101.643i	−0.204393	−	0.561565i	0.794566	−	0.607178i	$-0.207698\pi$
$181$	−36.9951	−	101.643i	−0.204393	−	0.561565i	−0.998959	+	0.0456123i	$0.985476\pi$
$182$	−32.5000	−	56.2917i	−0.178571	−	0.309295i
$183$	−124.900	−	72.1110i	−0.682513	−	0.394049i
$184$	−621.386	−	109.567i	−3.37710	−	0.595473i
$185$	−55.6225	−	66.2883i	−0.300662	−	0.358315i
$186$	301.288	−	359.062i	1.61983	−	1.93044i
$187$	−26.0472	−	147.721i	−0.139290	−	0.789953i
$188$	84.5723	+	30.7818i	0.449853	+	0.163733i
$189$			90.1388i			0.476925i
$190$		0			0
$191$	193.000			1.01047			0.505236	−	0.862981i	$-0.331406\pi$
$191$	193.000			1.01047			0.505236	+	0.862981i	$0.331406\pi$
$192$	1.23317	−	3.38811i	0.00642277	−	0.0176464i
$193$	−262.757	+	46.3312i	−1.36144	+	0.240058i	−0.806204	−	0.591637i	$-0.798482\pi$
$193$	−262.757	+	46.3312i	−1.36144	+	0.240058i	−0.555233	+	0.831695i	$0.687371\pi$
$194$	−338.592	−	284.112i	−1.74532	−	1.46450i
$195$	39.8343	−	33.4250i	0.204279	−	0.171410i
$196$	37.5080	−	212.718i	0.191367	−	1.08530i
$197$	−45.0000	+	77.9423i	−0.228426	+	0.395646i	−0.957342	−	0.288958i	$-0.906691\pi$
$197$	−45.0000	+	77.9423i	−0.228426	+	0.395646i	0.728916	+	0.684604i	$0.240025\pi$
$198$	124.900	−	72.1110i	0.630808	−	0.364197i
$199$	−115.582	+	42.0685i	−0.580815	+	0.211399i	−0.615685	−	0.787992i	$-0.711121\pi$
$199$	−115.582	+	42.0685i	−0.580815	+	0.211399i	0.0348698	+	0.999392i	$0.488898\pi$
$200$	−55.4927	−	152.465i	−0.277464	−	0.762325i
$201$	−71.5000	−	123.842i	−0.355721	−	0.616128i
$202$	156.125	+	90.1388i	0.772896	+	0.446232i
$203$	−88.7694	−	15.6524i	−0.437288	−	0.0771056i
$204$	312.876	+	372.872i	1.53371	+	1.82780i
$205$	−92.7041	+	110.481i	−0.452215	+	0.538929i
$206$	−36.1188	−	204.840i	−0.175334	−	0.994369i
$207$	131.557	+	47.8828i	0.635541	+	0.231318i
$208$			104.561i			0.502697i
$209$		0			0
$210$	−260.000			−1.23810
$211$	−80.1561	+	220.227i	−0.379887	+	1.04373i	0.591516	+	0.806293i	$0.298530\pi$
$211$	−80.1561	+	220.227i	−0.379887	+	1.04373i	−0.971403	+	0.237437i	$0.923693\pi$
$212$	−671.096	+	118.332i	−3.16555	+	0.558172i
$213$	298.757	+	250.687i	1.40262	+	1.17694i
$214$	−209.130	+	175.481i	−0.977244	+	0.820005i
$215$	−13.8919	+	78.7846i	−0.0646133	+	0.366440i
$216$	162.500	−	281.458i	0.752315	−	1.30305i
$217$	156.125	−	90.1388i	0.719470	−	0.415386i
$218$	−671.880	+	244.544i	−3.08202	+	1.12176i
$219$	129.483	+	355.752i	0.591246	+	1.62444i
$220$	−180.000	−	311.769i	−0.818182	−	1.41713i
$221$	−46.8375	−	27.0416i	−0.211934	−	0.122360i
$222$	−276.960	−	48.8356i	−1.24757	−	0.219980i
$223$	−129.786	−	154.673i	−0.581999	−	0.693600i	0.392048	−	0.919945i	$-0.371767\pi$
$223$	−129.786	−	154.673i	−0.581999	−	0.693600i	−0.974047	+	0.226345i	$0.927322\pi$
$224$	104.292	−	124.291i	0.465590	−	0.554869i
$225$	6.25133	+	35.4531i	0.0277837	+	0.157569i
$226$	−415.344	−	151.173i	−1.83781	−	0.668907i
$227$			255.994i			1.12773i	0.825868	+	0.563864i	$0.190686\pi$
$227$			255.994i			1.12773i	−0.825868	+	0.563864i	$0.809314\pi$
$228$		0			0
$229$	−160.000			−0.698690			−0.349345	−	0.936994i	$-0.613596\pi$
$229$	−160.000			−0.698690			−0.349345	+	0.936994i	$0.613596\pi$
$230$	172.644	−	474.335i	0.750626	−	2.06233i
$231$	177.539	−	31.3049i	0.768566	−	0.135519i
$232$	248.964	+	208.906i	1.07312	+	0.900457i
$233$	−206.832	+	173.553i	−0.887691	+	0.744861i	−0.967746	−	0.251929i	$-0.918935\pi$
$233$	−206.832	+	173.553i	−0.887691	+	0.744861i	0.0800547	+	0.996790i	$0.474491\pi$
$234$	9.02971	−	51.2100i	0.0385885	−	0.218846i
$235$	−20.0000	+	34.6410i	−0.0851064	+	0.147409i
$236$	−140.512	+	81.1249i	−0.595392	+	0.343750i
$237$	122.160	−	44.4626i	0.515443	−	0.187606i
$238$	92.4878	+	254.108i	0.388604	+	1.06768i
$239$	−98.5000	−	170.607i	−0.412134	−	0.713837i	0.582989	−	0.812480i	$-0.301883\pi$
$239$	−98.5000	−	170.607i	−0.412134	−	0.713837i	−0.995123	+	0.0986432i	$0.968550\pi$
$240$	362.210	+	209.122i	1.50921	+	0.871342i
$241$	390.585	+	68.8707i	1.62069	+	0.285771i	0.909021	−	0.416749i	$-0.136831\pi$
$241$	390.585	+	68.8707i	1.62069	+	0.285771i	0.711664	+	0.702520i	$0.247942\pi$
$242$	−48.6697	−	58.0023i	−0.201114	−	0.239679i
$243$	−129.786	+	154.673i	−0.534098	+	0.636513i
$244$	62.5133	+	354.531i	0.256202	+	1.45300i
$245$	90.2105	+	32.8339i	0.368206	+	0.134016i
$246$			468.722i			1.90537i
$247$		0			0
$248$	−650.000			−2.62097
$249$	49.3268	−	135.524i	0.198100	−	0.544275i
$250$	482.905	−	85.1492i	1.93162	−	0.340597i
$251$	−307.950	−	258.401i	−1.22689	−	1.02948i	−0.998435	−	0.0559306i	$-0.982187\pi$
$251$	−307.950	−	258.401i	−1.22689	−	1.02948i	−0.228457	−	0.973554i	$-0.573368\pi$
$252$	−137.888	+	115.702i	−0.547175	+	0.459134i
$253$	−60.7769	+	344.683i	−0.240225	+	1.36238i
$254$	−234.000	+	405.300i	−0.921260	+	1.59567i
$255$	−187.350	+	108.167i	−0.734706	+	0.424183i
$256$	431.319	−	156.987i	1.68484	−	0.613231i
$257$	143.048	+	393.021i	0.556606	+	1.52926i	0.824527	+	0.565823i	$0.191441\pi$
$257$	143.048	+	393.021i	0.556606	+	1.52926i	−0.267921	+	0.963441i	$0.586336\pi$
$258$	130.000	+	225.167i	0.503876	+	0.872739i
$259$	−93.6750	−	54.0833i	−0.361679	−	0.208816i
$260$	−127.828	−	22.5395i	−0.491646	−	0.0866904i
$261$	−46.3521	−	55.2403i	−0.177594	−	0.211648i
$262$	−259.572	+	309.345i	−0.990731	+	1.18071i
$263$	53.8309	+	305.290i	0.204680	+	1.16080i	0.897942	+	0.440114i	$0.145062\pi$
$263$	53.8309	+	305.290i	0.204680	+	1.16080i	−0.693262	+	0.720686i	$0.743827\pi$
$264$	−610.800	−	222.313i	−2.31364	−	0.842095i
$265$		−	302.866i		−	1.14289i
$266$		0			0
$267$		0			0
$268$	−122.084	+	335.423i	−0.455537	+	1.25158i
$269$	−106.523	+	18.7829i	−0.395997	+	0.0698250i	−0.368101	−	0.929786i	$-0.619992\pi$
$269$	−106.523	+	18.7829i	−0.395997	+	0.0698250i	−0.0278963	+	0.999611i	$0.508881\pi$
$270$	199.172	+	167.125i	0.737672	+	0.618981i
$271$	80.4347	−	67.4927i	0.296807	−	0.249051i	−0.482207	−	0.876057i	$-0.660165\pi$
$271$	80.4347	−	67.4927i	0.296807	−	0.249051i	0.779014	+	0.627007i	$0.215720\pi$
$272$	75.5370	−	428.391i	0.277709	−	1.57497i
$273$	32.5000	−	56.2917i	0.119048	−	0.206197i
$274$	390.312	−	225.347i	1.42450	−	0.822434i
$275$	−84.5723	+	30.7818i	−0.307536	+	0.111934i
$276$	−388.449	−	1067.25i	−1.40742	−	3.86686i
$277$	25.0000	+	43.3013i	0.0902527	+	0.156322i	0.907617	−	0.419798i	$-0.137899\pi$
$277$	25.0000	+	43.3013i	0.0902527	+	0.156322i	−0.817365	+	0.576121i	$0.804566\pi$
$278$	−156.125	−	90.1388i	−0.561601	−	0.324240i
$279$	142.031	+	25.0439i	0.509072	+	0.0897631i
$280$	231.760	+	276.201i	0.827716	+	0.986433i
$281$	185.408	−	220.961i	0.659816	−	0.786338i	−0.327543	−	0.944836i	$-0.606221\pi$
$281$	185.408	−	220.961i	0.659816	−	0.786338i	0.987359	+	0.158498i	$0.0506652\pi$
$282$	22.5743	+	128.025i	0.0800506	+	0.453989i
$283$	300.702	+	109.446i	1.06255	+	0.386737i	0.813386	−	0.581725i	$-0.197622\pi$
$283$	300.702	+	109.446i	1.06255	+	0.386737i	0.249164	+	0.968461i	$0.419844\pi$
$284$		−	973.499i		−	3.42781i
$285$		0			0
$286$	130.000			0.454545
$287$	−61.6586	+	169.405i	−0.214838	+	0.590263i
$288$	127.828	−	22.5395i	0.443847	−	0.0782622i
$289$	−49.0268	−	41.1384i	−0.169643	−	0.142347i
$290$	−199.172	+	167.125i	−0.686798	+	0.576292i
$291$	76.7525	−	435.285i	0.263754	−	1.49582i
$292$	472.500	−	818.394i	1.61815	−	2.80272i
$293$	−190.472	+	109.969i	−0.650077	+	0.375322i	−0.788486	−	0.615053i	$-0.789134\pi$
$293$	−190.472	+	109.969i	−0.650077	+	0.375322i	0.138409	+	0.990375i	$0.455801\pi$
$294$	293.184	−	106.710i	0.997225	−	0.362960i
$295$	−24.6634	−	67.7622i	−0.0836048	−	0.229702i
$296$	195.000	+	337.750i	0.658784	+	1.14105i
$297$	−156.125	−	90.1388i	−0.525673	−	0.303498i
$298$	248.554	+	43.8268i	0.834075	+	0.147070i
$299$	81.1161	+	96.6704i	0.271291	+	0.323313i
$300$	187.726	−	223.723i	0.625753	−	0.745743i
$301$	17.3648	+	98.4808i	0.0576904	+	0.327179i
$302$	122.160	+	44.4626i	0.404503	+	0.147227i
$303$			180.278i			0.594975i
$304$		0			0
$305$	−160.000			−0.524590
$306$	−73.9903	+	203.287i	−0.241798	+	0.664335i
$307$	−234.351	+	41.3224i	−0.763359	+	0.134601i	−0.541755	−	0.840536i	$-0.682240\pi$
$307$	−234.351	+	41.3224i	−0.763359	+	0.134601i	−0.221603	+	0.975137i	$0.571129\pi$
$308$	−344.720	−	289.254i	−1.11922	−	0.939138i
$309$	159.337	−	133.700i	0.515655	−	0.432686i
$310$	90.2971	−	512.100i	0.291281	−	1.65194i
$311$	−197.500	+	342.080i	−0.635048	+	1.09994i	0.351457	+	0.936204i	$0.385686\pi$
$311$	−197.500	+	342.080i	−0.635048	+	1.09994i	−0.986505	+	0.163732i	$0.947647\pi$
$312$	−202.962	+	117.180i	−0.650521	+	0.375578i
$313$	−117.462	+	42.7525i	−0.375277	+	0.136590i	−0.522771	−	0.852473i	$-0.675102\pi$
$313$	−117.462	+	42.7525i	−0.375277	+	0.136590i	0.147494	+	0.989063i	$0.452879\pi$
$314$	−12.3317	−	33.8811i	−0.0392730	−	0.107902i
$315$	−40.0000	−	69.2820i	−0.126984	−	0.219943i
$316$	−281.025	−	162.250i	−0.889319	−	0.513449i
$317$	3.55077	+	0.626097i	0.0112012	+	0.00197507i	0.179246	−	0.983804i	$-0.442634\pi$
$317$	3.55077	+	0.626097i	0.0112012	+	0.00197507i	−0.168045	+	0.985779i	$0.553745\pi$
$318$	−632.706	−	754.029i	−1.98964	−	2.37116i
$319$	115.880	−	138.101i	0.363261	−	0.432917i
$320$	−0.694593	−	3.93923i	−0.00217060	−	0.0123101i
$321$	−256.536	−	93.3715i	−0.799178	−	0.290877i
$322$		−	630.971i		−	1.95954i
$323$		0			0
$324$	909.000			2.80556
$325$	−11.0985	+	30.4930i	−0.0341494	+	0.0938246i
$326$	958.709	−	169.046i	2.94083	−	0.518547i
$327$	−547.722	−	459.593i	−1.67499	−	1.40548i
$328$	497.929	−	417.812i	1.51808	−	1.27382i
$329$	−8.68241	+	49.2404i	−0.0263903	+	0.149667i
$330$	260.000	−	450.333i	0.787879	−	1.36465i
$331$	−171.737	+	99.1527i	−0.518844	+	0.299555i	−0.736462	−	0.676479i	$-0.763505\pi$
$331$	−171.737	+	99.1527i	−0.518844	+	0.299555i	0.217617	+	0.976034i	$0.430171\pi$
$332$	−338.289	+	123.127i	−1.01894	+	0.370865i
$333$	−29.5961	−	81.3146i	−0.0888772	−	0.244188i
$334$	221.000	+	382.783i	0.661677	+	1.14606i
$335$	−137.390	−	79.3221i	−0.410119	−	0.236782i
$336$	514.862	+	90.7841i	1.53233	+	0.270191i
$337$	37.0817	+	44.1922i	0.110035	+	0.131134i	0.818251	−	0.574862i	$-0.194944\pi$
$337$	37.0817	+	44.1922i	0.110035	+	0.131134i	−0.708216	+	0.705996i	$0.750500\pi$
$338$	−361.546	+	430.874i	−1.06966	+	1.27478i
$339$	−76.7525	−	435.285i	−0.226409	−	1.28403i
$340$	507.434	+	184.691i	1.49245	+	0.543208i
$341$			360.555i			1.05735i
$342$		0			0
$343$	365.000			1.06414
$344$	123.317	−	338.811i	0.358480	−	0.984916i
$345$	497.108	−	87.6536i	1.44089	−	0.254069i
$346$	338.592	+	284.112i	0.978589	+	0.821133i
$347$	−30.6418	+	25.7115i	−0.0883048	+	0.0740966i	−0.685871	−	0.727723i	$-0.740579\pi$
$347$	−30.6418	+	25.7115i	−0.0883048	+	0.0740966i	0.597567	+	0.801819i	$0.296134\pi$
$348$	−101.584	+	576.113i	−0.291909	+	1.65550i
$349$	−49.0000	+	84.8705i	−0.140401	+	0.243182i	−0.927648	−	0.373456i	$-0.878173\pi$
$349$	−49.0000	+	84.8705i	−0.140401	+	0.243182i	0.787247	+	0.616638i	$0.211506\pi$
$350$	140.512	−	81.1249i	0.401464	−	0.231785i
$351$	−61.0800	+	22.2313i	−0.174017	+	0.0633371i
$352$	110.985	+	304.930i	0.315299	+	0.866278i
$353$	92.5000	+	160.215i	0.262040	+	0.453866i	0.966784	−	0.255596i	$-0.0822715\pi$
$353$	92.5000	+	160.215i	0.262040	+	0.453866i	−0.704744	+	0.709462i	$0.748938\pi$
$354$	−202.962	−	117.180i	−0.573340	−	0.331018i
$355$	426.093	+	75.1317i	1.20026	+	0.211639i
$356$		0			0
$357$	−173.820	+	207.151i	−0.486892	+	0.580255i
$358$	−22.5743	−	128.025i	−0.0630566	−	0.357612i
$359$	211.431	+	76.9545i	0.588944	+	0.214358i	0.619265	−	0.785182i	$-0.287431\pi$
$359$	211.431	+	76.9545i	0.588944	+	0.214358i	−0.0303210	+	0.999540i	$0.509653\pi$
$360$			288.444i			0.801234i
$361$		0			0
$362$	−390.000			−1.07735
$363$	25.8966	−	71.1503i	0.0713405	−	0.196006i
$364$	−159.785	+	28.1744i	−0.438969	+	0.0774022i
$365$	321.739	+	269.971i	0.881476	+	0.739646i
$366$	−398.343	+	334.250i	−1.08837	+	0.913250i
$367$	8.68241	−	49.2404i	0.0236578	−	0.134170i	−0.970691	−	0.240330i	$-0.922744\pi$
$367$	8.68241	−	49.2404i	0.0236578	−	0.134170i	0.994349	+	0.106160i	$0.0338555\pi$
$368$	−507.500	+	879.016i	−1.37908	+	2.38863i
$369$	−124.900	+	72.1110i	−0.338482	+	0.195423i
$370$	−293.184	+	106.710i	−0.792389	+	0.288406i
$371$	−129.483	−	355.752i	−0.349011	−	0.958899i
$372$	−585.000	−	1013.25i	−1.57258	−	2.72379i
$373$	377.822	+	218.136i	1.01293	+	0.584815i	0.912048	−	0.410084i	$-0.134501\pi$
$373$	377.822	+	218.136i	1.01293	+	0.584815i	0.100881	+	0.994899i	$0.467834\pi$
$374$	−532.616	−	93.9146i	−1.42411	−	0.251109i
$375$	315.194	+	375.634i	0.840518	+	1.00169i
$376$	115.880	−	138.101i	0.308192	−	0.367289i
$377$	−11.2871	−	64.0125i	−0.0299393	−	0.169794i
$378$	305.400	+	111.157i	0.807937	+	0.294065i
$379$		−	486.749i		−	1.28430i	−0.766579	−	0.642150i	$-0.778043\pi$
$379$		−	486.749i		−	1.28430i	0.766579	−	0.642150i	$-0.221957\pi$
$380$		0			0
$381$	−468.000			−1.22835
$382$	238.002	−	653.905i	0.623042	−	1.71179i
$383$	−198.843	+	35.0615i	−0.519173	+	0.0915443i	−0.427094	−	0.904207i	$-0.640463\pi$
$383$	−198.843	+	35.0615i	−0.519173	+	0.0915443i	−0.0920797	+	0.995752i	$0.529351\pi$
$384$	348.550	+	292.468i	0.907683	+	0.761636i
$385$	153.209	−	128.558i	0.397945	−	0.333916i
$386$	−167.050	+	947.385i	−0.432771	+	2.45437i
$387$	−40.0000	+	69.2820i	−0.103359	+	0.179023i
$388$	−955.485	+	551.649i	−2.46259	+	1.42178i
$389$	449.173	−	163.486i	1.15469	−	0.420272i	0.307490	−	0.951551i	$-0.400511\pi$
$389$	449.173	−	163.486i	1.15469	−	0.420272i	0.847196	+	0.531280i	$0.178289\pi$
$390$	−64.1249	−	176.182i	−0.164423	−	0.451748i
$391$	−262.500	−	454.663i	−0.671355	−	1.16282i
$392$	−374.700	−	216.333i	−0.955867	−	0.551870i
$393$	−397.687	−	70.1229i	−1.01193	−	0.178430i
$394$	208.584	+	248.581i	0.529402	+	0.630917i
$395$	92.7041	−	110.481i	0.234694	−	0.279697i
$396$	−62.5133	−	354.531i	−0.157862	−	0.895280i
$397$	−704.769	−	256.515i	−1.77524	−	0.646134i	−0.999893	−	0.0145952i	$-0.995354\pi$
$397$	−704.769	−	256.515i	−1.77524	−	0.646134i	−0.775344	−	0.631539i	$-0.782424\pi$
$398$			443.483i			1.11428i
$399$		0			0
$400$	−261.000			−0.652500
$401$	−98.6537	+	271.049i	−0.246019	+	0.675932i	0.753803	+	0.657100i	$0.228217\pi$
$401$	−98.6537	+	271.049i	−0.246019	+	0.675932i	−0.999823	+	0.0188322i	$0.994005\pi$
$402$	−507.761	+	89.5319i	−1.26309	+	0.222716i
$403$	99.5858	+	83.5624i	0.247111	+	0.207351i
$404$	344.720	−	289.254i	0.853267	−	0.715976i
$405$	−70.1539	+	397.862i	−0.173219	+	0.982376i
$406$	−162.500	+	281.458i	−0.400246	+	0.693247i
$407$	187.350	−	108.167i	0.460319	−	0.265765i
$408$	916.200	−	333.470i	2.24559	−	0.817328i
$409$	12.3317	+	33.8811i	0.0301509	+	0.0828389i	0.953855	−	0.300268i	$-0.0970762\pi$
$409$	12.3317	+	33.8811i	0.0301509	+	0.0828389i	−0.923704	+	0.383107i	$0.874854\pi$
$410$	260.000	+	450.333i	0.634146	+	1.09837i
$411$	390.312	+	225.347i	0.949665	+	0.548289i
$412$	−511.312	−	90.1580i	−1.24105	−	0.218830i
$413$	−57.9401	−	69.0503i	−0.140291	−	0.167192i
$414$	324.465	−	386.682i	0.783731	−	0.934014i
$415$	−27.7837	−	157.569i	−0.0669487	−	0.379685i
$416$	109.944	+	40.0164i	0.264289	+	0.0961932i
$417$		−	180.278i		−	0.432320i
$418$		0			0
$419$	112.000			0.267303			0.133652	−	0.991028i	$-0.457330\pi$
$419$	112.000			0.267303			0.133652	+	0.991028i	$0.457330\pi$
$420$	−221.971	+	609.860i	−0.528502	+	1.45205i
$421$	−621.386	+	109.567i	−1.47598	+	0.260254i	−0.852969	−	0.521962i	$-0.825200\pi$
$421$	−621.386	+	109.567i	−1.47598	+	0.260254i	−0.623007	+	0.782217i	$0.714089\pi$
$422$	647.308	+	543.156i	1.53390	+	1.28710i
$423$	−30.6418	+	25.7115i	−0.0724392	+	0.0607837i
$424$	−237.030	+	1344.26i	−0.559032	+	3.17043i
$425$	67.5000	−	116.913i	0.158824	−	0.275090i
$426$	1217.77	−	703.082i	2.85863	−	1.65043i
$427$	−187.939	+	68.4040i	−0.440137	+	0.160197i
$428$	233.069	+	640.353i	0.544555	+	1.49615i
$429$	65.0000	+	112.583i	0.151515	+	0.262432i
$430$	249.800	+	144.222i	0.580930	+	0.335400i
$431$	−426.093	−	75.1317i	−0.988615	−	0.174319i	−0.344118	−	0.938926i	$-0.611822\pi$
$431$	−426.093	−	75.1317i	−0.988615	−	0.174319i	−0.644497	+	0.764607i	$0.722933\pi$
$432$	−336.053	−	400.492i	−0.777899	−	0.927064i
$433$	472.791	−	563.451i	1.09190	−	1.30127i	0.141600	−	0.989924i	$-0.454775\pi$
$433$	472.791	−	563.451i	1.09190	−	1.30127i	0.950296	−	0.311348i	$-0.100780\pi$
$434$	−112.871	−	640.125i	−0.260072	−	1.47494i
$435$	−244.320	−	88.9252i	−0.561655	−	0.204426i
$436$			1784.75i			4.09346i
$437$		0			0
$438$	1365.00			3.11644
$439$	271.298	−	745.384i	0.617990	−	1.69791i	−0.0938627	−	0.995585i	$-0.529921\pi$
$439$	271.298	−	745.384i	0.617990	−	1.69791i	0.711853	−	0.702329i	$-0.247856\pi$
$440$	−710.155	+	125.219i	−1.61399	+	0.284590i
$441$	73.5403	+	61.7076i	0.166758	+	0.139927i
$442$	−149.379	+	125.344i	−0.337961	+	0.283583i
$443$	116.344	−	659.821i	0.262628	−	1.48944i	−0.513077	−	0.858343i	$-0.671494\pi$
$443$	116.344	−	659.821i	0.262628	−	1.48944i	0.775705	−	0.631096i	$-0.217394\pi$
$444$	−351.000	+	607.950i	−0.790541	+	1.36926i
$445$		0			0
$446$	−684.096	+	248.991i	−1.53385	+	0.558275i
$447$	86.3220	+	237.168i	0.193114	+	0.530576i
$448$	−2.50000	−	4.33013i	−0.00558036	−	0.00966546i
$449$	31.2250	+	18.0278i	0.0695434	+	0.0401509i	0.534369	−	0.845252i	$-0.320549\pi$
$449$	31.2250	+	18.0278i	0.0695434	+	0.0401509i	−0.464825	+	0.885403i	$0.653883\pi$
$450$	127.828	+	22.5395i	0.284062	+	0.0500878i
$451$	−231.760	−	276.201i	−0.513881	−	0.612420i
$452$	−709.187	+	845.176i	−1.56900	+	1.86986i
$453$	22.5743	+	128.025i	0.0498328	+	0.282616i
$454$	867.336	+	315.685i	1.91043	+	0.695341i
$455$		−	72.1110i		−	0.158486i
$456$		0			0
$457$	−755.000			−1.65208			−0.826039	−	0.563612i	$-0.809411\pi$
$457$	−755.000			−1.65208			−0.826039	+	0.563612i	$0.809411\pi$
$458$	−197.307	+	542.098i	−0.430802	+	1.18362i
$459$	266.308	−	46.9573i	0.580192	−	0.102303i
$460$	−965.216	−	809.912i	−2.09830	−	1.76068i
$461$	591.386	−	496.232i	1.28283	−	1.07643i	0.289987	−	0.957031i	$-0.406349\pi$
$461$	591.386	−	496.232i	1.28283	−	1.07643i	0.992847	−	0.119395i	$-0.0380954\pi$
$462$	112.871	−	640.125i	0.244310	−	1.38555i
$463$	175.000	−	303.109i	0.377970	−	0.654663i	−0.612797	−	0.790240i	$-0.709956\pi$
$463$	175.000	−	303.109i	0.377970	−	0.654663i	0.990767	+	0.135578i	$0.0432890\pi$
$464$	452.762	−	261.402i	0.975781	−	0.563367i
$465$	488.640	−	177.850i	1.05084	−	0.382474i
$466$	332.956	+	914.790i	0.714498	+	1.96307i
$467$	−35.0000	−	60.6218i	−0.0749465	−	0.129811i	0.826117	−	0.563499i	$-0.190545\pi$
$467$	−35.0000	−	60.6218i	−0.0749465	−	0.129811i	−0.901063	+	0.433688i	$0.857212\pi$
$468$	−112.410	−	64.8999i	−0.240192	−	0.138675i
$469$	−195.293	−	34.4354i	−0.416402	−	0.0734229i
$470$	92.7041	+	110.481i	0.197243	+	0.235065i
$471$	23.1760	−	27.6201i	0.0492060	−	0.0586415i
$472$	56.4357	+	320.063i	0.119567	+	0.678099i
$473$	−187.939	−	68.4040i	−0.397333	−	0.144617i
$474$		−	468.722i		−	0.988864i
$475$		0			0
$476$	675.000			1.41807
$477$	103.586	−	284.601i	0.217162	−	0.596648i
$478$	−699.503	+	123.341i	−1.46339	+	0.258036i
$479$	−283.436	−	237.831i	−0.591725	−	0.496517i	0.297049	−	0.954862i	$-0.403998\pi$
$479$	−283.436	−	237.831i	−0.591725	−	0.496517i	−0.888774	+	0.458346i	$0.848442\pi$
$480$	358.509	−	300.825i	0.746893	−	0.626718i
$481$	13.5446	−	76.8150i	0.0281592	−	0.159699i
$482$	715.000	−	1238.42i	1.48340	−	2.56933i
$483$	546.437	−	315.486i	1.13134	−	0.653180i
$484$	−177.602	+	64.6418i	−0.366946	+	0.133557i
$485$	−167.711	−	460.783i	−0.345796	−	0.950068i
$486$	364.000	+	630.466i	0.748971	+	1.29726i
$487$	449.640	+	259.600i	0.923285	+	0.533059i	0.884682	−	0.466196i	$-0.154376\pi$
$487$	449.640	+	259.600i	0.923285	+	0.533059i	0.0386035	+	0.999255i	$0.487709\pi$
$488$	710.155	+	125.219i	1.45524	+	0.256597i
$489$	625.753	+	745.743i	1.27966	+	1.52504i
$490$	222.490	−	265.153i	0.454061	−	0.541129i
$491$	−109.746	−	622.398i	−0.223515	−	1.26761i	−0.865505	−	0.500901i	$-0.833002\pi$
$491$	−109.746	−	622.398i	−0.223515	−	1.26761i	0.641990	−	0.766713i	$-0.278109\pi$
$492$	1099.44	+	400.164i	2.23463	+	0.813341i
$493$			270.416i			0.548512i
$494$		0			0
$495$	160.000			0.323232
$496$	−357.620	+	982.552i	−0.721007	+	1.98095i
$497$	532.616	−	93.9146i	1.07166	−	0.188963i
$498$	−398.343	−	334.250i	−0.799886	−	0.671184i
$499$	291.097	−	244.259i	0.583360	−	0.489498i	−0.302688	−	0.953090i	$-0.597884\pi$
$499$	291.097	−	244.259i	0.583360	−	0.489498i	0.886049	+	0.463592i	$0.153440\pi$
$500$	212.545	−	1205.40i	0.425091	−	2.41081i
$501$	−221.000	+	382.783i	−0.441118	+	0.764038i
$502$	−1255.24	+	724.716i	−2.50049	+	1.44366i
$503$	42.2862	−	15.3909i	0.0840679	−	0.0305982i	−0.299644	−	0.954051i	$-0.596868\pi$
$503$	42.2862	−	15.3909i	0.0840679	−	0.0305982i	0.383712	+	0.923453i	$0.374646\pi$
$504$	123.317	+	338.811i	0.244677	+	0.672244i
$505$	100.000	+	173.205i	0.198020	+	0.342980i
$506$	1092.87	+	630.971i	2.15983	+	1.24698i
$507$	−553.921	−	97.6712i	−1.09255	−	0.192645i
$508$	750.904	+	894.892i	1.47816	+	1.76160i
$509$	−533.049	+	635.263i	−1.04725	+	1.24806i	−0.0793149	+	0.996850i	$0.525273\pi$
$509$	−533.049	+	635.263i	−1.04725	+	1.24806i	−0.967932	+	0.251211i	$0.919171\pi$
$510$	135.446	+	768.150i	0.265580	+	1.50618i
$511$	493.339	+	179.561i	0.965438	+	0.351391i
$512$		−	1150.17i		−	2.24643i
$513$		0			0
$514$	1508.00			2.93385
$515$	78.9230	−	216.839i	0.153248	−	0.421047i
$516$	639.139	−	112.698i	1.23864	−	0.218406i
$517$	−76.6044	−	64.2788i	−0.148171	−	0.124330i
$518$	−298.757	+	250.687i	−0.576752	+	0.483952i
$519$	−76.7525	+	435.285i	−0.147885	+	0.838699i
$520$	−130.000	+	225.167i	−0.250000	+	0.433013i
$521$	530.825	−	306.472i	1.01886	−	0.588238i	0.105085	−	0.994463i	$-0.466489\pi$
$521$	530.825	−	306.472i	1.01886	−	0.588238i	0.913773	+	0.406226i	$0.133155\pi$
$522$	−244.320	+	88.9252i	−0.468046	+	0.170355i
$523$	−159.079	−	437.066i	−0.304167	−	0.835691i	−0.993765	−	0.111498i	$-0.964435\pi$
$523$	−159.079	−	437.066i	−0.304167	−	0.835691i	0.689598	−	0.724192i	$-0.257787\pi$
$524$	504.000	+	872.954i	0.961832	+	1.66594i
$525$	140.512	+	81.1249i	0.267643	+	0.154524i
$526$	1100.74	+	194.090i	2.09266	+	0.368993i
$527$	−347.641	−	414.302i	−0.659659	−	0.786152i
$528$	−672.105	+	800.984i	−1.27293	+	1.51701i
$529$	120.859	+	685.426i	0.228467	+	1.29570i
$530$	−1026.14	−	373.486i	−1.93612	−	0.704691i
$531$		−	72.1110i		−	0.135802i
$532$		0			0
$533$	−130.000			−0.243902
$534$		0			0
$535$	−298.265	+	52.5922i	−0.557505	+	0.0983031i
$536$	547.722	+	459.593i	1.02187	+	0.857450i
$537$	99.5858	−	83.5624i	0.185448	−	0.155610i
$538$	−67.7228	+	384.075i	−0.125879	+	0.713894i
$539$	−120.000	+	207.846i	−0.222635	+	0.385614i
$540$	562.050	−	324.500i	1.04083	−	0.600925i
$541$	563.816	−	205.212i	1.04217	−	0.379320i	0.236469	−	0.971639i	$-0.424010\pi$
$541$	563.816	−	205.212i	1.04217	−	0.379320i	0.805704	+	0.592319i	$0.201787\pi$
$542$	−129.483	−	355.752i	−0.238898	−	0.656368i
$543$	−195.000	−	337.750i	−0.359116	−	0.622007i
$544$	−421.537	−	243.375i	−0.774885	−	0.447380i
$545$	−781.170	−	137.741i	−1.43334	−	0.252737i
$546$	−150.644	−	179.531i	−0.275905	−	0.328811i
$547$	384.722	−	458.494i	0.703331	−	0.838198i	−0.289568	−	0.957158i	$-0.593512\pi$
$547$	384.722	−	458.494i	0.703331	−	0.838198i	0.992899	+	0.118960i	$0.0379560\pi$
$548$	−195.354	−	1107.91i	−0.356486	−	2.02173i
$549$	−150.351	−	54.7232i	−0.273863	−	0.0996780i
$550$			324.500i			0.589999i
$551$		0			0
$552$	−2275.00			−4.12138
$553$	61.6586	−	169.405i	0.111498	−	0.306339i
$554$	177.539	−	31.3049i	0.320467	−	0.0565070i
$555$	−239.006	−	200.550i	−0.430641	−	0.361351i
$556$	−344.720	+	289.254i	−0.620000	+	0.520242i
$557$	65.9863	−	374.227i	0.118467	−	0.671862i	−0.866508	−	0.499164i	$-0.833641\pi$
$557$	65.9863	−	374.227i	0.118467	−	0.671862i	0.984975	−	0.172698i	$-0.0552484\pi$
$558$	260.000	−	450.333i	0.465950	−	0.807049i
$559$	−62.4500	+	36.0555i	−0.111717	+	0.0645000i
$560$	545.022	−	198.372i	0.973253	−	0.354235i
$561$	−184.976	−	508.216i	−0.329725	−	0.905912i
$562$	−520.000	−	900.666i	−0.925267	−	1.60261i
$563$	−106.165	−	61.2944i	−0.188570	−	0.108871i	0.402743	−	0.915313i	$-0.368057\pi$
$563$	−106.165	−	61.2944i	−0.188570	−	0.108871i	−0.591313	+	0.806442i	$0.701390\pi$
$564$	319.570	+	56.3488i	0.566613	+	0.0999092i
$565$	−315.194	−	375.634i	−0.557866	−	0.664838i
$566$	741.633	−	883.844i	1.31031	−	1.56156i
$567$	87.6923	+	497.328i	0.154660	+	0.877122i
$568$	−1832.40	−	666.939i	−3.22606	−	1.17419i
$569$			36.0555i			0.0633665i	0.999498	+	0.0316832i	$0.0100868\pi$
$569$			36.0555i			0.0633665i	−0.999498	+	0.0316832i	$0.989913\pi$
$570$		0			0
$571$	−790.000			−1.38354			−0.691769	−	0.722119i	$-0.743168\pi$
$571$	−790.000			−1.38354			−0.691769	+	0.722119i	$0.743168\pi$
$572$	110.985	−	304.930i	0.194030	−	0.533094i
$573$	685.300	−	120.837i	1.19599	−	0.210884i
$574$	497.929	+	417.812i	0.867472	+	0.727895i
$575$	−241.304	+	202.478i	−0.419659	+	0.352136i
$576$	0.694593	−	3.93923i	0.00120589	−	0.00683894i
$577$	−337.500	+	584.567i	−0.584922	+	1.01311i	0.409963	+	0.912102i	$0.365542\pi$
$577$	−337.500	+	584.567i	−0.584922	+	1.01311i	−0.994885	+	0.101013i	$0.967792\pi$
$578$	−199.840	+	115.378i	−0.345744	+	0.199615i
$579$	−903.984	+	329.023i	−1.56129	+	0.568261i
$580$	221.971	+	609.860i	0.382708	+	1.05148i
$581$	−100.000	−	173.205i	−0.172117	−	0.298115i
$582$	−1380.14	−	796.827i	−2.37138	−	1.36912i
$583$	745.663	+	131.480i	1.27901	+	0.225524i
$584$	−1216.74	−	1450.06i	−2.08346	−	2.48297i
$585$	37.0817	−	44.1922i	0.0633875	−	0.0755422i
$586$	137.703	+	780.953i	0.234988	+	1.33268i
$587$	263.114	+	95.7656i	0.448235	+	0.163144i	0.556268	−	0.831003i	$-0.312233\pi$
$587$	263.114	+	95.7656i	0.448235	+	0.163144i	−0.108033	+	0.994147i	$0.534455\pi$
$588$		−	778.799i		−	1.32449i
$589$		0			0
$590$	−260.000			−0.440678
$591$	−110.985	+	304.930i	−0.187793	+	0.515956i
$592$	617.835	−	108.941i	1.04364	−	0.184022i
$593$	574.533	+	482.091i	0.968859	+	0.812969i	0.982371	−	0.186940i	$-0.0598569\pi$
$593$	574.533	+	482.091i	0.968859	+	0.812969i	−0.0135125	+	0.999909i	$0.504301\pi$
$594$	−497.929	+	417.812i	−0.838264	+	0.703387i
$595$	−52.0945	+	295.442i	−0.0875537	+	0.496542i
$596$	315.000	−	545.596i	0.528523	−	0.915430i
$597$	−384.067	+	221.741i	−0.643329	+	0.371426i
$598$	427.560	−	155.619i	0.714984	−	0.260233i
$599$	−172.644	−	474.335i	−0.288220	−	0.791879i	−0.996316	−	0.0857620i	$-0.972668\pi$
$599$	−172.644	−	474.335i	−0.288220	−	0.791879i	0.708095	−	0.706117i	$-0.249555\pi$
$600$	−292.500	−	506.625i	−0.487500	−	0.844375i
$601$	−530.825	−	306.472i	−0.883236	−	0.509937i	−0.0115120	−	0.999934i	$-0.503664\pi$
$601$	−530.825	−	306.472i	−0.883236	−	0.509937i	−0.871724	+	0.489997i	$0.836998\pi$
$602$	355.077	+	62.6097i	0.589830	+	0.104003i
$603$	−101.975	−	121.529i	−0.169112	−	0.201540i
$604$	208.584	−	248.581i	0.345338	−	0.411558i
$605$	−14.5864	−	82.7239i	−0.0241098	−	0.136734i
$606$	610.800	+	222.313i	1.00792	+	0.366853i
$607$		−	987.921i		−	1.62755i	−0.581182	−	0.813774i	$-0.697410\pi$
$607$		−	987.921i		−	1.62755i	0.581182	−	0.813774i	$-0.302590\pi$
$608$		0			0
$609$	−325.000			−0.533662
$610$	−197.307	+	542.098i	−0.323455	+	0.888685i
$611$	−35.5077	+	6.26097i	−0.0581142	+	0.0102471i
$612$	413.664	+	347.105i	0.675922	+	0.567166i
$613$	−919.253	+	771.345i	−1.49960	+	1.25831i	−0.618122	+	0.786082i	$0.712106\pi$
$613$	−919.253	+	771.345i	−1.49960	+	1.25831i	−0.881476	+	0.472230i	$0.843449\pi$
$614$	−148.990	+	844.965i	−0.242655	+	1.37616i
$615$	−260.000	+	450.333i	−0.422764	+	0.732249i
$616$	−780.625	+	450.694i	−1.26725	+	0.731646i
$617$	328.892	−	119.707i	0.533051	−	0.194015i	−0.0614492	−	0.998110i	$-0.519572\pi$
$617$	328.892	−	119.707i	0.533051	−	0.194015i	0.594500	+	0.804096i	$0.297350\pi$
$618$	−256.500	−	704.727i	−0.415048	−	1.14033i
$619$	−280.000	−	484.974i	−0.452342	−	0.783480i	0.546189	−	0.837662i	$-0.316078\pi$
$619$	−280.000	−	484.974i	−0.452342	−	0.783480i	−0.998531	+	0.0541821i	$0.982745\pi$
$620$	−1124.10	−	648.999i	−1.81306	−	1.04677i
$621$	−621.386	−	109.567i	−1.00062	−	0.176436i
$622$	915.453	+	1090.99i	1.47179	+	1.75401i
$623$		0			0
$624$	65.4654	+	371.273i	0.104912	+	0.594988i
$625$	299.762	+	109.104i	0.479619	+	0.174567i
$626$			450.694i			0.719958i
$627$		0			0
$628$	−90.0000			−0.143312
$629$	−110.985	+	304.930i	−0.176447	+	0.484785i
$630$	−284.062	+	50.0878i	−0.450892	+	0.0795044i
$631$	−804.347	−	674.927i	−1.27472	−	1.06961i	−0.993949	−	0.109839i	$-0.964966\pi$
$631$	−804.347	−	674.927i	−1.27472	−	1.06961i	−0.280768	−	0.959776i	$-0.590589\pi$
$632$	−497.929	+	417.812i	−0.787862	+	0.661095i
$633$	−146.733	+	832.163i	−0.231805	+	1.31463i
$634$	6.50000	−	11.2583i	0.0102524	−	0.0177576i
$635$	−449.640	+	259.600i	−0.708094	+	0.408818i
$636$	−2308.82	+	840.343i	−3.63023	+	1.32129i
$637$	29.5961	+	81.3146i	0.0464617	+	0.127652i
$638$	−325.000	−	562.917i	−0.509404	−	0.882314i
$639$	374.700	+	216.333i	0.586385	+	0.338549i
$640$	497.108	+	87.6536i	0.776732	+	0.136959i
$641$	787.985	+	939.084i	1.22931	+	1.46503i	0.838809	+	0.544426i	$0.183252\pi$
$641$	787.985	+	939.084i	1.22931	+	1.46503i	0.390497	+	0.920604i	$0.372303\pi$
$642$	−632.706	+	754.029i	−0.985523	+	1.17450i
$643$	−178.858	−	1014.35i	−0.278161	−	1.57753i	−0.728738	−	0.684793i	$-0.759893\pi$
$643$	−178.858	−	1014.35i	−0.278161	−	1.57753i	0.450577	−	0.892738i	$-0.351218\pi$
$644$	−1480.02	−	538.682i	−2.29816	−	0.836462i
$645$			288.444i			0.447200i
$646$		0			0
$647$	555.000			0.857805			0.428903	−	0.903351i	$-0.358900\pi$
$647$	555.000			0.857805			0.428903	+	0.903351i	$0.358900\pi$
$648$	622.751	−	1711.00i	0.961036	−	2.64043i
$649$	177.539	−	31.3049i	0.273557	−	0.0482355i
$650$	89.6272	+	75.2062i	0.137888	+	0.115702i
$651$	497.929	−	417.812i	0.764868	−	0.641800i
$652$	421.965	−	2393.08i	0.647186	−	3.67037i
$653$	−25.0000	+	43.3013i	−0.0382848	+	0.0663113i	−0.884533	−	0.466478i	$-0.845523\pi$
$653$	−25.0000	+	43.3013i	−0.0382848	+	0.0663113i	0.846248	+	0.532789i	$0.178856\pi$
$654$	−2232.59	+	1288.98i	−3.41374	+	1.97092i
$655$	−420.982	+	153.225i	−0.642721	+	0.233931i
$656$	−357.620	−	982.552i	−0.545152	−	1.49779i
$657$	210.000	+	363.731i	0.319635	+	0.553624i
$658$	156.125	+	90.1388i	0.237272	+	0.136989i
$659$	195.293	+	34.4354i	0.296347	+	0.0522540i	0.319845	−	0.947470i	$-0.396369\pi$
$659$	195.293	+	34.4354i	0.296347	+	0.0522540i	−0.0234979	+	0.999724i	$0.507480\pi$
$660$	−834.337	−	994.325i	−1.26415	−	1.50655i
$661$	−127.468	+	151.911i	−0.192841	+	0.229819i	−0.853798	−	0.520605i	$-0.825706\pi$
$661$	−127.468	+	151.911i	−0.192841	+	0.229819i	0.660956	+	0.750424i	$0.270151\pi$
$662$	124.158	+	704.138i	0.187551	+	1.06365i
$663$	−183.240	−	66.6939i	−0.276380	−	0.100594i
$664$			721.110i			1.08601i
$665$		0			0
$666$	−312.000			−0.468468
$667$	215.805	−	592.919i	0.323546	−	0.888934i
$668$	1086.54	−	191.586i	1.62655	−	0.286805i
$669$	−557.680	−	467.949i	−0.833603	−	0.699476i
$670$	−438.177	+	367.675i	−0.653996	+	0.548768i
$671$	69.4593	−	393.923i	0.103516	−	0.587069i
$672$	292.500	−	506.625i	0.435268	−	0.753906i
$673$	518.335	−	299.261i	0.770185	−	0.444667i	−0.0627553	−	0.998029i	$-0.519989\pi$
$673$	518.335	−	299.261i	0.770185	−	0.444667i	0.832941	+	0.553362i	$0.186655\pi$
$674$	195.456	−	71.1402i	0.289994	−	0.105549i
$675$	−55.4927	−	152.465i	−0.0822114	−	0.225874i
$676$	702.000	+	1215.90i	1.03846	+	1.79867i
$677$	−59.3275	−	34.2527i	−0.0876329	−	0.0505949i	0.455543	−	0.890214i	$-0.349445\pi$
$677$	−59.3275	−	34.2527i	−0.0876329	−	0.0505949i	−0.543176	+	0.839619i	$0.682778\pi$
$678$	−1569.44	−	276.735i	−2.31481	−	0.408164i
$679$	−393.993	−	469.542i	−0.580254	−	0.691520i
$680$	695.281	−	828.604i	1.02247	−	1.21853i
$681$	160.277	+	908.978i	0.235356	+	1.33477i
$682$	1221.60	+	444.626i	1.79120	+	0.651945i
$683$		−	237.966i		−	0.348413i	−0.984709	−	0.174207i	$-0.944264\pi$
$683$		−	237.966i		−	0.348413i	0.984709	−	0.174207i	$-0.0557361\pi$
$684$		0			0
$685$	500.000			0.729927
$686$	450.107	−	1236.66i	0.656133	−	1.80271i
$687$	−568.124	+	100.176i	−0.826964	+	0.145816i
$688$	−444.306	−	372.817i	−0.645793	−	0.541885i
$689$	209.130	−	175.481i	0.303527	−	0.254689i
$690$	316.040	−	1792.35i	0.458029	−	2.59761i
$691$	410.000	−	710.141i	0.593343	−	1.02770i	−0.400435	−	0.916325i	$-0.631141\pi$
$691$	410.000	−	710.141i	0.593343	−	1.02770i	0.993778	−	0.111375i	$-0.0355255\pi$
$692$	955.485	−	551.649i	1.38076	−	0.797181i
$693$	187.939	−	68.4040i	0.271196	−	0.0987071i
$694$	49.3268	+	135.524i	0.0710761	+	0.195280i
$695$	−100.000	−	173.205i	−0.143885	−	0.249216i
$696$	1014.81	+	585.902i	1.45806	+	0.841813i
$697$	532.616	+	93.9146i	0.764155	+	0.134741i
$698$	227.125	+	270.677i	0.325394	+	0.387790i
$699$	−625.753	+	745.743i	−0.895212	+	1.06687i
$700$	−70.3275	−	398.847i	−0.100468	−	0.569782i
$701$	507.434	+	184.691i	0.723872	+	0.263468i	0.677568	−	0.735460i	$-0.263034\pi$
$701$	507.434	+	184.691i	0.723872	+	0.263468i	0.0463032	+	0.998927i	$0.485256\pi$
$702$			234.361i			0.333847i
$703$		0			0
$704$	10.0000			0.0142045
$705$	−49.3268	+	135.524i	−0.0699672	+	0.192233i
$706$	656.893	−	115.828i	0.930444	−	0.164062i
$707$	191.511	+	160.697i	0.270879	+	0.227294i
$708$	−448.136	+	376.031i	−0.632960	+	0.531117i
$709$	46.5377	−	263.928i	0.0656385	−	0.372255i	−0.934240	−	0.356646i	$-0.883920\pi$
$709$	46.5377	−	263.928i	0.0656385	−	0.372255i	0.999878	−	0.0156087i	$-0.00496860\pi$
$710$	780.000	−	1351.00i	1.09859	−	1.90282i
$711$	124.900	−	72.1110i	0.175668	−	0.101422i
$712$		0			0
$713$	431.610	+	1185.84i	0.605343	+	1.66317i
$714$	487.500	+	844.375i	0.682773	+	1.18260i
$715$	124.900	+	72.1110i	0.174685	+	0.100855i
$716$	−319.570	−	56.3488i	−0.446326	−	0.0786994i
$717$	−456.568	−	544.116i	−0.636775	−	0.758879i
$718$	521.461	−	621.453i	0.726269	−	0.865533i
$719$	18.2331	+	103.405i	0.0253589	+	0.143818i	0.994858	−	0.101276i	$-0.0322925\pi$
$719$	18.2331	+	103.405i	0.0253589	+	0.143818i	−0.969499	+	0.245093i	$0.921181\pi$
$720$	436.017	+	158.697i	0.605580	+	0.220413i
$721$		−	288.444i		−	0.400061i
$722$		0			0
$723$	1430.00			1.97787
$724$	−332.956	+	914.790i	−0.459884	+	1.26352i
$725$	159.785	−	28.1744i	0.220393	−	0.0388612i
$726$	−209.130	−	175.481i	−0.288058	−	0.241709i
$727$	532.401	−	446.737i	0.732326	−	0.614494i	−0.198439	−	0.980113i	$-0.563587\pi$
$727$	532.401	−	446.737i	0.732326	−	0.614494i	0.930765	+	0.365619i	$0.119143\pi$
$728$	−56.4357	+	320.063i	−0.0775215	+	0.439646i
$729$	90.5000	−	156.751i	0.124143	−	0.215021i
$730$	1311.45	−	757.166i	1.79651	−	1.03721i
$731$	281.908	−	102.606i	0.385647	−	0.140364i
$732$	443.942	+	1219.72i	0.606478	+	1.66628i
$733$	−80.0000	−	138.564i	−0.109141	−	0.189037i	0.806282	−	0.591532i	$-0.201477\pi$
$733$	−80.0000	−	138.564i	−0.109141	−	0.189037i	−0.915422	+	0.402495i	$0.868143\pi$
$734$	−156.125	−	90.1388i	−0.212704	−	0.122805i
$735$	340.874	+	60.1054i	0.463775	+	0.0817760i
$736$	730.045	+	870.034i	0.991909	+	1.18211i
$737$	254.936	−	303.821i	0.345911	−	0.412241i
$738$	90.2971	+	512.100i	0.122354	+	0.693902i
$739$	−966.004	−	351.597i	−1.30718	−	0.475774i	−0.407850	−	0.913049i	$-0.633721\pi$
$739$	−966.004	−	351.597i	−1.30718	−	0.475774i	−0.899328	+	0.437275i	$0.855943\pi$
$740$			778.799i			1.05243i
$741$		0			0
$742$	−1365.00			−1.83962
$743$	−180.043	+	494.664i	−0.242319	+	0.665766i	0.757596	+	0.652724i	$0.226374\pi$
$743$	−180.043	+	494.664i	−0.242319	+	0.665766i	−0.999915	+	0.0130421i	$0.995848\pi$
$744$	−2308.00	+	406.963i	−3.10216	+	0.546994i
$745$	214.492	+	179.981i	0.287909	+	0.241585i
$746$	1204.99	−	1011.10i	1.61527	−	1.35537i
$747$	27.7837	−	157.569i	0.0371937	−	0.210936i
$748$	−675.000	+	1169.13i	−0.902406	+	1.56301i
$749$	−327.862	+	189.291i	−0.437734	+	0.252726i
$750$	1661.38	−	604.692i	2.21517	−	0.806255i
$751$	−12.3317	−	33.8811i	−0.0164204	−	0.0451146i	0.931212	−	0.364479i	$-0.118753\pi$
$751$	−12.3317	−	33.8811i	−0.0164204	−	0.0451146i	−0.947632	+	0.319364i	$0.896531\pi$
$752$	−145.000	−	251.147i	−0.192819	−	0.333973i
$753$	−1255.24	−	724.716i	−1.66699	−	0.962438i
$754$	−230.800	−	40.6963i	−0.306101	−	0.0539739i
$755$	92.7041	+	110.481i	0.122787	+	0.146332i
$756$	521.461	−	621.453i	0.689763	−	0.822028i
$757$	10.4189	+	59.0885i	0.0137634	+	0.0780561i	0.990916	−	0.134484i	$-0.0429376\pi$
$757$	10.4189	+	59.0885i	0.0137634	+	0.0780561i	−0.977152	+	0.212540i	$0.931826\pi$
$758$	−1649.16	−	600.245i	−2.17567	−	0.791880i
$759$			1261.94i			1.66264i
$760$		0			0
$761$	−655.000			−0.860710			−0.430355	−	0.902660i	$-0.641612\pi$
$761$	−655.000			−0.860710			−0.430355	+	0.902660i	$0.641612\pi$
$762$	−577.124	+	1585.64i	−0.757381	+	2.08089i
$763$	−976.463	+	172.177i	−1.27977	+	0.225658i
$764$	−1330.62	−	1116.52i	−1.74165	−	1.46142i
$765$	−183.851	+	154.269i	−0.240328	+	0.201659i
$766$	−126.416	+	716.940i	−0.165034	+	0.935953i
$767$	32.5000	−	56.2917i	0.0423729	−	0.0733920i
$768$	1433.23	−	827.474i	1.86618	−	1.07744i
$769$	173.843	−	63.2737i	0.226064	−	0.0822805i	−0.226505	−	0.974010i	$-0.572730\pi$
$769$	173.843	−	63.2737i	0.226064	−	0.0822805i	0.452569	+	0.891730i	$0.350508\pi$
$770$	−246.634	−	677.622i	−0.320304	−	0.880029i
$771$	754.000	+	1305.97i	0.977951	+	1.69386i
$772$	2079.58	+	1200.65i	2.69376	+	1.55524i
$773$	−316.019	−	55.7227i	−0.408821	−	0.0720862i	−0.0345443	−	0.999403i	$-0.510998\pi$
$773$	−316.019	−	55.7227i	−0.408821	−	0.0720862i	−0.374277	+	0.927317i	$0.622109\pi$
$774$	185.408	+	220.961i	0.239546	+	0.285479i
$775$	−208.584	+	248.581i	−0.269141	+	0.320750i
$776$	383.762	+	2176.43i	0.494539	+	2.80467i
$777$	−366.480	−	133.388i	−0.471660	−	0.171670i
$778$		−	1723.45i		−	2.21524i
$779$		0			0
$780$	−468.000			−0.600000
$781$	−369.951	+	1016.43i	−0.473689	+	1.30145i
$782$	−1864.16	+	328.701i	−2.38383	+	0.420334i
$783$	248.964	+	208.906i	0.317962	+	0.266802i
$784$	−533.167	+	447.380i	−0.680060	+	0.570638i
$785$	6.94593	−	39.3923i	0.00884831	−	0.0501813i
$786$	−728.000	+	1260.93i	−0.926209	+	1.60424i
$787$	59.3275	−	34.2527i	0.0753843	−	0.0435232i	−0.461834	−	0.886966i	$-0.652808\pi$
$787$	59.3275	−	34.2527i	0.0753843	−	0.0435232i	0.537218	+	0.843443i	$0.319475\pi$
$788$	761.151	−	277.036i	0.965928	−	0.351569i
$789$	382.283	+	1050.31i	0.484516	+	1.33120i
$790$	−260.000	−	450.333i	−0.329114	−	0.570042i
$791$	−530.825	−	306.472i	−0.671081	−	0.387449i
$792$	−710.155	−	125.219i	−0.896660	−	0.158105i
$793$	−92.7041	−	110.481i	−0.116903	−	0.139320i
$794$	−1738.20	+	2071.51i	−2.18917	+	2.60895i
$795$	−189.624	−	1075.41i	−0.238521	−	1.35272i
$796$	1040.24	+	378.616i	1.30683	+	0.475649i
$797$			1258.34i			1.57884i	0.613852	+	0.789421i	$0.289619\pi$
$797$			1258.34i			1.57884i	−0.613852	+	0.789421i	$0.710381\pi$
$798$		0			0
$799$	150.000			0.187735
$800$	−99.8869	+	274.437i	−0.124859	+	0.343046i
$801$		0			0
$802$	796.686	+	668.499i	0.993374	+	0.833540i
$803$	−804.347	+	674.927i	−1.00168	+	0.840507i
$804$	−223.485	+	1267.45i	−0.277967	+	1.57643i
$805$	350.000	−	606.218i	0.434783	−	0.753066i
$806$	405.925	−	234.361i	0.503629	−	0.290770i
$807$	−366.480	+	133.388i	−0.454127	+	0.165289i
$808$	−308.293	−	847.027i	−0.381550	−	1.04830i
$809$	3.50000	+	6.06218i	0.00432633	+	0.00749342i	0.868180	−	0.496249i	$-0.165290\pi$
$809$	3.50000	+	6.06218i	0.00432633	+	0.00749342i	−0.863854	+	0.503742i	$0.831956\pi$
$810$	1261.49	+	728.321i	1.55739	+	0.899162i
$811$	1011.97	+	178.438i	1.24781	+	0.220022i	0.758258	−	0.651954i	$-0.226051\pi$
$811$	1011.97	+	178.438i	1.24781	+	0.220022i	0.489548	+	0.871976i	$0.337162\pi$
$812$	521.461	+	621.453i	0.642193	+	0.765336i
$813$	243.348	−	290.011i	0.299322	−	0.356717i
$814$	−135.446	−	768.150i	−0.166395	−	0.943673i
$815$	1014.87	+	369.382i	1.24524	+	0.453229i
$816$		−	1568.41i		−	1.92208i
$817$		0			0
$818$	130.000			0.158924
$819$	24.6634	−	67.7622i	0.0301141	−	0.0827377i
$820$	1278.28	−	225.395i	1.55888	−	0.274872i
$821$	645.009	+	541.227i	0.785639	+	0.659229i	0.944662	−	0.328046i	$-0.106390\pi$
$821$	645.009	+	541.227i	0.785639	+	0.659229i	−0.159023	+	0.987275i	$0.550834\pi$
$822$	1244.82	−	1044.53i	1.51438	−	1.27072i
$823$	134.577	−	763.226i	0.163520	−	0.927371i	−0.787056	−	0.616881i	$-0.788396\pi$
$823$	134.577	−	763.226i	0.163520	−	0.927371i	0.950577	−	0.310489i	$-0.100493\pi$
$824$	−520.000	+	900.666i	−0.631068	+	1.09304i
$825$	−281.025	+	162.250i	−0.340636	+	0.196666i
$826$	−305.400	+	111.157i	−0.369734	+	0.134572i
$827$	432.843	+	1189.23i	0.523389	+	1.43800i	0.866724	+	0.498788i	$0.166221\pi$
$827$	432.843	+	1189.23i	0.523389	+	1.43800i	−0.343335	+	0.939213i	$0.611557\pi$
$828$	−630.000	−	1091.19i	−0.760870	−	1.31786i
$829$	1358.29	+	784.207i	1.63846	+	0.945968i	0.981362	+	0.192166i	$0.0615513\pi$
$829$	1358.29	+	784.207i	1.63846	+	0.945968i	0.657102	+	0.753802i	$0.271782\pi$
$830$	−568.124	−	100.176i	−0.684487	−	0.120693i
$831$	115.880	+	138.101i	0.139447	+	0.166186i
$832$	2.31760	−	2.76201i	0.00278558	−	0.00331973i
$833$	−62.5133	−	354.531i	−0.0750460	−	0.425607i
$834$	−610.800	−	222.313i	−0.732374	−	0.266562i
$835$			490.355i			0.587251i
$836$		0			0
$837$	−650.000			−0.776583
$838$	138.115	−	379.468i	0.164815	−	0.452826i
$839$	1136.25	−	200.351i	1.35429	−	0.238798i	0.551058	−	0.834467i	$-0.314224\pi$
$839$	1136.25	−	200.351i	1.35429	−	0.238798i	0.803230	+	0.595669i	$0.203113\pi$
$840$	995.858	+	835.624i	1.18554	+	0.994790i
$841$	395.279	−	331.678i	0.470011	−	0.394386i
$842$	−395.050	+	2240.44i	−0.469180	+	2.66085i
$843$	520.000	−	900.666i	0.616845	−	1.06841i
$844$	1826.66	−	1054.62i	2.16429	−	1.24955i
$845$	−586.368	+	213.421i	−0.693927	+	0.252569i
$846$	49.3268	+	135.524i	0.0583060	+	0.160194i
$847$	−52.5000	−	90.9327i	−0.0619835	−	0.107359i
$848$	1901.60	+	1097.89i	2.24246	+	1.29468i
$849$	1136.25	+	200.351i	1.33834	+	0.235985i
$850$	−312.876	−	372.872i	−0.368090	−	0.438673i
$851$	486.697	−	580.023i	0.571912	−	0.681578i
$852$	−609.505	−	3456.68i	−0.715382	−	4.05713i
$853$	−375.877	−	136.808i	−0.440653	−	0.160385i	0.112160	−	0.993690i	$-0.464223\pi$
$853$	−375.877	−	136.808i	−0.440653	−	0.160385i	−0.552813	+	0.833306i	$0.686445\pi$
$854$			721.110i			0.844391i
$855$		0			0
$856$	1365.00			1.59463
$857$	54.2595	−	149.077i	0.0633133	−	0.173952i	−0.904002	−	0.427528i	$-0.859385\pi$
$857$	54.2595	−	149.077i	0.0633133	−	0.173952i	0.967315	+	0.253576i	$0.0816068\pi$
$858$	461.601	−	81.3927i	0.537996	−	0.0948632i
$859$	1096.98	+	920.472i	1.27704	+	1.07156i	0.993645	+	0.112558i	$0.0359045\pi$
$859$	1096.98	+	920.472i	1.27704	+	1.07156i	0.283393	+	0.959004i	$0.408540\pi$
$860$	551.552	−	462.807i	0.641340	−	0.538148i
$861$	−112.871	+	640.125i	−0.131093	+	0.743467i
$862$	−780.000	+	1351.00i	−0.904872	+	1.56728i
$863$	−112.410	+	64.8999i	−0.130255	+	0.0752027i	−0.563712	−	0.825972i	$-0.690627\pi$
$863$	−112.410	+	64.8999i	−0.130255	+	0.0752027i	0.433457	+	0.901174i	$0.357294\pi$
$864$	−549.720	+	200.082i	−0.636250	+	0.231576i
$865$	167.711	+	460.783i	0.193886	+	0.532697i
$866$	−1326.00	−	2296.70i	−1.53118	−	2.65208i
$867$	−199.840	−	115.378i	−0.230496	−	0.133077i
$868$	−1597.85	−	281.744i	−1.84084	−	0.324590i
$869$	231.760	+	276.201i	0.266698	+	0.317838i
$870$	−602.577	+	718.123i	−0.692617	+	0.825429i
$871$	−24.8317	−	140.828i	−0.0285094	−	0.161685i
$872$	3359.40	+	1222.72i	3.85252	+	1.40220i
$873$		−	490.355i		−	0.561690i
$874$		0			0
$875$	680.000			0.777143
$876$	1165.35	−	3201.76i	1.33030	−	3.65498i
$877$	−387.034	+	68.2446i	−0.441316	+	0.0778160i	−0.389891	−	0.920861i	$-0.627487\pi$
$877$	−387.034	+	68.2446i	−0.441316	+	0.0778160i	−0.0514250	+	0.998677i	$0.516376\pi$
$878$	−2190.89	−	1838.37i	−2.49532	−	2.09382i
$879$	−607.473	+	509.731i	−0.691096	+	0.579898i
$880$	−201.432	+	1142.38i	−0.228900	+	1.29816i
$881$	−375.000	+	649.519i	−0.425653	+	0.737252i	−0.996481	−	0.0838173i	$-0.973289\pi$
$881$	−375.000	+	649.519i	−0.425653	+	0.737252i	0.570828	+	0.821069i	$0.306622\pi$
$882$	299.760	−	173.066i	0.339864	−	0.196220i
$883$	−112.763	+	41.0424i	−0.127705	+	0.0464807i	−0.405082	−	0.914280i	$-0.632757\pi$
$883$	−112.763	+	41.0424i	−0.127705	+	0.0464807i	0.277377	+	0.960761i	$0.410535\pi$
$884$	166.478	+	457.395i	0.188324	+	0.517415i
$885$	−130.000	−	225.167i	−0.146893	−	0.254426i
$886$	−2092.07	−	1207.86i	−2.36126	−	1.36327i
$887$	837.983	+	147.759i	0.944738	+	0.166583i	0.624738	−	0.780835i	$-0.285206\pi$
$887$	837.983	+	147.759i	0.944738	+	0.166583i	0.320000	+	0.947417i	$0.396317\pi$
$888$	903.865	+	1077.18i	1.01787	+	1.21305i
$889$	−417.169	+	497.162i	−0.469256	+	0.559238i
$890$		0			0
$891$	−949.090	−	345.440i	−1.06520	−	0.387700i
$892$			1817.20i			2.03722i
$893$		0			0
$894$	910.000			1.01790
$895$	49.3268	−	135.524i	0.0551138	−	0.151424i
$896$	621.386	−	109.567i	0.693511	−	0.122285i
$897$	348.550	+	292.468i	0.388573	+	0.326052i
$898$	99.5858	−	83.5624i	0.110897	−	0.0930539i
$899$	112.871	−	640.125i	0.125552	−	0.712041i
$900$	162.000	−	280.592i	0.180000	−	0.311769i
$901$	−983.587	+	567.874i	−1.09166	+	0.630271i
$902$	−1221.60	+	444.626i	−1.35432	+	0.492934i
$903$	123.317	+	338.811i	0.136564	+	0.375206i
$904$	1105.00	+	1913.92i	1.22235	+	2.11716i
$905$	−374.700	−	216.333i	−0.414033	−	0.239042i
$906$	461.601	+	81.3927i	0.509493	+	0.0898374i
$907$	−414.851	−	494.400i	−0.457388	−	0.545094i	0.487226	−	0.873276i	$-0.338009\pi$
$907$	−414.851	−	494.400i	−0.457388	−	0.545094i	−0.944615	+	0.328182i	$0.893564\pi$
$908$	1480.95	−	1764.93i	1.63100	−	1.94375i
$909$	34.7296	+	196.962i	0.0382064	+	0.216679i
$910$	−244.320	−	88.9252i	−0.268484	−	0.0977200i
$911$		−	1225.89i		−	1.34565i	−0.739802	−	0.672825i	$-0.765081\pi$
$911$		−	1225.89i		−	1.34565i	0.739802	−	0.672825i	$-0.234919\pi$
$912$		0			0
$913$	400.000			0.438116
$914$	−931.044	+	2558.02i	−1.01865	+	2.79871i
$915$	−568.124	+	100.176i	−0.620901	+	0.109482i
$916$	1103.10	+	925.614i	1.20426	+	1.01050i
$917$	−428.985	+	359.961i	−0.467813	+	0.392542i
$918$	169.307	−	960.188i	0.184430	−	1.04596i
$919$	256.500	−	444.271i	0.279108	−	0.483429i	−0.692056	−	0.721844i	$-0.743295\pi$
$919$	256.500	−	444.271i	0.279108	−	0.483429i	0.971163	+	0.238416i	$0.0766280\pi$
$920$	−2185.75	+	1261.94i	−2.37581	+	1.37168i
$921$	−806.256	+	293.453i	−0.875414	+	0.318625i
$922$	−952.008	−	2615.62i	−1.03255	−	2.83690i
$923$	195.000	+	337.750i	0.211268	+	0.365926i
$924$	−1405.12	−	811.249i	−1.52070	−	0.877975i
$925$	191.742	+	33.8093i	0.207288	+	0.0365506i
$926$	−811.161	−	966.704i	−0.875984	−	1.04396i
$927$	148.327	−	176.769i	0.160007	−	0.190689i
$928$	−101.584	−	576.113i	−0.109466	−	0.620811i
$929$	1143.61	+	416.239i	1.23101	+	0.448050i	0.873942	−	0.486029i	$-0.161555\pi$
$929$	1143.61	+	416.239i	1.23101	+	0.448050i	0.357065	+	0.934080i	$0.383777\pi$
$930$		−	1874.89i		−	2.01601i
$931$		0			0
$932$	2430.00			2.60730
$933$	−487.103	+	1338.30i	−0.522082	+	1.43441i
$934$	−248.554	+	43.8268i	−0.266118	+	0.0469238i
$935$	−459.627	−	385.673i	−0.491579	−	0.412484i
$936$	−199.172	+	167.125i	−0.212790	+	0.178552i
$937$	−190.145	+	1078.36i	−0.202929	+	1.15087i	0.697736	+	0.716355i	$0.254191\pi$
$937$	−190.145	+	1078.36i	−0.202929	+	1.15087i	−0.900665	+	0.434514i	$0.856920\pi$
$938$	−357.500	+	619.208i	−0.381130	+	0.660137i
$939$	−390.312	+	225.347i	−0.415668	+	0.239986i
$940$	338.289	−	123.127i	0.359882	−	0.130986i
$941$	−376.117	−	1033.37i	−0.399699	−	1.09817i	−0.962431	−	0.271526i	$-0.912472\pi$
$941$	−376.117	−	1033.37i	−0.399699	−	1.09817i	0.562732	−	0.826640i	$-0.309750\pi$
$942$	−65.0000	−	112.583i	−0.0690021	−	0.119515i
$943$	−1092.87	−	630.971i	−1.15893	−	0.669111i
$944$	514.862	+	90.7841i	0.545405	+	0.0961696i
$945$	231.760	+	276.201i	0.245249	+	0.292276i
$946$	−463.521	+	552.403i	−0.489980	+	0.583935i
$947$	111.135	+	630.277i	0.117355	+	0.665551i	0.985557	+	0.169342i	$0.0541641\pi$
$947$	111.135	+	630.277i	0.117355	+	0.665551i	−0.868203	+	0.496210i	$0.834725\pi$
$948$	−1099.44	−	400.164i	−1.15975	−	0.422113i
$949$			378.583i			0.398928i
$950$		0			0
$951$	13.0000			0.0136698
$952$	462.439	−	1270.54i	0.485755	−	1.33460i
$953$	−1150.45	+	202.856i	−1.20719	+	0.212860i	−0.740804	−	0.671722i	$-0.765555\pi$
$953$	−1150.45	+	202.856i	−1.20719	+	0.212860i	−0.466385	+	0.884582i	$0.654444\pi$
$954$	−836.521	−	701.924i	−0.876856	−	0.735769i
$955$	591.386	−	496.232i	0.619253	−	0.519615i
$956$	−307.878	+	1746.06i	−0.322048	+	1.82643i
$957$	325.000	−	562.917i	0.339603	−	0.588210i
$958$	−1155.32	+	667.027i	−1.20598	+	0.696270i
$959$	587.308	−	213.763i	0.612417	−	0.222902i
$960$	−4.93268	−	13.5524i	−0.00513821	−	0.0141171i
$961$	169.500	+	293.583i	0.176379	+	0.305497i
$962$	−243.555	−	140.616i	−0.253176	−	0.146171i
$963$	−298.265	−	52.5922i	−0.309725	−	0.0546129i
$964$	−2294.43	−	2734.39i	−2.38011	−	2.83651i
$965$	−686.011	+	817.556i	−0.710892	+	0.847208i
$966$	−395.050	−	2240.44i	−0.408954	−	2.31929i
$967$	949.090	+	345.440i	0.981478	+	0.357229i	0.782415	−	0.622758i	$-0.213988\pi$
$967$	949.090	+	345.440i	0.981478	+	0.357229i	0.199064	+	0.979987i	$0.436210\pi$
$968$			378.583i			0.391098i
$969$		0			0
$970$	−1768.00			−1.82268
$971$	−258.966	+	711.503i	−0.266700	+	0.732753i	0.731977	+	0.681330i	$0.238598\pi$
$971$	−258.966	+	711.503i	−0.266700	+	0.732753i	−0.998677	+	0.0514233i	$0.983624\pi$
$972$	1789.59	−	315.553i	1.84114	−	0.324643i
$973$	−191.511	−	160.697i	−0.196825	−	0.165156i
$974$	1434.04	−	1203.30i	1.47232	−	1.23542i
$975$	−20.3168	+	115.223i	−0.0208378	+	0.118177i
$976$	580.000	−	1004.59i	0.594262	−	1.02929i
$977$	518.335	−	299.261i	0.530537	−	0.306306i	−0.210698	−	0.977551i	$-0.567574\pi$
$977$	518.335	−	299.261i	0.530537	−	0.306306i	0.741235	+	0.671245i	$0.234240\pi$
$978$	3298.32	−	1200.49i	3.37252	−	1.22750i
$979$		0			0
$980$	−432.000	−	748.246i	−0.440816	−	0.763516i
$981$	−686.950	−	396.611i	−0.700255	−	0.404292i
$982$	−2244.09	−	395.694i	−2.28522	−	0.402947i
$983$	37.0817	+	44.1922i	0.0377229	+	0.0449565i	0.784576	−	0.620033i	$-0.212881\pi$
$983$	37.0817	+	44.1922i	0.0377229	+	0.0449565i	−0.746853	+	0.664989i	$0.768436\pi$
$984$	1506.44	−	1795.31i	1.53094	−	1.82450i
$985$	62.5133	+	354.531i	0.0634653	+	0.359930i
$986$	916.200	+	333.470i	0.929209	+	0.338205i
$987$			180.278i			0.182652i
$988$		0			0
$989$	−700.000			−0.707786
$990$	197.307	−	542.098i	0.199300	−	0.547573i
$991$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$991$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$992$	896.272	+	752.062i	0.903500	+	0.758127i
$993$	−547.722	+	459.593i	−0.551583	+	0.462833i
$994$	338.614	−	1920.38i	0.340658	−	1.93197i
$995$	−246.000	+	426.084i	−0.247236	+	0.428226i
$996$	−1124.10	+	648.999i	−1.12861	+	0.651606i
$997$	159.748	−	58.1434i	0.160228	−	0.0583184i	−0.260661	−	0.965430i	$-0.583940\pi$
$997$	159.748	−	58.1434i	0.160228	−	0.0583184i	0.420889	+	0.907112i	$0.361718\pi$
$998$	−468.605	−	1287.48i	−0.469544	−	1.29006i
$999$	195.000	+	337.750i	0.195195	+	0.338088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.3.f.d.262.2		12
19.2	odd	18	inner	361.3.f.d.307.2		12
19.3	odd	18	inner	361.3.f.d.116.1		12
19.4	even	9		361.3.d.b.69.2		4
19.5	even	9	inner	361.3.f.d.299.1		12
19.6	even	9		361.3.d.b.293.1		4
19.7	even	3	inner	361.3.f.d.127.2		12
19.8	odd	6	inner	361.3.f.d.333.2		12
19.9	even	9		19.3.b.b.18.2	yes	2
19.10	odd	18		19.3.b.b.18.1	✓	2
19.11	even	3	inner	361.3.f.d.333.1		12
19.12	odd	6	inner	361.3.f.d.127.1		12
19.13	odd	18		361.3.d.b.293.2		4
19.14	odd	18	inner	361.3.f.d.299.2		12
19.15	odd	18		361.3.d.b.69.1		4
19.16	even	9	inner	361.3.f.d.116.2		12
19.17	even	9	inner	361.3.f.d.307.1		12
19.18	odd	2	inner	361.3.f.d.262.1		12
57.29	even	18		171.3.c.b.37.2		2
57.47	odd	18		171.3.c.b.37.1		2
76.47	odd	18		304.3.e.d.113.2		2
76.67	even	18		304.3.e.d.113.1		2
95.9	even	18		475.3.c.b.151.1		2
95.28	odd	36		475.3.d.b.474.4		4
95.29	odd	18		475.3.c.b.151.2		2
95.47	odd	36		475.3.d.b.474.1		4
95.48	even	36		475.3.d.b.474.2		4
95.67	even	36		475.3.d.b.474.3		4
152.29	odd	18		1216.3.e.g.1025.1		2
152.67	even	18		1216.3.e.h.1025.2		2
152.85	even	18		1216.3.e.g.1025.2		2
152.123	odd	18		1216.3.e.h.1025.1		2
228.47	even	18		2736.3.o.d.721.2		2
228.143	odd	18		2736.3.o.d.721.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.3.b.b.18.1	✓	2	19.10	odd	18
19.3.b.b.18.2	yes	2	19.9	even	9
171.3.c.b.37.1		2	57.47	odd	18
171.3.c.b.37.2		2	57.29	even	18
304.3.e.d.113.1		2	76.67	even	18
304.3.e.d.113.2		2	76.47	odd	18
361.3.d.b.69.1		4	19.15	odd	18
361.3.d.b.69.2		4	19.4	even	9
361.3.d.b.293.1		4	19.6	even	9
361.3.d.b.293.2		4	19.13	odd	18
361.3.f.d.116.1		12	19.3	odd	18	inner
361.3.f.d.116.2		12	19.16	even	9	inner
361.3.f.d.127.1		12	19.12	odd	6	inner
361.3.f.d.127.2		12	19.7	even	3	inner
361.3.f.d.262.1		12	19.18	odd	2	inner
361.3.f.d.262.2		12	1.1	even	1	trivial
361.3.f.d.299.1		12	19.5	even	9	inner
361.3.f.d.299.2		12	19.14	odd	18	inner
361.3.f.d.307.1		12	19.17	even	9	inner
361.3.f.d.307.2		12	19.2	odd	18	inner
361.3.f.d.333.1		12	19.11	even	3	inner
361.3.f.d.333.2		12	19.8	odd	6	inner
475.3.c.b.151.1		2	95.9	even	18
475.3.c.b.151.2		2	95.29	odd	18
475.3.d.b.474.1		4	95.47	odd	36
475.3.d.b.474.2		4	95.48	even	36
475.3.d.b.474.3		4	95.67	even	36
475.3.d.b.474.4		4	95.28	odd	36
1216.3.e.g.1025.1		2	152.29	odd	18
1216.3.e.g.1025.2		2	152.85	even	18
1216.3.e.h.1025.1		2	152.123	odd	18
1216.3.e.h.1025.2		2	152.67	even	18
2736.3.o.d.721.1		2	228.143	odd	18
2736.3.o.d.721.2		2	228.47	even	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	361.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.23317 - 3.38811i) q^{2} +(3.55077 - 0.626097i) q^{3} +(-6.89440 - 5.78509i) q^{4} +(3.06418 - 2.57115i) q^{5} +(2.25743 - 12.8025i) q^{6} +(2.50000 - 4.33013i) q^{7} +(-15.6125 + 9.01388i) q^{8} +(3.75877 - 1.36808i) q^{9} +O(q^{10})\)	\(q+(1.23317 - 3.38811i) q^{2} +(3.55077 - 0.626097i) q^{3} +(-6.89440 - 5.78509i) q^{4} +(3.06418 - 2.57115i) q^{5} +(2.25743 - 12.8025i) q^{6} +(2.50000 - 4.33013i) q^{7} +(-15.6125 + 9.01388i) q^{8} +(3.75877 - 1.36808i) q^{9} +(-4.93268 - 13.5524i) q^{10} +(5.00000 + 8.66025i) q^{11} +(-28.1025 - 16.2250i) q^{12} +(3.55077 + 0.626097i) q^{13} +(-11.5880 - 13.8101i) q^{14} +(9.27041 - 11.0481i) q^{15} +(5.03580 + 28.5594i) q^{16} +(-14.0954 - 5.13030i) q^{17} -14.4222i q^{18} -36.0000 q^{20} +(6.16586 - 16.9405i) q^{21} +(35.5077 - 6.26097i) q^{22} +(26.8116 + 22.4976i) q^{23} +(-49.7929 + 41.7812i) q^{24} +(-1.56283 + 8.86327i) q^{25} +(6.50000 - 11.2583i) q^{26} +(-15.6125 + 9.01388i) q^{27} +(-42.2862 + 15.3909i) q^{28} +(-6.16586 - 16.9405i) q^{29} +(-26.0000 - 45.0333i) q^{30} +(31.2250 + 18.0278i) q^{31} +(31.9570 + 5.63488i) q^{32} +(23.1760 + 27.6201i) q^{33} +(-34.7641 + 41.4302i) q^{34} +(-3.47296 - 19.6962i) q^{35} +(-33.8289 - 12.3127i) q^{36} -21.6333i q^{37} +13.0000 q^{39} +(-24.6634 + 67.7622i) q^{40} +(-35.5077 + 6.26097i) q^{41} +(-49.7929 - 41.7812i) q^{42} +(-15.3209 + 12.8558i) q^{43} +(15.6283 - 88.6327i) q^{44} +(8.00000 - 13.8564i) q^{45} +(109.287 - 63.0971i) q^{46} +(-9.39693 + 3.42020i) q^{47} +(35.7620 + 98.2552i) q^{48} +(12.0000 + 20.7846i) q^{49} +(28.1025 + 16.2250i) q^{50} +(-53.2616 - 9.39146i) q^{51} +(-20.8584 - 24.8581i) q^{52} +(48.6697 - 58.0023i) q^{53} +(11.2871 + 64.0125i) q^{54} +(37.5877 + 13.6808i) q^{55} +90.1388i q^{56} -65.0000 q^{58} +(6.16586 - 16.9405i) q^{59} +(-127.828 + 22.5395i) q^{60} +(-30.6418 - 25.7115i) q^{61} +(99.5858 - 83.5624i) q^{62} +(3.47296 - 19.6962i) q^{63} +(0.500000 - 0.866025i) q^{64} +(12.4900 - 7.21110i) q^{65} +(122.160 - 44.4626i) q^{66} +(-13.5649 - 37.2692i) q^{67} +(67.5000 + 116.913i) q^{68} +(109.287 + 63.0971i) q^{69} +(-71.0155 - 12.5219i) q^{70} +(69.5281 + 82.8604i) q^{71} +(-46.3521 + 55.2403i) q^{72} +(18.2331 + 103.405i) q^{73} +(-73.2960 - 26.6776i) q^{74} +32.4500i q^{75} +50.0000 q^{77} +(16.0312 - 44.0454i) q^{78} +(35.5077 - 6.26097i) q^{79} +(88.8612 + 74.5634i) q^{80} +(-77.3705 + 64.9215i) q^{81} +(-22.5743 + 128.025i) q^{82} +(20.0000 - 34.6410i) q^{83} +(-140.512 + 81.1249i) q^{84} +(-56.3816 + 20.5212i) q^{85} +(24.6634 + 67.7622i) q^{86} +(-32.5000 - 56.2917i) q^{87} +(-156.125 - 90.1388i) q^{88} +(-37.0817 - 44.1922i) q^{90} +(11.5880 - 13.8101i) q^{91} +(-54.6992 - 310.214i) q^{92} +(122.160 + 44.4626i) q^{93} +36.0555i q^{94} +117.000 q^{96} +(41.9278 - 115.196i) q^{97} +(85.2186 - 15.0263i) q^{98} +(30.6418 + 25.7115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 30 q^{7}+O(q^{10}) \) 12 * q + 30 * q^7	\( 12 q + 30 q^{7} + 60 q^{11} - 432 q^{20} + 78 q^{26} - 312 q^{30} + 156 q^{39} + 96 q^{45} + 144 q^{49} - 780 q^{58} + 6 q^{64} + 810 q^{68} + 600 q^{77} + 240 q^{83} - 390 q^{87} + 1404 q^{96}+O(q^{100}) \) 12 * q + 30 * q^7 + 60 * q^11 - 432 * q^20 + 78 * q^26 - 312 * q^30 + 156 * q^39 + 96 * q^45 + 144 * q^49 - 780 * q^58 + 6 * q^64 + 810 * q^68 + 600 * q^77 + 240 * q^83 - 390 * q^87 + 1404 * q^96

Introduction

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