LMFDB - Embedded newform 30.3.f.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,3,Mod(7,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("30.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	30.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.817440793081$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.2
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	30.13
Dual form			30.3.f.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.89898 + 1.00000i) q^{5} +2.44949 q^{6} +(0.898979 - 0.898979i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.89898 + 1.00000i) q^{5} +2.44949 q^{6} +(0.898979 - 0.898979i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-3.89898 + 5.89898i) q^{10} -13.7980 q^{11} +(2.44949 - 2.44949i) q^{12} +(12.7980 + 12.7980i) q^{13} -1.79796i q^{14} +(-7.22474 - 4.77526i) q^{15} -4.00000 q^{16} +(15.8990 - 15.8990i) q^{17} +(3.00000 + 3.00000i) q^{18} -25.7980i q^{19} +(2.00000 + 9.79796i) q^{20} +2.20204 q^{21} +(-13.7980 + 13.7980i) q^{22} +(10.6969 + 10.6969i) q^{23} -4.89898i q^{24} +(23.0000 - 9.79796i) q^{25} +25.5959 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-1.79796 - 1.79796i) q^{28} +25.7980i q^{29} +(-12.0000 + 2.44949i) q^{30} -39.5959 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-16.8990 - 16.8990i) q^{33} -31.7980i q^{34} +(-3.50510 + 5.30306i) q^{35} +6.00000 q^{36} +(-27.0000 + 27.0000i) q^{37} +(-25.7980 - 25.7980i) q^{38} +31.3485i q^{39} +(11.7980 + 7.79796i) q^{40} +17.7980 q^{41} +(2.20204 - 2.20204i) q^{42} +(-12.4949 - 12.4949i) q^{43} +27.5959i q^{44} +(-3.00000 - 14.6969i) q^{45} +21.3939 q^{46} +(9.30306 - 9.30306i) q^{47} +(-4.89898 - 4.89898i) q^{48} +47.3837i q^{49} +(13.2020 - 32.7980i) q^{50} +38.9444 q^{51} +(25.5959 - 25.5959i) q^{52} +(-19.0908 - 19.0908i) q^{53} +7.34847i q^{54} +(67.5959 - 13.7980i) q^{55} -3.59592 q^{56} +(31.5959 - 31.5959i) q^{57} +(25.7980 + 25.7980i) q^{58} -20.0000i q^{59} +(-9.55051 + 14.4495i) q^{60} +15.1918 q^{61} +(-39.5959 + 39.5959i) q^{62} +(2.69694 + 2.69694i) q^{63} +8.00000i q^{64} +(-75.4949 - 49.8990i) q^{65} -33.7980 q^{66} +(-48.0908 + 48.0908i) q^{67} +(-31.7980 - 31.7980i) q^{68} +26.2020i q^{69} +(1.79796 + 8.80816i) q^{70} +6.20204 q^{71} +(6.00000 - 6.00000i) q^{72} +(-37.2020 - 37.2020i) q^{73} +54.0000i q^{74} +(40.1691 + 16.1691i) q^{75} -51.5959 q^{76} +(-12.4041 + 12.4041i) q^{77} +(31.3485 + 31.3485i) q^{78} -115.373i q^{79} +(19.5959 - 4.00000i) q^{80} -9.00000 q^{81} +(17.7980 - 17.7980i) q^{82} +(82.2929 + 82.2929i) q^{83} -4.40408i q^{84} +(-61.9898 + 93.7878i) q^{85} -24.9898 q^{86} +(-31.5959 + 31.5959i) q^{87} +(27.5959 + 27.5959i) q^{88} -117.394i q^{89} +(-17.6969 - 11.6969i) q^{90} +23.0102 q^{91} +(21.3939 - 21.3939i) q^{92} +(-48.4949 - 48.4949i) q^{93} -18.6061i q^{94} +(25.7980 + 126.384i) q^{95} -9.79796 q^{96} +(81.9898 - 81.9898i) q^{97} +(47.3837 + 47.3837i) q^{98} -41.3939i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 16 q^{7} - 8 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 16 * q^7 - 8 * q^8	$ 4 q + 4 q^{2} - 16 q^{7} - 8 q^{8} + 4 q^{10} - 16 q^{11} + 12 q^{13} - 24 q^{15} - 16 q^{16} + 44 q^{17} + 12 q^{18} + 8 q^{20} + 48 q^{21} - 16 q^{22} - 16 q^{23} + 92 q^{25} + 24 q^{26} + 32 q^{28} - 48 q^{30} - 80 q^{31} - 16 q^{32} - 48 q^{33} - 112 q^{35} + 24 q^{36} - 108 q^{37} - 64 q^{38} + 8 q^{40} + 32 q^{41} + 48 q^{42} + 48 q^{43} - 12 q^{45} - 32 q^{46} + 96 q^{47} + 92 q^{50} + 48 q^{51} + 24 q^{52} + 100 q^{53} + 192 q^{55} + 64 q^{56} + 48 q^{57} + 64 q^{58} - 48 q^{60} - 96 q^{61} - 80 q^{62} - 48 q^{63} - 204 q^{65} - 96 q^{66} - 16 q^{67} - 88 q^{68} - 32 q^{70} + 64 q^{71} + 24 q^{72} - 188 q^{73} + 48 q^{75} - 128 q^{76} - 128 q^{77} + 96 q^{78} - 36 q^{81} + 32 q^{82} + 192 q^{83} - 52 q^{85} + 96 q^{86} - 48 q^{87} + 32 q^{88} - 12 q^{90} + 288 q^{91} - 32 q^{92} - 96 q^{93} + 64 q^{95} + 132 q^{97} - 124 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 16 * q^7 - 8 * q^8 + 4 * q^10 - 16 * q^11 + 12 * q^13 - 24 * q^15 - 16 * q^16 + 44 * q^17 + 12 * q^18 + 8 * q^20 + 48 * q^21 - 16 * q^22 - 16 * q^23 + 92 * q^25 + 24 * q^26 + 32 * q^28 - 48 * q^30 - 80 * q^31 - 16 * q^32 - 48 * q^33 - 112 * q^35 + 24 * q^36 - 108 * q^37 - 64 * q^38 + 8 * q^40 + 32 * q^41 + 48 * q^42 + 48 * q^43 - 12 * q^45 - 32 * q^46 + 96 * q^47 + 92 * q^50 + 48 * q^51 + 24 * q^52 + 100 * q^53 + 192 * q^55 + 64 * q^56 + 48 * q^57 + 64 * q^58 - 48 * q^60 - 96 * q^61 - 80 * q^62 - 48 * q^63 - 204 * q^65 - 96 * q^66 - 16 * q^67 - 88 * q^68 - 32 * q^70 + 64 * q^71 + 24 * q^72 - 188 * q^73 + 48 * q^75 - 128 * q^76 - 128 * q^77 + 96 * q^78 - 36 * q^81 + 32 * q^82 + 192 * q^83 - 52 * q^85 + 96 * q^86 - 48 * q^87 + 32 * q^88 - 12 * q^90 + 288 * q^91 - 32 * q^92 - 96 * q^93 + 64 * q^95 + 132 * q^97 - 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	−4.89898	+	1.00000i	−0.979796	+	0.200000i
$5$	−4.89898	+	1.00000i	−0.979796	+	0.200000i
$6$	2.44949			0.408248
$7$	0.898979	−	0.898979i	0.128426	−	0.128426i	−0.639972	−	0.768398i	$-0.721054\pi$
$7$	0.898979	−	0.898979i	0.128426	−	0.128426i	0.768398	+	0.639972i	$0.221054\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$			3.00000i			0.333333i
$10$	−3.89898	+	5.89898i	−0.389898	+	0.589898i
$11$	−13.7980			−1.25436			−0.627180	−	0.778874i	$-0.715791\pi$
$11$	−13.7980			−1.25436			−0.627180	+	0.778874i	$0.715791\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	12.7980	+	12.7980i	0.984458	+	0.984458i	0.999881	−	0.0154227i	$-0.00490939\pi$
$13$	12.7980	+	12.7980i	0.984458	+	0.984458i	−0.0154227	+	0.999881i	$0.504909\pi$
$14$		−	1.79796i		−	0.128426i
$15$	−7.22474	−	4.77526i	−0.481650	−	0.318350i
$16$	−4.00000			−0.250000
$17$	15.8990	−	15.8990i	0.935234	−	0.935234i	−0.0627925	−	0.998027i	$-0.520001\pi$
$17$	15.8990	−	15.8990i	0.935234	−	0.935234i	0.998027	+	0.0627925i	$0.0200006\pi$
$18$	3.00000	+	3.00000i	0.166667	+	0.166667i
$19$		−	25.7980i		−	1.35779i	−0.734237	−	0.678894i	$-0.762460\pi$
$19$		−	25.7980i		−	1.35779i	0.734237	−	0.678894i	$-0.237540\pi$
$20$	2.00000	+	9.79796i	0.100000	+	0.489898i
$21$	2.20204			0.104859
$22$	−13.7980	+	13.7980i	−0.627180	+	0.627180i
$23$	10.6969	+	10.6969i	0.465084	+	0.465084i	0.900318	−	0.435233i	$-0.143334\pi$
$23$	10.6969	+	10.6969i	0.465084	+	0.465084i	−0.435233	+	0.900318i	$0.643334\pi$
$24$		−	4.89898i		−	0.204124i
$25$	23.0000	−	9.79796i	0.920000	−	0.391918i
$26$	25.5959			0.984458
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−1.79796	−	1.79796i	−0.0642128	−	0.0642128i
$29$			25.7980i			0.889585i	0.895634	+	0.444792i	$0.146723\pi$
$29$			25.7980i			0.889585i	−0.895634	+	0.444792i	$0.853277\pi$
$30$	−12.0000	+	2.44949i	−0.400000	+	0.0816497i
$31$	−39.5959			−1.27729			−0.638644	−	0.769502i	$-0.720504\pi$
$31$	−39.5959			−1.27729			−0.638644	+	0.769502i	$0.720504\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	−16.8990	−	16.8990i	−0.512090	−	0.512090i
$34$		−	31.7980i		−	0.935234i
$35$	−3.50510	+	5.30306i	−0.100146	+	0.151516i
$36$	6.00000			0.166667
$37$	−27.0000	+	27.0000i	−0.729730	+	0.729730i	−0.970566	−	0.240836i	$-0.922578\pi$
$37$	−27.0000	+	27.0000i	−0.729730	+	0.729730i	0.240836	+	0.970566i	$0.422578\pi$
$38$	−25.7980	−	25.7980i	−0.678894	−	0.678894i
$39$			31.3485i			0.803807i
$40$	11.7980	+	7.79796i	0.294949	+	0.194949i
$41$	17.7980			0.434097			0.217048	−	0.976161i	$-0.430357\pi$
$41$	17.7980			0.434097			0.217048	+	0.976161i	$0.430357\pi$
$42$	2.20204	−	2.20204i	0.0524295	−	0.0524295i
$43$	−12.4949	−	12.4949i	−0.290579	−	0.290579i	0.546730	−	0.837309i	$-0.315872\pi$
$43$	−12.4949	−	12.4949i	−0.290579	−	0.290579i	−0.837309	+	0.546730i	$0.815872\pi$
$44$			27.5959i			0.627180i
$45$	−3.00000	−	14.6969i	−0.0666667	−	0.326599i
$46$	21.3939			0.465084
$47$	9.30306	−	9.30306i	0.197937	−	0.197937i	−0.601178	−	0.799115i	$-0.705302\pi$
$47$	9.30306	−	9.30306i	0.197937	−	0.197937i	0.799115	+	0.601178i	$0.205302\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$			47.3837i			0.967014i
$50$	13.2020	−	32.7980i	0.264041	−	0.655959i
$51$	38.9444			0.763615
$52$	25.5959	−	25.5959i	0.492229	−	0.492229i
$53$	−19.0908	−	19.0908i	−0.360204	−	0.360204i	0.503684	−	0.863888i	$-0.331978\pi$
$53$	−19.0908	−	19.0908i	−0.360204	−	0.360204i	−0.863888	+	0.503684i	$0.831978\pi$
$54$			7.34847i			0.136083i
$55$	67.5959	−	13.7980i	1.22902	−	0.250872i
$56$	−3.59592			−0.0642128
$57$	31.5959	−	31.5959i	0.554314	−	0.554314i
$58$	25.7980	+	25.7980i	0.444792	+	0.444792i
$59$		−	20.0000i		−	0.338983i	−0.985532	−	0.169492i	$-0.945787\pi$
$59$		−	20.0000i		−	0.338983i	0.985532	−	0.169492i	$-0.0542125\pi$
$60$	−9.55051	+	14.4495i	−0.159175	+	0.240825i
$61$	15.1918			0.249046			0.124523	−	0.992217i	$-0.460260\pi$
$61$	15.1918			0.249046			0.124523	+	0.992217i	$0.460260\pi$
$62$	−39.5959	+	39.5959i	−0.638644	+	0.638644i
$63$	2.69694	+	2.69694i	0.0428085	+	0.0428085i
$64$			8.00000i			0.125000i
$65$	−75.4949	−	49.8990i	−1.16146	−	0.767677i
$66$	−33.7980			−0.512090
$67$	−48.0908	+	48.0908i	−0.717773	+	0.717773i	−0.968149	−	0.250375i	$-0.919446\pi$
$67$	−48.0908	+	48.0908i	−0.717773	+	0.717773i	0.250375	+	0.968149i	$0.419446\pi$
$68$	−31.7980	−	31.7980i	−0.467617	−	0.467617i
$69$			26.2020i			0.379740i
$70$	1.79796	+	8.80816i	0.0256851	+	0.125831i
$71$	6.20204			0.0873527			0.0436763	−	0.999046i	$-0.486093\pi$
$71$	6.20204			0.0873527			0.0436763	+	0.999046i	$0.486093\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	−37.2020	−	37.2020i	−0.509617	−	0.509617i	0.404792	−	0.914409i	$-0.367344\pi$
$73$	−37.2020	−	37.2020i	−0.509617	−	0.509617i	−0.914409	+	0.404792i	$0.867344\pi$
$74$			54.0000i			0.729730i
$75$	40.1691	+	16.1691i	0.535588	+	0.215588i
$76$	−51.5959			−0.678894
$77$	−12.4041	+	12.4041i	−0.161092	+	0.161092i
$78$	31.3485	+	31.3485i	0.401903	+	0.401903i
$79$		−	115.373i		−	1.46042i	−0.683221	−	0.730212i	$-0.739421\pi$
$79$		−	115.373i		−	1.46042i	0.683221	−	0.730212i	$-0.260579\pi$
$80$	19.5959	−	4.00000i	0.244949	−	0.0500000i
$81$	−9.00000			−0.111111
$82$	17.7980	−	17.7980i	0.217048	−	0.217048i
$83$	82.2929	+	82.2929i	0.991480	+	0.991480i	0.999964	−	0.00848381i	$-0.00270051\pi$
$83$	82.2929	+	82.2929i	0.991480	+	0.991480i	−0.00848381	+	0.999964i	$0.502701\pi$
$84$		−	4.40408i		−	0.0524295i
$85$	−61.9898	+	93.7878i	−0.729292	+	1.10339i
$86$	−24.9898			−0.290579
$87$	−31.5959	+	31.5959i	−0.363171	+	0.363171i
$88$	27.5959	+	27.5959i	0.313590	+	0.313590i
$89$		−	117.394i		−	1.31903i	−0.751690	−	0.659516i	$-0.770761\pi$
$89$		−	117.394i		−	1.31903i	0.751690	−	0.659516i	$-0.229239\pi$
$90$	−17.6969	−	11.6969i	−0.196633	−	0.129966i
$91$	23.0102			0.252859
$92$	21.3939	−	21.3939i	0.232542	−	0.232542i
$93$	−48.4949	−	48.4949i	−0.521451	−	0.521451i
$94$		−	18.6061i		−	0.197937i
$95$	25.7980	+	126.384i	0.271557	+	1.33035i
$96$	−9.79796			−0.102062
$97$	81.9898	−	81.9898i	0.845256	−	0.845256i	−0.144281	−	0.989537i	$-0.546087\pi$
$97$	81.9898	−	81.9898i	0.845256	−	0.845256i	0.989537	+	0.144281i	$0.0460870\pi$
$98$	47.3837	+	47.3837i	0.483507	+	0.483507i
$99$		−	41.3939i		−	0.418120i
$100$	−19.5959	−	46.0000i	−0.195959	−	0.460000i
$101$	28.3837			0.281026			0.140513	−	0.990079i	$-0.455125\pi$
$101$	28.3837			0.281026			0.140513	+	0.990079i	$0.455125\pi$
$102$	38.9444	−	38.9444i	0.381808	−	0.381808i
$103$	16.4949	+	16.4949i	0.160145	+	0.160145i	0.782631	−	0.622486i	$-0.213877\pi$
$103$	16.4949	+	16.4949i	0.160145	+	0.160145i	−0.622486	+	0.782631i	$0.713877\pi$
$104$		−	51.1918i		−	0.492229i
$105$	−10.7878	+	2.20204i	−0.102741	+	0.0209718i
$106$	−38.1816			−0.360204
$107$	15.1010	−	15.1010i	0.141131	−	0.141131i	−0.633011	−	0.774142i	$-0.718181\pi$
$107$	15.1010	−	15.1010i	0.141131	−	0.141131i	0.774142	+	0.633011i	$0.218181\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			130.000i			1.19266i	0.802739	+	0.596330i	$0.203375\pi$
$109$			130.000i			1.19266i	−0.802739	+	0.596330i	$0.796625\pi$
$110$	53.7980	−	81.3939i	0.489072	−	0.739944i
$111$	−66.1362			−0.595822
$112$	−3.59592	+	3.59592i	−0.0321064	+	0.0321064i
$113$	77.2929	+	77.2929i	0.684008	+	0.684008i	0.960901	−	0.276893i	$-0.0893048\pi$
$113$	77.2929	+	77.2929i	0.684008	+	0.684008i	−0.276893	+	0.960901i	$0.589305\pi$
$114$		−	63.1918i		−	0.554314i
$115$	−63.1010	−	41.7071i	−0.548705	−	0.362671i
$116$	51.5959			0.444792
$117$	−38.3939	+	38.3939i	−0.328153	+	0.328153i
$118$	−20.0000	−	20.0000i	−0.169492	−	0.169492i
$119$		−	28.5857i		−	0.240216i
$120$	4.89898	+	24.0000i	0.0408248	+	0.200000i
$121$	69.3837			0.573419
$122$	15.1918	−	15.1918i	0.124523	−	0.124523i
$123$	21.7980	+	21.7980i	0.177219	+	0.177219i
$124$			79.1918i			0.638644i
$125$	−102.879	+	71.0000i	−0.823029	+	0.568000i
$126$	5.39388			0.0428085
$127$	18.2929	−	18.2929i	0.144038	−	0.144038i	−0.631411	−	0.775449i	$-0.717524\pi$
$127$	18.2929	−	18.2929i	0.144038	−	0.144038i	0.775449	+	0.631411i	$0.217524\pi$
$128$	8.00000	+	8.00000i	0.0625000	+	0.0625000i
$129$		−	30.6061i		−	0.237257i
$130$	−125.394	+	25.5959i	−0.964568	+	0.196892i
$131$	−133.798			−1.02136			−0.510679	−	0.859771i	$-0.670606\pi$
$131$	−133.798			−1.02136			−0.510679	+	0.859771i	$0.670606\pi$
$132$	−33.7980	+	33.7980i	−0.256045	+	0.256045i
$133$	−23.1918	−	23.1918i	−0.174375	−	0.174375i
$134$			96.1816i			0.717773i
$135$	14.3258	−	21.6742i	0.106117	−	0.160550i
$136$	−63.5959			−0.467617
$137$	25.8990	−	25.8990i	0.189044	−	0.189044i	−0.606239	−	0.795283i	$-0.707322\pi$
$137$	25.8990	−	25.8990i	0.189044	−	0.189044i	0.795283	+	0.606239i	$0.207322\pi$
$138$	26.2020	+	26.2020i	0.189870	+	0.189870i
$139$			54.2020i			0.389943i	0.980809	+	0.194971i	$0.0624614\pi$
$139$			54.2020i			0.389943i	−0.980809	+	0.194971i	$0.937539\pi$
$140$	10.6061	+	7.01021i	0.0757580	+	0.0500729i
$141$	22.7878			0.161615
$142$	6.20204	−	6.20204i	0.0436763	−	0.0436763i
$143$	−176.586	−	176.586i	−1.23487	−	1.23487i
$144$		−	12.0000i		−	0.0833333i
$145$	−25.7980	−	126.384i	−0.177917	−	0.871612i
$146$	−74.4041			−0.509617
$147$	−58.0329	+	58.0329i	−0.394782	+	0.394782i
$148$	54.0000	+	54.0000i	0.364865	+	0.364865i
$149$			42.7673i			0.287029i	0.989648	+	0.143515i	$0.0458404\pi$
$149$			42.7673i			0.287029i	−0.989648	+	0.143515i	$0.954160\pi$
$150$	56.3383	−	24.0000i	0.375588	−	0.160000i
$151$	178.384			1.18135			0.590674	−	0.806910i	$-0.298862\pi$
$151$	178.384			1.18135			0.590674	+	0.806910i	$0.298862\pi$
$152$	−51.5959	+	51.5959i	−0.339447	+	0.339447i
$153$	47.6969	+	47.6969i	0.311745	+	0.311745i
$154$			24.8082i			0.161092i
$155$	193.980	−	39.5959i	1.25148	−	0.255458i
$156$	62.6969			0.401903
$157$	123.000	−	123.000i	0.783439	−	0.783439i	−0.196970	−	0.980410i	$-0.563110\pi$
$157$	123.000	−	123.000i	0.783439	−	0.783439i	0.980410	+	0.196970i	$0.0631102\pi$
$158$	−115.373	−	115.373i	−0.730212	−	0.730212i
$159$		−	46.7628i		−	0.294105i
$160$	15.5959	−	23.5959i	0.0974745	−	0.147474i
$161$	19.2327			0.119457
$162$	−9.00000	+	9.00000i	−0.0555556	+	0.0555556i
$163$	−63.5051	−	63.5051i	−0.389602	−	0.389602i	0.484944	−	0.874545i	$-0.338840\pi$
$163$	−63.5051	−	63.5051i	−0.389602	−	0.389602i	−0.874545	+	0.484944i	$0.838840\pi$
$164$		−	35.5959i		−	0.217048i
$165$	99.6867	+	65.8888i	0.604162	+	0.399326i
$166$	164.586			0.991480
$167$	−48.6765	+	48.6765i	−0.291476	+	0.291476i	−0.837663	−	0.546187i	$-0.816079\pi$
$167$	−48.6765	+	48.6765i	−0.291476	+	0.291476i	0.546187	+	0.837663i	$0.316079\pi$
$168$	−4.40408	−	4.40408i	−0.0262148	−	0.0262148i
$169$			158.576i			0.938317i
$170$	31.7980	+	155.778i	0.187047	+	0.916339i
$171$	77.3939			0.452596
$172$	−24.9898	+	24.9898i	−0.145290	+	0.145290i
$173$	35.1112	+	35.1112i	0.202955	+	0.202955i	0.801265	−	0.598310i	$-0.204161\pi$
$173$	35.1112	+	35.1112i	0.202955	+	0.202955i	−0.598310	+	0.801265i	$0.704161\pi$
$174$			63.1918i			0.363171i
$175$	11.8684	−	29.4847i	0.0678192	−	0.168484i
$176$	55.1918			0.313590
$177$	24.4949	−	24.4949i	0.138389	−	0.138389i
$178$	−117.394	−	117.394i	−0.659516	−	0.659516i
$179$		−	141.171i		−	0.788667i	−0.918967	−	0.394334i	$-0.870975\pi$
$179$		−	141.171i		−	0.788667i	0.918967	−	0.394334i	$-0.129025\pi$
$180$	−29.3939	+	6.00000i	−0.163299	+	0.0333333i
$181$	58.8082			0.324907			0.162453	−	0.986716i	$-0.448059\pi$
$181$	58.8082			0.324907			0.162453	+	0.986716i	$0.448059\pi$
$182$	23.0102	−	23.0102i	0.126430	−	0.126430i
$183$	18.6061	+	18.6061i	0.101673	+	0.101673i
$184$		−	42.7878i		−	0.232542i
$185$	105.272	−	159.272i	0.569040	−	0.860932i
$186$	−96.9898			−0.521451
$187$	−219.373	+	219.373i	−1.17312	+	1.17312i
$188$	−18.6061	−	18.6061i	−0.0989687	−	0.0989687i
$189$			6.60612i			0.0349530i
$190$	152.182	+	100.586i	0.800956	+	0.529398i
$191$	−325.394			−1.70363			−0.851816	−	0.523840i	$-0.824499\pi$
$191$	−325.394			−1.70363			−0.851816	+	0.523840i	$0.824499\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	−39.3837	−	39.3837i	−0.204060	−	0.204060i	0.597677	−	0.801737i	$-0.296091\pi$
$193$	−39.3837	−	39.3837i	−0.204060	−	0.204060i	−0.801737	+	0.597677i	$0.796091\pi$
$194$		−	163.980i		−	0.845256i
$195$	−31.3485	−	153.576i	−0.160761	−	0.787567i
$196$	94.7673			0.483507
$197$	−119.313	+	119.313i	−0.605651	+	0.605651i	−0.941807	−	0.336155i	$-0.890873\pi$
$197$	−119.313	+	119.313i	−0.605651	+	0.605651i	0.336155	+	0.941807i	$0.390873\pi$
$198$	−41.3939	−	41.3939i	−0.209060	−	0.209060i
$199$			178.565i			0.897313i	0.893704	+	0.448657i	$0.148097\pi$
$199$			178.565i			0.897313i	−0.893704	+	0.448657i	$0.851903\pi$
$200$	−65.5959	−	26.4041i	−0.327980	−	0.132020i
$201$	−117.798			−0.586059
$202$	28.3837	−	28.3837i	0.140513	−	0.140513i
$203$	23.1918	+	23.1918i	0.114245	+	0.114245i
$204$		−	77.8888i		−	0.381808i
$205$	−87.1918	+	17.7980i	−0.425326	+	0.0868193i
$206$	32.9898			0.160145
$207$	−32.0908	+	32.0908i	−0.155028	+	0.155028i
$208$	−51.1918	−	51.1918i	−0.246115	−	0.246115i
$209$			355.959i			1.70315i
$210$	−8.58571	+	12.9898i	−0.0408843	+	0.0618562i
$211$	−318.747			−1.51065			−0.755324	−	0.655351i	$-0.772521\pi$
$211$	−318.747			−1.51065			−0.755324	+	0.655351i	$0.772521\pi$
$212$	−38.1816	+	38.1816i	−0.180102	+	0.180102i
$213$	7.59592	+	7.59592i	0.0356616	+	0.0356616i
$214$		−	30.2020i		−	0.141131i
$215$	73.7071	+	48.7173i	0.342824	+	0.226592i
$216$	14.6969			0.0680414
$217$	−35.5959	+	35.5959i	−0.164036	+	0.164036i
$218$	130.000	+	130.000i	0.596330	+	0.596330i
$219$		−	91.1260i		−	0.416101i
$220$	−27.5959	−	135.192i	−0.125436	−	0.614508i
$221$	406.949			1.84140
$222$	−66.1362	+	66.1362i	−0.297911	+	0.297911i
$223$	208.677	+	208.677i	0.935769	+	0.935769i	0.998058	−	0.0622890i	$-0.0198400\pi$
$223$	208.677	+	208.677i	0.935769	+	0.935769i	−0.0622890	+	0.998058i	$0.519840\pi$
$224$			7.19184i			0.0321064i
$225$	29.3939	+	69.0000i	0.130639	+	0.306667i
$226$	154.586			0.684008
$227$	242.070	−	242.070i	1.06639	−	1.06639i	0.0687559	−	0.997634i	$-0.478097\pi$
$227$	242.070	−	242.070i	1.06639	−	1.06639i	0.997634	−	0.0687559i	$-0.0219030\pi$
$228$	−63.1918	−	63.1918i	−0.277157	−	0.277157i
$229$		−	413.939i		−	1.80759i	−0.427963	−	0.903796i	$-0.640769\pi$
$229$		−	413.939i		−	1.80759i	0.427963	−	0.903796i	$-0.359231\pi$
$230$	−104.808	+	21.3939i	−0.455688	+	0.0930169i
$231$	−30.3837			−0.131531
$232$	51.5959	−	51.5959i	0.222396	−	0.222396i
$233$	64.2622	+	64.2622i	0.275804	+	0.275804i	0.831431	−	0.555628i	$-0.187522\pi$
$233$	64.2622	+	64.2622i	0.275804	+	0.275804i	−0.555628	+	0.831431i	$0.687522\pi$
$234$			76.7878i			0.328153i
$235$	−36.2724	+	54.8786i	−0.154351	+	0.233526i
$236$	−40.0000			−0.169492
$237$	141.303	−	141.303i	0.596215	−	0.596215i
$238$	−28.5857	−	28.5857i	−0.120108	−	0.120108i
$239$			154.788i			0.647648i	0.946117	+	0.323824i	$0.104968\pi$
$239$			154.788i			0.647648i	−0.946117	+	0.323824i	$0.895032\pi$
$240$	28.8990	+	19.1010i	0.120412	+	0.0795876i
$241$	−421.939			−1.75078			−0.875392	−	0.483414i	$-0.839396\pi$
$241$	−421.939			−1.75078			−0.875392	+	0.483414i	$0.839396\pi$
$242$	69.3837	−	69.3837i	0.286709	−	0.286709i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		−	30.3837i		−	0.124523i
$245$	−47.3837	−	232.132i	−0.193403	−	0.947476i
$246$	43.5959			0.177219
$247$	330.161	−	330.161i	1.33669	−	1.33669i
$248$	79.1918	+	79.1918i	0.319322	+	0.319322i
$249$			201.576i			0.809540i
$250$	−31.8786	+	173.879i	−0.127514	+	0.695514i
$251$	392.586			1.56409			0.782043	−	0.623224i	$-0.214178\pi$
$251$	392.586			1.56409			0.782043	+	0.623224i	$0.214178\pi$
$252$	5.39388	−	5.39388i	0.0214043	−	0.0214043i
$253$	−147.596	−	147.596i	−0.583383	−	0.583383i
$254$		−	36.5857i		−	0.144038i
$255$	−190.788	+	38.9444i	−0.748187	+	0.152723i
$256$	16.0000			0.0625000
$257$	−123.515	+	123.515i	−0.480604	+	0.480604i	−0.905325	−	0.424720i	$-0.860372\pi$
$257$	−123.515	+	123.515i	−0.480604	+	0.480604i	0.424720	+	0.905325i	$0.360372\pi$
$258$	−30.6061	−	30.6061i	−0.118628	−	0.118628i
$259$			48.5449i			0.187432i
$260$	−99.7980	+	150.990i	−0.383838	+	0.580730i
$261$	−77.3939			−0.296528
$262$	−133.798	+	133.798i	−0.510679	+	0.510679i
$263$	30.6969	+	30.6969i	0.116718	+	0.116718i	0.763054	−	0.646335i	$-0.223699\pi$
$263$	30.6969	+	30.6969i	0.116718	+	0.116718i	−0.646335	+	0.763054i	$0.723699\pi$
$264$			67.5959i			0.256045i
$265$	112.616	+	74.4347i	0.424967	+	0.280886i
$266$	−46.3837			−0.174375
$267$	143.778	−	143.778i	0.538493	−	0.538493i
$268$	96.1816	+	96.1816i	0.358887	+	0.358887i
$269$		−	429.151i		−	1.59536i	−0.603083	−	0.797678i	$-0.706061\pi$
$269$		−	429.151i		−	1.59536i	0.603083	−	0.797678i	$-0.293939\pi$
$270$	−7.34847	−	36.0000i	−0.0272166	−	0.133333i
$271$	220.727			0.814489			0.407245	−	0.913319i	$-0.366490\pi$
$271$	220.727			0.814489			0.407245	+	0.913319i	$0.366490\pi$
$272$	−63.5959	+	63.5959i	−0.233809	+	0.233809i
$273$	28.1816	+	28.1816i	0.103229	+	0.103229i
$274$		−	51.7980i		−	0.189044i
$275$	−317.353	+	135.192i	−1.15401	+	0.491607i
$276$	52.4041			0.189870
$277$	−45.9898	+	45.9898i	−0.166028	+	0.166028i	−0.785231	−	0.619203i	$-0.787456\pi$
$277$	−45.9898	+	45.9898i	−0.166028	+	0.166028i	0.619203	+	0.785231i	$0.287456\pi$
$278$	54.2020	+	54.2020i	0.194971	+	0.194971i
$279$		−	118.788i		−	0.425763i
$280$	17.6163	−	3.59592i	0.0629155	−	0.0128426i
$281$	−482.524			−1.71717			−0.858584	−	0.512672i	$-0.828656\pi$
$281$	−482.524			−1.71717			−0.858584	+	0.512672i	$0.828656\pi$
$282$	22.7878	−	22.7878i	0.0808076	−	0.0808076i
$283$	271.283	+	271.283i	0.958596	+	0.958596i	0.999176	−	0.0405803i	$-0.0129207\pi$
$283$	271.283	+	271.283i	0.958596	+	0.958596i	−0.0405803	+	0.999176i	$0.512921\pi$
$284$		−	12.4041i		−	0.0436763i
$285$	−123.192	+	186.384i	−0.432252	+	0.653978i
$286$	−353.171			−1.23487
$287$	16.0000	−	16.0000i	0.0557491	−	0.0557491i
$288$	−12.0000	−	12.0000i	−0.0416667	−	0.0416667i
$289$		−	216.555i		−	0.749326i
$290$	−152.182	−	100.586i	−0.524764	−	0.346847i
$291$	200.833			0.690148
$292$	−74.4041	+	74.4041i	−0.254809	+	0.254809i
$293$	−149.091	−	149.091i	−0.508842	−	0.508842i	0.405329	−	0.914171i	$-0.367157\pi$
$293$	−149.091	−	149.091i	−0.508842	−	0.508842i	−0.914171	+	0.405329i	$0.867157\pi$
$294$			116.066i			0.394782i
$295$	20.0000	+	97.9796i	0.0677966	+	0.332134i
$296$	108.000			0.364865
$297$	50.6969	−	50.6969i	0.170697	−	0.170697i
$298$	42.7673	+	42.7673i	0.143515	+	0.143515i
$299$			273.798i			0.915712i
$300$	32.3383	−	80.3383i	0.107794	−	0.267794i
$301$	−22.4653			−0.0746356
$302$	178.384	−	178.384i	0.590674	−	0.590674i
$303$	34.7628	+	34.7628i	0.114729	+	0.114729i
$304$			103.192i			0.339447i
$305$	−74.4245	+	15.1918i	−0.244015	+	0.0498093i
$306$	95.3939			0.311745
$307$	−230.697	+	230.697i	−0.751456	+	0.751456i	−0.974751	−	0.223295i	$-0.928319\pi$
$307$	−230.697	+	230.697i	−0.751456	+	0.751456i	0.223295	+	0.974751i	$0.428319\pi$
$308$	24.8082	+	24.8082i	0.0805460	+	0.0805460i
$309$			40.4041i			0.130758i
$310$	154.384	−	233.576i	0.498012	−	0.753469i
$311$	−47.7367			−0.153494			−0.0767472	−	0.997051i	$-0.524453\pi$
$311$	−47.7367			−0.153494			−0.0767472	+	0.997051i	$0.524453\pi$
$312$	62.6969	−	62.6969i	0.200952	−	0.200952i
$313$	219.767	+	219.767i	0.702132	+	0.702132i	0.964868	−	0.262736i	$-0.0846247\pi$
$313$	219.767	+	219.767i	0.702132	+	0.702132i	−0.262736	+	0.964868i	$0.584625\pi$
$314$		−	246.000i		−	0.783439i
$315$	−15.9092	−	10.5153i	−0.0505053	−	0.0333819i
$316$	−230.747			−0.730212
$317$	−332.828	+	332.828i	−1.04993	+	1.04993i	−0.0512429	+	0.998686i	$0.516318\pi$
$317$	−332.828	+	332.828i	−1.04993	+	1.04993i	−0.998686	+	0.0512429i	$0.983682\pi$
$318$	−46.7628	−	46.7628i	−0.147053	−	0.147053i
$319$		−	355.959i		−	1.11586i
$320$	−8.00000	−	39.1918i	−0.0250000	−	0.122474i
$321$	36.9898			0.115233
$322$	19.2327	−	19.2327i	0.0597287	−	0.0597287i
$323$	−410.161	−	410.161i	−1.26985	−	1.26985i
$324$			18.0000i			0.0555556i
$325$	419.747	+	168.959i	1.29153	+	0.519874i
$326$	−127.010			−0.389602
$327$	−159.217	+	159.217i	−0.486902	+	0.486902i
$328$	−35.5959	−	35.5959i	−0.108524	−	0.108524i
$329$		−	16.7265i		−	0.0508405i
$330$	165.576	−	33.7980i	0.501744	−	0.102418i
$331$	209.980			0.634379			0.317190	−	0.948362i	$-0.397261\pi$
$331$	209.980			0.634379			0.317190	+	0.948362i	$0.397261\pi$
$332$	164.586	−	164.586i	0.495740	−	0.495740i
$333$	−81.0000	−	81.0000i	−0.243243	−	0.243243i
$334$			97.3531i			0.291476i
$335$	187.505	−	283.687i	0.559717	−	0.846826i
$336$	−8.80816			−0.0262148
$337$	88.3735	−	88.3735i	0.262236	−	0.262236i	−0.563726	−	0.825962i	$-0.690633\pi$
$337$	88.3735	−	88.3735i	0.262236	−	0.262236i	0.825962	+	0.563726i	$0.190633\pi$
$338$	158.576	+	158.576i	0.469158	+	0.469158i
$339$			189.328i			0.558490i
$340$	187.576	+	123.980i	0.551693	+	0.364646i
$341$	546.343			1.60218
$342$	77.3939	−	77.3939i	0.226298	−	0.226298i
$343$	86.6469	+	86.6469i	0.252615	+	0.252615i
$344$			49.9796i			0.145290i
$345$	−26.2020	−	128.363i	−0.0759479	−	0.372067i
$346$	70.2225			0.202955
$347$	212.495	−	212.495i	0.612377	−	0.612377i	−0.331188	−	0.943565i	$-0.607449\pi$
$347$	212.495	−	212.495i	0.612377	−	0.612377i	0.943565	+	0.331188i	$0.107449\pi$
$348$	63.1918	+	63.1918i	0.181586	+	0.181586i
$349$		−	280.000i		−	0.802292i	−0.916014	−	0.401146i	$-0.868612\pi$
$349$		−	280.000i		−	0.802292i	0.916014	−	0.401146i	$-0.131388\pi$
$350$	−17.6163	−	41.3531i	−0.0503324	−	0.118152i
$351$	−94.0454			−0.267936
$352$	55.1918	−	55.1918i	0.156795	−	0.156795i
$353$	212.505	+	212.505i	0.601997	+	0.601997i	0.940842	−	0.338845i	$-0.110036\pi$
$353$	212.505	+	212.505i	0.601997	+	0.601997i	−0.338845	+	0.940842i	$0.610036\pi$
$354$		−	48.9898i		−	0.138389i
$355$	−30.3837	+	6.20204i	−0.0855878	+	0.0174705i
$356$	−234.788			−0.659516
$357$	35.0102	−	35.0102i	0.0980678	−	0.0980678i
$358$	−141.171	−	141.171i	−0.394334	−	0.394334i
$359$			633.090i			1.76348i	0.471734	+	0.881741i	$0.343628\pi$
$359$			633.090i			1.76348i	−0.471734	+	0.881741i	$0.656372\pi$
$360$	−23.3939	+	35.3939i	−0.0649830	+	0.0983163i
$361$	−304.535			−0.843586
$362$	58.8082	−	58.8082i	0.162453	−	0.162453i
$363$	84.9773	+	84.9773i	0.234097	+	0.234097i
$364$		−	46.0204i		−	0.126430i
$365$	219.454	+	145.050i	0.601244	+	0.397397i
$366$	37.2122			0.101673
$367$	−267.505	+	267.505i	−0.728897	+	0.728897i	−0.970400	−	0.241503i	$-0.922360\pi$
$367$	−267.505	+	267.505i	−0.728897	+	0.728897i	0.241503	+	0.970400i	$0.422360\pi$
$368$	−42.7878	−	42.7878i	−0.116271	−	0.116271i
$369$			53.3939i			0.144699i
$370$	−54.0000	−	264.545i	−0.145946	−	0.714986i
$371$	−34.3245			−0.0925189
$372$	−96.9898	+	96.9898i	−0.260725	+	0.260725i
$373$	−376.939	−	376.939i	−1.01056	−	1.01056i	−0.999944	−	0.0106161i	$-0.996621\pi$
$373$	−376.939	−	376.939i	−1.01056	−	1.01056i	−0.0106161	−	0.999944i	$-0.503379\pi$
$374$			438.747i			1.17312i
$375$	−212.957	−	39.0431i	−0.567885	−	0.104115i
$376$	−37.2122			−0.0989687
$377$	−330.161	+	330.161i	−0.875759	+	0.875759i
$378$	6.60612	+	6.60612i	0.0174765	+	0.0174765i
$379$		−	167.818i		−	0.442793i	−0.975184	−	0.221396i	$-0.928939\pi$
$379$		−	167.818i		−	0.442793i	0.975184	−	0.221396i	$-0.0710614\pi$
$380$	252.767	−	51.5959i	0.665177	−	0.135779i
$381$	44.8082			0.117607
$382$	−325.394	+	325.394i	−0.851816	+	0.851816i
$383$	−478.293	−	478.293i	−1.24881	−	1.24881i	−0.956248	−	0.292559i	$-0.905493\pi$
$383$	−478.293	−	478.293i	−1.24881	−	1.24881i	−0.292559	−	0.956248i	$-0.594507\pi$
$384$			19.5959i			0.0510310i
$385$	48.3633	−	73.1714i	0.125619	−	0.190056i
$386$	−78.7673			−0.204060
$387$	37.4847	−	37.4847i	0.0968597	−	0.0968597i
$388$	−163.980	−	163.980i	−0.422628	−	0.422628i
$389$		−	169.151i		−	0.434836i	−0.976079	−	0.217418i	$-0.930237\pi$
$389$		−	169.151i		−	0.434836i	0.976079	−	0.217418i	$-0.0697634\pi$
$390$	−184.924	−	122.227i	−0.474164	−	0.313403i
$391$	340.141			0.869925
$392$	94.7673	−	94.7673i	0.241753	−	0.241753i
$393$	−163.868	−	163.868i	−0.416968	−	0.416968i
$394$			238.627i			0.605651i
$395$	115.373	+	565.212i	0.292085	+	1.43092i
$396$	−82.7878			−0.209060
$397$	−69.3429	+	69.3429i	−0.174667	+	0.174667i	−0.789026	−	0.614359i	$-0.789415\pi$
$397$	−69.3429	+	69.3429i	−0.174667	+	0.174667i	0.614359	+	0.789026i	$0.289415\pi$
$398$	178.565	+	178.565i	0.448657	+	0.448657i
$399$		−	56.8082i		−	0.142376i
$400$	−92.0000	+	39.1918i	−0.230000	+	0.0979796i
$401$	414.767			1.03433			0.517166	−	0.855885i	$-0.326987\pi$
$401$	414.767			1.03433			0.517166	+	0.855885i	$0.326987\pi$
$402$	−117.798	+	117.798i	−0.293030	+	0.293030i
$403$	−506.747	−	506.747i	−1.25744	−	1.25744i
$404$		−	56.7673i		−	0.140513i
$405$	44.0908	−	9.00000i	0.108866	−	0.0222222i
$406$	46.3837			0.114245
$407$	372.545	−	372.545i	0.915344	−	0.915344i
$408$	−77.8888	−	77.8888i	−0.190904	−	0.190904i
$409$			605.110i			1.47949i	0.672889	+	0.739744i	$0.265053\pi$
$409$			605.110i			1.47949i	−0.672889	+	0.739744i	$0.734947\pi$
$410$	−69.3939	+	104.990i	−0.169253	+	0.256073i
$411$	63.4393			0.154353
$412$	32.9898	−	32.9898i	0.0800723	−	0.0800723i
$413$	−17.9796	−	17.9796i	−0.0435341	−	0.0435341i
$414$			64.1816i			0.155028i
$415$	−485.444	−	320.858i	−1.16974	−	0.773152i
$416$	−102.384			−0.246115
$417$	−66.3837	+	66.3837i	−0.159193	+	0.159193i
$418$	355.959	+	355.959i	0.851577	+	0.851577i
$419$			15.9592i			0.0380887i	0.999819	+	0.0190444i	$0.00606238\pi$
$419$			15.9592i			0.0380887i	−0.999819	+	0.0190444i	$0.993938\pi$
$420$	4.40408	+	21.5755i	0.0104859	+	0.0513703i
$421$	433.171			1.02891			0.514455	−	0.857517i	$-0.327994\pi$
$421$	433.171			1.02891			0.514455	+	0.857517i	$0.327994\pi$
$422$	−318.747	+	318.747i	−0.755324	+	0.755324i
$423$	27.9092	+	27.9092i	0.0659792	+	0.0659792i
$424$			76.3633i			0.180102i
$425$	209.899	−	521.454i	0.493880	−	1.22695i
$426$	15.1918			0.0356616
$427$	13.6571	−	13.6571i	0.0319840	−	0.0319840i
$428$	−30.2020	−	30.2020i	−0.0705655	−	0.0705655i
$429$		−	432.545i		−	1.00826i
$430$	122.424	−	24.9898i	0.284708	−	0.0581158i
$431$	24.1816			0.0561059			0.0280529	−	0.999606i	$-0.491069\pi$
$431$	24.1816			0.0561059			0.0280529	+	0.999606i	$0.491069\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	528.918	+	528.918i	1.22152	+	1.22152i	0.967091	+	0.254429i	$0.0818875\pi$
$433$	528.918	+	528.918i	1.22152	+	1.22152i	0.254429	+	0.967091i	$0.418112\pi$
$434$			71.1918i			0.164036i
$435$	123.192	−	186.384i	0.283200	−	0.428468i
$436$	260.000			0.596330
$437$	275.959	−	275.959i	0.631486	−	0.631486i
$438$	−91.1260	−	91.1260i	−0.208050	−	0.208050i
$439$			44.6265i			0.101655i	0.998707	+	0.0508275i	$0.0161859\pi$
$439$			44.6265i			0.101655i	−0.998707	+	0.0508275i	$0.983814\pi$
$440$	−162.788	−	107.596i	−0.369972	−	0.244536i
$441$	−142.151			−0.322338
$442$	406.949	−	406.949i	0.920699	−	0.920699i
$443$	311.283	+	311.283i	0.702670	+	0.702670i	0.964983	−	0.262313i	$-0.0844853\pi$
$443$	311.283	+	311.283i	0.702670	+	0.702670i	−0.262313	+	0.964983i	$0.584485\pi$
$444$			132.272i			0.297911i
$445$	117.394	+	575.110i	0.263806	+	1.29238i
$446$	417.353			0.935769
$447$	−52.3791	+	52.3791i	−0.117179	+	0.117179i
$448$	7.19184	+	7.19184i	0.0160532	+	0.0160532i
$449$		−	141.273i		−	0.314640i	−0.987548	−	0.157320i	$-0.949715\pi$
$449$		−	141.273i		−	0.314640i	0.987548	−	0.157320i	$-0.0502855\pi$
$450$	98.3939	+	39.6061i	0.218653	+	0.0880136i
$451$	−245.576			−0.544513
$452$	154.586	−	154.586i	0.342004	−	0.342004i
$453$	218.474	+	218.474i	0.482284	+	0.482284i
$454$		−	484.141i		−	1.06639i
$455$	−112.727	+	23.0102i	−0.247751	+	0.0505719i
$456$	−126.384			−0.277157
$457$	20.3939	−	20.3939i	0.0446256	−	0.0446256i	−0.684442	−	0.729067i	$-0.739954\pi$
$457$	20.3939	−	20.3939i	0.0446256	−	0.0446256i	0.729067	+	0.684442i	$0.239954\pi$
$458$	−413.939	−	413.939i	−0.903796	−	0.903796i
$459$			116.833i			0.254538i
$460$	−83.4143	+	126.202i	−0.181335	+	0.274352i
$461$	−626.727			−1.35949			−0.679747	−	0.733447i	$-0.737910\pi$
$461$	−626.727			−1.35949			−0.679747	+	0.733447i	$0.737910\pi$
$462$	−30.3837	+	30.3837i	−0.0657655	+	0.0657655i
$463$	−314.515	−	314.515i	−0.679299	−	0.679299i	0.280543	−	0.959842i	$-0.409486\pi$
$463$	−314.515	−	314.515i	−0.679299	−	0.679299i	−0.959842	+	0.280543i	$0.909486\pi$
$464$		−	103.192i		−	0.222396i
$465$	286.070	+	189.081i	0.615205	+	0.406625i
$466$	128.524			0.275804
$467$	46.6969	−	46.6969i	0.0999934	−	0.0999934i	−0.655340	−	0.755334i	$-0.727475\pi$
$467$	46.6969	−	46.6969i	0.0999934	−	0.0999934i	0.755334	+	0.655340i	$0.227475\pi$
$468$	76.7878	+	76.7878i	0.164076	+	0.164076i
$469$			86.4653i			0.184361i
$470$	18.6061	+	91.1510i	0.0395875	+	0.193938i
$471$	301.287			0.639676
$472$	−40.0000	+	40.0000i	−0.0847458	+	0.0847458i
$473$	172.404	+	172.404i	0.364491	+	0.364491i
$474$		−	282.606i		−	0.596215i
$475$	−252.767	−	593.353i	−0.532142	−	1.24916i
$476$	−57.1714			−0.120108
$477$	57.2724	−	57.2724i	0.120068	−	0.120068i
$478$	154.788	+	154.788i	0.323824	+	0.323824i
$479$			71.2735i			0.148796i	0.997229	+	0.0743982i	$0.0237036\pi$
$479$			71.2735i			0.148796i	−0.997229	+	0.0743982i	$0.976296\pi$
$480$	48.0000	−	9.79796i	0.100000	−	0.0204124i
$481$	−691.090			−1.43678
$482$	−421.939	+	421.939i	−0.875392	+	0.875392i
$483$	23.5551	+	23.5551i	0.0487683	+	0.0487683i
$484$		−	138.767i		−	0.286709i
$485$	−319.677	+	483.656i	−0.659127	+	0.997229i
$486$	−22.0454			−0.0453609
$487$	295.423	−	295.423i	0.606619	−	0.606619i	−0.335442	−	0.942061i	$-0.608886\pi$
$487$	295.423	−	295.423i	0.606619	−	0.606619i	0.942061	+	0.335442i	$0.108886\pi$
$488$	−30.3837	−	30.3837i	−0.0622616	−	0.0622616i
$489$		−	155.555i		−	0.318109i
$490$	−279.515	−	184.748i	−0.570439	−	0.377037i
$491$	−910.080			−1.85352			−0.926761	−	0.375651i	$-0.877419\pi$
$491$	−910.080			−1.85352			−0.926761	+	0.375651i	$0.877419\pi$
$492$	43.5959	−	43.5959i	0.0886096	−	0.0886096i
$493$	410.161	+	410.161i	0.831970	+	0.831970i
$494$		−	660.322i		−	1.33669i
$495$	41.3939	+	202.788i	0.0836240	+	0.409672i
$496$	158.384			0.319322
$497$	5.57551	−	5.57551i	0.0112183	−	0.0112183i
$498$	201.576	+	201.576i	0.404770	+	0.404770i
$499$			970.161i			1.94421i	0.234544	+	0.972105i	$0.424640\pi$
$499$			970.161i			1.94421i	−0.234544	+	0.972105i	$0.575360\pi$
$500$	142.000	+	205.757i	0.284000	+	0.411514i
$501$	−119.233			−0.237989
$502$	392.586	−	392.586i	0.782043	−	0.782043i
$503$	276.817	+	276.817i	0.550333	+	0.550333i	0.926537	−	0.376204i	$-0.122771\pi$
$503$	276.817	+	276.817i	0.550333	+	0.550333i	−0.376204	+	0.926537i	$0.622771\pi$
$504$		−	10.7878i		−	0.0214043i
$505$	−139.051	+	28.3837i	−0.275349	+	0.0562053i
$506$	−295.192			−0.583383
$507$	−194.215	+	194.215i	−0.383066	+	0.383066i
$508$	−36.5857	−	36.5857i	−0.0720191	−	0.0720191i
$509$		−	900.059i		−	1.76829i	−0.467213	−	0.884145i	$-0.654742\pi$
$509$		−	900.059i		−	1.76829i	0.467213	−	0.884145i	$-0.345258\pi$
$510$	−151.843	+	229.732i	−0.297732	+	0.450455i
$511$	−66.8877			−0.130896
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	94.7878	+	94.7878i	0.184771	+	0.184771i
$514$			247.031i			0.480604i
$515$	−97.3031	−	64.3133i	−0.188938	−	0.124880i
$516$	−61.2122			−0.118628
$517$	−128.363	+	128.363i	−0.248285	+	0.248285i
$518$	48.5449	+	48.5449i	0.0937160	+	0.0937160i
$519$			86.0046i			0.165712i
$520$	51.1918	+	250.788i	0.0984458	+	0.482284i
$521$	−239.494			−0.459681			−0.229841	−	0.973228i	$-0.573820\pi$
$521$	−239.494			−0.459681			−0.229841	+	0.973228i	$0.573820\pi$
$522$	−77.3939	+	77.3939i	−0.148264	+	0.148264i
$523$	12.7173	+	12.7173i	0.0243162	+	0.0243162i	0.719160	−	0.694844i	$-0.244527\pi$
$523$	12.7173	+	12.7173i	0.0243162	+	0.0243162i	−0.694844	+	0.719160i	$0.744527\pi$
$524$			267.596i			0.510679i
$525$	50.6469	−	21.5755i	0.0964704	−	0.0410962i
$526$	61.3939			0.116718
$527$	−629.535	+	629.535i	−1.19456	+	1.19456i
$528$	67.5959	+	67.5959i	0.128023	+	0.128023i
$529$		−	300.151i		−	0.567393i
$530$	187.051	−	38.1816i	0.352926	−	0.0720408i
$531$	60.0000			0.112994
$532$	−46.3837	+	46.3837i	−0.0871874	+	0.0871874i
$533$	227.778	+	227.778i	0.427350	+	0.427350i
$534$		−	287.555i		−	0.538493i
$535$	−58.8786	+	89.0806i	−0.110053	+	0.166506i
$536$	192.363			0.358887
$537$	172.899	−	172.899i	0.321972	−	0.321972i
$538$	−429.151	−	429.151i	−0.797678	−	0.797678i
$539$		−	653.798i		−	1.21298i
$540$	−43.3485	−	28.6515i	−0.0802749	−	0.0530584i
$541$	477.110			0.881904			0.440952	−	0.897531i	$-0.354641\pi$
$541$	477.110			0.881904			0.440952	+	0.897531i	$0.354641\pi$
$542$	220.727	−	220.727i	0.407245	−	0.407245i
$543$	72.0250	+	72.0250i	0.132643	+	0.132643i
$544$			127.192i			0.233809i
$545$	−130.000	−	636.867i	−0.238532	−	1.16856i
$546$	56.3633			0.103229
$547$	720.372	−	720.372i	1.31695	−	1.31695i	0.400775	−	0.916177i	$-0.368741\pi$
$547$	720.372	−	720.372i	1.31695	−	1.31695i	0.916177	−	0.400775i	$-0.131259\pi$
$548$	−51.7980	−	51.7980i	−0.0945218	−	0.0945218i
$549$			45.5755i			0.0830155i
$550$	−182.161	+	452.545i	−0.331202	+	0.822809i
$551$	665.535			1.20787
$552$	52.4041	−	52.4041i	0.0949349	−	0.0949349i
$553$	−103.718	−	103.718i	−0.187556	−	0.187556i
$554$			91.9796i			0.166028i
$555$	324.000	−	66.1362i	0.583784	−	0.119164i
$556$	108.404			0.194971
$557$	−139.899	+	139.899i	−0.251165	+	0.251165i	−0.821448	−	0.570283i	$-0.806834\pi$
$557$	−139.899	+	139.899i	−0.251165	+	0.251165i	0.570283	+	0.821448i	$0.306834\pi$
$558$	−118.788	−	118.788i	−0.212881	−	0.212881i
$559$		−	319.818i		−	0.572126i
$560$	14.0204	−	21.2122i	0.0250364	−	0.0378790i
$561$	−537.353			−0.957849
$562$	−482.524	+	482.524i	−0.858584	+	0.858584i
$563$	461.121	+	461.121i	0.819043	+	0.819043i	0.985969	−	0.166926i	$-0.0533841\pi$
$563$	461.121	+	461.121i	0.819043	+	0.819043i	−0.166926	+	0.985969i	$0.553384\pi$
$564$		−	45.5755i		−	0.0808076i
$565$	−455.949	−	301.363i	−0.806989	−	0.533386i
$566$	542.565			0.958596
$567$	−8.09082	+	8.09082i	−0.0142695	+	0.0142695i
$568$	−12.4041	−	12.4041i	−0.0218382	−	0.0218382i
$569$			31.4939i			0.0553495i	0.999617	+	0.0276748i	$0.00881027\pi$
$569$			31.4939i			0.0553495i	−0.999617	+	0.0276748i	$0.991190\pi$
$570$	63.1918	+	309.576i	0.110863	+	0.543115i
$571$	139.233			0.243840			0.121920	−	0.992540i	$-0.461095\pi$
$571$	139.233			0.243840			0.121920	+	0.992540i	$0.461095\pi$
$572$	−353.171	+	353.171i	−0.617433	+	0.617433i
$573$	−398.524	−	398.524i	−0.695505	−	0.695505i
$574$		−	32.0000i		−	0.0557491i
$575$	350.838	+	141.221i	0.610153	+	0.245602i
$576$	−24.0000			−0.0416667
$577$	463.000	−	463.000i	0.802426	−	0.802426i	−0.181048	−	0.983474i	$-0.557949\pi$
$577$	463.000	−	463.000i	0.802426	−	0.802426i	0.983474	+	0.181048i	$0.0579489\pi$
$578$	−216.555	−	216.555i	−0.374663	−	0.374663i
$579$		−	96.4699i		−	0.166615i
$580$	−252.767	+	51.5959i	−0.435806	+	0.0889585i
$581$	147.959			0.254663
$582$	200.833	−	200.833i	0.345074	−	0.345074i
$583$	263.414	+	263.414i	0.451826	+	0.451826i
$584$			148.808i			0.254809i
$585$	149.697	−	226.485i	0.255892	−	0.387153i
$586$	−298.182			−0.508842
$587$	464.091	−	464.091i	0.790615	−	0.790615i	−0.190979	−	0.981594i	$-0.561166\pi$
$587$	464.091	−	464.091i	0.790615	−	0.790615i	0.981594	+	0.190979i	$0.0611664\pi$
$588$	116.066	+	116.066i	0.197391	+	0.197391i
$589$			1021.49i			1.73429i
$590$	117.980	+	77.9796i	0.199965	+	0.132169i
$591$	−292.257			−0.494512
$592$	108.000	−	108.000i	0.182432	−	0.182432i
$593$	120.646	+	120.646i	0.203450	+	0.203450i	0.801476	−	0.598026i	$-0.204048\pi$
$593$	120.646	+	120.646i	0.203450	+	0.203450i	−0.598026	+	0.801476i	$0.704048\pi$
$594$		−	101.394i		−	0.170697i
$595$	28.5857	+	140.041i	0.0480432	+	0.235363i
$596$	85.5347			0.143515
$597$	−218.697	+	218.697i	−0.366327	+	0.366327i
$598$	273.798	+	273.798i	0.457856	+	0.457856i
$599$			157.131i			0.262322i	0.991361	+	0.131161i	$0.0418704\pi$
$599$			157.131i			0.262322i	−0.991361	+	0.131161i	$0.958130\pi$
$600$	−48.0000	−	112.677i	−0.0800000	−	0.187794i
$601$	550.302			0.915644			0.457822	−	0.889044i	$-0.348630\pi$
$601$	550.302			0.915644			0.457822	+	0.889044i	$0.348630\pi$
$602$	−22.4653	+	22.4653i	−0.0373178	+	0.0373178i
$603$	−144.272	−	144.272i	−0.239258	−	0.239258i
$604$		−	356.767i		−	0.590674i
$605$	−339.909	+	69.3837i	−0.561833	+	0.114684i
$606$	69.5255			0.114729
$607$	−182.030	+	182.030i	−0.299884	+	0.299884i	−0.840968	−	0.541084i	$-0.818014\pi$
$607$	−182.030	+	182.030i	−0.299884	+	0.299884i	0.541084	+	0.840968i	$0.318014\pi$
$608$	103.192	+	103.192i	0.169723	+	0.169723i
$609$			56.8082i			0.0932811i
$610$	−59.2327	+	89.6163i	−0.0971027	+	0.146912i
$611$	238.120			0.389722
$612$	95.3939	−	95.3939i	0.155872	−	0.155872i
$613$	−788.110	−	788.110i	−1.28566	−	1.28566i	−0.937396	−	0.348265i	$-0.886771\pi$
$613$	−788.110	−	788.110i	−1.28566	−	1.28566i	−0.348265	−	0.937396i	$-0.613229\pi$
$614$			461.394i			0.751456i
$615$	−128.586	−	84.9898i	−0.209082	−	0.138195i
$616$	49.6163			0.0805460
$617$	356.221	−	356.221i	0.577344	−	0.577344i	−0.356826	−	0.934171i	$-0.616141\pi$
$617$	356.221	−	356.221i	0.577344	−	0.577344i	0.934171	+	0.356826i	$0.116141\pi$
$618$	40.4041	+	40.4041i	0.0653788	+	0.0653788i
$619$			73.8796i			0.119353i	0.998218	+	0.0596766i	$0.0190069\pi$
$619$			73.8796i			0.119353i	−0.998218	+	0.0596766i	$0.980993\pi$
$620$	−79.1918	−	387.959i	−0.127729	−	0.625741i
$621$	−78.6061			−0.126580
$622$	−47.7367	+	47.7367i	−0.0767472	+	0.0767472i
$623$	−105.535	−	105.535i	−0.169398	−	0.169398i
$624$		−	125.394i		−	0.200952i
$625$	433.000	−	450.706i	0.692800	−	0.721130i
$626$	439.535			0.702132
$627$	−435.959	+	435.959i	−0.695310	+	0.695310i
$628$	−246.000	−	246.000i	−0.391720	−	0.391720i
$629$			858.545i			1.36494i
$630$	−26.4245	+	5.39388i	−0.0419436	+	0.00856171i
$631$	−45.9796			−0.0728678			−0.0364339	−	0.999336i	$-0.511600\pi$
$631$	−45.9796			−0.0728678			−0.0364339	+	0.999336i	$0.511600\pi$
$632$	−230.747	+	230.747i	−0.365106	+	0.365106i
$633$	−390.384	−	390.384i	−0.616720	−	0.616720i
$634$			665.655i			1.04993i
$635$	−71.3235	+	107.909i	−0.112320	+	0.169936i
$636$	−93.5255			−0.147053
$637$	−606.414	+	606.414i	−0.951985	+	0.951985i
$638$	−355.959	−	355.959i	−0.557930	−	0.557930i
$639$			18.6061i			0.0291176i
$640$	−47.1918	−	31.1918i	−0.0737372	−	0.0487372i
$641$	−789.757			−1.23207			−0.616035	−	0.787719i	$-0.711262\pi$
$641$	−789.757			−1.23207			−0.616035	+	0.787719i	$0.711262\pi$
$642$	36.9898	−	36.9898i	0.0576165	−	0.0576165i
$643$	−530.474	−	530.474i	−0.824999	−	0.824999i	0.161821	−	0.986820i	$-0.448263\pi$
$643$	−530.474	−	530.474i	−0.824999	−	0.824999i	−0.986820	+	0.161821i	$0.948263\pi$
$644$		−	38.4653i		−	0.0597287i
$645$	30.6061	+	149.939i	0.0474514	+	0.232463i
$646$	−820.322			−1.26985
$647$	−135.323	+	135.323i	−0.209155	+	0.209155i	−0.803908	−	0.594753i	$-0.797250\pi$
$647$	−135.323	+	135.323i	−0.209155	+	0.209155i	0.594753	+	0.803908i	$0.297250\pi$
$648$	18.0000	+	18.0000i	0.0277778	+	0.0277778i
$649$			275.959i			0.425207i
$650$	588.706	−	250.788i	0.905702	−	0.385827i
$651$	−87.1918			−0.133935
$652$	−127.010	+	127.010i	−0.194801	+	0.194801i
$653$	−49.8377	−	49.8377i	−0.0763212	−	0.0763212i	0.667916	−	0.744237i	$-0.267187\pi$
$653$	−49.8377	−	49.8377i	−0.0763212	−	0.0763212i	−0.744237	+	0.667916i	$0.767187\pi$
$654$			318.434i			0.486902i
$655$	655.473	−	133.798i	1.00072	−	0.204272i
$656$	−71.1918			−0.108524
$657$	111.606	−	111.606i	0.169872	−	0.169872i
$658$	−16.7265	−	16.7265i	−0.0254202	−	0.0254202i
$659$			209.576i			0.318020i	0.987277	+	0.159010i	$0.0508303\pi$
$659$			209.576i			0.318020i	−0.987277	+	0.159010i	$0.949170\pi$
$660$	131.778	−	199.373i	0.199663	−	0.302081i
$661$	−119.273			−0.180444			−0.0902220	−	0.995922i	$-0.528758\pi$
$661$	−119.273			−0.180444			−0.0902220	+	0.995922i	$0.528758\pi$
$662$	209.980	−	209.980i	0.317190	−	0.317190i
$663$	498.409	+	498.409i	0.751748	+	0.751748i
$664$		−	329.171i		−	0.495740i
$665$	136.808	+	90.4245i	0.205727	+	0.135977i
$666$	−162.000			−0.243243
$667$	−275.959	+	275.959i	−0.413732	+	0.413732i
$668$	97.3531	+	97.3531i	0.145738	+	0.145738i
$669$			511.151i			0.764052i
$670$	−96.1816	−	471.192i	−0.143555	−	0.703271i
$671$	−209.616			−0.312394
$672$	−8.80816	+	8.80816i	−0.0131074	+	0.0131074i
$673$	−468.857	−	468.857i	−0.696667	−	0.696667i	0.267023	−	0.963690i	$-0.413960\pi$
$673$	−468.857	−	468.857i	−0.696667	−	0.696667i	−0.963690	+	0.267023i	$0.913960\pi$
$674$		−	176.747i		−	0.262236i
$675$	−48.5074	+	120.507i	−0.0718628	+	0.178529i
$676$	317.151			0.469158
$677$	−654.160	+	654.160i	−0.966263	+	0.966263i	−0.999449	−	0.0331860i	$-0.989435\pi$
$677$	−654.160	+	654.160i	−0.966263	+	0.966263i	0.0331860	+	0.999449i	$0.489435\pi$
$678$	189.328	+	189.328i	0.279245	+	0.279245i
$679$		−	147.414i		−	0.217105i
$680$	311.555	−	63.5959i	0.458169	−	0.0935234i
$681$	592.949			0.870703
$682$	546.343	−	546.343i	0.801089	−	0.801089i
$683$	286.070	+	286.070i	0.418844	+	0.418844i	0.884805	−	0.465961i	$-0.154291\pi$
$683$	286.070	+	286.070i	0.418844	+	0.418844i	−0.465961	+	0.884805i	$0.654291\pi$
$684$		−	154.788i		−	0.226298i
$685$	−100.980	+	152.778i	−0.147415	+	0.223033i
$686$	173.294			0.252615
$687$	506.969	−	506.969i	0.737947	−	0.737947i
$688$	49.9796	+	49.9796i	0.0726448	+	0.0726448i
$689$		−	488.647i		−	0.709212i
$690$	−154.565	−	102.161i	−0.224008	−	0.148060i
$691$	738.706			1.06904			0.534520	−	0.845156i	$-0.320493\pi$
$691$	738.706			1.06904			0.534520	+	0.845156i	$0.320493\pi$
$692$	70.2225	−	70.2225i	0.101478	−	0.101478i
$693$	−37.2122	−	37.2122i	−0.0536973	−	0.0536973i
$694$		−	424.990i		−	0.612377i
$695$	−54.2020	−	265.535i	−0.0779885	−	0.382064i
$696$	126.384			0.181586
$697$	282.969	−	282.969i	0.405982	−	0.405982i
$698$	−280.000	−	280.000i	−0.401146	−	0.401146i
$699$			157.410i			0.225193i
$700$	−58.9694	−	23.7367i	−0.0842420	−	0.0339096i
$701$	475.778			0.678713			0.339356	−	0.940658i	$-0.389791\pi$
$701$	475.778			0.678713			0.339356	+	0.940658i	$0.389791\pi$
$702$	−94.0454	+	94.0454i	−0.133968	+	0.133968i
$703$	696.545	+	696.545i	0.990818	+	0.990818i
$704$		−	110.384i		−	0.156795i
$705$	−111.637	+	22.7878i	−0.158350	+	0.0323231i
$706$	425.010			0.601997
$707$	25.5163	−	25.5163i	0.0360910	−	0.0360910i
$708$	−48.9898	−	48.9898i	−0.0691946	−	0.0691946i
$709$		−	504.363i		−	0.711373i	−0.934605	−	0.355686i	$-0.884247\pi$
$709$		−	504.363i		−	0.711373i	0.934605	−	0.355686i	$-0.115753\pi$
$710$	−24.1816	+	36.5857i	−0.0340586	+	0.0515292i
$711$	346.120			0.486808
$712$	−234.788	+	234.788i	−0.329758	+	0.329758i
$713$	−423.555	−	423.555i	−0.594046	−	0.594046i
$714$		−	70.0204i		−	0.0980678i
$715$	1041.68	+	688.504i	1.45689	+	0.962943i
$716$	−282.343			−0.394334
$717$	−189.576	+	189.576i	−0.264401	+	0.264401i
$718$	633.090	+	633.090i	0.881741	+	0.881741i
$719$		−	481.816i		−	0.670120i	−0.942197	−	0.335060i	$-0.891243\pi$
$719$		−	481.816i		−	0.670120i	0.942197	−	0.335060i	$-0.108757\pi$
$720$	12.0000	+	58.7878i	0.0166667	+	0.0816497i
$721$	29.6571			0.0411334
$722$	−304.535	+	304.535i	−0.421793	+	0.421793i
$723$	−516.767	−	516.767i	−0.714754	−	0.714754i
$724$		−	117.616i		−	0.162453i
$725$	252.767	+	593.353i	0.348645	+	0.818418i
$726$	169.955			0.234097
$727$	−782.352	+	782.352i	−1.07614	+	1.07614i	−0.0792856	+	0.996852i	$0.525264\pi$
$727$	−782.352	+	782.352i	−1.07614	+	1.07614i	−0.996852	+	0.0792856i	$0.974736\pi$
$728$	−46.0204	−	46.0204i	−0.0632148	−	0.0632148i
$729$		−	27.0000i		−	0.0370370i
$730$	364.504	−	74.4041i	0.499321	−	0.101923i
$731$	−397.312			−0.543519
$732$	37.2122	−	37.2122i	0.0508364	−	0.0508364i
$733$	537.586	+	537.586i	0.733405	+	0.733405i	0.971293	−	0.237888i	$-0.0764551\pi$
$733$	537.586	+	537.586i	0.733405	+	0.733405i	−0.237888	+	0.971293i	$0.576455\pi$
$734$			535.010i			0.728897i
$735$	226.269	−	342.335i	0.307849	−	0.465762i
$736$	−85.5755			−0.116271
$737$	663.555	−	663.555i	0.900346	−	0.900346i
$738$	53.3939	+	53.3939i	0.0723494	+	0.0723494i
$739$		−	833.353i		−	1.12768i	−0.825885	−	0.563838i	$-0.809324\pi$
$739$		−	833.353i		−	1.12768i	0.825885	−	0.563838i	$-0.190676\pi$
$740$	−318.545	−	210.545i	−0.430466	−	0.284520i
$741$	808.727			1.09140
$742$	−34.3245	+	34.3245i	−0.0462594	+	0.0462594i
$743$	−991.383	−	991.383i	−1.33430	−	1.33430i	−0.901484	−	0.432813i	$-0.857521\pi$
$743$	−991.383	−	991.383i	−1.33430	−	1.33430i	−0.432813	−	0.901484i	$-0.642479\pi$
$744$			193.980i			0.260725i
$745$	−42.7673	−	209.516i	−0.0574058	−	0.281230i
$746$	−753.878			−1.01056
$747$	−246.879	+	246.879i	−0.330493	+	0.330493i
$748$	438.747	+	438.747i	0.586560	+	0.586560i
$749$		−	27.1510i		−	0.0362497i
$750$	−252.000	+	173.914i	−0.336000	+	0.231885i
$751$	−1276.73			−1.70004			−0.850018	−	0.526754i	$-0.823409\pi$
$751$	−1276.73			−1.70004			−0.850018	+	0.526754i	$0.823409\pi$
$752$	−37.2122	+	37.2122i	−0.0494844	+	0.0494844i
$753$	480.817	+	480.817i	0.638536	+	0.638536i
$754$			660.322i			0.875759i
$755$	−873.898	+	178.384i	−1.15748	+	0.236270i
$756$	13.2122			0.0174765
$757$	−36.0918	+	36.0918i	−0.0476775	+	0.0476775i	−0.730544	−	0.682866i	$-0.760733\pi$
$757$	−36.0918	+	36.0918i	−0.0476775	+	0.0476775i	0.682866	+	0.730544i	$0.260733\pi$
$758$	−167.818	−	167.818i	−0.221396	−	0.221396i
$759$		−	361.535i		−	0.476330i
$760$	201.171	−	304.363i	0.264699	−	0.400478i
$761$	716.261			0.941211			0.470605	−	0.882344i	$-0.344036\pi$
$761$	716.261			0.941211			0.470605	+	0.882344i	$0.344036\pi$
$762$	44.8082	−	44.8082i	0.0588034	−	0.0588034i
$763$	116.867	+	116.867i	0.153168	+	0.153168i
$764$			650.788i			0.851816i
$765$	−281.363	−	185.969i	−0.367795	−	0.243097i
$766$	−956.586			−1.24881
$767$	255.959	−	255.959i	0.333715	−	0.333715i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	389.576i		−	0.506600i	−0.967388	−	0.253300i	$-0.918484\pi$
$769$		−	389.576i		−	0.506600i	0.967388	−	0.253300i	$-0.0815160\pi$
$770$	−24.8082	−	121.535i	−0.0322184	−	0.157837i
$771$	−302.549			−0.392412
$772$	−78.7673	+	78.7673i	−0.102030	+	0.102030i
$773$	−409.677	−	409.677i	−0.529983	−	0.529983i	0.390585	−	0.920567i	$-0.372273\pi$
$773$	−409.677	−	409.677i	−0.529983	−	0.529983i	−0.920567	+	0.390585i	$0.872273\pi$
$774$		−	74.9694i		−	0.0968597i
$775$	−910.706	+	387.959i	−1.17510	+	0.500592i
$776$	−327.959			−0.422628
$777$	−59.4551	+	59.4551i	−0.0765188	+	0.0765188i
$778$	−169.151	−	169.151i	−0.217418	−	0.217418i
$779$		−	459.151i		−	0.589411i
$780$	−307.151	+	62.6969i	−0.393783	+	0.0803807i
$781$	−85.5755			−0.109572
$782$	340.141	−	340.141i	0.434963	−	0.434963i
$783$	−94.7878	−	94.7878i	−0.121057	−	0.121057i
$784$		−	189.535i		−	0.241753i
$785$	−479.574	+	725.574i	−0.610923	+	0.924299i
$786$	−327.737			−0.416968
$787$	−383.142	+	383.142i	−0.486838	+	0.486838i	−0.907307	−	0.420469i	$-0.861866\pi$
$787$	−383.142	+	383.142i	−0.486838	+	0.486838i	0.420469	+	0.907307i	$0.361866\pi$
$788$	238.627	+	238.627i	0.302826	+	0.302826i
$789$			75.1918i			0.0953002i
$790$	680.586	+	449.839i	0.861501	+	0.569416i
$791$	138.969			0.175688
$792$	−82.7878	+	82.7878i	−0.104530	+	0.104530i
$793$	194.424	+	194.424i	0.245176	+	0.245176i
$794$			138.686i			0.174667i
$795$	46.7628	+	229.090i	0.0588211	+	0.288163i
$796$	357.131			0.448657
$797$	563.191	−	563.191i	0.706638	−	0.706638i	−0.259188	−	0.965827i	$-0.583455\pi$
$797$	563.191	−	563.191i	0.706638	−	0.706638i	0.965827	+	0.259188i	$0.0834551\pi$
$798$	−56.8082	−	56.8082i	−0.0711882	−	0.0711882i
$799$		−	295.818i		−	0.370236i
$800$	−52.8082	+	131.192i	−0.0660102	+	0.163990i
$801$	352.182			0.439677
$802$	414.767	−	414.767i	0.517166	−	0.517166i
$803$	513.312	+	513.312i	0.639243	+	0.639243i
$804$			235.596i			0.293030i
$805$	−94.2204	+	19.2327i	−0.117044	+	0.0238915i
$806$	−1013.49			−1.25744
$807$	525.601	−	525.601i	0.651302	−	0.651302i
$808$	−56.7673	−	56.7673i	−0.0702566	−	0.0702566i
$809$			770.161i			0.951992i	0.879448	+	0.475996i	$0.157912\pi$
$809$			770.161i			0.951992i	−0.879448	+	0.475996i	$0.842088\pi$
$810$	35.0908	−	53.0908i	0.0433220	−	0.0655442i
$811$	13.4939			0.0166386			0.00831928	−	0.999965i	$-0.497352\pi$
$811$	13.4939			0.0166386			0.00831928	+	0.999965i	$0.497352\pi$
$812$	46.3837	−	46.3837i	0.0571227	−	0.0571227i
$813$	270.334	+	270.334i	0.332514	+	0.332514i
$814$		−	745.090i		−	0.915344i
$815$	374.615	+	247.605i	0.459651	+	0.303810i
$816$	−155.778			−0.190904
$817$	−322.343	+	322.343i	−0.394544	+	0.394544i
$818$	605.110	+	605.110i	0.739744	+	0.739744i
$819$			69.0306i			0.0842865i
$820$	35.5959	+	174.384i	0.0434097	+	0.212663i
$821$	741.312			0.902938			0.451469	−	0.892287i	$-0.350900\pi$
$821$	741.312			0.902938			0.451469	+	0.892287i	$0.350900\pi$
$822$	63.4393	−	63.4393i	0.0771767	−	0.0771767i
$823$	−196.272	−	196.272i	−0.238484	−	0.238484i	0.577738	−	0.816222i	$-0.303936\pi$
$823$	−196.272	−	196.272i	−0.238484	−	0.238484i	−0.816222	+	0.577738i	$0.803936\pi$
$824$		−	65.9796i		−	0.0800723i
$825$	−554.252	−	223.101i	−0.671821	−	0.270425i
$826$	−35.9592			−0.0435341
$827$	−20.5357	+	20.5357i	−0.0248316	+	0.0248316i	−0.719414	−	0.694582i	$-0.755589\pi$
$827$	−20.5357	+	20.5357i	−0.0248316	+	0.0248316i	0.694582	+	0.719414i	$0.255589\pi$
$828$	64.1816	+	64.1816i	0.0775140	+	0.0775140i
$829$		−	264.465i		−	0.319017i	−0.987197	−	0.159509i	$-0.949009\pi$
$829$		−	264.465i		−	0.319017i	0.987197	−	0.159509i	$-0.0509910\pi$
$830$	−806.302	+	164.586i	−0.971448	+	0.198296i
$831$	−112.652			−0.135561
$832$	−102.384	+	102.384i	−0.123057	+	0.123057i
$833$	753.352	+	753.352i	0.904384	+	0.904384i
$834$			132.767i			0.159193i
$835$	189.789	−	287.142i	0.227292	−	0.343882i
$836$	711.918			0.851577
$837$	145.485	−	145.485i	0.173817	−	0.173817i
$838$	15.9592	+	15.9592i	0.0190444	+	0.0190444i
$839$		−	353.090i		−	0.420846i	−0.977610	−	0.210423i	$-0.932516\pi$
$839$		−	353.090i		−	0.420846i	0.977610	−	0.210423i	$-0.0674841\pi$
$840$	25.9796	+	17.1714i	0.0309281	+	0.0204422i
$841$	175.465			0.208639
$842$	433.171	−	433.171i	0.514455	−	0.514455i
$843$	−590.969	−	590.969i	−0.701031	−	0.701031i
$844$			637.494i			0.755324i
$845$	−158.576	−	776.858i	−0.187663	−	0.919359i
$846$	55.8184			0.0659792
$847$	62.3745	−	62.3745i	0.0736417	−	0.0736417i
$848$	76.3633	+	76.3633i	0.0900510	+	0.0900510i
$849$			664.504i			0.782690i
$850$	−311.555	−	731.353i	−0.366535	−	0.860415i
$851$	−577.635			−0.678772
$852$	15.1918	−	15.1918i	0.0178308	−	0.0178308i
$853$	19.4449	+	19.4449i	0.0227959	+	0.0227959i	0.718413	−	0.695617i	$-0.244869\pi$
$853$	19.4449	+	19.4449i	0.0227959	+	0.0227959i	−0.695617	+	0.718413i	$0.744869\pi$
$854$		−	27.3143i		−	0.0319840i
$855$	−379.151	+	77.3939i	−0.443451	+	0.0905192i
$856$	−60.4041			−0.0705655
$857$	602.444	−	602.444i	0.702968	−	0.702968i	−0.262078	−	0.965047i	$-0.584408\pi$
$857$	602.444	−	602.444i	0.702968	−	0.702968i	0.965047	+	0.262078i	$0.0844079\pi$
$858$	−432.545	−	432.545i	−0.504132	−	0.504132i
$859$		−	1099.53i		−	1.28001i	−0.768369	−	0.640007i	$-0.778931\pi$
$859$		−	1099.53i		−	1.28001i	0.768369	−	0.640007i	$-0.221069\pi$
$860$	97.4347	−	147.414i	0.113296	−	0.171412i
$861$	39.1918			0.0455190
$862$	24.1816	−	24.1816i	0.0280529	−	0.0280529i
$863$	694.797	+	694.797i	0.805095	+	0.805095i	0.983887	−	0.178792i	$-0.0572189\pi$
$863$	694.797	+	694.797i	0.805095	+	0.805095i	−0.178792	+	0.983887i	$0.557219\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−207.120	−	136.898i	−0.239446	−	0.158264i
$866$	1057.84			1.22152
$867$	265.225	−	265.225i	0.305911	−	0.305911i
$868$	71.1918	+	71.1918i	0.0820182	+	0.0820182i
$869$			1591.92i			1.83190i
$870$	−63.1918	−	309.576i	−0.0726343	−	0.355834i
$871$	−1230.93			−1.41324
$872$	260.000	−	260.000i	0.298165	−	0.298165i
$873$	245.969	+	245.969i	0.281752	+	0.281752i
$874$		−	551.918i		−	0.631486i
$875$	−28.6582	+	156.313i	−0.0327522	+	0.178644i
$876$	−182.252			−0.208050
$877$	1092.90	−	1092.90i	1.24618	−	1.24618i	0.288783	−	0.957394i	$-0.406749\pi$
$877$	1092.90	−	1092.90i	1.24618	−	1.24618i	0.957394	−	0.288783i	$-0.0932507\pi$
$878$	44.6265	+	44.6265i	0.0508275	+	0.0508275i
$879$		−	365.196i		−	0.415468i
$880$	−270.384	+	55.1918i	−0.307254	+	0.0627180i
$881$	138.443			0.157143			0.0785714	−	0.996908i	$-0.474964\pi$
$881$	138.443			0.157143			0.0785714	+	0.996908i	$0.474964\pi$
$882$	−142.151	+	142.151i	−0.161169	+	0.161169i
$883$	1008.41	+	1008.41i	1.14203	+	1.14203i	0.988078	+	0.153953i	$0.0492003\pi$
$883$	1008.41	+	1008.41i	1.14203	+	1.14203i	0.153953	+	0.988078i	$0.450800\pi$
$884$		−	813.898i		−	0.920699i
$885$	−95.5051	+	144.495i	−0.107915	+	0.163271i
$886$	622.565			0.702670
$887$	−639.687	+	639.687i	−0.721180	+	0.721180i	−0.968846	−	0.247666i	$-0.920337\pi$
$887$	−639.687	+	639.687i	−0.721180	+	0.721180i	0.247666	+	0.968846i	$0.420337\pi$
$888$	132.272	+	132.272i	0.148955	+	0.148955i
$889$		−	32.8898i		−	0.0369964i
$890$	692.504	+	457.716i	0.778094	+	0.514288i
$891$	124.182			0.139373
$892$	417.353	−	417.353i	0.467885	−	0.467885i
$893$	−240.000	−	240.000i	−0.268757	−	0.268757i
$894$			104.758i			0.117179i
$895$	141.171	+	691.596i	0.157733	+	0.772733i
$896$	14.3837			0.0160532
$897$	−335.333	+	335.333i	−0.373838	+	0.373838i
$898$	−141.273	−	141.273i	−0.157320	−	0.157320i
$899$		−	1021.49i		−	1.13626i
$900$	138.000	−	58.7878i	0.153333	−	0.0653197i
$901$	−607.049			−0.673750
$902$	−245.576	+	245.576i	−0.272257	+	0.272257i
$903$	−27.5143	−	27.5143i	−0.0304699	−	0.0304699i
$904$		−	309.171i		−	0.342004i
$905$	−288.100	+	58.8082i	−0.318343	+	0.0649814i
$906$	436.949			0.482284
$907$	−893.303	+	893.303i	−0.984899	+	0.984899i	−0.999888	−	0.0149890i	$-0.995229\pi$
$907$	−893.303	+	893.303i	−0.984899	+	0.984899i	0.0149890	+	0.999888i	$0.495229\pi$
$908$	−484.141	−	484.141i	−0.533195	−	0.533195i
$909$			85.1510i			0.0936755i
$910$	−89.7163	+	135.737i	−0.0985894	+	0.149161i
$911$	1045.03			1.14712			0.573562	−	0.819162i	$-0.305561\pi$
$911$	1045.03			1.14712			0.573562	+	0.819162i	$0.305561\pi$
$912$	−126.384	+	126.384i	−0.138579	+	0.138579i
$913$	−1135.47	−	1135.47i	−1.24367	−	1.24367i
$914$		−	40.7878i		−	0.0446256i
$915$	−109.757	−	72.5449i	−0.119953	−	0.0792840i
$916$	−827.878			−0.903796
$917$	−120.282	+	120.282i	−0.131169	+	0.131169i
$918$	116.833	+	116.833i	0.127269	+	0.127269i
$919$			803.573i			0.874400i	0.899364	+	0.437200i	$0.144030\pi$
$919$			803.573i			0.874400i	−0.899364	+	0.437200i	$0.855970\pi$
$920$	42.7878	+	209.616i	0.0465084	+	0.227844i
$921$	−565.090			−0.613561
$922$	−626.727	+	626.727i	−0.679747	+	0.679747i
$923$	79.3735	+	79.3735i	0.0859951	+	0.0859951i
$924$			60.7673i			0.0657655i
$925$	−356.455	+	885.545i	−0.385357	+	0.957346i
$926$	−629.031			−0.679299
$927$	−49.4847	+	49.4847i	−0.0533815	+	0.0533815i
$928$	−103.192	−	103.192i	−0.111198	−	0.111198i
$929$			1270.64i			1.36776i	0.729597	+	0.683878i	$0.239708\pi$
$929$			1270.64i			1.36776i	−0.729597	+	0.683878i	$0.760292\pi$
$930$	475.151	−	96.9898i	0.510915	−	0.104290i
$931$	1222.40			1.31300
$932$	128.524	−	128.524i	0.137902	−	0.137902i
$933$	−58.4653	−	58.4653i	−0.0626638	−	0.0626638i
$934$		−	93.3939i		−	0.0999934i
$935$	855.333	−	1294.08i	0.914794	−	1.38404i
$936$	153.576			0.164076
$937$	−970.616	+	970.616i	−1.03588	+	1.03588i	−0.0365445	+	0.999332i	$0.511635\pi$
$937$	−970.616	+	970.616i	−1.03588	+	1.03588i	−0.999332	+	0.0365445i	$0.988365\pi$
$938$	86.4653	+	86.4653i	0.0921805	+	0.0921805i
$939$			538.318i			0.573288i
$940$	109.757	+	72.5449i	0.116763	+	0.0771754i
$941$	−431.616			−0.458678			−0.229339	−	0.973347i	$-0.573656\pi$
$941$	−431.616			−0.458678			−0.229339	+	0.973347i	$0.573656\pi$
$942$	301.287	−	301.287i	0.319838	−	0.319838i
$943$	190.384	+	190.384i	0.201891	+	0.201891i
$944$			80.0000i			0.0847458i
$945$	−6.60612	−	32.3633i	−0.00699061	−	0.0342468i
$946$	344.808			0.364491
$947$	−721.121	+	721.121i	−0.761480	+	0.761480i	−0.976590	−	0.215110i	$-0.930989\pi$
$947$	−721.121	+	721.121i	−0.761480	+	0.761480i	0.215110	+	0.976590i	$0.430989\pi$
$948$	−282.606	−	282.606i	−0.298108	−	0.298108i
$949$		−	952.220i		−	1.00339i
$950$	−846.120	−	340.586i	−0.890653	−	0.358511i
$951$	−815.258			−0.857264
$952$	−57.1714	+	57.1714i	−0.0600540	+	0.0600540i
$953$	−737.291	−	737.291i	−0.773652	−	0.773652i	0.205091	−	0.978743i	$-0.434251\pi$
$953$	−737.291	−	737.291i	−0.773652	−	0.773652i	−0.978743	+	0.205091i	$0.934251\pi$
$954$		−	114.545i		−	0.120068i
$955$	1594.10	−	325.394i	1.66921	−	0.340727i
$956$	309.576			0.323824
$957$	435.959	−	435.959i	0.455548	−	0.455548i
$958$	71.2735	+	71.2735i	0.0743982	+	0.0743982i
$959$		−	46.5653i		−	0.0485561i
$960$	38.2020	−	57.7980i	0.0397938	−	0.0602062i
$961$	606.837			0.631464
$962$	−691.090	+	691.090i	−0.718389	+	0.718389i
$963$	45.3031	+	45.3031i	0.0470437	+	0.0470437i
$964$			843.878i			0.875392i
$965$	232.323	+	153.556i	0.240750	+	0.159126i
$966$	47.1102			0.0487683
$967$	958.879	−	958.879i	0.991601	−	0.991601i	−0.00836361	−	0.999965i	$-0.502662\pi$
$967$	958.879	−	958.879i	0.991601	−	0.991601i	0.999965	+	0.00836361i	$0.00266225\pi$
$968$	−138.767	−	138.767i	−0.143355	−	0.143355i
$969$		−	1004.69i		−	1.03683i
$970$	163.980	+	803.333i	0.169051	+	0.828178i
$971$	−1507.86			−1.55289			−0.776444	−	0.630186i	$-0.782979\pi$
$971$	−1507.86			−1.55289			−0.776444	+	0.630186i	$0.782979\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	48.7265	+	48.7265i	0.0500786	+	0.0500786i
$974$		−	590.847i		−	0.606619i
$975$	307.151	+	721.015i	0.315027	+	0.739502i
$976$	−60.7673			−0.0622616
$977$	−373.838	+	373.838i	−0.382638	+	0.382638i	−0.872052	−	0.489413i	$-0.837211\pi$
$977$	−373.838	+	373.838i	−0.382638	+	0.382638i	0.489413	+	0.872052i	$0.337211\pi$
$978$	−155.555	−	155.555i	−0.159054	−	0.159054i
$979$			1619.80i			1.65454i
$980$	−464.263	+	94.7673i	−0.473738	+	0.0967014i
$981$	−390.000			−0.397554
$982$	−910.080	+	910.080i	−0.926761	+	0.926761i
$983$	−1319.46	−	1319.46i	−1.34228	−	1.34228i	−0.893783	−	0.448501i	$-0.851958\pi$
$983$	−1319.46	−	1319.46i	−1.34228	−	1.34228i	−0.448501	−	0.893783i	$-0.648042\pi$
$984$		−	87.1918i		−	0.0886096i
$985$	465.200	−	703.827i	0.472284	−	0.714545i
$986$	820.322			0.831970
$987$	20.4857	−	20.4857i	0.0207555	−	0.0207555i
$988$	−660.322	−	660.322i	−0.668343	−	0.668343i
$989$		−	267.314i		−	0.270287i
$990$	244.182	+	161.394i	0.246648	+	0.163024i
$991$	−315.029			−0.317890			−0.158945	−	0.987287i	$-0.550809\pi$
$991$	−315.029			−0.317890			−0.158945	+	0.987287i	$0.550809\pi$
$992$	158.384	−	158.384i	0.159661	−	0.159661i
$993$	257.171	+	257.171i	0.258984	+	0.258984i
$994$		−	11.1510i		−	0.0112183i
$995$	−178.565	−	874.788i	−0.179463	−	0.879184i
$996$	403.151			0.404770
$997$	1009.38	−	1009.38i	1.01242	−	1.01242i	0.0124991	−	0.999922i	$-0.496021\pi$
$997$	1009.38	−	1009.38i	1.01242	−	1.01242i	0.999922	−	0.0124991i	$-0.00397868\pi$
$998$	970.161	+	970.161i	0.972105	+	0.972105i
$999$		−	198.409i		−	0.198607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.3.f.a.13.2	yes	4
3.2	odd	2		90.3.g.d.73.2		4
4.3	odd	2		240.3.bg.b.193.1		4
5.2	odd	4	inner	30.3.f.a.7.2	✓	4
5.3	odd	4		150.3.f.b.7.1		4
5.4	even	2		150.3.f.b.43.1		4
8.3	odd	2		960.3.bg.g.193.2		4
8.5	even	2		960.3.bg.e.193.1		4
12.11	even	2		720.3.bh.i.433.2		4
15.2	even	4		90.3.g.d.37.2		4
15.8	even	4		450.3.g.j.307.1		4
15.14	odd	2		450.3.g.j.343.1		4
20.3	even	4		1200.3.bg.d.1057.2		4
20.7	even	4		240.3.bg.b.97.1		4
20.19	odd	2		1200.3.bg.d.193.2		4
40.27	even	4		960.3.bg.g.577.2		4
40.37	odd	4		960.3.bg.e.577.1		4
60.47	odd	4		720.3.bh.i.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.f.a.7.2	✓	4	5.2	odd	4	inner
30.3.f.a.13.2	yes	4	1.1	even	1	trivial
90.3.g.d.37.2		4	15.2	even	4
90.3.g.d.73.2		4	3.2	odd	2
150.3.f.b.7.1		4	5.3	odd	4
150.3.f.b.43.1		4	5.4	even	2
240.3.bg.b.97.1		4	20.7	even	4
240.3.bg.b.193.1		4	4.3	odd	2
450.3.g.j.307.1		4	15.8	even	4
450.3.g.j.343.1		4	15.14	odd	2
720.3.bh.i.433.2		4	12.11	even	2
720.3.bh.i.577.2		4	60.47	odd	4
960.3.bg.e.193.1		4	8.5	even	2
960.3.bg.e.577.1		4	40.37	odd	4
960.3.bg.g.193.2		4	8.3	odd	2
960.3.bg.g.577.2		4	40.27	even	4
1200.3.bg.d.193.2		4	20.19	odd	2
1200.3.bg.d.1057.2		4	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	30.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.89898 + 1.00000i) q^{5} +2.44949 q^{6} +(0.898979 - 0.898979i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} +(-4.89898 + 1.00000i) q^{5} +2.44949 q^{6} +(0.898979 - 0.898979i) q^{7} +(-2.00000 - 2.00000i) q^{8} +3.00000i q^{9} +(-3.89898 + 5.89898i) q^{10} -13.7980 q^{11} +(2.44949 - 2.44949i) q^{12} +(12.7980 + 12.7980i) q^{13} -1.79796i q^{14} +(-7.22474 - 4.77526i) q^{15} -4.00000 q^{16} +(15.8990 - 15.8990i) q^{17} +(3.00000 + 3.00000i) q^{18} -25.7980i q^{19} +(2.00000 + 9.79796i) q^{20} +2.20204 q^{21} +(-13.7980 + 13.7980i) q^{22} +(10.6969 + 10.6969i) q^{23} -4.89898i q^{24} +(23.0000 - 9.79796i) q^{25} +25.5959 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-1.79796 - 1.79796i) q^{28} +25.7980i q^{29} +(-12.0000 + 2.44949i) q^{30} -39.5959 q^{31} +(-4.00000 + 4.00000i) q^{32} +(-16.8990 - 16.8990i) q^{33} -31.7980i q^{34} +(-3.50510 + 5.30306i) q^{35} +6.00000 q^{36} +(-27.0000 + 27.0000i) q^{37} +(-25.7980 - 25.7980i) q^{38} +31.3485i q^{39} +(11.7980 + 7.79796i) q^{40} +17.7980 q^{41} +(2.20204 - 2.20204i) q^{42} +(-12.4949 - 12.4949i) q^{43} +27.5959i q^{44} +(-3.00000 - 14.6969i) q^{45} +21.3939 q^{46} +(9.30306 - 9.30306i) q^{47} +(-4.89898 - 4.89898i) q^{48} +47.3837i q^{49} +(13.2020 - 32.7980i) q^{50} +38.9444 q^{51} +(25.5959 - 25.5959i) q^{52} +(-19.0908 - 19.0908i) q^{53} +7.34847i q^{54} +(67.5959 - 13.7980i) q^{55} -3.59592 q^{56} +(31.5959 - 31.5959i) q^{57} +(25.7980 + 25.7980i) q^{58} -20.0000i q^{59} +(-9.55051 + 14.4495i) q^{60} +15.1918 q^{61} +(-39.5959 + 39.5959i) q^{62} +(2.69694 + 2.69694i) q^{63} +8.00000i q^{64} +(-75.4949 - 49.8990i) q^{65} -33.7980 q^{66} +(-48.0908 + 48.0908i) q^{67} +(-31.7980 - 31.7980i) q^{68} +26.2020i q^{69} +(1.79796 + 8.80816i) q^{70} +6.20204 q^{71} +(6.00000 - 6.00000i) q^{72} +(-37.2020 - 37.2020i) q^{73} +54.0000i q^{74} +(40.1691 + 16.1691i) q^{75} -51.5959 q^{76} +(-12.4041 + 12.4041i) q^{77} +(31.3485 + 31.3485i) q^{78} -115.373i q^{79} +(19.5959 - 4.00000i) q^{80} -9.00000 q^{81} +(17.7980 - 17.7980i) q^{82} +(82.2929 + 82.2929i) q^{83} -4.40408i q^{84} +(-61.9898 + 93.7878i) q^{85} -24.9898 q^{86} +(-31.5959 + 31.5959i) q^{87} +(27.5959 + 27.5959i) q^{88} -117.394i q^{89} +(-17.6969 - 11.6969i) q^{90} +23.0102 q^{91} +(21.3939 - 21.3939i) q^{92} +(-48.4949 - 48.4949i) q^{93} -18.6061i q^{94} +(25.7980 + 126.384i) q^{95} -9.79796 q^{96} +(81.9898 - 81.9898i) q^{97} +(47.3837 + 47.3837i) q^{98} -41.3939i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 16 q^{7} - 8 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 16 * q^7 - 8 * q^8	\( 4 q + 4 q^{2} - 16 q^{7} - 8 q^{8} + 4 q^{10} - 16 q^{11} + 12 q^{13} - 24 q^{15} - 16 q^{16} + 44 q^{17} + 12 q^{18} + 8 q^{20} + 48 q^{21} - 16 q^{22} - 16 q^{23} + 92 q^{25} + 24 q^{26} + 32 q^{28} - 48 q^{30} - 80 q^{31} - 16 q^{32} - 48 q^{33} - 112 q^{35} + 24 q^{36} - 108 q^{37} - 64 q^{38} + 8 q^{40} + 32 q^{41} + 48 q^{42} + 48 q^{43} - 12 q^{45} - 32 q^{46} + 96 q^{47} + 92 q^{50} + 48 q^{51} + 24 q^{52} + 100 q^{53} + 192 q^{55} + 64 q^{56} + 48 q^{57} + 64 q^{58} - 48 q^{60} - 96 q^{61} - 80 q^{62} - 48 q^{63} - 204 q^{65} - 96 q^{66} - 16 q^{67} - 88 q^{68} - 32 q^{70} + 64 q^{71} + 24 q^{72} - 188 q^{73} + 48 q^{75} - 128 q^{76} - 128 q^{77} + 96 q^{78} - 36 q^{81} + 32 q^{82} + 192 q^{83} - 52 q^{85} + 96 q^{86} - 48 q^{87} + 32 q^{88} - 12 q^{90} + 288 q^{91} - 32 q^{92} - 96 q^{93} + 64 q^{95} + 132 q^{97} - 124 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 16 * q^7 - 8 * q^8 + 4 * q^10 - 16 * q^11 + 12 * q^13 - 24 * q^15 - 16 * q^16 + 44 * q^17 + 12 * q^18 + 8 * q^20 + 48 * q^21 - 16 * q^22 - 16 * q^23 + 92 * q^25 + 24 * q^26 + 32 * q^28 - 48 * q^30 - 80 * q^31 - 16 * q^32 - 48 * q^33 - 112 * q^35 + 24 * q^36 - 108 * q^37 - 64 * q^38 + 8 * q^40 + 32 * q^41 + 48 * q^42 + 48 * q^43 - 12 * q^45 - 32 * q^46 + 96 * q^47 + 92 * q^50 + 48 * q^51 + 24 * q^52 + 100 * q^53 + 192 * q^55 + 64 * q^56 + 48 * q^57 + 64 * q^58 - 48 * q^60 - 96 * q^61 - 80 * q^62 - 48 * q^63 - 204 * q^65 - 96 * q^66 - 16 * q^67 - 88 * q^68 - 32 * q^70 + 64 * q^71 + 24 * q^72 - 188 * q^73 + 48 * q^75 - 128 * q^76 - 128 * q^77 + 96 * q^78 - 36 * q^81 + 32 * q^82 + 192 * q^83 - 52 * q^85 + 96 * q^86 - 48 * q^87 + 32 * q^88 - 12 * q^90 + 288 * q^91 - 32 * q^92 - 96 * q^93 + 64 * q^95 + 132 * q^97 - 124 * q^98

Introduction

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