LMFDB - Embedded newform 30.3.f.a.7.2

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			7.2
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	30.7
Dual form			30.3.f.a.13.2

$q$-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 $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

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

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	0.768398	−	0.639972i	$-0.221054\pi$
$7$	0.898979	+	0.898979i	0.128426	+	0.128426i	−0.639972	+	0.768398i	$0.721054\pi$
$8$	−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	−0.0154227	−	0.999881i	$-0.504909\pi$
$13$	12.7980	−	12.7980i	0.984458	−	0.984458i	0.999881	+	0.0154227i	$0.00490939\pi$
$14$			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	0.998027	−	0.0627925i	$-0.0200006\pi$
$17$	15.8990	+	15.8990i	0.935234	+	0.935234i	−0.0627925	+	0.998027i	$0.520001\pi$
$18$	3.00000	−	3.00000i	0.166667	−	0.166667i
$19$			25.7980i			1.35779i	0.734237	+	0.678894i	$0.237540\pi$
$19$			25.7980i			1.35779i	−0.734237	+	0.678894i	$0.762460\pi$
$20$	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	−0.435233	−	0.900318i	$-0.643334\pi$
$23$	10.6969	−	10.6969i	0.465084	−	0.465084i	0.900318	+	0.435233i	$0.143334\pi$
$24$			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	$-0.853277\pi$
$29$		−	25.7980i		−	0.889585i	0.895634	−	0.444792i	$-0.146723\pi$
$30$	−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	0.240836	−	0.970566i	$-0.422578\pi$
$37$	−27.0000	−	27.0000i	−0.729730	−	0.729730i	−0.970566	+	0.240836i	$0.922578\pi$
$38$	−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	−0.837309	−	0.546730i	$-0.815872\pi$
$43$	−12.4949	+	12.4949i	−0.290579	+	0.290579i	0.546730	+	0.837309i	$0.315872\pi$
$44$		−	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	0.799115	−	0.601178i	$-0.205302\pi$
$47$	9.30306	+	9.30306i	0.197937	+	0.197937i	−0.601178	+	0.799115i	$0.705302\pi$
$48$	−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	−0.863888	−	0.503684i	$-0.831978\pi$
$53$	−19.0908	+	19.0908i	−0.360204	+	0.360204i	0.503684	+	0.863888i	$0.331978\pi$
$54$		−	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	$0.0542125\pi$
$59$			20.0000i			0.338983i	−0.985532	+	0.169492i	$0.945787\pi$
$60$	−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	0.250375	−	0.968149i	$-0.419446\pi$
$67$	−48.0908	−	48.0908i	−0.717773	−	0.717773i	−0.968149	+	0.250375i	$0.919446\pi$
$68$	−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	−0.914409	−	0.404792i	$-0.867344\pi$
$73$	−37.2020	+	37.2020i	−0.509617	+	0.509617i	0.404792	+	0.914409i	$0.367344\pi$
$74$		−	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	$0.260579\pi$
$79$			115.373i			1.46042i	−0.683221	+	0.730212i	$0.739421\pi$
$80$	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	−0.00848381	−	0.999964i	$-0.502701\pi$
$83$	82.2929	−	82.2929i	0.991480	−	0.991480i	0.999964	+	0.00848381i	$0.00270051\pi$
$84$			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	$0.229239\pi$
$89$			117.394i			1.31903i	−0.751690	+	0.659516i	$0.770761\pi$
$90$	−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	0.989537	−	0.144281i	$-0.0460870\pi$
$97$	81.9898	+	81.9898i	0.845256	+	0.845256i	−0.144281	+	0.989537i	$0.546087\pi$
$98$	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	−0.622486	−	0.782631i	$-0.713877\pi$
$103$	16.4949	−	16.4949i	0.160145	−	0.160145i	0.782631	+	0.622486i	$0.213877\pi$
$104$			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	0.774142	−	0.633011i	$-0.218181\pi$
$107$	15.1010	+	15.1010i	0.141131	+	0.141131i	−0.633011	+	0.774142i	$0.718181\pi$
$108$	7.34847	−	7.34847i	0.0680414	−	0.0680414i
$109$		−	130.000i		−	1.19266i	−0.802739	−	0.596330i	$-0.796625\pi$
$109$		−	130.000i		−	1.19266i	0.802739	−	0.596330i	$-0.203375\pi$
$110$	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	−0.276893	−	0.960901i	$-0.589305\pi$
$113$	77.2929	−	77.2929i	0.684008	−	0.684008i	0.960901	+	0.276893i	$0.0893048\pi$
$114$			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	0.775449	−	0.631411i	$-0.217524\pi$
$127$	18.2929	+	18.2929i	0.144038	+	0.144038i	−0.631411	+	0.775449i	$0.717524\pi$
$128$	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	0.795283	−	0.606239i	$-0.207322\pi$
$137$	25.8990	+	25.8990i	0.189044	+	0.189044i	−0.606239	+	0.795283i	$0.707322\pi$
$138$	26.2020	−	26.2020i	0.189870	−	0.189870i
$139$		−	54.2020i		−	0.389943i	−0.980809	−	0.194971i	$-0.937539\pi$
$139$		−	54.2020i		−	0.389943i	0.980809	−	0.194971i	$-0.0624614\pi$
$140$	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	$-0.954160\pi$
$149$		−	42.7673i		−	0.287029i	0.989648	−	0.143515i	$-0.0458404\pi$
$150$	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	0.980410	−	0.196970i	$-0.0631102\pi$
$157$	123.000	+	123.000i	0.783439	+	0.783439i	−0.196970	+	0.980410i	$0.563110\pi$
$158$	−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	−0.874545	−	0.484944i	$-0.838840\pi$
$163$	−63.5051	+	63.5051i	−0.389602	+	0.389602i	0.484944	+	0.874545i	$0.338840\pi$
$164$			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	0.546187	−	0.837663i	$-0.316079\pi$
$167$	−48.6765	−	48.6765i	−0.291476	−	0.291476i	−0.837663	+	0.546187i	$0.816079\pi$
$168$	−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	−0.598310	−	0.801265i	$-0.704161\pi$
$173$	35.1112	−	35.1112i	0.202955	−	0.202955i	0.801265	+	0.598310i	$0.204161\pi$
$174$		−	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	$0.129025\pi$
$179$			141.171i			0.788667i	−0.918967	+	0.394334i	$0.870975\pi$
$180$	−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	−0.801737	−	0.597677i	$-0.796091\pi$
$193$	−39.3837	+	39.3837i	−0.204060	+	0.204060i	0.597677	+	0.801737i	$0.296091\pi$
$194$			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	0.336155	−	0.941807i	$-0.390873\pi$
$197$	−119.313	−	119.313i	−0.605651	−	0.605651i	−0.941807	+	0.336155i	$0.890873\pi$
$198$	−41.3939	+	41.3939i	−0.209060	+	0.209060i
$199$		−	178.565i		−	0.897313i	−0.893704	−	0.448657i	$-0.851903\pi$
$199$		−	178.565i		−	0.897313i	0.893704	−	0.448657i	$-0.148097\pi$
$200$	−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	−0.0622890	−	0.998058i	$-0.519840\pi$
$223$	208.677	−	208.677i	0.935769	−	0.935769i	0.998058	+	0.0622890i	$0.0198400\pi$
$224$		−	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	0.997634	+	0.0687559i	$0.0219030\pi$
$227$	242.070	+	242.070i	1.06639	+	1.06639i	0.0687559	+	0.997634i	$0.478097\pi$
$228$	−63.1918	+	63.1918i	−0.277157	+	0.277157i
$229$			413.939i			1.80759i	0.427963	+	0.903796i	$0.359231\pi$
$229$			413.939i			1.80759i	−0.427963	+	0.903796i	$0.640769\pi$
$230$	−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	−0.555628	−	0.831431i	$-0.687522\pi$
$233$	64.2622	−	64.2622i	0.275804	−	0.275804i	0.831431	+	0.555628i	$0.187522\pi$
$234$		−	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	$-0.895032\pi$
$239$		−	154.788i		−	0.647648i	0.946117	−	0.323824i	$-0.104968\pi$
$240$	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	0.424720	−	0.905325i	$-0.360372\pi$
$257$	−123.515	−	123.515i	−0.480604	−	0.480604i	−0.905325	+	0.424720i	$0.860372\pi$
$258$	−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	−0.646335	−	0.763054i	$-0.723699\pi$
$263$	30.6969	−	30.6969i	0.116718	−	0.116718i	0.763054	+	0.646335i	$0.223699\pi$
$264$		−	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	$0.293939\pi$
$269$			429.151i			1.59536i	−0.603083	+	0.797678i	$0.706061\pi$
$270$	−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	0.619203	−	0.785231i	$-0.287456\pi$
$277$	−45.9898	−	45.9898i	−0.166028	−	0.166028i	−0.785231	+	0.619203i	$0.787456\pi$
$278$	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	−0.0405803	−	0.999176i	$-0.512921\pi$
$283$	271.283	−	271.283i	0.958596	−	0.958596i	0.999176	+	0.0405803i	$0.0129207\pi$
$284$			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	−0.914171	−	0.405329i	$-0.867157\pi$
$293$	−149.091	+	149.091i	−0.508842	+	0.508842i	0.405329	+	0.914171i	$0.367157\pi$
$294$		−	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	0.223295	−	0.974751i	$-0.428319\pi$
$307$	−230.697	−	230.697i	−0.751456	−	0.751456i	−0.974751	+	0.223295i	$0.928319\pi$
$308$	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	−0.262736	−	0.964868i	$-0.584625\pi$
$313$	219.767	−	219.767i	0.702132	−	0.702132i	0.964868	+	0.262736i	$0.0846247\pi$
$314$			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	−0.998686	−	0.0512429i	$-0.983682\pi$
$317$	−332.828	−	332.828i	−1.04993	−	1.04993i	−0.0512429	−	0.998686i	$-0.516318\pi$
$318$	−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	0.825962	−	0.563726i	$-0.190633\pi$
$337$	88.3735	+	88.3735i	0.262236	+	0.262236i	−0.563726	+	0.825962i	$0.690633\pi$
$338$	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	0.943565	−	0.331188i	$-0.107449\pi$
$347$	212.495	+	212.495i	0.612377	+	0.612377i	−0.331188	+	0.943565i	$0.607449\pi$
$348$	63.1918	−	63.1918i	0.181586	−	0.181586i
$349$			280.000i			0.802292i	0.916014	+	0.401146i	$0.131388\pi$
$349$			280.000i			0.802292i	−0.916014	+	0.401146i	$0.868612\pi$
$350$	−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	−0.338845	−	0.940842i	$-0.610036\pi$
$353$	212.505	−	212.505i	0.601997	−	0.601997i	0.940842	+	0.338845i	$0.110036\pi$
$354$			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	$-0.656372\pi$
$359$		−	633.090i		−	1.76348i	0.471734	−	0.881741i	$-0.343628\pi$
$360$	−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	0.241503	−	0.970400i	$-0.422360\pi$
$367$	−267.505	−	267.505i	−0.728897	−	0.728897i	−0.970400	+	0.241503i	$0.922360\pi$
$368$	−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	−0.0106161	+	0.999944i	$0.503379\pi$
$373$	−376.939	+	376.939i	−1.01056	+	1.01056i	−0.999944	+	0.0106161i	$0.996621\pi$
$374$		−	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	$0.0710614\pi$
$379$			167.818i			0.442793i	−0.975184	+	0.221396i	$0.928939\pi$
$380$	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	−0.292559	+	0.956248i	$0.594507\pi$
$383$	−478.293	+	478.293i	−1.24881	+	1.24881i	−0.956248	+	0.292559i	$0.905493\pi$
$384$		−	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	$0.0697634\pi$
$389$			169.151i			0.434836i	−0.976079	+	0.217418i	$0.930237\pi$
$390$	−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	0.614359	−	0.789026i	$-0.289415\pi$
$397$	−69.3429	−	69.3429i	−0.174667	−	0.174667i	−0.789026	+	0.614359i	$0.789415\pi$
$398$	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	$-0.734947\pi$
$409$		−	605.110i		−	1.47949i	0.672889	−	0.739744i	$-0.265053\pi$
$410$	−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	$-0.993938\pi$
$419$		−	15.9592i		−	0.0380887i	0.999819	−	0.0190444i	$-0.00606238\pi$
$420$	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	0.254429	−	0.967091i	$-0.418112\pi$
$433$	528.918	−	528.918i	1.22152	−	1.22152i	0.967091	−	0.254429i	$-0.0818875\pi$
$434$		−	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	$-0.983814\pi$
$439$		−	44.6265i		−	0.101655i	0.998707	−	0.0508275i	$-0.0161859\pi$
$440$	−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	−0.262313	−	0.964983i	$-0.584485\pi$
$443$	311.283	−	311.283i	0.702670	−	0.702670i	0.964983	+	0.262313i	$0.0844853\pi$
$444$		−	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	$0.0502855\pi$
$449$			141.273i			0.314640i	−0.987548	+	0.157320i	$0.949715\pi$
$450$	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	0.729067	−	0.684442i	$-0.239954\pi$
$457$	20.3939	+	20.3939i	0.0446256	+	0.0446256i	−0.684442	+	0.729067i	$0.739954\pi$
$458$	−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	−0.959842	−	0.280543i	$-0.909486\pi$
$463$	−314.515	+	314.515i	−0.679299	+	0.679299i	0.280543	+	0.959842i	$0.409486\pi$
$464$			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	0.755334	−	0.655340i	$-0.227475\pi$
$467$	46.6969	+	46.6969i	0.0999934	+	0.0999934i	−0.655340	+	0.755334i	$0.727475\pi$
$468$	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	$-0.976296\pi$
$479$		−	71.2735i		−	0.148796i	0.997229	−	0.0743982i	$-0.0237036\pi$
$480$	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	0.942061	−	0.335442i	$-0.108886\pi$
$487$	295.423	+	295.423i	0.606619	+	0.606619i	−0.335442	+	0.942061i	$0.608886\pi$
$488$	−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	$-0.575360\pi$
$499$		−	970.161i		−	1.94421i	0.234544	−	0.972105i	$-0.424640\pi$
$500$	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	−0.376204	−	0.926537i	$-0.622771\pi$
$503$	276.817	−	276.817i	0.550333	−	0.550333i	0.926537	+	0.376204i	$0.122771\pi$
$504$			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	$0.345258\pi$
$509$			900.059i			1.76829i	−0.467213	+	0.884145i	$0.654742\pi$
$510$	−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	−0.694844	−	0.719160i	$-0.744527\pi$
$523$	12.7173	−	12.7173i	0.0243162	−	0.0243162i	0.719160	+	0.694844i	$0.244527\pi$
$524$		−	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	0.916177	+	0.400775i	$0.131259\pi$
$547$	720.372	+	720.372i	1.31695	+	1.31695i	0.400775	+	0.916177i	$0.368741\pi$
$548$	−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	0.570283	−	0.821448i	$-0.306834\pi$
$557$	−139.899	−	139.899i	−0.251165	−	0.251165i	−0.821448	+	0.570283i	$0.806834\pi$
$558$	−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	−0.166926	−	0.985969i	$-0.553384\pi$
$563$	461.121	−	461.121i	0.819043	−	0.819043i	0.985969	+	0.166926i	$0.0533841\pi$
$564$			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	$-0.991190\pi$
$569$		−	31.4939i		−	0.0553495i	0.999617	−	0.0276748i	$-0.00881027\pi$
$570$	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	0.983474	−	0.181048i	$-0.0579489\pi$
$577$	463.000	+	463.000i	0.802426	+	0.802426i	−0.181048	+	0.983474i	$0.557949\pi$
$578$	−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	0.981594	−	0.190979i	$-0.0611664\pi$
$587$	464.091	+	464.091i	0.790615	+	0.790615i	−0.190979	+	0.981594i	$0.561166\pi$
$588$	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	−0.598026	−	0.801476i	$-0.704048\pi$
$593$	120.646	−	120.646i	0.203450	−	0.203450i	0.801476	+	0.598026i	$0.204048\pi$
$594$			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	$-0.958130\pi$
$599$		−	157.131i		−	0.262322i	0.991361	−	0.131161i	$-0.0418704\pi$
$600$	−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	0.541084	−	0.840968i	$-0.318014\pi$
$607$	−182.030	−	182.030i	−0.299884	−	0.299884i	−0.840968	+	0.541084i	$0.818014\pi$
$608$	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	−0.348265	+	0.937396i	$0.613229\pi$
$613$	−788.110	+	788.110i	−1.28566	+	1.28566i	−0.937396	+	0.348265i	$0.886771\pi$
$614$		−	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	0.934171	−	0.356826i	$-0.116141\pi$
$617$	356.221	+	356.221i	0.577344	+	0.577344i	−0.356826	+	0.934171i	$0.616141\pi$
$618$	40.4041	−	40.4041i	0.0653788	−	0.0653788i
$619$		−	73.8796i		−	0.119353i	−0.998218	−	0.0596766i	$-0.980993\pi$
$619$		−	73.8796i		−	0.119353i	0.998218	−	0.0596766i	$-0.0190069\pi$
$620$	−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	−0.986820	−	0.161821i	$-0.948263\pi$
$643$	−530.474	+	530.474i	−0.824999	+	0.824999i	0.161821	+	0.986820i	$0.448263\pi$
$644$			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	0.594753	−	0.803908i	$-0.297250\pi$
$647$	−135.323	−	135.323i	−0.209155	−	0.209155i	−0.803908	+	0.594753i	$0.797250\pi$
$648$	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	−0.744237	−	0.667916i	$-0.767187\pi$
$653$	−49.8377	+	49.8377i	−0.0763212	+	0.0763212i	0.667916	+	0.744237i	$0.267187\pi$
$654$		−	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	$-0.949170\pi$
$659$		−	209.576i		−	0.318020i	0.987277	−	0.159010i	$-0.0508303\pi$
$660$	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	−0.963690	−	0.267023i	$-0.913960\pi$
$673$	−468.857	+	468.857i	−0.696667	+	0.696667i	0.267023	+	0.963690i	$0.413960\pi$
$674$			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	0.0331860	−	0.999449i	$-0.489435\pi$
$677$	−654.160	−	654.160i	−0.966263	−	0.966263i	−0.999449	+	0.0331860i	$0.989435\pi$
$678$	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	−0.465961	−	0.884805i	$-0.654291\pi$
$683$	286.070	−	286.070i	0.418844	−	0.418844i	0.884805	+	0.465961i	$0.154291\pi$
$684$			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	$0.115753\pi$
$709$			504.363i			0.711373i	−0.934605	+	0.355686i	$0.884247\pi$
$710$	−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	$0.108757\pi$
$719$			481.816i			0.670120i	−0.942197	+	0.335060i	$0.891243\pi$
$720$	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	−0.996852	−	0.0792856i	$-0.974736\pi$
$727$	−782.352	−	782.352i	−1.07614	−	1.07614i	−0.0792856	−	0.996852i	$-0.525264\pi$
$728$	−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	−0.237888	−	0.971293i	$-0.576455\pi$
$733$	537.586	−	537.586i	0.733405	−	0.733405i	0.971293	+	0.237888i	$0.0764551\pi$
$734$		−	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	$0.190676\pi$
$739$			833.353i			1.12768i	−0.825885	+	0.563838i	$0.809324\pi$
$740$	−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	−0.432813	+	0.901484i	$0.642479\pi$
$743$	−991.383	+	991.383i	−1.33430	+	1.33430i	−0.901484	+	0.432813i	$0.857521\pi$
$744$		−	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	0.682866	−	0.730544i	$-0.260733\pi$
$757$	−36.0918	−	36.0918i	−0.0476775	−	0.0476775i	−0.730544	+	0.682866i	$0.760733\pi$
$758$	−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	$0.0815160\pi$
$769$			389.576i			0.506600i	−0.967388	+	0.253300i	$0.918484\pi$
$770$	−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	−0.920567	−	0.390585i	$-0.872273\pi$
$773$	−409.677	+	409.677i	−0.529983	+	0.529983i	0.390585	+	0.920567i	$0.372273\pi$
$774$			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	0.420469	−	0.907307i	$-0.361866\pi$
$787$	−383.142	−	383.142i	−0.486838	−	0.486838i	−0.907307	+	0.420469i	$0.861866\pi$
$788$	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	0.965827	−	0.259188i	$-0.0834551\pi$
$797$	563.191	+	563.191i	0.706638	+	0.706638i	−0.259188	+	0.965827i	$0.583455\pi$
$798$	−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	$-0.842088\pi$
$809$		−	770.161i		−	0.951992i	0.879448	−	0.475996i	$-0.157912\pi$
$810$	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	−0.816222	−	0.577738i	$-0.803936\pi$
$823$	−196.272	+	196.272i	−0.238484	+	0.238484i	0.577738	+	0.816222i	$0.303936\pi$
$824$			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	0.694582	−	0.719414i	$-0.255589\pi$
$827$	−20.5357	−	20.5357i	−0.0248316	−	0.0248316i	−0.719414	+	0.694582i	$0.755589\pi$
$828$	64.1816	−	64.1816i	0.0775140	−	0.0775140i
$829$			264.465i			0.319017i	0.987197	+	0.159509i	$0.0509910\pi$
$829$			264.465i			0.319017i	−0.987197	+	0.159509i	$0.949009\pi$
$830$	−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	$0.0674841\pi$
$839$			353.090i			0.420846i	−0.977610	+	0.210423i	$0.932516\pi$
$840$	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	−0.695617	−	0.718413i	$-0.744869\pi$
$853$	19.4449	−	19.4449i	0.0227959	−	0.0227959i	0.718413	+	0.695617i	$0.244869\pi$
$854$			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	0.965047	−	0.262078i	$-0.0844079\pi$
$857$	602.444	+	602.444i	0.702968	+	0.702968i	−0.262078	+	0.965047i	$0.584408\pi$
$858$	−432.545	+	432.545i	−0.504132	+	0.504132i
$859$			1099.53i			1.28001i	0.768369	+	0.640007i	$0.221069\pi$
$859$			1099.53i			1.28001i	−0.768369	+	0.640007i	$0.778931\pi$
$860$	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	−0.178792	−	0.983887i	$-0.557219\pi$
$863$	694.797	−	694.797i	0.805095	−	0.805095i	0.983887	+	0.178792i	$0.0572189\pi$
$864$			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	0.957394	+	0.288783i	$0.0932507\pi$
$877$	1092.90	+	1092.90i	1.24618	+	1.24618i	0.288783	+	0.957394i	$0.406749\pi$
$878$	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	0.153953	−	0.988078i	$-0.450800\pi$
$883$	1008.41	−	1008.41i	1.14203	−	1.14203i	0.988078	−	0.153953i	$-0.0492003\pi$
$884$			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	0.247666	−	0.968846i	$-0.420337\pi$
$887$	−639.687	−	639.687i	−0.721180	−	0.721180i	−0.968846	+	0.247666i	$0.920337\pi$
$888$	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	0.0149890	−	0.999888i	$-0.495229\pi$
$907$	−893.303	−	893.303i	−0.984899	−	0.984899i	−0.999888	+	0.0149890i	$0.995229\pi$
$908$	−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	$-0.855970\pi$
$919$		−	803.573i		−	0.874400i	0.899364	−	0.437200i	$-0.144030\pi$
$920$	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	$-0.760292\pi$
$929$		−	1270.64i		−	1.36776i	0.729597	−	0.683878i	$-0.239708\pi$
$930$	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	−0.999332	−	0.0365445i	$-0.988365\pi$
$937$	−970.616	−	970.616i	−1.03588	−	1.03588i	−0.0365445	−	0.999332i	$-0.511635\pi$
$938$	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	0.215110	−	0.976590i	$-0.430989\pi$
$947$	−721.121	−	721.121i	−0.761480	−	0.761480i	−0.976590	+	0.215110i	$0.930989\pi$
$948$	−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	−0.978743	−	0.205091i	$-0.934251\pi$
$953$	−737.291	+	737.291i	−0.773652	+	0.773652i	0.205091	+	0.978743i	$0.434251\pi$
$954$			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	0.999965	−	0.00836361i	$-0.00266225\pi$
$967$	958.879	+	958.879i	0.991601	+	0.991601i	−0.00836361	+	0.999965i	$0.502662\pi$
$968$	−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	0.489413	−	0.872052i	$-0.337211\pi$
$977$	−373.838	−	373.838i	−0.382638	−	0.382638i	−0.872052	+	0.489413i	$0.837211\pi$
$978$	−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	−0.448501	+	0.893783i	$0.648042\pi$
$983$	−1319.46	+	1319.46i	−1.34228	+	1.34228i	−0.893783	+	0.448501i	$0.851958\pi$
$984$			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	0.999922	+	0.0124991i	$0.00397868\pi$
$997$	1009.38	+	1009.38i	1.01242	+	1.01242i	0.0124991	+	0.999922i	$0.496021\pi$
$998$	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.7.2	✓	4
3.2	odd	2		90.3.g.d.37.2		4
4.3	odd	2		240.3.bg.b.97.1		4
5.2	odd	4		150.3.f.b.43.1		4
5.3	odd	4	inner	30.3.f.a.13.2	yes	4
5.4	even	2		150.3.f.b.7.1		4
8.3	odd	2		960.3.bg.g.577.2		4
8.5	even	2		960.3.bg.e.577.1		4
12.11	even	2		720.3.bh.i.577.2		4
15.2	even	4		450.3.g.j.343.1		4
15.8	even	4		90.3.g.d.73.2		4
15.14	odd	2		450.3.g.j.307.1		4
20.3	even	4		240.3.bg.b.193.1		4
20.7	even	4		1200.3.bg.d.193.2		4
20.19	odd	2		1200.3.bg.d.1057.2		4
40.3	even	4		960.3.bg.g.193.2		4
40.13	odd	4		960.3.bg.e.193.1		4
60.23	odd	4		720.3.bh.i.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.f.a.7.2	✓	4	1.1	even	1	trivial
30.3.f.a.13.2	yes	4	5.3	odd	4	inner
90.3.g.d.37.2		4	3.2	odd	2
90.3.g.d.73.2		4	15.8	even	4
150.3.f.b.7.1		4	5.4	even	2
150.3.f.b.43.1		4	5.2	odd	4
240.3.bg.b.97.1		4	4.3	odd	2
240.3.bg.b.193.1		4	20.3	even	4
450.3.g.j.307.1		4	15.14	odd	2
450.3.g.j.343.1		4	15.2	even	4
720.3.bh.i.433.2		4	60.23	odd	4
720.3.bh.i.577.2		4	12.11	even	2
960.3.bg.e.193.1		4	40.13	odd	4
960.3.bg.e.577.1		4	8.5	even	2
960.3.bg.g.193.2		4	40.3	even	4
960.3.bg.g.577.2		4	8.3	odd	2
1200.3.bg.d.193.2		4	20.7	even	4
1200.3.bg.d.1057.2		4	20.19	odd	2

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

L-functions

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