LMFDB - Embedded newform 15.3.f.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,3,Mod(7,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, 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("15.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	15.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:	$0.408720396540$
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			13.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	15.13
Dual form			15.3.f.a.7.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22474 + 2.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} -5.89898i q^{4} +(2.67423 - 4.22474i) q^{5} -5.44949 q^{6} +(-1.44949 + 1.44949i) q^{7} +(4.22474 + 4.22474i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-2.22474 + 2.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} -5.89898i q^{4} +(2.67423 - 4.22474i) q^{5} -5.44949 q^{6} +(-1.44949 + 1.44949i) q^{7} +(4.22474 + 4.22474i) q^{8} +3.00000i q^{9} +(3.44949 + 15.3485i) q^{10} -3.34847 q^{11} +(7.22474 - 7.22474i) q^{12} +(-10.4495 - 10.4495i) q^{13} -6.44949i q^{14} +(8.44949 - 1.89898i) q^{15} +4.79796 q^{16} +(-2.65153 + 2.65153i) q^{17} +(-6.67423 - 6.67423i) q^{18} +20.6969i q^{19} +(-24.9217 - 15.7753i) q^{20} -3.55051 q^{21} +(7.44949 - 7.44949i) q^{22} +(16.4495 + 16.4495i) q^{23} +10.3485i q^{24} +(-10.6969 - 22.5959i) q^{25} +46.4949 q^{26} +(-3.67423 + 3.67423i) q^{27} +(8.55051 + 8.55051i) q^{28} -0.853572i q^{29} +(-14.5732 + 23.0227i) q^{30} -18.6969 q^{31} +(-27.5732 + 27.5732i) q^{32} +(-4.10102 - 4.10102i) q^{33} -11.7980i q^{34} +(2.24745 + 10.0000i) q^{35} +17.6969 q^{36} +(38.0454 - 38.0454i) q^{37} +(-46.0454 - 46.0454i) q^{38} -25.5959i q^{39} +(29.1464 - 6.55051i) q^{40} -28.6969 q^{41} +(7.89898 - 7.89898i) q^{42} +(22.4949 + 22.4949i) q^{43} +19.7526i q^{44} +(12.6742 + 8.02270i) q^{45} -73.1918 q^{46} +(19.7526 - 19.7526i) q^{47} +(5.87628 + 5.87628i) q^{48} +44.7980i q^{49} +(74.0681 + 26.4722i) q^{50} -6.49490 q^{51} +(-61.6413 + 61.6413i) q^{52} +(28.6969 + 28.6969i) q^{53} -16.3485i q^{54} +(-8.95459 + 14.1464i) q^{55} -12.2474 q^{56} +(-25.3485 + 25.3485i) q^{57} +(1.89898 + 1.89898i) q^{58} -111.934i q^{59} +(-11.2020 - 49.8434i) q^{60} +94.0908 q^{61} +(41.5959 - 41.5959i) q^{62} +(-4.34847 - 4.34847i) q^{63} -103.495i q^{64} +(-72.0908 + 16.2020i) q^{65} +18.2474 q^{66} +(-54.8990 + 54.8990i) q^{67} +(15.6413 + 15.6413i) q^{68} +40.2929i q^{69} +(-27.2474 - 17.2474i) q^{70} -68.0000 q^{71} +(-12.6742 + 12.6742i) q^{72} +(-39.7878 - 39.7878i) q^{73} +169.283i q^{74} +(14.5732 - 40.7753i) q^{75} +122.091 q^{76} +(4.85357 - 4.85357i) q^{77} +(56.9444 + 56.9444i) q^{78} -24.4949i q^{79} +(12.8309 - 20.2702i) q^{80} -9.00000 q^{81} +(63.8434 - 63.8434i) q^{82} +(-21.1464 - 21.1464i) q^{83} +20.9444i q^{84} +(4.11123 + 18.2929i) q^{85} -100.091 q^{86} +(1.04541 - 1.04541i) q^{87} +(-14.1464 - 14.1464i) q^{88} +94.1816i q^{89} +(-46.0454 + 10.3485i) q^{90} +30.2929 q^{91} +(97.0352 - 97.0352i) q^{92} +(-22.8990 - 22.8990i) q^{93} +87.8888i q^{94} +(87.4393 + 55.3485i) q^{95} -67.5403 q^{96} +(14.5959 - 14.5959i) q^{97} +(-99.6640 - 99.6640i) q^{98} -10.0454i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{5} - 12 q^{6} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^5 - 12 * q^6 + 4 * q^7 + 12 * q^8	$ 4 q - 4 q^{2} - 4 q^{5} - 12 q^{6} + 4 q^{7} + 12 q^{8} + 4 q^{10} + 16 q^{11} + 24 q^{12} - 32 q^{13} + 24 q^{15} - 20 q^{16} - 40 q^{17} - 12 q^{18} - 36 q^{20} - 24 q^{21} + 20 q^{22} + 56 q^{23} + 16 q^{25} + 88 q^{26} + 44 q^{28} - 24 q^{30} - 16 q^{31} - 76 q^{32} - 36 q^{33} - 40 q^{35} + 12 q^{36} + 64 q^{37} - 96 q^{38} + 48 q^{40} - 56 q^{41} + 12 q^{42} - 8 q^{43} + 36 q^{45} - 136 q^{46} + 128 q^{47} + 48 q^{48} + 164 q^{50} + 72 q^{51} - 80 q^{52} + 56 q^{53} - 124 q^{55} - 72 q^{57} - 12 q^{58} - 84 q^{60} + 200 q^{61} + 88 q^{62} + 12 q^{63} - 112 q^{65} + 24 q^{66} - 200 q^{67} - 104 q^{68} - 60 q^{70} - 272 q^{71} - 36 q^{72} + 76 q^{73} + 24 q^{75} + 312 q^{76} + 88 q^{77} + 120 q^{78} + 164 q^{80} - 36 q^{81} + 128 q^{82} - 16 q^{83} + 232 q^{85} - 224 q^{86} - 84 q^{87} + 12 q^{88} - 96 q^{90} - 16 q^{91} + 104 q^{92} - 72 q^{93} + 144 q^{95} - 84 q^{96} - 20 q^{97} - 188 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^5 - 12 * q^6 + 4 * q^7 + 12 * q^8 + 4 * q^10 + 16 * q^11 + 24 * q^12 - 32 * q^13 + 24 * q^15 - 20 * q^16 - 40 * q^17 - 12 * q^18 - 36 * q^20 - 24 * q^21 + 20 * q^22 + 56 * q^23 + 16 * q^25 + 88 * q^26 + 44 * q^28 - 24 * q^30 - 16 * q^31 - 76 * q^32 - 36 * q^33 - 40 * q^35 + 12 * q^36 + 64 * q^37 - 96 * q^38 + 48 * q^40 - 56 * q^41 + 12 * q^42 - 8 * q^43 + 36 * q^45 - 136 * q^46 + 128 * q^47 + 48 * q^48 + 164 * q^50 + 72 * q^51 - 80 * q^52 + 56 * q^53 - 124 * q^55 - 72 * q^57 - 12 * q^58 - 84 * q^60 + 200 * q^61 + 88 * q^62 + 12 * q^63 - 112 * q^65 + 24 * q^66 - 200 * q^67 - 104 * q^68 - 60 * q^70 - 272 * q^71 - 36 * q^72 + 76 * q^73 + 24 * q^75 + 312 * q^76 + 88 * q^77 + 120 * q^78 + 164 * q^80 - 36 * q^81 + 128 * q^82 - 16 * q^83 + 232 * q^85 - 224 * q^86 - 84 * q^87 + 12 * q^88 - 96 * q^90 - 16 * q^91 + 104 * q^92 - 72 * q^93 + 144 * q^95 - 84 * q^96 - 20 * q^97 - 188 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.22474	+	2.22474i	−1.11237	+	1.11237i	−0.119543	+	0.992829i	$0.538143\pi$
$2$	−2.22474	+	2.22474i	−1.11237	+	1.11237i	−0.992829	+	0.119543i	$0.961857\pi$
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	5.89898i		−	1.47474i
$5$	2.67423	−	4.22474i	0.534847	−	0.844949i
$5$	2.67423	−	4.22474i	0.534847	−	0.844949i
$6$	−5.44949			−0.908248
$7$	−1.44949	+	1.44949i	−0.207070	+	0.207070i	−0.803021	−	0.595951i	$-0.796775\pi$
$7$	−1.44949	+	1.44949i	−0.207070	+	0.207070i	0.595951	+	0.803021i	$0.296775\pi$
$8$	4.22474	+	4.22474i	0.528093	+	0.528093i
$9$			3.00000i			0.333333i
$10$	3.44949	+	15.3485i	0.344949	+	1.53485i
$11$	−3.34847			−0.304406			−0.152203	−	0.988349i	$-0.548637\pi$
$11$	−3.34847			−0.304406			−0.152203	+	0.988349i	$0.548637\pi$
$12$	7.22474	−	7.22474i	0.602062	−	0.602062i
$13$	−10.4495	−	10.4495i	−0.803807	−	0.803807i	0.179881	−	0.983688i	$-0.442429\pi$
$13$	−10.4495	−	10.4495i	−0.803807	−	0.803807i	−0.983688	+	0.179881i	$0.942429\pi$
$14$		−	6.44949i		−	0.460678i
$15$	8.44949	−	1.89898i	0.563299	−	0.126599i
$16$	4.79796			0.299872
$17$	−2.65153	+	2.65153i	−0.155972	+	0.155972i	−0.780779	−	0.624807i	$-0.785178\pi$
$17$	−2.65153	+	2.65153i	−0.155972	+	0.155972i	0.624807	+	0.780779i	$0.285178\pi$
$18$	−6.67423	−	6.67423i	−0.370791	−	0.370791i
$19$			20.6969i			1.08931i	0.838659	+	0.544656i	$0.183340\pi$
$19$			20.6969i			1.08931i	−0.838659	+	0.544656i	$0.816660\pi$
$20$	−24.9217	−	15.7753i	−1.24608	−	0.788763i
$21$	−3.55051			−0.169072
$22$	7.44949	−	7.44949i	0.338613	−	0.338613i
$23$	16.4495	+	16.4495i	0.715195	+	0.715195i	0.967617	−	0.252422i	$-0.0812271\pi$
$23$	16.4495	+	16.4495i	0.715195	+	0.715195i	−0.252422	+	0.967617i	$0.581227\pi$
$24$			10.3485i			0.431186i
$25$	−10.6969	−	22.5959i	−0.427878	−	0.903837i
$26$	46.4949			1.78827
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	8.55051	+	8.55051i	0.305375	+	0.305375i
$29$		−	0.853572i		−	0.0294335i	−0.999892	−	0.0147168i	$-0.995315\pi$
$29$		−	0.853572i		−	0.0294335i	0.999892	−	0.0147168i	$-0.00468466\pi$
$30$	−14.5732	+	23.0227i	−0.485774	+	0.767423i
$31$	−18.6969			−0.603127			−0.301564	−	0.953446i	$-0.597509\pi$
$31$	−18.6969			−0.603127			−0.301564	+	0.953446i	$0.597509\pi$
$32$	−27.5732	+	27.5732i	−0.861663	+	0.861663i
$33$	−4.10102	−	4.10102i	−0.124273	−	0.124273i
$34$		−	11.7980i		−	0.346999i
$35$	2.24745	+	10.0000i	0.0642128	+	0.285714i
$36$	17.6969			0.491582
$37$	38.0454	−	38.0454i	1.02825	−	1.02825i	0.0286652	−	0.999589i	$-0.490874\pi$
$37$	38.0454	−	38.0454i	1.02825	−	1.02825i	0.999589	−	0.0286652i	$-0.00912566\pi$
$38$	−46.0454	−	46.0454i	−1.21172	−	1.21172i
$39$		−	25.5959i		−	0.656306i
$40$	29.1464	−	6.55051i	0.728661	−	0.163763i
$41$	−28.6969			−0.699925			−0.349963	−	0.936764i	$-0.613806\pi$
$41$	−28.6969			−0.699925			−0.349963	+	0.936764i	$0.613806\pi$
$42$	7.89898	−	7.89898i	0.188071	−	0.188071i
$43$	22.4949	+	22.4949i	0.523137	+	0.523137i	0.918517	−	0.395380i	$-0.129387\pi$
$43$	22.4949	+	22.4949i	0.523137	+	0.523137i	−0.395380	+	0.918517i	$0.629387\pi$
$44$			19.7526i			0.448922i
$45$	12.6742	+	8.02270i	0.281650	+	0.178282i
$46$	−73.1918			−1.59113
$47$	19.7526	−	19.7526i	0.420267	−	0.420267i	−0.465029	−	0.885296i	$-0.653956\pi$
$47$	19.7526	−	19.7526i	0.420267	−	0.420267i	0.885296	+	0.465029i	$0.153956\pi$
$48$	5.87628	+	5.87628i	0.122422	+	0.122422i
$49$			44.7980i			0.914244i
$50$	74.0681	+	26.4722i	1.48136	+	0.529444i
$51$	−6.49490			−0.127351
$52$	−61.6413	+	61.6413i	−1.18541	+	1.18541i
$53$	28.6969	+	28.6969i	0.541452	+	0.541452i	0.923954	−	0.382503i	$-0.124938\pi$
$53$	28.6969	+	28.6969i	0.541452	+	0.541452i	−0.382503	+	0.923954i	$0.624938\pi$
$54$		−	16.3485i		−	0.302749i
$55$	−8.95459	+	14.1464i	−0.162811	+	0.257208i
$56$	−12.2474			−0.218704
$57$	−25.3485	+	25.3485i	−0.444710	+	0.444710i
$58$	1.89898	+	1.89898i	0.0327410	+	0.0327410i
$59$		−	111.934i		−	1.89719i	−0.316493	−	0.948595i	$-0.602505\pi$
$59$		−	111.934i		−	1.89719i	0.316493	−	0.948595i	$-0.397495\pi$
$60$	−11.2020	−	49.8434i	−0.186701	−	0.830723i
$61$	94.0908			1.54247			0.771236	−	0.636549i	$-0.219639\pi$
$61$	94.0908			1.54247			0.771236	+	0.636549i	$0.219639\pi$
$62$	41.5959	−	41.5959i	0.670902	−	0.670902i
$63$	−4.34847	−	4.34847i	−0.0690233	−	0.0690233i
$64$		−	103.495i		−	1.61711i
$65$	−72.0908	+	16.2020i	−1.10909	+	0.249262i
$66$	18.2474			0.276476
$67$	−54.8990	+	54.8990i	−0.819388	+	0.819388i	−0.986019	−	0.166631i	$-0.946711\pi$
$67$	−54.8990	+	54.8990i	−0.819388	+	0.819388i	0.166631	+	0.986019i	$0.446711\pi$
$68$	15.6413	+	15.6413i	0.230019	+	0.230019i
$69$			40.2929i			0.583954i
$70$	−27.2474	−	17.2474i	−0.389249	−	0.246392i
$71$	−68.0000			−0.957746			−0.478873	−	0.877884i	$-0.658955\pi$
$71$	−68.0000			−0.957746			−0.478873	+	0.877884i	$0.658955\pi$
$72$	−12.6742	+	12.6742i	−0.176031	+	0.176031i
$73$	−39.7878	−	39.7878i	−0.545038	−	0.545038i	0.379964	−	0.925001i	$-0.375936\pi$
$73$	−39.7878	−	39.7878i	−0.545038	−	0.545038i	−0.925001	+	0.379964i	$0.875936\pi$
$74$			169.283i			2.28760i
$75$	14.5732	−	40.7753i	0.194310	−	0.543670i
$76$	122.091			1.60646
$77$	4.85357	−	4.85357i	0.0630334	−	0.0630334i
$78$	56.9444	+	56.9444i	0.730056	+	0.730056i
$79$		−	24.4949i		−	0.310062i	−0.987910	−	0.155031i	$-0.950452\pi$
$79$		−	24.4949i		−	0.310062i	0.987910	−	0.155031i	$-0.0495477\pi$
$80$	12.8309	−	20.2702i	0.160386	−	0.253377i
$81$	−9.00000			−0.111111
$82$	63.8434	−	63.8434i	0.778578	−	0.778578i
$83$	−21.1464	−	21.1464i	−0.254776	−	0.254776i	0.568149	−	0.822926i	$-0.307660\pi$
$83$	−21.1464	−	21.1464i	−0.254776	−	0.254776i	−0.822926	+	0.568149i	$0.807660\pi$
$84$			20.9444i			0.249338i
$85$	4.11123	+	18.2929i	0.0483674	+	0.215210i
$86$	−100.091			−1.16385
$87$	1.04541	−	1.04541i	0.0120162	−	0.0120162i
$88$	−14.1464	−	14.1464i	−0.160755	−	0.160755i
$89$			94.1816i			1.05822i	0.848553	+	0.529110i	$0.177474\pi$
$89$			94.1816i			1.05822i	−0.848553	+	0.529110i	$0.822526\pi$
$90$	−46.0454	+	10.3485i	−0.511616	+	0.114983i
$91$	30.2929			0.332889
$92$	97.0352	−	97.0352i	1.05473	−	1.05473i
$93$	−22.8990	−	22.8990i	−0.246226	−	0.246226i
$94$			87.8888i			0.934987i
$95$	87.4393	+	55.3485i	0.920414	+	0.582615i
$96$	−67.5403			−0.703545
$97$	14.5959	−	14.5959i	0.150473	−	0.150473i	−0.627856	−	0.778329i	$-0.716067\pi$
$97$	14.5959	−	14.5959i	0.150473	−	0.150473i	0.778329	+	0.627856i	$0.216067\pi$
$98$	−99.6640	−	99.6640i	−1.01698	−	1.01698i
$99$		−	10.0454i		−	0.101469i
$100$	−133.293	+	63.1010i	−1.33293	+	0.631010i
$101$	173.621			1.71902			0.859509	−	0.511120i	$-0.170769\pi$
$101$	173.621			1.71902			0.859509	+	0.511120i	$0.170769\pi$
$102$	14.4495	−	14.4495i	0.141662	−	0.141662i
$103$	−64.7526	−	64.7526i	−0.628666	−	0.628666i	0.319067	−	0.947732i	$-0.396631\pi$
$103$	−64.7526	−	64.7526i	−0.628666	−	0.628666i	−0.947732	+	0.319067i	$0.896631\pi$
$104$		−	88.2929i		−	0.848970i
$105$	−9.49490	+	15.0000i	−0.0904276	+	0.142857i
$106$	−127.687			−1.20459
$107$	−4.74235	+	4.74235i	−0.0443210	+	0.0443210i	−0.728920	−	0.684599i	$-0.759977\pi$
$107$	−4.74235	+	4.74235i	−0.0443210	+	0.0443210i	0.684599	+	0.728920i	$0.259977\pi$
$108$	21.6742	+	21.6742i	0.200687	+	0.200687i
$109$		−	39.3031i		−	0.360579i	−0.983614	−	0.180289i	$-0.942297\pi$
$109$		−	39.3031i		−	0.360579i	0.983614	−	0.180289i	$-0.0577034\pi$
$110$	−11.5505	−	51.3939i	−0.105005	−	0.467217i
$111$	93.1918			0.839566
$112$	−6.95459	+	6.95459i	−0.0620946	+	0.0620946i
$113$	14.3587	+	14.3587i	0.127068	+	0.127068i	0.767781	−	0.640713i	$-0.221361\pi$
$113$	14.3587	+	14.3587i	0.127068	+	0.127068i	−0.640713	+	0.767781i	$0.721361\pi$
$114$		−	112.788i		−	0.989366i
$115$	113.485	−	25.5051i	0.986823	−	0.221784i
$116$	−5.03520			−0.0434069
$117$	31.3485	−	31.3485i	0.267936	−	0.267936i
$118$	249.025	+	249.025i	2.11038	+	2.11038i
$119$		−	7.68673i		−	0.0645944i
$120$	43.7196	+	27.6742i	0.364330	+	0.230619i
$121$	−109.788			−0.907337
$122$	−209.328	+	209.328i	−1.71580	+	1.71580i
$123$	−35.1464	−	35.1464i	−0.285743	−	0.285743i
$124$			110.293i			0.889459i
$125$	−124.068	−	15.2350i	−0.992545	−	0.121880i
$126$	19.3485			0.153559
$127$	−114.621	+	114.621i	−0.902527	+	0.902527i	−0.995654	−	0.0931273i	$-0.970314\pi$
$127$	−114.621	+	114.621i	−0.902527	+	0.902527i	0.0931273	+	0.995654i	$0.470314\pi$
$128$	119.957	+	119.957i	0.937163	+	0.937163i
$129$			55.1010i			0.427140i
$130$	124.338	−	196.429i	0.956448	−	1.51099i
$131$	−26.1362			−0.199513			−0.0997566	−	0.995012i	$-0.531806\pi$
$131$	−26.1362			−0.199513			−0.0997566	+	0.995012i	$0.531806\pi$
$132$	−24.1918	+	24.1918i	−0.183271	+	0.183271i
$133$	−30.0000	−	30.0000i	−0.225564	−	0.225564i
$134$		−	244.272i		−	1.82293i
$135$	5.69694	+	25.3485i	0.0421995	+	0.187766i
$136$	−22.4041			−0.164736
$137$	14.6311	−	14.6311i	0.106796	−	0.106796i	−0.651689	−	0.758486i	$-0.725939\pi$
$137$	14.6311	−	14.6311i	0.106796	−	0.106796i	0.758486	+	0.651689i	$0.225939\pi$
$138$	−89.6413	−	89.6413i	−0.649575	−	0.649575i
$139$		−	83.1714i		−	0.598356i	−0.954197	−	0.299178i	$-0.903288\pi$
$139$		−	83.1714i		−	0.598356i	0.954197	−	0.299178i	$-0.0967124\pi$
$140$	58.9898	−	13.2577i	0.421356	−	0.0946975i
$141$	48.3837			0.343147
$142$	151.283	−	151.283i	1.06537	−	1.06537i
$143$	34.9898	+	34.9898i	0.244684	+	0.244684i
$144$			14.3939i			0.0999575i
$145$	−3.60612	−	2.28265i	−0.0248698	−	0.0157424i
$146$	177.035			1.21257
$147$	−54.8661	+	54.8661i	−0.373239	+	0.373239i
$148$	−224.429	−	224.429i	−1.51641	−	1.51641i
$149$		−	119.146i		−	0.799640i	−0.916594	−	0.399820i	$-0.869073\pi$
$149$		−	119.146i		−	0.799640i	0.916594	−	0.399820i	$-0.130927\pi$
$150$	58.2929	+	123.136i	0.388619	+	0.820908i
$151$	−144.969			−0.960062			−0.480031	−	0.877251i	$-0.659375\pi$
$151$	−144.969			−0.960062			−0.480031	+	0.877251i	$0.659375\pi$
$152$	−87.4393	+	87.4393i	−0.575258	+	0.575258i
$153$	−7.95459	−	7.95459i	−0.0519908	−	0.0519908i
$154$			21.5959i			0.140233i
$155$	−50.0000	+	78.9898i	−0.322581	+	0.509612i
$156$	−150.990			−0.967883
$157$	51.1464	−	51.1464i	0.325773	−	0.325773i	−0.525203	−	0.850977i	$-0.676011\pi$
$157$	51.1464	−	51.1464i	0.325773	−	0.325773i	0.850977	+	0.525203i	$0.176011\pi$
$158$	54.4949	+	54.4949i	0.344904	+	0.344904i
$159$			70.2929i			0.442093i
$160$	42.7526	+	190.227i	0.267203	+	1.18892i
$161$	−47.6867			−0.296191
$162$	20.0227	−	20.0227i	0.123597	−	0.123597i
$163$	189.394	+	189.394i	1.16193	+	1.16193i	0.984054	+	0.177872i	$0.0569213\pi$
$163$	189.394	+	189.394i	1.16193	+	1.16193i	0.177872	+	0.984054i	$0.443079\pi$
$164$			169.283i			1.03221i
$165$	−28.2929	+	6.35867i	−0.171472	+	0.0385374i
$166$	94.0908			0.566812
$167$	97.0352	−	97.0352i	0.581049	−	0.581049i	−0.354142	−	0.935192i	$-0.615227\pi$
$167$	97.0352	−	97.0352i	0.581049	−	0.581049i	0.935192	+	0.354142i	$0.115227\pi$
$168$	−15.0000	−	15.0000i	−0.0892857	−	0.0892857i
$169$			49.3837i			0.292211i
$170$	−49.8434	−	31.5505i	−0.293196	−	0.185591i
$171$	−62.0908			−0.363104
$172$	132.697	−	132.697i	0.771494	−	0.771494i
$173$	−34.6311	−	34.6311i	−0.200180	−	0.200180i	0.599897	−	0.800077i	$-0.295208\pi$
$173$	−34.6311	−	34.6311i	−0.200180	−	0.200180i	−0.800077	+	0.599897i	$0.795208\pi$
$174$			4.65153i			0.0267329i
$175$	48.2577	+	17.2474i	0.275758	+	0.0985568i
$176$	−16.0658			−0.0912831
$177$	137.091	−	137.091i	0.774524	−	0.774524i
$178$	−209.530	−	209.530i	−1.17714	−	1.17714i
$179$			183.712i			1.02632i	0.858292	+	0.513161i	$0.171526\pi$
$179$			183.712i			1.02632i	−0.858292	+	0.513161i	$0.828474\pi$
$180$	47.3258	−	74.7650i	0.262921	−	0.415361i
$181$	−21.7276			−0.120042			−0.0600209	−	0.998197i	$-0.519117\pi$
$181$	−21.7276			−0.120042			−0.0600209	+	0.998197i	$0.519117\pi$
$182$	−67.3939	+	67.3939i	−0.370296	+	0.370296i
$183$	115.237	+	115.237i	0.629712	+	0.629712i
$184$			138.990i			0.755379i
$185$	−58.9898	−	262.474i	−0.318864	−	1.41878i
$186$	101.889			0.547789
$187$	8.87857	−	8.87857i	0.0474790	−	0.0474790i
$188$	−116.520	−	116.520i	−0.619787	−	0.619787i
$189$		−	10.6515i		−	0.0563573i
$190$	−317.666	+	71.3939i	−1.67193	+	0.375757i
$191$	−40.0908			−0.209900			−0.104950	−	0.994478i	$-0.533468\pi$
$191$	−40.0908			−0.209900			−0.104950	+	0.994478i	$0.533468\pi$
$192$	126.755	−	126.755i	0.660181	−	0.660181i
$193$	77.5653	+	77.5653i	0.401893	+	0.401893i	0.878900	−	0.477007i	$-0.158278\pi$
$193$	77.5653	+	77.5653i	0.401893	+	0.401893i	−0.477007	+	0.878900i	$0.658278\pi$
$194$			64.9444i			0.334765i
$195$	−108.136	−	68.4495i	−0.554545	−	0.351023i
$196$	264.262			1.34828
$197$	−67.3031	+	67.3031i	−0.341640	+	0.341640i	−0.856984	−	0.515344i	$-0.827664\pi$
$197$	−67.3031	+	67.3031i	−0.341640	+	0.341640i	0.515344	+	0.856984i	$0.327664\pi$
$198$	22.3485	+	22.3485i	0.112871	+	0.112871i
$199$		−	251.394i		−	1.26329i	−0.775259	−	0.631643i	$-0.782381\pi$
$199$		−	251.394i		−	1.26329i	0.775259	−	0.631643i	$-0.217619\pi$
$200$	50.2702	−	140.654i	0.251351	−	0.703269i
$201$	−134.474			−0.669027
$202$	−386.262	+	386.262i	−1.91219	+	1.91219i
$203$	1.23724	+	1.23724i	0.00609480	+	0.00609480i
$204$			38.3133i			0.187810i
$205$	−76.7423	+	121.237i	−0.374353	+	0.591401i
$206$	288.116			1.39862
$207$	−49.3485	+	49.3485i	−0.238398	+	0.238398i
$208$	−50.1362	−	50.1362i	−0.241040	−	0.241040i
$209$		−	69.3031i		−	0.331594i
$210$	−12.2474	−	54.4949i	−0.0583212	−	0.259500i
$211$	264.788			1.25492			0.627459	−	0.778649i	$-0.284095\pi$
$211$	264.788			1.25492			0.627459	+	0.778649i	$0.284095\pi$
$212$	169.283	−	169.283i	0.798503	−	0.798503i
$213$	−83.2827	−	83.2827i	−0.390998	−	0.390998i
$214$		−	21.1010i		−	0.0986029i
$215$	155.192	−	34.8786i	0.721822	−	0.162226i
$216$	−31.0454			−0.143729
$217$	27.1010	−	27.1010i	0.124889	−	0.124889i
$218$	87.4393	+	87.4393i	0.401098	+	0.401098i
$219$		−	97.4597i		−	0.445021i
$220$	83.4495	+	52.8230i	0.379316	+	0.240104i
$221$	55.4143			0.250743
$222$	−207.328	+	207.328i	−0.933910	+	0.933910i
$223$	−33.4291	−	33.4291i	−0.149906	−	0.149906i	0.628170	−	0.778076i	$-0.283804\pi$
$223$	−33.4291	−	33.4291i	−0.149906	−	0.149906i	−0.778076	+	0.628170i	$0.783804\pi$
$224$		−	79.9342i		−	0.356849i
$225$	67.7878	−	32.0908i	0.301279	−	0.142626i
$226$	−63.8888			−0.282694
$227$	−21.1714	+	21.1714i	−0.0932662	+	0.0932662i	−0.752200	−	0.658934i	$-0.771008\pi$
$227$	−21.1714	+	21.1714i	−0.0932662	+	0.0932662i	0.658934	+	0.752200i	$0.271008\pi$
$228$	149.530	+	149.530i	0.655834	+	0.655834i
$229$			243.798i			1.06462i	0.846550	+	0.532310i	$0.178676\pi$
$229$			243.798i			1.06462i	−0.846550	+	0.532310i	$0.821324\pi$
$230$	−195.732	+	309.217i	−0.851009	+	1.34442i
$231$	11.8888			0.0514666
$232$	3.60612	−	3.60612i	0.0155436	−	0.0155436i
$233$	161.712	+	161.712i	0.694042	+	0.694042i	0.963119	−	0.269077i	$-0.0867186\pi$
$233$	161.712	+	161.712i	0.694042	+	0.694042i	−0.269077	+	0.963119i	$0.586719\pi$
$234$			139.485i			0.596088i
$235$	−30.6265	−	136.272i	−0.130326	−	0.579883i
$236$	−660.297			−2.79787
$237$	30.0000	−	30.0000i	0.126582	−	0.126582i
$238$	17.1010	+	17.1010i	0.0718530	+	0.0718530i
$239$			326.202i			1.36486i	0.730950	+	0.682431i	$0.239077\pi$
$239$			326.202i			1.36486i	−0.730950	+	0.682431i	$0.760923\pi$
$240$	40.5403	−	9.11123i	0.168918	−	0.0379634i
$241$	−133.576			−0.554255			−0.277128	−	0.960833i	$-0.589382\pi$
$241$	−133.576			−0.554255			−0.277128	+	0.960833i	$0.589382\pi$
$242$	244.250	−	244.250i	1.00930	−	1.00930i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$		−	555.040i		−	2.27475i
$245$	189.260	+	119.800i	0.772490	+	0.488981i
$246$	156.384			0.635706
$247$	216.272	−	216.272i	0.875597	−	0.875597i
$248$	−78.9898	−	78.9898i	−0.318507	−	0.318507i
$249$		−	51.7980i		−	0.208024i
$250$	309.914	−	242.126i	1.23966	−	0.968504i
$251$	−404.742			−1.61252			−0.806260	−	0.591562i	$-0.798512\pi$
$251$	−404.742			−1.61252			−0.806260	+	0.591562i	$0.798512\pi$
$252$	−25.6515	+	25.6515i	−0.101792	+	0.101792i
$253$	−55.0806	−	55.0806i	−0.217710	−	0.217710i
$254$		−	510.005i		−	2.00789i
$255$	−17.3689	+	27.4393i	−0.0681133	+	0.107605i
$256$	−119.767			−0.467841
$257$	−89.2372	+	89.2372i	−0.347227	+	0.347227i	−0.859076	−	0.511849i	$-0.828961\pi$
$257$	−89.2372	+	89.2372i	−0.347227	+	0.347227i	0.511849	+	0.859076i	$0.328961\pi$
$258$	−122.586	−	122.586i	−0.475138	−	0.475138i
$259$			110.293i			0.425841i
$260$	95.5755	+	425.262i	0.367598	+	1.63562i
$261$	2.56072			0.00981117
$262$	58.1464	−	58.1464i	0.221933	−	0.221933i
$263$	−341.843	−	341.843i	−1.29978	−	1.29978i	−0.928532	−	0.371253i	$-0.878928\pi$
$263$	−341.843	−	341.843i	−1.29978	−	1.29978i	−0.371253	−	0.928532i	$-0.621072\pi$
$264$		−	34.6515i		−	0.131256i
$265$	197.980	−	44.4949i	0.747093	−	0.167905i
$266$	133.485			0.501822
$267$	−115.348	+	115.348i	−0.432017	+	0.432017i
$268$	323.848	+	323.848i	1.20839	+	1.20839i
$269$			3.50052i			0.0130131i	0.999979	+	0.00650653i	$0.00207111\pi$
$269$			3.50052i			0.0130131i	−0.999979	+	0.00650653i	$0.997929\pi$
$270$	−69.0681	−	43.7196i	−0.255808	−	0.161925i
$271$	−103.576			−0.382197			−0.191099	−	0.981571i	$-0.561205\pi$
$271$	−103.576			−0.382197			−0.191099	+	0.981571i	$0.561205\pi$
$272$	−12.7219	+	12.7219i	−0.0467718	+	0.0467718i
$273$	37.1010	+	37.1010i	0.135901	+	0.135901i
$274$			65.1010i			0.237595i
$275$	35.8184	+	75.6617i	0.130249	+	0.275134i
$276$	237.687			0.861184
$277$	−285.510	+	285.510i	−1.03072	+	1.03072i	−0.0312080	+	0.999513i	$0.509935\pi$
$277$	−285.510	+	285.510i	−1.03072	+	1.03072i	−0.999513	+	0.0312080i	$0.990065\pi$
$278$	185.035	+	185.035i	0.665594	+	0.665594i
$279$		−	56.0908i		−	0.201042i
$280$	−32.7526	+	51.7423i	−0.116973	+	0.184794i
$281$	372.697			1.32632			0.663162	−	0.748476i	$-0.269214\pi$
$281$	372.697			1.32632			0.663162	+	0.748476i	$0.269214\pi$
$282$	−107.641	+	107.641i	−0.381707	+	0.381707i
$283$	−77.1918	−	77.1918i	−0.272763	−	0.272763i	0.557449	−	0.830211i	$-0.311780\pi$
$283$	−77.1918	−	77.1918i	−0.272763	−	0.272763i	−0.830211	+	0.557449i	$0.811780\pi$
$284$			401.131i			1.41243i
$285$	39.3031	+	174.879i	0.137905	+	0.613609i
$286$	−155.687			−0.544359
$287$	41.5959	−	41.5959i	0.144934	−	0.144934i
$288$	−82.7196	−	82.7196i	−0.287221	−	0.287221i
$289$			274.939i			0.951345i
$290$	13.1010	−	2.94439i	0.0451759	−	0.0101531i
$291$	35.7526			0.122861
$292$	−234.707	+	234.707i	−0.803792	+	0.803792i
$293$	−236.565	−	236.565i	−0.807390	−	0.807390i	0.176848	−	0.984238i	$-0.443410\pi$
$293$	−236.565	−	236.565i	−0.807390	−	0.807390i	−0.984238	+	0.176848i	$0.943410\pi$
$294$		−	244.126i		−	0.830361i
$295$	−472.893	−	299.338i	−1.60303	−	1.01471i
$296$	321.464			1.08603
$297$	12.3031	−	12.3031i	0.0414244	−	0.0414244i
$298$	265.070	+	265.070i	0.889498	+	0.889498i
$299$		−	343.778i		−	1.14976i
$300$	−240.532	−	85.9671i	−0.801775	−	0.286557i
$301$	−65.2122			−0.216652
$302$	322.520	−	322.520i	1.06795	−	1.06795i
$303$	212.641	+	212.641i	0.701787	+	0.701787i
$304$			99.3031i			0.326655i
$305$	251.621	−	397.510i	0.824987	−	1.30331i
$306$	35.3939			0.115666
$307$	168.969	−	168.969i	0.550389	−	0.550389i	−0.376164	−	0.926553i	$-0.622757\pi$
$307$	168.969	−	168.969i	0.550389	−	0.550389i	0.926553	+	0.376164i	$0.122757\pi$
$308$	−28.6311	−	28.6311i	−0.0929582	−	0.0929582i
$309$		−	158.611i		−	0.513303i
$310$	−64.4949	−	286.969i	−0.208048	−	0.925708i
$311$	354.302			1.13923			0.569617	−	0.821910i	$-0.307091\pi$
$311$	354.302			1.13923			0.569617	+	0.821910i	$0.307091\pi$
$312$	108.136	−	108.136i	0.346590	−	0.346590i
$313$	152.373	+	152.373i	0.486816	+	0.486816i	0.907300	−	0.420484i	$-0.138140\pi$
$313$	152.373	+	152.373i	0.486816	+	0.486816i	−0.420484	+	0.907300i	$0.638140\pi$
$314$			227.576i			0.724763i
$315$	−30.0000	+	6.74235i	−0.0952381	+	0.0214043i
$316$	−144.495			−0.457262
$317$	−427.217	+	427.217i	−1.34769	+	1.34769i	−0.459519	+	0.888168i	$0.651978\pi$
$317$	−427.217	+	427.217i	−1.34769	+	1.34769i	−0.888168	+	0.459519i	$0.848022\pi$
$318$	−156.384	−	156.384i	−0.491773	−	0.491773i
$319$			2.85816i			0.00895975i
$320$	−437.240	−	276.770i	−1.36637	−	0.864905i
$321$	−11.6163			−0.0361879
$322$	106.091	−	106.091i	0.329475	−	0.329475i
$323$	−54.8786	−	54.8786i	−0.169903	−	0.169903i
$324$			53.0908i			0.163861i
$325$	−124.338	+	347.893i	−0.382579	+	1.07044i
$326$	−842.706			−2.58499
$327$	48.1362	−	48.1362i	0.147206	−	0.147206i
$328$	−121.237	−	121.237i	−0.369626	−	0.369626i
$329$			57.2622i			0.174049i
$330$	48.7980	−	77.0908i	0.147873	−	0.233609i
$331$	489.423			1.47862			0.739310	−	0.673365i	$-0.235152\pi$
$331$	489.423			1.47862			0.739310	+	0.673365i	$0.235152\pi$
$332$	−124.742	+	124.742i	−0.375730	+	0.375730i
$333$	114.136	+	114.136i	0.342751	+	0.342751i
$334$			431.757i			1.29269i
$335$	85.1214	+	378.747i	0.254094	+	1.13059i
$336$	−17.0352			−0.0507000
$337$	292.192	−	292.192i	0.867038	−	0.867038i	−0.125105	−	0.992143i	$-0.539927\pi$
$337$	292.192	−	292.192i	0.867038	−	0.867038i	0.992143	+	0.125105i	$0.0399269\pi$
$338$	−109.866	−	109.866i	−0.325048	−	0.325048i
$339$			35.1714i			0.103751i
$340$	107.909	−	24.2520i	0.317380	−	0.0713295i
$341$	62.6061			0.183596
$342$	138.136	−	138.136i	0.403907	−	0.403907i
$343$	−135.959	−	135.959i	−0.396382	−	0.396382i
$344$			190.070i			0.552530i
$345$	170.227	+	107.753i	0.493412	+	0.312326i
$346$	154.091			0.445349
$347$	320.050	−	320.050i	0.922334	−	0.922334i	−0.0748598	−	0.997194i	$-0.523851\pi$
$347$	320.050	−	320.050i	0.922334	−	0.922334i	0.997194	+	0.0748598i	$0.0238509\pi$
$348$	−6.16684	−	6.16684i	−0.0177208	−	0.0177208i
$349$		−	574.009i		−	1.64473i	−0.568964	−	0.822363i	$-0.692655\pi$
$349$		−	574.009i		−	1.64473i	0.568964	−	0.822363i	$-0.307345\pi$
$350$	−145.732	+	68.9898i	−0.416378	+	0.197114i
$351$	76.7878			0.218769
$352$	92.3281	−	92.3281i	0.262296	−	0.262296i
$353$	266.520	+	266.520i	0.755014	+	0.755014i	0.975410	−	0.220396i	$-0.0707351\pi$
$353$	266.520	+	266.520i	0.755014	+	0.755014i	−0.220396	+	0.975410i	$0.570735\pi$
$354$			609.984i			1.72312i
$355$	−181.848	+	287.283i	−0.512248	+	0.809247i
$356$	555.576			1.56061
$357$	9.41429	−	9.41429i	0.0263706	−	0.0263706i
$358$	−408.712	−	408.712i	−1.14165	−	1.14165i
$359$			216.272i			0.602430i	0.953556	+	0.301215i	$0.0973922\pi$
$359$			216.272i			0.602430i	−0.953556	+	0.301215i	$0.902608\pi$
$360$	19.6515	+	87.4393i	0.0545876	+	0.242887i
$361$	−67.3633			−0.186602
$362$	48.3383	−	48.3383i	0.133531	−	0.133531i
$363$	−134.462	−	134.462i	−0.370419	−	0.370419i
$364$		−	178.697i		−	0.490926i
$365$	−274.495	+	61.6913i	−0.752041	+	0.169017i
$366$	−512.747			−1.40095
$367$	−240.510	+	240.510i	−0.655340	+	0.655340i	−0.954274	−	0.298934i	$-0.903369\pi$
$367$	−240.510	+	240.510i	−0.655340	+	0.655340i	0.298934	+	0.954274i	$0.403369\pi$
$368$	78.9240	+	78.9240i	0.214467	+	0.214467i
$369$		−	86.0908i		−	0.233308i
$370$	715.176	+	452.702i	1.93291	+	1.22352i
$371$	−83.1918			−0.224237
$372$	−135.081	+	135.081i	−0.363120	+	0.363120i
$373$	−330.207	−	330.207i	−0.885272	−	0.885272i	0.108792	−	0.994065i	$-0.465302\pi$
$373$	−330.207	−	330.207i	−0.885272	−	0.885272i	−0.994065	+	0.108792i	$0.965302\pi$
$374$			39.5051i			0.105629i
$375$	−133.293	−	170.611i	−0.355448	−	0.454962i
$376$	166.899			0.443880
$377$	−8.91939	+	8.91939i	−0.0236589	+	0.0236589i
$378$	23.6969	+	23.6969i	0.0626903	+	0.0626903i
$379$			210.000i			0.554090i	0.960857	+	0.277045i	$0.0893551\pi$
$379$			210.000i			0.554090i	−0.960857	+	0.277045i	$0.910645\pi$
$380$	326.499	−	515.803i	0.859209	−	1.35738i
$381$	−280.763			−0.736910
$382$	89.1918	−	89.1918i	0.233486	−	0.233486i
$383$	170.631	+	170.631i	0.445512	+	0.445512i	0.893859	−	0.448347i	$-0.147987\pi$
$383$	170.631	+	170.631i	0.445512	+	0.445512i	−0.448347	+	0.893859i	$0.647987\pi$
$384$			293.833i			0.765191i
$385$	−7.52551	−	33.4847i	−0.0195468	−	0.0869732i
$386$	−345.126			−0.894109
$387$	−67.4847	+	67.4847i	−0.174379	+	0.174379i
$388$	−86.1010	−	86.1010i	−0.221910	−	0.221910i
$389$		−	547.337i		−	1.40704i	−0.710677	−	0.703518i	$-0.751611\pi$
$389$		−	547.337i		−	1.40704i	0.710677	−	0.703518i	$-0.248389\pi$
$390$	392.858	−	88.2929i	1.00733	−	0.226392i
$391$	−87.2327			−0.223101
$392$	−189.260	+	189.260i	−0.482806	+	0.482806i
$393$	−32.0102	−	32.0102i	−0.0814509	−	0.0814509i
$394$		−	299.464i		−	0.760062i
$395$	−103.485	−	65.5051i	−0.261987	−	0.165836i
$396$	−59.2577			−0.149641
$397$	45.2577	−	45.2577i	0.113999	−	0.113999i	−0.647806	−	0.761805i	$-0.724313\pi$
$397$	45.2577	−	45.2577i	0.113999	−	0.113999i	0.761805	+	0.647806i	$0.224313\pi$
$398$	559.287	+	559.287i	1.40524	+	1.40524i
$399$		−	73.4847i		−	0.184172i
$400$	−51.3235	−	108.414i	−0.128309	−	0.271036i
$401$	−520.302			−1.29751			−0.648756	−	0.760997i	$-0.724710\pi$
$401$	−520.302			−1.29751			−0.648756	+	0.760997i	$0.724710\pi$
$402$	299.171	−	299.171i	0.744208	−	0.744208i
$403$	195.373	+	195.373i	0.484798	+	0.484798i
$404$		−	1024.19i		−	2.53511i
$405$	−24.0681	+	38.0227i	−0.0594274	+	0.0938832i
$406$	−5.50510			−0.0135594
$407$	−127.394	+	127.394i	−0.313007	+	0.313007i
$408$	−27.4393	−	27.4393i	−0.0672531	−	0.0672531i
$409$		−	347.110i		−	0.848680i	−0.905503	−	0.424340i	$-0.860506\pi$
$409$		−	347.110i		−	0.848680i	0.905503	−	0.424340i	$-0.139494\pi$
$410$	−98.9898	−	440.454i	−0.241439	−	1.07428i
$411$	35.8388			0.0871990
$412$	−381.974	+	381.974i	−0.927121	+	0.927121i
$413$	162.247	+	162.247i	0.392851	+	0.392851i
$414$		−	219.576i		−	0.530376i
$415$	−145.889	+	32.7878i	−0.351539	+	0.0790066i
$416$	576.252			1.38522
$417$	101.864	−	101.864i	0.244278	−	0.244278i
$418$	154.182	+	154.182i	0.368856	+	0.368856i
$419$			583.398i			1.39236i	0.717868	+	0.696180i	$0.245118\pi$
$419$			583.398i			1.39236i	−0.717868	+	0.696180i	$0.754882\pi$
$420$	88.4847	+	56.0102i	0.210678	+	0.133358i
$421$	213.151			0.506297			0.253148	−	0.967427i	$-0.418534\pi$
$421$	213.151			0.506297			0.253148	+	0.967427i	$0.418534\pi$
$422$	−589.085	+	589.085i	−1.39594	+	1.39594i
$423$	59.2577	+	59.2577i	0.140089	+	0.140089i
$424$			242.474i			0.571874i
$425$	88.2770	+	31.5505i	0.207711	+	0.0742365i
$426$	370.565			0.869872
$427$	−136.384	+	136.384i	−0.319400	+	0.319400i
$428$	27.9750	+	27.9750i	0.0653622	+	0.0653622i
$429$			85.7071i			0.199784i
$430$	−267.666	+	422.858i	−0.622480	+	0.983391i
$431$	187.364			0.434720			0.217360	−	0.976092i	$-0.430255\pi$
$431$	187.364			0.434720			0.217360	+	0.976092i	$0.430255\pi$
$432$	−17.6288	+	17.6288i	−0.0408075	+	0.0408075i
$433$	154.848	+	154.848i	0.357617	+	0.357617i	0.862934	−	0.505317i	$-0.168624\pi$
$433$	154.848	+	154.848i	0.357617	+	0.357617i	−0.505317	+	0.862934i	$0.668624\pi$
$434$			120.586i			0.277847i
$435$	−1.62092	−	7.21225i	−0.00372624	−	0.0165799i
$436$	−231.848			−0.531761
$437$	−340.454	+	340.454i	−0.779071	+	0.779071i
$438$	216.823	+	216.823i	0.495030	+	0.495030i
$439$			252.929i			0.576147i	0.957608	+	0.288074i	$0.0930148\pi$
$439$			252.929i			0.576147i	−0.957608	+	0.288074i	$0.906985\pi$
$440$	−97.5959	+	21.9342i	−0.221809	+	0.0498504i
$441$	−134.394			−0.304748
$442$	−123.283	+	123.283i	−0.278920	+	0.278920i
$443$	−421.131	−	421.131i	−0.950633	−	0.950633i	0.0482041	−	0.998838i	$-0.484650\pi$
$443$	−421.131	−	421.131i	−0.950633	−	0.950633i	−0.998838	+	0.0482041i	$0.984650\pi$
$444$		−	549.737i		−	1.23815i
$445$	397.893	+	251.864i	0.894142	+	0.565986i
$446$	148.742			0.333503
$447$	145.924	−	145.924i	0.326452	−	0.326452i
$448$	150.015	+	150.015i	0.334854	+	0.334854i
$449$		−	297.909i		−	0.663495i	−0.943368	−	0.331747i	$-0.892362\pi$
$449$		−	297.909i		−	0.663495i	0.943368	−	0.331747i	$-0.107638\pi$
$450$	−79.4166	+	222.204i	−0.176481	+	0.493787i
$451$	96.0908			0.213062
$452$	84.7015	−	84.7015i	0.187393	−	0.187393i
$453$	−177.551	−	177.551i	−0.391944	−	0.391944i
$454$		−	94.2020i		−	0.207493i
$455$	81.0102	−	127.980i	0.178044	−	0.281274i
$456$	−214.182			−0.469697
$457$	285.747	−	285.747i	0.625267	−	0.625267i	−0.321607	−	0.946873i	$-0.604223\pi$
$457$	285.747	−	285.747i	0.625267	−	0.625267i	0.946873	+	0.321607i	$0.104223\pi$
$458$	−542.388	−	542.388i	−1.18425	−	1.18425i
$459$		−	19.4847i		−	0.0424503i
$460$	−150.454	−	669.444i	−0.327074	−	1.45531i
$461$	526.620			1.14234			0.571171	−	0.820831i	$-0.306489\pi$
$461$	526.620			1.14234			0.571171	+	0.820831i	$0.306489\pi$
$462$	−26.4495	+	26.4495i	−0.0572500	+	0.0572500i
$463$	335.702	+	335.702i	0.725057	+	0.725057i	0.969631	−	0.244573i	$-0.0786479\pi$
$463$	335.702	+	335.702i	0.725057	+	0.725057i	−0.244573	+	0.969631i	$0.578648\pi$
$464$		−	4.09540i		−	0.00882630i
$465$	−157.980	+	35.5051i	−0.339741	+	0.0763551i
$466$	−719.535			−1.54407
$467$	488.742	−	488.742i	1.04656	−	1.04656i	0.0476956	−	0.998862i	$-0.484812\pi$
$467$	488.742	−	488.742i	1.04656	−	1.04656i	0.998862	−	0.0476956i	$-0.0151877\pi$
$468$	−184.924	−	184.924i	−0.395137	−	0.395137i
$469$		−	159.151i		−	0.339341i
$470$	371.308	+	235.035i	0.790016	+	0.500075i
$471$	125.283			0.265993
$472$	472.893	−	472.893i	1.00189	−	1.00189i
$473$	−75.3235	−	75.3235i	−0.159246	−	0.159246i
$474$			133.485i			0.281613i
$475$	467.666	−	221.394i	0.984561	−	0.466092i
$476$	−45.3439			−0.0952603
$477$	−86.0908	+	86.0908i	−0.180484	+	0.180484i
$478$	−725.716	−	725.716i	−1.51823	−	1.51823i
$479$			184.949i			0.386115i	0.981187	+	0.193057i	$0.0618404\pi$
$479$			184.949i			0.386115i	−0.981187	+	0.193057i	$0.938160\pi$
$480$	−180.619	+	285.341i	−0.376289	+	0.594459i
$481$	−795.110			−1.65304
$482$	297.171	−	297.171i	0.616538	−	0.616538i
$483$	−58.4041	−	58.4041i	−0.120919	−	0.120919i
$484$			647.636i			1.33809i
$485$	−22.6311	−	100.697i	−0.0466621	−	0.207623i
$486$	49.0454			0.100916
$487$	−120.682	+	120.682i	−0.247807	+	0.247807i	−0.820070	−	0.572263i	$-0.806066\pi$
$487$	−120.682	+	120.682i	−0.247807	+	0.247807i	0.572263	+	0.820070i	$0.306066\pi$
$488$	397.510	+	397.510i	0.814569	+	0.814569i
$489$			463.918i			0.948708i
$490$	−687.580	+	154.530i	−1.40322	+	0.315368i
$491$	−105.682			−0.215239			−0.107619	−	0.994192i	$-0.534323\pi$
$491$	−105.682			−0.215239			−0.107619	+	0.994192i	$0.534323\pi$
$492$	−207.328	+	207.328i	−0.421398	+	0.421398i
$493$	2.26327	+	2.26327i	0.00459082	+	0.00459082i
$494$			962.302i			1.94798i
$495$	−42.4393	−	26.8638i	−0.0857359	−	0.0542703i
$496$	−89.7071			−0.180861
$497$	98.5653	−	98.5653i	0.198321	−	0.198321i
$498$	115.237	+	115.237i	0.231400	+	0.231400i
$499$			739.585i			1.48213i	0.671431	+	0.741067i	$0.265680\pi$
$499$			739.585i			1.48213i	−0.671431	+	0.741067i	$0.734320\pi$
$500$	−89.8707	+	731.875i	−0.179741	+	1.46375i
$501$	237.687			0.474425
$502$	900.448	−	900.448i	1.79372	−	1.79372i
$503$	−406.409	−	406.409i	−0.807970	−	0.807970i	0.176357	−	0.984326i	$-0.443569\pi$
$503$	−406.409	−	406.409i	−0.807970	−	0.807970i	−0.984326	+	0.176357i	$0.943569\pi$
$504$		−	36.7423i		−	0.0729015i
$505$	464.303	−	733.504i	0.919412	−	1.45248i
$506$	245.081			0.484349
$507$	−60.4824	+	60.4824i	−0.119295	+	0.119295i
$508$	676.146	+	676.146i	1.33100	+	1.33100i
$509$		−	194.511i		−	0.382143i	−0.981576	−	0.191071i	$-0.938804\pi$
$509$		−	194.511i		−	0.382143i	0.981576	−	0.191071i	$-0.0611962\pi$
$510$	−22.4041	−	99.6867i	−0.0439296	−	0.195464i
$511$	115.344			0.225722
$512$	−213.376	+	213.376i	−0.416750	+	0.416750i
$513$	−76.0454	−	76.0454i	−0.148237	−	0.148237i
$514$		−	397.060i		−	0.772491i
$515$	−446.727	+	100.399i	−0.867430	+	0.194950i
$516$	325.040			0.629922
$517$	−66.1408	+	66.1408i	−0.127932	+	0.127932i
$518$	−245.373	−	245.373i	−0.473694	−	0.473694i
$519$		−	84.8286i		−	0.163446i
$520$	−373.015	−	236.116i	−0.717336	−	0.454069i
$521$	−589.605			−1.13168			−0.565840	−	0.824515i	$-0.691448\pi$
$521$	−589.605			−1.13168			−0.565840	+	0.824515i	$0.691448\pi$
$522$	−5.69694	+	5.69694i	−0.0109137	+	0.0109137i
$523$	−141.546	−	141.546i	−0.270642	−	0.270642i	0.558716	−	0.829359i	$-0.311294\pi$
$523$	−141.546	−	141.546i	−0.270642	−	0.270642i	−0.829359	+	0.558716i	$0.811294\pi$
$524$			154.177i			0.294231i
$525$	37.9796	+	80.2270i	0.0723421	+	0.152813i
$526$	1521.03			2.89169
$527$	49.5755	−	49.5755i	0.0940712	−	0.0940712i
$528$	−19.6765	−	19.6765i	−0.0372662	−	0.0372662i
$529$			12.1714i			0.0230084i
$530$	−341.464	+	539.444i	−0.644272	+	1.01782i
$531$	335.803			0.632397
$532$	−176.969	+	176.969i	−0.332649	+	0.332649i
$533$	299.868	+	299.868i	0.562605	+	0.562605i
$534$		−	513.242i		−	0.961127i
$535$	7.35306	+	32.7173i	0.0137440	+	0.0611539i
$536$	−463.868			−0.865426
$537$	−225.000	+	225.000i	−0.418994	+	0.418994i
$538$	−7.78775	−	7.78775i	−0.0144754	−	0.0144754i
$539$		−	150.005i		−	0.278302i
$540$	149.530	−	33.6061i	0.276908	−	0.0622336i
$541$	431.303			0.797233			0.398617	−	0.917118i	$-0.369490\pi$
$541$	431.303			0.797233			0.398617	+	0.917118i	$0.369490\pi$
$542$	230.429	−	230.429i	0.425146	−	0.425146i
$543$	−26.6107	−	26.6107i	−0.0490068	−	0.0490068i
$544$		−	146.222i		−	0.268791i
$545$	−166.045	−	105.106i	−0.304670	−	0.192854i
$546$	−165.081			−0.302345
$547$	−446.222	+	446.222i	−0.815763	+	0.815763i	−0.985491	−	0.169728i	$-0.945711\pi$
$547$	−446.222	+	446.222i	−0.815763	+	0.815763i	0.169728	+	0.985491i	$0.445711\pi$
$548$	−86.3087	−	86.3087i	−0.157498	−	0.157498i
$549$			282.272i			0.514157i
$550$	−248.015	−	88.6413i	−0.450936	−	0.161166i
$551$	17.6663			0.0320623
$552$	−170.227	+	170.227i	−0.308382	+	0.308382i
$553$	35.5051	+	35.5051i	0.0642045	+	0.0642045i
$554$		−	1270.37i		−	2.29309i
$555$	249.217	−	393.712i	0.449039	−	0.709391i
$556$	−490.627			−0.882422
$557$	214.091	−	214.091i	0.384364	−	0.384364i	−0.488308	−	0.872672i	$-0.662386\pi$
$557$	214.091	−	214.091i	0.384364	−	0.384364i	0.872672	+	0.488308i	$0.162386\pi$
$558$	124.788	+	124.788i	0.223634	+	0.223634i
$559$		−	470.120i		−	0.841003i
$560$	10.7832	+	47.9796i	0.0192557	+	0.0856778i
$561$	21.7480			0.0387664
$562$	−829.156	+	829.156i	−1.47537	+	1.47537i
$563$	672.009	+	672.009i	1.19362	+	1.19362i	0.976043	+	0.217579i	$0.0698161\pi$
$563$	672.009	+	672.009i	1.19362	+	1.19362i	0.217579	+	0.976043i	$0.430184\pi$
$564$		−	285.414i		−	0.506054i
$565$	99.0602	−	22.2633i	0.175328	−	0.0394040i
$566$	343.464			0.606827
$567$	13.0454	−	13.0454i	0.0230078	−	0.0230078i
$568$	−287.283	−	287.283i	−0.505779	−	0.505779i
$569$			972.161i			1.70854i	0.519827	+	0.854272i	$0.325997\pi$
$569$			972.161i			1.70854i	−0.519827	+	0.854272i	$0.674003\pi$
$570$	−476.499	−	301.621i	−0.835964	−	0.529160i
$571$	−924.030			−1.61827			−0.809133	−	0.587626i	$-0.800063\pi$
$571$	−924.030			−1.61827			−0.809133	+	0.587626i	$0.800063\pi$
$572$	206.404	−	206.404i	0.360846	−	0.360846i
$573$	−49.1010	−	49.1010i	−0.0856911	−	0.0856911i
$574$			185.081i			0.322440i
$575$	195.732	−	547.650i	0.340404	−	0.952436i
$576$	310.485			0.539036
$577$	−497.879	+	497.879i	−0.862874	+	0.862874i	−0.991671	−	0.128797i	$-0.958889\pi$
$577$	−497.879	+	497.879i	−0.862874	+	0.862874i	0.128797	+	0.991671i	$0.458889\pi$
$578$	−611.669	−	611.669i	−1.05825	−	1.05825i
$579$			189.995i			0.328144i
$580$	−13.4653	+	21.2724i	−0.0232161	+	0.0366766i
$581$	61.3031			0.105513
$582$	−79.5403	+	79.5403i	−0.136667	+	0.136667i
$583$	−96.0908	−	96.0908i	−0.164821	−	0.164821i
$584$		−	336.186i		−	0.575661i
$585$	−48.6061	−	216.272i	−0.0830874	−	0.369696i
$586$	1052.59			1.79624
$587$	292.783	−	292.783i	0.498779	−	0.498779i	−0.412279	−	0.911058i	$-0.635267\pi$
$587$	292.783	−	292.783i	0.498779	−	0.498779i	0.911058	+	0.412279i	$0.135267\pi$
$588$	323.654	+	323.654i	0.550432	+	0.550432i
$589$		−	386.969i		−	0.656994i
$590$	1718.02	−	386.116i	2.91190	−	0.654434i
$591$	−164.858			−0.278948
$592$	182.540	−	182.540i	0.308345	−	0.308345i
$593$	451.258	+	451.258i	0.760974	+	0.760974i	0.976498	−	0.215524i	$-0.0691461\pi$
$593$	451.258	+	451.258i	0.760974	+	0.760974i	−0.215524	+	0.976498i	$0.569146\pi$
$594$			54.7423i			0.0921588i
$595$	−32.4745	−	20.5561i	−0.0545790	−	0.0345481i
$596$	−702.842			−1.17927
$597$	307.893	−	307.893i	0.515734	−	0.515734i
$598$	764.817	+	764.817i	1.27896	+	1.27896i
$599$		−	32.8582i		−	0.0548550i	−0.999624	−	0.0274275i	$-0.991268\pi$
$599$		−	32.8582i		−	0.0548550i	0.999624	−	0.0274275i	$-0.00873154\pi$
$600$	233.833	−	110.697i	0.389722	−	0.184495i
$601$	−184.484			−0.306961			−0.153481	−	0.988152i	$-0.549048\pi$
$601$	−184.484			−0.306961			−0.153481	+	0.988152i	$0.549048\pi$
$602$	145.081	−	145.081i	0.240998	−	0.240998i
$603$	−164.697	−	164.697i	−0.273129	−	0.273129i
$604$			855.171i			1.41585i
$605$	−293.598	+	463.825i	−0.485286	+	0.766653i
$606$	−946.145			−1.56130
$607$	136.389	−	136.389i	0.224694	−	0.224694i	−0.585778	−	0.810472i	$-0.699211\pi$
$607$	136.389	−	136.389i	0.224694	−	0.224694i	0.810472	+	0.585778i	$0.199211\pi$
$608$	−570.681	−	570.681i	−0.938620	−	0.938620i
$609$			3.03062i			0.00497638i
$610$	324.565	+	1444.15i	0.532074	+	2.36746i
$611$	−412.808			−0.675627
$612$	−46.9240	+	46.9240i	−0.0766732	+	0.0766732i
$613$	−12.7128	−	12.7128i	−0.0207386	−	0.0207386i	0.696661	−	0.717400i	$-0.254668\pi$
$613$	−12.7128	−	12.7128i	−0.0207386	−	0.0207386i	−0.717400	+	0.696661i	$0.754668\pi$
$614$			751.828i			1.22447i
$615$	−242.474	+	54.4949i	−0.394267	+	0.0886096i
$616$	41.0102			0.0665750
$617$	−398.752	+	398.752i	−0.646275	+	0.646275i	−0.952091	−	0.305816i	$-0.901071\pi$
$617$	−398.752	+	398.752i	−0.646275	+	0.646275i	0.305816	+	0.952091i	$0.401071\pi$
$618$	352.868	+	352.868i	0.570984	+	0.570984i
$619$		−	819.131i		−	1.32331i	−0.749807	−	0.661656i	$-0.769854\pi$
$619$		−	819.131i		−	1.32331i	0.749807	−	0.661656i	$-0.230146\pi$
$620$	465.959	+	294.949i	0.751547	+	0.475724i
$621$	−120.879			−0.194651
$622$	−788.232	+	788.232i	−1.26725	+	1.26725i
$623$	−136.515	−	136.515i	−0.219126	−	0.219126i
$624$		−	122.808i		−	0.196808i
$625$	−396.151	+	483.414i	−0.633842	+	0.773463i
$626$	−677.984			−1.08304
$627$	84.8786	−	84.8786i	0.135373	−	0.135373i
$628$	−301.712	−	301.712i	−0.480433	−	0.480433i
$629$			201.757i			0.320759i
$630$	51.7423	−	81.7423i	0.0821307	−	0.129750i
$631$	105.485			0.167171			0.0835853	−	0.996501i	$-0.473363\pi$
$631$	105.485			0.167171			0.0835853	+	0.996501i	$0.473363\pi$
$632$	103.485	−	103.485i	0.163742	−	0.163742i
$633$	324.297	+	324.297i	0.512318	+	0.512318i
$634$		−	1900.90i		−	2.99826i
$635$	177.721	+	790.767i	0.279875	+	1.24530i
$636$	414.656			0.651975
$637$	468.116	−	468.116i	0.734876	−	0.734876i
$638$	−6.35867	−	6.35867i	−0.00996657	−	0.00996657i
$639$		−	204.000i		−	0.319249i
$640$	827.580	−	185.994i	1.29309	−	0.290616i
$641$	164.788			0.257079			0.128540	−	0.991704i	$-0.458971\pi$
$641$	164.788			0.257079			0.128540	+	0.991704i	$0.458971\pi$
$642$	25.8434	−	25.8434i	0.0402545	−	0.0402545i
$643$	−764.372	−	764.372i	−1.18876	−	1.18876i	−0.977411	−	0.211349i	$-0.932214\pi$
$643$	−764.372	−	764.372i	−1.18876	−	1.18876i	−0.211349	−	0.977411i	$-0.567786\pi$
$644$			281.303i			0.436806i
$645$	232.788	+	147.353i	0.360911	+	0.228454i
$646$	244.182			0.377990
$647$	321.287	−	321.287i	0.496580	−	0.496580i	−0.413792	−	0.910372i	$-0.635796\pi$
$647$	321.287	−	321.287i	0.496580	−	0.496580i	0.910372	+	0.413792i	$0.135796\pi$
$648$	−38.0227	−	38.0227i	−0.0586770	−	0.0586770i
$649$			374.808i			0.577516i
$650$	−497.353	−	1050.59i	−0.765159	−	1.61630i
$651$	66.3837			0.101972
$652$	1117.23	−	1117.23i	1.71354	−	1.71354i
$653$	−169.823	−	169.823i	−0.260066	−	0.260066i	0.565015	−	0.825081i	$-0.308870\pi$
$653$	−169.823	−	169.823i	−0.260066	−	0.260066i	−0.825081	+	0.565015i	$0.808870\pi$
$654$			214.182i			0.327495i
$655$	−69.8944	+	110.419i	−0.106709	+	0.168578i
$656$	−137.687			−0.209888
$657$	119.363	−	119.363i	0.181679	−	0.181679i
$658$	−127.394	−	127.394i	−0.193608	−	0.193608i
$659$		−	958.763i		−	1.45488i	−0.686174	−	0.727438i	$-0.740711\pi$
$659$		−	958.763i		−	1.45488i	0.686174	−	0.727438i	$-0.259289\pi$
$660$	37.5097	+	166.899i	0.0568329	+	0.252877i
$661$	396.393			0.599687			0.299843	−	0.953988i	$-0.403066\pi$
$661$	396.393			0.599687			0.299843	+	0.953988i	$0.403066\pi$
$662$	−1088.84	+	1088.84i	−1.64478	+	1.64478i
$663$	67.8684	+	67.8684i	0.102366	+	0.102366i
$664$		−	178.677i		−	0.269091i
$665$	−206.969	+	46.5153i	−0.311232	+	0.0699478i
$666$	−507.848			−0.762534
$667$	14.0408	−	14.0408i	0.0210507	−	0.0210507i
$668$	−572.409	−	572.409i	−0.856899	−	0.856899i
$669$		−	81.8842i		−	0.122398i
$670$	−1031.99	−	653.242i	−1.54028	−	0.974988i
$671$	−315.060			−0.469538
$672$	97.8990	−	97.8990i	0.145683	−	0.145683i
$673$	164.707	+	164.707i	0.244736	+	0.244736i	0.818806	−	0.574070i	$-0.194636\pi$
$673$	164.707	+	164.707i	0.244736	+	0.244736i	−0.574070	+	0.818806i	$0.694636\pi$
$674$			1300.10i			1.92894i
$675$	122.326	+	43.7196i	0.181223	+	0.0647698i
$676$	291.313			0.430937
$677$	544.388	−	544.388i	0.804119	−	0.804119i	−0.179618	−	0.983736i	$-0.557486\pi$
$677$	544.388	−	544.388i	0.804119	−	0.804119i	0.983736	+	0.179618i	$0.0574861\pi$
$678$	−78.2474	−	78.2474i	−0.115409	−	0.115409i
$679$			42.3133i			0.0623170i
$680$	−59.9138	+	94.6515i	−0.0881085	+	0.139193i
$681$	−51.8592			−0.0761515
$682$	−139.283	+	139.283i	−0.204227	+	0.204227i
$683$	786.590	+	786.590i	1.15167	+	1.15167i	0.986218	+	0.165452i	$0.0529082\pi$
$683$	786.590	+	786.590i	1.15167	+	1.15167i	0.165452	+	0.986218i	$0.447092\pi$
$684$			366.272i			0.535486i
$685$	−22.6857	−	100.940i	−0.0331178	−	0.147357i
$686$	604.949			0.881850
$687$	−298.590	+	298.590i	−0.434629	+	0.434629i
$688$	107.930	+	107.930i	0.156874	+	0.156874i
$689$		−	599.737i		−	0.870445i
$690$	−618.434	+	138.990i	−0.896281	+	0.201434i
$691$	356.879			0.516467			0.258233	−	0.966083i	$-0.416860\pi$
$691$	356.879			0.516467			0.258233	+	0.966083i	$0.416860\pi$
$692$	−204.288	+	204.288i	−0.295214	+	0.295214i
$693$	14.5607	+	14.5607i	0.0210111	+	0.0210111i
$694$			1424.06i			2.05196i
$695$	−351.378	−	222.420i	−0.505580	−	0.320029i
$696$	8.83316			0.0126913
$697$	76.0908	−	76.0908i	0.109169	−	0.109169i
$698$	1277.02	+	1277.02i	1.82955	+	1.82955i
$699$			396.111i			0.566683i
$700$	101.742	−	284.671i	0.145346	−	0.406673i
$701$	885.680			1.26345			0.631726	−	0.775192i	$-0.282347\pi$
$701$	885.680			1.26345			0.631726	+	0.775192i	$0.282347\pi$
$702$	−170.833	+	170.833i	−0.243352	+	0.243352i
$703$	787.423	+	787.423i	1.12009	+	1.12009i
$704$			346.549i			0.492258i
$705$	129.389	−	204.409i	0.183531	−	0.289941i
$706$	−1185.88			−1.67971
$707$	−251.662	+	251.662i	−0.355957	+	0.355957i
$708$	−808.696	−	808.696i	−1.14223	−	1.14223i
$709$			731.049i			1.03110i	0.856860	+	0.515549i	$0.172412\pi$
$709$			731.049i			1.03110i	−0.856860	+	0.515549i	$0.827588\pi$
$710$	−234.565	−	1043.70i	−0.330374	−	1.46999i
$711$	73.4847			0.103354
$712$	−397.893	+	397.893i	−0.558839	+	0.558839i
$713$	−307.555	−	307.555i	−0.431354	−	0.431354i
$714$			41.8888i			0.0586678i
$715$	241.394	−	54.2520i	0.337614	−	0.0758770i
$716$	1083.71			1.51356
$717$	−399.514	+	399.514i	−0.557203	+	0.557203i
$718$	−481.151	−	481.151i	−0.670127	−	0.670127i
$719$		−	629.271i		−	0.875204i	−0.899169	−	0.437602i	$-0.855828\pi$
$719$		−	629.271i		−	0.875204i	0.899169	−	0.437602i	$-0.144172\pi$
$720$	60.8105	+	38.4926i	0.0844590	+	0.0534619i
$721$	187.716			0.260356
$722$	149.866	−	149.866i	0.207571	−	0.207571i
$723$	−163.596	−	163.596i	−0.226274	−	0.226274i
$724$			128.170i			0.177031i
$725$	−19.2872	+	9.13061i	−0.0266031	+	0.0125939i
$726$	598.287			0.824087
$727$	−15.8740	+	15.8740i	−0.0218349	+	0.0218349i	−0.717940	−	0.696105i	$-0.754915\pi$
$727$	−15.8740	+	15.8740i	−0.0218349	+	0.0218349i	0.696105	+	0.717940i	$0.254915\pi$
$728$	127.980	+	127.980i	0.175796	+	0.175796i
$729$		−	27.0000i		−	0.0370370i
$730$	473.434	−	747.929i	0.648539	−	1.02456i
$731$	−119.292			−0.163190
$732$	679.782	−	679.782i	0.928664	−	0.928664i
$733$	−393.237	−	393.237i	−0.536476	−	0.536476i	0.386016	−	0.922492i	$-0.373851\pi$
$733$	−393.237	−	393.237i	−0.536476	−	0.536476i	−0.922492	+	0.386016i	$0.873851\pi$
$734$		−	1070.15i		−	1.45796i
$735$	85.0704	+	378.520i	0.115742	+	0.514993i
$736$	−907.131			−1.23251
$737$	183.828	−	183.828i	0.249427	−	0.249427i
$738$	191.530	+	191.530i	0.259526	+	0.259526i
$739$			192.334i			0.260262i	0.991497	+	0.130131i	$0.0415398\pi$
$739$			192.334i			0.260262i	−0.991497	+	0.130131i	$0.958460\pi$
$740$	−1548.33	+	347.980i	−2.09234	+	0.470243i
$741$	529.757			0.714922
$742$	185.081	−	185.081i	0.249435	−	0.249435i
$743$	−44.7015	−	44.7015i	−0.0601636	−	0.0601636i	0.676385	−	0.736548i	$-0.263546\pi$
$743$	−44.7015	−	44.7015i	−0.0601636	−	0.0601636i	−0.736548	+	0.676385i	$0.763546\pi$
$744$		−	193.485i		−	0.260060i
$745$	−503.363	−	318.626i	−0.675655	−	0.427685i
$746$	1469.25			1.96951
$747$	63.4393	−	63.4393i	0.0849254	−	0.0849254i
$748$	−52.3745	−	52.3745i	−0.0700194	−	0.0700194i
$749$		−	13.7480i		−	0.0183551i
$750$	676.108	+	83.0227i	0.901477	+	0.110697i
$751$	227.787			0.303311			0.151656	−	0.988433i	$-0.451540\pi$
$751$	227.787			0.303311			0.151656	+	0.988433i	$0.451540\pi$
$752$	94.7719	−	94.7719i	0.126027	−	0.126027i
$753$	−495.706	−	495.706i	−0.658308	−	0.658308i
$754$		−	39.6867i		−	0.0526349i
$755$	−387.682	+	612.459i	−0.513486	+	0.811204i
$756$	−62.8332			−0.0831126
$757$	−235.925	+	235.925i	−0.311658	+	0.311658i	−0.845552	−	0.533894i	$-0.820728\pi$
$757$	−235.925	+	235.925i	−0.311658	+	0.311658i	0.533894	+	0.845552i	$0.320728\pi$
$758$	−467.196	−	467.196i	−0.616354	−	0.616354i
$759$		−	134.919i		−	0.177759i
$760$	135.576	+	603.242i	0.178389	+	0.793739i
$761$	−881.242			−1.15801			−0.579003	−	0.815326i	$-0.696558\pi$
$761$	−881.242			−1.15801			−0.579003	+	0.815326i	$0.696558\pi$
$762$	624.626	−	624.626i	0.819719	−	0.819719i
$763$	56.9694	+	56.9694i	0.0746650	+	0.0746650i
$764$			236.495i			0.309548i
$765$	−54.8786	+	12.3337i	−0.0717367	+	0.0161225i
$766$	−759.221			−0.991151
$767$	−1169.66	+	1169.66i	−1.52497	+	1.52497i
$768$	−146.684	−	146.684i	−0.190995	−	0.190995i
$769$			1208.40i			1.57139i	0.618612	+	0.785697i	$0.287696\pi$
$769$			1208.40i			1.57139i	−0.618612	+	0.785697i	$0.712304\pi$
$770$	91.2372	+	57.7526i	0.118490	+	0.0750033i
$771$	−218.586			−0.283509
$772$	457.556	−	457.556i	0.592689	−	0.592689i
$773$	−815.226	−	815.226i	−1.05463	−	1.05463i	−0.998419	−	0.0562070i	$-0.982099\pi$
$773$	−815.226	−	815.226i	−1.05463	−	1.05463i	−0.0562070	−	0.998419i	$-0.517901\pi$
$774$		−	300.272i		−	0.387949i
$775$	200.000	+	422.474i	0.258065	+	0.545128i
$776$	123.328			0.158928
$777$	−135.081	+	135.081i	−0.173849	+	0.173849i
$778$	1217.69	+	1217.69i	1.56515	+	1.56515i
$779$		−	593.939i		−	0.762437i
$780$	−403.782	+	637.893i	−0.517669	+	0.817812i
$781$	227.696			0.291544
$782$	194.070	−	194.070i	0.248172	−	0.248172i
$783$	3.13622	+	3.13622i	0.00400539	+	0.00400539i
$784$			214.939i			0.274157i
$785$	−79.3031	−	352.858i	−0.101023	−	0.449501i
$786$	142.429			0.181207
$787$	813.010	−	813.010i	1.03305	−	1.03305i	0.0336150	−	0.999435i	$-0.489298\pi$
$787$	813.010	−	813.010i	1.03305	−	1.03305i	0.999435	−	0.0336150i	$-0.0107020\pi$
$788$	397.019	+	397.019i	0.503832	+	0.503832i
$789$		−	837.342i		−	1.06127i
$790$	375.959	−	84.4949i	0.475898	−	0.106956i
$791$	−41.6255			−0.0526239
$792$	42.4393	−	42.4393i	0.0535850	−	0.0535850i
$793$	−983.201	−	983.201i	−1.23985	−	1.23985i
$794$			201.373i			0.253619i
$795$	296.969	+	187.980i	0.373546	+	0.236452i
$796$	−1482.97			−1.86302
$797$	311.217	−	311.217i	0.390485	−	0.390485i	−0.484375	−	0.874860i	$-0.660953\pi$
$797$	311.217	−	311.217i	0.390485	−	0.390485i	0.874860	+	0.484375i	$0.160953\pi$
$798$	163.485	+	163.485i	0.204868	+	0.204868i
$799$			104.749i			0.131100i
$800$	917.991	+	328.093i	1.14749	+	0.410116i
$801$	−282.545			−0.352740
$802$	1157.54	−	1157.54i	1.44332	−	1.44332i
$803$	133.228	+	133.228i	0.165913	+	0.165913i
$804$			793.262i			0.986645i
$805$	−127.526	+	201.464i	−0.158417	+	0.250266i
$806$	−869.312			−1.07855
$807$	−4.28724	+	4.28724i	−0.00531256	+	0.00531256i
$808$	733.504	+	733.504i	0.907802	+	0.907802i
$809$			150.000i			0.185414i	0.995693	+	0.0927070i	$0.0295520\pi$
$809$			150.000i			0.185414i	−0.995693	+	0.0927070i	$0.970448\pi$
$810$	−31.0454	−	138.136i	−0.0383277	−	0.170539i
$811$	−132.847			−0.163806			−0.0819032	−	0.996640i	$-0.526100\pi$
$811$	−132.847			−0.163806			−0.0819032	+	0.996640i	$0.526100\pi$
$812$	7.29847	−	7.29847i	0.00898827	−	0.00898827i
$813$	−126.854	−	126.854i	−0.156031	−	0.156031i
$814$		−	566.838i		−	0.696361i
$815$	1306.62	−	293.657i	1.60322	−	0.360316i
$816$	−31.1623			−0.0381890
$817$	−465.576	+	465.576i	−0.569860	+	0.569860i
$818$	772.232	+	772.232i	0.944048	+	0.944048i
$819$			90.8786i			0.110963i
$820$	715.176	+	452.702i	0.872166	+	0.552075i
$821$	509.893			0.621064			0.310532	−	0.950563i	$-0.399493\pi$
$821$	509.893			0.621064			0.310532	+	0.950563i	$0.399493\pi$
$822$	−79.7321	+	79.7321i	−0.0969977	+	0.0969977i
$823$	300.369	+	300.369i	0.364968	+	0.364968i	0.865638	−	0.500670i	$-0.166913\pi$
$823$	300.369	+	300.369i	0.364968	+	0.364968i	−0.500670	+	0.865638i	$0.666913\pi$
$824$		−	547.126i		−	0.663988i
$825$	−48.7980	+	136.535i	−0.0591490	+	0.165497i
$826$	−721.918			−0.873993
$827$	−1030.76	+	1030.76i	−1.24638	+	1.24638i	−0.289073	+	0.957307i	$0.593347\pi$
$827$	−1030.76	+	1030.76i	−1.24638	+	1.24638i	−0.957307	+	0.289073i	$0.906653\pi$
$828$	291.106	+	291.106i	0.351577	+	0.351577i
$829$		−	37.4235i		−	0.0451429i	−0.999745	−	0.0225714i	$-0.992815\pi$
$829$		−	37.4235i		−	0.0451429i	0.999745	−	0.0225714i	$-0.00718533\pi$
$830$	251.621	−	397.510i	0.303158	−	0.478927i
$831$	−699.353			−0.841580
$832$	−1081.47	+	1081.47i	−1.29984	+	1.29984i
$833$	−118.783	−	118.783i	−0.142597	−	0.142597i
$834$			453.242i			0.543455i
$835$	−150.454	−	669.444i	−0.180185	−	0.801729i
$836$	−408.817			−0.489016
$837$	68.6969	−	68.6969i	0.0820752	−	0.0820752i
$838$	−1297.91	−	1297.91i	−1.54882	−	1.54882i
$839$			1152.37i			1.37351i	0.726890	+	0.686754i	$0.240965\pi$
$839$			1152.37i			1.37351i	−0.726890	+	0.686754i	$0.759035\pi$
$840$	−103.485	+	23.2577i	−0.123196	+	0.0276877i
$841$	840.271			0.999134
$842$	−474.207	+	474.207i	−0.563191	+	0.563191i
$843$	456.459	+	456.459i	0.541469	+	0.541469i
$844$		−	1561.98i		−	1.85068i
$845$	208.633	+	132.064i	0.246903	+	0.156288i
$846$	−263.666			−0.311662
$847$	159.136	−	159.136i	0.187882	−	0.187882i
$848$	137.687	+	137.687i	0.162366	+	0.162366i
$849$		−	189.081i		−	0.222710i
$850$	−266.586	+	126.202i	−0.313630	+	0.148473i
$851$	1251.66			1.47081
$852$	−491.283	+	491.283i	−0.576623	+	0.576623i
$853$	694.570	+	694.570i	0.814267	+	0.814267i	0.985270	−	0.171003i	$-0.0547009\pi$
$853$	694.570	+	694.570i	0.814267	+	0.814267i	−0.171003	+	0.985270i	$0.554701\pi$
$854$		−	606.838i		−	0.710583i
$855$	−166.045	+	262.318i	−0.194205	+	0.306805i
$856$	−40.0704			−0.0468112
$857$	417.176	−	417.176i	0.486786	−	0.486786i	−0.420504	−	0.907291i	$-0.638147\pi$
$857$	417.176	−	417.176i	0.486786	−	0.486786i	0.907291	+	0.420504i	$0.138147\pi$
$858$	−190.677	−	190.677i	−0.222234	−	0.222234i
$859$		−	486.867i		−	0.566784i	−0.959004	−	0.283392i	$-0.908540\pi$
$859$		−	486.867i		−	0.566784i	0.959004	−	0.283392i	$-0.0914597\pi$
$860$	−205.748	−	915.473i	−0.239242	−	1.06450i
$861$	101.889			0.118338
$862$	−416.838	+	416.838i	−0.483570	+	0.483570i
$863$	−411.319	−	411.319i	−0.476615	−	0.476615i	0.427432	−	0.904047i	$-0.359418\pi$
$863$	−411.319	−	411.319i	−0.476615	−	0.476615i	−0.904047	+	0.427432i	$0.859418\pi$
$864$		−	202.621i		−	0.234515i
$865$	−238.919	+	53.6959i	−0.276207	+	0.0620762i
$866$	−688.994			−0.795606
$867$	−336.730	+	336.730i	−0.388385	+	0.388385i
$868$	−159.868	−	159.868i	−0.184180	−	0.184180i
$869$			82.0204i			0.0943848i
$870$	19.6515	+	12.4393i	0.0225880	+	0.0142980i
$871$	1147.33			1.31726
$872$	166.045	−	166.045i	0.190419	−	0.190419i
$873$	43.7878	+	43.7878i	0.0501578	+	0.0501578i
$874$		−	1514.85i		−	1.73323i
$875$	201.918	−	157.753i	0.230764	−	0.180289i
$876$	−574.913			−0.656293
$877$	332.540	−	332.540i	0.379179	−	0.379179i	−0.491627	−	0.870806i	$-0.663598\pi$
$877$	332.540	−	332.540i	0.379179	−	0.379179i	0.870806	+	0.491627i	$0.163598\pi$
$878$	−562.702	−	562.702i	−0.640890	−	0.640890i
$879$		−	579.464i		−	0.659231i
$880$	−42.9638	+	67.8740i	−0.0488225	+	0.0771295i
$881$	533.151			0.605166			0.302583	−	0.953123i	$-0.402151\pi$
$881$	533.151			0.605166			0.302583	+	0.953123i	$0.402151\pi$
$882$	298.992	−	298.992i	0.338993	−	0.338993i
$883$	−745.939	−	745.939i	−0.844778	−	0.844778i	0.144698	−	0.989476i	$-0.453779\pi$
$883$	−745.939	−	745.939i	−0.844778	−	0.844778i	−0.989476	+	0.144698i	$0.953779\pi$
$884$		−	326.888i		−	0.369783i
$885$	−212.561	−	945.787i	−0.240182	−	1.06869i
$886$	1873.82			2.11492
$887$	−386.207	+	386.207i	−0.435408	+	0.435408i	−0.890463	−	0.455055i	$-0.849619\pi$
$887$	−386.207	+	386.207i	−0.435408	+	0.435408i	0.455055	+	0.890463i	$0.349619\pi$
$888$	393.712	+	393.712i	0.443369	+	0.443369i
$889$		−	332.284i		−	0.373772i
$890$	−1445.54	+	324.879i	−1.62421	+	0.365032i
$891$	30.1362			0.0338229
$892$	−197.197	+	197.197i	−0.221073	+	0.221073i
$893$	408.817	+	408.817i	0.457802	+	0.457802i
$894$			649.287i			0.726272i
$895$	776.135	+	491.288i	0.867190	+	0.548925i
$896$	−347.753			−0.388117
$897$	421.040	−	421.040i	0.469387	−	0.469387i
$898$	662.772	+	662.772i	0.738053	+	0.738053i
$899$			15.9592i			0.0177521i
$900$	−189.303	−	399.879i	−0.210337	−	0.444310i
$901$	−152.182			−0.168903
$902$	−213.778	+	213.778i	−0.237004	+	0.237004i
$903$	−79.8684	−	79.8684i	−0.0884478	−	0.0884478i
$904$			121.323i			0.134207i
$905$	−58.1046	+	91.7934i	−0.0642040	+	0.101429i
$906$	790.009			0.871975
$907$	−947.342	+	947.342i	−1.04448	+	1.04448i	−0.0455146	+	0.998964i	$0.514493\pi$
$907$	−947.342	+	947.342i	−1.04448	+	1.04448i	−0.998964	+	0.0455146i	$0.985507\pi$
$908$	124.890	+	124.890i	0.137544	+	0.137544i
$909$			520.863i			0.573006i
$910$	104.495	+	464.949i	0.114830	+	0.510933i
$911$	−1149.36			−1.26165			−0.630824	−	0.775926i	$-0.717283\pi$
$911$	−1149.36			−1.26165			−0.630824	+	0.775926i	$0.717283\pi$
$912$	−121.621	+	121.621i	−0.133356	+	0.133356i
$913$	70.8082	+	70.8082i	0.0775555	+	0.0775555i
$914$			1271.43i			1.39106i
$915$	795.019	−	178.677i	0.868874	−	0.195275i
$916$	1438.16			1.57004
$917$	37.8842	−	37.8842i	0.0413132	−	0.0413132i
$918$	43.3485	+	43.3485i	0.0472206	+	0.0472206i
$919$		−	412.577i		−	0.448941i	−0.974481	−	0.224470i	$-0.927935\pi$
$919$		−	412.577i		−	0.448941i	0.974481	−	0.224470i	$-0.0720652\pi$
$920$	587.196	+	371.691i	0.638257	+	0.404012i
$921$	413.889			0.449391
$922$	−1171.59	+	1171.59i	−1.27071	+	1.27071i
$923$	710.565	+	710.565i	0.769843	+	0.769843i
$924$		−	70.1316i		−	0.0759000i
$925$	−1266.64	−	452.702i	−1.36934	−	0.489407i
$926$	−1493.70			−1.61307
$927$	194.258	−	194.258i	0.209555	−	0.209555i
$928$	23.5357	+	23.5357i	0.0253618	+	0.0253618i
$929$			151.707i			0.163302i	0.996661	+	0.0816508i	$0.0260192\pi$
$929$			151.707i			0.163302i	−0.996661	+	0.0816508i	$0.973981\pi$
$930$	272.474	−	430.454i	0.292983	−	0.462854i
$931$	−927.181			−0.995898
$932$	953.934	−	953.934i	1.02353	−	1.02353i
$933$	433.930	+	433.930i	0.465091	+	0.465091i
$934$			2174.65i			2.32832i
$935$	−13.7663	−	61.2531i	−0.0147233	−	0.0655113i
$936$	264.879			0.282990
$937$	662.090	−	662.090i	0.706606	−	0.706606i	−0.259214	−	0.965820i	$-0.583463\pi$
$937$	662.090	−	662.090i	0.706606	−	0.706606i	0.965820	+	0.259214i	$0.0834635\pi$
$938$	354.070	+	354.070i	0.377474	+	0.377474i
$939$			373.237i			0.397484i
$940$	−803.868	+	180.665i	−0.855179	+	0.192197i
$941$	−1533.77			−1.62994			−0.814969	−	0.579505i	$-0.803246\pi$
$941$	−1533.77			−1.62994			−0.814969	+	0.579505i	$0.803246\pi$
$942$	−278.722	+	278.722i	−0.295883	+	0.295883i
$943$	−472.050	−	472.050i	−0.500583	−	0.500583i
$944$		−	537.056i		−	0.568915i
$945$	−45.0000	−	28.4847i	−0.0476190	−	0.0301425i
$946$	335.151			0.354282
$947$	1173.19	−	1173.19i	1.23885	−	1.23885i	0.278377	−	0.960472i	$-0.410204\pi$
$947$	1173.19	−	1173.19i	1.23885	−	1.23885i	0.960472	−	0.278377i	$-0.0897964\pi$
$948$	−176.969	−	176.969i	−0.186677	−	0.186677i
$949$			831.523i			0.876210i
$950$	−547.893	+	1532.98i	−0.576730	+	1.61367i
$951$	−1046.46			−1.10038
$952$	32.4745	−	32.4745i	0.0341119	−	0.0341119i
$953$	−145.501	−	145.501i	−0.152676	−	0.152676i	0.626636	−	0.779312i	$-0.284431\pi$
$953$	−145.501	−	145.501i	−0.152676	−	0.152676i	−0.779312	+	0.626636i	$0.784431\pi$
$954$		−	383.060i		−	0.401531i
$955$	−107.212	+	169.373i	−0.112264	+	0.177354i
$956$	1924.26			2.01282
$957$	−3.50052	+	3.50052i	−0.00365780	+	0.00365780i
$958$	−411.464	−	411.464i	−0.429503	−	0.429503i
$959$			42.4153i			0.0442287i
$960$	−196.535	−	874.479i	−0.204724	−	0.910916i
$961$	−611.424			−0.636238
$962$	1768.92	−	1768.92i	1.83879	−	1.83879i
$963$	−14.2270	−	14.2270i	−0.0147737	−	0.0147737i
$964$			787.959i			0.817385i
$965$	535.121	−	120.266i	0.554530	−	0.124628i
$966$	259.868			0.269015
$967$	1151.69	−	1151.69i	1.19099	−	1.19099i	0.214204	−	0.976789i	$-0.431284\pi$
$967$	1151.69	−	1151.69i	1.19099	−	1.19099i	0.976789	−	0.214204i	$-0.0687158\pi$
$968$	−463.825	−	463.825i	−0.479158	−	0.479158i
$969$		−	134.424i		−	0.138725i
$970$	274.373	+	173.677i	0.282859	+	0.179048i
$971$	72.4383			0.0746017			0.0373009	−	0.999304i	$-0.488124\pi$
$971$	72.4383			0.0746017			0.0373009	+	0.999304i	$0.488124\pi$
$972$	−65.0227	+	65.0227i	−0.0668958	+	0.0668958i
$973$	120.556	+	120.556i	0.123901	+	0.123901i
$974$		−	536.974i		−	0.551308i
$975$	−578.363	+	273.798i	−0.593193	+	0.280818i
$976$	451.444			0.462545
$977$	706.338	−	706.338i	0.722966	−	0.722966i	−0.246242	−	0.969208i	$-0.579196\pi$
$977$	706.338	−	706.338i	0.722966	−	0.722966i	0.969208	+	0.246242i	$0.0791958\pi$
$978$	−1032.10	−	1032.10i	−1.05532	−	1.05532i
$979$		−	315.364i		−	0.322129i
$980$	706.699	−	1116.44i	0.721122	−	1.13923i
$981$	117.909			0.120193
$982$	235.116	−	235.116i	0.239425	−	0.239425i
$983$	−134.663	−	134.663i	−0.136992	−	0.136992i	0.635286	−	0.772277i	$-0.280882\pi$
$983$	−134.663	−	134.663i	−0.136992	−	0.136992i	−0.772277	+	0.635286i	$0.780882\pi$
$984$		−	296.969i		−	0.301798i
$985$	104.354	+	464.322i	0.105943	+	0.471393i
$986$	−10.0704			−0.0102134
$987$	−70.1316	+	70.1316i	−0.0710554	+	0.0710554i
$988$	−1275.79	−	1275.79i	−1.29128	−	1.29128i
$989$			740.059i			0.748290i
$990$	154.182	−	34.6515i	0.155739	−	0.0350015i
$991$	−1131.94			−1.14222			−0.571109	−	0.820874i	$-0.693487\pi$
$991$	−1131.94			−1.14222			−0.571109	+	0.820874i	$0.693487\pi$
$992$	515.535	−	515.535i	0.519692	−	0.519692i
$993$	599.419	+	599.419i	0.603644	+	0.603644i
$994$			438.565i			0.441213i
$995$	−1062.07	−	672.286i	−1.06741	−	0.675665i
$996$	−305.555			−0.306782
$997$	−1115.27	+	1115.27i	−1.11862	+	1.11862i	−0.126679	+	0.991944i	$0.540432\pi$
$997$	−1115.27	+	1115.27i	−1.11862	+	1.11862i	−0.991944	+	0.126679i	$0.959568\pi$
$998$	−1645.39	−	1645.39i	−1.64868	−	1.64868i
$999$			279.576i			0.279855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.3.f.a.13.1	yes	4
3.2	odd	2		45.3.g.b.28.2		4
4.3	odd	2		240.3.bg.a.193.1		4
5.2	odd	4	inner	15.3.f.a.7.1	✓	4
5.3	odd	4		75.3.f.c.7.2		4
5.4	even	2		75.3.f.c.43.2		4
8.3	odd	2		960.3.bg.h.193.2		4
8.5	even	2		960.3.bg.i.193.1		4
9.2	odd	6		405.3.l.f.28.1		8
9.4	even	3		405.3.l.h.298.1		8
9.5	odd	6		405.3.l.f.298.2		8
9.7	even	3		405.3.l.h.28.2		8
12.11	even	2		720.3.bh.k.433.1		4
15.2	even	4		45.3.g.b.37.2		4
15.8	even	4		225.3.g.a.82.1		4
15.14	odd	2		225.3.g.a.118.1		4
20.3	even	4		1200.3.bg.k.1057.2		4
20.7	even	4		240.3.bg.a.97.1		4
20.19	odd	2		1200.3.bg.k.193.2		4
40.27	even	4		960.3.bg.h.577.2		4
40.37	odd	4		960.3.bg.i.577.1		4
45.2	even	12		405.3.l.f.352.2		8
45.7	odd	12		405.3.l.h.352.1		8
45.22	odd	12		405.3.l.h.217.2		8
45.32	even	12		405.3.l.f.217.1		8
60.47	odd	4		720.3.bh.k.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.1	✓	4	5.2	odd	4	inner
15.3.f.a.13.1	yes	4	1.1	even	1	trivial
45.3.g.b.28.2		4	3.2	odd	2
45.3.g.b.37.2		4	15.2	even	4
75.3.f.c.7.2		4	5.3	odd	4
75.3.f.c.43.2		4	5.4	even	2
225.3.g.a.82.1		4	15.8	even	4
225.3.g.a.118.1		4	15.14	odd	2
240.3.bg.a.97.1		4	20.7	even	4
240.3.bg.a.193.1		4	4.3	odd	2
405.3.l.f.28.1		8	9.2	odd	6
405.3.l.f.217.1		8	45.32	even	12
405.3.l.f.298.2		8	9.5	odd	6
405.3.l.f.352.2		8	45.2	even	12
405.3.l.h.28.2		8	9.7	even	3
405.3.l.h.217.2		8	45.22	odd	12
405.3.l.h.298.1		8	9.4	even	3
405.3.l.h.352.1		8	45.7	odd	12
720.3.bh.k.433.1		4	12.11	even	2
720.3.bh.k.577.1		4	60.47	odd	4
960.3.bg.h.193.2		4	8.3	odd	2
960.3.bg.h.577.2		4	40.27	even	4
960.3.bg.i.193.1		4	8.5	even	2
960.3.bg.i.577.1		4	40.37	odd	4
1200.3.bg.k.193.2		4	20.19	odd	2
1200.3.bg.k.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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	15.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.22474 + 2.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} -5.89898i q^{4} +(2.67423 - 4.22474i) q^{5} -5.44949 q^{6} +(-1.44949 + 1.44949i) q^{7} +(4.22474 + 4.22474i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-2.22474 + 2.22474i) q^{2} +(1.22474 + 1.22474i) q^{3} -5.89898i q^{4} +(2.67423 - 4.22474i) q^{5} -5.44949 q^{6} +(-1.44949 + 1.44949i) q^{7} +(4.22474 + 4.22474i) q^{8} +3.00000i q^{9} +(3.44949 + 15.3485i) q^{10} -3.34847 q^{11} +(7.22474 - 7.22474i) q^{12} +(-10.4495 - 10.4495i) q^{13} -6.44949i q^{14} +(8.44949 - 1.89898i) q^{15} +4.79796 q^{16} +(-2.65153 + 2.65153i) q^{17} +(-6.67423 - 6.67423i) q^{18} +20.6969i q^{19} +(-24.9217 - 15.7753i) q^{20} -3.55051 q^{21} +(7.44949 - 7.44949i) q^{22} +(16.4495 + 16.4495i) q^{23} +10.3485i q^{24} +(-10.6969 - 22.5959i) q^{25} +46.4949 q^{26} +(-3.67423 + 3.67423i) q^{27} +(8.55051 + 8.55051i) q^{28} -0.853572i q^{29} +(-14.5732 + 23.0227i) q^{30} -18.6969 q^{31} +(-27.5732 + 27.5732i) q^{32} +(-4.10102 - 4.10102i) q^{33} -11.7980i q^{34} +(2.24745 + 10.0000i) q^{35} +17.6969 q^{36} +(38.0454 - 38.0454i) q^{37} +(-46.0454 - 46.0454i) q^{38} -25.5959i q^{39} +(29.1464 - 6.55051i) q^{40} -28.6969 q^{41} +(7.89898 - 7.89898i) q^{42} +(22.4949 + 22.4949i) q^{43} +19.7526i q^{44} +(12.6742 + 8.02270i) q^{45} -73.1918 q^{46} +(19.7526 - 19.7526i) q^{47} +(5.87628 + 5.87628i) q^{48} +44.7980i q^{49} +(74.0681 + 26.4722i) q^{50} -6.49490 q^{51} +(-61.6413 + 61.6413i) q^{52} +(28.6969 + 28.6969i) q^{53} -16.3485i q^{54} +(-8.95459 + 14.1464i) q^{55} -12.2474 q^{56} +(-25.3485 + 25.3485i) q^{57} +(1.89898 + 1.89898i) q^{58} -111.934i q^{59} +(-11.2020 - 49.8434i) q^{60} +94.0908 q^{61} +(41.5959 - 41.5959i) q^{62} +(-4.34847 - 4.34847i) q^{63} -103.495i q^{64} +(-72.0908 + 16.2020i) q^{65} +18.2474 q^{66} +(-54.8990 + 54.8990i) q^{67} +(15.6413 + 15.6413i) q^{68} +40.2929i q^{69} +(-27.2474 - 17.2474i) q^{70} -68.0000 q^{71} +(-12.6742 + 12.6742i) q^{72} +(-39.7878 - 39.7878i) q^{73} +169.283i q^{74} +(14.5732 - 40.7753i) q^{75} +122.091 q^{76} +(4.85357 - 4.85357i) q^{77} +(56.9444 + 56.9444i) q^{78} -24.4949i q^{79} +(12.8309 - 20.2702i) q^{80} -9.00000 q^{81} +(63.8434 - 63.8434i) q^{82} +(-21.1464 - 21.1464i) q^{83} +20.9444i q^{84} +(4.11123 + 18.2929i) q^{85} -100.091 q^{86} +(1.04541 - 1.04541i) q^{87} +(-14.1464 - 14.1464i) q^{88} +94.1816i q^{89} +(-46.0454 + 10.3485i) q^{90} +30.2929 q^{91} +(97.0352 - 97.0352i) q^{92} +(-22.8990 - 22.8990i) q^{93} +87.8888i q^{94} +(87.4393 + 55.3485i) q^{95} -67.5403 q^{96} +(14.5959 - 14.5959i) q^{97} +(-99.6640 - 99.6640i) q^{98} -10.0454i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{5} - 12 q^{6} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^5 - 12 * q^6 + 4 * q^7 + 12 * q^8	\( 4 q - 4 q^{2} - 4 q^{5} - 12 q^{6} + 4 q^{7} + 12 q^{8} + 4 q^{10} + 16 q^{11} + 24 q^{12} - 32 q^{13} + 24 q^{15} - 20 q^{16} - 40 q^{17} - 12 q^{18} - 36 q^{20} - 24 q^{21} + 20 q^{22} + 56 q^{23} + 16 q^{25} + 88 q^{26} + 44 q^{28} - 24 q^{30} - 16 q^{31} - 76 q^{32} - 36 q^{33} - 40 q^{35} + 12 q^{36} + 64 q^{37} - 96 q^{38} + 48 q^{40} - 56 q^{41} + 12 q^{42} - 8 q^{43} + 36 q^{45} - 136 q^{46} + 128 q^{47} + 48 q^{48} + 164 q^{50} + 72 q^{51} - 80 q^{52} + 56 q^{53} - 124 q^{55} - 72 q^{57} - 12 q^{58} - 84 q^{60} + 200 q^{61} + 88 q^{62} + 12 q^{63} - 112 q^{65} + 24 q^{66} - 200 q^{67} - 104 q^{68} - 60 q^{70} - 272 q^{71} - 36 q^{72} + 76 q^{73} + 24 q^{75} + 312 q^{76} + 88 q^{77} + 120 q^{78} + 164 q^{80} - 36 q^{81} + 128 q^{82} - 16 q^{83} + 232 q^{85} - 224 q^{86} - 84 q^{87} + 12 q^{88} - 96 q^{90} - 16 q^{91} + 104 q^{92} - 72 q^{93} + 144 q^{95} - 84 q^{96} - 20 q^{97} - 188 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^5 - 12 * q^6 + 4 * q^7 + 12 * q^8 + 4 * q^10 + 16 * q^11 + 24 * q^12 - 32 * q^13 + 24 * q^15 - 20 * q^16 - 40 * q^17 - 12 * q^18 - 36 * q^20 - 24 * q^21 + 20 * q^22 + 56 * q^23 + 16 * q^25 + 88 * q^26 + 44 * q^28 - 24 * q^30 - 16 * q^31 - 76 * q^32 - 36 * q^33 - 40 * q^35 + 12 * q^36 + 64 * q^37 - 96 * q^38 + 48 * q^40 - 56 * q^41 + 12 * q^42 - 8 * q^43 + 36 * q^45 - 136 * q^46 + 128 * q^47 + 48 * q^48 + 164 * q^50 + 72 * q^51 - 80 * q^52 + 56 * q^53 - 124 * q^55 - 72 * q^57 - 12 * q^58 - 84 * q^60 + 200 * q^61 + 88 * q^62 + 12 * q^63 - 112 * q^65 + 24 * q^66 - 200 * q^67 - 104 * q^68 - 60 * q^70 - 272 * q^71 - 36 * q^72 + 76 * q^73 + 24 * q^75 + 312 * q^76 + 88 * q^77 + 120 * q^78 + 164 * q^80 - 36 * q^81 + 128 * q^82 - 16 * q^83 + 232 * q^85 - 224 * q^86 - 84 * q^87 + 12 * q^88 - 96 * q^90 - 16 * q^91 + 104 * q^92 - 72 * q^93 + 144 * q^95 - 84 * q^96 - 20 * q^97 - 188 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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