LMFDB - Embedded newform 15.3.f.a.7.1

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			7.1
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	15.7
Dual form			15.3.f.a.13.1

$q$-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 $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.22474	−	2.22474i	−1.11237	−	1.11237i	−0.992829	−	0.119543i	$-0.961857\pi$
$2$	−2.22474	−	2.22474i	−1.11237	−	1.11237i	−0.119543	−	0.992829i	$-0.538143\pi$
$3$	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	0.595951	−	0.803021i	$-0.296775\pi$
$7$	−1.44949	−	1.44949i	−0.207070	−	0.207070i	−0.803021	+	0.595951i	$0.796775\pi$
$8$	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	−0.983688	−	0.179881i	$-0.942429\pi$
$13$	−10.4495	+	10.4495i	−0.803807	+	0.803807i	0.179881	+	0.983688i	$0.442429\pi$
$14$			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	0.624807	−	0.780779i	$-0.285178\pi$
$17$	−2.65153	−	2.65153i	−0.155972	−	0.155972i	−0.780779	+	0.624807i	$0.785178\pi$
$18$	−6.67423	+	6.67423i	−0.370791	+	0.370791i
$19$		−	20.6969i		−	1.08931i	−0.838659	−	0.544656i	$-0.816660\pi$
$19$		−	20.6969i		−	1.08931i	0.838659	−	0.544656i	$-0.183340\pi$
$20$	−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	−0.252422	−	0.967617i	$-0.581227\pi$
$23$	16.4495	−	16.4495i	0.715195	−	0.715195i	0.967617	+	0.252422i	$0.0812271\pi$
$24$		−	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	$0.00468466\pi$
$29$			0.853572i			0.0294335i	−0.999892	+	0.0147168i	$0.995315\pi$
$30$	−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	0.999589	+	0.0286652i	$0.00912566\pi$
$37$	38.0454	+	38.0454i	1.02825	+	1.02825i	0.0286652	+	0.999589i	$0.490874\pi$
$38$	−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	−0.395380	−	0.918517i	$-0.629387\pi$
$43$	22.4949	−	22.4949i	0.523137	−	0.523137i	0.918517	+	0.395380i	$0.129387\pi$
$44$		−	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	0.885296	−	0.465029i	$-0.153956\pi$
$47$	19.7526	+	19.7526i	0.420267	+	0.420267i	−0.465029	+	0.885296i	$0.653956\pi$
$48$	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	−0.382503	−	0.923954i	$-0.624938\pi$
$53$	28.6969	−	28.6969i	0.541452	−	0.541452i	0.923954	+	0.382503i	$0.124938\pi$
$54$			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	$0.397495\pi$
$59$			111.934i			1.89719i	−0.316493	+	0.948595i	$0.602505\pi$
$60$	−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	0.166631	−	0.986019i	$-0.446711\pi$
$67$	−54.8990	−	54.8990i	−0.819388	−	0.819388i	−0.986019	+	0.166631i	$0.946711\pi$
$68$	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	−0.925001	−	0.379964i	$-0.875936\pi$
$73$	−39.7878	+	39.7878i	−0.545038	+	0.545038i	0.379964	+	0.925001i	$0.375936\pi$
$74$		−	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	$0.0495477\pi$
$79$			24.4949i			0.310062i	−0.987910	+	0.155031i	$0.950452\pi$
$80$	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	−0.822926	−	0.568149i	$-0.807660\pi$
$83$	−21.1464	+	21.1464i	−0.254776	+	0.254776i	0.568149	+	0.822926i	$0.307660\pi$
$84$		−	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	$-0.822526\pi$
$89$		−	94.1816i		−	1.05822i	0.848553	−	0.529110i	$-0.177474\pi$
$90$	−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	0.778329	−	0.627856i	$-0.216067\pi$
$97$	14.5959	+	14.5959i	0.150473	+	0.150473i	−0.627856	+	0.778329i	$0.716067\pi$
$98$	−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	−0.947732	−	0.319067i	$-0.896631\pi$
$103$	−64.7526	+	64.7526i	−0.628666	+	0.628666i	0.319067	+	0.947732i	$0.396631\pi$
$104$			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	0.684599	−	0.728920i	$-0.259977\pi$
$107$	−4.74235	−	4.74235i	−0.0443210	−	0.0443210i	−0.728920	+	0.684599i	$0.759977\pi$
$108$	21.6742	−	21.6742i	0.200687	−	0.200687i
$109$			39.3031i			0.360579i	0.983614	+	0.180289i	$0.0577034\pi$
$109$			39.3031i			0.360579i	−0.983614	+	0.180289i	$0.942297\pi$
$110$	−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	−0.640713	−	0.767781i	$-0.721361\pi$
$113$	14.3587	−	14.3587i	0.127068	−	0.127068i	0.767781	+	0.640713i	$0.221361\pi$
$114$			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	0.0931273	−	0.995654i	$-0.470314\pi$
$127$	−114.621	−	114.621i	−0.902527	−	0.902527i	−0.995654	+	0.0931273i	$0.970314\pi$
$128$	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	0.758486	−	0.651689i	$-0.225939\pi$
$137$	14.6311	+	14.6311i	0.106796	+	0.106796i	−0.651689	+	0.758486i	$0.725939\pi$
$138$	−89.6413	+	89.6413i	−0.649575	+	0.649575i
$139$			83.1714i			0.598356i	0.954197	+	0.299178i	$0.0967124\pi$
$139$			83.1714i			0.598356i	−0.954197	+	0.299178i	$0.903288\pi$
$140$	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	$0.130927\pi$
$149$			119.146i			0.799640i	−0.916594	+	0.399820i	$0.869073\pi$
$150$	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	0.850977	−	0.525203i	$-0.176011\pi$
$157$	51.1464	+	51.1464i	0.325773	+	0.325773i	−0.525203	+	0.850977i	$0.676011\pi$
$158$	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	0.177872	−	0.984054i	$-0.443079\pi$
$163$	189.394	−	189.394i	1.16193	−	1.16193i	0.984054	−	0.177872i	$-0.0569213\pi$
$164$		−	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	0.935192	−	0.354142i	$-0.115227\pi$
$167$	97.0352	+	97.0352i	0.581049	+	0.581049i	−0.354142	+	0.935192i	$0.615227\pi$
$168$	−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	−0.800077	−	0.599897i	$-0.795208\pi$
$173$	−34.6311	+	34.6311i	−0.200180	+	0.200180i	0.599897	+	0.800077i	$0.295208\pi$
$174$		−	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	$-0.828474\pi$
$179$		−	183.712i		−	1.02632i	0.858292	−	0.513161i	$-0.171526\pi$
$180$	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	−0.477007	−	0.878900i	$-0.658278\pi$
$193$	77.5653	−	77.5653i	0.401893	−	0.401893i	0.878900	+	0.477007i	$0.158278\pi$
$194$		−	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	0.515344	−	0.856984i	$-0.327664\pi$
$197$	−67.3031	−	67.3031i	−0.341640	−	0.341640i	−0.856984	+	0.515344i	$0.827664\pi$
$198$	22.3485	−	22.3485i	0.112871	−	0.112871i
$199$			251.394i			1.26329i	0.775259	+	0.631643i	$0.217619\pi$
$199$			251.394i			1.26329i	−0.775259	+	0.631643i	$0.782381\pi$
$200$	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	−0.778076	−	0.628170i	$-0.783804\pi$
$223$	−33.4291	+	33.4291i	−0.149906	+	0.149906i	0.628170	+	0.778076i	$0.283804\pi$
$224$			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	0.658934	−	0.752200i	$-0.271008\pi$
$227$	−21.1714	−	21.1714i	−0.0932662	−	0.0932662i	−0.752200	+	0.658934i	$0.771008\pi$
$228$	149.530	−	149.530i	0.655834	−	0.655834i
$229$		−	243.798i		−	1.06462i	−0.846550	−	0.532310i	$-0.821324\pi$
$229$		−	243.798i		−	1.06462i	0.846550	−	0.532310i	$-0.178676\pi$
$230$	−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	−0.269077	−	0.963119i	$-0.586719\pi$
$233$	161.712	−	161.712i	0.694042	−	0.694042i	0.963119	+	0.269077i	$0.0867186\pi$
$234$		−	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	$-0.760923\pi$
$239$		−	326.202i		−	1.36486i	0.730950	−	0.682431i	$-0.239077\pi$
$240$	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	0.511849	−	0.859076i	$-0.328961\pi$
$257$	−89.2372	−	89.2372i	−0.347227	−	0.347227i	−0.859076	+	0.511849i	$0.828961\pi$
$258$	−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	−0.371253	+	0.928532i	$0.621072\pi$
$263$	−341.843	+	341.843i	−1.29978	+	1.29978i	−0.928532	+	0.371253i	$0.878928\pi$
$264$			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	$-0.997929\pi$
$269$		−	3.50052i		−	0.0130131i	0.999979	−	0.00650653i	$-0.00207111\pi$
$270$	−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	−0.999513	−	0.0312080i	$-0.990065\pi$
$277$	−285.510	−	285.510i	−1.03072	−	1.03072i	−0.0312080	−	0.999513i	$-0.509935\pi$
$278$	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	−0.830211	−	0.557449i	$-0.811780\pi$
$283$	−77.1918	+	77.1918i	−0.272763	+	0.272763i	0.557449	+	0.830211i	$0.311780\pi$
$284$		−	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	−0.984238	−	0.176848i	$-0.943410\pi$
$293$	−236.565	+	236.565i	−0.807390	+	0.807390i	0.176848	+	0.984238i	$0.443410\pi$
$294$			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	0.926553	−	0.376164i	$-0.122757\pi$
$307$	168.969	+	168.969i	0.550389	+	0.550389i	−0.376164	+	0.926553i	$0.622757\pi$
$308$	−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	−0.420484	−	0.907300i	$-0.638140\pi$
$313$	152.373	−	152.373i	0.486816	−	0.486816i	0.907300	+	0.420484i	$0.138140\pi$
$314$		−	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	−0.888168	−	0.459519i	$-0.848022\pi$
$317$	−427.217	−	427.217i	−1.34769	−	1.34769i	−0.459519	−	0.888168i	$-0.651978\pi$
$318$	−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	0.992143	−	0.125105i	$-0.0399269\pi$
$337$	292.192	+	292.192i	0.867038	+	0.867038i	−0.125105	+	0.992143i	$0.539927\pi$
$338$	−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	0.997194	−	0.0748598i	$-0.0238509\pi$
$347$	320.050	+	320.050i	0.922334	+	0.922334i	−0.0748598	+	0.997194i	$0.523851\pi$
$348$	−6.16684	+	6.16684i	−0.0177208	+	0.0177208i
$349$			574.009i			1.64473i	0.568964	+	0.822363i	$0.307345\pi$
$349$			574.009i			1.64473i	−0.568964	+	0.822363i	$0.692655\pi$
$350$	−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	−0.220396	−	0.975410i	$-0.570735\pi$
$353$	266.520	−	266.520i	0.755014	−	0.755014i	0.975410	+	0.220396i	$0.0707351\pi$
$354$		−	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	$-0.902608\pi$
$359$		−	216.272i		−	0.602430i	0.953556	−	0.301215i	$-0.0973922\pi$
$360$	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	0.298934	−	0.954274i	$-0.403369\pi$
$367$	−240.510	−	240.510i	−0.655340	−	0.655340i	−0.954274	+	0.298934i	$0.903369\pi$
$368$	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	−0.994065	−	0.108792i	$-0.965302\pi$
$373$	−330.207	+	330.207i	−0.885272	+	0.885272i	0.108792	+	0.994065i	$0.465302\pi$
$374$		−	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	$-0.910645\pi$
$379$		−	210.000i		−	0.554090i	0.960857	−	0.277045i	$-0.0893551\pi$
$380$	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	−0.448347	−	0.893859i	$-0.647987\pi$
$383$	170.631	−	170.631i	0.445512	−	0.445512i	0.893859	+	0.448347i	$0.147987\pi$
$384$		−	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	$0.248389\pi$
$389$			547.337i			1.40704i	−0.710677	+	0.703518i	$0.751611\pi$
$390$	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	0.761805	−	0.647806i	$-0.224313\pi$
$397$	45.2577	+	45.2577i	0.113999	+	0.113999i	−0.647806	+	0.761805i	$0.724313\pi$
$398$	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	$0.139494\pi$
$409$			347.110i			0.848680i	−0.905503	+	0.424340i	$0.860506\pi$
$410$	−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	$-0.754882\pi$
$419$		−	583.398i		−	1.39236i	0.717868	−	0.696180i	$-0.245118\pi$
$420$	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	−0.505317	−	0.862934i	$-0.668624\pi$
$433$	154.848	−	154.848i	0.357617	−	0.357617i	0.862934	+	0.505317i	$0.168624\pi$
$434$		−	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	$-0.906985\pi$
$439$		−	252.929i		−	0.576147i	0.957608	−	0.288074i	$-0.0930148\pi$
$440$	−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	−0.998838	−	0.0482041i	$-0.984650\pi$
$443$	−421.131	+	421.131i	−0.950633	+	0.950633i	0.0482041	+	0.998838i	$0.484650\pi$
$444$			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	$0.107638\pi$
$449$			297.909i			0.663495i	−0.943368	+	0.331747i	$0.892362\pi$
$450$	−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	0.946873	−	0.321607i	$-0.104223\pi$
$457$	285.747	+	285.747i	0.625267	+	0.625267i	−0.321607	+	0.946873i	$0.604223\pi$
$458$	−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	−0.244573	−	0.969631i	$-0.578648\pi$
$463$	335.702	−	335.702i	0.725057	−	0.725057i	0.969631	+	0.244573i	$0.0786479\pi$
$464$			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	0.998862	+	0.0476956i	$0.0151877\pi$
$467$	488.742	+	488.742i	1.04656	+	1.04656i	0.0476956	+	0.998862i	$0.484812\pi$
$468$	−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	$-0.938160\pi$
$479$		−	184.949i		−	0.386115i	0.981187	−	0.193057i	$-0.0618404\pi$
$480$	−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	0.572263	−	0.820070i	$-0.306066\pi$
$487$	−120.682	−	120.682i	−0.247807	−	0.247807i	−0.820070	+	0.572263i	$0.806066\pi$
$488$	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	$-0.734320\pi$
$499$		−	739.585i		−	1.48213i	0.671431	−	0.741067i	$-0.265680\pi$
$500$	−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	−0.984326	−	0.176357i	$-0.943569\pi$
$503$	−406.409	+	406.409i	−0.807970	+	0.807970i	0.176357	+	0.984326i	$0.443569\pi$
$504$			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	$0.0611962\pi$
$509$			194.511i			0.382143i	−0.981576	+	0.191071i	$0.938804\pi$
$510$	−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	−0.829359	−	0.558716i	$-0.811294\pi$
$523$	−141.546	+	141.546i	−0.270642	+	0.270642i	0.558716	+	0.829359i	$0.311294\pi$
$524$		−	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	0.169728	−	0.985491i	$-0.445711\pi$
$547$	−446.222	−	446.222i	−0.815763	−	0.815763i	−0.985491	+	0.169728i	$0.945711\pi$
$548$	−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	0.872672	−	0.488308i	$-0.162386\pi$
$557$	214.091	+	214.091i	0.384364	+	0.384364i	−0.488308	+	0.872672i	$0.662386\pi$
$558$	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	0.217579	−	0.976043i	$-0.430184\pi$
$563$	672.009	−	672.009i	1.19362	−	1.19362i	0.976043	−	0.217579i	$-0.0698161\pi$
$564$			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	$-0.674003\pi$
$569$		−	972.161i		−	1.70854i	0.519827	−	0.854272i	$-0.325997\pi$
$570$	−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	0.128797	−	0.991671i	$-0.458889\pi$
$577$	−497.879	−	497.879i	−0.862874	−	0.862874i	−0.991671	+	0.128797i	$0.958889\pi$
$578$	−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	0.911058	−	0.412279i	$-0.135267\pi$
$587$	292.783	+	292.783i	0.498779	+	0.498779i	−0.412279	+	0.911058i	$0.635267\pi$
$588$	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	−0.215524	−	0.976498i	$-0.569146\pi$
$593$	451.258	−	451.258i	0.760974	−	0.760974i	0.976498	+	0.215524i	$0.0691461\pi$
$594$		−	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	$0.00873154\pi$
$599$			32.8582i			0.0548550i	−0.999624	+	0.0274275i	$0.991268\pi$
$600$	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	0.810472	−	0.585778i	$-0.199211\pi$
$607$	136.389	+	136.389i	0.224694	+	0.224694i	−0.585778	+	0.810472i	$0.699211\pi$
$608$	−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	−0.717400	−	0.696661i	$-0.754668\pi$
$613$	−12.7128	+	12.7128i	−0.0207386	+	0.0207386i	0.696661	+	0.717400i	$0.254668\pi$
$614$		−	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	0.305816	−	0.952091i	$-0.401071\pi$
$617$	−398.752	−	398.752i	−0.646275	−	0.646275i	−0.952091	+	0.305816i	$0.901071\pi$
$618$	352.868	−	352.868i	0.570984	−	0.570984i
$619$			819.131i			1.32331i	0.749807	+	0.661656i	$0.230146\pi$
$619$			819.131i			1.32331i	−0.749807	+	0.661656i	$0.769854\pi$
$620$	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	−0.211349	+	0.977411i	$0.567786\pi$
$643$	−764.372	+	764.372i	−1.18876	+	1.18876i	−0.977411	+	0.211349i	$0.932214\pi$
$644$		−	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	0.910372	−	0.413792i	$-0.135796\pi$
$647$	321.287	+	321.287i	0.496580	+	0.496580i	−0.413792	+	0.910372i	$0.635796\pi$
$648$	−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	−0.825081	−	0.565015i	$-0.808870\pi$
$653$	−169.823	+	169.823i	−0.260066	+	0.260066i	0.565015	+	0.825081i	$0.308870\pi$
$654$		−	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	$0.259289\pi$
$659$			958.763i			1.45488i	−0.686174	+	0.727438i	$0.740711\pi$
$660$	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	−0.574070	−	0.818806i	$-0.694636\pi$
$673$	164.707	−	164.707i	0.244736	−	0.244736i	0.818806	+	0.574070i	$0.194636\pi$
$674$		−	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	0.983736	−	0.179618i	$-0.0574861\pi$
$677$	544.388	+	544.388i	0.804119	+	0.804119i	−0.179618	+	0.983736i	$0.557486\pi$
$678$	−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	0.165452	−	0.986218i	$-0.447092\pi$
$683$	786.590	−	786.590i	1.15167	−	1.15167i	0.986218	−	0.165452i	$-0.0529082\pi$
$684$		−	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	$-0.827588\pi$
$709$		−	731.049i		−	1.03110i	0.856860	−	0.515549i	$-0.172412\pi$
$710$	−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	$0.144172\pi$
$719$			629.271i			0.875204i	−0.899169	+	0.437602i	$0.855828\pi$
$720$	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	0.696105	−	0.717940i	$-0.254915\pi$
$727$	−15.8740	−	15.8740i	−0.0218349	−	0.0218349i	−0.717940	+	0.696105i	$0.754915\pi$
$728$	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	−0.922492	−	0.386016i	$-0.873851\pi$
$733$	−393.237	+	393.237i	−0.536476	+	0.536476i	0.386016	+	0.922492i	$0.373851\pi$
$734$			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	$-0.958460\pi$
$739$		−	192.334i		−	0.260262i	0.991497	−	0.130131i	$-0.0415398\pi$
$740$	−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	−0.736548	−	0.676385i	$-0.763546\pi$
$743$	−44.7015	+	44.7015i	−0.0601636	+	0.0601636i	0.676385	+	0.736548i	$0.263546\pi$
$744$			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	0.533894	−	0.845552i	$-0.320728\pi$
$757$	−235.925	−	235.925i	−0.311658	−	0.311658i	−0.845552	+	0.533894i	$0.820728\pi$
$758$	−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	$-0.712304\pi$
$769$		−	1208.40i		−	1.57139i	0.618612	−	0.785697i	$-0.287696\pi$
$770$	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	−0.0562070	+	0.998419i	$0.517901\pi$
$773$	−815.226	+	815.226i	−1.05463	+	1.05463i	−0.998419	+	0.0562070i	$0.982099\pi$
$774$			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	0.999435	+	0.0336150i	$0.0107020\pi$
$787$	813.010	+	813.010i	1.03305	+	1.03305i	0.0336150	+	0.999435i	$0.489298\pi$
$788$	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	0.874860	−	0.484375i	$-0.160953\pi$
$797$	311.217	+	311.217i	0.390485	+	0.390485i	−0.484375	+	0.874860i	$0.660953\pi$
$798$	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	$-0.970448\pi$
$809$		−	150.000i		−	0.185414i	0.995693	−	0.0927070i	$-0.0295520\pi$
$810$	−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	−0.500670	−	0.865638i	$-0.666913\pi$
$823$	300.369	−	300.369i	0.364968	−	0.364968i	0.865638	+	0.500670i	$0.166913\pi$
$824$			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	−0.957307	−	0.289073i	$-0.906653\pi$
$827$	−1030.76	−	1030.76i	−1.24638	−	1.24638i	−0.289073	−	0.957307i	$-0.593347\pi$
$828$	291.106	−	291.106i	0.351577	−	0.351577i
$829$			37.4235i			0.0451429i	0.999745	+	0.0225714i	$0.00718533\pi$
$829$			37.4235i			0.0451429i	−0.999745	+	0.0225714i	$0.992815\pi$
$830$	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	$-0.759035\pi$
$839$		−	1152.37i		−	1.37351i	0.726890	−	0.686754i	$-0.240965\pi$
$840$	−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	−0.171003	−	0.985270i	$-0.554701\pi$
$853$	694.570	−	694.570i	0.814267	−	0.814267i	0.985270	+	0.171003i	$0.0547009\pi$
$854$			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	0.907291	−	0.420504i	$-0.138147\pi$
$857$	417.176	+	417.176i	0.486786	+	0.486786i	−0.420504	+	0.907291i	$0.638147\pi$
$858$	−190.677	+	190.677i	−0.222234	+	0.222234i
$859$			486.867i			0.566784i	0.959004	+	0.283392i	$0.0914597\pi$
$859$			486.867i			0.566784i	−0.959004	+	0.283392i	$0.908540\pi$
$860$	−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	−0.904047	−	0.427432i	$-0.859418\pi$
$863$	−411.319	+	411.319i	−0.476615	+	0.476615i	0.427432	+	0.904047i	$0.359418\pi$
$864$			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	0.870806	−	0.491627i	$-0.163598\pi$
$877$	332.540	+	332.540i	0.379179	+	0.379179i	−0.491627	+	0.870806i	$0.663598\pi$
$878$	−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	−0.989476	−	0.144698i	$-0.953779\pi$
$883$	−745.939	+	745.939i	−0.844778	+	0.844778i	0.144698	+	0.989476i	$0.453779\pi$
$884$			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	0.455055	−	0.890463i	$-0.349619\pi$
$887$	−386.207	−	386.207i	−0.435408	−	0.435408i	−0.890463	+	0.455055i	$0.849619\pi$
$888$	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	−0.998964	−	0.0455146i	$-0.985507\pi$
$907$	−947.342	−	947.342i	−1.04448	−	1.04448i	−0.0455146	−	0.998964i	$-0.514493\pi$
$908$	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	$0.0720652\pi$
$919$			412.577i			0.448941i	−0.974481	+	0.224470i	$0.927935\pi$
$920$	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	$-0.973981\pi$
$929$		−	151.707i		−	0.163302i	0.996661	−	0.0816508i	$-0.0260192\pi$
$930$	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	0.965820	−	0.259214i	$-0.0834635\pi$
$937$	662.090	+	662.090i	0.706606	+	0.706606i	−0.259214	+	0.965820i	$0.583463\pi$
$938$	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	0.960472	+	0.278377i	$0.0897964\pi$
$947$	1173.19	+	1173.19i	1.23885	+	1.23885i	0.278377	+	0.960472i	$0.410204\pi$
$948$	−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	−0.779312	−	0.626636i	$-0.784431\pi$
$953$	−145.501	+	145.501i	−0.152676	+	0.152676i	0.626636	+	0.779312i	$0.284431\pi$
$954$			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	0.976789	+	0.214204i	$0.0687158\pi$
$967$	1151.69	+	1151.69i	1.19099	+	1.19099i	0.214204	+	0.976789i	$0.431284\pi$
$968$	−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	0.969208	−	0.246242i	$-0.0791958\pi$
$977$	706.338	+	706.338i	0.722966	+	0.722966i	−0.246242	+	0.969208i	$0.579196\pi$
$978$	−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	−0.772277	−	0.635286i	$-0.780882\pi$
$983$	−134.663	+	134.663i	−0.136992	+	0.136992i	0.635286	+	0.772277i	$0.280882\pi$
$984$			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	−0.991944	−	0.126679i	$-0.959568\pi$
$997$	−1115.27	−	1115.27i	−1.11862	−	1.11862i	−0.126679	−	0.991944i	$-0.540432\pi$
$998$	−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.7.1	✓	4
3.2	odd	2		45.3.g.b.37.2		4
4.3	odd	2		240.3.bg.a.97.1		4
5.2	odd	4		75.3.f.c.43.2		4
5.3	odd	4	inner	15.3.f.a.13.1	yes	4
5.4	even	2		75.3.f.c.7.2		4
8.3	odd	2		960.3.bg.h.577.2		4
8.5	even	2		960.3.bg.i.577.1		4
9.2	odd	6		405.3.l.f.352.2		8
9.4	even	3		405.3.l.h.217.2		8
9.5	odd	6		405.3.l.f.217.1		8
9.7	even	3		405.3.l.h.352.1		8
12.11	even	2		720.3.bh.k.577.1		4
15.2	even	4		225.3.g.a.118.1		4
15.8	even	4		45.3.g.b.28.2		4
15.14	odd	2		225.3.g.a.82.1		4
20.3	even	4		240.3.bg.a.193.1		4
20.7	even	4		1200.3.bg.k.193.2		4
20.19	odd	2		1200.3.bg.k.1057.2		4
40.3	even	4		960.3.bg.h.193.2		4
40.13	odd	4		960.3.bg.i.193.1		4
45.13	odd	12		405.3.l.h.298.1		8
45.23	even	12		405.3.l.f.298.2		8
45.38	even	12		405.3.l.f.28.1		8
45.43	odd	12		405.3.l.h.28.2		8
60.23	odd	4		720.3.bh.k.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.3.f.a.7.1	✓	4	1.1	even	1	trivial
15.3.f.a.13.1	yes	4	5.3	odd	4	inner
45.3.g.b.28.2		4	15.8	even	4
45.3.g.b.37.2		4	3.2	odd	2
75.3.f.c.7.2		4	5.4	even	2
75.3.f.c.43.2		4	5.2	odd	4
225.3.g.a.82.1		4	15.14	odd	2
225.3.g.a.118.1		4	15.2	even	4
240.3.bg.a.97.1		4	4.3	odd	2
240.3.bg.a.193.1		4	20.3	even	4
405.3.l.f.28.1		8	45.38	even	12
405.3.l.f.217.1		8	9.5	odd	6
405.3.l.f.298.2		8	45.23	even	12
405.3.l.f.352.2		8	9.2	odd	6
405.3.l.h.28.2		8	45.43	odd	12
405.3.l.h.217.2		8	9.4	even	3
405.3.l.h.298.1		8	45.13	odd	12
405.3.l.h.352.1		8	9.7	even	3
720.3.bh.k.433.1		4	60.23	odd	4
720.3.bh.k.577.1		4	12.11	even	2
960.3.bg.h.193.2		4	40.3	even	4
960.3.bg.h.577.2		4	8.3	odd	2
960.3.bg.i.193.1		4	40.13	odd	4
960.3.bg.i.577.1		4	8.5	even	2
1200.3.bg.k.193.2		4	20.7	even	4
1200.3.bg.k.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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
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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