LMFDB - Embedded newform 1183.2.e.f.170.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 $ x^10 - x^9 + 8x^8 + 7x^7 + 41x^6 + 18x^5 + 58x^4 + 28x^3 + 64x^2 + 16x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.2
Root			$0.597828 - 1.03547i$ of defining polynomial
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.f.508.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0978281 + 0.169443i) q^{2} +(0.129894 + 0.224983i) q^{3} +(0.980859 + 1.69890i) q^{4} +(1.96625 - 3.40565i) q^{5} -0.0508292 q^{6} +(-1.12324 + 2.39548i) q^{7} -0.775135 q^{8} +(1.46625 - 2.53963i) q^{9} +O(q^{10})$	\(q+(-0.0978281 + 0.169443i) q^{2} +(0.129894 + 0.224983i) q^{3} +(0.980859 + 1.69890i) q^{4} +(1.96625 - 3.40565i) q^{5} -0.0508292 q^{6} +(-1.12324 + 2.39548i) q^{7} -0.775135 q^{8} +(1.46625 - 2.53963i) q^{9} +(0.384710 + 0.666337i) q^{10} +(2.25314 + 3.90255i) q^{11} +(-0.254816 + 0.441354i) q^{12} +(-0.296013 - 0.424671i) q^{14} +1.02162 q^{15} +(-1.88589 + 3.26645i) q^{16} +(1.14070 + 1.97576i) q^{17} +(0.286882 + 0.496894i) q^{18} +(-0.893841 + 1.54818i) q^{19} +7.71448 q^{20} +(-0.684846 + 0.0584481i) q^{21} -0.881681 q^{22} +(-0.870106 + 1.50707i) q^{23} +(-0.100686 - 0.174393i) q^{24} +(-5.23232 - 9.06264i) q^{25} +1.54120 q^{27} +(-5.17142 + 0.441354i) q^{28} +1.65110 q^{29} +(-0.0999432 + 0.173107i) q^{30} +(2.80262 + 4.85427i) q^{31} +(-1.14412 - 1.98168i) q^{32} +(-0.585339 + 1.01384i) q^{33} -0.446372 q^{34} +(5.94959 + 8.53550i) q^{35} +5.75276 q^{36} +(3.57204 - 6.18695i) q^{37} +(-0.174886 - 0.302911i) q^{38} +(-1.52411 + 2.63984i) q^{40} +8.11574 q^{41} +(0.0570936 - 0.121760i) q^{42} +6.81353 q^{43} +(-4.42002 + 7.65570i) q^{44} +(-5.76606 - 9.98711i) q^{45} +(-0.170242 - 0.294867i) q^{46} +(1.77271 - 3.07043i) q^{47} -0.979864 q^{48} +(-4.47665 - 5.38141i) q^{49} +2.04747 q^{50} +(-0.296342 + 0.513279i) q^{51} +(-1.64483 - 2.84892i) q^{53} +(-0.150772 + 0.261146i) q^{54} +17.7210 q^{55} +(0.870665 - 1.85682i) q^{56} -0.464419 q^{57} +(-0.161524 + 0.279768i) q^{58} +(2.25314 + 3.90255i) q^{59} +(1.00207 + 1.73563i) q^{60} +(-3.77234 + 6.53388i) q^{61} -1.09670 q^{62} +(4.43667 + 6.36500i) q^{63} -7.09585 q^{64} +(-0.114525 - 0.198364i) q^{66} +(-6.33263 - 10.9684i) q^{67} +(-2.23774 + 3.87588i) q^{68} -0.452087 q^{69} +(-2.02832 + 0.173107i) q^{70} -9.54869 q^{71} +(-1.13655 + 1.96855i) q^{72} +(0.540019 + 0.935340i) q^{73} +(0.698891 + 1.21052i) q^{74} +(1.35930 - 2.35437i) q^{75} -3.50693 q^{76} +(-11.8793 + 1.01384i) q^{77} +(-0.395849 + 0.685630i) q^{79} +(7.41628 + 12.8454i) q^{80} +(-4.19857 - 7.27214i) q^{81} +(-0.793947 + 1.37516i) q^{82} +7.14643 q^{83} +(-0.771035 - 1.10615i) q^{84} +8.97166 q^{85} +(-0.666555 + 1.15451i) q^{86} +(0.214468 + 0.371470i) q^{87} +(-1.74649 - 3.02500i) q^{88} +(-5.63281 + 9.75631i) q^{89} +2.25633 q^{90} -3.41381 q^{92} +(-0.728087 + 1.26108i) q^{93} +(0.346843 + 0.600749i) q^{94} +(3.51504 + 6.08823i) q^{95} +(0.297229 - 0.514816i) q^{96} +8.81353 q^{97} +(1.34979 - 0.232085i) q^{98} +13.2147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 18 q^{8} - 3 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 18 * q^8 - 3 * q^9	$ 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 18 q^{8} - 3 q^{9} + 5 q^{10} + 11 q^{11} - 5 q^{12} + 10 q^{14} - 10 q^{16} + 5 q^{17} + 9 q^{18} + 9 q^{19} - 2 q^{20} - 2 q^{21} + 16 q^{22} - 10 q^{23} - 9 q^{25} - 37 q^{28} - 6 q^{29} + 13 q^{30} - 6 q^{31} + 22 q^{32} + 8 q^{33} + 44 q^{34} - 4 q^{35} + 14 q^{36} + 4 q^{37} + 10 q^{38} - 28 q^{40} - 28 q^{41} + 52 q^{42} + 4 q^{43} - 32 q^{45} + 3 q^{46} + q^{47} - 46 q^{48} - 11 q^{49} - 18 q^{50} + 8 q^{51} - 17 q^{53} + 23 q^{54} - 21 q^{56} + 32 q^{57} - 27 q^{58} + 11 q^{59} - 29 q^{60} + 11 q^{61} - 46 q^{62} - 5 q^{63} + 18 q^{64} - 21 q^{66} + 13 q^{67} + 32 q^{68} + 36 q^{69} - 49 q^{70} - 30 q^{71} - 19 q^{72} + 33 q^{74} + 20 q^{75} - 16 q^{76} - 46 q^{77} - 2 q^{79} + 55 q^{80} + 19 q^{81} - 34 q^{82} - 12 q^{83} + 23 q^{84} + 44 q^{85} + 28 q^{86} + 8 q^{87} + 3 q^{88} - 4 q^{89} - 68 q^{90} + 42 q^{92} + 18 q^{93} - 20 q^{94} + 12 q^{95} - 37 q^{96} + 24 q^{97} + 7 q^{98} - 22 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 18 * q^8 - 3 * q^9 + 5 * q^10 + 11 * q^11 - 5 * q^12 + 10 * q^14 - 10 * q^16 + 5 * q^17 + 9 * q^18 + 9 * q^19 - 2 * q^20 - 2 * q^21 + 16 * q^22 - 10 * q^23 - 9 * q^25 - 37 * q^28 - 6 * q^29 + 13 * q^30 - 6 * q^31 + 22 * q^32 + 8 * q^33 + 44 * q^34 - 4 * q^35 + 14 * q^36 + 4 * q^37 + 10 * q^38 - 28 * q^40 - 28 * q^41 + 52 * q^42 + 4 * q^43 - 32 * q^45 + 3 * q^46 + q^47 - 46 * q^48 - 11 * q^49 - 18 * q^50 + 8 * q^51 - 17 * q^53 + 23 * q^54 - 21 * q^56 + 32 * q^57 - 27 * q^58 + 11 * q^59 - 29 * q^60 + 11 * q^61 - 46 * q^62 - 5 * q^63 + 18 * q^64 - 21 * q^66 + 13 * q^67 + 32 * q^68 + 36 * q^69 - 49 * q^70 - 30 * q^71 - 19 * q^72 + 33 * q^74 + 20 * q^75 - 16 * q^76 - 46 * q^77 - 2 * q^79 + 55 * q^80 + 19 * q^81 - 34 * q^82 - 12 * q^83 + 23 * q^84 + 44 * q^85 + 28 * q^86 + 8 * q^87 + 3 * q^88 - 4 * q^89 - 68 * q^90 + 42 * q^92 + 18 * q^93 - 20 * q^94 + 12 * q^95 - 37 * q^96 + 24 * q^97 + 7 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.0978281	+	0.169443i	−0.0691749	+	0.119815i	−0.898538	−	0.438895i	$-0.855370\pi$
$2$	−0.0978281	+	0.169443i	−0.0691749	+	0.119815i	0.829363	+	0.558710i	$0.188703\pi$
$3$	0.129894	+	0.224983i	0.0749945	+	0.129894i	0.901084	−	0.433645i	$-0.142773\pi$
$3$	0.129894	+	0.224983i	0.0749945	+	0.129894i	−0.826089	+	0.563539i	$0.809439\pi$
$4$	0.980859	+	1.69890i	0.490430	+	0.849449i
$5$	1.96625	−	3.40565i	0.879336	−	1.52305i	0.0272650	−	0.999628i	$-0.491320\pi$
$5$	1.96625	−	3.40565i	0.879336	−	1.52305i	0.852071	−	0.523426i	$-0.175346\pi$
$6$	−0.0508292			−0.0207509
$7$	−1.12324	+	2.39548i	−0.424546	+	0.905406i
$7$	−1.12324	+	2.39548i	−0.424546	+	0.905406i
$8$	−0.775135			−0.274052
$9$	1.46625	−	2.53963i	0.488752	−	0.846543i
$10$	0.384710	+	0.666337i	0.121656	+	0.210714i
$11$	2.25314	+	3.90255i	0.679346	+	1.17666i	0.975178	+	0.221422i	$0.0710699\pi$
$11$	2.25314	+	3.90255i	0.679346	+	1.17666i	−0.295832	+	0.955240i	$0.595597\pi$
$12$	−0.254816	+	0.441354i	−0.0735590	+	0.127408i
$13$		0			0
$13$		0			0
$14$	−0.296013	−	0.424671i	−0.0791129	−	0.113498i
$15$	1.02162			0.263781
$16$	−1.88589	+	3.26645i	−0.471472	+	0.816614i
$17$	1.14070	+	1.97576i	0.276661	+	0.479192i	0.970553	−	0.240888i	$-0.0774386\pi$
$17$	1.14070	+	1.97576i	0.276661	+	0.479192i	−0.693891	+	0.720080i	$0.744105\pi$
$18$	0.286882	+	0.496894i	0.0676187	+	0.117119i
$19$	−0.893841	+	1.54818i	−0.205061	+	0.355177i	−0.950152	−	0.311786i	$-0.899073\pi$
$19$	−0.893841	+	1.54818i	−0.205061	+	0.355177i	0.745091	+	0.666963i	$0.232406\pi$
$20$	7.71448			1.72501
$21$	−0.684846	+	0.0584481i	−0.149446	+	0.0127544i
$22$	−0.881681			−0.187975
$23$	−0.870106	+	1.50707i	−0.181430	+	0.314245i	−0.942368	−	0.334579i	$-0.891406\pi$
$23$	−0.870106	+	1.50707i	−0.181430	+	0.314245i	0.760938	+	0.648825i	$0.224739\pi$
$24$	−0.100686	−	0.174393i	−0.0205524	−	0.0355977i
$25$	−5.23232	−	9.06264i	−1.04646	−	1.81253i
$26$		0			0
$27$	1.54120			0.296604
$28$	−5.17142	+	0.441354i	−0.977307	+	0.0834081i
$29$	1.65110			0.306602			0.153301	−	0.988180i	$-0.451010\pi$
$29$	1.65110			0.306602			0.153301	+	0.988180i	$0.451010\pi$
$30$	−0.0999432	+	0.173107i	−0.0182471	+	0.0316048i
$31$	2.80262	+	4.85427i	0.503365	+	0.871853i	0.999992	+	0.00388953i	$0.00123808\pi$
$31$	2.80262	+	4.85427i	0.503365	+	0.871853i	−0.496628	+	0.867964i	$0.665429\pi$
$32$	−1.14412	−	1.98168i	−0.202254	−	0.350314i
$33$	−0.585339	+	1.01384i	−0.101894	+	0.176486i
$34$	−0.446372			−0.0765522
$35$	5.94959	+	8.53550i	1.00566	+	1.44276i
$36$	5.75276			0.958793
$37$	3.57204	−	6.18695i	0.587239	−	1.01713i	−0.407353	−	0.913271i	$-0.633548\pi$
$37$	3.57204	−	6.18695i	0.587239	−	1.01713i	0.994592	−	0.103857i	$-0.0331185\pi$
$38$	−0.174886	−	0.302911i	−0.0283702	−	0.0491386i
$39$		0			0
$40$	−1.52411	+	2.63984i	−0.240983	+	0.417396i
$41$	8.11574			1.26746			0.633732	−	0.773552i	$-0.281522\pi$
$41$	8.11574			1.26746			0.633732	+	0.773552i	$0.281522\pi$
$42$	0.0570936	−	0.121760i	0.00880973	−	0.0187880i
$43$	6.81353			1.03905			0.519527	−	0.854454i	$-0.326108\pi$
$43$	6.81353			1.03905			0.519527	+	0.854454i	$0.326108\pi$
$44$	−4.42002	+	7.65570i	−0.666343	+	1.15414i
$45$	−5.76606	−	9.98711i	−0.859554	−	1.48879i
$46$	−0.170242	−	0.294867i	−0.0251008	−	0.0434758i
$47$	1.77271	−	3.07043i	0.258577	−	0.447868i	−0.707284	−	0.706929i	$-0.750080\pi$
$47$	1.77271	−	3.07043i	0.258577	−	0.447868i	0.965861	+	0.259061i	$0.0834131\pi$
$48$	−0.979864			−0.141431
$49$	−4.47665	−	5.38141i	−0.639522	−	0.768773i
$50$	2.04747			0.289556
$51$	−0.296342	+	0.513279i	−0.0414962	+	0.0718735i
$52$		0			0
$53$	−1.64483	−	2.84892i	−0.225934	−	0.391330i	0.730665	−	0.682736i	$-0.239210\pi$
$53$	−1.64483	−	2.84892i	−0.225934	−	0.391330i	−0.956599	+	0.291406i	$0.905877\pi$
$54$	−0.150772	+	0.261146i	−0.0205175	+	0.0355374i
$55$	17.7210			2.38949
$56$	0.870665	−	1.85682i	0.116347	−	0.248128i
$57$	−0.464419			−0.0615138
$58$	−0.161524	+	0.279768i	−0.0212092	+	0.0367353i
$59$	2.25314	+	3.90255i	0.293333	+	0.508068i	0.974596	−	0.223971i	$-0.0719021\pi$
$59$	2.25314	+	3.90255i	0.293333	+	0.508068i	−0.681262	+	0.732039i	$0.738569\pi$
$60$	1.00207	+	1.73563i	0.129366	+	0.224069i
$61$	−3.77234	+	6.53388i	−0.482998	+	0.836577i	−0.999809	−	0.0195220i	$-0.993786\pi$
$61$	−3.77234	+	6.53388i	−0.482998	+	0.836577i	0.516811	+	0.856099i	$0.327119\pi$
$62$	−1.09670			−0.139281
$63$	4.43667	+	6.36500i	0.558968	+	0.801915i
$64$	−7.09585			−0.886981
$65$		0			0
$66$	−0.114525	−	0.198364i	−0.0140971	−	0.0244169i
$67$	−6.33263	−	10.9684i	−0.773653	−	1.34001i	−0.935548	−	0.353199i	$-0.885094\pi$
$67$	−6.33263	−	10.9684i	−0.773653	−	1.34001i	0.161895	−	0.986808i	$-0.448239\pi$
$68$	−2.23774	+	3.87588i	−0.271366	+	0.470020i
$69$	−0.452087			−0.0544249
$70$	−2.02832	+	0.173107i	−0.242431	+	0.0206902i
$71$	−9.54869			−1.13322			−0.566610	−	0.823986i	$-0.691746\pi$
$71$	−9.54869			−1.13322			−0.566610	+	0.823986i	$0.691746\pi$
$72$	−1.13655	+	1.96855i	−0.133943	+	0.231996i
$73$	0.540019	+	0.935340i	0.0632044	+	0.109473i	0.895896	−	0.444264i	$-0.146535\pi$
$73$	0.540019	+	0.935340i	0.0632044	+	0.109473i	−0.832692	+	0.553737i	$0.813201\pi$
$74$	0.698891	+	1.21052i	0.0812445	+	0.140720i
$75$	1.35930	−	2.35437i	0.156958	−	0.271859i
$76$	−3.50693			−0.402273
$77$	−11.8793	+	1.01384i	−1.35377	+	0.115537i
$78$		0			0
$79$	−0.395849	+	0.685630i	−0.0445365	+	0.0771394i	−0.887434	−	0.460934i	$-0.847514\pi$
$79$	−0.395849	+	0.685630i	−0.0445365	+	0.0771394i	0.842898	+	0.538074i	$0.180848\pi$
$80$	7.41628	+	12.8454i	0.829165	+	1.43616i
$81$	−4.19857	−	7.27214i	−0.466508	−	0.808016i
$82$	−0.793947	+	1.37516i	−0.0876768	+	0.151861i
$83$	7.14643			0.784422			0.392211	−	0.919875i	$-0.371710\pi$
$83$	7.14643			0.784422			0.392211	+	0.919875i	$0.371710\pi$
$84$	−0.771035	−	1.10615i	−0.0841268	−	0.120691i
$85$	8.97166			0.973114
$86$	−0.666555	+	1.15451i	−0.0718765	+	0.124494i
$87$	0.214468	+	0.371470i	0.0229934	+	0.0398258i
$88$	−1.74649	−	3.02500i	−0.186176	−	0.322466i
$89$	−5.63281	+	9.75631i	−0.597077	+	1.03417i	0.396174	+	0.918176i	$0.370338\pi$
$89$	−5.63281	+	9.75631i	−0.597077	+	1.03417i	−0.993250	+	0.115992i	$0.962995\pi$
$90$	2.25633			0.237838
$91$		0			0
$92$	−3.41381			−0.355914
$93$	−0.728087	+	1.26108i	−0.0754991	+	0.130768i
$94$	0.346843	+	0.600749i	0.0357741	+	0.0619625i
$95$	3.51504	+	6.08823i	0.360636	+	0.624639i
$96$	0.297229	−	0.514816i	0.0303358	−	0.0525432i
$97$	8.81353			0.894879			0.447439	−	0.894314i	$-0.352336\pi$
$97$	8.81353			0.894879			0.447439	+	0.894314i	$0.352336\pi$
$98$	1.34979	−	0.232085i	0.136349	−	0.0234441i
$99$	13.2147			1.32813
$100$	10.2643	−	17.7783i	1.02643	−	1.77783i
$101$	7.15855	+	12.3990i	0.712303	+	1.23374i	0.963991	+	0.265936i	$0.0856810\pi$
$101$	7.15855	+	12.3990i	0.712303	+	1.23374i	−0.251688	+	0.967808i	$0.580986\pi$
$102$	−0.0579811	−	0.100426i	−0.00574099	−	0.00994368i
$103$	3.74607	−	6.48839i	0.369111	−	0.639320i	−0.620315	−	0.784352i	$-0.712995\pi$
$103$	3.74607	−	6.48839i	0.369111	−	0.639320i	0.989427	+	0.145033i	$0.0463287\pi$
$104$		0			0
$105$	−1.14753	+	2.44727i	−0.111987	+	0.238829i
$106$	0.643641			0.0625160
$107$	−5.48919	+	9.50756i	−0.530660	+	0.919130i	0.468700	+	0.883357i	$0.344723\pi$
$107$	−5.48919	+	9.50756i	−0.530660	+	0.919130i	−0.999360	+	0.0357726i	$0.988611\pi$
$108$	1.51170	+	2.61834i	0.145463	+	0.251950i
$109$	−6.22314	−	10.7788i	−0.596068	−	1.03242i	−0.993395	−	0.114744i	$-0.963395\pi$
$109$	−6.22314	−	10.7788i	−0.596068	−	1.03242i	0.397327	−	0.917677i	$-0.369938\pi$
$110$	−1.73361	+	3.00270i	−0.165293	+	0.286296i
$111$	1.85595			0.176159
$112$	−5.70642	−	8.18663i	−0.539206	−	0.773564i
$113$	−1.65110			−0.155323			−0.0776613	−	0.996980i	$-0.524745\pi$
$113$	−1.65110			−0.155323			−0.0776613	+	0.996980i	$0.524745\pi$
$114$	0.0454333	−	0.0786927i	0.00425522	−	0.00737025i
$115$	3.42170	+	5.92656i	0.319075	+	0.552654i
$116$	1.61950	+	2.80505i	0.150367	+	0.260443i
$117$		0			0
$118$	−0.881681			−0.0811653
$119$	−6.01418	+	0.513279i	−0.551319	+	0.0470522i
$120$	−0.791894			−0.0722897
$121$	−4.65325	+	8.05967i	−0.423023	+	0.732697i
$122$	−0.738081	−	1.27839i	−0.0668227	−	0.115740i
$123$	1.05419	+	1.82591i	0.0950528	+	0.164636i
$124$	−5.49794	+	9.52272i	−0.493730	+	0.855165i
$125$	−21.4897			−1.92210
$126$	−1.51254	+	0.129087i	−0.134748	+	0.0115000i
$127$	−4.49297			−0.398687			−0.199343	−	0.979930i	$-0.563881\pi$
$127$	−4.49297			−0.398687			−0.199343	+	0.979930i	$0.563881\pi$
$128$	2.98242	−	5.16569i	0.263611	−	0.456587i
$129$	0.885039	+	1.53293i	0.0779233	+	0.134967i
$130$		0			0
$131$	6.32836	−	10.9610i	0.552911	−	0.957670i	−0.445151	−	0.895455i	$-0.646850\pi$
$131$	6.32836	−	10.9610i	0.552911	−	0.957670i	0.998063	−	0.0622152i	$-0.0198165\pi$
$132$	−2.29654			−0.199888
$133$	−2.70463	−	3.88016i	−0.234521	−	0.336453i
$134$	2.47804			0.214070
$135$	3.03039	−	5.24878i	0.260814	−	0.451743i
$136$	−0.884200	−	1.53148i	−0.0758195	−	0.131323i
$137$	−4.64321	−	8.04227i	−0.396696	−	0.687097i	0.596620	−	0.802524i	$-0.296510\pi$
$137$	−4.64321	−	8.04227i	−0.396696	−	0.687097i	−0.993316	+	0.115426i	$0.963177\pi$
$138$	0.0442268	−	0.0766031i	0.00376484	−	0.00652089i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−8.66523	+	18.4799i	−0.732346	+	1.56183i
$141$	0.921061			0.0775673
$142$	0.934130	−	1.61796i	0.0783905	−	0.135776i
$143$		0			0
$144$	5.53039	+	9.57891i	0.460866	+	0.798243i
$145$	3.24649	−	5.62308i	0.269606	−	0.466971i
$146$	−0.211316			−0.0174887
$147$	0.629237	−	1.70619i	0.0518986	−	0.140724i
$148$	14.0147			1.15200
$149$	−7.58243	+	13.1332i	−0.621177	+	1.07591i	0.368090	+	0.929790i	$0.380012\pi$
$149$	−7.58243	+	13.1332i	−0.621177	+	1.07591i	−0.989267	+	0.146120i	$0.953321\pi$
$150$	0.265955	+	0.460647i	0.0217151	+	0.0376117i
$151$	2.57079	+	4.45274i	0.209208	+	0.362359i	0.951465	−	0.307756i	$-0.0995780\pi$
$151$	2.57079	+	4.45274i	0.209208	+	0.362359i	−0.742257	+	0.670115i	$0.766245\pi$
$152$	0.692848	−	1.20005i	0.0561974	−	0.0973367i
$153$	6.69025			0.540875
$154$	0.990341	−	2.11205i	0.0798040	−	0.170194i
$155$	22.0426			1.77051
$156$		0			0
$157$	5.36557	+	9.29344i	0.428219	+	0.741697i	0.996715	−	0.0809889i	$-0.0258078\pi$
$157$	5.36557	+	9.29344i	0.428219	+	0.741697i	−0.568496	+	0.822686i	$0.692474\pi$
$158$	−0.0774503	−	0.134148i	−0.00616162	−	0.0106722i
$159$	0.427307	−	0.740117i	0.0338877	−	0.0586951i
$160$	−8.99853			−0.711397
$161$	−2.63281	−	3.77712i	−0.207495	−	0.297679i
$162$	1.64295			0.129083
$163$	1.18620	−	2.05455i	0.0929101	−	0.160925i	−0.815824	−	0.578300i	$-0.803716\pi$
$163$	1.18620	−	2.05455i	0.0929101	−	0.160925i	0.908734	+	0.417375i	$0.137050\pi$
$164$	7.96039	+	13.7878i	0.621602	+	1.07665i
$165$	2.30185	+	3.98692i	0.179199	+	0.310382i
$166$	−0.699122	+	1.21091i	−0.0542624	+	0.0939852i
$167$	−12.0784			−0.934653			−0.467327	−	0.884085i	$-0.654783\pi$
$167$	−12.0784			−0.934653			−0.467327	+	0.884085i	$0.654783\pi$
$168$	0.530848	−	0.0453052i	0.0409558	−	0.00349537i
$169$		0			0
$170$	−0.877681	+	1.52019i	−0.0673151	+	0.116593i
$171$	2.62120	+	4.54005i	0.200448	+	0.347186i
$172$	6.68312	+	11.5755i	0.509583	+	0.882624i
$173$	9.70485	−	16.8093i	0.737846	−	1.27799i	−0.215618	−	0.976478i	$-0.569176\pi$
$173$	9.70485	−	16.8093i	0.737846	−	1.27799i	0.953463	−	0.301509i	$-0.0974902\pi$
$174$	−0.0839242			−0.00636228
$175$	27.5865	−	2.35437i	2.08535	−	0.177974i
$176$	−16.9967			−1.28117
$177$	−0.585339	+	1.01384i	−0.0439968	+	0.0762046i
$178$	−1.10209	−	1.90888i	−0.0826055	−	0.143077i
$179$	−7.32219	−	12.6824i	−0.547286	−	0.947928i	−0.998459	−	0.0554912i	$-0.982328\pi$
$179$	−7.32219	−	12.6824i	−0.547286	−	0.947928i	0.451173	−	0.892437i	$-0.351006\pi$
$180$	11.3114	−	19.5919i	0.843101	−	1.46029i
$181$	−9.44627			−0.702136			−0.351068	−	0.936350i	$-0.614181\pi$
$181$	−9.44627			−0.702136			−0.351068	+	0.936350i	$0.614181\pi$
$182$		0			0
$183$	−1.96002			−0.144889
$184$	0.674450	−	1.16818i	0.0497211	−	0.0861194i
$185$	−14.0471	−	24.3302i	−1.03276	−	1.78879i
$186$	−0.142455	−	0.246739i	−0.0104453	−	0.0180918i
$187$	−5.14033	+	8.90331i	−0.375898	+	0.651074i
$188$	6.95513			0.507255
$189$	−1.73114	+	3.69191i	−0.125922	+	0.268547i
$190$	−1.37548			−0.0997878
$191$	−6.27687	+	10.8719i	−0.454179	+	0.786660i	−0.998641	−	0.0521252i	$-0.983401\pi$
$191$	−6.27687	+	10.8719i	−0.454179	+	0.786660i	0.544462	+	0.838786i	$0.316734\pi$
$192$	−0.921709	−	1.59645i	−0.0665186	−	0.115214i
$193$	−4.68430	−	8.11344i	−0.337183	−	0.584018i	0.646719	−	0.762729i	$-0.276141\pi$
$193$	−4.68430	−	8.11344i	−0.337183	−	0.584018i	−0.983902	+	0.178710i	$0.942807\pi$
$194$	−0.862212	+	1.49339i	−0.0619032	+	0.107219i
$195$		0			0
$196$	4.75151	−	12.8838i	0.339393	−	0.920270i
$197$	7.62276			0.543099			0.271550	−	0.962424i	$-0.412464\pi$
$197$	7.62276			0.543099			0.271550	+	0.962424i	$0.412464\pi$
$198$	−1.29277	+	2.23914i	−0.0918731	+	0.159129i
$199$	−6.76443	−	11.7163i	−0.479518	−	0.830549i	0.520206	−	0.854041i	$-0.325855\pi$
$199$	−6.76443	−	11.7163i	−0.479518	−	0.830549i	−0.999724	+	0.0234914i	$0.992522\pi$
$200$	4.05575	+	7.02477i	0.286785	+	0.496726i
$201$	1.64514	−	2.84947i	0.116039	−	0.200986i
$202$	−2.80123			−0.197094
$203$	−1.85459	+	3.95518i	−0.130167	+	0.277599i
$204$	−1.16268			−0.0814038
$205$	15.9576	−	27.6394i	1.11453	−	1.93042i
$206$	0.732942	+	1.26949i	0.0510665	+	0.0884498i
$207$	2.55159	+	4.41949i	0.177348	+	0.307176i
$208$		0			0
$209$	−8.05579			−0.557231
$210$	−0.302413	−	0.433853i	−0.0208685	−	0.0299387i
$211$	−15.7995			−1.08768			−0.543840	−	0.839189i	$-0.683030\pi$
$211$	−15.7995			−1.08768			−0.543840	+	0.839189i	$0.683030\pi$
$212$	3.22669	−	5.58879i	0.221610	−	0.383839i
$213$	−1.24032	−	2.14830i	−0.0849853	−	0.147199i
$214$	−1.07399	−	1.86021i	−0.0734167	−	0.127162i
$215$	13.3971	−	23.2045i	0.913678	−	1.58254i
$216$	−1.19464			−0.0812847
$217$	−14.7763	+	1.26108i	−1.00308	+	0.0856080i
$218$	2.43519			0.164932
$219$	−0.140291	+	0.242991i	−0.00947997	+	0.0164198i
$220$	17.3818	+	30.1061i	1.17188	+	2.02975i
$221$		0			0
$222$	−0.181564	+	0.314478i	−0.0121858	+	0.0211064i
$223$	−22.4737			−1.50495			−0.752474	−	0.658622i	$-0.771139\pi$
$223$	−22.4737			−1.50495			−0.752474	+	0.658622i	$0.771139\pi$
$224$	6.03219	−	0.514816i	0.403043	−	0.0343976i
$225$	−30.6876			−2.04584
$226$	0.161524	−	0.279768i	0.0107444	−	0.0186099i
$227$	−4.60124	−	7.96959i	−0.305395	−	0.528960i	0.671954	−	0.740593i	$-0.265455\pi$
$227$	−4.60124	−	7.96959i	−0.305395	−	0.528960i	−0.977349	+	0.211633i	$0.932122\pi$
$228$	−0.455530	−	0.789001i	−0.0301682	−	0.0522529i
$229$	7.64611	−	13.2435i	0.505269	−	0.875152i	−0.494712	−	0.869057i	$-0.664726\pi$
$229$	7.64611	−	13.2435i	0.505269	−	0.875152i	0.999981	−	0.00609528i	$-0.00194020\pi$
$230$	−1.33895			−0.0882880
$231$	−1.77115	−	2.54095i	−0.116533	−	0.167182i
$232$	−1.27983			−0.0840247
$233$	4.02789	−	6.97652i	0.263876	−	0.457047i	−0.703392	−	0.710802i	$-0.748332\pi$
$233$	4.02789	−	6.97652i	0.263876	−	0.457047i	0.967269	+	0.253755i	$0.0816656\pi$
$234$		0			0
$235$	−6.97121	−	12.0745i	−0.454752	−	0.787653i
$236$	−4.42002	+	7.65570i	−0.287719	+	0.498344i
$237$	−0.205674			−0.0133600
$238$	0.501384	−	1.06928i	0.0324999	−	0.0693108i
$239$	−21.7258			−1.40533			−0.702663	−	0.711523i	$-0.748006\pi$
$239$	−21.7258			−1.40533			−0.702663	+	0.711523i	$0.748006\pi$
$240$	−1.92666	+	3.33708i	−0.124366	+	0.215407i
$241$	−10.2490	−	17.7518i	−0.660195	−	1.14349i	−0.980564	−	0.196199i	$-0.937140\pi$
$241$	−10.2490	−	17.7518i	−0.660195	−	1.14349i	0.320369	−	0.947293i	$-0.396193\pi$
$242$	−0.910438	−	1.57692i	−0.0585252	−	0.101369i
$243$	3.40254	−	5.89337i	0.218273	−	0.378060i
$244$	−14.8005			−0.947507
$245$	−27.1295	+	4.66470i	−1.73324	+	0.298017i
$246$	−0.412517			−0.0263011
$247$		0			0
$248$	−2.17241	−	3.76272i	−0.137948	−	0.238933i
$249$	0.928280	+	1.60783i	0.0588273	+	0.101892i
$250$	2.10230	−	3.64129i	0.132961	−	0.230295i
$251$	2.60871			0.164660			0.0823301	−	0.996605i	$-0.473764\pi$
$251$	2.60871			0.164660			0.0823301	+	0.996605i	$0.473764\pi$
$252$	−6.46175	+	13.7806i	−0.407052	+	0.868098i
$253$	−7.84187			−0.493014
$254$	0.439539	−	0.761304i	0.0275791	−	0.0477685i
$255$	1.16537	+	2.01848i	0.0729781	+	0.126402i
$256$	−6.51232	−	11.2797i	−0.407020	−	0.704979i
$257$	4.49838	−	7.79142i	0.280601	−	0.486016i	−0.690932	−	0.722920i	$-0.742799\pi$
$257$	4.49838	−	7.79142i	0.280601	−	0.486016i	0.971533	+	0.236904i	$0.0761328\pi$
$258$	−0.346327			−0.0215614
$259$	10.8084	+	15.5062i	0.671604	+	0.963508i
$260$		0			0
$261$	2.42094	−	4.19318i	0.149852	−	0.259551i
$262$	1.23818	+	2.14460i	0.0764952	+	0.132494i
$263$	−0.716961	−	1.24181i	−0.0442097	−	0.0765735i	0.843074	−	0.537798i	$-0.180744\pi$
$263$	−0.716961	−	1.24181i	−0.0442097	−	0.0765735i	−0.887284	+	0.461224i	$0.847410\pi$
$264$	0.453717	−	0.785860i	0.0279243	−	0.0483664i
$265$	−12.9366			−0.794689
$266$	0.922056	−	0.0786927i	0.0565349	−	0.00482496i
$267$	−2.92668			−0.179110
$268$	12.4228	−	21.5170i	0.758845	−	1.31436i
$269$	4.08416	+	7.07397i	0.249016	+	0.431308i	0.963253	−	0.268596i	$-0.0865596\pi$
$269$	4.08416	+	7.07397i	0.249016	+	0.431308i	−0.714237	+	0.699904i	$0.753226\pi$
$270$	0.592914	+	1.02696i	0.0360836	+	0.0624986i
$271$	−0.106159	+	0.183872i	−0.00644867	+	0.0111694i	−0.869232	−	0.494405i	$-0.835386\pi$
$271$	−0.106159	+	0.183872i	−0.00644867	+	0.0111694i	0.862783	+	0.505574i	$0.168719\pi$
$272$	−8.60497			−0.521753
$273$		0			0
$274$	1.81695			0.109766
$275$	23.5783	−	40.8387i	1.42182	−	2.46267i
$276$	−0.443434	−	0.768049i	−0.0266916	−	0.0462311i
$277$	−11.4875	−	19.8969i	−0.690215	−	1.19549i	−0.971767	−	0.235942i	$-0.924182\pi$
$277$	−11.4875	−	19.8969i	−0.690215	−	1.19549i	0.281552	−	0.959546i	$-0.409151\pi$
$278$	0.391313	−	0.677773i	0.0234694	−	0.0406501i
$279$	16.4374			0.984081
$280$	−4.61174	−	6.61617i	−0.275604	−	0.395392i
$281$	0.345228			0.0205946			0.0102973	−	0.999947i	$-0.496722\pi$
$281$	0.345228			0.0205946			0.0102973	+	0.999947i	$0.496722\pi$
$282$	−0.0901057	+	0.156068i	−0.00536572	+	0.00929369i
$283$	14.4857	+	25.0900i	0.861087	+	1.49145i	0.870880	+	0.491495i	$0.163549\pi$
$283$	14.4857	+	25.0900i	0.861087	+	1.49145i	−0.00979277	+	0.999952i	$0.503117\pi$
$284$	−9.36592	−	16.2222i	−0.555765	−	0.962613i
$285$	−0.913167	+	1.58165i	−0.0540913	+	0.0936889i
$286$		0			0
$287$	−9.11594	+	19.4411i	−0.538097	+	1.14757i
$288$	−6.71029			−0.395408
$289$	5.89759	−	10.2149i	0.346917	−	0.600878i
$290$	0.635195	+	1.10019i	0.0372999	+	0.0646054i
$291$	1.14483	+	1.98290i	0.0671109	+	0.116240i
$292$	−1.05937	+	1.83487i	−0.0619947	+	0.107378i
$293$	−31.5427			−1.84274			−0.921372	−	0.388682i	$-0.872930\pi$
$293$	−31.5427			−1.84274			−0.921372	+	0.388682i	$0.872930\pi$
$294$	0.227545	+	0.273533i	0.0132707	+	0.0159528i
$295$	17.7210			1.03175
$296$	−2.76881	+	4.79572i	−0.160934	+	0.278746i
$297$	3.47253	+	6.01460i	0.201497	+	0.349002i
$298$	−1.48355	−	2.56958i	−0.0859398	−	0.148852i
$299$		0			0
$300$	5.33311			0.307907
$301$	−7.65325	+	16.3217i	−0.441126	+	0.940766i
$302$	−1.00598			−0.0578879
$303$	−1.85971	+	3.22111i	−0.106838	+	0.185048i
$304$	−3.37137	−	5.83939i	−0.193361	−	0.334912i
$305$	14.8348	+	25.6945i	0.849435	+	1.47127i
$306$	−0.654495	+	1.13362i	−0.0374150	+	0.0648047i
$307$	18.1941			1.03839			0.519197	−	0.854655i	$-0.326231\pi$
$307$	18.1941			1.03839			0.519197	+	0.854655i	$0.326231\pi$
$308$	−13.3743	−	19.1873i	−0.762073	−	1.09330i
$309$	1.94637			0.110725
$310$	−2.15639	+	3.73498i	−0.122475	+	0.212132i
$311$	0.188312	+	0.326165i	0.0106782	+	0.0184951i	0.871315	−	0.490724i	$-0.163268\pi$
$311$	0.188312	+	0.326165i	0.0106782	+	0.0184951i	−0.860637	+	0.509219i	$0.829934\pi$
$312$		0			0
$313$	−5.49415	+	9.51615i	−0.310548	+	0.537884i	−0.978481	−	0.206337i	$-0.933846\pi$
$313$	−5.49415	+	9.51615i	−0.310548	+	0.537884i	0.667933	+	0.744221i	$0.267179\pi$
$314$	−2.09961			−0.118488
$315$	30.4006	−	2.59454i	1.71288	−	0.146186i
$316$	−1.55309			−0.0873680
$317$	13.0903	−	22.6731i	0.735225	−	1.27345i	−0.219400	−	0.975635i	$-0.570410\pi$
$317$	13.0903	−	22.6731i	0.735225	−	1.27345i	0.954625	−	0.297812i	$-0.0962568\pi$
$318$	0.0836053	+	0.144809i	0.00468835	+	0.00812046i
$319$	3.72016	+	6.44350i	0.208289	+	0.360767i
$320$	−13.9522	+	24.1660i	−0.779954	+	1.35092i
$321$	−2.85206			−0.159186
$322$	0.897571	−	0.0766031i	0.0500197	−	0.00426892i
$323$	−4.07844			−0.226930
$324$	8.23642	−	14.2659i	0.457579	−	0.792550i
$325$		0			0
$326$	0.232087	+	0.401986i	0.0128541	+	0.0222639i
$327$	1.61670	−	2.80020i	0.0894037	−	0.154852i
$328$	−6.29079			−0.347351
$329$	5.36397	+	7.69534i	0.295725	+	0.424258i
$330$	−0.900743			−0.0495843
$331$	−17.0466	+	29.5256i	−0.936967	+	1.62287i	−0.165878	+	0.986146i	$0.553046\pi$
$331$	−17.0466	+	29.5256i	−0.936967	+	1.62287i	−0.771089	+	0.636728i	$0.780288\pi$
$332$	7.00964	+	12.1411i	0.384704	+	0.666327i
$333$	−10.4750	−	18.1433i	−0.574028	−	0.994246i
$334$	1.18161	−	2.04660i	0.0646546	−	0.111985i
$335$	−49.8062			−2.72120
$336$	1.10063	−	2.34725i	0.0600440	−	0.128053i
$337$	14.7532			0.803657			0.401829	−	0.915715i	$-0.368375\pi$
$337$	14.7532			0.803657			0.401829	+	0.915715i	$0.368375\pi$
$338$		0			0
$339$	−0.214468	−	0.371470i	−0.0116483	−	0.0201755i
$340$	8.79994	+	15.2419i	0.477244	+	0.826610i
$341$	−12.6294	+	21.8747i	−0.683918	+	1.18458i
$342$	−1.02571			−0.0554639
$343$	17.9194	−	4.67910i	0.967558	−	0.252648i
$344$	−5.28141			−0.284754
$345$	−0.888918	+	1.53965i	−0.0478577	+	0.0828920i
$346$	1.89881	+	3.28884i	0.102081	+	0.176809i
$347$	−14.9733	−	25.9345i	−0.803809	−	1.39224i	−0.917092	−	0.398675i	$-0.869470\pi$
$347$	−14.9733	−	25.9345i	−0.803809	−	1.39224i	0.113284	−	0.993563i	$-0.463863\pi$
$348$	−0.420727	+	0.728720i	−0.0225533	+	0.0390635i
$349$	13.4793			0.721532			0.360766	−	0.932656i	$-0.382515\pi$
$349$	13.4793			0.721532			0.360766	+	0.932656i	$0.382515\pi$
$350$	−2.29981	+	4.90468i	−0.122930	+	0.262166i
$351$		0			0
$352$	5.15572	−	8.92997i	0.274801	−	0.475969i
$353$	0.0817659	+	0.141623i	0.00435196	+	0.00753781i	0.868193	−	0.496226i	$-0.165281\pi$
$353$	0.0817659	+	0.141623i	0.00435196	+	0.00753781i	−0.863841	+	0.503764i	$0.831948\pi$
$354$	−0.114525	−	0.198364i	−0.00608695	−	0.0105429i
$355$	−18.7752	+	32.5195i	−0.996482	+	1.72596i
$356$	−22.1000			−1.17130
$357$	−0.896686	−	1.28642i	−0.0474577	−	0.0680845i
$358$	2.86527			0.151434
$359$	4.46065	−	7.72607i	0.235424	−	0.407766i	−0.723972	−	0.689830i	$-0.757685\pi$
$359$	4.46065	−	7.72607i	0.235424	−	0.407766i	0.959396	+	0.282063i	$0.0910188\pi$
$360$	4.46948	+	7.74136i	0.235562	+	0.408006i
$361$	7.90209	+	13.6868i	0.415900	+	0.720359i
$362$	0.924111	−	1.60061i	0.0485702	−	0.0841261i
$363$	−2.41772			−0.126898
$364$		0			0
$365$	4.24726			0.222312
$366$	0.191745	−	0.332112i	0.0100227	−	0.0173598i
$367$	−18.3276	−	31.7443i	−0.956693	−	1.65704i	−0.730445	−	0.682971i	$-0.760687\pi$
$367$	−18.3276	−	31.7443i	−0.956693	−	1.65704i	−0.226248	−	0.974070i	$-0.572646\pi$
$368$	−3.28185	−	5.68432i	−0.171078	−	0.296316i
$369$	11.8997	−	20.6110i	0.619476	−	1.07296i
$370$	5.49679			0.285765
$371$	8.67208	−	0.740117i	0.450232	−	0.0384250i
$372$	−2.85660			−0.148108
$373$	−13.5637	+	23.4930i	−0.702302	+	1.21642i	0.265355	+	0.964151i	$0.414511\pi$
$373$	−13.5637	+	23.4930i	−0.702302	+	1.21642i	−0.967656	+	0.252271i	$0.918822\pi$
$374$	−1.00574	−	1.74199i	−0.0520054	−	0.0900761i
$375$	−2.79139	−	4.83483i	−0.144147	−	0.249670i
$376$	−1.37409	+	2.38000i	−0.0708634	+	0.122739i
$377$		0			0
$378$	−0.456215	−	0.654502i	−0.0234652	−	0.0336640i
$379$	15.8943			0.816434			0.408217	−	0.912885i	$-0.366151\pi$
$379$	15.8943			0.816434			0.408217	+	0.912885i	$0.366151\pi$
$380$	−6.89552	+	11.9434i	−0.353733	+	0.612683i
$381$	−0.583611	−	1.01084i	−0.0298993	−	0.0517871i
$382$	−1.22811	−	2.12715i	−0.0628355	−	0.108834i
$383$	0.575394	−	0.996611i	0.0294013	−	0.0509245i	−0.850950	−	0.525246i	$-0.823973\pi$
$383$	0.575394	−	0.996611i	0.0294013	−	0.0509245i	0.880352	+	0.474322i	$0.157307\pi$
$384$	1.54959			0.0790774
$385$	−19.9049	+	42.4502i	−1.01445	+	2.16346i
$386$	1.83302			0.0932985
$387$	9.99038	−	17.3038i	0.507839	−	0.879604i
$388$	8.64484	+	14.9733i	0.438875	+	0.760154i
$389$	7.15651	+	12.3954i	0.362850	+	0.628474i	0.988429	−	0.151687i	$-0.0484705\pi$
$389$	7.15651	+	12.3954i	0.362850	+	0.628474i	−0.625579	+	0.780161i	$0.715137\pi$
$390$		0			0
$391$	−3.97013			−0.200778
$392$	3.47001	+	4.17132i	0.175262	+	0.210684i
$393$	3.28807			0.165861
$394$	−0.745721	+	1.29163i	−0.0375689	+	0.0650712i
$395$	1.55668	+	2.69625i	0.0783251	+	0.135663i
$396$	12.9618	+	22.4504i	0.651353	+	1.12818i
$397$	−12.9588	+	22.4453i	−0.650383	+	1.12650i	0.332647	+	0.943051i	$0.392058\pi$
$397$	−12.9588	+	22.4453i	−0.650383	+	1.12650i	−0.983030	+	0.183445i	$0.941275\pi$
$398$	2.64701			0.132682
$399$	0.521656	−	1.11251i	0.0261154	−	0.0556950i
$400$	39.4703			1.97351
$401$	−2.14816	+	3.72072i	−0.107274	+	0.185804i	−0.914665	−	0.404213i	$-0.867545\pi$
$401$	−2.14816	+	3.72072i	−0.107274	+	0.185804i	0.807391	+	0.590017i	$0.200879\pi$
$402$	0.321882	+	0.557517i	0.0160540	+	0.0278064i
$403$		0			0
$404$	−14.0431	+	24.3233i	−0.698669	+	1.21013i
$405$	−33.0219			−1.64087
$406$	−0.488748	−	0.701175i	−0.0242562	−	0.0347987i
$407$	32.1931			1.59575
$408$	0.229705	−	0.397861i	0.0113721	−	0.0196970i
$409$	−12.3536	−	21.3970i	−0.610844	−	1.05801i	−0.991098	−	0.133131i	$-0.957497\pi$
$409$	−12.3536	−	21.3970i	−0.610844	−	1.05801i	0.380255	−	0.924882i	$-0.375836\pi$
$410$	3.12221	+	5.40782i	0.154195	+	0.267073i
$411$	1.20625	−	2.08929i	0.0595000	−	0.103057i
$412$	14.6975			0.724093
$413$	−11.8793	+	1.01384i	−0.584542	+	0.0498876i
$414$	−0.998471			−0.0490722
$415$	14.0517	−	24.3383i	0.689771	−	1.19472i
$416$		0			0
$417$	−0.519577	−	0.899934i	−0.0254438	−	0.0440699i
$418$	0.788083	−	1.36500i	0.0385464	−	0.0667643i
$419$	−24.9293			−1.21787			−0.608937	−	0.793218i	$-0.708404\pi$
$419$	−24.9293			−1.21787			−0.608937	+	0.793218i	$0.708404\pi$
$420$	−5.28323	+	0.450896i	−0.257795	+	0.0220015i
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	1.54563	−	2.67712i	0.0752402	−	0.130320i
$423$	−5.19850	−	9.00407i	−0.252760	−	0.437793i
$424$	1.27496	+	2.20830i	0.0619177	+	0.107245i
$425$	11.9371	−	20.6756i	0.579032	−	1.00291i
$426$	0.485352			0.0235154
$427$	−11.4145	−	16.3757i	−0.552388	−	0.792475i
$428$	−21.5365			−1.04101
$429$		0			0
$430$	2.62124	+	4.54011i	0.126407	+	0.218944i
$431$	−2.84426	−	4.92639i	−0.137003	−	0.237296i	0.789358	−	0.613933i	$-0.210414\pi$
$431$	−2.84426	−	4.92639i	−0.137003	−	0.237296i	−0.926361	+	0.376637i	$0.877080\pi$
$432$	−2.90653	+	5.03425i	−0.139840	+	0.242211i
$433$	12.2598			0.589169			0.294584	−	0.955625i	$-0.404819\pi$
$433$	12.2598			0.589169			0.294584	+	0.955625i	$0.404819\pi$
$434$	1.23186	−	2.62712i	0.0591311	−	0.126106i
$435$	1.68680			0.0808758
$436$	12.2080	−	21.1450i	0.584659	−	1.01266i
$437$	−1.55547	−	2.69416i	−0.0744084	−	0.128879i
$438$	−0.0274487	−	0.0475426i	−0.00131155	−	0.00227167i
$439$	−2.51158	+	4.35019i	−0.119871	+	0.207623i	−0.919717	−	0.392583i	$-0.871582\pi$
$439$	−2.51158	+	4.35019i	−0.119871	+	0.207623i	0.799845	+	0.600206i	$0.204915\pi$
$440$	−13.7361			−0.654845
$441$	−20.2307	+	3.47851i	−0.963367	+	0.165643i
$442$		0			0
$443$	−0.289401	+	0.501258i	−0.0137499	+	0.0238155i	−0.872818	−	0.488045i	$-0.837710\pi$
$443$	−0.289401	+	0.501258i	−0.0137499	+	0.0238155i	0.859069	+	0.511860i	$0.171044\pi$
$444$	1.82042	+	3.15307i	0.0863935	+	0.149638i
$445$	22.1511	+	38.3668i	1.05006	+	1.81876i
$446$	2.19856	−	3.80801i	0.104105	−	0.180315i
$447$	−3.93966			−0.186339
$448$	7.97036	−	16.9980i	0.376564	−	0.803078i
$449$	7.36359			0.347509			0.173755	−	0.984789i	$-0.444410\pi$
$449$	7.36359			0.347509			0.173755	+	0.984789i	$0.444410\pi$
$450$	3.00212	−	5.19982i	0.141521	−	0.245122i
$451$	18.2859	+	31.6720i	0.861048	+	1.49138i
$452$	−1.61950	−	2.80505i	−0.0761748	−	0.131939i
$453$	−0.667862	+	1.15677i	−0.0313789	+	0.0543499i
$454$	1.80052			0.0845028
$455$		0			0
$456$	0.359988			0.0168580
$457$	3.95912	−	6.85739i	0.185200	−	0.320775i	−0.758444	−	0.651738i	$-0.774040\pi$
$457$	3.95912	−	6.85739i	0.185200	−	0.320775i	0.943644	+	0.330963i	$0.107373\pi$
$458$	1.49601	+	2.59117i	0.0699040	+	0.121077i
$459$	1.75805	+	3.04503i	0.0820588	+	0.142130i
$460$	−6.71241	+	11.6262i	−0.312968	+	0.542076i
$461$	9.53600			0.444136			0.222068	−	0.975031i	$-0.428719\pi$
$461$	9.53600			0.444136			0.222068	+	0.975031i	$0.428719\pi$
$462$	0.603816	−	0.0515325i	0.0280920	−	0.00239751i
$463$	−2.16049			−0.100406			−0.0502032	−	0.998739i	$-0.515987\pi$
$463$	−2.16049			−0.100406			−0.0502032	+	0.998739i	$0.515987\pi$
$464$	−3.11379	+	5.39325i	−0.144554	+	0.250375i
$465$	2.86321	+	4.95923i	0.132778	+	0.229979i
$466$	0.788083	+	1.36500i	0.0365072	+	0.0632324i
$467$	4.05950	−	7.03126i	0.187851	−	0.325368i	−0.756682	−	0.653783i	$-0.773181\pi$
$467$	4.05950	−	7.03126i	0.187851	−	0.325368i	0.944534	+	0.328415i	$0.106514\pi$
$468$		0			0
$469$	33.3877	−	2.84947i	1.54170	−	0.131576i
$470$	2.72792			0.125830
$471$	−1.39391	+	2.41433i	−0.0642281	+	0.111246i
$472$	−1.74649	−	3.02500i	−0.0803885	−	0.139237i
$473$	15.3518	+	26.5901i	0.705878	+	1.22262i
$474$	0.0201207	−	0.0348501i	0.000924174	−	0.00160072i
$475$	18.7074			0.858357
$476$	−6.77107	−	9.71402i	−0.310352	−	0.445241i
$477$	−9.64694			−0.441703
$478$	2.12540	−	3.68129i	0.0972133	−	0.168378i
$479$	7.27663	+	12.6035i	0.332478	+	0.575868i	0.982997	−	0.183621i	$-0.0587820\pi$
$479$	7.27663	+	12.6035i	0.332478	+	0.575868i	−0.650519	+	0.759490i	$0.725449\pi$
$480$	−1.16886	−	2.02452i	−0.0533508	−	0.0924063i
$481$		0			0
$482$	4.01056			0.182676
$483$	0.507803	−	1.08297i	0.0231058	−	0.0492766i
$484$	−18.2567			−0.829852
$485$	17.3297	−	30.0158i	0.786899	−	1.36295i
$486$	0.665728	+	1.15307i	0.0301980	+	0.0523045i
$487$	−16.6295	−	28.8031i	−0.753554	−	1.30519i	−0.946090	−	0.323904i	$-0.895005\pi$
$487$	−16.6295	−	28.8031i	−0.753554	−	1.30519i	0.192536	−	0.981290i	$-0.438329\pi$
$488$	2.92407	−	5.06464i	0.132366	−	0.229265i
$489$	0.616320			0.0278710
$490$	1.86362	−	5.05324i	0.0841899	−	0.228282i
$491$	−22.5563			−1.01795			−0.508977	−	0.860780i	$-0.669976\pi$
$491$	−22.5563			−1.01795			−0.508977	+	0.860780i	$0.669976\pi$
$492$	−2.06802	+	3.58191i	−0.0932335	+	0.161485i
$493$	1.88342	+	3.26218i	0.0848249	+	0.146921i
$494$		0			0
$495$	25.9835	−	45.0047i	1.16787	−	2.02281i
$496$	−21.1417			−0.949290
$497$	10.7255	−	22.8737i	0.481104	−	1.02603i
$498$	−0.363248			−0.0162775
$499$	−5.69271	+	9.86007i	−0.254841	+	0.441397i	−0.964852	−	0.262793i	$-0.915356\pi$
$499$	−5.69271	+	9.86007i	−0.254841	+	0.441397i	0.710011	+	0.704190i	$0.248690\pi$
$500$	−21.0784	−	36.5089i	−0.942655	−	1.63273i
$501$	−1.56891	−	2.71743i	−0.0700938	−	0.121406i
$502$	−0.255205	+	0.442028i	−0.0113904	+	0.0197287i
$503$	−8.81825			−0.393186			−0.196593	−	0.980485i	$-0.562988\pi$
$503$	−8.81825			−0.393186			−0.196593	+	0.980485i	$0.562988\pi$
$504$	−3.43902	−	4.93374i	−0.153186	−	0.219766i
$505$	56.3022			2.50541
$506$	0.767156	−	1.32875i	0.0341042	−	0.0590702i
$507$		0			0
$508$	−4.40697	−	7.63310i	−0.195528	−	0.338664i
$509$	9.64188	−	16.7002i	0.427369	−	0.740225i	−0.569269	−	0.822151i	$-0.692774\pi$
$509$	9.64188	−	16.7002i	0.427369	−	0.740225i	0.996638	+	0.0819263i	$0.0261072\pi$
$510$	−0.456023			−0.0201930
$511$	−2.84716	+	0.242991i	−0.125951	+	0.0107493i
$512$	14.4780			0.639844
$513$	−1.37759	+	2.38605i	−0.0608219	+	0.105347i
$514$	0.880136	+	1.52444i	0.0388211	+	0.0672402i
$515$	−14.7315	−	25.5156i	−0.649146	−	1.12435i
$516$	−1.73620	+	3.00718i	−0.0764318	+	0.132384i
$517$	15.9767			0.702653
$518$	−3.68479	+	0.314478i	−0.161900	+	0.0138174i
$519$	5.04241			0.221337
$520$		0			0
$521$	−12.5584	−	21.7518i	−0.550193	−	0.952963i	−0.998260	−	0.0589629i	$-0.981221\pi$
$521$	−12.5584	−	21.7518i	−0.550193	−	0.952963i	0.448067	−	0.894000i	$-0.352113\pi$
$522$	0.473671	+	0.820422i	0.0207320	+	0.0359089i
$523$	14.9824	−	25.9503i	0.655134	−	1.13473i	−0.326726	−	0.945119i	$-0.605946\pi$
$523$	14.9824	−	25.9503i	0.655134	−	1.13473i	0.981860	−	0.189606i	$-0.0607212\pi$
$524$	24.8289			1.08466
$525$	4.11303	+	5.90069i	0.179507	+	0.257527i
$526$	0.280556			0.0122328
$527$	−6.39391	+	11.0746i	−0.278523	+	0.482416i
$528$	−2.20777	−	3.82397i	−0.0960808	−	0.166417i
$529$	9.98583	+	17.2960i	0.434167	+	0.751999i
$530$	1.26556	−	2.19202i	0.0549726	−	0.0952153i
$531$	13.2147			0.573469
$532$	3.93913	−	8.40078i	0.170783	−	0.364220i
$533$		0			0
$534$	0.286311	−	0.495906i	0.0123899	−	0.0214599i
$535$	21.5863	+	37.3886i	0.933257	+	1.61645i
$536$	4.90864	+	8.50201i	0.212021	+	0.367231i
$537$	1.90222	−	3.29474i	0.0820869	−	0.142179i
$538$	−1.59818			−0.0689026
$539$	10.9147	−	29.5954i	0.470130	−	1.27476i
$540$	11.8895			0.511644
$541$	2.54987	−	4.41650i	0.109627	−	0.189880i	−0.805992	−	0.591926i	$-0.798368\pi$
$541$	2.54987	−	4.41650i	0.109627	−	0.189880i	0.915619	+	0.402046i	$0.131701\pi$
$542$	−0.0207706	−	0.0359757i	−0.000892173	−	0.00154529i
$543$	−1.22702	−	2.12525i	−0.0526563	−	0.0912034i
$544$	2.61021	−	4.52101i	0.111912	−	0.193837i
$545$	−48.9451			−2.09658
$546$		0			0
$547$	2.92025			0.124861			0.0624305	−	0.998049i	$-0.480115\pi$
$547$	2.92025			0.124861			0.0624305	+	0.998049i	$0.480115\pi$
$548$	9.10867	−	15.7767i	0.389103	−	0.673946i
$549$	11.0624	+	19.1607i	0.472132	+	0.817757i
$550$	4.61323	+	7.99035i	0.196709	+	0.340710i
$551$	−1.47582	+	2.55620i	−0.0628722	+	0.108898i
$552$	0.350428			0.0149152
$553$	−1.19778	−	1.71838i	−0.0509348	−	0.0730728i
$554$	4.49519			0.190982
$555$	3.64927	−	6.32071i	0.154903	−	0.268299i
$556$	−3.92344	−	6.79559i	−0.166391	−	0.288197i
$557$	12.9937	+	22.5058i	0.550561	+	0.953600i	0.998234	+	0.0594024i	$0.0189195\pi$
$557$	12.9937	+	22.5058i	0.550561	+	0.953600i	−0.447673	+	0.894197i	$0.647747\pi$
$558$	−1.60804	+	2.78521i	−0.0680738	+	0.117907i
$559$		0			0
$560$	−39.1011	+	3.33708i	−1.65232	+	0.141017i
$561$	−2.67079			−0.112761
$562$	−0.0337730	+	0.0584965i	−0.00142463	+	0.00246753i
$563$	−1.82534	−	3.16159i	−0.0769291	−	0.133245i	0.824994	−	0.565141i	$-0.191178\pi$
$563$	−1.82534	−	3.16159i	−0.0769291	−	0.133245i	−0.901924	+	0.431896i	$0.857845\pi$
$564$	0.903431	+	1.56479i	0.0380413	+	0.0658895i
$565$	−3.24649	+	5.62308i	−0.136581	+	0.236565i
$566$	−5.66845			−0.238263
$567$	22.1363	−	1.88922i	0.929637	−	0.0793397i
$568$	7.40152			0.310561
$569$	12.6766	−	21.9566i	0.531432	−	0.920468i	−0.467895	−	0.883784i	$-0.654987\pi$
$569$	12.6766	−	21.9566i	0.531432	−	0.920468i	0.999327	−	0.0366835i	$-0.0116793\pi$
$570$	−0.178667	−	0.309460i	−0.00748353	−	0.0129619i
$571$	−13.8626	−	24.0108i	−0.580133	−	1.00482i	−0.995463	−	0.0951493i	$-0.969667\pi$
$571$	−13.8626	−	24.0108i	−0.580133	−	1.00482i	0.415330	−	0.909671i	$-0.363666\pi$
$572$		0			0
$573$	−3.26132			−0.136244
$574$	−2.40237	−	3.44652i	−0.100273	−	0.143855i
$575$	18.2107			0.759438
$576$	−10.4043	+	18.0208i	−0.433513	+	0.750867i
$577$	19.7877	+	34.2733i	0.823773	+	1.42682i	0.902854	+	0.429948i	$0.141468\pi$
$577$	19.7877	+	34.2733i	0.823773	+	1.42682i	−0.0790809	+	0.996868i	$0.525199\pi$
$578$	1.15390	+	1.99861i	0.0479959	+	0.0831313i
$579$	1.21693	−	2.10778i	0.0505737	−	0.0875963i
$580$	12.7374			0.528891
$581$	−8.02717	+	17.1191i	−0.333023	+	0.710221i
$582$	−0.447985			−0.0185696
$583$	7.41204	−	12.8380i	0.306975	−	0.531697i
$584$	−0.418588	−	0.725015i	−0.0173213	−	0.0300013i
$585$		0			0
$586$	3.08576	−	5.34470i	0.127472	−	0.220787i
$587$	8.24177			0.340174			0.170087	−	0.985429i	$-0.445595\pi$
$587$	8.24177			0.340174			0.170087	+	0.985429i	$0.445595\pi$
$588$	3.51583	−	0.604519i	0.144990	−	0.0249299i
$589$	−10.0204			−0.412882
$590$	−1.73361	+	3.00270i	−0.0713716	+	0.123619i
$591$	0.990153	+	1.71500i	0.0407295	+	0.0705455i
$592$	13.4729	+	23.3358i	0.553734	+	0.959095i
$593$	−5.96149	+	10.3256i	−0.244809	+	0.424021i	−0.962078	−	0.272775i	$-0.912059\pi$
$593$	−5.96149	+	10.3256i	−0.244809	+	0.424021i	0.717269	+	0.696796i	$0.245392\pi$
$594$	−1.35884			−0.0557540
$595$	−10.0774	+	21.4914i	−0.413131	+	0.881063i
$596$	−29.7492			−1.21857
$597$	1.75732	−	3.04377i	0.0719224	−	0.124573i
$598$		0			0
$599$	17.8079	+	30.8442i	0.727611	+	1.26026i	0.957890	+	0.287135i	$0.0927027\pi$
$599$	17.8079	+	30.8442i	0.727611	+	1.26026i	−0.230279	+	0.973125i	$0.573964\pi$
$600$	−1.05364	+	1.82495i	−0.0430146	+	0.0745034i
$601$	38.9252			1.58779			0.793896	−	0.608054i	$-0.208050\pi$
$601$	38.9252			1.58779			0.793896	+	0.608054i	$0.208050\pi$
$602$	−2.01690	−	2.89351i	−0.0822026	−	0.117931i
$603$	−37.1410			−1.51250
$604$	−5.04317	+	8.73503i	−0.205204	+	0.355423i
$605$	18.2990	+	31.6947i	0.743959	+	1.28857i
$606$	−0.363864	−	0.630231i	−0.0147810	−	0.0256014i
$607$	6.84828	−	11.8616i	0.277963	−	0.481446i	−0.692915	−	0.721019i	$-0.743674\pi$
$607$	6.84828	−	11.8616i	0.277963	−	0.481446i	0.970878	+	0.239573i	$0.0770074\pi$
$608$	4.09065			0.165898
$609$	−1.13075	+	0.0965037i	−0.0458203	+	0.00391053i
$610$	−5.80502			−0.235039
$611$		0			0
$612$	6.56220	+	11.3661i	0.265261	+	0.459446i
$613$	1.58056	+	2.73761i	0.0638382	+	0.110571i	0.896178	−	0.443695i	$-0.146333\pi$
$613$	1.58056	+	2.73761i	0.0638382	+	0.110571i	−0.832340	+	0.554266i	$0.812999\pi$
$614$	−1.77990	+	3.08287i	−0.0718308	+	0.124415i
$615$	8.29120			0.334334
$616$	9.20806	−	0.785860i	0.371003	−	0.0316632i
$617$	−20.9297			−0.842597			−0.421299	−	0.906922i	$-0.638426\pi$
$617$	−20.9297			−0.842597			−0.421299	+	0.906922i	$0.638426\pi$
$618$	−0.190410	+	0.329800i	−0.00765941	+	0.0132665i
$619$	15.4772	+	26.8073i	0.622082	+	1.07748i	0.989097	+	0.147262i	$0.0470461\pi$
$619$	15.4772	+	26.8073i	0.622082	+	1.07748i	−0.367016	+	0.930215i	$0.619621\pi$
$620$	21.6207	+	37.4482i	0.868309	+	1.50396i
$621$	−1.34100	+	2.32269i	−0.0538127	+	0.0932063i
$622$	−0.0736887			−0.00295465
$623$	−17.0440	−	24.4520i	−0.682855	−	0.979648i
$624$		0			0
$625$	−16.0927	+	27.8734i	−0.643708	+	1.11494i
$626$	−1.07496	−	1.86189i	−0.0429642	−	0.0744162i
$627$	−1.04640	−	1.81242i	−0.0417892	−	0.0723810i
$628$	−10.5257	+	18.2311i	−0.420023	+	0.727501i
$629$	16.2986			0.649866
$630$	−2.53441	+	5.40500i	−0.100973	+	0.215340i
$631$	15.1218			0.601988			0.300994	−	0.953626i	$-0.402682\pi$
$631$	15.1218			0.601988			0.300994	+	0.953626i	$0.402682\pi$
$632$	0.306836	−	0.531456i	0.0122053	−	0.0211402i
$633$	−2.05226	−	3.55462i	−0.0815700	−	0.141283i
$634$	2.56120	+	4.43613i	0.101718	+	0.176181i
$635$	−8.83433	+	15.3015i	−0.350580	+	0.607222i
$636$	1.67651			0.0664780
$637$		0			0
$638$	−1.45574			−0.0576335
$639$	−14.0008	+	24.2501i	−0.553864	+	0.959320i
$640$	−11.7284	−	20.3141i	−0.463605	−	0.802987i
$641$	23.6207	+	40.9123i	0.932962	+	1.61594i	0.778229	+	0.627981i	$0.216118\pi$
$641$	23.6207	+	40.9123i	0.932962	+	1.61594i	0.154733	+	0.987956i	$0.450548\pi$
$642$	0.279011	−	0.483262i	0.0110117	−	0.0190728i
$643$	−39.9249			−1.57448			−0.787241	−	0.616645i	$-0.788491\pi$
$643$	−39.9249			−1.57448			−0.787241	+	0.616645i	$0.788491\pi$
$644$	3.83453	−	8.17770i	0.151102	−	0.322247i
$645$	6.96085			0.274083
$646$	0.398986	−	0.691064i	0.0156979	−	0.0271895i
$647$	14.9139	+	25.8317i	0.586327	+	1.01555i	0.994709	+	0.102736i	$0.0327598\pi$
$647$	14.9139	+	25.8317i	0.586327	+	1.01555i	−0.408382	+	0.912811i	$0.633907\pi$
$648$	3.25446	+	5.63689i	0.127847	+	0.221438i
$649$	−10.1533	+	17.5859i	−0.398550	+	0.690309i
$650$		0			0
$651$	−2.20308	−	3.16062i	−0.0863456	−	0.123875i
$652$	4.65397			0.182263
$653$	−12.5774	+	21.7848i	−0.492194	+	0.852504i	−0.999960	−	0.00899079i	$-0.997138\pi$
$653$	−12.5774	+	21.7848i	−0.492194	+	0.852504i	0.507766	+	0.861495i	$0.330471\pi$
$654$	0.316317	+	0.547878i	0.0123690	+	0.0214237i
$655$	−24.8863	−	43.1044i	−0.972390	−	1.68423i
$656$	−15.3054	+	26.5097i	−0.597574	+	1.03503i
$657$	3.16722			0.123565
$658$	−1.82867	+	0.156068i	−0.0712890	+	0.00608415i
$659$	17.3155			0.674517			0.337258	−	0.941412i	$-0.390500\pi$
$659$	17.3155			0.674517			0.337258	+	0.941412i	$0.390500\pi$
$660$	−4.51558	+	7.82122i	−0.175769	+	0.304441i
$661$	−4.60037	−	7.96808i	−0.178934	−	0.309922i	0.762582	−	0.646892i	$-0.223931\pi$
$661$	−4.60037	−	7.96808i	−0.178934	−	0.309922i	−0.941516	+	0.336969i	$0.890598\pi$
$662$	−3.33528	−	5.77687i	−0.129629	−	0.224524i
$663$		0			0
$664$	−5.53945			−0.214972
$665$	−18.5325	+	1.58165i	−0.718659	+	0.0613338i
$666$	4.09901			0.158833
$667$	−1.43663	+	2.48832i	−0.0556266	+	0.0963482i
$668$	−11.8472	−	20.5199i	−0.458382	−	0.793940i
$669$	−2.91920	−	5.05620i	−0.112863	−	0.195484i
$670$	4.87245	−	8.43933i	0.188239	−	0.326040i
$671$	−33.9984			−1.31249
$672$	0.899372	+	1.29027i	0.0346940	+	0.0497733i
$673$	17.3609			0.669212			0.334606	−	0.942358i	$-0.391397\pi$
$673$	17.3609			0.669212			0.334606	+	0.942358i	$0.391397\pi$
$674$	−1.44328	+	2.49983i	−0.0555930	+	0.0962898i
$675$	−8.06403	−	13.9673i	−0.310385	−	0.537602i
$676$		0			0
$677$	−24.9913	+	43.2861i	−0.960492	+	1.66362i	−0.239225	+	0.970964i	$0.576893\pi$
$677$	−24.9913	+	43.2861i	−0.960492	+	1.66362i	−0.721267	+	0.692657i	$0.756440\pi$
$678$	0.0839242			0.00322309
$679$	−9.89974	+	21.1126i	−0.379917	+	0.810229i
$680$	−6.95425			−0.266683
$681$	1.19535	−	2.07041i	0.0458059	−	0.0793382i
$682$	−2.47101	−	4.27992i	−0.0946200	−	0.163887i
$683$	16.8077	+	29.1117i	0.643128	+	1.11393i	0.984731	+	0.174086i	$0.0556969\pi$
$683$	16.8077	+	29.1117i	0.643128	+	1.11393i	−0.341603	+	0.939844i	$0.610970\pi$
$684$	−5.14205	+	8.90630i	−0.196611	+	0.340541i
$685$	−36.5189			−1.39532
$686$	−0.960183	+	3.49408i	−0.0366599	+	0.133404i
$687$	3.97274			0.151570
$688$	−12.8496	+	22.2561i	−0.489885	+	0.848506i
$689$		0			0
$690$	−0.173922	−	0.301242i	−0.00662111	−	0.0114681i
$691$	−7.56545	+	13.1038i	−0.287803	+	0.498490i	−0.973285	−	0.229600i	$-0.926258\pi$
$691$	−7.56545	+	13.1038i	−0.287803	+	0.498490i	0.685482	+	0.728090i	$0.259592\pi$
$692$	38.0764			1.44745
$693$	−14.8433	+	31.6555i	−0.563851	+	1.20249i
$694$	5.85924			0.222414
$695$	−7.86502	+	13.6226i	−0.298337	+	0.516735i
$696$	−0.166242	−	0.287940i	−0.00630139	−	0.0109143i
$697$	9.25766	+	16.0347i	0.350659	+	0.607359i
$698$	−1.31866	+	2.28398i	−0.0499119	+	0.0864500i
$699$	2.09280			0.0791570
$700$	31.0583	+	44.5574i	1.17390	+	1.68411i
$701$	2.02467			0.0764705			0.0382353	−	0.999269i	$-0.487826\pi$
$701$	2.02467			0.0764705			0.0382353	+	0.999269i	$0.487826\pi$
$702$		0			0
$703$	6.38567	+	11.0603i	0.240840	+	0.417147i
$704$	−15.9879	−	27.6919i	−0.602567	−	1.04368i
$705$	1.81104	−	3.13681i	0.0682077	−	0.118139i
$706$	−0.0319960			−0.00120419
$707$	−37.7423	+	3.22111i	−1.41945	+	0.121142i
$708$	−2.29654			−0.0863093
$709$	−15.2276	+	26.3751i	−0.571886	+	0.990536i	0.424486	+	0.905434i	$0.360455\pi$
$709$	−15.2276	+	26.3751i	−0.571886	+	0.990536i	−0.996372	+	0.0851015i	$0.972879\pi$
$710$	−3.67348	−	6.36265i	−0.137863	−	0.238786i
$711$	1.16083	+	2.01062i	0.0435346	+	0.0754041i
$712$	4.36619	−	7.56246i	0.163630	−	0.283415i
$713$	−9.75429			−0.365301
$714$	0.305696	−	0.0260896i	0.0114404	−	0.000976378i
$715$		0			0
$716$	14.3641	−	24.8793i	0.536811	−	0.929784i
$717$	−2.82206	−	4.88795i	−0.105392	−	0.182544i
$718$	0.872754	+	1.51165i	0.0325709	+	0.0564144i
$719$	12.2123	−	21.1523i	0.455442	−	0.788848i	−0.543272	−	0.839557i	$-0.682815\pi$
$719$	12.2123	−	21.1523i	0.455442	−	0.788848i	0.998713	+	0.0507089i	$0.0161481\pi$
$720$	43.4966			1.62102
$721$	11.3351	+	16.2617i	0.422139	+	0.605616i
$722$	−3.09219			−0.115079
$723$	2.66257	−	4.61170i	0.0990220	−	0.171511i
$724$	−9.26547	−	16.0483i	−0.344348	−	0.596429i
$725$	−8.63908	−	14.9633i	−0.320848	−	0.555724i
$726$	0.236521	−	0.409667i	0.00877813	−	0.0152042i
$727$	−3.09307			−0.114716			−0.0573578	−	0.998354i	$-0.518268\pi$
$727$	−3.09307			−0.114716			−0.0573578	+	0.998354i	$0.518268\pi$
$728$		0			0
$729$	−23.4236			−0.867539
$730$	−0.415501	+	0.719670i	−0.0153784	+	0.0266362i
$731$	7.77223	+	13.4619i	0.287466	+	0.497906i
$732$	−1.92250	−	3.32987i	−0.0710577	−	0.123076i
$733$	−4.20713	+	7.28697i	−0.155394	+	0.269150i	−0.933202	−	0.359351i	$-0.882998\pi$
$733$	−4.20713	+	7.28697i	−0.155394	+	0.269150i	0.777808	+	0.628501i	$0.216331\pi$
$734$	7.17182			0.264717
$735$	−4.57344	−	5.49776i	−0.168694	−	0.202788i
$736$	3.98203			0.146779
$737$	28.5365	−	49.4267i	1.05116	−	1.82066i
$738$	2.32826	+	4.03266i	0.0857044	+	0.148444i
$739$	−3.61379	−	6.25927i	−0.132936	−	0.230251i	0.791871	−	0.610688i	$-0.209107\pi$
$739$	−3.61379	−	6.25927i	−0.132936	−	0.230251i	−0.924807	+	0.380437i	$0.875774\pi$
$740$	27.5564	−	47.7291i	1.01299	−	1.75456i
$741$		0			0
$742$	−0.722966	+	1.54183i	−0.0265409	+	0.0566024i
$743$	53.9092			1.97774			0.988869	−	0.148791i	$-0.0475383\pi$
$743$	53.9092			1.97774			0.988869	+	0.148791i	$0.0475383\pi$
$744$	0.564366	−	0.977510i	0.0206907	−	0.0358373i
$745$	29.8180	+	51.6463i	1.09245	+	1.89217i
$746$	−2.65382	−	4.59656i	−0.0971634	−	0.168292i
$747$	10.4785	−	18.1493i	0.383388	−	0.664047i
$748$	−20.1678			−0.737406
$749$	−16.6095	−	23.8285i	−0.606897	−	0.870676i
$750$	1.09231			0.0398854
$751$	−14.6221	+	25.3262i	−0.533568	+	0.924168i	0.465663	+	0.884962i	$0.345816\pi$
$751$	−14.6221	+	25.3262i	−0.533568	+	0.924168i	−0.999231	+	0.0392053i	$0.987517\pi$
$752$	6.68628	+	11.5810i	0.243824	+	0.422315i
$753$	0.338856	+	0.586916i	0.0123486	+	0.0213884i
$754$		0			0
$755$	20.2193			0.735857
$756$	−7.97018	+	0.680214i	−0.289873	+	0.0247391i
$757$	−22.0597			−0.801773			−0.400887	−	0.916128i	$-0.631298\pi$
$757$	−22.0597			−0.801773			−0.400887	+	0.916128i	$0.631298\pi$
$758$	−1.55491	+	2.69318i	−0.0564768	+	0.0978206i
$759$	−1.01861	−	1.76429i	−0.0369733	−	0.0640397i
$760$	−2.72463	−	4.71920i	−0.0988328	−	0.171183i
$761$	8.90805	−	15.4292i	0.322917	−	0.559308i	−0.658172	−	0.752868i	$-0.728670\pi$
$761$	8.90805	−	15.4292i	0.322917	−	0.559308i	0.981089	+	0.193560i	$0.0620033\pi$
$762$	0.228374			0.00827313
$763$	32.8105	−	2.80020i	1.18782	−	0.101374i
$764$	−24.6269			−0.890971
$765$	13.1547	−	22.7847i	0.475611	−	0.823782i
$766$	0.112579	+	0.194993i	0.00406766	+	0.00704539i
$767$		0			0
$768$	1.69182	−	2.93033i	0.0610485	−	0.105739i
$769$	11.3069			0.407738			0.203869	−	0.978998i	$-0.434648\pi$
$769$	11.3069			0.407738			0.203869	+	0.978998i	$0.434648\pi$
$770$	−5.24564	−	7.52559i	−0.189040	−	0.271203i
$771$	2.33725			0.0841741
$772$	9.18927	−	15.9163i	0.330729	−	0.572840i
$773$	−0.964104	−	1.66988i	−0.0346764	−	0.0600613i	0.848166	−	0.529730i	$-0.177707\pi$
$773$	−0.964104	−	1.66988i	−0.0346764	−	0.0600613i	−0.882843	+	0.469669i	$0.844373\pi$
$774$	1.95468	+	3.38561i	0.0702595	+	0.121693i
$775$	29.3284	−	50.7982i	1.05351	−	1.82472i
$776$	−6.83168			−0.245243
$777$	−2.08468	+	4.44588i	−0.0747875	+	0.159495i
$778$	−2.80043			−0.100400
$779$	−7.25418	+	12.5646i	−0.259908	+	0.450174i
$780$		0			0
$781$	−21.5145	−	37.2642i	−0.769849	−	1.33342i
$782$	0.388391	−	0.672713i	0.0138888	−	0.0240562i
$783$	2.54467			0.0909392
$784$	26.0206	−	4.47404i	0.929307	−	0.159787i
$785$	42.2003			1.50619
$786$	−0.321666	+	0.557141i	−0.0114734	+	0.0198726i
$787$	2.76577	+	4.79046i	0.0985892	+	0.170761i	0.911101	−	0.412183i	$-0.135234\pi$
$787$	2.76577	+	4.79046i	0.0985892	+	0.170761i	−0.812512	+	0.582945i	$0.801900\pi$
$788$	7.47686	+	12.9503i	0.266352	+	0.461335i
$789$	0.186258	−	0.322609i	0.00663097	−	0.0114852i
$790$	−0.609148			−0.0216725
$791$	1.85459	−	3.95518i	0.0659415	−	0.140630i
$792$	−10.2432			−0.363975
$793$		0			0
$794$	−2.53547	−	4.39156i	−0.0899804	−	0.155851i
$795$	−1.68039	−	2.91052i	−0.0595973	−	0.103225i
$796$	13.2699	−	22.9842i	0.470340	−	0.814652i
$797$	−13.8038			−0.488955			−0.244477	−	0.969655i	$-0.578616\pi$
$797$	−13.8038			−0.488955			−0.244477	+	0.969655i	$0.578616\pi$
$798$	0.137474	+	0.197226i	0.00486654	+	0.00698171i
$799$	8.08857			0.286153
$800$	−11.9728	+	20.7375i	−0.423303	+	0.733182i
$801$	16.5183	+	28.6105i	0.583644	+	1.01090i
$802$	−0.420300	−	0.727982i	−0.0148413	−	0.0257059i
$803$	−2.43347	+	4.21490i	−0.0858754	+	0.148741i
$804$	6.45461			0.227637
$805$	−18.0404	+	1.53965i	−0.635839	+	0.0542656i
$806$		0			0
$807$	−1.06102	+	1.83774i	−0.0373496	+	0.0646914i
$808$	−5.54885	−	9.61088i	−0.195208	−	0.338110i
$809$	−14.1498	−	24.5082i	−0.497480	−	0.861661i	0.502515	−	0.864568i	$-0.332408\pi$
$809$	−14.1498	−	24.5082i	−0.497480	−	0.861661i	−0.999996	+	0.00290700i	$0.999075\pi$
$810$	3.23047	−	5.59533i	0.113507	−	0.196600i
$811$	12.2124			0.428837			0.214418	−	0.976742i	$-0.431214\pi$
$811$	12.2124			0.428837			0.214418	+	0.976742i	$0.431214\pi$
$812$	−8.53854	+	0.728720i	−0.299644	+	0.0255731i
$813$	−0.0551575			−0.00193446
$814$	−3.14940	+	5.45491i	−0.110386	+	0.191195i
$815$	−4.66473	−	8.07955i	−0.163398	−	0.283014i
$816$	−1.11774	−	1.93597i	−0.0391286	−	0.0677727i
$817$	−6.09022	+	10.5486i	−0.213070	+	0.369048i
$818$	4.83410			0.169020
$819$		0			0
$820$	62.6087			2.18639
$821$	−20.7005	+	35.8544i	−0.722453	+	1.25133i	0.237560	+	0.971373i	$0.423652\pi$
$821$	−20.7005	+	35.8544i	−0.722453	+	1.25133i	−0.960014	+	0.279953i	$0.909681\pi$
$822$	0.236011	+	0.408782i	0.00823182	+	0.0142579i
$823$	−23.5876	−	40.8550i	−0.822213	−	1.42411i	−0.904031	−	0.427467i	$-0.859406\pi$
$823$	−23.5876	−	40.8550i	−0.822213	−	1.42411i	0.0818184	−	0.996647i	$-0.473927\pi$
$824$	−2.90371	+	5.02938i	−0.101156	+	0.175207i
$825$	12.2507			0.426515
$826$	0.990341	−	2.11205i	0.0344584	−	0.0734876i
$827$	−21.1124			−0.734150			−0.367075	−	0.930191i	$-0.619641\pi$
$827$	−21.1124			−0.734150			−0.367075	+	0.930191i	$0.619641\pi$
$828$	−5.00551	+	8.66980i	−0.173953	+	0.301296i
$829$	0.318376	+	0.551444i	0.0110577	+	0.0191524i	0.871501	−	0.490393i	$-0.163147\pi$
$829$	0.318376	+	0.551444i	0.0110577	+	0.0191524i	−0.860444	+	0.509546i	$0.829813\pi$
$830$	2.74930	+	4.76193i	0.0954297	+	0.165289i
$831$	2.98431	−	5.16898i	0.103525	−	0.179310i
$832$		0			0
$833$	5.52583	−	14.9834i	0.191459	−	0.519143i
$834$	0.203317			0.00704029
$835$	−23.7492	+	41.1348i	−0.821874	+	1.42353i
$836$	−7.90160	−	13.6860i	−0.273282	−	0.473339i
$837$	4.31938	+	7.48139i	0.149300	+	0.258595i
$838$	2.43878	−	4.22410i	0.0842464	−	0.145919i
$839$	26.9432			0.930183			0.465092	−	0.885263i	$-0.346021\pi$
$839$	26.9432			0.930183			0.465092	+	0.885263i	$0.346021\pi$
$840$	0.889489	−	1.89697i	0.0306903	−	0.0654516i
$841$	−26.2739			−0.905995
$842$	−0.978281	+	1.69443i	−0.0337138	+	0.0583940i
$843$	0.0448431	+	0.0776705i	0.00154448	+	0.00267511i
$844$	−15.4971	−	26.8417i	−0.533431	−	0.923929i
$845$		0			0
$846$	2.03424			0.0699386
$847$	−14.0800	−	20.1997i	−0.483796	−	0.694071i
$848$	12.4078			0.426087
$849$	−3.76323	+	6.51810i	−0.129154	+	0.223701i
$850$	2.33556	+	4.04531i	0.0801090	+	0.138753i
$851$	6.21610	+	10.7666i	0.213085	+	0.369074i
$852$	2.43316	−	4.21435i	0.0833586	−	0.144381i
$853$	−6.74784			−0.231042			−0.115521	−	0.993305i	$-0.536854\pi$
$853$	−6.74784			−0.231042			−0.115521	+	0.993305i	$0.536854\pi$
$854$	3.89141	−	0.332112i	0.133161	−	0.0113646i
$855$	20.6158			0.705045
$856$	4.25486	−	7.36964i	0.145428	−	0.251889i
$857$	22.5134	+	38.9943i	0.769043	+	1.33202i	0.938082	+	0.346412i	$0.112600\pi$
$857$	22.5134	+	38.9943i	0.769043	+	1.33202i	−0.169040	+	0.985609i	$0.554067\pi$
$858$		0			0
$859$	18.3635	−	31.8065i	0.626554	−	1.08522i	−0.361684	−	0.932301i	$-0.617798\pi$
$859$	18.3635	−	31.8065i	0.626554	−	1.08522i	0.988238	−	0.152923i	$-0.0488687\pi$
$860$	52.5629			1.79238
$861$	−5.55803	+	0.474349i	−0.189417	+	0.0161658i
$862$	1.11299			0.0379087
$863$	−21.7137	+	37.6093i	−0.739144	+	1.28024i	0.213737	+	0.976891i	$0.431437\pi$
$863$	−21.7137	+	37.6093i	−0.739144	+	1.28024i	−0.952881	+	0.303344i	$0.901897\pi$
$864$	−1.76332	−	3.05415i	−0.0599892	−	0.103904i
$865$	−38.1644	−	66.1027i	−1.29763	−	2.24756i
$866$	−1.19935	+	2.07734i	−0.0407557	+	0.0705910i
$867$	3.06425			0.104067
$868$	−16.6360	−	23.8665i	−0.564661	−	0.810083i
$869$	−3.56761			−0.121023
$870$	−0.165016	+	0.285817i	−0.00559458	+	0.00969010i
$871$		0			0
$872$	4.82377	+	8.35502i	0.163354	+	0.282937i
$873$	12.9229	−	22.3831i	0.437373	−	0.757553i
$874$	0.608676			0.0205888
$875$	24.1382	−	51.4782i	0.816020	−	1.74028i
$876$	−0.550422			−0.0185970
$877$	20.0040	−	34.6480i	0.675488	−	1.16998i	−0.300838	−	0.953675i	$-0.597266\pi$
$877$	20.0040	−	34.6480i	0.675488	−	1.16998i	0.976326	−	0.216304i	$-0.0694004\pi$
$878$	−0.491407	−	0.851142i	−0.0165842	−	0.0287247i
$879$	−4.09721	−	7.09658i	−0.138196	−	0.239362i
$880$	−33.4198	+	57.8847i	−1.12658	+	1.95129i
$881$	35.4308			1.19370			0.596848	−	0.802355i	$-0.296420\pi$
$881$	35.4308			1.19370			0.596848	+	0.802355i	$0.296420\pi$
$882$	1.38972	−	3.76825i	0.0467944	−	0.126884i
$883$	22.6654			0.762751			0.381375	−	0.924420i	$-0.375451\pi$
$883$	22.6654			0.762751			0.381375	+	0.924420i	$0.375451\pi$
$884$		0			0
$885$	2.30185	+	3.98692i	0.0773759	+	0.134019i
$886$	−0.0566232	−	0.0980742i	−0.00190229	−	0.00329487i
$887$	−22.3440	+	38.7010i	−0.750240	+	1.29945i	0.197467	+	0.980310i	$0.436729\pi$
$887$	−22.3440	+	38.7010i	−0.750240	+	1.29945i	−0.947706	+	0.319144i	$0.896605\pi$
$888$	−1.43861			−0.0482766
$889$	5.04670	−	10.7628i	0.169261	−	0.360974i
$890$	−8.66800			−0.290552
$891$	18.9199	−	32.7703i	0.633841	−	1.09784i
$892$	−22.0435	−	38.1804i	−0.738071	−	1.27838i
$893$	3.16905	+	5.48896i	0.106048	+	0.183681i
$894$	0.385409	−	0.667548i	0.0128900	−	0.0223262i
$895$	−57.5892			−1.92499
$896$	9.02434	+	12.9466i	0.301482	+	0.432517i
$897$		0			0
$898$	−0.720366	+	1.24771i	−0.0240389	+	0.0416366i
$899$	4.62740	+	8.01489i	0.154332	+	0.267312i
$900$	−30.1003	−	52.1352i	−1.00334	−	1.73784i
$901$	3.75252	−	6.49956i	0.125015	−	0.216532i
$902$	−7.15549			−0.238252
$903$	−4.66622	+	0.398238i	−0.155282	+	0.0132525i
$904$	1.27983			0.0425664
$905$	−18.5738	+	32.1707i	−0.617413	+	1.06939i
$906$	−0.130671	−	0.226330i	−0.00434127	−	0.00751930i
$907$	−27.2374	−	47.1766i	−0.904403	−	1.56647i	−0.821717	−	0.569896i	$-0.806983\pi$
$907$	−27.2374	−	47.1766i	−0.904403	−	1.56647i	−0.0826860	−	0.996576i	$-0.526350\pi$
$908$	9.02635	−	15.6341i	0.299550	−	0.518836i
$909$	41.9851			1.39256
$910$		0			0
$911$	−27.4793			−0.910431			−0.455215	−	0.890381i	$-0.650438\pi$
$911$	−27.4793			−0.910431			−0.455215	+	0.890381i	$0.650438\pi$
$912$	0.875843	−	1.51700i	0.0290021	−	0.0502330i
$913$	16.1019	+	27.8893i	0.532895	+	0.923000i
$914$	0.774626	+	1.34169i	0.0256224	+	0.0443792i
$915$	−3.85390	+	6.67514i	−0.127406	+	0.220673i
$916$	29.9990			0.991196
$917$	19.1487	+	27.4714i	0.632345	+	0.907184i
$918$	−0.687947			−0.0227056
$919$	24.1440	−	41.8186i	0.796437	−	1.37947i	−0.125486	−	0.992095i	$-0.540049\pi$
$919$	24.1440	−	41.8186i	0.796437	−	1.37947i	0.921923	−	0.387374i	$-0.126618\pi$
$920$	−2.65228	−	4.59388i	−0.0874431	−	0.151456i
$921$	2.36331	+	4.09337i	0.0778737	+	0.134881i
$922$	−0.932889	+	1.61581i	−0.0307231	+	0.0532139i
$923$		0			0
$924$	2.57957	−	5.50132i	0.0848617	−	0.180980i
$925$	−74.7601			−2.45810
$926$	0.211356	−	0.366080i	0.00694560	−	0.0120301i
$927$	−10.9854	−	19.0273i	−0.360808	−	0.624937i
$928$	−1.88906	−	3.27195i	−0.0620114	−	0.107407i
$929$	21.6577	−	37.5122i	0.710566	−	1.23074i	−0.254079	−	0.967183i	$-0.581772\pi$
$929$	21.6577	−	37.5122i	0.710566	−	1.23074i	0.964645	−	0.263553i	$-0.0848943\pi$
$930$	−1.12041			−0.0367397
$931$	12.3328	−	2.12053i	0.404191	−	0.0694975i
$932$	15.8032			0.517651
$933$	−0.0489212	+	0.0847339i	−0.00160161	+	0.00277406i
$934$	0.794266	+	1.37571i	0.0259892	+	0.0450146i
$935$	20.2144	+	35.0123i	0.661081	+	1.14503i
$936$		0			0
$937$	−37.2211			−1.21596			−0.607980	−	0.793952i	$-0.708020\pi$
$937$	−37.2211			−1.21596			−0.607980	+	0.793952i	$0.708020\pi$
$938$	−2.78344	+	5.93609i	−0.0908824	+	0.193820i
$939$	−2.85463			−0.0931574
$940$	13.6756	−	23.6868i	0.446048	−	0.772577i
$941$	7.98754	+	13.8348i	0.260386	+	0.451002i	0.966345	−	0.257251i	$-0.0828167\pi$
$941$	7.98754	+	13.8348i	0.260386	+	0.451002i	−0.705958	+	0.708253i	$0.749483\pi$
$942$	−0.272728	−	0.472378i	−0.00888595	−	0.0153909i
$943$	−7.06155	+	12.2310i	−0.229956	+	0.398295i
$944$	−16.9967			−0.553194
$945$	9.16950	+	13.1549i	0.298284	+	0.427929i
$946$	−6.00736			−0.195316
$947$	13.8786	−	24.0384i	0.450994	−	0.781144i	−0.547454	−	0.836836i	$-0.684403\pi$
$947$	13.8786	−	24.0384i	0.450994	−	0.781144i	0.998448	+	0.0556912i	$0.0177363\pi$
$948$	−0.201737	−	0.349419i	−0.00655212	−	0.0113486i
$949$		0			0
$950$	−1.83011	+	3.16985i	−0.0593768	+	0.102844i
$951$	6.80142			0.220551
$952$	4.66180	−	0.397861i	0.151090	−	0.0128947i
$953$	12.0303			0.389700			0.194850	−	0.980833i	$-0.437578\pi$
$953$	12.0303			0.389700			0.194850	+	0.980833i	$0.437578\pi$
$954$	0.943742	−	1.63461i	0.0305548	−	0.0529224i
$955$	24.6839	+	42.7537i	0.798751	+	1.38348i
$956$	−21.3100	−	36.9099i	−0.689213	−	1.19375i
$957$	−0.966454	+	1.67395i	−0.0312410	+	0.0541110i
$958$	−2.84744			−0.0919965
$959$	24.4805	−	2.08929i	0.790518	−	0.0674666i
$960$	−7.24926			−0.233969
$961$	−0.209310	+	0.362536i	−0.00675194	+	0.0116947i
$962$		0			0
$963$	16.0971	+	27.8810i	0.518722	+	0.898453i
$964$	20.1056	−	34.8240i	0.647559	−	1.12160i
$965$	−36.8421			−1.18599
$966$	0.133824	+	0.191988i	0.00430571	+	0.00617712i
$967$	−5.40788			−0.173906			−0.0869528	−	0.996212i	$-0.527713\pi$
$967$	−5.40788			−0.173906			−0.0869528	+	0.996212i	$0.527713\pi$
$968$	3.60690	−	6.24733i	0.115930	−	0.200797i
$969$	−0.529765	−	0.917580i	−0.0170185	−	0.0294769i
$970$	3.39066	+	5.87279i	0.108867	+	0.188564i
$971$	−21.1376	+	36.6114i	−0.678338	+	1.17492i	0.297143	+	0.954833i	$0.403966\pi$
$971$	−21.1376	+	36.6114i	−0.678338	+	1.17492i	−0.975481	+	0.220083i	$0.929367\pi$
$972$	13.3496			0.428190
$973$	4.49297	−	9.58192i	0.144038	−	0.307182i
$974$	6.50733			0.208508
$975$		0			0
$976$	−14.2284	−	24.6443i	−0.455440	−	0.788846i
$977$	−5.41508	−	9.37920i	−0.173244	−	0.300067i	0.766308	−	0.642473i	$-0.222092\pi$
$977$	−5.41508	−	9.37920i	−0.173244	−	0.300067i	−0.939552	+	0.342406i	$0.888758\pi$
$978$	−0.0602935	+	0.104431i	−0.00192797	+	0.00333935i
$979$	−50.7660			−1.62249
$980$	−34.5350	−	41.5148i	−1.10318	−	1.32614i
$981$	−36.4988			−1.16532
$982$	2.20664	−	3.82202i	0.0704169	−	0.121966i
$983$	10.7805	+	18.6723i	0.343844	+	0.595555i	0.985143	−	0.171736i	$-0.0549375\pi$
$983$	10.7805	+	18.6723i	0.343844	+	0.595555i	−0.641299	+	0.767291i	$0.721604\pi$
$984$	−0.817137	−	1.41532i	−0.0260494	−	0.0451189i
$985$	14.9883	−	25.9605i	0.477567	−	0.827170i
$986$	−0.737005			−0.0234710
$987$	−1.03458	+	2.20638i	−0.0329309	+	0.0702300i
$988$		0			0
$989$	−5.92850	+	10.2685i	−0.188515	+	0.326518i
$990$	5.08383	+	8.80545i	0.161575	+	0.279855i
$991$	−4.31312	−	7.47054i	−0.137011	−	0.237310i	0.789353	−	0.613940i	$-0.210416\pi$
$991$	−4.31312	−	7.47054i	−0.137011	−	0.237310i	−0.926364	+	0.376630i	$0.877083\pi$
$992$	6.41306	−	11.1078i	0.203615	−	0.352671i
$993$	−8.85703			−0.281069
$994$	2.82654	+	4.05505i	0.0896524	+	0.128618i
$995$	−53.2024			−1.68663
$996$	−1.82102	+	3.15411i	−0.0577013	+	0.0999417i
$997$	−10.8484	−	18.7899i	−0.343571	−	0.595082i	0.641522	−	0.767105i	$-0.278303\pi$
$997$	−10.8484	−	18.7899i	−0.343571	−	0.595082i	−0.985093	+	0.172022i	$0.944970\pi$
$998$	−1.11381	−	1.92918i	−0.0352572	−	0.0610672i
$999$	5.50521	−	9.53531i	0.174177	−	0.301684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.f.170.2		10
7.2	even	3		8281.2.a.bw.1.4		5
7.4	even	3	inner	1183.2.e.f.508.2		10
7.5	odd	6		8281.2.a.bx.1.4		5
13.12	even	2		91.2.e.c.79.4	yes	10
39.38	odd	2		819.2.j.h.352.2		10
52.51	odd	2		1456.2.r.p.625.3		10
91.12	odd	6		637.2.a.k.1.2		5
91.25	even	6		91.2.e.c.53.4	✓	10
91.38	odd	6		637.2.e.m.508.4		10
91.51	even	6		637.2.a.l.1.2		5
91.90	odd	2		637.2.e.m.79.4		10
273.116	odd	6		819.2.j.h.235.2		10
273.194	even	6		5733.2.a.bm.1.4		5
273.233	odd	6		5733.2.a.bl.1.4		5
364.207	odd	6		1456.2.r.p.417.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.e.c.53.4	✓	10	91.25	even	6
91.2.e.c.79.4	yes	10	13.12	even	2
637.2.a.k.1.2		5	91.12	odd	6
637.2.a.l.1.2		5	91.51	even	6
637.2.e.m.79.4		10	91.90	odd	2
637.2.e.m.508.4		10	91.38	odd	6
819.2.j.h.235.2		10	273.116	odd	6
819.2.j.h.352.2		10	39.38	odd	2
1183.2.e.f.170.2		10	1.1	even	1	trivial
1183.2.e.f.508.2		10	7.4	even	3	inner
1456.2.r.p.417.3		10	364.207	odd	6
1456.2.r.p.625.3		10	52.51	odd	2
5733.2.a.bl.1.4		5	273.233	odd	6
5733.2.a.bm.1.4		5	273.194	even	6
8281.2.a.bw.1.4		5	7.2	even	3
8281.2.a.bx.1.4		5	7.5	odd	6

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0978281 + 0.169443i) q^{2} +(0.129894 + 0.224983i) q^{3} +(0.980859 + 1.69890i) q^{4} +(1.96625 - 3.40565i) q^{5} -0.0508292 q^{6} +(-1.12324 + 2.39548i) q^{7} -0.775135 q^{8} +(1.46625 - 2.53963i) q^{9} +O(q^{10})\)	\(q+(-0.0978281 + 0.169443i) q^{2} +(0.129894 + 0.224983i) q^{3} +(0.980859 + 1.69890i) q^{4} +(1.96625 - 3.40565i) q^{5} -0.0508292 q^{6} +(-1.12324 + 2.39548i) q^{7} -0.775135 q^{8} +(1.46625 - 2.53963i) q^{9} +(0.384710 + 0.666337i) q^{10} +(2.25314 + 3.90255i) q^{11} +(-0.254816 + 0.441354i) q^{12} +(-0.296013 - 0.424671i) q^{14} +1.02162 q^{15} +(-1.88589 + 3.26645i) q^{16} +(1.14070 + 1.97576i) q^{17} +(0.286882 + 0.496894i) q^{18} +(-0.893841 + 1.54818i) q^{19} +7.71448 q^{20} +(-0.684846 + 0.0584481i) q^{21} -0.881681 q^{22} +(-0.870106 + 1.50707i) q^{23} +(-0.100686 - 0.174393i) q^{24} +(-5.23232 - 9.06264i) q^{25} +1.54120 q^{27} +(-5.17142 + 0.441354i) q^{28} +1.65110 q^{29} +(-0.0999432 + 0.173107i) q^{30} +(2.80262 + 4.85427i) q^{31} +(-1.14412 - 1.98168i) q^{32} +(-0.585339 + 1.01384i) q^{33} -0.446372 q^{34} +(5.94959 + 8.53550i) q^{35} +5.75276 q^{36} +(3.57204 - 6.18695i) q^{37} +(-0.174886 - 0.302911i) q^{38} +(-1.52411 + 2.63984i) q^{40} +8.11574 q^{41} +(0.0570936 - 0.121760i) q^{42} +6.81353 q^{43} +(-4.42002 + 7.65570i) q^{44} +(-5.76606 - 9.98711i) q^{45} +(-0.170242 - 0.294867i) q^{46} +(1.77271 - 3.07043i) q^{47} -0.979864 q^{48} +(-4.47665 - 5.38141i) q^{49} +2.04747 q^{50} +(-0.296342 + 0.513279i) q^{51} +(-1.64483 - 2.84892i) q^{53} +(-0.150772 + 0.261146i) q^{54} +17.7210 q^{55} +(0.870665 - 1.85682i) q^{56} -0.464419 q^{57} +(-0.161524 + 0.279768i) q^{58} +(2.25314 + 3.90255i) q^{59} +(1.00207 + 1.73563i) q^{60} +(-3.77234 + 6.53388i) q^{61} -1.09670 q^{62} +(4.43667 + 6.36500i) q^{63} -7.09585 q^{64} +(-0.114525 - 0.198364i) q^{66} +(-6.33263 - 10.9684i) q^{67} +(-2.23774 + 3.87588i) q^{68} -0.452087 q^{69} +(-2.02832 + 0.173107i) q^{70} -9.54869 q^{71} +(-1.13655 + 1.96855i) q^{72} +(0.540019 + 0.935340i) q^{73} +(0.698891 + 1.21052i) q^{74} +(1.35930 - 2.35437i) q^{75} -3.50693 q^{76} +(-11.8793 + 1.01384i) q^{77} +(-0.395849 + 0.685630i) q^{79} +(7.41628 + 12.8454i) q^{80} +(-4.19857 - 7.27214i) q^{81} +(-0.793947 + 1.37516i) q^{82} +7.14643 q^{83} +(-0.771035 - 1.10615i) q^{84} +8.97166 q^{85} +(-0.666555 + 1.15451i) q^{86} +(0.214468 + 0.371470i) q^{87} +(-1.74649 - 3.02500i) q^{88} +(-5.63281 + 9.75631i) q^{89} +2.25633 q^{90} -3.41381 q^{92} +(-0.728087 + 1.26108i) q^{93} +(0.346843 + 0.600749i) q^{94} +(3.51504 + 6.08823i) q^{95} +(0.297229 - 0.514816i) q^{96} +8.81353 q^{97} +(1.34979 - 0.232085i) q^{98} +13.2147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 18 q^{8} - 3 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 18 * q^8 - 3 * q^9	\( 10 q + 4 q^{2} - 8 q^{4} + 2 q^{5} + 10 q^{6} - q^{7} - 18 q^{8} - 3 q^{9} + 5 q^{10} + 11 q^{11} - 5 q^{12} + 10 q^{14} - 10 q^{16} + 5 q^{17} + 9 q^{18} + 9 q^{19} - 2 q^{20} - 2 q^{21} + 16 q^{22} - 10 q^{23} - 9 q^{25} - 37 q^{28} - 6 q^{29} + 13 q^{30} - 6 q^{31} + 22 q^{32} + 8 q^{33} + 44 q^{34} - 4 q^{35} + 14 q^{36} + 4 q^{37} + 10 q^{38} - 28 q^{40} - 28 q^{41} + 52 q^{42} + 4 q^{43} - 32 q^{45} + 3 q^{46} + q^{47} - 46 q^{48} - 11 q^{49} - 18 q^{50} + 8 q^{51} - 17 q^{53} + 23 q^{54} - 21 q^{56} + 32 q^{57} - 27 q^{58} + 11 q^{59} - 29 q^{60} + 11 q^{61} - 46 q^{62} - 5 q^{63} + 18 q^{64} - 21 q^{66} + 13 q^{67} + 32 q^{68} + 36 q^{69} - 49 q^{70} - 30 q^{71} - 19 q^{72} + 33 q^{74} + 20 q^{75} - 16 q^{76} - 46 q^{77} - 2 q^{79} + 55 q^{80} + 19 q^{81} - 34 q^{82} - 12 q^{83} + 23 q^{84} + 44 q^{85} + 28 q^{86} + 8 q^{87} + 3 q^{88} - 4 q^{89} - 68 q^{90} + 42 q^{92} + 18 q^{93} - 20 q^{94} + 12 q^{95} - 37 q^{96} + 24 q^{97} + 7 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 8 * q^4 + 2 * q^5 + 10 * q^6 - q^7 - 18 * q^8 - 3 * q^9 + 5 * q^10 + 11 * q^11 - 5 * q^12 + 10 * q^14 - 10 * q^16 + 5 * q^17 + 9 * q^18 + 9 * q^19 - 2 * q^20 - 2 * q^21 + 16 * q^22 - 10 * q^23 - 9 * q^25 - 37 * q^28 - 6 * q^29 + 13 * q^30 - 6 * q^31 + 22 * q^32 + 8 * q^33 + 44 * q^34 - 4 * q^35 + 14 * q^36 + 4 * q^37 + 10 * q^38 - 28 * q^40 - 28 * q^41 + 52 * q^42 + 4 * q^43 - 32 * q^45 + 3 * q^46 + q^47 - 46 * q^48 - 11 * q^49 - 18 * q^50 + 8 * q^51 - 17 * q^53 + 23 * q^54 - 21 * q^56 + 32 * q^57 - 27 * q^58 + 11 * q^59 - 29 * q^60 + 11 * q^61 - 46 * q^62 - 5 * q^63 + 18 * q^64 - 21 * q^66 + 13 * q^67 + 32 * q^68 + 36 * q^69 - 49 * q^70 - 30 * q^71 - 19 * q^72 + 33 * q^74 + 20 * q^75 - 16 * q^76 - 46 * q^77 - 2 * q^79 + 55 * q^80 + 19 * q^81 - 34 * q^82 - 12 * q^83 + 23 * q^84 + 44 * q^85 + 28 * q^86 + 8 * q^87 + 3 * q^88 - 4 * q^89 - 68 * q^90 + 42 * q^92 + 18 * q^93 - 20 * q^94 + 12 * q^95 - 37 * q^96 + 24 * q^97 + 7 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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