LMFDB - Embedded newform 91.2.e.c.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(53,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("91.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.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:	$0.726638658394$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			53.4
Root			$0.597828 + 1.03547i$ of defining polynomial
Character	$\chi$	$=$	91.53
Dual form			91.2.e.c.79.4

$q$-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} +1.00000 q^{13} +(-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} +(0.0978281 + 0.169443i) q^{26} +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} +(0.129894 - 0.224983i) q^{39} +(-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} +(0.980859 - 1.69890i) q^{52} +(-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} +(-1.96625 - 3.40565i) q^{65} +(-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} +0.0508292 q^{78} +(-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} +(1.12324 + 2.39548i) q^{91} -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	\( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9} + 5 q^{10} - 11 q^{11} - 5 q^{12} + 10 q^{13} + 10 q^{14} - 10 q^{16} + 5 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 2 q^{21} + 16 q^{22} - 10 q^{23} - 9 q^{25} - 4 q^{26} + 37 q^{28} - 6 q^{29} + 13 q^{30} + 6 q^{31} - 22 q^{32} - 8 q^{33} - 44 q^{34} - 4 q^{35} + 14 q^{36} - 4 q^{37} + 10 q^{38} - 28 q^{40} + 28 q^{41} + 52 q^{42} + 4 q^{43} + 32 q^{45} - 3 q^{46} - q^{47} - 46 q^{48} - 11 q^{49} + 18 q^{50} + 8 q^{51} - 8 q^{52} - 17 q^{53} - 23 q^{54} - 21 q^{56} - 32 q^{57} + 27 q^{58} - 11 q^{59} + 29 q^{60} + 11 q^{61} - 46 q^{62} + 5 q^{63} + 18 q^{64} - 2 q^{65} - 21 q^{66} - 13 q^{67} + 32 q^{68} + 36 q^{69} + 49 q^{70} + 30 q^{71} + 19 q^{72} + 33 q^{74} + 20 q^{75} + 16 q^{76} - 46 q^{77} - 10 q^{78} - 2 q^{79} - 55 q^{80} + 19 q^{81} - 34 q^{82} + 12 q^{83} - 23 q^{84} - 44 q^{85} - 28 q^{86} + 8 q^{87} + 3 q^{88} + 4 q^{89} - 68 q^{90} + q^{91} + 42 q^{92} - 18 q^{93} - 20 q^{94} + 12 q^{95} + 37 q^{96} - 24 q^{97} - 7 q^{98} + 22 q^{99}+O(q^{100}) \) 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^13 + 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 - 4 * q^26 + 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 - 8 * q^52 - 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 - 2 * q^65 - 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 - 10 * q^78 - 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 + q^91 + 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 $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	$-0.144630\pi$
$2$	0.0978281	+	0.169443i	0.0691749	+	0.119815i	−0.829363	+	0.558710i	$0.811297\pi$
$3$	0.129894	−	0.224983i	0.0749945	−	0.129894i	−0.826089	−	0.563539i	$-0.809439\pi$
$3$	0.129894	−	0.224983i	0.0749945	−	0.129894i	0.901084	+	0.433645i	$0.142773\pi$
$4$	0.980859	−	1.69890i	0.490430	−	0.849449i
$5$	−1.96625	−	3.40565i	−0.879336	−	1.52305i	−0.852071	−	0.523426i	$-0.824654\pi$
$5$	−1.96625	−	3.40565i	−0.879336	−	1.52305i	−0.0272650	−	0.999628i	$-0.508680\pi$
$6$	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	0.295832	+	0.955240i	$0.404403\pi$
$11$	−2.25314	+	3.90255i	−0.679346	+	1.17666i	−0.975178	+	0.221422i	$0.928930\pi$
$12$	−0.254816	−	0.441354i	−0.0735590	−	0.127408i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−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	−0.693891	−	0.720080i	$-0.744105\pi$
$17$	1.14070	−	1.97576i	0.276661	−	0.479192i	0.970553	+	0.240888i	$0.0774386\pi$
$18$	−0.286882	+	0.496894i	−0.0676187	+	0.117119i
$19$	0.893841	+	1.54818i	0.205061	+	0.355177i	0.950152	−	0.311786i	$-0.100927\pi$
$19$	0.893841	+	1.54818i	0.205061	+	0.355177i	−0.745091	+	0.666963i	$0.767594\pi$
$20$	−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	0.760938	−	0.648825i	$-0.224739\pi$
$23$	−0.870106	−	1.50707i	−0.181430	−	0.314245i	−0.942368	+	0.334579i	$0.891406\pi$
$24$	0.100686	−	0.174393i	0.0205524	−	0.0355977i
$25$	−5.23232	+	9.06264i	−1.04646	+	1.81253i
$26$	0.0978281	+	0.169443i	0.0191857	+	0.0332306i
$27$	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	0.496628	+	0.867964i	$0.334571\pi$
$31$	−2.80262	+	4.85427i	−0.503365	+	0.871853i	−0.999992	+	0.00388953i	$0.998762\pi$
$32$	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	−0.994592	−	0.103857i	$-0.966881\pi$
$37$	−3.57204	−	6.18695i	−0.587239	−	1.01713i	0.407353	−	0.913271i	$-0.366452\pi$
$38$	−0.174886	+	0.302911i	−0.0283702	+	0.0491386i
$39$	0.129894	−	0.224983i	0.0207997	−	0.0360262i
$40$	−1.52411	−	2.63984i	−0.240983	−	0.417396i
$41$	−8.11574			−1.26746			−0.633732	−	0.773552i	$-0.718478\pi$
$41$	−8.11574			−1.26746			−0.633732	+	0.773552i	$0.718478\pi$
$42$	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	$-0.249920\pi$
$47$	−1.77271	−	3.07043i	−0.258577	−	0.447868i	−0.965861	+	0.259061i	$0.916587\pi$
$48$	−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
$52$	0.980859	−	1.69890i	0.136021	−	0.235595i
$53$	−1.64483	+	2.84892i	−0.225934	+	0.391330i	−0.956599	−	0.291406i	$-0.905877\pi$
$53$	−1.64483	+	2.84892i	−0.225934	+	0.391330i	0.730665	+	0.682736i	$0.239210\pi$
$54$	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	$-0.928098\pi$
$59$	−2.25314	+	3.90255i	−0.293333	+	0.508068i	0.681262	+	0.732039i	$0.261431\pi$
$60$	−1.00207	+	1.73563i	−0.129366	+	0.224069i
$61$	−3.77234	−	6.53388i	−0.482998	−	0.836577i	0.516811	−	0.856099i	$-0.327119\pi$
$61$	−3.77234	−	6.53388i	−0.482998	−	0.836577i	−0.999809	+	0.0195220i	$0.993786\pi$
$62$	−1.09670			−0.139281
$63$	−4.43667	+	6.36500i	−0.558968	+	0.801915i
$64$	−7.09585			−0.886981
$65$	−1.96625	−	3.40565i	−0.243884	−	0.422419i
$66$	−0.114525	+	0.198364i	−0.0140971	+	0.0244169i
$67$	6.33263	−	10.9684i	0.773653	−	1.34001i	−0.161895	−	0.986808i	$-0.551761\pi$
$67$	6.33263	−	10.9684i	0.773653	−	1.34001i	0.935548	−	0.353199i	$-0.114906\pi$
$68$	−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	$-0.308254\pi$
$71$	9.54869			1.13322			0.566610	+	0.823986i	$0.308254\pi$
$72$	1.13655	+	1.96855i	0.133943	+	0.231996i
$73$	−0.540019	+	0.935340i	−0.0632044	+	0.109473i	−0.895896	−	0.444264i	$-0.853465\pi$
$73$	−0.540019	+	0.935340i	−0.0632044	+	0.109473i	0.832692	+	0.553737i	$0.186799\pi$
$74$	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
$78$	0.0508292			0.00575528
$79$	−0.395849	−	0.685630i	−0.0445365	−	0.0771394i	0.842898	−	0.538074i	$-0.180848\pi$
$79$	−0.395849	−	0.685630i	−0.0445365	−	0.0771394i	−0.887434	+	0.460934i	$0.847514\pi$
$80$	−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	$-0.628290\pi$
$83$	−7.14643			−0.784422			−0.392211	+	0.919875i	$0.628290\pi$
$84$	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	0.993250	+	0.115992i	$0.0370045\pi$
$89$	5.63281	+	9.75631i	0.597077	+	1.03417i	−0.396174	+	0.918176i	$0.629662\pi$
$90$	2.25633			0.237838
$91$	1.12324	+	2.39548i	0.117748	+	0.251115i
$92$	−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	$-0.647664\pi$
$97$	−8.81353			−0.894879			−0.447439	+	0.894314i	$0.647664\pi$
$98$	−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	−0.251688	−	0.967808i	$-0.580986\pi$
$101$	7.15855	−	12.3990i	0.712303	−	1.23374i	0.963991	−	0.265936i	$-0.0856810\pi$
$102$	0.0579811	−	0.100426i	0.00574099	−	0.00994368i
$103$	3.74607	+	6.48839i	0.369111	+	0.639320i	0.989427	−	0.145033i	$-0.0463287\pi$
$103$	3.74607	+	6.48839i	0.369111	+	0.639320i	−0.620315	+	0.784352i	$0.712995\pi$
$104$	0.775135			0.0760082
$105$	−1.14753	−	2.44727i	−0.111987	−	0.238829i
$106$	−0.643641			−0.0625160
$107$	−5.48919	−	9.50756i	−0.530660	−	0.919130i	−0.999360	−	0.0357726i	$-0.988611\pi$
$107$	−5.48919	−	9.50756i	−0.530660	−	0.919130i	0.468700	−	0.883357i	$-0.344723\pi$
$108$	1.51170	−	2.61834i	0.145463	−	0.251950i
$109$	6.22314	−	10.7788i	0.596068	−	1.03242i	−0.397327	−	0.917677i	$-0.630062\pi$
$109$	6.22314	−	10.7788i	0.596068	−	1.03242i	0.993395	−	0.114744i	$-0.0366046\pi$
$110$	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
$117$	1.46625	+	2.53963i	0.135555	+	0.234789i
$118$	−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
$130$	0.384710	−	0.666337i	0.0337413	−	0.0584417i
$131$	6.32836	+	10.9610i	0.552911	+	0.957670i	0.998063	+	0.0622152i	$0.0198165\pi$
$131$	6.32836	+	10.9610i	0.552911	+	0.957670i	−0.445151	+	0.895455i	$0.646850\pi$
$132$	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	$-0.703490\pi$
$137$	4.64321	−	8.04227i	0.396696	−	0.687097i	0.993316	+	0.115426i	$0.0368234\pi$
$138$	−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
$143$	−2.25314	+	3.90255i	−0.188417	+	0.326347i
$144$	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	0.989267	+	0.146120i	$0.0466786\pi$
$149$	7.58243	+	13.1332i	0.621177	+	1.07591i	−0.368090	+	0.929790i	$0.619988\pi$
$150$	−0.265955	+	0.460647i	−0.0217151	+	0.0376117i
$151$	−2.57079	+	4.45274i	−0.209208	+	0.362359i	−0.951465	−	0.307756i	$-0.900422\pi$
$151$	−2.57079	+	4.45274i	−0.209208	+	0.362359i	0.742257	+	0.670115i	$0.233755\pi$
$152$	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
$156$	−0.254816	−	0.441354i	−0.0204016	−	0.0353366i
$157$	5.36557	−	9.29344i	0.428219	−	0.741697i	−0.568496	−	0.822686i	$-0.692474\pi$
$157$	5.36557	−	9.29344i	0.428219	−	0.741697i	0.996715	+	0.0809889i	$0.0258078\pi$
$158$	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	$-0.196284\pi$
$163$	−1.18620	−	2.05455i	−0.0929101	−	0.160925i	−0.908734	+	0.417375i	$0.862950\pi$
$164$	−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	$-0.345217\pi$
$167$	12.0784			0.934653			0.467327	+	0.884085i	$0.345217\pi$
$168$	0.530848	+	0.0453052i	0.0409558	+	0.00349537i
$169$	1.00000			0.0769231
$170$	−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	0.953463	+	0.301509i	$0.0974902\pi$
$173$	9.70485	+	16.8093i	0.737846	+	1.27799i	−0.215618	+	0.976478i	$0.569176\pi$
$174$	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	0.451173	+	0.892437i	$0.351006\pi$
$179$	−7.32219	+	12.6824i	−0.547286	+	0.947928i	−0.998459	+	0.0554912i	$0.982328\pi$
$180$	−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	$0.614181\pi$
$182$	−0.296013	+	0.424671i	−0.0219420	+	0.0314787i
$183$	−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	0.544462	−	0.838786i	$-0.316734\pi$
$191$	−6.27687	−	10.8719i	−0.454179	−	0.786660i	−0.998641	+	0.0521252i	$0.983401\pi$
$192$	−0.921709	+	1.59645i	−0.0665186	+	0.115214i
$193$	4.68430	−	8.11344i	0.337183	−	0.584018i	−0.646719	−	0.762729i	$-0.723859\pi$
$193$	4.68430	−	8.11344i	0.337183	−	0.584018i	0.983902	+	0.178710i	$0.0571925\pi$
$194$	−0.862212	−	1.49339i	−0.0619032	−	0.107219i
$195$	−1.02162			−0.0731598
$196$	4.75151	+	12.8838i	0.339393	+	0.920270i
$197$	−7.62276			−0.543099			−0.271550	−	0.962424i	$-0.587536\pi$
$197$	−7.62276			−0.543099			−0.271550	+	0.962424i	$0.587536\pi$
$198$	−1.29277	−	2.23914i	−0.0918731	−	0.159129i
$199$	−6.76443	+	11.7163i	−0.479518	+	0.830549i	−0.999724	−	0.0234914i	$-0.992522\pi$
$199$	−6.76443	+	11.7163i	−0.479518	+	0.830549i	0.520206	+	0.854041i	$0.325855\pi$
$200$	−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
$208$	−1.88589	−	3.26645i	−0.130763	−	0.226488i
$209$	−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
$221$	1.14070	−	1.97576i	0.0767321	−	0.132904i
$222$	−0.181564	−	0.314478i	−0.0121858	−	0.0211064i
$223$	22.4737			1.50495			0.752474	−	0.658622i	$-0.228861\pi$
$223$	22.4737			1.50495			0.752474	+	0.658622i	$0.228861\pi$
$224$	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	$-0.734545\pi$
$227$	4.60124	−	7.96959i	0.305395	−	0.528960i	0.977349	+	0.211633i	$0.0678781\pi$
$228$	0.455530	−	0.789001i	0.0301682	−	0.0522529i
$229$	−7.64611	−	13.2435i	−0.505269	−	0.875152i	−0.999981	−	0.00609528i	$-0.998060\pi$
$229$	−7.64611	−	13.2435i	−0.505269	−	0.875152i	0.494712	−	0.869057i	$-0.335274\pi$
$230$	−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	0.967269	−	0.253755i	$-0.0816656\pi$
$233$	4.02789	+	6.97652i	0.263876	+	0.457047i	−0.703392	+	0.710802i	$0.748332\pi$
$234$	−0.286882	+	0.496894i	−0.0187541	+	0.0324830i
$235$	−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	$-0.251994\pi$
$239$	21.7258			1.40533			0.702663	+	0.711523i	$0.251994\pi$
$240$	1.92666	+	3.33708i	0.124366	+	0.215407i
$241$	10.2490	−	17.7518i	0.660195	−	1.14349i	−0.320369	−	0.947293i	$-0.603807\pi$
$241$	10.2490	−	17.7518i	0.660195	−	1.14349i	0.980564	−	0.196199i	$-0.0628598\pi$
$242$	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
$247$	0.893841	+	1.54818i	0.0568738	+	0.0985083i
$248$	−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	0.971533	−	0.236904i	$-0.0761328\pi$
$257$	4.49838	+	7.79142i	0.280601	+	0.486016i	−0.690932	+	0.722920i	$0.742799\pi$
$258$	0.346327			0.0215614
$259$	10.8084	−	15.5062i	0.671604	−	0.963508i
$260$	−7.71448			−0.478432
$261$	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	−0.887284	−	0.461224i	$-0.847410\pi$
$263$	−0.716961	+	1.24181i	−0.0442097	+	0.0765735i	0.843074	+	0.537798i	$0.180744\pi$
$264$	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	−0.714237	−	0.699904i	$-0.753226\pi$
$269$	4.08416	−	7.07397i	0.249016	−	0.431308i	0.963253	+	0.268596i	$0.0865596\pi$
$270$	0.592914	−	1.02696i	0.0360836	−	0.0624986i
$271$	0.106159	+	0.183872i	0.00644867	+	0.0111694i	0.869232	−	0.494405i	$-0.164614\pi$
$271$	0.106159	+	0.183872i	0.00644867	+	0.0111694i	−0.862783	+	0.505574i	$0.831281\pi$
$272$	−8.60497			−0.521753
$273$	0.684846	+	0.0584481i	0.0414488	+	0.00353744i
$274$	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	0.281552	+	0.959546i	$0.409151\pi$
$277$	−11.4875	+	19.8969i	−0.690215	+	1.19549i	−0.971767	+	0.235942i	$0.924182\pi$
$278$	−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	$-0.503278\pi$
$281$	−0.345228			−0.0205946			−0.0102973	+	0.999947i	$0.503278\pi$
$282$	−0.0901057	−	0.156068i	−0.00536572	−	0.00929369i
$283$	14.4857	−	25.0900i	0.861087	−	1.49145i	−0.00979277	−	0.999952i	$-0.503117\pi$
$283$	14.4857	−	25.0900i	0.861087	−	1.49145i	0.870880	−	0.491495i	$-0.163549\pi$
$284$	9.36592	−	16.2222i	0.555765	−	0.962613i
$285$	−0.913167	−	1.58165i	−0.0540913	−	0.0936889i
$286$	−0.881681			−0.0521349
$287$	−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	$-0.127070\pi$
$293$	31.5427			1.84274			0.921372	+	0.388682i	$0.127070\pi$
$294$	−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
$299$	−0.870106	−	1.50707i	−0.0503195	−	0.0871560i
$300$	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	$-0.673769\pi$
$307$	−18.1941			−1.03839			−0.519197	+	0.854655i	$0.673769\pi$
$308$	−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	−0.860637	−	0.509219i	$-0.829934\pi$
$311$	0.188312	−	0.326165i	0.0106782	−	0.0184951i	0.871315	+	0.490724i	$0.163268\pi$
$312$	0.100686	−	0.174393i	0.00570020	−	0.00987303i
$313$	−5.49415	−	9.51615i	−0.310548	−	0.537884i	0.667933	−	0.744221i	$-0.267179\pi$
$313$	−5.49415	−	9.51615i	−0.310548	−	0.537884i	−0.978481	+	0.206337i	$0.933846\pi$
$314$	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	−0.954625	−	0.297812i	$-0.903743\pi$
$317$	−13.0903	−	22.6731i	−0.735225	−	1.27345i	0.219400	−	0.975635i	$-0.429590\pi$
$318$	−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
$325$	−5.23232	+	9.06264i	−0.290237	+	0.502705i
$326$	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	0.771089	+	0.636728i	$0.219712\pi$
$331$	17.0466	+	29.5256i	0.936967	+	1.62287i	0.165878	+	0.986146i	$0.446954\pi$
$332$	−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	$0.368375\pi$
$338$	0.0978281	+	0.169443i	0.00532115	+	0.00921650i
$339$	−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	0.113284	+	0.993563i	$0.463863\pi$
$347$	−14.9733	+	25.9345i	−0.803809	+	1.39224i	−0.917092	+	0.398675i	$0.869470\pi$
$348$	−0.420727	−	0.728720i	−0.0225533	−	0.0390635i
$349$	−13.4793			−0.721532			−0.360766	−	0.932656i	$-0.617485\pi$
$349$	−13.4793			−0.721532			−0.360766	+	0.932656i	$0.617485\pi$
$350$	−2.29981	−	4.90468i	−0.122930	−	0.262166i
$351$	1.54120			0.0822630
$352$	5.15572	+	8.92997i	0.274801	+	0.475969i
$353$	−0.0817659	+	0.141623i	−0.00435196	+	0.00753781i	−0.868193	−	0.496226i	$-0.834719\pi$
$353$	−0.0817659	+	0.141623i	−0.00435196	+	0.00753781i	0.863841	+	0.503764i	$0.168052\pi$
$354$	−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	$-0.242315\pi$
$359$	−4.46065	−	7.72607i	−0.235424	−	0.407766i	−0.959396	+	0.282063i	$0.908981\pi$
$360$	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
$364$	5.17142	+	0.441354i	0.271056	+	0.0231332i
$365$	4.24726			0.222312
$366$	−0.191745	−	0.332112i	−0.0100227	−	0.0173598i
$367$	−18.3276	+	31.7443i	−0.956693	+	1.65704i	−0.226248	+	0.974070i	$0.572646\pi$
$367$	−18.3276	+	31.7443i	−0.956693	+	1.65704i	−0.730445	+	0.682971i	$0.760687\pi$
$368$	−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	−0.967656	−	0.252271i	$-0.918822\pi$
$373$	−13.5637	−	23.4930i	−0.702302	−	1.21642i	0.265355	−	0.964151i	$-0.414511\pi$
$374$	−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
$377$	1.65110			0.0850360
$378$	−0.456215	+	0.654502i	−0.0234652	+	0.0336640i
$379$	−15.8943			−0.816434			−0.408217	−	0.912885i	$-0.633849\pi$
$379$	−15.8943			−0.816434			−0.408217	+	0.912885i	$0.633849\pi$
$380$	−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	$-0.176027\pi$
$383$	−0.575394	−	0.996611i	−0.0294013	−	0.0509245i	−0.880352	+	0.474322i	$0.842693\pi$
$384$	−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	−0.625579	−	0.780161i	$-0.715137\pi$
$389$	7.15651	−	12.3954i	0.362850	−	0.628474i	0.988429	+	0.151687i	$0.0484705\pi$
$390$	−0.0999432	−	0.173107i	−0.00506082	−	0.00876560i
$391$	−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	0.983030	+	0.183445i	$0.0587248\pi$
$397$	12.9588	+	22.4453i	0.650383	+	1.12650i	−0.332647	+	0.943051i	$0.607942\pi$
$398$	−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	$-0.132455\pi$
$401$	2.14816	+	3.72072i	0.107274	+	0.185804i	−0.807391	+	0.590017i	$0.799121\pi$
$402$	0.321882	−	0.557517i	0.0160540	−	0.0278064i
$403$	−2.80262	+	4.85427i	−0.139608	+	0.241809i
$404$	−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	−0.380255	−	0.924882i	$-0.624164\pi$
$409$	12.3536	−	21.3970i	0.610844	−	1.05801i	0.991098	−	0.133131i	$-0.0425030\pi$
$410$	−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
$416$	1.14412	−	1.98168i	0.0560951	−	0.0971596i
$417$	−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	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−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
$429$	0.585339	+	1.01384i	0.0282604	+	0.0489485i
$430$	2.62124	−	4.54011i	0.126407	−	0.218944i
$431$	2.84426	−	4.92639i	0.137003	−	0.237296i	−0.789358	−	0.613933i	$-0.789586\pi$
$431$	2.84426	−	4.92639i	0.137003	−	0.237296i	0.926361	+	0.376637i	$0.122920\pi$
$432$	−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	0.799845	−	0.600206i	$-0.204915\pi$
$439$	−2.51158	−	4.35019i	−0.119871	−	0.207623i	−0.919717	+	0.392583i	$0.871582\pi$
$440$	13.7361			0.654845
$441$	−20.2307	−	3.47851i	−0.963367	−	0.165643i
$442$	0.446372			0.0212317
$443$	−0.289401	−	0.501258i	−0.0137499	−	0.0238155i	0.859069	−	0.511860i	$-0.171044\pi$
$443$	−0.289401	−	0.501258i	−0.0137499	−	0.0238155i	−0.872818	+	0.488045i	$0.837710\pi$
$444$	−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	$-0.555590\pi$
$449$	−7.36359			−0.347509			−0.173755	+	0.984789i	$0.555590\pi$
$450$	−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
$455$	5.94959	−	8.53550i	0.278921	−	0.400150i
$456$	0.359988			0.0168580
$457$	−3.95912	−	6.85739i	−0.185200	−	0.320775i	0.758444	−	0.651738i	$-0.225960\pi$
$457$	−3.95912	−	6.85739i	−0.185200	−	0.320775i	−0.943644	+	0.330963i	$0.892627\pi$
$458$	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	$-0.571281\pi$
$461$	−9.53600			−0.444136			−0.222068	+	0.975031i	$0.571281\pi$
$462$	−0.603816	−	0.0515325i	−0.0280920	−	0.00239751i
$463$	2.16049			0.100406			0.0502032	−	0.998739i	$-0.484013\pi$
$463$	2.16049			0.100406			0.0502032	+	0.998739i	$0.484013\pi$
$464$	−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	0.944534	−	0.328415i	$-0.106514\pi$
$467$	4.05950	+	7.03126i	0.187851	+	0.325368i	−0.756682	+	0.653783i	$0.773181\pi$
$468$	5.75276			0.265921
$469$	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	$-0.941218\pi$
$479$	−7.27663	+	12.6035i	−0.332478	+	0.575868i	0.650519	+	0.759490i	$0.274551\pi$
$480$	−1.16886	+	2.02452i	−0.0533508	+	0.0924063i
$481$	−3.57204	−	6.18695i	−0.162871	−	0.282101i
$482$	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	−0.192536	−	0.981290i	$-0.561671\pi$
$487$	16.6295	−	28.8031i	0.753554	−	1.30519i	0.946090	−	0.323904i	$-0.104995\pi$
$488$	−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
$494$	−0.174886	+	0.302911i	−0.00786848	+	0.0136286i
$495$	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	$-0.0846436\pi$
$499$	5.69271	+	9.86007i	0.254841	+	0.441397i	−0.710011	+	0.704190i	$0.751310\pi$
$500$	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
$507$	0.129894	−	0.224983i	0.00576880	−	0.00999186i
$508$	−4.40697	+	7.63310i	−0.195528	+	0.338664i
$509$	−9.64188	−	16.7002i	−0.427369	−	0.740225i	0.569269	−	0.822151i	$-0.307226\pi$
$509$	−9.64188	−	16.7002i	−0.427369	−	0.740225i	−0.996638	+	0.0819263i	$0.973893\pi$
$510$	−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
$520$	−1.52411	−	2.63984i	−0.0668368	−	0.115765i
$521$	−12.5584	+	21.7518i	−0.550193	+	0.952963i	0.448067	+	0.894000i	$0.352113\pi$
$521$	−12.5584	+	21.7518i	−0.550193	+	0.952963i	−0.998260	+	0.0589629i	$0.981221\pi$
$522$	−0.473671	+	0.820422i	−0.0207320	+	0.0359089i
$523$	14.9824	+	25.9503i	0.655134	+	1.13473i	0.981860	+	0.189606i	$0.0607212\pi$
$523$	14.9824	+	25.9503i	0.655134	+	1.13473i	−0.326726	+	0.945119i	$0.605946\pi$
$524$	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
$533$	−8.11574			−0.351532
$534$	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	$-0.201632\pi$
$541$	−2.54987	−	4.41650i	−0.109627	−	0.189880i	−0.915619	+	0.402046i	$0.868299\pi$
$542$	−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
$546$	0.0570936	+	0.121760i	0.00244338	+	0.00521087i
$547$	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	0.447673	+	0.894197i	$0.352253\pi$
$557$	−12.9937	+	22.5058i	−0.550561	+	0.953600i	−0.998234	+	0.0594024i	$0.981080\pi$
$558$	−1.60804	−	2.78521i	−0.0680738	−	0.117907i
$559$	6.81353			0.288182
$560$	−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	−0.901924	−	0.431896i	$-0.857845\pi$
$563$	−1.82534	+	3.16159i	−0.0769291	+	0.133245i	0.824994	+	0.565141i	$0.191178\pi$
$564$	−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	0.999327	+	0.0366835i	$0.0116793\pi$
$569$	12.6766	+	21.9566i	0.531432	+	0.920468i	−0.467895	+	0.883784i	$0.654987\pi$
$570$	0.178667	−	0.309460i	0.00748353	−	0.0129619i
$571$	−13.8626	+	24.0108i	−0.580133	+	1.00482i	0.415330	+	0.909671i	$0.363666\pi$
$571$	−13.8626	+	24.0108i	−0.580133	+	1.00482i	−0.995463	+	0.0951493i	$0.969667\pi$
$572$	4.42002	+	7.65570i	0.184810	+	0.320101i
$573$	−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	0.0790809	+	0.996868i	$0.474801\pi$
$577$	−19.7877	+	34.2733i	−0.823773	+	1.42682i	−0.902854	+	0.429948i	$0.858532\pi$
$578$	−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
$585$	5.76606	−	9.98711i	0.238397	−	0.412916i
$586$	3.08576	+	5.34470i	0.127472	+	0.220787i
$587$	−8.24177			−0.340174			−0.170087	−	0.985429i	$-0.554405\pi$
$587$	−8.24177			−0.340174			−0.170087	+	0.985429i	$0.554405\pi$
$588$	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	$-0.0879415\pi$
$593$	5.96149	+	10.3256i	0.244809	+	0.424021i	−0.717269	+	0.696796i	$0.754608\pi$
$594$	−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
$598$	0.170242	−	0.294867i	0.00696170	−	0.0120580i
$599$	17.8079	−	30.8442i	0.727611	−	1.26026i	−0.230279	−	0.973125i	$-0.573964\pi$
$599$	17.8079	−	30.8442i	0.727611	−	1.26026i	0.957890	−	0.287135i	$-0.0927027\pi$
$600$	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	0.970878	−	0.239573i	$-0.0770074\pi$
$607$	6.84828	+	11.8616i	0.277963	+	0.481446i	−0.692915	+	0.721019i	$0.743674\pi$
$608$	4.09065			0.165898
$609$	1.13075	+	0.0965037i	0.0458203	+	0.00391053i
$610$	−5.80502			−0.235039
$611$	−1.77271	−	3.07043i	−0.0717163	−	0.124216i
$612$	6.56220	−	11.3661i	0.265261	−	0.459446i
$613$	−1.58056	+	2.73761i	−0.0638382	+	0.110571i	−0.896178	−	0.443695i	$-0.853667\pi$
$613$	−1.58056	+	2.73761i	−0.0638382	+	0.110571i	0.832340	+	0.554266i	$0.187001\pi$
$614$	−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	$-0.361574\pi$
$617$	20.9297			0.842597			0.421299	+	0.906922i	$0.361574\pi$
$618$	0.190410	+	0.329800i	0.00765941	+	0.0132665i
$619$	−15.4772	+	26.8073i	−0.622082	+	1.07748i	0.367016	+	0.930215i	$0.380379\pi$
$619$	−15.4772	+	26.8073i	−0.622082	+	1.07748i	−0.989097	+	0.147262i	$0.952954\pi$
$620$	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
$624$	−0.979864			−0.0392260
$625$	−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	$-0.597318\pi$
$631$	−15.1218			−0.601988			−0.300994	+	0.953626i	$0.597318\pi$
$632$	−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
$637$	−4.47665	+	5.38141i	−0.177371	+	0.213219i
$638$	−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	0.154733	−	0.987956i	$-0.450548\pi$
$641$	23.6207	−	40.9123i	0.932962	−	1.61594i	0.778229	−	0.627981i	$-0.216118\pi$
$642$	−0.279011	−	0.483262i	−0.0110117	−	0.0190728i
$643$	39.9249			1.57448			0.787241	−	0.616645i	$-0.211509\pi$
$643$	39.9249			1.57448			0.787241	+	0.616645i	$0.211509\pi$
$644$	−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	−0.408382	−	0.912811i	$-0.633907\pi$
$647$	14.9139	−	25.8317i	0.586327	−	1.01555i	0.994709	−	0.102736i	$-0.0327598\pi$
$648$	−3.25446	+	5.63689i	−0.127847	+	0.221438i
$649$	−10.1533	−	17.5859i	−0.398550	−	0.690309i
$650$	−2.04747			−0.0803084
$651$	−2.20308	+	3.16062i	−0.0863456	+	0.123875i
$652$	−4.65397			−0.182263
$653$	−12.5774	−	21.7848i	−0.492194	−	0.852504i	0.507766	−	0.861495i	$-0.330471\pi$
$653$	−12.5774	−	21.7848i	−0.492194	−	0.852504i	−0.999960	+	0.00899079i	$0.997138\pi$
$654$	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	$-0.776069\pi$
$661$	4.60037	−	7.96808i	0.178934	−	0.309922i	0.941516	+	0.336969i	$0.109402\pi$
$662$	−3.33528	+	5.77687i	−0.129629	+	0.224524i
$663$	−0.296342	−	0.513279i	−0.0115090	−	0.0199341i
$664$	−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
$676$	0.980859	−	1.69890i	0.0377254	−	0.0653422i
$677$	−24.9913	−	43.2861i	−0.960492	−	1.66362i	−0.721267	−	0.692657i	$-0.756440\pi$
$677$	−24.9913	−	43.2861i	−0.960492	−	1.66362i	−0.239225	−	0.970964i	$-0.576893\pi$
$678$	−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	0.341603	+	0.939844i	$0.389030\pi$
$683$	−16.8077	+	29.1117i	−0.643128	+	1.11393i	−0.984731	+	0.174086i	$0.944303\pi$
$684$	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
$689$	−1.64483	+	2.84892i	−0.0626629	+	0.108535i
$690$	−0.173922	+	0.301242i	−0.00662111	+	0.0114681i
$691$	7.56545	+	13.1038i	0.287803	+	0.498490i	0.973285	−	0.229600i	$-0.0737417\pi$
$691$	7.56545	+	13.1038i	0.287803	+	0.498490i	−0.685482	+	0.728090i	$0.740408\pi$
$692$	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	$0.487826\pi$
$702$	0.150772	+	0.261146i	0.00569054	+	0.00985630i
$703$	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	0.996372	+	0.0851015i	$0.0271215\pi$
$709$	15.2276	+	26.3751i	0.571886	+	0.990536i	−0.424486	+	0.905434i	$0.639545\pi$
$710$	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
$715$	17.7210			0.662727
$716$	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	0.998713	−	0.0507089i	$-0.0161481\pi$
$719$	12.2123	+	21.1523i	0.455442	+	0.788848i	−0.543272	+	0.839557i	$0.682815\pi$
$720$	−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	$0.518268\pi$
$728$	0.870665	+	1.85682i	0.0322690	+	0.0688184i
$729$	−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	$-0.117002\pi$
$733$	4.20713	+	7.28697i	0.155394	+	0.269150i	−0.777808	+	0.628501i	$0.783669\pi$
$734$	−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	$-0.790893\pi$
$739$	3.61379	−	6.25927i	0.132936	−	0.230251i	0.924807	+	0.380437i	$0.124226\pi$
$740$	27.5564	+	47.7291i	1.01299	+	1.75456i
$741$	0.464419			0.0170609
$742$	−0.722966	−	1.54183i	−0.0265409	−	0.0566024i
$743$	−53.9092			−1.97774			−0.988869	−	0.148791i	$-0.952462\pi$
$743$	−53.9092			−1.97774			−0.988869	+	0.148791i	$0.952462\pi$
$744$	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	−0.999231	−	0.0392053i	$-0.987517\pi$
$751$	−14.6221	−	25.3262i	−0.533568	−	0.924168i	0.465663	−	0.884962i	$-0.345816\pi$
$752$	−6.68628	+	11.5810i	−0.243824	+	0.422315i
$753$	0.338856	−	0.586916i	0.0123486	−	0.0213884i
$754$	0.161524	+	0.279768i	0.00588236	+	0.0101885i
$755$	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	$-0.271330\pi$
$761$	−8.90805	−	15.4292i	−0.322917	−	0.559308i	−0.981089	+	0.193560i	$0.937997\pi$
$762$	−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
$767$	−2.25314	+	3.90255i	−0.0813561	+	0.140913i
$768$	1.69182	+	2.93033i	0.0610485	+	0.105739i
$769$	−11.3069

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.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} +1.00000 q^{13} +(-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} +(0.0978281 + 0.169443i) q^{26} +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} +(0.129894 - 0.224983i) q^{39} +(-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} +(0.980859 - 1.69890i) q^{52} +(-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} +(-1.96625 - 3.40565i) q^{65} +(-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} +0.0508292 q^{78} +(-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} +(1.12324 + 2.39548i) q^{91} -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	\( 10 q - 4 q^{2} - 8 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 18 q^{8} - 3 q^{9} + 5 q^{10} - 11 q^{11} - 5 q^{12} + 10 q^{13} + 10 q^{14} - 10 q^{16} + 5 q^{17} - 9 q^{18} - 9 q^{19} + 2 q^{20} + 2 q^{21} + 16 q^{22} - 10 q^{23} - 9 q^{25} - 4 q^{26} + 37 q^{28} - 6 q^{29} + 13 q^{30} + 6 q^{31} - 22 q^{32} - 8 q^{33} - 44 q^{34} - 4 q^{35} + 14 q^{36} - 4 q^{37} + 10 q^{38} - 28 q^{40} + 28 q^{41} + 52 q^{42} + 4 q^{43} + 32 q^{45} - 3 q^{46} - q^{47} - 46 q^{48} - 11 q^{49} + 18 q^{50} + 8 q^{51} - 8 q^{52} - 17 q^{53} - 23 q^{54} - 21 q^{56} - 32 q^{57} + 27 q^{58} - 11 q^{59} + 29 q^{60} + 11 q^{61} - 46 q^{62} + 5 q^{63} + 18 q^{64} - 2 q^{65} - 21 q^{66} - 13 q^{67} + 32 q^{68} + 36 q^{69} + 49 q^{70} + 30 q^{71} + 19 q^{72} + 33 q^{74} + 20 q^{75} + 16 q^{76} - 46 q^{77} - 10 q^{78} - 2 q^{79} - 55 q^{80} + 19 q^{81} - 34 q^{82} + 12 q^{83} - 23 q^{84} - 44 q^{85} - 28 q^{86} + 8 q^{87} + 3 q^{88} + 4 q^{89} - 68 q^{90} + q^{91} + 42 q^{92} - 18 q^{93} - 20 q^{94} + 12 q^{95} + 37 q^{96} - 24 q^{97} - 7 q^{98} + 22 q^{99}+O(q^{100}) \) 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^13 + 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 - 4 * q^26 + 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 - 8 * q^52 - 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 - 2 * q^65 - 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 - 10 * q^78 - 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 + q^91 + 42 * q^92 - 18 * q^93 - 20 * q^94 + 12 * q^95 + 37 * q^96 - 24 * q^97 - 7 * q^98 + 22 * q^99

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