LMFDB - Embedded newform 315.2.i.f.106.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(106,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.i (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 8 x^{14} - 10 x^{13} + 40 x^{12} - 45 x^{11} + 159 x^{10} - 180 x^{9} + 576 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 8x^14 - 10x^13 + 40x^12 - 45x^11 + 159x^10 - 180x^9 + 576x^8 - 540x^7 + 1431x^6 - 1215x^5 + 3240x^4 - 2430x^3 + 5832x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.7
Root			$1.14603 - 1.29869i$ of defining polynomial
Character	$\chi$	$=$	315.106
Dual form			315.2.i.f.211.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09035 - 1.88855i) q^{2} +(-0.551686 - 1.64184i) q^{3} +(-1.37775 - 2.38633i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.70223 - 0.748302i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.64751 q^{8} +(-2.39128 + 1.81156i) q^{9} +O(q^{10})$	\(q+(1.09035 - 1.88855i) q^{2} +(-0.551686 - 1.64184i) q^{3} +(-1.37775 - 2.38633i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.70223 - 0.748302i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.64751 q^{8} +(-2.39128 + 1.81156i) q^{9} -2.18071 q^{10} +(1.12065 - 1.94102i) q^{11} +(-3.15788 + 3.57854i) q^{12} +(2.15591 + 3.73415i) q^{13} +(-1.09035 - 1.88855i) q^{14} +(-1.14603 + 1.29869i) q^{15} +(0.959124 - 1.66125i) q^{16} -7.61793 q^{17} +(0.813877 + 6.49130i) q^{18} +2.77290 q^{19} +(-1.37775 + 2.38633i) q^{20} +(-1.69772 - 0.343146i) q^{21} +(-2.44381 - 4.23280i) q^{22} +(3.45490 + 5.98406i) q^{23} +(0.908908 + 2.70495i) q^{24} +(-0.500000 + 0.866025i) q^{25} +9.40283 q^{26} +(4.29354 + 2.92670i) q^{27} -2.75549 q^{28} +(5.17399 - 8.96162i) q^{29} +(1.20307 + 3.58038i) q^{30} +(-0.920737 - 1.59476i) q^{31} +(-3.73908 - 6.47627i) q^{32} +(-3.80509 - 0.769092i) q^{33} +(-8.30624 + 14.3868i) q^{34} -1.00000 q^{35} +(7.61756 + 3.21051i) q^{36} +5.36764 q^{37} +(3.02345 - 5.23677i) q^{38} +(4.94149 - 5.59974i) q^{39} +(0.823754 + 1.42678i) q^{40} +(-3.46153 - 5.99554i) q^{41} +(-2.49916 + 2.83208i) q^{42} +(-2.98159 + 5.16427i) q^{43} -6.17587 q^{44} +(2.76450 + 1.16513i) q^{45} +15.0683 q^{46} +(1.59299 - 2.75914i) q^{47} +(-3.25665 - 0.658239i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(1.09035 + 1.88855i) q^{50} +(4.20270 + 12.5074i) q^{51} +(5.94059 - 10.2894i) q^{52} +4.14054 q^{53} +(10.2087 - 4.91742i) q^{54} -2.24130 q^{55} +(-0.823754 + 1.42678i) q^{56} +(-1.52977 - 4.55267i) q^{57} +(-11.2830 - 19.5427i) q^{58} +(-1.41722 - 2.45469i) q^{59} +(4.67805 + 0.945537i) q^{60} +(-5.59684 + 9.69401i) q^{61} -4.01572 q^{62} +(0.373217 + 2.97669i) q^{63} -12.4712 q^{64} +(2.15591 - 3.73415i) q^{65} +(-5.60137 + 6.34752i) q^{66} +(0.966006 + 1.67317i) q^{67} +(10.4956 + 18.1789i) q^{68} +(7.91885 - 8.97372i) q^{69} +(-1.09035 + 1.88855i) q^{70} +8.17768 q^{71} +(3.93966 - 2.98456i) q^{72} +3.51994 q^{73} +(5.85263 - 10.1370i) q^{74} +(1.69772 + 0.343146i) q^{75} +(-3.82036 - 6.61705i) q^{76} +(-1.12065 - 1.94102i) q^{77} +(-5.18741 - 15.4379i) q^{78} +(-3.74388 + 6.48459i) q^{79} -1.91825 q^{80} +(2.43648 - 8.66392i) q^{81} -15.0972 q^{82} +(-6.16529 + 10.6786i) q^{83} +(1.52017 + 4.52408i) q^{84} +(3.80896 + 6.59732i) q^{85} +(6.50199 + 11.2618i) q^{86} +(-17.5680 - 3.55087i) q^{87} +(-1.84628 + 3.19784i) q^{88} +11.7158 q^{89} +(5.21470 - 3.95049i) q^{90} +4.31182 q^{91} +(9.51994 - 16.4890i) q^{92} +(-2.11039 + 2.39151i) q^{93} +(-3.47385 - 6.01688i) q^{94} +(-1.38645 - 2.40141i) q^{95} +(-8.57021 + 9.71184i) q^{96} +(0.988659 - 1.71241i) q^{97} -2.18071 q^{98} +(0.836489 + 6.67165i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} - 2 q^{15} - 21 q^{16} + 8 q^{17} + 26 q^{18} + 6 q^{19} - 11 q^{20} - q^{21} - 23 q^{22} + 8 q^{23} - 38 q^{24} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 22 q^{28} - 19 q^{29} - 13 q^{30} + 12 q^{32} - 21 q^{33} - 9 q^{34} - 16 q^{35} + 70 q^{36} + 42 q^{37} + 28 q^{38} + 32 q^{39} + 3 q^{40} - 20 q^{41} - 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{45} + 34 q^{46} + 11 q^{47} - 18 q^{48} - 8 q^{49} + q^{50} - 14 q^{51} - 13 q^{52} - 16 q^{53} + 8 q^{55} - 3 q^{56} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 9 q^{60} - 24 q^{61} - 30 q^{62} + 12 q^{63} + 110 q^{64} - 5 q^{65} - 11 q^{66} - 16 q^{67} - 5 q^{68} + 21 q^{69} - q^{70} - 10 q^{71} + 17 q^{72} + 20 q^{73} - 21 q^{74} + q^{75} - 25 q^{76} + 4 q^{77} - 61 q^{78} - 27 q^{79} + 42 q^{80} + 11 q^{81} + 72 q^{82} - 5 q^{83} + 6 q^{84} - 4 q^{85} + 27 q^{86} - 46 q^{87} - 67 q^{88} + 54 q^{89} - 7 q^{90} - 10 q^{91} + 93 q^{92} - 9 q^{93} + 17 q^{94} - 3 q^{95} - 98 q^{96} - 27 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^11 - 3 * q^12 - 5 * q^13 - q^14 - 2 * q^15 - 21 * q^16 + 8 * q^17 + 26 * q^18 + 6 * q^19 - 11 * q^20 - q^21 - 23 * q^22 + 8 * q^23 - 38 * q^24 - 8 * q^25 - 6 * q^26 + 10 * q^27 - 22 * q^28 - 19 * q^29 - 13 * q^30 + 12 * q^32 - 21 * q^33 - 9 * q^34 - 16 * q^35 + 70 * q^36 + 42 * q^37 + 28 * q^38 + 32 * q^39 + 3 * q^40 - 20 * q^41 - 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^45 + 34 * q^46 + 11 * q^47 - 18 * q^48 - 8 * q^49 + q^50 - 14 * q^51 - 13 * q^52 - 16 * q^53 + 8 * q^55 - 3 * q^56 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 9 * q^60 - 24 * q^61 - 30 * q^62 + 12 * q^63 + 110 * q^64 - 5 * q^65 - 11 * q^66 - 16 * q^67 - 5 * q^68 + 21 * q^69 - q^70 - 10 * q^71 + 17 * q^72 + 20 * q^73 - 21 * q^74 + q^75 - 25 * q^76 + 4 * q^77 - 61 * q^78 - 27 * q^79 + 42 * q^80 + 11 * q^81 + 72 * q^82 - 5 * q^83 + 6 * q^84 - 4 * q^85 + 27 * q^86 - 46 * q^87 - 67 * q^88 + 54 * q^89 - 7 * q^90 - 10 * q^91 + 93 * q^92 - 9 * q^93 + 17 * q^94 - 3 * q^95 - 98 * q^96 - 27 * q^97 - 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.09035	−	1.88855i	0.770997	−	1.33541i	−0.166020	−	0.986122i	$-0.553092\pi$
$2$	1.09035	−	1.88855i	0.770997	−	1.33541i	0.937017	−	0.349284i	$-0.113575\pi$
$3$	−0.551686	−	1.64184i	−0.318516	−	0.947917i
$3$	−0.551686	−	1.64184i	−0.318516	−	0.947917i
$4$	−1.37775	−	2.38633i	−0.688873	−	1.19316i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−3.70223	−	0.748302i	−1.51143	−	0.305493i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−1.64751			−0.582482
$9$	−2.39128	+	1.81156i	−0.797095	+	0.603854i
$10$	−2.18071			−0.689601
$11$	1.12065	−	1.94102i	0.337888	−	0.585239i	−0.646147	−	0.763213i	$-0.723621\pi$
$11$	1.12065	−	1.94102i	0.337888	−	0.585239i	0.984035	+	0.177974i	$0.0569542\pi$
$12$	−3.15788	+	3.57854i	−0.911603	+	1.03304i
$13$	2.15591	+	3.73415i	0.597942	+	1.03567i	0.993124	+	0.117063i	$0.0373480\pi$
$13$	2.15591	+	3.73415i	0.597942	+	1.03567i	−0.395183	+	0.918603i	$0.629319\pi$
$14$	−1.09035	−	1.88855i	−0.291410	−	0.504736i
$15$	−1.14603	+	1.29869i	−0.295904	+	0.335322i
$16$	0.959124	−	1.66125i	0.239781	−	0.415313i
$17$	−7.61793			−1.84762			−0.923809	−	0.382853i	$-0.874941\pi$
$17$	−7.61793			−1.84762			−0.923809	+	0.382853i	$0.874941\pi$
$18$	0.813877	+	6.49130i	0.191833	+	1.53002i
$19$	2.77290			0.636148			0.318074	−	0.948066i	$-0.396964\pi$
$19$	2.77290			0.636148			0.318074	+	0.948066i	$0.396964\pi$
$20$	−1.37775	+	2.38633i	−0.308073	+	0.533599i
$21$	−1.69772	−	0.343146i	−0.370473	−	0.0748807i
$22$	−2.44381	−	4.23280i	−0.521021	−	0.902435i
$23$	3.45490	+	5.98406i	0.720396	+	1.24776i	0.960841	+	0.277100i	$0.0893733\pi$
$23$	3.45490	+	5.98406i	0.720396	+	1.24776i	−0.240445	+	0.970663i	$0.577293\pi$
$24$	0.908908	+	2.70495i	0.185530	+	0.552145i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	9.40283			1.84405
$27$	4.29354	+	2.92670i	0.826291	+	0.563243i
$28$	−2.75549			−0.520739
$29$	5.17399	−	8.96162i	0.960786	−	1.66413i	0.240254	−	0.970710i	$-0.422769\pi$
$29$	5.17399	−	8.96162i	0.960786	−	1.66413i	0.720533	−	0.693421i	$-0.243897\pi$
$30$	1.20307	+	3.58038i	0.219649	+	0.653685i
$31$	−0.920737	−	1.59476i	−0.165369	−	0.286428i	0.771417	−	0.636330i	$-0.219548\pi$
$31$	−0.920737	−	1.59476i	−0.165369	−	0.286428i	−0.936786	+	0.349902i	$0.886215\pi$
$32$	−3.73908	−	6.47627i	−0.660982	−	1.14485i
$33$	−3.80509	−	0.769092i	−0.662381	−	0.133882i
$34$	−8.30624	+	14.3868i	−1.42451	+	2.46732i
$35$	−1.00000			−0.169031
$36$	7.61756	+	3.21051i	1.26959	+	0.535085i
$37$	5.36764			0.882434			0.441217	−	0.897401i	$-0.354547\pi$
$37$	5.36764			0.882434			0.441217	+	0.897401i	$0.354547\pi$
$38$	3.02345	−	5.23677i	0.490468	−	0.849516i
$39$	4.94149	−	5.59974i	0.791271	−	0.896676i
$40$	0.823754	+	1.42678i	0.130247	+	0.225594i
$41$	−3.46153	−	5.99554i	−0.540600	−	0.936346i	−0.998870	−	0.0475330i	$-0.984864\pi$
$41$	−3.46153	−	5.99554i	−0.540600	−	0.936346i	0.458270	−	0.888813i	$-0.348469\pi$
$42$	−2.49916	+	2.83208i	−0.385629	+	0.436999i
$43$	−2.98159	+	5.16427i	−0.454689	+	0.787544i	−0.998670	−	0.0515530i	$-0.983583\pi$
$43$	−2.98159	+	5.16427i	−0.454689	+	0.787544i	0.543981	+	0.839097i	$0.316916\pi$
$44$	−6.17587			−0.931048
$45$	2.76450	+	1.16513i	0.412108	+	0.173688i
$46$	15.0683			2.22169
$47$	1.59299	−	2.75914i	0.232362	−	0.402462i	−0.726141	−	0.687546i	$-0.758688\pi$
$47$	1.59299	−	2.75914i	0.232362	−	0.402462i	0.958503	+	0.285084i	$0.0920214\pi$
$48$	−3.25665	−	0.658239i	−0.470056	−	0.0950087i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	1.09035	+	1.88855i	0.154199	+	0.267081i
$51$	4.20270	+	12.5074i	0.588496	+	1.75139i
$52$	5.94059	−	10.2894i	0.823812	−	1.42688i
$53$	4.14054			0.568747			0.284373	−	0.958714i	$-0.408214\pi$
$53$	4.14054			0.568747			0.284373	+	0.958714i	$0.408214\pi$
$54$	10.2087	−	4.91742i	1.38923	−	0.669176i
$55$	−2.24130			−0.302216
$56$	−0.823754	+	1.42678i	−0.110079	+	0.190662i
$57$	−1.52977	−	4.55267i	−0.202623	−	0.603016i
$58$	−11.2830	−	19.5427i	−1.48153	−	2.56608i
$59$	−1.41722	−	2.45469i	−0.184506	−	0.319574i	0.758904	−	0.651203i	$-0.225735\pi$
$59$	−1.41722	−	2.45469i	−0.184506	−	0.319574i	−0.943410	+	0.331629i	$0.892402\pi$
$60$	4.67805	+	0.945537i	0.603934	+	0.122068i
$61$	−5.59684	+	9.69401i	−0.716602	+	1.24119i	0.245736	+	0.969337i	$0.420970\pi$
$61$	−5.59684	+	9.69401i	−0.716602	+	1.24119i	−0.962338	+	0.271855i	$0.912363\pi$
$62$	−4.01572			−0.509997
$63$	0.373217	+	2.97669i	0.0470209	+	0.375028i
$64$	−12.4712			−1.55890
$65$	2.15591	−	3.73415i	0.267408	−	0.463164i
$66$	−5.60137	+	6.34752i	−0.689480	+	0.781325i
$67$	0.966006	+	1.67317i	0.118016	+	0.204410i	0.918982	−	0.394301i	$-0.129013\pi$
$67$	0.966006	+	1.67317i	0.118016	+	0.204410i	−0.800965	+	0.598711i	$0.795680\pi$
$68$	10.4956	+	18.1789i	1.27277	+	2.20451i
$69$	7.91885	−	8.97372i	0.953318	−	1.08031i
$70$	−1.09035	+	1.88855i	−0.130322	+	0.225725i
$71$	8.17768			0.970513			0.485256	−	0.874372i	$-0.338726\pi$
$71$	8.17768			0.970513			0.485256	+	0.874372i	$0.338726\pi$
$72$	3.93966	−	2.98456i	0.464294	−	0.351734i
$73$	3.51994			0.411978			0.205989	−	0.978554i	$-0.433959\pi$
$73$	3.51994			0.411978			0.205989	+	0.978554i	$0.433959\pi$
$74$	5.85263	−	10.1370i	0.680354	−	1.17841i
$75$	1.69772	+	0.343146i	0.196036	+	0.0396231i
$76$	−3.82036	−	6.61705i	−0.438225	−	0.759028i
$77$	−1.12065	−	1.94102i	−0.127710	−	0.221200i
$78$	−5.18741	−	15.4379i	−0.587359	−	1.74800i
$79$	−3.74388	+	6.48459i	−0.421219	+	0.729573i	−0.996059	−	0.0886928i	$-0.971731\pi$
$79$	−3.74388	+	6.48459i	−0.421219	+	0.729573i	0.574840	+	0.818266i	$0.305064\pi$
$80$	−1.91825			−0.214467
$81$	2.43648	−	8.66392i	0.270720	−	0.962658i
$82$	−15.0972			−1.66720
$83$	−6.16529	+	10.6786i	−0.676728	+	1.17213i	0.299232	+	0.954180i	$0.403269\pi$
$83$	−6.16529	+	10.6786i	−0.676728	+	1.17213i	−0.975961	+	0.217947i	$0.930064\pi$
$84$	1.52017	+	4.52408i	0.165864	+	0.493618i
$85$	3.80896	+	6.59732i	0.413140	+	0.715579i
$86$	6.50199	+	11.2618i	0.701128	+	1.21439i
$87$	−17.5680	−	3.55087i	−1.88348	−	0.380694i
$88$	−1.84628	+	3.19784i	−0.196814	+	0.340891i
$89$	11.7158			1.24187			0.620936	−	0.783861i	$-0.286753\pi$
$89$	11.7158			1.24187			0.620936	+	0.783861i	$0.286753\pi$
$90$	5.21470	−	3.95049i	0.549677	−	0.416418i
$91$	4.31182			0.452002
$92$	9.51994	−	16.4890i	0.992523	−	1.71910i
$93$	−2.11039	+	2.39151i	−0.218837	+	0.247988i
$94$	−3.47385	−	6.01688i	−0.358300	−	0.620594i
$95$	−1.38645	−	2.40141i	−0.142247	−	0.246379i
$96$	−8.57021	+	9.71184i	−0.874694	+	0.991211i
$97$	0.988659	−	1.71241i	0.100383	−	0.173869i	−0.811459	−	0.584409i	$-0.801326\pi$
$97$	0.988659	−	1.71241i	0.100383	−	0.173869i	0.911843	+	0.410540i	$0.134660\pi$
$98$	−2.18071			−0.220285
$99$	0.836489	+	6.67165i	0.0840703	+	0.670526i
$100$	2.75549			0.275549
$101$	−2.81743	+	4.87994i	−0.280345	+	0.485572i	−0.971470	−	0.237164i	$-0.923782\pi$
$101$	−2.81743	+	4.87994i	−0.280345	+	0.485572i	0.691125	+	0.722736i	$0.257116\pi$
$102$	28.2033	+	5.70051i	2.79255	+	0.564435i
$103$	−0.758994	−	1.31462i	−0.0747859	−	0.129533i	0.826207	−	0.563366i	$-0.190494\pi$
$103$	−0.758994	−	1.31462i	−0.0747859	−	0.129533i	−0.900993	+	0.433833i	$0.857161\pi$
$104$	−3.55188	−	6.15204i	−0.348291	−	0.603257i
$105$	0.551686	+	1.64184i	0.0538391	+	0.160227i
$106$	4.51466	−	7.81961i	0.438502	−	0.759508i
$107$	−3.74650			−0.362188			−0.181094	−	0.983466i	$-0.557964\pi$
$107$	−3.74650			−0.362188			−0.181094	+	0.983466i	$0.557964\pi$
$108$	1.06865	−	14.2780i	0.102831	−	1.37390i
$109$	3.39165			0.324861			0.162431	−	0.986720i	$-0.448067\pi$
$109$	3.39165			0.324861			0.162431	+	0.986720i	$0.448067\pi$
$110$	−2.44381	+	4.23280i	−0.233008	+	0.403581i
$111$	−2.96125	−	8.81280i	−0.281069	−	0.836474i
$112$	−0.959124	−	1.66125i	−0.0906287	−	0.156973i
$113$	4.85694	+	8.41246i	0.456902	+	0.791378i	0.998795	−	0.0490695i	$-0.0156256\pi$
$113$	4.85694	+	8.41246i	0.456902	+	0.791378i	−0.541893	+	0.840447i	$0.682292\pi$
$114$	−10.2659	−	2.07497i	−0.961493	−	0.194339i
$115$	3.45490	−	5.98406i	0.322171	−	0.558016i
$116$	−28.5138			−2.64744
$117$	−11.9200	−	5.02384i	−1.10201	−	0.464454i
$118$	−6.18108			−0.569014
$119$	−3.80896	+	6.59732i	−0.349167	+	0.604775i
$120$	1.88810	−	2.13961i	0.172359	−	0.195319i
$121$	2.98830	+	5.17588i	0.271663	+	0.470535i
$122$	12.2051	+	21.1398i	1.10500	+	1.91391i
$123$	−7.93405	+	8.99093i	−0.715389	+	0.810685i
$124$	−2.53708	+	4.39436i	−0.227837	+	0.394625i
$125$	1.00000			0.0894427
$126$	6.02857	+	2.54081i	0.537068	+	0.226354i
$127$	1.20990			0.107361			0.0536807	−	0.998558i	$-0.482905\pi$
$127$	1.20990			0.107361			0.0536807	+	0.998558i	$0.482905\pi$
$128$	−6.11986	+	10.5999i	−0.540924	+	0.936909i
$129$	10.1238	+	2.04625i	0.891353	+	0.180162i
$130$	−4.70141	−	8.14309i	−0.412341	−	0.714196i
$131$	0.571554	+	0.989961i	0.0499369	+	0.0864933i	0.889913	−	0.456130i	$-0.150765\pi$
$131$	0.571554	+	0.989961i	0.0499369	+	0.0864933i	−0.839976	+	0.542623i	$0.817431\pi$
$132$	3.40714	+	10.1398i	0.296554	+	0.882556i
$133$	1.38645	−	2.40141i	0.120221	−	0.208228i
$134$	4.21316			0.363961
$135$	0.387825	−	5.18166i	0.0333786	−	0.445966i
$136$	12.5506			1.07620
$137$	−7.34482	+	12.7216i	−0.627510	+	1.08688i	0.360539	+	0.932744i	$0.382593\pi$
$137$	−7.34482	+	12.7216i	−0.627510	+	1.08688i	−0.988050	+	0.154136i	$0.950741\pi$
$138$	−8.31295	−	24.7397i	−0.707645	−	2.10598i
$139$	8.93371	+	15.4736i	0.757748	+	1.31246i	0.943997	+	0.329955i	$0.107033\pi$
$139$	8.93371	+	15.4736i	0.757748	+	1.31246i	−0.186249	+	0.982503i	$0.559633\pi$
$140$	1.37775	+	2.38633i	0.116441	+	0.201681i
$141$	−5.40890	−	1.09326i	−0.455512	−	0.0920689i
$142$	8.91657	−	15.4440i	0.748262	−	1.29603i
$143$	9.66406			0.808149
$144$	0.715922	+	5.71004i	0.0596602	+	0.475836i
$145$	−10.3480			−0.859354
$146$	3.83799	−	6.64759i	0.317634	−	0.550158i
$147$	−1.14603	+	1.29869i	−0.0945232	+	0.107115i
$148$	−7.39524	−	12.8089i	−0.607885	−	1.05289i
$149$	−9.06272	−	15.6971i	−0.742447	−	1.28596i	−0.951378	−	0.308026i	$-0.900332\pi$
$149$	−9.06272	−	15.6971i	−0.742447	−	1.28596i	0.208931	−	0.977930i	$-0.433002\pi$
$150$	2.49916	−	2.83208i	0.204056	−	0.231238i
$151$	−4.42211	+	7.65933i	−0.359867	+	0.623307i	−0.987938	−	0.154848i	$-0.950511\pi$
$151$	−4.42211	+	7.65933i	−0.359867	+	0.623307i	0.628072	+	0.778155i	$0.283844\pi$
$152$	−4.56838			−0.370545
$153$	18.2166	−	13.8003i	1.47273	−	1.11569i
$154$	−4.88761			−0.393855
$155$	−0.920737	+	1.59476i	−0.0739554	+	0.128095i
$156$	−20.1709	−	4.07699i	−1.61497	−	0.326420i
$157$	5.92742	+	10.2666i	0.473060	+	0.819364i	0.999525	−	0.0308332i	$-0.00981608\pi$
$157$	5.92742	+	10.2666i	0.473060	+	0.819364i	−0.526465	+	0.850197i	$0.676483\pi$
$158$	8.16431	+	14.1410i	0.649518	+	1.12500i
$159$	−2.28428	−	6.79811i	−0.181155	−	0.539125i
$160$	−3.73908	+	6.47627i	−0.295600	+	0.511994i
$161$	6.90980			0.544568
$162$	−13.7056	−	14.0482i	−1.07681	−	1.10373i
$163$	7.83231			0.613473			0.306737	−	0.951794i	$-0.400763\pi$
$163$	7.83231			0.613473			0.306737	+	0.951794i	$0.400763\pi$
$164$	−9.53821	+	16.5207i	−0.744809	+	1.29005i
$165$	1.23649	+	3.67985i	0.0962607	+	0.286476i
$166$	13.4447	+	23.2869i	1.04351	+	1.80741i
$167$	5.17768	+	8.96801i	0.400661	+	0.693965i	0.993806	−	0.111130i	$-0.0354472\pi$
$167$	5.17768	+	8.96801i	0.400661	+	0.693965i	−0.593145	+	0.805096i	$0.702114\pi$
$168$	2.79701	+	0.565336i	0.215794	+	0.0436167i
$169$	−2.79590	+	4.84264i	−0.215069	+	0.372511i
$170$	16.6125			1.27412
$171$	−6.63080	+	5.02329i	−0.507070	+	0.384140i
$172$	16.4315			1.25289
$173$	2.64167	−	4.57551i	0.200843	−	0.347870i	−0.747957	−	0.663747i	$-0.768965\pi$
$173$	2.64167	−	4.57551i	0.200843	−	0.347870i	0.948800	+	0.315877i	$0.102299\pi$
$174$	−25.8613	+	29.3063i	−1.96054	+	2.22170i
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	−2.14968	−	3.72335i	−0.162038	−	0.280658i
$177$	−3.24836	+	3.68107i	−0.244161	+	0.276686i
$178$	12.7744	−	22.1259i	0.957480	−	1.65840i
$179$	−25.0325			−1.87102			−0.935508	−	0.353304i	$-0.885058\pi$
$179$	−25.0325			−1.87102			−0.935508	+	0.353304i	$0.885058\pi$
$180$	−1.02840	−	8.20226i	−0.0766521	−	0.611360i
$181$	−13.7059			−1.01875			−0.509376	−	0.860544i	$-0.670124\pi$
$181$	−13.7059			−1.01875			−0.509376	+	0.860544i	$0.670124\pi$
$182$	4.70141	−	8.14309i	0.348492	−	0.603606i
$183$	19.0037	+	3.84107i	1.40480	+	0.283940i
$184$	−5.69197	−	9.85879i	−0.419618	−	0.726799i
$185$	−2.68382	−	4.64851i	−0.197318	−	0.341765i
$186$	2.21542	+	6.59317i	0.162442	+	0.483435i
$187$	−8.53701	+	14.7865i	−0.624288	+	1.08130i
$188$	−8.77895			−0.640270
$189$	4.68136	−	2.25496i	0.340519	−	0.164024i
$190$	−6.04690			−0.438688
$191$	−11.4891	+	19.8997i	−0.831322	+	1.43989i	0.0656691	+	0.997841i	$0.479082\pi$
$191$	−11.4891	+	19.8997i	−0.831322	+	1.43989i	−0.896991	+	0.442050i	$0.854252\pi$
$192$	6.88018	+	20.4757i	0.496534	+	1.47771i
$193$	−8.22741	−	14.2503i	−0.592222	−	1.02576i	−0.993933	−	0.109991i	$-0.964918\pi$
$193$	−8.22741	−	14.2503i	−0.592222	−	1.02576i	0.401711	−	0.915767i	$-0.368416\pi$
$194$	−2.15598	−	3.73426i	−0.154790	−	0.268104i
$195$	−7.32026	−	1.47959i	−0.524215	−	0.105955i
$196$	−1.37775	+	2.38633i	−0.0984104	+	0.170452i
$197$	−17.4103			−1.24043			−0.620215	−	0.784431i	$-0.712955\pi$
$197$	−17.4103			−1.24043			−0.620215	+	0.784431i	$0.712955\pi$
$198$	13.5118	+	5.69471i	0.960243	+	0.404706i
$199$	8.46662			0.600183			0.300091	−	0.953910i	$-0.402983\pi$
$199$	8.46662			0.600183			0.300091	+	0.953910i	$0.402983\pi$
$200$	0.823754	−	1.42678i	0.0582482	−	0.100889i
$201$	2.21415	−	2.50909i	0.156174	−	0.176978i
$202$	6.14400	+	10.6417i	0.432291	+	0.748749i
$203$	−5.17399	−	8.96162i	−0.363143	−	0.628982i
$204$	24.0565	−	27.2611i	1.68429	−	1.90866i
$205$	−3.46153	+	5.99554i	−0.241763	+	0.418747i
$206$	−3.31029			−0.230639
$207$	−19.1021	−	8.05083i	−1.32769	−	0.559571i
$208$	8.27114			0.573500
$209$	3.10745	−	5.38226i	0.214947	−	0.372299i
$210$	3.70223	+	0.748302i	0.255478	+	0.0516378i
$211$	−2.70546	−	4.68600i	−0.186252	−	0.322597i	0.757746	−	0.652550i	$-0.226301\pi$
$211$	−2.70546	−	4.68600i	−0.186252	−	0.322597i	−0.943998	+	0.329952i	$0.892967\pi$
$212$	−5.70461	−	9.88068i	−0.391794	−	0.678608i
$213$	−4.51152	−	13.4265i	−0.309124	−	0.919966i
$214$	−4.08501	+	7.07544i	−0.279246	+	0.483667i
$215$	5.96319			0.406686
$216$	−7.07364	−	4.82176i	−0.481300	−	0.328079i
$217$	−1.84147			−0.125007
$218$	3.69810	−	6.40530i	0.250467	−	0.433822i
$219$	−1.94190	−	5.77919i	−0.131222	−	0.390521i
$220$	3.08794	+	5.34846i	0.208189	+	0.360593i
$221$	−16.4236	−	28.4464i	−1.10477	−	1.91352i
$222$	−19.8722	−	4.01661i	−1.33374	−	0.269577i
$223$	−1.74534	+	3.02301i	−0.116876	+	0.202436i	−0.918528	−	0.395355i	$-0.870621\pi$
$223$	−1.74534	+	3.02301i	−0.116876	+	0.202436i	0.801652	+	0.597791i	$0.203955\pi$
$224$	−7.47816			−0.499655
$225$	−0.373217	−	2.97669i	−0.0248811	−	0.198446i
$226$	21.1831			1.40908
$227$	7.45673	−	12.9154i	0.494920	−	0.857227i	−0.505062	−	0.863083i	$-0.668531\pi$
$227$	7.45673	−	12.9154i	0.494920	−	0.857227i	0.999983	+	0.00585555i	$0.00186389\pi$
$228$	−8.75651	+	9.92296i	−0.579914	+	0.657164i
$229$	−13.4650	−	23.3221i	−0.889795	−	1.54117i	−0.840117	−	0.542405i	$-0.817514\pi$
$229$	−13.4650	−	23.3221i	−0.889795	−	1.54117i	−0.0496776	−	0.998765i	$-0.515819\pi$
$230$	−7.53413	−	13.0495i	−0.496786	−	0.860458i
$231$	−2.56860	+	2.91076i	−0.169001	+	0.191514i
$232$	−8.52420	+	14.7643i	−0.559641	+	0.969327i
$233$	−18.5716			−1.21666			−0.608332	−	0.793682i	$-0.708161\pi$
$233$	−18.5716			−1.21666			−0.608332	+	0.793682i	$0.708161\pi$
$234$	−22.4848	+	17.0338i	−1.46988	+	1.11353i
$235$	−3.18598			−0.207831
$236$	−3.90513	+	6.76388i	−0.254202	+	0.440291i
$237$	12.7121	+	2.56940i	0.825740	+	0.166900i
$238$	8.30624	+	14.3868i	0.538414	+	0.932560i
$239$	−2.51211	−	4.35109i	−0.162495	−	0.281449i	0.773268	−	0.634079i	$-0.218621\pi$
$239$	−2.51211	−	4.35109i	−0.162495	−	0.281449i	−0.935763	+	0.352630i	$0.885287\pi$
$240$	1.05827	+	3.14946i	0.0683111	+	0.203297i
$241$	13.1745	−	22.8189i	0.848645	−	1.46990i	−0.0337737	−	0.999430i	$-0.510753\pi$
$241$	13.1745	−	22.8189i	0.848645	−	1.46990i	0.882418	−	0.470466i	$-0.155914\pi$
$242$	13.0332			0.837807
$243$	−15.5690	+	0.779446i	−0.998749	+	0.0500015i
$244$	30.8441			1.97459
$245$	−0.500000	+	0.866025i	−0.0319438	+	0.0553283i
$246$	8.32890	+	24.7871i	0.531031	+	1.58037i
$247$	5.97813	+	10.3544i	0.380379	+	0.658837i
$248$	1.51692	+	2.62739i	0.0963247	+	0.166839i
$249$	20.9339	+	4.23119i	1.32663	+	0.268141i
$250$	1.09035	−	1.88855i	0.0689601	−	0.119442i
$251$	25.2530			1.59395			0.796977	−	0.604010i	$-0.206431\pi$
$251$	25.2530			1.59395			0.796977	+	0.604010i	$0.206431\pi$
$252$	6.58917	−	4.99175i	0.415078	−	0.314450i
$253$	15.4869			0.973653
$254$	1.31922	−	2.28496i	0.0827753	−	0.143371i
$255$	8.73039	−	9.89336i	0.546718	−	0.619546i
$256$	0.874447	+	1.51459i	0.0546530	+	0.0946617i
$257$	−10.0125	−	17.3422i	−0.624563	−	1.08178i	−0.988625	−	0.150400i	$-0.951944\pi$
$257$	−10.0125	−	17.3422i	−0.624563	−	1.08178i	0.364062	−	0.931375i	$-0.381390\pi$
$258$	14.9030	−	16.8882i	0.927820	−	1.05141i
$259$	2.68382	−	4.64851i	0.166764	−	0.288844i
$260$	−11.8812			−0.736840
$261$	3.86204	+	30.8028i	0.239054	+	1.90665i
$262$	2.49279			0.154005
$263$	−1.19957	+	2.07772i	−0.0739688	+	0.128118i	−0.900637	−	0.434571i	$-0.856900\pi$
$263$	−1.19957	+	2.07772i	−0.0739688	+	0.128118i	0.826669	+	0.562689i	$0.190233\pi$
$264$	6.26892	+	1.26709i	0.385825	+	0.0779837i
$265$	−2.07027	−	3.58581i	−0.127176	−	0.220275i
$266$	−3.02345	−	5.23677i	−0.185380	−	0.321087i
$267$	−6.46344	−	19.2355i	−0.395556	−	1.17719i
$268$	2.66182	−	4.61041i	0.162597	−	0.281626i
$269$	−0.951237			−0.0579980			−0.0289990	−	0.999579i	$-0.509232\pi$
$269$	−0.951237			−0.0579980			−0.0289990	+	0.999579i	$0.509232\pi$
$270$	−9.36295	−	6.38227i	−0.569811	−	0.388413i
$271$	3.73331			0.226782			0.113391	−	0.993550i	$-0.463829\pi$
$271$	3.73331			0.226782			0.113391	+	0.993550i	$0.463829\pi$
$272$	−7.30653	+	12.6553i	−0.443024	+	0.767339i
$273$	−2.37877	−	7.07932i	−0.143970	−	0.428460i
$274$	16.0169	+	27.7421i	0.967617	+	1.67596i
$275$	1.12065	+	1.94102i	0.0675776	+	0.117048i
$276$	−32.3244	−	6.53347i	−1.94570	−	0.393268i
$277$	−2.52867	+	4.37978i	−0.151933	+	0.263155i	−0.931938	−	0.362618i	$-0.881883\pi$
$277$	−2.52867	+	4.37978i	−0.151933	+	0.263155i	0.780005	+	0.625773i	$0.215216\pi$
$278$	38.9637			2.33688
$279$	5.09076	+	2.14556i	0.304776	+	0.128451i
$280$	1.64751			0.0984575
$281$	10.4296	−	18.0647i	0.622181	−	1.07765i	−0.366898	−	0.930261i	$-0.619580\pi$
$281$	10.4296	−	18.0647i	0.622181	−	1.07765i	0.989079	−	0.147387i	$-0.0470864\pi$
$282$	−7.96229	+	9.02294i	−0.474148	+	0.537308i
$283$	5.03189	+	8.71549i	0.299115	+	0.518082i	0.975934	−	0.218068i	$-0.0699753\pi$
$283$	5.03189	+	8.71549i	0.299115	+	0.518082i	−0.676819	+	0.736150i	$0.736642\pi$
$284$	−11.2668	−	19.5146i	−0.668560	−	1.15798i
$285$	−3.17784	+	3.60116i	−0.188239	+	0.213314i
$286$	10.5373	−	18.2511i	0.623081	−	1.07921i
$287$	−6.92305			−0.408655
$288$	20.6734	+	8.71304i	1.21819	+	0.513421i
$289$	41.0328			2.41369
$290$	−11.2830	+	19.5427i	−0.662559	+	1.14759i
$291$	−3.35693	−	0.678509i	−0.196787	−	0.0397749i
$292$	−4.84959	−	8.39973i	−0.283801	−	0.491557i
$293$	3.35009	+	5.80252i	0.195714	+	0.338987i	0.947134	−	0.320837i	$-0.103964\pi$
$293$	3.35009	+	5.80252i	0.195714	+	0.338987i	−0.751420	+	0.659824i	$0.770631\pi$
$294$	1.20307	+	3.58038i	0.0701643	+	0.208812i
$295$	−1.41722	+	2.45469i	−0.0825136	+	0.142918i
$296$	−8.84322			−0.514002
$297$	10.4923	−	5.05404i	0.608826	−	0.293265i
$298$	−39.5263			−2.28970
$299$	−14.8969	+	25.8022i	−0.861510	+	1.49218i
$300$	−1.52017	−	4.52408i	−0.0877669	−	0.261198i
$301$	2.98159	+	5.16427i	0.171856	+	0.297664i
$302$	9.64335	+	16.7028i	0.554912	+	0.961136i
$303$	9.56642	+	1.93358i	0.549577	+	0.111082i
$304$	2.65956	−	4.60649i	0.152536	−	0.264200i
$305$	11.1937			0.640948
$306$	−6.20005	−	49.4503i	−0.354433	−	2.82688i
$307$	−7.70802			−0.439920			−0.219960	−	0.975509i	$-0.570593\pi$
$307$	−7.70802			−0.439920			−0.219960	+	0.975509i	$0.570593\pi$
$308$	−3.08794	+	5.34846i	−0.175951	+	0.304757i
$309$	−1.73966	+	1.97140i	−0.0989661	+	0.112149i
$310$	2.00786	+	3.47772i	0.114039	+	0.197521i
$311$	1.51588	+	2.62558i	0.0859576	+	0.148883i	0.905799	−	0.423708i	$-0.139272\pi$
$311$	1.51588	+	2.62558i	0.0859576	+	0.148883i	−0.819841	+	0.572591i	$0.805938\pi$
$312$	−8.14114	+	9.22562i	−0.460902	+	0.522298i
$313$	−8.45007	+	14.6360i	−0.477626	+	0.827273i	−0.999671	−	0.0256449i	$-0.991836\pi$
$313$	−8.45007	+	14.6360i	−0.477626	+	0.827273i	0.522045	+	0.852918i	$0.325169\pi$
$314$	25.8520			1.45891
$315$	2.39128	−	1.81156i	0.134734	−	0.102070i
$316$	20.6325			1.16067
$317$	−1.67659	+	2.90394i	−0.0941668	+	0.163102i	−0.909261	−	0.416227i	$-0.863352\pi$
$317$	−1.67659	+	2.90394i	−0.0941668	+	0.163102i	0.815094	+	0.579329i	$0.196685\pi$
$318$	−15.3292	−	3.09837i	−0.859621	−	0.173748i
$319$	−11.5964	−	20.0856i	−0.649276	−	1.12458i
$320$	6.23559	+	10.8004i	0.348580	+	0.603759i
$321$	2.06689	+	6.15115i	0.115363	+	0.343324i
$322$	7.53413	−	13.0495i	0.419861	−	0.727220i
$323$	−21.1238			−1.17536
$324$	−24.0318	+	6.12244i	−1.33510	+	0.340135i
$325$	−4.31182			−0.239177
$326$	8.53999	−	14.7917i	0.472986	−	0.819236i
$327$	−1.87113	−	5.56856i	−0.103474	−	0.307942i
$328$	5.70289	+	9.87770i	0.314890	+	0.545405i
$329$	−1.59299	−	2.75914i	−0.0878244	−	0.152116i
$330$	8.29779	+	1.67717i	0.456779	+	0.0923250i
$331$	0.842998	−	1.46011i	0.0463353	−	0.0802552i	−0.841928	−	0.539591i	$-0.818579\pi$
$331$	0.842998	−	1.46011i	0.0463353	−	0.0802552i	0.888263	+	0.459335i	$0.151912\pi$
$332$	33.9768			1.86472
$333$	−12.8355	+	9.72381i	−0.703383	+	0.532861i
$334$	22.5820			1.23563
$335$	0.966006	−	1.67317i	0.0527786	−	0.0914151i
$336$	−2.19837	+	2.49122i	−0.119931	+	0.135907i
$337$	11.9127	+	20.6334i	0.648926	+	1.12397i	0.983380	+	0.181561i	$0.0581148\pi$
$337$	11.9127	+	20.6334i	0.648926	+	1.12397i	−0.334454	+	0.942412i	$0.608552\pi$
$338$	6.09704	+	10.5604i	0.331635	+	0.574409i
$339$	11.1324	−	12.6154i	0.604630	−	0.685172i
$340$	10.4956	−	18.1789i	0.569202	−	0.985887i
$341$	−4.12729			−0.223505
$342$	2.25680	+	17.9998i	0.122034	+	0.973316i
$343$	−1.00000			−0.0539949
$344$	4.91220	−	8.50818i	0.264848	−	0.458731i
$345$	−11.7309	−	2.37107i	−0.631570	−	0.127654i
$346$	−5.76072	−	9.97787i	−0.309698	−	0.536413i
$347$	0.645825	+	1.11860i	0.0346697	+	0.0600497i	0.882840	−	0.469675i	$-0.155629\pi$
$347$	0.645825	+	1.11860i	0.0346697	+	0.0600497i	−0.848170	+	0.529724i	$0.822295\pi$
$348$	15.7307	+	46.8151i	0.843252	+	2.50955i
$349$	3.12436	−	5.41155i	0.167243	−	0.289674i	−0.770206	−	0.637795i	$-0.779847\pi$
$349$	3.12436	−	5.41155i	0.167243	−	0.289674i	0.937450	+	0.348121i	$0.113180\pi$
$350$	2.18071			0.116564
$351$	−1.67223	+	22.3424i	−0.0892570	+	1.19255i
$352$	−16.7608			−0.893351
$353$	−8.49825	+	14.7194i	−0.452316	+	0.783434i	−0.998529	−	0.0542116i	$-0.982735\pi$
$353$	−8.49825	+	14.7194i	−0.452316	+	0.783434i	0.546213	+	0.837646i	$0.316069\pi$
$354$	3.41001	+	10.1483i	0.181240	+	0.539379i
$355$	−4.08884	−	7.08208i	−0.217013	−	0.375878i
$356$	−16.1414	−	27.9577i	−0.855492	−	1.48176i
$357$	12.9331	+	2.61406i	0.684492	+	0.138351i
$358$	−27.2943	+	47.2751i	−1.44255	+	2.49857i
$359$	29.7739			1.57141			0.785704	−	0.618603i	$-0.212301\pi$
$359$	29.7739			1.57141			0.785704	+	0.618603i	$0.212301\pi$
$360$	−4.55454	−	1.91956i	−0.240045	−	0.101170i
$361$	−11.3110			−0.595316
$362$	−14.9443	+	25.8843i	−0.785455	+	1.36045i
$363$	6.84938	−	7.76178i	0.359499	−	0.407388i
$364$	−5.94059	−	10.2894i	−0.311372	−	0.539312i
$365$	−1.75997	−	3.04836i	−0.0921211	−	0.159558i
$366$	27.9749	−	31.7014i	1.46227	−	1.65706i
$367$	8.85900	−	15.3442i	0.462436	−	0.800963i	−0.536646	−	0.843808i	$-0.680309\pi$
$367$	8.85900	−	15.3442i	0.462436	−	0.800963i	0.999082	+	0.0428448i	$0.0136421\pi$
$368$	13.2547			0.690949
$369$	19.1388	+	8.06627i	0.996326	+	0.419913i
$370$	−11.7053			−0.608527
$371$	2.07027	−	3.58581i	0.107483	−	0.186166i
$372$	8.61451	+	1.74118i	0.446642	+	0.0902761i
$373$	−14.8054	−	25.6437i	−0.766593	−	1.32778i	−0.939400	−	0.342823i	$-0.888617\pi$
$373$	−14.8054	−	25.6437i	−0.766593	−	1.32778i	0.172807	−	0.984956i	$-0.444716\pi$
$374$	18.6167	+	32.2451i	0.962648	+	1.66736i
$375$	−0.551686	−	1.64184i	−0.0284890	−	0.0847843i
$376$	−2.62447	+	4.54571i	−0.135346	+	0.234427i
$377$	44.6187			2.29798
$378$	0.845732	−	11.2997i	0.0434998	−	0.581193i
$379$	−2.27795			−0.117010			−0.0585052	−	0.998287i	$-0.518633\pi$
$379$	−2.27795			−0.117010			−0.0585052	+	0.998287i	$0.518633\pi$
$380$	−3.82036	+	6.61705i	−0.195980	+	0.339448i
$381$	−0.667486	−	1.98647i	−0.0341963	−	0.101770i
$382$	25.0544	+	43.3954i	1.28189	+	2.22030i
$383$	−10.9616	−	18.9861i	−0.560114	−	0.970145i	−0.997486	−	0.0708648i	$-0.977424\pi$
$383$	−10.9616	−	18.9861i	−0.560114	−	0.970145i	0.437372	−	0.899281i	$-0.355909\pi$
$384$	20.7796	+	4.20002i	1.06041	+	0.214331i
$385$	−1.12065	+	1.94102i	−0.0571135	+	0.0989235i
$386$	−35.8832			−1.82640
$387$	−2.22556	−	17.7506i	−0.113132	−	0.902313i
$388$	−5.44848			−0.276605
$389$	−17.4567	+	30.2358i	−0.885088	+	1.53302i	−0.0394758	+	0.999221i	$0.512569\pi$
$389$	−17.4567	+	30.2358i	−0.885088	+	1.53302i	−0.845612	+	0.533797i	$0.820765\pi$
$390$	−10.7759	+	12.2114i	−0.545661	+	0.618348i
$391$	−26.3192	−	45.5861i	−1.33102	−	2.30539i
$392$	0.823754	+	1.42678i	0.0416059	+	0.0720635i
$393$	1.31004	−	1.48455i	0.0660828	−	0.0748856i
$394$	−18.9834	+	32.8802i	−0.956369	+	1.65648i
$395$	7.48776			0.376750
$396$	14.7683	−	11.1880i	0.742133	−	0.562217i
$397$	13.8960			0.697418			0.348709	−	0.937231i	$-0.386620\pi$
$397$	13.8960			0.697418			0.348709	+	0.937231i	$0.386620\pi$
$398$	9.23162	−	15.9896i	0.462739	−	0.801488i
$399$	−4.70761	−	0.951512i	−0.235675	−	0.0476352i
$400$	0.959124	+	1.66125i	0.0479562	+	0.0830626i
$401$	−10.2369	−	17.7309i	−0.511208	−	0.885438i	−0.999916	−	0.0129905i	$-0.995865\pi$
$401$	−10.2369	−	17.7309i	−0.511208	−	0.885438i	0.488708	−	0.872448i	$-0.337468\pi$
$402$	−2.32434	−	6.91733i	−0.115928	−	0.345005i
$403$	3.97005	−	6.87633i	0.197762	−	0.342535i
$404$	15.5268			0.772489
$405$	−8.72142	+	2.22190i	−0.433371	+	0.110407i
$406$	−22.5659			−1.11993
$407$	6.01523	−	10.4187i	0.298164	−	0.516435i
$408$	−6.92399	−	20.6061i	−0.342789	−	1.02015i
$409$	−17.7600	−	30.7613i	−0.878177	−	1.52105i	−0.853340	−	0.521355i	$-0.825427\pi$
$409$	−17.7600	−	30.7613i	−0.878177	−	1.52105i	−0.0248367	−	0.999692i	$-0.507907\pi$
$410$	7.54858	+	13.0745i	0.372798	+	0.645705i
$411$	24.9389	+	5.04070i	1.23014	+	0.248639i
$412$	−2.09140	+	3.62242i	−0.103036	+	0.178464i
$413$	−2.83443			−0.139473
$414$	−36.0325	+	27.2971i	−1.77090	+	1.34158i
$415$	12.3306			0.605284
$416$	16.1222	−	27.9245i	0.790458	−	1.36911i
$417$	20.4767	−	23.2043i	1.00275	−	1.13632i
$418$	−6.77644	−	11.7371i	−0.331447	−	0.574082i
$419$	18.4391	+	31.9375i	0.900809	+	1.56025i	0.826446	+	0.563016i	$0.190359\pi$
$419$	18.4391	+	31.9375i	0.900809	+	1.56025i	0.0743630	+	0.997231i	$0.476308\pi$
$420$	3.15788	−	3.57854i	0.154089	−	0.174615i
$421$	−7.55889	+	13.0924i	−0.368398	+	0.638084i	−0.989315	−	0.145792i	$-0.953427\pi$
$421$	−7.55889	+	13.0924i	−0.368398	+	0.638084i	0.620917	+	0.783876i	$0.286760\pi$
$422$	−11.7996			−0.574398
$423$	1.18906	+	9.48369i	0.0578141	+	0.461113i
$424$	−6.82157			−0.331285
$425$	3.80896	−	6.59732i	0.184762	−	0.320017i
$426$	−30.2757	−	6.11938i	−1.46686	−	0.296485i
$427$	5.59684	+	9.69401i	0.270850	+	0.469126i
$428$	5.16172	+	8.94036i	0.249501	+	0.432149i
$429$	−5.33153	−	15.8669i	−0.257409	−	0.766059i
$430$	6.50199	−	11.2618i	0.313554	−	0.543091i
$431$	−16.1660			−0.778687			−0.389343	−	0.921093i	$-0.627298\pi$
$431$	−16.1660			−0.778687			−0.389343	+	0.921093i	$0.627298\pi$
$432$	8.98001	−	4.32558i	0.432051	−	0.208114i
$433$	−2.70113			−0.129808			−0.0649040	−	0.997892i	$-0.520674\pi$
$433$	−2.70113			−0.129808			−0.0649040	+	0.997892i	$0.520674\pi$
$434$	−2.00786	+	3.47772i	−0.0963804	+	0.166936i
$435$	5.70884	+	16.9898i	0.273718	+	0.814596i
$436$	−4.67284	−	8.09359i	−0.223788	−	0.387613i
$437$	9.58010	+	16.5932i	0.458278	+	0.793761i
$438$	−13.0316	−	2.63398i	−0.622676	−	0.125857i
$439$	20.3448	−	35.2383i	0.971006	−	1.68183i	0.278474	−	0.960444i	$-0.410171\pi$
$439$	20.3448	−	35.2383i	0.971006	−	1.68183i	0.692532	−	0.721388i	$-0.256495\pi$
$440$	3.69255			0.176036
$441$	2.76450	+	1.16513i	0.131643	+	0.0554825i
$442$	−71.6300			−3.40709
$443$	−16.4399	+	28.4747i	−0.781082	+	1.35287i	0.150229	+	0.988651i	$0.451999\pi$
$443$	−16.4399	+	28.4747i	−0.781082	+	1.35287i	−0.931312	+	0.364223i	$0.881335\pi$
$444$	−16.9504	+	19.2083i	−0.804429	+	0.911586i
$445$	−5.85790	−	10.1462i	−0.277691	−	0.480975i
$446$	3.80607	+	6.59231i	0.180223	+	0.312155i
$447$	−20.7724	+	23.5394i	−0.982499	+	1.11338i
$448$	−6.23559	+	10.8004i	−0.294604	+	0.510269i
$449$	9.73241			0.459301			0.229650	−	0.973273i	$-0.426242\pi$
$449$	9.73241			0.459301			0.229650	+	0.973273i	$0.426242\pi$
$450$	−6.02857	−	2.54081i	−0.284190	−	0.119775i
$451$	−15.5166			−0.730648
$452$	13.3833	−	23.1805i	0.629495	−	1.09032i
$453$	15.0150	+	3.03486i	0.705467	+	0.142590i
$454$	−16.2610	−	28.1648i	−0.763164	−	1.32184i
$455$	−2.15591	−	3.73415i	−0.101071	−	0.175059i
$456$	2.52031	+	7.50056i	0.118025	+	0.351246i
$457$	8.45929	−	14.6519i	0.395709	−	0.685388i	−0.597482	−	0.801882i	$-0.703832\pi$
$457$	8.45929	−	14.6519i	0.395709	−	0.685388i	0.993191	+	0.116494i	$0.0371656\pi$
$458$	−58.7267			−2.74412
$459$	−32.7078	−	22.2953i	−1.52667	−	1.04066i
$460$	−19.0399			−0.887739
$461$	−2.25463	+	3.90514i	−0.105009	+	0.181881i	−0.913742	−	0.406295i	$-0.866820\pi$
$461$	−2.25463	+	3.90514i	−0.105009	+	0.181881i	0.808733	+	0.588176i	$0.200154\pi$
$462$	2.69643	+	8.02468i	0.125449	+	0.373342i
$463$	−5.57748	−	9.66047i	−0.259207	−	0.448960i	0.706823	−	0.707391i	$-0.250128\pi$
$463$	−5.57748	−	9.66047i	−0.259207	−	0.448960i	−0.966030	+	0.258431i	$0.916795\pi$
$464$	−9.92500	−	17.1906i	−0.460757	−	0.798054i
$465$	3.12631	+	0.631895i	0.144979	+	0.0293034i
$466$	−20.2496	+	35.0734i	−0.938045	+	1.62474i
$467$	−27.5639			−1.27551			−0.637753	−	0.770241i	$-0.720136\pi$
$467$	−27.5639			−1.27551			−0.637753	+	0.770241i	$0.720136\pi$
$468$	4.43426	+	35.3667i	0.204974	+	1.63482i
$469$	1.93201			0.0892120
$470$	−3.47385	+	6.01688i	−0.160237	+	0.277538i
$471$	13.5860	−	15.3958i	0.626012	−	0.709402i
$472$	2.33488	+	4.04413i	0.107471	+	0.186146i
$473$	6.68263	+	11.5747i	0.307268	+	0.532203i
$474$	18.7131	−	21.2059i	0.859523	−	0.974019i
$475$	−1.38645	+	2.40141i	−0.0636148	+	0.110184i
$476$	20.9911			0.962127
$477$	−9.90121	+	7.50084i	−0.453345	+	0.343440i
$478$	−10.9563			−0.501132
$479$	−9.87108	+	17.0972i	−0.451021	+	0.781191i	−0.998450	−	0.0556610i	$-0.982273\pi$
$479$	−9.87108	+	17.0972i	−0.451021	+	0.781191i	0.547429	+	0.836852i	$0.315607\pi$
$480$	12.6958	+	2.56610i	0.579482	+	0.117126i
$481$	11.5721	+	20.0435i	0.527644	+	0.913906i
$482$	−28.7298	−	49.7614i	−1.30860	−	2.26657i
$483$	−3.81204	−	11.3448i	−0.173454	−	0.516206i
$484$	8.23423	−	14.2621i	0.374283	−	0.648278i
$485$	−1.97732			−0.0897854
$486$	−15.5037	+	30.2526i	−0.703260	+	1.37229i
$487$	−8.95864			−0.405955			−0.202977	−	0.979183i	$-0.565062\pi$
$487$	−8.95864			−0.405955			−0.202977	+	0.979183i	$0.565062\pi$
$488$	9.22084	−	15.9710i	0.417408	−	0.722972i
$489$	−4.32097	−	12.8594i	−0.195401	−	0.581522i
$490$	1.09035	+	1.88855i	0.0492572	+	0.0853160i
$491$	4.68693	+	8.11800i	0.211518	+	0.366360i	0.952190	−	0.305507i	$-0.0988259\pi$
$491$	4.68693	+	8.11800i	0.211518	+	0.366360i	−0.740672	+	0.671867i	$0.765493\pi$
$492$	32.3864	+	6.54600i	1.46009	+	0.295117i
$493$	−39.4151	+	68.2690i	−1.77517	+	3.07468i
$494$	26.0731			1.17309
$495$	5.35957	−	4.06025i	0.240895	−	0.182494i
$496$	−3.53240			−0.158610
$497$	4.08884	−	7.08208i	0.183410	−	0.317675i
$498$	30.8161	−	34.9211i	1.38090	−	1.56485i
$499$	2.14437	+	3.71416i	0.0959952	+	0.166269i	0.910024	−	0.414557i	$-0.136063\pi$
$499$	2.14437	+	3.71416i	0.0959952	+	0.166269i	−0.814028	+	0.580825i	$0.802730\pi$
$500$	−1.37775	−	2.38633i	−0.0616147	−	0.106720i
$501$	11.8676	−	13.4485i	0.530205	−	0.600833i
$502$	27.5347	−	47.6915i	1.22893	−	2.12858i
$503$	−36.9907			−1.64934			−0.824668	−	0.565618i	$-0.808638\pi$
$503$	−36.9907			−1.64934			−0.824668	+	0.565618i	$0.808638\pi$
$504$	−0.614878	−	4.90413i	−0.0273888	−	0.218447i
$505$	5.63487			0.250748
$506$	16.8862	−	29.2478i	0.750683	−	1.30022i
$507$	9.49330	+	1.91880i	0.421612	+	0.0852171i
$508$	−1.66694	−	2.88722i	−0.0739584	−	0.128100i
$509$	−11.3917	−	19.7310i	−0.504927	−	0.874560i	−0.999984	−	0.00569908i	$-0.998186\pi$
$509$	−11.3917	−	19.7310i	−0.504927	−	0.874560i	0.495056	−	0.868861i	$-0.335147\pi$
$510$	−9.16488	−	27.2751i	−0.405828	−	1.20776i
$511$	1.75997	−	3.04836i	0.0778566	−	0.134852i
$512$	−20.6656			−0.913300
$513$	11.9056	+	8.11545i	0.525643	+	0.358306i
$514$	−43.6687			−1.92615
$515$	−0.758994	+	1.31462i	−0.0334453	+	0.0579289i
$516$	−9.06504	−	26.9779i	−0.399066	−	1.18764i
$517$	−3.57036	−	6.18405i	−0.157024	−	0.271974i
$518$	−5.85263	−	10.1370i	−0.257150	−	0.445396i
$519$	−8.96964	−	1.81296i	−0.393724	−	0.0795802i
$520$	−3.55188	+	6.15204i	−0.155760	+	0.269785i
$521$	1.49492			0.0654937			0.0327469	−	0.999464i	$-0.489574\pi$
$521$	1.49492			0.0654937			0.0327469	+	0.999464i	$0.489574\pi$
$522$	62.3836	+	26.2923i	2.73046	+	1.15078i
$523$	−20.0430			−0.876419			−0.438210	−	0.898873i	$-0.644387\pi$
$523$	−20.0430			−0.876419			−0.438210	+	0.898873i	$0.644387\pi$
$524$	1.57491	−	2.72783i	0.0688004	−	0.119166i
$525$	1.14603	−	1.29869i	0.0500170	−	0.0566797i
$526$	2.61592	+	4.53091i	0.114060	+	0.197557i
$527$	7.01411	+	12.1488i	0.305539	+	0.529210i
$528$	−4.92721	+	5.58355i	−0.214429	+	0.242993i
$529$	−12.3726	+	21.4300i	−0.537941	+	0.931741i
$530$	−9.02931			−0.392208
$531$	7.83580	+	3.30249i	0.340045	+	0.143316i
$532$	−7.64072			−0.331267
$533$	14.9255	−	25.8517i	0.646494	−	1.11976i
$534$	−43.3746	−	8.76696i	−1.87700	−	0.379383i
$535$	1.87325	+	3.24456i	0.0809876	+	0.140275i
$536$	−1.59150	−	2.75656i	−0.0687425	−	0.119065i
$537$	13.8101	+	41.0994i	0.595949	+	1.77357i
$538$	−1.03719	+	1.79646i	−0.0447163	+	0.0774508i
$539$	−2.24130			−0.0965394
$540$	−12.8995	+	6.21353i	−0.555104	+	0.267388i
$541$	−40.0421			−1.72154			−0.860772	−	0.508991i	$-0.830019\pi$
$541$	−40.0421			−1.72154			−0.860772	+	0.508991i	$0.830019\pi$
$542$	4.07063	−	7.05054i	0.174849	−	0.302847i
$543$	7.56136	+	22.5029i	0.324489	+	0.965693i
$544$	28.4840	+	49.3358i	1.22124	+	2.11525i
$545$	−1.69583	−	2.93726i	−0.0726412	−	0.125818i
$546$	−15.9634	−	3.22654i	−0.683169	−	0.138083i
$547$	3.97959	−	6.89286i	0.170155	−	0.294717i	−0.768319	−	0.640067i	$-0.778906\pi$
$547$	3.97959	−	6.89286i	0.170155	−	0.294717i	0.938474	+	0.345350i	$0.112240\pi$
$548$	40.4772			1.72910
$549$	−4.17767	−	33.3202i	−0.178299	−	1.42207i
$550$	4.88761			0.208408
$551$	14.3470	−	24.8497i	0.611202	−	1.05863i
$552$	−13.0464	+	14.7843i	−0.555291	+	0.629260i
$553$	3.74388	+	6.48459i	0.159206	+	0.275753i
$554$	5.51428	+	9.55102i	0.234279	+	0.405784i
$555$	−6.15149	+	6.97092i	−0.261116	+	0.295899i
$556$	24.6168	−	42.6375i	1.04398	−	1.80823i
$557$	9.86962			0.418189			0.209095	−	0.977895i	$-0.432948\pi$
$557$	9.86962			0.418189			0.209095	+	0.977895i	$0.432948\pi$
$558$	9.60273	−	7.27473i	0.406516	−	0.307964i
$559$	−25.7122			−1.08751
$560$	−0.959124	+	1.66125i	−0.0405304	+	0.0702007i
$561$	28.9869	+	5.85889i	1.22383	+	0.247362i
$562$	−22.7440	−	39.3938i	−0.959399	−	1.66173i
$563$	15.7836	+	27.3380i	0.665198	+	1.15216i	0.979231	+	0.202745i	$0.0649864\pi$
$563$	15.7836	+	27.3380i	0.665198	+	1.15216i	−0.314033	+	0.949412i	$0.601680\pi$
$564$	4.84322	+	14.4136i	0.203937	+	0.606924i
$565$	4.85694	−	8.41246i	0.204333	−	0.353915i
$566$	21.9462			0.922466
$567$	−6.28493	−	6.44202i	−0.263942	−	0.270539i
$568$	−13.4728			−0.565306
$569$	4.87154	−	8.43776i	0.204226	−	0.353729i	−0.745660	−	0.666327i	$-0.767866\pi$
$569$	4.87154	−	8.43776i	0.204226	−	0.353729i	0.949886	+	0.312597i	$0.101199\pi$
$570$	3.33599	+	9.92804i	0.139729	+	0.415840i
$571$	16.6746	+	28.8813i	0.697812	+	1.20865i	0.969223	+	0.246183i	$0.0791763\pi$
$571$	16.6746	+	28.8813i	0.697812	+	1.20865i	−0.271411	+	0.962463i	$0.587490\pi$
$572$	−13.3146	−	23.0616i	−0.556712	−	0.964254i
$573$	39.0105	+	7.88488i	1.62969	+	0.329396i
$574$	−7.54858	+	13.0745i	−0.315072	+	0.545720i
$575$	−6.90980			−0.288158
$576$	29.8222	−	22.5923i	1.24259	−	0.941347i
$577$	−7.27210			−0.302741			−0.151371	−	0.988477i	$-0.548369\pi$
$577$	−7.27210			−0.302741			−0.151371	+	0.988477i	$0.548369\pi$
$578$	44.7403	−	77.4924i	1.86095	−	3.22326i
$579$	−18.8578	+	21.3698i	−0.783702	+	0.888098i
$580$	14.2569	+	24.6937i	0.591985	+	1.02535i
$581$	6.16529	+	10.6786i	0.255779	+	0.443023i
$582$	−4.94164	+	5.59991i	−0.204838	+	0.232124i
$583$	4.64008	−	8.03686i	0.192173	−	0.332853i
$584$	−5.79914			−0.239970
$585$	1.60924	+	12.8350i	0.0665340	+	0.530661i
$586$	14.6111			0.603581
$587$	−16.6837	+	28.8971i	−0.688611	+	1.19271i	0.283676	+	0.958920i	$0.408446\pi$
$587$	−16.6837	+	28.8971i	−0.688611	+	1.19271i	−0.972287	+	0.233789i	$0.924887\pi$
$588$	4.67805	+	0.945537i	0.192920	+	0.0389933i
$589$	−2.55312	−	4.42213i	−0.105199	−	0.182211i
$590$	3.09054	+	5.35297i	0.127235	+	0.220378i
$591$	9.60501	+	28.5849i	0.395097	+	1.17583i
$592$	5.14823	−	8.91699i	0.211591	−	0.366486i
$593$	25.9070			1.06387			0.531936	−	0.846784i	$-0.321465\pi$
$593$	25.9070			1.06387			0.531936	+	0.846784i	$0.321465\pi$
$594$	1.89554	−	25.3259i	0.0777748	−	1.03914i
$595$	7.61793			0.312304
$596$	−24.9723	+	43.2532i	−1.02290	+	1.77172i
$597$	−4.67092	−	13.9008i	−0.191168	−	0.568924i
$598$	32.4858	+	56.2671i	1.32844	+	2.30093i
$599$	18.1085	+	31.3648i	0.739891	+	1.28153i	0.952544	+	0.304401i	$0.0984564\pi$
$599$	18.1085	+	31.3648i	0.739891	+	1.28153i	−0.212653	+	0.977128i	$0.568210\pi$
$600$	−2.79701	−	0.565336i	−0.114187	−	0.0230798i
$601$	−17.8417	+	30.9027i	−0.727777	+	1.26055i	0.230043	+	0.973180i	$0.426113\pi$
$601$	−17.8417	+	30.9027i	−0.727777	+	1.26055i	−0.957821	+	0.287367i	$0.907220\pi$
$602$	13.0040			0.530003
$603$	−5.34105	−	2.25105i	−0.217504	−	0.0916698i
$604$	24.3702			0.991610
$605$	2.98830	−	5.17588i	0.121492	−	0.210430i
$606$	14.0825	−	15.9584i	0.572061	−	0.648265i
$607$	2.85878	+	4.95156i	0.116034	+	0.200977i	0.918193	−	0.396134i	$-0.129648\pi$
$607$	2.85878	+	4.95156i	0.116034	+	0.200977i	−0.802158	+	0.597111i	$0.796315\pi$
$608$	−10.3681	−	17.9581i	−0.420482	−	0.728297i
$609$	−11.8591	+	13.4389i	−0.480556	+	0.544571i
$610$	12.2051	−	21.1398i	0.494169	−	0.855926i
$611$	13.7374			0.555755
$612$	−58.0300	−	24.4574i	−2.34572	−	0.988634i
$613$	16.8207			0.679380			0.339690	−	0.940538i	$-0.389678\pi$
$613$	16.8207			0.679380			0.339690	+	0.940538i	$0.389678\pi$
$614$	−8.40448	+	14.5570i	−0.339177	+	0.587472i
$615$	11.7534	+	2.37562i	0.473943	+	0.0957942i
$616$	1.84628	+	3.19784i	0.0743886	+	0.128845i
$617$	3.00727	+	5.20875i	0.121068	+	0.209696i	0.920189	−	0.391474i	$-0.128035\pi$
$617$	3.00727	+	5.20875i	0.121068	+	0.209696i	−0.799121	+	0.601170i	$0.794701\pi$
$618$	1.82624	+	5.43497i	0.0734622	+	0.218627i
$619$	17.1943	−	29.7813i	0.691096	−	1.19701i	−0.280383	−	0.959888i	$-0.590462\pi$
$619$	17.1943	−	29.7813i	0.691096	−	1.19701i	0.971479	−	0.237125i	$-0.0762051\pi$
$620$	5.07417			0.203784
$621$	−2.67979	+	35.8042i	−0.107536	+	1.43677i
$622$	6.61138			0.265092
$623$	5.85790	−	10.1462i	0.234692	−	0.406498i
$624$	−4.56307	−	13.5799i	−0.182669	−	0.543631i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	18.4272	+	31.9168i	0.736497	+	1.27565i
$627$	−10.5511	−	2.13262i	−0.421372	−	0.0851686i
$628$	16.3330	−	28.2895i	0.651756	−	1.12888i
$629$	−40.8902			−1.63040
$630$	−0.813877	−	6.49130i	−0.0324256	−	0.258620i
$631$	9.70897			0.386508			0.193254	−	0.981149i	$-0.438096\pi$
$631$	9.70897			0.386508			0.193254	+	0.981149i	$0.438096\pi$
$632$	6.16807	−	10.6834i	0.245353	−	0.424963i
$633$	−6.20110	+	7.02714i	−0.246471	+	0.279304i
$634$	3.65616	+	6.33265i	0.145205	+	0.251502i
$635$	−0.604951	−	1.04781i	−0.0240067	−	0.0415809i
$636$	−13.0753	+	14.8171i	−0.518471	+	0.587536i
$637$	2.15591	−	3.73415i	0.0854203	−	0.147952i
$638$	−50.5770			−2.00236
$639$	−19.5552	+	14.8144i	−0.773591	+	0.586048i
$640$	12.2397			0.483817
$641$	−10.9181	+	18.9106i	−0.431238	+	0.746926i	−0.996980	−	0.0776563i	$-0.975256\pi$
$641$	−10.9181	+	18.9106i	−0.431238	+	0.746926i	0.565742	+	0.824582i	$0.308590\pi$
$642$	13.8704	+	2.80351i	0.547421	+	0.110646i
$643$	−5.94667	−	10.2999i	−0.234514	−	0.406189i	0.724618	−	0.689151i	$-0.242016\pi$
$643$	−5.94667	−	10.2999i	−0.234514	−	0.406189i	−0.959131	+	0.282962i	$0.908683\pi$
$644$	−9.51994	−	16.4890i	−0.375138	−	0.649759i
$645$	−3.28981	−	9.79061i	−0.129536	−	0.385505i
$646$	−23.0324	+	39.8933i	−0.906198	+	1.56958i
$647$	1.04181			0.0409576			0.0204788	−	0.999790i	$-0.493481\pi$
$647$	1.04181			0.0409576			0.0204788	+	0.999790i	$0.493481\pi$
$648$	−4.01413	+	14.2739i	−0.157690	+	0.560731i
$649$	−6.35280			−0.249369
$650$	−4.70141	+	8.14309i	−0.184405	+	0.319398i
$651$	1.01592	+	3.02341i	0.0398169	+	0.118497i
$652$	−10.7909	−	18.6904i	−0.422605	−	0.731974i
$653$	−10.1491	−	17.5788i	−0.397165	−	0.687910i	0.596210	−	0.802829i	$-0.296673\pi$
$653$	−10.1491	−	17.5788i	−0.397165	−	0.687910i	−0.993375	+	0.114919i	$0.963339\pi$
$654$	−12.5567	−	2.53798i	−0.491005	−	0.0992429i
$655$	0.571554	−	0.989961i	0.0223325	−	0.0386810i
$656$	−13.2801			−0.518502
$657$	−8.41719	+	6.37660i	−0.328386	+	0.248775i
$658$	−6.94770			−0.270849
$659$	1.66525	−	2.88429i	0.0648688	−	0.112356i	−0.831767	−	0.555125i	$-0.812670\pi$
$659$	1.66525	−	2.88429i	0.0648688	−	0.112356i	0.896636	+	0.442769i	$0.146004\pi$
$660$	7.07775	−	8.02057i	0.275501	−	0.312200i
$661$	−2.80569	−	4.85960i	−0.109129	−	0.189016i	0.806289	−	0.591522i	$-0.201473\pi$
$661$	−2.80569	−	4.85960i	−0.109129	−	0.189016i	−0.915418	+	0.402506i	$0.868139\pi$
$662$	−1.83833	−	3.18408i	−0.0714488	−	0.123753i
$663$	−37.6439	+	42.6584i	−1.46197	+	1.65671i
$664$	10.1574	−	17.5931i	0.394182	−	0.682744i
$665$	−2.77290			−0.107529
$666$	4.36859	+	34.8430i	0.169280	+	1.35014i
$667$	71.5025			2.76859
$668$	14.2671	−	24.7113i	0.552009	−	0.956108i
$669$	5.92619	+	1.19781i	0.229120	+	0.0463101i
$670$	−2.10658	−	3.64870i	−0.0813842	−	0.140962i
$671$	12.5442	+	21.7271i	0.484262	+	0.838767i
$672$	4.12560	+	12.2779i	0.159148	+	0.473632i
$673$	12.1050	−	20.9665i	0.466613	−	0.808198i	−0.532659	−	0.846330i	$-0.678807\pi$
$673$	12.1050	−	20.9665i	0.466613	−	0.808198i	0.999273	+	0.0381315i	$0.0121406\pi$
$674$	51.9563			2.00128
$675$	−4.68136	+	2.25496i	−0.180186	+	0.0867936i
$676$	15.4082			0.592621
$677$	−0.522991	+	0.905848i	−0.0201002	+	0.0348146i	−0.875901	−	0.482492i	$-0.839732\pi$
$677$	−0.522991	+	0.905848i	−0.0201002	+	0.0348146i	0.855800	+	0.517306i	$0.173065\pi$
$678$	−11.6864	−	34.7793i	−0.448815	−	1.33569i
$679$	−0.988659	−	1.71241i	−0.0379412	−	0.0657162i
$680$	−6.27530	−	10.8691i	−0.240647	−	0.416812i
$681$	−25.3189	−	5.11750i	−0.970221	−	0.196103i
$682$	−4.50021	+	7.79459i	−0.172322	+	0.298470i
$683$	34.7509			1.32971			0.664853	−	0.746974i	$-0.268494\pi$
$683$	34.7509			1.32971			0.664853	+	0.746974i	$0.268494\pi$
$684$	21.1228	+	8.90244i	0.807649	+	0.340393i
$685$	14.6896			0.561262
$686$	−1.09035	+	1.88855i	−0.0416299	+	0.0721052i
$687$	−30.8628	+	34.9740i	−1.17749	+	1.33434i
$688$	5.71944	+	9.90635i	0.218051	+	0.377676i
$689$	8.92663	+	15.4614i	0.340078	+	0.589032i
$690$	−17.2687	+	19.5691i	−0.657409	+	0.744982i
$691$	6.87128	−	11.9014i	0.261396	−	0.452751i	−0.705217	−	0.708991i	$-0.749151\pi$
$691$	6.87128	−	11.9014i	0.261396	−	0.452751i	0.966613	+	0.256240i	$0.0824839\pi$
$692$	−14.5582			−0.553421
$693$	6.19606	+	2.61140i	0.235369	+	0.0991991i
$694$	2.81671			0.106921
$695$	8.93371	−	15.4736i	0.338875	−	0.586949i
$696$	28.9434	+	5.85009i	1.09710	+	0.221747i
$697$	26.3696	+	45.6736i	0.998822	+	1.73001i
$698$	−6.81332	−	11.8010i	−0.257888	−	0.446675i
$699$	10.2457	+	30.4916i	0.387527	+	1.15330i
$700$	1.37775	−	2.38633i	0.0520739	−	0.0901947i
$701$	−34.0700			−1.28681			−0.643403	−	0.765528i	$-0.722478\pi$
$701$	−34.0700			−1.28681			−0.643403	+	0.765528i	$0.722478\pi$
$702$	40.3714	+	27.5192i	1.52372	+	1.03865i
$703$	14.8839			0.561358
$704$	−13.9758	+	24.2068i	−0.526733	+	0.912328i
$705$	1.75766	+	5.23088i	0.0661974	+	0.197006i
$706$	18.5322	+	32.0987i	0.697469	+	1.20805i
$707$	2.81743	+	4.87994i	0.105961	+	0.183529i
$708$	13.2596	+	2.68006i	0.498327	+	0.100723i
$709$	−6.85533	+	11.8738i	−0.257457	+	0.445929i	−0.965560	−	0.260180i	$-0.916218\pi$
$709$	−6.85533	+	11.8738i	−0.257457	+	0.445929i	0.708103	+	0.706109i	$0.249551\pi$
$710$	−17.8331			−0.669266
$711$	−2.79456	−	22.2888i	−0.104804	−	0.835894i
$712$	−19.3019			−0.723368
$713$	6.36211	−	11.0195i	0.238263	−	0.412683i
$714$	19.0384	−	21.5745i	0.712496	−	0.807407i
$715$	−4.83203	−	8.36932i	−0.180708	−	0.312995i
$716$	34.4884	+	59.7357i	1.28889	+	2.23243i
$717$	−5.75791	+	6.52492i	−0.215033	+	0.243678i
$718$	32.4641	−	56.2295i	1.21155	−	2.09847i
$719$	12.7162			0.474234			0.237117	−	0.971481i	$-0.423797\pi$
$719$	12.7162			0.474234			0.237117	+	0.971481i	$0.423797\pi$
$720$	4.58708	−	3.47502i	0.170950	−	0.129507i
$721$	−1.51799			−0.0565328
$722$	−12.3330	+	21.3614i	−0.458987	+	0.794989i
$723$	−44.7332	−	9.04157i	−1.66365	−	0.336259i
$724$	18.8833	+	32.7068i	0.701791	+	1.21554i
$725$	5.17399	+	8.96162i	0.192157	+	0.332826i
$726$	−7.19025	−	21.3985i	−0.266855	−	0.794172i
$727$	18.5958	−	32.2089i	0.689681	−	1.19456i	−0.282260	−	0.959338i	$-0.591084\pi$
$727$	18.5958	−	32.2089i	0.689681	−	1.19456i	0.971941	−	0.235224i	$-0.0755825\pi$
$728$	−7.10376			−0.263283
$729$	9.86891	+	25.1317i	0.365515	+	0.930805i
$730$	−7.67597			−0.284101
$731$	22.7136	−	39.3410i	0.840092	−	1.45508i
$732$	−17.0163	−	50.6411i	−0.628939	−	1.87175i
$733$	−18.8723	−	32.6878i	−0.697066	−	1.20735i	−0.969479	−	0.245173i	$-0.921155\pi$
$733$	−18.8723	−	32.6878i	−0.697066	−	1.20735i	0.272414	−	0.962180i	$-0.412178\pi$
$734$	−19.3189	−	33.4613i	−0.713074	−	1.23508i
$735$	1.69772	+	0.343146i	0.0626213	+	0.0126571i
$736$	25.8363	−	44.7497i	0.952337	−	1.64950i
$737$	4.33021			0.159505
$738$	36.1016	−	27.3495i	1.32892	−	1.00675i
$739$	−19.4670			−0.716105			−0.358053	−	0.933701i	$-0.616559\pi$
$739$	−19.4670			−0.716105			−0.358053	+	0.933701i	$0.616559\pi$
$740$	−7.39524	+	12.8089i	−0.271854	+	0.470866i
$741$	13.7023	−	15.5275i	0.503366	−	0.570418i
$742$	−4.51466	−	7.81961i	−0.165738	−	0.287067i
$743$	−15.1251	−	26.1975i	−0.554887	−	0.961093i	−0.997912	−	0.0645835i	$-0.979428\pi$
$743$	−15.1251	−	26.1975i	−0.554887	−	0.961093i	0.443025	−	0.896509i	$-0.353905\pi$
$744$	3.47689	−	3.94004i	0.127469	−	0.144449i
$745$	−9.06272	+	15.6971i	−0.332032	+	0.575097i
$746$	−64.5724			−2.36416
$747$	−4.60198	−	36.7044i	−0.168377	−	1.34294i
$748$	47.0473			1.72022
$749$	−1.87325	+	3.24456i	−0.0684470	+	0.118554i
$750$	−3.70223	−	0.748302i	−0.135186	−	0.0273241i
$751$	24.1257	+	41.7870i	0.880360	+	1.52483i	0.850942	+	0.525260i	$0.176032\pi$
$751$	24.1257	+	41.7870i	0.880360	+	1.52483i	0.0294180	+	0.999567i	$0.490635\pi$
$752$	−3.05575	−	5.29272i	−0.111432	−	0.193005i
$753$	−13.9317	−	41.4614i	−0.507700	−	1.51094i
$754$	48.6502	−	84.2646i	1.77173	−	3.06873i
$755$	8.84423			0.321874
$756$	−11.8308	−	8.06449i	−0.430282	−	0.293303i
$757$	0.914075			0.0332226			0.0166113	−	0.999862i	$-0.494712\pi$
$757$	0.914075			0.0332226			0.0166113	+	0.999862i	$0.494712\pi$
$758$	−2.48377	+	4.30202i	−0.0902147	+	0.156257i
$759$	−8.54390	−	25.4270i	−0.310124	−	0.922942i
$760$	2.28419	+	3.95634i	0.0828563	+	0.143511i
$761$	−4.74612	−	8.22052i	−0.172047	−	0.297994i	0.767089	−	0.641541i	$-0.221705\pi$
$761$	−4.74612	−	8.22052i	−0.172047	−	0.297994i	−0.939135	+	0.343547i	$0.888371\pi$
$762$	−4.47933	−	0.905372i	−0.162269	−	0.0327982i
$763$	1.69583	−	2.93726i	0.0613930	−	0.106336i
$764$	63.3162			2.29070
$765$	−21.0598	−	8.87589i	−0.761417	−	0.320908i
$766$	−47.8083			−1.72738
$767$	6.11079	−	10.5842i	0.220648	−	0.382173i
$768$	2.00429	−	2.27128i	0.0723236	−	0.0819578i
$769$	9.32546	+	16.1522i	0.336285	+	0.582462i	0.983731	−	0.179649i	$-0.0574962\pi$
$769$	9.32546	+	16.1522i	0.336285	+	0.582462i	−0.647446	+	0.762111i	$0.724163\pi$
$770$	2.44381	+	4.23280i	0.0880687	+	0.152539i
$771$	−22.9493	+	26.0064i	−0.826500	+	0.936597i
$772$	−22.6706	+	39.2665i	−0.815931	+	1.41323i
$773$	−11.4567			−0.412068			−0.206034	−	0.978545i	$-0.566056\pi$
$773$	−11.4567			−0.412068			−0.206034	+	0.978545i	$0.566056\pi$
$774$	−35.9495	−	15.1514i	−1.29218	−	0.544604i
$775$	1.84147			0.0661477
$776$	−1.62882	+	2.82121i	−0.0584714	+	0.101275i
$777$	−9.11274	−	1.84188i	−0.326918	−	0.0660772i
$778$	38.0679	+	65.9356i	1.36480	+	2.36390i
$779$	−9.59848	−	16.6251i	−0.343901	−	0.595654i
$780$	6.55469	+	19.5070i	0.234695	+	0.698463i
$781$	9.16430	−	15.8730i	0.327924	−	0.567982i
$782$	−114.789			−4.10484
$783$	48.4427	−	23.3343i	1.73120	−	0.833901i
$784$	−1.91825			−0.0685088
$785$	5.92742	−	10.2666i	0.211559	−	0.366431i
$786$	−1.37524	−	4.09276i	−0.0490531	−	0.145984i
$787$	1.46240	+	2.53296i	0.0521291	+	0.0902902i	0.890912	−	0.454175i	$-0.150066\pi$
$787$	1.46240	+	2.53296i	0.0521291	+	0.0902902i	−0.838783	+	0.544465i	$0.816733\pi$
$788$	23.9869	+	41.5466i	0.854499	+	1.48004i
$789$	4.07308	+	0.823258i	0.145005	+	0.0293088i
$790$	8.16431	−	14.1410i	0.290473	−	0.503114i
$791$	9.71388			0.345386
$792$	−1.37812	−	10.9916i	−0.0489694	−	0.390570i
$793$	−48.2652			−1.71395
$794$	15.1515	−	26.2432i	0.537708	−	0.931337i
$795$	−4.74519	+	5.37730i	−0.168295	+	0.190713i
$796$	−11.6649	−	20.2041i	−0.413450	−	0.716116i
$797$	−7.81975	−	13.5442i	−0.276990	−	0.479760i	0.693645	−	0.720317i	$-0.256003\pi$
$797$	−7.81975	−	13.5442i	−0.276990	−	0.479760i	−0.970635	+	0.240556i	$0.922670\pi$
$798$	−6.92994	+	7.85307i	−0.245317	+	0.277996i
$799$	−12.1353	+	21.0189i	−0.429316	+	0.743596i
$800$	7.47816			0.264393
$801$	−28.0158	+	21.2239i	−0.989890	+	0.749909i
$802$	−44.6475			−1.57656
$803$	3.94462	−	6.83228i	0.139202	−	0.241106i
$804$	−9.03805	−	1.82679i	−0.318748	−	0.0644259i
$805$	−3.45490	−	5.98406i	−0.121769	−	0.210910i
$806$	−8.65753	−	14.9953i	−0.304949	−	0.528186i
$807$	0.524784	+	1.56178i	0.0184733	+	0.0549773i
$808$	4.64175	−	8.03974i	0.163296	−	0.282837i
$809$	−2.74465			−0.0964968			−0.0482484	−	0.998835i	$-0.515364\pi$
$809$	−2.74465			−0.0964968			−0.0482484	+	0.998835i	$0.515364\pi$
$810$	−5.31326	+	18.8935i	−0.186689	+	0.663850i
$811$	−7.26277			−0.255030			−0.127515	−	0.991837i	$-0.540700\pi$
$811$	−7.26277			−0.255030			−0.127515	+	0.991837i	$0.540700\pi$
$812$	−14.2569	+	24.6937i	−0.500319	+	0.866578i
$813$	−2.05962	−	6.12950i	−0.0722339	−	0.214971i
$814$	−13.1175	−	22.7201i	−0.459767	−	0.796339i
$815$	−3.91615	−	6.78298i	−0.137177	−	0.237597i
$816$	24.8089	+	5.01442i	0.868485	+	0.175540i
$817$	−8.26768	+	14.3200i	−0.289249	+	0.500995i
$818$	−77.4589			−2.70829
$819$	−10.3108	+	7.81113i	−0.360288	+	0.272943i
$820$	19.0764			0.666177
$821$	−2.29735	+	3.97913i	−0.0801781	+	0.138873i	−0.903326	−	0.428954i	$-0.858882\pi$
$821$	−2.29735	+	3.97913i	−0.0801781	+	0.138873i	0.823148	+	0.567827i	$0.192216\pi$
$822$	36.7118	−	41.6022i	1.28047	−	1.45104i
$823$	−16.1501	−	27.9728i	−0.562958	−	0.975072i	−0.997236	−	0.0742934i	$-0.976330\pi$
$823$	−16.1501	−	27.9728i	−0.562958	−	0.975072i	0.434278	−	0.900779i	$-0.357003\pi$
$824$	1.25045	+	2.16584i	0.0435615	+	0.0754507i
$825$	2.56860	−	2.91076i	0.0894271	−	0.101340i
$826$	−3.09054	+	5.35297i	−0.107534	+	0.186254i
$827$	51.0236			1.77426			0.887132	−	0.461516i	$-0.152694\pi$
$827$	51.0236			1.77426			0.887132	+	0.461516i	$0.152694\pi$
$828$	7.10600	+	56.6759i	0.246951	+	1.96962i
$829$	36.8581			1.28013			0.640067	−	0.768319i	$-0.278907\pi$
$829$	36.8581			1.28013			0.640067	+	0.768319i	$0.278907\pi$
$830$	13.4447	−	23.2869i	0.466672	−	0.808300i
$831$	8.58593	+	1.73540i	0.297842	+	0.0602005i
$832$	−26.8868	−	46.5692i	−0.932131	−	1.61450i
$833$	3.80896	+	6.59732i	0.131973	+	0.228583i
$834$	−21.4957	−	63.9721i	−0.744336	−	2.21517i
$835$	5.17768	−	8.96801i	0.179181	−	0.310351i
$836$	−17.1251			−0.592284
$837$	0.714169	−	9.54189i	0.0246853	−	0.329816i
$838$	80.4206			2.77808
$839$	21.8271	−	37.8057i	0.753557	−	1.30520i	−0.192532	−	0.981291i	$-0.561670\pi$
$839$	21.8271	−	37.8057i	0.753557	−	1.30520i	0.946089	−	0.323908i	$-0.104997\pi$
$840$	−0.908908	−	2.70495i	−0.0313603	−	0.0933295i
$841$	−39.0404	−	67.6200i	−1.34622	−	2.33172i
$842$	16.4837	+	28.5507i	0.568067	+	0.983922i
$843$	−35.4132	−	7.15779i	−1.21970	−	0.246527i
$844$	−7.45488	+	12.9122i	−0.256607	+	0.444457i
$845$	5.59180			0.192364
$846$	19.2069	+	8.09499i	0.660348	+	0.278311i
$847$	5.97660			0.205358
$848$	3.97129	−	6.87847i	0.136375	−	0.236208i
$849$	11.5334	−	13.0698i	0.395826	−	0.448554i
$850$	−8.30624	−	14.3868i	−0.284902	−	0.493464i
$851$	18.5446	+	32.1202i	0.635702	+	1.10107i
$852$	−25.8242	+	29.2642i	−0.884722	+	1.00257i
$853$	−25.4519	+	44.0840i	−0.871456	+	1.50941i	−0.0109649	+	0.999940i	$0.503490\pi$
$853$	−25.4519	+	44.0840i	−0.871456	+	1.50941i	−0.860491	+	0.509466i	$0.829843\pi$
$854$	24.4102			0.835299
$855$	7.66570	+	3.23080i	0.262161	+	0.110491i
$856$	6.17239			0.210968
$857$	−4.30667	+	7.45937i	−0.147113	+	0.254807i	−0.930159	−	0.367156i	$-0.880331\pi$
$857$	−4.30667	+	7.45937i	−0.147113	+	0.254807i	0.783046	+	0.621963i	$0.213665\pi$
$858$	−35.7786	−	7.23164i	−1.22146	−	0.246884i
$859$	7.88495	+	13.6571i	0.269031	+	0.465976i	0.968612	−	0.248578i	$-0.0799632\pi$
$859$	7.88495	+	13.6571i	0.269031	+	0.465976i	−0.699581	+	0.714554i	$0.746630\pi$
$860$	−8.21576	−	14.2301i	−0.280155	−	0.485243i
$861$	3.81935	+	11.3666i	0.130163	+	0.387371i
$862$	−17.6266	+	30.5302i	−0.600365	+	1.03986i
$863$	10.7856			0.367146			0.183573	−	0.983006i	$-0.441234\pi$
$863$	10.7856			0.367146			0.183573	+	0.983006i	$0.441234\pi$
$864$	2.90021	−	38.7493i	0.0986672	−	1.31828i
$865$	−5.28335			−0.179639
$866$	−2.94519	+	5.10122i	−0.100082	+	0.173346i
$867$	−22.6372	−	67.3693i	−0.768800	−	2.28798i
$868$	2.53708	+	4.39436i	0.0861142	+	0.149154i
$869$	8.39114	+	14.5339i	0.284650	+	0.493028i
$870$	38.3106	+	7.74342i	1.29885	+	0.262527i
$871$	−4.16525	+	7.21442i	−0.141134	+	0.244451i
$872$	−5.58778			−0.189226
$873$	0.737968	+	5.88587i	0.0249764	+	0.199207i
$874$	41.7828			1.41333
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$	−11.1156	+	12.5963i	−0.375561	+	0.425589i
$877$	−4.52605	−	7.83935i	−0.152834	−	0.264716i	0.779434	−	0.626484i	$-0.215507\pi$
$877$	−4.52605	−	7.83935i	−0.152834	−	0.264716i	−0.932268	+	0.361768i	$0.882173\pi$
$878$	−44.3662	−	76.8444i	−1.49729	−	2.59337i
$879$	7.67863	−	8.70149i	0.258994	−	0.293494i
$880$	−2.14968	+	3.72335i	−0.0724657	+	0.125514i
$881$	−2.19535			−0.0739632			−0.0369816	−	0.999316i	$-0.511774\pi$
$881$	−2.19535			−0.0739632			−0.0369816	+	0.999316i	$0.511774\pi$
$882$	5.21470	−	3.95049i	0.175588	−	0.133020i
$883$	49.0216			1.64971			0.824855	−	0.565345i	$-0.191257\pi$
$883$	49.0216			1.64971			0.824855	+	0.565345i	$0.191257\pi$
$884$	−45.2550	+	78.3840i	−1.52209	+	2.63634i
$885$	4.81207	+	0.972626i	0.161756	+	0.0326945i
$886$	35.8506	+	62.0951i	1.20442	+	2.08612i
$887$	−8.60485	−	14.9040i	−0.288923	−	0.500428i	0.684630	−	0.728890i	$-0.259964\pi$
$887$	−8.60485	−	14.9040i	−0.288923	−	0.500428i	−0.973553	+	0.228462i	$0.926630\pi$
$888$	4.87868	+	14.5192i	0.163718	+	0.487231i
$889$	0.604951	−	1.04781i	0.0202894	−	0.0351423i
$890$	−25.5487			−0.856396
$891$	−14.0864	−	14.4385i	−0.471912	−	0.483707i
$892$	9.61853			0.322052
$893$	4.41721	−	7.65083i	0.147816	−	0.256025i
$894$	21.8061	+	64.8959i	0.729306	+	2.17045i
$895$	12.5163	+	21.6788i	0.418372	+	0.724642i
$896$	6.11986	+	10.5999i	0.204450	+	0.354118i
$897$	50.5815	+	10.2236i	1.68887	+	0.341357i
$898$	10.6118	−	18.3801i	0.354120	−	0.613353i
$899$	−19.0556			−0.635538
$900$	−6.58917	+	4.99175i	−0.219639	+	0.166392i
$901$	−31.5423			−1.05083
$902$	−16.9186	+	29.3039i	−0.563328	+	0.975712i
$903$	6.83401	−	7.74436i	0.227422	−	0.257716i
$904$	−8.00185	−	13.8596i	−0.266137	−	0.460964i
$905$	6.85295	+	11.8697i	0.227800	+	0.394561i
$906$	22.1032	−	25.0475i	0.734329	−	0.832148i
$907$	−18.6827	+	32.3594i	−0.620348	+	1.07447i	0.369073	+	0.929401i	$0.379675\pi$
$907$	−18.6827	+	32.3594i	−0.620348	+	1.07447i	−0.989421	+	0.145074i	$0.953658\pi$
$908$	−41.0939			−1.36375
$909$	−2.10303	−	16.7733i	−0.0697530	−	0.556335i
$910$	−9.40283			−0.311701
$911$	0.477937	−	0.827812i	0.0158348	−	0.0274266i	−0.857999	−	0.513651i	$-0.828293\pi$
$911$	0.477937	−	0.827812i	0.0158348	−	0.0274266i	0.873834	+	0.486224i	$0.161626\pi$
$912$	−9.03037	−	1.82523i	−0.299025	−	0.0604396i
$913$	13.8182	+	23.9339i	0.457317	+	0.792096i
$914$	−18.4473	−	31.9516i	−0.610181	−	1.05686i
$915$	−6.17540	−	18.3782i	−0.204152	−	0.607566i
$916$	−37.1028	+	64.2640i	−1.22591	+	2.12334i
$917$	1.14311			0.0377488
$918$	−77.7690	+	37.4605i	−2.56676	+	1.23638i
$919$	−46.0759			−1.51991			−0.759953	−	0.649978i	$-0.774778\pi$
$919$	−46.0759			−1.51991			−0.759953	+	0.649978i	$0.774778\pi$
$920$	−5.69197	+	9.85879i	−0.187659	+	0.325035i
$921$	4.25241	+	12.6553i	0.140122	+	0.417008i
$922$	4.91670	+	8.51598i	0.161923	+	0.280459i
$923$	17.6304	+	30.5367i	0.580310	+	1.00513i
$924$	10.4849	+	2.11923i	0.344928	+	0.0697175i
$925$	−2.68382	+	4.64851i	−0.0882434	+	0.152842i
$926$	−24.3257			−0.799392
$927$	4.19648	+	1.76866i	0.137831	+	0.0580903i
$928$	−77.3839			−2.54025
$929$	−5.97047	+	10.3412i	−0.195885	+	0.339282i	−0.947190	−	0.320672i	$-0.896091\pi$
$929$	−5.97047	+	10.3412i	−0.195885	+	0.339282i	0.751306	+	0.659955i	$0.229424\pi$
$930$	4.60215	−	5.21520i	0.150910	−	0.171013i
$931$	−1.38645	−	2.40141i	−0.0454391	−	0.0787029i
$932$	25.5869	+	44.3179i	0.838128	+	1.45168i
$933$	3.47450	−	3.93733i	0.113750	−	0.128902i
$934$	−30.0544	+	52.0558i	−0.983411	+	1.70332i
$935$	17.0740			0.558380
$936$	19.6384	+	8.27682i	0.641900	+	0.270536i
$937$	9.17467			0.299723			0.149862	−	0.988707i	$-0.452117\pi$
$937$	9.17467			0.299723			0.149862	+	0.988707i	$0.452117\pi$
$938$	2.10658	−	3.64870i	0.0687822	−	0.119134i
$939$	28.6917	+	5.79922i	0.936319	+	0.189251i
$940$	4.38947	+	7.60279i	0.143169	+	0.247976i
$941$	16.8605	+	29.2032i	0.549636	+	0.951998i	0.998299	+	0.0582971i	$0.0185671\pi$
$941$	16.8605	+	29.2032i	0.549636	+	0.951998i	−0.448663	+	0.893701i	$0.648100\pi$
$942$	−14.2622	−	42.4448i	−0.464687	−	1.38293i
$943$	23.9184	−	41.4280i	0.778892	−	1.34908i
$944$	−5.43715			−0.176964
$945$	−4.29354	−	2.92670i	−0.139669	−	0.0952054i
$946$	29.1458			0.947610
$947$	8.13954	−	14.0981i	0.264499	−	0.458127i	−0.702933	−	0.711256i	$-0.748127\pi$
$947$	8.13954	−	14.0981i	0.264499	−	0.458127i	0.967432	+	0.253130i	$0.0814599\pi$
$948$	−11.3826	−	33.8752i	−0.369691	−	1.10022i
$949$	7.58868	+	13.1440i	0.246339	+	0.426672i
$950$	3.02345	+	5.23677i	0.0980936	+	0.169903i
$951$	5.69276	+	1.15063i	0.184600	+	0.0373118i
$952$	6.27530	−	10.8691i	0.203384	−	0.352271i
$953$	3.83943			0.124371			0.0621857	−	0.998065i	$-0.480193\pi$
$953$	3.83943			0.124371			0.0621857	+	0.998065i	$0.480193\pi$
$954$	3.36989	+	26.8775i	0.109104	+	0.870191i
$955$	22.9782			0.743557
$956$	−6.92209	+	11.9894i	−0.223876	+	0.387765i
$957$	−26.5798	+	30.1205i	−0.859204	+	0.973657i
$958$	21.5259	+	37.2840i	0.695472	+	1.20459i
$959$	7.34482	+	12.7216i	0.237177	+	0.410802i
$960$	14.2924	−	16.1963i	0.461285	−	0.522732i
$961$	13.8045	−	23.9101i	0.445306	−	0.771293i
$962$	50.4709			1.62725
$963$	8.95894	−	6.78701i	0.288698	−	0.218708i
$964$	−72.6045			−2.33843
$965$	−8.22741	+	14.2503i	−0.264850	+	0.458733i
$966$	−25.5817	−	5.17062i	−0.823077	−	0.166362i
$967$	−7.24500	−	12.5487i	−0.232983	−	0.403539i	0.725701	−	0.688010i	$-0.241515\pi$
$967$	−7.24500	−	12.5487i	−0.232983	−	0.403539i	−0.958685	+	0.284471i	$0.908182\pi$
$968$	−4.92325	−	8.52731i	−0.158239	−	0.274078i
$969$	11.6537	+	34.6819i	0.374371	+	1.11414i
$970$	−2.15598	+	3.73426i	−0.0692243	+	0.119900i
$971$	45.7613			1.46855			0.734276	−	0.678851i	$-0.237522\pi$
$971$	45.7613			1.46855			0.734276	+	0.678851i	$0.237522\pi$
$972$	23.3101	+	36.0787i	0.747671	+	1.15723i
$973$	17.8674			0.572803
$974$	−9.76810	+	16.9188i	−0.312990	+	0.542115i
$975$	2.37877	+	7.07932i	0.0761817	+	0.226720i
$976$	10.7361	+	18.5955i	0.343655	+	0.595228i
$977$	−26.0424	−	45.1068i	−0.833172	−	1.44310i	−0.895510	−	0.445041i	$-0.853189\pi$
$977$	−26.0424	−	45.1068i	−0.833172	−	1.44310i	0.0623385	−	0.998055i	$-0.480144\pi$
$978$	−28.9970	−	5.86093i	−0.927222	−	0.187412i
$979$	13.1293	−	22.7406i	0.419614	−	0.726792i
$980$	2.75549			0.0880210
$981$	−8.11041	+	6.14419i	−0.258945	+	0.196169i
$982$	20.4417			0.652319
$983$	−25.5195	+	44.2010i	−0.813945	+	1.40979i	0.0961383	+	0.995368i	$0.469351\pi$
$983$	−25.5195	+	44.2010i	−0.813945	+	1.40979i	−0.910083	+	0.414426i	$0.863982\pi$
$984$	13.0714	−	14.8126i	0.416701	−	0.472210i
$985$	8.70514	+	15.0777i	0.277369	+	0.480417i
$986$	85.9529	+	148.875i	2.73730	+	4.74114i
$987$	−3.65124	+	4.13762i	−0.116220	+	0.131702i
$988$	16.4727	−	28.5315i	0.524066	−	0.907709i
$989$	−41.2044			−1.31022
$990$	−1.82414	−	14.5489i	−0.0579749	−	0.462395i
$991$	−2.14863			−0.0682536			−0.0341268	−	0.999418i	$-0.510865\pi$
$991$	−2.14863			−0.0682536			−0.0341268	+	0.999418i	$0.510865\pi$
$992$	−6.88542	+	11.9259i	−0.218612	+	0.378647i
$993$	−2.86235	−	0.578543i	−0.0908338	−	0.0183595i
$994$	−8.91657	−	15.4440i	−0.282817	−	0.489853i
$995$	−4.23331	−	7.33231i	−0.134205	−	0.232450i
$996$	−18.7445	−	55.7845i	−0.593943	−	1.76760i
$997$	−25.1842	+	43.6204i	−0.797593	+	1.38147i	0.123587	+	0.992334i	$0.460560\pi$
$997$	−25.1842	+	43.6204i	−0.797593	+	1.38147i	−0.921180	+	0.389137i	$0.872773\pi$
$998$	9.35249			0.296048
$999$	23.0461	+	15.7094i	0.729147	+	0.497024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.f.106.7	✓	16
3.2	odd	2		945.2.i.f.316.2		16
9.2	odd	6		2835.2.a.y.1.7		8
9.4	even	3	inner	315.2.i.f.211.7	yes	16
9.5	odd	6		945.2.i.f.631.2		16
9.7	even	3		2835.2.a.x.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.f.106.7	✓	16	1.1	even	1	trivial
315.2.i.f.211.7	yes	16	9.4	even	3	inner
945.2.i.f.316.2		16	3.2	odd	2
945.2.i.f.631.2		16	9.5	odd	6
2835.2.a.x.1.2		8	9.7	even	3
2835.2.a.y.1.7		8	9.2	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09035 - 1.88855i) q^{2} +(-0.551686 - 1.64184i) q^{3} +(-1.37775 - 2.38633i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.70223 - 0.748302i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.64751 q^{8} +(-2.39128 + 1.81156i) q^{9} +O(q^{10})\)	\(q+(1.09035 - 1.88855i) q^{2} +(-0.551686 - 1.64184i) q^{3} +(-1.37775 - 2.38633i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-3.70223 - 0.748302i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.64751 q^{8} +(-2.39128 + 1.81156i) q^{9} -2.18071 q^{10} +(1.12065 - 1.94102i) q^{11} +(-3.15788 + 3.57854i) q^{12} +(2.15591 + 3.73415i) q^{13} +(-1.09035 - 1.88855i) q^{14} +(-1.14603 + 1.29869i) q^{15} +(0.959124 - 1.66125i) q^{16} -7.61793 q^{17} +(0.813877 + 6.49130i) q^{18} +2.77290 q^{19} +(-1.37775 + 2.38633i) q^{20} +(-1.69772 - 0.343146i) q^{21} +(-2.44381 - 4.23280i) q^{22} +(3.45490 + 5.98406i) q^{23} +(0.908908 + 2.70495i) q^{24} +(-0.500000 + 0.866025i) q^{25} +9.40283 q^{26} +(4.29354 + 2.92670i) q^{27} -2.75549 q^{28} +(5.17399 - 8.96162i) q^{29} +(1.20307 + 3.58038i) q^{30} +(-0.920737 - 1.59476i) q^{31} +(-3.73908 - 6.47627i) q^{32} +(-3.80509 - 0.769092i) q^{33} +(-8.30624 + 14.3868i) q^{34} -1.00000 q^{35} +(7.61756 + 3.21051i) q^{36} +5.36764 q^{37} +(3.02345 - 5.23677i) q^{38} +(4.94149 - 5.59974i) q^{39} +(0.823754 + 1.42678i) q^{40} +(-3.46153 - 5.99554i) q^{41} +(-2.49916 + 2.83208i) q^{42} +(-2.98159 + 5.16427i) q^{43} -6.17587 q^{44} +(2.76450 + 1.16513i) q^{45} +15.0683 q^{46} +(1.59299 - 2.75914i) q^{47} +(-3.25665 - 0.658239i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(1.09035 + 1.88855i) q^{50} +(4.20270 + 12.5074i) q^{51} +(5.94059 - 10.2894i) q^{52} +4.14054 q^{53} +(10.2087 - 4.91742i) q^{54} -2.24130 q^{55} +(-0.823754 + 1.42678i) q^{56} +(-1.52977 - 4.55267i) q^{57} +(-11.2830 - 19.5427i) q^{58} +(-1.41722 - 2.45469i) q^{59} +(4.67805 + 0.945537i) q^{60} +(-5.59684 + 9.69401i) q^{61} -4.01572 q^{62} +(0.373217 + 2.97669i) q^{63} -12.4712 q^{64} +(2.15591 - 3.73415i) q^{65} +(-5.60137 + 6.34752i) q^{66} +(0.966006 + 1.67317i) q^{67} +(10.4956 + 18.1789i) q^{68} +(7.91885 - 8.97372i) q^{69} +(-1.09035 + 1.88855i) q^{70} +8.17768 q^{71} +(3.93966 - 2.98456i) q^{72} +3.51994 q^{73} +(5.85263 - 10.1370i) q^{74} +(1.69772 + 0.343146i) q^{75} +(-3.82036 - 6.61705i) q^{76} +(-1.12065 - 1.94102i) q^{77} +(-5.18741 - 15.4379i) q^{78} +(-3.74388 + 6.48459i) q^{79} -1.91825 q^{80} +(2.43648 - 8.66392i) q^{81} -15.0972 q^{82} +(-6.16529 + 10.6786i) q^{83} +(1.52017 + 4.52408i) q^{84} +(3.80896 + 6.59732i) q^{85} +(6.50199 + 11.2618i) q^{86} +(-17.5680 - 3.55087i) q^{87} +(-1.84628 + 3.19784i) q^{88} +11.7158 q^{89} +(5.21470 - 3.95049i) q^{90} +4.31182 q^{91} +(9.51994 - 16.4890i) q^{92} +(-2.11039 + 2.39151i) q^{93} +(-3.47385 - 6.01688i) q^{94} +(-1.38645 - 2.40141i) q^{95} +(-8.57021 + 9.71184i) q^{96} +(0.988659 - 1.71241i) q^{97} -2.18071 q^{98} +(0.836489 + 6.67165i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9	\( 16 q + q^{2} + q^{3} - 11 q^{4} - 8 q^{5} + 8 q^{6} + 8 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} - 4 q^{11} - 3 q^{12} - 5 q^{13} - q^{14} - 2 q^{15} - 21 q^{16} + 8 q^{17} + 26 q^{18} + 6 q^{19} - 11 q^{20} - q^{21} - 23 q^{22} + 8 q^{23} - 38 q^{24} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 22 q^{28} - 19 q^{29} - 13 q^{30} + 12 q^{32} - 21 q^{33} - 9 q^{34} - 16 q^{35} + 70 q^{36} + 42 q^{37} + 28 q^{38} + 32 q^{39} + 3 q^{40} - 20 q^{41} - 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{45} + 34 q^{46} + 11 q^{47} - 18 q^{48} - 8 q^{49} + q^{50} - 14 q^{51} - 13 q^{52} - 16 q^{53} + 8 q^{55} - 3 q^{56} + 8 q^{57} - 37 q^{58} - 7 q^{59} + 9 q^{60} - 24 q^{61} - 30 q^{62} + 12 q^{63} + 110 q^{64} - 5 q^{65} - 11 q^{66} - 16 q^{67} - 5 q^{68} + 21 q^{69} - q^{70} - 10 q^{71} + 17 q^{72} + 20 q^{73} - 21 q^{74} + q^{75} - 25 q^{76} + 4 q^{77} - 61 q^{78} - 27 q^{79} + 42 q^{80} + 11 q^{81} + 72 q^{82} - 5 q^{83} + 6 q^{84} - 4 q^{85} + 27 q^{86} - 46 q^{87} - 67 q^{88} + 54 q^{89} - 7 q^{90} - 10 q^{91} + 93 q^{92} - 9 q^{93} + 17 q^{94} - 3 q^{95} - 98 q^{96} - 27 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + q^2 + q^3 - 11 * q^4 - 8 * q^5 + 8 * q^6 + 8 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 - 4 * q^11 - 3 * q^12 - 5 * q^13 - q^14 - 2 * q^15 - 21 * q^16 + 8 * q^17 + 26 * q^18 + 6 * q^19 - 11 * q^20 - q^21 - 23 * q^22 + 8 * q^23 - 38 * q^24 - 8 * q^25 - 6 * q^26 + 10 * q^27 - 22 * q^28 - 19 * q^29 - 13 * q^30 + 12 * q^32 - 21 * q^33 - 9 * q^34 - 16 * q^35 + 70 * q^36 + 42 * q^37 + 28 * q^38 + 32 * q^39 + 3 * q^40 - 20 * q^41 - 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^45 + 34 * q^46 + 11 * q^47 - 18 * q^48 - 8 * q^49 + q^50 - 14 * q^51 - 13 * q^52 - 16 * q^53 + 8 * q^55 - 3 * q^56 + 8 * q^57 - 37 * q^58 - 7 * q^59 + 9 * q^60 - 24 * q^61 - 30 * q^62 + 12 * q^63 + 110 * q^64 - 5 * q^65 - 11 * q^66 - 16 * q^67 - 5 * q^68 + 21 * q^69 - q^70 - 10 * q^71 + 17 * q^72 + 20 * q^73 - 21 * q^74 + q^75 - 25 * q^76 + 4 * q^77 - 61 * q^78 - 27 * q^79 + 42 * q^80 + 11 * q^81 + 72 * q^82 - 5 * q^83 + 6 * q^84 - 4 * q^85 + 27 * q^86 - 46 * q^87 - 67 * q^88 + 54 * q^89 - 7 * q^90 - 10 * q^91 + 93 * q^92 - 9 * q^93 + 17 * q^94 - 3 * q^95 - 98 * q^96 - 27 * q^97 - 2 * q^98 - 4 * q^99

Introduction

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