LMFDB - Embedded newform 315.2.i.d.106.1

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	315.106
Dual form			315.2.i.d.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.978148 + 1.69420i) q^{2} +(1.72256 + 0.181049i) q^{3} +(-0.913545 - 1.58231i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.99165 + 2.74128i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.338261 q^{8} +(2.93444 + 0.623735i) q^{9} +O(q^{10})$	\(q+(-0.978148 + 1.69420i) q^{2} +(1.72256 + 0.181049i) q^{3} +(-0.913545 - 1.58231i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.99165 + 2.74128i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.338261 q^{8} +(2.93444 + 0.623735i) q^{9} -1.95630 q^{10} +(-1.97815 + 3.42625i) q^{11} +(-1.28716 - 2.89102i) q^{12} +(1.77366 + 3.07207i) q^{13} +(0.978148 + 1.69420i) q^{14} +(0.704489 + 1.58231i) q^{15} +(2.15796 - 3.73770i) q^{16} -1.95630 q^{17} +(-3.92705 + 4.36143i) q^{18} +0.231398 q^{19} +(0.913545 - 1.58231i) q^{20} +(1.01807 - 1.40126i) q^{21} +(-3.86984 - 6.70276i) q^{22} +(3.86527 + 6.69485i) q^{23} +(-0.582676 - 0.0612417i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.93960 q^{26} +(4.94183 + 1.60570i) q^{27} -1.82709 q^{28} +(3.88791 - 6.73407i) q^{29} +(-3.36984 - 0.354185i) q^{30} +(-3.00973 - 5.21300i) q^{31} +(3.88335 + 6.72615i) q^{32} +(-4.02780 + 5.54379i) q^{33} +(1.91355 - 3.31436i) q^{34} +1.00000 q^{35} +(-1.69381 - 5.21300i) q^{36} -7.31592 q^{37} +(-0.226341 + 0.392034i) q^{38} +(2.49904 + 5.61295i) q^{39} +(-0.169131 - 0.292943i) q^{40} +(-4.29173 - 7.43350i) q^{41} +(1.37819 + 3.09546i) q^{42} +(3.72539 - 6.45256i) q^{43} +7.22851 q^{44} +(0.927051 + 2.85317i) q^{45} -15.1232 q^{46} +(-0.124148 + 0.215030i) q^{47} +(4.39393 - 6.04772i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.978148 - 1.69420i) q^{50} +(-3.36984 - 0.354185i) q^{51} +(3.24064 - 5.61295i) q^{52} -2.16982 q^{53} +(-7.55422 + 6.80185i) q^{54} -3.95630 q^{55} +(-0.169131 + 0.292943i) q^{56} +(0.398597 + 0.0418942i) q^{57} +(7.60591 + 13.1738i) q^{58} +(-0.323966 - 0.561125i) q^{59} +(1.86011 - 2.56023i) q^{60} +(3.83603 - 6.64420i) q^{61} +11.7758 q^{62} +(2.00739 - 2.22943i) q^{63} -6.56210 q^{64} +(-1.77366 + 3.07207i) q^{65} +(-5.45252 - 12.2466i) q^{66} +(3.30902 + 5.73139i) q^{67} +(1.78716 + 3.09546i) q^{68} +(5.44608 + 12.2321i) q^{69} +(-0.978148 + 1.69420i) q^{70} +4.05751 q^{71} +(-0.992608 - 0.210985i) q^{72} +13.5639 q^{73} +(7.15605 - 12.3946i) q^{74} +(-1.01807 + 1.40126i) q^{75} +(-0.211392 - 0.366142i) q^{76} +(1.97815 + 3.42625i) q^{77} +(-11.9539 - 1.25641i) q^{78} +(2.84049 - 4.91988i) q^{79} +4.31592 q^{80} +(8.22191 + 3.66063i) q^{81} +16.7918 q^{82} +(7.40599 - 12.8275i) q^{83} +(-3.14728 - 0.330792i) q^{84} +(-0.978148 - 1.69420i) q^{85} +(7.28795 + 12.6231i) q^{86} +(7.91637 - 10.8959i) q^{87} +(0.669131 - 1.15897i) q^{88} +6.12611 q^{89} +(-5.74064 - 1.22021i) q^{90} +3.54732 q^{91} +(7.06220 - 12.2321i) q^{92} +(-4.24064 - 9.52463i) q^{93} +(-0.242870 - 0.420662i) q^{94} +(0.115699 + 0.200396i) q^{95} +(5.47155 + 12.2893i) q^{96} +(-3.10154 + 5.37202i) q^{97} +1.95630 q^{98} +(-7.94183 + 8.82030i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9	$ 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9} + 2 q^{10} - 7 q^{11} + 3 q^{12} + 8 q^{13} - q^{14} + 3 q^{15} + 9 q^{16} + 2 q^{17} - 18 q^{18} + 6 q^{19} + q^{20} - 7 q^{22} + 8 q^{23} + 6 q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{28} - q^{29} - 3 q^{30} + 9 q^{34} + 8 q^{35} - 6 q^{36} - 42 q^{37} - 8 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} + 3 q^{42} + 7 q^{43} + 6 q^{44} - 6 q^{45} - 46 q^{46} + 2 q^{47} + 30 q^{48} - 4 q^{49} + q^{50} - 3 q^{51} + 7 q^{52} - 16 q^{53} - 36 q^{54} - 14 q^{55} + 3 q^{56} - 24 q^{57} + 19 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 30 q^{62} + 3 q^{63} - 14 q^{64} - 8 q^{65} - 9 q^{66} + 22 q^{67} + q^{68} + 51 q^{69} + q^{70} + 26 q^{71} - 21 q^{72} - 8 q^{73} - 9 q^{74} + 13 q^{76} + 7 q^{77} - 21 q^{78} + 24 q^{79} + 18 q^{80} + 9 q^{81} + 19 q^{83} - 12 q^{84} + q^{85} + 27 q^{86} + 45 q^{87} + q^{88} + 30 q^{89} - 27 q^{90} + 16 q^{91} - 3 q^{92} - 15 q^{93} + 7 q^{94} + 3 q^{95} + 30 q^{96} + 12 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) $ 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9 + 2 * q^10 - 7 * q^11 + 3 * q^12 + 8 * q^13 - q^14 + 3 * q^15 + 9 * q^16 + 2 * q^17 - 18 * q^18 + 6 * q^19 + q^20 - 7 * q^22 + 8 * q^23 + 6 * q^24 - 4 * q^25 - 6 * q^26 - 2 * q^28 - q^29 - 3 * q^30 + 9 * q^34 + 8 * q^35 - 6 * q^36 - 42 * q^37 - 8 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 + 3 * q^42 + 7 * q^43 + 6 * q^44 - 6 * q^45 - 46 * q^46 + 2 * q^47 + 30 * q^48 - 4 * q^49 + q^50 - 3 * q^51 + 7 * q^52 - 16 * q^53 - 36 * q^54 - 14 * q^55 + 3 * q^56 - 24 * q^57 + 19 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 30 * q^62 + 3 * q^63 - 14 * q^64 - 8 * q^65 - 9 * q^66 + 22 * q^67 + q^68 + 51 * q^69 + q^70 + 26 * q^71 - 21 * q^72 - 8 * q^73 - 9 * q^74 + 13 * q^76 + 7 * q^77 - 21 * q^78 + 24 * q^79 + 18 * q^80 + 9 * q^81 + 19 * q^83 - 12 * q^84 + q^85 + 27 * q^86 + 45 * q^87 + q^88 + 30 * q^89 - 27 * q^90 + 16 * q^91 - 3 * q^92 - 15 * q^93 + 7 * q^94 + 3 * q^95 + 30 * q^96 + 12 * q^97 - 2 * q^98 - 24 * 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 $

$2$	−0.978148	+	1.69420i	−0.691655	+	1.19798i	0.279641	+	0.960105i	$0.409785\pi$
$2$	−0.978148	+	1.69420i	−0.691655	+	1.19798i	−0.971295	+	0.237877i	$0.923549\pi$
$3$	1.72256	+	0.181049i	0.994522	+	0.104528i
$3$	1.72256	+	0.181049i	0.994522	+	0.104528i
$4$	−0.913545	−	1.58231i	−0.456773	−	0.791154i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.99165	+	2.74128i	−0.813089	+	1.11912i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−0.338261			−0.119593
$9$	2.93444	+	0.623735i	0.978148	+	0.207912i
$10$	−1.95630			−0.618635
$11$	−1.97815	+	3.42625i	−0.596434	+	1.03305i	0.396909	+	0.917858i	$0.370083\pi$
$11$	−1.97815	+	3.42625i	−0.596434	+	1.03305i	−0.993343	+	0.115196i	$0.963250\pi$
$12$	−1.28716	−	2.89102i	−0.371572	−	0.834565i
$13$	1.77366	+	3.07207i	0.491925	+	0.852038i	0.999957	−	0.00929980i	$-0.00296026\pi$
$13$	1.77366	+	3.07207i	0.491925	+	0.852038i	−0.508032	+	0.861338i	$0.669627\pi$
$14$	0.978148	+	1.69420i	0.261421	+	0.452794i
$15$	0.704489	+	1.58231i	0.181898	+	0.408550i
$16$	2.15796	−	3.73770i	0.539490	−	0.934424i
$17$	−1.95630			−0.474471			−0.237236	−	0.971452i	$-0.576241\pi$
$17$	−1.95630			−0.474471			−0.237236	+	0.971452i	$0.576241\pi$
$18$	−3.92705	+	4.36143i	−0.925615	+	1.02800i
$19$	0.231398			0.0530862			0.0265431	−	0.999648i	$-0.491550\pi$
$19$	0.231398			0.0530862			0.0265431	+	0.999648i	$0.491550\pi$
$20$	0.913545	−	1.58231i	0.204275	−	0.353815i
$21$	1.01807	−	1.40126i	0.222162	−	0.305780i
$22$	−3.86984	−	6.70276i	−0.825053	−	1.42903i
$23$	3.86527	+	6.69485i	0.805965	+	1.39597i	0.915638	+	0.402005i	$0.131686\pi$
$23$	3.86527	+	6.69485i	0.805965	+	1.39597i	−0.109673	+	0.993968i	$0.534980\pi$
$24$	−0.582676	−	0.0612417i	−0.118938	−	0.0125009i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−6.93960			−1.36097
$27$	4.94183	+	1.60570i	0.951057	+	0.309017i
$28$	−1.82709			−0.345288
$29$	3.88791	−	6.73407i	0.721968	−	1.25048i	−0.238242	−	0.971206i	$-0.576571\pi$
$29$	3.88791	−	6.73407i	0.721968	−	1.25048i	0.960210	−	0.279279i	$-0.0900954\pi$
$30$	−3.36984	−	0.354185i	−0.615246	−	0.0646650i
$31$	−3.00973	−	5.21300i	−0.540563	−	0.936282i	−0.998872	−	0.0474894i	$-0.984878\pi$
$31$	−3.00973	−	5.21300i	−0.540563	−	0.936282i	0.458309	−	0.888793i	$-0.348455\pi$
$32$	3.88335	+	6.72615i	0.686485	+	1.18903i
$33$	−4.02780	+	5.54379i	−0.701150	+	0.965050i
$34$	1.91355	−	3.31436i	0.328170	−	0.568408i
$35$	1.00000			0.169031
$36$	−1.69381	−	5.21300i	−0.282301	−	0.868833i
$37$	−7.31592			−1.20273			−0.601365	−	0.798974i	$-0.705376\pi$
$37$	−7.31592			−1.20273			−0.601365	+	0.798974i	$0.705376\pi$
$38$	−0.226341	+	0.392034i	−0.0367173	+	0.0635963i
$39$	2.49904	+	5.61295i	0.400167	+	0.898791i
$40$	−0.169131	−	0.292943i	−0.0267419	−	0.0463183i
$41$	−4.29173	−	7.43350i	−0.670256	−	1.16092i	−0.977831	−	0.209394i	$-0.932851\pi$
$41$	−4.29173	−	7.43350i	−0.670256	−	1.16092i	0.307575	−	0.951524i	$-0.400482\pi$
$42$	1.37819	+	3.09546i	0.212659	+	0.477640i
$43$	3.72539	−	6.45256i	0.568116	−	0.984006i	−0.428636	−	0.903477i	$-0.641006\pi$
$43$	3.72539	−	6.45256i	0.568116	−	0.984006i	0.996752	−	0.0805287i	$-0.0256609\pi$
$44$	7.22851			1.08974
$45$	0.927051	+	2.85317i	0.138197	+	0.425325i
$46$	−15.1232			−2.22980
$47$	−0.124148	+	0.215030i	−0.0181088	+	0.0313654i	−0.874938	−	0.484235i	$-0.839098\pi$
$47$	−0.124148	+	0.215030i	−0.0181088	+	0.0313654i	0.856829	+	0.515601i	$0.172431\pi$
$48$	4.39393	−	6.04772i	0.634209	−	0.872913i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.978148	−	1.69420i	−0.138331	−	0.239596i
$51$	−3.36984	−	0.354185i	−0.471872	−	0.0495958i
$52$	3.24064	−	5.61295i	0.449395	−	0.778376i
$53$	−2.16982			−0.298047			−0.149024	−	0.988834i	$-0.547613\pi$
$53$	−2.16982			−0.298047			−0.149024	+	0.988834i	$0.547613\pi$
$54$	−7.55422	+	6.80185i	−1.02800	+	0.925615i
$55$	−3.95630			−0.533467
$56$	−0.169131	+	0.292943i	−0.0226010	+	0.0391461i
$57$	0.398597	+	0.0418942i	0.0527954	+	0.00554902i
$58$	7.60591	+	13.1738i	0.998705	+	1.72981i
$59$	−0.323966	−	0.561125i	−0.0421768	−	0.0730523i	0.844166	−	0.536081i	$-0.180096\pi$
$59$	−0.323966	−	0.561125i	−0.0421768	−	0.0730523i	−0.886343	+	0.463029i	$0.846763\pi$
$60$	1.86011	−	2.56023i	0.240140	−	0.330524i
$61$	3.83603	−	6.64420i	0.491153	−	0.850702i	−0.508795	−	0.860888i	$-0.669909\pi$
$61$	3.83603	−	6.64420i	0.491153	−	0.850702i	0.999948	+	0.0101856i	$0.00324224\pi$
$62$	11.7758			1.49553
$63$	2.00739	−	2.22943i	0.252908	−	0.280882i
$64$	−6.56210			−0.820263
$65$	−1.77366	+	3.07207i	−0.219995	+	0.381043i
$66$	−5.45252	−	12.2466i	−0.671158	−	1.50745i
$67$	3.30902	+	5.73139i	0.404261	+	0.700200i	0.994235	−	0.107222i	$-0.0341955\pi$
$67$	3.30902	+	5.73139i	0.404261	+	0.700200i	−0.589974	+	0.807422i	$0.700862\pi$
$68$	1.78716	+	3.09546i	0.216726	+	0.375380i
$69$	5.44608	+	12.2321i	0.655631	+	1.47257i
$70$	−0.978148	+	1.69420i	−0.116911	+	0.202496i
$71$	4.05751			0.481538			0.240769	−	0.970582i	$-0.422600\pi$
$71$	4.05751			0.481538			0.240769	+	0.970582i	$0.422600\pi$
$72$	−0.992608	−	0.210985i	−0.116980	−	0.0248649i
$73$	13.5639			1.58753			0.793766	−	0.608223i	$-0.208117\pi$
$73$	13.5639			1.58753			0.793766	+	0.608223i	$0.208117\pi$
$74$	7.15605	−	12.3946i	0.831874	−	1.44085i
$75$	−1.01807	+	1.40126i	−0.117557	+	0.161803i
$76$	−0.211392	−	0.366142i	−0.0242483	−	0.0419994i
$77$	1.97815	+	3.42625i	0.225431	+	0.390458i
$78$	−11.9539	−	1.25641i	−1.35351	−	0.142260i
$79$	2.84049	−	4.91988i	0.319581	−	0.553530i	−0.660820	−	0.750544i	$-0.729791\pi$
$79$	2.84049	−	4.91988i	0.319581	−	0.553530i	0.980401	+	0.197015i	$0.0631247\pi$
$80$	4.31592			0.482535
$81$	8.22191	+	3.66063i	0.913545	+	0.406737i
$82$	16.7918			1.85434
$83$	7.40599	−	12.8275i	0.812913	−	1.40801i	−0.0979041	−	0.995196i	$-0.531214\pi$
$83$	7.40599	−	12.8275i	0.812913	−	1.40801i	0.910817	−	0.412810i	$-0.135453\pi$
$84$	−3.14728	−	0.330792i	−0.343396	−	0.0360924i
$85$	−0.978148	−	1.69420i	−0.106095	−	0.183762i
$86$	7.28795	+	12.6231i	0.785880	+	1.36118i
$87$	7.91637	−	10.8959i	0.848724	−	1.16817i
$88$	0.669131	−	1.15897i	0.0713296	−	0.123546i
$89$	6.12611			0.649367			0.324683	−	0.945823i	$-0.394742\pi$
$89$	6.12611			0.649367			0.324683	+	0.945823i	$0.394742\pi$
$90$	−5.74064	−	1.22021i	−0.605116	−	0.128621i
$91$	3.54732			0.371860
$92$	7.06220	−	12.2321i	0.736286	−	1.27528i
$93$	−4.24064	−	9.52463i	−0.439734	−	0.987658i
$94$	−0.242870	−	0.420662i	−0.0250501	−	0.0433880i
$95$	0.115699	+	0.200396i	0.0118704	+	0.0205602i
$96$	5.47155	+	12.2893i	0.558437	+	1.25427i
$97$	−3.10154	+	5.37202i	−0.314914	+	0.545446i	−0.979419	−	0.201837i	$-0.935309\pi$
$97$	−3.10154	+	5.37202i	−0.314914	+	0.545446i	0.664505	+	0.747283i	$0.268642\pi$
$98$	1.95630			0.197616
$99$	−7.94183	+	8.82030i	−0.798184	+	0.886474i
$100$	1.82709			0.182709
$101$	−1.53332	+	2.65580i	−0.152571	+	0.264262i	−0.932172	−	0.362015i	$-0.882089\pi$
$101$	−1.53332	+	2.65580i	−0.152571	+	0.264262i	0.779601	+	0.626277i	$0.215422\pi$
$102$	3.89626	−	5.36274i	0.385787	−	0.530991i
$103$	8.30507	+	14.3848i	0.818323	+	1.41738i	0.906917	+	0.421310i	$0.138429\pi$
$103$	8.30507	+	14.3848i	0.818323	+	1.41738i	−0.0885937	+	0.996068i	$0.528237\pi$
$104$	−0.599960	−	1.03916i	−0.0588309	−	0.101898i
$105$	1.72256	+	0.181049i	0.168105	+	0.0176685i
$106$	2.12240	−	3.67611i	0.206146	−	0.357055i
$107$	−19.2470			−1.86068			−0.930338	−	0.366702i	$-0.880487\pi$
$107$	−19.2470			−1.86068			−0.930338	+	0.366702i	$0.880487\pi$
$108$	−1.97388	−	9.28638i	−0.189937	−	0.893582i
$109$	−16.6132			−1.59126			−0.795630	−	0.605783i	$-0.792860\pi$
$109$	−16.6132			−1.59126			−0.795630	+	0.605783i	$0.792860\pi$
$110$	3.86984	−	6.70276i	0.368975	−	0.639083i
$111$	−12.6021	−	1.32454i	−1.19614	−	0.125720i
$112$	−2.15796	−	3.73770i	−0.203908	−	0.353179i
$113$	−6.50674	−	11.2700i	−0.612102	−	1.06019i	−0.990885	−	0.134707i	$-0.956991\pi$
$113$	−6.50674	−	11.2700i	−0.612102	−	1.06019i	0.378783	−	0.925486i	$-0.376343\pi$
$114$	−0.460864	+	0.634324i	−0.0431638	+	0.0594099i
$115$	−3.86527	+	6.69485i	−0.360438	+	0.624298i
$116$	−14.2071			−1.31910
$117$	3.28854	+	10.1211i	0.304026	+	0.935696i
$118$	1.26755			0.116687
$119$	−0.978148	+	1.69420i	−0.0896666	+	0.155307i
$120$	−0.238301	−	0.535233i	−0.0217538	−	0.0488599i
$121$	−2.32614	−	4.02899i	−0.211467	−	0.366271i
$122$	7.50440	+	12.9980i	0.679417	+	1.17678i
$123$	−6.04695	−	13.5817i	−0.545235	−	1.22462i
$124$	−5.49904	+	9.52463i	−0.493829	+	0.855337i
$125$	−1.00000			−0.0894427
$126$	1.81359	+	5.58164i	0.161567	+	0.497252i
$127$	10.8009			0.958428			0.479214	−	0.877698i	$-0.340922\pi$
$127$	10.8009			0.958428			0.479214	+	0.877698i	$0.340922\pi$
$128$	−1.34799	+	2.33478i	−0.119146	+	0.206368i
$129$	7.58544	−	10.4405i	0.667860	−	0.919231i
$130$	−3.46980	−	6.00987i	−0.304322	−	0.527101i
$131$	−6.98186	−	12.0929i	−0.610008	−	1.05657i	−0.991238	−	0.132085i	$-0.957833\pi$
$131$	−6.98186	−	12.0929i	−0.610008	−	1.05657i	0.381230	−	0.924480i	$-0.375501\pi$
$132$	12.4516	+	1.30871i	1.08377	+	0.113909i
$133$	0.115699	−	0.200396i	0.0100324	−	0.0173765i
$134$	−12.9468			−1.11844
$135$	1.08034	+	5.08260i	0.0929809	+	0.437441i
$136$	0.661739			0.0567436
$137$	1.61064	−	2.78971i	0.137606	−	0.238341i	−0.788984	−	0.614414i	$-0.789392\pi$
$137$	1.61064	−	2.78971i	0.137606	−	0.238341i	0.926590	+	0.376073i	$0.122726\pi$
$138$	−26.0507	−	2.73804i	−2.21758	−	0.233077i
$139$	5.39074	+	9.33703i	0.457236	+	0.791957i	0.998814	−	0.0486942i	$-0.0155060\pi$
$139$	5.39074	+	9.33703i	0.457236	+	0.791957i	−0.541577	+	0.840651i	$0.682173\pi$
$140$	−0.913545	−	1.58231i	−0.0772087	−	0.133729i
$141$	−0.252783	+	0.347926i	−0.0212882	+	0.0293007i
$142$	−3.96885	+	6.87424i	−0.333058	+	0.576874i
$143$	−14.0342			−1.17360
$144$	8.66374	−	9.62206i	0.721979	−	0.801839i
$145$	7.77583			0.645747
$146$	−13.2675	+	22.9800i	−1.09802	+	1.90183i
$147$	−0.704489	−	1.58231i	−0.0581052	−	0.130506i
$148$	6.68343	+	11.5760i	0.549374	+	0.951544i
$149$	−7.08783	−	12.2765i	−0.580658	−	1.00573i	−0.995401	−	0.0957908i	$-0.969462\pi$
$149$	−7.08783	−	12.2765i	−0.580658	−	1.00573i	0.414743	−	0.909938i	$-0.363871\pi$
$150$	−1.37819	−	3.09546i	−0.112529	−	0.252743i
$151$	−3.59523	+	6.22712i	−0.292575	+	0.506755i	−0.974418	−	0.224744i	$-0.927846\pi$
$151$	−3.59523	+	6.22712i	−0.292575	+	0.506755i	0.681843	+	0.731499i	$0.261179\pi$
$152$	−0.0782728			−0.00634876
$153$	−5.74064	−	1.22021i	−0.464103	−	0.0986481i
$154$	−7.73968			−0.623681
$155$	3.00973	−	5.21300i	0.241747	−	0.418718i
$156$	6.59841	−	9.08194i	0.528296	−	0.727137i
$157$	0.923438	+	1.59944i	0.0736983	+	0.127649i	0.900519	−	0.434816i	$-0.143186\pi$
$157$	0.923438	+	1.59944i	0.0736983	+	0.127649i	−0.826821	+	0.562465i	$0.809853\pi$
$158$	5.55685	+	9.62474i	0.442079	+	0.765703i
$159$	−3.73765	−	0.392843i	−0.296415	−	0.0311544i
$160$	−3.88335	+	6.72615i	−0.307005	+	0.531749i
$161$	7.73054			0.609252
$162$	−14.2441	+	10.3489i	−1.11912	+	0.813089i
$163$	−15.9000			−1.24538			−0.622691	−	0.782468i	$-0.713960\pi$
$163$	−15.9000			−1.24538			−0.622691	+	0.782468i	$0.713960\pi$
$164$	−7.84139	+	13.5817i	−0.612309	+	1.06055i
$165$	−6.81497	−	0.716282i	−0.530544	−	0.0557625i
$166$	14.4883	+	25.0945i	1.12451	+	1.94771i
$167$	0.679813	+	1.17747i	0.0526055	+	0.0911154i	0.891129	−	0.453750i	$-0.149914\pi$
$167$	0.679813	+	1.17747i	0.0526055	+	0.0911154i	−0.838524	+	0.544865i	$0.816581\pi$
$168$	−0.344375	+	0.473991i	−0.0265691	+	0.0365692i
$169$	0.208267	−	0.360729i	0.0160205	−	0.0277484i
$170$	3.82709			0.293524
$171$	0.679023	+	0.144331i	0.0519262	+	0.0110372i
$172$	−13.6132			−1.03800
$173$	−2.49953	+	4.32932i	−0.190036	+	0.329152i	−0.945262	−	0.326313i	$-0.894194\pi$
$173$	−2.49953	+	4.32932i	−0.190036	+	0.329152i	0.755226	+	0.655465i	$0.227527\pi$
$174$	10.7166	+	24.0698i	0.812420	+	1.82472i
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	8.53753	+	14.7874i	0.643540	+	1.11464i
$177$	−0.456460	−	1.02523i	−0.0343097	−	0.0770608i
$178$	−5.99224	+	10.3789i	−0.449138	+	0.777929i
$179$	20.8475			1.55822			0.779108	−	0.626889i	$-0.215672\pi$
$179$	20.8475			1.55822			0.779108	+	0.626889i	$0.215672\pi$
$180$	3.66769	−	4.07338i	0.273373	−	0.303612i
$181$	−7.64696			−0.568394			−0.284197	−	0.958766i	$-0.591727\pi$
$181$	−7.64696			−0.568394			−0.284197	+	0.958766i	$0.591727\pi$
$182$	−3.46980	+	6.00987i	−0.257199	+	0.445481i
$183$	7.81072	−	10.7505i	0.577385	−	0.794702i
$184$	−1.30747	−	2.26461i	−0.0963881	−	0.166949i
$185$	−3.65796	−	6.33577i	−0.268939	−	0.465815i
$186$	20.2846	+	2.13200i	1.48734	+	0.156326i
$187$	3.86984	−	6.70276i	0.282991	−	0.490154i
$188$	0.453658			0.0330864
$189$	3.86149	−	3.47690i	0.280882	−	0.252908i
$190$	−0.452682			−0.0328410
$191$	−5.41194	+	9.37375i	−0.391594	+	0.678261i	−0.992660	−	0.120939i	$-0.961410\pi$
$191$	−5.41194	+	9.37375i	−0.391594	+	0.678261i	0.601066	+	0.799199i	$0.294743\pi$
$192$	−11.3036	−	1.18806i	−0.815769	−	0.0857408i
$193$	−4.35380	−	7.54100i	−0.313393	−	0.542813i	0.665701	−	0.746218i	$-0.268133\pi$
$193$	−4.35380	−	7.54100i	−0.313393	−	0.542813i	−0.979095	+	0.203405i	$0.934799\pi$
$194$	−6.06753	−	10.5093i	−0.435623	−	0.754521i
$195$	−3.61143	+	4.97071i	−0.258620	+	0.355960i
$196$	−0.913545	+	1.58231i	−0.0652532	+	0.113022i
$197$	−26.1081			−1.86013			−0.930063	−	0.367400i	$-0.880248\pi$
$197$	−26.1081			−1.86013			−0.930063	+	0.367400i	$0.880248\pi$
$198$	−7.17508	−	22.0826i	−0.509911	−	1.56934i
$199$	−3.79757			−0.269202			−0.134601	−	0.990900i	$-0.542975\pi$
$199$	−3.79757			−0.269202			−0.134601	+	0.990900i	$0.542975\pi$
$200$	0.169131	−	0.292943i	0.0119593	−	0.0207142i
$201$	4.66233	+	10.4718i	0.328855	+	0.738621i
$202$	−2.99964	−	5.19552i	−0.211054	−	0.365556i
$203$	−3.88791	−	6.73407i	−0.272878	−	0.472639i
$204$	2.51807	+	5.65569i	0.176300	+	0.395977i
$205$	4.29173	−	7.43350i	0.299748	−	0.519178i
$206$	−32.4944			−2.26399
$207$	7.16661	+	22.0566i	0.498114	+	1.53304i
$208$	15.3099			1.06155
$209$	−0.457738	+	0.792826i	−0.0316624	+	0.0548409i
$210$	−1.99165	+	2.74128i	−0.137437	+	0.189166i
$211$	−3.75473	−	6.50339i	−0.258486	−	0.447712i	0.707350	−	0.706863i	$-0.249890\pi$
$211$	−3.75473	−	6.50339i	−0.258486	−	0.447712i	−0.965837	+	0.259152i	$0.916557\pi$
$212$	1.98223	+	3.43332i	0.136140	+	0.235801i
$213$	6.98932	+	0.734607i	0.478900	+	0.0503344i
$214$	18.8264	−	32.6083i	1.28695	−	2.22906i
$215$	7.45077			0.508138
$216$	−1.67163	−	0.543146i	−0.113740	−	0.0369564i
$217$	−6.01945			−0.408627
$218$	16.2502	−	28.1462i	1.10060	−	1.90630i
$219$	23.3646	+	2.45572i	1.57884	+	0.165942i
$220$	3.61426	+	6.26007i	0.243673	+	0.422054i
$221$	−3.46980	−	6.00987i	−0.233404	−	0.404268i
$222$	14.5708	−	20.0550i	0.977926	−	1.34600i
$223$	−9.16391	+	15.8724i	−0.613661	+	1.06289i	0.376957	+	0.926231i	$0.376970\pi$
$223$	−9.16391	+	15.8724i	−0.613661	+	1.06289i	−0.990618	+	0.136661i	$0.956363\pi$
$224$	7.76669			0.518934
$225$	−2.00739	+	2.22943i	−0.133826	+	0.148629i
$226$	25.4582			1.69345
$227$	−6.31293	+	10.9343i	−0.419004	+	0.725736i	−0.995840	−	0.0911241i	$-0.970954\pi$
$227$	−6.31293	+	10.9343i	−0.419004	+	0.725736i	0.576836	+	0.816860i	$0.304287\pi$
$228$	−0.297847	−	0.668975i	−0.0197254	−	0.0443039i
$229$	−0.0782097	−	0.135463i	−0.00516824	−	0.00895166i	0.863430	−	0.504469i	$-0.168312\pi$
$229$	−0.0782097	−	0.135463i	−0.00516824	−	0.00895166i	−0.868598	+	0.495517i	$0.834978\pi$
$230$	−7.56161	−	13.0971i	−0.498598	−	0.863597i
$231$	2.78716	+	6.26007i	0.183382	+	0.411883i
$232$	−1.31513	+	2.27787i	−0.0863426	+	0.149550i
$233$	20.9785			1.37435			0.687174	−	0.726493i	$-0.258851\pi$
$233$	20.9785			1.37435			0.687174	+	0.726493i	$0.258851\pi$
$234$	−20.3639	−	4.32847i	−1.33123	−	0.282961i
$235$	−0.248295			−0.0161970
$236$	−0.591915	+	1.02523i	−0.0385304	+	0.0667366i
$237$	5.78367	−	7.96053i	0.375690	−	0.517092i
$238$	−1.91355	−	3.31436i	−0.124037	−	0.214838i
$239$	1.67856	+	2.90734i	0.108577	+	0.188060i	0.915194	−	0.403014i	$-0.132037\pi$
$239$	1.67856	+	2.90734i	0.108577	+	0.188060i	−0.806617	+	0.591074i	$0.798704\pi$
$240$	7.43444	+	0.781391i	0.479891	+	0.0504386i
$241$	5.36277	−	9.28859i	0.345447	−	0.598331i	−0.639988	−	0.768385i	$-0.721061\pi$
$241$	5.36277	−	9.28859i	0.345447	−	0.598331i	0.985435	+	0.170054i	$0.0543941\pi$
$242$	9.10122			0.585048
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	−14.0175			−0.897381
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$	28.9249	+	3.04013i	1.84419	+	0.193832i
$247$	0.410420	+	0.710869i	0.0261144	+	0.0452315i
$248$	1.01807	+	1.76336i	0.0646478	+	0.111973i
$249$	15.0797	−	20.7554i	0.955636	−	1.31532i
$250$	0.978148	−	1.69420i	0.0618635	−	0.107151i
$251$	9.63655			0.608254			0.304127	−	0.952632i	$-0.401635\pi$
$251$	9.63655			0.608254			0.304127	+	0.952632i	$0.401635\pi$
$252$	−5.36149	−	1.13962i	−0.337742	−	0.0717894i
$253$	−30.5843			−1.92282
$254$	−10.5649	+	18.2990i	−0.662901	+	1.14818i
$255$	−1.37819	−	3.09546i	−0.0863055	−	0.193845i
$256$	−9.19916	−	15.9334i	−0.574948	−	0.995839i
$257$	−12.3196	−	21.3381i	−0.768473	−	1.33103i	−0.938391	−	0.345576i	$-0.887684\pi$
$257$	−12.3196	−	21.3381i	−0.768473	−	1.33103i	0.169918	−	0.985458i	$-0.445650\pi$
$258$	10.2686	+	23.0636i	0.639293	+	1.43587i
$259$	−3.65796	+	6.33577i	−0.227295	+	0.393686i
$260$	6.48127			0.401951
$261$	15.6091	−	17.3357i	0.966181	−	1.07305i
$262$	27.3172			1.68766
$263$	−7.19210	+	12.4571i	−0.443484	+	0.768136i	−0.997945	−	0.0640731i	$-0.979591\pi$
$263$	−7.19210	+	12.4571i	−0.443484	+	0.768136i	0.554462	+	0.832209i	$0.312924\pi$
$264$	1.36245	−	1.87525i	0.0838529	−	0.115414i
$265$	−1.08491	−	1.87912i	−0.0666454	−	0.115433i
$266$	0.226341	+	0.392034i	0.0138779	+	0.0240371i
$267$	10.5526	+	1.10912i	0.645809	+	0.0678773i
$268$	6.04587	−	10.4718i	0.369311	−	0.639665i
$269$	13.6989			0.835234			0.417617	−	0.908623i	$-0.362865\pi$
$269$	13.6989			0.835234			0.417617	+	0.908623i	$0.362865\pi$
$270$	−9.66769	−	3.14122i	−0.588357	−	0.191169i
$271$	−1.43854			−0.0873853			−0.0436927	−	0.999045i	$-0.513912\pi$
$271$	−1.43854			−0.0873853			−0.0436927	+	0.999045i	$0.513912\pi$
$272$	−4.22161	+	7.31204i	−0.255973	+	0.443357i
$273$	6.11048	+	0.642237i	0.369823	+	0.0388700i
$274$	3.15089	+	5.45750i	0.190352	+	0.329700i
$275$	−1.97815	−	3.42625i	−0.119287	−	0.206611i
$276$	14.3797	−	19.7919i	0.865556	−	1.19134i
$277$	−9.12713	+	15.8087i	−0.548396	+	0.949850i	0.449989	+	0.893034i	$0.351428\pi$
$277$	−9.12713	+	15.8087i	−0.548396	+	0.949850i	−0.998385	+	0.0568155i	$0.981905\pi$
$278$	−21.0917			−1.26500
$279$	−5.58034	−	17.1745i	−0.334086	−	1.02821i
$280$	−0.338261			−0.0202150
$281$	−2.91684	+	5.05211i	−0.174004	+	0.301383i	−0.939816	−	0.341681i	$-0.889004\pi$
$281$	−2.91684	+	5.05211i	−0.174004	+	0.301383i	0.765812	+	0.643064i	$0.222337\pi$
$282$	−0.342198	−	0.768588i	−0.0203776	−	0.0457688i
$283$	6.90764	+	11.9644i	0.410616	+	0.711208i	0.994957	−	0.100300i	$-0.0319802\pi$
$283$	6.90764	+	11.9644i	0.410616	+	0.711208i	−0.584341	+	0.811508i	$0.698647\pi$
$284$	−3.70672	−	6.42023i	−0.219953	−	0.380971i
$285$	0.163017	+	0.366142i	0.00965629	+	0.0216884i
$286$	13.7276	−	23.7768i	0.811727	−	1.40595i
$287$	−8.58347			−0.506666
$288$	7.20012	+	22.1597i	0.424271	+	1.30577i
$289$	−13.1729			−0.774877
$290$	−7.60591	+	13.1738i	−0.446634	+	0.773593i
$291$	−6.31519	+	8.69212i	−0.370203	+	0.509541i
$292$	−12.3912	−	21.4622i	−0.725142	−	1.25598i
$293$	−6.92449	−	11.9936i	−0.404533	−	0.700672i	0.589734	−	0.807597i	$-0.299233\pi$
$293$	−6.92449	−	11.9936i	−0.404533	−	0.700672i	−0.994267	+	0.106926i	$0.965899\pi$
$294$	3.36984	+	0.354185i	0.196533	+	0.0206565i
$295$	0.323966	−	0.561125i	0.0188620	−	0.0326700i
$296$	2.47469			0.143839
$297$	−15.2772	+	13.7557i	−0.886474	+	0.798184i
$298$	27.7318			1.60646
$299$	−13.7114	+	23.7488i	−0.792948	+	1.37343i
$300$	3.14728	+	0.330792i	0.181708	+	0.0190983i
$301$	−3.72539	−	6.45256i	−0.214728	−	0.371919i
$302$	−7.03332	−	12.1821i	−0.404722	−	0.701000i
$303$	−3.12208	+	4.29717i	−0.179359	+	0.246866i
$304$	0.499347	−	0.864894i	0.0286395	−	0.0496051i
$305$	7.67206			0.439301
$306$	7.68247	−	8.53225i	0.439178	−	0.487756i
$307$	32.4126			1.84988			0.924942	−	0.380108i	$-0.124113\pi$
$307$	32.4126			1.84988			0.924942	+	0.380108i	$0.124113\pi$
$308$	3.61426	−	6.26007i	0.205941	−	0.356701i
$309$	11.7017	+	26.2824i	0.665684	+	1.49515i
$310$	5.88791	+	10.1982i	0.334411	+	0.579217i
$311$	15.1887	+	26.3076i	0.861273	+	1.49177i	0.870700	+	0.491814i	$0.163666\pi$
$311$	15.1887	+	26.3076i	0.861273	+	1.49177i	−0.00942711	+	0.999956i	$0.503001\pi$
$312$	−0.845330	−	1.89864i	−0.0478574	−	0.107489i
$313$	12.3176	−	21.3348i	0.696233	−	1.20591i	−0.273530	−	0.961863i	$-0.588191\pi$
$313$	12.3176	−	21.3348i	0.696233	−	1.20591i	0.969763	−	0.244048i	$-0.0784754\pi$
$314$	−3.61303			−0.203895
$315$	2.93444	+	0.623735i	0.165337	+	0.0351435i
$316$	−10.3797			−0.583903
$317$	−9.54823	+	16.5380i	−0.536282	+	0.928868i	0.462818	+	0.886453i	$0.346838\pi$
$317$	−9.54823	+	16.5380i	−0.536282	+	0.928868i	−0.999100	+	0.0424145i	$0.986495\pi$
$318$	4.32153	−	5.94807i	0.242339	−	0.333551i
$319$	15.3817	+	26.6420i	0.861212	+	1.49166i
$320$	−3.28105	−	5.68295i	−0.183416	−	0.317686i
$321$	−33.1541	−	3.48464i	−1.85048	−	0.194494i
$322$	−7.56161	+	13.0971i	−0.421392	+	0.729873i
$323$	−0.452682			−0.0251879
$324$	−1.71885	−	16.3537i	−0.0954915	−	0.908541i
$325$	−3.54732			−0.196770
$326$	15.5525	−	26.9377i	0.861374	−	1.49194i
$327$	−28.6173	−	3.00780i	−1.58254	−	0.166332i
$328$	1.45173	+	2.51446i	0.0801582	+	0.138838i
$329$	0.124148	+	0.215030i	0.00684448	+	0.0118550i
$330$	7.87957	−	10.8453i	0.433756	−	0.597014i
$331$	−6.02149	+	10.4295i	−0.330971	+	0.573258i	−0.982702	−	0.185191i	$-0.940710\pi$
$331$	−6.02149	+	10.4295i	−0.330971	+	0.573258i	0.651732	+	0.758450i	$0.274043\pi$
$332$	−27.0628			−1.48527
$333$	−21.4682	−	4.56320i	−1.17645	−	0.250062i
$334$	−2.65983			−0.145539
$335$	−3.30902	+	5.73139i	−0.180791	+	0.313139i
$336$	−3.04052	−	6.82911i	−0.165874	−	0.372559i
$337$	−5.50956	−	9.54284i	−0.300125	−	0.519832i	0.676039	−	0.736866i	$-0.263695\pi$
$337$	−5.50956	−	9.54284i	−0.300125	−	0.519832i	−0.976164	+	0.217034i	$0.930362\pi$
$338$	0.407432	+	0.705692i	0.0221614	+	0.0383846i
$339$	−9.16785	−	20.5913i	−0.497929	−	1.11837i
$340$	−1.78716	+	3.09546i	−0.0969226	+	0.167875i
$341$	23.8147			1.28964
$342$	−0.908710	+	1.00922i	−0.0491374	+	0.0545726i
$343$	−1.00000			−0.0539949
$344$	−1.26015	+	2.18265i	−0.0679429	+	0.117681i
$345$	−7.87027	+	10.8325i	−0.423721	+	0.583202i
$346$	−4.88982	−	8.46942i	−0.262879	−	0.455319i
$347$	−15.4307	−	26.7268i	−0.828364	−	1.43477i	−0.899321	−	0.437288i	$-0.855939\pi$
$347$	−15.4307	−	26.7268i	−0.828364	−	1.43477i	0.0709578	−	0.997479i	$-0.477394\pi$
$348$	−24.4727	−	2.57218i	−1.31187	−	0.137884i
$349$	3.94403	−	6.83127i	0.211119	−	0.365669i	−0.740946	−	0.671565i	$-0.765622\pi$
$349$	3.94403	−	6.83127i	0.211119	−	0.365669i	0.952065	+	0.305896i	$0.0989558\pi$
$350$	−1.95630			−0.104568
$351$	3.83231	+	18.0296i	0.204554	+	0.962350i
$352$	−30.7273			−1.63777
$353$	13.0468	−	22.5977i	0.694410	−	1.20275i	−0.275969	−	0.961167i	$-0.588999\pi$
$353$	13.0468	−	22.5977i	0.694410	−	1.20275i	0.970379	−	0.241588i	$-0.0776681\pi$
$354$	2.18343	+	0.229487i	0.116048	+	0.0121971i
$355$	2.02876	+	3.51391i	0.107675	+	0.186499i
$356$	−5.59648	−	9.69339i	−0.296613	−	0.513749i
$357$	−1.99165	+	2.74128i	−0.105409	+	0.145084i
$358$	−20.3920	+	35.3199i	−1.07775	+	1.86671i
$359$	−26.1440			−1.37983			−0.689913	−	0.723892i	$-0.742351\pi$
$359$	−26.1440			−1.37983			−0.689913	+	0.723892i	$0.742351\pi$
$360$	−0.313585	−	0.965117i	−0.0165274	−	0.0508661i
$361$	−18.9465			−0.997182
$362$	7.47985	−	12.9555i	0.393132	−	0.680925i
$363$	−3.27747	−	7.36132i	−0.172023	−	0.386369i
$364$	−3.24064	−	5.61295i	−0.169855	−	0.294198i
$365$	6.78194	+	11.7467i	0.354983	+	0.614849i
$366$	10.5735	+	23.7485i	0.552687	+	1.24136i
$367$	−3.20323	+	5.54816i	−0.167207	+	0.289612i	−0.937437	−	0.348155i	$-0.886808\pi$
$367$	−3.20323	+	5.54816i	−0.167207	+	0.289612i	0.770230	+	0.637767i	$0.220142\pi$
$368$	33.3644			1.73924
$369$	−7.95731	−	24.4901i	−0.414241	−	1.27490i
$370$	14.3121			0.744051
$371$	−1.08491	+	1.87912i	−0.0563257	+	0.0975589i
$372$	−11.1969	+	15.4112i	−0.580531	+	0.799032i
$373$	6.65658	+	11.5295i	0.344665	+	0.596977i	0.985293	−	0.170875i	$-0.0546593\pi$
$373$	6.65658	+	11.5295i	0.344665	+	0.596977i	−0.640628	+	0.767851i	$0.721326\pi$
$374$	7.57055	+	13.1126i	0.391464	+	0.678035i
$375$	−1.72256	−	0.181049i	−0.0889527	−	0.00934931i
$376$	0.0419943	−	0.0727363i	0.00216569	−	0.00375109i
$377$	27.5833			1.42061
$378$	2.11347	+	9.94307i	0.108705	+	0.511417i
$379$	−9.14013			−0.469497			−0.234748	−	0.972056i	$-0.575427\pi$
$379$	−9.14013			−0.469497			−0.234748	+	0.972056i	$0.575427\pi$
$380$	0.211392	−	0.366142i	0.0108442	−	0.0187827i
$381$	18.6053	+	1.95549i	0.953177	+	0.100183i
$382$	−10.5873	−	18.3378i	−0.541696	−	0.938245i
$383$	4.83416	+	8.37301i	0.247014	+	0.427841i	0.962696	−	0.270586i	$-0.0872173\pi$
$383$	4.83416	+	8.37301i	0.247014	+	0.427841i	−0.715682	+	0.698426i	$0.753884\pi$
$384$	−2.74470	+	3.77776i	−0.140065	+	0.192783i
$385$	−1.97815	+	3.42625i	−0.100816	+	0.174618i
$386$	17.0346			0.867040
$387$	14.9566	−	16.6110i	0.760288	−	0.844385i
$388$	11.3336			0.575376
$389$	−3.70041	+	6.40930i	−0.187618	+	0.324964i	−0.944456	−	0.328639i	$-0.893410\pi$
$389$	−3.70041	+	6.40930i	−0.187618	+	0.324964i	0.756837	+	0.653603i	$0.226743\pi$
$390$	−4.88887	−	10.9806i	−0.247558	−	0.556023i
$391$	−7.56161	−	13.0971i	−0.382407	−	0.662349i
$392$	0.169131	+	0.292943i	0.00854239	+	0.0147958i
$393$	−9.83728	−	22.0949i	−0.496225	−	1.11454i
$394$	25.5376	−	44.2324i	1.28657	−	2.22840i
$395$	5.68099			0.285842
$396$	21.2117	+	4.50868i	1.06593	+	0.226569i
$397$	−20.6228			−1.03503			−0.517514	−	0.855675i	$-0.673142\pi$
$397$	−20.6228			−1.03503			−0.517514	+	0.855675i	$0.673142\pi$
$398$	3.71458	−	6.43384i	0.186195	−	0.322499i
$399$	0.235580	−	0.324248i	0.0117937	−	0.0162327i
$400$	2.15796	+	3.73770i	0.107898	+	0.186885i
$401$	−5.58454	−	9.67271i	−0.278879	−	0.483032i	0.692228	−	0.721679i	$-0.256629\pi$
$401$	−5.58454	−	9.67271i	−0.278879	−	0.483032i	−0.971106	+	0.238647i	$0.923296\pi$
$402$	−22.3017	−	2.34401i	−1.11231	−	0.116908i
$403$	10.6765	−	18.4922i	0.531832	−	0.921161i
$404$	5.60305			0.278762
$405$	0.940756	+	8.95070i	0.0467465	+	0.444764i
$406$	15.2118			0.754950
$407$	14.4720	−	25.0662i	0.717349	−	1.24248i
$408$	1.13989	+	0.119807i	0.0564328	+	0.00593132i
$409$	14.6875	+	25.4394i	0.726248	+	1.25790i	0.958458	+	0.285233i	$0.0920711\pi$
$409$	14.6875	+	25.4394i	0.726248	+	1.25790i	−0.232210	+	0.972666i	$0.574596\pi$
$410$	8.39590	+	14.5421i	0.414644	+	0.718184i
$411$	3.27951	−	4.51385i	0.161766	−	0.222652i
$412$	15.1741	−	26.2824i	0.747575	−	1.29484i
$413$	−0.647932			−0.0318826
$414$	−44.3782	−	9.43289i	−2.18107	−	0.463601i
$415$	14.8120			0.727091
$416$	−13.7755	+	23.8598i	−0.675398	+	1.16982i
$417$	7.59543	+	17.0596i	0.371950	+	0.835413i
$418$	−0.895472	−	1.55100i	−0.0437989	−	0.0758620i
$419$	6.64380	+	11.5074i	0.324571	+	0.562173i	0.981425	−	0.191844i	$-0.0614468\pi$
$419$	6.64380	+	11.5074i	0.324571	+	0.562173i	−0.656854	+	0.754017i	$0.728113\pi$
$420$	−1.28716	−	2.89102i	−0.0628072	−	0.141067i
$421$	8.12385	−	14.0709i	0.395932	−	0.685774i	−0.597288	−	0.802027i	$-0.703755\pi$
$421$	8.12385	−	14.0709i	0.395932	−	0.685774i	0.993220	+	0.116253i	$0.0370883\pi$
$422$	14.6907			0.715133
$423$	−0.498426	+	0.553558i	−0.0242343	+	0.0269149i
$424$	0.733965			0.0356445
$425$	0.978148	−	1.69420i	0.0474471	−	0.0821808i
$426$	−8.08116	+	11.1228i	−0.391533	+	0.538899i
$427$	−3.83603	−	6.64420i	−0.185638	−	0.321535i
$428$	17.5830	+	30.4546i	0.849906	+	1.47208i
$429$	−24.1749	−	2.54088i	−1.16717	−	0.122675i
$430$	−7.28795	+	12.6231i	−0.351456	+	0.608740i
$431$	−7.28753			−0.351028			−0.175514	−	0.984477i	$-0.556159\pi$
$431$	−7.28753			−0.351028			−0.175514	+	0.984477i	$0.556159\pi$
$432$	16.6659	−	15.0060i	0.801839	−	0.721979i
$433$	−33.6740			−1.61827			−0.809133	−	0.587625i	$-0.800063\pi$
$433$	−33.6740			−1.61827			−0.809133	+	0.587625i	$0.800063\pi$
$434$	5.88791	−	10.1982i	0.282629	−	0.489528i
$435$	13.3944	+	1.40780i	0.642210	+	0.0674990i
$436$	15.1769	+	26.2872i	0.726844	+	1.25893i
$437$	0.894414	+	1.54917i	0.0427856	+	0.0741069i
$438$	−27.0146	+	37.1823i	−1.29081	+	1.77664i
$439$	−18.1856	+	31.4984i	−0.867952	+	1.50334i	−0.00386647	+	0.999993i	$0.501231\pi$
$439$	−18.1856	+	31.4984i	−0.867952	+	1.50334i	−0.864086	+	0.503345i	$0.832103\pi$
$440$	1.33826			0.0637991
$441$	−0.927051	−	2.85317i	−0.0441453	−	0.135865i
$442$	13.5759			0.645740
$443$	−2.19973	+	3.81005i	−0.104513	+	0.181021i	−0.913539	−	0.406751i	$-0.866662\pi$
$443$	−2.19973	+	3.81005i	−0.104513	+	0.181021i	0.809026	+	0.587772i	$0.199995\pi$
$444$	9.41679	+	21.1505i	0.446901	+	1.00376i
$445$	3.06306	+	5.30537i	0.145203	+	0.251499i
$446$	−17.9273	−	31.0510i	−0.848883	−	1.47031i
$447$	−9.98660	−	22.4303i	−0.472350	−	1.06092i
$448$	−3.28105	+	5.68295i	−0.155015	+	0.268494i
$449$	−5.79317			−0.273397			−0.136698	−	0.990613i	$-0.543649\pi$
$449$	−5.79317			−0.273397			−0.136698	+	0.990613i	$0.543649\pi$
$450$	−1.81359	−	5.58164i	−0.0854932	−	0.263121i
$451$	33.9587			1.59905
$452$	−11.8884	+	20.5913i	−0.559183	+	0.968534i
$453$	−7.32041	+	10.0757i	−0.343943	+	0.473397i
$454$	−12.3500	−	21.3908i	−0.579612	−	1.00392i
$455$	1.77366	+	3.07207i	0.0831504	+	0.144021i
$456$	−0.134830	−	0.0141712i	−0.00631398	−	0.000663626i
$457$	−7.04153	+	12.1963i	−0.329389	+	0.570518i	−0.982391	−	0.186838i	$-0.940176\pi$
$457$	−7.04153	+	12.1963i	−0.329389	+	0.570518i	0.653002	+	0.757356i	$0.273509\pi$
$458$	0.306003			0.0142986
$459$	−9.66769	−	3.14122i	−0.451249	−	0.146620i
$460$	14.1244			0.658554
$461$	11.8443	−	20.5149i	0.551645	−	0.955476i	−0.446512	−	0.894778i	$-0.647334\pi$
$461$	11.8443	−	20.5149i	0.551645	−	0.955476i	0.998156	−	0.0606986i	$-0.0193328\pi$
$462$	−13.3321	−	1.40126i	−0.620265	−	0.0651924i
$463$	7.56095	+	13.0959i	0.351387	+	0.608620i	0.986493	−	0.163805i	$-0.0523768\pi$
$463$	7.56095	+	13.0959i	0.351387	+	0.608620i	−0.635106	+	0.772425i	$0.719043\pi$
$464$	−16.7799	−	29.0637i	−0.778989	−	1.34925i
$465$	6.12825	−	8.43481i	0.284191	−	0.391155i
$466$	−20.5201	+	35.5418i	−0.950574	+	1.64644i
$467$	13.8433			0.640593			0.320296	−	0.947317i	$-0.396217\pi$
$467$	13.8433			0.640593			0.320296	+	0.947317i	$0.396217\pi$
$468$	13.0105	−	14.4496i	0.601408	−	0.667932i
$469$	6.61803			0.305592
$470$	0.242870	−	0.420662i	0.0112027	−	0.0194037i
$471$	1.30110	+	2.92232i	0.0599516	+	0.134654i
$472$	0.109585	+	0.189807i	0.00504406	+	0.00873657i
$473$	14.7387	+	25.5282i	0.677687	+	1.17379i
$474$	7.82947	+	17.5853i	0.359619	+	0.807718i
$475$	−0.115699	+	0.200396i	−0.00530862	+	0.00919481i
$476$	3.57433			0.163829
$477$	−6.36721	−	1.35339i	−0.291534	−	0.0619676i
$478$	−6.56750			−0.300391
$479$	6.78407	−	11.7504i	0.309972	−	0.536888i	−0.668384	−	0.743817i	$-0.733014\pi$
$479$	6.78407	−	11.7504i	0.309972	−	0.536888i	0.978356	+	0.206929i	$0.0663469\pi$
$480$	−7.90707	+	10.8831i	−0.360907	+	0.496745i
$481$	−12.9759	−	22.4750i	−0.591652	−	1.02477i
$482$	10.4912	+	18.1712i	0.477859	+	0.827677i
$483$	13.3163	+	1.39960i	0.605915	+	0.0636842i
$484$	−4.25006	+	7.36132i	−0.193185	+	0.334606i
$485$	−6.20308			−0.281667
$486$	−26.4100	+	15.2478i	−1.19798	+	0.691655i
$487$	5.48843			0.248705			0.124352	−	0.992238i	$-0.460315\pi$
$487$	5.48843			0.248705			0.124352	+	0.992238i	$0.460315\pi$
$488$	−1.29758	+	2.24747i	−0.0587387	+	0.101738i
$489$	−27.3887	−	2.87867i	−1.23856	−	0.130178i
$490$	0.978148	+	1.69420i	0.0441882	+	0.0765362i
$491$	18.5490	+	32.1277i	0.837103	+	1.44990i	0.892307	+	0.451429i	$0.149086\pi$
$491$	18.5490	+	32.1277i	0.837103	+	1.44990i	−0.0552041	+	0.998475i	$0.517581\pi$
$492$	−15.9662	+	21.9756i	−0.719813	+	0.990737i
$493$	−7.60591	+	13.1738i	−0.342553	+	0.593319i
$494$	−1.60581			−0.0722487
$495$	−11.6095	−	2.46768i	−0.521809	−	0.110914i
$496$	−25.9795			−1.16651
$497$	2.02876	−	3.51391i	0.0910021	−	0.157620i
$498$	20.4137	+	45.8499i	0.914759	+	2.05458i
$499$	10.8042	+	18.7135i	0.483663	+	0.837729i	0.999824	−	0.0187623i	$-0.00597259\pi$
$499$	10.8042	+	18.7135i	0.483663	+	0.837729i	−0.516161	+	0.856492i	$0.672639\pi$
$500$	0.913545	+	1.58231i	0.0408550	+	0.0707629i
$501$	0.957841	+	2.15135i	0.0427932	+	0.0961150i
$502$	−9.42597	+	16.3263i	−0.420702	+	0.728677i
$503$	21.4561			0.956681			0.478340	−	0.878174i	$-0.341239\pi$
$503$	21.4561			0.956681			0.478340	+	0.878174i	$0.341239\pi$
$504$	−0.679023	+	0.754131i	−0.0302461	+	0.0335917i
$505$	−3.06665			−0.136464
$506$	29.9160	−	51.8160i	1.32993	−	2.30350i
$507$	0.424062	−	0.583672i	0.0188333	−	0.0259218i
$508$	−9.86714	−	17.0904i	−0.437784	−	0.758263i
$509$	7.45748	+	12.9167i	0.330547	+	0.572524i	0.982619	−	0.185633i	$-0.0594335\pi$
$509$	7.45748	+	12.9167i	0.330547	+	0.572524i	−0.652072	+	0.758157i	$0.726100\pi$
$510$	6.59240	+	0.692889i	0.291917	+	0.0306817i
$511$	6.78194	−	11.7467i	0.300015	−	0.519642i
$512$	30.6006			1.35237
$513$	1.14353	+	0.371555i	0.0504880	+	0.0164045i
$514$	48.2014			2.12607
$515$	−8.30507	+	14.3848i	−0.365965	+	0.633870i
$516$	−23.4497	−	2.46466i	−1.03231	−	0.108501i
$517$	−0.491165	−	0.850723i	−0.0216014	−	0.0374147i
$518$	−7.15605	−	12.3946i	−0.314419	−	0.544589i
$519$	−5.08942	+	7.00498i	−0.223401	+	0.307485i
$520$	0.599960	−	1.03916i	0.0263100	−	0.0455702i
$521$	22.6100			0.990563			0.495281	−	0.868733i	$-0.335065\pi$
$521$	22.6100			0.990563			0.495281	+	0.868733i	$0.335065\pi$
$522$	14.1021	+	43.4019i	0.617233	+	1.89965i
$523$	−37.1387			−1.62396			−0.811982	−	0.583683i	$-0.801611\pi$
$523$	−37.1387			−1.62396			−0.811982	+	0.583683i	$0.801611\pi$
$524$	−12.7565	+	22.0949i	−0.557270	+	0.965220i
$525$	0.704489	+	1.58231i	0.0307464	+	0.0690575i
$526$	−14.0699	−	24.3697i	−0.613475	−	1.06257i
$527$	5.88791	+	10.1982i	0.256482	+	0.444239i
$528$	12.0292	+	27.0180i	0.523503	+	1.17581i
$529$	−18.3807	+	31.8362i	−0.799159	+	1.38418i
$530$	4.24481			0.184383
$531$	−0.600666	−	1.84866i	−0.0260667	−	0.0802249i
$532$	−0.422784			−0.0183300
$533$	15.2241	−	26.3690i	0.659431	−	1.14217i
$534$	−12.2011	+	16.7934i	−0.527993	+	0.726720i
$535$	−9.62349	−	16.6684i	−0.416060	−	0.720637i
$536$	−1.11931	−	1.93871i	−0.0483469	−	0.0837393i
$537$	35.9112	+	3.77441i	1.54968	+	0.162878i
$538$	−13.3995	+	23.2086i	−0.577694	+	1.00060i
$539$	3.95630			0.170410
$540$	7.05530	−	6.35262i	0.303612	−	0.273373i
$541$	−38.7201			−1.66471			−0.832355	−	0.554244i	$-0.813008\pi$
$541$	−38.7201			−1.66471			−0.832355	+	0.554244i	$0.813008\pi$
$542$	1.40711	−	2.43718i	0.0604405	−	0.104686i
$543$	−13.1724	−	1.38447i	−0.565280	−	0.0594133i
$544$	−7.59697	−	13.1583i	−0.325717	−	0.564159i
$545$	−8.30662	−	14.3875i	−0.355816	−	0.616292i
$546$	−7.06503	+	9.72418i	−0.302355	+	0.416156i
$547$	8.96478	−	15.5275i	0.383306	−	0.663906i	−0.608226	−	0.793764i	$-0.708119\pi$
$547$	8.96478	−	15.5275i	0.383306	−	0.663906i	0.991533	+	0.129858i	$0.0414521\pi$
$548$	−5.88558			−0.251419
$549$	15.4008	−	17.1043i	0.657291	−	0.729996i
$550$	7.73968			0.330021
$551$	0.899654	−	1.55825i	0.0383265	−	0.0663835i
$552$	−1.84220	−	4.13764i	−0.0784091	−	0.176110i
$553$	−2.84049	−	4.91988i	−0.120790	−	0.209215i
$554$	−17.8554	−	30.9264i	−0.758602	−	1.31394i
$555$	−5.15398	−	11.5760i	−0.218774	−	0.491375i
$556$	9.84937	−	17.0596i	0.417706	−	0.723488i
$557$	−18.9035			−0.800968			−0.400484	−	0.916304i	$-0.631158\pi$
$557$	−18.9035			−0.800968			−0.400484	+	0.916304i	$0.631158\pi$
$558$	34.5555	+	7.34500i	1.46285	+	0.310939i
$559$	26.4303			1.11788
$560$	2.15796	−	3.73770i	0.0911905	−	0.157947i
$561$	7.87957	−	10.8453i	0.332676	−	0.457889i
$562$	−5.70619	−	9.88341i	−0.240701	−	0.416907i
$563$	−17.1129	−	29.6405i	−0.721224	−	1.24920i	−0.960509	−	0.278248i	$-0.910246\pi$
$563$	−17.1129	−	29.6405i	−0.721224	−	1.24920i	0.239285	−	0.970949i	$-0.423087\pi$
$564$	0.781455	+	0.0821342i	0.0329052	+	0.00345847i
$565$	6.50674	−	11.2700i	0.273741	−	0.474133i
$566$	−27.0267			−1.13602
$567$	7.28115	−	5.29007i	0.305780	−	0.222162i
$568$	−1.37250			−0.0575888
$569$	−5.87973	+	10.1840i	−0.246491	+	0.426935i	−0.962550	−	0.271105i	$-0.912611\pi$
$569$	−5.87973	+	10.1840i	−0.246491	+	0.426935i	0.716059	+	0.698040i	$0.245944\pi$
$570$	−0.779773	−	0.0819574i	−0.0326611	−	0.00343282i
$571$	9.85140	+	17.0631i	0.412268	+	0.714070i	0.995137	−	0.0984964i	$-0.0314033\pi$
$571$	9.85140	+	17.0631i	0.412268	+	0.714070i	−0.582869	+	0.812566i	$0.698070\pi$
$572$	12.8209	+	22.2065i	0.536069	+	0.928499i
$573$	−11.0195	+	15.1670i	−0.460346	+	0.633612i
$574$	8.39590	−	14.5421i	0.350438	−	0.606976i
$575$	−7.73054			−0.322386
$576$	−19.2561	−	4.09301i	−0.802338	−	0.170542i
$577$	21.9439			0.913538			0.456769	−	0.889585i	$-0.349007\pi$
$577$	21.9439			0.913538			0.456769	+	0.889585i	$0.349007\pi$
$578$	12.8850	−	22.3176i	0.535947	−	0.928288i
$579$	−6.13440	−	13.7781i	−0.254937	−	0.572598i
$580$	−7.10357	−	12.3038i	−0.294960	−	0.510885i
$581$	−7.40599	−	12.8275i	−0.307252	−	0.532176i
$582$	−8.54901	−	19.2014i	−0.354368	−	0.795923i
$583$	4.29222	−	7.43435i	0.177766	−	0.307899i
$584$	−4.58814			−0.189858
$585$	−7.12086	+	7.90851i	−0.294411	+	0.326977i
$586$	27.0927			1.11919
$587$	−0.427820	+	0.741005i	−0.0176580	+	0.0305846i	−0.874719	−	0.484630i	$-0.838954\pi$
$587$	−0.427820	+	0.741005i	−0.0176580	+	0.0305846i	0.857061	+	0.515214i	$0.172288\pi$
$588$	−1.86011	+	2.56023i	−0.0767098	+	0.105582i
$589$	−0.696443	−	1.20628i	−0.0286964	−	0.0497037i
$590$	0.633773	+	1.09773i	0.0260920	+	0.0451927i
$591$	−44.9729	−	4.72684i	−1.84994	−	0.194436i
$592$	−15.7875	+	27.3447i	−0.648861	+	1.12386i
$593$	12.4833			0.512628			0.256314	−	0.966594i	$-0.417492\pi$
$593$	12.4833			0.512628			0.256314	+	0.966594i	$0.417492\pi$
$594$	−8.36149	−	39.3377i	−0.343076	−	1.61405i
$595$	−1.95630			−0.0802003
$596$	−12.9501	+	22.4303i	−0.530458	+	0.918779i
$597$	−6.54155	−	0.687544i	−0.267728	−	0.0281393i
$598$	−26.8234	−	46.4596i	−1.09689	−	1.89987i
$599$	1.86633	+	3.23258i	0.0762562	+	0.132080i	0.901632	−	0.432504i	$-0.142370\pi$
$599$	1.86633	+	3.23258i	0.0762562	+	0.132080i	−0.825376	+	0.564584i	$0.809037\pi$
$600$	0.344375	−	0.473991i	0.0140590	−	0.0193506i
$601$	8.95613	−	15.5125i	0.365328	−	0.632767i	−0.623501	−	0.781823i	$-0.714290\pi$
$601$	8.95613	−	15.5125i	0.365328	−	0.632767i	0.988829	+	0.149056i	$0.0476234\pi$
$602$	14.5759			0.594070
$603$	6.13525	+	18.8824i	0.249847	+	0.768950i
$604$	13.1376			0.534562
$605$	2.32614	−	4.02899i	0.0945709	−	0.163802i
$606$	−4.22642	−	9.49269i	−0.171686	−	0.385614i
$607$	−22.2438	−	38.5274i	−0.902849	−	1.56378i	−0.823779	−	0.566911i	$-0.808138\pi$
$607$	−22.2438	−	38.5274i	−0.902849	−	1.56378i	−0.0790694	−	0.996869i	$-0.525195\pi$
$608$	0.898597	+	1.55642i	0.0364429	+	0.0631210i
$609$	−5.47798	−	12.3038i	−0.221979	−	0.498573i
$610$	−7.50440	+	12.9980i	−0.303844	+	0.526274i
$611$	−0.880783			−0.0356327
$612$	3.31359	+	10.1982i	0.133944	+	0.412236i
$613$	27.1824			1.09789			0.548943	−	0.835860i	$-0.315031\pi$
$613$	27.1824			1.09789			0.548943	+	0.835860i	$0.315031\pi$
$614$	−31.7043	+	54.9134i	−1.27948	+	2.21613i
$615$	8.73860	−	12.0277i	0.352374	−	0.485002i
$616$	−0.669131	−	1.15897i	−0.0269600	−	0.0466962i
$617$	18.4977	+	32.0390i	0.744690	+	1.28984i	0.950339	+	0.311216i	$0.100736\pi$
$617$	18.4977	+	32.0390i	0.744690	+	1.28984i	−0.205649	+	0.978626i	$0.565930\pi$
$618$	−55.9735	−	5.88306i	−2.25159	−	0.236651i
$619$	12.7730	−	22.1234i	0.513389	−	0.889215i	−0.486491	−	0.873686i	$-0.661723\pi$
$619$	12.7730	−	22.1234i	0.513389	−	0.889215i	0.999879	−	0.0155296i	$-0.00494344\pi$
$620$	−10.9981			−0.441694
$621$	8.35162	+	39.2913i	0.335139	+	1.57671i
$622$	−59.4272			−2.38282
$623$	3.06306	−	5.30537i	0.122719	−	0.212555i
$624$	26.3723	+	2.77184i	1.05574	+	0.110963i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	24.0969	+	41.7371i	0.963106	+	1.66815i
$627$	−0.932023	+	1.28282i	−0.0372214	+	0.0512309i
$628$	1.68720	−	2.92232i	0.0673268	−	0.116613i
$629$	14.3121			0.570661
$630$	−3.92705	+	4.36143i	−0.156457	+	0.173764i
$631$	−24.6348			−0.980696			−0.490348	−	0.871527i	$-0.663130\pi$
$631$	−24.6348			−0.980696			−0.490348	+	0.871527i	$0.663130\pi$
$632$	−0.960829	+	1.66420i	−0.0382197	+	0.0661985i
$633$	−5.29033	−	11.8823i	−0.210272	−	0.472278i
$634$	−18.6792	−	32.3533i	−0.741844	−	1.28491i
$635$	5.40047	+	9.35388i	0.214311	+	0.371197i
$636$	2.79291	+	6.27299i	0.110746	+	0.248740i
$637$	1.77366	−	3.07207i	0.0702749	−	0.121720i
$638$	−60.1824			−2.38265
$639$	11.9065	+	2.53081i	0.471015	+	0.100117i
$640$	−2.69598			−0.106568
$641$	20.5715	−	35.6309i	0.812525	−	1.40734i	−0.0985659	−	0.995131i	$-0.531426\pi$
$641$	20.5715	−	35.6309i	0.812525	−	1.40734i	0.911091	−	0.412205i	$-0.135241\pi$
$642$	38.3333	−	52.7613i	1.51290	−	2.08232i
$643$	−3.80747	−	6.59473i	−0.150152	−	0.260071i	0.781131	−	0.624367i	$-0.214643\pi$
$643$	−3.80747	−	6.59473i	−0.150152	−	0.260071i	−0.931283	+	0.364296i	$0.881310\pi$
$644$	−7.06220	−	12.2321i	−0.278290	−	0.482012i
$645$	12.8344	+	1.34895i	0.505355	+	0.0531149i
$646$	0.442790	−	0.766934i	0.0174213	−	0.0301746i
$647$	−22.2127			−0.873270			−0.436635	−	0.899639i	$-0.643830\pi$
$647$	−22.2127			−0.873270			−0.436635	+	0.899639i	$0.643830\pi$
$648$	−2.78115	−	1.23825i	−0.109254	−	0.0486430i
$649$	2.56341			0.100623
$650$	3.46980	−	6.00987i	0.136097	−	0.235727i
$651$	−10.3689	−	1.08981i	−0.406389	−	0.0427132i
$652$	14.5253	+	25.1586i	0.568856	+	0.985288i
$653$	−2.17886	−	3.77389i	−0.0852653	−	0.147684i	0.820239	−	0.572021i	$-0.193840\pi$
$653$	−2.17886	−	3.77389i	−0.0852653	−	0.147684i	−0.905504	+	0.424337i	$0.860507\pi$
$654$	33.0878	−	45.5415i	1.29384	−	1.78081i
$655$	6.98186	−	12.0929i	0.272804	−	0.472510i
$656$	−37.0456			−1.44639
$657$	39.8024	+	8.46027i	1.55284	+	0.330067i
$658$	−0.485739			−0.0189361
$659$	−14.8386	+	25.7011i	−0.578028	+	1.00117i	0.417677	+	0.908596i	$0.362844\pi$
$659$	−14.8386	+	25.7011i	−0.578028	+	1.00117i	−0.995705	+	0.0925789i	$0.970489\pi$
$660$	5.09240	+	11.4377i	0.198222	+	0.445213i
$661$	0.458240	+	0.793695i	0.0178235	+	0.0308711i	0.874800	−	0.484485i	$-0.160993\pi$
$661$	0.458240	+	0.793695i	0.0178235	+	0.0308711i	−0.856976	+	0.515356i	$0.827660\pi$
$662$	−11.7798	−	20.4032i	−0.457835	−	0.792994i
$663$	−4.88887	−	10.9806i	−0.189868	−	0.426450i
$664$	−2.50516	+	4.33906i	−0.0972190	+	0.168388i
$665$	0.231398			0.00897321
$666$	28.7300	−	31.9079i	1.11326	−	1.23641i
$667$	60.1114			2.32752
$668$	1.24208	−	2.15135i	0.0480575	−	0.0832380i
$669$	−18.6591	+	25.6820i	−0.721401	+	0.992924i
$670$	−6.47341	−	11.2123i	−0.250090	−	0.433168i
$671$	15.1765	+	26.2864i	0.585881	+	1.01478i
$672$	13.3786	+	1.40615i	0.516091	+	0.0542434i
$673$	14.6539	−	25.3813i	0.564867	−	0.978378i	−0.432195	−	0.901780i	$-0.642261\pi$
$673$	14.6539	−	25.3813i	0.564867	−	0.978378i	0.997062	−	0.0765981i	$-0.0244058\pi$
$674$	21.5567			0.830331
$675$	−3.86149	+	3.47690i	−0.148629	+	0.133826i
$676$	−0.761046			−0.0292710
$677$	−13.7620	+	23.8364i	−0.528915	+	0.916108i	0.470516	+	0.882391i	$0.344068\pi$
$677$	−13.7620	+	23.8364i	−0.528915	+	0.916108i	−0.999431	+	0.0337165i	$0.989266\pi$
$678$	43.8533	+	4.60917i	1.68418	+	0.177014i
$679$	3.10154	+	5.37202i	0.119026	+	0.206159i
$680$	0.330869	+	0.573083i	0.0126883	+	0.0219767i
$681$	−12.8541	+	17.6921i	−0.492569	+	0.677963i
$682$	−23.2943	+	40.3470i	−0.891986	+	1.54496i
$683$	−36.1320			−1.38255			−0.691276	−	0.722591i	$-0.742951\pi$
$683$	−36.1320			−1.38255			−0.691276	+	0.722591i	$0.742951\pi$
$684$	−0.391943	−	1.20628i	−0.0149863	−	0.0461231i
$685$	3.22128			0.123079
$686$	0.978148	−	1.69420i	0.0373458	−	0.0646849i
$687$	−0.110196	−	0.247504i	−0.00420423	−	0.00944285i
$688$	−16.0785	−	27.8487i	−0.612986	−	1.06172i
$689$	−3.84852	−	6.66583i	−0.146617	−	0.253948i
$690$	−10.6541	−	23.9296i	−0.405596	−	0.910984i
$691$	−13.7504	+	23.8163i	−0.523088	+	0.906015i	0.476551	+	0.879147i	$0.341887\pi$
$691$	−13.7504	+	23.8163i	−0.523088	+	0.906015i	−0.999639	+	0.0268681i	$0.991447\pi$
$692$	9.13375			0.347213
$693$	3.66769	+	11.2880i	0.139324	+	0.428795i
$694$	60.3740			2.29177
$695$	−5.39074	+	9.33703i	−0.204482	+	0.354174i
$696$	−2.67780	+	3.68568i	−0.101502	+	0.139705i
$697$	8.39590	+	14.5421i	0.318017	+	0.550822i
$698$	7.71569	+	13.3640i	0.292043	+	0.505834i
$699$	36.1368	+	3.79813i	1.36682	+	0.143658i
$700$	0.913545	−	1.58231i	0.0345288	−	0.0598056i
$701$	0.206128			0.00778534			0.00389267	−	0.999992i	$-0.498761\pi$
$701$	0.206128			0.00778534			0.00389267	+	0.999992i	$0.498761\pi$
$702$	−34.2944	−	11.1429i	−1.29436	−	0.420562i
$703$	−1.69289			−0.0638484
$704$	12.9808	−	22.4834i	0.489233	−	0.847376i
$705$	−0.427704	−	0.0449535i	−0.0161083	−	0.00169305i
$706$	25.5234	+	44.2078i	0.960585	+	1.66378i
$707$	1.53332	+	2.65580i	0.0576666	+	0.0998815i
$708$	−1.20523	+	1.65885i	−0.0452952	+	0.0623435i
$709$	23.1935	−	40.1723i	0.871049	−	1.50870i	0.0101367	−	0.999949i	$-0.496773\pi$
$709$	23.1935	−	40.1723i	0.871049	−	1.50870i	0.860913	−	0.508753i	$-0.169893\pi$
$710$	−7.93769			−0.297896
$711$	11.4040	−	12.6654i	0.427682	−	0.474989i
$712$	−2.07223			−0.0776600
$713$	23.2668	−	40.2993i	0.871350	−	1.50922i
$714$	−2.69614	−	6.05563i	−0.100901	−	0.226626i
$715$	−7.01712	−	12.1540i	−0.262425	−	0.454534i
$716$	−19.0452	−	32.9872i	−0.711751	−	1.23279i
$717$	2.36505	+	5.31198i	0.0883243	+	0.198380i
$718$	25.5727	−	44.2932i	0.954364	−	1.65301i
$719$	18.5632			0.692292			0.346146	−	0.938181i	$-0.387490\pi$
$719$	18.5632			0.692292			0.346146	+	0.938181i	$0.387490\pi$
$720$	12.6648	+	2.69199i	0.471990	+	0.100325i
$721$	16.6101			0.618594
$722$	18.5324	−	32.0991i	0.689706	−	1.19461i
$723$	10.9194	−	15.0293i	0.406097	−	0.558944i
$724$	6.98584	+	12.0998i	0.259627	+	0.449687i
$725$	3.88791	+	6.73407i	0.144394	+	0.250097i
$726$	15.6774	+	1.64776i	0.581843	+	0.0611542i
$727$	17.6537	−	30.5770i	0.654738	−	1.13404i	−0.327222	−	0.944948i	$-0.606112\pi$
$727$	17.6537	−	30.5770i	0.654738	−	1.13404i	0.981959	−	0.189091i	$-0.0605542\pi$
$728$	−1.19992			−0.0444720
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$	−26.5350			−0.982103
$731$	−7.28795	+	12.6231i	−0.269555	+	0.466882i
$732$	−24.1461	−	2.53786i	−0.892465	−	0.0938019i
$733$	−8.85865	−	15.3436i	−0.327202	−	0.566730i	0.654754	−	0.755842i	$-0.272772\pi$
$733$	−8.85865	−	15.3436i	−0.327202	−	0.566730i	−0.981955	+	0.189112i	$0.939439\pi$
$734$	−6.26647	−	10.8538i	−0.231300	−	0.400623i
$735$	1.01807	−	1.40126i	0.0375522	−	0.0516862i
$736$	−30.0204	+	51.9968i	−1.10657	+	1.91663i
$737$	−26.1829			−0.964459
$738$	49.2746	+	10.4736i	1.81382	+	0.385540i
$739$	21.8311			0.803068			0.401534	−	0.915844i	$-0.368477\pi$
$739$	21.8311			0.803068			0.401534	+	0.915844i	$0.368477\pi$
$740$	−6.68343	+	11.5760i	−0.245688	+	0.425543i
$741$	0.578273	+	1.29882i	0.0212434	+	0.0477134i
$742$	−2.12240	−	3.67611i	−0.0779159	−	0.134954i
$743$	20.8738	+	36.1545i	0.765786	+	1.32638i	0.939830	+	0.341642i	$0.110983\pi$
$743$	20.8738	+	36.1545i	0.765786	+	1.32638i	−0.174044	+	0.984738i	$0.555683\pi$
$744$	1.43444	+	3.22181i	0.0525892	+	0.118117i
$745$	7.08783	−	12.2765i	0.259678	−	0.449776i
$746$	−26.0445			−0.953556
$747$	29.7334	−	33.0223i	1.08789	−	1.20822i
$748$	−14.1411			−0.517050
$749$	−9.62349	+	16.6684i	−0.351635	+	0.609049i
$750$	1.99165	−	2.74128i	0.0727249	−	0.100097i
$751$	3.83979	+	6.65070i	0.140116	+	0.242688i	0.927540	−	0.373724i	$-0.121919\pi$
$751$	3.83979	+	6.65070i	0.140116	+	0.242688i	−0.787424	+	0.616411i	$0.788586\pi$
$752$	0.535812	+	0.928053i	0.0195390	+	0.0338426i
$753$	16.5996	+	1.74468i	0.604922	+	0.0635798i
$754$	−26.9806	+	46.7317i	−0.982575	+	1.70187i
$755$	−7.19045			−0.261687
$756$	−9.02918	−	2.93376i	−0.328388	−	0.106700i
$757$	18.4236			0.669617			0.334808	−	0.942286i	$-0.391328\pi$
$757$	18.4236			0.669617			0.334808	+	0.942286i	$0.391328\pi$
$758$	8.94039	−	15.4852i	0.324730	−	0.562448i
$759$	−52.6834	−	5.53725i	−1.91229	−	0.200989i
$760$	−0.0391364	−	0.0677862i	−0.00141963	−	0.00245887i
$761$	19.4522	+	33.6921i	0.705140	+	1.22134i	0.966641	+	0.256135i	$0.0824492\pi$
$761$	19.4522	+	33.6921i	0.705140	+	1.22134i	−0.261501	+	0.965203i	$0.584217\pi$
$762$	−21.5117	+	29.6083i	−0.779287	+	1.07260i
$763$	−8.30662	+	14.3875i	−0.300720	+	0.520862i
$764$	19.7762			0.715478
$765$	−1.81359	−	5.58164i	−0.0655703	−	0.201805i
$766$	−18.9141			−0.683394
$767$	1.14921	−	1.99049i	0.0414956	−	0.0718724i
$768$	−12.9614	−	29.1118i	−0.467705	−	1.05048i
$769$	4.40099	+	7.62275i	0.158704	+	0.274883i	0.934402	−	0.356221i	$-0.115935\pi$
$769$	4.40099	+	7.62275i	0.158704	+	0.274883i	−0.775698	+	0.631105i	$0.782602\pi$
$770$	−3.86984	−	6.70276i	−0.139459	−	0.241551i
$771$	−17.3580	−	38.9866i	−0.625132	−	1.40407i
$772$	−7.95479	+	13.7781i	−0.286299	+	0.495885i
$773$	−25.5896			−0.920394			−0.460197	−	0.887817i	$-0.652221\pi$
$773$	−25.5896			−0.920394			−0.460197	+	0.887817i	$0.652221\pi$
$774$	13.5126	+	41.5875i	0.485701	+	1.49483i
$775$	6.01945			0.216225
$776$	1.04913	−	1.81715i	0.0376616	−	0.0652318i
$777$	−7.44815	+	10.2515i	−0.267201	+	0.367770i
$778$	−7.23909	−	12.5385i	−0.259534	−	0.449526i
$779$	−0.993096	−	1.72009i	−0.0355814	−	0.0616287i
$780$	11.1644	+	1.17343i	0.399750	+	0.0420154i
$781$	−8.02636	+	13.9021i	−0.287206	+	0.497455i
$782$	29.5855			1.05798
$783$	30.0263	−	27.0358i	1.07305	−	0.966181i
$784$	−4.31592			−0.154140
$785$	−0.923438	+	1.59944i	−0.0329589	+	0.0570865i
$786$	47.0555	+	4.94574i	1.67842	+	0.176409i
$787$	−1.25597	−	2.17541i	−0.0447705	−	0.0775449i	0.842772	−	0.538271i	$-0.180922\pi$
$787$	−1.25597	−	2.17541i	−0.0447705	−	0.0775449i	−0.887542	+	0.460726i	$0.847589\pi$
$788$	23.8509	+	41.3111i	0.849655	+	1.47165i
$789$	−14.6442	+	20.1560i	−0.521346	+	0.717572i
$790$	−5.55685	+	9.62474i	−0.197704	+	0.342433i
$791$	−13.0135			−0.462706
$792$	2.68641	−	2.98357i	0.0954576	−	0.106016i
$793$	27.2152			0.966441
$794$	20.1721	−	34.9391i	0.715882	−	1.23994i
$795$	−1.52861	−	3.43332i	−0.0542143	−	0.121767i
$796$	3.46925	+	6.00892i	0.122964	+	0.212980i
$797$	−16.9635	−	29.3816i	−0.600878	−	1.04075i	−0.992688	−	0.120705i	$-0.961484\pi$
$797$	−16.9635	−	29.3816i	−0.600878	−	1.04075i	0.391810	−	0.920046i	$-0.371849\pi$
$798$	0.318909	+	0.716282i	0.0112893	+	0.0253561i
$799$	0.242870	−	0.420662i	0.00859211	−	0.0148820i
$800$	−7.76669			−0.274594
$801$	17.9767	+	3.82107i	0.635177	+	0.135011i
$802$	21.8500			0.771552
$803$	−26.8314	+	46.4733i	−0.946858	+	1.64001i
$804$	12.3103	−	16.9437i	0.434151	−	0.597557i
$805$	3.86527	+	6.69485i	0.136233	+	0.235962i
$806$	20.8863	+	36.1761i	0.735689	+	1.27425i
$807$	23.5971	+	2.48016i	0.830659	+	0.0873058i
$808$	0.518664	−	0.898353i	0.0182465	−	0.0316039i
$809$	−19.0145			−0.668513			−0.334256	−	0.942482i	$-0.608485\pi$
$809$	−19.0145			−0.668513			−0.334256	+	0.942482i	$0.608485\pi$
$810$	−16.0845	−	7.16127i	−0.565151	−	0.251621i
$811$	47.0454			1.65199			0.825994	−	0.563679i	$-0.190614\pi$
$811$	47.0454			1.65199			0.825994	+	0.563679i	$0.190614\pi$
$812$	−7.10357	+	12.3038i	−0.249287	+	0.431777i
$813$	−2.47798	−	0.260446i	−0.0869066	−	0.00913426i
$814$	28.3114	+	49.0369i	0.992316	+	1.71874i
$815$	−7.94998	−	13.7698i	−0.278476	−	0.482334i
$816$	−8.59582	+	11.8311i	−0.300914	+	0.414172i
$817$	0.862045	−	1.49311i	0.0301591	−	0.0522372i
$818$	−57.4660			−2.00925
$819$	10.4094	+	2.21259i	0.363734	+	0.0773140i
$820$	−15.6828			−0.547666
$821$	−3.14464	+	5.44668i	−0.109749	+	0.190090i	−0.915668	−	0.401934i	$-0.868338\pi$
$821$	−3.14464	+	5.44668i	−0.109749	+	0.190090i	0.805920	+	0.592025i	$0.201671\pi$
$822$	4.43953	+	9.97136i	0.154847	+	0.347791i
$823$	−15.9300	−	27.5916i	−0.555285	−	0.961783i	−0.997881	−	0.0650614i	$-0.979276\pi$
$823$	−15.9300	−	27.5916i	−0.555285	−	0.961783i	0.442596	−	0.896721i	$-0.354058\pi$
$824$	−2.80928	−	4.86582i	−0.0978661	−	0.169509i
$825$	−2.78716	−	6.26007i	−0.0970366	−	0.217948i
$826$	0.633773	−	1.09773i	0.0220518	−	0.0381948i
$827$	−15.0182			−0.522235			−0.261117	−	0.965307i	$-0.584091\pi$
$827$	−15.0182			−0.522235			−0.261117	+	0.965307i	$0.584091\pi$
$828$	28.3532	−	31.4894i	0.985343	−	1.09433i
$829$	−45.7077			−1.58749			−0.793747	−	0.608248i	$-0.791873\pi$
$829$	−45.7077			−1.58749			−0.793747	+	0.608248i	$0.791873\pi$
$830$	−14.4883	+	25.0945i	−0.502896	+	0.871042i
$831$	−18.5842	+	25.5789i	−0.644678	+	0.887323i
$832$	−11.6389	−	20.1592i	−0.403507	−	0.698895i
$833$	0.978148	+	1.69420i	0.0338908	+	0.0587006i
$834$	−36.3319	−	3.81863i	−1.25807	−	0.132228i
$835$	−0.679813	+	1.17747i	−0.0235259	+	0.0407480i
$836$	1.67266			0.0578501
$837$	−6.50306	−	30.5945i	−0.224779	−	1.05750i
$838$	−25.9945			−0.897964
$839$	10.7054	−	18.5424i	0.369593	−	0.640153i	−0.619909	−	0.784674i	$-0.712831\pi$
$839$	10.7054	−	18.5424i	0.369593	−	0.640153i	0.989502	+	0.144520i	$0.0461639\pi$
$840$	−0.582676	−	0.0612417i	−0.0201042	−	0.00211304i
$841$	−15.7318	−	27.2482i	−0.542474	−	0.939593i
$842$	15.8926	+	27.5269i	0.547697	+	0.948638i
$843$	−5.93911	+	8.17448i	−0.204554	+	0.281544i
$844$	−6.86024	+	11.8823i	−0.236139	+	0.409005i
$845$	0.416534			0.0143292
$846$	−0.450305	−	1.38590i	−0.0154818	−	0.0476481i
$847$	−4.65227			−0.159854
$848$	−4.68238	+	8.11012i	−0.160794	+	0.278503i
$849$	9.73270	+	21.8600i	0.334025	+	0.750233i
$850$	1.91355	+	3.31436i	0.0656341	+	0.113682i
$851$	−28.2780	−	48.9790i	−0.969358	−	1.67898i
$852$	−5.22269	−	11.7303i	−0.178926	−	0.401875i
$853$	−20.0193	+	34.6745i	−0.685448	+	1.18723i	0.287848	+	0.957676i	$0.407060\pi$
$853$	−20.0193	+	34.6745i	−0.685448	+	1.18723i	−0.973296	+	0.229555i	$0.926273\pi$
$854$	15.0088			0.513591
$855$	0.214517	+	0.660216i	0.00733634	+	0.0225789i
$856$	6.51051			0.222525
$857$	22.9609	−	39.7695i	0.784330	−	1.35850i	−0.145068	−	0.989422i	$-0.546340\pi$
$857$	22.9609	−	39.7695i	0.784330	−	1.35850i	0.929398	−	0.369078i	$-0.120327\pi$
$858$	27.9513	−	38.4717i	0.954243	−	1.31340i
$859$	−25.6958	−	44.5065i	−0.876730	−	1.51854i	−0.854909	−	0.518779i	$-0.826387\pi$
$859$	−25.6958	−	44.5065i	−0.876730	−	1.51854i	−0.0218212	−	0.999762i	$-0.506946\pi$
$860$	−6.80662	−	11.7894i	−0.232104	−	0.402016i
$861$	−14.7856	−	1.55402i	−0.503890	−	0.0529610i
$862$	7.12828	−	12.3465i	0.242790	−	0.420525i
$863$	33.9778			1.15662			0.578308	−	0.815818i	$-0.303713\pi$
$863$	33.9778			1.15662			0.578308	+	0.815818i	$0.303713\pi$
$864$	8.39067	+	39.4750i	0.285457	+	1.34297i
$865$	−4.99907			−0.169973
$866$	32.9381	−	57.0505i	1.11928	−	1.93865i
$867$	−22.6912	−	2.38494i	−0.770632	−	0.0809967i
$868$	5.49904	+	9.52463i	0.186650	+	0.323287i
$869$	11.2378	+	19.4645i	0.381217	+	0.660288i
$870$	−15.4868	+	21.3157i	−0.525050	+	0.722670i
$871$	−11.7381	+	20.3310i	−0.397732	+	0.688891i
$872$	5.61961			0.190304
$873$	−12.4520	+	13.8294i	−0.421437	+	0.468053i
$874$	−3.49948			−0.118372
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	−17.4590	−	39.2135i	−0.589883	−	1.32490i
$877$	15.7416	+	27.2653i	0.531558	+	0.920685i	0.999321	+	0.0368314i	$0.0117264\pi$
$877$	15.7416	+	27.2653i	0.531558	+	0.920685i	−0.467764	+	0.883853i	$0.654940\pi$
$878$	−35.5764	−	61.6202i	−1.20065	−	2.07958i
$879$	−9.75644	−	21.9133i	−0.329077	−	0.739118i
$880$	−8.53753	+	14.7874i	−0.287800	+	0.498484i
$881$	17.4293			0.587209			0.293605	−	0.955927i	$-0.405145\pi$
$881$	17.4293			0.587209			0.293605	+	0.955927i	$0.405145\pi$
$882$	5.74064	+	1.22021i	0.193297	+	0.0410866i
$883$	−17.2534			−0.580623			−0.290312	−	0.956932i	$-0.593759\pi$
$883$	−17.2534			−0.580623			−0.290312	+	0.956932i	$0.593759\pi$
$884$	−6.33964	+	10.9806i	−0.213225	+	0.369317i
$885$	0.659642	−	0.907920i	0.0221736	−	0.0305194i
$886$	−4.30333	−	7.45358i	−0.144573	−	0.250408i
$887$	2.37120	+	4.10704i	0.0796171	+	0.137901i	0.903085	−	0.429462i	$-0.141297\pi$
$887$	2.37120	+	4.10704i	0.0796171	+	0.137901i	−0.823468	+	0.567363i	$0.807964\pi$
$888$	4.26281	+	0.448040i	0.143051	+	0.0150352i
$889$	5.40047	−	9.35388i	0.181126	−	0.313719i
$890$	−11.9845			−0.401721
$891$	−28.8064	+	20.9291i	−0.965050	+	0.701150i
$892$	33.4866			1.12121
$893$	−0.0287275	+	0.0497574i	−0.000961328	+	0.00166507i
$894$	47.7697	+	5.02080i	1.59766	+	0.167921i
$895$	10.4238	+	18.0545i	0.348428	+	0.603495i
$896$	1.34799	+	2.33478i	0.0450331	+	0.0779997i
$897$	−27.9183	+	38.4263i	−0.932166	+	1.28302i
$898$	5.66657	−	9.81479i	0.189096	−	0.327524i
$899$	−46.8062			−1.56108
$900$	5.36149	+	1.13962i	0.178716	+	0.0379874i
$901$	4.24481			0.141415
$902$	−33.2166	+	57.5329i	−1.10599	+	1.91564i
$903$	−5.24898	−	11.7894i	−0.174675	−	0.392327i
$904$	2.20098	+	3.81220i	0.0732034	+	0.126792i
$905$	−3.82348	−	6.62246i	−0.127097	−	0.220138i
$906$	−9.90979	−	22.2578i	−0.329231	−	0.739465i
$907$	−9.24073	+	16.0054i	−0.306833	+	0.531451i	−0.977668	−	0.210156i	$-0.932603\pi$
$907$	−9.24073	+	16.0054i	−0.306833	+	0.531451i	0.670835	+	0.741607i	$0.265936\pi$
$908$	23.0686			0.765558
$909$	−6.15597	+	6.83689i	−0.204180	+	0.226765i
$910$	−6.93960			−0.230046
$911$	−4.31637	+	7.47618i	−0.143008	+	0.247697i	−0.928628	−	0.371012i	$-0.879011\pi$
$911$	−4.31637	+	7.47618i	−0.143008	+	0.247697i	0.785620	+	0.618709i	$0.212344\pi$
$912$	1.01674	−	1.39943i	0.0336677	−	0.0463397i
$913$	29.3003	+	50.7496i	0.969698	+	1.67957i
$914$	−13.7753	−	23.8595i	−0.455647	−	0.789203i
$915$	13.2156	+	1.38902i	0.436894	+	0.0459194i
$916$	−0.142896	+	0.247504i	−0.00472143	+	0.00817775i
$917$	−13.9637			−0.461123
$918$	14.7783	−	13.3064i	0.487756	−	0.439178i
$919$	−10.5715			−0.348721			−0.174361	−	0.984682i	$-0.555786\pi$
$919$	−10.5715			−0.348721			−0.174361	+	0.984682i	$0.555786\pi$
$920$	1.30747	−	2.26461i	0.0431061	−	0.0746619i
$921$	55.8327	+	5.86825i	1.83975	+	0.193366i
$922$	23.1710	+	40.1333i	0.763095	+	1.32172i
$923$	7.19664	+	12.4650i	0.236880	+	0.410289i
$924$	7.35916	−	10.1290i	0.242099	−	0.333220i
$925$	3.65796	−	6.33577i	0.120273	−	0.208319i
$926$	−29.5829			−0.972154
$927$	15.3985	+	47.3916i	0.505752	+	1.55654i
$928$	60.3925			1.98248
$929$	−5.86050	+	10.1507i	−0.192277	+	0.333033i	−0.946004	−	0.324154i	$-0.894921\pi$
$929$	−5.86050	+	10.1507i	−0.192277	+	0.333033i	0.753728	+	0.657187i	$0.228254\pi$
$930$	8.29594	+	18.6330i	0.272034	+	0.610999i
$931$	−0.115699	−	0.200396i	−0.00379187	−	0.00656772i
$932$	−19.1648	−	33.1944i	−0.627765	−	1.08732i
$933$	21.4006	+	48.0664i	0.700623	+	1.57362i
$934$	−13.5408	+	23.4534i	−0.443069	+	0.767418i
$935$	7.73968			0.253115
$936$	−1.11239	−	3.42358i	−0.0363595	−	0.111903i
$937$	−20.3067			−0.663392			−0.331696	−	0.943386i	$-0.607621\pi$
$937$	−20.3067			−0.663392			−0.331696	+	0.943386i	$0.607621\pi$
$938$	−6.47341	+	11.2123i	−0.211364	+	0.366094i
$939$	25.0805	−	34.5204i	0.818471	−	1.12653i
$940$	0.226829	+	0.392880i	0.00739835	+	0.0128143i
$941$	13.0889	+	22.6707i	0.426686	+	0.739042i	0.996576	−	0.0826786i	$-0.0263475\pi$
$941$	13.0889	+	22.6707i	0.426686	+	0.739042i	−0.569890	+	0.821721i	$0.693014\pi$
$942$	−6.22368	−	0.654135i	−0.202778	−	0.0213129i
$943$	33.1774	−	57.4650i	1.08041	−	1.87132i
$944$	−2.79642			−0.0910158
$945$	4.94183	+	1.60570i	0.160758	+	0.0522334i
$946$	−57.6666			−1.87490
$947$	3.82695	−	6.62848i	0.124359	−	0.215397i	−0.797123	−	0.603817i	$-0.793646\pi$
$947$	3.82695	−	6.62848i	0.124359	−	0.215397i	0.921482	+	0.388420i	$0.126979\pi$
$948$	−17.8797	−	1.87923i	−0.580704	−	0.0610345i
$949$	24.0577	+	41.6692i	0.780946	+	1.35264i
$950$	−0.226341	−	0.392034i	−0.00734347	−	0.0127193i
$951$	−19.4416	+	26.7591i	−0.630437	+	0.867723i
$952$	0.330869	−	0.573083i	0.0107235	−	0.0185737i
$953$	−23.3548			−0.756536			−0.378268	−	0.925696i	$-0.623480\pi$
$953$	−23.3548			−0.756536			−0.378268	+	0.925696i	$0.623480\pi$
$954$	8.52099	−	9.46352i	0.275877	−	0.306393i
$955$	−10.8239			−0.350252
$956$	3.06687	−	5.31198i	0.0991898	−	0.171802i
$957$	21.6725	+	48.6773i	0.700573	+	1.57351i
$958$	13.2717	+	22.9872i	0.428788	+	0.742682i
$959$	−1.61064	−	2.78971i	−0.0520103	−	0.0900846i
$960$	−4.62293	−	10.3833i	−0.149204	−	0.335118i
$961$	−2.61691	+	4.53263i	−0.0844166	+	0.146214i
$962$	50.7696			1.63688
$963$	−56.4792	−	12.0050i	−1.82002	−	0.386856i
$964$	−19.5965			−0.631162
$965$	4.35380	−	7.54100i	0.140154	−	0.242753i
$966$	−15.3966	+	21.1916i	−0.495376	+	0.681827i
$967$	14.7240	+	25.5028i	0.473493	+	0.820115i	0.999540	−	0.0303414i	$-0.00965946\pi$
$967$	14.7240	+	25.5028i	0.473493	+	0.820115i	−0.526046	+	0.850456i	$0.676326\pi$
$968$	0.786842	+	1.36285i	0.0252900	+	0.0438036i
$969$	−0.779773	−	0.0819574i	−0.0250499	−	0.00263285i
$970$	6.06753	−	10.5093i	0.194817	−	0.337432i
$971$	−48.9293			−1.57022			−0.785108	−	0.619359i	$-0.787393\pi$
$971$	−48.9293			−1.57022			−0.785108	+	0.619359i	$0.787393\pi$
$972$		−	28.4815i		−	0.913545i
$973$	10.7815			0.345638
$974$	−5.36850	+	9.29851i	−0.172018	+	0.297943i
$975$	−6.11048	−	0.642237i	−0.195692	−	0.0205680i
$976$	−16.5560	−	28.6758i	−0.529944	−	0.917891i
$977$	−19.8045	−	34.3024i	−0.633603	−	1.09743i	−0.986809	−	0.161887i	$-0.948242\pi$
$977$	−19.8045	−	34.3024i	−0.633603	−	1.09743i	0.353207	−	0.935545i	$-0.385091\pi$
$978$	31.6672	−	43.5862i	1.01261	−	1.39373i
$979$	−12.1184	+	20.9896i	−0.387304	+	0.670831i
$980$	−1.82709			−0.0583643
$981$	−48.7506	−	10.3623i	−1.55649	−	0.330841i
$982$	−72.5745			−2.31594
$983$	−17.3953	+	30.1295i	−0.554823	+	0.960982i	0.443094	+	0.896475i	$0.353881\pi$
$983$	−17.3953	+	30.1295i	−0.554823	+	0.960982i	−0.997917	+	0.0645066i	$0.979453\pi$
$984$	2.04545	+	4.59416i	0.0652066	+	0.146456i
$985$	−13.0541	−	22.6103i	−0.415937	−	0.720424i
$986$	−14.8794	−	25.7719i	−0.473857	−	0.820744i
$987$	0.174921	+	0.392880i	0.00556780	+	0.0125055i
$988$	0.749875	−	1.29882i	0.0238567	−	0.0413210i
$989$	57.5985			1.83153
$990$	15.5366	−	17.2551i	0.493785	−	0.548403i
$991$	10.3214			0.327870			0.163935	−	0.986471i	$-0.447581\pi$
$991$	10.3214			0.327870			0.163935	+	0.986471i	$0.447581\pi$
$992$	23.3756	−	40.4878i	0.742177	−	1.28549i
$993$	−12.2606	+	16.8753i	−0.389080	+	0.535522i
$994$	3.96885	+	6.87424i	0.125884	+	0.218038i
$995$	−1.89878	−	3.28879i	−0.0601955	−	0.104262i
$996$	−46.6174	−	4.89969i	−1.47713	−	0.155253i
$997$	3.73355	−	6.46669i	0.118243	−	0.204802i	−0.800829	−	0.598893i	$-0.795607\pi$
$997$	3.73355	−	6.46669i	0.118243	−	0.204802i	0.919071	+	0.394091i	$0.128941\pi$
$998$	−42.2725			−1.33811
$999$	−36.1541	−	11.7472i	−1.14386	−	0.371664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.d.106.1	✓	8
3.2	odd	2		945.2.i.c.316.4		8
9.2	odd	6		2835.2.a.q.1.1		4
9.4	even	3	inner	315.2.i.d.211.1	yes	8
9.5	odd	6		945.2.i.c.631.4		8
9.7	even	3		2835.2.a.l.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.d.106.1	✓	8	1.1	even	1	trivial
315.2.i.d.211.1	yes	8	9.4	even	3	inner
945.2.i.c.316.4		8	3.2	odd	2
945.2.i.c.631.4		8	9.5	odd	6
2835.2.a.l.1.4		4	9.7	even	3
2835.2.a.q.1.1		4	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)

\(f(q)\)	\(=\)	\(q+(-0.978148 + 1.69420i) q^{2} +(1.72256 + 0.181049i) q^{3} +(-0.913545 - 1.58231i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.99165 + 2.74128i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.338261 q^{8} +(2.93444 + 0.623735i) q^{9} +O(q^{10})\)	\(q+(-0.978148 + 1.69420i) q^{2} +(1.72256 + 0.181049i) q^{3} +(-0.913545 - 1.58231i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.99165 + 2.74128i) q^{6} +(0.500000 - 0.866025i) q^{7} -0.338261 q^{8} +(2.93444 + 0.623735i) q^{9} -1.95630 q^{10} +(-1.97815 + 3.42625i) q^{11} +(-1.28716 - 2.89102i) q^{12} +(1.77366 + 3.07207i) q^{13} +(0.978148 + 1.69420i) q^{14} +(0.704489 + 1.58231i) q^{15} +(2.15796 - 3.73770i) q^{16} -1.95630 q^{17} +(-3.92705 + 4.36143i) q^{18} +0.231398 q^{19} +(0.913545 - 1.58231i) q^{20} +(1.01807 - 1.40126i) q^{21} +(-3.86984 - 6.70276i) q^{22} +(3.86527 + 6.69485i) q^{23} +(-0.582676 - 0.0612417i) q^{24} +(-0.500000 + 0.866025i) q^{25} -6.93960 q^{26} +(4.94183 + 1.60570i) q^{27} -1.82709 q^{28} +(3.88791 - 6.73407i) q^{29} +(-3.36984 - 0.354185i) q^{30} +(-3.00973 - 5.21300i) q^{31} +(3.88335 + 6.72615i) q^{32} +(-4.02780 + 5.54379i) q^{33} +(1.91355 - 3.31436i) q^{34} +1.00000 q^{35} +(-1.69381 - 5.21300i) q^{36} -7.31592 q^{37} +(-0.226341 + 0.392034i) q^{38} +(2.49904 + 5.61295i) q^{39} +(-0.169131 - 0.292943i) q^{40} +(-4.29173 - 7.43350i) q^{41} +(1.37819 + 3.09546i) q^{42} +(3.72539 - 6.45256i) q^{43} +7.22851 q^{44} +(0.927051 + 2.85317i) q^{45} -15.1232 q^{46} +(-0.124148 + 0.215030i) q^{47} +(4.39393 - 6.04772i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.978148 - 1.69420i) q^{50} +(-3.36984 - 0.354185i) q^{51} +(3.24064 - 5.61295i) q^{52} -2.16982 q^{53} +(-7.55422 + 6.80185i) q^{54} -3.95630 q^{55} +(-0.169131 + 0.292943i) q^{56} +(0.398597 + 0.0418942i) q^{57} +(7.60591 + 13.1738i) q^{58} +(-0.323966 - 0.561125i) q^{59} +(1.86011 - 2.56023i) q^{60} +(3.83603 - 6.64420i) q^{61} +11.7758 q^{62} +(2.00739 - 2.22943i) q^{63} -6.56210 q^{64} +(-1.77366 + 3.07207i) q^{65} +(-5.45252 - 12.2466i) q^{66} +(3.30902 + 5.73139i) q^{67} +(1.78716 + 3.09546i) q^{68} +(5.44608 + 12.2321i) q^{69} +(-0.978148 + 1.69420i) q^{70} +4.05751 q^{71} +(-0.992608 - 0.210985i) q^{72} +13.5639 q^{73} +(7.15605 - 12.3946i) q^{74} +(-1.01807 + 1.40126i) q^{75} +(-0.211392 - 0.366142i) q^{76} +(1.97815 + 3.42625i) q^{77} +(-11.9539 - 1.25641i) q^{78} +(2.84049 - 4.91988i) q^{79} +4.31592 q^{80} +(8.22191 + 3.66063i) q^{81} +16.7918 q^{82} +(7.40599 - 12.8275i) q^{83} +(-3.14728 - 0.330792i) q^{84} +(-0.978148 - 1.69420i) q^{85} +(7.28795 + 12.6231i) q^{86} +(7.91637 - 10.8959i) q^{87} +(0.669131 - 1.15897i) q^{88} +6.12611 q^{89} +(-5.74064 - 1.22021i) q^{90} +3.54732 q^{91} +(7.06220 - 12.2321i) q^{92} +(-4.24064 - 9.52463i) q^{93} +(-0.242870 - 0.420662i) q^{94} +(0.115699 + 0.200396i) q^{95} +(5.47155 + 12.2893i) q^{96} +(-3.10154 + 5.37202i) q^{97} +1.95630 q^{98} +(-7.94183 + 8.82030i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9	\( 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9} + 2 q^{10} - 7 q^{11} + 3 q^{12} + 8 q^{13} - q^{14} + 3 q^{15} + 9 q^{16} + 2 q^{17} - 18 q^{18} + 6 q^{19} + q^{20} - 7 q^{22} + 8 q^{23} + 6 q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{28} - q^{29} - 3 q^{30} + 9 q^{34} + 8 q^{35} - 6 q^{36} - 42 q^{37} - 8 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} + 3 q^{42} + 7 q^{43} + 6 q^{44} - 6 q^{45} - 46 q^{46} + 2 q^{47} + 30 q^{48} - 4 q^{49} + q^{50} - 3 q^{51} + 7 q^{52} - 16 q^{53} - 36 q^{54} - 14 q^{55} + 3 q^{56} - 24 q^{57} + 19 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 30 q^{62} + 3 q^{63} - 14 q^{64} - 8 q^{65} - 9 q^{66} + 22 q^{67} + q^{68} + 51 q^{69} + q^{70} + 26 q^{71} - 21 q^{72} - 8 q^{73} - 9 q^{74} + 13 q^{76} + 7 q^{77} - 21 q^{78} + 24 q^{79} + 18 q^{80} + 9 q^{81} + 19 q^{83} - 12 q^{84} + q^{85} + 27 q^{86} + 45 q^{87} + q^{88} + 30 q^{89} - 27 q^{90} + 16 q^{91} - 3 q^{92} - 15 q^{93} + 7 q^{94} + 3 q^{95} + 30 q^{96} + 12 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9 + 2 * q^10 - 7 * q^11 + 3 * q^12 + 8 * q^13 - q^14 + 3 * q^15 + 9 * q^16 + 2 * q^17 - 18 * q^18 + 6 * q^19 + q^20 - 7 * q^22 + 8 * q^23 + 6 * q^24 - 4 * q^25 - 6 * q^26 - 2 * q^28 - q^29 - 3 * q^30 + 9 * q^34 + 8 * q^35 - 6 * q^36 - 42 * q^37 - 8 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 + 3 * q^42 + 7 * q^43 + 6 * q^44 - 6 * q^45 - 46 * q^46 + 2 * q^47 + 30 * q^48 - 4 * q^49 + q^50 - 3 * q^51 + 7 * q^52 - 16 * q^53 - 36 * q^54 - 14 * q^55 + 3 * q^56 - 24 * q^57 + 19 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 30 * q^62 + 3 * q^63 - 14 * q^64 - 8 * q^65 - 9 * q^66 + 22 * q^67 + q^68 + 51 * q^69 + q^70 + 26 * q^71 - 21 * q^72 - 8 * q^73 - 9 * q^74 + 13 * q^76 + 7 * q^77 - 21 * q^78 + 24 * q^79 + 18 * q^80 + 9 * q^81 + 19 * q^83 - 12 * q^84 + q^85 + 27 * q^86 + 45 * q^87 + q^88 + 30 * q^89 - 27 * q^90 + 16 * q^91 - 3 * q^92 - 15 * q^93 + 7 * q^94 + 3 * q^95 + 30 * q^96 + 12 * q^97 - 2 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more