LMFDB - Embedded newform 315.2.l.b.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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([2, 0, 2]))

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Character	$\chi$	$=$	315.151
Dual form			315.2.l.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56008 q^{2} +(-1.18219 - 1.26587i) q^{3} +4.55403 q^{4} +(0.500000 - 0.866025i) q^{5} +(3.02651 + 3.24073i) q^{6} +(-0.992363 + 2.45259i) q^{7} -6.53853 q^{8} +(-0.204852 + 2.99300i) q^{9} +O(q^{10})$	\(q-2.56008 q^{2} +(-1.18219 - 1.26587i) q^{3} +4.55403 q^{4} +(0.500000 - 0.866025i) q^{5} +(3.02651 + 3.24073i) q^{6} +(-0.992363 + 2.45259i) q^{7} -6.53853 q^{8} +(-0.204852 + 2.99300i) q^{9} +(-1.28004 + 2.21710i) q^{10} +(-1.90524 - 3.29997i) q^{11} +(-5.38373 - 5.76481i) q^{12} +(-0.798588 - 1.38320i) q^{13} +(2.54053 - 6.27885i) q^{14} +(-1.68737 + 0.390872i) q^{15} +7.63112 q^{16} +(-1.84010 + 3.18715i) q^{17} +(0.524439 - 7.66233i) q^{18} +(1.68636 + 2.92086i) q^{19} +(2.27701 - 3.94390i) q^{20} +(4.27783 - 1.64323i) q^{21} +(4.87757 + 8.44820i) q^{22} +(-0.452249 + 0.783319i) q^{23} +(7.72978 + 8.27692i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.04445 + 3.54110i) q^{26} +(4.03092 - 3.27898i) q^{27} +(-4.51925 + 11.1692i) q^{28} +(-4.97559 + 8.61797i) q^{29} +(4.31981 - 1.00067i) q^{30} -4.55044 q^{31} -6.45926 q^{32} +(-1.92498 + 6.31298i) q^{33} +(4.71081 - 8.15936i) q^{34} +(1.62783 + 2.08571i) q^{35} +(-0.932902 + 13.6302i) q^{36} +(3.90897 + 6.77053i) q^{37} +(-4.31722 - 7.47764i) q^{38} +(-0.806862 + 2.64611i) q^{39} +(-3.26926 + 5.66253i) q^{40} +(6.38119 + 11.0525i) q^{41} +(-10.9516 + 4.20681i) q^{42} +(0.849513 - 1.47140i) q^{43} +(-8.67652 - 15.0282i) q^{44} +(2.48959 + 1.67391i) q^{45} +(1.15780 - 2.00536i) q^{46} +9.68162 q^{47} +(-9.02144 - 9.66001i) q^{48} +(-5.03043 - 4.86773i) q^{49} +(1.28004 + 2.21710i) q^{50} +(6.20986 - 1.43849i) q^{51} +(-3.63679 - 6.29911i) q^{52} +(-1.61768 + 2.80191i) q^{53} +(-10.3195 + 8.39446i) q^{54} -3.81048 q^{55} +(6.48859 - 16.0364i) q^{56} +(1.70383 - 5.58772i) q^{57} +(12.7379 - 22.0627i) q^{58} +2.25833 q^{59} +(-7.68433 + 1.78004i) q^{60} +10.2522 q^{61} +11.6495 q^{62} +(-7.13732 - 3.47256i) q^{63} +1.27399 q^{64} -1.59718 q^{65} +(4.92811 - 16.1618i) q^{66} -3.66677 q^{67} +(-8.37987 + 14.5144i) q^{68} +(1.52622 - 0.353543i) q^{69} +(-4.16737 - 5.33959i) q^{70} -13.8231 q^{71} +(1.33943 - 19.5698i) q^{72} +(-1.47850 + 2.56083i) q^{73} +(-10.0073 - 17.3331i) q^{74} +(-0.505180 + 1.65674i) q^{75} +(7.67972 + 13.3017i) q^{76} +(9.98418 - 1.39801i) q^{77} +(2.06563 - 6.77426i) q^{78} -13.9679 q^{79} +(3.81556 - 6.60875i) q^{80} +(-8.91607 - 1.22624i) q^{81} +(-16.3364 - 28.2954i) q^{82} +(-2.67992 + 4.64177i) q^{83} +(19.4813 - 7.48332i) q^{84} +(1.84010 + 3.18715i) q^{85} +(-2.17483 + 3.76691i) q^{86} +(16.7913 - 3.88963i) q^{87} +(12.4575 + 21.5770i) q^{88} +(-0.998354 - 1.72920i) q^{89} +(-6.37355 - 4.28534i) q^{90} +(4.18491 - 0.585980i) q^{91} +(-2.05956 + 3.56726i) q^{92} +(5.37948 + 5.76026i) q^{93} -24.7858 q^{94} +3.37272 q^{95} +(7.63607 + 8.17658i) q^{96} +(-5.25748 + 9.10623i) q^{97} +(12.8783 + 12.4618i) q^{98} +(10.2671 - 5.02637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.56008			−1.81025			−0.905126	−	0.425143i	$-0.860224\pi$
$2$	−2.56008			−1.81025			−0.905126	+	0.425143i	$0.860224\pi$
$3$	−1.18219	−	1.26587i	−0.682538	−	0.730850i
$3$	−1.18219	−	1.26587i	−0.682538	−	0.730850i
$4$	4.55403			2.27701
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	3.02651	+	3.24073i	1.23557	+	1.32302i
$7$	−0.992363	+	2.45259i	−0.375078	+	0.926993i
$7$	−0.992363	+	2.45259i	−0.375078	+	0.926993i
$8$	−6.53853			−2.31172
$9$	−0.204852	+	2.99300i	−0.0682840	+	0.997666i
$10$	−1.28004	+	2.21710i	−0.404785	+	0.701108i
$11$	−1.90524	−	3.29997i	−0.574451	−	0.994979i	−0.996101	−	0.0882201i	$-0.971882\pi$
$11$	−1.90524	−	3.29997i	−0.574451	−	0.994979i	0.421650	−	0.906759i	$-0.361451\pi$
$12$	−5.38373	−	5.76481i	−1.55415	−	1.66416i
$13$	−0.798588	−	1.38320i	−0.221488	−	0.383629i	0.733772	−	0.679396i	$-0.237758\pi$
$13$	−0.798588	−	1.38320i	−0.221488	−	0.383629i	−0.955260	+	0.295767i	$0.904425\pi$
$14$	2.54053	−	6.27885i	0.678986	−	1.67809i
$15$	−1.68737	+	0.390872i	−0.435677	+	0.100923i
$16$	7.63112			1.90778
$17$	−1.84010	+	3.18715i	−0.446290	+	0.772997i	−0.998141	−	0.0609458i	$-0.980588\pi$
$17$	−1.84010	+	3.18715i	−0.446290	+	0.772997i	0.551851	+	0.833943i	$0.313922\pi$
$18$	0.524439	−	7.66233i	0.123611	−	1.80603i
$19$	1.68636	+	2.92086i	0.386877	+	0.670091i	0.992028	−	0.126020i	$-0.0402204\pi$
$19$	1.68636	+	2.92086i	0.386877	+	0.670091i	−0.605151	+	0.796111i	$0.706887\pi$
$20$	2.27701	−	3.94390i	0.509156	−	0.881884i
$21$	4.27783	−	1.64323i	0.933498	−	0.358582i
$22$	4.87757	+	8.44820i	1.03990	+	1.80116i
$23$	−0.452249	+	0.783319i	−0.0943005	+	0.163333i	−0.909316	−	0.416105i	$-0.863395\pi$
$23$	−0.452249	+	0.783319i	−0.0943005	+	0.163333i	0.815016	+	0.579439i	$0.196728\pi$
$24$	7.72978	+	8.27692i	1.57784	+	1.68952i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.04445	+	3.54110i	0.400950	+	0.694466i
$27$	4.03092	−	3.27898i	0.775751	−	0.631039i
$28$	−4.51925	+	11.1692i	−0.854058	+	2.11078i
$29$	−4.97559	+	8.61797i	−0.923943	+	1.60032i	−0.130691	+	0.991423i	$0.541719\pi$
$29$	−4.97559	+	8.61797i	−0.923943	+	1.60032i	−0.793252	+	0.608893i	$0.791614\pi$
$30$	4.31981	−	1.00067i	0.788686	−	0.182696i
$31$	−4.55044			−0.817283			−0.408641	−	0.912695i	$-0.633997\pi$
$31$	−4.55044			−0.817283			−0.408641	+	0.912695i	$0.633997\pi$
$32$	−6.45926			−1.14185
$33$	−1.92498	+	6.31298i	−0.335096	+	1.09895i
$34$	4.71081	−	8.15936i	0.807897	−	1.39932i
$35$	1.62783	+	2.08571i	0.275153	+	0.352549i
$36$	−0.932902	+	13.6302i	−0.155484	+	2.27170i
$37$	3.90897	+	6.77053i	0.642630	+	1.11307i	0.984843	+	0.173446i	$0.0554901\pi$
$37$	3.90897	+	6.77053i	0.642630	+	1.11307i	−0.342213	+	0.939622i	$0.611177\pi$
$38$	−4.31722	−	7.47764i	−0.700345	−	1.21303i
$39$	−0.806862	+	2.64611i	−0.129201	+	0.423716i
$40$	−3.26926	+	5.66253i	−0.516916	+	0.895325i
$41$	6.38119	+	11.0525i	0.996574	+	1.72612i	0.569914	+	0.821704i	$0.306976\pi$
$41$	6.38119	+	11.0525i	0.996574	+	1.72612i	0.426660	+	0.904412i	$0.359690\pi$
$42$	−10.9516	+	4.20681i	−1.68987	+	0.649124i
$43$	0.849513	−	1.47140i	0.129550	−	0.224386i	−0.793953	−	0.607980i	$-0.791980\pi$
$43$	0.849513	−	1.47140i	0.129550	−	0.224386i	0.923502	+	0.383593i	$0.125314\pi$
$44$	−8.67652	−	15.0282i	−1.30803	−	2.26558i
$45$	2.48959	+	1.67391i	0.371126	+	0.249531i
$46$	1.15780	−	2.00536i	0.170708	−	0.295675i
$47$	9.68162			1.41221			0.706105	−	0.708107i	$-0.250451\pi$
$47$	9.68162			1.41221			0.706105	+	0.708107i	$0.250451\pi$
$48$	−9.02144	−	9.66001i	−1.30213	−	1.39430i
$49$	−5.03043	−	4.86773i	−0.718633	−	0.695390i
$50$	1.28004	+	2.21710i	0.181025	+	0.313545i
$51$	6.20986	−	1.43849i	0.869555	−	0.201429i
$52$	−3.63679	−	6.29911i	−0.504333	−	0.873530i
$53$	−1.61768	+	2.80191i	−0.222206	+	0.384871i	−0.955477	−	0.295064i	$-0.904659\pi$
$53$	−1.61768	+	2.80191i	−0.222206	+	0.384871i	0.733272	+	0.679936i	$0.237992\pi$
$54$	−10.3195	+	8.39446i	−1.40430	+	1.14234i
$55$	−3.81048			−0.513805
$56$	6.48859	−	16.0364i	0.867075	−	2.14295i
$57$	1.70383	−	5.58772i	0.225678	−	0.740112i
$58$	12.7379	−	22.0627i	1.67257	−	2.89698i
$59$	2.25833			0.294010			0.147005	−	0.989136i	$-0.453037\pi$
$59$	2.25833			0.294010			0.147005	+	0.989136i	$0.453037\pi$
$60$	−7.68433	+	1.78004i	−0.992043	+	0.229802i
$61$	10.2522			1.31266			0.656330	−	0.754474i	$-0.272108\pi$
$61$	10.2522			1.31266			0.656330	+	0.754474i	$0.272108\pi$
$62$	11.6495			1.47949
$63$	−7.13732	−	3.47256i	−0.899218	−	0.437501i
$64$	1.27399			0.159249
$65$	−1.59718			−0.198105
$66$	4.92811	−	16.1618i	0.606608	−	1.98937i
$67$	−3.66677			−0.447967			−0.223984	−	0.974593i	$-0.571906\pi$
$67$	−3.66677			−0.447967			−0.223984	+	0.974593i	$0.571906\pi$
$68$	−8.37987	+	14.5144i	−1.01621	+	1.76012i
$69$	1.52622	−	0.353543i	0.183736	−	0.0425616i
$70$	−4.16737	−	5.33959i	−0.498096	−	0.638203i
$71$	−13.8231			−1.64050			−0.820251	−	0.572004i	$-0.806166\pi$
$71$	−13.8231			−1.64050			−0.820251	+	0.572004i	$0.806166\pi$
$72$	1.33943	−	19.5698i	0.157853	−	2.30632i
$73$	−1.47850	+	2.56083i	−0.173045	+	0.299723i	−0.939483	−	0.342595i	$-0.888694\pi$
$73$	−1.47850	+	2.56083i	−0.173045	+	0.299723i	0.766438	+	0.642318i	$0.222027\pi$
$74$	−10.0073	−	17.3331i	−1.16332	−	2.01493i
$75$	−0.505180	+	1.65674i	−0.0583332	+	0.191304i
$76$	7.67972	+	13.3017i	0.880925	+	1.52581i
$77$	9.98418	−	1.39801i	1.13780	−	0.159318i
$78$	2.06563	−	6.77426i	0.233887	−	0.767034i
$79$	−13.9679			−1.57151			−0.785755	−	0.618537i	$-0.787726\pi$
$79$	−13.9679			−1.57151			−0.785755	+	0.618537i	$0.787726\pi$
$80$	3.81556	−	6.60875i	0.426593	−	0.738880i
$81$	−8.91607	−	1.22624i	−0.990675	−	0.136249i
$82$	−16.3364	−	28.2954i	−1.80405	−	3.12471i
$83$	−2.67992	+	4.64177i	−0.294160	+	0.509500i	−0.974789	−	0.223128i	$-0.928373\pi$
$83$	−2.67992	+	4.64177i	−0.294160	+	0.509500i	0.680629	+	0.732628i	$0.261707\pi$
$84$	19.4813	−	7.48332i	2.12559	−	0.816497i
$85$	1.84010	+	3.18715i	0.199587	+	0.345695i
$86$	−2.17483	+	3.76691i	−0.234517	+	0.406196i
$87$	16.7913	−	3.88963i	1.80022	−	0.417013i
$88$	12.4575	+	21.5770i	1.32797	+	2.30011i
$89$	−0.998354	−	1.72920i	−0.105825	−	0.183295i	0.808250	−	0.588840i	$-0.200415\pi$
$89$	−0.998354	−	1.72920i	−0.105825	−	0.183295i	−0.914075	+	0.405545i	$0.867082\pi$
$90$	−6.37355	−	4.28534i	−0.671831	−	0.451714i
$91$	4.18491	−	0.585980i	0.438697	−	0.0614274i
$92$	−2.05956	+	3.56726i	−0.214724	+	0.371912i
$93$	5.37948	+	5.76026i	0.557827	+	0.597311i
$94$	−24.7858			−2.55646
$95$	3.37272			0.346033
$96$	7.63607	+	8.17658i	0.779353	+	0.834518i
$97$	−5.25748	+	9.10623i	−0.533816	+	0.924597i	0.465403	+	0.885099i	$0.345909\pi$
$97$	−5.25748	+	9.10623i	−0.533816	+	0.924597i	−0.999220	+	0.0394984i	$0.987424\pi$
$98$	12.8783	+	12.4618i	1.30091	+	1.25883i
$99$	10.2671	−	5.02637i	1.03188	−	0.505169i
$100$	−2.27701	−	3.94390i	−0.227701	−	0.394390i
$101$	0.438328	+	0.759207i	0.0436153	+	0.0755439i	0.887009	−	0.461752i	$-0.152779\pi$
$101$	0.438328	+	0.759207i	0.0436153	+	0.0755439i	−0.843394	+	0.537296i	$0.819446\pi$
$102$	−15.8978	+	3.68265i	−1.57411	+	0.364637i
$103$	1.82289	−	3.15734i	0.179615	−	0.311102i	−0.762134	−	0.647419i	$-0.775848\pi$
$103$	1.82289	−	3.15734i	0.179615	−	0.311102i	0.941749	+	0.336318i	$0.109182\pi$
$104$	5.22159	+	9.04406i	0.512019	+	0.886843i
$105$	0.715834	−	4.52632i	0.0698583	−	0.441724i
$106$	4.14140	−	7.17311i	0.402248	−	0.696714i
$107$	−0.844077	−	1.46198i	−0.0816000	−	0.141335i	0.822337	−	0.569000i	$-0.192670\pi$
$107$	−0.844077	−	1.46198i	−0.0816000	−	0.141335i	−0.903937	+	0.427665i	$0.859336\pi$
$108$	18.3569	−	14.9326i	1.76640	−	1.43689i
$109$	2.47929	−	4.29426i	0.237473	−	0.411315i	−0.722516	−	0.691355i	$-0.757014\pi$
$109$	2.47929	−	4.29426i	0.237473	−	0.411315i	0.959988	+	0.280039i	$0.0903475\pi$
$110$	9.75515			0.930117
$111$	3.94946	−	12.9523i	0.374867	−	1.22938i
$112$	−7.57284	+	18.7160i	−0.715567	+	1.76850i
$113$	1.48453	+	2.57129i	0.139653	+	0.241886i	0.927365	−	0.374157i	$-0.122068\pi$
$113$	1.48453	+	2.57129i	0.139653	+	0.241886i	−0.787712	+	0.616043i	$0.788735\pi$
$114$	−4.36195	+	14.3050i	−0.408534	+	1.33979i
$115$	0.452249	+	0.783319i	0.0421725	+	0.0730449i
$116$	−22.6590	+	39.2465i	−2.10383	+	3.64394i
$117$	4.30349	−	2.10682i	0.397858	−	0.194776i
$118$	−5.78153			−0.532233
$119$	−5.99073	−	7.67583i	−0.549169	−	0.703642i
$120$	11.0329	−	2.55573i	1.00716	−	0.233305i
$121$	−1.75988	+	3.04819i	−0.159989	+	0.277108i
$122$	−26.2465			−2.37625
$123$	6.44730	−	21.1440i	0.581333	−	1.90649i
$124$	−20.7228			−1.86097
$125$	−1.00000			−0.0894427
$126$	18.2721	+	8.89004i	1.62781	+	0.791988i
$127$	−17.5038			−1.55321			−0.776606	−	0.629987i	$-0.783060\pi$
$127$	−17.5038			−1.55321			−0.776606	+	0.629987i	$0.783060\pi$
$128$	9.65699			0.853565
$129$	−2.86689	+	0.664102i	−0.252415	+	0.0584709i
$130$	4.08891			0.358621
$131$	−0.416773	+	0.721872i	−0.0364136	+	0.0630703i	−0.883658	−	0.468133i	$-0.844927\pi$
$131$	−0.416773	+	0.721872i	−0.0364136	+	0.0630703i	0.847244	+	0.531204i	$0.178260\pi$
$132$	−8.76641	+	28.7495i	−0.763018	+	2.50232i
$133$	−8.83716	+	1.23740i	−0.766279	+	0.107296i
$134$	9.38724			0.810934
$135$	−0.824218	−	5.13037i	−0.0709374	−	0.441552i
$136$	12.0315	−	20.8393i	1.03170	−	1.78695i
$137$	2.55340	+	4.42261i	0.218151	+	0.377849i	0.954243	−	0.299033i	$-0.0966640\pi$
$137$	2.55340	+	4.42261i	0.218151	+	0.377849i	−0.736091	+	0.676882i	$0.763331\pi$
$138$	−3.90726	+	0.905100i	−0.332608	+	0.0770473i
$139$	3.11308	+	5.39202i	0.264048	+	0.457345i	0.967314	−	0.253582i	$-0.0816088\pi$
$139$	3.11308	+	5.39202i	0.264048	+	0.457345i	−0.703265	+	0.710927i	$0.748275\pi$
$140$	7.41317	+	9.49838i	0.626527	+	0.802759i
$141$	−11.4455	−	12.2557i	−0.963887	−	1.03211i
$142$	35.3883			2.96972
$143$	−3.04300	+	5.27064i	−0.254469	+	0.440753i
$144$	−1.56325	+	22.8399i	−0.130271	+	1.90333i
$145$	4.97559	+	8.61797i	0.413200	+	0.715683i
$146$	3.78508	−	6.55595i	0.313255	−	0.542574i
$147$	−0.214982	+	12.1224i	−0.0177314	+	0.999843i
$148$	17.8015	+	30.8332i	1.46328	+	2.53447i
$149$	2.93153	−	5.07756i	0.240160	−	0.415970i	−0.720599	−	0.693352i	$-0.756133\pi$
$149$	2.93153	−	5.07756i	0.240160	−	0.415970i	0.960760	+	0.277382i	$0.0894667\pi$
$150$	1.29330	−	4.24140i	0.105598	−	0.346309i
$151$	9.13466	+	15.8217i	0.743368	+	1.28755i	0.950953	+	0.309335i	$0.100106\pi$
$151$	9.13466	+	15.8217i	0.743368	+	1.28755i	−0.207585	+	0.978217i	$0.566560\pi$
$152$	−11.0263	−	19.0981i	−0.894351	−	1.54906i
$153$	−9.16218	−	6.16031i	−0.740718	−	0.498032i
$154$	−25.5603	+	3.57902i	−2.05971	+	0.288405i
$155$	−2.27522	+	3.94080i	−0.182750	+	0.316532i
$156$	−3.67447	+	12.0505i	−0.294193	+	0.964809i
$157$	−6.61702			−0.528095			−0.264048	−	0.964510i	$-0.585058\pi$
$157$	−6.61702			−0.528095			−0.264048	+	0.964510i	$0.585058\pi$
$158$	35.7590			2.84483
$159$	5.45925	−	1.26461i	0.432947	−	0.100290i
$160$	−3.22963	+	5.59388i	−0.255324	+	0.442235i
$161$	−1.47237	−	1.88652i	−0.116039	−	0.148679i
$162$	22.8259	+	3.13929i	1.79337	+	0.246646i
$163$	−1.21749	−	2.10876i	−0.0953615	−	0.165171i	0.814398	−	0.580307i	$-0.197067\pi$
$163$	−1.21749	−	2.10876i	−0.0953615	−	0.165171i	−0.909759	+	0.415136i	$0.863734\pi$
$164$	29.0601	+	50.3336i	2.26921	+	3.93039i
$165$	4.50471	+	4.82357i	0.350691	+	0.375514i
$166$	6.86083	−	11.8833i	0.532504	−	0.922324i
$167$	−9.56538	−	16.5677i	−0.740191	−	1.28205i	−0.952408	−	0.304826i	$-0.901402\pi$
$167$	−9.56538	−	16.5677i	−0.740191	−	1.28205i	0.212217	−	0.977223i	$-0.431932\pi$
$168$	−27.9707	+	10.7443i	−2.15799	+	0.828941i
$169$	5.22451	−	9.04912i	0.401886	−	0.696086i
$170$	−4.71081	−	8.15936i	−0.361303	−	0.625795i
$171$	−9.08758	+	4.44892i	−0.694944	+	0.340218i
$172$	3.86871	−	6.70080i	0.294986	−	0.510931i
$173$	−20.8553			−1.58560			−0.792800	−	0.609482i	$-0.791378\pi$
$173$	−20.8553			−1.58560			−0.792800	+	0.609482i	$0.791378\pi$
$174$	−42.9872	+	9.95779i	−3.25885	+	0.754898i
$175$	2.62019	−	0.366885i	0.198068	−	0.0277339i
$176$	−14.5391	−	25.1825i	−1.09593	−	1.89820i
$177$	−2.66978	−	2.85876i	−0.200673	−	0.214877i
$178$	2.55587	+	4.42690i	0.191570	+	0.331810i
$179$	4.83593	−	8.37608i	0.361455	−	0.626058i	−0.626746	−	0.779224i	$-0.715614\pi$
$179$	4.83593	−	8.37608i	0.361455	−	0.626058i	0.988200	+	0.153166i	$0.0489469\pi$
$180$	11.3376	+	7.62302i	0.845058	+	0.568186i
$181$	9.86830			0.733505			0.366752	−	0.930319i	$-0.380470\pi$
$181$	9.86830			0.733505			0.366752	+	0.930319i	$0.380470\pi$
$182$	−10.7137	+	1.50016i	−0.794153	+	0.111199i
$183$	−12.1201	−	12.9780i	−0.895940	−	0.959358i
$184$	2.95705	−	5.12175i	0.217996	−	0.377581i
$185$	7.81793			0.574786
$186$	−13.7719	−	14.7468i	−1.00981	−	1.08128i
$187$	14.0233			1.02549
$188$	44.0904			3.21562
$189$	4.04186	+	13.1401i	0.294002	+	0.955805i
$190$	−8.63444			−0.626408
$191$	−26.5636			−1.92207			−0.961037	−	0.276418i	$-0.910852\pi$
$191$	−26.5636			−1.92207			−0.961037	+	0.276418i	$0.910852\pi$
$192$	−1.50610	−	1.61271i	−0.108693	−	0.116387i
$193$	−14.4974			−1.04355			−0.521774	−	0.853084i	$-0.674730\pi$
$193$	−14.4974			−1.04355			−0.521774	+	0.853084i	$0.674730\pi$
$194$	13.4596	−	23.3127i	0.966343	−	1.67375i
$195$	1.88817	+	2.02182i	0.135214	+	0.144785i
$196$	−22.9087	−	22.1678i	−1.63634	−	1.58341i
$197$	17.2702			1.23045			0.615227	−	0.788350i	$-0.289065\pi$
$197$	17.2702			1.23045			0.615227	+	0.788350i	$0.289065\pi$
$198$	−26.2846	+	12.8679i	−1.86797	+	0.914484i
$199$	6.81936	−	11.8115i	0.483411	−	0.837293i	−0.516407	−	0.856343i	$-0.672731\pi$
$199$	6.81936	−	11.8115i	0.483411	−	0.837293i	0.999819	+	0.0190501i	$0.00606420\pi$
$200$	3.26926	+	5.66253i	0.231172	+	0.400401i
$201$	4.33482	+	4.64165i	0.305755	+	0.327397i
$202$	−1.12216	−	1.94363i	−0.0789547	−	0.136754i
$203$	−16.1988	−	20.7552i	−1.13693	−	1.45673i
$204$	28.2799	−	6.55091i	1.97999	−	0.458656i
$205$	12.7624			0.891363
$206$	−4.66675	+	8.08304i	−0.325148	+	0.563172i
$207$	−2.25183	−	1.51405i	−0.156513	−	0.105233i
$208$	−6.09412	−	10.5553i	−0.422551	−	0.731881i
$209$	6.42583	−	11.1299i	0.444484	−	0.769869i
$210$	−1.83260	+	11.5878i	−0.126461	+	0.799631i
$211$	−8.11825	−	14.0612i	−0.558883	−	0.968014i	−0.997590	−	0.0693840i	$-0.977897\pi$
$211$	−8.11825	−	14.0612i	−0.558883	−	0.968014i	0.438707	−	0.898630i	$-0.355437\pi$
$212$	−7.36697	+	12.7600i	−0.505965	+	0.876358i
$213$	16.3415	+	17.4983i	1.11970	+	1.19896i
$214$	2.16091	+	3.74280i	0.147717	+	0.255853i
$215$	−0.849513	−	1.47140i	−0.0579363	−	0.100349i
$216$	−26.3563	+	21.4397i	−1.79332	+	1.45879i
$217$	4.51569	−	11.1604i	0.306545	−	0.757616i
$218$	−6.34719	+	10.9937i	−0.429886	+	0.744585i
$219$	4.98955	−	1.15581i	0.337163	−	0.0781022i
$220$	−17.3530			−1.16994
$221$	5.87793			0.395392
$222$	−10.1110	+	33.1590i	−0.678603	+	2.22548i
$223$	−2.64925	+	4.58864i	−0.177407	+	0.307278i	−0.940992	−	0.338430i	$-0.890104\pi$
$223$	−2.64925	+	4.58864i	−0.177407	+	0.307278i	0.763585	+	0.645708i	$0.223438\pi$
$224$	6.40993	−	15.8419i	0.428281	−	1.05848i
$225$	2.69444	−	1.31909i	0.179629	−	0.0879395i
$226$	−3.80053	−	6.58271i	−0.252808	−	0.437876i
$227$	12.4412	+	21.5487i	0.825749	+	1.43024i	0.901346	+	0.433101i	$0.142581\pi$
$227$	12.4412	+	21.5487i	0.825749	+	1.43024i	−0.0755967	+	0.997138i	$0.524086\pi$
$228$	7.75929	−	25.4466i	0.513871	−	1.68524i
$229$	−8.22112	+	14.2394i	−0.543267	+	0.940966i	0.455447	+	0.890263i	$0.349479\pi$
$229$	−8.22112	+	14.2394i	−0.543267	+	0.940966i	−0.998714	+	0.0507029i	$0.983854\pi$
$230$	−1.15780	−	2.00536i	−0.0763428	−	0.132230i
$231$	−13.5729	−	10.9860i	−0.893031	−	0.722823i
$232$	32.5330	−	56.3488i	2.13590	−	3.69948i
$233$	2.70224	+	4.68042i	0.177030	+	0.306624i	0.940862	−	0.338791i	$-0.110018\pi$
$233$	2.70224	+	4.68042i	0.177030	+	0.306624i	−0.763832	+	0.645415i	$0.776684\pi$
$234$	−11.0173	+	5.39364i	−0.720224	+	0.352593i
$235$	4.84081	−	8.38453i	0.315780	−	0.546946i
$236$	10.2845			0.669465
$237$	16.5127	+	17.6815i	1.07262	+	1.14854i
$238$	15.3368	+	19.6508i	0.994135	+	1.27377i
$239$	5.37499	+	9.30975i	0.347679	+	0.602198i	0.985837	−	0.167708i	$-0.0536365\pi$
$239$	5.37499	+	9.30975i	0.347679	+	0.602198i	−0.638158	+	0.769906i	$0.720303\pi$
$240$	−12.8765	+	2.98279i	−0.831176	+	0.192538i
$241$	−5.50687	−	9.53817i	−0.354728	−	0.614408i	0.632343	−	0.774689i	$-0.282093\pi$
$241$	−5.50687	−	9.53817i	−0.354728	−	0.614408i	−0.987071	+	0.160281i	$0.948760\pi$
$242$	4.50543	−	7.80363i	0.289620	−	0.501636i
$243$	8.98823	+	12.7362i	0.576595	+	0.817030i
$244$	46.6888			2.98895
$245$	−6.73079	+	1.92262i	−0.430014	+	0.122832i
$246$	−16.5056	+	54.1303i	−1.05236	+	3.45122i
$247$	2.69341	−	4.66513i	0.171378	−	0.296835i
$248$	29.7532			1.88933
$249$	9.04405	−	2.09502i	0.573144	−	0.132766i
$250$	2.56008			0.161914
$251$	3.43070			0.216544			0.108272	−	0.994121i	$-0.465468\pi$
$251$	3.43070			0.216544			0.108272	+	0.994121i	$0.465468\pi$
$252$	−32.5036	−	15.8141i	−2.04753	−	0.996197i
$253$	3.44657			0.216684
$254$	44.8112			2.81171
$255$	1.85916	−	6.09714i	0.116425	−	0.381818i
$256$	−27.2707			−1.70442
$257$	6.01749	−	10.4226i	0.375361	−	0.650144i	−0.615020	−	0.788512i	$-0.710852\pi$
$257$	6.01749	−	10.4226i	0.375361	−	0.650144i	0.990381	+	0.138367i	$0.0441854\pi$
$258$	7.33947	−	1.70016i	0.456936	−	0.105847i
$259$	−20.4845	+	2.86828i	−1.27284	+	0.178226i
$260$	−7.27359			−0.451089
$261$	−24.7743	−	16.6573i	−1.53349	−	1.03106i
$262$	1.06697	−	1.84805i	0.0659179	−	0.114173i
$263$	−8.88295	−	15.3857i	−0.547746	−	0.948725i	−0.998429	−	0.0560401i	$-0.982153\pi$
$263$	−8.88295	−	15.3857i	−0.547746	−	0.948725i	0.450682	−	0.892684i	$-0.351181\pi$
$264$	12.5865	−	41.2776i	0.774647	−	2.54046i
$265$	1.61768	+	2.80191i	0.0993733	+	0.172120i
$266$	22.6239	−	3.16785i	1.38716	−	0.194233i
$267$	−1.00870	+	3.30803i	−0.0617313	+	0.202448i
$268$	−16.6986			−1.02003
$269$	1.63482	−	2.83159i	0.0996766	−	0.172645i	−0.811874	−	0.583832i	$-0.801553\pi$
$269$	1.63482	−	2.83159i	0.0996766	−	0.172645i	0.911551	+	0.411187i	$0.134886\pi$
$270$	2.11007	+	13.1342i	0.128415	+	0.799320i
$271$	15.1243	+	26.1960i	0.918735	+	1.59129i	0.801340	+	0.598210i	$0.204121\pi$
$271$	15.1243	+	26.1960i	0.918735	+	1.59129i	0.117395	+	0.993085i	$0.462546\pi$
$272$	−14.0420	+	24.3215i	−0.851423	+	1.47471i
$273$	−5.68913	−	4.60480i	−0.344322	−	0.278695i
$274$	−6.53691	−	11.3223i	−0.394909	−	0.684002i
$275$	−1.90524	+	3.29997i	−0.114890	+	0.198996i
$276$	6.95047	−	1.61005i	0.418369	−	0.0969134i
$277$	−8.23293	−	14.2598i	−0.494669	−	0.856791i	0.505313	−	0.862936i	$-0.331377\pi$
$277$	−8.23293	−	14.2598i	−0.494669	−	0.856791i	−0.999981	+	0.00614527i	$0.998044\pi$
$278$	−7.96976	−	13.8040i	−0.477994	−	0.827910i
$279$	0.932167	−	13.6195i	0.0558074	−	0.815375i
$280$	−10.6436	−	13.6375i	−0.636076	−	0.814994i
$281$	6.92464	−	11.9938i	0.413089	−	0.715492i	−0.582136	−	0.813091i	$-0.697783\pi$
$281$	6.92464	−	11.9938i	0.413089	−	0.715492i	0.995226	+	0.0975993i	$0.0311164\pi$
$282$	29.3015	+	31.3755i	1.74488	+	1.86839i
$283$	6.16676			0.366576			0.183288	−	0.983059i	$-0.441326\pi$
$283$	6.16676			0.366576			0.183288	+	0.983059i	$0.441326\pi$
$284$	−62.9508			−3.73545
$285$	−3.98719	−	4.26942i	−0.236181	−	0.252899i
$286$	7.79034	−	13.4933i	0.460653	−	0.797874i
$287$	−33.4398	+	4.68232i	−1.97389	+	0.276389i
$288$	1.32319	−	19.3325i	0.0779698	−	1.13918i
$289$	1.72806	+	2.99309i	0.101651	+	0.176064i
$290$	−12.7379	−	22.0627i	−0.747996	−	1.29557i
$291$	17.7426	−	4.11000i	1.04009	−	0.240933i
$292$	−6.73313	+	11.6621i	−0.394026	+	0.682474i
$293$	3.33662	+	5.77920i	0.194927	+	0.337624i	0.946877	−	0.321597i	$-0.104220\pi$
$293$	3.33662	+	5.77920i	0.194927	+	0.337624i	−0.751949	+	0.659221i	$0.770886\pi$
$294$	0.550372	−	31.0345i	0.0320983	−	1.80997i
$295$	1.12917	−	1.95578i	0.0657427	−	0.113870i
$296$	−25.5589	−	44.2693i	−1.48558	−	2.57310i
$297$	−18.5004	−	7.05468i	−1.07350	−	0.409354i
$298$	−7.50496	+	12.9990i	−0.434751	+	0.753011i
$299$	1.44464			0.0835459
$300$	−2.30061	+	7.54485i	−0.132825	+	0.435602i
$301$	2.76572	+	3.54367i	0.159413	+	0.204254i
$302$	−23.3855	−	40.5049i	−1.34568	−	2.33079i
$303$	0.442870	−	1.45239i	0.0254422	−	0.0834379i
$304$	12.8688	+	22.2894i	0.738077	+	1.27839i
$305$	5.12610	−	8.87867i	0.293520	−	0.508391i
$306$	23.4559	+	15.7709i	1.34089	+	0.901563i
$307$	0.973998			0.0555890			0.0277945	−	0.999614i	$-0.491152\pi$
$307$	0.973998			0.0555890			0.0277945	+	0.999614i	$0.491152\pi$
$308$	45.4682	−	6.36657i	2.59079	−	0.362769i
$309$	−6.15178	+	1.42503i	−0.349962	+	0.0810672i
$310$	5.82475	−	10.0888i	0.330824	−	0.573003i
$311$	−12.3644			−0.701119			−0.350559	−	0.936541i	$-0.614009\pi$
$311$	−12.3644			−0.701119			−0.350559	+	0.936541i	$0.614009\pi$
$312$	5.27569	−	17.3017i	0.298677	−	0.979513i
$313$	7.77919			0.439706			0.219853	−	0.975533i	$-0.429442\pi$
$313$	7.77919			0.439706			0.219853	+	0.975533i	$0.429442\pi$
$314$	16.9401			0.955986
$315$	−6.57598	+	4.44482i	−0.370515	+	0.250437i
$316$	−63.6102			−3.57835
$317$	−14.2806			−0.802079			−0.401040	−	0.916061i	$-0.631351\pi$
$317$	−14.2806			−0.802079			−0.401040	+	0.916061i	$0.631351\pi$
$318$	−13.9761	+	3.23751i	−0.783743	+	0.181551i
$319$	37.9187			2.12304
$320$	0.636996	−	1.10331i	0.0356091	−	0.0616768i
$321$	−0.852822	+	2.79684i	−0.0475999	+	0.156104i
$322$	3.76938	+	4.82965i	0.210060	+	0.269146i
$323$	−12.4123			−0.690637
$324$	−40.6040	−	5.58435i	−2.25578	−	0.310242i
$325$	−0.798588	+	1.38320i	−0.0442977	+	0.0767259i
$326$	3.11689	+	5.39861i	0.172628	+	0.299001i
$327$	−8.36696	+	1.93817i	−0.462694	+	0.107181i
$328$	−41.7236	−	72.2673i	−2.30380	−	3.99030i
$329$	−9.60769	+	23.7451i	−0.529689	+	1.30911i
$330$	−11.5324	−	12.3487i	−0.634840	−	0.679776i
$331$	4.66354			0.256331			0.128166	−	0.991753i	$-0.459091\pi$
$331$	4.66354			0.256331			0.128166	+	0.991753i	$0.459091\pi$
$332$	−12.2045	+	21.1387i	−0.669807	+	1.16014i
$333$	−21.0649	+	10.3126i	−1.15435	+	0.565125i
$334$	24.4882	+	42.4147i	1.33993	+	2.32083i
$335$	−1.83338	+	3.17552i	−0.100169	+	0.173497i
$336$	32.6446	−	12.5397i	1.78091	−	0.684096i
$337$	7.05834	+	12.2254i	0.384492	+	0.665960i	0.991699	−	0.128584i	$-0.0410432\pi$
$337$	7.05834	+	12.2254i	0.384492	+	0.665960i	−0.607206	+	0.794544i	$0.707710\pi$
$338$	−13.3752	+	23.1665i	−0.727515	+	1.26009i
$339$	1.49991	−	4.91898i	0.0814642	−	0.267162i
$340$	8.37987	+	14.5144i	0.454462	+	0.787152i
$341$	8.66968	+	15.0163i	0.469489	+	0.813179i
$342$	23.2650	−	11.3896i	1.25802	−	0.615880i
$343$	16.9306	−	7.50705i	0.914165	−	0.405343i
$344$	−5.55457	+	9.62079i	−0.299482	+	0.518718i
$345$	0.456935	−	1.49852i	0.0246005	−	0.0806777i
$346$	53.3914			2.87034
$347$	21.7861			1.16954			0.584770	−	0.811199i	$-0.301185\pi$
$347$	21.7861			1.16954			0.584770	+	0.811199i	$0.301185\pi$
$348$	76.4681	−	17.7135i	4.09912	−	0.949544i
$349$	−9.11575	+	15.7889i	−0.487955	+	0.845163i	−0.999904	−	0.0138529i	$-0.995590\pi$
$349$	−9.11575	+	15.7889i	−0.487955	+	0.845163i	0.511949	+	0.859016i	$0.328924\pi$
$350$	−6.70791	+	0.939257i	−0.358553	+	0.0502054i
$351$	−7.75451	−	2.95700i	−0.413905	−	0.157833i
$352$	12.3064	+	21.3154i	0.655935	+	1.13611i
$353$	−1.16964	−	2.02587i	−0.0622536	−	0.107826i	0.833219	−	0.552943i	$-0.186495\pi$
$353$	−1.16964	−	2.02587i	−0.0622536	−	0.107826i	−0.895472	+	0.445117i	$0.853162\pi$
$354$	6.83486	+	7.31866i	0.363269	+	0.388982i
$355$	−6.91156	+	11.9712i	−0.366827	+	0.635363i
$356$	−4.54653	−	7.87482i	−0.240966	−	0.417365i
$357$	−2.63441	+	16.6578i	−0.139428	+	0.881623i
$358$	−12.3804	+	21.4435i	−0.654324	+	1.13332i
$359$	5.36666	+	9.29533i	0.283242	+	0.490589i	0.972181	−	0.234230i	$-0.0752569\pi$
$359$	5.36666	+	9.29533i	0.283242	+	0.490589i	−0.688940	+	0.724819i	$0.741924\pi$
$360$	−16.2782	−	10.9449i	−0.857938	−	0.576846i
$361$	3.81239	−	6.60326i	0.200652	−	0.347540i
$362$	−25.2637			−1.32783
$363$	5.93912	−	1.37577i	0.311723	−	0.0722093i
$364$	19.0582	−	2.66857i	0.998920	−	0.139871i
$365$	1.47850	+	2.56083i	0.0773882	+	0.134040i
$366$	31.0284	+	33.2247i	1.62188	+	1.73668i
$367$	5.45729	+	9.45230i	0.284868	+	0.493406i	0.972577	−	0.232580i	$-0.0747169\pi$
$367$	5.45729	+	9.45230i	0.284868	+	0.493406i	−0.687709	+	0.725986i	$0.741384\pi$
$368$	−3.45117	+	5.97760i	−0.179905	+	0.311604i
$369$	−34.3874	+	16.8347i	−1.79014	+	0.876382i
$370$	−20.0146			−1.04051
$371$	−5.26661	−	6.74802i	−0.273429	−	0.350340i
$372$	24.4983	+	26.2324i	1.27018	+	1.36009i
$373$	−5.89282	+	10.2067i	−0.305119	+	0.528481i	−0.977288	−	0.211916i	$-0.932030\pi$
$373$	−5.89282	+	10.2067i	−0.305119	+	0.528481i	0.672169	+	0.740398i	$0.265363\pi$
$374$	−35.9009			−1.85639
$375$	1.18219	+	1.26587i	0.0610480	+	0.0653692i
$376$	−63.3036			−3.26463
$377$	15.8938			0.818571
$378$	−10.3475	−	33.6399i	−0.532218	−	1.73025i
$379$	−7.94613			−0.408165			−0.204083	−	0.978954i	$-0.565421\pi$
$379$	−7.94613			−0.408165			−0.204083	+	0.978954i	$0.565421\pi$
$380$	15.3594			0.787923
$381$	20.6928	+	22.1575i	1.06013	+	1.13517i
$382$	68.0050			3.47944
$383$	11.9354	−	20.6727i	0.609871	−	1.05633i	−0.381391	−	0.924414i	$-0.624555\pi$
$383$	11.9354	−	20.6727i	0.609871	−	1.05633i	0.991261	−	0.131913i	$-0.0421119\pi$
$384$	−11.4164	−	12.2245i	−0.582591	−	0.623828i
$385$	3.78138	−	9.34556i	0.192717	−	0.476294i
$386$	37.1147			1.88909
$387$	4.22987	+	2.84401i	0.215017	+	0.144569i
$388$	−23.9427	+	41.4700i	−1.21551	+	2.10532i
$389$	−14.9182	−	25.8390i	−0.756381	−	1.31009i	−0.944685	−	0.327980i	$-0.893632\pi$
$389$	−14.9182	−	25.8390i	−0.756381	−	1.31009i	0.188303	−	0.982111i	$-0.439701\pi$
$390$	−4.83386	−	5.17602i	−0.244772	−	0.262098i
$391$	−1.66437	−	2.88277i	−0.0841707	−	0.145788i
$392$	32.8916	+	31.8278i	1.66128	+	1.60755i
$393$	1.40650	−	0.325810i	0.0709486	−	0.0164349i
$394$	−44.2132			−2.22743
$395$	−6.98395	+	12.0966i	−0.351401	+	0.608644i
$396$	46.7567	−	22.8902i	2.34961	−	1.15028i
$397$	−0.889325	−	1.54036i	−0.0446339	−	0.0773083i	0.842845	−	0.538156i	$-0.180879\pi$
$397$	−0.889325	−	1.54036i	−0.0446339	−	0.0773083i	−0.887479	+	0.460848i	$0.847545\pi$
$398$	−17.4581	+	30.2384i	−0.875097	+	1.51571i
$399$	12.0136	+	9.72385i	0.601432	+	0.486801i
$400$	−3.81556	−	6.60875i	−0.190778	−	0.330437i
$401$	−8.12407	+	14.0713i	−0.405697	+	0.702687i	−0.994402	−	0.105660i	$-0.966304\pi$
$401$	−8.12407	+	14.0713i	−0.405697	+	0.702687i	0.588706	+	0.808348i	$0.299638\pi$
$402$	−11.0975	−	11.8830i	−0.553493	−	0.592671i
$403$	3.63393	+	6.29415i	0.181019	+	0.313534i
$404$	1.99616	+	3.45745i	0.0993127	+	0.172015i
$405$	−5.51999	+	7.10842i	−0.274291	+	0.353220i
$406$	41.4702	+	53.1352i	2.05813	+	2.63705i
$407$	14.8950	−	25.7990i	0.738319	−	1.27881i
$408$	−40.6034	+	9.40559i	−2.01017	+	0.465646i
$409$	14.2048			0.702382			0.351191	−	0.936304i	$-0.385777\pi$
$409$	14.2048			0.702382			0.351191	+	0.936304i	$0.385777\pi$
$410$	−32.6727			−1.61359
$411$	2.57985	−	8.46063i	0.127255	−	0.417332i
$412$	8.30149	−	14.3786i	0.408985	−	0.708383i
$413$	−2.24109	+	5.53878i	−0.110277	+	0.272545i
$414$	5.76487	+	3.87608i	0.283328	+	0.190499i
$415$	2.67992	+	4.64177i	0.131552	+	0.227855i
$416$	5.15828	+	8.93441i	0.252906	+	0.438046i
$417$	3.14534	−	10.3152i	0.154028	−	0.505135i
$418$	−16.4507	+	28.4934i	−0.804629	+	1.39366i
$419$	−14.5093	−	25.1308i	−0.708825	−	1.22772i	−0.965293	−	0.261168i	$-0.915892\pi$
$419$	−14.5093	−	25.1308i	−0.708825	−	1.22772i	0.256469	−	0.966552i	$-0.417441\pi$
$420$	3.25993	−	20.6130i	0.159068	−	1.00581i
$421$	−10.3003	+	17.8406i	−0.502004	+	0.869497i	0.497993	+	0.867181i	$0.334070\pi$
$421$	−10.3003	+	17.8406i	−0.502004	+	0.869497i	−0.999997	+	0.00231578i	$0.999263\pi$
$422$	20.7834	+	35.9979i	1.01172	+	1.75235i
$423$	−1.98330	+	28.9771i	−0.0964314	+	1.40891i
$424$	10.5773	−	18.3203i	0.513677	−	0.889714i
$425$	3.68020			0.178516
$426$	−41.8357	−	44.7970i	−2.02695	−	2.17042i
$427$	−10.1739	+	25.1445i	−0.492350	+	1.21683i
$428$	−3.84395	−	6.65792i	−0.185804	−	0.321823i
$429$	10.2693	−	2.37885i	0.495809	−	0.114852i
$430$	2.17483	+	3.76691i	0.104879	+	0.181656i
$431$	0.890812	−	1.54293i	0.0429089	−	0.0743204i	−0.843773	−	0.536700i	$-0.819671\pi$
$431$	0.890812	−	1.54293i	0.0429089	−	0.0743204i	0.886682	+	0.462379i	$0.153004\pi$
$432$	30.7604	−	25.0223i	1.47996	−	1.20388i
$433$	−8.58391			−0.412516			−0.206258	−	0.978498i	$-0.566129\pi$
$433$	−8.58391			−0.412516			−0.206258	+	0.978498i	$0.566129\pi$
$434$	−11.5605	+	28.5715i	−0.554924	+	1.37148i
$435$	5.02713	−	16.4865i	0.241033	−	0.790468i
$436$	11.2908	−	19.5562i	0.540729	−	0.936571i
$437$	−3.05062			−0.145931
$438$	−12.7737	+	2.95896i	−0.610349	+	0.141385i
$439$	19.3179			0.921995			0.460998	−	0.887401i	$-0.347492\pi$
$439$	19.3179			0.921995			0.460998	+	0.887401i	$0.347492\pi$
$440$	24.9149			1.18777
$441$	15.5996	−	14.0589i	0.742838	−	0.669472i
$442$	−15.0480			−0.715760
$443$	21.4144			1.01743			0.508715	−	0.860935i	$-0.330121\pi$
$443$	21.4144			1.01743			0.508715	+	0.860935i	$0.330121\pi$
$444$	17.9860	−	58.9851i	0.853577	−	2.79931i
$445$	−1.99671			−0.0946530
$446$	6.78231	−	11.7473i	0.321151	−	0.556251i
$447$	−9.89316	+	2.29171i	−0.467930	+	0.108394i
$448$	−1.26426	+	3.12458i	−0.0597308	+	0.147623i
$449$	5.39942			0.254814			0.127407	−	0.991850i	$-0.459335\pi$
$449$	5.39942			0.254814			0.127407	+	0.991850i	$0.459335\pi$
$450$	−6.89799	+	3.37699i	−0.325174	+	0.159193i
$451$	24.3154	−	42.1155i	1.14497	−	1.98314i
$452$	6.76061	+	11.7097i	0.317992	+	0.550779i
$453$	9.22930	−	30.2676i	0.433630	−	1.42209i
$454$	−31.8504	−	55.1665i	−1.49481	−	2.58909i
$455$	1.58498	−	3.91722i	0.0743050	−	0.183642i
$456$	−11.1405	+	36.5355i	−0.521703	+	1.71093i
$457$	−35.0988			−1.64185			−0.820925	−	0.571035i	$-0.806542\pi$
$457$	−35.0988			−1.64185			−0.820925	+	0.571035i	$0.806542\pi$
$458$	21.0468	−	36.4540i	0.983450	−	1.70339i
$459$	3.03329	+	18.8808i	0.141582	+	0.881279i
$460$	2.05956	+	3.56726i	0.0960273	+	0.166324i
$461$	−17.7822	+	30.7997i	−0.828201	+	1.43449i	0.0712469	+	0.997459i	$0.477302\pi$
$461$	−17.7822	+	30.7997i	−0.828201	+	1.43449i	−0.899448	+	0.437028i	$0.856031\pi$
$462$	34.7477	+	28.1250i	1.61661	+	1.30849i
$463$	4.54343	+	7.86945i	0.211151	+	0.365724i	0.952075	−	0.305865i	$-0.0989455\pi$
$463$	4.54343	+	7.86945i	0.211151	+	0.365724i	−0.740924	+	0.671589i	$0.765612\pi$
$464$	−37.9693	+	65.7648i	−1.76268	+	3.05305i
$465$	7.67828	−	1.77864i	0.356072	−	0.0824824i
$466$	−6.91796	−	11.9823i	−0.320468	−	0.555067i
$467$	−5.32092	−	9.21610i	−0.246223	−	0.426470i	0.716252	−	0.697842i	$-0.245856\pi$
$467$	−5.32092	−	9.21610i	−0.246223	−	0.426470i	−0.962475	+	0.271372i	$0.912523\pi$
$468$	19.5982	−	9.59453i	0.905929	−	0.443507i
$469$	3.63877	−	8.99310i	0.168023	−	0.415263i
$470$	−12.3929	+	21.4651i	−0.571641	+	0.990111i
$471$	7.82257	+	8.37628i	0.360445	+	0.385959i
$472$	−14.7662			−0.679669
$473$	−6.47410			−0.297680
$474$	−42.2739	−	45.2662i	−1.94171	−	2.07915i
$475$	1.68636	−	2.92086i	0.0773754	−	0.134018i
$476$	−27.2820	−	34.9559i	−1.25047	−	1.60220i
$477$	−8.05471	−	5.41569i	−0.368800	−	0.247967i
$478$	−13.7604	−	23.8338i	−0.629387	−	1.09013i
$479$	9.23963	+	16.0035i	0.422169	+	0.731219i	0.996151	−	0.0876492i	$-0.0279355\pi$
$479$	9.23963	+	16.0035i	0.422169	+	0.731219i	−0.573982	+	0.818868i	$0.694602\pi$
$480$	10.8992	−	2.52474i	0.497476	−	0.115238i
$481$	6.24331	−	10.8137i	0.284670	−	0.493063i
$482$	14.0980	+	24.4185i	0.642148	+	1.11223i
$483$	−0.647471	+	4.09405i	−0.0294610	+	0.186286i
$484$	−8.01452	+	13.8816i	−0.364296	+	0.630980i
$485$	5.25748	+	9.10623i	0.238730	+	0.413492i
$486$	−23.0106	−	32.6058i	−1.04378	−	1.47903i
$487$	−10.5477	+	18.2692i	−0.477963	+	0.827856i	−0.999681	−	0.0252619i	$-0.991958\pi$
$487$	−10.5477	+	18.2692i	−0.477963	+	0.827856i	0.521718	+	0.853118i	$0.325291\pi$
$488$	−67.0343			−3.03450
$489$	−1.23011	+	4.03415i	−0.0556274	+	0.182430i
$490$	17.2314	−	4.92206i	0.778435	−	0.222356i
$491$	14.3348	+	24.8287i	0.646922	+	1.12050i	0.983854	+	0.178973i	$0.0572775\pi$
$491$	14.3348	+	24.8287i	0.646922	+	1.12050i	−0.336932	+	0.941529i	$0.609389\pi$
$492$	29.3612	−	96.2902i	1.32370	−	4.34110i
$493$	−18.3112	−	31.7158i	−0.824693	−	1.42841i
$494$	−6.89536	+	11.9431i	−0.310237	+	0.537346i
$495$	0.780585	−	11.4048i	0.0350847	−	0.512606i
$496$	−34.7250			−1.55920
$497$	13.7175	−	33.9025i	0.615316	−	1.52073i
$498$	−23.1535	+	5.36341i	−1.03753	+	0.240340i
$499$	16.7758	−	29.0565i	0.750986	−	1.30075i	−0.196360	−	0.980532i	$-0.562912\pi$
$499$	16.7758	−	29.0565i	0.750986	−	1.30075i	0.947345	−	0.320214i	$-0.103755\pi$
$500$	−4.55403			−0.203662
$501$	−9.66448	+	31.6947i	−0.431777	+	1.41602i
$502$	−8.78287			−0.391999
$503$	25.8519			1.15268			0.576339	−	0.817211i	$-0.304481\pi$
$503$	25.8519			1.15268			0.576339	+	0.817211i	$0.304481\pi$
$504$	46.6676	+	22.7054i	2.07874	+	1.01138i
$505$	0.876657			0.0390107
$506$	−8.82352			−0.392253
$507$	−17.6314	+	4.08423i	−0.783037	+	0.181387i
$508$	−79.7129			−3.53669
$509$	16.1400	−	27.9554i	0.715394	−	1.23910i	−0.247413	−	0.968910i	$-0.579580\pi$
$509$	16.1400	−	27.9554i	0.715394	−	1.23910i	0.962807	−	0.270189i	$-0.0870863\pi$
$510$	−4.75962	+	15.6092i	−0.210759	+	0.691187i
$511$	−4.81348	−	6.16743i	−0.212936	−	0.272831i
$512$	50.5012			2.23186
$513$	16.3750	+	6.24421i	0.722974	+	0.275689i
$514$	−15.4053	+	26.6827i	−0.679498	+	1.17693i
$515$	−1.82289	−	3.15734i	−0.0803261	−	0.139129i
$516$	−13.0559	+	3.02434i	−0.574753	+	0.133139i
$517$	−18.4458	−	31.9491i	−0.811246	−	1.40512i
$518$	52.4420	−	7.34304i	2.30417	−	0.322635i
$519$	24.6550	+	26.4001i	1.08223	+	1.15884i
$520$	10.4432			0.457964
$521$	−4.34708	+	7.52936i	−0.190449	+	0.329867i	−0.945399	−	0.325915i	$-0.894328\pi$
$521$	−4.34708	+	7.52936i	−0.190449	+	0.329867i	0.754950	+	0.655782i	$0.227661\pi$
$522$	63.4243	+	42.6441i	2.77601	+	1.86648i
$523$	−10.2798	−	17.8052i	−0.449505	−	0.778566i	0.548849	−	0.835922i	$-0.315066\pi$
$523$	−10.2798	−	17.8052i	−0.449505	−	0.778566i	−0.998354	+	0.0573560i	$0.981733\pi$
$524$	−1.89800	+	3.28743i	−0.0829144	+	0.143612i
$525$	−3.56199	−	2.88309i	−0.155458	−	0.125828i
$526$	22.7411	+	39.3888i	0.991559	+	1.71743i
$527$	8.37326	−	14.5029i	0.364745	−	0.631757i
$528$	−14.6897	+	48.1751i	−0.639289	+	2.09655i
$529$	11.0909	+	19.2101i	0.482215	+	0.835221i
$530$	−4.14140	−	7.17311i	−0.179891	−	0.311580i
$531$	−0.462625	+	6.75919i	−0.0200762	+	0.293324i
$532$	−40.2447	+	5.63515i	−1.74483	+	0.244315i
$533$	10.1919	−	17.6529i	0.441459	−	0.764630i
$534$	2.58235	−	8.46883i	0.111749	−	0.366482i
$535$	−1.68815			−0.0729853
$536$	23.9753			1.03557
$537$	−16.3200	+	3.78046i	−0.704261	+	0.163139i
$538$	−4.18527	+	7.24910i	−0.180440	+	0.312531i
$539$	−6.47919	+	25.8745i	−0.279078	+	1.11449i
$540$	−3.75351	−	23.3638i	−0.161525	−	1.00542i
$541$	11.4358	+	19.8073i	0.491662	+	0.851583i	0.999954	−	0.00960144i	$-0.00305628\pi$
$541$	11.4358	+	19.8073i	0.491662	+	0.851583i	−0.508292	+	0.861185i	$0.669723\pi$
$542$	−38.7194	−	67.0640i	−1.66314	−	2.88065i
$543$	−11.6662	−	12.4920i	−0.500645	−	0.536082i
$544$	11.8857	−	20.5866i	0.509594	−	0.882643i
$545$	−2.47929	−	4.29426i	−0.106201	−	0.183946i
$546$	14.5646	+	11.7887i	0.623309	+	0.504509i
$547$	−11.1030	+	19.2310i	−0.474730	+	0.822256i	−0.999581	−	0.0289375i	$-0.990788\pi$
$547$	−11.1030	+	19.2310i	−0.474730	+	0.822256i	0.524851	+	0.851194i	$0.324121\pi$
$548$	11.6282	+	20.1407i	0.496734	+	0.860368i
$549$	−2.10019	+	30.6848i	−0.0896338	+	1.30960i
$550$	4.87757	−	8.44820i	0.207980	−	0.360233i
$551$	−33.5625			−1.42981
$552$	−9.97926	+	2.31165i	−0.424746	+	0.0983905i
$553$	13.8612	−	34.2576i	0.589439	−	1.45678i
$554$	21.0770	+	36.5064i	0.895475	+	1.55101i
$555$	−9.24228	−	9.89648i	−0.392313	−	0.420082i
$556$	14.1771	+	24.5554i	0.601242	+	1.04138i
$557$	6.29353	−	10.9007i	0.266666	−	0.461878i	−0.701333	−	0.712834i	$-0.747411\pi$
$557$	6.29353	−	10.9007i	0.266666	−	0.461878i	0.967999	+	0.250955i	$0.0807448\pi$
$558$	−2.38643	+	34.8669i	−0.101025	+	1.47604i
$559$	−2.71364			−0.114775
$560$	12.4221	+	15.9163i	0.524931	+	0.672586i
$561$	−16.5782	−	17.7517i	−0.699934	−	0.749478i
$562$	−17.7277	+	30.7052i	−0.747796	+	1.29522i
$563$	−16.3000			−0.686962			−0.343481	−	0.939160i	$-0.611606\pi$
$563$	−16.3000			−0.686962			−0.343481	+	0.939160i	$0.611606\pi$
$564$	−52.1232	−	55.8127i	−2.19478	−	2.35014i
$565$	2.96907			0.124910
$566$	−15.7874			−0.663595
$567$	11.8555	−	20.6506i	0.497882	−	0.867245i
$568$	90.3828			3.79238
$569$	−15.2784			−0.640504			−0.320252	−	0.947332i	$-0.603768\pi$
$569$	−15.2784			−0.640504			−0.320252	+	0.947332i	$0.603768\pi$
$570$	10.2075	+	10.9301i	0.427547	+	0.457810i
$571$	−28.4312			−1.18981			−0.594903	−	0.803797i	$-0.702810\pi$
$571$	−28.4312			−1.18981			−0.594903	+	0.803797i	$0.702810\pi$
$572$	−13.8579	+	24.0026i	−0.579429	+	1.00360i
$573$	31.4032	+	33.6261i	1.31189	+	1.40475i
$574$	85.6088	−	11.9871i	3.57324	−	0.500334i
$575$	0.904499			0.0377202
$576$	−0.260980	+	3.81305i	−0.0108742	+	0.158877i
$577$	10.3126	−	17.8619i	0.429317	−	0.743599i	−0.567495	−	0.823377i	$-0.692088\pi$
$577$	10.3126	−	17.8619i	0.429317	−	0.743599i	0.996813	+	0.0797772i	$0.0254209\pi$
$578$	−4.42398	−	7.66256i	−0.184013	−	0.318721i
$579$	17.1387	+	18.3519i	0.712262	+	0.762678i
$580$	22.6590	+	39.2465i	0.940862	+	1.62962i
$581$	−8.72491	−	11.1791i	−0.361970	−	0.463787i
$582$	−45.4226	+	10.5220i	−1.88283	+	0.436149i
$583$	12.3283			0.510585
$584$	9.66721	−	16.7441i	0.400032	−	0.692875i
$585$	0.327185	−	4.78035i	0.0135274	−	0.197643i
$586$	−8.54203	−	14.7952i	−0.352868	−	0.611185i
$587$	1.59958	−	2.77056i	0.0660218	−	0.114353i	−0.831125	−	0.556086i	$-0.812303\pi$
$587$	1.59958	−	2.77056i	0.0660218	−	0.114353i	0.897147	+	0.441733i	$0.145636\pi$
$588$	−0.979034	+	55.2060i	−0.0403747	+	2.27666i
$589$	−7.67367	−	13.2912i	−0.316188	−	0.547654i
$590$	−2.89076	+	5.00695i	−0.119011	+	0.206133i
$591$	−20.4167	−	21.8619i	−0.839831	−	0.899277i
$592$	29.8298	+	51.6667i	1.22600	+	2.12349i
$593$	−14.8761	−	25.7662i	−0.610888	−	1.05809i	−0.991091	−	0.133186i	$-0.957479\pi$
$593$	−14.8761	−	25.7662i	−0.610888	−	1.05809i	0.380203	−	0.924903i	$-0.375854\pi$
$594$	47.3626	+	18.0606i	1.94331	+	0.741035i
$595$	−9.64282	+	1.35021i	−0.395317	+	0.0553532i
$596$	13.3503	−	23.1234i	0.546849	−	0.947169i
$597$	−23.0136	+	5.33099i	−0.941882	+	0.218183i
$598$	−3.69841			−0.151239
$599$	−0.823533			−0.0336486			−0.0168243	−	0.999858i	$-0.505356\pi$
$599$	−0.823533			−0.0336486			−0.0168243	+	0.999858i	$0.505356\pi$
$600$	3.30313	−	10.8327i	0.134850	−	0.442241i
$601$	10.0885	−	17.4737i	0.411517	−	0.712769i	−0.583539	−	0.812085i	$-0.698332\pi$
$601$	10.0885	−	17.4737i	0.411517	−	0.712769i	0.995056	+	0.0993166i	$0.0316657\pi$
$602$	−7.08048	−	9.07210i	−0.288579	−	0.369751i
$603$	0.751146	−	10.9746i	0.0305890	−	0.446922i
$604$	41.5995	+	72.0525i	1.69266	+	2.93177i
$605$	1.75988	+	3.04819i	0.0715491	+	0.123927i
$606$	−1.13378	+	3.71825i	−0.0460568	+	0.151044i
$607$	−5.63403	+	9.75842i	−0.228678	+	0.396082i	−0.957417	−	0.288710i	$-0.906774\pi$
$607$	−5.63403	+	9.75842i	−0.228678	+	0.396082i	0.728738	+	0.684792i	$0.240107\pi$
$608$	−10.8926	−	18.8666i	−0.441754	−	0.765140i
$609$	−7.12339	+	45.0422i	−0.288654	+	1.82520i
$610$	−13.1233	+	22.7301i	−0.531345	+	0.920316i
$611$	−7.73163	−	13.3916i	−0.312788	−	0.541765i
$612$	−41.7248	−	28.0542i	−1.68663	−	1.13403i
$613$	−16.0167	+	27.7417i	−0.646906	+	1.12047i	0.336951	+	0.941522i	$0.390604\pi$
$613$	−16.0167	+	27.7417i	−0.646906	+	1.12047i	−0.983858	+	0.178953i	$0.942729\pi$
$614$	−2.49352			−0.100630
$615$	−15.0876	−	16.1555i	−0.608389	−	0.651453i
$616$	−65.2818	+	9.14091i	−2.63028	+	0.368298i
$617$	−1.74570	−	3.02363i	−0.0702790	−	0.121727i	0.828745	−	0.559627i	$-0.189056\pi$
$617$	−1.74570	−	3.02363i	−0.0702790	−	0.121727i	−0.899024	+	0.437900i	$0.855722\pi$
$618$	15.7491	−	3.64820i	0.633520	−	0.146752i
$619$	16.3582	+	28.3332i	0.657491	+	1.13881i	0.981263	+	0.192672i	$0.0617154\pi$
$619$	16.3582	+	28.3332i	0.657491	+	1.13881i	−0.323772	+	0.946135i	$0.604951\pi$
$620$	−10.3614	+	17.9465i	−0.416124	+	0.720749i
$621$	0.745504	+	4.64041i	0.0299160	+	0.186213i
$622$	31.6538			1.26920
$623$	5.23175	−	0.732562i	0.209606	−	0.0293495i
$624$	−6.15726	+	20.1928i	−0.246488	+	0.808358i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−19.9154			−0.795978
$627$	−21.6855	+	5.02336i	−0.866036	+	0.200614i
$628$	−30.1341			−1.20248
$629$	−28.7716			−1.14720
$630$	16.8351	−	11.3791i	0.670725	−	0.453355i
$631$	18.3017			0.728578			0.364289	−	0.931286i	$-0.381312\pi$
$631$	18.3017			0.728578			0.364289	+	0.931286i	$0.381312\pi$
$632$	91.3295			3.63289
$633$	−8.20236	+	26.8997i	−0.326014	+	1.06917i
$634$	36.5596			1.45197
$635$	−8.75190	+	15.1587i	−0.347309	+	0.601556i
$636$	24.8616	−	5.75908i	0.985827	−	0.228362i
$637$	−2.71577	+	10.8454i	−0.107603	+	0.429709i
$638$	−97.0751			−3.84324
$639$	2.83169	−	41.3725i	0.112020	−	1.63667i
$640$	4.82849	−	8.36320i	0.190863	−	0.330584i
$641$	21.3988	+	37.0638i	0.845203	+	1.46393i	0.885445	+	0.464744i	$0.153854\pi$
$641$	21.3988	+	37.0638i	0.845203	+	1.46393i	−0.0402425	+	0.999190i	$0.512813\pi$
$642$	2.18330	−	7.16013i	0.0861678	−	0.282588i
$643$	19.0608	+	33.0143i	0.751686	+	1.30196i	0.947005	+	0.321218i	$0.104092\pi$
$643$	19.0608	+	33.0143i	0.751686	+	1.30196i	−0.195319	+	0.980740i	$0.562574\pi$
$644$	−6.70520	−	8.59127i	−0.264222	−	0.338544i
$645$	−0.858314	+	2.81485i	−0.0337961	+	0.110835i
$646$	31.7765			1.25023
$647$	−6.43473	+	11.1453i	−0.252975	+	0.438166i	−0.964344	−	0.264653i	$-0.914742\pi$
$647$	−6.43473	+	11.1453i	−0.252975	+	0.438166i	0.711368	+	0.702819i	$0.248076\pi$
$648$	58.2980	+	8.01783i	2.29016	+	0.314970i
$649$	−4.30267	−	7.45244i	−0.168894	−	0.292534i
$650$	2.04445	−	3.54110i	0.0801900	−	0.138893i
$651$	−19.4660	+	7.47742i	−0.762932	+	0.293063i
$652$	−5.54450	−	9.60336i	−0.217140	−	0.376097i
$653$	−4.45267	+	7.71225i	−0.174246	+	0.301804i	−0.939900	−	0.341449i	$-0.889082\pi$
$653$	−4.45267	+	7.71225i	−0.174246	+	0.301804i	0.765654	+	0.643253i	$0.222416\pi$
$654$	21.4201	−	4.96188i	0.837593	−	0.194025i
$655$	0.416773	+	0.721872i	0.0162847	+	0.0282059i
$656$	48.6956	+	84.3433i	1.90124	+	3.29305i
$657$	−7.36170	−	4.94974i	−0.287207	−	0.193108i
$658$	24.5965	−	60.7894i	0.958871	−	2.36982i
$659$	10.4637	−	18.1237i	0.407609	−	0.706000i	−0.587012	−	0.809578i	$-0.699696\pi$
$659$	10.4637	−	18.1237i	0.407609	−	0.706000i	0.994621	+	0.103578i	$0.0330292\pi$
$660$	20.5146	+	21.9667i	0.798529	+	0.855052i
$661$	−4.08024			−0.158703			−0.0793516	−	0.996847i	$-0.525285\pi$
$661$	−4.08024			−0.158703			−0.0793516	+	0.996847i	$0.525285\pi$
$662$	−11.9390			−0.464024
$663$	−6.94883	−	7.44069i	−0.269870	−	0.288973i
$664$	17.5228	−	30.3503i	0.680015	−	1.17782i
$665$	−3.34696	+	8.27190i	−0.129790	+	0.320771i
$666$	53.9280	−	26.4010i	2.08967	−	1.02302i
$667$	−4.50041	−	7.79494i	−0.174257	−	0.301821i
$668$	−43.5610	−	75.4499i	−1.68543	−	2.91924i
$669$	8.94054	−	2.07104i	0.345661	−	0.0800709i
$670$	4.69362	−	8.12959i	0.181330	−	0.314073i
$671$	−19.5329	−	33.8320i	−0.754060	−	1.30607i
$672$	−27.6316	+	10.6140i	−1.06591	+	0.409446i
$673$	13.4792	−	23.3467i	0.519587	−	0.899951i	−0.480154	−	0.877184i	$-0.659419\pi$
$673$	13.4792	−	23.3467i	0.519587	−	0.899951i	0.999741	−	0.0227666i	$-0.00724746\pi$
$674$	−18.0699	−	31.2981i	−0.696028	−	1.20556i
$675$	−4.85514	−	1.85139i	−0.186874	−	0.0712600i
$676$	23.7926	−	41.2100i	0.915100	−	1.58500i
$677$	42.0684			1.61682			0.808409	−	0.588621i	$-0.200329\pi$
$677$	42.0684			1.61682			0.808409	+	0.588621i	$0.200329\pi$
$678$	−3.83991	+	12.5930i	−0.147471	+	0.483631i
$679$	−17.1165	−	21.9311i	−0.656872	−	0.841640i
$680$	−12.0315	−	20.8393i	−0.461389	−	0.799149i
$681$	12.5701	−	41.2236i	0.481686	−	1.57969i
$682$	−22.1951	−	38.4430i	−0.849894	−	1.47206i
$683$	−8.98495	+	15.5624i	−0.343799	+	0.595478i	−0.985135	−	0.171782i	$-0.945047\pi$
$683$	−8.98495	+	15.5624i	−0.343799	+	0.595478i	0.641335	+	0.767261i	$0.278381\pi$
$684$	−41.3851	+	20.2605i	−1.58240	+	0.774680i
$685$	5.10679			0.195120
$686$	−43.3437	+	19.2187i	−1.65487	+	0.733772i
$687$	27.7441	−	6.42681i	1.05851	−	0.245198i
$688$	6.48274	−	11.2284i	0.247152	−	0.428080i
$689$	5.16744			0.196864
$690$	−1.16979	+	3.83634i	−0.0445332	+	0.146047i
$691$	17.6389			0.671015			0.335508	−	0.942037i	$-0.391092\pi$
$691$	17.6389			0.671015			0.335508	+	0.942037i	$0.391092\pi$
$692$	−94.9757			−3.61044
$693$	2.13895	+	30.1690i	0.0812522	+	1.14603i
$694$	−55.7742			−2.11716
$695$	6.22617			0.236172
$696$	−109.790	+	25.4325i	−4.16160	+	0.964016i
$697$	−46.9681			−1.77904
$698$	23.3371	−	40.4210i	0.883322	−	1.52996i
$699$	2.73024	−	8.95383i	0.103267	−	0.338665i
$700$	11.9324	−	1.67081i	0.451003	−	0.0631505i
$701$	33.4458			1.26323			0.631614	−	0.775283i	$-0.282393\pi$
$701$	33.4458			1.26323			0.631614	+	0.775283i	$0.282393\pi$
$702$	19.8522	+	7.57016i	0.749273	+	0.285717i
$703$	−13.1838	+	22.8351i	−0.497238	+	0.861241i
$704$	−2.42726	−	4.20413i	−0.0914807	−	0.158449i
$705$	−16.3365	+	3.78428i	−0.615268	+	0.142524i
$706$	2.99437	+	5.18640i	0.112695	+	0.195193i
$707$	−2.29701	+	0.321632i	−0.0863879	+	0.0120962i
$708$	−12.1583	−	13.0189i	−0.456935	−	0.489279i
$709$	10.4551			0.392649			0.196325	−	0.980539i	$-0.437099\pi$
$709$	10.4551			0.392649			0.196325	+	0.980539i	$0.437099\pi$
$710$	17.6942	−	30.6472i	0.664050	−	1.15017i
$711$	2.86135	−	41.8059i	0.107309	−	1.56784i
$712$	6.52776	+	11.3064i	0.244638	+	0.423726i
$713$	2.05793	−	3.56445i	0.0770702	−	0.133490i
$714$	6.74432	−	42.6453i	0.252400	−	1.59596i
$715$	3.04300	+	5.27064i	0.113802	+	0.197111i
$716$	22.0230	−	38.1449i	0.823038	−	1.42554i
$717$	5.43068	−	17.8099i	0.202812	−	0.665124i
$718$	−13.7391	−	23.7968i	−0.512739	−	0.888089i
$719$	−0.970052	−	1.68018i	−0.0361768	−	0.0626601i	0.847370	−	0.531003i	$-0.178185\pi$
$719$	−0.970052	−	1.68018i	−0.0361768	−	0.0626601i	−0.883547	+	0.468343i	$0.844851\pi$
$720$	18.9983	+	12.7738i	0.708026	+	0.476051i
$721$	5.93469	+	7.60403i	0.221020	+	0.283189i
$722$	−9.76004	+	16.9049i	−0.363231	+	0.629135i
$723$	−5.56392	+	18.2469i	−0.206924	+	0.678610i
$724$	44.9405			1.67020
$725$	9.95117			0.369577
$726$	−15.2047	+	3.52209i	−0.564298	+	0.130717i
$727$	−8.52702	+	14.7692i	−0.316250	+	0.547760i	−0.979702	−	0.200458i	$-0.935757\pi$
$727$	−8.52702	+	14.7692i	−0.316250	+	0.547760i	0.663453	+	0.748218i	$0.269090\pi$
$728$	−27.3631	+	3.83145i	−1.01414	+	0.142003i
$729$	5.49662	−	26.4346i	0.203579	−	0.979059i
$730$	−3.78508	−	6.55595i	−0.140092	−	0.242647i
$731$	3.12638	+	5.41505i	0.115633	+	0.200283i
$732$	−55.1951	−	59.1020i	−2.04007	−	2.18447i
$733$	23.3804	−	40.4960i	0.863575	−	1.49576i	−0.00488069	−	0.999988i	$-0.501554\pi$
$733$	23.3804	−	40.4960i	0.863575	−	1.49576i	0.868455	−	0.495767i	$-0.165113\pi$
$734$	−13.9711	−	24.1987i	−0.515683	−	0.893189i
$735$	10.3909	+	6.24740i	0.383273	+	0.230439i
$736$	2.92119	−	5.05966i	0.107677	−	0.186501i
$737$	6.98607	+	12.1002i	0.257335	+	0.445718i
$738$	88.0347	−	43.0983i	3.24060	−	1.58647i
$739$	16.2283	−	28.1082i	0.596968	−	1.03398i	−0.396298	−	0.918122i	$-0.629705\pi$
$739$	16.2283	−	28.1082i	0.596968	−	1.03398i	0.993266	−	0.115857i	$-0.0369613\pi$
$740$	35.6031			1.30880
$741$	−9.08957	+	2.10556i	−0.333914	+	0.0773496i
$742$	13.4830	+	17.2755i	0.494975	+	0.634204i
$743$	13.6220	+	23.5940i	0.499743	+	0.865580i	1.00000		0.000296896i	$-9.45049e-5\pi$
$743$	13.6220	+	23.5940i	0.499743	+	0.865580i	−0.500257	+	0.865877i	$0.666761\pi$
$744$	−35.1739	−	37.6636i	−1.28954	−	1.38082i
$745$	−2.93153	−	5.07756i	−0.107403	−	0.186027i
$746$	15.0861	−	26.1299i	0.552342	−	0.956685i
$747$	−13.3438	−	8.97188i	−0.488224	−	0.328264i
$748$	63.8626			2.33505
$749$	4.42329	−	0.619359i	0.161623	−	0.0226309i
$750$	−3.02651	−	3.24073i	−0.110512	−	0.118335i
$751$	−22.7174	+	39.3477i	−0.828969	+	1.43582i	0.0698786	+	0.997556i	$0.477739\pi$
$751$	−22.7174	+	39.3477i	−0.828969	+	1.43582i	−0.898848	+	0.438261i	$0.855595\pi$
$752$	73.8816			2.69419
$753$	−4.05574	−	4.34281i	−0.147799	−	0.158261i
$754$	−40.6894			−1.48182
$755$	18.2693			0.664889
$756$	18.4068	+	59.8406i	0.669447	+	2.17638i
$757$	−8.45039			−0.307135			−0.153567	−	0.988138i	$-0.549076\pi$
$757$	−8.45039			−0.307135			−0.153567	+	0.988138i	$0.549076\pi$
$758$	20.3428			0.738882
$759$	−4.07451	−	4.36291i	−0.147895	−	0.158364i
$760$	−22.0526			−0.799932
$761$	5.56115	−	9.63220i	0.201592	−	0.349167i	−0.747450	−	0.664318i	$-0.768722\pi$
$761$	5.56115	−	9.63220i	0.201592	−	0.349167i	0.949041	+	0.315151i	$0.102055\pi$
$762$	−52.9754	−	56.7252i	−1.91910	−	2.05494i
$763$	8.07171	+	10.3422i	0.292216	+	0.374411i
$764$	−120.971			−4.37659
$765$	−9.91607	+	4.85452i	−0.358516	+	0.175516i
$766$	−30.5556	+	52.9239i	−1.10402	+	1.91222i
$767$	−1.80348	−	3.12372i	−0.0651199	−	0.112791i
$768$	32.2391	+	34.5211i	1.16333	+	1.24567i
$769$	−6.38900	−	11.0661i	−0.230393	−	0.399053i	0.727531	−	0.686075i	$-0.240668\pi$
$769$	−6.38900	−	11.0661i	−0.230393	−	0.399053i	−0.957924	+	0.287022i	$0.907335\pi$
$770$	−9.68065	+	23.9254i	−0.348866	+	0.862212i
$771$	−20.3075	+	4.70414i	−0.731356	+	0.169415i
$772$	−66.0218			−2.37618
$773$	12.6787	−	21.9601i	0.456020	−	0.789851i	−0.542726	−	0.839910i	$-0.682608\pi$
$773$	12.6787	−	21.9601i	0.456020	−	0.789851i	0.998746	+	0.0500593i	$0.0159410\pi$
$774$	−10.8288	−	7.28091i	−0.389234	−	0.261707i
$775$	2.27522	+	3.94080i	0.0817283	+	0.141558i
$776$	34.3762	−	59.5413i	1.23403	−	2.13741i
$777$	27.8474	+	22.5398i	0.999020	+	0.808611i
$778$	38.1918	+	66.1501i	1.36924	+	2.37160i
$779$	−21.5219	+	37.2771i	−0.771103	+	1.33559i
$780$	8.59876	+	9.20741i	0.307885	+	0.329678i
$781$	26.3363	+	45.6159i	0.942388	+	1.63226i
$782$	4.26092	+	7.38014i	0.152370	+	0.263913i
$783$	8.20193	+	51.0532i	0.293113	+	1.82449i
$784$	−38.3878	−	37.1462i	−1.37099	−	1.32665i
$785$	−3.30851	+	5.73050i	−0.118086	+	0.204530i
$786$	−3.60076	+	0.834101i	−0.128435	+	0.0297514i
$787$	10.5191			0.374964			0.187482	−	0.982268i	$-0.439967\pi$
$787$	10.5191			0.374964			0.187482	+	0.982268i	$0.439967\pi$
$788$	78.6491			2.80176
$789$	−8.97498	+	29.4335i	−0.319518	+	1.04786i
$790$	17.8795	−	30.9682i	0.636124	−	1.10180i
$791$	−7.77952	+	1.08931i	−0.276608	+	0.0387313i
$792$	−67.1317	+	32.8651i	−2.38542	+	1.16781i
$793$	−8.18729	−	14.1808i	−0.290739	−	0.503575i
$794$	2.27675	+	3.94344i	0.0807987	+	0.139947i
$795$	1.63444	−	5.36016i	0.0579676	−	0.190105i
$796$	31.0555	−	53.7898i	1.10073	−	1.90653i
$797$	15.6493	+	27.1053i	0.554325	+	0.960120i	0.997956	+	0.0639099i	$0.0203570\pi$
$797$	15.6493	+	27.1053i	0.554325	+	0.960120i	−0.443630	+	0.896210i	$0.646310\pi$
$798$	−30.7558	−	24.8939i	−1.08874	−	0.881233i
$799$	−17.8152	+	30.8568i	−0.630255	+	1.09163i
$800$	3.22963	+	5.59388i	0.114185	+	0.197774i
$801$	5.38000	−	2.63384i	0.190093	−	0.0930622i
$802$	20.7983	−	36.0237i	0.734414	−	1.27204i
$803$	11.2676			0.397624
$804$	19.7409	+	21.1382i	0.696208	+	0.745488i
$805$	−2.36996	+	0.331847i	−0.0835301	+	0.0116961i
$806$	−9.30316	−	16.1135i	−0.327690	−	0.567575i
$807$	−5.51709	+	1.27801i	−0.194211	+	0.0449880i
$808$	−2.86602	−	4.96410i	−0.100826	−	0.174636i
$809$	−15.2977	+	26.4964i	−0.537839	+	0.931565i	0.461181	+	0.887306i	$0.347426\pi$
$809$	−15.2977	+	26.4964i	−0.537839	+	0.931565i	−0.999020	+	0.0442585i	$0.985907\pi$
$810$	14.1316	−	18.1982i	0.496535	−	0.639418i
$811$	−16.0194			−0.562519			−0.281259	−	0.959632i	$-0.590752\pi$
$811$	−16.0194			−0.562519			−0.281259	+	0.959632i	$0.590752\pi$
$812$	−73.7697	−	94.5200i	−2.58881	−	3.31700i
$813$	15.2810	−	50.1140i	0.535927	−	1.75758i
$814$	−38.1325	+	66.0475i	−1.33654	+	2.31496i
$815$	−2.43499			−0.0852939
$816$	47.3882	−	10.9773i	1.65892	−	0.384281i
$817$	5.73033			0.200479
$818$	−36.3655			−1.27149
$819$	0.896551	+	12.6455i	0.0313280	+	0.441868i
$820$	58.1202			2.02965
$821$	5.50033			0.191963			0.0959814	−	0.995383i	$-0.469401\pi$
$821$	5.50033			0.191963			0.0959814	+	0.995383i	$0.469401\pi$
$822$	−6.60463	+	21.6599i	−0.230363	+	0.755477i
$823$	12.5384			0.437063			0.218531	−	0.975830i	$-0.429873\pi$
$823$	12.5384			0.437063			0.218531	+	0.975830i	$0.429873\pi$
$824$	−11.9190	+	20.6443i	−0.415218	+	0.719179i
$825$	6.42969	−	1.48941i	0.223853	−	0.0518546i
$826$	5.73737	−	14.1797i	0.199629	−	0.493376i
$827$	−23.6999			−0.824126			−0.412063	−	0.911155i	$-0.635192\pi$
$827$	−23.6999			−0.824126			−0.412063	+	0.911155i	$0.635192\pi$
$828$	−10.2549	−	6.89501i	−0.356382	−	0.239618i
$829$	11.5755	−	20.0494i	0.402034	−	0.696344i	−0.591937	−	0.805984i	$-0.701637\pi$
$829$	11.5755	−	20.0494i	0.402034	−	0.696344i	0.993971	+	0.109640i	$0.0349699\pi$
$830$	−6.86083	−	11.8833i	−0.238143	−	0.412476i
$831$	−8.31822	+	27.2797i	−0.288556	+	0.946321i
$832$	−1.01739	−	1.76218i	−0.0352718	−	0.0610925i
$833$	24.7707	−	7.07562i	0.858253	−	0.245156i
$834$	−8.05233	+	26.4077i	−0.278829	+	0.914422i
$835$	−19.1308			−0.662047
$836$	29.2634	−	50.6857i	1.01210	−	1.75300i
$837$	−18.3425	+	14.9208i	−0.634008	+	0.515738i
$838$	37.1450	+	64.3370i	1.28315	+	2.22248i
$839$	5.35125	−	9.26864i	0.184746	−	0.319989i	−0.758745	−	0.651388i	$-0.774187\pi$
$839$	5.35125	−	9.26864i	0.184746	−	0.319989i	0.943491	+	0.331399i	$0.107521\pi$
$840$	−4.68050	+	29.5955i	−0.161493	+	1.02114i
$841$	−35.0129	−	60.6441i	−1.20734	−	2.09118i
$842$	26.3695	−	45.6734i	0.908754	−	1.57401i
$843$	−23.3689	+	5.41330i	−0.804867	+	0.186444i
$844$	−36.9707	−	64.0352i	−1.27259	−	2.20418i
$845$	−5.22451	−	9.04912i	−0.179729	−	0.311299i
$846$	5.07742	−	74.1837i	0.174565	−	2.55049i
$847$	−5.72954	−	7.34117i	−0.196869	−	0.252246i
$848$	−12.3447	+	21.3817i	−0.423919	+	0.734250i
$849$	−7.29028	−	7.80631i	−0.250202	−	0.267912i
$850$	−9.42162			−0.323159
$851$	−7.07131			−0.242401
$852$	74.4199	+	79.6876i	2.54958	+	2.73005i
$853$	−4.90183	+	8.49022i	−0.167835	+	0.290700i	−0.937659	−	0.347558i	$-0.887011\pi$
$853$	−4.90183	+	8.49022i	−0.167835	+	0.290700i	0.769823	+	0.638257i	$0.220344\pi$
$854$	26.0461	−	64.3720i	0.891278	−	2.20276i
$855$	−0.690908	+	10.0945i	−0.0236286	+	0.345226i
$856$	5.51902	+	9.55923i	0.188636	+	0.326728i
$857$	1.06326	+	1.84162i	0.0363202	+	0.0629084i	0.883614	−	0.468216i	$-0.155103\pi$
$857$	1.06326	+	1.84162i	0.0363202	+	0.0629084i	−0.847294	+	0.531124i	$0.821770\pi$
$858$	−26.2904	+	6.09005i	−0.897539	+	0.207911i
$859$	−1.45019	+	2.51179i	−0.0494797	+	0.0857013i	−0.889704	−	0.456537i	$-0.849090\pi$
$859$	−1.45019	+	2.51179i	−0.0494797	+	0.0857013i	0.840225	+	0.542238i	$0.182423\pi$
$860$	−3.86871	−	6.70080i	−0.131922	−	0.228495i
$861$	45.4595	+	36.7951i	1.54925	+	1.25397i
$862$	−2.28055	+	3.95003i	−0.0776760	+	0.134539i
$863$	12.8885	+	22.3236i	0.438731	+	0.759905i	0.997592	−	0.0693567i	$-0.0220947\pi$
$863$	12.8885	+	22.3236i	0.438731	+	0.759905i	−0.558861	+	0.829262i	$0.688761\pi$
$864$	−26.0367	+	21.1797i	−0.885788	+	0.720550i
$865$	−10.4277	+	18.0612i	−0.354551	+	0.614100i
$866$	21.9755			0.746759
$867$	1.74596	−	5.72590i	0.0592961	−	0.194462i
$868$	20.5646	−	50.8247i	0.698007	−	1.72510i
$869$	26.6122	+	46.0937i	0.902757	+	1.56362i
$870$	−12.8699	+	42.2069i	−0.436330	+	1.43095i
$871$	2.92824	+	5.07186i	0.0992196	+	0.171853i
$872$	−16.2109	+	28.0781i	−0.548971	+	0.950845i
$873$	−26.1779	−	17.6011i	−0.885988	−	0.595706i
$874$	7.80984			0.264172
$875$	0.992363	−	2.45259i	0.0335480	−	0.0829128i
$876$	22.7226	−	5.26358i	0.767724	−	0.177840i
$877$	−7.23327	+	12.5284i	−0.244250	+	0.423053i	−0.961920	−	0.273329i	$-0.911875\pi$
$877$	−7.23327	+	12.5284i	−0.244250	+	0.423053i	0.717670	+	0.696383i	$0.245208\pi$
$878$	−49.4556			−1.66904
$879$	3.37119	−	11.0558i	0.113707	−	0.372904i
$880$	−29.0782			−0.980227
$881$	46.8921			1.57983			0.789917	−	0.613214i	$-0.210124\pi$
$881$	46.8921			1.57983			0.789917	+	0.613214i	$0.210124\pi$
$882$	−39.9363	+	35.9920i	−1.34472	+	1.21191i
$883$	−21.7458			−0.731806			−0.365903	−	0.930653i	$-0.619240\pi$
$883$	−21.7458			−0.731806			−0.365903	+	0.930653i	$0.619240\pi$
$884$	26.7683			0.900314
$885$	−3.81065	+	0.882720i	−0.128093	+	0.0296723i
$886$	−54.8227			−1.84180
$887$	−15.6500	+	27.1066i	−0.525475	+	0.910149i	0.474085	+	0.880479i	$0.342779\pi$
$887$	−15.6500	+	27.1066i	−0.525475	+	0.910149i	−0.999560	+	0.0296701i	$0.990554\pi$
$888$	−25.8237	+	84.6889i	−0.866586	+	2.84197i
$889$	17.3701	−	42.9297i	0.582576	−	1.43982i
$890$	5.11174			0.171346
$891$	12.9407	+	31.7591i	0.433529	+	1.06397i
$892$	−12.0648	+	20.8968i	−0.403958	+	0.699676i
$893$	16.3267	+	28.2786i	0.546352	+	0.946309i
$894$	25.3273	−	5.86696i	0.847072	−	0.196220i
$895$	−4.83593	−	8.37608i	−0.161647	−	0.279982i
$896$	−9.58324	+	23.6847i	−0.320154	+	0.791249i
$897$	−1.70784	−	1.82873i	−0.0570233	−	0.0610596i
$898$	−13.8230			−0.461278
$899$	22.6411	−	39.2155i	0.755123	−	1.30791i
$900$	12.2705	−	6.00718i	0.409018	−	0.200239i
$901$	−5.95339	−	10.3116i	−0.198336	−	0.343528i
$902$	−62.2494	+	107.819i	−2.07268	+	3.58998i
$903$	1.21622	−	7.69034i	0.0404733	−	0.255918i
$904$	−9.70667	−	16.8124i	−0.322839	−	0.559173i
$905$	4.93415	−	8.54620i	0.164017	−	0.284085i
$906$	−23.6278	+	77.4875i	−0.784980	+	2.57435i
$907$	4.85043	+	8.40120i	0.161056	+	0.278957i	0.935248	−	0.353994i	$-0.115177\pi$
$907$	4.85043	+	8.40120i	0.161056	+	0.278957i	−0.774192	+	0.632951i	$0.781843\pi$
$908$	56.6574	+	98.1335i	1.88024	+	3.25668i
$909$	−2.36210	+	1.15639i	−0.0783458	+	0.0383551i
$910$	−4.05768	+	10.0284i	−0.134511	+	0.332439i
$911$	−0.720390	+	1.24775i	−0.0238676	+	0.0413399i	−0.877712	−	0.479188i	$-0.840931\pi$
$911$	−0.720390	+	1.24775i	−0.0238676	+	0.0413399i	0.853845	+	0.520528i	$0.174265\pi$
$912$	13.0021	−	42.6406i	0.430544	−	1.41197i
$913$	20.4236			0.675922
$914$	89.8558			2.97216
$915$	−17.2993	+	4.00730i	−0.571896	+	0.132477i
$916$	−37.4392	+	64.8466i	−1.23703	+	2.14259i
$917$	−1.35687	−	1.73853i	−0.0448078	−	0.0574115i
$918$	−7.76547	−	48.3364i	−0.256299	−	1.59534i
$919$	−2.33645	−	4.04686i	−0.0770725	−	0.133494i	0.824913	−	0.565260i	$-0.191224\pi$
$919$	−2.33645	−	4.04686i	−0.0770725	−	0.133494i	−0.901986	+	0.431766i	$0.857891\pi$
$920$	−2.95705	−	5.12175i	−0.0974909	−	0.168859i
$921$	−1.15145	−	1.23296i	−0.0379416	−	0.0406272i
$922$	45.5240	−	78.8499i	1.49925	−	2.59678i
$923$	11.0390	+	19.1201i	0.363352	+	0.629344i
$924$	−61.8114	−	50.0304i	−2.03344	−	1.64588i
$925$	3.90897	−	6.77053i	0.128526	−	0.222614i
$926$	−11.6316	−	20.1465i	−0.382237	−	0.662053i
$927$	9.07648	+	6.10269i	0.298111	+	0.200439i
$928$	32.1386	−	55.6656i	1.05500	−	1.82731i
$929$	17.4673			0.573082			0.286541	−	0.958068i	$-0.407494\pi$
$929$	17.4673			0.573082			0.286541	+	0.958068i	$0.407494\pi$
$930$	−19.6570	+	4.55347i	−0.644579	+	0.149314i
$931$	5.73483	−	22.9019i	0.187952	−	0.750580i
$932$	12.3061	+	21.3148i	0.403099	+	0.698188i
$933$	14.6170	+	15.6517i	0.478540	+	0.512413i
$934$	13.6220	+	23.5940i	0.445725	+	0.772018i
$935$	7.01166	−	12.1446i	0.229306	−	0.397170i
$936$	−28.1385	+	13.7755i	−0.919736	+	0.450267i
$937$	11.5939			0.378757			0.189378	−	0.981904i	$-0.439353\pi$
$937$	11.5939			0.378757			0.189378	+	0.981904i	$0.439353\pi$
$938$	−9.31555	+	23.0231i	−0.304163	+	0.751730i
$939$	−9.19648	−	9.84744i	−0.300116	−	0.321359i
$940$	22.0452	−	38.1834i	0.719035	−	1.24541i
$941$	18.2134			0.593738			0.296869	−	0.954918i	$-0.404057\pi$
$941$	18.2134			0.593738			0.296869	+	0.954918i	$0.404057\pi$
$942$	−20.0264	−	21.4440i	−0.652497	−	0.698683i
$943$	−11.5436			−0.375910
$944$	17.2336			0.560907
$945$	13.4006	+	3.06972i	0.435922	+	0.0998579i
$946$	16.5743			0.538875
$947$	23.3446			0.758597			0.379299	−	0.925274i	$-0.376165\pi$
$947$	23.3446			0.758597			0.379299	+	0.925274i	$0.376165\pi$
$948$	75.1994	+	80.5222i	2.44236	+	2.61524i
$949$	4.72285			0.153310
$950$	−4.31722	+	7.47764i	−0.140069	+	0.242607i
$951$	16.8824	+	18.0774i	0.547450	+	0.586200i
$952$	39.1706	+	50.1886i	1.26952	+	1.62662i
$953$	25.2729			0.818671			0.409335	−	0.912384i	$-0.365761\pi$
$953$	25.2729			0.818671			0.409335	+	0.912384i	$0.365761\pi$
$954$	20.6207	+	13.8646i	0.667621	+	0.448884i
$955$	−13.2818	+	23.0048i	−0.429789	+	0.744416i
$956$	24.4779	+	42.3969i	0.791670	+	1.37121i
$957$	−44.8272	−	48.0002i	−1.44906	−	1.55163i
$958$	−23.6542	−	40.9703i	−0.764233	−	1.32369i
$959$	−13.3808	+	1.87361i	−0.432087	+	0.0605019i
$960$	−2.14969	+	0.497967i	−0.0693811	+	0.0160718i
$961$	−10.2935			−0.332049
$962$	−15.9834	+	27.6840i	−0.515325	+	0.892569i
$963$	4.54863	−	2.22683i	0.146577	−	0.0717586i
$964$	−25.0784	−	43.4371i	−0.807722	−	1.39902i
$965$	−7.24872	+	12.5552i	−0.233345	+	0.404165i
$966$	1.65758	−	10.4811i	0.0533318	−	0.337224i
$967$	−3.95319	−	6.84713i	−0.127126	−	0.220189i	0.795436	−	0.606038i	$-0.207242\pi$
$967$	−3.95319	−	6.84713i	−0.127126	−	0.220189i	−0.922562	+	0.385849i	$0.873909\pi$
$968$	11.5070	−	19.9307i	0.369849	−	0.640597i
$969$	14.6737	+	15.7123i	0.471386	+	0.504752i
$970$	−13.4596	−	23.3127i	−0.432162	−	0.748526i
$971$	0.623277	+	1.07955i	0.0200019	+	0.0346443i	0.875853	−	0.482578i	$-0.160299\pi$
$971$	0.623277	+	1.07955i	0.0200019	+	0.0346443i	−0.855851	+	0.517222i	$0.826966\pi$
$972$	40.9327	+	58.0012i	1.31292	+	1.86039i
$973$	−16.3137	+	2.28429i	−0.522995	+	0.0732309i
$974$	27.0031	−	46.7707i	0.865234	−	1.49863i
$975$	2.69503	−	0.624291i	0.0863100	−	0.0199933i
$976$	78.2358			2.50427
$977$	−23.2018			−0.742292			−0.371146	−	0.928575i	$-0.621035\pi$
$977$	−23.2018			−0.742292			−0.371146	+	0.928575i	$0.621035\pi$
$978$	3.14918	−	10.3278i	0.100700	−	0.330245i
$979$	−3.80421	+	6.58908i	−0.121583	+	0.210588i
$980$	−30.6522	+	8.75565i	−0.979149	+	0.279689i
$981$	12.3448	+	8.30020i	0.394140	+	0.265005i
$982$	−36.6984	−	63.5635i	−1.17109	−	2.02839i
$983$	19.0514	+	32.9979i	0.607644	+	1.05247i	0.991628	+	0.129131i	$0.0412186\pi$
$983$	19.0514	+	32.9979i	0.607644	+	1.05247i	−0.383983	+	0.923340i	$0.625448\pi$
$984$	−42.1558	+	138.250i	−1.34388	+	4.40726i
$985$	8.63512	−	14.9565i	0.275138	−	0.476553i
$986$	46.8781	+	81.1952i	1.49290	+	2.58578i
$987$	41.4163	−	15.9091i	1.31830	−	0.506393i
$988$	12.2659	−	21.2451i	0.390229	−	0.675897i
$989$	0.768384	+	1.33088i	0.0244332	+	0.0423195i
$990$	−1.99836	+	29.1971i	−0.0635121	+	0.927946i
$991$	2.53513	−	4.39098i	0.0805312	−	0.139484i	−0.822947	−	0.568118i	$-0.807672\pi$
$991$	2.53513	−	4.39098i	0.0805312	−	0.139484i	0.903478	+	0.428634i	$0.141005\pi$
$992$	29.3924			0.933211
$993$	−5.51319	−	5.90343i	−0.174956	−	0.187340i
$994$	−35.1181	+	86.7932i	−1.11388	+	2.75291i
$995$	−6.81936	−	11.8115i	−0.216188	−	0.374449i
$996$	41.1869	−	9.54076i	1.30506	−	0.302311i
$997$	−15.7537	−	27.2863i	−0.498926	−	0.864165i	0.501073	−	0.865405i	$-0.332939\pi$
$997$	−15.7537	−	27.2863i	−0.498926	−	0.864165i	−0.999999	+	0.00123985i	$0.999605\pi$
$998$	−42.9473	+	74.3870i	−1.35947	+	2.35468i
$999$	37.9571	+	14.4740i	1.20091	+	0.457938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.b.151.1	yes	24
3.2	odd	2		945.2.l.b.46.12		24
7.2	even	3		315.2.k.b.16.12	✓	24
9.4	even	3		315.2.k.b.256.12	yes	24
9.5	odd	6		945.2.k.b.361.1		24
21.2	odd	6		945.2.k.b.856.1		24
63.23	odd	6		945.2.l.b.226.12		24
63.58	even	3	inner	315.2.l.b.121.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.12	✓	24	7.2	even	3
315.2.k.b.256.12	yes	24	9.4	even	3
315.2.l.b.121.1	yes	24	63.58	even	3	inner
315.2.l.b.151.1	yes	24	1.1	even	1	trivial
945.2.k.b.361.1		24	9.5	odd	6
945.2.k.b.856.1		24	21.2	odd	6
945.2.l.b.46.12		24	3.2	odd	2
945.2.l.b.226.12		24	63.23	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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.56008 q^{2} +(-1.18219 - 1.26587i) q^{3} +4.55403 q^{4} +(0.500000 - 0.866025i) q^{5} +(3.02651 + 3.24073i) q^{6} +(-0.992363 + 2.45259i) q^{7} -6.53853 q^{8} +(-0.204852 + 2.99300i) q^{9} +O(q^{10})\)	\(q-2.56008 q^{2} +(-1.18219 - 1.26587i) q^{3} +4.55403 q^{4} +(0.500000 - 0.866025i) q^{5} +(3.02651 + 3.24073i) q^{6} +(-0.992363 + 2.45259i) q^{7} -6.53853 q^{8} +(-0.204852 + 2.99300i) q^{9} +(-1.28004 + 2.21710i) q^{10} +(-1.90524 - 3.29997i) q^{11} +(-5.38373 - 5.76481i) q^{12} +(-0.798588 - 1.38320i) q^{13} +(2.54053 - 6.27885i) q^{14} +(-1.68737 + 0.390872i) q^{15} +7.63112 q^{16} +(-1.84010 + 3.18715i) q^{17} +(0.524439 - 7.66233i) q^{18} +(1.68636 + 2.92086i) q^{19} +(2.27701 - 3.94390i) q^{20} +(4.27783 - 1.64323i) q^{21} +(4.87757 + 8.44820i) q^{22} +(-0.452249 + 0.783319i) q^{23} +(7.72978 + 8.27692i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.04445 + 3.54110i) q^{26} +(4.03092 - 3.27898i) q^{27} +(-4.51925 + 11.1692i) q^{28} +(-4.97559 + 8.61797i) q^{29} +(4.31981 - 1.00067i) q^{30} -4.55044 q^{31} -6.45926 q^{32} +(-1.92498 + 6.31298i) q^{33} +(4.71081 - 8.15936i) q^{34} +(1.62783 + 2.08571i) q^{35} +(-0.932902 + 13.6302i) q^{36} +(3.90897 + 6.77053i) q^{37} +(-4.31722 - 7.47764i) q^{38} +(-0.806862 + 2.64611i) q^{39} +(-3.26926 + 5.66253i) q^{40} +(6.38119 + 11.0525i) q^{41} +(-10.9516 + 4.20681i) q^{42} +(0.849513 - 1.47140i) q^{43} +(-8.67652 - 15.0282i) q^{44} +(2.48959 + 1.67391i) q^{45} +(1.15780 - 2.00536i) q^{46} +9.68162 q^{47} +(-9.02144 - 9.66001i) q^{48} +(-5.03043 - 4.86773i) q^{49} +(1.28004 + 2.21710i) q^{50} +(6.20986 - 1.43849i) q^{51} +(-3.63679 - 6.29911i) q^{52} +(-1.61768 + 2.80191i) q^{53} +(-10.3195 + 8.39446i) q^{54} -3.81048 q^{55} +(6.48859 - 16.0364i) q^{56} +(1.70383 - 5.58772i) q^{57} +(12.7379 - 22.0627i) q^{58} +2.25833 q^{59} +(-7.68433 + 1.78004i) q^{60} +10.2522 q^{61} +11.6495 q^{62} +(-7.13732 - 3.47256i) q^{63} +1.27399 q^{64} -1.59718 q^{65} +(4.92811 - 16.1618i) q^{66} -3.66677 q^{67} +(-8.37987 + 14.5144i) q^{68} +(1.52622 - 0.353543i) q^{69} +(-4.16737 - 5.33959i) q^{70} -13.8231 q^{71} +(1.33943 - 19.5698i) q^{72} +(-1.47850 + 2.56083i) q^{73} +(-10.0073 - 17.3331i) q^{74} +(-0.505180 + 1.65674i) q^{75} +(7.67972 + 13.3017i) q^{76} +(9.98418 - 1.39801i) q^{77} +(2.06563 - 6.77426i) q^{78} -13.9679 q^{79} +(3.81556 - 6.60875i) q^{80} +(-8.91607 - 1.22624i) q^{81} +(-16.3364 - 28.2954i) q^{82} +(-2.67992 + 4.64177i) q^{83} +(19.4813 - 7.48332i) q^{84} +(1.84010 + 3.18715i) q^{85} +(-2.17483 + 3.76691i) q^{86} +(16.7913 - 3.88963i) q^{87} +(12.4575 + 21.5770i) q^{88} +(-0.998354 - 1.72920i) q^{89} +(-6.37355 - 4.28534i) q^{90} +(4.18491 - 0.585980i) q^{91} +(-2.05956 + 3.56726i) q^{92} +(5.37948 + 5.76026i) q^{93} -24.7858 q^{94} +3.37272 q^{95} +(7.63607 + 8.17658i) q^{96} +(-5.25748 + 9.10623i) q^{97} +(12.8783 + 12.4618i) q^{98} +(10.2671 - 5.02637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

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