LMFDB - Embedded newform 210.2.r.a.131.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(101,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("210.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.r (of order $6$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.1
Root			$-0.111613 - 1.72845i$ of defining polynomial
Character	$\chi$	$=$	210.131
Dual form			210.2.r.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.72845 + 0.111613i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.55269 + 0.767566i) q^{6} +(-1.91871 + 1.82168i) q^{7} -1.00000i q^{8} +(2.97509 - 0.385834i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72845 + 0.111613i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.55269 + 0.767566i) q^{6} +(-1.91871 + 1.82168i) q^{7} -1.00000i q^{8} +(2.97509 - 0.385834i) q^{9} +(-0.866025 + 0.500000i) q^{10} +(-1.99775 + 1.15340i) q^{11} +(-0.960885 - 1.44108i) q^{12} +5.00084i q^{13} +(2.57250 - 0.618268i) q^{14} +(-0.767566 + 1.55269i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.15115 + 5.45795i) q^{17} +(-2.76942 - 1.15340i) q^{18} +(6.54470 + 3.77859i) q^{19} +1.00000 q^{20} +(3.11308 - 3.36285i) q^{21} +2.30680 q^{22} +(-5.51880 - 3.18628i) q^{23} +(0.111613 + 1.72845i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.50042 - 4.33086i) q^{26} +(-5.09922 + 0.998953i) q^{27} +(-2.53698 - 0.750813i) q^{28} +3.83533i q^{29} +(1.44108 - 0.960885i) q^{30} +(-3.79452 + 2.19077i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.32428 - 2.21657i) q^{33} -6.30230i q^{34} +(0.618268 + 2.57250i) q^{35} +(1.82168 + 2.38358i) q^{36} +(3.45465 - 5.98363i) q^{37} +(-3.77859 - 6.54470i) q^{38} +(-0.558158 - 8.64371i) q^{39} +(-0.866025 - 0.500000i) q^{40} -9.79371 q^{41} +(-4.37743 + 1.35577i) q^{42} +2.55278 q^{43} +(-1.99775 - 1.15340i) q^{44} +(1.15340 - 2.76942i) q^{45} +(3.18628 + 5.51880i) q^{46} +(0.828416 - 1.43486i) q^{47} +(0.767566 - 1.55269i) q^{48} +(0.362928 - 6.99059i) q^{49} +1.00000i q^{50} +(-6.05578 - 9.08209i) q^{51} +(-4.33086 + 2.50042i) q^{52} +(2.81699 - 1.62639i) q^{53} +(4.91553 + 1.68449i) q^{54} +2.30680i q^{55} +(1.82168 + 1.91871i) q^{56} +(-11.7339 - 5.80063i) q^{57} +(1.91767 - 3.32150i) q^{58} +(4.96573 + 8.60089i) q^{59} +(-1.72845 + 0.111613i) q^{60} +(-5.18202 - 2.99184i) q^{61} +4.38153 q^{62} +(-5.00547 + 6.15997i) q^{63} -1.00000 q^{64} +(4.33086 + 2.50042i) q^{65} +(-3.98719 + 0.257468i) q^{66} +(1.38358 + 2.39643i) q^{67} +(-3.15115 + 5.45795i) q^{68} +(9.89460 + 4.89136i) q^{69} +(0.750813 - 2.53698i) q^{70} -2.85910i q^{71} +(-0.385834 - 2.97509i) q^{72} +(-3.18851 + 1.84089i) q^{73} +(-5.98363 + 3.45465i) q^{74} +(0.960885 + 1.44108i) q^{75} +7.55717i q^{76} +(1.73198 - 5.85231i) q^{77} +(-3.83848 + 7.76475i) q^{78} +(-1.27945 + 2.21607i) q^{79} +(0.500000 + 0.866025i) q^{80} +(8.70226 - 2.29578i) q^{81} +(8.48160 + 4.89686i) q^{82} +1.83743 q^{83} +(4.46885 + 1.01458i) q^{84} +6.30230 q^{85} +(-2.21077 - 1.27639i) q^{86} +(-0.428072 - 6.62919i) q^{87} +(1.15340 + 1.99775i) q^{88} +(2.94387 - 5.09894i) q^{89} +(-2.38358 + 1.82168i) q^{90} +(-9.10996 - 9.59518i) q^{91} -6.37256i q^{92} +(6.31412 - 4.21015i) q^{93} +(-1.43486 + 0.828416i) q^{94} +(6.54470 - 3.77859i) q^{95} +(-1.44108 + 0.960885i) q^{96} -4.61723i q^{97} +(-3.80960 + 5.87256i) q^{98} +(-5.49845 + 4.20226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9	$ 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9} - 12 q^{11} + 2 q^{12} + 12 q^{14} - 4 q^{15} - 6 q^{16} + 12 q^{17} - 4 q^{18} + 12 q^{20} - 18 q^{21} - 24 q^{23} - 4 q^{24} - 6 q^{25} - 4 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} + 12 q^{31} - 22 q^{33} + 4 q^{35} + 6 q^{36} - 8 q^{37} + 8 q^{38} + 30 q^{39} - 4 q^{41} - 20 q^{42} - 12 q^{44} + 2 q^{46} + 16 q^{47} + 4 q^{48} - 14 q^{49} + 4 q^{51} - 12 q^{52} - 48 q^{53} - 4 q^{54} + 6 q^{56} - 36 q^{57} + 8 q^{58} + 12 q^{59} - 2 q^{60} - 30 q^{61} + 8 q^{62} - 4 q^{63} - 12 q^{64} + 12 q^{65} - 34 q^{66} - 4 q^{67} - 12 q^{68} + 50 q^{69} + 6 q^{70} + 4 q^{72} - 2 q^{75} + 20 q^{77} + 32 q^{78} - 4 q^{79} + 6 q^{80} + 50 q^{81} - 40 q^{83} - 12 q^{84} + 24 q^{85} - 54 q^{86} + 8 q^{87} + 26 q^{89} - 8 q^{90} + 28 q^{91} - 32 q^{93} + 24 q^{94} - 2 q^{96} + 16 q^{98} + 48 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9 - 12 * q^11 + 2 * q^12 + 12 * q^14 - 4 * q^15 - 6 * q^16 + 12 * q^17 - 4 * q^18 + 12 * q^20 - 18 * q^21 - 24 * q^23 - 4 * q^24 - 6 * q^25 - 4 * q^26 - 8 * q^27 + 4 * q^28 + 2 * q^30 + 12 * q^31 - 22 * q^33 + 4 * q^35 + 6 * q^36 - 8 * q^37 + 8 * q^38 + 30 * q^39 - 4 * q^41 - 20 * q^42 - 12 * q^44 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 14 * q^49 + 4 * q^51 - 12 * q^52 - 48 * q^53 - 4 * q^54 + 6 * q^56 - 36 * q^57 + 8 * q^58 + 12 * q^59 - 2 * q^60 - 30 * q^61 + 8 * q^62 - 4 * q^63 - 12 * q^64 + 12 * q^65 - 34 * q^66 - 4 * q^67 - 12 * q^68 + 50 * q^69 + 6 * q^70 + 4 * q^72 - 2 * q^75 + 20 * q^77 + 32 * q^78 - 4 * q^79 + 6 * q^80 + 50 * q^81 - 40 * q^83 - 12 * q^84 + 24 * q^85 - 54 * q^86 + 8 * q^87 + 26 * q^89 - 8 * q^90 + 28 * q^91 - 32 * q^93 + 24 * q^94 - 2 * q^96 + 16 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.72845	+	0.111613i	−0.997922	+	0.0644396i
$3$	−1.72845	+	0.111613i	−0.997922	+	0.0644396i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.55269	+	0.767566i	0.633883	+	0.313358i
$7$	−1.91871	+	1.82168i	−0.725206	+	0.688532i
$7$	−1.91871	+	1.82168i	−0.725206	+	0.688532i
$8$		−	1.00000i		−	0.353553i
$9$	2.97509	−	0.385834i	0.991695	−	0.128611i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$	−1.99775	+	1.15340i	−0.602344	+	0.347763i	−0.769963	−	0.638089i	$-0.779725\pi$
$11$	−1.99775	+	1.15340i	−0.602344	+	0.347763i	0.167619	+	0.985852i	$0.446392\pi$
$12$	−0.960885	−	1.44108i	−0.277384	−	0.416003i
$13$			5.00084i			1.38698i	0.720464	+	0.693492i	$0.243929\pi$
$13$			5.00084i			1.38698i	−0.720464	+	0.693492i	$0.756071\pi$
$14$	2.57250	−	0.618268i	0.687529	−	0.165239i
$15$	−0.767566	+	1.55269i	−0.198185	+	0.400903i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.15115	+	5.45795i	0.764266	+	1.32375i	0.940634	+	0.339423i	$0.110232\pi$
$17$	3.15115	+	5.45795i	0.764266	+	1.32375i	−0.176368	+	0.984324i	$0.556435\pi$
$18$	−2.76942	−	1.15340i	−0.652758	−	0.271859i
$19$	6.54470	+	3.77859i	1.50146	+	0.866867i	0.999999	+	0.00168616i	$0.000536721\pi$
$19$	6.54470	+	3.77859i	1.50146	+	0.866867i	0.501460	+	0.865181i	$0.332797\pi$
$20$	1.00000			0.223607
$21$	3.11308	−	3.36285i	0.679330	−	0.733833i
$22$	2.30680			0.491812
$23$	−5.51880	−	3.18628i	−1.15075	−	0.664385i	−0.201679	−	0.979452i	$-0.564640\pi$
$23$	−5.51880	−	3.18628i	−1.15075	−	0.664385i	−0.949070	+	0.315066i	$0.897973\pi$
$24$	0.111613	+	1.72845i	0.0227829	+	0.352819i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	2.50042	−	4.33086i	0.490373	−	0.849351i
$27$	−5.09922	+	0.998953i	−0.981346	+	0.192249i
$28$	−2.53698	−	0.750813i	−0.479445	−	0.141890i
$29$			3.83533i			0.712204i	0.934447	+	0.356102i	$0.115894\pi$
$29$			3.83533i			0.712204i	−0.934447	+	0.356102i	$0.884106\pi$
$30$	1.44108	−	0.960885i	0.263103	−	0.175433i
$31$	−3.79452	+	2.19077i	−0.681516	+	0.393473i	−0.800426	−	0.599432i	$-0.795393\pi$
$31$	−3.79452	+	2.19077i	−0.681516	+	0.393473i	0.118910	+	0.992905i	$0.462060\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.32428	−	2.21657i	0.578682	−	0.385855i
$34$		−	6.30230i		−	1.08083i
$35$	0.618268	+	2.57250i	0.104506	+	0.434831i
$36$	1.82168	+	2.38358i	0.303614	+	0.397264i
$37$	3.45465	−	5.98363i	0.567941	−	0.983703i	−0.428828	−	0.903386i	$-0.641074\pi$
$37$	3.45465	−	5.98363i	0.567941	−	0.983703i	0.996769	−	0.0803166i	$-0.0255931\pi$
$38$	−3.77859	−	6.54470i	−0.612968	−	1.06169i
$39$	−0.558158	−	8.64371i	−0.0893767	−	1.38410i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	−9.79371			−1.52952			−0.764760	−	0.644315i	$-0.777143\pi$
$41$	−9.79371			−1.52952			−0.764760	+	0.644315i	$0.777143\pi$
$42$	−4.37743	+	1.35577i	−0.675452	+	0.209200i
$43$	2.55278			0.389296			0.194648	−	0.980873i	$-0.437644\pi$
$43$	2.55278			0.389296			0.194648	+	0.980873i	$0.437644\pi$
$44$	−1.99775	−	1.15340i	−0.301172	−	0.173882i
$45$	1.15340	−	2.76942i	0.171939	−	0.412840i
$46$	3.18628	+	5.51880i	0.469791	+	0.813703i
$47$	0.828416	−	1.43486i	0.120837	−	0.209296i	−0.799261	−	0.600984i	$-0.794776\pi$
$47$	0.828416	−	1.43486i	0.120837	−	0.209296i	0.920098	+	0.391688i	$0.128109\pi$
$48$	0.767566	−	1.55269i	0.110789	−	0.224111i
$49$	0.362928	−	6.99059i	0.0518469	−	0.998655i
$50$			1.00000i			0.141421i
$51$	−6.05578	−	9.08209i	−0.847979	−	1.27175i
$52$	−4.33086	+	2.50042i	−0.600582	+	0.346746i
$53$	2.81699	−	1.62639i	0.386944	−	0.223402i	−0.293891	−	0.955839i	$-0.594950\pi$
$53$	2.81699	−	1.62639i	0.386944	−	0.223402i	0.680835	+	0.732437i	$0.261617\pi$
$54$	4.91553	+	1.68449i	0.668920	+	0.229231i
$55$			2.30680i			0.311049i
$56$	1.82168	+	1.91871i	0.243433	+	0.256399i
$57$	−11.7339	−	5.80063i	−1.55420	−	0.768312i
$58$	1.91767	−	3.32150i	0.251802	−	0.436134i
$59$	4.96573	+	8.60089i	0.646483	+	1.11974i	0.983957	+	0.178406i	$0.0570940\pi$
$59$	4.96573	+	8.60089i	0.646483	+	1.11974i	−0.337474	+	0.941335i	$0.609573\pi$
$60$	−1.72845	+	0.111613i	−0.223142	+	0.0144091i
$61$	−5.18202	−	2.99184i	−0.663489	−	0.383066i	0.130116	−	0.991499i	$-0.458465\pi$
$61$	−5.18202	−	2.99184i	−0.663489	−	0.383066i	−0.793605	+	0.608433i	$0.791798\pi$
$62$	4.38153			0.556455
$63$	−5.00547	+	6.15997i	−0.630630	+	0.776084i
$64$	−1.00000			−0.125000
$65$	4.33086	+	2.50042i	0.537176	+	0.310139i
$66$	−3.98719	+	0.257468i	−0.490789	+	0.0316922i
$67$	1.38358	+	2.39643i	0.169031	+	0.292771i	0.938080	−	0.346420i	$-0.112603\pi$
$67$	1.38358	+	2.39643i	0.169031	+	0.292771i	−0.769048	+	0.639191i	$0.779269\pi$
$68$	−3.15115	+	5.45795i	−0.382133	+	0.661874i
$69$	9.89460	+	4.89136i	1.19117	+	0.588851i
$70$	0.750813	−	2.53698i	0.0897393	−	0.303227i
$71$		−	2.85910i		−	0.339312i	−0.985503	−	0.169656i	$-0.945734\pi$
$71$		−	2.85910i		−	0.339312i	0.985503	−	0.169656i	$-0.0542657\pi$
$72$	−0.385834	−	2.97509i	−0.0454710	−	0.350617i
$73$	−3.18851	+	1.84089i	−0.373187	+	0.215459i	−0.674850	−	0.737955i	$-0.735792\pi$
$73$	−3.18851	+	1.84089i	−0.373187	+	0.215459i	0.301663	+	0.953415i	$0.402458\pi$
$74$	−5.98363	+	3.45465i	−0.695583	+	0.401595i
$75$	0.960885	+	1.44108i	0.110953	+	0.166401i
$76$			7.55717i			0.866867i
$77$	1.73198	−	5.85231i	0.197377	−	0.666933i
$78$	−3.83848	+	7.76475i	−0.434622	+	0.879185i
$79$	−1.27945	+	2.21607i	−0.143949	+	0.249327i	−0.928980	−	0.370129i	$-0.879313\pi$
$79$	−1.27945	+	2.21607i	−0.143949	+	0.249327i	0.785031	+	0.619456i	$0.212647\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	8.70226	−	2.29578i	0.966918	−	0.255087i
$82$	8.48160	+	4.89686i	0.936636	+	0.540767i
$83$	1.83743			0.201684			0.100842	−	0.994902i	$-0.467846\pi$
$83$	1.83743			0.201684			0.100842	+	0.994902i	$0.467846\pi$
$84$	4.46885	+	1.01458i	0.487592	+	0.110700i
$85$	6.30230			0.683580
$86$	−2.21077	−	1.27639i	−0.238394	−	0.137637i
$87$	−0.428072	−	6.62919i	−0.0458942	−	0.710723i
$88$	1.15340	+	1.99775i	0.122953	+	0.212961i
$89$	2.94387	−	5.09894i	0.312050	−	0.540486i	−0.666756	−	0.745276i	$-0.732318\pi$
$89$	2.94387	−	5.09894i	0.312050	−	0.540486i	0.978806	+	0.204790i	$0.0656511\pi$
$90$	−2.38358	+	1.82168i	−0.251252	+	0.192022i
$91$	−9.10996	−	9.59518i	−0.954983	−	1.00585i
$92$		−	6.37256i		−	0.664385i
$93$	6.31412	−	4.21015i	0.654744	−	0.436572i
$94$	−1.43486	+	0.828416i	−0.147994	+	0.0854446i
$95$	6.54470	−	3.77859i	0.671472	−	0.387675i
$96$	−1.44108	+	0.960885i	−0.147079	+	0.0980699i
$97$		−	4.61723i		−	0.468808i	−0.972139	−	0.234404i	$-0.924686\pi$
$97$		−	4.61723i		−	0.468808i	0.972139	−	0.234404i	$-0.0753139\pi$
$98$	−3.80960	+	5.87256i	−0.384827	+	0.593218i
$99$	−5.49845	+	4.20226i	−0.552615	+	0.422343i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	5.65702	+	9.79825i	0.562894	+	0.974962i	0.997242	+	0.0742165i	$0.0236456\pi$
$101$	5.65702	+	9.79825i	0.562894	+	0.974962i	−0.434348	+	0.900745i	$0.643021\pi$
$102$	0.703417	+	10.8932i	0.0696486	+	1.07859i
$103$	6.37747	+	3.68203i	0.628391	+	0.362802i	0.780129	−	0.625619i	$-0.215154\pi$
$103$	6.37747	+	3.68203i	0.628391	+	0.362802i	−0.151738	+	0.988421i	$0.548487\pi$
$104$	5.00084			0.490373
$105$	−1.35577	−	4.37743i	−0.132310	−	0.427193i
$106$	−3.25278			−0.315938
$107$	7.29084	+	4.20937i	0.704832	+	0.406935i	0.809145	−	0.587609i	$-0.199931\pi$
$107$	7.29084	+	4.20937i	0.704832	+	0.406935i	−0.104312	+	0.994545i	$0.533264\pi$
$108$	−3.41473	−	3.91658i	−0.328583	−	0.376873i
$109$	3.33156	+	5.77043i	0.319105	+	0.552707i	0.980302	−	0.197506i	$-0.0632843\pi$
$109$	3.33156	+	5.77043i	0.319105	+	0.552707i	−0.661196	+	0.750213i	$0.729951\pi$
$110$	1.15340	−	1.99775i	0.109972	−	0.190478i
$111$	−5.30334	+	10.7280i	−0.503371	+	1.01826i
$112$	−0.618268	−	2.57250i	−0.0584209	−	0.243078i
$113$			4.45505i			0.419096i	0.977798	+	0.209548i	$0.0671992\pi$
$113$			4.45505i			0.419096i	−0.977798	+	0.209548i	$0.932801\pi$
$114$	7.26157	+	10.8905i	0.680109	+	1.01999i
$115$	−5.51880	+	3.18628i	−0.514631	+	0.297122i
$116$	−3.32150	+	1.91767i	−0.308393	+	0.178051i
$117$	1.92950	+	14.8779i	0.178382	+	1.37546i
$118$		−	9.93145i		−	0.914264i
$119$	−15.9888	−	4.73184i	−1.46569	−	0.433767i
$120$	1.55269	+	0.767566i	0.141740	+	0.0700689i
$121$	−2.83934	+	4.91787i	−0.258121	+	0.447079i
$122$	2.99184	+	5.18202i	0.270868	+	0.469158i
$123$	16.9279	−	1.09310i	1.52634	−	0.0985618i
$124$	−3.79452	−	2.19077i	−0.340758	−	0.196737i
$125$	−1.00000			−0.0894427
$126$	7.41485	−	2.83196i	0.660567	−	0.252291i
$127$	−1.83694			−0.163002			−0.0815011	−	0.996673i	$-0.525971\pi$
$127$	−1.83694			−0.163002			−0.0815011	+	0.996673i	$0.525971\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−4.41236	+	0.284923i	−0.388487	+	0.0250861i
$130$	−2.50042	−	4.33086i	−0.219301	−	0.379841i
$131$	2.76942	−	4.79677i	0.241965	−	0.419096i	−0.719309	−	0.694690i	$-0.755541\pi$
$131$	2.76942	−	4.79677i	0.241965	−	0.419096i	0.961274	+	0.275595i	$0.0888747\pi$
$132$	3.58174	+	1.77062i	0.311751	+	0.154113i
$133$	−19.4408	+	4.67236i	−1.68573	+	0.405145i
$134$		−	2.76716i		−	0.239047i
$135$	−1.68449	+	4.91553i	−0.144978	+	0.423062i
$136$	5.45795	−	3.15115i	0.468015	−	0.270209i
$137$	−1.07477	+	0.620520i	−0.0918240	+	0.0530146i	−0.545209	−	0.838300i	$-0.683550\pi$
$137$	−1.07477	+	0.620520i	−0.0918240	+	0.0530146i	0.453385	+	0.891315i	$0.350216\pi$
$138$	−6.12330	−	9.18334i	−0.521250	−	0.781738i
$139$		−	12.5344i		−	1.06315i	−0.847011	−	0.531576i	$-0.821600\pi$
$139$		−	12.5344i		−	1.06315i	0.847011	−	0.531576i	$-0.178400\pi$
$140$	−1.91871	+	1.82168i	−0.162161	+	0.153960i
$141$	−1.27173	+	2.57255i	−0.107099	+	0.216647i
$142$	−1.42955	+	2.47605i	−0.119965	+	0.207786i
$143$	−5.76797	−	9.99042i	−0.482342	−	0.835441i
$144$	−1.15340	+	2.76942i	−0.0961167	+	0.230785i
$145$	3.32150	+	1.91767i	0.275835	+	0.159254i
$146$	3.68177			0.304706
$147$	0.152935	+	12.1234i	0.0126138	+	0.999920i
$148$	6.90930			0.567941
$149$	−13.5058	−	7.79757i	−1.10644	−	0.638802i	−0.168533	−	0.985696i	$-0.553903\pi$
$149$	−13.5058	−	7.79757i	−1.10644	−	0.638802i	−0.937904	+	0.346894i	$0.887236\pi$
$150$	−0.111613	−	1.72845i	−0.00911314	−	0.141127i
$151$	−1.51958	−	2.63198i	−0.123661	−	0.214188i	0.797548	−	0.603256i	$-0.206130\pi$
$151$	−1.51958	−	2.63198i	−0.123661	−	0.214188i	−0.921209	+	0.389068i	$0.872797\pi$
$152$	3.77859	−	6.54470i	0.306484	−	0.530846i
$153$	11.4808	+	15.0220i	0.928168	+	1.21446i
$154$	−4.42609	+	4.20226i	−0.356665	+	0.338628i
$155$			4.38153i			0.351933i
$156$	7.20659	−	4.80523i	0.576989	−	0.384727i
$157$	13.7050	−	7.91260i	1.09378	−	0.631494i	0.159200	−	0.987246i	$-0.449109\pi$
$157$	13.7050	−	7.91260i	1.09378	−	0.631494i	0.934580	+	0.355752i	$0.115775\pi$
$158$	2.21607	−	1.27945i	0.176301	−	0.101787i
$159$	−4.68751	+	3.12555i	−0.371744	+	0.247872i
$160$		−	1.00000i		−	0.0790569i
$161$	16.3934	−	3.93995i	1.29198	−	0.310512i
$162$	−8.68427	−	2.36293i	−0.682301	−	0.185649i
$163$	4.30841	−	7.46238i	0.337461	−	0.584499i	−0.646494	−	0.762919i	$-0.723765\pi$
$163$	4.30841	−	7.46238i	0.337461	−	0.584499i	0.983954	+	0.178420i	$0.0570987\pi$
$164$	−4.89686	−	8.48160i	−0.382380	−	0.662302i
$165$	−0.257468	−	3.98719i	−0.0200439	−	0.310402i
$166$	−1.59126	−	0.918714i	−0.123506	−	0.0713060i
$167$	8.64948			0.669317			0.334658	−	0.942339i	$-0.391379\pi$
$167$	8.64948			0.669317			0.334658	+	0.942339i	$0.391379\pi$
$168$	−3.36285	−	3.11308i	−0.259449	−	0.240179i
$169$	−12.0084			−0.923724
$170$	−5.45795	−	3.15115i	−0.418606	−	0.241682i
$171$	20.9290	+	8.71645i	1.60048	+	0.666563i
$172$	1.27639	+	2.21077i	0.0973239	+	0.168570i
$173$	−8.96573	+	15.5291i	−0.681652	+	1.18066i	0.292825	+	0.956166i	$0.405405\pi$
$173$	−8.96573	+	15.5291i	−0.681652	+	1.18066i	−0.974477	+	0.224489i	$0.927929\pi$
$174$	−2.94387	+	5.95508i	−0.223174	+	0.451454i
$175$	2.53698	+	0.750813i	0.191778	+	0.0567561i
$176$		−	2.30680i		−	0.173882i
$177$	−9.54298	−	14.3120i	−0.717295	−	1.07575i
$178$	−5.09894	+	2.94387i	−0.382181	+	0.220653i
$179$	−10.4070	+	6.00848i	−0.777855	+	0.449095i	−0.835670	−	0.549233i	$-0.814920\pi$
$179$	−10.4070	+	6.00848i	−0.777855	+	0.449095i	0.0578145	+	0.998327i	$0.481587\pi$
$180$	2.97509	−	0.385834i	0.221750	−	0.0287584i
$181$		−	9.52612i		−	0.708071i	−0.935232	−	0.354036i	$-0.884809\pi$
$181$		−	9.52612i		−	0.708071i	0.935232	−	0.354036i	$-0.115191\pi$
$182$	3.09186	+	12.8647i	0.229184	+	0.953591i
$183$	9.29079	+	4.59287i	0.686795	+	0.339514i
$184$	−3.18628	+	5.51880i	−0.234896	+	0.406851i
$185$	−3.45465	−	5.98363i	−0.253991	−	0.439925i
$186$	−7.57326	+	0.489035i	−0.555299	+	0.0358578i
$187$	−12.5904	−	7.26907i	−0.920701	−	0.531567i
$188$	1.65683			0.120837
$189$	7.96418	−	11.2059i	0.579309	−	0.815108i
$190$	−7.55717			−0.548255
$191$	−4.30564	−	2.48586i	−0.311545	−	0.179871i	0.336073	−	0.941836i	$-0.390901\pi$
$191$	−4.30564	−	2.48586i	−0.311545	−	0.179871i	−0.647618	+	0.761965i	$0.724235\pi$
$192$	1.72845	−	0.111613i	0.124740	−	0.00805496i
$193$	−3.01660	−	5.22491i	−0.217140	−	0.376097i	0.736793	−	0.676119i	$-0.236339\pi$
$193$	−3.01660	−	5.22491i	−0.217140	−	0.376097i	−0.953932	+	0.300022i	$0.903006\pi$
$194$	−2.30861	+	3.99864i	−0.165749	+	0.287085i
$195$	−7.76475	−	3.83848i	−0.556045	−	0.274879i
$196$	6.23549	−	3.18099i	0.445392	−	0.227213i
$197$		−	14.2144i		−	1.01273i	−0.862318	−	0.506366i	$-0.830988\pi$
$197$		−	14.2144i		−	1.01273i	0.862318	−	0.506366i	$-0.169012\pi$
$198$	6.86293	−	0.890043i	0.487727	−	0.0632526i
$199$	1.94932	−	1.12544i	0.138183	−	0.0797802i	−0.429315	−	0.903155i	$-0.641245\pi$
$199$	1.94932	−	1.12544i	0.138183	−	0.0797802i	0.567498	+	0.823375i	$0.307911\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−2.65893	−	3.98769i	−0.187546	−	0.281270i
$202$		−	11.3140i		−	0.796053i
$203$	−6.98677	−	7.35891i	−0.490375	−	0.516494i
$204$	4.83743	−	9.78550i	0.338688	−	0.685122i
$205$	−4.89686	+	8.48160i	−0.342011	+	0.592381i
$206$	−3.68203	−	6.37747i	−0.256540	−	0.444339i
$207$	−17.6483	−	7.35011i	−1.22664	−	0.510868i
$208$	−4.33086	−	2.50042i	−0.300291	−	0.173373i
$209$	−17.4329			−1.20586
$210$	−1.01458	+	4.46885i	−0.0700129	+	0.308380i
$211$	27.6034			1.90029			0.950147	−	0.311804i	$-0.100933\pi$
$211$	27.6034			1.90029			0.950147	+	0.311804i	$0.100933\pi$
$212$	2.81699	+	1.62639i	0.193472	+	0.111701i
$213$	0.319112	+	4.94181i	0.0218652	+	0.338607i
$214$	−4.20937	−	7.29084i	−0.287747	−	0.498392i
$215$	1.27639	−	2.21077i	0.0870492	−	0.150774i
$216$	0.998953	+	5.09922i	0.0679701	+	0.346958i
$217$	3.28971	−	11.1159i	0.223320	−	0.754594i
$218$		−	6.66311i		−	0.451283i
$219$	5.30571	−	3.53776i	0.358527	−	0.239060i
$220$	−1.99775	+	1.15340i	−0.134688	+	0.0777622i
$221$	−27.2943	+	15.7584i	−1.83602	+	1.06002i
$222$	9.95683	−	6.63904i	0.668258	−	0.445583i
$223$		−	23.0777i		−	1.54539i	−0.634775	−	0.772697i	$-0.718907\pi$
$223$		−	23.0777i		−	1.54539i	0.634775	−	0.772697i	$-0.281093\pi$
$224$	−0.750813	+	2.53698i	−0.0501658	+	0.169509i
$225$	−1.82168	−	2.38358i	−0.121446	−	0.158905i
$226$	2.22752	−	3.85818i	0.148173	−	0.256643i
$227$	10.0175	+	17.3509i	0.664887	+	1.15162i	0.979316	+	0.202337i	$0.0648538\pi$
$227$	10.0175	+	17.3509i	0.664887	+	1.15162i	−0.314429	+	0.949281i	$0.601813\pi$
$228$	−0.843477	−	13.0622i	−0.0558606	−	0.865066i
$229$	24.9111	+	14.3824i	1.64617	+	0.950417i	0.978575	+	0.205892i	$0.0660097\pi$
$229$	24.9111	+	14.3824i	1.64617	+	0.950417i	0.667595	+	0.744524i	$0.267324\pi$
$230$	6.37256			0.420194
$231$	−2.34044	+	10.3087i	−0.153990	+	0.678266i
$232$	3.83533			0.251802
$233$	22.2668	+	12.8558i	1.45875	+	0.842209i	0.998950	−	0.0458133i	$-0.0145879\pi$
$233$	22.2668	+	12.8558i	1.45875	+	0.842209i	0.459799	+	0.888023i	$0.347921\pi$
$234$	5.76797	−	13.8494i	0.377064	−	0.905364i
$235$	−0.828416	−	1.43486i	−0.0540399	−	0.0935999i
$236$	−4.96573	+	8.60089i	−0.323241	+	0.559870i
$237$	1.96412	−	3.97317i	0.127583	−	0.258085i
$238$	11.4808	+	12.0923i	0.744190	+	0.783828i
$239$		−	10.7220i		−	0.693551i	−0.937948	−	0.346776i	$-0.887277\pi$
$239$		−	10.7220i		−	0.693551i	0.937948	−	0.346776i	$-0.112723\pi$
$240$	−0.960885	−	1.44108i	−0.0620249	−	0.0930211i
$241$	1.02594	−	0.592325i	0.0660864	−	0.0381550i	−0.466593	−	0.884472i	$-0.654519\pi$
$241$	1.02594	−	0.592325i	0.0660864	−	0.0381550i	0.532679	+	0.846317i	$0.321185\pi$
$242$	4.91787	−	2.83934i	0.316133	−	0.182519i
$243$	−14.7852	+	4.93943i	−0.948471	+	0.316864i
$244$		−	5.98368i		−	0.383066i
$245$	−5.87256	−	3.80960i	−0.375184	−	0.243386i
$246$	−15.2066	−	7.51732i	−0.969536	−	0.479287i
$247$	−18.8961	+	32.7290i	−1.20233	+	2.08250i
$248$	2.19077	+	3.79452i	0.139114	+	0.240952i
$249$	−3.17590	+	0.205080i	−0.201265	+	0.0129964i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	14.3689			0.906958			0.453479	−	0.891267i	$-0.350183\pi$
$251$	14.3689			0.906958			0.453479	+	0.891267i	$0.350183\pi$
$252$	−7.83743	−	1.25488i	−0.493712	−	0.0790498i
$253$	14.7002			0.924195
$254$	1.59084	+	0.918471i	0.0998181	+	0.0576300i
$255$	−10.8932	+	0.703417i	−0.682159	+	0.0440497i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.26802	+	14.3206i	−0.515745	+	0.893297i	0.484088	+	0.875019i	$0.339152\pi$
$257$	−8.26802	+	14.3206i	−0.515745	+	0.893297i	−0.999833	+	0.0182774i	$0.994182\pi$
$258$	3.96368	+	1.95943i	0.246768	+	0.121989i
$259$	4.27180	+	17.7742i	0.265437	+	1.10443i
$260$			5.00084i			0.310139i
$261$	1.47980	+	11.4104i	0.0915975	+	0.706289i
$262$	−4.79677	+	2.76942i	−0.296345	+	0.171095i
$263$	26.7948	−	15.4700i	1.65224	−	0.953920i	0.676089	−	0.736820i	$-0.263673\pi$
$263$	26.7948	−	15.4700i	1.65224	−	0.953920i	0.976149	−	0.217100i	$-0.0696599\pi$
$264$	−2.21657	−	3.32428i	−0.136420	−	0.204595i
$265$		−	3.25278i		−	0.199817i
$266$	19.1724	+	5.67402i	1.17554	+	0.347897i
$267$	−4.51923	+	9.14184i	−0.276573	+	0.559471i
$268$	−1.38358	+	2.39643i	−0.0845157	+	0.146386i
$269$	2.05211	+	3.55436i	0.125119	+	0.216713i	0.921780	−	0.387714i	$-0.126735\pi$
$269$	2.05211	+	3.55436i	0.125119	+	0.216713i	−0.796660	+	0.604427i	$0.793402\pi$
$270$	3.91658	−	3.41473i	0.238356	−	0.207814i
$271$	−7.86071	−	4.53838i	−0.477504	−	0.275687i	0.241872	−	0.970308i	$-0.422239\pi$
$271$	−7.86071	−	4.53838i	−0.477504	−	0.275687i	−0.719376	+	0.694621i	$0.755572\pi$
$272$	−6.30230			−0.382133
$273$	16.8171	+	15.5680i	1.01781	+	0.942219i
$274$	1.24104			0.0749740
$275$	1.99775	+	1.15340i	0.120469	+	0.0695527i
$276$	0.711259	+	11.0147i	0.0428128	+	0.663004i
$277$	−0.108238	−	0.187473i	−0.00650338	−	0.0112642i	0.862755	−	0.505622i	$-0.168737\pi$
$277$	−0.108238	−	0.187473i	−0.00650338	−	0.0112642i	−0.869259	+	0.494357i	$0.835403\pi$
$278$	−6.26718	+	10.8551i	−0.375881	+	0.651044i
$279$	−10.4437	+	7.98177i	−0.625250	+	0.477856i
$280$	2.57250	−	0.618268i	0.153736	−	0.0369486i
$281$		−	18.8498i		−	1.12448i	−0.826973	−	0.562241i	$-0.809939\pi$
$281$		−	18.8498i		−	1.12448i	0.826973	−	0.562241i	$-0.190061\pi$
$282$	2.38762	−	1.59203i	0.142181	−	0.0948037i
$283$	−1.73059	+	0.999159i	−0.102873	+	0.0593939i	−0.550554	−	0.834800i	$-0.685583\pi$
$283$	−1.73059	+	0.999159i	−0.102873	+	0.0593939i	0.447681	+	0.894193i	$0.352250\pi$
$284$	2.47605	−	1.42955i	0.146927	−	0.0848281i
$285$	−10.8905	+	7.26157i	−0.645095	+	0.430139i
$286$			11.5359i			0.682135i
$287$	18.7913	−	17.8411i	1.10922	−	1.05312i
$288$	2.38358	−	1.82168i	0.140454	−	0.107344i
$289$	−11.3595	+	19.6752i	−0.668204	+	1.15736i
$290$	−1.91767	−	3.32150i	−0.112609	−	0.195045i
$291$	0.515341	+	7.98065i	0.0302099	+	0.467834i
$292$	−3.18851	−	1.84089i	−0.186593	−	0.107730i
$293$	−9.28117			−0.542212			−0.271106	−	0.962550i	$-0.587389\pi$
$293$	−9.28117			−0.542212			−0.271106	+	0.962550i	$0.587389\pi$
$294$	5.92925	−	10.5756i	0.345801	−	0.616783i
$295$	9.93145			0.578232
$296$	−5.98363	−	3.45465i	−0.347791	−	0.200797i
$297$	9.03477	−	7.87710i	0.524251	−	0.457076i
$298$	7.79757	+	13.5058i	0.451701	+	0.782370i
$299$	15.9341	−	27.5986i	0.921492	−	1.59607i
$300$	−0.767566	+	1.55269i	−0.0443154	+	0.0896445i
$301$	−4.89806	+	4.65037i	−0.282319	+	0.268043i
$302$			3.03915i			0.174883i
$303$	−10.8715	−	16.3044i	−0.624551	−	0.936663i
$304$	−6.54470	+	3.77859i	−0.375365	+	0.216717i
$305$	−5.18202	+	2.99184i	−0.296721	+	0.171312i
$306$	−2.43164	−	18.7499i	−0.139008	−	1.07186i
$307$			26.9282i			1.53687i	0.639927	+	0.768436i	$0.278965\pi$
$307$			26.9282i			1.53687i	−0.639927	+	0.768436i	$0.721035\pi$
$308$	5.93424	−	1.42622i	0.338135	−	0.0812665i
$309$	−11.4341	−	5.65241i	−0.650464	−	0.321554i
$310$	2.19077	−	3.79452i	0.124427	−	0.215514i
$311$	−1.41065	−	2.44331i	−0.0799905	−	0.138548i	0.823255	−	0.567672i	$-0.192156\pi$
$311$	−1.41065	−	2.44331i	−0.0799905	−	0.138548i	−0.903246	+	0.429124i	$0.858822\pi$
$312$	−8.64371	+	0.558158i	−0.489354	+	0.0315994i
$313$	−9.90967	−	5.72135i	−0.560128	−	0.323390i	0.193069	−	0.981185i	$-0.438156\pi$
$313$	−9.90967	−	5.72135i	−0.560128	−	0.323390i	−0.753197	+	0.657795i	$0.771489\pi$
$314$	−15.8252			−0.893068
$315$	2.83196	+	7.41485i	0.159563	+	0.417780i
$316$	−2.55889			−0.143949
$317$	8.06254	+	4.65491i	0.452837	+	0.261446i	0.709028	−	0.705181i	$-0.249134\pi$
$317$	8.06254	+	4.65491i	0.452837	+	0.261446i	−0.256190	+	0.966626i	$0.582467\pi$
$318$	5.62228	−	0.363052i	0.315282	−	0.0203589i
$319$	−4.42368	−	7.66203i	−0.247678	−	0.428991i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−13.0717	−	6.46194i	−0.729590	−	0.360670i
$322$	−16.1671	−	4.78460i	−0.900956	−	0.266635i
$323$			47.6275i			2.65007i
$324$	6.33934	+	6.38849i	0.352185	+	0.354916i
$325$	4.33086	−	2.50042i	0.240233	−	0.138698i
$326$	−7.46238	+	4.30841i	−0.413303	+	0.238621i
$327$	−6.40249	−	9.60205i	−0.354058	−	0.530995i
$328$			9.79371i			0.540767i
$329$	1.02437	+	4.26220i	0.0564752	+	0.234983i
$330$	−1.77062	+	3.58174i	−0.0974695	+	0.197168i
$331$	−9.14801	+	15.8448i	−0.502820	+	0.870910i	0.497175	+	0.867650i	$0.334371\pi$
$331$	−9.14801	+	15.8448i	−0.502820	+	0.870910i	−0.999995	+	0.00325921i	$0.998963\pi$
$332$	0.918714	+	1.59126i	0.0504210	+	0.0873317i
$333$	7.96919	−	19.1347i	0.436709	−	1.04858i
$334$	−7.49067	−	4.32474i	−0.409871	−	0.236639i
$335$	2.76716			0.151186
$336$	1.35577	+	4.37743i	0.0739633	+	0.238808i
$337$	7.84516			0.427353			0.213676	−	0.976904i	$-0.431456\pi$
$337$	7.84516			0.427353			0.213676	+	0.976904i	$0.431456\pi$
$338$	10.3996	+	6.00420i	0.565663	+	0.326586i
$339$	−0.497240	−	7.70033i	−0.0270064	−	0.418225i
$340$	3.15115	+	5.45795i	0.170895	+	0.295999i
$341$	5.05366	−	8.75320i	0.273671	−	0.474012i
$342$	−13.7668	−	18.0131i	−0.744423	−	0.974039i
$343$	12.0383	+	14.0741i	0.650006	+	0.759929i
$344$		−	2.55278i		−	0.137637i
$345$	9.18334	−	6.12330i	0.494415	−	0.329667i
$346$	15.5291	−	8.96573i	0.834849	−	0.482000i
$347$	0.201172	−	0.116147i	0.0107995	−	0.00623509i	−0.494591	−	0.869126i	$-0.664682\pi$
$347$	0.201172	−	0.116147i	0.0107995	−	0.00623509i	0.505390	+	0.862891i	$0.331349\pi$
$348$	5.52701	−	3.68532i	0.296279	−	0.197554i
$349$			11.5685i			0.619249i	0.950859	+	0.309624i	$0.100203\pi$
$349$			11.5685i			0.619249i	−0.950859	+	0.309624i	$0.899797\pi$
$350$	−1.82168	−	1.91871i	−0.0973732	−	0.102560i
$351$	−4.99561	−	25.5004i	−0.266646	−	1.36111i
$352$	−1.15340	+	1.99775i	−0.0614764	+	0.106480i
$353$	−17.3537	−	30.0575i	−0.923646	−	1.59980i	−0.793725	−	0.608277i	$-0.791861\pi$
$353$	−17.3537	−	30.0575i	−0.923646	−	1.59980i	−0.129921	−	0.991524i	$-0.541472\pi$
$354$	1.10848	+	17.1660i	0.0589149	+	0.912364i
$355$	−2.47605	−	1.42955i	−0.131415	−	0.0758725i
$356$	5.88774			0.312050
$357$	28.1640	+	6.39421i	1.49060	+	0.338417i
$358$	12.0170			0.635116
$359$	−15.1834	−	8.76612i	−0.801347	−	0.462658i	0.0425949	−	0.999092i	$-0.486438\pi$
$359$	−15.1834	−	8.76612i	−0.801347	−	0.462658i	−0.843942	+	0.536434i	$0.819771\pi$
$360$	−2.76942	−	1.15340i	−0.145961	−	0.0607895i
$361$	19.0554	+	33.0050i	1.00292	+	1.73710i
$362$	−4.76306	+	8.24987i	−0.250341	+	0.433603i
$363$	4.35875	−	8.81721i	0.228775	−	0.462783i
$364$	3.75470	−	12.6870i	0.196799	−	0.664982i
$365$			3.68177i			0.192713i
$366$	−5.74962	−	8.62293i	−0.300538	−	0.450728i
$367$	−8.69505	+	5.02009i	−0.453878	+	0.262047i	−0.709467	−	0.704739i	$-0.751064\pi$
$367$	−8.69505	+	5.02009i	−0.453878	+	0.262047i	0.255589	+	0.966786i	$0.417731\pi$
$368$	5.51880	−	3.18628i	0.287687	−	0.166096i
$369$	−29.1371	+	3.77875i	−1.51682	+	0.196714i
$370$			6.90930i			0.359197i
$371$	−2.44223	+	8.25225i	−0.126794	+	0.428436i
$372$	6.80316	+	3.36311i	0.352727	+	0.174369i
$373$	0.00241034	−	0.00417483i	0.000124803	−	0.000216164i	−0.865963	−	0.500108i	$-0.833294\pi$
$373$	0.00241034	−	0.00417483i	0.000124803	−	0.000216164i	0.866088	+	0.499892i	$0.166627\pi$
$374$	7.26907	+	12.5904i	0.375875	+	0.651034i
$375$	1.72845	−	0.111613i	0.0892568	−	0.00576366i
$376$	−1.43486	−	0.828416i	−0.0739972	−	0.0427223i
$377$	−19.1799			−0.987815
$378$	−12.5001	+	5.72249i	−0.642937	+	0.294333i
$379$	18.6572			0.958356			0.479178	−	0.877718i	$-0.340935\pi$
$379$	18.6572			0.958356			0.479178	+	0.877718i	$0.340935\pi$
$380$	6.54470	+	3.77859i	0.335736	+	0.193837i
$381$	3.17506	−	0.205026i	0.162663	−	0.0105038i
$382$	2.48586	+	4.30564i	0.127188	+	0.220296i
$383$	9.42316	−	16.3214i	0.481501	−	0.833984i	−0.518274	−	0.855215i	$-0.673425\pi$
$383$	9.42316	−	16.3214i	0.481501	−	0.833984i	0.999775	+	0.0212308i	$0.00675849\pi$
$384$	−1.55269	−	0.767566i	−0.0792353	−	0.0391697i
$385$	−4.20226	−	4.42609i	−0.214167	−	0.225574i
$386$			6.03321i			0.307082i
$387$	7.59475	−	0.984951i	0.386063	−	0.0500679i
$388$	3.99864	−	2.30861i	0.203000	−	0.117202i
$389$	9.40510	−	5.43003i	0.476857	−	0.275314i	−0.242249	−	0.970214i	$-0.577885\pi$
$389$	9.40510	−	5.43003i	0.476857	−	0.275314i	0.719106	+	0.694901i	$0.244552\pi$
$390$	4.80523	+	7.20659i	0.243322	+	0.364920i
$391$		−	40.1618i		−	2.03107i
$392$	−6.99059	−	0.362928i	−0.353078	−	0.0183306i
$393$	−4.25142	+	8.60008i	−0.214456	+	0.433817i
$394$	−7.10719	+	12.3100i	−0.358055	+	0.620170i
$395$	1.27945	+	2.21607i	0.0643760	+	0.111502i
$396$	−6.38849	−	2.66066i	−0.321034	−	0.133703i
$397$	−23.4180	−	13.5204i	−1.17532	−	0.678570i	−0.220391	−	0.975412i	$-0.570733\pi$
$397$	−23.4180	−	13.5204i	−1.17532	−	0.678570i	−0.954927	+	0.296841i	$0.904067\pi$
$398$	−2.25088			−0.112826
$399$	33.0810	−	10.2458i	1.65612	−	0.512931i
$400$	1.00000			0.0500000
$401$	21.2396	+	12.2627i	1.06066	+	0.612371i	0.925614	−	0.378469i	$-0.123549\pi$
$401$	21.2396	+	12.2627i	1.06066	+	0.612371i	0.135043	+	0.990840i	$0.456883\pi$
$402$	0.308851	+	4.78291i	0.0154041	+	0.238550i
$403$	−10.9557	−	18.9758i	−0.545741	−	0.945251i
$404$	−5.65702	+	9.79825i	−0.281447	+	0.487481i
$405$	2.36293	−	8.68427i	0.117415	−	0.431525i
$406$	2.37127	+	9.86639i	0.117684	+	0.489661i
$407$			15.9384i			0.790036i
$408$	−9.08209	+	6.05578i	−0.449630	+	0.299806i
$409$	4.67954	−	2.70173i	0.231388	−	0.133592i	−0.379824	−	0.925059i	$-0.624015\pi$
$409$	4.67954	−	2.70173i	0.231388	−	0.133592i	0.611212	+	0.791467i	$0.290682\pi$
$410$	8.48160	−	4.89686i	0.418876	−	0.241838i
$411$	1.78843	−	1.19250i	0.0882170	−	0.0588216i
$412$			7.36407i			0.362802i
$413$	−25.1959	−	7.45666i	−1.23981	−	0.366918i
$414$	11.6088	+	15.1895i	0.570541	+	0.746524i
$415$	0.918714	−	1.59126i	0.0450979	−	0.0781119i
$416$	2.50042	+	4.33086i	0.122593	+	0.212338i
$417$	1.39899	+	21.6650i	0.0685091	+	1.06094i
$418$	15.0973	+	8.71645i	0.738434	+	0.426335i
$419$	28.2930			1.38220			0.691101	−	0.722758i	$-0.257126\pi$
$419$	28.2930			1.38220			0.691101	+	0.722758i	$0.257126\pi$
$420$	3.11308	−	3.36285i	0.151903	−	0.164090i
$421$	−25.1687			−1.22665			−0.613323	−	0.789832i	$-0.710168\pi$
$421$	−25.1687			−1.22665			−0.613323	+	0.789832i	$0.710168\pi$
$422$	−23.9052	−	13.8017i	−1.16369	−	0.671855i
$423$	1.91099	−	4.58846i	0.0929156	−	0.223099i
$424$	−1.62639	−	2.81699i	−0.0789846	−	0.136805i
$425$	3.15115	−	5.45795i	0.152853	−	0.264749i
$426$	2.19455	−	4.43929i	0.106326	−	0.215084i
$427$	15.3930	−	3.69952i	0.744919	−	0.179032i
$428$			8.41874i			0.406935i
$429$	11.0847	+	16.6242i	0.535175	+	0.802622i
$430$	−2.21077	+	1.27639i	−0.106613	+	0.0615531i
$431$	9.71524	−	5.60910i	0.467967	−	0.270181i	−0.247421	−	0.968908i	$-0.579583\pi$
$431$	9.71524	−	5.60910i	0.467967	−	0.270181i	0.715388	+	0.698727i	$0.246250\pi$
$432$	1.68449	−	4.91553i	0.0810452	−	0.236499i
$433$		−	0.639592i		−	0.0307368i	−0.999882	−	0.0153684i	$-0.995108\pi$
$433$		−	0.639592i		−	0.0307368i	0.999882	−	0.0153684i	$-0.00489211\pi$
$434$	−8.40691	+	7.98177i	−0.403544	+	0.383137i
$435$	−5.95508	−	2.94387i	−0.285524	−	0.141148i
$436$	−3.33156	+	5.77043i	−0.159553	+	0.276353i
$437$	−24.0793	−	41.7065i	−1.15187	−	1.99509i
$438$	−6.36376	+	0.410933i	−0.304072	+	0.0196351i
$439$	−11.3999	−	6.58174i	−0.544088	−	0.314129i	0.202646	−	0.979252i	$-0.435046\pi$
$439$	−11.3999	−	6.58174i	−0.544088	−	0.314129i	−0.746734	+	0.665123i	$0.768379\pi$
$440$	2.30680			0.109972
$441$	−1.61747	−	20.9376i	−0.0770221	−	0.997029i
$442$	31.5168			1.49910
$443$	22.3821	+	12.9223i	1.06341	+	0.613957i	0.926372	−	0.376609i	$-0.122910\pi$
$443$	22.3821	+	12.9223i	1.06341	+	0.613957i	0.137033	+	0.990566i	$0.456243\pi$
$444$	−11.9424	+	0.771166i	−0.566761	+	0.0365979i
$445$	−2.94387	−	5.09894i	−0.139553	−	0.241713i
$446$	−11.5388	+	19.9858i	−0.546380	+	0.946357i
$447$	24.2144	+	11.9703i	1.14530	+	0.566176i
$448$	1.91871	−	1.82168i	0.0906507	−	0.0860665i
$449$			28.3586i			1.33833i	0.743116	+	0.669163i	$0.233347\pi$
$449$			28.3586i			1.33833i	−0.743116	+	0.669163i	$0.766653\pi$
$450$	0.385834	+	2.97509i	0.0181884	+	0.140247i
$451$	19.5654	−	11.2961i	0.921297	−	0.531911i
$452$	−3.85818	+	2.22752i	−0.181474	+	0.104774i
$453$	2.92027	+	4.37965i	0.137206	+	0.205774i
$454$		−	20.0351i		−	0.940293i
$455$	−12.8647	+	3.09186i	−0.603104	+	0.144949i
$456$	−5.80063	+	11.7339i	−0.271639	+	0.549492i
$457$	14.5953	−	25.2797i	0.682737	−	1.18254i	−0.291405	−	0.956600i	$-0.594123\pi$
$457$	14.5953	−	25.2797i	0.682737	−	1.18254i	0.974142	−	0.225936i	$-0.0725440\pi$
$458$	−14.3824	−	24.9111i	−0.672046	−	1.16402i
$459$	−21.5206	−	24.6835i	−1.00450	−	1.15213i
$460$	−5.51880	−	3.18628i	−0.257315	−	0.148561i
$461$	−31.0968			−1.44832			−0.724162	−	0.689630i	$-0.757773\pi$
$461$	−31.0968			−1.44832			−0.724162	+	0.689630i	$0.757773\pi$
$462$	7.18125	−	7.75741i	0.334102	−	0.360908i
$463$	−33.4915			−1.55648			−0.778240	−	0.627967i	$-0.783887\pi$
$463$	−33.4915			−1.55648			−0.778240	+	0.627967i	$0.783887\pi$
$464$	−3.32150	−	1.91767i	−0.154197	−	0.0890255i
$465$	−0.489035	−	7.57326i	−0.0226784	−	0.351202i
$466$	−12.8558	−	22.2668i	−0.595532	−	1.03149i
$467$	7.41254	−	12.8389i	0.343012	−	0.594113i	−0.641979	−	0.766722i	$-0.721886\pi$
$467$	7.41254	−	12.8389i	0.343012	−	0.594113i	0.984990	+	0.172609i	$0.0552197\pi$
$468$	−11.9199	+	9.10996i	−0.550998	+	0.421108i
$469$	−7.02025	−	2.07762i	−0.324165	−	0.0959357i
$470$			1.65683i			0.0764240i
$471$	−22.8053	+	15.2062i	−1.05081	+	0.700664i
$472$	8.60089	−	4.96573i	0.395888	−	0.228566i
$473$	−5.09982	+	2.94438i	−0.234490	+	0.135383i
$474$	−3.68756	+	2.45880i	−0.169375	+	0.112937i
$475$		−	7.55717i		−	0.346747i
$476$	−3.89651	−	16.2126i	−0.178596	−	0.743105i
$477$	7.75328	−	5.92555i	0.354998	−	0.271312i
$478$	−5.36102	+	9.28556i	−0.245207	+	0.424712i
$479$	11.5223	+	19.9573i	0.526469	+	0.911871i	0.999524	+	0.0308386i	$0.00981778\pi$
$479$	11.5223	+	19.9573i	0.526469	+	0.911871i	−0.473055	+	0.881033i	$0.656849\pi$
$480$	0.111613	+	1.72845i	0.00509440	+	0.0788926i
$481$	29.9232	+	17.2762i	1.36438	+	0.787725i
$482$	−1.18465			−0.0539593
$483$	−27.8954	+	8.63973i	−1.26929	+	0.393121i
$484$	−5.67867			−0.258121
$485$	−3.99864	−	2.30861i	−0.181569	−	0.104829i
$486$	15.2741	+	3.11493i	0.692846	+	0.141296i
$487$	5.31384	+	9.20383i	0.240793	+	0.417066i	0.960940	−	0.276756i	$-0.0892592\pi$
$487$	5.31384	+	9.20383i	0.240793	+	0.417066i	−0.720147	+	0.693821i	$0.755926\pi$
$488$	−2.99184	+	5.18202i	−0.135434	+	0.234579i
$489$	−6.61397	+	13.3792i	−0.299094	+	0.605030i
$490$	3.18099	+	6.23549i	0.143702	+	0.281691i
$491$		−	22.4687i		−	1.01400i	−0.861947	−	0.506998i	$-0.830755\pi$
$491$		−	22.4687i		−	1.01400i	0.861947	−	0.506998i	$-0.169245\pi$
$492$	9.41063	+	14.1135i	0.424264	+	0.636285i
$493$	−20.9331	+	12.0857i	−0.942778	+	0.544313i
$494$	32.7290	−	18.8961i	1.47255	−	0.850176i
$495$	0.890043	+	6.86293i	0.0400044	+	0.308466i
$496$		−	4.38153i		−	0.196737i
$497$	5.20837	+	5.48579i	0.233627	+	0.246071i
$498$	2.85295	+	1.41035i	0.127844	+	0.0631992i
$499$	19.8794	−	34.4322i	0.889925	−	1.54140i	0.0499622	−	0.998751i	$-0.484090\pi$
$499$	19.8794	−	34.4322i	0.889925	−	1.54140i	0.839963	−	0.542644i	$-0.182577\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−14.9502	+	0.965392i	−0.667926	+	0.0431305i
$502$	−12.4438	−	7.18445i	−0.555396	−	0.320658i
$503$	−18.6717			−0.832530			−0.416265	−	0.909243i	$-0.636661\pi$
$503$	−18.6717			−0.832530			−0.416265	+	0.909243i	$0.636661\pi$
$504$	6.15997	+	5.00547i	0.274387	+	0.222961i
$505$	11.3140			0.503468
$506$	−12.7308	−	7.35011i	−0.565952	−	0.326752i
$507$	20.7559	−	1.34029i	0.921804	−	0.0595244i
$508$	−0.918471	−	1.59084i	−0.0407506	−	0.0705820i
$509$	−2.01643	+	3.49256i	−0.0893768	+	0.154805i	−0.907248	−	0.420596i	$-0.861821\pi$
$509$	−2.01643	+	3.49256i	−0.0893768	+	0.154805i	0.817871	+	0.575402i	$0.195154\pi$
$510$	9.78550	+	4.83743i	0.433309	+	0.214205i
$511$	2.76432	−	9.34059i	0.122286	−	0.413203i
$512$			1.00000i			0.0441942i
$513$	−37.1475	−	12.7300i	−1.64010	−	0.562044i
$514$	14.3206	−	8.26802i	0.631656	−	0.364687i
$515$	6.37747	−	3.68203i	0.281025	−	0.162250i
$516$	−2.45293	−	3.67875i	−0.107984	−	0.161948i
$517$			3.82198i			0.168091i
$518$	5.18759	−	17.5288i	0.227930	−	0.770170i
$519$	13.7636	−	27.8420i	0.604154	−	1.22213i
$520$	2.50042	−	4.33086i	0.109651	−	0.189921i
$521$	5.27733	+	9.14060i	0.231204	+	0.400457i	0.958163	−	0.286224i	$-0.0924002\pi$
$521$	5.27733	+	9.14060i	0.231204	+	0.400457i	−0.726959	+	0.686681i	$0.759067\pi$
$522$	4.42368	−	10.6216i	0.193619	−	0.464896i
$523$	−17.7815	−	10.2661i	−0.777529	−	0.448907i	0.0580246	−	0.998315i	$-0.481520\pi$
$523$	−17.7815	−	10.2661i	−0.777529	−	0.448907i	−0.835554	+	0.549408i	$0.814853\pi$
$524$	5.53883			0.241965
$525$	−4.46885	−	1.01458i	−0.195037	−	0.0442801i
$526$	−30.9400			−1.34905
$527$	−23.9142	−	13.8069i	−1.04172	−	0.601436i
$528$	0.257468	+	3.98719i	0.0112049	+	0.173520i
$529$	8.80476	+	15.2503i	0.382816	+	0.663056i
$530$	−1.62639	+	2.81699i	−0.0706459	+	0.122362i
$531$	18.0920	+	23.6724i	0.785125	+	1.02730i
$532$	−13.7668	−	14.5001i	−0.596866	−	0.628657i
$533$		−	48.9768i		−	2.12142i
$534$	8.48469	−	5.65745i	0.367168	−	0.244822i
$535$	7.29084	−	4.20937i	0.315211	−	0.181987i
$536$	2.39643	−	1.38358i	0.103510	−	0.0597616i
$537$	17.3174	−	11.5469i	0.747299	−	0.498286i
$538$		−	4.10422i		−	0.176946i
$539$	7.33790	+	14.3840i	0.316066	+	0.619564i
$540$	−5.09922	+	0.998953i	−0.219436	+	0.0429881i
$541$	4.59255	−	7.95454i	0.197449	−	0.341992i	−0.750251	−	0.661153i	$-0.770068\pi$
$541$	4.59255	−	7.95454i	0.197449	−	0.341992i	0.947701	+	0.319160i	$0.103401\pi$
$542$	4.53838	+	7.86071i	0.194940	+	0.337646i
$543$	1.06324	+	16.4654i	0.0456279	+	0.706600i
$544$	5.45795	+	3.15115i	0.234008	+	0.135104i
$545$	6.66311			0.285416
$546$	−6.77999	−	21.8908i	−0.290157	−	0.936841i
$547$	−5.21319			−0.222900			−0.111450	−	0.993770i	$-0.535550\pi$
$547$	−5.21319			−0.222900			−0.111450	+	0.993770i	$0.535550\pi$
$548$	−1.07477	−	0.620520i	−0.0459120	−	0.0265073i
$549$	−16.5713	−	6.90157i	−0.707246	−	0.294552i
$550$	−1.15340	−	1.99775i	−0.0491812	−	0.0851843i
$551$	−14.4921	+	25.1011i	−0.617386	+	1.06934i
$552$	4.89136	−	9.89460i	0.208190	−	0.421142i
$553$	−1.58208	−	6.58275i	−0.0672770	−	0.279927i
$554$			0.216476i			0.00919717i
$555$	6.63904	+	9.95683i	0.281812	+	0.422644i
$556$	10.8551	−	6.26718i	0.460358	−	0.265788i
$557$	−22.3550	+	12.9066i	−0.947210	+	0.546872i	−0.892213	−	0.451614i	$-0.850848\pi$
$557$	−22.3550	+	12.9066i	−0.947210	+	0.546872i	−0.0549970	+	0.998487i	$0.517515\pi$
$558$	13.0354	−	1.69055i	0.551834	−	0.0715665i
$559$			12.7661i			0.539947i
$560$	−2.53698	−	0.750813i	−0.107207	−	0.0317276i
$561$	22.5732	+	11.1590i	0.953042	+	0.471133i
$562$	−9.42488	+	16.3244i	−0.397565	+	0.688602i
$563$	−18.7468	−	32.4704i	−0.790084	−	1.36847i	−0.925914	−	0.377733i	$-0.876704\pi$
$563$	−18.7468	−	32.4704i	−0.790084	−	1.36847i	0.135831	−	0.990732i	$-0.456630\pi$
$564$	−2.86375	+	0.184924i	−0.120586	+	0.00778669i
$565$	3.85818	+	2.22752i	0.162315	+	0.0937126i
$566$	1.99832			0.0839956
$567$	−12.5150	+	20.2577i	−0.525579	+	0.850745i
$568$	−2.85910			−0.119965
$569$	35.0352	+	20.2276i	1.46875	+	0.847985i	0.999387	−	0.0350177i	$-0.0111488\pi$
$569$	35.0352	+	20.2276i	1.46875	+	0.847985i	0.469367	+	0.883003i	$0.344482\pi$
$570$	13.0622	−	0.843477i	0.547115	−	0.0353294i
$571$	14.5551	+	25.2101i	0.609111	+	1.05501i	0.991387	+	0.130963i	$0.0418070\pi$
$571$	14.5551	+	25.2101i	0.609111	+	1.05501i	−0.382276	+	0.924048i	$0.624860\pi$
$572$	5.76797	−	9.99042i	0.241171	−	0.417720i
$573$	7.71954	+	3.81613i	0.322488	+	0.159421i
$574$	−25.1943	+	6.05514i	−1.05159	+	0.252737i
$575$			6.37256i			0.265754i
$576$	−2.97509	+	0.385834i	−0.123962	+	0.0160764i
$577$	−13.1423	+	7.58769i	−0.547120	+	0.315880i	−0.747959	−	0.663744i	$-0.768966\pi$
$577$	−13.1423	+	7.58769i	−0.547120	+	0.315880i	0.200840	+	0.979624i	$0.435633\pi$
$578$	19.6752	−	11.3595i	0.818380	−	0.472492i
$579$	5.79722	+	8.69431i	0.240924	+	0.361323i
$580$			3.83533i			0.159254i
$581$	−3.52550	+	3.34722i	−0.146262	+	0.138866i
$582$	3.54403	−	7.16912i	0.146905	−	0.297169i
$583$	−3.75176	+	6.49824i	−0.155382	+	0.269130i
$584$	1.84089	+	3.18851i	0.0761764	+	0.131941i
$585$	13.8494	+	5.76797i	0.572603	+	0.238476i
$586$	8.03773	+	4.64059i	0.332036	+	0.191701i
$587$	3.22807			0.133237			0.0666183	−	0.997779i	$-0.478779\pi$
$587$	3.22807			0.133237			0.0666183	+	0.997779i	$0.478779\pi$
$588$	−10.4227	+	6.19414i	−0.429825	+	0.255442i
$589$	−33.1120			−1.36436
$590$	−8.60089	−	4.96573i	−0.354093	−	0.204436i
$591$	1.58651	+	24.5689i	0.0652601	+	1.01063i
$592$	3.45465	+	5.98363i	0.141985	+	0.245926i
$593$	−21.8653	+	37.8717i	−0.897899	+	1.55521i	−0.0677234	+	0.997704i	$0.521574\pi$
$593$	−21.8653	+	37.8717i	−0.897899	+	1.55521i	−0.830175	+	0.557502i	$0.811760\pi$
$594$	−11.7629	+	2.30439i	−0.482637	+	0.0945501i
$595$	−12.0923	+	11.4808i	−0.495736	+	0.470667i
$596$		−	15.5951i		−	0.638802i
$597$	−3.24369	+	2.16283i	−0.132755	+	0.0885189i
$598$	−27.5986	+	15.9341i	−1.12859	+	0.651593i
$599$	−6.96777	+	4.02284i	−0.284695	+	0.164369i	−0.635547	−	0.772062i	$-0.719225\pi$
$599$	−6.96777	+	4.02284i	−0.284695	+	0.164369i	0.350852	+	0.936431i	$0.385892\pi$
$600$	1.44108	−	0.960885i	0.0588317	−	0.0392280i
$601$			8.38546i			0.342050i	0.985267	+	0.171025i	$0.0547079\pi$
$601$			8.38546i			0.342050i	−0.985267	+	0.171025i	$0.945292\pi$
$602$	6.56703	−	1.57830i	0.267652	−	0.0643269i
$603$	5.04090	+	6.59576i	0.205281	+	0.268600i
$604$	1.51958	−	2.63198i	0.0618306	−	0.107094i
$605$	2.83934	+	4.91787i	0.115435	+	0.199940i
$606$	1.26279	+	19.5558i	0.0512974	+	0.794398i
$607$	14.6650	+	8.46682i	0.595232	+	0.343658i	0.767164	−	0.641451i	$-0.221667\pi$
$607$	14.6650	+	8.46682i	0.595232	+	0.343658i	−0.171931	+	0.985109i	$0.555001\pi$
$608$	7.55717			0.306484
$609$	12.8976	+	11.9397i	0.522639	+	0.483821i
$610$	5.98368			0.242272
$611$	7.17550	+	4.14278i	0.290290	+	0.167599i
$612$	−7.26907	+	17.4537i	−0.293835	+	0.705523i
$613$	−16.9432	−	29.3464i	−0.684328	−	1.18529i	−0.973647	−	0.228058i	$-0.926762\pi$
$613$	−16.9432	−	29.3464i	−0.684328	−	1.18529i	0.289319	−	0.957233i	$-0.406571\pi$
$614$	13.4641	−	23.3205i	0.543366	−	0.941138i
$615$	7.51732	−	15.2066i	0.303128	−	0.613189i
$616$	−5.85231	−	1.73198i	−0.235796	−	0.0697833i
$617$			37.5359i			1.51114i	0.655068	+	0.755570i	$0.272640\pi$
$617$			37.5359i			1.51114i	−0.655068	+	0.755570i	$0.727360\pi$
$618$	7.07602	+	10.6122i	0.284639	+	0.426885i
$619$	14.6497	−	8.45802i	0.588822	−	0.339957i	−0.175809	−	0.984424i	$-0.556254\pi$
$619$	14.6497	−	8.45802i	0.588822	−	0.339957i	0.764632	+	0.644468i	$0.222921\pi$
$620$	−3.79452	+	2.19077i	−0.152392	+	0.0879833i
$621$	31.3245	+	10.7345i	1.25701	+	0.430762i
$622$			2.82130i			0.113124i
$623$	3.64021	+	15.1462i	0.145842	+	0.606820i
$624$	7.76475	+	3.83848i	0.310839	+	0.153662i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.72135	+	9.90967i	0.228671	+	0.396070i
$627$	30.1319	−	1.94573i	1.20335	−	0.0777051i
$628$	13.7050	+	7.91260i	0.546890	+	0.315747i
$629$	43.5445			1.73623
$630$	1.25488	−	7.83743i	0.0499955	−	0.312251i
$631$	−29.1879			−1.16195			−0.580977	−	0.813920i	$-0.697329\pi$
$631$	−29.1879			−1.16195			−0.580977	+	0.813920i	$0.697329\pi$
$632$	2.21607	+	1.27945i	0.0881504	+	0.0508937i
$633$	−47.7110	+	3.08089i	−1.89634	+	0.122454i
$634$	−4.65491	−	8.06254i	−0.184870	−	0.320204i
$635$	−0.918471	+	1.59084i	−0.0364484	+	0.0631305i
$636$	−5.05056	−	2.49673i	−0.200268	−	0.0990016i
$637$	34.9588	+	1.81495i	1.38512	+	0.0719108i
$638$			8.84735i			0.350270i
$639$	−1.10314	−	8.50606i	−0.0436394	−	0.336494i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	3.95871	−	2.28556i	0.156360	−	0.0902743i	−0.419779	−	0.907627i	$-0.637892\pi$
$641$	3.95871	−	2.28556i	0.156360	−	0.0902743i	0.576138	+	0.817352i	$0.304559\pi$
$642$	8.08944	+	12.1320i	0.319265	+	0.478814i
$643$			24.0758i			0.949457i	0.880132	+	0.474728i	$0.157454\pi$
$643$			24.0758i			0.949457i	−0.880132	+	0.474728i	$0.842546\pi$
$644$	11.6088	+	12.2271i	0.457451	+	0.481816i
$645$	−1.95943	+	3.96368i	−0.0771524	+	0.156070i
$646$	23.8138	−	41.2467i	0.936940	−	1.62283i
$647$	8.71205	+	15.0897i	0.342506	+	0.593238i	0.984897	−	0.173139i	$-0.0553909\pi$
$647$	8.71205	+	15.0897i	0.342506	+	0.593238i	−0.642391	+	0.766377i	$0.722058\pi$
$648$	−2.29578	−	8.70226i	−0.0901867	−	0.341857i
$649$	−19.8405	−	11.4549i	−0.778809	−	0.449646i
$650$	−5.00084			−0.196149
$651$	−4.44543	+	19.5804i	−0.174230	+	0.767417i
$652$	8.61682			0.337461
$653$	32.8146	+	18.9455i	1.28414	+	0.741396i	0.977602	−	0.210464i	$-0.0674973\pi$
$653$	32.8146	+	18.9455i	1.28414	+	0.741396i	0.306534	+	0.951860i	$0.400831\pi$
$654$	0.743688	+	11.5169i	0.0290805	+	0.450345i
$655$	−2.76942	−	4.79677i	−0.108210	−	0.187425i
$656$	4.89686	−	8.48160i	0.191190	−	0.331151i
$657$	−8.77580	+	6.70703i	−0.342377	+	0.261666i
$658$	1.24397	−	4.20336i	0.0484950	−	0.163864i
$659$			24.7262i			0.963197i	0.876392	+	0.481599i	$0.159944\pi$
$659$			24.7262i			0.963197i	−0.876392	+	0.481599i	$0.840056\pi$
$660$	3.32428	−	2.21657i	0.129397	−	0.0862799i
$661$	−37.8348	+	21.8439i	−1.47160	+	0.849631i	−0.999491	−	0.0319070i	$-0.989842\pi$
$661$	−37.8348	+	21.8439i	−1.47160	+	0.849631i	−0.472113	+	0.881538i	$0.656509\pi$
$662$	15.8448	−	9.14801i	0.615826	−	0.355547i
$663$	45.4181	−	30.2840i	1.76389	−	1.17613i
$664$		−	1.83743i		−	0.0713060i
$665$	−5.67402	+	19.1724i	−0.220029	+	0.743474i
$666$	−16.4689	+	12.5866i	−0.638156	+	0.487720i
$667$	12.2205	−	21.1664i	0.473178	−	0.819568i
$668$	4.32474	+	7.49067i	0.167329	+	0.289823i
$669$	2.57576	+	39.8886i	0.0995847	+	1.54218i
$670$	−2.39643	−	1.38358i	−0.0925823	−	0.0534524i
$671$	13.8031			0.532865
$672$	1.01458	−	4.46885i	0.0391384	−	0.172390i
$673$	34.1588			1.31673			0.658363	−	0.752701i	$-0.271249\pi$
$673$	34.1588			1.31673			0.658363	+	0.752701i	$0.271249\pi$
$674$	−6.79410	−	3.92258i	−0.261699	−	0.151092i
$675$	3.41473	+	3.91658i	0.131433	+	0.150749i
$676$	−6.00420	−	10.3996i	−0.230931	−	0.399984i
$677$	6.56630	−	11.3732i	0.252364	−	0.437106i	−0.711813	−	0.702369i	$-0.752125\pi$
$677$	6.56630	−	11.3732i	0.252364	−	0.437106i	0.964176	+	0.265263i	$0.0854588\pi$
$678$	−3.41954	+	6.91730i	−0.131327	+	0.265657i
$679$	8.41113	+	8.85914i	0.322790	+	0.339983i
$680$		−	6.30230i		−	0.241682i
$681$	−19.2514	−	28.8721i	−0.737715	−	1.10638i
$682$	−8.75320	+	5.05366i	−0.335177	+	0.193515i
$683$	−39.7352	+	22.9411i	−1.52043	+	0.877818i	−0.520716	+	0.853730i	$0.674335\pi$
$683$	−39.7352	+	22.9411i	−1.52043	+	0.877818i	−0.999710	+	0.0240882i	$0.992332\pi$
$684$	2.91582	+	22.4832i	0.111489	+	0.859668i
$685$			1.24104i			0.0474177i
$686$	−3.38843	−	18.2077i	−0.129371	−	0.695171i
$687$	−44.6628	−	22.0789i	−1.70399	−	0.842363i
$688$	−1.27639	+	2.21077i	−0.0486620	+	0.0842850i
$689$	8.13333	+	14.0873i	0.309855	+	0.536685i
$690$	−11.0147	+	0.711259i	−0.419321	+	0.0270772i
$691$	−15.2114	−	8.78233i	−0.578671	−	0.334096i	0.181934	−	0.983311i	$-0.441764\pi$
$691$	−15.2114	−	8.78233i	−0.578671	−	0.334096i	−0.760605	+	0.649215i	$0.775098\pi$
$692$	−17.9315			−0.681652
$693$	2.89475	−	18.0794i	0.109963	−	0.686779i
$694$	−0.232294			−0.00881775
$695$	−10.8551	−	6.26718i	−0.411757	−	0.237728i
$696$	−6.62919	+	0.428072i	−0.251279	+	0.0162260i
$697$	−30.8614	−	53.4536i	−1.16896	−	2.02470i
$698$	5.78426	−	10.0186i	0.218938	−	0.379211i
$699$	−39.9220	−	19.7353i	−1.50999	−	0.746458i
$700$	0.618268	+	2.57250i	0.0233683	+	0.0972313i
$701$		−	39.2501i		−	1.48246i	−0.671253	−	0.741228i	$-0.734244\pi$
$701$		−	39.2501i		−	1.48246i	0.671253	−	0.741228i	$-0.265756\pi$
$702$	−8.42388	+	24.5818i	−0.317939	+	0.927780i
$703$	45.2193	−	26.1074i	1.70548	−	0.984659i
$704$	1.99775	−	1.15340i	0.0752930	−	0.0434704i
$705$	1.59203	+	2.38762i	0.0599592	+	0.0899230i
$706$			34.7075i			1.30623i
$707$	−28.7035	−	8.49472i	−1.07951	−	0.319477i
$708$	7.62305	−	15.4205i	0.286492	−	0.579536i
$709$	23.8340	−	41.2817i	0.895105	−	1.55037i	0.0614314	−	0.998111i	$-0.480433\pi$
$709$	23.8340	−	41.2817i	0.895105	−	1.55037i	0.833674	−	0.552257i	$-0.186233\pi$
$710$	1.42955	+	2.47605i	0.0536500	+	0.0929245i
$711$	−2.95143	+	7.08664i	−0.110687	+	0.265770i
$712$	−5.09894	−	2.94387i	−0.191091	−	0.110326i
$713$	27.9216			1.04567
$714$	−21.1937	−	19.6196i	−0.793152	−	0.734243i
$715$	−11.5359			−0.431420
$716$	−10.4070	−	6.00848i	−0.388928	−	0.224547i
$717$	1.19672	+	18.5325i	0.0446922	+	0.692110i
$718$	8.76612	+	15.1834i	0.327149	+	0.566638i
$719$	16.7107	−	28.9438i	0.623205	−	1.07942i	−0.365680	−	0.930740i	$-0.619164\pi$
$719$	16.7107	−	28.9438i	0.623205	−	1.07942i	0.988885	−	0.148682i	$-0.0475030\pi$
$720$	1.82168	+	2.38358i	0.0678902	+	0.0888309i
$721$	−18.9441	+	4.55297i	−0.705513	+	0.169561i
$722$		−	38.1109i		−	1.41834i
$723$	−1.70717	+	1.13831i	−0.0634904	+	0.0423343i
$724$	8.24987	−	4.76306i	0.306604	−	0.177018i
$725$	3.32150	−	1.91767i	0.123357	−	0.0712204i
$726$	−8.18340	+	5.45655i	−0.303714	+	0.202512i
$727$			31.9845i			1.18624i	0.805115	+	0.593119i	$0.202104\pi$
$727$			31.9845i			1.18624i	−0.805115	+	0.593119i	$0.797896\pi$
$728$	−9.59518	+	9.10996i	−0.355621	+	0.337637i
$729$	25.0042	−	10.1878i	0.926081	−	0.377325i
$730$	1.84089	−	3.18851i	0.0681342	−	0.118012i
$731$	8.04420	+	13.9330i	0.297525	+	0.515329i
$732$	0.667855	+	10.3425i	0.0246846	+	0.382269i
$733$	33.9483	+	19.6001i	1.25391	+	0.723945i	0.971884	−	0.235461i	$-0.0756601\pi$
$733$	33.9483	+	19.6001i	1.25391	+	0.723945i	0.282026	+	0.959407i	$0.408993\pi$
$734$	10.0402			0.370590
$735$	10.5756	+	5.92925i	0.390088	+	0.218704i
$736$	−6.37256			−0.234896
$737$	−5.52810	−	3.19165i	−0.203630	−	0.117566i
$738$	27.1229	+	11.2961i	0.998406	+	0.415814i
$739$	16.8814	+	29.2394i	0.620992	+	1.07559i	0.989301	+	0.145886i	$0.0466033\pi$
$739$	16.8814	+	29.2394i	0.620992	+	1.07559i	−0.368310	+	0.929703i	$0.620063\pi$
$740$	3.45465	−	5.98363i	0.126995	−	0.219963i
$741$	29.0080	−	58.6796i	1.06564	−	2.15565i
$742$	6.24116	−	5.92555i	0.229120	−	0.217534i
$743$			14.3933i			0.528038i	0.964517	+	0.264019i	$0.0850482\pi$
$743$			14.3933i			0.528038i	−0.964517	+	0.264019i	$0.914952\pi$
$744$	−4.21015	−	6.31412i	−0.154352	−	0.231487i
$745$	−13.5058	+	7.79757i	−0.494814	+	0.285681i
$746$	−0.00417483	+	0.00241034i	−0.000152851	+	8.82487e-5i
$747$	5.46651	−	0.708943i	0.200009	−	0.0259389i
$748$		−	14.5381i		−	0.531567i
$749$	−21.6572	+	5.20504i	−0.791336	+	0.190188i
$750$	−1.55269	−	0.767566i	−0.0566962	−	0.0280275i
$751$	−8.92040	+	15.4506i	−0.325510	+	0.563800i	−0.981615	−	0.190869i	$-0.938869\pi$
$751$	−8.92040	+	15.4506i	−0.325510	+	0.563800i	0.656105	+	0.754669i	$0.272203\pi$
$752$	0.828416	+	1.43486i	0.0302092	+	0.0523239i
$753$	−24.8360	+	1.60375i	−0.905073	+	0.0584440i
$754$	16.6103	+	9.58995i	0.604911	+	0.349245i
$755$	−3.03915			−0.110606
$756$	13.6867	+	1.29424i	0.497779	+	0.0470709i
$757$	−1.90604			−0.0692760			−0.0346380	−	0.999400i	$-0.511028\pi$
$757$	−1.90604			−0.0692760			−0.0346380	+	0.999400i	$0.511028\pi$
$758$	−16.1576	−	9.32860i	−0.586871	−	0.338830i
$759$	−25.4086	+	1.64073i	−0.922274	+	0.0595548i
$760$	−3.77859	−	6.54470i	−0.137064	−	0.237401i
$761$	14.1364	−	24.4850i	0.512445	−	0.887581i	−0.487451	−	0.873150i	$-0.662073\pi$
$761$	14.1364	−	24.4850i	0.512445	−	0.887581i	0.999896	−	0.0144304i	$-0.00459350\pi$
$762$	−2.85220	−	1.40997i	−0.103324	−	0.0510780i
$763$	−16.9042	−	5.00275i	−0.611973	−	0.181112i
$764$		−	4.97173i		−	0.179871i
$765$	18.7499	−	2.43164i	0.677903	−	0.0879162i
$766$	−16.3214	+	9.42316i	−0.589716	+	0.340473i
$767$	−43.0117	+	24.8328i	−1.55306	+	0.896661i
$768$	0.960885	+	1.44108i	0.0346729	+	0.0520004i
$769$		−	1.43146i		−	0.0516197i	−0.999667	−	0.0258098i	$-0.991784\pi$
$769$		−	1.43146i		−	0.0516197i	0.999667	−	0.0258098i	$-0.00821644\pi$
$770$	1.42622	+	5.93424i	0.0513975	+	0.213855i
$771$	12.6925	−	25.6753i	0.457109	−	0.924675i
$772$	3.01660	−	5.22491i	0.108570	−	0.188049i
$773$	17.4088	+	30.1528i	0.626149	+	1.08452i	0.988317	+	0.152410i	$0.0487033\pi$
$773$	17.4088	+	30.1528i	0.626149	+	1.08452i	−0.362168	+	0.932113i	$0.617963\pi$
$774$	−7.06972	−	2.94438i	−0.254116	−	0.105834i
$775$	3.79452	+	2.19077i	0.136303	+	0.0786946i
$776$	−4.61723			−0.165749
$777$	−9.36742	−	30.2450i	−0.336054	−	1.08503i
$778$	−10.8601			−0.389352
$779$	−64.0969	−	37.0064i	−2.29651	−	1.32589i
$780$	−0.558158	−	8.64371i	−0.0199852	−	0.309494i
$781$	3.29768	+	5.71175i	0.118000	+	0.204383i
$782$	−20.0809	+	34.7811i	−0.718091	+	1.24377i
$783$	−3.83132	−	19.5572i	−0.136920	−	0.698918i
$784$	5.87256	+	3.80960i	0.209734	+	0.136057i
$785$		−	15.8252i		−	0.564826i
$786$	7.98188	−	5.32218i	0.284704	−	0.189836i
$787$	−43.0486	+	24.8541i	−1.53452	+	0.885953i	−0.535370	+	0.844617i	$0.679828\pi$
$787$	−43.0486	+	24.8541i	−1.53452	+	0.885953i	−0.999145	+	0.0413355i	$0.986839\pi$
$788$	12.3100	−	7.10719i	0.438526	−	0.253183i
$789$	−44.5869	+	29.7298i	−1.58733	+	1.05841i
$790$		−	2.55889i		−	0.0910414i
$791$	−8.11569	−	8.54796i	−0.288561	−	0.303931i
$792$	4.20226	+	5.49845i	0.149321	+	0.195379i
$793$	14.9617	−	25.9144i	0.531306	−	0.920249i
$794$	13.5204	+	23.4180i	0.479822	+	0.831075i
$795$	0.363052	+	5.62228i	0.0128761	+	0.199402i
$796$	1.94932	+	1.12544i	0.0690917	+	0.0398901i
$797$	−8.43295			−0.298710			−0.149355	−	0.988784i	$-0.547720\pi$
$797$	−8.43295			−0.298710			−0.149355	+	0.988784i	$0.547720\pi$
$798$	−33.7719	−	7.66738i	−1.19551	−	0.271422i
$799$	10.4419			0.369406
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	6.79093	−	16.3056i	0.239946	−	0.576131i
$802$	−12.2627	−	21.2396i	−0.433012	−	0.749998i
$803$	4.24656	−	7.35525i	0.149858	−	0.259561i
$804$	2.12398	−	4.29655i	0.0749070	−	0.151527i
$805$	4.78460	−	16.1671i	0.168635	−	0.569814i
$806$			21.9113i			0.771794i
$807$	−3.94368	−	5.91449i	−0.138824	−	0.208200i
$808$	9.79825	−	5.65702i	0.344701	−	0.199013i
$809$	33.7531	−	19.4873i	1.18669	−	0.685138i	0.229141	−	0.973393i	$-0.426408\pi$
$809$	33.7531	−	19.4873i	1.18669	−	0.685138i	0.957554	+	0.288255i	$0.0930751\pi$
$810$	−6.38849	+	6.33934i	−0.224469	+	0.222742i
$811$		−	29.5668i		−	1.03823i	−0.854704	−	0.519116i	$-0.826261\pi$
$811$		−	29.5668i		−	1.03823i	0.854704	−	0.519116i	$-0.173739\pi$
$812$	2.87962	−	9.73018i	0.101055	−	0.341462i
$813$	14.0934	+	6.96702i	0.494277	+	0.244344i
$814$	7.96919	−	13.8030i	0.279320	−	0.483796i
$815$	−4.30841	−	7.46238i	−0.150917	−	0.261396i
$816$	10.8932	−	0.703417i	0.381339	−	0.0246245i
$817$	16.7072	+	9.64591i	0.584511	+	0.337468i
$818$	−5.40347			−0.188928
$819$	−30.8050	−	25.0316i	−1.07642	−	0.874673i
$820$	−9.79371			−0.342011
$821$	29.1479	+	16.8285i	1.01727	+	0.587320i	0.913311	−	0.407262i	$-0.133516\pi$
$821$	29.1479	+	16.8285i	1.01727	+	0.587320i	0.103956	+	0.994582i	$0.466850\pi$
$822$	−2.14508	+	0.138516i	−0.0748182	+	0.00483130i
$823$	6.27024	+	10.8604i	0.218567	+	0.378569i	0.954370	−	0.298627i	$-0.0965285\pi$
$823$	6.27024	+	10.8604i	0.218567	+	0.378569i	−0.735803	+	0.677195i	$0.763195\pi$
$824$	3.68203	−	6.37747i	0.128270	−	0.222170i
$825$	−3.58174	−	1.77062i	−0.124700	−	0.0616451i
$826$	18.0920	+	19.0556i	0.629501	+	0.663030i
$827$		−	15.6875i		−	0.545506i	−0.962084	−	0.272753i	$-0.912066\pi$
$827$		−	15.6875i		−	0.545506i	0.962084	−	0.272753i	$-0.0879342\pi$
$828$	−2.45875	−	18.9589i	−0.0854476	−	0.658868i
$829$	−4.91198	+	2.83593i	−0.170600	+	0.0984959i	−0.582869	−	0.812566i	$-0.698070\pi$
$829$	−4.91198	+	2.83593i	−0.170600	+	0.0984959i	0.412269	+	0.911062i	$0.364736\pi$
$830$	−1.59126	+	0.918714i	−0.0552334	+	0.0318890i
$831$	0.208008	+	0.311958i	0.00721572	+	0.0108217i
$832$		−	5.00084i		−	0.173373i
$833$	39.2979	−	20.0475i	1.36159	−	0.694606i
$834$	9.62095	−	19.4620i	0.333146	−	0.673913i
$835$	4.32474	−	7.49067i	0.149664	−	0.259225i
$836$	−8.71645	−	15.0973i	−0.301465	−	0.522152i
$837$	17.1606	−	14.9618i	0.593158	−	0.517154i
$838$	−24.5024	−	14.1465i	−0.846422	−	0.488682i
$839$	14.5217			0.501346			0.250673	−	0.968072i	$-0.419348\pi$
$839$	14.5217			0.501346			0.250673	+	0.968072i	$0.419348\pi$
$840$	−4.37743	+	1.35577i	−0.151036	+	0.0467785i
$841$	14.2902			0.492766
$842$	21.7967	+	12.5843i	0.751165	+	0.433685i
$843$	2.10387	+	32.5809i	0.0724613	+	1.12215i
$844$	13.8017	+	23.9052i	0.475073	+	0.822851i
$845$	−6.00420	+	10.3996i	−0.206551	+	0.357757i
$846$	−3.94920	+	3.01823i	−0.135776	+	0.103769i
$847$	−3.51094	−	14.6084i	−0.120637	−	0.501949i
$848$			3.25278i			0.111701i
$849$	2.87973	−	1.92015i	0.0988320	−	0.0658995i
$850$	−5.45795	+	3.15115i	−0.187206	+	0.108083i
$851$	−38.1310	+	22.0150i	−1.30712	+	0.754663i
$852$	−4.12018	+	2.74726i	−0.141155	+	0.0941197i
$853$			3.66698i			0.125555i	0.998028	+	0.0627775i	$0.0199958\pi$
$853$			3.66698i			0.125555i	−0.998028	+	0.0627775i	$0.980004\pi$
$854$	−15.1805	−	4.49262i	−0.519465	−	0.153734i
$855$	18.0131	−	13.7668i	0.616037	−	0.470814i
$856$	4.20937	−	7.29084i	0.143873	−	0.249196i
$857$	−5.78149	−	10.0138i	−0.197492	−	0.342066i	0.750223	−	0.661185i	$-0.229946\pi$
$857$	−5.78149	−	10.0138i	−0.197492	−	0.342066i	−0.947715	+	0.319119i	$0.896613\pi$
$858$	−1.28756	−	19.9393i	−0.0439565	−	0.680717i
$859$	−12.9614	−	7.48325i	−0.442236	−	0.255325i	0.262310	−	0.964984i	$-0.415516\pi$
$859$	−12.9614	−	7.48325i	−0.442236	−	0.255325i	−0.704546	+	0.709659i	$0.748849\pi$
$860$	2.55278			0.0870492
$861$	−30.4886	+	32.9347i	−1.03905	+	1.12241i
$862$	−11.2182			−0.382093
$863$	−8.11706	−	4.68639i	−0.276308	−	0.159526i	0.355443	−	0.934698i	$-0.384330\pi$
$863$	−8.11706	−	4.68639i	−0.276308	−	0.159526i	−0.631751	+	0.775172i	$0.717663\pi$
$864$	−3.91658	+	3.41473i	−0.133245	+	0.116172i
$865$	8.96573	+	15.5291i	0.304844	+	0.528005i
$866$	−0.319796	+	0.553903i	−0.0108671	+	0.0188224i
$867$	17.4383	−	35.2754i	0.592235	−	1.19802i
$868$	11.2715	−	2.70896i	0.382579	−	0.0919482i
$869$		−	5.90286i		−	0.200241i
$870$	3.68532	+	5.52701i	0.124944	+	0.187383i
$871$	−11.9842	+	6.91907i	−0.406069	+	0.234444i
$872$	5.77043	−	3.33156i	0.195411	−	0.112821i
$873$	−1.78148	−	13.7366i	−0.0602941	−	0.464915i
$874$			48.1585i			1.62899i
$875$	1.91871	−	1.82168i	0.0648644	−	0.0615842i
$876$	5.71664	+	2.82600i	0.193148	+	0.0954818i
$877$	7.81117	−	13.5293i	0.263764	−	0.456853i	−0.703475	−	0.710720i	$-0.748369\pi$
$877$	7.81117	−	13.5293i	0.263764	−	0.456853i	0.967239	+	0.253867i	$0.0817025\pi$
$878$	6.58174	+	11.3999i	0.222123	+	0.384728i
$879$	16.0420	−	1.03590i	0.541085	−	0.0349399i
$880$	−1.99775	−	1.15340i	−0.0673441	−	0.0388811i
$881$	−4.54709			−0.153195			−0.0765977	−	0.997062i	$-0.524406\pi$
$881$	−4.54709			−0.153195			−0.0765977	+	0.997062i	$0.524406\pi$
$882$	−9.06804	+	18.9412i	−0.305337	+	0.637785i
$883$	−48.8190			−1.64289			−0.821445	−	0.570288i	$-0.806831\pi$
$883$	−48.8190			−1.64289			−0.821445	+	0.570288i	$0.806831\pi$
$884$	−27.2943	−	15.7584i	−0.918008	−	0.530012i
$885$	−17.1660	+	1.10848i	−0.577030	+	0.0372610i
$886$	−12.9223	−	22.3821i	−0.434133	−	0.751941i
$887$	−3.64168	+	6.30758i	−0.122276	+	0.211788i	−0.920665	−	0.390354i	$-0.872353\pi$
$887$	−3.64168	+	6.30758i	−0.122276	+	0.211788i	0.798389	+	0.602142i	$0.205686\pi$
$888$	10.7280	+	5.30334i	0.360008	+	0.177969i
$889$	3.52457	−	3.34633i	0.118210	−	0.112232i
$890$			5.88774i			0.197358i
$891$	−14.7370	+	14.6236i	−0.493707	+	0.489908i
$892$	19.9858	−	11.5388i	0.669176	−	0.386349i
$893$	10.8435	−	6.26049i	0.362863	−	0.209499i
$894$	−14.9851	−	22.4738i	−0.501178	−	0.751636i
$895$			12.0170i			0.401683i
$896$	−2.57250	+	0.618268i	−0.0859411	+	0.0206549i
$897$	−24.4609	+	49.4813i	−0.816726	+	1.65213i
$898$	14.1793	−	24.5593i	0.473170	−	0.819554i
$899$	−8.40232	−	14.5532i	−0.280233	−	0.485378i
$900$	1.15340	−	2.76942i	0.0384467	−	0.0923139i
$901$	17.7535	+	10.2500i	0.591456	+	0.341477i
$902$	−22.5921			−0.752236
$903$	7.94702	−	8.58461i	0.264460	−	0.285678i
$904$	4.45505			0.148173
$905$	−8.24987	−	4.76306i	−0.274235	−	0.158330i
$906$	−0.339208	−	5.25302i	−0.0112694	−	0.174520i
$907$	13.4481	+	23.2928i	0.446537	+	0.773425i	0.998158	−	0.0606703i	$-0.0193238\pi$
$907$	13.4481	+	23.2928i	0.446537	+	0.773425i	−0.551621	+	0.834095i	$0.685990\pi$
$908$	−10.0175	+	17.3509i	−0.332444	+	0.575809i
$909$	20.6106	+	26.9679i	0.683611	+	0.894470i
$910$	12.6870	+	3.75470i	0.420571	+	0.124467i
$911$			46.4059i			1.53750i	0.639552	+	0.768748i	$0.279120\pi$
$911$			46.4059i			1.53750i	−0.639552	+	0.768748i	$0.720880\pi$
$912$	10.8905	−	7.26157i	0.360619	−	0.240455i
$913$	−3.67072	+	2.11929i	−0.121483	+	0.0701383i
$914$	−25.2797	+	14.5953i	−0.836179	+	0.482768i
$915$	8.62293	−	5.74962i	0.285065	−	0.190077i
$916$			28.7648i			0.950417i
$917$	3.42448	+	14.2486i	0.113086	+	0.470531i
$918$	6.29570	+	32.1368i	0.207789	+	1.06067i
$919$	2.26073	−	3.91570i	0.0745746	−	0.129167i	−0.826327	−	0.563191i	$-0.809573\pi$
$919$	2.26073	−	3.91570i	0.0745746	−	0.129167i	0.900901	+	0.434024i	$0.142907\pi$
$920$	3.18628	+	5.51880i	0.105049	+	0.181949i
$921$	−3.00553	−	46.5440i	−0.0990355	−	1.53368i
$922$	26.9306	+	15.5484i	0.886913	+	0.512060i
$923$	14.2979			0.470621
$924$	−10.0979	+	3.12749i	−0.332195	+	0.102887i
$925$	−6.90930			−0.227176
$926$	29.0045	+	16.7457i	0.953146	+	0.550299i
$927$	20.3942	+	8.49372i	0.669833	+	0.278970i
$928$	1.91767	+	3.32150i	0.0629505	+	0.109033i
$929$	8.30472	−	14.3842i	0.272469	−	0.471930i	−0.697025	−	0.717047i	$-0.745493\pi$
$929$	8.30472	−	14.3842i	0.272469	−	0.471930i	0.969493	+	0.245117i	$0.0788265\pi$
$930$	−3.36311	+	6.80316i	−0.110281	+	0.223084i
$931$	28.7898	−	44.3800i	0.943547	−	1.45449i
$932$			25.7115i			0.842209i
$933$	2.71094	+	4.06570i	0.0887522	+	0.133105i
$934$	−12.8389	+	7.41254i	−0.420102	+	0.242546i
$935$	−12.5904	+	7.26907i	−0.411750	+	0.237724i
$936$	14.8779	−	1.92950i	0.486300	−	0.0630675i
$937$			20.5347i			0.670839i	0.942069	+	0.335419i	$0.108878\pi$
$937$			20.5347i			0.670839i	−0.942069	+	0.335419i	$0.891122\pi$
$938$	5.04090	+	5.30940i	0.164591	+	0.173358i
$939$	17.7670	+	8.78303i	0.579803	+	0.286623i
$940$	0.828416	−	1.43486i	0.0270200	−	0.0467999i
$941$	−12.1992	−	21.1296i	−0.397682	−	0.688805i	0.595758	−	0.803164i	$-0.296852\pi$
$941$	−12.1992	−	21.1296i	−0.397682	−	0.688805i	−0.993439	+	0.114359i	$0.963519\pi$
$942$	27.3531	−	1.76629i	0.891211	−	0.0575490i
$943$	54.0495	+	31.2055i	1.76009	+	1.01619i
$944$	−9.93145			−0.323241
$945$	−5.72249	−	12.5001i	−0.186153	−	0.406629i
$946$	5.88876			0.191460
$947$	−16.5526	−	9.55667i	−0.537888	−	0.310550i	0.206334	−	0.978482i	$-0.433847\pi$
$947$	−16.5526	−	9.55667i	−0.537888	−	0.310550i	−0.744223	+	0.667932i	$0.767180\pi$
$948$	4.42292	−	0.285605i	0.143650	−	0.00927602i
$949$	−9.20598	−	15.9452i	−0.298839	−	0.517604i
$950$	−3.77859	+	6.54470i	−0.122594	+	0.212338i
$951$	−14.4553	−	7.14590i	−0.468744	−	0.231722i
$952$	−4.73184	+	15.9888i	−0.153360	+	0.518200i
$953$		−	7.20297i		−	0.233327i	−0.993171	−	0.116664i	$-0.962780\pi$
$953$		−	7.20297i		−	0.233327i	0.993171	−	0.116664i	$-0.0372199\pi$
$954$	−9.67731	+	1.25504i	−0.313314	+	0.0406333i
$955$	−4.30564	+	2.48586i	−0.139327	+	0.0804406i
$956$	9.28556	−	5.36102i	0.300317	−	0.173388i
$957$	8.50129	+	12.7497i	0.274808	+	0.412139i
$958$		−	23.0447i		−	0.744540i
$959$	0.931789	−	3.14850i	0.0300890	−	0.101670i
$960$	0.767566	−	1.55269i	0.0247731	−	0.0501128i
$961$	−5.90109	+	10.2210i	−0.190358	+	0.329709i
$962$	−17.2762	−	29.9232i	−0.557006	−	0.964762i
$963$	23.3150	+	9.71018i	0.751315	+	0.312906i
$964$	1.02594	+	0.592325i	0.0330432	+	0.0190775i
$965$	−6.03321			−0.194216
$966$	28.4780	+	6.46549i	0.916265	+	0.208024i
$967$	−12.2448			−0.393765			−0.196883	−	0.980427i	$-0.563082\pi$
$967$	−12.2448			−0.393765			−0.196883	+	0.980427i	$0.563082\pi$
$968$	4.91787	+	2.83934i	0.158066	+	0.0912597i
$969$	−5.31584	−	82.3219i	−0.170769	−	2.64456i
$970$	2.30861	+	3.99864i	0.0741251	+	0.128388i
$971$	13.4388	−	23.2768i	0.431273	−	0.746987i	−0.565710	−	0.824604i	$-0.691398\pi$
$971$	13.4388	−	23.2768i	0.431273	−	0.746987i	0.996983	+	0.0776173i	$0.0247312\pi$
$972$	−11.6703	−	10.3346i	−0.374324	−	0.331484i
$973$	22.8337	+	24.0499i	0.732014	+	0.771003i
$974$		−	10.6277i		−	0.340533i
$975$	−7.20659	+	4.80523i	−0.230796	+	0.153891i
$976$	5.18202	−	2.99184i	0.165872	−	0.0957664i
$977$	31.8298	−	18.3770i	1.01833	−	0.587931i	0.104707	−	0.994503i	$-0.466609\pi$
$977$	31.8298	−	18.3770i	1.01833	−	0.587931i	0.913619	+	0.406572i	$0.133276\pi$
$978$	12.4175	−	8.27977i	0.397067	−	0.264758i
$979$			13.5819i			0.434078i
$980$	0.362928	−	6.99059i	0.0115933	−	0.223306i
$981$	12.1381	+	15.8821i	0.387540	+	0.507076i
$982$	−11.2343	+	19.4584i	−0.358502	+	0.620943i
$983$	−6.68519	−	11.5791i	−0.213224	−	0.369315i	0.739498	−	0.673159i	$-0.235063\pi$
$983$	−6.68519	−	11.5791i	−0.213224	−	0.369315i	−0.952722	+	0.303844i	$0.901730\pi$
$984$	−1.09310	−	16.9279i	−0.0348468	−	0.539643i
$985$	−12.3100	−	7.10719i	−0.392230	−	0.226454i
$986$	24.1714			0.769775
$987$	−2.24628	−	7.25267i	−0.0715000	−	0.230855i
$988$	−37.7922			−1.20233
$989$	−14.0883	−	8.13388i	−0.447982	−	0.258642i
$990$	2.66066	−	6.38849i	0.0845615	−	0.203040i
$991$	−8.34843	−	14.4599i	−0.265197	−	0.459334i	0.702419	−	0.711764i	$-0.252104\pi$
$991$	−8.34843	−	14.4599i	−0.265197	−	0.459334i	−0.967615	+	0.252430i	$0.918770\pi$
$992$	−2.19077	+	3.79452i	−0.0695569	+	0.120476i
$993$	14.0434	−	28.4080i	0.445654	−	0.901501i
$994$	−1.76769	−	7.35502i	−0.0560677	−	0.233287i
$995$		−	2.25088i		−	0.0713576i
$996$	−1.76556	−	2.64787i	−0.0559438	−	0.0839011i
$997$	42.5957	−	24.5927i	1.34902	−	0.778857i	0.360910	−	0.932601i	$-0.382466\pi$
$997$	42.5957	−	24.5927i	1.34902	−	0.778857i	0.988111	+	0.153743i	$0.0491329\pi$
$998$	−34.4322	+	19.8794i	−1.08993	+	0.629272i
$999$	−11.6387	+	33.9629i	−0.368231	+	1.07454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.r.a.131.1	yes	12
3.2	odd	2		210.2.r.b.131.4	yes	12
5.2	odd	4		1050.2.u.g.299.4		12
5.3	odd	4		1050.2.u.f.299.3		12
5.4	even	2		1050.2.s.g.551.6		12
7.2	even	3		1470.2.b.b.881.10		12
7.3	odd	6		210.2.r.b.101.4	yes	12
7.5	odd	6		1470.2.b.a.881.9		12
15.2	even	4		1050.2.u.e.299.6		12
15.8	even	4		1050.2.u.h.299.1		12
15.14	odd	2		1050.2.s.f.551.3		12
21.2	odd	6		1470.2.b.a.881.3		12
21.5	even	6		1470.2.b.b.881.4		12
21.17	even	6	inner	210.2.r.a.101.1	✓	12
35.3	even	12		1050.2.u.e.899.6		12
35.17	even	12		1050.2.u.h.899.1		12
35.24	odd	6		1050.2.s.f.101.3		12
105.17	odd	12		1050.2.u.f.899.3		12
105.38	odd	12		1050.2.u.g.899.4		12
105.59	even	6		1050.2.s.g.101.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.1	✓	12	21.17	even	6	inner
210.2.r.a.131.1	yes	12	1.1	even	1	trivial
210.2.r.b.101.4	yes	12	7.3	odd	6
210.2.r.b.131.4	yes	12	3.2	odd	2
1050.2.s.f.101.3		12	35.24	odd	6
1050.2.s.f.551.3		12	15.14	odd	2
1050.2.s.g.101.6		12	105.59	even	6
1050.2.s.g.551.6		12	5.4	even	2
1050.2.u.e.299.6		12	15.2	even	4
1050.2.u.e.899.6		12	35.3	even	12
1050.2.u.f.299.3		12	5.3	odd	4
1050.2.u.f.899.3		12	105.17	odd	12
1050.2.u.g.299.4		12	5.2	odd	4
1050.2.u.g.899.4		12	105.38	odd	12
1050.2.u.h.299.1		12	15.8	even	4
1050.2.u.h.899.1		12	35.17	even	12
1470.2.b.a.881.3		12	21.2	odd	6
1470.2.b.a.881.9		12	7.5	odd	6
1470.2.b.b.881.4		12	21.5	even	6
1470.2.b.b.881.10		12	7.2	even	3

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72845 + 0.111613i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.55269 + 0.767566i) q^{6} +(-1.91871 + 1.82168i) q^{7} -1.00000i q^{8} +(2.97509 - 0.385834i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.72845 + 0.111613i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.55269 + 0.767566i) q^{6} +(-1.91871 + 1.82168i) q^{7} -1.00000i q^{8} +(2.97509 - 0.385834i) q^{9} +(-0.866025 + 0.500000i) q^{10} +(-1.99775 + 1.15340i) q^{11} +(-0.960885 - 1.44108i) q^{12} +5.00084i q^{13} +(2.57250 - 0.618268i) q^{14} +(-0.767566 + 1.55269i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.15115 + 5.45795i) q^{17} +(-2.76942 - 1.15340i) q^{18} +(6.54470 + 3.77859i) q^{19} +1.00000 q^{20} +(3.11308 - 3.36285i) q^{21} +2.30680 q^{22} +(-5.51880 - 3.18628i) q^{23} +(0.111613 + 1.72845i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(2.50042 - 4.33086i) q^{26} +(-5.09922 + 0.998953i) q^{27} +(-2.53698 - 0.750813i) q^{28} +3.83533i q^{29} +(1.44108 - 0.960885i) q^{30} +(-3.79452 + 2.19077i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.32428 - 2.21657i) q^{33} -6.30230i q^{34} +(0.618268 + 2.57250i) q^{35} +(1.82168 + 2.38358i) q^{36} +(3.45465 - 5.98363i) q^{37} +(-3.77859 - 6.54470i) q^{38} +(-0.558158 - 8.64371i) q^{39} +(-0.866025 - 0.500000i) q^{40} -9.79371 q^{41} +(-4.37743 + 1.35577i) q^{42} +2.55278 q^{43} +(-1.99775 - 1.15340i) q^{44} +(1.15340 - 2.76942i) q^{45} +(3.18628 + 5.51880i) q^{46} +(0.828416 - 1.43486i) q^{47} +(0.767566 - 1.55269i) q^{48} +(0.362928 - 6.99059i) q^{49} +1.00000i q^{50} +(-6.05578 - 9.08209i) q^{51} +(-4.33086 + 2.50042i) q^{52} +(2.81699 - 1.62639i) q^{53} +(4.91553 + 1.68449i) q^{54} +2.30680i q^{55} +(1.82168 + 1.91871i) q^{56} +(-11.7339 - 5.80063i) q^{57} +(1.91767 - 3.32150i) q^{58} +(4.96573 + 8.60089i) q^{59} +(-1.72845 + 0.111613i) q^{60} +(-5.18202 - 2.99184i) q^{61} +4.38153 q^{62} +(-5.00547 + 6.15997i) q^{63} -1.00000 q^{64} +(4.33086 + 2.50042i) q^{65} +(-3.98719 + 0.257468i) q^{66} +(1.38358 + 2.39643i) q^{67} +(-3.15115 + 5.45795i) q^{68} +(9.89460 + 4.89136i) q^{69} +(0.750813 - 2.53698i) q^{70} -2.85910i q^{71} +(-0.385834 - 2.97509i) q^{72} +(-3.18851 + 1.84089i) q^{73} +(-5.98363 + 3.45465i) q^{74} +(0.960885 + 1.44108i) q^{75} +7.55717i q^{76} +(1.73198 - 5.85231i) q^{77} +(-3.83848 + 7.76475i) q^{78} +(-1.27945 + 2.21607i) q^{79} +(0.500000 + 0.866025i) q^{80} +(8.70226 - 2.29578i) q^{81} +(8.48160 + 4.89686i) q^{82} +1.83743 q^{83} +(4.46885 + 1.01458i) q^{84} +6.30230 q^{85} +(-2.21077 - 1.27639i) q^{86} +(-0.428072 - 6.62919i) q^{87} +(1.15340 + 1.99775i) q^{88} +(2.94387 - 5.09894i) q^{89} +(-2.38358 + 1.82168i) q^{90} +(-9.10996 - 9.59518i) q^{91} -6.37256i q^{92} +(6.31412 - 4.21015i) q^{93} +(-1.43486 + 0.828416i) q^{94} +(6.54470 - 3.77859i) q^{95} +(-1.44108 + 0.960885i) q^{96} -4.61723i q^{97} +(-3.80960 + 5.87256i) q^{98} +(-5.49845 + 4.20226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9	\( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{9} - 12 q^{11} + 2 q^{12} + 12 q^{14} - 4 q^{15} - 6 q^{16} + 12 q^{17} - 4 q^{18} + 12 q^{20} - 18 q^{21} - 24 q^{23} - 4 q^{24} - 6 q^{25} - 4 q^{26} - 8 q^{27} + 4 q^{28} + 2 q^{30} + 12 q^{31} - 22 q^{33} + 4 q^{35} + 6 q^{36} - 8 q^{37} + 8 q^{38} + 30 q^{39} - 4 q^{41} - 20 q^{42} - 12 q^{44} + 2 q^{46} + 16 q^{47} + 4 q^{48} - 14 q^{49} + 4 q^{51} - 12 q^{52} - 48 q^{53} - 4 q^{54} + 6 q^{56} - 36 q^{57} + 8 q^{58} + 12 q^{59} - 2 q^{60} - 30 q^{61} + 8 q^{62} - 4 q^{63} - 12 q^{64} + 12 q^{65} - 34 q^{66} - 4 q^{67} - 12 q^{68} + 50 q^{69} + 6 q^{70} + 4 q^{72} - 2 q^{75} + 20 q^{77} + 32 q^{78} - 4 q^{79} + 6 q^{80} + 50 q^{81} - 40 q^{83} - 12 q^{84} + 24 q^{85} - 54 q^{86} + 8 q^{87} + 26 q^{89} - 8 q^{90} + 28 q^{91} - 32 q^{93} + 24 q^{94} - 2 q^{96} + 16 q^{98} + 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^9 - 12 * q^11 + 2 * q^12 + 12 * q^14 - 4 * q^15 - 6 * q^16 + 12 * q^17 - 4 * q^18 + 12 * q^20 - 18 * q^21 - 24 * q^23 - 4 * q^24 - 6 * q^25 - 4 * q^26 - 8 * q^27 + 4 * q^28 + 2 * q^30 + 12 * q^31 - 22 * q^33 + 4 * q^35 + 6 * q^36 - 8 * q^37 + 8 * q^38 + 30 * q^39 - 4 * q^41 - 20 * q^42 - 12 * q^44 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 14 * q^49 + 4 * q^51 - 12 * q^52 - 48 * q^53 - 4 * q^54 + 6 * q^56 - 36 * q^57 + 8 * q^58 + 12 * q^59 - 2 * q^60 - 30 * q^61 + 8 * q^62 - 4 * q^63 - 12 * q^64 + 12 * q^65 - 34 * q^66 - 4 * q^67 - 12 * q^68 + 50 * q^69 + 6 * q^70 + 4 * q^72 - 2 * q^75 + 20 * q^77 + 32 * q^78 - 4 * q^79 + 6 * q^80 + 50 * q^81 - 40 * q^83 - 12 * q^84 + 24 * q^85 - 54 * q^86 + 8 * q^87 + 26 * q^89 - 8 * q^90 + 28 * q^91 - 32 * q^93 + 24 * q^94 - 2 * q^96 + 16 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more