LMFDB - Embedded newform 930.2.r.a.119.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(119,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("930.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.20
Character	$\chi$	$=$	930.119
Dual form			930.2.r.a.719.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.681795 + 1.59222i) q^{3} +1.00000 q^{4} +(-0.949262 - 2.02457i) q^{5} +(-0.681795 - 1.59222i) q^{6} +(-1.56394 - 0.902941i) q^{7} -1.00000 q^{8} +(-2.07031 + 2.17113i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.681795 + 1.59222i) q^{3} +1.00000 q^{4} +(-0.949262 - 2.02457i) q^{5} +(-0.681795 - 1.59222i) q^{6} +(-1.56394 - 0.902941i) q^{7} -1.00000 q^{8} +(-2.07031 + 2.17113i) q^{9} +(0.949262 + 2.02457i) q^{10} +(1.36676 + 2.36730i) q^{11} +(0.681795 + 1.59222i) q^{12} +(1.89509 + 3.28240i) q^{13} +(1.56394 + 0.902941i) q^{14} +(2.57636 - 2.89178i) q^{15} +1.00000 q^{16} +(-5.50887 - 3.18055i) q^{17} +(2.07031 - 2.17113i) q^{18} +(0.217690 - 0.377051i) q^{19} +(-0.949262 - 2.02457i) q^{20} +(0.371391 - 3.10575i) q^{21} +(-1.36676 - 2.36730i) q^{22} -2.68202i q^{23} +(-0.681795 - 1.59222i) q^{24} +(-3.19780 + 3.84370i) q^{25} +(-1.89509 - 3.28240i) q^{26} +(-4.86844 - 1.81611i) q^{27} +(-1.56394 - 0.902941i) q^{28} -3.54035 q^{29} +(-2.57636 + 2.89178i) q^{30} +(-0.925384 + 5.49032i) q^{31} -1.00000 q^{32} +(-2.83741 + 3.79020i) q^{33} +(5.50887 + 3.18055i) q^{34} +(-0.343482 + 4.02344i) q^{35} +(-2.07031 + 2.17113i) q^{36} +(-5.35919 + 9.28239i) q^{37} +(-0.217690 + 0.377051i) q^{38} +(-3.93422 + 5.25532i) q^{39} +(0.949262 + 2.02457i) q^{40} +(2.25018 - 1.29914i) q^{41} +(-0.371391 + 3.10575i) q^{42} +(-0.848315 + 1.46932i) q^{43} +(1.36676 + 2.36730i) q^{44} +(6.36089 + 2.13052i) q^{45} +2.68202i q^{46} -1.54613 q^{47} +(0.681795 + 1.59222i) q^{48} +(-1.86940 - 3.23789i) q^{49} +(3.19780 - 3.84370i) q^{50} +(1.30820 - 10.9398i) q^{51} +(1.89509 + 3.28240i) q^{52} +(-8.31697 + 4.80180i) q^{53} +(4.86844 + 1.81611i) q^{54} +(3.49537 - 5.01430i) q^{55} +(1.56394 + 0.902941i) q^{56} +(0.748767 + 0.0895387i) q^{57} +3.54035 q^{58} +(-10.8827 - 6.28315i) q^{59} +(2.57636 - 2.89178i) q^{60} -3.25814i q^{61} +(0.925384 - 5.49032i) q^{62} +(5.19824 - 1.52615i) q^{63} +1.00000 q^{64} +(4.84651 - 6.95261i) q^{65} +(2.83741 - 3.79020i) q^{66} +(-7.83494 + 4.52350i) q^{67} +(-5.50887 - 3.18055i) q^{68} +(4.27036 - 1.82859i) q^{69} +(0.343482 - 4.02344i) q^{70} +(-5.72140 + 3.30325i) q^{71} +(2.07031 - 2.17113i) q^{72} +(3.73631 + 6.47149i) q^{73} +(5.35919 - 9.28239i) q^{74} +(-8.30026 - 2.47098i) q^{75} +(0.217690 - 0.377051i) q^{76} -4.93642i q^{77} +(3.93422 - 5.25532i) q^{78} +(0.884726 + 0.510797i) q^{79} +(-0.949262 - 2.02457i) q^{80} +(-0.427634 - 8.98983i) q^{81} +(-2.25018 + 1.29914i) q^{82} +(1.00160 - 0.578276i) q^{83} +(0.371391 - 3.10575i) q^{84} +(-1.20989 + 14.1723i) q^{85} +(0.848315 - 1.46932i) q^{86} +(-2.41379 - 5.63700i) q^{87} +(-1.36676 - 2.36730i) q^{88} +2.32751 q^{89} +(-6.36089 - 2.13052i) q^{90} -6.84462i q^{91} -2.68202i q^{92} +(-9.37271 + 2.26987i) q^{93} +1.54613 q^{94} +(-0.970012 - 0.0828103i) q^{95} +(-0.681795 - 1.59222i) q^{96} -11.8138i q^{97} +(1.86940 + 3.23789i) q^{98} +(-7.96935 - 1.93363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9}+O(q^{10}) $ 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9	$ 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} - 6 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 2 q^{25} + 18 q^{31} - 64 q^{32} + 8 q^{33} + 6 q^{34} - 16 q^{35} - 4 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 5 q^{45} + 4 q^{47} + 30 q^{49} - 2 q^{50} - 8 q^{51} + 6 q^{53} - 6 q^{57} - 18 q^{62} - 12 q^{63} + 64 q^{64} - 8 q^{66} - 6 q^{68} - 10 q^{69} + 16 q^{70} + 4 q^{72} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 q^{90} + 18 q^{93} - 4 q^{94} + 56 q^{95} - 30 q^{98} - 102 q^{99}+O(q^{100}) $ 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 - 6 * q^17 + 4 * q^18 + 4 * q^19 - 2 * q^20 + 2 * q^25 + 18 * q^31 - 64 * q^32 + 8 * q^33 + 6 * q^34 - 16 * q^35 - 4 * q^36 - 4 * q^38 - 8 * q^39 + 2 * q^40 + 5 * q^45 + 4 * q^47 + 30 * q^49 - 2 * q^50 - 8 * q^51 + 6 * q^53 - 6 * q^57 - 18 * q^62 - 12 * q^63 + 64 * q^64 - 8 * q^66 - 6 * q^68 - 10 * q^69 + 16 * q^70 + 4 * q^72 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * q^90 + 18 * q^93 - 4 * q^94 + 56 * q^95 - 30 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.681795	+	1.59222i	0.393635	+	0.919267i
$3$	0.681795	+	1.59222i	0.393635	+	0.919267i
$4$	1.00000			0.500000
$5$	−0.949262	−	2.02457i	−0.424523	−	0.905417i
$5$	−0.949262	−	2.02457i	−0.424523	−	0.905417i
$6$	−0.681795	−	1.59222i	−0.278342	−	0.650020i
$7$	−1.56394	−	0.902941i	−0.591113	−	0.341279i	0.174424	−	0.984671i	$-0.444194\pi$
$7$	−1.56394	−	0.902941i	−0.591113	−	0.341279i	−0.765538	+	0.643391i	$0.777527\pi$
$8$	−1.00000			−0.353553
$9$	−2.07031	+	2.17113i	−0.690103	+	0.723711i
$10$	0.949262	+	2.02457i	0.300183	+	0.640227i
$11$	1.36676	+	2.36730i	0.412095	+	0.713769i	0.995119	−	0.0986861i	$-0.0314640\pi$
$11$	1.36676	+	2.36730i	0.412095	+	0.713769i	−0.583024	+	0.812455i	$0.698131\pi$
$12$	0.681795	+	1.59222i	0.196817	+	0.459633i
$13$	1.89509	+	3.28240i	0.525604	+	0.910373i	0.999555	+	0.0298216i	$0.00949392\pi$
$13$	1.89509	+	3.28240i	0.525604	+	0.910373i	−0.473951	+	0.880551i	$0.657173\pi$
$14$	1.56394	+	0.902941i	0.417980	+	0.241321i
$15$	2.57636	−	2.89178i	0.665213	−	0.746654i
$16$	1.00000			0.250000
$17$	−5.50887	−	3.18055i	−1.33610	−	0.771397i	−0.349872	−	0.936798i	$-0.613775\pi$
$17$	−5.50887	−	3.18055i	−1.33610	−	0.771397i	−0.986226	+	0.165401i	$0.947108\pi$
$18$	2.07031	−	2.17113i	0.487977	−	0.511741i
$19$	0.217690	−	0.377051i	0.0499416	−	0.0865013i	−0.839974	−	0.542627i	$-0.817430\pi$
$19$	0.217690	−	0.377051i	0.0499416	−	0.0865013i	0.889916	+	0.456125i	$0.150763\pi$
$20$	−0.949262	−	2.02457i	−0.212261	−	0.452709i
$21$	0.371391	−	3.10575i	0.0810441	−	0.677730i
$22$	−1.36676	−	2.36730i	−0.291395	−	0.504711i
$23$		−	2.68202i		−	0.559240i	−0.960111	−	0.279620i	$-0.909791\pi$
$23$		−	2.68202i		−	0.559240i	0.960111	−	0.279620i	$-0.0902085\pi$
$24$	−0.681795	−	1.59222i	−0.139171	−	0.325010i
$25$	−3.19780	+	3.84370i	−0.639561	+	0.768741i
$26$	−1.89509	−	3.28240i	−0.371658	−	0.643731i
$27$	−4.86844	−	1.81611i	−0.936932	−	0.349511i
$28$	−1.56394	−	0.902941i	−0.295557	−	0.170640i
$29$	−3.54035			−0.657426			−0.328713	−	0.944430i	$-0.606615\pi$
$29$	−3.54035			−0.657426			−0.328713	+	0.944430i	$0.606615\pi$
$30$	−2.57636	+	2.89178i	−0.470377	+	0.527964i
$31$	−0.925384	+	5.49032i	−0.166204	+	0.986091i
$31$	−0.925384	+	5.49032i	−0.166204	+	0.986091i
$32$	−1.00000			−0.176777
$33$	−2.83741	+	3.79020i	−0.493929	+	0.659789i
$34$	5.50887	+	3.18055i	0.944764	+	0.545460i
$35$	−0.343482	+	4.02344i	−0.0580591	+	0.680085i
$36$	−2.07031	+	2.17113i	−0.345052	+	0.361855i
$37$	−5.35919	+	9.28239i	−0.881045	+	1.52602i	−0.0308649	+	0.999524i	$0.509826\pi$
$37$	−5.35919	+	9.28239i	−0.881045	+	1.52602i	−0.850180	+	0.526492i	$0.823507\pi$
$38$	−0.217690	+	0.377051i	−0.0353140	+	0.0611657i
$39$	−3.93422	+	5.25532i	−0.629979	+	0.841525i
$40$	0.949262	+	2.02457i	0.150092	+	0.320113i
$41$	2.25018	−	1.29914i	0.351420	−	0.202892i	−0.313891	−	0.949459i	$-0.601633\pi$
$41$	2.25018	−	1.29914i	0.351420	−	0.202892i	0.665310	+	0.746567i	$0.268299\pi$
$42$	−0.371391	+	3.10575i	−0.0573068	+	0.479228i
$43$	−0.848315	+	1.46932i	−0.129367	+	0.224070i	−0.923431	−	0.383763i	$-0.874628\pi$
$43$	−0.848315	+	1.46932i	−0.129367	+	0.224070i	0.794065	+	0.607833i	$0.207961\pi$
$44$	1.36676	+	2.36730i	0.206047	+	0.356884i
$45$	6.36089	+	2.13052i	0.948225	+	0.317600i
$46$			2.68202i			0.395443i
$47$	−1.54613			−0.225526			−0.112763	−	0.993622i	$-0.535970\pi$
$47$	−1.54613			−0.225526			−0.112763	+	0.993622i	$0.535970\pi$
$48$	0.681795	+	1.59222i	0.0984087	+	0.229817i
$49$	−1.86940	−	3.23789i	−0.267057	−	0.462556i
$50$	3.19780	−	3.84370i	0.452238	−	0.543582i
$51$	1.30820	−	10.9398i	0.183185	−	1.53188i
$52$	1.89509	+	3.28240i	0.262802	+	0.455186i
$53$	−8.31697	+	4.80180i	−1.14242	+	0.659578i	−0.947030	−	0.321146i	$-0.895932\pi$
$53$	−8.31697	+	4.80180i	−1.14242	+	0.659578i	−0.195394	+	0.980725i	$0.562599\pi$
$54$	4.86844	+	1.81611i	0.662511	+	0.247142i
$55$	3.49537	−	5.01430i	0.471315	−	0.676129i
$56$	1.56394	+	0.902941i	0.208990	+	0.120661i
$57$	0.748767	+	0.0895387i	0.0991766	+	0.0118597i
$58$	3.54035			0.464871
$59$	−10.8827	−	6.28315i	−1.41681	−	0.817997i	−0.420794	−	0.907156i	$-0.638249\pi$
$59$	−10.8827	−	6.28315i	−1.41681	−	0.817997i	−0.996017	+	0.0891593i	$0.971582\pi$
$60$	2.57636	−	2.89178i	0.332607	−	0.373327i
$61$		−	3.25814i		−	0.417163i	−0.978005	−	0.208581i	$-0.933115\pi$
$61$		−	3.25814i		−	0.417163i	0.978005	−	0.208581i	$-0.0668846\pi$
$62$	0.925384	−	5.49032i	0.117524	−	0.697272i
$63$	5.19824	−	1.52615i	0.654917	−	0.192277i
$64$	1.00000			0.125000
$65$	4.84651	−	6.95261i	0.601136	−	0.862365i
$66$	2.83741	−	3.79020i	0.349261	−	0.466541i
$67$	−7.83494	+	4.52350i	−0.957190	+	0.552634i	−0.895307	−	0.445449i	$-0.853044\pi$
$67$	−7.83494	+	4.52350i	−0.957190	+	0.552634i	−0.0618830	+	0.998083i	$0.519711\pi$
$68$	−5.50887	−	3.18055i	−0.668049	−	0.385698i
$69$	4.27036	−	1.82859i	0.514091	−	0.220136i
$70$	0.343482	−	4.02344i	0.0410540	−	0.480893i
$71$	−5.72140	+	3.30325i	−0.679005	+	0.392024i	−0.799480	−	0.600692i	$-0.794892\pi$
$71$	−5.72140	+	3.30325i	−0.679005	+	0.392024i	0.120475	+	0.992716i	$0.461558\pi$
$72$	2.07031	−	2.17113i	0.243988	−	0.255870i
$73$	3.73631	+	6.47149i	0.437302	+	0.757430i	0.997480	−	0.0709422i	$-0.0226006\pi$
$73$	3.73631	+	6.47149i	0.437302	+	0.757430i	−0.560178	+	0.828372i	$0.689267\pi$
$74$	5.35919	−	9.28239i	0.622993	−	1.07906i
$75$	−8.30026	−	2.47098i	−0.958431	−	0.285324i
$76$	0.217690	−	0.377051i	0.0249708	−	0.0432507i
$77$		−	4.93642i		−	0.562558i
$78$	3.93422	−	5.25532i	0.445463	−	0.595048i
$79$	0.884726	+	0.510797i	0.0995395	+	0.0574692i	0.548943	−	0.835860i	$-0.315030\pi$
$79$	0.884726	+	0.510797i	0.0995395	+	0.0574692i	−0.449404	+	0.893329i	$0.648364\pi$
$80$	−0.949262	−	2.02457i	−0.106131	−	0.226354i
$81$	−0.427634	−	8.98983i	−0.0475149	−	0.998871i
$82$	−2.25018	+	1.29914i	−0.248491	+	0.143466i
$83$	1.00160	−	0.578276i	0.109940	−	0.0634740i	−0.444022	−	0.896016i	$-0.646449\pi$
$83$	1.00160	−	0.578276i	0.109940	−	0.0634740i	0.553962	+	0.832542i	$0.313115\pi$
$84$	0.371391	−	3.10575i	0.0405221	−	0.338865i
$85$	−1.20989	+	14.1723i	−0.131232	+	1.53720i
$86$	0.848315	−	1.46932i	0.0914761	−	0.158441i
$87$	−2.41379	−	5.63700i	−0.258786	−	0.604350i
$88$	−1.36676	−	2.36730i	−0.145697	−	0.252355i
$89$	2.32751			0.246715			0.123358	−	0.992362i	$-0.460634\pi$
$89$	2.32751			0.246715			0.123358	+	0.992362i	$0.460634\pi$
$90$	−6.36089	−	2.13052i	−0.670496	−	0.224577i
$91$		−	6.84462i		−	0.717511i
$92$		−	2.68202i		−	0.279620i
$93$	−9.37271	+	2.26987i	−0.971905	+	0.235374i
$94$	1.54613			0.159471
$95$	−0.970012	−	0.0828103i	−0.0995211	−	0.00849616i
$96$	−0.681795	−	1.59222i	−0.0695855	−	0.162505i
$97$		−	11.8138i		−	1.19951i	−0.800183	−	0.599755i	$-0.795265\pi$
$97$		−	11.8138i		−	1.19951i	0.800183	−	0.599755i	$-0.204735\pi$
$98$	1.86940	+	3.23789i	0.188838	+	0.327076i
$99$	−7.96935	−	1.93363i	−0.800950	−	0.194337i
$100$	−3.19780	+	3.84370i	−0.319780	+	0.384370i
$101$			15.5501i			1.54729i	0.633620	+	0.773645i	$0.281568\pi$
$101$			15.5501i			1.54729i	−0.633620	+	0.773645i	$0.718432\pi$
$102$	−1.30820	+	10.9398i	−0.129531	+	1.08320i
$103$	14.1597	−	8.17508i	1.39519	−	0.805515i	0.401308	−	0.915943i	$-0.368556\pi$
$103$	14.1597	−	8.17508i	1.39519	−	0.805515i	0.993884	+	0.110428i	$0.0352223\pi$
$104$	−1.89509	−	3.28240i	−0.185829	−	0.321865i
$105$	−6.64037	+	2.19626i	−0.648034	+	0.214333i
$106$	8.31697	−	4.80180i	0.807815	−	0.466392i
$107$	2.70745	−	4.68944i	0.261739	−	0.453345i	−0.704965	−	0.709242i	$-0.749037\pi$
$107$	2.70745	−	4.68944i	0.261739	−	0.453345i	0.966704	+	0.255897i	$0.0823707\pi$
$108$	−4.86844	−	1.81611i	−0.468466	−	0.174756i
$109$	−3.08751			−0.295730			−0.147865	−	0.989008i	$-0.547240\pi$
$109$	−3.08751			−0.295730			−0.147865	+	0.989008i	$0.547240\pi$
$110$	−3.49537	+	5.01430i	−0.333270	+	0.478095i
$111$	−18.4334	−	2.20430i	−1.74963	−	0.209223i
$112$	−1.56394	−	0.902941i	−0.147778	−	0.0853199i
$113$	5.84956	+	10.1317i	0.550280	+	0.953113i	0.998254	+	0.0590664i	$0.0188124\pi$
$113$	5.84956	+	10.1317i	0.550280	+	0.953113i	−0.447974	+	0.894047i	$0.647854\pi$
$114$	−0.748767	−	0.0895387i	−0.0701284	−	0.00838607i
$115$	−5.42995	+	2.54594i	−0.506346	+	0.237410i
$116$	−3.54035			−0.328713
$117$	−11.0499	−	2.68108i	−1.02157	−	0.247866i
$118$	10.8827	+	6.28315i	1.00184	+	0.578411i
$119$	5.74370	+	9.94837i	0.526524	+	0.911966i
$120$	−2.57636	+	2.89178i	−0.235188	+	0.263982i
$121$	1.76392	−	3.05519i	0.160356	−	0.277745i
$122$			3.25814i			0.294979i
$123$	3.60268	+	2.69703i	0.324843	+	0.243183i
$124$	−0.925384	+	5.49032i	−0.0831019	+	0.493046i
$125$	10.8174	+	2.82551i	0.967539	+	0.252721i
$126$	−5.19824	+	1.52615i	−0.463096	+	0.135960i
$127$	−2.92334	+	5.06337i	−0.259404	+	0.449301i	−0.966082	−	0.258234i	$-0.916859\pi$
$127$	−2.92334	+	5.06337i	−0.259404	+	0.449301i	0.706678	+	0.707535i	$0.250193\pi$
$128$	−1.00000			−0.0883883
$129$	−2.91786	−	0.348923i	−0.256903	−	0.0307209i
$130$	−4.84651	+	6.95261i	−0.425067	+	0.609784i
$131$	−13.3521	−	7.70881i	−1.16657	−	0.673522i	−0.213704	−	0.976899i	$-0.568553\pi$
$131$	−13.3521	−	7.70881i	−1.16657	−	0.673522i	−0.952871	+	0.303376i	$0.901886\pi$
$132$	−2.83741	+	3.79020i	−0.246965	+	0.329895i
$133$	−0.680908	+	0.393123i	−0.0590423	+	0.0340881i
$134$	7.83494	−	4.52350i	0.676836	−	0.390771i
$135$	0.944569	+	11.5805i	0.0812956	+	0.996690i
$136$	5.50887	+	3.18055i	0.472382	+	0.272730i
$137$	5.75226	−	3.32107i	0.491448	−	0.283738i	−0.233727	−	0.972302i	$-0.575092\pi$
$137$	5.75226	−	3.32107i	0.491448	−	0.283738i	0.725175	+	0.688564i	$0.241759\pi$
$138$	−4.27036	+	1.82859i	−0.363517	+	0.155660i
$139$			10.0512i			0.852531i	0.904598	+	0.426266i	$0.140171\pi$
$139$			10.0512i			0.852531i	−0.904598	+	0.426266i	$0.859829\pi$
$140$	−0.343482	+	4.02344i	−0.0290296	+	0.340043i
$141$	−1.05414	−	2.46177i	−0.0887748	−	0.207318i
$142$	5.72140	−	3.30325i	0.480129	−	0.277203i
$143$	−5.18028	+	8.97251i	−0.433197	+	0.750319i
$144$	−2.07031	+	2.17113i	−0.172526	+	0.180928i
$145$	3.36072	+	7.16770i	0.279093	+	0.595245i
$146$	−3.73631	−	6.47149i	−0.309220	−	0.535584i
$147$	3.88088	−	5.18406i	0.320089	−	0.427574i
$148$	−5.35919	+	9.28239i	−0.440523	+	0.763008i
$149$	6.45518	+	3.72690i	0.528829	+	0.305320i	0.740540	−	0.672013i	$-0.234570\pi$
$149$	6.45518	+	3.72690i	0.528829	+	0.305320i	−0.211710	+	0.977332i	$0.567903\pi$
$150$	8.30026	+	2.47098i	0.677713	+	0.201754i
$151$		−	18.6368i		−	1.51664i	−0.651880	−	0.758322i	$-0.726019\pi$
$151$		−	18.6368i		−	1.51664i	0.651880	−	0.758322i	$-0.273981\pi$
$152$	−0.217690	+	0.377051i	−0.0176570	+	0.0305828i
$153$	18.3105	−	5.37577i	1.48031	−	0.434605i
$154$			4.93642i			0.397788i
$155$	11.9940	−	3.33825i	0.963381	−	0.268135i
$156$	−3.93422	+	5.25532i	−0.314990	+	0.420762i
$157$			11.8145i			0.942901i	0.881893	+	0.471450i	$0.156269\pi$
$157$			11.8145i			0.942901i	−0.881893	+	0.471450i	$0.843731\pi$
$158$	−0.884726	−	0.510797i	−0.0703851	−	0.0406368i
$159$	−13.3160	−	9.96857i	−1.05603	−	0.790559i
$160$	0.949262	+	2.02457i	0.0750458	+	0.160057i
$161$	−2.42171	+	4.19452i	−0.190857	+	0.330574i
$162$	0.427634	+	8.98983i	0.0335981	+	0.706308i
$163$		−	20.5432i		−	1.60906i	−0.593909	−	0.804532i	$-0.702416\pi$
$163$		−	20.5432i		−	1.60906i	0.593909	−	0.804532i	$-0.297584\pi$
$164$	2.25018	−	1.29914i	0.175710	−	0.101446i
$165$	10.3670	+	2.14665i	0.807069	+	0.167116i
$166$	−1.00160	+	0.578276i	−0.0777395	+	0.0448829i
$167$	9.55459	+	5.51635i	0.739356	+	0.426868i	0.821835	−	0.569725i	$-0.192950\pi$
$167$	9.55459	+	5.51635i	0.739356	+	0.426868i	−0.0824789	+	0.996593i	$0.526284\pi$
$168$	−0.371391	+	3.10575i	−0.0286534	+	0.239614i
$169$	−0.682746	+	1.18255i	−0.0525189	+	0.0909654i
$170$	1.20989	−	14.1723i	0.0927947	−	1.08697i
$171$	0.367941	+	1.25325i	0.0281371	+	0.0958381i
$172$	−0.848315	+	1.46932i	−0.0646834	+	0.112035i
$173$	13.0225	+	22.5556i	0.990079	+	1.71487i	0.616727	+	0.787177i	$0.288458\pi$
$173$	13.0225	+	22.5556i	0.990079	+	1.71487i	0.373351	+	0.927690i	$0.378209\pi$
$174$	2.41379	+	5.63700i	0.182989	+	0.427340i
$175$	8.47180	−	3.12389i	0.640408	−	0.236144i
$176$	1.36676	+	2.36730i	0.103024	+	0.178442i
$177$	2.58434	−	21.6115i	0.194251	−	1.62442i
$178$	−2.32751			−0.174454
$179$	2.35224	−	4.07419i	0.175814	−	0.304519i	−0.764628	−	0.644471i	$-0.777078\pi$
$179$	2.35224	−	4.07419i	0.175814	−	0.304519i	0.940443	+	0.339952i	$0.110411\pi$
$180$	6.36089	+	2.13052i	0.474112	+	0.158800i
$181$	−2.33559	+	1.34845i	−0.173603	+	0.100230i	−0.584284	−	0.811549i	$-0.698624\pi$
$181$	−2.33559	+	1.34845i	−0.173603	+	0.100230i	0.410681	+	0.911779i	$0.365291\pi$
$182$			6.84462i			0.507357i
$183$	5.18767	−	2.22139i	0.383484	−	0.164210i
$184$			2.68202i			0.197721i
$185$	23.8802	+	2.03866i	1.75570	+	0.149885i
$186$	9.37271	−	2.26987i	0.687240	−	0.166435i
$187$		−	17.3882i		−	1.27155i
$188$	−1.54613			−0.112763
$189$	5.97410	+	7.23621i	0.434552	+	0.526356i
$190$	0.970012	+	0.0828103i	0.0703721	+	0.00600769i
$191$	−14.5902	+	8.42368i	−1.05571	+	0.609516i	−0.924243	−	0.381804i	$-0.875303\pi$
$191$	−14.5902	+	8.42368i	−1.05571	+	0.609516i	−0.131470	+	0.991320i	$0.541970\pi$
$192$	0.681795	+	1.59222i	0.0492044	+	0.114908i
$193$	−14.2645	−	8.23560i	−1.02678	−	0.592811i	−0.110719	−	0.993852i	$-0.535315\pi$
$193$	−14.2645	−	8.23560i	−1.02678	−	0.592811i	−0.916060	+	0.401041i	$0.868649\pi$
$194$			11.8138i			0.848182i
$195$	14.3744	+	2.97645i	1.02937	+	0.213148i
$196$	−1.86940	−	3.23789i	−0.133528	−	0.231278i
$197$	0.508531	−	0.293601i	0.0362313	−	0.0209182i	−0.481775	−	0.876295i	$-0.660008\pi$
$197$	0.508531	−	0.293601i	0.0362313	−	0.0209182i	0.518006	+	0.855377i	$0.326674\pi$
$198$	7.96935	+	1.93363i	0.566357	+	0.137417i
$199$	0.625276	−	0.361003i	0.0443246	−	0.0255908i	−0.477674	−	0.878537i	$-0.658520\pi$
$199$	0.625276	−	0.361003i	0.0443246	−	0.0255908i	0.521999	+	0.852946i	$0.325187\pi$
$200$	3.19780	−	3.84370i	0.226119	−	0.271791i
$201$	−12.5442	−	9.39082i	−0.884801	−	0.662377i
$202$		−	15.5501i		−	1.09410i
$203$	5.53689	+	3.19672i	0.388613	+	0.224366i
$204$	1.30820	−	10.9398i	0.0915923	−	0.765940i
$205$	−4.76623	−	3.32244i	−0.332888	−	0.232049i
$206$	−14.1597	+	8.17508i	−0.986550	+	0.569585i
$207$	5.82303	+	5.55262i	0.404728	+	0.385934i
$208$	1.89509	+	3.28240i	0.131401	+	0.227593i
$209$	1.19012			0.0823226
$210$	6.64037	−	2.19626i	0.458229	−	0.151557i
$211$	−12.8281	+	22.2190i	−0.883124	+	1.52962i	−0.0352755	+	0.999378i	$0.511231\pi$
$211$	−12.8281	+	22.2190i	−0.883124	+	1.52962i	−0.847849	+	0.530238i	$0.822102\pi$
$212$	−8.31697	+	4.80180i	−0.571212	+	0.329789i
$213$	−9.16032	−	6.85757i	−0.627655	−	0.469873i
$214$	−2.70745	+	4.68944i	−0.185077	+	0.320564i
$215$	3.78003	+	0.322703i	0.257796	+	0.0220081i
$216$	4.86844	+	1.81611i	0.331256	+	0.123571i
$217$	6.40468	−	7.75097i	0.434778	−	0.526170i
$218$	3.08751			0.209112
$219$	−7.75661	+	10.3613i	−0.524143	+	0.700148i
$220$	3.49537	−	5.01430i	0.235657	−	0.338064i
$221$		−	24.1097i		−	1.62180i
$222$	18.4334	+	2.20430i	1.23717	+	0.147943i
$223$	2.25149	−	3.89969i	0.150771	−	0.261143i	−0.780740	−	0.624856i	$-0.785158\pi$
$223$	2.25149	−	3.89969i	0.150771	−	0.261143i	0.931511	+	0.363713i	$0.118491\pi$
$224$	1.56394	+	0.902941i	0.104495	+	0.0603303i
$225$	−1.72475	−	14.9005i	−0.114983	−	0.993367i
$226$	−5.84956	−	10.1317i	−0.389107	−	0.673953i
$227$	7.02539	+	12.1683i	0.466292	+	0.807641i	0.999259	−	0.0384951i	$-0.0122564\pi$
$227$	7.02539	+	12.1683i	0.466292	+	0.807641i	−0.532967	+	0.846136i	$0.678923\pi$
$228$	0.748767	+	0.0895387i	0.0495883	+	0.00592985i
$229$	18.8343	+	10.8740i	1.24461	+	0.718574i	0.970029	−	0.242990i	$-0.0781283\pi$
$229$	18.8343	+	10.8740i	1.24461	+	0.718574i	0.274579	+	0.961565i	$0.411462\pi$
$230$	5.42995	−	2.54594i	0.358041	−	0.167874i
$231$	7.85986	−	3.36563i	0.517141	−	0.221442i
$232$	3.54035			0.232435
$233$	−8.80114			−0.576582			−0.288291	−	0.957543i	$-0.593087\pi$
$233$	−8.80114			−0.576582			−0.288291	+	0.957543i	$0.593087\pi$
$234$	11.0499	+	2.68108i	0.722357	+	0.175268i
$235$	1.46768	+	3.13025i	0.0957408	+	0.204195i
$236$	−10.8827	−	6.28315i	−0.708406	−	0.408998i
$237$	−0.210097	+	1.75694i	−0.0136473	+	0.114125i
$238$	−5.74370	−	9.94837i	−0.372308	−	0.644857i
$239$	7.39846	+	12.8145i	0.478567	+	0.828902i	0.999698	−	0.0245746i	$-0.00782311\pi$
$239$	7.39846	+	12.8145i	0.478567	+	0.828902i	−0.521131	+	0.853477i	$0.674490\pi$
$240$	2.57636	−	2.89178i	0.166303	−	0.186663i
$241$	7.91848	+	4.57174i	0.510074	+	0.294491i	0.732864	−	0.680375i	$-0.238183\pi$
$241$	7.91848	+	4.57174i	0.510074	+	0.294491i	−0.222790	+	0.974866i	$0.571516\pi$
$242$	−1.76392	+	3.05519i	−0.113389	+	0.196395i
$243$	14.0222	−	6.81012i	0.899525	−	0.436869i
$244$		−	3.25814i		−	0.208581i
$245$	−4.78080	+	6.85834i	−0.305434	+	0.438163i
$246$	−3.60268	−	2.69703i	−0.229699	−	0.171956i
$247$	1.65017			0.104998
$248$	0.925384	−	5.49032i	0.0587619	−	0.348636i
$249$	1.60363	+	1.20050i	0.101626	+	0.0760789i
$250$	−10.8174	−	2.82551i	−0.684153	−	0.178701i
$251$	11.7310	−	20.3187i	0.740454	−	1.28250i	−0.211835	−	0.977305i	$-0.567944\pi$
$251$	11.7310	−	20.3187i	0.740454	−	1.28250i	0.952289	−	0.305198i	$-0.0987226\pi$
$252$	5.19824	−	1.52615i	0.327458	−	0.0961385i
$253$	6.34916	−	3.66569i	0.399168	−	0.230460i
$254$	2.92334	−	5.06337i	0.183426	−	0.317704i
$255$	−23.3903	+	7.73620i	−1.46476	+	0.484459i
$256$	1.00000			0.0625000
$257$	9.45976	+	16.3848i	0.590084	+	1.02206i	0.994221	+	0.107357i	$0.0342387\pi$
$257$	9.45976	+	16.3848i	0.590084	+	1.02206i	−0.404137	+	0.914699i	$0.632428\pi$
$258$	2.91786	+	0.348923i	0.181658	+	0.0217230i
$259$	16.7629	−	9.67806i	1.04160	−	0.601365i
$260$	4.84651	−	6.95261i	0.300568	−	0.431182i
$261$	7.32962	−	7.68657i	0.453692	−	0.475787i
$262$	13.3521	+	7.70881i	0.824893	+	0.476252i
$263$		−	9.36711i		−	0.577600i	−0.957389	−	0.288800i	$-0.906744\pi$
$263$		−	9.36711i		−	0.577600i	0.957389	−	0.288800i	$-0.0932563\pi$
$264$	2.83741	−	3.79020i	0.174630	−	0.233271i
$265$	17.6166	+	12.2802i	1.08218	+	0.754364i
$266$	0.680908	−	0.393123i	0.0417492	−	0.0241039i
$267$	1.58688	+	3.70589i	0.0971157	+	0.226797i
$268$	−7.83494	+	4.52350i	−0.478595	+	0.276317i
$269$	−4.99236	−	8.64703i	−0.304390	−	0.527219i	0.672735	−	0.739883i	$-0.265119\pi$
$269$	−4.99236	−	8.64703i	−0.304390	−	0.527219i	−0.977125	+	0.212664i	$0.931786\pi$
$270$	−0.944569	−	11.5805i	−0.0574847	−	0.704766i
$271$		−	14.3826i		−	0.873678i	−0.899540	−	0.436839i	$-0.856098\pi$
$271$		−	14.3826i		−	0.873678i	0.899540	−	0.436839i	$-0.143902\pi$
$272$	−5.50887	−	3.18055i	−0.334025	−	0.192849i
$273$	10.8981	−	4.66663i	0.659584	−	0.282437i
$274$	−5.75226	+	3.32107i	−0.347506	+	0.200633i
$275$	−13.4699	−	2.31674i	−0.812263	−	0.139705i
$276$	4.27036	−	1.82859i	0.257046	−	0.110068i
$277$	10.7709			0.647163			0.323581	−	0.946200i	$-0.395113\pi$
$277$	10.7709			0.647163			0.323581	+	0.946200i	$0.395113\pi$
$278$		−	10.0512i		−	0.602831i
$279$	−10.0044	−	13.3758i	−0.598947	−	0.800788i
$280$	0.343482	−	4.02344i	0.0205270	−	0.240446i
$281$		−	15.1194i		−	0.901949i	−0.892537	−	0.450975i	$-0.851076\pi$
$281$		−	15.1194i		−	0.901949i	0.892537	−	0.450975i	$-0.148924\pi$
$282$	1.05414	+	2.46177i	0.0627732	+	0.146596i
$283$			15.4123i			0.916167i	0.888909	+	0.458083i	$0.151464\pi$
$283$			15.4123i			0.916167i	−0.888909	+	0.458083i	$0.848536\pi$
$284$	−5.72140	+	3.30325i	−0.339503	+	0.196012i
$285$	−0.529498	−	1.60093i	−0.0313647	−	0.0948309i
$286$	5.18028	−	8.97251i	0.306317	−	0.530556i
$287$	−4.69220			−0.276972
$288$	2.07031	−	2.17113i	0.121994	−	0.127935i
$289$	11.7318	+	20.3201i	0.690106	+	1.19530i
$290$	−3.36072	−	7.16770i	−0.197348	−	0.420902i
$291$	18.8101	−	8.05460i	1.10267	−	0.472169i
$292$	3.73631	+	6.47149i	0.218651	+	0.378715i
$293$	−16.8667	+	29.2139i	−0.985361	+	1.70670i	−0.345039	+	0.938588i	$0.612134\pi$
$293$	−16.8667	+	29.2139i	−0.985361	+	1.70670i	−0.640322	+	0.768107i	$0.721199\pi$
$294$	−3.88088	+	5.18406i	−0.226337	+	0.302341i
$295$	−2.39014	+	27.9973i	−0.139159	+	1.63006i
$296$	5.35919	−	9.28239i	0.311497	−	0.539528i
$297$	−2.35471	−	14.0073i	−0.136634	−	0.812785i
$298$	−6.45518	−	3.72690i	−0.373939	−	0.215894i
$299$	8.80346	−	5.08268i	0.509117	−	0.293939i
$300$	−8.30026	−	2.47098i	−0.479216	−	0.142662i
$301$	2.65343	−	1.53196i	0.152941	−	0.0883005i
$302$			18.6368i			1.07243i
$303$	−24.7591	+	10.6020i	−1.42237	+	0.609067i
$304$	0.217690	−	0.377051i	0.0124854	−	0.0216253i
$305$	−6.59636	+	3.09283i	−0.377706	+	0.177095i
$306$	−18.3105	+	5.37577i	−1.04674	+	0.307312i
$307$	−10.3344	−	5.96659i	−0.589818	−	0.340532i	0.175208	−	0.984532i	$-0.443940\pi$
$307$	−10.3344	−	5.96659i	−0.589818	−	0.340532i	−0.765025	+	0.644000i	$0.777274\pi$
$308$		−	4.93642i		−	0.281279i
$309$	22.6705	+	16.9715i	1.28968	+	0.965475i
$310$	−11.9940	+	3.33825i	−0.681214	+	0.189600i
$311$			0.401203i			0.0227501i	0.999935	+	0.0113751i	$0.00362088\pi$
$311$			0.401203i			0.0227501i	−0.999935	+	0.0113751i	$0.996379\pi$
$312$	3.93422	−	5.25532i	0.222731	−	0.297524i
$313$	10.0123	−	17.3418i	0.565930	−	0.980219i	−0.431033	−	0.902336i	$-0.641851\pi$
$313$	10.0123	−	17.3418i	0.565930	−	0.980219i	0.996963	−	0.0778829i	$-0.0248160\pi$
$314$		−	11.8145i		−	0.666732i
$315$	−8.02430	−	9.07551i	−0.452118	−	0.511347i
$316$	0.884726	+	0.510797i	0.0497697	+	0.0287346i
$317$	14.0966	−	24.4161i	0.791746	−	1.37134i	−0.133139	−	0.991097i	$-0.542506\pi$
$317$	14.0966	−	24.4161i	0.791746	−	1.37134i	0.924885	−	0.380247i	$-0.124161\pi$
$318$	13.3160	+	9.96857i	0.746723	+	0.559010i
$319$	−4.83882	−	8.38108i	−0.270922	−	0.469250i
$320$	−0.949262	−	2.02457i	−0.0530654	−	0.113177i
$321$	9.31253	+	1.11361i	0.519775	+	0.0621555i
$322$	2.42171	−	4.19452i	0.134956	−	0.233751i
$323$	−2.39846	+	1.38475i	−0.133454	+	0.0770495i
$324$	−0.427634	−	8.98983i	−0.0237575	−	0.499435i
$325$	−18.6767	−	3.21228i	−1.03600	−	0.178185i
$326$			20.5432i			1.13778i
$327$	−2.10505	−	4.91598i	−0.116410	−	0.271855i
$328$	−2.25018	+	1.29914i	−0.124246	+	0.0717332i
$329$	2.41805	+	1.39606i	0.133311	+	0.0769673i
$330$	−10.3670	−	2.14665i	−0.570684	−	0.118169i
$331$	7.83238	−	4.52202i	0.430506	−	0.248553i	−0.269056	−	0.963125i	$-0.586712\pi$
$331$	7.83238	−	4.52202i	0.430506	−	0.248553i	0.699562	+	0.714572i	$0.253378\pi$
$332$	1.00160	−	0.578276i	0.0549701	−	0.0317370i
$333$	−9.05811	−	30.8529i	−0.496382	−	1.69073i
$334$	−9.55459	−	5.51635i	−0.522804	−	0.301841i
$335$	16.5956	+	11.5684i	0.906713	+	0.632051i
$336$	0.371391	−	3.10575i	0.0202610	−	0.169433i
$337$	24.7796			1.34983			0.674916	−	0.737894i	$-0.264180\pi$
$337$	24.7796			1.34983			0.674916	+	0.737894i	$0.264180\pi$
$338$	0.682746	−	1.18255i	0.0371365	−	0.0643222i
$339$	−12.1437	+	16.2215i	−0.659556	+	0.881033i
$340$	−1.20989	+	14.1723i	−0.0656158	+	0.768601i
$341$	−14.2620	+	5.31331i	−0.772333	+	0.287732i
$342$	−0.367941	−	1.25325i	−0.0198959	−	0.0677678i
$343$			19.3930i			1.04712i
$344$	0.848315	−	1.46932i	0.0457381	−	0.0792207i
$345$	−7.75581	−	6.90985i	−0.417559	−	0.372014i
$346$	−13.0225	−	22.5556i	−0.700091	−	1.21259i
$347$	1.62104	+	0.935905i	0.0870217	+	0.0502420i	0.542879	−	0.839811i	$-0.317334\pi$
$347$	1.62104	+	0.935905i	0.0870217	+	0.0502420i	−0.455858	+	0.890053i	$0.650667\pi$
$348$	−2.41379	−	5.63700i	−0.129393	−	0.302175i
$349$	7.55278			0.404291			0.202146	−	0.979356i	$-0.435209\pi$
$349$	7.55278			0.404291			0.202146	+	0.979356i	$0.435209\pi$
$350$	−8.47180	+	3.12389i	−0.452837	+	0.166979i
$351$	−3.26494	−	19.4219i	−0.174270	−	1.03666i
$352$	−1.36676	−	2.36730i	−0.0728487	−	0.126178i
$353$	10.3150	+	5.95534i	0.549010	+	0.316971i	0.748722	−	0.662884i	$-0.230668\pi$
$353$	10.3150	+	5.95534i	0.549010	+	0.316971i	−0.199713	+	0.979854i	$0.564001\pi$
$354$	−2.58434	+	21.6115i	−0.137356	+	1.14864i
$355$	12.1188	+	8.44775i	0.643199	+	0.448360i
$356$	2.32751			0.123358
$357$	−11.9239	+	15.9280i	−0.631082	+	0.842997i
$358$	−2.35224	+	4.07419i	−0.124319	+	0.215328i
$359$	−30.4010	+	17.5520i	−1.60450	+	0.926361i	−0.613934	+	0.789357i	$0.710414\pi$
$359$	−30.4010	+	17.5520i	−1.60450	+	0.926361i	−0.990570	+	0.137004i	$0.956253\pi$
$360$	−6.36089	−	2.13052i	−0.335248	−	0.112288i
$361$	9.40522	+	16.2903i	0.495012	+	0.857385i
$362$	2.33559	−	1.34845i	0.122756	−	0.0708732i
$363$	6.06716	+	0.725521i	0.318443	+	0.0380800i
$364$		−	6.84462i		−	0.358756i
$365$	9.55526	−	13.7076i	0.500145	−	0.717488i
$366$	−5.18767	+	2.22139i	−0.271164	+	0.116114i
$367$	10.3863	+	17.9896i	0.542159	+	0.939047i	0.998780	+	0.0493855i	$0.0157263\pi$
$367$	10.3863	+	17.9896i	0.542159	+	0.939047i	−0.456621	+	0.889661i	$0.650940\pi$
$368$		−	2.68202i		−	0.139810i
$369$	−1.83796	+	7.57508i	−0.0956805	+	0.394343i
$370$	−23.8802	−	2.03866i	−1.24147	−	0.105985i
$371$	17.3430			0.900402
$372$	−9.37271	+	2.26987i	−0.485952	+	0.117687i
$373$			17.6858i			0.915738i	0.889020	+	0.457869i	$0.151387\pi$
$373$			17.6858i			0.915738i	−0.889020	+	0.457869i	$0.848613\pi$
$374$			17.3882i			0.899124i
$375$	2.87644	+	19.1501i	0.148539	+	0.988907i
$376$	1.54613			0.0797354
$377$	−6.70929	−	11.6208i	−0.345546	−	0.598503i
$378$	−5.97410	−	7.23621i	−0.307275	−	0.372190i
$379$	4.38746	−	7.59930i	0.225369	−	0.390350i	−0.731061	−	0.682312i	$-0.760975\pi$
$379$	4.38746	−	7.59930i	0.225369	−	0.390350i	0.956430	+	0.291962i	$0.0943081\pi$
$380$	−0.970012	−	0.0828103i	−0.0497606	−	0.00424808i
$381$	−10.0551	−	1.20240i	−0.515138	−	0.0616011i
$382$	14.5902	−	8.42368i	0.746502	−	0.430993i
$383$	−32.0004	+	18.4754i	−1.63514	+	0.944050i	−0.652671	+	0.757642i	$0.726352\pi$
$383$	−32.0004	+	18.4754i	−1.63514	+	0.944050i	−0.982472	+	0.186409i	$0.940315\pi$
$384$	−0.681795	−	1.59222i	−0.0347927	−	0.0812525i
$385$	−9.99416	+	4.68596i	−0.509349	+	0.238819i
$386$	14.2645	+	8.23560i	0.726042	+	0.419181i
$387$	−1.43382	−	4.88376i	−0.0728854	−	0.248256i
$388$		−	11.8138i		−	0.599755i
$389$	15.0730	−	26.1072i	0.764232	−	1.32369i	−0.176420	−	0.984315i	$-0.556452\pi$
$389$	15.0730	−	26.1072i	0.764232	−	1.32369i	0.940652	−	0.339374i	$-0.110215\pi$
$390$	−14.3744	−	2.97645i	−0.727876	−	0.150718i
$391$	−8.53031	+	14.7749i	−0.431396	+	0.747200i
$392$	1.86940	+	3.23789i	0.0944188	+	0.163538i
$393$	3.17073	−	26.5152i	0.159942	−	1.33752i
$394$	−0.508531	+	0.293601i	−0.0256194	+	0.0147914i
$395$	0.194309	−	2.27607i	0.00977677	−	0.114522i
$396$	−7.96935	−	1.93363i	−0.400475	−	0.0971684i
$397$	−18.5049	−	10.6838i	−0.928732	−	0.536204i	−0.0423219	−	0.999104i	$-0.513475\pi$
$397$	−18.5049	−	10.6838i	−0.928732	−	0.536204i	−0.886410	+	0.462900i	$0.846809\pi$
$398$	−0.625276	+	0.361003i	−0.0313422	+	0.0180954i
$399$	−1.09018	−	0.816125i	−0.0545771	−	0.0408573i
$400$	−3.19780	+	3.84370i	−0.159890	+	0.192185i
$401$	−10.2194			−0.510331			−0.255165	−	0.966897i	$-0.582130\pi$
$401$	−10.2194			−0.510331			−0.255165	+	0.966897i	$0.582130\pi$
$402$	12.5442	+	9.39082i	0.625649	+	0.468371i
$403$	−19.7751	+	7.36719i	−0.985068	+	0.366986i
$404$			15.5501i			0.773645i
$405$	−17.7947	+	9.39949i	−0.884223	+	0.467064i
$406$	−5.53689	−	3.19672i	−0.274791	−	0.158651i
$407$	−29.2990			−1.45230
$408$	−1.30820	+	10.9398i	−0.0647656	+	0.541601i
$409$	−21.7788	−	12.5740i	−1.07689	−	0.621744i	−0.146836	−	0.989161i	$-0.546909\pi$
$409$	−21.7788	−	12.5740i	−1.07689	−	0.621744i	−0.930056	+	0.367417i	$0.880242\pi$
$410$	4.76623	+	3.32244i	0.235387	+	0.164083i
$411$	9.20972	+	6.89455i	0.454282	+	0.340083i
$412$	14.1597	−	8.17508i	0.697596	−	0.402757i
$413$	11.3466	+	19.6529i	0.558331	+	0.967058i
$414$	−5.82303	−	5.55262i	−0.286186	−	0.272896i
$415$	−2.12155	−	1.47889i	−0.104143	−	0.0725956i
$416$	−1.89509	−	3.28240i	−0.0929145	−	0.160933i
$417$	−16.0037	+	6.85286i	−0.783704	+	0.335586i
$418$	−1.19012			−0.0582109
$419$			21.1866i			1.03503i	0.855673	+	0.517516i	$0.173143\pi$
$419$			21.1866i			1.03503i	−0.855673	+	0.517516i	$0.826857\pi$
$420$	−6.64037	+	2.19626i	−0.324017	+	0.107167i
$421$	−3.99936	−	6.92709i	−0.194917	−	0.337606i	0.751956	−	0.659213i	$-0.229110\pi$
$421$	−3.99936	−	6.92709i	−0.194917	−	0.337606i	−0.946873	+	0.321607i	$0.895777\pi$
$422$	12.8281	−	22.2190i	0.624463	−	1.08160i
$423$	3.20096	−	3.35685i	0.155636	−	0.163215i
$424$	8.31697	−	4.80180i	0.403908	−	0.233196i
$425$	29.8414	−	11.0037i	1.44752	−	0.533758i
$426$	9.16032	+	6.85757i	0.443819	+	0.332250i
$427$	−2.94191	+	5.09554i	−0.142369	+	0.246590i
$428$	2.70745	−	4.68944i	0.130870	−	0.226673i
$429$	−17.8181	−	2.13072i	−0.860265	−	0.102872i
$430$	−3.78003	−	0.322703i	−0.182289	−	0.0155621i
$431$	20.4694	+	11.8180i	0.985976	+	0.569253i	0.904069	−	0.427387i	$-0.140566\pi$
$431$	20.4694	+	11.8180i	0.985976	+	0.569253i	0.0819068	+	0.996640i	$0.473899\pi$
$432$	−4.86844	−	1.81611i	−0.234233	−	0.0873778i
$433$	10.0836			0.484588			0.242294	−	0.970203i	$-0.422100\pi$
$433$	10.0836			0.484588			0.242294	+	0.970203i	$0.422100\pi$
$434$	−6.40468	+	7.75097i	−0.307434	+	0.372058i
$435$	−9.12121	+	10.2379i	−0.437329	+	0.490870i
$436$	−3.08751			−0.147865
$437$	−1.01126	−	0.583850i	−0.0483750	−	0.0279293i
$438$	7.75661	−	10.3613i	0.370625	−	0.495080i
$439$	−19.2622	−	33.3630i	−0.919332	−	1.59233i	−0.800432	−	0.599424i	$-0.795396\pi$
$439$	−19.2622	−	33.3630i	−0.919332	−	1.59233i	−0.118901	−	0.992906i	$-0.537937\pi$
$440$	−3.49537	+	5.01430i	−0.166635	+	0.239048i
$441$	10.9001	+	2.64473i	0.519053	+	0.125939i
$442$			24.1097i			1.14678i
$443$	−11.5516	−	20.0079i	−0.548831	−	0.950603i	−0.998355	−	0.0573347i	$-0.981740\pi$
$443$	−11.5516	−	20.0079i	−0.548831	−	0.950603i	0.449524	−	0.893268i	$-0.351594\pi$
$444$	−18.4334	−	2.20430i	−0.874813	−	0.104612i
$445$	−2.20941	−	4.71221i	−0.104736	−	0.223380i
$446$	−2.25149	+	3.89969i	−0.106611	+	0.184656i
$447$	−1.53292	+	12.8190i	−0.0725047	+	0.606320i
$448$	−1.56394	−	0.902941i	−0.0738892	−	0.0426599i
$449$	15.1659			0.715722			0.357861	−	0.933775i	$-0.383506\pi$
$449$	15.1659			0.715722			0.357861	+	0.933775i	$0.383506\pi$
$450$	1.72475	+	14.9005i	0.0813053	+	0.702417i
$451$	6.15094	+	3.55124i	0.289636	+	0.167222i
$452$	5.84956	+	10.1317i	0.275140	+	0.476556i
$453$	29.6739	−	12.7065i	1.39420	−	0.597004i
$454$	−7.02539	−	12.1683i	−0.329718	−	0.571088i
$455$	−13.8574	+	6.49734i	−0.649647	+	0.304600i
$456$	−0.748767	−	0.0895387i	−0.0350642	−	0.00419304i
$457$	−39.7824			−1.86094			−0.930471	−	0.366366i	$-0.880602\pi$
$457$	−39.7824			−1.86094			−0.930471	+	0.366366i	$0.880602\pi$
$458$	−18.8343	−	10.8740i	−0.880070	−	0.508109i
$459$	21.0434	+	25.4891i	0.982222	+	1.18973i
$460$	−5.42995	+	2.54594i	−0.253173	+	0.118705i
$461$	−23.1667			−1.07898			−0.539490	−	0.841992i	$-0.681383\pi$
$461$	−23.1667			−1.07898			−0.539490	+	0.841992i	$0.681383\pi$
$462$	−7.85986	+	3.36563i	−0.365674	+	0.156583i
$463$	−30.4160			−1.41355			−0.706775	−	0.707438i	$-0.749851\pi$
$463$	−30.4160			−1.41355			−0.706775	+	0.707438i	$0.749851\pi$
$464$	−3.54035			−0.164357
$465$	13.4927	+	16.8211i	0.625708	+	0.780058i
$466$	8.80114			0.407705
$467$	−7.94617			−0.367705			−0.183852	−	0.982954i	$-0.558857\pi$
$467$	−7.94617			−0.367705			−0.183852	+	0.982954i	$0.558857\pi$
$468$	−11.0499	−	2.68108i	−0.510784	−	0.123933i
$469$	16.3378			0.754410
$470$	−1.46768	−	3.13025i	−0.0676990	−	0.144388i
$471$	−18.8113	+	8.05508i	−0.866778	+	0.371159i
$472$	10.8827	+	6.28315i	0.500919	+	0.289206i
$473$	−4.63778			−0.213245
$474$	0.210097	−	1.75694i	0.00965009	−	0.0806987i
$475$	0.753140	+	2.04247i	0.0345564	+	0.0937150i
$476$	5.74370	+	9.94837i	0.263262	+	0.455983i
$477$	6.79335	−	27.9985i	0.311046	−	1.28196i
$478$	−7.39846	−	12.8145i	−0.338398	−	0.586122i
$479$	−24.5119	−	14.1519i	−1.11998	−	0.646618i	−0.178581	−	0.983925i	$-0.557151\pi$
$479$	−24.5119	−	14.1519i	−1.11998	−	0.646618i	−0.941395	+	0.337307i	$0.890484\pi$
$480$	−2.57636	+	2.89178i	−0.117594	+	0.131991i
$481$	−40.6246			−1.85232
$482$	−7.91848	−	4.57174i	−0.360677	−	0.208237i
$483$	−8.32969	−	0.996078i	−0.379014	−	0.0453231i
$484$	1.76392	−	3.05519i	0.0801780	−	0.138872i
$485$	−23.9179	+	11.2144i	−1.08606	+	0.509220i
$486$	−14.0222	+	6.81012i	−0.636060	+	0.308913i
$487$	0.193235	+	0.334692i	0.00875630	+	0.0151664i	0.870370	−	0.492398i	$-0.163879\pi$
$487$	0.193235	+	0.334692i	0.00875630	+	0.0151664i	−0.861614	+	0.507564i	$0.830546\pi$
$488$			3.25814i			0.147489i
$489$	32.7092	−	14.0062i	1.47916	−	0.633384i
$490$	4.78080	−	6.85834i	0.215975	−	0.309828i
$491$	10.1542	+	17.5877i	0.458255	+	0.793721i	0.998869	−	0.0475501i	$-0.0151414\pi$
$491$	10.1542	+	17.5877i	0.458255	+	0.793721i	−0.540614	+	0.841271i	$0.681808\pi$
$492$	3.60268	+	2.69703i	0.162422	+	0.121592i
$493$	19.5033	+	11.2603i	0.878386	+	0.507137i
$494$	−1.65017			−0.0742447
$495$	3.65023	+	17.9701i	0.164066	+	0.807694i
$496$	−0.925384	+	5.49032i	−0.0415509	+	0.246523i
$497$	11.9306			0.535159
$498$	−1.60363	−	1.20050i	−0.0718604	−	0.0537959i
$499$	−5.94228	−	3.43078i	−0.266013	−	0.153583i	0.361061	−	0.932542i	$-0.382414\pi$
$499$	−5.94228	−	3.43078i	−0.266013	−	0.153583i	−0.627074	+	0.778959i	$0.715748\pi$
$500$	10.8174	+	2.82551i	0.483770	+	0.126361i
$501$	−2.26894	+	18.9740i	−0.101369	+	0.847696i
$502$	−11.7310	+	20.3187i	−0.523580	+	0.906867i
$503$	10.3142	−	17.8646i	0.459885	−	0.796545i	−0.539069	−	0.842262i	$-0.681224\pi$
$503$	10.3142	−	17.8646i	0.459885	−	0.796545i	0.998954	+	0.0457166i	$0.0145571\pi$
$504$	−5.19824	+	1.52615i	−0.231548	+	0.0679802i
$505$	31.4823	−	14.7611i	1.40094	−	0.656860i
$506$	−6.34916	+	3.66569i	−0.282255	+	0.162960i
$507$	−2.34837	−	0.280822i	−0.104295	−	0.0124717i
$508$	−2.92334	+	5.06337i	−0.129702	+	0.224651i
$509$	−2.25242	−	3.90131i	−0.0998370	−	0.172923i	0.811780	−	0.583963i	$-0.198499\pi$
$509$	−2.25242	−	3.90131i	−0.0998370	−	0.172923i	−0.911617	+	0.411041i	$0.865165\pi$
$510$	23.3903	−	7.73620i	1.03574	−	0.342565i
$511$		−	13.4947i		−	0.596969i
$512$	−1.00000			−0.0441942
$513$	−1.74458	+	1.44030i	−0.0770251	+	0.0635907i
$514$	−9.45976	−	16.3848i	−0.417252	−	0.722702i
$515$	−29.9923	−	20.9070i	−1.32162	−	0.921272i
$516$	−2.91786	−	0.348923i	−0.128452	−	0.0153605i
$517$	−2.11319	−	3.66015i	−0.0929379	−	0.160973i
$518$	−16.7629	+	9.67806i	−0.736519	+	0.425229i
$519$	−27.0347	+	36.1128i	−1.18669	+	1.58518i
$520$	−4.84651	+	6.95261i	−0.212534	+	0.304892i
$521$	−4.65889	−	2.68981i	−0.204110	−	0.117843i	0.394461	−	0.918913i	$-0.370931\pi$
$521$	−4.65889	−	2.68981i	−0.204110	−	0.117843i	−0.598571	+	0.801070i	$0.704265\pi$
$522$	−7.32962	+	7.68657i	−0.320809	+	0.336432i
$523$	−3.08855			−0.135053			−0.0675265	−	0.997717i	$-0.521511\pi$
$523$	−3.08855			−0.135053			−0.0675265	+	0.997717i	$0.521511\pi$
$524$	−13.3521	−	7.70881i	−0.583287	−	0.336761i
$525$	10.7500	+	11.3591i	0.469166	+	0.495752i
$526$			9.36711i			0.408425i
$527$	22.5601	−	27.3023i	0.982732	−	1.18931i
$528$	−2.83741	+	3.79020i	−0.123482	+	0.164947i
$529$	15.8068			0.687250
$530$	−17.6166	−	12.2802i	−0.765216	−	0.533416i
$531$	36.1722	−	10.6198i	1.56974	−	0.460860i
$532$	−0.680908	+	0.393123i	−0.0295211	+	0.0170440i
$533$	8.52861	+	4.92399i	0.369415	+	0.213282i
$534$	−1.58688	−	3.70589i	−0.0686711	−	0.160370i
$535$	−12.0642	−	1.02993i	−0.521581	−	0.0445276i
$536$	7.83494	−	4.52350i	0.338418	−	0.195386i
$537$	8.09074	+	0.967504i	0.349141	+	0.0417509i
$538$	4.99236	+	8.64703i	0.215236	+	0.372800i
$539$	5.11005	−	8.85086i	0.220105	−	0.381233i
$540$	0.944569	+	11.5805i	0.0406478	+	0.498345i
$541$	7.60401	−	13.1705i	0.326922	−	0.566245i	−0.654978	−	0.755648i	$-0.727322\pi$
$541$	7.60401	−	13.1705i	0.326922	−	0.566245i	0.981899	+	0.189403i	$0.0606553\pi$
$542$			14.3826i			0.617784i
$543$	−3.73943	−	2.79940i	−0.160474	−	0.120134i
$544$	5.50887	+	3.18055i	0.236191	+	0.136365i
$545$	2.93085	+	6.25089i	0.125544	+	0.267759i
$546$	−10.8981	+	4.66663i	−0.466397	+	0.199713i
$547$	10.7704	−	6.21829i	0.460509	−	0.265875i	−0.251749	−	0.967792i	$-0.581006\pi$
$547$	10.7704	−	6.21829i	0.460509	−	0.265875i	0.712258	+	0.701917i	$0.247672\pi$
$548$	5.75226	−	3.32107i	0.245724	−	0.141869i
$549$	7.07386	+	6.74537i	0.301905	+	0.287885i
$550$	13.4699	+	2.31674i	0.574356	+	0.0987860i
$551$	−0.770700	+	1.33489i	−0.0328329	+	0.0568683i
$552$	−4.27036	+	1.82859i	−0.181759	+	0.0778300i
$553$	−0.922439	−	1.59771i	−0.0392261	−	0.0679416i
$554$	−10.7709			−0.457613
$555$	13.0354	+	39.4123i	0.553322	+	1.67296i
$556$			10.0512i			0.426266i
$557$			5.01476i			0.212482i	0.994340	+	0.106241i	$0.0338815\pi$
$557$			5.01476i			0.212482i	−0.994340	+	0.106241i	$0.966118\pi$
$558$	10.0044	+	13.3758i	0.423520	+	0.566243i
$559$	−6.43054			−0.271983
$560$	−0.343482	+	4.02344i	−0.0145148	+	0.170021i
$561$	27.6858	−	11.8552i	1.16890	−	0.500528i
$562$			15.1194i			0.637774i
$563$	1.82585	+	3.16246i	0.0769503	+	0.133282i	0.901933	−	0.431877i	$-0.142148\pi$
$563$	1.82585	+	3.16246i	0.0769503	+	0.133282i	−0.824982	+	0.565158i	$0.808815\pi$
$564$	−1.05414	−	2.46177i	−0.0443874	−	0.103659i
$565$	14.9597	−	21.4605i	0.629358	−	0.902851i
$566$		−	15.4123i		−	0.647828i
$567$	−7.44849	+	14.4457i	−0.312807	+	0.606662i
$568$	5.72140	−	3.30325i	0.240065	−	0.138601i
$569$	12.6503	+	21.9110i	0.530328	+	0.918555i	0.999374	+	0.0353813i	$0.0112646\pi$
$569$	12.6503	+	21.9110i	0.530328	+	0.918555i	−0.469046	+	0.883174i	$0.655402\pi$
$570$	0.529498	+	1.60093i	0.0221782	+	0.0670556i
$571$	−13.7614	+	7.94517i	−0.575898	+	0.332495i	−0.759502	−	0.650505i	$-0.774557\pi$
$571$	−13.7614	+	7.94517i	−0.575898	+	0.332495i	0.183603	+	0.983000i	$0.441224\pi$
$572$	−5.18028	+	8.97251i	−0.216599	+	0.375160i
$573$	−23.3599	−	17.4876i	−0.975874	−	0.730556i
$574$	4.69220			0.195849
$575$	10.3089	+	8.57658i	0.429911	+	0.357668i
$576$	−2.07031	+	2.17113i	−0.0862629	+	0.0904639i
$577$	−30.6800	−	17.7131i	−1.27723	−	0.737406i	−0.300888	−	0.953660i	$-0.597283\pi$
$577$	−30.6800	−	17.7131i	−1.27723	−	0.737406i	−0.976337	+	0.216253i	$0.930616\pi$
$578$	−11.7318	−	20.3201i	−0.487978	−	0.845204i
$579$	3.38740	−	28.3271i	0.140776	−	1.17724i
$580$	3.36072	+	7.16770i	0.139546	+	0.297623i
$581$	−2.08860			−0.0866495
$582$	−18.8101	+	8.05460i	−0.779706	+	0.333874i
$583$	−22.7347	−	13.1259i	−0.941573	−	0.543617i
$584$	−3.73631	−	6.47149i	−0.154610	−	0.267792i
$585$	5.06125	+	24.9165i	0.209257	+	1.03017i
$586$	16.8667	−	29.2139i	0.696755	−	1.20682i
$587$		−	47.0276i		−	1.94104i	−0.241024	−	0.970519i	$-0.577483\pi$
$587$		−	47.0276i		−	1.94104i	0.241024	−	0.970519i	$-0.422517\pi$
$588$	3.88088	−	5.18406i	0.160045	−	0.213787i
$589$	1.86868	+	1.54411i	0.0769977	+	0.0636238i
$590$	2.39014	−	27.9973i	0.0984004	−	1.15263i
$591$	0.814190	+	0.609516i	0.0334913	+	0.0250722i
$592$	−5.35919	+	9.28239i	−0.220261	+	0.381504i
$593$	−15.5928			−0.640320			−0.320160	−	0.947363i	$-0.603737\pi$
$593$	−15.5928			−0.640320			−0.320160	+	0.947363i	$0.603737\pi$
$594$	2.35471	+	14.0073i	0.0966151	+	0.574726i
$595$	14.6889	−	21.0722i	0.602188	−	0.863874i
$596$	6.45518	+	3.72690i	0.264415	+	0.152660i
$597$	1.00111	+	0.749444i	0.0409725	+	0.0306727i
$598$	−8.80346	+	5.08268i	−0.360000	+	0.207846i
$599$	19.2164	−	11.0946i	0.785162	−	0.453313i	−0.0530949	−	0.998589i	$-0.516909\pi$
$599$	19.2164	−	11.0946i	0.785162	−	0.453313i	0.838256	+	0.545276i	$0.183575\pi$
$600$	8.30026	+	2.47098i	0.338857	+	0.100877i
$601$	17.2042	+	9.93286i	0.701775	+	0.405170i	0.808008	−	0.589171i	$-0.200546\pi$
$601$	17.2042	+	9.93286i	0.701775	+	0.405170i	−0.106233	+	0.994341i	$0.533879\pi$
$602$	−2.65343	+	1.53196i	−0.108146	+	0.0624379i
$603$	6.39962	−	26.3757i	0.260613	−	1.07410i
$604$		−	18.6368i		−	0.758322i
$605$	−7.85989	−	0.671002i	−0.319550	−	0.0272801i
$606$	24.7591	−	10.6020i	1.00577	−	0.430675i
$607$	−9.96246	+	5.75183i	−0.404364	+	0.233460i	−0.688365	−	0.725364i	$-0.741671\pi$
$607$	−9.96246	+	5.75183i	−0.404364	+	0.233460i	0.284001	+	0.958824i	$0.408338\pi$
$608$	−0.217690	+	0.377051i	−0.00882851	+	0.0152914i
$609$	−1.31485	+	10.9954i	−0.0532805	+	0.445558i
$610$	6.59636	−	3.09283i	0.267079	−	0.125225i
$611$	−2.93005	−	5.07500i	−0.118537	−	0.205312i
$612$	18.3105	−	5.37577i	0.740157	−	0.217303i
$613$	−6.19651	+	10.7327i	−0.250275	+	0.433488i	−0.963601	−	0.267343i	$-0.913854\pi$
$613$	−6.19651	+	10.7327i	−0.250275	+	0.433488i	0.713327	+	0.700832i	$0.247188\pi$
$614$	10.3344	+	5.96659i	0.417064	+	0.240792i
$615$	2.04045	−	9.85409i	0.0822787	−	0.397355i
$616$			4.93642i			0.198894i
$617$	2.85076	−	4.93766i	0.114767	−	0.198783i	−0.802919	−	0.596087i	$-0.796721\pi$
$617$	2.85076	−	4.93766i	0.114767	−	0.198783i	0.917687	+	0.397305i	$0.130054\pi$
$618$	−22.6705	−	16.9715i	−0.911941	−	0.682694i
$619$		−	31.2487i		−	1.25599i	−0.778217	−	0.627995i	$-0.783876\pi$
$619$		−	31.2487i		−	1.25599i	0.778217	−	0.627995i	$-0.216124\pi$
$620$	11.9940	−	3.33825i	0.481691	−	0.134067i
$621$	−4.87086	+	13.0573i	−0.195461	+	0.523970i
$622$		−	0.401203i		−	0.0160868i
$623$	−3.64008	−	2.10160i	−0.145837	−	0.0841988i
$624$	−3.93422	+	5.25532i	−0.157495	+	0.210381i
$625$	−4.54811	−	24.5828i	−0.181924	−	0.983313i
$626$	−10.0123	+	17.3418i	−0.400173	+	0.693120i
$627$	0.811421	+	1.89494i	0.0324050	+	0.0756764i
$628$			11.8145i			0.471450i
$629$	59.0462	−	34.0903i	2.35433	−	1.35927i
$630$	8.02430	+	9.07551i	0.319696	+	0.361577i
$631$	−16.5180	+	9.53670i	−0.657573	+	0.379650i	−0.791352	−	0.611361i	$-0.790622\pi$
$631$	−16.5180	+	9.53670i	−0.657573	+	0.379650i	0.133779	+	0.991011i	$0.457289\pi$
$632$	−0.884726	−	0.510797i	−0.0351925	−	0.0203184i
$633$	−44.1236	−	5.27637i	−1.75375	−	0.209717i
$634$	−14.0966	+	24.4161i	−0.559849	+	0.969687i
$635$	13.0262	+	1.11205i	0.516928	+	0.0441303i
$636$	−13.3160	−	9.96857i	−0.528013	−	0.395280i
$637$	7.08536	−	12.2722i	0.280732	−	0.486242i
$638$	4.83882	+	8.38108i	0.191571	+	0.331810i
$639$	4.67327	−	19.2607i	0.184872	−	0.761941i
$640$	0.949262	+	2.02457i	0.0375229	+	0.0800283i
$641$	−12.2113	−	21.1506i	−0.482318	−	0.835400i	0.517475	−	0.855698i	$-0.326872\pi$
$641$	−12.2113	−	21.1506i	−0.482318	−	0.835400i	−0.999794	+	0.0202979i	$0.993539\pi$
$642$	−9.31253	−	1.11361i	−0.367536	−	0.0439506i
$643$	−26.0049			−1.02553			−0.512767	−	0.858528i	$-0.671379\pi$
$643$	−26.0049			−1.02553			−0.512767	+	0.858528i	$0.671379\pi$
$644$	−2.42171	+	4.19452i	−0.0954286	+	0.165287i
$645$	2.06339	+	6.23864i	0.0812461	+	0.245646i
$646$	2.39846	−	1.38475i	0.0943660	−	0.0544822i
$647$			40.9565i			1.61016i	0.593163	+	0.805082i	$0.297879\pi$
$647$			40.9565i			1.61016i	−0.593163	+	0.805082i	$0.702121\pi$
$648$	0.427634	+	8.98983i	0.0167991	+	0.353154i
$649$		−	34.3503i		−	1.34837i
$650$	18.6767	+	3.21228i	0.732560	+	0.125996i
$651$	16.7079	+	4.91307i	0.654834	+	0.192558i
$652$		−	20.5432i		−	0.804532i
$653$	−47.4222			−1.85577			−0.927886	−	0.372863i	$-0.878376\pi$
$653$	−47.4222			−1.85577			−0.927886	+	0.372863i	$0.878376\pi$
$654$	2.10505	+	4.91598i	0.0823140	+	0.192230i
$655$	−2.93247	+	34.3499i	−0.114581	+	1.34216i
$656$	2.25018	−	1.29914i	0.0878549	−	0.0507231i
$657$	−21.7858	−	5.28595i	−0.849944	−	0.206224i
$658$	−2.41805	−	1.39606i	−0.0942653	−	0.0544241i
$659$			16.2173i			0.631737i	0.948803	+	0.315868i	$0.102296\pi$
$659$			16.2173i			0.631737i	−0.948803	+	0.315868i	$0.897704\pi$
$660$	10.3670	+	2.14665i	0.403534	+	0.0835582i
$661$	6.59103	+	11.4160i	0.256361	+	0.444031i	0.965264	−	0.261275i	$-0.0841430\pi$
$661$	6.59103	+	11.4160i	0.256361	+	0.444031i	−0.708903	+	0.705306i	$0.750810\pi$
$662$	−7.83238	+	4.52202i	−0.304414	+	0.175753i
$663$	38.3879	−	16.4379i	1.49086	−	0.638396i
$664$	−1.00160	+	0.578276i	−0.0388698	+	0.0224415i
$665$	1.44227	+	1.00537i	0.0559287	+	0.0389867i
$666$	9.05811	+	30.8529i	0.350995	+	1.19553i
$667$			9.49530i			0.367659i
$668$	9.55459	+	5.51635i	0.369678	+	0.213434i
$669$	7.74422	+	0.926066i	0.299409	+	0.0358038i
$670$	−16.5956	−	11.5684i	−0.641143	−	0.446927i
$671$	7.71302	−	4.45311i	0.297758	−	0.171910i
$672$	−0.371391	+	3.10575i	−0.0143267	+	0.119807i
$673$	9.84175	+	17.0464i	0.379371	+	0.657091i	0.990971	−	0.134077i	$-0.0428069\pi$
$673$	9.84175	+	17.0464i	0.379371	+	0.657091i	−0.611600	+	0.791168i	$0.709474\pi$
$674$	−24.7796			−0.954476
$675$	22.5489	−	12.9053i	0.867908	−	0.496724i
$676$	−0.682746	+	1.18255i	−0.0262594	+	0.0454827i
$677$	8.27505	−	4.77760i	0.318036	−	0.183618i	−0.332481	−	0.943110i	$-0.607886\pi$
$677$	8.27505	−	4.77760i	0.318036	−	0.183618i	0.650517	+	0.759492i	$0.274552\pi$
$678$	12.1437	−	16.2215i	0.466376	−	0.622984i
$679$	−10.6672	+	18.4761i	−0.409368	+	0.709047i
$680$	1.20989	−	14.1723i	0.0463974	−	0.543483i
$681$	−14.5848	+	19.4823i	−0.558889	+	0.746562i
$682$	14.2620	−	5.31331i	0.546122	−	0.203457i
$683$	−4.31865			−0.165249			−0.0826244	−	0.996581i	$-0.526330\pi$
$683$	−4.31865			−0.165249			−0.0826244	+	0.996581i	$0.526330\pi$
$684$	0.367941	+	1.25325i	0.0140686	+	0.0479191i
$685$	−12.1841	−	8.49331i	−0.465532	−	0.324513i
$686$		−	19.3930i		−	0.740428i
$687$	−4.47261	+	37.4022i	−0.170641	+	1.42698i
$688$	−0.848315	+	1.46932i	−0.0323417	+	0.0560175i
$689$	−31.5228	−	18.1997i	−1.20092	−	0.693354i
$690$	7.75581	+	6.90985i	0.295259	+	0.263054i
$691$	1.62251	+	2.81027i	0.0617232	+	0.106908i	0.895236	−	0.445593i	$-0.147007\pi$
$691$	1.62251	+	2.81027i	0.0617232	+	0.106908i	−0.833513	+	0.552501i	$0.813674\pi$
$692$	13.0225	+	22.5556i	0.495039	+	0.857433i
$693$	10.7176	+	10.2199i	0.407129	+	0.388223i
$694$	−1.62104	−	0.935905i	−0.0615337	−	0.0355265i
$695$	20.3494	−	9.54122i	0.771897	−	0.361919i
$696$	2.41379	+	5.63700i	0.0914946	+	0.213670i
$697$	−16.5280			−0.626042
$698$	−7.55278			−0.285877
$699$	−6.00058	−	14.0133i	−0.226963	−	0.530033i
$700$	8.47180	−	3.12389i	0.320204	−	0.118072i
$701$	39.4575	+	22.7808i	1.49029	+	0.860419i	0.999938	−	0.0111057i	$-0.00353513\pi$
$701$	39.4575	+	22.7808i	1.49029	+	0.860419i	0.490351	+	0.871525i	$0.336868\pi$
$702$	3.26494	+	19.4219i	0.123227	+	0.733031i
$703$	2.33329	+	4.04137i	0.0880016	+	0.152423i
$704$	1.36676	+	2.36730i	0.0515118	+	0.0892211i
$705$	−3.98338	+	4.47105i	−0.150023	+	0.168390i
$706$	−10.3150	−	5.95534i	−0.388208	−	0.224132i
$707$	14.0408	−	24.3193i	0.528058	−	0.914623i
$708$	2.58434	−	21.6115i	0.0971254	−	0.812210i
$709$		−	11.3089i		−	0.424715i	−0.977192	−	0.212357i	$-0.931886\pi$
$709$		−	11.3089i		−	0.424715i	0.977192	−	0.212357i	$-0.0681141\pi$
$710$	−12.1188	−	8.44775i	−0.454810	−	0.317038i
$711$	−2.94067	+	0.863350i	−0.110284	+	0.0323782i
$712$	−2.32751			−0.0872270
$713$	14.7252	+	2.48190i	0.551462	+	0.0929479i
$714$	11.9239	−	15.9280i	0.446242	−	0.596089i
$715$	23.0830	+	1.97060i	0.863254	+	0.0736963i
$716$	2.35224	−	4.07419i	0.0879071	−	0.152260i
$717$	−15.3592	+	20.5168i	−0.573602	+	0.766215i
$718$	30.4010	−	17.5520i	1.13456	−	0.655036i
$719$	−9.66837	+	16.7461i	−0.360570	+	0.624525i	−0.988055	−	0.154104i	$-0.950751\pi$
$719$	−9.66837	+	16.7461i	−0.360570	+	0.624525i	0.627485	+	0.778629i	$0.284084\pi$
$720$	6.36089	+	2.13052i	0.237056	+	0.0793999i
$721$	−29.5264			−1.09962
$722$	−9.40522	−	16.2903i	−0.350026	−	0.606263i
$723$	−1.88041	+	15.7249i	−0.0699333	+	0.584816i
$724$	−2.33559	+	1.34845i	−0.0868016	+	0.0501149i
$725$	11.3213	−	13.6081i	0.420464	−	0.505390i
$726$	−6.06716	−	0.725521i	−0.225173	−	0.0269266i
$727$	6.15704	+	3.55477i	0.228352	+	0.131839i	0.609812	−	0.792546i	$-0.291245\pi$
$727$	6.15704	+	3.55477i	0.228352	+	0.131839i	−0.381460	+	0.924386i	$0.624578\pi$
$728$			6.84462i			0.253679i
$729$	20.4035	+	17.6833i	0.755684	+	0.654937i
$730$	−9.55526	+	13.7076i	−0.353656	+	0.507340i
$731$	9.34652	−	5.39622i	0.345694	−	0.199586i
$732$	5.18767	−	2.22139i	0.191742	−	0.0821049i
$733$	38.5132	−	22.2356i	1.42252	−	0.821290i	0.426002	−	0.904722i	$-0.359922\pi$
$733$	38.5132	−	22.2356i	1.42252	−	0.821290i	0.996513	+	0.0834322i	$0.0265882\pi$
$734$	−10.3863	−	17.9896i	−0.383364	−	0.664006i
$735$	−14.1795	−	2.93609i	−0.523018	−	0.108299i
$736$			2.68202i			0.0988607i
$737$	−21.4170	−	12.3651i	−0.788906	−	0.455475i
$738$	1.83796	−	7.57508i	0.0676564	−	0.278842i
$739$	23.8106	−	13.7470i	0.875886	−	0.505693i	0.00658608	−	0.999978i	$-0.497904\pi$
$739$	23.8106	−	13.7470i	0.875886	−	0.505693i	0.869300	+	0.494285i	$0.164570\pi$
$740$	23.8802	+	2.03866i	0.877852	+	0.0749426i
$741$	1.12508	+	2.62743i	0.0413308	+	0.0965211i
$742$	−17.3430			−0.636681
$743$		−	21.7557i		−	0.798138i	−0.916921	−	0.399069i	$-0.869333\pi$
$743$		−	21.7557i		−	0.798138i	0.916921	−	0.399069i	$-0.130667\pi$
$744$	9.37271	−	2.26987i	0.343620	−	0.0832174i
$745$	1.41773	−	16.6068i	0.0519416	−	0.608426i
$746$		−	17.6858i		−	0.647524i
$747$	−0.818116	+	3.37182i	−0.0299333	+	0.123369i
$748$		−	17.3882i		−	0.635777i
$749$	−8.46857	+	4.88933i	−0.309435	+	0.178652i
$750$	−2.87644	−	19.1501i	−0.105033	−	0.699263i
$751$	−6.82872	+	11.8277i	−0.249184	+	0.431599i	−0.963300	−	0.268429i	$-0.913496\pi$
$751$	−6.82872	+	11.8277i	−0.249184	+	0.431599i	0.714116	+	0.700028i	$0.246829\pi$
$752$	−1.54613			−0.0563814
$753$	40.3499	+	4.82510i	1.47043	+	0.175837i
$754$	6.70929	+	11.6208i	0.244338	+	0.423206i
$755$	−37.7317	+	17.6912i	−1.37320	+	0.643850i
$756$	5.97410	+	7.23621i	0.217276	+	0.263178i
$757$	23.9396	+	41.4647i	0.870101	+	1.50706i	0.861892	+	0.507093i	$0.169280\pi$
$757$	23.9396	+	41.4647i	0.870101	+	1.50706i	0.00820943	+	0.999966i	$0.497387\pi$
$758$	−4.38746	+	7.59930i	−0.159360	+	0.276019i
$759$	10.1654	+	7.60999i	0.368981	+	0.276225i
$760$	0.970012	+	0.0828103i	0.0351860	+	0.00300385i
$761$	−10.0986	+	17.4912i	−0.366073	+	0.634057i	−0.988948	−	0.148265i	$-0.952631\pi$
$761$	−10.0986	+	17.4912i	−0.366073	+	0.634057i	0.622875	+	0.782321i	$0.285965\pi$
$762$	10.0551	+	1.20240i	0.364258	+	0.0435585i
$763$	4.82868	+	2.78784i	0.174810	+	0.100926i
$764$	−14.5902	+	8.42368i	−0.527857	+	0.304758i
$765$	−28.2651	−	31.9679i	−1.02193	−	1.15580i
$766$	32.0004	−	18.4754i	1.15622	−	0.667544i
$767$		−	47.6286i		−	1.71977i
$768$	0.681795	+	1.59222i	0.0246022	+	0.0574542i
$769$	−9.43636	+	16.3443i	−0.340284	+	0.589389i	−0.984485	−	0.175467i	$-0.943856\pi$
$769$	−9.43636	+	16.3443i	−0.340284	+	0.589389i	0.644201	+	0.764856i	$0.277190\pi$
$770$	9.99416	−	4.68596i	0.360164	−	0.168870i
$771$	−19.6385	+	26.2331i	−0.707264	+	0.944761i
$772$	−14.2645	−	8.23560i	−0.513390	−	0.296406i
$773$			41.2864i			1.48497i	0.669863	+	0.742485i	$0.266353\pi$
$773$			41.2864i			1.48497i	−0.669863	+	0.742485i	$0.733647\pi$
$774$	1.43382	+	4.88376i	0.0515377	+	0.175543i
$775$	−18.1440	−	21.1139i	−0.651751	−	0.758433i
$776$			11.8138i			0.424091i
$777$	26.8384	+	20.0917i	0.962823	+	0.720786i
$778$	−15.0730	+	26.1072i	−0.540394	+	0.935989i
$779$		−	1.13124i		−	0.0405310i
$780$	14.3744	+	2.97645i	0.514686	+	0.106574i
$781$	−15.6396	−	9.02953i	−0.559629	−	0.323102i
$782$	8.53031	−	14.7749i	0.305043	−	0.528350i
$783$	17.2360	+	6.42968i	0.615964	+	0.229778i
$784$	−1.86940	−	3.23789i	−0.0667642	−	0.115639i
$785$	23.9194	−	11.2151i	0.853719	−	0.400283i
$786$	−3.17073	+	26.5152i	−0.113096	+	0.945766i
$787$	27.0761	−	46.8971i	0.965157	−	1.67170i	0.255966	−	0.966686i	$-0.417607\pi$
$787$	27.0761	−	46.8971i	0.965157	−	1.67170i	0.709192	−	0.705016i	$-0.249060\pi$
$788$	0.508531	−	0.293601i	0.0181157	−	0.0104591i
$789$	14.9145	−	6.38645i	0.530969	−	0.227364i
$790$	−0.194309	+	2.27607i	−0.00691322	+	0.0809791i
$791$		−	21.1272i		−	0.751197i
$792$	7.96935	+	1.93363i	0.283179	+	0.0687084i
$793$	10.6945	−	6.17448i	0.379773	−	0.219262i
$794$	18.5049	+	10.6838i	0.656713	+	0.379153i
$795$	−7.54175	+	36.4220i	−0.267478	+	1.29175i
$796$	0.625276	−	0.361003i	0.0221623	−	0.0127954i
$797$	34.2218	−	19.7580i	1.21220	−	0.699864i	0.248962	−	0.968513i	$-0.419911\pi$
$797$	34.2218	−	19.7580i	1.21220	−	0.699864i	0.963238	+	0.268649i	$0.0865773\pi$
$798$	1.09018	+	0.816125i	0.0385918	+	0.0288905i
$799$	8.51742	+	4.91753i	0.301325	+	0.173970i
$800$	3.19780	−	3.84370i	0.113059	−	0.135895i
$801$	−4.81866	+	5.05332i	−0.170259	+	0.178550i
$802$	10.2194			0.360858
$803$	−10.2133	+	17.6900i	−0.360420	+	0.624266i
$804$	−12.5442	−	9.39082i	−0.442401	−	0.331189i
$805$	10.7909	+	0.921228i	0.380331	+	0.0324690i
$806$	19.7751	−	7.36719i	0.696548	−	0.259498i
$807$	10.3642	−	13.8444i	0.364836	−	0.487347i
$808$		−	15.5501i		−	0.547049i
$809$	−15.4256	+	26.7179i	−0.542335	+	0.939352i	0.456434	+	0.889757i	$0.349126\pi$
$809$	−15.4256	+	26.7179i	−0.542335	+	0.939352i	−0.998769	+	0.0495948i	$0.984207\pi$
$810$	17.7947	−	9.39949i	0.625240	−	0.330264i
$811$	18.5015	+	32.0456i	0.649676	+	1.12527i	0.983200	+	0.182531i	$0.0584289\pi$
$811$	18.5015	+	32.0456i	0.649676	+	1.12527i	−0.333524	+	0.942742i	$0.608238\pi$
$812$	5.53689	+	3.19672i	0.194307	+	0.112183i
$813$	22.9002	−	9.80597i	0.803144	−	0.343910i
$814$	29.2990			1.02693
$815$	−41.5912	+	19.5008i	−1.45687	+	0.683085i
$816$	1.30820	−	10.9398i	0.0457962	−	0.382970i
$817$	0.369340	+	0.639715i	0.0129216	+	0.0223808i
$818$	21.7788	+	12.5740i	0.761478	+	0.439639i
$819$	14.8606	+	14.1705i	0.519271	+	0.495157i
$820$	−4.76623	−	3.32244i	−0.166444	−	0.116025i
$821$	−27.5335			−0.960924			−0.480462	−	0.877016i	$-0.659531\pi$
$821$	−27.5335			−0.960924			−0.480462	+	0.877016i	$0.659531\pi$
$822$	−9.20972	−	6.89455i	−0.321226	−	0.240475i
$823$	27.1266	−	46.9846i	0.945573	−	1.63778i	0.190972	−	0.981596i	$-0.438836\pi$
$823$	27.1266	−	46.9846i	0.945573	−	1.63778i	0.754601	−	0.656184i	$-0.227831\pi$
$824$	−14.1597	+	8.17508i	−0.493275	+	0.284792i
$825$	−5.49493	−	23.0265i	−0.191309	−	0.801679i
$826$	−11.3466	−	19.6529i	−0.394800	−	0.683813i
$827$	−28.8678	+	16.6668i	−1.00383	+	0.579562i	−0.909380	−	0.415967i	$-0.863443\pi$
$827$	−28.8678	+	16.6668i	−1.00383	+	0.579562i	−0.0944515	+	0.995529i	$0.530110\pi$
$828$	5.82303	+	5.55262i	0.202364	+	0.192967i
$829$			21.4599i			0.745334i	0.927965	+	0.372667i	$0.121557\pi$
$829$			21.4599i			0.745334i	−0.927965	+	0.372667i	$0.878443\pi$
$830$	2.12155	+	1.47889i	0.0736400	+	0.0513329i
$831$	7.34358	+	17.1497i	0.254746	+	0.594915i
$832$	1.89509	+	3.28240i	0.0657005	+	0.113797i
$833$			23.7828i			0.824027i
$834$	16.0037	−	6.85286i	0.554162	−	0.237295i
$835$	2.09844	−	24.5804i	0.0726196	−	0.850641i
$836$	1.19012			0.0411613
$837$	14.4762	−	25.0487i	0.500372	−	0.865811i
$838$		−	21.1866i		−	0.731878i
$839$			10.3784i			0.358302i	0.983822	+	0.179151i	$0.0573350\pi$
$839$			10.3784i			0.358302i	−0.983822	+	0.179151i	$0.942665\pi$
$840$	6.64037	−	2.19626i	0.229115	−	0.0757783i
$841$	−16.4659			−0.567791
$842$	3.99936	+	6.92709i	0.137827	+	0.238723i
$843$	24.0734	−	10.3084i	0.829132	−	0.355039i
$844$	−12.8281	+	22.2190i	−0.441562	+	0.764808i
$845$	3.04226	+	0.259719i	0.104657	+	0.00893462i
$846$	−3.20096	+	3.35685i	−0.110051	+	0.115411i
$847$	−5.51732	+	3.18542i	−0.189577	+	0.109452i
$848$	−8.31697	+	4.80180i	−0.285606	+	0.164895i
$849$	−24.5397	+	10.5080i	−0.842202	+	0.360635i
$850$	−29.8414	+	11.0037i	−1.02355	+	0.377424i
$851$	24.8956	+	14.3735i	0.853409	+	0.492716i
$852$	−9.16032	−	6.85757i	−0.313827	−	0.234936i
$853$			31.6014i			1.08201i	0.841019	+	0.541005i	$0.181956\pi$
$853$			31.6014i			1.08201i	−0.841019	+	0.541005i	$0.818044\pi$
$854$	2.94191	−	5.09554i	0.100670	−	0.174366i
$855$	2.18802	−	1.93458i	0.0748286	−	0.0661613i
$856$	−2.70745	+	4.68944i	−0.0925387	+	0.160282i
$857$	−8.70164	−	15.0717i	−0.297242	−	0.514839i	0.678262	−	0.734821i	$-0.262734\pi$
$857$	−8.70164	−	15.0717i	−0.297242	−	0.514839i	−0.975504	+	0.219981i	$0.929400\pi$
$858$	17.8181	+	2.13072i	0.608299	+	0.0727414i
$859$	−14.3943	+	8.31055i	−0.491127	+	0.283552i	−0.725042	−	0.688705i	$-0.758180\pi$
$859$	−14.3943	+	8.31055i	−0.491127	+	0.283552i	0.233915	+	0.972257i	$0.424846\pi$
$860$	3.78003	+	0.322703i	0.128898	+	0.0110041i
$861$	−3.19912	−	7.47100i	−0.109026	−	0.254611i
$862$	−20.4694	−	11.8180i	−0.697190	−	0.402523i
$863$	24.2209	−	13.9839i	0.824488	−	0.476018i	−0.0274739	−	0.999623i	$-0.508746\pi$
$863$	24.2209	−	13.9839i	0.824488	−	0.476018i	0.851962	+	0.523604i	$0.175413\pi$
$864$	4.86844	+	1.81611i	0.165628	+	0.0617855i
$865$	33.3037	−	47.7761i	1.13236	−	1.62443i
$866$	−10.0836			−0.342656
$867$	−24.3553	+	32.5337i	−0.827148	+	1.10490i
$868$	6.40468	−	7.75097i	0.217389	−	0.263085i
$869$			2.79255i			0.0947309i
$870$	9.12121	−	10.2379i	0.309238	−	0.347097i
$871$	−29.6959	−	17.1449i	−1.00621	−	0.580933i
$872$	3.08751			0.104556
$873$	25.6493	+	24.4582i	0.868099	+	0.827786i
$874$	1.01126	+	0.583850i	0.0342063	+	0.0197490i
$875$	−14.3665	−	14.1864i	−0.485677	−	0.479588i
$876$	−7.75661	+	10.3613i	−0.262071	+	0.350074i
$877$	−38.0665	+	21.9777i	−1.28541	+	0.742134i	−0.977833	−	0.209388i	$-0.932853\pi$
$877$	−38.0665	+	21.9777i	−1.28541	+	0.742134i	−0.307581	+	0.951522i	$0.599519\pi$
$878$	19.2622	+	33.3630i	0.650066	+	1.12595i
$879$	−58.0145	−	6.93747i	−1.95678	−	0.233995i
$880$	3.49537	−	5.01430i	0.117829	−	0.169032i
$881$	13.9628	+	24.1844i	0.470420	+	0.814792i	0.999428	−	0.0338253i	$-0.0107690\pi$
$881$	13.9628	+	24.1844i	0.470420	+	0.814792i	−0.529007	+	0.848617i	$0.677436\pi$
$882$	−10.9001	−	2.64473i	−0.367026	−	0.0890526i
$883$	−24.3754			−0.820297			−0.410148	−	0.912019i	$-0.634523\pi$
$883$	−24.3754			−0.820297			−0.410148	+	0.912019i	$0.634523\pi$
$884$		−	24.1097i		−	0.810898i
$885$	−46.2073	+	15.2828i	−1.55324	+	0.513725i
$886$	11.5516	+	20.0079i	0.388082	+	0.672178i
$887$	4.78670	−	8.29081i	0.160722	−	0.278378i	−0.774406	−	0.632689i	$-0.781951\pi$
$887$	4.78670	−	8.29081i	0.160722	−	0.278378i	0.935128	+	0.354311i	$0.115285\pi$
$888$	18.4334	+	2.20430i	0.618586	+	0.0739715i
$889$	9.14384	−	5.27920i	0.306674	−	0.177059i
$890$	2.20941	+	4.71221i	0.0740597	+	0.157954i
$891$	20.6972	−	13.2993i	0.693382	−	0.445544i
$892$	2.25149	−	3.89969i	0.0753855	−	0.130571i
$893$	−0.336577	+	0.582968i	−0.0112631	+	0.0195083i
$894$	1.53292	−	12.8190i	0.0512686	−	0.428733i
$895$	−10.4814	−	0.894800i	−0.350354	−	0.0299099i
$896$	1.56394	+	0.902941i	0.0522475	+	0.0301651i
$897$	14.0949	+	10.5517i	0.470614	+	0.352310i
$898$	−15.1659			−0.506092
$899$	3.27618	−	19.4377i	0.109267	−	0.648283i
$900$	−1.72475	−	14.9005i	−0.0574916	−	0.496684i
$901$	61.0895			2.03519
$902$	−6.15094	−	3.55124i	−0.204804	−	0.118244i
$903$	4.24830	+	3.18035i	0.141375	+	0.105835i
$904$	−5.84956	−	10.1317i	−0.194553	−	0.336976i
$905$	4.94713	+	3.44854i	0.164448	+	0.114633i
$906$	−29.6739	+	12.7065i	−0.985849	+	0.422146i
$907$			51.8786i			1.72260i	0.508095	+	0.861301i	$0.330350\pi$
$907$			51.8786i			1.72260i	−0.508095	+	0.861301i	$0.669650\pi$
$908$	7.02539	+	12.1683i	0.233146	+	0.403820i
$909$	−33.7613	−	32.1935i	−1.11979	−	1.06779i
$910$	13.8574	−	6.49734i	0.459370	−	0.215385i
$911$	12.2756	−	21.2619i	0.406708	−	0.704439i	−0.587810	−	0.808999i	$-0.700010\pi$
$911$	12.2756	−	21.2619i	0.406708	−	0.704439i	0.994519	+	0.104559i	$0.0333432\pi$
$912$	0.748767	+	0.0895387i	0.0247941	+	0.00296492i
$913$	2.73791	+	1.58073i	0.0906116	+	0.0523146i
$914$	39.7824			1.31588
$915$	−9.42183	−	8.39415i	−0.311476	−	0.277502i
$916$	18.8343	+	10.8740i	0.622304	+	0.359287i
$917$	13.9212	+	24.1122i	0.459719	+	0.796256i
$918$	−21.0434	−	25.4891i	−0.694536	−	0.841265i
$919$	−18.2267	−	31.5695i	−0.601243	−	1.04138i	−0.992633	−	0.121158i	$-0.961339\pi$
$919$	−18.2267	−	31.5695i	−0.601243	−	1.04138i	0.391390	−	0.920225i	$-0.371994\pi$
$920$	5.42995	−	2.54594i	0.179020	−	0.0839372i
$921$	2.45414	−	20.5227i	0.0808665	−	0.676245i
$922$	23.1667			0.762954
$923$	−21.6852	−	12.5199i	−0.713776	−	0.412099i
$924$	7.85986	−	3.36563i	0.258570	−	0.110721i
$925$	−18.5411	−	50.2824i	−0.609628	−	1.65327i
$926$	30.4160			0.999531
$927$	−11.5657	+	47.6674i	−0.379867	+	1.56560i
$928$	3.54035			0.116218
$929$	−49.3802			−1.62011			−0.810056	−	0.586353i	$-0.800563\pi$
$929$	−49.3802			−1.62011			−0.810056	+	0.586353i	$0.800563\pi$
$930$	−13.4927	−	16.8211i	−0.442442	−	0.551584i
$931$	−1.62780			−0.0533489
$932$	−8.80114			−0.288291
$933$	−0.638802	+	0.273538i	−0.0209135	+	0.00895525i
$934$	7.94617			0.260007
$935$	−35.2038	+	16.5060i	−1.15129	+	0.539804i
$936$	11.0499	+	2.68108i	0.361179	+	0.0876338i
$937$	−11.3636	−	6.56077i	−0.371232	−	0.214331i	0.302764	−	0.953065i	$-0.402090\pi$
$937$	−11.3636	−	6.56077i	−0.371232	−	0.214331i	−0.673997	+	0.738734i	$0.735424\pi$
$938$	−16.3378			−0.533449
$939$	34.4383	+	4.11819i	1.12385	+	0.134392i
$940$	1.46768	+	3.13025i	0.0478704	+	0.102097i
$941$	18.2683	+	31.6415i	0.595528	+	1.03148i	0.993472	+	0.114075i	$0.0363905\pi$
$941$	18.2683	+	31.6415i	0.595528	+	1.03148i	−0.397944	+	0.917410i	$0.630276\pi$
$942$	18.8113	−	8.05508i	0.612904	−	0.262449i
$943$	−3.48433	−	6.03504i	−0.113466	−	0.196528i
$944$	−10.8827	−	6.28315i	−0.354203	−	0.204499i
$945$	8.97925	−	18.9641i	0.292095	−	0.616901i
$946$	4.63778			0.150787
$947$	6.64300	+	3.83534i	0.215868	+	0.124632i	0.604036	−	0.796957i	$-0.293558\pi$
$947$	6.64300	+	3.83534i	0.215868	+	0.124632i	−0.388167	+	0.921589i	$0.626892\pi$
$948$	−0.210097	+	1.75694i	−0.00682364	+	0.0570626i
$949$	−14.1613	+	24.5281i	−0.459696	+	0.796216i
$950$	−0.753140	−	2.04247i	−0.0244351	−	0.0662665i
$951$	48.4867	+	5.79812i	1.57229	+	0.188017i
$952$	−5.74370	−	9.94837i	−0.186154	−	0.322429i
$953$			35.0031i			1.13386i	0.823765	+	0.566931i	$0.191870\pi$
$953$			35.0031i			1.13386i	−0.823765	+	0.566931i	$0.808130\pi$
$954$	−6.79335	+	27.9985i	−0.219943	+	0.906484i
$955$	30.9043	+	21.5428i	1.00004	+	0.697107i
$956$	7.39846	+	12.8145i	0.239283	+	0.414451i
$957$	10.0454	−	13.4186i	0.324722	−	0.433763i
$958$	24.5119	+	14.1519i	0.791942	+	0.457228i
$959$	−11.9949			−0.387336
$960$	2.57636	−	2.89178i	0.0831516	−	0.0933317i
$961$	−29.2873	−	10.1613i	−0.944753	−	0.327784i
$962$	40.6246			1.30979
$963$	4.57614	+	15.5868i	0.147464	+	0.502278i
$964$	7.91848	+	4.57174i	0.255037	+	0.147246i
$965$	−3.13286	+	36.6972i	−0.100850	+	1.18133i
$966$	8.32969	+	0.996078i	0.268003	+	0.0320483i
$967$	21.3722	−	37.0178i	0.687285	−	1.19041i	−0.285428	−	0.958400i	$-0.592136\pi$
$967$	21.3722	−	37.0178i	0.687285	−	1.19041i	0.972713	−	0.232012i	$-0.0745310\pi$
$968$	−1.76392	+	3.05519i	−0.0566944	+	0.0981976i
$969$	−3.84008	−	2.87475i	−0.123361	−	0.0923502i
$970$	23.9179	−	11.2144i	0.767959	−	0.360073i
$971$	−35.6432	+	20.5786i	−1.14384	+	0.660398i	−0.947379	−	0.320113i	$-0.896279\pi$
$971$	−35.6432	+	20.5786i	−1.14384	+	0.660398i	−0.196464	+	0.980511i	$0.562946\pi$
$972$	14.0222	−	6.81012i	0.449763	−	0.218435i
$973$	9.07563	−	15.7195i	0.290951	−	0.503943i
$974$	−0.193235	−	0.334692i	−0.00619164	−	0.0107242i
$975$	−7.61903	−	31.9275i	−0.244004	−	1.02250i
$976$		−	3.25814i		−	0.104291i
$977$	−16.9620			−0.542662			−0.271331	−	0.962486i	$-0.587464\pi$
$977$	−16.9620			−0.542662			−0.271331	+	0.962486i	$0.587464\pi$
$978$	−32.7092	+	14.0062i	−1.04592	+	0.447870i
$979$	3.18115	+	5.50991i	0.101670	+	0.176098i
$980$	−4.78080	+	6.85834i	−0.152717	+	0.219082i
$981$	6.39210	−	6.70339i	0.204084	−	0.214023i
$982$	−10.1542	−	17.5877i	−0.324035	−	0.561245i
$983$	22.0203	−	12.7134i	0.702338	−	0.405495i	−0.105880	−	0.994379i	$-0.533766\pi$
$983$	22.0203	−	12.7134i	0.702338	−	0.405495i	0.808218	+	0.588884i	$0.200432\pi$
$984$	−3.60268	−	2.69703i	−0.114849	−	0.0859782i
$985$	−1.07715	−	0.750855i	−0.0343207	−	0.0239242i
$986$	−19.5033	−	11.2603i	−0.621113	−	0.358600i
$987$	−0.574217	+	4.80188i	−0.0182775	+	0.152846i
$988$	1.65017			0.0524990
$989$	3.94076	+	2.27520i	0.125309	+	0.0723471i
$990$	−3.65023	−	17.9701i	−0.116012	−	0.571126i
$991$		−	20.4866i		−	0.650778i	−0.945580	−	0.325389i	$-0.894505\pi$
$991$		−	20.4866i		−	0.650778i	0.945580	−	0.325389i	$-0.105495\pi$
$992$	0.925384	−	5.49032i	0.0293810	−	0.174318i
$993$	12.5401	+	9.38775i	0.397949	+	0.297911i
$994$	−11.9306			−0.378414
$995$	−1.32443	−	0.923230i	−0.0419872	−	0.0292684i
$996$	1.60363	+	1.20050i	0.0508129	+	0.0380394i
$997$	−17.1606	+	9.90769i	−0.543482	+	0.313780i	−0.746489	−	0.665398i	$-0.768262\pi$
$997$	−17.1606	+	9.90769i	−0.543482	+	0.313780i	0.203007	+	0.979177i	$0.434929\pi$
$998$	5.94228	+	3.43078i	0.188100	+	0.108599i
$999$	42.9488	−	35.4579i	1.35884	−	1.12184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.r.a.119.20	✓	64
3.2	odd	2		930.2.r.b.119.2	yes	64
5.4	even	2		930.2.r.b.119.13	yes	64
15.14	odd	2	inner	930.2.r.a.119.31	yes	64
31.6	odd	6	inner	930.2.r.a.719.31	yes	64
93.68	even	6		930.2.r.b.719.13	yes	64
155.99	odd	6		930.2.r.b.719.2	yes	64
465.254	even	6	inner	930.2.r.a.719.20	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.20	✓	64	1.1	even	1	trivial
930.2.r.a.119.31	yes	64	15.14	odd	2	inner
930.2.r.a.719.20	yes	64	465.254	even	6	inner
930.2.r.a.719.31	yes	64	31.6	odd	6	inner
930.2.r.b.119.2	yes	64	3.2	odd	2
930.2.r.b.119.13	yes	64	5.4	even	2
930.2.r.b.719.2	yes	64	155.99	odd	6
930.2.r.b.719.13	yes	64	93.68	even	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.681795 + 1.59222i) q^{3} +1.00000 q^{4} +(-0.949262 - 2.02457i) q^{5} +(-0.681795 - 1.59222i) q^{6} +(-1.56394 - 0.902941i) q^{7} -1.00000 q^{8} +(-2.07031 + 2.17113i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.681795 + 1.59222i) q^{3} +1.00000 q^{4} +(-0.949262 - 2.02457i) q^{5} +(-0.681795 - 1.59222i) q^{6} +(-1.56394 - 0.902941i) q^{7} -1.00000 q^{8} +(-2.07031 + 2.17113i) q^{9} +(0.949262 + 2.02457i) q^{10} +(1.36676 + 2.36730i) q^{11} +(0.681795 + 1.59222i) q^{12} +(1.89509 + 3.28240i) q^{13} +(1.56394 + 0.902941i) q^{14} +(2.57636 - 2.89178i) q^{15} +1.00000 q^{16} +(-5.50887 - 3.18055i) q^{17} +(2.07031 - 2.17113i) q^{18} +(0.217690 - 0.377051i) q^{19} +(-0.949262 - 2.02457i) q^{20} +(0.371391 - 3.10575i) q^{21} +(-1.36676 - 2.36730i) q^{22} -2.68202i q^{23} +(-0.681795 - 1.59222i) q^{24} +(-3.19780 + 3.84370i) q^{25} +(-1.89509 - 3.28240i) q^{26} +(-4.86844 - 1.81611i) q^{27} +(-1.56394 - 0.902941i) q^{28} -3.54035 q^{29} +(-2.57636 + 2.89178i) q^{30} +(-0.925384 + 5.49032i) q^{31} -1.00000 q^{32} +(-2.83741 + 3.79020i) q^{33} +(5.50887 + 3.18055i) q^{34} +(-0.343482 + 4.02344i) q^{35} +(-2.07031 + 2.17113i) q^{36} +(-5.35919 + 9.28239i) q^{37} +(-0.217690 + 0.377051i) q^{38} +(-3.93422 + 5.25532i) q^{39} +(0.949262 + 2.02457i) q^{40} +(2.25018 - 1.29914i) q^{41} +(-0.371391 + 3.10575i) q^{42} +(-0.848315 + 1.46932i) q^{43} +(1.36676 + 2.36730i) q^{44} +(6.36089 + 2.13052i) q^{45} +2.68202i q^{46} -1.54613 q^{47} +(0.681795 + 1.59222i) q^{48} +(-1.86940 - 3.23789i) q^{49} +(3.19780 - 3.84370i) q^{50} +(1.30820 - 10.9398i) q^{51} +(1.89509 + 3.28240i) q^{52} +(-8.31697 + 4.80180i) q^{53} +(4.86844 + 1.81611i) q^{54} +(3.49537 - 5.01430i) q^{55} +(1.56394 + 0.902941i) q^{56} +(0.748767 + 0.0895387i) q^{57} +3.54035 q^{58} +(-10.8827 - 6.28315i) q^{59} +(2.57636 - 2.89178i) q^{60} -3.25814i q^{61} +(0.925384 - 5.49032i) q^{62} +(5.19824 - 1.52615i) q^{63} +1.00000 q^{64} +(4.84651 - 6.95261i) q^{65} +(2.83741 - 3.79020i) q^{66} +(-7.83494 + 4.52350i) q^{67} +(-5.50887 - 3.18055i) q^{68} +(4.27036 - 1.82859i) q^{69} +(0.343482 - 4.02344i) q^{70} +(-5.72140 + 3.30325i) q^{71} +(2.07031 - 2.17113i) q^{72} +(3.73631 + 6.47149i) q^{73} +(5.35919 - 9.28239i) q^{74} +(-8.30026 - 2.47098i) q^{75} +(0.217690 - 0.377051i) q^{76} -4.93642i q^{77} +(3.93422 - 5.25532i) q^{78} +(0.884726 + 0.510797i) q^{79} +(-0.949262 - 2.02457i) q^{80} +(-0.427634 - 8.98983i) q^{81} +(-2.25018 + 1.29914i) q^{82} +(1.00160 - 0.578276i) q^{83} +(0.371391 - 3.10575i) q^{84} +(-1.20989 + 14.1723i) q^{85} +(0.848315 - 1.46932i) q^{86} +(-2.41379 - 5.63700i) q^{87} +(-1.36676 - 2.36730i) q^{88} +2.32751 q^{89} +(-6.36089 - 2.13052i) q^{90} -6.84462i q^{91} -2.68202i q^{92} +(-9.37271 + 2.26987i) q^{93} +1.54613 q^{94} +(-0.970012 - 0.0828103i) q^{95} +(-0.681795 - 1.59222i) q^{96} -11.8138i q^{97} +(1.86940 + 3.23789i) q^{98} +(-7.96935 - 1.93363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9}+O(q^{10}) \) 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9	\( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} - 6 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 2 q^{25} + 18 q^{31} - 64 q^{32} + 8 q^{33} + 6 q^{34} - 16 q^{35} - 4 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 5 q^{45} + 4 q^{47} + 30 q^{49} - 2 q^{50} - 8 q^{51} + 6 q^{53} - 6 q^{57} - 18 q^{62} - 12 q^{63} + 64 q^{64} - 8 q^{66} - 6 q^{68} - 10 q^{69} + 16 q^{70} + 4 q^{72} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 q^{90} + 18 q^{93} - 4 q^{94} + 56 q^{95} - 30 q^{98} - 102 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 + 64 * q^4 - 2 * q^5 - 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 - 6 * q^17 + 4 * q^18 + 4 * q^19 - 2 * q^20 + 2 * q^25 + 18 * q^31 - 64 * q^32 + 8 * q^33 + 6 * q^34 - 16 * q^35 - 4 * q^36 - 4 * q^38 - 8 * q^39 + 2 * q^40 + 5 * q^45 + 4 * q^47 + 30 * q^49 - 2 * q^50 - 8 * q^51 + 6 * q^53 - 6 * q^57 - 18 * q^62 - 12 * q^63 + 64 * q^64 - 8 * q^66 - 6 * q^68 - 10 * q^69 + 16 * q^70 + 4 * q^72 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * q^90 + 18 * q^93 - 4 * q^94 + 56 * q^95 - 30 * q^98 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more