LMFDB - Embedded newform 1110.2.o.a.253.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (of order $4$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.12
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.407420 + 2.19864i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.64494 - 1.64494i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.407420 + 2.19864i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.64494 - 1.64494i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-0.407420 - 2.19864i) q^{10} -5.09841i q^{11} +(0.707107 - 0.707107i) q^{12} -5.90090 q^{13} +(-1.64494 + 1.64494i) q^{14} +(1.84276 + 1.26658i) q^{15} +1.00000 q^{16} -0.720684i q^{17} +1.00000i q^{18} +(-5.20267 - 5.20267i) q^{19} +(0.407420 + 2.19864i) q^{20} -2.32629i q^{21} +5.09841i q^{22} +2.47151 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.66802 + 1.79154i) q^{25} +5.90090 q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.64494 - 1.64494i) q^{28} +(-2.09433 + 2.09433i) q^{29} +(-1.84276 - 1.26658i) q^{30} +(-6.99049 - 6.99049i) q^{31} -1.00000 q^{32} +(-3.60512 - 3.60512i) q^{33} +0.720684i q^{34} +(4.28681 + 2.94644i) q^{35} -1.00000i q^{36} +(0.654393 - 6.04746i) q^{37} +(5.20267 + 5.20267i) q^{38} +(-4.17257 + 4.17257i) q^{39} +(-0.407420 - 2.19864i) q^{40} +6.58809i q^{41} +2.32629i q^{42} +10.4051 q^{43} -5.09841i q^{44} +(2.19864 - 0.407420i) q^{45} -2.47151 q^{46} +(6.69776 - 6.69776i) q^{47} +(0.707107 - 0.707107i) q^{48} +1.58835i q^{49} +(4.66802 - 1.79154i) q^{50} +(-0.509601 - 0.509601i) q^{51} -5.90090 q^{52} +(6.02669 + 6.02669i) q^{53} +(0.707107 + 0.707107i) q^{54} +(11.2096 - 2.07719i) q^{55} +(-1.64494 + 1.64494i) q^{56} -7.35769 q^{57} +(2.09433 - 2.09433i) q^{58} +(-1.31697 - 1.31697i) q^{59} +(1.84276 + 1.26658i) q^{60} +(-0.136297 - 0.136297i) q^{61} +(6.99049 + 6.99049i) q^{62} +(-1.64494 - 1.64494i) q^{63} +1.00000 q^{64} +(-2.40415 - 12.9740i) q^{65} +(3.60512 + 3.60512i) q^{66} +(-8.82528 - 8.82528i) q^{67} -0.720684i q^{68} +(1.74762 - 1.74762i) q^{69} +(-4.28681 - 2.94644i) q^{70} +0.630243 q^{71} +1.00000i q^{72} +(0.800728 - 0.800728i) q^{73} +(-0.654393 + 6.04746i) q^{74} +(-2.03398 + 4.56760i) q^{75} +(-5.20267 - 5.20267i) q^{76} +(-8.38658 - 8.38658i) q^{77} +(4.17257 - 4.17257i) q^{78} +(1.35715 + 1.35715i) q^{79} +(0.407420 + 2.19864i) q^{80} -1.00000 q^{81} -6.58809i q^{82} +(0.0877629 + 0.0877629i) q^{83} -2.32629i q^{84} +(1.58452 - 0.293621i) q^{85} -10.4051 q^{86} +2.96182i q^{87} +5.09841i q^{88} +(0.651916 - 0.651916i) q^{89} +(-2.19864 + 0.407420i) q^{90} +(-9.70663 + 9.70663i) q^{91} +2.47151 q^{92} -9.88605 q^{93} +(-6.69776 + 6.69776i) q^{94} +(9.31912 - 13.5585i) q^{95} +(-0.707107 + 0.707107i) q^{96} +5.99946i q^{97} -1.58835i q^{98} -5.09841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	0.407420	+	2.19864i	0.182204	+	0.983261i
$5$	0.407420	+	2.19864i	0.182204	+	0.983261i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	1.64494	−	1.64494i	0.621728	−	0.621728i	−0.324245	−	0.945973i	$-0.605110\pi$
$7$	1.64494	−	1.64494i	0.621728	−	0.621728i	0.945973	+	0.324245i	$0.105110\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−0.407420	−	2.19864i	−0.128837	−	0.695270i
$11$		−	5.09841i		−	1.53723i	−0.639712	−	0.768614i	$-0.720947\pi$
$11$		−	5.09841i		−	1.53723i	0.639712	−	0.768614i	$-0.279053\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−5.90090			−1.63662			−0.818308	−	0.574780i	$-0.805088\pi$
$13$	−5.90090			−1.63662			−0.818308	+	0.574780i	$0.805088\pi$
$14$	−1.64494	+	1.64494i	−0.439628	+	0.439628i
$15$	1.84276	+	1.26658i	0.475799	+	0.327030i
$16$	1.00000			0.250000
$17$		−	0.720684i		−	0.174792i	−0.996174	−	0.0873958i	$-0.972146\pi$
$17$		−	0.720684i		−	0.174792i	0.996174	−	0.0873958i	$-0.0278545\pi$
$18$			1.00000i			0.235702i
$19$	−5.20267	−	5.20267i	−1.19357	−	1.19357i	−0.976056	−	0.217519i	$-0.930204\pi$
$19$	−5.20267	−	5.20267i	−1.19357	−	1.19357i	−0.217519	−	0.976056i	$-0.569796\pi$
$20$	0.407420	+	2.19864i	0.0911019	+	0.491630i
$21$		−	2.32629i		−	0.507639i
$22$			5.09841i			1.08698i
$23$	2.47151			0.515346			0.257673	−	0.966232i	$-0.417044\pi$
$23$	2.47151			0.515346			0.257673	+	0.966232i	$0.417044\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−4.66802	+	1.79154i	−0.933604	+	0.358308i
$26$	5.90090			1.15726
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.64494	−	1.64494i	0.310864	−	0.310864i
$29$	−2.09433	+	2.09433i	−0.388907	+	0.388907i	−0.874297	−	0.485391i	$-0.838677\pi$
$29$	−2.09433	+	2.09433i	−0.388907	+	0.388907i	0.485391	+	0.874297i	$0.338677\pi$
$30$	−1.84276	−	1.26658i	−0.336441	−	0.231245i
$31$	−6.99049	−	6.99049i	−1.25553	−	1.25553i	−0.953205	−	0.302324i	$-0.902238\pi$
$31$	−6.99049	−	6.99049i	−1.25553	−	1.25553i	−0.302324	−	0.953205i	$-0.597762\pi$
$32$	−1.00000			−0.176777
$33$	−3.60512	−	3.60512i	−0.627571	−	0.627571i
$34$			0.720684i			0.123596i
$35$	4.28681	+	2.94644i	0.724602	+	0.498040i
$36$		−	1.00000i		−	0.166667i
$37$	0.654393	−	6.04746i	0.107582	−	0.994196i
$37$	0.654393	−	6.04746i	0.107582	−	0.994196i
$38$	5.20267	+	5.20267i	0.843985	+	0.843985i
$39$	−4.17257	+	4.17257i	−0.668146	+	0.668146i
$40$	−0.407420	−	2.19864i	−0.0644187	−	0.347635i
$41$			6.58809i			1.02889i	0.857524	+	0.514444i	$0.172001\pi$
$41$			6.58809i			1.02889i	−0.857524	+	0.514444i	$0.827999\pi$
$42$			2.32629i			0.358955i
$43$	10.4051			1.58676			0.793380	−	0.608726i	$-0.208319\pi$
$43$	10.4051			1.58676			0.793380	+	0.608726i	$0.208319\pi$
$44$		−	5.09841i		−	0.768614i
$45$	2.19864	−	0.407420i	0.327754	−	0.0607346i
$46$	−2.47151			−0.364405
$47$	6.69776	−	6.69776i	0.976969	−	0.976969i	−0.0227714	−	0.999741i	$-0.507249\pi$
$47$	6.69776	−	6.69776i	0.976969	−	0.976969i	0.999741	+	0.0227714i	$0.00724897\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			1.58835i			0.226907i
$50$	4.66802	−	1.79154i	0.660157	−	0.253362i
$51$	−0.509601	−	0.509601i	−0.0713584	−	0.0713584i
$52$	−5.90090			−0.818308
$53$	6.02669	+	6.02669i	0.827829	+	0.827829i	0.987216	−	0.159387i	$-0.0509518\pi$
$53$	6.02669	+	6.02669i	0.827829	+	0.827829i	−0.159387	+	0.987216i	$0.550952\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	11.2096	−	2.07719i	1.51150	−	0.280089i
$56$	−1.64494	+	1.64494i	−0.219814	+	0.219814i
$57$	−7.35769			−0.974550
$58$	2.09433	−	2.09433i	0.274999	−	0.274999i
$59$	−1.31697	−	1.31697i	−0.171455	−	0.171455i	0.616163	−	0.787619i	$-0.288686\pi$
$59$	−1.31697	−	1.31697i	−0.171455	−	0.171455i	−0.787619	+	0.616163i	$0.788686\pi$
$60$	1.84276	+	1.26658i	0.237899	+	0.163515i
$61$	−0.136297	−	0.136297i	−0.0174510	−	0.0174510i	0.698327	−	0.715778i	$-0.253928\pi$
$61$	−0.136297	−	0.136297i	−0.0174510	−	0.0174510i	−0.715778	+	0.698327i	$0.753928\pi$
$62$	6.99049	+	6.99049i	0.887793	+	0.887793i
$63$	−1.64494	−	1.64494i	−0.207243	−	0.207243i
$64$	1.00000			0.125000
$65$	−2.40415	−	12.9740i	−0.298198	−	1.60922i
$66$	3.60512	+	3.60512i	0.443760	+	0.443760i
$67$	−8.82528	−	8.82528i	−1.07818	−	1.07818i	−0.996673	−	0.0815072i	$-0.974027\pi$
$67$	−8.82528	−	8.82528i	−1.07818	−	1.07818i	−0.0815072	−	0.996673i	$-0.525973\pi$
$68$		−	0.720684i		−	0.0873958i
$69$	1.74762	−	1.74762i	0.210389	−	0.210389i
$70$	−4.28681	−	2.94644i	−0.512371	−	0.352167i
$71$	0.630243			0.0747961			0.0373980	−	0.999300i	$-0.488093\pi$
$71$	0.630243			0.0747961			0.0373980	+	0.999300i	$0.488093\pi$
$72$			1.00000i			0.117851i
$73$	0.800728	−	0.800728i	0.0937181	−	0.0937181i	−0.658693	−	0.752411i	$-0.728891\pi$
$73$	0.800728	−	0.800728i	0.0937181	−	0.0937181i	0.752411	+	0.658693i	$0.228891\pi$
$74$	−0.654393	+	6.04746i	−0.0760717	+	0.703003i
$75$	−2.03398	+	4.56760i	−0.234864	+	0.527421i
$76$	−5.20267	−	5.20267i	−0.596787	−	0.596787i
$77$	−8.38658	−	8.38658i	−0.955739	−	0.955739i
$78$	4.17257	−	4.17257i	0.472451	−	0.472451i
$79$	1.35715	+	1.35715i	0.152691	+	0.152691i	0.779319	−	0.626628i	$-0.215565\pi$
$79$	1.35715	+	1.35715i	0.152691	+	0.152691i	−0.626628	+	0.779319i	$0.715565\pi$
$80$	0.407420	+	2.19864i	0.0455509	+	0.245815i
$81$	−1.00000			−0.111111
$82$		−	6.58809i		−	0.727533i
$83$	0.0877629	+	0.0877629i	0.00963323	+	0.00963323i	0.711907	−	0.702274i	$-0.247832\pi$
$83$	0.0877629	+	0.0877629i	0.00963323	+	0.00963323i	−0.702274	+	0.711907i	$0.747832\pi$
$84$		−	2.32629i		−	0.253820i
$85$	1.58452	−	0.293621i	0.171866	−	0.0318477i
$86$	−10.4051			−1.12201
$87$			2.96182i			0.317541i
$88$			5.09841i			0.543492i
$89$	0.651916	−	0.651916i	0.0691030	−	0.0691030i	−0.671711	−	0.740814i	$-0.734440\pi$
$89$	0.651916	−	0.651916i	0.0691030	−	0.0691030i	0.740814	+	0.671711i	$0.234440\pi$
$90$	−2.19864	+	0.407420i	−0.231757	+	0.0429458i
$91$	−9.70663	+	9.70663i	−1.01753	+	1.01753i
$92$	2.47151			0.257673
$93$	−9.88605			−1.02514
$94$	−6.69776	+	6.69776i	−0.690822	+	0.690822i
$95$	9.31912	−	13.5585i	0.956122	−	1.39107i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$			5.99946i			0.609153i	0.952488	+	0.304577i	$0.0985150\pi$
$97$			5.99946i			0.609153i	−0.952488	+	0.304577i	$0.901485\pi$
$98$		−	1.58835i		−	0.160448i
$99$	−5.09841			−0.512410
$100$	−4.66802	+	1.79154i	−0.466802	+	0.179154i
$101$		−	0.764728i		−	0.0760932i	−0.999276	−	0.0380466i	$-0.987886\pi$
$101$		−	0.764728i		−	0.0760932i	0.999276	−	0.0380466i	$-0.0121135\pi$
$102$	0.509601	+	0.509601i	0.0504580	+	0.0504580i
$103$			2.86283i			0.282083i	0.990004	+	0.141041i	$0.0450451\pi$
$103$			2.86283i			0.282083i	−0.990004	+	0.141041i	$0.954955\pi$
$104$	5.90090			0.578631
$105$	5.11468	−	0.947779i	0.499142	−	0.0924938i
$106$	−6.02669	−	6.02669i	−0.585363	−	0.585363i
$107$	7.65897	−	7.65897i	0.740421	−	0.740421i	−0.232238	−	0.972659i	$-0.574605\pi$
$107$	7.65897	−	7.65897i	0.740421	−	0.740421i	0.972659	+	0.232238i	$0.0746048\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−1.40152	−	1.40152i	−0.134241	−	0.134241i	0.636793	−	0.771034i	$-0.280260\pi$
$109$	−1.40152	−	1.40152i	−0.134241	−	0.134241i	−0.771034	+	0.636793i	$0.780260\pi$
$110$	−11.2096	+	2.07719i	−1.06879	+	0.198053i
$111$	−3.81347	−	4.73893i	−0.361959	−	0.449799i
$112$	1.64494	−	1.64494i	0.155432	−	0.155432i
$113$			15.5998i			1.46751i	0.679416	+	0.733753i	$0.262233\pi$
$113$			15.5998i			1.46751i	−0.679416	+	0.733753i	$0.737767\pi$
$114$	7.35769			0.689111
$115$	1.00694	+	5.43396i	0.0938980	+	0.506720i
$116$	−2.09433	+	2.09433i	−0.194453	+	0.194453i
$117$			5.90090i			0.545539i
$118$	1.31697	+	1.31697i	0.121237	+	0.121237i
$119$	−1.18548	−	1.18548i	−0.108673	−	0.108673i
$120$	−1.84276	−	1.26658i	−0.168220	−	0.115623i
$121$	−14.9938			−1.36307
$122$	0.136297	+	0.136297i	0.0123397	+	0.0123397i
$123$	4.65848	+	4.65848i	0.420041	+	0.420041i
$124$	−6.99049	−	6.99049i	−0.627765	−	0.627765i
$125$	−5.84079	−	9.53337i	−0.522416	−	0.852691i
$126$	1.64494	+	1.64494i	0.146543	+	0.146543i
$127$	14.2375	−	14.2375i	1.26337	−	1.26337i	0.313928	−	0.949447i	$-0.398355\pi$
$127$	14.2375	−	14.2375i	1.26337	−	1.26337i	0.949447	−	0.313928i	$-0.101645\pi$
$128$	−1.00000			−0.0883883
$129$	7.35750	−	7.35750i	0.647792	−	0.647792i
$130$	2.40415	+	12.9740i	0.210858	+	1.13789i
$131$	−9.64243	−	9.64243i	−0.842463	−	0.842463i	0.146716	−	0.989179i	$-0.453130\pi$
$131$	−9.64243	−	9.64243i	−0.842463	−	0.842463i	−0.989179	+	0.146716i	$0.953130\pi$
$132$	−3.60512	−	3.60512i	−0.313786	−	0.313786i
$133$	−17.1162			−1.48416
$134$	8.82528	+	8.82528i	0.762388	+	0.762388i
$135$	1.26658	−	1.84276i	0.109010	−	0.158600i
$136$			0.720684i			0.0617982i
$137$	−5.63532	+	5.63532i	−0.481458	+	0.481458i	−0.905597	−	0.424139i	$-0.860577\pi$
$137$	−5.63532	+	5.63532i	−0.481458	+	0.481458i	0.424139	+	0.905597i	$0.360577\pi$
$138$	−1.74762	+	1.74762i	−0.148768	+	0.148768i
$139$	−18.1510			−1.53955			−0.769775	−	0.638315i	$-0.779632\pi$
$139$	−18.1510			−1.53955			−0.769775	+	0.638315i	$0.779632\pi$
$140$	4.28681	+	2.94644i	0.362301	+	0.249020i
$141$		−	9.47207i		−	0.797692i
$142$	−0.630243			−0.0528888
$143$			30.0852i			2.51585i
$144$		−	1.00000i		−	0.0833333i
$145$	−5.45794	−	3.75140i	−0.453257	−	0.311536i
$146$	−0.800728	+	0.800728i	−0.0662687	+	0.0662687i
$147$	1.12313	+	1.12313i	0.0926346	+	0.0926346i
$148$	0.654393	−	6.04746i	0.0537908	−	0.497098i
$149$		−	19.7092i		−	1.61464i	−0.590112	−	0.807322i	$-0.700916\pi$
$149$		−	19.7092i		−	1.61464i	0.590112	−	0.807322i	$-0.299084\pi$
$150$	2.03398	−	4.56760i	0.166074	−	0.372943i
$151$			5.28263i			0.429895i	0.976626	+	0.214947i	$0.0689580\pi$
$151$			5.28263i			0.429895i	−0.976626	+	0.214947i	$0.931042\pi$
$152$	5.20267	+	5.20267i	0.421992	+	0.421992i
$153$	−0.720684			−0.0582639
$154$	8.38658	+	8.38658i	0.675809	+	0.675809i
$155$	12.5215	−	18.2176i	1.00575	−	1.46327i
$156$	−4.17257	+	4.17257i	−0.334073	+	0.334073i
$157$	16.6599	−	16.6599i	1.32961	−	1.32961i	0.423893	−	0.905712i	$-0.360663\pi$
$157$	16.6599	−	16.6599i	1.32961	−	1.32961i	0.905712	−	0.423893i	$-0.139337\pi$
$158$	−1.35715	−	1.35715i	−0.107969	−	0.107969i
$159$	8.52302			0.675920
$160$	−0.407420	−	2.19864i	−0.0322094	−	0.173818i
$161$	4.06549	−	4.06549i	0.320405	−	0.320405i
$162$	1.00000			0.0785674
$163$			15.8733i			1.24330i	0.783297	+	0.621648i	$0.213537\pi$
$163$			15.8733i			1.24330i	−0.783297	+	0.621648i	$0.786463\pi$
$164$			6.58809i			0.514444i
$165$	6.45756	−	9.39515i	0.502720	−	0.731412i
$166$	−0.0877629	−	0.0877629i	−0.00681172	−	0.00681172i
$167$			16.1399i			1.24894i	0.781048	+	0.624471i	$0.214686\pi$
$167$			16.1399i			1.24894i	−0.781048	+	0.624471i	$0.785314\pi$
$168$			2.32629i			0.179478i
$169$	21.8207			1.67851
$170$	−1.58452	+	0.293621i	−0.121527	+	0.0225197i
$171$	−5.20267	+	5.20267i	−0.397858	+	0.397858i
$172$	10.4051			0.793380
$173$	7.18619	−	7.18619i	0.546356	−	0.546356i	−0.379029	−	0.925385i	$-0.623742\pi$
$173$	7.18619	−	7.18619i	0.546356	−	0.546356i	0.925385	+	0.379029i	$0.123742\pi$
$174$		−	2.96182i		−	0.224535i
$175$	−4.73163	+	10.6256i	−0.357678	+	0.803218i
$176$		−	5.09841i		−	0.384307i
$177$	−1.86248			−0.139993
$178$	−0.651916	+	0.651916i	−0.0488632	+	0.0488632i
$179$	1.27828	−	1.27828i	0.0955432	−	0.0955432i	−0.657720	−	0.753263i	$-0.728479\pi$
$179$	1.27828	−	1.27828i	0.0955432	−	0.0955432i	0.753263	+	0.657720i	$0.228479\pi$
$180$	2.19864	−	0.407420i	0.163877	−	0.0303673i
$181$	6.63253			0.492992			0.246496	−	0.969144i	$-0.420721\pi$
$181$	6.63253			0.492992			0.246496	+	0.969144i	$0.420721\pi$
$182$	9.70663	−	9.70663i	0.719503	−	0.719503i
$183$	−0.192753			−0.0142487
$184$	−2.47151			−0.182202
$185$	13.5628	−	1.02508i	0.997156	−	0.0753655i
$186$	9.88605			0.724880
$187$	−3.67435			−0.268695
$188$	6.69776	−	6.69776i	0.488485	−	0.488485i
$189$	−2.32629			−0.169213
$190$	−9.31912	+	13.5585i	−0.676080	+	0.983634i
$191$	13.4202	−	13.4202i	0.971054	−	0.971054i	−0.0285382	−	0.999593i	$-0.509085\pi$
$191$	13.4202	−	13.4202i	0.971054	−	0.971054i	0.999593	+	0.0285382i	$0.00908524\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	9.65236			0.694792			0.347396	−	0.937719i	$-0.387066\pi$
$193$	9.65236			0.694792			0.347396	+	0.937719i	$0.387066\pi$
$194$		−	5.99946i		−	0.430736i
$195$	−10.8740	−	7.47398i	−0.778700	−	0.535223i
$196$			1.58835i			0.113454i
$197$	1.88877	−	1.88877i	0.134569	−	0.134569i	−0.636614	−	0.771183i	$-0.719665\pi$
$197$	1.88877	−	1.88877i	0.134569	−	0.134569i	0.771183	+	0.636614i	$0.219665\pi$
$198$	5.09841			0.362328
$199$	5.38735	−	5.38735i	0.381899	−	0.381899i	−0.489887	−	0.871786i	$-0.662962\pi$
$199$	5.38735	−	5.38735i	0.381899	−	0.381899i	0.871786	+	0.489887i	$0.162962\pi$
$200$	4.66802	−	1.79154i	0.330079	−	0.126681i
$201$	−12.4808			−0.880330
$202$			0.764728i			0.0538060i
$203$			6.89008i			0.483589i
$204$	−0.509601	−	0.509601i	−0.0356792	−	0.0356792i
$205$	−14.4848	+	2.68412i	−1.01166	+	0.187467i
$206$		−	2.86283i		−	0.199463i
$207$		−	2.47151i		−	0.171782i
$208$	−5.90090			−0.409154
$209$	−26.5254	+	26.5254i	−1.83480	+	1.83480i
$210$	−5.11468	+	0.947779i	−0.352946	+	0.0654030i
$211$	−2.70038			−0.185902			−0.0929510	−	0.995671i	$-0.529630\pi$
$211$	−2.70038			−0.185902			−0.0929510	+	0.995671i	$0.529630\pi$
$212$	6.02669	+	6.02669i	0.413914	+	0.413914i
$213$	0.445649	−	0.445649i	0.0305354	−	0.0305354i
$214$	−7.65897	+	7.65897i	−0.523557	+	0.523557i
$215$	4.23924	+	22.8770i	0.289114	+	1.56020i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−22.9979			−1.56120
$218$	1.40152	+	1.40152i	0.0949228	+	0.0949228i
$219$		−	1.13240i		−	0.0765205i
$220$	11.2096	−	2.07719i	0.755748	−	0.140044i
$221$			4.25269i			0.286067i
$222$	3.81347	+	4.73893i	0.255944	+	0.318056i
$223$	0.836925	+	0.836925i	0.0560447	+	0.0560447i	0.734574	−	0.678529i	$-0.237382\pi$
$223$	0.836925	+	0.836925i	0.0560447	+	0.0560447i	−0.678529	+	0.734574i	$0.737382\pi$
$224$	−1.64494	+	1.64494i	−0.109907	+	0.109907i
$225$	1.79154	+	4.66802i	0.119436	+	0.311201i
$226$		−	15.5998i		−	1.03768i
$227$			2.55431i			0.169535i	0.996401	+	0.0847677i	$0.0270148\pi$
$227$			2.55431i			0.169535i	−0.996401	+	0.0847677i	$0.972985\pi$
$228$	−7.35769			−0.487275
$229$			2.55867i			0.169082i	0.996420	+	0.0845409i	$0.0269424\pi$
$229$			2.55867i			0.169082i	−0.996420	+	0.0845409i	$0.973058\pi$
$230$	−1.00694	−	5.43396i	−0.0663959	−	0.358305i
$231$	−11.8604			−0.780358
$232$	2.09433	−	2.09433i	0.137499	−	0.137499i
$233$	5.68879	−	5.68879i	0.372685	−	0.372685i	−0.495769	−	0.868454i	$-0.665114\pi$
$233$	5.68879	−	5.68879i	0.372685	−	0.372685i	0.868454	+	0.495769i	$0.165114\pi$
$234$		−	5.90090i		−	0.385754i
$235$	17.4548	+	11.9972i	1.13862	+	0.782608i
$236$	−1.31697	−	1.31697i	−0.0857277	−	0.0857277i
$237$	1.91930			0.124672
$238$	1.18548	+	1.18548i	0.0768434	+	0.0768434i
$239$	−8.30333	−	8.30333i	−0.537098	−	0.537098i	0.385577	−	0.922675i	$-0.374002\pi$
$239$	−8.30333	−	8.30333i	−0.537098	−	0.537098i	−0.922675	+	0.385577i	$0.874002\pi$
$240$	1.84276	+	1.26658i	0.118950	+	0.0817575i
$241$	2.03835	−	2.03835i	0.131302	−	0.131302i	−0.638402	−	0.769703i	$-0.720404\pi$
$241$	2.03835	−	2.03835i	0.131302	−	0.131302i	0.769703	+	0.638402i	$0.220404\pi$
$242$	14.9938			0.963838
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−0.136297	−	0.136297i	−0.00872550	−	0.00872550i
$245$	−3.49221	+	0.647126i	−0.223109	+	0.0413434i
$246$	−4.65848	−	4.65848i	−0.297014	−	0.297014i
$247$	30.7005	+	30.7005i	1.95342	+	1.95342i
$248$	6.99049	+	6.99049i	0.443897	+	0.443897i
$249$	0.124116			0.00786550
$250$	5.84079	+	9.53337i	0.369404	+	0.602943i
$251$	18.1430	+	18.1430i	1.14518	+	1.14518i	0.987489	+	0.157690i	$0.0504048\pi$
$251$	18.1430	+	18.1430i	1.14518	+	1.14518i	0.157690	+	0.987489i	$0.449595\pi$
$252$	−1.64494	−	1.64494i	−0.103621	−	0.103621i
$253$		−	12.6008i		−	0.792205i
$254$	−14.2375	+	14.2375i	−0.893341	+	0.893341i
$255$	0.912806	−	1.32805i	0.0571621	−	0.0831657i
$256$	1.00000			0.0625000
$257$			13.8117i			0.861552i	0.902459	+	0.430776i	$0.141760\pi$
$257$			13.8117i			0.861552i	−0.902459	+	0.430776i	$0.858240\pi$
$258$	−7.35750	+	7.35750i	−0.458058	+	0.458058i
$259$	−8.87127	−	11.0241i	−0.551234	−	0.685007i
$260$	−2.40415	−	12.9740i	−0.149099	−	0.804610i
$261$	2.09433	+	2.09433i	0.129636	+	0.129636i
$262$	9.64243	+	9.64243i	0.595711	+	0.595711i
$263$	−14.0744	+	14.0744i	−0.867867	+	0.867867i	−0.992236	−	0.124369i	$-0.960309\pi$
$263$	−14.0744	+	14.0744i	−0.867867	+	0.867867i	0.124369	+	0.992236i	$0.460309\pi$
$264$	3.60512	+	3.60512i	0.221880	+	0.221880i
$265$	−10.7951	+	15.7059i	−0.663138	+	0.964805i
$266$	17.1162			1.04946
$267$		−	0.921949i		−	0.0564224i
$268$	−8.82528	−	8.82528i	−0.539090	−	0.539090i
$269$			18.2296i			1.11148i	0.831357	+	0.555738i	$0.187564\pi$
$269$			18.2296i			1.11148i	−0.831357	+	0.555738i	$0.812436\pi$
$270$	−1.26658	+	1.84276i	−0.0770818	+	0.112147i
$271$	−12.8081			−0.778034			−0.389017	−	0.921231i	$-0.627185\pi$
$271$	−12.8081			−0.778034			−0.389017	+	0.921231i	$0.627185\pi$
$272$		−	0.720684i		−	0.0436979i
$273$			13.7272i			0.830811i
$274$	5.63532	−	5.63532i	0.340442	−	0.340442i
$275$	9.13400	+	23.7995i	0.550801	+	1.43516i
$276$	1.74762	−	1.74762i	0.105195	−	0.105195i
$277$	30.4939			1.83220			0.916099	−	0.400952i	$-0.131321\pi$
$277$	30.4939			1.83220			0.916099	+	0.400952i	$0.131321\pi$
$278$	18.1510			1.08863
$279$	−6.99049	+	6.99049i	−0.418510	+	0.418510i
$280$	−4.28681	−	2.94644i	−0.256186	−	0.176084i
$281$	−7.94084	+	7.94084i	−0.473711	+	0.473711i	−0.903113	−	0.429402i	$-0.858724\pi$
$281$	−7.94084	+	7.94084i	−0.473711	+	0.473711i	0.429402	+	0.903113i	$0.358724\pi$
$282$			9.47207i			0.564054i
$283$			3.46807i			0.206155i	0.994673	+	0.103078i	$0.0328690\pi$
$283$			3.46807i			0.206155i	−0.994673	+	0.103078i	$0.967131\pi$
$284$	0.630243			0.0373980
$285$	−2.99767	−	16.1769i	−0.177567	−	0.958237i
$286$		−	30.0852i		−	1.77898i
$287$	10.8370	+	10.8370i	0.639688	+	0.639688i
$288$			1.00000i			0.0589256i
$289$	16.4806			0.969448
$290$	5.45794	+	3.75140i	0.320501	+	0.220290i
$291$	4.24226	+	4.24226i	0.248686	+	0.248686i
$292$	0.800728	−	0.800728i	0.0468590	−	0.0468590i
$293$	6.68632	+	6.68632i	0.390619	+	0.390619i	0.874908	−	0.484289i	$-0.160922\pi$
$293$	6.68632	+	6.68632i	0.390619	+	0.390619i	−0.484289	+	0.874908i	$0.660922\pi$
$294$	−1.12313	−	1.12313i	−0.0655025	−	0.0655025i
$295$	2.35899	−	3.43211i	0.137346	−	0.199825i
$296$	−0.654393	+	6.04746i	−0.0380358	+	0.351501i
$297$	−3.60512	+	3.60512i	−0.209190	+	0.209190i
$298$			19.7092i			1.14173i
$299$	−14.5842			−0.843424
$300$	−2.03398	+	4.56760i	−0.117432	+	0.263710i
$301$	17.1157	−	17.1157i	0.986534	−	0.986534i
$302$		−	5.28263i		−	0.303981i
$303$	−0.540744	−	0.540744i	−0.0310649	−	0.0310649i
$304$	−5.20267	−	5.20267i	−0.298394	−	0.298394i
$305$	0.244137	−	0.355197i	0.0139792	−	0.0203385i
$306$	0.720684			0.0411988
$307$	−24.0972	−	24.0972i	−1.37530	−	1.37530i	−0.852382	−	0.522919i	$-0.824843\pi$
$307$	−24.0972	−	24.0972i	−1.37530	−	1.37530i	−0.522919	−	0.852382i	$-0.675157\pi$
$308$	−8.38658	−	8.38658i	−0.477869	−	0.477869i
$309$	2.02432	+	2.02432i	0.115160	+	0.115160i
$310$	−12.5215	+	18.2176i	−0.711173	+	1.03469i
$311$	7.00421	+	7.00421i	0.397172	+	0.397172i	0.877234	−	0.480062i	$-0.159386\pi$
$311$	7.00421	+	7.00421i	0.397172	+	0.397172i	−0.480062	+	0.877234i	$0.659386\pi$
$312$	4.17257	−	4.17257i	0.236225	−	0.236225i
$313$	0.610621			0.0345144			0.0172572	−	0.999851i	$-0.494507\pi$
$313$	0.610621			0.0345144			0.0172572	+	0.999851i	$0.494507\pi$
$314$	−16.6599	+	16.6599i	−0.940173	+	0.940173i
$315$	2.94644	−	4.28681i	0.166013	−	0.241534i
$316$	1.35715	+	1.35715i	0.0763455	+	0.0763455i
$317$	13.6669	+	13.6669i	0.767608	+	0.767608i	0.977685	−	0.210077i	$-0.0673715\pi$
$317$	13.6669	+	13.6669i	0.767608	+	0.767608i	−0.210077	+	0.977685i	$0.567372\pi$
$318$	−8.52302			−0.477947
$319$	10.6777	+	10.6777i	0.597839	+	0.597839i
$320$	0.407420	+	2.19864i	0.0227755	+	0.122908i
$321$		−	10.8314i		−	0.604551i
$322$	−4.06549	+	4.06549i	−0.226561	+	0.226561i
$323$	−3.74948	+	3.74948i	−0.208627	+	0.208627i
$324$	−1.00000			−0.0555556
$325$	27.5455	−	10.5717i	1.52795	−	0.586412i
$326$		−	15.8733i		−	0.879143i
$327$	−1.98205			−0.109607
$328$		−	6.58809i		−	0.363767i
$329$		−	22.0348i		−	1.21482i
$330$	−6.45756	+	9.39515i	−0.355477	+	0.517186i
$331$	−4.46154	+	4.46154i	−0.245228	+	0.245228i	−0.819009	−	0.573781i	$-0.805476\pi$
$331$	−4.46154	+	4.46154i	−0.245228	+	0.245228i	0.573781	+	0.819009i	$0.305476\pi$
$332$	0.0877629	+	0.0877629i	0.00481662	+	0.00481662i
$333$	−6.04746	−	0.654393i	−0.331399	−	0.0358605i
$334$		−	16.1399i		−	0.883136i
$335$	15.8080	−	22.9992i	0.863684	−	1.25658i
$336$		−	2.32629i		−	0.126910i
$337$	0.254872	+	0.254872i	0.0138838	+	0.0138838i	0.714015	−	0.700131i	$-0.246875\pi$
$337$	0.254872	+	0.254872i	0.0138838	+	0.0138838i	−0.700131	+	0.714015i	$0.746875\pi$
$338$	−21.8207			−1.18689
$339$	11.0307	+	11.0307i	0.599107	+	0.599107i
$340$	1.58452	−	0.293621i	0.0859329	−	0.0159238i
$341$	−35.6404	+	35.6404i	−1.93004	+	1.93004i
$342$	5.20267	−	5.20267i	0.281328	−	0.281328i
$343$	14.1273	+	14.1273i	0.762803	+	0.762803i
$344$	−10.4051			−0.561004
$345$	4.55441	+	3.13038i	0.245201	+	0.168534i
$346$	−7.18619	+	7.18619i	−0.386332	+	0.386332i
$347$	−28.6170			−1.53624			−0.768122	−	0.640304i	$-0.778808\pi$
$347$	−28.6170			−1.53624			−0.768122	+	0.640304i	$0.778808\pi$
$348$			2.96182i			0.158770i
$349$		−	15.9860i		−	0.855710i	−0.903847	−	0.427855i	$-0.859269\pi$
$349$		−	15.9860i		−	0.855710i	0.903847	−	0.427855i	$-0.140731\pi$
$350$	4.73163	−	10.6256i	0.252916	−	0.567961i
$351$	4.17257	+	4.17257i	0.222715	+	0.222715i
$352$			5.09841i			0.271746i
$353$		−	16.4429i		−	0.875170i	−0.899177	−	0.437585i	$-0.855834\pi$
$353$		−	16.4429i		−	0.875170i	0.899177	−	0.437585i	$-0.144166\pi$
$354$	1.86248			0.0989899
$355$	0.256774	+	1.38568i	0.0136281	+	0.0735440i
$356$	0.651916	−	0.651916i	0.0345515	−	0.0345515i
$357$	−1.67652			−0.0887311
$358$	−1.27828	+	1.27828i	−0.0675593	+	0.0675593i
$359$		−	17.3539i		−	0.915904i	−0.888977	−	0.457952i	$-0.848583\pi$
$359$		−	17.3539i		−	0.915904i	0.888977	−	0.457952i	$-0.151417\pi$
$360$	−2.19864	+	0.407420i	−0.115878	+	0.0214729i
$361$			35.1356i			1.84924i
$362$	−6.63253			−0.348598
$363$	−10.6022	+	10.6022i	−0.556472	+	0.556472i
$364$	−9.70663	+	9.70663i	−0.508766	+	0.508766i
$365$	2.08674	+	1.43428i	0.109225	+	0.0750735i
$366$	0.192753			0.0100753
$367$	−9.80219	+	9.80219i	−0.511670	+	0.511670i	−0.915038	−	0.403368i	$-0.867840\pi$
$367$	−9.80219	+	9.80219i	−0.511670	+	0.511670i	0.403368	+	0.915038i	$0.367840\pi$
$368$	2.47151			0.128837
$369$	6.58809			0.342962
$370$	−13.5628	+	1.02508i	−0.705096	+	0.0532915i
$371$	19.8271			1.02937
$372$	−9.88605			−0.512568
$373$	−1.82136	+	1.82136i	−0.0943063	+	0.0943063i	−0.752686	−	0.658380i	$-0.771242\pi$
$373$	−1.82136	+	1.82136i	−0.0943063	+	0.0943063i	0.658380	+	0.752686i	$0.271242\pi$
$374$	3.67435			0.189996
$375$	−10.8712	−	2.61105i	−0.561385	−	0.134834i
$376$	−6.69776	+	6.69776i	−0.345411	+	0.345411i
$377$	12.3584	−	12.3584i	0.636491	−	0.636491i
$378$	2.32629			0.119652
$379$			23.5189i			1.20808i	0.796953	+	0.604041i	$0.206444\pi$
$379$			23.5189i			1.20808i	−0.796953	+	0.604041i	$0.793556\pi$
$380$	9.31912	−	13.5585i	0.478061	−	0.695535i
$381$		−	20.1349i		−	1.03154i
$382$	−13.4202	+	13.4202i	−0.686639	+	0.686639i
$383$	−31.0387			−1.58600			−0.793001	−	0.609220i	$-0.791482\pi$
$383$	−31.0387			−1.58600			−0.793001	+	0.609220i	$0.791482\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	15.0222	−	21.8559i	0.765601	−	1.11388i
$386$	−9.65236			−0.491292
$387$		−	10.4051i		−	0.528920i
$388$			5.99946i			0.304577i
$389$	23.1210	+	23.1210i	1.17228	+	1.17228i	0.981665	+	0.190615i	$0.0610484\pi$
$389$	23.1210	+	23.1210i	1.17228	+	1.17228i	0.190615	+	0.981665i	$0.438952\pi$
$390$	10.8740	+	7.47398i	0.550624	+	0.378460i
$391$		−	1.78118i		−	0.0900782i
$392$		−	1.58835i		−	0.0802239i
$393$	−13.6365			−0.687868
$394$	−1.88877	+	1.88877i	−0.0951547	+	0.0951547i
$395$	−2.43095	+	3.53681i	−0.122314	+	0.177956i
$396$	−5.09841			−0.256205
$397$	−6.35301	−	6.35301i	−0.318848	−	0.318848i	0.529476	−	0.848325i	$-0.322388\pi$
$397$	−6.35301	−	6.35301i	−0.318848	−	0.318848i	−0.848325	+	0.529476i	$0.822388\pi$
$398$	−5.38735	+	5.38735i	−0.270043	+	0.270043i
$399$	−12.1030	+	12.1030i	−0.605905	+	0.605905i
$400$	−4.66802	+	1.79154i	−0.233401	+	0.0895769i
$401$	−23.0255	−	23.0255i	−1.14984	−	1.14984i	−0.986584	−	0.163256i	$-0.947800\pi$
$401$	−23.0255	−	23.0255i	−1.14984	−	1.14984i	−0.163256	−	0.986584i	$-0.552200\pi$
$402$	12.4808			0.622487
$403$	41.2502	+	41.2502i	2.05482	+	2.05482i
$404$		−	0.764728i		−	0.0380466i
$405$	−0.407420	−	2.19864i	−0.0202449	−	0.109251i
$406$		−	6.89008i		−	0.341949i
$407$	−30.8324	−	3.33637i	−1.52831	−	0.165377i
$408$	0.509601	+	0.509601i	0.0252290	+	0.0252290i
$409$	2.34868	−	2.34868i	0.116135	−	0.116135i	−0.646651	−	0.762786i	$-0.723831\pi$
$409$	2.34868	−	2.34868i	0.116135	−	0.116135i	0.762786	+	0.646651i	$0.223831\pi$
$410$	14.4848	−	2.68412i	0.715355	−	0.132559i
$411$			7.96955i			0.393109i
$412$			2.86283i			0.141041i
$413$	−4.33269			−0.213197
$414$			2.47151i			0.121468i
$415$	−0.157203	+	0.228715i	−0.00771677	+	0.0112272i
$416$	5.90090			0.289316
$417$	−12.8347	+	12.8347i	−0.628519	+	0.628519i
$418$	26.5254	−	26.5254i	1.29740	−	1.29740i
$419$			11.9631i			0.584434i	0.956352	+	0.292217i	$0.0943930\pi$
$419$			11.9631i			0.584434i	−0.956352	+	0.292217i	$0.905607\pi$
$420$	5.11468	−	0.947779i	0.249571	−	0.0462469i
$421$	−18.2560	−	18.2560i	−0.889744	−	0.889744i	0.104754	−	0.994498i	$-0.466594\pi$
$421$	−18.2560	−	18.2560i	−0.889744	−	0.889744i	−0.994498	+	0.104754i	$0.966594\pi$
$422$	2.70038			0.131453
$423$	−6.69776	−	6.69776i	−0.325656	−	0.325656i
$424$	−6.02669	−	6.02669i	−0.292682	−	0.292682i
$425$	1.29113	+	3.36417i	0.0626292	+	0.163186i
$426$	−0.445649	+	0.445649i	−0.0215918	+	0.0215918i
$427$	−0.448399			−0.0216996
$428$	7.65897	−	7.65897i	0.370210	−	0.370210i
$429$	21.2735	+	21.2735i	1.02709	+	1.02709i
$430$	−4.23924	−	22.8770i	−0.204434	−	1.10323i
$431$	−13.3451	−	13.3451i	−0.642811	−	0.642811i	0.308435	−	0.951245i	$-0.400195\pi$
$431$	−13.3451	−	13.3451i	−0.642811	−	0.642811i	−0.951245	+	0.308435i	$0.900195\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−12.4634	−	12.4634i	−0.598952	−	0.598952i	0.341082	−	0.940034i	$-0.389207\pi$
$433$	−12.4634	−	12.4634i	−0.598952	−	0.598952i	−0.940034	+	0.341082i	$0.889207\pi$
$434$	22.9979			1.10393
$435$	−6.51198	+	1.20671i	−0.312226	+	0.0578572i
$436$	−1.40152	−	1.40152i	−0.0671206	−	0.0671206i
$437$	−12.8585	−	12.8585i	−0.615104	−	0.615104i
$438$			1.13240i			0.0541082i
$439$	24.4496	−	24.4496i	1.16692	−	1.16692i	0.183987	−	0.982929i	$-0.441100\pi$
$439$	24.4496	−	24.4496i	1.16692	−	1.16692i	0.982929	−	0.183987i	$-0.0589005\pi$
$440$	−11.2096	+	2.07719i	−0.534395	+	0.0990264i
$441$	1.58835			0.0756358
$442$		−	4.25269i		−	0.202280i
$443$	19.6237	−	19.6237i	0.932352	−	0.932352i	−0.0655007	−	0.997853i	$-0.520864\pi$
$443$	19.6237	−	19.6237i	0.932352	−	0.932352i	0.997853	+	0.0655007i	$0.0208645\pi$
$444$	−3.81347	−	4.73893i	−0.180979	−	0.224899i
$445$	1.69893	+	1.16772i	0.0805371	+	0.0553555i
$446$	−0.836925	−	0.836925i	−0.0396296	−	0.0396296i
$447$	−13.9365	−	13.9365i	−0.659175	−	0.659175i
$448$	1.64494	−	1.64494i	0.0777161	−	0.0777161i
$449$	26.1134	+	26.1134i	1.23237	+	1.23237i	0.963052	+	0.269315i	$0.0867974\pi$
$449$	26.1134	+	26.1134i	1.23237	+	1.23237i	0.269315	+	0.963052i	$0.413203\pi$
$450$	−1.79154	−	4.66802i	−0.0844539	−	0.220052i
$451$	33.5888			1.58163
$452$			15.5998i			0.733753i
$453$	3.73539	+	3.73539i	0.175504	+	0.175504i
$454$		−	2.55431i		−	0.119880i
$455$	−25.2960	−	17.3867i	−1.18590	−	0.815100i
$456$	7.35769			0.344555
$457$			0.148390i			0.00694138i	0.999994	+	0.00347069i	$0.00110476\pi$
$457$			0.148390i			0.00694138i	−0.999994	+	0.00347069i	$0.998895\pi$
$458$		−	2.55867i		−	0.119559i
$459$	−0.509601	+	0.509601i	−0.0237861	+	0.0237861i
$460$	1.00694	+	5.43396i	0.0469490	+	0.253360i
$461$	20.8196	−	20.8196i	0.969665	−	0.969665i	−0.0298885	−	0.999553i	$-0.509515\pi$
$461$	20.8196	−	20.8196i	0.969665	−	0.969665i	0.999553	+	0.0298885i	$0.00951521\pi$
$462$	11.8604			0.551796
$463$	29.5512			1.37336			0.686681	−	0.726959i	$-0.259067\pi$
$463$	29.5512			1.37336			0.686681	+	0.726959i	$0.259067\pi$
$464$	−2.09433	+	2.09433i	−0.0972267	+	0.0972267i
$465$	−4.02777	−	21.7358i	−0.186783	−	1.00798i
$466$	−5.68879	+	5.68879i	−0.263528	+	0.263528i
$467$		−	12.6036i		−	0.583225i	−0.956537	−	0.291613i	$-0.905808\pi$
$467$		−	12.6036i		−	0.583225i	0.956537	−	0.291613i	$-0.0941918\pi$
$468$			5.90090i			0.272769i
$469$	−29.0341			−1.34067
$470$	−17.4548	−	11.9972i	−0.805128	−	0.553388i
$471$		−	23.5607i		−	1.08562i
$472$	1.31697	+	1.31697i	0.0606187	+	0.0606187i
$473$		−	53.0494i		−	2.43921i
$474$	−1.91930			−0.0881562
$475$	33.6070	+	14.9654i	1.54199	+	0.686659i
$476$	−1.18548	−	1.18548i	−0.0543365	−	0.0543365i
$477$	6.02669	−	6.02669i	0.275943	−	0.275943i
$478$	8.30333	+	8.30333i	0.379786	+	0.379786i
$479$	−0.298466	−	0.298466i	−0.0136373	−	0.0136373i	0.700255	−	0.713893i	$-0.253070\pi$
$479$	−0.298466	−	0.298466i	−0.0136373	−	0.0136373i	−0.713893	+	0.700255i	$0.753070\pi$
$480$	−1.84276	−	1.26658i	−0.0841102	−	0.0578113i
$481$	−3.86151	+	35.6855i	−0.176070	+	1.62712i
$482$	−2.03835	+	2.03835i	−0.0928442	+	0.0928442i
$483$		−	5.74947i		−	0.261610i
$484$	−14.9938			−0.681536
$485$	−13.1906	+	2.44430i	−0.598957	+	0.110990i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$			13.5324i			0.613209i	0.951837	+	0.306605i	$0.0991930\pi$
$487$			13.5324i			0.613209i	−0.951837	+	0.306605i	$0.900807\pi$
$488$	0.136297	+	0.136297i	0.00616986	+	0.00616986i
$489$	11.2241	+	11.2241i	0.507573	+	0.507573i
$490$	3.49221	−	0.647126i	0.157762	−	0.0292342i
$491$	0.261520			0.0118022			0.00590111	−	0.999983i	$-0.498122\pi$
$491$	0.261520			0.0118022			0.00590111	+	0.999983i	$0.498122\pi$
$492$	4.65848	+	4.65848i	0.210021	+	0.210021i
$493$	1.50935	+	1.50935i	0.0679776	+	0.0679776i
$494$	−30.7005	−	30.7005i	−1.38128	−	1.38128i
$495$	−2.07719	−	11.2096i	−0.0933629	−	0.503832i
$496$	−6.99049	−	6.99049i	−0.313882	−	0.313882i
$497$	1.03671	−	1.03671i	0.0465028	−	0.0465028i
$498$	−0.124116			−0.00556175
$499$	11.3438	−	11.3438i	0.507819	−	0.507819i	−0.406037	−	0.913856i	$-0.633090\pi$
$499$	11.3438	−	11.3438i	0.507819	−	0.507819i	0.913856	+	0.406037i	$0.133090\pi$
$500$	−5.84079	−	9.53337i	−0.261208	−	0.426345i
$501$	11.4126	+	11.4126i	0.509879	+	0.509879i
$502$	−18.1430	−	18.1430i	−0.809764	−	0.809764i
$503$	−40.5994			−1.81024			−0.905118	−	0.425160i	$-0.860218\pi$
$503$	−40.5994			−1.81024			−0.905118	+	0.425160i	$0.860218\pi$
$504$	1.64494	+	1.64494i	0.0732714	+	0.0732714i
$505$	1.68136	−	0.311565i	0.0748195	−	0.0138645i
$506$			12.6008i			0.560174i
$507$	15.4295	−	15.4295i	0.685250	−	0.685250i
$508$	14.2375	−	14.2375i	0.631687	−	0.631687i
$509$	19.0305			0.843513			0.421756	−	0.906709i	$-0.361414\pi$
$509$	19.0305			0.843513			0.421756	+	0.906709i	$0.361414\pi$
$510$	−0.912806	+	1.32805i	−0.0404197	+	0.0588070i
$511$		−	2.63430i		−	0.116534i
$512$	−1.00000			−0.0441942
$513$			7.35769i			0.324850i
$514$		−	13.8117i		−	0.609209i
$515$	−6.29432	+	1.16637i	−0.277361	+	0.0513965i
$516$	7.35750	−	7.35750i	0.323896	−	0.323896i
$517$	−34.1480	−	34.1480i	−1.50183	−	1.50183i
$518$	8.87127	+	11.0241i	0.389781	+	0.484373i
$519$		−	10.1628i		−	0.446098i
$520$	2.40415	+	12.9740i	0.105429	+	0.568946i
$521$		−	28.7069i		−	1.25767i	−0.777539	−	0.628835i	$-0.783532\pi$
$521$		−	28.7069i		−	1.25767i	0.777539	−	0.628835i	$-0.216468\pi$
$522$	−2.09433	−	2.09433i	−0.0916662	−	0.0916662i
$523$	19.7783			0.864845			0.432423	−	0.901671i	$-0.357659\pi$
$523$	19.7783			0.864845			0.432423	+	0.901671i	$0.357659\pi$
$524$	−9.64243	−	9.64243i	−0.421231	−	0.421231i
$525$	4.16765	+	10.8592i	0.181891	+	0.473934i
$526$	14.0744	−	14.0744i	0.613674	−	0.613674i
$527$	−5.03794	+	5.03794i	−0.219456	+	0.219456i
$528$	−3.60512	−	3.60512i	−0.156893	−	0.156893i
$529$	−16.8916			−0.734418
$530$	10.7951	−	15.7059i	0.468910	−	0.682220i
$531$	−1.31697	+	1.31697i	−0.0571518	+	0.0571518i
$532$	−17.1162			−0.742080
$533$		−	38.8757i		−	1.68389i
$534$			0.921949i			0.0398966i
$535$	19.9597	+	13.7189i	0.862934	+	0.593119i
$536$	8.82528	+	8.82528i	0.381194	+	0.381194i
$537$		−	1.80776i		−	0.0780107i
$538$		−	18.2296i		−	0.785932i
$539$	8.09807			0.348809
$540$	1.26658	−	1.84276i	0.0545050	−	0.0792998i
$541$	13.1613	−	13.1613i	0.565851	−	0.565851i	−0.365113	−	0.930963i	$-0.618970\pi$
$541$	13.1613	−	13.1613i	0.565851	−	0.565851i	0.930963	+	0.365113i	$0.118970\pi$
$542$	12.8081			0.550153
$543$	4.68991	−	4.68991i	0.201263	−	0.201263i
$544$			0.720684i			0.0308991i
$545$	2.51043	−	3.65244i	0.107535	−	0.156453i
$546$		−	13.7272i		−	0.587472i
$547$	25.1974			1.07736			0.538682	−	0.842509i	$-0.318923\pi$
$547$	25.1974			1.07736			0.538682	+	0.842509i	$0.318923\pi$
$548$	−5.63532	+	5.63532i	−0.240729	+	0.240729i
$549$	−0.136297	+	0.136297i	−0.00581700	+	0.00581700i
$550$	−9.13400	−	23.7995i	−0.389475	−	1.01481i
$551$	21.7922			0.928378
$552$	−1.74762	+	1.74762i	−0.0743838	+	0.0743838i
$553$	4.46485			0.189865
$554$	−30.4939			−1.29556
$555$	8.86550	−	10.3152i	0.376319	−	0.437855i
$556$	−18.1510			−0.769775
$557$	7.96504			0.337490			0.168745	−	0.985660i	$-0.446029\pi$
$557$	7.96504			0.337490			0.168745	+	0.985660i	$0.446029\pi$
$558$	6.99049	−	6.99049i	0.295931	−	0.295931i
$559$	−61.3994			−2.59692
$560$	4.28681	+	2.94644i	0.181151	+	0.124510i
$561$	−2.59815	+	2.59815i	−0.109694	+	0.109694i
$562$	7.94084	−	7.94084i	0.334964	−	0.334964i
$563$	−19.0142			−0.801352			−0.400676	−	0.916220i	$-0.631225\pi$
$563$	−19.0142			−0.801352			−0.400676	+	0.916220i	$0.631225\pi$
$564$		−	9.47207i		−	0.398846i
$565$	−34.2983	+	6.35567i	−1.44294	+	0.267385i
$566$		−	3.46807i		−	0.145774i
$567$	−1.64494	+	1.64494i	−0.0690809	+	0.0690809i
$568$	−0.630243			−0.0264444
$569$	−0.615232	+	0.615232i	−0.0257918	+	0.0257918i	−0.719885	−	0.694093i	$-0.755806\pi$
$569$	−0.615232	+	0.615232i	−0.0257918	+	0.0257918i	0.694093	+	0.719885i	$0.255806\pi$
$570$	2.99767	+	16.1769i	0.125559	+	0.677576i
$571$	−42.1498			−1.76391			−0.881957	−	0.471330i	$-0.843774\pi$
$571$	−42.1498			−1.76391			−0.881957	+	0.471330i	$0.843774\pi$
$572$			30.0852i			1.25793i
$573$		−	18.9791i		−	0.792863i
$574$	−10.8370	−	10.8370i	−0.452328	−	0.452328i
$575$	−11.5371	+	4.42781i	−0.481129	+	0.184652i
$576$		−	1.00000i		−	0.0416667i
$577$			7.37152i			0.306881i	0.988158	+	0.153440i	$0.0490353\pi$
$577$			7.37152i			0.306881i	−0.988158	+	0.153440i	$0.950965\pi$
$578$	−16.4806			−0.685503
$579$	6.82525	−	6.82525i	0.283648	−	0.283648i
$580$	−5.45794	−	3.75140i	−0.226628	−	0.155768i
$581$	0.288729			0.0119785
$582$	−4.24226	−	4.24226i	−0.175847	−	0.175847i
$583$	30.7265	−	30.7265i	1.27256	−	1.27256i
$584$	−0.800728	+	0.800728i	−0.0331343	+	0.0331343i
$585$	−12.9740	+	2.40415i	−0.536407	+	0.0993992i
$586$	−6.68632	−	6.68632i	−0.276209	−	0.276209i
$587$	44.0572			1.81844			0.909218	−	0.416319i	$-0.136680\pi$
$587$	44.0572			1.81844			0.909218	+	0.416319i	$0.136680\pi$
$588$	1.12313	+	1.12313i	0.0463173	+	0.0463173i
$589$			72.7385i			2.99714i
$590$	−2.35899	+	3.43211i	−0.0971180	+	0.141298i
$591$		−	2.67112i		−	0.109875i
$592$	0.654393	−	6.04746i	0.0268954	−	0.248549i
$593$	−4.89452	−	4.89452i	−0.200994	−	0.200994i	0.599432	−	0.800426i	$-0.295393\pi$
$593$	−4.89452	−	4.89452i	−0.200994	−	0.200994i	−0.800426	+	0.599432i	$0.795393\pi$
$594$	3.60512	−	3.60512i	0.147920	−	0.147920i
$595$	2.12346	−	3.08943i	0.0870532	−	0.126654i
$596$		−	19.7092i		−	0.807322i
$597$		−	7.61886i		−	0.311819i
$598$	14.5842			0.596391
$599$			34.6454i			1.41557i	0.706427	+	0.707785i	$0.250306\pi$
$599$			34.6454i			1.41557i	−0.706427	+	0.707785i	$0.749694\pi$
$600$	2.03398	−	4.56760i	0.0830368	−	0.186471i
$601$	−3.11150			−0.126921			−0.0634604	−	0.997984i	$-0.520214\pi$
$601$	−3.11150			−0.126921			−0.0634604	+	0.997984i	$0.520214\pi$
$602$	−17.1157	+	17.1157i	−0.697585	+	0.697585i
$603$	−8.82528	+	8.82528i	−0.359393	+	0.359393i
$604$			5.28263i			0.214947i
$605$	−6.10877	−	32.9659i	−0.248357	−	1.34026i
$606$	0.540744	+	0.540744i	0.0219662	+	0.0219662i
$607$	−38.6760			−1.56981			−0.784906	−	0.619615i	$-0.787289\pi$
$607$	−38.6760			−1.56981			−0.784906	+	0.619615i	$0.787289\pi$
$608$	5.20267	+	5.20267i	0.210996	+	0.210996i
$609$	4.87202	+	4.87202i	0.197424	+	0.197424i
$610$	−0.244137	+	0.355197i	−0.00988482	+	0.0143815i
$611$	−39.5229	+	39.5229i	−1.59892	+	1.59892i
$612$	−0.720684			−0.0291319
$613$	−19.7218	+	19.7218i	−0.796557	+	0.796557i	−0.982551	−	0.185994i	$-0.940449\pi$
$613$	−19.7218	+	19.7218i	−0.796557	+	0.796557i	0.185994	+	0.982551i	$0.440449\pi$
$614$	24.0972	+	24.0972i	0.972485	+	0.972485i
$615$	−8.34436	+	12.1403i	−0.336477	+	0.489543i
$616$	8.38658	+	8.38658i	0.337905	+	0.337905i
$617$	23.5004	+	23.5004i	0.946091	+	0.946091i	0.998619	−	0.0525282i	$-0.0167280\pi$
$617$	23.5004	+	23.5004i	0.946091	+	0.946091i	−0.0525282	+	0.998619i	$0.516728\pi$
$618$	−2.02432	−	2.02432i	−0.0814303	−	0.0814303i
$619$	31.4805			1.26531			0.632654	−	0.774434i	$-0.281965\pi$
$619$	31.4805			1.26531			0.632654	+	0.774434i	$0.281965\pi$
$620$	12.5215	−	18.2176i	0.502875	−	0.731637i
$621$	−1.74762	−	1.74762i	−0.0701297	−	0.0701297i
$622$	−7.00421	−	7.00421i	−0.280843	−	0.280843i
$623$		−	2.14473i		−	0.0859266i
$624$	−4.17257	+	4.17257i	−0.167036	+	0.167036i
$625$	18.5808	−	16.7259i	0.743231	−	0.669034i
$626$	−0.610621			−0.0244053
$627$			37.5125i			1.49811i
$628$	16.6599	−	16.6599i	0.664803	−	0.664803i
$629$	−4.35831	−	0.471611i	−0.173777	−	0.0188044i
$630$	−2.94644	+	4.28681i	−0.117389	+	0.170790i
$631$	23.3413	+	23.3413i	0.929204	+	0.929204i	0.997654	−	0.0684508i	$-0.0218056\pi$
$631$	23.3413	+	23.3413i	0.929204	+	0.929204i	−0.0684508	+	0.997654i	$0.521806\pi$
$632$	−1.35715	−	1.35715i	−0.0539844	−	0.0539844i
$633$	−1.90946	+	1.90946i	−0.0758942	+	0.0758942i
$634$	−13.6669	−	13.6669i	−0.542781	−	0.542781i
$635$	37.1038	+	25.5025i	1.47242	+	1.01204i
$636$	8.52302			0.337960
$637$		−	9.37271i		−	0.371360i
$638$	−10.6777	−	10.6777i	−0.422736	−	0.422736i
$639$		−	0.630243i		−	0.0249320i
$640$	−0.407420	−	2.19864i	−0.0161047	−	0.0869088i
$641$	9.30102			0.367368			0.183684	−	0.982985i	$-0.441198\pi$
$641$	9.30102			0.367368			0.183684	+	0.982985i	$0.441198\pi$
$642$			10.8314i			0.427482i
$643$			17.5936i			0.693823i	0.937898	+	0.346911i	$0.112770\pi$
$643$			17.5936i			0.693823i	−0.937898	+	0.346911i	$0.887230\pi$
$644$	4.06549	−	4.06549i	0.160203	−	0.160203i
$645$	19.1741	+	13.1789i	0.754979	+	0.518919i
$646$	3.74948	−	3.74948i	0.147521	−	0.147521i
$647$	−38.2288			−1.50293			−0.751466	−	0.659772i	$-0.770653\pi$
$647$	−38.2288			−1.50293			−0.751466	+	0.659772i	$0.770653\pi$
$648$	1.00000			0.0392837
$649$	−6.71448	+	6.71448i	−0.263566	+	0.263566i
$650$	−27.5455	+	10.5717i	−1.08042	+	0.414656i
$651$	−16.2619	+	16.2619i	−0.637356	+	0.637356i
$652$			15.8733i			0.621648i
$653$		−	2.43786i		−	0.0954008i	−0.998862	−	0.0477004i	$-0.984811\pi$
$653$		−	2.43786i		−	0.0954008i	0.998862	−	0.0477004i	$-0.0151893\pi$
$654$	1.98205			0.0775041
$655$	17.2717	−	25.1287i	0.674861	−	0.981861i
$656$			6.58809i			0.257222i
$657$	−0.800728	−	0.800728i	−0.0312394	−	0.0312394i
$658$			22.0348i			0.859007i
$659$	−10.7505			−0.418779			−0.209390	−	0.977832i	$-0.567148\pi$
$659$	−10.7505			−0.418779			−0.209390	+	0.977832i	$0.567148\pi$
$660$	6.45756	−	9.39515i	0.251360	−	0.365706i
$661$	−28.1910	−	28.1910i	−1.09650	−	1.09650i	−0.994817	−	0.101686i	$-0.967576\pi$
$661$	−28.1910	−	28.1910i	−1.09650	−	1.09650i	−0.101686	−	0.994817i	$-0.532424\pi$
$662$	4.46154	−	4.46154i	0.173403	−	0.173403i
$663$	3.00711	+	3.00711i	0.116786	+	0.116786i
$664$	−0.0877629	−	0.0877629i	−0.00340586	−	0.00340586i
$665$	−6.97346	−	37.6322i	−0.270419	−	1.45932i
$666$	6.04746	+	0.654393i	0.234334	+	0.0253572i
$667$	−5.17616	+	5.17616i	−0.200422	+	0.200422i
$668$			16.1399i			0.624471i
$669$	1.18359			0.0457603
$670$	−15.8080	+	22.9992i	−0.610717	+	0.888537i
$671$	−0.694897	+	0.694897i	−0.0268262	+	0.0268262i
$672$			2.32629i			0.0897388i
$673$	−9.84759	−	9.84759i	−0.379597	−	0.379597i	0.491360	−	0.870957i	$-0.336500\pi$
$673$	−9.84759	−	9.84759i	−0.379597	−	0.379597i	−0.870957	+	0.491360i	$0.836500\pi$
$674$	−0.254872	−	0.254872i	−0.00981731	−	0.00981731i
$675$	4.56760	+	2.03398i	0.175807	+	0.0782879i
$676$	21.8207			0.839257
$677$	−2.68587	−	2.68587i	−0.103226	−	0.103226i	0.653607	−	0.756834i	$-0.273255\pi$
$677$	−2.68587	−	2.68587i	−0.103226	−	0.103226i	−0.756834	+	0.653607i	$0.773255\pi$
$678$	−11.0307	−	11.0307i	−0.423632	−	0.423632i
$679$	9.86875	+	9.86875i	0.378728	+	0.378728i
$680$	−1.58452	+	0.293621i	−0.0607637	+	0.0112599i
$681$	1.80617	+	1.80617i	0.0692125	+	0.0692125i
$682$	35.6404	−	35.6404i	1.36474	−	1.36474i
$683$	−21.4016			−0.818910			−0.409455	−	0.912330i	$-0.634281\pi$
$683$	−21.4016			−0.818910			−0.409455	+	0.912330i	$0.634281\pi$
$684$	−5.20267	+	5.20267i	−0.198929	+	0.198929i
$685$	−14.6860	−	10.0941i	−0.561123	−	0.385676i
$686$	−14.1273	−	14.1273i	−0.539383	−	0.539383i
$687$	1.80926	+	1.80926i	0.0690274	+	0.0690274i
$688$	10.4051			0.396690
$689$	−35.5629	−	35.5629i	−1.35484	−	1.35484i
$690$	−4.55441	−	3.13038i	−0.173383	−	0.119171i
$691$		−	2.78114i		−	0.105800i	−0.998600	−	0.0528998i	$-0.983154\pi$
$691$		−	2.78114i		−	0.105800i	0.998600	−	0.0528998i	$-0.0168464\pi$
$692$	7.18619	−	7.18619i	0.273178	−	0.273178i
$693$	−8.38658	+	8.38658i	−0.318580	+	0.318580i
$694$	28.6170			1.08629
$695$	−7.39509	−	39.9075i	−0.280512	−	1.51378i
$696$		−	2.96182i		−	0.112268i
$697$	4.74793			0.179841
$698$			15.9860i			0.605078i
$699$		−	8.04517i		−	0.304296i
$700$	−4.73163	+	10.6256i	−0.178839	+	0.401609i
$701$	−0.336016	+	0.336016i	−0.0126911	+	0.0126911i	−0.713424	−	0.700733i	$-0.752857\pi$
$701$	−0.336016	+	0.336016i	−0.0126911	+	0.0126911i	0.700733	+	0.713424i	$0.252857\pi$
$702$	−4.17257	−	4.17257i	−0.157484	−	0.157484i
$703$	−34.8675	+	28.0584i	−1.31505	+	1.05824i
$704$		−	5.09841i		−	0.192154i
$705$	20.8257	−	3.85911i	0.784339	−	0.145342i
$706$			16.4429i			0.618839i
$707$	−1.25793	−	1.25793i	−0.0473093	−	0.0473093i
$708$	−1.86248			−0.0699964
$709$	−34.2461	−	34.2461i	−1.28614	−	1.28614i	−0.937114	−	0.349024i	$-0.886513\pi$
$709$	−34.2461	−	34.2461i	−1.28614	−	1.28614i	−0.349024	−	0.937114i	$-0.613487\pi$
$710$	−0.256774	−	1.38568i	−0.00963654	−	0.0520035i
$711$	1.35715	−	1.35715i	0.0508970	−	0.0508970i
$712$	−0.651916	+	0.651916i	−0.0244316	+	0.0244316i
$713$	−17.2771	−	17.2771i	−0.647032	−	0.647032i
$714$	1.67652			0.0627423
$715$	−66.1466	+	12.2573i	−2.47374	+	0.458398i
$716$	1.27828	−	1.27828i	0.0477716	−	0.0477716i
$717$	−11.7427			−0.438539
$718$			17.3539i			0.647642i
$719$		−	7.34855i		−	0.274055i	−0.990567	−	0.137027i	$-0.956245\pi$
$719$		−	7.34855i		−	0.274055i	0.990567	−	0.137027i	$-0.0437548\pi$
$720$	2.19864	−	0.407420i	0.0819384	−	0.0151836i
$721$	4.70918	+	4.70918i	0.175379	+	0.175379i
$722$		−	35.1356i		−	1.30761i
$723$		−	2.88266i		−	0.107207i
$724$	6.63253			0.246496
$725$	6.02429	−	13.5284i	0.223736	−	0.502433i
$726$	10.6022	−	10.6022i	0.393485	−	0.393485i
$727$	46.5833			1.72768			0.863839	−	0.503768i	$-0.168053\pi$
$727$	46.5833			1.72768			0.863839	+	0.503768i	$0.168053\pi$
$728$	9.70663	−	9.70663i	0.359752	−	0.359752i
$729$			1.00000i			0.0370370i
$730$	−2.08674	−	1.43428i	−0.0772338	−	0.0530850i
$731$		−	7.49878i		−	0.277352i
$732$	−0.192753			−0.00712434
$733$	12.4565	−	12.4565i	0.460092	−	0.460092i	−0.438594	−	0.898685i	$-0.644523\pi$
$733$	12.4565	−	12.4565i	0.460092	−	0.460092i	0.898685	+	0.438594i	$0.144523\pi$
$734$	9.80219	−	9.80219i	0.361805	−	0.361805i
$735$	−2.01178	+	2.92695i	−0.0742056	+	0.107962i
$736$	−2.47151			−0.0911012
$737$	−44.9949	+	44.9949i	−1.65741	+	1.65741i
$738$	−6.58809			−0.242511
$739$	−27.0728			−0.995889			−0.497945	−	0.867209i	$-0.665912\pi$
$739$	−27.0728			−0.995889			−0.497945	+	0.867209i	$0.665912\pi$
$740$	13.5628	−	1.02508i	0.498578	−	0.0376828i
$741$	43.4170			1.59496
$742$	−19.8271			−0.727874
$743$	−21.9556	+	21.9556i	−0.805471	+	0.805471i	−0.983945	−	0.178474i	$-0.942884\pi$
$743$	−21.9556	+	21.9556i	−0.805471	+	0.805471i	0.178474	+	0.983945i	$0.442884\pi$
$744$	9.88605			0.362440
$745$	43.3335	−	8.02993i	1.58762	−	0.294194i
$746$	1.82136	−	1.82136i	0.0666846	−	0.0666846i
$747$	0.0877629	−	0.0877629i	0.00321108	−	0.00321108i
$748$	−3.67435			−0.134347
$749$		−	25.1971i		−	0.920682i
$750$	10.8712	+	2.61105i	0.396959	+	0.0953422i
$751$		−	8.35224i		−	0.304778i	−0.988321	−	0.152389i	$-0.951303\pi$
$751$		−	8.35224i		−	0.304778i	0.988321	−	0.152389i	$-0.0486966\pi$
$752$	6.69776	−	6.69776i	0.244242	−	0.244242i
$753$	25.6581			0.935035
$754$	−12.3584	+	12.3584i	−0.450067	+	0.450067i
$755$	−11.6146	+	2.15225i	−0.422698	+	0.0783284i
$756$	−2.32629			−0.0846065
$757$		−	6.78896i		−	0.246749i	−0.992360	−	0.123374i	$-0.960628\pi$
$757$		−	6.78896i		−	0.246749i	0.992360	−	0.123374i	$-0.0393716\pi$
$758$		−	23.5189i		−	0.854244i
$759$	−8.91011	−	8.91011i	−0.323416	−	0.323416i
$760$	−9.31912	+	13.5585i	−0.338040	+	0.491817i
$761$		−	11.1352i		−	0.403651i	−0.979421	−	0.201826i	$-0.935313\pi$
$761$		−	11.1352i		−	0.403651i	0.979421	−	0.201826i	$-0.0646874\pi$
$762$			20.1349i			0.729410i
$763$	−4.61082			−0.166923
$764$	13.4202	−	13.4202i	0.485527	−	0.485527i
$765$	−0.293621	−	1.58452i	−0.0106159	−	0.0572886i
$766$	31.0387			1.12147
$767$	7.77134	+	7.77134i	0.280607	+	0.280607i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−26.8144	+	26.8144i	−0.966950	+	0.966950i	−0.999471	−	0.0325207i	$-0.989647\pi$
$769$	−26.8144	+	26.8144i	−0.966950	+	0.966950i	0.0325207	+	0.999471i	$0.489647\pi$
$770$	−15.0222	+	21.8559i	−0.541362	+	0.787632i
$771$	9.76637	+	9.76637i	0.351727	+	0.351727i
$772$	9.65236			0.347396
$773$	25.7542	+	25.7542i	0.926315	+	0.926315i	0.997466	−	0.0711506i	$-0.0226671\pi$
$773$	25.7542	+	25.7542i	0.926315	+	0.926315i	−0.0711506	+	0.997466i	$0.522667\pi$
$774$			10.4051i			0.374003i
$775$	45.1555	+	20.1080i	1.62203	+	0.722301i
$776$		−	5.99946i		−	0.215368i
$777$	−14.0682	−	1.52231i	−0.504693	−	0.0546126i
$778$	−23.1210	−	23.1210i	−0.828927	−	0.828927i
$779$	34.2757	−	34.2757i	1.22805	−	1.22805i
$780$	−10.8740	−	7.47398i	−0.389350	−	0.267611i
$781$		−	3.21324i		−	0.114979i
$782$			1.78118i			0.0636949i
$783$	2.96182			0.105847
$784$			1.58835i			0.0567269i
$785$	43.4167	+	29.8415i	1.54961	+	1.06509i
$786$	13.6365			0.486396
$787$	30.8842	−	30.8842i	1.10090	−	1.10090i	0.106601	−	0.994302i	$-0.466003\pi$
$787$	30.8842	−	30.8842i	1.10090	−	1.10090i	0.994302	−	0.106601i	$-0.0339967\pi$
$788$	1.88877	−	1.88877i	0.0672846	−	0.0672846i
$789$			19.9043i			0.708610i
$790$	2.43095	−	3.53681i	0.0864892	−	0.125834i
$791$	25.6607	+	25.6607i	0.912390	+	0.912390i
$792$	5.09841			0.181164
$793$	0.804274	+	0.804274i	0.0285606	+	0.0285606i
$794$	6.35301	+	6.35301i	0.225460	+	0.225460i
$795$	3.47245	+	18.7390i	0.123155	+	0.664605i
$796$	5.38735	−	5.38735i	0.190949	−	0.190949i
$797$	−39.3542			−1.39400			−0.696998	−	0.717073i	$-0.745481\pi$
$797$	−39.3542			−1.39400			−0.696998	+	0.717073i	$0.745481\pi$
$798$	12.1030	−	12.1030i	0.428440	−	0.428440i
$799$	−4.82697	−	4.82697i	−0.170766	−	0.170766i
$800$	4.66802	−	1.79154i	0.165039	−	0.0633404i
$801$	−0.651916	−	0.651916i	−0.0230343	−	0.0230343i
$802$	23.0255	+	23.0255i	0.813059	+	0.813059i
$803$	−4.08244	−	4.08244i	−0.144066	−	0.144066i
$804$	−12.4808			−0.440165
$805$	10.5949	+	7.28218i	0.373421	+	0.256663i
$806$	−41.2502	−	41.2502i	−1.45298	−	1.45298i
$807$	12.8902	+	12.8902i	0.453758	+	0.453758i
$808$			0.764728i			0.0269030i
$809$	−13.8822	+	13.8822i	−0.488072	+	0.488072i	−0.907697	−	0.419626i	$-0.862161\pi$
$809$	−13.8822	+	13.8822i	−0.488072	+	0.488072i	0.419626	+	0.907697i	$0.362161\pi$
$810$	0.407420	+	2.19864i	0.0143153	+	0.0772523i
$811$	−28.3944			−0.997061			−0.498530	−	0.866872i	$-0.666127\pi$
$811$	−28.3944			−0.997061			−0.498530	+	0.866872i	$0.666127\pi$
$812$			6.89008i			0.241794i
$813$	−9.05666	+	9.05666i	−0.317631	+	0.317631i
$814$	30.8324	+	3.33637i	1.08068	+	0.116940i
$815$	−34.8997	+	6.46711i	−1.22248	+	0.226533i
$816$	−0.509601	−	0.509601i	−0.0178396	−	0.0178396i
$817$	−54.1342	−	54.1342i	−1.89392	−	1.89392i
$818$	−2.34868	+	2.34868i	−0.0821196	+	0.0821196i
$819$	9.70663	+	9.70663i	0.339177	+	0.339177i
$820$	−14.4848	+	2.68412i	−0.505832	+	0.0937335i
$821$	32.3278			1.12825			0.564124	−	0.825690i	$-0.309214\pi$
$821$	32.3278			1.12825			0.564124	+	0.825690i	$0.309214\pi$
$822$		−	7.96955i		−	0.277970i
$823$	30.8079	+	30.8079i	1.07390	+	1.07390i	0.997042	+	0.0768541i	$0.0244876\pi$
$823$	30.8079	+	30.8079i	1.07390	+	1.07390i	0.0768541	+	0.997042i	$0.475512\pi$
$824$		−	2.86283i		−	0.0997313i
$825$	23.2875	+	10.3701i	0.810766	+	0.361039i
$826$	4.33269			0.150753
$827$		−	7.86712i		−	0.273567i	−0.990601	−	0.136783i	$-0.956324\pi$
$827$		−	7.86712i		−	0.273567i	0.990601	−	0.136783i	$-0.0436764\pi$
$828$		−	2.47151i		−	0.0858910i
$829$	32.7613	−	32.7613i	1.13785	−	1.13785i	0.149011	−	0.988836i	$-0.452391\pi$
$829$	32.7613	−	32.7613i	1.13785	−	1.13785i	0.988836	−	0.149011i	$-0.0476088\pi$
$830$	0.157203	−	0.228715i	0.00545658	−	0.00793882i
$831$	21.5624	−	21.5624i	0.747992	−	0.747992i
$832$	−5.90090			−0.204577
$833$	1.14470			0.0396615
$834$	12.8347	−	12.8347i	0.444430	−	0.444430i
$835$	−35.4858	+	6.57572i	−1.22804	+	0.227562i
$836$	−26.5254	+	26.5254i	−0.917399	+	0.917399i
$837$			9.88605i			0.341712i
$838$		−	11.9631i		−	0.413257i
$839$	10.9095			0.376639			0.188320	−	0.982108i	$-0.439696\pi$
$839$	10.9095			0.376639			0.188320	+	0.982108i	$0.439696\pi$
$840$	−5.11468	+	0.947779i	−0.176473	+	0.0327015i
$841$			20.2276i			0.697503i
$842$	18.2560	+	18.2560i	0.629144	+	0.629144i
$843$			11.2300i			0.386783i
$844$	−2.70038			−0.0929510
$845$	8.89018	+	47.9758i	0.305831	+	1.65042i
$846$	6.69776	+	6.69776i	0.230274	+	0.230274i
$847$	−24.6639	+	24.6639i	−0.847461	+	0.847461i
$848$	6.02669	+	6.02669i	0.206957	+	0.206957i
$849$	2.45229	+	2.45229i	0.0841625	+	0.0841625i
$850$	−1.29113	−	3.36417i	−0.0442855	−	0.115390i
$851$	1.61734	−	14.9464i	0.0554418	−	0.512355i
$852$	0.445649	−	0.445649i	0.0152677	−	0.0152677i
$853$			10.6249i			0.363791i	0.983318	+	0.181895i	$0.0582232\pi$
$853$			10.6249i			0.363791i	−0.983318	+	0.181895i	$0.941777\pi$
$854$	0.448399			0.0153439
$855$	−13.5585	−	9.31912i	−0.463690	−	0.318707i
$856$	−7.65897	+	7.65897i	−0.261778	+	0.261778i
$857$			46.1841i			1.57762i	0.614639	+	0.788809i	$0.289302\pi$
$857$			46.1841i			1.57762i	−0.614639	+	0.788809i	$0.710698\pi$
$858$	−21.2735	−	21.2735i	−0.726265	−	0.726265i
$859$	2.85826	+	2.85826i	0.0975227	+	0.0975227i	0.754185	−	0.656662i	$-0.228032\pi$
$859$	2.85826	+	2.85826i	0.0975227	+	0.0975227i	−0.656662	+	0.754185i	$0.728032\pi$
$860$	4.23924	+	22.8770i	0.144557	+	0.780100i
$861$	15.3258			0.522303
$862$	13.3451	+	13.3451i	0.454536	+	0.454536i
$863$	14.1450	+	14.1450i	0.481501	+	0.481501i	0.905611	−	0.424110i	$-0.139413\pi$
$863$	14.1450	+	14.1450i	0.481501	+	0.481501i	−0.424110	+	0.905611i	$0.639413\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	18.7276	+	12.8720i	0.636759	+	0.437662i
$866$	12.4634	+	12.4634i	0.423523	+	0.423523i
$867$	11.6536	−	11.6536i	0.395775	−	0.395775i
$868$	−22.9979			−0.780598
$869$	6.91930	−	6.91930i	0.234721	−	0.234721i
$870$	6.51198	−	1.20671i	0.220777	−	0.0409112i
$871$	52.0772	+	52.0772i	1.76457	+	1.76457i
$872$	1.40152	+	1.40152i	0.0474614	+	0.0474614i
$873$	5.99946			0.203051
$874$	12.8585	+	12.8585i	0.434944	+	0.434944i
$875$	−25.2896	−	6.07408i	−0.854943	−	0.205341i
$876$		−	1.13240i		−	0.0382602i
$877$	7.98772	−	7.98772i	0.269726	−	0.269726i	−0.559264	−	0.828990i	$-0.688916\pi$
$877$	7.98772	−	7.98772i	0.269726	−	0.269726i	0.828990	+	0.559264i	$0.188916\pi$
$878$	−24.4496	+	24.4496i	−0.825134	+	0.825134i
$879$	9.45589			0.318939
$880$	11.2096	−	2.07719i	0.377874	−	0.0700222i
$881$		−	18.1937i		−	0.612961i	−0.951877	−	0.306480i	$-0.900849\pi$
$881$		−	18.1937i		−	0.612961i	0.951877	−	0.306480i	$-0.0991514\pi$
$882$	−1.58835			−0.0534826
$883$		−	35.7275i		−	1.20233i	−0.799126	−	0.601164i	$-0.794704\pi$
$883$		−	35.7275i		−	1.20233i	0.799126	−	0.601164i	$-0.205296\pi$
$884$			4.25269i			0.143033i
$885$	−0.758813	−	4.09493i	−0.0255072	−	0.137649i
$886$	−19.6237	+	19.6237i	−0.659272	+	0.659272i
$887$	11.6967	+	11.6967i	0.392735	+	0.392735i	0.875661	−	0.482926i	$-0.160426\pi$
$887$	11.6967	+	11.6967i	0.392735	+	0.392735i	−0.482926	+	0.875661i	$0.660426\pi$
$888$	3.81347	+	4.73893i	0.127972	+	0.159028i
$889$		−	46.8397i		−	1.57095i
$890$	−1.69893	−	1.16772i	−0.0569483	−	0.0391422i
$891$			5.09841i			0.170803i
$892$	0.836925	+	0.836925i	0.0280223	+	0.0280223i
$893$	−69.6925			−2.33217
$894$	13.9365	+	13.9365i	0.466107	+	0.466107i
$895$	3.33127	+	2.28968i	0.111352	+	0.0765356i
$896$	−1.64494	+	1.64494i	−0.0549536	+	0.0549536i
$897$	−10.3126	+	10.3126i	−0.344327	+	0.344327i
$898$	−26.1134	−	26.1134i	−0.871415	−	0.871415i
$899$	29.2807			0.976567
$900$	1.79154	+	4.66802i	0.0597179	+	0.155601i
$901$	4.34334	−	4.34334i	0.144698	−	0.144698i
$902$	−33.5888			−1.11838
$903$		−	24.2053i		−	0.805502i
$904$		−	15.5998i		−	0.518842i
$905$	2.70222	+	14.5825i	0.0898250	+	0.484740i
$906$	−3.73539	−	3.73539i	−0.124100	−	0.124100i
$907$			11.6158i			0.385697i	0.981229	+	0.192848i	$0.0617726\pi$
$907$			11.6158i			0.385697i	−0.981229	+	0.192848i	$0.938227\pi$
$908$			2.55431i			0.0847677i
$909$	−0.764728			−0.0253644
$910$	25.2960	+	17.3867i	0.838555	+	0.576363i
$911$	−25.8802	+	25.8802i	−0.857449	+	0.857449i	−0.991037	−	0.133588i	$-0.957350\pi$
$911$	−25.8802	+	25.8802i	−0.857449	+	0.857449i	0.133588	+	0.991037i	$0.457350\pi$
$912$	−7.35769			−0.243637
$913$	0.447452	−	0.447452i	0.0148085	−	0.0148085i
$914$		−	0.148390i		−	0.00490830i
$915$	−0.0785313	−	0.423793i	−0.00259616	−	0.0140102i
$916$			2.55867i			0.0845409i
$917$	−31.7224			−1.04757
$918$	0.509601	−	0.509601i	0.0168193	−	0.0168193i
$919$	32.1526	−	32.1526i	1.06062	−	1.06062i	0.0625766	−	0.998040i	$-0.480068\pi$
$919$	32.1526	−	32.1526i	1.06062	−	1.06062i	0.998040	−	0.0625766i	$-0.0199318\pi$
$920$	−1.00694	−	5.43396i	−0.0331980	−	0.179153i
$921$	−34.0786			−1.12293
$922$	−20.8196	+	20.8196i	−0.685657	+	0.685657i
$923$	−3.71900			−0.122412
$924$	−11.8604			−0.390179
$925$	7.77953	+	29.4020i	0.255790	+	0.966732i
$926$	−29.5512			−0.971114
$927$	2.86283			0.0940276
$928$	2.09433	−	2.09433i	0.0687496	−	0.0687496i
$929$	−21.7314			−0.712984			−0.356492	−	0.934298i	$-0.616027\pi$
$929$	−21.7314			−0.712984			−0.356492	+	0.934298i	$0.616027\pi$
$930$	4.02777	+	21.7358i	0.132076	+	0.712746i
$931$	8.26368	−	8.26368i	0.270831	−	0.270831i
$932$	5.68879	−	5.68879i	0.186343	−	0.186343i
$933$	9.90544			0.324290
$934$			12.6036i			0.412402i
$935$	−1.49700	−	8.07855i	−0.0489572	−	0.264197i
$936$		−	5.90090i		−	0.192877i
$937$	−0.780889	+	0.780889i	−0.0255105	+	0.0255105i	−0.719747	−	0.694236i	$-0.755742\pi$
$937$	−0.780889	+	0.780889i	−0.0255105	+	0.0255105i	0.694236	+	0.719747i	$0.255742\pi$
$938$	29.0341			0.947997
$939$	0.431774	−	0.431774i	0.0140904	−	0.0140904i
$940$	17.4548	+	11.9972i	0.569312	+	0.391304i
$941$	17.4265			0.568089			0.284045	−	0.958811i	$-0.408324\pi$
$941$	17.4265			0.568089			0.284045	+	0.958811i	$0.408324\pi$
$942$			23.5607i			0.767648i
$943$			16.2826i			0.530233i
$944$	−1.31697	−	1.31697i	−0.0428639	−	0.0428639i
$945$	−0.947779	−	5.11468i	−0.0308313	−	0.166381i
$946$			53.0494i			1.72478i
$947$		−	22.4456i		−	0.729383i	−0.931128	−	0.364691i	$-0.881175\pi$
$947$		−	22.4456i		−	0.729383i	0.931128	−	0.364691i	$-0.118825\pi$
$948$	1.91930			0.0623359
$949$	−4.72502	+	4.72502i	−0.153381	+	0.153381i
$950$	−33.6070	−	14.9654i	−1.09035	−	0.485541i
$951$	19.3279			0.626749
$952$	1.18548	+	1.18548i	0.0384217	+	0.0384217i
$953$	16.5339	−	16.5339i	0.535586	−	0.535586i	−0.386643	−	0.922229i	$-0.626366\pi$
$953$	16.5339	−	16.5339i	0.535586	−	0.535586i	0.922229	+	0.386643i	$0.126366\pi$
$954$	−6.02669	+	6.02669i	−0.195121	+	0.195121i
$955$	34.9739	+	24.0386i	1.13173	+	0.777870i
$956$	−8.30333	−	8.30333i	−0.268549	−	0.268549i
$957$	15.1006			0.488133
$958$	0.298466	+	0.298466i	0.00964299	+	0.00964299i
$959$			18.5395i			0.598673i
$960$	1.84276	+	1.26658i	0.0594749	+	0.0408788i
$961$			66.7339i			2.15271i
$962$	3.86151	−	35.6855i	0.124500	−	1.15055i
$963$	−7.65897	−	7.65897i	−0.246807	−	0.246807i
$964$	2.03835	−	2.03835i	0.0656508	−	0.0656508i
$965$	3.93256	+	21.2220i	0.126594	+	0.683162i
$966$			5.74947i			0.184986i
$967$		−	38.9960i		−	1.25403i	−0.779008	−	0.627014i	$-0.784277\pi$
$967$		−	38.9960i		−	1.25403i	0.779008	−	0.627014i	$-0.215723\pi$
$968$	14.9938			0.481919
$969$			5.30257i			0.170343i
$970$	13.1906	−	2.44430i	0.423526	−	0.0784818i
$971$	−1.85210			−0.0594368			−0.0297184	−	0.999558i	$-0.509461\pi$
$971$	−1.85210			−0.0594368			−0.0297184	+	0.999558i	$0.509461\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−29.8573	+	29.8573i	−0.957182	+	0.957182i
$974$		−	13.5324i		−	0.433605i
$975$	12.0023	−	26.9529i	0.384382	−	0.863185i
$976$	−0.136297	−	0.136297i	−0.00436275	−	0.00436275i
$977$	48.1560			1.54065			0.770323	−	0.637654i	$-0.220095\pi$
$977$	48.1560			1.54065			0.770323	+	0.637654i	$0.220095\pi$
$978$	−11.2241	−	11.2241i	−0.358909	−	0.358909i
$979$	−3.32374	−	3.32374i	−0.106227	−	0.106227i
$980$	−3.49221	+	0.647126i	−0.111555	+	0.0206717i
$981$	−1.40152	+	1.40152i	−0.0447470	+	0.0447470i
$982$	−0.261520			−0.00834544
$983$	1.15966	−	1.15966i	0.0369873	−	0.0369873i	−0.688371	−	0.725359i	$-0.741674\pi$
$983$	1.15966	−	1.15966i	0.0369873	−	0.0369873i	0.725359	+	0.688371i	$0.241674\pi$
$984$	−4.65848	−	4.65848i	−0.148507	−	0.148507i
$985$	4.92224	+	3.38319i	0.156836	+	0.107798i
$986$	−1.50935	−	1.50935i	−0.0480674	−	0.0480674i
$987$	−15.5810	−	15.5810i	−0.495948	−	0.495948i
$988$	30.7005	+	30.7005i	0.976712	+	0.976712i
$989$	25.7163			0.817731
$990$	2.07719	+	11.2096i	0.0660176	+	0.356263i
$991$	−40.0639	−	40.0639i	−1.27267	−	1.27267i	−0.944680	−	0.327993i	$-0.893628\pi$
$991$	−40.0639	−	40.0639i	−1.27267	−	1.27267i	−0.327993	−	0.944680i	$-0.606372\pi$
$992$	6.99049	+	6.99049i	0.221948	+	0.221948i
$993$			6.30957i			0.200228i
$994$	−1.03671	+	1.03671i	−0.0328825	+	0.0328825i
$995$	14.0397	+	9.64991i	0.445089	+	0.305923i
$996$	0.124116			0.00393275
$997$		−	31.5835i		−	1.00026i	−0.865951	−	0.500129i	$-0.833286\pi$
$997$		−	31.5835i		−	1.00026i	0.865951	−	0.500129i	$-0.166714\pi$
$998$	−11.3438	+	11.3438i	−0.359082	+	0.359082i
$999$	−4.73893	+	3.81347i	−0.149933	+	0.120653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.253.12	yes	36
5.2	odd	4		1110.2.l.a.697.7	yes	36
37.6	odd	4		1110.2.l.a.43.7	✓	36
185.117	even	4	inner	1110.2.o.a.487.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.7	✓	36	37.6	odd	4
1110.2.l.a.697.7	yes	36	5.2	odd	4
1110.2.o.a.253.12	yes	36	1.1	even	1	trivial
1110.2.o.a.487.12	yes	36	185.117	even	4	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.407420 + 2.19864i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.64494 - 1.64494i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(0.407420 + 2.19864i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(1.64494 - 1.64494i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(-0.407420 - 2.19864i) q^{10} -5.09841i q^{11} +(0.707107 - 0.707107i) q^{12} -5.90090 q^{13} +(-1.64494 + 1.64494i) q^{14} +(1.84276 + 1.26658i) q^{15} +1.00000 q^{16} -0.720684i q^{17} +1.00000i q^{18} +(-5.20267 - 5.20267i) q^{19} +(0.407420 + 2.19864i) q^{20} -2.32629i q^{21} +5.09841i q^{22} +2.47151 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.66802 + 1.79154i) q^{25} +5.90090 q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.64494 - 1.64494i) q^{28} +(-2.09433 + 2.09433i) q^{29} +(-1.84276 - 1.26658i) q^{30} +(-6.99049 - 6.99049i) q^{31} -1.00000 q^{32} +(-3.60512 - 3.60512i) q^{33} +0.720684i q^{34} +(4.28681 + 2.94644i) q^{35} -1.00000i q^{36} +(0.654393 - 6.04746i) q^{37} +(5.20267 + 5.20267i) q^{38} +(-4.17257 + 4.17257i) q^{39} +(-0.407420 - 2.19864i) q^{40} +6.58809i q^{41} +2.32629i q^{42} +10.4051 q^{43} -5.09841i q^{44} +(2.19864 - 0.407420i) q^{45} -2.47151 q^{46} +(6.69776 - 6.69776i) q^{47} +(0.707107 - 0.707107i) q^{48} +1.58835i q^{49} +(4.66802 - 1.79154i) q^{50} +(-0.509601 - 0.509601i) q^{51} -5.90090 q^{52} +(6.02669 + 6.02669i) q^{53} +(0.707107 + 0.707107i) q^{54} +(11.2096 - 2.07719i) q^{55} +(-1.64494 + 1.64494i) q^{56} -7.35769 q^{57} +(2.09433 - 2.09433i) q^{58} +(-1.31697 - 1.31697i) q^{59} +(1.84276 + 1.26658i) q^{60} +(-0.136297 - 0.136297i) q^{61} +(6.99049 + 6.99049i) q^{62} +(-1.64494 - 1.64494i) q^{63} +1.00000 q^{64} +(-2.40415 - 12.9740i) q^{65} +(3.60512 + 3.60512i) q^{66} +(-8.82528 - 8.82528i) q^{67} -0.720684i q^{68} +(1.74762 - 1.74762i) q^{69} +(-4.28681 - 2.94644i) q^{70} +0.630243 q^{71} +1.00000i q^{72} +(0.800728 - 0.800728i) q^{73} +(-0.654393 + 6.04746i) q^{74} +(-2.03398 + 4.56760i) q^{75} +(-5.20267 - 5.20267i) q^{76} +(-8.38658 - 8.38658i) q^{77} +(4.17257 - 4.17257i) q^{78} +(1.35715 + 1.35715i) q^{79} +(0.407420 + 2.19864i) q^{80} -1.00000 q^{81} -6.58809i q^{82} +(0.0877629 + 0.0877629i) q^{83} -2.32629i q^{84} +(1.58452 - 0.293621i) q^{85} -10.4051 q^{86} +2.96182i q^{87} +5.09841i q^{88} +(0.651916 - 0.651916i) q^{89} +(-2.19864 + 0.407420i) q^{90} +(-9.70663 + 9.70663i) q^{91} +2.47151 q^{92} -9.88605 q^{93} +(-6.69776 + 6.69776i) q^{94} +(9.31912 - 13.5585i) q^{95} +(-0.707107 + 0.707107i) q^{96} +5.99946i q^{97} -1.58835i q^{98} -5.09841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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