LMFDB - Embedded newform 560.2.bc.a.251.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(251,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("560.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bc (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.12
Character	$\chi$	$=$	560.251
Dual form			560.2.bc.a.531.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16313 + 0.804438i) q^{2} +(1.78548 - 1.78548i) q^{3} +(0.705760 - 1.87134i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.640444 + 3.51306i) q^{6} +(-0.850060 - 2.50547i) q^{7} +(0.684482 + 2.74436i) q^{8} -3.37588i q^{9} +O(q^{10})$	\(q+(-1.16313 + 0.804438i) q^{2} +(1.78548 - 1.78548i) q^{3} +(0.705760 - 1.87134i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.640444 + 3.51306i) q^{6} +(-0.850060 - 2.50547i) q^{7} +(0.684482 + 2.74436i) q^{8} -3.37588i q^{9} +(0.253636 - 1.39128i) q^{10} +(0.0703262 - 0.0703262i) q^{11} +(-2.08112 - 4.60135i) q^{12} +(-1.06297 - 1.06297i) q^{13} +(3.00423 + 2.23038i) q^{14} +2.52505i q^{15} +(-3.00381 - 2.64143i) q^{16} -2.50969i q^{17} +(2.71568 + 3.92660i) q^{18} +(4.58790 - 4.58790i) q^{19} +(0.824188 + 1.82228i) q^{20} +(-5.99124 - 2.95571i) q^{21} +(-0.0252257 + 0.138372i) q^{22} -2.70670 q^{23} +(6.12212 + 3.67786i) q^{24} -1.00000i q^{25} +(2.09147 + 0.381283i) q^{26} +(-0.671121 - 0.671121i) q^{27} +(-5.28852 - 0.177514i) q^{28} +(-0.166794 + 0.166794i) q^{29} +(-2.03125 - 2.93697i) q^{30} +0.412650 q^{31} +(5.61869 + 0.655959i) q^{32} -0.251132i q^{33} +(2.01889 + 2.91910i) q^{34} +(2.37272 + 1.17055i) q^{35} +(-6.31740 - 2.38256i) q^{36} +(-7.93663 - 7.93663i) q^{37} +(-1.64566 + 9.02702i) q^{38} -3.79582 q^{39} +(-2.42455 - 1.45655i) q^{40} -6.16803 q^{41} +(9.34629 - 1.38169i) q^{42} +(0.690526 - 0.690526i) q^{43} +(-0.0819707 - 0.181238i) q^{44} +(2.38711 + 2.38711i) q^{45} +(3.14825 - 2.17737i) q^{46} -0.817267 q^{47} +(-10.0795 + 0.647018i) q^{48} +(-5.55480 + 4.25960i) q^{49} +(0.804438 + 1.16313i) q^{50} +(-4.48100 - 4.48100i) q^{51} +(-2.73938 + 1.23897i) q^{52} +(-0.0169281 - 0.0169281i) q^{53} +(1.32048 + 0.240728i) q^{54} +0.0994563i q^{55} +(6.29406 - 4.04782i) q^{56} -16.3832i q^{57} +(0.0598284 - 0.328179i) q^{58} +(6.42990 + 6.42990i) q^{59} +(4.72522 + 1.78208i) q^{60} +(4.40167 + 4.40167i) q^{61} +(-0.479968 + 0.331952i) q^{62} +(-8.45817 + 2.86970i) q^{63} +(-7.06297 + 3.75692i) q^{64} +1.50327 q^{65} +(0.202020 + 0.292100i) q^{66} +(-3.75060 - 3.75060i) q^{67} +(-4.69648 - 1.77124i) q^{68} +(-4.83275 + 4.83275i) q^{69} +(-3.70143 + 0.547194i) q^{70} +14.9974 q^{71} +(9.26460 - 2.31073i) q^{72} +15.8463 q^{73} +(15.6159 + 2.84684i) q^{74} +(-1.78548 - 1.78548i) q^{75} +(-5.34755 - 11.8235i) q^{76} +(-0.235982 - 0.116419i) q^{77} +(4.41505 - 3.05351i) q^{78} +0.410639i q^{79} +(3.99178 - 0.256240i) q^{80} +7.73109 q^{81} +(7.17424 - 4.96179i) q^{82} +(3.76295 - 3.76295i) q^{83} +(-9.75950 + 9.12561i) q^{84} +(1.77462 + 1.77462i) q^{85} +(-0.247689 + 1.35866i) q^{86} +0.595615i q^{87} +(0.241137 + 0.144863i) q^{88} +7.55362 q^{89} +(-4.69680 - 0.856245i) q^{90} +(-1.75966 + 3.56683i) q^{91} +(-1.91028 + 5.06514i) q^{92} +(0.736779 - 0.736779i) q^{93} +(0.950591 - 0.657440i) q^{94} +6.48827i q^{95} +(11.2033 - 8.86086i) q^{96} -16.3192i q^{97} +(3.03439 - 9.42298i) q^{98} +(-0.237413 - 0.237413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 4 q^{4}+O(q^{10}) $ 128 * q - 4 * q^4	$ 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.16313	+	0.804438i	−0.822460	+	0.568823i
$2$	−1.16313	+	0.804438i	−0.822460	+	0.568823i
$3$	1.78548	−	1.78548i	1.03085	−	1.03085i	0.0313385	−	0.999509i	$-0.490023\pi$
$3$	1.78548	−	1.78548i	1.03085	−	1.03085i	0.999509	−	0.0313385i	$-0.00997698\pi$
$4$	0.705760	−	1.87134i	0.352880	−	0.935669i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.640444	+	3.51306i	−0.261460	+	1.43420i
$7$	−0.850060	−	2.50547i	−0.321292	−	0.946980i
$7$	−0.850060	−	2.50547i	−0.321292	−	0.946980i
$8$	0.684482	+	2.74436i	0.242001	+	0.970276i
$9$		−	3.37588i		−	1.12529i
$10$	0.253636	−	1.39128i	0.0802068	−	0.439962i
$11$	0.0703262	−	0.0703262i	0.0212042	−	0.0212042i	−0.696425	−	0.717629i	$-0.745227\pi$
$11$	0.0703262	−	0.0703262i	0.0212042	−	0.0212042i	0.717629	+	0.696425i	$0.245227\pi$
$12$	−2.08112	−	4.60135i	−0.600766	−	1.32830i
$13$	−1.06297	−	1.06297i	−0.294815	−	0.294815i	0.544164	−	0.838979i	$-0.316847\pi$
$13$	−1.06297	−	1.06297i	−0.294815	−	0.294815i	−0.838979	+	0.544164i	$0.816847\pi$
$14$	3.00423	+	2.23038i	0.802914	+	0.596094i
$15$			2.52505i			0.651965i
$16$	−3.00381	−	2.64143i	−0.750952	−	0.660357i
$17$		−	2.50969i		−	0.608689i	−0.952562	−	0.304345i	$-0.901563\pi$
$17$		−	2.50969i		−	0.608689i	0.952562	−	0.304345i	$-0.0984374\pi$
$18$	2.71568	+	3.92660i	0.640093	+	0.925508i
$19$	4.58790	−	4.58790i	1.05254	−	1.05254i	0.0539952	−	0.998541i	$-0.482804\pi$
$19$	4.58790	−	4.58790i	1.05254	−	1.05254i	0.998541	−	0.0539952i	$-0.0171956\pi$
$20$	0.824188	+	1.82228i	0.184294	+	0.407475i
$21$	−5.99124	−	2.95571i	−1.30740	−	0.644989i
$22$	−0.0252257	+	0.138372i	−0.00537814	+	0.0295010i
$23$	−2.70670			−0.564385			−0.282192	−	0.959358i	$-0.591062\pi$
$23$	−2.70670			−0.564385			−0.282192	+	0.959358i	$0.591062\pi$
$24$	6.12212	+	3.67786i	1.24967	+	0.750741i
$25$		−	1.00000i		−	0.200000i
$26$	2.09147	+	0.381283i	0.410171	+	0.0747758i
$27$	−0.671121	−	0.671121i	−0.129157	−	0.129157i
$28$	−5.28852	−	0.177514i	−0.999437	−	0.0335471i
$29$	−0.166794	+	0.166794i	−0.0309729	+	0.0309729i	−0.722424	−	0.691451i	$-0.756972\pi$
$29$	−0.166794	+	0.166794i	−0.0309729	+	0.0309729i	0.691451	+	0.722424i	$0.256972\pi$
$30$	−2.03125	−	2.93697i	−0.370853	−	0.536215i
$31$	0.412650			0.0741142			0.0370571	−	0.999313i	$-0.488202\pi$
$31$	0.412650			0.0741142			0.0370571	+	0.999313i	$0.488202\pi$
$32$	5.61869	+	0.655959i	0.993254	+	0.115958i
$33$		−	0.251132i		−	0.0437165i
$34$	2.01889	+	2.91910i	0.346237	+	0.500622i
$35$	2.37272	+	1.17055i	0.401063	+	0.197860i
$36$	−6.31740	−	2.38256i	−1.05290	−	0.397093i
$37$	−7.93663	−	7.93663i	−1.30477	−	1.30477i	−0.925134	−	0.379640i	$-0.876048\pi$
$37$	−7.93663	−	7.93663i	−1.30477	−	1.30477i	−0.379640	−	0.925134i	$-0.623952\pi$
$38$	−1.64566	+	9.02702i	−0.266961	+	1.46438i
$39$	−3.79582			−0.607818
$40$	−2.42455	−	1.45655i	−0.383356	−	0.230301i
$41$	−6.16803			−0.963284			−0.481642	−	0.876368i	$-0.659959\pi$
$41$	−6.16803			−0.963284			−0.481642	+	0.876368i	$0.659959\pi$
$42$	9.34629	−	1.38169i	1.44216	−	0.213200i
$43$	0.690526	−	0.690526i	0.105304	−	0.105304i	−0.652492	−	0.757796i	$-0.726276\pi$
$43$	0.690526	−	0.690526i	0.105304	−	0.105304i	0.757796	+	0.652492i	$0.226276\pi$
$44$	−0.0819707	−	0.181238i	−0.0123575	−	0.0273226i
$45$	2.38711	+	2.38711i	0.355849	+	0.355849i
$46$	3.14825	−	2.17737i	0.464184	−	0.321035i
$47$	−0.817267			−0.119211			−0.0596053	−	0.998222i	$-0.518984\pi$
$47$	−0.817267			−0.119211			−0.0596053	+	0.998222i	$0.518984\pi$
$48$	−10.0795	+	0.647018i	−1.45484	+	0.0933890i
$49$	−5.55480	+	4.25960i	−0.793543	+	0.608515i
$50$	0.804438	+	1.16313i	0.113765	+	0.164492i
$51$	−4.48100	−	4.48100i	−0.627466	−	0.627466i
$52$	−2.73938	+	1.23897i	−0.379883	+	0.171815i
$53$	−0.0169281	−	0.0169281i	−0.00232525	−	0.00232525i	0.705943	−	0.708268i	$-0.250523\pi$
$53$	−0.0169281	−	0.0169281i	−0.00232525	−	0.00232525i	−0.708268	+	0.705943i	$0.750523\pi$
$54$	1.32048	+	0.240728i	0.179694	+	0.0327590i
$55$			0.0994563i			0.0134107i
$56$	6.29406	−	4.04782i	0.841079	−	0.540912i
$57$		−	16.3832i		−	2.17001i
$58$	0.0598284	−	0.328179i	0.00785585	−	0.0430921i
$59$	6.42990	+	6.42990i	0.837102	+	0.837102i	0.988477	−	0.151374i	$-0.0483699\pi$
$59$	6.42990	+	6.42990i	0.837102	+	0.837102i	−0.151374	+	0.988477i	$0.548370\pi$
$60$	4.72522	+	1.78208i	0.610023	+	0.230065i
$61$	4.40167	+	4.40167i	0.563576	+	0.563576i	0.930321	−	0.366745i	$-0.119528\pi$
$61$	4.40167	+	4.40167i	0.563576	+	0.563576i	−0.366745	+	0.930321i	$0.619528\pi$
$62$	−0.479968	+	0.331952i	−0.0609559	+	0.0421579i
$63$	−8.45817	+	2.86970i	−1.06563	+	0.361548i
$64$	−7.06297	+	3.75692i	−0.882871	+	0.469615i
$65$	1.50327			0.186457
$66$	0.202020	+	0.292100i	0.0248670	+	0.0359551i
$67$	−3.75060	−	3.75060i	−0.458209	−	0.458209i	0.439858	−	0.898067i	$-0.355029\pi$
$67$	−3.75060	−	3.75060i	−0.458209	−	0.458209i	−0.898067	+	0.439858i	$0.855029\pi$
$68$	−4.69648	−	1.77124i	−0.569531	−	0.214794i
$69$	−4.83275	+	4.83275i	−0.581795	+	0.581795i
$70$	−3.70143	+	0.547194i	−0.442405	+	0.0654022i
$71$	14.9974			1.77986			0.889932	−	0.456093i	$-0.150752\pi$
$71$	14.9974			1.77986			0.889932	+	0.456093i	$0.150752\pi$
$72$	9.26460	−	2.31073i	1.09184	−	0.272322i
$73$	15.8463			1.85467			0.927336	−	0.374229i	$-0.122092\pi$
$73$	15.8463			1.85467			0.927336	+	0.374229i	$0.122092\pi$
$74$	15.6159	+	2.84684i	1.81531	+	0.330938i
$75$	−1.78548	−	1.78548i	−0.206169	−	0.206169i
$76$	−5.34755	−	11.8235i	−0.613406	−	1.35624i
$77$	−0.235982	−	0.116419i	−0.0268926	−	0.0132672i
$78$	4.41505	−	3.05351i	0.499906	−	0.345741i
$79$			0.410639i			0.0462005i	0.999733	+	0.0231003i	$0.00735370\pi$
$79$			0.410639i			0.0462005i	−0.999733	+	0.0231003i	$0.992646\pi$
$80$	3.99178	−	0.256240i	0.446295	−	0.0286485i
$81$	7.73109			0.859010
$82$	7.17424	−	4.96179i	0.792262	−	0.547938i
$83$	3.76295	−	3.76295i	0.413038	−	0.413038i	−0.469758	−	0.882795i	$-0.655659\pi$
$83$	3.76295	−	3.76295i	0.413038	−	0.413038i	0.882795	+	0.469758i	$0.155659\pi$
$84$	−9.75950	+	9.12561i	−1.06485	+	0.995685i
$85$	1.77462	+	1.77462i	0.192484	+	0.192484i
$86$	−0.247689	+	1.35866i	−0.0267090	+	0.146508i
$87$			0.595615i			0.0638567i
$88$	0.241137	+	0.144863i	0.0257053	+	0.0154425i
$89$	7.55362			0.800683			0.400341	−	0.916366i	$-0.368892\pi$
$89$	7.55362			0.800683			0.400341	+	0.916366i	$0.368892\pi$
$90$	−4.69680	−	0.856245i	−0.495086	−	0.0902561i
$91$	−1.75966	+	3.56683i	−0.184462	+	0.373906i
$92$	−1.91028	+	5.06514i	−0.199160	+	0.528077i
$93$	0.736779	−	0.736779i	0.0764004	−	0.0764004i
$94$	0.950591	−	0.657440i	0.0980459	−	0.0678098i
$95$			6.48827i			0.665682i
$96$	11.2033	−	8.86086i	1.14343	−	0.904358i
$97$		−	16.3192i		−	1.65696i	−0.560016	−	0.828482i	$-0.689205\pi$
$97$		−	16.3192i		−	1.65696i	0.560016	−	0.828482i	$-0.310795\pi$
$98$	3.03439	−	9.42298i	0.306519	−	0.951864i
$99$	−0.237413	−	0.237413i	−0.0238609	−	0.0238609i
$100$	−1.87134	−	0.705760i	−0.187134	−	0.0705760i
$101$	6.02420	−	6.02420i	0.599431	−	0.599431i	−0.340730	−	0.940161i	$-0.610674\pi$
$101$	6.02420	−	6.02420i	0.599431	−	0.599431i	0.940161	+	0.340730i	$0.110674\pi$
$102$	8.81669	+	1.60732i	0.872982	+	0.159148i
$103$			5.29227i			0.521463i	0.965411	+	0.260731i	$0.0839637\pi$
$103$			5.29227i			0.521463i	−0.965411	+	0.260731i	$0.916036\pi$
$104$	2.18958	−	3.64475i	0.214706	−	0.357397i
$105$	6.32645	−	2.14644i	0.617398	−	0.209471i
$106$	0.0333072	+	0.00607204i	0.00323509	+	0.000589769i
$107$	−10.0631	+	10.0631i	−0.972838	+	0.972838i	−0.999641	−	0.0268025i	$-0.991467\pi$
$107$	−10.0631	+	10.0631i	−0.972838	+	0.972838i	0.0268025	+	0.999641i	$0.491467\pi$
$108$	−1.72954	+	0.782243i	−0.166425	+	0.0752714i
$109$	−13.0851	+	13.0851i	−1.25332	+	1.25332i	−0.299104	+	0.954221i	$0.596688\pi$
$109$	−13.0851	+	13.0851i	−1.25332	+	1.25332i	−0.954221	+	0.299104i	$0.903312\pi$
$110$	−0.0800064	−	0.115681i	−0.00762831	−	0.0110297i
$111$	−28.3414			−2.69005
$112$	−4.06462	+	9.77133i	−0.384070	+	0.923304i
$113$	13.1388			1.23599			0.617996	−	0.786181i	$-0.287945\pi$
$113$	13.1388			1.23599			0.617996	+	0.786181i	$0.287945\pi$
$114$	13.1793	+	19.0559i	1.23435	+	1.78474i
$115$	1.91392	−	1.91392i	0.178474	−	0.178474i
$116$	0.194412	+	0.429845i	0.0180507	+	0.0399101i
$117$	−3.58846	+	3.58846i	−0.331753	+	0.331753i
$118$	−12.6513	−	2.30638i	−1.16465	−	0.212319i
$119$	−6.28796	+	2.13339i	−0.576417	+	0.195567i
$120$	−6.92963	+	1.72835i	−0.632586	+	0.157776i
$121$			10.9901i			0.999101i
$122$	−8.66060	−	1.57886i	−0.784094	−	0.142943i
$123$	−11.0129	+	11.0129i	−0.992999	+	0.992999i
$124$	0.291232	−	0.772208i	0.0261534	−	0.0693463i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	7.52949	−	10.1419i	0.670780	−	0.903513i
$127$			17.3811i			1.54232i	0.636640	+	0.771161i	$0.280324\pi$
$127$			17.3811i			1.54232i	−0.636640	+	0.771161i	$0.719676\pi$
$128$	5.19297	−	10.0515i	0.458998	−	0.888437i
$129$		−	2.46584i		−	0.217105i
$130$	−1.74850	+	1.20929i	−0.153354	+	0.106061i
$131$	−4.96637	+	4.96637i	−0.433913	+	0.433913i	−0.889957	−	0.456044i	$-0.849266\pi$
$131$	−4.96637	+	4.96637i	−0.433913	+	0.433913i	0.456044	+	0.889957i	$0.349266\pi$
$132$	−0.469953	−	0.177239i	−0.0409042	−	0.0154267i
$133$	−15.3949	−	7.59487i	−1.33490	−	0.658559i
$134$	7.37958	+	1.34533i	0.637499	+	0.116218i
$135$	0.949108			0.0816862
$136$	6.88748	−	1.71784i	0.590597	−	0.147303i
$137$		−	11.6933i		−	0.999027i	−0.866306	−	0.499513i	$-0.833512\pi$
$137$		−	11.6933i		−	0.999027i	0.866306	−	0.499513i	$-0.166488\pi$
$138$	1.73349	−	9.50878i	0.147564	−	0.809441i
$139$	14.3160	+	14.3160i	1.21426	+	1.21426i	0.969611	+	0.244652i	$0.0786739\pi$
$139$	14.3160	+	14.3160i	1.21426	+	1.21426i	0.244652	+	0.969611i	$0.421326\pi$
$140$	3.86507	−	3.61403i	0.326658	−	0.305441i
$141$	−1.45921	+	1.45921i	−0.122888	+	0.122888i
$142$	−17.4440	+	12.0645i	−1.46387	+	1.01243i
$143$	−0.149509			−0.0125026
$144$	−8.91714	+	10.1405i	−0.743095	+	0.845040i
$145$		−	0.235883i		−	0.0195890i
$146$	−18.4314	+	12.7474i	−1.52539	+	1.05498i
$147$	−2.31254	+	17.5234i	−0.190735	+	1.44531i
$148$	−20.4535	+	9.25076i	−1.68126	+	0.760408i
$149$	16.9746	+	16.9746i	1.39061	+	1.39061i	0.823947	+	0.566667i	$0.191767\pi$
$149$	16.9746	+	16.9746i	1.39061	+	1.39061i	0.566667	+	0.823947i	$0.308233\pi$
$150$	3.51306	+	0.640444i	0.286840	+	0.0522921i
$151$	11.6481			0.947912			0.473956	−	0.880549i	$-0.342826\pi$
$151$	11.6481			0.947912			0.473956	+	0.880549i	$0.342826\pi$
$152$	15.7312	+	9.45049i	1.27597	+	0.766536i
$153$	−8.47240			−0.684953
$154$	0.368130	−	0.0544219i	0.0296648	−	0.00438544i
$155$	−0.291788	+	0.291788i	−0.0234370	+	0.0234370i
$156$	−2.67894	+	7.10327i	−0.214487	+	0.568717i
$157$	−6.81929	−	6.81929i	−0.544239	−	0.544239i	0.380530	−	0.924769i	$-0.375742\pi$
$157$	−6.81929	−	6.81929i	−0.544239	−	0.544239i	−0.924769	+	0.380530i	$0.875742\pi$
$158$	−0.330334	−	0.477629i	−0.0262800	−	0.0379981i
$159$	−0.0604496			−0.00479396
$160$	−4.43685	+	3.50918i	−0.350764	+	0.277425i
$161$	2.30085	+	6.78155i	0.181333	+	0.534461i
$162$	−8.99229	+	6.21918i	−0.706501	+	0.488625i
$163$	−4.97611	−	4.97611i	−0.389759	−	0.389759i	0.484842	−	0.874602i	$-0.338877\pi$
$163$	−4.97611	−	4.97611i	−0.389759	−	0.389759i	−0.874602	+	0.484842i	$0.838877\pi$
$164$	−4.35314	+	11.5425i	−0.339924	+	0.901315i
$165$	0.177577	+	0.177577i	0.0138244	+	0.0138244i
$166$	−1.34976	+	7.40388i	−0.104761	+	0.574652i
$167$		−	0.412599i		−	0.0319279i	−0.999873	−	0.0159639i	$-0.994918\pi$
$167$		−	0.412599i		−	0.0319279i	0.999873	−	0.0159639i	$-0.00508169\pi$
$168$	4.01062	−	18.4652i	0.309426	−	1.42462i
$169$		−	10.7402i		−	0.826168i
$170$	−3.49169	−	0.636548i	−0.267800	−	0.0488210i
$171$	−15.4882	−	15.4882i	−1.18441	−	1.18441i
$172$	−0.804862	−	1.77955i	−0.0613701	−	0.135690i
$173$	−5.16055	−	5.16055i	−0.392350	−	0.392350i	0.483174	−	0.875524i	$-0.339484\pi$
$173$	−5.16055	−	5.16055i	−0.392350	−	0.392350i	−0.875524	+	0.483174i	$0.839484\pi$
$174$	−0.479136	−	0.692780i	−0.0363232	−	0.0525195i
$175$	−2.50547	+	0.850060i	−0.189396	+	0.0642585i
$176$	−0.397008	+	0.0254846i	−0.0299256	+	0.00192098i
$177$	22.9609			1.72585
$178$	−8.78587	+	6.07642i	−0.658529	+	0.455447i
$179$	−12.6682	−	12.6682i	−0.946869	−	0.946869i	0.0517891	−	0.998658i	$-0.483508\pi$
$179$	−12.6682	−	12.6682i	−0.946869	−	0.946869i	−0.998658	+	0.0517891i	$0.983508\pi$
$180$	6.15180	−	2.78236i	0.458528	−	0.207385i
$181$	−7.23983	+	7.23983i	−0.538132	+	0.538132i	−0.922980	−	0.384848i	$-0.874254\pi$
$181$	−7.23983	+	7.23983i	−0.538132	+	0.538132i	0.384848	+	0.922980i	$0.374254\pi$
$182$	−0.822579	−	5.56424i	−0.0609736	−	0.412449i
$183$	15.7182			1.16192
$184$	−1.85268	−	7.42813i	−0.136582	−	0.547609i
$185$	11.2241			0.825212
$186$	−0.264280	+	1.44967i	−0.0193779	+	0.106295i
$187$	−0.176497	−	0.176497i	−0.0129067	−	0.0129067i
$188$	−0.576794	+	1.52938i	−0.0420670	+	0.111542i
$189$	−1.11098	+	2.25197i	−0.0808121	+	0.163807i
$190$	−5.21941	−	7.54673i	−0.378656	−	0.547497i
$191$			9.45391i			0.684061i	0.939689	+	0.342031i	$0.111115\pi$
$191$			9.45391i			0.684061i	−0.939689	+	0.342031i	$0.888885\pi$
$192$	−5.90288	+	19.3187i	−0.426004	+	1.39421i
$193$	6.37384			0.458799			0.229399	−	0.973332i	$-0.426324\pi$
$193$	6.37384			0.458799			0.229399	+	0.973332i	$0.426324\pi$
$194$	13.1278	+	18.9814i	0.942520	+	1.36279i
$195$	2.68405	−	2.68405i	0.192209	−	0.192209i
$196$	4.05080	+	13.4012i	0.289343	+	0.957225i
$197$	−7.27131	−	7.27131i	−0.518059	−	0.518059i	0.398925	−	0.916984i	$-0.369384\pi$
$197$	−7.27131	−	7.27131i	−0.518059	−	0.518059i	−0.916984	+	0.398925i	$0.869384\pi$
$198$	0.467126	+	0.0851589i	0.0331972	+	0.00605198i
$199$		−	5.34393i		−	0.378821i	−0.981898	−	0.189411i	$-0.939342\pi$
$199$		−	5.34393i		−	0.378821i	0.981898	−	0.189411i	$-0.0606578\pi$
$200$	2.74436	−	0.684482i	0.194055	−	0.0484002i
$201$	−13.3933			−0.944687
$202$	−2.16086	+	11.8530i	−0.152037	+	0.833978i
$203$	0.559683	+	0.276113i	0.0392821	+	0.0193794i
$204$	−11.5480	+	5.22295i	−0.808520	+	0.365680i
$205$	4.36145	−	4.36145i	0.304617	−	0.304617i
$206$	−4.25730	−	6.15562i	−0.296620	−	0.428882i
$207$			9.13747i			0.635098i
$208$	0.385197	+	6.00072i	0.0267086	+	0.416075i
$209$		−	0.645299i		−	0.0446363i
$210$	−5.63182	+	7.58583i	−0.388633	+	0.523472i
$211$	8.08871	+	8.08871i	0.556850	+	0.556850i	0.928409	−	0.371559i	$-0.121177\pi$
$211$	8.08871	+	8.08871i	0.556850	+	0.556850i	−0.371559	+	0.928409i	$0.621177\pi$
$212$	−0.0436254	+	0.0197310i	−0.00299620	+	0.00135513i
$213$	26.7776	−	26.7776i	1.83477	−	1.83477i
$214$	3.60960	−	19.7999i	0.246747	−	1.35349i
$215$			0.976552i			0.0666003i
$216$	1.38242	−	2.30116i	0.0940620	−	0.156574i
$217$	−0.350777	−	1.03388i	−0.0238123	−	0.0701847i
$218$	4.69357	−	25.7458i	0.317888	−	1.74373i
$219$	28.2933	−	28.2933i	1.91188	−	1.91188i
$220$	0.186116	+	0.0701923i	0.0125480	+	0.00473236i
$221$	−2.66773	+	2.66773i	−0.179451	+	0.179451i
$222$	32.9648	−	22.7989i	2.21245	−	1.53016i
$223$	20.5733			1.37769			0.688844	−	0.724910i	$-0.258119\pi$
$223$	20.5733			1.37769			0.688844	+	0.724910i	$0.258119\pi$
$224$	−3.13273	−	14.6351i	−0.209315	−	0.977848i
$225$	−3.37588			−0.225058
$226$	−15.2822	+	10.5693i	−1.01655	+	0.703061i
$227$	−12.3146	+	12.3146i	−0.817346	+	0.817346i	−0.985723	−	0.168376i	$-0.946148\pi$
$227$	−12.3146	+	12.3146i	−0.817346	+	0.817346i	0.168376	+	0.985723i	$0.446148\pi$
$228$	−30.6585	−	11.5626i	−2.03041	−	0.765752i
$229$	14.4211	−	14.4211i	0.952976	−	0.952976i	−0.0459674	−	0.998943i	$-0.514637\pi$
$229$	14.4211	−	14.4211i	0.952976	−	0.952976i	0.998943	+	0.0459674i	$0.0146370\pi$
$230$	−0.686516	+	3.76578i	−0.0452675	+	0.248308i
$231$	−0.629205	+	0.213477i	−0.0413986	+	0.0140458i
$232$	−0.571910	−	0.343575i	−0.0375477	−	0.0225568i
$233$			23.8952i			1.56543i	0.622383	+	0.782713i	$0.286165\pi$
$233$			23.8952i			1.56543i	−0.622383	+	0.782713i	$0.713835\pi$
$234$	1.28716	−	7.06055i	0.0841446	−	0.461562i
$235$	0.577895	−	0.577895i	0.0376977	−	0.0376977i
$236$	16.5705	−	7.49455i	1.07865	−	0.487854i
$237$	0.733188	+	0.733188i	0.0476257	+	0.0476257i
$238$	5.59756	−	7.53969i	0.362836	−	0.488725i
$239$			15.0229i			0.971750i	0.874028	+	0.485875i	$0.161499\pi$
$239$			15.0229i			0.971750i	−0.874028	+	0.485875i	$0.838501\pi$
$240$	6.66974	−	7.58476i	0.430530	−	0.489594i
$241$		−	1.81039i		−	0.116618i	−0.998299	−	0.0583089i	$-0.981429\pi$
$241$		−	1.81039i		−	0.116618i	0.998299	−	0.0583089i	$-0.0185708\pi$
$242$	−8.84086	−	12.7830i	−0.568312	−	0.821720i
$243$	15.8171	−	15.8171i	1.01466	−	1.01466i
$244$	11.3435	−	5.13049i	0.726195	−	0.328446i
$245$	0.915841	−	6.93983i	0.0585109	−	0.443369i
$246$	3.95028	−	21.6686i	0.251860	−	1.38154i
$247$	−9.75360			−0.620607
$248$	0.282452	+	1.13246i	0.0179357	+	0.0719112i
$249$		−	13.4373i		−	0.851557i
$250$	−1.39128	−	0.253636i	−0.0879925	−	0.0160414i
$251$	−8.95299	−	8.95299i	−0.565108	−	0.565108i	0.365646	−	0.930754i	$-0.380848\pi$
$251$	−8.95299	−	8.95299i	−0.565108	−	0.565108i	−0.930754	+	0.365646i	$0.880848\pi$
$252$	−0.599267	+	17.8534i	−0.0377503	+	1.12466i
$253$	−0.190352	+	0.190352i	−0.0119673	+	0.0119673i
$254$	−13.9820	−	20.2165i	−0.877309	−	1.26850i
$255$	6.33709			0.396844
$256$	2.04571	+	15.8687i	0.127857	+	0.991793i
$257$			16.2096i			1.01113i	0.862789	+	0.505564i	$0.168715\pi$
$257$			16.2096i			1.01113i	−0.862789	+	0.505564i	$0.831285\pi$
$258$	1.98362	+	2.86810i	0.123495	+	0.178560i
$259$	−13.1384	+	26.6316i	−0.816381	+	1.65481i
$260$	1.06095	−	2.81312i	0.0657970	−	0.174462i
$261$	0.563077	+	0.563077i	0.0348536	+	0.0348536i
$262$	1.78141	−	9.77168i	0.110056	−	0.603696i
$263$	19.7944			1.22057			0.610287	−	0.792181i	$-0.291054\pi$
$263$	19.7944			1.22057			0.610287	+	0.792181i	$0.291054\pi$
$264$	0.689196	−	0.171895i	0.0424171	−	0.0105794i
$265$	0.0239399			0.00147062
$266$	24.0159	−	3.55035i	1.47251	−	0.217686i
$267$	13.4868	−	13.4868i	0.825382	−	0.825382i
$268$	−9.66567	+	4.37162i	−0.590425	+	0.267039i
$269$	−12.9634	−	12.9634i	−0.790391	−	0.790391i	0.191167	−	0.981558i	$-0.438773\pi$
$269$	−12.9634	−	12.9634i	−0.790391	−	0.790391i	−0.981558	+	0.191167i	$0.938773\pi$
$270$	−1.10394	+	0.763498i	−0.0671836	+	0.0464650i
$271$	5.46458			0.331950			0.165975	−	0.986130i	$-0.446923\pi$
$271$	5.46458			0.331950			0.165975	+	0.986130i	$0.446923\pi$
$272$	−6.62917	+	7.53862i	−0.401952	+	0.457096i
$273$	3.22668	+	9.51034i	0.195287	+	0.575592i
$274$	9.40654	+	13.6009i	0.568270	+	0.821659i
$275$	−0.0703262	−	0.0703262i	−0.00424083	−	0.00424083i
$276$	5.63294	+	12.4545i	0.339063	+	0.749671i
$277$	4.35299	+	4.35299i	0.261546	+	0.261546i	0.825682	−	0.564136i	$-0.190791\pi$
$277$	4.35299	+	4.35299i	0.261546	+	0.261546i	−0.564136	+	0.825682i	$0.690791\pi$
$278$	−28.1677	−	5.13507i	−1.68938	−	0.307981i
$279$		−	1.39306i		−	0.0834001i
$280$	−1.58833	+	7.31281i	−0.0949211	+	0.437024i
$281$		−	4.12957i		−	0.246349i	−0.992385	−	0.123175i	$-0.960692\pi$
$281$		−	4.12957i		−	0.246349i	0.992385	−	0.123175i	$-0.0393076\pi$
$282$	0.523414	−	2.87111i	0.0311688	−	0.170972i
$283$	−10.2581	−	10.2581i	−0.609778	−	0.609778i	0.333110	−	0.942888i	$-0.391902\pi$
$283$	−10.2581	−	10.2581i	−0.609778	−	0.609778i	−0.942888	+	0.333110i	$0.891902\pi$
$284$	10.5846	−	28.0652i	0.628078	−	1.66536i
$285$	11.5847	+	11.5847i	0.686217	+	0.686217i
$286$	0.173899	−	0.120271i	0.0102829	−	0.00711177i
$287$	5.24319	+	15.4538i	0.309496	+	0.912211i
$288$	2.21444	−	18.9680i	0.130487	−	1.11770i
$289$	10.7015			0.629497
$290$	0.189753	+	0.274363i	0.0111427	+	0.0161112i
$291$	−29.1376	−	29.1376i	−1.70808	−	1.70808i
$292$	11.1837	−	29.6538i	0.654477	−	1.73536i
$293$	−6.90025	+	6.90025i	−0.403117	+	0.403117i	−0.879330	−	0.476213i	$-0.842009\pi$
$293$	−6.90025	+	6.90025i	−0.403117	+	0.403117i	0.476213	+	0.879330i	$0.342009\pi$
$294$	−11.4067	−	22.2424i	−0.665252	−	1.29720i
$295$	−9.09326			−0.529430
$296$	16.3485	−	27.2134i	0.950235	−	1.58175i
$297$	−0.0943947			−0.00547734
$298$	−33.3987	−	6.08872i	−1.93474	−	0.352710i
$299$	2.87714	+	2.87714i	0.166389	+	0.166389i
$300$	−4.60135	+	2.08112i	−0.265659	+	0.120153i
$301$	−2.31708	−	1.14311i	−0.133554	−	0.0658876i
$302$	−13.5483	+	9.37020i	−0.779619	+	0.539194i
$303$		−	21.5122i		−	1.23584i
$304$	−25.8998	+	1.66255i	−1.48545	+	0.0953539i
$305$	−6.22490			−0.356437
$306$	9.85454	−	6.81552i	0.563346	−	0.389617i
$307$	13.8551	−	13.8551i	0.790755	−	0.790755i	−0.190862	−	0.981617i	$-0.561128\pi$
$307$	13.8551	−	13.8551i	0.790755	−	0.790755i	0.981617	+	0.190862i	$0.0611284\pi$
$308$	−0.384406	+	0.359438i	−0.0219036	+	0.0204809i
$309$	9.44924	+	9.44924i	0.537549	+	0.537549i
$310$	0.104663	−	0.574114i	0.00594447	−	0.0326075i
$311$		−	22.7602i		−	1.29061i	−0.763925	−	0.645305i	$-0.776730\pi$
$311$		−	22.7602i		−	1.29061i	0.763925	−	0.645305i	$-0.223270\pi$
$312$	−2.59817	−	10.4171i	−0.147093	−	0.589752i
$313$	−17.6504			−0.997657			−0.498828	−	0.866701i	$-0.666236\pi$
$313$	−17.6504			−0.997657			−0.498828	+	0.866701i	$0.666236\pi$
$314$	13.4174	+	2.44605i	0.757190	+	0.138039i
$315$	3.95165	−	8.01001i	0.222650	−	0.451313i
$316$	0.768445	+	0.289813i	0.0432284	+	0.0163032i
$317$	5.01748	−	5.01748i	0.281810	−	0.281810i	−0.552021	−	0.833831i	$-0.686143\pi$
$317$	5.01748	−	5.01748i	0.281810	−	0.281810i	0.833831	+	0.552021i	$0.186143\pi$
$318$	0.0703109	−	0.0486279i	0.00394284	−	0.00272692i
$319$			0.0234600i			0.00131351i
$320$	2.33773	−	7.65082i	0.130683	−	0.427694i
$321$			35.9350i			2.00570i
$322$	−8.13154	−	6.03696i	−0.453153	−	0.336427i
$323$	−11.5142	−	11.5142i	−0.640668	−	0.640668i
$324$	5.45629	−	14.4675i	0.303127	−	0.803748i
$325$	−1.06297	+	1.06297i	−0.0589630	+	0.0589630i
$326$	9.79086	+	1.78491i	0.542265	+	0.0988571i
$327$			46.7263i			2.58397i
$328$	−4.22190	−	16.9273i	−0.233115	−	0.934651i
$329$	0.694726	+	2.04764i	0.0383015	+	0.112890i
$330$	−0.349396	−	0.0636962i	−0.0192336	−	0.00350636i
$331$	6.77902	−	6.77902i	0.372609	−	0.372609i	−0.495818	−	0.868427i	$-0.665132\pi$
$331$	6.77902	−	6.77902i	0.372609	−	0.372609i	0.868427	+	0.495818i	$0.165132\pi$
$332$	−4.38601	−	9.69749i	−0.240714	−	0.532219i
$333$	−26.7931	+	26.7931i	−1.46825	+	1.46825i
$334$	0.331910	+	0.479908i	0.0181613	+	0.0262594i
$335$	5.30415			0.289797
$336$	10.1892	+	24.7038i	0.555868	+	1.34770i
$337$	−20.8461			−1.13556			−0.567779	−	0.823181i	$-0.692197\pi$
$337$	−20.8461			−1.13556			−0.567779	+	0.823181i	$0.692197\pi$
$338$	8.63981	+	12.4923i	0.469944	+	0.679490i
$339$	23.4590	−	23.4590i	1.27412	−	1.27412i
$340$	4.57337	−	2.06846i	0.248026	−	0.112178i
$341$	0.0290201	−	0.0290201i	0.00157153	−	0.00157153i
$342$	30.4741	+	5.55555i	1.64785	+	0.300410i
$343$	15.3942	+	10.2965i	0.831210	+	0.555958i
$344$	2.36770	+	1.42240i	0.127658	+	0.0766905i
$345$		−	6.83454i		−	0.367959i
$346$	10.1538	+	1.85107i	0.545869	+	0.0995141i
$347$	−13.1727	+	13.1727i	−0.707146	+	0.707146i	−0.965934	−	0.258788i	$-0.916677\pi$
$347$	−13.1727	+	13.1727i	−0.707146	+	0.707146i	0.258788	+	0.965934i	$0.416677\pi$
$348$	1.11460	+	0.420361i	0.0597487	+	0.0225337i
$349$	−20.1813	−	20.1813i	−1.08028	−	1.08028i	−0.996483	−	0.0837975i	$-0.973295\pi$
$349$	−20.1813	−	20.1813i	−1.08028	−	1.08028i	−0.0837975	−	0.996483i	$-0.526705\pi$
$350$	2.23038	−	3.00423i	0.119219	−	0.160583i
$351$			1.42676i			0.0761550i
$352$	0.441273	−	0.349010i	0.0235199	−	0.0186023i
$353$			21.8630i			1.16365i	0.813314	+	0.581825i	$0.197661\pi$
$353$			21.8630i			1.16365i	−0.813314	+	0.581825i	$0.802339\pi$
$354$	−26.7066	+	18.4706i	−1.41944	+	0.981703i
$355$	−10.6048	+	10.6048i	−0.562843	+	0.562843i
$356$	5.33104	−	14.1354i	0.282545	−	0.749174i
$357$	−7.41791	+	15.0361i	−0.392598	+	0.795797i
$358$	24.9257	+	4.54405i	1.31736	+	0.240160i
$359$	−21.1907			−1.11840			−0.559200	−	0.829032i	$-0.688892\pi$
$359$	−21.1907			−1.11840			−0.559200	+	0.829032i	$0.688892\pi$
$360$	−4.91714	+	8.18499i	−0.259156	+	0.431387i
$361$		−	23.0976i		−	1.21567i
$362$	2.59690	−	14.2449i	0.136490	−	0.748694i
$363$	19.6226	+	19.6226i	1.02992	+	1.02992i
$364$	5.43285	+	5.81024i	0.284759	+	0.304539i
$365$	−11.2050	+	11.2050i	−0.586499	+	0.586499i
$366$	−18.2824	+	12.6443i	−0.955634	+	0.660928i
$367$	9.46718			0.494183			0.247091	−	0.968992i	$-0.420525\pi$
$367$	9.46718			0.494183			0.247091	+	0.968992i	$0.420525\pi$
$368$	8.13039	+	7.14954i	0.423826	+	0.372696i
$369$			20.8225i			1.08398i
$370$	−13.0551	+	9.02908i	−0.678703	+	0.469400i
$371$	−0.0280230	+	0.0568028i	−0.00145488	+	0.00294905i
$372$	−0.858773	−	1.89875i	−0.0445253	−	0.0984457i
$373$	−2.20729	−	2.20729i	−0.114289	−	0.114289i	0.647649	−	0.761938i	$-0.275752\pi$
$373$	−2.20729	−	2.20729i	−0.114289	−	0.114289i	−0.761938	+	0.647649i	$0.775752\pi$
$374$	0.347271	+	0.0633088i	0.0179569	+	0.00327362i
$375$	2.52505			0.130393
$376$	−0.559404	−	2.24287i	−0.0288491	−	0.115667i
$377$	0.354595			0.0182626
$378$	−0.519346	−	3.51306i	−0.0267123	−	0.180692i
$379$	5.12226	−	5.12226i	0.263113	−	0.263113i	−0.563205	−	0.826317i	$-0.690432\pi$
$379$	5.12226	−	5.12226i	0.263113	−	0.263113i	0.826317	+	0.563205i	$0.190432\pi$
$380$	12.1417	+	4.57916i	0.622858	+	0.234906i
$381$	31.0336	+	31.0336i	1.58990	+	1.58990i
$382$	−7.60508	−	10.9962i	−0.389110	−	0.562613i
$383$	29.9707			1.53143			0.765716	−	0.643179i	$-0.222385\pi$
$383$	29.9707			1.53143			0.765716	+	0.643179i	$0.222385\pi$
$384$	−8.67485	−	27.2187i	−0.442686	−	1.38900i
$385$	0.249185	−	0.0845438i	0.0126997	−	0.00430875i
$386$	−7.41362	+	5.12735i	−0.377343	+	0.260975i
$387$	−2.33113	−	2.33113i	−0.118498	−	0.118498i
$388$	−30.5387	−	11.5174i	−1.55037	−	0.584709i
$389$	22.0266	+	22.0266i	1.11679	+	1.11679i	0.992209	+	0.124582i	$0.0397590\pi$
$389$	22.0266	+	22.0266i	1.11679	+	1.11679i	0.124582	+	0.992209i	$0.460241\pi$
$390$	−0.962759	+	5.28107i	−0.0487512	+	0.267417i
$391$			6.79297i			0.343535i
$392$	−15.4920	−	12.3287i	−0.782465	−	0.622694i
$393$			17.7347i			0.894597i
$394$	14.3068	+	2.60819i	0.720767	+	0.131399i
$395$	−0.290366	−	0.290366i	−0.0146099	−	0.0146099i
$396$	−0.611836	+	0.276723i	−0.0307459	+	0.0139058i
$397$	−10.6623	−	10.6623i	−0.535125	−	0.535125i	0.386968	−	0.922093i	$-0.373522\pi$
$397$	−10.6623	−	10.6623i	−0.535125	−	0.535125i	−0.922093	+	0.386968i	$0.873522\pi$
$398$	4.29886	+	6.21571i	0.215482	+	0.311565i
$399$	−41.0477	+	13.9267i	−2.05495	+	0.697207i
$400$	−2.64143	+	3.00381i	−0.132071	+	0.150190i
$401$	−24.9352			−1.24521			−0.622603	−	0.782538i	$-0.713925\pi$
$401$	−24.9352			−1.24521			−0.622603	+	0.782538i	$0.713925\pi$
$402$	15.5781	−	10.7740i	0.776967	−	0.537360i
$403$	−0.438635	−	0.438635i	−0.0218500	−	0.0218500i
$404$	−7.02168	−	15.5250i	−0.349341	−	0.772395i
$405$	−5.46670	+	5.46670i	−0.271643	+	0.271643i
$406$	−0.873103	+	0.129074i	−0.0433314	+	0.00640582i
$407$	−1.11631			−0.0553333
$408$	9.23030	−	15.3646i	0.456968	−	0.760662i
$409$	−20.5944			−1.01833			−0.509163	−	0.860670i	$-0.670045\pi$
$409$	−20.5944			−1.01833			−0.509163	+	0.860670i	$0.670045\pi$
$410$	−1.56444	+	8.58147i	−0.0772620	+	0.423809i
$411$	−20.8782	−	20.8782i	−1.02984	−	1.02984i
$412$	9.90362	+	3.73507i	0.487917	+	0.184014i
$413$	10.6442	−	21.5758i	0.523765	−	1.06167i
$414$	−7.35053	−	10.6281i	−0.361259	−	0.522342i
$415$			5.32162i			0.261228i
$416$	−5.27524	−	6.66977i	−0.258640	−	0.327012i
$417$	51.1217			2.50344
$418$	0.519103	+	0.750569i	0.0253902	+	0.0367115i
$419$	3.70374	−	3.70374i	0.180939	−	0.180939i	−0.610826	−	0.791765i	$-0.709162\pi$
$419$	3.70374	−	3.70374i	0.180939	−	0.180939i	0.791765	+	0.610826i	$0.209162\pi$
$420$	0.448233	−	13.3538i	0.0218715	−	0.651598i
$421$	−17.7296	−	17.7296i	−0.864086	−	0.864086i	0.127724	−	0.991810i	$-0.459233\pi$
$421$	−17.7296	−	17.7296i	−0.864086	−	0.864086i	−0.991810	+	0.127724i	$0.959233\pi$
$422$	−15.9151	−	2.90139i	−0.774736	−	0.141237i
$423$			2.75899i			0.134147i
$424$	0.0348697	−	0.0580437i	0.00169342	−	0.00281885i
$425$	−2.50969			−0.121738
$426$	−9.60500	+	52.6868i	−0.465364	+	2.55268i
$427$	7.28659	−	14.7700i	0.352623	−	0.714768i
$428$	11.7293	+	25.9336i	0.566959	+	1.25355i
$429$	−0.266946	+	0.266946i	−0.0128883	+	0.0128883i
$430$	−0.785575	−	1.13586i	−0.0378838	−	0.0547760i
$431$		−	35.7191i		−	1.72053i	−0.509848	−	0.860265i	$-0.670298\pi$
$431$		−	35.7191i		−	1.72053i	0.509848	−	0.860265i	$-0.329702\pi$
$432$	0.243199	+	3.78863i	0.0117009	+	0.182281i
$433$		−	11.0602i		−	0.531520i	−0.964039	−	0.265760i	$-0.914377\pi$
$433$		−	11.0602i		−	0.531520i	0.964039	−	0.265760i	$-0.0856229\pi$
$434$	1.23970	+	0.920368i	0.0595074	+	0.0441791i
$435$	−0.421164	−	0.421164i	−0.0201933	−	0.0201933i
$436$	15.2517	+	33.7215i	0.730423	+	1.61497i
$437$	−12.4180	+	12.4180i	−0.594036	+	0.594036i
$438$	−10.1487	+	55.6691i	−0.484923	+	2.65997i
$439$		−	4.80803i		−	0.229475i	−0.993396	−	0.114737i	$-0.963397\pi$
$439$		−	4.80803i		−	0.229475i	0.993396	−	0.114737i	$-0.0366026\pi$
$440$	−0.272943	+	0.0680760i	−0.0130121	+	0.00324540i
$441$	14.3799	+	18.7523i	0.684757	+	0.892967i
$442$	0.956902	−	5.24894i	0.0455152	−	0.249667i
$443$	−11.2754	+	11.2754i	−0.535709	+	0.535709i	−0.922266	−	0.386557i	$-0.873664\pi$
$443$	−11.2754	+	11.2754i	−0.535709	+	0.535709i	0.386557	+	0.922266i	$0.373664\pi$
$444$	−20.0022	+	53.0363i	−0.949263	+	2.51699i
$445$	−5.34122	+	5.34122i	−0.253198	+	0.253198i
$446$	−23.9294	+	16.5499i	−1.13309	+	0.783661i
$447$	60.6156			2.86702
$448$	15.4168	+	14.5025i	0.728376	+	0.685178i
$449$	−25.1066			−1.18485			−0.592426	−	0.805625i	$-0.701830\pi$
$449$	−25.1066			−1.18485			−0.592426	+	0.805625i	$0.701830\pi$
$450$	3.92660	−	2.71568i	0.185102	−	0.128019i
$451$	−0.433774	+	0.433774i	−0.0204256	+	0.0204256i
$452$	9.27282	−	24.5871i	0.436157	−	1.15648i
$453$	20.7975	−	20.7975i	0.977152	−	0.977152i
$454$	4.41718	−	24.2298i	0.207309	−	1.13716i
$455$	−1.27787	−	3.76640i	−0.0599073	−	0.176571i
$456$	44.9613	−	11.2140i	2.10551	−	0.525144i
$457$			21.7097i			1.01554i	0.861494	+	0.507768i	$0.169529\pi$
$457$			21.7097i			1.01554i	−0.861494	+	0.507768i	$0.830471\pi$
$458$	−5.17280	+	28.3746i	−0.241709	+	1.32586i
$459$	−1.68430	+	1.68430i	−0.0786166	+	0.0786166i
$460$	−2.23083	−	4.93236i	−0.104013	−	0.229973i
$461$	−27.3774	−	27.3774i	−1.27509	−	1.27509i	−0.943381	−	0.331712i	$-0.892374\pi$
$461$	−27.3774	−	27.3774i	−1.27509	−	1.27509i	−0.331712	−	0.943381i	$-0.607626\pi$
$462$	0.560120	−	0.754459i	0.0260592	−	0.0351006i
$463$		−	4.16423i		−	0.193528i	−0.995307	−	0.0967641i	$-0.969151\pi$
$463$		−	4.16423i		−	0.193528i	0.995307	−	0.0967641i	$-0.0308492\pi$
$464$	0.941592	−	0.0604425i	0.0437123	−	0.00280597i
$465$			1.04196i			0.0483199i
$466$	−19.2222	−	27.7933i	−0.890451	−	1.28750i
$467$	−14.9813	+	14.9813i	−0.693250	+	0.693250i	−0.962946	−	0.269695i	$-0.913077\pi$
$467$	−14.9813	+	14.9813i	−0.693250	+	0.693250i	0.269695	+	0.962946i	$0.413077\pi$
$468$	4.18263	+	9.24780i	0.193342	+	0.427480i
$469$	−6.20880	+	12.5853i	−0.286696	+	0.581134i
$470$	−0.207289	+	1.13705i	−0.00956151	+	0.0524482i
$471$	−24.3514			−1.12205
$472$	−13.2448	+	22.0471i	−0.609641	+	1.01480i
$473$		−	0.0971242i		−	0.00446578i
$474$	−1.44260	−	0.262992i	−0.0662608	−	0.0120796i
$475$	−4.58790	−	4.58790i	−0.210507	−	0.210507i
$476$	−0.445506	+	13.2726i	−0.0204197	+	0.608347i
$477$	−0.0571472	+	0.0571472i	−0.00261659	+	0.00261659i
$478$	−12.0850	−	17.4736i	−0.552754	−	0.799225i
$479$	6.50906			0.297406			0.148703	−	0.988882i	$-0.452490\pi$
$479$	6.50906			0.297406			0.148703	+	0.988882i	$0.452490\pi$
$480$	−1.65633	+	14.1875i	−0.0756008	+	0.647567i
$481$			16.8728i			0.769334i
$482$	1.45635	+	2.10573i	0.0663349	+	0.0959134i
$483$	16.2165	+	8.00020i	0.737874	+	0.364022i
$484$	20.5662	+	7.75638i	0.934827	+	0.352563i
$485$	11.5394	+	11.5394i	0.523978	+	0.523978i
$486$	−5.67351	+	31.1212i	−0.257356	+	1.41169i
$487$	36.0662			1.63432			0.817158	−	0.576414i	$-0.195548\pi$
$487$	36.0662			1.63432			0.817158	+	0.576414i	$0.195548\pi$
$488$	−9.06689	+	15.0926i	−0.410439	+	0.683210i
$489$	−17.7695			−0.803564
$490$	4.51742	+	8.80869i	0.204076	+	0.397936i
$491$	−19.9630	+	19.9630i	−0.900920	+	0.900920i	−0.995516	−	0.0945960i	$-0.969844\pi$
$491$	−19.9630	+	19.9630i	−0.900920	+	0.900920i	0.0945960	+	0.995516i	$0.469844\pi$
$492$	12.8364	+	28.3813i	0.578709	+	1.27953i
$493$	0.418602	+	0.418602i	0.0188529	+	0.0188529i
$494$	11.3447	−	7.84617i	0.510424	−	0.353016i
$495$	0.335752			0.0150909
$496$	−1.23952	−	1.08999i	−0.0556562	−	0.0489418i
$497$	−12.7487	−	37.5756i	−0.571857	−	1.68550i
$498$	10.8095	+	15.6294i	0.484386	+	0.700372i
$499$	16.1714	+	16.1714i	0.723929	+	0.723929i	0.969403	−	0.245474i	$-0.0789436\pi$
$499$	16.1714	+	16.1714i	0.723929	+	0.723929i	−0.245474	+	0.969403i	$0.578944\pi$
$500$	1.82228	−	0.824188i	0.0814950	−	0.0368588i
$501$	−0.736687	−	0.736687i	−0.0329127	−	0.0329127i
$502$	17.6157	+	3.21140i	0.786225	+	0.143332i
$503$		−	25.1976i		−	1.12350i	−0.827306	−	0.561752i	$-0.810128\pi$
$503$		−	25.1976i		−	1.12350i	0.827306	−	0.561752i	$-0.189872\pi$
$504$	−13.6649	−	21.2480i	−0.608684	−	0.946460i
$505$			8.51951i			0.379113i
$506$	0.0682783	−	0.374530i	0.00303534	−	0.0166499i
$507$	−19.1764	−	19.1764i	−0.851653	−	0.851653i
$508$	32.5259	+	12.2669i	1.44310	+	0.544255i
$509$	−15.4434	−	15.4434i	−0.684515	−	0.684515i	0.276499	−	0.961014i	$-0.410826\pi$
$509$	−15.4434	−	15.4434i	−0.684515	−	0.684515i	−0.961014	+	0.276499i	$0.910826\pi$
$510$	−7.37089	+	5.09780i	−0.326388	+	0.225734i
$511$	−13.4703	−	39.7026i	−0.595892	−	1.75634i
$512$	−15.1448	−	16.8118i	−0.669312	−	0.742982i
$513$	−6.15807			−0.271885
$514$	−13.0396	−	18.8539i	−0.575153	−	0.831612i
$515$	−3.74220	−	3.74220i	−0.164901	−	0.164901i
$516$	−4.61442	−	1.74029i	−0.203139	−	0.0766121i
$517$	−0.0574753	+	0.0574753i	−0.00252776	+	0.00252776i
$518$	−6.14176	−	41.5452i	−0.269853	−	1.82539i
$519$	−18.4281			−0.808905
$520$	1.02896	+	4.12550i	0.0451228	+	0.180915i
$521$	32.4120			1.42000			0.709998	−	0.704204i	$-0.248696\pi$
$521$	32.4120			1.42000			0.709998	+	0.704204i	$0.248696\pi$
$522$	−1.10789	−	0.201973i	−0.0484912	−	0.00884013i
$523$	17.7256	+	17.7256i	0.775087	+	0.775087i	0.978991	−	0.203904i	$-0.0653630\pi$
$523$	17.7256	+	17.7256i	0.775087	+	0.775087i	−0.203904	+	0.978991i	$0.565363\pi$
$524$	5.78868	+	12.7988i	0.252880	+	0.559118i
$525$	−2.95571	+	5.99124i	−0.128998	+	0.261479i
$526$	−23.0235	+	15.9233i	−1.00387	+	0.694291i
$527$		−	1.03562i		−	0.0451125i
$528$	−0.663348	+	0.754352i	−0.0288685	+	0.0328290i
$529$	−15.6738			−0.681470
$530$	−0.0278454	+	0.0192582i	−0.00120953	+	0.000836523i
$531$	21.7066	−	21.7066i	0.941985	−	0.941985i
$532$	−25.0776	+	23.4488i	−1.08725	+	1.01663i
$533$	6.55643	+	6.55643i	0.283991	+	0.283991i
$534$	−4.83768	+	26.5363i	−0.209347	+	1.14834i
$535$		−	14.2314i		−	0.615277i
$536$	7.72577	−	12.8602i	0.333702	−	0.555476i
$537$	−45.2378			−1.95215
$538$	25.5064	+	4.64991i	1.09966	+	0.200472i
$539$	−0.0910861	+	0.690210i	−0.00392336	+	0.0297294i
$540$	0.669842	−	1.77610i	0.0288254	−	0.0764312i
$541$	−6.61753	+	6.61753i	−0.284510	+	0.284510i	−0.834905	−	0.550395i	$-0.814477\pi$
$541$	−6.61753	+	6.61753i	−0.284510	+	0.284510i	0.550395	+	0.834905i	$0.314477\pi$
$542$	−6.35604	+	4.39591i	−0.273015	+	0.188821i
$543$			25.8531i			1.10946i
$544$	1.64625	−	14.1012i	0.0705826	−	0.604583i
$545$		−	18.5051i		−	0.792672i
$546$	−11.4035	−	8.46614i	−0.488026	−	0.362317i
$547$	−24.9955	−	24.9955i	−1.06873	−	1.06873i	−0.997457	−	0.0712747i	$-0.977293\pi$
$547$	−24.9955	−	24.9955i	−1.06873	−	1.06873i	−0.0712747	−	0.997457i	$-0.522707\pi$
$548$	−21.8821	−	8.25267i	−0.934758	−	0.352536i
$549$	14.8595	−	14.8595i	0.634188	−	0.634188i
$550$	0.138372	+	0.0252257i	0.00590020	+	0.00107563i
$551$			1.53047i			0.0652002i
$552$	−16.5707	−	9.95485i	−0.705296	−	0.423707i
$553$	1.02885	−	0.349068i	0.0437510	−	0.0148439i
$554$	−8.56482	−	1.56140i	−0.363884	−	0.0663375i
$555$	20.0404	−	20.0404i	0.850667	−	0.850667i
$556$	36.8936	−	16.6864i	1.56464	−	0.707659i
$557$	−16.5922	+	16.5922i	−0.703033	+	0.703033i	−0.965060	−	0.262027i	$-0.915609\pi$
$557$	−16.5922	+	16.5922i	−0.703033	+	0.703033i	0.262027	+	0.965060i	$0.415609\pi$
$558$	1.12063	+	1.62031i	0.0474400	+	0.0685933i
$559$	−1.46802			−0.0620906
$560$	−4.03526	−	9.78349i	−0.170521	−	0.413428i
$561$	−0.630264			−0.0266098
$562$	3.32198	+	4.80324i	0.140129	+	0.202612i
$563$	4.54880	−	4.54880i	0.191709	−	0.191709i	−0.604725	−	0.796434i	$-0.706717\pi$
$563$	4.54880	−	4.54880i	0.191709	−	0.191709i	0.796434	+	0.604725i	$0.206717\pi$
$564$	1.70083	+	3.76054i	0.0716177	+	0.158347i
$565$	−9.29052	+	9.29052i	−0.390855	+	0.390855i
$566$	20.1835	+	3.67952i	0.848374	+	0.154662i
$567$	−6.57188	−	19.3700i	−0.275993	−	0.813465i
$568$	10.2654	+	41.1582i	0.430729	+	1.72696i
$569$		−	3.91496i		−	0.164124i	−0.996627	−	0.0820619i	$-0.973849\pi$
$569$		−	3.91496i		−	0.164124i	0.996627	−	0.0820619i	$-0.0261505\pi$
$570$	−22.7937	−	4.15538i	−0.954722	−	0.174050i
$571$	23.8199	−	23.8199i	0.996831	−	0.996831i	−0.00316410	−	0.999995i	$-0.501007\pi$
$571$	23.8199	−	23.8199i	0.996831	−	0.996831i	0.999995	+	0.00316410i	$0.00100717\pi$
$572$	−0.105518	+	0.279783i	−0.00441192	+	0.0116983i
$573$	16.8798	+	16.8798i	0.705162	+	0.705162i
$574$	−18.5302	−	13.7570i	−0.773435	−	0.574208i
$575$			2.70670i			0.112877i
$576$	12.6829	+	23.8437i	0.528454	+	0.993488i
$577$		−	40.1244i		−	1.67040i	−0.549946	−	0.835200i	$-0.685352\pi$
$577$		−	40.1244i		−	1.67040i	0.549946	−	0.835200i	$-0.314648\pi$
$578$	−12.4472	+	8.60866i	−0.517736	+	0.358073i
$579$	11.3804	−	11.3804i	0.472951	−	0.472951i
$580$	−0.441416	−	0.166476i	−0.0183288	−	0.00691256i
$581$	−12.6267	−	6.22924i	−0.523844	−	0.258433i
$582$	57.3303	+	10.4515i	2.37642	+	0.433230i
$583$	−0.00238098			−9.86101e−5
$584$	10.8465	+	43.4880i	0.448832	+	1.79954i
$585$		−	5.07485i		−	0.209819i
$586$	2.47509	−	13.5767i	0.102245	−	0.560850i
$587$	16.7702	+	16.7702i	0.692180	+	0.692180i	0.962711	−	0.270531i	$-0.0871993\pi$
$587$	16.7702	+	16.7702i	0.692180	+	0.692180i	−0.270531	+	0.962711i	$0.587199\pi$
$588$	31.1601	+	16.6949i	1.28502	+	0.688485i
$589$	1.89320	−	1.89320i	0.0780079	−	0.0780079i
$590$	10.5767	−	7.31496i	0.435435	−	0.301152i
$591$	−25.9655			−1.06808
$592$	2.87606	+	44.8041i	0.118205	+	1.84144i
$593$		−	2.50323i		−	0.102795i	−0.998678	−	0.0513976i	$-0.983632\pi$
$593$		−	2.50323i		−	0.102795i	0.998678	−	0.0513976i	$-0.0163676\pi$
$594$	0.109794	−	0.0759347i	0.00450489	−	0.00311564i
$595$	2.93773	−	5.95479i	0.120435	−	0.244123i
$596$	43.7452	−	19.7852i	1.79187	−	0.810434i
$597$	−9.54149	−	9.54149i	−0.390507	−	0.390507i
$598$	−5.66097	−	1.03202i	−0.231494	−	0.0422023i
$599$	38.9264			1.59049			0.795244	−	0.606289i	$-0.207343\pi$
$599$	38.9264			1.59049			0.795244	+	0.606289i	$0.207343\pi$
$600$	3.67786	−	6.12212i	0.150148	−	0.249934i
$601$	42.0261			1.71428			0.857141	−	0.515082i	$-0.172239\pi$
$601$	42.0261			1.71428			0.857141	+	0.515082i	$0.172239\pi$
$602$	3.61464	−	0.534364i	0.147322	−	0.0217790i
$603$	−12.6616	+	12.6616i	−0.515619	+	0.515619i
$604$	8.22078	−	21.7976i	0.334499	−	0.886931i
$605$	−7.77118	−	7.77118i	−0.315943	−	0.315943i
$606$	17.3052	+	25.0215i	0.702976	+	1.01643i
$607$	11.8025			0.479049			0.239525	−	0.970890i	$-0.423008\pi$
$607$	11.8025			0.479049			0.239525	+	0.970890i	$0.423008\pi$
$608$	28.7875	−	22.7685i	1.16749	−	0.923386i
$609$	1.49230	−	0.506308i	0.0604710	−	0.0205167i
$610$	7.24039	−	5.00755i	0.293155	−	0.202750i
$611$	0.868731	+	0.868731i	0.0351451	+	0.0351451i
$612$	−5.97948	+	15.8547i	−0.241706	+	0.640889i
$613$	5.34258	+	5.34258i	0.215785	+	0.215785i	0.806719	−	0.590935i	$-0.201241\pi$
$613$	5.34258	+	5.34258i	0.215785	+	0.215785i	−0.590935	+	0.806719i	$0.701241\pi$
$614$	−4.96978	+	27.2610i	−0.200564	+	1.10016i
$615$		−	15.5746i		−	0.628028i
$616$	0.157970	−	0.727305i	0.00636479	−	0.0293040i
$617$			8.22219i			0.331013i	0.986209	+	0.165506i	$0.0529259\pi$
$617$			8.22219i			0.331013i	−0.986209	+	0.165506i	$0.947074\pi$
$618$	−18.5921	−	3.38940i	−0.747882	−	0.136342i
$619$	13.4184	+	13.4184i	0.539333	+	0.539333i	0.923333	−	0.384000i	$-0.125454\pi$
$619$	13.4184	+	13.4184i	0.539333	+	0.539333i	−0.384000	+	0.923333i	$0.625454\pi$
$620$	0.340101	+	0.751966i	0.0136588	+	0.0301997i
$621$	1.81652	+	1.81652i	0.0728944	+	0.0728944i
$622$	18.3091	+	26.4731i	0.734130	+	1.06148i
$623$	−6.42103	−	18.9254i	−0.257253	−	0.758230i
$624$	11.4019	+	10.0264i	0.456442	+	0.401377i
$625$	−1.00000			−0.0400000
$626$	20.5297	−	14.1986i	0.820532	−	0.567491i
$627$	−1.15217	−	1.15217i	−0.0460132	−	0.0460132i
$628$	−17.5740	+	7.94841i	−0.701278	+	0.317176i
$629$	−19.9185	+	19.9185i	−0.794202	+	0.794202i
$630$	1.84726	+	12.4956i	0.0735966	+	0.497835i
$631$	12.8354			0.510971			0.255486	−	0.966813i	$-0.417765\pi$
$631$	12.8354			0.510971			0.255486	+	0.966813i	$0.417765\pi$
$632$	−1.12694	+	0.281075i	−0.0448273	+	0.0111806i
$633$	28.8845			1.14805
$634$	−1.79975	+	9.87226i	−0.0714772	+	0.392077i
$635$	−12.2903	−	12.2903i	−0.487725	−	0.487725i
$636$	−0.0426629	+	0.113122i	−0.00169169	+	0.00448556i
$637$	10.4324	+	1.37675i	0.413348	+	0.0545489i
$638$	−0.0188721	−	0.0272871i	−0.000747154	−	0.00108031i
$639$		−	50.6294i		−	2.00287i
$640$	3.43552	+	10.7795i	0.135801	+	0.426096i
$641$	5.60861			0.221527			0.110763	−	0.993847i	$-0.464670\pi$
$641$	5.60861			0.221527			0.110763	+	0.993847i	$0.464670\pi$
$642$	−28.9075	−	41.7972i	−1.14089	−	1.64960i
$643$	−31.7453	+	31.7453i	−1.25191	+	1.25191i	−0.297052	+	0.954861i	$0.596003\pi$
$643$	−31.7453	+	31.7453i	−1.25191	+	1.25191i	−0.954861	+	0.297052i	$0.903997\pi$
$644$	14.3144	+	0.480477i	0.564067	+	0.0189335i
$645$	1.74361	+	1.74361i	0.0686547	+	0.0686547i
$646$	22.6550	+	4.13010i	0.891350	+	0.162497i
$647$			32.4679i			1.27644i	0.769853	+	0.638222i	$0.220330\pi$
$647$			32.4679i			1.27644i	−0.769853	+	0.638222i	$0.779670\pi$
$648$	5.29179	+	21.2168i	0.207881	+	0.833476i
$649$	0.904382			0.0355001
$650$	0.381283	−	2.09147i	0.0149552	−	0.0820342i
$651$	−2.47229	−	1.21967i	−0.0968965	−	0.0478028i
$652$	−12.8239	+	5.80004i	−0.502224	+	0.227147i
$653$	10.2586	−	10.2586i	0.401451	−	0.401451i	−0.477293	−	0.878744i	$-0.658382\pi$
$653$	10.2586	−	10.2586i	0.401451	−	0.401451i	0.878744	+	0.477293i	$0.158382\pi$
$654$	−37.5884	−	54.3490i	−1.46982	−	2.12521i
$655$		−	7.02350i		−	0.274431i
$656$	18.5276	+	16.2924i	0.723380	+	0.636112i
$657$		−	53.4953i		−	2.08705i
$658$	−2.45526	−	1.82282i	−0.0957159	−	0.0710608i
$659$	−14.0257	−	14.0257i	−0.546364	−	0.546364i	0.379023	−	0.925387i	$-0.376260\pi$
$659$	−14.0257	−	14.0257i	−0.546364	−	0.546364i	−0.925387	+	0.379023i	$0.876260\pi$
$660$	0.457634	−	0.206980i	0.0178134	−	0.00805669i
$661$	20.0421	−	20.0421i	0.779547	−	0.779547i	−0.200206	−	0.979754i	$-0.564161\pi$
$661$	20.0421	−	20.0421i	0.779547	−	0.779547i	0.979754	+	0.200206i	$0.0641612\pi$
$662$	−2.43161	+	13.3382i	−0.0945071	+	0.518404i
$663$			9.52634i			0.369973i
$664$	12.9025	+	7.75120i	0.500716	+	0.300805i
$665$	16.2562	−	5.51542i	0.630388	−	0.213879i
$666$	9.61057	−	52.7173i	0.372402	−	2.04275i
$667$	0.451461	−	0.451461i	0.0174806	−	0.0174806i
$668$	−0.772112	−	0.291196i	−0.0298739	−	0.0112667i
$669$	36.7331	−	36.7331i	1.42018	−	1.42018i
$670$	−6.16944	+	4.26686i	−0.238346	+	0.164843i
$671$	0.619106			0.0239003
$672$	−31.7241	−	20.5372i	−1.22378	−	0.792241i
$673$	4.44272			0.171254			0.0856272	−	0.996327i	$-0.472711\pi$
$673$	4.44272			0.171254			0.0856272	+	0.996327i	$0.472711\pi$
$674$	24.2468	−	16.7694i	0.933951	−	0.645932i
$675$	−0.671121	+	0.671121i	−0.0258314	+	0.0258314i
$676$	−20.0985	−	7.57999i	−0.773020	−	0.291538i
$677$	−28.0949	+	28.0949i	−1.07977	+	1.07977i	−0.0832446	+	0.996529i	$0.526528\pi$
$677$	−28.0949	+	28.0949i	−1.07977	+	1.07977i	−0.996529	+	0.0832446i	$0.973472\pi$
$678$	−8.41465	+	46.1573i	−0.323163	+	1.77266i
$679$	−40.8873	+	13.8723i	−1.56911	+	0.532370i
$680$	−3.65549	+	6.08488i	−0.140182	+	0.233344i
$681$			43.9748i			1.68512i
$682$	−0.0104094	+	0.0570992i	−0.000398597	+	0.00218644i
$683$	−21.9011	+	21.9011i	−0.838021	+	0.838021i	−0.988598	−	0.150577i	$-0.951887\pi$
$683$	−21.9011	+	21.9011i	−0.838021	+	0.838021i	0.150577	+	0.988598i	$0.451887\pi$
$684$	−39.9146	+	18.0527i	−1.52617	+	0.690262i
$685$	8.26842	+	8.26842i	0.315920	+	0.315920i
$686$	−26.1884	+	0.407517i	−0.999879	+	0.0155591i
$687$		−	51.4973i		−	1.96474i
$688$	−3.89818	+	0.250231i	−0.148617	+	0.00953998i
$689$			0.0359881i			0.00137104i
$690$	5.49796	+	7.94948i	0.209304	+	0.302632i
$691$	−3.18326	+	3.18326i	−0.121097	+	0.121097i	−0.765058	−	0.643961i	$-0.777290\pi$
$691$	−3.18326	+	3.18326i	−0.121097	+	0.121097i	0.643961	+	0.765058i	$0.277290\pi$
$692$	−13.2992	+	6.01503i	−0.505562	+	0.228657i
$693$	−0.393016	+	0.796646i	−0.0149295	+	0.0302621i
$694$	4.72498	−	25.9182i	0.179358	−	0.983840i
$695$	−20.2458			−0.767968
$696$	−1.63458	+	0.407688i	−0.0619586	+	0.0154534i
$697$			15.4798i			0.586341i
$698$	39.7082	+	7.23895i	1.50298	+	0.273998i
$699$	42.6644	+	42.6644i	1.61371	+	1.61371i
$700$	−0.177514	+	5.28852i	−0.00670941	+	0.199887i
$701$	−18.5095	+	18.5095i	−0.699092	+	0.699092i	−0.964215	−	0.265122i	$-0.914588\pi$
$701$	−18.5095	+	18.5095i	−0.699092	+	0.699092i	0.265122	+	0.964215i	$0.414588\pi$
$702$	−1.14774	−	1.65952i	−0.0433187	−	0.0626344i
$703$	−72.8249			−2.74664
$704$	−0.232502	+	0.760922i	−0.00876275	+	0.0286783i
$705$		−	2.06364i		−	0.0777212i
$706$	−17.5874	−	25.4296i	−0.661911	−	0.957055i
$707$	−20.2144	−	9.97255i	−0.760241	−	0.375056i
$708$	16.2049	−	42.9676i	0.609017	−	1.61482i
$709$	−31.6483	−	31.6483i	−1.18858	−	1.18858i	−0.977462	−	0.211114i	$-0.932291\pi$
$709$	−31.6483	−	31.6483i	−1.18858	−	1.18858i	−0.211114	−	0.977462i	$-0.567709\pi$
$710$	3.80389	−	20.8656i	0.142757	−	0.783073i
$711$	1.38627			0.0519891
$712$	5.17032	+	20.7298i	0.193766	+	0.776883i
$713$	−1.11692			−0.0418289
$714$	−3.46762	−	23.4563i	−0.129772	−	0.877830i
$715$	0.105719	−	0.105719i	0.00395367	−	0.00395367i
$716$	−32.6473	+	14.7658i	−1.22009	+	0.551825i
$717$	26.8231	+	26.8231i	1.00173	+	1.00173i
$718$	24.6476	−	17.0466i	0.919840	−	0.636173i
$719$	−46.1237			−1.72012			−0.860062	−	0.510190i	$-0.829575\pi$
$719$	−46.1237			−1.72012			−0.860062	+	0.510190i	$0.829575\pi$
$720$	−0.865034	−	13.4758i	−0.0322379	−	0.502212i
$721$	13.2596	−	4.49875i	0.493815	−	0.167542i
$722$	18.5806	+	26.8657i	0.691499	+	0.999836i
$723$	−3.23242	−	3.23242i	−0.120215	−	0.120215i
$724$	8.43858	+	18.6577i	0.313617	+	0.693409i
$725$	0.166794	+	0.166794i	0.00619458	+	0.00619458i
$726$	−38.6089	−	7.03855i	−1.43291	−	0.261225i
$727$		−	6.75173i		−	0.250408i	−0.992131	−	0.125204i	$-0.960041\pi$
$727$		−	6.75173i		−	0.250408i	0.992131	−	0.125204i	$-0.0399585\pi$
$728$	−10.9931	−	2.38769i	−0.407432	−	0.0884937i
$729$		−	33.2888i		−	1.23292i
$730$	4.01920	−	22.0467i	0.148757	−	0.815986i
$731$	−1.73301	−	1.73301i	−0.0640976	−	0.0640976i
$732$	11.0933	−	29.4140i	0.410019	−	1.08717i
$733$	19.2989	+	19.2989i	0.712821	+	0.712821i	0.967124	−	0.254304i	$-0.0818462\pi$
$733$	19.2989	+	19.2989i	0.712821	+	0.712821i	−0.254304	+	0.967124i	$0.581846\pi$
$734$	−11.0116	+	7.61576i	−0.406446	+	0.281103i
$735$	−10.7557	−	14.0261i	−0.396730	−	0.517362i
$736$	−15.2081	−	1.77548i	−0.560578	−	0.0654451i
$737$	−0.527532			−0.0194319
$738$	−16.7504	−	24.2193i	−0.616591	−	0.891527i
$739$	17.5826	+	17.5826i	0.646785	+	0.646785i	0.952215	−	0.305430i	$-0.0988001\pi$
$739$	17.5826	+	17.5826i	0.646785	+	0.646785i	−0.305430	+	0.952215i	$0.598800\pi$
$740$	7.92151	−	21.0041i	0.291201	−	0.772125i
$741$	−17.4149	+	17.4149i	−0.639751	+	0.639751i
$742$	−0.0130998	−	0.0886120i	−0.000480909	−	0.00325305i
$743$	−39.4758			−1.44823			−0.724113	−	0.689681i	$-0.757751\pi$
$743$	−39.4758			−1.44823			−0.724113	+	0.689681i	$0.757751\pi$
$744$	2.52629	+	1.51767i	0.0926185	+	0.0556405i
$745$	−24.0057			−0.879501
$746$	4.34299	+	0.791745i	0.159008	+	0.0289878i
$747$	−12.7033	−	12.7033i	−0.464788	−	0.464788i
$748$	−0.454850	+	0.205721i	−0.0166310	+	0.00752190i
$749$	33.7671	+	16.6586i	1.23382	+	0.608693i
$750$	−2.93697	+	2.03125i	−0.107243	+	0.0741706i
$751$			33.5961i			1.22594i	0.790107	+	0.612970i	$0.210025\pi$
$751$			33.5961i			1.22594i	−0.790107	+	0.612970i	$0.789975\pi$
$752$	2.45491	+	2.15875i	0.0895214	+	0.0787216i
$753$	−31.9708			−1.16508
$754$	−0.412441	+	0.285249i	−0.0150202	+	0.0103882i
$755$	−8.23647	+	8.23647i	−0.299756	+	0.299756i
$756$	3.43010	+	3.66837i	0.124752	+	0.133417i
$757$	−0.530996	−	0.530996i	−0.0192994	−	0.0192994i	0.697391	−	0.716691i	$-0.254344\pi$
$757$	−0.530996	−	0.530996i	−0.0192994	−	0.0192994i	−0.716691	+	0.697391i	$0.754344\pi$
$758$	−1.83733	+	10.0784i	−0.0667349	+	0.366064i
$759$			0.679738i			0.0246729i
$760$	−17.8061	+	4.44110i	−0.645896	+	0.161096i
$761$	−24.0667			−0.872418			−0.436209	−	0.899845i	$-0.643679\pi$
$761$	−24.0667			−0.872418			−0.436209	+	0.899845i	$0.643679\pi$
$762$	−61.0608	−	11.1316i	−2.21200	−	0.403256i
$763$	43.9075	+	21.6612i	1.58956	+	0.784190i
$764$	17.6915	+	6.67219i	0.640054	+	0.241391i
$765$	5.99089	−	5.99089i	0.216601	−	0.216601i
$766$	−34.8599	+	24.1096i	−1.25954	+	0.871114i
$767$		−	13.6696i		−	0.493580i
$768$	31.9858	+	24.6806i	1.15419	+	0.890586i
$769$			21.9377i			0.791093i	0.918446	+	0.395546i	$0.129445\pi$
$769$			21.9377i			0.791093i	−0.918446	+	0.395546i	$0.870555\pi$
$770$	−0.221825	+	0.298790i	−0.00799403	+	0.0107676i
$771$	28.9419	+	28.9419i	1.04232	+	1.04232i
$772$	4.49840	−	11.9276i	0.161901	−	0.429284i
$773$	12.8103	−	12.8103i	0.460755	−	0.460755i	−0.438148	−	0.898903i	$-0.644365\pi$
$773$	12.8103	−	12.8103i	0.460755	−	0.460755i	0.898903	+	0.438148i	$0.144365\pi$
$774$	4.58667	+	0.836167i	0.164864	+	0.0300554i
$775$		−	0.412650i		−	0.0148228i
$776$	44.7857	−	11.1702i	1.60771	−	0.400987i
$777$	24.0919	+	71.0086i	0.864291	+	2.54742i
$778$	−43.3388	−	7.90084i	−1.55377	−	0.283259i
$779$	−28.2983	+	28.2983i	−1.01389	+	1.01389i
$780$	−3.12847	−	6.91707i	−0.112017	−	0.247671i
$781$	1.05471	−	1.05471i	0.0377405	−	0.0377405i
$782$	−5.46452	−	7.90113i	−0.195411	−	0.282544i
$783$	0.223878			0.00800075
$784$	27.9370	+	1.87758i	0.997749	+	0.0670564i
$785$	9.64393			0.344207
$786$	−14.2665	−	20.6278i	−0.508868	−	0.735770i
$787$	−3.80179	+	3.80179i	−0.135519	+	0.135519i	−0.771612	−	0.636093i	$-0.780549\pi$
$787$	−3.80179	+	3.80179i	−0.135519	+	0.135519i	0.636093	+	0.771612i	$0.280549\pi$
$788$	−18.7389	+	8.47527i	−0.667544	+	0.301919i
$789$	35.3425	−	35.3425i	1.25822	−	1.25822i
$790$	0.571316	+	0.104153i	0.0203265	+	0.00370560i
$791$	−11.1687	−	32.9189i	−0.397115	−	1.17046i
$792$	0.489040	−	0.814049i	0.0173773	−	0.0289260i
$793$		−	9.35769i		−	0.332301i
$794$	20.9788	+	3.82452i	0.744511	+	0.135727i
$795$	0.0427443	−	0.0427443i	0.00151598	−	0.00151598i
$796$	−10.0003	−	3.77153i	−0.354451	−	0.133678i
$797$	−18.0285	−	18.0285i	−0.638601	−	0.638601i	0.311610	−	0.950210i	$-0.399132\pi$
$797$	−18.0285	−	18.0285i	−0.638601	−	0.638601i	−0.950210	+	0.311610i	$0.899132\pi$
$798$	36.5408	−	49.2189i	1.29353	−	1.74233i
$799$			2.05109i			0.0725622i
$800$	0.655959	−	5.61869i	0.0231917	−	0.198651i
$801$		−	25.5001i		−	0.901002i
$802$	29.0030	−	20.0588i	1.02413	−	0.708302i
$803$	1.11441	−	1.11441i	0.0393268	−	0.0393268i
$804$	−9.45242	+	25.0633i	−0.333361	+	0.883914i
$805$	−6.42223	−	3.16833i	−0.226354	−	0.111669i
$806$	0.863046	+	0.157337i	0.0303995	+	0.00554195i
$807$	−46.2917			−1.62954
$808$	20.6560	+	12.4091i	0.726676	+	0.436550i
$809$		−	0.874043i		−	0.0307297i	−0.999882	−	0.0153649i	$-0.995109\pi$
$809$		−	0.874043i		−	0.0307297i	0.999882	−	0.0153649i	$-0.00489098\pi$
$810$	1.96088	−	10.7561i	0.0688984	−	0.377932i
$811$	36.6436	+	36.6436i	1.28673	+	1.28673i	0.936761	+	0.349970i	$0.113808\pi$
$811$	36.6436	+	36.6436i	1.28673	+	1.28673i	0.349970	+	0.936761i	$0.386192\pi$
$812$	0.911704	−	0.852487i	0.0319945	−	0.0299164i
$813$	9.75690	−	9.75690i	0.342189	−	0.342189i
$814$	1.29841	−	0.897999i	0.0455094	−	0.0314749i
$815$	7.03729			0.246505
$816$	1.62381	+	25.2963i	0.0568449	+	0.885548i
$817$		−	6.33613i		−	0.221673i
$818$	23.9540	−	16.5669i	0.837532	−	0.579248i
$819$	12.0412	+	5.94038i	0.420753	+	0.207574i
$820$	−5.08361	−	11.2399i	−0.177527	−	0.392514i
$821$	20.2505	+	20.2505i	0.706747	+	0.706747i	0.965850	−	0.259103i	$-0.0834269\pi$
$821$	20.2505	+	20.2505i	0.706747	+	0.706747i	−0.259103	+	0.965850i	$0.583427\pi$
$822$	41.0793	+	7.48891i	1.43280	+	0.261206i
$823$	−17.3081			−0.603323			−0.301662	−	0.953415i	$-0.597541\pi$
$823$	−17.3081			−0.603323			−0.301662	+	0.953415i	$0.597541\pi$
$824$	−14.5239	+	3.62246i	−0.505963	+	0.126194i
$825$	−0.251132			−0.00874330
$826$	4.97578	+	33.6580i	0.173129	+	1.17111i
$827$	8.03881	−	8.03881i	0.279537	−	0.279537i	−0.553387	−	0.832924i	$-0.686665\pi$
$827$	8.03881	−	8.03881i	0.279537	−	0.279537i	0.832924	+	0.553387i	$0.186665\pi$
$828$	17.0993	+	6.44886i	0.594241	+	0.224113i
$829$	−10.6662	−	10.6662i	−0.370451	−	0.370451i	0.497190	−	0.867641i	$-0.334365\pi$
$829$	−10.6662	−	10.6662i	−0.370451	−	0.370451i	−0.867641	+	0.497190i	$0.834365\pi$
$830$	−4.28091	−	6.18975i	−0.148593	−	0.214849i
$831$	15.5444			0.539228
$832$	11.5012	+	3.51423i	0.398733	+	0.121834i
$833$	10.6903	+	13.9408i	0.370396	+	0.483021i
$834$	−59.4614	+	41.1242i	−2.05898	+	1.42402i
$835$	0.291751	+	0.291751i	0.0100965	+	0.0100965i
$836$	−1.20757	−	0.455426i	−0.0417648	−	0.0157512i
$837$	−0.276938	−	0.276938i	−0.00957238	−	0.00957238i
$838$	−1.32851	+	7.28736i	−0.0458928	+	0.251738i
$839$		−	27.4218i		−	0.946704i	−0.880873	−	0.473352i	$-0.843044\pi$
$839$		−	27.4218i		−	0.946704i	0.880873	−	0.473352i	$-0.156956\pi$
$840$	10.2209	+	15.8928i	0.352656	+	0.548354i
$841$			28.9444i			0.998081i
$842$	34.8842	+	6.35952i	1.20219	+	0.219164i
$843$	−7.37326	−	7.37326i	−0.253949	−	0.253949i
$844$	20.8454	−	9.42802i	0.717528	−	0.324526i
$845$	7.59446	+	7.59446i	0.261257	+	0.261257i
$846$	−2.21944	−	3.20908i	−0.0763058	−	0.110330i
$847$	27.5354	−	9.34225i	0.946129	−	0.321003i
$848$	0.00613436	+	0.0955631i	0.000210655	+	0.00328165i
$849$	−36.6311			−1.25718
$850$	2.91910	−	2.01889i	0.100124	−	0.0692473i
$851$	21.4820	+	21.4820i	0.736395	+	0.736395i
$852$	−31.2113	−	69.0084i	−1.06928	−	2.36419i
$853$	−6.88948	+	6.88948i	−0.235891	+	0.235891i	−0.815146	−	0.579255i	$-0.803344\pi$
$853$	−6.88948	+	6.88948i	−0.235891	+	0.235891i	0.579255	+	0.815146i	$0.303344\pi$
$854$	3.40623	+	23.0410i	0.116559	+	0.788448i
$855$	21.9036			0.749087
$856$	−34.5048	−	20.7287i	−1.17935	−	0.708494i
$857$	2.51601			0.0859451			0.0429726	−	0.999076i	$-0.486317\pi$
$857$	2.51601			0.0859451			0.0429726	+	0.999076i	$0.486317\pi$
$858$	0.0957524	−	0.525235i	0.00326893	−	0.0179312i
$859$	−26.2967	−	26.2967i	−0.897231	−	0.897231i	0.0979594	−	0.995190i	$-0.468768\pi$
$859$	−26.2967	−	26.2967i	−0.897231	−	0.897231i	−0.995190	+	0.0979594i	$0.968768\pi$
$860$	1.82746	+	0.689211i	0.0623158	+	0.0235019i
$861$	36.9541	+	18.2309i	1.25939	+	0.621307i
$862$	28.7338	+	41.5461i	0.978677	+	1.41507i
$863$		−	21.3047i		−	0.725221i	−0.931941	−	0.362611i	$-0.881886\pi$
$863$		−	21.3047i		−	0.725221i	0.931941	−	0.362611i	$-0.118114\pi$
$864$	−3.33059	−	4.21105i	−0.113309	−	0.143263i
$865$	7.29813			0.248144
$866$	8.89726	+	12.8645i	0.302341	+	0.437154i
$867$	19.1072	−	19.1072i	0.648916	−	0.648916i
$868$	−2.18231	−	0.0732514i	−0.0740725	−	0.00248631i
$869$	0.0288787	+	0.0288787i	0.000979643	+	0.000979643i
$870$	0.828670	+	0.151070i	0.0280945	+	0.00512174i
$871$			7.97356i			0.270174i
$872$	−44.8666	−	26.9536i	−1.51938	−	0.912765i
$873$	−55.0916			−1.86457
$874$	4.45430	−	24.4334i	0.150669	−	0.826472i
$875$	1.17055	−	2.37272i	0.0395720	−	0.0802126i
$876$	−32.9780	−	72.9146i	−1.11422	−	2.46356i
$877$	11.7170	−	11.7170i	0.395655	−	0.395655i	−0.481043	−	0.876697i	$-0.659742\pi$
$877$	11.7170	−	11.7170i	0.395655	−	0.395655i	0.876697	+	0.481043i	$0.159742\pi$
$878$	3.86776	+	5.59238i	0.130531	+	0.188734i
$879$			24.6405i			0.831105i
$880$	0.262707	−	0.298747i	0.00885584	−	0.0100708i
$881$		−	0.972466i		−	0.0327632i	−0.999866	−	0.0163816i	$-0.994785\pi$
$881$		−	0.972466i		−	0.0327632i	0.999866	−	0.0163816i	$-0.00521466\pi$
$882$	−31.8108	−	10.2437i	−1.07113	−	0.344924i
$883$	5.81134	+	5.81134i	0.195567	+	0.195567i	0.798097	−	0.602529i	$-0.205840\pi$
$883$	5.81134	+	5.81134i	0.195567	+	0.195567i	−0.602529	+	0.798097i	$0.705840\pi$
$884$	3.10944	+	6.87499i	0.104582	+	0.231231i
$885$	−16.2358	+	16.2358i	−0.545761	+	0.545761i
$886$	4.04443	−	22.1851i	0.135875	−	0.745323i
$887$			33.3171i			1.11868i	0.828938	+	0.559340i	$0.188945\pi$
$887$			33.3171i			1.11868i	−0.828938	+	0.559340i	$0.811055\pi$
$888$	−19.3992	−	77.7788i	−0.650993	−	2.61009i
$889$	43.5479	−	14.7750i	1.46055	−	0.495536i
$890$	1.91587	−	10.5092i	0.0642202	−	0.352270i
$891$	0.543698	−	0.543698i	0.0182146	−	0.0182146i
$892$	14.5198	−	38.4995i	0.486158	−	1.28906i
$893$	−3.74954	+	3.74954i	−0.125474	+	0.125474i
$894$	−70.5041	+	48.7615i	−2.35801	+	1.63083i
$895$	17.9156			0.598853
$896$	−29.5982	−	4.46646i	−0.988805	−	0.149214i
$897$	10.2741			0.343044
$898$	29.2023	−	20.1967i	0.974493	−	0.673971i
$899$	−0.0688277	+	0.0688277i	−0.00229553	+	0.00229553i
$900$	−2.38256	+	6.31740i	−0.0794186	+	0.210580i
$901$	−0.0424843	+	0.0424843i	−0.00141536	+	0.00141536i
$902$	0.155593	−	0.853481i	0.00518068	−	0.0284178i
$903$	−6.17810	+	2.09611i	−0.205594	+	0.0697542i
$904$	8.99325	+	36.0575i	0.299111	+	1.19925i
$905$		−	10.2387i		−	0.340345i
$906$	−7.45998	+	40.9206i	−0.247841	+	1.35950i
$907$	12.6037	−	12.6037i	0.418497	−	0.418497i	−0.466188	−	0.884686i	$-0.654373\pi$
$907$	12.6037	−	12.6037i	0.418497	−	0.418497i	0.884686	+	0.466188i	$0.154373\pi$
$908$	14.3536	+	31.7358i	0.476340	+	1.05319i
$909$	−20.3370	−	20.3370i	−0.674535	−	0.674535i
$910$	4.51616	+	3.35286i	0.149709	+	0.111146i
$911$			9.79230i			0.324433i	0.986755	+	0.162217i	$0.0518644\pi$
$911$			9.79230i			0.324433i	−0.986755	+	0.162217i	$0.948136\pi$
$912$	−43.2751	+	49.2120i	−1.43298	+	1.62957i
$913$		−	0.529268i		−	0.0175162i
$914$	−17.4641	−	25.2513i	−0.577661	−	0.835238i
$915$	−11.1144	+	11.1144i	−0.367432	+	0.367432i
$916$	−16.8090	−	37.1647i	−0.555383	−	1.22796i
$917$	16.6648	+	8.22139i	0.550320	+	0.271494i
$918$	0.604153	−	3.31399i	0.0199400	−	0.109378i
$919$	39.6951			1.30942			0.654710	−	0.755880i	$-0.272791\pi$
$919$	39.6951			1.30942			0.654710	+	0.755880i	$0.272791\pi$
$920$	6.56253	+	3.94244i	0.216360	+	0.129978i
$921$		−	49.4762i		−	1.63029i
$922$	53.8670	+	9.82016i	1.77402	+	0.323410i
$923$	−15.9418	−	15.9418i	−0.524731	−	0.524731i
$924$	−0.0445796	+	1.32812i	−0.00146656	+	0.0436919i
$925$	−7.93663	+	7.93663i	−0.260955	+	0.260955i
$926$	3.34986	+	4.84356i	0.110083	+	0.159169i
$927$	17.8661			0.586798
$928$	−1.04658	+	0.827755i	−0.0343555	+	0.0271724i
$929$		−	21.4883i		−	0.705008i	−0.935810	−	0.352504i	$-0.885330\pi$
$929$		−	21.4883i		−	0.705008i	0.935810	−	0.352504i	$-0.114670\pi$
$930$	−0.838194	−	1.21194i	−0.0274855	−	0.0397411i
$931$	−5.94222	+	45.0275i	−0.194748	+	1.47572i
$932$	44.7160	+	16.8643i	1.46472	+	0.552407i
$933$	−40.6378	−	40.6378i	−1.33042	−	1.33042i
$934$	5.37372	−	29.4767i	0.175833	−	0.964508i
$935$	0.249605			0.00816294
$936$	−12.3042	−	7.39177i	−0.402177	−	0.241608i
$937$	−2.65817			−0.0868387			−0.0434194	−	0.999057i	$-0.513825\pi$
$937$	−2.65817			−0.0868387			−0.0434194	+	0.999057i	$0.513825\pi$
$938$	−2.90240	−	19.6330i	−0.0947668	−	0.641039i
$939$	−31.5143	+	31.5143i	−1.02843	+	1.02843i
$940$	−0.673581	−	1.48929i	−0.0219698	−	0.0485753i
$941$	35.7636	+	35.7636i	1.16586	+	1.16586i	0.983171	+	0.182689i	$0.0584800\pi$
$941$	35.7636	+	35.7636i	1.16586	+	1.16586i	0.182689	+	0.983171i	$0.441520\pi$
$942$	28.3239	−	19.5892i	0.922844	−	0.638250i
$943$	16.6950			0.543663
$944$	−2.33005	−	36.2983i	−0.0758368	−	1.18141i
$945$	−0.806798	−	2.37796i	−0.0262451	−	0.0773552i
$946$	0.0781304	+	0.112968i	0.00254024	+	0.00367292i
$947$	21.5158	+	21.5158i	0.699169	+	0.699169i	0.964231	−	0.265062i	$-0.0853925\pi$
$947$	21.5158	+	21.5158i	0.699169	+	0.699169i	−0.265062	+	0.964231i	$0.585392\pi$
$948$	1.88950	−	0.854588i	0.0613680	−	0.0277557i
$949$	−16.8442	−	16.8442i	−0.546785	−	0.546785i
$950$	9.02702	+	1.64566i	0.292875	+	0.0533923i
$951$		−	17.9172i		−	0.581006i
$952$	−10.1588	−	15.7961i	−0.329247	−	0.511956i
$953$		−	44.4498i		−	1.43987i	−0.694041	−	0.719935i	$-0.744171\pi$
$953$		−	44.4498i		−	1.43987i	0.694041	−	0.719935i	$-0.255829\pi$
$954$	0.0204985	−	0.112441i	0.000663662	−	0.00364042i
$955$	−6.68492	−	6.68492i	−0.216319	−	0.216319i
$956$	28.1129	+	10.6026i	0.909236	+	0.342911i
$957$	0.0418874	+	0.0418874i	0.00135403	+	0.00135403i
$958$	−7.57090	+	5.23613i	−0.244605	+	0.169172i
$959$	−29.2973	+	9.94001i	−0.946059	+	0.320980i
$960$	−9.48641	−	17.8344i	−0.306173	−	0.575601i
$961$	−30.8297			−0.994507
$962$	−13.5731	−	19.6253i	−0.437615	−	0.632746i
$963$	33.9718	+	33.9718i	1.09473	+	1.09473i
$964$	−3.38786	−	1.27770i	−0.109116	−	0.0411521i
$965$	−4.50698	+	4.50698i	−0.145085	+	0.145085i
$966$	−25.2976	+	3.73982i	−0.813936	+	0.120327i
$967$	44.1096			1.41847			0.709235	−	0.704972i	$-0.249040\pi$
$967$	44.1096			1.41847			0.709235	+	0.704972i	$0.249040\pi$
$968$	−30.1608	+	7.52253i	−0.969404	+	0.241783i
$969$	−41.1168			−1.32086
$970$	−22.7046	−	4.13914i	−0.729002	−	0.132900i
$971$	−2.91952	−	2.91952i	−0.0936918	−	0.0936918i	0.658707	−	0.752399i	$-0.271104\pi$
$971$	−2.91952	−	2.91952i	−0.0936918	−	0.0936918i	−0.752399	+	0.658707i	$0.771104\pi$
$972$	−18.4360	−	40.7621i	−0.591335	−	1.30744i
$973$	23.6988	−	48.0377i	0.759750	−	1.54002i
$974$	−41.9498	+	29.0130i	−1.34416	+	0.929637i
$975$			3.79582i			0.121564i
$976$	−1.59507	−	24.8485i	−0.0510568	−	0.795380i
$977$	−48.0839			−1.53834			−0.769170	−	0.639044i	$-0.779330\pi$
$977$	−48.0839			−1.53834			−0.769170	+	0.639044i	$0.779330\pi$
$978$	20.6683	−	14.2945i	0.660899	−	0.457086i
$979$	0.531218	−	0.531218i	0.0169778	−	0.0169778i
$980$	−12.3404	−	6.61170i	−0.394200	−	0.211203i
$981$	44.1737	+	44.1737i	1.41036	+	1.41036i
$982$	7.16066	−	39.2787i	0.228506	−	1.25343i
$983$			15.1230i			0.482348i	0.970482	+	0.241174i	$0.0775325\pi$
$983$			15.1230i			0.482348i	−0.970482	+	0.241174i	$0.922468\pi$
$984$	−37.7614	−	22.6852i	−1.20379	−	0.723176i
$985$	10.2832			0.327649
$986$	−0.823629	−	0.150151i	−0.0262297	−	0.00478177i
$987$	4.89644	+	2.41560i	0.155855	+	0.0768895i
$988$	−6.88370	+	18.2523i	−0.219000	+	0.580683i
$989$	−1.86904	+	1.86904i	−0.0594321	+	0.0594321i
$990$	−0.390525	+	0.270092i	−0.0124117	+	0.00858408i
$991$		−	12.2956i		−	0.390584i	−0.980745	−	0.195292i	$-0.937435\pi$
$991$		−	12.2956i		−	0.390584i	0.980745	−	0.195292i	$-0.0625654\pi$
$992$	2.31856	+	0.270682i	0.0736142	+	0.00859416i
$993$		−	24.2076i		−	0.768206i
$994$	45.0557	+	33.4499i	1.42908	+	1.06097i
$995$	3.77873	+	3.77873i	0.119794	+	0.119794i
$996$	−25.1458	−	9.48354i	−0.796776	−	0.300497i
$997$	11.5255	−	11.5255i	0.365016	−	0.365016i	−0.500640	−	0.865656i	$-0.666902\pi$
$997$	11.5255	−	11.5255i	0.365016	−	0.365016i	0.865656	+	0.500640i	$0.166902\pi$
$998$	−31.8183	−	5.80060i	−1.00719	−	0.183615i
$999$			10.6529i			0.337042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bc.a.251.12	yes	128
7.6	odd	2	inner	560.2.bc.a.251.11	✓	128
16.3	odd	4	inner	560.2.bc.a.531.11	yes	128
112.83	even	4	inner	560.2.bc.a.531.12	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bc.a.251.11	✓	128	7.6	odd	2	inner
560.2.bc.a.251.12	yes	128	1.1	even	1	trivial
560.2.bc.a.531.11	yes	128	16.3	odd	4	inner
560.2.bc.a.531.12	yes	128	112.83	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16313 + 0.804438i) q^{2} +(1.78548 - 1.78548i) q^{3} +(0.705760 - 1.87134i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.640444 + 3.51306i) q^{6} +(-0.850060 - 2.50547i) q^{7} +(0.684482 + 2.74436i) q^{8} -3.37588i q^{9} +O(q^{10})\)	\(q+(-1.16313 + 0.804438i) q^{2} +(1.78548 - 1.78548i) q^{3} +(0.705760 - 1.87134i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.640444 + 3.51306i) q^{6} +(-0.850060 - 2.50547i) q^{7} +(0.684482 + 2.74436i) q^{8} -3.37588i q^{9} +(0.253636 - 1.39128i) q^{10} +(0.0703262 - 0.0703262i) q^{11} +(-2.08112 - 4.60135i) q^{12} +(-1.06297 - 1.06297i) q^{13} +(3.00423 + 2.23038i) q^{14} +2.52505i q^{15} +(-3.00381 - 2.64143i) q^{16} -2.50969i q^{17} +(2.71568 + 3.92660i) q^{18} +(4.58790 - 4.58790i) q^{19} +(0.824188 + 1.82228i) q^{20} +(-5.99124 - 2.95571i) q^{21} +(-0.0252257 + 0.138372i) q^{22} -2.70670 q^{23} +(6.12212 + 3.67786i) q^{24} -1.00000i q^{25} +(2.09147 + 0.381283i) q^{26} +(-0.671121 - 0.671121i) q^{27} +(-5.28852 - 0.177514i) q^{28} +(-0.166794 + 0.166794i) q^{29} +(-2.03125 - 2.93697i) q^{30} +0.412650 q^{31} +(5.61869 + 0.655959i) q^{32} -0.251132i q^{33} +(2.01889 + 2.91910i) q^{34} +(2.37272 + 1.17055i) q^{35} +(-6.31740 - 2.38256i) q^{36} +(-7.93663 - 7.93663i) q^{37} +(-1.64566 + 9.02702i) q^{38} -3.79582 q^{39} +(-2.42455 - 1.45655i) q^{40} -6.16803 q^{41} +(9.34629 - 1.38169i) q^{42} +(0.690526 - 0.690526i) q^{43} +(-0.0819707 - 0.181238i) q^{44} +(2.38711 + 2.38711i) q^{45} +(3.14825 - 2.17737i) q^{46} -0.817267 q^{47} +(-10.0795 + 0.647018i) q^{48} +(-5.55480 + 4.25960i) q^{49} +(0.804438 + 1.16313i) q^{50} +(-4.48100 - 4.48100i) q^{51} +(-2.73938 + 1.23897i) q^{52} +(-0.0169281 - 0.0169281i) q^{53} +(1.32048 + 0.240728i) q^{54} +0.0994563i q^{55} +(6.29406 - 4.04782i) q^{56} -16.3832i q^{57} +(0.0598284 - 0.328179i) q^{58} +(6.42990 + 6.42990i) q^{59} +(4.72522 + 1.78208i) q^{60} +(4.40167 + 4.40167i) q^{61} +(-0.479968 + 0.331952i) q^{62} +(-8.45817 + 2.86970i) q^{63} +(-7.06297 + 3.75692i) q^{64} +1.50327 q^{65} +(0.202020 + 0.292100i) q^{66} +(-3.75060 - 3.75060i) q^{67} +(-4.69648 - 1.77124i) q^{68} +(-4.83275 + 4.83275i) q^{69} +(-3.70143 + 0.547194i) q^{70} +14.9974 q^{71} +(9.26460 - 2.31073i) q^{72} +15.8463 q^{73} +(15.6159 + 2.84684i) q^{74} +(-1.78548 - 1.78548i) q^{75} +(-5.34755 - 11.8235i) q^{76} +(-0.235982 - 0.116419i) q^{77} +(4.41505 - 3.05351i) q^{78} +0.410639i q^{79} +(3.99178 - 0.256240i) q^{80} +7.73109 q^{81} +(7.17424 - 4.96179i) q^{82} +(3.76295 - 3.76295i) q^{83} +(-9.75950 + 9.12561i) q^{84} +(1.77462 + 1.77462i) q^{85} +(-0.247689 + 1.35866i) q^{86} +0.595615i q^{87} +(0.241137 + 0.144863i) q^{88} +7.55362 q^{89} +(-4.69680 - 0.856245i) q^{90} +(-1.75966 + 3.56683i) q^{91} +(-1.91028 + 5.06514i) q^{92} +(0.736779 - 0.736779i) q^{93} +(0.950591 - 0.657440i) q^{94} +6.48827i q^{95} +(11.2033 - 8.86086i) q^{96} -16.3192i q^{97} +(3.03439 - 9.42298i) q^{98} +(-0.237413 - 0.237413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 4 q^{4}+O(q^{10}) \) 128 * q - 4 * q^4	\( 128 q - 4 q^{4} + 8 q^{11} - 8 q^{14} + 20 q^{16} + 20 q^{18} - 52 q^{22} - 16 q^{23} + 44 q^{28} + 16 q^{29} + 40 q^{32} + 16 q^{37} + 60 q^{42} - 8 q^{43} - 108 q^{44} - 40 q^{46} - 4 q^{50} + 80 q^{51} + 16 q^{53} + 12 q^{56} - 76 q^{58} - 56 q^{60} - 52 q^{64} + 40 q^{67} - 8 q^{70} - 64 q^{71} - 36 q^{72} + 60 q^{74} - 48 q^{78} - 128 q^{81} - 32 q^{84} + 76 q^{86} + 20 q^{88} - 32 q^{91} + 64 q^{92} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 128 * q - 4 * q^4 + 8 * q^11 - 8 * q^14 + 20 * q^16 + 20 * q^18 - 52 * q^22 - 16 * q^23 + 44 * q^28 + 16 * q^29 + 40 * q^32 + 16 * q^37 + 60 * q^42 - 8 * q^43 - 108 * q^44 - 40 * q^46 - 4 * q^50 + 80 * q^51 + 16 * q^53 + 12 * q^56 - 76 * q^58 - 56 * q^60 - 52 * q^64 + 40 * q^67 - 8 * q^70 - 64 * q^71 - 36 * q^72 + 60 * q^74 - 48 * q^78 - 128 * q^81 - 32 * q^84 + 76 * q^86 + 20 * q^88 - 32 * q^91 + 64 * q^92 - 76 * q^98 - 40 * q^99

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