LMFDB - Embedded newform 390.2.bn.c.67.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

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("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.7
Character	$\chi$	$=$	390.67
Dual form			390.2.bn.c.163.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.83584 + 1.27660i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.838691 + 0.484219i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.83584 + 1.27660i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.838691 + 0.484219i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(0.187644 - 2.22818i) q^{10} +(-1.30003 + 4.85177i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-1.46581 + 3.29414i) q^{13} -0.968437i q^{14} +(1.44288 + 1.70825i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.82001 - 6.79237i) q^{17} -1.00000i q^{18} +(2.91467 - 0.780983i) q^{19} +(-2.02348 + 0.951586i) q^{20} +(0.684788 + 0.684788i) q^{21} +(4.85177 - 1.30003i) q^{22} +(-1.01946 + 3.80468i) q^{23} +(0.965926 + 0.258819i) q^{24} +(1.74061 + 4.68725i) q^{25} +(3.58572 - 0.377640i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.838691 + 0.484219i) q^{28} +(-3.52151 + 2.03314i) q^{29} +(0.757946 - 2.10369i) q^{30} +(6.94843 - 6.94843i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.51146 + 4.34998i) q^{33} +(-4.97236 + 4.97236i) q^{34} +(0.921551 + 1.95962i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(7.90395 - 4.56335i) q^{37} +(-2.13369 - 2.13369i) q^{38} +(-2.26845 + 2.80252i) q^{39} +(1.83584 + 1.27660i) q^{40} +(-7.00720 - 1.87757i) q^{41} +(0.250650 - 0.935438i) q^{42} +(9.01668 - 2.41601i) q^{43} +(-3.55175 - 3.55175i) q^{44} +(0.951586 + 2.02348i) q^{45} +(3.80468 - 1.01946i) q^{46} -10.2669i q^{47} +(-0.258819 - 0.965926i) q^{48} +(-3.03106 - 5.24996i) q^{49} +(3.18897 - 3.85104i) q^{50} -7.03198i q^{51} +(-2.11991 - 2.91650i) q^{52} +(4.84444 - 4.84444i) q^{53} +(0.258819 - 0.965926i) q^{54} +(-8.58040 + 7.24747i) q^{55} +(0.838691 + 0.484219i) q^{56} +3.01749 q^{57} +(3.52151 + 2.03314i) q^{58} +(1.32954 + 4.96190i) q^{59} +(-2.20082 + 0.395445i) q^{60} +(-6.98358 + 12.0959i) q^{61} +(-9.49174 - 2.54330i) q^{62} +(0.484219 + 0.838691i) q^{63} +1.00000 q^{64} +(-6.89629 + 4.17627i) q^{65} +5.02293 q^{66} +(-1.94887 - 3.37554i) q^{67} +(6.79237 + 1.82001i) q^{68} +(-1.96945 + 3.41118i) q^{69} +(1.23630 - 1.77789i) q^{70} +(-0.745580 - 2.78254i) q^{71} +(0.866025 + 0.500000i) q^{72} -5.28998 q^{73} +(-7.90395 - 4.56335i) q^{74} +(0.468152 + 4.97804i) q^{75} +(-0.780983 + 2.91467i) q^{76} +(-3.43964 + 3.43964i) q^{77} +(3.56128 + 0.563280i) q^{78} +8.53983i q^{79} +(0.187644 - 2.22818i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.87757 + 7.00720i) q^{82} -7.83085i q^{83} +(-0.935438 + 0.250650i) q^{84} +(5.32986 - 14.7931i) q^{85} +(-6.60067 - 6.60067i) q^{86} +(-3.92773 + 1.05243i) q^{87} +(-1.30003 + 4.85177i) q^{88} +(-9.75961 - 2.61508i) q^{89} +(1.27660 - 1.83584i) q^{90} +(-2.82445 + 2.05300i) q^{91} +(-2.78522 - 2.78522i) q^{92} +(8.51006 - 4.91328i) q^{93} +(-8.89142 + 5.13346i) q^{94} +(6.34786 + 2.28709i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(5.23050 - 9.05950i) q^{97} +(-3.03106 + 5.24996i) q^{98} +(-3.55175 + 3.55175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.83584	+	1.27660i	0.821012	+	0.570911i
$5$	1.83584	+	1.27660i	0.821012	+	0.570911i
$6$	−0.258819	−	0.965926i	−0.105662	−	0.394338i
$7$	0.838691	+	0.484219i	0.316995	+	0.183017i	0.650053	−	0.759889i	$-0.274747\pi$
$7$	0.838691	+	0.484219i	0.316995	+	0.183017i	−0.333057	+	0.942907i	$0.608080\pi$
$8$	1.00000			0.353553
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	0.187644	−	2.22818i	0.0593383	−	0.704613i
$11$	−1.30003	+	4.85177i	−0.391974	+	1.46287i	0.434901	+	0.900478i	$0.356783\pi$
$11$	−1.30003	+	4.85177i	−0.391974	+	1.46287i	−0.826874	+	0.562387i	$0.809883\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−1.46581	+	3.29414i	−0.406544	+	0.913631i
$13$	−1.46581	+	3.29414i	−0.406544	+	0.913631i
$14$		−	0.968437i		−	0.258826i
$15$	1.44288	+	1.70825i	0.372549	+	0.441067i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.82001	−	6.79237i	−0.441418	−	1.64739i	−0.725225	−	0.688512i	$-0.758264\pi$
$17$	−1.82001	−	6.79237i	−0.441418	−	1.64739i	0.283808	−	0.958881i	$-0.408402\pi$
$18$		−	1.00000i		−	0.235702i
$19$	2.91467	−	0.780983i	0.668671	−	0.179170i	0.0915147	−	0.995804i	$-0.470829\pi$
$19$	2.91467	−	0.780983i	0.668671	−	0.179170i	0.577156	+	0.816634i	$0.304162\pi$
$20$	−2.02348	+	0.951586i	−0.452465	+	0.212781i
$21$	0.684788	+	0.684788i	0.149433	+	0.149433i
$22$	4.85177	−	1.30003i	1.03440	−	0.277167i
$23$	−1.01946	+	3.80468i	−0.212572	+	0.793330i	0.774435	+	0.632654i	$0.218034\pi$
$23$	−1.01946	+	3.80468i	−0.212572	+	0.793330i	−0.987007	+	0.160677i	$0.948632\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$	1.74061	+	4.68725i	0.348122	+	0.937449i
$26$	3.58572	−	0.377640i	0.703218	−	0.0740614i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.838691	+	0.484219i	−0.158498	+	0.0915087i
$29$	−3.52151	+	2.03314i	−0.653928	+	0.377545i	−0.789959	−	0.613159i	$-0.789898\pi$
$29$	−3.52151	+	2.03314i	−0.653928	+	0.377545i	0.136032	+	0.990704i	$0.456565\pi$
$30$	0.757946	−	2.10369i	0.138381	−	0.384080i
$31$	6.94843	−	6.94843i	1.24798	−	1.24798i	0.291363	−	0.956613i	$-0.405891\pi$
$31$	6.94843	−	6.94843i	1.24798	−	1.24798i	0.956613	−	0.291363i	$-0.0941087\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.51146	+	4.34998i	−0.437190	+	0.757235i
$34$	−4.97236	+	4.97236i	−0.852753	+	0.852753i
$35$	0.921551	+	1.95962i	0.155771	+	0.331236i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	7.90395	−	4.56335i	1.29940	−	0.750210i	0.319101	−	0.947721i	$-0.396619\pi$
$37$	7.90395	−	4.56335i	1.29940	−	0.750210i	0.980301	+	0.197511i	$0.0632859\pi$
$38$	−2.13369	−	2.13369i	−0.346129	−	0.346129i
$39$	−2.26845	+	2.80252i	−0.363243	+	0.448762i
$40$	1.83584	+	1.27660i	0.290272	+	0.201847i
$41$	−7.00720	−	1.87757i	−1.09434	−	0.293228i	−0.333883	−	0.942615i	$-0.608359\pi$
$41$	−7.00720	−	1.87757i	−1.09434	−	0.293228i	−0.760458	+	0.649387i	$0.775026\pi$
$42$	0.250650	−	0.935438i	0.0386761	−	0.144341i
$43$	9.01668	−	2.41601i	1.37503	−	0.368438i	0.505717	−	0.862699i	$-0.331228\pi$
$43$	9.01668	−	2.41601i	1.37503	−	0.368438i	0.869313	+	0.494261i	$0.164561\pi$
$44$	−3.55175	−	3.55175i	−0.535446	−	0.535446i
$45$	0.951586	+	2.02348i	0.141854	+	0.301643i
$46$	3.80468	−	1.01946i	0.560969	−	0.150311i
$47$		−	10.2669i		−	1.49759i	−0.662804	−	0.748793i	$-0.730634\pi$
$47$		−	10.2669i		−	1.49759i	0.662804	−	0.748793i	$-0.269366\pi$
$48$	−0.258819	−	0.965926i	−0.0373573	−	0.139419i
$49$	−3.03106	−	5.24996i	−0.433009	−	0.749994i
$50$	3.18897	−	3.85104i	0.450988	−	0.544619i
$51$		−	7.03198i		−	0.984675i
$52$	−2.11991	−	2.91650i	−0.293978	−	0.404446i
$53$	4.84444	−	4.84444i	0.665436	−	0.665436i	−0.291220	−	0.956656i	$-0.594061\pi$
$53$	4.84444	−	4.84444i	0.665436	−	0.665436i	0.956656	+	0.291220i	$0.0940613\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	−8.58040	+	7.24747i	−1.15698	+	0.977248i
$56$	0.838691	+	0.484219i	0.112075	+	0.0647064i
$57$	3.01749			0.399676
$58$	3.52151	+	2.03314i	0.462397	+	0.266965i
$59$	1.32954	+	4.96190i	0.173091	+	0.645984i	0.996869	+	0.0790717i	$0.0251956\pi$
$59$	1.32954	+	4.96190i	0.173091	+	0.645984i	−0.823778	+	0.566913i	$0.808138\pi$
$60$	−2.20082	+	0.395445i	−0.284125	+	0.0510518i
$61$	−6.98358	+	12.0959i	−0.894156	+	1.54872i	−0.0593112	+	0.998240i	$0.518890\pi$
$61$	−6.98358	+	12.0959i	−0.894156	+	1.54872i	−0.834845	+	0.550485i	$0.814443\pi$
$62$	−9.49174	−	2.54330i	−1.20545	−	0.323000i
$63$	0.484219	+	0.838691i	0.0610058	+	0.105665i
$64$	1.00000			0.125000
$65$	−6.89629	+	4.17627i	−0.855379	+	0.518002i
$66$	5.02293			0.618280
$67$	−1.94887	−	3.37554i	−0.238092	−	0.412387i	0.722075	−	0.691815i	$-0.243189\pi$
$67$	−1.94887	−	3.37554i	−0.238092	−	0.412387i	−0.960167	+	0.279428i	$0.909855\pi$
$68$	6.79237	+	1.82001i	0.823696	+	0.220709i
$69$	−1.96945	+	3.41118i	−0.237094	+	0.410658i
$70$	1.23630	−	1.77789i	0.147766	−	0.212499i
$71$	−0.745580	−	2.78254i	−0.0884841	−	0.330227i	0.907467	−	0.420123i	$-0.138013\pi$
$71$	−0.745580	−	2.78254i	−0.0884841	−	0.330227i	−0.995951	+	0.0898962i	$0.971346\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−5.28998			−0.619146			−0.309573	−	0.950876i	$-0.600186\pi$
$73$	−5.28998			−0.619146			−0.309573	+	0.950876i	$0.600186\pi$
$74$	−7.90395	−	4.56335i	−0.918815	−	0.530478i
$75$	0.468152	+	4.97804i	0.0540575	+	0.574814i
$76$	−0.780983	+	2.91467i	−0.0895849	+	0.334335i
$77$	−3.43964	+	3.43964i	−0.391984	+	0.391984i
$78$	3.56128	+	0.563280i	0.403236	+	0.0637789i
$79$			8.53983i			0.960806i	0.877048	+	0.480403i	$0.159510\pi$
$79$			8.53983i			0.960806i	−0.877048	+	0.480403i	$0.840490\pi$
$80$	0.187644	−	2.22818i	0.0209793	−	0.249118i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.87757	+	7.00720i	0.207343	+	0.773816i
$83$		−	7.83085i		−	0.859548i	−0.902937	−	0.429774i	$-0.858593\pi$
$83$		−	7.83085i		−	0.859548i	0.902937	−	0.429774i	$-0.141407\pi$
$84$	−0.935438	+	0.250650i	−0.102065	+	0.0273482i
$85$	5.32986	−	14.7931i	0.578105	−	1.60454i
$86$	−6.60067	−	6.60067i	−0.711768	−	0.711768i
$87$	−3.92773	+	1.05243i	−0.421097	+	0.112833i
$88$	−1.30003	+	4.85177i	−0.138584	+	0.517201i
$89$	−9.75961	−	2.61508i	−1.03452	−	0.277198i	−0.298677	−	0.954354i	$-0.596545\pi$
$89$	−9.75961	−	2.61508i	−1.03452	−	0.277198i	−0.735839	+	0.677156i	$0.763212\pi$
$90$	1.27660	−	1.83584i	0.134565	−	0.193514i
$91$	−2.82445	+	2.05300i	−0.296083	+	0.215212i
$92$	−2.78522	−	2.78522i	−0.290379	−	0.290379i
$93$	8.51006	−	4.91328i	0.882452	−	0.509484i
$94$	−8.89142	+	5.13346i	−0.917080	+	0.529476i
$95$	6.34786	+	2.28709i	0.651277	+	0.234651i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	5.23050	−	9.05950i	0.531077	−	0.919853i	−0.468265	−	0.883588i	$-0.655121\pi$
$97$	5.23050	−	9.05950i	0.531077	−	0.919853i	0.999342	−	0.0362647i	$-0.0115460\pi$
$98$	−3.03106	+	5.24996i	−0.306184	+	0.530326i
$99$	−3.55175	+	3.55175i	−0.356964	+	0.356964i
$100$	−4.92958	−	0.836210i	−0.492958	−	0.0836210i
$101$	−5.81959	+	3.35994i	−0.579071	+	0.334327i	−0.760764	−	0.649029i	$-0.775176\pi$
$101$	−5.81959	+	3.35994i	−0.579071	+	0.334327i	0.181693	+	0.983355i	$0.441842\pi$
$102$	−6.08988	+	3.51599i	−0.602988	+	0.348135i
$103$	−2.73124	−	2.73124i	−0.269118	−	0.269118i	0.559627	−	0.828745i	$-0.310944\pi$
$103$	−2.73124	−	2.73124i	−0.269118	−	0.269118i	−0.828745	+	0.559627i	$0.810944\pi$
$104$	−1.46581	+	3.29414i	−0.143735	+	0.323017i
$105$	0.382964	+	2.13136i	0.0373734	+	0.207999i
$106$	−6.61763	−	1.77319i	−0.642761	−	0.172227i
$107$	−4.15969	+	15.5242i	−0.402133	+	1.50078i	0.407151	+	0.913361i	$0.366522\pi$
$107$	−4.15969	+	15.5242i	−0.402133	+	1.50078i	−0.809283	+	0.587418i	$0.800144\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	−7.13680	−	7.13680i	−0.683582	−	0.683582i	0.277224	−	0.960805i	$-0.410586\pi$
$109$	−7.13680	−	7.13680i	−0.683582	−	0.683582i	−0.960805	+	0.277224i	$0.910586\pi$
$110$	10.5667	+	3.80711i	1.00749	+	0.362993i
$111$	8.81571	−	2.36216i	0.836750	−	0.224207i
$112$		−	0.968437i		−	0.0915087i
$113$	−0.280295	−	1.04608i	−0.0263679	−	0.0984065i	0.951488	−	0.307686i	$-0.0995547\pi$
$113$	−0.280295	−	1.04608i	−0.0263679	−	0.0984065i	−0.977856	+	0.209280i	$0.932888\pi$
$114$	−1.50874	−	2.61322i	−0.141307	−	0.244750i
$115$	−6.72860	+	5.68334i	−0.627445	+	0.529974i
$116$		−	4.06629i		−	0.377545i
$117$	−2.91650	+	2.11991i	−0.269631	+	0.195985i
$118$	3.63236	−	3.63236i	0.334386	−	0.334386i
$119$	1.76257	−	6.57799i	0.161574	−	0.603003i
$120$	1.44288	+	1.70825i	0.131716	+	0.155941i
$121$	−12.3234	−	7.11490i	−1.12031	−	0.646809i
$122$	13.9672			1.26453
$123$	−6.28248	−	3.62719i	−0.566472	−	0.327053i
$124$	2.54330	+	9.49174i	0.228395	+	0.852383i
$125$	−2.78823	+	10.8271i	−0.249387	+	0.968404i
$126$	0.484219	−	0.838691i	0.0431376	−	0.0747165i
$127$	−0.614358	−	0.164617i	−0.0545155	−	0.0146074i	0.231458	−	0.972845i	$-0.425650\pi$
$127$	−0.614358	−	0.164617i	−0.0545155	−	0.0146074i	−0.285974	+	0.958237i	$0.592317\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	9.33475			0.821879
$130$	7.06490	+	3.88423i	0.619633	+	0.340669i
$131$	0.518007			0.0452584			0.0226292	−	0.999744i	$-0.492796\pi$
$131$	0.518007			0.0452584			0.0226292	+	0.999744i	$0.492796\pi$
$132$	−2.51146	−	4.34998i	−0.218595	−	0.378617i
$133$	2.82267	+	0.756333i	0.244757	+	0.0655824i
$134$	−1.94887	+	3.37554i	−0.168356	+	0.291602i
$135$	0.395445	+	2.20082i	0.0340345	+	0.189417i
$136$	−1.82001	−	6.79237i	−0.156065	−	0.582441i
$137$	8.53881	+	4.92988i	0.729520	+	0.421188i	0.818246	−	0.574868i	$-0.194946\pi$
$137$	8.53881	+	4.92988i	0.729520	+	0.421188i	−0.0887268	+	0.996056i	$0.528280\pi$
$138$	3.93889			0.335301
$139$	0.123541	+	0.0713262i	0.0104786	+	0.00604981i	0.505230	−	0.862985i	$-0.331408\pi$
$139$	0.123541	+	0.0713262i	0.0104786	+	0.00604981i	−0.494752	+	0.869034i	$0.664741\pi$
$140$	−2.15785	−	0.181722i	−0.182372	−	0.0153583i
$141$	2.65728	−	9.91709i	0.223783	−	0.835170i
$142$	−2.03696	+	2.03696i	−0.170938	+	0.170938i
$143$	−14.0768	−	11.3943i	−1.17717	−	0.952838i
$144$		−	1.00000i		−	0.0833333i
$145$	−9.06043	−	0.763015i	−0.752427	−	0.0633650i
$146$	2.64499	+	4.58126i	0.218901	+	0.379148i
$147$	−1.56899	−	5.85557i	−0.129408	−	0.482959i
$148$			9.12669i			0.750210i
$149$	2.12794	−	0.570179i	0.174327	−	0.0467109i	−0.170599	−	0.985340i	$-0.554570\pi$
$149$	2.12794	−	0.570179i	0.174327	−	0.0467109i	0.344927	+	0.938630i	$0.387904\pi$
$150$	4.07703	−	2.89445i	0.332888	−	0.236331i
$151$	6.94204	+	6.94204i	0.564935	+	0.564935i	0.930705	−	0.365770i	$-0.119194\pi$
$151$	6.94204	+	6.94204i	0.564935	+	0.564935i	−0.365770	+	0.930705i	$0.619194\pi$
$152$	2.91467	−	0.780983i	0.236411	−	0.0633461i
$153$	1.82001	−	6.79237i	0.147139	−	0.549131i
$154$	4.69864	+	1.25900i	0.378627	+	0.101453i
$155$	21.6265	−	3.88587i	1.73709	−	0.312121i
$156$	−1.29283	−	3.36580i	−0.103509	−	0.269480i
$157$	−9.27595	−	9.27595i	−0.740302	−	0.740302i	0.232334	−	0.972636i	$-0.425364\pi$
$157$	−9.27595	−	9.27595i	−0.740302	−	0.740302i	−0.972636	+	0.232334i	$0.925364\pi$
$158$	7.39571	−	4.26992i	0.588371	−	0.339696i
$159$	5.93321	−	3.42554i	0.470534	−	0.271663i
$160$	−2.02348	+	0.951586i	−0.159970	+	0.0752295i
$161$	−2.69731	+	2.69731i	−0.212578	+	0.212578i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	0.167540	−	0.290188i	0.0131227	−	0.0227292i	−0.859389	−	0.511322i	$-0.829156\pi$
$163$	0.167540	−	0.290188i	0.0131227	−	0.0227292i	0.872512	+	0.488592i	$0.162489\pi$
$164$	5.12963	−	5.12963i	0.400556	−	0.400556i
$165$	−10.1638	+	4.77975i	−0.791251	+	0.372103i
$166$	−6.78172	+	3.91543i	−0.526363	+	0.303896i
$167$	15.8294	−	9.13911i	1.22492	−	0.707206i	0.258954	−	0.965890i	$-0.416622\pi$
$167$	15.8294	−	9.13911i	1.22492	−	0.707206i	0.965962	+	0.258684i	$0.0832887\pi$
$168$	0.684788	+	0.684788i	0.0528326	+	0.0528326i
$169$	−8.70278	−	9.65721i	−0.669445	−	0.742862i
$170$	−15.4762	+	2.78076i	−1.18697	+	0.213275i
$171$	2.91467	+	0.780983i	0.222890	+	0.0597233i
$172$	−2.41601	+	9.01668i	−0.184219	+	0.687515i
$173$	−2.00714	+	0.537812i	−0.152600	+	0.0408891i	−0.334310	−	0.942463i	$-0.608503\pi$
$173$	−2.00714	+	0.537812i	−0.152600	+	0.0408891i	0.181710	+	0.983352i	$0.441837\pi$
$174$	2.87530	+	2.87530i	0.217976	+	0.217976i
$175$	−0.809817	+	4.77399i	−0.0612164	+	0.360880i
$176$	4.85177	−	1.30003i	0.365716	−	0.0979934i
$177$			5.13694i			0.386116i
$178$	2.61508	+	9.75961i	0.196008	+	0.731513i
$179$	4.87549	+	8.44459i	0.364411	+	0.631178i	0.988681	−	0.150030i	$-0.0479370\pi$
$179$	4.87549	+	8.44459i	0.364411	+	0.631178i	−0.624271	+	0.781208i	$0.714604\pi$
$180$	−2.22818	−	0.187644i	−0.166079	−	0.0139862i
$181$		−	7.04690i		−	0.523792i	−0.965096	−	0.261896i	$-0.915652\pi$
$181$		−	7.04690i		−	0.523792i	0.965096	−	0.261896i	$-0.0843477\pi$
$182$	3.19017	+	1.41955i	0.236471	+	0.105224i
$183$	−9.87628	+	9.87628i	−0.730076	+	0.730076i
$184$	−1.01946	+	3.80468i	−0.0751556	+	0.280485i
$185$	20.3359	+	1.71257i	1.49513	+	0.125911i
$186$	−8.51006	−	4.91328i	−0.623988	−	0.360260i
$187$	35.3211			2.58294
$188$	8.89142	+	5.13346i	0.648474	+	0.374396i
$189$	0.250650	+	0.935438i	0.0182321	+	0.0680431i
$190$	−1.19325	−	6.64095i	−0.0865675	−	0.481785i
$191$	6.31127	−	10.9314i	0.456667	−	0.790971i	−0.542115	−	0.840304i	$-0.682376\pi$
$191$	6.31127	−	10.9314i	0.456667	−	0.790971i	0.998782	+	0.0493335i	$0.0157097\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	11.3631	+	19.6816i	0.817937	+	1.41671i	0.907199	+	0.420701i	$0.138216\pi$
$193$	11.3631	+	19.6816i	0.817937	+	1.41671i	−0.0892620	+	0.996008i	$0.528451\pi$
$194$	−10.4610			−0.751057
$195$	−7.74220	+	2.24908i	−0.554430	+	0.161060i
$196$	6.06213			0.433009
$197$	−8.41170	−	14.5695i	−0.599309	−	1.03803i	−0.992923	−	0.118758i	$-0.962109\pi$
$197$	−8.41170	−	14.5695i	−0.599309	−	1.03803i	0.393614	−	0.919276i	$-0.371225\pi$
$198$	4.85177	+	1.30003i	0.344801	+	0.0923891i
$199$	7.60612	−	13.1742i	0.539184	−	0.933893i	−0.459765	−	0.888041i	$-0.652066\pi$
$199$	7.60612	−	13.1742i	0.539184	−	0.933893i	0.998948	−	0.0458525i	$-0.0146004\pi$
$200$	1.74061	+	4.68725i	0.123080	+	0.331438i
$201$	−1.00881	−	3.76492i	−0.0711558	−	0.265557i
$202$	5.81959	+	3.35994i	0.409465	+	0.236405i
$203$	−3.93794			−0.276390
$204$	6.08988	+	3.51599i	0.426377	+	0.246169i
$205$	−10.4672	−	12.3923i	−0.731060	−	0.865514i
$206$	−0.999705	+	3.73095i	−0.0696527	+	0.259948i
$207$	−2.78522	+	2.78522i	−0.193586	+	0.193586i
$208$	3.58572	−	0.377640i	0.248625	−	0.0261846i
$209$			15.1566i			1.04840i
$210$	1.65433	−	1.39734i	0.114160	−	0.0964253i
$211$	−0.811524	−	1.40560i	−0.0558676	−	0.0967656i	0.836739	−	0.547602i	$-0.184459\pi$
$211$	−0.811524	−	1.40560i	−0.0558676	−	0.0967656i	−0.892607	+	0.450836i	$0.851126\pi$
$212$	1.77319	+	6.61763i	0.121783	+	0.454501i
$213$		−	2.88070i		−	0.197382i
$214$	15.5242	−	4.15969i	1.06121	−	0.284351i
$215$	19.6374	+	7.07524i	1.33926	+	0.482527i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	9.19215	−	2.46303i	0.624004	−	0.167201i
$218$	−2.61225	+	9.74905i	−0.176924	+	0.660289i
$219$	−5.10973	−	1.36915i	−0.345284	−	0.0925185i
$220$	−1.98629	−	11.0546i	−0.133916	−	0.745299i
$221$	25.0429	+	3.96098i	1.68457	+	0.266444i
$222$	−6.45355	−	6.45355i	−0.433134	−	0.433134i
$223$	6.15595	−	3.55414i	0.412233	−	0.238003i	−0.279516	−	0.960141i	$-0.590174\pi$
$223$	6.15595	−	3.55414i	0.412233	−	0.238003i	0.691749	+	0.722138i	$0.256841\pi$
$224$	−0.838691	+	0.484219i	−0.0560374	+	0.0323532i
$225$	−0.836210	+	4.92958i	−0.0557474	+	0.328639i
$226$	−0.765780	+	0.765780i	−0.0509389	+	0.0509389i
$227$	−9.05181	+	15.6782i	−0.600790	+	1.04060i	0.391912	+	0.920003i	$0.371814\pi$
$227$	−9.05181	+	15.6782i	−0.600790	+	1.04060i	−0.992702	+	0.120595i	$0.961520\pi$
$228$	−1.50874	+	2.61322i	−0.0999190	+	0.173065i
$229$	1.37446	−	1.37446i	0.0908268	−	0.0908268i	−0.660234	−	0.751060i	$-0.729543\pi$
$229$	1.37446	−	1.37446i	0.0908268	−	0.0908268i	0.751060	+	0.660234i	$0.229543\pi$
$230$	8.28622	+	2.98547i	0.546377	+	0.196856i
$231$	−4.21268	+	2.43219i	−0.277174	+	0.160027i
$232$	−3.52151	+	2.03314i	−0.231198	+	0.133482i
$233$	−6.51837	−	6.51837i	−0.427033	−	0.427033i	0.460583	−	0.887616i	$-0.347640\pi$
$233$	−6.51837	−	6.51837i	−0.427033	−	0.427033i	−0.887616	+	0.460583i	$0.847640\pi$
$234$	3.29414	+	1.46581i	0.215345	+	0.0958233i
$235$	13.1067	−	18.8484i	0.854988	−	1.22954i
$236$	−4.96190	−	1.32954i	−0.322992	−	0.0865455i
$237$	−2.21027	+	8.24884i	−0.143573	+	0.535820i
$238$	−6.57799	+	1.76257i	−0.426388	+	0.114250i
$239$	18.8066	+	18.8066i	1.21650	+	1.21650i	0.968849	+	0.247651i	$0.0796586\pi$
$239$	18.8066	+	18.8066i	1.21650	+	1.21650i	0.247651	+	0.968849i	$0.420341\pi$
$240$	0.757946	−	2.10369i	0.0489252	−	0.135793i
$241$	−13.7699	+	3.68964i	−0.886999	+	0.237671i	−0.673424	−	0.739256i	$-0.735177\pi$
$241$	−13.7699	+	3.68964i	−0.886999	+	0.237671i	−0.213575	+	0.976927i	$0.568511\pi$
$242$			14.2298i			0.914726i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−6.98358	−	12.0959i	−0.447078	−	0.774362i
$245$	1.13752	−	13.5075i	0.0726737	−	0.862964i
$246$			7.25439i			0.462523i
$247$	−1.69969	+	10.7461i	−0.108149	+	0.683759i
$248$	6.94843	−	6.94843i	0.441226	−	0.441226i
$249$	2.02677	−	7.56402i	0.128442	−	0.479351i
$250$	10.7706	−	2.99886i	0.681196	−	0.189665i
$251$	−7.79832	−	4.50236i	−0.492226	−	0.284187i	0.233272	−	0.972412i	$-0.425057\pi$
$251$	−7.79832	−	4.50236i	−0.492226	−	0.284187i	−0.725497	+	0.688225i	$0.758390\pi$
$252$	−0.968437			−0.0610058
$253$	−17.1341	−	9.89239i	−1.07721	−	0.621929i
$254$	0.164617	+	0.614358i	0.0103290	+	0.0385483i
$255$	8.97700	−	12.9096i	0.562161	−	0.808430i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.8720	−	3.18110i	−0.740557	−	0.198432i	−0.131231	−	0.991352i	$-0.541893\pi$
$257$	−11.8720	−	3.18110i	−0.740557	−	0.198432i	−0.609326	+	0.792920i	$0.708560\pi$
$258$	−4.66738	−	8.08413i	−0.290578	−	0.503296i
$259$	8.83863			0.549206
$260$	−0.168611	−	8.06049i	−0.0104568	−	0.499891i
$261$	−4.06629			−0.251697
$262$	−0.259003	−	0.448607i	−0.0160013	−	0.0277150i
$263$	−8.27374	−	2.21694i	−0.510181	−	0.136703i	−0.00545995	−	0.999985i	$-0.501738\pi$
$263$	−8.27374	−	2.21694i	−0.510181	−	0.136703i	−0.504721	+	0.863283i	$0.668405\pi$
$264$	−2.51146	+	4.34998i	−0.154570	+	0.267723i
$265$	15.0780	−	2.70923i	0.926235	−	0.166426i
$266$	−0.756333	−	2.82267i	−0.0463737	−	0.173069i
$267$	−8.75022	−	5.05194i	−0.535505	−	0.309174i
$268$	3.89773			0.238092
$269$	15.7848	+	9.11334i	0.962415	+	0.555650i	0.896915	−	0.442202i	$-0.145803\pi$
$269$	15.7848	+	9.11334i	0.962415	+	0.555650i	0.0654992	+	0.997853i	$0.479136\pi$
$270$	1.70825	−	1.44288i	0.103961	−	0.0878107i
$271$	−2.55088	+	9.52000i	−0.154955	+	0.578299i	0.844155	+	0.536100i	$0.180103\pi$
$271$	−2.55088	+	9.52000i	−0.154955	+	0.578299i	−0.999109	+	0.0421988i	$0.986564\pi$
$272$	−4.97236	+	4.97236i	−0.301494	+	0.301494i
$273$	−3.25956	+	1.25202i	−0.197278	+	0.0757757i
$274$		−	9.85977i		−	0.595650i
$275$	−25.0043	+	2.35149i	−1.50782	+	0.141800i
$276$	−1.96945	−	3.41118i	−0.118547	−	0.205329i
$277$	−1.69998	−	6.34441i	−0.102142	−	0.381198i	0.895863	−	0.444330i	$-0.146558\pi$
$277$	−1.69998	−	6.34441i	−0.102142	−	0.381198i	−0.998005	+	0.0631311i	$0.979891\pi$
$278$		−	0.142652i		−	0.00855573i
$279$	9.49174	−	2.54330i	0.568255	−	0.152264i
$280$	0.921551	+	1.95962i	0.0550732	+	0.117109i
$281$	0.181386	+	0.181386i	0.0108206	+	0.0108206i	0.712496	−	0.701676i	$-0.247564\pi$
$281$	0.181386	+	0.181386i	0.0108206	+	0.0108206i	−0.701676	+	0.712496i	$0.747564\pi$
$282$	−9.91709	+	2.65728i	−0.590554	+	0.158239i
$283$	−3.47765	+	12.9788i	−0.206725	+	0.771507i	0.782192	+	0.623037i	$0.214102\pi$
$283$	−3.47765	+	12.9788i	−0.206725	+	0.771507i	−0.988917	+	0.148470i	$0.952565\pi$
$284$	2.78254	+	0.745580i	0.165114	+	0.0442420i
$285$	5.53962	+	3.85211i	0.328139	+	0.228179i
$286$	−2.82931	+	17.8880i	−0.167301	+	1.05774i
$287$	−4.96772	−	4.96772i	−0.293235	−	0.293235i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−28.1015	+	16.2244i	−1.65303	+	0.954376i
$290$	3.86942	+	8.22807i	0.227220	+	0.483169i
$291$	7.39705	−	7.39705i	0.433623	−	0.433623i
$292$	2.64499	−	4.58126i	0.154786	−	0.268098i
$293$	4.51894	−	7.82703i	0.263999	−	0.457260i	−0.703302	−	0.710891i	$-0.748292\pi$
$293$	4.51894	−	7.82703i	0.263999	−	0.457260i	0.967301	+	0.253632i	$0.0816251\pi$
$294$	−4.28657	+	4.28657i	−0.249998	+	0.249998i
$295$	−3.89352	+	10.8065i	−0.226689	+	0.629180i
$296$	7.90395	−	4.56335i	0.459408	−	0.265239i
$297$	−4.34998	+	2.51146i	−0.252412	+	0.145730i
$298$	−1.55776	−	1.55776i	−0.0902384	−	0.0902384i
$299$	−11.0388	−	8.93520i	−0.638392	−	0.516736i
$300$	−4.54518	−	2.08359i	−0.262416	−	0.120296i
$301$	8.73208	+	2.33976i	0.503309	+	0.134861i
$302$	2.54096	−	9.48301i	0.146216	−	0.545686i
$303$	−6.49091	+	1.73923i	−0.372893	+	0.0999164i
$304$	−2.13369	−	2.13369i	−0.122375	−	0.122375i
$305$	−28.2623	+	13.2910i	−1.61830	+	0.761038i
$306$	−6.79237	+	1.82001i	−0.388294	+	0.104043i
$307$			15.9810i			0.912081i	0.889959	+	0.456041i	$0.150733\pi$
$307$			15.9810i			0.912081i	−0.889959	+	0.456041i	$0.849267\pi$
$308$	−1.25900	−	4.69864i	−0.0717380	−	0.267730i
$309$	−1.93128	−	3.34508i	−0.109867	−	0.190295i
$310$	−14.1785	−	16.7862i	−0.805287	−	0.953392i
$311$			7.63498i			0.432940i	0.976289	+	0.216470i	$0.0694544\pi$
$311$			7.63498i			0.432940i	−0.976289	+	0.216470i	$0.930546\pi$
$312$	−2.26845	+	2.80252i	−0.128426	+	0.158661i
$313$	−18.2617	+	18.2617i	−1.03221	+	1.03221i	−0.0327483	+	0.999464i	$0.510426\pi$
$313$	−18.2617	+	18.2617i	−1.03221	+	1.03221i	−0.999464	+	0.0327483i	$0.989574\pi$
$314$	−3.39523	+	12.6712i	−0.191604	+	0.715077i
$315$	−0.181722	+	2.15785i	−0.0102389	+	0.121581i
$316$	−7.39571	−	4.26992i	−0.416041	−	0.240202i
$317$	−0.262214			−0.0147274			−0.00736370	−	0.999973i	$-0.502344\pi$
$317$	−0.262214			−0.0147274			−0.00736370	+	0.999973i	$0.502344\pi$
$318$	−5.93321	−	3.42554i	−0.332718	−	0.192095i
$319$	−5.28629	−	19.7287i	−0.295976	−	1.10460i
$320$	1.83584	+	1.27660i	0.102627	+	0.0713638i
$321$	−8.03591	+	13.9186i	−0.448521	+	0.776861i
$322$	3.68459	+	0.987284i	0.205334	+	0.0550192i
$323$	−10.6095	−	18.3761i	−0.590326	−	1.02247i
$324$	−1.00000			−0.0555556
$325$	−17.9919	−	1.13681i	−0.998010	−	0.0630588i
$326$	−0.335080			−0.0185584
$327$	−5.04648	−	8.74076i	−0.279071	−	0.483365i
$328$	−7.00720	−	1.87757i	−0.386908	−	0.103672i
$329$	4.97144	−	8.61078i	0.274084	−	0.474728i
$330$	9.22129	+	6.41224i	0.507615	+	0.352982i
$331$	1.35608	+	5.06097i	0.0745370	+	0.278176i	0.993128	−	0.117034i	$-0.0373386\pi$
$331$	1.35608	+	5.06097i	0.0745370	+	0.278176i	−0.918591	+	0.395210i	$0.870672\pi$
$332$	6.78172	+	3.91543i	0.372195	+	0.214887i
$333$	9.12669			0.500140
$334$	−15.8294	−	9.13911i	−0.866147	−	0.500070i
$335$	0.731387	−	8.68486i	0.0399599	−	0.474504i
$336$	0.250650	−	0.935438i	0.0136741	−	0.0510323i
$337$	6.70084	−	6.70084i	0.365018	−	0.365018i	−0.500638	−	0.865656i	$-0.666901\pi$
$337$	6.70084	−	6.70084i	0.365018	−	0.365018i	0.865656	+	0.500638i	$0.166901\pi$
$338$	−4.01200	+	12.3654i	−0.218224	+	0.672591i
$339$		−	1.08298i		−	0.0588192i
$340$	10.1463	+	12.0124i	0.550260	+	0.651462i
$341$	24.6791	+	42.7454i	1.33645	+	2.31479i
$342$	−0.780983	−	2.91467i	−0.0422307	−	0.157607i
$343$		−	12.6499i		−	0.683028i
$344$	9.01668	−	2.41601i	0.486147	−	0.130263i
$345$	−7.97029	+	3.74820i	−0.429106	+	0.201796i
$346$	1.46933	+	1.46933i	0.0789917	+	0.0789917i
$347$	−16.9766	+	4.54887i	−0.911353	+	0.244196i	−0.683885	−	0.729589i	$-0.739711\pi$
$347$	−16.9766	+	4.54887i	−0.911353	+	0.244196i	−0.227467	+	0.973786i	$0.573045\pi$
$348$	1.05243	−	3.92773i	0.0564163	−	0.210549i
$349$	21.5167	+	5.76539i	1.15176	+	0.308614i	0.783672	−	0.621175i	$-0.213344\pi$
$349$	21.5167	+	5.76539i	1.15176	+	0.308614i	0.368093	+	0.929789i	$0.380011\pi$
$350$	4.53930	−	1.68567i	0.242636	−	0.0901029i
$351$	−3.36580	+	1.29283i	−0.179653	+	0.0690059i
$352$	−3.55175	−	3.55175i	−0.189309	−	0.189309i
$353$	−3.04814	+	1.75984i	−0.162236	+	0.0936671i	−0.578920	−	0.815384i	$-0.696526\pi$
$353$	−3.04814	+	1.75984i	−0.162236	+	0.0936671i	0.416684	+	0.909052i	$0.363192\pi$
$354$	4.44872	−	2.56847i	0.236447	−	0.136513i
$355$	2.18341	−	6.06010i	0.115884	−	0.321637i
$356$	7.14453	−	7.14453i	0.378659	−	0.378659i
$357$	3.40502	−	5.89766i	0.180213	−	0.312137i
$358$	4.87549	−	8.44459i	0.257677	−	0.446310i
$359$	17.0305	−	17.0305i	0.898833	−	0.898833i	−0.0964997	−	0.995333i	$-0.530765\pi$
$359$	17.0305	−	17.0305i	0.898833	−	0.898833i	0.995333	+	0.0964997i	$0.0307647\pi$
$360$	0.951586	+	2.02348i	0.0501530	+	0.106647i
$361$	−8.56913	+	4.94739i	−0.451007	+	0.260389i
$362$	−6.10279	+	3.52345i	−0.320756	+	0.185188i
$363$	−10.0620	−	10.0620i	−0.528117	−	0.528117i
$364$	−0.365721	−	3.47254i	−0.0191690	−	0.182011i
$365$	−9.71156	−	6.75316i	−0.508326	−	0.353477i
$366$	13.4912	+	3.61497i	0.705199	+	0.188957i
$367$	−2.24663	+	8.38454i	−0.117273	+	0.437670i	−0.999447	−	0.0332546i	$-0.989413\pi$
$367$	−2.24663	+	8.38454i	−0.117273	+	0.437670i	0.882174	+	0.470924i	$0.156079\pi$
$368$	3.80468	−	1.01946i	0.198333	−	0.0531431i
$369$	−5.12963	−	5.12963i	−0.267038	−	0.267038i
$370$	−8.68483	−	18.4677i	−0.451503	−	0.960091i
$371$	6.40876	−	1.71722i	0.332726	−	0.0891538i
$372$			9.82657i			0.509484i
$373$	−4.64238	−	17.3256i	−0.240373	−	0.897086i	−0.975653	−	0.219322i	$-0.929616\pi$
$373$	−4.64238	−	17.3256i	−0.240373	−	0.897086i	0.735279	−	0.677764i	$-0.237051\pi$
$374$	−17.6606	−	30.5890i	−0.913206	−	1.58172i
$375$	−5.49548	+	9.73651i	−0.283786	+	0.502791i
$376$		−	10.2669i		−	0.529476i
$377$	−1.53559	−	14.5806i	−0.0790871	−	0.750938i
$378$	0.684788	−	0.684788i	0.0352217	−	0.0352217i
$379$	2.23134	−	8.32746i	0.114616	−	0.427753i	−0.884642	−	0.466271i	$-0.845597\pi$
$379$	2.23134	−	8.32746i	0.114616	−	0.427753i	0.999258	+	0.0385183i	$0.0122638\pi$
$380$	−5.15461	+	4.35386i	−0.264426	+	0.223348i
$381$	−0.550819	−	0.318015i	−0.0282193	−	0.0162924i
$382$	−12.6225			−0.645825
$383$	15.3541	+	8.86469i	0.784557	+	0.452964i	0.838043	−	0.545604i	$-0.183700\pi$
$383$	15.3541	+	8.86469i	0.784557	+	0.452964i	−0.0534856	+	0.998569i	$0.517033\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	−10.7057	+	1.92360i	−0.545611	+	0.0980357i
$386$	11.3631	−	19.6816i	0.578369	−	1.00176i
$387$	9.01668	+	2.41601i	0.458343	+	0.122813i
$388$	5.23050	+	9.05950i	0.265539	+	0.459926i
$389$	30.1978			1.53109			0.765545	−	0.643382i	$-0.222469\pi$
$389$	30.1978			1.53109			0.765545	+	0.643382i	$0.222469\pi$
$390$	5.81886	+	5.58040i	0.294649	+	0.282575i
$391$	27.6982			1.40076
$392$	−3.03106	−	5.24996i	−0.153092	−	0.265163i
$393$	0.500356	+	0.134070i	0.0252396	+	0.00676293i
$394$	−8.41170	+	14.5695i	−0.423775	+	0.734000i
$395$	−10.9019	+	15.6778i	−0.548534	+	0.788833i
$396$	−1.30003	−	4.85177i	−0.0653289	−	0.243811i
$397$	2.58338	+	1.49152i	0.129656	+	0.0748570i	0.563425	−	0.826167i	$-0.309483\pi$
$397$	2.58338	+	1.49152i	0.129656	+	0.0748570i	−0.433769	+	0.901024i	$0.642817\pi$
$398$	−15.2122			−0.762521
$399$	2.53074	+	1.46112i	0.126695	+	0.0731476i
$400$	3.18897	−	3.85104i	0.159448	−	0.192552i
$401$	2.21585	−	8.26965i	0.110654	−	0.412967i	−0.888271	−	0.459320i	$-0.848093\pi$
$401$	2.21585	−	8.26965i	0.110654	−	0.412967i	0.998925	+	0.0463531i	$0.0147599\pi$
$402$	−2.75611	+	2.75611i	−0.137462	+	0.137462i
$403$	12.7040	+	33.0743i	0.632833	+	1.64755i
$404$		−	6.71988i		−	0.334327i
$405$	−0.187644	+	2.22818i	−0.00932411	+	0.110719i
$406$	1.96897	+	3.41036i	0.0977185	+	0.169253i
$407$	11.8650	+	44.2807i	0.588125	+	2.19491i
$408$		−	7.03198i		−	0.348135i
$409$	−6.47345	+	1.73455i	−0.320091	+	0.0857682i	−0.415287	−	0.909690i	$-0.636319\pi$
$409$	−6.47345	+	1.73455i	−0.320091	+	0.0857682i	0.0951959	+	0.995459i	$0.469652\pi$
$410$	−5.49843	+	15.2610i	−0.271548	+	0.753687i
$411$	6.97191	+	6.97191i	0.343899	+	0.343899i
$412$	3.73095	−	0.999705i	0.183811	−	0.0492519i
$413$	−1.28757	+	4.80529i	−0.0633573	+	0.236453i
$414$	3.80468	+	1.01946i	0.186990	+	0.0501038i
$415$	9.99683	−	14.3762i	0.490725	−	0.705699i
$416$	−2.11991	−	2.91650i	−0.103937	−	0.142993i
$417$	0.100871	+	0.100871i	0.00493965	+	0.00493965i
$418$	13.1260	−	7.57831i	0.642014	−	0.370667i
$419$	−12.7429	+	7.35714i	−0.622533	+	0.359420i	−0.777855	−	0.628444i	$-0.783692\pi$
$419$	−12.7429	+	7.35714i	−0.622533	+	0.359420i	0.155321	+	0.987864i	$0.450359\pi$
$420$	−2.03729	−	0.734023i	−0.0994097	−	0.0358167i
$421$	−19.5854	+	19.5854i	−0.954536	+	0.954536i	−0.999011	−	0.0444742i	$-0.985839\pi$
$421$	−19.5854	+	19.5854i	−0.954536	+	0.954536i	0.0444742	+	0.999011i	$0.485839\pi$
$422$	−0.811524	+	1.40560i	−0.0395044	+	0.0684236i
$423$	5.13346	−	8.89142i	0.249598	−	0.432316i
$424$	4.84444	−	4.84444i	0.235267	−	0.235267i
$425$	28.6696	−	20.3537i	1.39068	−	0.987300i
$426$	−2.49476	+	1.44035i	−0.120871	+	0.0697852i
$427$	−11.7141	+	6.76316i	−0.566887	+	0.327292i
$428$	−11.3645	−	11.3645i	−0.549323	−	0.549323i
$429$	−10.6481	−	14.6494i	−0.514097	−	0.707279i
$430$	−3.69138	−	20.5441i	−0.178014	−	0.990726i
$431$	−20.3176	−	5.44408i	−0.978663	−	0.262232i	−0.266182	−	0.963923i	$-0.585762\pi$
$431$	−20.3176	−	5.44408i	−0.978663	−	0.262232i	−0.712481	+	0.701691i	$0.752429\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	−4.13203	+	1.10718i	−0.198573	+	0.0532075i	−0.356735	−	0.934206i	$-0.616110\pi$
$433$	−4.13203	+	1.10718i	−0.198573	+	0.0532075i	0.158162	+	0.987413i	$0.449443\pi$
$434$	−6.72912	−	6.72912i	−0.323008	−	0.323008i
$435$	−8.55422	−	3.08203i	−0.410143	−	0.147772i
$436$	9.74905	−	2.61225i	0.466895	−	0.125104i
$437$			11.8856i			0.568563i
$438$	1.36915	+	5.10973i	0.0654204	+	0.244152i
$439$	5.94011	+	10.2886i	0.283506	+	0.491047i	0.972246	−	0.233962i	$-0.0751690\pi$
$439$	5.94011	+	10.2886i	0.283506	+	0.491047i	−0.688740	+	0.725009i	$0.741836\pi$
$440$	−8.58040	+	7.24747i	−0.409054	+	0.345509i
$441$		−	6.06213i		−	0.288673i
$442$	−9.09113	−	23.6682i	−0.432421	−	1.12578i
$443$	4.53987	−	4.53987i	0.215696	−	0.215696i	−0.590986	−	0.806682i	$-0.701261\pi$
$443$	4.53987	−	4.53987i	0.215696	−	0.215696i	0.806682	+	0.590986i	$0.201261\pi$
$444$	−2.36216	+	8.81571i	−0.112103	+	0.418375i
$445$	−14.5787	−	17.2599i	−0.691095	−	0.818199i
$446$	−6.15595	−	3.55414i	−0.291493	−	0.168293i
$447$	2.20300			0.104198
$448$	0.838691	+	0.484219i	0.0396244	+	0.0228772i
$449$	0.188899	+	0.704981i	0.00891470	+	0.0332701i	0.970240	−	0.242146i	$-0.0778512\pi$
$449$	0.188899	+	0.704981i	0.00891470	+	0.0332701i	−0.961325	+	0.275416i	$0.911185\pi$
$450$	4.68725	−	1.74061i	0.220959	−	0.0820532i
$451$	18.2191	−	31.5565i	0.857905	−	1.48594i
$452$	1.04608	+	0.280295i	0.0492032	+	0.0131840i
$453$	4.90877	+	8.50223i	0.230634	+	0.399470i
$454$	18.1036			0.849645
$455$	−7.80608	+	0.163290i	−0.365955	+	0.00765513i
$456$	3.01749			0.141307
$457$	−7.39796	−	12.8136i	−0.346062	−	0.599397i	0.639484	−	0.768804i	$-0.279148\pi$
$457$	−7.39796	−	12.8136i	−0.346062	−	0.599397i	−0.985546	+	0.169407i	$0.945815\pi$
$458$	−1.87755	−	0.503087i	−0.0877320	−	0.0235077i
$459$	3.51599	−	6.08988i	0.164112	−	0.284251i
$460$	−1.55762	−	8.66881i	−0.0726243	−	0.404185i
$461$	−6.00079	−	22.3953i	−0.279485	−	1.04305i	−0.952776	−	0.303674i	$-0.901787\pi$
$461$	−6.00079	−	22.3953i	−0.279485	−	1.04305i	0.673291	−	0.739377i	$-0.264880\pi$
$462$	4.21268	+	2.43219i	0.195992	+	0.113156i
$463$	−22.3697			−1.03961			−0.519803	−	0.854286i	$-0.673995\pi$
$463$	−22.3697			−1.03961			−0.519803	+	0.854286i	$0.673995\pi$
$464$	3.52151	+	2.03314i	0.163482	+	0.0943864i
$465$	21.8954	+	1.84390i	1.01537	+	0.0855087i
$466$	−2.38589	+	8.90427i	−0.110524	+	0.412482i
$467$	−6.99272	+	6.99272i	−0.323584	+	0.323584i	−0.850140	−	0.526556i	$-0.823483\pi$
$467$	−6.99272	+	6.99272i	−0.323584	+	0.323584i	0.526556	+	0.850140i	$0.323483\pi$
$468$	−0.377640	−	3.58572i	−0.0174564	−	0.165750i
$469$		−	3.77471i		−	0.174300i
$470$	−22.8766	−	1.92653i	−1.05522	−	0.0888642i
$471$	−6.55909	−	11.3607i	−0.302227	−	0.523472i
$472$	1.32954	+	4.96190i	0.0611969	+	0.228390i
$473$			46.8878i			2.15590i
$474$	8.24884	−	2.21027i	0.378882	−	0.101521i
$475$	8.73396	+	12.3024i	0.400742	+	0.564472i
$476$	4.81542	+	4.81542i	0.220714	+	0.220714i
$477$	6.61763	−	1.77319i	0.303001	−	0.0811888i
$478$	6.88371	−	25.6903i	0.314853	−	1.17505i
$479$	6.48925	+	1.73879i	0.296501	+	0.0794473i	0.404003	−	0.914758i	$-0.367618\pi$
$479$	6.48925	+	1.73879i	0.296501	+	0.0794473i	−0.107502	+	0.994205i	$0.534285\pi$
$480$	−2.20082	+	0.395445i	−0.100453	+	0.0180495i
$481$	3.44661	+	32.7258i	0.157152	+	1.49217i
$482$	10.0803	+	10.0803i	0.459145	+	0.459145i
$483$	−3.30352	+	1.90729i	−0.150315	+	0.0867845i
$484$	12.3234	−	7.11490i	0.560153	−	0.323404i
$485$	21.1677	−	9.95455i	0.961175	−	0.452013i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	−5.17331	+	8.96044i	−0.234425	+	0.406036i	−0.959105	−	0.283049i	$-0.908654\pi$
$487$	−5.17331	+	8.96044i	−0.234425	+	0.406036i	0.724680	+	0.689085i	$0.241987\pi$
$488$	−6.98358	+	12.0959i	−0.316132	+	0.547557i
$489$	0.236937	−	0.236937i	0.0107147	−	0.0107147i
$490$	−12.2666	+	5.76864i	−0.554149	+	0.260600i
$491$	−32.8883	+	18.9881i	−1.48423	+	0.856920i	−0.999839	−	0.0179318i	$-0.994292\pi$
$491$	−32.8883	+	18.9881i	−1.48423	+	0.856920i	−0.484390	+	0.874852i	$0.660959\pi$
$492$	6.28248	−	3.62719i	0.283236	−	0.163527i
$493$	20.2191	+	20.2191i	0.910621	+	0.910621i
$494$	10.1563	−	3.90108i	0.456951	−	0.175518i
$495$	−11.0546	+	1.98629i	−0.496866	+	0.0892772i
$496$	−9.49174	−	2.54330i	−0.426192	−	0.114198i
$497$	0.722047	−	2.69472i	0.0323882	−	0.120875i
$498$	−7.56402	+	2.02677i	−0.338952	+	0.0908219i
$499$	−4.94763	−	4.94763i	−0.221486	−	0.221486i	0.587638	−	0.809124i	$-0.300058\pi$
$499$	−4.94763	−	4.94763i	−0.221486	−	0.221486i	−0.809124	+	0.587638i	$0.800058\pi$
$500$	−7.98241	−	7.82822i	−0.356984	−	0.350089i
$501$	17.6554	−	4.73075i	0.788786	−	0.211354i
$502$			9.00472i			0.401901i
$503$	−10.1161	−	37.7538i	−0.451055	−	1.68336i	−0.699435	−	0.714696i	$-0.746565\pi$
$503$	−10.1161	−	37.7538i	−0.451055	−	1.68336i	0.248381	−	0.968662i	$-0.420102\pi$
$504$	0.484219	+	0.838691i	0.0215688	+	0.0373583i
$505$	−14.9731	−	1.26095i	−0.666295	−	0.0561114i
$506$			19.7848i			0.879541i
$507$	−5.90677	−	11.5806i	−0.262329	−	0.514312i
$508$	0.449741	−	0.449741i	0.0199541	−	0.0199541i
$509$	−0.0662437	+	0.247225i	−0.00293620	+	0.0109581i	−0.967378	−	0.253336i	$-0.918472\pi$
$509$	−0.0662437	+	0.247225i	−0.00293620	+	0.0109581i	0.964442	+	0.264294i	$0.0851389\pi$
$510$	−15.6685	−	1.31951i	−0.693814	−	0.0584289i
$511$	−4.43666	−	2.56151i	−0.196266	−	0.113314i
$512$	1.00000			0.0441942
$513$	2.61322	+	1.50874i	0.115376	+	0.0666126i
$514$	3.18110	+	11.8720i	0.140312	+	0.523653i
$515$	−1.52743	−	8.50082i	−0.0673067	−	0.374591i
$516$	−4.66738	+	8.08413i	−0.205470	+	0.355884i
$517$	49.8128	+	13.3473i	2.19077	+	0.587014i
$518$	−4.41931	−	7.65448i	−0.194174	−	0.336318i
$519$	−2.07795			−0.0912118
$520$	−6.89629	+	4.17627i	−0.302422	+	0.183142i
$521$	−17.2469			−0.755599			−0.377799	−	0.925887i	$-0.623319\pi$
$521$	−17.2469			−0.755599			−0.377799	+	0.925887i	$0.623319\pi$
$522$	2.03314	+	3.52151i	0.0889883	+	0.154132i
$523$	3.90702	+	1.04688i	0.170842	+	0.0457770i	0.343226	−	0.939253i	$-0.388480\pi$
$523$	3.90702	+	1.04688i	0.170842	+	0.0457770i	−0.172384	+	0.985030i	$0.555147\pi$
$524$	−0.259003	+	0.448607i	−0.0113146	+	0.0195975i
$525$	−2.01782	+	4.40172i	−0.0880650	+	0.192107i
$526$	2.21694	+	8.27374i	0.0966633	+	0.360752i
$527$	−59.8426	−	34.5501i	−2.60678	−	1.50503i
$528$	5.02293			0.218595
$529$	6.48230	+	3.74256i	0.281839	+	0.162720i
$530$	−9.88527	−	11.7033i	−0.429388	−	0.508360i
$531$	−1.32954	+	4.96190i	−0.0576970	+	0.215328i
$532$	−2.06634	+	2.06634i	−0.0895872	+	0.0895872i
$533$	16.4562	−	20.3306i	0.712799	−	0.880614i
$534$			10.1039i			0.437238i
$535$	−27.4546	+	23.1897i	−1.18697	+	1.00258i
$536$	−1.94887	−	3.37554i	−0.0841782	−	0.145801i
$537$	2.52374	+	9.41871i	0.108907	+	0.406448i
$538$		−	18.2267i		−	0.785808i
$539$	29.4121	−	7.88095i	1.26687	−	0.339456i
$540$	−2.10369	−	0.757946i	−0.0905285	−	0.0326168i
$541$	13.3085	+	13.3085i	0.572176	+	0.572176i	0.932736	−	0.360560i	$-0.117414\pi$
$541$	13.3085	+	13.3085i	0.572176	+	0.572176i	−0.360560	+	0.932736i	$0.617414\pi$
$542$	9.52000	−	2.55088i	0.408919	−	0.109569i
$543$	1.82387	−	6.80678i	0.0782698	−	0.292107i
$544$	6.79237	+	1.82001i	0.291221	+	0.0780323i
$545$	−3.99121	−	22.2128i	−0.170965	−	0.951493i
$546$	2.71406	+	2.19686i	0.116151	+	0.0940167i
$547$	−3.01689	−	3.01689i	−0.128993	−	0.128993i	0.639663	−	0.768656i	$-0.279074\pi$
$547$	−3.01689	−	3.01689i	−0.128993	−	0.128993i	−0.768656	+	0.639663i	$0.779074\pi$
$548$	−8.53881	+	4.92988i	−0.364760	+	0.210594i
$549$	−12.0959	+	6.98358i	−0.516241	+	0.298052i
$550$	14.5386	+	20.4786i	0.619928	+	0.873211i
$551$	−8.67618	+	8.67618i	−0.369618	+	0.369618i
$552$	−1.96945	+	3.41118i	−0.0838252	+	0.145190i
$553$	−4.13514	+	7.16228i	−0.175844	+	0.304571i
$554$	−4.64443	+	4.64443i	−0.197323	+	0.197323i
$555$	19.1998	+	6.91754i	0.814984	+	0.293633i
$556$	−0.123541	+	0.0713262i	−0.00523929	+	0.00302491i
$557$	23.7513	−	13.7128i	1.00638	−	0.581031i	0.0962474	−	0.995357i	$-0.469316\pi$
$557$	23.7513	−	13.7128i	1.00638	−	0.581031i	0.910129	+	0.414326i	$0.135983\pi$
$558$	−6.94843	−	6.94843i	−0.294151	−	0.294151i
$559$	−5.25808	+	33.2437i	−0.222393	+	1.40606i
$560$	1.23630	−	1.77789i	0.0522433	−	0.0751298i
$561$	34.1176	+	9.14178i	1.44045	+	0.385966i
$562$	0.0663920	−	0.247778i	0.00280058	−	0.0104519i
$563$	27.3970	−	7.34100i	1.15464	−	0.309386i	0.369820	−	0.929103i	$-0.379419\pi$
$563$	27.3970	−	7.34100i	1.15464	−	0.309386i	0.784825	+	0.619717i	$0.212753\pi$
$564$	7.25982	+	7.25982i	0.305693	+	0.305693i
$565$	0.820838	−	2.27825i	0.0345329	−	0.0958467i
$566$	12.9788	−	3.47765i	0.545538	−	0.146177i
$567$			0.968437i			0.0406705i
$568$	−0.745580	−	2.78254i	−0.0312838	−	0.116753i
$569$	21.2013	+	36.7217i	0.888804	+	1.53945i	0.841290	+	0.540584i	$0.181797\pi$
$569$	21.2013	+	36.7217i	0.888804	+	1.53945i	0.0475143	+	0.998871i	$0.484870\pi$
$570$	0.566214	−	6.72351i	0.0237161	−	0.281617i
$571$			44.0026i			1.84145i	0.390210	+	0.920726i	$0.372403\pi$
$571$			44.0026i			1.84145i	−0.390210	+	0.920726i	$0.627597\pi$
$572$	16.9062	−	6.49377i	0.706882	−	0.271518i
$573$	8.92548	−	8.92548i	0.372867	−	0.372867i
$574$	−1.81831	+	6.78603i	−0.0758949	+	0.283243i
$575$	−19.6080	+	1.84400i	−0.817708	+	0.0769001i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	43.9761			1.83075			0.915375	−	0.402603i	$-0.131894\pi$
$577$	43.9761			1.83075			0.915375	+	0.402603i	$0.131894\pi$
$578$	28.1015	+	16.2244i	1.16887	+	0.674846i
$579$	5.88200	+	21.9519i	0.244448	+	0.912291i
$580$	5.19100	−	7.46505i	0.215545	−	0.309969i
$581$	3.79184	−	6.56767i	0.157312	−	0.272473i
$582$	−10.1046	−	2.70751i	−0.418847	−	0.112230i
$583$	17.2062	+	29.8021i	0.712609	+	1.23428i
$584$	−5.28998			−0.218901
$585$	−8.06049	+	0.168611i	−0.333260	+	0.00697123i
$586$	−9.03787			−0.373351
$587$	−17.8974	−	30.9992i	−0.738704	−	1.27947i	−0.953079	−	0.302721i	$-0.902105\pi$
$587$	−17.8974	−	30.9992i	−0.738704	−	1.27947i	0.214376	−	0.976751i	$-0.431228\pi$
$588$	5.85557	+	1.56899i	0.241480	+	0.0647042i
$589$	14.8258	−	25.6790i	0.610885	−	1.05808i
$590$	11.3055	−	2.03138i	0.465440	−	0.0836305i
$591$	−4.35422	−	16.2502i	−0.179109	−	0.668442i
$592$	−7.90395	−	4.56335i	−0.324850	−	0.187552i
$593$	−6.11440			−0.251088			−0.125544	−	0.992088i	$-0.540068\pi$
$593$	−6.11440			−0.251088			−0.125544	+	0.992088i	$0.540068\pi$
$594$	4.34998	+	2.51146i	0.178482	+	0.103047i
$595$	11.6332	−	9.82604i	0.476915	−	0.402828i
$596$	−0.570179	+	2.12794i	−0.0233554	+	0.0871636i
$597$	10.7567	−	10.7567i	0.440241	−	0.440241i
$598$	−2.21870	+	14.0275i	−0.0907294	+	0.573627i
$599$			2.16515i			0.0884655i	0.999021	+	0.0442327i	$0.0140843\pi$
$599$			2.16515i			0.0884655i	−0.999021	+	0.0442327i	$0.985916\pi$
$600$	0.468152	+	4.97804i	0.0191122	+	0.203227i
$601$	−20.1099	−	34.8314i	−0.820301	−	1.42080i	−0.905458	−	0.424436i	$-0.860472\pi$
$601$	−20.1099	−	34.8314i	−0.820301	−	1.42080i	0.0851569	−	0.996368i	$-0.472861\pi$
$602$	−2.33976	−	8.73208i	−0.0953613	−	0.355893i
$603$		−	3.89773i		−	0.158728i
$604$	−9.48301	+	2.54096i	−0.385858	+	0.103390i
$605$	−13.5409	−	28.7938i	−0.550515	−	1.17063i
$606$	4.75167	+	4.75167i	0.193024	+	0.193024i
$607$	−26.4057	+	7.07540i	−1.07178	+	0.287182i	−0.751223	−	0.660049i	$-0.770536\pi$
$607$	−26.4057	+	7.07540i	−1.07178	+	0.287182i	−0.320553	+	0.947230i	$0.603869\pi$
$608$	−0.780983	+	2.91467i	−0.0316730	+	0.118205i
$609$	−3.80376	−	1.01922i	−0.154136	−	0.0413007i
$610$	25.6415	+	17.8304i	1.03819	+	0.721933i
$611$	33.8208	+	15.0494i	1.36824	+	0.608834i
$612$	4.97236	+	4.97236i	0.200996	+	0.200996i
$613$	18.6017	−	10.7397i	0.751317	−	0.433773i	−0.0748527	−	0.997195i	$-0.523849\pi$
$613$	18.6017	−	10.7397i	0.751317	−	0.433773i	0.826170	+	0.563422i	$0.190515\pi$
$614$	13.8399	−	7.99048i	0.558533	−	0.322469i
$615$	−6.90317	−	14.6791i	−0.278363	−	0.591920i
$616$	−3.43964	+	3.43964i	−0.138587	+	0.138587i
$617$	−22.2821	+	38.5938i	−0.897045	+	1.55373i	−0.0657925	+	0.997833i	$0.520958\pi$
$617$	−22.2821	+	38.5938i	−0.897045	+	1.55373i	−0.831253	+	0.555895i	$0.812376\pi$
$618$	−1.93128	+	3.34508i	−0.0776875	+	0.134559i
$619$	18.5236	−	18.5236i	0.744526	−	0.744526i	−0.228920	−	0.973445i	$-0.573519\pi$
$619$	18.5236	−	18.5236i	0.744526	−	0.744526i	0.973445	+	0.228920i	$0.0735193\pi$
$620$	−7.44801	+	20.6721i	−0.299119	+	0.830210i
$621$	−3.41118	+	1.96945i	−0.136886	+	0.0790312i
$622$	6.61209	−	3.81749i	0.265121	−	0.153067i
$623$	−6.91903	−	6.91903i	−0.277205	−	0.277205i
$624$	3.56128	+	0.563280i	0.142565	+	0.0225492i
$625$	−18.9406	+	16.3173i	−0.757622	+	0.652694i
$626$	24.9459	+	6.68424i	0.997040	+	0.267156i
$627$	−3.92282	+	14.6402i	−0.156662	+	0.584672i
$628$	12.6712	−	3.39523i	0.505635	−	0.135485i
$629$	−45.3812	−	45.3812i	−1.80947	−	1.80947i
$630$	1.95962	−	0.921551i	0.0780730	−	0.0367155i
$631$	−17.9811	+	4.81802i	−0.715816	+	0.191802i	−0.598304	−	0.801269i	$-0.704159\pi$
$631$	−17.9811	+	4.81802i	−0.715816	+	0.191802i	−0.117512	+	0.993071i	$0.537492\pi$
$632$			8.53983i			0.339696i
$633$	−0.420076	−	1.56774i	−0.0166965	−	0.0623122i
$634$	0.131107	+	0.227084i	0.00520692	+	0.00901865i
$635$	−0.917714	−	1.08650i	−0.0364184	−	0.0431163i
$636$			6.85108i			0.271663i
$637$	21.7371	−	2.28930i	0.861255	−	0.0907056i
$638$	−14.4424	+	14.4424i	−0.571781	+	0.571781i
$639$	0.745580	−	2.78254i	0.0294947	−	0.110076i
$640$	0.187644	−	2.22818i	0.00741729	−	0.0880766i
$641$	32.8986	+	18.9940i	1.29942	+	0.750219i	0.980303	−	0.197497i	$-0.0632813\pi$
$641$	32.8986	+	18.9940i	1.29942	+	0.750219i	0.319114	+	0.947716i	$0.396615\pi$
$642$	16.0718			0.634304
$643$	−35.4883	−	20.4892i	−1.39952	−	0.808015i	−0.405180	−	0.914237i	$-0.632791\pi$
$643$	−35.4883	−	20.4892i	−1.39952	−	0.808015i	−0.994342	+	0.106222i	$0.966125\pi$
$644$	−0.987284	−	3.68459i	−0.0389044	−	0.145193i
$645$	17.1371	+	11.9167i	0.674773	+	0.469219i
$646$	−10.6095	+	18.3761i	−0.417424	+	0.722999i
$647$	5.78218	+	1.54933i	0.227321	+	0.0609104i	0.370681	−	0.928760i	$-0.379124\pi$
$647$	5.78218	+	1.54933i	0.227321	+	0.0609104i	−0.143361	+	0.989671i	$0.545791\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−25.8025			−1.01283
$650$	8.01143	+	16.1498i	0.314234	+	0.633448i
$651$	9.51641			0.372978
$652$	0.167540	+	0.290188i	0.00656137	+	0.0113646i
$653$	19.4525	+	5.21228i	0.761235	+	0.203972i	0.618496	−	0.785788i	$-0.287742\pi$
$653$	19.4525	+	5.21228i	0.761235	+	0.203972i	0.142739	+	0.989760i	$0.454409\pi$
$654$	−5.04648	+	8.74076i	−0.197333	+	0.341791i
$655$	0.950977	+	0.661285i	0.0371577	+	0.0258385i
$656$	1.87757	+	7.00720i	0.0733069	+	0.273585i
$657$	−4.58126	−	2.64499i	−0.178732	−	0.103191i
$658$	−9.94288			−0.387614
$659$	−1.77563	−	1.02516i	−0.0691686	−	0.0399345i	0.465017	−	0.885302i	$-0.346048\pi$
$659$	−1.77563	−	1.02516i	−0.0691686	−	0.0399345i	−0.534185	+	0.845367i	$0.679382\pi$
$660$	0.942523	−	11.1920i	0.0366877	−	0.435648i
$661$	8.09043	−	30.1939i	0.314681	−	1.17441i	−0.609605	−	0.792706i	$-0.708672\pi$
$661$	8.09043	−	30.1939i	0.314681	−	1.17441i	0.924286	−	0.381701i	$-0.124662\pi$
$662$	3.70489	−	3.70489i	0.143994	−	0.143994i
$663$	23.1644	+	10.3076i	0.899630	+	0.400313i
$664$		−	7.83085i		−	0.303896i
$665$	4.21644	+	4.99192i	0.163507	+	0.193578i
$666$	−4.56335	−	7.90395i	−0.176826	−	0.306272i
$667$	−4.14542	−	15.4709i	−0.160511	−	0.599037i
$668$			18.2782i			0.707206i
$669$	6.86607	−	1.83976i	0.265458	−	0.0711291i
$670$	−7.88700	+	3.70903i	−0.304701	+	0.143292i
$671$	−49.6078	−	49.6078i	−1.91509	−	1.91509i
$672$	−0.935438	+	0.250650i	−0.0360853	+	0.00966903i
$673$	−6.80591	+	25.4000i	−0.262349	+	0.979098i	0.701505	+	0.712665i	$0.252512\pi$
$673$	−6.80591	+	25.4000i	−0.262349	+	0.979098i	−0.963853	+	0.266433i	$0.914155\pi$
$674$	−9.15352	−	2.45268i	−0.352580	−	0.0944736i
$675$	−2.08359	+	4.54518i	−0.0801973	+	0.174944i
$676$	12.7148	−	2.70822i	0.489030	−	0.104162i
$677$	−9.72941	−	9.72941i	−0.373931	−	0.373931i	0.494975	−	0.868907i	$-0.335177\pi$
$677$	−9.72941	−	9.72941i	−0.373931	−	0.373931i	−0.868907	+	0.494975i	$0.835177\pi$
$678$	−0.937885	+	0.541488i	−0.0360193	+	0.0207957i
$679$	8.77356	−	5.06541i	0.336698	−	0.194393i
$680$	5.32986	−	14.7931i	0.204391	−	0.567290i
$681$	−12.8012	+	12.8012i	−0.490543	+	0.490543i
$682$	24.6791	−	42.7454i	0.945010	−	1.63681i
$683$	−8.76902	+	15.1884i	−0.335537	+	0.581167i	−0.983588	−	0.180430i	$-0.942251\pi$
$683$	−8.76902	+	15.1884i	−0.335537	+	0.581167i	0.648051	+	0.761597i	$0.275584\pi$
$684$	−2.13369	+	2.13369i	−0.0815835	+	0.0815835i
$685$	9.38241	+	19.9511i	0.358484	+	0.762291i
$686$	−10.9551	+	6.32493i	−0.418267	+	0.241487i
$687$	1.68336	−	0.971890i	0.0642243	−	0.0370799i
$688$	−6.60067	−	6.60067i	−0.251648	−	0.251648i
$689$	8.85725	+	23.0594i	0.337434	+	0.878491i
$690$	7.23118	+	5.02837i	0.275286	+	0.191427i
$691$	22.8048	+	6.11053i	0.867535	+	0.232455i	0.665022	−	0.746824i	$-0.268422\pi$
$691$	22.8048	+	6.11053i	0.867535	+	0.232455i	0.202514	+	0.979279i	$0.435089\pi$
$692$	0.537812	−	2.00714i	0.0204446	−	0.0763001i
$693$	−4.69864	+	1.25900i	−0.178487	+	0.0478253i
$694$	12.4277	+	12.4277i	0.471751	+	0.471751i
$695$	0.135746	+	0.288655i	0.00514914	+	0.0109493i
$696$	−3.92773	+	1.05243i	−0.148880	+	0.0398924i
$697$			51.0127i			1.93224i
$698$	−5.76539	−	21.5167i	−0.218223	−	0.814421i
$699$	−4.60919	−	7.98335i	−0.174335	−	0.301958i
$700$	−3.72949	−	3.08832i	−0.140961	−	0.116727i
$701$		−	24.3673i		−	0.920339i	−0.887831	−	0.460169i	$-0.847789\pi$
$701$		−	24.3673i		−	0.920339i	0.887831	−	0.460169i	$-0.152211\pi$
$702$	2.80252	+	2.26845i	0.105774	+	0.0856173i
$703$	19.4735	−	19.4735i	0.734457	−	0.734457i
$704$	−1.30003	+	4.85177i	−0.0489967	+	0.182858i
$705$	17.5384	−	14.8139i	0.660536	−	0.557924i
$706$	3.04814	+	1.75984i	0.114718	+	0.0662326i
$707$	−6.50778			−0.244750
$708$	−4.44872	−	2.56847i	−0.167193	−	0.0965289i
$709$	7.79534	+	29.0926i	0.292760	+	1.09260i	0.942980	+	0.332850i	$0.108010\pi$
$709$	7.79534	+	29.0926i	0.292760	+	1.09260i	−0.650220	+	0.759746i	$0.725323\pi$
$710$	−6.33991	+	1.13916i	−0.237933	+	0.0427519i
$711$	−4.26992	+	7.39571i	−0.160134	+	0.277361i
$712$	−9.75961	−	2.61508i	−0.365757	−	0.0980042i
$713$	19.3529	+	33.5202i	0.724772	+	1.25534i
$714$	−6.81003			−0.254859
$715$	−11.2969	−	38.8885i	−0.422482	−	1.45435i
$716$	−9.75097			−0.364411
$717$	13.2983	+	23.0333i	0.496634	+	0.860196i
$718$	−23.2640	−	6.23358i	−0.868206	−	0.232635i
$719$	1.28175	−	2.22005i	0.0478012	−	0.0827941i	−0.841135	−	0.540825i	$-0.818112\pi$
$719$	1.28175	−	2.22005i	0.0478012	−	0.0827941i	0.888936	+	0.458031i	$0.151445\pi$
$720$	1.27660	−	1.83584i	0.0475759	−	0.0684177i
$721$	−0.968151	−	3.61319i	−0.0360558	−	0.134562i
$722$	8.56913	+	4.94739i	0.318910	+	0.184123i
$723$	−14.2557			−0.530174
$724$	6.10279	+	3.52345i	0.226809	+	0.130948i
$725$	−15.6594	−	12.9673i	−0.581576	−	0.481592i
$726$	−3.68294	+	13.7449i	−0.136687	+	0.510122i
$727$	−28.9717	+	28.9717i	−1.07450	+	1.07450i	−0.0775074	+	0.996992i	$0.524696\pi$
$727$	−28.9717	+	28.9717i	−1.07450	+	1.07450i	−0.996992	+	0.0775074i	$0.975304\pi$
$728$	−2.82445	+	2.05300i	−0.104681	+	0.0760891i
$729$			1.00000i			0.0370370i
$730$	−0.992634	+	11.7870i	−0.0367390	+	0.436258i
$731$	−32.8209	−	56.8475i	−1.21393	−	2.10258i
$732$	−3.61497	−	13.4912i	−0.133613	−	0.498651i
$733$		−	34.5040i		−	1.27443i	−0.770684	−	0.637217i	$-0.780086\pi$
$733$		−	34.5040i		−	1.27443i	0.770684	−	0.637217i	$-0.219914\pi$
$734$	8.38454	−	2.24663i	0.309479	−	0.0829247i
$735$	4.59477	−	12.7529i	0.169481	−	0.470396i
$736$	−2.78522	−	2.78522i	−0.102665	−	0.102665i
$737$	18.9109	−	5.06717i	0.696593	−	0.186652i
$738$	−1.87757	+	7.00720i	−0.0691144	+	0.257939i
$739$	−24.8848	−	6.66786i	−0.915402	−	0.245281i	−0.229783	−	0.973242i	$-0.573802\pi$
$739$	−24.8848	−	6.66786i	−0.915402	−	0.245281i	−0.685619	+	0.727961i	$0.740468\pi$
$740$	−11.6511	+	16.7551i	−0.428303	+	0.615931i
$741$	−4.42307	+	9.94004i	−0.162486	+	0.365156i
$742$	−4.69154	−	4.69154i	−0.172232	−	0.172232i
$743$	27.2626	−	15.7401i	1.00017	−	0.577447i	0.0918703	−	0.995771i	$-0.470715\pi$
$743$	27.2626	−	15.7401i	1.00017	−	0.577447i	0.908298	+	0.418324i	$0.137382\pi$
$744$	8.51006	−	4.91328i	0.311994	−	0.180130i
$745$	4.63443	+	1.66976i	0.169793	+	0.0611751i
$746$	−12.6832	+	12.6832i	−0.464366	+	0.464366i
$747$	3.91543	−	6.78172i	0.143258	−	0.248130i
$748$	−17.6606	+	30.5890i	−0.645734	+	1.11844i
$749$	−11.0058	+	11.0058i	−0.402143	+	0.402143i
$750$	11.1798	−	0.109028i	0.408229	−	0.00398113i
$751$	15.8501	−	9.15103i	0.578377	−	0.333926i	−0.182111	−	0.983278i	$-0.558293\pi$
$751$	15.8501	−	9.15103i	0.578377	−	0.333926i	0.760488	+	0.649352i	$0.224960\pi$
$752$	−8.89142	+	5.13346i	−0.324237	+	0.187198i
$753$	−6.36730	−	6.36730i	−0.232037	−	0.232037i
$754$	−11.8593	+	8.62015i	−0.431892	+	0.313927i
$755$	3.88230	+	21.6066i	0.141291	+	0.786346i
$756$	−0.935438	−	0.250650i	−0.0340216	−	0.00911605i
$757$	9.92258	−	37.0316i	0.360642	−	1.34594i	−0.512591	−	0.858633i	$-0.671314\pi$
$757$	9.92258	−	37.0316i	0.360642	−	1.34594i	0.873233	−	0.487302i	$-0.162019\pi$
$758$	−8.32746	+	2.23134i	−0.302467	+	0.0810458i
$759$	−13.9899	−	13.9899i	−0.507803	−	0.507803i
$760$	6.34786	+	2.28709i	0.230261	+	0.0829615i
$761$	17.5406	−	4.69998i	0.635845	−	0.170374i	0.0735244	−	0.997293i	$-0.476575\pi$
$761$	17.5406	−	4.69998i	0.635845	−	0.170374i	0.562321	+	0.826919i	$0.309909\pi$
$762$			0.636030i			0.0230410i
$763$	−2.52980	−	9.44134i	−0.0915849	−	0.341800i
$764$	6.31127	+	10.9314i	0.228334	+	0.395485i
$765$	12.0124	−	10.1463i	0.434308	−	0.366840i
$766$		−	17.7294i		−	0.640588i
$767$	−18.2941	−	2.89353i	−0.660560	−	0.104479i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−0.0660613	+	0.246544i	−0.00238223	+	0.00889061i	−0.967107	−	0.254371i	$-0.918132\pi$
$769$	−0.0660613	+	0.246544i	−0.00238223	+	0.00889061i	0.964724	+	0.263262i	$0.0847982\pi$
$770$	7.01872	+	8.30957i	0.252937	+	0.299456i
$771$	−10.6442	−	6.14542i	−0.383341	−	0.221322i
$772$	−22.7263			−0.817937
$773$	18.8493	+	10.8826i	0.677961	+	0.391421i	0.799086	−	0.601216i	$-0.205317\pi$
$773$	18.8493	+	10.8826i	0.677961	+	0.391421i	−0.121126	+	0.992637i	$0.538650\pi$
$774$	−2.41601	−	9.01668i	−0.0868417	−	0.324098i
$775$	44.6635	+	20.4745i	1.60436	+	0.735466i
$776$	5.23050	−	9.05950i	0.187764	−	0.325217i
$777$	8.53746	+	2.28761i	0.306280	+	0.0820674i
$778$	−15.0989	−	26.1521i	−0.541322	−	0.937597i
$779$	−21.8900			−0.784291
$780$	1.92334	−	7.82948i	0.0688667	−	0.280340i
$781$	14.4695			0.517761
$782$	−13.8491	−	23.9874i	−0.495243	−	0.857787i
$783$	−3.92773	−	1.05243i	−0.140366	−	0.0376109i
$784$	−3.03106	+	5.24996i	−0.108252	+	0.187499i
$785$	−5.18752	−	28.8708i	−0.185151	−	1.03044i
$786$	−0.134070	−	0.500356i	−0.00478212	−	0.0178471i
$787$	18.4712	+	10.6643i	0.658426	+	0.380142i	0.791677	−	0.610940i	$-0.209208\pi$
$787$	18.4712	+	10.6643i	0.658426	+	0.380142i	−0.133251	+	0.991082i	$0.542542\pi$
$788$	16.8234			0.599309
$789$	−7.41804	−	4.28281i	−0.264089	−	0.152472i
$790$	19.0283	+	1.60245i	0.676996	+	0.0570126i
$791$	0.271448	−	1.01306i	0.00965158	−	0.0360202i
$792$	−3.55175	+	3.55175i	−0.126206	+	0.126206i
$793$	−29.6091	−	40.7353i	−1.05145	−	1.44655i
$794$		−	2.98303i		−	0.105864i
$795$	15.2654	+	1.28556i	0.541409	+	0.0455943i
$796$	7.60612	+	13.1742i	0.269592	+	0.466947i
$797$	0.356228	+	1.32946i	0.0126182	+	0.0470919i	0.971948	−	0.235196i	$-0.0755733\pi$
$797$	0.356228	+	1.32946i	0.0126182	+	0.0470919i	−0.959330	+	0.282288i	$0.908907\pi$
$798$		−	2.92225i		−	0.103446i
$799$	−69.7368	+	18.6859i	−2.46711	+	0.661061i
$800$	−4.92958	−	0.836210i	−0.174287	−	0.0295645i
$801$	−7.14453	−	7.14453i	−0.252439	−	0.252439i
$802$	−8.26965	+	2.21585i	−0.292011	+	0.0782442i
$803$	6.87713	−	25.6658i	0.242689	−	0.905727i
$804$	3.76492	+	1.00881i	0.132779	+	0.0355779i
$805$	−8.39520	+	1.50845i	−0.295892	+	0.0531660i
$806$	22.2911	−	27.5391i	0.785172	−	0.970025i
$807$	12.8882	+	12.8882i	0.453687	+	0.453687i
$808$	−5.81959	+	3.35994i	−0.204732	+	0.118202i
$809$	14.5594	−	8.40588i	0.511881	−	0.295535i	−0.221725	−	0.975109i	$-0.571169\pi$
$809$	14.5594	−	8.40588i	0.511881	−	0.295535i	0.733607	+	0.679574i	$0.237835\pi$
$810$	2.02348	−	0.951586i	0.0710980	−	0.0334353i
$811$	−0.120225	+	0.120225i	−0.00422166	+	0.00422166i	−0.709214	−	0.704993i	$-0.750950\pi$
$811$	−0.120225	+	0.120225i	−0.00422166	+	0.00422166i	0.704993	+	0.709214i	$0.250950\pi$
$812$	1.96897	−	3.41036i	0.0690974	−	0.119680i
$813$	−4.92791	+	8.53540i	−0.172829	+	0.299349i
$814$	32.4157	−	32.4157i	1.13617	−	1.13617i
$815$	0.678028	−	0.318857i	0.0237503	−	0.0111691i
$816$	−6.08988	+	3.51599i	−0.213188	+	0.123084i
$817$	24.3938	−	14.0837i	0.853430	−	0.492728i
$818$	4.73889	+	4.73889i	0.165691	+	0.165691i
$819$	−3.47254	+	0.365721i	−0.121341	+	0.0127793i
$820$	15.9656	−	2.86871i	0.557544	−	0.100180i
$821$	−14.4304	−	3.86660i	−0.503623	−	0.134945i	−0.00194202	−	0.999998i	$-0.500618\pi$
$821$	−14.4304	−	3.86660i	−0.503623	−	0.134945i	−0.501681	+	0.865053i	$0.667285\pi$
$822$	2.55190	−	9.52380i	0.0890076	−	0.332181i
$823$	−5.11609	+	1.37085i	−0.178336	+	0.0477849i	−0.346882	−	0.937909i	$-0.612759\pi$
$823$	−5.11609	+	1.37085i	−0.178336	+	0.0477849i	0.168546	+	0.985694i	$0.446093\pi$
$824$	−2.73124	−	2.73124i	−0.0951474	−	0.0951474i
$825$	−24.7609	−	4.20022i	−0.862064	−	0.146233i
$826$	4.80529	−	1.28757i	0.167197	−	0.0448004i
$827$		−	25.3351i		−	0.880988i	−0.897756	−	0.440494i	$-0.854803\pi$
$827$		−	25.3351i		−	0.880988i	0.897756	−	0.440494i	$-0.145197\pi$
$828$	−1.01946	−	3.80468i	−0.0354287	−	0.132222i
$829$	−9.76498	−	16.9134i	−0.339152	−	0.587428i	0.645122	−	0.764080i	$-0.276807\pi$
$829$	−9.76498	−	16.9134i	−0.339152	−	0.587428i	−0.984273	+	0.176652i	$0.943473\pi$
$830$	−17.4486	−	1.46941i	−0.605648	−	0.0510041i
$831$		−	6.56821i		−	0.227849i
$832$	−1.46581	+	3.29414i	−0.0508180	+	0.114204i
$833$	−30.1431	+	30.1431i	−1.04440	+	1.04440i
$834$	0.0369212	−	0.137792i	0.00127848	−	0.00477134i
$835$	40.7272	+	3.42980i	1.40942	+	0.118693i
$836$	−13.1260	−	7.57831i	−0.453973	−	0.262101i
$837$	9.82657			0.339656
$838$	12.7429	+	7.35714i	0.440198	+	0.254148i
$839$	−4.81738	−	17.9787i	−0.166314	−	0.620694i	−0.997869	−	0.0652508i	$-0.979215\pi$
$839$	−4.81738	−	17.9787i	−0.166314	−	0.620694i	0.831554	−	0.555443i	$-0.187451\pi$
$840$	0.382964	+	2.13136i	0.0132135	+	0.0735389i
$841$	−6.23265	+	10.7953i	−0.214919	+	0.372250i
$842$	26.7542	+	7.16877i	0.922011	+	0.247052i
$843$	0.128259	+	0.222152i	0.00441749	+	0.00765132i
$844$	1.62305			0.0558676
$845$	−3.64856	−	28.8390i	−0.125514	−	0.992092i
$846$	−10.2669			−0.352984
$847$	−6.89033	−	11.9344i	−0.236755	−	0.410071i
$848$	−6.61763	−	1.77319i	−0.227250	−	0.0608916i
$849$	−6.71830	+	11.6364i	−0.230572	+	0.399362i
$850$	−31.9616	−	14.6517i	−1.09628	−	0.502551i
$851$	9.30431	+	34.7241i	0.318948	+	1.19033i
$852$	2.49476	+	1.44035i	0.0854690	+	0.0493456i
$853$	23.1899			0.794007			0.397003	−	0.917817i	$-0.370050\pi$
$853$	23.1899			0.794007			0.397003	+	0.917817i	$0.370050\pi$
$854$	11.7141	+	6.76316i	0.400850	+	0.231431i
$855$	4.35386	+	5.15461i	0.148899	+	0.176284i
$856$	−4.15969	+	15.5242i	−0.142175	+	0.530606i
$857$	−31.6975	+	31.6975i	−1.08277	+	1.08277i	−0.0865171	+	0.996250i	$0.527574\pi$
$857$	−31.6975	+	31.6975i	−1.08277	+	1.08277i	−0.996250	+	0.0865171i	$0.972426\pi$
$858$	−7.36268	+	16.5462i	−0.251358	+	0.564880i
$859$			40.3734i			1.37752i	0.724988	+	0.688762i	$0.241845\pi$
$859$			40.3734i			1.37752i	−0.724988	+	0.688762i	$0.758155\pi$
$860$	−15.9461	+	13.4689i	−0.543756	+	0.459286i
$861$	−3.51271	−	6.08419i	−0.119713	−	0.207349i
$862$	5.44408	+	20.3176i	0.185426	+	0.692019i
$863$			44.2139i			1.50506i	0.658558	+	0.752530i	$0.271167\pi$
$863$			44.2139i			1.50506i	−0.658558	+	0.752530i	$0.728833\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	−4.37136	−	1.57497i	−0.148631	−	0.0535506i
$866$	3.02486	+	3.02486i	0.102789	+	0.102789i
$867$	−31.3431	+	8.39837i	−1.06447	+	0.285223i
$868$	−2.46303	+	9.19215i	−0.0836007	+	0.312002i
$869$	−41.4333	−	11.1020i	−1.40553	−	0.376611i
$870$	1.60799	+	8.94918i	0.0545161	+	0.303406i
$871$	13.9762	−	1.47194i	0.473565	−	0.0498748i
$872$	−7.13680	−	7.13680i	−0.241683	−	0.241683i
$873$	9.05950	−	5.23050i	0.306618	−	0.177026i
$874$	10.2932	−	5.94278i	0.348173	−	0.201018i
$875$	−7.58114	+	7.73046i	−0.256289	+	0.261337i
$876$	3.74058	−	3.74058i	0.126383	−	0.126383i
$877$	−12.8301	+	22.2223i	−0.433241	+	0.750395i	−0.997150	−	0.0754417i	$-0.975963\pi$
$877$	−12.8301	+	22.2223i	−0.433241	+	0.750395i	0.563910	+	0.825837i	$0.309297\pi$
$878$	5.94011	−	10.2886i	0.200469	−	0.347223i
$879$	6.39074	−	6.39074i	0.215554	−	0.215554i
$880$	10.5667	+	3.80711i	0.356203	+	0.128338i
$881$	−8.52485	+	4.92183i	−0.287210	+	0.165821i	−0.636683	−	0.771126i	$-0.719694\pi$
$881$	−8.52485	+	4.92183i	−0.287210	+	0.165821i	0.349473	+	0.936946i	$0.386361\pi$
$882$	−5.24996	+	3.03106i	−0.176775	+	0.102061i
$883$	−24.7435	−	24.7435i	−0.832686	−	0.832686i	0.155197	−	0.987884i	$-0.450399\pi$
$883$	−24.7435	−	24.7435i	−0.832686	−	0.832686i	−0.987884	+	0.155197i	$0.950399\pi$
$884$	−15.9517	+	19.7073i	−0.536515	+	0.662827i
$885$	−6.55779	+	9.43059i	−0.220438	+	0.317006i
$886$	−6.20158	−	1.66171i	−0.208346	−	0.0558262i
$887$	−0.845112	+	3.15400i	−0.0283761	+	0.105901i	−0.978661	−	0.205479i	$-0.934125\pi$
$887$	−0.845112	+	3.15400i	−0.0283761	+	0.105901i	0.950285	+	0.311380i	$0.100791\pi$
$888$	8.81571	−	2.36216i	0.295836	−	0.0792690i
$889$	−0.435546	−	0.435546i	−0.0146078	−	0.0146078i
$890$	−7.65820	+	21.2555i	−0.256704	+	0.712485i
$891$	−4.85177	+	1.30003i	−0.162541	+	0.0435526i
$892$			7.10828i			0.238003i
$893$	−8.01830	−	29.9247i	−0.268322	−	1.00139i
$894$	−1.10150	−	1.90785i	−0.0368397	−	0.0638082i
$895$	−1.82971	+	21.7269i	−0.0611606	+	0.726251i
$896$		−	0.968437i		−	0.0323532i
$897$	−8.35009	−	11.4878i	−0.278801	−	0.383567i
$898$	0.516082	−	0.516082i	0.0172219	−	0.0172219i
$899$	−10.3418	+	38.5961i	−0.344919	+	1.28725i
$900$	−3.85104	−	3.18897i	−0.128368	−	0.106299i
$901$	−41.7222	−	24.0883i	−1.38997	−	0.802499i
$902$	−36.4383			−1.21326
$903$	7.82897	+	4.52006i	0.260532	+	0.150418i
$904$	−0.280295	−	1.04608i	−0.00932247	−	0.0347919i
$905$	8.99604	−	12.9370i	0.299038	−	0.430039i
$906$	4.90877	−	8.50223i	0.163083	−	0.282468i
$907$	−14.3045	−	3.83288i	−0.474973	−	0.127269i	0.0133879	−	0.999910i	$-0.495738\pi$
$907$	−14.3045	−	3.83288i	−0.474973	−	0.127269i	−0.488361	+	0.872642i	$0.662405\pi$
$908$	−9.05181	−	15.6782i	−0.300395	−	0.520299i
$909$	−6.71988			−0.222884
$910$	4.04445	+	6.67862i	0.134072	+	0.221394i
$911$	49.7322			1.64770			0.823850	−	0.566807i	$-0.191822\pi$
$911$	49.7322			1.64770			0.823850	+	0.566807i	$0.191822\pi$
$912$	−1.50874	−	2.61322i	−0.0499595	−	0.0865324i
$913$	37.9935	+	10.1803i	1.25740	+	0.336920i
$914$	−7.39796	+	12.8136i	−0.244703	+	0.423837i
$915$	−30.7393	+	5.52325i	−1.01621	+	0.182593i
$916$	0.503087	+	1.87755i	0.0166225	+	0.0620359i
$917$	0.434447	+	0.250828i	0.0143467	+	0.00828308i
$918$	−7.03198			−0.232090
$919$	−16.1605	−	9.33028i	−0.533087	−	0.307778i	0.209186	−	0.977876i	$-0.432919\pi$
$919$	−16.1605	−	9.33028i	−0.533087	−	0.307778i	−0.742272	+	0.670098i	$0.766252\pi$
$920$	−6.72860	+	5.68334i	−0.221835	+	0.187374i
$921$	−4.13617	+	15.4364i	−0.136292	+	0.508647i
$922$	−16.3945	+	16.3945i	−0.539923	+	0.539923i
$923$	10.2590	+	1.62264i	0.337678	+	0.0534099i
$924$		−	4.86439i		−	0.160027i
$925$	35.1472	+	29.1047i	1.15563	+	0.956958i
$926$	11.1848	+	19.3727i	0.367557	+	0.636627i
$927$	−0.999705	−	3.73095i	−0.0328346	−	0.122540i
$928$		−	4.06629i		−	0.133482i
$929$	6.61307	−	1.77197i	0.216968	−	0.0581364i	−0.148698	−	0.988883i	$-0.547508\pi$
$929$	6.61307	−	1.77197i	0.216968	−	0.0581364i	0.365665	+	0.930746i	$0.380841\pi$
$930$	−9.35082	−	19.8839i	−0.306626	−	0.652019i
$931$	−12.9347	−	12.9347i	−0.423917	−	0.423917i
$932$	8.90427	−	2.38589i	0.291669	−	0.0781524i
$933$	−1.97608	+	7.37482i	−0.0646939	+	0.241441i
$934$	9.55223	+	2.55951i	0.312558	+	0.0837498i
$935$	64.8439	+	45.0908i	2.12062	+	1.47463i
$936$	−2.91650	+	2.11991i	−0.0953289	+	0.0692913i
$937$	−28.4459	−	28.4459i	−0.929288	−	0.929288i	0.0683721	−	0.997660i	$-0.478220\pi$
$937$	−28.4459	−	28.4459i	−0.929288	−	0.929288i	−0.997660	+	0.0683721i	$0.978220\pi$
$938$	−3.26900	+	1.88736i	−0.106736	+	0.0616243i
$939$	−22.3659	+	12.9130i	−0.729884	+	0.421399i
$940$	9.76986	+	20.7750i	0.318658	+	0.677605i
$941$	−30.0593	+	30.0593i	−0.979904	+	0.979904i	−0.999802	−	0.0198978i	$-0.993666\pi$
$941$	−30.0593	+	30.0593i	−0.979904	+	0.979904i	0.0198978	+	0.999802i	$0.493666\pi$
$942$	−6.55909	+	11.3607i	−0.213707	+	0.370151i
$943$	14.2871	−	24.7460i	0.465253	−	0.805842i
$944$	3.63236	−	3.63236i	0.118223	−	0.118223i
$945$	−0.734023	+	2.03729i	−0.0238778	+	0.0662731i
$946$	40.6060	−	23.4439i	1.32022	−	0.762227i
$947$	−3.49284	+	2.01659i	−0.113502	+	0.0655304i	−0.555676	−	0.831399i	$-0.687541\pi$
$947$	−3.49284	+	2.01659i	−0.113502	+	0.0655304i	0.442174	+	0.896929i	$0.354207\pi$
$948$	−6.03857	−	6.03857i	−0.196124	−	0.196124i
$949$	7.75413	−	17.4260i	0.251710	−	0.565671i
$950$	6.28719	−	13.7150i	0.203983	−	0.444974i
$951$	−0.253279	−	0.0678659i	−0.00821314	−	0.00220070i
$952$	1.76257	−	6.57799i	0.0571251	−	0.213194i
$953$	−32.3913	+	8.67923i	−1.04926	+	0.281148i	−0.741945	−	0.670460i	$-0.766097\pi$
$953$	−32.3913	+	8.67923i	−1.04926	+	0.281148i	−0.307313	+	0.951608i	$0.599430\pi$
$954$	−4.84444	−	4.84444i	−0.156845	−	0.156845i
$955$	25.5415	−	12.0114i	0.826503	−	0.388680i
$956$	−25.6903	+	6.88371i	−0.830885	+	0.222635i
$957$		−	20.4247i		−	0.660236i
$958$	−1.73879	−	6.48925i	−0.0561777	−	0.209658i
$959$	4.77428	+	8.26930i	0.154170	+	0.267030i
$960$	1.44288	+	1.70825i	0.0465687	+	0.0551334i
$961$		−	65.5615i		−	2.11489i
$962$	26.6180	−	19.3477i	0.858200	−	0.623796i
$963$	−11.3645	+	11.3645i	−0.366216	+	0.366216i
$964$	3.68964	−	13.7699i	0.118835	−	0.443500i
$965$	−4.26446	+	50.6383i	−0.137278	+	1.63010i
$966$	3.30352	+	1.90729i	0.106289	+	0.0613659i
$967$	−27.8211			−0.894666			−0.447333	−	0.894368i	$-0.647626\pi$
$967$	−27.8211			−0.894666			−0.447333	+	0.894368i	$0.647626\pi$
$968$	−12.3234	−	7.11490i	−0.396088	−	0.228681i
$969$	−5.49186	−	20.4959i	−0.176424	−	0.658423i
$970$	−19.2047	−	13.3545i	−0.616627	−	0.428786i
$971$	−3.36942	+	5.83601i	−0.108130	+	0.187287i	−0.915013	−	0.403425i	$-0.867820\pi$
$971$	−3.36942	+	5.83601i	−0.108130	+	0.187287i	0.806883	+	0.590712i	$0.201153\pi$
$972$	−0.965926	−	0.258819i	−0.0309821	−	0.00830162i
$973$	0.0690750	+	0.119641i	0.00221444	+	0.00383553i
$974$	10.3466			0.331527
$975$	−17.0846	−	5.75471i	−0.547145	−	0.184298i
$976$	13.9672			0.447078
$977$	12.0528	+	20.8760i	0.385602	+	0.667882i	0.991852	−	0.127392i	$-0.0406606\pi$
$977$	12.0528	+	20.8760i	0.385602	+	0.667882i	−0.606251	+	0.795274i	$0.707327\pi$
$978$	−0.323662	−	0.0867250i	−0.0103496	−	0.00277316i
$979$	25.3755	−	43.9517i	0.811006	−	1.40470i
$980$	11.1291	+	7.73888i	0.355506	+	0.247210i
$981$	−2.61225	−	9.74905i	−0.0834028	−	0.311263i
$982$	32.8883	+	18.9881i	1.04951	+	0.605934i
$983$	−17.6577			−0.563194			−0.281597	−	0.959533i	$-0.590864\pi$
$983$	−17.6577			−0.563194			−0.281597	+	0.959533i	$0.590864\pi$
$984$	−6.28248	−	3.62719i	−0.200278	−	0.115631i
$985$	3.15681	−	37.4856i	0.100584	−	1.19439i
$986$	7.40069	−	27.6198i	0.235686	−	0.879592i
$987$	7.03067	−	7.03067i	0.223789	−	0.223789i
$988$	−8.45656	−	6.84503i	−0.269039	−	0.217769i
$989$			36.7686i			1.16917i
$990$	7.24747	+	8.58040i	0.230340	+	0.272703i
$991$	−15.1479	−	26.2369i	−0.481188	−	0.833442i	0.518579	−	0.855030i	$-0.326461\pi$
$991$	−15.1479	−	26.2369i	−0.481188	−	0.833442i	−0.999767	+	0.0215876i	$0.993128\pi$
$992$	2.54330	+	9.49174i	0.0807500	+	0.301363i
$993$			5.23950i			0.166271i
$994$	−2.69472	+	0.722047i	−0.0854712	+	0.0229019i
$995$	30.7817	−	14.4758i	0.975846	−	0.458912i
$996$	5.53725	+	5.53725i	0.175454	+	0.175454i
$997$	−38.8213	+	10.4021i	−1.22948	+	0.329439i	−0.814378	−	0.580335i	$-0.802922\pi$
$997$	−38.8213	+	10.4021i	−1.22948	+	0.329439i	−0.415105	+	0.909774i	$0.636255\pi$
$998$	−1.81096	+	6.75859i	−0.0573249	+	0.213939i
$999$	8.81571	+	2.36216i	0.278917	+	0.0747355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.c.67.7	yes	32
5.3	odd	4		390.2.bd.c.223.2	yes	32
13.7	odd	12		390.2.bd.c.7.2	✓	32
65.33	even	12	inner	390.2.bn.c.163.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.c.7.2	✓	32	13.7	odd	12
390.2.bd.c.223.2	yes	32	5.3	odd	4
390.2.bn.c.67.7	yes	32	1.1	even	1	trivial
390.2.bn.c.163.7	yes	32	65.33	even	12	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.83584 + 1.27660i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.838691 + 0.484219i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.83584 + 1.27660i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(0.838691 + 0.484219i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(0.187644 - 2.22818i) q^{10} +(-1.30003 + 4.85177i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-1.46581 + 3.29414i) q^{13} -0.968437i q^{14} +(1.44288 + 1.70825i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.82001 - 6.79237i) q^{17} -1.00000i q^{18} +(2.91467 - 0.780983i) q^{19} +(-2.02348 + 0.951586i) q^{20} +(0.684788 + 0.684788i) q^{21} +(4.85177 - 1.30003i) q^{22} +(-1.01946 + 3.80468i) q^{23} +(0.965926 + 0.258819i) q^{24} +(1.74061 + 4.68725i) q^{25} +(3.58572 - 0.377640i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.838691 + 0.484219i) q^{28} +(-3.52151 + 2.03314i) q^{29} +(0.757946 - 2.10369i) q^{30} +(6.94843 - 6.94843i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.51146 + 4.34998i) q^{33} +(-4.97236 + 4.97236i) q^{34} +(0.921551 + 1.95962i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(7.90395 - 4.56335i) q^{37} +(-2.13369 - 2.13369i) q^{38} +(-2.26845 + 2.80252i) q^{39} +(1.83584 + 1.27660i) q^{40} +(-7.00720 - 1.87757i) q^{41} +(0.250650 - 0.935438i) q^{42} +(9.01668 - 2.41601i) q^{43} +(-3.55175 - 3.55175i) q^{44} +(0.951586 + 2.02348i) q^{45} +(3.80468 - 1.01946i) q^{46} -10.2669i q^{47} +(-0.258819 - 0.965926i) q^{48} +(-3.03106 - 5.24996i) q^{49} +(3.18897 - 3.85104i) q^{50} -7.03198i q^{51} +(-2.11991 - 2.91650i) q^{52} +(4.84444 - 4.84444i) q^{53} +(0.258819 - 0.965926i) q^{54} +(-8.58040 + 7.24747i) q^{55} +(0.838691 + 0.484219i) q^{56} +3.01749 q^{57} +(3.52151 + 2.03314i) q^{58} +(1.32954 + 4.96190i) q^{59} +(-2.20082 + 0.395445i) q^{60} +(-6.98358 + 12.0959i) q^{61} +(-9.49174 - 2.54330i) q^{62} +(0.484219 + 0.838691i) q^{63} +1.00000 q^{64} +(-6.89629 + 4.17627i) q^{65} +5.02293 q^{66} +(-1.94887 - 3.37554i) q^{67} +(6.79237 + 1.82001i) q^{68} +(-1.96945 + 3.41118i) q^{69} +(1.23630 - 1.77789i) q^{70} +(-0.745580 - 2.78254i) q^{71} +(0.866025 + 0.500000i) q^{72} -5.28998 q^{73} +(-7.90395 - 4.56335i) q^{74} +(0.468152 + 4.97804i) q^{75} +(-0.780983 + 2.91467i) q^{76} +(-3.43964 + 3.43964i) q^{77} +(3.56128 + 0.563280i) q^{78} +8.53983i q^{79} +(0.187644 - 2.22818i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.87757 + 7.00720i) q^{82} -7.83085i q^{83} +(-0.935438 + 0.250650i) q^{84} +(5.32986 - 14.7931i) q^{85} +(-6.60067 - 6.60067i) q^{86} +(-3.92773 + 1.05243i) q^{87} +(-1.30003 + 4.85177i) q^{88} +(-9.75961 - 2.61508i) q^{89} +(1.27660 - 1.83584i) q^{90} +(-2.82445 + 2.05300i) q^{91} +(-2.78522 - 2.78522i) q^{92} +(8.51006 - 4.91328i) q^{93} +(-8.89142 + 5.13346i) q^{94} +(6.34786 + 2.28709i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(5.23050 - 9.05950i) q^{97} +(-3.03106 + 5.24996i) q^{98} +(-3.55175 + 3.55175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

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