LMFDB - Embedded newform 560.2.bd.b.141.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(141,560)]

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([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("560.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bd (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:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			141.7
Character	$\chi$	$=$	560.141
Dual form			560.2.bd.b.421.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.908304 + 1.08397i) q^{2} +(0.523494 + 0.523494i) q^{3} +(-0.349967 - 1.96914i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.04294 + 0.0919583i) q^{6} +1.00000i q^{7} +(2.45236 + 1.40923i) q^{8} -2.45191i q^{9} +O(q^{10})$	\(q+(-0.908304 + 1.08397i) q^{2} +(0.523494 + 0.523494i) q^{3} +(-0.349967 - 1.96914i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.04294 + 0.0919583i) q^{6} +1.00000i q^{7} +(2.45236 + 1.40923i) q^{8} -2.45191i q^{9} +(0.124212 + 1.40875i) q^{10} +(-4.66793 + 4.66793i) q^{11} +(0.847630 - 1.21404i) q^{12} +(0.715365 + 0.715365i) q^{13} +(-1.08397 - 0.908304i) q^{14} +0.740333 q^{15} +(-3.75505 + 1.37827i) q^{16} +7.33275 q^{17} +(2.65779 + 2.22708i) q^{18} +(3.02223 + 3.02223i) q^{19} +(-1.63986 - 1.14493i) q^{20} +(-0.523494 + 0.523494i) q^{21} +(-0.819980 - 9.29979i) q^{22} +2.66840i q^{23} +(0.546074 + 2.02152i) q^{24} -1.00000i q^{25} +(-1.42520 + 0.125663i) q^{26} +(2.85404 - 2.85404i) q^{27} +(1.96914 - 0.349967i) q^{28} +(7.42579 + 7.42579i) q^{29} +(-0.672448 + 0.802496i) q^{30} +6.82577 q^{31} +(1.91673 - 5.32223i) q^{32} -4.88728 q^{33} +(-6.66036 + 7.94845i) q^{34} +(0.707107 + 0.707107i) q^{35} +(-4.82816 + 0.858086i) q^{36} +(-4.94014 + 4.94014i) q^{37} +(-6.02111 + 0.530893i) q^{38} +0.748979i q^{39} +(2.73056 - 0.737607i) q^{40} +1.19522i q^{41} +(-0.0919583 - 1.04294i) q^{42} +(4.05319 - 4.05319i) q^{43} +(10.8255 + 7.55821i) q^{44} +(-1.73376 - 1.73376i) q^{45} +(-2.89246 - 2.42372i) q^{46} -7.36041 q^{47} +(-2.68726 - 1.24423i) q^{48} -1.00000 q^{49} +(1.08397 + 0.908304i) q^{50} +(3.83865 + 3.83865i) q^{51} +(1.15830 - 1.65901i) q^{52} +(3.63832 - 3.63832i) q^{53} +(0.501348 + 5.68603i) q^{54} +6.60146i q^{55} +(-1.40923 + 2.45236i) q^{56} +3.16425i q^{57} +(-14.7942 + 1.30443i) q^{58} +(-4.60355 + 4.60355i) q^{59} +(-0.259092 - 1.45782i) q^{60} +(-9.38988 - 9.38988i) q^{61} +(-6.19988 + 7.39891i) q^{62} +2.45191 q^{63} +(4.02815 + 6.91187i) q^{64} +1.01168 q^{65} +(4.43913 - 5.29764i) q^{66} +(-4.19222 - 4.19222i) q^{67} +(-2.56622 - 14.4392i) q^{68} +(-1.39689 + 1.39689i) q^{69} +(-1.40875 + 0.124212i) q^{70} +1.04179i q^{71} +(3.45530 - 6.01296i) q^{72} -4.30389i q^{73} +(-0.867796 - 9.84209i) q^{74} +(0.523494 - 0.523494i) q^{75} +(4.89353 - 7.00889i) q^{76} +(-4.66793 - 4.66793i) q^{77} +(-0.811869 - 0.680301i) q^{78} -7.26030 q^{79} +(-1.68063 + 3.62980i) q^{80} -4.36757 q^{81} +(-1.29557 - 1.08562i) q^{82} +(8.17526 + 8.17526i) q^{83} +(1.21404 + 0.847630i) q^{84} +(5.18503 - 5.18503i) q^{85} +(0.711993 + 8.07505i) q^{86} +7.77472i q^{87} +(-18.0256 + 4.86928i) q^{88} +0.532249i q^{89} +(3.45412 - 0.304556i) q^{90} +(-0.715365 + 0.715365i) q^{91} +(5.25447 - 0.933853i) q^{92} +(3.57325 + 3.57325i) q^{93} +(6.68549 - 7.97843i) q^{94} +4.27408 q^{95} +(3.78955 - 1.78276i) q^{96} +6.49177 q^{97} +(0.908304 - 1.08397i) q^{98} +(11.4453 + 11.4453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) $ 52 * q - 8 * q^4 + 12 * q^6	$ 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) $ 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.908304	+	1.08397i	−0.642268	+	0.766480i
$2$	−0.908304	+	1.08397i	−0.642268	+	0.766480i
$3$	0.523494	+	0.523494i	0.302240	+	0.302240i	0.841890	−	0.539650i	$-0.181443\pi$
$3$	0.523494	+	0.523494i	0.302240	+	0.302240i	−0.539650	+	0.841890i	$0.681443\pi$
$4$	−0.349967	−	1.96914i	−0.174983	−	0.984571i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	−1.04294	+	0.0919583i	−0.425780	+	0.0375418i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.45236	+	1.40923i	0.867041	+	0.498237i
$9$		−	2.45191i		−	0.817302i
$10$	0.124212	+	1.40875i	0.0392793	+	0.445485i
$11$	−4.66793	+	4.66793i	−1.40744	+	1.40744i	−0.634568	+	0.772867i	$0.718822\pi$
$11$	−4.66793	+	4.66793i	−1.40744	+	1.40744i	−0.772867	+	0.634568i	$0.781178\pi$
$12$	0.847630	−	1.21404i	0.244690	−	0.350463i
$13$	0.715365	+	0.715365i	0.198407	+	0.198407i	0.799317	−	0.600910i	$-0.205195\pi$
$13$	0.715365	+	0.715365i	0.198407	+	0.198407i	−0.600910	+	0.799317i	$0.705195\pi$
$14$	−1.08397	−	0.908304i	−0.289702	−	0.242755i
$15$	0.740333			0.191153
$16$	−3.75505	+	1.37827i	−0.938762	+	0.344567i
$17$	7.33275			1.77845			0.889226	−	0.457468i	$-0.151244\pi$
$17$	7.33275			1.77845			0.889226	+	0.457468i	$0.151244\pi$
$18$	2.65779	+	2.22708i	0.626446	+	0.524927i
$19$	3.02223	+	3.02223i	0.693348	+	0.693348i	0.962967	−	0.269619i	$-0.0868978\pi$
$19$	3.02223	+	3.02223i	0.693348	+	0.693348i	−0.269619	+	0.962967i	$0.586898\pi$
$20$	−1.63986	−	1.14493i	−0.366683	−	0.256014i
$21$	−0.523494	+	0.523494i	−0.114236	+	0.114236i
$22$	−0.819980	−	9.29979i	−0.174820	−	1.98272i
$23$			2.66840i			0.556401i	0.960523	+	0.278200i	$0.0897379\pi$
$23$			2.66840i			0.556401i	−0.960523	+	0.278200i	$0.910262\pi$
$24$	0.546074	+	2.02152i	0.111467	+	0.412641i
$25$		−	1.00000i		−	0.200000i
$26$	−1.42520	+	0.125663i	−0.279505	+	0.0246445i
$27$	2.85404	−	2.85404i	0.549261	−	0.549261i
$28$	1.96914	−	0.349967i	0.372133	−	0.0661375i
$29$	7.42579	+	7.42579i	1.37893	+	1.37893i	0.846422	+	0.532513i	$0.178752\pi$
$29$	7.42579	+	7.42579i	1.37893	+	1.37893i	0.532513	+	0.846422i	$0.321248\pi$
$30$	−0.672448	+	0.802496i	−0.122772	+	0.146515i
$31$	6.82577			1.22594			0.612972	−	0.790104i	$-0.289974\pi$
$31$	6.82577			1.22594			0.612972	+	0.790104i	$0.289974\pi$
$32$	1.91673	−	5.32223i	0.338832	−	0.940847i
$33$	−4.88728			−0.850765
$34$	−6.66036	+	7.94845i	−1.14224	+	1.36315i
$35$	0.707107	+	0.707107i	0.119523	+	0.119523i
$36$	−4.82816	+	0.858086i	−0.804693	+	0.143014i
$37$	−4.94014	+	4.94014i	−0.812154	+	0.812154i	−0.984956	−	0.172803i	$-0.944718\pi$
$37$	−4.94014	+	4.94014i	−0.812154	+	0.812154i	0.172803	+	0.984956i	$0.444718\pi$
$38$	−6.02111	+	0.530893i	−0.976753	+	0.0861222i
$39$			0.748979i			0.119933i
$40$	2.73056	−	0.737607i	0.431739	−	0.116626i
$41$			1.19522i			0.186661i	0.995635	+	0.0933306i	$0.0297514\pi$
$41$			1.19522i			0.186661i	−0.995635	+	0.0933306i	$0.970249\pi$
$42$	−0.0919583	−	1.04294i	−0.0141895	−	0.160930i
$43$	4.05319	−	4.05319i	0.618106	−	0.618106i	−0.326940	−	0.945045i	$-0.606017\pi$
$43$	4.05319	−	4.05319i	0.618106	−	0.618106i	0.945045	+	0.326940i	$0.106017\pi$
$44$	10.8255	+	7.55821i	1.63200	+	1.13944i
$45$	−1.73376	−	1.73376i	−0.258454	−	0.258454i
$46$	−2.89246	−	2.42372i	−0.426470	−	0.357358i
$47$	−7.36041			−1.07363			−0.536813	−	0.843701i	$-0.680372\pi$
$47$	−7.36041			−1.07363			−0.536813	+	0.843701i	$0.680372\pi$
$48$	−2.68726	−	1.24423i	−0.387873	−	0.179589i
$49$	−1.00000			−0.142857
$50$	1.08397	+	0.908304i	0.153296	+	0.128454i
$51$	3.83865	+	3.83865i	0.537519	+	0.537519i
$52$	1.15830	−	1.65901i	0.160628	−	0.230063i
$53$	3.63832	−	3.63832i	0.499762	−	0.499762i	−0.411602	−	0.911364i	$-0.635031\pi$
$53$	3.63832	−	3.63832i	0.499762	−	0.499762i	0.911364	+	0.411602i	$0.135031\pi$
$54$	0.501348	+	5.68603i	0.0682248	+	0.773770i
$55$			6.60146i			0.890140i
$56$	−1.40923	+	2.45236i	−0.188316	+	0.327711i
$57$			3.16425i			0.419115i
$58$	−14.7942	+	1.30443i	−1.94257	+	0.171280i
$59$	−4.60355	+	4.60355i	−0.599331	+	0.599331i	−0.940135	−	0.340803i	$-0.889301\pi$
$59$	−4.60355	+	4.60355i	−0.599331	+	0.599331i	0.340803	+	0.940135i	$0.389301\pi$
$60$	−0.259092	−	1.45782i	−0.0334486	−	0.188204i
$61$	−9.38988	−	9.38988i	−1.20225	−	1.20225i	−0.973481	−	0.228770i	$-0.926530\pi$
$61$	−9.38988	−	9.38988i	−1.20225	−	1.20225i	−0.228770	−	0.973481i	$-0.573470\pi$
$62$	−6.19988	+	7.39891i	−0.787385	+	0.939662i
$63$	2.45191			0.308911
$64$	4.02815	+	6.91187i	0.503519	+	0.863984i
$65$	1.01168			0.125483
$66$	4.43913	−	5.29764i	0.546419	−	0.652095i
$67$	−4.19222	−	4.19222i	−0.512162	−	0.512162i	0.403027	−	0.915188i	$-0.367958\pi$
$67$	−4.19222	−	4.19222i	−0.512162	−	0.512162i	−0.915188	+	0.403027i	$0.867958\pi$
$68$	−2.56622	−	14.4392i	−0.311200	−	1.75101i
$69$	−1.39689	+	1.39689i	−0.168166	+	0.168166i
$70$	−1.40875	+	0.124212i	−0.168378	+	0.0148462i
$71$			1.04179i			0.123638i	0.998087	+	0.0618189i	$0.0196901\pi$
$71$			1.04179i			0.123638i	−0.998087	+	0.0618189i	$0.980310\pi$
$72$	3.45530	−	6.01296i	0.407211	−	0.708634i
$73$		−	4.30389i		−	0.503732i	−0.967762	−	0.251866i	$-0.918956\pi$
$73$		−	4.30389i		−	0.503732i	0.967762	−	0.251866i	$-0.0810443\pi$
$74$	−0.867796	−	9.84209i	−0.100879	−	1.14412i
$75$	0.523494	−	0.523494i	0.0604479	−	0.0604479i
$76$	4.89353	−	7.00889i	0.561326	−	0.803975i
$77$	−4.66793	−	4.66793i	−0.531960	−	0.531960i
$78$	−0.811869	−	0.680301i	−0.0919260	−	0.0770289i
$79$	−7.26030			−0.816847			−0.408424	−	0.912792i	$-0.633921\pi$
$79$	−7.26030			−0.816847			−0.408424	+	0.912792i	$0.633921\pi$
$80$	−1.68063	+	3.62980i	−0.187901	+	0.405824i
$81$	−4.36757			−0.485286
$82$	−1.29557	−	1.08562i	−0.143072	−	0.119887i
$83$	8.17526	+	8.17526i	0.897352	+	0.897352i	0.995201	−	0.0978495i	$-0.0311964\pi$
$83$	8.17526	+	8.17526i	0.897352	+	0.897352i	−0.0978495	+	0.995201i	$0.531196\pi$
$84$	1.21404	+	0.847630i	0.132463	+	0.0924840i
$85$	5.18503	−	5.18503i	0.562396	−	0.562396i
$86$	0.711993	+	8.07505i	0.0767762	+	0.870755i
$87$			7.77472i			0.833538i
$88$	−18.0256	+	4.86928i	−1.92154	+	0.519067i
$89$			0.532249i			0.0564183i	0.999602	+	0.0282091i	$0.00898044\pi$
$89$			0.532249i			0.0564183i	−0.999602	+	0.0282091i	$0.991020\pi$
$90$	3.45412	−	0.304556i	0.364096	−	0.0321031i
$91$	−0.715365	+	0.715365i	−0.0749906	+	0.0749906i
$92$	5.25447	−	0.933853i	0.547816	−	0.0973609i
$93$	3.57325	+	3.57325i	0.370529	+	0.370529i
$94$	6.68549	−	7.97843i	0.689555	−	0.822913i
$95$	4.27408			0.438512
$96$	3.78955	−	1.78276i	0.386770	−	0.181953i
$97$	6.49177			0.659139			0.329570	−	0.944131i	$-0.393096\pi$
$97$	6.49177			0.659139			0.329570	+	0.944131i	$0.393096\pi$
$98$	0.908304	−	1.08397i	0.0917526	−	0.109497i
$99$	11.4453	+	11.4453i	1.15030	+	1.15030i
$100$	−1.96914	+	0.349967i	−0.196914	+	0.0349967i
$101$	−7.58678	+	7.58678i	−0.754913	+	0.754913i	−0.975392	−	0.220479i	$-0.929238\pi$
$101$	−7.58678	+	7.58678i	−0.754913	+	0.754913i	0.220479	+	0.975392i	$0.429238\pi$
$102$	−7.64763	+	0.674307i	−0.757229	+	0.0667663i
$103$		−	0.802846i		−	0.0791068i	−0.999217	−	0.0395534i	$-0.987406\pi$
$103$		−	0.802846i		−	0.0791068i	0.999217	−	0.0395534i	$-0.0125935\pi$
$104$	0.746221	+	2.76245i	0.0731730	+	0.270880i
$105$			0.740333i			0.0722491i
$106$	0.639116	+	7.24852i	0.0620764	+	0.704038i
$107$	10.7228	−	10.7228i	1.03661	−	1.03661i	0.0373043	−	0.999304i	$-0.488123\pi$
$107$	10.7228	−	10.7228i	1.03661	−	1.03661i	0.999304	−	0.0373043i	$-0.0118771\pi$
$108$	−6.61884	−	4.62120i	−0.636898	−	0.444675i
$109$	2.22159	+	2.22159i	0.212790	+	0.212790i	0.805451	−	0.592662i	$-0.201923\pi$
$109$	2.22159	+	2.22159i	0.212790	+	0.212790i	−0.592662	+	0.805451i	$0.701923\pi$
$110$	−7.15576	−	5.99613i	−0.682275	−	0.571709i
$111$	−5.17227			−0.490930
$112$	−1.37827	−	3.75505i	−0.130234	−	0.354819i
$113$	8.10483			0.762438			0.381219	−	0.924485i	$-0.375504\pi$
$113$	8.10483			0.762438			0.381219	+	0.924485i	$0.375504\pi$
$114$	−3.42994	−	2.87410i	−0.321243	−	0.269184i
$115$	1.88685	+	1.88685i	0.175949	+	0.175949i
$116$	12.0237	−	17.2212i	1.11637	−	1.59895i
$117$	1.75401	−	1.75401i	0.162158	−	0.162158i
$118$	−0.808671	−	9.17152i	−0.0744442	−	0.844307i
$119$			7.33275i			0.672192i
$120$	1.81556	+	1.04330i	0.165738	+	0.0952396i
$121$		−	32.5792i		−	2.96175i
$122$	18.7072	−	1.64945i	1.69367	−	0.149334i
$123$	−0.625689	+	0.625689i	−0.0564164	+	0.0564164i
$124$	−2.38879	−	13.4409i	−0.214520	−	1.20703i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	−2.22708	+	2.65779i	−0.198404	+	0.236774i
$127$	−17.2293			−1.52885			−0.764425	−	0.644712i	$-0.776977\pi$
$127$	−17.2293			−1.52885			−0.764425	+	0.644712i	$0.776977\pi$
$128$	−11.1510	−	1.91170i	−0.985621	−	0.168972i
$129$	4.24365			0.373632
$130$	−0.918912	+	1.09663i	−0.0805939	+	0.0961805i
$131$	0.509280	+	0.509280i	0.0444960	+	0.0444960i	0.729005	−	0.684509i	$-0.239983\pi$
$131$	0.509280	+	0.509280i	0.0444960	+	0.0444960i	−0.684509	+	0.729005i	$0.739983\pi$
$132$	1.71038	+	9.62374i	0.148870	+	0.837639i
$133$	−3.02223	+	3.02223i	−0.262061	+	0.262061i
$134$	8.35204	−	0.736416i	0.721507	−	0.0636166i
$135$		−	4.03623i		−	0.347383i
$136$	17.9825	+	10.3335i	1.54199	+	0.886091i
$137$		−	10.5643i		−	0.902569i	−0.892380	−	0.451285i	$-0.850966\pi$
$137$		−	10.5643i		−	0.902569i	0.892380	−	0.451285i	$-0.149034\pi$
$138$	−0.245382	−	2.78299i	−0.0208883	−	0.236904i
$139$	7.89402	−	7.89402i	0.669562	−	0.669562i	−0.288053	−	0.957615i	$-0.593008\pi$
$139$	7.89402	−	7.89402i	0.669562	−	0.669562i	0.957615	+	0.288053i	$0.0930079\pi$
$140$	1.14493	−	1.63986i	0.0967643	−	0.138593i
$141$	−3.85313	−	3.85313i	−0.324492	−	0.324492i
$142$	−1.12927	−	0.946262i	−0.0947658	−	0.0794085i
$143$	−6.67855			−0.558489
$144$	3.37939	+	9.20702i	0.281616	+	0.767252i
$145$	10.5017			0.872115
$146$	4.66527	+	3.90924i	0.386101	+	0.323531i
$147$	−0.523494	−	0.523494i	−0.0431771	−	0.0431771i
$148$	11.4567	+	7.99895i	0.941737	+	0.657510i
$149$	−0.728824	+	0.728824i	−0.0597076	+	0.0597076i	−0.736330	−	0.676622i	$-0.763443\pi$
$149$	−0.728824	+	0.728824i	−0.0597076	+	0.0597076i	0.676622	+	0.736330i	$0.263443\pi$
$150$	0.0919583	+	1.04294i	0.00750836	+	0.0851559i
$151$		−	2.60194i		−	0.211742i	−0.994380	−	0.105871i	$-0.966237\pi$
$151$		−	2.60194i		−	0.211742i	0.994380	−	0.105871i	$-0.0337631\pi$
$152$	3.15259	+	11.6706i	0.255709	+	0.946613i
$153$		−	17.9792i		−	1.45353i
$154$	9.29979	−	0.819980i	0.749398	−	0.0660759i
$155$	4.82655	−	4.82655i	0.387678	−	0.387678i
$156$	1.47485	−	0.262118i	0.118082	−	0.0209862i
$157$	−6.73128	−	6.73128i	−0.537214	−	0.537214i	0.385495	−	0.922710i	$-0.374031\pi$
$157$	−6.73128	−	6.73128i	−0.537214	−	0.537214i	−0.922710	+	0.385495i	$0.874031\pi$
$158$	6.59456	−	7.86992i	0.524635	−	0.626097i
$159$	3.80928			0.302096
$160$	−2.40806	−	5.11872i	−0.190374	−	0.404670i
$161$	−2.66840			−0.210300
$162$	3.96708	−	4.73430i	0.311683	−	0.371962i
$163$	−7.68987	−	7.68987i	−0.602317	−	0.602317i	0.338610	−	0.940927i	$-0.390043\pi$
$163$	−7.68987	−	7.68987i	−0.602317	−	0.602317i	−0.940927	+	0.338610i	$0.890043\pi$
$164$	2.35355	−	0.418286i	0.183781	−	0.0326626i
$165$	−3.45583	+	3.45583i	−0.269036	+	0.269036i
$166$	−16.2873	+	1.43609i	−1.26414	+	0.111462i
$167$		−	14.6831i		−	1.13621i	−0.822956	−	0.568106i	$-0.807676\pi$
$167$		−	14.6831i		−	1.13621i	0.822956	−	0.568106i	$-0.192324\pi$
$168$	−2.02152	+	0.546074i	−0.155964	+	0.0421306i
$169$		−	11.9765i		−	0.921270i
$170$	0.910815	+	10.3300i	0.0698563	+	0.792274i
$171$	7.41024	−	7.41024i	0.566675	−	0.566675i
$172$	−9.39979	−	6.56283i	−0.716727	−	0.500411i
$173$	5.61702	+	5.61702i	0.427054	+	0.427054i	0.887624	−	0.460570i	$-0.152355\pi$
$173$	5.61702	+	5.61702i	0.427054	+	0.427054i	−0.460570	+	0.887624i	$0.652355\pi$
$174$	−8.42754	−	7.06181i	−0.638890	−	0.535355i
$175$	1.00000			0.0755929
$176$	11.0946	−	23.9620i	0.836290	−	1.80620i
$177$	−4.81987			−0.362283
$178$	−0.576940	−	0.483444i	−0.0432435	−	0.0362357i
$179$	8.84480	+	8.84480i	0.661091	+	0.661091i	0.955637	−	0.294546i	$-0.0951684\pi$
$179$	8.84480	+	8.84480i	0.661091	+	0.661091i	−0.294546	+	0.955637i	$0.595168\pi$
$180$	−2.80726	+	4.02078i	−0.209241	+	0.299691i
$181$	−17.2445	+	17.2445i	−1.28177	+	1.28177i	−0.342114	+	0.939659i	$0.611143\pi$
$181$	−17.2445	+	17.2445i	−1.28177	+	1.28177i	−0.939659	+	0.342114i	$0.888857\pi$
$182$	−0.125663	−	1.42520i	−0.00931474	−	0.105643i
$183$		−	9.83110i		−	0.726736i
$184$	−3.76039	+	6.54389i	−0.277220	+	0.482422i
$185$			6.98641i			0.513651i
$186$	−7.11889	+	0.627686i	−0.521982	+	0.0460242i
$187$	−34.2288	+	34.2288i	−2.50306	+	2.50306i
$188$	2.57590	+	14.4937i	0.187867	+	1.05706i
$189$	2.85404	+	2.85404i	0.207601	+	0.207601i
$190$	−3.88217	+	4.63296i	−0.281642	+	0.336111i
$191$	−3.29294			−0.238269			−0.119134	−	0.992878i	$-0.538012\pi$
$191$	−3.29294			−0.238269			−0.119134	+	0.992878i	$0.538012\pi$
$192$	−1.50961	+	5.72704i	−0.108947	+	0.413314i
$193$	9.65935			0.695295			0.347648	−	0.937625i	$-0.386981\pi$
$193$	9.65935			0.695295			0.347648	+	0.937625i	$0.386981\pi$
$194$	−5.89650	+	7.03686i	−0.423344	+	0.505217i
$195$	0.529608	+	0.529608i	0.0379260	+	0.0379260i
$196$	0.349967	+	1.96914i	0.0249976	+	0.140653i
$197$	4.96271	−	4.96271i	0.353578	−	0.353578i	−0.507861	−	0.861439i	$-0.669564\pi$
$197$	4.96271	−	4.96271i	0.353578	−	0.353578i	0.861439	+	0.507861i	$0.169564\pi$
$198$	−22.8022	+	2.01052i	−1.62048	+	0.142881i
$199$		−	6.09643i		−	0.432164i	−0.976375	−	0.216082i	$-0.930672\pi$
$199$		−	6.09643i		−	0.432164i	0.976375	−	0.216082i	$-0.0693279\pi$
$200$	1.40923	−	2.45236i	0.0996475	−	0.173408i
$201$		−	4.38921i		−	0.309591i
$202$	−1.33271	−	15.1149i	−0.0937693	−	1.06348i
$203$	−7.42579	+	7.42579i	−0.521188	+	0.521188i
$204$	6.21545	−	8.90226i	0.435169	−	0.623283i
$205$	0.845145	+	0.845145i	0.0590275	+	0.0590275i
$206$	0.870258	+	0.729228i	0.0606338	+	0.0508077i
$207$	6.54268			0.454747
$208$	−3.67220	−	1.70026i	−0.254621	−	0.117892i
$209$	−28.2152			−1.95168
$210$	−0.802496	−	0.672448i	−0.0553775	−	0.0464033i
$211$	9.32682	+	9.32682i	0.642084	+	0.642084i	0.951068	−	0.308983i	$-0.0999886\pi$
$211$	9.32682	+	9.32682i	0.642084	+	0.642084i	−0.308983	+	0.951068i	$0.599989\pi$
$212$	−8.43766	−	5.89108i	−0.579501	−	0.404601i
$213$	−0.545371	+	0.545371i	−0.0373682	+	0.0373682i
$214$	1.88359	+	21.3626i	0.128759	+	1.46032i
$215$		−	5.73208i		−	0.390924i
$216$	11.0211	−	2.97715i	0.749894	−	0.202569i
$217$			6.82577i			0.463364i
$218$	−4.42600	+	0.390249i	−0.299767	+	0.0264310i
$219$	2.25306	−	2.25306i	0.152248	−	0.152248i
$220$	12.9992	−	2.31029i	0.876406	−	0.155760i
$221$	5.24559	+	5.24559i	0.352857	+	0.352857i
$222$	4.69800	−	5.60657i	0.315309	−	0.376288i
$223$	16.1112			1.07888			0.539441	−	0.842023i	$-0.318635\pi$
$223$	16.1112			1.07888			0.539441	+	0.842023i	$0.318635\pi$
$224$	5.32223	+	1.91673i	0.355607	+	0.128067i
$225$	−2.45191			−0.163460
$226$	−7.36165	+	8.78537i	−0.489690	+	0.584394i
$227$	7.69190	+	7.69190i	0.510529	+	0.510529i	0.914689	−	0.404159i	$-0.132436\pi$
$227$	7.69190	+	7.69190i	0.510529	+	0.510529i	−0.404159	+	0.914689i	$0.632436\pi$
$228$	6.23085	−	1.10738i	0.412648	−	0.0733381i
$229$	−11.7964	+	11.7964i	−0.779528	+	0.779528i	−0.979750	−	0.200223i	$-0.935833\pi$
$229$	−11.7964	+	11.7964i	−0.779528	+	0.779528i	0.200223	+	0.979750i	$0.435833\pi$
$230$	−3.75911	+	0.331448i	−0.247868	+	0.0218550i
$231$		−	4.88728i		−	0.321559i
$232$	7.74609	+	28.6754i	0.508556	+	1.88263i
$233$		−	12.5498i		−	0.822163i	−0.911599	−	0.411081i	$-0.865151\pi$
$233$		−	12.5498i		−	0.822163i	0.911599	−	0.411081i	$-0.134849\pi$
$234$	0.308113	+	3.49446i	0.0201420	+	0.228440i
$235$	−5.20459	+	5.20459i	−0.339510	+	0.339510i
$236$	10.6761	+	7.45396i	0.694958	+	0.485211i
$237$	−3.80073	−	3.80073i	−0.246884	−	0.246884i
$238$	−7.94845	−	6.66036i	−0.515222	−	0.431727i
$239$	6.25932			0.404881			0.202441	−	0.979295i	$-0.435113\pi$
$239$	6.25932			0.404881			0.202441	+	0.979295i	$0.435113\pi$
$240$	−2.77998	+	1.02038i	−0.179447	+	0.0658652i
$241$	−28.4304			−1.83136			−0.915680	−	0.401907i	$-0.868347\pi$
$241$	−28.4304			−1.83136			−0.915680	+	0.401907i	$0.868347\pi$
$242$	35.3148	+	29.5918i	2.27012	+	1.90224i
$243$	−10.8485	−	10.8485i	−0.695933	−	0.695933i
$244$	−15.2039	+	21.7762i	−0.973327	+	1.39408i
$245$	−0.707107	+	0.707107i	−0.0451754	+	0.0451754i
$246$	−0.109910	−	1.24654i	−0.00700760	−	0.0794765i
$247$			4.32400i			0.275130i
$248$	16.7393	+	9.61907i	1.06294	+	0.610811i
$249$			8.55941i			0.542431i
$250$	1.40875	−	0.124212i	0.0890971	−	0.00785586i
$251$	−2.66268	+	2.66268i	−0.168067	+	0.168067i	−0.786129	−	0.618062i	$-0.787918\pi$
$251$	−2.66268	+	2.66268i	−0.168067	+	0.168067i	0.618062	+	0.786129i	$0.287918\pi$
$252$	−0.858086	−	4.82816i	−0.0540544	−	0.304145i
$253$	−12.4559	−	12.4559i	−0.783098	−	0.783098i
$254$	15.6494	−	18.6760i	0.981932	−	1.17183i
$255$	5.42867			0.339957
$256$	12.2007	−	10.3509i	0.762547	−	0.646933i
$257$	18.2131			1.13610			0.568052	−	0.822993i	$-0.307697\pi$
$257$	18.2131			1.13610			0.568052	+	0.822993i	$0.307697\pi$
$258$	−3.85452	+	4.59997i	−0.239972	+	0.286382i
$259$	−4.94014	−	4.94014i	−0.306965	−	0.306965i
$260$	−0.354054	−	1.99214i	−0.0219575	−	0.123547i
$261$	18.2073	−	18.2073i	1.12701	−	1.12701i
$262$	−1.01462	+	0.0894614i	−0.0626837	+	0.00552694i
$263$			1.84322i			0.113658i	0.998384	+	0.0568288i	$0.0180989\pi$
$263$			1.84322i			0.113658i	−0.998384	+	0.0568288i	$0.981901\pi$
$264$	−11.9854	−	6.88729i	−0.737648	−	0.423883i
$265$		−	5.14536i		−	0.316077i
$266$	−0.530893	−	6.02111i	−0.0325511	−	0.369178i
$267$	−0.278629	+	0.278629i	−0.0170518	+	0.0170518i
$268$	−6.78795	+	9.72223i	−0.414640	+	0.593880i
$269$	−8.91181	−	8.91181i	−0.543362	−	0.543362i	0.381151	−	0.924513i	$-0.375528\pi$
$269$	−8.91181	−	8.91181i	−0.543362	−	0.543362i	−0.924513	+	0.381151i	$0.875528\pi$
$270$	4.37513	+	3.66612i	0.266262	+	0.223113i
$271$	−25.2309			−1.53267			−0.766334	−	0.642442i	$-0.777921\pi$
$271$	−25.2309			−1.53267			−0.766334	+	0.642442i	$0.777921\pi$
$272$	−27.5348	+	10.1065i	−1.66954	+	0.612797i
$273$	−0.748979			−0.0453303
$274$	11.4514	+	9.59560i	0.691801	+	0.579691i
$275$	4.66793	+	4.66793i	0.281487	+	0.281487i
$276$	3.23955	+	2.26182i	0.194998	+	0.136145i
$277$	2.42569	−	2.42569i	0.145746	−	0.145746i	−0.630469	−	0.776215i	$-0.717137\pi$
$277$	2.42569	−	2.42569i	0.145746	−	0.145746i	0.776215	+	0.630469i	$0.217137\pi$
$278$	1.38668	+	15.7270i	0.0831676	+	0.943244i
$279$		−	16.7362i		−	1.00197i
$280$	0.737607	+	2.73056i	0.0440804	+	0.163182i
$281$			12.3096i			0.734332i	0.930155	+	0.367166i	$0.119672\pi$
$281$			12.3096i			0.734332i	−0.930155	+	0.367166i	$0.880328\pi$
$282$	7.67648	−	0.676850i	0.457128	−	0.0403058i
$283$	15.6166	−	15.6166i	0.928313	−	0.928313i	−0.0692840	−	0.997597i	$-0.522071\pi$
$283$	15.6166	−	15.6166i	0.928313	−	0.928313i	0.997597	+	0.0692840i	$0.0220715\pi$
$284$	2.05143	−	0.364592i	0.121730	−	0.0216346i
$285$	2.23746	+	2.23746i	0.132536	+	0.132536i
$286$	6.06616	−	7.23933i	0.358700	−	0.428071i
$287$	−1.19522			−0.0705513
$288$	−13.0496	−	4.69963i	−0.768956	−	0.276929i
$289$	36.7692			2.16289
$290$	−9.53870	+	11.3834i	−0.560132	+	0.668459i
$291$	3.39841	+	3.39841i	0.199218	+	0.199218i
$292$	−8.47497	+	1.50622i	−0.495960	+	0.0881448i
$293$	−11.1786	+	11.1786i	−0.653060	+	0.653060i	−0.953729	−	0.300669i	$-0.902790\pi$
$293$	−11.1786	+	11.1786i	−0.653060	+	0.653060i	0.300669	+	0.953729i	$0.402790\pi$
$294$	1.04294	−	0.0919583i	0.0608257	−	0.00536312i
$295$			6.51040i			0.379050i
$296$	−19.0768	+	5.15322i	−1.10882	+	0.299525i
$297$			26.6450i			1.54610i
$298$	−0.128027	−	1.45202i	−0.00741640	−	0.0841130i
$299$	−1.90888	+	1.90888i	−0.110394	+	0.110394i
$300$	−1.21404	−	0.847630i	−0.0700927	−	0.0489379i
$301$	4.05319	+	4.05319i	0.233622	+	0.233622i
$302$	2.82041	+	2.36335i	0.162296	+	0.135995i
$303$	−7.94327			−0.456329
$304$	−15.5141	−	7.18318i	−0.889794	−	0.411983i
$305$	−13.2793			−0.760370
$306$	19.4889	+	16.3306i	1.11410	+	0.933558i
$307$	−9.62280	−	9.62280i	−0.549202	−	0.549202i	0.377008	−	0.926210i	$-0.376953\pi$
$307$	−9.62280	−	9.62280i	−0.549202	−	0.549202i	−0.926210	+	0.377008i	$0.876953\pi$
$308$	−7.55821	+	10.8255i	−0.430669	+	0.616837i
$309$	0.420285	−	0.420285i	0.0239092	−	0.0239092i
$310$	0.847843	+	9.61579i	0.0481542	+	0.546140i
$311$			4.18947i			0.237563i	0.992920	+	0.118782i	$0.0378988\pi$
$311$			4.18947i			0.237563i	−0.992920	+	0.118782i	$0.962101\pi$
$312$	−1.05548	+	1.83677i	−0.0597550	+	0.103987i
$313$		−	10.7975i		−	0.610311i	−0.952302	−	0.305156i	$-0.901292\pi$
$313$		−	10.7975i		−	0.610311i	0.952302	−	0.305156i	$-0.0987085\pi$
$314$	13.4105	−	1.18243i	0.756800	−	0.0667285i
$315$	1.73376	−	1.73376i	0.0976863	−	0.0976863i
$316$	2.54086	+	14.2966i	0.142935	+	0.804245i
$317$	5.17115	+	5.17115i	0.290441	+	0.290441i	0.837254	−	0.546813i	$-0.184159\pi$
$317$	5.17115	+	5.17115i	0.290441	+	0.290441i	−0.546813	+	0.837254i	$0.684159\pi$
$318$	−3.45999	+	4.12913i	−0.194026	+	0.231550i
$319$	−69.3262			−3.88152
$320$	7.73577	+	2.03910i	0.432442	+	0.113989i
$321$	11.2266			0.626608
$322$	2.42372	−	2.89246i	0.135069	−	0.161190i
$323$	22.1613	+	22.1613i	1.23309	+	1.23309i
$324$	1.52851	+	8.60037i	0.0849169	+	0.477798i
$325$	0.715365	−	0.715365i	0.0396813	−	0.0396813i
$326$	15.3203	−	1.35082i	0.848513	−	0.0748150i
$327$			2.32598i			0.128627i
$328$	−1.68433	+	2.93110i	−0.0930016	+	0.161843i
$329$		−	7.36041i		−	0.405792i
$330$	−0.607058	−	6.88494i	−0.0334175	−	0.379003i
$331$	−0.463443	+	0.463443i	−0.0254731	+	0.0254731i	−0.719729	−	0.694256i	$-0.755734\pi$
$331$	−0.463443	+	0.463443i	−0.0254731	+	0.0254731i	0.694256	+	0.719729i	$0.255734\pi$
$332$	13.2372	−	18.9593i	0.726485	−	1.04053i
$333$	12.1128	+	12.1128i	0.663775	+	0.663775i
$334$	15.9160	+	13.3367i	0.870884	+	0.729752i
$335$	−5.92870			−0.323919
$336$	1.24423	−	2.68726i	0.0678783	−	0.146602i
$337$	4.94317			0.269272			0.134636	−	0.990895i	$-0.457014\pi$
$337$	4.94317			0.269272			0.134636	+	0.990895i	$0.457014\pi$
$338$	12.9821	+	10.8783i	0.706135	+	0.591702i
$339$	4.24283	+	4.24283i	0.230439	+	0.230439i
$340$	−12.0247	−	8.39548i	−0.652129	−	0.455309i
$341$	−31.8622	+	31.8622i	−1.72544	+	1.72544i
$342$	1.30170	+	14.7632i	0.0703879	+	0.798302i
$343$		−	1.00000i		−	0.0539949i
$344$	15.6518	−	4.22802i	0.843886	−	0.227959i
$345$			1.97551i			0.106358i
$346$	−11.1906	+	0.986699i	−0.601612	+	0.0530453i
$347$	−22.9118	+	22.9118i	−1.22997	+	1.22997i	−0.265993	+	0.963975i	$0.585700\pi$
$347$	−22.9118	+	22.9118i	−1.22997	+	1.22997i	−0.963975	+	0.265993i	$0.914300\pi$
$348$	15.3095	−	2.72090i	0.820677	−	0.145855i
$349$	12.3468	+	12.3468i	0.660908	+	0.660908i	0.955594	−	0.294686i	$-0.0952152\pi$
$349$	12.3468	+	12.3468i	0.660908	+	0.660908i	−0.294686	+	0.955594i	$0.595215\pi$
$350$	−0.908304	+	1.08397i	−0.0485509	+	0.0579404i
$351$	4.08337			0.217954
$352$	15.8967	+	33.7910i	0.847296	+	1.80107i
$353$	−5.58127			−0.297061			−0.148530	−	0.988908i	$-0.547454\pi$
$353$	−5.58127			−0.297061			−0.148530	+	0.988908i	$0.547454\pi$
$354$	4.37791	−	5.22457i	0.232683	−	0.277683i
$355$	0.736657	+	0.736657i	0.0390977	+	0.0390977i
$356$	1.04807	−	0.186270i	0.0555478	−	0.00987226i
$357$	−3.83865	+	3.83865i	−0.203163	+	0.203163i
$358$	−17.6212	+	1.55370i	−0.931311	+	0.0821155i
$359$		−	14.8019i		−	0.781215i	−0.920557	−	0.390608i	$-0.872265\pi$
$359$		−	14.8019i		−	0.781215i	0.920557	−	0.390608i	$-0.127735\pi$
$360$	−1.80854	−	6.69507i	−0.0953186	−	0.352861i
$361$		−	0.732201i		−	0.0385369i
$362$	−3.02921	−	34.3557i	−0.159212	−	1.80569i
$363$	17.0550	−	17.0550i	0.895157	−	0.895157i
$364$	1.65901	+	1.15830i	0.0869558	+	0.0607115i
$365$	−3.04331	−	3.04331i	−0.159294	−	0.159294i
$366$	10.6566	+	8.92963i	0.557028	+	0.466759i
$367$	−2.51958			−0.131521			−0.0657605	−	0.997835i	$-0.520947\pi$
$367$	−2.51958			−0.131521			−0.0657605	+	0.997835i	$0.520947\pi$
$368$	−3.67778	−	10.0200i	−0.191718	−	0.522327i
$369$	2.93056			0.152559
$370$	−7.57304	−	6.34579i	−0.393703	−	0.329902i
$371$	3.63832	+	3.63832i	0.188892	+	0.188892i
$372$	5.78573	−	8.28677i	0.299976	−	0.429649i
$373$	3.51836	−	3.51836i	0.182174	−	0.182174i	−0.610129	−	0.792302i	$-0.708882\pi$
$373$	3.51836	−	3.51836i	0.182174	−	0.182174i	0.792302	+	0.610129i	$0.208882\pi$
$374$	−6.01271	−	68.1930i	−0.310910	−	3.52618i
$375$		−	0.740333i		−	0.0382306i
$376$	−18.0504	−	10.3725i	−0.930877	−	0.534920i
$377$			10.6243i			0.547180i
$378$	−5.68603	+	0.501348i	−0.292458	+	0.0257866i
$379$	24.5112	−	24.5112i	1.25906	−	1.25906i	0.307514	−	0.951543i	$-0.400503\pi$
$379$	24.5112	−	24.5112i	1.25906	−	1.25906i	0.951543	−	0.307514i	$-0.0994972\pi$
$380$	−1.49579	−	8.41628i	−0.0767323	−	0.431746i
$381$	−9.01943	−	9.01943i	−0.462079	−	0.462079i
$382$	2.99099	−	3.56944i	0.153032	−	0.182628i
$383$	−1.60372			−0.0819463			−0.0409731	−	0.999160i	$-0.513046\pi$
$383$	−1.60372			−0.0819463			−0.0409731	+	0.999160i	$0.513046\pi$
$384$	−4.83674	−	6.83827i	−0.246824	−	0.348964i
$385$	−6.60146			−0.336441
$386$	−8.77363	+	10.4704i	−0.446566	+	0.532930i
$387$	−9.93805	−	9.93805i	−0.505179	−	0.505179i
$388$	−2.27191	−	12.7832i	−0.115339	−	0.648970i
$389$	19.6804	−	19.6804i	0.997835	−	0.997835i	−0.00216282	−	0.999998i	$-0.500688\pi$
$389$	19.6804	−	19.6804i	0.997835	−	0.997835i	0.999998	+	0.00216282i	$0.000688449\pi$
$390$	−1.05512	+	0.0930323i	−0.0534282	+	0.00471087i
$391$			19.5667i			0.989532i
$392$	−2.45236	−	1.40923i	−0.123863	−	0.0711768i
$393$			0.533211i			0.0268969i
$394$	0.871761	+	9.88706i	0.0439187	+	0.498103i
$395$	−5.13381	+	5.13381i	−0.258310	+	0.258310i
$396$	18.5320	−	26.5430i	0.931269	−	1.33384i
$397$	27.4925	+	27.4925i	1.37981	+	1.37981i	0.844925	+	0.534884i	$0.179645\pi$
$397$	27.4925	+	27.4925i	1.37981	+	1.37981i	0.534884	+	0.844925i	$0.320355\pi$
$398$	6.60832	+	5.53741i	0.331245	+	0.277565i
$399$	−3.16425			−0.158410
$400$	1.37827	+	3.75505i	0.0689135	+	0.187752i
$401$	−21.2200			−1.05967			−0.529837	−	0.848099i	$-0.677747\pi$
$401$	−21.2200			−1.05967			−0.529837	+	0.848099i	$0.677747\pi$
$402$	4.75776	+	3.98674i	0.237295	+	0.198840i
$403$	4.88292	+	4.88292i	0.243235	+	0.243235i
$404$	17.5946	+	12.2843i	0.875363	+	0.611168i
$405$	−3.08834	+	3.08834i	−0.153461	+	0.153461i
$406$	−1.30443	−	14.7942i	−0.0647379	−	0.734223i
$407$		−	46.1205i		−	2.28611i
$408$	4.00423	+	14.8233i	0.198239	+	0.733863i
$409$			10.2539i			0.507025i	0.967332	+	0.253512i	$0.0815859\pi$
$409$			10.2539i			0.507025i	−0.967332	+	0.253512i	$0.918414\pi$
$410$	−1.68376	+	0.148460i	−0.0831548	+	0.00733192i
$411$	5.53035	−	5.53035i	0.272792	−	0.272792i
$412$	−1.58092	+	0.280970i	−0.0778862	+	0.0138424i
$413$	−4.60355	−	4.60355i	−0.226526	−	0.226526i
$414$	−5.94274	+	7.09204i	−0.292070	+	0.348555i
$415$	11.5616			0.567535
$416$	5.17850	−	2.43618i	0.253897	−	0.119444i
$417$	8.26495			0.404736
$418$	25.6280	−	30.5843i	1.25350	−	1.49593i
$419$	−18.0676	−	18.0676i	−0.882660	−	0.882660i	0.111144	−	0.993804i	$-0.464548\pi$
$419$	−18.0676	−	18.0676i	−0.882660	−	0.882660i	−0.993804	+	0.111144i	$0.964548\pi$
$420$	1.45782	−	0.259092i	0.0711344	−	0.0126424i
$421$	3.50014	−	3.50014i	0.170586	−	0.170586i	−0.616651	−	0.787237i	$-0.711511\pi$
$421$	3.50014	−	3.50014i	0.170586	−	0.170586i	0.787237	+	0.616651i	$0.211511\pi$
$422$	−18.5815	+	1.63837i	−0.904535	+	0.0797546i
$423$			18.0470i			0.877477i
$424$	14.0497	−	3.79525i	0.682314	−	0.184314i
$425$		−	7.33275i		−	0.355690i
$426$	−0.0958012	−	1.08653i	−0.00464158	−	0.0526424i
$427$	9.38988	−	9.38988i	0.454408	−	0.454408i
$428$	−24.8673	−	17.3620i	−1.20200	−	0.839226i
$429$	−3.49619	−	3.49619i	−0.168797	−	0.168797i
$430$	6.21338	+	5.20647i	0.299636	+	0.251078i
$431$	5.32832			0.256656			0.128328	−	0.991732i	$-0.459039\pi$
$431$	5.32832			0.256656			0.128328	+	0.991732i	$0.459039\pi$
$432$	−6.78342	+	14.6507i	−0.326368	+	0.704882i
$433$	18.5191			0.889972			0.444986	−	0.895538i	$-0.353209\pi$
$433$	18.5191			0.889972			0.444986	+	0.895538i	$0.353209\pi$
$434$	−7.39891	−	6.19988i	−0.355159	−	0.297604i
$435$	5.49756	+	5.49756i	0.263588	+	0.263588i
$436$	3.59714	−	5.15211i	0.172272	−	0.246741i
$437$	−8.06454	+	8.06454i	−0.385779	+	0.385779i
$438$	0.395778	+	4.48871i	0.0189110	+	0.214479i
$439$		−	3.52437i		−	0.168209i	−0.996457	−	0.0841044i	$-0.973197\pi$
$439$		−	3.52437i		−	0.168209i	0.996457	−	0.0841044i	$-0.0268029\pi$
$440$	−9.30296	+	16.1892i	−0.443501	+	0.771788i
$441$			2.45191i			0.116757i
$442$	−10.4506	+	0.921453i	−0.497086	+	0.0438290i
$443$	2.48325	−	2.48325i	0.117983	−	0.117983i	−0.645650	−	0.763633i	$-0.723414\pi$
$443$	2.48325	−	2.48325i	0.117983	−	0.117983i	0.763633	+	0.645650i	$0.223414\pi$
$444$	1.81012	+	10.1849i	0.0859047	+	0.483356i
$445$	0.376357	+	0.376357i	0.0178410	+	0.0178410i
$446$	−14.6338	+	17.4640i	−0.692932	+	0.826942i
$447$	−0.763071			−0.0360920
$448$	−6.91187	+	4.02815i	−0.326555	+	0.190312i
$449$	−15.5502			−0.733858			−0.366929	−	0.930249i	$-0.619591\pi$
$449$	−15.5502			−0.733858			−0.366929	+	0.930249i	$0.619591\pi$
$450$	2.22708	−	2.65779i	0.104985	−	0.125289i
$451$	−5.57919	−	5.57919i	−0.262714	−	0.262714i
$452$	−2.83642	−	15.9596i	−0.133414	−	0.750675i
$453$	1.36210	−	1.36210i	0.0639970	−	0.0639970i
$454$	−15.3243	+	1.35118i	−0.719207	+	0.0634139i
$455$			1.01168i			0.0474282i
$456$	−4.45914	+	7.75987i	−0.208819	+	0.363389i
$457$			20.0603i			0.938382i	0.883097	+	0.469191i	$0.155454\pi$
$457$			20.0603i			0.938382i	−0.883097	+	0.469191i	$0.844546\pi$
$458$	−2.07218	−	23.5016i	−0.0968268	−	1.09816i
$459$	20.9280	−	20.9280i	0.976834	−	0.976834i
$460$	3.05514	−	4.37580i	0.142446	−	0.204023i
$461$	−18.8405	−	18.8405i	−0.877492	−	0.877492i	0.115783	−	0.993275i	$-0.463062\pi$
$461$	−18.8405	−	18.8405i	−0.877492	−	0.877492i	−0.993275	+	0.115783i	$0.963062\pi$
$462$	5.29764	+	4.43913i	0.246469	+	0.206527i
$463$	9.28334			0.431433			0.215717	−	0.976456i	$-0.430791\pi$
$463$	9.28334			0.431433			0.215717	+	0.976456i	$0.430791\pi$
$464$	−38.1189	−	17.6494i	−1.76963	−	0.819355i
$465$	5.05334			0.234343
$466$	13.6035	+	11.3990i	0.630171	+	0.528049i
$467$	−25.6203	−	25.6203i	−1.18557	−	1.18557i	−0.978280	−	0.207288i	$-0.933536\pi$
$467$	−25.6203	−	25.6203i	−1.18557	−	1.18557i	−0.207288	−	0.978280i	$-0.566464\pi$
$468$	−4.06774	−	2.84005i	−0.188031	−	0.131281i
$469$	4.19222	−	4.19222i	0.193579	−	0.193579i
$470$	−0.914251	−	10.3690i	−0.0421713	−	0.478284i
$471$		−	7.04757i		−	0.324735i
$472$	−17.7770	+	4.80212i	−0.818254	+	0.221035i
$473$			37.8400i			1.73989i
$474$	7.57208	−	0.667645i	0.347797	−	0.0306659i
$475$	3.02223	−	3.02223i	0.138670	−	0.138670i
$476$	14.4392	−	2.56622i	0.661821	−	0.117622i
$477$	−8.92082	−	8.92082i	−0.408456	−	0.408456i
$478$	−5.68536	+	6.78489i	−0.260042	+	0.310334i
$479$	−13.0222			−0.594999			−0.297499	−	0.954722i	$-0.596153\pi$
$479$	−13.0222			−0.594999			−0.297499	+	0.954722i	$0.596153\pi$
$480$	1.41902	−	3.94022i	0.0647689	−	0.179846i
$481$	−7.06801			−0.322273
$482$	25.8234	−	30.8176i	1.17622	−	1.40370i
$483$	−1.39689	−	1.39689i	−0.0635609	−	0.0635609i
$484$	−64.1531	+	11.4016i	−2.91605	+	0.518257i
$485$	4.59037	−	4.59037i	0.208438	−	0.208438i
$486$	21.6132	−	1.90568i	0.980395	−	0.0864433i
$487$		−	32.0720i		−	1.45332i	−0.686996	−	0.726661i	$-0.741071\pi$
$487$		−	32.0720i		−	1.45332i	0.686996	−	0.726661i	$-0.258929\pi$
$488$	−9.79489	−	36.2598i	−0.443394	−	1.64141i
$489$		−	8.05121i		−	0.364088i
$490$	−0.124212	−	1.40875i	−0.00561133	−	0.0636408i
$491$	−15.7984	+	15.7984i	−0.712972	+	0.712972i	−0.967156	−	0.254184i	$-0.918193\pi$
$491$	−15.7984	+	15.7984i	−0.712972	+	0.712972i	0.254184	+	0.967156i	$0.418193\pi$
$492$	1.45104	+	1.01310i	0.0654179	+	0.0456741i
$493$	54.4514	+	54.4514i	2.45237	+	2.45237i
$494$	−4.68707	−	3.92751i	−0.210881	−	0.176707i
$495$	16.1862			0.727514
$496$	−25.6311	+	9.40775i	−1.15087	+	0.422421i
$497$	−1.04179			−0.0467307
$498$	−9.27811	−	7.77455i	−0.415762	−	0.348386i
$499$	−5.62700	−	5.62700i	−0.251899	−	0.251899i	0.569850	−	0.821749i	$-0.307001\pi$
$499$	−5.62700	−	5.62700i	−0.251899	−	0.251899i	−0.821749	+	0.569850i	$0.807001\pi$
$500$	−1.14493	+	1.63986i	−0.0512028	+	0.0733367i
$501$	7.68652	−	7.68652i	0.343408	−	0.343408i
$502$	−0.467732	−	5.30477i	−0.0208759	−	0.236763i
$503$		−	35.1271i		−	1.56624i	−0.621871	−	0.783120i	$-0.713627\pi$
$503$		−	35.1271i		−	1.56624i	0.621871	−	0.783120i	$-0.286373\pi$
$504$	6.01296	+	3.45530i	0.267839	+	0.153911i
$505$			10.7293i			0.477449i
$506$	24.8156	−	2.18804i	1.10319	−	0.0972702i
$507$	6.26963	−	6.26963i	0.278444	−	0.278444i
$508$	6.02967	+	33.9269i	0.267524	+	1.50526i
$509$	0.883173	+	0.883173i	0.0391460	+	0.0391460i	0.726409	−	0.687263i	$-0.241188\pi$
$509$	0.883173	+	0.883173i	0.0391460	+	0.0391460i	−0.687263	+	0.726409i	$0.741188\pi$
$510$	−4.93089	+	5.88450i	−0.218343	+	0.260570i
$511$	4.30389			0.190393
$512$	0.138078	+	22.6270i	0.00610226	+	0.999981i
$513$	17.2512			0.761658
$514$	−16.5431	+	19.7424i	−0.729683	+	0.870801i
$515$	−0.567698	−	0.567698i	−0.0250158	−	0.0250158i
$516$	−1.48514	−	8.35634i	−0.0653795	−	0.367867i
$517$	34.3579	−	34.3579i	1.51106	−	1.51106i
$518$	9.84209	−	0.867796i	0.432437	−	0.0381288i
$519$			5.88096i			0.258145i
$520$	2.48100	+	1.42569i	0.108799	+	0.0625205i
$521$		−	23.8372i		−	1.04433i	−0.852846	−	0.522163i	$-0.825125\pi$
$521$		−	23.8372i		−	1.04433i	0.852846	−	0.522163i	$-0.174875\pi$
$522$	3.19835	+	36.2740i	0.139988	+	1.58767i
$523$	23.0198	−	23.0198i	1.00659	−	1.00659i	0.00660936	−	0.999978i	$-0.497896\pi$
$523$	23.0198	−	23.0198i	1.00659	−	1.00659i	0.999978	−	0.00660936i	$-0.00210384\pi$
$524$	0.824614	−	1.18108i	0.0360234	−	0.0515956i
$525$	0.523494	+	0.523494i	0.0228472	+	0.0228472i
$526$	−1.99799	−	1.67420i	−0.0871164	−	0.0729987i
$527$	50.0516			2.18028
$528$	18.3519	−	6.73598i	0.798666	−	0.293146i
$529$	15.8796			0.690418
$530$	5.57740	+	4.67355i	0.242267	+	0.203006i
$531$	11.2875	+	11.2875i	0.489835	+	0.489835i
$532$	7.00889	+	4.89353i	0.303874	+	0.212161i
$533$	−0.855015	+	0.855015i	−0.0370348	+	0.0370348i
$534$	−0.0489447	−	0.555105i	−0.00211804	−	0.0240217i
$535$		−	15.1643i		−	0.655609i
$536$	−4.37305	−	16.1886i	−0.188887	−	0.699243i
$537$			9.26041i			0.399616i
$538$	17.7547	−	1.56547i	0.765461	−	0.0674922i
$539$	4.66793	−	4.66793i	0.201062	−	0.201062i
$540$	−7.94791	+	1.41255i	−0.342023	+	0.0607863i
$541$	−1.68387	−	1.68387i	−0.0723950	−	0.0723950i	0.669982	−	0.742377i	$-0.266302\pi$
$541$	−1.68387	−	1.68387i	−0.0723950	−	0.0723950i	−0.742377	+	0.669982i	$0.766302\pi$
$542$	22.9173	−	27.3495i	0.984384	−	1.17476i
$543$	−18.0548			−0.774805
$544$	14.0549	−	39.0266i	0.602597	−	1.67325i
$545$	3.14180			0.134580
$546$	0.680301	−	0.811869i	0.0291142	−	0.0347448i
$547$	−10.9752	−	10.9752i	−0.469265	−	0.469265i	0.432411	−	0.901676i	$-0.357663\pi$
$547$	−10.9752	−	10.9752i	−0.469265	−	0.469265i	−0.901676	+	0.432411i	$0.857663\pi$
$548$	−20.8026	+	3.69716i	−0.888644	+	0.157935i
$549$	−23.0231	+	23.0231i	−0.982602	+	0.982602i
$550$	−9.29979	+	0.819980i	−0.396544	+	0.0349641i
$551$			44.8850i			1.91216i
$552$	−5.39423	+	1.45715i	−0.229594	+	0.0620203i
$553$		−	7.26030i		−	0.308739i
$554$	0.426103	+	4.83264i	0.0181034	+	0.205319i
$555$	−3.65735	+	3.65735i	−0.155246	+	0.155246i
$556$	−18.3071	−	12.7818i	−0.776393	−	0.542069i
$557$	15.5831	+	15.5831i	0.660278	+	0.660278i	0.955446	−	0.295167i	$-0.0953754\pi$
$557$	15.5831	+	15.5831i	0.660278	+	0.660278i	−0.295167	+	0.955446i	$0.595375\pi$
$558$	18.1414	+	15.2015i	0.767988	+	0.643532i
$559$	5.79902			0.245273
$560$	−3.62980	−	1.68063i	−0.153387	−	0.0710198i
$561$	−35.8371			−1.51305
$562$	−13.3432	−	11.1809i	−0.562851	−	0.471638i
$563$	−1.69406	−	1.69406i	−0.0713961	−	0.0713961i	0.670507	−	0.741903i	$-0.266077\pi$
$563$	−1.69406	−	1.69406i	−0.0713961	−	0.0713961i	−0.741903	+	0.670507i	$0.766077\pi$
$564$	−6.23890	+	8.93584i	−0.262705	+	0.376267i
$565$	5.73098	−	5.73098i	0.241104	−	0.241104i
$566$	2.74326	+	31.1126i	0.115308	+	1.30776i
$567$		−	4.36757i		−	0.183421i
$568$	−1.46812	+	2.55485i	−0.0616009	+	0.107199i
$569$			17.7540i			0.744288i	0.928175	+	0.372144i	$0.121377\pi$
$569$			17.7540i			0.744288i	−0.928175	+	0.372144i	$0.878623\pi$
$570$	−4.45763	+	0.393037i	−0.186709	+	0.0164625i
$571$	6.13860	−	6.13860i	0.256892	−	0.256892i	−0.566897	−	0.823789i	$-0.691856\pi$
$571$	6.13860	−	6.13860i	0.256892	−	0.256892i	0.823789	+	0.566897i	$0.191856\pi$
$572$	2.33727	+	13.1510i	0.0977263	+	0.549872i
$573$	−1.72384	−	1.72384i	−0.0720143	−	0.0720143i
$574$	1.08562	−	1.29557i	0.0453129	−	0.0540762i
$575$	2.66840			0.111280
$576$	16.9473	−	9.87665i	0.706136	−	0.411527i
$577$	−32.9457			−1.37155			−0.685773	−	0.727816i	$-0.740536\pi$
$577$	−32.9457			−1.37155			−0.685773	+	0.727816i	$0.740536\pi$
$578$	−33.3976	+	39.8565i	−1.38916	+	1.65781i
$579$	5.05662	+	5.05662i	0.210146	+	0.210146i
$580$	−3.67523	−	20.6793i	−0.152606	−	0.858659i
$581$	−8.17526	+	8.17526i	−0.339167	+	0.339167i
$582$	−6.77054	+	0.596972i	−0.280648	+	0.0247453i
$583$			33.9669i			1.40676i
$584$	6.06516	−	10.5547i	0.250978	−	0.436756i
$585$		−	2.48054i		−	0.102558i
$586$	−1.96366	−	22.2708i	−0.0811179	−	0.919997i
$587$	−24.1542	+	24.1542i	−0.996952	+	0.996952i	−0.999995	−	0.00304373i	$-0.999031\pi$
$587$	−24.1542	+	24.1542i	−0.996952	+	0.996952i	0.00304373	+	0.999995i	$0.499031\pi$
$588$	−0.847630	+	1.21404i	−0.0349557	+	0.0500662i
$589$	20.6291	+	20.6291i	0.850006	+	0.850006i
$590$	−7.05706	−	5.91343i	−0.290535	−	0.243452i
$591$	5.19590			0.213731
$592$	11.7416	−	25.3593i	0.482577	−	1.04226i
$593$	35.4351			1.45515			0.727573	−	0.686031i	$-0.240648\pi$
$593$	35.4351			1.45515			0.727573	+	0.686031i	$0.240648\pi$
$594$	−28.8823	−	24.2017i	−1.18505	−	0.993009i
$595$	5.18503	+	5.18503i	0.212566	+	0.212566i
$596$	1.69022	+	1.18009i	0.0692342	+	0.0483386i
$597$	3.19145	−	3.19145i	0.130617	−	0.130617i
$598$	−0.335319	−	3.80301i	−0.0137122	−	0.155517i
$599$			43.3503i			1.77124i	0.464407	+	0.885622i	$0.346267\pi$
$599$			43.3503i			1.77124i	−0.464407	+	0.885622i	$0.653733\pi$
$600$	2.02152	−	0.546074i	0.0825282	−	0.0222934i
$601$		−	5.74682i		−	0.234418i	−0.993107	−	0.117209i	$-0.962605\pi$
$601$		−	5.74682i		−	0.234418i	0.993107	−	0.117209i	$-0.0373947\pi$
$602$	−8.07505	+	0.711993i	−0.329115	+	0.0290187i
$603$	−10.2789	+	10.2789i	−0.418591	+	0.418591i
$604$	−5.12358	+	0.910591i	−0.208476	+	0.0370514i
$605$	−23.0370	−	23.0370i	−0.936587	−	0.936587i
$606$	7.21491	−	8.61024i	0.293086	−	0.349767i
$607$	22.4098			0.909586			0.454793	−	0.890597i	$-0.349713\pi$
$607$	22.4098			0.909586			0.454793	+	0.890597i	$0.349713\pi$
$608$	21.8778	−	10.2922i	0.887263	−	0.417405i
$609$	−7.77472			−0.315048
$610$	12.0616	−	14.3943i	0.488361	−	0.582808i
$611$	−5.26538	−	5.26538i	−0.213014	−	0.213014i
$612$	−35.4036	+	6.29213i	−1.43111	+	0.254344i
$613$	3.46505	−	3.46505i	0.139952	−	0.139952i	−0.633660	−	0.773612i	$-0.718448\pi$
$613$	3.46505	−	3.46505i	0.139952	−	0.139952i	0.773612	+	0.633660i	$0.218448\pi$
$614$	19.1712	−	1.69036i	0.773687	−	0.0682175i
$615$			0.884857i			0.0356809i
$616$	−4.86928	−	18.0256i	−0.196189	−	0.726274i
$617$			6.16713i			0.248279i	0.992265	+	0.124140i	$0.0396171\pi$
$617$			6.16713i			0.248279i	−0.992265	+	0.124140i	$0.960383\pi$
$618$	0.0738283	+	0.837322i	0.00296981	+	0.0336820i
$619$	−16.4738	+	16.4738i	−0.662136	+	0.662136i	−0.955883	−	0.293747i	$-0.905098\pi$
$619$	−16.4738	+	16.4738i	−0.662136	+	0.662136i	0.293747	+	0.955883i	$0.405098\pi$
$620$	−11.1933	−	7.81503i	−0.449534	−	0.313859i
$621$	7.61574	+	7.61574i	0.305609	+	0.305609i
$622$	−4.54125	−	3.80531i	−0.182087	−	0.152579i
$623$	−0.532249			−0.0213241
$624$	−1.03230	−	2.81245i	−0.0413249	−	0.112588i
$625$	−1.00000			−0.0400000
$626$	11.7041	+	9.80742i	0.467791	+	0.391983i
$627$	−14.7705	−	14.7705i	−0.589877	−	0.589877i
$628$	−10.8991	+	15.6106i	−0.434922	+	0.622930i
$629$	−36.2248	+	36.2248i	−1.44438	+	1.44438i
$630$	0.304556	+	3.45412i	0.0121338	+	0.137615i
$631$		−	4.55878i		−	0.181482i	−0.995875	−	0.0907410i	$-0.971076\pi$
$631$		−	4.55878i		−	0.181482i	0.995875	−	0.0907410i	$-0.0289235\pi$
$632$	−17.8049	−	10.2314i	−0.708240	−	0.406984i
$633$			9.76507i			0.388127i
$634$	−10.3023	+	0.908377i	−0.409158	+	0.0360763i
$635$	−12.1829	+	12.1829i	−0.483465	+	0.483465i
$636$	−1.33312	−	7.50102i	−0.0528617	−	0.297435i
$637$	−0.715365	−	0.715365i	−0.0283438	−	0.0283438i
$638$	62.9693	−	75.1473i	2.49298	−	2.97511i
$639$	2.55437			0.101049
$640$	−9.23674	+	6.53319i	−0.365114	+	0.258247i
$641$	40.9220			1.61632			0.808161	−	0.588962i	$-0.200463\pi$
$641$	40.9220			1.61632			0.808161	+	0.588962i	$0.200463\pi$
$642$	−10.1972	+	12.1693i	−0.402450	+	0.480283i
$643$	1.05107	+	1.05107i	0.0414502	+	0.0414502i	0.727528	−	0.686078i	$-0.240669\pi$
$643$	1.05107	+	1.05107i	0.0414502	+	0.0414502i	−0.686078	+	0.727528i	$0.740669\pi$
$644$	0.933853	+	5.25447i	0.0367990	+	0.207055i
$645$	3.00071	−	3.00071i	0.118153	−	0.118153i
$646$	−44.1513	+	3.89290i	−1.73711	+	0.153164i
$647$		−	2.47501i		−	0.0973029i	−0.998816	−	0.0486514i	$-0.984508\pi$
$647$		−	2.47501i		−	0.0973029i	0.998816	−	0.0486514i	$-0.0154923\pi$
$648$	−10.7109	−	6.15490i	−0.420762	−	0.241787i
$649$		−	42.9781i		−	1.68704i
$650$	0.125663	+	1.42520i	0.00492890	+	0.0559010i
$651$	−3.57325	+	3.57325i	−0.140047	+	0.140047i
$652$	−12.4512	+	17.8336i	−0.487629	+	0.698420i
$653$	−2.66386	−	2.66386i	−0.104245	−	0.104245i	0.653061	−	0.757306i	$-0.273485\pi$
$653$	−2.66386	−	2.66386i	−0.104245	−	0.104245i	−0.757306	+	0.653061i	$0.773485\pi$
$654$	−2.52128	−	2.11270i	−0.0985899	−	0.0826129i
$655$	0.720231			0.0281418
$656$	−1.64733	−	4.48809i	−0.0643174	−	0.175230i
$657$	−10.5527			−0.411702
$658$	7.97843	+	6.68549i	0.311032	+	0.260627i
$659$	−7.78249	−	7.78249i	−0.303163	−	0.303163i	0.539087	−	0.842250i	$-0.318769\pi$
$659$	−7.78249	−	7.78249i	−0.303163	−	0.303163i	−0.842250	+	0.539087i	$0.818769\pi$
$660$	8.01444	+	5.59559i	0.311962	+	0.217808i
$661$	32.2608	−	32.2608i	1.25480	−	1.25480i	0.301256	−	0.953543i	$-0.402594\pi$
$661$	32.2608	−	32.2608i	1.25480	−	1.25480i	0.953543	−	0.301256i	$-0.0974059\pi$
$662$	−0.0814094	−	0.923303i	−0.00316407	−	0.0358852i
$663$			5.49208i			0.213295i
$664$	8.52789	+	31.5695i	0.330946	+	1.22513i
$665$			4.27408i			0.165742i
$666$	−24.1319	+	2.12776i	−0.935092	+	0.0824489i
$667$	−19.8150	+	19.8150i	−0.767240	+	0.767240i
$668$	−28.9131	+	5.13860i	−1.11868	+	0.198818i
$669$	8.43410	+	8.43410i	0.326081	+	0.326081i
$670$	5.38506	−	6.42651i	0.208043	−	0.248278i
$671$	87.6626			3.38418
$672$	1.78276	+	3.78955i	0.0687716	+	0.146185i
$673$	−1.77922			−0.0685839			−0.0342919	−	0.999412i	$-0.510918\pi$
$673$	−1.77922			−0.0685839			−0.0342919	+	0.999412i	$0.510918\pi$
$674$	−4.48991	+	5.35823i	−0.172945	+	0.206391i
$675$	−2.85404	−	2.85404i	−0.109852	−	0.109852i
$676$	−23.5834	+	4.19138i	−0.907056	+	0.161207i
$677$	−15.9568	+	15.9568i	−0.613268	+	0.613268i	−0.943796	−	0.330528i	$-0.892773\pi$
$677$	−15.9568	+	15.9568i	−0.613268	+	0.613268i	0.330528	+	0.943796i	$0.392773\pi$
$678$	−8.45288	+	0.745306i	−0.324631	+	0.0286233i
$679$			6.49177i			0.249131i
$680$	20.0225	−	5.40868i	0.767827	−	0.207413i
$681$			8.05333i			0.308604i
$682$	−5.59700	−	63.4782i	−0.214320	−	2.43071i
$683$	−22.8749	+	22.8749i	−0.875283	+	0.875283i	−0.993042	−	0.117759i	$-0.962429\pi$
$683$	−22.8749	+	22.8749i	−0.875283	+	0.875283i	0.117759	+	0.993042i	$0.462429\pi$
$684$	−17.1852	−	11.9985i	−0.657091	−	0.458773i
$685$	−7.47009	−	7.47009i	−0.285417	−	0.285417i
$686$	1.08397	+	0.908304i	0.0413860	+	0.0346792i
$687$	−12.3507			−0.471209
$688$	−9.63353	+	20.8063i	−0.367275	+	0.793233i
$689$	5.20545			0.198312
$690$	−2.14138	−	1.79436i	−0.0815211	−	0.0683102i
$691$	14.1498	+	14.1498i	0.538284	+	0.538284i	0.923025	−	0.384741i	$-0.125709\pi$
$691$	14.1498	+	14.1498i	0.538284	+	0.538284i	−0.384741	+	0.923025i	$0.625709\pi$
$692$	9.09494	−	13.0265i	0.345738	−	0.495193i
$693$	−11.4453	+	11.4453i	−0.434773	+	0.434773i
$694$	−4.02473	−	45.6464i	−0.152777	−	1.73271i
$695$		−	11.1638i		−	0.423468i
$696$	−10.9564	+	19.0664i	−0.415300	+	0.722711i
$697$			8.76421i			0.331968i
$698$	−24.5981	+	2.16886i	−0.931052	+	0.0820927i
$699$	6.56974	−	6.56974i	0.248490	−	0.248490i
$700$	−0.349967	−	1.96914i	−0.0132275	−	0.0744266i
$701$	−6.63595	−	6.63595i	−0.250636	−	0.250636i	0.570595	−	0.821231i	$-0.306713\pi$
$701$	−6.63595	−	6.63595i	−0.250636	−	0.250636i	−0.821231	+	0.570595i	$0.806713\pi$
$702$	−3.70894	+	4.42623i	−0.139985	+	0.167057i
$703$	−29.8605			−1.12621
$704$	−51.0673	−	13.4610i	−1.92467	−	0.507331i
$705$	−5.44915			−0.205227
$706$	5.06949	−	6.04991i	0.190793	−	0.227691i
$707$	−7.58678	−	7.58678i	−0.285330	−	0.285330i
$708$	1.68679	+	9.49101i	0.0633936	+	0.356694i
$709$	21.7743	−	21.7743i	0.817750	−	0.817750i	−0.168032	−	0.985782i	$-0.553741\pi$
$709$	21.7743	−	21.7743i	0.817750	−	0.817750i	0.985782	+	0.168032i	$0.0537412\pi$
$710$	−1.46762	+	0.129403i	−0.0550788	+	0.00485640i
$711$			17.8016i			0.667611i
$712$	−0.750060	+	1.30527i	−0.0281097	+	0.0489169i
$713$			18.2139i			0.682116i
$714$	−0.674307	−	7.64763i	−0.0252353	−	0.286206i
$715$	−4.72245	+	4.72245i	−0.176610	+	0.176610i
$716$	14.3213	−	20.5121i	0.535211	−	0.766572i
$717$	3.27672	+	3.27672i	0.122371	+	0.122371i
$718$	16.0448	+	13.4446i	0.598786	+	0.501750i
$719$	−13.3886			−0.499309			−0.249655	−	0.968335i	$-0.580317\pi$
$719$	−13.3886			−0.499309			−0.249655	+	0.968335i	$0.580317\pi$
$720$	8.89994	+	4.12076i	0.331681	+	0.153572i
$721$	0.802846			0.0298995
$722$	0.793681	+	0.665061i	0.0295377	+	0.0247510i
$723$	−14.8831	−	14.8831i	−0.553510	−	0.553510i
$724$	39.9918	+	27.9218i	1.48629	+	1.03771i
$725$	7.42579	−	7.42579i	0.275787	−	0.275787i
$726$	2.99593	+	33.9783i	0.111189	+	1.26105i
$727$			28.9563i			1.07393i	0.843604	+	0.536965i	$0.180429\pi$
$727$			28.9563i			1.07393i	−0.843604	+	0.536965i	$0.819571\pi$
$728$	−2.76245	+	0.746221i	−0.102383	+	0.0276568i
$729$			1.74442i			0.0646081i
$730$	6.06310	−	0.534595i	0.224405	−	0.0197862i
$731$	29.7210	−	29.7210i	1.09927	−	1.09927i
$732$	−19.3588	+	3.44056i	−0.715523	+	0.127167i
$733$	−12.1661	−	12.1661i	−0.449366	−	0.449366i	0.445778	−	0.895144i	$-0.352927\pi$
$733$	−12.1661	−	12.1661i	−0.449366	−	0.449366i	−0.895144	+	0.445778i	$0.852927\pi$
$734$	2.28855	−	2.73114i	0.0844718	−	0.100808i
$735$	−0.740333			−0.0273076
$736$	14.2019	+	5.11460i	0.523488	+	0.188527i
$737$	39.1380			1.44167
$738$	−2.66184	+	3.17663i	−0.0979836	+	0.116933i
$739$	−27.4242	−	27.4242i	−1.00882	−	1.00882i	−0.999961	−	0.00885446i	$-0.997182\pi$
$739$	−27.4242	−	27.4242i	−1.00882	−	1.00882i	−0.00885446	−	0.999961i	$-0.502818\pi$
$740$	13.7572	−	2.44501i	0.505726	−	0.0898805i
$741$	−2.26359	+	2.26359i	−0.0831551	+	0.0831551i
$742$	−7.24852	+	0.639116i	−0.266101	+	0.0234627i
$743$		−	34.4746i		−	1.26475i	−0.774663	−	0.632374i	$-0.782080\pi$
$743$		−	34.4746i		−	1.26475i	0.774663	−	0.632374i	$-0.217920\pi$
$744$	3.72738	+	13.7984i	0.136652	+	0.505875i
$745$			1.03071i			0.0377624i
$746$	0.618044	+	7.00953i	0.0226282	+	0.256637i
$747$	20.0450	−	20.0450i	0.733408	−	0.733408i
$748$	79.3803	+	55.4224i	2.90243	+	2.02644i
$749$	10.7228	+	10.7228i	0.391801	+	0.391801i
$750$	0.802496	+	0.672448i	0.0293030	+	0.0245543i
$751$	28.3477			1.03442			0.517211	−	0.855858i	$-0.326970\pi$
$751$	28.3477			1.03442			0.517211	+	0.855858i	$0.326970\pi$
$752$	27.6387	−	10.1446i	1.00788	−	0.369936i
$753$	−2.78779			−0.101593
$754$	−11.5164	−	9.65010i	−0.419402	−	0.351436i
$755$	−1.83985	−	1.83985i	−0.0669589	−	0.0669589i
$756$	4.62120	−	6.61884i	0.168071	−	0.240725i
$757$	−2.02393	+	2.02393i	−0.0735609	+	0.0735609i	−0.742930	−	0.669369i	$-0.766564\pi$
$757$	−2.02393	+	2.02393i	−0.0735609	+	0.0735609i	0.669369	+	0.742930i	$0.266564\pi$
$758$	4.30570	+	48.8330i	0.156390	+	1.77370i
$759$		−	13.0412i		−	0.473366i
$760$	10.4816	+	6.02316i	0.380208	+	0.218483i
$761$			7.82114i			0.283516i	0.989901	+	0.141758i	$0.0452755\pi$
$761$			7.82114i			0.283516i	−0.989901	+	0.141758i	$0.954725\pi$
$762$	17.9691	−	1.58437i	0.650953	−	0.0573958i
$763$	−2.22159	+	2.22159i	−0.0804269	+	0.0804269i
$764$	1.15242	+	6.48427i	0.0416931	+	0.234593i
$765$	−12.7132	−	12.7132i	−0.459648	−	0.459648i
$766$	1.45667	−	1.73838i	0.0526315	−	0.0628102i
$767$	−6.58644			−0.237823
$768$	11.8057	+	0.968366i	0.426001	+	0.0349429i
$769$	−28.8481			−1.04029			−0.520145	−	0.854078i	$-0.674122\pi$
$769$	−28.8481			−1.04029			−0.520145	+	0.854078i	$0.674122\pi$
$770$	5.99613	−	7.15576i	0.216086	−	0.257876i
$771$	9.53447	+	9.53447i	0.343376	+	0.343376i
$772$	−3.38045	−	19.0206i	−0.121665	−	0.684568i
$773$	−26.7540	+	26.7540i	−0.962275	+	0.962275i	−0.999314	−	0.0370387i	$-0.988208\pi$
$773$	−26.7540	+	26.7540i	−0.962275	+	0.962275i	0.0370387	+	0.999314i	$0.488208\pi$
$774$	19.7993	−	1.74574i	0.711670	−	0.0627493i
$775$		−	6.82577i		−	0.245189i
$776$	15.9202	+	9.14838i	0.571501	+	0.328408i
$777$		−	5.17227i		−	0.185554i
$778$	3.45710	+	39.2086i	0.123943	+	1.40570i
$779$	−3.61222	+	3.61222i	−0.129421	+	0.129421i
$780$	0.857529	−	1.22822i	0.0307045	−	0.0439773i
$781$	−4.86301	−	4.86301i	−0.174012	−	0.174012i
$782$	−21.2097	−	17.7725i	−0.758456	−	0.635545i
$783$	42.3871			1.51479
$784$	3.75505	−	1.37827i	0.134109	−	0.0492239i
$785$	−9.51946			−0.339764
$786$	−0.577983	−	0.484318i	−0.0206160	−	0.0172750i
$787$	11.0127	+	11.0127i	0.392562	+	0.392562i	0.875600	−	0.483038i	$-0.160467\pi$
$787$	11.0127	+	11.0127i	0.392562	+	0.392562i	−0.483038	+	0.875600i	$0.660467\pi$
$788$	−11.5091	−	8.03550i	−0.409994	−	0.286253i
$789$	−0.964914	+	0.964914i	−0.0343519	+	0.0343519i
$790$	−0.901817	−	10.2279i	−0.0320852	−	0.363894i
$791$			8.10483i			0.288175i
$792$	11.9390	+	44.1972i	0.424234	+	1.57048i
$793$		−	13.4344i		−	0.477069i
$794$	−54.7725	+	4.82940i	−1.94380	+	0.171389i
$795$	2.69357	−	2.69357i	0.0955310	−	0.0955310i
$796$	−12.0047	+	2.13355i	−0.425497	+	0.0756216i
$797$	−13.9484	−	13.9484i	−0.494076	−	0.494076i	0.415512	−	0.909588i	$-0.363602\pi$
$797$	−13.9484	−	13.9484i	−0.494076	−	0.494076i	−0.909588	+	0.415512i	$0.863602\pi$
$798$	2.87410	−	3.42994i	0.101742	−	0.121418i
$799$	−53.9720			−1.90939
$800$	−5.32223	−	1.91673i	−0.188169	−	0.0677665i
$801$	1.30502			0.0461108
$802$	19.2742	−	23.0017i	0.680595	−	0.812220i
$803$	20.0903	+	20.0903i	0.708970	+	0.708970i
$804$	−8.64298	+	1.53608i	−0.304815	+	0.0541733i
$805$	−1.88685	+	1.88685i	−0.0665026	+	0.0665026i
$806$	−9.72810	+	0.857745i	−0.342658	+	0.0302128i
$807$		−	9.33056i		−	0.328451i
$808$	−29.2970	+	7.91402i	−1.03067	+	0.278414i
$809$		−	5.75714i		−	0.202410i	−0.994866	−	0.101205i	$-0.967730\pi$
$809$		−	5.75714i		−	0.202410i	0.994866	−	0.101205i	$-0.0322699\pi$
$810$	−0.542505	−	6.15281i	−0.0190617	−	0.216188i
$811$	17.9676	−	17.9676i	0.630927	−	0.630927i	−0.317373	−	0.948301i	$-0.602801\pi$
$811$	17.9676	−	17.9676i	0.630927	−	0.630927i	0.948301	+	0.317373i	$0.102801\pi$
$812$	17.2212	+	12.0237i	0.604346	+	0.421948i
$813$	−13.2082	−	13.2082i	−0.463233	−	0.463233i
$814$	49.9931	+	41.8914i	1.75226	+	1.46829i
$815$	−10.8751			−0.380939
$816$	−19.7050	−	9.12362i	−0.689813	−	0.319391i
$817$	24.4994			0.857125
$818$	−11.1149	−	9.31370i	−0.388625	−	0.325646i
$819$	1.75401	+	1.75401i	0.0612900	+	0.0612900i
$820$	1.36844	−	1.95998i	0.0477879	−	0.0684456i
$821$	−21.1975	+	21.1975i	−0.739797	+	0.739797i	−0.972539	−	0.232741i	$-0.925230\pi$
$821$	−21.1975	+	21.1975i	−0.739797	+	0.739797i	0.232741	+	0.972539i	$0.425230\pi$
$822$	0.971475	+	11.0180i	0.0338841	+	0.384296i
$823$			9.54791i			0.332819i	0.986057	+	0.166410i	$0.0532174\pi$
$823$			9.54791i			0.332819i	−0.986057	+	0.166410i	$0.946783\pi$
$824$	1.13139	−	1.96887i	0.0394139	−	0.0685888i
$825$			4.88728i			0.170153i
$826$	9.17152	−	0.808671i	0.319118	−	0.0281372i
$827$	14.5549	−	14.5549i	0.506125	−	0.506125i	−0.407210	−	0.913335i	$-0.633498\pi$
$827$	14.5549	−	14.5549i	0.506125	−	0.506125i	0.913335	+	0.407210i	$0.133498\pi$
$828$	−2.28972	−	12.8835i	−0.0795733	−	0.447731i
$829$	−7.31235	−	7.31235i	−0.253969	−	0.253969i	0.568627	−	0.822596i	$-0.307475\pi$
$829$	−7.31235	−	7.31235i	−0.253969	−	0.253969i	−0.822596	+	0.568627i	$0.807475\pi$
$830$	−10.5014	+	12.5324i	−0.364510	+	0.435004i
$831$	2.53967			0.0881003
$832$	−2.06291	+	7.82611i	−0.0715187	+	0.271322i
$833$	−7.33275			−0.254065
$834$	−7.50709	+	8.95893i	−0.259949	+	0.310222i
$835$	−10.3825	−	10.3825i	−0.359302	−	0.359302i
$836$	9.87438	+	55.5597i	0.341513	+	1.92157i
$837$	19.4810	−	19.4810i	0.673363	−	0.673363i
$838$	35.9955	−	3.17380i	1.24345	−	0.109637i
$839$		−	13.9321i		−	0.480989i	−0.970651	−	0.240494i	$-0.922690\pi$
$839$		−	13.9321i		−	0.480989i	0.970651	−	0.240494i	$-0.0773096\pi$
$840$	−1.04330	+	1.81556i	−0.0359972	+	0.0626429i
$841$			81.2847i			2.80292i
$842$	0.614843	+	6.97322i	0.0211889	+	0.240313i
$843$	−6.44403	+	6.44403i	−0.221944	+	0.221944i
$844$	15.1018	−	21.6299i	0.519824	−	0.744532i
$845$	−8.46867	−	8.46867i	−0.291331	−	0.291331i
$846$	−19.5624	−	16.3922i	−0.672568	−	0.563575i
$847$	32.5792			1.11944
$848$	−8.64747	+	18.6766i	−0.296955	+	0.641359i
$849$	16.3505			0.561146
$850$	7.94845	+	6.66036i	0.272630	+	0.228449i
$851$	−13.1823	−	13.1823i	−0.451883	−	0.451883i
$852$	1.26478	+	0.883052i	0.0433305	+	0.0302529i
$853$	−0.934477	+	0.934477i	−0.0319959	+	0.0319959i	−0.722924	−	0.690928i	$-0.757202\pi$
$853$	−0.934477	+	0.934477i	−0.0319959	+	0.0319959i	0.690928	+	0.722924i	$0.257202\pi$
$854$	1.64945	+	18.7072i	0.0564429	+	0.640146i
$855$		−	10.4797i		−	0.358397i
$856$	41.4069	−	11.1853i	1.41526	−	0.382305i
$857$			41.7519i			1.42622i	0.701053	+	0.713109i	$0.252714\pi$
$857$			41.7519i			1.42622i	−0.701053	+	0.713109i	$0.747286\pi$
$858$	6.96535	−	0.614148i	0.237793	−	0.0209667i
$859$	−26.1634	+	26.1634i	−0.892684	+	0.892684i	−0.994775	−	0.102091i	$-0.967447\pi$
$859$	−26.1634	+	26.1634i	−0.892684	+	0.892684i	0.102091	+	0.994775i	$0.467447\pi$
$860$	−11.2873	+	2.00604i	−0.384893	+	0.0684053i
$861$	−0.625689	−	0.625689i	−0.0213234	−	0.0213234i
$862$	−4.83973	+	5.77572i	−0.164842	+	0.196722i
$863$	−8.72689			−0.297067			−0.148533	−	0.988907i	$-0.547455\pi$
$863$	−8.72689			−0.297067			−0.148533	+	0.988907i	$0.547455\pi$
$864$	−9.71946	−	20.6603i	−0.330663	−	0.702878i
$865$	7.94367			0.270093
$866$	−16.8210	+	20.0741i	−0.571600	+	0.682146i
$867$	19.2485	+	19.2485i	0.653712	+	0.653712i
$868$	13.4409	−	2.38879i	0.456214	−	0.0810810i
$869$	33.8906	−	33.8906i	1.14966	−	1.14966i
$870$	−10.9526	+	0.965714i	−0.371329	+	0.0327408i
$871$		−	5.99794i		−	0.203233i
$872$	2.31741	+	8.57886i	0.0784775	+	0.290517i
$873$		−	15.9172i		−	0.538716i
$874$	−1.41664	−	16.0667i	−0.0479184	−	0.543466i
$875$	0.707107	−	0.707107i	0.0239046	−	0.0239046i
$876$	−5.22510	−	3.64810i	−0.176540	−	0.123258i
$877$	2.43549	+	2.43549i	0.0822405	+	0.0822405i	0.747030	−	0.664790i	$-0.231479\pi$
$877$	2.43549	+	2.43549i	0.0822405	+	0.0822405i	−0.664790	+	0.747030i	$0.731479\pi$
$878$	3.82030	+	3.20120i	0.128929	+	0.108035i
$879$	−11.7039			−0.394761
$880$	−9.09859	−	24.7888i	−0.306713	−	0.835629i
$881$	−1.48856			−0.0501509			−0.0250754	−	0.999686i	$-0.507983\pi$
$881$	−1.48856			−0.0501509			−0.0250754	+	0.999686i	$0.507983\pi$
$882$	−2.65779	−	2.22708i	−0.0894923	−	0.0749896i
$883$	9.09384	+	9.09384i	0.306032	+	0.306032i	0.843368	−	0.537336i	$-0.180569\pi$
$883$	9.09384	+	9.09384i	0.306032	+	0.306032i	−0.537336	+	0.843368i	$0.680569\pi$
$884$	8.49353	−	12.1651i	0.285668	−	0.409157i
$885$	−3.40816	+	3.40816i	−0.114564	+	0.114564i
$886$	0.436214	+	4.94731i	0.0146549	+	0.166208i
$887$			19.4625i			0.653487i	0.945113	+	0.326743i	$0.105951\pi$
$887$			19.4625i			0.653487i	−0.945113	+	0.326743i	$0.894049\pi$
$888$	−12.6843	−	7.28891i	−0.425656	−	0.244600i
$889$		−	17.2293i		−	0.577851i
$890$	−0.749805	+	0.0661117i	−0.0251335	+	0.00221607i
$891$	20.3875	−	20.3875i	0.683008	−	0.683008i
$892$	−5.63837	−	31.7252i	−0.188787	−	1.06224i
$893$	−22.2449	−	22.2449i	−0.744396	−	0.744396i
$894$	0.693100	−	0.827143i	0.0231807	−	0.0276638i
$895$	12.5084			0.418111
$896$	1.91170	−	11.1510i	0.0638655	−	0.372530i
$897$	−1.99858			−0.0667306
$898$	14.1243	−	16.8559i	0.471334	−	0.562488i
$899$	50.6867	+	50.6867i	1.69050	+	1.69050i
$900$	0.858086	+	4.82816i	0.0286029	+	0.160939i
$901$	26.6789	−	26.6789i	0.888802	−	0.888802i
$902$	11.1152	−	0.980053i	0.370097	−	0.0326322i
$903$			4.24365i			0.141220i
$904$	19.8760	+	11.4216i	0.661065	+	0.379875i
$905$			24.3874i			0.810664i
$906$	0.239269	+	2.71367i	0.00794920	+	0.0901556i
$907$	−8.21831	+	8.21831i	−0.272884	+	0.272884i	−0.830260	−	0.557376i	$-0.811808\pi$
$907$	−8.21831	+	8.21831i	−0.272884	+	0.272884i	0.557376	+	0.830260i	$0.311808\pi$
$908$	12.4545	−	17.8384i	0.413318	−	0.591987i
$909$	18.6021	+	18.6021i	0.616992	+	0.616992i
$910$	−1.09663	−	0.918912i	−0.0363528	−	0.0304616i
$911$	−32.2531			−1.06859			−0.534296	−	0.845298i	$-0.679423\pi$
$911$	−32.2531			−1.06859			−0.534296	+	0.845298i	$0.679423\pi$
$912$	−4.36118	−	11.8819i	−0.144413	−	0.393449i
$913$	−76.3232			−2.52593
$914$	−21.7447	−	18.2209i	−0.719251	−	0.602693i
$915$	−6.95164	−	6.95164i	−0.229814	−	0.229814i
$916$	27.3571	+	19.1004i	0.903905	+	0.631096i
$917$	−0.509280	+	0.509280i	−0.0168179	+	0.0168179i
$918$	3.67626	+	41.6942i	0.121335	+	1.37611i
$919$			17.6609i			0.582579i	0.956635	+	0.291289i	$0.0940842\pi$
$919$			17.6609i			0.582579i	−0.956635	+	0.291289i	$0.905916\pi$
$920$	1.96823	+	7.28622i	0.0648907	+	0.240220i
$921$		−	10.0750i		−	0.331981i
$922$	37.5355	−	3.30957i	1.23616	−	0.108995i
$923$	−0.745260	+	0.745260i	−0.0245305	+	0.0245305i
$924$	−9.62374	+	1.71038i	−0.316598	+	0.0562675i
$925$	4.94014	+	4.94014i	0.162431	+	0.162431i
$926$	−8.43210	+	10.0628i	−0.277096	+	0.330685i
$927$	−1.96850			−0.0646541
$928$	53.7550	−	25.2886i	1.76459	−	0.830138i
$929$	14.4346			0.473584			0.236792	−	0.971560i	$-0.423904\pi$
$929$	14.4346			0.473584			0.236792	+	0.971560i	$0.423904\pi$
$930$	−4.58997	+	5.47765i	−0.150511	+	0.179619i
$931$	−3.02223	−	3.02223i	−0.0990497	−	0.0990497i
$932$	−24.7123	+	4.39201i	−0.809478	+	0.143865i
$933$	−2.19316	+	2.19316i	−0.0718010	+	0.0718010i
$934$	51.0427	−	4.50053i	1.67017	−	0.147262i
$935$			48.4068i			1.58307i
$936$	6.77326	−	1.82966i	0.221391	−	0.0598045i
$937$			2.84643i			0.0929887i	0.998919	+	0.0464943i	$0.0148049\pi$
$937$			2.84643i			0.0929887i	−0.998919	+	0.0464943i	$0.985195\pi$
$938$	0.736416	+	8.35204i	0.0240448	+	0.272704i
$939$	5.65244	−	5.65244i	0.184460	−	0.184460i
$940$	12.0700	+	8.42715i	0.393681	+	0.274863i
$941$	−18.2562	−	18.2562i	−0.595135	−	0.595135i	0.343879	−	0.939014i	$-0.388259\pi$
$941$	−18.2562	−	18.2562i	−0.595135	−	0.595135i	−0.939014	+	0.343879i	$0.888259\pi$
$942$	7.63933	+	6.40134i	0.248903	+	0.208567i
$943$	−3.18932			−0.103858
$944$	10.9416	−	23.6315i	0.356119	−	0.769139i
$945$	4.03623			0.131298
$946$	−41.0173	−	34.3703i	−1.33359	−	1.11747i
$947$	−38.6855	−	38.6855i	−1.25711	−	1.25711i	−0.952466	−	0.304644i	$-0.901463\pi$
$947$	−38.6855	−	38.6855i	−1.25711	−	1.25711i	−0.304644	−	0.952466i	$-0.598537\pi$
$948$	−6.15404	+	8.81430i	−0.199874	+	0.286275i
$949$	3.07885	−	3.07885i	0.0999438	−	0.0999438i
$950$	0.530893	+	6.02111i	0.0172244	+	0.195351i
$951$			5.41414i			0.175566i
$952$	−10.3335	+	17.9825i	−0.334911	+	0.582818i
$953$			12.7057i			0.411579i	0.978596	+	0.205789i	$0.0659761\pi$
$953$			12.7057i			0.411579i	−0.978596	+	0.205789i	$0.934024\pi$
$954$	17.7727	−	1.56705i	0.575412	−	0.0507352i
$955$	−2.32846	+	2.32846i	−0.0753472	+	0.0753472i
$956$	−2.19055	−	12.3255i	−0.0708476	−	0.398635i
$957$	−36.2919	−	36.2919i	−1.17315	−	1.17315i
$958$	11.8281	−	14.1156i	0.382149	−	0.456055i
$959$	10.5643			0.341139
$960$	2.98217	+	5.11709i	0.0962492	+	0.165153i
$961$	15.5911			0.502940
$962$	6.41990	−	7.66148i	0.206986	−	0.247016i
$963$	−26.2912	−	26.2912i	−0.847222	−	0.847222i
$964$	9.94969	+	55.9834i	0.320458	+	1.80311i
$965$	6.83019	−	6.83019i	0.219872	−	0.219872i
$966$	2.78299	−	0.245382i	0.0895413	−	0.00789503i
$967$			10.3646i			0.333303i	0.986016	+	0.166651i	$0.0532954\pi$
$967$			10.3646i			0.333303i	−0.986016	+	0.166651i	$0.946705\pi$
$968$	45.9115	−	79.8960i	1.47565	−	2.56795i
$969$			23.2026i			0.745375i
$970$	0.806356	+	9.14527i	0.0258905	+	0.293637i
$971$	−32.3406	+	32.3406i	−1.03786	+	1.03786i	−0.0386042	+	0.999255i	$0.512291\pi$
$971$	−32.3406	+	32.3406i	−1.03786	+	1.03786i	−0.999255	+	0.0386042i	$0.987709\pi$
$972$	−17.5657	+	25.1589i	−0.563419	+	0.806973i
$973$	7.89402	+	7.89402i	0.253071	+	0.253071i
$974$	34.7650	+	29.1312i	1.11394	+	0.933423i
$975$	0.748979			0.0239865
$976$	48.2012	+	22.3176i	1.54288	+	0.714370i
$977$	10.9227			0.349448			0.174724	−	0.984617i	$-0.444097\pi$
$977$	10.9227			0.349448			0.174724	+	0.984617i	$0.444097\pi$
$978$	8.72724	+	7.31295i	0.279066	+	0.233842i
$979$	−2.48450	−	2.48450i	−0.0794050	−	0.0794050i
$980$	1.63986	+	1.14493i	0.0523833	+	0.0365735i
$981$	5.44713	−	5.44713i	0.173913	−	0.173913i
$982$	−2.77518	−	31.4747i	−0.0885597	−	1.00440i
$983$			13.2103i			0.421344i	0.977557	+	0.210672i	$0.0675651\pi$
$983$			13.2103i			0.421344i	−0.977557	+	0.210672i	$0.932435\pi$
$984$	−2.41615	+	0.652676i	−0.0770241	+	0.0208066i
$985$		−	7.01833i		−	0.223623i
$986$	−108.482	+	9.56507i	−3.45477	+	0.304614i
$987$	3.85313	−	3.85313i	0.122647	−	0.122647i
$988$	8.51458	−	1.51326i	0.270885	−	0.0481431i
$989$	10.8155	+	10.8155i	0.343914	+	0.343914i
$990$	−14.7020	+	17.5453i	−0.467259	+	0.557625i
$991$	−36.2638			−1.15196			−0.575979	−	0.817465i	$-0.695379\pi$
$991$	−36.2638			−1.15196			−0.575979	+	0.817465i	$0.695379\pi$
$992$	13.0831	−	36.3283i	0.415390	−	1.15343i
$993$	−0.485219			−0.0153980
$994$	0.946262	−	1.12927i	0.0300136	−	0.0358181i
$995$	−4.31083	−	4.31083i	−0.136662	−	0.136662i
$996$	16.8547	−	2.99551i	0.534062	−	0.0949164i
$997$	29.1722	−	29.1722i	0.923892	−	0.923892i	−0.0734101	−	0.997302i	$-0.523388\pi$
$997$	29.1722	−	29.1722i	0.923892	−	0.923892i	0.997302	+	0.0734101i	$0.0233882\pi$
$998$	11.2105	−	0.988453i	0.354863	−	0.0312889i
$999$			28.1987i			0.892169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bd.b.141.7	✓	52
4.3	odd	2		2240.2.bd.b.1681.9		52
16.5	even	4	inner	560.2.bd.b.421.7	yes	52
16.11	odd	4		2240.2.bd.b.561.9		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.b.141.7	✓	52	1.1	even	1	trivial
560.2.bd.b.421.7	yes	52	16.5	even	4	inner
2240.2.bd.b.561.9		52	16.11	odd	4
2240.2.bd.b.1681.9		52	4.3	odd	2

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.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.908304 + 1.08397i) q^{2} +(0.523494 + 0.523494i) q^{3} +(-0.349967 - 1.96914i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.04294 + 0.0919583i) q^{6} +1.00000i q^{7} +(2.45236 + 1.40923i) q^{8} -2.45191i q^{9} +O(q^{10})\)	\(q+(-0.908304 + 1.08397i) q^{2} +(0.523494 + 0.523494i) q^{3} +(-0.349967 - 1.96914i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-1.04294 + 0.0919583i) q^{6} +1.00000i q^{7} +(2.45236 + 1.40923i) q^{8} -2.45191i q^{9} +(0.124212 + 1.40875i) q^{10} +(-4.66793 + 4.66793i) q^{11} +(0.847630 - 1.21404i) q^{12} +(0.715365 + 0.715365i) q^{13} +(-1.08397 - 0.908304i) q^{14} +0.740333 q^{15} +(-3.75505 + 1.37827i) q^{16} +7.33275 q^{17} +(2.65779 + 2.22708i) q^{18} +(3.02223 + 3.02223i) q^{19} +(-1.63986 - 1.14493i) q^{20} +(-0.523494 + 0.523494i) q^{21} +(-0.819980 - 9.29979i) q^{22} +2.66840i q^{23} +(0.546074 + 2.02152i) q^{24} -1.00000i q^{25} +(-1.42520 + 0.125663i) q^{26} +(2.85404 - 2.85404i) q^{27} +(1.96914 - 0.349967i) q^{28} +(7.42579 + 7.42579i) q^{29} +(-0.672448 + 0.802496i) q^{30} +6.82577 q^{31} +(1.91673 - 5.32223i) q^{32} -4.88728 q^{33} +(-6.66036 + 7.94845i) q^{34} +(0.707107 + 0.707107i) q^{35} +(-4.82816 + 0.858086i) q^{36} +(-4.94014 + 4.94014i) q^{37} +(-6.02111 + 0.530893i) q^{38} +0.748979i q^{39} +(2.73056 - 0.737607i) q^{40} +1.19522i q^{41} +(-0.0919583 - 1.04294i) q^{42} +(4.05319 - 4.05319i) q^{43} +(10.8255 + 7.55821i) q^{44} +(-1.73376 - 1.73376i) q^{45} +(-2.89246 - 2.42372i) q^{46} -7.36041 q^{47} +(-2.68726 - 1.24423i) q^{48} -1.00000 q^{49} +(1.08397 + 0.908304i) q^{50} +(3.83865 + 3.83865i) q^{51} +(1.15830 - 1.65901i) q^{52} +(3.63832 - 3.63832i) q^{53} +(0.501348 + 5.68603i) q^{54} +6.60146i q^{55} +(-1.40923 + 2.45236i) q^{56} +3.16425i q^{57} +(-14.7942 + 1.30443i) q^{58} +(-4.60355 + 4.60355i) q^{59} +(-0.259092 - 1.45782i) q^{60} +(-9.38988 - 9.38988i) q^{61} +(-6.19988 + 7.39891i) q^{62} +2.45191 q^{63} +(4.02815 + 6.91187i) q^{64} +1.01168 q^{65} +(4.43913 - 5.29764i) q^{66} +(-4.19222 - 4.19222i) q^{67} +(-2.56622 - 14.4392i) q^{68} +(-1.39689 + 1.39689i) q^{69} +(-1.40875 + 0.124212i) q^{70} +1.04179i q^{71} +(3.45530 - 6.01296i) q^{72} -4.30389i q^{73} +(-0.867796 - 9.84209i) q^{74} +(0.523494 - 0.523494i) q^{75} +(4.89353 - 7.00889i) q^{76} +(-4.66793 - 4.66793i) q^{77} +(-0.811869 - 0.680301i) q^{78} -7.26030 q^{79} +(-1.68063 + 3.62980i) q^{80} -4.36757 q^{81} +(-1.29557 - 1.08562i) q^{82} +(8.17526 + 8.17526i) q^{83} +(1.21404 + 0.847630i) q^{84} +(5.18503 - 5.18503i) q^{85} +(0.711993 + 8.07505i) q^{86} +7.77472i q^{87} +(-18.0256 + 4.86928i) q^{88} +0.532249i q^{89} +(3.45412 - 0.304556i) q^{90} +(-0.715365 + 0.715365i) q^{91} +(5.25447 - 0.933853i) q^{92} +(3.57325 + 3.57325i) q^{93} +(6.68549 - 7.97843i) q^{94} +4.27408 q^{95} +(3.78955 - 1.78276i) q^{96} +6.49177 q^{97} +(0.908304 - 1.08397i) q^{98} +(11.4453 + 11.4453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 8 q^{4} + 12 q^{6}+O(q^{10}) \) 52 * q - 8 * q^4 + 12 * q^6	\( 52 q - 8 q^{4} + 12 q^{6} - 4 q^{10} - 4 q^{11} + 40 q^{12} + 8 q^{15} - 4 q^{16} + 8 q^{19} + 32 q^{22} + 12 q^{24} - 12 q^{26} - 24 q^{27} + 4 q^{28} + 4 q^{29} - 16 q^{34} + 4 q^{36} - 12 q^{37} + 16 q^{38} - 4 q^{42} + 36 q^{43} + 28 q^{44} - 16 q^{46} + 32 q^{48} - 52 q^{49} - 8 q^{51} - 80 q^{52} - 4 q^{53} + 48 q^{54} - 12 q^{56} - 56 q^{58} + 24 q^{59} - 16 q^{61} - 72 q^{62} - 68 q^{63} + 4 q^{64} + 40 q^{65} - 12 q^{66} - 12 q^{67} - 72 q^{69} - 8 q^{72} + 68 q^{74} - 4 q^{77} - 4 q^{78} - 16 q^{79} - 32 q^{80} - 116 q^{81} + 104 q^{82} + 16 q^{85} - 68 q^{86} - 48 q^{88} + 36 q^{90} + 64 q^{92} + 8 q^{93} - 72 q^{94} - 32 q^{95} - 52 q^{99}+O(q^{100}) \) 52 * q - 8 * q^4 + 12 * q^6 - 4 * q^10 - 4 * q^11 + 40 * q^12 + 8 * q^15 - 4 * q^16 + 8 * q^19 + 32 * q^22 + 12 * q^24 - 12 * q^26 - 24 * q^27 + 4 * q^28 + 4 * q^29 - 16 * q^34 + 4 * q^36 - 12 * q^37 + 16 * q^38 - 4 * q^42 + 36 * q^43 + 28 * q^44 - 16 * q^46 + 32 * q^48 - 52 * q^49 - 8 * q^51 - 80 * q^52 - 4 * q^53 + 48 * q^54 - 12 * q^56 - 56 * q^58 + 24 * q^59 - 16 * q^61 - 72 * q^62 - 68 * q^63 + 4 * q^64 + 40 * q^65 - 12 * q^66 - 12 * q^67 - 72 * q^69 - 8 * q^72 + 68 * q^74 - 4 * q^77 - 4 * q^78 - 16 * q^79 - 32 * q^80 - 116 * q^81 + 104 * q^82 + 16 * q^85 - 68 * q^86 - 48 * q^88 + 36 * q^90 + 64 * q^92 + 8 * q^93 - 72 * q^94 - 32 * q^95 - 52 * q^99

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