LMFDB - Embedded newform 504.2.cs.b.85.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.8
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.b.421.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14188 + 0.834337i) q^{2} +(-1.71270 - 0.258185i) q^{3} +(0.607763 - 1.90542i) q^{4} +(-1.96075 - 1.13204i) q^{5} +(2.17110 - 1.13415i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(0.895772 + 2.68283i) q^{8} +(2.86668 + 0.884386i) q^{9} +O(q^{10})$	\(q+(-1.14188 + 0.834337i) q^{2} +(-1.71270 - 0.258185i) q^{3} +(0.607763 - 1.90542i) q^{4} +(-1.96075 - 1.13204i) q^{5} +(2.17110 - 1.13415i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(0.895772 + 2.68283i) q^{8} +(2.86668 + 0.884386i) q^{9} +(3.18343 - 0.343276i) q^{10} +(3.65532 - 2.11040i) q^{11} +(-1.53287 + 3.10650i) q^{12} +(3.07695 + 1.77648i) q^{13} +(1.29350 + 0.571725i) q^{14} +(3.06589 + 2.44507i) q^{15} +(-3.26125 - 2.31609i) q^{16} -7.49338 q^{17} +(-4.01127 + 1.38192i) q^{18} -5.45165i q^{19} +(-3.34867 + 3.04803i) q^{20} +(0.632755 + 1.61233i) q^{21} +(-2.41314 + 5.45959i) q^{22} +(-1.93659 + 3.35428i) q^{23} +(-0.841521 - 4.82616i) q^{24} +(0.0630143 + 0.109144i) q^{25} +(-4.99568 + 0.538696i) q^{26} +(-4.68143 - 2.25482i) q^{27} +(-1.95402 + 0.426371i) q^{28} +(-7.98124 + 4.60797i) q^{29} +(-5.54089 - 0.233984i) q^{30} +(0.819268 - 1.41901i) q^{31} +(5.65634 - 0.0762932i) q^{32} +(-6.80535 + 2.67074i) q^{33} +(8.55652 - 6.25201i) q^{34} +2.26407i q^{35} +(3.42739 - 4.92473i) q^{36} +3.52689i q^{37} +(4.54851 + 6.22511i) q^{38} +(-4.81124 - 3.83700i) q^{39} +(1.28069 - 6.27440i) q^{40} +(-1.72349 + 2.98517i) q^{41} +(-2.06776 - 1.31315i) q^{42} +(-3.85599 + 2.22625i) q^{43} +(-1.79963 - 8.24755i) q^{44} +(-4.61967 - 4.97924i) q^{45} +(-0.587248 - 5.44594i) q^{46} +(-0.203881 - 0.353133i) q^{47} +(4.98756 + 4.80877i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.163017 - 0.0720538i) q^{50} +(12.8339 + 1.93468i) q^{51} +(5.25500 - 4.78321i) q^{52} -0.628310i q^{53} +(7.22689 - 1.33116i) q^{54} -9.55621 q^{55} +(1.87552 - 2.11718i) q^{56} +(-1.40753 + 9.33703i) q^{57} +(5.26899 - 11.9208i) q^{58} +(-9.94910 - 5.74412i) q^{59} +(6.52223 - 4.35579i) q^{60} +(-8.13933 + 4.69924i) q^{61} +(0.248433 + 2.30388i) q^{62} +(-0.667440 - 2.92481i) q^{63} +(-6.39519 + 4.80641i) q^{64} +(-4.02208 - 6.96645i) q^{65} +(5.54257 - 8.72761i) q^{66} +(4.32209 + 2.49536i) q^{67} +(-4.55420 + 14.2780i) q^{68} +(4.18283 - 5.24487i) q^{69} +(-1.88900 - 2.58529i) q^{70} +2.93942 q^{71} +(0.195232 + 8.48304i) q^{72} -7.06301 q^{73} +(-2.94262 - 4.02728i) q^{74} +(-0.0797453 - 0.203200i) q^{75} +(-10.3877 - 3.31331i) q^{76} +(-3.65532 - 2.11040i) q^{77} +(8.69519 + 0.367185i) q^{78} +(-3.06682 - 5.31188i) q^{79} +(3.77258 + 8.23311i) q^{80} +(7.43572 + 5.07051i) q^{81} +(-0.522628 - 4.84667i) q^{82} +(2.39680 - 1.38379i) q^{83} +(3.45674 - 0.225747i) q^{84} +(14.6926 + 8.48279i) q^{85} +(2.54561 - 5.75930i) q^{86} +(14.8592 - 5.83144i) q^{87} +(8.93619 + 7.91619i) q^{88} +15.3141 q^{89} +(9.42946 + 1.83132i) q^{90} -3.55296i q^{91} +(5.21432 + 5.72863i) q^{92} +(-1.76953 + 2.21882i) q^{93} +(0.527439 + 0.233128i) q^{94} +(-6.17146 + 10.6893i) q^{95} +(-9.70731 - 1.32971i) q^{96} +(-1.25455 - 2.17294i) q^{97} +(-0.151619 - 1.40606i) q^{98} +(12.3451 - 2.81713i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.14188	+	0.834337i	−0.807429	+	0.589965i
$2$	−1.14188	+	0.834337i	−0.807429	+	0.589965i
$3$	−1.71270	−	0.258185i	−0.988828	−	0.149063i
$3$	−1.71270	−	0.258185i	−0.988828	−	0.149063i
$4$	0.607763	−	1.90542i	0.303882	−	0.952710i
$5$	−1.96075	−	1.13204i	−0.876872	−	0.506262i	−0.00724614	−	0.999974i	$-0.502307\pi$
$5$	−1.96075	−	1.13204i	−0.876872	−	0.506262i	−0.869626	+	0.493712i	$0.835640\pi$
$6$	2.17110	−	1.13415i	0.886350	−	0.463016i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	0.895772	+	2.68283i	0.316703	+	0.948525i
$9$	2.86668	+	0.884386i	0.955560	+	0.294795i
$10$	3.18343	−	0.343276i	1.00669	−	0.108554i
$11$	3.65532	−	2.11040i	1.10212	−	0.636310i	0.165344	−	0.986236i	$-0.447126\pi$
$11$	3.65532	−	2.11040i	1.10212	−	0.636310i	0.936778	+	0.349926i	$0.113793\pi$
$12$	−1.53287	+	3.10650i	−0.442500	+	0.896768i
$13$	3.07695	+	1.77648i	0.853393	+	0.492707i	0.861794	−	0.507258i	$-0.169341\pi$
$13$	3.07695	+	1.77648i	0.853393	+	0.492707i	−0.00840106	+	0.999965i	$0.502674\pi$
$14$	1.29350	+	0.571725i	0.345701	+	0.152800i
$15$	3.06589	+	2.44507i	0.791610	+	0.631315i
$16$	−3.26125	−	2.31609i	−0.815312	−	0.579022i
$17$	−7.49338			−1.81741			−0.908706	−	0.417436i	$-0.862929\pi$
$17$	−7.49338			−1.81741			−0.908706	+	0.417436i	$0.862929\pi$
$18$	−4.01127	+	1.38192i	−0.945466	+	0.325721i
$19$		−	5.45165i		−	1.25069i	−0.780347	−	0.625347i	$-0.784958\pi$
$19$		−	5.45165i		−	1.25069i	0.780347	−	0.625347i	$-0.215042\pi$
$20$	−3.34867	+	3.04803i	−0.748786	+	0.681561i
$21$	0.632755	+	1.61233i	0.138079	+	0.351840i
$22$	−2.41314	+	5.45959i	−0.514484	+	1.16399i
$23$	−1.93659	+	3.35428i	−0.403808	+	0.699415i	−0.994182	−	0.107714i	$-0.965647\pi$
$23$	−1.93659	+	3.35428i	−0.403808	+	0.699415i	0.590374	+	0.807130i	$0.298980\pi$
$24$	−0.841521	−	4.82616i	−0.171775	−	0.985136i
$25$	0.0630143	+	0.109144i	0.0126029	+	0.0218288i
$26$	−4.99568	+	0.538696i	−0.979734	+	0.105647i
$27$	−4.68143	−	2.25482i	−0.900942	−	0.433941i
$28$	−1.95402	+	0.426371i	−0.369276	+	0.0805766i
$29$	−7.98124	+	4.60797i	−1.48208	+	0.855679i	−0.999793	−	0.0203354i	$-0.993527\pi$
$29$	−7.98124	+	4.60797i	−1.48208	+	0.855679i	−0.482286	+	0.876014i	$0.660193\pi$
$30$	−5.54089	−	0.233984i	−1.01162	−	0.0427193i
$31$	0.819268	−	1.41901i	0.147145	−	0.254862i	−0.783026	−	0.621989i	$-0.786325\pi$
$31$	0.819268	−	1.41901i	0.147145	−	0.254862i	0.930171	+	0.367126i	$0.119658\pi$
$32$	5.65634	−	0.0762932i	0.999909	−	0.0134869i
$33$	−6.80535	+	2.67074i	−1.18466	+	0.464916i
$34$	8.55652	−	6.25201i	1.46743	−	1.07221i
$35$			2.26407i			0.382698i
$36$	3.42739	−	4.92473i	0.571232	−	0.820789i
$37$			3.52689i			0.579818i	0.957054	+	0.289909i	$0.0936250\pi$
$37$			3.52689i			0.579818i	−0.957054	+	0.289909i	$0.906375\pi$
$38$	4.54851	+	6.22511i	0.737866	+	1.00985i
$39$	−4.81124	−	3.83700i	−0.770414	−	0.614412i
$40$	1.28069	−	6.27440i	0.202494	−	0.992069i
$41$	−1.72349	+	2.98517i	−0.269164	+	0.466206i	−0.968646	−	0.248444i	$-0.920081\pi$
$41$	−1.72349	+	2.98517i	−0.269164	+	0.466206i	0.699482	+	0.714650i	$0.253414\pi$
$42$	−2.06776	−	1.31315i	−0.319062	−	0.202624i
$43$	−3.85599	+	2.22625i	−0.588032	+	0.339501i	−0.764319	−	0.644838i	$-0.776925\pi$
$43$	−3.85599	+	2.22625i	−0.588032	+	0.339501i	0.176287	+	0.984339i	$0.443591\pi$
$44$	−1.79963	−	8.24755i	−0.271304	−	1.24337i
$45$	−4.61967	−	4.97924i	−0.688660	−	0.742262i
$46$	−0.587248	−	5.44594i	−0.0865850	−	0.802960i
$47$	−0.203881	−	0.353133i	−0.0297392	−	0.0515097i	0.850773	−	0.525534i	$-0.176134\pi$
$47$	−0.203881	−	0.353133i	−0.0297392	−	0.0515097i	−0.880512	+	0.474024i	$0.842801\pi$
$48$	4.98756	+	4.80877i	0.719892	+	0.694086i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.163017	−	0.0720538i	−0.0230542	−	0.0101899i
$51$	12.8339	+	1.93468i	1.79711	+	0.270909i
$52$	5.25500	−	4.78321i	0.728737	−	0.663312i
$53$		−	0.628310i		−	0.0863050i	−0.999068	−	0.0431525i	$-0.986260\pi$
$53$		−	0.628310i		−	0.0863050i	0.999068	−	0.0431525i	$-0.0137401\pi$
$54$	7.22689	−	1.33116i	0.983456	−	0.181148i
$55$	−9.55621			−1.28856
$56$	1.87552	−	2.11718i	0.250626	−	0.282920i
$57$	−1.40753	+	9.33703i	−0.186432	+	1.23672i
$58$	5.26899	−	11.9208i	0.691852	−	1.56527i
$59$	−9.94910	−	5.74412i	−1.29526	−	0.747820i	−0.315681	−	0.948865i	$-0.602233\pi$
$59$	−9.94910	−	5.74412i	−1.29526	−	0.747820i	−0.979582	+	0.201045i	$0.935566\pi$
$60$	6.52223	−	4.35579i	0.842016	−	0.562330i
$61$	−8.13933	+	4.69924i	−1.04213	+	0.601676i	−0.920437	−	0.390891i	$-0.872167\pi$
$61$	−8.13933	+	4.69924i	−1.04213	+	0.601676i	−0.121697	+	0.992567i	$0.538834\pi$
$62$	0.248433	+	2.30388i	0.0315510	+	0.292594i
$63$	−0.667440	−	2.92481i	−0.0840895	−	0.368492i
$64$	−6.39519	+	4.80641i	−0.799398	+	0.600801i
$65$	−4.02208	−	6.96645i	−0.498878	−	0.864082i
$66$	5.54257	−	8.72761i	0.682243	−	1.07429i
$67$	4.32209	+	2.49536i	0.528027	+	0.304857i	0.740213	−	0.672373i	$-0.234725\pi$
$67$	4.32209	+	2.49536i	0.528027	+	0.304857i	−0.212186	+	0.977229i	$0.568058\pi$
$68$	−4.55420	+	14.2780i	−0.552278	+	1.73147i
$69$	4.18283	−	5.24487i	0.503553	−	0.631408i
$70$	−1.88900	−	2.58529i	−0.225779	−	0.309001i
$71$	2.93942			0.348845			0.174422	−	0.984671i	$-0.444194\pi$
$71$	2.93942			0.348845			0.174422	+	0.984671i	$0.444194\pi$
$72$	0.195232	+	8.48304i	0.0230083	+	0.999735i
$73$	−7.06301			−0.826663			−0.413331	−	0.910581i	$-0.635635\pi$
$73$	−7.06301			−0.826663			−0.413331	+	0.910581i	$0.635635\pi$
$74$	−2.94262	−	4.02728i	−0.342072	−	0.468161i
$75$	−0.0797453	−	0.203200i	−0.00920820	−	0.0234635i
$76$	−10.3877	−	3.31331i	−1.19155	−	0.380063i
$77$	−3.65532	−	2.11040i	−0.416563	−	0.240503i
$78$	8.69519	+	0.367185i	0.984536	+	0.0415755i
$79$	−3.06682	−	5.31188i	−0.345044	−	0.597634i	0.640318	−	0.768110i	$-0.278803\pi$
$79$	−3.06682	−	5.31188i	−0.345044	−	0.597634i	−0.985362	+	0.170476i	$0.945469\pi$
$80$	3.77258	+	8.23311i	0.421787	+	0.920490i
$81$	7.43572	+	5.07051i	0.826191	+	0.563390i
$82$	−0.522628	−	4.84667i	−0.0577146	−	0.535225i
$83$	2.39680	−	1.38379i	0.263083	−	0.151891i	−0.362657	−	0.931923i	$-0.618130\pi$
$83$	2.39680	−	1.38379i	0.263083	−	0.151891i	0.625740	+	0.780032i	$0.284797\pi$
$84$	3.45674	−	0.225747i	0.377161	−	0.0246310i
$85$	14.6926	+	8.48279i	1.59364	+	0.920087i
$86$	2.54561	−	5.75930i	0.274500	−	0.621041i
$87$	14.8592	−	5.83144i	1.59307	−	0.625196i
$88$	8.93619	+	7.91619i	0.952602	+	0.843868i
$89$	15.3141			1.62329			0.811645	−	0.584151i	$-0.198572\pi$
$89$	15.3141			1.62329			0.811645	+	0.584151i	$0.198572\pi$
$90$	9.42946	+	1.83132i	0.993953	+	0.193038i
$91$		−	3.55296i		−	0.372451i
$92$	5.21432	+	5.72863i	0.543630	+	0.597251i
$93$	−1.76953	+	2.21882i	−0.183491	+	0.230081i
$94$	0.527439	+	0.233128i	0.0544012	+	0.0240454i
$95$	−6.17146	+	10.6893i	−0.633179	+	1.09670i
$96$	−9.70731	−	1.32971i	−0.990748	−	0.135713i
$97$	−1.25455	−	2.17294i	−0.127380	−	0.220628i	0.795281	−	0.606241i	$-0.207323\pi$
$97$	−1.25455	−	2.17294i	−0.127380	−	0.220628i	−0.922661	+	0.385613i	$0.873990\pi$
$98$	−0.151619	−	1.40606i	−0.0153158	−	0.142034i
$99$	12.3451	−	2.81713i	1.24073	−	0.283133i
$100$	0.246263	−	0.0537350i	0.0246263	−	0.00537350i
$101$	−5.33689	+	3.08125i	−0.531040	+	0.306596i	−0.741440	−	0.671019i	$-0.765857\pi$
$101$	−5.33689	+	3.08125i	−0.531040	+	0.306596i	0.210400	+	0.977615i	$0.432523\pi$
$102$	−16.2689	+	8.49865i	−1.61086	+	0.841492i
$103$	−8.95144	+	15.5043i	−0.882011	+	1.52769i	−0.0329099	+	0.999458i	$0.510477\pi$
$103$	−8.95144	+	15.5043i	−0.882011	+	1.52769i	−0.849101	+	0.528230i	$0.822856\pi$
$104$	−2.00975	+	9.84627i	−0.197072	+	0.965506i
$105$	0.584549	−	3.87768i	0.0570462	−	0.378423i
$106$	0.524222	+	0.717452i	0.0509170	+	0.0696851i
$107$		−	18.5677i		−	1.79501i	−0.441005	−	0.897505i	$-0.645378\pi$
$107$		−	18.5677i		−	1.79501i	0.441005	−	0.897505i	$-0.354622\pi$
$108$	−7.14158	+	7.54969i	−0.687199	+	0.726469i
$109$			12.0266i			1.15194i	0.817471	+	0.575969i	$0.195375\pi$
$109$			12.0266i			1.15194i	−0.817471	+	0.575969i	$0.804625\pi$
$110$	10.9120	−	7.97310i	1.04042	−	0.760206i
$111$	0.910590	−	6.04051i	0.0864294	−	0.573340i
$112$	−0.375168	+	3.98237i	−0.0354500	+	0.376298i
$113$	−7.06305	+	12.2336i	−0.664436	+	1.15084i	0.315002	+	0.949091i	$0.397995\pi$
$113$	−7.06305	+	12.2336i	−0.664436	+	1.15084i	−0.979438	+	0.201745i	$0.935339\pi$
$114$	−6.18301	−	11.8361i	−0.579092	−	1.10855i
$115$	7.59433	−	4.38459i	0.708175	−	0.408865i
$116$	3.92941	+	18.0082i	0.364837	+	1.67202i
$117$	7.24955	+	7.81382i	0.670221	+	0.722387i
$118$	16.1532	−	1.74183i	1.48702	−	0.160349i
$119$	3.74669	+	6.48946i	0.343459	+	0.594888i
$120$	−3.81338	+	10.4155i	−0.348113	+	0.950801i
$121$	3.40760	−	5.90214i	0.309782	−	0.536558i
$122$	5.37335	−	12.1569i	0.486481	−	1.10063i
$123$	3.72255	−	4.66773i	0.335651	−	0.420875i
$124$	−2.20590	−	2.42347i	−0.198095	−	0.217634i
$125$			11.0350i			0.987003i
$126$	3.20241	+	2.78290i	0.285294	+	0.247921i
$127$	2.38763			0.211868			0.105934	−	0.994373i	$-0.466217\pi$
$127$	2.38763			0.211868			0.105934	+	0.994373i	$0.466217\pi$
$128$	3.29235	−	10.8241i	0.291005	−	0.956722i
$129$	7.17893	−	2.81735i	0.632070	−	0.248054i
$130$	10.4051	+	4.59905i	0.912586	+	0.403363i
$131$	−8.35765	−	4.82529i	−0.730212	−	0.421588i	0.0882880	−	0.996095i	$-0.471860\pi$
$131$	−8.35765	−	4.82529i	−0.730212	−	0.421588i	−0.818500	+	0.574507i	$0.805194\pi$
$132$	0.952834	+	14.5902i	0.0829336	+	1.26992i
$133$	−4.72126	+	2.72582i	−0.409386	+	0.236359i
$134$	−7.01726	+	0.756687i	−0.606199	+	0.0653678i
$135$	6.62655	+	9.72068i	0.570323	+	0.836623i
$136$	−6.71236	−	20.1035i	−0.575580	−	1.72386i
$137$	−8.75245	−	15.1597i	−0.747773	−	1.29518i	−0.948888	−	0.315613i	$-0.897790\pi$
$137$	−8.75245	−	15.1597i	−0.747773	−	1.29518i	0.201116	−	0.979568i	$-0.435543\pi$
$138$	−0.400279	+	9.47888i	−0.0340740	+	0.806896i
$139$	5.76034	+	3.32573i	0.488585	+	0.282085i	0.723987	−	0.689813i	$-0.242307\pi$
$139$	5.76034	+	3.32573i	0.488585	+	0.282085i	−0.235402	+	0.971898i	$0.575641\pi$
$140$	4.31401	+	1.37602i	0.364600	+	0.116295i
$141$	0.258014	+	0.657450i	0.0217287	+	0.0553673i
$142$	−3.35645	+	2.45246i	−0.281667	+	0.205806i
$143$	14.9964			1.25406
$144$	−7.30064	−	9.52369i	−0.608387	−	0.793641i
$145$	20.8656			1.73279
$146$	8.06508	−	5.89293i	0.667471	−	0.487702i
$147$	1.07994	−	1.35415i	0.0890723	−	0.111688i
$148$	6.72021	+	2.14352i	0.552398	+	0.176196i
$149$	0.00641770	+	0.00370526i	0.000525758	+	0.000303547i	0.500263	−	0.865874i	$-0.333237\pi$
$149$	0.00641770	+	0.00370526i	0.000525758	+	0.000303547i	−0.499737	+	0.866177i	$0.666570\pi$
$150$	0.260597	+	0.165495i	0.0212776	+	0.0135126i
$151$	−9.02738	−	15.6359i	−0.734638	−	1.27243i	−0.954882	−	0.296985i	$-0.904019\pi$
$151$	−9.02738	−	15.6359i	−0.734638	−	1.27243i	0.220245	−	0.975445i	$-0.429314\pi$
$152$	14.6259	−	4.88343i	1.18631	−	0.396098i
$153$	−21.4811	−	6.62704i	−1.73665	−	0.535765i
$154$	5.93472	−	0.639954i	0.478233	−	0.0515690i
$155$	−3.21275	+	1.85488i	−0.258054	+	0.148988i
$156$	−10.2352	+	6.83544i	−0.819471	+	0.547273i
$157$	−17.2287	−	9.94700i	−1.37500	−	0.793857i	−0.383449	−	0.923562i	$-0.625264\pi$
$157$	−17.2287	−	9.94700i	−1.37500	−	0.793857i	−0.991553	+	0.129705i	$0.958597\pi$
$158$	7.93383	+	3.50676i	0.631181	+	0.278982i
$159$	−0.162220	+	1.07611i	−0.0128649	+	0.0853408i
$160$	−11.1770	−	6.25359i	−0.883620	−	0.494390i
$161$	3.87319			0.305250
$162$	−12.7212	+	0.414008i	−0.999471	+	0.0325276i
$163$			5.21403i			0.408395i	0.978930	+	0.204197i	$0.0654584\pi$
$163$			5.21403i			0.408395i	−0.978930	+	0.204197i	$0.934542\pi$
$164$	4.64053	+	5.09825i	0.362365	+	0.398107i
$165$	16.3669	+	2.46727i	1.27416	+	0.192077i
$166$	−1.58230	+	3.57985i	−0.122810	+	0.277851i
$167$	−5.89086	+	10.2033i	−0.455849	+	0.789553i	−0.998737	−	0.0502521i	$-0.983998\pi$
$167$	−5.89086	+	10.2033i	−0.455849	+	0.789553i	0.542888	+	0.839805i	$0.317331\pi$
$168$	−3.75882	+	3.14186i	−0.289999	+	0.242400i
$169$	−0.188240	−	0.326041i	−0.0144800	−	0.0250801i
$170$	−23.8547	+	2.57230i	−1.82957	+	0.197287i
$171$	4.82136	−	15.6281i	0.368699	−	1.19511i
$172$	1.89842	+	8.70031i	0.144753	+	0.663392i
$173$	19.7139	−	11.3818i	1.49882	−	0.865343i	0.498818	−	0.866706i	$-0.333767\pi$
$173$	19.7139	−	11.3818i	1.49882	−	0.865343i	0.999999	+	0.00136376i	$0.000434098\pi$
$174$	−12.1020	+	19.0563i	−0.917447	+	1.44466i
$175$	0.0630143	−	0.109144i	0.00476344	−	0.00825051i
$176$	−16.8088	−	1.58351i	−1.26701	−	0.119361i
$177$	15.5568	+	12.4067i	1.16932	+	0.932541i
$178$	−17.4868	+	12.7771i	−1.31069	+	0.957685i
$179$		−	0.753462i		−	0.0563164i	−0.999603	−	0.0281582i	$-0.991036\pi$
$179$		−	0.753462i		−	0.0563164i	0.999603	−	0.0281582i	$-0.00896422\pi$
$180$	−12.2952	+	5.77622i	−0.916431	+	0.430534i
$181$		−	6.56605i		−	0.488051i	−0.969769	−	0.244025i	$-0.921532\pi$
$181$		−	6.56605i		−	0.488051i	0.969769	−	0.244025i	$-0.0784680\pi$
$182$	2.96437	+	4.05704i	0.219733	+	0.300728i
$183$	15.1535	−	5.94694i	1.12018	−	0.439611i
$184$	−10.7337	−	2.19089i	−0.791300	−	0.161514i
$185$	3.99257	−	6.91534i	0.293540	−	0.508426i
$186$	0.169337	−	4.01000i	0.0124164	−	0.294028i
$187$	−27.3908	+	15.8141i	−2.00301	+	1.15644i
$188$	−0.796778	+	0.173858i	−0.0581110	+	0.0126799i
$189$	0.387982	+	5.18165i	0.0282216	+	0.376909i
$190$	−1.87142	−	17.3549i	−0.135767	−	1.25906i
$191$	8.55130	+	14.8113i	0.618751	+	1.07171i	0.989714	+	0.143060i	$0.0456942\pi$
$191$	8.55130	+	14.8113i	0.618751	+	1.07171i	−0.370963	+	0.928648i	$0.620972\pi$
$192$	12.1940	−	6.58080i	0.880024	−	0.474928i
$193$	4.89015	−	8.46998i	0.352001	−	0.609683i	−0.634599	−	0.772841i	$-0.718835\pi$
$193$	4.89015	−	8.46998i	0.352001	−	0.609683i	0.986600	+	0.163159i	$0.0521682\pi$
$194$	3.24550	+	1.43451i	0.233013	+	0.102992i
$195$	5.08999	+	12.9699i	0.364501	+	0.928792i
$196$	1.34626	+	1.47905i	0.0961614	+	0.105646i
$197$		−	11.3694i		−	0.810040i	−0.914308	−	0.405020i	$-0.867265\pi$
$197$		−	11.3694i		−	0.810040i	0.914308	−	0.405020i	$-0.132735\pi$
$198$	−11.7461	+	13.5168i	−0.834759	+	0.960594i
$199$	−12.8114			−0.908176			−0.454088	−	0.890957i	$-0.650035\pi$
$199$	−12.8114			−0.908176			−0.454088	+	0.890957i	$0.650035\pi$
$200$	−0.236369	+	0.266825i	−0.0167138	+	0.0188674i
$201$	−6.75817	−	5.38970i	−0.476685	−	0.380160i
$202$	3.52326	−	7.97118i	0.247896	−	0.560850i
$203$	7.98124	+	4.60797i	0.560173	+	0.323416i
$204$	11.4864	−	23.2782i	0.804206	−	1.62980i
$205$	6.75865	−	3.90211i	0.472045	−	0.272535i
$206$	−2.71441	−	25.1726i	−0.189122	−	1.75386i
$207$	−8.51807	+	7.90295i	−0.592047	+	0.549293i
$208$	−5.92022	−	12.9200i	−0.410494	−	0.895843i
$209$	−11.5052	−	19.9275i	−0.795829	−	1.37842i
$210$	2.56781	+	4.91554i	0.177196	+	0.339205i
$211$	10.8618	+	6.27108i	0.747759	+	0.431719i	0.824884	−	0.565303i	$-0.191241\pi$
$211$	10.8618	+	6.27108i	0.747759	+	0.431719i	−0.0771245	+	0.997021i	$0.524574\pi$
$212$	−1.19719	−	0.381864i	−0.0822236	−	0.0262265i
$213$	−5.03434	−	0.758913i	−0.344947	−	0.0519998i
$214$	15.4917	+	21.2020i	1.05899	+	1.44934i
$215$	10.0808			0.687505
$216$	1.85582	−	14.5793i	0.126272	−	0.991996i
$217$	−1.63854			−0.111231
$218$	−10.0342	−	13.7329i	−0.679604	−	0.930108i
$219$	12.0968	+	1.82356i	0.817427	+	0.123225i
$220$	−5.80792	+	18.2086i	−0.391570	+	1.22762i
$221$	−23.0568	−	13.3118i	−1.55097	−	0.895452i
$222$	4.00004	+	7.65725i	0.268465	+	0.513921i
$223$	−2.76437	−	4.78803i	−0.185116	−	0.320630i	0.758500	−	0.651674i	$-0.225933\pi$
$223$	−2.76437	−	4.78803i	−0.185116	−	0.320630i	−0.943616	+	0.331043i	$0.892599\pi$
$224$	−2.89424	−	4.86039i	−0.193380	−	0.324748i
$225$	0.0841166	+	0.368610i	0.00560777	+	0.0245740i
$226$	−2.14178	−	19.8622i	−0.142469	−	1.32121i
$227$	−11.5422	+	6.66392i	−0.766086	+	0.442300i	−0.831477	−	0.555560i	$-0.812504\pi$
$227$	−11.5422	+	6.66392i	−0.766086	+	0.442300i	0.0653906	+	0.997860i	$0.479171\pi$
$228$	16.9355	+	8.35665i	1.12158	+	0.553432i
$229$	5.56648	+	3.21381i	0.367843	+	0.212374i	0.672516	−	0.740083i	$-0.265214\pi$
$229$	5.56648	+	3.21381i	0.367843	+	0.212374i	−0.304673	+	0.952457i	$0.598547\pi$
$230$	−5.01356	+	11.3429i	−0.330584	+	0.747928i
$231$	5.71560	+	4.55824i	0.376059	+	0.299910i
$232$	−19.5118	−	17.2846i	−1.28101	−	1.13479i
$233$	6.48830			0.425063			0.212531	−	0.977154i	$-0.431829\pi$
$233$	6.48830			0.425063			0.212531	+	0.977154i	$0.431829\pi$
$234$	−14.7974	−	2.87384i	−0.967339	−	0.187869i
$235$			0.923205i			0.0602233i
$236$	−16.9916	+	15.4661i	−1.10606	+	1.00676i
$237$	3.88109	+	9.88947i	0.252104	+	0.642390i
$238$	−9.69266	−	4.28416i	−0.628282	−	0.277701i
$239$	12.1917	−	21.1167i	0.788616	−	1.36592i	−0.138198	−	0.990405i	$-0.544131\pi$
$239$	12.1917	−	21.1167i	0.788616	−	1.36592i	0.926815	−	0.375519i	$-0.122536\pi$
$240$	−4.33563	−	15.0749i	−0.279864	−	0.973079i
$241$	2.25185	+	3.90032i	0.145054	+	0.251241i	0.929393	−	0.369091i	$-0.120331\pi$
$241$	2.25185	+	3.90032i	0.145054	+	0.251241i	−0.784339	+	0.620333i	$0.786998\pi$
$242$	1.03331	+	9.58260i	0.0664239	+	0.615993i
$243$	−11.4260	−	10.6040i	−0.732980	−	0.680250i
$244$	4.00725	+	18.3649i	0.256538	+	1.17569i
$245$	1.96075	−	1.13204i	0.125267	−	0.0723232i
$246$	−0.356233	+	8.43583i	−0.0227126	+	0.537849i
$247$	9.68474	−	16.7745i	0.616225	−	1.06733i
$248$	4.54085	+	0.926847i	0.288345	+	0.0588548i
$249$	−4.46227	+	1.75120i	−0.282785	+	0.110978i
$250$	−9.20693	−	12.6006i	−0.582298	−	0.796934i
$251$		−	5.56536i		−	0.351282i	−0.984454	−	0.175641i	$-0.943800\pi$
$251$		−	5.56536i		−	0.351282i	0.984454	−	0.175641i	$-0.0561998\pi$
$252$	−5.97864	−	0.505840i	−0.376619	−	0.0318649i
$253$			16.3480i			1.02779i
$254$	−2.72638	+	1.99209i	−0.171068	+	0.124995i
$255$	−22.9739	−	18.3219i	−1.43868	−	1.14736i
$256$	5.27147	+	15.1067i	0.329467	+	0.944167i
$257$	12.2550	−	21.2262i	0.764443	−	1.32405i	−0.176097	−	0.984373i	$-0.556347\pi$
$257$	12.2550	−	21.2262i	0.764443	−	1.32405i	0.940540	−	0.339682i	$-0.110319\pi$
$258$	−5.84683	+	9.20671i	−0.364008	+	0.573185i
$259$	3.05438	−	1.76345i	0.189790	−	0.109575i
$260$	−15.7185	+	3.42980i	−0.974819	+	0.212707i
$261$	−26.9549	+	6.15109i	−1.66847	+	0.380743i
$262$	13.5693	−	1.46321i	0.838316	−	0.0903975i
$263$	−5.85004	−	10.1326i	−0.360729	−	0.624800i	0.627352	−	0.778736i	$-0.284139\pi$
$263$	−5.85004	−	10.1326i	−0.360729	−	0.624800i	−0.988081	+	0.153935i	$0.950805\pi$
$264$	−13.2612	−	15.8652i	−0.816169	−	0.976438i
$265$	−0.711270	+	1.23196i	−0.0436930	+	0.0756784i
$266$	3.11684	−	7.05168i	0.191106	−	0.432366i
$267$	−26.2284	−	3.95386i	−1.60515	−	0.241973i
$268$	7.38151	−	6.71880i	0.450897	−	0.410416i
$269$			0.932616i			0.0568626i	0.999596	+	0.0284313i	$0.00905118\pi$
$269$			0.932616i			0.0568626i	−0.999596	+	0.0284313i	$0.990949\pi$
$270$	−15.6770	−	5.57104i	−0.954073	−	0.339043i
$271$	2.29201			0.139230			0.0696150	−	0.997574i	$-0.477823\pi$
$271$	2.29201			0.139230			0.0696150	+	0.997574i	$0.477823\pi$
$272$	24.4378	+	17.3553i	1.48176	+	1.05232i
$273$	−0.917320	+	6.08515i	−0.0555187	+	0.368290i
$274$	22.6425	+	10.0080i	1.36788	+	0.604605i
$275$	0.460676	+	0.265971i	0.0277798	+	0.0160387i
$276$	−7.45151	−	11.1577i	−0.448528	−	0.671613i
$277$	−24.8567	+	14.3510i	−1.49350	+	0.862270i	−0.999972	−	0.00746305i	$-0.997624\pi$
$277$	−24.8567	+	14.3510i	−1.49350	+	0.862270i	−0.493523	+	0.869733i	$0.664291\pi$
$278$	−9.35237	+	1.00849i	−0.560918	+	0.0604851i
$279$	3.60354	−	3.34331i	0.215738	−	0.200159i
$280$	−6.07413	+	2.02809i	−0.362999	+	0.121202i
$281$	−13.5665	−	23.4979i	−0.809310	−	1.40177i	−0.913343	−	0.407192i	$-0.866508\pi$
$281$	−13.5665	−	23.4979i	−0.809310	−	1.40177i	0.104033	−	0.994574i	$-0.466825\pi$
$282$	−0.843155	−	0.535456i	−0.0502092	−	0.0318859i
$283$	15.0226	+	8.67332i	0.893003	+	0.515575i	0.874923	−	0.484261i	$-0.160912\pi$
$283$	15.0226	+	8.67332i	0.893003	+	0.515575i	0.0180792	+	0.999837i	$0.494245\pi$
$284$	1.78647	−	5.60082i	0.106007	−	0.332348i
$285$	13.3297	−	16.7142i	0.789582	−	0.990062i
$286$	−17.1240	+	12.5120i	−1.01256	+	0.739851i
$287$	3.44698			0.203469
$288$	16.2824	+	4.78368i	0.959449	+	0.281881i
$289$	39.1508			2.30299
$290$	−23.8259	+	17.4089i	−1.39910	+	1.02229i
$291$	1.58764	+	4.04549i	0.0930692	+	0.237151i
$292$	−4.29264	+	13.4580i	−0.251208	+	0.787570i
$293$	0.975764	+	0.563358i	0.0570047	+	0.0329117i	0.528232	−	0.849100i	$-0.322855\pi$
$293$	0.975764	+	0.563358i	0.0570047	+	0.0329117i	−0.471227	+	0.882012i	$0.656189\pi$
$294$	−0.103346	+	2.44731i	−0.00602728	+	0.142730i
$295$	13.0051	+	22.5255i	0.757186	+	1.31149i
$296$	−9.46207	+	3.15929i	−0.549971	+	0.183630i
$297$	−21.8707	+	1.63760i	−1.26907	+	0.0950230i
$298$	−0.0104196	+	0.00112357i	−0.000603594	+	6.50869e-5i
$299$	−11.9176	+	6.88064i	−0.689213	+	0.397917i
$300$	−0.435648	+	0.0284506i	−0.0251522	+	0.00164260i
$301$	3.85599	+	2.22625i	0.222255	+	0.128319i
$302$	23.3537	+	10.3224i	1.34386	+	0.593985i
$303$	9.93602	−	3.89936i	0.570810	−	0.224012i
$304$	−12.6265	+	17.7792i	−0.724179	+	1.01971i
$305$	21.2789			1.21842
$306$	30.0580	−	10.3552i	1.71830	−	0.591970i
$307$		−	17.5054i		−	0.999085i	−0.866289	−	0.499542i	$-0.833501\pi$
$307$		−	17.5054i		−	0.999085i	0.866289	−	0.499542i	$-0.166499\pi$
$308$	−6.24277	+	5.68230i	−0.355715	+	0.323779i
$309$	19.3341	−	24.2432i	1.09988	−	1.37915i
$310$	2.12097	−	4.79856i	0.120463	−	0.272540i
$311$	0.763492	−	1.32241i	0.0432937	−	0.0749868i	−0.843567	−	0.537025i	$-0.819548\pi$
$311$	0.763492	−	1.32241i	0.0432937	−	0.0749868i	0.886860	+	0.462038i	$0.152882\pi$
$312$	5.98426	−	16.3448i	0.338792	−	0.925343i
$313$	12.6224	+	21.8626i	0.713460	+	1.23575i	0.963550	+	0.267527i	$0.0862064\pi$
$313$	12.6224	+	21.8626i	0.713460	+	1.23575i	−0.250090	+	0.968223i	$0.580460\pi$
$314$	27.9722	−	3.01631i	1.57856	−	0.170220i
$315$	−2.00231	+	6.49038i	−0.112818	+	0.365691i
$316$	−11.9853	+	2.61521i	−0.674224	+	0.147117i
$317$	3.92560	−	2.26645i	0.220484	−	0.127296i	−0.385690	−	0.922628i	$-0.626037\pi$
$317$	3.92560	−	2.26645i	0.220484	−	0.127296i	0.606174	+	0.795332i	$0.292703\pi$
$318$	−0.712600	−	1.36413i	−0.0399606	−	0.0764964i
$319$	−19.4493	+	33.6873i	−1.08895	+	1.88612i
$320$	17.9804	−	2.18456i	1.00513	−	0.122121i
$321$	−4.79390	+	31.8009i	−0.267570	+	1.77496i
$322$	−4.42270	+	3.23154i	−0.246467	+	0.180087i
$323$			40.8513i			2.27303i
$324$	14.1806	−	11.0865i	0.787811	−	0.615917i
$325$			0.447775i			0.0248381i
$326$	−4.35026	−	5.95378i	−0.240939	−	0.329749i
$327$	3.10508	−	20.5979i	0.171712	−	1.13907i
$328$	−9.55258	−	1.94980i	−0.527453	−	0.107660i
$329$	−0.203881	+	0.353133i	−0.0112403	+	0.0194689i
$330$	−20.7475	+	10.8382i	−1.14211	+	0.596624i
$331$	−20.1650	+	11.6422i	−1.10837	+	0.639915i	−0.938406	−	0.345536i	$-0.887697\pi$
$331$	−20.1650	+	11.6422i	−1.10837	+	0.639915i	−0.169960	+	0.985451i	$0.554364\pi$
$332$	−1.18002	−	5.40792i	−0.0647619	−	0.296798i
$333$	−3.11914	+	10.1105i	−0.170928	+	0.554051i
$334$	−1.78633	−	16.5658i	−0.0977438	−	0.906443i
$335$	−5.64967	−	9.78552i	−0.308675	−	0.534640i
$336$	1.67074	−	6.72374i	0.0911461	−	0.366810i
$337$	−3.30034	+	5.71636i	−0.179781	+	0.311390i	−0.941806	−	0.336158i	$-0.890872\pi$
$337$	−3.30034	+	5.71636i	−0.179781	+	0.311390i	0.762024	+	0.647548i	$0.224206\pi$
$338$	0.486974	+	0.215243i	0.0264879	+	0.0117077i
$339$	15.2554	−	19.1288i	0.828560	−	1.03894i
$340$	25.0929	−	22.8401i	1.36085	−	1.23868i
$341$		−	6.91594i		−	0.374519i
$342$	7.53373	+	21.8680i	0.407378	+	1.18249i
$343$	1.00000			0.0539949
$344$	−9.42675	−	8.35075i	−0.508256	−	0.450242i
$345$	−14.1388	+	5.54874i	−0.761210	+	0.298734i
$346$	−13.0145	+	29.4446i	−0.699666	+	1.58295i
$347$	0.810460	+	0.467919i	0.0435078	+	0.0251192i	0.521596	−	0.853193i	$-0.325337\pi$
$347$	0.810460	+	0.467919i	0.0435078	+	0.0251192i	−0.478088	+	0.878312i	$0.658670\pi$
$348$	−2.08047	−	31.8571i	−0.111525	−	1.70772i
$349$	12.1326	−	7.00479i	0.649446	−	0.374958i	−0.138798	−	0.990321i	$-0.544324\pi$
$349$	12.1326	−	7.00479i	0.649446	−	0.374958i	0.788244	+	0.615363i	$0.210991\pi$
$350$	0.0191083	+	0.177204i	0.00102138	+	0.00947196i
$351$	−10.3989	−	15.2544i	−0.555052	−	0.814222i
$352$	20.5147	−	12.2160i	1.09344	−	0.651117i
$353$	6.66766	+	11.5487i	0.354884	+	0.614677i	0.987098	−	0.160117i	$-0.0511871\pi$
$353$	6.66766	+	11.5487i	0.354884	+	0.614677i	−0.632214	+	0.774794i	$0.717854\pi$
$354$	−28.1152	−	1.18727i	−1.49431	−	0.0631025i
$355$	−5.76345	−	3.32753i	−0.305892	−	0.176607i
$356$	9.30734	−	29.1798i	0.493288	−	1.54652i
$357$	−4.74148	−	12.0818i	−0.250946	−	0.639439i
$358$	0.628642	+	0.860361i	0.0332247	+	0.0454715i
$359$	−22.1015			−1.16647			−0.583237	−	0.812302i	$-0.698214\pi$
$359$	−22.1015			−1.16647			−0.583237	+	0.812302i	$0.698214\pi$
$360$	9.22031	−	16.8541i	0.485953	−	0.888288i
$361$	−10.7204			−0.564234
$362$	5.47830	+	7.49762i	0.287933	+	0.394066i
$363$	−7.36004	+	9.22880i	−0.386302	+	0.484386i
$364$	−6.76988	−	2.15936i	−0.354838	−	0.113181i
$365$	13.8488	+	7.99559i	0.724877	+	0.418508i
$366$	−12.3417	+	19.4338i	−0.645109	+	1.01582i
$367$	6.69889	+	11.6028i	0.349679	+	0.605662i	0.986192	−	0.165603i	$-0.0529572\pi$
$367$	6.69889	+	11.6028i	0.349679	+	0.605662i	−0.636513	+	0.771266i	$0.719624\pi$
$368$	14.0845	−	6.45381i	0.734206	−	0.336428i
$369$	−7.58074	+	7.03331i	−0.394638	+	0.366139i
$370$	1.21070	+	11.2276i	0.0629412	+	0.583696i
$371$	−0.544132	+	0.314155i	−0.0282499	+	0.0163101i
$372$	3.15233	+	4.72021i	0.163441	+	0.244732i
$373$	−13.5531	−	7.82489i	−0.701753	−	0.405157i	0.106247	−	0.994340i	$-0.466117\pi$
$373$	−13.5531	−	7.82489i	−0.701753	−	0.405157i	−0.808000	+	0.589182i	$0.799450\pi$
$374$	18.0826	−	40.9108i	0.935029	−	2.11545i
$375$	2.84908	−	18.8997i	0.147126	−	0.975976i
$376$	0.764766	−	0.863306i	0.0394398	−	0.0445216i
$377$	−32.7439			−1.68639
$378$	−4.76627	−	5.59309i	−0.245150	−	0.287678i
$379$		−	13.2858i		−	0.682446i	−0.939982	−	0.341223i	$-0.889159\pi$
$379$		−	13.2858i		−	0.682446i	0.939982	−	0.341223i	$-0.110841\pi$
$380$	16.6168	+	18.2558i	0.852423	+	0.936502i
$381$	−4.08929	−	0.616449i	−0.209501	−	0.0315817i
$382$	−22.1221	−	9.77800i	−1.13187	−	0.500286i
$383$	−0.242336	+	0.419738i	−0.0123828	+	0.0214476i	−0.872150	−	0.489238i	$-0.837275\pi$
$383$	−0.242336	+	0.419738i	−0.0123828	+	0.0214476i	0.859768	+	0.510685i	$0.170608\pi$
$384$	−8.43341	+	17.6883i	−0.430366	+	0.902655i
$385$	4.77811	+	8.27592i	0.243515	+	0.421780i
$386$	1.48288	+	13.7517i	0.0754765	+	0.699943i
$387$	−13.0228	+	2.97178i	−0.661984	+	0.151064i
$388$	−4.90283	+	1.06980i	−0.248903	+	0.0543111i
$389$	1.26506	−	0.730384i	0.0641412	−	0.0370319i	−0.467586	−	0.883947i	$-0.654876\pi$
$389$	1.26506	−	0.730384i	0.0641412	−	0.0370319i	0.531728	+	0.846915i	$0.321543\pi$
$390$	−16.6334	−	10.5632i	−0.842264	−	0.534890i
$391$	14.5116	−	25.1349i	0.733885	−	1.27113i
$392$	−2.77129	−	0.565656i	−0.139971	−	0.0285699i
$393$	13.0683	+	10.4221i	0.659210	+	0.525725i
$394$	9.48595	+	12.9825i	0.477895	+	0.654049i
$395$			13.8870i			0.698731i
$396$	2.13505	−	25.2347i	0.107290	−	1.26809i
$397$		−	14.1622i		−	0.710782i	−0.934718	−	0.355391i	$-0.884348\pi$
$397$		−	14.1622i		−	0.710782i	0.934718	−	0.355391i	$-0.115652\pi$
$398$	14.6290	−	10.6890i	0.733287	−	0.535792i
$399$	8.78987	−	3.44956i	0.440044	−	0.172694i
$400$	0.0472819	−	0.501892i	0.00236409	−	0.0250946i
$401$	−12.7115	+	22.0170i	−0.634784	+	1.09948i	0.351776	+	0.936084i	$0.385578\pi$
$401$	−12.7115	+	22.0170i	−0.634784	+	1.09948i	−0.986561	+	0.163395i	$0.947756\pi$
$402$	12.2138	+	0.515772i	0.609170	+	0.0257244i
$403$	5.04170	−	2.91083i	0.251145	−	0.144999i
$404$	2.62752	+	12.0417i	0.130724	+	0.599096i
$405$	−8.83956	−	18.3595i	−0.439241	−	0.912290i
$406$	−12.9582	+	1.39731i	−0.643104	+	0.0693474i
$407$	7.44317	+	12.8919i	0.368944	+	0.639030i
$408$	6.30584	+	36.1643i	0.312186	+	1.79040i
$409$	0.236004	−	0.408770i	0.0116696	−	0.0202124i	−0.860132	−	0.510072i	$-0.829619\pi$
$409$	0.236004	−	0.408770i	0.0116696	−	0.0202124i	0.871801	+	0.489860i	$0.162952\pi$
$410$	−4.46187	+	10.0947i	−0.220356	+	0.498543i
$411$	11.0763	+	28.2238i	0.546355	+	1.39218i
$412$	24.1019	+	26.4792i	1.18742	+	1.30454i
$413$			11.4882i			0.565299i
$414$	3.13286	−	16.1311i	0.153972	−	0.792802i
$415$	−6.26601			−0.307586
$416$	17.5398	+	9.81362i	0.859961	+	0.481152i
$417$	−9.00707	−	7.18321i	−0.441078	−	0.351763i
$418$	29.7638	+	13.1556i	1.45579	+	0.643461i
$419$	9.76183	+	5.63599i	0.476896	+	0.275336i	0.719122	−	0.694884i	$-0.244544\pi$
$419$	9.76183	+	5.63599i	0.476896	+	0.275336i	−0.242226	+	0.970220i	$0.577877\pi$
$420$	−7.03334	−	3.47052i	−0.343192	−	0.169344i
$421$	22.8845	−	13.2124i	1.11532	−	0.643932i	0.175120	−	0.984547i	$-0.443969\pi$
$421$	22.8845	−	13.2124i	1.11532	−	0.643932i	0.940203	+	0.340615i	$0.110635\pi$
$422$	−17.6351	+	1.90163i	−0.858461	+	0.0925698i
$423$	−0.272157	−	1.19263i	−0.0132327	−	0.0579876i
$424$	1.68565	−	0.562822i	0.0818624	−	0.0273331i
$425$	−0.472191	−	0.817858i	−0.0229046	−	0.0396719i
$426$	6.38178	−	3.33375i	0.309198	−	0.161521i
$427$	8.13933	+	4.69924i	0.393890	+	0.227412i
$428$	−35.3793	−	11.2848i	−1.71012	−	0.545471i
$429$	−25.6842	−	3.87183i	−1.24005	−	0.186934i
$430$	−11.5110	+	8.41079i	−0.555111	+	0.405604i
$431$	34.7290			1.67284			0.836418	−	0.548092i	$-0.184645\pi$
$431$	34.7290			1.67284			0.836418	+	0.548092i	$0.184645\pi$
$432$	10.0449	+	18.1961i	0.483287	+	0.875462i
$433$	9.19096			0.441689			0.220845	−	0.975309i	$-0.429119\pi$
$433$	9.19096			0.441689			0.220845	+	0.975309i	$0.429119\pi$
$434$	1.87101	−	1.36709i	0.0898111	−	0.0656225i
$435$	−35.7365	−	5.38717i	−1.71343	−	0.258295i
$436$	22.9157	+	7.30932i	1.09746	+	0.350053i
$437$	18.2863	+	10.5576i	0.874754	+	0.505039i
$438$	−15.3345	+	8.01054i	−0.732712	+	0.382758i
$439$	−18.2847	−	31.6701i	−0.872682	−	1.51153i	−0.859212	−	0.511620i	$-0.829046\pi$
$439$	−18.2847	−	31.6701i	−0.872682	−	1.51153i	−0.0134701	−	0.999909i	$-0.504288\pi$
$440$	−8.56018	−	25.6377i	−0.408091	−	1.22223i
$441$	−2.19924	+	2.04043i	−0.104726	+	0.0971631i
$442$	37.4346	−	4.03665i	1.78058	−	0.192004i
$443$	−0.680151	+	0.392685i	−0.0323149	+	0.0186570i	−0.516070	−	0.856546i	$-0.672606\pi$
$443$	−0.680151	+	0.392685i	−0.0323149	+	0.0186570i	0.483755	+	0.875203i	$0.339272\pi$
$444$	−10.9563	−	5.40626i	−0.519962	−	0.256570i
$445$	−30.0270	−	17.3361i	−1.42342	−	0.821811i
$446$	7.15141	+	3.16092i	0.338629	+	0.149674i
$447$	−0.0100349	−	0.00800295i	−0.000474637	−	0.000378526i
$448$	7.36007	+	3.13519i	0.347731	+	0.148124i
$449$	14.8026			0.698577			0.349288	−	0.937015i	$-0.386423\pi$
$449$	14.8026			0.698577			0.349288	+	0.937015i	$0.386423\pi$
$450$	−0.403596	−	0.350726i	−0.0190257	−	0.0165334i
$451$			14.5490i			0.685087i
$452$	19.0174	+	20.8932i	0.894503	+	0.982732i
$453$	11.4242	+	29.1103i	0.536758	+	1.36772i
$454$	7.61987	−	17.2395i	0.357618	−	0.809090i
$455$	−4.02208	+	6.96645i	−0.188558	+	0.326592i
$456$	−26.3105	+	4.58768i	−1.23210	+	0.214838i
$457$	−3.12688	−	5.41591i	−0.146269	−	0.253345i	0.783577	−	0.621295i	$-0.213393\pi$
$457$	−3.12688	−	5.41591i	−0.146269	−	0.253345i	−0.929846	+	0.367950i	$0.880060\pi$
$458$	−9.03763	+	0.974548i	−0.422301	+	0.0455376i
$459$	35.0798	+	16.8962i	1.63738	+	0.788649i
$460$	−3.73893	−	17.1352i	−0.174328	−	0.798932i
$461$	15.8425	−	9.14669i	0.737860	−	0.426004i	−0.0834305	−	0.996514i	$-0.526588\pi$
$461$	15.8425	−	9.14669i	0.737860	−	0.426004i	0.821291	+	0.570510i	$0.193254\pi$
$462$	−10.3296	−	0.436204i	−0.480577	−	0.0202941i
$463$	−7.74794	+	13.4198i	−0.360077	+	0.623672i	−0.987973	−	0.154625i	$-0.950583\pi$
$463$	−7.74794	+	13.4198i	−0.360077	+	0.623672i	0.627896	+	0.778297i	$0.283916\pi$
$464$	36.7013	+	3.45752i	1.70381	+	0.160511i
$465$	5.98138	−	2.34737i	0.277380	−	0.108857i
$466$	−7.40884	+	5.41343i	−0.343208	+	0.250772i
$467$		−	7.07138i		−	0.327224i	−0.986525	−	0.163612i	$-0.947685\pi$
$467$		−	7.07138i		−	0.327224i	0.986525	−	0.163612i	$-0.0523146\pi$
$468$	19.2946	−	9.06448i	0.891894	−	0.419006i
$469$		−	4.99072i		−	0.230450i
$470$	−0.770264	−	1.05419i	−0.0355296	−	0.0486260i
$471$	26.9395	+	21.4844i	1.24130	+	0.989950i
$472$	6.49838	−	31.8372i	0.299112	−	1.46543i
$473$	−9.39659	+	16.2754i	−0.432056	+	0.748342i
$474$	−12.6829	−	8.05441i	−0.582544	−	0.369951i
$475$	0.595015	−	0.343532i	0.0273011	−	0.0157623i
$476$	14.6422	−	3.19496i	0.671126	−	0.146441i
$477$	0.555668	−	1.80116i	0.0254423	−	0.0824696i
$478$	3.69699	+	34.2846i	0.169096	+	1.56814i
$479$	−0.637387	−	1.10399i	−0.0291229	−	0.0504424i	0.851097	−	0.525009i	$-0.175938\pi$
$479$	−0.637387	−	1.10399i	−0.0291229	−	0.0504424i	−0.880220	+	0.474567i	$0.842605\pi$
$480$	17.5283	+	13.5963i	0.800053	+	0.620582i
$481$	−6.26545	+	10.8521i	−0.285680	+	0.494812i
$482$	−5.82551	−	2.57488i	−0.265345	−	0.117282i
$483$	−6.63360	−	0.999998i	−0.301839	−	0.0455015i
$484$	−9.17503	−	10.0800i	−0.417047	−	0.458182i
$485$			5.68077i			0.257950i
$486$	21.8945	+	2.57534i	0.993153	+	0.116820i
$487$	−26.1875			−1.18667			−0.593335	−	0.804955i	$-0.702189\pi$
$487$	−26.1875			−1.18667			−0.593335	+	0.804955i	$0.702189\pi$
$488$	−19.8983	−	17.6270i	−0.900752	−	0.797937i
$489$	1.34618	−	8.93007i	0.0608765	−	0.403832i
$490$	−1.29443	+	2.92857i	−0.0584763	+	0.132299i
$491$	−17.5996	−	10.1612i	−0.794260	−	0.458566i	0.0472000	−	0.998885i	$-0.484970\pi$
$491$	−17.5996	−	10.1612i	−0.794260	−	0.458566i	−0.841460	+	0.540319i	$0.818304\pi$
$492$	−6.63155	−	9.92989i	−0.298973	−	0.447674i
$493$	59.8065	−	34.5293i	2.69355	−	1.55512i
$494$	2.93678	+	27.2347i	0.132132	+	1.22535i
$495$	−27.3946	−	8.45138i	−1.23130	−	0.379861i
$496$	−5.95840	+	2.73026i	−0.267540	+	0.122592i
$497$	−1.46971	−	2.54561i	−0.0659254	−	0.114186i
$498$	3.63426	−	5.72269i	0.162855	−	0.256440i
$499$	28.7967	+	16.6258i	1.28912	+	0.744271i	0.978496	−	0.206263i	$-0.0661304\pi$
$499$	28.7967	+	16.6258i	1.28912	+	0.744271i	0.310619	+	0.950535i	$0.399464\pi$
$500$	21.0264	+	6.70669i	0.940327	+	0.299932i
$501$	12.7236	−	15.9542i	0.568449	−	0.712782i
$502$	4.64338	+	6.35495i	0.207244	+	0.283635i
$503$	−16.6887			−0.744110			−0.372055	−	0.928211i	$-0.621347\pi$
$503$	−16.6887			−0.744110			−0.372055	+	0.928211i	$0.621347\pi$
$504$	7.24891	−	4.41059i	0.322892	−	0.196463i
$505$	13.9524			0.620872
$506$	−13.6397	−	18.6674i	−0.606359	−	0.829865i
$507$	0.238219	+	0.607010i	0.0105797	+	0.0269583i
$508$	1.45111	−	4.54943i	0.0643827	−	0.201849i
$509$	35.9654	+	20.7646i	1.59414	+	0.920376i	0.992586	+	0.121542i	$0.0387840\pi$
$509$	35.9654	+	20.7646i	1.59414	+	0.920376i	0.601552	+	0.798834i	$0.294549\pi$
$510$	41.5200	+	1.75333i	1.83854	+	0.0776387i
$511$	3.53150	+	6.11675i	0.156225	+	0.270589i
$512$	−18.6234	−	12.8518i	−0.823047	−	0.567973i
$513$	−12.2925	+	25.5215i	−0.542727	+	1.12680i
$514$	3.71617	+	34.4625i	0.163913	+	1.52007i
$515$	35.1030	−	20.2667i	1.54682	−	0.893058i
$516$	−1.00514	−	15.3912i	−0.0442488	−	0.677558i
$517$	−1.49051	−	0.860544i	−0.0655524	−	0.0378467i
$518$	−2.01641	+	4.56202i	−0.0885962	+	0.200444i
$519$	−36.7025	+	14.4038i	−1.61106	+	0.632257i
$520$	15.0870	−	17.0309i	0.661607	−	0.746855i
$521$	−15.8991			−0.696553			−0.348276	−	0.937392i	$-0.613233\pi$
$521$	−15.8991			−0.696553			−0.348276	+	0.937392i	$0.613233\pi$
$522$	25.6471	−	29.5132i	1.12254	−	1.29176i
$523$		−	9.26392i		−	0.405083i	−0.979274	−	0.202542i	$-0.935080\pi$
$523$		−	9.26392i		−	0.405083i	0.979274	−	0.202542i	$-0.0649201\pi$
$524$	−14.2737	+	12.9922i	−0.623549	+	0.567567i
$525$	−0.136104	+	0.170662i	−0.00594006	+	0.00744828i
$526$	15.1340	+	6.68923i	0.659873	+	0.291664i
$527$	−6.13909	+	10.6332i	−0.267423	+	0.463190i
$528$	28.3796	+	7.05185i	1.23506	+	0.306892i
$529$	3.99922	+	6.92684i	0.173879	+	0.301167i
$530$	−0.215684	−	2.00018i	−0.00936871	−	0.0868822i
$531$	−23.4409	−	25.2654i	−1.01725	−	1.09642i
$532$	2.32443	+	10.6526i	0.100777	+	0.461851i
$533$	−10.6062	+	6.12349i	−0.459405	+	0.265238i
$534$	33.2485	−	17.3685i	1.43880	−	0.751610i
$535$	−21.0193	+	36.4066i	−0.908746	+	1.57399i
$536$	−2.82303	+	13.8307i	−0.121936	+	0.597396i
$537$	−0.194532	+	1.29045i	−0.00839470	+	0.0556872i
$538$	−0.778116	−	1.06493i	−0.0335470	−	0.0459125i
$539$			4.22081i			0.181803i
$540$	22.5493	−	6.71848i	0.970369	−	0.289118i
$541$		−	12.0472i		−	0.517951i	−0.965884	−	0.258975i	$-0.916615\pi$
$541$		−	12.0472i		−	0.517951i	0.965884	−	0.258975i	$-0.0833849\pi$
$542$	−2.61720	+	1.91231i	−0.112418	+	0.0821409i
$543$	−1.69525	+	11.2457i	−0.0727503	+	0.482598i
$544$	−42.3851	+	0.571694i	−1.81725	+	0.0245112i
$545$	13.6145	−	23.5811i	0.583183	−	1.01010i
$546$	−4.02960	−	7.71385i	−0.172451	−	0.330122i
$547$	8.27364	−	4.77679i	0.353755	−	0.204241i	−0.312583	−	0.949891i	$-0.601194\pi$
$547$	8.27364	−	4.77679i	0.353755	−	0.204241i	0.666338	+	0.745650i	$0.267861\pi$
$548$	−34.2050	+	7.46359i	−1.46117	+	0.318829i
$549$	−27.4888	+	6.27292i	−1.17319	+	0.267722i
$550$	−0.747944	+	0.0806525i	−0.0318925	+	0.00343904i
$551$	25.1210	+	43.5109i	1.07019	+	1.85363i
$552$	17.8180	+	6.52362i	0.758383	+	0.277664i
$553$	−3.06682	+	5.31188i	−0.130414	+	0.225884i
$554$	16.4097	−	37.1260i	0.697181	−	1.57733i
$555$	−8.62351	+	10.8131i	−0.366048	+	0.458990i
$556$	9.83784	−	8.95460i	0.417217	−	0.379760i
$557$		−	34.7953i		−	1.47432i	−0.675716	−	0.737162i	$-0.736165\pi$
$557$		−	34.7953i		−	1.47432i	0.675716	−	0.737162i	$-0.263835\pi$
$558$	−1.32534	+	6.82421i	−0.0561063	+	0.288892i
$559$	−15.8196			−0.669097
$560$	5.24379	−	7.38370i	0.221591	−	0.312018i
$561$	50.9951	−	20.0129i	2.15301	−	0.844944i
$562$	35.0964	+	15.5126i	1.48045	+	0.654361i
$563$	26.7953	+	15.4703i	1.12929	+	0.651995i	0.943756	−	0.330643i	$-0.107265\pi$
$563$	26.7953	+	15.4703i	1.12929	+	0.651995i	0.185533	+	0.982638i	$0.440599\pi$
$564$	1.40953	−	0.0920512i	0.0593519	−	0.00387606i
$565$	27.6977	−	15.9913i	1.16525	−	0.672757i
$566$	−24.3905	+	2.63008i	−1.02521	+	0.110550i
$567$	0.673325	−	8.97478i	0.0282770	−	0.376905i
$568$	2.63305	+	7.88596i	0.110480	+	0.330888i
$569$	−19.5116	−	33.7950i	−0.817968	−	1.41676i	−0.907177	−	0.420749i	$-0.861767\pi$
$569$	−19.5116	−	33.7950i	−0.817968	−	1.41676i	0.0892096	−	0.996013i	$-0.471566\pi$
$570$	−1.27560	+	30.2070i	−0.0534288	+	1.26523i
$571$	−34.3138	−	19.8111i	−1.43599	−	0.829069i	−0.438421	−	0.898770i	$-0.644462\pi$
$571$	−34.3138	−	19.8111i	−1.43599	−	0.829069i	−0.997568	+	0.0697013i	$0.977795\pi$
$572$	9.11423	−	28.5743i	0.381085	−	1.19475i
$573$	−10.8218	−	27.5751i	−0.452086	−	1.15197i
$574$	−3.93603	+	2.87594i	−0.164287	+	0.120040i
$575$	−0.488132			−0.0203565
$576$	−22.5837	+	8.12264i	−0.940987	+	0.338443i
$577$	−2.66874			−0.111101			−0.0555506	−	0.998456i	$-0.517691\pi$
$577$	−2.66874			−0.111101			−0.0555506	+	0.998456i	$0.517691\pi$
$578$	−44.7054	+	32.6650i	−1.85950	+	1.35868i
$579$	−10.5622	+	13.2440i	−0.438949	+	0.550401i
$580$	12.6813	−	39.7577i	0.526563	−	1.65085i
$581$	−2.39680	−	1.38379i	−0.0994359	−	0.0574093i
$582$	−5.18820	−	3.29483i	−0.215058	−	0.136575i
$583$	−1.32599	−	2.29668i	−0.0549168	−	0.0951186i
$584$	−6.32684	−	18.9489i	−0.261807	−	0.784110i
$585$	−5.36899	−	23.5277i	−0.221981	−	0.972749i
$586$	−1.58423	+	0.170831i	−0.0654440	+	0.00705698i
$587$	−14.7287	+	8.50359i	−0.607917	+	0.350981i	−0.772150	−	0.635441i	$-0.780818\pi$
$587$	−14.7287	+	8.50359i	−0.607917	+	0.350981i	0.164233	+	0.986422i	$0.447485\pi$
$588$	−1.92387	−	2.88075i	−0.0793391	−	0.118800i
$589$	−7.73596	−	4.46636i	−0.318755	−	0.184033i
$590$	−33.6441	−	14.8707i	−1.38510	−	0.612217i
$591$	−2.93542	+	19.4725i	−0.120747	+	0.800990i
$592$	8.16860	−	11.5021i	0.335727	−	0.472732i
$593$	−21.1967			−0.870445			−0.435223	−	0.900323i	$-0.643330\pi$
$593$	−21.1967			−0.870445			−0.435223	+	0.900323i	$0.643330\pi$
$594$	23.6074	−	20.1175i	0.968622	−	0.825431i
$595$		−	16.9656i		−	0.695521i
$596$	0.0109605	−	0.00997648i	0.000448960	−	0.000408653i
$597$	21.9421	+	3.30771i	0.898029	+	0.135375i
$598$	7.86767	−	17.8001i	0.321733	−	0.727902i
$599$	−12.5142	+	21.6753i	−0.511318	+	0.885629i	0.488596	+	0.872510i	$0.337509\pi$
$599$	−12.5142	+	21.6753i	−0.511318	+	0.885629i	−0.999914	+	0.0131186i	$0.995824\pi$
$600$	0.473719	−	0.395964i	0.0193395	−	0.0161652i
$601$	−2.88320	−	4.99384i	−0.117608	−	0.203703i	0.801211	−	0.598382i	$-0.204189\pi$
$601$	−2.88320	−	4.99384i	−0.117608	−	0.203703i	−0.918819	+	0.394678i	$0.870856\pi$
$602$	−6.26051	+	0.675085i	−0.255159	+	0.0275144i
$603$	10.1832	+	10.9758i	0.414691	+	0.446969i
$604$	−35.2794	+	7.69803i	−1.43550	+	0.313228i
$605$	−13.3629	+	7.71506i	−0.543278	+	0.313662i
$606$	−8.09233	+	12.7426i	−0.328728	+	0.517632i
$607$	14.3209	−	24.8045i	0.581267	−	1.00678i	−0.414063	−	0.910248i	$-0.635891\pi$
$607$	14.3209	−	24.8045i	0.581267	−	1.00678i	0.995330	−	0.0965356i	$-0.0307762\pi$
$608$	−0.415924	−	30.8364i	−0.0168679	−	1.25058i
$609$	−12.4798	−	9.95270i	−0.505705	−	0.403304i
$610$	−24.2978	+	17.7537i	−0.983791	+	0.718828i
$611$		−	1.44876i		−	0.0586108i
$612$	−25.6828	+	36.9029i	−1.03816	+	1.49171i
$613$			27.3006i			1.10266i	0.834287	+	0.551330i	$0.185879\pi$
$613$			27.3006i			1.10266i	−0.834287	+	0.551330i	$0.814121\pi$
$614$	14.6054	+	19.9890i	0.589426	+	0.806690i
$615$	−12.5830	+	4.93816i	−0.507396	+	0.199126i
$616$	2.38752	−	11.6971i	0.0961960	−	0.471288i
$617$	−12.7201	+	22.0318i	−0.512091	+	0.886968i	0.487811	+	0.872950i	$0.337796\pi$
$617$	−12.7201	+	22.0318i	−0.512091	+	0.886968i	−0.999902	+	0.0140184i	$0.995538\pi$
$618$	−1.85019	+	43.8139i	−0.0744257	+	1.76245i
$619$	−15.6501	+	9.03562i	−0.629033	+	0.363172i	−0.780377	−	0.625309i	$-0.784973\pi$
$619$	−15.6501	+	9.03562i	−0.629033	+	0.363172i	0.151345	+	0.988481i	$0.451640\pi$
$620$	1.58174	+	7.24897i	0.0635241	+	0.291126i
$621$	16.6293	−	11.3361i	0.667312	−	0.454904i
$622$	0.231520	+	2.14704i	0.00928310	+	0.0860883i
$623$	−7.65704	−	13.2624i	−0.306773	−	0.531346i
$624$	6.80381	+	23.6567i	0.272370	+	0.947024i
$625$	12.8071	−	22.1826i	0.512285	−	0.887304i
$626$	−32.6540	−	14.4331i	−1.30512	−	0.576863i
$627$	14.5599	+	37.1003i	0.581467	+	1.48165i
$628$	−29.4242	+	26.7825i	−1.17415	+	1.06874i
$629$		−	26.4284i		−	1.05377i
$630$	−3.12877	−	9.08181i	−0.124653	−	0.361828i
$631$	16.3488			0.650834			0.325417	−	0.945571i	$-0.394495\pi$
$631$	16.3488			0.650834			0.325417	+	0.945571i	$0.394495\pi$
$632$	11.5037	−	12.9860i	0.457594	−	0.516555i
$633$	−16.9840	−	13.5448i	−0.675052	−	0.538359i
$634$	−2.59157	+	5.86328i	−0.102924	+	0.232861i
$635$	−4.68153	−	2.70288i	−0.185781	−	0.107261i
$636$	1.95184	+	0.963115i	0.0773956	+	0.0381900i
$637$	−3.07695	+	1.77648i	−0.121913	+	0.0703867i
$638$	−5.89778	−	54.6940i	−0.233495	−	2.16536i
$639$	8.42637	+	2.59958i	0.333342	+	0.102838i
$640$	−18.7087	+	17.4962i	−0.739526	+	0.691597i
$641$	15.1808	+	26.2939i	0.599606	+	1.03855i	0.992879	+	0.119126i	$0.0380094\pi$
$641$	15.1808	+	26.2939i	0.599606	+	1.03855i	−0.393273	+	0.919422i	$0.628657\pi$
$642$	−21.0587	−	40.3125i	−0.831119	−	1.59101i
$643$	−11.7101	−	6.76085i	−0.461803	−	0.266622i	0.250999	−	0.967987i	$-0.419241\pi$
$643$	−11.7101	−	6.76085i	−0.461803	−	0.266622i	−0.712802	+	0.701365i	$0.752574\pi$
$644$	2.35398	−	7.38004i	0.0927598	−	0.290814i
$645$	−17.2654	−	2.60271i	−0.679824	−	0.102482i
$646$	−34.0837	−	46.6471i	−1.34101	−	1.83531i
$647$	5.13135			0.201734			0.100867	−	0.994900i	$-0.467838\pi$
$647$	5.13135			0.201734			0.100867	+	0.994900i	$0.467838\pi$
$648$	−6.94261	+	24.4908i	−0.272732	+	0.962090i
$649$	−48.4896			−1.90338
$650$	−0.373595	−	0.511303i	−0.0146536	−	0.0200550i
$651$	2.80632	+	0.423045i	0.109988	+	0.0165804i
$652$	9.93492	+	3.16890i	0.389081	+	0.124104i
$653$	−32.7835	−	18.9275i	−1.28292	−	0.740692i	−0.305535	−	0.952181i	$-0.598835\pi$
$653$	−32.7835	−	18.9275i	−1.28292	−	0.740692i	−0.977380	+	0.211489i	$0.932169\pi$
$654$	13.6400	+	26.1110i	0.533367	+	1.02102i
$655$	10.9248	+	18.9223i	0.426868	+	0.739357i
$656$	12.5347	−	5.74363i	0.489396	−	0.224251i
$657$	−20.2474	−	6.24643i	−0.789926	−	0.243696i
$658$	−0.0618246	−	0.573340i	−0.00241017	−	0.0223511i
$659$	6.64637	−	3.83729i	0.258906	−	0.149479i	−0.364929	−	0.931035i	$-0.618907\pi$
$659$	6.64637	−	3.83729i	0.258906	−	0.149479i	0.623835	+	0.781556i	$0.285574\pi$
$660$	14.6484	−	29.6863i	0.570188	−	1.15554i
$661$	−19.5778	−	11.3033i	−0.761489	−	0.439646i	0.0683414	−	0.997662i	$-0.478229\pi$
$661$	−19.5778	−	11.3033i	−0.761489	−	0.439646i	−0.829830	+	0.558016i	$0.811563\pi$
$662$	13.3123	−	30.1184i	0.517398	−	1.17058i
$663$	36.0524	+	28.7521i	1.40016	+	1.11664i
$664$	5.85946	+	5.19064i	0.227391	+	0.201436i
$665$	12.3429			0.478638
$666$	−4.87388	−	14.1473i	−0.188859	−	0.548198i
$667$		−	35.6951i		−	1.38212i
$668$	15.8613	+	17.4257i	0.613691	+	0.674222i
$669$	3.49834	+	8.91418i	0.135254	+	0.344642i
$670$	14.6157	+	6.46012i	0.564652	+	0.249576i
$671$	−19.8346	+	34.3545i	−0.765706	+	1.32624i
$672$	3.70209	+	9.07163i	0.142811	+	0.349946i
$673$	−17.9356	−	31.0654i	−0.691366	−	1.19748i	−0.971390	−	0.237488i	$-0.923676\pi$
$673$	−17.9356	−	31.0654i	−0.691366	−	1.19748i	0.280024	−	0.959993i	$-0.409658\pi$
$674$	−1.00079	−	9.28098i	−0.0385490	−	0.357490i
$675$	−0.0488969	−	0.653036i	−0.00188204	−	0.0251354i
$676$	−0.735649	+	0.160520i	−0.0282942	+	0.00617385i
$677$	12.2522	−	7.07381i	0.470890	−	0.271869i	−0.245722	−	0.969340i	$-0.579025\pi$
$677$	12.2522	−	7.07381i	0.470890	−	0.271869i	0.716612	+	0.697472i	$0.245692\pi$
$678$	−1.45988	+	34.5709i	−0.0560663	+	1.32769i
$679$	−1.25455	+	2.17294i	−0.0481451	+	0.0833897i
$680$	−9.59667	+	47.0165i	−0.368016	+	1.80300i
$681$	21.4889	−	8.43326i	0.823458	−	0.323163i
$682$	5.77023	+	7.89715i	0.220953	+	0.302398i
$683$		−	18.2747i		−	0.699261i	−0.936888	−	0.349631i	$-0.886307\pi$
$683$		−	18.2747i		−	0.699261i	0.936888	−	0.349631i	$-0.113693\pi$
$684$	−26.8479	−	18.6849i	−1.02656	−	0.714436i
$685$			39.6324i			1.51428i
$686$	−1.14188	+	0.834337i	−0.0435970	+	0.0318551i
$687$	−8.70395	−	6.94147i	−0.332076	−	0.264834i
$688$	17.7315	+	1.67044i	0.676008	+	0.0636848i
$689$	1.11618	−	1.93328i	0.0425231	−	0.0736521i
$690$	11.5153	−	18.1325i	0.438379	−	0.690294i
$691$	−35.7979	+	20.6679i	−1.36182	+	0.786244i	−0.989865	−	0.142009i	$-0.954644\pi$
$691$	−35.7979	+	20.6679i	−1.36182	+	0.786244i	−0.371950	+	0.928253i	$0.621311\pi$
$692$	−9.70575	−	44.4806i	−0.368957	−	1.69090i
$693$	−8.61224	−	9.28257i	−0.327152	−	0.352616i
$694$	−1.31585	+	0.141891i	−0.0499489	+	0.00538610i
$695$	−7.52970	−	13.0418i	−0.285618	−	0.494705i
$696$	28.9552	+	34.6410i	1.09754	+	1.31307i
$697$	12.9148	−	22.3691i	0.489182	−	0.847288i
$698$	−8.00963	+	18.1213i	−0.303169	+	0.685902i
$699$	−11.1125	−	1.67518i	−0.420314	−	0.0633611i
$700$	−0.169667	−	0.186402i	−0.00641282	−	0.00704535i
$701$			27.0061i			1.02001i	0.860172	+	0.510004i	$0.170356\pi$
$701$			27.0061i			1.02001i	−0.860172	+	0.510004i	$0.829644\pi$
$702$	24.6016	+	8.74251i	0.928528	+	0.329965i
$703$	19.2274			0.725174
$704$	−13.2330	+	31.0654i	−0.498738	+	1.17082i
$705$	0.238357	−	1.58117i	0.00897706	−	0.0595504i
$706$	−17.2492	−	7.62414i	−0.649181	−	0.286938i
$707$	5.33689	+	3.08125i	0.200714	+	0.115882i
$708$	33.0947	−	22.1019i	1.24378	−	0.830640i
$709$	−38.4454	+	22.1965i	−1.44385	+	0.833607i	−0.998104	−	0.0615534i	$-0.980395\pi$
$709$	−38.4454	+	22.1965i	−1.44385	+	0.833607i	−0.445745	+	0.895160i	$0.647061\pi$
$710$	9.35742	−	1.00903i	0.351178	−	0.0378683i
$711$	−4.09383	−	17.9397i	−0.153531	−	0.672792i
$712$	13.7179	+	41.0851i	0.514101	+	1.53973i
$713$	3.17318	+	5.49610i	0.118836	+	0.205831i
$714$	15.4945	+	9.83997i	0.579867	+	0.368252i
$715$	−29.4040	−	16.9764i	−1.09965	−	0.634882i
$716$	−1.43566	−	0.457927i	−0.0536532	−	0.0171135i
$717$	−26.3327	+	33.0188i	−0.983415	+	1.23311i
$718$	25.2372	−	18.4401i	0.941845	−	0.688180i
$719$	−1.76124			−0.0656832			−0.0328416	−	0.999461i	$-0.510456\pi$
$719$	−1.76124			−0.0656832			−0.0328416	+	0.999461i	$0.510456\pi$
$720$	3.53353	+	26.9381i	0.131687	+	1.00392i
$721$	17.9029			0.666738
$722$	12.2414	−	8.94446i	0.455579	−	0.332879i
$723$	−2.84974	−	7.26146i	−0.105983	−	0.270057i
$724$	−12.5111	−	3.99060i	−0.464970	−	0.148310i
$725$	−1.00586	−	0.580736i	−0.0373569	−	0.0215680i
$726$	0.704325	−	16.6789i	0.0261400	−	0.619012i
$727$	−16.9314	−	29.3260i	−0.627950	−	1.08764i	−0.987962	−	0.154694i	$-0.950561\pi$
$727$	−16.9314	−	29.3260i	−0.627950	−	1.08764i	0.360012	−	0.932948i	$-0.382773\pi$
$728$	9.53200	−	3.18264i	0.353279	−	0.117956i
$729$	16.8316	+	21.1116i	0.623391	+	0.781910i
$730$	−22.4846	+	2.42456i	−0.832192	+	0.0897371i
$731$	28.8944	−	16.6822i	1.06870	−	0.617013i
$732$	−2.12168	−	32.4881i	−0.0784195	−	1.20080i
$733$	4.01087	+	2.31568i	0.148145	+	0.0855314i	0.572240	−	0.820086i	$-0.306075\pi$
$733$	4.01087	+	2.31568i	0.148145	+	0.0855314i	−0.424095	+	0.905618i	$0.639408\pi$
$734$	−17.3300	−	7.65986i	−0.639661	−	0.282730i
$735$	−3.65044	+	1.43260i	−0.134649	+	0.0528424i
$736$	−10.6981	+	19.1207i	−0.394338	+	0.704798i
$737$	21.0648			0.775933
$738$	2.78812	−	14.3561i	0.102632	−	0.528454i
$739$			2.01009i			0.0739422i	0.999316	+	0.0369711i	$0.0117710\pi$
$739$			2.01009i			0.0739422i	−0.999316	+	0.0369711i	$0.988229\pi$
$740$	−10.7501	−	11.8104i	−0.395181	−	0.434160i
$741$	−20.9180	+	26.2292i	−0.768440	+	0.963552i
$742$	0.359221	−	0.812716i	0.0131874	−	0.0298357i
$743$	−2.42210	+	4.19521i	−0.0888584	+	0.153907i	−0.907029	−	0.421068i	$-0.861655\pi$
$743$	−2.42210	+	4.19521i	−0.0888584	+	0.153907i	0.818170	+	0.574976i	$0.194989\pi$
$744$	−7.53782	−	2.75979i	−0.276350	−	0.101179i
$745$	−0.00838898	−	0.0145301i	−0.000307348	−	0.000532343i
$746$	22.0046	−	2.37280i	0.805644	−	0.0868745i
$747$	8.09466	−	1.84719i	0.296168	−	0.0675853i
$748$	13.4853	+	61.8021i	0.493072	+	2.25971i
$749$	−16.0801	+	9.28386i	−0.587555	+	0.339225i
$750$	12.5154	+	23.9582i	0.456999	+	0.874830i
$751$	1.23547	−	2.13990i	0.0450830	−	0.0780860i	−0.842603	−	0.538535i	$-0.818978\pi$
$751$	1.23547	−	2.13990i	0.0450830	−	0.0780860i	0.887686	+	0.460449i	$0.152311\pi$
$752$	−0.152979	+	1.62386i	−0.00557858	+	0.0592161i
$753$	−1.43689	+	9.53178i	−0.0523632	+	0.347358i
$754$	37.3894	−	27.3194i	1.36164	−	0.994915i
$755$			40.8773i			1.48768i
$756$	10.1090	+	2.40995i	0.367661	+	0.0876489i
$757$		−	27.0867i		−	0.984482i	−0.870459	−	0.492241i	$-0.836178\pi$
$757$		−	27.0867i		−	0.984482i	0.870459	−	0.492241i	$-0.163822\pi$
$758$	11.0848	+	15.1707i	0.402619	+	0.551026i
$759$	4.22080	−	27.9992i	0.153205	−	1.01630i
$760$	−34.2058	−	6.98185i	−1.24077	−	0.253258i
$761$	6.81649	−	11.8065i	0.247097	−	0.427985i	−0.715622	−	0.698488i	$-0.753857\pi$
$761$	6.81649	−	11.8065i	0.247097	−	0.427985i	0.962719	+	0.270503i	$0.0871899\pi$
$762$	5.18379	−	2.70794i	0.187789	−	0.0980983i
$763$	10.4153	−	6.01330i	0.377061	−	0.217696i
$764$	33.4189	−	7.29206i	1.20905	−	0.263818i
$765$	34.6170	+	37.3114i	1.25158	+	1.34900i
$766$	−0.0734854	−	0.681478i	−0.00265513	−	0.0246228i
$767$	−20.4086	−	35.3488i	−0.736912	−	1.27637i
$768$	−5.12813	−	27.2342i	−0.185046	−	0.982730i
$769$	−10.0983	+	17.4908i	−0.364154	+	0.630734i	−0.988640	−	0.150303i	$-0.951975\pi$
$769$	−10.0983	+	17.4908i	−0.364154	+	0.630734i	0.624486	+	0.781036i	$0.285309\pi$
$770$	−12.3609	−	5.46353i	−0.445457	−	0.196892i
$771$	−26.4694	+	33.1901i	−0.953270	+	1.19531i
$772$	−13.1668	−	14.4655i	−0.473884	−	0.520626i
$773$			51.3765i			1.84788i	0.382532	+	0.923942i	$0.375052\pi$
$773$			51.3765i			1.84788i	−0.382532	+	0.923942i	$0.624948\pi$
$774$	12.3909	−	14.2588i	0.445382	−	0.512521i
$775$	0.206503			0.00741779
$776$	4.70584	−	5.31219i	0.168930	−	0.190697i
$777$	−5.68653	+	2.23166i	−0.204003	+	0.0800604i
$778$	−0.835158	+	1.88950i	−0.0299419	+	0.0677417i
$779$	16.2741	+	9.39586i	0.583080	+	0.336642i
$780$	27.8066	−	1.81594i	0.995635	−	0.0650213i
$781$	10.7445	−	6.20335i	0.384469	−	0.221973i
$782$	4.40048	+	40.8085i	0.157361	+	1.45931i
$783$	47.7538	−	3.57562i	1.70658	−	0.127782i
$784$	3.63642	−	1.66628i	0.129872	−	0.0595100i
$785$	22.5207	+	39.0071i	0.803800	+	1.39222i
$786$	−23.6180	−	0.997352i	−0.842425	−	0.0355744i
$787$	6.57442	+	3.79574i	0.234353	+	0.135304i	0.612578	−	0.790410i	$-0.290132\pi$
$787$	6.57442	+	3.79574i	0.234353	+	0.135304i	−0.378226	+	0.925713i	$0.623466\pi$
$788$	−21.6636	−	6.90993i	−0.771733	−	0.246156i
$789$	7.40328	+	18.8644i	0.263564	+	0.671591i
$790$	−11.5864	−	15.8572i	−0.412227	−	0.564175i
$791$	14.1261			0.502266
$792$	18.6163	+	30.5962i	0.661500	+	1.08719i
$793$	−33.3924			−1.18580
$794$	11.8161	+	16.1715i	0.419337	+	0.573905i
$795$	1.53626	−	1.92633i	0.0544857	−	0.0683199i
$796$	−7.78629	+	24.4111i	−0.275978	+	0.865228i
$797$	0.895966	+	0.517286i	0.0317368	+	0.0183232i	0.515784	−	0.856718i	$-0.327501\pi$
$797$	0.895966	+	0.517286i	0.0317368	+	0.0183232i	−0.484048	+	0.875042i	$0.660834\pi$
$798$	−7.15886	+	11.2727i	−0.253421	+	0.399049i
$799$	1.52776	+	2.64616i	0.0540483	+	0.0936145i
$800$	0.364757	+	0.612548i	0.0128961	+	0.0216568i
$801$	43.9006	+	13.5436i	1.55115	+	0.478538i
$802$	−3.85462	−	35.7465i	−0.136111	−	1.26225i
$803$	−25.8176	+	14.9058i	−0.911083	+	0.526014i
$804$	−14.3770	+	9.60150i	−0.507038	+	0.338619i
$805$	−7.59433	−	4.38459i	−0.267665	−	0.154536i
$806$	−3.32839	+	7.53028i	−0.117237	+	0.265243i
$807$	0.240787	−	1.59729i	0.00847611	−	0.0562273i
$808$	−13.0471	−	11.5579i	−0.458996	−	0.406605i
$809$	−9.22818			−0.324445			−0.162223	−	0.986754i	$-0.551866\pi$
$809$	−9.22818			−0.324445			−0.162223	+	0.986754i	$0.551866\pi$
$810$	25.4117	+	13.5891i	0.892875	+	0.477472i
$811$		−	7.10280i		−	0.249413i	−0.992194	−	0.124707i	$-0.960201\pi$
$811$		−	7.10280i		−	0.249413i	0.992194	−	0.124707i	$-0.0397989\pi$
$812$	13.6308	−	12.4071i	0.478348	−	0.435402i
$813$	−3.92553	−	0.591763i	−0.137674	−	0.0207540i
$814$	−19.2554	−	8.51089i	−0.674901	−	0.298307i
$815$	5.90248	−	10.2234i	0.206755	−	0.358110i
$816$	−37.3737	−	36.0340i	−1.30834	−	1.26144i
$817$	12.1368	+	21.0215i	0.424611	+	0.735448i
$818$	0.0715653	+	0.663672i	0.00250222	+	0.0232047i
$819$	3.14219	−	10.1852i	0.109797	−	0.355900i
$820$	−3.32749	−	15.2496i	−0.116201	−	0.532540i
$821$	1.28103	−	0.739602i	0.0447082	−	0.0258123i	−0.477479	−	0.878643i	$-0.658449\pi$
$821$	1.28103	−	0.739602i	0.0447082	−	0.0258123i	0.522187	+	0.852831i	$0.325116\pi$
$822$	−36.1959	−	22.9867i	−1.26248	−	0.801752i
$823$	26.1957	−	45.3722i	0.913124	−	1.58158i	0.103498	−	0.994630i	$-0.466996\pi$
$823$	26.1957	−	45.3722i	0.913124	−	1.58158i	0.809625	−	0.586947i	$-0.199670\pi$
$824$	−49.6140	−	10.1269i	−1.72839	−	0.352786i
$825$	−0.720329	−	0.574468i	−0.0250787	−	0.0200004i
$826$	−9.58506	−	13.1181i	−0.333507	−	0.456438i
$827$		−	33.7993i		−	1.17532i	−0.809109	−	0.587658i	$-0.800050\pi$
$827$		−	33.7993i		−	1.17532i	0.809109	−	0.587658i	$-0.199950\pi$
$828$	9.88146	+	21.0336i	0.343405	+	0.730969i
$829$			30.3899i			1.05549i	0.849404	+	0.527743i	$0.176962\pi$
$829$			30.3899i			1.05549i	−0.849404	+	0.527743i	$0.823038\pi$
$830$	7.15501	−	5.22796i	0.248354	−	0.181465i
$831$	46.2773	−	18.1614i	1.60534	−	0.630011i
$832$	−28.2162	+	3.42818i	−0.978220	+	0.118851i
$833$	3.74669	−	6.48946i	0.129815	−	0.224847i
$834$	16.2782	+	0.687404i	0.563667	+	0.0238028i
$835$	23.1010	−	13.3373i	0.799442	−	0.461558i
$836$	−44.9627	+	9.81095i	−1.55507	+	0.339319i
$837$	−7.03497	+	4.79571i	−0.243164	+	0.165764i
$838$	−15.8491	+	1.70905i	−0.547499	+	0.0590380i
$839$	−8.58303	−	14.8662i	−0.296319	−	0.513240i	0.678972	−	0.734164i	$-0.262426\pi$
$839$	−8.58303	−	14.8662i	−0.296319	−	0.513240i	−0.975291	+	0.220925i	$0.929093\pi$
$840$	10.9268	−	1.90527i	0.377010	−	0.0657379i
$841$	27.9668	−	48.4399i	0.964372	−	1.67034i
$842$	−15.1077	+	34.1803i	−0.520646	+	1.17793i
$843$	17.1686	+	43.7475i	0.591317	+	1.50674i
$844$	18.5505	−	16.8850i	0.638533	−	0.581206i
$845$			0.852377i			0.0293227i
$846$	1.30582	+	1.13476i	0.0448952	+	0.0390140i
$847$	−6.81520			−0.234173
$848$	−1.45522	+	2.04907i	−0.0499725	+	0.0703655i
$849$	−23.4899	−	18.7334i	−0.806173	−	0.642929i
$850$	1.22155	+	0.539927i	0.0418989	+	0.0185193i
$851$	−11.8302	−	6.83016i	−0.405533	−	0.234135i
$852$	−4.50573	+	9.13129i	−0.154364	+	0.312833i
$853$	43.7227	−	25.2433i	1.49704	−	0.864314i	0.497042	−	0.867726i	$-0.334419\pi$
$853$	43.7227	−	25.2433i	1.49704	−	0.864314i	0.999994	+	0.00341211i	$0.00108611\pi$
$854$	−13.2149	+	1.42499i	−0.452203	+	0.0487621i
$855$	−27.1451	+	25.1848i	−0.928342	+	0.861303i
$856$	49.8141	−	16.6324i	1.70261	−	0.568485i
$857$	9.84470	+	17.0515i	0.336288	+	0.582469i	0.983731	−	0.179645i	$-0.0574950\pi$
$857$	9.84470	+	17.0515i	0.336288	+	0.582469i	−0.647443	+	0.762114i	$0.724162\pi$
$858$	32.5586	−	17.0082i	1.11153	−	0.580649i
$859$	14.4055	+	8.31701i	0.491509	+	0.283773i	0.725200	−	0.688538i	$-0.241747\pi$
$859$	14.4055	+	8.31701i	0.491509	+	0.283773i	−0.233691	+	0.972311i	$0.575080\pi$
$860$	6.12674	−	19.2082i	0.208920	−	0.654993i
$861$	−5.90364	−	0.889958i	−0.201196	−	0.0303297i
$862$	−39.6562	+	28.9757i	−1.35070	+	0.986916i
$863$	−13.9636			−0.475327			−0.237663	−	0.971348i	$-0.576381\pi$
$863$	−13.9636			−0.475327			−0.237663	+	0.971348i	$0.576381\pi$
$864$	−26.6518	−	12.3969i	−0.906712	−	0.421750i
$865$	−51.5385			−1.75236
$866$	−10.4949	+	7.66836i	−0.356633	+	0.260581i
$867$	−67.0536	−	10.1081i	−2.27726	−	0.343291i
$868$	−0.995842	+	3.12210i	−0.0338011	+	0.105971i
$869$	−22.4204	−	12.9444i	−0.760561	−	0.439110i
$870$	45.3013	−	23.6648i	1.53586	−	0.802311i
$871$	8.86591	+	15.3562i	0.300410	+	0.520325i
$872$	−32.2653	+	10.7731i	−1.09264	+	0.364823i
$873$	−1.67467	−	7.33862i	−0.0566789	−	0.248375i
$874$	−29.6893	+	3.20147i	−1.00426	+	0.108291i
$875$	9.55662	−	5.51751i	0.323073	−	0.186526i
$876$	10.8266	−	21.9412i	0.365799	−	0.741325i
$877$	−12.8832	−	7.43810i	−0.435034	−	0.251167i	0.266455	−	0.963847i	$-0.414148\pi$
$877$	−12.8832	−	7.43810i	−0.435034	−	0.251167i	−0.701489	+	0.712680i	$0.747481\pi$
$878$	47.3024	+	20.9077i	1.59638	+	0.705600i
$879$	−1.52574	−	1.21679i	−0.0514619	−	0.0410413i
$880$	31.1652	+	22.1330i	1.05058	+	0.746104i
$881$	22.8798			0.770841			0.385420	−	0.922741i	$-0.374056\pi$
$881$	22.8798			0.770841			0.385420	+	0.922741i	$0.374056\pi$
$882$	0.808859	−	4.16482i	0.0272357	−	0.140237i
$883$		−	10.7941i		−	0.363251i	−0.983368	−	0.181625i	$-0.941864\pi$
$883$		−	10.7941i		−	0.363251i	0.983368	−	0.181625i	$-0.0581358\pi$
$884$	−39.3777	+	35.8424i	−1.32442	+	1.20551i
$885$	−16.4581	−	41.9371i	−0.553233	−	1.40970i
$886$	0.449016	−	1.01587i	0.0150850	−	0.0341289i
$887$	−16.3887	+	28.3861i	−0.550279	+	0.953111i	0.447975	+	0.894046i	$0.352145\pi$
$887$	−16.3887	+	28.3861i	−0.550279	+	0.953111i	−0.998254	+	0.0590648i	$0.981188\pi$
$888$	17.0214	−	2.96796i	0.571199	−	0.0995981i
$889$	−1.19381	−	2.06775i	−0.0400393	−	0.0693500i
$890$	48.7513	−	5.25696i	1.63415	−	0.176214i
$891$	37.8808	+	2.84198i	1.26905	+	0.0952098i
$892$	−10.8033	+	2.35730i	−0.361721	+	0.0789282i
$893$	−1.92516	+	1.11149i	−0.0644229	+	0.0371946i
$894$	0.0181358		0.000765849i	0.000606553		2.56138e-5i
$895$	−0.852947	+	1.47735i	−0.0285109	+	0.0493823i
$896$	−11.0201	+	2.56078i	−0.368155	+	0.0855496i
$897$	22.1878	−	8.70752i	0.740828	−	0.290736i
$898$	−16.9027	+	12.3503i	−0.564051	+	0.412136i
$899$			15.1007i			0.503635i
$900$	0.753480	+	0.0637504i	0.0251160	+	0.00212501i
$901$			4.70817i			0.156852i
$902$	−12.1388	−	16.6132i	−0.404178	−	0.553159i
$903$	−6.02936	−	4.80846i	−0.200645	−	0.160016i
$904$	−39.1475	−	7.99051i	−1.30203	−	0.265760i
$905$	−7.43301	+	12.8743i	−0.247082	+	0.427958i
$906$	−37.3329	−	23.7087i	−1.24030	−	0.787668i
$907$	−22.0575	+	12.7349i	−0.732407	+	0.422855i	−0.819302	−	0.573362i	$-0.805639\pi$
$907$	−22.0575	+	12.7349i	−0.732407	+	0.422855i	0.0868954	+	0.996217i	$0.472305\pi$
$908$	5.68261	+	26.0429i	0.188584	+	0.864264i
$909$	−18.0242	+	4.11310i	−0.597824	+	0.136423i
$910$	−1.21965	−	11.3106i	−0.0404309	−	0.374943i
$911$	−25.7238	−	44.5550i	−0.852268	−	1.47617i	−0.879156	−	0.476533i	$-0.841893\pi$
$911$	−25.7238	−	44.5550i	−0.852268	−	1.47617i	0.0268883	−	0.999638i	$-0.491440\pi$
$912$	26.2157	−	27.1904i	0.868089	−	0.900364i
$913$	5.84071	−	10.1164i	0.193299	−	0.334804i
$914$	8.08920	+	3.57543i	0.267567	+	0.118265i
$915$	−36.4443	−	5.49388i	−1.20481	−	0.181622i
$916$	9.50675	−	8.65324i	0.314112	−	0.285911i
$917$			9.65059i			0.318690i
$918$	−54.1539	+	9.97492i	−1.78735	+	0.329221i
$919$	36.4531			1.20248			0.601239	−	0.799069i	$-0.294674\pi$
$919$	36.4531			1.20248			0.601239	+	0.799069i	$0.294674\pi$
$920$	18.5659	+	16.4467i	0.612100	+	0.542233i
$921$	−4.51962	+	29.9815i	−0.148927	+	0.987923i
$922$	−10.4588	+	23.6624i	−0.344442	+	0.779280i
$923$	9.04445	+	5.22181i	0.297702	+	0.171878i
$924$	12.1591	−	8.12029i	0.400004	−	0.267138i
$925$	−0.384939	+	0.222245i	−0.0126567	+	0.00730736i
$926$	−2.34947	−	21.7882i	−0.0772083	−	0.716004i
$927$	−39.3727	+	36.5295i	−1.29317	+	1.19979i
$928$	−44.7930	+	26.6732i	−1.47040	+	0.875589i
$929$	27.8331	+	48.2084i	0.913175	+	1.58166i	0.809552	+	0.587048i	$0.199710\pi$
$929$	27.8331	+	48.2084i	0.913175	+	1.58166i	0.103623	+	0.994617i	$0.466957\pi$
$930$	−4.87150	+	7.67090i	−0.159743	+	0.251539i
$931$	4.72126	+	2.72582i	0.154733	+	0.0893352i
$932$	3.94335	−	12.3629i	0.129169	−	0.404961i
$933$	−1.64906	+	2.06776i	−0.0539878	+	0.0676956i
$934$	5.89991	+	8.07464i	0.193051	+	0.264210i
$935$	71.6084			2.34184
$936$	−14.4692	+	26.4487i	−0.472941	+	0.864504i
$937$	29.8908			0.976491			0.488245	−	0.872706i	$-0.337637\pi$
$937$	29.8908			0.976491			0.488245	+	0.872706i	$0.337637\pi$
$938$	4.16394	+	5.69878i	0.135957	+	0.186072i
$939$	−15.9738	−	40.7031i	−0.521285	−	1.32829i
$940$	1.75909	+	0.561090i	0.0573753	+	0.0183007i
$941$	37.4181	+	21.6034i	1.21980	+	0.704250i	0.964874	−	0.262712i	$-0.0846169\pi$
$941$	37.4181	+	21.6034i	1.21980	+	0.704250i	0.254922	+	0.966962i	$0.417950\pi$
$942$	−48.6868	−	2.05597i	−1.58630	−	0.0669872i
$943$	−6.67540	−	11.5621i	−0.217381	−	0.376515i
$944$	19.1426	+	41.7760i	0.623039	+	1.35969i
$945$	5.10508	−	10.5991i	0.166068	−	0.344789i
$946$	−2.84940	−	26.4244i	−0.0926420	−	0.859131i
$947$	21.7150	−	12.5371i	0.705641	−	0.407402i	−0.103804	−	0.994598i	$-0.533101\pi$
$947$	21.7150	−	12.5371i	0.705641	−	0.407402i	0.809445	+	0.587196i	$0.199768\pi$
$948$	21.2024	−	1.38465i	0.688621	−	0.0449713i
$949$	−21.7325	−	12.5473i	−0.705468	−	0.407302i
$950$	−0.392812	+	0.888714i	−0.0127445	+	0.0288337i
$951$	−7.30854	+	2.86821i	−0.236996	+	0.0930082i
$952$	−14.0540	+	15.8648i	−0.455491	+	0.514182i
$953$	−58.6905			−1.90117			−0.950587	−	0.310460i	$-0.899517\pi$
$953$	−58.6905			−1.90117			−0.950587	+	0.310460i	$0.899517\pi$
$954$	0.868273	+	2.52032i	0.0281114	+	0.0815984i
$955$		−	38.7216i		−	1.25300i
$956$	−32.8264	−	36.0643i	−1.06168	−	1.16640i
$957$	42.0084	−	52.6746i	1.35794	−	1.70273i
$958$	1.64891	+	0.728820i	0.0532740	+	0.0235471i
$959$	−8.75245	+	15.1597i	−0.282631	+	0.489532i
$960$	−31.3590	−	0.900758i	−1.01211	−	0.0290718i
$961$	14.1576	+	24.5217i	0.456697	+	0.791022i
$962$	−1.89992	−	17.6192i	−0.0612560	−	0.568067i
$963$	16.4210	−	53.2277i	0.529160	−	1.71524i
$964$	8.80033	−	1.92025i	0.283440	−	0.0618470i
$965$	−19.1767	+	11.0717i	−0.617319	+	0.356409i
$966$	8.40909	−	4.39279i	0.270558	−	0.141336i
$967$	8.39908	−	14.5476i	0.270096	−	0.467820i	−0.698790	−	0.715327i	$-0.746278\pi$
$967$	8.39908	−	14.5476i	0.270096	−	0.467820i	0.968886	+	0.247507i	$0.0796112\pi$
$968$	18.8869	+	3.85506i	0.607047	+	0.123906i
$969$	10.5472	−	69.9660i	0.338824	−	2.24763i
$970$	−4.73968	−	6.48674i	−0.152182	−	0.208277i
$971$		−	42.7773i		−	1.37279i	−0.727230	−	0.686394i	$-0.759193\pi$
$971$		−	42.7773i		−	1.37279i	0.727230	−	0.686394i	$-0.240807\pi$
$972$	−27.1495	+	15.3266i	−0.870820	+	0.491602i
$973$		−	6.65146i		−	0.213236i
$974$	29.9029	−	21.8492i	0.958152	−	0.700094i
$975$	0.115609	−	0.766904i	0.00370244	−	0.0245606i
$976$	37.4282	+	3.52601i	1.19805	+	0.112865i
$977$	17.5565	−	30.4087i	0.561682	−	0.972862i	−0.435668	−	0.900107i	$-0.643488\pi$
$977$	17.5565	−	30.4087i	0.561682	−	0.972862i	0.997350	−	0.0727542i	$-0.0231789\pi$
$978$	5.91351	+	11.3202i	0.189093	+	0.361980i
$979$	55.9780	−	32.3189i	1.78906	−	1.03292i
$980$	−0.965336	−	4.42405i	−0.0308365	−	0.141321i
$981$	−10.6362	+	34.4764i	−0.339586	+	1.10075i
$982$	28.5744	−	3.08125i	0.911847	−	0.0983265i
$983$	−19.7504	−	34.2087i	−0.629940	−	1.09109i	−0.987563	−	0.157222i	$-0.949746\pi$
$983$	−19.7504	−	34.2087i	−0.629940	−	1.09109i	0.357623	−	0.933866i	$-0.383587\pi$
$984$	15.8573	+	5.80576i	0.505512	+	0.185081i
$985$	−12.8706	+	22.2926i	−0.410092	+	0.710301i
$986$	−39.4826	+	89.3270i	−1.25738	+	2.84475i
$987$	0.440361	−	0.552172i	0.0140169	−	0.0175758i
$988$	−26.0764	−	28.6484i	−0.829599	−	0.911427i
$989$		−	17.2454i		−	0.548372i
$990$	38.3326	−	13.2059i	1.21829	−	0.419711i
$991$	49.7949			1.58179			0.790894	−	0.611954i	$-0.209616\pi$
$991$	49.7949			1.58179			0.790894	+	0.611954i	$0.209616\pi$
$992$	4.52580	−	8.08893i	0.143694	−	0.256824i
$993$	37.5424	−	14.7334i	1.19137	−	0.467550i
$994$	3.80212	+	1.68054i	0.120596	+	0.0533035i
$995$	25.1199	+	14.5030i	0.796354	+	0.459775i
$996$	0.624773	+	9.56681i	0.0197967	+	0.303136i
$997$	4.55530	−	2.63000i	0.144268	−	0.0832931i	−0.426129	−	0.904663i	$-0.640123\pi$
$997$	4.55530	−	2.63000i	0.144268	−	0.0832931i	0.570396	+	0.821370i	$0.306790\pi$
$998$	−46.7537	+	5.04156i	−1.47996	+	0.159588i
$999$	7.95251	−	16.5109i	0.251606	−	0.522382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.85.8	✓	72
8.5	even	2	inner	504.2.cs.b.85.32	yes	72
9.7	even	3	inner	504.2.cs.b.421.32	yes	72
72.61	even	6	inner	504.2.cs.b.421.8	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.8	✓	72	1.1	even	1	trivial
504.2.cs.b.85.32	yes	72	8.5	even	2	inner
504.2.cs.b.421.8	yes	72	72.61	even	6	inner
504.2.cs.b.421.32	yes	72	9.7	even	3	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14188 + 0.834337i) q^{2} +(-1.71270 - 0.258185i) q^{3} +(0.607763 - 1.90542i) q^{4} +(-1.96075 - 1.13204i) q^{5} +(2.17110 - 1.13415i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(0.895772 + 2.68283i) q^{8} +(2.86668 + 0.884386i) q^{9} +O(q^{10})\)	\(q+(-1.14188 + 0.834337i) q^{2} +(-1.71270 - 0.258185i) q^{3} +(0.607763 - 1.90542i) q^{4} +(-1.96075 - 1.13204i) q^{5} +(2.17110 - 1.13415i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(0.895772 + 2.68283i) q^{8} +(2.86668 + 0.884386i) q^{9} +(3.18343 - 0.343276i) q^{10} +(3.65532 - 2.11040i) q^{11} +(-1.53287 + 3.10650i) q^{12} +(3.07695 + 1.77648i) q^{13} +(1.29350 + 0.571725i) q^{14} +(3.06589 + 2.44507i) q^{15} +(-3.26125 - 2.31609i) q^{16} -7.49338 q^{17} +(-4.01127 + 1.38192i) q^{18} -5.45165i q^{19} +(-3.34867 + 3.04803i) q^{20} +(0.632755 + 1.61233i) q^{21} +(-2.41314 + 5.45959i) q^{22} +(-1.93659 + 3.35428i) q^{23} +(-0.841521 - 4.82616i) q^{24} +(0.0630143 + 0.109144i) q^{25} +(-4.99568 + 0.538696i) q^{26} +(-4.68143 - 2.25482i) q^{27} +(-1.95402 + 0.426371i) q^{28} +(-7.98124 + 4.60797i) q^{29} +(-5.54089 - 0.233984i) q^{30} +(0.819268 - 1.41901i) q^{31} +(5.65634 - 0.0762932i) q^{32} +(-6.80535 + 2.67074i) q^{33} +(8.55652 - 6.25201i) q^{34} +2.26407i q^{35} +(3.42739 - 4.92473i) q^{36} +3.52689i q^{37} +(4.54851 + 6.22511i) q^{38} +(-4.81124 - 3.83700i) q^{39} +(1.28069 - 6.27440i) q^{40} +(-1.72349 + 2.98517i) q^{41} +(-2.06776 - 1.31315i) q^{42} +(-3.85599 + 2.22625i) q^{43} +(-1.79963 - 8.24755i) q^{44} +(-4.61967 - 4.97924i) q^{45} +(-0.587248 - 5.44594i) q^{46} +(-0.203881 - 0.353133i) q^{47} +(4.98756 + 4.80877i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.163017 - 0.0720538i) q^{50} +(12.8339 + 1.93468i) q^{51} +(5.25500 - 4.78321i) q^{52} -0.628310i q^{53} +(7.22689 - 1.33116i) q^{54} -9.55621 q^{55} +(1.87552 - 2.11718i) q^{56} +(-1.40753 + 9.33703i) q^{57} +(5.26899 - 11.9208i) q^{58} +(-9.94910 - 5.74412i) q^{59} +(6.52223 - 4.35579i) q^{60} +(-8.13933 + 4.69924i) q^{61} +(0.248433 + 2.30388i) q^{62} +(-0.667440 - 2.92481i) q^{63} +(-6.39519 + 4.80641i) q^{64} +(-4.02208 - 6.96645i) q^{65} +(5.54257 - 8.72761i) q^{66} +(4.32209 + 2.49536i) q^{67} +(-4.55420 + 14.2780i) q^{68} +(4.18283 - 5.24487i) q^{69} +(-1.88900 - 2.58529i) q^{70} +2.93942 q^{71} +(0.195232 + 8.48304i) q^{72} -7.06301 q^{73} +(-2.94262 - 4.02728i) q^{74} +(-0.0797453 - 0.203200i) q^{75} +(-10.3877 - 3.31331i) q^{76} +(-3.65532 - 2.11040i) q^{77} +(8.69519 + 0.367185i) q^{78} +(-3.06682 - 5.31188i) q^{79} +(3.77258 + 8.23311i) q^{80} +(7.43572 + 5.07051i) q^{81} +(-0.522628 - 4.84667i) q^{82} +(2.39680 - 1.38379i) q^{83} +(3.45674 - 0.225747i) q^{84} +(14.6926 + 8.48279i) q^{85} +(2.54561 - 5.75930i) q^{86} +(14.8592 - 5.83144i) q^{87} +(8.93619 + 7.91619i) q^{88} +15.3141 q^{89} +(9.42946 + 1.83132i) q^{90} -3.55296i q^{91} +(5.21432 + 5.72863i) q^{92} +(-1.76953 + 2.21882i) q^{93} +(0.527439 + 0.233128i) q^{94} +(-6.17146 + 10.6893i) q^{95} +(-9.70731 - 1.32971i) q^{96} +(-1.25455 - 2.17294i) q^{97} +(-0.151619 - 1.40606i) q^{98} +(12.3451 - 2.81713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

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