LMFDB - Embedded newform 950.2.n.a.39.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.16
Character	$\chi$	$=$	950.39
Dual form			950.2.n.a.609.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-1.33501 - 0.433772i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.407477 + 2.19863i) q^{5} +(-0.433772 - 1.33501i) q^{6} -1.42943i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.832948 - 0.605172i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-1.33501 - 0.433772i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.407477 + 2.19863i) q^{5} +(-0.433772 - 1.33501i) q^{6} -1.42943i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.832948 - 0.605172i) q^{9} +(-1.53922 + 1.62198i) q^{10} +(-0.311502 + 0.226320i) q^{11} +(0.825084 - 1.13563i) q^{12} +(-1.28246 + 1.76515i) q^{13} +(1.15643 - 0.840199i) q^{14} +(0.409717 - 3.11195i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-3.52613 + 1.14571i) q^{17} -1.02958i q^{18} +(0.309017 + 0.951057i) q^{19} +(-2.21694 - 0.291880i) q^{20} +(-0.620048 + 1.90831i) q^{21} +(-0.366193 - 0.118983i) q^{22} +(-2.85907 - 3.93518i) q^{23} +1.40372 q^{24} +(-4.66793 + 1.79178i) q^{25} -2.18184 q^{26} +(3.32474 + 4.57611i) q^{27} +(1.35947 + 0.441719i) q^{28} +(-0.490958 + 1.51101i) q^{29} +(2.75845 - 1.49769i) q^{30} +(-3.08959 - 9.50877i) q^{31} -1.00000i q^{32} +(0.514031 - 0.167019i) q^{33} +(-2.99950 - 2.17927i) q^{34} +(3.14279 - 0.582460i) q^{35} +(0.832948 - 0.605172i) q^{36} +(-0.691464 + 0.951718i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(2.47777 - 1.80020i) q^{39} +(-1.06695 - 1.96510i) q^{40} +(-9.08241 - 6.59875i) q^{41} +(-1.90831 + 0.620048i) q^{42} +3.88613i q^{43} +(-0.118983 - 0.366193i) q^{44} +(0.991141 - 2.07794i) q^{45} +(1.50310 - 4.62608i) q^{46} +(-1.87701 - 0.609877i) q^{47} +(0.825084 + 1.13563i) q^{48} +4.95672 q^{49} +(-4.19332 - 2.72325i) q^{50} +5.20441 q^{51} +(-1.28246 - 1.76515i) q^{52} +(-10.9266 - 3.55026i) q^{53} +(-1.74792 + 5.37954i) q^{54} +(-0.624522 - 0.592657i) q^{55} +(0.441719 + 1.35947i) q^{56} -1.40372i q^{57} +(-1.51101 + 0.490958i) q^{58} +(4.17081 + 3.03027i) q^{59} +(2.83303 + 1.35131i) q^{60} +(0.294533 - 0.213991i) q^{61} +(5.87674 - 8.08864i) q^{62} +(-0.865052 + 1.19064i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-4.40348 - 2.10039i) q^{65} +(0.437261 + 0.317688i) q^{66} +(-2.85217 + 0.926727i) q^{67} -3.70759i q^{68} +(2.10993 + 6.49370i) q^{69} +(2.31851 + 2.20021i) q^{70} +(-0.629945 + 1.93877i) q^{71} +(0.979189 + 0.318158i) q^{72} +(-3.25454 - 4.47950i) q^{73} -1.17639 q^{74} +(7.00897 - 0.367233i) q^{75} -1.00000 q^{76} +(0.323508 + 0.445271i) q^{77} +(2.91279 + 0.946424i) q^{78} +(-0.406201 + 1.25016i) q^{79} +(0.962665 - 2.01824i) q^{80} +(-1.49911 - 4.61379i) q^{81} -11.2265i q^{82} +(-5.74336 + 1.86613i) q^{83} +(-1.62331 - 1.17940i) q^{84} +(-3.95580 - 7.28579i) q^{85} +(-3.14395 + 2.28421i) q^{86} +(1.31087 - 1.80426i) q^{87} +(0.226320 - 0.311502i) q^{88} +(10.0616 - 7.31017i) q^{89} +(2.26366 - 0.419530i) q^{90} +(2.52316 + 1.83318i) q^{91} +(4.62608 - 1.50310i) q^{92} +14.0345i q^{93} +(-0.609877 - 1.87701i) q^{94} +(-1.96510 + 1.06695i) q^{95} +(-0.433772 + 1.33501i) q^{96} +(0.285978 + 0.0929199i) q^{97} +(2.91349 + 4.01007i) q^{98} +0.396427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−1.33501	−	0.433772i	−0.770771	−	0.250439i	−0.102876	−	0.994694i	$-0.532804\pi$
$3$	−1.33501	−	0.433772i	−0.770771	−	0.250439i	−0.667895	+	0.744256i	$0.732804\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	0.407477	+	2.19863i	0.182229	+	0.983256i
$5$	0.407477	+	2.19863i	0.182229	+	0.983256i
$6$	−0.433772	−	1.33501i	−0.177087	−	0.545017i
$7$		−	1.42943i		−	0.540275i	−0.962822	−	0.270137i	$-0.912931\pi$
$7$		−	1.42943i		−	0.540275i	0.962822	−	0.270137i	$-0.0870691\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−0.832948	−	0.605172i	−0.277649	−	0.201724i
$10$	−1.53922	+	1.62198i	−0.486744	+	0.512914i
$11$	−0.311502	+	0.226320i	−0.0939214	+	0.0682379i	−0.633755	−	0.773534i	$-0.718487\pi$
$11$	−0.311502	+	0.226320i	−0.0939214	+	0.0682379i	0.539833	+	0.841772i	$0.318487\pi$
$12$	0.825084	−	1.13563i	0.238181	−	0.327828i
$13$	−1.28246	+	1.76515i	−0.355689	+	0.489564i	−0.948941	−	0.315452i	$-0.897844\pi$
$13$	−1.28246	+	1.76515i	−0.355689	+	0.489564i	0.593252	+	0.805017i	$0.297844\pi$
$14$	1.15643	−	0.840199i	0.309070	−	0.224553i
$15$	0.409717	−	3.11195i	0.105788	−	0.803502i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−3.52613	+	1.14571i	−0.855212	+	0.277875i	−0.703627	−	0.710569i	$-0.748437\pi$
$17$	−3.52613	+	1.14571i	−0.855212	+	0.277875i	−0.151584	+	0.988444i	$0.548437\pi$
$18$		−	1.02958i		−	0.242674i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	−2.21694	−	0.291880i	−0.495722	−	0.0652663i
$21$	−0.620048	+	1.90831i	−0.135306	+	0.416428i
$22$	−0.366193	−	0.118983i	−0.0780726	−	0.0253673i
$23$	−2.85907	−	3.93518i	−0.596158	−	0.820541i	0.399192	−	0.916868i	$-0.369291\pi$
$23$	−2.85907	−	3.93518i	−0.596158	−	0.820541i	−0.995350	+	0.0963262i	$0.969291\pi$
$24$	1.40372			0.286532
$25$	−4.66793	+	1.79178i	−0.933585	+	0.358356i
$26$	−2.18184			−0.427895
$27$	3.32474	+	4.57611i	0.639847	+	0.880674i
$28$	1.35947	+	0.441719i	0.256916	+	0.0834770i
$29$	−0.490958	+	1.51101i	−0.0911687	+	0.280588i	−0.986236	−	0.165342i	$-0.947127\pi$
$29$	−0.490958	+	1.51101i	−0.0911687	+	0.280588i	0.895068	+	0.445931i	$0.147127\pi$
$30$	2.75845	−	1.49769i	0.503621	−	0.273440i
$31$	−3.08959	−	9.50877i	−0.554906	−	1.70782i	−0.696192	−	0.717856i	$-0.745124\pi$
$31$	−3.08959	−	9.50877i	−0.554906	−	1.70782i	0.141286	−	0.989969i	$-0.454876\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.514031	−	0.167019i	0.0894813	−	0.0290742i
$34$	−2.99950	−	2.17927i	−0.514411	−	0.373741i
$35$	3.14279	−	0.582460i	0.531228	−	0.0984538i
$36$	0.832948	−	0.605172i	0.138825	−	0.100862i
$37$	−0.691464	+	0.951718i	−0.113676	+	0.156462i	−0.862064	−	0.506800i	$-0.830828\pi$
$37$	−0.691464	+	0.951718i	−0.113676	+	0.156462i	0.748388	+	0.663261i	$0.230828\pi$
$38$	−0.587785	+	0.809017i	−0.0953514	+	0.131240i
$39$	2.47777	−	1.80020i	0.396761	−	0.288263i
$40$	−1.06695	−	1.96510i	−0.168699	−	0.310710i
$41$	−9.08241	−	6.59875i	−1.41843	−	1.03055i	−0.992028	−	0.126020i	$-0.959780\pi$
$41$	−9.08241	−	6.59875i	−1.41843	−	1.03055i	−0.426406	−	0.904532i	$-0.640220\pi$
$42$	−1.90831	+	0.620048i	−0.294459	+	0.0956755i
$43$			3.88613i			0.592630i	0.955090	+	0.296315i	$0.0957578\pi$
$43$			3.88613i			0.592630i	−0.955090	+	0.296315i	$0.904242\pi$
$44$	−0.118983	−	0.366193i	−0.0179374	−	0.0552056i
$45$	0.991141	−	2.07794i	0.147751	−	0.309760i
$46$	1.50310	−	4.62608i	0.221621	−	0.682078i
$47$	−1.87701	−	0.609877i	−0.273790	−	0.0889597i	0.168904	−	0.985632i	$-0.445977\pi$
$47$	−1.87701	−	0.609877i	−0.273790	−	0.0889597i	−0.442694	+	0.896673i	$0.645977\pi$
$48$	0.825084	+	1.13563i	0.119091	+	0.163914i
$49$	4.95672			0.708103
$50$	−4.19332	−	2.72325i	−0.593025	−	0.385126i
$51$	5.20441			0.728762
$52$	−1.28246	−	1.76515i	−0.177845	−	0.244782i
$53$	−10.9266	−	3.55026i	−1.50088	−	0.487666i	−0.560607	−	0.828082i	$-0.689432\pi$
$53$	−10.9266	−	3.55026i	−1.50088	−	0.487666i	−0.940275	+	0.340416i	$0.889432\pi$
$54$	−1.74792	+	5.37954i	−0.237862	+	0.732063i
$55$	−0.624522	−	0.592657i	−0.0842106	−	0.0799139i
$56$	0.441719	+	1.35947i	0.0590272	+	0.181667i
$57$		−	1.40372i		−	0.185927i
$58$	−1.51101	+	0.490958i	−0.198406	+	0.0644660i
$59$	4.17081	+	3.03027i	0.542993	+	0.394508i	0.825196	−	0.564847i	$-0.191065\pi$
$59$	4.17081	+	3.03027i	0.542993	+	0.394508i	−0.282202	+	0.959355i	$0.591065\pi$
$60$	2.83303	+	1.35131i	0.365743	+	0.174453i
$61$	0.294533	−	0.213991i	0.0377111	−	0.0273987i	−0.568770	−	0.822497i	$-0.692581\pi$
$61$	0.294533	−	0.213991i	0.0377111	−	0.0273987i	0.606481	+	0.795098i	$0.292581\pi$
$62$	5.87674	−	8.08864i	0.746347	−	1.02726i
$63$	−0.865052	+	1.19064i	−0.108986	+	0.150007i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−4.40348	−	2.10039i	−0.546184	−	0.260521i
$66$	0.437261	+	0.317688i	0.0538231	+	0.0391048i
$67$	−2.85217	+	0.926727i	−0.348448	+	0.113218i	−0.478012	−	0.878353i	$-0.658642\pi$
$67$	−2.85217	+	0.926727i	−0.348448	+	0.113218i	0.129564	+	0.991571i	$0.458642\pi$
$68$		−	3.70759i		−	0.449611i
$69$	2.10993	+	6.49370i	0.254006	+	0.781750i
$70$	2.31851	+	2.20021i	0.277114	+	0.262975i
$71$	−0.629945	+	1.93877i	−0.0747607	+	0.230090i	−0.981453	−	0.191703i	$-0.938599\pi$
$71$	−0.629945	+	1.93877i	−0.0747607	+	0.230090i	0.906692	+	0.421793i	$0.138599\pi$
$72$	0.979189	+	0.318158i	0.115399	+	0.0374952i
$73$	−3.25454	−	4.47950i	−0.380916	−	0.524285i	0.574911	−	0.818216i	$-0.305037\pi$
$73$	−3.25454	−	4.47950i	−0.380916	−	0.524285i	−0.955827	+	0.293930i	$0.905037\pi$
$74$	−1.17639			−0.136752
$75$	7.00897	−	0.367233i	0.809326	−	0.0424044i
$76$	−1.00000			−0.114708
$77$	0.323508	+	0.445271i	0.0368672	+	0.0507434i
$78$	2.91279	+	0.946424i	0.329809	+	0.107161i
$79$	−0.406201	+	1.25016i	−0.0457012	+	0.140654i	−0.971303	−	0.237844i	$-0.923559\pi$
$79$	−0.406201	+	1.25016i	−0.0457012	+	0.140654i	0.925602	+	0.378498i	$0.123559\pi$
$80$	0.962665	−	2.01824i	0.107629	−	0.225646i
$81$	−1.49911	−	4.61379i	−0.166568	−	0.512643i
$82$		−	11.2265i		−	1.23976i
$83$	−5.74336	+	1.86613i	−0.630415	+	0.204834i	−0.606759	−	0.794886i	$-0.707531\pi$
$83$	−5.74336	+	1.86613i	−0.630415	+	0.204834i	−0.0236562	+	0.999720i	$0.507531\pi$
$84$	−1.62331	−	1.17940i	−0.177117	−	0.128683i
$85$	−3.95580	−	7.28579i	−0.429067	−	0.790255i
$86$	−3.14395	+	2.28421i	−0.339021	+	0.246313i
$87$	1.31087	−	1.80426i	0.140540	−	0.193437i
$88$	0.226320	−	0.311502i	0.0241257	−	0.0332062i
$89$	10.0616	−	7.31017i	1.06653	−	0.774877i	0.0912415	−	0.995829i	$-0.470916\pi$
$89$	10.0616	−	7.31017i	1.06653	−	0.774877i	0.975285	+	0.220952i	$0.0709165\pi$
$90$	2.26366	−	0.419530i	0.238611	−	0.0442223i
$91$	2.52316	+	1.83318i	0.264499	+	0.192170i
$92$	4.62608	−	1.50310i	0.482302	−	0.156709i
$93$			14.0345i			1.45531i
$94$	−0.609877	−	1.87701i	−0.0629040	−	0.193599i
$95$	−1.96510	+	1.06695i	−0.201615	+	0.109466i
$96$	−0.433772	+	1.33501i	−0.0442717	+	0.136254i
$97$	0.285978	+	0.0929199i	0.0290367	+	0.00943459i	0.323499	−	0.946228i	$-0.395141\pi$
$97$	0.285978	+	0.0929199i	0.0290367	+	0.00943459i	−0.294463	+	0.955663i	$0.595141\pi$
$98$	2.91349	+	4.01007i	0.294307	+	0.405079i
$99$	0.396427			0.0398424
$100$	−0.261615	−	4.99315i	−0.0261615	−	0.499315i
$101$	−17.4200			−1.73335			−0.866677	−	0.498869i	$-0.833749\pi$
$101$	−17.4200			−1.73335			−0.866677	+	0.498869i	$0.833749\pi$
$102$	3.05907	+	4.21045i	0.302893	+	0.416897i
$103$	−1.63667	−	0.531785i	−0.161266	−	0.0523984i	0.227272	−	0.973831i	$-0.427019\pi$
$103$	−1.63667	−	0.531785i	−0.161266	−	0.0523984i	−0.388537	+	0.921433i	$0.627019\pi$
$104$	0.674227	−	2.07506i	0.0661134	−	0.203476i
$105$	−4.44832	−	0.585662i	−0.434112	−	0.0571548i
$106$	−3.55026	−	10.9266i	−0.344832	−	1.06128i
$107$			3.76483i			0.363960i	0.983302	+	0.181980i	$0.0582506\pi$
$107$			3.76483i			0.363960i	−0.983302	+	0.181980i	$0.941749\pi$
$108$	−5.37954	+	1.74792i	−0.517647	+	0.168194i
$109$	5.59051	+	4.06174i	0.535474	+	0.389045i	0.822401	−	0.568908i	$-0.192634\pi$
$109$	5.59051	+	4.06174i	0.535474	+	0.389045i	−0.286927	+	0.957952i	$0.592634\pi$
$110$	0.112385	−	0.853604i	0.0107155	−	0.0813880i
$111$	1.33594	−	0.970619i	0.126802	−	0.0921271i
$112$	−0.840199	+	1.15643i	−0.0793914	+	0.109273i
$113$	−7.79975	+	10.7354i	−0.733739	+	1.00990i	0.265216	+	0.964189i	$0.414557\pi$
$113$	−7.79975	+	10.7354i	−0.733739	+	1.00990i	−0.998954	+	0.0457158i	$0.985443\pi$
$114$	1.13563	−	0.825084i	0.106362	−	0.0772762i
$115$	7.48698	−	7.88953i	0.698165	−	0.735703i
$116$	−1.28535	−	0.933859i	−0.119341	−	0.0867066i
$117$	2.13644	−	0.694171i	0.197514	−	0.0641761i
$118$			5.15541i			0.474594i
$119$	1.63771	+	5.04036i	0.150129	+	0.462049i
$120$	0.571982	+	3.08625i	0.0522146	+	0.281735i
$121$	−3.35337	+	10.3206i	−0.304852	+	0.938239i
$122$	0.346244	+	0.112502i	0.0313475	+	0.0101854i
$123$	9.26278	+	12.7491i	0.835197	+	1.14955i
$124$	9.99811			0.897857
$125$	−5.84153	−	9.53292i	−0.522482	−	0.852650i
$126$	−1.47171			−0.131111
$127$	10.5187	+	14.4777i	0.933380	+	1.28469i	0.958526	+	0.285004i	$0.0919948\pi$
$127$	10.5187	+	14.4777i	0.933380	+	1.28469i	−0.0251464	+	0.999684i	$0.508005\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	1.68570	−	5.18804i	0.148417	−	0.456782i
$130$	−0.889051	−	4.79706i	−0.0779749	−	0.420730i
$131$	1.79495	+	5.52428i	0.156825	+	0.482658i	0.998341	−	0.0575739i	$-0.0183365\pi$
$131$	1.79495	+	5.52428i	0.156825	+	0.482658i	−0.841516	+	0.540232i	$0.818336\pi$
$132$			0.540484i			0.0470431i
$133$	1.35947	−	0.441719i	0.117881	−	0.0383019i
$134$	−2.42620	−	1.76274i	−0.209592	−	0.152277i
$135$	−8.70642	+	9.17453i	−0.749329	+	0.789618i
$136$	2.99950	−	2.17927i	0.257205	−	0.186871i
$137$	−6.84284	+	9.41836i	−0.584623	+	0.804664i	−0.994193	−	0.107614i	$-0.965679\pi$
$137$	−6.84284	+	9.41836i	−0.584623	+	0.804664i	0.409570	+	0.912279i	$0.365679\pi$
$138$	−4.01333	+	5.52387i	−0.341637	+	0.470223i
$139$	5.79852	−	4.21287i	0.491824	−	0.357331i	−0.314061	−	0.949403i	$-0.601690\pi$
$139$	5.79852	−	4.21287i	0.491824	−	0.357331i	0.805885	+	0.592072i	$0.201690\pi$
$140$	−0.417222	+	3.16896i	−0.0352617	+	0.267826i
$141$	2.24129	+	1.62839i	0.188750	+	0.137135i
$142$	−1.93877	+	0.629945i	−0.162698	+	0.0528638i
$143$		−	0.840093i		−	0.0702521i
$144$	0.318158	+	0.979189i	0.0265131	+	0.0815991i
$145$	−3.52221	−	0.463731i	−0.292504	−	0.0385108i
$146$	1.71102	−	5.26596i	0.141605	−	0.435814i
$147$	−6.61729	−	2.15009i	−0.545785	−	0.177336i
$148$	−0.691464	−	0.951718i	−0.0568380	−	0.0782308i
$149$	3.66183			0.299989			0.149994	−	0.988687i	$-0.452074\pi$
$149$	3.66183			0.299989			0.149994	+	0.988687i	$0.452074\pi$
$150$	4.41687	+	5.45452i	0.360636	+	0.445360i
$151$	19.5808			1.59347			0.796733	−	0.604331i	$-0.206560\pi$
$151$	19.5808			1.59347			0.796733	+	0.604331i	$0.206560\pi$
$152$	−0.587785	−	0.809017i	−0.0476757	−	0.0656199i
$153$	3.63043	+	1.17960i	0.293503	+	0.0953649i
$154$	−0.170078	+	0.523448i	−0.0137053	+	0.0421806i
$155$	19.6473	−	10.6674i	1.57811	−	0.856830i
$156$	0.946424	+	2.91279i	0.0757745	+	0.233210i
$157$			8.60781i			0.686978i	0.939157	+	0.343489i	$0.111609\pi$
$157$			8.60781i			0.686978i	−0.939157	+	0.343489i	$0.888391\pi$
$158$	−1.25016	+	0.406201i	−0.0994572	+	0.0323156i
$159$	13.0471	+	9.47930i	1.03471	+	0.751757i
$160$	2.19863	−	0.407477i	0.173817	−	0.0322139i
$161$	−5.62507	+	4.08685i	−0.443318	+	0.322089i
$162$	2.85148	−	3.92472i	0.224033	−	0.308355i
$163$	−2.16832	+	2.98444i	−0.169836	+	0.233759i	−0.885448	−	0.464739i	$-0.846148\pi$
$163$	−2.16832	+	2.98444i	−0.169836	+	0.233759i	0.715611	+	0.698499i	$0.246148\pi$
$164$	9.08241	−	6.59875i	0.709217	−	0.515276i
$165$	0.576668	+	1.06211i	0.0448935	+	0.0826848i
$166$	−4.88559	−	3.54959i	−0.379195	−	0.275502i
$167$	−16.4604	+	5.34832i	−1.27375	+	0.413865i	−0.866373	−	0.499397i	$-0.833555\pi$
$167$	−16.4604	+	5.34832i	−1.27375	+	0.413865i	−0.407373	+	0.913262i	$0.633555\pi$
$168$		−	2.00652i		−	0.154806i
$169$	2.54616	+	7.83628i	0.195859	+	0.602791i
$170$	3.56917	−	7.48279i	0.273743	−	0.573904i
$171$	0.318158	−	0.979189i	0.0243301	−	0.0748804i
$172$	−3.69593	−	1.20088i	−0.281812	−	0.0915663i
$173$	8.22963	+	11.3271i	0.625687	+	0.861184i	0.997751	−	0.0670227i	$-0.0213500\pi$
$173$	8.22963	+	11.3271i	0.625687	+	0.861184i	−0.372065	+	0.928207i	$0.621350\pi$
$174$	2.23019			0.169070
$175$	2.56123	+	6.67248i	0.193611	+	0.504392i
$176$	0.385038			0.0290233
$177$	−4.25364	−	5.85464i	−0.319723	−	0.440061i
$178$	11.8281	+	3.84318i	0.886554	+	0.288059i
$179$	−0.640865	+	1.97238i	−0.0479005	+	0.147423i	−0.972146	−	0.234376i	$-0.924695\pi$
$179$	−0.640865	+	1.97238i	−0.0479005	+	0.147423i	0.924245	+	0.381799i	$0.124695\pi$
$180$	1.66995	+	1.58475i	0.124471	+	0.118120i
$181$	1.51176	+	4.65270i	0.112368	+	0.345833i	0.991389	−	0.130950i	$-0.0418028\pi$
$181$	1.51176	+	4.65270i	0.112368	+	0.345833i	−0.879021	+	0.476783i	$0.841803\pi$
$182$			3.11880i			0.231181i
$183$	−0.486029	+	0.157920i	−0.0359283	+	0.0116738i
$184$	3.93518	+	2.85907i	0.290105	+	0.210774i
$185$	−2.37423	−	1.13247i	−0.174557	−	0.0832607i
$186$	−11.3542	+	8.24928i	−0.832527	+	0.604866i
$187$	0.839100	−	1.15492i	0.0613611	−	0.0844563i
$188$	1.16006	−	1.59668i	0.0846057	−	0.116450i
$189$	6.54124	−	4.75249i	0.475806	−	0.345693i
$190$	−2.01824	−	0.962665i	−0.146418	−	0.0698391i
$191$	12.4460	+	9.04257i	0.900563	+	0.654297i	0.938611	−	0.344979i	$-0.112114\pi$
$191$	12.4460	+	9.04257i	0.900563	+	0.654297i	−0.0380474	+	0.999276i	$0.512114\pi$
$192$	−1.33501	+	0.433772i	−0.0963463	+	0.0313048i
$193$		−	20.6914i		−	1.48940i	−0.667400	−	0.744699i	$-0.732593\pi$
$193$		−	20.6914i		−	1.48940i	0.667400	−	0.744699i	$-0.267407\pi$
$194$	0.0929199	+	0.285978i	0.00667126	+	0.0205320i
$195$	4.96761	+	4.71415i	0.355738	+	0.337587i
$196$	−1.53171	+	4.71412i	−0.109408	+	0.336723i
$197$	15.6488	+	5.08460i	1.11493	+	0.362263i	0.807831	−	0.589414i	$-0.200641\pi$
$197$	15.6488	+	5.08460i	1.11493	+	0.362263i	0.307100	+	0.951677i	$0.400641\pi$
$198$	0.233014	+	0.320716i	0.0165596	+	0.0227923i
$199$	3.02063			0.214127			0.107063	−	0.994252i	$-0.465855\pi$
$199$	3.02063			0.214127			0.107063	+	0.994252i	$0.465855\pi$
$200$	3.88577	−	3.14655i	0.274765	−	0.222495i
$201$	4.20968			0.296928
$202$	−10.2392	−	14.0931i	−0.720429	−	0.991585i
$203$	2.15989	+	0.701792i	0.151595	+	0.0492561i
$204$	−1.60825	+	4.94968i	−0.112600	+	0.346547i
$205$	10.8073	−	22.6577i	0.754817	−	1.58248i
$206$	−0.531785	−	1.63667i	−0.0370512	−	0.114032i
$207$			5.00803i			0.348082i
$208$	2.07506	−	0.674227i	0.143879	−	0.0467492i
$209$	−0.311502	−	0.226320i	−0.0215471	−	0.0156549i
$210$	−2.14085	−	3.94301i	−0.147732	−	0.272094i
$211$	19.1417	−	13.9073i	1.31777	−	0.957416i	0.317812	−	0.948154i	$-0.397052\pi$
$211$	19.1417	−	13.9073i	1.31777	−	0.957416i	0.999957	−	0.00926191i	$-0.00294820\pi$
$212$	6.75300	−	9.29471i	0.463798	−	0.638363i
$213$	1.68197	−	2.31503i	0.115247	−	0.158623i
$214$	−3.04581	+	2.21291i	−0.208208	+	0.151272i
$215$	−8.54416	+	1.58351i	−0.582707	+	0.107994i
$216$	−4.57611	−	3.32474i	−0.311365	−	0.226220i
$217$	−13.5921	+	4.41635i	−0.922694	+	0.299802i
$218$			6.91025i			0.468021i
$219$	2.40178	+	7.39192i	0.162297	+	0.499500i
$220$	0.756639	−	0.410815i	0.0510126	−	0.0276971i
$221$	2.49976	−	7.69346i	0.168152	−	0.517518i
$222$	1.57049	+	0.510285i	0.105405	+	0.0342481i
$223$	−4.25763	−	5.86013i	−0.285112	−	0.392423i	0.642307	−	0.766448i	$-0.277978\pi$
$223$	−4.25763	−	5.86013i	−0.285112	−	0.392423i	−0.927419	+	0.374025i	$0.877978\pi$
$224$	−1.42943			−0.0955080
$225$	4.97247	+	1.33244i	0.331498	+	0.0888293i
$226$	−13.2697			−0.882689
$227$	0.357834	+	0.492516i	0.0237503	+	0.0326894i	0.820727	−	0.571321i	$-0.193569\pi$
$227$	0.357834	+	0.492516i	0.0237503	+	0.0326894i	−0.796977	+	0.604010i	$0.793569\pi$
$228$	1.33501	+	0.433772i	0.0884134	+	0.0287273i
$229$	−6.14445	+	18.9107i	−0.406037	+	1.24965i	0.513989	+	0.857797i	$0.328167\pi$
$229$	−6.14445	+	18.9107i	−0.406037	+	1.24965i	−0.920026	+	0.391857i	$0.871833\pi$
$230$	10.7835	+	1.41975i	0.711043	+	0.0936153i
$231$	−0.238742	−	0.734772i	−0.0157081	−	0.0483445i
$232$		−	1.58878i		−	0.104308i
$233$	−10.5168	+	3.41711i	−0.688977	+	0.223862i	−0.632522	−	0.774543i	$-0.717980\pi$
$233$	−10.5168	+	3.41711i	−0.688977	+	0.223862i	−0.0564559	+	0.998405i	$0.517980\pi$
$234$	1.81736	+	1.32039i	0.118805	+	0.0863167i
$235$	0.576055	−	4.37535i	0.0375777	−	0.285417i
$236$	−4.17081	+	3.03027i	−0.271497	+	0.197254i
$237$	1.08457	−	1.49278i	0.0704502	−	0.0969664i
$238$	−3.11511	+	4.28759i	−0.201923	+	0.277923i
$239$	19.0696	−	13.8549i	1.23351	−	0.896198i	0.236362	−	0.971665i	$-0.424045\pi$
$239$	19.0696	−	13.8549i	1.23351	−	0.896198i	0.997148	+	0.0754672i	$0.0240448\pi$
$240$	−2.16063	+	2.27679i	−0.139468	+	0.146966i
$241$	−16.7758	−	12.1884i	−1.08063	−	0.785122i	−0.102835	−	0.994698i	$-0.532791\pi$
$241$	−16.7758	−	12.1884i	−1.08063	−	0.785122i	−0.977792	+	0.209577i	$0.932791\pi$
$242$	−10.3206	+	3.35337i	−0.663435	+	0.215563i
$243$		−	10.1594i		−	0.651727i
$244$	0.112502	+	0.346244i	0.00720218	+	0.0221660i
$245$	2.01975	+	10.8980i	0.129037	+	0.696247i
$246$	−4.86973	+	14.9875i	−0.310483	+	0.955568i
$247$	−2.07506	−	0.674227i	−0.132033	−	0.0429000i
$248$	5.87674	+	8.08864i	0.373173	+	0.513629i
$249$	8.47694			0.537204
$250$	4.27873	−	10.3292i	0.270611	−	0.653276i
$251$	−13.7674			−0.868988			−0.434494	−	0.900675i	$-0.643073\pi$
$251$	−13.7674			−0.868988			−0.434494	+	0.900675i	$0.643073\pi$
$252$	−0.865052	−	1.19064i	−0.0544932	−	0.0750034i
$253$	1.78122	+	0.578752i	0.111984	+	0.0363858i
$254$	−5.52999	+	17.0195i	−0.346982	+	1.06790i
$255$	2.12067	+	11.4425i	0.132802	+	0.716560i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			27.0774i			1.68904i	0.535523	+	0.844520i	$0.320114\pi$
$257$			27.0774i			1.68904i	−0.535523	+	0.844520i	$0.679886\pi$
$258$	5.18804	−	1.68570i	0.322993	−	0.104947i
$259$	1.36042	+	0.988400i	0.0845322	+	0.0614162i
$260$	3.35834	−	3.53890i	0.208275	−	0.219473i
$261$	1.32337	−	0.961482i	0.0819143	−	0.0595143i
$262$	−3.41419	+	4.69923i	−0.210929	+	0.290319i
$263$	−8.53910	+	11.7531i	−0.526543	+	0.724725i	−0.986599	−	0.163165i	$-0.947830\pi$
$263$	−8.53910	+	11.7531i	−0.526543	+	0.724725i	0.460055	+	0.887890i	$0.347830\pi$
$264$	−0.437261	+	0.317688i	−0.0269115	+	0.0195524i
$265$	3.35338	−	25.4701i	0.205996	−	1.56462i
$266$	1.15643	+	0.840199i	0.0709056	+	0.0515159i
$267$	−16.6033	+	5.39474i	−1.01611	+	0.330153i
$268$		−	2.99895i		−	0.183190i
$269$	−3.08376	−	9.49084i	−0.188020	−	0.578666i	0.811967	−	0.583703i	$-0.198397\pi$
$269$	−3.08376	−	9.49084i	−0.188020	−	0.578666i	−0.999987	+	0.00503661i	$0.998397\pi$
$270$	−12.5399	−	1.65099i	−0.763151	−	0.100476i
$271$	−7.29303	+	22.4456i	−0.443020	+	1.36348i	0.441621	+	0.897202i	$0.354404\pi$
$271$	−7.29303	+	22.4456i	−0.443020	+	1.36348i	−0.884641	+	0.466274i	$0.845596\pi$
$272$	3.52613	+	1.14571i	0.213803	+	0.0694688i
$273$	−2.57327	−	3.54180i	−0.155741	−	0.214360i
$274$	−11.6417			−0.703302
$275$	1.04855	−	1.61459i	0.0632302	−	0.0973632i
$276$	−6.82788			−0.410990
$277$	−11.2285	−	15.4548i	−0.674658	−	0.928587i	0.325197	−	0.945646i	$-0.394570\pi$
$277$	−11.2285	−	15.4548i	−0.674658	−	0.928587i	−0.999854	+	0.0170596i	$0.994570\pi$
$278$	6.81657	+	2.21484i	0.408830	+	0.132837i
$279$	−3.18098	+	9.79004i	−0.190440	+	0.586114i
$280$	−2.80898	+	1.52513i	−0.167869	+	0.0911438i
$281$	−6.28749	−	19.3509i	−0.375080	−	1.15438i	−0.943424	−	0.331588i	$-0.892416\pi$
$281$	−6.28749	−	19.3509i	−0.375080	−	1.15438i	0.568344	−	0.822791i	$-0.307584\pi$
$282$			2.77038i			0.164974i
$283$	−15.2308	+	4.94880i	−0.905379	+	0.294175i	−0.724455	−	0.689322i	$-0.757909\pi$
$283$	−15.2308	+	4.94880i	−0.905379	+	0.294175i	−0.180923	+	0.983497i	$0.557909\pi$
$284$	−1.64922	−	1.19823i	−0.0978630	−	0.0711017i
$285$	3.08625	−	0.571982i	0.182814	−	0.0338813i
$286$	0.679649	−	0.493794i	0.0401885	−	0.0291987i
$287$	−9.43247	+	12.9827i	−0.556781	+	0.766343i
$288$	−0.605172	+	0.832948i	−0.0356601	+	0.0490819i
$289$	−2.63236	+	1.91252i	−0.154845	+	0.112501i
$290$	−1.69514	−	3.12210i	−0.0995419	−	0.183336i
$291$	−0.341479	−	0.248099i	−0.0200178	−	0.0145438i
$292$	5.26596	−	1.71102i	0.308167	−	0.100130i
$293$		−	13.6809i		−	0.799244i	−0.916680	−	0.399622i	$-0.869141\pi$
$293$		−	13.6809i		−	0.799244i	0.916680	−	0.399622i	$-0.130859\pi$
$294$	−2.15009	−	6.61729i	−0.125396	−	0.385928i
$295$	−4.96293	+	10.4048i	−0.288953	+	0.605792i
$296$	0.363524	−	1.11881i	0.0211294	−	0.0650296i
$297$	−2.07133	−	0.673015i	−0.120191	−	0.0390523i
$298$	2.15237	+	2.96248i	0.124683	+	0.171612i
$299$	10.6128			0.613755
$300$	−1.81663	+	6.77941i	−0.104883	+	0.391409i
$301$	5.55496			0.320183
$302$	11.5093	+	15.8412i	0.662288	+	0.911561i
$303$	23.2559	+	7.55631i	1.33602	+	0.434099i
$304$	0.309017	−	0.951057i	0.0177233	−	0.0545468i
$305$	0.590501	+	0.560372i	0.0338120	+	0.0320868i
$306$	1.17960	+	3.63043i	0.0674332	+	0.207538i
$307$		−	18.7570i		−	1.07052i	−0.844687	−	0.535260i	$-0.820214\pi$
$307$		−	18.7570i		−	1.07052i	0.844687	−	0.535260i	$-0.179786\pi$
$308$	−0.523448	+	0.170078i	−0.0298262	+	0.00969112i
$309$	1.95430	+	1.41988i	0.111176	+	0.0807742i
$310$	20.1785	+	9.62483i	1.14606	+	0.546654i
$311$	8.15619	−	5.92582i	0.462495	−	0.336022i	−0.332014	−	0.943274i	$-0.607728\pi$
$311$	8.15619	−	5.92582i	0.462495	−	0.336022i	0.794509	+	0.607252i	$0.207728\pi$
$312$	−1.80020	+	2.47777i	−0.101917	+	0.140276i
$313$	−9.91731	+	13.6500i	−0.560559	+	0.771544i	−0.991397	−	0.130886i	$-0.958218\pi$
$313$	−9.91731	+	13.6500i	−0.560559	+	0.771544i	0.430838	+	0.902429i	$0.358218\pi$
$314$	−6.96386	+	5.05954i	−0.392994	+	0.285527i
$315$	−2.97027	−	1.41677i	−0.167356	−	0.0798259i
$316$	−1.06345	−	0.772640i	−0.0598236	−	0.0434644i
$317$	−5.34016	+	1.73512i	−0.299933	+	0.0974542i	−0.455118	−	0.890431i	$-0.650403\pi$
$317$	−5.34016	+	1.73512i	−0.299933	+	0.0974542i	0.155184	+	0.987886i	$0.450403\pi$
$318$			16.1271i			0.904366i
$319$	−0.189038	−	0.581798i	−0.0105841	−	0.0325744i
$320$	1.62198	+	1.53922i	0.0906712	+	0.0860449i
$321$	1.63308	−	5.02610i	0.0911497	−	0.280530i
$322$	−6.61267	−	2.14859i	−0.368509	−	0.119736i
$323$	−2.17927	−	2.99950i	−0.121258	−	0.166897i
$324$	4.85122			0.269512
$325$	2.82365	−	10.5375i	0.156628	−	0.584513i
$326$	−3.68897			−0.204313
$327$	−5.70154	−	7.84749i	−0.315296	−	0.433967i
$328$	10.6770	+	3.46917i	0.589539	+	0.191553i
$329$	−0.871778	+	2.68306i	−0.0480627	+	0.147922i
$330$	−0.520305	+	1.09082i	−0.0286419	+	0.0600479i
$331$	−4.68419	−	14.4164i	−0.257466	−	0.792400i	−0.993334	−	0.115274i	$-0.963225\pi$
$331$	−4.68419	−	14.4164i	−0.257466	−	0.792400i	0.735868	−	0.677126i	$-0.236775\pi$
$332$		−	6.03892i		−	0.331429i
$333$	1.15191	−	0.374277i	0.0631241	−	0.0205103i
$334$	−14.0021	−	10.1731i	−0.766160	−	0.556647i
$335$	−3.19972	−	5.89324i	−0.174819	−	0.321982i
$336$	1.62331	−	1.17940i	0.0885586	−	0.0643416i
$337$	0.738192	−	1.01603i	0.0402119	−	0.0553469i	−0.788438	−	0.615115i	$-0.789110\pi$
$337$	0.738192	−	1.01603i	0.0402119	−	0.0553469i	0.828649	+	0.559768i	$0.189110\pi$
$338$	−4.84309	+	6.66594i	−0.263429	+	0.362579i
$339$	15.0695	−	10.9486i	0.818463	−	0.594648i
$340$	8.15161	−	1.51076i	0.442083	−	0.0819323i
$341$	3.11443	+	2.26277i	0.168656	+	0.122536i
$342$	0.979189	−	0.318158i	0.0529485	−	0.0172040i
$343$		−	17.0913i		−	0.922845i
$344$	−1.20088	−	3.69593i	−0.0647472	−	0.199271i
$345$	−13.4175	+	7.28499i	−0.722373	+	0.392211i
$346$	−4.32657	+	13.3158i	−0.232598	+	0.715863i
$347$	−17.1334	−	5.56697i	−0.919768	−	0.298851i	−0.189396	−	0.981901i	$-0.560653\pi$
$347$	−17.1334	−	5.56697i	−0.919768	−	0.298851i	−0.730371	+	0.683050i	$0.760653\pi$
$348$	1.31087	+	1.80426i	0.0702701	+	0.0967186i
$349$	−23.5895			−1.26272			−0.631359	−	0.775490i	$-0.717503\pi$
$349$	−23.5895			−1.26272			−0.631359	+	0.775490i	$0.717503\pi$
$350$	−3.89270	+	5.99406i	−0.208074	+	0.320396i
$351$	−12.3414			−0.658733
$352$	0.226320	+	0.311502i	0.0120629	+	0.0166031i
$353$	−13.2715	−	4.31216i	−0.706369	−	0.229513i	−0.0662656	−	0.997802i	$-0.521108\pi$
$353$	−13.2715	−	4.31216i	−0.706369	−	0.229513i	−0.640103	+	0.768289i	$0.721108\pi$
$354$	2.23627	−	6.88254i	0.118857	−	0.365803i
$355$	−4.51932	−	0.595010i	−0.239861	−	0.0315799i
$356$	3.84318	+	11.8281i	0.203688	+	0.626888i
$357$		−	7.43934i		−	0.393732i
$358$	−1.97238	+	0.640865i	−0.104243	+	0.0338708i
$359$	−21.9068	−	15.9162i	−1.15620	−	0.840027i	−0.166905	−	0.985973i	$-0.553377\pi$
$359$	−21.9068	−	15.9162i	−1.15620	−	0.840027i	−0.989293	+	0.145946i	$0.953377\pi$
$360$	−0.300514	+	2.28251i	−0.0158385	+	0.120299i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−2.87553	+	3.95783i	−0.151134	+	0.208019i
$363$	8.95360	−	12.3236i	0.469942	−	0.646820i
$364$	−2.52316	+	1.83318i	−0.132250	+	0.0960850i
$365$	8.52259	−	8.98082i	0.446093	−	0.470078i
$366$	−0.413441	−	0.300382i	−0.0216109	−	0.0157012i
$367$	−6.16163	+	2.00204i	−0.321635	+	0.104505i	−0.465384	−	0.885109i	$-0.654084\pi$
$367$	−6.16163	+	2.00204i	−0.321635	+	0.104505i	0.143750	+	0.989614i	$0.454084\pi$
$368$			4.86415i			0.253561i
$369$	3.57179	+	10.9928i	0.185940	+	0.572264i
$370$	−0.479351	−	2.58644i	−0.0249203	−	0.134463i
$371$	−5.07486	+	15.6188i	−0.263474	+	0.810888i
$372$	−13.3476	−	4.33690i	−0.692041	−	0.224858i
$373$	5.15763	+	7.09886i	0.267052	+	0.367565i	0.921392	−	0.388635i	$-0.127053\pi$
$373$	5.15763	+	7.09886i	0.267052	+	0.367565i	−0.654340	+	0.756201i	$0.727053\pi$
$374$	1.42756			0.0738175
$375$	3.66340	+	15.2605i	0.189177	+	0.788047i
$376$	1.97360			0.101781
$377$	−2.03753	−	2.80443i	−0.104938	−	0.144435i
$378$	7.68969	+	2.49853i	0.395515	+	0.128511i
$379$	−2.54165	+	7.82239i	−0.130556	+	0.401809i	−0.994872	−	0.101139i	$-0.967751\pi$
$379$	−2.54165	+	7.82239i	−0.130556	+	0.401809i	0.864317	+	0.502948i	$0.167751\pi$
$380$	−0.407477	−	2.19863i	−0.0209031	−	0.112787i
$381$	−7.76253	−	23.8906i	−0.397687	−	1.22395i
$382$			15.3841i			0.787121i
$383$	20.2213	−	6.57031i	1.03326	−	0.335727i	0.257183	−	0.966363i	$-0.417206\pi$
$383$	20.2213	−	6.57031i	1.03326	−	0.335727i	0.776079	+	0.630636i	$0.217206\pi$
$384$	−1.13563	−	0.825084i	−0.0579524	−	0.0421049i
$385$	−0.847163	+	0.892712i	−0.0431754	+	0.0454968i
$386$	16.7397	−	12.1621i	0.852027	−	0.619034i
$387$	2.35178	−	3.23695i	0.119548	−	0.164543i
$388$	−0.176744	+	0.243268i	−0.00897283	+	0.0123500i
$389$	3.05550	−	2.21995i	0.154920	−	0.112556i	−0.507625	−	0.861578i	$-0.669476\pi$
$389$	3.05550	−	2.21995i	0.154920	−	0.112556i	0.662545	+	0.749022i	$0.269476\pi$
$390$	−0.893938	+	6.78979i	−0.0452663	+	0.343814i
$391$	14.5900	+	10.6003i	0.737849	+	0.536079i
$392$	−4.71412	+	1.53171i	−0.238099	+	0.0773631i
$393$		−	8.15358i		−	0.411294i
$394$	5.08460	+	15.6488i	0.256159	+	0.788375i
$395$	−2.91415	−	0.383674i	−0.146627	−	0.0193047i
$396$	−0.122503	+	0.377025i	−0.00615600	+	0.0189462i
$397$	−15.2244	−	4.94669i	−0.764088	−	0.248267i	−0.0990559	−	0.995082i	$-0.531582\pi$
$397$	−15.2244	−	4.94669i	−0.764088	−	0.248267i	−0.665032	+	0.746815i	$0.731582\pi$
$398$	1.77548	+	2.44374i	0.0889969	+	0.122494i
$399$	−2.00652			−0.100452
$400$	4.82961	+	1.29416i	0.241481	+	0.0647079i
$401$	6.79105			0.339129			0.169564	−	0.985519i	$-0.445764\pi$
$401$	6.79105			0.339129			0.169564	+	0.985519i	$0.445764\pi$
$402$	2.47439	+	3.40570i	0.123411	+	0.169861i
$403$	20.7467	+	6.74100i	1.03346	+	0.335793i
$404$	5.38308	−	16.5674i	0.267818	−	0.824259i
$405$	9.53315	−	5.17600i	0.473706	−	0.257197i
$406$	0.701792	+	2.15989i	0.0348293	+	0.107194i
$407$		−	0.452954i		−	0.0224521i
$408$	−4.94968	+	1.60825i	−0.245046	+	0.0796202i
$409$	−6.47152	−	4.70183i	−0.319996	−	0.232491i	0.416178	−	0.909283i	$-0.363369\pi$
$409$	−6.47152	−	4.70183i	−0.319996	−	0.232491i	−0.736174	+	0.676793i	$0.763369\pi$
$410$	24.6828	−	4.57452i	1.21900	−	0.225920i
$411$	13.2207	−	9.60540i	0.652129	−	0.473799i
$412$	1.01152	−	1.39223i	0.0498338	−	0.0685903i
$413$	4.33157	−	5.96189i	0.213143	−	0.293366i
$414$	−4.05158	+	2.94365i	−0.199124	+	0.144672i
$415$	−6.44321	−	11.8671i	−0.316285	−	0.582533i
$416$	1.76515	+	1.28246i	0.0865436	+	0.0628776i
$417$	−9.56853	+	3.10900i	−0.468573	+	0.152248i
$418$		−	0.385038i		−	0.0188328i
$419$	3.55877	+	10.9528i	0.173857	+	0.535078i	0.999579	−	0.0289994i	$-0.00923210\pi$
$419$	3.55877	+	10.9528i	0.173857	+	0.535078i	−0.825722	+	0.564077i	$0.809232\pi$
$420$	1.93160	−	4.04963i	0.0942527	−	0.197601i
$421$	10.8798	−	33.4847i	0.530250	−	1.63194i	−0.223444	−	0.974717i	$-0.571730\pi$
$421$	10.8798	−	33.4847i	0.530250	−	1.63194i	0.753694	−	0.657226i	$-0.228270\pi$
$422$	22.5024	+	7.31148i	1.09540	+	0.355917i
$423$	1.19437	+	1.64391i	0.0580723	+	0.0799296i
$424$	11.4889			0.557950
$425$	14.4068	−	11.6661i	0.698835	−	0.565890i
$426$	2.86154			0.138642
$427$	−0.305885	−	0.421015i	−0.0148028	−	0.0203743i
$428$	−3.58057	−	1.16340i	−0.173073	−	0.0562349i
$429$	−0.364409	+	1.12154i	−0.0175938	+	0.0541482i
$430$	−6.30322	−	5.98161i	−0.303968	−	0.288459i
$431$	−7.82941	−	24.0965i	−0.377130	−	1.16069i	−0.942031	−	0.335527i	$-0.891086\pi$
$431$	−7.82941	−	24.0965i	−0.377130	−	1.16069i	0.564901	−	0.825159i	$-0.308914\pi$
$432$		−	5.65639i		−	0.272143i
$433$	38.2582	−	12.4308i	1.83857	−	0.597388i	0.840081	−	0.542461i	$-0.182507\pi$
$433$	38.2582	−	12.4308i	1.83857	−	0.597388i	0.998490	−	0.0549268i	$-0.0174925\pi$
$434$	−11.5622	−	8.40040i	−0.555001	−	0.403232i
$435$	4.50105	+	2.14693i	0.215809	+	0.102937i
$436$	−5.59051	+	4.06174i	−0.267737	+	0.194522i
$437$	2.85907	−	3.93518i	0.136768	−	0.188245i
$438$	−4.56846	+	6.28794i	−0.218289	+	0.300450i
$439$	18.8087	−	13.6653i	0.897691	−	0.652211i	−0.0401810	−	0.999192i	$-0.512793\pi$
$439$	18.8087	−	13.6653i	0.897691	−	0.652211i	0.937872	+	0.346982i	$0.112793\pi$
$440$	0.777097	+	0.370663i	0.0370467	+	0.0176706i
$441$	−4.12869	−	2.99967i	−0.196604	−	0.142841i
$442$	7.69346	−	2.49976i	0.365941	−	0.118901i
$443$			14.5196i			0.689849i	0.938630	+	0.344925i	$0.112095\pi$
$443$			14.5196i			0.689849i	−0.938630	+	0.344925i	$0.887905\pi$
$444$	0.510285	+	1.57049i	0.0242170	+	0.0745324i
$445$	20.1722	+	19.1430i	0.956254	+	0.907463i
$446$	2.23837	−	6.88899i	0.105990	−	0.326203i
$447$	−4.88860	−	1.58840i	−0.231223	−	0.0751288i
$448$	−0.840199	−	1.15643i	−0.0396957	−	0.0546364i
$449$	−3.60787			−0.170266			−0.0851331	−	0.996370i	$-0.527132\pi$
$449$	−3.60787			−0.170266			−0.0851331	+	0.996370i	$0.527132\pi$
$450$	1.84478	+	4.80600i	0.0869638	+	0.226557i
$451$	4.32262			0.203544
$452$	−7.79975	−	10.7354i	−0.366869	−	0.504952i
$453$	−26.1407	−	8.49363i	−1.22820	−	0.399065i
$454$	−0.188124	+	0.578987i	−0.00882911	+	0.0271732i
$455$	−3.00236	+	6.29447i	−0.140753	+	0.295089i
$456$	0.433772	+	1.33501i	0.0203132	+	0.0625177i
$457$		−	25.0363i		−	1.17115i	−0.810618	−	0.585575i	$-0.800869\pi$
$457$		−	25.0363i		−	1.17115i	0.810618	−	0.585575i	$-0.199131\pi$
$458$	−18.9107	+	6.14445i	−0.883638	+	0.287111i
$459$	−16.9664	−	12.3268i	−0.791922	−	0.575365i
$460$	5.18979	+	9.55855i	0.241975	+	0.445669i
$461$	14.9114	−	10.8337i	0.694492	−	0.504578i	−0.183642	−	0.982993i	$-0.558789\pi$
$461$	14.9114	−	10.8337i	0.694492	−	0.504578i	0.878134	+	0.478415i	$0.158789\pi$
$462$	0.454114	−	0.625035i	0.0211273	−	0.0290792i
$463$	−0.232229	+	0.319635i	−0.0107926	+	0.0148547i	−0.814379	−	0.580333i	$-0.802922\pi$
$463$	−0.232229	+	0.319635i	−0.0107926	+	0.0148547i	0.803587	+	0.595188i	$0.202922\pi$
$464$	1.28535	−	0.933859i	0.0596707	−	0.0433533i
$465$	−30.8567	+	5.71874i	−1.43094	+	0.265200i
$466$	−8.94611	−	6.49973i	−0.414421	−	0.301094i
$467$	−11.6868	+	3.79726i	−0.540799	+	0.175716i	−0.566663	−	0.823949i	$-0.691766\pi$
$467$	−11.6868	+	3.79726i	−0.540799	+	0.175716i	0.0258649	+	0.999665i	$0.491766\pi$
$468$			2.24638i			0.103839i
$469$	1.32469	+	4.07699i	0.0611686	+	0.188258i
$470$	3.87833	−	2.10573i	0.178894	−	0.0971301i
$471$	3.73383	−	11.4915i	0.172046	−	0.529502i
$472$	−4.90308	−	1.59311i	−0.225683	−	0.0733288i
$473$	−0.879508	−	1.21054i	−0.0404398	−	0.0556606i
$474$	1.84518			0.0847518
$475$	−3.14655	−	3.88577i	−0.144374	−	0.178291i
$476$	−5.29975			−0.242914
$477$	6.95276	+	9.56965i	0.318345	+	0.438164i
$478$	22.4177	+	7.28394i	1.02536	+	0.333160i
$479$	−13.4065	+	41.2609i	−0.612557	+	1.88526i	−0.179947	+	0.983676i	$0.557593\pi$
$479$	−13.4065	+	41.2609i	−0.612557	+	1.88526i	−0.432610	+	0.901581i	$0.642407\pi$
$480$	−3.11195	−	0.409717i	−0.142040	−	0.0187009i
$481$	−0.793153	−	2.44107i	−0.0361647	−	0.111303i
$482$		−	20.7361i		−	0.944503i
$483$	9.28231	−	3.01600i	0.422360	−	0.137233i
$484$	−8.77925	−	6.37850i	−0.399057	−	0.289932i
$485$	−0.0877669	+	0.666622i	−0.00398529	+	0.0302698i
$486$	8.21914	−	5.97156i	0.372828	−	0.270875i
$487$	9.38390	−	12.9158i	0.425225	−	0.585272i	−0.541624	−	0.840621i	$-0.682190\pi$
$487$	9.38390	−	12.9158i	0.425225	−	0.585272i	0.966849	+	0.255349i	$0.0821903\pi$
$488$	−0.213991	+	0.294533i	−0.00968690	+	0.0133329i
$489$	4.18931	−	3.04371i	0.189447	−	0.137641i
$490$	−7.62948	+	8.03969i	−0.344665	+	0.363196i
$491$	28.4286	+	20.6546i	1.28296	+	0.932128i	0.999638	−	0.0268952i	$-0.00856205\pi$
$491$	28.4286	+	20.6546i	1.28296	+	0.932128i	0.283326	+	0.959024i	$0.408562\pi$
$492$	−14.9875	+	4.86973i	−0.675688	+	0.219544i
$493$		−	5.89053i		−	0.265296i
$494$	−0.674227	−	2.07506i	−0.0303349	−	0.0933613i
$495$	0.161535	+	0.871596i	0.00726045	+	0.0391753i
$496$	−3.08959	+	9.50877i	−0.138726	+	0.426956i
$497$	2.77134	+	0.900464i	0.124312	+	0.0403913i
$498$	4.98262	+	6.85798i	0.223276	+	0.307314i
$499$	0.694679			0.0310981			0.0155491	−	0.999879i	$-0.495050\pi$
$499$	0.694679			0.0310981			0.0155491	+	0.999879i	$0.495050\pi$
$500$	10.8715	−	2.60979i	0.486187	−	0.116713i
$501$	24.2948			1.08541
$502$	−8.09225	−	11.1380i	−0.361175	−	0.497115i
$503$	−6.88966	−	2.23859i	−0.307195	−	0.0998136i	0.151363	−	0.988478i	$-0.451634\pi$
$503$	−6.88966	−	2.23859i	−0.307195	−	0.0998136i	−0.458558	+	0.888665i	$0.651634\pi$
$504$	0.454785	−	1.39968i	0.0202577	−	0.0623469i
$505$	−7.09824	−	38.3001i	−0.315868	−	1.70433i
$506$	0.578752	+	1.78122i	0.0257287	+	0.0791847i
$507$		−	11.5660i		−	0.513664i
$508$	−17.0195	+	5.52999i	−0.755120	+	0.245353i
$509$	16.8506	+	12.2427i	0.746891	+	0.542648i	0.894862	−	0.446344i	$-0.147274\pi$
$509$	16.8506	+	12.2427i	0.746891	+	0.542648i	−0.147971	+	0.988992i	$0.547274\pi$
$510$	−8.01071	+	8.44142i	−0.354720	+	0.373792i
$511$	−6.40314	+	4.65215i	−0.283258	+	0.205799i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−3.32474	+	4.57611i	−0.146791	+	0.202040i
$514$	−21.9061	+	15.9157i	−0.966235	+	0.702011i
$515$	0.502294	−	3.81511i	0.0221337	−	0.168114i
$516$	4.41321	+	3.20639i	0.194281	+	0.141153i
$517$	0.722720	−	0.234826i	0.0317852	−	0.0103276i
$518$			1.68157i			0.0738838i
$519$	−6.07328	−	18.6916i	−0.266587	−	0.820471i
$520$	4.83701	+	0.636837i	0.212117	+	0.0279271i
$521$	−11.3940	+	35.0671i	−0.499180	+	1.53632i	0.311160	+	0.950357i	$0.399282\pi$
$521$	−11.3940	+	35.0671i	−0.499180	+	1.53632i	−0.810340	+	0.585960i	$0.800718\pi$
$522$	1.55571	+	0.505481i	0.0680916	+	0.0221243i
$523$	−13.8570	−	19.0725i	−0.605925	−	0.833984i	0.390310	−	0.920684i	$-0.372368\pi$
$523$	−13.8570	−	19.0725i	−0.605925	−	0.833984i	−0.996234	+	0.0866999i	$0.972368\pi$
$524$	−5.80857			−0.253748
$525$	−0.524934	−	10.0188i	−0.0229100	−	0.437258i
$526$	−14.5276			−0.633433
$527$	21.7885	+	29.9894i	0.949124	+	1.30636i
$528$	−0.514031	−	0.167019i	−0.0223703	−	0.00726856i
$529$	−0.203930	+	0.627633i	−0.00886653	+	0.0272884i
$530$	22.5768	−	12.2580i	0.980675	−	0.532455i
$531$	−1.64023	−	5.04812i	−0.0711800	−	0.219070i
$532$			1.42943i			0.0619737i
$533$	23.2956	−	7.56919i	1.00904	−	0.327858i
$534$	−14.1236	−	10.2614i	−0.611189	−	0.444055i
$535$	−8.27747	+	1.53408i	−0.357866	+	0.0663241i
$536$	2.42620	−	1.76274i	0.104796	−	0.0761387i
$537$	1.71113	−	2.35516i	0.0738406	−	0.101633i
$538$	5.86566	−	8.07339i	0.252887	−	0.348068i
$539$	−1.54403	+	1.12180i	−0.0665061	+	0.0483195i
$540$	−6.03506	−	11.1154i	−0.259708	−	0.478330i
$541$	7.56217	+	5.49424i	0.325123	+	0.236216i	0.738358	−	0.674408i	$-0.235601\pi$
$541$	7.56217	+	5.49424i	0.325123	+	0.236216i	−0.413235	+	0.910624i	$0.635601\pi$
$542$	−22.4456	+	7.29303i	−0.964123	+	0.313262i
$543$		−	6.86718i		−	0.294699i
$544$	1.14571	+	3.52613i	0.0491218	+	0.151181i
$545$	−6.65226	+	13.9465i	−0.284951	+	0.597403i
$546$	1.35285	−	4.16364i	0.0578966	−	0.178187i
$547$	20.4358	+	6.63998i	0.873770	+	0.283905i	0.711368	−	0.702820i	$-0.248076\pi$
$547$	20.4358	+	6.63998i	0.873770	+	0.283905i	0.162402	+	0.986725i	$0.448076\pi$
$548$	−6.84284	−	9.41836i	−0.292311	−	0.402332i
$549$	−0.374832			−0.0159974
$550$	1.92255	−	0.100732i	0.0819779	−	0.00429521i
$551$	−1.58878			−0.0676841
$552$	−4.01333	−	5.52387i	−0.170819	−	0.235112i
$553$	1.78702	+	0.580637i	0.0759916	+	0.0246912i
$554$	5.90319	−	18.1682i	0.250803	−	0.771891i
$555$	2.67840	+	2.54174i	0.113692	+	0.107891i
$556$	2.21484	+	6.81657i	0.0939300	+	0.289087i
$557$			42.7444i			1.81114i	0.424198	+	0.905569i	$0.360556\pi$
$557$			42.7444i			1.81114i	−0.424198	+	0.905569i	$0.639444\pi$
$558$	−9.79004	+	3.18098i	−0.414445	+	0.134661i
$559$	−6.85961	−	4.98380i	−0.290130	−	0.210792i
$560$	−2.88493	−	1.37606i	−0.121911	−	0.0581493i
$561$	−1.62118	+	1.17786i	−0.0684464	+	0.0497292i
$562$	11.9595	−	16.4609i	0.504482	−	0.694360i
$563$	2.70440	−	3.72229i	0.113977	−	0.156876i	−0.748217	−	0.663454i	$-0.769090\pi$
$563$	2.70440	−	3.72229i	0.113977	−	0.156876i	0.862194	+	0.506578i	$0.169090\pi$
$564$	−2.24129	+	1.62839i	−0.0943751	+	0.0685675i
$565$	−26.7814	−	12.7743i	−1.12670	−	0.537419i
$566$	−12.9561	−	9.41317i	−0.544586	−	0.395665i
$567$	−6.59510	+	2.14288i	−0.276968	+	0.0899924i
$568$		−	2.03854i		−	0.0855354i
$569$	−3.27229	−	10.0711i	−0.137182	−	0.422202i	0.858741	−	0.512409i	$-0.171247\pi$
$569$	−3.27229	−	10.0711i	−0.137182	−	0.422202i	−0.995923	+	0.0902077i	$0.971247\pi$
$570$	2.27679	+	2.16063i	0.0953644	+	0.0904987i
$571$	9.11216	−	28.0443i	0.381332	−	1.17362i	−0.557775	−	0.829992i	$-0.688345\pi$
$571$	9.11216	−	28.0443i	0.381332	−	1.17362i	0.939106	−	0.343626i	$-0.111655\pi$
$572$	0.798976	+	0.259603i	0.0334069	+	0.0108545i
$573$	−12.6932	−	17.4707i	−0.530266	−	0.729849i
$574$	−16.0475			−0.669809
$575$	20.3969	+	13.2463i	0.850610	+	0.552408i
$576$	−1.02958			−0.0428992
$577$	4.86354	+	6.69410i	0.202472	+	0.278679i	0.898163	−	0.439662i	$-0.144902\pi$
$577$	4.86354	+	6.69410i	0.202472	+	0.278679i	−0.695691	+	0.718341i	$0.744902\pi$
$578$	−3.09453	−	1.00547i	−0.128715	−	0.0418221i
$579$	−8.97535	+	27.6233i	−0.373003	+	1.14798i
$580$	1.52946	−	3.20652i	0.0635073	−	0.133144i
$581$	2.66751	+	8.20974i	0.110667	+	0.340597i
$582$		−	0.422091i		−	0.0174962i
$583$	4.20715	−	1.36699i	0.174242	−	0.0566148i
$584$	4.47950	+	3.25454i	0.185363	+	0.134674i
$585$	2.39677	+	4.41437i	0.0990943	+	0.182512i
$586$	11.0680	−	8.04141i	0.457217	−	0.332187i
$587$	−13.6182	+	18.7439i	−0.562084	+	0.773642i	−0.991590	−	0.129422i	$-0.958688\pi$
$587$	−13.6182	+	18.7439i	−0.562084	+	0.773642i	0.429506	+	0.903064i	$0.358688\pi$
$588$	4.08971	−	5.62901i	0.168657	−	0.232136i
$589$	8.08864	−	5.87674i	0.333287	−	0.242147i
$590$	−11.3348	+	2.10071i	−0.466647	+	0.0864848i
$591$	−18.6858	−	13.5760i	−0.768631	−	0.558443i
$592$	1.11881	−	0.363524i	0.0459829	−	0.0149407i
$593$			8.03877i			0.330113i	0.986284	+	0.165056i	$0.0527806\pi$
$593$			8.03877i			0.330113i	−0.986284	+	0.165056i	$0.947219\pi$
$594$	−0.673015	−	2.07133i	−0.0276142	−	0.0849876i
$595$	−10.4145	+	5.65455i	−0.426955	+	0.231814i
$596$	−1.13157	+	3.48261i	−0.0463508	+	0.142653i
$597$	−4.03259	−	1.31027i	−0.165043	−	0.0536256i
$598$	6.23806	+	8.58595i	0.255093	+	0.351106i
$599$	−11.8399			−0.483766			−0.241883	−	0.970305i	$-0.577765\pi$
$599$	−11.8399			−0.483766			−0.241883	+	0.970305i	$0.577765\pi$
$600$	−6.55244	+	2.51515i	−0.267502	+	0.102681i
$601$	−33.9067			−1.38308			−0.691542	−	0.722336i	$-0.743068\pi$
$601$	−33.9067			−1.38308			−0.691542	+	0.722336i	$0.743068\pi$
$602$	3.26513	+	4.49406i	0.133077	+	0.183164i
$603$	2.93654	+	0.954139i	0.119585	+	0.0388556i
$604$	−6.05081	+	18.6225i	−0.246204	+	0.757738i
$605$	−24.0576	−	3.16741i	−0.978082	−	0.128773i
$606$	7.55631	+	23.2559i	0.306954	+	0.944708i
$607$		−	22.3408i		−	0.906784i	−0.891311	−	0.453392i	$-0.850214\pi$
$607$		−	22.3408i		−	0.906784i	0.891311	−	0.453392i	$-0.149786\pi$
$608$	0.951057	−	0.309017i	0.0385704	−	0.0125323i
$609$	−2.57907	−	1.87380i	−0.104509	−	0.0759303i
$610$	−0.106263	+	0.807104i	−0.00430245	+	0.0326787i
$611$	3.48371	−	2.53106i	0.140936	−	0.102396i
$612$	−2.24373	+	3.08823i	−0.0906974	+	0.124834i
$613$	−0.719608	+	0.990455i	−0.0290647	+	0.0400041i	−0.823302	−	0.567604i	$-0.807871\pi$
$613$	−0.719608	+	0.990455i	−0.0290647	+	0.0400041i	0.794237	+	0.607608i	$0.207871\pi$
$614$	15.1748	−	11.0251i	0.612403	−	0.444937i
$615$	−24.2562	+	25.5604i	−0.978104	+	1.03069i
$616$	−0.445271	−	0.323508i	−0.0179405	−	0.0130345i
$617$	3.48971	−	1.13388i	0.140491	−	0.0456482i	−0.237928	−	0.971283i	$-0.576468\pi$
$617$	3.48971	−	1.13388i	0.140491	−	0.0456482i	0.378418	+	0.925635i	$0.376468\pi$
$618$			2.41565i			0.0971715i
$619$	−10.6931	−	32.9098i	−0.429790	−	1.32276i	−0.898332	−	0.439317i	$-0.855221\pi$
$619$	−10.6931	−	32.9098i	−0.429790	−	1.32276i	0.468542	−	0.883441i	$-0.344779\pi$
$620$	4.07400	+	21.9821i	0.163616	+	0.882823i
$621$	8.50214	−	26.1669i	0.341179	−	1.05004i
$622$	9.58817	+	3.11539i	0.384451	+	0.124916i
$623$	−10.4494	−	14.3824i	−0.418646	−	0.576217i
$624$	−3.06269			−0.122606
$625$	18.5791	−	16.7278i	0.743162	−	0.669111i
$626$	−16.8723			−0.674354
$627$	0.317688	+	0.437261i	0.0126873	+	0.0174625i
$628$	−8.18651	−	2.65996i	−0.326677	−	0.106144i
$629$	1.34780	−	4.14810i	0.0537402	−	0.165395i
$630$	−0.599689	−	3.23575i	−0.0238922	−	0.128915i
$631$	−1.33756	−	4.11657i	−0.0532472	−	0.163878i	0.920897	−	0.389807i	$-0.127458\pi$
$631$	−1.33756	−	4.11657i	−0.0532472	−	0.163878i	−0.974144	+	0.225929i	$0.927458\pi$
$632$		−	1.31449i		−	0.0522877i
$633$	−31.5870	+	10.2632i	−1.25547	+	0.407927i
$634$	−4.54261	−	3.30040i	−0.180410	−	0.131076i
$635$	−27.5449	+	29.0259i	−1.09309	+	1.15186i
$636$	−13.0471	+	9.47930i	−0.517353	+	0.375879i
$637$	−6.35678	+	8.74936i	−0.251865	+	0.346662i
$638$	0.359571	−	0.494907i	0.0142355	−	0.0195935i
$639$	1.69800	−	1.23367i	0.0671719	−	0.0488032i
$640$	−0.291880	+	2.21694i	−0.0115376	+	0.0876321i
$641$	−20.5014	−	14.8951i	−0.809757	−	0.588323i	0.104003	−	0.994577i	$-0.466835\pi$
$641$	−20.5014	−	14.8951i	−0.809757	−	0.588323i	−0.913760	+	0.406254i	$0.866835\pi$
$642$	5.02610	−	1.63308i	0.198365	−	0.0644525i
$643$		−	13.0934i		−	0.516354i	−0.966098	−	0.258177i	$-0.916878\pi$
$643$		−	13.0934i		−	0.516354i	0.966098	−	0.258177i	$-0.0831218\pi$
$644$	−2.14859	−	6.61267i	−0.0846661	−	0.260576i
$645$	12.0935	+	1.59221i	0.476179	+	0.0626933i
$646$	1.14571	−	3.52613i	0.0450773	−	0.138734i
$647$	34.8051	+	11.3089i	1.36833	+	0.444597i	0.898815	−	0.438328i	$-0.144429\pi$
$647$	34.8051	+	11.3089i	1.36833	+	0.444597i	0.469514	+	0.882925i	$0.344429\pi$
$648$	2.85148	+	3.92472i	0.112017	+	0.154178i
$649$	−1.98503			−0.0779191
$650$	10.1847	−	3.90938i	0.399476	−	0.153339i
$651$	20.0614			0.786267
$652$	−2.16832	−	2.98444i	−0.0849181	−	0.116880i
$653$	2.04410	+	0.664168i	0.0799918	+	0.0259909i	0.348740	−	0.937220i	$-0.386610\pi$
$653$	2.04410	+	0.664168i	0.0799918	+	0.0259909i	−0.268748	+	0.963211i	$0.586610\pi$
$654$	2.99748	−	9.22528i	0.117211	−	0.360737i
$655$	−11.4144	+	6.19743i	−0.445998	+	0.242154i
$656$	3.46917	+	10.6770i	0.135448	+	0.416867i
$657$			5.70075i			0.222407i
$658$	−2.68306	+	0.871778i	−0.104596	+	0.0339855i
$659$	−16.0023	−	11.6264i	−0.623362	−	0.452899i	0.230733	−	0.973017i	$-0.425888\pi$
$659$	−16.0023	−	11.6264i	−0.623362	−	0.452899i	−0.854094	+	0.520119i	$0.825888\pi$
$660$	−1.18832	+	0.220235i	−0.0462554	+	0.00857262i
$661$	−31.9903	+	23.2423i	−1.24428	+	0.904022i	−0.997876	−	0.0651454i	$-0.979249\pi$
$661$	−31.9903	+	23.2423i	−1.24428	+	0.904022i	−0.246404	+	0.969167i	$0.579249\pi$
$662$	8.90985	−	12.2634i	0.346291	−	0.476629i
$663$	−6.67442	+	9.18655i	−0.259213	+	0.356776i
$664$	4.88559	−	3.54959i	0.189598	−	0.137751i
$665$	1.52513	+	2.80898i	0.0591419	+	0.108928i
$666$	0.979870	+	0.711917i	0.0379692	+	0.0275862i
$667$	7.34980	−	2.38809i	0.284585	−	0.0924674i
$668$		−	17.3075i		−	0.669648i
$669$	3.14204	+	9.67020i	0.121478	+	0.373871i
$670$	2.88699	−	6.05259i	0.111534	−	0.233832i
$671$	−0.0433174	+	0.133317i	−0.00167225	+	0.00514665i
$672$	1.90831	+	0.620048i	0.0736147	+	0.0239189i
$673$	28.2149	+	38.8345i	1.08761	+	1.49696i	0.850862	+	0.525389i	$0.176080\pi$
$673$	28.2149	+	38.8345i	1.08761	+	1.49696i	0.236744	+	0.971572i	$0.423920\pi$
$674$	1.25589			0.0483750
$675$	−23.7190	−	15.4038i	−0.912946	−	0.592891i
$676$	−8.23955			−0.316906
$677$	3.06994	+	4.22542i	0.117988	+	0.162396i	0.863926	−	0.503619i	$-0.167999\pi$
$677$	3.06994	+	4.22542i	0.117988	+	0.162396i	−0.745938	+	0.666015i	$0.767999\pi$
$678$	17.7153	+	5.75604i	0.680351	+	0.221059i
$679$	0.132823	−	0.408786i	0.00509727	−	0.0156878i
$680$	6.01362	+	5.70679i	0.230612	+	0.218845i
$681$	−0.264073	−	0.812734i	−0.0101193	−	0.0311440i
$682$			3.84965i			0.147411i
$683$	24.1332	−	7.84135i	0.923431	−	0.300041i	0.191558	−	0.981481i	$-0.438646\pi$
$683$	24.1332	−	7.84135i	0.923431	−	0.300041i	0.731874	+	0.681440i	$0.238646\pi$
$684$	0.832948	+	0.605172i	0.0318486	+	0.0231393i
$685$	−23.4958	−	11.2071i	−0.897726	−	0.428201i
$686$	13.8272	−	10.0460i	0.527924	−	0.383559i
$687$	16.4059	−	22.5807i	0.625923	−	0.861508i
$688$	2.28421	−	3.14395i	0.0870848	−	0.119862i
$689$	20.2796	−	14.7340i	0.772592	−	0.561321i
$690$	−13.7803	−	6.57297i	−0.524606	−	0.250229i
$691$	−18.3588	−	13.3385i	−0.698402	−	0.507419i	0.181009	−	0.983481i	$-0.442064\pi$
$691$	−18.3588	−	13.3385i	−0.698402	−	0.507419i	−0.879411	+	0.476062i	$0.842064\pi$
$692$	−13.3158	+	4.32657i	−0.506191	+	0.164472i
$693$		−	0.566666i		−	0.0215259i
$694$	−5.56697	−	17.1334i	−0.211319	−	0.650374i
$695$	11.6253	+	11.0321i	0.440972	+	0.418473i
$696$	−0.689167	+	2.12104i	−0.0261228	+	0.0803977i
$697$	39.5860	+	12.8623i	1.49943	+	0.487193i
$698$	−13.8656	−	19.0843i	−0.524820	−	0.722353i
$699$	15.5223			0.587107
$700$	−7.13737	+	0.373960i	−0.269767	+	0.0141344i
$701$	−27.9010			−1.05381			−0.526904	−	0.849925i	$-0.676647\pi$
$701$	−27.9010			−1.05381			−0.526904	+	0.849925i	$0.676647\pi$
$702$	−7.25407	−	9.98437i	−0.273787	−	0.376836i
$703$	−1.11881	−	0.363524i	−0.0421968	−	0.0137106i
$704$	−0.118983	+	0.366193i	−0.00448435	+	0.0138014i
$705$	−2.66695	+	5.59128i	−0.100443	+	0.210580i
$706$	−4.31216	−	13.2715i	−0.162290	−	0.499478i
$707$			24.9007i			0.936488i
$708$	6.88254	−	2.23627i	0.258662	−	0.0840443i
$709$	21.7356	+	15.7918i	0.816296	+	0.593074i	0.915649	−	0.401978i	$-0.131677\pi$
$709$	21.7356	+	15.7918i	0.816296	+	0.593074i	−0.0993529	+	0.995052i	$0.531677\pi$
$710$	−2.17502	−	4.00595i	−0.0816270	−	0.150341i
$711$	1.09490	−	0.795495i	0.0410621	−	0.0298334i
$712$	−7.31017	+	10.0616i	−0.273960	+	0.377074i
$713$	−28.5853	+	39.3443i	−1.07053	+	1.47346i
$714$	6.01856	−	4.37274i	0.225239	−	0.163646i
$715$	1.84705	−	0.342318i	0.0690758	−	0.0128020i
$716$	−1.67781	−	1.21900i	−0.0627025	−	0.0455561i
$717$	−31.4681	+	10.2246i	−1.17520	+	0.381844i
$718$		−	27.0783i		−	1.01055i
$719$	−7.98348	−	24.5706i	−0.297733	−	0.916329i	−0.982290	−	0.187369i	$-0.940004\pi$
$719$	−7.98348	−	24.5706i	−0.297733	−	0.916329i	0.684556	−	0.728960i	$-0.259996\pi$
$720$	−2.02323	+	1.09851i	−0.0754013	+	0.0409389i
$721$	−0.760151	+	2.33950i	−0.0283095	+	0.0871277i
$722$	−0.951057	−	0.309017i	−0.0353947	−	0.0115004i
$723$	17.1090	+	23.5485i	0.636291	+	0.875779i
$724$	−4.89214			−0.181815
$725$	−0.415647	−	7.93299i	−0.0154367	−	0.294624i
$726$	15.2328			0.565341
$727$	−29.7664	−	40.9699i	−1.10397	−	1.51949i	−0.830010	−	0.557748i	$-0.811666\pi$
$727$	−29.7664	−	40.9699i	−1.10397	−	1.51949i	−0.273963	−	0.961740i	$-0.588334\pi$
$728$	−2.96615	−	0.963762i	−0.109933	−	0.0357194i
$729$	−8.90421	+	27.4043i	−0.329785	+	1.01498i
$730$	12.2751	+	1.61613i	0.454322	+	0.0598156i
$731$	−4.45238	−	13.7030i	−0.164677	−	0.506824i
$732$		−	0.511041i		−	0.0188886i
$733$	19.9481	−	6.48154i	0.736801	−	0.239401i	0.0835089	−	0.996507i	$-0.473387\pi$
$733$	19.9481	−	6.48154i	0.736801	−	0.239401i	0.653292	+	0.757106i	$0.273387\pi$
$734$	−5.24140	−	3.80810i	−0.193464	−	0.140559i
$735$	2.03085	−	15.4251i	0.0749091	−	0.568962i
$736$	−3.93518	+	2.85907i	−0.145053	+	0.105387i
$737$	0.678721	−	0.934180i	0.0250010	−	0.0344109i
$738$	−6.79394	+	9.35106i	−0.250089	+	0.344217i
$739$	−32.7285	+	23.7786i	−1.20394	+	0.874710i	−0.994666	−	0.103148i	$-0.967109\pi$
$739$	−32.7285	+	23.7786i	−1.20394	+	0.874710i	−0.209270	+	0.977858i	$0.567109\pi$
$740$	1.81072	−	1.90807i	0.0665633	−	0.0701422i
$741$	2.47777	+	1.80020i	0.0910231	+	0.0661322i
$742$	−15.6188	+	5.07486i	−0.573385	+	0.186304i
$743$			7.16937i			0.263019i	0.991315	+	0.131509i	$0.0419823\pi$
$743$			7.16937i			0.263019i	−0.991315	+	0.131509i	$0.958018\pi$
$744$	−4.33690	−	13.3476i	−0.158999	−	0.489347i
$745$	1.49211	+	8.05100i	0.0546667	+	0.294966i
$746$	−2.71153	+	8.34522i	−0.0992760	+	0.305540i
$747$	5.91325	+	1.92133i	0.216354	+	0.0702978i
$748$	0.839100	+	1.15492i	0.0306805	+	0.0422281i
$749$	5.38157			0.196638
$750$	−10.1927	+	11.9336i	−0.372184	+	0.435755i
$751$	51.1506			1.86651			0.933255	−	0.359214i	$-0.116955\pi$
$751$	51.1506			1.86651			0.933255	+	0.359214i	$0.116955\pi$
$752$	1.16006	+	1.59668i	0.0423029	+	0.0582249i
$753$	18.3796	+	5.97190i	0.669791	+	0.217628i
$754$	1.07120	−	3.29680i	0.0390106	−	0.120062i
$755$	7.97874	+	43.0510i	0.290376	+	1.56679i
$756$	2.49853	+	7.68969i	0.0908708	+	0.279671i
$757$			1.76028i			0.0639784i	0.999488	+	0.0319892i	$0.0101842\pi$
$757$			1.76028i			0.0639784i	−0.999488	+	0.0319892i	$0.989816\pi$
$758$	−7.82239	+	2.54165i	−0.284122	+	0.0923169i
$759$	−2.12690	−	1.54528i	−0.0772016	−	0.0560902i
$760$	1.53922	−	1.62198i	0.0558333	−	0.0588353i
$761$	−5.26139	+	3.82262i	−0.190725	+	0.138570i	−0.679050	−	0.734092i	$-0.737608\pi$
$761$	−5.26139	+	3.82262i	−0.190725	+	0.138570i	0.488325	+	0.872662i	$0.337608\pi$
$762$	14.7652	−	20.3226i	0.534887	−	0.736209i
$763$	5.80599	−	7.99126i	0.210191	−	0.289303i
$764$	−12.4460	+	9.04257i	−0.450282	+	0.327149i
$765$	−1.11418	+	8.46262i	−0.0402833	+	0.305967i
$766$	17.2013	+	12.4975i	0.621508	+	0.451552i
$767$	−10.6978	+	3.47592i	−0.386274	+	0.125508i
$768$		−	1.40372i		−	0.0506523i
$769$	12.3079	+	37.8799i	0.443835	+	1.36598i	0.883757	+	0.467947i	$0.155006\pi$
$769$	12.3079	+	37.8799i	0.443835	+	1.36598i	−0.439922	+	0.898036i	$0.644994\pi$
$770$	−1.22017	−	0.160646i	−0.0439719	−	0.00578930i
$771$	11.7454	−	36.1487i	0.423001	−	1.30186i
$772$	19.6787	+	6.39399i	0.708251	+	0.230125i
$773$	−30.6319	−	42.1612i	−1.10175	−	1.51643i	−0.833040	−	0.553213i	$-0.813402\pi$
$773$	−30.6319	−	42.1612i	−1.10175	−	1.51643i	−0.268713	−	0.963220i	$-0.586598\pi$
$774$	4.00109			0.143816
$775$	31.4596	+	38.8504i	1.13006	+	1.39555i
$776$	−0.300695			−0.0107943
$777$	−1.38743	−	1.90964i	−0.0497739	−	0.0685079i
$778$	3.59195	+	1.16710i	0.128778	+	0.0418424i
$779$	3.46917	−	10.6770i	0.124296	−	0.382543i
$780$	−6.01850	+	3.26773i	−0.215497	+	0.117003i
$781$	−0.242553	−	0.746500i	−0.00867922	−	0.0267119i
$782$			18.0343i			0.644904i
$783$	−8.54689	+	2.77705i	−0.305441	+	0.0992437i
$784$	−4.01007	−	2.91349i	−0.143217	−	0.104053i
$785$	−18.9254	+	3.50748i	−0.675475	+	0.125187i
$786$	6.59639	−	4.79255i	0.235285	−	0.170945i
$787$	26.7810	−	36.8608i	0.954638	−	1.31395i	0.00520208	−	0.999986i	$-0.498344\pi$
$787$	26.7810	−	36.8608i	0.954638	−	1.31395i	0.949436	−	0.313960i	$-0.101656\pi$
$788$	−9.67149	+	13.3117i	−0.344533	+	0.474208i
$789$	16.4980	−	11.9865i	0.587343	−	0.426730i
$790$	−1.40249	−	2.58311i	−0.0498985	−	0.0919031i
$791$	15.3456	+	11.1492i	0.545626	+	0.396420i
$792$	−0.377025	+	0.122503i	−0.0133970	+	0.00435295i
$793$			0.794328i			0.0282074i
$794$	−4.94669	−	15.2244i	−0.175552	−	0.540292i
$795$	−15.5250	+	32.5484i	−0.550617	+	1.15437i
$796$	−0.933427	+	2.87279i	−0.0330844	+	0.101823i
$797$	25.2451	+	8.20263i	0.894228	+	0.290552i	0.719852	−	0.694127i	$-0.244209\pi$
$797$	25.2451	+	8.20263i	0.894228	+	0.290552i	0.174375	+	0.984679i	$0.444209\pi$
$798$	−1.17940	−	1.62331i	−0.0417504	−	0.0574644i
$799$	7.31732			0.258868
$800$	1.79178	+	4.66793i	0.0633490	+	0.165036i
$801$	−12.8047			−0.452431
$802$	3.99168	+	5.49407i	0.140951	+	0.194002i
$803$	2.02760	+	0.658806i	0.0715523	+	0.0232487i
$804$	−1.30086	+	4.00364i	−0.0458779	+	0.141198i
$805$	−11.2776	−	10.7021i	−0.397481	−	0.377201i
$806$	6.74100	+	20.7467i	0.237441	+	0.730770i
$807$			14.0080i			0.493107i
$808$	16.5674	−	5.38308i	0.582839	−	0.189376i
$809$	−8.37184	−	6.08250i	−0.294338	−	0.213849i	0.430809	−	0.902443i	$-0.358228\pi$
$809$	−8.37184	−	6.08250i	−0.294338	−	0.213849i	−0.725147	+	0.688594i	$0.758228\pi$
$810$	9.79092	+	4.67011i	0.344018	+	0.164091i
$811$	−0.793778	+	0.576713i	−0.0278733	+	0.0202511i	−0.601635	−	0.798771i	$-0.705484\pi$
$811$	−0.793778	+	0.576713i	−0.0278733	+	0.0202511i	0.573761	+	0.819023i	$0.305484\pi$
$812$	−1.33489	+	1.83731i	−0.0468454	+	0.0644771i
$813$	19.4726	−	26.8017i	0.682934	−	0.939977i
$814$	0.366447	−	0.266240i	0.0128440	−	0.00933170i
$815$	−7.44521	−	3.55124i	−0.260795	−	0.124395i
$816$	−4.21045	−	3.05907i	−0.147395	−	0.107089i
$817$	−3.69593	+	1.20088i	−0.129304	+	0.0420135i
$818$		−	7.99924i		−	0.279687i
$819$	−0.992270	−	3.05389i	−0.0346727	−	0.106712i
$820$	18.2091	+	17.2800i	0.635888	+	0.603443i
$821$	−15.0137	+	46.2074i	−0.523982	+	1.61265i	0.242339	+	0.970192i	$0.422085\pi$
$821$	−15.0137	+	46.2074i	−0.523982	+	1.61265i	−0.766321	+	0.642458i	$0.777915\pi$
$822$	15.5419	+	5.04986i	0.542085	+	0.176134i
$823$	−4.25328	−	5.85414i	−0.148260	−	0.204063i	0.728427	−	0.685123i	$-0.240252\pi$
$823$	−4.25328	−	5.85414i	−0.148260	−	0.204063i	−0.876687	+	0.481061i	$0.840252\pi$
$824$	1.72089			0.0599501
$825$	−2.10020	+	1.70066i	−0.0731195	+	0.0592094i
$826$	7.36930			0.256411
$827$	−16.7063	−	22.9942i	−0.580934	−	0.799588i	0.412863	−	0.910793i	$-0.364529\pi$
$827$	−16.7063	−	22.9942i	−0.580934	−	0.799588i	−0.993797	+	0.111206i	$0.964529\pi$
$828$	−4.76292	−	1.54757i	−0.165523	−	0.0537816i
$829$	−7.35269	+	22.6293i	−0.255370	+	0.785947i	0.738387	+	0.674377i	$0.235588\pi$
$829$	−7.35269	+	22.6293i	−0.255370	+	0.785947i	−0.993757	+	0.111570i	$0.964412\pi$
$830$	5.81346	−	12.1880i	0.201788	−	0.423051i
$831$	8.28641	+	25.5030i	0.287452	+	0.884688i
$832$			2.18184i			0.0756419i
$833$	−17.4780	+	5.67896i	−0.605578	+	0.196764i
$834$	−8.13947	−	5.91367i	−0.281847	−	0.204774i
$835$	−18.4662	−	34.0110i	−0.639049	−	1.17700i
$836$	0.311502	−	0.226320i	0.0107735	−	0.00782743i
$837$	33.2411	−	45.7525i	1.14898	−	1.58144i
$838$	−6.76918	+	9.31698i	−0.233837	+	0.321850i
$839$	−24.8034	+	18.0207i	−0.856307	+	0.622143i	−0.926878	−	0.375363i	$-0.877518\pi$
$839$	−24.8034	+	18.0207i	−0.856307	+	0.622143i	0.0705709	+	0.997507i	$0.477518\pi$
$840$	4.41158	−	0.817609i	0.152214	−	0.0282102i
$841$	21.4194	+	15.5621i	0.738599	+	0.536623i
$842$	33.4847	−	10.8798i	1.15396	−	0.374944i
$843$			28.5611i			0.983696i
$844$	7.31148	+	22.5024i	0.251672	+	0.774565i
$845$	−16.1916	+	8.79116i	−0.557007	+	0.302425i
$846$	−0.627917	+	1.93253i	−0.0215882	+	0.0664418i
$847$	14.7526	+	4.79342i	0.506906	+	0.164704i
$848$	6.75300	+	9.29471i	0.231899	+	0.319182i
$849$	22.4800			0.771512
$850$	17.9062	+	4.79821i	0.614178	+	0.164577i
$851$	5.72213			0.196152
$852$	1.68197	+	2.31503i	0.0576234	+	0.0793117i
$853$	−32.8556	−	10.6754i	−1.12495	−	0.365519i	−0.313297	−	0.949655i	$-0.601434\pi$
$853$	−32.8556	−	10.6754i	−1.12495	−	0.365519i	−0.811656	+	0.584136i	$0.801434\pi$
$854$	0.160813	−	0.494933i	0.00550292	−	0.0169362i
$855$	2.28251	+	0.300514i	0.0780603	+	0.0102774i
$856$	−1.16340	−	3.58057i	−0.0397641	−	0.122381i
$857$			1.00665i			0.0343865i	0.999852	+	0.0171932i	$0.00547305\pi$
$857$			1.00665i			0.0343865i	−0.999852	+	0.0171932i	$0.994527\pi$
$858$	−1.12154	+	0.364409i	−0.0382886	+	0.0124407i
$859$	−25.0444	−	18.1958i	−0.854505	−	0.620834i	0.0718796	−	0.997413i	$-0.477100\pi$
$859$	−25.0444	−	18.1958i	−0.854505	−	0.620834i	−0.926384	+	0.376579i	$0.877100\pi$
$860$	1.13428	−	8.61531i	0.0386788	−	0.293780i
$861$	18.2240	−	13.2405i	0.621072	−	0.451236i
$862$	14.8924	−	20.4977i	0.507238	−	0.698153i
$863$	26.9158	−	37.0465i	0.916226	−	1.26108i	−0.0487693	−	0.998810i	$-0.515530\pi$
$863$	26.9158	−	37.0465i	0.916226	−	1.26108i	0.964995	−	0.262267i	$-0.0844701\pi$
$864$	4.57611	−	3.32474i	0.155683	−	0.113110i
$865$	−21.5507	+	22.7094i	−0.732746	+	0.772143i
$866$	32.5444	+	23.6449i	1.10590	+	0.803485i
$867$	4.34384	−	1.41140i	0.147524	−	0.0479336i
$868$		−	14.2916i		−	0.485089i
$869$	−0.156403	−	0.481358i	−0.00530560	−	0.0163290i
$870$	0.908750	+	4.90336i	0.0308095	+	0.166239i
$871$	2.02197	−	6.22300i	0.0685120	−	0.210858i
$872$	−6.57204	−	2.13539i	−0.222557	−	0.0723133i
$873$	−0.181972	−	0.250463i	−0.00615883	−	0.00847690i
$874$	4.86415			0.164532
$875$	−13.6267	+	8.35006i	−0.460665	+	0.282284i
$876$	−7.77233			−0.262603
$877$	11.7073	+	16.1137i	0.395328	+	0.544122i	0.959564	−	0.281492i	$-0.0908292\pi$
$877$	11.7073	+	16.1137i	0.395328	+	0.544122i	−0.564236	+	0.825614i	$0.690829\pi$
$878$	22.1110	+	7.18429i	0.746209	+	0.242458i
$879$	−5.93438	+	18.2641i	−0.200162	+	0.616034i
$880$	0.156894	+	0.846555i	0.00528889	+	0.0285374i
$881$	0.533438	+	1.64175i	0.0179720	+	0.0553121i	0.959640	−	0.281230i	$-0.0907425\pi$
$881$	0.533438	+	1.64175i	0.0179720	+	0.0553121i	−0.941668	+	0.336542i	$0.890742\pi$
$882$		−	5.10334i		−	0.171839i
$883$	18.5636	−	6.03168i	0.624715	−	0.202982i	0.0204824	−	0.999790i	$-0.493480\pi$
$883$	18.5636	−	6.03168i	0.624715	−	0.202982i	0.604233	+	0.796808i	$0.293480\pi$
$884$	6.54445	+	4.75482i	0.220114	+	0.159922i
$885$	11.1389	−	11.7378i	0.374430	−	0.394562i
$886$	−11.7466	+	8.53443i	−0.394636	+	0.286720i
$887$	−20.1431	+	27.7245i	−0.676338	+	0.930899i	−0.999883	−	0.0153136i	$-0.995125\pi$
$887$	−20.1431	+	27.7245i	−0.676338	+	0.930899i	0.323545	+	0.946213i	$0.395125\pi$
$888$	−0.970619	+	1.33594i	−0.0325718	+	0.0448313i
$889$	20.6949	−	15.0357i	0.694084	−	0.504281i
$890$	−3.63005	+	27.5716i	−0.121680	+	0.924202i
$891$	1.51117	+	1.09793i	0.0506260	+	0.0367819i
$892$	6.88899	−	2.23837i	0.230661	−	0.0749462i
$893$		−	1.97360i		−	0.0660442i
$894$	−1.58840	−	4.88860i	−0.0531241	−	0.163499i
$895$	−4.59766	−	0.605324i	−0.153683	−	0.0202338i
$896$	0.441719	−	1.35947i	0.0147568	−	0.0454167i
$897$	−14.1683	−	4.60354i	−0.473064	−	0.153708i
$898$	−2.12066	−	2.91883i	−0.0707672	−	0.0974027i
$899$	15.8847			0.529786
$900$	−2.80380	+	4.31736i	−0.0934601	+	0.143912i
$901$	42.5961			1.41908
$902$	2.54077	+	3.49707i	0.0845984	+	0.116440i
$903$	−7.41595	−	2.40959i	−0.246787	−	0.0801861i
$904$	4.10057	−	12.6203i	0.136383	−	0.419744i
$905$	−9.61356	+	5.21965i	−0.319565	+	0.173507i
$906$	−8.49363	−	26.1407i	−0.282182	−	0.868467i
$907$			53.9788i			1.79234i	0.443713	+	0.896169i	$0.353661\pi$
$907$			53.9788i			1.79234i	−0.443713	+	0.896169i	$0.646339\pi$
$908$	−0.578987	+	0.188124i	−0.0192144	+	0.00624313i
$909$	14.5100	+	10.5421i	0.481265	+	0.349659i
$910$	−6.85708	+	1.27084i	−0.227310	+	0.0421279i
$911$	−5.42038	+	3.93814i	−0.179585	+	0.130476i	−0.673946	−	0.738780i	$-0.735402\pi$
$911$	−5.42038	+	3.93814i	−0.179585	+	0.130476i	0.494361	+	0.869257i	$0.335402\pi$
$912$	−0.825084	+	1.13563i	−0.0273213	+	0.0376045i
$913$	1.36673	−	1.88114i	0.0452320	−	0.0622566i
$914$	20.2548	−	14.7160i	0.669970	−	0.486762i
$915$	−0.545253	−	1.00425i	−0.0180255	−	0.0331994i
$916$	−16.0864	−	11.6874i	−0.531509	−	0.386164i
$917$	7.89658	−	2.56575i	0.260768	−	0.0847286i
$918$		−	20.9716i		−	0.692165i
$919$	−16.1299	−	49.6427i	−0.532076	−	1.63756i	−0.749883	−	0.661571i	$-0.769890\pi$
$919$	−16.1299	−	49.6427i	−0.532076	−	1.63756i	0.217806	−	0.975992i	$-0.430110\pi$
$920$	−4.68255	+	9.81700i	−0.154379	+	0.323657i
$921$	−8.13628	+	25.0409i	−0.268100	+	0.825125i
$922$	17.5294	+	5.69564i	0.577299	+	0.187576i
$923$	−2.61434	−	3.59834i	−0.0860522	−	0.118441i
$924$	0.772585			0.0254162
$925$	1.52243	−	5.68150i	0.0500573	−	0.186807i
$926$	−0.395091			−0.0129835
$927$	1.04144	+	1.43341i	0.0342053	+	0.0470795i
$928$	1.51101	+	0.490958i	0.0496015	+	0.0161165i
$929$	−2.98561	+	9.18877i	−0.0979548	+	0.301474i	−0.988012	−	0.154374i	$-0.950664\pi$
$929$	−2.98561	+	9.18877i	−0.0979548	+	0.301474i	0.890058	+	0.455848i	$0.150664\pi$
$930$	−22.7636	−	21.6022i	−0.746449	−	0.708363i
$931$	1.53171	+	4.71412i	0.0501998	+	0.154499i
$932$		−	11.0580i		−	0.362217i
$933$	−13.4591	+	4.37312i	−0.440630	+	0.143170i
$934$	−9.94135	−	7.22281i	−0.325291	−	0.236338i
$935$	2.88116	+	1.37426i	0.0942239	+	0.0449433i
$936$	−1.81736	+	1.32039i	−0.0594024	+	0.0431583i
$937$	5.33290	−	7.34011i	0.174218	−	0.239791i	−0.712974	−	0.701190i	$-0.752652\pi$
$937$	5.33290	−	7.34011i	0.174218	−	0.239791i	0.887193	+	0.461399i	$0.152652\pi$
$938$	−2.51972	+	3.46809i	−0.0822716	+	0.113237i
$939$	19.1607	−	13.9211i	0.625287	−	0.454297i
$940$	3.98320	+	1.89992i	0.129918	+	0.0619686i
$941$	8.87741	+	6.44981i	0.289395	+	0.210258i	0.723005	−	0.690843i	$-0.242760\pi$
$941$	8.87741	+	6.44981i	0.289395	+	0.210258i	−0.433610	+	0.901101i	$0.642760\pi$
$942$	11.4915	−	3.73383i	0.374415	−	0.121655i
$943$			54.6072i			1.77826i
$944$	−1.59311	−	4.90308i	−0.0518513	−	0.159582i
$945$	13.1144	+	12.4452i	0.426610	+	0.404843i
$946$	0.462385	−	1.42307i	0.0150334	−	0.0462681i
$947$	50.6091	+	16.4439i	1.64458	+	0.534355i	0.977554	−	0.210684i	$-0.0675690\pi$
$947$	50.6091	+	16.4439i	1.64458	+	0.534355i	0.667021	+	0.745039i	$0.267569\pi$
$948$	1.08457	+	1.49278i	0.0352251	+	0.0484832i
$949$	12.0808			0.392159
$950$	1.29416	−	4.82961i	0.0419880	−	0.156693i
$951$	7.88183			0.255586
$952$	−3.11511	−	4.28759i	−0.100961	−	0.138961i
$953$	−38.8204	−	12.6135i	−1.25752	−	0.408591i	−0.396907	−	0.917859i	$-0.629916\pi$
$953$	−38.8204	−	12.6135i	−1.25752	−	0.408591i	−0.860608	+	0.509267i	$0.829916\pi$
$954$	−3.65528	+	11.2498i	−0.118344	+	0.364226i
$955$	−14.8098	+	31.0488i	−0.479233	+	1.00472i
$956$	7.28394	+	22.4177i	0.235580	+	0.725039i
$957$			0.858707i			0.0277581i
$958$	−41.2609	+	13.4065i	−1.33308	+	0.433143i
$959$	13.4629	+	9.78137i	0.434740	+	0.315857i
$960$	−1.49769	−	2.75845i	−0.0483378	−	0.0890285i
$961$	−55.7916	+	40.5349i	−1.79973	+	1.30758i
$962$	1.50867	−	2.07650i	0.0486414	−	0.0669491i
$963$	2.27837	−	3.13591i	0.0734195	−	0.101053i
$964$	16.7758	−	12.1884i	0.540314	−	0.392561i
$965$	45.4926	−	8.43126i	1.46446	−	0.271412i
$966$	7.89600	+	5.73678i	0.254050	+	0.184578i
$967$	−22.3811	+	7.27205i	−0.719727	+	0.233853i	−0.645905	−	0.763418i	$-0.723520\pi$
$967$	−22.3811	+	7.27205i	−0.719727	+	0.233853i	−0.0738221	+	0.997271i	$0.523520\pi$
$968$		−	10.8517i		−	0.348788i
$969$	1.60825	+	4.94968i	0.0516644	+	0.159007i
$970$	−0.590897	+	0.320826i	−0.0189725	+	0.0103011i
$971$	13.4450	−	41.3794i	0.431470	−	1.32793i	−0.465192	−	0.885210i	$-0.654015\pi$
$971$	13.4450	−	41.3794i	0.431470	−	1.32793i	0.896661	−	0.442717i	$-0.145985\pi$
$972$	9.66218	+	3.13943i	0.309915	+	0.100697i
$973$	−6.02201	−	8.28859i	−0.193057	−	0.265720i
$974$	15.9648			0.511546
$975$	−8.34047	+	12.8428i	−0.267109	+	0.411300i
$976$	−0.364063			−0.0116534
$977$	18.5458	+	25.5262i	0.593334	+	0.816654i	0.995078	−	0.0990981i	$-0.0315958\pi$
$977$	18.5458	+	25.5262i	0.593334	+	0.816654i	−0.401744	+	0.915752i	$0.631596\pi$
$978$	4.92483	+	1.60017i	0.157479	+	0.0511679i
$979$	−1.47977	+	4.55427i	−0.0472937	+	0.145555i
$980$	−10.9887	−	1.44677i	−0.351022	−	0.0462153i
$981$	−2.19855	−	6.76644i	−0.0701943	−	0.216036i
$982$			35.1397i			1.12135i
$983$	−2.02076	+	0.656584i	−0.0644522	+	0.0209418i	−0.341066	−	0.940039i	$-0.610788\pi$
$983$	−2.02076	+	0.656584i	−0.0644522	+	0.0209418i	0.276613	+	0.960981i	$0.410788\pi$
$984$	−12.7491	−	9.26278i	−0.406427	−	0.295287i
$985$	−4.80263	+	36.4777i	−0.153024	+	1.16228i
$986$	4.76554	−	3.46236i	0.151766	−	0.110264i
$987$	2.32767	−	3.20377i	0.0740906	−	0.101977i
$988$	1.28246	−	1.76515i	0.0408004	−	0.0561569i
$989$	15.2926	−	11.1107i	0.486277	−	0.353301i
$990$	−0.610188	+	0.642996i	−0.0193930	+	0.0204357i
$991$	20.1185	+	14.6169i	0.639085	+	0.464323i	0.859536	−	0.511075i	$-0.170753\pi$
$991$	20.1185	+	14.6169i	0.639085	+	0.464323i	−0.220450	+	0.975398i	$0.570753\pi$
$992$	−9.50877	+	3.08959i	−0.301904	+	0.0980944i
$993$			21.2780i			0.675238i
$994$	0.900464	+	2.77134i	0.0285610	+	0.0879016i
$995$	1.23084	+	6.64125i	0.0390202	+	0.210542i
$996$	−2.61952	+	8.06204i	−0.0830026	+	0.255456i
$997$	1.36179	+	0.442474i	0.0431285	+	0.0140133i	0.330502	−	0.943805i	$-0.392782\pi$
$997$	1.36179	+	0.442474i	0.0431285	+	0.0140133i	−0.287373	+	0.957819i	$0.592782\pi$
$998$	0.408322	+	0.562007i	0.0129252	+	0.0177900i
$999$	−6.65411			−0.210527

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.a.39.16	✓	88
25.9	even	10	inner	950.2.n.a.609.16	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.a.39.16	✓	88	1.1	even	1	trivial
950.2.n.a.609.16	yes	88	25.9	even	10	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-1.33501 - 0.433772i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.407477 + 2.19863i) q^{5} +(-0.433772 - 1.33501i) q^{6} -1.42943i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.832948 - 0.605172i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-1.33501 - 0.433772i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.407477 + 2.19863i) q^{5} +(-0.433772 - 1.33501i) q^{6} -1.42943i q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.832948 - 0.605172i) q^{9} +(-1.53922 + 1.62198i) q^{10} +(-0.311502 + 0.226320i) q^{11} +(0.825084 - 1.13563i) q^{12} +(-1.28246 + 1.76515i) q^{13} +(1.15643 - 0.840199i) q^{14} +(0.409717 - 3.11195i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-3.52613 + 1.14571i) q^{17} -1.02958i q^{18} +(0.309017 + 0.951057i) q^{19} +(-2.21694 - 0.291880i) q^{20} +(-0.620048 + 1.90831i) q^{21} +(-0.366193 - 0.118983i) q^{22} +(-2.85907 - 3.93518i) q^{23} +1.40372 q^{24} +(-4.66793 + 1.79178i) q^{25} -2.18184 q^{26} +(3.32474 + 4.57611i) q^{27} +(1.35947 + 0.441719i) q^{28} +(-0.490958 + 1.51101i) q^{29} +(2.75845 - 1.49769i) q^{30} +(-3.08959 - 9.50877i) q^{31} -1.00000i q^{32} +(0.514031 - 0.167019i) q^{33} +(-2.99950 - 2.17927i) q^{34} +(3.14279 - 0.582460i) q^{35} +(0.832948 - 0.605172i) q^{36} +(-0.691464 + 0.951718i) q^{37} +(-0.587785 + 0.809017i) q^{38} +(2.47777 - 1.80020i) q^{39} +(-1.06695 - 1.96510i) q^{40} +(-9.08241 - 6.59875i) q^{41} +(-1.90831 + 0.620048i) q^{42} +3.88613i q^{43} +(-0.118983 - 0.366193i) q^{44} +(0.991141 - 2.07794i) q^{45} +(1.50310 - 4.62608i) q^{46} +(-1.87701 - 0.609877i) q^{47} +(0.825084 + 1.13563i) q^{48} +4.95672 q^{49} +(-4.19332 - 2.72325i) q^{50} +5.20441 q^{51} +(-1.28246 - 1.76515i) q^{52} +(-10.9266 - 3.55026i) q^{53} +(-1.74792 + 5.37954i) q^{54} +(-0.624522 - 0.592657i) q^{55} +(0.441719 + 1.35947i) q^{56} -1.40372i q^{57} +(-1.51101 + 0.490958i) q^{58} +(4.17081 + 3.03027i) q^{59} +(2.83303 + 1.35131i) q^{60} +(0.294533 - 0.213991i) q^{61} +(5.87674 - 8.08864i) q^{62} +(-0.865052 + 1.19064i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-4.40348 - 2.10039i) q^{65} +(0.437261 + 0.317688i) q^{66} +(-2.85217 + 0.926727i) q^{67} -3.70759i q^{68} +(2.10993 + 6.49370i) q^{69} +(2.31851 + 2.20021i) q^{70} +(-0.629945 + 1.93877i) q^{71} +(0.979189 + 0.318158i) q^{72} +(-3.25454 - 4.47950i) q^{73} -1.17639 q^{74} +(7.00897 - 0.367233i) q^{75} -1.00000 q^{76} +(0.323508 + 0.445271i) q^{77} +(2.91279 + 0.946424i) q^{78} +(-0.406201 + 1.25016i) q^{79} +(0.962665 - 2.01824i) q^{80} +(-1.49911 - 4.61379i) q^{81} -11.2265i q^{82} +(-5.74336 + 1.86613i) q^{83} +(-1.62331 - 1.17940i) q^{84} +(-3.95580 - 7.28579i) q^{85} +(-3.14395 + 2.28421i) q^{86} +(1.31087 - 1.80426i) q^{87} +(0.226320 - 0.311502i) q^{88} +(10.0616 - 7.31017i) q^{89} +(2.26366 - 0.419530i) q^{90} +(2.52316 + 1.83318i) q^{91} +(4.62608 - 1.50310i) q^{92} +14.0345i q^{93} +(-0.609877 - 1.87701i) q^{94} +(-1.96510 + 1.06695i) q^{95} +(-0.433772 + 1.33501i) q^{96} +(0.285978 + 0.0929199i) q^{97} +(2.91349 + 4.01007i) q^{98} +0.396427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

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