LMFDB - Embedded newform 273.2.t.c.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.3
Root			$1.21245 - 0.727987i$ of defining polynomial
Character	$\chi$	$=$	273.4
Dual form			273.2.t.c.205.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.45597i q^{2} +(-0.500000 - 0.866025i) q^{3} -0.119863 q^{4} +(-3.67267 + 2.12042i) q^{5} +(-1.26091 + 0.727987i) q^{6} +(-0.357777 - 2.62145i) q^{7} -2.73743i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.45597i q^{2} +(-0.500000 - 0.866025i) q^{3} -0.119863 q^{4} +(-3.67267 + 2.12042i) q^{5} +(-1.26091 + 0.727987i) q^{6} +(-0.357777 - 2.62145i) q^{7} -2.73743i q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.08727 + 5.34732i) q^{10} +(-3.49469 + 2.01766i) q^{11} +(0.0599314 + 0.103804i) q^{12} +(-3.50498 - 0.845633i) q^{13} +(-3.81676 + 0.520915i) q^{14} +(3.67267 + 2.12042i) q^{15} -4.22536 q^{16} -0.0484615 q^{17} +(1.26091 + 0.727987i) q^{18} +(-1.10977 - 0.640729i) q^{19} +(0.440217 - 0.254159i) q^{20} +(-2.09135 + 1.62057i) q^{21} +(2.93766 + 5.08818i) q^{22} +3.59569 q^{23} +(-2.37069 + 1.36872i) q^{24} +(6.49234 - 11.2451i) q^{25} +(-1.23122 + 5.10317i) q^{26} +1.00000 q^{27} +(0.0428842 + 0.314214i) q^{28} +(1.08299 - 1.87579i) q^{29} +(3.08727 - 5.34732i) q^{30} +(4.50804 + 2.60272i) q^{31} +0.677151i q^{32} +(3.49469 + 2.01766i) q^{33} +0.0705587i q^{34} +(6.87256 + 8.86908i) q^{35} +(0.0599314 - 0.103804i) q^{36} -4.30401i q^{37} +(-0.932885 + 1.61580i) q^{38} +(1.02015 + 3.45822i) q^{39} +(5.80450 + 10.0537i) q^{40} +(-10.5963 - 6.11775i) q^{41} +(2.35951 + 3.04496i) q^{42} +(-2.51030 - 4.34796i) q^{43} +(0.418883 - 0.241842i) q^{44} -4.24083i q^{45} -5.23524i q^{46} +(0.819767 - 0.473293i) q^{47} +(2.11268 + 3.65927i) q^{48} +(-6.74399 + 1.87579i) q^{49} +(-16.3725 - 9.45268i) q^{50} +(0.0242308 + 0.0419689i) q^{51} +(0.420117 + 0.101360i) q^{52} +(2.66425 - 4.61461i) q^{53} -1.45597i q^{54} +(8.55656 - 14.8204i) q^{55} +(-7.17604 + 0.979391i) q^{56} +1.28146i q^{57} +(-2.73110 - 1.57680i) q^{58} -3.17187i q^{59} +(-0.440217 - 0.254159i) q^{60} +(-1.90786 + 3.30451i) q^{61} +(3.78949 - 6.56359i) q^{62} +(2.44913 + 1.00088i) q^{63} -7.46480 q^{64} +(14.6657 - 4.32630i) q^{65} +(2.93766 - 5.08818i) q^{66} +(-10.5072 + 6.06634i) q^{67} +0.00580873 q^{68} +(-1.79785 - 3.11396i) q^{69} +(12.9132 - 10.0063i) q^{70} +(5.69604 - 3.28861i) q^{71} +(2.37069 + 1.36872i) q^{72} +(12.1155 + 6.99486i) q^{73} -6.26653 q^{74} -12.9847 q^{75} +(0.133021 + 0.0767995i) q^{76} +(6.53951 + 8.43927i) q^{77} +(5.03508 - 1.48532i) q^{78} +(6.29441 + 10.9022i) q^{79} +(15.5183 - 8.95952i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.90729 + 15.4279i) q^{82} -3.47006i q^{83} +(0.250675 - 0.194246i) q^{84} +(0.177983 - 0.102759i) q^{85} +(-6.33052 + 3.65493i) q^{86} -2.16598 q^{87} +(5.52320 + 9.56647i) q^{88} -7.47988i q^{89} -6.17455 q^{90} +(-0.962780 + 9.49068i) q^{91} -0.430990 q^{92} -5.20543i q^{93} +(-0.689102 - 1.19356i) q^{94} +5.43445 q^{95} +(0.586430 - 0.338575i) q^{96} +(3.63599 - 2.09924i) q^{97} +(2.73110 + 9.81908i) q^{98} -4.03532i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.45597i		−	1.02953i	−0.857331	−	0.514765i	$-0.827879\pi$
$2$		−	1.45597i		−	1.02953i	0.857331	−	0.514765i	$-0.172121\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.119863			−0.0599314
$5$	−3.67267	+	2.12042i	−1.64247	+	0.948279i	−0.662516	+	0.749048i	$0.730511\pi$
$5$	−3.67267	+	2.12042i	−1.64247	+	0.948279i	−0.979952	+	0.199231i	$0.936155\pi$
$6$	−1.26091	+	0.727987i	−0.514765	+	0.297200i
$7$	−0.357777	−	2.62145i	−0.135227	−	0.990815i
$7$	−0.357777	−	2.62145i	−0.135227	−	0.990815i
$8$		−	2.73743i		−	0.967829i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	3.08727	+	5.34732i	0.976282	+	1.69097i
$11$	−3.49469	+	2.01766i	−1.05369	+	0.608347i	−0.923680	−	0.383166i	$-0.874834\pi$
$11$	−3.49469	+	2.01766i	−1.05369	+	0.608347i	−0.130008	+	0.991513i	$0.541500\pi$
$12$	0.0599314	+	0.103804i	0.0173007	+	0.0299657i
$13$	−3.50498	−	0.845633i	−0.972107	−	0.234536i
$13$	−3.50498	−	0.845633i	−0.972107	−	0.234536i
$14$	−3.81676	+	0.520915i	−1.02007	+	0.139220i
$15$	3.67267	+	2.12042i	0.948279	+	0.547489i
$16$	−4.22536			−1.05634
$17$	−0.0484615			−0.0117536			−0.00587682	−	0.999983i	$-0.501871\pi$
$17$	−0.0484615			−0.0117536			−0.00587682	+	0.999983i	$0.501871\pi$
$18$	1.26091	+	0.727987i	0.297200	+	0.171588i
$19$	−1.10977	−	0.640729i	−0.254600	−	0.146993i	0.367269	−	0.930115i	$-0.380293\pi$
$19$	−1.10977	−	0.640729i	−0.254600	−	0.146993i	−0.621869	+	0.783122i	$0.713626\pi$
$20$	0.440217	−	0.254159i	0.0984354	−	0.0568317i
$21$	−2.09135	+	1.62057i	−0.456371	+	0.353637i
$22$	2.93766	+	5.08818i	0.626311	+	1.08480i
$23$	3.59569			0.749754			0.374877	−	0.927075i	$-0.377685\pi$
$23$	3.59569			0.749754			0.374877	+	0.927075i	$0.377685\pi$
$24$	−2.37069	+	1.36872i	−0.483914	+	0.279388i
$25$	6.49234	−	11.2451i	1.29847	−	2.24901i
$26$	−1.23122	+	5.10317i	−0.241462	+	1.00081i
$27$	1.00000			0.192450
$28$	0.0428842	+	0.314214i	0.00810435	+	0.0593809i
$29$	1.08299	−	1.87579i	0.201106	−	0.348325i	−0.747779	−	0.663947i	$-0.768880\pi$
$29$	1.08299	−	1.87579i	0.201106	−	0.348325i	0.948885	+	0.315622i	$0.102213\pi$
$30$	3.08727	−	5.34732i	0.563657	−	0.976282i
$31$	4.50804	+	2.60272i	0.809667	+	0.467461i	0.846840	−	0.531847i	$-0.178502\pi$
$31$	4.50804	+	2.60272i	0.809667	+	0.467461i	−0.0371732	+	0.999309i	$0.511835\pi$
$32$			0.677151i			0.119704i
$33$	3.49469	+	2.01766i	0.608347	+	0.351229i
$34$			0.0705587i			0.0121007i
$35$	6.87256	+	8.86908i	1.16168	+	1.49915i
$36$	0.0599314	−	0.103804i	0.00998857	−	0.0173007i
$37$		−	4.30401i		−	0.707574i	−0.935326	−	0.353787i	$-0.884894\pi$
$37$		−	4.30401i		−	0.707574i	0.935326	−	0.353787i	$-0.115106\pi$
$38$	−0.932885	+	1.61580i	−0.151334	+	0.262118i
$39$	1.02015	+	3.45822i	0.163355	+	0.553758i
$40$	5.80450	+	10.0537i	0.917772	+	1.58963i
$41$	−10.5963	−	6.11775i	−1.65486	−	0.955432i	−0.975034	−	0.222056i	$-0.928723\pi$
$41$	−10.5963	−	6.11775i	−1.65486	−	0.955432i	−0.679823	−	0.733376i	$-0.737943\pi$
$42$	2.35951	+	3.04496i	0.364080	+	0.469847i
$43$	−2.51030	−	4.34796i	−0.382816	−	0.663058i	0.608647	−	0.793441i	$-0.291713\pi$
$43$	−2.51030	−	4.34796i	−0.382816	−	0.663058i	−0.991464	+	0.130383i	$0.958379\pi$
$44$	0.418883	−	0.241842i	0.0631490	−	0.0364591i
$45$		−	4.24083i		−	0.632186i
$46$		−	5.23524i		−	0.771894i
$47$	0.819767	−	0.473293i	0.119575	−	0.0690368i	−0.439019	−	0.898478i	$-0.644674\pi$
$47$	0.819767	−	0.473293i	0.119575	−	0.0690368i	0.558595	+	0.829441i	$0.311341\pi$
$48$	2.11268	+	3.65927i	0.304939	+	0.528170i
$49$	−6.74399	+	1.87579i	−0.963427	+	0.267970i
$50$	−16.3725	−	9.45268i	−2.31542	−	1.33681i
$51$	0.0242308	+	0.0419689i	0.00339298	+	0.00587682i
$52$	0.420117	+	0.101360i	0.0582598	+	0.0140561i
$53$	2.66425	−	4.61461i	0.365962	−	0.633865i	−0.622968	−	0.782247i	$-0.714073\pi$
$53$	2.66425	−	4.61461i	0.365962	−	0.633865i	0.988930	+	0.148382i	$0.0474066\pi$
$54$		−	1.45597i		−	0.198133i
$55$	8.55656	−	14.8204i	1.15377	−	1.99838i
$56$	−7.17604	+	0.979391i	−0.958939	+	0.130877i
$57$			1.28146i			0.169733i
$58$	−2.73110	−	1.57680i	−0.358611	−	0.207044i
$59$		−	3.17187i		−	0.412943i	−0.978453	−	0.206471i	$-0.933802\pi$
$59$		−	3.17187i		−	0.412943i	0.978453	−	0.206471i	$-0.0661980\pi$
$60$	−0.440217	−	0.254159i	−0.0568317	−	0.0328118i
$61$	−1.90786	+	3.30451i	−0.244276	+	0.423099i	−0.961928	−	0.273303i	$-0.911884\pi$
$61$	−1.90786	+	3.30451i	−0.244276	+	0.423099i	0.717652	+	0.696402i	$0.245217\pi$
$62$	3.78949	−	6.56359i	0.481265	−	0.833576i
$63$	2.44913	+	1.00088i	0.308561	+	0.126099i
$64$	−7.46480			−0.933100
$65$	14.6657	−	4.32630i	1.81906	−	0.536611i
$66$	2.93766	−	5.08818i	0.361601	−	0.626311i
$67$	−10.5072	+	6.06634i	−1.28366	+	0.741121i	−0.977515	−	0.210864i	$-0.932372\pi$
$67$	−10.5072	+	6.06634i	−1.28366	+	0.741121i	−0.306144	+	0.951985i	$0.599039\pi$
$68$	0.00580873			0.000704412
$69$	−1.79785	−	3.11396i	−0.216435	−	0.374877i
$70$	12.9132	−	10.0063i	1.54342	−	1.19598i
$71$	5.69604	−	3.28861i	0.675996	−	0.390287i	−0.122349	−	0.992487i	$-0.539043\pi$
$71$	5.69604	−	3.28861i	0.675996	−	0.390287i	0.798345	+	0.602201i	$0.205709\pi$
$72$	2.37069	+	1.36872i	0.279388	+	0.161305i
$73$	12.1155	+	6.99486i	1.41801	+	0.818687i	0.996124	−	0.0879632i	$-0.0280358\pi$
$73$	12.1155	+	6.99486i	1.41801	+	0.818687i	0.421883	+	0.906650i	$0.361369\pi$
$74$	−6.26653			−0.728469
$75$	−12.9847			−1.49934
$76$	0.133021	+	0.0767995i	0.0152585	+	0.00880951i
$77$	6.53951	+	8.43927i	0.745246	+	0.961744i
$78$	5.03508	−	1.48532i	0.570111	−	0.168179i
$79$	6.29441	+	10.9022i	0.708177	+	1.22660i	0.965533	+	0.260281i	$0.0838153\pi$
$79$	6.29441	+	10.9022i	0.708177	+	1.22660i	−0.257356	+	0.966317i	$0.582851\pi$
$80$	15.5183	−	8.95952i	1.73500	−	1.00171i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.90729	+	15.4279i	−0.983646	+	1.70372i
$83$		−	3.47006i		−	0.380889i	−0.981698	−	0.190444i	$-0.939007\pi$
$83$		−	3.47006i		−	0.380889i	0.981698	−	0.190444i	$-0.0609929\pi$
$84$	0.250675	−	0.194246i	0.0273509	−	0.0211940i
$85$	0.177983	−	0.102759i	0.0193050	−	0.0111457i
$86$	−6.33052	+	3.65493i	−0.682638	+	0.394121i
$87$	−2.16598			−0.232217
$88$	5.52320	+	9.56647i	0.588776	+	1.01979i
$89$		−	7.47988i		−	0.792866i	−0.918064	−	0.396433i	$-0.870248\pi$
$89$		−	7.47988i		−	0.792866i	0.918064	−	0.396433i	$-0.129752\pi$
$90$	−6.17455			−0.650855
$91$	−0.962780	+	9.49068i	−0.100927	+	0.994894i
$92$	−0.430990			−0.0449338
$93$		−	5.20543i		−	0.539778i
$94$	−0.689102	−	1.19356i	−0.0710754	−	0.123106i
$95$	5.43445			0.557563
$96$	0.586430	−	0.338575i	0.0598522	−	0.0345557i
$97$	3.63599	−	2.09924i	0.369179	−	0.213145i	−0.303921	−	0.952697i	$-0.598296\pi$
$97$	3.63599	−	2.09924i	0.369179	−	0.213145i	0.673100	+	0.739552i	$0.264963\pi$
$98$	2.73110	+	9.81908i	0.275883	+	0.991877i
$99$		−	4.03532i		−	0.405565i
$100$	−0.778190	+	1.34786i	−0.0778190	+	0.134786i
$101$	−7.94673	−	13.7641i	−0.790729	−	1.36958i	−0.925516	−	0.378708i	$-0.876368\pi$
$101$	−7.94673	−	13.7641i	−0.790729	−	1.36958i	0.134787	−	0.990875i	$-0.456965\pi$
$102$	0.0611057	−	0.0352794i	0.00605036	−	0.00349318i
$103$	−3.27155	−	5.66650i	−0.322356	−	0.558336i	0.658618	−	0.752477i	$-0.271141\pi$
$103$	−3.27155	−	5.66650i	−0.322356	−	0.558336i	−0.980974	+	0.194141i	$0.937808\pi$
$104$	−2.31486	+	9.59465i	−0.226991	+	0.940833i
$105$	4.24457	−	10.3864i	0.414227	−	1.01360i
$106$	−6.71875	−	3.87907i	−0.652583	−	0.376769i
$107$	−7.15958			−0.692143			−0.346072	−	0.938208i	$-0.612485\pi$
$107$	−7.15958			−0.692143			−0.346072	+	0.938208i	$0.612485\pi$
$108$	−0.119863			−0.0115338
$109$	0.693532	+	0.400411i	0.0664283	+	0.0383524i	0.532846	−	0.846212i	$-0.321122\pi$
$109$	0.693532	+	0.400411i	0.0664283	+	0.0383524i	−0.466418	+	0.884564i	$0.654456\pi$
$110$	−21.5781	−	12.4581i	−2.05739	−	1.18784i
$111$	−3.72738	+	2.15200i	−0.353787	+	0.204259i
$112$	1.51174	+	11.0766i	0.142846	+	1.04664i
$113$	−0.289689	−	0.501755i	−0.0272516	−	0.0472012i	0.852078	−	0.523415i	$-0.175342\pi$
$113$	−0.289689	−	0.501755i	−0.0272516	−	0.0472012i	−0.879330	+	0.476214i	$0.842009\pi$
$114$	1.86577			0.174745
$115$	−13.2058	+	7.62437i	−1.23145	+	0.710976i
$116$	−0.129810	+	0.224837i	−0.0120526	+	0.0208756i
$117$	2.48483	−	2.61259i	0.229723	−	0.241534i
$118$	−4.61817			−0.425137
$119$	0.0173384	+	0.127039i	0.00158941	+	0.0116457i
$120$	5.80450	−	10.0537i	0.529876	−	0.917772i
$121$	2.64189	−	4.57589i	0.240172	−	0.415990i
$122$	4.81128	+	2.77780i	0.435593	+	0.251490i
$123$			12.2355i			1.10324i
$124$	−0.540346	−	0.311969i	−0.0485245	−	0.0280156i
$125$			33.8617i			3.02868i
$126$	1.45726	−	3.56587i	0.129823	−	0.317673i
$127$	0.797934	−	1.38206i	0.0708052	−	0.122638i	−0.828449	−	0.560064i	$-0.810776\pi$
$127$	0.797934	−	1.38206i	0.0708052	−	0.122638i	0.899254	+	0.437426i	$0.144110\pi$
$128$			12.2229i			1.08036i
$129$	−2.51030	+	4.34796i	−0.221019	+	0.382816i
$130$	−6.29898	−	21.3530i	−0.552457	−	1.87278i
$131$	2.97143	+	5.14667i	0.259615	+	0.449666i	0.966139	−	0.258023i	$-0.0830710\pi$
$131$	2.97143	+	5.14667i	0.259615	+	0.449666i	−0.706524	+	0.707689i	$0.749738\pi$
$132$	−0.418883	−	0.241842i	−0.0364591	−	0.0210497i
$133$	−1.28259	+	3.13846i	−0.111214	+	0.272139i
$134$	8.83244	+	15.2982i	0.763006	+	1.32157i
$135$	−3.67267	+	2.12042i	−0.316093	+	0.182496i
$136$			0.132660i			0.0113755i
$137$			16.0660i			1.37261i	0.727315	+	0.686304i	$0.240768\pi$
$137$			16.0660i			1.37261i	−0.727315	+	0.686304i	$0.759232\pi$
$138$	−4.53385	+	2.61762i	−0.385947	+	0.222826i
$139$	5.62726	+	9.74671i	0.477298	+	0.826705i	0.999661	−	0.0260182i	$-0.00828280\pi$
$139$	5.62726	+	9.74671i	0.477298	+	0.826705i	−0.522363	+	0.852723i	$0.674949\pi$
$140$	−0.823765	−	1.06307i	−0.0696208	−	0.0898461i
$141$	−0.819767	−	0.473293i	−0.0690368	−	0.0398584i
$142$	−4.78814	−	8.29330i	−0.401812	−	0.695958i
$143$	13.9550	−	4.11664i	1.16698	−	0.344251i
$144$	2.11268	−	3.65927i	0.176057	−	0.304939i
$145$			9.18554i			0.762818i
$146$	10.1843	−	17.6398i	0.842862	−	1.45988i
$147$	4.99648	+	4.90257i	0.412102	+	0.404357i
$148$			0.515890i			0.0424059i
$149$	4.83224	+	2.78990i	0.395873	+	0.228557i	0.684702	−	0.728823i	$-0.259933\pi$
$149$	4.83224	+	2.78990i	0.395873	+	0.228557i	−0.288829	+	0.957381i	$0.593266\pi$
$150$			18.9054i			1.54362i
$151$	−11.1069	−	6.41258i	−0.903868	−	0.521849i	−0.0254151	−	0.999677i	$-0.508091\pi$
$151$	−11.1069	−	6.41258i	−0.903868	−	0.521849i	−0.878453	+	0.477828i	$0.841424\pi$
$152$	−1.75395	+	3.03793i	−0.142264	+	0.246409i
$153$	0.0242308	−	0.0419689i	0.00195894	−	0.00339298i
$154$	12.2874	−	9.52136i	0.990144	−	0.767253i
$155$	−22.0754			−1.77314
$156$	−0.122278	−	0.414512i	−0.00979010	−	0.0331875i
$157$	1.87821	−	3.25315i	0.149897	−	0.259630i	−0.781292	−	0.624166i	$-0.785439\pi$
$157$	1.87821	−	3.25315i	0.149897	−	0.259630i	0.931189	+	0.364536i	$0.118772\pi$
$158$	15.8734	−	9.16450i	1.26282	−	0.729089i
$159$	−5.32849			−0.422577
$160$	−1.43584	−	2.48695i	−0.113513	−	0.196611i
$161$	−1.28646	−	9.42592i	−0.101387	−	0.742867i
$162$	−1.26091	+	0.727987i	−0.0990665	+	0.0571961i
$163$	−16.2233	−	9.36652i	−1.27071	−	0.733642i	−0.295585	−	0.955316i	$-0.595515\pi$
$163$	−16.2233	−	9.36652i	−1.27071	−	0.733642i	−0.975121	+	0.221674i	$0.928848\pi$
$164$	1.27010	+	0.733291i	0.0991779	+	0.0572604i
$165$	−17.1131			−1.33225
$166$	−5.05232			−0.392136
$167$	8.22069	+	4.74622i	0.636136	+	0.367273i	0.783124	−	0.621865i	$-0.213625\pi$
$167$	8.22069	+	4.74622i	0.636136	+	0.367273i	−0.146989	+	0.989138i	$0.546958\pi$
$168$	4.43620	+	5.72494i	0.342260	+	0.441689i
$169$	11.5698	+	5.92786i	0.889985	+	0.455989i
$170$	−0.149614	−	0.259139i	−0.0114749	−	0.0198751i
$171$	1.10977	−	0.640729i	0.0848666	−	0.0489978i
$172$	0.300891	+	0.521159i	0.0229427	+	0.0397380i
$173$	8.79700	−	15.2368i	0.668823	−	1.15844i	−0.309410	−	0.950929i	$-0.600132\pi$
$173$	8.79700	−	15.2368i	0.668823	−	1.15844i	0.978233	−	0.207507i	$-0.0665350\pi$
$174$			3.15361i			0.239074i
$175$	−31.8012	−	12.9961i	−2.40394	−	0.982413i
$176$	14.7663	−	8.52533i	1.11305	−	0.642621i
$177$	−2.74692	+	1.58594i	−0.206471	+	0.119206i
$178$	−10.8905			−0.816279
$179$	8.98969	+	15.5706i	0.671921	+	1.16380i	0.977359	+	0.211590i	$0.0678640\pi$
$179$	8.98969	+	15.5706i	0.671921	+	1.16380i	−0.305437	+	0.952212i	$0.598803\pi$
$180$			0.508318i			0.0378878i
$181$	9.08741			0.675462			0.337731	−	0.941243i	$-0.390341\pi$
$181$	9.08741			0.675462			0.337731	+	0.941243i	$0.390341\pi$
$182$	13.8182	+	1.40178i	1.02427	+	0.103907i
$183$	3.81572			0.282066
$184$		−	9.84296i		−	0.725633i
$185$	9.12629	+	15.8072i	0.670978	+	1.16217i
$186$	−7.57898			−0.555717
$187$	0.169358	−	0.0977788i	0.0123847	−	0.00715029i
$188$	−0.0982595	+	0.0567302i	−0.00716631	+	0.00413747i
$189$	−0.357777	−	2.62145i	−0.0260245	−	0.190682i
$190$		−	7.91242i		−	0.574027i
$191$	−10.0660	+	17.4349i	−0.728352	+	1.26154i	0.229227	+	0.973373i	$0.426380\pi$
$191$	−10.0660	+	17.4349i	−0.728352	+	1.26154i	−0.957579	+	0.288170i	$0.906953\pi$
$192$	3.73240	+	6.46471i	0.269363	+	0.466550i
$193$	−2.76578	+	1.59682i	−0.199085	+	0.114942i	−0.596229	−	0.802815i	$-0.703335\pi$
$193$	−2.76578	+	1.59682i	−0.199085	+	0.114942i	0.397144	+	0.917756i	$0.370001\pi$
$194$	−3.05644	−	5.29391i	−0.219440	−	0.380080i
$195$	−11.0796	−	10.5378i	−0.793423	−	0.754624i
$196$	0.808354	−	0.224837i	0.0577395	−	0.0160598i
$197$	−12.7261	−	7.34744i	−0.906700	−	0.523483i	−0.0273321	−	0.999626i	$-0.508701\pi$
$197$	−12.7261	−	7.34744i	−0.906700	−	0.523483i	−0.879368	+	0.476143i	$0.842034\pi$
$198$	−5.87532			−0.417541
$199$	−23.1495			−1.64102			−0.820511	−	0.571630i	$-0.806311\pi$
$199$	−23.1495			−1.64102			−0.820511	+	0.571630i	$0.806311\pi$
$200$	−30.7826	−	17.7723i	−2.17666	−	1.25669i
$201$	10.5072	+	6.06634i	0.741121	+	0.427887i
$202$	−20.0402	+	11.5702i	−1.41003	+	0.814079i
$203$	−5.30476	−	2.16788i	−0.372321	−	0.152156i
$204$	−0.00290437	−	0.00503051i	−0.000203346	−	0.000352206i
$205$	51.8887			3.62407
$206$	−8.25027	+	4.76330i	−0.574824	+	0.331875i
$207$	−1.79785	+	3.11396i	−0.124959	+	0.216435i
$208$	14.8098	+	3.57310i	1.02688	+	0.247750i
$209$	5.17109			0.357692
$210$	−15.1223	−	6.17998i	−1.04354	−	0.426459i
$211$	4.58765	−	7.94604i	0.315827	−	0.547028i	−0.663786	−	0.747923i	$-0.731051\pi$
$211$	4.58765	−	7.94604i	0.315827	−	0.547028i	0.979613	+	0.200894i	$0.0643848\pi$
$212$	−0.319344	+	0.553120i	−0.0219326	+	0.0379884i
$213$	−5.69604	−	3.28861i	−0.390287	−	0.225332i
$214$			10.4242i			0.712582i
$215$	18.4390	+	10.6457i	1.25753	+	0.726034i
$216$		−	2.73743i		−	0.186259i
$217$	5.21001	−	12.7488i	0.353679	−	0.865443i
$218$	0.582988	−	1.00976i	0.0394849	−	0.0683899i
$219$		−	13.9897i		−	0.945338i
$220$	−1.02561	+	1.77641i	−0.0691468	+	0.119766i
$221$	0.169857	+	0.0409806i	0.0114258	+	0.00275666i
$222$	3.13326	+	5.42697i	0.210291	+	0.364234i
$223$	1.96256	+	1.13309i	0.131423	+	0.0758770i	0.564270	−	0.825590i	$-0.309158\pi$
$223$	1.96256	+	1.13309i	0.131423	+	0.0758770i	−0.432847	+	0.901467i	$0.642491\pi$
$224$	1.77512	−	0.242269i	0.118605	−	0.0161873i
$225$	6.49234	+	11.2451i	0.432823	+	0.749671i
$226$	−0.730543	+	0.421779i	−0.0485950	+	0.0280563i
$227$			8.35130i			0.554295i	0.960827	+	0.277148i	$0.0893891\pi$
$227$			8.35130i			0.554295i	−0.960827	+	0.277148i	$0.910611\pi$
$228$		−	0.153599i		−	0.0101723i
$229$	−6.05361	+	3.49506i	−0.400034	+	0.230960i	−0.686499	−	0.727131i	$-0.740853\pi$
$229$	−6.05361	+	3.49506i	−0.400034	+	0.230960i	0.286465	+	0.958091i	$0.407520\pi$
$230$	11.1009	+	19.2273i	0.731971	+	1.26781i
$231$	4.03887	−	9.88302i	0.265738	−	0.650255i
$232$	−5.13485	−	2.96461i	−0.337119	−	0.194636i
$233$	−11.1643	−	19.3371i	−0.731395	−	1.26681i	−0.956287	−	0.292429i	$-0.905536\pi$
$233$	−11.1643	−	19.3371i	−0.731395	−	1.26681i	0.224892	−	0.974384i	$-0.427797\pi$
$234$	−3.80386	−	3.61785i	−0.248666	−	0.236506i
$235$	−2.00716	+	3.47649i	−0.130932	+	0.226782i
$236$			0.380190i			0.0247482i
$237$	6.29441	−	10.9022i	0.408866	−	0.708177i
$238$	0.184966	−	0.0252443i	0.0119896	−	0.00163635i
$239$		−	12.8510i		−	0.831264i	−0.909533	−	0.415632i	$-0.863560\pi$
$239$		−	12.8510i		−	0.831264i	0.909533	−	0.415632i	$-0.136440\pi$
$240$	−15.5183	−	8.95952i	−1.00171	−	0.578335i
$241$		−	14.9262i		−	0.961483i	−0.876862	−	0.480742i	$-0.840367\pi$
$241$		−	14.9262i		−	0.961483i	0.876862	−	0.480742i	$-0.159633\pi$
$242$	−6.66238	−	3.84653i	−0.428274	−	0.247264i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.228681	−	0.396088i	0.0146398	−	0.0253569i
$245$	20.7910	−	21.1892i	1.32829	−	1.35373i
$246$	17.8146			1.13582
$247$	3.34792	+	3.18421i	0.213023	+	0.202606i
$248$	7.12476	−	12.3404i	0.452423	−	0.783619i
$249$	−3.00516	+	1.73503i	−0.190444	+	0.109953i
$250$	49.3018			3.11812
$251$	−5.86990	−	10.1670i	−0.370505	−	0.641733i	0.619138	−	0.785282i	$-0.287482\pi$
$251$	−5.86990	−	10.1670i	−0.370505	−	0.641733i	−0.989643	+	0.143549i	$0.954149\pi$
$252$	−0.293560	−	0.119968i	−0.0184925	−	0.00755729i
$253$	−12.5658	+	7.25488i	−0.790006	+	0.456110i
$254$	−2.01225	−	1.16177i	−0.126260	−	0.0728961i
$255$	−0.177983	−	0.102759i	−0.0111457	−	0.00643499i
$256$	2.86658			0.179161
$257$	−30.6013			−1.90885			−0.954427	−	0.298445i	$-0.903532\pi$
$257$	−30.6013			−1.90885			−0.954427	+	0.298445i	$0.903532\pi$
$258$	6.33052	+	3.65493i	0.394121	+	0.227546i
$259$	−11.2827	+	1.53988i	−0.701075	+	0.0956833i
$260$	−1.75788	+	0.518562i	−0.109019	+	0.0321598i
$261$	1.08299	+	1.87579i	0.0670353	+	0.116108i
$262$	7.49342	−	4.32633i	0.462945	−	0.267281i
$263$	9.08377	+	15.7336i	0.560129	+	0.970173i	0.997485	+	0.0708837i	$0.0225819\pi$
$263$	9.08377	+	15.7336i	0.560129	+	0.970173i	−0.437355	+	0.899289i	$0.644085\pi$
$264$	5.52320	−	9.56647i	0.339930	−	0.588776i
$265$			22.5973i			1.38814i
$266$	4.56951	+	1.86741i	0.280175	+	0.114498i
$267$	−6.47777	+	3.73994i	−0.396433	+	0.228881i
$268$	1.25942	−	0.727128i	0.0769315	−	0.0444164i
$269$	10.1222			0.617163			0.308581	−	0.951198i	$-0.400146\pi$
$269$	10.1222			0.617163			0.308581	+	0.951198i	$0.400146\pi$
$270$	3.08727	+	5.34732i	0.187886	+	0.325427i
$271$		−	26.5527i		−	1.61296i	−0.591260	−	0.806481i	$-0.701369\pi$
$271$		−	26.5527i		−	1.61296i	0.591260	−	0.806481i	$-0.298631\pi$
$272$	0.204767			0.0124158
$273$	8.70056	−	3.91155i	0.526582	−	0.236738i
$274$	23.3916			1.41314
$275$			52.3973i			3.15968i
$276$	0.215495	+	0.373248i	0.0129713	+	0.0224669i
$277$	29.3101			1.76107			0.880537	−	0.473977i	$-0.157182\pi$
$277$	29.3101			1.76107			0.880537	+	0.473977i	$0.157182\pi$
$278$	14.1910	−	8.19315i	0.851117	−	0.491393i
$279$	−4.50804	+	2.60272i	−0.269889	+	0.155820i
$280$	24.2785	−	18.8132i	1.45092	−	1.12430i
$281$		−	6.74332i		−	0.402273i	−0.979563	−	0.201136i	$-0.935537\pi$
$281$		−	6.74332i		−	0.402273i	0.979563	−	0.201136i	$-0.0644635\pi$
$282$	−0.689102	+	1.19356i	−0.0410354	+	0.0710754i
$283$	−8.69346	−	15.0575i	−0.516772	−	0.895076i	−0.999810	−	0.0194766i	$-0.993800\pi$
$283$	−8.69346	−	15.0575i	−0.516772	−	0.895076i	0.483038	−	0.875599i	$-0.339533\pi$
$284$	−0.682744	+	0.394182i	−0.0405134	+	0.0233904i
$285$	−2.71722	−	4.70637i	−0.160955	−	0.278781i
$286$	−5.99372	−	20.3182i	−0.354416	−	1.20144i
$287$	−12.2463	+	29.9663i	−0.722875	+	1.76886i
$288$	−0.586430	−	0.338575i	−0.0345557	−	0.0199507i
$289$	−16.9977			−0.999862
$290$	13.3739			0.785344
$291$	−3.63599	−	2.09924i	−0.213145	−	0.123060i
$292$	−1.45219	−	0.838424i	−0.0849831	−	0.0490650i
$293$	15.2346	−	8.79572i	0.890017	−	0.513852i	0.0160689	−	0.999871i	$-0.494885\pi$
$293$	15.2346	−	8.79572i	0.890017	−	0.513852i	0.873948	+	0.486019i	$0.161552\pi$
$294$	7.13802	−	7.27475i	0.416298	−	0.424272i
$295$	6.72570	+	11.6492i	0.391585	+	0.678245i
$296$	−11.7819			−0.684811
$297$	−3.49469	+	2.01766i	−0.202782	+	0.117076i
$298$	4.06202	−	7.03562i	0.235306	−	0.407563i
$299$	−12.6028	−	3.04063i	−0.728841	−	0.175844i
$300$	1.55638			0.0898576
$301$	−10.4998	+	8.13621i	−0.605200	+	0.468964i
$302$	−9.33656	+	16.1714i	−0.537259	+	0.930559i
$303$	−7.94673	+	13.7641i	−0.456528	+	0.790729i
$304$	4.68920	+	2.70731i	0.268944	+	0.155275i
$305$		−	16.1818i		−	0.926569i
$306$	−0.0611057	−	0.0352794i	−0.00349318	−	0.00201679i
$307$		−	0.0778605i		−	0.00444373i	−0.999998	−	0.00222187i	$-0.999293\pi$
$307$		−	0.0778605i		−	0.00444373i	0.999998	−	0.00222187i	$-0.000707243\pi$
$308$	−0.783844	−	1.01155i	−0.0446636	−	0.0576387i
$309$	−3.27155	+	5.66650i	−0.186112	+	0.322356i
$310$			32.1412i			1.82550i
$311$	15.0689	−	26.1002i	0.854482	−	1.48001i	−0.0226436	−	0.999744i	$-0.507208\pi$
$311$	15.0689	−	26.1002i	0.854482	−	1.48001i	0.877125	−	0.480262i	$-0.159458\pi$
$312$	9.46665	−	2.79260i	0.535943	−	0.158100i
$313$	−10.0024	−	17.3247i	−0.565371	−	0.979252i	−0.997015	−	0.0772078i	$-0.975400\pi$
$313$	−10.0024	−	17.3247i	−0.565371	−	0.979252i	0.431644	−	0.902044i	$-0.357934\pi$
$314$	−4.73650	−	2.73462i	−0.267296	−	0.154324i
$315$	−11.1171	+	1.51727i	−0.626379	+	0.0854887i
$316$	−0.754466	−	1.30677i	−0.0424420	−	0.0735117i
$317$	20.7932	−	12.0050i	1.16786	−	0.674266i	0.214688	−	0.976683i	$-0.431127\pi$
$317$	20.7932	−	12.0050i	1.16786	−	0.674266i	0.953176	+	0.302416i	$0.0977933\pi$
$318$			7.75815i			0.435055i
$319$			8.74040i			0.489368i
$320$	27.4158	−	15.8285i	1.53259	−	0.884840i
$321$	3.57979	+	6.20038i	0.199805	+	0.346072i
$322$	−13.7239	+	1.87305i	−0.764803	+	0.104381i
$323$	0.0537814	+	0.0310507i	0.00299247	+	0.00172771i
$324$	0.0599314	+	0.103804i	0.00332952	+	0.00576690i
$325$	−32.2647	+	33.9236i	−1.78973	+	1.88174i
$326$	−13.6374	+	23.6207i	−0.755306	+	1.30823i
$327$		−	0.800821i		−	0.0442855i
$328$	−16.7469	+	29.0065i	−0.924694	+	1.60162i
$329$	−1.53401	−	1.97964i	−0.0845725	−	0.109141i
$330$			24.9163i			1.37160i
$331$	−7.74452	−	4.47130i	−0.425677	−	0.245765i	0.271826	−	0.962346i	$-0.412372\pi$
$331$	−7.74452	−	4.47130i	−0.425677	−	0.245765i	−0.697503	+	0.716582i	$0.745706\pi$
$332$			0.415931i			0.0228272i
$333$	3.72738	+	2.15200i	0.204259	+	0.117929i
$334$	6.91037	−	11.9691i	0.378119	−	0.654921i
$335$	25.7263	−	44.5593i	1.40558	−	2.43454i
$336$	8.83672	−	6.84748i	0.482082	−	0.373561i
$337$	−6.95546			−0.378888			−0.189444	−	0.981892i	$-0.560669\pi$
$337$	−6.95546			−0.378888			−0.189444	+	0.981892i	$0.560669\pi$
$338$	8.63081	−	16.8454i	0.469454	−	0.916266i
$339$	−0.289689	+	0.501755i	−0.0157337	+	0.0272516i
$340$	−0.0213336	+	0.0123169i	−0.00115697	+	0.000667980i
$341$	−21.0056			−1.13752
$342$	−0.932885	−	1.61580i	−0.0504446	−	0.0873727i
$343$	7.33014	+	17.0079i	0.395790	+	0.918341i
$344$	−11.9022	+	6.87176i	−0.641726	+	0.370501i
$345$	13.2058	+	7.62437i	0.710976	+	0.410482i
$346$	−22.1845	−	12.8082i	−1.19264	−	0.688573i
$347$	14.6491			0.786407			0.393204	−	0.919451i	$-0.371367\pi$
$347$	14.6491			0.786407			0.393204	+	0.919451i	$0.371367\pi$
$348$	0.259620			0.0139171
$349$	9.58341	+	5.53298i	0.512988	+	0.296174i	0.734061	−	0.679083i	$-0.237623\pi$
$349$	9.58341	+	5.53298i	0.512988	+	0.296174i	−0.221073	+	0.975257i	$0.570956\pi$
$350$	−18.9220	+	46.3017i	−1.01142	+	2.47493i
$351$	−3.50498	−	0.845633i	−0.187082	−	0.0451365i
$352$	−1.36626	−	2.36643i	−0.0728218	−	0.126131i
$353$	−2.71822	+	1.56937i	−0.144676	+	0.0835290i	−0.570591	−	0.821234i	$-0.693286\pi$
$353$	−2.71822	+	1.56937i	−0.144676	+	0.0835290i	0.425914	+	0.904763i	$0.359952\pi$
$354$	2.30908	+	3.99945i	0.122726	+	0.212568i
$355$	−13.9465	+	24.1560i	−0.740201	+	1.28207i
$356$			0.896559i			0.0475176i
$357$	0.101350	−	0.0785352i	0.00536402	−	0.00415652i
$358$	22.6704	−	13.0888i	1.19817	−	0.691763i
$359$	11.4388	−	6.60421i	0.603719	−	0.348557i	−0.166785	−	0.985993i	$-0.553338\pi$
$359$	11.4388	−	6.60421i	0.603719	−	0.348557i	0.770503	+	0.637436i	$0.220005\pi$
$360$	−11.6090			−0.611848
$361$	−8.67893	−	15.0324i	−0.456786	−	0.791176i
$362$		−	13.2310i		−	0.695408i
$363$	−5.28379			−0.277327
$364$	0.115401	−	1.13758i	0.00604868	−	0.0596254i
$365$	−59.3281			−3.10538
$366$		−	5.55559i		−	0.290395i
$367$	2.82967	+	4.90112i	0.147707	+	0.255837i	0.930380	−	0.366597i	$-0.119477\pi$
$367$	2.82967	+	4.90112i	0.147707	+	0.255837i	−0.782672	+	0.622434i	$0.786144\pi$
$368$	−15.1931			−0.791994
$369$	10.5963	−	6.11775i	0.551619	−	0.318477i
$370$	23.0149	−	13.2877i	1.19649	−	0.690792i
$371$	−13.0502	−	5.33318i	−0.677531	−	0.276885i
$372$			0.623937i			0.0323496i
$373$	5.56866	−	9.64521i	0.288334	−	0.499410i	−0.685078	−	0.728470i	$-0.740232\pi$
$373$	5.56866	−	9.64521i	0.288334	−	0.499410i	0.973412	+	0.229060i	$0.0735652\pi$
$374$	−0.142363	−	0.246581i	−0.00736144	−	0.0127504i
$375$	29.3251	−	16.9308i	1.51434	−	0.874305i
$376$	−1.29561	−	2.24406i	−0.0668158	−	0.115728i
$377$	−5.38208	+	5.65880i	−0.277191	+	0.291443i
$378$	−3.81676	+	0.520915i	−0.196313	+	0.0267930i
$379$	3.15893	+	1.82381i	0.162263	+	0.0936828i	0.578933	−	0.815375i	$-0.303469\pi$
$379$	3.15893	+	1.82381i	0.162263	+	0.0936828i	−0.416669	+	0.909058i	$0.636803\pi$
$380$	−0.651388			−0.0334155
$381$	−1.59587			−0.0817588
$382$	25.3847	+	14.6559i	1.29880	+	0.749860i
$383$	17.5134	+	10.1114i	0.894895	+	0.516668i	0.875540	−	0.483145i	$-0.160506\pi$
$383$	17.5134	+	10.1114i	0.894895	+	0.516668i	0.0193546	+	0.999813i	$0.493839\pi$
$384$	10.5853	−	6.11143i	0.540179	−	0.311873i
$385$	−41.9122	−	17.1282i	−2.13605	−	0.872933i
$386$	2.32493	+	4.02690i	0.118336	+	0.204964i
$387$	5.02059			0.255211
$388$	−0.435820	+	0.251621i	−0.0221254	+	0.0127741i
$389$	−2.17109	+	3.76044i	−0.110079	+	0.190662i	−0.915802	−	0.401631i	$-0.868444\pi$
$389$	−2.17109	+	3.76044i	−0.110079	+	0.190662i	0.805723	+	0.592292i	$0.201777\pi$
$390$	−15.3427	+	16.1316i	−0.776908	+	0.816853i
$391$	−0.174253			−0.00881233
$392$	5.13485	+	18.4612i	0.259349	+	0.932432i
$393$	2.97143	−	5.14667i	0.149889	−	0.259615i
$394$	−10.6977	+	18.5289i	−0.538942	+	0.933475i
$395$	−46.2346	−	26.6936i	−2.32632	−	1.34310i
$396$			0.483684i			0.0243061i
$397$	0.739259	+	0.426812i	0.0371024	+	0.0214211i	0.518436	−	0.855116i	$-0.326514\pi$
$397$	0.739259	+	0.426812i	0.0371024	+	0.0214211i	−0.481334	+	0.876537i	$0.659848\pi$
$398$			33.7051i			1.68948i
$399$	3.35928	−	0.458476i	0.168174	−	0.0229525i
$400$	−27.4325	+	47.5144i	−1.37162	+	2.37572i
$401$			14.2417i			0.711199i	0.934638	+	0.355600i	$0.115723\pi$
$401$			14.2417i			0.711199i	−0.934638	+	0.355600i	$0.884277\pi$
$402$	8.83244	−	15.2982i	0.440522	−	0.763006i
$403$	−13.5996	−	12.9346i	−0.677447	−	0.644319i
$404$	0.952517	+	1.64981i	0.0473895	+	0.0820810i
$405$	3.67267	+	2.12042i	0.182496	+	0.105364i
$406$	−3.15638	+	7.72359i	−0.156649	+	0.383315i
$407$	8.68402	+	15.0412i	0.430451	+	0.745563i
$408$	0.114887	−	0.0663300i	0.00568775	−	0.00328383i
$409$			9.05933i			0.447955i	0.974594	+	0.223978i	$0.0719042\pi$
$409$			9.05933i			0.447955i	−0.974594	+	0.223978i	$0.928096\pi$
$410$		−	75.5487i		−	3.73108i
$411$	13.9135	−	8.03298i	0.686304	−	0.396238i
$412$	0.392137	+	0.679202i	0.0193192	+	0.0334619i
$413$	−8.31491	+	1.13482i	−0.409150	+	0.0558411i
$414$	4.53385	+	2.61762i	0.222826	+	0.128649i
$415$	7.35798	+	12.7444i	0.361189	+	0.625598i
$416$	0.572621	−	2.37340i	0.0280750	−	0.116366i
$417$	5.62726	−	9.74671i	0.275568	−	0.477298i
$418$		−	7.52897i		−	0.368254i
$419$	−10.9547	+	18.9741i	−0.535171	+	0.926944i	0.463984	+	0.885844i	$0.346420\pi$
$419$	−10.9547	+	18.9741i	−0.535171	+	0.926944i	−0.999155	+	0.0411002i	$0.986914\pi$
$420$	−0.508766	+	1.24494i	−0.0248252	+	0.0607467i
$421$			6.13705i			0.299102i	0.988754	+	0.149551i	$0.0477827\pi$
$421$			6.13705i			0.299102i	−0.988754	+	0.149551i	$0.952217\pi$
$422$	−11.5692	−	6.67950i	−0.563182	−	0.325153i
$423$			0.946585i			0.0460245i
$424$	−12.6322	−	7.29319i	−0.613473	−	0.354189i
$425$	−0.314628	+	0.544953i	−0.0152617	+	0.0264341i
$426$	−4.78814	+	8.29330i	−0.231986	+	0.401812i
$427$	9.34519	+	3.81908i	0.452246	+	0.184818i
$428$	0.858168			0.0414811
$429$	−10.5426	−	10.0271i	−0.509003	−	0.484112i
$430$	15.4999	−	26.8467i	0.747474	−	1.29466i
$431$	22.2097	−	12.8228i	1.06980	−	0.617651i	0.141675	−	0.989913i	$-0.454751\pi$
$431$	22.2097	−	12.8228i	1.06980	−	0.617651i	0.928128	+	0.372262i	$0.121418\pi$
$432$	−4.22536			−0.203293
$433$	−9.98231	−	17.2899i	−0.479719	−	0.830898i	0.520010	−	0.854160i	$-0.325928\pi$
$433$	−9.98231	−	17.2899i	−0.479719	−	0.830898i	−0.999729	+	0.0232619i	$0.992595\pi$
$434$	−18.5619	−	7.58565i	−0.891000	−	0.364123i
$435$	7.95492	−	4.59277i	0.381409	−	0.220207i
$436$	−0.0831286	−	0.0479943i	−0.00398114	−	0.00229851i
$437$	−3.99041	−	2.30386i	−0.190887	−	0.110209i
$438$	−20.3687			−0.973254
$439$	23.2057			1.10755			0.553774	−	0.832667i	$-0.313187\pi$
$439$	23.2057			1.10755			0.553774	+	0.832667i	$0.313187\pi$
$440$	−40.5698	−	23.4230i	−1.93409	−	1.11665i
$441$	1.74751	−	6.77836i	0.0832149	−	0.322779i
$442$	0.0596668	−	0.247307i	0.00283806	−	0.0117632i
$443$	−1.72662	−	2.99059i	−0.0820340	−	0.142087i	0.822089	−	0.569358i	$-0.192808\pi$
$443$	−1.72662	−	2.99059i	−0.0820340	−	0.142087i	−0.904124	+	0.427271i	$0.859475\pi$
$444$	0.446774	−	0.257945i	0.0212030	−	0.0122415i
$445$	15.8605	+	27.4711i	0.751858	+	1.30226i
$446$	1.64974	−	2.85744i	0.0781176	−	0.135304i
$447$		−	5.57979i		−	0.263915i
$448$	2.67074	+	19.5686i	0.126180	+	0.924529i
$449$	−16.9875	+	9.80772i	−0.801688	+	0.462855i	−0.844061	−	0.536247i	$-0.819842\pi$
$449$	−16.9875	+	9.80772i	−0.801688	+	0.462855i	0.0423728	+	0.999102i	$0.486508\pi$
$450$	16.3725	−	9.45268i	0.771808	−	0.445604i
$451$	49.3741			2.32494
$452$	0.0347229	+	0.0601418i	0.00163323	+	0.00282883i
$453$			12.8252i			0.602579i
$454$	12.1593			0.570663
$455$	−16.5882	−	36.8976i	−0.777668	−	1.72979i
$456$	3.50790			0.164273
$457$		−	39.1402i		−	1.83090i	−0.402428	−	0.915452i	$-0.631834\pi$
$457$		−	39.1402i		−	1.83090i	0.402428	−	0.915452i	$-0.368166\pi$
$458$	5.08871	+	8.81391i	0.237780	+	0.411847i
$459$	−0.0484615			−0.00226199
$460$	1.58288	−	0.913878i	0.0738023	−	0.0426098i
$461$	13.2521	−	7.65108i	0.617210	−	0.356346i	−0.158572	−	0.987347i	$-0.550689\pi$
$461$	13.2521	−	7.65108i	0.617210	−	0.356346i	0.775782	+	0.631001i	$0.217356\pi$
$462$	−14.3894	−	5.88049i	−0.669457	−	0.273585i
$463$		−	6.98877i		−	0.324796i	−0.986725	−	0.162398i	$-0.948077\pi$
$463$		−	6.98877i		−	0.324796i	0.986725	−	0.162398i	$-0.0519228\pi$
$464$	−4.57601	+	7.92589i	−0.212436	+	0.367950i
$465$	11.0377	+	19.1178i	0.511860	+	0.886568i
$466$	−28.1543	+	16.2549i	−1.30422	+	0.752993i
$467$	7.25825	+	12.5716i	0.335872	+	0.581747i	0.983652	−	0.180081i	$-0.0576359\pi$
$467$	7.25825	+	12.5716i	0.335872	+	0.581747i	−0.647780	+	0.761827i	$0.724303\pi$
$468$	−0.297839	+	0.313152i	−0.0137676	+	0.0144755i
$469$	19.6618	+	25.3737i	0.907899	+	1.17165i
$470$	5.06169	+	2.92237i	0.233478	+	0.134799i
$471$	−3.75641			−0.173086
$472$	−8.68279			−0.399658
$473$	17.5454	+	10.1298i	0.806738	+	0.465771i
$474$	−15.8734	−	9.16450i	−0.729089	−	0.420940i
$475$	−14.4101	+	8.31966i	−0.661179	+	0.381732i
$476$	−0.00207823	−	0.0152273i	−9.52556e−5	−	0.000697942i
$477$	2.66425	+	4.61461i	0.121987	+	0.211288i
$478$	−18.7108			−0.855811
$479$	−14.6591	+	8.46346i	−0.669793	+	0.386705i	−0.795998	−	0.605299i	$-0.793054\pi$
$479$	−14.6591	+	8.46346i	−0.669793	+	0.386705i	0.126205	+	0.992004i	$0.459720\pi$
$480$	−1.43584	+	2.48695i	−0.0655369	+	0.113513i
$481$	−3.63961	+	15.0855i	−0.165952	+	0.687838i
$482$	−21.7322			−0.989876
$483$	−7.51986	+	5.82707i	−0.342165	+	0.265141i
$484$	−0.316665	+	0.548479i	−0.0143938	+	0.0249309i
$485$	−8.90253	+	15.4196i	−0.404243	+	0.700169i
$486$	1.26091	+	0.727987i	0.0571961	+	0.0330222i
$487$			25.4528i			1.15338i	0.816965	+	0.576688i	$0.195655\pi$
$487$			25.4528i			1.15338i	−0.816965	+	0.576688i	$0.804345\pi$
$488$	9.04587	+	5.22264i	0.409487	+	0.236418i
$489$			18.7330i			0.847137i
$490$	−30.8510	−	30.2712i	−1.39371	−	1.36751i
$491$	−0.0663605	+	0.114940i	−0.00299481	+	0.00518716i	−0.867519	−	0.497404i	$-0.834287\pi$
$491$	−0.0663605	+	0.114940i	−0.00299481	+	0.00518716i	0.864524	+	0.502591i	$0.167620\pi$
$492$		−	1.46658i		−	0.0661186i
$493$	−0.0524832	+	0.0909036i	−0.00236373	+	0.00409409i
$494$	4.63612	−	4.87449i	0.208589	−	0.219314i
$495$	8.55656	+	14.8204i	0.384589	+	0.666127i
$496$	−19.0481	−	10.9974i	−0.855283	−	0.493798i
$497$	−10.6588	−	13.7553i	−0.478115	−	0.617009i
$498$	2.52616	+	4.37544i	0.113200	+	0.196068i
$499$	−3.97198	+	2.29323i	−0.177810	+	0.102659i	−0.586264	−	0.810120i	$-0.699402\pi$
$499$	−3.97198	+	2.29323i	−0.177810	+	0.102659i	0.408453	+	0.912779i	$0.366068\pi$
$500$		−	4.05876i		−	0.181513i
$501$		−	9.49243i		−	0.424091i
$502$	−14.8028	+	8.54643i	−0.660683	+	0.381446i
$503$	−10.9290	−	18.9296i	−0.487301	−	0.844029i	0.512593	−	0.858632i	$-0.328685\pi$
$503$	−10.9290	−	18.9296i	−0.487301	−	0.844029i	−0.999893	+	0.0146024i	$0.995352\pi$
$504$	2.73984	−	6.70433i	0.122042	−	0.298635i
$505$	58.3714	+	33.7008i	2.59749	+	1.49966i
$506$	10.5629	+	18.2955i	0.469579	+	0.813335i
$507$	−0.651232	−	12.9837i	−0.0289222	−	0.576625i
$508$	−0.0956426	+	0.165658i	−0.00424345	+	0.00734988i
$509$		−	35.1753i		−	1.55912i	−0.626329	−	0.779559i	$-0.715443\pi$
$509$		−	35.1753i		−	1.55912i	0.626329	−	0.779559i	$-0.284557\pi$
$510$	−0.149614	+	0.259139i	−0.00662502	+	0.0114749i
$511$	14.0020	−	34.2627i	0.619414	−	1.51569i
$512$			20.2721i			0.895907i
$513$	−1.10977	−	0.640729i	−0.0489978	−	0.0282889i
$514$			44.5547i			1.96522i
$515$	24.0307	+	13.8741i	1.05892	+	0.611366i
$516$	0.300891	−	0.521159i	0.0132460	−	0.0229427i
$517$	−1.90989	+	3.30802i	−0.0839967	+	0.145486i
$518$	2.24202	+	16.4274i	0.0985088	+	0.721778i
$519$	−17.5940			−0.772291
$520$	−11.8429	−	40.1465i	−0.519347	−	1.76054i
$521$	−9.16197	+	15.8690i	−0.401393	+	0.695233i	−0.993894	−	0.110336i	$-0.964807\pi$
$521$	−9.16197	+	15.8690i	−0.401393	+	0.695233i	0.592501	+	0.805570i	$0.298141\pi$
$522$	2.73110	−	1.57680i	0.119537	−	0.0690148i
$523$	−8.29587			−0.362753			−0.181376	−	0.983414i	$-0.558055\pi$
$523$	−8.29587			−0.362753			−0.181376	+	0.983414i	$0.558055\pi$
$524$	−0.356164	−	0.616894i	−0.0155591	−	0.0269491i
$525$	4.64562	+	34.0387i	0.202752	+	1.48557i
$526$	22.9077	−	13.2257i	0.998822	−	0.576670i
$527$	−0.218466	−	0.126131i	−0.00951654	−	0.00549437i
$528$	−14.7663	−	8.52533i	−0.642621	−	0.371017i
$529$	−10.0710			−0.437870
$530$	32.9010			1.42913
$531$	2.74692	+	1.58594i	0.119206	+	0.0688238i
$532$	0.153734	−	0.376184i	0.00666523	−	0.0163097i
$533$	31.9663	+	30.4032i	1.38462	+	1.31691i
$534$	5.44526	+	9.43147i	0.235639	+	0.408139i
$535$	26.2948	−	15.1813i	1.13682	−	0.656345i
$536$	16.6062	+	28.7628i	0.717278	+	1.24236i
$537$	8.98969	−	15.5706i	0.387934	−	0.671921i
$538$		−	14.7377i		−	0.635388i
$539$	19.7834	−	20.1624i	0.852133	−	0.868455i
$540$	0.440217	−	0.254159i	0.0189439	−	0.0109373i
$541$	−15.6366	+	9.02781i	−0.672271	+	0.388136i	−0.796937	−	0.604063i	$-0.793548\pi$
$541$	−15.6366	+	9.02781i	−0.672271	+	0.388136i	0.124665	+	0.992199i	$0.460214\pi$
$542$	−38.6601			−1.66059
$543$	−4.54370	−	7.86993i	−0.194989	−	0.337731i
$544$		−	0.0328157i		−	0.00140696i
$545$	−3.39615			−0.145475
$546$	−5.69512	−	12.6678i	−0.243729	−	0.542132i
$547$	39.4973			1.68878			0.844391	−	0.535727i	$-0.179962\pi$
$547$	39.4973			1.68878			0.844391	+	0.535727i	$0.179962\pi$
$548$		−	1.92571i		−	0.0822623i
$549$	−1.90786	−	3.30451i	−0.0814255	−	0.141033i
$550$	76.2891			3.25298
$551$	−2.40375	+	1.38780i	−0.102403	+	0.0591224i
$552$	−8.52426	+	4.92148i	−0.362816	+	0.209472i
$553$	26.3277	−	20.4011i	1.11957	−	0.867541i
$554$		−	42.6748i		−	1.81308i
$555$	9.12629	−	15.8072i	0.387390	−	0.670978i
$556$	−0.674500	−	1.16827i	−0.0286052	−	0.0495456i
$557$	21.9234	−	12.6575i	0.928925	−	0.536315i	0.0424534	−	0.999098i	$-0.486483\pi$
$557$	21.9234	−	12.6575i	0.928925	−	0.536315i	0.886471	+	0.462783i	$0.153149\pi$
$558$	3.78949	+	6.56359i	0.160422	+	0.277859i
$559$	5.12177	+	17.3623i	0.216628	+	0.734348i
$560$	−29.0390	−	37.4750i	−1.22712	−	1.58361i
$561$	−0.169358	−	0.0977788i	−0.00715029	−	0.00412822i
$562$	−9.81811			−0.414152
$563$	13.5622			0.571577			0.285789	−	0.958293i	$-0.407744\pi$
$563$	13.5622			0.571577			0.285789	+	0.958293i	$0.407744\pi$
$564$	0.0982595	+	0.0567302i	0.00413747	+	0.00238877i
$565$	2.12786	+	1.22852i	0.0895198	+	0.0516843i
$566$	−21.9234	+	12.6575i	−0.921507	+	0.532032i
$567$	−2.09135	+	1.62057i	−0.0878286	+	0.0680575i
$568$	−9.00236	−	15.5925i	−0.377730	−	0.654248i
$569$	12.5214			0.524922			0.262461	−	0.964943i	$-0.415466\pi$
$569$	12.5214			0.524922			0.262461	+	0.964943i	$0.415466\pi$
$570$	−6.85236	+	3.95621i	−0.287014	+	0.165707i
$571$	−4.44524	+	7.69938i	−0.186028	+	0.322209i	−0.943922	−	0.330168i	$-0.892895\pi$
$571$	−4.44524	+	7.69938i	−0.186028	+	0.322209i	0.757895	+	0.652377i	$0.226228\pi$
$572$	−1.67269	+	0.493432i	−0.0699386	+	0.0206314i
$573$	20.1321			0.841029
$574$	43.6302	+	17.8303i	1.82109	+	0.744221i
$575$	23.3444	−	40.4338i	0.973531	−	1.68620i
$576$	3.73240	−	6.46471i	0.155517	−	0.269363i
$577$	−24.6718	−	14.2443i	−1.02710	−	0.592997i	−0.110948	−	0.993826i	$-0.535389\pi$
$577$	−24.6718	−	14.2443i	−1.02710	−	0.592997i	−0.916153	+	0.400829i	$0.868722\pi$
$578$			24.7482i			1.02939i
$579$	2.76578	+	1.59682i	0.114942	+	0.0663616i
$580$		−	1.10101i		−	0.0457167i
$581$	−9.09659	+	1.24151i	−0.377390	+	0.0515065i
$582$	−3.05644	+	5.29391i	−0.126693	+	0.219440i
$583$			21.5022i			0.890528i
$584$	19.1480	−	33.1653i	0.792348	−	1.37239i
$585$	−3.58619	+	14.8641i	−0.148271	+	0.614553i
$586$	−12.8063	−	22.1812i	−0.529025	−	0.916299i
$587$	13.5984	+	7.85103i	0.561266	+	0.324047i	0.753653	−	0.657272i	$-0.228290\pi$
$587$	13.5984	+	7.85103i	0.561266	+	0.324047i	−0.192388	+	0.981319i	$0.561623\pi$
$588$	−0.598892	−	0.587636i	−0.0246979	−	0.0242337i
$589$	−3.33527	−	5.77686i	−0.137427	−	0.238031i
$590$	16.9610	−	9.79244i	0.698274	−	0.403149i
$591$			14.6949i			0.604467i
$592$			18.1860i			0.747439i
$593$	−14.8094	+	8.55019i	−0.608148	+	0.351114i	−0.772240	−	0.635331i	$-0.780864\pi$
$593$	−14.8094	+	8.55019i	−0.608148	+	0.351114i	0.164092	+	0.986445i	$0.447530\pi$
$594$	2.93766	+	5.08818i	0.120534	+	0.208770i
$595$	−0.333055	−	0.429809i	−0.0136539	−	0.0176205i
$596$	−0.579206	−	0.334405i	−0.0237252	−	0.0136978i
$597$	11.5747	+	20.0480i	0.473722	+	0.820511i
$598$	−4.42709	+	18.3494i	−0.181037	+	0.750363i
$599$	−21.8381	+	37.8247i	−0.892280	+	1.54547i	−0.0551452	+	0.998478i	$0.517562\pi$
$599$	−21.8381	+	37.8247i	−0.892280	+	1.54547i	−0.837135	+	0.546996i	$0.815771\pi$
$600$			35.5447i			1.45111i
$601$	14.9028	−	25.8124i	0.607898	−	1.05291i	−0.383688	−	0.923463i	$-0.625346\pi$
$601$	14.9028	−	25.8124i	0.607898	−	1.05291i	0.991586	−	0.129448i	$-0.0413205\pi$
$602$	11.8461	+	15.2875i	0.482812	+	0.623071i
$603$		−	12.1327i		−	0.494081i
$604$	1.33131	+	0.768630i	0.0541701	+	0.0312751i
$605$			22.4077i			0.911001i
$606$	20.0402	+	11.5702i	0.814079	+	0.470009i
$607$	−0.375968	+	0.651196i	−0.0152601	+	0.0264312i	−0.873555	−	0.486726i	$-0.838191\pi$
$607$	−0.375968	+	0.651196i	−0.0152601	+	0.0264312i	0.858295	+	0.513157i	$0.171524\pi$
$608$	0.433870	−	0.751485i	0.0175958	−	0.0304767i
$609$	0.774937	+	5.67800i	0.0314020	+	0.230084i
$610$	−23.5603			−0.953930
$611$	−3.27350	+	0.965661i	−0.132432	+	0.0390665i
$612$	−0.00290437	+	0.00503051i	−0.000117402	+	0.000203346i
$613$	−23.5664	+	13.6061i	−0.951837	+	0.549543i	−0.893651	−	0.448762i	$-0.851865\pi$
$613$	−23.5664	+	13.6061i	−0.951837	+	0.549543i	−0.0581859	+	0.998306i	$0.518532\pi$
$614$	−0.113363			−0.00457495
$615$	−25.9444	−	44.9370i	−1.04618	−	1.81203i
$616$	23.1019	−	17.9015i	0.930804	−	0.721271i
$617$	13.3489	−	7.70701i	0.537408	−	0.310272i	−0.206620	−	0.978421i	$-0.566246\pi$
$617$	13.3489	−	7.70701i	0.537408	−	0.310272i	0.744028	+	0.668149i	$0.232913\pi$
$618$	8.25027	+	4.76330i	0.331875	+	0.191608i
$619$	37.4700	+	21.6333i	1.50605	+	0.869516i	0.999975	+	0.00702301i	$0.00223551\pi$
$619$	37.4700	+	21.6333i	1.50605	+	0.869516i	0.506070	+	0.862493i	$0.331098\pi$
$620$	2.64602			0.106267
$621$	3.59569			0.144290
$622$	−38.0012	−	21.9400i	−1.52371	−	0.879714i
$623$	−19.6081	+	2.67613i	−0.785583	+	0.107217i
$624$	−4.31051	−	14.6122i	−0.172558	−	0.584957i
$625$	−39.3392	−	68.1375i	−1.57357	−	2.72550i
$626$	−25.2244	+	14.5633i	−1.00817	+	0.582067i
$627$	−2.58554	−	4.47829i	−0.103257	−	0.178846i
$628$	−0.225127	+	0.389932i	−0.00898355	+	0.0155600i
$629$			0.208579i			0.00831658i
$630$	2.20911	+	16.1863i	0.0880132	+	0.644876i
$631$	−13.6641	+	7.88896i	−0.543958	+	0.314054i	−0.746682	−	0.665182i	$-0.768354\pi$
$631$	−13.6641	+	7.88896i	−0.543958	+	0.314054i	0.202723	+	0.979236i	$0.435021\pi$
$632$	29.8441	−	17.2305i	1.18714	−	0.685394i
$633$	−9.17530			−0.364685
$634$	−17.4789	−	30.2744i	−0.694177	−	1.20235i
$635$			6.76781i			0.268572i
$636$	0.638688			0.0253256
$637$	25.2238	−	0.871673i	0.999403	−	0.0345370i
$638$	12.7258			0.503819
$639$			6.57723i			0.260191i
$640$	−25.9176	−	44.8906i	−1.02448	−	1.77446i
$641$	−16.1808			−0.639104			−0.319552	−	0.947569i	$-0.603532\pi$
$641$	−16.1808			−0.639104			−0.319552	+	0.947569i	$0.603532\pi$
$642$	9.02760	−	5.21209i	0.356291	−	0.205705i
$643$	10.1953	−	5.88625i	0.402063	−	0.232131i	−0.285311	−	0.958435i	$-0.592097\pi$
$643$	10.1953	−	5.88625i	0.402063	−	0.232131i	0.687374	+	0.726304i	$0.258763\pi$
$644$	0.154198	+	1.12982i	0.00607627	+	0.0445210i
$645$		−	21.2915i		−	0.838352i
$646$	0.0452090	−	0.0783043i	0.00177872	−	0.00308084i
$647$	−8.77908	−	15.2058i	−0.345141	−	0.597802i	0.640238	−	0.768176i	$-0.278836\pi$
$647$	−8.77908	−	15.2058i	−0.345141	−	0.597802i	−0.985379	+	0.170374i	$0.945502\pi$
$648$	−2.37069	+	1.36872i	−0.0931293	+	0.0537683i
$649$	6.39976	+	11.0847i	0.251213	+	0.435113i
$650$	49.3919	+	46.9766i	1.93731	+	1.84258i
$651$	−13.6458	+	1.86239i	−0.534820	+	0.0729926i
$652$	1.94457	+	1.12270i	0.0761552	+	0.0439682i
$653$	−30.9961			−1.21297			−0.606485	−	0.795095i	$-0.707421\pi$
$653$	−30.9961			−1.21297			−0.606485	+	0.795095i	$0.707421\pi$
$654$	−1.16598			−0.0455933
$655$	−21.8262	−	12.6013i	−0.852819	−	0.492375i
$656$	44.7730	+	25.8497i	1.74809	+	1.00926i
$657$	−12.1155	+	6.99486i	−0.472669	+	0.272896i
$658$	−2.88231	+	2.23347i	−0.112364	+	0.0870699i
$659$	3.05016	+	5.28303i	0.118817	+	0.205797i	0.919299	−	0.393559i	$-0.128756\pi$
$659$	3.05016	+	5.28303i	0.118817	+	0.205797i	−0.800482	+	0.599357i	$0.795423\pi$
$660$	2.05123			0.0798438
$661$	32.8669	−	18.9757i	1.27837	−	0.738070i	0.301825	−	0.953363i	$-0.402404\pi$
$661$	32.8669	−	18.9757i	1.27837	−	0.738070i	0.976549	+	0.215293i	$0.0690708\pi$
$662$	−6.51010	+	11.2758i	−0.253022	+	0.438247i
$663$	−0.0494381	−	0.167591i	−0.00192002	−	0.00650868i
$664$	−9.49906			−0.368635
$665$	−1.94432	−	14.2461i	−0.0753976	−	0.552441i
$666$	3.13326	−	5.42697i	0.121411	−	0.210291i
$667$	3.89409	−	6.74476i	0.150780	−	0.261158i
$668$	−0.985354	−	0.568895i	−0.0381245	−	0.0220112i
$669$		−	2.26617i		−	0.0876152i
$670$	−64.8773	−	37.4569i	−2.50643	−	1.44709i
$671$		−	15.3976i		−	0.594419i
$672$	−1.09737	−	1.41616i	−0.0423319	−	0.0546296i
$673$	8.90401	−	15.4222i	0.343225	−	0.594482i	−0.641805	−	0.766868i	$-0.721814\pi$
$673$	8.90401	−	15.4222i	0.343225	−	0.594482i	0.985030	+	0.172386i	$0.0551475\pi$
$674$			10.1270i			0.390077i
$675$	6.49234	−	11.2451i	0.249890	−	0.432823i
$676$	−1.38679	−	0.710529i	−0.0533381	−	0.0273281i
$677$	−2.24699	−	3.89190i	−0.0863589	−	0.149578i	0.819611	−	0.572921i	$-0.194190\pi$
$677$	−2.24699	−	3.89190i	−0.0863589	−	0.149578i	−0.905969	+	0.423343i	$0.860857\pi$
$678$	0.730543	+	0.421779i	0.0280563	+	0.0161983i
$679$	−6.80392	−	8.78050i	−0.261111	−	0.336965i
$680$	−0.281295	−	0.487217i	−0.0107872	−	0.0186839i
$681$	7.23244	−	4.17565i	0.277148	−	0.160011i
$682$			30.5836i			1.17111i
$683$		−	18.8903i		−	0.722816i	−0.932408	−	0.361408i	$-0.882296\pi$
$683$		−	18.8903i		−	0.722816i	0.932408	−	0.361408i	$-0.117704\pi$
$684$	−0.133021	+	0.0767995i	−0.00508617	+	0.00293650i
$685$	−34.0665	−	59.0050i	−1.30162	−	2.25446i
$686$	24.7631	−	10.6725i	0.945459	−	0.407478i
$687$	6.05361	+	3.49506i	0.230960	+	0.133345i
$688$	10.6069	+	18.3717i	0.404384	+	0.700414i
$689$	−13.2404	+	13.9212i	−0.504419	+	0.530354i
$690$	11.1009	−	19.2273i	0.422604	−	0.731971i
$691$		−	36.0946i		−	1.37310i	−0.727081	−	0.686551i	$-0.759124\pi$
$691$		−	36.0946i		−	1.37310i	0.727081	−	0.686551i	$-0.240876\pi$
$692$	−1.05443	+	1.82633i	−0.0400835	+	0.0694267i
$693$	−10.5784	+	1.44374i	−0.401839	+	0.0548433i
$694$		−	21.3288i		−	0.809630i
$695$	−41.3342	−	23.8643i	−1.56789	−	0.905224i
$696$			5.92921i			0.224746i
$697$	0.513510	+	0.296475i	0.0194506	+	0.0112298i
$698$	8.05588	−	13.9532i	0.304920	−	0.528136i
$699$	−11.1643	+	19.3371i	−0.422271	+	0.731395i
$700$	3.81178	+	1.55775i	0.144072	+	0.0588774i
$701$	7.46818			0.282069			0.141035	−	0.990005i	$-0.454957\pi$
$701$	7.46818			0.282069			0.141035	+	0.990005i	$0.454957\pi$
$702$	−1.23122	+	5.10317i	−0.0464694	+	0.192607i
$703$	−2.75770	+	4.77648i	−0.104009	+	0.180148i
$704$	26.0872	−	15.0614i	0.983196	−	0.567649i
$705$	4.01431			0.151188
$706$	2.28496	+	3.95766i	0.0859955	+	0.148949i
$707$	−33.2388	+	25.7564i	−1.25007	+	0.968671i
$708$	0.329254	−	0.190095i	0.0123741	−	0.00714420i
$709$	13.9053	+	8.02823i	0.522225	+	0.301506i	0.737844	−	0.674971i	$-0.235844\pi$
$709$	13.9053	+	8.02823i	0.522225	+	0.301506i	−0.215620	+	0.976477i	$0.569177\pi$
$710$	35.1705	+	20.3057i	1.31993	+	0.762059i
$711$	−12.5888			−0.472118
$712$	−20.4757			−0.767358
$713$	16.2095	+	9.35856i	0.607051	+	0.350481i
$714$	−0.114345	−	0.147563i	−0.00427926	−	0.00552241i
$715$	−42.5232	+	44.7095i	−1.59028	+	1.67204i
$716$	−1.07753	−	1.86634i	−0.0402692	−	0.0697483i
$717$	−11.1293	+	6.42552i	−0.415632	+	0.239965i
$718$	−9.61557	−	16.6547i	−0.358850	−	0.621546i
$719$	−7.60447	+	13.1713i	−0.283599	+	0.491208i	−0.972268	−	0.233868i	$-0.924862\pi$
$719$	−7.60447	+	13.1713i	−0.283599	+	0.491208i	0.688670	+	0.725075i	$0.258195\pi$
$720$			17.9190i			0.667803i
$721$	−13.6839	+	10.6036i	−0.509617	+	0.394897i
$722$	−21.8867	+	12.6363i	−0.814540	+	0.470275i
$723$	−12.9265	+	7.46312i	−0.480742	+	0.277556i
$724$	−1.08924			−0.0404814
$725$	−14.0622	−	24.3565i	−0.522259	−	0.904579i
$726$			7.69306i			0.285516i
$727$	40.3565			1.49674			0.748369	−	0.663282i	$-0.230837\pi$
$727$	40.3565			1.49674			0.748369	+	0.663282i	$0.230837\pi$
$728$	25.9801	+	2.63554i	0.962887	+	0.0976798i
$729$	1.00000			0.0370370
$730$			86.3802i			3.19708i
$731$	0.121653	+	0.210709i	0.00449949	+	0.00779334i
$732$	−0.457363			−0.0169046
$733$	−33.4424	+	19.3080i	−1.23522	+	0.713156i	−0.968114	−	0.250510i	$-0.919402\pi$
$733$	−33.4424	+	19.3080i	−1.23522	+	0.713156i	−0.267109	+	0.963666i	$0.586068\pi$
$734$	7.13591	−	4.11992i	0.263391	−	0.152069i
$735$	−28.7459	−	7.41092i	−1.06031	−	0.273356i
$736$			2.43483i			0.0897489i
$737$	24.4796	−	42.3999i	0.901718	−	1.56182i
$738$	−8.90729	−	15.4279i	−0.327882	−	0.567908i
$739$	8.88879	−	5.13195i	0.326980	−	0.188782i	−0.327520	−	0.944844i	$-0.606213\pi$
$739$	8.88879	−	5.13195i	0.326980	−	0.188782i	0.654499	+	0.756063i	$0.272879\pi$
$740$	−1.09390	−	1.89470i	−0.0402127	−	0.0696504i
$741$	1.08364	−	4.49149i	0.0398086	−	0.164999i
$742$	−7.76498	+	19.0007i	−0.285061	+	0.697538i
$743$	−1.51273	−	0.873374i	−0.0554966	−	0.0320410i	0.471995	−	0.881601i	$-0.343534\pi$
$743$	−1.51273	−	0.873374i	−0.0554966	−	0.0320410i	−0.527492	+	0.849560i	$0.676867\pi$
$744$	−14.2495			−0.522413
$745$	−23.6630			−0.866945
$746$	−14.0432	−	8.10783i	−0.514157	−	0.296849i
$747$	3.00516	+	1.73503i	0.109953	+	0.0634815i
$748$	−0.0202997	+	0.0117200i	−0.000742230	+	0.000428527i
$749$	2.56154	+	18.7685i	0.0935965	+	0.685786i
$750$	−24.6509	−	42.6966i	−0.900123	−	1.55906i
$751$	24.6041			0.897816			0.448908	−	0.893578i	$-0.351813\pi$
$751$	24.6041			0.897816			0.448908	+	0.893578i	$0.351813\pi$
$752$	−3.46381	+	1.99983i	−0.126312	+	0.0729263i
$753$	−5.86990	+	10.1670i	−0.213911	+	0.370505i
$754$	8.23907	+	7.83618i	0.300049	+	0.285377i
$755$	54.3894			1.97943
$756$	0.0428842	+	0.314214i	0.00155968	+	0.0114279i
$757$	6.03229	−	10.4482i	0.219247	−	0.379747i	−0.735331	−	0.677708i	$-0.762973\pi$
$757$	6.03229	−	10.4482i	0.219247	−	0.379747i	0.954578	+	0.297961i	$0.0963065\pi$
$758$	2.65542	−	4.59932i	0.0964492	−	0.167055i
$759$	12.5658	+	7.25488i	0.456110	+	0.263335i
$760$		−	14.8764i		−	0.539625i
$761$	8.96051	+	5.17335i	0.324818	+	0.187534i	0.653538	−	0.756894i	$-0.273284\pi$
$761$	8.96051	+	5.17335i	0.324818	+	0.187534i	−0.328720	+	0.944427i	$0.606617\pi$
$762$			2.32354i			0.0841731i
$763$	0.801526	−	1.96132i	0.0290172	−	0.0710044i
$764$	1.20654	−	2.08979i	0.0436512	−	0.0756060i
$765$			0.205517i			0.00743049i
$766$	14.7219	−	25.4991i	0.531925	−	0.921321i
$767$	−2.68224	+	11.1174i	−0.0968501	+	0.401425i
$768$	−1.43329	−	2.48253i	−0.0517194	−	0.0895807i
$769$	25.6321	+	14.7987i	0.924316	+	0.533654i	0.885010	−	0.465573i	$-0.154152\pi$
$769$	25.6321	+	14.7987i	0.924316	+	0.533654i	0.0393069	+	0.999227i	$0.487485\pi$
$770$	−24.9382	+	61.0232i	−0.898710	+	2.19912i
$771$	15.3006	+	26.5015i	0.551039	+	0.954427i
$772$	0.331514	−	0.191399i	0.0119314	−	0.00688862i
$773$		−	33.5754i		−	1.20762i	−0.797128	−	0.603811i	$-0.793648\pi$
$773$		−	33.5754i		−	1.20762i	0.797128	−	0.603811i	$-0.206352\pi$
$774$		−	7.30985i		−	0.262747i
$775$	58.5354	−	33.7954i	2.10265	−	1.21397i
$776$	−5.74653	−	9.95327i	−0.206288	−	0.357302i
$777$	6.97494	+	9.00120i	0.250225	+	0.322916i
$778$	5.47510	+	3.16105i	0.196292	+	0.113329i
$779$	7.83964	+	13.5787i	0.280884	+	0.486506i
$780$	1.32803	+	1.26308i	0.0475510	+	0.0452257i
$781$	−13.2706	+	22.9853i	−0.474859	+	0.822480i
$782$			0.253707i			0.00907256i
$783$	1.08299	−	1.87579i	0.0387028	−	0.0670353i
$784$	28.4958	−	7.92589i	1.01771	−	0.283067i
$785$			15.9303i			0.568578i
$786$	−7.49342	−	4.32633i	−0.267281	−	0.154315i
$787$			21.9610i			0.782824i	0.920216	+	0.391412i	$0.128013\pi$
$787$			21.9610i			0.782824i	−0.920216	+	0.391412i	$0.871987\pi$
$788$	1.52539	+	0.880685i	0.0543398	+	0.0313731i
$789$	9.08377	−	15.7336i	0.323391	−	0.560129i
$790$	−38.8651	+	67.3164i	−1.38276	+	2.39501i
$791$	−1.21168	+	0.938921i	−0.0430825	+	0.0333842i
$792$	−11.0464			−0.392517
$793$	9.48142	−	9.96890i	0.336695	−	0.354006i
$794$	0.621427	−	1.07634i	0.0220536	−	0.0381980i
$795$	19.5698	−	11.2986i	0.694069	−	0.400721i
$796$	2.77476			0.0983488
$797$	1.40719	+	2.43732i	0.0498451	+	0.0863343i	0.889871	−	0.456211i	$-0.150794\pi$
$797$	1.40719	+	2.43732i	0.0498451	+	0.0863343i	−0.840026	+	0.542546i	$0.817461\pi$
$798$	−0.667530	−	4.89102i	−0.0236303	−	0.173140i
$799$	−0.0397271	+	0.0229365i	−0.00140544	+	0.000811434i
$800$	7.61460	+	4.39629i	0.269217	+	0.155432i
$801$	6.47777	+	3.73994i	0.228881	+	0.132144i
$802$	20.7356			0.732201
$803$	−56.4530			−1.99218
$804$	−1.25942	−	0.727128i	−0.0444164	−	0.0256438i
$805$	24.7116	+	31.8905i	0.870970	+	1.12399i
$806$	−18.8325	+	19.8007i	−0.663346	+	0.697451i
$807$	−5.06111	−	8.76610i	−0.178160	−	0.308581i
$808$	−37.6784	+	21.7536i	−1.32552	+	0.765290i
$809$	−19.9724	−	34.5932i	−0.702192	−	1.21623i	−0.967695	−	0.252122i	$-0.918871\pi$
$809$	−19.9724	−	34.5932i	−0.702192	−	1.21623i	0.265503	−	0.964110i	$-0.414462\pi$
$810$	3.08727	−	5.34732i	0.108476	−	0.187886i
$811$			45.8322i			1.60939i	0.593691	+	0.804693i	$0.297670\pi$
$811$			45.8322i			1.60939i	−0.593691	+	0.804693i	$0.702330\pi$
$812$	0.635843	+	0.259848i	0.0223137	+	0.00911889i
$813$	−22.9953	+	13.2763i	−0.806481	+	0.465622i
$814$	21.8996	−	12.6437i	0.767579	−	0.443162i
$815$	79.4437			2.78279
$816$	−0.102384	−	0.177334i	−0.00358414	−	0.00620792i
$817$			6.43368i			0.225086i
$818$	13.1902			0.461183
$819$	−7.73778	−	5.57913i	−0.270380	−	0.194951i
$820$	−6.21953			−0.217195
$821$			54.5859i			1.90506i	0.304443	+	0.952531i	$0.401530\pi$
$821$			54.5859i			1.90506i	−0.304443	+	0.952531i	$0.598470\pi$
$822$	−11.6958	−	20.2578i	−0.407938	−	0.706570i
$823$	−50.0972			−1.74628			−0.873139	−	0.487471i	$-0.837919\pi$
$823$	−50.0972			−1.74628			−0.873139	+	0.487471i	$0.837919\pi$
$824$	−15.5116	+	8.95565i	−0.540374	+	0.311985i
$825$	45.3774	−	26.1986i	1.57984	−	0.912120i
$826$	1.65228	+	12.1063i	0.0574900	+	0.421232i
$827$			19.4771i			0.677284i	0.940915	+	0.338642i	$0.109967\pi$
$827$			19.4771i			0.677284i	−0.940915	+	0.338642i	$0.890033\pi$
$828$	0.215495	−	0.373248i	0.00748896	−	0.0129713i
$829$	−7.40473	−	12.8254i	−0.257177	−	0.445444i	0.708308	−	0.705904i	$-0.249459\pi$
$829$	−7.40473	−	12.8254i	−0.257177	−	0.445444i	−0.965485	+	0.260460i	$0.916126\pi$
$830$	18.5555	−	10.7130i	0.644071	−	0.371855i
$831$	−14.6551	−	25.3833i	−0.508378	−	0.880537i
$832$	26.1640	+	6.31248i	0.907074	+	0.218846i
$833$	0.326824	−	0.0909036i	0.0113238	−	0.00314962i
$834$	−14.1910	−	8.19315i	−0.491393	−	0.283706i
$835$	−40.2558			−1.39311
$836$	−0.619821			−0.0214370
$837$	4.50804	+	2.60272i	0.155820	+	0.0899630i
$838$	27.6258	+	15.9497i	0.954316	+	0.550975i
$839$	−41.3739	+	23.8872i	−1.42839	+	0.824679i	−0.996994	−	0.0774846i	$-0.975311\pi$
$839$	−41.3739	+	23.8872i	−1.42839	+	0.824679i	−0.431393	+	0.902164i	$0.641978\pi$
$840$	−28.4319	−	11.6192i	−0.980995	−	0.400901i
$841$	12.1543	+	21.0518i	0.419113	+	0.725925i
$842$	8.93539			0.307934
$843$	−5.83989	+	3.37166i	−0.201136	+	0.116126i
$844$	−0.549889	+	0.952435i	−0.0189279	+	0.0327842i
$845$	−55.0616	+	2.76177i	−1.89418	+	0.0950076i
$846$	1.37820			0.0473836
$847$	−12.9407	−	5.28844i	−0.444647	−	0.181713i
$848$	−11.2574	+	19.4984i	−0.386580	+	0.669577i
$849$	−8.69346	+	15.0575i	−0.298359	+	0.516772i
$850$	0.793437	+	0.458091i	0.0272147	+	0.0157124i
$851$		−	15.4759i		−	0.530506i
$852$	0.682744	+	0.394182i	0.0233904	+	0.0135045i
$853$		−	20.3132i		−	0.695509i	−0.937586	−	0.347755i	$-0.886944\pi$
$853$		−	20.3132i		−	0.695509i	0.937586	−	0.347755i	$-0.113056\pi$
$854$	5.56048	−	13.6064i	0.190276	−	0.465600i
$855$	−2.71722	+	4.70637i	−0.0929271	+	0.160955i
$856$			19.5989i			0.669876i
$857$	−3.72976	+	6.46014i	−0.127406	+	0.220674i	−0.922671	−	0.385588i	$-0.873999\pi$
$857$	−3.72976	+	6.46014i	−0.127406	+	0.220674i	0.795265	+	0.606262i	$0.207332\pi$
$858$	−14.5992	+	15.3498i	−0.498408	+	0.524033i
$859$	−3.78123	−	6.54929i	−0.129014	−	0.223459i	0.794281	−	0.607551i	$-0.207848\pi$
$859$	−3.78123	−	6.54929i	−0.129014	−	0.223459i	−0.923295	+	0.384092i	$0.874515\pi$
$860$	−2.21015	−	1.27603i	−0.0753654	−	0.0435122i
$861$	32.0747	−	4.37758i	1.09310	−	0.149188i
$862$	−18.6696	−	32.3367i	−0.635890	−	1.10139i
$863$	17.3688	−	10.0279i	0.591239	−	0.341352i	−0.174348	−	0.984684i	$-0.555782\pi$
$863$	17.3688	−	10.0279i	0.591239	−	0.341352i	0.765587	+	0.643332i	$0.222448\pi$
$864$			0.677151i			0.0230371i
$865$			74.6132i			2.53693i
$866$	−25.1736	+	14.5340i	−0.855434	+	0.493885i
$867$	8.49883	+	14.7204i	0.288635	+	0.499931i
$868$	−0.624487	+	1.52810i	−0.0211965	+	0.0518672i
$869$	−43.9940	−	25.3999i	−1.49239	−	0.861634i
$870$	−6.68696	−	11.5822i	−0.226709	−	0.392672i
$871$	41.9575	−	12.3772i	1.42167	−	0.419385i
$872$	1.09610	−	1.89850i	0.0371185	−	0.0642912i
$873$			4.19848i			0.142097i
$874$	−3.35437	+	5.80993i	−0.113463	+	0.196524i
$875$	88.7667	−	12.1149i	3.00086	−	0.409560i
$876$			1.67685i			0.0566554i
$877$	24.4425	+	14.1119i	0.825365	+	0.476525i	0.852263	−	0.523113i	$-0.175230\pi$
$877$	24.4425	+	14.1119i	0.825365	+	0.476525i	−0.0268979	+	0.999638i	$0.508563\pi$
$878$		−	33.7870i		−	1.14025i
$879$	−15.2346	−	8.79572i	−0.513852	−	0.296672i
$880$	−36.1545	+	62.6215i	−1.21877	+	2.11097i
$881$	−15.5671	+	26.9631i	−0.524470	+	0.908409i	0.475124	+	0.879919i	$0.342403\pi$
$881$	−15.5671	+	26.9631i	−0.524470	+	0.908409i	−0.999594	+	0.0284903i	$0.990930\pi$
$882$	−9.86913	−	2.54434i	−0.332311	−	0.0856722i
$883$	−48.8522			−1.64401			−0.822004	−	0.569482i	$-0.807144\pi$
$883$	−48.8522			−1.64401			−0.822004	+	0.569482i	$0.807144\pi$
$884$	−0.0203595	−	0.00491205i	−0.000684764	−	0.000165210i
$885$	6.72570	−	11.6492i	0.226082	−	0.391585i
$886$	−4.35422	+	2.51391i	−0.146283	+	0.0844565i
$887$	15.6735			0.526266			0.263133	−	0.964760i	$-0.415244\pi$
$887$	15.6735			0.526266			0.263133	+	0.964760i	$0.415244\pi$
$888$	5.89096	+	10.2035i	0.197688	+	0.342405i
$889$	−3.90849	−	1.59727i	−0.131087	−	0.0535708i
$890$	39.9973	−	23.0924i	1.34071	−	0.774060i
$891$	3.49469	+	2.01766i	0.117076	+	0.0675941i
$892$	−0.235238	−	0.135815i	−0.00787635	−	0.00454741i
$893$	−1.21301			−0.0405918
$894$	−8.12404			−0.271709
$895$	−66.0324	−	38.1238i	−2.20722	−	1.27434i
$896$	32.0416	−	4.37306i	1.07044	−	0.146094i
$897$	3.66815	+	12.4347i	0.122476	+	0.415182i
$898$	14.2798	+	24.7333i	0.476523	+	0.825362i
$899$	9.76430	−	5.63742i	0.325657	−	0.188018i
$900$	−0.778190	−	1.34786i	−0.0259397	−	0.0449288i
$901$	−0.129113	+	0.223631i	−0.00430139	+	0.00745022i
$902$		−	71.8875i		−	2.39359i
$903$	12.2961	+	5.02501i	0.409188	+	0.167222i
$904$	−1.37352	+	0.793003i	−0.0456827	+	0.0263749i
$905$	−33.3751	+	19.2691i	−1.10942	+	0.640527i
$906$	18.6731			0.620373
$907$	1.57527	+	2.72845i	0.0523060	+	0.0905967i	0.890993	−	0.454017i	$-0.150010\pi$
$907$	1.57527	+	2.72845i	0.0523060	+	0.0905967i	−0.838687	+	0.544614i	$0.816676\pi$
$908$		−	1.00101i		−	0.0332197i
$909$	15.8935			0.527153
$910$	−53.7220	+	24.1521i	−1.78087	+	0.800633i
$911$	−1.18315			−0.0391996			−0.0195998	−	0.999808i	$-0.506239\pi$
$911$	−1.18315			−0.0391996			−0.0195998	+	0.999808i	$0.506239\pi$
$912$		−	5.41462i		−	0.179296i
$913$	7.00140	+	12.1268i	0.231713	+	0.401338i
$914$	−56.9872			−1.88497
$915$	−14.0139	+	8.09092i	−0.463285	+	0.267477i
$916$	0.725603	−	0.418927i	0.0239746	−	0.0138417i
$917$	12.4286	−	9.63081i	0.410429	−	0.318038i
$918$			0.0705587i			0.00232879i
$919$	2.56154	−	4.43672i	0.0844974	−	0.146354i	−0.820680	−	0.571389i	$-0.806405\pi$
$919$	2.56154	−	4.43672i	0.0844974	−	0.146354i	0.905177	+	0.425035i	$0.139738\pi$
$920$	20.8712	+	36.1500i	0.688103	+	1.19183i
$921$	−0.0674292	+	0.0389302i	−0.00222187	+	0.00128280i
$922$	−11.1398	−	19.2947i	−0.366869	−	0.635436i
$923$	−22.7455	+	6.70977i	−0.748677	+	0.220855i
$924$	−0.484110	+	1.18461i	−0.0159261	+	0.0389707i
$925$	−48.3988	−	27.9431i	−1.59134	−	0.918763i
$926$	−10.1755			−0.334387
$927$	6.54310			0.214904
$928$	1.27019	+	0.733346i	0.0416961	+	0.0240733i
$929$	27.2201	+	15.7155i	0.893063	+	0.515610i	0.874943	−	0.484226i	$-0.160899\pi$
$929$	27.2201	+	15.7155i	0.893063	+	0.515610i	0.0181195	+	0.999836i	$0.494232\pi$
$930$	27.8351	−	16.0706i	0.912748	−	0.526975i
$931$	8.68618	+	2.23936i	0.284678	+	0.0733922i
$932$	1.33818	+	2.31779i	0.0438335	+	0.0759219i
$933$	−30.1379			−0.986670
$934$	18.3040	−	10.5678i	0.598925	−	0.345790i
$935$	−0.414664	+	0.718218i	−0.0135609	+	0.0234883i
$936$	−7.15178	−	6.80206i	−0.233763	−	0.222332i
$937$	−1.86220			−0.0608355			−0.0304178	−	0.999537i	$-0.509684\pi$
$937$	−1.86220			−0.0608355			−0.0304178	+	0.999537i	$0.509684\pi$
$938$	36.9435	−	28.6271i	1.20625	−	0.934709i
$939$	−10.0024	+	17.3247i	−0.326417	+	0.565371i
$940$	0.240583	−	0.416702i	0.00784696	−	0.0135913i
$941$	43.4248	+	25.0713i	1.41561	+	0.817303i	0.995909	−	0.0903602i	$-0.0288018\pi$
$941$	43.4248	+	25.0713i	1.41561	+	0.817303i	0.419700	+	0.907663i	$0.362135\pi$
$942$			5.46924i			0.178198i
$943$	−38.1009	−	21.9975i	−1.24073	−	0.716339i
$944$			13.4023i			0.436208i
$945$	6.87256	+	8.86908i	0.223565	+	0.288511i
$946$	14.7488	−	25.5457i	0.479525	−	0.830561i
$947$		0	0.000321344i		0	1.04423e-5i	1.00000		5.22114e-6i	$1.66194e-6\pi$
$947$		0	0.000321344i		0	1.04423e-5i	−1.00000		5.22114e-6i	$0.999998\pi$
$948$	−0.754466	+	1.30677i	−0.0245039	+	0.0424420i
$949$	−36.5494	−	34.7621i	−1.18644	−	1.12843i
$950$	12.1132	+	20.9807i	0.393004	+	0.680704i
$951$	−20.7932	−	12.0050i	−0.674266	−	0.389288i
$952$	0.347762	−	0.0474628i	0.0112710	−	0.00153828i
$953$	−28.6176	−	49.5671i	−0.927015	−	1.60564i	−0.788288	−	0.615306i	$-0.789032\pi$
$953$	−28.6176	−	49.5671i	−0.927015	−	1.60564i	−0.138727	−	0.990331i	$-0.544301\pi$
$954$	6.71875	−	3.87907i	0.217528	−	0.125590i
$955$		−	85.3767i		−	2.76273i
$956$			1.54036i			0.0498188i
$957$	7.56941	−	4.37020i	0.244684	−	0.141268i
$958$	12.3226	+	21.3433i	0.398125	+	0.689572i
$959$	42.1161	−	5.74804i	1.36000	−	0.185614i
$960$	−27.4158	−	15.8285i	−0.884840	−	0.510863i
$961$	−1.95175	−	3.38052i	−0.0629595	−	0.109049i
$962$	21.9641	+	5.29918i	0.708150	+	0.170852i
$963$	3.57979	−	6.20038i	0.115357	−	0.199805i
$964$			1.78910i			0.0576230i
$965$	6.77185	−	11.7292i	0.217994	−	0.377576i
$966$	8.48406	+	10.9487i	0.272970	+	0.352270i
$967$		−	13.9192i		−	0.447610i	−0.974634	−	0.223805i	$-0.928152\pi$
$967$		−	13.9192i		−	0.447610i	0.974634	−	0.223805i	$-0.0718478\pi$
$968$	−12.5262	−	7.23200i	−0.402607	−	0.232445i
$969$		−	0.0621014i		−	0.00199498i
$970$	22.4506	+	12.9619i	0.720845	+	0.416180i
$971$	−10.4459	+	18.0928i	−0.335224	+	0.580625i	−0.983528	−	0.180757i	$-0.942145\pi$
$971$	−10.4459	+	18.0928i	−0.335224	+	0.580625i	0.648304	+	0.761382i	$0.275479\pi$
$972$	0.0599314	−	0.103804i	0.00192230	−	0.00332952i
$973$	23.5372	−	18.2387i	0.754568	−	0.584707i
$974$	37.0586			1.18743
$975$	45.5111	+	10.9803i	1.45752	+	0.351650i
$976$	8.06139	−	13.9627i	0.258039	−	0.446936i
$977$	−7.43409	+	4.29208i	−0.237838	+	0.137316i	−0.614183	−	0.789164i	$-0.710514\pi$
$977$	−7.43409	+	4.29208i	−0.237838	+	0.137316i	0.376345	+	0.926480i	$0.377181\pi$
$978$	27.2748			0.872153
$979$	15.0918	+	26.1398i	0.482338	+	0.835433i
$980$	−2.49207	+	2.53980i	−0.0796062	+	0.0811310i
$981$	−0.693532	+	0.400411i	−0.0221428	+	0.0127841i
$982$	0.167350	+	0.0966193i	0.00534034	+	0.00308325i
$983$	2.72691	+	1.57438i	0.0869750	+	0.0502150i	0.542857	−	0.839825i	$-0.317343\pi$
$983$	2.72691	+	1.57438i	0.0869750	+	0.0502150i	−0.455882	+	0.890040i	$0.650676\pi$
$984$	33.4939			1.06775
$985$	62.3186			1.98563
$986$	0.132353	+	0.0764143i	0.00421499	+	0.00243353i
$987$	−0.947418	+	2.31831i	−0.0301567	+	0.0737926i
$988$	−0.401291	−	0.381668i	−0.0127668	−	0.0121425i
$989$	−9.02625	−	15.6339i	−0.287018	−	0.497130i
$990$	21.5781	−	12.4581i	0.685798	−	0.395945i
$991$	−3.10422	−	5.37666i	−0.0986088	−	0.170795i	0.812500	−	0.582961i	$-0.198106\pi$
$991$	−3.10422	−	5.37666i	−0.0986088	−	0.170795i	−0.911109	+	0.412165i	$0.864773\pi$
$992$	−1.76243	+	3.05262i	−0.0559572	+	0.0969208i
$993$			8.94260i			0.283785i
$994$	−20.0274	+	15.5190i	−0.635230	+	0.492233i
$995$	85.0204	−	49.0865i	2.69533	−	1.55615i
$996$	0.360207	−	0.207966i	0.0114136	−	0.00658964i
$997$	−22.5169			−0.713116			−0.356558	−	0.934273i	$-0.616050\pi$
$997$	−22.5169			−0.713116			−0.356558	+	0.934273i	$0.616050\pi$
$998$	3.33888	+	5.78311i	0.105690	+	0.183061i
$999$		−	4.30401i		−	0.136173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.c.4.3	✓	12
3.2	odd	2		819.2.bm.e.550.4		12
7.2	even	3		273.2.bl.c.121.3	yes	12
13.10	even	6		273.2.bl.c.88.3	yes	12
21.2	odd	6		819.2.do.f.667.4		12
39.23	odd	6		819.2.do.f.361.4		12
91.23	even	6	inner	273.2.t.c.205.4	yes	12
273.23	odd	6		819.2.bm.e.478.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.3	✓	12	1.1	even	1	trivial
273.2.t.c.205.4	yes	12	91.23	even	6	inner
273.2.bl.c.88.3	yes	12	13.10	even	6
273.2.bl.c.121.3	yes	12	7.2	even	3
819.2.bm.e.478.3		12	273.23	odd	6
819.2.bm.e.550.4		12	3.2	odd	2
819.2.do.f.361.4		12	39.23	odd	6
819.2.do.f.667.4		12	21.2	odd	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.45597i q^{2} +(-0.500000 - 0.866025i) q^{3} -0.119863 q^{4} +(-3.67267 + 2.12042i) q^{5} +(-1.26091 + 0.727987i) q^{6} +(-0.357777 - 2.62145i) q^{7} -2.73743i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.45597i q^{2} +(-0.500000 - 0.866025i) q^{3} -0.119863 q^{4} +(-3.67267 + 2.12042i) q^{5} +(-1.26091 + 0.727987i) q^{6} +(-0.357777 - 2.62145i) q^{7} -2.73743i q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.08727 + 5.34732i) q^{10} +(-3.49469 + 2.01766i) q^{11} +(0.0599314 + 0.103804i) q^{12} +(-3.50498 - 0.845633i) q^{13} +(-3.81676 + 0.520915i) q^{14} +(3.67267 + 2.12042i) q^{15} -4.22536 q^{16} -0.0484615 q^{17} +(1.26091 + 0.727987i) q^{18} +(-1.10977 - 0.640729i) q^{19} +(0.440217 - 0.254159i) q^{20} +(-2.09135 + 1.62057i) q^{21} +(2.93766 + 5.08818i) q^{22} +3.59569 q^{23} +(-2.37069 + 1.36872i) q^{24} +(6.49234 - 11.2451i) q^{25} +(-1.23122 + 5.10317i) q^{26} +1.00000 q^{27} +(0.0428842 + 0.314214i) q^{28} +(1.08299 - 1.87579i) q^{29} +(3.08727 - 5.34732i) q^{30} +(4.50804 + 2.60272i) q^{31} +0.677151i q^{32} +(3.49469 + 2.01766i) q^{33} +0.0705587i q^{34} +(6.87256 + 8.86908i) q^{35} +(0.0599314 - 0.103804i) q^{36} -4.30401i q^{37} +(-0.932885 + 1.61580i) q^{38} +(1.02015 + 3.45822i) q^{39} +(5.80450 + 10.0537i) q^{40} +(-10.5963 - 6.11775i) q^{41} +(2.35951 + 3.04496i) q^{42} +(-2.51030 - 4.34796i) q^{43} +(0.418883 - 0.241842i) q^{44} -4.24083i q^{45} -5.23524i q^{46} +(0.819767 - 0.473293i) q^{47} +(2.11268 + 3.65927i) q^{48} +(-6.74399 + 1.87579i) q^{49} +(-16.3725 - 9.45268i) q^{50} +(0.0242308 + 0.0419689i) q^{51} +(0.420117 + 0.101360i) q^{52} +(2.66425 - 4.61461i) q^{53} -1.45597i q^{54} +(8.55656 - 14.8204i) q^{55} +(-7.17604 + 0.979391i) q^{56} +1.28146i q^{57} +(-2.73110 - 1.57680i) q^{58} -3.17187i q^{59} +(-0.440217 - 0.254159i) q^{60} +(-1.90786 + 3.30451i) q^{61} +(3.78949 - 6.56359i) q^{62} +(2.44913 + 1.00088i) q^{63} -7.46480 q^{64} +(14.6657 - 4.32630i) q^{65} +(2.93766 - 5.08818i) q^{66} +(-10.5072 + 6.06634i) q^{67} +0.00580873 q^{68} +(-1.79785 - 3.11396i) q^{69} +(12.9132 - 10.0063i) q^{70} +(5.69604 - 3.28861i) q^{71} +(2.37069 + 1.36872i) q^{72} +(12.1155 + 6.99486i) q^{73} -6.26653 q^{74} -12.9847 q^{75} +(0.133021 + 0.0767995i) q^{76} +(6.53951 + 8.43927i) q^{77} +(5.03508 - 1.48532i) q^{78} +(6.29441 + 10.9022i) q^{79} +(15.5183 - 8.95952i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.90729 + 15.4279i) q^{82} -3.47006i q^{83} +(0.250675 - 0.194246i) q^{84} +(0.177983 - 0.102759i) q^{85} +(-6.33052 + 3.65493i) q^{86} -2.16598 q^{87} +(5.52320 + 9.56647i) q^{88} -7.47988i q^{89} -6.17455 q^{90} +(-0.962780 + 9.49068i) q^{91} -0.430990 q^{92} -5.20543i q^{93} +(-0.689102 - 1.19356i) q^{94} +5.43445 q^{95} +(0.586430 - 0.338575i) q^{96} +(3.63599 - 2.09924i) q^{97} +(2.73110 + 9.81908i) q^{98} -4.03532i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} - 10 q^{4} - 6 q^{5} - 3 q^{6} - 3 q^{7} - 6 q^{9} - 7 q^{10} - 18 q^{11} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} - 6 q^{16} + 3 q^{18} + 9 q^{19} - 27 q^{20} - 3 q^{21} + 7 q^{22} + 32 q^{23} + 6 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{27} + 36 q^{28} - 5 q^{29} - 7 q^{30} - 15 q^{31} + 18 q^{33} - 2 q^{35} + 5 q^{36} + 24 q^{38} - 10 q^{39} + 21 q^{40} - 15 q^{41} + 5 q^{42} - 13 q^{43} + 30 q^{44} + 9 q^{47} + 3 q^{48} - 3 q^{49} - 63 q^{50} + 32 q^{52} + 18 q^{53} + 13 q^{55} + 3 q^{56} - 57 q^{58} + 27 q^{60} + 26 q^{61} - 13 q^{62} + 6 q^{63} - 4 q^{64} + 10 q^{65} + 7 q^{66} - 24 q^{67} - 16 q^{69} + 42 q^{70} - 15 q^{71} - 6 q^{72} + 18 q^{73} - 76 q^{74} - 20 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 39 q^{80} - 6 q^{81} - 14 q^{82} - 12 q^{84} - 12 q^{85} + 15 q^{86} + 10 q^{87} + 16 q^{88} + 14 q^{90} + 4 q^{91} - 40 q^{92} - 3 q^{94} + 56 q^{95} + 6 q^{96} + 45 q^{97} + 57 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 - 10 * q^4 - 6 * q^5 - 3 * q^6 - 3 * q^7 - 6 * q^9 - 7 * q^10 - 18 * q^11 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 - 6 * q^16 + 3 * q^18 + 9 * q^19 - 27 * q^20 - 3 * q^21 + 7 * q^22 + 32 * q^23 + 6 * q^24 + 10 * q^25 - 7 * q^26 + 12 * q^27 + 36 * q^28 - 5 * q^29 - 7 * q^30 - 15 * q^31 + 18 * q^33 - 2 * q^35 + 5 * q^36 + 24 * q^38 - 10 * q^39 + 21 * q^40 - 15 * q^41 + 5 * q^42 - 13 * q^43 + 30 * q^44 + 9 * q^47 + 3 * q^48 - 3 * q^49 - 63 * q^50 + 32 * q^52 + 18 * q^53 + 13 * q^55 + 3 * q^56 - 57 * q^58 + 27 * q^60 + 26 * q^61 - 13 * q^62 + 6 * q^63 - 4 * q^64 + 10 * q^65 + 7 * q^66 - 24 * q^67 - 16 * q^69 + 42 * q^70 - 15 * q^71 - 6 * q^72 + 18 * q^73 - 76 * q^74 - 20 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 39 * q^80 - 6 * q^81 - 14 * q^82 - 12 * q^84 - 12 * q^85 + 15 * q^86 + 10 * q^87 + 16 * q^88 + 14 * q^90 + 4 * q^91 - 40 * q^92 - 3 * q^94 + 56 * q^95 + 6 * q^96 + 45 * q^97 + 57 * q^98

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