LMFDB - Embedded newform 273.2.bl.c.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(88,273)]

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, 5]))

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

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

chi := DirichletCharacter("273.88");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bl (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.3
Root			$1.21245 - 0.727987i$ of defining polynomial
Character	$\chi$	$=$	273.121
Dual form			273.2.bl.c.88.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26091 + 0.727987i) q^{2} +1.00000 q^{3} +(0.0599314 - 0.103804i) q^{4} +(3.67267 + 2.12042i) q^{5} +(-1.26091 + 0.727987i) q^{6} +(2.09135 + 1.62057i) q^{7} -2.73743i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.26091 + 0.727987i) q^{2} +1.00000 q^{3} +(0.0599314 - 0.103804i) q^{4} +(3.67267 + 2.12042i) q^{5} +(-1.26091 + 0.727987i) q^{6} +(2.09135 + 1.62057i) q^{7} -2.73743i q^{8} +1.00000 q^{9} -6.17455 q^{10} -4.03532i 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} +(2.11268 + 3.65927i) q^{16} +(0.0242308 - 0.0419689i) q^{17} +(-1.26091 + 0.727987i) q^{18} +1.28146i q^{19} +(0.440217 - 0.254159i) q^{20} +(2.09135 + 1.62057i) q^{21} +(2.93766 + 5.08818i) q^{22} +(-1.79785 - 3.11396i) q^{23} -2.73743i q^{24} +(6.49234 + 11.2451i) q^{25} +(5.03508 - 1.48532i) q^{26} +1.00000 q^{27} +(0.293560 - 0.119968i) q^{28} +(1.08299 - 1.87579i) q^{29} -6.17455 q^{30} +(-4.50804 + 2.60272i) q^{31} +(-0.586430 - 0.338575i) q^{32} -4.03532i q^{33} +0.0705587i q^{34} +(4.24457 + 10.3864i) q^{35} +(0.0599314 - 0.103804i) q^{36} +(-3.72738 + 2.15200i) q^{37} +(-0.932885 - 1.61580i) q^{38} +(-3.50498 - 0.845633i) q^{39} +(5.80450 - 10.0537i) q^{40} +(-10.5963 - 6.11775i) q^{41} +(-3.81676 - 0.520915i) q^{42} +(-2.51030 - 4.34796i) q^{43} +(-0.418883 - 0.241842i) q^{44} +(3.67267 + 2.12042i) q^{45} +(4.53385 + 2.61762i) q^{46} +(-0.819767 - 0.473293i) q^{47} +(2.11268 + 3.65927i) q^{48} +(1.74751 + 6.77836i) q^{49} +(-16.3725 - 9.45268i) q^{50} +(0.0242308 - 0.0419689i) q^{51} +(-0.297839 + 0.313152i) q^{52} +(2.66425 + 4.61461i) q^{53} +(-1.26091 + 0.727987i) q^{54} +(8.55656 - 14.8204i) q^{55} +(4.43620 - 5.72494i) q^{56} +1.28146i q^{57} +3.15361i q^{58} +(2.74692 + 1.58594i) q^{59} +(0.440217 - 0.254159i) q^{60} +3.81572 q^{61} +(3.78949 - 6.56359i) q^{62} +(2.09135 + 1.62057i) q^{63} -7.46480 q^{64} +(-11.0796 - 10.5378i) q^{65} +(2.93766 + 5.08818i) q^{66} -12.1327i q^{67} +(-0.00290437 - 0.00503051i) q^{68} +(-1.79785 - 3.11396i) q^{69} +(-12.9132 - 10.0063i) q^{70} +(5.69604 - 3.28861i) q^{71} -2.73743i q^{72} +(-12.1155 + 6.99486i) q^{73} +(3.13326 - 5.42697i) q^{74} +(6.49234 + 11.2451i) 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} +17.9190i q^{80} +1.00000 q^{81} +17.8146 q^{82} -3.47006i q^{83} +(0.293560 - 0.119968i) q^{84} +(0.177983 - 0.102759i) q^{85} +(6.33052 + 3.65493i) q^{86} +(1.08299 - 1.87579i) q^{87} -11.0464 q^{88} +(-6.47777 + 3.73994i) q^{89} -6.17455 q^{90} +(-5.95975 - 7.44858i) q^{91} -0.430990 q^{92} +(-4.50804 + 2.60272i) q^{93} +1.37820 q^{94} +(-2.71722 + 4.70637i) q^{95} +(-0.586430 - 0.338575i) q^{96} +(3.63599 - 2.09924i) q^{97} +(-7.13802 - 7.27475i) q^{98} -4.03532i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9	$ 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9} + 14 q^{10} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 27 q^{20} + 3 q^{21} + 7 q^{22} - 16 q^{23} + 10 q^{25} - q^{26} + 12 q^{27} + 24 q^{28} - 5 q^{29} + 14 q^{30} + 15 q^{31} - 6 q^{32} - 2 q^{35} + 5 q^{36} + 6 q^{37} + 24 q^{38} - q^{39} + 21 q^{40} - 15 q^{41} - 16 q^{42} - 13 q^{43} - 30 q^{44} + 6 q^{45} - 9 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} - 63 q^{50} - 55 q^{52} + 18 q^{53} - 3 q^{54} + 13 q^{55} - 21 q^{56} - 33 q^{59} - 27 q^{60} - 52 q^{61} - 13 q^{62} + 3 q^{63} - 4 q^{64} - 41 q^{65} + 7 q^{66} - 16 q^{69} - 42 q^{70} - 15 q^{71} - 18 q^{73} + 38 q^{74} + 10 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 12 q^{81} + 28 q^{82} + 24 q^{84} - 12 q^{85} - 15 q^{86} - 5 q^{87} - 32 q^{88} + 12 q^{89} + 14 q^{90} + 49 q^{91} - 40 q^{92} + 15 q^{93} + 6 q^{94} - 28 q^{95} - 6 q^{96} + 45 q^{97} + 48 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9 + 14 * q^10 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 27 * q^20 + 3 * q^21 + 7 * q^22 - 16 * q^23 + 10 * q^25 - q^26 + 12 * q^27 + 24 * q^28 - 5 * q^29 + 14 * q^30 + 15 * q^31 - 6 * q^32 - 2 * q^35 + 5 * q^36 + 6 * q^37 + 24 * q^38 - q^39 + 21 * q^40 - 15 * q^41 - 16 * q^42 - 13 * q^43 - 30 * q^44 + 6 * q^45 - 9 * q^46 - 9 * q^47 + 3 * q^48 + 9 * q^49 - 63 * q^50 - 55 * q^52 + 18 * q^53 - 3 * q^54 + 13 * q^55 - 21 * q^56 - 33 * q^59 - 27 * q^60 - 52 * q^61 - 13 * q^62 + 3 * q^63 - 4 * q^64 - 41 * q^65 + 7 * q^66 - 16 * q^69 - 42 * q^70 - 15 * q^71 - 18 * q^73 + 38 * q^74 + 10 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 12 * q^81 + 28 * q^82 + 24 * q^84 - 12 * q^85 - 15 * q^86 - 5 * q^87 - 32 * q^88 + 12 * q^89 + 14 * q^90 + 49 * q^91 - 40 * q^92 + 15 * q^93 + 6 * q^94 - 28 * q^95 - 6 * q^96 + 45 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.26091	+	0.727987i	−0.891599	+	0.514765i	−0.874465	−	0.485088i	$-0.838787\pi$
$2$	−1.26091	+	0.727987i	−0.891599	+	0.514765i	−0.0171337	+	0.999853i	$0.505454\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.0599314	−	0.103804i	0.0299657	−	0.0519021i
$5$	3.67267	+	2.12042i	1.64247	+	0.948279i	0.979952	+	0.199231i	$0.0638445\pi$
$5$	3.67267	+	2.12042i	1.64247	+	0.948279i	0.662516	+	0.749048i	$0.269489\pi$
$6$	−1.26091	+	0.727987i	−0.514765	+	0.297200i
$7$	2.09135	+	1.62057i	0.790457	+	0.612517i
$7$	2.09135	+	1.62057i	0.790457	+	0.612517i
$8$		−	2.73743i		−	0.967829i
$9$	1.00000			0.333333
$10$	−6.17455			−1.95256
$11$		−	4.03532i		−	1.21669i	−0.793671	−	0.608347i	$-0.791833\pi$
$11$		−	4.03532i		−	1.21669i	0.793671	−	0.608347i	$-0.208167\pi$
$12$	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
$16$	2.11268	+	3.65927i	0.528170	+	0.914817i
$17$	0.0242308	−	0.0419689i	0.00587682	−	0.0101790i	−0.863072	−	0.505081i	$-0.831463\pi$
$17$	0.0242308	−	0.0419689i	0.00587682	−	0.0101790i	0.868949	+	0.494902i	$0.164796\pi$
$18$	−1.26091	+	0.727987i	−0.297200	+	0.171588i
$19$			1.28146i			0.293987i	0.989137	+	0.146993i	$0.0469596\pi$
$19$			1.28146i			0.293987i	−0.989137	+	0.146993i	$0.953040\pi$
$20$	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
$23$	−1.79785	−	3.11396i	−0.374877	−	0.649306i	0.615432	−	0.788190i	$-0.288982\pi$
$23$	−1.79785	−	3.11396i	−0.374877	−	0.649306i	−0.990309	+	0.138884i	$0.955648\pi$
$24$		−	2.73743i		−	0.558776i
$25$	6.49234	+	11.2451i	1.29847	+	2.24901i
$26$	5.03508	−	1.48532i	0.987461	−	0.291294i
$27$	1.00000			0.192450
$28$	0.293560	−	0.119968i	0.0554775	−	0.0226719i
$29$	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	$0.102213\pi$
$30$	−6.17455			−1.12731
$31$	−4.50804	+	2.60272i	−0.809667	+	0.467461i	−0.846840	−	0.531847i	$-0.821498\pi$
$31$	−4.50804	+	2.60272i	−0.809667	+	0.467461i	0.0371732	+	0.999309i	$0.488165\pi$
$32$	−0.586430	−	0.338575i	−0.103667	−	0.0598522i
$33$		−	4.03532i		−	0.702459i
$34$			0.0705587i			0.0121007i
$35$	4.24457	+	10.3864i	0.717463	+	1.75561i
$36$	0.0599314	−	0.103804i	0.00998857	−	0.0173007i
$37$	−3.72738	+	2.15200i	−0.612777	+	0.353787i	−0.774052	−	0.633122i	$-0.781773\pi$
$37$	−3.72738	+	2.15200i	−0.612777	+	0.353787i	0.161274	+	0.986910i	$0.448440\pi$
$38$	−0.932885	−	1.61580i	−0.151334	−	0.262118i
$39$	−3.50498	−	0.845633i	−0.561246	−	0.135410i
$40$	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	$-0.737943\pi$
$42$	−3.81676	−	0.520915i	−0.588939	−	0.0803789i
$43$	−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
$45$	3.67267	+	2.12042i	0.547489	+	0.316093i
$46$	4.53385	+	2.61762i	0.668479	+	0.385947i
$47$	−0.819767	−	0.473293i	−0.119575	−	0.0690368i	0.439019	−	0.898478i	$-0.355326\pi$
$47$	−0.819767	−	0.473293i	−0.119575	−	0.0690368i	−0.558595	+	0.829441i	$0.688659\pi$
$48$	2.11268	+	3.65927i	0.304939	+	0.528170i
$49$	1.74751	+	6.77836i	0.249645	+	0.968337i
$50$	−16.3725	−	9.45268i	−2.31542	−	1.33681i
$51$	0.0242308	−	0.0419689i	0.00339298	−	0.00587682i
$52$	−0.297839	+	0.313152i	−0.0413028	+	0.0434264i
$53$	2.66425	+	4.61461i	0.365962	+	0.633865i	0.988930	−	0.148382i	$-0.0474066\pi$
$53$	2.66425	+	4.61461i	0.365962	+	0.633865i	−0.622968	+	0.782247i	$0.714073\pi$
$54$	−1.26091	+	0.727987i	−0.171588	+	0.0990665i
$55$	8.55656	−	14.8204i	1.15377	−	1.99838i
$56$	4.43620	−	5.72494i	0.592812	−	0.765027i
$57$			1.28146i			0.169733i
$58$			3.15361i			0.414089i
$59$	2.74692	+	1.58594i	0.357619	+	0.206471i	0.668036	−	0.744129i	$-0.267135\pi$
$59$	2.74692	+	1.58594i	0.357619	+	0.206471i	−0.310417	+	0.950601i	$0.600469\pi$
$60$	0.440217	−	0.254159i	0.0568317	−	0.0328118i
$61$	3.81572			0.488553			0.244276	−	0.969706i	$-0.421450\pi$
$61$	3.81572			0.488553			0.244276	+	0.969706i	$0.421450\pi$
$62$	3.78949	−	6.56359i	0.481265	−	0.833576i
$63$	2.09135	+	1.62057i	0.263486	+	0.204172i
$64$	−7.46480			−0.933100
$65$	−11.0796	−	10.5378i	−1.37425	−	1.30705i
$66$	2.93766	+	5.08818i	0.361601	+	0.626311i
$67$		−	12.1327i		−	1.48224i	−0.671371	−	0.741121i	$-0.734294\pi$
$67$		−	12.1327i		−	1.48224i	0.671371	−	0.741121i	$-0.265706\pi$
$68$	−0.00290437	−	0.00503051i	−0.000352206	−	0.000610039i
$69$	−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	$0.205709\pi$
$72$		−	2.73743i		−	0.322610i
$73$	−12.1155	+	6.99486i	−1.41801	+	0.818687i	−0.996124	−	0.0879632i	$-0.971964\pi$
$73$	−12.1155	+	6.99486i	−1.41801	+	0.818687i	−0.421883	+	0.906650i	$0.638631\pi$
$74$	3.13326	−	5.42697i	0.364234	−	0.630873i
$75$	6.49234	+	11.2451i	0.749671	+	1.29847i
$76$	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	−0.257356	−	0.966317i	$-0.582851\pi$
$79$	6.29441	−	10.9022i	0.708177	−	1.22660i	0.965533	−	0.260281i	$-0.0838153\pi$
$80$			17.9190i			2.00341i
$81$	1.00000			0.111111
$82$	17.8146			1.96729
$83$		−	3.47006i		−	0.380889i	−0.981698	−	0.190444i	$-0.939007\pi$
$83$		−	3.47006i		−	0.380889i	0.981698	−	0.190444i	$-0.0609929\pi$
$84$	0.293560	−	0.119968i	0.0320300	−	0.0130896i
$85$	0.177983	−	0.102759i	0.0193050	−	0.0111457i
$86$	6.33052	+	3.65493i	0.682638	+	0.394121i
$87$	1.08299	−	1.87579i	0.116108	−	0.201106i
$88$	−11.0464			−1.17755
$89$	−6.47777	+	3.73994i	−0.686642	+	0.396433i	−0.802353	−	0.596850i	$-0.796419\pi$
$89$	−6.47777	+	3.73994i	−0.686642	+	0.396433i	0.115711	+	0.993283i	$0.463085\pi$
$90$	−6.17455			−0.650855
$91$	−5.95975	−	7.44858i	−0.624752	−	0.780824i
$92$	−0.430990			−0.0449338
$93$	−4.50804	+	2.60272i	−0.467461	+	0.269889i
$94$	1.37820			0.142151
$95$	−2.71722	+	4.70637i	−0.278781	+	0.482864i
$96$	−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	$0.264963\pi$
$98$	−7.13802	−	7.27475i	−0.721049	−	0.734860i
$99$		−	4.03532i		−	0.405565i
$100$	1.55638			0.155638
$101$	15.8935			1.58146			0.790729	−	0.612166i	$-0.209702\pi$
$101$	15.8935			1.58146			0.790729	+	0.612166i	$0.209702\pi$
$102$			0.0705587i			0.00698636i
$103$	−3.27155	+	5.66650i	−0.322356	+	0.558336i	−0.980974	−	0.194141i	$-0.937808\pi$
$103$	−3.27155	+	5.66650i	−0.322356	+	0.558336i	0.658618	+	0.752477i	$0.271141\pi$
$104$	−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
$107$	3.57979	+	6.20038i	0.346072	+	0.599414i	0.985548	−	0.169397i	$-0.0541821\pi$
$107$	3.57979	+	6.20038i	0.346072	+	0.599414i	−0.639476	+	0.768811i	$0.720849\pi$
$108$	0.0599314	−	0.103804i	0.00576690	−	0.00998857i
$109$	−0.693532	+	0.400411i	−0.0664283	+	0.0383524i	−0.532846	−	0.846212i	$-0.678878\pi$
$109$	−0.693532	+	0.400411i	−0.0664283	+	0.0383524i	0.466418	+	0.884564i	$0.345544\pi$
$110$			24.9163i			2.37567i
$111$	−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	$0.842009\pi$
$114$	−0.932885	−	1.61580i	−0.0873727	−	0.151334i
$115$		−	15.2487i		−	1.42195i
$116$	−0.129810	−	0.224837i	−0.0120526	−	0.0208756i
$117$	−3.50498	−	0.845633i	−0.324036	−	0.0781788i
$118$	−4.61817			−0.425137
$119$	0.118689	−	0.0485042i	0.0108802	−	0.00444637i
$120$	5.80450	−	10.0537i	0.529876	−	0.917772i
$121$	−5.28379			−0.480344
$122$	−4.81128	+	2.77780i	−0.435593	+	0.251490i
$123$	−10.5963	−	6.11775i	−0.955432	−	0.551619i
$124$			0.623937i			0.0560312i
$125$			33.8617i			3.02868i
$126$	−3.81676	−	0.520915i	−0.340024	−	0.0464068i
$127$	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	$0.144110\pi$
$128$	10.5853	−	6.11143i	0.935618	−	0.540179i
$129$	−2.51030	−	4.34796i	−0.221019	−	0.382816i
$130$	21.6417	+	5.22140i	1.89810	+	0.457947i
$131$	2.97143	−	5.14667i	0.259615	−	0.449666i	−0.706524	−	0.707689i	$-0.749738\pi$
$131$	2.97143	−	5.14667i	0.259615	−	0.449666i	0.966139	+	0.258023i	$0.0830710\pi$
$132$	−0.418883	−	0.241842i	−0.0364591	−	0.0210497i
$133$	−2.07669	+	2.67998i	−0.180072	+	0.232384i
$134$	8.83244	+	15.2982i	0.763006	+	1.32157i
$135$	3.67267	+	2.12042i	0.316093	+	0.182496i
$136$	−0.114887	−	0.0663300i	−0.00985148	−	0.00568775i
$137$	−13.9135	−	8.03298i	−1.18871	−	0.686304i	−0.230699	−	0.973025i	$-0.574101\pi$
$137$	−13.9135	−	8.03298i	−1.18871	−	0.686304i	−0.958014	+	0.286721i	$0.907435\pi$
$138$	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	$0.674949\pi$
$140$	1.33253	+	0.181865i	0.112619	+	0.0153704i
$141$	−0.819767	−	0.473293i	−0.0690368	−	0.0398584i
$142$	−4.78814	+	8.29330i	−0.401812	+	0.695958i
$143$	−3.41240	+	14.1437i	−0.285359	+	1.18276i
$144$	2.11268	+	3.65927i	0.176057	+	0.304939i
$145$	7.95492	−	4.59277i	0.660620	−	0.381409i
$146$	10.1843	−	17.6398i	0.842862	−	1.45988i
$147$	1.74751	+	6.77836i	0.144132	+	0.559070i
$148$			0.515890i			0.0424059i
$149$		−	5.57979i		−	0.457115i	−0.973530	−	0.228557i	$-0.926599\pi$
$149$		−	5.57979i		−	0.457115i	0.973530	−	0.228557i	$-0.0734008\pi$
$150$	−16.3725	−	9.45268i	−1.33681	−	0.771808i
$151$	11.1069	−	6.41258i	0.903868	−	0.521849i	0.0254151	−	0.999677i	$-0.491909\pi$
$151$	11.1069	−	6.41258i	0.903868	−	0.521849i	0.878453	+	0.477828i	$0.158576\pi$
$152$	3.50790			0.284529
$153$	0.0242308	−	0.0419689i	0.00195894	−	0.00339298i
$154$	−2.10206	+	15.4019i	−0.169389	+	1.24112i
$155$	−22.0754			−1.77314
$156$	−0.297839	+	0.313152i	−0.0238462	+	0.0250722i
$157$	1.87821	+	3.25315i	0.149897	+	0.259630i	0.931189	−	0.364536i	$-0.118772\pi$
$157$	1.87821	+	3.25315i	0.149897	+	0.259630i	−0.781292	+	0.624166i	$0.785439\pi$
$158$			18.3290i			1.45818i
$159$	2.66425	+	4.61461i	0.211288	+	0.365962i
$160$	−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
$163$			18.7330i			1.46728i	0.679536	+	0.733642i	$0.262181\pi$
$163$			18.7330i			1.46728i	−0.679536	+	0.733642i	$0.737819\pi$
$164$	−1.27010	+	0.733291i	−0.0991779	+	0.0572604i
$165$	8.55656	−	14.8204i	0.666127	−	1.15377i
$166$	2.52616	+	4.37544i	0.196068	+	0.339600i
$167$	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
$171$			1.28146i			0.0979955i
$172$	−0.601782			−0.0458855
$173$	−17.5940			−1.33765			−0.668823	−	0.743421i	$-0.733202\pi$
$173$	−17.5940			−1.33765			−0.668823	+	0.743421i	$0.733202\pi$
$174$			3.15361i			0.239074i
$175$	−4.64562	+	34.0387i	−0.351176	+	2.57308i
$176$	14.7663	−	8.52533i	1.11305	−	0.642621i
$177$	2.74692	+	1.58594i	0.206471	+	0.119206i
$178$	5.44526	−	9.43147i	0.408139	−	0.706918i
$179$	−17.9794			−1.34384			−0.671921	−	0.740623i	$-0.734531\pi$
$179$	−17.9794			−1.34384			−0.671921	+	0.740623i	$0.734531\pi$
$180$	0.440217	−	0.254159i	0.0328118	−	0.0189439i
$181$	9.08741			0.675462			0.337731	−	0.941243i	$-0.390341\pi$
$181$	9.08741			0.675462			0.337731	+	0.941243i	$0.390341\pi$
$182$	12.9372	+	5.05338i	0.958968	+	0.374581i
$183$	3.81572			0.282066
$184$	−8.52426	+	4.92148i	−0.628417	+	0.362816i
$185$	−18.2526			−1.34196
$186$	3.78949	−	6.56359i	0.277859	−	0.481265i
$187$	−0.169358	−	0.0977788i	−0.0123847	−	0.00715029i
$188$	−0.0982595	+	0.0567302i	−0.00716631	+	0.00413747i
$189$	2.09135	+	1.62057i	0.152124	+	0.117879i
$190$		−	7.91242i		−	0.574027i
$191$	20.1321			1.45670			0.728352	−	0.685203i	$-0.240287\pi$
$191$	20.1321			1.45670			0.728352	+	0.685203i	$0.240287\pi$
$192$	−7.46480			−0.538726
$193$		−	3.19364i		−	0.229883i	−0.993372	−	0.114942i	$-0.963332\pi$
$193$		−	3.19364i		−	0.229883i	0.993372	−	0.114942i	$-0.0366681\pi$
$194$	−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	$0.842034\pi$
$198$	2.93766	+	5.08818i	0.208770	+	0.361601i
$199$	11.5747	−	20.0480i	0.820511	−	1.42117i	−0.0847907	−	0.996399i	$-0.527022\pi$
$199$	11.5747	−	20.0480i	0.820511	−	1.42117i	0.905302	−	0.424769i	$-0.139645\pi$
$200$	30.7826	−	17.7723i	2.17666	−	1.25669i
$201$		−	12.1327i		−	0.855773i
$202$	−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
$205$	−25.9444	−	44.9370i	−1.81203	−	3.13853i
$206$		−	9.52660i		−	0.663749i
$207$	−1.79785	−	3.11396i	−0.124959	−	0.216435i
$208$	−4.31051	−	14.6122i	−0.298880	−	1.01318i
$209$	5.17109			0.357692
$210$	−12.9132	−	10.0063i	−0.891093	−	0.690499i
$211$	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	$0.0643848\pi$
$212$	0.638688			0.0438653
$213$	5.69604	−	3.28861i	0.390287	−	0.225332i
$214$	−9.02760	−	5.21209i	−0.617114	−	0.356291i
$215$		−	21.2915i		−	1.45207i
$216$		−	2.73743i		−	0.186259i
$217$	−13.6458	−	1.86239i	−0.926335	−	0.126427i
$218$	0.582988	−	1.00976i	0.0394849	−	0.0683899i
$219$	−12.1155	+	6.99486i	−0.818687	+	0.472669i
$220$	−1.02561	−	1.77641i	−0.0691468	−	0.119766i
$221$	−0.120419	+	0.126610i	−0.00810023	+	0.00851671i
$222$	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	$0.642491\pi$
$224$	−0.677747	−	1.65843i	−0.0452839	−	0.110809i
$225$	6.49234	+	11.2451i	0.432823	+	0.749671i
$226$	0.730543	+	0.421779i	0.0485950	+	0.0280563i
$227$	−7.23244	−	4.17565i	−0.480034	−	0.277148i	0.240397	−	0.970675i	$-0.422722\pi$
$227$	−7.23244	−	4.17565i	−0.480034	−	0.277148i	−0.720430	+	0.693527i	$0.756056\pi$
$228$	0.133021	+	0.0767995i	0.00880951	+	0.00508617i
$229$	6.05361	+	3.49506i	0.400034	+	0.230960i	0.686499	−	0.727131i	$-0.259147\pi$
$229$	6.05361	+	3.49506i	0.400034	+	0.230960i	−0.286465	+	0.958091i	$0.592480\pi$
$230$	11.1009	+	19.2273i	0.731971	+	1.26781i
$231$	6.53951	−	8.43927i	0.430268	−	0.555263i
$232$	−5.13485	−	2.96461i	−0.337119	−	0.194636i
$233$	−11.1643	+	19.3371i	−0.731395	+	1.26681i	0.224892	+	0.974384i	$0.427797\pi$
$233$	−11.1643	+	19.3371i	−0.731395	+	1.26681i	−0.956287	+	0.292429i	$0.905536\pi$
$234$	5.03508	−	1.48532i	0.329154	−	0.0970981i
$235$	−2.00716	−	3.47649i	−0.130932	−	0.226782i
$236$	0.329254	−	0.190095i	0.0214326	−	0.0123741i
$237$	6.29441	−	10.9022i	0.408866	−	0.708177i
$238$	−0.114345	+	0.147563i	−0.00741190	+	0.00956510i
$239$		−	12.8510i		−	0.831264i	−0.909533	−	0.415632i	$-0.863560\pi$
$239$		−	12.8510i		−	0.831264i	0.909533	−	0.415632i	$-0.136440\pi$
$240$			17.9190i			1.15667i
$241$	12.9265	+	7.46312i	0.832669	+	0.480742i	0.854766	−	0.519014i	$-0.173701\pi$
$241$	12.9265	+	7.46312i	0.832669	+	0.480742i	−0.0220967	+	0.999756i	$0.507034\pi$
$242$	6.66238	−	3.84653i	0.428274	−	0.247264i
$243$	1.00000			0.0641500
$244$	0.228681	−	0.396088i	0.0146398	−	0.0253569i
$245$	−7.95492	+	28.6001i	−0.508221	+	1.82720i
$246$	17.8146			1.13582
$247$	1.08364	−	4.49149i	0.0689505	−	0.285786i
$248$	7.12476	+	12.3404i	0.452423	+	0.783619i
$249$		−	3.47006i		−	0.219906i
$250$	−24.6509	−	42.6966i	−1.55906	−	2.70037i
$251$	−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
$254$			2.32354i			0.145792i
$255$	0.177983	−	0.102759i	0.0111457	−	0.00643499i
$256$	−1.43329	+	2.48253i	−0.0895807	+	0.155158i
$257$	15.3006	+	26.5015i	0.954427	+	1.65312i	0.735674	+	0.677335i	$0.236865\pi$
$257$	15.3006	+	26.5015i	0.954427	+	1.65312i	0.218752	+	0.975780i	$0.429801\pi$
$258$	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
$262$			8.65266i			0.534563i
$263$	−18.1675			−1.12026			−0.560129	−	0.828405i	$-0.689249\pi$
$263$	−18.1675			−1.12026			−0.560129	+	0.828405i	$0.689249\pi$
$264$	−11.0464			−0.679859
$265$			22.5973i			1.38814i
$266$	0.667530	−	4.89102i	0.0409289	−	0.299888i
$267$	−6.47777	+	3.73994i	−0.396433	+	0.228881i
$268$	−1.25942	−	0.727128i	−0.0769315	−	0.0444164i
$269$	−5.06111	+	8.76610i	−0.308581	+	0.534479i	−0.978052	−	0.208360i	$-0.933188\pi$
$269$	−5.06111	+	8.76610i	−0.308581	+	0.534479i	0.669471	+	0.742838i	$0.266521\pi$
$270$	−6.17455			−0.375771
$271$	−22.9953	+	13.2763i	−1.39687	+	0.806481i	−0.994063	−	0.108806i	$-0.965297\pi$
$271$	−22.9953	+	13.2763i	−1.39687	+	0.806481i	−0.402803	+	0.915287i	$0.631964\pi$
$272$	0.204767			0.0124158
$273$	−5.95975	−	7.44858i	−0.360700	−	0.450809i
$274$	23.3916			1.41314
$275$	45.3774	−	26.1986i	2.73636	−	1.57984i
$276$	−0.430990			−0.0259425
$277$	−14.6551	+	25.3833i	−0.880537	+	1.52514i	−0.0297927	+	0.999556i	$0.509485\pi$
$277$	−14.6551	+	25.3833i	−0.880537	+	1.52514i	−0.850745	+	0.525579i	$0.823849\pi$
$278$	−14.1910	−	8.19315i	−0.851117	−	0.491393i
$279$	−4.50804	+	2.60272i	−0.269889	+	0.155820i
$280$	28.4319	−	11.6192i	1.69913	−	0.694381i
$281$		−	6.74332i		−	0.402273i	−0.979563	−	0.201136i	$-0.935537\pi$
$281$		−	6.74332i		−	0.402273i	0.979563	−	0.201136i	$-0.0644635\pi$
$282$	1.37820			0.0820709
$283$	17.3869			1.03354			0.516772	−	0.856123i	$-0.327133\pi$
$283$	17.3869			1.03354			0.516772	+	0.856123i	$0.327133\pi$
$284$		−	0.788365i		−	0.0467808i
$285$	−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
$289$	8.49883	+	14.7204i	0.499931	+	0.865906i
$290$	−6.68696	+	11.5822i	−0.392672	+	0.680128i
$291$	3.63599	−	2.09924i	0.213145	−	0.123060i
$292$			1.67685i			0.0981301i
$293$	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
$296$	5.89096	+	10.2035i	0.342405	+	0.593064i
$297$		−	4.03532i		−	0.234153i
$298$	4.06202	+	7.03562i	0.235306	+	0.407563i
$299$	3.66815	+	12.4347i	0.212135	+	0.719117i
$300$	1.55638			0.0898576
$301$	1.79625	−	13.1612i	0.103534	−	0.758600i
$302$	−9.33656	+	16.1714i	−0.537259	+	0.930559i
$303$	15.8935			0.913055
$304$	−4.68920	+	2.70731i	−0.268944	+	0.155275i
$305$	14.0139	+	8.09092i	0.802432	+	0.463285i
$306$			0.0705587i			0.00403357i
$307$		−	0.0778605i		−	0.00444373i	−0.999998	−	0.00222187i	$-0.999293\pi$
$307$		−	0.0778605i		−	0.00444373i	0.999998	−	0.00222187i	$-0.000707243\pi$
$308$	−0.484110	−	1.18461i	−0.0275847	−	0.0674992i
$309$	−3.27155	+	5.66650i	−0.186112	+	0.322356i
$310$	27.8351	−	16.0706i	1.58093	−	0.912748i
$311$	15.0689	+	26.1002i	0.854482	+	1.48001i	0.877125	+	0.480262i	$0.159458\pi$
$311$	15.0689	+	26.1002i	0.854482	+	1.48001i	−0.0226436	+	0.999744i	$0.507208\pi$
$312$	−2.31486	+	9.59465i	−0.131053	+	0.543190i
$313$	−10.0024	+	17.3247i	−0.565371	+	0.979252i	0.431644	+	0.902044i	$0.357934\pi$
$313$	−10.0024	+	17.3247i	−0.565371	+	0.979252i	−0.997015	+	0.0772078i	$0.975400\pi$
$314$	−4.73650	−	2.73462i	−0.267296	−	0.154324i
$315$	4.24457	+	10.3864i	0.239154	+	0.585205i
$316$	−0.754466	−	1.30677i	−0.0424420	−	0.0735117i
$317$	−20.7932	−	12.0050i	−1.16786	−	0.674266i	−0.214688	−	0.976683i	$-0.568873\pi$
$317$	−20.7932	−	12.0050i	−1.16786	−	0.674266i	−0.953176	+	0.302416i	$0.902207\pi$
$318$	−6.71875	−	3.87907i	−0.376769	−	0.217528i
$319$	−7.56941	−	4.37020i	−0.423805	−	0.244684i
$320$	−27.4158	−	15.8285i	−1.53259	−	0.884840i
$321$	3.57979	+	6.20038i	0.199805	+	0.346072i
$322$	5.23985	+	12.8218i	0.292005	+	0.714530i
$323$	0.0537814	+	0.0310507i	0.00299247	+	0.00172771i
$324$	0.0599314	−	0.103804i	0.00332952	−	0.00576690i
$325$	−13.2463	−	44.9039i	−0.734775	−	2.49082i
$326$	−13.6374	−	23.6207i	−0.755306	−	1.30823i
$327$	−0.693532	+	0.400411i	−0.0383524	+	0.0221428i
$328$	−16.7469	+	29.0065i	−0.924694	+	1.60162i
$329$	−0.947418	−	2.31831i	−0.0522329	−	0.127813i
$330$			24.9163i			1.37160i
$331$			8.94260i			0.491530i	0.969329	+	0.245765i	$0.0790391\pi$
$331$			8.94260i			0.491530i	−0.969329	+	0.245765i	$0.920961\pi$
$332$	−0.360207	−	0.207966i	−0.0197689	−	0.0114136i
$333$	−3.72738	+	2.15200i	−0.204259	+	0.117929i
$334$	−13.8207			−0.756237
$335$	25.7263	−	44.5593i	1.40558	−	2.43454i
$336$	−1.51174	+	11.0766i	−0.0824720	+	0.604276i
$337$	−6.95546			−0.378888			−0.189444	−	0.981892i	$-0.560669\pi$
$337$	−6.95546			−0.378888			−0.189444	+	0.981892i	$0.560669\pi$
$338$	−18.9039	+	0.948177i	−1.02824	+	0.0515740i
$339$	−0.289689	−	0.501755i	−0.0157337	−	0.0272516i
$340$		−	0.0246339i		−	0.00133596i
$341$	10.5028	+	18.1914i	0.568758	+	0.985117i
$342$	−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
$345$		−	15.2487i		−	0.820964i
$346$	22.1845	−	12.8082i	1.19264	−	0.688573i
$347$	−7.32457	+	12.6865i	−0.393204	+	0.681049i	−0.992870	−	0.119201i	$-0.961967\pi$
$347$	−7.32457	+	12.6865i	−0.393204	+	0.681049i	0.599666	+	0.800250i	$0.295300\pi$
$348$	−0.129810	−	0.224837i	−0.00695854	−	0.0120526i
$349$	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
$353$		−	3.13873i		−	0.167058i	−0.996505	−	0.0835290i	$-0.973381\pi$
$353$		−	3.13873i		−	0.167058i	0.996505	−	0.0835290i	$-0.0266191\pi$
$354$	−4.61817			−0.245453
$355$	27.8929			1.48040
$356$			0.896559i			0.0475176i
$357$	0.118689	−	0.0485042i	0.00628166	−	0.00256711i
$358$	22.6704	−	13.0888i	1.19817	−	0.691763i
$359$	−11.4388	−	6.60421i	−0.603719	−	0.348557i	0.166785	−	0.985993i	$-0.446662\pi$
$359$	−11.4388	−	6.60421i	−0.603719	−	0.348557i	−0.770503	+	0.637436i	$0.779995\pi$
$360$	5.80450	−	10.0537i	0.305924	−	0.529876i
$361$	17.3579			0.913572
$362$	−11.4584	+	6.61552i	−0.602241	+	0.347704i
$363$	−5.28379			−0.277327
$364$	−1.13037	+	0.172243i	−0.0592475	+	0.00902800i
$365$	−59.3281			−3.10538
$366$	−4.81128	+	2.77780i	−0.251490	+	0.145198i
$367$	−5.65933			−0.295415			−0.147707	−	0.989031i	$-0.547189\pi$
$367$	−5.65933			−0.295415			−0.147707	+	0.989031i	$0.547189\pi$
$368$	7.59654	−	13.1576i	0.395997	−	0.685887i
$369$	−10.5963	−	6.11775i	−0.551619	−	0.318477i
$370$	23.0149	−	13.2877i	1.19649	−	0.690792i
$371$	−1.90641	+	13.9684i	−0.0989760	+	0.725202i
$372$			0.623937i			0.0323496i
$373$	−11.1373			−0.576669			−0.288334	−	0.957530i	$-0.593101\pi$
$373$	−11.1373			−0.576669			−0.288334	+	0.957530i	$0.593101\pi$
$374$	0.284727			0.0147229
$375$			33.8617i			1.74861i
$376$	−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	$0.636803\pi$
$380$	0.325694	+	0.564119i	0.0167078	+	0.0289387i
$381$	0.797934	−	1.38206i	0.0408794	−	0.0708052i
$382$	−25.3847	+	14.6559i	−1.29880	+	0.749860i
$383$		−	20.2228i		−	1.03334i	−0.856186	−	0.516668i	$-0.827172\pi$
$383$		−	20.2228i		−	1.03334i	0.856186	−	0.516668i	$-0.172828\pi$
$384$	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
$387$	−2.51030	−	4.34796i	−0.127605	−	0.221019i
$388$		−	0.503241i		−	0.0255482i
$389$	−2.17109	−	3.76044i	−0.110079	−	0.190662i	0.805723	−	0.592292i	$-0.201777\pi$
$389$	−2.17109	−	3.76044i	−0.110079	−	0.190662i	−0.915802	+	0.401631i	$0.868444\pi$
$390$	21.6417	+	5.22140i	1.09587	+	0.264396i
$391$	−0.174253			−0.00881233
$392$	18.5553	−	4.78370i	0.937185	−	0.241613i
$393$	2.97143	−	5.14667i	0.149889	−	0.259615i
$394$	21.3954			1.07788
$395$	46.2346	−	26.6936i	2.32632	−	1.34310i
$396$	−0.418883	−	0.241842i	−0.0210497	−	0.0121530i
$397$		−	0.853623i		−	0.0428421i	−0.999771	−	0.0214211i	$-0.993181\pi$
$397$		−	0.853623i		−	0.0428421i	0.999771	−	0.0214211i	$-0.00681906\pi$
$398$			33.7051i			1.68948i
$399$	−2.07669	+	2.67998i	−0.103965	+	0.134167i
$400$	−27.4325	+	47.5144i	−1.37162	+	2.37572i
$401$	12.3337	−	7.12087i	0.615916	−	0.355600i	−0.159361	−	0.987220i	$-0.550943\pi$
$401$	12.3337	−	7.12087i	0.615916	−	0.355600i	0.775277	+	0.631621i	$0.217610\pi$
$402$	8.83244	+	15.2982i	0.440522	+	0.763006i
$403$	18.0015	−	5.31033i	0.896720	−	0.264526i
$404$	0.952517	−	1.64981i	0.0473895	−	0.0820810i
$405$	3.67267	+	2.12042i	0.182496	+	0.105364i
$406$	−5.11064	+	6.59530i	−0.253637	+	0.327319i
$407$	8.68402	+	15.0412i	0.430451	+	0.745563i
$408$	−0.114887	−	0.0663300i	−0.00568775	−	0.00328383i
$409$	−7.84561	−	4.52967i	−0.387941	−	0.223978i	0.293327	−	0.956012i	$-0.405238\pi$
$409$	−7.84561	−	4.52967i	−0.387941	−	0.223978i	−0.681267	+	0.732035i	$0.738571\pi$
$410$	65.4271	+	37.7743i	3.23121	+	1.86554i
$411$	−13.9135	−	8.03298i	−0.686304	−	0.396238i
$412$	0.392137	+	0.679202i	0.0193192	+	0.0334619i
$413$	3.17467	+	7.76833i	0.156215	+	0.382255i
$414$	4.53385	+	2.61762i	0.222826	+	0.128649i
$415$	7.35798	−	12.7444i	0.361189	−	0.625598i
$416$	1.76912	+	1.68260i	0.0867380	+	0.0824965i
$417$	5.62726	+	9.74671i	0.275568	+	0.477298i
$418$	−6.52028	+	3.76449i	−0.318917	+	0.184127i
$419$	−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	$0.986914\pi$
$420$	1.33253	+	0.181865i	0.0650208	+	0.00887409i
$421$			6.13705i			0.299102i	0.988754	+	0.149551i	$0.0477827\pi$
$421$			6.13705i			0.299102i	−0.988754	+	0.149551i	$0.952217\pi$
$422$			13.3590i			0.650306i
$423$	−0.819767	−	0.473293i	−0.0398584	−	0.0230123i
$424$	12.6322	−	7.29319i	0.613473	−	0.354189i
$425$	0.629257			0.0305234
$426$	−4.78814	+	8.29330i	−0.231986	+	0.401812i
$427$	7.98001	+	6.18363i	0.386180	+	0.299247i
$428$	0.858168			0.0414811
$429$	−3.41240	+	14.1437i	−0.164752	+	0.682865i
$430$	15.4999	+	26.8467i	0.747474	+	1.29466i
$431$			25.6455i			1.23530i	0.786452	+	0.617651i	$0.211916\pi$
$431$			25.6455i			1.23530i	−0.786452	+	0.617651i	$0.788084\pi$
$432$	2.11268	+	3.65927i	0.101646	+	0.176057i
$433$	−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
$436$			0.0959887i			0.00459702i
$437$	3.99041	−	2.30386i	0.190887	−	0.110209i
$438$	10.1843	−	17.6398i	0.486627	−	0.842862i
$439$	−11.6029	−	20.0967i	−0.553774	−	0.959165i	−0.997998	−	0.0632494i	$-0.979854\pi$
$439$	−11.6029	−	20.0967i	−0.553774	−	0.959165i	0.444223	−	0.895916i	$-0.353480\pi$
$440$	−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	−0.904124	−	0.427271i	$-0.859475\pi$
$443$	−1.72662	+	2.99059i	−0.0820340	+	0.142087i	0.822089	+	0.569358i	$0.192808\pi$
$444$			0.515890i			0.0244831i
$445$	−31.7209			−1.50372
$446$	−3.29949			−0.156235
$447$		−	5.57979i		−	0.263915i
$448$	−15.6115	−	12.0972i	−0.737576	−	0.571540i
$449$	−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
$451$	−24.6871	+	42.7593i	−1.16247	+	2.01345i
$452$	−0.0694458			−0.00326645
$453$	11.1069	−	6.41258i	0.521849	−	0.301289i
$454$	12.1593			0.570663
$455$	−6.09410	−	39.9933i	−0.285696	−	1.87492i
$456$	3.50790			0.164273
$457$	−33.8964	+	19.5701i	−1.58561	+	0.915452i	−0.591590	+	0.806239i	$0.701500\pi$
$457$	−33.8964	+	19.5701i	−1.58561	+	0.915452i	−0.994018	+	0.109213i	$0.965167\pi$
$458$	−10.1774			−0.475560
$459$	0.0242308	−	0.0419689i	0.00113099	−	0.00195894i
$460$	−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	$0.217356\pi$
$462$	−2.10206	+	15.4019i	−0.0977965	+	0.716559i
$463$		−	6.98877i		−	0.324796i	−0.986725	−	0.162398i	$-0.948077\pi$
$463$		−	6.98877i		−	0.324796i	0.986725	−	0.162398i	$-0.0519228\pi$
$464$	9.15202			0.424872
$465$	−22.0754			−1.02372
$466$		−	32.5098i		−	1.50599i
$467$	7.25825	−	12.5716i	0.335872	−	0.581747i	−0.647780	−	0.761827i	$-0.724303\pi$
$467$	7.25825	−	12.5716i	0.335872	−	0.581747i	0.983652	+	0.180081i	$0.0576359\pi$
$468$	−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
$471$	1.87821	+	3.25315i	0.0865432	+	0.149897i
$472$	4.34140	−	7.51952i	0.199829	−	0.346114i
$473$	−17.5454	+	10.1298i	−0.806738	+	0.465771i
$474$			18.3290i			0.841879i
$475$	−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
$478$	9.35539	+	16.2040i	0.427906	+	0.741154i
$479$		−	16.9269i		−	0.773411i	−0.922203	−	0.386705i	$-0.873613\pi$
$479$		−	16.9269i		−	0.773411i	0.922203	−	0.386705i	$-0.126387\pi$
$480$	−1.43584	−	2.48695i	−0.0655369	−	0.113513i
$481$	14.8842	−	4.39074i	0.678661	−	0.200201i
$482$	−21.7322			−0.989876
$483$	1.28646	−	9.42592i	0.0585358	−	0.428894i
$484$	−0.316665	+	0.548479i	−0.0143938	+	0.0249309i
$485$	17.8051			0.808486
$486$	−1.26091	+	0.727987i	−0.0571961	+	0.0330222i
$487$	−22.0428	−	12.7264i	−0.998853	−	0.576688i	−0.0909440	−	0.995856i	$-0.528988\pi$
$487$	−22.0428	−	12.7264i	−0.998853	−	0.576688i	−0.907909	+	0.419168i	$0.862322\pi$
$488$		−	10.4453i		−	0.472835i
$489$			18.7330i			0.847137i
$490$	−10.7901	−	41.8533i	−0.487447	−	1.89074i
$491$	−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	$0.167620\pi$
$492$	−1.27010	+	0.733291i	−0.0572604	+	0.0330593i
$493$	−0.0524832	−	0.0909036i	−0.00236373	−	0.00409409i
$494$	1.90337	+	6.45224i	0.0856366	+	0.290300i
$495$	8.55656	−	14.8204i	0.384589	−	0.666127i
$496$	−19.0481	−	10.9974i	−0.855283	−	0.493798i
$497$	17.2419	+	2.35318i	0.773403	+	0.105555i
$498$	2.52616	+	4.37544i	0.113200	+	0.196068i
$499$	3.97198	+	2.29323i	0.177810	+	0.102659i	0.586264	−	0.810120i	$-0.300598\pi$
$499$	3.97198	+	2.29323i	0.177810	+	0.102659i	−0.408453	+	0.912779i	$0.633932\pi$
$500$	3.51499	+	2.02938i	0.157195	+	0.0907566i
$501$	8.22069	+	4.74622i	0.367273	+	0.212045i
$502$	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	$0.995352\pi$
$504$	4.43620	−	5.72494i	0.197604	−	0.255009i
$505$	58.3714	+	33.7008i	2.59749	+	1.49966i
$506$	10.5629	−	18.2955i	0.469579	−	0.813335i
$507$	11.5698	+	5.92786i	0.513833	+	0.263265i
$508$	−0.0956426	−	0.165658i	−0.00424345	−	0.00734988i
$509$	−30.4627	+	17.5876i	−1.35024	+	0.779559i	−0.988282	−	0.152638i	$-0.951223\pi$
$509$	−30.4627	+	17.5876i	−1.35024	+	0.779559i	−0.361953	+	0.932196i	$0.617890\pi$
$510$	−0.149614	+	0.259139i	−0.00662502	+	0.0114749i
$511$	−36.6734	−	5.00521i	−1.62233	−	0.221417i
$512$			20.2721i			0.895907i
$513$			1.28146i			0.0565777i
$514$	−38.5855	−	22.2773i	−1.70193	−	0.982611i
$515$	−24.0307	+	13.8741i	−1.05892	+	0.611366i
$516$	−0.601782			−0.0264920
$517$	−1.90989	+	3.30802i	−0.0839967	+	0.145486i
$518$	15.3475	−	6.27204i	0.674332	−	0.275578i
$519$	−17.5940			−0.772291
$520$	−28.8464	+	30.3295i	−1.26500	+	1.33004i
$521$	−9.16197	−	15.8690i	−0.401393	−	0.695233i	0.592501	−	0.805570i	$-0.298141\pi$
$521$	−9.16197	−	15.8690i	−0.401393	−	0.695233i	−0.993894	+	0.110336i	$0.964807\pi$
$522$			3.15361i			0.138030i
$523$	4.14793	+	7.18443i	0.181376	+	0.314153i	0.942350	−	0.334630i	$-0.108611\pi$
$523$	4.14793	+	7.18443i	0.181376	+	0.314153i	−0.760973	+	0.648783i	$0.775278\pi$
$524$	−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
$527$			0.252263i			0.0109887i
$528$	14.7663	−	8.52533i	0.642621	−	0.371017i
$529$	5.03550	−	8.72174i	0.218935	−	0.379206i
$530$	−16.4505	−	28.4931i	−0.714565	−	1.23766i
$531$	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
$535$			30.3626i			1.31269i
$536$	−33.2124			−1.43456
$537$	−17.9794			−0.775868
$538$		−	14.7377i		−	0.635388i
$539$	27.3528	−	7.05177i	1.17817	−	0.303741i
$540$	0.440217	−	0.254159i	0.0189439	−	0.0109373i
$541$	15.6366	+	9.02781i	0.672271	+	0.388136i	0.796937	−	0.604063i	$-0.206452\pi$
$541$	15.6366	+	9.02781i	0.672271	+	0.388136i	−0.124665	+	0.992199i	$0.539786\pi$
$542$	19.3300	−	33.4806i	0.830296	−	1.43811i
$543$	9.08741			0.389978
$544$	−0.0284193	+	0.0164079i	−0.00121847	+	0.000703482i
$545$	−3.39615			−0.145475
$546$	12.9372	+	5.05338i	0.553661	+	0.216265i
$547$	39.4973			1.68878			0.844391	−	0.535727i	$-0.179962\pi$
$547$	39.4973			1.68878			0.844391	+	0.535727i	$0.179962\pi$
$548$	−1.66771	+	0.962855i	−0.0712412	+	0.0411311i
$549$	3.81572			0.162851
$550$	−38.1446	+	66.0683i	−1.62649	+	2.81716i
$551$	2.40375	+	1.38780i	0.102403	+	0.0591224i
$552$	−8.52426	+	4.92148i	−0.362816	+	0.209472i
$553$	30.8317	−	12.5999i	1.31110	−	0.535802i
$554$		−	42.6748i		−	1.81308i
$555$	−18.2526			−0.774779
$556$	1.34900			0.0572103
$557$			25.3150i			1.07263i	0.844018	+	0.536315i	$0.180184\pi$
$557$			25.3150i			1.07263i	−0.844018	+	0.536315i	$0.819816\pi$
$558$	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
$562$	4.90905	+	8.50273i	0.207076	+	0.358666i
$563$	−6.78108	+	11.7452i	−0.285789	+	0.495000i	−0.972800	−	0.231646i	$-0.925589\pi$
$563$	−6.78108	+	11.7452i	−0.285789	+	0.495000i	0.687011	+	0.726647i	$0.258922\pi$
$564$	−0.0982595	+	0.0567302i	−0.00413747	+	0.00238877i
$565$		−	2.45704i		−	0.103369i
$566$	−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
$569$	−6.26068	−	10.8438i	−0.262461	−	0.454596i	0.704434	−	0.709769i	$-0.251201\pi$
$569$	−6.26068	−	10.8438i	−0.262461	−	0.454596i	−0.966895	+	0.255173i	$0.917867\pi$
$570$		−	7.91242i		−	0.331415i
$571$	−4.44524	−	7.69938i	−0.186028	−	0.322209i	0.757895	−	0.652377i	$-0.226228\pi$
$571$	−4.44524	−	7.69938i	−0.186028	−	0.322209i	−0.943922	+	0.330168i	$0.892895\pi$
$572$	1.26367	+	1.20187i	0.0528366	+	0.0502529i
$573$	20.1321			0.841029
$574$	37.2566	+	28.8698i	1.55506	+	1.20500i
$575$	23.3444	−	40.4338i	0.973531	−	1.68620i
$576$	−7.46480			−0.311033
$577$	24.6718	−	14.2443i	1.02710	−	0.592997i	0.110948	−	0.993826i	$-0.464611\pi$
$577$	24.6718	−	14.2443i	1.02710	−	0.592997i	0.916153	+	0.400829i	$0.131278\pi$
$578$	−21.4325	−	12.3741i	−0.891476	−	0.514694i
$579$		−	3.19364i		−	0.132723i
$580$		−	1.10101i		−	0.0457167i
$581$	5.62347	−	7.25712i	0.233301	−	0.301076i
$582$	−3.05644	+	5.29391i	−0.126693	+	0.219440i
$583$	18.6214	−	10.7511i	0.771220	−	0.445264i
$584$	19.1480	+	33.1653i	0.792348	+	1.37239i
$585$	−11.0796	−	10.5378i	−0.458083	−	0.435683i
$586$	−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	$0.561623\pi$
$588$	0.808354	+	0.224837i	0.0333359	+	0.00927214i
$589$	−3.33527	−	5.77686i	−0.137427	−	0.238031i
$590$	−16.9610	−	9.79244i	−0.698274	−	0.403149i
$591$	−12.7261	−	7.34744i	−0.523483	−	0.302233i
$592$	−15.7495	−	9.09299i	−0.647301	−	0.373719i
$593$	14.8094	+	8.55019i	0.608148	+	0.351114i	0.772240	−	0.635331i	$-0.219136\pi$
$593$	14.8094	+	8.55019i	0.608148	+	0.351114i	−0.164092	+	0.986445i	$0.552470\pi$
$594$	2.93766	+	5.08818i	0.120534	+	0.208770i
$595$	0.538753	+	0.0735294i	0.0220867	+	0.00301441i
$596$	−0.579206	−	0.334405i	−0.0237252	−	0.0136978i
$597$	11.5747	−	20.0480i	0.473722	−	0.820511i
$598$	−13.6775	−	13.0087i	−0.559315	−	0.531964i
$599$	−21.8381	−	37.8247i	−0.892280	−	1.54547i	−0.837135	−	0.546996i	$-0.815771\pi$
$599$	−21.8381	−	37.8247i	−0.892280	−	1.54547i	−0.0551452	−	0.998478i	$-0.517562\pi$
$600$	30.7826	−	17.7723i	1.25669	−	0.725553i
$601$	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	$-0.0413205\pi$
$602$	7.31629	+	17.9028i	0.298190	+	0.729663i
$603$		−	12.1327i		−	0.494081i
$604$		−	1.53726i		−	0.0625502i
$605$	−19.4056	−	11.2038i	−0.788950	−	0.455500i
$606$	−20.0402	+	11.5702i	−0.814079	+	0.470009i
$607$	0.751936			0.0305201			0.0152601	−	0.999884i	$-0.495142\pi$
$607$	0.751936			0.0305201			0.0152601	+	0.999884i	$0.495142\pi$
$608$	0.433870	−	0.751485i	0.0175958	−	0.0304767i
$609$	5.30476	−	2.16788i	0.214960	−	0.0878470i
$610$	−23.5603			−0.953930
$611$	2.47304	+	2.35210i	0.100048	+	0.0951559i
$612$	−0.00290437	−	0.00503051i	−0.000117402	−	0.000203346i
$613$		−	27.2121i		−	1.09909i	−0.835465	−	0.549543i	$-0.814802\pi$
$613$		−	27.2121i		−	1.09909i	0.835465	−	0.549543i	$-0.185198\pi$
$614$	0.0566815	+	0.0981752i	0.00228748	+	0.00396203i
$615$	−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	$0.232913\pi$
$618$		−	9.52660i		−	0.383216i
$619$	−37.4700	+	21.6333i	−1.50605	+	0.869516i	−0.506070	+	0.862493i	$0.668902\pi$
$619$	−37.4700	+	21.6333i	−1.50605	+	0.869516i	−0.999975	+	0.00702301i	$0.997764\pi$
$620$	−1.32301	+	2.29152i	−0.0531333	+	0.0920295i
$621$	−1.79785	−	3.11396i	−0.0721451	−	0.124959i
$622$	−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
$626$		−	29.1266i		−	1.16413i
$627$	5.17109			0.206513
$628$	0.450254			0.0179671
$629$			0.208579i			0.00831658i
$630$	−12.9132	−	10.0063i	−0.514473	−	0.398660i
$631$	−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
$633$	4.58765	−	7.94604i	0.182343	−	0.315827i
$634$	34.9579			1.38835
$635$	5.86110	−	3.38391i	0.232591	−	0.134286i
$636$	0.638688			0.0253256
$637$	−0.393001	−	25.2358i	−0.0155713	−	0.999879i
$638$	12.7258			0.503819
$639$	5.69604	−	3.28861i	0.225332	−	0.130096i
$640$	51.8352			2.04896
$641$	8.09040	−	14.0130i	0.319552	−	0.553480i	−0.660843	−	0.750524i	$-0.729801\pi$
$641$	8.09040	−	14.0130i	0.319552	−	0.553480i	0.980395	+	0.197044i	$0.0631343\pi$
$642$	−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	$0.258763\pi$
$644$	−0.901351	−	0.698448i	−0.0355182	−	0.0275227i
$645$		−	21.2915i		−	0.838352i
$646$	−0.0904180			−0.00355745
$647$	17.5582			0.690282			0.345141	−	0.938551i	$-0.387831\pi$
$647$	17.5582			0.690282			0.345141	+	0.938551i	$0.387831\pi$
$648$		−	2.73743i		−	0.107537i
$649$	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
$653$	15.4980	+	26.8434i	0.606485	+	1.05046i	0.991815	+	0.127684i	$0.0407544\pi$
$653$	15.4980	+	26.8434i	0.606485	+	1.05046i	−0.385330	+	0.922779i	$0.625912\pi$
$654$	0.582988	−	1.00976i	0.0227966	−	0.0394849i
$655$	21.8262	−	12.6013i	0.852819	−	0.492375i
$656$		−	51.6994i		−	2.01852i
$657$	−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	$0.795423\pi$
$660$	−1.02561	−	1.77641i	−0.0399219	−	0.0691468i
$661$			37.9514i			1.47614i	0.674724	+	0.738070i	$0.264263\pi$
$661$			37.9514i			1.47614i	−0.674724	+	0.738070i	$0.735737\pi$
$662$	−6.51010	−	11.2758i	−0.253022	−	0.438247i
$663$	−0.120419	+	0.126610i	−0.00467667	+	0.00491712i
$664$	−9.49906			−0.368635
$665$	−13.3097	+	5.43923i	−0.516127	+	0.210924i
$666$	3.13326	−	5.42697i	0.121411	−	0.210291i
$667$	−7.78818			−0.301560
$668$	0.985354	−	0.568895i	0.0381245	−	0.0220112i
$669$	1.96256	+	1.13309i	0.0758770	+	0.0438076i
$670$			74.9138i			2.89417i
$671$		−	15.3976i		−	0.594419i
$672$	−0.677747	−	1.65843i	−0.0261447	−	0.0639753i
$673$	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	$0.0551475\pi$
$674$	8.77022	−	5.06349i	0.337816	−	0.195038i
$675$	6.49234	+	11.2451i	0.249890	+	0.432823i
$676$	1.30873	−	0.845731i	0.0503358	−	0.0325281i
$677$	−2.24699	+	3.89190i	−0.0863589	+	0.149578i	−0.905969	−	0.423343i	$-0.860857\pi$
$677$	−2.24699	+	3.89190i	−0.0863589	+	0.149578i	0.819611	+	0.572921i	$0.194190\pi$
$678$	0.730543	+	0.421779i	0.0280563	+	0.0161983i
$679$	11.0061	+	1.50212i	0.422375	+	0.0576461i
$680$	−0.281295	−	0.487217i	−0.0107872	−	0.0186839i
$681$	−7.23244	−	4.17565i	−0.277148	−	0.160011i
$682$	−26.4862	−	15.2918i	−1.01421	−	0.585553i
$683$	16.3595	+	9.44514i	0.625977	+	0.361408i	0.779192	−	0.626785i	$-0.215629\pi$
$683$	16.3595	+	9.44514i	0.625977	+	0.361408i	−0.153215	+	0.988193i	$0.548963\pi$
$684$	0.133021	+	0.0767995i	0.00508617	+	0.00293650i
$685$	−34.0665	−	59.0050i	−1.30162	−	2.25446i
$686$	−3.13890	−	26.7817i	−0.119844	−	1.02253i
$687$	6.05361	+	3.49506i	0.230960	+	0.133345i
$688$	10.6069	−	18.3717i	0.404384	−	0.700414i
$689$	−5.43587	−	18.4271i	−0.207090	−	0.702017i
$690$	11.1009	+	19.2273i	0.422604	+	0.731971i
$691$	−31.2588	+	18.0473i	−1.18914	+	0.686551i	−0.958112	−	0.286395i	$-0.907543\pi$
$691$	−31.2588	+	18.0473i	−1.18914	+	0.686551i	−0.231030	+	0.972947i	$0.574210\pi$
$692$	−1.05443	+	1.82633i	−0.0400835	+	0.0694267i
$693$	6.53951	−	8.43927i	0.248415	−	0.320581i
$694$		−	21.3288i		−	0.809630i
$695$			47.7286i			1.81045i
$696$	−5.13485	−	2.96461i	−0.194636	−	0.112373i
$697$	−0.513510	+	0.296475i	−0.0194506	+	0.0112298i
$698$	−16.1118			−0.609839
$699$	−11.1643	+	19.3371i	−0.422271	+	0.731395i
$700$	3.25494	+	2.52222i	0.123025	+	0.0953310i
$701$	7.46818			0.282069			0.141035	−	0.990005i	$-0.454957\pi$
$701$	7.46818			0.282069			0.141035	+	0.990005i	$0.454957\pi$
$702$	5.03508	−	1.48532i	0.190037	−	0.0560596i
$703$	−2.75770	−	4.77648i	−0.104009	−	0.180148i
$704$			30.1228i			1.13530i
$705$	−2.00716	−	3.47649i	−0.0755938	−	0.130932i
$706$	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
$709$		−	16.0565i		−	0.603013i	−0.953464	−	0.301506i	$-0.902511\pi$
$709$		−	16.0565i		−	0.603013i	0.953464	−	0.301506i	$-0.0974895\pi$
$710$	−35.1705	+	20.3057i	−1.31993	+	0.762059i
$711$	6.29441	−	10.9022i	0.236059	−	0.408866i
$712$	10.2378	+	17.7324i	0.383679	+	0.664552i
$713$	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
$717$		−	12.8510i		−	0.479931i
$718$	19.2311			0.717700
$719$	15.2089			0.567198			0.283599	−	0.958943i	$-0.408472\pi$
$719$	15.2089			0.567198			0.283599	+	0.958943i	$0.408472\pi$
$720$			17.9190i			0.667803i
$721$	−16.0249	+	6.54886i	−0.596799	+	0.243892i
$722$	−21.8867	+	12.6363i	−0.814540	+	0.470275i
$723$	12.9265	+	7.46312i	0.480742	+	0.277556i
$724$	0.544621	−	0.943311i	0.0202407	−	0.0350579i
$725$	28.1245			1.04452
$726$	6.66238	−	3.84653i	0.247264	−	0.142758i
$727$	40.3565			1.49674			0.748369	−	0.663282i	$-0.230837\pi$
$727$	40.3565			1.49674			0.748369	+	0.663282i	$0.230837\pi$
$728$	−20.3900	+	16.3144i	−0.755703	+	0.604652i
$729$	1.00000			0.0370370
$730$	74.8075	−	43.1901i	2.76875	−	1.59854i
$731$	−0.243305			−0.00899898
$732$	0.228681	−	0.396088i	0.00845231	−	0.0146398i
$733$	33.4424	+	19.3080i	1.23522	+	0.713156i	0.968114	−	0.250510i	$-0.0805983\pi$
$733$	33.4424	+	19.3080i	1.23522	+	0.713156i	0.267109	+	0.963666i	$0.413932\pi$
$734$	7.13591	−	4.11992i	0.263391	−	0.152069i
$735$	−7.95492	+	28.6001i	−0.293421	+	1.05493i
$736$			2.43483i			0.0897489i
$737$	−48.9592			−1.80344
$738$	17.8146			0.655764
$739$			10.2639i			0.377563i	0.982019	+	0.188782i	$0.0604539\pi$
$739$			10.2639i			0.377563i	−0.982019	+	0.188782i	$0.939546\pi$
$740$	−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	$0.676867\pi$
$744$	7.12476	+	12.3404i	0.261206	+	0.452423i
$745$	11.8315	−	20.4927i	0.433472	−	0.750796i
$746$	14.0432	−	8.10783i	0.514157	−	0.296849i
$747$		−	3.47006i		−	0.126963i
$748$	−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
$751$	−12.3020	−	21.3078i	−0.448908	−	0.777532i	0.549407	−	0.835555i	$-0.314854\pi$
$751$	−12.3020	−	21.3078i	−0.448908	−	0.777532i	−0.998315	+	0.0580232i	$0.981520\pi$
$752$		−	3.99966i		−	0.145853i
$753$	−5.86990	−	10.1670i	−0.213911	−	0.370505i
$754$	2.66679	−	11.0533i	0.0971189	−	0.402539i
$755$	54.3894			1.97943
$756$	0.293560	−	0.119968i	0.0106767	−	0.00436321i
$757$	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	$0.0963065\pi$
$758$	−5.31084			−0.192898
$759$	−12.5658	+	7.25488i	−0.456110	+	0.263335i
$760$	12.8834	+	7.43822i	0.467329	+	0.269813i
$761$		−	10.3467i		−	0.375068i	−0.982258	−	0.187534i	$-0.939951\pi$
$761$		−	10.3467i		−	0.375068i	0.982258	−	0.187534i	$-0.0600494\pi$
$762$			2.32354i			0.0841731i
$763$	−2.09931	−	0.286516i	−0.0760002	−	0.0103726i
$764$	1.20654	−	2.08979i	0.0436512	−	0.0756060i
$765$	0.177983	−	0.102759i	0.00643499	−	0.00371525i
$766$	14.7219	+	25.4991i	0.531925	+	0.921321i
$767$	−8.28680	−	7.88157i	−0.299219	−	0.284587i
$768$	−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	$0.487485\pi$
$770$	−40.3785	+	52.1087i	−1.45514	+	1.87787i
$771$	15.3006	+	26.5015i	0.551039	+	0.954427i
$772$	−0.331514	−	0.191399i	−0.0119314	−	0.00688862i
$773$	29.0771	+	16.7877i	1.04583	+	0.603811i	0.921479	−	0.388427i	$-0.126982\pi$
$773$	29.0771	+	16.7877i	1.04583	+	0.603811i	0.124352	+	0.992238i	$0.460315\pi$
$774$	6.33052	+	3.65493i	0.227546	+	0.131374i
$775$	−58.5354	−	33.7954i	−2.10265	−	1.21397i
$776$	−5.74653	−	9.95327i	−0.206288	−	0.357302i
$777$	−11.2827	−	1.53988i	−0.404766	−	0.0552428i
$778$	5.47510	+	3.16105i	0.196292	+	0.113329i
$779$	7.83964	−	13.5787i	0.280884	−	0.486506i
$780$	−1.75788	+	0.518562i	−0.0629421	+	0.0185675i
$781$	−13.2706	−	22.9853i	−0.474859	−	0.822480i
$782$	0.219717	−	0.126854i	0.00785707	−	0.00453628i
$783$	1.08299	−	1.87579i	0.0387028	−	0.0670353i
$784$	−21.1119	+	20.7151i	−0.753997	+	0.739826i
$785$			15.9303i			0.568578i
$786$			8.65266i			0.308630i
$787$	−19.0187	−	10.9805i	−0.677945	−	0.391412i	0.121135	−	0.992636i	$-0.461347\pi$
$787$	−19.0187	−	10.9805i	−0.677945	−	0.391412i	−0.799080	+	0.601224i	$0.794680\pi$
$788$	−1.52539	+	0.880685i	−0.0543398	+	0.0313731i
$789$	−18.1675			−0.646782
$790$	−38.8651	+	67.3164i	−1.38276	+	2.39501i
$791$	0.207288	−	1.51881i	0.00737032	−	0.0540026i
$792$	−11.0464			−0.392517
$793$	−13.3740	−	3.22670i	−0.474926	−	0.114583i
$794$	0.621427	+	1.07634i	0.0220536	+	0.0381980i
$795$			22.5973i			0.801442i
$796$	−1.38738	−	2.40301i	−0.0491744	−	0.0851725i
$797$	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
$800$		−	8.79258i		−	0.310865i
$801$	−6.47777	+	3.73994i	−0.228881	+	0.132144i
$802$	−10.3678	+	17.9576i	−0.366100	+	0.634104i
$803$	28.2265	+	48.8897i	0.996091	+	1.72528i
$804$	−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
$808$		−	43.5073i		−	1.53058i
$809$	39.9448			1.40438			0.702192	−	0.711988i	$-0.252205\pi$
$809$	39.9448			1.40438			0.702192	+	0.711988i	$0.252205\pi$
$810$	−6.17455			−0.216952
$811$			45.8322i			1.60939i	0.593691	+	0.804693i	$0.297670\pi$
$811$			45.8322i			1.60939i	−0.593691	+	0.804693i	$0.702330\pi$
$812$	0.0928861	−	0.680580i	0.00325966	−	0.0238837i
$813$	−22.9953	+	13.2763i	−0.806481	+	0.465622i
$814$	−21.8996	−	12.6437i	−0.767579	−	0.443162i
$815$	−39.7218	+	68.8003i	−1.39140	+	2.40997i
$816$	0.204767			0.00716829
$817$	5.57173	−	3.21684i	0.194930	−	0.112543i
$818$	13.1902			0.461183
$819$	−5.95975	−	7.44858i	−0.208251	−	0.260275i
$820$	−6.21953			−0.217195
$821$	47.2728	−	27.2930i	1.64983	−	0.952531i	0.672694	−	0.739921i	$-0.265137\pi$
$821$	47.2728	−	27.2930i	1.64983	−	0.952531i	0.977137	−	0.212610i	$-0.0681964\pi$
$822$	23.3916			0.815877
$823$	25.0486	−	43.3854i	0.873139	−	1.51232i	0.0144071	−	0.999896i	$-0.495414\pi$
$823$	25.0486	−	43.3854i	0.873139	−	1.51232i	0.858732	−	0.512425i	$-0.171253\pi$
$824$	15.5116	+	8.95565i	0.540374	+	0.311985i
$825$	45.3774	−	26.1986i	1.57984	−	0.912120i
$826$	−9.65822	−	7.48406i	−0.336052	−	0.260404i
$827$			19.4771i			0.677284i	0.940915	+	0.338642i	$0.109967\pi$
$827$			19.4771i			0.677284i	−0.940915	+	0.338642i	$0.890033\pi$
$828$	−0.430990			−0.0149779
$829$	14.8095			0.514354			0.257177	−	0.966364i	$-0.417208\pi$
$829$	14.8095			0.514354			0.257177	+	0.966364i	$0.417208\pi$
$830$			21.4261i			0.743710i
$831$	−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
$835$	20.1279	+	34.8626i	0.696555	+	1.20647i
$836$	0.309911	−	0.536781i	0.0107185	−	0.0185650i
$837$	−4.50804	+	2.60272i	−0.155820	+	0.0899630i
$838$		−	31.8995i		−	1.10195i
$839$	−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
$842$	−4.46770	−	7.73828i	−0.153967	−	0.266679i
$843$		−	6.74332i		−	0.232252i
$844$	−0.549889	−	0.952435i	−0.0189279	−	0.0327842i
$845$	29.9226	+	46.3039i	1.02937	+	1.59290i
$846$	1.37820			0.0473836
$847$	−11.0503	−	8.56274i	−0.379691	−	0.294219i
$848$	−11.2574	+	19.4984i	−0.386580	+	0.669577i
$849$	17.3869			0.596717
$850$	−0.793437	+	0.458091i	−0.0272147	+	0.0157124i
$851$	13.4025	+	7.73794i	0.459432	+	0.265253i
$852$		−	0.788365i		−	0.0270089i
$853$		−	20.3132i		−	0.695509i	−0.937586	−	0.347755i	$-0.886944\pi$
$853$		−	20.3132i		−	0.695509i	0.937586	−	0.347755i	$-0.113056\pi$
$854$	−14.5637	−	1.98766i	−0.498359	−	0.0680165i
$855$	−2.71722	+	4.70637i	−0.0929271	+	0.160955i
$856$	16.9731	−	9.79944i	0.580130	−	0.334938i
$857$	−3.72976	−	6.46014i	−0.127406	−	0.220674i	0.795265	−	0.606262i	$-0.207332\pi$
$857$	−3.72976	−	6.46014i	−0.127406	−	0.220674i	−0.922671	+	0.385588i	$0.873999\pi$
$858$	−5.99372	−	20.3182i	−0.204622	−	0.693650i
$859$	−3.78123	+	6.54929i	−0.129014	+	0.223459i	−0.923295	−	0.384092i	$-0.874515\pi$
$859$	−3.78123	+	6.54929i	−0.129014	+	0.223459i	0.794281	+	0.607551i	$0.207848\pi$
$860$	−2.21015	−	1.27603i	−0.0753654	−	0.0435122i
$861$	−12.2463	−	29.9663i	−0.417352	−	1.02125i
$862$	−18.6696	−	32.3367i	−0.635890	−	1.10139i
$863$	−17.3688	−	10.0279i	−0.591239	−	0.341352i	0.174348	−	0.984684i	$-0.444218\pi$
$863$	−17.3688	−	10.0279i	−0.591239	−	0.341352i	−0.765587	+	0.643332i	$0.777552\pi$
$864$	−0.586430	−	0.338575i	−0.0199507	−	0.0115186i
$865$	−64.6169	−	37.3066i	−2.19704	−	1.26846i
$866$	25.1736	+	14.5340i	0.855434	+	0.493885i
$867$	8.49883	+	14.7204i	0.288635	+	0.499931i
$868$	−1.01113	+	1.30487i	−0.0343201	+	0.0442903i
$869$	−43.9940	−	25.3999i	−1.49239	−	0.861634i
$870$	−6.68696	+	11.5822i	−0.226709	+	0.392672i
$871$	−10.2598	+	42.5248i	−0.347640	+	1.44090i
$872$	1.09610	+	1.89850i	0.0371185	+	0.0642912i
$873$	3.63599	−	2.09924i	0.123060	−	0.0710485i
$874$	−3.35437	+	5.80993i	−0.113463	+	0.196524i
$875$	−54.8752	+	70.8168i	−1.85512	+	2.39404i
$876$			1.67685i			0.0566554i
$877$		−	28.2238i		−	0.953050i	−0.879161	−	0.476525i	$-0.841896\pi$
$877$		−	28.2238i		−	0.953050i	0.879161	−	0.476525i	$-0.158104\pi$
$878$	29.2604	+	16.8935i	0.987489	+	0.570127i
$879$	15.2346	−	8.79572i	0.513852	−	0.296672i
$880$	72.3090			2.43754
$881$	−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	$0.990930\pi$
$882$	−7.13802	−	7.27475i	−0.240350	−	0.244953i
$883$	−48.8522			−1.64401			−0.822004	−	0.569482i	$-0.807144\pi$
$883$	−48.8522			−1.64401			−0.822004	+	0.569482i	$0.807144\pi$
$884$	0.00592579	+	0.0200879i	0.000199306	+	0.000675628i
$885$	6.72570	+	11.6492i	0.226082	+	0.391585i
$886$		−	5.02782i		−	0.168913i
$887$	−7.83677	−	13.5737i	−0.263133	−	0.455760i	0.703940	−	0.710260i	$-0.251422\pi$
$887$	−7.83677	−	13.5737i	−0.263133	−	0.455760i	−0.967073	+	0.254500i	$0.918089\pi$
$888$	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
$891$		−	4.03532i		−	0.135188i
$892$	0.235238	−	0.135815i	0.00787635	−	0.00454741i
$893$	0.606504	−	1.05050i	0.0202959	−	0.0351535i
$894$	4.06202	+	7.03562i	0.135854	+	0.235306i
$895$	−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
$899$			11.2748i			0.376037i
$900$	1.55638			0.0518793
$901$	0.258227			0.00860278
$902$		−	71.8875i		−	2.39359i
$903$	1.79625	−	13.1612i	0.0597756	−	0.437978i
$904$	−1.37352	+	0.793003i	−0.0456827	+	0.0263749i
$905$	33.3751	+	19.2691i	1.10942	+	0.640527i
$906$	−9.33656	+	16.1714i	−0.310186	+	0.537259i
$907$	−3.15054			−0.104612			−0.0523060	−	0.998631i	$-0.516657\pi$
$907$	−3.15054			−0.104612			−0.0523060	+	0.998631i	$0.516657\pi$
$908$	−0.866900	+	0.500505i	−0.0287691	+	0.0166098i
$909$	15.8935			0.527153
$910$	36.7988	+	45.9916i	1.21987	+	1.52461i
$911$	−1.18315			−0.0391996			−0.0195998	−	0.999808i	$-0.506239\pi$
$911$	−1.18315			−0.0391996			−0.0195998	+	0.999808i	$0.506239\pi$
$912$	−4.68920	+	2.70731i	−0.155275	+	0.0896480i
$913$	−14.0028			−0.463425
$914$	28.4936	−	49.3524i	0.942485	−	1.63243i
$915$	14.0139	+	8.09092i	0.463285	+	0.267477i
$916$	0.725603	−	0.418927i	0.0239746	−	0.0138417i
$917$	14.5548	−	5.94809i	0.480643	−	0.196423i
$918$			0.0705587i			0.00232879i
$919$	−5.12308			−0.168995			−0.0844974	−	0.996424i	$-0.526928\pi$
$919$	−5.12308			−0.168995			−0.0844974	+	0.996424i	$0.526928\pi$
$920$	−41.7424			−1.37621
$921$		−	0.0778605i		−	0.00256559i
$922$	−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
$926$	5.08774	+	8.81222i	0.167193	+	0.289587i
$927$	−3.27155	+	5.66650i	−0.107452	+	0.186112i
$928$	−1.27019	+	0.733346i	−0.0416961	+	0.0240733i
$929$		−	31.4311i		−	1.03122i	−0.856823	−	0.515610i	$-0.827565\pi$
$929$		−	31.4311i		−	1.03122i	0.856823	−	0.515610i	$-0.172435\pi$
$930$	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
$933$	15.0689	+	26.1002i	0.493335	+	0.854482i
$934$			21.1356i			0.691579i
$935$	−0.414664	−	0.718218i	−0.0135609	−	0.0234883i
$936$	−2.31486	+	9.59465i	−0.0756636	+	0.313611i
$937$	−1.86220			−0.0608355			−0.0304178	−	0.999537i	$-0.509684\pi$
$937$	−1.86220			−0.0608355			−0.0304178	+	0.999537i	$0.509684\pi$
$938$	−6.32009	+	46.3076i	−0.206358	+	1.51200i
$939$	−10.0024	+	17.3247i	−0.326417	+	0.565371i
$940$	−0.481166			−0.0156939
$941$	−43.4248	+	25.0713i	−1.41561	+	0.817303i	−0.995909	−	0.0903602i	$-0.971198\pi$
$941$	−43.4248	+	25.0713i	−1.41561	+	0.817303i	−0.419700	+	0.907663i	$0.637865\pi$
$942$	−4.73650	−	2.73462i	−0.154324	−	0.0890988i
$943$			43.9951i			1.43268i
$944$			13.4023i			0.436208i
$945$	4.24457	+	10.3864i	0.138076	+	0.337868i
$946$	14.7488	−	25.5457i	0.479525	−	0.830561i
$947$	0.000278292	0	0.000160672i	9.04328e−6	0	5.22114e-6i	−0.499995	−	0.866028i	$-0.666665\pi$
$947$	0.000278292	0	0.000160672i	9.04328e−6	0	5.22114e-6i	0.500005	+	0.866023i	$0.333332\pi$
$948$	−0.754466	−	1.30677i	−0.0245039	−	0.0424420i
$949$	48.3796	−	14.2716i	1.57047	−	0.463277i
$950$	12.1132	−	20.9807i	0.393004	−	0.680704i
$951$	−20.7932	−	12.0050i	−0.674266	−	0.389288i
$952$	−0.132777	−	0.324902i	−0.00430332	−	0.0105301i
$953$	−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
$955$	73.9384	+	42.6884i	2.39259	+	1.38136i
$956$	−1.33399	−	0.770180i	−0.0431444	−	0.0249094i
$957$	−7.56941	−	4.37020i	−0.244684	−	0.141268i
$958$	12.3226	+	21.3433i	0.398125	+	0.689572i
$959$	−16.0801	−	39.3476i	−0.519254	−	1.27060i
$960$	−27.4158	−	15.8285i	−0.884840	−	0.510863i
$961$	−1.95175	+	3.38052i	−0.0629595	+	0.109049i
$962$	−15.5713	+	16.3719i	−0.502038	+	0.527850i
$963$	3.57979	+	6.20038i	0.115357	+	0.199805i
$964$	1.54941	−	0.894550i	0.0499030	−	0.0288115i
$965$	6.77185	−	11.7292i	0.217994	−	0.377576i
$966$	5.23985	+	12.8218i	0.168589	+	0.412534i
$967$		−	13.9192i		−	0.447610i	−0.974634	−	0.223805i	$-0.928152\pi$
$967$		−	13.9192i		−	0.447610i	0.974634	−	0.223805i	$-0.0718478\pi$
$968$			14.4640i			0.464891i
$969$	0.0537814	+	0.0310507i	0.00172771	+	0.000997492i
$970$	−22.4506	+	12.9619i	−0.720845	+	0.416180i
$971$	20.8917			0.670447			0.335224	−	0.942139i	$-0.391188\pi$
$971$	20.8917			0.670447			0.335224	+	0.942139i	$0.391188\pi$
$972$	0.0599314	−	0.103804i	0.00192230	−	0.00332952i
$973$	−4.02661	+	29.5032i	−0.129087	+	0.945828i
$974$	37.0586			1.18743
$975$	−13.2463	−	44.9039i	−0.424223	−	1.43808i
$976$	8.06139	+	13.9627i	0.258039	+	0.446936i
$977$		−	8.58415i		−	0.274631i	−0.990527	−	0.137316i	$-0.956153\pi$
$977$		−	8.58415i		−	0.274631i	0.990527	−	0.137316i	$-0.0438475\pi$
$978$	−13.6374	−	23.6207i	−0.436076	−	0.755306i
$979$	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
$982$		−	0.193239i		−	0.00616649i
$983$	−2.72691	+	1.57438i	−0.0869750	+	0.0502150i	−0.542857	−	0.839825i	$-0.682657\pi$
$983$	−2.72691	+	1.57438i	−0.0869750	+	0.0502150i	0.455882	+	0.890040i	$0.349324\pi$
$984$	−16.7469	+	29.0065i	−0.533873	+	0.924694i
$985$	−31.1593	−	53.9695i	−0.992817	−	1.71961i
$986$	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
$990$			24.9163i			0.791891i
$991$	6.20844			0.197218			0.0986088	−	0.995126i	$-0.468561\pi$
$991$	6.20844			0.197218			0.0986088	+	0.995126i	$0.468561\pi$
$992$	3.52486			0.111914
$993$			8.94260i			0.283785i
$994$	−23.4535	+	9.58470i	−0.743901	+	0.304008i
$995$	85.0204	−	49.0865i	2.69533	−	1.55615i
$996$	−0.360207	−	0.207966i	−0.0114136	−	0.00658964i
$997$	11.2584	−	19.5002i	0.356558	−	0.617576i	−0.630825	−	0.775925i	$-0.717284\pi$
$997$	11.2584	−	19.5002i	0.356558	−	0.617576i	0.987383	+	0.158348i	$0.0506169\pi$
$998$	−6.67776			−0.211381
$999$	−3.72738	+	2.15200i	−0.117929	+	0.0680864i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.3	✓	12	7.4	even	3
273.2.t.c.205.4	yes	12	13.10	even	6
273.2.bl.c.88.3	yes	12	91.88	even	6	inner
273.2.bl.c.121.3	yes	12	1.1	even	1	trivial
819.2.bm.e.478.3		12	39.23	odd	6
819.2.bm.e.550.4		12	21.11	odd	6
819.2.do.f.361.4		12	273.179	odd	6
819.2.do.f.667.4		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.26091 + 0.727987i) q^{2} +1.00000 q^{3} +(0.0599314 - 0.103804i) q^{4} +(3.67267 + 2.12042i) q^{5} +(-1.26091 + 0.727987i) q^{6} +(2.09135 + 1.62057i) q^{7} -2.73743i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.26091 + 0.727987i) q^{2} +1.00000 q^{3} +(0.0599314 - 0.103804i) q^{4} +(3.67267 + 2.12042i) q^{5} +(-1.26091 + 0.727987i) q^{6} +(2.09135 + 1.62057i) q^{7} -2.73743i q^{8} +1.00000 q^{9} -6.17455 q^{10} -4.03532i 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} +(2.11268 + 3.65927i) q^{16} +(0.0242308 - 0.0419689i) q^{17} +(-1.26091 + 0.727987i) q^{18} +1.28146i q^{19} +(0.440217 - 0.254159i) q^{20} +(2.09135 + 1.62057i) q^{21} +(2.93766 + 5.08818i) q^{22} +(-1.79785 - 3.11396i) q^{23} -2.73743i q^{24} +(6.49234 + 11.2451i) q^{25} +(5.03508 - 1.48532i) q^{26} +1.00000 q^{27} +(0.293560 - 0.119968i) q^{28} +(1.08299 - 1.87579i) q^{29} -6.17455 q^{30} +(-4.50804 + 2.60272i) q^{31} +(-0.586430 - 0.338575i) q^{32} -4.03532i q^{33} +0.0705587i q^{34} +(4.24457 + 10.3864i) q^{35} +(0.0599314 - 0.103804i) q^{36} +(-3.72738 + 2.15200i) q^{37} +(-0.932885 - 1.61580i) q^{38} +(-3.50498 - 0.845633i) q^{39} +(5.80450 - 10.0537i) q^{40} +(-10.5963 - 6.11775i) q^{41} +(-3.81676 - 0.520915i) q^{42} +(-2.51030 - 4.34796i) q^{43} +(-0.418883 - 0.241842i) q^{44} +(3.67267 + 2.12042i) q^{45} +(4.53385 + 2.61762i) q^{46} +(-0.819767 - 0.473293i) q^{47} +(2.11268 + 3.65927i) q^{48} +(1.74751 + 6.77836i) q^{49} +(-16.3725 - 9.45268i) q^{50} +(0.0242308 - 0.0419689i) q^{51} +(-0.297839 + 0.313152i) q^{52} +(2.66425 + 4.61461i) q^{53} +(-1.26091 + 0.727987i) q^{54} +(8.55656 - 14.8204i) q^{55} +(4.43620 - 5.72494i) q^{56} +1.28146i q^{57} +3.15361i q^{58} +(2.74692 + 1.58594i) q^{59} +(0.440217 - 0.254159i) q^{60} +3.81572 q^{61} +(3.78949 - 6.56359i) q^{62} +(2.09135 + 1.62057i) q^{63} -7.46480 q^{64} +(-11.0796 - 10.5378i) q^{65} +(2.93766 + 5.08818i) q^{66} -12.1327i q^{67} +(-0.00290437 - 0.00503051i) q^{68} +(-1.79785 - 3.11396i) q^{69} +(-12.9132 - 10.0063i) q^{70} +(5.69604 - 3.28861i) q^{71} -2.73743i q^{72} +(-12.1155 + 6.99486i) q^{73} +(3.13326 - 5.42697i) q^{74} +(6.49234 + 11.2451i) 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} +17.9190i q^{80} +1.00000 q^{81} +17.8146 q^{82} -3.47006i q^{83} +(0.293560 - 0.119968i) q^{84} +(0.177983 - 0.102759i) q^{85} +(6.33052 + 3.65493i) q^{86} +(1.08299 - 1.87579i) q^{87} -11.0464 q^{88} +(-6.47777 + 3.73994i) q^{89} -6.17455 q^{90} +(-5.95975 - 7.44858i) q^{91} -0.430990 q^{92} +(-4.50804 + 2.60272i) q^{93} +1.37820 q^{94} +(-2.71722 + 4.70637i) q^{95} +(-0.586430 - 0.338575i) q^{96} +(3.63599 - 2.09924i) q^{97} +(-7.13802 - 7.27475i) q^{98} -4.03532i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9	\( 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9} + 14 q^{10} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 27 q^{20} + 3 q^{21} + 7 q^{22} - 16 q^{23} + 10 q^{25} - q^{26} + 12 q^{27} + 24 q^{28} - 5 q^{29} + 14 q^{30} + 15 q^{31} - 6 q^{32} - 2 q^{35} + 5 q^{36} + 6 q^{37} + 24 q^{38} - q^{39} + 21 q^{40} - 15 q^{41} - 16 q^{42} - 13 q^{43} - 30 q^{44} + 6 q^{45} - 9 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} - 63 q^{50} - 55 q^{52} + 18 q^{53} - 3 q^{54} + 13 q^{55} - 21 q^{56} - 33 q^{59} - 27 q^{60} - 52 q^{61} - 13 q^{62} + 3 q^{63} - 4 q^{64} - 41 q^{65} + 7 q^{66} - 16 q^{69} - 42 q^{70} - 15 q^{71} - 18 q^{73} + 38 q^{74} + 10 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 12 q^{81} + 28 q^{82} + 24 q^{84} - 12 q^{85} - 15 q^{86} - 5 q^{87} - 32 q^{88} + 12 q^{89} + 14 q^{90} + 49 q^{91} - 40 q^{92} + 15 q^{93} + 6 q^{94} - 28 q^{95} - 6 q^{96} + 45 q^{97} + 48 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 + 12 * q^3 + 5 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 + 12 * q^9 + 14 * q^10 + 5 * q^12 - q^13 - 16 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 27 * q^20 + 3 * q^21 + 7 * q^22 - 16 * q^23 + 10 * q^25 - q^26 + 12 * q^27 + 24 * q^28 - 5 * q^29 + 14 * q^30 + 15 * q^31 - 6 * q^32 - 2 * q^35 + 5 * q^36 + 6 * q^37 + 24 * q^38 - q^39 + 21 * q^40 - 15 * q^41 - 16 * q^42 - 13 * q^43 - 30 * q^44 + 6 * q^45 - 9 * q^46 - 9 * q^47 + 3 * q^48 + 9 * q^49 - 63 * q^50 - 55 * q^52 + 18 * q^53 - 3 * q^54 + 13 * q^55 - 21 * q^56 - 33 * q^59 - 27 * q^60 - 52 * q^61 - 13 * q^62 + 3 * q^63 - 4 * q^64 - 41 * q^65 + 7 * q^66 - 16 * q^69 - 42 * q^70 - 15 * q^71 - 18 * q^73 + 38 * q^74 + 10 * q^75 - 30 * q^76 + 20 * q^77 - q^78 - 4 * q^79 + 12 * q^81 + 28 * q^82 + 24 * q^84 - 12 * q^85 - 15 * q^86 - 5 * q^87 - 32 * q^88 + 12 * q^89 + 14 * q^90 + 49 * q^91 - 40 * q^92 + 15 * q^93 + 6 * q^94 - 28 * q^95 - 6 * q^96 + 45 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more