LMFDB - Embedded newform 276.2.c.a.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (of order $2$, degree $1$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.7
Character	$\chi$	$=$	276.47
Dual form			276.2.c.a.47.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.565709 - 1.29614i) q^{2} +(-1.40231 - 1.01662i) q^{3} +(-1.35995 + 1.46647i) q^{4} -0.662888i q^{5} +(-0.524382 + 2.39270i) q^{6} +4.60297i q^{7} +(2.67009 + 0.933083i) q^{8} +(0.932961 + 2.85124i) q^{9} +O(q^{10})$	\(q+(-0.565709 - 1.29614i) q^{2} +(-1.40231 - 1.01662i) q^{3} +(-1.35995 + 1.46647i) q^{4} -0.662888i q^{5} +(-0.524382 + 2.39270i) q^{6} +4.60297i q^{7} +(2.67009 + 0.933083i) q^{8} +(0.932961 + 2.85124i) q^{9} +(-0.859194 + 0.375001i) q^{10} -1.50207 q^{11} +(3.39792 - 0.673902i) q^{12} +1.18533 q^{13} +(5.96608 - 2.60394i) q^{14} +(-0.673906 + 0.929576i) q^{15} +(-0.301087 - 3.98865i) q^{16} +1.95053i q^{17} +(3.16782 - 2.82222i) q^{18} +0.0109530i q^{19} +(0.972107 + 0.901492i) q^{20} +(4.67948 - 6.45480i) q^{21} +(0.849734 + 1.94689i) q^{22} +1.00000 q^{23} +(-2.79570 - 4.02294i) q^{24} +4.56058 q^{25} +(-0.670551 - 1.53635i) q^{26} +(1.59033 - 4.94680i) q^{27} +(-6.75013 - 6.25979i) q^{28} +8.65051i q^{29} +(1.58609 + 0.347606i) q^{30} +6.06917i q^{31} +(-4.99952 + 2.64667i) q^{32} +(2.10637 + 1.52704i) q^{33} +(2.52816 - 1.10343i) q^{34} +3.05125 q^{35} +(-5.45005 - 2.50938i) q^{36} -7.04924 q^{37} +(0.0141966 - 0.00619620i) q^{38} +(-1.66220 - 1.20503i) q^{39} +(0.618529 - 1.76997i) q^{40} +7.37072i q^{41} +(-11.0135 - 2.41371i) q^{42} -4.67459i q^{43} +(2.04274 - 2.20275i) q^{44} +(1.89005 - 0.618448i) q^{45} +(-0.565709 - 1.29614i) q^{46} +10.0495 q^{47} +(-3.63273 + 5.89943i) q^{48} -14.1873 q^{49} +(-2.57996 - 5.91114i) q^{50} +(1.98296 - 2.73526i) q^{51} +(-1.61199 + 1.73825i) q^{52} +0.825339i q^{53} +(-7.31140 + 0.737158i) q^{54} +0.995704i q^{55} +(-4.29495 + 12.2903i) q^{56} +(0.0111350 - 0.0153595i) q^{57} +(11.2123 - 4.89367i) q^{58} -6.63799 q^{59} +(-0.446721 - 2.25244i) q^{60} +12.1170 q^{61} +(7.86648 - 3.43338i) q^{62} +(-13.1242 + 4.29439i) q^{63} +(6.25871 + 4.98282i) q^{64} -0.785740i q^{65} +(0.787658 - 3.59401i) q^{66} +0.812332i q^{67} +(-2.86041 - 2.65262i) q^{68} +(-1.40231 - 1.01662i) q^{69} +(-1.72612 - 3.95484i) q^{70} -8.94527 q^{71} +(-0.169361 + 8.48359i) q^{72} -13.3072 q^{73} +(3.98782 + 9.13679i) q^{74} +(-6.39536 - 4.63638i) q^{75} +(-0.0160623 - 0.0148955i) q^{76} -6.91398i q^{77} +(-0.621565 + 2.83614i) q^{78} +9.43225i q^{79} +(-2.64403 + 0.199587i) q^{80} +(-7.25917 + 5.32019i) q^{81} +(9.55347 - 4.16968i) q^{82} -1.34462 q^{83} +(3.10195 + 15.6405i) q^{84} +1.29299 q^{85} +(-6.05891 + 2.64445i) q^{86} +(8.79430 - 12.1307i) q^{87} +(-4.01066 - 1.40156i) q^{88} -6.30424i q^{89} +(-1.87081 - 2.09991i) q^{90} +5.45603i q^{91} +(-1.35995 + 1.46647i) q^{92} +(6.17005 - 8.51087i) q^{93} +(-5.68507 - 13.0255i) q^{94} +0.00726060 q^{95} +(9.70154 + 1.37117i) q^{96} +16.5457 q^{97} +(8.02588 + 18.3887i) q^{98} +(-1.40137 - 4.28277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.565709	−	1.29614i	−0.400016	−	0.916508i
$2$	−0.565709	−	1.29614i	−0.400016	−	0.916508i
$3$	−1.40231	−	1.01662i	−0.809625	−	0.586947i
$3$	−1.40231	−	1.01662i	−0.809625	−	0.586947i
$4$	−1.35995	+	1.46647i	−0.679974	+	0.733237i
$5$		−	0.662888i		−	0.296452i	−0.988953	−	0.148226i	$-0.952644\pi$
$5$		−	0.662888i		−	0.296452i	0.988953	−	0.148226i	$-0.0473564\pi$
$6$	−0.524382	+	2.39270i	−0.214078	+	0.976817i
$7$			4.60297i			1.73976i	0.493265	+	0.869879i	$0.335803\pi$
$7$			4.60297i			1.73976i	−0.493265	+	0.869879i	$0.664197\pi$
$8$	2.67009	+	0.933083i	0.944018	+	0.329895i
$9$	0.932961	+	2.85124i	0.310987	+	0.950414i
$10$	−0.859194	+	0.375001i	−0.271701	+	0.118586i
$11$	−1.50207			−0.452891			−0.226446	−	0.974024i	$-0.572711\pi$
$11$	−1.50207			−0.452891			−0.226446	+	0.974024i	$0.572711\pi$
$12$	3.39792	−	0.673902i	0.980895	−	0.194539i
$13$	1.18533			0.328751			0.164376	−	0.986398i	$-0.447439\pi$
$13$	1.18533			0.328751			0.164376	+	0.986398i	$0.447439\pi$
$14$	5.96608	−	2.60394i	1.59450	−	0.695932i
$15$	−0.673906	+	0.929576i	−0.174002	+	0.240015i
$16$	−0.301087	−	3.98865i	−0.0752717	−	0.997163i
$17$			1.95053i			0.473074i	0.971622	+	0.236537i	$0.0760125\pi$
$17$			1.95053i			0.473074i	−0.971622	+	0.236537i	$0.923988\pi$
$18$	3.16782	−	2.82222i	0.746662	−	0.665203i
$19$			0.0109530i			0.00251279i	0.999999	+	0.00125639i	$0.000399923\pi$
$19$			0.0109530i			0.00251279i	−0.999999	+	0.00125639i	$0.999600\pi$
$20$	0.972107	+	0.901492i	0.217370	+	0.201580i
$21$	4.67948	−	6.45480i	1.02115	−	1.40855i
$22$	0.849734	+	1.94689i	0.181164	+	0.415078i
$23$	1.00000			0.208514
$23$	1.00000			0.208514
$24$	−2.79570	−	4.02294i	−0.570670	−	0.821179i
$25$	4.56058			0.912116
$26$	−0.670551	−	1.53635i	−0.131506	−	0.301303i
$27$	1.59033	−	4.94680i	0.306060	−	0.952012i
$28$	−6.75013	−	6.25979i	−1.27565	−	1.18299i
$29$			8.65051i			1.60636i	0.595736	+	0.803180i	$0.296860\pi$
$29$			8.65051i			1.60636i	−0.595736	+	0.803180i	$0.703140\pi$
$30$	1.58609	+	0.347606i	0.289580	+	0.0634639i
$31$			6.06917i			1.09006i	0.838418	+	0.545028i	$0.183481\pi$
$31$			6.06917i			1.09006i	−0.838418	+	0.545028i	$0.816519\pi$
$32$	−4.99952	+	2.64667i	−0.883798	+	0.467869i
$33$	2.10637	+	1.52704i	0.366672	+	0.265823i
$34$	2.52816	−	1.10343i	0.433576	−	0.189237i
$35$	3.05125			0.515755
$36$	−5.45005	−	2.50938i	−0.908341	−	0.418230i
$37$	−7.04924			−1.15889			−0.579444	−	0.815012i	$-0.696730\pi$
$37$	−7.04924			−1.15889			−0.579444	+	0.815012i	$0.696730\pi$
$38$	0.0141966	−	0.00619620i	0.00230299	−	0.00100516i
$39$	−1.66220	−	1.20503i	−0.266165	−	0.192959i
$40$	0.618529	−	1.76997i	0.0977980	−	0.279856i
$41$			7.37072i			1.15111i	0.817762	+	0.575556i	$0.195214\pi$
$41$			7.37072i			1.15111i	−0.817762	+	0.575556i	$0.804786\pi$
$42$	−11.0135	−	2.41371i	−1.69942	−	0.372444i
$43$		−	4.67459i		−	0.712868i	−0.934321	−	0.356434i	$-0.883993\pi$
$43$		−	4.67459i		−	0.712868i	0.934321	−	0.356434i	$-0.116007\pi$
$44$	2.04274	−	2.20275i	0.307954	−	0.332076i
$45$	1.89005	−	0.618448i	0.281753	−	0.0921928i
$46$	−0.565709	−	1.29614i	−0.0834092	−	0.191105i
$47$	10.0495			1.46587			0.732933	−	0.680301i	$-0.238151\pi$
$47$	10.0495			1.46587			0.732933	+	0.680301i	$0.238151\pi$
$48$	−3.63273	+	5.89943i	−0.524340	+	0.851509i
$49$	−14.1873			−2.02676
$50$	−2.57996	−	5.91114i	−0.364861	−	0.835962i
$51$	1.98296	−	2.73526i	0.277669	−	0.383013i
$52$	−1.61199	+	1.73825i	−0.223542	+	0.241052i
$53$			0.825339i			0.113369i	0.998392	+	0.0566845i	$0.0180529\pi$
$53$			0.825339i			0.113369i	−0.998392	+	0.0566845i	$0.981947\pi$
$54$	−7.31140	+	0.737158i	−0.994956	+	0.100314i
$55$			0.995704i			0.134261i
$56$	−4.29495	+	12.2903i	−0.573937	+	1.64236i
$57$	0.0111350	−	0.0153595i	0.00147487	−	0.00203442i
$58$	11.2123	−	4.89367i	1.47224	−	0.642571i
$59$	−6.63799			−0.864193			−0.432096	−	0.901827i	$-0.642226\pi$
$59$	−6.63799			−0.864193			−0.432096	+	0.901827i	$0.642226\pi$
$60$	−0.446721	−	2.25244i	−0.0576715	−	0.290789i
$61$	12.1170			1.55142			0.775710	−	0.631090i	$-0.217392\pi$
$61$	12.1170			1.55142			0.775710	+	0.631090i	$0.217392\pi$
$62$	7.86648	−	3.43338i	0.999044	−	0.436040i
$63$	−13.1242	+	4.29439i	−1.65349	+	0.541042i
$64$	6.25871	+	4.98282i	0.782339	+	0.622853i
$65$		−	0.785740i		−	0.0974591i
$66$	0.787658	−	3.59401i	0.0969540	−	0.442392i
$67$			0.812332i			0.0992421i	0.998768	+	0.0496211i	$0.0158014\pi$
$67$			0.812332i			0.0992421i	−0.998768	+	0.0496211i	$0.984199\pi$
$68$	−2.86041	−	2.65262i	−0.346875	−	0.321678i
$69$	−1.40231	−	1.01662i	−0.168819	−	0.122387i
$70$	−1.72612	−	3.95484i	−0.206311	−	0.472694i
$71$	−8.94527			−1.06161			−0.530804	−	0.847495i	$-0.678110\pi$
$71$	−8.94527			−1.06161			−0.530804	+	0.847495i	$0.678110\pi$
$72$	−0.169361	+	8.48359i	−0.0199593	+	0.999801i
$73$	−13.3072			−1.55749			−0.778747	−	0.627338i	$-0.784144\pi$
$73$	−13.3072			−1.55749			−0.778747	+	0.627338i	$0.784144\pi$
$74$	3.98782	+	9.13679i	0.463574	+	1.06213i
$75$	−6.39536	−	4.63638i	−0.738472	−	0.535364i
$76$	−0.0160623	−	0.0148955i	−0.00184247	−	0.00170863i
$77$		−	6.91398i		−	0.787921i
$78$	−0.621565	+	2.83614i	−0.0703784	+	0.321130i
$79$			9.43225i			1.06121i	0.847619	+	0.530606i	$0.178036\pi$
$79$			9.43225i			1.06121i	−0.847619	+	0.530606i	$0.821964\pi$
$80$	−2.64403	+	0.199587i	−0.295611	+	0.0223145i
$81$	−7.25917	+	5.32019i	−0.806574	+	0.591133i
$82$	9.55347	−	4.16968i	1.05500	−	0.460464i
$83$	−1.34462			−0.147591			−0.0737956	−	0.997273i	$-0.523511\pi$
$83$	−1.34462			−0.147591			−0.0737956	+	0.997273i	$0.523511\pi$
$84$	3.10195	+	15.6405i	0.338450	+	1.70652i
$85$	1.29299			0.140244
$86$	−6.05891	+	2.64445i	−0.653349	+	0.285159i
$87$	8.79430	−	12.1307i	0.942848	−	1.30055i
$88$	−4.01066	−	1.40156i	−0.427537	−	0.149406i
$89$		−	6.30424i		−	0.668248i	−0.942529	−	0.334124i	$-0.891560\pi$
$89$		−	6.30424i		−	0.668248i	0.942529	−	0.334124i	$-0.108440\pi$
$90$	−1.87081	−	2.09991i	−0.197201	−	0.221350i
$91$			5.45603i			0.571948i
$92$	−1.35995	+	1.46647i	−0.141784	+	0.152890i
$93$	6.17005	−	8.51087i	0.639805	−	0.882537i
$94$	−5.68507	−	13.0255i	−0.586371	−	1.34348i
$95$	0.00726060			0.000744922
$96$	9.70154	+	1.37117i	0.990159	+	0.139944i
$97$	16.5457			1.67996			0.839982	−	0.542614i	$-0.182565\pi$
$97$	16.5457			1.67996			0.839982	+	0.542614i	$0.182565\pi$
$98$	8.02588	+	18.3887i	0.810736	+	1.85754i
$99$	−1.40137	−	4.28277i	−0.140843	−	0.430434i
$100$	−6.20215	+	6.68797i	−0.620215	+	0.668797i
$101$			1.89168i			0.188229i	0.995561	+	0.0941147i	$0.0300020\pi$
$101$			1.89168i			0.188229i	−0.995561	+	0.0941147i	$0.969998\pi$
$102$	−4.66705	−	1.02282i	−0.462107	−	0.101275i
$103$		−	14.5242i		−	1.43111i	−0.698557	−	0.715554i	$-0.746174\pi$
$103$		−	14.5242i		−	1.43111i	0.698557	−	0.715554i	$-0.253826\pi$
$104$	3.16493	+	1.10601i	0.310347	+	0.108453i
$105$	−4.27881	−	3.10197i	−0.417569	−	0.302721i
$106$	1.06975	−	0.466902i	0.103904	−	0.0453495i
$107$	10.9726			1.06076			0.530378	−	0.847761i	$-0.322050\pi$
$107$	10.9726			1.06076			0.530378	+	0.847761i	$0.322050\pi$
$108$	5.09158	+	9.05957i	0.489938	+	0.871757i
$109$	−3.04054			−0.291231			−0.145616	−	0.989341i	$-0.546516\pi$
$109$	−3.04054			−0.291231			−0.145616	+	0.989341i	$0.546516\pi$
$110$	1.29057	−	0.563278i	0.123051	−	0.0537065i
$111$	9.88524	+	7.16641i	0.938266	+	0.680206i
$112$	18.3596	−	1.38589i	1.73482	−	0.130955i
$113$		−	17.1766i		−	1.61584i	−0.589293	−	0.807919i	$-0.700594\pi$
$113$		−	17.1766i		−	1.61584i	0.589293	−	0.807919i	$-0.299406\pi$
$114$	−0.0262072	−	0.00574355i	−0.00245453	−	0.000537932i
$115$		−	0.662888i		−	0.0618146i
$116$	−12.6857	−	11.7642i	−1.17784	−	1.09228i
$117$	1.10587	+	3.37966i	0.102237	+	0.312450i
$118$	3.75517	+	8.60375i	0.345691	+	0.792039i
$119$	−8.97825			−0.823035
$120$	−2.66676	+	1.85324i	−0.243441	+	0.169177i
$121$	−8.74379			−0.794890
$122$	−6.85468	−	15.7053i	−0.620593	−	1.42189i
$123$	7.49323	−	10.3360i	0.675642	−	0.931970i
$124$	−8.90028	−	8.25375i	−0.799268	−	0.741209i
$125$		−	6.33759i		−	0.566851i
$126$	12.9906	+	14.5814i	1.15729	+	1.29901i
$127$		−	6.32247i		−	0.561028i	−0.959850	−	0.280514i	$-0.909495\pi$
$127$		−	6.32247i		−	0.561028i	0.959850	−	0.280514i	$-0.0905050\pi$
$128$	2.91782	−	10.9310i	0.257901	−	0.966171i
$129$	−4.75229	+	6.55523i	−0.418415	+	0.577156i
$130$	−1.01843	+	0.444500i	−0.0893220	+	0.0389852i
$131$	10.8645			0.949234			0.474617	−	0.880193i	$-0.342587\pi$
$131$	10.8645			0.949234			0.474617	+	0.880193i	$0.342587\pi$
$132$	−5.10391	+	1.01225i	−0.444239	+	0.0881048i
$133$	−0.0504163			−0.00437164
$134$	1.05289	−	0.459543i	0.0909562	−	0.0396985i
$135$	−3.27917	−	1.05421i	−0.282226	−	0.0907321i
$136$	−1.82001	+	5.20810i	−0.156065	+	0.446590i
$137$		−	1.95202i		−	0.166772i	−0.996517	−	0.0833860i	$-0.973427\pi$
$137$		−	1.95202i		−	0.166772i	0.996517	−	0.0833860i	$-0.0265734\pi$
$138$	−0.524382	+	2.39270i	−0.0446383	+	0.203680i
$139$			17.2077i			1.45954i	0.683693	+	0.729770i	$0.260373\pi$
$139$			17.2077i			1.45954i	−0.683693	+	0.729770i	$0.739627\pi$
$140$	−4.14954	+	4.47458i	−0.350700	+	0.378171i
$141$	−14.0925	−	10.2165i	−1.18680	−	0.860385i
$142$	5.06042	+	11.5943i	0.424661	+	0.972972i
$143$	−1.78045			−0.148889
$144$	11.0917	−	4.57973i	0.924309	−	0.381644i
$145$	5.73432			0.476209
$146$	7.52802	+	17.2480i	0.623023	+	1.42746i
$147$	19.8950	+	14.4231i	1.64091	+	1.18960i
$148$	9.58660	−	10.3375i	0.788014	−	0.849739i
$149$		−	18.5582i		−	1.52035i	−0.649718	−	0.760175i	$-0.725113\pi$
$149$		−	18.5582i		−	1.52035i	0.649718	−	0.760175i	$-0.274887\pi$
$150$	−2.39148	+	10.9121i	−0.195264	+	0.890970i
$151$			2.12461i			0.172898i	0.996256	+	0.0864490i	$0.0275520\pi$
$151$			2.12461i			0.172898i	−0.996256	+	0.0864490i	$0.972448\pi$
$152$	−0.0102200	+	0.0292454i	−0.000828955	+	0.00237212i
$153$	−5.56145	+	1.81977i	−0.449616	+	0.147120i
$154$	−8.96147	+	3.91130i	−0.722136	+	0.315181i
$155$	4.02318			0.323150
$156$	4.02765	−	0.798795i	0.322470	−	0.0639548i
$157$	4.55043			0.363164			0.181582	−	0.983376i	$-0.441878\pi$
$157$	4.55043			0.363164			0.181582	+	0.983376i	$0.441878\pi$
$158$	12.2255	−	5.33591i	0.972609	−	0.424502i
$159$	0.839058	−	1.15738i	0.0665416	−	0.0917865i
$160$	1.75444	+	3.31412i	0.138701	+	0.262004i
$161$			4.60297i			0.362765i
$162$	11.0023	+	6.39920i	0.864421	+	0.502769i
$163$			8.14951i			0.638319i	0.947701	+	0.319159i	$0.103401\pi$
$163$			8.14951i			0.638319i	−0.947701	+	0.319159i	$0.896599\pi$
$164$	−10.8090	−	10.0238i	−0.844038	−	0.782726i
$165$	1.01225	−	1.39629i	0.0788039	−	0.108701i
$166$	0.760664	+	1.74281i	0.0590389	+	0.135269i
$167$	9.55842			0.739652			0.369826	−	0.929101i	$-0.379417\pi$
$167$	9.55842			0.739652			0.369826	+	0.929101i	$0.379417\pi$
$168$	18.5175	−	12.8685i	1.42865	−	0.992828i
$169$	−11.5950			−0.891923
$170$	−0.731453	−	1.67589i	−0.0560999	−	0.128535i
$171$	−0.0312296	+	0.0102187i	−0.00238819	+	0.000781444i
$172$	6.85515	+	6.35719i	0.522701	+	0.484731i
$173$			8.00339i			0.608487i	0.952594	+	0.304243i	$0.0984036\pi$
$173$			8.00339i			0.608487i	−0.952594	+	0.304243i	$0.901596\pi$
$174$	−20.6981	−	4.53617i	−1.56912	−	0.343886i
$175$			20.9922i			1.58686i
$176$	0.452253	+	5.99124i	0.0340899	+	0.451606i
$177$	9.30854	+	6.74832i	0.699672	+	0.507235i
$178$	−8.17117	+	3.56636i	−0.612455	+	0.267310i
$179$	−10.0014			−0.747541			−0.373771	−	0.927521i	$-0.621935\pi$
$179$	−10.0014			−0.747541			−0.373771	+	0.927521i	$0.621935\pi$
$180$	−1.66344	+	3.61277i	−0.123985	+	0.269280i
$181$	9.98514			0.742189			0.371095	−	0.928595i	$-0.378983\pi$
$181$	9.98514			0.742189			0.371095	+	0.928595i	$0.378983\pi$
$182$	7.07177	−	3.08652i	0.524194	−	0.228788i
$183$	−16.9918	−	12.3184i	−1.25607	−	0.910601i
$184$	2.67009	+	0.933083i	0.196841	+	0.0687878i
$185$			4.67286i			0.343555i
$186$	−14.5217	−	3.18256i	−1.06478	−	0.233357i
$187$		−	2.92984i		−	0.214251i
$188$	−13.6668	+	14.7373i	−0.996750	+	1.07483i
$189$	22.7700	+	7.32025i	1.65627	+	0.532470i
$190$	−0.00410739	−	0.00941075i	−0.000297981	−	0.000682727i
$191$	20.2203			1.46309			0.731544	−	0.681794i	$-0.238800\pi$
$191$	20.2203			1.46309			0.731544	+	0.681794i	$0.238800\pi$
$192$	−3.71103	−	13.3502i	−0.267820	−	0.963469i
$193$	−12.3457			−0.888666			−0.444333	−	0.895862i	$-0.646559\pi$
$193$	−12.3457			−0.888666			−0.444333	+	0.895862i	$0.646559\pi$
$194$	−9.36006	−	21.4455i	−0.672013	−	1.53970i
$195$	−0.798801	+	1.10185i	−0.0572033	+	0.0789054i
$196$	19.2940	−	20.8053i	1.37814	−	1.48609i
$197$		−	3.79311i		−	0.270248i	−0.990829	−	0.135124i	$-0.956857\pi$
$197$		−	3.79311i		−	0.270248i	0.990829	−	0.135124i	$-0.0431433\pi$
$198$	−4.75829	+	4.23917i	−0.338157	+	0.301265i
$199$		−	17.7972i		−	1.26161i	−0.775942	−	0.630804i	$-0.782725\pi$
$199$		−	17.7972i		−	1.26161i	0.775942	−	0.630804i	$-0.217275\pi$
$200$	12.1771	+	4.25540i	0.861054	+	0.300902i
$201$	0.825834	−	1.13914i	0.0582499	−	0.0803490i
$202$	2.45188	−	1.07014i	0.172514	−	0.0752948i
$203$	−39.8180			−2.79468
$204$	1.31447	+	6.62776i	0.0920312	+	0.464036i
$205$	4.88596			0.341250
$206$	−18.8253	+	8.21645i	−1.31162	+	0.572467i
$207$	0.932961	+	2.85124i	0.0648452	+	0.198175i
$208$	−0.356887	−	4.72787i	−0.0247457	−	0.327819i
$209$		−	0.0164522i		−	0.00113802i
$210$	−1.60002	+	7.30073i	−0.110412	+	0.503799i
$211$		−	7.20311i		−	0.495883i	−0.968775	−	0.247941i	$-0.920246\pi$
$211$		−	7.20311i		−	0.495883i	0.968775	−	0.247941i	$-0.0797540\pi$
$212$	−1.21034	−	1.12242i	−0.0831263	−	0.0770880i
$213$	12.5441	+	9.09395i	0.859505	+	0.623108i
$214$	−6.20727	−	14.2219i	−0.424320	−	0.972192i
$215$	−3.09873			−0.211331
$216$	8.86210	−	11.7245i	0.602989	−	0.797749i
$217$	−27.9362			−1.89643
$218$	1.72006	+	3.94096i	0.116497	+	0.266916i
$219$	18.6609	+	13.5284i	1.26099	+	0.914166i
$220$	−1.46017	−	1.35410i	−0.0984449	−	0.0912937i
$221$			2.31203i			0.155524i
$222$	3.69649	−	16.8667i	0.248092	−	1.13202i
$223$		−	15.3568i		−	1.02836i	−0.857681	−	0.514182i	$-0.828095\pi$
$223$		−	15.3568i		−	1.02836i	0.857681	−	0.514182i	$-0.171905\pi$
$224$	−12.1825	−	23.0126i	−0.813978	−	1.53759i
$225$	4.25484	+	13.0033i	0.283656	+	0.866888i
$226$	−22.2632	+	9.71695i	−1.48093	+	0.646362i
$227$	3.00133			0.199205			0.0996026	−	0.995027i	$-0.468243\pi$
$227$	3.00133			0.199205			0.0996026	+	0.995027i	$0.468243\pi$
$228$	0.00738124	+	0.0372174i	0.000488834	+	0.00246478i
$229$	10.8128			0.714528			0.357264	−	0.934003i	$-0.383710\pi$
$229$	10.8128			0.714528			0.357264	+	0.934003i	$0.383710\pi$
$230$	−0.859194	+	0.375001i	−0.0566536	+	0.0247269i
$231$	−7.02890	+	9.69556i	−0.462468	+	0.637921i
$232$	−8.07165	+	23.0976i	−0.529930	+	1.51643i
$233$			5.74427i			0.376319i	0.982138	+	0.188160i	$0.0602523\pi$
$233$			5.74427i			0.376319i	−0.982138	+	0.188160i	$0.939748\pi$
$234$	3.75491	−	3.34526i	0.245466	−	0.218686i
$235$		−	6.66167i		−	0.434560i
$236$	9.02732	−	9.73443i	0.587628	−	0.633658i
$237$	9.58903	−	13.2270i	0.622875	−	0.859184i
$238$	5.07907	+	11.6370i	0.329227	+	0.754318i
$239$	−12.1163			−0.783737			−0.391868	−	0.920021i	$-0.628171\pi$
$239$	−12.1163			−0.783737			−0.391868	+	0.920021i	$0.628171\pi$
$240$	3.91066	+	2.40809i	0.252432	+	0.155442i
$241$	−4.39939			−0.283390			−0.141695	−	0.989910i	$-0.545255\pi$
$241$	−4.39939			−0.283390			−0.141695	+	0.989910i	$0.545255\pi$
$242$	4.94644	+	11.3332i	0.317969	+	0.728523i
$243$	15.5882	−	0.0807457i	0.999987	−	0.00517984i
$244$	−16.4784	+	17.7692i	−1.05492	+	1.13756i
$245$			9.40459i			0.600837i
$246$	−17.6359	−	3.86507i	−1.12443	−	0.246428i
$247$			0.0129829i			0.000826082i
$248$	−5.66304	+	16.2052i	−0.359603	+	1.02903i
$249$	1.88558	+	1.36697i	0.119494	+	0.0866282i
$250$	−8.21439	+	3.58523i	−0.519524	+	0.226750i
$251$	−23.2910			−1.47011			−0.735056	−	0.678006i	$-0.762844\pi$
$251$	−23.2910			−1.47011			−0.735056	+	0.678006i	$0.762844\pi$
$252$	11.5506	−	25.0864i	0.727618	−	1.58029i
$253$	−1.50207			−0.0944343
$254$	−8.19479	+	3.57667i	−0.514187	+	0.224421i
$255$	−1.81317	−	1.31448i	−0.113545	−	0.0823158i
$256$	−15.8187	+	2.40186i	−0.988668	+	0.150116i
$257$			4.92895i			0.307459i	0.988113	+	0.153730i	$0.0491285\pi$
$257$			4.92895i			0.307459i	−0.988113	+	0.153730i	$0.950871\pi$
$258$	11.1849	+	2.45127i	0.696341	+	0.152609i
$259$		−	32.4474i		−	2.01619i
$260$	1.15227	+	1.06857i	0.0714606	+	0.0662696i
$261$	−24.6647	+	8.07059i	−1.52671	+	0.499557i
$262$	−6.14613	−	14.0819i	−0.379709	−	0.869980i
$263$	29.8066			1.83795			0.918977	−	0.394312i	$-0.129017\pi$
$263$	29.8066			1.83795			0.918977	+	0.394312i	$0.129017\pi$
$264$	4.19934	+	6.04274i	0.258452	+	0.371905i
$265$	0.547107			0.0336085
$266$	0.0285209	+	0.0653464i	0.00174873	+	0.00400665i
$267$	−6.40903	+	8.84052i	−0.392226	+	0.541031i
$268$	−1.19126	−	1.10473i	−0.0727680	−	0.0674820i
$269$			15.3961i			0.938717i	0.883008	+	0.469359i	$0.155515\pi$
$269$			15.3961i			0.938717i	−0.883008	+	0.469359i	$0.844485\pi$
$270$	0.488653	+	4.84664i	0.0297385	+	0.294957i
$271$			13.6927i			0.831772i	0.909417	+	0.415886i	$0.136529\pi$
$271$			13.6927i			0.831772i	−0.909417	+	0.415886i	$0.863471\pi$
$272$	7.78001	−	0.587280i	0.471732	−	0.0356091i
$273$	5.54672	−	7.65106i	0.335703	−	0.463063i
$274$	−2.53008	+	1.10427i	−0.152848	+	0.0667115i
$275$	−6.85031			−0.413089
$276$	3.39792	−	0.673902i	0.204531	−	0.0405641i
$277$	−6.21349			−0.373333			−0.186666	−	0.982423i	$-0.559768\pi$
$277$	−6.21349			−0.373333			−0.186666	+	0.982423i	$0.559768\pi$
$278$	22.3036	−	9.73456i	1.33768	−	0.583840i
$279$	−17.3047	+	5.66230i	−1.03600	+	0.338993i
$280$	8.14710	+	2.84707i	0.486882	+	0.170145i
$281$			27.9379i			1.66664i	0.552794	+	0.833318i	$0.313562\pi$
$281$			27.9379i			1.66664i	−0.552794	+	0.833318i	$0.686438\pi$
$282$	−5.26976	+	24.0454i	−0.313809	+	1.43188i
$283$			18.8589i			1.12105i	0.828139	+	0.560523i	$0.189400\pi$
$283$			18.8589i			1.12105i	−0.828139	+	0.560523i	$0.810600\pi$
$284$	12.1651	−	13.1180i	0.721866	−	0.778410i
$285$	−0.0101816	−	0.00738129i	−0.000603108	−	0.000437230i
$286$	1.00721	+	2.30771i	0.0595579	+	0.136458i
$287$	−33.9272			−2.00266
$288$	−12.2106	−	11.7856i	−0.719519	−	0.694473i
$289$	13.1954			0.776201
$290$	−3.24396	−	7.43247i	−0.190492	−	0.436450i
$291$	−23.2023	−	16.8207i	−1.36014	−	0.986050i
$292$	18.0971	−	19.5147i	1.05905	−	1.14201i
$293$		−	29.3313i		−	1.71355i	−0.515688	−	0.856776i	$-0.672464\pi$
$293$		−	29.3313i		−	1.71355i	0.515688	−	0.856776i	$-0.327536\pi$
$294$	7.43956	−	33.9460i	0.433884	−	1.97977i
$295$			4.40024i			0.256192i
$296$	−18.8221	−	6.57753i	−1.09401	−	0.382311i
$297$	−2.38879	+	7.43044i	−0.138612	+	0.431158i
$298$	−24.0541	+	10.4986i	−1.39341	+	0.608165i
$299$	1.18533			0.0685494
$300$	15.4965	−	3.07338i	0.894690	−	0.177442i
$301$	21.5170			1.24022
$302$	2.75378	−	1.20191i	0.158462	−	0.0691621i
$303$	1.92312	−	2.65273i	0.110481	−	0.152395i
$304$	0.0436877	−	0.00329780i	0.00250566	−	0.000189142i
$305$		−	8.03220i		−	0.459922i
$306$	5.50484	+	6.17894i	0.314691	+	0.353227i
$307$			0.897213i			0.0512066i	0.999672	+	0.0256033i	$0.00815068\pi$
$307$			0.897213i			0.0512066i	−0.999672	+	0.0256033i	$0.991849\pi$
$308$	10.1392	+	9.40265i	0.577733	+	0.535766i
$309$	−14.7656	+	20.3674i	−0.839985	+	1.15866i
$310$	−2.27595	−	5.21460i	−0.129265	−	0.296169i
$311$	24.0397			1.36316			0.681582	−	0.731741i	$-0.261292\pi$
$311$	24.0397			1.36316			0.681582	+	0.731741i	$0.261292\pi$
$312$	−3.31383	−	4.76851i	−0.187609	−	0.269964i
$313$	10.4861			0.592710			0.296355	−	0.955078i	$-0.404229\pi$
$313$	10.4861			0.592710			0.296355	+	0.955078i	$0.404229\pi$
$314$	−2.57422	−	5.89798i	−0.145271	−	0.332842i
$315$	2.84670	+	8.69986i	0.160393	+	0.490181i
$316$	−13.8321	−	12.8274i	−0.778119	−	0.721596i
$317$		−	32.4751i		−	1.82399i	−0.410206	−	0.911993i	$-0.634543\pi$
$317$		−	32.4751i		−	1.82399i	0.410206	−	0.911993i	$-0.365457\pi$
$318$	−1.97479	−	0.432793i	−0.110741	−	0.0242698i
$319$		−	12.9937i		−	0.727506i
$320$	3.30305	−	4.14882i	0.184646	−	0.231926i
$321$	−15.3869	−	11.1549i	−0.858816	−	0.622608i
$322$	5.96608	−	2.60394i	0.332477	−	0.145112i
$323$	−0.0213642			−0.00118874
$324$	2.07017	−	17.8806i	0.115009	−	0.993364i
$325$	5.40579			0.299859
$326$	10.5629	−	4.61025i	0.585024	−	0.255338i
$327$	4.26379	+	3.09108i	0.235788	+	0.170937i
$328$	−6.87749	+	19.6804i	−0.379746	+	1.08667i
$329$			46.2574i			2.55025i
$330$	−2.38242	−	0.522129i	−0.131148	−	0.0287422i
$331$		−	0.698432i		−	0.0383893i	−0.999816	−	0.0191946i	$-0.993890\pi$
$331$		−	0.698432i		−	0.0383893i	0.999816	−	0.0191946i	$-0.00611022\pi$
$332$	1.82861	−	1.97185i	0.100358	−	0.108219i
$333$	−6.57667	−	20.0991i	−0.360399	−	1.10142i
$334$	−5.40728	−	12.3890i	−0.295873	−	0.677897i
$335$	0.538485			0.0294206
$336$	−27.1549	−	16.7213i	−1.48142	−	0.912224i
$337$	14.7092			0.801259			0.400630	−	0.916240i	$-0.368791\pi$
$337$	14.7092			0.801259			0.400630	+	0.916240i	$0.368791\pi$
$338$	6.55939	+	15.0287i	0.356784	+	0.817454i
$339$	−17.4621	+	24.0870i	−0.948411	+	1.30822i
$340$	−1.75839	+	1.89613i	−0.0953622	+	0.102832i
$341$		−	9.11632i		−	0.493676i
$342$	0.0309117	+	0.0346971i	0.00167152	+	0.00187620i
$343$		−	33.0829i		−	1.78631i
$344$	4.36177	−	12.4815i	0.235171	−	0.672960i
$345$	−0.673906	+	0.929576i	−0.0362819	+	0.0500467i
$346$	10.3735	−	4.52759i	0.557683	−	0.243405i
$347$	−2.73153			−0.146636			−0.0733181	−	0.997309i	$-0.523359\pi$
$347$	−2.73153			−0.146636			−0.0733181	+	0.997309i	$0.523359\pi$
$348$	5.82960	+	29.3938i	0.312499	+	1.57567i
$349$	17.7670			0.951047			0.475524	−	0.879703i	$-0.342259\pi$
$349$	17.7670			0.951047			0.475524	+	0.879703i	$0.342259\pi$
$350$	27.2088	−	11.8755i	1.45437	−	0.634771i
$351$	1.88507	−	5.86359i	0.100618	−	0.312975i
$352$	7.50962	−	3.97548i	0.400264	−	0.211894i
$353$			4.77529i			0.254163i	0.991892	+	0.127082i	$0.0405610\pi$
$353$			4.77529i			0.254163i	−0.991892	+	0.127082i	$0.959439\pi$
$354$	3.48084	−	15.8827i	0.185005	−	0.844158i
$355$			5.92971i			0.314716i
$356$	9.24500	+	8.57344i	0.489984	+	0.454391i
$357$	12.5903	+	9.12748i	0.666350	+	0.483078i
$358$	5.65789	+	12.9632i	0.299029	+	0.685128i
$359$	29.5385			1.55898			0.779492	−	0.626413i	$-0.215477\pi$
$359$	29.5385			1.55898			0.779492	+	0.626413i	$0.215477\pi$
$360$	5.62367	+	0.112267i	0.296393	+	0.00591700i
$361$	18.9999			0.999994
$362$	−5.64868	−	12.9421i	−0.296888	−	0.680223i
$363$	12.2615	+	8.88912i	0.643563	+	0.466558i
$364$	−8.00112	−	7.41992i	−0.419373	−	0.388909i
$365$			8.82120i			0.461723i
$366$	−6.35392	+	28.9923i	−0.332125	+	1.51545i
$367$			10.8651i			0.567152i	0.958950	+	0.283576i	$0.0915208\pi$
$367$			10.8651i			0.567152i	−0.958950	+	0.283576i	$0.908479\pi$
$368$	−0.301087	−	3.98865i	−0.0156952	−	0.207923i
$369$	−21.0157	+	6.87659i	−1.09403	+	0.357981i
$370$	6.05667	−	2.64348i	0.314871	−	0.137428i
$371$	−3.79901			−0.197235
$372$	4.09002	+	20.6226i	0.212058	+	1.06923i
$373$	−24.5952			−1.27349			−0.636745	−	0.771074i	$-0.719720\pi$
$373$	−24.5952			−1.27349			−0.636745	+	0.771074i	$0.719720\pi$
$374$	−3.79748	+	1.65744i	−0.196363	+	0.0857040i
$375$	−6.44293	+	8.88728i	−0.332712	+	0.458937i
$376$	26.8329	+	9.37699i	1.38380	+	0.483581i
$377$			10.2537i			0.528093i
$378$	−3.39311	−	33.6541i	−0.174523	−	1.73098i
$379$		−	34.9695i		−	1.79626i	−0.439729	−	0.898131i	$-0.644925\pi$
$379$		−	34.9695i		−	1.79626i	0.439729	−	0.898131i	$-0.355075\pi$
$380$	−0.00987404	+	0.0106475i	−0.000506528	+	0.000546204i
$381$	−6.42756	+	8.86607i	−0.329294	+	0.454223i
$382$	−11.4388	−	26.2083i	−0.585260	−	1.34093i
$383$	9.03605			0.461721			0.230860	−	0.972987i	$-0.425846\pi$
$383$	9.03605			0.461721			0.230860	+	0.972987i	$0.425846\pi$
$384$	−15.2044	+	12.3623i	−0.775894	+	0.630863i
$385$	−4.58319			−0.233581
$386$	6.98410	+	16.0018i	0.355481	+	0.814470i
$387$	13.3284	−	4.36120i	0.677520	−	0.221692i
$388$	−22.5013	+	24.2639i	−1.14233	+	1.23181i
$389$			31.5958i			1.60197i	0.598683	+	0.800986i	$0.295691\pi$
$389$			31.5958i			1.60197i	−0.598683	+	0.800986i	$0.704309\pi$
$390$	1.88004	+	0.412028i	0.0951997	+	0.0208638i
$391$			1.95053i			0.0986428i
$392$	−37.8813	−	13.2379i	−1.91330	−	0.668616i
$393$	−15.2354	−	11.0451i	−0.768524	−	0.557150i
$394$	−4.91640	+	2.14580i	−0.247685	+	0.108104i
$395$	6.25253			0.314599
$396$	8.18635	+	3.76926i	0.411380	+	0.189413i
$397$	37.1411			1.86406			0.932028	−	0.362386i	$-0.118038\pi$
$397$	37.1411			1.86406			0.932028	+	0.362386i	$0.118038\pi$
$398$	−23.0676	+	10.0680i	−1.15627	+	0.504664i
$399$	0.0706993	+	0.0512543i	0.00353939	+	0.00256592i
$400$	−1.37313	−	18.1906i	−0.0686565	−	0.909528i
$401$		−	15.9102i		−	0.794518i	−0.917707	−	0.397259i	$-0.869962\pi$
$401$		−	15.9102i		−	0.794518i	0.917707	−	0.397259i	$-0.130038\pi$
$402$	−1.94367	−	0.425972i	−0.0969414	−	0.0212455i
$403$			7.19397i			0.358357i
$404$	−2.77410	−	2.57259i	−0.138017	−	0.127991i
$405$	3.52669	+	4.81201i	0.175243	+	0.239111i
$406$	22.5254	+	51.6097i	1.11792	+	2.56134i
$407$	10.5885			0.524850
$408$	7.84689	−	5.45311i	0.388479	−	0.269969i
$409$	30.7839			1.52217			0.761084	−	0.648653i	$-0.224667\pi$
$409$	30.7839			1.52217			0.761084	+	0.648653i	$0.224667\pi$
$410$	−2.76403	−	6.33288i	−0.136506	−	0.312758i
$411$	−1.98446	+	2.73734i	−0.0978863	+	0.135023i
$412$	21.2993	+	19.7521i	1.04934	+	0.973116i
$413$		−	30.5544i		−	1.50349i
$414$	3.16782	−	2.82222i	0.155690	−	0.138704i
$415$			0.891333i			0.0437538i
$416$	−5.92607	+	3.13717i	−0.290550	+	0.153812i
$417$	17.4937	−	24.1306i	0.856672	−	1.18168i
$418$	−0.0213243	+	0.00930713i	−0.00104300	+	0.000455227i
$419$	8.53577			0.417000			0.208500	−	0.978022i	$-0.433142\pi$
$419$	8.53577			0.417000			0.208500	+	0.978022i	$0.433142\pi$
$420$	10.3679	−	2.05624i	0.505902	−	0.100334i
$421$	−2.20696			−0.107560			−0.0537802	−	0.998553i	$-0.517127\pi$
$421$	−2.20696			−0.107560			−0.0537802	+	0.998553i	$0.517127\pi$
$422$	−9.33623	+	4.07486i	−0.454480	+	0.198361i
$423$	9.37576	+	28.6535i	0.455865	+	1.39318i
$424$	−0.770110	+	2.20373i	−0.0373998	+	0.107022i
$425$			8.89557i			0.431499i
$426$	4.69073	−	21.4034i	0.227267	−	1.03700i
$427$			55.7740i			2.69909i
$428$	−14.9221	+	16.0910i	−0.721287	+	0.777786i
$429$	2.49674	+	1.81004i	0.120544	+	0.0873897i
$430$	1.75298	+	4.01638i	0.0845360	+	0.193687i
$431$	34.5893			1.66611			0.833055	−	0.553191i	$-0.186590\pi$
$431$	34.5893			1.66611			0.833055	+	0.553191i	$0.186590\pi$
$432$	−20.2099	−	4.85387i	−0.972349	−	0.233532i
$433$	−10.2039			−0.490370			−0.245185	−	0.969476i	$-0.578849\pi$
$433$	−10.2039			−0.490370			−0.245185	+	0.969476i	$0.578849\pi$
$434$	15.8037	+	36.2092i	0.758604	+	1.73810i
$435$	−8.04131	−	5.82963i	−0.385551	−	0.279510i
$436$	4.13498	−	4.45888i	0.198030	−	0.213541i
$437$			0.0109530i			0.000523953i
$438$	6.97807	−	31.8402i	0.333425	−	1.52139i
$439$		−	3.84509i		−	0.183516i	−0.995781	−	0.0917581i	$-0.970751\pi$
$439$		−	3.84509i		−	0.183516i	0.995781	−	0.0917581i	$-0.0292487\pi$
$440$	−0.929074	+	2.65861i	−0.0442919	+	0.126744i
$441$	−13.2362	−	40.4514i	−0.630295	−	1.92626i
$442$	2.99671	−	1.30793i	0.142539	−	0.0622121i
$443$	−10.6221			−0.504673			−0.252336	−	0.967640i	$-0.581199\pi$
$443$	−10.6221			−0.504673			−0.252336	+	0.967640i	$0.581199\pi$
$444$	−23.9528	+	4.75050i	−1.13675	+	0.225449i
$445$	−4.17900			−0.198104
$446$	−19.9045	+	8.68745i	−0.942504	+	0.411363i
$447$	−18.8667	+	26.0245i	−0.892365	+	1.23091i
$448$	−22.9358	+	28.8087i	−1.08361	+	1.36108i
$449$		−	8.69064i		−	0.410137i	−0.978748	−	0.205068i	$-0.934258\pi$
$449$		−	8.69064i		−	0.410137i	0.978748	−	0.205068i	$-0.0657417\pi$
$450$	14.4471	−	12.8710i	0.681043	−	0.606743i
$451$		−	11.0713i		−	0.521329i
$452$	25.1890	+	23.3593i	1.18479	+	1.09873i
$453$	2.15992	−	2.97936i	0.101482	−	0.139983i
$454$	−1.69788	−	3.89014i	−0.0796854	−	0.182573i
$455$	3.61674			0.169555
$456$	0.0440632	−	0.0306213i	0.00206345	−	0.00143397i
$457$	−31.0123			−1.45069			−0.725346	−	0.688384i	$-0.758320\pi$
$457$	−31.0123			−1.45069			−0.725346	+	0.688384i	$0.758320\pi$
$458$	−6.11688	−	14.0148i	−0.285823	−	0.654871i
$459$	9.64891	+	3.10200i	0.450372	+	0.144789i
$460$	0.972107	+	0.901492i	0.0453247	+	0.0420323i
$461$			26.3970i			1.22943i	0.788750	+	0.614715i	$0.210729\pi$
$461$			26.3970i			1.22943i	−0.788750	+	0.614715i	$0.789271\pi$
$462$	16.5431	+	3.62556i	0.769654	+	0.168676i
$463$			8.59067i			0.399242i	0.979873	+	0.199621i	$0.0639711\pi$
$463$			8.59067i			0.399242i	−0.979873	+	0.199621i	$0.936029\pi$
$464$	34.5039	−	2.60456i	1.60180	−	0.120913i
$465$	−5.64175	−	4.09005i	−0.261630	−	0.189672i
$466$	7.44536	−	3.24958i	0.344900	−	0.150534i
$467$	1.43602			0.0664512			0.0332256	−	0.999448i	$-0.489422\pi$
$467$	1.43602			0.0664512			0.0332256	+	0.999448i	$0.489422\pi$
$468$	−6.46010	−	2.97444i	−0.298618	−	0.137494i
$469$	−3.73914			−0.172657
$470$	−8.63445	+	3.76857i	−0.398277	+	0.173831i
$471$	−6.38112	−	4.62606i	−0.294027	−	0.213158i
$472$	−17.7240	−	6.19379i	−0.815813	−	0.285092i
$473$			7.02156i			0.322851i
$474$	−22.5686	−	4.94610i	−1.03661	−	0.227182i
$475$			0.0499520i			0.00229195i
$476$	12.2099	−	13.1664i	0.559642	−	0.603479i
$477$	−2.35324	+	0.770009i	−0.107748	+	0.0352563i
$478$	6.85428	+	15.7044i	0.313508	+	0.718301i
$479$	−24.9935			−1.14198			−0.570991	−	0.820956i	$-0.693441\pi$
$479$	−24.9935			−1.14198			−0.570991	+	0.820956i	$0.693441\pi$
$480$	0.908929	−	6.43103i	0.0414867	−	0.293535i
$481$	−8.35567			−0.380986
$482$	2.48878	+	5.70222i	0.113361	+	0.259729i
$483$	4.67948	−	6.45480i	0.212924	−	0.293703i
$484$	11.8911	−	12.8225i	0.540504	−	0.582842i
$485$		−	10.9680i		−	0.498029i
$486$	−8.92307	−	20.1588i	−0.404758	−	0.914424i
$487$		−	0.418538i		−	0.0189658i	−0.999955	−	0.00948288i	$-0.996981\pi$
$487$		−	0.418538i		−	0.0189658i	0.999955	−	0.00948288i	$-0.00301854\pi$
$488$	32.3534	+	11.3061i	1.46457	+	0.511805i
$489$	8.28497	−	11.4282i	0.374659	−	0.516799i
$490$	12.1896	−	5.32026i	0.550672	−	0.240345i
$491$	−18.0648			−0.815251			−0.407626	−	0.913149i	$-0.633643\pi$
$491$	−18.0648			−0.815251			−0.407626	+	0.913149i	$0.633643\pi$
$492$	4.96714	+	25.0451i	0.223936	+	1.12912i
$493$	−16.8731			−0.759928
$494$	0.0168276	−	0.00734454i	0.000757111	−	0.000330447i
$495$	−2.83899	+	0.928953i	−0.127603	+	0.0417533i
$496$	24.2078	−	1.82735i	1.08696	−	0.0820503i
$497$		−	41.1748i		−	1.84694i
$498$	0.705094	−	3.21728i	0.0315960	−	0.144170i
$499$		−	16.1076i		−	0.721075i	−0.932745	−	0.360538i	$-0.882593\pi$
$499$		−	16.1076i		−	0.721075i	0.932745	−	0.360538i	$-0.117407\pi$
$500$	9.29391	+	8.61879i	0.415636	+	0.385444i
$501$	−13.4039	−	9.71729i	−0.598842	−	0.434137i
$502$	13.1759	+	30.1883i	0.588069	+	1.34737i
$503$	2.28839			0.102034			0.0510172	−	0.998698i	$-0.483754\pi$
$503$	2.28839			0.102034			0.0510172	+	0.998698i	$0.483754\pi$
$504$	−39.0497	−	0.779561i	−1.73941	−	0.0347244i
$505$	1.25397			0.0558011
$506$	0.849734	+	1.94689i	0.0377753	+	0.0865498i
$507$	16.2598	+	11.7877i	0.722123	+	0.523511i
$508$	9.27173	+	8.59822i	0.411366	+	0.381484i
$509$		−	8.08033i		−	0.358154i	−0.983835	−	0.179077i	$-0.942689\pi$
$509$		−	8.08033i		−	0.358154i	0.983835	−	0.179077i	$-0.0573111\pi$
$510$	−0.678018	+	3.09373i	−0.0300231	+	0.136993i
$511$		−	61.2528i		−	2.70966i
$512$	12.0619	+	19.1445i	0.533066	+	0.846073i
$513$	0.0541823	+	0.0174189i	0.00239221	+	0.000769063i
$514$	6.38860	−	2.78835i	0.281789	−	0.122989i
$515$	−9.62789			−0.424256
$516$	−3.15021	−	15.8839i	−0.138680	−	0.699248i
$517$	−15.0950			−0.663878
$518$	−42.0563	+	18.3558i	−1.84785	+	0.806507i
$519$	8.13642	−	11.2233i	0.357149	−	0.492646i
$520$	0.733161	−	2.09799i	0.0321512	−	0.0920031i
$521$		−	3.68353i		−	0.161378i	−0.996739	−	0.0806891i	$-0.974288\pi$
$521$		−	3.68353i		−	0.161378i	0.996739	−	0.0806891i	$-0.0257121\pi$
$522$	24.4136	+	27.4033i	1.06856	+	1.19941i
$523$			2.10377i			0.0919913i	0.998942	+	0.0459956i	$0.0146460\pi$
$523$			2.10377i			0.0919913i	−0.998942	+	0.0459956i	$0.985354\pi$
$524$	−14.7751	+	15.9325i	−0.645454	+	0.696013i
$525$	21.3411	−	29.4376i	0.931403	−	1.28476i
$526$	−16.8619	−	38.6335i	−0.735212	−	1.68450i
$527$	−11.8381			−0.515677
$528$	5.45662	−	8.86136i	0.237469	−	0.385641i
$529$	1.00000			0.0434783
$530$	−0.309503	−	0.709126i	−0.0134440	−	0.0308025i
$531$	−6.19298	−	18.9265i	−0.268753	−	0.821341i
$532$	0.0685635	−	0.0739341i	0.00297260	−	0.00320545i
$533$			8.73673i			0.378430i
$534$	15.0842	+	3.30583i	0.652756	+	0.143057i
$535$		−	7.27357i		−	0.314464i
$536$	−0.757973	+	2.16900i	−0.0327394	+	0.0936863i
$537$	14.0251	+	10.1677i	0.605228	+	0.438767i
$538$	19.9555	−	8.70971i	0.860342	−	0.375502i
$539$	21.3103			0.917901
$540$	6.00548	−	3.37515i	0.258435	−	0.145243i
$541$	−11.2674			−0.484422			−0.242211	−	0.970224i	$-0.577873\pi$
$541$	−11.2674			−0.484422			−0.242211	+	0.970224i	$0.577873\pi$
$542$	17.7476	−	7.74608i	0.762326	−	0.332723i
$543$	−14.0023	−	10.1511i	−0.600896	−	0.435626i
$544$	−5.16241	−	9.75173i	−0.221337	−	0.418102i
$545$			2.01554i			0.0863362i
$546$	−13.0547	−	2.86104i	−0.558688	−	0.122441i
$547$		−	19.8194i		−	0.847414i	−0.905799	−	0.423707i	$-0.860729\pi$
$547$		−	19.8194i		−	0.847414i	0.905799	−	0.423707i	$-0.139271\pi$
$548$	2.86258	+	2.65464i	0.122283	+	0.113401i
$549$	11.3047	+	34.5484i	0.482471	+	1.47449i
$550$	3.87528	+	8.87895i	0.165243	+	0.378600i
$551$	−0.0947490			−0.00403644
$552$	−2.79570	−	4.02294i	−0.118993	−	0.171228i
$553$	−43.4164			−1.84625
$554$	3.51503	+	8.05355i	0.149339	+	0.342162i
$555$	4.75053	−	6.55281i	0.201649	−	0.278151i
$556$	−25.2347	−	23.4016i	−1.07019	−	0.992448i
$557$		−	21.1102i		−	0.894470i	−0.894417	−	0.447235i	$-0.852409\pi$
$557$		−	21.1102i		−	0.894470i	0.894417	−	0.447235i	$-0.147591\pi$
$558$	17.1285	+	19.2260i	0.725108	+	0.813903i
$559$		−	5.54092i		−	0.234356i
$560$	−0.918691	−	12.1704i	−0.0388218	−	0.514292i
$561$	−2.97854	+	4.10855i	−0.125754	+	0.173463i
$562$	36.2114	−	15.8047i	1.52749	−	0.666682i
$563$	4.72361			0.199077			0.0995383	−	0.995034i	$-0.468263\pi$
$563$	4.72361			0.199077			0.0995383	+	0.995034i	$0.468263\pi$
$564$	34.1473	−	6.77235i	1.43786	−	0.285168i
$565$	−11.3862			−0.479019
$566$	24.4438	−	10.6687i	1.02745	−	0.448437i
$567$	−24.4887	−	33.4137i	−1.02843	−	1.40324i
$568$	−23.8846	−	8.34668i	−1.00218	−	0.350219i
$569$		−	8.91556i		−	0.373760i	−0.982383	−	0.186880i	$-0.940162\pi$
$569$		−	8.91556i		−	0.373760i	0.982383	−	0.186880i	$-0.0598375\pi$
$570$	−0.00380733	+	0.0173725i	−0.000159471	+	0.000727652i
$571$		−	19.5692i		−	0.818946i	−0.912322	−	0.409473i	$-0.865713\pi$
$571$		−	19.5692i		−	0.818946i	0.912322	−	0.409473i	$-0.134287\pi$
$572$	2.42132	−	2.61098i	0.101240	−	0.109171i
$573$	−28.3552	−	20.5564i	−1.18455	−	0.858755i
$574$	19.1929	+	43.9743i	0.801096	+	1.83545i
$575$	4.56058			0.190189
$576$	−8.36810	+	22.4939i	−0.348671	+	0.937245i
$577$	−2.05849			−0.0856961			−0.0428481	−	0.999082i	$-0.513643\pi$
$577$	−2.05849			−0.0856961			−0.0428481	+	0.999082i	$0.513643\pi$
$578$	−7.46476	−	17.1031i	−0.310493	−	0.711394i
$579$	17.3126	+	12.5510i	0.719487	+	0.521600i
$580$	−7.79837	+	8.40923i	−0.323810	+	0.349174i
$581$		−	6.18924i		−	0.256773i
$582$	−8.67627	+	39.5890i	−0.359643	+	1.64102i
$583$		−	1.23972i		−	0.0513438i
$584$	−35.5315	−	12.4168i	−1.47030	−	0.513809i
$585$	2.24034	−	0.733065i	0.0926265	−	0.0303085i
$586$	−38.0174	+	16.5930i	−1.57048	+	0.685449i
$587$	23.3188			0.962471			0.481236	−	0.876591i	$-0.340188\pi$
$587$	23.3188			0.962471			0.481236	+	0.876591i	$0.340188\pi$
$588$	−48.2073	+	9.56085i	−1.98804	+	0.394283i
$589$	−0.0664756			−0.00273908
$590$	5.70332	−	2.48926i	0.234802	−	0.102481i
$591$	−3.85616	+	5.31913i	−0.158621	+	0.218800i
$592$	2.12243	+	28.1170i	0.0872315	+	1.15560i
$593$			24.7929i			1.01812i	0.860731	+	0.509061i	$0.170007\pi$
$593$			24.7929i			1.01812i	−0.860731	+	0.509061i	$0.829993\pi$
$594$	10.9822	−	1.10726i	0.450607	−	0.0454315i
$595$			5.95157i			0.243991i
$596$	27.2152	+	25.2382i	1.11478	+	1.03380i
$597$	−18.0930	+	24.9572i	−0.740497	+	1.02143i
$598$	−0.670551	−	1.53635i	−0.0274209	−	0.0628260i
$599$	−8.16134			−0.333463			−0.166732	−	0.986002i	$-0.553321\pi$
$599$	−8.16134			−0.333463			−0.166732	+	0.986002i	$0.553321\pi$
$600$	−12.7500	−	18.3469i	−0.520517	−	0.749011i
$601$	5.23414			0.213505			0.106752	−	0.994286i	$-0.465955\pi$
$601$	5.23414			0.213505			0.106752	+	0.994286i	$0.465955\pi$
$602$	−12.1723	−	27.8890i	−0.496107	−	1.13667i
$603$	−2.31616	+	0.757874i	−0.0943211	+	0.0308630i
$604$	−3.11568	−	2.88935i	−0.126775	−	0.117566i
$605$			5.79615i			0.235647i
$606$	−4.52623	−	0.991963i	−0.183866	−	0.0402957i
$607$			13.2731i			0.538738i	0.963037	+	0.269369i	$0.0868151\pi$
$607$			13.2731i			0.538738i	−0.963037	+	0.269369i	$0.913185\pi$
$608$	−0.0289889	−	0.0547597i	−0.00117566	−	0.00222080i
$609$	55.8373	+	40.4799i	2.26264	+	1.64033i
$610$	−10.4108	+	4.54388i	−0.421522	+	0.183976i
$611$	11.9119			0.481905
$612$	4.89463	−	10.6305i	0.197854	−	0.429713i
$613$	3.86868			0.156255			0.0781273	−	0.996943i	$-0.475106\pi$
$613$	3.86868			0.156255			0.0781273	+	0.996943i	$0.475106\pi$
$614$	1.16291	−	0.507561i	0.0469313	−	0.0204835i
$615$	−6.85164	−	4.96717i	−0.276285	−	0.200296i
$616$	6.45131	−	18.4609i	0.259931	−	0.743812i
$617$			10.7763i			0.433838i	0.976190	+	0.216919i	$0.0696008\pi$
$617$			10.7763i			0.433838i	−0.976190	+	0.216919i	$0.930399\pi$
$618$	34.7520	+	7.61620i	1.39793	+	0.306369i
$619$			8.55306i			0.343776i	0.985116	+	0.171888i	$0.0549868\pi$
$619$			8.55306i			0.343776i	−0.985116	+	0.171888i	$0.945013\pi$
$620$	−5.47131	+	5.89988i	−0.219733	+	0.236945i
$621$	1.59033	−	4.94680i	0.0638179	−	0.198508i
$622$	−13.5995	−	31.1587i	−0.545288	−	1.24935i
$623$	29.0182			1.16259
$624$	−4.30599	+	6.99277i	−0.172377	+	0.279935i
$625$	18.6018			0.744071
$626$	−5.93208	−	13.5914i	−0.237094	−	0.543223i
$627$	−0.0167256	+	0.0230711i	−0.000667957	+	0.000921370i
$628$	−6.18834	+	6.67308i	−0.246942	+	0.266285i
$629$		−	13.7498i		−	0.548240i
$630$	9.66581	−	8.61130i	0.385095	−	0.343082i
$631$			25.3560i			1.00940i	0.863293	+	0.504702i	$0.168398\pi$
$631$			25.3560i			1.00940i	−0.863293	+	0.504702i	$0.831602\pi$
$632$	−8.80107	+	25.1849i	−0.350088	+	1.00180i
$633$	−7.32284	+	10.1010i	−0.291057	+	0.401479i
$634$	−42.0923	+	18.3715i	−1.67170	+	0.729624i
$635$	−4.19109			−0.166318
$636$	0.556197	+	2.80444i	0.0220547	+	0.111203i
$637$	−16.8166			−0.666299
$638$	−16.8416	+	7.35064i	−0.666765	+	0.291015i
$639$	−8.34558	−	25.5051i	−0.330146	−	1.00897i
$640$	−7.24601	−	1.93418i	−0.286424	−	0.0764553i
$641$		−	38.1941i		−	1.50858i	−0.656543	−	0.754289i	$-0.727982\pi$
$641$		−	38.1941i		−	1.50858i	0.656543	−	0.754289i	$-0.272018\pi$
$642$	−5.75380	+	26.2541i	−0.227085	+	1.03616i
$643$		−	0.331795i		−	0.0130847i	−0.999979	−	0.00654235i	$-0.997917\pi$
$643$		−	0.331795i		−	0.0130847i	0.999979	−	0.00654235i	$-0.00208251\pi$
$644$	−6.75013	−	6.25979i	−0.265992	−	0.246670i
$645$	4.34538	+	3.15023i	0.171099	+	0.124040i
$646$	0.0120859	+	0.0276909i	0.000475514	+	0.00108949i
$647$	−27.6906			−1.08863			−0.544315	−	0.838881i	$-0.683210\pi$
$647$	−27.6906			−1.08863			−0.544315	+	0.838881i	$0.683210\pi$
$648$	−24.3468	+	7.43197i	−0.956432	+	0.291955i
$649$	9.97073			0.391385
$650$	−3.05810	−	7.00665i	−0.119949	−	0.274823i
$651$	39.1753	+	28.4005i	1.53540	+	1.11310i
$652$	−11.9510	−	11.0829i	−0.468039	−	0.434040i
$653$		−	13.4782i		−	0.527444i	−0.964599	−	0.263722i	$-0.915050\pi$
$653$		−	13.4782i		−	0.527444i	0.964599	−	0.263722i	$-0.0849502\pi$
$654$	1.59441	−	7.27512i	0.0623462	−	0.284480i
$655$		−	7.20193i		−	0.281403i
$656$	29.3992	−	2.21922i	1.14785	−	0.0866462i
$657$	−12.4151	−	37.9422i	−0.484360	−	1.48026i
$658$	59.9559	−	26.1682i	2.33733	−	1.02014i
$659$	−35.9892			−1.40194			−0.700971	−	0.713190i	$-0.747250\pi$
$659$	−35.9892			−1.40194			−0.700971	+	0.713190i	$0.747250\pi$
$660$	0.671007	+	3.38332i	0.0261189	+	0.131696i
$661$	−38.0263			−1.47905			−0.739525	−	0.673129i	$-0.764950\pi$
$661$	−38.0263			−1.47905			−0.739525	+	0.673129i	$0.764950\pi$
$662$	−0.905264	+	0.395109i	−0.0351841	+	0.0153563i
$663$	2.35046	−	3.24218i	0.0912842	−	0.125916i
$664$	−3.59025	−	1.25464i	−0.139329	−	0.0486896i
$665$			0.0334203i			0.00129598i
$666$	−22.3307	+	19.8945i	−0.865298	+	0.770896i
$667$			8.65051i			0.334949i
$668$	−12.9989	+	14.0172i	−0.502944	+	0.542340i
$669$	−15.6120	+	21.5350i	−0.603595	+	0.832590i
$670$	−0.304626	−	0.697951i	−0.0117687	−	0.0269642i
$671$	−18.2005			−0.702624
$672$	−6.31143	+	44.6559i	−0.243469	+	1.72264i
$673$	13.7751			0.530990			0.265495	−	0.964112i	$-0.414465\pi$
$673$	13.7751			0.530990			0.265495	+	0.964112i	$0.414465\pi$
$674$	−8.32110	−	19.0651i	−0.320517	−	0.734360i
$675$	7.25284	−	22.5603i	0.279162	−	0.868346i
$676$	15.7686	−	17.0037i	0.606484	−	0.653990i
$677$			22.1570i			0.851562i	0.904826	+	0.425781i	$0.140001\pi$
$677$			22.1570i			0.851562i	−0.904826	+	0.425781i	$0.859999\pi$
$678$	41.0985	+	9.00709i	1.57838	+	0.345915i
$679$			76.1594i			2.92273i
$680$	3.45238	+	1.20646i	0.132393	+	0.0462657i
$681$	−4.20880	−	3.05122i	−0.161282	−	0.116923i
$682$	−11.8160	+	5.15718i	−0.452458	+	0.197479i
$683$	−30.3631			−1.16181			−0.580907	−	0.813970i	$-0.697302\pi$
$683$	−30.3631			−1.16181			−0.580907	+	0.813970i	$0.697302\pi$
$684$	0.0274852	−	0.0596943i	0.00105092	−	0.00228247i
$685$	−1.29397			−0.0494400
$686$	−42.8800	+	18.7153i	−1.63717	+	0.714553i
$687$	−15.1629	−	10.9925i	−0.578500	−	0.419390i
$688$	−18.6453	+	1.40746i	−0.710845	+	0.0536587i
$689$			0.978299i			0.0372702i
$690$	1.58609	+	0.347606i	0.0603815	+	0.0132331i
$691$			24.4059i			0.928442i	0.885719	+	0.464221i	$0.153666\pi$
$691$			24.4059i			0.928442i	−0.885719	+	0.464221i	$0.846334\pi$
$692$	−11.7368	−	10.8842i	−0.446165	−	0.413755i
$693$	19.7134	−	6.45047i	0.748851	−	0.245033i
$694$	1.54525	+	3.54044i	0.0586569	+	0.134393i
$695$	11.4068			0.432684
$696$	34.8005	−	24.1843i	1.31911	−	0.916702i
$697$	−14.3768			−0.544562
$698$	−10.0510	−	23.0285i	−0.380434	−	0.871642i
$699$	5.83975	−	8.05526i	0.220880	−	0.304678i
$700$	−30.7845	−	28.5483i	−1.16354	−	1.07902i
$701$		−	21.7606i		−	0.821888i	−0.911661	−	0.410944i	$-0.865199\pi$
$701$		−	21.7606i		−	0.821888i	0.911661	−	0.410944i	$-0.134801\pi$
$702$	−8.66642	+	0.873775i	−0.327093	+	0.0329785i
$703$		−	0.0772103i		−	0.00291204i
$704$	−9.40103	−	7.48455i	−0.354315	−	0.282084i
$705$	−6.77240	+	9.34174i	−0.255063	+	0.351830i
$706$	6.18944	−	2.70142i	0.232943	−	0.101669i
$707$	−8.70735			−0.327474
$708$	−22.5554	+	4.47335i	−0.847682	+	0.168119i
$709$	−20.6926			−0.777127			−0.388564	−	0.921422i	$-0.627029\pi$
$709$	−20.6926			−0.777127			−0.388564	+	0.921422i	$0.627029\pi$
$710$	7.68572	−	3.35449i	0.288440	−	0.125892i
$711$	−26.8936	+	8.79992i	−1.00859	+	0.330023i
$712$	5.88238	−	16.8329i	0.220451	−	0.630838i
$713$			6.06917i			0.227292i
$714$	4.70803	−	21.4823i	0.176194	−	0.803954i
$715$			1.18024i			0.0441384i
$716$	13.6014	−	14.6668i	0.508308	−	0.548125i
$717$	16.9908	+	12.3177i	0.634533	+	0.460012i
$718$	−16.7102	−	38.2860i	−0.623619	−	1.42882i
$719$	−20.6957			−0.771818			−0.385909	−	0.922537i	$-0.626112\pi$
$719$	−20.6957			−0.771818			−0.385909	+	0.922537i	$0.626112\pi$
$720$	−3.03584	−	7.35256i	−0.113139	−	0.274014i
$721$	66.8542			2.48978
$722$	−10.7484	−	24.6265i	−0.400014	−	0.916502i
$723$	6.16933	+	4.47252i	0.229440	+	0.166335i
$724$	−13.5793	+	14.6429i	−0.504669	+	0.544200i
$725$			39.4514i			1.46519i
$726$	4.58508	−	20.9213i	0.170168	−	0.776461i
$727$			17.7962i			0.660023i	0.943977	+	0.330011i	$0.107053\pi$
$727$			17.7962i			0.660023i	−0.943977	+	0.330011i	$0.892947\pi$
$728$	−5.09093	+	14.5681i	−0.188682	+	0.539929i
$729$	−21.9417	−	15.7341i	−0.812655	−	0.582745i
$730$	11.4335	−	4.99023i	0.423173	−	0.184697i
$731$	9.11794			0.337239
$732$	41.1725	−	8.16565i	1.52178	−	0.301811i
$733$	−2.58476			−0.0954703			−0.0477352	−	0.998860i	$-0.515200\pi$
$733$	−2.58476			−0.0954703			−0.0477352	+	0.998860i	$0.515200\pi$
$734$	14.0826	−	6.14646i	0.519799	−	0.226870i
$735$	9.56091	−	13.1882i	0.352660	−	0.486453i
$736$	−4.99952	+	2.64667i	−0.184285	+	0.0975574i
$737$		−	1.22018i		−	0.0449459i
$738$	20.8018	+	23.3491i	0.765724	+	0.859492i
$739$		−	40.7287i		−	1.49823i	−0.662441	−	0.749114i	$-0.730480\pi$
$739$		−	40.7287i		−	1.49823i	0.662441	−	0.749114i	$-0.269520\pi$
$740$	−6.85262	−	6.35484i	−0.251907	−	0.233609i
$741$	0.0131987	−	0.0182061i	0.000484866	−	0.000668817i
$742$	2.14913	+	4.92404i	0.0788971	+	0.180767i
$743$	−3.12875			−0.114783			−0.0573913	−	0.998352i	$-0.518278\pi$
$743$	−3.12875			−0.114783			−0.0573913	+	0.998352i	$0.518278\pi$
$744$	24.4159	−	16.9676i	0.895131	−	0.622062i
$745$	−12.3020			−0.450712
$746$	13.9137	+	31.8788i	0.509417	+	1.16716i
$747$	−1.25448	−	3.83384i	−0.0458989	−	0.140273i
$748$	4.29653	+	3.98443i	0.157097	+	0.145685i
$749$			50.5063i			1.84546i
$750$	15.1640	+	3.32332i	0.553710	+	0.121350i
$751$			25.2002i			0.919568i	0.888031	+	0.459784i	$0.152073\pi$
$751$			25.2002i			0.919568i	−0.888031	+	0.459784i	$0.847927\pi$
$752$	−3.02576	−	40.0838i	−0.110338	−	1.46171i
$753$	32.6612	+	23.6781i	1.19024	+	0.862878i
$754$	13.2902	−	5.80061i	0.484001	−	0.211246i
$755$	1.40838			0.0512560
$756$	−41.7009	+	23.4364i	−1.51665	+	0.852373i
$757$	16.7595			0.609135			0.304567	−	0.952491i	$-0.401488\pi$
$757$	16.7595			0.609135			0.304567	+	0.952491i	$0.401488\pi$
$758$	−45.3253	+	19.7825i	−1.64629	+	0.718534i
$759$	2.10637	+	1.52704i	0.0764565	+	0.0554279i
$760$	0.0193864	+	0.00677474i	0.000703220	+	0.000245746i
$761$		−	19.5908i		−	0.710165i	−0.934835	−	0.355082i	$-0.884453\pi$
$761$		−	19.5908i		−	0.710165i	0.934835	−	0.355082i	$-0.115547\pi$
$762$	15.1278	+	3.31539i	0.548022	+	0.120104i
$763$		−	13.9955i		−	0.506672i
$764$	−27.4985	+	29.6525i	−0.994862	+	1.07279i
$765$	1.20630	+	3.68662i	0.0436140	+	0.133290i
$766$	−5.11177	−	11.7120i	−0.184696	−	0.423171i
$767$	−7.86820			−0.284104
$768$	24.6245	+	12.7135i	0.888561	+	0.458758i
$769$	43.5836			1.57166			0.785832	−	0.618441i	$-0.212235\pi$
$769$	43.5836			1.57166			0.785832	+	0.618441i	$0.212235\pi$
$770$	2.59275	+	5.94045i	0.0934363	+	0.214079i
$771$	5.01088	−	6.91193i	0.180462	−	0.248927i
$772$	16.7896	−	18.1047i	0.604270	−	0.651602i
$773$			42.0157i			1.51120i	0.655035	+	0.755599i	$0.272654\pi$
$773$			42.0157i			1.51120i	−0.655035	+	0.755599i	$0.727346\pi$
$774$	−13.1927	−	14.8082i	−0.474202	−	0.532271i
$775$			27.6789i			0.994257i
$776$	44.1785	+	15.4385i	1.58592	+	0.554211i
$777$	−32.9868	+	45.5014i	−1.18339	+	1.63235i
$778$	40.9525	−	17.8740i	1.46822	−	0.640815i
$779$	−0.0807314			−0.00289250
$780$	−0.529512	−	2.66988i	−0.0189596	−	0.0955971i
$781$	13.4364			0.480793
$782$	2.52816	−	1.10343i	0.0904069	−	0.0394587i
$783$	42.7924	+	13.7572i	1.52927	+	0.491642i
$784$	4.27161	+	56.5882i	0.152557	+	2.02101i
$785$		−	3.01642i		−	0.107661i
$786$	−5.69713	+	25.9955i	−0.203210	+	0.927227i
$787$			38.5386i			1.37375i	0.726774	+	0.686877i	$0.241019\pi$
$787$			38.5386i			1.37375i	−0.726774	+	0.686877i	$0.758981\pi$
$788$	5.56250	+	5.15843i	0.198156	+	0.183762i
$789$	−41.7982	−	30.3020i	−1.48805	−	1.07878i
$790$	−3.53711	−	8.10414i	−0.125845	−	0.288332i
$791$	79.0633			2.81117
$792$	0.254392	−	12.7429i	0.00903941	−	0.452801i
$793$	14.3626			0.510031
$794$	−21.0110	−	48.1399i	−0.745653	−	1.70842i
$795$	−0.767215	−	0.556201i	−0.0272103	−	0.0197264i
$796$	26.0991	+	24.2032i	0.925057	+	0.857860i
$797$		−	30.0832i		−	1.06560i	−0.846241	−	0.532800i	$-0.821140\pi$
$797$		−	30.0832i		−	1.06560i	0.846241	−	0.532800i	$-0.178860\pi$
$798$	0.0264374	−	0.120631i	0.000935872	−	0.00427029i
$799$			19.6018i			0.693463i
$800$	−22.8007	+	12.0703i	−0.806126	+	0.426751i
$801$	17.9749	−	5.88161i	0.635113	−	0.207816i
$802$	−20.6218	+	9.00054i	−0.728182	+	0.317820i
$803$	19.9884			0.705375
$804$	0.547432	+	2.76024i	0.0193064	+	0.0973461i
$805$	3.05125			0.107542
$806$	9.32437	−	4.06969i	0.328437	−	0.143349i
$807$	15.6520	−	21.5901i	0.550977	−	0.760009i
$808$	−1.76510	+	5.05095i	−0.0620958	+	0.177692i
$809$			32.0544i			1.12697i	0.826126	+	0.563486i	$0.190540\pi$
$809$			32.0544i			1.12697i	−0.826126	+	0.563486i	$0.809460\pi$
$810$	4.24195	−	7.29328i	0.149047	−	0.256260i
$811$		−	43.4869i		−	1.52703i	−0.645789	−	0.763516i	$-0.723471\pi$
$811$		−	43.4869i		−	1.52703i	0.645789	−	0.763516i	$-0.276529\pi$
$812$	54.1504	−	58.3921i	1.90031	−	2.04916i
$813$	13.9203	−	19.2014i	0.488206	−	0.673424i
$814$	−5.98998	−	13.7241i	−0.209949	−	0.481030i
$815$	5.40221			0.189231
$816$	−11.5070	−	7.08577i	−0.402827	−	0.248052i
$817$	0.0512007			0.00179129
$818$	−17.4147	−	39.9002i	−0.608892	−	1.39508i
$819$	−15.5565	+	5.09026i	−0.543587	+	0.177868i
$820$	−6.64465	+	7.16513i	−0.232041	+	0.250217i
$821$		−	7.67640i		−	0.267908i	−0.990988	−	0.133954i	$-0.957233\pi$
$821$		−	7.67640i		−	0.267908i	0.990988	−	0.133954i	$-0.0427675\pi$
$822$	4.67059	+	1.02360i	0.162906	+	0.0357022i
$823$			30.4699i			1.06211i	0.847336	+	0.531057i	$0.178205\pi$
$823$			30.4699i			1.06211i	−0.847336	+	0.531057i	$0.821795\pi$
$824$	13.5522	−	38.7808i	0.472115	−	1.35099i
$825$	9.60628	+	6.96417i	0.334448	+	0.242461i
$826$	−39.6028	+	17.2849i	−1.37796	+	0.601419i
$827$	−23.2164			−0.807312			−0.403656	−	0.914911i	$-0.632261\pi$
$827$	−23.2164			−0.807312			−0.403656	+	0.914911i	$0.632261\pi$
$828$	−5.45005	−	2.50938i	−0.189402	−	0.0872069i
$829$	40.2010			1.39624			0.698118	−	0.715982i	$-0.254021\pi$
$829$	40.2010			1.39624			0.698118	+	0.715982i	$0.254021\pi$
$830$	1.15529	−	0.504235i	0.0401007	−	0.0175022i
$831$	8.71326	+	6.31677i	0.302260	+	0.219126i
$832$	7.41864	+	5.90628i	0.257195	+	0.204764i
$833$		−	27.6728i		−	0.958807i
$834$	−41.1729	−	9.02341i	−1.42570	−	0.312455i
$835$		−	6.33616i		−	0.219272i
$836$	0.0241267	+	0.0223741i	0.000834438	+	0.000773824i
$837$	30.0230	+	9.65200i	1.03775	+	0.333622i
$838$	−4.82876	−	11.0635i	−0.166807	−	0.382183i
$839$	−9.40046			−0.324540			−0.162270	−	0.986746i	$-0.551882\pi$
$839$	−9.40046			−0.324540			−0.162270	+	0.986746i	$0.551882\pi$
$840$	−8.53039	−	12.2750i	−0.294326	−	0.423528i
$841$	−45.8314			−1.58039
$842$	1.24849	+	2.86052i	0.0430260	+	0.0985801i
$843$	28.4023	−	39.1777i	0.978227	−	1.34935i
$844$	10.5632	+	9.79585i	0.363599	+	0.337187i
$845$			7.68618i			0.264413i
$846$	31.8349	−	28.3618i	1.09451	−	0.975099i
$847$		−	40.2474i		−	1.38292i
$848$	3.29199	−	0.248499i	0.113047	−	0.00853348i
$849$	19.1724	−	26.4461i	0.657995	−	0.907628i
$850$	11.5299	−	5.03230i	0.395472	−	0.172607i
$851$	−7.04924			−0.241645
$852$	−30.3953	+	6.02823i	−1.04133	+	0.206524i
$853$	−7.38619			−0.252898			−0.126449	−	0.991973i	$-0.540358\pi$
$853$	−7.38619			−0.252898			−0.126449	+	0.991973i	$0.540358\pi$
$854$	72.2908	−	31.5519i	2.47374	−	1.07968i
$855$	0.00677386	+	0.0207017i	0.000231661	+	0.000707985i
$856$	29.2977	+	10.2383i	1.00137	+	0.349938i
$857$		−	40.2854i		−	1.37612i	−0.725652	−	0.688062i	$-0.758462\pi$
$857$		−	40.2854i		−	1.37612i	0.725652	−	0.688062i	$-0.241538\pi$
$858$	0.933634	−	4.26008i	0.0318737	−	0.145437i
$859$			26.0548i			0.888977i	0.895785	+	0.444488i	$0.146615\pi$
$859$			26.0548i			0.888977i	−0.895785	+	0.444488i	$0.853385\pi$
$860$	4.21410	−	4.54420i	0.143700	−	0.154956i
$861$	47.5765	+	34.4911i	1.62140	+	1.17545i
$862$	−19.5675	−	44.8325i	−0.666471	−	1.52700i
$863$	−12.4780			−0.424756			−0.212378	−	0.977188i	$-0.568121\pi$
$863$	−12.4780			−0.424756			−0.212378	+	0.977188i	$0.568121\pi$
$864$	5.14163	+	28.9407i	0.174922	+	0.984582i
$865$	5.30535			0.180387
$866$	5.77245	+	13.2257i	0.196156	+	0.449428i
$867$	−18.5041	−	13.4147i	−0.628432	−	0.455589i
$868$	37.9918	−	40.9677i	1.28952	−	1.39053i
$869$		−	14.1679i		−	0.480613i
$870$	−3.00697	+	13.7205i	−0.101946	+	0.465169i
$871$			0.962881i			0.0326260i
$872$	−8.11851	−	2.83708i	−0.274928	−	0.0960756i
$873$	15.4365	+	47.1759i	0.522447	+	1.59666i
$874$	0.0141966	−	0.00619620i	0.000480207	−	0.000209590i
$875$	29.1717			0.986184
$876$	−45.2169	+	8.96777i	−1.52774	+	0.302993i
$877$	4.48172			0.151337			0.0756685	−	0.997133i	$-0.475891\pi$
$877$	4.48172			0.151337			0.0756685	+	0.997133i	$0.475891\pi$
$878$	−4.98377	+	2.17520i	−0.168194	+	0.0734095i
$879$	−29.8188	+	41.1316i	−1.00576	+	1.38734i
$880$	3.97152	−	0.299793i	0.133880	−	0.0101060i
$881$		−	0.826411i		−	0.0278425i	−0.999903	−	0.0139212i	$-0.995569\pi$
$881$		−	0.826411i		−	0.0278425i	0.999903	−	0.0139212i	$-0.00443141\pi$
$882$	−44.9428	+	40.0397i	−1.51330	+	1.34821i
$883$			2.87077i			0.0966090i	0.998833	+	0.0483045i	$0.0153818\pi$
$883$			2.87077i			0.0966090i	−0.998833	+	0.0483045i	$0.984618\pi$
$884$	−3.39052	−	3.14423i	−0.114036	−	0.105752i
$885$	4.47338	−	6.17051i	0.150371	−	0.207420i
$886$	6.00903	+	13.7677i	0.201877	+	0.462536i
$887$	4.77944			0.160478			0.0802389	−	0.996776i	$-0.474432\pi$
$887$	4.77944			0.160478			0.0802389	+	0.996776i	$0.474432\pi$
$888$	19.7076	+	28.3587i	0.661343	+	0.951655i
$889$	29.1021			0.976053
$890$	2.36410	+	5.41657i	0.0792448	+	0.181564i
$891$	10.9038	−	7.99131i	0.365290	−	0.267719i
$892$	22.5203	+	20.8844i	0.754035	+	0.699261i
$893$			0.110072i			0.00368341i
$894$	44.4044	+	9.73160i	1.48510	+	0.325474i
$895$			6.62982i			0.221610i
$896$	50.3149	+	13.4306i	1.68090	+	0.448685i
$897$	−1.66220	−	1.20503i	−0.0554993	−	0.0402348i
$898$	−11.2643	+	4.91637i	−0.375894	+	0.164061i
$899$	−52.5015			−1.75102
$900$	−24.8554	−	11.4442i	−0.828513	−	0.381474i
$901$	−1.60985			−0.0536320
$902$	−14.3500	+	6.26315i	−0.477802	+	0.208540i
$903$	−30.1735	−	21.8746i	−1.00411	−	0.727941i
$904$	16.0272	−	45.8630i	0.533056	−	1.52538i
$905$		−	6.61903i		−	0.220024i
$906$	−5.08355	−	1.11410i	−0.168890	−	0.0370136i
$907$			27.4514i			0.911508i	0.890106	+	0.455754i	$0.150630\pi$
$907$			27.4514i			0.911508i	−0.890106	+	0.455754i	$0.849370\pi$
$908$	−4.08165	+	4.40137i	−0.135454	+	0.146065i
$909$	−5.39364	+	1.76486i	−0.178896	+	0.0585369i
$910$	−2.04602	−	4.68779i	−0.0678249	−	0.155399i
$911$	−2.48679			−0.0823910			−0.0411955	−	0.999151i	$-0.513117\pi$
$911$	−2.48679			−0.0823910			−0.0411955	+	0.999151i	$0.513117\pi$
$912$	−0.0646164	−	0.0397893i	−0.00213966	−	0.00131756i
$913$	2.01971			0.0668428
$914$	17.5439	+	40.1962i	0.580301	+	1.32957i
$915$	−8.16570	+	11.2636i	−0.269950	+	0.372365i
$916$	−14.7048	+	15.8566i	−0.485860	+	0.523918i
$917$			50.0088i			1.65144i
$918$	−1.43785	−	14.2611i	−0.0474562	−	0.470688i
$919$		−	22.6168i		−	0.746060i	−0.927819	−	0.373030i	$-0.878319\pi$
$919$		−	22.6168i		−	0.746060i	0.927819	−	0.373030i	$-0.121681\pi$
$920$	0.618529	−	1.76997i	0.0203923	−	0.0583541i
$921$	0.912126	−	1.25817i	0.0300556	−	0.0414582i
$922$	34.2141	−	14.9330i	1.12678	−	0.491792i
$923$	−10.6031			−0.349005
$924$	−4.65934	−	23.4931i	−0.153281	−	0.772868i
$925$	−32.1486			−1.05704
$926$	11.1347	−	4.85982i	0.365909	−	0.159703i
$927$	41.4119	−	13.5505i	1.36015	−	0.445056i
$928$	−22.8950	−	43.2484i	−0.751566	−	1.41970i
$929$		−	13.8280i		−	0.453683i	−0.973932	−	0.226842i	$-0.927160\pi$
$929$		−	13.8280i		−	0.453683i	0.973932	−	0.226842i	$-0.0728400\pi$
$930$	−2.10968	+	9.62627i	−0.0691792	+	0.315658i
$931$		−	0.155393i		−	0.00509281i
$932$	−8.42381	−	7.81190i	−0.275931	−	0.255887i
$933$	−33.7111	−	24.4393i	−1.10365	−	0.800105i
$934$	−0.812371	−	1.86128i	−0.0265816	−	0.0609031i
$935$	−1.94216			−0.0635153
$936$	−0.200748	+	10.0558i	−0.00656166	+	0.328686i
$937$	2.30323			0.0752434			0.0376217	−	0.999292i	$-0.488022\pi$
$937$	2.30323			0.0752434			0.0376217	+	0.999292i	$0.488022\pi$
$938$	2.11526	+	4.84644i	0.0690658	+	0.158242i
$939$	−14.7048	−	10.6604i	−0.479873	−	0.347889i
$940$	9.76916	+	9.05952i	0.318635	+	0.295489i
$941$			13.9365i			0.454318i	0.973858	+	0.227159i	$0.0729438\pi$
$941$			13.9365i			0.454318i	−0.973858	+	0.227159i	$0.927056\pi$
$942$	−2.38616	+	10.8878i	−0.0777453	+	0.354744i
$943$			7.37072i			0.240024i
$944$	1.99861	+	26.4766i	0.0650492	+	0.861741i
$945$	4.85250	−	15.0939i	0.157852	−	0.491006i
$946$	9.10090	−	3.97216i	0.295896	−	0.129146i
$947$	−43.1835			−1.40328			−0.701638	−	0.712533i	$-0.747548\pi$
$947$	−43.1835			−1.40328			−0.701638	+	0.712533i	$0.747548\pi$
$948$	6.35641	+	32.0500i	0.206447	+	1.04094i
$949$	−15.7735			−0.512028
$950$	0.0647447	−	0.0282583i	0.00210059	−	0.000916820i
$951$	−33.0149	+	45.5403i	−1.07058	+	1.47675i
$952$	−23.9727	−	8.37745i	−0.776959	−	0.271515i
$953$		−	55.6088i		−	1.80134i	−0.434499	−	0.900672i	$-0.643075\pi$
$953$		−	55.6088i		−	1.80134i	0.434499	−	0.900672i	$-0.356925\pi$
$954$	2.32929	+	2.61453i	0.0754135	+	0.0846484i
$955$		−	13.4038i		−	0.433736i
$956$	16.4775	−	17.7682i	0.532920	−	0.574664i
$957$	−13.2097	+	18.2212i	−0.427008	+	0.589008i
$958$	14.1390	+	32.3950i	0.456812	+	1.04664i
$959$	8.98506			0.290143
$960$	−8.84970	+	2.45999i	−0.285623	+	0.0793960i
$961$	−5.83484			−0.188221
$962$	4.72688	+	10.8301i	0.152401	+	0.349177i
$963$	10.2370	+	31.2854i	0.329881	+	1.00816i
$964$	5.98294	−	6.45159i	0.192698	−	0.207792i
$965$			8.18384i			0.263447i
$966$	−11.0135	−	2.41371i	−0.354354	−	0.0776599i
$967$			9.62160i			0.309410i	0.987961	+	0.154705i	$0.0494427\pi$
$967$			9.62160i			0.309410i	−0.987961	+	0.154705i	$0.950557\pi$
$968$	−23.3467	−	8.15867i	−0.750390	−	0.262230i
$969$	0.0299593	+	0.0217193i	0.000962431	+	0.000697725i
$970$	−14.2160	+	6.20467i	−0.456448	+	0.199220i
$971$	−52.4944			−1.68463			−0.842313	−	0.538989i	$-0.818806\pi$
$971$	−52.4944			−1.68463			−0.842313	+	0.538989i	$0.818806\pi$
$972$	−21.0808	+	22.9696i	−0.676166	+	0.736749i
$973$	−79.2066			−2.53925
$974$	−0.542483	+	0.236770i	−0.0173823	+	0.00758661i
$975$	−7.58061	−	5.49564i	−0.242774	−	0.176001i
$976$	−3.64826	−	48.3304i	−0.116778	−	1.54702i
$977$			37.8221i			1.21004i	0.796212	+	0.605018i	$0.206834\pi$
$977$			37.8221i			1.21004i	−0.796212	+	0.605018i	$0.793166\pi$
$978$	−19.4994	−	4.27345i	−0.623520	−	0.136650i
$979$			9.46941i			0.302644i
$980$	−13.7916	−	12.7897i	−0.440556	−	0.408554i
$981$	−2.83671	−	8.66933i	−0.0905691	−	0.276790i
$982$	10.2194	+	23.4144i	0.326114	+	0.747184i
$983$	−30.2061			−0.963424			−0.481712	−	0.876330i	$-0.659985\pi$
$983$	−30.2061			−0.963424			−0.481712	+	0.876330i	$0.659985\pi$
$984$	29.6520	−	20.6063i	0.945270	−	0.656906i
$985$	−2.51441			−0.0801157
$986$	9.54528	+	21.8699i	0.303984	+	0.696480i
$987$	47.0263	−	64.8673i	1.49686	−	2.06475i
$988$	−0.0190391	−	0.0176561i	−0.000605714	−	0.000561714i
$989$		−	4.67459i		−	0.148643i
$990$	2.81009	+	3.15421i	0.0893107	+	0.100247i
$991$			5.10465i			0.162155i	0.996708	+	0.0810773i	$0.0258361\pi$
$991$			5.10465i			0.162155i	−0.996708	+	0.0810773i	$0.974164\pi$
$992$	−16.0631	−	30.3429i	−0.510003	−	0.963389i
$993$	−0.710041	+	0.979419i	−0.0225325	+	0.0310809i
$994$	−53.3682	+	23.2929i	−1.69274	+	0.738807i
$995$	−11.7975			−0.374007
$996$	−4.56891	+	0.906142i	−0.144772	+	0.0287122i
$997$	31.9741			1.01263			0.506315	−	0.862349i	$-0.331007\pi$
$997$	31.9741			1.01263			0.506315	+	0.862349i	$0.331007\pi$
$998$	−20.8777	+	9.11221i	−0.660871	+	0.288442i
$999$	−11.2106	+	34.8712i	−0.354689	+	1.10328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.a.47.7	✓	22
3.2	odd	2		276.2.c.b.47.16	yes	22
4.3	odd	2		276.2.c.b.47.15	yes	22
12.11	even	2	inner	276.2.c.a.47.8	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.7	✓	22	1.1	even	1	trivial
276.2.c.a.47.8	yes	22	12.11	even	2	inner
276.2.c.b.47.15	yes	22	4.3	odd	2
276.2.c.b.47.16	yes	22	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.565709 - 1.29614i) q^{2} +(-1.40231 - 1.01662i) q^{3} +(-1.35995 + 1.46647i) q^{4} -0.662888i q^{5} +(-0.524382 + 2.39270i) q^{6} +4.60297i q^{7} +(2.67009 + 0.933083i) q^{8} +(0.932961 + 2.85124i) q^{9} +O(q^{10})\)	\(q+(-0.565709 - 1.29614i) q^{2} +(-1.40231 - 1.01662i) q^{3} +(-1.35995 + 1.46647i) q^{4} -0.662888i q^{5} +(-0.524382 + 2.39270i) q^{6} +4.60297i q^{7} +(2.67009 + 0.933083i) q^{8} +(0.932961 + 2.85124i) q^{9} +(-0.859194 + 0.375001i) q^{10} -1.50207 q^{11} +(3.39792 - 0.673902i) q^{12} +1.18533 q^{13} +(5.96608 - 2.60394i) q^{14} +(-0.673906 + 0.929576i) q^{15} +(-0.301087 - 3.98865i) q^{16} +1.95053i q^{17} +(3.16782 - 2.82222i) q^{18} +0.0109530i q^{19} +(0.972107 + 0.901492i) q^{20} +(4.67948 - 6.45480i) q^{21} +(0.849734 + 1.94689i) q^{22} +1.00000 q^{23} +(-2.79570 - 4.02294i) q^{24} +4.56058 q^{25} +(-0.670551 - 1.53635i) q^{26} +(1.59033 - 4.94680i) q^{27} +(-6.75013 - 6.25979i) q^{28} +8.65051i q^{29} +(1.58609 + 0.347606i) q^{30} +6.06917i q^{31} +(-4.99952 + 2.64667i) q^{32} +(2.10637 + 1.52704i) q^{33} +(2.52816 - 1.10343i) q^{34} +3.05125 q^{35} +(-5.45005 - 2.50938i) q^{36} -7.04924 q^{37} +(0.0141966 - 0.00619620i) q^{38} +(-1.66220 - 1.20503i) q^{39} +(0.618529 - 1.76997i) q^{40} +7.37072i q^{41} +(-11.0135 - 2.41371i) q^{42} -4.67459i q^{43} +(2.04274 - 2.20275i) q^{44} +(1.89005 - 0.618448i) q^{45} +(-0.565709 - 1.29614i) q^{46} +10.0495 q^{47} +(-3.63273 + 5.89943i) q^{48} -14.1873 q^{49} +(-2.57996 - 5.91114i) q^{50} +(1.98296 - 2.73526i) q^{51} +(-1.61199 + 1.73825i) q^{52} +0.825339i q^{53} +(-7.31140 + 0.737158i) q^{54} +0.995704i q^{55} +(-4.29495 + 12.2903i) q^{56} +(0.0111350 - 0.0153595i) q^{57} +(11.2123 - 4.89367i) q^{58} -6.63799 q^{59} +(-0.446721 - 2.25244i) q^{60} +12.1170 q^{61} +(7.86648 - 3.43338i) q^{62} +(-13.1242 + 4.29439i) q^{63} +(6.25871 + 4.98282i) q^{64} -0.785740i q^{65} +(0.787658 - 3.59401i) q^{66} +0.812332i q^{67} +(-2.86041 - 2.65262i) q^{68} +(-1.40231 - 1.01662i) q^{69} +(-1.72612 - 3.95484i) q^{70} -8.94527 q^{71} +(-0.169361 + 8.48359i) q^{72} -13.3072 q^{73} +(3.98782 + 9.13679i) q^{74} +(-6.39536 - 4.63638i) q^{75} +(-0.0160623 - 0.0148955i) q^{76} -6.91398i q^{77} +(-0.621565 + 2.83614i) q^{78} +9.43225i q^{79} +(-2.64403 + 0.199587i) q^{80} +(-7.25917 + 5.32019i) q^{81} +(9.55347 - 4.16968i) q^{82} -1.34462 q^{83} +(3.10195 + 15.6405i) q^{84} +1.29299 q^{85} +(-6.05891 + 2.64445i) q^{86} +(8.79430 - 12.1307i) q^{87} +(-4.01066 - 1.40156i) q^{88} -6.30424i q^{89} +(-1.87081 - 2.09991i) q^{90} +5.45603i q^{91} +(-1.35995 + 1.46647i) q^{92} +(6.17005 - 8.51087i) q^{93} +(-5.68507 - 13.0255i) q^{94} +0.00726060 q^{95} +(9.70154 + 1.37117i) q^{96} +16.5457 q^{97} +(8.02588 + 18.3887i) q^{98} +(-1.40137 - 4.28277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * q^96 - 4 * q^97 + 64 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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