LMFDB - Embedded newform 276.2.c.b.47.16

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			47.16
Character	$\chi$	$=$	276.47
Dual form			276.2.c.b.47.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.565709 + 1.29614i) q^{2} +(1.40231 - 1.01662i) q^{3} +(-1.35995 + 1.46647i) q^{4} +0.662888i q^{5} +(2.11098 + 1.24248i) q^{6} +4.60297i q^{7} +(-2.67009 - 0.933083i) q^{8} +(0.932961 - 2.85124i) q^{9} +O(q^{10})$	\(q+(0.565709 + 1.29614i) q^{2} +(1.40231 - 1.01662i) q^{3} +(-1.35995 + 1.46647i) q^{4} +0.662888i q^{5} +(2.11098 + 1.24248i) 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} +(-0.416223 + 3.43901i) 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} +(4.22339 - 0.403727i) 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} +(-4.69289 + 1.40599i) 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} +(-0.823624 + 1.39934i) 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} +(2.91249 + 5.24570i) 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} +(-5.71909 + 9.71678i) 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} +(-4.47717 - 5.28725i) 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} +(5.51207 - 4.85974i) 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} +(-2.27967 - 0.275909i) 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} +(3.17084 + 1.86629i) 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} +(-5.15153 + 6.74253i) 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} +(2.50221 + 1.47275i) 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} +(-15.8296 - 1.91586i) 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} +(0.267626 + 2.79963i) 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} +(4.32023 - 8.79407i) 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 + 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q + 9 * q^8 - 2 * q^9	$ 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) $ 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * 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	$0.0473564\pi$
$5$			0.662888i			0.296452i	−0.988953	+	0.148226i	$0.952644\pi$
$6$	2.11098	+	1.24248i	0.861805	+	0.507240i
$7$			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	$-0.427289\pi$
$11$	1.50207			0.452891			0.226446	+	0.974024i	$0.427289\pi$
$12$	−0.416223	+	3.43901i	−0.120153	+	0.992755i
$13$	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	$-0.923988\pi$
$17$		−	1.95053i		−	0.473074i	0.971622	−	0.236537i	$-0.0760125\pi$
$18$	4.22339	−	0.403727i	0.995462	−	0.0951594i
$19$			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
$24$	−4.69289	+	1.40599i	−0.957931	+	0.286997i
$25$	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	$-0.703140\pi$
$29$		−	8.65051i		−	1.60636i	0.595736	−	0.803180i	$-0.296860\pi$
$30$	−0.823624	+	1.39934i	−0.150372	+	0.255484i
$31$			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
$36$	2.91249	+	5.24570i	0.485416	+	0.874284i
$37$	−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	$-0.804786\pi$
$41$		−	7.37072i		−	1.15111i	0.817762	−	0.575556i	$-0.195214\pi$
$42$	−5.71909	+	9.71678i	−0.882474	+	1.49933i
$43$		−	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	$-0.761849\pi$
$47$	−10.0495			−1.46587			−0.732933	+	0.680301i	$0.761849\pi$
$48$	−4.47717	−	5.28725i	−0.646224	−	0.763148i
$49$	−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	$-0.981947\pi$
$53$		−	0.825339i		−	0.113369i	0.998392	−	0.0566845i	$-0.0180529\pi$
$54$	5.51207	−	4.85974i	0.750098	−	0.661327i
$55$			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	$-0.357774\pi$
$59$	6.63799			0.864193			0.432096	+	0.901827i	$0.357774\pi$
$60$	−2.27967	−	0.275909i	−0.294305	−	0.0356197i
$61$	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
$66$	3.17084	+	1.86629i	0.390304	+	0.229724i
$67$			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	$-0.321890\pi$
$71$	8.94527			1.06161			0.530804	+	0.847495i	$0.321890\pi$
$72$	−5.15153	+	6.74253i	−0.607114	+	0.794615i
$73$	−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
$78$	2.50221	+	1.47275i	0.283319	+	0.166756i
$79$			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	$-0.476489\pi$
$83$	1.34462			0.147591			0.0737956	+	0.997273i	$0.476489\pi$
$84$	−15.8296	−	1.91586i	−1.72715	−	0.209037i
$85$	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	$0.108440\pi$
$89$			6.30424i			0.668248i	−0.942529	+	0.334124i	$0.891560\pi$
$90$	0.267626	+	2.79963i	0.0282102	+	0.295107i
$91$			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
$96$	4.32023	−	8.79407i	0.440931	−	0.897541i
$97$	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	$-0.969998\pi$
$101$		−	1.89168i		−	0.188229i	0.995561	−	0.0941147i	$-0.0300020\pi$
$102$	2.42350	−	4.11754i	0.239962	−	0.407698i
$103$		−	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	$-0.677950\pi$
$107$	−10.9726			−1.06076			−0.530378	+	0.847761i	$0.677950\pi$
$108$	9.41712	+	4.39521i	0.906163	+	0.422929i
$109$	−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	$0.299406\pi$
$113$			17.1766i			1.61584i	−0.589293	+	0.807919i	$0.700594\pi$
$114$	−0.0136089	+	0.0231216i	−0.00127459	+	0.00216553i
$115$		−	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
$120$	−0.932016	−	3.11086i	−0.0850810	−	0.283981i
$121$	−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
$126$	1.85834	+	19.4401i	0.165554	+	1.73186i
$127$		−	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	$-0.657413\pi$
$131$	−10.8645			−0.949234			−0.474617	+	0.880193i	$0.657413\pi$
$132$	−0.625196	+	5.16563i	−0.0544163	+	0.449610i
$133$	−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	$0.0265734\pi$
$137$			1.95202i			0.166772i	−0.996517	+	0.0833860i	$0.973427\pi$
$138$	−2.11098	−	1.24248i	−0.179699	−	0.105767i
$139$			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
$144$	−11.6535	−	2.86278i	−0.971126	−	0.238565i
$145$	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	$0.274887\pi$
$149$			18.5582i			1.52035i	−0.649718	+	0.760175i	$0.725113\pi$
$150$	9.62730	+	5.66642i	0.786066	+	0.462662i
$151$			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
$156$	−0.493361	+	4.07635i	−0.0395005	+	0.326370i
$157$	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
$162$	2.78913	−	12.4186i	0.219135	−	0.975695i
$163$			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	$-0.620583\pi$
$167$	−9.55842			−0.739652			−0.369826	+	0.929101i	$0.620583\pi$
$168$	−6.47174	−	21.6012i	−0.499306	−	1.66657i
$169$	−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	$-0.901596\pi$
$173$		−	8.00339i		−	0.608487i	0.952594	−	0.304243i	$-0.0984036\pi$
$174$	10.7481	−	18.2611i	0.814810	−	1.38437i
$175$			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	$-0.378065\pi$
$179$	10.0014			0.747541			0.373771	+	0.927521i	$0.378065\pi$
$180$	−3.47731	+	1.93066i	−0.259183	+	0.143903i
$181$	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
$186$	−7.54082	+	12.8119i	−0.552919	+	0.939415i
$187$		−	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	$-0.761200\pi$
$191$	−20.2203			−1.46309			−0.731544	+	0.681794i	$0.761200\pi$
$192$	13.8423	+	0.624729i	0.998983	+	0.0450859i
$193$	−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	$0.0431433\pi$
$197$			3.79311i			0.270248i	−0.990829	+	0.135124i	$0.956857\pi$
$198$	6.34382	−	0.606427i	0.450836	−	0.0430969i
$199$		−	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
$204$	6.70790	+	0.811857i	0.469647	+	0.0568413i
$205$	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
$210$	−6.44114	−	3.79111i	−0.444481	−	0.261612i
$211$		−	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
$216$	−0.369450	+	14.6923i	−0.0251379	+	0.999684i
$217$	−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
$222$	−14.8808	−	8.75853i	−0.998736	−	0.587834i
$223$		−	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	$-0.531757\pi$
$227$	−3.00133			−0.199205			−0.0996026	+	0.995027i	$0.531757\pi$
$228$	−0.0376674	−	0.00455888i	−0.00249458	−	0.000301919i
$229$	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	$-0.939748\pi$
$233$		−	5.74427i		−	0.376319i	0.982138	−	0.188160i	$-0.0602523\pi$
$234$	5.00611	−	0.478550i	0.327259	−	0.0312838i
$235$		−	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	$-0.371829\pi$
$239$	12.1163			0.783737			0.391868	+	0.920021i	$0.371829\pi$
$240$	3.50485	−	2.96786i	0.226237	−	0.191575i
$241$	−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
$246$	9.15796	−	15.5595i	0.583890	−	0.992035i
$247$			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	$-0.237156\pi$
$251$	23.2910			1.47011			0.735056	+	0.678006i	$0.237156\pi$
$252$	−24.1458	+	13.4061i	−1.52104	+	0.844506i
$253$	−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	$-0.950871\pi$
$257$		−	4.92895i		−	0.307459i	0.988113	−	0.153730i	$-0.0491285\pi$
$258$	5.80807	−	9.86797i	0.361595	−	0.614353i
$259$		−	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	$-0.870983\pi$
$263$	−29.8066			−1.83795			−0.918977	+	0.394312i	$0.870983\pi$
$264$	−7.04904	+	2.11190i	−0.433839	+	0.129979i
$265$	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	$-0.844485\pi$
$269$		−	15.3961i		−	0.938717i	0.883008	−	0.469359i	$-0.155515\pi$
$270$	3.22146	+	3.65388i	0.196052	+	0.222368i
$271$			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
$276$	0.416223	−	3.43901i	0.0250537	−	0.207004i
$277$	−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	$-0.686438\pi$
$281$		−	27.9379i		−	1.66664i	0.552794	−	0.833318i	$-0.313562\pi$
$282$	−21.2143	−	12.4863i	−1.26329	−	0.743546i
$283$			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
$288$	−2.88193	−	16.7241i	−0.169820	−	0.985475i
$289$	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	$0.327536\pi$
$293$			29.3313i			1.71355i	−0.515688	+	0.856776i	$0.672464\pi$
$294$	−29.9492	−	17.6274i	−1.74667	−	1.02805i
$295$			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
$300$	−1.89822	+	15.6839i	−0.109594	+	0.905508i
$301$	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
$306$	−0.787484	−	8.23787i	−0.0450175	−	0.470927i
$307$			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	$-0.738708\pi$
$311$	−24.0397			−1.36316			−0.681582	+	0.731741i	$0.738708\pi$
$312$	−5.56262	+	1.66657i	−0.314921	+	0.0943507i
$313$	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	$0.365457\pi$
$317$			32.4751i			1.82399i	−0.410206	+	0.911993i	$0.634543\pi$
$318$	1.02547	−	1.74228i	0.0575053	−	0.0977020i
$319$		−	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
$324$	17.6740	−	3.41019i	0.981889	−	0.189455i
$325$	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
$330$	−1.23714	+	2.10191i	−0.0681024	+	0.115707i
$331$		−	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
$336$	24.3370	−	20.6083i	1.32769	−	1.12427i
$337$	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
$342$	0.00442202	+	0.0462587i	0.000239115	+	0.00250139i
$343$		−	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	$-0.476641\pi$
$347$	2.73153			0.146636			0.0733181	+	0.997309i	$0.476641\pi$
$348$	29.7492	+	3.60054i	1.59472	+	0.193009i
$349$	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	$-0.959439\pi$
$353$		−	4.77529i		−	0.254163i	0.991892	−	0.127082i	$-0.0405610\pi$
$354$	14.0127	+	8.24756i	0.744766	+	0.438353i
$355$			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	$-0.784523\pi$
$359$	−29.5385			−1.55898			−0.779492	+	0.626413i	$0.784523\pi$
$360$	−4.46954	−	3.41489i	−0.235566	−	0.179980i
$361$	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
$366$	25.5787	+	15.0551i	1.33702	+	0.786942i
$367$			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
$372$	−20.8719	−	2.52613i	−1.08216	−	0.130974i
$373$	−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
$378$	22.3692	+	25.3719i	1.15055	+	1.30499i
$379$		−	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	$-0.574154\pi$
$383$	−9.03605			−0.461721			−0.230860	+	0.972987i	$0.574154\pi$
$384$	7.02098	+	18.2950i	0.358288	+	0.933611i
$385$	−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	$-0.704309\pi$
$389$		−	31.5958i		−	1.60197i	0.598683	−	0.800986i	$-0.295691\pi$
$390$	−0.976266	+	1.65868i	−0.0494351	+	0.0839907i
$391$			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
$396$	4.37477	+	7.87941i	0.219840	+	0.395955i
$397$	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	$0.130038\pi$
$401$			15.9102i			0.794518i	−0.917707	+	0.397259i	$0.869962\pi$
$402$	−1.00931	+	1.71482i	−0.0503396	+	0.0855274i
$403$			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
$408$	2.74244	+	9.15364i	0.135771	+	0.453173i
$409$	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
$414$	−4.22339	+	0.403727i	−0.207568	+	0.0198421i
$415$			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	$-0.566858\pi$
$419$	−8.53577			−0.417000			−0.208500	+	0.978022i	$0.566858\pi$
$420$	1.27000	−	10.4933i	0.0619696	−	0.512019i
$421$	−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
$426$	18.8833	+	11.1143i	0.914899	+	0.538490i
$427$			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	$-0.813410\pi$
$431$	−34.5893			−1.66611			−0.833055	+	0.553191i	$0.813410\pi$
$432$	−19.2522	+	7.83270i	−0.926274	+	0.376851i
$433$	−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
$438$	−28.0913	−	16.5340i	−1.34226	−	0.790023i
$439$		−	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	$-0.418801\pi$
$443$	10.6221			0.504673			0.252336	+	0.967640i	$0.418801\pi$
$444$	2.93405	−	24.2424i	0.139244	−	1.15049i
$445$	−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	$0.0657417\pi$
$449$			8.69064i			0.410137i	−0.978748	+	0.205068i	$0.934258\pi$
$450$	19.2611	−	1.84123i	0.907977	−	0.0867964i
$451$		−	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
$456$	−0.0153998	−	0.0514011i	−0.000721163	−	0.00240708i
$457$	−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	$-0.789271\pi$
$461$		−	26.3970i		−	1.22943i	0.788750	−	0.614715i	$-0.210729\pi$
$462$	−8.59047	+	14.5953i	−0.399665	+	0.679034i
$463$			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	$-0.510578\pi$
$467$	−1.43602			−0.0664512			−0.0332256	+	0.999448i	$0.510578\pi$
$468$	3.45226	+	6.21788i	0.159581	+	0.287422i
$469$	−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
$474$	−11.7194	+	19.9113i	−0.538289	+	0.914557i
$475$			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	$-0.306559\pi$
$479$	24.9935			1.14198			0.570991	+	0.820956i	$0.306559\pi$
$480$	5.82948	+	2.86383i	0.266078	+	0.130715i
$481$	−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
$486$	−8.71375	−	20.2502i	−0.395264	−	0.918568i
$487$		−	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	$-0.366357\pi$
$491$	18.0648			0.815251			0.407626	+	0.913149i	$0.366357\pi$
$492$	25.3479	+	3.06786i	1.14277	+	0.138310i
$493$	−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
$498$	2.83847	+	1.67066i	0.127195	+	0.0748642i
$499$		−	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	$-0.516246\pi$
$503$	−2.28839			−0.102034			−0.0510172	+	0.998698i	$0.516246\pi$
$504$	−31.0357	−	23.7123i	−1.38244	−	1.05623i
$505$	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	$0.0573111\pi$
$509$			8.08033i			0.358154i	−0.983835	+	0.179077i	$0.942689\pi$
$510$	2.72947	+	1.60651i	0.120863	+	0.0711373i
$511$		−	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
$516$	16.0759	+	1.94567i	0.707703	+	0.0856533i
$517$	−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	$0.0257121\pi$
$521$			3.68353i			0.161378i	−0.996739	+	0.0806891i	$0.974288\pi$
$522$	−3.49245	−	36.5345i	−0.152860	−	1.59907i
$523$			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
$528$	−6.72502	−	7.94181i	−0.292669	−	0.345623i
$529$	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
$534$	−7.83289	+	13.3081i	−0.338962	+	0.575900i
$535$		−	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
$540$	−2.91353	+	6.24249i	−0.125378	+	0.268634i
$541$	−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
$546$	−6.77900	+	11.5176i	−0.290115	+	0.492907i
$547$		−	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
$552$	4.69289	−	1.40599i	0.199743	−	0.0598431i
$553$	−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	$0.147591\pi$
$557$			21.1102i			0.894470i	−0.894417	+	0.447235i	$0.852409\pi$
$558$	2.45029	+	25.6325i	0.103729	+	1.08511i
$559$		−	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	$-0.531737\pi$
$563$	−4.72361			−0.199077			−0.0995383	+	0.995034i	$0.531737\pi$
$564$	4.18282	−	34.5602i	0.176128	−	1.45525i
$565$	−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	$0.0598375\pi$
$569$			8.91556i			0.373760i	−0.982383	+	0.186880i	$0.940162\pi$
$570$	−0.0153270	−	0.00902115i	−0.000641978	−	0.000377854i
$571$		−	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
$576$	20.0464	−	13.1963i	0.835265	−	0.549847i
$577$	−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
$582$	34.9277	+	20.5577i	1.44780	+	0.852145i
$583$		−	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	$-0.659812\pi$
$587$	−23.3188			−0.962471			−0.481236	+	0.876591i	$0.659812\pi$
$588$	5.90508	−	48.7902i	0.243521	−	2.01207i
$589$	−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	$-0.829993\pi$
$593$		−	24.7929i		−	1.01812i	0.860731	−	0.509061i	$-0.170007\pi$
$594$	8.27952	−	7.29967i	0.339713	−	0.299509i
$595$			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	$-0.446679\pi$
$599$	8.16134			0.333463			0.166732	+	0.986002i	$0.446679\pi$
$600$	−21.4023	+	6.41214i	−0.873745	+	0.261775i
$601$	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
$606$	2.35037	−	3.99331i	0.0954774	−	0.162217i
$607$			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
$612$	10.2319	−	5.68092i	0.413601	−	0.229638i
$613$	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	$-0.930399\pi$
$617$		−	10.7763i		−	0.433838i	0.976190	−	0.216919i	$-0.0696008\pi$
$618$	18.0460	−	30.6603i	0.725915	−	1.23334i
$619$			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
$624$	−5.30692	−	6.26713i	−0.212447	−	0.250886i
$625$	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
$630$	−12.8866	+	1.23187i	−0.513415	+	0.0490790i
$631$			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
$636$	2.83835	+	0.343525i	0.112548	+	0.0136216i
$637$	−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	$0.272018\pi$
$641$			38.1941i			1.50858i	−0.656543	+	0.754289i	$0.727982\pi$
$642$	−23.1629	−	13.6332i	−0.914165	−	0.538058i
$643$		−	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	$-0.316790\pi$
$647$	27.6906			1.08863			0.544315	+	0.838881i	$0.316790\pi$
$648$	14.4184	+	20.9788i	0.566409	+	0.824124i
$649$	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	$0.0849502\pi$
$653$			13.4782i			0.527444i	−0.964599	+	0.263722i	$0.915050\pi$
$654$	−6.41853	−	3.77781i	−0.250985	−	0.147724i
$655$		−	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	$-0.252750\pi$
$659$	35.9892			1.40194			0.700971	+	0.713190i	$0.252750\pi$
$660$	−3.42423	−	0.414435i	−0.133288	−	0.0161318i
$661$	−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
$666$	−29.7717	+	2.84597i	−1.15363	+	0.110279i
$667$			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
$672$	40.4788	+	19.8859i	1.56150	+	0.767114i
$673$	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	$-0.859999\pi$
$677$		−	22.1570i		−	0.851562i	0.904826	−	0.425781i	$-0.140001\pi$
$678$	−21.3416	+	36.2595i	−0.819617	+	1.39254i
$679$			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	$-0.302698\pi$
$683$	30.3631			1.16181			0.580907	+	0.813970i	$0.302698\pi$
$684$	−0.0574561	+	0.0319005i	−0.00219689	+	0.00121975i
$685$	−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
$690$	0.823624	−	1.39934i	0.0313548	−	0.0532721i
$691$			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
$696$	12.1626	+	40.5959i	0.461021	+	1.53878i
$697$	−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	$0.134801\pi$
$701$			21.7606i			0.821888i	−0.911661	+	0.410944i	$0.865199\pi$
$702$	6.53362	−	5.76039i	0.246596	−	0.217412i
$703$		−	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
$708$	−2.76288	+	22.8281i	−0.103835	+	0.857932i
$709$	−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
$714$	18.9529	+	11.1553i	0.709295	+	0.417476i
$715$			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	$-0.373888\pi$
$719$	20.6957			0.771818			0.385909	+	0.922537i	$0.373888\pi$
$720$	1.89770	−	7.72497i	0.0707233	−	0.287893i
$721$	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
$726$	−18.4580	−	10.8640i	−0.685040	−	0.403200i
$727$			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
$732$	−5.04336	+	41.6703i	−0.186408	+	1.54018i
$733$	−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
$738$	−2.97576	−	31.1294i	−0.109539	−	1.14589i
$739$		−	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	$-0.481722\pi$
$743$	3.12875			0.114783			0.0573913	+	0.998352i	$0.481722\pi$
$744$	−8.53321	−	28.4819i	−0.312843	−	1.04420i
$745$	−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
$750$	−7.87432	+	13.3785i	−0.287530	+	0.488515i
$751$			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
$756$	−20.2310	+	43.3467i	−0.735794	+	1.57650i
$757$	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	$0.115547\pi$
$761$			19.5908i			0.710165i	−0.934835	+	0.355082i	$0.884453\pi$
$762$	7.85553	−	13.3466i	0.284576	−	0.483497i
$763$		−	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
$768$	−19.7410	+	19.4498i	−0.712341	+	0.701834i
$769$	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	$-0.727346\pi$
$773$		−	42.0157i		−	1.51120i	0.655035	−	0.755599i	$-0.272654\pi$
$774$	−1.88726	−	19.7426i	−0.0678361	−	0.709633i
$775$			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
$780$	−2.70217	−	0.327043i	−0.0967530	−	0.0117100i
$781$	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
$786$	−22.9347	−	13.4989i	−0.818054	−	0.481489i
$787$			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
$792$	−7.73796	+	10.1278i	−0.274956	+	0.359874i
$793$	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	$0.178860\pi$
$797$			30.0832i			1.06560i	−0.846241	+	0.532800i	$0.821140\pi$
$798$	−0.106428	−	0.0626411i	−0.00376750	−	0.00221747i
$799$			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
$804$	−2.79361	−	0.338111i	−0.0985232	−	0.0119243i
$805$	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	$-0.809460\pi$
$809$		−	32.0544i		−	1.12697i	0.826126	−	0.563486i	$-0.190540\pi$
$810$	8.23212	+	1.84888i	0.289247	+	0.0649630i
$811$		−	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
$816$	−10.3130	+	8.73287i	−0.361026	+	0.305712i
$817$	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	$0.0427675\pi$
$821$			7.67640i			0.267908i	−0.990988	+	0.133954i	$0.957233\pi$
$822$	−2.42534	+	4.12067i	−0.0845934	+	0.143725i
$823$			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	$-0.367739\pi$
$827$	23.2164			0.807312			0.403656	+	0.914911i	$0.367739\pi$
$828$	−2.91249	−	5.24570i	−0.101216	−	0.182301i
$829$	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
$834$	−21.3802	+	36.3252i	−0.740337	+	1.25784i
$835$		−	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	$-0.448118\pi$
$839$	9.40046			0.324540			0.162270	+	0.986746i	$0.448118\pi$
$840$	14.3192	−	4.29004i	0.494058	−	0.148020i
$841$	−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
$846$	−42.4428	+	4.05724i	−1.45921	+	0.139491i
$847$		−	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
$852$	−3.72322	+	30.7628i	−0.127556	+	1.05392i
$853$	−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	$0.241538\pi$
$857$			40.2854i			1.37612i	−0.725652	+	0.688062i	$0.758462\pi$
$858$	3.75849	+	2.21217i	0.128313	+	0.0755222i
$859$			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	$-0.431879\pi$
$863$	12.4780			0.424756			0.212378	+	0.977188i	$0.431879\pi$
$864$	−21.0434	−	20.5225i	−0.715912	−	0.698191i
$865$	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
$870$	12.1051	+	7.12477i	0.410400	+	0.241552i
$871$			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
$876$	5.53877	−	45.7637i	0.187138	−	1.54621i
$877$	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	$0.00443141\pi$
$881$			0.826411i			0.0278425i	−0.999903	+	0.0139212i	$0.995569\pi$
$882$	−59.9185	+	5.72780i	−2.01756	+	0.192865i
$883$			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	$-0.525568\pi$
$887$	−4.77944			−0.160478			−0.0802389	+	0.996776i	$0.525568\pi$
$888$	33.0813	−	9.91119i	1.11014	−	0.332598i
$889$	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
$894$	−23.0582	+	39.1761i	−0.771183	+	1.31025i
$895$			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
$900$	13.2827	+	23.9234i	0.442755	+	0.797448i
$901$	−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
$906$	−2.63978	+	4.48501i	−0.0877008	+	0.149004i
$907$			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	$-0.486883\pi$
$911$	2.48679			0.0823910			0.0411955	+	0.999151i	$0.486883\pi$
$912$	0.0579112	−	0.0490384i	0.00191763	−	0.00162382i
$913$	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
$918$	−9.47909	−	10.7515i	−0.312857	−	0.354852i
$919$		−	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
$924$	−23.7772	−	2.87776i	−0.782213	−	0.0946712i
$925$	−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	$0.0728400\pi$
$929$			13.8280i			0.453683i	−0.973932	+	0.226842i	$0.927160\pi$
$930$	−8.49286	−	4.99871i	−0.278492	−	0.163914i
$931$		−	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
$936$	−6.10626	+	7.99212i	−0.199589	+	0.261231i
$937$	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	$-0.927056\pi$
$941$		−	13.9365i		−	0.454318i	0.973858	−	0.227159i	$-0.0729438\pi$
$942$	9.60587	+	5.65381i	0.312976	+	0.184211i
$943$			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	$-0.252452\pi$
$947$	43.1835			1.40328			0.701638	+	0.712533i	$0.252452\pi$
$948$	−32.4376	−	3.92592i	−1.05352	−	0.127508i
$949$	−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	$0.356925\pi$
$953$			55.6088i			1.80134i	−0.434499	+	0.900672i	$0.643075\pi$
$954$	−0.333212	−	3.48573i	−0.0107881	−	0.112855i
$955$		−	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
$960$	−0.414125	+	9.17590i	−0.0133658	+	0.296151i
$961$	−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
$966$	5.71909	−	9.71678i	0.184009	−	0.312632i
$967$			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	$-0.181194\pi$
$971$	52.4944			1.68463			0.842313	+	0.538989i	$0.181194\pi$
$972$	21.3176	−	22.7499i	0.683763	−	0.729705i
$973$	−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	$-0.793166\pi$
$977$		−	37.8221i		−	1.21004i	0.796212	−	0.605018i	$-0.206834\pi$
$978$	−10.1256	+	17.2035i	−0.323781	+	0.550106i
$979$			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	$-0.340015\pi$
$983$	30.2061			0.963424			0.481712	+	0.876330i	$0.340015\pi$
$984$	10.3632	+	34.5899i	0.330366	+	1.10269i
$985$	−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
$990$	0.401993	+	4.20524i	0.0127762	+	0.133651i
$991$			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
$996$	−0.559662	+	4.62416i	−0.0177336	+	0.146522i
$997$	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.b.47.16	yes	22
3.2	odd	2		276.2.c.a.47.7	✓	22
4.3	odd	2		276.2.c.a.47.8	yes	22
12.11	even	2	inner	276.2.c.b.47.15	yes	22

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

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)

\(f(q)\)	\(=\)	\(q+(0.565709 + 1.29614i) q^{2} +(1.40231 - 1.01662i) q^{3} +(-1.35995 + 1.46647i) q^{4} +0.662888i q^{5} +(2.11098 + 1.24248i) q^{6} +4.60297i q^{7} +(-2.67009 - 0.933083i) q^{8} +(0.932961 - 2.85124i) q^{9} +O(q^{10})\)	\(q+(0.565709 + 1.29614i) q^{2} +(1.40231 - 1.01662i) q^{3} +(-1.35995 + 1.46647i) q^{4} +0.662888i q^{5} +(2.11098 + 1.24248i) 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} +(-0.416223 + 3.43901i) 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} +(4.22339 - 0.403727i) 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} +(-4.69289 + 1.40599i) 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} +(-0.823624 + 1.39934i) 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} +(2.91249 + 5.24570i) 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} +(-5.71909 + 9.71678i) 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} +(-4.47717 - 5.28725i) 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} +(5.51207 - 4.85974i) 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} +(-2.27967 - 0.275909i) 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} +(3.17084 + 1.86629i) 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} +(-5.15153 + 6.74253i) 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} +(2.50221 + 1.47275i) 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} +(-15.8296 - 1.91586i) 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} +(0.267626 + 2.79963i) 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} +(4.32023 - 8.79407i) q^{96} +16.5457 q^{97} +(-8.02588 - 18.3887i) q^{98} +(1.40137 - 4.28277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q + 9 * q^8 - 2 * q^9	\( 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) \) 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * 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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