LMFDB - Embedded newform 731.2.m.c.87.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.15
Character	$\chi$	$=$	731.87
Dual form			731.2.m.c.689.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.150441 - 0.150441i) q^{2} +(0.303692 - 0.125793i) q^{3} -1.95474i q^{4} +(0.0508915 + 0.122863i) q^{5} +(-0.0646121 - 0.0267632i) q^{6} +(-0.398942 + 0.963131i) q^{7} +(-0.594953 + 0.594953i) q^{8} +(-2.04492 + 2.04492i) q^{9} +O(q^{10})$	\(q+(-0.150441 - 0.150441i) q^{2} +(0.303692 - 0.125793i) q^{3} -1.95474i q^{4} +(0.0508915 + 0.122863i) q^{5} +(-0.0646121 - 0.0267632i) q^{6} +(-0.398942 + 0.963131i) q^{7} +(-0.594953 + 0.594953i) q^{8} +(-2.04492 + 2.04492i) q^{9} +(0.0108274 - 0.0261397i) q^{10} +(-3.09848 - 1.28343i) q^{11} +(-0.245893 - 0.593638i) q^{12} -2.84947i q^{13} +(0.204911 - 0.0848770i) q^{14} +(0.0309107 + 0.0309107i) q^{15} -3.73046 q^{16} +(3.93446 - 1.23290i) q^{17} +0.615277 q^{18} +(-5.85784 - 5.85784i) q^{19} +(0.240165 - 0.0994794i) q^{20} +0.342680i q^{21} +(0.273057 + 0.659217i) q^{22} +(-3.45185 - 1.42980i) q^{23} +(-0.105841 + 0.255524i) q^{24} +(3.52303 - 3.52303i) q^{25} +(-0.428677 + 0.428677i) q^{26} +(-0.741168 + 1.78934i) q^{27} +(1.88267 + 0.779826i) q^{28} +(-0.414650 - 1.00105i) q^{29} -0.00930046i q^{30} +(-9.11474 + 3.77545i) q^{31} +(1.75112 + 1.75112i) q^{32} -1.10243 q^{33} +(-0.777380 - 0.406425i) q^{34} -0.138636 q^{35} +(3.99727 + 3.99727i) q^{36} +(0.751315 - 0.311205i) q^{37} +1.76252i q^{38} +(-0.358445 - 0.865363i) q^{39} +(-0.103376 - 0.0428197i) q^{40} +(-1.51500 + 3.65754i) q^{41} +(0.0515530 - 0.0515530i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-2.50877 + 6.05670i) q^{44} +(-0.355313 - 0.147176i) q^{45} +(0.304198 + 0.734399i) q^{46} -6.37430i q^{47} +(-1.13291 + 0.469267i) q^{48} +(4.18128 + 4.18128i) q^{49} -1.06001 q^{50} +(1.03977 - 0.869350i) q^{51} -5.56997 q^{52} +(-0.612552 - 0.612552i) q^{53} +(0.380691 - 0.157687i) q^{54} -0.446004i q^{55} +(-0.335666 - 0.810370i) q^{56} +(-2.51586 - 1.04210i) q^{57} +(-0.0882189 + 0.212979i) q^{58} +(-2.00046 + 2.00046i) q^{59} +(0.0604222 - 0.0604222i) q^{60} +(-3.32494 + 8.02713i) q^{61} +(1.93921 + 0.803246i) q^{62} +(-1.15372 - 2.78533i) q^{63} +6.93404i q^{64} +(0.350095 - 0.145014i) q^{65} +(0.165850 + 0.165850i) q^{66} +2.76281 q^{67} +(-2.40999 - 7.69083i) q^{68} -1.22816 q^{69} +(0.0208565 + 0.0208565i) q^{70} +(13.3659 - 5.53634i) q^{71} -2.43326i q^{72} +(-5.05611 - 12.2065i) q^{73} +(-0.159846 - 0.0662105i) q^{74} +(0.626742 - 1.51309i) q^{75} +(-11.4505 + 11.4505i) q^{76} +(2.47223 - 2.47223i) q^{77} +(-0.0762611 + 0.184110i) q^{78} +(-8.71221 - 3.60872i) q^{79} +(-0.189849 - 0.458336i) q^{80} -8.03920i q^{81} +(0.778161 - 0.322325i) q^{82} +(7.79734 + 7.79734i) q^{83} +0.669848 q^{84} +(0.351708 + 0.420655i) q^{85} +0.212755 q^{86} +(-0.251852 - 0.251852i) q^{87} +(2.60703 - 1.07987i) q^{88} -11.8211i q^{89} +(0.0313124 + 0.0755948i) q^{90} +(2.74442 + 1.13678i) q^{91} +(-2.79489 + 6.74745i) q^{92} +(-2.29315 + 2.29315i) q^{93} +(-0.958954 + 0.958954i) q^{94} +(0.421598 - 1.01783i) q^{95} +(0.752080 + 0.311522i) q^{96} +(-3.00086 - 7.24472i) q^{97} -1.25807i q^{98} +(8.96063 - 3.71162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.150441	−	0.150441i	−0.106378	−	0.106378i	0.651915	−	0.758292i	$-0.273966\pi$
$2$	−0.150441	−	0.150441i	−0.106378	−	0.106378i	−0.758292	+	0.651915i	$0.773966\pi$
$3$	0.303692	−	0.125793i	0.175337	−	0.0726269i	−0.293288	−	0.956024i	$-0.594750\pi$
$3$	0.303692	−	0.125793i	0.175337	−	0.0726269i	0.468625	+	0.883397i	$0.344750\pi$
$4$		−	1.95474i		−	0.977368i
$5$	0.0508915	+	0.122863i	0.0227594	+	0.0549460i	0.934851	−	0.355041i	$-0.115533\pi$
$5$	0.0508915	+	0.122863i	0.0227594	+	0.0549460i	−0.912091	+	0.409987i	$0.865533\pi$
$6$	−0.0646121	−	0.0267632i	−0.0263778	−	0.0109260i
$7$	−0.398942	+	0.963131i	−0.150786	+	0.364029i	−0.981166	−	0.193169i	$-0.938124\pi$
$7$	−0.398942	+	0.963131i	−0.150786	+	0.364029i	0.830380	+	0.557198i	$0.188124\pi$
$8$	−0.594953	+	0.594953i	−0.210348	+	0.210348i
$9$	−2.04492	+	2.04492i	−0.681638	+	0.681638i
$10$	0.0108274	−	0.0261397i	0.00342394	−	0.00826611i
$11$	−3.09848	−	1.28343i	−0.934226	−	0.386969i	−0.136946	−	0.990579i	$-0.543729\pi$
$11$	−3.09848	−	1.28343i	−0.934226	−	0.386969i	−0.797280	+	0.603609i	$0.793729\pi$
$12$	−0.245893	−	0.593638i	−0.0709831	−	0.171368i
$13$		−	2.84947i		−	0.790302i	−0.918616	−	0.395151i	$-0.870692\pi$
$13$		−	2.84947i		−	0.790302i	0.918616	−	0.395151i	$-0.129308\pi$
$14$	0.204911	−	0.0848770i	0.0547648	−	0.0226843i
$15$	0.0309107	+	0.0309107i	0.00798111	+	0.00798111i
$16$	−3.73046			−0.932615
$17$	3.93446	−	1.23290i	0.954246	−	0.299021i
$17$	3.93446	−	1.23290i	0.954246	−	0.299021i
$18$	0.615277			0.145022
$19$	−5.85784	−	5.85784i	−1.34388	−	1.34388i	−0.892158	−	0.451724i	$-0.850809\pi$
$19$	−5.85784	−	5.85784i	−1.34388	−	1.34388i	−0.451724	−	0.892158i	$-0.649191\pi$
$20$	0.240165	−	0.0994794i	0.0537024	−	0.0222443i
$21$			0.342680i			0.0747788i
$22$	0.273057	+	0.659217i	0.0582159	+	0.140546i
$23$	−3.45185	−	1.42980i	−0.719760	−	0.298135i	−0.00742376	−	0.999972i	$-0.502363\pi$
$23$	−3.45185	−	1.42980i	−0.719760	−	0.298135i	−0.712337	+	0.701838i	$0.752363\pi$
$24$	−0.105841	+	0.255524i	−0.0216048	+	0.0521586i
$25$	3.52303	−	3.52303i	0.704606	−	0.704606i
$26$	−0.428677	+	0.428677i	−0.0840704	+	0.0840704i
$27$	−0.741168	+	1.78934i	−0.142638	+	0.344358i
$28$	1.88267	+	0.779826i	0.355791	+	0.147373i
$29$	−0.414650	−	1.00105i	−0.0769985	−	0.185891i	0.880693	−	0.473687i	$-0.157077\pi$
$29$	−0.414650	−	1.00105i	−0.0769985	−	0.185891i	−0.957692	+	0.287797i	$0.907077\pi$
$30$		−	0.00930046i		−	0.00169802i
$31$	−9.11474	+	3.77545i	−1.63706	+	0.678091i	−0.995996	−	0.0894005i	$-0.971505\pi$
$31$	−9.11474	+	3.77545i	−1.63706	+	0.678091i	−0.641060	+	0.767491i	$0.721505\pi$
$32$	1.75112	+	1.75112i	0.309557	+	0.309557i
$33$	−1.10243			−0.191908
$34$	−0.777380	−	0.406425i	−0.133320	−	0.0697013i
$35$	−0.138636			−0.0234338
$36$	3.99727	+	3.99727i	0.666211	+	0.666211i
$37$	0.751315	−	0.311205i	0.123515	−	0.0511618i	−0.320070	−	0.947394i	$-0.603706\pi$
$37$	0.751315	−	0.311205i	0.123515	−	0.0511618i	0.443585	+	0.896232i	$0.353706\pi$
$38$			1.76252i			0.285918i
$39$	−0.358445	−	0.865363i	−0.0573971	−	0.138569i
$40$	−0.103376	−	0.0428197i	−0.0163451	−	0.00677038i
$41$	−1.51500	+	3.65754i	−0.236604	+	0.571212i	−0.996927	−	0.0783325i	$-0.975040\pi$
$41$	−1.51500	+	3.65754i	−0.236604	+	0.571212i	0.760324	+	0.649545i	$0.225040\pi$
$42$	0.0515530	−	0.0515530i	0.00795480	−	0.00795480i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$44$	−2.50877	+	6.05670i	−0.378211	+	0.913082i
$45$	−0.355313	−	0.147176i	−0.0529670	−	0.0219396i
$46$	0.304198	+	0.734399i	0.0448516	+	0.108281i
$47$		−	6.37430i		−	0.929787i	−0.885367	−	0.464894i	$-0.846093\pi$
$47$		−	6.37430i		−	0.929787i	0.885367	−	0.464894i	$-0.153907\pi$
$48$	−1.13291	+	0.469267i	−0.163522	+	0.0677329i
$49$	4.18128	+	4.18128i	0.597326	+	0.597326i
$50$	−1.06001			−0.149909
$51$	1.03977	−	0.869350i	0.145597	−	0.121733i
$52$	−5.56997			−0.772415
$53$	−0.612552	−	0.612552i	−0.0841405	−	0.0841405i	0.663784	−	0.747924i	$-0.268949\pi$
$53$	−0.612552	−	0.612552i	−0.0841405	−	0.0841405i	−0.747924	+	0.663784i	$0.768949\pi$
$54$	0.380691	−	0.157687i	0.0518055	−	0.0214585i
$55$		−	0.446004i		−	0.0601392i
$56$	−0.335666	−	0.810370i	−0.0448553	−	0.108290i
$57$	−2.51586	−	1.04210i	−0.333234	−	0.138030i
$58$	−0.0882189	+	0.212979i	−0.0115837	+	0.0279655i
$59$	−2.00046	+	2.00046i	−0.260438	+	0.260438i	−0.825232	−	0.564794i	$-0.808956\pi$
$59$	−2.00046	+	2.00046i	−0.260438	+	0.260438i	0.564794	+	0.825232i	$0.308956\pi$
$60$	0.0604222	−	0.0604222i	0.00780048	−	0.00780048i
$61$	−3.32494	+	8.02713i	−0.425715	+	1.02777i	0.554916	+	0.831906i	$0.312750\pi$
$61$	−3.32494	+	8.02713i	−0.425715	+	1.02777i	−0.980632	+	0.195862i	$0.937250\pi$
$62$	1.93921	+	0.803246i	0.246280	+	0.102012i
$63$	−1.15372	−	2.78533i	−0.145355	−	0.350918i
$64$			6.93404i			0.866755i
$65$	0.350095	−	0.145014i	0.0434239	−	0.0179868i
$66$	0.165850	+	0.165850i	0.0204148	+	0.0204148i
$67$	2.76281			0.337531			0.168766	−	0.985656i	$-0.446022\pi$
$67$	2.76281			0.337531			0.168766	+	0.985656i	$0.446022\pi$
$68$	−2.40999	−	7.69083i	−0.292254	−	0.932650i
$69$	−1.22816			−0.147853
$70$	0.0208565	+	0.0208565i	0.00249283	+	0.00249283i
$71$	13.3659	−	5.53634i	1.58624	−	0.657042i	0.596854	−	0.802350i	$-0.296417\pi$
$71$	13.3659	−	5.53634i	1.58624	−	0.657042i	0.989387	+	0.145308i	$0.0464172\pi$
$72$		−	2.43326i		−	0.286762i
$73$	−5.05611	−	12.2065i	−0.591773	−	1.42867i	−0.881789	−	0.471645i	$-0.843660\pi$
$73$	−5.05611	−	12.2065i	−0.591773	−	1.42867i	0.290015	−	0.957022i	$-0.406340\pi$
$74$	−0.159846	−	0.0662105i	−0.0185817	−	0.00769681i
$75$	0.626742	−	1.51309i	0.0723700	−	0.174717i
$76$	−11.4505	+	11.4505i	−1.31347	+	1.31347i
$77$	2.47223	−	2.47223i	0.281736	−	0.281736i
$78$	−0.0762611	+	0.184110i	−0.00863486	+	0.0208464i
$79$	−8.71221	−	3.60872i	−0.980201	−	0.406012i	−0.165701	−	0.986176i	$-0.552989\pi$
$79$	−8.71221	−	3.60872i	−0.980201	−	0.406012i	−0.814500	+	0.580164i	$0.802989\pi$
$80$	−0.189849	−	0.458336i	−0.0212257	−	0.0512435i
$81$		−	8.03920i		−	0.893244i
$82$	0.778161	−	0.322325i	0.0859335	−	0.0355948i
$83$	7.79734	+	7.79734i	0.855870	+	0.855870i	0.990848	−	0.134979i	$-0.0430966\pi$
$83$	7.79734	+	7.79734i	0.855870	+	0.855870i	−0.134979	+	0.990848i	$0.543097\pi$
$84$	0.669848			0.0730864
$85$	0.351708	+	0.420655i	0.0381481	+	0.0456265i
$86$	0.212755			0.0229420
$87$	−0.251852	−	0.251852i	−0.0270013	−	0.0270013i
$88$	2.60703	−	1.07987i	0.277910	−	0.115114i
$89$		−	11.8211i		−	1.25304i	−0.779406	−	0.626519i	$-0.784479\pi$
$89$		−	11.8211i		−	1.25304i	0.779406	−	0.626519i	$-0.215521\pi$
$90$	0.0313124	+	0.0755948i	0.00330061	+	0.00796839i
$91$	2.74442	+	1.13678i	0.287693	+	0.119166i
$92$	−2.79489	+	6.74745i	−0.291387	+	0.703471i
$93$	−2.29315	+	2.29315i	−0.237788	+	0.237788i
$94$	−0.958954	+	0.958954i	−0.0989085	+	0.0989085i
$95$	0.421598	−	1.01783i	0.0432550	−	0.104427i
$96$	0.752080	+	0.311522i	0.0767589	+	0.0317946i
$97$	−3.00086	−	7.24472i	−0.304691	−	0.735590i	−0.999860	−	0.0167433i	$-0.994670\pi$
$97$	−3.00086	−	7.24472i	−0.304691	−	0.735590i	0.695168	−	0.718847i	$-0.255330\pi$
$98$		−	1.25807i		−	0.127084i
$99$	8.96063	−	3.71162i	0.900577	−	0.373031i
$100$	−6.88659	−	6.88659i	−0.688659	−	0.688659i
$101$	12.0201			1.19605			0.598025	−	0.801478i	$-0.295952\pi$
$101$	12.0201			1.19605			0.598025	+	0.801478i	$0.295952\pi$
$102$	−0.287210	−	0.0256387i	−0.0284380	−	0.00253861i
$103$	11.6091			1.14388			0.571938	−	0.820297i	$-0.306192\pi$
$103$	11.6091			1.14388			0.571938	+	0.820297i	$0.306192\pi$
$104$	1.69530	+	1.69530i	0.166238	+	0.166238i
$105$	−0.0421027	+	0.0174395i	−0.00410880	+	0.00170192i
$106$			0.184306i			0.0179013i
$107$	−0.114256	−	0.275838i	−0.0110455	−	0.0266663i	0.918261	−	0.395977i	$-0.129594\pi$
$107$	−0.114256	−	0.275838i	−0.0110455	−	0.0266663i	−0.929306	+	0.369310i	$0.879594\pi$
$108$	3.49768	+	1.44879i	0.336565	+	0.139410i
$109$	0.209794	−	0.506487i	0.0200946	−	0.0485126i	−0.913514	−	0.406808i	$-0.866642\pi$
$109$	0.209794	−	0.506487i	0.0200946	−	0.0485126i	0.933608	+	0.358295i	$0.116642\pi$
$110$	−0.0670971	+	0.0670971i	−0.00639746	+	0.00639746i
$111$	0.189021	−	0.189021i	0.0179411	−	0.0179411i
$112$	1.48824	−	3.59292i	0.140625	−	0.339499i
$113$	1.68831	+	0.699321i	0.158823	+	0.0657866i	0.460679	−	0.887567i	$-0.347606\pi$
$113$	1.68831	+	0.699321i	0.158823	+	0.0657866i	−0.301856	+	0.953354i	$0.597606\pi$
$114$	0.221713	+	0.535262i	0.0207653	+	0.0501319i
$115$		−	0.496869i		−	0.0463333i
$116$	−1.95679	+	0.810530i	−0.181684	+	0.0752558i
$117$	5.82693	+	5.82693i	0.538700	+	0.538700i
$118$	0.601902			0.0554095
$119$	−0.382180	+	4.28126i	−0.0350343	+	0.392462i
$120$	−0.0367808			−0.00335762
$121$	0.175191	+	0.175191i	0.0159264	+	0.0159264i
$122$	1.70781	−	0.707399i	0.154618	−	0.0640449i
$123$			1.30134i			0.117338i
$124$	7.38000	+	17.8169i	0.662744	+	1.60000i
$125$	1.22646	+	0.508015i	0.109698	+	0.0454383i
$126$	−0.245460	+	0.592593i	−0.0218673	+	0.0527923i
$127$	−4.30246	+	4.30246i	−0.381782	+	0.381782i	−0.871744	−	0.489962i	$-0.837011\pi$
$127$	−4.30246	+	4.30246i	−0.381782	+	0.381782i	0.489962	+	0.871744i	$0.337011\pi$
$128$	4.54540	−	4.54540i	0.401760	−	0.401760i
$129$	−0.125793	+	0.303692i	−0.0110755	+	0.0267386i
$130$	−0.0744845	−	0.0308525i	−0.00653273	−	0.00270594i
$131$	2.66173	+	6.42600i	0.232557	+	0.561442i	0.996477	−	0.0838691i	$-0.0267278\pi$
$131$	2.66173	+	6.42600i	0.232557	+	0.561442i	−0.763920	+	0.645311i	$0.776728\pi$
$132$			2.15496i			0.187565i
$133$	7.97882	−	3.30493i	0.691851	−	0.286574i
$134$	−0.415639	−	0.415639i	−0.0359058	−	0.0359058i
$135$	−0.257563			−0.0221675
$136$	−1.60730	+	3.07433i	−0.137825	+	0.263622i
$137$	−15.7774			−1.34795			−0.673976	−	0.738753i	$-0.735415\pi$
$137$	−15.7774			−1.34795			−0.673976	+	0.738753i	$0.735415\pi$
$138$	0.184765	+	0.184765i	0.0157283	+	0.0157283i
$139$	6.27653	−	2.59982i	0.532368	−	0.220514i	−0.100272	−	0.994960i	$-0.531971\pi$
$139$	6.27653	−	2.59982i	0.532368	−	0.220514i	0.632640	+	0.774446i	$0.281971\pi$
$140$			0.270997i			0.0229034i
$141$	−0.801845	−	1.93582i	−0.0675275	−	0.163026i
$142$	−2.84367	−	1.17788i	−0.238635	−	0.0988459i
$143$	−3.65710	+	8.82903i	−0.305822	+	0.738321i
$144$	7.62848	−	7.62848i	0.635706	−	0.635706i
$145$	0.101890	−	0.101890i	0.00846152	−	0.00846152i
$146$	−1.07571	+	2.59700i	−0.0890268	+	0.214930i
$147$	1.79580	+	0.743844i	0.148115	+	0.0613513i
$148$	−0.608323	−	1.46862i	−0.0500038	−	0.120720i
$149$		−	5.69766i		−	0.466771i	−0.972384	−	0.233385i	$-0.925020\pi$
$149$		−	5.69766i		−	0.466771i	0.972384	−	0.233385i	$-0.0749804\pi$
$150$	−0.321918	+	0.133343i	−0.0262845	+	0.0108874i
$151$	−8.42508	−	8.42508i	−0.685624	−	0.685624i	0.275638	−	0.961262i	$-0.411111\pi$
$151$	−8.42508	−	8.42508i	−0.685624	−	0.685624i	−0.961262	+	0.275638i	$0.911111\pi$
$152$	6.97029			0.565365
$153$	−5.52447	+	10.5668i	−0.446627	+	0.854276i
$154$	−0.743847			−0.0599409
$155$	−0.927726	−	0.927726i	−0.0745167	−	0.0745167i
$156$	−1.69156	+	0.700665i	−0.135433	+	0.0560981i
$157$			13.8098i			1.10214i	0.834458	+	0.551072i	$0.185781\pi$
$157$			13.8098i			1.10214i	−0.834458	+	0.551072i	$0.814219\pi$
$158$	0.767774	+	1.85357i	0.0610808	+	0.147462i
$159$	−0.263082	−	0.108972i	−0.0208638	−	0.00864206i
$160$	−0.126031	+	0.304265i	−0.00996360	+	0.0240542i
$161$	2.75418	−	2.75418i	0.217060	−	0.217060i
$162$	−1.20942	+	1.20942i	−0.0950212	+	0.0950212i
$163$	−2.78063	+	6.71303i	−0.217796	+	0.525805i	−0.994582	−	0.103960i	$-0.966849\pi$
$163$	−2.78063	+	6.71303i	−0.217796	+	0.525805i	0.776786	+	0.629765i	$0.216849\pi$
$164$	7.14953	+	2.96143i	0.558284	+	0.231249i
$165$	−0.0561044	−	0.135448i	−0.00436772	−	0.0105446i
$166$		−	2.34608i		−	0.182091i
$167$	−8.55211	+	3.54240i	−0.661782	+	0.274119i	−0.688188	−	0.725532i	$-0.741594\pi$
$167$	−8.55211	+	3.54240i	−0.661782	+	0.274119i	0.0264063	+	0.999651i	$0.491594\pi$
$168$	−0.203878	−	0.203878i	−0.0157296	−	0.0157296i
$169$	4.88050			0.375423
$170$	0.0103725	−	0.116195i	0.000795534	−	0.00891174i
$171$	23.9576			1.83208
$172$	1.38221	+	1.38221i	0.105392	+	0.105392i
$173$	18.0938	−	7.49470i	1.37565	−	0.569811i	0.432333	−	0.901714i	$-0.357691\pi$
$173$	18.0938	−	7.49470i	1.37565	−	0.569811i	0.943314	+	0.331903i	$0.107691\pi$
$174$			0.0757775i			0.00574467i
$175$	1.98766	+	4.79862i	0.150253	+	0.362742i
$176$	11.5587	+	4.78779i	0.871273	+	0.360893i
$177$	−0.355880	+	0.859169i	−0.0267495	+	0.0645791i
$178$	−1.77838	+	1.77838i	−0.133295	+	0.133295i
$179$	5.70430	−	5.70430i	0.426359	−	0.426359i	−0.461027	−	0.887386i	$-0.652519\pi$
$179$	5.70430	−	5.70430i	0.426359	−	0.426359i	0.887386	+	0.461027i	$0.152519\pi$
$180$	−0.287689	+	0.694543i	−0.0214431	+	0.0517682i
$181$	5.86498	+	2.42935i	0.435940	+	0.180572i	0.589851	−	0.807512i	$-0.299187\pi$
$181$	5.86498	+	2.42935i	0.435940	+	0.180572i	−0.153910	+	0.988085i	$0.549187\pi$
$182$	−0.241855	−	0.583889i	−0.0179275	−	0.0432808i
$183$			2.85603i			0.211124i
$184$	2.90435	−	1.20302i	0.214112	−	0.0886880i
$185$	0.0764711	+	0.0764711i	0.00562227	+	0.00562227i
$186$	0.689965			0.0505907
$187$	−13.7732	−	1.22951i	−1.00719	−	0.0899103i
$188$	−12.4601			−0.908744
$189$	−1.42768	−	1.42768i	−0.103849	−	0.103849i
$190$	−0.216548	+	0.0896971i	−0.0157100	+	0.00650731i
$191$		−	25.7157i		−	1.86072i	−0.366642	−	0.930362i	$-0.619493\pi$
$191$		−	25.7157i		−	1.86072i	0.366642	−	0.930362i	$-0.380507\pi$
$192$	0.872257	+	2.10581i	0.0629497	+	0.151974i
$193$	8.59927	+	3.56193i	0.618989	+	0.256394i	0.670067	−	0.742301i	$-0.266266\pi$
$193$	8.59927	+	3.56193i	0.618989	+	0.256394i	−0.0510776	+	0.998695i	$0.516266\pi$
$194$	−0.638449	+	1.54135i	−0.0458380	+	0.110663i
$195$	0.0880793	−	0.0880793i	0.00630749	−	0.00630749i
$196$	8.17330	−	8.17330i	0.583807	−	0.583807i
$197$	−4.20607	+	10.1543i	−0.299670	+	0.723467i	0.700284	+	0.713864i	$0.253057\pi$
$197$	−4.20607	+	10.1543i	−0.299670	+	0.723467i	−0.999954	+	0.00960263i	$0.996943\pi$
$198$	−1.90642	−	0.789666i	−0.135483	−	0.0561191i
$199$	−5.89812	−	14.2393i	−0.418106	−	1.00940i	−0.982896	−	0.184163i	$-0.941043\pi$
$199$	−5.89812	−	14.2393i	−0.418106	−	1.00940i	0.564789	−	0.825235i	$-0.308957\pi$
$200$			4.19207i			0.296424i
$201$	0.839044	−	0.347543i	0.0591816	−	0.0245138i
$202$	−1.80832	−	1.80832i	−0.127233	−	0.127233i
$203$	1.12957			0.0792800
$204$	−1.69935	−	2.03248i	−0.118978	−	0.142302i
$205$	−0.526477			−0.0367708
$206$	−1.74648	−	1.74648i	−0.121683	−	0.121683i
$207$	9.98257	−	4.13491i	0.693836	−	0.287396i
$208$			10.6298i			0.737047i
$209$	10.6323	+	25.6685i	0.735449	+	1.77553i
$210$	0.00895756	+	0.00371034i	0.000618130	+	0.000256038i
$211$	−3.16315	+	7.63651i	−0.217760	+	0.525719i	−0.994576	−	0.104008i	$-0.966833\pi$
$211$	−3.16315	+	7.63651i	−0.217760	+	0.525719i	0.776817	+	0.629727i	$0.216833\pi$
$212$	−1.19738	+	1.19738i	−0.0822362	+	0.0822362i
$213$	3.36268	−	3.36268i	0.230407	−	0.230407i
$214$	−0.0243085	+	0.0586860i	−0.00166170	+	0.00401169i
$215$	−0.122863	−	0.0508915i	−0.00837919	−	0.00347077i
$216$	−0.623612	−	1.50553i	−0.0424314	−	0.102438i
$217$		−	10.2849i		−	0.698183i
$218$	−0.107758	+	0.0446347i	−0.00729827	+	0.00302304i
$219$	−3.07100	−	3.07100i	−0.207519	−	0.207519i
$220$	−0.871820			−0.0587781
$221$	−3.51311	−	11.2111i	−0.236317	−	0.754143i
$222$	−0.0568729			−0.00381706
$223$	−12.6605	−	12.6605i	−0.847813	−	0.847813i	0.142047	−	0.989860i	$-0.454632\pi$
$223$	−12.6605	−	12.6605i	−0.847813	−	0.847813i	−0.989860	+	0.142047i	$0.954632\pi$
$224$	−2.38515	+	0.987963i	−0.159365	+	0.0660110i
$225$			14.4086i			0.960573i
$226$	−0.148784	−	0.359197i	−0.00989698	−	0.0238934i
$227$	22.2475	+	9.21521i	1.47662	+	0.611635i	0.968357	−	0.249568i	$-0.0802886\pi$
$227$	22.2475	+	9.21521i	1.47662	+	0.611635i	0.508261	+	0.861203i	$0.330289\pi$
$228$	−2.03704	+	4.91784i	−0.134906	+	0.325692i
$229$	−2.20965	+	2.20965i	−0.146018	+	0.146018i	−0.776337	−	0.630319i	$-0.782924\pi$
$229$	−2.20965	+	2.20965i	−0.146018	+	0.146018i	0.630319	+	0.776337i	$0.282924\pi$
$230$	−0.0747494	+	0.0747494i	−0.00492883	+	0.00492883i
$231$	0.439806	−	1.06179i	0.0289371	−	0.0698603i
$232$	0.842276	+	0.348882i	0.0552981	+	0.0229052i
$233$	−1.19841	−	2.89323i	−0.0785107	−	0.189542i	0.879751	−	0.475435i	$-0.157709\pi$
$233$	−1.19841	−	2.89323i	−0.0785107	−	0.189542i	−0.958261	+	0.285894i	$0.907709\pi$
$234$		−	1.75322i		−	0.114611i
$235$	0.783165	−	0.324398i	0.0510881	−	0.0211614i
$236$	3.91037	+	3.91037i	0.254544	+	0.254544i
$237$	−3.09978			−0.201353
$238$	0.701570	−	0.586580i	0.0454760	−	0.0380223i
$239$	−0.787860			−0.0509624			−0.0254812	−	0.999675i	$-0.508112\pi$
$239$	−0.787860			−0.0509624			−0.0254812	+	0.999675i	$0.508112\pi$
$240$	−0.115311	−	0.115311i	−0.00744330	−	0.00744330i
$241$	0.683409	−	0.283077i	0.0440223	−	0.0182346i	−0.360564	−	0.932735i	$-0.617416\pi$
$241$	0.683409	−	0.283077i	0.0440223	−	0.0182346i	0.404586	+	0.914500i	$0.367416\pi$
$242$		−	0.0527116i		−	0.00338843i
$243$	−3.23478	−	7.80946i	−0.207511	−	0.500977i
$244$	15.6909	+	6.49939i	1.00451	+	0.416081i
$245$	−0.300933	+	0.726516i	−0.0192259	+	0.0464154i
$246$	0.195775	−	0.195775i	0.0124822	−	0.0124822i
$247$	−16.6918	+	16.6918i	−1.06207	+	1.06207i
$248$	3.17663	−	7.66906i	0.201716	−	0.486986i
$249$	3.34885	+	1.38714i	0.212225	+	0.0879063i
$250$	−0.108083	−	0.260935i	−0.00683576	−	0.0165030i
$251$			1.50455i			0.0949662i	0.998872	+	0.0474831i	$0.0151200\pi$
$251$			1.50455i			0.0949662i	−0.998872	+	0.0474831i	$0.984880\pi$
$252$	−5.44457	+	2.25522i	−0.342976	+	0.142065i
$253$	8.86042	+	8.86042i	0.557050	+	0.557050i
$254$	1.29453			0.0812261
$255$	0.159727	+	0.0835072i	0.0100025	+	0.00522942i
$256$	12.5005			0.781278
$257$	1.38741	+	1.38741i	0.0865441	+	0.0865441i	0.749054	−	0.662509i	$-0.230509\pi$
$257$	1.38741	+	1.38741i	0.0865441	+	0.0865441i	−0.662509	+	0.749054i	$0.730509\pi$
$258$	0.0646121	−	0.0267632i	0.00402257	−	0.00166620i
$259$			0.847768i			0.0526777i
$260$	−0.283464	−	0.684343i	−0.0175797	−	0.0424411i
$261$	2.89499	+	1.19914i	0.179195	+	0.0742252i
$262$	0.566298	−	1.36716i	0.0349860	−	0.0844637i
$263$	9.37079	−	9.37079i	0.577828	−	0.577828i	−0.356476	−	0.934304i	$-0.616022\pi$
$263$	9.37079	−	9.37079i	0.577828	−	0.577828i	0.934304	+	0.356476i	$0.116022\pi$
$264$	0.655894	−	0.655894i	0.0403675	−	0.0403675i
$265$	0.0440863	−	0.106434i	0.00270820	−	0.00653817i
$266$	−1.69753	−	0.703142i	−0.104083	−	0.0431124i
$267$	−1.48702	−	3.58998i	−0.0910042	−	0.219703i
$268$		−	5.40056i		−	0.329892i
$269$	−17.7373	+	7.34705i	−1.08147	+	0.447958i	−0.851023	−	0.525128i	$-0.824017\pi$
$269$	−17.7373	+	7.34705i	−1.08147	+	0.447958i	−0.230442	+	0.973086i	$0.574017\pi$
$270$	0.0387479	+	0.0387479i	0.00235812	+	0.00235812i
$271$	−17.3772			−1.05559			−0.527796	−	0.849371i	$-0.676981\pi$
$271$	−17.3772			−1.05559			−0.527796	+	0.849371i	$0.676981\pi$
$272$	−14.6773	+	4.59927i	−0.889945	+	0.278872i
$273$	0.976457			0.0590979
$274$	2.37356	+	2.37356i	0.143392	+	0.143392i
$275$	−15.4376	+	6.39446i	−0.930922	+	0.385600i
$276$			2.40073i			0.144507i
$277$	0.238839	+	0.576609i	0.0143505	+	0.0346451i	0.930892	−	0.365294i	$-0.119031\pi$
$277$	0.238839	+	0.576609i	0.0143505	+	0.0346451i	−0.916542	+	0.399939i	$0.869031\pi$
$278$	−1.33536	−	0.553126i	−0.0800898	−	0.0331743i
$279$	10.9184	−	26.3593i	0.653667	−	1.57809i
$280$	0.0824819	−	0.0824819i	0.00492924	−	0.00492924i
$281$	18.6500	−	18.6500i	1.11256	−	1.11256i	0.119762	−	0.992803i	$-0.461787\pi$
$281$	18.6500	−	18.6500i	1.11256	−	1.11256i	0.992803	−	0.119762i	$-0.0382130\pi$
$282$	−0.170597	+	0.411857i	−0.0101589	+	0.0245257i
$283$	−15.0105	−	6.21755i	−0.892281	−	0.369595i	−0.111034	−	0.993817i	$-0.535416\pi$
$283$	−15.0105	−	6.21755i	−0.892281	−	0.369595i	−0.781247	+	0.624222i	$0.785416\pi$
$284$	−10.8221	−	26.1268i	−0.642172	−	1.55034i
$285$		−	0.362140i		−	0.0214513i
$286$	1.87842	−	0.778068i	0.111073	−	0.0460081i
$287$	−2.91829	−	2.91829i	−0.172261	−	0.172261i
$288$	−7.16178			−0.422012
$289$	13.9599	−	9.70156i	0.821172	−	0.570680i
$290$	−0.0306569			−0.00180023
$291$	−1.82268	−	1.82268i	−0.106847	−	0.106847i
$292$	−23.8605	+	9.88336i	−1.39633	+	0.578380i
$293$		−	25.3108i		−	1.47867i	−0.673336	−	0.739337i	$-0.735139\pi$
$293$		−	25.3108i		−	1.47867i	0.673336	−	0.739337i	$-0.264861\pi$
$294$	−0.158257	−	0.382066i	−0.00922972	−	0.0222825i
$295$	−0.347589	−	0.143976i	−0.0202374	−	0.00838262i
$296$	−0.261845	+	0.632149i	−0.0152194	+	0.0367429i
$297$	4.59298	−	4.59298i	0.266512	−	0.266512i
$298$	−0.857160	+	0.857160i	−0.0496540	+	0.0496540i
$299$	−4.07419	+	9.83596i	−0.235616	+	0.568828i
$300$	−2.95769	−	1.22512i	−0.170762	−	0.0707321i
$301$	−0.398942	−	0.963131i	−0.0229946	−	0.0555140i
$302$			2.53495i			0.145870i
$303$	3.65042	−	1.51206i	0.209711	−	0.0868653i
$304$	21.8525	+	21.8525i	1.25332	+	1.25332i
$305$	−1.15545			−0.0661608
$306$	2.42078	−	0.758573i	0.138387	−	0.0433647i
$307$	−12.4504			−0.710581			−0.355291	−	0.934756i	$-0.615618\pi$
$307$	−12.4504			−0.710581			−0.355291	+	0.934756i	$0.615618\pi$
$308$	−4.83255	−	4.83255i	−0.275360	−	0.275360i
$309$	3.52559	−	1.46035i	0.200564	−	0.0830762i
$310$			0.279135i			0.0158538i
$311$	6.32748	+	15.2759i	0.358799	+	0.866217i	0.995470	+	0.0950810i	$0.0303110\pi$
$311$	6.32748	+	15.2759i	0.358799	+	0.866217i	−0.636671	+	0.771136i	$0.719689\pi$
$312$	0.728108	+	0.301592i	0.0412210	+	0.0170743i
$313$	7.36528	−	17.7814i	0.416310	−	1.00506i	−0.567097	−	0.823651i	$-0.691934\pi$
$313$	7.36528	−	17.7814i	0.416310	−	1.00506i	0.983407	−	0.181411i	$-0.0580663\pi$
$314$	2.07756	−	2.07756i	0.117243	−	0.117243i
$315$	0.283499	−	0.283499i	0.0159734	−	0.0159734i
$316$	−7.05409	+	17.0301i	−0.396823	+	0.958016i
$317$	16.0283	+	6.63912i	0.900237	+	0.372890i	0.784311	−	0.620368i	$-0.213017\pi$
$317$	16.0283	+	6.63912i	0.900237	+	0.372890i	0.115926	+	0.993258i	$0.463017\pi$
$318$	0.0231844	+	0.0559722i	0.00130012	+	0.00313876i
$319$			3.63391i			0.203460i
$320$	−0.851937	+	0.352884i	−0.0476247	+	0.0197268i
$321$	−0.0693972	−	0.0693972i	−0.00387337	−	0.00387337i
$322$	−0.828680			−0.0461806
$323$	−30.2696	−	15.8253i	−1.68424	−	0.880545i
$324$	−15.7145			−0.873028
$325$	−10.0388	−	10.0388i	−0.556851	−	0.556851i
$326$	1.42823	−	0.591593i	0.0791024	−	0.0327653i
$327$		−	0.180207i		−	0.00996545i
$328$	−1.27471	−	3.07742i	−0.0703841	−	0.169922i
$329$	6.13929	+	2.54298i	0.338470	+	0.140199i
$330$	−0.0119365	+	0.0288173i	−0.000657083	+	0.00158634i
$331$	−9.18058	+	9.18058i	−0.504610	+	0.504610i	−0.912867	−	0.408257i	$-0.866137\pi$
$331$	−9.18058	+	9.18058i	−0.504610	+	0.504610i	0.408257	+	0.912867i	$0.366137\pi$
$332$	15.2417	−	15.2417i	0.836499	−	0.836499i
$333$	−0.899988	+	2.17276i	−0.0493190	+	0.119067i
$334$	1.81951	+	0.753664i	0.0995589	+	0.0412387i
$335$	0.140604	+	0.339447i	0.00768200	+	0.0185460i
$336$		−	1.27835i		−	0.0697399i
$337$	−26.8338	+	11.1149i	−1.46173	+	0.605467i	−0.964956	−	0.262414i	$-0.915482\pi$
$337$	−26.8338	+	11.1149i	−1.46173	+	0.605467i	−0.496772	+	0.867881i	$0.665482\pi$
$338$	−0.734226	−	0.734226i	−0.0399366	−	0.0399366i
$339$	0.600697			0.0326254
$340$	0.822270	−	0.687496i	0.0445938	−	0.0372847i
$341$	33.0873			1.79178
$342$	−3.60420	−	3.60420i	−0.194893	−	0.194893i
$343$	−12.4371	+	5.15163i	−0.671542	+	0.278162i
$344$		−	0.841391i		−	0.0453647i
$345$	−0.0625029	−	0.150895i	−0.00336504	−	0.00812393i
$346$	−3.84955	−	1.59454i	−0.206953	−	0.0857228i
$347$	−5.77945	+	13.9528i	−0.310257	+	0.749027i	0.689438	+	0.724345i	$0.257858\pi$
$347$	−5.77945	+	13.9528i	−0.310257	+	0.749027i	−0.999695	+	0.0246828i	$0.992142\pi$
$348$	−0.492303	+	0.492303i	−0.0263902	+	0.0263902i
$349$	−16.9584	+	16.9584i	−0.907765	+	0.907765i	−0.996092	−	0.0883268i	$-0.971848\pi$
$349$	−16.9584	+	16.9584i	−0.907765	+	0.907765i	0.0883268	+	0.996092i	$0.471848\pi$
$350$	0.422884	−	1.02093i	0.0226041	−	0.0545711i
$351$	5.09867	+	2.11194i	0.272147	+	0.112727i
$352$	−3.17836	−	7.67324i	−0.169407	−	0.408985i
$353$		−	34.7163i		−	1.84776i	−0.382683	−	0.923880i	$-0.625000\pi$
$353$		−	34.7163i		−	1.84776i	0.382683	−	0.923880i	$-0.375000\pi$
$354$	0.182793	−	0.0757153i	0.00971533	−	0.00402422i
$355$	1.36042	+	1.36042i	0.0722037	+	0.0722037i
$356$	−23.1072			−1.22468
$357$	0.422489	+	1.34826i	0.0223605	+	0.0713574i
$358$	−1.71632			−0.0907102
$359$	−6.65294	−	6.65294i	−0.351129	−	0.351129i	0.509401	−	0.860529i	$-0.329867\pi$
$359$	−6.65294	−	6.65294i	−0.351129	−	0.351129i	−0.860529	+	0.509401i	$0.829867\pi$
$360$	0.298957	−	0.123832i	0.0157564	−	0.00652653i
$361$			49.6287i			2.61204i
$362$	−0.516858	−	1.24781i	−0.0271654	−	0.0655832i
$363$	0.0752419	+	0.0311662i	0.00394917	+	0.00163580i
$364$	2.22209	−	5.36461i	0.116469	−	0.281182i
$365$	1.24242	−	1.24242i	0.0650311	−	0.0650311i
$366$	0.429663	−	0.429663i	0.0224589	−	0.0224589i
$367$	−13.2023	+	31.8731i	−0.689153	+	1.66376i	0.0573279	+	0.998355i	$0.481742\pi$
$367$	−13.2023	+	31.8731i	−0.689153	+	1.66376i	−0.746481	+	0.665407i	$0.768258\pi$
$368$	12.8770	+	5.33382i	0.671259	+	0.278045i
$369$	−4.38131	−	10.5774i	−0.228082	−	0.550638i
$370$		−	0.0230087i		−	0.00119617i
$371$	0.834341	−	0.345595i	0.0433168	−	0.0179424i
$372$	4.48250	+	4.48250i	0.232407	+	0.232407i
$373$	−13.1404			−0.680382			−0.340191	−	0.940356i	$-0.610492\pi$
$373$	−13.1404			−0.680382			−0.340191	+	0.940356i	$0.610492\pi$
$374$	1.88708	+	2.25701i	0.0975784	+	0.116707i
$375$	0.436370			0.0225341
$376$	3.79241	+	3.79241i	0.195579	+	0.195579i
$377$	−2.85247	+	1.18153i	−0.146910	+	0.0608520i
$378$			0.429564i			0.0220944i
$379$	−10.1758	−	24.5665i	−0.522694	−	1.26189i	−0.936224	−	0.351404i	$-0.885704\pi$
$379$	−10.1758	−	24.5665i	−0.522694	−	1.26189i	0.413530	−	0.910490i	$-0.364296\pi$
$380$	−1.98958	−	0.824112i	−0.102063	−	0.0422761i
$381$	−0.765402	+	1.84784i	−0.0392127	+	0.0946680i
$382$	−3.86869	+	3.86869i	−0.197939	+	0.197939i
$383$	5.58884	−	5.58884i	0.285576	−	0.285576i	−0.549752	−	0.835328i	$-0.685278\pi$
$383$	5.58884	−	5.58884i	0.285576	−	0.285576i	0.835328	+	0.549752i	$0.185278\pi$
$384$	0.808621	−	1.95218i	0.0412648	−	0.0996220i
$385$	0.429560	+	0.177930i	0.0218924	+	0.00906814i
$386$	−0.757820	−	1.82954i	−0.0385720	−	0.0931211i
$387$		−	2.89195i		−	0.147006i
$388$	−14.1615	+	5.86589i	−0.718942	+	0.297796i
$389$	−3.67423	−	3.67423i	−0.186291	−	0.186291i	0.607800	−	0.794090i	$-0.292052\pi$
$389$	−3.67423	−	3.67423i	−0.186291	−	0.186291i	−0.794090	+	0.607800i	$0.792052\pi$
$390$	−0.0265014			−0.00134195
$391$	−15.3440	−	1.36973i	−0.775977	−	0.0692701i
$392$	−4.97533			−0.251292
$393$	1.61670	+	1.61670i	0.0815515	+	0.0815515i
$394$	2.16039	−	0.894863i	0.108839	−	0.0450825i
$395$		−	1.25406i		−	0.0630987i
$396$	−7.25523	−	17.5157i	−0.364589	−	0.880195i
$397$	10.1627	+	4.20952i	0.510050	+	0.211270i	0.622840	−	0.782349i	$-0.285979\pi$
$397$	10.1627	+	4.20952i	0.510050	+	0.211270i	−0.112790	+	0.993619i	$0.535979\pi$
$398$	−1.25486	+	3.02949i	−0.0629002	+	0.151855i
$399$	2.00736	−	2.00736i	0.100494	−	0.100494i
$400$	−13.1425	+	13.1425i	−0.657126	+	0.657126i
$401$	−9.04541	+	21.8375i	−0.451706	+	1.09051i	0.519967	+	0.854186i	$0.325944\pi$
$401$	−9.04541	+	21.8375i	−0.451706	+	1.09051i	−0.971673	+	0.236329i	$0.924056\pi$
$402$	−0.178511	−	0.0739417i	−0.00890332	−	0.00368788i
$403$	10.7580	+	25.9722i	0.535896	+	1.29377i
$404$		−	23.4962i		−	1.16898i
$405$	0.987720	−	0.409127i	0.0490802	−	0.0203297i
$406$	−0.169933	−	0.169933i	−0.00843362	−	0.00843362i
$407$	−2.72734			−0.135189
$408$	−0.101394	+	1.13584i	−0.00501976	+	0.0562324i
$409$	11.8377			0.585339			0.292669	−	0.956214i	$-0.405457\pi$
$409$	11.8377			0.585339			0.292669	+	0.956214i	$0.405457\pi$
$410$	0.0792036	+	0.0792036i	0.00391159	+	0.00391159i
$411$	−4.79146	+	1.98469i	−0.236345	+	0.0978975i
$412$		−	22.6927i		−	1.11799i
$413$	−1.12864	−	2.72478i	−0.0555367	−	0.134077i
$414$	−2.12384	−	0.879725i	−0.104381	−	0.0432361i
$415$	−0.561186	+	1.35482i	−0.0275476	+	0.0665057i
$416$	4.98977	−	4.98977i	0.244644	−	0.244644i
$417$	1.57909	−	1.57909i	0.0773284	−	0.0773284i
$418$	2.26207	−	5.46112i	0.110641	−	0.267112i
$419$	−7.63120	−	3.16095i	−0.372808	−	0.154422i	0.188409	−	0.982091i	$-0.439667\pi$
$419$	−7.63120	−	3.16095i	−0.372808	−	0.154422i	−0.561218	+	0.827668i	$0.689667\pi$
$420$	0.0340896	+	0.0822995i	0.00166340	+	0.00401581i
$421$		−	7.16292i		−	0.349099i	−0.984648	−	0.174550i	$-0.944153\pi$
$421$		−	7.16292i		−	0.349099i	0.984648	−	0.174550i	$-0.0558470\pi$
$422$	1.62471	−	0.672976i	0.0790895	−	0.0327599i
$423$	13.0349	+	13.0349i	0.633779	+	0.633779i
$424$	0.728880			0.0353975
$425$	9.51768	−	18.2047i	0.461675	−	0.883060i
$426$	−1.01177			−0.0490204
$427$	−6.40472	−	6.40472i	−0.309946	−	0.309946i
$428$	−0.539190	+	0.223340i	−0.0260627	+	0.0107955i
$429$			3.14135i			0.151666i
$430$	0.0108274	+	0.0261397i	0.000522145	+	0.00126057i
$431$	−28.7685	−	11.9163i	−1.38573	−	0.573988i	−0.439722	−	0.898134i	$-0.644923\pi$
$431$	−28.7685	−	11.9163i	−1.38573	−	0.573988i	−0.946007	+	0.324146i	$0.894923\pi$
$432$	2.76490	−	6.67505i	0.133026	−	0.321154i
$433$	−19.2154	+	19.2154i	−0.923434	+	0.923434i	−0.997270	−	0.0738367i	$-0.976476\pi$
$433$	−19.2154	+	19.2154i	−0.923434	+	0.923434i	0.0738367	+	0.997270i	$0.476476\pi$
$434$	−1.54726	+	1.54726i	−0.0742710	+	0.0742710i
$435$	0.0181261	−	0.0437604i	0.000869081	−	0.00209815i
$436$	−0.990047	−	0.410091i	−0.0474147	−	0.0196398i
$437$	11.8448	+	28.5960i	0.566615	+	1.36793i
$438$			0.924008i			0.0441508i
$439$	1.49314	−	0.618478i	0.0712636	−	0.0295183i	−0.346767	−	0.937951i	$-0.612721\pi$
$439$	1.49314	−	0.618478i	0.0712636	−	0.0295183i	0.418031	+	0.908433i	$0.362721\pi$
$440$	0.265351	+	0.265351i	0.0126501	+	0.0126501i
$441$	−17.1007			−0.814320
$442$	−1.15810	+	2.21513i	−0.0550851	+	0.105363i
$443$	12.8517			0.610604			0.305302	−	0.952256i	$-0.401243\pi$
$443$	12.8517			0.610604			0.305302	+	0.952256i	$0.401243\pi$
$444$	−0.369486	−	0.369486i	−0.0175350	−	0.0175350i
$445$	1.45238	−	0.601595i	0.0688494	−	0.0285184i
$446$			3.80932i			0.180377i
$447$	−0.716728	−	1.73034i	−0.0339001	−	0.0818421i
$448$	−6.67839	−	2.76628i	−0.315524	−	0.130694i
$449$	−0.490889	+	1.18511i	−0.0231665	+	0.0559288i	−0.935039	−	0.354544i	$-0.884636\pi$
$449$	−0.490889	+	1.18511i	−0.0231665	+	0.0559288i	0.911873	+	0.410473i	$0.134636\pi$
$450$	2.16764	−	2.16764i	0.102183	−	0.102183i
$451$	9.38841	−	9.38841i	0.442083	−	0.442083i
$452$	1.36699	−	3.30020i	0.0642977	−	0.155228i
$453$	−3.61845	−	1.49881i	−0.170010	−	0.0704203i
$454$	−1.96059	−	4.73327i	−0.0920148	−	0.222143i
$455$			0.395040i			0.0185197i
$456$	2.11682	−	0.876816i	0.0991292	−	0.0410607i
$457$	−9.12503	−	9.12503i	−0.426851	−	0.426851i	0.460703	−	0.887554i	$-0.347597\pi$
$457$	−9.12503	−	9.12503i	−0.426851	−	0.426851i	−0.887554	+	0.460703i	$0.847597\pi$
$458$	0.664844			0.0310661
$459$	−0.710026	+	7.95386i	−0.0331412	+	0.371254i
$460$	−0.971248			−0.0452847
$461$	12.5781	+	12.5781i	0.585822	+	0.585822i	0.936497	−	0.350675i	$-0.114048\pi$
$461$	12.5781	+	12.5781i	0.585822	+	0.585822i	−0.350675	+	0.936497i	$0.614048\pi$
$462$	−0.225900	+	0.0935710i	−0.0105098	+	0.00435332i
$463$			9.44043i			0.438734i	0.975642	+	0.219367i	$0.0703992\pi$
$463$			9.44043i			0.438734i	−0.975642	+	0.219367i	$0.929601\pi$
$464$	1.54683	+	3.73439i	0.0718099	+	0.173365i
$465$	−0.398445	−	0.165041i	−0.0184774	−	0.00765360i
$466$	−0.254969	+	0.615549i	−0.0118112	+	0.0285148i
$467$	−29.8659	+	29.8659i	−1.38203	+	1.38203i	−0.541020	+	0.841010i	$0.681962\pi$
$467$	−29.8659	+	29.8659i	−1.38203	+	1.38203i	−0.841010	+	0.541020i	$0.818038\pi$
$468$	11.3901	−	11.3901i	0.526508	−	0.526508i
$469$	−1.10220	+	2.66095i	−0.0508949	+	0.122871i
$470$	−0.166623	−	0.0690173i	−0.00768573	−	0.00318353i
$471$	1.73718	+	4.19393i	0.0800452	+	0.193246i
$472$		−	2.38036i		−	0.109565i
$473$	3.09848	−	1.28343i	0.142468	−	0.0590122i
$474$	0.466334	+	0.466334i	0.0214194	+	0.0214194i
$475$	−41.2747			−1.89381
$476$	8.36872	+	0.747060i	0.383580	+	0.0342414i
$477$	2.50524			0.114707
$478$	0.118526	+	0.118526i	0.00542126	+	0.00542126i
$479$	18.4299	−	7.63393i	0.842086	−	0.348803i	0.0804102	−	0.996762i	$-0.474377\pi$
$479$	18.4299	−	7.63393i	0.842086	−	0.348803i	0.761676	+	0.647959i	$0.224377\pi$
$480$			0.108257i			0.00494122i
$481$	−0.886770	−	2.14085i	−0.0404332	−	0.0976144i
$482$	−0.145399	−	0.0602262i	−0.00662274	−	0.00274323i
$483$	0.489964	−	1.18288i	0.0222942	−	0.0538229i
$484$	0.342451	−	0.342451i	0.0155660	−	0.0155660i
$485$	0.737390	−	0.737390i	0.0334832	−	0.0334832i
$486$	−0.688217	+	1.66150i	−0.0312182	+	0.0753673i
$487$	−6.60416	−	2.73553i	−0.299263	−	0.123959i	0.227999	−	0.973661i	$-0.426782\pi$
$487$	−6.60416	−	2.73553i	−0.299263	−	0.123959i	−0.527263	+	0.849702i	$0.676782\pi$
$488$	−2.79758	−	6.75395i	−0.126640	−	0.305737i
$489$			2.38848i			0.108011i
$490$	0.154570	−	0.0640251i	0.00698277	−	0.00289236i
$491$	−11.8204	−	11.8204i	−0.533448	−	0.533448i	0.388149	−	0.921597i	$-0.373115\pi$
$491$	−11.8204	−	11.8204i	−0.533448	−	0.533448i	−0.921597	+	0.388149i	$0.873115\pi$
$492$	2.54378			0.114683
$493$	−2.86562	−	3.42738i	−0.129061	−	0.154361i
$494$	5.02224			0.225961
$495$	0.912040	+	0.912040i	0.0409932	+	0.0409932i
$496$	34.0022	−	14.0842i	1.52674	−	0.632397i
$497$			15.0818i			0.676511i
$498$	−0.295121	−	0.712485i	−0.0132247	−	0.0319272i
$499$	33.9249	+	14.0521i	1.51869	+	0.629060i	0.977328	−	0.211733i	$-0.0679106\pi$
$499$	33.9249	+	14.0521i	1.51869	+	0.629060i	0.541357	+	0.840793i	$0.317911\pi$
$500$	0.993035	−	2.39740i	0.0444099	−	0.107215i
$501$	−2.15160	+	2.15160i	−0.0961263	+	0.0961263i
$502$	0.226345	−	0.226345i	0.0101023	−	0.0101023i
$503$	13.3339	−	32.1909i	0.594529	−	1.43532i	−0.284558	−	0.958659i	$-0.591847\pi$
$503$	13.3339	−	32.1909i	0.594529	−	1.43532i	0.879087	−	0.476661i	$-0.158153\pi$
$504$	2.34355	+	0.970729i	0.104390	+	0.0432397i
$505$	0.611724	+	1.47683i	0.0272213	+	0.0657181i
$506$		−	2.66594i		−	0.118515i
$507$	1.48217	−	0.613935i	0.0658254	−	0.0272658i
$508$	8.41017	+	8.41017i	0.373141	+	0.373141i
$509$	−10.0942			−0.447419			−0.223710	−	0.974656i	$-0.571817\pi$
$509$	−10.0942			−0.447419			−0.223710	+	0.974656i	$0.571817\pi$
$510$	−0.0114665	−	0.0365923i	−0.000507745	−	0.00162033i
$511$	13.7736			0.609308
$512$	−10.9714	−	10.9714i	−0.484871	−	0.484871i
$513$	14.8233	−	6.14002i	0.654465	−	0.271088i
$514$		−	0.417445i		−	0.0184127i
$515$	0.590804	+	1.42633i	0.0260339	+	0.0628515i
$516$	0.593638	+	0.245893i	0.0261334	+	0.0108248i
$517$	−8.18097	+	19.7506i	−0.359799	+	0.868631i
$518$	0.127539	−	0.127539i	0.00560373	−	0.00560373i
$519$	4.55216	−	4.55216i	0.199818	−	0.199818i
$520$	−0.122013	+	0.294567i	−0.00535064	+	0.0129176i
$521$	13.1679	+	5.45434i	0.576898	+	0.238959i	0.652003	−	0.758217i	$-0.273929\pi$
$521$	13.1679	+	5.45434i	0.576898	+	0.238959i	−0.0751048	+	0.997176i	$0.523929\pi$
$522$	−0.255124	−	0.615925i	−0.0111665	−	0.0269583i
$523$		−	24.1989i		−	1.05814i	−0.848577	−	0.529072i	$-0.822540\pi$
$523$		−	24.1989i		−	1.05814i	0.848577	−	0.529072i	$-0.177460\pi$
$524$	12.5611	−	5.20299i	0.548735	−	0.227294i
$525$	1.20727	+	1.20727i	0.0526896	+	0.0526896i
$526$	−2.81950			−0.122936
$527$	−31.2068	+	26.0919i	−1.35939	+	1.13658i
$528$	4.11257			0.178977
$529$	−6.39253	−	6.39253i	−0.277936	−	0.277936i
$530$	−0.0226443	+	0.00937959i	−0.000983607	+	0.000407423i
$531$		−	8.18155i		−	0.355049i
$532$	−6.46027	−	15.5965i	−0.280088	−	0.676193i
$533$	10.4221	+	4.31696i	0.451430	+	0.186988i
$534$	−0.316371	+	0.763788i	−0.0136907	+	0.0330523i
$535$	0.0280756	−	0.0280756i	0.00121382	−	0.00121382i
$536$	−1.64374	+	1.64374i	−0.0709989	+	0.0709989i
$537$	1.01479	−	2.44991i	0.0437913	−	0.105722i
$538$	3.77371	+	1.56312i	0.162696	+	0.0673910i
$539$	−7.58922	−	18.3220i	−0.326891	−	0.789184i
$540$			0.503467i			0.0216658i
$541$	23.0182	−	9.53444i	0.989629	−	0.409918i	0.171645	−	0.985159i	$-0.445092\pi$
$541$	23.0182	−	9.53444i	0.989629	−	0.409918i	0.817984	+	0.575241i	$0.195092\pi$
$542$	2.61424	+	2.61424i	0.112291	+	0.112291i
$543$	2.08674			0.0895508
$544$	9.04865	+	4.73076i	0.387958	+	0.202830i
$545$	0.0729052			0.00312291
$546$	−0.146899	−	0.146899i	−0.00628669	−	0.00628669i
$547$	33.7875	−	13.9952i	1.44465	−	0.598393i	0.483728	−	0.875218i	$-0.339282\pi$
$547$	33.7875	−	13.9952i	1.44465	−	0.598393i	0.960920	+	0.276825i	$0.0892823\pi$
$548$			30.8406i			1.31744i
$549$	−9.61556	−	23.2140i	−0.410382	−	0.990750i
$550$	3.28443	+	1.36045i	0.140048	+	0.0580100i
$551$	−3.43506	+	8.29296i	−0.146338	+	0.353292i
$552$	0.730697	−	0.730697i	0.0311005	−	0.0311005i
$553$	6.95134	−	6.95134i	0.295601	−	0.295601i
$554$	0.0508144	−	0.122677i	0.00215889	−	0.00521203i
$555$	0.0328432	+	0.0136041i	0.00139412	+	0.000577462i
$556$	−5.08196	−	12.2689i	−0.215523	−	0.520319i
$557$		−	5.29376i		−	0.224304i	−0.993691	−	0.112152i	$-0.964226\pi$
$557$		−	5.29376i		−	0.224304i	0.993691	−	0.112152i	$-0.0357743\pi$
$558$	−5.60809	+	2.32295i	−0.237409	+	0.0983382i
$559$	2.01488	+	2.01488i	0.0852204	+	0.0852204i
$560$	0.517176			0.0218547
$561$	−4.33747	+	1.35918i	−0.183128	+	0.0573847i
$562$	−5.61143			−0.236704
$563$	4.67853	+	4.67853i	0.197177	+	0.197177i	0.798789	−	0.601612i	$-0.205475\pi$
$563$	4.67853	+	4.67853i	0.197177	+	0.197177i	−0.601612	+	0.798789i	$0.705475\pi$
$564$	−3.78402	+	1.56739i	−0.159336	+	0.0659992i
$565$			0.243020i			0.0102239i
$566$	1.32282	+	3.19356i	0.0556021	+	0.134235i
$567$	7.74281	+	3.20717i	0.325167	+	0.134689i
$568$	−4.65822	+	11.2459i	−0.195455	+	0.471869i
$569$	−0.410189	+	0.410189i	−0.0171960	+	0.0171960i	−0.715653	−	0.698456i	$-0.753871\pi$
$569$	−0.410189	+	0.410189i	−0.0171960	+	0.0171960i	0.698456	+	0.715653i	$0.253871\pi$
$570$	−0.0544806	+	0.0544806i	−0.00228194	+	0.00228194i
$571$	12.6569	−	30.5565i	0.529676	−	1.27875i	−0.402059	−	0.915614i	$-0.631705\pi$
$571$	12.6569	−	30.5565i	0.529676	−	1.27875i	0.931735	−	0.363138i	$-0.118295\pi$
$572$	17.2584	+	7.14867i	0.721611	+	0.298901i
$573$	−3.23487	−	7.80966i	−0.135139	−	0.326253i
$574$			0.878061i			0.0366495i
$575$	−17.1982	+	7.12373i	−0.717215	+	0.297080i
$576$	−14.1795	−	14.1795i	−0.590814	−	0.590814i
$577$	−17.9672			−0.747984			−0.373992	−	0.927432i	$-0.622011\pi$
$577$	−17.9672			−0.747984			−0.373992	+	0.927432i	$0.622011\pi$
$578$	−3.55965	−	0.640632i	−0.148062	−	0.0266468i
$579$	3.05960			0.127153
$580$	−0.199168	−	0.199168i	−0.00827001	−	0.00827001i
$581$	−10.6206	+	4.39918i	−0.440615	+	0.182509i
$582$			0.548409i			0.0227323i
$583$	1.11181	+	2.68415i	0.0460465	+	0.111166i
$584$	10.2705	+	4.25417i	0.424995	+	0.176039i
$585$	−0.419373	+	1.01246i	−0.0173389	+	0.0418599i
$586$	−3.80778	+	3.80778i	−0.157298	+	0.157298i
$587$	−1.26028	+	1.26028i	−0.0520172	+	0.0520172i	−0.732637	−	0.680620i	$-0.761711\pi$
$587$	−1.26028	+	1.26028i	−0.0520172	+	0.0520172i	0.680620	+	0.732637i	$0.261711\pi$
$588$	1.45402	−	3.51031i	0.0599627	−	0.144763i
$589$	75.5087	+	31.2767i	3.11128	+	1.28874i
$590$	0.0306317	+	0.0739514i	0.00126109	+	0.00304453i
$591$			3.61289i			0.148614i
$592$	−2.80275	+	1.16094i	−0.115192	+	0.0477142i
$593$	−32.5955	−	32.5955i	−1.33854	−	1.33854i	−0.897478	−	0.441059i	$-0.854603\pi$
$593$	−32.5955	−	32.5955i	−1.33854	−	1.33854i	−0.441059	−	0.897478i	$-0.645397\pi$
$594$	−1.38194			−0.0567018
$595$	−0.545458	+	0.170924i	−0.0223616	+	0.00700719i
$596$	−11.1374			−0.456207
$597$	−3.58242	−	3.58242i	−0.146619	−	0.146619i
$598$	2.09265	−	0.866805i	0.0855749	−	0.0354463i
$599$			20.0848i			0.820643i	0.911941	+	0.410321i	$0.134583\pi$
$599$			20.0848i			0.820643i	−0.911941	+	0.410321i	$0.865417\pi$
$600$	0.527335	+	1.27310i	0.0215284	+	0.0519741i
$601$	−8.66060	−	3.58734i	−0.353273	−	0.146331i	0.198987	−	0.980002i	$-0.436235\pi$
$601$	−8.66060	−	3.58734i	−0.353273	−	0.146331i	−0.552261	+	0.833671i	$0.686235\pi$
$602$	−0.0848770	+	0.204911i	−0.00345933	+	0.00835156i
$603$	−5.64972	+	5.64972i	−0.230074	+	0.230074i
$604$	−16.4688	+	16.4688i	−0.670106	+	0.670106i
$605$	−0.0126087	+	0.0304402i	−0.000512618	+	0.00123757i
$606$	−0.776647	−	0.321698i	−0.0315491	−	0.0130681i
$607$	−6.95391	−	16.7882i	−0.282251	−	0.681413i	0.717637	−	0.696417i	$-0.245224\pi$
$607$	−6.95391	−	16.7882i	−0.282251	−	0.681413i	−0.999887	+	0.0150044i	$0.995224\pi$
$608$		−	20.5156i		−	0.832016i
$609$	0.343040	−	0.142092i	0.0139007	−	0.00575786i
$610$	0.173826	+	0.173826i	0.00703803	+	0.00703803i
$611$	−18.1634			−0.734812
$612$	20.6553	+	10.7989i	0.834941	+	0.436518i
$613$	1.09456			0.0442087			0.0221044	−	0.999756i	$-0.492963\pi$
$613$	1.09456			0.0442087			0.0221044	+	0.999756i	$0.492963\pi$
$614$	1.87304	+	1.87304i	0.0755899	+	0.0755899i
$615$	−0.159887	+	0.0662274i	−0.00644727	+	0.00267055i
$616$			2.94172i			0.118525i
$617$	13.2425	+	31.9703i	0.533124	+	1.28707i	0.929444	+	0.368962i	$0.120287\pi$
$617$	13.2425	+	31.9703i	0.533124	+	1.28707i	−0.396321	+	0.918112i	$0.629713\pi$
$618$	−0.750087	−	0.310696i	−0.0301729	−	0.0124980i
$619$	10.9143	−	26.3495i	0.438684	−	1.05908i	−0.537719	−	0.843124i	$-0.680714\pi$
$619$	10.9143	−	26.3495i	0.438684	−	1.05908i	0.976404	−	0.215954i	$-0.0692860\pi$
$620$	−1.81346	+	1.81346i	−0.0728302	+	0.0728302i
$621$	5.11680	−	5.11680i	0.205330	−	0.205330i
$622$	1.34621	−	3.25003i	0.0539779	−	0.130314i
$623$	11.3853	+	4.71595i	0.456142	+	0.188940i
$624$	1.33716	+	3.22820i	0.0535294	+	0.129231i
$625$		−	24.7350i		−	0.989401i
$626$	−3.78308	+	1.56700i	−0.151202	+	0.0626300i
$627$	6.45787	+	6.45787i	0.257902	+	0.257902i
$628$	26.9945			1.07720
$629$	2.57233	−	2.15072i	0.102566	−	0.0857547i
$630$	−0.0852995			−0.00339841
$631$	9.11639	+	9.11639i	0.362918	+	0.362918i	0.864886	−	0.501968i	$-0.167391\pi$
$631$	9.11639	+	9.11639i	0.362918	+	0.362918i	−0.501968	+	0.864886i	$0.667391\pi$
$632$	7.33038	−	3.03634i	0.291587	−	0.120779i
$633$			2.71705i			0.107993i
$634$	−1.41251	−	3.41010i	−0.0560979	−	0.135432i
$635$	−0.747572	−	0.309654i	−0.0296665	−	0.0122883i
$636$	−0.213012	+	0.514256i	−0.00844647	+	0.0203916i
$637$	11.9144	−	11.9144i	0.472068	−	0.472068i
$638$	0.546688	−	0.546688i	0.0216436	−	0.0216436i
$639$	−16.0108	+	38.6535i	−0.633377	+	1.52911i
$640$	0.789784	+	0.327139i	0.0312189	+	0.0129313i
$641$	12.8904	+	31.1201i	0.509140	+	1.22917i	0.944380	+	0.328857i	$0.106663\pi$
$641$	12.8904	+	31.1201i	0.509140	+	1.22917i	−0.435240	+	0.900314i	$0.643337\pi$
$642$			0.0208803i			0.000824081i
$643$	22.4989	−	9.31937i	0.887272	−	0.367520i	0.107959	−	0.994155i	$-0.465568\pi$
$643$	22.4989	−	9.31937i	0.887272	−	0.367520i	0.779313	+	0.626635i	$0.215568\pi$
$644$	−5.38369	−	5.38369i	−0.212147	−	0.212147i
$645$	−0.0437143			−0.00172125
$646$	2.17300	+	6.93455i	0.0854956	+	0.272836i
$647$	−18.8348			−0.740473			−0.370236	−	0.928938i	$-0.620723\pi$
$647$	−18.8348			−0.740473			−0.370236	+	0.928938i	$0.620723\pi$
$648$	4.78295	+	4.78295i	0.187892	+	0.187892i
$649$	8.76584	−	3.63093i	0.344089	−	0.142526i
$650$			3.02048i			0.118473i
$651$	−1.29377	−	3.12344i	−0.0507068	−	0.122417i
$652$	13.1222	+	5.43539i	0.513905	+	0.212866i
$653$	−16.4018	+	39.5974i	−0.641852	+	1.54957i	0.182327	+	0.983238i	$0.441637\pi$
$653$	−16.4018	+	39.5974i	−0.641852	+	1.54957i	−0.824179	+	0.566330i	$0.808363\pi$
$654$	−0.0271104	+	0.0271104i	−0.00106010	+	0.00106010i
$655$	−0.654057	+	0.654057i	−0.0255561	+	0.0255561i
$656$	5.65166	−	13.6443i	0.220660	−	0.532721i
$657$	35.3007	+	14.6220i	1.37721	+	0.570459i
$658$	−0.541032	−	1.30617i	−0.0210916	−	0.0509196i
$659$			18.8170i			0.733006i	0.930417	+	0.366503i	$0.119445\pi$
$659$			18.8170i			0.733006i	−0.930417	+	0.366503i	$0.880555\pi$
$660$	−0.264765	+	0.109669i	−0.0103060	+	0.00426887i
$661$	14.4767	+	14.4767i	0.563078	+	0.563078i	0.930181	−	0.367102i	$-0.119650\pi$
$661$	14.4767	+	14.4767i	0.563078	+	0.563078i	−0.367102	+	0.930181i	$0.619650\pi$
$662$	2.76226			0.107358
$663$	−2.47719	−	2.96281i	−0.0962061	−	0.115066i
$664$	−9.27811			−0.360060
$665$	0.812108	+	0.812108i	0.0314922	+	0.0314922i
$666$	0.462267	−	0.191477i	0.0179125	−	0.00741959i
$667$			4.04835i			0.156753i
$668$	6.92445	+	16.7171i	0.267915	+	0.646804i
$669$	−5.43752	−	2.25230i	−0.210227	−	0.0870788i
$670$	0.0299142	−	0.0722192i	0.00115569	−	0.00279007i
$671$	20.6045	−	20.6045i	0.795429	−	0.795429i
$672$	−0.600073	+	0.600073i	−0.0231483	+	0.0231483i
$673$	−0.499976	+	1.20705i	−0.0192727	+	0.0465284i	−0.933223	−	0.359298i	$-0.883016\pi$
$673$	−0.499976	+	1.20705i	−0.0192727	+	0.0465284i	0.913950	+	0.405826i	$0.133016\pi$
$674$	5.70902	+	2.36475i	0.219903	+	0.0910869i
$675$	3.69273	+	8.91504i	0.142133	+	0.343140i
$676$		−	9.54008i		−	0.366926i
$677$	−11.4191	+	4.72993i	−0.438870	+	0.181786i	−0.591168	−	0.806549i	$-0.701333\pi$
$677$	−11.4191	+	4.72993i	−0.438870	+	0.181786i	0.152297	+	0.988335i	$0.451333\pi$
$678$	−0.0903692	−	0.0903692i	−0.00347061	−	0.00347061i
$679$	8.17479			0.313720
$680$	−0.459520	−	0.0410205i	−0.0176218	−	0.00157306i
$681$	7.91560			0.303327
$682$	−4.97768	−	4.97768i	−0.190605	−	0.190605i
$683$	24.5166	−	10.1551i	0.938102	−	0.388575i	0.139356	−	0.990242i	$-0.455497\pi$
$683$	24.5166	−	10.1551i	0.938102	−	0.388575i	0.798746	+	0.601668i	$0.205497\pi$
$684$		−	46.8308i		−	1.79062i
$685$	−0.802934	−	1.93845i	−0.0306785	−	0.0740645i
$686$	2.64606	+	1.09604i	0.101027	+	0.0418468i
$687$	−0.393095	+	0.949015i	−0.0149975	+	0.0362072i
$688$	2.63783	−	2.63783i	0.100566	−	0.100566i
$689$	−1.74545	+	1.74545i	−0.0664964	+	0.0664964i
$690$	−0.0132978	+	0.0321038i	−0.000506239	+	0.00122217i
$691$	−35.3460	−	14.6408i	−1.34462	−	0.556962i	−0.409834	−	0.912160i	$-0.634413\pi$
$691$	−35.3460	−	14.6408i	−1.34462	−	0.556962i	−0.934791	+	0.355198i	$0.884413\pi$
$692$	−14.6502	−	35.3686i	−0.556915	−	1.34451i
$693$			10.1110i			0.384085i
$694$	2.96854	−	1.22961i	0.112684	−	0.0466753i
$695$	0.638844	+	0.638844i	0.0242327	+	0.0242327i
$696$	0.299680			0.0113593
$697$	−1.45135	+	16.2583i	−0.0549737	+	0.615827i
$698$	5.10248			0.193132
$699$	−0.727897	−	0.727897i	−0.0275316	−	0.0275316i
$700$	9.38004	−	3.88534i	0.354532	−	0.146852i
$701$			26.3920i			0.996813i	0.866943	+	0.498407i	$0.166081\pi$
$701$			26.3920i			0.996813i	−0.866943	+	0.498407i	$0.833919\pi$
$702$	−0.449326	−	1.08477i	−0.0169587	−	0.0409420i
$703$	−6.22408	−	2.57810i	−0.234745	−	0.0972347i
$704$	8.89937	−	21.4850i	0.335407	−	0.809745i
$705$	0.197034	−	0.197034i	0.00742073	−	0.00742073i
$706$	−5.22274	+	5.22274i	−0.196560	+	0.196560i
$707$	−4.79534	+	11.5770i	−0.180347	+	0.435397i
$708$	1.67945	+	0.695650i	0.0631175	+	0.0261441i
$709$	9.52199	+	22.9881i	0.357606	+	0.863337i	0.995636	+	0.0933251i	$0.0297496\pi$
$709$	9.52199	+	22.9881i	0.357606	+	0.863337i	−0.638030	+	0.770012i	$0.720250\pi$
$710$		−	0.409326i		−	0.0153617i
$711$	25.1953	−	10.4362i	0.944896	−	0.391389i
$712$	7.03302	+	7.03302i	0.263573	+	0.263573i
$713$	36.8609			1.38045
$714$	0.139274	−	0.266393i	0.00521218	−	0.00996949i
$715$	−1.27088			−0.0475281
$716$	−11.1504	−	11.1504i	−0.416710	−	0.416710i
$717$	−0.239267	+	0.0991076i	−0.00893559	+	0.00370124i
$718$			2.00174i			0.0747044i
$719$	−2.38620	−	5.76081i	−0.0889904	−	0.214842i	0.873118	−	0.487509i	$-0.162094\pi$
$719$	−2.38620	−	5.76081i	−0.0889904	−	0.214842i	−0.962108	+	0.272667i	$0.912094\pi$
$720$	1.32548	+	0.549033i	0.0493978	+	0.0204612i
$721$	−4.63135	+	11.1811i	−0.172481	+	0.416405i
$722$	7.46617	−	7.46617i	0.277862	−	0.277862i
$723$	0.171937	−	0.171937i	0.00639440	−	0.00639440i
$724$	4.74874	−	11.4645i	0.176486	−	0.426074i
$725$	−4.98756	−	2.06591i	−0.185233	−	0.0767261i
$726$	−0.00663077	−	0.0160081i	−0.000246091	−	0.000594116i
$727$			17.0963i			0.634068i	0.948414	+	0.317034i	$0.102687\pi$
$727$			17.0963i			0.634068i	−0.948414	+	0.317034i	$0.897313\pi$
$728$	−2.30913	+	0.956472i	−0.0855820	+	0.0354492i
$729$	15.0890	+	15.0890i	0.558850	+	0.558850i
$730$	−0.373821			−0.0138357
$731$	−1.91029	+	3.65387i	−0.0706547	+	0.135143i
$732$	5.58278			0.206346
$733$	−1.67138	−	1.67138i	−0.0617338	−	0.0617338i	0.675566	−	0.737300i	$-0.263899\pi$
$733$	−1.67138	−	1.67138i	−0.0617338	−	0.0617338i	−0.737300	+	0.675566i	$0.763899\pi$
$734$	6.78117	−	2.80885i	0.250298	−	0.103677i
$735$			0.258493i			0.00953465i
$736$	−3.54084	−	8.54836i	−0.130517	−	0.315097i
$737$	−8.56051	−	3.54588i	−0.315330	−	0.130614i
$738$	−0.932147	+	2.25040i	−0.0343128	+	0.0828384i
$739$	−30.7155	+	30.7155i	−1.12989	+	1.12989i	−0.139691	+	0.990195i	$0.544611\pi$
$739$	−30.7155	+	30.7155i	−1.12989	+	1.12989i	−0.990195	+	0.139691i	$0.955389\pi$
$740$	0.149481	−	0.149481i	0.00549502	−	0.00549502i
$741$	−2.96945	+	7.16888i	−0.109085	+	0.263355i
$742$	−0.177510	−	0.0735272i	−0.00651661	−	0.00269927i
$743$	14.3830	+	34.7236i	0.527660	+	1.27388i	0.933052	+	0.359741i	$0.117135\pi$
$743$	14.3830	+	34.7236i	0.527660	+	1.27388i	−0.405392	+	0.914143i	$0.632865\pi$
$744$		−	2.72863i		−	0.100036i
$745$	0.700032	−	0.289963i	0.0256472	−	0.0106234i
$746$	1.97685	+	1.97685i	0.0723775	+	0.0723775i
$747$	−31.8898			−1.16679
$748$	−2.40336	+	26.9229i	−0.0878754	+	0.984399i
$749$	0.311250			0.0113728
$750$	−0.0656479	−	0.0656479i	−0.00239712	−	0.00239712i
$751$	−22.6903	+	9.39863i	−0.827980	+	0.342961i	−0.756103	−	0.654453i	$-0.772899\pi$
$751$	−22.6903	+	9.39863i	−0.827980	+	0.342961i	−0.0718775	+	0.997413i	$0.522899\pi$
$752$			23.7791i			0.867133i
$753$	0.189262	+	0.456919i	0.00689710	+	0.0166511i
$754$	0.606879	+	0.251377i	0.0221012	+	0.00915462i
$755$	0.606366	−	1.46390i	0.0220679	−	0.0532766i
$756$	−2.79075	+	2.79075i	−0.101498	+	0.101498i
$757$	−12.6091	+	12.6091i	−0.458284	+	0.458284i	−0.898092	−	0.439808i	$-0.855047\pi$
$757$	−12.6091	+	12.6091i	−0.458284	+	0.458284i	0.439808	+	0.898092i	$0.355047\pi$
$758$	−2.16495	+	5.22664i	−0.0786344	+	0.189840i
$759$	3.80542	+	1.57626i	0.138128	+	0.0572145i
$760$	0.354728	+	0.856390i	0.0128674	+	0.0310645i
$761$		−	45.5897i		−	1.65262i	−0.563213	−	0.826312i	$-0.690435\pi$
$761$		−	45.5897i		−	1.65262i	0.563213	−	0.826312i	$-0.309565\pi$
$762$	0.393139	−	0.162843i	0.0142419	−	0.00589919i
$763$	0.404118	+	0.404118i	0.0146300	+	0.0146300i
$764$	−50.2674			−1.81861
$765$	−1.57942	−	0.140992i	−0.0571040	−	0.00509756i
$766$	−1.68158			−0.0607579
$767$	5.70026	+	5.70026i	0.205825	+	0.205825i
$768$	3.79629	−	1.57247i	0.136987	−	0.0567418i
$769$		−	33.0527i		−	1.19191i	−0.803018	−	0.595955i	$-0.796774\pi$
$769$		−	33.0527i		−	1.19191i	0.803018	−	0.595955i	$-0.203226\pi$
$770$	−0.0378555	−	0.0913912i	−0.00136422	−	0.00329351i
$771$	0.595871	+	0.246818i	0.0214598	+	0.00888893i
$772$	6.96264	−	16.8093i	0.250591	−	0.604980i
$773$	29.8007	−	29.8007i	1.07186	−	1.07186i	0.0746462	−	0.997210i	$-0.476217\pi$
$773$	29.8007	−	29.8007i	1.07186	−	1.07186i	0.997210	−	0.0746462i	$-0.0237827\pi$
$774$	−0.435067	+	0.435067i	−0.0156381	+	0.0156381i
$775$	−18.8105	+	45.4125i	−0.675692	+	1.63127i
$776$	6.09564	+	2.52490i	0.218821	+	0.0906386i
$777$	0.106644	+	0.257460i	0.00382582	+	0.00923634i
$778$			1.10551i			0.0396343i
$779$	30.3000	−	12.5507i	1.08561	−	0.449674i
$780$	−0.172172	−	0.172172i	−0.00616473	−	0.00616473i
$781$	−48.5194			−1.73616
$782$	2.10229	+	2.51442i	0.0751779	+	0.0899154i
$783$	2.09855			0.0749959
$784$	−15.5981	−	15.5981i	−0.557075	−	0.557075i
$785$	−1.69672	+	0.702802i	−0.0605584	+	0.0250841i
$786$		−	0.486434i		−	0.0173505i
$787$	−14.0323	−	33.8769i	−0.500196	−	1.20758i	−0.949377	−	0.314139i	$-0.898284\pi$
$787$	−14.0323	−	33.8769i	−0.500196	−	1.20758i	0.449181	−	0.893441i	$-0.351716\pi$
$788$	19.8490	+	8.22175i	0.707093	+	0.292888i
$789$	1.66705	−	4.02462i	0.0593486	−	0.143280i
$790$	−0.188662	+	0.188662i	−0.00671229	+	0.00671229i
$791$	−1.34708	+	1.34708i	−0.0478965	+	0.0478965i
$792$	−3.12292	+	7.53939i	−0.110968	+	0.267901i
$793$	22.8731	+	9.47434i	0.812247	+	0.336444i
$794$	−0.895598	−	2.16216i	−0.0317836	−	0.0767323i
$795$		−	0.0378689i		−	0.00134307i
$796$	−27.8341	+	11.5293i	−0.986553	+	0.408644i
$797$	3.41658	+	3.41658i	0.121021	+	0.121021i	0.765024	−	0.644002i	$-0.222727\pi$
$797$	3.41658	+	3.41658i	0.121021	+	0.121021i	−0.644002	+	0.765024i	$0.722727\pi$
$798$	−0.603979			−0.0213806
$799$	−7.85885	−	25.0794i	−0.278026	−	0.887246i
$800$	12.3385			0.436231
$801$	24.1732	+	24.1732i	0.854118	+	0.854118i
$802$	4.64605	−	1.92446i	0.164058	−	0.0679550i
$803$			44.3108i			1.56370i
$804$	−0.679355	−	1.64011i	−0.0239590	−	0.0578422i
$805$	0.478551	+	0.198222i	0.0168667	+	0.00698641i
$806$	2.28883	−	5.52572i	0.0806206	−	0.194635i
$807$	−4.46248	+	4.46248i	−0.157087	+	0.157087i
$808$	−7.15142	+	7.15142i	−0.251586	+	0.251586i
$809$	5.72281	−	13.8161i	0.201203	−	0.485748i	−0.790783	−	0.612097i	$-0.790326\pi$
$809$	5.72281	−	13.8161i	0.201203	−	0.485748i	0.991986	+	0.126350i	$0.0403261\pi$
$810$	−0.210143	−	0.0870439i	−0.00738366	−	0.00305841i
$811$	−7.59727	−	18.3414i	−0.266776	−	0.644054i	0.732552	−	0.680711i	$-0.238329\pi$
$811$	−7.59727	−	18.3414i	−0.266776	−	0.644054i	−0.999328	+	0.0366568i	$0.988329\pi$
$812$		−	2.20800i		−	0.0774857i
$813$	−5.27733	+	2.18594i	−0.185084	+	0.0766643i
$814$	0.410303	+	0.410303i	0.0143811	+	0.0143811i
$815$	−0.966293			−0.0338478
$816$	−3.87884	+	3.24308i	−0.135786	+	0.113530i
$817$	8.28424			0.289829
$818$	−1.78088	−	1.78088i	−0.0622669	−	0.0622669i
$819$	−7.93671	+	3.28749i	−0.277331	+	0.114874i
$820$			1.02912i			0.0359386i
$821$	−4.73037	−	11.4201i	−0.165091	−	0.398565i	0.819585	−	0.572957i	$-0.194204\pi$
$821$	−4.73037	−	11.4201i	−0.165091	−	0.398565i	−0.984676	+	0.174392i	$0.944204\pi$
$822$	1.01941	+	0.422253i	0.0355560	+	0.0147278i
$823$	−17.9728	+	43.3901i	−0.626492	+	1.51249i	0.217462	+	0.976069i	$0.430222\pi$
$823$	−17.9728	+	43.3901i	−0.626492	+	1.51249i	−0.843954	+	0.536416i	$0.819778\pi$
$824$	−6.90686	+	6.90686i	−0.240612	+	0.240612i
$825$	−3.88389	+	3.88389i	−0.135220	+	0.135220i
$826$	−0.240124	+	0.579710i	−0.00835498	+	0.0201707i
$827$	14.7685	+	6.11733i	0.513552	+	0.212720i	0.624382	−	0.781119i	$-0.285351\pi$
$827$	14.7685	+	6.11733i	0.513552	+	0.212720i	−0.110830	+	0.993839i	$0.535351\pi$
$828$	−8.08266	−	19.5133i	−0.280892	−	0.678133i
$829$		−	46.3531i		−	1.60991i	−0.593336	−	0.804955i	$-0.702189\pi$
$829$		−	46.3531i		−	1.60991i	0.593336	−	0.804955i	$-0.297811\pi$
$830$	0.288246	−	0.119395i	0.0100052	−	0.00414427i
$831$	0.145067	+	0.145067i	0.00503233	+	0.00503233i
$832$	19.7584			0.684998
$833$	21.6062	+	11.2960i	0.748609	+	0.391383i
$834$	−0.475119			−0.0164520
$835$	−0.870459	−	0.870459i	−0.0301235	−	0.0301235i
$836$	50.1752	−	20.7832i	1.73535	−	0.718804i
$837$		−	19.1076i		−	0.660455i
$838$	0.672508	+	1.62358i	0.0232314	+	0.0560855i
$839$	42.7061	+	17.6894i	1.47438	+	0.610707i	0.967853	−	0.251518i	$-0.0809298\pi$
$839$	42.7061	+	17.6894i	1.47438	+	0.610707i	0.506525	+	0.862225i	$0.330930\pi$
$840$	0.0146734	−	0.0354248i	0.000506281	−	0.00122227i
$841$	19.6759	−	19.6759i	0.678480	−	0.678480i
$842$	−1.07759	+	1.07759i	−0.0371364	+	0.0371364i
$843$	3.31781	−	8.00989i	0.114271	−	0.275875i
$844$	14.9274	+	6.18311i	0.513821	+	0.212831i
$845$	0.248376	+	0.599633i	0.00854439	+	0.0206280i
$846$		−	3.92196i		−	0.134840i
$847$	−0.238623	+	0.0988407i	−0.00819917	+	0.00339621i
$848$	2.28510	+	2.28510i	0.0784707	+	0.0784707i
$849$	−5.34069			−0.183292
$850$	−4.17058	+	1.30689i	−0.143050	+	0.0448259i
$851$	−3.03839			−0.104155
$852$	−6.57316	−	6.57316i	−0.225193	−	0.225193i
$853$	−45.6086	+	18.8917i	−1.56161	+	0.646839i	−0.985368	−	0.170441i	$-0.945481\pi$
$853$	−45.6086	+	18.8917i	−1.56161	+	0.646839i	−0.576240	+	0.817280i	$0.695481\pi$
$854$			1.92706i			0.0659426i
$855$	1.21924	+	2.94350i	0.0416971	+	0.100666i
$856$	0.232088	+	0.0961338i	0.00793259	+	0.00328579i
$857$	14.1456	−	34.1504i	0.483203	−	1.16656i	−0.474876	−	0.880052i	$-0.657507\pi$
$857$	14.1456	−	34.1504i	0.483203	−	1.16656i	0.958079	−	0.286503i	$-0.0924927\pi$
$858$	0.472586	−	0.472586i	0.0161338	−	0.0161338i
$859$	23.0852	−	23.0852i	0.787657	−	0.787657i	−0.193452	−	0.981110i	$-0.561969\pi$
$859$	23.0852	−	23.0852i	0.787657	−	0.787657i	0.981110	+	0.193452i	$0.0619685\pi$
$860$	−0.0994794	+	0.240165i	−0.00339222	+	0.00818955i
$861$	−1.25337	−	0.519161i	−0.0427146	−	0.0176930i
$862$	2.53526	+	6.12065i	0.0863511	+	0.208470i
$863$		−	0.0581099i		−	0.00197808i	−1.00000		0.000989042i	$-0.999685\pi$
$863$		−	0.0581099i		−	0.00197808i	1.00000		0.000989042i	$-0.000314822\pi$
$864$	−4.43122	+	1.83547i	−0.150753	+	0.0624440i
$865$	1.84164	+	1.84164i	0.0626177	+	0.0626177i
$866$	5.78156			0.196465
$867$	3.01913	−	4.70236i	0.102535	−	0.159700i
$868$	−20.1042			−0.682381
$869$	22.3631	+	22.3631i	0.758615	+	0.758615i
$870$	−0.00931024	+	0.00385643i	−0.000315647	+	0.000130745i
$871$		−	7.87256i		−	0.266751i
$872$	0.176518	+	0.426153i	0.00597767	+	0.0144314i
$873$	20.9514	+	8.67834i	0.709096	+	0.293717i
$874$	2.52005	−	6.08394i	0.0852420	−	0.205792i
$875$	−0.978571	+	0.978571i	−0.0330817	+	0.0330817i
$876$	−6.00300	+	6.00300i	−0.202823	+	0.202823i
$877$	15.3040	−	36.9472i	0.516781	−	1.24762i	−0.423090	−	0.906088i	$-0.639054\pi$
$877$	15.3040	−	36.9472i	0.516781	−	1.24762i	0.939870	−	0.341531i	$-0.110946\pi$
$878$	−0.317673	−	0.131584i	−0.0107209	−	0.00444076i
$879$	−3.18393	−	7.68670i	−0.107391	−	0.259266i
$880$			1.66380i			0.0560867i
$881$	7.40642	−	3.06784i	0.249529	−	0.103358i	−0.254414	−	0.967096i	$-0.581882\pi$
$881$	7.40642	−	3.06784i	0.249529	−	0.103358i	0.503942	+	0.863737i	$0.331882\pi$
$882$	2.57265	+	2.57265i	0.0866255	+	0.0866255i
$883$	55.9108			1.88155			0.940774	−	0.339035i	$-0.110100\pi$
$883$	55.9108			1.88155			0.940774	+	0.339035i	$0.110100\pi$
$884$	−21.9148	+	6.86719i	−0.737075	+	0.230969i
$885$	−0.123671			−0.00415717
$886$	−1.93342	−	1.93342i	−0.0649546	−	0.0649546i
$887$	−33.1353	+	13.7251i	−1.11257	+	0.460843i	−0.861823	−	0.507209i	$-0.830677\pi$
$887$	−33.1353	+	13.7251i	−1.11257	+	0.460843i	−0.250750	+	0.968052i	$0.580677\pi$
$888$			0.224917i			0.00754772i
$889$	−2.42740	−	5.86027i	−0.0814125	−	0.196547i
$890$	−0.309001	−	0.127993i	−0.0103577	−	0.00429032i
$891$	−10.3178	+	24.9093i	−0.345658	+	0.834492i
$892$	−24.7480	+	24.7480i	−0.828625	+	0.828625i
$893$	−37.3397	+	37.3397i	−1.24952	+	1.24952i
$894$	−0.152488	+	0.368138i	−0.00509995	+	0.0123124i
$895$	0.991148	+	0.410547i	0.0331304	+	0.0137231i
$896$	2.56447	+	6.19117i	0.0856728	+	0.206832i
$897$			3.49961i			0.116849i
$898$	0.252139	−	0.104439i	0.00841397	−	0.00348518i
$899$	7.55884	+	7.55884i	0.252102	+	0.252102i
$900$	28.1650			0.938833
$901$	−3.16528	−	1.65485i	−0.105451	−	0.0551310i
$902$	−2.82480			−0.0940554
$903$	−0.242311	−	0.242311i	−0.00806361	−	0.00806361i
$904$	−1.42053	+	0.588402i	−0.0472461	+	0.0195700i
$905$			0.844222i			0.0280629i
$906$	0.318880	+	0.769845i	0.0105941	+	0.0255764i
$907$	4.44561	+	1.84143i	0.147614	+	0.0611437i	0.455267	−	0.890355i	$-0.349544\pi$
$907$	4.44561	+	1.84143i	0.147614	+	0.0611437i	−0.307653	+	0.951499i	$0.599544\pi$
$908$	18.0133	−	43.4880i	0.597792	−	1.44320i
$909$	−24.5802	+	24.5802i	−0.815273	+	0.815273i
$910$	0.0594300	−	0.0594300i	0.00197009	−	0.00197009i
$911$	−12.4417	+	30.0369i	−0.412212	+	0.995169i	0.572330	+	0.820023i	$0.306040\pi$
$911$	−12.4417	+	30.0369i	−0.412212	+	0.995169i	−0.984543	+	0.175145i	$0.943960\pi$
$912$	9.38531	+	3.88752i	0.310779	+	0.128729i
$913$	−14.1525	−	34.1672i	−0.468381	−	1.13077i
$914$			2.74555i			0.0908148i
$915$	−0.350901	+	0.145348i	−0.0116004	+	0.00480505i
$916$	4.31929	+	4.31929i	0.142713	+	0.142713i
$917$	−7.25096			−0.239448
$918$	1.30340	−	1.08977i	0.0430186	−	0.0359677i
$919$	1.11093			0.0366461			0.0183231	−	0.999832i	$-0.494167\pi$
$919$	1.11093			0.0366461			0.0183231	+	0.999832i	$0.494167\pi$
$920$	0.295614	+	0.295614i	0.00974611	+	0.00974611i
$921$	−3.78108	+	1.56618i	−0.124591	+	0.0516073i
$922$		−	3.78452i		−	0.124637i
$923$	−15.7756	−	38.0858i	−0.519262	−	1.25361i
$924$	−2.07551	−	0.859704i	−0.0682792	−	0.0282822i
$925$	1.55052	−	3.74329i	0.0509808	−	0.123079i
$926$	1.42022	−	1.42022i	0.0466715	−	0.0466715i
$927$	−23.7396	+	23.7396i	−0.779711	+	0.779711i
$928$	1.02686	−	2.47906i	0.0337084	−	0.0813792i
$929$	−0.0224670	−	0.00930612i	−0.000737117	−	0.000305324i	0.382315	−	0.924032i	$-0.375127\pi$
$929$	−0.0224670	−	0.00930612i	−0.000737117	−	0.000305324i	−0.383052	+	0.923727i	$0.625127\pi$
$930$	0.0351134	+	0.0847712i	0.00115141	+	0.00277976i
$931$		−	48.9866i		−	1.60547i
$932$	−5.65549	+	2.34258i	−0.185252	+	0.0767338i
$933$	3.84321	+	3.84321i	0.125821	+	0.125821i
$934$	8.98610			0.294034
$935$	−0.549877	−	1.75478i	−0.0179829	−	0.0573876i
$936$	−6.93350			−0.226629
$937$	−3.51737	−	3.51737i	−0.114907	−	0.114907i	0.647315	−	0.762222i	$-0.275892\pi$
$937$	−3.51737	−	3.51737i	−0.114907	−	0.114907i	−0.762222	+	0.647315i	$0.775892\pi$
$938$	0.566131	−	0.234499i	0.0184848	−	0.00765667i
$939$		−	6.32656i		−	0.206459i
$940$	−0.634112	−	1.53088i	−0.0206824	−	0.0499318i
$941$	5.28011	+	2.18709i	0.172127	+	0.0712972i	0.467083	−	0.884214i	$-0.345305\pi$
$941$	5.28011	+	2.18709i	0.172127	+	0.0712972i	−0.294956	+	0.955511i	$0.595305\pi$
$942$	0.369595	−	0.892281i	0.0120421	−	0.0290721i
$943$	10.4591	−	10.4591i	0.340596	−	0.340596i
$944$	7.46264	−	7.46264i	0.242888	−	0.242888i
$945$	0.102753	−	0.248067i	0.00334254	−	0.00806961i
$946$	−0.659217	−	0.273057i	−0.0214330	−	0.00887784i
$947$	−21.9899	−	53.0883i	−0.714575	−	1.72514i	−0.688239	−	0.725484i	$-0.741616\pi$
$947$	−21.9899	−	53.0883i	−0.714575	−	1.72514i	−0.0263363	−	0.999653i	$-0.508384\pi$
$948$			6.05926i			0.196796i
$949$	−34.7822	+	14.4073i	−1.12908	+	0.467679i
$950$	6.20940	+	6.20940i	0.201459	+	0.201459i
$951$	5.70281			0.184926
$952$	−2.31977	−	2.77452i	−0.0751841	−	0.0899229i
$953$	−28.9354			−0.937309			−0.468655	−	0.883382i	$-0.655261\pi$
$953$	−28.9354			−0.937309			−0.468655	+	0.883382i	$0.655261\pi$
$954$	−0.376889	−	0.376889i	−0.0122022	−	0.0122022i
$955$	3.15951	−	1.30871i	0.102239	−	0.0423489i
$956$			1.54006i			0.0498090i
$957$	0.457122	+	1.10359i	0.0147767	+	0.0356740i
$958$	−3.92107	−	1.62416i	−0.126684	−	0.0524742i
$959$	6.29426	−	15.1957i	0.203252	−	0.490694i
$960$	−0.214336	+	0.214336i	−0.00691767	+	0.00691767i
$961$	46.9041	−	46.9041i	1.51304	−	1.51304i
$962$	−0.188665	+	0.455478i	−0.00608280	+	0.0146852i
$963$	0.797709	+	0.330422i	0.0257058	+	0.0106477i
$964$	−0.553341	−	1.33588i	−0.0178219	−	0.0430259i
$965$			1.23780i			0.0398463i
$966$	−0.251664	+	0.104243i	−0.00809715	+	0.00335395i
$967$	−22.6308	−	22.6308i	−0.727758	−	0.727758i	0.242415	−	0.970173i	$-0.422061\pi$
$967$	−22.6308	−	22.6308i	−0.727758	−	0.727758i	−0.970173	+	0.242415i	$0.922061\pi$
$968$	−0.208460			−0.00670017
$969$	−11.1834	−	0.998317i	−0.359261	−	0.0320706i
$970$	−0.221867			−0.00712372
$971$	−34.5039	−	34.5039i	−1.10728	−	1.10728i	−0.993507	−	0.113775i	$-0.963706\pi$
$971$	−34.5039	−	34.5039i	−1.10728	−	1.10728i	−0.113775	−	0.993507i	$-0.536294\pi$
$972$	−15.2654	+	6.32314i	−0.489638	+	0.202815i
$973$			7.08230i			0.227048i
$974$	0.581999	+	1.40507i	0.0186485	+	0.0450214i
$975$	−4.31151	−	1.78589i	−0.138079	−	0.0571941i
$976$	12.4036	−	29.9449i	0.397029	−	0.958512i
$977$	−1.14773	+	1.14773i	−0.0367192	+	0.0367192i	−0.725228	−	0.688509i	$-0.758266\pi$
$977$	−1.14773	+	1.14773i	−0.0367192	+	0.0367192i	0.688509	+	0.725228i	$0.258266\pi$
$978$	0.359324	−	0.359324i	0.0114899	−	0.0114899i
$979$	−15.1716	+	36.6275i	−0.484887	+	1.17062i
$980$	1.42015	+	0.588244i	0.0453649	+	0.0187908i
$981$	0.606712	+	1.46473i	0.0193708	+	0.0467653i
$982$			3.55654i			0.113494i
$983$	−52.7716	+	21.8587i	−1.68315	+	0.697185i	−0.999469	−	0.0325928i	$-0.989624\pi$
$983$	−52.7716	+	21.8587i	−1.68315	+	0.697185i	−0.683684	+	0.729778i	$0.739624\pi$
$984$	−0.774239	−	0.774239i	−0.0246818	−	0.0246818i
$985$	−1.46165			−0.0465719
$986$	−0.0845121	+	0.946723i	−0.00269142	+	0.0301498i
$987$	2.18434			0.0695284
$988$	32.6280	+	32.6280i	1.03804	+	1.03804i
$989$	3.45185	−	1.42980i	0.109762	−	0.0454651i
$990$		−	0.274416i		−	0.00872151i
$991$	−8.18627	−	19.7634i	−0.260045	−	0.627805i	0.738895	−	0.673820i	$-0.235348\pi$
$991$	−8.18627	−	19.7634i	−0.260045	−	0.627805i	−0.998941	+	0.0460151i	$0.985348\pi$
$992$	−22.5723	−	9.34973i	−0.716670	−	0.296854i
$993$	−1.63321	+	3.94292i	−0.0518284	+	0.125125i
$994$	2.26892	−	2.26892i	0.0719656	−	0.0719656i
$995$	1.44932	−	1.44932i	0.0459465	−	0.0459465i
$996$	2.71149	−	6.54611i	0.0859167	−	0.207421i
$997$	−50.2716	−	20.8232i	−1.59212	−	0.659476i	−0.601843	−	0.798614i	$-0.705567\pi$
$997$	−50.2716	−	20.8232i	−1.59212	−	0.659476i	−0.990273	+	0.139138i	$0.955567\pi$
$998$	−2.98967	−	7.21769i	−0.0946362	−	0.228472i
$999$			1.57501i			0.0498312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.87.15	✓	128
17.9	even	8	inner	731.2.m.c.689.15	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.15	✓	128	1.1	even	1	trivial
731.2.m.c.689.15	yes	128	17.9	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.150441 - 0.150441i) q^{2} +(0.303692 - 0.125793i) q^{3} -1.95474i q^{4} +(0.0508915 + 0.122863i) q^{5} +(-0.0646121 - 0.0267632i) q^{6} +(-0.398942 + 0.963131i) q^{7} +(-0.594953 + 0.594953i) q^{8} +(-2.04492 + 2.04492i) q^{9} +O(q^{10})\)	\(q+(-0.150441 - 0.150441i) q^{2} +(0.303692 - 0.125793i) q^{3} -1.95474i q^{4} +(0.0508915 + 0.122863i) q^{5} +(-0.0646121 - 0.0267632i) q^{6} +(-0.398942 + 0.963131i) q^{7} +(-0.594953 + 0.594953i) q^{8} +(-2.04492 + 2.04492i) q^{9} +(0.0108274 - 0.0261397i) q^{10} +(-3.09848 - 1.28343i) q^{11} +(-0.245893 - 0.593638i) q^{12} -2.84947i q^{13} +(0.204911 - 0.0848770i) q^{14} +(0.0309107 + 0.0309107i) q^{15} -3.73046 q^{16} +(3.93446 - 1.23290i) q^{17} +0.615277 q^{18} +(-5.85784 - 5.85784i) q^{19} +(0.240165 - 0.0994794i) q^{20} +0.342680i q^{21} +(0.273057 + 0.659217i) q^{22} +(-3.45185 - 1.42980i) q^{23} +(-0.105841 + 0.255524i) q^{24} +(3.52303 - 3.52303i) q^{25} +(-0.428677 + 0.428677i) q^{26} +(-0.741168 + 1.78934i) q^{27} +(1.88267 + 0.779826i) q^{28} +(-0.414650 - 1.00105i) q^{29} -0.00930046i q^{30} +(-9.11474 + 3.77545i) q^{31} +(1.75112 + 1.75112i) q^{32} -1.10243 q^{33} +(-0.777380 - 0.406425i) q^{34} -0.138636 q^{35} +(3.99727 + 3.99727i) q^{36} +(0.751315 - 0.311205i) q^{37} +1.76252i q^{38} +(-0.358445 - 0.865363i) q^{39} +(-0.103376 - 0.0428197i) q^{40} +(-1.51500 + 3.65754i) q^{41} +(0.0515530 - 0.0515530i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-2.50877 + 6.05670i) q^{44} +(-0.355313 - 0.147176i) q^{45} +(0.304198 + 0.734399i) q^{46} -6.37430i q^{47} +(-1.13291 + 0.469267i) q^{48} +(4.18128 + 4.18128i) q^{49} -1.06001 q^{50} +(1.03977 - 0.869350i) q^{51} -5.56997 q^{52} +(-0.612552 - 0.612552i) q^{53} +(0.380691 - 0.157687i) q^{54} -0.446004i q^{55} +(-0.335666 - 0.810370i) q^{56} +(-2.51586 - 1.04210i) q^{57} +(-0.0882189 + 0.212979i) q^{58} +(-2.00046 + 2.00046i) q^{59} +(0.0604222 - 0.0604222i) q^{60} +(-3.32494 + 8.02713i) q^{61} +(1.93921 + 0.803246i) q^{62} +(-1.15372 - 2.78533i) q^{63} +6.93404i q^{64} +(0.350095 - 0.145014i) q^{65} +(0.165850 + 0.165850i) q^{66} +2.76281 q^{67} +(-2.40999 - 7.69083i) q^{68} -1.22816 q^{69} +(0.0208565 + 0.0208565i) q^{70} +(13.3659 - 5.53634i) q^{71} -2.43326i q^{72} +(-5.05611 - 12.2065i) q^{73} +(-0.159846 - 0.0662105i) q^{74} +(0.626742 - 1.51309i) q^{75} +(-11.4505 + 11.4505i) q^{76} +(2.47223 - 2.47223i) q^{77} +(-0.0762611 + 0.184110i) q^{78} +(-8.71221 - 3.60872i) q^{79} +(-0.189849 - 0.458336i) q^{80} -8.03920i q^{81} +(0.778161 - 0.322325i) q^{82} +(7.79734 + 7.79734i) q^{83} +0.669848 q^{84} +(0.351708 + 0.420655i) q^{85} +0.212755 q^{86} +(-0.251852 - 0.251852i) q^{87} +(2.60703 - 1.07987i) q^{88} -11.8211i q^{89} +(0.0313124 + 0.0755948i) q^{90} +(2.74442 + 1.13678i) q^{91} +(-2.79489 + 6.74745i) q^{92} +(-2.29315 + 2.29315i) q^{93} +(-0.958954 + 0.958954i) q^{94} +(0.421598 - 1.01783i) q^{95} +(0.752080 + 0.311522i) q^{96} +(-3.00086 - 7.24472i) q^{97} -1.25807i q^{98} +(8.96063 - 3.71162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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