LMFDB - Embedded newform 731.2.m.c.689.6

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			689.6
Character	$\chi$	$=$	731.689
Dual form			731.2.m.c.87.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15376 + 1.15376i) q^{2} +(0.645285 + 0.267286i) q^{3} -0.662305i q^{4} +(0.125261 - 0.302406i) q^{5} +(-1.05288 + 0.436119i) q^{6} +(0.205763 + 0.496757i) q^{7} +(-1.54337 - 1.54337i) q^{8} +(-1.77637 - 1.77637i) q^{9} +O(q^{10})$	\(q+(-1.15376 + 1.15376i) q^{2} +(0.645285 + 0.267286i) q^{3} -0.662305i q^{4} +(0.125261 - 0.302406i) q^{5} +(-1.05288 + 0.436119i) q^{6} +(0.205763 + 0.496757i) q^{7} +(-1.54337 - 1.54337i) q^{8} +(-1.77637 - 1.77637i) q^{9} +(0.204383 + 0.493423i) q^{10} +(5.51981 - 2.28638i) q^{11} +(0.177025 - 0.427376i) q^{12} +3.02723i q^{13} +(-0.810537 - 0.335735i) q^{14} +(0.161658 - 0.161658i) q^{15} +4.88596 q^{16} +(0.0210706 + 4.12305i) q^{17} +4.09899 q^{18} +(-1.54151 + 1.54151i) q^{19} +(-0.200285 - 0.0829608i) q^{20} +0.375547i q^{21} +(-3.73059 + 9.00643i) q^{22} +(6.80846 - 2.82016i) q^{23} +(-0.583394 - 1.40844i) q^{24} +(3.45977 + 3.45977i) q^{25} +(-3.49269 - 3.49269i) q^{26} +(-1.47332 - 3.55692i) q^{27} +(0.329004 - 0.136278i) q^{28} +(-3.74945 + 9.05197i) q^{29} +0.373027i q^{30} +(7.55856 + 3.13086i) q^{31} +(-2.55046 + 2.55046i) q^{32} +4.17296 q^{33} +(-4.78131 - 4.73268i) q^{34} +0.175996 q^{35} +(-1.17650 + 1.17650i) q^{36} +(-7.45467 - 3.08782i) q^{37} -3.55706i q^{38} +(-0.809137 + 1.95343i) q^{39} +(-0.660049 + 0.273401i) q^{40} +(2.26733 + 5.47382i) q^{41} +(-0.433290 - 0.433290i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(-1.51428 - 3.65580i) q^{44} +(-0.759694 + 0.314676i) q^{45} +(-4.60153 + 11.1091i) q^{46} -5.04755i q^{47} +(3.15284 + 1.30595i) q^{48} +(4.74532 - 4.74532i) q^{49} -7.98347 q^{50} +(-1.08844 + 2.66618i) q^{51} +2.00495 q^{52} +(4.11065 - 4.11065i) q^{53} +(5.80367 + 2.40396i) q^{54} -1.95562i q^{55} +(0.449111 - 1.08425i) q^{56} +(-1.40674 + 0.582691i) q^{57} +(-6.11781 - 14.7697i) q^{58} +(8.90947 + 8.90947i) q^{59} +(-0.107067 - 0.107067i) q^{60} +(-1.54398 - 3.72750i) q^{61} +(-12.3330 + 5.10848i) q^{62} +(0.516912 - 1.24794i) q^{63} +3.88671i q^{64} +(0.915454 + 0.379193i) q^{65} +(-4.81458 + 4.81458i) q^{66} -9.13376 q^{67} +(2.73072 - 0.0139552i) q^{68} +5.14719 q^{69} +(-0.203057 + 0.203057i) q^{70} +(7.17245 + 2.97093i) q^{71} +5.48320i q^{72} +(-2.55372 + 6.16522i) q^{73} +(12.1635 - 5.03827i) q^{74} +(1.30779 + 3.15729i) q^{75} +(1.02095 + 1.02095i) q^{76} +(2.27155 + 2.27155i) q^{77} +(-1.32023 - 3.18733i) q^{78} +(-10.1769 + 4.21542i) q^{79} +(0.612019 - 1.47754i) q^{80} +4.84747i q^{81} +(-8.93139 - 3.69950i) q^{82} +(3.94233 - 3.94233i) q^{83} +0.248727 q^{84} +(1.24948 + 0.510084i) q^{85} +1.63166 q^{86} +(-4.83893 + 4.83893i) q^{87} +(-12.0479 - 4.99039i) q^{88} -4.71666i q^{89} +(0.513443 - 1.23956i) q^{90} +(-1.50380 + 0.622894i) q^{91} +(-1.86780 - 4.50928i) q^{92} +(4.04059 + 4.04059i) q^{93} +(5.82364 + 5.82364i) q^{94} +(0.273072 + 0.659254i) q^{95} +(-2.32748 + 0.964072i) q^{96} +(-1.78681 + 4.31373i) q^{97} +10.9499i q^{98} +(-13.8667 - 5.74376i) 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 $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.15376	+	1.15376i	−0.815829	+	0.815829i	−0.985501	−	0.169672i	$-0.945729\pi$
$2$	−1.15376	+	1.15376i	−0.815829	+	0.815829i	0.169672	+	0.985501i	$0.445729\pi$
$3$	0.645285	+	0.267286i	0.372555	+	0.154318i	0.561102	−	0.827747i	$-0.310378\pi$
$3$	0.645285	+	0.267286i	0.372555	+	0.154318i	−0.188546	+	0.982064i	$0.560378\pi$
$4$		−	0.662305i		−	0.331153i
$5$	0.125261	−	0.302406i	0.0560183	−	0.135240i	−0.893392	−	0.449277i	$-0.851682\pi$
$5$	0.125261	−	0.302406i	0.0560183	−	0.135240i	0.949411	+	0.314037i	$0.101682\pi$
$6$	−1.05288	+	0.436119i	−0.429838	+	0.178045i
$7$	0.205763	+	0.496757i	0.0777712	+	0.187756i	0.957983	−	0.286824i	$-0.0925996\pi$
$7$	0.205763	+	0.496757i	0.0777712	+	0.187756i	−0.880212	+	0.474581i	$0.842600\pi$
$8$	−1.54337	−	1.54337i	−0.545665	−	0.545665i
$9$	−1.77637	−	1.77637i	−0.592123	−	0.592123i
$10$	0.204383	+	0.493423i	0.0646314	+	0.156034i
$11$	5.51981	−	2.28638i	1.66428	−	0.689369i	0.665892	−	0.746048i	$-0.268051\pi$
$11$	5.51981	−	2.28638i	1.66428	−	0.689369i	0.998392	+	0.0566792i	$0.0180512\pi$
$12$	0.177025	−	0.427376i	0.0511026	−	0.123373i
$13$			3.02723i			0.839604i	0.907616	+	0.419802i	$0.137900\pi$
$13$			3.02723i			0.839604i	−0.907616	+	0.419802i	$0.862100\pi$
$14$	−0.810537	−	0.335735i	−0.216625	−	0.0897290i
$15$	0.161658	−	0.161658i	0.0417398	−	0.0417398i
$16$	4.88596			1.22149
$17$	0.0210706	+	4.12305i	0.00511038	+	0.999987i
$17$	0.0210706	+	4.12305i	0.00511038	+	0.999987i
$18$	4.09899			0.966142
$19$	−1.54151	+	1.54151i	−0.353647	+	0.353647i	−0.861465	−	0.507817i	$-0.830452\pi$
$19$	−1.54151	+	1.54151i	−0.353647	+	0.353647i	0.507817	+	0.861465i	$0.330452\pi$
$20$	−0.200285	−	0.0829608i	−0.0447851	−	0.0185506i
$21$			0.375547i			0.0819511i
$22$	−3.73059	+	9.00643i	−0.795364	+	1.92018i
$23$	6.80846	−	2.82016i	1.41966	−	0.588043i	0.464887	−	0.885370i	$-0.346095\pi$
$23$	6.80846	−	2.82016i	1.41966	−	0.588043i	0.954776	+	0.297327i	$0.0960951\pi$
$24$	−0.583394	−	1.40844i	−0.119085	−	0.287496i
$25$	3.45977	+	3.45977i	0.691955	+	0.691955i
$26$	−3.49269	−	3.49269i	−0.684973	−	0.684973i
$27$	−1.47332	−	3.55692i	−0.283541	−	0.684529i
$28$	0.329004	−	0.136278i	0.0621760	−	0.0257541i
$29$	−3.74945	+	9.05197i	−0.696255	+	1.68091i	0.0355262	+	0.999369i	$0.488689\pi$
$29$	−3.74945	+	9.05197i	−0.696255	+	1.68091i	−0.731781	+	0.681540i	$0.761311\pi$
$30$			0.373027i			0.0681051i
$31$	7.55856	+	3.13086i	1.35756	+	0.562318i	0.938386	−	0.345589i	$-0.112321\pi$
$31$	7.55856	+	3.13086i	1.35756	+	0.562318i	0.419171	+	0.907907i	$0.362321\pi$
$32$	−2.55046	+	2.55046i	−0.450862	+	0.450862i
$33$	4.17296			0.726420
$34$	−4.78131	−	4.73268i	−0.819987	−	0.811649i
$35$	0.175996			0.0297488
$36$	−1.17650	+	1.17650i	−0.196083	+	0.196083i
$37$	−7.45467	−	3.08782i	−1.22554	−	0.507635i	−0.326373	−	0.945241i	$-0.605827\pi$
$37$	−7.45467	−	3.08782i	−1.22554	−	0.507635i	−0.899167	+	0.437606i	$0.855827\pi$
$38$		−	3.55706i		−	0.577031i
$39$	−0.809137	+	1.95343i	−0.129566	+	0.312799i
$40$	−0.660049	+	0.273401i	−0.104363	+	0.0432286i
$41$	2.26733	+	5.47382i	0.354097	+	0.854867i	0.996106	+	0.0881688i	$0.0281015\pi$
$41$	2.26733	+	5.47382i	0.354097	+	0.854867i	−0.642008	+	0.766698i	$0.721899\pi$
$42$	−0.433290	−	0.433290i	−0.0668581	−	0.0668581i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$44$	−1.51428	−	3.65580i	−0.228286	−	0.551132i
$45$	−0.759694	+	0.314676i	−0.113249	+	0.0469091i
$46$	−4.60153	+	11.1091i	−0.678459	+	1.63794i
$47$		−	5.04755i		−	0.736260i	−0.929774	−	0.368130i	$-0.879998\pi$
$47$		−	5.04755i		−	0.736260i	0.929774	−	0.368130i	$-0.120002\pi$
$48$	3.15284	+	1.30595i	0.455073	+	0.188497i
$49$	4.74532	−	4.74532i	0.677903	−	0.677903i
$50$	−7.98347			−1.12903
$51$	−1.08844	+	2.66618i	−0.152412	+	0.373339i
$52$	2.00495			0.278037
$53$	4.11065	−	4.11065i	0.564642	−	0.564642i	−0.365981	−	0.930622i	$-0.619266\pi$
$53$	4.11065	−	4.11065i	0.564642	−	0.564642i	0.930622	+	0.365981i	$0.119266\pi$
$54$	5.80367	+	2.40396i	0.789779	+	0.327137i
$55$		−	1.95562i		−	0.263695i
$56$	0.449111	−	1.08425i	0.0600150	−	0.144889i
$57$	−1.40674	+	0.582691i	−0.186327	+	0.0771792i
$58$	−6.11781	−	14.7697i	−0.803308	−	1.93936i
$59$	8.90947	+	8.90947i	1.15991	+	1.15991i	0.984494	+	0.175420i	$0.0561283\pi$
$59$	8.90947	+	8.90947i	1.15991	+	1.15991i	0.175420	+	0.984494i	$0.443872\pi$
$60$	−0.107067	−	0.107067i	−0.0138223	−	0.0138223i
$61$	−1.54398	−	3.72750i	−0.197686	−	0.477257i	0.793687	−	0.608326i	$-0.208159\pi$
$61$	−1.54398	−	3.72750i	−0.197686	−	0.477257i	−0.991373	+	0.131070i	$0.958159\pi$
$62$	−12.3330	+	5.10848i	−1.56629	+	0.648778i
$63$	0.516912	−	1.24794i	0.0651247	−	0.157225i
$64$			3.88671i			0.485838i
$65$	0.915454	+	0.379193i	0.113548	+	0.0470332i
$66$	−4.81458	+	4.81458i	−0.592634	+	0.592634i
$67$	−9.13376			−1.11587			−0.557933	−	0.829886i	$-0.688405\pi$
$67$	−9.13376			−1.11587			−0.557933	+	0.829886i	$0.688405\pi$
$68$	2.73072	−	0.0139552i	0.331148	−	0.00169231i
$69$	5.14719			0.619648
$70$	−0.203057	+	0.203057i	−0.0242699	+	0.0242699i
$71$	7.17245	+	2.97093i	0.851213	+	0.352584i	0.765265	−	0.643716i	$-0.222608\pi$
$71$	7.17245	+	2.97093i	0.851213	+	0.352584i	0.0859484	+	0.996300i	$0.472608\pi$
$72$			5.48320i			0.646202i
$73$	−2.55372	+	6.16522i	−0.298890	+	0.721585i	0.701074	+	0.713089i	$0.252704\pi$
$73$	−2.55372	+	6.16522i	−0.298890	+	0.721585i	−0.999964	+	0.00849609i	$0.997296\pi$
$74$	12.1635	−	5.03827i	1.41397	−	0.585687i
$75$	1.30779	+	3.15729i	0.151011	+	0.364572i
$76$	1.02095	+	1.02095i	0.117111	+	0.117111i
$77$	2.27155	+	2.27155i	0.258867	+	0.258867i
$78$	−1.32023	−	3.18733i	−0.149487	−	0.360894i
$79$	−10.1769	+	4.21542i	−1.14499	+	0.474272i	−0.872852	−	0.487985i	$-0.837732\pi$
$79$	−10.1769	+	4.21542i	−1.14499	+	0.474272i	−0.272142	+	0.962257i	$0.587732\pi$
$80$	0.612019	−	1.47754i	0.0684258	−	0.165195i
$81$			4.84747i			0.538608i
$82$	−8.93139	−	3.69950i	−0.986307	−	0.408542i
$83$	3.94233	−	3.94233i	0.432727	−	0.432727i	−0.456828	−	0.889555i	$-0.651014\pi$
$83$	3.94233	−	3.94233i	0.432727	−	0.432727i	0.889555	+	0.456828i	$0.151014\pi$
$84$	0.248727			0.0271383
$85$	1.24948	+	0.510084i	0.135525	+	0.0553264i
$86$	1.63166			0.175946
$87$	−4.83893	+	4.83893i	−0.518787	+	0.518787i
$88$	−12.0479	−	4.99039i	−1.28431	−	0.531977i
$89$		−	4.71666i		−	0.499965i	−0.968250	−	0.249982i	$-0.919575\pi$
$89$		−	4.71666i		−	0.499965i	0.968250	−	0.249982i	$-0.0804248\pi$
$90$	0.513443	−	1.23956i	0.0541216	−	0.130661i
$91$	−1.50380	+	0.622894i	−0.157641	+	0.0652970i
$92$	−1.86780	−	4.50928i	−0.194732	−	0.470125i
$93$	4.04059	+	4.04059i	0.418990	+	0.418990i
$94$	5.82364	+	5.82364i	0.600662	+	0.600662i
$95$	0.273072	+	0.659254i	0.0280166	+	0.0676380i
$96$	−2.32748	+	0.964072i	−0.237547	+	0.0983952i
$97$	−1.78681	+	4.31373i	−0.181423	+	0.437993i	−0.988260	−	0.152780i	$-0.951177\pi$
$97$	−1.78681	+	4.31373i	−0.181423	+	0.437993i	0.806838	+	0.590773i	$0.201177\pi$
$98$			10.9499i			1.10610i
$99$	−13.8667	−	5.74376i	−1.39365	−	0.577270i
$100$	2.29143	−	2.29143i	0.229143	−	0.229143i
$101$	−9.20709			−0.916140			−0.458070	−	0.888916i	$-0.651459\pi$
$101$	−9.20709			−0.916140			−0.458070	+	0.888916i	$0.651459\pi$
$102$	−1.82033	−	4.33191i	−0.180239	−	0.428923i
$103$	−3.32995			−0.328109			−0.164055	−	0.986451i	$-0.552457\pi$
$103$	−3.32995			−0.328109			−0.164055	+	0.986451i	$0.552457\pi$
$104$	4.67215	−	4.67215i	0.458142	−	0.458142i
$105$	0.113568	+	0.0470413i	0.0110831	+	0.00459076i
$106$			9.48538i			0.921302i
$107$	1.48056	−	3.57439i	0.143131	−	0.345550i	−0.836015	−	0.548707i	$-0.815120\pi$
$107$	1.48056	−	3.57439i	0.143131	−	0.345550i	0.979146	+	0.203157i	$0.0651203\pi$
$108$	−2.35576	+	0.975790i	−0.226684	+	0.0938954i
$109$	4.93976	+	11.9256i	0.473143	+	1.14227i	0.962766	+	0.270335i	$0.0871343\pi$
$109$	4.93976	+	11.9256i	0.473143	+	1.14227i	−0.489623	+	0.871934i	$0.662866\pi$
$110$	2.25630	+	2.25630i	0.215130	+	0.215130i
$111$	−3.98505	−	3.98505i	−0.378245	−	0.378245i
$112$	1.00535	+	2.42713i	0.0949968	+	0.229343i
$113$	8.91910	−	3.69441i	0.839038	−	0.347541i	0.0785638	−	0.996909i	$-0.474967\pi$
$113$	8.91910	−	3.69441i	0.839038	−	0.347541i	0.760474	+	0.649368i	$0.224967\pi$
$114$	0.950751	−	2.29532i	0.0890460	−	0.214976i
$115$		−	2.41217i		−	0.224936i
$116$	5.99516	+	2.48328i	0.556637	+	0.230567i
$117$	5.37749	−	5.37749i	0.497149	−	0.497149i
$118$	−20.5587			−1.89258
$119$	−2.04382	+	0.858840i	−0.187356	+	0.0787297i
$120$	−0.498996			−0.0455519
$121$	17.4626	−	17.4626i	1.58751	−	1.58751i
$122$	6.08199	+	2.51924i	0.550638	+	0.228082i
$123$			4.13820i			0.373129i
$124$	2.07358	−	5.00607i	0.186213	−	0.449558i
$125$	2.99166	−	1.23919i	0.267582	−	0.110836i
$126$	0.843423	+	2.03620i	0.0751381	+	0.181399i
$127$	−11.3470	−	11.3470i	−1.00688	−	1.00688i	−0.999976	−	0.00690833i	$-0.997801\pi$
$127$	−11.3470	−	11.3470i	−1.00688	−	1.00688i	−0.00690833	−	0.999976i	$-0.502199\pi$
$128$	−9.58523	−	9.58523i	−0.847223	−	0.847223i
$129$	−0.267286	−	0.645285i	−0.0235332	−	0.0568142i
$130$	−1.49371	+	0.618714i	−0.131007	+	0.0542648i
$131$	−5.21314	+	12.5856i	−0.455474	+	1.09961i	0.514736	+	0.857349i	$0.327890\pi$
$131$	−5.21314	+	12.5856i	−0.455474	+	1.09961i	−0.970210	+	0.242264i	$0.922110\pi$
$132$		−	2.76378i		−	0.240556i
$133$	−1.08294	−	0.448570i	−0.0939031	−	0.0388959i
$134$	10.5381	−	10.5381i	0.910356	−	0.910356i
$135$	−1.26018			−0.108459
$136$	6.33089	−	6.39593i	0.542869	−	0.548446i
$137$	6.15344			0.525724			0.262862	−	0.964833i	$-0.415334\pi$
$137$	6.15344			0.525724			0.262862	+	0.964833i	$0.415334\pi$
$138$	−5.93860	+	5.93860i	−0.505527	+	0.505527i
$139$	2.30651	+	0.955387i	0.195636	+	0.0810349i	0.478350	−	0.878169i	$-0.341235\pi$
$139$	2.30651	+	0.955387i	0.195636	+	0.0810349i	−0.282715	+	0.959204i	$0.591235\pi$
$140$		−	0.116563i		−	0.00985139i
$141$	1.34914	−	3.25711i	0.113618	−	0.274298i
$142$	−11.7030	+	4.84753i	−0.982092	+	0.406796i
$143$	6.92140	+	16.7097i	0.578797	+	1.39734i
$144$	−8.67927	−	8.67927i	−0.723273	−	0.723273i
$145$	2.26771	+	2.26771i	0.188323	+	0.188323i
$146$	−4.16680	−	10.0595i	−0.344846	−	0.832533i
$147$	4.33044	−	1.79373i	0.357169	−	0.147944i
$148$	−2.04508	+	4.93726i	−0.168105	+	0.405841i
$149$		−	19.3522i		−	1.58539i	−0.609618	−	0.792695i	$-0.708677\pi$
$149$		−	19.3522i		−	1.58539i	0.609618	−	0.792695i	$-0.291323\pi$
$150$	−5.15161	−	2.13387i	−0.420628	−	0.174230i
$151$	9.07898	−	9.07898i	0.738837	−	0.738837i	−0.233516	−	0.972353i	$-0.575023\pi$
$151$	9.07898	−	9.07898i	0.738837	−	0.738837i	0.972353	+	0.233516i	$0.0750232\pi$
$152$	4.75826			0.385946
$153$	7.28663	−	7.36149i	0.589089	−	0.595141i
$154$	−5.24162			−0.422382
$155$	1.89358	−	1.89358i	0.152096	−	0.152096i
$156$	1.29377	+	0.535895i	0.103584	+	0.0429060i
$157$		−	8.36326i		−	0.667461i	−0.942669	−	0.333730i	$-0.891692\pi$
$157$		−	8.36326i		−	0.667461i	0.942669	−	0.333730i	$-0.108308\pi$
$158$	6.87813	−	16.6053i	0.547194	−	1.32104i
$159$	3.75126	−	1.55382i	0.297494	−	0.123226i
$160$	0.451802	+	1.09075i	0.0357181	+	0.0862311i
$161$	2.80186	+	2.80186i	0.220818	+	0.220818i
$162$	−5.59280	−	5.59280i	−0.439412	−	0.439412i
$163$	−5.59774	−	13.5141i	−0.438449	−	1.05851i	−0.976485	−	0.215587i	$-0.930833\pi$
$163$	−5.59774	−	13.5141i	−0.438449	−	1.05851i	0.538036	−	0.842922i	$-0.319167\pi$
$164$	3.62534	−	1.50166i	0.283091	−	0.117260i
$165$	0.522708	−	1.26193i	0.0406928	−	0.0982411i
$166$			9.09698i			0.706063i
$167$	21.6244	+	8.95711i	1.67334	+	0.693122i	0.998975	−	0.0452727i	$-0.0144157\pi$
$167$	21.6244	+	8.95711i	1.67334	+	0.693122i	0.674369	+	0.738394i	$0.264416\pi$
$168$	0.579610	−	0.579610i	0.0447179	−	0.0447179i
$169$	3.83585			0.295066
$170$	−2.03010	+	0.853076i	−0.155702	+	0.0654280i
$171$	5.47659			0.418805
$172$	−0.468320	+	0.468320i	−0.0357091	+	0.0357091i
$173$	−2.83629	−	1.17483i	−0.215639	−	0.0893208i	0.272249	−	0.962227i	$-0.412233\pi$
$173$	−2.83629	−	1.17483i	−0.215639	−	0.0893208i	−0.487888	+	0.872906i	$0.662233\pi$
$174$		−	11.1659i		−	0.846483i
$175$	−1.00677	+	2.43056i	−0.0761048	+	0.183733i
$176$	26.9696	−	11.1712i	2.03291	−	0.842058i
$177$	3.36777	+	8.13052i	0.253137	+	0.611127i
$178$	5.44187	+	5.44187i	0.407885	+	0.407885i
$179$	11.5287	+	11.5287i	0.861694	+	0.861694i	0.991535	−	0.129841i	$-0.0414467\pi$
$179$	11.5287	+	11.5287i	0.861694	+	0.861694i	−0.129841	+	0.991535i	$0.541447\pi$
$180$	0.208411	+	0.503149i	0.0155341	+	0.0375025i
$181$	10.9212	−	4.52373i	0.811770	−	0.336246i	0.0621100	−	0.998069i	$-0.480217\pi$
$181$	10.9212	−	4.52373i	0.811770	−	0.336246i	0.749660	+	0.661823i	$0.230217\pi$
$182$	1.01635	−	2.45368i	0.0753368	−	0.181879i
$183$		−	2.81798i		−	0.208311i
$184$	−14.8606	−	6.15544i	−1.09553	−	0.453785i
$185$	−1.86755	+	1.86755i	−0.137305	+	0.137305i
$186$	−9.32371			−0.683647
$187$	9.54316	+	22.7103i	0.697865	+	1.66074i
$188$	−3.34302			−0.243814
$189$	1.46377	−	1.46377i	0.106473	−	0.106473i
$190$	−1.07568	−	0.445560i	−0.0780377	−	0.0323243i
$191$		−	6.86465i		−	0.496708i	−0.968669	−	0.248354i	$-0.920110\pi$
$191$		−	6.86465i		−	0.496708i	0.968669	−	0.248354i	$-0.0798897\pi$
$192$	−1.03886	+	2.50803i	−0.0749734	+	0.181002i
$193$	−16.3854	+	6.78705i	−1.17945	+	0.488542i	−0.884304	−	0.466911i	$-0.845367\pi$
$193$	−16.3854	+	6.78705i	−1.17945	+	0.488542i	−0.295141	+	0.955454i	$0.595367\pi$
$194$	−2.91545	−	7.03853i	−0.209317	−	0.505337i
$195$	0.489376	+	0.489376i	0.0350449	+	0.0350449i
$196$	−3.14285	−	3.14285i	−0.224489	−	0.224489i
$197$	−1.07703	−	2.60018i	−0.0767351	−	0.185255i	0.880857	−	0.473383i	$-0.156967\pi$
$197$	−1.07703	−	2.60018i	−0.0767351	−	0.185255i	−0.957592	+	0.288128i	$0.906967\pi$
$198$	22.6256	−	9.37185i	1.60793	−	0.666028i
$199$	7.25981	−	17.5267i	0.514634	−	1.24244i	−0.426526	−	0.904475i	$-0.640263\pi$
$199$	7.25981	−	17.5267i	0.514634	−	1.24244i	0.941160	−	0.337962i	$-0.109737\pi$
$200$		−	10.6794i		−	0.755151i
$201$	−5.89388	−	2.44132i	−0.415722	−	0.172198i
$202$	10.6227	−	10.6227i	0.747413	−	0.747413i
$203$	−5.26812			−0.369750
$204$	1.76582	+	0.720877i	0.123632	+	0.0504715i
$205$	1.93932			0.135448
$206$	3.84194	−	3.84194i	0.267681	−	0.267681i
$207$	−17.1040	−	7.08470i	−1.18881	−	0.492421i
$208$			14.7910i			1.02557i
$209$	−4.98437	+	12.0333i	−0.344776	+	0.832363i
$210$	−0.185304	+	0.0767553i	−0.0127872	+	0.00529662i
$211$	−2.54310	−	6.13958i	−0.175074	−	0.422666i	0.811847	−	0.583870i	$-0.198462\pi$
$211$	−2.54310	−	6.13958i	−0.175074	−	0.422666i	−0.986921	+	0.161204i	$0.948462\pi$
$212$	−2.72251	−	2.72251i	−0.186983	−	0.186983i
$213$	3.83419	+	3.83419i	0.262714	+	0.262714i
$214$	2.41577	+	5.83219i	0.165139	+	0.398680i
$215$	−0.302406	+	0.125261i	−0.0206239	+	0.00854271i
$216$	−3.21576	+	7.76354i	−0.218805	+	0.528242i
$217$			4.39898i			0.298622i
$218$	−19.4585	−	8.06000i	−1.31790	−	0.545892i
$219$	−3.29575	+	3.29575i	−0.222706	+	0.222706i
$220$	−1.29521			−0.0873233
$221$	−12.4814	+	0.0637857i	−0.839593	+	0.00429069i
$222$	9.19556			0.617166
$223$	−20.2197	+	20.2197i	−1.35401	+	1.35401i	−0.472885	+	0.881124i	$0.656787\pi$
$223$	−20.2197	+	20.2197i	−1.35401	+	1.35401i	−0.881124	+	0.472885i	$0.843213\pi$
$224$	−1.79175	−	0.742167i	−0.119716	−	0.0495881i
$225$		−	12.2917i		−	0.819445i
$226$	−6.02801	+	14.5529i	−0.400977	+	0.968045i
$227$	23.8421	−	9.87573i	1.58246	−	0.655475i	0.593656	−	0.804719i	$-0.297684\pi$
$227$	23.8421	−	9.87573i	1.58246	−	0.655475i	0.988800	+	0.149243i	$0.0476838\pi$
$228$	0.385919	+	0.931691i	0.0255581	+	0.0617027i
$229$	−6.57048	−	6.57048i	−0.434190	−	0.434190i	0.455861	−	0.890051i	$-0.349331\pi$
$229$	−6.57048	−	6.57048i	−0.434190	−	0.434190i	−0.890051	+	0.455861i	$0.849331\pi$
$230$	2.78306	+	2.78306i	0.183510	+	0.183510i
$231$	0.858643	+	2.07295i	0.0564946	+	0.136390i
$232$	19.7574	−	8.18377i	1.29713	−	0.537291i
$233$	7.46254	−	18.0162i	0.488887	−	1.18028i	−0.466394	−	0.884577i	$-0.654447\pi$
$233$	7.46254	−	18.0162i	0.488887	−	1.18028i	0.955281	−	0.295700i	$-0.0955530\pi$
$234$			12.4086i			0.811176i
$235$	−1.52641	−	0.632259i	−0.0995719	−	0.0412440i
$236$	5.90078	−	5.90078i	0.384108	−	0.384108i
$237$	−7.69375			−0.499762
$238$	1.36718	−	3.34896i	0.0886208	−	0.217081i
$239$	−3.87346			−0.250554			−0.125277	−	0.992122i	$-0.539982\pi$
$239$	−3.87346			−0.250554			−0.125277	+	0.992122i	$0.539982\pi$
$240$	0.789853	−	0.789853i	0.0509848	−	0.0509848i
$241$	−11.2877	−	4.67553i	−0.727106	−	0.301177i	−0.0117441	−	0.999931i	$-0.503738\pi$
$241$	−11.2877	−	4.67553i	−0.727106	−	0.301177i	−0.715362	+	0.698754i	$0.753738\pi$
$242$			40.2951i			2.59026i
$243$	−5.71563	+	13.7988i	−0.366658	+	0.885191i
$244$	−2.46874	+	1.02259i	−0.158045	+	0.0654643i
$245$	−0.840611	−	2.02942i	−0.0537047	−	0.129655i
$246$	−4.77447	−	4.77447i	−0.304409	−	0.304409i
$247$	−4.66652	−	4.66652i	−0.296924	−	0.296924i
$248$	−6.83359	−	16.4978i	−0.433934	−	1.04761i
$249$	3.59766	−	1.49020i	0.227992	−	0.0944375i
$250$	−2.02193	+	4.88136i	−0.127878	+	0.308725i
$251$		−	1.28167i		−	0.0808982i	−0.999182	−	0.0404491i	$-0.987121\pi$
$251$		−	1.28167i		−	0.0808982i	0.999182	−	0.0404491i	$-0.0128789\pi$
$252$	−0.826514	−	0.342353i	−0.0520655	−	0.0215662i
$253$	31.1334	−	31.1334i	1.95734	−	1.95734i
$254$	26.1834			1.64289
$255$	0.669929	+	0.663117i	0.0419526	+	0.0415260i
$256$	14.3446			0.896539
$257$	−12.3644	+	12.3644i	−0.771271	+	0.771271i	−0.978329	−	0.207058i	$-0.933611\pi$
$257$	−12.3644	+	12.3644i	−0.771271	+	0.771271i	0.207058	+	0.978329i	$0.433611\pi$
$258$	1.05288	+	0.436119i	0.0655497	+	0.0271516i
$259$		−	4.33852i		−	0.269582i
$260$	0.251142	−	0.606310i	0.0155752	−	0.0376017i
$261$	22.7400	−	9.41923i	1.40757	−	0.583036i
$262$	−8.50606	−	20.5354i	−0.525506	−	1.26868i
$263$	−10.8970	−	10.8970i	−0.671936	−	0.671936i	0.286226	−	0.958162i	$-0.407599\pi$
$263$	−10.8970	−	10.8970i	−0.671936	−	0.671936i	−0.958162	+	0.286226i	$0.907599\pi$
$264$	−6.44044	−	6.44044i	−0.396382	−	0.396382i
$265$	−0.728183	−	1.75799i	−0.0447319	−	0.107992i
$266$	1.76699	−	0.731912i	0.108341	−	0.0448764i
$267$	1.26070	−	3.04359i	0.0771533	−	0.186265i
$268$			6.04934i			0.369522i
$269$	−21.9560	−	9.09445i	−1.33868	−	0.554499i	−0.405560	−	0.914068i	$-0.632923\pi$
$269$	−21.9560	−	9.09445i	−1.33868	−	0.554499i	−0.933118	+	0.359570i	$0.882923\pi$
$270$	1.45394	−	1.45394i	0.0884842	−	0.0884842i
$271$	−24.7707			−1.50471			−0.752355	−	0.658757i	$-0.771082\pi$
$271$	−24.7707			−1.50471			−0.752355	+	0.658757i	$0.771082\pi$
$272$	0.102950	+	20.1451i	0.00624228	+	1.22147i
$273$	−1.13687			−0.0688065
$274$	−7.09957	+	7.09957i	−0.428901	+	0.428901i
$275$	27.0076	+	11.1869i	1.62862	+	0.674597i
$276$		−	3.40901i		−	0.205198i
$277$	−1.18405	+	2.85855i	−0.0711426	+	0.171753i	−0.955451	−	0.295150i	$-0.904630\pi$
$277$	−1.18405	+	2.85855i	−0.0711426	+	0.171753i	0.884308	+	0.466903i	$0.154630\pi$
$278$	−3.76343	+	1.55886i	−0.225716	+	0.0934945i
$279$	−7.86523	−	18.9883i	−0.470879	−	1.13680i
$280$	−0.271628	−	0.271628i	−0.0162329	−	0.0162329i
$281$	−11.9689	−	11.9689i	−0.714003	−	0.714003i	0.253367	−	0.967370i	$-0.418462\pi$
$281$	−11.9689	−	11.9689i	−0.714003	−	0.714003i	−0.967370	+	0.253367i	$0.918462\pi$
$282$	2.20133	+	5.31448i	0.131087	+	0.316473i
$283$	−4.96523	+	2.05667i	−0.295152	+	0.122256i	−0.525346	−	0.850889i	$-0.676064\pi$
$283$	−4.96523	+	2.05667i	−0.295152	+	0.122256i	0.230193	+	0.973145i	$0.426064\pi$
$284$	1.96766	−	4.75035i	0.116759	−	0.281881i
$285$			0.498395i			0.0295224i
$286$	−27.2646	−	11.2934i	−1.61219	−	0.667790i
$287$	−2.25262	+	2.25262i	−0.132968	+	0.132968i
$288$	9.06112			0.533932
$289$	−16.9991	+	0.173751i	−0.999948	+	0.0102206i
$290$	−5.23277			−0.307279
$291$	−2.30600	+	2.30600i	−0.135180	+	0.135180i
$292$	4.08326	+	1.69134i	0.238955	+	0.0989783i
$293$		−	5.06070i		−	0.295649i	−0.989014	−	0.147825i	$-0.952773\pi$
$293$		−	5.06070i		−	0.295649i	0.989014	−	0.147825i	$-0.0472272\pi$
$294$	−2.92675	+	7.06579i	−0.170691	+	0.412085i
$295$	3.81028	−	1.57827i	0.221843	−	0.0918905i
$296$	6.73967	+	16.2710i	0.391735	+	0.945733i
$297$	−16.2649	−	16.2649i	−0.943786	−	0.943786i
$298$	22.3277	+	22.3277i	1.29341	+	1.29341i
$299$	8.53728	+	20.6108i	0.493723	+	1.19195i
$300$	2.09109	−	0.866157i	0.120729	−	0.0500076i
$301$	0.205763	−	0.496757i	0.0118600	−	0.0286326i
$302$			20.9498i			1.20553i
$303$	−5.94120	−	2.46093i	−0.341313	−	0.141376i
$304$	−7.53177	+	7.53177i	−0.431977	+	0.431977i
$305$	−1.32062			−0.0756183
$306$	0.0863684	+	16.9004i	0.00493735	+	0.966129i
$307$	−7.95370			−0.453942			−0.226971	−	0.973902i	$-0.572882\pi$
$307$	−7.95370			−0.453942			−0.226971	+	0.973902i	$0.572882\pi$
$308$	1.50446	−	1.50446i	0.0857244	−	0.0857244i
$309$	−2.14876	−	0.890047i	−0.122239	−	0.0506330i
$310$			4.36946i			0.248169i
$311$	−4.40264	+	10.6289i	−0.249651	+	0.602710i	−0.998174	−	0.0603978i	$-0.980763\pi$
$311$	−4.40264	+	10.6289i	−0.249651	+	0.602710i	0.748524	+	0.663108i	$0.230763\pi$
$312$	4.26367	−	1.76607i	0.241383	−	0.0999840i
$313$	6.05898	+	14.6277i	0.342474	+	0.826804i	0.997464	+	0.0711674i	$0.0226725\pi$
$313$	6.05898	+	14.6277i	0.342474	+	0.826804i	−0.654991	+	0.755637i	$0.727328\pi$
$314$	9.64916	+	9.64916i	0.544534	+	0.544534i
$315$	−0.312634	−	0.312634i	−0.0176150	−	0.0176150i
$316$	2.79190	+	6.74023i	0.157056	+	0.379168i
$317$	−12.6327	+	5.23263i	−0.709522	+	0.293894i	−0.708107	−	0.706105i	$-0.750450\pi$
$317$	−12.6327	+	5.23263i	−0.709522	+	0.293894i	−0.00141523	+	0.999999i	$0.500450\pi$
$318$	−2.53531	+	6.12077i	−0.142173	+	0.343236i
$319$			58.5378i			3.27749i
$320$	1.17536	+	0.486852i	0.0657048	+	0.0272158i
$321$	1.91077	−	1.91077i	0.106649	−	0.106649i
$322$	−6.46533			−0.360299
$323$	−6.38822	−	6.32326i	−0.355450	−	0.351835i
$324$	3.21051			0.178361
$325$	−10.4735	+	10.4735i	−0.580968	+	0.580968i
$326$	22.0504	+	9.13359i	1.22126	+	0.505863i
$327$			9.01576i			0.498573i
$328$	4.94881	−	11.9475i	0.273252	−	0.659689i
$329$	2.50740	−	1.03860i	0.138238	−	0.0572599i
$330$	0.852881	+	2.05904i	0.0469496	+	0.113346i
$331$	20.4194	+	20.4194i	1.12235	+	1.12235i	0.991387	+	0.130963i	$0.0418070\pi$
$331$	20.4194	+	20.4194i	1.12235	+	1.12235i	0.130963	+	0.991387i	$0.458193\pi$
$332$	−2.61103	−	2.61103i	−0.143299	−	0.143299i
$333$	7.75713	+	18.7274i	0.425088	+	1.02625i
$334$	−35.2836	+	14.6149i	−1.93063	+	0.799693i
$335$	−1.14410	+	2.76210i	−0.0625089	+	0.150910i
$336$			1.83491i			0.100103i
$337$	−11.3617	−	4.70618i	−0.618913	−	0.256362i	0.0511211	−	0.998692i	$-0.483721\pi$
$337$	−11.3617	−	4.70618i	−0.618913	−	0.256362i	−0.670034	+	0.742330i	$0.733721\pi$
$338$	−4.42564	+	4.42564i	−0.240723	+	0.240723i
$339$	6.74282			0.366220
$340$	0.337832	−	0.827534i	0.0183215	−	0.0448793i
$341$	48.8801			2.64701
$342$	−6.31865	+	6.31865i	−0.341673	+	0.341673i
$343$	6.81098	+	2.82120i	0.367758	+	0.152330i
$344$			2.18266i			0.117681i
$345$	0.644740	−	1.55654i	0.0347116	−	0.0838013i
$346$	4.62786	−	1.91692i	0.248795	−	0.103054i
$347$	−2.33375	−	5.63417i	−0.125282	−	0.302458i	0.848777	−	0.528751i	$-0.177339\pi$
$347$	−2.33375	−	5.63417i	−0.125282	−	0.302458i	−0.974059	+	0.226293i	$0.927339\pi$
$348$	3.20484	+	3.20484i	0.171798	+	0.171798i
$349$	0.0592157	+	0.0592157i	0.00316974	+	0.00316974i	0.708690	−	0.705520i	$-0.249287\pi$
$349$	0.0592157	+	0.0592157i	0.00316974	+	0.00316974i	−0.705520	+	0.708690i	$0.749287\pi$
$350$	−1.64271	−	3.96584i	−0.0878063	−	0.211983i
$351$	10.7676	−	4.46010i	0.574733	−	0.238062i
$352$	−8.24673	+	19.9094i	−0.439552	+	1.06117i
$353$		−	8.41416i		−	0.447841i	−0.974607	−	0.223920i	$-0.928114\pi$
$353$		−	8.41416i		−	0.447841i	0.974607	−	0.223920i	$-0.0718855\pi$
$354$	−13.2662	−	5.49505i	−0.705092	−	0.292058i
$355$	1.79685	−	1.79685i	0.0953670	−	0.0953670i
$356$	−3.12387			−0.165565
$357$	−1.54840	+	0.00791302i	−0.0819501	+	0.000418801i
$358$	−26.6026			−1.40599
$359$	−14.6139	+	14.6139i	−0.771290	+	0.771290i	−0.978332	−	0.207042i	$-0.933616\pi$
$359$	−14.6139	+	14.6139i	−0.771290	+	0.771290i	0.207042	+	0.978332i	$0.433616\pi$
$360$	1.65815	+	0.686830i	0.0873924	+	0.0361991i
$361$			14.2475i			0.749867i
$362$	−7.38117	+	17.8197i	−0.387946	+	0.936584i
$363$	15.9358	−	6.60083i	0.836414	−	0.346454i
$364$	0.412546	+	0.995974i	0.0216233	+	0.0522032i
$365$	1.54452	+	1.54452i	0.0808439	+	0.0808439i
$366$	3.25126	+	3.25126i	0.169946	+	0.169946i
$367$	−7.91202	−	19.1013i	−0.413004	−	0.997080i	−0.984327	−	0.176355i	$-0.943569\pi$
$367$	−7.91202	−	19.1013i	−0.413004	−	0.997080i	0.571322	−	0.820726i	$-0.306431\pi$
$368$	33.2659	−	13.7792i	1.73410	−	0.718289i
$369$	5.69591	−	13.7511i	0.296517	−	0.715855i
$370$		−	4.30940i		−	0.224035i
$371$	2.88782	+	1.19617i	0.149928	+	0.0621022i
$372$	2.67610	−	2.67610i	0.138749	−	0.138749i
$373$	−6.08555			−0.315098			−0.157549	−	0.987511i	$-0.550359\pi$
$373$	−6.08555			−0.315098			−0.157549	+	0.987511i	$0.550359\pi$
$374$	−37.2126	−	15.1916i	−1.92422	−	0.785540i
$375$	2.26169			0.116793
$376$	−7.79025	+	7.79025i	−0.401751	+	0.401751i
$377$	−27.4024	−	11.3505i	−1.41130	−	0.584578i
$378$			3.37766i			0.173728i
$379$	4.97969	−	12.0220i	0.255789	−	0.617530i	−0.742862	−	0.669444i	$-0.766532\pi$
$379$	4.97969	−	12.0220i	0.255789	−	0.617530i	0.998652	+	0.0519141i	$0.0165322\pi$
$380$	0.436627	−	0.180857i	0.0223985	−	0.00927776i
$381$	−4.28916	−	10.3550i	−0.219740	−	0.530500i
$382$	7.92012	+	7.92012i	0.405229	+	0.405229i
$383$	−6.02568	−	6.02568i	−0.307898	−	0.307898i	0.536196	−	0.844094i	$-0.319861\pi$
$383$	−6.02568	−	6.02568i	−0.307898	−	0.307898i	−0.844094	+	0.536196i	$0.819861\pi$
$384$	−3.62321	−	8.74720i	−0.184896	−	0.446379i
$385$	0.971465	−	0.402394i	0.0495105	−	0.0205079i
$386$	11.0741	−	26.7353i	0.563658	−	1.36079i
$387$			2.51217i			0.127701i
$388$	2.85701	+	1.18341i	0.145042	+	0.0600786i
$389$	−3.45704	+	3.45704i	−0.175279	+	0.175279i	−0.789294	−	0.614015i	$-0.789553\pi$
$389$	−3.45704	+	3.45704i	−0.175279	+	0.175279i	0.614015	+	0.789294i	$0.289553\pi$
$390$	−1.12924			−0.0571813
$391$	11.7711	+	28.0122i	0.595291	+	1.41664i
$392$	−14.6476			−0.739815
$393$	−6.72792	+	6.72792i	−0.339379	+	0.339379i
$394$	4.24260	+	1.75734i	0.213739	+	0.0885336i
$395$			3.60559i			0.181417i
$396$	−3.80412	+	9.18396i	−0.191164	+	0.461512i
$397$	−2.04767	+	0.848174i	−0.102770	+	0.0425686i	−0.433476	−	0.901165i	$-0.642713\pi$
$397$	−2.04767	+	0.848174i	−0.102770	+	0.0425686i	0.330706	+	0.943734i	$0.392713\pi$
$398$	11.8455	+	28.5976i	0.593762	+	1.43347i
$399$	−0.578911	−	0.578911i	−0.0289818	−	0.0289818i
$400$	16.9043	+	16.9043i	0.845216	+	0.845216i
$401$	−11.0745	−	26.7363i	−0.553036	−	1.33515i	−0.915188	−	0.403027i	$-0.867958\pi$
$401$	−11.0745	−	26.7363i	−0.553036	−	1.33515i	0.362152	−	0.932119i	$-0.382042\pi$
$402$	9.61679	−	3.98340i	0.479642	−	0.198674i
$403$	−9.47784	+	22.8815i	−0.472125	+	1.13981i
$404$			6.09790i			0.303382i
$405$	1.46591	+	0.607198i	0.0728414	+	0.0301719i
$406$	6.07813	−	6.07813i	0.301653	−	0.301653i
$407$	−48.2083			−2.38960
$408$	5.79477	−	2.43504i	0.286884	−	0.120552i
$409$	37.0789			1.83343			0.916717	−	0.399537i	$-0.130829\pi$
$409$	37.0789			1.83343			0.916717	+	0.399537i	$0.130829\pi$
$410$	−2.23750	+	2.23750i	−0.110502	+	0.110502i
$411$	3.97072	+	1.64473i	0.195861	+	0.0811284i
$412$			2.20544i			0.108654i
$413$	−2.59260	+	6.25908i	−0.127573	+	0.307989i
$414$	27.9078	−	11.5598i	1.37160	−	0.568133i
$415$	−0.698366	−	1.68601i	−0.0342815	−	0.0827628i
$416$	−7.72084	−	7.72084i	−0.378545	−	0.378545i
$417$	1.23299	+	1.23299i	0.0603800	+	0.0603800i
$418$	−8.13278	−	19.6343i	−0.397787	−	0.960344i
$419$	−21.0814	+	8.73221i	−1.02990	+	0.426597i	−0.832675	−	0.553763i	$-0.813191\pi$
$419$	−21.0814	+	8.73221i	−1.02990	+	0.426597i	−0.197221	+	0.980359i	$0.563191\pi$
$420$	0.0311557	−	0.0752165i	0.00152024	−	0.00367019i
$421$		−	11.2815i		−	0.549828i	−0.961469	−	0.274914i	$-0.911351\pi$
$421$		−	11.2815i		−	0.549828i	0.961469	−	0.274914i	$-0.0886494\pi$
$422$	10.0177	+	4.14946i	0.487654	+	0.201993i
$423$	−8.96631	+	8.96631i	−0.435957	+	0.435957i
$424$	−12.6885			−0.616210
$425$	−14.1919	+	14.3377i	−0.688410	+	0.695482i
$426$	−8.84743			−0.428660
$427$	1.53396	−	1.53396i	0.0742337	−	0.0742337i
$428$	−2.36734	−	0.980584i	−0.114430	−	0.0473983i
$429$			12.6325i			0.609905i
$430$	0.204383	−	0.493423i	0.00985620	−	0.0237950i
$431$	30.6132	−	12.6804i	1.47458	−	0.610793i	0.506685	−	0.862132i	$-0.330871\pi$
$431$	30.6132	−	12.6804i	1.47458	−	0.610793i	0.967899	+	0.251339i	$0.0808709\pi$
$432$	−7.19860	−	17.3790i	−0.346343	−	0.836146i
$433$	25.5113	+	25.5113i	1.22599	+	1.22599i	0.965466	+	0.260529i	$0.0838968\pi$
$433$	25.5113	+	25.5113i	1.22599	+	1.22599i	0.260529	+	0.965466i	$0.416103\pi$
$434$	−5.07535	−	5.07535i	−0.243624	−	0.243624i
$435$	0.857193	+	2.06945i	0.0410993	+	0.0992224i
$436$	7.89841	−	3.27163i	0.378265	−	0.156683i
$437$	−6.14802	+	14.8426i	−0.294100	+	0.710020i
$438$		−	7.60499i		−	0.363381i
$439$	34.3548	+	14.2302i	1.63967	+	0.679172i	0.996264	−	0.0863569i	$-0.0275225\pi$
$439$	34.3548	+	14.2302i	1.63967	+	0.679172i	0.643402	+	0.765529i	$0.277523\pi$
$440$	−3.01825	+	3.01825i	−0.143889	+	0.143889i
$441$	−16.8589			−0.802804
$442$	14.3269	−	14.4741i	0.681463	−	0.688464i
$443$	1.24983			0.0593814			0.0296907	−	0.999559i	$-0.490548\pi$
$443$	1.24983			0.0593814			0.0296907	+	0.999559i	$0.490548\pi$
$444$	−2.63932	+	2.63932i	−0.125257	+	0.125257i
$445$	−1.42635	−	0.590812i	−0.0676153	−	0.0280072i
$446$		−	46.6571i		−	2.20928i
$447$	5.17256	−	12.4877i	0.244654	−	0.590646i
$448$	−1.93075	+	0.799742i	−0.0912192	+	0.0377842i
$449$	−7.88708	−	19.0411i	−0.372214	−	0.898605i	−0.993375	−	0.114921i	$-0.963338\pi$
$449$	−7.88708	−	19.0411i	−0.372214	−	0.898605i	0.621160	−	0.783684i	$-0.286662\pi$
$450$	14.1816	+	14.1816i	0.668527	+	0.668527i
$451$	25.0304	+	25.0304i	1.17864	+	1.17864i
$452$	−2.44683	−	5.90716i	−0.115089	−	0.277850i
$453$	8.28521	−	3.43185i	0.389273	−	0.161242i
$454$	−16.1138	+	38.9022i	−0.756258	+	1.82577i
$455$			0.532782i			0.0249772i
$456$	3.07043	+	1.27182i	0.143786	+	0.0595582i
$457$	−3.75562	+	3.75562i	−0.175680	+	0.175680i	−0.789470	−	0.613789i	$-0.789644\pi$
$457$	−3.75562	+	3.75562i	−0.175680	+	0.175680i	0.613789	+	0.789470i	$0.289644\pi$
$458$	15.1615			0.708449
$459$	14.6343	−	6.14954i	0.683071	−	0.287036i
$460$	−1.59760			−0.0744883
$461$	−7.16371	+	7.16371i	−0.333647	+	0.333647i	−0.853970	−	0.520323i	$-0.825812\pi$
$461$	−7.16371	+	7.16371i	−0.333647	+	0.333647i	0.520323	+	0.853970i	$0.325812\pi$
$462$	−3.38234	−	1.40101i	−0.157361	−	0.0651809i
$463$			31.3449i			1.45672i	0.685194	+	0.728360i	$0.259717\pi$
$463$			31.3449i			1.45672i	−0.685194	+	0.728360i	$0.740283\pi$
$464$	−18.3197	+	44.2276i	−0.850469	+	2.05321i
$465$	1.72803	−	0.715772i	0.0801353	−	0.0331931i
$466$	12.1763	+	29.3962i	0.564056	+	1.36175i
$467$	−19.4068	−	19.4068i	−0.898037	−	0.898037i	0.0972251	−	0.995262i	$-0.469003\pi$
$467$	−19.4068	−	19.4068i	−0.898037	−	0.898037i	−0.995262	+	0.0972251i	$0.969003\pi$
$468$	−3.56154	−	3.56154i	−0.164632	−	0.164632i
$469$	−1.87939	−	4.53726i	−0.0867823	−	0.209511i
$470$	2.49058	−	1.03163i	0.114882	−	0.0475856i
$471$	2.23538	−	5.39669i	0.103001	−	0.248666i
$472$		−	27.5013i		−	1.26585i
$473$	−5.51981	−	2.28638i	−0.253801	−	0.105128i
$474$	8.87670	−	8.87670i	0.407721	−	0.407721i
$475$	−10.6666			−0.489416
$476$	0.568814	+	1.35363i	0.0260715	+	0.0620436i
$477$	−14.6041			−0.668675
$478$	4.46903	−	4.46903i	0.204409	−	0.204409i
$479$	−28.5871	−	11.8412i	−1.30618	−	0.541037i	−0.382413	−	0.923992i	$-0.624907\pi$
$479$	−28.5871	−	11.8412i	−1.30618	−	0.541037i	−0.923767	+	0.382954i	$0.874907\pi$
$480$			0.824603i			0.0376378i
$481$	9.34757	−	22.5670i	0.426212	−	1.02897i
$482$	18.4177	−	7.62886i	0.838903	−	0.347485i
$483$	1.05910	+	2.55690i	0.0481908	+	0.116343i
$484$	−11.5655	−	11.5655i	−0.525706	−	0.525706i
$485$	1.08068	+	1.08068i	0.0490712	+	0.0490712i
$486$	−9.32595	−	22.5148i	−0.423034	−	1.02129i
$487$	−18.6601	+	7.72929i	−0.845572	+	0.350247i	−0.763048	−	0.646342i	$-0.776298\pi$
$487$	−18.6601	+	7.72929i	−0.845572	+	0.350247i	−0.0825238	+	0.996589i	$0.526298\pi$
$488$	−3.36998	+	8.13585i	−0.152552	+	0.368293i
$489$		−	10.2167i		−	0.462014i
$490$	3.31131	+	1.37159i	0.149590	+	0.0619621i
$491$	4.00630	−	4.00630i	0.180802	−	0.180802i	−0.610903	−	0.791705i	$-0.709194\pi$
$491$	4.00630	−	4.00630i	0.180802	−	0.180802i	0.791705	+	0.610903i	$0.209194\pi$
$492$	2.74075			0.123562
$493$	−37.4007	−	15.2684i	−1.68444	−	0.687656i
$494$	10.7680			0.484477
$495$	−3.47390	+	3.47390i	−0.156140	+	0.156140i
$496$	36.9308	+	15.2972i	1.65824	+	0.686867i
$497$			4.17427i			0.187242i
$498$	−2.43149	+	5.87015i	−0.108958	+	0.263048i
$499$	−12.6303	+	5.23164i	−0.565410	+	0.234201i	−0.647032	−	0.762463i	$-0.723990\pi$
$499$	−12.6303	+	5.23164i	−0.565410	+	0.234201i	0.0816219	+	0.996663i	$0.473990\pi$
$500$	−0.820720	−	1.98139i	−0.0367037	−	0.0886106i
$501$	11.5598	+	11.5598i	0.516453	+	0.516453i
$502$	1.47873	+	1.47873i	0.0659991	+	0.0659991i
$503$	−11.0296	−	26.6278i	−0.491786	−	1.18728i	−0.953811	−	0.300409i	$-0.902877\pi$
$503$	−11.0296	−	26.6278i	−0.491786	−	1.18728i	0.462025	−	0.886867i	$-0.347123\pi$
$504$	−2.72382	+	1.12824i	−0.121328	+	0.0502559i
$505$	−1.15329	+	2.78428i	−0.0513206	+	0.123899i
$506$			71.8408i			3.19371i
$507$	2.47522	+	1.02527i	0.109928	+	0.0455338i
$508$	−7.51518	+	7.51518i	−0.333432	+	0.333432i
$509$	4.01945			0.178159			0.0890795	−	0.996025i	$-0.471607\pi$
$509$	4.01945			0.178159			0.0890795	+	0.996025i	$0.471607\pi$
$510$	−1.53801	+	0.00785991i	−0.0681042	+	0.000348043i
$511$	−3.58808			−0.158727
$512$	2.62027	−	2.62027i	0.115801	−	0.115801i
$513$	7.75418	+	3.21189i	0.342355	+	0.141808i
$514$		−	28.5310i		−	1.25845i
$515$	−0.417111	+	1.00700i	−0.0183801	+	0.0443735i
$516$	−0.427376	+	0.177025i	−0.0188142	+	0.00779308i
$517$	−11.5406	−	27.8615i	−0.507555	−	1.22535i
$518$	5.00559	+	5.00559i	0.219933	+	0.219933i
$519$	−1.51620	−	1.51620i	−0.0665539	−	0.0665539i
$520$	−0.827650	−	1.99812i	−0.0362949	−	0.0876236i
$521$	6.79537	−	2.81474i	0.297711	−	0.123316i	−0.228828	−	0.973467i	$-0.573489\pi$
$521$	6.79537	−	2.81474i	0.297711	−	0.123316i	0.526539	+	0.850151i	$0.323489\pi$
$522$	−15.3690	+	37.1040i	−0.672681	+	1.62400i
$523$		−	15.8427i		−	0.692754i	−0.938095	−	0.346377i	$-0.887412\pi$
$523$		−	15.8427i		−	0.692754i	0.938095	−	0.346377i	$-0.112588\pi$
$524$	8.33553	+	3.45269i	0.364139	+	0.150831i
$525$	−1.29931	+	1.29931i	−0.0567065	+	0.0567065i
$526$	25.1449			1.09637
$527$	−12.7494	+	31.2303i	−0.555373	+	1.36041i
$528$	20.3889			0.887315
$529$	22.1384	−	22.1384i	0.962539	−	0.962539i
$530$	2.86844	+	1.18815i	0.124597	+	0.0516097i
$531$		−	31.6530i		−	1.37362i
$532$	−0.297090	+	0.717239i	−0.0128805	+	0.0310963i
$533$	−16.5705	+	6.86374i	−0.717749	+	0.297301i
$534$	2.05702	+	4.96609i	0.0890161	+	0.214904i
$535$	−0.895462	−	0.895462i	−0.0387142	−	0.0387142i
$536$	14.0968	+	14.0968i	0.608889	+	0.608889i
$537$	4.35783	+	10.5207i	0.188054	+	0.454003i
$538$	35.8246	−	14.8390i	1.54451	−	0.639756i
$539$	15.3436	−	37.0428i	0.660898	−	1.59555i
$540$			0.834626i			0.0359166i
$541$	−34.0066	−	14.0860i	−1.46206	−	0.605605i	−0.497027	−	0.867735i	$-0.665575\pi$
$541$	−34.0066	−	14.0860i	−1.46206	−	0.605605i	−0.965032	+	0.262130i	$0.915575\pi$
$542$	28.5793	−	28.5793i	1.22759	−	1.22759i
$543$	8.25645			0.354318
$544$	−10.5694	−	10.4619i	−0.453160	−	0.448552i
$545$	4.22514			0.180985
$546$	1.31167	−	1.31167i	0.0561343	−	0.0561343i
$547$	−19.8639	−	8.22792i	−0.849321	−	0.351800i	−0.0847992	−	0.996398i	$-0.527025\pi$
$547$	−19.8639	−	8.22792i	−0.849321	−	0.351800i	−0.764522	+	0.644598i	$0.777025\pi$
$548$		−	4.07546i		−	0.174095i
$549$	−3.87873	+	9.36408i	−0.165540	+	0.399649i
$550$	−44.0672	+	18.2532i	−1.87903	+	0.778321i
$551$	−8.17390	−	19.7335i	−0.348220	−	0.840677i
$552$	−7.94403	−	7.94403i	−0.338120	−	0.338120i
$553$	−4.18808	−	4.18808i	−0.178095	−	0.178095i
$554$	−1.93196	−	4.66417i	−0.0820812	−	0.198162i
$555$	−1.70428	+	0.705934i	−0.0723425	+	0.0299652i
$556$	0.632758	−	1.52761i	0.0268349	−	0.0647852i
$557$			8.88046i			0.376277i	0.982142	+	0.188139i	$0.0602454\pi$
$557$			8.88046i			0.376277i	−0.982142	+	0.188139i	$0.939755\pi$
$558$	30.9825	+	12.8334i	1.31159	+	0.543279i
$559$	2.14058	−	2.14058i	0.0905368	−	0.0905368i
$560$	0.859911			0.0363379
$561$	0.0879270	+	17.2053i	0.00371228	+	0.726410i
$562$	27.6183			1.16501
$563$	30.9006	−	30.9006i	1.30230	−	1.30230i	0.375469	−	0.926835i	$-0.377482\pi$
$563$	30.9006	−	30.9006i	1.30230	−	1.30230i	0.926835	−	0.375469i	$-0.122518\pi$
$564$	−2.15720	−	0.893541i	−0.0908344	−	0.0376248i
$565$		−	3.15995i		−	0.132940i
$566$	3.35578	−	8.10156i	0.141054	−	0.340534i
$567$	−2.40801	+	0.997432i	−0.101127	+	0.0418882i
$568$	−6.48452	−	15.6550i	−0.272084	−	0.656870i
$569$	1.67923	+	1.67923i	0.0703970	+	0.0703970i	0.741429	−	0.671032i	$-0.234149\pi$
$569$	1.67923	+	1.67923i	0.0703970	+	0.0703970i	−0.671032	+	0.741429i	$0.734149\pi$
$570$	−0.575026	−	0.575026i	−0.0240852	−	0.0240852i
$571$	−15.1196	−	36.5020i	−0.632736	−	1.52756i	−0.836170	−	0.548471i	$-0.815210\pi$
$571$	−15.1196	−	36.5020i	−0.632736	−	1.52756i	0.203434	−	0.979089i	$-0.434790\pi$
$572$	11.0670	−	4.58408i	0.462732	−	0.191670i
$573$	1.83482	−	4.42965i	0.0766508	−	0.185051i
$574$		−	5.19795i		−	0.216958i
$575$	33.3129	+	13.7986i	1.38924	+	0.575443i
$576$	6.90423	−	6.90423i	0.287676	−	0.287676i
$577$	0.0418987			0.00174427			0.000872133	−	1.00000i	$-0.499722\pi$
$577$	0.0418987			0.00174427			0.000872133		1.00000i	$0.499722\pi$
$578$	19.4124	−	19.8133i	0.807448	−	0.824124i
$579$	−12.3873			−0.514799
$580$	1.50192	−	1.50192i	0.0623637	−	0.0623637i
$581$	2.76957	+	1.14719i	0.114901	+	0.0475936i
$582$		−	5.32112i		−	0.220567i
$583$	13.2915	−	32.0885i	0.550478	−	1.32897i
$584$	13.4566	−	5.57390i	0.556838	−	0.230650i
$585$	−0.952597	−	2.29977i	−0.0393850	−	0.0950839i
$586$	5.83882	+	5.83882i	0.241199	+	0.241199i
$587$	27.2656	+	27.2656i	1.12537	+	1.12537i	0.990920	+	0.134453i	$0.0429278\pi$
$587$	27.2656	+	27.2656i	1.12537	+	1.12537i	0.134453	+	0.990920i	$0.457072\pi$
$588$	−1.18799	−	2.86807i	−0.0489921	−	0.118277i
$589$	−16.4779	+	6.82536i	−0.678959	+	0.281234i
$590$	−2.57520	+	6.21707i	−0.106019	+	0.255953i
$591$		−	1.96573i		−	0.0808593i
$592$	−36.4232	−	15.0870i	−1.49699	−	0.620072i
$593$	−20.5224	+	20.5224i	−0.842753	+	0.842753i	−0.989216	−	0.146463i	$-0.953211\pi$
$593$	−20.5224	+	20.5224i	−0.842753	+	0.842753i	0.146463	+	0.989216i	$0.453211\pi$
$594$	37.5315			1.53994
$595$	0.00370835	+	0.725642i	0.000152028	+	0.0297484i
$596$	−12.8170			−0.525006
$597$	9.36929	−	9.36929i	0.383460	−	0.383460i
$598$	−33.6298	−	13.9299i	−1.37522	−	0.569636i
$599$		−	6.72419i		−	0.274743i	−0.990520	−	0.137372i	$-0.956135\pi$
$599$		−	6.72419i		−	0.274743i	0.990520	−	0.137372i	$-0.0438654\pi$
$600$	2.85446	−	6.89129i	0.116533	−	0.281336i
$601$	40.1868	−	16.6459i	1.63925	−	0.679002i	0.643032	−	0.765839i	$-0.277676\pi$
$601$	40.1868	−	16.6459i	1.63925	−	0.679002i	0.996222	+	0.0868376i	$0.0276761\pi$
$602$	0.335735	+	0.810537i	0.0136835	+	0.0330350i
$603$	16.2249	+	16.2249i	0.660730	+	0.660730i
$604$	−6.01305	−	6.01305i	−0.244668	−	0.244668i
$605$	−3.09341	−	7.46816i	−0.125765	−	0.303624i
$606$	9.69400	−	4.01539i	0.393792	−	0.163114i
$607$	−0.513115	+	1.23877i	−0.0208267	+	0.0502800i	−0.933951	−	0.357402i	$-0.883663\pi$
$607$	−0.513115	+	1.23877i	−0.0208267	+	0.0502800i	0.913124	+	0.407682i	$0.133663\pi$
$608$		−	7.86313i		−	0.318892i
$609$	−3.39944	−	1.40809i	−0.137752	−	0.0570589i
$610$	1.52367	−	1.52367i	0.0616916	−	0.0616916i
$611$	15.2801			0.618167
$612$	−4.87555	−	4.82597i	−0.197083	−	0.195078i
$613$	−8.39331			−0.339003			−0.169501	−	0.985530i	$-0.554216\pi$
$613$	−8.39331			−0.339003			−0.169501	+	0.985530i	$0.554216\pi$
$614$	9.17663	−	9.17663i	0.370339	−	0.370339i
$615$	1.25142	+	0.518353i	0.0504620	+	0.0209020i
$616$		−	7.01169i		−	0.282509i
$617$	2.61672	−	6.31733i	0.105345	−	0.254326i	−0.862414	−	0.506204i	$-0.831048\pi$
$617$	2.61672	−	6.31733i	0.105345	−	0.254326i	0.967759	+	0.251878i	$0.0810482\pi$
$618$	3.50605	−	1.45225i	0.141034	−	0.0584181i
$619$	11.9922	+	28.9517i	0.482007	+	1.16367i	0.958654	+	0.284573i	$0.0918518\pi$
$619$	11.9922	+	28.9517i	0.482007	+	1.16367i	−0.476648	+	0.879094i	$0.658148\pi$
$620$	−1.25413	−	1.25413i	−0.0503670	−	0.0503670i
$621$	−20.0621	−	20.0621i	−0.805066	−	0.805066i
$622$	−7.18360	−	17.3427i	−0.288036	−	0.695381i
$623$	2.34303	−	0.970515i	0.0938716	−	0.0388829i
$624$	−3.95341	+	9.54438i	−0.158263	+	0.382081i
$625$			23.4044i			0.936175i
$626$	−23.8673	−	9.88617i	−0.953930	−	0.395131i
$627$	−6.43268	+	6.43268i	−0.256896	+	0.256896i
$628$	−5.53903			−0.221031
$629$	12.5742	−	30.8010i	0.501366	−	1.22812i
$630$	0.721408			0.0287416
$631$	−9.01190	+	9.01190i	−0.358758	+	0.358758i	−0.863355	−	0.504597i	$-0.831641\pi$
$631$	−9.01190	+	9.01190i	−0.358758	+	0.358758i	0.504597	+	0.863355i	$0.331641\pi$
$632$	22.2128	+	9.20084i	0.883577	+	0.365990i
$633$		−	4.64151i		−	0.184484i
$634$	8.53785	−	20.6122i	0.339082	−	0.818615i
$635$	−4.85274	+	2.01007i	−0.192575	+	0.0797672i
$636$	−1.02911	−	2.48448i	−0.0408067	−	0.0985160i
$637$	14.3652	+	14.3652i	0.569170	+	0.569170i
$638$	−67.5383	−	67.5383i	−2.67387	−	2.67387i
$639$	−7.46346	−	18.0184i	−0.295250	−	0.712796i
$640$	−4.09928	+	1.69798i	−0.162038	+	0.0671185i
$641$	−8.63996	+	20.8587i	−0.341258	+	0.823870i	0.656331	+	0.754473i	$0.272107\pi$
$641$	−8.63996	+	20.8587i	−0.341258	+	0.823870i	−0.997589	+	0.0693968i	$0.977893\pi$
$642$			4.40912i			0.174014i
$643$	−36.4120	−	15.0823i	−1.43595	−	0.594789i	−0.477136	−	0.878829i	$-0.658325\pi$
$643$	−36.4120	−	15.0823i	−1.43595	−	0.594789i	−0.958812	+	0.284040i	$0.908325\pi$
$644$	1.85569	−	1.85569i	0.0731244	−	0.0731244i
$645$	−0.228619			−0.00900184
$646$	14.6659	−	0.0749495i	0.577024	−	0.00294885i
$647$	14.1537			0.556441			0.278221	−	0.960517i	$-0.410255\pi$
$647$	14.1537			0.556441			0.278221	+	0.960517i	$0.410255\pi$
$648$	7.48146	−	7.48146i	0.293900	−	0.293900i
$649$	69.5489	+	28.8081i	2.73003	+	1.13082i
$650$		−	24.1678i		−	0.947941i
$651$	−1.17578	+	2.83860i	−0.0460826	+	0.111253i
$652$	−8.95049	+	3.70741i	−0.350528	+	0.145193i
$653$	0.166231	+	0.401317i	0.00650512	+	0.0157047i	0.927099	−	0.374817i	$-0.122295\pi$
$653$	0.166231	+	0.401317i	0.00650512	+	0.0157047i	−0.920594	+	0.390522i	$0.872295\pi$
$654$	−10.4020	−	10.4020i	−0.406750	−	0.406750i
$655$	3.15297	+	3.15297i	0.123197	+	0.123197i
$656$	11.0781	+	26.7449i	0.432527	+	1.04421i
$657$	15.4881	−	6.41537i	0.604247	−	0.250287i
$658$	−1.69464	+	4.09122i	−0.0660639	+	0.159492i
$659$			26.0136i			1.01335i	0.862139	+	0.506673i	$0.169125\pi$
$659$			26.0136i			1.01335i	−0.862139	+	0.506673i	$0.830875\pi$
$660$	−0.835783	−	0.346192i	−0.0325328	−	0.0134755i
$661$	−3.82032	+	3.82032i	−0.148593	+	0.148593i	−0.777489	−	0.628896i	$-0.783507\pi$
$661$	−3.82032	+	3.82032i	−0.148593	+	0.148593i	0.628896	+	0.777489i	$0.283507\pi$
$662$	−47.1180			−1.83129
$663$	−8.07114	−	3.29495i	−0.313457	−	0.127965i
$664$	−12.1690			−0.472248
$665$	−0.271301	+	0.271301i	−0.0105206	+	0.0105206i
$666$	−30.5566	−	12.6570i	−1.18405	−	0.490448i
$667$			72.2040i			2.79575i
$668$	5.93234	−	14.3219i	0.229529	−	0.554132i
$669$	−18.4519	+	7.64302i	−0.713391	+	0.295496i
$670$	−1.86678	−	4.50681i	−0.0721200	−	0.174113i
$671$	−17.0449	−	17.0449i	−0.658012	−	0.658012i
$672$	−0.957819	−	0.957819i	−0.0369487	−	0.0369487i
$673$	−9.83632	−	23.7470i	−0.379162	−	0.915379i	−0.992123	−	0.125266i	$-0.960022\pi$
$673$	−9.83632	−	23.7470i	−0.379162	−	0.915379i	0.612961	−	0.790113i	$-0.289978\pi$
$674$	18.5385	−	7.67888i	0.714075	−	0.295779i
$675$	7.20877	−	17.4035i	0.277466	−	0.669861i
$676$		−	2.54050i		−	0.0977117i
$677$	2.59087	+	1.07317i	0.0995750	+	0.0412453i	0.431915	−	0.901914i	$-0.357838\pi$
$677$	2.59087	+	1.07317i	0.0995750	+	0.0412453i	−0.332340	+	0.943160i	$0.607838\pi$
$678$	−7.77957	+	7.77957i	−0.298773	+	0.298773i
$679$	−2.51053			−0.0963454
$680$	−1.14116	−	2.71566i	−0.0437613	−	0.104141i
$681$	18.0246			0.690704
$682$	−56.3957	+	56.3957i	−2.15950	+	2.15950i
$683$	4.03853	+	1.67281i	0.154530	+	0.0640084i	0.458608	−	0.888639i	$-0.348348\pi$
$683$	4.03853	+	1.67281i	0.154530	+	0.0640084i	−0.304078	+	0.952647i	$0.598348\pi$
$684$		−	3.62717i		−	0.138688i
$685$	0.770784	−	1.86084i	0.0294502	−	0.0710990i
$686$	−11.1132	+	4.60323i	−0.424303	+	0.175752i
$687$	−2.48364	−	5.99603i	−0.0947567	−	0.228763i
$688$	−3.45490	−	3.45490i	−0.131717	−	0.131717i
$689$	12.4439	+	12.4439i	0.474075	+	0.474075i
$690$	1.05199	+	2.53974i	0.0400488	+	0.0966863i
$691$	−24.4631	+	10.1329i	−0.930620	+	0.385475i	−0.795913	−	0.605410i	$-0.793009\pi$
$691$	−24.4631	+	10.1329i	−0.930620	+	0.385475i	−0.134706	+	0.990886i	$0.543009\pi$
$692$	−0.778097	+	1.87849i	−0.0295788	+	0.0714096i
$693$		−	8.07022i		−	0.306562i
$694$	9.19304	+	3.80788i	0.348963	+	0.144545i
$695$	0.577830	−	0.577830i	0.0219183	−	0.0219183i
$696$	14.9365			0.566168
$697$	−22.5211	+	9.46365i	−0.853046	+	0.358461i
$698$	−0.136641			−0.00517194
$699$	9.63092	−	9.63092i	0.364275	−	0.364275i
$700$	1.60977	+	0.666790i	0.0608437	+	0.0252023i
$701$		−	21.9116i		−	0.827589i	−0.910370	−	0.413795i	$-0.864203\pi$
$701$		−	21.9116i		−	0.827589i	0.910370	−	0.413795i	$-0.135797\pi$
$702$	−7.27735	+	17.5691i	−0.274666	+	0.663102i
$703$	16.2514	−	6.73155i	0.612933	−	0.253885i
$704$	8.88648	+	21.4539i	0.334922	+	0.808573i
$705$	−0.815975	−	0.815975i	−0.0307314	−	0.0307314i
$706$	9.70789	+	9.70789i	0.365361	+	0.365361i
$707$	−1.89448	−	4.57368i	−0.0712493	−	0.172011i
$708$	5.38488	−	2.23049i	0.202376	−	0.0838270i
$709$	8.78340	−	21.2050i	0.329867	−	0.796370i	−0.668734	−	0.743502i	$-0.733164\pi$
$709$	8.78340	−	21.2050i	0.329867	−	0.796370i	0.998601	−	0.0528687i	$-0.0168365\pi$
$710$			4.14626i			0.155606i
$711$	25.5661	+	10.5898i	0.958805	+	0.397150i
$712$	−7.27956	+	7.27956i	−0.272813	+	0.272813i
$713$	60.2916			2.25794
$714$	1.77735	−	1.79561i	0.0665155	−	0.0671989i
$715$	5.92011			0.221400
$716$	7.63550	−	7.63550i	0.285352	−	0.285352i
$717$	−2.49949	−	1.03532i	−0.0933451	−	0.0386648i
$718$		−	33.7217i		−	1.25848i
$719$	3.77644	−	9.11714i	0.140838	−	0.340012i	−0.837684	−	0.546155i	$-0.816091\pi$
$719$	3.77644	−	9.11714i	0.140838	−	0.340012i	0.978522	+	0.206143i	$0.0660911\pi$
$720$	−3.71184	+	1.53749i	−0.138332	+	0.0572990i
$721$	−0.685181	−	1.65417i	−0.0255175	−	0.0616046i
$722$	−16.4381	−	16.4381i	−0.611763	−	0.611763i
$723$	−6.03410	−	6.03410i	−0.224411	−	0.224411i
$724$	−2.99609	−	7.23320i	−0.111349	−	0.268820i
$725$	−44.2900	+	18.3455i	−1.64489	+	0.681336i
$726$	−10.7703	+	26.0018i	−0.399723	+	0.965017i
$727$			15.9121i			0.590148i	0.955474	+	0.295074i	$0.0953443\pi$
$727$			15.9121i			0.590148i	−0.955474	+	0.295074i	$0.904656\pi$
$728$	3.28228	+	1.35957i	0.121649	+	0.0503888i
$729$	2.90662	−	2.90662i	0.107653	−	0.107653i
$730$	−3.56400			−0.131910
$731$	2.90054	−	2.93034i	0.107280	−	0.108382i
$732$	−1.86636			−0.0689827
$733$	−14.2549	+	14.2549i	−0.526516	+	0.526516i	−0.919532	−	0.393016i	$-0.871432\pi$
$733$	−14.2549	+	14.2549i	−0.526516	+	0.526516i	0.393016	+	0.919532i	$0.371432\pi$
$734$	31.1668	+	12.9097i	1.15039	+	0.476506i
$735$		−	1.53423i		−	0.0565911i
$736$	−10.1720	+	24.5574i	−0.374945	+	0.905198i
$737$	−50.4166	+	20.8832i	−1.85712	+	0.769244i
$738$	9.29377	+	22.4371i	0.342108	+	0.825922i
$739$	−7.81517	−	7.81517i	−0.287486	−	0.287486i	0.548600	−	0.836085i	$-0.315161\pi$
$739$	−7.81517	−	7.81517i	−0.287486	−	0.287486i	−0.836085	+	0.548600i	$0.815161\pi$
$740$	1.23689	+	1.23689i	0.0454690	+	0.0454690i
$741$	−1.76394	−	4.25853i	−0.0648000	−	0.156441i
$742$	−4.71193	+	1.95174i	−0.172980	+	0.0716508i
$743$	−13.1572	+	31.7643i	−0.482691	+	1.16532i	0.475635	+	0.879643i	$0.342218\pi$
$743$	−13.1572	+	31.7643i	−0.482691	+	1.16532i	−0.958326	+	0.285676i	$0.907782\pi$
$744$		−	12.4723i		−	0.457256i
$745$	−5.85221	−	2.42406i	−0.214408	−	0.0888109i
$746$	7.02124	−	7.02124i	0.257066	−	0.257066i
$747$	−14.0061			−0.512456
$748$	15.0411	−	6.32049i	0.549958	−	0.231100i
$749$	2.08025			0.0760107
$750$	−2.60944	+	2.60944i	−0.0952832	+	0.0952832i
$751$	0.854618	+	0.353994i	0.0311854	+	0.0129174i	0.398222	−	0.917289i	$-0.369627\pi$
$751$	0.854618	+	0.353994i	0.0311854	+	0.0129174i	−0.367036	+	0.930207i	$0.619627\pi$
$752$		−	24.6621i		−	0.899335i
$753$	0.342572	−	0.827042i	0.0124840	−	0.0301391i
$754$	44.7114	−	18.5201i	1.62829	−	0.674461i
$755$	−1.60830	−	3.88278i	−0.0585320	−	0.141309i
$756$	−0.969460	−	0.969460i	−0.0352589	−	0.0352589i
$757$	−6.72666	−	6.72666i	−0.244485	−	0.244485i	0.574218	−	0.818703i	$-0.305306\pi$
$757$	−6.72666	−	6.72666i	−0.244485	−	0.244485i	−0.818703	+	0.574218i	$0.805306\pi$
$758$	8.12515	+	19.6158i	0.295119	+	0.712479i
$759$	28.4115	−	11.7684i	1.03127	−	0.427166i
$760$	0.596023	−	1.43893i	0.0216200	−	0.0521953i
$761$		−	27.4658i		−	0.995633i	−0.867282	−	0.497816i	$-0.834135\pi$
$761$		−	27.4658i		−	0.995633i	0.867282	−	0.497816i	$-0.165865\pi$
$762$	16.8957	+	6.99844i	0.612068	+	0.253527i
$763$	−4.90772	+	4.90772i	−0.177671	+	0.177671i
$764$	−4.54649			−0.164486
$765$	−1.31343	−	3.12563i	−0.0474872	−	0.113007i
$766$	13.9043			0.502383
$767$	−26.9710	+	26.9710i	−0.973868	+	0.973868i
$768$	9.25637	+	3.83411i	0.334010	+	0.138352i
$769$		−	45.9487i		−	1.65695i	−0.560025	−	0.828476i	$-0.689208\pi$
$769$		−	45.9487i		−	1.65695i	0.560025	−	0.828476i	$-0.310792\pi$
$770$	−0.656569	+	1.58510i	−0.0236611	+	0.0571230i
$771$	−11.2834	+	4.67374i	−0.406362	+	0.168320i
$772$	4.49509	+	10.8521i	0.161782	+	0.390576i
$773$	−24.9327	−	24.9327i	−0.896767	−	0.896767i	0.0983814	−	0.995149i	$-0.468633\pi$
$773$	−24.9327	−	24.9327i	−0.896767	−	0.896767i	−0.995149	+	0.0983814i	$0.968633\pi$
$774$	−2.89843	−	2.89843i	−0.104182	−	0.104182i
$775$	15.3188	+	36.9830i	0.550269	+	1.32847i
$776$	9.41541	−	3.89999i	0.337993	−	0.140001i
$777$	1.15962	−	2.79958i	0.0416013	−	0.100434i
$778$		−	7.97715i		−	0.285995i
$779$	−11.9331	−	4.94284i	−0.427547	−	0.177096i
$780$	0.324116	−	0.324116i	0.0116052	−	0.0116052i
$781$	46.3832			1.65972
$782$	−45.9002	−	18.7383i	−1.64139	−	0.670079i
$783$	37.7213			1.34805
$784$	23.1854	−	23.1854i	0.828052	−	0.828052i
$785$	−2.52910	−	1.04759i	−0.0902675	−	0.0373900i
$786$		−	15.5248i		−	0.553750i
$787$	−6.29764	+	15.2038i	−0.224486	+	0.541958i	−0.995489	−	0.0948734i	$-0.969755\pi$
$787$	−6.29764	+	15.2038i	−0.224486	+	0.541958i	0.771003	+	0.636832i	$0.219755\pi$
$788$	−1.72211	+	0.713322i	−0.0613477	+	0.0254110i
$789$	−4.11905	−	9.94426i	−0.146642	−	0.354025i
$790$	−4.15997	−	4.15997i	−0.148005	−	0.148005i
$791$	3.67045	+	3.67045i	0.130506	+	0.130506i
$792$	12.5367	+	30.2662i	0.445471	+	1.07546i
$793$	11.2840	−	4.67399i	0.400707	−	0.165978i
$794$	1.38393	−	3.34110i	0.0491138	−	0.118571i
$795$		−	1.32904i		−	0.0471361i
$796$	−11.6080	−	4.80821i	−0.411436	−	0.170422i
$797$	−23.9248	+	23.9248i	−0.847460	+	0.847460i	−0.989816	−	0.142356i	$-0.954532\pi$
$797$	−23.9248	+	23.9248i	−0.847460	+	0.847460i	0.142356	+	0.989816i	$0.454532\pi$
$798$	1.33584			0.0472884
$799$	20.8113	−	0.106355i	0.736251	−	0.00376257i
$800$	−17.6480			−0.623952
$801$	−8.37852	+	8.37852i	−0.296041	+	0.296041i
$802$	43.6244	+	18.0698i	1.54043	+	0.638068i
$803$			39.8696i			1.40697i
$804$	−1.61690	+	3.90355i	−0.0570237	+	0.137667i
$805$	1.19826	−	0.496337i	0.0422333	−	0.0174936i
$806$	−15.4646	−	37.3348i	−0.544717	−	1.31506i
$807$	−11.7370	−	11.7370i	−0.413163	−	0.413163i
$808$	14.2100	+	14.2100i	0.499905	+	0.499905i
$809$	1.55583	+	3.75610i	0.0546999	+	0.132057i	0.948867	−	0.315676i	$-0.102231\pi$
$809$	1.55583	+	3.75610i	0.0546999	+	0.132057i	−0.894167	+	0.447733i	$0.852231\pi$
$810$	−2.39185	+	0.990739i	−0.0840412	+	0.0348110i
$811$	−6.60680	+	15.9502i	−0.231996	+	0.560088i	−0.996412	−	0.0846353i	$-0.973027\pi$
$811$	−6.60680	+	15.9502i	−0.231996	+	0.560088i	0.764416	+	0.644724i	$0.223027\pi$
$812$			3.48911i			0.122444i
$813$	−15.9841	−	6.62085i	−0.560588	−	0.232203i
$814$	55.6206	−	55.6206i	1.94950	−	1.94950i
$815$	−4.78794			−0.167714
$816$	−5.31806	+	13.0268i	−0.186169	+	0.456030i
$817$	2.18003			0.0762695
$818$	−42.7800	+	42.7800i	−1.49577	+	1.49577i
$819$	3.77779	+	1.56481i	0.132007	+	0.0546790i
$820$		−	1.28442i		−	0.0448540i
$821$	−8.33365	+	20.1192i	−0.290846	+	0.702165i	−0.999996	−	0.00289282i	$-0.999079\pi$
$821$	−8.33365	+	20.1192i	−0.290846	+	0.702165i	0.709149	+	0.705058i	$0.249079\pi$
$822$	−6.47886	+	2.68363i	−0.225976	+	0.0936024i
$823$	6.21370	+	15.0012i	0.216596	+	0.522909i	0.994410	−	0.105585i	$-0.0336716\pi$
$823$	6.21370	+	15.0012i	0.216596	+	0.522909i	−0.777814	+	0.628494i	$0.783672\pi$
$824$	5.13935	+	5.13935i	0.179038	+	0.179038i
$825$	14.4375	+	14.4375i	0.502650	+	0.502650i
$826$	−4.23023	−	10.2127i	−0.147188	−	0.355344i
$827$	−23.7788	+	9.84950i	−0.826870	+	0.342501i	−0.755663	−	0.654961i	$-0.772685\pi$
$827$	−23.7788	+	9.84950i	−0.826870	+	0.342501i	−0.0712071	+	0.997462i	$0.522685\pi$
$828$	−4.69223	+	11.3281i	−0.163066	+	0.393677i
$829$			44.2855i			1.53810i	0.639189	+	0.769050i	$0.279270\pi$
$829$			44.2855i			1.53810i	−0.639189	+	0.769050i	$0.720730\pi$
$830$	2.75098	+	1.13949i	0.0954880	+	0.0395524i
$831$	−1.52810	+	1.52810i	−0.0530091	+	0.0530091i
$832$	−11.7660			−0.407912
$833$	19.6652	+	19.4652i	0.681358	+	0.674429i
$834$	−2.84515			−0.0985194
$835$	5.41737	−	5.41737i	0.187476	−	0.187476i
$836$	7.96974	+	3.30117i	0.275639	+	0.114173i
$837$		−	31.4979i		−	1.08873i
$838$	14.2480	−	34.3977i	0.492188	−	1.18825i
$839$	−0.407300	+	0.168709i	−0.0140616	+	0.00582449i	−0.389703	−	0.920941i	$-0.627422\pi$
$839$	−0.407300	+	0.168709i	−0.0140616	+	0.00582449i	0.375642	+	0.926765i	$0.377422\pi$
$840$	−0.102675	−	0.247880i	−0.00354263	−	0.00855266i
$841$	−47.3737	−	47.3737i	−1.63357	−	1.63357i
$842$	13.0161	+	13.0161i	0.448565	+	0.448565i
$843$	−4.52422	−	10.9224i	−0.155823	−	0.376189i
$844$	−4.06628	+	1.68431i	−0.139967	+	0.0579762i
$845$	0.480482	−	1.15999i	0.0165291	−	0.0399047i
$846$		−	20.6899i		−	0.711332i
$847$	12.2678	+	5.08149i	0.421527	+	0.174602i
$848$	20.0845	−	20.0845i	0.689704	−	0.689704i
$849$	−3.75371			−0.128827
$850$	−0.168217	−	32.9163i	−0.00576979	−	1.12902i
$851$	−59.4630			−2.03836
$852$	2.53940	−	2.53940i	0.0869985	−	0.0869985i
$853$	27.8503	+	11.5360i	0.953575	+	0.394984i	0.804573	−	0.593853i	$-0.202394\pi$
$853$	27.8503	+	11.5360i	0.953575	+	0.394984i	0.149001	+	0.988837i	$0.452394\pi$
$854$			3.53964i			0.121124i
$855$	0.686002	−	1.65615i	0.0234608	−	0.0566393i
$856$	−7.80168	+	3.23156i	−0.266656	+	0.110453i
$857$	−4.93842	−	11.9224i	−0.168693	−	0.407261i	0.816813	−	0.576903i	$-0.195739\pi$
$857$	−4.93842	−	11.9224i	−0.168693	−	0.407261i	−0.985506	+	0.169642i	$0.945739\pi$
$858$	−14.5749	−	14.5749i	−0.497578	−	0.497578i
$859$	−18.8093	−	18.8093i	−0.641765	−	0.641765i	0.309224	−	0.950989i	$-0.399931\pi$
$859$	−18.8093	−	18.8093i	−0.641765	−	0.641765i	−0.950989	+	0.309224i	$0.899931\pi$
$860$	0.0829608	+	0.200285i	0.00282894	+	0.00682966i
$861$	−2.05568	+	0.851489i	−0.0700573	+	0.0290187i
$862$	−20.6900	+	49.9502i	−0.704705	+	1.70131i
$863$		−	19.4174i		−	0.660977i	−0.943810	−	0.330488i	$-0.892787\pi$
$863$		−	19.4174i		−	0.660977i	0.943810	−	0.330488i	$-0.107213\pi$
$864$	12.8294	+	5.31412i	0.436466	+	0.180790i
$865$	−0.710552	+	0.710552i	−0.0241595	+	0.0241595i
$866$	−58.8676			−2.00040
$867$	−11.0157	−	4.43150i	−0.374113	−	0.150502i
$868$	2.91347			0.0988895
$869$	−46.5366	+	46.5366i	−1.57865	+	1.57865i
$870$	−3.37663	−	1.39865i	−0.114478	−	0.0474185i
$871$		−	27.6500i		−	0.936886i
$872$	10.7818	−	26.0296i	0.365118	−	0.881474i
$873$	10.8368	−	4.48875i	0.366770	−	0.151921i
$874$	−10.0315	−	24.2181i	−0.339319	−	0.819189i
$875$	1.23115	+	1.23115i	0.0416204	+	0.0416204i
$876$	2.18279	+	2.18279i	0.0737498	+	0.0737498i
$877$	−4.78972	−	11.5634i	−0.161737	−	0.390468i	0.822147	−	0.569275i	$-0.192776\pi$
$877$	−4.78972	−	11.5634i	−0.161737	−	0.390468i	−0.983884	+	0.178807i	$0.942776\pi$
$878$	−56.0553	+	23.2189i	−1.89177	+	0.783598i
$879$	1.35265	−	3.26560i	0.0456239	−	0.110146i
$880$		−	9.55507i		−	0.322101i
$881$	42.2426	+	17.4975i	1.42319	+	0.589504i	0.955660	−	0.294473i	$-0.0951442\pi$
$881$	42.2426	+	17.4975i	1.42319	+	0.589504i	0.467529	+	0.883977i	$0.345144\pi$
$882$	19.4510	−	19.4510i	0.654950	−	0.654950i
$883$	1.13705			0.0382648			0.0191324	−	0.999817i	$-0.493910\pi$
$883$	1.13705			0.0382648			0.0191324	+	0.999817i	$0.493910\pi$
$884$	0.0422456	+	8.26652i	0.00142087	+	0.278033i
$885$	2.88057			0.0968292
$886$	−1.44200	+	1.44200i	−0.0484451	+	0.0484451i
$887$	−42.9733	−	17.8001i	−1.44290	−	0.597670i	−0.482402	−	0.875950i	$-0.660236\pi$
$887$	−42.9733	−	17.8001i	−1.44290	−	0.597670i	−0.960500	+	0.278280i	$0.910236\pi$
$888$			12.3009i			0.412790i
$889$	3.30190	−	7.97150i	0.110742	−	0.267356i
$890$	2.32731	−	0.964002i	0.0780115	−	0.0323134i
$891$	11.0832	+	26.7571i	0.371300	+	0.896397i
$892$	13.3916	+	13.3916i	0.448384	+	0.448384i
$893$	7.78086	+	7.78086i	0.260376	+	0.260376i
$894$	8.43984	+	20.3756i	0.282270	+	0.681461i
$895$	4.93043	−	2.04225i	0.164806	−	0.0682650i
$896$	2.78924	−	6.73382i	0.0931819	−	0.224961i
$897$			15.5817i			0.520259i
$898$	31.0685	+	12.8690i	1.03677	+	0.429444i
$899$	−56.6808	+	56.6808i	−1.89041	+	1.89041i
$900$	−8.14084			−0.271361
$901$	17.0350	+	16.8618i	0.567520	+	0.561749i
$902$	−57.7580			−1.92313
$903$	0.265552	−	0.265552i	0.00883702	−	0.00883702i
$904$	−19.4673	−	8.06364i	−0.647474	−	0.268193i
$905$		−	3.86930i		−	0.128620i
$906$	−5.59960	+	13.5186i	−0.186034	+	0.449126i
$907$	37.6298	−	15.5868i	1.24948	−	0.517550i	0.342812	−	0.939404i	$-0.388621\pi$
$907$	37.6298	−	15.5868i	1.24948	−	0.517550i	0.906664	+	0.421854i	$0.138621\pi$
$908$	−6.54074	−	15.7908i	−0.217062	−	0.524035i
$909$	16.3552	+	16.3552i	0.542468	+	0.542468i
$910$	−0.614700	−	0.614700i	−0.0203771	−	0.0203771i
$911$	2.37983	+	5.74541i	0.0788471	+	0.190354i	0.958388	−	0.285470i	$-0.0921498\pi$
$911$	2.37983	+	5.74541i	0.0788471	+	0.190354i	−0.879540	+	0.475824i	$0.842150\pi$
$912$	−6.87328	+	2.84700i	−0.227597	+	0.0942737i
$913$	12.7473	−	30.7746i	0.421873	−	1.01849i
$914$		−	8.66613i		−	0.286650i
$915$	−0.852174	−	0.352982i	−0.0281720	−	0.0116692i
$916$	−4.35166	+	4.35166i	−0.143783	+	0.143783i
$917$	−7.32467			−0.241882
$918$	−9.78936	+	23.9795i	−0.323097	+	0.791441i
$919$	−2.13630			−0.0704700			−0.0352350	−	0.999379i	$-0.511218\pi$
$919$	−2.13630			−0.0704700			−0.0352350	+	0.999379i	$0.511218\pi$
$920$	−3.72289	+	3.72289i	−0.122740	+	0.122740i
$921$	−5.13241	−	2.12591i	−0.169119	−	0.0700512i
$922$		−	16.5303i		−	0.544398i
$923$	−8.99369	+	21.7127i	−0.296031	+	0.714682i
$924$	1.37292	−	0.568684i	0.0451659	−	0.0187083i
$925$	−15.1083	−	36.4747i	−0.496758	−	1.19928i
$926$	−36.1643	−	36.1643i	−1.18843	−	1.18843i
$927$	5.91521	+	5.91521i	0.194281	+	0.194281i
$928$	−13.5239	−	32.6495i	−0.443943	−	1.07177i
$929$	53.4843	−	22.1539i	1.75476	−	0.726847i	0.757508	−	0.652826i	$-0.226417\pi$
$929$	53.4843	−	22.1539i	1.75476	−	0.726847i	0.997257	−	0.0740207i	$-0.0235831\pi$
$930$	−1.16789	+	2.81955i	−0.0382968	+	0.0924565i
$931$			14.6299i			0.479477i
$932$	−11.9322	−	4.94247i	−0.390852	−	0.161896i
$933$	−5.68192	+	5.68192i	−0.186018	+	0.186018i
$934$	44.7813			1.46529
$935$	8.06311	−	0.0412061i	0.263692	−	0.00134758i
$936$	−16.5989			−0.542553
$937$	4.31034	−	4.31034i	0.140813	−	0.140813i	−0.633187	−	0.773999i	$-0.718253\pi$
$937$	4.31034	−	4.31034i	0.140813	−	0.140813i	0.773999	+	0.633187i	$0.218253\pi$
$938$	7.40325	+	3.06653i	0.241725	+	0.100126i
$939$			11.0585i			0.360880i
$940$	−0.418748	+	1.01095i	−0.0136581	+	0.0329735i
$941$	25.9806	−	10.7615i	0.846942	−	0.350815i	0.0833554	−	0.996520i	$-0.473436\pi$
$941$	25.9806	−	10.7615i	0.846942	−	0.350815i	0.763587	+	0.645705i	$0.223436\pi$
$942$	3.64738	+	8.80554i	0.118838	+	0.286900i
$943$	30.8740	+	30.8740i	1.00540	+	1.00540i
$944$	43.5313	+	43.5313i	1.41682	+	1.41682i
$945$	−0.259299	−	0.626004i	−0.00843501	−	0.0203639i
$946$	9.00643	−	3.73059i	0.292824	−	0.121292i
$947$	3.55105	−	8.57299i	0.115394	−	0.278585i	−0.855622	−	0.517601i	$-0.826825\pi$
$947$	3.55105	−	8.57299i	0.115394	−	0.278585i	0.971015	+	0.239017i	$0.0768250\pi$
$948$			5.09561i			0.165498i
$949$	−18.6636	−	7.73071i	−0.605845	−	0.250949i
$950$	12.3066	−	12.3066i	0.399280	−	0.399280i
$951$	−9.55029			−0.309689
$952$	4.47988	+	1.82886i	0.145194	+	0.0592738i
$953$	28.4495			0.921570			0.460785	−	0.887512i	$-0.347568\pi$
$953$	28.4495			0.921570			0.460785	+	0.887512i	$0.347568\pi$
$954$	16.8495	−	16.8495i	0.545524	−	0.545524i
$955$	−2.07591	−	0.859870i	−0.0671749	−	0.0278247i
$956$			2.56542i			0.0829715i
$957$	−15.6463	+	37.7735i	−0.505774	+	1.22105i
$958$	46.6444	−	19.3207i	1.50701	−	0.624225i
$959$	1.26615	+	3.05676i	0.0408862	+	0.0987081i
$960$	0.628316	+	0.628316i	0.0202788	+	0.0202788i
$961$	25.4092	+	25.4092i	0.819652	+	0.819652i
$962$	15.2520	+	36.8217i	0.491745	+	1.18718i
$963$	−8.97947	+	3.71942i	−0.289359	+	0.119857i
$964$	−3.09663	+	7.47592i	−0.0997356	+	0.240783i
$965$			5.80519i			0.186876i
$966$	−4.17198	−	1.72809i	−0.134231	−	0.0556004i
$967$	−8.60132	+	8.60132i	−0.276600	+	0.276600i	−0.831750	−	0.555150i	$-0.812661\pi$
$967$	−8.60132	+	8.60132i	−0.276600	+	0.276600i	0.555150	+	0.831750i	$0.312661\pi$
$968$	−53.9025			−1.73249
$969$	−2.43210	−	5.78778i	−0.0781304	−	0.185930i
$970$	−2.49369			−0.0800674
$971$	18.0139	−	18.0139i	0.578094	−	0.578094i	−0.356284	−	0.934378i	$-0.615956\pi$
$971$	18.0139	−	18.0139i	0.578094	−	0.578094i	0.934378	+	0.356284i	$0.115956\pi$
$972$	9.13898	+	3.78549i	0.293133	+	0.121420i
$973$			1.34236i			0.0430340i
$974$	12.6115	−	30.4470i	0.404100	−	0.975584i
$975$	−9.55785	+	3.95899i	−0.306096	+	0.126789i
$976$	−7.54382	−	18.2124i	−0.241472	−	0.582965i
$977$	−30.4274	−	30.4274i	−0.973459	−	0.973459i	0.0261978	−	0.999657i	$-0.491660\pi$
$977$	−30.4274	−	30.4274i	−0.973459	−	0.973459i	−0.999657	+	0.0261978i	$0.991660\pi$
$978$	11.7875	+	11.7875i	0.376924	+	0.376924i
$979$	−10.7841	−	26.0350i	−0.344660	−	0.832083i
$980$	−1.34409	+	0.556741i	−0.0429354	+	0.0177844i
$981$	12.4095	−	29.9592i	0.396205	−	0.956523i
$982$			9.24457i			0.295006i
$983$	−18.4974	−	7.66189i	−0.589976	−	0.244376i	0.0676640	−	0.997708i	$-0.478445\pi$
$983$	−18.4974	−	7.66189i	−0.589976	−	0.244376i	−0.657641	+	0.753332i	$0.728445\pi$
$984$	6.38678	−	6.38678i	0.203603	−	0.203603i
$985$	−0.921219			−0.0293525
$986$	60.7674	−	25.5353i	1.93523	−	0.813209i
$987$	1.89559			0.0603374
$988$	−3.09066	+	3.09066i	−0.0983270	+	0.0983270i
$989$	−6.80846	−	2.82016i	−0.216496	−	0.0896758i
$990$		−	8.01606i		−	0.254767i
$991$	−10.6713	+	25.7628i	−0.338985	+	0.818383i	0.658828	+	0.752293i	$0.271052\pi$
$991$	−10.6713	+	25.7628i	−0.338985	+	0.818383i	−0.997814	+	0.0660895i	$0.978948\pi$
$992$	−27.2629	+	11.2927i	−0.865599	+	0.358543i
$993$	7.71851	+	18.6341i	0.244939	+	0.591336i
$994$	−4.81609	−	4.81609i	−0.152757	−	0.152757i
$995$	−4.39082	−	4.39082i	−0.139198	−	0.139198i
$996$	−0.986967	−	2.38275i	−0.0312732	−	0.0755003i
$997$	52.1843	−	21.6155i	1.65269	−	0.684568i	0.655209	−	0.755447i	$-0.272580\pi$
$997$	52.1843	−	21.6155i	1.65269	−	0.684568i	0.997485	+	0.0708790i	$0.0225804\pi$
$998$	8.53625	−	20.6083i	0.270210	−	0.652345i
$999$			31.0650i			0.982853i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.689.6	yes	128
17.2	even	8	inner	731.2.m.c.87.6	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.6	✓	128	17.2	even	8	inner
731.2.m.c.689.6	yes	128	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15376 + 1.15376i) q^{2} +(0.645285 + 0.267286i) q^{3} -0.662305i q^{4} +(0.125261 - 0.302406i) q^{5} +(-1.05288 + 0.436119i) q^{6} +(0.205763 + 0.496757i) q^{7} +(-1.54337 - 1.54337i) q^{8} +(-1.77637 - 1.77637i) q^{9} +O(q^{10})\)	\(q+(-1.15376 + 1.15376i) q^{2} +(0.645285 + 0.267286i) q^{3} -0.662305i q^{4} +(0.125261 - 0.302406i) q^{5} +(-1.05288 + 0.436119i) q^{6} +(0.205763 + 0.496757i) q^{7} +(-1.54337 - 1.54337i) q^{8} +(-1.77637 - 1.77637i) q^{9} +(0.204383 + 0.493423i) q^{10} +(5.51981 - 2.28638i) q^{11} +(0.177025 - 0.427376i) q^{12} +3.02723i q^{13} +(-0.810537 - 0.335735i) q^{14} +(0.161658 - 0.161658i) q^{15} +4.88596 q^{16} +(0.0210706 + 4.12305i) q^{17} +4.09899 q^{18} +(-1.54151 + 1.54151i) q^{19} +(-0.200285 - 0.0829608i) q^{20} +0.375547i q^{21} +(-3.73059 + 9.00643i) q^{22} +(6.80846 - 2.82016i) q^{23} +(-0.583394 - 1.40844i) q^{24} +(3.45977 + 3.45977i) q^{25} +(-3.49269 - 3.49269i) q^{26} +(-1.47332 - 3.55692i) q^{27} +(0.329004 - 0.136278i) q^{28} +(-3.74945 + 9.05197i) q^{29} +0.373027i q^{30} +(7.55856 + 3.13086i) q^{31} +(-2.55046 + 2.55046i) q^{32} +4.17296 q^{33} +(-4.78131 - 4.73268i) q^{34} +0.175996 q^{35} +(-1.17650 + 1.17650i) q^{36} +(-7.45467 - 3.08782i) q^{37} -3.55706i q^{38} +(-0.809137 + 1.95343i) q^{39} +(-0.660049 + 0.273401i) q^{40} +(2.26733 + 5.47382i) q^{41} +(-0.433290 - 0.433290i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(-1.51428 - 3.65580i) q^{44} +(-0.759694 + 0.314676i) q^{45} +(-4.60153 + 11.1091i) q^{46} -5.04755i q^{47} +(3.15284 + 1.30595i) q^{48} +(4.74532 - 4.74532i) q^{49} -7.98347 q^{50} +(-1.08844 + 2.66618i) q^{51} +2.00495 q^{52} +(4.11065 - 4.11065i) q^{53} +(5.80367 + 2.40396i) q^{54} -1.95562i q^{55} +(0.449111 - 1.08425i) q^{56} +(-1.40674 + 0.582691i) q^{57} +(-6.11781 - 14.7697i) q^{58} +(8.90947 + 8.90947i) q^{59} +(-0.107067 - 0.107067i) q^{60} +(-1.54398 - 3.72750i) q^{61} +(-12.3330 + 5.10848i) q^{62} +(0.516912 - 1.24794i) q^{63} +3.88671i q^{64} +(0.915454 + 0.379193i) q^{65} +(-4.81458 + 4.81458i) q^{66} -9.13376 q^{67} +(2.73072 - 0.0139552i) q^{68} +5.14719 q^{69} +(-0.203057 + 0.203057i) q^{70} +(7.17245 + 2.97093i) q^{71} +5.48320i q^{72} +(-2.55372 + 6.16522i) q^{73} +(12.1635 - 5.03827i) q^{74} +(1.30779 + 3.15729i) q^{75} +(1.02095 + 1.02095i) q^{76} +(2.27155 + 2.27155i) q^{77} +(-1.32023 - 3.18733i) q^{78} +(-10.1769 + 4.21542i) q^{79} +(0.612019 - 1.47754i) q^{80} +4.84747i q^{81} +(-8.93139 - 3.69950i) q^{82} +(3.94233 - 3.94233i) q^{83} +0.248727 q^{84} +(1.24948 + 0.510084i) q^{85} +1.63166 q^{86} +(-4.83893 + 4.83893i) q^{87} +(-12.0479 - 4.99039i) q^{88} -4.71666i q^{89} +(0.513443 - 1.23956i) q^{90} +(-1.50380 + 0.622894i) q^{91} +(-1.86780 - 4.50928i) q^{92} +(4.04059 + 4.04059i) q^{93} +(5.82364 + 5.82364i) q^{94} +(0.273072 + 0.659254i) q^{95} +(-2.32748 + 0.964072i) q^{96} +(-1.78681 + 4.31373i) q^{97} +10.9499i q^{98} +(-13.8667 - 5.74376i) 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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