LMFDB - Embedded newform 750.2.l.b.743.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, not 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			743.7
Character	$\chi$	$=$	750.743
Dual form			750.2.l.b.107.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 - 0.453990i) q^{2} +(-0.983013 + 1.42607i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-0.228447 + 1.71692i) q^{6} +(-0.462249 + 0.462249i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.06737 - 2.80370i) q^{9} +O(q^{10})$	\(q+(0.891007 - 0.453990i) q^{2} +(-0.983013 + 1.42607i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-0.228447 + 1.71692i) q^{6} +(-0.462249 + 0.462249i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.06737 - 2.80370i) q^{9} +(2.73512 + 0.888693i) q^{11} +(0.575917 + 1.63350i) q^{12} +(-1.97121 + 3.86872i) q^{13} +(-0.202010 + 0.621723i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(5.75574 + 0.911620i) q^{17} +(-2.22389 - 2.01354i) q^{18} +(4.28299 + 5.89503i) q^{19} +(-0.204804 - 1.11360i) q^{21} +(2.84047 - 0.449885i) q^{22} +(0.316926 + 0.622003i) q^{23} +(1.25474 + 1.19400i) q^{24} +4.34197i q^{26} +(5.04752 + 1.23392i) q^{27} +(0.102264 + 0.645670i) q^{28} +(-2.60237 - 1.89073i) q^{29} +(-4.82678 + 3.50686i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.95600 + 3.02688i) q^{33} +(5.54227 - 1.80079i) q^{34} +(-2.89562 - 0.784450i) q^{36} +(1.93977 + 0.988365i) q^{37} +(6.49246 + 3.30807i) q^{38} +(-3.57936 - 6.61410i) q^{39} +(-6.34331 + 2.06107i) q^{41} +(-0.688045 - 0.899243i) q^{42} +(5.08751 + 5.08751i) q^{43} +(2.32663 - 1.69040i) q^{44} +(0.564767 + 0.410327i) q^{46} +(-0.474965 - 2.99881i) q^{47} +(1.66004 + 0.494220i) q^{48} +6.57265i q^{49} +(-6.95800 + 7.31198i) q^{51} +(1.97121 + 3.86872i) q^{52} +(2.23241 - 0.353579i) q^{53} +(5.05756 - 1.19210i) q^{54} +(0.384246 + 0.528869i) q^{56} +(-12.6170 + 0.312969i) q^{57} +(-3.17710 - 0.503203i) q^{58} +(2.66341 + 8.19714i) q^{59} +(2.77903 - 8.55298i) q^{61} +(-2.70861 + 5.31594i) q^{62} +(1.78940 + 0.802614i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-2.15064 + 4.49296i) q^{66} +(2.22497 - 14.0479i) q^{67} +(4.12066 - 4.12066i) q^{68} +(-1.19856 - 0.159477i) q^{69} +(7.15246 - 9.84451i) q^{71} +(-2.93615 + 0.615636i) q^{72} +(-0.498794 + 0.254148i) q^{73} +2.17706 q^{74} +7.28665 q^{76} +(-1.67510 + 0.853507i) q^{77} +(-6.19197 - 4.26821i) q^{78} +(6.00067 - 8.25922i) q^{79} +(-6.72143 + 5.98518i) q^{81} +(-4.71623 + 4.71623i) q^{82} +(-0.742236 + 4.68629i) q^{83} +(-1.02130 - 0.488866i) q^{84} +(6.84269 + 2.22332i) q^{86} +(5.25448 - 1.85256i) q^{87} +(1.30562 - 2.56242i) q^{88} +(1.78693 - 5.49959i) q^{89} +(-0.877122 - 2.69950i) q^{91} +(0.689496 + 0.109205i) q^{92} +(-0.256256 - 10.3306i) q^{93} +(-1.78463 - 2.45633i) q^{94} +(1.70348 - 0.313291i) q^{96} +(-5.26300 + 0.833578i) q^{97} +(2.98392 + 5.85628i) q^{98} +(-0.427760 - 8.61700i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$-1$

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 $

$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$2$	0.891007	−	0.453990i	0.630037	−	0.321020i
$3$	−0.983013	+	1.42607i	−0.567543	+	0.823344i
$3$	−0.983013	+	1.42607i	−0.567543	+	0.823344i
$4$	0.587785	−	0.809017i	0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	−0.228447	+	1.71692i	−0.0932630	+	0.700929i
$7$	−0.462249	+	0.462249i	−0.174714	+	0.174714i	−0.789047	−	0.614333i	$-0.789425\pi$
$7$	−0.462249	+	0.462249i	−0.174714	+	0.174714i	0.614333	+	0.789047i	$0.289425\pi$
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$	−1.06737	−	2.80370i	−0.355791	−	0.934566i
$10$		0			0
$11$	2.73512	+	0.888693i	0.824669	+	0.267951i	0.690798	−	0.723048i	$-0.257259\pi$
$11$	2.73512	+	0.888693i	0.824669	+	0.267951i	0.133871	+	0.990999i	$0.457259\pi$
$12$	0.575917	+	1.63350i	0.166253	+	0.471551i
$13$	−1.97121	+	3.86872i	−0.546716	+	1.07299i	0.438025	+	0.898963i	$0.355678\pi$
$13$	−1.97121	+	3.86872i	−0.546716	+	1.07299i	−0.984741	+	0.174028i	$0.944322\pi$
$14$	−0.202010	+	0.621723i	−0.0539895	+	0.166163i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	5.75574	+	0.911620i	1.39597	+	0.221100i	0.808668	−	0.588266i	$-0.200189\pi$
$17$	5.75574	+	0.911620i	1.39597	+	0.221100i	0.587305	+	0.809366i	$0.300189\pi$
$18$	−2.22389	−	2.01354i	−0.524175	−	0.474595i
$19$	4.28299	+	5.89503i	0.982585	+	1.35241i	0.935425	+	0.353525i	$0.115017\pi$
$19$	4.28299	+	5.89503i	0.982585	+	1.35241i	0.0471595	+	0.998887i	$0.484983\pi$
$20$		0			0
$21$	−0.204804	−	1.11360i	−0.0446920	−	0.243007i
$22$	2.84047	−	0.449885i	0.605589	−	0.0959159i
$23$	0.316926	+	0.622003i	0.0660837	+	0.129697i	0.921685	−	0.387938i	$-0.126813\pi$
$23$	0.316926	+	0.622003i	0.0660837	+	0.129697i	−0.855602	+	0.517635i	$0.826813\pi$
$24$	1.25474	+	1.19400i	0.256123	+	0.243724i
$25$		0			0
$26$			4.34197i			0.851530i
$27$	5.04752	+	1.23392i	0.971395	+	0.237468i
$28$	0.102264	+	0.645670i	0.0193261	+	0.122020i
$29$	−2.60237	−	1.89073i	−0.483247	−	0.351100i	0.319334	−	0.947642i	$-0.396541\pi$
$29$	−2.60237	−	1.89073i	−0.483247	−	0.351100i	−0.802582	+	0.596542i	$0.796541\pi$
$30$		0			0
$31$	−4.82678	+	3.50686i	−0.866915	+	0.629850i	−0.929757	−	0.368173i	$-0.879983\pi$
$31$	−4.82678	+	3.50686i	−0.866915	+	0.629850i	0.0628427	+	0.998023i	$0.479983\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.95600	+	3.02688i	−0.688651	+	0.526912i
$34$	5.54227	−	1.80079i	0.950491	−	0.308833i
$35$		0			0
$36$	−2.89562	−	0.784450i	−0.482604	−	0.130742i
$37$	1.93977	+	0.988365i	0.318897	+	0.162486i	0.606110	−	0.795380i	$-0.292729\pi$
$37$	1.93977	+	0.988365i	0.318897	+	0.162486i	−0.287213	+	0.957867i	$0.592729\pi$
$38$	6.49246	+	3.30807i	1.05322	+	0.536640i
$39$	−3.57936	−	6.61410i	−0.573156	−	1.05910i
$40$		0			0
$41$	−6.34331	+	2.06107i	−0.990659	+	0.321884i	−0.759127	−	0.650943i	$-0.774374\pi$
$41$	−6.34331	+	2.06107i	−0.990659	+	0.321884i	−0.231532	+	0.972827i	$0.574374\pi$
$42$	−0.688045	−	0.899243i	−0.106168	−	0.138756i
$43$	5.08751	+	5.08751i	0.775838	+	0.775838i	0.979120	−	0.203282i	$-0.0651609\pi$
$43$	5.08751	+	5.08751i	0.775838	+	0.775838i	−0.203282	+	0.979120i	$0.565161\pi$
$44$	2.32663	−	1.69040i	0.350753	−	0.254837i
$45$		0			0
$46$	0.564767	+	0.410327i	0.0832703	+	0.0604994i
$47$	−0.474965	−	2.99881i	−0.0692808	−	0.437422i	−0.997809	−	0.0661599i	$-0.978925\pi$
$47$	−0.474965	−	2.99881i	−0.0692808	−	0.437422i	0.928528	−	0.371262i	$-0.121075\pi$
$48$	1.66004	+	0.494220i	0.239607	+	0.0713345i
$49$			6.57265i			0.938950i
$50$		0			0
$51$	−6.95800	+	7.31198i	−0.974315	+	1.02388i
$52$	1.97121	+	3.86872i	0.273358	+	0.536495i
$53$	2.23241	−	0.353579i	0.306645	−	0.0485679i	−0.00121543	−	0.999999i	$-0.500387\pi$
$53$	2.23241	−	0.353579i	0.306645	−	0.0485679i	0.307861	+	0.951431i	$0.400387\pi$
$54$	5.05756	−	1.19210i	0.688247	−	0.162224i
$55$		0			0
$56$	0.384246	+	0.528869i	0.0513470	+	0.0706731i
$57$	−12.6170	+	0.312969i	−1.67116	+	0.0414538i
$58$	−3.17710	−	0.503203i	−0.417174	−	0.0660738i
$59$	2.66341	+	8.19714i	0.346747	+	1.06718i	0.960642	+	0.277790i	$0.0896018\pi$
$59$	2.66341	+	8.19714i	0.346747	+	1.06718i	−0.613895	+	0.789388i	$0.710398\pi$
$60$		0			0
$61$	2.77903	−	8.55298i	0.355818	−	1.09510i	−0.599715	−	0.800214i	$-0.704719\pi$
$61$	2.77903	−	8.55298i	0.355818	−	1.09510i	0.955533	−	0.294883i	$-0.0952806\pi$
$62$	−2.70861	+	5.31594i	−0.343994	+	0.675126i
$63$	1.78940	+	0.802614i	0.225443	+	0.101120i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$		0			0
$66$	−2.15064	+	4.49296i	−0.264726	+	0.553045i
$67$	2.22497	−	14.0479i	0.271823	−	1.71622i	−0.353141	−	0.935570i	$-0.614886\pi$
$67$	2.22497	−	14.0479i	0.271823	−	1.71622i	0.624964	−	0.780654i	$-0.285114\pi$
$68$	4.12066	−	4.12066i	0.499703	−	0.499703i
$69$	−1.19856	−	0.159477i	−0.144290	−	0.0191987i
$70$		0			0
$71$	7.15246	−	9.84451i	0.848840	−	1.16833i	−0.135277	−	0.990808i	$-0.543192\pi$
$71$	7.15246	−	9.84451i	0.848840	−	1.16833i	0.984117	−	0.177521i	$-0.0568077\pi$
$72$	−2.93615	+	0.615636i	−0.346029	+	0.0725534i
$73$	−0.498794	+	0.254148i	−0.0583794	+	0.0297458i	−0.482937	−	0.875655i	$-0.660430\pi$
$73$	−0.498794	+	0.254148i	−0.0583794	+	0.0297458i	0.424557	+	0.905401i	$0.360430\pi$
$74$	2.17706			0.253078
$75$		0			0
$76$	7.28665			0.835837
$77$	−1.67510	+	0.853507i	−0.190896	+	0.0972661i
$78$	−6.19197	−	4.26821i	−0.701102	−	0.483280i
$79$	6.00067	−	8.25922i	0.675128	−	0.929234i	−0.324734	−	0.945805i	$-0.605275\pi$
$79$	6.00067	−	8.25922i	0.675128	−	0.929234i	0.999863	+	0.0165708i	$0.00527490\pi$
$80$		0			0
$81$	−6.72143	+	5.98518i	−0.746826	+	0.665019i
$82$	−4.71623	+	4.71623i	−0.520820	+	0.520820i
$83$	−0.742236	+	4.68629i	−0.0814709	+	0.514387i	0.912879	+	0.408231i	$0.133854\pi$
$83$	−0.742236	+	4.68629i	−0.0814709	+	0.514387i	−0.994349	+	0.106156i	$0.966146\pi$
$84$	−1.02130	−	0.488866i	−0.111433	−	0.0533396i
$85$		0			0
$86$	6.84269	+	2.22332i	0.737866	+	0.239747i
$87$	5.25448	−	1.85256i	0.563340	−	0.198615i
$88$	1.30562	−	2.56242i	0.139179	−	0.273155i
$89$	1.78693	−	5.49959i	0.189414	−	0.582956i	−0.810583	−	0.585624i	$-0.800849\pi$
$89$	1.78693	−	5.49959i	0.189414	−	0.582956i	0.999996	+	0.00266864i	$0.000849456\pi$
$90$		0			0
$91$	−0.877122	−	2.69950i	−0.0919473	−	0.282985i
$92$	0.689496	+	0.109205i	0.0718849	+	0.0113854i
$93$	−0.256256	−	10.3306i	−0.0265725	−	1.07124i
$94$	−1.78463	−	2.45633i	−0.184070	−	0.253351i
$95$		0			0
$96$	1.70348	−	0.313291i	0.173861	−	0.0319752i
$97$	−5.26300	+	0.833578i	−0.534377	+	0.0846370i	−0.417790	−	0.908544i	$-0.637195\pi$
$97$	−5.26300	+	0.833578i	−0.534377	+	0.0846370i	−0.116587	+	0.993181i	$0.537195\pi$
$98$	2.98392	+	5.85628i	0.301422	+	0.591573i
$99$	−0.427760	−	8.61700i	−0.0429915	−	0.866042i
$100$		0			0
$101$		−	12.5590i		−	1.24967i	−0.780758	−	0.624833i	$-0.785167\pi$
$101$		−	12.5590i		−	1.24967i	0.780758	−	0.624833i	$-0.214833\pi$
$102$	−2.88006	+	9.67389i	−0.285168	+	0.957858i
$103$	0.958193	+	6.04979i	0.0944135	+	0.596104i	0.988851	+	0.148910i	$0.0475765\pi$
$103$	0.958193	+	6.04979i	0.0944135	+	0.596104i	−0.894437	+	0.447194i	$0.852424\pi$
$104$	3.51273	+	2.55215i	0.344451	+	0.250258i
$105$		0			0
$106$	1.82857	−	1.32854i	0.177607	−	0.129039i
$107$	0.411529	+	0.411529i	0.0397840	+	0.0397840i	0.726719	−	0.686935i	$-0.241044\pi$
$107$	0.411529	+	0.411529i	0.0397840	+	0.0397840i	−0.686935	+	0.726719i	$0.741044\pi$
$108$	3.96512	−	3.35825i	0.381544	−	0.323148i
$109$	−11.0499	+	3.59033i	−1.05839	+	0.343891i	−0.785955	−	0.618284i	$-0.787828\pi$
$109$	−11.0499	+	3.59033i	−1.05839	+	0.343891i	−0.272433	+	0.962175i	$0.587828\pi$
$110$		0			0
$111$	−3.31630	+	1.79469i	−0.314770	+	0.170344i
$112$	0.582467	+	0.296782i	0.0550380	+	0.0280433i
$113$	−12.6233	−	6.43189i	−1.18750	−	0.605061i	−0.255249	−	0.966875i	$-0.582158\pi$
$113$	−12.6233	−	6.43189i	−1.18750	−	0.605061i	−0.932250	+	0.361814i	$0.882158\pi$
$114$	−11.0997	+	6.00684i	−1.03958	+	0.562592i
$115$		0			0
$116$	−3.05927	+	0.994016i	−0.284046	+	0.0922921i
$117$	12.9507	+	1.39732i	1.19730	+	0.129182i
$118$	6.09455	+	6.09455i	0.561048	+	0.561048i
$119$	−3.08198	+	2.23919i	−0.282525	+	0.205266i
$120$		0			0
$121$	−2.20810	−	1.60428i	−0.200736	−	0.145844i
$122$	−1.40684	−	8.88241i	−0.127369	−	0.804176i
$123$	3.29632	−	11.0721i	0.297219	−	0.998336i
$124$			5.96622i			0.535783i
$125$		0			0
$126$	1.95874	−	0.0972348i	0.174499	−	0.00866236i
$127$	−6.58036	−	12.9147i	−0.583912	−	1.14599i	−0.974282	−	0.225334i	$-0.927653\pi$
$127$	−6.58036	−	12.9147i	−0.583912	−	1.14599i	0.390369	−	0.920658i	$-0.372347\pi$
$128$	−0.987688	+	0.156434i	−0.0873001	+	0.0138270i
$129$	−12.2563	+	2.25408i	−1.07910	+	0.198460i
$130$		0			0
$131$	−3.23088	−	4.44693i	−0.282283	−	0.388530i	0.644205	−	0.764853i	$-0.277188\pi$
$131$	−3.23088	−	4.44693i	−0.282283	−	0.388530i	−0.926489	+	0.376323i	$0.877188\pi$
$132$	0.123522	+	4.97962i	0.0107512	+	0.433421i
$133$	−4.70477	−	0.745163i	−0.407956	−	0.0646138i
$134$	−4.39515	−	13.5269i	−0.379683	−	1.16854i
$135$		0			0
$136$	1.80079	−	5.54227i	0.154417	−	0.475246i
$137$	−9.55034	+	18.7436i	−0.815941	+	1.60137i	−0.0170834	+	0.999854i	$0.505438\pi$
$137$	−9.55034	+	18.7436i	−0.815941	+	1.60137i	−0.798858	+	0.601520i	$0.794562\pi$
$138$	−1.14033	+	0.402042i	−0.0970713	+	0.0342241i
$139$	11.0917	+	3.60392i	0.940788	+	0.305681i	0.738967	−	0.673742i	$-0.235314\pi$
$139$	11.0917	+	3.60392i	0.940788	+	0.305681i	0.201821	+	0.979422i	$0.435314\pi$
$140$		0			0
$141$	4.74342	+	2.27053i	0.399468	+	0.191214i
$142$	1.90357	−	12.0187i	0.159744	−	1.00858i
$143$	−8.82961	+	8.82961i	−0.738369	+	0.738369i
$144$	−2.33664	+	1.88152i	−0.194720	+	0.156793i
$145$		0			0
$146$	−0.329048	+	0.452896i	−0.0272322	+	0.0374819i
$147$	−9.37309	−	6.46100i	−0.773079	−	0.532894i
$148$	1.93977	−	0.988365i	0.159449	−	0.0812431i
$149$	−10.0289			−0.821602			−0.410801	−	0.911725i	$-0.634751\pi$
$149$	−10.0289			−0.821602			−0.410801	+	0.911725i	$0.634751\pi$
$150$		0			0
$151$	17.9175			1.45811			0.729054	−	0.684456i	$-0.239960\pi$
$151$	17.9175			1.45811			0.729054	+	0.684456i	$0.239960\pi$
$152$	6.49246	−	3.30807i	0.526608	−	0.268320i
$153$	−3.58761	−	17.1104i	−0.290041	−	1.38329i
$154$	−1.10504	+	1.52096i	−0.0890469	+	0.122562i
$155$		0			0
$156$	−7.45481	−	0.991909i	−0.596863	−	0.0794163i
$157$	6.42991	−	6.42991i	0.513163	−	0.513163i	−0.402331	−	0.915494i	$-0.631800\pi$
$157$	6.42991	−	6.42991i	0.513163	−	0.513163i	0.915494	+	0.402331i	$0.131800\pi$
$158$	1.59703	−	10.0833i	0.127053	−	0.802181i
$159$	−1.69026	+	3.53116i	−0.134046	+	0.280039i
$160$		0			0
$161$	−0.434019	−	0.141021i	−0.0342055	−	0.0111140i
$162$	−3.27163	+	8.38430i	−0.257043	+	0.658733i
$163$	4.21139	−	8.26532i	0.329862	−	0.647390i	−0.665198	−	0.746667i	$-0.731653\pi$
$163$	4.21139	−	8.26532i	0.329862	−	0.647390i	0.995060	+	0.0992767i	$0.0316529\pi$
$164$	−2.06107	+	6.34331i	−0.160942	+	0.495329i
$165$		0			0
$166$	1.46619	+	4.51248i	0.113799	+	0.350237i
$167$	5.01819	+	0.794803i	0.388319	+	0.0615037i	0.347542	−	0.937665i	$-0.387017\pi$
$167$	5.01819	+	0.794803i	0.388319	+	0.0615037i	0.0407774	+	0.999168i	$0.487017\pi$
$168$	−1.13193	+	0.0280779i	−0.0873299	+	0.00216626i
$169$	−3.44013	−	4.73493i	−0.264625	−	0.364226i
$170$		0			0
$171$	11.9563	−	18.3004i	0.914323	−	1.39947i
$172$	7.10625	−	1.12552i	0.541846	−	0.0858200i
$173$	−8.65954	−	16.9953i	−0.658373	−	1.29213i	−0.942777	−	0.333425i	$-0.891796\pi$
$173$	−8.65954	−	16.9953i	−0.658373	−	1.29213i	0.284404	−	0.958705i	$-0.408204\pi$
$174$	3.84073	−	4.03612i	0.291165	−	0.305978i
$175$		0			0
$176$		−	2.87587i		−	0.216777i
$177$	−14.3079	−	4.25967i	−1.07545	−	0.320177i
$178$	−0.904600	−	5.71142i	−0.0678026	−	0.428089i
$179$	3.24712	+	2.35917i	0.242701	+	0.176332i	0.702486	−	0.711698i	$-0.252073\pi$
$179$	3.24712	+	2.35917i	0.242701	+	0.176332i	−0.459785	+	0.888030i	$0.652073\pi$
$180$		0			0
$181$	3.30770	−	2.40319i	0.245860	−	0.178628i	−0.458030	−	0.888937i	$-0.651445\pi$
$181$	3.30770	−	2.40319i	0.245860	−	0.178628i	0.703890	+	0.710309i	$0.251445\pi$
$182$	−2.00707	−	2.00707i	−0.148774	−	0.148774i
$183$	9.46535	+	12.3708i	0.699699	+	0.914475i
$184$	0.663923	−	0.215722i	0.0489451	−	0.0159032i
$185$		0			0
$186$	−4.91833	−	9.08832i	−0.360629	−	0.666388i
$187$	14.9325	+	7.60848i	1.09197	+	0.556387i
$188$	−2.70527	−	1.37840i	−0.197302	−	0.100530i
$189$	−2.90359	+	1.76283i	−0.211205	+	0.128227i
$190$		0			0
$191$	−11.5725	+	3.76012i	−0.837354	+	0.272073i	−0.696140	−	0.717906i	$-0.745101\pi$
$191$	−11.5725	+	3.76012i	−0.837354	+	0.272073i	−0.141214	+	0.989979i	$0.545101\pi$
$192$	1.37558	−	1.05251i	0.0992741	−	0.0759583i
$193$	9.01719	+	9.01719i	0.649071	+	0.649071i	0.952769	−	0.303697i	$-0.0982211\pi$
$193$	9.01719	+	9.01719i	0.649071	+	0.649071i	−0.303697	+	0.952769i	$0.598221\pi$
$194$	−4.31093	+	3.13208i	−0.309507	+	0.224870i
$195$		0			0
$196$	5.31739	+	3.86331i	0.379813	+	0.275951i
$197$	−0.0641446	−	0.404993i	−0.00457012	−	0.0288546i	0.985298	−	0.170845i	$-0.0546498\pi$
$197$	−0.0641446	−	0.404993i	−0.00457012	−	0.0288546i	−0.989868	+	0.141990i	$0.954650\pi$
$198$	−4.29318	−	7.48361i	−0.305103	−	0.531837i
$199$		−	10.9949i		−	0.779406i	−0.920941	−	0.389703i	$-0.872578\pi$
$199$		−	10.9949i		−	0.779406i	0.920941	−	0.389703i	$-0.127422\pi$
$200$		0			0
$201$	17.8462	+	16.9822i	1.25877	+	1.19783i
$202$	−5.70166	−	11.1901i	−0.401168	−	0.787336i
$203$	2.07693	−	0.328953i	0.145772	−	0.0230880i
$204$	1.82570	+	9.92702i	0.127825	+	0.695030i
$205$		0			0
$206$	3.60030	+	4.95539i	0.250845	+	0.345259i
$207$	1.40563	−	1.55247i	0.0976980	−	0.107904i
$208$	4.28851	+	0.679234i	0.297355	+	0.0470964i
$209$	6.47560	+	19.9298i	0.447927	+	1.37858i
$210$		0			0
$211$	6.64735	−	20.4585i	0.457623	−	1.40842i	−0.410406	−	0.911903i	$-0.634613\pi$
$211$	6.64735	−	20.4585i	0.457623	−	1.40842i	0.868028	−	0.496515i	$-0.165387\pi$
$212$	1.02613	−	2.01389i	0.0704747	−	0.138314i
$213$	7.00804	+	19.8772i	0.480183	+	1.36196i
$214$	0.553505	+	0.179845i	0.0378368	+	0.0122939i
$215$		0			0
$216$	2.00833	−	4.79235i	0.136650	−	0.326078i
$217$	0.610130	−	3.85221i	0.0414184	−	0.261505i
$218$	−8.21555	+	8.21555i	−0.556427	+	0.556427i
$219$	0.127887	−	0.961148i	0.00864179	−	0.0649484i
$220$		0			0
$221$	−14.8726	+	20.4704i	−1.00044	+	1.37699i
$222$	−2.14008	+	3.10465i	−0.143633	+	0.208370i
$223$	−5.65554	+	2.88164i	−0.378723	+	0.192969i	−0.632981	−	0.774167i	$-0.718169\pi$
$223$	−5.65554	+	2.88164i	−0.378723	+	0.192969i	0.254258	+	0.967137i	$0.418169\pi$
$224$	0.653718			0.0436784
$225$		0			0
$226$	−14.1675			−0.942405
$227$	−12.5844	+	6.41208i	−0.835257	+	0.425584i	−0.818660	−	0.574278i	$-0.805283\pi$
$227$	−12.5844	+	6.41208i	−0.835257	+	0.425584i	−0.0165960	+	0.999862i	$0.505283\pi$
$228$	−7.16287	+	10.3913i	−0.474373	+	0.688181i
$229$	−8.94288	+	12.3088i	−0.590962	+	0.813389i	−0.994844	−	0.101422i	$-0.967661\pi$
$229$	−8.94288	+	12.3088i	−0.590962	+	0.813389i	0.403882	+	0.914811i	$0.367661\pi$
$230$		0			0
$231$	0.429482	−	3.22783i	0.0282579	−	0.212375i
$232$	−2.27455	+	2.27455i	−0.149332	+	0.149332i
$233$	1.18798	−	7.50060i	0.0778271	−	0.491381i	−0.917729	−	0.397208i	$-0.869979\pi$
$233$	1.18798	−	7.50060i	0.0778271	−	0.491381i	0.995556	−	0.0941731i	$-0.0300207\pi$
$234$	12.1736	−	4.63450i	0.795811	−	0.302967i
$235$		0			0
$236$	8.19714	+	2.66341i	0.533589	+	0.173373i
$237$	5.87951	+	16.6763i	0.381915	+	1.08324i
$238$	−1.72949	+	3.39432i	−0.112106	+	0.220021i
$239$	−3.85885	+	11.8763i	−0.249608	+	0.768215i	0.745236	+	0.666801i	$0.232337\pi$
$239$	−3.85885	+	11.8763i	−0.249608	+	0.768215i	−0.994844	+	0.101414i	$0.967663\pi$
$240$		0			0
$241$	7.01360	+	21.5856i	0.451786	+	1.39045i	0.874868	+	0.484362i	$0.160948\pi$
$241$	7.01360	+	21.5856i	0.451786	+	1.39045i	−0.423082	+	0.906092i	$0.639052\pi$
$242$	−2.69576	−	0.426966i	−0.173290	−	0.0274464i
$243$	−1.92805	−	15.4688i	−0.123684	−	0.992322i
$244$	−5.28603	−	7.27560i	−0.338403	−	0.465772i
$245$		0			0
$246$	−2.08958	−	11.3618i	−0.133226	−	0.724402i
$247$	−31.2489	+	4.94934i	−1.98832	+	0.314919i
$248$	2.70861	+	5.31594i	0.171997	+	0.337563i
$249$	−5.95337	−	5.66517i	−0.377279	−	0.359015i
$250$		0			0
$251$			8.40399i			0.530455i	0.964186	+	0.265228i	$0.0854471\pi$
$251$			8.40399i			0.530455i	−0.964186	+	0.265228i	$0.914553\pi$
$252$	1.70111	−	0.975888i	0.107160	−	0.0614751i
$253$	0.314061	+	1.98290i	0.0197448	+	0.124664i
$254$	−11.7263	−	8.51964i	−0.735773	−	0.534570i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−21.2293	−	21.2293i	−1.32425	−	1.32425i	−0.910303	−	0.413942i	$-0.864152\pi$
$257$	−21.2293	−	21.2293i	−1.32425	−	1.32425i	−0.413942	−	0.910303i	$-0.635848\pi$
$258$	−9.89707	+	7.57262i	−0.616165	+	0.471451i
$259$	−1.35353	+	0.439788i	−0.0841042	+	0.0273271i
$260$		0			0
$261$	−2.52334	+	9.31436i	−0.156191	+	0.576545i
$262$	−4.89760	−	2.49545i	−0.302575	−	0.154169i
$263$	−3.75527	−	1.91341i	−0.231560	−	0.117986i	0.334361	−	0.942445i	$-0.391479\pi$
$263$	−3.75527	−	1.91341i	−0.231560	−	0.117986i	−0.565921	+	0.824459i	$0.691479\pi$
$264$	2.37076	+	4.38080i	0.145910	+	0.269620i
$265$		0			0
$266$	−4.53028	+	1.47198i	−0.277769	+	0.0902527i
$267$	6.08625	+	7.95446i	0.372473	+	0.486805i
$268$	−10.0572	−	10.0572i	−0.614340	−	0.614340i
$269$	16.4085	−	11.9215i	1.00044	−	0.726865i	0.0382610	−	0.999268i	$-0.487818\pi$
$269$	16.4085	−	11.9215i	1.00044	−	0.726865i	0.962183	+	0.272402i	$0.0878182\pi$
$270$		0			0
$271$	−5.48031	−	3.98168i	−0.332905	−	0.241870i	0.408757	−	0.912643i	$-0.365962\pi$
$271$	−5.48031	−	3.98168i	−0.332905	−	0.241870i	−0.741662	+	0.670773i	$0.765962\pi$
$272$	−0.911620	−	5.75574i	−0.0552751	−	0.348993i
$273$	4.71191	+	1.40281i	0.285178	+	0.0849017i
$274$			21.0364i			1.27086i
$275$		0			0
$276$	−0.833518	+	0.875921i	−0.0501719	+	0.0527243i
$277$	11.1150	+	21.8145i	0.667837	+	1.31070i	0.937579	+	0.347772i	$0.113062\pi$
$277$	11.1150	+	21.8145i	0.667837	+	1.31070i	−0.269742	+	0.962933i	$0.586938\pi$
$278$	11.5189	−	1.82442i	0.690861	−	0.109422i
$279$	14.9841	+	9.78970i	0.897077	+	0.586094i
$280$		0			0
$281$	−11.8968	−	16.3745i	−0.709702	−	0.976820i	−0.999803	−	0.0198246i	$-0.993689\pi$
$281$	−11.8968	−	16.3745i	−0.709702	−	0.976820i	0.290102	−	0.956996i	$-0.406311\pi$
$282$	5.25722	−	0.130408i	0.313063	−	0.00776566i
$283$	8.20158	+	1.29900i	0.487533	+	0.0772177i	0.395362	−	0.918525i	$-0.370619\pi$
$283$	8.20158	+	1.29900i	0.487533	+	0.0772177i	0.0921715	+	0.995743i	$0.470619\pi$
$284$	−3.76027	−	11.5729i	−0.223131	−	0.686726i
$285$		0			0
$286$	−3.85868	+	11.8758i	−0.228168	+	0.702230i
$287$	1.97946	−	3.88491i	0.116844	−	0.229319i
$288$	−1.22777	+	2.73726i	−0.0723469	+	0.161295i
$289$	16.1295	+	5.24081i	0.948797	+	0.308283i
$290$		0			0
$291$	3.98486	−	8.32485i	0.233596	−	0.488011i
$292$	−0.0875735	+	0.552918i	−0.00512485	+	0.0323571i
$293$	1.20804	−	1.20804i	0.0705747	−	0.0705747i	−0.670938	−	0.741513i	$-0.734109\pi$
$293$	1.20804	−	1.20804i	0.0705747	−	0.0705747i	0.741513	+	0.670938i	$0.234109\pi$
$294$	−11.2847	−	1.50150i	−0.658138	−	0.0875694i
$295$		0			0
$296$	1.27964	−	1.76128i	0.0743778	−	0.102372i
$297$	12.7090	+	7.86061i	0.737450	+	0.456119i
$298$	−8.93584	+	4.55304i	−0.517639	+	0.263750i
$299$	−3.03109			−0.175292
$300$		0			0
$301$	−4.70339			−0.271099
$302$	15.9646	−	8.13439i	0.918661	−	0.468081i
$303$	17.9100	+	12.3456i	1.02891	+	0.709239i
$304$	4.28299	−	5.89503i	0.245646	−	0.338103i
$305$		0			0
$306$	−10.9645	−	13.6167i	−0.626801	−	0.778417i
$307$	−4.52656	+	4.52656i	−0.258344	+	0.258344i	−0.824380	−	0.566036i	$-0.808476\pi$
$307$	−4.52656	+	4.52656i	−0.258344	+	0.258344i	0.566036	+	0.824380i	$0.308476\pi$
$308$	−0.294098	+	1.85686i	−0.0167578	+	0.105805i
$309$	−9.56936	−	4.58057i	−0.544382	−	0.260579i
$310$		0			0
$311$	32.9364	+	10.7017i	1.86765	+	0.606838i	0.992381	+	0.123210i	$0.0393188\pi$
$311$	32.9364	+	10.7017i	1.86765	+	0.606838i	0.875274	+	0.483628i	$0.160681\pi$
$312$	−7.09260	+	2.50062i	−0.401540	+	0.141569i
$313$	11.8701	−	23.2965i	0.670940	−	1.31679i	−0.264869	−	0.964285i	$-0.585329\pi$
$313$	11.8701	−	23.2965i	0.670940	−	1.31679i	0.935808	−	0.352509i	$-0.114671\pi$
$314$	2.80998	−	8.64821i	0.158576	−	0.488047i
$315$		0			0
$316$	−3.15474	−	9.70929i	−0.177468	−	0.546190i
$317$	13.4990	+	2.13804i	0.758181	+	0.120084i	0.523544	−	0.851999i	$-0.324610\pi$
$317$	13.4990	+	2.13804i	0.758181	+	0.120084i	0.234638	+	0.972083i	$0.424610\pi$
$318$	0.0970796	+	3.91365i	0.00544396	+	0.219466i
$319$	−5.43750	−	7.48407i	−0.304441	−	0.419028i
$320$		0			0
$321$	−0.991408	+	0.182332i	−0.0553350	+	0.0101768i
$322$	−0.450736	+	0.0713896i	−0.0251185	+	0.00397838i
$323$	19.2777	+	37.8347i	1.07264	+	2.10518i
$324$	0.891349	+	8.95575i	0.0495194	+	0.497542i
$325$		0			0
$326$		−	9.27639i		−	0.513772i
$327$	5.74211	−	19.2873i	0.317540	−	1.06659i
$328$	1.04338	+	6.58764i	0.0576110	+	0.363741i
$329$	1.60575	+	1.16664i	0.0885278	+	0.0643192i
$330$		0			0
$331$	−8.55071	+	6.21245i	−0.469989	+	0.341467i	−0.797437	−	0.603402i	$-0.793811\pi$
$331$	−8.55071	+	6.21245i	−0.469989	+	0.341467i	0.327448	+	0.944869i	$0.393811\pi$
$332$	3.35501	+	3.35501i	0.184130	+	0.184130i
$333$	0.700614	−	6.49349i	0.0383934	−	0.355841i
$334$	4.83207	−	1.57004i	0.264399	−	0.0859085i
$335$		0			0
$336$	−0.995806	+	0.538901i	−0.0543257	+	0.0293995i
$337$	28.0951	+	14.3152i	1.53044	+	0.779796i	0.997784	−	0.0665380i	$-0.0211954\pi$
$337$	28.0951	+	14.3152i	1.53044	+	0.779796i	0.532652	+	0.846334i	$0.321195\pi$
$338$	−5.21479	−	2.65707i	−0.283647	−	0.144526i
$339$	21.5812	−	11.6791i	1.17213	−	0.634323i
$340$		0			0
$341$	−16.3183	+	5.30214i	−0.883686	+	0.287127i
$342$	2.34496	−	21.7338i	0.126801	−	1.17523i
$343$	−6.27394	−	6.27394i	−0.338761	−	0.338761i
$344$	5.82074	−	4.22901i	0.313833	−	0.228013i
$345$		0			0
$346$	−15.4314	−	11.2116i	−0.829598	−	0.602738i
$347$	2.04407	+	12.9057i	0.109731	+	0.692816i	0.979814	+	0.199911i	$0.0640652\pi$
$347$	2.04407	+	12.9057i	0.109731	+	0.692816i	−0.870083	+	0.492905i	$0.835935\pi$
$348$	1.58976	−	5.33987i	0.0852200	−	0.286247i
$349$		−	30.4326i		−	1.62902i	−0.580151	−	0.814509i	$-0.697007\pi$
$349$		−	30.4326i		−	1.62902i	0.580151	−	0.814509i	$-0.302993\pi$
$350$		0			0
$351$	−14.7234	+	17.0951i	−0.785878	+	0.912471i
$352$	−1.30562	−	2.56242i	−0.0695897	−	0.136577i
$353$	2.87776	−	0.455793i	0.153168	−	0.0242594i	−0.0793796	−	0.996844i	$-0.525294\pi$
$353$	2.87776	−	0.455793i	0.153168	−	0.0242594i	0.232547	+	0.972585i	$0.425294\pi$
$354$	−14.6823	+	2.70025i	−0.780355	+	0.143517i
$355$		0			0
$356$	−3.39893	−	4.67823i	−0.180143	−	0.247946i
$357$	−0.163624	−	6.59628i	−0.00865988	−	0.349112i
$358$	3.96424	+	0.627874i	0.209517	+	0.0331842i
$359$	−2.44510	−	7.52523i	−0.129047	−	0.397167i	0.865569	−	0.500789i	$-0.166957\pi$
$359$	−2.44510	−	7.52523i	−0.129047	−	0.397167i	−0.994617	+	0.103622i	$0.966957\pi$
$360$		0			0
$361$	−10.5360	+	32.4266i	−0.554528	+	1.70666i
$362$	1.85616	−	3.64292i	0.0975577	−	0.191468i
$363$	4.45841	−	1.57189i	0.234006	−	0.0825027i
$364$	−2.69950	−	0.877122i	−0.141492	−	0.0459737i
$365$		0			0
$366$	14.0499	+	6.72527i	0.734401	+	0.351536i
$367$	−3.44380	+	21.7433i	−0.179765	+	1.13499i	0.718497	+	0.695530i	$0.244830\pi$
$367$	−3.44380	+	21.7433i	−0.179765	+	1.13499i	−0.898262	+	0.439460i	$0.855170\pi$
$368$	0.493624	−	0.493624i	0.0257319	−	0.0257319i
$369$	12.5493	+	15.5848i	0.653289	+	0.811312i
$370$		0			0
$371$	−0.868488	+	1.19537i	−0.0450897	+	0.0620606i
$372$	−8.50827	−	5.86487i	−0.441133	−	0.304080i
$373$	−19.0344	+	9.69853i	−0.985566	+	0.502171i	−0.871020	−	0.491247i	$-0.836541\pi$
$373$	−19.0344	+	9.69853i	−0.985566	+	0.502171i	−0.114545	+	0.993418i	$0.536541\pi$
$374$	16.7591			0.866593
$375$		0			0
$376$	−3.03619			−0.156580
$377$	12.4445	−	6.34081i	0.640926	−	0.326568i
$378$	−1.78681	+	2.88890i	−0.0919034	+	0.148589i
$379$	−0.581554	+	0.800441i	−0.0298724	+	0.0411159i	−0.823692	−	0.567038i	$-0.808089\pi$
$379$	−0.581554	+	0.800441i	−0.0298724	+	0.0411159i	0.793820	+	0.608153i	$0.208089\pi$
$380$		0			0
$381$	24.8859	+	3.31122i	1.27494	+	0.169639i
$382$	−8.60408	+	8.60408i	−0.440223	+	0.440223i
$383$	1.97847	−	12.4916i	0.101095	−	0.638289i	−0.884158	−	0.467187i	$-0.845267\pi$
$383$	1.97847	−	12.4916i	0.101095	−	0.638289i	0.985253	−	0.171102i	$-0.0547326\pi$
$384$	0.747823	−	1.56229i	0.0381622	−	0.0797254i
$385$		0			0
$386$	12.1281	+	3.94066i	0.617304	+	0.200574i
$387$	8.83357	−	19.6941i	0.449036	−	1.00111i
$388$	−2.41914	+	4.74782i	−0.122813	+	0.241034i
$389$	8.45598	−	26.0248i	0.428735	−	1.31951i	−0.470636	−	0.882327i	$-0.655976\pi$
$389$	8.45598	−	26.0248i	0.428735	−	1.31951i	0.899372	−	0.437185i	$-0.144024\pi$
$390$		0			0
$391$	1.25712	+	3.86900i	0.0635751	+	0.195664i
$392$	6.49173	+	1.02819i	0.327882	+	0.0519314i
$393$	9.51764	−	0.236089i	0.480102	−	0.0119091i
$394$	−0.241016	−	0.331731i	−0.0121422	−	0.0167123i
$395$		0			0
$396$	−7.22273	−	4.71888i	−0.362956	−	0.237133i
$397$	−3.51235	+	0.556301i	−0.176280	+	0.0279199i	−0.243950	−	0.969788i	$-0.578443\pi$
$397$	−3.51235	+	0.556301i	−0.176280	+	0.0279199i	0.0676706	+	0.997708i	$0.478443\pi$
$398$	−4.99157	−	9.79650i	−0.250205	−	0.491054i
$399$	5.68751	−	5.97685i	0.284732	−	0.299217i
$400$		0			0
$401$		−	16.6499i		−	0.831458i	−0.909489	−	0.415729i	$-0.863527\pi$
$401$		−	16.6499i		−	0.831458i	0.909489	−	0.415729i	$-0.136473\pi$
$402$	23.6108	+	7.02929i	1.17760	+	0.350589i
$403$	−4.05246	−	25.5862i	−0.201867	−	1.27454i
$404$	−10.1604	−	7.38199i	−0.505501	−	0.367268i
$405$		0			0
$406$	1.70122	−	1.23601i	0.0844299	−	0.0613419i
$407$	4.42716	+	4.42716i	0.219446	+	0.219446i
$408$	6.13348	+	8.01618i	0.303653	+	0.396860i
$409$	−4.09420	+	1.33029i	−0.202445	+	0.0657784i	−0.408484	−	0.912765i	$-0.633943\pi$
$409$	−4.09420	+	1.33029i	−0.202445	+	0.0657784i	0.206039	+	0.978544i	$0.433943\pi$
$410$		0			0
$411$	−17.3417	−	32.0447i	−0.855401	−	1.58065i
$412$	5.45760	+	2.78078i	0.268876	+	0.136999i
$413$	−5.02028	−	2.55796i	−0.247032	−	0.125869i
$414$	0.547617	−	2.02141i	0.0269139	−	0.0993467i
$415$		0			0
$416$	4.12946	−	1.34174i	0.202463	−	0.0657843i
$417$	−16.0428	+	12.2749i	−0.785618	+	0.601105i
$418$	14.8178	+	14.8178i	0.724761	+	0.724761i
$419$	5.84455	−	4.24631i	0.285525	−	0.207446i	−0.435799	−	0.900044i	$-0.643534\pi$
$419$	5.84455	−	4.24631i	0.285525	−	0.207446i	0.721324	+	0.692598i	$0.243534\pi$
$420$		0			0
$421$	−11.7630	−	8.54631i	−0.573293	−	0.416521i	0.263007	−	0.964794i	$-0.415286\pi$
$421$	−11.7630	−	8.54631i	−0.573293	−	0.416521i	−0.836300	+	0.548272i	$0.815286\pi$
$422$	−3.36511	−	21.2464i	−0.163811	−	1.03426i
$423$	−7.90079	+	4.53251i	−0.384150	+	0.220378i
$424$		−	2.26024i		−	0.109767i
$425$		0			0
$426$	15.2683	+	14.5291i	0.739750	+	0.703939i
$427$	2.66900	+	5.23821i	0.129162	+	0.253495i
$428$	0.574824	−	0.0910432i	0.0277852	−	0.00440074i
$429$	−3.91205	−	21.2713i	−0.188876	−	1.02699i
$430$		0			0
$431$	2.43967	+	3.35792i	0.117515	+	0.161745i	0.863722	−	0.503968i	$-0.168127\pi$
$431$	2.43967	+	3.35792i	0.117515	+	0.161745i	−0.746207	+	0.665714i	$0.768127\pi$
$432$	−0.386242	−	5.18178i	−0.0185831	−	0.249308i
$433$	−28.8682	−	4.57227i	−1.38732	−	0.219729i	−0.582296	−	0.812977i	$-0.697846\pi$
$433$	−28.8682	−	4.57227i	−1.38732	−	0.219729i	−0.805020	+	0.593248i	$0.797846\pi$
$434$	−1.20524	−	3.70934i	−0.0578532	−	0.178054i
$435$		0			0
$436$	−3.59033	+	11.0499i	−0.171945	+	0.529194i
$437$	−2.30933	+	4.53232i	−0.110470	+	0.216810i
$438$	−0.322404	−	0.914449i	−0.0154051	−	0.0436941i
$439$	10.7432	+	3.49067i	0.512744	+	0.166601i	0.553950	−	0.832550i	$-0.313120\pi$
$439$	10.7432	+	3.49067i	0.512744	+	0.166601i	−0.0412056	+	0.999151i	$0.513120\pi$
$440$		0			0
$441$	18.4277	−	7.01546i	0.877511	−	0.334070i
$442$	−3.95823	+	24.9913i	−0.188274	+	1.18871i
$443$	−12.3286	+	12.3286i	−0.585749	+	0.585749i	−0.936477	−	0.350728i	$-0.885934\pi$
$443$	−12.3286	+	12.3286i	−0.585749	+	0.585749i	0.350728	+	0.936477i	$0.385934\pi$
$444$	−0.497343	+	3.73784i	−0.0236028	+	0.177390i
$445$		0			0
$446$	−3.73089	+	5.13513i	−0.176663	+	0.243155i
$447$	9.85857	−	14.3020i	0.466294	−	0.676461i
$448$	0.582467	−	0.296782i	0.0275190	−	0.0140216i
$449$	11.4060			0.538284			0.269142	−	0.963101i	$-0.413260\pi$
$449$	11.4060			0.538284			0.269142	+	0.963101i	$0.413260\pi$
$450$		0			0
$451$	−19.1813			−0.903214
$452$	−12.6233	+	6.43189i	−0.593750	+	0.302531i
$453$	−17.6132	+	25.5517i	−0.827538	+	1.20052i
$454$	−8.30177	+	11.4264i	−0.389621	+	0.536268i
$455$		0			0
$456$	−1.66461	+	12.5106i	−0.0779527	+	0.585862i
$457$	4.54539	−	4.54539i	0.212624	−	0.212624i	−0.592757	−	0.805381i	$-0.701961\pi$
$457$	4.54539	−	4.54539i	0.212624	−	0.212624i	0.805381	+	0.592757i	$0.201961\pi$
$458$	−2.38008	+	15.0272i	−0.111214	+	0.702176i
$459$	27.9273	+	11.7035i	1.30354	+	0.546274i
$460$		0			0
$461$	18.3653	+	5.96726i	0.855359	+	0.277923i	0.703689	−	0.710508i	$-0.251535\pi$
$461$	18.3653	+	5.96726i	0.855359	+	0.277923i	0.151670	+	0.988431i	$0.451535\pi$
$462$	−1.08273	−	3.07100i	−0.0503732	−	0.142876i
$463$	−2.03171	+	3.98746i	−0.0944216	+	0.185313i	−0.933387	−	0.358873i	$-0.883161\pi$
$463$	−2.03171	+	3.98746i	−0.0944216	+	0.185313i	0.838965	+	0.544186i	$0.183161\pi$
$464$	−0.994016	+	3.05927i	−0.0461460	+	0.142023i
$465$		0			0
$466$	−2.34671	−	7.22242i	−0.108709	−	0.334572i
$467$	−1.74215	−	0.275929i	−0.0806170	−	0.0127685i	0.115996	−	0.993250i	$-0.462994\pi$
$467$	−1.74215	−	0.275929i	−0.0806170	−	0.0127685i	−0.196613	+	0.980481i	$0.562994\pi$
$468$	8.74271	−	9.65605i	0.404132	−	0.446351i
$469$	5.46513	+	7.52211i	0.252356	+	0.347339i
$470$		0			0
$471$	2.84884	+	15.4902i	0.131268	+	0.713752i
$472$	8.51287	−	1.34831i	0.391837	−	0.0620609i
$473$	9.39370	+	18.4362i	0.431923	+	0.847696i
$474$	12.8096	+	12.1895i	0.588363	+	0.559881i
$475$		0			0
$476$			3.80954i			0.174610i
$477$	−3.37414	−	5.88161i	−0.154491	−	0.269300i
$478$	1.95347	+	12.3338i	0.0893498	+	0.564133i
$479$	13.7743	+	10.0076i	0.629363	+	0.457259i	0.856179	−	0.516679i	$-0.172832\pi$
$479$	13.7743	+	10.0076i	0.629363	+	0.457259i	−0.226817	+	0.973937i	$0.572832\pi$
$480$		0			0
$481$	−7.64742	+	5.55617i	−0.348692	+	0.253340i
$482$	16.0488	+	16.0488i	0.731005	+	0.731005i
$483$	0.627753	−	0.480317i	0.0285637	−	0.0218552i
$484$	−2.59578	+	0.843419i	−0.117990	+	0.0383372i
$485$		0			0
$486$	−8.74057	−	12.9075i	−0.396480	−	0.585494i
$487$	−25.0891	−	12.7835i	−1.13690	−	0.579277i	−0.218852	−	0.975758i	$-0.570231\pi$
$487$	−25.0891	−	12.7835i	−1.13690	−	0.579277i	−0.918043	+	0.396481i	$0.870231\pi$
$488$	−8.01294	−	4.08280i	−0.362729	−	0.184820i
$489$	7.64711	+	14.1307i	0.345814	+	0.639011i
$490$		0			0
$491$	8.69557	−	2.82536i	0.392426	−	0.127507i	−0.106156	−	0.994349i	$-0.533854\pi$
$491$	8.69557	−	2.82536i	0.392426	−	0.127507i	0.498582	+	0.866843i	$0.333854\pi$
$492$	−7.01997	−	9.17479i	−0.316485	−	0.413631i
$493$	−13.2549	−	13.2549i	−0.596972	−	0.596972i
$494$	−25.5960	+	18.5966i	−1.15162	+	0.836701i
$495$		0			0
$496$	4.82678	+	3.50686i	0.216729	+	0.157463i
$497$	1.24440	+	7.85683i	0.0558189	+	0.352427i
$498$	−7.87642	−	2.34493i	−0.352951	−	0.105079i
$499$			12.9235i			0.578536i	0.957248	+	0.289268i	$0.0934119\pi$
$499$			12.9235i			0.578536i	−0.957248	+	0.289268i	$0.906588\pi$
$500$		0			0
$501$	−6.06639	+	6.37500i	−0.271026	+	0.284814i
$502$	3.81533	+	7.48801i	0.170287	+	0.334206i
$503$	22.2567	−	3.52512i	0.992379	−	0.157177i	0.360928	−	0.932594i	$-0.382460\pi$
$503$	22.2567	−	3.52512i	0.992379	−	0.157177i	0.631450	+	0.775416i	$0.282460\pi$
$504$	1.07266	−	1.64181i	0.0477799	−	0.0731320i
$505$		0			0
$506$	1.18005	+	1.62420i	0.0524595	+	0.0722044i
$507$	10.1341	−	0.251380i	0.450069	−	0.0111642i
$508$	−14.3160	−	2.26744i	−0.635171	−	0.100601i
$509$	−1.15005	−	3.53949i	−0.0509750	−	0.156885i	0.922329	−	0.386407i	$-0.126284\pi$
$509$	−1.15005	−	3.53949i	−0.0509750	−	0.156885i	−0.973304	+	0.229522i	$0.926284\pi$
$510$		0			0
$511$	0.113087	−	0.348047i	0.00500268	−	0.0153967i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$	14.3445	+	35.0401i	0.633324	+	1.54706i
$514$	−28.5533	−	9.27753i	−1.25943	−	0.409214i
$515$		0			0
$516$	−5.38046	+	11.2404i	−0.236861	+	0.494832i
$517$	1.36594	−	8.62420i	0.0600739	−	0.379292i
$518$	−1.00634	+	1.00634i	−0.0442162	+	0.0442162i
$519$	32.7490	+	4.35746i	1.43752	+	0.191271i
$520$		0			0
$521$	−25.0327	+	34.4546i	−1.09670	+	1.50948i	−0.257021	+	0.966406i	$0.582741\pi$
$521$	−25.0327	+	34.4546i	−1.09670	+	1.50948i	−0.839683	+	0.543077i	$0.817259\pi$
$522$	1.98032	+	9.44473i	0.0866762	+	0.413385i
$523$	19.8847	−	10.1317i	0.869495	−	0.443030i	0.0384667	−	0.999260i	$-0.487753\pi$
$523$	19.8847	−	10.1317i	0.869495	−	0.443030i	0.831028	+	0.556230i	$0.187753\pi$
$524$	−5.49670			−0.240125
$525$		0			0
$526$	−4.21464			−0.183767
$527$	−30.9786	+	15.7844i	−1.34945	+	0.687579i
$528$	4.10120	+	2.82702i	0.178482	+	0.123030i
$529$	13.2326	−	18.2131i	0.575331	−	0.791875i
$530$		0			0
$531$	20.1395	−	16.2168i	0.873978	−	0.703750i
$532$	−3.36825	+	3.36825i	−0.146032	+	0.146032i
$533$	4.53032	−	28.6033i	0.196230	−	1.23895i
$534$	9.03414	+	4.32437i	0.390945	+	0.187134i
$535$		0			0
$536$	−13.5269	−	4.39515i	−0.584272	−	0.189842i
$537$	−6.55630	+	2.31153i	−0.282925	+	0.0997501i
$538$	9.20785	−	18.0714i	0.396979	−	0.779114i
$539$	−5.84107	+	17.9770i	−0.251593	+	0.774323i
$540$		0			0
$541$	0.576378	+	1.77391i	0.0247804	+	0.0762663i	0.962682	−	0.270635i	$-0.0872338\pi$
$541$	0.576378	+	1.77391i	0.0247804	+	0.0762663i	−0.937902	+	0.346902i	$0.887234\pi$
$542$	−6.69064	−	1.05969i	−0.287387	−	0.0455177i
$543$	0.175607	+	7.07940i	0.00753604	+	0.303806i
$544$	−3.42531	−	4.71454i	−0.146859	−	0.202134i
$545$		0			0
$546$	4.83520	−	0.889254i	0.206928	−	0.0380566i
$547$	24.0199	−	3.80438i	1.02702	−	0.162663i	0.379878	−	0.925036i	$-0.375966\pi$
$547$	24.0199	−	3.80438i	1.02702	−	0.162663i	0.647138	+	0.762373i	$0.275966\pi$
$548$	9.55034	+	18.7436i	0.407970	+	0.800687i
$549$	−26.9462	+	1.33765i	−1.15004	+	0.0570894i
$550$		0			0
$551$		−	23.4390i		−	0.998535i
$552$	−0.345010	+	1.15886i	−0.0146846	+	0.0493244i
$553$	1.04401	+	6.59162i	0.0443958	+	0.280304i
$554$	19.8071	+	14.3907i	0.841524	+	0.611403i
$555$		0			0
$556$	9.43519	−	6.85506i	0.400141	−	0.290720i
$557$	18.2820	+	18.2820i	0.774632	+	0.774632i	0.978912	−	0.204281i	$-0.0654855\pi$
$557$	18.2820	+	18.2820i	0.774632	+	0.774632i	−0.204281	+	0.978912i	$0.565485\pi$
$558$	17.7954	+	1.92003i	0.753339	+	0.0812813i
$559$	−29.7107	+	9.65360i	−1.25663	+	0.408304i
$560$		0			0
$561$	−25.5291	+	13.8156i	−1.07784	+	0.583294i
$562$	−18.0340	−	9.18876i	−0.760717	−	0.387604i
$563$	−0.869364	−	0.442963i	−0.0366393	−	0.0186687i	0.435575	−	0.900153i	$-0.356545\pi$
$563$	−0.869364	−	0.442963i	−0.0366393	−	0.0186687i	−0.472214	+	0.881484i	$0.656545\pi$
$564$	4.62502	−	2.50292i	0.194748	−	0.105392i
$565$		0			0
$566$	7.89740	−	2.56602i	0.331952	−	0.107858i
$567$	0.340335	−	5.87361i	0.0142927	−	0.246669i
$568$	−8.60442	−	8.60442i	−0.361033	−	0.361033i
$569$	−22.6112	+	16.4280i	−0.947909	+	0.688696i	−0.950311	−	0.311301i	$-0.899235\pi$
$569$	−22.6112	+	16.4280i	−0.947909	+	0.688696i	0.00240243	+	0.999997i	$0.499235\pi$
$570$		0			0
$571$	−4.29121	−	3.11775i	−0.179582	−	0.130474i	0.494363	−	0.869256i	$-0.335401\pi$
$571$	−4.29121	−	3.11775i	−0.179582	−	0.130474i	−0.673945	+	0.738782i	$0.735401\pi$
$572$	1.95339	+	12.3332i	0.0816753	+	0.515678i
$573$	6.01367	−	20.1994i	0.251224	−	0.843843i
$574$		−	4.36014i		−	0.181989i
$575$		0			0
$576$	0.148741	+	2.99631i	0.00619754	+	0.124846i
$577$	3.71857	+	7.29810i	0.154806	+	0.303824i	0.955364	−	0.295432i	$-0.0954634\pi$
$577$	3.71857	+	7.29810i	0.154806	+	0.303824i	−0.800558	+	0.599255i	$0.795463\pi$
$578$	16.7508	−	2.65307i	0.696742	−	0.110353i
$579$	−21.7232	+	3.99516i	−0.902785	+	0.166033i
$580$		0			0
$581$	−1.82313	−	2.50933i	−0.0756364	−	0.104105i
$582$	−0.228869	−	9.22658i	−0.00948694	−	0.382454i
$583$	6.42013	+	1.01685i	0.265895	+	0.0421136i
$584$	0.172991	+	0.532411i	0.00715841	+	0.0220313i
$585$		0			0
$586$	0.527935	−	1.62482i	0.0218088	−	0.0671205i
$587$	15.9900	−	31.3821i	0.659978	−	1.29528i	−0.281939	−	0.959432i	$-0.590977\pi$
$587$	15.9900	−	31.3821i	0.659978	−	1.29528i	0.941917	−	0.335847i	$-0.109023\pi$
$588$	−10.7364	+	3.78530i	−0.442763	+	0.156103i
$589$	−41.3460	−	13.4341i	−1.70363	−	0.553544i
$590$		0			0
$591$	0.640605	+	0.306639i	0.0263510	+	0.0126134i
$592$	0.340567	−	2.15026i	0.0139972	−	0.0883750i
$593$	2.52481	−	2.52481i	0.103681	−	0.103681i	−0.653363	−	0.757045i	$-0.726643\pi$
$593$	2.52481	−	2.52481i	0.103681	−	0.103681i	0.757045	+	0.653363i	$0.226643\pi$
$594$	14.8924	+	1.23410i	0.611043	+	0.0506357i
$595$		0			0
$596$	−5.89486	+	8.11358i	−0.241463	+	0.332345i
$597$	15.6795	+	10.8081i	0.641719	+	0.442346i
$598$	−2.70072	+	1.37608i	−0.110441	+	0.0562723i
$599$	−39.4333			−1.61120			−0.805600	−	0.592460i	$-0.798157\pi$
$599$	−39.4333			−1.61120			−0.805600	+	0.592460i	$0.798157\pi$
$600$		0			0
$601$	28.0191			1.14292			0.571462	−	0.820629i	$-0.306376\pi$
$601$	28.0191			1.14292			0.571462	+	0.820629i	$0.306376\pi$
$602$	−4.19075	+	2.13529i	−0.170802	+	0.0870281i
$603$	−41.7609	+	8.75620i	−1.70064	+	0.356580i
$604$	10.5317	−	14.4956i	0.428527	−	0.589817i
$605$		0			0
$606$	21.5628	+	2.86906i	0.875928	+	0.116548i
$607$	3.59236	−	3.59236i	0.145809	−	0.145809i	−0.630434	−	0.776243i	$-0.717123\pi$
$607$	3.59236	−	3.59236i	0.145809	−	0.145809i	0.776243	+	0.630434i	$0.217123\pi$
$608$	1.13988	−	7.19694i	0.0462284	−	0.291875i
$609$	−1.57254	+	3.28522i	−0.0637224	+	0.133124i
$610$		0			0
$611$	12.5378	+	4.07379i	0.507226	+	0.164808i
$612$	−15.9513	−	7.15480i	−0.644795	−	0.289216i
$613$	−6.96688	+	13.6733i	−0.281390	+	0.552258i	−0.987834	−	0.155510i	$-0.950298\pi$
$613$	−6.96688	+	13.6733i	−0.281390	+	0.552258i	0.706445	+	0.707768i	$0.250298\pi$
$614$	−1.97818	+	6.08821i	−0.0798328	+	0.245700i
$615$		0			0
$616$	0.580955	+	1.78800i	0.0234074	+	0.0720404i
$617$	−7.10625	−	1.12552i	−0.286087	−	0.0453117i	0.0117417	−	0.999931i	$-0.496262\pi$
$617$	−7.10625	−	1.12552i	−0.286087	−	0.0453117i	−0.297829	+	0.954619i	$0.596262\pi$
$618$	−10.6059	+	0.263084i	−0.426632	+	0.0105828i
$619$	−7.42133	−	10.2146i	−0.298288	−	0.410559i	0.633396	−	0.773828i	$-0.281661\pi$
$619$	−7.42133	−	10.2146i	−0.298288	−	0.410559i	−0.931684	+	0.363269i	$0.881661\pi$
$620$		0			0
$621$	0.832190	+	3.53063i	0.0333946	+	0.141679i
$622$	34.2051	−	5.41755i	1.37150	−	0.217224i
$623$	1.71618	+	3.36818i	0.0687571	+	0.134943i
$624$	−5.18430	+	5.44804i	−0.207538	+	0.218096i
$625$		0			0
$626$		−	26.1462i		−	1.04501i
$627$	−34.7870	−	10.3566i	−1.38926	−	0.413603i
$628$	−1.42250	−	8.98132i	−0.0567640	−	0.358394i
$629$	10.2638	+	7.45711i	0.409246	+	0.297334i
$630$		0			0
$631$	−2.09574	+	1.52265i	−0.0834301	+	0.0606155i	−0.628718	−	0.777633i	$-0.716420\pi$
$631$	−2.09574	+	1.52265i	−0.0834301	+	0.0606155i	0.545288	+	0.838249i	$0.316420\pi$
$632$	−7.21882	−	7.21882i	−0.287149	−	0.287149i
$633$	22.6408	+	29.5905i	0.899892	+	1.17612i
$634$	12.9984	−	4.22343i	0.516231	−	0.167734i
$635$		0			0
$636$	1.86326	+	3.44301i	0.0738829	+	0.136524i
$637$	−25.4278	−	12.9561i	−1.00748	−	0.513339i
$638$	−8.24255	−	4.19979i	−0.326326	−	0.166271i
$639$	−35.2354	−	9.54557i	−1.39389	−	0.377617i
$640$		0			0
$641$	−3.49095	+	1.13428i	−0.137884	+	0.0448012i	−0.377146	−	0.926154i	$-0.623095\pi$
$641$	−3.49095	+	1.13428i	−0.137884	+	0.0448012i	0.239262	+	0.970955i	$0.423095\pi$
$642$	−0.800574	+	0.612549i	−0.0315961	+	0.0241754i
$643$	−9.94703	−	9.94703i	−0.392273	−	0.392273i	0.483224	−	0.875497i	$-0.339466\pi$
$643$	−9.94703	−	9.94703i	−0.392273	−	0.392273i	−0.875497	+	0.483224i	$0.839466\pi$
$644$	−0.369198	+	0.268238i	−0.0145485	+	0.0105701i
$645$		0			0
$646$	34.3532	+	24.9591i	1.35161	+	0.982001i
$647$	0.617590	+	3.89931i	0.0242800	+	0.153298i	0.996850	−	0.0793138i	$-0.0252729\pi$
$647$	0.617590	+	3.89931i	0.0242800	+	0.153298i	−0.972570	+	0.232612i	$0.925273\pi$
$648$	4.86002	+	7.57497i	0.190920	+	0.297573i
$649$			24.7871i			0.972979i
$650$		0			0
$651$	4.89377	+	4.65686i	0.191802	+	0.182517i
$652$	−4.21139	−	8.26532i	−0.164931	−	0.323695i
$653$	−14.3859	+	2.27850i	−0.562962	+	0.0891644i	−0.431428	−	0.902147i	$-0.641990\pi$
$653$	−14.3859	+	2.27850i	−0.562962	+	0.0891644i	−0.131534	+	0.991312i	$0.541990\pi$
$654$	−3.63999	−	19.7920i	−0.142335	−	0.773927i
$655$		0			0
$656$	3.92038	+	5.39594i	0.153065	+	0.210676i
$657$	1.24495	+	1.12720i	0.0485703	+	0.0439761i
$658$	1.96038	+	0.310493i	0.0764235	+	0.0121043i
$659$	4.21526	+	12.9732i	0.164203	+	0.505365i	0.998977	−	0.0452283i	$-0.0144015\pi$
$659$	4.21526	+	12.9732i	0.164203	+	0.505365i	−0.834774	+	0.550593i	$0.814402\pi$
$660$		0			0
$661$	−2.48143	+	7.63705i	−0.0965164	+	0.297047i	−0.987646	−	0.156702i	$-0.949914\pi$
$661$	−2.48143	+	7.63705i	−0.0965164	+	0.297047i	0.891130	+	0.453749i	$0.149914\pi$
$662$	−4.79834	+	9.41728i	−0.186493	+	0.366013i
$663$	−14.5723	−	41.3321i	−0.565942	−	1.60520i
$664$	4.51248	+	1.46619i	0.175118	+	0.0568994i
$665$		0			0
$666$	−2.32373	−	6.10382i	−0.0900428	−	0.236518i
$667$	0.351281	−	2.21790i	0.0136017	−	0.0858775i
$668$	3.59263	−	3.59263i	0.139003	−	0.139003i
$669$	1.45004	−	10.8979i	0.0560616	−	0.421338i
$670$		0			0
$671$	15.2019	−	20.9237i	0.586865	−	0.807750i
$672$	−0.642614	+	0.932251i	−0.0247894	+	0.0359623i
$673$	24.0809	−	12.2698i	0.928251	−	0.472967i	0.0765912	−	0.997063i	$-0.475596\pi$
$673$	24.0809	−	12.2698i	0.928251	−	0.472967i	0.851660	+	0.524095i	$0.175596\pi$
$674$	31.5318			1.21456
$675$		0			0
$676$	−5.85270			−0.225104
$677$	16.4613	−	8.38747i	0.632660	−	0.322357i	−0.108086	−	0.994142i	$-0.534472\pi$
$677$	16.4613	−	8.38747i	0.632660	−	0.322357i	0.740746	+	0.671785i	$0.234472\pi$
$678$	13.9268	−	20.2038i	0.534855	−	0.775924i
$679$	2.04750	−	2.81814i	0.0785757	−	0.108150i
$680$		0			0
$681$	3.22654	−	24.2494i	0.123641	−	0.929241i
$682$	−12.1326	+	12.1326i	−0.464581	+	0.464581i
$683$	5.94046	−	37.5066i	0.227305	−	1.43515i	−0.565033	−	0.825068i	$-0.691137\pi$
$683$	5.94046	−	37.5066i	0.227305	−	1.43515i	0.792338	−	0.610082i	$-0.208863\pi$
$684$	−7.77757	−	20.4296i	−0.297383	−	0.781144i
$685$		0			0
$686$	−8.43843	−	2.74181i	−0.322181	−	0.104683i
$687$	−8.76231	−	24.8529i	−0.334303	−	0.948198i
$688$	3.26638	−	6.41064i	0.124530	−	0.244403i
$689$	−3.03266	+	9.33356i	−0.115535	+	0.355580i
$690$		0			0
$691$	−2.65184	−	8.16151i	−0.100881	−	0.310479i	0.887861	−	0.460112i	$-0.152191\pi$
$691$	−2.65184	−	8.16151i	−0.100881	−	0.310479i	−0.988742	+	0.149633i	$0.952191\pi$
$692$	−18.8394	−	2.98388i	−0.716168	−	0.113430i
$693$	4.18093	+	3.78547i	0.158820	+	0.143798i
$694$	7.68036	+	10.5711i	0.291542	+	0.401274i
$695$		0			0
$696$	−1.00777	−	5.47959i	−0.0381992	−	0.207703i
$697$	−38.3894	+	6.08028i	−1.45410	+	0.230307i
$698$	−13.8161	−	27.1156i	−0.522947	−	1.02634i
$699$	9.52861	+	9.06733i	0.360405	+	0.342958i
$700$		0			0
$701$		−	52.4507i		−	1.98104i	−0.137384	−	0.990518i	$-0.543869\pi$
$701$		−	52.4507i		−	1.98104i	0.137384	−	0.990518i	$-0.456131\pi$
$702$	−5.35764	+	21.9162i	−0.202211	+	0.827173i
$703$	2.48160	+	15.6682i	0.0935951	+	0.590937i
$704$	−2.32663	−	1.69040i	−0.0876881	−	0.0637092i
$705$		0			0
$706$	2.35718	−	1.71259i	0.0887136	−	0.0644542i
$707$	5.80538	+	5.80538i	0.218334	+	0.218334i
$708$	−11.8561	+	9.07156i	−0.445580	+	0.340930i
$709$	5.89184	−	1.91438i	0.221273	−	0.0718959i	−0.196283	−	0.980547i	$-0.562887\pi$
$709$	5.89184	−	1.91438i	0.221273	−	0.0718959i	0.417555	+	0.908652i	$0.362887\pi$
$710$		0			0
$711$	−29.5613	−	8.00841i	−1.10863	−	0.300339i
$712$	−5.15235	−	2.62525i	−0.193092	−	0.0983855i
$713$	−3.71101	−	1.89085i	−0.138978	−	0.0708130i
$714$	−3.14044	−	5.80305i	−0.117528	−	0.217174i
$715$		0			0
$716$	3.81721	−	1.24029i	0.142656	−	0.0463517i
$717$	−13.1432	−	17.1776i	−0.490842	−	0.641508i
$718$	−5.59498	−	5.59498i	−0.208803	−	0.208803i
$719$	−3.26095	+	2.36922i	−0.121613	+	0.0883570i	−0.646929	−	0.762550i	$-0.723947\pi$
$719$	−3.26095	+	2.36922i	−0.121613	+	0.0883570i	0.525316	+	0.850907i	$0.323947\pi$
$720$		0			0
$721$	−3.23943	−	2.35359i	−0.120643	−	0.0876521i
$722$	5.33368	+	33.6756i	0.198499	+	1.25327i
$723$	−37.6772	−	11.2171i	−1.40123	−	0.417167i
$724$		−	4.08855i		−	0.151950i
$725$		0			0
$726$	3.25885	−	3.42464i	0.120947	−	0.127100i
$727$	13.8279	+	27.1388i	0.512850	+	1.00652i	0.991693	+	0.128624i	$0.0410560\pi$
$727$	13.8279	+	27.1388i	0.512850	+	1.00652i	−0.478844	+	0.877900i	$0.658944\pi$
$728$	−2.80348	+	0.444028i	−0.103904	+	0.0164568i
$729$	23.9549	+	12.4565i	0.887218	+	0.461350i
$730$		0			0
$731$	24.6445	+	33.9203i	0.911510	+	1.25459i
$732$	15.5718	−	0.386264i	0.575549	−	0.0142767i
$733$	13.6402	+	2.16039i	0.503812	+	0.0797960i	0.403167	−	0.915126i	$-0.367909\pi$
$733$	13.6402	+	2.16039i	0.503812	+	0.0797960i	0.100645	+	0.994922i	$0.467909\pi$
$734$	6.80279	+	20.9368i	0.251096	+	0.772793i
$735$		0			0
$736$	0.215722	−	0.663923i	0.00795161	−	0.0244725i
$737$	18.5698	−	36.4453i	0.684028	−	1.34248i
$738$	18.2568	+	8.18890i	0.672043	+	0.301438i
$739$	−25.2888	−	8.21683i	−0.930264	−	0.302261i	−0.195593	−	0.980685i	$-0.562663\pi$
$739$	−25.2888	−	8.21683i	−0.930264	−	0.302261i	−0.734671	+	0.678424i	$0.762663\pi$
$740$		0			0
$741$	23.6599	−	49.4285i	0.869170	−	1.81580i
$742$	−0.231141	+	1.45937i	−0.00848547	+	0.0535751i
$743$	−19.0708	+	19.0708i	−0.699641	+	0.699641i	−0.964333	−	0.264692i	$-0.914730\pi$
$743$	−19.0708	+	19.0708i	−0.699641	+	0.699641i	0.264692	+	0.964333i	$0.414730\pi$
$744$	−10.2435	−	1.36297i	−0.375546	−	0.0499687i
$745$		0			0
$746$	−12.5568	+	17.2829i	−0.459736	+	0.632772i
$747$	13.9312	−	2.92101i	0.509715	−	0.106874i
$748$	14.9325	−	7.60848i	0.545985	−	0.278193i
$749$	−0.380457			−0.0139016
$750$		0			0
$751$	−27.8529			−1.01637			−0.508183	−	0.861249i	$-0.669683\pi$
$751$	−27.8529			−1.01637			−0.508183	+	0.861249i	$0.669683\pi$
$752$	−2.70527	+	1.37840i	−0.0986509	+	0.0502652i
$753$	−11.9847	−	8.26123i	−0.436747	−	0.301056i
$754$	8.20949	−	11.2994i	0.298972	−	0.411500i
$755$		0			0
$756$	−0.280525	+	3.38522i	−0.0102026	+	0.123119i
$757$	14.2550	−	14.2550i	0.518108	−	0.518108i	−0.398891	−	0.916998i	$-0.630605\pi$
$757$	14.2550	−	14.2550i	0.518108	−	0.518108i	0.916998	+	0.398891i	$0.130605\pi$
$758$	−0.154776	+	0.977218i	−0.00562172	+	0.0354942i
$759$	−3.13649	−	1.50134i	−0.113847	−	0.0544953i
$760$		0			0
$761$	−20.4602	−	6.64792i	−0.741681	−	0.240987i	−0.0862835	−	0.996271i	$-0.527499\pi$
$761$	−20.4602	−	6.64792i	−0.741681	−	0.240987i	−0.655398	+	0.755284i	$0.727499\pi$
$762$	23.6767	−	8.34763i	0.857717	−	0.302403i
$763$	3.44817	−	6.76742i	0.124832	−	0.244997i
$764$	−3.76012	+	11.5725i	−0.136036	+	0.418677i
$765$		0			0
$766$	−3.90822	−	12.0283i	−0.141210	−	0.434599i
$767$	−36.9626	−	5.85431i	−1.33464	−	0.211387i
$768$	−0.0429510	−	1.73152i	−0.00154986	−	0.0624808i
$769$	5.35630	+	7.37231i	0.193153	+	0.265852i	0.894599	−	0.446871i	$-0.147462\pi$
$769$	5.35630	+	7.37231i	0.193153	+	0.265852i	−0.701446	+	0.712723i	$0.747462\pi$
$770$		0			0
$771$	51.1431	−	9.40586i	1.84188	−	0.338744i
$772$	12.5952	−	1.99489i	0.453312	−	0.0717976i
$773$	−20.4388	−	40.1134i	−0.735132	−	1.44278i	−0.890529	−	0.454926i	$-0.849666\pi$
$773$	−20.4388	−	40.1134i	−0.735132	−	1.44278i	0.155397	−	0.987852i	$-0.450334\pi$
$774$	−1.07017	−	21.5579i	−0.0384663	−	0.774884i
$775$		0			0
$776$			5.32861i			0.191286i
$777$	0.703366	−	2.36255i	0.0252331	−	0.0847560i
$778$	−4.28069	−	27.0272i	−0.153470	−	0.968973i
$779$	−39.3184	−	28.5665i	−1.40873	−	1.02350i
$780$		0			0
$781$	28.3116	−	20.5695i	1.01307	−	0.736036i
$782$	2.87659	+	2.87659i	0.102867	+	0.102867i
$783$	−10.8025	−	12.7546i	−0.386049	−	0.455813i
$784$	6.25096	−	2.03106i	0.223249	−	0.0725379i
$785$		0			0
$786$	8.37310	−	4.53128i	0.298659	−	0.161625i
$787$	−22.6577	−	11.5447i	−0.807659	−	0.411523i	0.000855029	−	1.00000i	$-0.499728\pi$
$787$	−22.6577	−	11.5447i	−0.807659	−	0.411523i	−0.808514	+	0.588477i	$0.799728\pi$
$788$	−0.365350	−	0.186155i	−0.0130150	−	0.00663150i
$789$	6.42014	−	3.47439i	0.228563	−	0.123692i
$790$		0			0
$791$	8.80823	−	2.86197i	0.313185	−	0.101760i
$792$	−8.57783	−	0.925503i	−0.304800	−	0.0328863i
$793$	27.6110	+	27.6110i	0.980497	+	0.980497i
$794$	−2.87697	+	2.09024i	−0.102100	+	0.0741798i
$795$		0			0
$796$	−8.89504	−	6.46262i	−0.315276	−	0.229062i
$797$	1.71644	+	10.8372i	0.0607996	+	0.383874i	0.999259	+	0.0384845i	$0.0122530\pi$
$797$	1.71644	+	10.8372i	0.0607996	+	0.383874i	−0.938460	+	0.345389i	$0.887747\pi$
$798$	2.35418	−	7.90749i	0.0833369	−	0.279922i
$799$		−	17.6934i		−	0.625946i
$800$		0			0
$801$	−17.3265	+	0.860112i	−0.612202	+	0.0303906i
$802$	−7.55891	−	14.8352i	−0.266914	−	0.523849i
$803$	−1.59012	+	0.251850i	−0.0561141	+	0.00888760i
$804$	24.2286	−	4.45595i	0.854478	−	0.157149i
$805$		0			0
$806$	−15.2267	−	20.9577i	−0.536337	−	0.738204i
$807$	0.871135	+	35.1187i	0.0306654	+	1.23624i
$808$	−12.4044	−	1.96466i	−0.436384	−	0.0691165i
$809$	−13.0207	−	40.0735i	−0.457782	−	1.40891i	−0.867838	−	0.496848i	$-0.834491\pi$
$809$	−13.0207	−	40.0735i	−0.457782	−	1.40891i	0.410056	−	0.912060i	$-0.365509\pi$
$810$		0			0
$811$	4.38556	−	13.4974i	0.153998	−	0.473957i	−0.844060	−	0.536249i	$-0.819841\pi$
$811$	4.38556	−	13.4974i	0.153998	−	0.473957i	0.998058	+	0.0622916i	$0.0198409\pi$
$812$	0.954659	−	1.87362i	0.0335020	−	0.0657513i
$813$	11.0654	−	3.90128i	0.388080	−	0.136824i
$814$	5.95451	+	1.93474i	0.208706	+	0.0678126i
$815$		0			0
$816$	9.10425	+	4.35793i	0.318712	+	0.152558i
$817$	−8.20127	+	51.7808i	−0.286926	+	1.81158i
$818$	−3.04402	+	3.04402i	−0.106432	+	0.106432i
$819$	−6.63237	+	5.34056i	−0.231754	+	0.186614i
$820$		0			0
$821$	9.28341	−	12.7775i	0.323993	−	0.445939i	−0.615688	−	0.787990i	$-0.711122\pi$
$821$	9.28341	−	12.7775i	0.323993	−	0.445939i	0.939681	+	0.342052i	$0.111122\pi$
$822$	−29.9995	−	20.6791i	−1.04635	−	0.721266i
$823$	−21.3898	+	10.8987i	−0.745603	+	0.379904i	−0.785143	−	0.619314i	$-0.787411\pi$
$823$	−21.3898	+	10.8987i	−0.745603	+	0.379904i	0.0395404	+	0.999218i	$0.487411\pi$
$824$	6.12520			0.213382
$825$		0			0
$826$	−5.63439			−0.196046
$827$	23.7234	−	12.0877i	0.824944	−	0.420330i	0.0100569	−	0.999949i	$-0.496799\pi$
$827$	23.7234	−	12.0877i	0.824944	−	0.420330i	0.814887	+	0.579619i	$0.196799\pi$
$828$	−0.429769	−	2.04970i	−0.0149355	−	0.0712320i
$829$	−9.16301	+	12.6118i	−0.318245	+	0.438026i	−0.937930	−	0.346824i	$-0.887260\pi$
$829$	−9.16301	+	12.6118i	−0.318245	+	0.438026i	0.619686	+	0.784850i	$0.287260\pi$
$830$		0			0
$831$	−42.0352	−	5.59305i	−1.45819	−	0.194021i
$832$	3.07024	−	3.07024i	0.106441	−	0.106441i
$833$	−5.99176	+	37.8305i	−0.207602	+	1.31075i
$834$	−8.72151	+	18.2203i	−0.302001	+	0.630917i
$835$		0			0
$836$	19.9298	+	6.47560i	0.689288	+	0.223963i
$837$	−28.6904	+	11.7451i	−0.991686	+	0.405969i
$838$	3.27974	−	6.43686i	0.113297	−	0.222358i
$839$	4.03893	−	12.4305i	0.139439	−	0.429150i	−0.856815	−	0.515624i	$-0.827560\pi$
$839$	4.03893	−	12.4305i	0.139439	−	0.429150i	0.996254	+	0.0864743i	$0.0275600\pi$
$840$		0			0
$841$	−5.76404	−	17.7399i	−0.198760	−	0.611720i
$842$	−14.3608	−	2.27453i	−0.494907	−	0.0783856i
$843$	35.0459	−	0.869329i	1.20705	−	0.0299413i
$844$	−12.6440	−	17.4030i	−0.435225	−	0.599036i
$845$		0			0
$846$	−4.98194	+	7.62538i	−0.171283	+	0.262166i
$847$	1.76227	−	0.279116i	0.0605522	−	0.00959053i
$848$	−1.02613	−	2.01389i	−0.0352374	−	0.0691572i
$849$	−9.91473	+	10.4191i	−0.340273	+	0.357583i
$850$		0			0
$851$			1.51978i			0.0520975i
$852$	20.2002	+	6.01391i	0.692048	+	0.206033i
$853$	−6.36392	−	40.1802i	−0.217897	−	1.37574i	−0.817722	−	0.575614i	$-0.804763\pi$
$853$	−6.36392	−	40.1802i	−0.217897	−	1.37574i	0.599825	−	0.800131i	$-0.295237\pi$
$854$	4.75619	+	3.45558i	0.162754	+	0.118247i
$855$		0			0
$856$	0.470839	−	0.342085i	0.0160930	−	0.0116922i
$857$	−24.0957	−	24.0957i	−0.823093	−	0.823093i	0.163457	−	0.986550i	$-0.447735\pi$
$857$	−24.0957	−	24.0957i	−0.823093	−	0.823093i	−0.986550	+	0.163457i	$0.947735\pi$
$858$	−13.1426	−	17.1768i	−0.448682	−	0.586407i
$859$	−17.4179	+	5.65942i	−0.594291	+	0.193097i	−0.590693	−	0.806897i	$-0.701145\pi$
$859$	−17.4179	+	5.65942i	−0.594291	+	0.193097i	−0.00359858	+	0.999994i	$0.501145\pi$
$860$		0			0
$861$	3.59434	+	6.64178i	0.122495	+	0.226351i
$862$	3.69822	+	1.88434i	0.125962	+	0.0641808i
$863$	7.06405	+	3.59931i	0.240463	+	0.122522i	0.570070	−	0.821596i	$-0.306916\pi$
$863$	7.06405	+	3.59931i	0.240463	+	0.122522i	−0.329607	+	0.944118i	$0.606916\pi$
$864$	−2.69662	−	4.44165i	−0.0917410	−	0.151108i
$865$		0			0
$866$	−27.7975	+	9.03196i	−0.944598	+	0.306918i
$867$	−23.3293	+	17.8501i	−0.792306	+	0.606223i
$868$	−2.75788	−	2.75788i	−0.0936085	−	0.0936085i
$869$	23.7524	−	17.2572i	0.805747	−	0.585409i
$870$		0			0
$871$	49.9615	+	36.2992i	1.69288	+	1.22995i
$872$	1.81754	+	11.4755i	0.0615497	+	0.388609i
$873$	7.95468	+	13.8661i	0.269225	+	0.469297i
$874$			5.08674i			0.172062i
$875$		0			0
$876$	−0.702415	−	0.668411i	−0.0237324	−	0.0225835i
$877$	−23.3612	−	45.8490i	−0.788853	−	1.54821i	−0.835621	−	0.549306i	$-0.814892\pi$
$877$	−23.3612	−	45.8490i	−0.788853	−	1.54821i	0.0467683	−	0.998906i	$-0.485108\pi$
$878$	11.1570	−	1.76709i	0.376530	−	0.0596365i
$879$	0.535237	+	2.91028i	0.0180531	+	0.0981614i
$880$		0			0
$881$	1.69050	+	2.32677i	0.0569544	+	0.0783909i	0.836544	−	0.547900i	$-0.184572\pi$
$881$	1.69050	+	2.32677i	0.0569544	+	0.0783909i	−0.779590	+	0.626290i	$0.784572\pi$
$882$	13.2343	−	14.6168i	0.445621	−	0.492175i
$883$	36.4793	+	5.77775i	1.22763	+	0.194437i	0.736370	−	0.676579i	$-0.236538\pi$
$883$	36.4793	+	5.77775i	1.22763	+	0.194437i	0.491255	+	0.871016i	$0.336538\pi$
$884$	7.81899	+	24.0644i	0.262981	+	0.809372i
$885$		0			0
$886$	−5.38779	+	16.5819i	−0.181006	+	0.557081i
$887$	−2.57475	+	5.05323i	−0.0864515	+	0.169671i	−0.930184	−	0.367093i	$-0.880353\pi$
$887$	−2.57475	+	5.05323i	−0.0864515	+	0.169671i	0.843733	+	0.536763i	$0.180353\pi$
$888$	1.25381	+	3.55623i	0.0420750	+	0.119339i
$889$	9.01156	+	2.92803i	0.302238	+	0.0982031i
$890$		0			0
$891$	−23.7029	+	10.3969i	−0.794077	+	0.348308i
$892$	−0.992947	+	6.26922i	−0.0332463	+	0.209909i
$893$	15.6438	−	15.6438i	0.523500	−	0.523500i
$894$	2.29108	−	17.2189i	0.0766251	−	0.575885i
$895$		0			0
$896$	0.384246	−	0.528869i	0.0128368	−	0.0176683i
$897$	2.97960	−	4.32255i	0.0994858	−	0.144326i
$898$	10.1628	−	5.17823i	0.339138	−	0.172800i
$899$	19.1916			0.640075
$900$		0			0
$901$	13.1715			0.438807
$902$	−17.0907	+	8.70815i	−0.569058	+	0.289950i
$903$	4.62349	−	6.70738i	0.153860	−	0.223208i
$904$	−8.32742	+	11.4617i	−0.276966	+	0.381211i
$905$		0			0
$906$	−4.09320	+	30.7629i	−0.135988	+	1.02203i
$907$	23.6056	−	23.6056i	0.783811	−	0.783811i	−0.196661	−	0.980472i	$-0.563010\pi$
$907$	23.6056	−	23.6056i	0.783811	−	0.783811i	0.980472	+	0.196661i	$0.0630097\pi$
$908$	−2.20945	+	13.9499i	−0.0733232	+	0.462944i
$909$	−35.2116	+	13.4051i	−1.16790	+	0.444620i
$910$		0			0
$911$	−40.8162	−	13.2620i	−1.35230	−	0.439390i	−0.458837	−	0.888521i	$-0.651734\pi$
$911$	−40.8162	−	13.2620i	−1.35230	−	0.439390i	−0.893466	+	0.449131i	$0.851734\pi$
$912$	4.19651	+	11.9027i	0.138960	+	0.394139i
$913$	−6.19478	+	12.1579i	−0.205017	+	0.402369i
$914$	1.98641	−	6.11354i	0.0657046	−	0.202218i
$915$		0			0
$916$	4.70155	+	14.4699i	0.155344	+	0.478098i
$917$	3.54906	+	0.562115i	0.117200	+	0.0185627i
$918$	30.1967	−	2.25082i	0.996641	−	0.0742882i
$919$	7.08527	+	9.75204i	0.233722	+	0.321690i	0.909727	−	0.415206i	$-0.136291\pi$
$919$	7.08527	+	9.75204i	0.233722	+	0.321690i	−0.676006	+	0.736896i	$0.736291\pi$
$920$		0			0
$921$	−2.00554	−	10.9049i	−0.0660848	−	0.359328i
$922$	19.0727	−	3.02082i	0.628126	−	0.0994854i
$923$	23.9867	+	47.0765i	0.789531	+	1.54954i
$924$	−2.35892	−	2.24473i	−0.0776029	−	0.0738461i
$925$		0			0
$926$			4.47523i			0.147065i
$927$	15.9390	−	9.14386i	0.523507	−	0.300324i
$928$	0.503203	+	3.17710i	0.0165185	+	0.104293i
$929$	15.3269	+	11.1356i	0.502859	+	0.365349i	0.810108	−	0.586280i	$-0.199408\pi$
$929$	15.3269	+	11.1356i	0.502859	+	0.365349i	−0.307249	+	0.951629i	$0.599408\pi$
$930$		0			0
$931$	−38.7460	+	28.1506i	−1.26985	+	0.922598i
$932$	−5.36984	−	5.36984i	−0.175895	−	0.175895i
$933$	−47.6384	+	36.4499i	−1.55961	+	1.19332i
$934$	−1.67753	+	0.545064i	−0.0548906	+	0.0178350i
$935$		0			0
$936$	3.40606	−	12.5727i	0.111330	−	0.410952i
$937$	−34.7728	−	17.7176i	−1.13598	−	0.578809i	−0.218199	−	0.975904i	$-0.570018\pi$
$937$	−34.7728	−	17.7176i	−1.13598	−	0.578809i	−0.917778	+	0.397095i	$0.870018\pi$
$938$	8.28444	+	4.22113i	0.270497	+	0.137825i
$939$	21.5540	+	39.8284i	0.703387	+	1.29975i
$940$		0			0
$941$	26.0266	−	8.45656i	0.848443	−	0.275676i	0.147649	−	0.989040i	$-0.452829\pi$
$941$	26.0266	−	8.45656i	0.848443	−	0.275676i	0.700794	+	0.713364i	$0.252829\pi$
$942$	9.57075	+	12.5085i	0.311832	+	0.407550i
$943$	−3.29235	−	3.29235i	−0.107214	−	0.107214i
$944$	6.97291	−	5.06611i	0.226949	−	0.164888i
$945$		0			0
$946$	16.7397	+	12.1621i	0.544254	+	0.395424i
$947$	4.63200	+	29.2453i	0.150520	+	0.950344i	0.941135	+	0.338031i	$0.109761\pi$
$947$	4.63200	+	29.2453i	0.150520	+	0.950344i	−0.790615	+	0.612313i	$0.790239\pi$
$948$	16.9473	+	5.04547i	0.550423	+	0.163869i
$949$		−	2.43068i		−	0.0789031i
$950$		0			0
$951$	−16.3187	+	17.1489i	−0.529171	+	0.556091i
$952$	1.72949	+	3.39432i	0.0560532	+	0.110011i
$953$	8.50033	−	1.34632i	0.275353	−	0.0436116i	−0.0172309	−	0.999852i	$-0.505485\pi$
$953$	8.50033	−	1.34632i	0.275353	−	0.0436116i	0.292584	+	0.956240i	$0.405485\pi$
$954$	−5.67658	−	3.70872i	−0.183786	−	0.120074i
$955$		0			0
$956$	7.33996	+	10.1026i	0.237391	+	0.326741i
$957$	16.0180	−	0.397333i	0.517788	−	0.0128439i
$958$	16.8163	+	2.66344i	0.543311	+	0.0860519i
$959$	−4.24957	−	13.0788i	−0.137226	−	0.422338i
$960$		0			0
$961$	1.42019	−	4.37089i	0.0458125	−	0.140996i
$962$	−4.29145	+	8.42244i	−0.138362	+	0.271550i
$963$	0.714547	−	1.59306i	0.0230260	−	0.0513355i
$964$	21.5856	+	7.01360i	0.695227	+	0.225893i
$965$		0			0
$966$	0.341272	−	0.712959i	0.0109803	−	0.0229391i
$967$	4.89692	−	30.9179i	0.157474	−	0.994254i	−0.774722	−	0.632302i	$-0.782110\pi$
$967$	4.89692	−	30.9179i	0.157474	−	0.994254i	0.932197	−	0.361952i	$-0.117890\pi$
$968$	−1.92995	+	1.92995i	−0.0620309	+	0.0620309i
$969$	−72.9053	−	9.70051i	−2.34206	−	0.311625i
$970$		0			0
$971$	−16.9971	+	23.3945i	−0.545463	+	0.750765i	−0.989388	−	0.145299i	$-0.953586\pi$
$971$	−16.9971	+	23.3945i	−0.545463	+	0.750765i	0.443925	+	0.896064i	$0.353586\pi$
$972$	−13.6478	−	7.53249i	−0.437752	−	0.241605i
$973$	−6.79305	+	3.46123i	−0.217775	+	0.110962i
$974$	−28.1581			−0.902245
$975$		0			0
$976$	−8.99313			−0.287863
$977$	1.82021	−	0.927445i	0.0582338	−	0.0296716i	−0.424631	−	0.905366i	$-0.639596\pi$
$977$	1.82021	−	0.927445i	0.0582338	−	0.0296716i	0.482865	+	0.875695i	$0.339596\pi$
$978$	13.2288	+	9.11881i	0.423011	+	0.291587i
$979$	9.77490	−	13.4540i	0.312407	−	0.429992i
$980$		0			0
$981$	21.8605	+	27.1483i	0.697953	+	0.866780i
$982$	6.46512	−	6.46512i	0.206310	−	0.206310i
$983$	−4.54655	+	28.7058i	−0.145012	+	0.915572i	0.802685	+	0.596403i	$0.203404\pi$
$983$	−4.54655	+	28.7058i	−0.145012	+	0.915572i	−0.947698	+	0.319169i	$0.896596\pi$
$984$	−10.4201	−	4.98779i	−0.332181	−	0.159005i
$985$		0			0
$986$	−17.8278	−	5.79262i	−0.567754	−	0.184474i
$987$	−3.24219	+	1.14309i	−0.103200	+	0.0363849i
$988$	−14.3635	+	28.1900i	−0.456965	+	0.896845i
$989$	−1.55208	+	4.77681i	−0.0493533	+	0.151894i
$990$		0			0
$991$	−4.33291	−	13.3353i	−0.137640	−	0.423611i	0.858352	−	0.513062i	$-0.171489\pi$
$991$	−4.33291	−	13.3353i	−0.137640	−	0.423611i	−0.995991	+	0.0894508i	$0.971489\pi$
$992$	5.89277	+	0.933323i	0.187096	+	0.0296330i
$993$	−0.453961	−	18.3009i	−0.0144060	−	0.580760i
$994$	4.67569	+	6.43554i	0.148304	+	0.204123i
$995$		0			0
$996$	−8.08252	+	1.48648i	−0.256104	+	0.0471008i
$997$	35.5407	−	5.62909i	1.12558	−	0.178275i	0.434238	−	0.900798i	$-0.357018\pi$
$997$	35.5407	−	5.62909i	1.12558	−	0.178275i	0.691347	+	0.722523i	$0.257018\pi$
$998$	5.86715	+	11.5149i	0.185722	+	0.364499i
$999$	8.57149	+	7.38231i	0.271190	+	0.233566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.b.743.7		80
3.2	odd	2	inner	750.2.l.b.743.4		80
5.2	odd	4		750.2.l.a.257.9		80
5.3	odd	4		750.2.l.c.257.2		80
5.4	even	2		150.2.l.a.53.4	yes	80
15.2	even	4		750.2.l.a.257.4		80
15.8	even	4		750.2.l.c.257.7		80
15.14	odd	2		150.2.l.a.53.7	yes	80
25.6	even	5		750.2.l.a.143.4		80
25.8	odd	20		150.2.l.a.17.7	yes	80
25.17	odd	20	inner	750.2.l.b.107.4		80
25.19	even	10		750.2.l.c.143.7		80
75.8	even	20		150.2.l.a.17.4	✓	80
75.17	even	20	inner	750.2.l.b.107.7		80
75.44	odd	10		750.2.l.c.143.2		80
75.56	odd	10		750.2.l.a.143.9		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.4	✓	80	75.8	even	20
150.2.l.a.17.7	yes	80	25.8	odd	20
150.2.l.a.53.4	yes	80	5.4	even	2
150.2.l.a.53.7	yes	80	15.14	odd	2
750.2.l.a.143.4		80	25.6	even	5
750.2.l.a.143.9		80	75.56	odd	10
750.2.l.a.257.4		80	15.2	even	4
750.2.l.a.257.9		80	5.2	odd	4
750.2.l.b.107.4		80	25.17	odd	20	inner
750.2.l.b.107.7		80	75.17	even	20	inner
750.2.l.b.743.4		80	3.2	odd	2	inner
750.2.l.b.743.7		80	1.1	even	1	trivial
750.2.l.c.143.2		80	75.44	odd	10
750.2.l.c.143.7		80	25.19	even	10
750.2.l.c.257.2		80	5.3	odd	4
750.2.l.c.257.7		80	15.8	even	4

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.891007 - 0.453990i) q^{2} +(-0.983013 + 1.42607i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-0.228447 + 1.71692i) q^{6} +(-0.462249 + 0.462249i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.06737 - 2.80370i) q^{9} +O(q^{10})\)	\(q+(0.891007 - 0.453990i) q^{2} +(-0.983013 + 1.42607i) q^{3} +(0.587785 - 0.809017i) q^{4} +(-0.228447 + 1.71692i) q^{6} +(-0.462249 + 0.462249i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-1.06737 - 2.80370i) q^{9} +(2.73512 + 0.888693i) q^{11} +(0.575917 + 1.63350i) q^{12} +(-1.97121 + 3.86872i) q^{13} +(-0.202010 + 0.621723i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(5.75574 + 0.911620i) q^{17} +(-2.22389 - 2.01354i) q^{18} +(4.28299 + 5.89503i) q^{19} +(-0.204804 - 1.11360i) q^{21} +(2.84047 - 0.449885i) q^{22} +(0.316926 + 0.622003i) q^{23} +(1.25474 + 1.19400i) q^{24} +4.34197i q^{26} +(5.04752 + 1.23392i) q^{27} +(0.102264 + 0.645670i) q^{28} +(-2.60237 - 1.89073i) q^{29} +(-4.82678 + 3.50686i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.95600 + 3.02688i) q^{33} +(5.54227 - 1.80079i) q^{34} +(-2.89562 - 0.784450i) q^{36} +(1.93977 + 0.988365i) q^{37} +(6.49246 + 3.30807i) q^{38} +(-3.57936 - 6.61410i) q^{39} +(-6.34331 + 2.06107i) q^{41} +(-0.688045 - 0.899243i) q^{42} +(5.08751 + 5.08751i) q^{43} +(2.32663 - 1.69040i) q^{44} +(0.564767 + 0.410327i) q^{46} +(-0.474965 - 2.99881i) q^{47} +(1.66004 + 0.494220i) q^{48} +6.57265i q^{49} +(-6.95800 + 7.31198i) q^{51} +(1.97121 + 3.86872i) q^{52} +(2.23241 - 0.353579i) q^{53} +(5.05756 - 1.19210i) q^{54} +(0.384246 + 0.528869i) q^{56} +(-12.6170 + 0.312969i) q^{57} +(-3.17710 - 0.503203i) q^{58} +(2.66341 + 8.19714i) q^{59} +(2.77903 - 8.55298i) q^{61} +(-2.70861 + 5.31594i) q^{62} +(1.78940 + 0.802614i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-2.15064 + 4.49296i) q^{66} +(2.22497 - 14.0479i) q^{67} +(4.12066 - 4.12066i) q^{68} +(-1.19856 - 0.159477i) q^{69} +(7.15246 - 9.84451i) q^{71} +(-2.93615 + 0.615636i) q^{72} +(-0.498794 + 0.254148i) q^{73} +2.17706 q^{74} +7.28665 q^{76} +(-1.67510 + 0.853507i) q^{77} +(-6.19197 - 4.26821i) q^{78} +(6.00067 - 8.25922i) q^{79} +(-6.72143 + 5.98518i) q^{81} +(-4.71623 + 4.71623i) q^{82} +(-0.742236 + 4.68629i) q^{83} +(-1.02130 - 0.488866i) q^{84} +(6.84269 + 2.22332i) q^{86} +(5.25448 - 1.85256i) q^{87} +(1.30562 - 2.56242i) q^{88} +(1.78693 - 5.49959i) q^{89} +(-0.877122 - 2.69950i) q^{91} +(0.689496 + 0.109205i) q^{92} +(-0.256256 - 10.3306i) q^{93} +(-1.78463 - 2.45633i) q^{94} +(1.70348 - 0.313291i) q^{96} +(-5.26300 + 0.833578i) q^{97} +(2.98392 + 5.85628i) q^{98} +(-0.427760 - 8.61700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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