LMFDB - Embedded newform 750.2.l.b.107.4

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			107.4
Character	$\chi$	$=$	750.107
Dual form			750.2.l.b.743.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(1.37558 - 1.05251i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.70348 + 0.313291i) q^{6} +(-0.462249 - 0.462249i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.784450 - 2.89562i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(1.37558 - 1.05251i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.70348 + 0.313291i) q^{6} +(-0.462249 - 0.462249i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.784450 - 2.89562i) q^{9} +(-2.73512 + 0.888693i) q^{11} +(1.66004 + 0.494220i) 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} +(-2.01354 + 2.22389i) q^{18} +(4.28299 - 5.89503i) q^{19} +(-1.12238 - 0.149340i) q^{21} +(2.84047 + 0.449885i) q^{22} +(-0.316926 + 0.622003i) q^{23} +(-1.25474 - 1.19400i) q^{24} +4.34197i q^{26} +(-1.96860 - 4.80881i) 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} +(-2.82702 + 4.10120i) q^{33} +(5.54227 + 1.80079i) q^{34} +(2.80370 - 1.06737i) q^{36} +(1.93977 - 0.988365i) q^{37} +(-6.49246 + 3.30807i) q^{38} +(-6.78343 - 3.24703i) q^{39} +(6.34331 + 2.06107i) q^{41} +(0.932251 + 0.642614i) 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} +(0.575917 + 1.63350i) q^{48} -6.57265i q^{49} +(-6.95800 + 7.31198i) q^{51} +(1.97121 - 3.86872i) q^{52} +(-2.23241 - 0.353579i) q^{53} +(-0.429121 + 5.17840i) q^{54} +(-0.384246 + 0.528869i) q^{56} +(-0.312969 - 12.6170i) 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} +(-1.70111 + 0.975888i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(4.38080 - 2.37076i) q^{66} +(2.22497 + 14.0479i) q^{67} +(-4.12066 - 4.12066i) q^{68} +(0.218706 + 1.18918i) q^{69} +(-7.15246 - 9.84451i) q^{71} +(-2.98269 - 0.321816i) q^{72} +(-0.498794 - 0.254148i) q^{73} -2.17706 q^{74} +7.28665 q^{76} +(1.67510 + 0.853507i) q^{77} +(4.56996 + 5.97273i) q^{78} +(6.00067 + 8.25922i) q^{79} +(-7.76928 - 4.54294i) q^{81} +(-4.71623 - 4.71623i) q^{82} +(0.742236 + 4.68629i) q^{83} +(-0.538901 - 0.995806i) q^{84} +(-6.84269 + 2.22332i) q^{86} +(1.58976 - 5.33987i) 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} +(-10.3306 + 0.256256i) q^{93} +(-1.78463 + 2.45633i) q^{94} +(0.228447 - 1.71692i) 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$-1$

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
$3$	1.37558	−	1.05251i	0.794192	−	0.607666i
$3$	1.37558	−	1.05251i	0.794192	−	0.607666i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	−1.70348	+	0.313291i	−0.695443	+	0.127901i
$7$	−0.462249	−	0.462249i	−0.174714	−	0.174714i	0.614333	−	0.789047i	$-0.289425\pi$
$7$	−0.462249	−	0.462249i	−0.174714	−	0.174714i	−0.789047	+	0.614333i	$0.789425\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	0.784450	−	2.89562i	0.261483	−	0.965208i
$10$		0			0
$11$	−2.73512	+	0.888693i	−0.824669	+	0.267951i	−0.690798	−	0.723048i	$-0.742741\pi$
$11$	−2.73512	+	0.888693i	−0.824669	+	0.267951i	−0.133871	+	0.990999i	$0.542741\pi$
$12$	1.66004	+	0.494220i	0.479213	+	0.142669i
$13$	−1.97121	−	3.86872i	−0.546716	−	1.07299i	−0.984741	−	0.174028i	$-0.944322\pi$
$13$	−1.97121	−	3.86872i	−0.546716	−	1.07299i	0.438025	−	0.898963i	$-0.355678\pi$
$14$	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	$-0.799811\pi$
$17$	−5.75574	+	0.911620i	−1.39597	+	0.221100i	−0.587305	+	0.809366i	$0.699811\pi$
$18$	−2.01354	+	2.22389i	−0.474595	+	0.524175i
$19$	4.28299	−	5.89503i	0.982585	−	1.35241i	0.0471595	−	0.998887i	$-0.484983\pi$
$19$	4.28299	−	5.89503i	0.982585	−	1.35241i	0.935425	−	0.353525i	$-0.115017\pi$
$20$		0			0
$21$	−1.12238	−	0.149340i	−0.244924	−	0.0325886i
$22$	2.84047	+	0.449885i	0.605589	+	0.0959159i
$23$	−0.316926	+	0.622003i	−0.0660837	+	0.129697i	−0.921685	−	0.387938i	$-0.873187\pi$
$23$	−0.316926	+	0.622003i	−0.0660837	+	0.129697i	0.855602	+	0.517635i	$0.173187\pi$
$24$	−1.25474	−	1.19400i	−0.256123	−	0.243724i
$25$		0			0
$26$			4.34197i			0.851530i
$27$	−1.96860	−	4.80881i	−0.378856	−	0.925455i
$28$	0.102264	−	0.645670i	0.0193261	−	0.122020i
$29$	2.60237	−	1.89073i	0.483247	−	0.351100i	−0.319334	−	0.947642i	$-0.603459\pi$
$29$	2.60237	−	1.89073i	0.483247	−	0.351100i	0.802582	+	0.596542i	$0.203459\pi$
$30$		0			0
$31$	−4.82678	−	3.50686i	−0.866915	−	0.629850i	0.0628427	−	0.998023i	$-0.479983\pi$
$31$	−4.82678	−	3.50686i	−0.866915	−	0.629850i	−0.929757	+	0.368173i	$0.879983\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−2.82702	+	4.10120i	−0.492121	+	0.713928i
$34$	5.54227	+	1.80079i	0.950491	+	0.308833i
$35$		0			0
$36$	2.80370	−	1.06737i	0.467283	−	0.177895i
$37$	1.93977	−	0.988365i	0.318897	−	0.162486i	−0.287213	−	0.957867i	$-0.592729\pi$
$37$	1.93977	−	0.988365i	0.318897	−	0.162486i	0.606110	+	0.795380i	$0.292729\pi$
$38$	−6.49246	+	3.30807i	−1.05322	+	0.536640i
$39$	−6.78343	−	3.24703i	−1.08622	−	0.519940i
$40$		0			0
$41$	6.34331	+	2.06107i	0.990659	+	0.321884i	0.759127	−	0.650943i	$-0.225626\pi$
$41$	6.34331	+	2.06107i	0.990659	+	0.321884i	0.231532	+	0.972827i	$0.425626\pi$
$42$	0.932251	+	0.642614i	0.143849	+	0.0991574i
$43$	5.08751	−	5.08751i	0.775838	−	0.775838i	−0.203282	−	0.979120i	$-0.565161\pi$
$43$	5.08751	−	5.08751i	0.775838	−	0.775838i	0.979120	+	0.203282i	$0.0651609\pi$
$44$	−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	−0.928528	−	0.371262i	$-0.878925\pi$
$47$	0.474965	−	2.99881i	0.0692808	−	0.437422i	0.997809	−	0.0661599i	$-0.0210747\pi$
$48$	0.575917	+	1.63350i	0.0831265	+	0.235775i
$49$		−	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	$-0.499613\pi$
$53$	−2.23241	−	0.353579i	−0.306645	−	0.0485679i	−0.307861	+	0.951431i	$0.599613\pi$
$54$	−0.429121	+	5.17840i	−0.0583960	+	0.704691i
$55$		0			0
$56$	−0.384246	+	0.528869i	−0.0513470	+	0.0706731i
$57$	−0.312969	−	12.6170i	−0.0414538	−	1.67116i
$58$	−3.17710	+	0.503203i	−0.417174	+	0.0660738i
$59$	−2.66341	+	8.19714i	−0.346747	+	1.06718i	0.613895	+	0.789388i	$0.289602\pi$
$59$	−2.66341	+	8.19714i	−0.346747	+	1.06718i	−0.960642	+	0.277790i	$0.910398\pi$
$60$		0			0
$61$	2.77903	+	8.55298i	0.355818	+	1.09510i	0.955533	+	0.294883i	$0.0952806\pi$
$61$	2.77903	+	8.55298i	0.355818	+	1.09510i	−0.599715	+	0.800214i	$0.704719\pi$
$62$	2.70861	+	5.31594i	0.343994	+	0.675126i
$63$	−1.70111	+	0.975888i	−0.214320	+	0.122950i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$		0			0
$66$	4.38080	−	2.37076i	0.539239	−	0.291820i
$67$	2.22497	+	14.0479i	0.271823	+	1.71622i	0.624964	+	0.780654i	$0.285114\pi$
$67$	2.22497	+	14.0479i	0.271823	+	1.71622i	−0.353141	+	0.935570i	$0.614886\pi$
$68$	−4.12066	−	4.12066i	−0.499703	−	0.499703i
$69$	0.218706	+	1.18918i	0.0263291	+	0.143161i
$70$		0			0
$71$	−7.15246	−	9.84451i	−0.848840	−	1.16833i	−0.984117	−	0.177521i	$-0.943192\pi$
$71$	−7.15246	−	9.84451i	−0.848840	−	1.16833i	0.135277	−	0.990808i	$-0.456808\pi$
$72$	−2.98269	−	0.321816i	−0.351513	−	0.0379264i
$73$	−0.498794	−	0.254148i	−0.0583794	−	0.0297458i	0.424557	−	0.905401i	$-0.360430\pi$
$73$	−0.498794	−	0.254148i	−0.0583794	−	0.0297458i	−0.482937	+	0.875655i	$0.660430\pi$
$74$	−2.17706			−0.253078
$75$		0			0
$76$	7.28665			0.835837
$77$	1.67510	+	0.853507i	0.190896	+	0.0972661i
$78$	4.56996	+	5.97273i	0.517446	+	0.676279i
$79$	6.00067	+	8.25922i	0.675128	+	0.929234i	0.999863	−	0.0165708i	$-0.00527490\pi$
$79$	6.00067	+	8.25922i	0.675128	+	0.929234i	−0.324734	+	0.945805i	$0.605275\pi$
$80$		0			0
$81$	−7.76928	−	4.54294i	−0.863253	−	0.504771i
$82$	−4.71623	−	4.71623i	−0.520820	−	0.520820i
$83$	0.742236	+	4.68629i	0.0814709	+	0.514387i	0.994349	+	0.106156i	$0.0338543\pi$
$83$	0.742236	+	4.68629i	0.0814709	+	0.514387i	−0.912879	+	0.408231i	$0.866146\pi$
$84$	−0.538901	−	0.995806i	−0.0587989	−	0.108651i
$85$		0			0
$86$	−6.84269	+	2.22332i	−0.737866	+	0.239747i
$87$	1.58976	−	5.33987i	0.170440	−	0.572494i
$88$	1.30562	+	2.56242i	0.139179	+	0.273155i
$89$	−1.78693	−	5.49959i	−0.189414	−	0.582956i	0.810583	−	0.585624i	$-0.199151\pi$
$89$	−1.78693	−	5.49959i	−0.189414	−	0.582956i	−0.999996	+	0.00266864i	$0.999151\pi$
$90$		0			0
$91$	−0.877122	+	2.69950i	−0.0919473	+	0.282985i
$92$	−0.689496	+	0.109205i	−0.0718849	+	0.0113854i
$93$	−10.3306	+	0.256256i	−1.07124	+	0.0265725i
$94$	−1.78463	+	2.45633i	−0.184070	+	0.253351i
$95$		0			0
$96$	0.228447	−	1.71692i	0.0233158	−	0.175232i
$97$	−5.26300	−	0.833578i	−0.534377	−	0.0846370i	−0.116587	−	0.993181i	$-0.537195\pi$
$97$	−5.26300	−	0.833578i	−0.534377	−	0.0846370i	−0.417790	+	0.908544i	$0.637195\pi$
$98$	−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	$-0.214833\pi$
$102$	9.51920	−	3.35615i	0.942541	−	0.332309i
$103$	0.958193	−	6.04979i	0.0944135	−	0.596104i	−0.894437	−	0.447194i	$-0.852424\pi$
$103$	0.958193	−	6.04979i	0.0944135	−	0.596104i	0.988851	−	0.148910i	$-0.0475765\pi$
$104$	−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	$-0.758956\pi$
$107$	−0.411529	+	0.411529i	−0.0397840	+	0.0397840i	0.686935	+	0.726719i	$0.258956\pi$
$108$	2.73330	−	4.41917i	0.263011	−	0.425235i
$109$	−11.0499	−	3.59033i	−1.05839	−	0.343891i	−0.272433	−	0.962175i	$-0.587828\pi$
$109$	−11.0499	−	3.59033i	−1.05839	−	0.343891i	−0.785955	+	0.618284i	$0.787828\pi$
$110$		0			0
$111$	1.62806	−	3.40121i	0.154528	−	0.322828i
$112$	0.582467	−	0.296782i	0.0550380	−	0.0280433i
$113$	12.6233	−	6.43189i	1.18750	−	0.605061i	0.255249	−	0.966875i	$-0.417842\pi$
$113$	12.6233	−	6.43189i	1.18750	−	0.605061i	0.932250	+	0.361814i	$0.117842\pi$
$114$	−5.44913	+	11.3839i	−0.510358	+	1.06620i
$115$		0			0
$116$	3.05927	+	0.994016i	0.284046	+	0.0922921i
$117$	−12.7487	+	2.67307i	−1.17862	+	0.247126i
$118$	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
$123$	10.8950	−	3.84123i	0.982372	−	0.346352i
$124$		−	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	0.390369	+	0.920658i	$0.372347\pi$
$127$	−6.58036	+	12.9147i	−0.583912	+	1.14599i	−0.974282	+	0.225334i	$0.927653\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	1.64364	−	12.3529i	0.144714	−	1.08762i
$130$		0			0
$131$	3.23088	−	4.44693i	0.282283	−	0.388530i	−0.644205	−	0.764853i	$-0.722812\pi$
$131$	3.23088	−	4.44693i	0.282283	−	0.388530i	0.926489	+	0.376323i	$0.122812\pi$
$132$	−4.97962	+	0.123522i	−0.433421	+	0.0107512i
$133$	−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	0.798858	+	0.601520i	$0.205438\pi$
$137$	9.55034	+	18.7436i	0.815941	+	1.60137i	0.0170834	+	0.999854i	$0.494562\pi$
$138$	0.345010	−	1.15886i	0.0293692	−	0.0986488i
$139$	11.0917	−	3.60392i	0.940788	−	0.305681i	0.201821	−	0.979422i	$-0.435314\pi$
$139$	11.0917	−	3.60392i	0.940788	−	0.305681i	0.738967	+	0.673742i	$0.235314\pi$
$140$		0			0
$141$	−2.50292	−	4.62502i	−0.210784	−	0.389497i
$142$	1.90357	+	12.0187i	0.159744	+	1.00858i
$143$	8.82961	+	8.82961i	0.738369	+	0.738369i
$144$	2.51149	+	1.64085i	0.209291	+	0.136738i
$145$		0			0
$146$	0.329048	+	0.452896i	0.0272322	+	0.0374819i
$147$	−6.91778	−	9.04122i	−0.570569	−	0.745707i
$148$	1.93977	+	0.988365i	0.159449	+	0.0812431i
$149$	10.0289			0.821602			0.410801	−	0.911725i	$-0.365249\pi$
$149$	10.0289			0.821602			0.410801	+	0.911725i	$0.365249\pi$
$150$		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
$153$	−1.87538	+	17.3816i	−0.151616	+	1.40522i
$154$	−1.10504	−	1.52096i	−0.0890469	−	0.122562i
$155$		0			0
$156$	−1.36030	−	7.39646i	−0.108911	−	0.592191i
$157$	6.42991	+	6.42991i	0.513163	+	0.513163i	0.915494	−	0.402331i	$-0.131800\pi$
$157$	6.42991	+	6.42991i	0.513163	+	0.513163i	−0.402331	+	0.915494i	$0.631800\pi$
$158$	−1.59703	−	10.0833i	−0.127053	−	0.802181i
$159$	−3.44301	+	1.86326i	−0.273049	+	0.147766i
$160$		0			0
$161$	0.434019	−	0.141021i	0.0342055	−	0.0111140i
$162$	4.86002	+	7.57497i	0.381840	+	0.595146i
$163$	4.21139	+	8.26532i	0.329862	+	0.647390i	0.995060	−	0.0992767i	$-0.0316529\pi$
$163$	4.21139	+	8.26532i	0.329862	+	0.647390i	−0.665198	+	0.746667i	$0.731653\pi$
$164$	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	$-0.612983\pi$
$167$	−5.01819	+	0.794803i	−0.388319	+	0.0615037i	−0.0407774	+	0.999168i	$0.512983\pi$
$168$	0.0280779	+	1.13193i	0.00216626	+	0.0873299i
$169$	−3.44013	+	4.73493i	−0.264625	+	0.364226i
$170$		0			0
$171$	−13.7100	−	17.0263i	−1.04843	−	1.30203i
$172$	7.10625	+	1.12552i	0.541846	+	0.0858200i
$173$	8.65954	−	16.9953i	0.658373	−	1.29213i	−0.284404	−	0.958705i	$-0.591796\pi$
$173$	8.65954	−	16.9953i	0.658373	−	1.29213i	0.942777	−	0.333425i	$-0.108204\pi$
$174$	−3.84073	+	4.03612i	−0.291165	+	0.305978i
$175$		0			0
$176$		−	2.87587i		−	0.216777i
$177$	4.96383	+	14.0791i	0.373104	+	1.05825i
$178$	−0.904600	+	5.71142i	−0.0678026	+	0.428089i
$179$	−3.24712	+	2.35917i	−0.242701	+	0.176332i	−0.702486	−	0.711698i	$-0.747927\pi$
$179$	−3.24712	+	2.35917i	−0.242701	+	0.176332i	0.459785	+	0.888030i	$0.347927\pi$
$180$		0			0
$181$	3.30770	+	2.40319i	0.245860	+	0.178628i	0.703890	−	0.710309i	$-0.251445\pi$
$181$	3.30770	+	2.40319i	0.245860	+	0.178628i	−0.458030	+	0.888937i	$0.651445\pi$
$182$	2.00707	−	2.00707i	0.148774	−	0.148774i
$183$	12.8249	+	8.84036i	0.948042	+	0.653498i
$184$	0.663923	+	0.215722i	0.0489451	+	0.0159032i
$185$		0			0
$186$	9.32099	+	4.46168i	0.683448	+	0.327146i
$187$	14.9325	−	7.60848i	1.09197	−	0.556387i
$188$	2.70527	−	1.37840i	0.197302	−	0.100530i
$189$	−1.31288	+	3.13285i	−0.0954983	+	0.227881i
$190$		0			0
$191$	11.5725	+	3.76012i	0.837354	+	0.272073i	0.696140	−	0.717906i	$-0.254899\pi$
$191$	11.5725	+	3.76012i	0.837354	+	0.272073i	0.141214	+	0.989979i	$0.454899\pi$
$192$	−0.983013	+	1.42607i	−0.0709428	+	0.102918i
$193$	9.01719	−	9.01719i	0.649071	−	0.649071i	−0.303697	−	0.952769i	$-0.598221\pi$
$193$	9.01719	−	9.01719i	0.649071	−	0.649071i	0.952769	+	0.303697i	$0.0982211\pi$
$194$	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	$-0.945350\pi$
$197$	0.0641446	−	0.404993i	0.00457012	−	0.0288546i	0.989868	+	0.141990i	$0.0453502\pi$
$198$	3.53090	−	7.87201i	0.250930	−	0.559439i
$199$			10.9949i			0.779406i	0.920941	+	0.389703i	$0.127422\pi$
$199$			10.9949i			0.779406i	−0.920941	+	0.389703i	$0.872578\pi$
$200$		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
$204$	−10.0053	−	1.33127i	−0.700513	−	0.0932076i
$205$		0			0
$206$	−3.60030	+	4.95539i	−0.250845	+	0.345259i
$207$	1.55247	+	1.40563i	0.107904	+	0.0976980i
$208$	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	0.868028	+	0.496515i	$0.165387\pi$
$211$	6.64735	+	20.4585i	0.457623	+	1.40842i	−0.410406	+	0.911903i	$0.634613\pi$
$212$	−1.02613	−	2.01389i	−0.0704747	−	0.138314i
$213$	−20.2002	−	6.01391i	−1.38410	−	0.412066i
$214$	0.553505	−	0.179845i	0.0378368	−	0.0122939i
$215$		0			0
$216$	−4.44165	+	2.69662i	−0.302216	+	0.183482i
$217$	0.610130	+	3.85221i	0.0414184	+	0.261505i
$218$	8.21555	+	8.21555i	0.556427	+	0.556427i
$219$	−0.953626	+	0.175384i	−0.0644400	+	0.0118513i
$220$		0			0
$221$	14.8726	+	20.4704i	1.00044	+	1.37699i
$222$	−2.99472	+	2.29138i	−0.200993	+	0.153787i
$223$	−5.65554	−	2.88164i	−0.378723	−	0.192969i	0.254258	−	0.967137i	$-0.418169\pi$
$223$	−5.65554	−	2.88164i	−0.378723	−	0.192969i	−0.632981	+	0.774167i	$0.718169\pi$
$224$	−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	$-0.194717\pi$
$227$	12.5844	+	6.41208i	0.835257	+	0.425584i	0.0165960	+	0.999862i	$0.494717\pi$
$228$	10.0234	−	7.66927i	0.663815	−	0.507910i
$229$	−8.94288	−	12.3088i	−0.590962	−	0.813389i	0.403882	−	0.914811i	$-0.367661\pi$
$229$	−8.94288	−	12.3088i	−0.590962	−	0.813389i	−0.994844	+	0.101422i	$0.967661\pi$
$230$		0			0
$231$	3.20256	−	0.588991i	0.210713	−	0.0387528i
$232$	−2.27455	−	2.27455i	−0.149332	−	0.149332i
$233$	−1.18798	−	7.50060i	−0.0778271	−	0.491381i	−0.995556	−	0.0941731i	$-0.969979\pi$
$233$	−1.18798	−	7.50060i	−0.0778271	−	0.491381i	0.917729	−	0.397208i	$-0.130021\pi$
$234$	12.5727	+	3.40606i	0.821904	+	0.222661i
$235$		0			0
$236$	−8.19714	+	2.66341i	−0.533589	+	0.173373i
$237$	16.9473	+	5.04547i	1.10085	+	0.327738i
$238$	−1.72949	−	3.39432i	−0.112106	−	0.220021i
$239$	3.85885	+	11.8763i	0.249608	+	0.768215i	0.994844	+	0.101414i	$0.0323367\pi$
$239$	3.85885	+	11.8763i	0.249608	+	0.768215i	−0.745236	+	0.666801i	$0.767663\pi$
$240$		0			0
$241$	7.01360	−	21.5856i	0.451786	−	1.39045i	−0.423082	−	0.906092i	$-0.639052\pi$
$241$	7.01360	−	21.5856i	0.451786	−	1.39045i	0.874868	−	0.484362i	$-0.160948\pi$
$242$	2.69576	−	0.426966i	0.173290	−	0.0274464i
$243$	−15.4688	+	1.92805i	−0.992322	+	0.123684i
$244$	−5.28603	+	7.27560i	−0.338403	+	0.465772i
$245$		0			0
$246$	−11.4514	−	1.52368i	−0.730116	−	0.0971465i
$247$	−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	$0.914553\pi$
$252$	−1.78940	−	0.802614i	−0.112721	−	0.0505599i
$253$	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	0.413942	−	0.910303i	$-0.364152\pi$
$257$	21.2293	−	21.2293i	1.32425	−	1.32425i	0.910303	−	0.413942i	$-0.135848\pi$
$258$	−7.07261	+	10.2604i	−0.440321	+	0.638782i
$259$	−1.35353	−	0.439788i	−0.0841042	−	0.0273271i
$260$		0			0
$261$	−3.43342	−	9.01866i	−0.212523	−	0.558241i
$262$	−4.89760	+	2.49545i	−0.302575	+	0.154169i
$263$	3.75527	−	1.91341i	0.231560	−	0.117986i	−0.334361	−	0.942445i	$-0.608521\pi$
$263$	3.75527	−	1.91341i	0.231560	−	0.117986i	0.565921	+	0.824459i	$0.308521\pi$
$264$	4.49296	+	2.15064i	0.276522	+	0.132363i
$265$		0			0
$266$	4.53028	+	1.47198i	0.277769	+	0.0902527i
$267$	−8.24643	−	5.68438i	−0.504673	−	0.347879i
$268$	−10.0572	+	10.0572i	−0.614340	+	0.614340i
$269$	−16.4085	−	11.9215i	−1.00044	−	0.726865i	−0.0382610	−	0.999268i	$-0.512182\pi$
$269$	−16.4085	−	11.9215i	−1.00044	−	0.726865i	−0.962183	+	0.272402i	$0.912182\pi$
$270$		0			0
$271$	−5.48031	+	3.98168i	−0.332905	+	0.241870i	−0.741662	−	0.670773i	$-0.765962\pi$
$271$	−5.48031	+	3.98168i	−0.332905	+	0.241870i	0.408757	+	0.912643i	$0.365962\pi$
$272$	0.911620	−	5.75574i	0.0552751	−	0.348993i
$273$	1.63470	+	4.63657i	0.0989365	+	0.280618i
$274$		−	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	−0.269742	−	0.962933i	$-0.586938\pi$
$277$	11.1150	−	21.8145i	0.667837	−	1.31070i	0.937579	−	0.347772i	$-0.113062\pi$
$278$	−11.5189	−	1.82442i	−0.690861	−	0.109422i
$279$	−13.9409	+	11.2256i	−0.834620	+	0.672058i
$280$		0			0
$281$	11.8968	−	16.3745i	0.709702	−	0.976820i	−0.290102	−	0.956996i	$-0.593689\pi$
$281$	11.8968	−	16.3745i	0.709702	−	0.976820i	0.999803	−	0.0198246i	$-0.00631077\pi$
$282$	0.130408	+	5.25722i	0.00776566	+	0.313063i
$283$	8.20158	−	1.29900i	0.487533	−	0.0772177i	0.0921715	−	0.995743i	$-0.470619\pi$
$283$	8.20158	−	1.29900i	0.487533	−	0.0772177i	0.395362	+	0.918525i	$0.370619\pi$
$284$	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
$288$	−1.49283	−	2.60221i	−0.0879656	−	0.153336i
$289$	16.1295	−	5.24081i	0.948797	−	0.308283i
$290$		0			0
$291$	−8.11704	+	4.39270i	−0.475829	+	0.257505i
$292$	−0.0875735	−	0.552918i	−0.00512485	−	0.0323571i
$293$	−1.20804	−	1.20804i	−0.0705747	−	0.0705747i	0.670938	−	0.741513i	$-0.265891\pi$
$293$	−1.20804	−	1.20804i	−0.0705747	−	0.0705747i	−0.741513	+	0.670938i	$0.765891\pi$
$294$	2.05916	+	11.1964i	0.120092	+	0.652987i
$295$		0			0
$296$	−1.27964	−	1.76128i	−0.0743778	−	0.102372i
$297$	9.65789	+	11.4032i	0.560408	+	0.661679i
$298$	−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
$303$	−13.2185	−	17.2759i	−0.759380	−	0.992475i
$304$	4.28299	+	5.89503i	0.245646	+	0.338103i
$305$		0			0
$306$	9.56205	−	14.6357i	0.546626	−	0.836667i
$307$	−4.52656	−	4.52656i	−0.258344	−	0.258344i	0.566036	−	0.824380i	$-0.308476\pi$
$307$	−4.52656	−	4.52656i	−0.258344	−	0.258344i	−0.824380	+	0.566036i	$0.808476\pi$
$308$	0.294098	+	1.85686i	0.0167578	+	0.105805i
$309$	−5.04939	−	9.33049i	−0.287250	−	0.530793i
$310$		0			0
$311$	−32.9364	+	10.7017i	−1.86765	+	0.606838i	−0.875274	+	0.483628i	$0.839319\pi$
$311$	−32.9364	+	10.7017i	−1.86765	+	0.606838i	−0.992381	+	0.123210i	$0.960681\pi$
$312$	−2.14589	+	7.20786i	−0.121487	+	0.408065i
$313$	11.8701	+	23.2965i	0.670940	+	1.31679i	0.935808	+	0.352509i	$0.114671\pi$
$313$	11.8701	+	23.2965i	0.670940	+	1.31679i	−0.264869	+	0.964285i	$0.585329\pi$
$314$	−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	$-0.675390\pi$
$317$	−13.4990	+	2.13804i	−0.758181	+	0.120084i	−0.234638	+	0.972083i	$0.575390\pi$
$318$	3.91365	−	0.0970796i	0.219466	−	0.00544396i
$319$	−5.43750	+	7.48407i	−0.304441	+	0.419028i
$320$		0			0
$321$	−0.132954	+	0.999229i	−0.00742075	+	0.0557715i
$322$	−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
$327$	−18.9789	+	6.69132i	−1.04953	+	0.370031i
$328$	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	0.327448	−	0.944869i	$-0.393811\pi$
$331$	−8.55071	−	6.21245i	−0.469989	−	0.341467i	−0.797437	+	0.603402i	$0.793811\pi$
$332$	−3.35501	+	3.35501i	−0.184130	+	0.184130i
$333$	−1.34028	−	6.39218i	−0.0734467	−	0.350289i
$334$	4.83207	+	1.57004i	0.264399	+	0.0859085i
$335$		0			0
$336$	0.488866	−	1.02130i	0.0266698	−	0.0557165i
$337$	28.0951	−	14.3152i	1.53044	−	0.779796i	0.532652	−	0.846334i	$-0.321195\pi$
$337$	28.0951	−	14.3152i	1.53044	−	0.779796i	0.997784	+	0.0665380i	$0.0211954\pi$
$338$	5.21479	−	2.65707i	0.283647	−	0.144526i
$339$	10.5947	−	22.1337i	0.575428	−	1.20214i
$340$		0			0
$341$	16.3183	+	5.30214i	0.883686	+	0.287127i
$342$	4.48593	+	21.3947i	0.242571	+	1.15689i
$343$	−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	0.870083	+	0.492905i	$0.164065\pi$
$347$	−2.04407	+	12.9057i	−0.109731	+	0.692816i	−0.979814	+	0.199911i	$0.935935\pi$
$348$	5.25448	−	1.85256i	0.281670	−	0.0993074i
$349$			30.4326i			1.62902i	0.580151	+	0.814509i	$0.302993\pi$
$349$			30.4326i			1.62902i	−0.580151	+	0.814509i	$0.697007\pi$
$350$		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	$-0.474706\pi$
$353$	−2.87776	−	0.455793i	−0.153168	−	0.0242594i	−0.232547	+	0.972585i	$0.574706\pi$
$354$	1.96898	−	14.7981i	0.104650	−	0.786511i
$355$		0			0
$356$	3.39893	−	4.67823i	0.180143	−	0.247946i
$357$	6.59628	−	0.163624i	0.349112	−	0.00865988i
$358$	3.96424	−	0.627874i	0.209517	−	0.0331842i
$359$	2.44510	−	7.52523i	0.129047	−	0.397167i	−0.865569	−	0.500789i	$-0.833043\pi$
$359$	2.44510	−	7.52523i	0.129047	−	0.397167i	0.994617	+	0.103622i	$0.0330433\pi$
$360$		0			0
$361$	−10.5360	−	32.4266i	−0.554528	−	1.70666i
$362$	−1.85616	−	3.64292i	−0.0975577	−	0.191468i
$363$	−1.34890	+	4.53086i	−0.0707991	+	0.237809i
$364$	−2.69950	+	0.877122i	−0.141492	+	0.0459737i
$365$		0			0
$366$	−7.41360	−	13.6992i	−0.387515	−	0.716068i
$367$	−3.44380	−	21.7433i	−0.179765	−	1.13499i	−0.898262	−	0.439460i	$-0.855170\pi$
$367$	−3.44380	−	21.7433i	−0.179765	−	1.13499i	0.718497	−	0.695530i	$-0.244830\pi$
$368$	−0.493624	−	0.493624i	−0.0257319	−	0.0257319i
$369$	10.9441	−	16.7510i	0.569726	−	0.872024i
$370$		0			0
$371$	0.868488	+	1.19537i	0.0450897	+	0.0620606i
$372$	−6.27950	−	8.20703i	−0.325577	−	0.425515i
$373$	−19.0344	−	9.69853i	−0.985566	−	0.502171i	−0.114545	−	0.993418i	$-0.536541\pi$
$373$	−19.0344	−	9.69853i	−0.985566	−	0.502171i	−0.871020	+	0.491247i	$0.836541\pi$
$374$	−16.7591			−0.866593
$375$		0			0
$376$	−3.03619			−0.156580
$377$	−12.4445	−	6.34081i	−0.640926	−	0.326568i
$378$	2.59207	−	2.19535i	0.133322	−	0.112917i
$379$	−0.581554	−	0.800441i	−0.0298724	−	0.0411159i	0.793820	−	0.608153i	$-0.208089\pi$
$379$	−0.581554	−	0.800441i	−0.0298724	−	0.0411159i	−0.823692	+	0.567038i	$0.808089\pi$
$380$		0			0
$381$	4.54100	+	24.6911i	0.232642	+	1.26496i
$382$	−8.60408	−	8.60408i	−0.440223	−	0.440223i
$383$	−1.97847	−	12.4916i	−0.101095	−	0.638289i	−0.985253	−	0.171102i	$-0.945267\pi$
$383$	−1.97847	−	12.4916i	−0.101095	−	0.638289i	0.884158	−	0.467187i	$-0.154733\pi$
$384$	1.52329	−	0.824362i	0.0777353	−	0.0420681i
$385$		0			0
$386$	−12.1281	+	3.94066i	−0.617304	+	0.200574i
$387$	−10.7406	−	18.7224i	−0.545976	−	0.951714i
$388$	−2.41914	−	4.74782i	−0.122813	−	0.241034i
$389$	−8.45598	−	26.0248i	−0.428735	−	1.31951i	−0.899372	−	0.437185i	$-0.855976\pi$
$389$	−8.45598	−	26.0248i	−0.428735	−	1.31951i	0.470636	−	0.882327i	$-0.344024\pi$
$390$		0			0
$391$	1.25712	−	3.86900i	0.0635751	−	0.195664i
$392$	−6.49173	+	1.02819i	−0.327882	+	0.0519314i
$393$	−0.236089	−	9.51764i	−0.0119091	−	0.480102i
$394$	−0.241016	+	0.331731i	−0.0121422	+	0.0167123i
$395$		0			0
$396$	−6.71987	+	5.41101i	−0.337686	+	0.271914i
$397$	−3.51235	−	0.556301i	−0.176280	−	0.0279199i	0.0676706	−	0.997708i	$-0.478443\pi$
$397$	−3.51235	−	0.556301i	−0.176280	−	0.0279199i	−0.243950	+	0.969788i	$0.578443\pi$
$398$	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	$-0.136473\pi$
$402$	−8.19128	−	23.2333i	−0.408544	−	1.15877i
$403$	−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
$408$	8.31043	+	5.72849i	0.411427	+	0.283603i
$409$	−4.09420	−	1.33029i	−0.202445	−	0.0657784i	0.206039	−	0.978544i	$-0.433943\pi$
$409$	−4.09420	−	1.33029i	−0.202445	−	0.0657784i	−0.408484	+	0.912765i	$0.633943\pi$
$410$		0			0
$411$	32.8651	+	15.7315i	1.62112	+	0.775979i
$412$	5.45760	−	2.78078i	0.268876	−	0.136999i
$413$	5.02028	−	2.55796i	0.247032	−	0.125869i
$414$	−0.745122	−	1.95723i	−0.0366207	−	0.0961928i
$415$		0			0
$416$	−4.12946	−	1.34174i	−0.202463	−	0.0657843i
$417$	11.4644	−	16.6316i	0.561415	−	0.814454i
$418$	14.8178	−	14.8178i	0.724761	−	0.724761i
$419$	−5.84455	−	4.24631i	−0.285525	−	0.207446i	0.435799	−	0.900044i	$-0.356466\pi$
$419$	−5.84455	−	4.24631i	−0.285525	−	0.207446i	−0.721324	+	0.692598i	$0.756466\pi$
$420$		0			0
$421$	−11.7630	+	8.54631i	−0.573293	+	0.416521i	−0.836300	−	0.548272i	$-0.815286\pi$
$421$	−11.7630	+	8.54631i	−0.573293	+	0.416521i	0.263007	+	0.964794i	$0.415286\pi$
$422$	3.36511	−	21.2464i	0.163811	−	1.03426i
$423$	−8.31084	−	3.72774i	−0.404087	−	0.181249i
$424$			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
$429$	21.4391	+	2.85260i	1.03509	+	0.137725i
$430$		0			0
$431$	−2.43967	+	3.35792i	−0.117515	+	0.161745i	−0.863722	−	0.503968i	$-0.831873\pi$
$431$	−2.43967	+	3.35792i	−0.117515	+	0.161745i	0.746207	+	0.665714i	$0.231873\pi$
$432$	5.18178	−	0.386242i	0.249308	−	0.0185831i
$433$	−28.8682	+	4.57227i	−1.38732	+	0.219729i	−0.805020	−	0.593248i	$-0.797846\pi$
$433$	−28.8682	+	4.57227i	−1.38732	+	0.219729i	−0.582296	+	0.812977i	$0.697846\pi$
$434$	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
$438$	0.929309	+	0.276669i	0.0444041	+	0.0132198i
$439$	10.7432	−	3.49067i	0.512744	−	0.166601i	−0.0412056	−	0.999151i	$-0.513120\pi$
$439$	10.7432	−	3.49067i	0.512744	−	0.166601i	0.553950	+	0.832550i	$0.313120\pi$
$440$		0			0
$441$	−19.0319	−	5.15592i	−0.906282	−	0.245520i
$442$	−3.95823	−	24.9913i	−0.188274	−	1.18871i
$443$	12.3286	+	12.3286i	0.585749	+	0.585749i	0.936477	−	0.350728i	$-0.114066\pi$
$443$	12.3286	+	12.3286i	0.585749	+	0.585749i	−0.350728	+	0.936477i	$0.614066\pi$
$444$	3.70858	−	0.682054i	0.176001	−	0.0323689i
$445$		0			0
$446$	3.73089	+	5.13513i	0.176663	+	0.243155i
$447$	13.7956	−	10.5555i	0.652510	−	0.499260i
$448$	0.582467	+	0.296782i	0.0275190	+	0.0140216i
$449$	−11.4060			−0.538284			−0.269142	−	0.963101i	$-0.586740\pi$
$449$	−11.4060			−0.538284			−0.269142	+	0.963101i	$0.586740\pi$
$450$		0			0
$451$	−19.1813			−0.903214
$452$	12.6233	+	6.43189i	0.593750	+	0.302531i
$453$	24.6470	−	18.8584i	1.15802	−	0.886043i
$454$	−8.30177	−	11.4264i	−0.389621	−	0.536268i
$455$		0			0
$456$	−12.4127	+	2.28285i	−0.581277	+	0.106904i
$457$	4.54539	+	4.54539i	0.212624	+	0.212624i	0.805381	−	0.592757i	$-0.201961\pi$
$457$	4.54539	+	4.54539i	0.212624	+	0.212624i	−0.592757	+	0.805381i	$0.701961\pi$
$458$	2.38008	+	15.0272i	0.111214	+	0.702176i
$459$	15.7145	+	25.8836i	0.733492	+	1.20814i
$460$		0			0
$461$	−18.3653	+	5.96726i	−0.855359	+	0.277923i	−0.703689	−	0.710508i	$-0.748465\pi$
$461$	−18.3653	+	5.96726i	−0.855359	+	0.277923i	−0.151670	+	0.988431i	$0.548465\pi$
$462$	−3.12090	−	0.929138i	−0.145197	−	0.0432274i
$463$	−2.03171	−	3.98746i	−0.0944216	−	0.185313i	0.838965	−	0.544186i	$-0.183161\pi$
$463$	−2.03171	−	3.98746i	−0.0944216	−	0.185313i	−0.933387	+	0.358873i	$0.883161\pi$
$464$	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	$-0.537006\pi$
$467$	1.74215	−	0.275929i	0.0806170	−	0.0127685i	0.196613	+	0.980481i	$0.437006\pi$
$468$	−9.65605	−	8.74271i	−0.446351	−	0.404132i
$469$	5.46513	−	7.52211i	0.252356	−	0.347339i
$470$		0			0
$471$	15.6124	+	2.07733i	0.719382	+	0.0957183i
$472$	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
$477$	−2.77505	+	6.18686i	−0.127061	+	0.283277i
$478$	1.95347	−	12.3338i	0.0893498	−	0.564133i
$479$	−13.7743	+	10.0076i	−0.629363	+	0.457259i	−0.856179	−	0.516679i	$-0.827168\pi$
$479$	−13.7743	+	10.0076i	−0.629363	+	0.457259i	0.226817	+	0.973937i	$0.427168\pi$
$480$		0			0
$481$	−7.64742	−	5.55617i	−0.348692	−	0.253340i
$482$	−16.0488	+	16.0488i	−0.731005	+	0.731005i
$483$	0.448602	−	0.650795i	0.0204121	−	0.0296122i
$484$	−2.59578	−	0.843419i	−0.117990	−	0.0383372i
$485$		0			0
$486$	14.6581	+	5.30477i	0.664904	+	0.240629i
$487$	−25.0891	+	12.7835i	−1.13690	+	0.579277i	−0.918043	−	0.396481i	$-0.870231\pi$
$487$	−25.0891	+	12.7835i	−1.13690	+	0.579277i	−0.218852	+	0.975758i	$0.570231\pi$
$488$	8.01294	−	4.08280i	0.362729	−	0.184820i
$489$	14.4924	+	6.93710i	0.655371	+	0.313706i
$490$		0			0
$491$	−8.69557	−	2.82536i	−0.392426	−	0.127507i	0.106156	−	0.994349i	$-0.466146\pi$
$491$	−8.69557	−	2.82536i	−0.392426	−	0.127507i	−0.498582	+	0.866843i	$0.666146\pi$
$492$	9.51156	+	6.55645i	0.428814	+	0.295588i
$493$	−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
$498$	−2.73256	−	7.75047i	−0.122449	−	0.347307i
$499$		−	12.9235i		−	0.578536i	−0.957248	−	0.289268i	$-0.906588\pi$
$499$		−	12.9235i		−	0.578536i	0.957248	−	0.289268i	$-0.0934119\pi$
$500$		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	$-0.617540\pi$
$503$	−22.2567	−	3.52512i	−0.992379	−	0.157177i	−0.631450	+	0.775416i	$0.717540\pi$
$504$	1.22999	+	1.52750i	0.0547879	+	0.0680404i
$505$		0			0
$506$	−1.18005	+	1.62420i	−0.0524595	+	0.0722044i
$507$	0.251380	+	10.1341i	0.0111642	+	0.450069i
$508$	−14.3160	+	2.26744i	−0.635171	+	0.100601i
$509$	1.15005	−	3.53949i	0.0509750	−	0.156885i	−0.922329	−	0.386407i	$-0.873716\pi$
$509$	1.15005	−	3.53949i	0.0509750	−	0.156885i	0.973304	+	0.229522i	$0.0737162\pi$
$510$		0			0
$511$	0.113087	+	0.348047i	0.00500268	+	0.0153967i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	−36.7795	−	8.99114i	−1.62386	−	0.396969i
$514$	−28.5533	+	9.27753i	−1.25943	+	0.409214i
$515$		0			0
$516$	10.9598	−	5.93114i	0.482480	−	0.261104i
$517$	1.36594	+	8.62420i	0.0600739	+	0.379292i
$518$	1.00634	+	1.00634i	0.0442162	+	0.0442162i
$519$	−5.97581	−	32.4927i	−0.262309	−	1.42627i
$520$		0			0
$521$	25.0327	+	34.4546i	1.09670	+	1.50948i	0.839683	+	0.543077i	$0.182741\pi$
$521$	25.0327	+	34.4546i	1.09670	+	1.50948i	0.257021	+	0.966406i	$0.417259\pi$
$522$	−1.03519	+	9.59442i	−0.0453089	+	0.419937i
$523$	19.8847	+	10.1317i	0.869495	+	0.443030i	0.831028	−	0.556230i	$-0.187753\pi$
$523$	19.8847	+	10.1317i	0.869495	+	0.443030i	0.0384667	+	0.999260i	$0.487753\pi$
$524$	5.49670			0.240125
$525$		0			0
$526$	−4.21464			−0.183767
$527$	30.9786	+	15.7844i	1.34945	+	0.687579i
$528$	−3.02688	−	3.95600i	−0.131728	−	0.172163i
$529$	13.2326	+	18.2131i	0.575331	+	0.791875i
$530$		0			0
$531$	21.6465	+	14.1425i	0.939380	+	0.613732i
$532$	−3.36825	−	3.36825i	−0.146032	−	0.146032i
$533$	−4.53032	−	28.6033i	−0.196230	−	1.23895i
$534$	4.76697	+	8.80862i	0.206287	+	0.381186i
$535$		0			0
$536$	13.5269	−	4.39515i	0.584272	−	0.189842i
$537$	−1.98363	+	6.66285i	−0.0855999	+	0.287523i
$538$	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	−0.937902	−	0.346902i	$-0.887234\pi$
$541$	0.576378	−	1.77391i	0.0247804	−	0.0762663i	0.962682	+	0.270635i	$0.0872338\pi$
$542$	6.69064	−	1.05969i	0.287387	−	0.0455177i
$543$	7.07940	−	0.175607i	0.303806	−	0.00753604i
$544$	−3.42531	+	4.71454i	−0.146859	+	0.202134i
$545$		0			0
$546$	0.648429	−	4.87335i	0.0277502	−	0.208560i
$547$	24.0199	+	3.80438i	1.02702	+	0.162663i	0.647138	−	0.762373i	$-0.275966\pi$
$547$	24.0199	+	3.80438i	1.02702	+	0.162663i	0.379878	+	0.925036i	$0.375966\pi$
$548$	−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
$552$	1.14033	−	0.402042i	0.0485357	−	0.0171121i
$553$	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	$-0.934515\pi$
$557$	−18.2820	+	18.2820i	−0.774632	+	0.774632i	0.204281	+	0.978912i	$0.434515\pi$
$558$	17.5177	−	3.67302i	0.741585	−	0.155491i
$559$	−29.7107	−	9.65360i	−1.25663	−	0.408304i
$560$		0			0
$561$	12.5328	−	26.1826i	0.529137	−	1.10543i
$562$	−18.0340	+	9.18876i	−0.760717	+	0.387604i
$563$	0.869364	−	0.442963i	0.0366393	−	0.0186687i	−0.435575	−	0.900153i	$-0.643455\pi$
$563$	0.869364	−	0.442963i	0.0366393	−	0.0186687i	0.472214	+	0.881484i	$0.343455\pi$
$564$	2.27053	−	4.74342i	0.0956068	−	0.199734i
$565$		0			0
$566$	−7.89740	−	2.56602i	−0.331952	−	0.107858i
$567$	1.49137	+	5.69131i	0.0626316	+	0.239012i
$568$	−8.60442	+	8.60442i	−0.361033	+	0.361033i
$569$	22.6112	+	16.4280i	0.947909	+	0.688696i	0.950311	−	0.311301i	$-0.100765\pi$
$569$	22.6112	+	16.4280i	0.947909	+	0.688696i	−0.00240243	+	0.999997i	$0.500765\pi$
$570$		0			0
$571$	−4.29121	+	3.11775i	−0.179582	+	0.130474i	−0.673945	−	0.738782i	$-0.735401\pi$
$571$	−4.29121	+	3.11775i	−0.179582	+	0.130474i	0.494363	+	0.869256i	$0.335401\pi$
$572$	−1.95339	+	12.3332i	−0.0816753	+	0.515678i
$573$	19.8764	−	7.00776i	0.830349	−	0.292754i
$574$			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	−0.800558	−	0.599255i	$-0.795463\pi$
$577$	3.71857	−	7.29810i	0.154806	−	0.303824i	0.955364	+	0.295432i	$0.0954634\pi$
$578$	−16.7508	−	2.65307i	−0.696742	−	0.110353i
$579$	2.91321	−	21.8946i	0.121069	−	0.909907i
$580$		0			0
$581$	1.82313	−	2.50933i	0.0756364	−	0.104105i
$582$	9.22658	−	0.228869i	0.382454	−	0.00948694i
$583$	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	−0.941917	−	0.335847i	$-0.890977\pi$
$587$	−15.9900	−	31.3821i	−0.659978	−	1.29528i	0.281939	−	0.959432i	$-0.409023\pi$
$588$	3.24833	−	10.9109i	0.133959	−	0.449958i
$589$	−41.3460	+	13.4341i	−1.70363	+	0.553544i
$590$		0			0
$591$	−0.338023	−	0.624614i	−0.0139044	−	0.0256932i
$592$	0.340567	+	2.15026i	0.0139972	+	0.0883750i
$593$	−2.52481	−	2.52481i	−0.103681	−	0.103681i	0.653363	−	0.757045i	$-0.273357\pi$
$593$	−2.52481	−	2.52481i	−0.103681	−	0.103681i	−0.757045	+	0.653363i	$0.773357\pi$
$594$	−3.42831	−	14.5449i	−0.140665	−	0.596784i
$595$		0			0
$596$	5.89486	+	8.11358i	0.241463	+	0.332345i
$597$	11.5722	+	15.1243i	0.473619	+	0.618998i
$598$	−2.70072	−	1.37608i	−0.110441	−	0.0562723i
$599$	39.4333			1.61120			0.805600	−	0.592460i	$-0.201843\pi$
$599$	39.4333			1.61120			0.805600	+	0.592460i	$0.201843\pi$
$600$		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
$603$	42.4228	+	4.57720i	1.72759	+	0.186398i
$604$	10.5317	+	14.4956i	0.428527	+	0.589817i
$605$		0			0
$606$	3.93462	+	21.3940i	0.159833	+	0.869072i
$607$	3.59236	+	3.59236i	0.145809	+	0.145809i	0.776243	−	0.630434i	$-0.217123\pi$
$607$	3.59236	+	3.59236i	0.145809	+	0.145809i	−0.630434	+	0.776243i	$0.717123\pi$
$608$	−1.13988	−	7.19694i	−0.0462284	−	0.291875i
$609$	−3.20321	+	1.73348i	−0.129801	+	0.0702443i
$610$		0			0
$611$	−12.5378	+	4.07379i	−0.507226	+	0.164808i
$612$	−15.1643	+	8.69942i	−0.612981	+	0.351653i
$613$	−6.96688	−	13.6733i	−0.281390	−	0.552258i	0.706445	−	0.707768i	$-0.250298\pi$
$613$	−6.96688	−	13.6733i	−0.281390	−	0.552258i	−0.987834	+	0.155510i	$0.950298\pi$
$614$	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	$-0.503738\pi$
$617$	7.10625	−	1.12552i	0.286087	−	0.0453117i	0.297829	+	0.954619i	$0.403738\pi$
$618$	0.263084	+	10.6059i	0.0105828	+	0.426632i
$619$	−7.42133	+	10.2146i	−0.298288	+	0.410559i	−0.931684	−	0.363269i	$-0.881661\pi$
$619$	−7.42133	+	10.2146i	−0.298288	+	0.410559i	0.633396	+	0.773828i	$0.281661\pi$
$620$		0			0
$621$	3.61499	+	0.299565i	0.145065	+	0.0120211i
$622$	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
$627$	12.0686	+	34.2308i	0.481975	+	1.36704i
$628$	−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	0.545288	−	0.838249i	$-0.316420\pi$
$631$	−2.09574	−	1.52265i	−0.0834301	−	0.0606155i	−0.628718	+	0.777633i	$0.716420\pi$
$632$	7.21882	−	7.21882i	0.287149	−	0.287149i
$633$	30.6767	+	21.1459i	1.21929	+	0.840473i
$634$	12.9984	+	4.22343i	0.516231	+	0.167734i
$635$		0			0
$636$	−3.53116	−	1.69026i	−0.140019	−	0.0670231i
$637$	−25.4278	+	12.9561i	−1.00748	+	0.513339i
$638$	8.24255	−	4.19979i	0.326326	−	0.166271i
$639$	−34.1167	+	12.9883i	−1.34964	+	0.513809i
$640$		0			0
$641$	3.49095	+	1.13428i	0.137884	+	0.0448012i	0.377146	−	0.926154i	$-0.376905\pi$
$641$	3.49095	+	1.13428i	0.137884	+	0.0448012i	−0.239262	+	0.970955i	$0.576905\pi$
$642$	0.572103	−	0.829960i	0.0225791	−	0.0327559i
$643$	−9.94703	+	9.94703i	−0.392273	+	0.392273i	−0.875497	−	0.483224i	$-0.839466\pi$
$643$	−9.94703	+	9.94703i	−0.392273	+	0.392273i	0.483224	+	0.875497i	$0.339466\pi$
$644$	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	$-0.974727\pi$
$647$	−0.617590	+	3.89931i	−0.0242800	+	0.153298i	0.972570	+	0.232612i	$0.0747271\pi$
$648$	−3.27163	+	8.38430i	−0.128522	+	0.329366i
$649$		−	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	$-0.358010\pi$
$653$	14.3859	+	2.27850i	0.562962	+	0.0891644i	0.131534	+	0.991312i	$0.458010\pi$
$654$	19.9481	+	2.65422i	0.780033	+	0.103788i
$655$		0			0
$656$	−3.92038	+	5.39594i	−0.153065	+	0.210676i
$657$	−1.12720	+	1.24495i	−0.0439761	+	0.0485703i
$658$	1.96038	−	0.310493i	0.0764235	−	0.0121043i
$659$	−4.21526	+	12.9732i	−0.164203	+	0.505365i	−0.998977	−	0.0452283i	$-0.985598\pi$
$659$	−4.21526	+	12.9732i	−0.164203	+	0.505365i	0.834774	+	0.550593i	$0.185598\pi$
$660$		0			0
$661$	−2.48143	−	7.63705i	−0.0965164	−	0.297047i	0.891130	−	0.453749i	$-0.149914\pi$
$661$	−2.48143	−	7.63705i	−0.0965164	−	0.297047i	−0.987646	+	0.156702i	$0.949914\pi$
$662$	4.79834	+	9.41728i	0.186493	+	0.366013i
$663$	42.0037	+	12.5051i	1.63129	+	0.485659i
$664$	4.51248	−	1.46619i	0.175118	−	0.0568994i
$665$		0			0
$666$	−1.70779	+	6.30395i	−0.0661757	+	0.244273i
$667$	0.351281	+	2.21790i	0.0136017	+	0.0858775i
$668$	−3.59263	−	3.59263i	−0.139003	−	0.139003i
$669$	−10.8126	+	1.98857i	−0.418040	+	0.0768828i
$670$		0			0
$671$	−15.2019	−	20.9237i	−0.586865	−	0.807750i
$672$	−0.899243	+	0.688045i	−0.0346891	+	0.0265419i
$673$	24.0809	+	12.2698i	0.928251	+	0.472967i	0.851660	−	0.524095i	$-0.175596\pi$
$673$	24.0809	+	12.2698i	0.928251	+	0.472967i	0.0765912	+	0.997063i	$0.475596\pi$
$674$	−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	$-0.465528\pi$
$677$	−16.4613	−	8.38747i	−0.632660	−	0.322357i	−0.740746	+	0.671785i	$0.765528\pi$
$678$	−19.4885	+	14.9114i	−0.748451	+	0.572668i
$679$	2.04750	+	2.81814i	0.0785757	+	0.108150i
$680$		0			0
$681$	24.0596	−	4.42487i	0.921968	−	0.169561i
$682$	−12.1326	−	12.1326i	−0.464581	−	0.464581i
$683$	−5.94046	−	37.5066i	−0.227305	−	1.43515i	−0.792338	−	0.610082i	$-0.791137\pi$
$683$	−5.94046	−	37.5066i	−0.227305	−	1.43515i	0.565033	−	0.825068i	$-0.308863\pi$
$684$	5.71601	−	21.0994i	0.218557	−	0.806756i
$685$		0			0
$686$	8.43843	−	2.74181i	0.322181	−	0.104683i
$687$	−25.2568	−	7.51932i	−0.963607	−	0.286880i
$688$	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	−0.988742	−	0.149633i	$-0.952191\pi$
$691$	−2.65184	+	8.16151i	−0.100881	+	0.310479i	0.887861	+	0.460112i	$0.152191\pi$
$692$	18.8394	−	2.98388i	0.716168	−	0.113430i
$693$	3.78547	−	4.18093i	0.143798	−	0.158820i
$694$	7.68036	−	10.5711i	0.291542	−	0.401274i
$695$		0			0
$696$	−5.52282	−	0.734846i	−0.209342	−	0.0278543i
$697$	−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	$-0.456131\pi$
$702$	20.8797	−	8.54758i	0.788053	−	0.322608i
$703$	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
$708$	−8.47258	+	12.2913i	−0.318419	+	0.461936i
$709$	5.89184	+	1.91438i	0.221273	+	0.0718959i	0.417555	−	0.908652i	$-0.362887\pi$
$709$	5.89184	+	1.91438i	0.221273	+	0.0718959i	−0.196283	+	0.980547i	$0.562887\pi$
$710$		0			0
$711$	28.6228	−	10.8967i	1.07344	−	0.408660i
$712$	−5.15235	+	2.62525i	−0.193092	+	0.0983855i
$713$	3.71101	−	1.89085i	0.138978	−	0.0708130i
$714$	−5.95161	−	2.84886i	−0.222734	−	0.106616i
$715$		0			0
$716$	−3.81721	−	1.24029i	−0.142656	−	0.0463517i
$717$	17.8081	+	12.2754i	0.665055	+	0.458432i
$718$	−5.59498	+	5.59498i	−0.208803	+	0.208803i
$719$	3.26095	+	2.36922i	0.121613	+	0.0883570i	0.646929	−	0.762550i	$-0.276053\pi$
$719$	3.26095	+	2.36922i	0.121613	+	0.0883570i	−0.525316	+	0.850907i	$0.676053\pi$
$720$		0			0
$721$	−3.23943	+	2.35359i	−0.120643	+	0.0876521i
$722$	−5.33368	+	33.6756i	−0.198499	+	1.25327i
$723$	−13.0713	−	37.0747i	−0.486127	−	1.37882i
$724$			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	−0.478844	−	0.877900i	$-0.658944\pi$
$727$	13.8279	−	27.1388i	0.512850	−	1.00652i	0.991693	−	0.128624i	$-0.0410560\pi$
$728$	2.80348	+	0.444028i	0.103904	+	0.0164568i
$729$	−19.2493	+	18.9332i	−0.712936	+	0.701229i
$730$		0			0
$731$	−24.6445	+	33.9203i	−0.911510	+	1.25459i
$732$	0.386264	+	15.5718i	0.0142767	+	0.575549i
$733$	13.6402	−	2.16039i	0.503812	−	0.0797960i	0.100645	−	0.994922i	$-0.467909\pi$
$733$	13.6402	−	2.16039i	0.503812	−	0.0797960i	0.403167	+	0.915126i	$0.367909\pi$
$734$	−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
$738$	−17.3561	+	9.95678i	−0.638885	+	0.366514i
$739$	−25.2888	+	8.21683i	−0.930264	+	0.302261i	−0.734671	−	0.678424i	$-0.762663\pi$
$739$	−25.2888	+	8.21683i	−0.930264	+	0.302261i	−0.195593	+	0.980685i	$0.562663\pi$
$740$		0			0
$741$	−48.1946	+	26.0815i	−1.77047	+	0.958129i
$742$	−0.231141	−	1.45937i	−0.00848547	−	0.0535751i
$743$	19.0708	+	19.0708i	0.699641	+	0.699641i	0.964333	−	0.264692i	$-0.0852703\pi$
$743$	19.0708	+	19.0708i	0.699641	+	0.699641i	−0.264692	+	0.964333i	$0.585270\pi$
$744$	1.86917	+	10.1633i	0.0685270	+	0.372606i
$745$		0			0
$746$	12.5568	+	17.2829i	0.459736	+	0.632772i
$747$	14.1520	+	1.52692i	0.517794	+	0.0558672i
$748$	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
$753$	8.84528	+	11.5604i	0.322340	+	0.421283i
$754$	8.20949	+	11.2994i	0.298972	+	0.411500i
$755$		0			0
$756$	−3.30622	+	0.779295i	−0.120246	+	0.0283427i
$757$	14.2550	+	14.2550i	0.518108	+	0.518108i	0.916998	−	0.398891i	$-0.130605\pi$
$757$	14.2550	+	14.2550i	0.518108	+	0.518108i	−0.398891	+	0.916998i	$0.630605\pi$
$758$	0.154776	+	0.977218i	0.00562172	+	0.0354942i
$759$	−1.65500	−	3.05819i	−0.0600729	−	0.111005i
$760$		0			0
$761$	20.4602	−	6.64792i	0.741681	−	0.240987i	0.0862835	−	0.996271i	$-0.472501\pi$
$761$	20.4602	−	6.64792i	0.741681	−	0.240987i	0.655398	+	0.755284i	$0.272501\pi$
$762$	7.16346	−	24.0615i	0.259505	−	0.871656i
$763$	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
$768$	−1.73152	+	0.0429510i	−0.0624808	+	0.00154986i
$769$	5.35630	−	7.37231i	0.193153	−	0.265852i	−0.701446	−	0.712723i	$-0.747462\pi$
$769$	5.35630	−	7.37231i	0.193153	−	0.265852i	0.894599	+	0.446871i	$0.147462\pi$
$770$		0			0
$771$	6.85860	−	51.5466i	0.247006	−	1.85641i
$772$	12.5952	+	1.99489i	0.453312	+	0.0717976i
$773$	20.4388	−	40.1134i	0.735132	−	1.44278i	−0.155397	−	0.987852i	$-0.549666\pi$
$773$	20.4388	−	40.1134i	0.735132	−	1.44278i	0.890529	−	0.454926i	$-0.150334\pi$
$774$	1.07017	+	21.5579i	0.0384663	+	0.774884i
$775$		0			0
$776$			5.32861i			0.191286i
$777$	−2.32477	+	0.819637i	−0.0834007	+	0.0294043i
$778$	−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
$783$	−14.2152	−	8.79220i	−0.508009	−	0.314208i
$784$	6.25096	+	2.03106i	0.223249	+	0.0725379i
$785$		0			0
$786$	−4.11056	+	8.58746i	−0.146619	+	0.306305i
$787$	−22.6577	+	11.5447i	−0.807659	+	0.411523i	−0.808514	−	0.588477i	$-0.799728\pi$
$787$	−22.6577	+	11.5447i	−0.807659	+	0.411523i	0.000855029		1.00000i	$0.499728\pi$
$788$	0.365350	−	0.186155i	0.0130150	−	0.00663150i
$789$	3.15181	−	6.58451i	0.112207	−	0.234415i
$790$		0			0
$791$	−8.80823	−	2.86197i	−0.313185	−	0.101760i
$792$	8.44400	−	1.77049i	0.300044	−	0.0629116i
$793$	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	0.938460	+	0.345389i	$0.112253\pi$
$797$	−1.71644	+	10.8372i	−0.0607996	+	0.383874i	−0.999259	+	0.0384845i	$0.987747\pi$
$798$	7.78104	−	2.74334i	0.275446	−	0.0971131i
$799$			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
$804$	−3.24920	+	24.4198i	−0.114591	+	0.861218i
$805$		0			0
$806$	15.2267	−	20.9577i	0.536337	−	0.738204i
$807$	−35.1187	+	0.871135i	−1.23624	+	0.0306654i
$808$	−12.4044	+	1.96466i	−0.436384	+	0.0691165i
$809$	13.0207	−	40.0735i	0.457782	−	1.40891i	−0.410056	−	0.912060i	$-0.634491\pi$
$809$	13.0207	−	40.0735i	0.457782	−	1.40891i	0.867838	−	0.496848i	$-0.165509\pi$
$810$		0			0
$811$	4.38556	+	13.4974i	0.153998	+	0.473957i	0.998058	−	0.0622916i	$-0.0198409\pi$
$811$	4.38556	+	13.4974i	0.153998	+	0.473957i	−0.844060	+	0.536249i	$0.819841\pi$
$812$	−0.954659	−	1.87362i	−0.0335020	−	0.0657513i
$813$	−3.34786	+	11.2452i	−0.117415	+	0.394386i
$814$	5.95451	−	1.93474i	0.208706	−	0.0678126i
$815$		0			0
$816$	−4.80396	−	8.87698i	−0.168172	−	0.310756i
$817$	−8.20127	−	51.7808i	−0.286926	−	1.81158i
$818$	3.04402	+	3.04402i	0.106432	+	0.106432i
$819$	7.12869	+	4.65744i	0.249097	+	0.162744i
$820$		0			0
$821$	−9.28341	−	12.7775i	−0.323993	−	0.445939i	0.615688	−	0.787990i	$-0.288878\pi$
$821$	−9.28341	−	12.7775i	−0.323993	−	0.445939i	−0.939681	+	0.342052i	$0.888878\pi$
$822$	−22.1410	−	28.9373i	−0.772258	−	1.00931i
$823$	−21.3898	−	10.8987i	−0.745603	−	0.379904i	0.0395404	−	0.999218i	$-0.487411\pi$
$823$	−21.3898	−	10.8987i	−0.745603	−	0.379904i	−0.785143	+	0.619314i	$0.787411\pi$
$824$	−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	$-0.503201\pi$
$827$	−23.7234	−	12.0877i	−0.824944	−	0.420330i	−0.814887	+	0.579619i	$0.803201\pi$
$828$	−0.224657	+	2.08219i	−0.00780737	+	0.0723610i
$829$	−9.16301	−	12.6118i	−0.318245	−	0.438026i	0.619686	−	0.784850i	$-0.287260\pi$
$829$	−9.16301	−	12.6118i	−0.318245	−	0.438026i	−0.937930	+	0.346824i	$0.887260\pi$
$830$		0			0
$831$	−7.67030	−	41.7062i	−0.266080	−	1.44677i
$832$	3.07024	+	3.07024i	0.106441	+	0.106441i
$833$	5.99176	+	37.8305i	0.207602	+	1.31075i
$834$	−17.7655	+	9.61415i	−0.615168	+	0.332911i
$835$		0			0
$836$	−19.9298	+	6.47560i	−0.689288	+	0.223963i
$837$	−7.36184	+	30.1146i	−0.254462	+	1.04091i
$838$	3.27974	+	6.43686i	0.113297	+	0.222358i
$839$	−4.03893	−	12.4305i	−0.139439	−	0.429150i	0.856815	−	0.515624i	$-0.172440\pi$
$839$	−4.03893	−	12.4305i	−0.139439	−	0.429150i	−0.996254	+	0.0864743i	$0.972440\pi$
$840$		0			0
$841$	−5.76404	+	17.7399i	−0.198760	+	0.611720i
$842$	14.3608	−	2.27453i	0.494907	−	0.0783856i
$843$	−0.869329	−	35.0459i	−0.0299413	−	1.20705i
$844$	−12.6440	+	17.4030i	−0.435225	+	0.599036i
$845$		0			0
$846$	5.71266	+	7.09448i	0.196405	+	0.243913i
$847$	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
$852$	−7.00804	−	19.8772i	−0.240092	−	0.680982i
$853$	−6.36392	+	40.1802i	−0.217897	+	1.37574i	0.599825	+	0.800131i	$0.295237\pi$
$853$	−6.36392	+	40.1802i	−0.217897	+	1.37574i	−0.817722	+	0.575614i	$0.804763\pi$
$854$	−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	$-0.552265\pi$
$857$	24.0957	−	24.0957i	0.823093	−	0.823093i	0.986550	+	0.163457i	$0.0522646\pi$
$858$	−17.8073	−	12.2748i	−0.607931	−	0.419056i
$859$	−17.4179	−	5.65942i	−0.594291	−	0.193097i	−0.00359858	−	0.999994i	$-0.501145\pi$
$859$	−17.4179	−	5.65942i	−0.594291	−	0.193097i	−0.590693	+	0.806897i	$0.701145\pi$
$860$		0			0
$861$	−6.81182	−	3.26061i	−0.232146	−	0.111121i
$862$	3.69822	−	1.88434i	0.125962	−	0.0641808i
$863$	−7.06405	+	3.59931i	−0.240463	+	0.122522i	−0.570070	−	0.821596i	$-0.693084\pi$
$863$	−7.06405	+	3.59931i	−0.240463	+	0.122522i	0.329607	+	0.944118i	$0.393084\pi$
$864$	−4.79235	−	2.00833i	−0.163039	−	0.0683249i
$865$		0			0
$866$	27.7975	+	9.03196i	0.944598	+	0.306918i
$867$	16.6715	−	24.1857i	0.566194	−	0.821388i
$868$	−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
$873$	−6.54229	+	14.5858i	−0.221423	+	0.493654i
$874$		−	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	0.0467683	+	0.998906i	$0.485108\pi$
$877$	−23.3612	+	45.8490i	−0.788853	+	1.54821i	−0.835621	+	0.549306i	$0.814892\pi$
$878$	−11.1570	−	1.76709i	−0.376530	−	0.0596365i
$879$	−2.93324	−	0.390286i	−0.0989358	−	0.0131640i
$880$		0			0
$881$	−1.69050	+	2.32677i	−0.0569544	+	0.0783909i	−0.836544	−	0.547900i	$-0.815428\pi$
$881$	−1.69050	+	2.32677i	−0.0569544	+	0.0783909i	0.779590	+	0.626290i	$0.215428\pi$
$882$	14.6168	+	13.2343i	0.492175	+	0.445621i
$883$	36.4793	−	5.77775i	1.22763	−	0.194437i	0.491255	−	0.871016i	$-0.336538\pi$
$883$	36.4793	−	5.77775i	1.22763	−	0.194437i	0.736370	+	0.676579i	$0.236538\pi$
$884$	−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	$-0.119647\pi$
$887$	2.57475	+	5.05323i	0.0864515	+	0.169671i	−0.843733	+	0.536763i	$0.819647\pi$
$888$	−3.61402	−	1.07595i	−0.121278	−	0.0361064i
$889$	9.01156	−	2.92803i	0.302238	−	0.0982031i
$890$		0			0
$891$	25.2872	+	5.52097i	0.847152	+	0.184960i
$892$	−0.992947	−	6.26922i	−0.0332463	−	0.209909i
$893$	−15.6438	−	15.6438i	−0.523500	−	0.523500i
$894$	−17.0841	+	3.14198i	−0.571378	+	0.105083i
$895$		0			0
$896$	−0.384246	−	0.528869i	−0.0128368	−	0.0176683i
$897$	4.16951	−	3.19025i	0.139216	−	0.106519i
$898$	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
$903$	−6.46990	+	4.95036i	−0.215305	+	0.164738i
$904$	−8.32742	−	11.4617i	−0.276966	−	0.381211i
$905$		0			0
$906$	−30.5222	+	5.61341i	−1.01403	+	0.186493i
$907$	23.6056	+	23.6056i	0.783811	+	0.783811i	0.980472	−	0.196661i	$-0.0630097\pi$
$907$	23.6056	+	23.6056i	0.783811	+	0.783811i	−0.196661	+	0.980472i	$0.563010\pi$
$908$	2.20945	+	13.9499i	0.0733232	+	0.462944i
$909$	−36.3661	−	9.85190i	−1.20619	−	0.326767i
$910$		0			0
$911$	40.8162	−	13.2620i	1.35230	−	0.439390i	0.458837	−	0.888521i	$-0.348266\pi$
$911$	40.8162	−	13.2620i	1.35230	−	0.439390i	0.893466	+	0.449131i	$0.148266\pi$
$912$	12.0962	+	3.60121i	0.400544	+	0.119248i
$913$	−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
$918$	−2.25082	−	30.1967i	−0.0742882	−	0.996641i
$919$	7.08527	−	9.75204i	0.233722	−	0.321690i	−0.676006	−	0.736896i	$-0.736291\pi$
$919$	7.08527	−	9.75204i	0.233722	−	0.321690i	0.909727	+	0.415206i	$0.136291\pi$
$920$		0			0
$921$	−10.9909	−	1.46241i	−0.362162	−	0.0481880i
$922$	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
$927$	−16.7663	−	7.52032i	−0.550676	−	0.247000i
$928$	0.503203	−	3.17710i	0.0165185	−	0.104293i
$929$	−15.3269	+	11.1356i	−0.502859	+	0.365349i	−0.810108	−	0.586280i	$-0.800592\pi$
$929$	−15.3269	+	11.1356i	−0.502859	+	0.365349i	0.307249	+	0.951629i	$0.400592\pi$
$930$		0			0
$931$	−38.7460	−	28.1506i	−1.26985	−	0.922598i
$932$	5.36984	−	5.36984i	0.175895	−	0.175895i
$933$	−34.0431	+	49.3870i	−1.11452	+	1.61686i
$934$	−1.67753	−	0.545064i	−0.0548906	−	0.0178350i
$935$		0			0
$936$	4.63450	+	12.1736i	0.151483	+	0.397905i
$937$	−34.7728	+	17.7176i	−1.13598	+	0.578809i	−0.917778	−	0.397095i	$-0.870018\pi$
$937$	−34.7728	+	17.7176i	−1.13598	+	0.578809i	−0.218199	+	0.975904i	$0.570018\pi$
$938$	−8.28444	+	4.22113i	−0.270497	+	0.137825i
$939$	40.8481	+	19.5528i	1.33303	+	0.638080i
$940$		0			0
$941$	−26.0266	−	8.45656i	−0.848443	−	0.275676i	−0.147649	−	0.989040i	$-0.547171\pi$
$941$	−26.0266	−	8.45656i	−0.848443	−	0.275676i	−0.700794	+	0.713364i	$0.747171\pi$
$942$	−12.9677	−	8.93880i	−0.422510	−	0.291242i
$943$	−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	0.790615	+	0.612313i	$0.209761\pi$
$947$	−4.63200	+	29.2453i	−0.150520	+	0.950344i	−0.941135	+	0.338031i	$0.890239\pi$
$948$	5.87951	+	16.6763i	0.190958	+	0.541622i
$949$			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	$-0.494515\pi$
$953$	−8.50033	−	1.34632i	−0.275353	−	0.0436116i	−0.292584	+	0.956240i	$0.594515\pi$
$954$	5.28136	−	4.25269i	0.170990	−	0.137686i
$955$		0			0
$956$	−7.33996	+	10.1026i	−0.237391	+	0.326741i
$957$	0.397333	+	16.0180i	0.0128439	+	0.517788i
$958$	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
$963$	0.868809	+	1.51446i	0.0279970	+	0.0488027i
$964$	21.5856	−	7.01360i	0.695227	−	0.225893i
$965$		0			0
$966$	−0.695162	+	0.376201i	−0.0223665	+	0.0121041i
$967$	4.89692	+	30.9179i	0.157474	+	0.994254i	0.932197	+	0.361952i	$0.117890\pi$
$967$	4.89692	+	30.9179i	0.157474	+	0.994254i	−0.774722	+	0.632302i	$0.782110\pi$
$968$	1.92995	+	1.92995i	0.0620309	+	0.0620309i
$969$	13.3033	+	72.3347i	0.427362	+	2.32373i
$970$		0			0
$971$	16.9971	+	23.3945i	0.545463	+	0.750765i	0.989388	−	0.145299i	$-0.0464143\pi$
$971$	16.9971	+	23.3945i	0.545463	+	0.750765i	−0.443925	+	0.896064i	$0.646414\pi$
$972$	−10.6521	−	11.3812i	−0.341667	−	0.365053i
$973$	−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	$-0.360404\pi$
$977$	−1.82021	−	0.927445i	−0.0582338	−	0.0296716i	−0.482865	+	0.875695i	$0.660404\pi$
$978$	−9.76348	−	12.7604i	−0.312202	−	0.408034i
$979$	9.77490	+	13.4540i	0.312407	+	0.429992i
$980$		0			0
$981$	−19.0643	+	29.1799i	−0.608677	+	0.931643i
$982$	6.46512	+	6.46512i	0.206310	+	0.206310i
$983$	4.54655	+	28.7058i	0.145012	+	0.915572i	0.947698	+	0.319169i	$0.103404\pi$
$983$	4.54655	+	28.7058i	0.145012	+	0.915572i	−0.802685	+	0.596403i	$0.796596\pi$
$984$	−5.49829	−	10.1600i	−0.175279	−	0.323889i
$985$		0			0
$986$	17.8278	−	5.79262i	0.567754	−	0.184474i
$987$	−0.980934	+	3.29488i	−0.0312235	+	0.104877i
$988$	−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	−0.995991	−	0.0894508i	$-0.971489\pi$
$991$	−4.33291	+	13.3353i	−0.137640	+	0.423611i	0.858352	+	0.513062i	$0.171489\pi$
$992$	−5.89277	+	0.933323i	−0.187096	+	0.0296330i
$993$	−18.3009	+	0.453961i	−0.580760	+	0.0144060i
$994$	4.67569	−	6.43554i	0.148304	−	0.204123i
$995$		0			0
$996$	−1.08391	+	8.14628i	−0.0343451	+	0.258125i
$997$	35.5407	+	5.62909i	1.12558	+	0.178275i	0.691347	−	0.722523i	$-0.257018\pi$
$997$	35.5407	+	5.62909i	1.12558	+	0.178275i	0.434238	+	0.900798i	$0.357018\pi$
$998$	−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.107.4		80
3.2	odd	2	inner	750.2.l.b.107.7		80
5.2	odd	4		750.2.l.c.143.7		80
5.3	odd	4		750.2.l.a.143.4		80
5.4	even	2		150.2.l.a.17.7	yes	80
15.2	even	4		750.2.l.c.143.2		80
15.8	even	4		750.2.l.a.143.9		80
15.14	odd	2		150.2.l.a.17.4	✓	80
25.3	odd	20	inner	750.2.l.b.743.7		80
25.4	even	10		750.2.l.c.257.2		80
25.21	even	5		750.2.l.a.257.9		80
25.22	odd	20		150.2.l.a.53.4	yes	80
75.29	odd	10		750.2.l.c.257.7		80
75.47	even	20		150.2.l.a.53.7	yes	80
75.53	even	20	inner	750.2.l.b.743.4		80
75.71	odd	10		750.2.l.a.257.4		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.4	✓	80	15.14	odd	2
150.2.l.a.17.7	yes	80	5.4	even	2
150.2.l.a.53.4	yes	80	25.22	odd	20
150.2.l.a.53.7	yes	80	75.47	even	20
750.2.l.a.143.4		80	5.3	odd	4
750.2.l.a.143.9		80	15.8	even	4
750.2.l.a.257.4		80	75.71	odd	10
750.2.l.a.257.9		80	25.21	even	5
750.2.l.b.107.4		80	1.1	even	1	trivial
750.2.l.b.107.7		80	3.2	odd	2	inner
750.2.l.b.743.4		80	75.53	even	20	inner
750.2.l.b.743.7		80	25.3	odd	20	inner
750.2.l.c.143.2		80	15.2	even	4
750.2.l.c.143.7		80	5.2	odd	4
750.2.l.c.257.2		80	25.4	even	10
750.2.l.c.257.7		80	75.29	odd	10

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)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(1.37558 - 1.05251i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.70348 + 0.313291i) q^{6} +(-0.462249 - 0.462249i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.784450 - 2.89562i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(1.37558 - 1.05251i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-1.70348 + 0.313291i) q^{6} +(-0.462249 - 0.462249i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.784450 - 2.89562i) q^{9} +(-2.73512 + 0.888693i) q^{11} +(1.66004 + 0.494220i) 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} +(-2.01354 + 2.22389i) q^{18} +(4.28299 - 5.89503i) q^{19} +(-1.12238 - 0.149340i) q^{21} +(2.84047 + 0.449885i) q^{22} +(-0.316926 + 0.622003i) q^{23} +(-1.25474 - 1.19400i) q^{24} +4.34197i q^{26} +(-1.96860 - 4.80881i) 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} +(-2.82702 + 4.10120i) q^{33} +(5.54227 + 1.80079i) q^{34} +(2.80370 - 1.06737i) q^{36} +(1.93977 - 0.988365i) q^{37} +(-6.49246 + 3.30807i) q^{38} +(-6.78343 - 3.24703i) q^{39} +(6.34331 + 2.06107i) q^{41} +(0.932251 + 0.642614i) 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} +(0.575917 + 1.63350i) q^{48} -6.57265i q^{49} +(-6.95800 + 7.31198i) q^{51} +(1.97121 - 3.86872i) q^{52} +(-2.23241 - 0.353579i) q^{53} +(-0.429121 + 5.17840i) q^{54} +(-0.384246 + 0.528869i) q^{56} +(-0.312969 - 12.6170i) 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} +(-1.70111 + 0.975888i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(4.38080 - 2.37076i) q^{66} +(2.22497 + 14.0479i) q^{67} +(-4.12066 - 4.12066i) q^{68} +(0.218706 + 1.18918i) q^{69} +(-7.15246 - 9.84451i) q^{71} +(-2.98269 - 0.321816i) q^{72} +(-0.498794 - 0.254148i) q^{73} -2.17706 q^{74} +7.28665 q^{76} +(1.67510 + 0.853507i) q^{77} +(4.56996 + 5.97273i) q^{78} +(6.00067 + 8.25922i) q^{79} +(-7.76928 - 4.54294i) q^{81} +(-4.71623 - 4.71623i) q^{82} +(0.742236 + 4.68629i) q^{83} +(-0.538901 - 0.995806i) q^{84} +(-6.84269 + 2.22332i) q^{86} +(1.58976 - 5.33987i) 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} +(-10.3306 + 0.256256i) q^{93} +(-1.78463 + 2.45633i) q^{94} +(0.228447 - 1.71692i) 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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