LMFDB - Embedded newform 750.2.l.c.143.2

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			143.2
Character	$\chi$	$=$	750.143
Dual form			750.2.l.c.257.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-1.42607 + 0.983013i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.228447 - 1.71692i) q^{6} +(0.462249 - 0.462249i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.06737 - 2.80370i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.42607 + 0.983013i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.228447 - 1.71692i) q^{6} +(0.462249 - 0.462249i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.06737 - 2.80370i) q^{9} +(2.73512 - 0.888693i) q^{11} +(1.63350 + 0.575917i) q^{12} +(-3.86872 + 1.97121i) q^{13} +(0.202010 + 0.621723i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.911620 + 5.75574i) q^{17} +(2.01354 + 2.22389i) q^{18} +(-4.28299 + 5.89503i) q^{19} +(-0.204804 + 1.11360i) q^{21} +(-0.449885 + 2.84047i) q^{22} +(-0.622003 - 0.316926i) q^{23} +(-1.25474 + 1.19400i) q^{24} -4.34197i q^{26} +(1.23392 + 5.04752i) q^{27} +(-0.645670 - 0.102264i) q^{28} +(2.60237 - 1.89073i) q^{29} +(-4.82678 - 3.50686i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.02688 + 3.95600i) q^{33} +(-5.54227 - 1.80079i) q^{34} +(-2.89562 + 0.784450i) q^{36} +(0.988365 + 1.93977i) q^{37} +(-3.30807 - 6.49246i) q^{38} +(3.57936 - 6.61410i) q^{39} +(-6.34331 - 2.06107i) q^{41} +(-0.899243 - 0.688045i) q^{42} +(-5.08751 - 5.08751i) q^{43} +(-2.32663 - 1.69040i) q^{44} +(0.564767 - 0.410327i) q^{46} +(-2.99881 - 0.474965i) q^{47} +(-0.494220 - 1.66004i) q^{48} +6.57265i q^{49} +(-6.95800 - 7.31198i) q^{51} +(3.86872 + 1.97121i) q^{52} +(0.353579 - 2.23241i) q^{53} +(-5.05756 - 1.19210i) q^{54} +(0.384246 - 0.528869i) q^{56} +(0.312969 - 12.6170i) q^{57} +(0.503203 + 3.17710i) q^{58} +(-2.66341 + 8.19714i) q^{59} +(2.77903 + 8.55298i) q^{61} +(5.31594 - 2.70861i) q^{62} +(-0.802614 - 1.78940i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-2.15064 - 4.49296i) q^{66} +(-14.0479 + 2.22497i) q^{67} +(4.12066 - 4.12066i) q^{68} +(1.19856 - 0.159477i) q^{69} +(7.15246 + 9.84451i) q^{71} +(0.615636 - 2.93615i) q^{72} +(-0.254148 + 0.498794i) q^{73} -2.17706 q^{74} +7.28665 q^{76} +(0.853507 - 1.67510i) q^{77} +(4.26821 + 6.19197i) q^{78} +(-6.00067 - 8.25922i) q^{79} +(-6.72143 - 5.98518i) q^{81} +(4.71623 - 4.71623i) q^{82} +(-4.68629 + 0.742236i) q^{83} +(1.02130 - 0.488866i) q^{84} +(6.84269 - 2.22332i) q^{86} +(-1.85256 + 5.25448i) q^{87} +(2.56242 - 1.30562i) q^{88} +(-1.78693 - 5.49959i) q^{89} +(-0.877122 + 2.69950i) q^{91} +(0.109205 + 0.689496i) q^{92} +(10.3306 + 0.256256i) q^{93} +(1.78463 - 2.45633i) q^{94} +(1.70348 + 0.313291i) q^{96} +(0.833578 - 5.26300i) q^{97} +(-5.85628 - 2.98392i) 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} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−1.42607	+	0.983013i	−0.823344	+	0.567543i
$3$	−1.42607	+	0.983013i	−0.823344	+	0.567543i
$4$	−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	−0.614333	−	0.789047i	$-0.710575\pi$
$7$	0.462249	−	0.462249i	0.174714	−	0.174714i	0.789047	+	0.614333i	$0.210575\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	1.06737	−	2.80370i	0.355791	−	0.934566i
$10$		0			0
$11$	2.73512	−	0.888693i	0.824669	−	0.267951i	0.133871	−	0.990999i	$-0.457259\pi$
$11$	2.73512	−	0.888693i	0.824669	−	0.267951i	0.690798	+	0.723048i	$0.257259\pi$
$12$	1.63350	+	0.575917i	0.471551	+	0.166253i
$13$	−3.86872	+	1.97121i	−1.07299	+	0.546716i	−0.898963	−	0.438025i	$-0.855678\pi$
$13$	−3.86872	+	1.97121i	−1.07299	+	0.546716i	−0.174028	+	0.984741i	$0.555678\pi$
$14$	0.202010	+	0.621723i	0.0539895	+	0.166163i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.911620	+	5.75574i	0.221100	+	1.39597i	0.809366	+	0.587305i	$0.199811\pi$
$17$	0.911620	+	5.75574i	0.221100	+	1.39597i	−0.588266	+	0.808668i	$0.700189\pi$
$18$	2.01354	+	2.22389i	0.474595	+	0.524175i
$19$	−4.28299	+	5.89503i	−0.982585	+	1.35241i	−0.0471595	+	0.998887i	$0.515017\pi$
$19$	−4.28299	+	5.89503i	−0.982585	+	1.35241i	−0.935425	+	0.353525i	$0.884983\pi$
$20$		0			0
$21$	−0.204804	+	1.11360i	−0.0446920	+	0.243007i
$22$	−0.449885	+	2.84047i	−0.0959159	+	0.605589i
$23$	−0.622003	−	0.316926i	−0.129697	−	0.0660837i	0.387938	−	0.921685i	$-0.373187\pi$
$23$	−0.622003	−	0.316926i	−0.129697	−	0.0660837i	−0.517635	+	0.855602i	$0.673187\pi$
$24$	−1.25474	+	1.19400i	−0.256123	+	0.243724i
$25$		0			0
$26$		−	4.34197i		−	0.851530i
$27$	1.23392	+	5.04752i	0.237468	+	0.971395i
$28$	−0.645670	−	0.102264i	−0.122020	−	0.0193261i
$29$	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
$33$	−3.02688	+	3.95600i	−0.526912	+	0.688651i
$34$	−5.54227	−	1.80079i	−0.950491	−	0.308833i
$35$		0			0
$36$	−2.89562	+	0.784450i	−0.482604	+	0.130742i
$37$	0.988365	+	1.93977i	0.162486	+	0.318897i	0.957867	−	0.287213i	$-0.0927289\pi$
$37$	0.988365	+	1.93977i	0.162486	+	0.318897i	−0.795380	+	0.606110i	$0.792729\pi$
$38$	−3.30807	−	6.49246i	−0.536640	−	1.05322i
$39$	3.57936	−	6.61410i	0.573156	−	1.05910i
$40$		0			0
$41$	−6.34331	−	2.06107i	−0.990659	−	0.321884i	−0.231532	−	0.972827i	$-0.574374\pi$
$41$	−6.34331	−	2.06107i	−0.990659	−	0.321884i	−0.759127	+	0.650943i	$0.774374\pi$
$42$	−0.899243	−	0.688045i	−0.138756	−	0.106168i
$43$	−5.08751	−	5.08751i	−0.775838	−	0.775838i	0.203282	−	0.979120i	$-0.434839\pi$
$43$	−5.08751	−	5.08751i	−0.775838	−	0.775838i	−0.979120	+	0.203282i	$0.934839\pi$
$44$	−2.32663	−	1.69040i	−0.350753	−	0.254837i
$45$		0			0
$46$	0.564767	−	0.410327i	0.0832703	−	0.0604994i
$47$	−2.99881	−	0.474965i	−0.437422	−	0.0692808i	−0.0661599	−	0.997809i	$-0.521075\pi$
$47$	−2.99881	−	0.474965i	−0.437422	−	0.0692808i	−0.371262	+	0.928528i	$0.621075\pi$
$48$	−0.494220	−	1.66004i	−0.0713345	−	0.239607i
$49$			6.57265i			0.938950i
$50$		0			0
$51$	−6.95800	−	7.31198i	−0.974315	−	1.02388i
$52$	3.86872	+	1.97121i	0.536495	+	0.273358i
$53$	0.353579	−	2.23241i	0.0485679	−	0.306645i	−0.951431	−	0.307861i	$-0.900387\pi$
$53$	0.353579	−	2.23241i	0.0485679	−	0.306645i	0.999999	+	0.00121543i	$0.000386884\pi$
$54$	−5.05756	−	1.19210i	−0.688247	−	0.162224i
$55$		0			0
$56$	0.384246	−	0.528869i	0.0513470	−	0.0706731i
$57$	0.312969	−	12.6170i	0.0414538	−	1.67116i
$58$	0.503203	+	3.17710i	0.0660738	+	0.417174i
$59$	−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	$0.704719\pi$
$62$	5.31594	−	2.70861i	0.675126	−	0.343994i
$63$	−0.802614	−	1.78940i	−0.101120	−	0.225443i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	−2.15064	−	4.49296i	−0.264726	−	0.553045i
$67$	−14.0479	+	2.22497i	−1.71622	+	0.271823i	−0.935570	−	0.353141i	$-0.885114\pi$
$67$	−14.0479	+	2.22497i	−1.71622	+	0.271823i	−0.780654	+	0.624964i	$0.785114\pi$
$68$	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	0.984117	+	0.177521i	$0.0568077\pi$
$71$	7.15246	+	9.84451i	0.848840	+	1.16833i	−0.135277	+	0.990808i	$0.543192\pi$
$72$	0.615636	−	2.93615i	0.0725534	−	0.346029i
$73$	−0.254148	+	0.498794i	−0.0297458	+	0.0583794i	−0.905401	−	0.424557i	$-0.860430\pi$
$73$	−0.254148	+	0.498794i	−0.0297458	+	0.0583794i	0.875655	+	0.482937i	$0.160430\pi$
$74$	−2.17706			−0.253078
$75$		0			0
$76$	7.28665			0.835837
$77$	0.853507	−	1.67510i	0.0972661	−	0.190896i
$78$	4.26821	+	6.19197i	0.483280	+	0.701102i
$79$	−6.00067	−	8.25922i	−0.675128	−	0.929234i	0.324734	−	0.945805i	$-0.394725\pi$
$79$	−6.00067	−	8.25922i	−0.675128	−	0.929234i	−0.999863	+	0.0165708i	$0.994725\pi$
$80$		0			0
$81$	−6.72143	−	5.98518i	−0.746826	−	0.665019i
$82$	4.71623	−	4.71623i	0.520820	−	0.520820i
$83$	−4.68629	+	0.742236i	−0.514387	+	0.0814709i	−0.408231	−	0.912879i	$-0.633854\pi$
$83$	−4.68629	+	0.742236i	−0.514387	+	0.0814709i	−0.106156	+	0.994349i	$0.533854\pi$
$84$	1.02130	−	0.488866i	0.111433	−	0.0533396i
$85$		0			0
$86$	6.84269	−	2.22332i	0.737866	−	0.239747i
$87$	−1.85256	+	5.25448i	−0.198615	+	0.563340i
$88$	2.56242	−	1.30562i	0.273155	−	0.139179i
$89$	−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
$92$	0.109205	+	0.689496i	0.0113854	+	0.0718849i
$93$	10.3306	+	0.256256i	1.07124	+	0.0265725i
$94$	1.78463	−	2.45633i	0.184070	−	0.253351i
$95$		0			0
$96$	1.70348	+	0.313291i	0.173861	+	0.0319752i
$97$	0.833578	−	5.26300i	0.0846370	−	0.534377i	−0.908544	−	0.417790i	$-0.862805\pi$
$97$	0.833578	−	5.26300i	0.0846370	−	0.534377i	0.993181	−	0.116587i	$-0.0371953\pi$
$98$	−5.85628	−	2.98392i	−0.591573	−	0.301422i
$99$	0.427760	−	8.61700i	0.0429915	−	0.866042i
$100$		0			0
$101$			12.5590i			1.24967i	0.780758	+	0.624833i	$0.214833\pi$
$101$			12.5590i			1.24967i	−0.780758	+	0.624833i	$0.785167\pi$
$102$	9.67389	−	2.88006i	0.957858	−	0.285168i
$103$	−6.04979	−	0.958193i	−0.596104	−	0.0944135i	−0.148910	−	0.988851i	$-0.547576\pi$
$103$	−6.04979	−	0.958193i	−0.596104	−	0.0944135i	−0.447194	+	0.894437i	$0.647576\pi$
$104$	−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	$0.741044\pi$
$108$	3.35825	−	3.96512i	0.323148	−	0.381544i
$109$	11.0499	+	3.59033i	1.05839	+	0.343891i	0.785955	−	0.618284i	$-0.212172\pi$
$109$	11.0499	+	3.59033i	1.05839	+	0.343891i	0.272433	+	0.962175i	$0.412172\pi$
$110$		0			0
$111$	−3.31630	−	1.79469i	−0.314770	−	0.170344i
$112$	0.296782	+	0.582467i	0.0280433	+	0.0550380i
$113$	6.43189	+	12.6233i	0.605061	+	1.18750i	0.966875	+	0.255249i	$0.0821575\pi$
$113$	6.43189	+	12.6233i	0.605061	+	1.18750i	−0.361814	+	0.932250i	$0.617842\pi$
$114$	11.0997	+	6.00684i	1.03958	+	0.562592i
$115$		0			0
$116$	−3.05927	−	0.994016i	−0.284046	−	0.0922921i
$117$	1.39732	+	12.9507i	0.129182	+	1.19730i
$118$	−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
$122$	−8.88241	−	1.40684i	−0.804176	−	0.127369i
$123$	11.0721	−	3.29632i	0.998336	−	0.297219i
$124$			5.96622i			0.535783i
$125$		0			0
$126$	1.95874	+	0.0972348i	0.174499	+	0.00866236i
$127$	−12.9147	−	6.58036i	−1.14599	−	0.583912i	−0.225334	−	0.974282i	$-0.572347\pi$
$127$	−12.9147	−	6.58036i	−1.14599	−	0.583912i	−0.920658	+	0.390369i	$0.872347\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	12.2563	+	2.25408i	1.07910	+	0.198460i
$130$		0			0
$131$	−3.23088	+	4.44693i	−0.282283	+	0.388530i	−0.926489	−	0.376323i	$-0.877188\pi$
$131$	−3.23088	+	4.44693i	−0.282283	+	0.388530i	0.644205	+	0.764853i	$0.277188\pi$
$132$	4.97962	+	0.123522i	0.433421	+	0.0107512i
$133$	0.745163	+	4.70477i	0.0646138	+	0.407956i
$134$	4.39515	−	13.5269i	0.379683	−	1.16854i
$135$		0			0
$136$	1.80079	+	5.54227i	0.154417	+	0.475246i
$137$	18.7436	−	9.55034i	1.60137	−	0.815941i	0.601520	−	0.798858i	$-0.294562\pi$
$137$	18.7436	−	9.55034i	1.60137	−	0.815941i	0.999854	−	0.0170834i	$-0.00543808\pi$
$138$	−0.402042	+	1.14033i	−0.0342241	+	0.0970713i
$139$	−11.0917	+	3.60392i	−0.940788	+	0.305681i	−0.738967	−	0.673742i	$-0.764686\pi$
$139$	−11.0917	+	3.60392i	−0.940788	+	0.305681i	−0.201821	+	0.979422i	$0.564686\pi$
$140$		0			0
$141$	4.74342	−	2.27053i	0.399468	−	0.191214i
$142$	−12.0187	+	1.90357i	−1.00858	+	0.159744i
$143$	−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
$147$	−6.46100	−	9.37309i	−0.532894	−	0.773079i
$148$	0.988365	−	1.93977i	0.0812431	−	0.159449i
$149$	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	$0.239960\pi$
$152$	−3.30807	+	6.49246i	−0.268320	+	0.526608i
$153$	17.1104	+	3.58761i	1.38329	+	0.290041i
$154$	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	−0.915494	−	0.402331i	$-0.868200\pi$
$157$	−6.42991	+	6.42991i	−0.513163	+	0.513163i	0.402331	+	0.915494i	$0.368200\pi$
$158$	10.0833	−	1.59703i	0.802181	−	0.127053i
$159$	1.69026	+	3.53116i	0.134046	+	0.280039i
$160$		0			0
$161$	−0.434019	+	0.141021i	−0.0342055	+	0.0111140i
$162$	8.38430	−	3.27163i	0.658733	−	0.257043i
$163$	8.26532	−	4.21139i	0.647390	−	0.329862i	−0.0992767	−	0.995060i	$-0.531653\pi$
$163$	8.26532	−	4.21139i	0.647390	−	0.329862i	0.746667	+	0.665198i	$0.231653\pi$
$164$	2.06107	+	6.34331i	0.160942	+	0.495329i
$165$		0			0
$166$	1.46619	−	4.51248i	0.113799	−	0.350237i
$167$	0.794803	+	5.01819i	0.0615037	+	0.388319i	0.999168	+	0.0407774i	$0.0129835\pi$
$167$	0.794803	+	5.01819i	0.0615037	+	0.388319i	−0.937665	+	0.347542i	$0.887017\pi$
$168$	−0.0280779	+	1.13193i	−0.00216626	+	0.0873299i
$169$	3.44013	−	4.73493i	0.264625	−	0.364226i
$170$		0			0
$171$	11.9563	+	18.3004i	0.914323	+	1.39947i
$172$	−1.12552	+	7.10625i	−0.0858200	+	0.541846i
$173$	16.9953	+	8.65954i	1.29213	+	0.658373i	0.958705	−	0.284404i	$-0.0917956\pi$
$173$	16.9953	+	8.65954i	1.29213	+	0.658373i	0.333425	+	0.942777i	$0.391796\pi$
$174$	−3.84073	−	4.03612i	−0.291165	−	0.305978i
$175$		0			0
$176$			2.87587i			0.216777i
$177$	−4.25967	−	14.3079i	−0.320177	−	1.07545i
$178$	5.71142	+	0.904600i	0.428089	+	0.0678026i
$179$	−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
$183$	−12.3708	−	9.46535i	−0.914475	−	0.699699i
$184$	−0.663923	−	0.215722i	−0.0489451	−	0.0159032i
$185$		0			0
$186$	−4.91833	+	9.08832i	−0.360629	+	0.666388i
$187$	7.60848	+	14.9325i	0.556387	+	1.09197i
$188$	1.37840	+	2.70527i	0.100530	+	0.197302i
$189$	2.90359	+	1.76283i	0.211205	+	0.128227i
$190$		0			0
$191$	−11.5725	−	3.76012i	−0.837354	−	0.272073i	−0.141214	−	0.989979i	$-0.545101\pi$
$191$	−11.5725	−	3.76012i	−0.837354	−	0.272073i	−0.696140	+	0.717906i	$0.745101\pi$
$192$	−1.05251	+	1.37558i	−0.0759583	+	0.0992741i
$193$	−9.01719	−	9.01719i	−0.649071	−	0.649071i	0.303697	−	0.952769i	$-0.401779\pi$
$193$	−9.01719	−	9.01719i	−0.649071	−	0.649071i	−0.952769	+	0.303697i	$0.901779\pi$
$194$	4.31093	+	3.13208i	0.309507	+	0.224870i
$195$		0			0
$196$	5.31739	−	3.86331i	0.379813	−	0.275951i
$197$	−0.404993	−	0.0641446i	−0.0288546	−	0.00457012i	0.141990	−	0.989868i	$-0.454650\pi$
$197$	−0.404993	−	0.0641446i	−0.0288546	−	0.00457012i	−0.170845	+	0.985298i	$0.554650\pi$
$198$	7.48361	+	4.29318i	0.531837	+	0.305103i
$199$		−	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
$202$	−11.1901	−	5.70166i	−0.787336	−	0.401168i
$203$	0.328953	−	2.07693i	0.0230880	−	0.145772i
$204$	−1.82570	+	9.92702i	−0.127825	+	0.695030i
$205$		0			0
$206$	3.60030	−	4.95539i	0.250845	−	0.345259i
$207$	−1.55247	+	1.40563i	−0.107904	+	0.0976980i
$208$	−0.679234	−	4.28851i	−0.0470964	−	0.297355i
$209$	−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	$0.634613\pi$
$212$	−2.01389	+	1.02613i	−0.138314	+	0.0704747i
$213$	−19.8772	−	7.00804i	−1.36196	−	0.480183i
$214$	−0.553505	+	0.179845i	−0.0378368	+	0.0122939i
$215$		0			0
$216$	2.00833	+	4.79235i	0.136650	+	0.326078i
$217$	−3.85221	+	0.610130i	−0.261505	+	0.0414184i
$218$	−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
$222$	3.10465	−	2.14008i	0.208370	−	0.143633i
$223$	−2.88164	+	5.65554i	−0.192969	+	0.378723i	−0.967137	−	0.254258i	$-0.918169\pi$
$223$	−2.88164	+	5.65554i	−0.192969	+	0.378723i	0.774167	+	0.632981i	$0.218169\pi$
$224$	−0.653718			−0.0436784
$225$		0			0
$226$	−14.1675			−0.942405
$227$	6.41208	−	12.5844i	0.425584	−	0.835257i	−0.574278	−	0.818660i	$-0.694717\pi$
$227$	6.41208	−	12.5844i	0.425584	−	0.835257i	0.999862	−	0.0165960i	$-0.00528292\pi$
$228$	−10.3913	+	7.16287i	−0.688181	+	0.474373i
$229$	8.94288	+	12.3088i	0.590962	+	0.813389i	0.994844	−	0.101422i	$-0.0323392\pi$
$229$	8.94288	+	12.3088i	0.590962	+	0.813389i	−0.403882	+	0.914811i	$0.632339\pi$
$230$		0			0
$231$	0.429482	+	3.22783i	0.0282579	+	0.212375i
$232$	2.27455	−	2.27455i	0.149332	−	0.149332i
$233$	7.50060	−	1.18798i	0.491381	−	0.0778271i	0.0941731	−	0.995556i	$-0.469979\pi$
$233$	7.50060	−	1.18798i	0.491381	−	0.0778271i	0.397208	+	0.917729i	$0.369979\pi$
$234$	−12.1736	−	4.63450i	−0.795811	−	0.302967i
$235$		0			0
$236$	8.19714	−	2.66341i	0.533589	−	0.173373i
$237$	16.6763	+	5.87951i	1.08324	+	0.381915i
$238$	−3.39432	+	1.72949i	−0.220021	+	0.112106i
$239$	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	$-0.160948\pi$
$242$	−0.426966	−	2.69576i	−0.0274464	−	0.173290i
$243$	15.4688	+	1.92805i	0.992322	+	0.123684i
$244$	5.28603	−	7.27560i	0.338403	−	0.465772i
$245$		0			0
$246$	−2.08958	+	11.3618i	−0.133226	+	0.724402i
$247$	4.94934	−	31.2489i	0.314919	−	1.98832i
$248$	−5.31594	−	2.70861i	−0.337563	−	0.171997i
$249$	5.95337	−	5.66517i	0.377279	−	0.359015i
$250$		0			0
$251$		−	8.40399i		−	0.530455i	−0.964186	−	0.265228i	$-0.914553\pi$
$251$		−	8.40399i		−	0.530455i	0.964186	−	0.265228i	$-0.0854471\pi$
$252$	−0.975888	+	1.70111i	−0.0614751	+	0.107160i
$253$	−1.98290	−	0.314061i	−0.124664	−	0.0197448i
$254$	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	$-0.635848\pi$
$258$	−7.57262	+	9.89707i	−0.471451	+	0.616165i
$259$	1.35353	+	0.439788i	0.0841042	+	0.0273271i
$260$		0			0
$261$	−2.52334	−	9.31436i	−0.156191	−	0.576545i
$262$	−2.49545	−	4.89760i	−0.154169	−	0.302575i
$263$	1.91341	+	3.75527i	0.117986	+	0.231560i	0.942445	−	0.334361i	$-0.108521\pi$
$263$	1.91341	+	3.75527i	0.117986	+	0.231560i	−0.824459	+	0.565921i	$0.808521\pi$
$264$	−2.37076	+	4.38080i	−0.145910	+	0.269620i
$265$		0			0
$266$	−4.53028	−	1.47198i	−0.277769	−	0.0902527i
$267$	7.95446	+	6.08625i	0.486805	+	0.372473i
$268$	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	$0.365962\pi$
$272$	−5.75574	−	0.911620i	−0.348993	−	0.0552751i
$273$	−1.40281	−	4.71191i	−0.0849017	−	0.285178i
$274$			21.0364i			1.27086i
$275$		0			0
$276$	−0.833518	−	0.875921i	−0.0501719	−	0.0527243i
$277$	21.8145	+	11.1150i	1.31070	+	0.667837i	0.962933	−	0.269742i	$-0.0869384\pi$
$277$	21.8145	+	11.1150i	1.31070	+	0.667837i	0.347772	+	0.937579i	$0.386938\pi$
$278$	1.82442	−	11.5189i	0.109422	−	0.690861i
$279$	−14.9841	+	9.78970i	−0.897077	+	0.586094i
$280$		0			0
$281$	−11.8968	+	16.3745i	−0.709702	+	0.976820i	0.290102	+	0.956996i	$0.406311\pi$
$281$	−11.8968	+	16.3745i	−0.709702	+	0.976820i	−0.999803	+	0.0198246i	$0.993689\pi$
$282$	−0.130408	+	5.25722i	−0.00776566	+	0.313063i
$283$	−1.29900	−	8.20158i	−0.0772177	−	0.487533i	−0.995743	−	0.0921715i	$-0.970619\pi$
$283$	−1.29900	−	8.20158i	−0.0772177	−	0.487533i	0.918525	−	0.395362i	$-0.129381\pi$
$284$	3.76027	−	11.5729i	0.223131	−	0.686726i
$285$		0			0
$286$	−3.85868	−	11.8758i	−0.228168	−	0.702230i
$287$	−3.88491	+	1.97946i	−0.229319	+	0.116844i
$288$	−2.73726	+	1.22777i	−0.161295	+	0.0723469i
$289$	−16.1295	+	5.24081i	−0.948797	+	0.308283i
$290$		0			0
$291$	3.98486	+	8.32485i	0.233596	+	0.488011i
$292$	0.552918	−	0.0875735i	0.0323571	−	0.00512485i
$293$	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
$297$	7.86061	+	12.7090i	0.456119	+	0.737450i
$298$	−4.55304	+	8.93584i	−0.263750	+	0.517639i
$299$	3.03109			0.175292
$300$		0			0
$301$	−4.70339			−0.271099
$302$	−8.13439	+	15.9646i	−0.468081	+	0.918661i
$303$	−12.3456	−	17.9100i	−0.709239	−	1.02891i
$304$	−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	−0.566036	−	0.824380i	$-0.691524\pi$
$307$	4.52656	−	4.52656i	0.258344	−	0.258344i	0.824380	+	0.566036i	$0.191524\pi$
$308$	−1.85686	+	0.294098i	−0.105805	+	0.0167578i
$309$	9.56936	−	4.58057i	0.544382	−	0.260579i
$310$		0			0
$311$	32.9364	−	10.7017i	1.86765	−	0.606838i	0.875274	−	0.483628i	$-0.160681\pi$
$311$	32.9364	−	10.7017i	1.86765	−	0.606838i	0.992381	−	0.123210i	$-0.0393188\pi$
$312$	2.50062	−	7.09260i	0.141569	−	0.401540i
$313$	23.2965	−	11.8701i	1.31679	−	0.670940i	0.352509	−	0.935808i	$-0.385329\pi$
$313$	23.2965	−	11.8701i	1.31679	−	0.670940i	0.964285	+	0.264869i	$0.0853286\pi$
$314$	−2.80998	−	8.64821i	−0.158576	−	0.488047i
$315$		0			0
$316$	−3.15474	+	9.70929i	−0.177468	+	0.546190i
$317$	2.13804	+	13.4990i	0.120084	+	0.758181i	0.972083	+	0.234638i	$0.0753903\pi$
$317$	2.13804	+	13.4990i	0.120084	+	0.758181i	−0.851999	+	0.523544i	$0.824610\pi$
$318$	−3.91365	−	0.0970796i	−0.219466	−	0.00544396i
$319$	5.43750	−	7.48407i	0.304441	−	0.419028i
$320$		0			0
$321$	−0.991408	−	0.182332i	−0.0553350	−	0.0101768i
$322$	0.0713896	−	0.450736i	0.00397838	−	0.0251185i
$323$	−37.8347	−	19.2777i	−2.10518	−	1.07264i
$324$	−0.891349	+	8.95575i	−0.0495194	+	0.497542i
$325$		0			0
$326$			9.27639i			0.513772i
$327$	−19.2873	+	5.74211i	−1.06659	+	0.317540i
$328$	−6.58764	−	1.04338i	−0.363741	−	0.0576110i
$329$	−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
$333$	6.49349	−	0.700614i	0.355841	−	0.0383934i
$334$	−4.83207	−	1.57004i	−0.264399	−	0.0859085i
$335$		0			0
$336$	−0.995806	−	0.538901i	−0.0543257	−	0.0293995i
$337$	14.3152	+	28.0951i	0.779796	+	1.53044i	0.846334	+	0.532652i	$0.178805\pi$
$337$	14.3152	+	28.0951i	0.779796	+	1.53044i	−0.0665380	+	0.997784i	$0.521195\pi$
$338$	2.65707	+	5.21479i	0.144526	+	0.283647i
$339$	−21.5812	−	11.6791i	−1.17213	−	0.634323i
$340$		0			0
$341$	−16.3183	−	5.30214i	−0.883686	−	0.287127i
$342$	−21.7338	+	2.34496i	−1.17523	+	0.126801i
$343$	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
$347$	12.9057	+	2.04407i	0.692816	+	0.109731i	0.492905	−	0.870083i	$-0.335935\pi$
$347$	12.9057	+	2.04407i	0.692816	+	0.109731i	0.199911	+	0.979814i	$0.435935\pi$
$348$	5.33987	−	1.58976i	0.286247	−	0.0852200i
$349$		−	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
$352$	−2.56242	−	1.30562i	−0.136577	−	0.0695897i
$353$	0.455793	−	2.87776i	0.0242594	−	0.153168i	−0.972585	−	0.232547i	$-0.925294\pi$
$353$	0.455793	−	2.87776i	0.0242594	−	0.153168i	0.996844	+	0.0793796i	$0.0252939\pi$
$354$	14.6823	+	2.70025i	0.780355	+	0.143517i
$355$		0			0
$356$	−3.39893	+	4.67823i	−0.180143	+	0.247946i
$357$	−6.59628	−	0.163624i	−0.349112	−	0.00865988i
$358$	−0.627874	−	3.96424i	−0.0331842	−	0.209517i
$359$	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
$362$	−3.64292	+	1.85616i	−0.191468	+	0.0975577i
$363$	1.57189	−	4.45841i	0.0825027	−	0.234006i
$364$	2.69950	−	0.877122i	0.141492	−	0.0459737i
$365$		0			0
$366$	14.0499	−	6.72527i	0.734401	−	0.351536i
$367$	21.7433	−	3.44380i	1.13499	−	0.179765i	0.439460	−	0.898262i	$-0.355170\pi$
$367$	21.7433	−	3.44380i	1.13499	−	0.179765i	0.695530	+	0.718497i	$0.255170\pi$
$368$	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
$372$	−5.86487	−	8.50827i	−0.304080	−	0.441133i
$373$	−9.69853	+	19.0344i	−0.502171	+	0.985566i	0.491247	+	0.871020i	$0.336541\pi$
$373$	−9.69853	+	19.0344i	−0.502171	+	0.985566i	−0.993418	+	0.114545i	$0.963459\pi$
$374$	−16.7591			−0.866593
$375$		0			0
$376$	−3.03619			−0.156580
$377$	−6.34081	+	12.4445i	−0.326568	+	0.640926i
$378$	−2.88890	+	1.78681i	−0.148589	+	0.0919034i
$379$	0.581554	+	0.800441i	0.0298724	+	0.0411159i	0.823692	−	0.567038i	$-0.191911\pi$
$379$	0.581554	+	0.800441i	0.0298724	+	0.0411159i	−0.793820	+	0.608153i	$0.791911\pi$
$380$		0			0
$381$	24.8859	−	3.31122i	1.27494	−	0.169639i
$382$	8.60408	−	8.60408i	0.440223	−	0.440223i
$383$	12.4916	−	1.97847i	0.638289	−	0.101095i	0.171102	−	0.985253i	$-0.445267\pi$
$383$	12.4916	−	1.97847i	0.638289	−	0.101095i	0.467187	+	0.884158i	$0.345267\pi$
$384$	−0.747823	−	1.56229i	−0.0381622	−	0.0797254i
$385$		0			0
$386$	12.1281	−	3.94066i	0.617304	−	0.200574i
$387$	−19.6941	+	8.83357i	−1.00111	+	0.449036i
$388$	−4.74782	+	2.41914i	−0.241034	+	0.122813i
$389$	−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
$392$	1.02819	+	6.49173i	0.0519314	+	0.327882i
$393$	0.236089	−	9.51764i	0.0119091	−	0.480102i
$394$	0.241016	−	0.331731i	0.0121422	−	0.0167123i
$395$		0			0
$396$	−7.22273	+	4.71888i	−0.362956	+	0.237133i
$397$	0.556301	−	3.51235i	0.0279199	−	0.176280i	−0.969788	−	0.243950i	$-0.921557\pi$
$397$	0.556301	−	3.51235i	0.0279199	−	0.176280i	0.997708	+	0.0676706i	$0.0215567\pi$
$398$	9.79650	+	4.99157i	0.491054	+	0.250205i
$399$	−5.68751	−	5.97685i	−0.284732	−	0.299217i
$400$		0			0
$401$			16.6499i			0.831458i	0.909489	+	0.415729i	$0.136473\pi$
$401$			16.6499i			0.831458i	−0.909489	+	0.415729i	$0.863527\pi$
$402$	7.02929	+	23.6108i	0.350589	+	1.17760i
$403$	25.5862	+	4.05246i	1.27454	+	0.201867i
$404$	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
$408$	−8.01618	−	6.13348i	−0.396860	−	0.303653i
$409$	4.09420	+	1.33029i	0.202445	+	0.0657784i	0.408484	−	0.912765i	$-0.366057\pi$
$409$	4.09420	+	1.33029i	0.202445	+	0.0657784i	−0.206039	+	0.978544i	$0.566057\pi$
$410$		0			0
$411$	−17.3417	+	32.0447i	−0.855401	+	1.58065i
$412$	2.78078	+	5.45760i	0.136999	+	0.268876i
$413$	2.55796	+	5.02028i	0.125869	+	0.247032i
$414$	−0.547617	−	2.02141i	−0.0269139	−	0.0993467i
$415$		0			0
$416$	4.12946	+	1.34174i	0.202463	+	0.0657843i
$417$	12.2749	−	16.0428i	0.601105	−	0.785618i
$418$	−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	$0.415286\pi$
$422$	−21.2464	−	3.36511i	−1.03426	−	0.163811i
$423$	−4.53251	+	7.90079i	−0.220378	+	0.384150i
$424$		−	2.26024i		−	0.109767i
$425$		0			0
$426$	15.2683	−	14.5291i	0.739750	−	0.703939i
$427$	5.23821	+	2.66900i	0.253495	+	0.129162i
$428$	0.0910432	−	0.574824i	0.00440074	−	0.0277852i
$429$	3.91205	−	21.2713i	0.188876	−	1.02699i
$430$		0			0
$431$	2.43967	−	3.35792i	0.117515	−	0.161745i	−0.746207	−	0.665714i	$-0.768127\pi$
$431$	2.43967	−	3.35792i	0.117515	−	0.161745i	0.863722	+	0.503968i	$0.168127\pi$
$432$	−5.18178	−	0.386242i	−0.249308	−	0.0185831i
$433$	4.57227	+	28.8682i	0.219729	+	1.38732i	0.812977	+	0.582296i	$0.197846\pi$
$433$	4.57227	+	28.8682i	0.219729	+	1.38732i	−0.593248	+	0.805020i	$0.702154\pi$
$434$	1.20524	−	3.70934i	0.0578532	−	0.178054i
$435$		0			0
$436$	−3.59033	−	11.0499i	−0.171945	−	0.529194i
$437$	4.53232	−	2.30933i	0.216810	−	0.110470i
$438$	0.914449	+	0.322404i	0.0436941	+	0.0154051i
$439$	−10.7432	+	3.49067i	−0.512744	+	0.166601i	−0.553950	−	0.832550i	$-0.686880\pi$
$439$	−10.7432	+	3.49067i	−0.512744	+	0.166601i	0.0412056	+	0.999151i	$0.486880\pi$
$440$		0			0
$441$	18.4277	+	7.01546i	0.877511	+	0.334070i
$442$	24.9913	−	3.95823i	1.18871	−	0.188274i
$443$	−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
$447$	−14.3020	+	9.85857i	−0.676461	+	0.466294i
$448$	0.296782	−	0.582467i	0.0140216	−	0.0275190i
$449$	−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
$452$	6.43189	−	12.6233i	0.302531	−	0.593750i
$453$	−25.5517	+	17.6132i	−1.20052	+	0.827538i
$454$	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	−0.805381	−	0.592757i	$-0.798039\pi$
$457$	−4.54539	+	4.54539i	−0.212624	+	0.212624i	0.592757	+	0.805381i	$0.298039\pi$
$458$	−15.0272	+	2.38008i	−0.702176	+	0.111214i
$459$	−27.9273	+	11.7035i	−1.30354	+	0.546274i
$460$		0			0
$461$	18.3653	−	5.96726i	0.855359	−	0.277923i	0.151670	−	0.988431i	$-0.451535\pi$
$461$	18.3653	−	5.96726i	0.855359	−	0.277923i	0.703689	+	0.710508i	$0.251535\pi$
$462$	−3.07100	−	1.08273i	−0.142876	−	0.0503732i
$463$	−3.98746	+	2.03171i	−0.185313	+	0.0944216i	−0.544186	−	0.838965i	$-0.683161\pi$
$463$	−3.98746	+	2.03171i	−0.185313	+	0.0944216i	0.358873	+	0.933387i	$0.383161\pi$
$464$	0.994016	+	3.05927i	0.0461460	+	0.142023i
$465$		0			0
$466$	−2.34671	+	7.22242i	−0.108709	+	0.334572i
$467$	−0.275929	−	1.74215i	−0.0127685	−	0.0806170i	0.980481	−	0.196613i	$-0.0629941\pi$
$467$	−0.275929	−	1.74215i	−0.0127685	−	0.0806170i	−0.993250	+	0.115996i	$0.962994\pi$
$468$	9.65605	−	8.74271i	0.446351	−	0.404132i
$469$	−5.46513	+	7.52211i	−0.252356	+	0.347339i
$470$		0			0
$471$	2.84884	−	15.4902i	0.131268	−	0.713752i
$472$	−1.34831	+	8.51287i	−0.0620609	+	0.391837i
$473$	−18.4362	−	9.39370i	−0.847696	−	0.431923i
$474$	−12.8096	+	12.1895i	−0.588363	+	0.559881i
$475$		0			0
$476$		−	3.80954i		−	0.174610i
$477$	−5.88161	−	3.37414i	−0.269300	−	0.154491i
$478$	−12.3338	−	1.95347i	−0.564133	−	0.0893498i
$479$	−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
$483$	0.480317	−	0.627753i	0.0218552	−	0.0285637i
$484$	2.59578	+	0.843419i	0.117990	+	0.0383372i
$485$		0			0
$486$	−8.74057	+	12.9075i	−0.396480	+	0.585494i
$487$	−12.7835	−	25.0891i	−0.579277	−	1.13690i	−0.975758	−	0.218852i	$-0.929769\pi$
$487$	−12.7835	−	25.0891i	−0.579277	−	1.13690i	0.396481	−	0.918043i	$-0.370231\pi$
$488$	4.08280	+	8.01294i	0.184820	+	0.362729i
$489$	−7.64711	+	14.1307i	−0.345814	+	0.639011i
$490$		0			0
$491$	8.69557	+	2.82536i	0.392426	+	0.127507i	0.498582	−	0.866843i	$-0.333854\pi$
$491$	8.69557	+	2.82536i	0.392426	+	0.127507i	−0.106156	+	0.994349i	$0.533854\pi$
$492$	−9.17479	−	7.01997i	−0.413631	−	0.316485i
$493$	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
$497$	7.85683	+	1.24440i	0.352427	+	0.0558189i
$498$	2.34493	+	7.87642i	0.105079	+	0.352951i
$499$			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
$502$	7.48801	+	3.81533i	0.334206	+	0.170287i
$503$	3.52512	−	22.2567i	0.157177	−	0.992379i	−0.775416	−	0.631450i	$-0.782460\pi$
$503$	3.52512	−	22.2567i	0.157177	−	0.992379i	0.932594	−	0.360928i	$-0.117540\pi$
$504$	−1.07266	−	1.64181i	−0.0477799	−	0.0731320i
$505$		0			0
$506$	1.18005	−	1.62420i	0.0524595	−	0.0722044i
$507$	−0.251380	+	10.1341i	−0.0111642	+	0.450069i
$508$	2.26744	+	14.3160i	0.100601	+	0.635171i
$509$	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
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−35.0401	−	14.3445i	−1.54706	−	0.633324i
$514$	28.5533	−	9.27753i	1.25943	−	0.409214i
$515$		0			0
$516$	−5.38046	−	11.2404i	−0.236861	−	0.494832i
$517$	−8.62420	+	1.36594i	−0.379292	+	0.0600739i
$518$	−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	−0.839683	−	0.543077i	$-0.817259\pi$
$521$	−25.0327	−	34.4546i	−1.09670	−	1.50948i	−0.257021	−	0.966406i	$-0.582741\pi$
$522$	9.44473	+	1.98032i	0.413385	+	0.0866762i
$523$	10.1317	−	19.8847i	0.443030	−	0.869495i	−0.556230	−	0.831028i	$-0.687753\pi$
$523$	10.1317	−	19.8847i	0.443030	−	0.869495i	0.999260	−	0.0384667i	$-0.0122474\pi$
$524$	5.49670			0.240125
$525$		0			0
$526$	−4.21464			−0.183767
$527$	15.7844	−	30.9786i	0.687579	−	1.34945i
$528$	−2.82702	−	4.10120i	−0.123030	−	0.178482i
$529$	−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
$533$	28.6033	−	4.53032i	1.23895	−	0.196230i
$534$	−9.03414	+	4.32437i	−0.390945	+	0.187134i
$535$		0			0
$536$	−13.5269	+	4.39515i	−0.584272	+	0.189842i
$537$	2.31153	−	6.55630i	0.0997501	−	0.282925i
$538$	18.0714	−	9.20785i	0.779114	−	0.396979i
$539$	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	$0.0872338\pi$
$542$	−1.05969	−	6.69064i	−0.0455177	−	0.287387i
$543$	−7.07940	−	0.175607i	−0.303806	−	0.00753604i
$544$	3.42531	−	4.71454i	0.146859	−	0.202134i
$545$		0			0
$546$	4.83520	+	0.889254i	0.206928	+	0.0380566i
$547$	−3.80438	+	24.0199i	−0.162663	+	1.02702i	0.762373	+	0.647138i	$0.224034\pi$
$547$	−3.80438	+	24.0199i	−0.162663	+	1.02702i	−0.925036	+	0.379878i	$0.875966\pi$
$548$	−18.7436	−	9.55034i	−0.800687	−	0.407970i
$549$	26.9462	+	1.33765i	1.15004	+	0.0570894i
$550$		0			0
$551$			23.4390i			0.998535i
$552$	1.15886	−	0.345010i	0.0493244	−	0.0146846i
$553$	−6.59162	−	1.04401i	−0.280304	−	0.0443958i
$554$	−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	$0.565485\pi$
$558$	−1.92003	−	17.7954i	−0.0812813	−	0.753339i
$559$	29.7107	+	9.65360i	1.25663	+	0.408304i
$560$		0			0
$561$	−25.5291	−	13.8156i	−1.07784	−	0.583294i
$562$	−9.18876	−	18.0340i	−0.387604	−	0.760717i
$563$	0.442963	+	0.869364i	0.0186687	+	0.0366393i	0.900153	−	0.435575i	$-0.143455\pi$
$563$	0.442963	+	0.869364i	0.0186687	+	0.0366393i	−0.881484	+	0.472214i	$0.843455\pi$
$564$	−4.62502	−	2.50292i	−0.194748	−	0.105392i
$565$		0			0
$566$	7.89740	+	2.56602i	0.331952	+	0.107858i
$567$	−5.87361	+	0.340335i	−0.246669	+	0.0142927i
$568$	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	$0.335401\pi$
$572$	12.3332	+	1.95339i	0.515678	+	0.0816753i
$573$	20.1994	−	6.01367i	0.843843	−	0.251224i
$574$		−	4.36014i		−	0.181989i
$575$		0			0
$576$	0.148741	−	2.99631i	0.00619754	−	0.124846i
$577$	7.29810	+	3.71857i	0.303824	+	0.154806i	0.599255	−	0.800558i	$-0.295463\pi$
$577$	7.29810	+	3.71857i	0.303824	+	0.154806i	−0.295432	+	0.955364i	$0.595463\pi$
$578$	2.65307	−	16.7508i	0.110353	−	0.696742i
$579$	21.7232	+	3.99516i	0.902785	+	0.166033i
$580$		0			0
$581$	−1.82313	+	2.50933i	−0.0756364	+	0.104105i
$582$	−9.22658	−	0.228869i	−0.382454	−	0.00948694i
$583$	−1.01685	−	6.42013i	−0.0421136	−	0.265895i
$584$	−0.172991	+	0.532411i	−0.00715841	+	0.0220313i
$585$		0			0
$586$	0.527935	+	1.62482i	0.0218088	+	0.0671205i
$587$	−31.3821	+	15.9900i	−1.29528	+	0.659978i	−0.959432	−	0.281939i	$-0.909023\pi$
$587$	−31.3821	+	15.9900i	−1.29528	+	0.659978i	−0.335847	+	0.941917i	$0.609023\pi$
$588$	−3.78530	+	10.7364i	−0.156103	+	0.442763i
$589$	41.3460	−	13.4341i	1.70363	−	0.553544i
$590$		0			0
$591$	0.640605	−	0.306639i	0.0263510	−	0.0126134i
$592$	−2.15026	+	0.340567i	−0.0883750	+	0.0139972i
$593$	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
$597$	10.8081	+	15.6795i	0.442346	+	0.641719i
$598$	−1.37608	+	2.70072i	−0.0562723	+	0.110441i
$599$	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	$0.306376\pi$
$602$	2.13529	−	4.19075i	0.0870281	−	0.170802i
$603$	−8.75620	+	41.7609i	−0.356580	+	1.70064i
$604$	−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	−0.776243	−	0.630434i	$-0.782877\pi$
$607$	−3.59236	+	3.59236i	−0.145809	+	0.145809i	0.630434	+	0.776243i	$0.282877\pi$
$608$	7.19694	−	1.13988i	0.291875	−	0.0462284i
$609$	1.57254	+	3.28522i	0.0637224	+	0.133124i
$610$		0			0
$611$	12.5378	−	4.07379i	0.507226	−	0.164808i
$612$	−7.15480	−	15.9513i	−0.289216	−	0.644795i
$613$	−13.6733	+	6.96688i	−0.552258	+	0.281390i	−0.707768	−	0.706445i	$-0.750298\pi$
$613$	−13.6733	+	6.96688i	−0.552258	+	0.281390i	0.155510	+	0.987834i	$0.450298\pi$
$614$	1.97818	+	6.08821i	0.0798328	+	0.245700i
$615$		0			0
$616$	0.580955	−	1.78800i	0.0234074	−	0.0720404i
$617$	−1.12552	−	7.10625i	−0.0453117	−	0.286087i	0.954619	−	0.297829i	$-0.0962624\pi$
$617$	−1.12552	−	7.10625i	−0.0453117	−	0.286087i	−0.999931	+	0.0117417i	$0.996262\pi$
$618$	−0.263084	+	10.6059i	−0.0105828	+	0.426632i
$619$	7.42133	−	10.2146i	0.298288	−	0.410559i	−0.633396	−	0.773828i	$-0.718339\pi$
$619$	7.42133	−	10.2146i	0.298288	−	0.410559i	0.931684	+	0.363269i	$0.118339\pi$
$620$		0			0
$621$	0.832190	−	3.53063i	0.0333946	−	0.141679i
$622$	−5.41755	+	34.2051i	−0.217224	+	1.37150i
$623$	−3.36818	−	1.71618i	−0.134943	−	0.0687571i
$624$	5.18430	+	5.44804i	0.207538	+	0.218096i
$625$		0			0
$626$			26.1462i			1.04501i
$627$	−10.3566	−	34.7870i	−0.413603	−	1.38926i
$628$	8.98132	+	1.42250i	0.358394	+	0.0567640i
$629$	−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
$633$	−29.5905	−	22.6408i	−1.17612	−	0.899892i
$634$	−12.9984	−	4.22343i	−0.516231	−	0.167734i
$635$		0			0
$636$	1.86326	−	3.44301i	0.0738829	−	0.136524i
$637$	−12.9561	−	25.4278i	−0.513339	−	1.00748i
$638$	4.19979	+	8.24255i	0.166271	+	0.326326i
$639$	35.2354	−	9.54557i	1.39389	−	0.377617i
$640$		0			0
$641$	−3.49095	−	1.13428i	−0.137884	−	0.0448012i	0.239262	−	0.970955i	$-0.423095\pi$
$641$	−3.49095	−	1.13428i	−0.137884	−	0.0448012i	−0.377146	+	0.926154i	$0.623095\pi$
$642$	0.612549	−	0.800574i	0.0241754	−	0.0315961i
$643$	9.94703	+	9.94703i	0.392273	+	0.392273i	0.875497	−	0.483224i	$-0.160534\pi$
$643$	9.94703	+	9.94703i	0.392273	+	0.392273i	−0.483224	+	0.875497i	$0.660534\pi$
$644$	0.369198	+	0.268238i	0.0145485	+	0.0105701i
$645$		0			0
$646$	34.3532	−	24.9591i	1.35161	−	0.982001i
$647$	3.89931	+	0.617590i	0.153298	+	0.0242800i	0.232612	−	0.972570i	$-0.425273\pi$
$647$	3.89931	+	0.617590i	0.153298	+	0.0242800i	−0.0793138	+	0.996850i	$0.525273\pi$
$648$	−7.57497	−	4.86002i	−0.297573	−	0.190920i
$649$			24.7871i			0.972979i
$650$		0			0
$651$	4.89377	−	4.65686i	0.191802	−	0.182517i
$652$	−8.26532	−	4.21139i	−0.323695	−	0.164931i
$653$	−2.27850	+	14.3859i	−0.0891644	+	0.562962i	0.902147	+	0.431428i	$0.141990\pi$
$653$	−2.27850	+	14.3859i	−0.0891644	+	0.562962i	−0.991312	+	0.131534i	$0.958010\pi$
$654$	3.63999	−	19.7920i	0.142335	−	0.773927i
$655$		0			0
$656$	3.92038	−	5.39594i	0.153065	−	0.210676i
$657$	1.12720	+	1.24495i	0.0439761	+	0.0485703i
$658$	−0.310493	−	1.96038i	−0.0121043	−	0.0764235i
$659$	−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	$0.949914\pi$
$662$	9.41728	−	4.79834i	0.366013	−	0.186493i
$663$	41.3321	+	14.5723i	1.60520	+	0.565942i
$664$	−4.51248	+	1.46619i	−0.175118	+	0.0568994i
$665$		0			0
$666$	−2.32373	+	6.10382i	−0.0900428	+	0.236518i
$667$	−2.21790	+	0.351281i	−0.0858775	+	0.0136017i
$668$	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
$672$	0.932251	−	0.642614i	0.0359623	−	0.0247894i
$673$	12.2698	−	24.0809i	0.472967	−	0.928251i	−0.524095	−	0.851660i	$-0.675596\pi$
$673$	12.2698	−	24.0809i	0.472967	−	0.928251i	0.997063	−	0.0765912i	$-0.0244036\pi$
$674$	−31.5318			−1.21456
$675$		0			0
$676$	−5.85270			−0.225104
$677$	−8.38747	+	16.4613i	−0.322357	+	0.632660i	−0.994142	−	0.108086i	$-0.965528\pi$
$677$	−8.38747	+	16.4613i	−0.322357	+	0.632660i	0.671785	+	0.740746i	$0.265528\pi$
$678$	20.2038	−	13.9268i	0.775924	−	0.534855i
$679$	−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
$683$	37.5066	−	5.94046i	1.43515	−	0.227305i	0.610082	−	0.792338i	$-0.291137\pi$
$683$	37.5066	−	5.94046i	1.43515	−	0.227305i	0.825068	+	0.565033i	$0.191137\pi$
$684$	7.77757	−	20.4296i	0.297383	−	0.781144i
$685$		0			0
$686$	−8.43843	+	2.74181i	−0.322181	+	0.104683i
$687$	−24.8529	−	8.76231i	−0.948198	−	0.334303i
$688$	6.41064	−	3.26638i	0.244403	−	0.124530i
$689$	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	$0.152191\pi$
$692$	−2.98388	−	18.8394i	−0.113430	−	0.716168i
$693$	−3.78547	−	4.18093i	−0.143798	−	0.158820i
$694$	−7.68036	+	10.5711i	−0.291542	+	0.401274i
$695$		0			0
$696$	−1.00777	+	5.47959i	−0.0381992	+	0.207703i
$697$	6.08028	−	38.3894i	0.230307	−	1.45410i
$698$	27.1156	+	13.8161i	1.02634	+	0.522947i
$699$	−9.52861	+	9.06733i	−0.360405	+	0.342958i
$700$		0			0
$701$			52.4507i			1.98104i	0.137384	+	0.990518i	$0.456131\pi$
$701$			52.4507i			1.98104i	−0.137384	+	0.990518i	$0.543869\pi$
$702$	21.9162	−	5.35764i	0.827173	−	0.202211i
$703$	−15.6682	−	2.48160i	−0.590937	−	0.0935951i
$704$	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
$708$	−9.07156	+	11.8561i	−0.340930	+	0.445580i
$709$	−5.89184	−	1.91438i	−0.221273	−	0.0718959i	0.196283	−	0.980547i	$-0.437113\pi$
$709$	−5.89184	−	1.91438i	−0.221273	−	0.0718959i	−0.417555	+	0.908652i	$0.637113\pi$
$710$		0			0
$711$	−29.5613	+	8.00841i	−1.10863	+	0.300339i
$712$	−2.62525	−	5.15235i	−0.0983855	−	0.193092i
$713$	1.89085	+	3.71101i	0.0708130	+	0.138978i
$714$	3.14044	−	5.80305i	0.117528	−	0.217174i
$715$		0			0
$716$	3.81721	+	1.24029i	0.142656	+	0.0463517i
$717$	−17.1776	−	13.1432i	−0.641508	−	0.490842i
$718$	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
$722$	33.6756	+	5.33368i	1.25327	+	0.198499i
$723$	11.2171	+	37.6772i	0.417167	+	1.40123i
$724$		−	4.08855i		−	0.151950i
$725$		0			0
$726$	3.25885	+	3.42464i	0.120947	+	0.127100i
$727$	27.1388	+	13.8279i	1.00652	+	0.512850i	0.877900	−	0.478844i	$-0.158944\pi$
$727$	27.1388	+	13.8279i	1.00652	+	0.512850i	0.128624	+	0.991693i	$0.458944\pi$
$728$	−0.444028	+	2.80348i	−0.0164568	+	0.103904i
$729$	−23.9549	+	12.4565i	−0.887218	+	0.461350i
$730$		0			0
$731$	24.6445	−	33.9203i	0.911510	−	1.25459i
$732$	−0.386264	+	15.5718i	−0.0142767	+	0.575549i
$733$	−2.16039	−	13.6402i	−0.0797960	−	0.503812i	−0.994922	−	0.100645i	$-0.967909\pi$
$733$	−2.16039	−	13.6402i	−0.0797960	−	0.503812i	0.915126	−	0.403167i	$-0.132091\pi$
$734$	−6.80279	+	20.9368i	−0.251096	+	0.772793i
$735$		0			0
$736$	0.215722	+	0.663923i	0.00795161	+	0.0244725i
$737$	−36.4453	+	18.5698i	−1.34248	+	0.684028i
$738$	−8.18890	−	18.2568i	−0.301438	−	0.672043i
$739$	25.2888	−	8.21683i	0.930264	−	0.302261i	0.195593	−	0.980685i	$-0.437337\pi$
$739$	25.2888	−	8.21683i	0.930264	−	0.302261i	0.734671	+	0.678424i	$0.237337\pi$
$740$		0			0
$741$	23.6599	+	49.4285i	0.869170	+	1.81580i
$742$	1.45937	−	0.231141i	0.0535751	−	0.00848547i
$743$	−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
$747$	−2.92101	+	13.9312i	−0.106874	+	0.509715i
$748$	7.60848	−	14.9325i	0.278193	−	0.545985i
$749$	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	$0.669683\pi$
$752$	1.37840	−	2.70527i	0.0502652	−	0.0986509i
$753$	8.26123	+	11.9847i	0.301056	+	0.436747i
$754$	−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	−0.916998	−	0.398891i	$-0.869395\pi$
$757$	−14.2550	+	14.2550i	−0.518108	+	0.518108i	0.398891	+	0.916998i	$0.369395\pi$
$758$	−0.977218	+	0.154776i	−0.0354942	+	0.00562172i
$759$	3.13649	−	1.50134i	0.113847	−	0.0544953i
$760$		0			0
$761$	−20.4602	+	6.64792i	−0.741681	+	0.240987i	−0.655398	−	0.755284i	$-0.727499\pi$
$761$	−20.4602	+	6.64792i	−0.741681	+	0.240987i	−0.0862835	+	0.996271i	$0.527499\pi$
$762$	−8.34763	+	23.6767i	−0.302403	+	0.857717i
$763$	6.76742	−	3.44817i	0.244997	−	0.124832i
$764$	3.76012	+	11.5725i	0.136036	+	0.418677i
$765$		0			0
$766$	−3.90822	+	12.0283i	−0.141210	+	0.434599i
$767$	−5.85431	−	36.9626i	−0.211387	−	1.33464i
$768$	1.73152	+	0.0429510i	0.0624808	+	0.00154986i
$769$	−5.35630	+	7.37231i	−0.193153	+	0.265852i	−0.894599	−	0.446871i	$-0.852538\pi$
$769$	−5.35630	+	7.37231i	−0.193153	+	0.265852i	0.701446	+	0.712723i	$0.252538\pi$
$770$		0			0
$771$	51.1431	+	9.40586i	1.84188	+	0.338744i
$772$	−1.99489	+	12.5952i	−0.0717976	+	0.453312i
$773$	40.1134	+	20.4388i	1.44278	+	0.735132i	0.987852	−	0.155397i	$-0.0496657\pi$
$773$	40.1134	+	20.4388i	1.44278	+	0.735132i	0.454926	+	0.890529i	$0.349666\pi$
$774$	1.07017	−	21.5579i	0.0384663	−	0.774884i
$775$		0			0
$776$		−	5.32861i		−	0.191286i
$777$	−2.36255	+	0.703366i	−0.0847560	+	0.0252331i
$778$	27.0272	+	4.28069i	0.968973	+	0.153470i
$779$	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
$783$	12.7546	+	10.8025i	0.455813	+	0.386049i
$784$	−6.25096	−	2.03106i	−0.223249	−	0.0725379i
$785$		0			0
$786$	8.37310	+	4.53128i	0.298659	+	0.161625i
$787$	−11.5447	−	22.6577i	−0.411523	−	0.807659i	0.588477	−	0.808514i	$-0.299728\pi$
$787$	−11.5447	−	22.6577i	−0.411523	−	0.807659i	−1.00000		0.000855029i	$0.999728\pi$
$788$	0.186155	+	0.365350i	0.00663150	+	0.0130150i
$789$	−6.42014	−	3.47439i	−0.228563	−	0.123692i
$790$		0			0
$791$	8.80823	+	2.86197i	0.313185	+	0.101760i
$792$	−0.925503	−	8.57783i	−0.0328863	−	0.304800i
$793$	−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
$797$	10.8372	+	1.71644i	0.383874	+	0.0607996i	0.345389	−	0.938460i	$-0.387747\pi$
$797$	10.8372	+	1.71644i	0.383874	+	0.0607996i	0.0384845	+	0.999259i	$0.487747\pi$
$798$	7.90749	−	2.35418i	0.279922	−	0.0833369i
$799$		−	17.6934i		−	0.625946i
$800$		0			0
$801$	−17.3265	−	0.860112i	−0.612202	−	0.0303906i
$802$	−14.8352	−	7.55891i	−0.523849	−	0.266914i
$803$	−0.251850	+	1.59012i	−0.00888760	+	0.0561141i
$804$	−24.2286	−	4.45595i	−0.854478	−	0.157149i
$805$		0			0
$806$	−15.2267	+	20.9577i	−0.536337	+	0.738204i
$807$	35.1187	+	0.871135i	1.23624	+	0.0306654i
$808$	1.96466	+	12.4044i	0.0691165	+	0.436384i
$809$	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	$0.819841\pi$
$812$	−1.87362	+	0.954659i	−0.0657513	+	0.0335020i
$813$	3.90128	−	11.0654i	0.136824	−	0.388080i
$814$	−5.95451	+	1.93474i	−0.208706	+	0.0678126i
$815$		0			0
$816$	9.10425	−	4.35793i	0.318712	−	0.152558i
$817$	51.7808	−	8.20127i	1.81158	−	0.286926i
$818$	−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	0.939681	−	0.342052i	$-0.111122\pi$
$821$	9.28341	+	12.7775i	0.323993	+	0.445939i	−0.615688	+	0.787990i	$0.711122\pi$
$822$	−20.6791	−	29.9995i	−0.721266	−	1.04635i
$823$	−10.8987	+	21.3898i	−0.379904	+	0.745603i	−0.999218	−	0.0395404i	$-0.987411\pi$
$823$	−10.8987	+	21.3898i	−0.379904	+	0.745603i	0.619314	+	0.785143i	$0.287411\pi$
$824$	−6.12520			−0.213382
$825$		0			0
$826$	−5.63439			−0.196046
$827$	−12.0877	+	23.7234i	−0.420330	+	0.824944i	0.579619	+	0.814887i	$0.303201\pi$
$827$	−12.0877	+	23.7234i	−0.420330	+	0.824944i	−0.999949	+	0.0100569i	$0.996799\pi$
$828$	2.04970	+	0.429769i	0.0712320	+	0.0149355i
$829$	9.16301	+	12.6118i	0.318245	+	0.438026i	0.937930	−	0.346824i	$-0.112740\pi$
$829$	9.16301	+	12.6118i	0.318245	+	0.438026i	−0.619686	+	0.784850i	$0.712740\pi$
$830$		0			0
$831$	−42.0352	+	5.59305i	−1.45819	+	0.194021i
$832$	−3.07024	+	3.07024i	−0.106441	+	0.106441i
$833$	−37.8305	+	5.99176i	−1.31075	+	0.207602i
$834$	8.72151	+	18.2203i	0.302001	+	0.630917i
$835$		0			0
$836$	19.9298	−	6.47560i	0.689288	−	0.223963i
$837$	11.7451	−	28.6904i	0.405969	−	0.991686i
$838$	6.43686	−	3.27974i	0.222358	−	0.113297i
$839$	−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
$842$	−2.27453	−	14.3608i	−0.0783856	−	0.494907i
$843$	0.869329	−	35.0459i	0.0299413	−	1.20705i
$844$	12.6440	−	17.4030i	0.435225	−	0.599036i
$845$		0			0
$846$	−4.98194	−	7.62538i	−0.171283	−	0.262166i
$847$	−0.279116	+	1.76227i	−0.00959053	+	0.0605522i
$848$	2.01389	+	1.02613i	0.0691572	+	0.0352374i
$849$	9.91473	+	10.4191i	0.340273	+	0.357583i
$850$		0			0
$851$		−	1.51978i		−	0.0520975i
$852$	6.01391	+	20.2002i	0.206033	+	0.692048i
$853$	40.1802	+	6.36392i	1.37574	+	0.217897i	0.800131	−	0.599825i	$-0.204763\pi$
$853$	40.1802	+	6.36392i	1.37574	+	0.217897i	0.575614	+	0.817722i	$0.304763\pi$
$854$	−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	$0.947735\pi$
$858$	17.1768	+	13.1426i	0.586407	+	0.448682i
$859$	17.4179	+	5.65942i	0.594291	+	0.193097i	0.590693	−	0.806897i	$-0.298855\pi$
$859$	17.4179	+	5.65942i	0.594291	+	0.193097i	0.00359858	+	0.999994i	$0.498855\pi$
$860$		0			0
$861$	3.59434	−	6.64178i	0.122495	−	0.226351i
$862$	1.88434	+	3.69822i	0.0641808	+	0.125962i
$863$	−3.59931	−	7.06405i	−0.122522	−	0.240463i	0.821596	−	0.570070i	$-0.193084\pi$
$863$	−3.59931	−	7.06405i	−0.122522	−	0.240463i	−0.944118	+	0.329607i	$0.893084\pi$
$864$	2.69662	−	4.44165i	0.0917410	−	0.151108i
$865$		0			0
$866$	−27.7975	−	9.03196i	−0.944598	−	0.306918i
$867$	17.8501	−	23.3293i	0.606223	−	0.792306i
$868$	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
$872$	11.4755	+	1.81754i	0.388609	+	0.0615497i
$873$	−13.8661	−	7.95468i	−0.469297	−	0.269225i
$874$			5.08674i			0.172062i
$875$		0			0
$876$	−0.702415	+	0.668411i	−0.0237324	+	0.0225835i
$877$	−45.8490	−	23.3612i	−1.54821	−	0.788853i	−0.549306	−	0.835621i	$-0.685108\pi$
$877$	−45.8490	−	23.3612i	−1.54821	−	0.788853i	−0.998906	+	0.0467683i	$0.985108\pi$
$878$	1.76709	−	11.1570i	0.0596365	−	0.376530i
$879$	−0.535237	+	2.91028i	−0.0180531	+	0.0981614i
$880$		0			0
$881$	1.69050	−	2.32677i	0.0569544	−	0.0783909i	−0.779590	−	0.626290i	$-0.784572\pi$
$881$	1.69050	−	2.32677i	0.0569544	−	0.0783909i	0.836544	+	0.547900i	$0.184572\pi$
$882$	−14.6168	+	13.2343i	−0.492175	+	0.445621i
$883$	−5.77775	−	36.4793i	−0.194437	−	1.22763i	−0.871016	−	0.491255i	$-0.836538\pi$
$883$	−5.77775	−	36.4793i	−0.194437	−	1.22763i	0.676579	−	0.736370i	$-0.263462\pi$
$884$	−7.81899	+	24.0644i	−0.262981	+	0.809372i
$885$		0			0
$886$	−5.38779	−	16.5819i	−0.181006	−	0.557081i
$887$	5.05323	−	2.57475i	0.169671	−	0.0864515i	−0.367093	−	0.930184i	$-0.619647\pi$
$887$	5.05323	−	2.57475i	0.169671	−	0.0864515i	0.536763	+	0.843733i	$0.319647\pi$
$888$	−3.55623	−	1.25381i	−0.119339	−	0.0420750i
$889$	−9.01156	+	2.92803i	−0.302238	+	0.0982031i
$890$		0			0
$891$	−23.7029	−	10.3969i	−0.794077	−	0.348308i
$892$	6.26922	−	0.992947i	0.209909	−	0.0332463i
$893$	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
$897$	−4.32255	+	2.97960i	−0.144326	+	0.0994858i
$898$	5.17823	−	10.1628i	0.172800	−	0.339138i
$899$	−19.1916			−0.640075
$900$		0			0
$901$	13.1715			0.438807
$902$	8.70815	−	17.0907i	0.289950	−	0.569058i
$903$	6.70738	−	4.62349i	0.223208	−	0.153860i
$904$	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	−0.980472	−	0.196661i	$-0.936990\pi$
$907$	−23.6056	+	23.6056i	−0.783811	+	0.783811i	0.196661	+	0.980472i	$0.436990\pi$
$908$	−13.9499	+	2.20945i	−0.462944	+	0.0733232i
$909$	35.2116	+	13.4051i	1.16790	+	0.444620i
$910$		0			0
$911$	−40.8162	+	13.2620i	−1.35230	+	0.439390i	−0.893466	−	0.449131i	$-0.851734\pi$
$911$	−40.8162	+	13.2620i	−1.35230	+	0.439390i	−0.458837	+	0.888521i	$0.651734\pi$
$912$	11.9027	+	4.19651i	0.394139	+	0.138960i
$913$	−12.1579	+	6.19478i	−0.402369	+	0.205017i
$914$	−1.98641	−	6.11354i	−0.0657046	−	0.202218i
$915$		0			0
$916$	4.70155	−	14.4699i	0.155344	−	0.478098i
$917$	0.562115	+	3.54906i	0.0185627	+	0.117200i
$918$	2.25082	−	30.1967i	0.0742882	−	0.996641i
$919$	−7.08527	+	9.75204i	−0.233722	+	0.321690i	−0.909727	−	0.415206i	$-0.863709\pi$
$919$	−7.08527	+	9.75204i	−0.233722	+	0.321690i	0.676006	+	0.736896i	$0.263709\pi$
$920$		0			0
$921$	−2.00554	+	10.9049i	−0.0660848	+	0.359328i
$922$	−3.02082	+	19.0727i	−0.0994854	+	0.628126i
$923$	−47.0765	−	23.9867i	−1.54954	−	0.789531i
$924$	2.35892	−	2.24473i	0.0776029	−	0.0738461i
$925$		0			0
$926$		−	4.47523i		−	0.147065i
$927$	−9.14386	+	15.9390i	−0.300324	+	0.523507i
$928$	−3.17710	−	0.503203i	−0.104293	−	0.0165185i
$929$	−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
$933$	−36.4499	+	47.6384i	−1.19332	+	1.55961i
$934$	1.67753	+	0.545064i	0.0548906	+	0.0178350i
$935$		0			0
$936$	3.40606	+	12.5727i	0.111330	+	0.410952i
$937$	−17.7176	−	34.7728i	−0.578809	−	1.13598i	−0.975904	−	0.218199i	$-0.929982\pi$
$937$	−17.7176	−	34.7728i	−0.578809	−	1.13598i	0.397095	−	0.917778i	$-0.370018\pi$
$938$	−4.22113	−	8.28444i	−0.137825	−	0.270497i
$939$	−21.5540	+	39.8284i	−0.703387	+	1.29975i
$940$		0			0
$941$	26.0266	+	8.45656i	0.848443	+	0.275676i	0.700794	−	0.713364i	$-0.252829\pi$
$941$	26.0266	+	8.45656i	0.848443	+	0.275676i	0.147649	+	0.989040i	$0.452829\pi$
$942$	12.5085	+	9.57075i	0.407550	+	0.311832i
$943$	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
$947$	29.2453	+	4.63200i	0.950344	+	0.150520i	0.612313	−	0.790615i	$-0.290239\pi$
$947$	29.2453	+	4.63200i	0.950344	+	0.150520i	0.338031	+	0.941135i	$0.390239\pi$
$948$	−5.04547	−	16.9473i	−0.163869	−	0.550423i
$949$		−	2.43068i		−	0.0789031i
$950$		0			0
$951$	−16.3187	−	17.1489i	−0.529171	−	0.556091i
$952$	3.39432	+	1.72949i	0.110011	+	0.0560532i
$953$	1.34632	−	8.50033i	0.0436116	−	0.275353i	−0.956240	−	0.292584i	$-0.905485\pi$
$953$	1.34632	−	8.50033i	0.0436116	−	0.275353i	0.999852	+	0.0172309i	$0.00548503\pi$
$954$	5.67658	−	3.70872i	0.183786	−	0.120074i
$955$		0			0
$956$	7.33996	−	10.1026i	0.237391	−	0.326741i
$957$	−0.397333	+	16.0180i	−0.0128439	+	0.517788i
$958$	−2.66344	−	16.8163i	−0.0860519	−	0.543311i
$959$	4.24957	−	13.0788i	0.137226	−	0.422338i
$960$		0			0
$961$	1.42019	+	4.37089i	0.0458125	+	0.140996i
$962$	8.42244	−	4.29145i	0.271550	−	0.138362i
$963$	1.59306	−	0.714547i	0.0513355	−	0.0230260i
$964$	−21.5856	+	7.01360i	−0.695227	+	0.225893i
$965$		0			0
$966$	0.341272	+	0.712959i	0.0109803	+	0.0229391i
$967$	−30.9179	+	4.89692i	−0.994254	+	0.157474i	−0.632302	−	0.774722i	$-0.717890\pi$
$967$	−30.9179	+	4.89692i	−0.994254	+	0.157474i	−0.361952	+	0.932197i	$0.617890\pi$
$968$	−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	0.443925	−	0.896064i	$-0.353586\pi$
$971$	−16.9971	−	23.3945i	−0.545463	−	0.750765i	−0.989388	+	0.145299i	$0.953586\pi$
$972$	−7.53249	−	13.6478i	−0.241605	−	0.437752i
$973$	−3.46123	+	6.79305i	−0.110962	+	0.217775i
$974$	28.1581			0.902245
$975$		0			0
$976$	−8.99313			−0.287863
$977$	−0.927445	+	1.82021i	−0.0296716	+	0.0582338i	−0.905366	−	0.424631i	$-0.860404\pi$
$977$	−0.927445	+	1.82021i	−0.0296716	+	0.0582338i	0.875695	+	0.482865i	$0.160404\pi$
$978$	−9.11881	−	13.2288i	−0.291587	−	0.423011i
$979$	−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
$983$	−28.7058	+	4.54655i	−0.915572	+	0.145012i	−0.596403	−	0.802685i	$-0.703404\pi$
$983$	−28.7058	+	4.54655i	−0.915572	+	0.145012i	−0.319169	+	0.947698i	$0.603404\pi$
$984$	10.4201	−	4.98779i	0.332181	−	0.159005i
$985$		0			0
$986$	−17.8278	+	5.79262i	−0.567754	+	0.184474i
$987$	1.14309	−	3.24219i	0.0363849	−	0.103200i
$988$	−28.1900	+	14.3635i	−0.896845	+	0.456965i
$989$	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	$0.171489\pi$
$992$	0.933323	+	5.89277i	0.0296330	+	0.187096i
$993$	18.3009	+	0.453961i	0.580760	+	0.0144060i
$994$	−4.67569	+	6.43554i	−0.148304	+	0.204123i
$995$		0			0
$996$	−8.08252	−	1.48648i	−0.256104	−	0.0471008i
$997$	−5.62909	+	35.5407i	−0.178275	+	1.12558i	0.722523	+	0.691347i	$0.242982\pi$
$997$	−5.62909	+	35.5407i	−0.178275	+	1.12558i	−0.900798	+	0.434238i	$0.857018\pi$
$998$	−11.5149	−	5.86715i	−0.364499	−	0.185722i
$999$	−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.c.143.2		80
3.2	odd	2	inner	750.2.l.c.143.7		80
5.2	odd	4		150.2.l.a.17.4	✓	80
5.3	odd	4		750.2.l.b.107.7		80
5.4	even	2		750.2.l.a.143.9		80
15.2	even	4		150.2.l.a.17.7	yes	80
15.8	even	4		750.2.l.b.107.4		80
15.14	odd	2		750.2.l.a.143.4		80
25.3	odd	20		750.2.l.a.257.4		80
25.4	even	10		750.2.l.b.743.4		80
25.21	even	5		150.2.l.a.53.7	yes	80
25.22	odd	20	inner	750.2.l.c.257.7		80
75.29	odd	10		750.2.l.b.743.7		80
75.47	even	20	inner	750.2.l.c.257.2		80
75.53	even	20		750.2.l.a.257.9		80
75.71	odd	10		150.2.l.a.53.4	yes	80

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.42607 + 0.983013i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.228447 - 1.71692i) q^{6} +(0.462249 - 0.462249i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.06737 - 2.80370i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-1.42607 + 0.983013i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.228447 - 1.71692i) q^{6} +(0.462249 - 0.462249i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.06737 - 2.80370i) q^{9} +(2.73512 - 0.888693i) q^{11} +(1.63350 + 0.575917i) q^{12} +(-3.86872 + 1.97121i) q^{13} +(0.202010 + 0.621723i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.911620 + 5.75574i) q^{17} +(2.01354 + 2.22389i) q^{18} +(-4.28299 + 5.89503i) q^{19} +(-0.204804 + 1.11360i) q^{21} +(-0.449885 + 2.84047i) q^{22} +(-0.622003 - 0.316926i) q^{23} +(-1.25474 + 1.19400i) q^{24} -4.34197i q^{26} +(1.23392 + 5.04752i) q^{27} +(-0.645670 - 0.102264i) q^{28} +(2.60237 - 1.89073i) q^{29} +(-4.82678 - 3.50686i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.02688 + 3.95600i) q^{33} +(-5.54227 - 1.80079i) q^{34} +(-2.89562 + 0.784450i) q^{36} +(0.988365 + 1.93977i) q^{37} +(-3.30807 - 6.49246i) q^{38} +(3.57936 - 6.61410i) q^{39} +(-6.34331 - 2.06107i) q^{41} +(-0.899243 - 0.688045i) q^{42} +(-5.08751 - 5.08751i) q^{43} +(-2.32663 - 1.69040i) q^{44} +(0.564767 - 0.410327i) q^{46} +(-2.99881 - 0.474965i) q^{47} +(-0.494220 - 1.66004i) q^{48} +6.57265i q^{49} +(-6.95800 - 7.31198i) q^{51} +(3.86872 + 1.97121i) q^{52} +(0.353579 - 2.23241i) q^{53} +(-5.05756 - 1.19210i) q^{54} +(0.384246 - 0.528869i) q^{56} +(0.312969 - 12.6170i) q^{57} +(0.503203 + 3.17710i) q^{58} +(-2.66341 + 8.19714i) q^{59} +(2.77903 + 8.55298i) q^{61} +(5.31594 - 2.70861i) q^{62} +(-0.802614 - 1.78940i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-2.15064 - 4.49296i) q^{66} +(-14.0479 + 2.22497i) q^{67} +(4.12066 - 4.12066i) q^{68} +(1.19856 - 0.159477i) q^{69} +(7.15246 + 9.84451i) q^{71} +(0.615636 - 2.93615i) q^{72} +(-0.254148 + 0.498794i) q^{73} -2.17706 q^{74} +7.28665 q^{76} +(0.853507 - 1.67510i) q^{77} +(4.26821 + 6.19197i) q^{78} +(-6.00067 - 8.25922i) q^{79} +(-6.72143 - 5.98518i) q^{81} +(4.71623 - 4.71623i) q^{82} +(-4.68629 + 0.742236i) q^{83} +(1.02130 - 0.488866i) q^{84} +(6.84269 - 2.22332i) q^{86} +(-1.85256 + 5.25448i) q^{87} +(2.56242 - 1.30562i) q^{88} +(-1.78693 - 5.49959i) q^{89} +(-0.877122 + 2.69950i) q^{91} +(0.109205 + 0.689496i) q^{92} +(10.3306 + 0.256256i) q^{93} +(1.78463 - 2.45633i) q^{94} +(1.70348 + 0.313291i) q^{96} +(0.833578 - 5.26300i) q^{97} +(-5.85628 - 2.98392i) 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	\( 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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