LMFDB - Embedded newform 750.2.l.a.143.4

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			143.4
Character	$\chi$	$=$	750.143
Dual form			750.2.l.a.257.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(1.05251 + 1.37558i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.70348 + 0.313291i) q^{6} +(-0.462249 + 0.462249i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-0.784450 + 2.89562i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(1.05251 + 1.37558i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.70348 + 0.313291i) q^{6} +(-0.462249 + 0.462249i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-0.784450 + 2.89562i) q^{9} +(-2.73512 + 0.888693i) q^{11} +(0.494220 - 1.66004i) 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} +(-2.22389 - 2.01354i) q^{18} +(-4.28299 + 5.89503i) q^{19} +(-1.12238 - 0.149340i) q^{21} +(0.449885 - 2.84047i) q^{22} +(-0.622003 - 0.316926i) q^{23} +(1.25474 + 1.19400i) q^{24} +4.34197i q^{26} +(-4.80881 + 1.96860i) 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} +(-4.10120 - 2.82702i) q^{33} +(-5.54227 - 1.80079i) q^{34} +(2.80370 - 1.06737i) q^{36} +(-0.988365 - 1.93977i) q^{37} +(-3.30807 - 6.49246i) q^{38} +(6.78343 + 3.24703i) q^{39} +(6.34331 + 2.06107i) q^{41} +(0.642614 - 0.932251i) 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} +(-1.63350 + 0.575917i) q^{48} +6.57265i q^{49} +(-6.95800 + 7.31198i) q^{51} +(-3.86872 - 1.97121i) q^{52} +(0.353579 - 2.23241i) q^{53} +(0.429121 - 5.17840i) q^{54} +(-0.384246 + 0.528869i) q^{56} +(-12.6170 + 0.312969i) 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} +(-0.975888 - 1.70111i) q^{63} +(0.951057 - 0.309017i) q^{64} +(4.38080 - 2.37076i) q^{66} +(14.0479 - 2.22497i) q^{67} +(4.12066 - 4.12066i) q^{68} +(-0.218706 - 1.18918i) q^{69} +(-7.15246 - 9.84451i) q^{71} +(-0.321816 + 2.98269i) q^{72} +(0.254148 - 0.498794i) q^{73} +2.17706 q^{74} +7.28665 q^{76} +(0.853507 - 1.67510i) q^{77} +(-5.97273 + 4.56996i) q^{78} +(-6.00067 - 8.25922i) q^{79} +(-7.76928 - 4.54294i) q^{81} +(-4.71623 + 4.71623i) q^{82} +(-4.68629 + 0.742236i) q^{83} +(0.538901 + 0.995806i) q^{84} +(-6.84269 + 2.22332i) q^{86} +(-5.33987 - 1.58976i) 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} +(-0.256256 - 10.3306i) q^{93} +(1.78463 - 2.45633i) q^{94} +(0.228447 - 1.71692i) 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
$3$	1.05251	+	1.37558i	0.607666	+	0.794192i
$3$	1.05251	+	1.37558i	0.607666	+	0.794192i
$4$	−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	−0.789047	−	0.614333i	$-0.789425\pi$
$7$	−0.462249	+	0.462249i	−0.174714	+	0.174714i	0.614333	+	0.789047i	$0.289425\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−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	$0.542741\pi$
$12$	0.494220	−	1.66004i	0.142669	−	0.479213i
$13$	3.86872	−	1.97121i	1.07299	−	0.546716i	0.174028	−	0.984741i	$-0.444322\pi$
$13$	3.86872	−	1.97121i	1.07299	−	0.546716i	0.898963	+	0.438025i	$0.144322\pi$
$14$	−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	$0.700189\pi$
$18$	−2.22389	−	2.01354i	−0.524175	−	0.474595i
$19$	−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
$21$	−1.12238	−	0.149340i	−0.244924	−	0.0325886i
$22$	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
$27$	−4.80881	+	1.96860i	−0.925455	+	0.378856i
$28$	0.645670	+	0.102264i	0.122020	+	0.0193261i
$29$	−2.60237	+	1.89073i	−0.483247	+	0.351100i	−0.802582	−	0.596542i	$-0.796541\pi$
$29$	−2.60237	+	1.89073i	−0.483247	+	0.351100i	0.319334	+	0.947642i	$0.396541\pi$
$30$		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
$33$	−4.10120	−	2.82702i	−0.713928	−	0.492121i
$34$	−5.54227	−	1.80079i	−0.950491	−	0.308833i
$35$		0			0
$36$	2.80370	−	1.06737i	0.467283	−	0.177895i
$37$	−0.988365	−	1.93977i	−0.162486	−	0.318897i	0.795380	−	0.606110i	$-0.207271\pi$
$37$	−0.988365	−	1.93977i	−0.162486	−	0.318897i	−0.957867	+	0.287213i	$0.907271\pi$
$38$	−3.30807	−	6.49246i	−0.536640	−	1.05322i
$39$	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	$0.425626\pi$
$42$	0.642614	−	0.932251i	0.0991574	−	0.143849i
$43$	5.08751	+	5.08751i	0.775838	+	0.775838i	0.979120	−	0.203282i	$-0.0651609\pi$
$43$	5.08751	+	5.08751i	0.775838	+	0.775838i	−0.203282	+	0.979120i	$0.565161\pi$
$44$	2.32663	+	1.69040i	0.350753	+	0.254837i
$45$		0			0
$46$	0.564767	−	0.410327i	0.0832703	−	0.0604994i
$47$	−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	$0.621075\pi$
$48$	−1.63350	+	0.575917i	−0.235775	+	0.0831265i
$49$			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	$0.000386884\pi$
$54$	0.429121	−	5.17840i	0.0583960	−	0.704691i
$55$		0			0
$56$	−0.384246	+	0.528869i	−0.0513470	+	0.0706731i
$57$	−12.6170	+	0.312969i	−1.67116	+	0.0414538i
$58$	−0.503203	−	3.17710i	−0.0660738	−	0.417174i
$59$	2.66341	−	8.19714i	0.346747	−	1.06718i	−0.613895	−	0.789388i	$-0.710398\pi$
$59$	2.66341	−	8.19714i	0.346747	−	1.06718i	0.960642	−	0.277790i	$-0.0896018\pi$
$60$		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
$63$	−0.975888	−	1.70111i	−0.122950	−	0.214320i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	4.38080	−	2.37076i	0.539239	−	0.291820i
$67$	14.0479	−	2.22497i	1.71622	−	0.271823i	0.780654	−	0.624964i	$-0.214886\pi$
$67$	14.0479	−	2.22497i	1.71622	−	0.271823i	0.935570	+	0.353141i	$0.114886\pi$
$68$	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	$-0.456808\pi$
$72$	−0.321816	+	2.98269i	−0.0379264	+	0.351513i
$73$	0.254148	−	0.498794i	0.0297458	−	0.0583794i	−0.875655	−	0.482937i	$-0.839570\pi$
$73$	0.254148	−	0.498794i	0.0297458	−	0.0583794i	0.905401	+	0.424557i	$0.139570\pi$
$74$	2.17706			0.253078
$75$		0			0
$76$	7.28665			0.835837
$77$	0.853507	−	1.67510i	0.0972661	−	0.190896i
$78$	−5.97273	+	4.56996i	−0.676279	+	0.517446i
$79$	−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
$81$	−7.76928	−	4.54294i	−0.863253	−	0.504771i
$82$	−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	$0.533854\pi$
$84$	0.538901	+	0.995806i	0.0587989	+	0.108651i
$85$		0			0
$86$	−6.84269	+	2.22332i	−0.737866	+	0.239747i
$87$	−5.33987	−	1.58976i	−0.572494	−	0.170440i
$88$	−2.56242	+	1.30562i	−0.273155	+	0.139179i
$89$	1.78693	+	5.49959i	0.189414	+	0.582956i	0.999996	−	0.00266864i	$-0.000849456\pi$
$89$	1.78693	+	5.49959i	0.189414	+	0.582956i	−0.810583	+	0.585624i	$0.800849\pi$
$90$		0			0
$91$	−0.877122	+	2.69950i	−0.0919473	+	0.282985i
$92$	0.109205	+	0.689496i	0.0113854	+	0.0718849i
$93$	−0.256256	−	10.3306i	−0.0265725	−	1.07124i
$94$	1.78463	−	2.45633i	0.184070	−	0.253351i
$95$		0			0
$96$	0.228447	−	1.71692i	0.0233158	−	0.175232i
$97$	−0.833578	+	5.26300i	−0.0846370	+	0.534377i	0.908544	+	0.417790i	$0.137195\pi$
$97$	−0.833578	+	5.26300i	−0.0846370	+	0.534377i	−0.993181	+	0.116587i	$0.962805\pi$
$98$	−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	$-0.785167\pi$
$101$		−	12.5590i		−	1.24967i	0.780758	−	0.624833i	$-0.214833\pi$
$102$	−3.35615	−	9.51920i	−0.332309	−	0.942541i
$103$	6.04979	+	0.958193i	0.596104	+	0.0944135i	0.447194	−	0.894437i	$-0.352424\pi$
$103$	6.04979	+	0.958193i	0.596104	+	0.0944135i	0.148910	+	0.988851i	$0.452424\pi$
$104$	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	$0.741044\pi$
$108$	4.41917	+	2.73330i	0.425235	+	0.263011i
$109$	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
$111$	1.62806	−	3.40121i	0.154528	−	0.322828i
$112$	−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	$0.617842\pi$
$114$	5.44913	−	11.3839i	0.510358	−	1.06620i
$115$		0			0
$116$	3.05927	+	0.994016i	0.284046	+	0.0922921i
$117$	2.67307	+	12.7487i	0.247126	+	1.17862i
$118$	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
$123$	3.84123	+	10.8950i	0.346352	+	0.982372i
$124$			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	0.920658	−	0.390369i	$-0.127653\pi$
$127$	12.9147	+	6.58036i	1.14599	+	0.583912i	0.225334	+	0.974282i	$0.427653\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	−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	$0.122812\pi$
$132$	0.123522	+	4.97962i	0.0107512	+	0.433421i
$133$	−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	$-0.00543808\pi$
$138$	1.15886	+	0.345010i	0.0986488	+	0.0293692i
$139$	−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
$141$	−2.50292	−	4.62502i	−0.210784	−	0.389497i
$142$	12.0187	−	1.90357i	1.00858	−	0.159744i
$143$	−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
$147$	−9.04122	+	6.91778i	−0.745707	+	0.570569i
$148$	−0.988365	+	1.93977i	−0.0812431	+	0.159449i
$149$	−10.0289			−0.821602			−0.410801	−	0.911725i	$-0.634751\pi$
$149$	−10.0289			−0.821602			−0.410801	+	0.911725i	$0.634751\pi$
$150$		0			0
$151$	17.9175			1.45811			0.729054	−	0.684456i	$-0.239960\pi$
$151$	17.9175			1.45811			0.729054	+	0.684456i	$0.239960\pi$
$152$	−3.30807	+	6.49246i	−0.268320	+	0.526608i
$153$	−17.3816	−	1.87538i	−1.40522	−	0.151616i
$154$	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	−0.402331	−	0.915494i	$-0.631800\pi$
$157$	6.42991	−	6.42991i	0.513163	−	0.513163i	0.915494	+	0.402331i	$0.131800\pi$
$158$	10.0833	−	1.59703i	0.802181	−	0.127053i
$159$	3.44301	−	1.86326i	0.273049	−	0.147766i
$160$		0			0
$161$	0.434019	−	0.141021i	0.0342055	−	0.0111140i
$162$	7.57497	−	4.86002i	0.595146	−	0.381840i
$163$	−8.26532	+	4.21139i	−0.647390	+	0.329862i	−0.746667	−	0.665198i	$-0.768347\pi$
$163$	−8.26532	+	4.21139i	−0.647390	+	0.329862i	0.0992767	+	0.995060i	$0.468347\pi$
$164$	−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	$0.887017\pi$
$168$	−1.13193	+	0.0280779i	−0.0873299	+	0.00216626i
$169$	3.44013	−	4.73493i	0.264625	−	0.364226i
$170$		0			0
$171$	−13.7100	−	17.0263i	−1.04843	−	1.30203i
$172$	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
$177$	14.0791	−	4.96383i	1.05825	−	0.373104i
$178$	−5.71142	−	0.904600i	−0.428089	−	0.0678026i
$179$	3.24712	−	2.35917i	0.242701	−	0.176332i	−0.459785	−	0.888030i	$-0.652073\pi$
$179$	3.24712	−	2.35917i	0.242701	−	0.176332i	0.702486	+	0.711698i	$0.252073\pi$
$180$		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
$183$	−8.84036	+	12.8249i	−0.653498	+	0.948042i
$184$	−0.663923	−	0.215722i	−0.0489451	−	0.0159032i
$185$		0			0
$186$	9.32099	+	4.46168i	0.683448	+	0.327146i
$187$	−7.60848	−	14.9325i	−0.556387	−	1.09197i
$188$	1.37840	+	2.70527i	0.100530	+	0.197302i
$189$	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	$0.454899\pi$
$192$	1.42607	+	0.983013i	0.102918	+	0.0709428i
$193$	9.01719	+	9.01719i	0.649071	+	0.649071i	0.952769	−	0.303697i	$-0.0982211\pi$
$193$	9.01719	+	9.01719i	0.649071	+	0.649071i	−0.303697	+	0.952769i	$0.598221\pi$
$194$	−4.31093	−	3.13208i	−0.309507	−	0.224870i
$195$		0			0
$196$	5.31739	−	3.86331i	0.379813	−	0.275951i
$197$	−0.404993	−	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	$0.554650\pi$
$198$	7.87201	+	3.53090i	0.559439	+	0.250930i
$199$		−	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
$204$	10.0053	+	1.33127i	0.700513	+	0.0932076i
$205$		0			0
$206$	−3.60030	+	4.95539i	−0.250845	+	0.345259i
$207$	1.40563	−	1.55247i	0.0976980	−	0.107904i
$208$	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
$213$	6.01391	−	20.2002i	0.412066	−	1.38410i
$214$	−0.553505	+	0.179845i	−0.0378368	+	0.0122939i
$215$		0			0
$216$	−4.44165	+	2.69662i	−0.302216	+	0.183482i
$217$	3.85221	−	0.610130i	0.261505	−	0.0414184i
$218$	−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
$222$	2.29138	+	2.99472i	0.153787	+	0.200993i
$223$	2.88164	−	5.65554i	0.192969	−	0.378723i	−0.774167	−	0.632981i	$-0.781831\pi$
$223$	2.88164	−	5.65554i	0.192969	−	0.378723i	0.967137	+	0.254258i	$0.0818311\pi$
$224$	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	$-0.00528292\pi$
$228$	7.66927	+	10.0234i	0.507910	+	0.663815i
$229$	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
$231$	3.20256	−	0.588991i	0.210713	−	0.0387528i
$232$	−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	$0.369979\pi$
$234$	−12.5727	−	3.40606i	−0.821904	−	0.222661i
$235$		0			0
$236$	−8.19714	+	2.66341i	−0.533589	+	0.173373i
$237$	5.04547	−	16.9473i	0.327738	−	1.10085i
$238$	3.39432	−	1.72949i	0.220021	−	0.112106i
$239$	−3.85885	−	11.8763i	−0.249608	−	0.768215i	−0.994844	−	0.101414i	$-0.967663\pi$
$239$	−3.85885	−	11.8763i	−0.249608	−	0.768215i	0.745236	−	0.666801i	$-0.232337\pi$
$240$		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
$243$	−1.92805	−	15.4688i	−0.123684	−	0.992322i
$244$	5.28603	−	7.27560i	0.338403	−	0.465772i
$245$		0			0
$246$	−11.4514	−	1.52368i	−0.730116	−	0.0971465i
$247$	−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	$0.0854471\pi$
$251$			8.40399i			0.530455i	−0.964186	+	0.265228i	$0.914553\pi$
$252$	−0.802614	+	1.78940i	−0.0505599	+	0.112721i
$253$	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	$-0.635848\pi$
$258$	−10.2604	−	7.07261i	−0.638782	−	0.440321i
$259$	1.35353	+	0.439788i	0.0841042	+	0.0273271i
$260$		0			0
$261$	−3.43342	−	9.01866i	−0.212523	−	0.558241i
$262$	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	$0.808521\pi$
$264$	−4.49296	−	2.15064i	−0.276522	−	0.132363i
$265$		0			0
$266$	4.53028	+	1.47198i	0.277769	+	0.0902527i
$267$	−5.68438	+	8.24643i	−0.347879	+	0.504673i
$268$	−10.0572	−	10.0572i	−0.614340	−	0.614340i
$269$	16.4085	+	11.9215i	1.00044	+	0.726865i	0.962183	−	0.272402i	$-0.0878182\pi$
$269$	16.4085	+	11.9215i	1.00044	+	0.726865i	0.0382610	+	0.999268i	$0.487818\pi$
$270$		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
$273$	−4.63657	+	1.63470i	−0.280618	+	0.0989365i
$274$			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	−0.347772	−	0.937579i	$-0.613062\pi$
$277$	−21.8145	−	11.1150i	−1.31070	−	0.667837i	−0.962933	+	0.269742i	$0.913062\pi$
$278$	1.82442	−	11.5189i	0.109422	−	0.690861i
$279$	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	$-0.00631077\pi$
$282$	5.25722	−	0.130408i	0.313063	−	0.00776566i
$283$	1.29900	+	8.20158i	0.0772177	+	0.487533i	0.995743	+	0.0921715i	$0.0293808\pi$
$283$	1.29900	+	8.20158i	0.0772177	+	0.487533i	−0.918525	+	0.395362i	$0.870619\pi$
$284$	−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
$288$	2.60221	−	1.49283i	0.153336	−	0.0879656i
$289$	−16.1295	+	5.24081i	−0.948797	+	0.308283i
$290$		0			0
$291$	−8.11704	+	4.39270i	−0.475829	+	0.257505i
$292$	−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	$0.234109\pi$
$294$	−2.05916	−	11.1964i	−0.120092	−	0.652987i
$295$		0			0
$296$	−1.27964	−	1.76128i	−0.0743778	−	0.102372i
$297$	11.4032	−	9.65789i	0.661679	−	0.560408i
$298$	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
$303$	17.2759	−	13.2185i	0.992475	−	0.759380i
$304$	−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	−0.824380	−	0.566036i	$-0.808476\pi$
$307$	−4.52656	+	4.52656i	−0.258344	+	0.258344i	0.566036	+	0.824380i	$0.308476\pi$
$308$	−1.85686	+	0.294098i	−0.105805	+	0.0167578i
$309$	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	$0.960681\pi$
$312$	7.20786	+	2.14589i	0.408065	+	0.121487i
$313$	−23.2965	+	11.8701i	−1.31679	+	0.670940i	−0.964285	−	0.264869i	$-0.914671\pi$
$313$	−23.2965	+	11.8701i	−1.31679	+	0.670940i	−0.352509	+	0.935808i	$0.614671\pi$
$314$	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	$0.824610\pi$
$318$	0.0970796	+	3.91365i	0.00544396	+	0.219466i
$319$	5.43750	−	7.48407i	0.304441	−	0.419028i
$320$		0			0
$321$	−0.132954	+	0.999229i	−0.00742075	+	0.0557715i
$322$	−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
$327$	6.69132	+	18.9789i	0.370031	+	1.04953i
$328$	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
$333$	6.39218	−	1.34028i	0.350289	−	0.0734467i
$334$	−4.83207	−	1.57004i	−0.264399	−	0.0859085i
$335$		0			0
$336$	0.488866	−	1.02130i	0.0266698	−	0.0557165i
$337$	−14.3152	−	28.0951i	−0.779796	−	1.53044i	−0.846334	−	0.532652i	$-0.821195\pi$
$337$	−14.3152	−	28.0951i	−0.779796	−	1.53044i	0.0665380	−	0.997784i	$-0.478805\pi$
$338$	2.65707	+	5.21479i	0.144526	+	0.283647i
$339$	−10.5947	+	22.1337i	−0.575428	+	1.20214i
$340$		0			0
$341$	16.3183	+	5.30214i	0.883686	+	0.287127i
$342$	21.3947	−	4.48593i	1.15689	−	0.242571i
$343$	−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	$0.435935\pi$
$348$	1.85256	+	5.25448i	0.0993074	+	0.281670i
$349$		−	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	$0.0252939\pi$
$354$	−1.96898	+	14.7981i	−0.104650	+	0.786511i
$355$		0			0
$356$	3.39893	−	4.67823i	0.180143	−	0.247946i
$357$	−0.163624	−	6.59628i	−0.00865988	−	0.349112i
$358$	0.627874	+	3.96424i	0.0331842	+	0.209517i
$359$	−2.44510	+	7.52523i	−0.129047	+	0.397167i	−0.994617	−	0.103622i	$-0.966957\pi$
$359$	−2.44510	+	7.52523i	−0.129047	+	0.397167i	0.865569	+	0.500789i	$0.166957\pi$
$360$		0			0
$361$	−10.5360	−	32.4266i	−0.554528	−	1.70666i
$362$	−3.64292	+	1.85616i	−0.191468	+	0.0975577i
$363$	−4.53086	−	1.34890i	−0.237809	−	0.0707991i
$364$	2.69950	−	0.877122i	0.141492	−	0.0459737i
$365$		0			0
$366$	−7.41360	−	13.6992i	−0.387515	−	0.716068i
$367$	−21.7433	+	3.44380i	−1.13499	+	0.179765i	−0.695530	−	0.718497i	$-0.744830\pi$
$367$	−21.7433	+	3.44380i	−1.13499	+	0.179765i	−0.439460	+	0.898262i	$0.644830\pi$
$368$	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
$372$	−8.20703	+	6.27950i	−0.425515	+	0.325577i
$373$	9.69853	−	19.0344i	0.502171	−	0.985566i	−0.491247	−	0.871020i	$-0.663459\pi$
$373$	9.69853	−	19.0344i	0.502171	−	0.985566i	0.993418	−	0.114545i	$-0.0365412\pi$
$374$	16.7591			0.866593
$375$		0			0
$376$	−3.03619			−0.156580
$377$	−6.34081	+	12.4445i	−0.326568	+	0.640926i
$378$	2.19535	+	2.59207i	0.112917	+	0.133322i
$379$	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
$381$	4.54100	+	24.6911i	0.232642	+	1.26496i
$382$	−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	$0.345267\pi$
$384$	−1.52329	+	0.824362i	−0.0777353	+	0.0420681i
$385$		0			0
$386$	−12.1281	+	3.94066i	−0.617304	+	0.200574i
$387$	−18.7224	+	10.7406i	−0.951714	+	0.545976i
$388$	4.74782	−	2.41914i	0.241034	−	0.122813i
$389$	8.45598	+	26.0248i	0.428735	+	1.31951i	0.899372	+	0.437185i	$0.144024\pi$
$389$	8.45598	+	26.0248i	0.428735	+	1.31951i	−0.470636	+	0.882327i	$0.655976\pi$
$390$		0			0
$391$	1.25712	−	3.86900i	0.0635751	−	0.195664i
$392$	1.02819	+	6.49173i	0.0519314	+	0.327882i
$393$	9.51764	−	0.236089i	0.480102	−	0.0119091i
$394$	0.241016	−	0.331731i	0.0121422	−	0.0167123i
$395$		0			0
$396$	−6.71987	+	5.41101i	−0.337686	+	0.271914i
$397$	−0.556301	+	3.51235i	−0.0279199	+	0.176280i	−0.997708	−	0.0676706i	$-0.978443\pi$
$397$	−0.556301	+	3.51235i	−0.0279199	+	0.176280i	0.969788	+	0.243950i	$0.0784433\pi$
$398$	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	$-0.863527\pi$
$401$		−	16.6499i		−	0.831458i	0.909489	−	0.415729i	$-0.136473\pi$
$402$	−23.2333	+	8.19128i	−1.15877	+	0.408544i
$403$	−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
$408$	−5.72849	+	8.31043i	−0.283603	+	0.411427i
$409$	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
$411$	32.8651	+	15.7315i	1.62112	+	0.775979i
$412$	−2.78078	−	5.45760i	−0.136999	−	0.268876i
$413$	2.55796	+	5.02028i	0.125869	+	0.247032i
$414$	0.745122	+	1.95723i	0.0366207	+	0.0961928i
$415$		0			0
$416$	−4.12946	−	1.34174i	−0.202463	−	0.0657843i
$417$	−16.6316	−	11.4644i	−0.814454	−	0.561415i
$418$	14.8178	+	14.8178i	0.724761	+	0.724761i
$419$	5.84455	+	4.24631i	0.285525	+	0.207446i	0.721324	−	0.692598i	$-0.243534\pi$
$419$	5.84455	+	4.24631i	0.285525	+	0.207446i	−0.435799	+	0.900044i	$0.643534\pi$
$420$		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
$423$	3.72774	−	8.31084i	0.181249	−	0.404087i
$424$		−	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
$429$	−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	$0.231873\pi$
$432$	−0.386242	−	5.18178i	−0.0185831	−	0.249308i
$433$	−4.57227	−	28.8682i	−0.219729	−	1.38732i	−0.812977	−	0.582296i	$-0.802154\pi$
$433$	−4.57227	−	28.8682i	−0.219729	−	1.38732i	0.593248	−	0.805020i	$-0.297846\pi$
$434$	−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
$438$	−0.276669	+	0.929309i	−0.0132198	+	0.0444041i
$439$	−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
$441$	−19.0319	−	5.15592i	−0.906282	−	0.245520i
$442$	−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	$0.385934\pi$
$444$	−3.70858	+	0.682054i	−0.176001	+	0.0323689i
$445$		0			0
$446$	3.73089	+	5.13513i	0.176663	+	0.243155i
$447$	−10.5555	−	13.7956i	−0.499260	−	0.652510i
$448$	−0.296782	+	0.582467i	−0.0140216	+	0.0275190i
$449$	11.4060			0.538284			0.269142	−	0.963101i	$-0.413260\pi$
$449$	11.4060			0.538284			0.269142	+	0.963101i	$0.413260\pi$
$450$		0			0
$451$	−19.1813			−0.903214
$452$	6.43189	−	12.6233i	0.302531	−	0.593750i
$453$	18.8584	+	24.6470i	0.886043	+	1.15802i
$454$	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	−0.592757	−	0.805381i	$-0.701961\pi$
$457$	4.54539	−	4.54539i	0.212624	−	0.212624i	0.805381	+	0.592757i	$0.201961\pi$
$458$	−15.0272	+	2.38008i	−0.702176	+	0.111214i
$459$	−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	$0.548465\pi$
$462$	−0.929138	+	3.12090i	−0.0432274	+	0.145197i
$463$	3.98746	−	2.03171i	0.185313	−	0.0944216i	−0.358873	−	0.933387i	$-0.616839\pi$
$463$	3.98746	−	2.03171i	0.185313	−	0.0944216i	0.544186	+	0.838965i	$0.316839\pi$
$464$	−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	$0.962994\pi$
$468$	8.74271	−	9.65605i	0.404132	−	0.446351i
$469$	−5.46513	+	7.52211i	−0.252356	+	0.347339i
$470$		0			0
$471$	15.6124	+	2.07733i	0.719382	+	0.0957183i
$472$	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
$477$	6.18686	+	2.77505i	0.283277	+	0.127061i
$478$	12.3338	+	1.95347i	0.564133	+	0.0893498i
$479$	13.7743	−	10.0076i	0.629363	−	0.457259i	−0.226817	−	0.973937i	$-0.572832\pi$
$479$	13.7743	−	10.0076i	0.629363	−	0.457259i	0.856179	+	0.516679i	$0.172832\pi$
$480$		0			0
$481$	−7.64742	−	5.55617i	−0.348692	−	0.253340i
$482$	16.0488	+	16.0488i	0.731005	+	0.731005i
$483$	0.650795	+	0.448602i	0.0296122	+	0.0204121i
$484$	2.59578	+	0.843419i	0.117990	+	0.0383372i
$485$		0			0
$486$	14.6581	+	5.30477i	0.664904	+	0.240629i
$487$	12.7835	+	25.0891i	0.579277	+	1.13690i	0.975758	+	0.218852i	$0.0702313\pi$
$487$	12.7835	+	25.0891i	0.579277	+	1.13690i	−0.396481	+	0.918043i	$0.629769\pi$
$488$	4.08280	+	8.01294i	0.184820	+	0.362729i
$489$	−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	$0.666146\pi$
$492$	6.55645	−	9.51156i	0.295588	−	0.428814i
$493$	−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
$498$	7.75047	−	2.73256i	0.347307	−	0.122449i
$499$			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	$-0.117540\pi$
$504$	−1.22999	−	1.52750i	−0.0547879	−	0.0680404i
$505$		0			0
$506$	−1.18005	+	1.62420i	−0.0524595	+	0.0722044i
$507$	10.1341	−	0.251380i	0.450069	−	0.0111642i
$508$	−2.26744	−	14.3160i	−0.100601	−	0.635171i
$509$	−1.15005	+	3.53949i	−0.0509750	+	0.156885i	−0.973304	−	0.229522i	$-0.926284\pi$
$509$	−1.15005	+	3.53949i	−0.0509750	+	0.156885i	0.922329	+	0.386407i	$0.126284\pi$
$510$		0			0
$511$	0.113087	+	0.348047i	0.00500268	+	0.0153967i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	8.99114	−	36.7795i	0.396969	−	1.62386i
$514$	28.5533	−	9.27753i	1.25943	−	0.409214i
$515$		0			0
$516$	10.9598	−	5.93114i	0.482480	−	0.261104i
$517$	8.62420	−	1.36594i	0.379292	−	0.0600739i
$518$	−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	$0.417259\pi$
$522$	9.59442	+	1.03519i	0.419937	+	0.0453089i
$523$	−10.1317	+	19.8847i	−0.443030	+	0.869495i	0.556230	+	0.831028i	$0.312247\pi$
$523$	−10.1317	+	19.8847i	−0.443030	+	0.869495i	−0.999260	+	0.0384667i	$0.987753\pi$
$524$	−5.49670			−0.240125
$525$		0			0
$526$	−4.21464			−0.183767
$527$	15.7844	−	30.9786i	0.687579	−	1.34945i
$528$	3.95600	−	3.02688i	0.172163	−	0.131728i
$529$	−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
$533$	28.6033	−	4.53032i	1.23895	−	0.196230i
$534$	−4.76697	−	8.80862i	−0.206287	−	0.381186i
$535$		0			0
$536$	13.5269	−	4.39515i	0.584272	−	0.189842i
$537$	6.66285	+	1.98363i	0.287523	+	0.0855999i
$538$	−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
$543$	0.175607	+	7.07940i	0.00753604	+	0.303806i
$544$	3.42531	−	4.71454i	0.146859	−	0.202134i
$545$		0			0
$546$	0.648429	−	4.87335i	0.0277502	−	0.208560i
$547$	3.80438	−	24.0199i	0.162663	−	1.02702i	−0.762373	−	0.647138i	$-0.775966\pi$
$547$	3.80438	−	24.0199i	0.162663	−	1.02702i	0.925036	−	0.379878i	$-0.124034\pi$
$548$	−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
$552$	−0.402042	−	1.14033i	−0.0171121	−	0.0485357i
$553$	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	$0.565485\pi$
$558$	3.67302	+	17.5177i	0.155491	+	0.741585i
$559$	29.7107	+	9.65360i	1.25663	+	0.408304i
$560$		0			0
$561$	12.5328	−	26.1826i	0.529137	−	1.10543i
$562$	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	$0.843455\pi$
$564$	−2.27053	+	4.74342i	−0.0956068	+	0.199734i
$565$		0			0
$566$	−7.89740	−	2.56602i	−0.331952	−	0.107858i
$567$	5.69131	−	1.49137i	0.239012	−	0.0626316i
$568$	−8.60442	−	8.60442i	−0.361033	−	0.361033i
$569$	−22.6112	−	16.4280i	−0.947909	−	0.688696i	0.00240243	−	0.999997i	$-0.499235\pi$
$569$	−22.6112	−	16.4280i	−0.947909	−	0.688696i	−0.950311	+	0.311301i	$0.899235\pi$
$570$		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
$573$	7.00776	+	19.8764i	0.292754	+	0.830349i
$574$		−	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	0.295432	−	0.955364i	$-0.404537\pi$
$577$	−7.29810	−	3.71857i	−0.303824	−	0.154806i	−0.599255	+	0.800558i	$0.704537\pi$
$578$	2.65307	−	16.7508i	0.110353	−	0.696742i
$579$	−2.91321	+	21.8946i	−0.121069	+	0.909907i
$580$		0			0
$581$	1.82313	−	2.50933i	0.0756364	−	0.104105i
$582$	−0.228869	−	9.22658i	−0.00948694	−	0.382454i
$583$	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	$0.609023\pi$
$588$	10.9109	+	3.24833i	0.449958	+	0.133959i
$589$	41.3460	−	13.4341i	1.70363	−	0.553544i
$590$		0			0
$591$	−0.338023	−	0.624614i	−0.0139044	−	0.0256932i
$592$	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	$0.226643\pi$
$594$	3.42831	+	14.5449i	0.140665	+	0.596784i
$595$		0			0
$596$	5.89486	+	8.11358i	0.241463	+	0.332345i
$597$	15.1243	−	11.5722i	0.618998	−	0.473619i
$598$	1.37608	−	2.70072i	0.0562723	−	0.110441i
$599$	−39.4333			−1.61120			−0.805600	−	0.592460i	$-0.798157\pi$
$599$	−39.4333			−1.61120			−0.805600	+	0.592460i	$0.798157\pi$
$600$		0			0
$601$	28.0191			1.14292			0.571462	−	0.820629i	$-0.306376\pi$
$601$	28.0191			1.14292			0.571462	+	0.820629i	$0.306376\pi$
$602$	2.13529	−	4.19075i	0.0870281	−	0.170802i
$603$	−4.57720	+	42.4228i	−0.186398	+	1.72759i
$604$	−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	−0.630434	−	0.776243i	$-0.717123\pi$
$607$	3.59236	−	3.59236i	0.145809	−	0.145809i	0.776243	+	0.630434i	$0.217123\pi$
$608$	7.19694	−	1.13988i	0.291875	−	0.0462284i
$609$	3.20321	−	1.73348i	0.129801	−	0.0702443i
$610$		0			0
$611$	−12.5378	+	4.07379i	−0.507226	+	0.164808i
$612$	8.69942	+	15.1643i	0.351653	+	0.612981i
$613$	13.6733	−	6.96688i	0.552258	−	0.281390i	−0.155510	−	0.987834i	$-0.549702\pi$
$613$	13.6733	−	6.96688i	0.552258	−	0.281390i	0.707768	+	0.706445i	$0.249702\pi$
$614$	−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	$0.996262\pi$
$618$	−10.6059	+	0.263084i	−0.426632	+	0.0105828i
$619$	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
$621$	3.61499	+	0.299565i	0.145065	+	0.0120211i
$622$	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
$627$	34.2308	−	12.0686i	1.36704	−	0.481975i
$628$	−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
$633$	−21.1459	+	30.6767i	−0.840473	+	1.21929i
$634$	−12.9984	−	4.22343i	−0.516231	−	0.167734i
$635$		0			0
$636$	−3.53116	−	1.69026i	−0.140019	−	0.0670231i
$637$	12.9561	+	25.4278i	0.513339	+	1.00748i
$638$	4.19979	+	8.24255i	0.166271	+	0.326326i
$639$	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	$0.576905\pi$
$642$	−0.829960	−	0.572103i	−0.0327559	−	0.0225791i
$643$	−9.94703	−	9.94703i	−0.392273	−	0.392273i	0.483224	−	0.875497i	$-0.339466\pi$
$643$	−9.94703	−	9.94703i	−0.392273	−	0.392273i	−0.875497	+	0.483224i	$0.839466\pi$
$644$	−0.369198	−	0.268238i	−0.0145485	−	0.0105701i
$645$		0			0
$646$	34.3532	−	24.9591i	1.35161	−	0.982001i
$647$	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	$0.525273\pi$
$648$	−8.38430	−	3.27163i	−0.329366	−	0.128522i
$649$			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	$0.958010\pi$
$654$	−19.9481	−	2.65422i	−0.780033	−	0.103788i
$655$		0			0
$656$	−3.92038	+	5.39594i	−0.153065	+	0.210676i
$657$	1.24495	+	1.12720i	0.0485703	+	0.0439761i
$658$	0.310493	+	1.96038i	0.0121043	+	0.0764235i
$659$	4.21526	−	12.9732i	0.164203	−	0.505365i	−0.834774	−	0.550593i	$-0.814402\pi$
$659$	4.21526	−	12.9732i	0.164203	−	0.505365i	0.998977	+	0.0452283i	$0.0144015\pi$
$660$		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
$663$	−12.5051	+	42.0037i	−0.485659	+	1.63129i
$664$	−4.51248	+	1.46619i	−0.175118	+	0.0568994i
$665$		0			0
$666$	−1.70779	+	6.30395i	−0.0661757	+	0.244273i
$667$	2.21790	−	0.351281i	0.0858775	−	0.0136017i
$668$	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
$672$	0.688045	+	0.899243i	0.0265419	+	0.0346891i
$673$	−12.2698	+	24.0809i	−0.472967	+	0.928251i	0.524095	+	0.851660i	$0.324404\pi$
$673$	−12.2698	+	24.0809i	−0.472967	+	0.928251i	−0.997063	+	0.0765912i	$0.975596\pi$
$674$	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	$0.265528\pi$
$678$	−14.9114	−	19.4885i	−0.572668	−	0.748451i
$679$	−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
$683$	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	$0.191137\pi$
$684$	−5.71601	+	21.0994i	−0.218557	+	0.806756i
$685$		0			0
$686$	8.43843	−	2.74181i	0.322181	−	0.104683i
$687$	−7.51932	+	25.2568i	−0.286880	+	0.963607i
$688$	−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
$693$	4.18093	+	3.78547i	0.158820	+	0.143798i
$694$	−7.68036	+	10.5711i	−0.291542	+	0.401274i
$695$		0			0
$696$	−5.52282	−	0.734846i	−0.209342	−	0.0278543i
$697$	−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	$-0.543869\pi$
$701$		−	52.4507i		−	1.98104i	0.137384	−	0.990518i	$-0.456131\pi$
$702$	−8.54758	−	20.8797i	−0.322608	−	0.788053i
$703$	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
$708$	−12.2913	−	8.47258i	−0.461936	−	0.318419i
$709$	−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
$711$	28.6228	−	10.8967i	1.07344	−	0.408660i
$712$	2.62525	+	5.15235i	0.0983855	+	0.193092i
$713$	1.89085	+	3.71101i	0.0708130	+	0.138978i
$714$	5.95161	+	2.84886i	0.222734	+	0.106616i
$715$		0			0
$716$	−3.81721	−	1.24029i	−0.142656	−	0.0463517i
$717$	12.2754	−	17.8081i	0.458432	−	0.665055i
$718$	−5.59498	−	5.59498i	−0.208803	−	0.208803i
$719$	−3.26095	−	2.36922i	−0.121613	−	0.0883570i	0.525316	−	0.850907i	$-0.323947\pi$
$719$	−3.26095	−	2.36922i	−0.121613	−	0.0883570i	−0.646929	+	0.762550i	$0.723947\pi$
$720$		0			0
$721$	−3.23943	+	2.35359i	−0.120643	+	0.0876521i
$722$	33.6756	+	5.33368i	1.25327	+	0.198499i
$723$	37.0747	−	13.0713i	1.37882	−	0.486127i
$724$		−	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	−0.128624	−	0.991693i	$-0.541056\pi$
$727$	−27.1388	−	13.8279i	−1.00652	−	0.512850i	−0.877900	+	0.478844i	$0.841056\pi$
$728$	−0.444028	+	2.80348i	−0.0164568	+	0.103904i
$729$	19.2493	−	18.9332i	0.712936	−	0.701229i
$730$		0			0
$731$	−24.6445	+	33.9203i	−0.911510	+	1.25459i
$732$	15.5718	−	0.386264i	0.575549	−	0.0142767i
$733$	2.16039	+	13.6402i	0.0797960	+	0.503812i	0.994922	+	0.100645i	$0.0320906\pi$
$733$	2.16039	+	13.6402i	0.0797960	+	0.503812i	−0.915126	+	0.403167i	$0.867909\pi$
$734$	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
$738$	−9.95678	−	17.3561i	−0.366514	−	0.638885i
$739$	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
$741$	−48.1946	+	26.0815i	−1.77047	+	0.958129i
$742$	−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	$0.414730\pi$
$744$	−1.86917	−	10.1633i	−0.0685270	−	0.372606i
$745$		0			0
$746$	12.5568	+	17.2829i	0.459736	+	0.632772i
$747$	1.52692	−	14.1520i	0.0558672	−	0.517794i
$748$	−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
$753$	−11.5604	+	8.84528i	−0.421283	+	0.322340i
$754$	−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	−0.398891	−	0.916998i	$-0.630605\pi$
$757$	14.2550	−	14.2550i	0.518108	−	0.518108i	0.916998	+	0.398891i	$0.130605\pi$
$758$	−0.977218	+	0.154776i	−0.0354942	+	0.00562172i
$759$	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	$0.272501\pi$
$762$	−24.0615	−	7.16346i	−0.871656	−	0.259505i
$763$	−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
$768$	−0.0429510	−	1.73152i	−0.00154986	−	0.0624808i
$769$	−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
$771$	6.85860	−	51.5466i	0.247006	−	1.85641i
$772$	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
$777$	0.819637	+	2.32477i	0.0294043	+	0.0834007i
$778$	−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
$783$	8.79220	−	14.2152i	0.314208	−	0.508009i
$784$	−6.25096	−	2.03106i	−0.223249	−	0.0725379i
$785$		0			0
$786$	−4.11056	+	8.58746i	−0.146619	+	0.306305i
$787$	11.5447	+	22.6577i	0.411523	+	0.807659i	1.00000		0.000855029i	$-0.000272164\pi$
$787$	11.5447	+	22.6577i	0.411523	+	0.807659i	−0.588477	+	0.808514i	$0.700272\pi$
$788$	0.186155	+	0.365350i	0.00663150	+	0.0130150i
$789$	−3.15181	+	6.58451i	−0.112207	+	0.234415i
$790$		0			0
$791$	−8.80823	−	2.86197i	−0.313185	−	0.101760i
$792$	−1.77049	−	8.44400i	−0.0629116	−	0.300044i
$793$	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	$0.487747\pi$
$798$	2.74334	+	7.78104i	0.0971131	+	0.275446i
$799$		−	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
$804$	3.24920	−	24.4198i	0.114591	−	0.861218i
$805$		0			0
$806$	15.2267	−	20.9577i	0.536337	−	0.738204i
$807$	0.871135	+	35.1187i	0.0306654	+	1.23624i
$808$	−1.96466	−	12.4044i	−0.0691165	−	0.436384i
$809$	−13.0207	+	40.0735i	−0.457782	+	1.40891i	0.410056	+	0.912060i	$0.365509\pi$
$809$	−13.0207	+	40.0735i	−0.457782	+	1.40891i	−0.867838	+	0.496848i	$0.834491\pi$
$810$		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
$813$	−11.2452	−	3.34786i	−0.394386	−	0.117415i
$814$	−5.95451	+	1.93474i	−0.208706	+	0.0678126i
$815$		0			0
$816$	−4.80396	−	8.87698i	−0.168172	−	0.310756i
$817$	−51.7808	+	8.20127i	−1.81158	+	0.286926i
$818$	−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	$0.888878\pi$
$822$	−28.9373	+	22.1410i	−1.00931	+	0.772258i
$823$	10.8987	−	21.3898i	0.379904	−	0.745603i	−0.619314	−	0.785143i	$-0.712589\pi$
$823$	10.8987	−	21.3898i	0.379904	−	0.745603i	0.999218	+	0.0395404i	$0.0125894\pi$
$824$	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	$0.996799\pi$
$828$	−2.08219	−	0.224657i	−0.0723610	−	0.00780737i
$829$	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
$831$	−7.67030	−	41.7062i	−0.266080	−	1.44677i
$832$	3.07024	−	3.07024i	0.106441	−	0.106441i
$833$	−37.8305	+	5.99176i	−1.31075	+	0.207602i
$834$	17.7655	−	9.61415i	0.615168	−	0.332911i
$835$		0			0
$836$	−19.9298	+	6.47560i	−0.689288	+	0.223963i
$837$	30.1146	+	7.36184i	1.04091	+	0.254462i
$838$	−6.43686	+	3.27974i	−0.222358	+	0.113297i
$839$	4.03893	+	12.4305i	0.139439	+	0.429150i	0.996254	−	0.0864743i	$-0.0275600\pi$
$839$	4.03893	+	12.4305i	0.139439	+	0.429150i	−0.856815	+	0.515624i	$0.827560\pi$
$840$		0			0
$841$	−5.76404	+	17.7399i	−0.198760	+	0.611720i
$842$	−2.27453	−	14.3608i	−0.0783856	−	0.494907i
$843$	35.0459	−	0.869329i	1.20705	−	0.0299413i
$844$	12.6440	−	17.4030i	0.435225	−	0.599036i
$845$		0			0
$846$	5.71266	+	7.09448i	0.196405	+	0.243913i
$847$	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
$852$	−19.8772	+	7.00804i	−0.680982	+	0.240092i
$853$	−40.1802	−	6.36392i	−1.37574	−	0.217897i	−0.575614	−	0.817722i	$-0.695237\pi$
$853$	−40.1802	−	6.36392i	−1.37574	−	0.217897i	−0.800131	+	0.599825i	$0.795237\pi$
$854$	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	$0.947735\pi$
$858$	12.2748	−	17.8073i	0.419056	−	0.607931i
$859$	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
$861$	−6.81182	−	3.26061i	−0.232146	−	0.111121i
$862$	−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	$0.893084\pi$
$864$	4.79235	+	2.00833i	0.163039	+	0.0683249i
$865$		0			0
$866$	27.7975	+	9.03196i	0.944598	+	0.306918i
$867$	−24.1857	−	16.6715i	−0.821388	−	0.566194i
$868$	−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
$873$	−14.5858	−	6.54229i	−0.493654	−	0.221423i
$874$			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	0.998906	−	0.0467683i	$-0.0148922\pi$
$877$	45.8490	+	23.3612i	1.54821	+	0.788853i	0.549306	+	0.835621i	$0.314892\pi$
$878$	1.76709	−	11.1570i	0.0596365	−	0.376530i
$879$	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	$0.215428\pi$
$882$	13.2343	−	14.6168i	0.445621	−	0.492175i
$883$	5.77775	+	36.4793i	0.194437	+	1.22763i	0.871016	+	0.491255i	$0.163462\pi$
$883$	5.77775	+	36.4793i	0.194437	+	1.22763i	−0.676579	+	0.736370i	$0.736538\pi$
$884$	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	$0.319647\pi$
$888$	1.07595	−	3.61402i	0.0361064	−	0.121278i
$889$	−9.01156	+	2.92803i	−0.302238	+	0.0982031i
$890$		0			0
$891$	25.2872	+	5.52097i	0.847152	+	0.184960i
$892$	−6.26922	+	0.992947i	−0.209909	+	0.0332463i
$893$	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
$897$	−3.19025	−	4.16951i	−0.106519	−	0.139216i
$898$	−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
$903$	−4.95036	−	6.46990i	−0.164738	−	0.215305i
$904$	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	−0.196661	−	0.980472i	$-0.563010\pi$
$907$	23.6056	−	23.6056i	0.783811	−	0.783811i	0.980472	+	0.196661i	$0.0630097\pi$
$908$	−13.9499	+	2.20945i	−0.462944	+	0.0733232i
$909$	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	$0.148266\pi$
$912$	3.60121	−	12.0962i	0.119248	−	0.400544i
$913$	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
$918$	30.1967	−	2.25082i	0.996641	−	0.0742882i
$919$	−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
$921$	−10.9909	−	1.46241i	−0.362162	−	0.0481880i
$922$	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
$927$	−7.52032	+	16.7663i	−0.247000	+	0.550676i
$928$	3.17710	+	0.503203i	0.104293	+	0.0165185i
$929$	15.3269	−	11.1356i	0.502859	−	0.365349i	−0.307249	−	0.951629i	$-0.599408\pi$
$929$	15.3269	−	11.1356i	0.502859	−	0.365349i	0.810108	+	0.586280i	$0.199408\pi$
$930$		0			0
$931$	−38.7460	−	28.1506i	−1.26985	−	0.922598i
$932$	−5.36984	−	5.36984i	−0.175895	−	0.175895i
$933$	−49.3870	−	34.0431i	−1.61686	−	1.11452i
$934$	1.67753	+	0.545064i	0.0548906	+	0.0178350i
$935$		0			0
$936$	4.63450	+	12.1736i	0.151483	+	0.397905i
$937$	17.7176	+	34.7728i	0.578809	+	1.13598i	0.975904	+	0.218199i	$0.0700183\pi$
$937$	17.7176	+	34.7728i	0.578809	+	1.13598i	−0.397095	+	0.917778i	$0.629982\pi$
$938$	−4.22113	−	8.28444i	−0.137825	−	0.270497i
$939$	−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	$0.747171\pi$
$942$	−8.93880	+	12.9677i	−0.291242	+	0.422510i
$943$	−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	$0.390239\pi$
$948$	−16.6763	+	5.87951i	−0.541622	+	0.190958i
$949$		−	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	$0.00548503\pi$
$954$	−5.28136	+	4.25269i	−0.170990	+	0.137686i
$955$		0			0
$956$	−7.33996	+	10.1026i	−0.237391	+	0.326741i
$957$	16.0180	−	0.397333i	0.517788	−	0.0128439i
$958$	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
$963$	−1.51446	+	0.868809i	−0.0488027	+	0.0279970i
$964$	−21.5856	+	7.01360i	−0.695227	+	0.225893i
$965$		0			0
$966$	−0.695162	+	0.376201i	−0.0223665	+	0.0121041i
$967$	30.9179	−	4.89692i	0.994254	−	0.157474i	0.361952	−	0.932197i	$-0.382110\pi$
$967$	30.9179	−	4.89692i	0.994254	−	0.157474i	0.632302	+	0.774722i	$0.282110\pi$
$968$	−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	$0.646414\pi$
$972$	−11.3812	+	10.6521i	−0.365053	+	0.341667i
$973$	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	$0.160404\pi$
$978$	12.7604	−	9.76348i	0.408034	−	0.312202i
$979$	−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
$983$	−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	$0.603404\pi$
$984$	5.49829	+	10.1600i	0.175279	+	0.323889i
$985$		0			0
$986$	17.8278	−	5.79262i	0.567754	−	0.184474i
$987$	3.29488	+	0.980934i	0.104877	+	0.0312235i
$988$	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
$993$	−0.453961	−	18.3009i	−0.0144060	−	0.580760i
$994$	−4.67569	+	6.43554i	−0.148304	+	0.204123i
$995$		0			0
$996$	−1.08391	+	8.14628i	−0.0343451	+	0.258125i
$997$	5.62909	−	35.5407i	0.178275	−	1.12558i	−0.722523	−	0.691347i	$-0.757018\pi$
$997$	5.62909	−	35.5407i	0.178275	−	1.12558i	0.900798	−	0.434238i	$-0.142982\pi$
$998$	−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.a.143.4		80
3.2	odd	2	inner	750.2.l.a.143.9		80
5.2	odd	4		750.2.l.b.107.4		80
5.3	odd	4		150.2.l.a.17.7	yes	80
5.4	even	2		750.2.l.c.143.7		80
15.2	even	4		750.2.l.b.107.7		80
15.8	even	4		150.2.l.a.17.4	✓	80
15.14	odd	2		750.2.l.c.143.2		80
25.3	odd	20		750.2.l.c.257.2		80
25.4	even	10		150.2.l.a.53.4	yes	80
25.21	even	5		750.2.l.b.743.7		80
25.22	odd	20	inner	750.2.l.a.257.9		80
75.29	odd	10		150.2.l.a.53.7	yes	80
75.47	even	20	inner	750.2.l.a.257.4		80
75.53	even	20		750.2.l.c.257.7		80
75.71	odd	10		750.2.l.b.743.4		80

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

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)

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