LMFDB - Embedded newform 273.2.bj.d.142.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(25,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("273.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bj (of order $6$, degree $2$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 85x^{12} - 310x^{10} + 807x^{8} - 1196x^{6} + 1273x^{4} - 688x^{2} + 256 $ x^16 - 11x^14 + 85x^12 - 310x^10 + 807x^8 - 1196x^6 + 1273x^4 - 688*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			142.2
Root			$1.02312 - 0.590698i$ of defining polynomial
Character	$\chi$	$=$	273.142
Dual form			273.2.bj.d.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69305 - 0.977485i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.910952 + 1.57782i) q^{4} +(0.130553 + 0.0753750i) q^{5} -1.95497i q^{6} +(0.807080 - 2.51965i) q^{7} +0.348171i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.69305 - 0.977485i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.910952 + 1.57782i) q^{4} +(0.130553 + 0.0753750i) q^{5} -1.95497i q^{6} +(0.807080 - 2.51965i) q^{7} +0.348171i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.147356 - 0.255228i) q^{10} +(-0.669934 + 0.386787i) q^{11} +(-0.910952 + 1.57782i) q^{12} +(3.25910 - 1.54216i) q^{13} +(-3.82934 + 3.47699i) q^{14} +0.150750i q^{15} +(2.16224 - 3.74510i) q^{16} +(0.461444 + 0.799245i) q^{17} +(1.69305 - 0.977485i) q^{18} +(6.54095 + 3.77642i) q^{19} +0.274652i q^{20} +(2.58562 - 0.560872i) q^{21} +1.51231 q^{22} +(3.61624 - 6.26351i) q^{23} +(-0.301525 + 0.174086i) q^{24} +(-2.48864 - 4.31045i) q^{25} +(-7.02527 - 0.574757i) q^{26} -1.00000 q^{27} +(4.71075 - 1.02186i) q^{28} +1.68142 q^{29} +(0.147356 - 0.255228i) q^{30} +(0.532789 - 0.307606i) q^{31} +(-6.71851 + 3.87893i) q^{32} +(-0.669934 - 0.386787i) q^{33} -1.80422i q^{34} +(0.295285 - 0.268115i) q^{35} -1.82190 q^{36} +(3.09117 + 1.78469i) q^{37} +(-7.38278 - 12.7874i) q^{38} +(2.96510 + 2.05138i) q^{39} +(-0.0262434 + 0.0454549i) q^{40} -10.5905i q^{41} +(-4.92583 - 1.57782i) q^{42} -0.868503 q^{43} +(-1.22056 - 0.704688i) q^{44} +(-0.130553 + 0.0753750i) q^{45} +(-12.2450 + 7.06964i) q^{46} +(4.89695 + 2.82725i) q^{47} +4.32447 q^{48} +(-5.69725 - 4.06711i) q^{49} +9.73042i q^{50} +(-0.461444 + 0.799245i) q^{51} +(5.40213 + 3.73742i) q^{52} +(4.65125 + 8.05620i) q^{53} +(1.69305 + 0.977485i) q^{54} -0.116616 q^{55} +(0.877269 + 0.281002i) q^{56} +7.55284i q^{57} +(-2.84673 - 1.64356i) q^{58} +(-7.07374 + 4.08402i) q^{59} +(-0.237856 + 0.137326i) q^{60} +(-5.90253 + 10.2235i) q^{61} -1.20272 q^{62} +(1.77854 + 1.95878i) q^{63} +6.51745 q^{64} +(0.541727 + 0.0443202i) q^{65} +(0.756156 + 1.30970i) q^{66} +(-4.56962 + 2.63827i) q^{67} +(-0.840708 + 1.45615i) q^{68} +7.23248 q^{69} +(-0.762012 + 0.165296i) q^{70} +9.73042i q^{71} +(-0.301525 - 0.174086i) q^{72} +(4.19319 - 2.42094i) q^{73} +(-3.48901 - 6.04315i) q^{74} +(2.48864 - 4.31045i) q^{75} +13.7605i q^{76} +(0.433876 + 2.00017i) q^{77} +(-3.01488 - 6.37144i) q^{78} +(-6.82897 + 11.8281i) q^{79} +(0.564575 - 0.325957i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.3520 + 17.9303i) q^{82} -3.57563i q^{83} +(3.24033 + 3.56870i) q^{84} +0.139126i q^{85} +(1.47042 + 0.848948i) q^{86} +(0.840708 + 1.45615i) q^{87} +(-0.134668 - 0.233252i) q^{88} +(-8.95299 - 5.16901i) q^{89} +0.294712 q^{90} +(-1.25535 - 9.45643i) q^{91} +13.1769 q^{92} +(0.532789 + 0.307606i) q^{93} +(-5.52719 - 9.57338i) q^{94} +(0.569295 + 0.986048i) q^{95} +(-6.71851 - 3.87893i) q^{96} -4.78983i q^{97} +(5.67020 + 12.4548i) q^{98} -0.773573i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9} - 16 q^{10} - 8 q^{12} + 6 q^{13} - 10 q^{14} - 28 q^{16} - 2 q^{17} + 60 q^{22} + 24 q^{23} + 10 q^{25} + 14 q^{26} - 16 q^{27} + 24 q^{29} + 16 q^{30} - 30 q^{35} - 16 q^{36} + 3 q^{39} + 26 q^{40} + 4 q^{42} - 76 q^{43} - 56 q^{48} + 2 q^{49} + 2 q^{51} + 10 q^{53} - 16 q^{55} + 72 q^{56} + 26 q^{61} - 104 q^{62} - 84 q^{64} - 32 q^{65} + 30 q^{66} - 12 q^{68} + 48 q^{69} - 54 q^{74} - 10 q^{75} - 10 q^{77} + 28 q^{78} - 10 q^{79} - 8 q^{81} - 48 q^{82} + 12 q^{87} + 68 q^{88} + 32 q^{90} - 57 q^{91} + 16 q^{92} - 48 q^{94} + 18 q^{95}+O(q^{100}) $ 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9 - 16 * q^10 - 8 * q^12 + 6 * q^13 - 10 * q^14 - 28 * q^16 - 2 * q^17 + 60 * q^22 + 24 * q^23 + 10 * q^25 + 14 * q^26 - 16 * q^27 + 24 * q^29 + 16 * q^30 - 30 * q^35 - 16 * q^36 + 3 * q^39 + 26 * q^40 + 4 * q^42 - 76 * q^43 - 56 * q^48 + 2 * q^49 + 2 * q^51 + 10 * q^53 - 16 * q^55 + 72 * q^56 + 26 * q^61 - 104 * q^62 - 84 * q^64 - 32 * q^65 + 30 * q^66 - 12 * q^68 + 48 * q^69 - 54 * q^74 - 10 * q^75 - 10 * q^77 + 28 * q^78 - 10 * q^79 - 8 * q^81 - 48 * q^82 + 12 * q^87 + 68 * q^88 + 32 * q^90 - 57 * q^91 + 16 * q^92 - 48 * q^94 + 18 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.69305	−	0.977485i	−1.19717	−	0.691186i	−0.237246	−	0.971450i	$-0.576245\pi$
$2$	−1.69305	−	0.977485i	−1.19717	−	0.691186i	−0.959923	+	0.280264i	$0.909578\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.910952	+	1.57782i	0.455476	+	0.788908i
$5$	0.130553	+	0.0753750i	0.0583852	+	0.0337087i	0.528908	−	0.848679i	$-0.322601\pi$
$5$	0.130553	+	0.0753750i	0.0583852	+	0.0337087i	−0.470523	+	0.882388i	$0.655935\pi$
$6$		−	1.95497i		−	0.798113i
$7$	0.807080	−	2.51965i	0.305047	−	0.952337i
$7$	0.807080	−	2.51965i	0.305047	−	0.952337i
$8$			0.348171i			0.123097i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.147356	−	0.255228i	−0.0465980	−	0.0807101i
$11$	−0.669934	+	0.386787i	−0.201993	+	0.116621i	−0.597585	−	0.801806i	$-0.703873\pi$
$11$	−0.669934	+	0.386787i	−0.201993	+	0.116621i	0.395592	+	0.918426i	$0.370539\pi$
$12$	−0.910952	+	1.57782i	−0.262969	+	0.455476i
$13$	3.25910	−	1.54216i	0.903912	−	0.427719i
$13$	3.25910	−	1.54216i	0.903912	−	0.427719i
$14$	−3.82934	+	3.47699i	−1.02344	+	0.929264i
$15$			0.150750i			0.0389235i
$16$	2.16224	−	3.74510i	0.540559	−	0.936276i
$17$	0.461444	+	0.799245i	0.111917	+	0.193845i	0.916543	−	0.399936i	$-0.130968\pi$
$17$	0.461444	+	0.799245i	0.111917	+	0.193845i	−0.804626	+	0.593782i	$0.797634\pi$
$18$	1.69305	−	0.977485i	0.399056	−	0.230395i
$19$	6.54095	+	3.77642i	1.50060	+	0.866370i	1.00000		0.000689073i	$0.000219339\pi$
$19$	6.54095	+	3.77642i	1.50060	+	0.866370i	0.500597	+	0.865681i	$0.333114\pi$
$20$			0.274652i			0.0614141i
$21$	2.58562	−	0.560872i	0.564228	−	0.122392i
$22$	1.51231			0.322426
$23$	3.61624	−	6.26351i	0.754038	−	1.30603i	−0.191813	−	0.981432i	$-0.561437\pi$
$23$	3.61624	−	6.26351i	0.754038	−	1.30603i	0.945851	−	0.324601i	$-0.105230\pi$
$24$	−0.301525	+	0.174086i	−0.0615485	+	0.0355351i
$25$	−2.48864	−	4.31045i	−0.497727	−	0.862089i
$26$	−7.02527	−	0.574757i	−1.37777	−	0.112719i
$27$	−1.00000			−0.192450
$28$	4.71075	−	1.02186i	0.890248	−	0.193113i
$29$	1.68142			0.312231			0.156115	−	0.987739i	$-0.450103\pi$
$29$	1.68142			0.312231			0.156115	+	0.987739i	$0.450103\pi$
$30$	0.147356	−	0.255228i	0.0269034	−	0.0465980i
$31$	0.532789	−	0.307606i	0.0956917	−	0.0552476i	−0.451390	−	0.892327i	$-0.649072\pi$
$31$	0.532789	−	0.307606i	0.0956917	−	0.0552476i	0.547082	+	0.837079i	$0.315739\pi$
$32$	−6.71851	+	3.87893i	−1.18768	+	0.685705i
$33$	−0.669934	−	0.386787i	−0.116621	−	0.0673309i
$34$		−	1.80422i		−	0.309421i
$35$	0.295285	−	0.268115i	0.0499123	−	0.0453197i
$36$	−1.82190			−0.303651
$37$	3.09117	+	1.78469i	0.508186	+	0.293401i	0.732088	−	0.681211i	$-0.238546\pi$
$37$	3.09117	+	1.78469i	0.508186	+	0.293401i	−0.223902	+	0.974612i	$0.571880\pi$
$38$	−7.38278	−	12.7874i	−1.19765	−	2.07438i
$39$	2.96510	+	2.05138i	0.474796	+	0.328484i
$40$	−0.0262434	+	0.0454549i	−0.00414945	+	0.00718705i
$41$		−	10.5905i		−	1.65396i	−0.562234	−	0.826978i	$-0.690058\pi$
$41$		−	10.5905i		−	1.65396i	0.562234	−	0.826978i	$-0.309942\pi$
$42$	−4.92583	−	1.57782i	−0.760073	−	0.243462i
$43$	−0.868503			−0.132445			−0.0662227	−	0.997805i	$-0.521095\pi$
$43$	−0.868503			−0.132445			−0.0662227	+	0.997805i	$0.521095\pi$
$44$	−1.22056	−	0.704688i	−0.184006	−	0.106236i
$45$	−0.130553	+	0.0753750i	−0.0194617	+	0.0112362i
$46$	−12.2450	+	7.06964i	−1.80542	+	1.04236i
$47$	4.89695	+	2.82725i	0.714293	+	0.412397i	0.812649	−	0.582754i	$-0.198025\pi$
$47$	4.89695	+	2.82725i	0.714293	+	0.412397i	−0.0983556	+	0.995151i	$0.531358\pi$
$48$	4.32447			0.624184
$49$	−5.69725	−	4.06711i	−0.813892	−	0.581016i
$50$			9.73042i			1.37609i
$51$	−0.461444	+	0.799245i	−0.0646151	+	0.111917i
$52$	5.40213	+	3.73742i	0.749141	+	0.518287i
$53$	4.65125	+	8.05620i	0.638898	+	1.10660i	0.985675	+	0.168656i	$0.0539428\pi$
$53$	4.65125	+	8.05620i	0.638898	+	1.10660i	−0.346777	+	0.937948i	$0.612724\pi$
$54$	1.69305	+	0.977485i	0.230395	+	0.133019i
$55$	−0.116616			−0.0157245
$56$	0.877269	+	0.281002i	0.117230	+	0.0375504i
$57$			7.55284i			1.00040i
$58$	−2.84673	−	1.64356i	−0.373793	−	0.215810i
$59$	−7.07374	+	4.08402i	−0.920922	+	0.531695i	−0.883929	−	0.467621i	$-0.845111\pi$
$59$	−7.07374	+	4.08402i	−0.920922	+	0.531695i	−0.0369930	+	0.999316i	$0.511778\pi$
$60$	−0.237856	+	0.137326i	−0.0307070	+	0.0177287i
$61$	−5.90253	+	10.2235i	−0.755742	+	1.30898i	0.189263	+	0.981927i	$0.439390\pi$
$61$	−5.90253	+	10.2235i	−0.755742	+	1.30898i	−0.945005	+	0.327057i	$0.893943\pi$
$62$	−1.20272			−0.152746
$63$	1.77854	+	1.95878i	0.224075	+	0.246782i
$64$	6.51745			0.814681
$65$	0.541727	+	0.0443202i	0.0671930	+	0.00549725i
$66$	0.756156	+	1.30970i	0.0930764	+	0.161213i
$67$	−4.56962	+	2.63827i	−0.558268	+	0.322316i	−0.752450	−	0.658649i	$-0.771128\pi$
$67$	−4.56962	+	2.63827i	−0.558268	+	0.322316i	0.194182	+	0.980966i	$0.437795\pi$
$68$	−0.840708	+	1.45615i	−0.101951	+	0.176584i
$69$	7.23248			0.870688
$70$	−0.762012	+	0.165296i	−0.0910779	+	0.0197566i
$71$			9.73042i			1.15479i	0.816466	+	0.577394i	$0.195930\pi$
$71$			9.73042i			1.15479i	−0.816466	+	0.577394i	$0.804070\pi$
$72$	−0.301525	−	0.174086i	−0.0355351	−	0.0205162i
$73$	4.19319	−	2.42094i	0.490775	−	0.283349i	−0.234121	−	0.972208i	$-0.575221\pi$
$73$	4.19319	−	2.42094i	0.490775	−	0.283349i	0.724896	+	0.688858i	$0.241888\pi$
$74$	−3.48901	−	6.04315i	−0.405590	−	0.702502i
$75$	2.48864	−	4.31045i	0.287363	−	0.497727i
$76$			13.7605i			1.57844i
$77$	0.433876	+	2.00017i	0.0494447	+	0.227940i
$78$	−3.01488	−	6.37144i	−0.341368	−	0.721424i
$79$	−6.82897	+	11.8281i	−0.768319	+	1.33077i	0.170155	+	0.985417i	$0.445573\pi$
$79$	−6.82897	+	11.8281i	−0.768319	+	1.33077i	−0.938474	+	0.345350i	$0.887760\pi$
$80$	0.564575	−	0.325957i	0.0631214	−	0.0364431i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−10.3520	+	17.9303i	−1.14319	+	1.98007i
$83$		−	3.57563i		−	0.392477i	−0.980556	−	0.196238i	$-0.937127\pi$
$83$		−	3.57563i		−	0.392477i	0.980556	−	0.196238i	$-0.0628727\pi$
$84$	3.24033	+	3.56870i	0.353549	+	0.389377i
$85$			0.139126i			0.0150903i
$86$	1.47042	+	0.848948i	0.158560	+	0.0915445i
$87$	0.840708	+	1.45615i	0.0901333	+	0.156115i
$88$	−0.134668	−	0.233252i	−0.0143557	−	0.0248647i
$89$	−8.95299	−	5.16901i	−0.949015	−	0.547914i	−0.0562399	−	0.998417i	$-0.517911\pi$
$89$	−8.95299	−	5.16901i	−0.949015	−	0.547914i	−0.892775	+	0.450503i	$0.851245\pi$
$90$	0.294712			0.0310653
$91$	−1.25535	−	9.45643i	−0.131597	−	0.991303i
$92$	13.1769			1.37379
$93$	0.532789	+	0.307606i	0.0552476	+	0.0318972i
$94$	−5.52719	−	9.57338i	−0.570086	−	0.987419i
$95$	0.569295	+	0.986048i	0.0584085	+	0.101166i
$96$	−6.71851	−	3.87893i	−0.685705	−	0.395892i
$97$		−	4.78983i		−	0.486334i	−0.969984	−	0.243167i	$-0.921814\pi$
$97$		−	4.78983i		−	0.486334i	0.969984	−	0.243167i	$-0.0781863\pi$
$98$	5.67020	+	12.4548i	0.572777	+	1.25813i
$99$		−	0.773573i		−	0.0777471i
$100$	4.53406	−	7.85322i	0.453406	−	0.785322i
$101$	−8.35948	−	14.4790i	−0.831800	−	1.44072i	−0.896610	−	0.442821i	$-0.853978\pi$
$101$	−8.35948	−	14.4790i	−0.831800	−	1.44072i	0.0648103	−	0.997898i	$-0.479356\pi$
$102$	1.56250	−	0.902110i	0.154711	−	0.0893222i
$103$	2.73248	−	4.73280i	0.269239	−	0.466336i	−0.699426	−	0.714705i	$-0.746561\pi$
$103$	2.73248	−	4.73280i	0.269239	−	0.466336i	0.968666	+	0.248369i	$0.0798944\pi$
$104$	0.536937	+	1.13472i	0.0526510	+	0.111269i
$105$	0.379837	+	0.121667i	0.0370683	+	0.0118735i
$106$		−	18.1861i		−	1.76639i
$107$	−3.74774	+	6.49127i	−0.362307	+	0.627535i	−0.988340	−	0.152262i	$-0.951344\pi$
$107$	−3.74774	+	6.49127i	−0.362307	+	0.627535i	0.626033	+	0.779797i	$0.284678\pi$
$108$	−0.910952	−	1.57782i	−0.0876564	−	0.151825i
$109$	−3.77312	+	2.17841i	−0.361399	+	0.208654i	−0.669694	−	0.742637i	$-0.733575\pi$
$109$	−3.77312	+	2.17841i	−0.361399	+	0.208654i	0.308295	+	0.951291i	$0.400242\pi$
$110$	0.197437	+	0.113991i	0.0188249	+	0.0108686i
$111$			3.56938i			0.338790i
$112$	−7.69124	−	8.47067i	−0.726754	−	0.800403i
$113$	8.82854			0.830520			0.415260	−	0.909703i	$-0.363691\pi$
$113$	8.82854			0.830520			0.415260	+	0.909703i	$0.363691\pi$
$114$	7.38278	−	12.7874i	0.691461	−	1.19765i
$115$	0.944225	−	0.545148i	0.0880494	−	0.0508354i
$116$	1.53169	+	2.65296i	0.142214	+	0.246321i
$117$	−0.293998	+	3.59354i	−0.0271801	+	0.332223i
$118$	15.9683			1.47000
$119$	2.38624	−	0.517623i	0.218746	−	0.0474504i
$120$	−0.0524868			−0.00479137
$121$	−5.20079	+	9.00804i	−0.472799	+	0.818912i
$122$	19.9866	−	11.5393i	1.80950	−	1.04472i
$123$	9.17163	−	5.29525i	0.826978	−	0.477456i
$124$	0.970691	+	0.560428i	0.0871706	+	0.0503280i
$125$		−	1.50407i		−	0.134529i
$126$	−1.09649	−	5.05480i	−0.0976829	−	0.450318i
$127$	−11.4035			−1.01190			−0.505948	−	0.862564i	$-0.668857\pi$
$127$	−11.4035			−1.01190			−0.505948	+	0.862564i	$0.668857\pi$
$128$	2.40264	+	1.38716i	0.212365	+	0.122609i
$129$	−0.434252	−	0.752146i	−0.0382337	−	0.0662227i
$130$	−0.873850	−	0.604566i	−0.0766417	−	0.0530240i
$131$	−2.98864	+	5.17647i	−0.261118	+	0.452270i	−0.966539	−	0.256518i	$-0.917425\pi$
$131$	−2.98864	+	5.17647i	−0.261118	+	0.452270i	0.705421	+	0.708789i	$0.250758\pi$
$132$		−	1.40938i		−	0.122671i
$133$	14.7943	−	13.4330i	1.28283	−	1.16479i
$134$	10.3155			0.891122
$135$	−0.130553	−	0.0753750i	−0.0112362	−	0.00648725i
$136$	−0.278274	+	0.160662i	−0.0238618	+	0.0137766i
$137$	11.5074	−	6.64379i	0.983142	−	0.567618i	0.0799250	−	0.996801i	$-0.474532\pi$
$137$	11.5074	−	6.64379i	0.983142	−	0.567618i	0.903217	+	0.429183i	$0.141199\pi$
$138$	−12.2450	−	7.06964i	−1.04236	−	0.601808i
$139$	−14.0454			−1.19131			−0.595657	−	0.803239i	$-0.703108\pi$
$139$	−14.0454			−1.19131			−0.595657	+	0.803239i	$0.703108\pi$
$140$	0.692027	+	0.221666i	0.0584869	+	0.0187342i
$141$			5.65451i			0.476195i
$142$	9.51133	−	16.4741i	0.798173	−	1.38248i
$143$	−1.58689	+	2.29372i	−0.132703	+	0.191811i
$144$	2.16224	+	3.74510i	0.180186	+	0.312092i
$145$	0.219514	+	0.126737i	0.0182297	+	0.0105249i
$146$	−9.46571			−0.783388
$147$	0.673599	−	6.96751i	0.0555575	−	0.574671i
$148$			6.50307i			0.534549i
$149$	−9.79389	−	5.65451i	−0.802347	−	0.463235i	0.0419442	−	0.999120i	$-0.486645\pi$
$149$	−9.79389	−	5.65451i	−0.802347	−	0.463235i	−0.844291	+	0.535885i	$0.819978\pi$
$150$	−8.42679	+	4.86521i	−0.688044	+	0.397243i
$151$	0.693185	−	0.400211i	0.0564106	−	0.0325687i	−0.471529	−	0.881850i	$-0.656298\pi$
$151$	0.693185	−	0.400211i	0.0564106	−	0.0325687i	0.527940	+	0.849282i	$0.322965\pi$
$152$	−1.31484	+	2.27737i	−0.106648	+	0.184719i
$153$	−0.922889			−0.0746111
$154$	1.22056	−	3.81049i	0.0983552	−	0.307058i
$155$	0.0927432			0.00744931
$156$	−0.535636	+	6.54710i	−0.0428852	+	0.524187i
$157$	−0.0964880	−	0.167122i	−0.00770058	−	0.0133378i	0.862149	−	0.506654i	$-0.169118\pi$
$157$	−0.0964880	−	0.167122i	−0.00770058	−	0.0133378i	−0.869850	+	0.493316i	$0.835785\pi$
$158$	23.1236	−	13.3504i	1.83962	−	1.06210i
$159$	−4.65125	+	8.05620i	−0.368868	+	0.638898i
$160$	−1.16950			−0.0924570
$161$	−12.8632	−	14.1668i	−1.01377	−	1.11650i
$162$			1.95497i			0.153597i
$163$	13.3834	+	7.72692i	1.04827	+	0.605219i	0.922165	−	0.386798i	$-0.126419\pi$
$163$	13.3834	+	7.72692i	1.04827	+	0.605219i	0.126106	+	0.992017i	$0.459752\pi$
$164$	16.7098	−	9.64743i	1.30482	−	0.753338i
$165$	−0.0583081	−	0.100993i	−0.00453928	−	0.00786226i
$166$	−3.49513	+	6.05374i	−0.271275	+	0.469861i
$167$			4.18223i			0.323631i	0.986821	+	0.161815i	$0.0517349\pi$
$167$			4.18223i			0.323631i	−0.986821	+	0.161815i	$0.948265\pi$
$168$	0.195280	+	0.900238i	0.0150661	+	0.0694549i
$169$	8.24347	−	10.0521i	0.634113	−	0.773240i
$170$	0.135993	−	0.235547i	0.0104302	−	0.0180656i
$171$	−6.54095	+	3.77642i	−0.500199	+	0.288790i
$172$	−0.791165	−	1.37034i	−0.0603258	−	0.104487i
$173$	10.8135	−	18.7295i	0.822134	−	1.42398i	−0.0819559	−	0.996636i	$-0.526117\pi$
$173$	10.8135	−	18.7295i	0.822134	−	1.42398i	0.904090	−	0.427342i	$-0.140550\pi$
$174$		−	3.28712i		−	0.249196i
$175$	−12.8693	+	2.79162i	−0.972830	+	0.211026i
$176$			3.34530i			0.252161i
$177$	−7.07374	−	4.08402i	−0.531695	−	0.306974i
$178$	10.1053	+	17.5028i	0.757421	+	1.31189i
$179$	9.29373	+	16.0972i	0.694646	+	1.20316i	0.970300	+	0.241906i	$0.0777724\pi$
$179$	9.29373	+	16.0972i	0.694646	+	1.20316i	−0.275654	+	0.961257i	$0.588894\pi$
$180$	−0.237856	−	0.137326i	−0.0177287	−	0.0102357i
$181$	−2.54992			−0.189534			−0.0947670	−	0.995499i	$-0.530211\pi$
$181$	−2.54992			−0.189534			−0.0947670	+	0.995499i	$0.530211\pi$
$182$	−7.11814	+	17.2373i	−0.527631	+	1.27772i
$183$	−11.8051			−0.872656
$184$	2.18077	+	1.25907i	0.160769	+	0.0928199i
$185$	0.269042	+	0.465994i	0.0197804	+	0.0342606i
$186$	−0.601360	−	1.04159i	−0.0440938	−	0.0763728i
$187$	−0.618275	−	0.356961i	−0.0452127	−	0.0261036i
$188$			10.3020i			0.751348i
$189$	−0.807080	+	2.51965i	−0.0587064	+	0.183277i
$190$		−	2.22591i		−	0.161484i
$191$	−0.995504	+	1.72426i	−0.0720321	+	0.124763i	−0.899792	−	0.436320i	$-0.856282\pi$
$191$	−0.995504	+	1.72426i	−0.0720321	+	0.124763i	0.827760	+	0.561083i	$0.189615\pi$
$192$	3.25872	+	5.64428i	0.235178	+	0.407341i
$193$	−15.1267	+	8.73340i	−1.08884	+	0.628644i	−0.933268	−	0.359180i	$-0.883056\pi$
$193$	−15.1267	+	8.73340i	−1.08884	+	0.628644i	−0.155575	+	0.987824i	$0.549723\pi$
$194$	−4.68199	+	8.10944i	−0.336147	+	0.582224i
$195$	0.232481	+	0.491310i	0.0166483	+	0.0351834i
$196$	1.22723	−	12.6941i	0.0876595	−	0.906725i
$197$		−	13.5807i		−	0.967585i	−0.875183	−	0.483793i	$-0.839259\pi$
$197$		−	13.5807i		−	0.967585i	0.875183	−	0.483793i	$-0.160741\pi$
$198$	−0.756156	+	1.30970i	−0.0537377	+	0.0930764i
$199$	0.751660	+	1.30191i	0.0532838	+	0.0922902i	0.891437	−	0.453145i	$-0.149698\pi$
$199$	0.751660	+	1.30191i	0.0532838	+	0.0922902i	−0.838153	+	0.545435i	$0.816365\pi$
$200$	1.50077	−	0.866472i	0.106121	−	0.0612688i
$201$	−4.56962	−	2.63827i	−0.322316	−	0.186089i
$202$			32.6851i			2.29971i
$203$	1.35704	−	4.23657i	0.0952452	−	0.297349i
$204$	−1.68142			−0.117723
$205$	0.798259	−	1.38262i	0.0557528	−	0.0965667i
$206$	−9.25247	+	5.34192i	−0.644650	+	0.372189i
$207$	3.61624	+	6.26351i	0.251346	+	0.435344i
$208$	1.27139	−	15.5402i	0.0881548	−	1.07752i
$209$	−5.84267			−0.404146
$210$	−0.524156	−	0.577274i	−0.0361702	−	0.0398357i
$211$	24.0919			1.65856			0.829279	−	0.558835i	$-0.188752\pi$
$211$	24.0919			1.65856			0.829279	+	0.558835i	$0.188752\pi$
$212$	−8.47413	+	14.6776i	−0.582006	+	1.00806i
$213$	−8.42679	+	4.86521i	−0.577394	+	0.333359i
$214$	12.6902	−	7.32671i	0.867487	−	0.500844i
$215$	−0.113386	−	0.0654634i	−0.00773286	−	0.00446457i
$216$		−	0.348171i		−	0.0236900i
$217$	−0.345055	−	1.59070i	−0.0234239	−	0.107984i
$218$	8.51745			0.576874
$219$	4.19319	+	2.42094i	0.283349	+	0.163592i
$220$	−0.106232	−	0.183999i	−0.00716215	−	0.0124052i
$221$	2.73646	+	1.89320i	0.184074	+	0.127350i
$222$	3.48901	−	6.04315i	0.234167	−	0.405590i
$223$			11.1398i			0.745976i	0.927836	+	0.372988i	$0.121667\pi$
$223$			11.1398i			0.745976i	−0.927836	+	0.372988i	$0.878333\pi$
$224$	4.35117	+	20.0589i	0.290725	+	1.34024i
$225$	4.97727			0.331818
$226$	−14.9472	−	8.62977i	−0.994272	−	0.574043i
$227$	−2.21721	+	1.28011i	−0.147161	+	0.0849636i	−0.571773	−	0.820412i	$-0.693744\pi$
$227$	−2.21721	+	1.28011i	−0.147161	+	0.0849636i	0.424611	+	0.905376i	$0.360411\pi$
$228$	−11.9170	+	6.88027i	−0.789221	+	0.455657i
$229$	2.08405	+	1.20323i	0.137718	+	0.0795114i	0.567276	−	0.823528i	$-0.307997\pi$
$229$	2.08405	+	1.20323i	0.137718	+	0.0795114i	−0.429558	+	0.903039i	$0.641331\pi$
$230$	−2.13150			−0.140547
$231$	−1.51526	+	1.37583i	−0.0996965	+	0.0905230i
$232$			0.585420i			0.0384347i
$233$	−9.28924	+	16.0894i	−0.608558	+	1.05405i	0.382920	+	0.923781i	$0.374918\pi$
$233$	−9.28924	+	16.0894i	−0.608558	+	1.05405i	−0.991478	+	0.130272i	$0.958415\pi$
$234$	4.01039	−	5.79668i	0.262167	−	0.378941i
$235$	0.426209	+	0.738215i	0.0278028	+	0.0481558i
$236$	−12.8877	−	7.44070i	−0.838916	−	0.484348i
$237$	−13.6579			−0.887178
$238$	−4.54600	−	1.45615i	−0.294673	−	0.0943881i
$239$			18.5657i			1.20092i	0.799656	+	0.600458i	$0.205015\pi$
$239$			18.5657i			1.20092i	−0.799656	+	0.600458i	$0.794985\pi$
$240$	0.564575	+	0.325957i	0.0364431	+	0.0210405i
$241$	−22.1422	+	12.7838i	−1.42630	+	0.823477i	−0.996827	−	0.0796012i	$-0.974635\pi$
$241$	−22.1422	+	12.7838i	−1.42630	+	0.823477i	−0.429477	+	0.903078i	$0.641302\pi$
$242$	17.6104	−	10.1674i	1.13204	−	0.653584i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−21.5077			−1.37689
$245$	−0.437236	−	0.960405i	−0.0279340	−	0.0613580i
$246$	−20.7041			−1.32004
$247$	27.1415	+	2.22052i	1.72697	+	0.141288i
$248$	0.107099	+	0.185502i	0.00680082	+	0.0117794i
$249$	3.09659	−	1.78782i	0.196238	−	0.113298i
$250$	−1.47021	+	2.54648i	−0.0929842	+	0.161053i
$251$	1.34056			0.0846153			0.0423077	−	0.999105i	$-0.486529\pi$
$251$	1.34056			0.0846153			0.0423077	+	0.999105i	$0.486529\pi$
$252$	−1.47042	+	4.59056i	−0.0926279	+	0.289178i
$253$			5.59486i			0.351746i
$254$	19.3067	+	11.1467i	1.21141	+	0.699408i
$255$	−0.120486	+	0.0695628i	−0.00754514	+	0.00435619i
$256$	−9.22931	−	15.9856i	−0.576832	−	0.999102i
$257$	10.0147	−	17.3459i	0.624697	−	1.08201i	−0.363902	−	0.931437i	$-0.618556\pi$
$257$	10.0147	−	17.3459i	0.624697	−	1.08201i	0.988599	−	0.150570i	$-0.0481108\pi$
$258$			1.69790i			0.105706i
$259$	6.99161	−	6.34828i	0.434438	−	0.394463i
$260$	0.423558	+	0.895119i	0.0262680	+	0.0555129i
$261$	−0.840708	+	1.45615i	−0.0520385	+	0.0901333i
$262$	10.1198	−	5.84269i	0.625206	−	0.360963i
$263$	−10.8649	−	18.8186i	−0.669960	−	1.16040i	−0.977915	−	0.209004i	$-0.932978\pi$
$263$	−10.8649	−	18.8186i	−0.669960	−	1.16040i	0.307955	−	0.951401i	$-0.400355\pi$
$264$	0.134668	−	0.233252i	0.00828824	−	0.0143557i
$265$			1.40235i			0.0861458i
$266$	−38.1781	+	8.28159i	−2.34085	+	0.507777i
$267$		−	10.3380i		−	0.632676i
$268$	−8.32541	−	4.80668i	−0.508556	−	0.293615i
$269$	0.783952	+	1.35784i	0.0477984	+	0.0827892i	0.888935	−	0.458034i	$-0.151446\pi$
$269$	0.783952	+	1.35784i	0.0477984	+	0.0827892i	−0.841136	+	0.540823i	$0.818113\pi$
$270$	0.147356	+	0.255228i	0.00896779	+	0.0155327i
$271$	3.15341	+	1.82062i	0.191556	+	0.110595i	0.592711	−	0.805415i	$-0.298058\pi$
$271$	3.15341	+	1.82062i	0.191556	+	0.110595i	−0.401155	+	0.916010i	$0.631391\pi$
$272$	3.99101			0.241990
$273$	7.56183	−	5.81538i	0.457663	−	0.351963i
$274$	−25.9768			−1.56932
$275$	3.33445	+	1.92514i	0.201075	+	0.116091i
$276$	6.58845	+	11.4115i	0.396578	+	0.686893i
$277$	−4.03856	−	6.99498i	−0.242653	−	0.420288i	0.718816	−	0.695200i	$-0.244684\pi$
$277$	−4.03856	−	6.99498i	−0.242653	−	0.420288i	−0.961469	+	0.274913i	$0.911351\pi$
$278$	23.7796	+	13.7292i	1.42621	+	0.823420i
$279$			0.615212i			0.0368318i
$280$	0.0933498	+	0.102810i	0.00557872	+	0.00614407i
$281$			0.685719i			0.0409065i	0.999791	+	0.0204533i	$0.00651093\pi$
$281$			0.685719i			0.0409065i	−0.999791	+	0.0204533i	$0.993489\pi$
$282$	5.52719	−	9.57338i	0.329140	−	0.570086i
$283$	7.69275	+	13.3242i	0.457286	+	0.792043i	0.998816	−	0.0486380i	$-0.0154881\pi$
$283$	7.69275	+	13.3242i	0.457286	+	0.792043i	−0.541530	+	0.840681i	$0.682155\pi$
$284$	−15.3528	+	8.86395i	−0.911021	+	0.525978i
$285$	−0.569295	+	0.986048i	−0.0337221	+	0.0584085i
$286$	4.92878	−	2.33223i	0.291445	−	0.137908i
$287$	−26.6843	−	8.54737i	−1.57512	−	0.504535i
$288$		−	7.75787i		−	0.457137i
$289$	8.07414	−	13.9848i	0.474949	−	0.822636i
$290$	−0.247766	−	0.429144i	−0.0145493	−	0.0252002i
$291$	4.14812	−	2.39492i	0.243167	−	0.140393i
$292$	7.63958	+	4.41072i	0.447073	+	0.258118i
$293$			12.1224i			0.708199i	0.935208	+	0.354099i	$0.115213\pi$
$293$			12.1224i			0.708199i	−0.935208	+	0.354099i	$0.884787\pi$
$294$	−7.95108	+	11.1379i	−0.463716	+	0.649578i
$295$	−1.23133			−0.0716910
$296$	−0.621377	+	1.07626i	−0.0361168	+	0.0625562i
$297$	0.669934	−	0.386787i	0.0388735	−	0.0224436i
$298$	11.0544	+	19.1468i	0.640363	+	1.10914i
$299$	2.12633	−	25.9902i	0.122969	−	1.50305i
$300$	9.06812			0.523548
$301$	−0.700951	+	2.18832i	−0.0404022	+	0.126133i
$302$	−1.56480			−0.0900441
$303$	8.35948	−	14.4790i	0.480240	−	0.831800i
$304$	28.2862	−	16.3310i	1.62232	−	0.936648i
$305$	−1.54119	+	0.889807i	−0.0882484	+	0.0509502i
$306$	1.56250	+	0.902110i	0.0893222	+	0.0515702i
$307$		−	19.3806i		−	1.10611i	−0.833145	−	0.553054i	$-0.813462\pi$
$307$		−	19.3806i		−	1.10611i	0.833145	−	0.553054i	$-0.186538\pi$
$308$	−2.76065	+	2.50663i	−0.157303	+	0.142829i
$309$	5.46496			0.310891
$310$	−0.157019	−	0.0906550i	−0.00891809	−	0.00514886i
$311$	−5.03074	−	8.71350i	−0.285267	−	0.494097i	0.687407	−	0.726273i	$-0.258749\pi$
$311$	−5.03074	−	8.71350i	−0.285267	−	0.494097i	−0.972674	+	0.232176i	$0.925416\pi$
$312$	−0.714232	+	1.03236i	−0.0404354	+	0.0584461i
$313$	9.30155	−	16.1108i	0.525755	−	0.910634i	−0.473795	−	0.880635i	$-0.657116\pi$
$313$	9.30155	−	16.1108i	0.525755	−	0.910634i	0.999550	−	0.0299988i	$-0.00955033\pi$
$314$			0.377262i			0.0212901i
$315$	0.0845515	+	0.389782i	0.00476394	+	0.0219617i
$316$	−24.8835			−1.39980
$317$	−2.96604	−	1.71244i	−0.166589	−	0.0961804i	0.414387	−	0.910101i	$-0.363996\pi$
$317$	−2.96604	−	1.71244i	−0.166589	−	0.0961804i	−0.580977	+	0.813920i	$0.697329\pi$
$318$	15.7496	−	9.09305i	0.883195	−	0.509913i
$319$	−1.12644	+	0.650349i	−0.0630684	+	0.0364126i
$320$	0.850875	+	0.491253i	0.0475654	+	0.0274619i
$321$	−7.49547			−0.418357
$322$	7.93033	+	36.5588i	0.441940	+	2.03734i
$323$			6.97043i			0.387845i
$324$	0.910952	−	1.57782i	0.0506085	−	0.0876564i
$325$	−14.7581	−	10.2103i	−0.818634	−	0.566365i
$326$	−15.1059	−	26.1642i	−0.836638	−	1.44910i
$327$	−3.77312	−	2.17841i	−0.208654	−	0.120466i
$328$	3.68730			0.203597
$329$	11.0759	−	10.0568i	0.610634	−	0.554447i
$330$			0.227981i			0.0125499i
$331$	15.3310	+	8.85135i	0.842667	+	0.486514i	0.858170	−	0.513366i	$-0.171602\pi$
$331$	15.3310	+	8.85135i	0.842667	+	0.486514i	−0.0155026	+	0.999880i	$0.504935\pi$
$332$	5.64169	−	3.25723i	0.309628	−	0.178764i
$333$	−3.09117	+	1.78469i	−0.169395	+	0.0978004i
$334$	4.08807	−	7.08074i	0.223689	−	0.387441i
$335$	−0.795439			−0.0434595
$336$	3.49019	−	10.8961i	0.190406	−	0.594434i
$337$	−19.9495			−1.08672			−0.543361	−	0.839499i	$-0.682848\pi$
$337$	−19.9495			−1.08672			−0.543361	+	0.839499i	$0.682848\pi$
$338$	−23.7824	+	8.96092i	−1.29359	+	0.487410i
$339$	4.41427	+	7.64574i	0.239750	+	0.415260i
$340$	−0.219514	+	0.126737i	−0.0119048	+	0.00687326i
$341$	−0.237956	+	0.412151i	−0.0128860	+	0.0223192i
$342$	14.7656			0.798430
$343$	−14.8458	+	11.0726i	−0.801599	+	0.597862i
$344$		−	0.302388i		−	0.0163037i
$345$	0.944225	+	0.545148i	0.0508354	+	0.0293498i
$346$	−36.6156	+	21.1400i	−1.96847	+	1.13650i
$347$	−1.59686	−	2.76585i	−0.0857241	−	0.148479i	0.819975	−	0.572399i	$-0.193987\pi$
$347$	−1.59686	−	2.76585i	−0.0857241	−	0.148479i	−0.905700	+	0.423920i	$0.860654\pi$
$348$	−1.53169	+	2.65296i	−0.0821072	+	0.142214i
$349$		−	21.4556i		−	1.14849i	−0.818682	−	0.574247i	$-0.805295\pi$
$349$		−	21.4556i		−	1.14849i	0.818682	−	0.574247i	$-0.194705\pi$
$350$	24.5172	+	7.85322i	1.31050	+	0.419772i
$351$	−3.25910	+	1.54216i	−0.173958	+	0.0823146i
$352$	3.00064	−	5.19726i	0.159935	−	0.277015i
$353$	−23.3191	+	13.4633i	−1.24115	+	0.716579i	−0.969329	−	0.245769i	$-0.920960\pi$
$353$	−23.3191	+	13.4633i	−1.24115	+	0.716579i	−0.271822	+	0.962347i	$0.587626\pi$
$354$	7.98414	+	13.8289i	0.424352	+	0.735000i
$355$	−0.733431	+	1.27034i	−0.0389265	+	0.0674226i
$356$		−	18.8349i		−	0.998247i
$357$	1.64139	+	1.80773i	0.0868718	+	0.0956753i
$358$		−	36.3379i		−	1.92052i
$359$	−2.64852	−	1.52912i	−0.139783	−	0.0807040i	0.428477	−	0.903553i	$-0.359050\pi$
$359$	−2.64852	−	1.52912i	−0.139783	−	0.0807040i	−0.568261	+	0.822849i	$0.692384\pi$
$360$	−0.0262434	−	0.0454549i	−0.00138315	−	0.00239568i
$361$	19.0227	+	32.9482i	1.00119	+	1.73412i
$362$	4.31715	+	2.49251i	0.226904	+	0.131003i
$363$	−10.4016			−0.545942
$364$	13.7769	−	10.5951i	0.722108	−	0.555333i
$365$	0.729913			0.0382054
$366$	19.9866	+	11.5393i	1.04472	+	0.603167i
$367$	11.2300	+	19.4509i	0.586200	+	1.01533i	0.994725	+	0.102581i	$0.0327101\pi$
$367$	11.2300	+	19.4509i	0.586200	+	1.01533i	−0.408524	+	0.912747i	$0.633957\pi$
$368$	−15.6383	−	27.0864i	−0.815205	−	1.41198i
$369$	9.17163	+	5.29525i	0.477456	+	0.275659i
$370$		−	1.05194i		−	0.0546876i
$371$	24.0527	−	5.21751i	1.24875	−	0.270880i
$372$			1.12086i			0.0581137i
$373$	−16.2812	+	28.1999i	−0.843008	+	1.46013i	0.0443314	+	0.999017i	$0.485884\pi$
$373$	−16.2812	+	28.1999i	−0.843008	+	1.46013i	−0.887340	+	0.461116i	$0.847449\pi$
$374$	0.697848	+	1.20871i	0.0360849	+	0.0625008i
$375$	1.30257	−	0.752037i	0.0672643	−	0.0388350i
$376$	−0.984368	+	1.70498i	−0.0507649	+	0.0879274i
$377$	5.47990	−	2.59302i	0.282229	−	0.133547i
$378$	3.82934	−	3.47699i	0.196960	−	0.178837i
$379$		−	30.6652i		−	1.57516i	−0.616209	−	0.787582i	$-0.711333\pi$
$379$		−	30.6652i		−	1.57516i	0.616209	−	0.787582i	$-0.288667\pi$
$380$	−1.03720	+	1.79649i	−0.0532073	+	0.0921578i
$381$	−5.70174	−	9.87571i	−0.292109	−	0.505948i
$382$	3.37088	−	1.94618i	0.172469	−	0.0995752i
$383$	23.6125	+	13.6327i	1.20654	+	0.696598i	0.962002	−	0.273041i	$-0.0880296\pi$
$383$	23.6125	+	13.6327i	1.20654	+	0.696598i	0.244541	+	0.969639i	$0.421363\pi$
$384$			2.77433i			0.141577i
$385$	−0.0941186	+	0.293832i	−0.00479673	+	0.0149751i
$386$	34.1471			1.73804
$387$	0.434252	−	0.752146i	0.0220742	−	0.0382337i
$388$	7.55747	−	4.36331i	0.383673	−	0.221514i
$389$	15.2847	+	26.4739i	0.774967	+	1.34228i	0.934813	+	0.355140i	$0.115567\pi$
$389$	15.2847	+	26.4739i	0.774967	+	1.34228i	−0.159846	+	0.987142i	$0.551100\pi$
$390$	0.0866447	−	1.05906i	0.00438742	−	0.0536276i
$391$	6.67478			0.337558
$392$	1.41605	−	1.98362i	0.0715214	−	0.100188i
$393$	−5.97727			−0.301514
$394$	−13.2749	+	22.9929i	−0.668781	+	1.15836i
$395$	−1.78309	+	1.02947i	−0.0897170	+	0.0517981i
$396$	1.22056	−	0.704688i	0.0613353	−	0.0354119i
$397$	−19.3546	−	11.1744i	−0.971378	−	0.560826i	−0.0717222	−	0.997425i	$-0.522850\pi$
$397$	−19.3546	−	11.1744i	−0.971378	−	0.560826i	−0.899656	+	0.436599i	$0.856183\pi$
$398$		−	2.93894i		−	0.147316i
$399$	19.0305	+	6.09574i	0.952716	+	0.305169i
$400$	−21.5241			−1.07620
$401$	−24.6356	−	14.2234i	−1.23024	−	0.710282i	−0.263164	−	0.964751i	$-0.584766\pi$
$401$	−24.6356	−	14.2234i	−1.23024	−	0.710282i	−0.967081	+	0.254469i	$0.918099\pi$
$402$	5.15774	+	8.93347i	0.257245	+	0.445561i
$403$	1.26203	−	1.82417i	0.0628664	−	0.0908682i
$404$	15.2302	−	26.3794i	0.757730	−	1.31243i
$405$		−	0.150750i		−	0.00749083i
$406$	−6.43872	+	5.84626i	−0.319548	+	0.290145i
$407$	−2.76118			−0.136866
$408$	−0.278274	−	0.160662i	−0.0137766	−	0.00795394i
$409$	13.0772	−	7.55015i	0.646628	−	0.373331i	−0.140535	−	0.990076i	$-0.544882\pi$
$409$	13.0772	−	7.55015i	0.646628	−	0.373331i	0.787163	+	0.616745i	$0.211549\pi$
$410$	−2.70299	+	1.56057i	−0.133491	+	0.0770711i
$411$	11.5074	+	6.64379i	0.567618	+	0.327714i
$412$	9.95664			0.490528
$413$	4.58123	+	21.1195i	0.225428	+	1.03922i
$414$		−	14.1393i		−	0.694908i
$415$	0.269514	−	0.466811i	0.0132299	−	0.0229149i
$416$	−15.9144	+	23.0029i	−0.780265	+	1.12781i
$417$	−7.02270	−	12.1637i	−0.343903	−	0.595657i
$418$	9.89196	+	5.71112i	0.483831	+	0.279340i
$419$	−8.52484			−0.416466			−0.208233	−	0.978079i	$-0.566771\pi$
$419$	−8.52484			−0.416466			−0.208233	+	0.978079i	$0.566771\pi$
$420$	0.154045	+	0.710146i	0.00751662	+	0.0346516i
$421$			35.9003i			1.74967i	0.484417	+	0.874837i	$0.339032\pi$
$421$			35.9003i			1.74967i	−0.484417	+	0.874837i	$0.660968\pi$
$422$	−40.7889	−	23.5495i	−1.98557	−	1.14637i
$423$	−4.89695	+	2.82725i	−0.238098	+	0.137466i
$424$	−2.80494	+	1.61943i	−0.136220	+	0.0786465i
$425$	2.29674	−	3.97806i	0.111408	−	0.192964i
$426$	19.0227			0.921651
$427$	20.9958	+	23.1235i	1.01606	+	1.11902i
$428$	−13.6560			−0.660090
$429$	−2.77987	−	0.227429i	−0.134213	−	0.0109804i
$430$	0.127979	+	0.221666i	0.00617170	+	0.0106897i
$431$	−34.9245	+	20.1637i	−1.68225	+	0.971250i	−0.722096	+	0.691793i	$0.756821\pi$
$431$	−34.9245	+	20.1637i	−1.68225	+	0.971250i	−0.960158	+	0.279456i	$0.909846\pi$
$432$	−2.16224	+	3.74510i	−0.104031	+	0.180186i
$433$	7.65839			0.368039			0.184019	−	0.982923i	$-0.441089\pi$
$433$	7.65839			0.368039			0.184019	+	0.982923i	$0.441089\pi$
$434$	−0.970691	+	3.03043i	−0.0465946	+	0.145465i
$435$			0.253473i			0.0121531i
$436$	−6.87426	−	3.96886i	−0.329217	−	0.190074i
$437$	47.3073	−	27.3129i	2.26301	−	1.30655i
$438$	−4.73286	−	8.19755i	−0.226145	−	0.391694i
$439$	−9.44132	+	16.3528i	−0.450609	+	0.780478i	−0.998424	−	0.0561214i	$-0.982127\pi$
$439$	−9.44132	+	16.3528i	−0.450609	+	0.780478i	0.547815	+	0.836600i	$0.315460\pi$
$440$		−	0.0406024i		−	0.00193564i
$441$	6.37084	−	2.90040i	0.303374	−	0.138114i
$442$	−2.78240	−	5.88013i	−0.132345	−	0.279689i
$443$	−7.89924	+	13.6819i	−0.375304	+	0.650046i	−0.990373	−	0.138428i	$-0.955795\pi$
$443$	−7.89924	+	13.6819i	−0.375304	+	0.650046i	0.615068	+	0.788474i	$0.289128\pi$
$444$	−5.63182	+	3.25153i	−0.267274	+	0.154311i
$445$	−0.779228	−	1.34966i	−0.0369390	−	0.0639802i
$446$	10.8890	−	18.8603i	0.515608	−	0.893059i
$447$		−	11.3090i		−	0.534898i
$448$	5.26010	−	16.4217i	0.248516	−	0.775851i
$449$		−	23.5766i		−	1.11265i	−0.830966	−	0.556324i	$-0.812211\pi$
$449$		−	23.5766i		−	1.11265i	0.830966	−	0.556324i	$-0.187789\pi$
$450$	−8.42679	−	4.86521i	−0.397243	−	0.229348i
$451$	4.09626	+	7.09493i	0.192885	+	0.334087i
$452$	8.04238	+	13.9298i	0.378282	+	0.655203i
$453$	0.693185	+	0.400211i	0.0325687	+	0.0188035i
$454$	5.00514			0.234903
$455$	0.548888	−	1.32919i	0.0257323	−	0.0623134i
$456$	−2.62968			−0.123146
$457$	−22.1748	−	12.8026i	−1.03730	−	0.598883i	−0.118229	−	0.992986i	$-0.537722\pi$
$457$	−22.1748	−	12.8026i	−1.03730	−	0.598883i	−0.919066	+	0.394104i	$0.871055\pi$
$458$	−2.35227	−	4.07425i	−0.109914	−	0.190377i
$459$	−0.461444	−	0.799245i	−0.0215384	−	0.0373056i
$460$	1.72029	+	0.993208i	0.0802088	+	0.0463086i
$461$		−	9.31900i		−	0.434029i	−0.976168	−	0.217014i	$-0.930368\pi$
$461$		−	9.31900i		−	0.434029i	0.976168	−	0.217014i	$-0.0696319\pi$
$462$	3.91026	−	0.848214i	0.181922	−	0.0394625i
$463$			22.9646i			1.06726i	0.845719	+	0.533628i	$0.179172\pi$
$463$			22.9646i			1.06726i	−0.845719	+	0.533628i	$0.820828\pi$
$464$	3.63562	−	6.29707i	0.168779	−	0.292334i
$465$	0.0463716	+	0.0803180i	0.00215043	+	0.00372466i
$466$	31.4543	−	18.1602i	1.45709	−	0.841254i
$467$	−9.64755	+	16.7101i	−0.446436	+	0.773249i	−0.998151	−	0.0607834i	$-0.980640\pi$
$467$	−9.64755	+	16.7101i	−0.446436	+	0.773249i	0.551715	+	0.834032i	$0.313973\pi$
$468$	−5.93777	+	2.80967i	−0.274473	+	0.129877i
$469$	2.95947	+	13.6431i	0.136655	+	0.629981i
$470$		−	1.66645i		−	0.0768676i
$471$	0.0964880	−	0.167122i	0.00444593	−	0.00770058i
$472$	−1.42194	−	2.46287i	−0.0654501	−	0.113363i
$473$	0.581840	−	0.335925i	0.0267530	−	0.0154459i
$474$	23.1236	+	13.3504i	1.06210	+	0.613205i
$475$		−	37.5925i		−	1.72486i
$476$	2.99046	+	3.29351i	0.137068	+	0.150958i
$477$	−9.30250			−0.425932
$478$	18.1477	−	31.4327i	0.830057	−	1.43770i
$479$	−14.6709	+	8.47023i	−0.670329	+	0.387014i	−0.796201	−	0.605032i	$-0.793160\pi$
$479$	−14.6709	+	8.47023i	−0.670329	+	0.387014i	0.125872	+	0.992046i	$0.459827\pi$
$480$	−0.584750	−	1.01282i	−0.0266900	−	0.0462285i
$481$	12.8267	+	1.04939i	0.584848	+	0.0478481i
$482$	49.9839			2.27670
$483$	5.83719	−	18.2233i	0.265601	−	0.829189i
$484$	−18.9507			−0.861395
$485$	0.361034	−	0.625329i	0.0163937	−	0.0283947i
$486$	−1.69305	+	0.977485i	−0.0767984	+	0.0443396i
$487$	11.7638	−	6.79182i	0.533068	−	0.307767i	−0.209197	−	0.977874i	$-0.567085\pi$
$487$	11.7638	−	6.79182i	0.533068	−	0.307767i	0.742265	+	0.670107i	$0.233752\pi$
$488$	−3.55952	−	2.05509i	−0.161132	−	0.0930296i
$489$			15.4538i			0.698847i
$490$	−0.198518	+	2.05341i	−0.00896811	+	0.0927635i
$491$	−7.89307			−0.356209			−0.178105	−	0.984012i	$-0.556997\pi$
$491$	−7.89307			−0.356209			−0.178105	+	0.984012i	$0.556997\pi$
$492$	16.7098	+	9.64743i	0.753338	+	0.434940i
$493$	0.775880	+	1.34386i	0.0349439	+	0.0605245i
$494$	−43.7814	−	30.2898i	−1.96982	−	1.36280i
$495$	0.0583081	−	0.100993i	0.00262075	−	0.00453928i
$496$		−	2.66047i		−	0.119458i
$497$	24.5172	+	7.85322i	1.09975	+	0.352265i
$498$	−6.99026			−0.313241
$499$	−29.5229	−	17.0450i	−1.32162	−	0.763041i	−0.337637	−	0.941276i	$-0.609628\pi$
$499$	−29.5229	−	17.0450i	−1.32162	−	0.763041i	−0.983988	+	0.178236i	$0.942961\pi$
$500$	2.37315	−	1.37014i	0.106131	−	0.0612745i
$501$	−3.62192	+	2.09112i	−0.161815	+	0.0934242i
$502$	−2.26964	−	1.31038i	−0.101299	−	0.0584849i
$503$	−30.0070			−1.33795			−0.668974	−	0.743286i	$-0.733266\pi$
$503$	−30.0070			−1.33795			−0.668974	+	0.743286i	$0.733266\pi$
$504$	−0.681989	+	0.619236i	−0.0303782	+	0.0275830i
$505$		−	2.52038i		−	0.112156i
$506$	5.46888	−	9.47239i	0.243122	−	0.421099i
$507$	12.8271	+	2.11299i	0.569673	+	0.0938412i
$508$	−10.3880	−	17.9926i	−0.460894	−	0.798292i
$509$	17.7454	+	10.2453i	0.786550	+	0.454115i	0.838747	−	0.544522i	$-0.183289\pi$
$509$	17.7454	+	10.2453i	0.786550	+	0.454115i	−0.0521966	+	0.998637i	$0.516622\pi$
$510$	0.271986			0.0120437
$511$	−2.71567	−	12.5192i	−0.120134	−	0.553818i
$512$			30.5374i			1.34957i
$513$	−6.54095	−	3.77642i	−0.288790	−	0.166733i
$514$	−33.9107	+	19.5783i	−1.49574	+	0.863564i
$515$	0.713469	−	0.411922i	0.0314392	−	0.0181514i
$516$	0.791165	−	1.37034i	0.0348291	−	0.0603258i
$517$	−4.37418			−0.192376
$518$	−18.0425	+	3.91378i	−0.792742	+	0.171962i
$519$	21.6270			0.949319
$520$	−0.0154310	+	0.188614i	−0.000676695	+	0.00827126i
$521$	−20.6778	−	35.8151i	−0.905913	−	1.56909i	−0.819688	−	0.572811i	$-0.805853\pi$
$521$	−20.6778	−	35.8151i	−0.905913	−	1.56909i	−0.0862251	−	0.996276i	$-0.527480\pi$
$522$	2.84673	−	1.64356i	0.124598	−	0.0719366i
$523$	6.73305	−	11.6620i	0.294416	−	0.509943i	−0.680433	−	0.732810i	$-0.738208\pi$
$523$	6.73305	−	11.6620i	0.294416	−	0.509943i	0.974849	+	0.222867i	$0.0715416\pi$
$524$	−10.8900			−0.475733
$525$	−8.85228	−	9.74936i	−0.386345	−	0.425497i
$526$			42.4812i			1.85227i
$527$	0.491705	+	0.283886i	0.0214190	+	0.0123663i
$528$	−2.89711	+	1.67265i	−0.126081	+	0.0727927i
$529$	−14.6544	−	25.3822i	−0.637147	−	1.10357i
$530$	1.37078	−	2.37426i	0.0595428	−	0.103131i
$531$		−	8.16805i		−	0.354463i
$532$	34.6717	+	11.1059i	1.50321	+	0.481500i
$533$	−16.3323	−	34.5155i	−0.707429	−	1.49503i
$534$	−10.1053	+	17.5028i	−0.437297	+	0.757421i
$535$	−0.978560	+	0.564972i	−0.0423068	+	0.0244259i
$536$	−0.918570	−	1.59101i	−0.0396762	−	0.0687212i
$537$	−9.29373	+	16.0972i	−0.401054	+	0.694646i
$538$		−	3.06520i		−	0.132150i
$539$	5.38988	+	0.521078i	0.232159	+	0.0224444i
$540$		−	0.274652i		−	0.0118191i
$541$	24.8152	+	14.3271i	1.06689	+	0.615969i	0.927330	−	0.374244i	$-0.122098\pi$
$541$	24.8152	+	14.3271i	1.06689	+	0.615969i	0.139560	+	0.990214i	$0.455431\pi$
$542$	−3.55926	−	6.16481i	−0.152883	−	0.264801i
$543$	−1.27496	−	2.20829i	−0.0547137	−	0.0947670i
$544$	−6.20044	−	3.57983i	−0.265842	−	0.153484i
$545$	−0.656791			−0.0281338
$546$	−18.4870	+	2.45418i	−0.791172	+	0.105029i
$547$	14.1081			0.603218			0.301609	−	0.953432i	$-0.402476\pi$
$547$	14.1081			0.603218			0.301609	+	0.953432i	$0.402476\pi$
$548$	20.9654	+	12.1044i	0.895596	+	0.517072i
$549$	−5.90253	−	10.2235i	−0.251914	−	0.436328i
$550$	−3.76360	−	6.51874i	−0.160480	−	0.277960i
$551$	10.9980	+	6.34973i	0.468533	+	0.270507i
$552$			2.51814i			0.107179i
$553$	24.2912	+	26.7528i	1.03297	+	1.13765i
$554$			15.7905i			0.670874i
$555$	−0.269042	+	0.465994i	−0.0114202	+	0.0197804i
$556$	−12.7947	−	22.1610i	−0.542615	−	0.939837i
$557$	−1.09997	+	0.635069i	−0.0466073	+	0.0269087i	−0.523123	−	0.852257i	$-0.675233\pi$
$557$	−1.09997	+	0.635069i	−0.0466073	+	0.0269087i	0.476515	+	0.879166i	$0.341900\pi$
$558$	0.601360	−	1.04159i	0.0254576	−	0.0440938i
$559$	−2.83054	+	1.33937i	−0.119719	+	0.0566494i
$560$	−0.365641	−	1.68560i	−0.0154511	−	0.0712297i
$561$		−	0.713922i		−	0.0301418i
$562$	0.670279	−	1.16096i	0.0282740	−	0.0489721i
$563$	11.7278	+	20.3131i	0.494267	+	0.856096i	0.999978	−	0.00660697i	$-0.00210308\pi$
$563$	11.7278	+	20.3131i	0.494267	+	0.856096i	−0.505711	+	0.862703i	$0.668770\pi$
$564$	−8.92177	+	5.15099i	−0.375674	+	0.216896i
$565$	1.15260	+	0.665452i	0.0484901	+	0.0279958i
$566$		−	30.0782i		−	1.26428i
$567$	−2.58562	+	0.560872i	−0.108586	+	0.0235544i
$568$	−3.38785			−0.142151
$569$	0.0264704	−	0.0458481i	0.00110970	−	0.00192205i	−0.865470	−	0.500961i	$-0.832980\pi$
$569$	0.0264704	−	0.0458481i	0.00110970	−	0.00192205i	0.866580	+	0.499039i	$0.166313\pi$
$570$	1.92769	−	1.11295i	0.0807422	−	0.0466165i
$571$	2.43580	+	4.21894i	0.101935	+	0.176557i	0.912482	−	0.409117i	$-0.134163\pi$
$571$	2.43580	+	4.21894i	0.101935	+	0.176557i	−0.810547	+	0.585674i	$0.800830\pi$
$572$	−5.06466	−	0.414354i	−0.211764	−	0.0173250i
$573$	−1.99101			−0.0831755
$574$	36.8230	+	40.5546i	1.53696	+	1.69272i
$575$	−35.9980			−1.50122
$576$	−3.25872	+	5.64428i	−0.135780	+	0.235178i
$577$	38.0743	−	21.9822i	1.58505	−	0.915131i	0.590948	−	0.806710i	$-0.298754\pi$
$577$	38.0743	−	21.9822i	1.58505	−	0.915131i	0.994105	−	0.108421i	$-0.0345795\pi$
$578$	−27.3399	+	15.7847i	−1.13719	+	0.656557i
$579$	−15.1267	−	8.73340i	−0.628644	−	0.362948i
$580$			0.461804i			0.0191754i
$581$	−9.00934	−	2.88582i	−0.373770	−	0.119724i
$582$	−9.36398			−0.388149
$583$	−6.23206	−	3.59808i	−0.258106	−	0.149017i
$584$	0.842900	+	1.45995i	0.0348795	+	0.0604130i
$585$	−0.309246	+	0.446989i	−0.0127857	+	0.0184807i
$586$	11.8495	−	20.5239i	0.489497	−	0.847834i
$587$			27.3732i			1.12981i	0.825155	+	0.564906i	$0.191087\pi$
$587$			27.3732i			1.12981i	−0.825155	+	0.564906i	$0.808913\pi$
$588$	11.6071	−	5.28426i	0.478668	−	0.217919i
$589$	4.64659			0.191460
$590$	2.08471	+	1.20361i	0.0858263	+	0.0495518i
$591$	11.7612	−	6.79035i	0.483793	−	0.279318i
$592$	13.3677	−	7.71784i	0.549409	−	0.317201i
$593$	35.6228	+	20.5669i	1.46285	+	0.844580i	0.999142	−	0.0414062i	$-0.0131838\pi$
$593$	35.6228	+	20.5669i	1.46285	+	0.844580i	0.463712	+	0.885986i	$0.346517\pi$
$594$	−1.51231			−0.0620509
$595$	0.350547	+	0.112285i	0.0143710	+	0.00460325i
$596$		−	20.6039i		−	0.843970i
$597$	−0.751660	+	1.30191i	−0.0307634	+	0.0532838i
$598$	−29.0051	+	41.9244i	−1.18611	+	1.71442i
$599$	8.87901	+	15.3789i	0.362786	+	0.628364i	0.988418	−	0.151754i	$-0.0484921\pi$
$599$	8.87901	+	15.3789i	0.362786	+	0.628364i	−0.625632	+	0.780118i	$0.715159\pi$
$600$	1.50077	+	0.866472i	0.0612688	+	0.0353736i
$601$	11.7901			0.480929			0.240465	−	0.970658i	$-0.422700\pi$
$601$	11.7901			0.480929			0.240465	+	0.970658i	$0.422700\pi$
$602$	3.32580	−	3.01978i	0.135549	−	0.123077i
$603$		−	5.27654i		−	0.214877i
$604$	1.26292	+	0.729146i	0.0513874	+	0.0296685i
$605$	−1.35796	+	0.784020i	−0.0552090	+	0.0318749i
$606$	−28.3061	+	16.3425i	−1.14986	+	0.663870i
$607$	8.03071	−	13.9096i	0.325956	−	0.564573i	−0.655749	−	0.754979i	$-0.727647\pi$
$607$	8.03071	−	13.9096i	0.325956	−	0.564573i	0.981705	+	0.190406i	$0.0609804\pi$
$608$	−58.5939			−2.37630
$609$	4.34750	−	0.943059i	0.176170	−	0.0382147i
$610$	3.47909			0.140864
$611$	20.3197	+	1.66241i	0.822048	+	0.0672541i
$612$	−0.840708	−	1.45615i	−0.0339836	−	0.0588613i
$613$	−16.7067	+	9.64563i	−0.674778	+	0.389583i	−0.797885	−	0.602810i	$-0.794048\pi$
$613$	−16.7067	+	9.64563i	−0.674778	+	0.389583i	0.123106	+	0.992393i	$0.460714\pi$
$614$	−18.9442	+	32.8124i	−0.764527	+	1.32420i
$615$	1.59652			0.0643778
$616$	−0.696400	+	0.151063i	−0.0280588	+	0.00608650i
$617$			34.6180i			1.39367i	0.717233	+	0.696833i	$0.245408\pi$
$617$			34.6180i			1.39367i	−0.717233	+	0.696833i	$0.754592\pi$
$618$	−9.25247	−	5.34192i	−0.372189	−	0.214883i
$619$	−13.7392	+	7.93230i	−0.552223	+	0.318826i	−0.750018	−	0.661417i	$-0.769955\pi$
$619$	−13.7392	+	7.93230i	−0.552223	+	0.318826i	0.197795	+	0.980243i	$0.436622\pi$
$620$	0.0844846	+	0.146332i	0.00339298	+	0.00587682i
$621$	−3.61624	+	6.26351i	−0.145115	+	0.251346i
$622$			19.6699i			0.788690i
$623$	−20.2499	+	18.3866i	−0.811293	+	0.736642i
$624$	14.0939	−	6.66904i	0.564207	−	0.266975i
$625$	−12.3298	+	21.3559i	−0.493193	+	0.854235i
$626$	−31.4960	+	18.1842i	−1.25883	+	0.726788i
$627$	−2.92134	−	5.05990i	−0.116667	−	0.202073i
$628$	0.175792	−	0.304481i	0.00701486	−	0.0121501i
$629$			3.29414i			0.131346i
$630$	0.237856	−	0.742570i	0.00947640	−	0.0295847i
$631$		−	5.72803i		−	0.228029i	−0.993479	−	0.114015i	$-0.963629\pi$
$631$		−	5.72803i		−	0.228029i	0.993479	−	0.114015i	$-0.0363710\pi$
$632$	−4.11821	−	2.37765i	−0.163814	−	0.0945778i
$633$	12.0460	+	20.8642i	0.478784	+	0.829279i
$634$	3.34777	+	5.79851i	0.132957	+	0.230288i
$635$	−1.48876	−	0.859538i	−0.0590798	−	0.0341097i
$636$	−16.9483			−0.672042
$637$	−24.8400	−	4.46904i	−0.984198	−	0.177070i
$638$	2.54282			0.100671
$639$	−8.42679	−	4.86521i	−0.333359	−	0.192465i
$640$	0.209115	+	0.362198i	0.00826599	+	0.0143171i
$641$	9.27361	+	16.0624i	0.366285	+	0.634425i	0.988982	−	0.148039i	$-0.0472961\pi$
$641$	9.27361	+	16.0624i	0.366285	+	0.634425i	−0.622696	+	0.782464i	$0.713963\pi$
$642$	12.6902	+	7.32671i	0.500844	+	0.289162i
$643$		−	43.4949i		−	1.71527i	−0.514257	−	0.857636i	$-0.671932\pi$
$643$		−	43.4949i		−	1.71527i	0.514257	−	0.857636i	$-0.328068\pi$
$644$	10.6348	−	33.2011i	0.419070	−	1.30831i
$645$		−	0.130927i		−	0.00515524i
$646$	6.81349	−	11.8013i	0.268073	−	0.464316i
$647$	7.97924	+	13.8204i	0.313696	+	0.543338i	0.979160	−	0.203093i	$-0.0650993\pi$
$647$	7.97924	+	13.8204i	0.313696	+	0.543338i	−0.665463	+	0.746431i	$0.731766\pi$
$648$	0.301525	−	0.174086i	0.0118450	−	0.00683873i
$649$	3.15929	−	5.47205i	0.124013	−	0.214797i
$650$	15.0059	+	31.7124i	0.588579	+	1.24386i
$651$	1.20506	−	1.09418i	0.0472301	−	0.0428842i
$652$			28.1554i			1.10265i
$653$	11.4443	−	19.8220i	0.447849	−	0.775696i	−0.550397	−	0.834903i	$-0.685524\pi$
$653$	11.4443	−	19.8220i	0.447849	−	0.775696i	0.998246	+	0.0592065i	$0.0188571\pi$
$654$	4.25872	+	7.37633i	0.166529	+	0.288437i
$655$	−0.780353	+	0.450537i	−0.0304909	+	0.0176039i
$656$	−39.6625	−	22.8991i	−1.54856	−	0.894061i
$657$			4.84187i			0.188899i
$658$	−28.5824	+	6.20010i	−1.11426	+	0.241705i
$659$	19.2602			0.750269			0.375134	−	0.926970i	$-0.377597\pi$
$659$	19.2602			0.750269			0.375134	+	0.926970i	$0.377597\pi$
$660$	0.106232	−	0.183999i	0.00413507	−	0.00716215i
$661$	2.86323	−	1.65308i	0.111367	−	0.0642975i	−0.443282	−	0.896382i	$-0.646186\pi$
$661$	2.86323	−	1.65308i	0.111367	−	0.0642975i	0.554649	+	0.832085i	$0.312853\pi$
$662$	−17.3041	−	29.9716i	−0.672544	−	1.16488i
$663$	−0.271327	+	3.31644i	−0.0105375	+	0.128800i
$664$	1.24493			0.0483128
$665$	2.94396	−	0.638604i	0.114162	−	0.0247640i
$666$	6.97803			0.270393
$667$	6.08040	−	10.5316i	0.235434	−	0.407784i
$668$	−6.59879	+	3.80982i	−0.255315	+	0.147406i
$669$	−9.64735	+	5.56990i	−0.372988	+	0.215345i
$670$	1.34672	+	0.777530i	0.0520284	+	0.0300386i
$671$		−	9.13209i		−	0.352540i
$672$	−15.1959	+	13.7977i	−0.586195	+	0.532257i
$673$	20.7526			0.799953			0.399977	−	0.916525i	$-0.369018\pi$
$673$	20.7526			0.799953			0.399977	+	0.916525i	$0.369018\pi$
$674$	33.7756	+	19.5004i	1.30099	+	0.751126i
$675$	2.48864	+	4.31045i	0.0957877	+	0.165909i
$676$	23.3698	+	3.84967i	0.898839	+	0.148064i
$677$	−20.4176	+	35.3643i	−0.784711	+	1.35916i	0.144461	+	0.989510i	$0.453855\pi$
$677$	−20.4176	+	35.3643i	−0.784711	+	1.35916i	−0.929172	+	0.369648i	$0.879478\pi$
$678$		−	17.2595i		−	0.662848i
$679$	−12.0687	−	3.86578i	−0.463154	−	0.148355i
$680$	−0.0484395			−0.00185757
$681$	−2.21721	−	1.28011i	−0.0849636	−	0.0490538i
$682$	0.805743	−	0.465196i	0.0308535	−	0.0178133i
$683$	13.7114	−	7.91625i	0.524650	−	0.302907i	−0.214185	−	0.976793i	$-0.568710\pi$
$683$	13.7114	−	7.91625i	0.524650	−	0.302907i	0.738835	+	0.673886i	$0.235376\pi$
$684$	−11.9170	−	6.88027i	−0.455657	−	0.263074i
$685$	2.00310			0.0765347
$686$	35.9580	−	4.23488i	1.37288	−	0.161689i
$687$			2.40645i			0.0918118i
$688$	−1.87791	+	3.25263i	−0.0715946	+	0.124006i
$689$	27.5829	+	19.0830i	1.05082	+	0.727004i
$690$	−1.06575	−	1.84593i	−0.0405723	−	0.0702734i
$691$	−34.5351	−	19.9389i	−1.31378	−	0.758510i	−0.331059	−	0.943610i	$-0.607406\pi$
$691$	−34.5351	−	19.9389i	−1.31378	−	0.758510i	−0.982720	+	0.185100i	$0.940739\pi$
$692$	39.4023			1.49785
$693$	−1.94913	−	0.624335i	−0.0740414	−	0.0237165i
$694$			6.24364i			0.237005i
$695$	−1.83367	−	1.05867i	−0.0695552	−	0.0401577i
$696$	−0.506989	+	0.292710i	−0.0192174	+	0.0110951i
$697$	8.46440	−	4.88692i	0.320612	−	0.185105i
$698$	−20.9726	+	36.3255i	−0.793823	+	1.37494i
$699$	−18.5785			−0.702702
$700$	−16.1280	−	17.7624i	−0.609581	−	0.671356i
$701$	25.8419			0.976034			0.488017	−	0.872834i	$-0.337720\pi$
$701$	25.8419			0.976034			0.488017	+	0.872834i	$0.337720\pi$
$702$	7.02527	+	0.574757i	0.265152	+	0.0216928i
$703$	13.4795	+	23.3471i	0.508388	+	0.880553i
$704$	−4.36626	+	2.52086i	−0.164560	+	0.0950086i
$705$	−0.426209	+	0.738215i	−0.0160519	+	0.0278028i
$706$	52.6406			1.98116
$707$	−43.2289	+	9.37720i	−1.62579	+	0.352666i
$708$		−	14.8814i		−	0.559277i
$709$	9.94974	+	5.74448i	0.373670	+	0.215739i	0.675061	−	0.737762i	$-0.264117\pi$
$709$	9.94974	+	5.74448i	0.373670	+	0.215739i	−0.301390	+	0.953501i	$0.597451\pi$
$710$	2.48347	−	1.43383i	0.0932031	−	0.0538108i
$711$	−6.82897	−	11.8281i	−0.256106	−	0.443589i
$712$	1.79970	−	3.11717i	0.0674466	−	0.116821i
$713$		−	4.44951i		−	0.166635i
$714$	−1.01194	−	4.66502i	−0.0378708	−	0.174584i
$715$	−0.380064	+	0.179841i	−0.0142136	+	0.00672568i
$716$	−16.9323	+	29.3276i	−0.632790	+	1.09602i
$717$	−16.0784	+	9.28286i	−0.600458	+	0.346675i
$718$	2.98939	+	5.17777i	0.111563	+	0.193233i
$719$	12.4830	−	21.6211i	0.465536	−	0.806332i	−0.533690	−	0.845680i	$-0.679195\pi$
$719$	12.4830	−	21.6211i	0.465536	−	0.806332i	0.999226	+	0.0393484i	$0.0125282\pi$
$720$			0.651915i			0.0242954i
$721$	−9.71965	−	10.7046i	−0.361979	−	0.398661i
$722$		−	74.3775i		−	2.76804i
$723$	−22.1422	−	12.7838i	−0.823477	−	0.475435i
$724$	−2.32285	−	4.02330i	−0.0863282	−	0.149525i
$725$	−4.18443	−	7.24765i	−0.155406	−	0.269171i
$726$	17.6104	+	10.1674i	0.653584	+	0.377347i
$727$	−37.9518			−1.40756			−0.703778	−	0.710420i	$-0.748505\pi$
$727$	−37.9518			−1.40756			−0.703778	+	0.710420i	$0.748505\pi$
$728$	3.29246	−	0.437078i	0.122027	−	0.0161992i
$729$	1.00000			0.0370370
$730$	−1.23578	−	0.713478i	−0.0457383	−	0.0264070i
$731$	−0.400766	−	0.694147i	−0.0148229	−	0.0256740i
$732$	−10.7539	−	18.6262i	−0.397474	−	0.688445i
$733$	−26.8008	−	15.4734i	−0.989909	−	0.571524i	−0.0846618	−	0.996410i	$-0.526981\pi$
$733$	−26.8008	−	15.4734i	−0.989909	−	0.571524i	−0.905247	+	0.424886i	$0.860314\pi$
$734$		−	43.9085i		−	1.62069i
$735$	0.613117	−	0.858860i	0.0226152	−	0.0316795i
$736$			56.1086i			2.06819i
$737$	2.04090	−	3.53494i	0.0751774	−	0.130211i
$738$	−10.3520	−	17.9303i	−0.381064	−	0.660022i
$739$	16.9505	−	9.78635i	0.623533	−	0.359997i	−0.154710	−	0.987960i	$-0.549444\pi$
$739$	16.9505	−	9.78635i	0.623533	−	0.359997i	0.778243	+	0.627963i	$0.216111\pi$
$740$	−0.490169	+	0.848997i	−0.0180190	+	0.0312098i
$741$	11.6477	+	24.6155i	0.427889	+	0.904271i
$742$	−45.8226	−	14.6776i	−1.68220	−	0.538833i
$743$			34.0186i			1.24802i	0.781416	+	0.624010i	$0.214498\pi$
$743$			34.0186i			1.24802i	−0.781416	+	0.624010i	$0.785502\pi$
$744$	−0.107099	+	0.185502i	−0.00392646	+	0.00680082i
$745$	−0.852417	−	1.47643i	−0.0312301	−	0.0540922i
$746$	55.1298	−	31.8292i	2.01845	−	1.16535i
$747$	3.09659	+	1.78782i	0.113298	+	0.0654128i
$748$		−	1.30070i		−	0.0475582i
$749$	13.3310	+	14.6819i	0.487104	+	0.536467i
$750$	−2.94042			−0.107369
$751$	20.6159	−	35.7077i	0.752284	−	1.30299i	−0.194430	−	0.980916i	$-0.562286\pi$
$751$	20.6159	−	35.7077i	0.752284	−	1.30299i	0.946713	−	0.322077i	$-0.104381\pi$
$752$	21.1767	−	12.2264i	0.772235	−	0.445850i
$753$	0.670279	+	1.16096i	0.0244263	+	0.0423077i
$754$	−11.8124	−	0.966405i	−0.430182	−	0.0351944i
$755$	0.120664			0.00439140
$756$	−4.71075	+	1.02186i	−0.171328	+	0.0371645i
$757$	4.10877			0.149336			0.0746679	−	0.997208i	$-0.476210\pi$
$757$	4.10877			0.149336			0.0746679	+	0.997208i	$0.476210\pi$
$758$	−29.9747	+	51.9178i	−1.08873	+	1.88574i
$759$	−4.84529	+	2.79743i	−0.175873	+	0.101540i
$760$	−0.343314	+	0.198212i	−0.0124533	+	0.00718991i
$761$	18.2651	+	10.5454i	0.662111	+	0.382270i	0.793081	−	0.609116i	$-0.208476\pi$
$761$	18.2651	+	10.5454i	0.662111	+	0.382270i	−0.130970	+	0.991386i	$0.541809\pi$
$762$			22.2935i			0.807607i
$763$	2.44362	+	11.2651i	0.0884650	+	0.407823i
$764$	−3.62743			−0.131236
$765$	−0.120486	−	0.0695628i	−0.00435619	−	0.00251505i
$766$	−26.6515	−	46.1617i	−0.962957	−	1.66789i
$767$	−16.7558	+	24.2191i	−0.605016	+	0.874501i
$768$	9.22931	−	15.9856i	0.333034	−	0.576832i
$769$			31.6857i			1.14262i	0.820735	+	0.571309i	$0.193564\pi$
$769$			31.6857i			1.14262i	−0.820735	+	0.571309i	$0.806436\pi$
$770$	0.446564	−	0.405473i	0.0160930	−	0.0146122i
$771$	20.0293			0.721338
$772$	−27.5594	−	15.9114i	−0.991885	−	0.572665i
$773$	45.2445	−	26.1219i	1.62733	−	0.939540i	0.642446	−	0.766331i	$-0.277920\pi$
$773$	45.2445	−	26.1219i	1.62733	−	0.939540i	0.984885	−	0.173209i	$-0.0554137\pi$
$774$	−1.47042	+	0.848948i	−0.0528532	+	0.0305148i
$775$	−2.65184	−	1.53104i	−0.0952568	−	0.0549965i
$776$	1.66768			0.0598663
$777$	8.99358	+	2.88077i	0.322643	+	0.103347i
$778$		−	59.7624i		−	2.14259i
$779$	39.9941	−	69.2718i	1.43294	−	2.48192i
$780$	−0.563417	+	0.814372i	−0.0201736	+	0.0291592i
$781$	−3.76360	−	6.51874i	−0.134672	−	0.233259i
$782$	−11.3007	−	6.52449i	−0.404114	−	0.233315i
$783$	−1.68142			−0.0600889
$784$	−27.5505	+	12.5427i	−0.983948	+	0.447954i
$785$		−	0.0290912i		−	0.00103831i
$786$	10.1198	+	5.84269i	0.360963	+	0.208402i
$787$	19.5495	−	11.2869i	0.696863	−	0.402334i	−0.109315	−	0.994007i	$-0.534866\pi$
$787$	19.5495	−	11.2869i	0.696863	−	0.402334i	0.806178	+	0.591673i	$0.201532\pi$
$788$	21.4278	−	12.3714i	0.763336	−	0.440712i
$789$	10.8649	−	18.8186i	0.386802	−	0.669960i
$790$	4.02515			0.143209
$791$	7.12534	−	22.2448i	0.253348	−	0.790935i
$792$	0.269336			0.00957044
$793$	−3.47067	+	42.4220i	−0.123247	+	1.50645i
$794$	21.8456	+	37.8376i	0.775270	+	1.34281i
$795$	−1.21447	+	0.701176i	−0.0430729	+	0.0248682i
$796$	−1.36945	+	2.37196i	−0.0485390	+	0.0840719i
$797$	−11.0947			−0.392996			−0.196498	−	0.980504i	$-0.562957\pi$
$797$	−11.0947			−0.392996			−0.196498	+	0.980504i	$0.562957\pi$
$798$	−26.2611	−	28.9224i	−0.929634	−	1.02384i
$799$			5.21848i			0.184617i
$800$	33.4399	+	19.3065i	1.18228	+	0.682589i
$801$	8.95299	−	5.16901i	0.316338	−	0.182638i
$802$	27.8063	+	48.1619i	0.981874	+	1.70066i
$803$	−1.87277	+	3.24374i	−0.0660887	+	0.114469i
$804$		−	9.61336i		−	0.339037i
$805$	−0.611517	−	2.81909i	−0.0215532	−	0.0993599i
$806$	−3.91978	+	1.85479i	−0.138069	+	0.0653322i
$807$	−0.783952	+	1.35784i	−0.0275964	+	0.0477984i
$808$	5.04119	−	2.91053i	0.177348	−	0.102392i
$809$	12.6465	+	21.9044i	0.444628	+	0.770119i	0.998026	−	0.0627983i	$-0.0200025\pi$
$809$	12.6465	+	21.9044i	0.444628	+	0.770119i	−0.553398	+	0.832917i	$0.686669\pi$
$810$	−0.147356	+	0.255228i	−0.00517756	+	0.00896779i
$811$			14.1042i			0.495267i	0.968854	+	0.247633i	$0.0796528\pi$
$811$			14.1042i			0.495267i	−0.968854	+	0.247633i	$0.920347\pi$
$812$	7.92073	−	1.71816i	0.277963	−	0.0602957i
$813$			3.64124i			0.127704i
$814$	4.67482	+	2.69901i	0.163852	+	0.0946002i
$815$	1.16483	+	2.01755i	0.0408024	+	0.0706717i
$816$	1.99550	+	3.45631i	0.0698566	+	0.120995i
$817$	−5.68083	−	3.27983i	−0.198747	−	0.114747i
$818$	−29.5206			−1.03216
$819$	8.81719	+	3.64105i	0.308097	+	0.127229i
$820$	2.90870			0.101576
$821$	47.5632	+	27.4606i	1.65997	+	0.958383i	0.972727	+	0.231954i	$0.0745119\pi$
$821$	47.5632	+	27.4606i	1.65997	+	0.958383i	0.687242	+	0.726429i	$0.258821\pi$
$822$	−12.9884	−	22.4966i	−0.453023	−	0.784659i
$823$	−5.48342	−	9.49756i	−0.191140	−	0.331064i	0.754488	−	0.656313i	$-0.227885\pi$
$823$	−5.48342	−	9.49756i	−0.191140	−	0.331064i	−0.945628	+	0.325249i	$0.894552\pi$
$824$	1.64782	+	0.951371i	0.0574046	+	0.0331426i
$825$			3.85029i			0.134050i
$826$	12.8877	−	40.2344i	0.448420	−	1.39994i
$827$		−	47.0639i		−	1.63657i	−0.574810	−	0.818287i	$-0.694924\pi$
$827$		−	47.0639i		−	1.63657i	0.574810	−	0.818287i	$-0.305076\pi$
$828$	−6.58845	+	11.4115i	−0.228964	+	0.396578i
$829$	−13.4513	−	23.2983i	−0.467182	−	0.809183i	0.532115	−	0.846672i	$-0.321397\pi$
$829$	−13.4513	−	23.2983i	−0.467182	−	0.809183i	−0.999297	+	0.0374890i	$0.988064\pi$
$830$	−0.912602	+	0.526891i	−0.0316769	+	0.0182886i
$831$	4.03856	−	6.99498i	0.140096	−	0.242653i
$832$	21.2410	−	10.0510i	0.736400	−	0.348455i
$833$	0.621657	−	6.43024i	0.0215391	−	0.222795i
$834$			27.4583i			0.950804i
$835$	−0.315236	+	0.546005i	−0.0109092	+	0.0188953i
$836$	−5.32240	−	9.21866i	−0.184079	−	0.318834i
$837$	−0.532789	+	0.307606i	−0.0184159	+	0.0106324i
$838$	14.4330	+	8.33290i	0.498580	+	0.287855i
$839$			35.4835i			1.22503i	0.790460	+	0.612514i	$0.209842\pi$
$839$			35.4835i			1.22503i	−0.790460	+	0.612514i	$0.790158\pi$
$840$	−0.0423610	+	0.132248i	−0.00146159	+	0.00456300i
$841$	−26.1728			−0.902512
$842$	35.0920	−	60.7811i	1.20935	−	2.09466i
$843$	−0.593850	+	0.342859i	−0.0204533	+	0.0118087i
$844$	21.9466	+	38.0126i	0.755433	+	1.30845i
$845$	1.83389	−	0.690987i	0.0630878	−	0.0237707i
$846$	11.0544			0.380058
$847$	18.4996	+	20.3744i	0.635655	+	0.700071i
$848$	40.2284			1.38145
$849$	−7.69275	+	13.3242i	−0.264014	+	0.457286i
$850$	−7.77699	+	4.49005i	−0.266749	+	0.154007i
$851$	22.3568	−	12.9077i	0.766383	−	0.442471i
$852$	−15.3528	−	8.86395i	−0.525978	−	0.303674i
$853$			3.39402i			0.116209i	0.998311	+	0.0581046i	$0.0185057\pi$
$853$			3.39402i			0.116209i	−0.998311	+	0.0581046i	$0.981494\pi$
$854$	−12.9441	−	59.6723i	−0.442938	−	2.04194i
$855$	−1.13859			−0.0389390
$856$	−2.26007	−	1.30485i	−0.0772477	−	0.0445990i
$857$	−18.3203	−	31.7317i	−0.625810	−	1.08394i	−0.988384	−	0.151980i	$-0.951435\pi$
$857$	−18.3203	−	31.7317i	−0.625810	−	1.08394i	0.362573	−	0.931955i	$-0.381898\pi$
$858$	4.48416	+	3.10233i	0.153087	+	0.105912i
$859$	4.69785	−	8.13691i	0.160289	−	0.277628i	−0.774684	−	0.632349i	$-0.782091\pi$
$859$	4.69785	−	8.13691i	0.160289	−	0.277628i	0.934972	+	0.354721i	$0.115424\pi$
$860$		−	0.238536i		−	0.00813402i
$861$	−5.93991	−	27.3830i	−0.202432	−	0.933209i
$862$	78.8387			2.68526
$863$	−22.8030	−	13.1653i	−0.776222	−	0.448152i	0.0588674	−	0.998266i	$-0.481251\pi$
$863$	−22.8030	−	13.1653i	−0.776222	−	0.448152i	−0.835090	+	0.550114i	$0.814584\pi$
$864$	6.71851	−	3.87893i	0.228568	−	0.131964i
$865$	2.82347	−	1.63013i	0.0960010	−	0.0554262i
$866$	−12.9661	−	7.48596i	−0.440605	−	0.254383i
$867$	16.1483			0.548424
$868$	2.19551	−	1.99349i	0.0745203	−	0.0676634i
$869$		−	10.5654i		−	0.358407i
$870$	0.247766	−	0.429144i	0.00840007	−	0.0145493i
$871$	−10.8242	+	15.6455i	−0.366764	+	0.530127i
$872$	−0.758460	−	1.31369i	−0.0256847	−	0.0444872i
$873$	4.14812	+	2.39492i	0.140393	+	0.0810557i
$874$	−106.792			−3.61228
$875$	−3.78974	−	1.21391i	−0.128117	−	0.0410376i
$876$			8.82143i			0.298049i
$877$	−31.8523	−	18.3900i	−1.07558	−	0.620985i	−0.145877	−	0.989303i	$-0.546600\pi$
$877$	−31.8523	−	18.3900i	−1.07558	−	0.620985i	−0.929700	+	0.368318i	$0.879934\pi$
$878$	31.9693	−	18.4575i	1.07891	−	0.622910i
$879$	−10.4983	+	6.06121i	−0.354099	+	0.204439i
$880$	−0.252152	+	0.436740i	−0.00850004	+	0.0147225i
$881$	−31.1520			−1.04954			−0.524768	−	0.851245i	$-0.675848\pi$
$881$	−31.1520			−1.04954			−0.524768	+	0.851245i	$0.675848\pi$
$882$	−13.6213	−	1.31687i	−0.458652	−	0.0443412i
$883$	−35.2516			−1.18631			−0.593155	−	0.805089i	$-0.702118\pi$
$883$	−35.2516			−1.18631			−0.593155	+	0.805089i	$0.702118\pi$
$884$	−0.494333	+	6.04224i	−0.0166262	+	0.203223i
$885$	−0.615667	−	1.06637i	−0.0206954	−	0.0358455i
$886$	26.7477	−	15.4428i	0.898606	−	0.518810i
$887$	16.2604	−	28.1638i	0.545971	−	0.945649i	−0.452574	−	0.891727i	$-0.649494\pi$
$887$	16.2604	−	28.1638i	0.545971	−	0.945649i	0.998545	−	0.0539223i	$-0.0171723\pi$
$888$	−1.24275			−0.0417041
$889$	−9.20352	+	28.7328i	−0.308676	+	0.963666i
$890$			3.04673i			0.102127i
$891$	0.669934	+	0.386787i	0.0224436	+	0.0129578i
$892$	−17.5765	+	10.1478i	−0.588506	+	0.339774i
$893$	21.3538	+	36.9858i	0.714577	+	1.23768i
$894$	−11.0544	+	19.1468i	−0.369714	+	0.640363i
$895$			2.80206i			0.0936626i
$896$	5.43428	−	4.93425i	0.181547	−	0.164842i
$897$	23.5714	−	11.1537i	0.787025	−	0.372410i
$898$	−23.0457	+	39.9164i	−0.769046	+	1.33203i
$899$	0.895839	−	0.517213i	0.0298779	−	0.0172500i
$900$	4.53406	+	7.85322i	0.151135	+	0.261774i
$901$	−4.29259	+	7.43498i	−0.143007	+	0.247695i
$902$		−	16.0161i		−	0.533279i
$903$	−2.24562	+	0.487119i	−0.0747295	+	0.0162103i
$904$			3.07384i			0.102235i
$905$	−0.332900	−	0.192200i	−0.0110660	−	0.00638895i
$906$	−0.782400	−	1.35516i	−0.0259935	−	0.0450220i
$907$	−25.7504	−	44.6010i	−0.855029	−	1.48095i	−0.876618	−	0.481186i	$-0.840206\pi$
$907$	−25.7504	−	44.6010i	−0.855029	−	1.48095i	0.0215894	−	0.999767i	$-0.493127\pi$
$908$	−4.03954	−	2.33223i	−0.134057	−	0.0773978i
$909$	16.7190			0.554533
$910$	−2.22856	+	1.71386i	−0.0738761	+	0.0568140i
$911$	45.9134			1.52118			0.760589	−	0.649234i	$-0.224910\pi$
$911$	45.9134			1.52118			0.760589	+	0.649234i	$0.224910\pi$
$912$	28.2862	+	16.3310i	0.936648	+	0.540774i
$913$	1.38301	+	2.39544i	0.0457709	+	0.0792775i
$914$	25.0288	+	43.3511i	0.827879	+	1.43393i
$915$	−1.54119	−	0.889807i	−0.0509502	−	0.0294161i
$916$			4.38432i			0.144862i
$917$	10.6308	+	11.7081i	0.351060	+	0.386637i
$918$			1.80422i			0.0595481i
$919$	12.5947	−	21.8147i	0.415461	−	0.719600i	−0.580016	−	0.814605i	$-0.696954\pi$
$919$	12.5947	−	21.8147i	0.415461	−	0.719600i	0.995477	+	0.0950056i	$0.0302869\pi$
$920$	0.189805	+	0.328752i	0.00625768	+	0.0108386i
$921$	16.7841	−	9.69030i	0.553054	−	0.319306i
$922$	−9.10918	+	15.7776i	−0.299995	+	0.519606i
$923$	15.0059	+	31.7124i	0.493925	+	1.04383i
$924$	−3.55113	−	1.13748i	−0.116824	−	0.0374203i
$925$		−	17.7658i		−	0.584135i
$926$	22.4476	−	38.8803i	0.737672	−	1.27769i
$927$	2.73248	+	4.73280i	0.0897465	+	0.155445i
$928$	−11.2966	+	6.52210i	−0.370829	+	0.214098i
$929$	−32.2348	−	18.6108i	−1.05759	−	0.610599i	−0.132825	−	0.991140i	$-0.542405\pi$
$929$	−32.2348	−	18.6108i	−1.05759	−	0.610599i	−0.924764	+	0.380540i	$0.875738\pi$
$930$		−	0.181310i		−	0.00594539i
$931$	−21.9063	−	48.1179i	−0.717949	−	1.57700i
$932$	−33.8482			−1.10873
$933$	5.03074	−	8.71350i	0.164699	−	0.285267i
$934$	32.6676	−	18.8607i	1.06892	−	0.617140i
$935$	−0.0538119	−	0.0932050i	−0.00175984	−	0.00304813i
$936$	−1.25117	−	0.102362i	−0.0408957	−	0.00334579i
$937$	7.76176			0.253566			0.126783	−	0.991930i	$-0.459535\pi$
$937$	7.76176			0.253566			0.126783	+	0.991930i	$0.459535\pi$
$938$	8.32541	−	25.9914i	0.271834	−	0.848648i
$939$	18.6031			0.607089
$940$	−0.776511	+	1.34496i	−0.0253270	+	0.0438677i
$941$	21.1138	−	12.1901i	0.688291	−	0.397385i	−0.114681	−	0.993402i	$-0.536585\pi$
$941$	21.1138	−	12.1901i	0.688291	−	0.397385i	0.802971	+	0.596018i	$0.203251\pi$
$942$	−0.326719	+	0.188631i	−0.0106451	+	0.00614594i
$943$	−66.3337	−	38.2978i	−2.16012	−	1.24715i
$944$			35.3225i			1.14965i
$945$	−0.295285	+	0.268115i	−0.00960564	+	0.00872178i
$946$	−1.31345			−0.0427039
$947$	−8.89648	−	5.13638i	−0.289097	−	0.166910i	0.348438	−	0.937332i	$-0.386712\pi$
$947$	−8.89648	−	5.13638i	−0.289097	−	0.166910i	−0.637534	+	0.770422i	$0.720046\pi$
$948$	−12.4417	−	21.5497i	−0.404089	−	0.699902i
$949$	9.93253	−	14.3566i	0.322424	−	0.466037i
$950$	−36.7461	+	63.6462i	−1.19220	+	2.06495i
$951$		−	3.42488i		−	0.111060i
$952$	0.180221	+	0.830819i	0.00584101	+	0.0269270i
$953$	−45.5757			−1.47634			−0.738170	−	0.674614i	$-0.764310\pi$
$953$	−45.5757			−1.47634			−0.738170	+	0.674614i	$0.764310\pi$
$954$	15.7496	+	9.09305i	0.509913	+	0.294398i
$955$	−0.259933	+	0.150072i	−0.00841123	+	0.00485622i
$956$	−29.2933	+	16.9125i	−0.947412	+	0.546989i
$957$	−1.12644	−	0.650349i	−0.0364126	−	0.0210228i
$958$	33.1181			1.07000
$959$	−7.45264	−	34.3566i	−0.240658	−	1.10943i
$960$			0.982506i			0.0317102i
$961$	−15.3108	+	26.5190i	−0.493895	+	0.855452i
$962$	−20.6906	−	14.3146i	−0.667090	−	0.461521i
$963$	−3.74774	−	6.49127i	−0.120769	−	0.209178i
$964$	−40.3409	−	23.2909i	−1.29929	−	0.750148i
$965$	−2.63312			−0.0847632
$966$	−27.6957	+	25.1473i	−0.891093	+	0.809100i
$967$		−	44.8970i		−	1.44379i	−0.692003	−	0.721895i	$-0.743271\pi$
$967$		−	44.8970i		−	1.44379i	0.692003	−	0.721895i	$-0.256729\pi$
$968$	−3.13634	−	1.81077i	−0.100806	−	0.0582002i
$969$	−6.03657	+	3.48521i	−0.193922	+	0.111961i
$970$	−1.22250	+	0.705810i	−0.0392521	+	0.0226622i
$971$	−0.842100	+	1.45856i	−0.0270243	+	0.0468074i	−0.879221	−	0.476414i	$-0.841936\pi$
$971$	−0.842100	+	1.45856i	−0.0270243	+	0.0468074i	0.852197	+	0.523221i	$0.175270\pi$
$972$	1.82190			0.0584376
$973$	−11.3357	+	35.3894i	−0.363407	+	1.13453i
$974$	−26.5556			−0.850897
$975$	1.46331	−	17.8861i	0.0468634	−	0.572812i
$976$	25.5253	+	44.2112i	0.817046	+	1.41517i
$977$	−34.2101	+	19.7512i	−1.09448	+	0.631897i	−0.934765	−	0.355266i	$-0.884390\pi$
$977$	−34.2101	+	19.7512i	−1.09448	+	0.631897i	−0.159713	+	0.987163i	$0.551057\pi$
$978$	15.1059	−	26.1642i	0.483033	−	0.836638i
$979$	7.99722			0.255592
$980$	1.11704	−	1.56476i	0.0356826	−	0.0499845i
$981$		−	4.35682i		−	0.139103i
$982$	13.3634	+	7.71535i	0.426443	+	0.246207i
$983$	−10.9155	+	6.30206i	−0.348150	+	0.201004i	−0.663870	−	0.747848i	$-0.731087\pi$
$983$	−10.9155	+	6.30206i	−0.348150	+	0.201004i	0.315720	+	0.948852i	$0.397754\pi$
$984$	1.84365	+	3.19330i	0.0587735	+	0.101799i
$985$	1.02365	−	1.77301i	0.0326161	−	0.0564927i
$986$		−	3.03364i		−	0.0966108i
$987$	14.2474	+	4.56364i	0.453499	+	0.145262i
$988$	21.2210	+	44.8470i	0.675130	+	1.42677i
$989$	−3.14072	+	5.43988i	−0.0998690	+	0.172978i
$990$	−0.197437	+	0.113991i	−0.00627497	+	0.00362286i
$991$	22.1789	+	38.4150i	0.704535	+	1.22029i	0.966859	+	0.255311i	$0.0821779\pi$
$991$	22.1789	+	38.4150i	0.704535	+	1.22029i	−0.262323	+	0.964980i	$0.584489\pi$
$992$	−2.38637	+	4.13331i	−0.0757672	+	0.131233i
$993$			17.7027i			0.561778i
$994$	−33.8326	−	37.2611i	−1.07310	−	1.18185i
$995$			0.226626i			0.00718451i
$996$	5.64169	+	3.25723i	0.178764	+	0.103209i
$997$	−15.0675	−	26.0977i	−0.477193	−	0.826523i	0.522465	−	0.852661i	$-0.325012\pi$
$997$	−15.0675	−	26.0977i	−0.477193	−	0.826523i	−0.999658	+	0.0261380i	$0.991679\pi$
$998$	33.3225	+	57.7163i	1.05481	+	1.82698i
$999$	−3.09117	−	1.78469i	−0.0978004	−	0.0564651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bj.d.142.2	yes	16
3.2	odd	2		819.2.dl.g.415.7		16
7.2	even	3		1911.2.c.j.883.7		8
7.4	even	3	inner	273.2.bj.d.25.7	yes	16
7.5	odd	6		1911.2.c.m.883.7		8
13.12	even	2	inner	273.2.bj.d.142.7	yes	16
21.11	odd	6		819.2.dl.g.298.2		16
39.38	odd	2		819.2.dl.g.415.2		16
91.12	odd	6		1911.2.c.m.883.2		8
91.25	even	6	inner	273.2.bj.d.25.2	✓	16
91.51	even	6		1911.2.c.j.883.2		8
273.116	odd	6		819.2.dl.g.298.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bj.d.25.2	✓	16	91.25	even	6	inner
273.2.bj.d.25.7	yes	16	7.4	even	3	inner
273.2.bj.d.142.2	yes	16	1.1	even	1	trivial
273.2.bj.d.142.7	yes	16	13.12	even	2	inner
819.2.dl.g.298.2		16	21.11	odd	6
819.2.dl.g.298.7		16	273.116	odd	6
819.2.dl.g.415.2		16	39.38	odd	2
819.2.dl.g.415.7		16	3.2	odd	2
1911.2.c.j.883.2		8	91.51	even	6
1911.2.c.j.883.7		8	7.2	even	3
1911.2.c.m.883.2		8	91.12	odd	6
1911.2.c.m.883.7		8	7.5	odd	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69305 - 0.977485i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.910952 + 1.57782i) q^{4} +(0.130553 + 0.0753750i) q^{5} -1.95497i q^{6} +(0.807080 - 2.51965i) q^{7} +0.348171i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.69305 - 0.977485i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.910952 + 1.57782i) q^{4} +(0.130553 + 0.0753750i) q^{5} -1.95497i q^{6} +(0.807080 - 2.51965i) q^{7} +0.348171i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.147356 - 0.255228i) q^{10} +(-0.669934 + 0.386787i) q^{11} +(-0.910952 + 1.57782i) q^{12} +(3.25910 - 1.54216i) q^{13} +(-3.82934 + 3.47699i) q^{14} +0.150750i q^{15} +(2.16224 - 3.74510i) q^{16} +(0.461444 + 0.799245i) q^{17} +(1.69305 - 0.977485i) q^{18} +(6.54095 + 3.77642i) q^{19} +0.274652i q^{20} +(2.58562 - 0.560872i) q^{21} +1.51231 q^{22} +(3.61624 - 6.26351i) q^{23} +(-0.301525 + 0.174086i) q^{24} +(-2.48864 - 4.31045i) q^{25} +(-7.02527 - 0.574757i) q^{26} -1.00000 q^{27} +(4.71075 - 1.02186i) q^{28} +1.68142 q^{29} +(0.147356 - 0.255228i) q^{30} +(0.532789 - 0.307606i) q^{31} +(-6.71851 + 3.87893i) q^{32} +(-0.669934 - 0.386787i) q^{33} -1.80422i q^{34} +(0.295285 - 0.268115i) q^{35} -1.82190 q^{36} +(3.09117 + 1.78469i) q^{37} +(-7.38278 - 12.7874i) q^{38} +(2.96510 + 2.05138i) q^{39} +(-0.0262434 + 0.0454549i) q^{40} -10.5905i q^{41} +(-4.92583 - 1.57782i) q^{42} -0.868503 q^{43} +(-1.22056 - 0.704688i) q^{44} +(-0.130553 + 0.0753750i) q^{45} +(-12.2450 + 7.06964i) q^{46} +(4.89695 + 2.82725i) q^{47} +4.32447 q^{48} +(-5.69725 - 4.06711i) q^{49} +9.73042i q^{50} +(-0.461444 + 0.799245i) q^{51} +(5.40213 + 3.73742i) q^{52} +(4.65125 + 8.05620i) q^{53} +(1.69305 + 0.977485i) q^{54} -0.116616 q^{55} +(0.877269 + 0.281002i) q^{56} +7.55284i q^{57} +(-2.84673 - 1.64356i) q^{58} +(-7.07374 + 4.08402i) q^{59} +(-0.237856 + 0.137326i) q^{60} +(-5.90253 + 10.2235i) q^{61} -1.20272 q^{62} +(1.77854 + 1.95878i) q^{63} +6.51745 q^{64} +(0.541727 + 0.0443202i) q^{65} +(0.756156 + 1.30970i) q^{66} +(-4.56962 + 2.63827i) q^{67} +(-0.840708 + 1.45615i) q^{68} +7.23248 q^{69} +(-0.762012 + 0.165296i) q^{70} +9.73042i q^{71} +(-0.301525 - 0.174086i) q^{72} +(4.19319 - 2.42094i) q^{73} +(-3.48901 - 6.04315i) q^{74} +(2.48864 - 4.31045i) q^{75} +13.7605i q^{76} +(0.433876 + 2.00017i) q^{77} +(-3.01488 - 6.37144i) q^{78} +(-6.82897 + 11.8281i) q^{79} +(0.564575 - 0.325957i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-10.3520 + 17.9303i) q^{82} -3.57563i q^{83} +(3.24033 + 3.56870i) q^{84} +0.139126i q^{85} +(1.47042 + 0.848948i) q^{86} +(0.840708 + 1.45615i) q^{87} +(-0.134668 - 0.233252i) q^{88} +(-8.95299 - 5.16901i) q^{89} +0.294712 q^{90} +(-1.25535 - 9.45643i) q^{91} +13.1769 q^{92} +(0.532789 + 0.307606i) q^{93} +(-5.52719 - 9.57338i) q^{94} +(0.569295 + 0.986048i) q^{95} +(-6.71851 - 3.87893i) q^{96} -4.78983i q^{97} +(5.67020 + 12.4548i) q^{98} -0.773573i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9} - 16 q^{10} - 8 q^{12} + 6 q^{13} - 10 q^{14} - 28 q^{16} - 2 q^{17} + 60 q^{22} + 24 q^{23} + 10 q^{25} + 14 q^{26} - 16 q^{27} + 24 q^{29} + 16 q^{30} - 30 q^{35} - 16 q^{36} + 3 q^{39} + 26 q^{40} + 4 q^{42} - 76 q^{43} - 56 q^{48} + 2 q^{49} + 2 q^{51} + 10 q^{53} - 16 q^{55} + 72 q^{56} + 26 q^{61} - 104 q^{62} - 84 q^{64} - 32 q^{65} + 30 q^{66} - 12 q^{68} + 48 q^{69} - 54 q^{74} - 10 q^{75} - 10 q^{77} + 28 q^{78} - 10 q^{79} - 8 q^{81} - 48 q^{82} + 12 q^{87} + 68 q^{88} + 32 q^{90} - 57 q^{91} + 16 q^{92} - 48 q^{94} + 18 q^{95}+O(q^{100}) \) 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9 - 16 * q^10 - 8 * q^12 + 6 * q^13 - 10 * q^14 - 28 * q^16 - 2 * q^17 + 60 * q^22 + 24 * q^23 + 10 * q^25 + 14 * q^26 - 16 * q^27 + 24 * q^29 + 16 * q^30 - 30 * q^35 - 16 * q^36 + 3 * q^39 + 26 * q^40 + 4 * q^42 - 76 * q^43 - 56 * q^48 + 2 * q^49 + 2 * q^51 + 10 * q^53 - 16 * q^55 + 72 * q^56 + 26 * q^61 - 104 * q^62 - 84 * q^64 - 32 * q^65 + 30 * q^66 - 12 * q^68 + 48 * q^69 - 54 * q^74 - 10 * q^75 - 10 * q^77 + 28 * q^78 - 10 * q^79 - 8 * q^81 - 48 * q^82 + 12 * q^87 + 68 * q^88 + 32 * q^90 - 57 * q^91 + 16 * q^92 - 48 * q^94 + 18 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more