LMFDB - Embedded newform 273.2.l.c.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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, 2, 2]))

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 18 x^{18} - 4 x^{17} + 211 x^{16} - 59 x^{15} + 1458 x^{14} - 526 x^{13} + 7324 x^{12} + \cdots + 1369 $ x^20 + 18x^18 - 4x^17 + 211x^16 - 59x^15 + 1458x^14 - 526x^13 + 7324x^12 - 2645x^11 + 23428x^10 - 8506x^9 + 54235x^8 - 18801x^7 + 74141x^6 - 25533x^5 + 68867x^4 - 16327x^3 + 16588x^2 + 2997x + 1369
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.2
Root			$-1.27537 - 2.20901i$ of defining polynomial
Character	$\chi$	$=$	273.16
Dual form			273.2.l.c.256.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55074 q^{2} +(-0.500000 + 0.866025i) q^{3} +4.50630 q^{4} +(-1.40932 + 2.44101i) q^{5} +(1.27537 - 2.20901i) q^{6} +(-2.27422 + 1.35201i) q^{7} -6.39292 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-2.55074 q^{2} +(-0.500000 + 0.866025i) q^{3} +4.50630 q^{4} +(-1.40932 + 2.44101i) q^{5} +(1.27537 - 2.20901i) q^{6} +(-2.27422 + 1.35201i) q^{7} -6.39292 q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.59481 - 6.22639i) q^{10} +(-0.265601 + 0.460034i) q^{11} +(-2.25315 + 3.90257i) q^{12} +(2.71760 + 2.36953i) q^{13} +(5.80095 - 3.44863i) q^{14} +(-1.40932 - 2.44101i) q^{15} +7.29411 q^{16} +0.405918 q^{17} +(1.27537 + 2.20901i) q^{18} +(-1.83699 - 3.18176i) q^{19} +(-6.35080 + 10.9999i) q^{20} +(-0.0337632 - 2.64554i) q^{21} +(0.677479 - 1.17343i) q^{22} -2.54593 q^{23} +(3.19646 - 5.53643i) q^{24} +(-1.47234 - 2.55018i) q^{25} +(-6.93190 - 6.04406i) q^{26} +1.00000 q^{27} +(-10.2483 + 6.09255i) q^{28} +(-4.44357 - 7.69648i) q^{29} +(3.59481 + 6.22639i) q^{30} +(-4.44201 - 7.69379i) q^{31} -5.81958 q^{32} +(-0.265601 - 0.460034i) q^{33} -1.03539 q^{34} +(-0.0951659 - 7.45679i) q^{35} +(-2.25315 - 3.90257i) q^{36} -8.95466 q^{37} +(4.68569 + 8.11585i) q^{38} +(-3.41087 + 1.16874i) q^{39} +(9.00965 - 15.6052i) q^{40} +(5.44846 + 9.43700i) q^{41} +(0.0861212 + 6.74809i) q^{42} +(-4.52174 + 7.83189i) q^{43} +(-1.19687 + 2.07305i) q^{44} +2.81863 q^{45} +6.49401 q^{46} +(4.45669 - 7.71921i) q^{47} +(-3.64706 + 6.31689i) q^{48} +(3.34415 - 6.14953i) q^{49} +(3.75558 + 6.50485i) q^{50} +(-0.202959 + 0.351536i) q^{51} +(12.2463 + 10.6778i) q^{52} +(-3.51589 - 6.08971i) q^{53} -2.55074 q^{54} +(-0.748630 - 1.29667i) q^{55} +(14.5389 - 8.64328i) q^{56} +3.67398 q^{57} +(11.3344 + 19.6318i) q^{58} +0.0728735 q^{59} +(-6.35080 - 10.9999i) q^{60} +(4.87445 + 8.44280i) q^{61} +(11.3304 + 19.6249i) q^{62} +(2.30798 + 1.29353i) q^{63} +0.256025 q^{64} +(-9.61399 + 3.29426i) q^{65} +(0.677479 + 1.17343i) q^{66} +(-3.98061 + 6.89462i) q^{67} +1.82919 q^{68} +(1.27296 - 2.20484i) q^{69} +(0.242744 + 19.0204i) q^{70} +(-0.535997 + 0.928375i) q^{71} +(3.19646 + 5.53643i) q^{72} +(0.729382 + 1.26333i) q^{73} +22.8410 q^{74} +2.94469 q^{75} +(-8.27801 - 14.3379i) q^{76} +(-0.0179350 - 1.40531i) q^{77} +(8.70026 - 2.98117i) q^{78} +(3.53872 - 6.12924i) q^{79} +(-10.2797 + 17.8050i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-13.8976 - 24.0714i) q^{82} +0.449091 q^{83} +(-0.152147 - 11.9216i) q^{84} +(-0.572068 + 0.990850i) q^{85} +(11.5338 - 19.9771i) q^{86} +8.88713 q^{87} +(1.69796 - 2.94096i) q^{88} -0.922870 q^{89} -7.18961 q^{90} +(-9.38403 - 1.71461i) q^{91} -11.4727 q^{92} +8.88402 q^{93} +(-11.3679 + 19.6897i) q^{94} +10.3556 q^{95} +(2.90979 - 5.03990i) q^{96} +(-0.0841208 + 0.145702i) q^{97} +(-8.53007 + 15.6859i) q^{98} +0.531201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	$ 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) $ 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.55074			−1.80365			−0.901824	−	0.432103i	$-0.857772\pi$
$2$	−2.55074			−1.80365			−0.901824	+	0.432103i	$0.857772\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	4.50630			2.25315
$5$	−1.40932	+	2.44101i	−0.630265	+	1.09165i	0.357232	+	0.934016i	$0.383721\pi$
$5$	−1.40932	+	2.44101i	−0.630265	+	1.09165i	−0.987497	+	0.157636i	$0.949613\pi$
$6$	1.27537	−	2.20901i	0.520668	−	0.901824i
$7$	−2.27422	+	1.35201i	−0.859574	+	0.511011i
$7$	−2.27422	+	1.35201i	−0.859574	+	0.511011i
$8$	−6.39292			−2.26024
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	3.59481	−	6.22639i	1.13678	−	1.96896i
$11$	−0.265601	+	0.460034i	−0.0800816	+	0.138705i	−0.903285	−	0.429041i	$-0.858851\pi$
$11$	−0.265601	+	0.460034i	−0.0800816	+	0.138705i	0.823203	+	0.567747i	$0.192185\pi$
$12$	−2.25315	+	3.90257i	−0.650428	+	1.12657i
$13$	2.71760	+	2.36953i	0.753726	+	0.657189i
$13$	2.71760	+	2.36953i	0.753726	+	0.657189i
$14$	5.80095	−	3.44863i	1.55037	−	0.921684i
$15$	−1.40932	−	2.44101i	−0.363884	−	0.630265i
$16$	7.29411			1.82353
$17$	0.405918			0.0984497			0.0492248	−	0.998788i	$-0.484325\pi$
$17$	0.405918			0.0984497			0.0492248	+	0.998788i	$0.484325\pi$
$18$	1.27537	+	2.20901i	0.300608	+	0.520668i
$19$	−1.83699	−	3.18176i	−0.421434	−	0.729945i	0.574646	−	0.818402i	$-0.305140\pi$
$19$	−1.83699	−	3.18176i	−0.421434	−	0.729945i	−0.996080	+	0.0884570i	$0.971806\pi$
$20$	−6.35080	+	10.9999i	−1.42008	+	2.45965i
$21$	−0.0337632	−	2.64554i	−0.00736772	−	0.577303i
$22$	0.677479	−	1.17343i	0.144439	−	0.250176i
$23$	−2.54593			−0.530863			−0.265431	−	0.964130i	$-0.585514\pi$
$23$	−2.54593			−0.530863			−0.265431	+	0.964130i	$0.585514\pi$
$24$	3.19646	−	5.53643i	0.652475	−	1.13012i
$25$	−1.47234	−	2.55018i	−0.294469	−	0.510035i
$26$	−6.93190	−	6.04406i	−1.35946	−	1.18534i
$27$	1.00000			0.192450
$28$	−10.2483	+	6.09255i	−1.93675	+	1.15138i
$29$	−4.44357	−	7.69648i	−0.825150	−	1.42920i	−0.901805	−	0.432143i	$-0.857757\pi$
$29$	−4.44357	−	7.69648i	−0.825150	−	1.42920i	0.0766554	−	0.997058i	$-0.475576\pi$
$30$	3.59481	+	6.22639i	0.656319	+	1.13678i
$31$	−4.44201	−	7.69379i	−0.797809	−	1.38185i	−0.921040	−	0.389468i	$-0.872659\pi$
$31$	−4.44201	−	7.69379i	−0.797809	−	1.38185i	0.123231	−	0.992378i	$-0.460674\pi$
$32$	−5.81958			−1.02877
$33$	−0.265601	−	0.460034i	−0.0462351	−	0.0800816i
$34$	−1.03539			−0.177569
$35$	−0.0951659	−	7.45679i	−0.0160860	−	1.26043i
$36$	−2.25315	−	3.90257i	−0.375525	−	0.650428i
$37$	−8.95466			−1.47214			−0.736068	−	0.676907i	$-0.763320\pi$
$37$	−8.95466			−1.47214			−0.736068	+	0.676907i	$0.763320\pi$
$38$	4.68569	+	8.11585i	0.760119	+	1.31656i
$39$	−3.41087	+	1.16874i	−0.546176	+	0.187149i
$40$	9.00965	−	15.6052i	1.42455	−	2.46739i
$41$	5.44846	+	9.43700i	0.850906	+	1.47381i	0.880392	+	0.474247i	$0.157280\pi$
$41$	5.44846	+	9.43700i	0.850906	+	1.47381i	−0.0294859	+	0.999565i	$0.509387\pi$
$42$	0.0861212	+	6.74809i	0.0132888	+	1.04125i
$43$	−4.52174	+	7.83189i	−0.689559	+	1.19435i	0.282421	+	0.959290i	$0.408862\pi$
$43$	−4.52174	+	7.83189i	−0.689559	+	1.19435i	−0.971981	+	0.235061i	$0.924471\pi$
$44$	−1.19687	+	2.07305i	−0.180436	+	0.312524i
$45$	2.81863			0.420177
$46$	6.49401			0.957490
$47$	4.45669	−	7.71921i	0.650074	−	1.12596i	−0.333030	−	0.942916i	$-0.608071\pi$
$47$	4.45669	−	7.71921i	0.650074	−	1.12596i	0.983104	−	0.183046i	$-0.0585957\pi$
$48$	−3.64706	+	6.31689i	−0.526407	+	0.911764i
$49$	3.34415	−	6.14953i	0.477736	−	0.878504i
$50$	3.75558	+	6.50485i	0.531119	+	0.919924i
$51$	−0.202959	+	0.351536i	−0.0284200	+	0.0492248i
$52$	12.2463	+	10.6778i	1.69826	+	1.48074i
$53$	−3.51589	−	6.08971i	−0.482945	−	0.836486i	0.516863	−	0.856068i	$-0.327100\pi$
$53$	−3.51589	−	6.08971i	−0.482945	−	0.836486i	−0.999808	+	0.0195824i	$0.993766\pi$
$54$	−2.55074			−0.347112
$55$	−0.748630	−	1.29667i	−0.100945	−	0.174842i
$56$	14.5389	−	8.64328i	1.94284	−	1.15501i
$57$	3.67398			0.486630
$58$	11.3344	+	19.6318i	1.48828	+	2.57778i
$59$	0.0728735			0.00948732			0.00474366	−	0.999989i	$-0.498490\pi$
$59$	0.0728735			0.00948732			0.00474366	+	0.999989i	$0.498490\pi$
$60$	−6.35080	−	10.9999i	−0.819884	−	1.42008i
$61$	4.87445	+	8.44280i	0.624110	+	1.08099i	0.988712	+	0.149827i	$0.0478715\pi$
$61$	4.87445	+	8.44280i	0.624110	+	1.08099i	−0.364603	+	0.931163i	$0.618795\pi$
$62$	11.3304	+	19.6249i	1.43897	+	2.49236i
$63$	2.30798	+	1.29353i	0.290779	+	0.162969i
$64$	0.256025			0.0320031
$65$	−9.61399	+	3.29426i	−1.19247	+	0.408603i
$66$	0.677479	+	1.17343i	0.0833919	+	0.144439i
$67$	−3.98061	+	6.89462i	−0.486309	+	0.842312i	−0.999876	−	0.0157374i	$-0.994990\pi$
$67$	−3.98061	+	6.89462i	−0.486309	+	0.842312i	0.513567	+	0.858049i	$0.328324\pi$
$68$	1.82919			0.221822
$69$	1.27296	−	2.20484i	0.153247	−	0.265431i
$70$	0.242744	+	19.0204i	0.0290135	+	2.27337i
$71$	−0.535997	+	0.928375i	−0.0636112	+	0.110178i	−0.896077	−	0.443898i	$-0.853595\pi$
$71$	−0.535997	+	0.928375i	−0.0636112	+	0.110178i	0.832466	+	0.554076i	$0.186928\pi$
$72$	3.19646	+	5.53643i	0.376706	+	0.652475i
$73$	0.729382	+	1.26333i	0.0853677	+	0.147861i	0.905548	−	0.424244i	$-0.139460\pi$
$73$	0.729382	+	1.26333i	0.0853677	+	0.147861i	−0.820180	+	0.572105i	$0.806127\pi$
$74$	22.8410			2.65522
$75$	2.94469			0.340023
$76$	−8.27801	−	14.3379i	−0.949553	−	1.64467i
$77$	−0.0179350	−	1.40531i	−0.00204389	−	0.160150i
$78$	8.70026	−	2.98117i	0.985110	−	0.337551i
$79$	3.53872	−	6.12924i	0.398137	−	0.689594i	−0.595359	−	0.803460i	$-0.702990\pi$
$79$	3.53872	−	6.12924i	0.398137	−	0.689594i	0.993496	+	0.113866i	$0.0363235\pi$
$80$	−10.2797	+	17.8050i	−1.14931	+	1.99066i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−13.8976	−	24.0714i	−1.53474	−	2.65824i
$83$	0.449091			0.0492942			0.0246471	−	0.999696i	$-0.492154\pi$
$83$	0.449091			0.0492942			0.0246471	+	0.999696i	$0.492154\pi$
$84$	−0.152147	−	11.9216i	−0.0166006	−	1.30075i
$85$	−0.572068	+	0.990850i	−0.0620494	+	0.107473i
$86$	11.5338	−	19.9771i	1.24372	−	2.15419i
$87$	8.88713			0.952801
$88$	1.69796	−	2.94096i	0.181003	−	0.313507i
$89$	−0.922870			−0.0978240			−0.0489120	−	0.998803i	$-0.515575\pi$
$89$	−0.922870			−0.0978240			−0.0489120	+	0.998803i	$0.515575\pi$
$90$	−7.18961			−0.757852
$91$	−9.38403	−	1.71461i	−0.983714	−	0.179740i
$92$	−11.4727			−1.19611
$93$	8.88402			0.921230
$94$	−11.3679	+	19.6897i	−1.17251	+	2.03084i
$95$	10.3556			1.06246
$96$	2.90979	−	5.03990i	0.296979	−	0.514383i
$97$	−0.0841208	+	0.145702i	−0.00854117	+	0.0147937i	−0.870264	−	0.492585i	$-0.836052\pi$
$97$	−0.0841208	+	0.145702i	−0.00854117	+	0.0147937i	0.861723	+	0.507379i	$0.169385\pi$
$98$	−8.53007	+	15.6859i	−0.861667	+	1.58451i
$99$	0.531201			0.0533877
$100$	−6.63482	−	11.4918i	−0.663482	−	1.14918i
$101$	−1.81430	+	3.14245i	−0.180529	+	0.312686i	−0.942061	−	0.335442i	$-0.891114\pi$
$101$	−1.81430	+	3.14245i	−0.180529	+	0.312686i	0.761532	+	0.648128i	$0.224448\pi$
$102$	0.517697	−	0.896678i	0.0512597	−	0.0887843i
$103$	−4.47902	+	7.75790i	−0.441331	+	0.764408i	−0.997789	−	0.0664681i	$-0.978827\pi$
$103$	−4.47902	+	7.75790i	−0.441331	+	0.764408i	0.556457	+	0.830876i	$0.312160\pi$
$104$	−17.3734	−	15.1482i	−1.70360	−	1.48540i
$105$	6.50536	+	3.64598i	0.634858	+	0.355811i
$106$	8.96815	+	15.5333i	0.871064	+	1.50873i
$107$	−1.88820			−0.182539			−0.0912695	−	0.995826i	$-0.529092\pi$
$107$	−1.88820			−0.182539			−0.0912695	+	0.995826i	$0.529092\pi$
$108$	4.50630			0.433619
$109$	4.90716	+	8.49945i	0.470021	+	0.814100i	0.999412	−	0.0342776i	$-0.0109130\pi$
$109$	4.90716	+	8.49945i	0.470021	+	0.814100i	−0.529391	+	0.848378i	$0.677580\pi$
$110$	1.90956	+	3.30746i	0.182070	+	0.315354i
$111$	4.47733	−	7.75496i	0.424969	−	0.736068i
$112$	−16.5884	+	9.86170i	−1.56746	+	0.931843i
$113$	−3.53026	+	6.11459i	−0.332099	+	0.575212i	−0.982923	−	0.184016i	$-0.941090\pi$
$113$	−3.53026	+	6.11459i	−0.332099	+	0.575212i	0.650824	+	0.759228i	$0.274423\pi$
$114$	−9.37137			−0.877710
$115$	3.58802	−	6.21463i	0.334584	−	0.579517i
$116$	−20.0240	−	34.6826i	−1.85918	−	3.22020i
$117$	0.693272	−	3.53827i	0.0640930	−	0.327113i
$118$	−0.185882			−0.0171118
$119$	−0.923148	+	0.548805i	−0.0846248	+	0.0503089i
$120$	9.00965	+	15.6052i	0.822465	+	1.42455i
$121$	5.35891	+	9.28191i	0.487174	+	0.843810i
$122$	−12.4335	−	21.5354i	−1.12567	−	1.94973i
$123$	−10.8969			−0.982541
$124$	−20.0170	−	34.6705i	−1.79758	−	3.11350i
$125$	−5.79316			−0.518156
$126$	−5.88707	−	3.29946i	−0.524462	−	0.293939i
$127$	−9.40239	−	16.2854i	−0.834327	−	1.44510i	−0.894577	−	0.446914i	$-0.852523\pi$
$127$	−9.40239	−	16.2854i	−0.834327	−	1.44510i	0.0602500	−	0.998183i	$-0.480810\pi$
$128$	10.9861			0.971043
$129$	−4.52174	−	7.83189i	−0.398117	−	0.689559i
$130$	24.5228	−	8.40282i	2.15079	−	0.736976i
$131$	−11.3156	+	19.5992i	−0.988647	+	1.71239i	−0.364197	+	0.931322i	$0.618657\pi$
$131$	−11.3156	+	19.5992i	−0.988647	+	1.71239i	−0.624450	+	0.781065i	$0.714677\pi$
$132$	−1.19687	−	2.07305i	−0.104175	−	0.180436i
$133$	8.47947	+	4.75239i	0.735264	+	0.412085i
$134$	10.1535	−	17.5864i	0.877131	−	1.51924i
$135$	−1.40932	+	2.44101i	−0.121295	+	0.210088i
$136$	−2.59500			−0.222520
$137$	−8.54892			−0.730384			−0.365192	−	0.930932i	$-0.618997\pi$
$137$	−8.54892			−0.730384			−0.365192	+	0.930932i	$0.618997\pi$
$138$	−3.24701	+	5.62398i	−0.276403	+	0.478745i
$139$	−3.47181	+	6.01335i	−0.294475	+	0.510045i	−0.974863	−	0.222807i	$-0.928478\pi$
$139$	−3.47181	+	6.01335i	−0.294475	+	0.510045i	0.680388	+	0.732852i	$0.261811\pi$
$140$	−0.428846	−	33.6025i	−0.0362441	−	2.83993i
$141$	4.45669	+	7.71921i	0.375321	+	0.650074i
$142$	1.36719	−	2.36805i	0.114732	−	0.198722i
$143$	−1.81186	+	0.620838i	−0.151515	+	0.0519171i
$144$	−3.64706	−	6.31689i	−0.303921	−	0.526407i
$145$	25.0496			2.08025
$146$	−1.86047	−	3.22242i	−0.153973	−	0.266690i
$147$	3.65357	+	5.97088i	0.301341	+	0.492470i
$148$	−40.3523			−3.31694
$149$	6.25373	+	10.8318i	0.512325	+	0.887373i	0.999898	+	0.0142909i	$0.00454908\pi$
$149$	6.25373	+	10.8318i	0.512325	+	0.887373i	−0.487573	+	0.873082i	$0.662118\pi$
$150$	−7.51115			−0.613283
$151$	−3.96347	−	6.86494i	−0.322543	−	0.558661i	0.658469	−	0.752608i	$-0.271204\pi$
$151$	−3.96347	−	6.86494i	−0.322543	−	0.558661i	−0.981012	+	0.193947i	$0.937871\pi$
$152$	11.7437	+	20.3407i	0.952541	+	1.64985i
$153$	−0.202959	−	0.351536i	−0.0164083	−	0.0284200i
$154$	0.0457477	+	3.58459i	0.00368645	+	0.288854i
$155$	25.0408			2.01133
$156$	−15.3704	+	5.26671i	−1.23062	+	0.421674i
$157$	−5.56829	−	9.64457i	−0.444398	−	0.769720i	0.553612	−	0.832775i	$-0.313249\pi$
$157$	−5.56829	−	9.64457i	−0.444398	−	0.769720i	−0.998010	+	0.0630545i	$0.979916\pi$
$158$	−9.02637	+	15.6341i	−0.718099	+	1.24378i
$159$	7.03179			0.557657
$160$	8.20162	−	14.2056i	0.648395	−	1.12305i
$161$	5.79000	−	3.44211i	0.456316	−	0.271277i
$162$	1.27537	−	2.20901i	0.100203	−	0.173556i
$163$	−8.26484	−	14.3151i	−0.647352	−	1.12125i	−0.983753	−	0.179528i	$-0.942543\pi$
$163$	−8.26484	−	14.3151i	−0.647352	−	1.12125i	0.336401	−	0.941719i	$-0.390790\pi$
$164$	24.5524	+	42.5259i	1.91722	+	3.32072i
$165$	1.49726			0.116562
$166$	−1.14552			−0.0889094
$167$	−5.73954	−	9.94117i	−0.444139	−	0.769271i	0.553853	−	0.832615i	$-0.313157\pi$
$167$	−5.73954	−	9.94117i	−0.444139	−	0.769271i	−0.997992	+	0.0633434i	$0.979824\pi$
$168$	0.215845	+	16.9127i	0.0166528	+	1.30484i
$169$	1.77068	+	12.8788i	0.136206	+	0.990681i
$170$	1.45920	−	2.52741i	0.111915	−	0.193843i
$171$	−1.83699	+	3.18176i	−0.140478	+	0.243315i
$172$	−20.3763	+	35.2928i	−1.55368	+	2.69105i
$173$	8.62688	+	14.9422i	0.655889	+	1.13603i	0.981670	+	0.190588i	$0.0610396\pi$
$173$	8.62688	+	14.9422i	0.655889	+	1.13603i	−0.325781	+	0.945445i	$0.605627\pi$
$174$	−22.6688			−1.71852
$175$	6.79629	+	3.80904i	0.513752	+	0.287936i
$176$	−1.93732	+	3.35554i	−0.146031	+	0.252933i
$177$	−0.0364367	+	0.0631103i	−0.00273875	+	0.00474366i
$178$	2.35401			0.176440
$179$	−11.9330	+	20.6686i	−0.891914	+	1.54484i	−0.0543368	+	0.998523i	$0.517304\pi$
$179$	−11.9330	+	20.6686i	−0.891914	+	1.54484i	−0.837578	+	0.546318i	$0.816029\pi$
$180$	12.7016			0.946721
$181$	16.8430			1.25193			0.625964	−	0.779852i	$-0.284706\pi$
$181$	16.8430			1.25193			0.625964	+	0.779852i	$0.284706\pi$
$182$	23.9363	+	4.37354i	1.77427	+	0.324188i
$183$	−9.74891			−0.720660
$184$	16.2759			1.19988
$185$	12.6199	−	21.8584i	0.927837	−	1.60706i
$186$	−22.6609			−1.66158
$187$	−0.107812	+	0.186736i	−0.00788401	+	0.0136555i
$188$	20.0831	−	34.7850i	1.46471	−	2.53696i
$189$	−2.27422	+	1.35201i	−0.165425	+	0.0983441i
$190$	−26.4145			−1.91631
$191$	−2.12621	−	3.68270i	−0.153847	−	0.266470i	0.778792	−	0.627283i	$-0.215833\pi$
$191$	−2.12621	−	3.68270i	−0.153847	−	0.266470i	−0.932639	+	0.360812i	$0.882500\pi$
$192$	−0.128012	+	0.221724i	−0.00923850	+	0.0160015i
$193$	0.876346	−	1.51788i	0.0630807	−	0.109259i	−0.832760	−	0.553634i	$-0.813241\pi$
$193$	0.876346	−	1.51788i	0.0630807	−	0.109259i	0.895841	+	0.444375i	$0.146574\pi$
$194$	0.214571	−	0.371647i	0.0154053	−	0.0266827i
$195$	1.95408	−	9.97309i	0.139935	−	0.714188i
$196$	15.0697	−	27.7116i	1.07641	−	1.97940i
$197$	−3.29158	−	5.70119i	−0.234516	−	0.406193i	0.724616	−	0.689153i	$-0.242017\pi$
$197$	−3.29158	−	5.70119i	−0.234516	−	0.406193i	−0.959132	+	0.282960i	$0.908684\pi$
$198$	−1.35496			−0.0962927
$199$	−4.52366			−0.320674			−0.160337	−	0.987062i	$-0.551258\pi$
$199$	−4.52366			−0.320674			−0.160337	+	0.987062i	$0.551258\pi$
$200$	9.41258	+	16.3031i	0.665570	+	1.15280i
$201$	−3.98061	−	6.89462i	−0.280771	−	0.486309i
$202$	4.62781	−	8.01560i	0.325611	−	0.563976i
$203$	20.5113	+	11.4958i	1.43961	+	0.806844i
$204$	−0.914594	+	1.58412i	−0.0640344	+	0.110911i
$205$	−30.7144			−2.14519
$206$	11.4248	−	19.7884i	0.796006	−	1.37872i
$207$	1.27296	+	2.20484i	0.0884771	+	0.153247i
$208$	19.8225	+	17.2836i	1.37444	+	1.19840i
$209$	1.95162			0.134996
$210$	−16.5935	−	9.29996i	−1.14506	−	0.641759i
$211$	−4.47171	−	7.74522i	−0.307845	−	0.533203i	0.670046	−	0.742320i	$-0.266274\pi$
$211$	−4.47171	−	7.74522i	−0.307845	−	0.533203i	−0.977891	+	0.209117i	$0.932941\pi$
$212$	−15.8437	−	27.4420i	−1.08815	−	1.88473i
$213$	−0.535997	−	0.928375i	−0.0367259	−	0.0636112i
$214$	4.81631			0.329236
$215$	−12.7451	−	22.0752i	−0.869211	−	1.50552i
$216$	−6.39292			−0.434983
$217$	20.5042	+	11.4917i	1.39191	+	0.780110i
$218$	−12.5169	−	21.6799i	−0.847752	−	1.46835i
$219$	−1.45876			−0.0985741
$220$	−3.37355	−	5.84316i	−0.227445	−	0.393946i
$221$	1.10312	+	0.961835i	0.0742041	+	0.0647000i
$222$	−11.4205	+	19.7809i	−0.766495	+	1.32761i
$223$	−4.63460	−	8.02737i	−0.310356	−	0.537552i	0.668083	−	0.744086i	$-0.267115\pi$
$223$	−4.63460	−	8.02737i	−0.310356	−	0.537552i	−0.978439	+	0.206534i	$0.933782\pi$
$224$	13.2350	−	7.86811i	0.884300	−	0.525710i
$225$	−1.47234	+	2.55018i	−0.0981563	+	0.170012i
$226$	9.00479	−	15.5968i	0.598990	−	1.03748i
$227$	16.8333			1.11726			0.558631	−	0.829416i	$-0.311327\pi$
$227$	16.8333			1.11726			0.558631	+	0.829416i	$0.311327\pi$
$228$	16.5560			1.09645
$229$	0.853294	−	1.47795i	0.0563873	−	0.0976656i	−0.836454	−	0.548037i	$-0.815375\pi$
$229$	0.853294	−	1.47795i	0.0563873	−	0.0976656i	0.892841	+	0.450372i	$0.148709\pi$
$230$	−9.15211	+	15.8519i	−0.603473	+	1.04525i
$231$	1.22600	+	0.687123i	0.0806651	+	0.0452094i
$232$	28.4074	+	49.2030i	1.86504	+	3.23034i
$233$	−12.0571	+	20.8834i	−0.789884	+	1.36812i	0.136154	+	0.990688i	$0.456526\pi$
$233$	−12.0571	+	20.8834i	−0.789884	+	1.36812i	−0.926038	+	0.377431i	$0.876808\pi$
$234$	−1.76836	+	9.02523i	−0.115601	+	0.589998i
$235$	12.5618	+	21.7576i	0.819439	+	1.41931i
$236$	0.328390			0.0213763
$237$	3.53872	+	6.12924i	0.229865	+	0.398137i
$238$	2.35471	−	1.39986i	0.152633	−	0.0907395i
$239$	−20.7572			−1.34267			−0.671337	−	0.741152i	$-0.734280\pi$
$239$	−20.7572			−1.34267			−0.671337	+	0.741152i	$0.734280\pi$
$240$	−10.2797	−	17.8050i	−0.663553	−	1.14931i
$241$	−20.0188			−1.28952			−0.644761	−	0.764384i	$-0.723043\pi$
$241$	−20.0188			−1.28952			−0.644761	+	0.764384i	$0.723043\pi$
$242$	−13.6692	−	23.6758i	−0.878690	−	1.52194i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	21.9657	+	38.0458i	1.40621	+	2.43563i
$245$	10.2981	+	16.8297i	0.657920	+	1.07521i
$246$	27.7952			1.77216
$247$	2.54707	−	12.9995i	0.162066	−	0.827140i
$248$	28.3974	+	49.1858i	1.80324	+	3.12330i
$249$	−0.224546	+	0.388924i	−0.0142300	+	0.0246471i
$250$	14.7769			0.934572
$251$	10.4342	−	18.0725i	0.658599	−	1.14073i	−0.322380	−	0.946610i	$-0.604483\pi$
$251$	10.4342	−	18.0725i	0.658599	−	1.14073i	0.980979	−	0.194116i	$-0.0621838\pi$
$252$	10.4005	+	5.82902i	0.655167	+	0.367194i
$253$	0.676200	−	1.17121i	0.0425123	−	0.0736335i
$254$	23.9831	+	41.5399i	1.50483	+	2.60645i
$255$	−0.572068	−	0.990850i	−0.0358243	−	0.0620494i
$256$	−28.5348			−1.78342
$257$	−9.24177			−0.576486			−0.288243	−	0.957557i	$-0.593071\pi$
$257$	−9.24177			−0.576486			−0.288243	+	0.957557i	$0.593071\pi$
$258$	11.5338	+	19.9771i	0.718064	+	1.24372i
$259$	20.3649	−	12.1068i	1.26541	−	0.752278i
$260$	−43.3235	+	14.8449i	−2.68681	+	0.920643i
$261$	−4.44357	+	7.69648i	−0.275050	+	0.476400i
$262$	28.8632	−	49.9925i	1.78317	−	3.08854i
$263$	0.0930831	−	0.161225i	0.00573975	−	0.00994154i	−0.863141	−	0.504963i	$-0.831506\pi$
$263$	0.0930831	−	0.161225i	0.00573975	−	0.00994154i	0.868881	+	0.495021i	$0.164840\pi$
$264$	1.69796	+	2.94096i	0.104502	+	0.181003i
$265$	19.8200			1.21753
$266$	−21.6290	−	12.1221i	−1.32616	−	0.743256i
$267$	0.461435	−	0.799229i	0.0282394	−	0.0489120i
$268$	−17.9378	+	31.0692i	−1.09573	+	1.89785i
$269$	−12.7816			−0.779310			−0.389655	−	0.920961i	$-0.627406\pi$
$269$	−12.7816			−0.779310			−0.389655	+	0.920961i	$0.627406\pi$
$270$	3.59481	−	6.22639i	0.218773	−	0.378926i
$271$	−3.24190			−0.196932			−0.0984658	−	0.995140i	$-0.531393\pi$
$271$	−3.24190			−0.196932			−0.0984658	+	0.995140i	$0.531393\pi$
$272$	2.96082			0.179526
$273$	6.17692	−	7.26951i	0.373844	−	0.439970i
$274$	21.8061			1.31736
$275$	1.56422			0.0943261
$276$	5.73635	−	9.93565i	0.345288	−	0.598056i
$277$	23.8799			1.43480			0.717401	−	0.696660i	$-0.245332\pi$
$277$	23.8799			1.43480			0.717401	+	0.696660i	$0.245332\pi$
$278$	8.85569	−	15.3385i	0.531129	−	0.919943i
$279$	−4.44201	+	7.69379i	−0.265936	+	0.460615i
$280$	0.608388	+	47.6707i	0.0363582	+	2.84887i
$281$	−2.18620			−0.130417			−0.0652087	−	0.997872i	$-0.520771\pi$
$281$	−2.18620			−0.130417			−0.0652087	+	0.997872i	$0.520771\pi$
$282$	−11.3679	−	19.6897i	−0.676947	−	1.17251i
$283$	−8.57724	+	14.8562i	−0.509864	+	0.883111i	0.490070	+	0.871683i	$0.336971\pi$
$283$	−8.57724	+	14.8562i	−0.509864	+	0.883111i	−0.999935	+	0.0114279i	$0.996362\pi$
$284$	−2.41536	+	4.18353i	−0.143325	+	0.248247i
$285$	−5.17779	+	8.96820i	−0.306706	+	0.531231i
$286$	4.62159	−	1.58360i	0.273280	−	0.0936402i
$287$	−25.1499	−	14.0955i	−1.48455	−	0.832029i
$288$	2.90979	+	5.03990i	0.171461	+	0.296979i
$289$	−16.8352			−0.990308
$290$	−63.8950			−3.75205
$291$	−0.0841208	−	0.145702i	−0.00493125	−	0.00854117i
$292$	3.28681	+	5.69292i	0.192346	+	0.333153i
$293$	−1.83891	+	3.18509i	−0.107430	+	0.186075i	−0.914729	−	0.404069i	$-0.867596\pi$
$293$	−1.83891	+	3.18509i	−0.107430	+	0.186075i	0.807298	+	0.590144i	$0.200929\pi$
$294$	−9.31932	−	15.2302i	−0.543514	−	0.888243i
$295$	−0.102702	+	0.177885i	−0.00597953	+	0.0103568i
$296$	57.2464			3.32738
$297$	−0.265601	+	0.460034i	−0.0154117	+	0.0266939i
$298$	−15.9517	−	27.6291i	−0.924055	−	1.60051i
$299$	−6.91881	−	6.03265i	−0.400125	−	0.348877i
$300$	13.2696			0.766123
$301$	−0.305337	−	23.9249i	−0.0175993	−	1.37901i
$302$	10.1098	+	17.5107i	0.581754	+	1.00763i
$303$	−1.81430	−	3.14245i	−0.104229	−	0.180529i
$304$	−13.3992	−	23.2081i	−0.768497	−	1.33108i
$305$	−27.4786			−1.57342
$306$	0.517697	+	0.896678i	0.0295948	+	0.0512597i
$307$	14.6014			0.833347			0.416673	−	0.909056i	$-0.363196\pi$
$307$	14.6014			0.833347			0.416673	+	0.909056i	$0.363196\pi$
$308$	−0.0808205	−	6.33275i	−0.00460518	−	0.360842i
$309$	−4.47902	−	7.75790i	−0.254803	−	0.441331i
$310$	−63.8727			−3.62772
$311$	−3.03815	−	5.26223i	−0.172278	−	0.298393i	0.766938	−	0.641721i	$-0.221779\pi$
$311$	−3.03815	−	5.26223i	−0.172278	−	0.298393i	−0.939216	+	0.343328i	$0.888446\pi$
$312$	21.8054	−	7.47169i	1.23449	−	0.423001i
$313$	−1.61084	+	2.79006i	−0.0910501	+	0.157703i	−0.907953	−	0.419071i	$-0.862356\pi$
$313$	−1.61084	+	2.79006i	−0.0910501	+	0.157703i	0.816903	+	0.576775i	$0.195689\pi$
$314$	14.2033	+	24.6008i	0.801538	+	1.38831i
$315$	−6.41019	+	3.81081i	−0.361173	+	0.214715i
$316$	15.9465	−	27.6202i	0.897062	−	1.55376i
$317$	−5.62276	+	9.73891i	−0.315806	+	0.546992i	−0.979608	−	0.200916i	$-0.935608\pi$
$317$	−5.62276	+	9.73891i	−0.315806	+	0.546992i	0.663803	+	0.747908i	$0.268941\pi$
$318$	−17.9363			−1.00582
$319$	4.72085			0.264317
$320$	−0.360820	+	0.624958i	−0.0201704	+	0.0349362i
$321$	0.944099	−	1.63523i	0.0526944	−	0.0912695i
$322$	−14.7688	+	8.77995i	−0.823033	+	0.489288i
$323$	−0.745667	−	1.29153i	−0.0414900	−	0.0718629i
$324$	−2.25315	+	3.90257i	−0.125175	+	0.216809i
$325$	2.04147	−	10.4191i	0.113240	−	0.577949i
$326$	21.0815	+	36.5142i	1.16760	+	2.02233i
$327$	−9.81432			−0.542733
$328$	−34.8315	−	60.3300i	−1.92325	−	3.33117i
$329$	0.300944	+	23.5806i	0.0165916	+	1.30004i
$330$	−3.81913			−0.210236
$331$	−1.84302	−	3.19220i	−0.101301	−	0.175459i	0.810920	−	0.585157i	$-0.198967\pi$
$331$	−1.84302	−	3.19220i	−0.101301	−	0.175459i	−0.912221	+	0.409698i	$0.865634\pi$
$332$	2.02374			0.111067
$333$	4.47733	+	7.75496i	0.245356	+	0.424969i
$334$	14.6401	+	25.3574i	0.801070	+	1.38749i
$335$	−11.2199	−	19.4334i	−0.613008	−	1.06176i
$336$	−0.246272	−	19.2968i	−0.0134353	−	1.05273i
$337$	31.9053			1.73799			0.868996	−	0.494819i	$-0.164766\pi$
$337$	31.9053			1.73799			0.868996	+	0.494819i	$0.164766\pi$
$338$	−4.51654	−	32.8506i	−0.245667	−	1.78684i
$339$	−3.53026	−	6.11459i	−0.191737	−	0.332099i
$340$	−2.57791	+	4.46506i	−0.139807	+	0.242152i
$341$	4.71920			0.255559
$342$	4.68569	−	8.11585i	0.253373	−	0.438855i
$343$	0.708872	+	18.5067i	0.0382755	+	0.999267i
$344$	28.9071	−	50.0686i	1.55857	−	2.69952i
$345$	3.58802	+	6.21463i	0.193172	+	0.334584i
$346$	−22.0050	−	38.1137i	−1.18299	−	2.04901i
$347$	−25.4851			−1.36811			−0.684057	−	0.729429i	$-0.739786\pi$
$347$	−25.4851			−1.36811			−0.684057	+	0.729429i	$0.739786\pi$
$348$	40.0481			2.14680
$349$	0.936682	+	1.62238i	0.0501394	+	0.0868440i	0.890006	−	0.455949i	$-0.150700\pi$
$349$	0.936682	+	1.62238i	0.0501394	+	0.0868440i	−0.839866	+	0.542793i	$0.817367\pi$
$350$	−17.3356	−	9.71589i	−0.926627	−	0.519336i
$351$	2.71760	+	2.36953i	0.145055	+	0.126476i
$352$	1.54568	−	2.67720i	0.0823852	−	0.142695i
$353$	6.53786	−	11.3239i	0.347975	−	0.602710i	−0.637915	−	0.770107i	$-0.720203\pi$
$353$	6.53786	−	11.3239i	0.347975	−	0.602710i	0.985890	+	0.167397i	$0.0535361\pi$
$354$	0.0929408	−	0.160978i	0.00493975	−	0.00855590i
$355$	−1.51078	−	2.61675i	−0.0801839	−	0.138883i
$356$	−4.15873			−0.220412
$357$	−0.0137051	−	1.07387i	−0.000725350	−	0.0568353i
$358$	30.4380	−	52.7202i	1.60870	−	2.78635i
$359$	−1.93310	+	3.34823i	−0.102025	+	0.176713i	−0.912519	−	0.409034i	$-0.865866\pi$
$359$	−1.93310	+	3.34823i	−0.102025	+	0.176713i	0.810494	+	0.585747i	$0.199199\pi$
$360$	−18.0193			−0.949700
$361$	2.75095	−	4.76478i	0.144787	−	0.250778i
$362$	−42.9621			−2.25804
$363$	−10.7178			−0.562540
$364$	−42.2872	−	7.72656i	−2.21645	−	0.404982i
$365$	−4.11172			−0.215217
$366$	24.8670			1.29982
$367$	−9.78135	+	16.9418i	−0.510582	+	0.884354i	0.489343	+	0.872092i	$0.337237\pi$
$367$	−9.78135	+	16.9418i	−0.510582	+	0.884354i	−0.999925	+	0.0122627i	$0.996097\pi$
$368$	−18.5703			−0.968043
$369$	5.44846	−	9.43700i	0.283635	−	0.491271i
$370$	−32.1903	+	55.7552i	−1.67349	+	2.89857i
$371$	16.2292	+	9.09582i	0.842581	+	0.472231i
$372$	40.0340			2.07567
$373$	−8.47735	−	14.6832i	−0.438941	−	0.760267i	0.558667	−	0.829392i	$-0.311313\pi$
$373$	−8.47735	−	14.6832i	−0.438941	−	0.760267i	−0.997608	+	0.0691243i	$0.977979\pi$
$374$	0.275001	−	0.476316i	0.0142200	−	0.0246297i
$375$	2.89658	−	5.01703i	0.149579	−	0.259078i
$376$	−28.4912	+	49.3483i	−1.46932	+	2.54494i
$377$	6.16120	−	31.4451i	0.317318	−	1.61950i
$378$	5.80095	−	3.44863i	0.298369	−	0.177378i
$379$	17.0145	+	29.4699i	0.873974	+	1.51377i	0.857851	+	0.513898i	$0.171799\pi$
$379$	17.0145	+	29.4699i	0.873974	+	1.51377i	0.0161228	+	0.999870i	$0.494868\pi$
$380$	46.6654			2.39388
$381$	18.8048			0.963398
$382$	5.42341	+	9.39361i	0.277486	+	0.480619i
$383$	10.3742	+	17.9686i	0.530095	+	0.918152i	0.999384	+	0.0351070i	$0.0111772\pi$
$383$	10.3742	+	17.9686i	0.530095	+	0.918152i	−0.469288	+	0.883045i	$0.655489\pi$
$384$	−5.49305	+	9.51424i	−0.280316	+	0.485522i
$385$	3.45565	+	1.93675i	0.176116	+	0.0987059i
$386$	−2.23533	+	3.87171i	−0.113775	+	0.197065i
$387$	9.04348			0.459706
$388$	−0.379073	+	0.656574i	−0.0192445	+	0.0333325i
$389$	−7.60442	−	13.1712i	−0.385559	−	0.667808i	0.606287	−	0.795246i	$-0.292658\pi$
$389$	−7.60442	−	13.1712i	−0.385559	−	0.667808i	−0.991847	+	0.127437i	$0.959325\pi$
$390$	−4.98436	+	25.4388i	−0.252393	+	1.28814i
$391$	−1.03344			−0.0522633
$392$	−21.3789	+	39.3134i	−1.07980	+	1.98563i
$393$	−11.3156	−	19.5992i	−0.570796	−	0.988647i
$394$	8.39599	+	14.5423i	0.422984	+	0.732629i
$395$	9.97435	+	17.2761i	0.501864	+	0.869254i
$396$	2.39375			0.120290
$397$	7.00699	+	12.1365i	0.351671	+	0.609112i	0.986542	−	0.163506i	$-0.0522803\pi$
$397$	7.00699	+	12.1365i	0.351671	+	0.609112i	−0.634871	+	0.772618i	$0.718947\pi$
$398$	11.5387			0.578383
$399$	−8.35543	+	4.96724i	−0.418295	+	0.248673i
$400$	−10.7395	−	18.6013i	−0.536973	−	0.930064i
$401$	13.9219			0.695224			0.347612	−	0.937638i	$-0.386993\pi$
$401$	13.9219			0.695224			0.347612	+	0.937638i	$0.386993\pi$
$402$	10.1535	+	17.5864i	0.506412	+	0.877131i
$403$	6.15905	−	31.4341i	0.306804	−	1.56584i
$404$	−8.17576	+	14.1608i	−0.406759	+	0.704528i
$405$	−1.40932	−	2.44101i	−0.0700295	−	0.121295i
$406$	−52.3192	−	29.3227i	−2.59656	−	1.45526i
$407$	2.37836	−	4.11944i	0.117891	−	0.204193i
$408$	1.29750	−	2.24734i	0.0642359	−	0.111260i
$409$	17.9660			0.888362			0.444181	−	0.895937i	$-0.353495\pi$
$409$	17.9660			0.888362			0.444181	+	0.895937i	$0.353495\pi$
$410$	78.3446			3.86916
$411$	4.27446	−	7.40359i	0.210844	−	0.365192i
$412$	−20.1838	+	34.9594i	−0.994385	+	1.72232i
$413$	−0.165730	+	0.0985255i	−0.00815506	+	0.00484812i
$414$	−3.24701	−	5.62398i	−0.159582	−	0.276403i
$415$	−0.632912	+	1.09624i	−0.0310684	+	0.0538121i
$416$	−15.8153	−	13.7896i	−0.775407	−	0.676093i
$417$	−3.47181	−	6.01335i	−0.170015	−	0.294475i
$418$	−4.97808			−0.243486
$419$	7.04438	+	12.2012i	0.344140	+	0.596069i	0.985197	−	0.171425i	$-0.0548370\pi$
$419$	7.04438	+	12.2012i	0.344140	+	0.596069i	−0.641057	+	0.767493i	$0.721504\pi$
$420$	29.3151	+	16.4299i	1.43043	+	0.801696i
$421$	4.42295			0.215562			0.107781	−	0.994175i	$-0.465626\pi$
$421$	4.42295			0.215562			0.107781	+	0.994175i	$0.465626\pi$
$422$	11.4062	+	19.7561i	0.555244	+	0.961711i
$423$	−8.91337			−0.433383
$424$	22.4768	+	38.9310i	1.09157	+	1.89066i
$425$	−0.597652	−	1.03516i	−0.0289904	−	0.0502128i
$426$	1.36719	+	2.36805i	0.0662407	+	0.114732i
$427$	−22.5003	−	12.6105i	−1.08887	−	0.610264i
$428$	−8.50878			−0.411287
$429$	0.368267	−	1.87953i	0.0177801	−	0.0907448i
$430$	32.5096	+	56.3082i	1.56775	+	2.71542i
$431$	−3.22218	+	5.58098i	−0.155207	+	0.268826i	−0.933134	−	0.359528i	$-0.882938\pi$
$431$	−3.22218	+	5.58098i	−0.155207	+	0.268826i	0.777927	+	0.628354i	$0.216271\pi$
$432$	7.29411			0.350938
$433$	−10.4321	+	18.0689i	−0.501333	+	0.868335i	0.498665	+	0.866795i	$0.333824\pi$
$433$	−10.4321	+	18.0689i	−0.501333	+	0.868335i	−0.999999	+	0.00154042i	$0.999510\pi$
$434$	−52.3009	−	29.3125i	−2.51052	−	1.40704i
$435$	−12.5248	+	21.6936i	−0.600517	+	1.04013i
$436$	22.1131	+	38.3011i	1.05903	+	1.83429i
$437$	4.67684	+	8.10052i	0.223724	+	0.387501i
$438$	3.72093			0.177793
$439$	−5.27897			−0.251951			−0.125976	−	0.992033i	$-0.540206\pi$
$439$	−5.27897			−0.251951			−0.125976	+	0.992033i	$0.540206\pi$
$440$	4.78593	+	8.28948i	0.228160	+	0.395185i
$441$	−6.99772	+	0.178643i	−0.333225	+	0.00850682i
$442$	−2.81379	−	2.45340i	−0.133838	−	0.116696i
$443$	11.9653	−	20.7245i	0.568488	−	0.984649i	−0.428228	−	0.903671i	$-0.640862\pi$
$443$	11.9653	−	20.7245i	0.568488	−	0.984649i	0.996716	−	0.0809788i	$-0.0258046\pi$
$444$	20.1762	−	34.9462i	0.957519	−	1.65847i
$445$	1.30062	−	2.25273i	0.0616551	−	0.106790i
$446$	11.8217	+	20.4758i	0.559773	+	0.969555i
$447$	−12.5075			−0.591582
$448$	−0.582257	+	0.346147i	−0.0275090	+	0.0163539i
$449$	12.6967	−	21.9913i	0.599195	−	1.03784i	−0.393746	−	0.919219i	$-0.628821\pi$
$449$	12.6967	−	21.9913i	0.599195	−	1.03784i	0.992940	−	0.118616i	$-0.0378457\pi$
$450$	3.75558	−	6.50485i	0.177040	−	0.306641i
$451$	−5.78845			−0.272568
$452$	−15.9084	+	27.5542i	−0.748268	+	1.29604i
$453$	7.92695			0.372440
$454$	−42.9373			−2.01515
$455$	17.4105	−	20.4901i	0.816215	−	0.960589i
$456$	−23.4874			−1.09990
$457$	−2.24579			−0.105053			−0.0525267	−	0.998620i	$-0.516727\pi$
$457$	−2.24579			−0.105053			−0.0525267	+	0.998620i	$0.516727\pi$
$458$	−2.17654	+	3.76987i	−0.101703	+	0.176154i
$459$	0.405918			0.0189467
$460$	16.1687	−	28.0050i	0.753868	−	1.30574i
$461$	−9.36702	+	16.2242i	−0.436266	+	0.755634i	−0.997398	−	0.0720917i	$-0.977033\pi$
$461$	−9.36702	+	16.2242i	−0.436266	+	0.755634i	0.561132	+	0.827726i	$0.310366\pi$
$462$	−3.12722	−	1.75268i	−0.145491	−	0.0815419i
$463$	2.51845			0.117042			0.0585212	−	0.998286i	$-0.481361\pi$
$463$	2.51845			0.117042			0.0585212	+	0.998286i	$0.481361\pi$
$464$	−32.4119	−	56.1390i	−1.50468	−	2.60619i
$465$	−12.5204	+	21.6860i	−0.580620	+	1.00566i
$466$	30.7545	−	53.2683i	1.42467	−	2.46761i
$467$	0.988420	−	1.71199i	0.0457386	−	0.0792216i	−0.842250	−	0.539088i	$-0.818769\pi$
$467$	0.988420	−	1.71199i	0.0457386	−	0.0792216i	0.887988	+	0.459866i	$0.152103\pi$
$468$	3.12409	−	15.9445i	0.144411	−	0.737035i
$469$	−0.268796	−	21.0617i	−0.0124118	−	0.972539i
$470$	−32.0418	−	55.4981i	−1.47798	−	2.55994i
$471$	11.1366			0.513147
$472$	−0.465874			−0.0214436
$473$	−2.40195	−	4.16031i	−0.110442	−	0.191291i
$474$	−9.02637	−	15.6341i	−0.414595	−	0.718099i
$475$	−5.40936	+	9.36929i	−0.248198	+	0.429892i
$476$	−4.15998	+	2.47308i	−0.190672	+	0.113353i
$477$	−3.51589	+	6.08971i	−0.160982	+	0.278829i
$478$	52.9464			2.42171
$479$	−8.61806	+	14.9269i	−0.393769	+	0.682029i	−0.992943	−	0.118590i	$-0.962162\pi$
$479$	−8.61806	+	14.9269i	−0.393769	+	0.682029i	0.599174	+	0.800619i	$0.295496\pi$
$480$	8.20162	+	14.2056i	0.374351	+	0.648395i
$481$	−24.3352	−	21.2183i	−1.10959	−	0.967472i
$482$	51.0627			2.32584
$483$	0.0859586	+	6.73534i	0.00391125	+	0.306469i
$484$	24.1488	+	41.8270i	1.09767	+	1.90123i
$485$	−0.237106	−	0.410679i	−0.0107664	−	0.0186480i
$486$	1.27537	+	2.20901i	0.0578521	+	0.100203i
$487$	25.2962			1.14628			0.573141	−	0.819457i	$-0.305725\pi$
$487$	25.2962			1.14628			0.573141	+	0.819457i	$0.305725\pi$
$488$	−31.1620	−	53.9742i	−1.41064	−	2.44330i
$489$	16.5297			0.747498
$490$	−26.2677	−	42.9283i	−1.18666	−	1.93930i
$491$	17.6390	+	30.5517i	0.796039	+	1.37878i	0.922177	+	0.386767i	$0.126408\pi$
$491$	17.6390	+	30.5517i	0.796039	+	1.37878i	−0.126138	+	0.992013i	$0.540258\pi$
$492$	−49.1047			−2.21381
$493$	−1.80373	−	3.12414i	−0.0812357	−	0.140704i
$494$	−6.49691	+	33.1585i	−0.292310	+	1.49187i
$495$	−0.748630	+	1.29667i	−0.0336484	+	0.0582808i
$496$	−32.4005	−	56.1194i	−1.45483	−	2.51983i
$497$	−0.0361939	−	2.83600i	−0.00162352	−	0.127212i
$498$	0.572758	−	0.992047i	0.0256659	−	0.0444547i
$499$	−5.71040	+	9.89071i	−0.255633	+	0.442769i	−0.965067	−	0.262002i	$-0.915617\pi$
$499$	−5.71040	+	9.89071i	−0.255633	+	0.442769i	0.709434	+	0.704771i	$0.248950\pi$
$500$	−26.1057			−1.16748
$501$	11.4791			0.512847
$502$	−26.6149	+	46.0983i	−1.18788	+	2.05747i
$503$	6.49637	−	11.2520i	0.289659	−	0.501704i	−0.684070	−	0.729417i	$-0.739792\pi$
$503$	6.49637	−	11.2520i	0.289659	−	0.501704i	0.973728	+	0.227713i	$0.0731249\pi$
$504$	−14.7548	−	8.26942i	−0.657229	−	0.368349i
$505$	−5.11384	−	8.85743i	−0.227563	−	0.394150i
$506$	−1.72481	+	2.98746i	−0.0766773	+	0.132809i
$507$	−12.0387	−	4.90597i	−0.534660	−	0.217882i
$508$	−42.3699	−	73.3869i	−1.87986	−	3.25602i
$509$	37.8070			1.67577			0.837884	−	0.545849i	$-0.183793\pi$
$509$	37.8070			1.67577			0.837884	+	0.545849i	$0.183793\pi$
$510$	1.45920	+	2.52741i	0.0646144	+	0.111915i
$511$	−3.36680	−	1.88695i	−0.148939	−	0.0834738i
$512$	50.8127			2.24563
$513$	−1.83699	−	3.18176i	−0.0811050	−	0.140478i
$514$	23.5734			1.03978
$515$	−12.6247	−	21.8667i	−0.556312	−	0.963560i
$516$	−20.3763	−	35.2928i	−0.897017	−	1.55368i
$517$	2.36740	+	4.10045i	0.104118	+	0.180338i
$518$	−51.9456	+	30.8813i	−2.28236	+	1.35685i
$519$	−17.2538			−0.757356
$520$	61.4615	−	21.0600i	2.69526	−	0.923540i
$521$	3.83608	+	6.64429i	0.168062	+	0.291092i	0.937738	−	0.347342i	$-0.112916\pi$
$521$	3.83608	+	6.64429i	0.168062	+	0.291092i	−0.769676	+	0.638434i	$0.779582\pi$
$522$	11.3344	−	19.6318i	0.496093	−	0.859259i
$523$	36.5981			1.60032			0.800161	−	0.599785i	$-0.204747\pi$
$523$	36.5981			1.60032			0.800161	+	0.599785i	$0.204747\pi$
$524$	−50.9914	+	88.3196i	−2.22757	+	3.85826i
$525$	−6.69687	+	3.98124i	−0.292275	+	0.173756i
$526$	−0.237431	+	0.411243i	−0.0103525	+	0.0179310i
$527$	−1.80309	−	3.12305i	−0.0785440	−	0.136042i
$528$	−1.93732	−	3.35554i	−0.0843110	−	0.146031i
$529$	−16.5183			−0.718185
$530$	−50.5558			−2.19600
$531$	−0.0364367	−	0.0631103i	−0.00158122	−	0.00273875i
$532$	38.2110	+	21.4157i	1.65666	+	0.928488i
$533$	−7.55453	+	38.5562i	−0.327223	+	1.67006i
$534$	−1.17700	+	2.03863i	−0.0509339	+	0.0882201i
$535$	2.66107	−	4.60910i	0.115048	−	0.199269i
$536$	25.4477	−	44.0768i	1.09917	−	1.90383i
$537$	−11.9330	−	20.6686i	−0.514947	−	0.891914i
$538$	32.6027			1.40560
$539$	1.94078	+	3.17174i	0.0835953	+	0.136616i
$540$	−6.35080	+	10.9999i	−0.273295	+	0.473360i
$541$	7.93930	−	13.7513i	0.341337	−	0.591214i	−0.643344	−	0.765577i	$-0.722453\pi$
$541$	7.93930	−	13.7513i	0.341337	−	0.591214i	0.984681	+	0.174364i	$0.0557868\pi$
$542$	8.26926			0.355195
$543$	−8.42149	+	14.5864i	−0.361401	+	0.625964i
$544$	−2.36227			−0.101282
$545$	−27.6630			−1.18495
$546$	−15.7557	+	18.5426i	−0.674283	+	0.793552i
$547$	−22.5218			−0.962962			−0.481481	−	0.876456i	$-0.659901\pi$
$547$	−22.5218			−0.962962			−0.481481	+	0.876456i	$0.659901\pi$
$548$	−38.5240			−1.64566
$549$	4.87445	−	8.44280i	0.208037	−	0.360330i
$550$	−3.98993			−0.170131
$551$	−16.3256	+	28.2767i	−0.695492	+	1.20463i
$552$	−8.13796	+	14.0954i	−0.346374	+	0.599938i
$553$	0.238957	+	18.7236i	0.0101615	+	0.796209i
$554$	−60.9114			−2.58788
$555$	12.6199	+	21.8584i	0.535687	+	0.927837i
$556$	−15.6450	+	27.0979i	−0.663495	+	1.14921i
$557$	−0.136366	+	0.236193i	−0.00577802	+	0.0100078i	−0.868900	−	0.494988i	$-0.835173\pi$
$557$	−0.136366	+	0.236193i	−0.00577802	+	0.0100078i	0.863122	+	0.504996i	$0.168506\pi$
$558$	11.3304	−	19.6249i	0.479656	−	0.830788i
$559$	−30.8462	+	10.5695i	−1.30465	+	0.447043i
$560$	−0.694151	−	54.3907i	−0.0293332	−	2.29843i
$561$	−0.107812	−	0.186736i	−0.00455183	−	0.00788401i
$562$	5.57643			0.235227
$563$	3.08887			0.130180			0.0650901	−	0.997879i	$-0.479267\pi$
$563$	3.08887			0.130180			0.0650901	+	0.997879i	$0.479267\pi$
$564$	20.0831	+	34.7850i	0.845653	+	1.46471i
$565$	−9.95051	−	17.2348i	−0.418621	−	0.725073i
$566$	21.8784	−	37.8944i	0.919616	−	1.59282i
$567$	−0.0337632	−	2.64554i	−0.00141792	−	0.111102i
$568$	3.42659	−	5.93503i	0.143776	−	0.249028i
$569$	24.5857			1.03069			0.515343	−	0.856984i	$-0.327664\pi$
$569$	24.5857			1.03069			0.515343	+	0.856984i	$0.327664\pi$
$570$	13.2072	−	22.8756i	0.553190	−	0.958153i
$571$	14.4509	+	25.0297i	0.604751	+	1.04746i	0.992091	+	0.125523i	$0.0400609\pi$
$571$	14.4509	+	25.0297i	0.604751	+	1.04746i	−0.387339	+	0.921937i	$0.626606\pi$
$572$	−8.16477	+	2.79768i	−0.341386	+	0.116977i
$573$	4.25241			0.177647
$574$	64.1509	+	35.9539i	2.67761	+	1.50069i
$575$	3.74848	+	6.49256i	0.156323	+	0.270759i
$576$	−0.128012	−	0.221724i	−0.00533385	−	0.00923850i
$577$	−2.80534	−	4.85899i	−0.116788	−	0.202283i	0.801705	−	0.597720i	$-0.203926\pi$
$577$	−2.80534	−	4.85899i	−0.116788	−	0.202283i	−0.918493	+	0.395437i	$0.870593\pi$
$578$	42.9424			1.78617
$579$	0.876346	+	1.51788i	0.0364197	+	0.0630807i
$580$	112.881			4.68712
$581$	−1.02133	+	0.607175i	−0.0423720	+	0.0251899i
$582$	0.214571	+	0.371647i	0.00889424	+	0.0154053i
$583$	3.73529			0.154700
$584$	−4.66288	−	8.07635i	−0.192951	−	0.334202i
$585$	7.65991	+	6.67883i	0.316698	+	0.276136i
$586$	4.69059	−	8.12434i	0.193767	−	0.335614i
$587$	−15.9496	−	27.6256i	−0.658313	−	1.14023i	−0.981052	−	0.193743i	$-0.937937\pi$
$587$	−15.9496	−	27.6256i	−0.658313	−	1.14023i	0.322740	−	0.946488i	$-0.395396\pi$
$588$	16.4641	+	26.9066i	0.678967	+	1.10961i
$589$	−16.3198	+	28.2668i	−0.672448	+	1.16471i
$590$	0.261966	−	0.453738i	0.0107850	−	0.0186801i
$591$	6.58317			0.270795
$592$	−65.3163			−2.68448
$593$	6.97018	−	12.0727i	0.286231	−	0.495766i	−0.686676	−	0.726963i	$-0.740931\pi$
$593$	6.97018	−	12.0727i	0.286231	−	0.495766i	0.972907	+	0.231197i	$0.0742643\pi$
$594$	0.677479	−	1.17343i	0.0277973	−	0.0481463i
$595$	−0.0386296	−	3.02685i	−0.00158366	−	0.124089i
$596$	28.1811	+	48.8112i	1.15434	+	1.99938i
$597$	2.26183	−	3.91760i	0.0925705	−	0.160337i
$598$	17.6481	+	15.3877i	0.721685	+	0.629251i
$599$	2.84098	+	4.92072i	0.116079	+	0.201055i	0.918211	−	0.396092i	$-0.129634\pi$
$599$	2.84098	+	4.92072i	0.116079	+	0.201055i	−0.802131	+	0.597148i	$0.796301\pi$
$600$	−18.8252			−0.768534
$601$	−15.2347	−	26.3873i	−0.621436	−	1.07636i	−0.989219	−	0.146447i	$-0.953216\pi$
$601$	−15.2347	−	26.3873i	−0.621436	−	1.07636i	0.367783	−	0.929912i	$-0.380117\pi$
$602$	0.778836	+	61.0262i	0.0317430	+	2.48724i
$603$	7.96122			0.324206
$604$	−17.8606	−	30.9354i	−0.726737	−	1.25875i
$605$	−30.2096			−1.22820
$606$	4.62781	+	8.01560i	0.187992	+	0.325611i
$607$	9.72757	+	16.8486i	0.394830	+	0.683865i	0.993079	−	0.117444i	$-0.0374702\pi$
$607$	9.72757	+	16.8486i	0.394830	+	0.683865i	−0.598250	+	0.801310i	$0.704137\pi$
$608$	10.6905	+	18.5165i	0.433557	+	0.750942i
$609$	−20.2113	+	12.0155i	−0.819003	+	0.486891i
$610$	70.0908			2.83790
$611$	30.4024	−	10.4175i	1.22995	−	0.421445i
$612$	−0.914594	−	1.58412i	−0.0369703	−	0.0640344i
$613$	−22.9781	+	39.7992i	−0.928075	+	1.60747i	−0.141535	+	0.989933i	$0.545204\pi$
$613$	−22.9781	+	39.7992i	−0.928075	+	1.60747i	−0.786540	+	0.617540i	$0.788129\pi$
$614$	−37.2445			−1.50306
$615$	15.3572	−	26.5994i	0.619262	−	1.07259i
$616$	0.114657	+	8.98404i	0.00461967	+	0.361977i
$617$	0.910424	−	1.57690i	0.0366523	−	0.0634837i	−0.847117	−	0.531406i	$-0.821664\pi$
$617$	0.910424	−	1.57690i	0.0366523	−	0.0634837i	0.883770	+	0.467922i	$0.154997\pi$
$618$	11.4248	+	19.7884i	0.459575	+	0.796006i
$619$	9.04766	+	15.6710i	0.363656	+	0.629871i	0.988560	−	0.150831i	$-0.0481949\pi$
$619$	9.04766	+	15.6710i	0.363656	+	0.629871i	−0.624903	+	0.780702i	$0.714862\pi$
$620$	112.841			4.53181
$621$	−2.54593			−0.102165
$622$	7.74954	+	13.4226i	0.310728	+	0.538197i
$623$	2.09881	−	1.24773i	0.0840870	−	0.0499891i
$624$	−24.8793	+	8.52496i	−0.995968	+	0.341271i
$625$	15.5261	−	26.8920i	0.621045	−	1.07568i
$626$	4.10884	−	7.11672i	0.164222	−	0.284441i
$627$	−0.975810	+	1.69015i	−0.0389701	+	0.0674982i
$628$	−25.0924	−	43.4613i	−1.00130	−	1.73429i
$629$	−3.63486			−0.144931
$630$	16.3508	−	9.72041i	0.651430	−	0.387270i
$631$	−4.72173	+	8.17827i	−0.187969	+	0.325572i	−0.944573	−	0.328301i	$-0.893524\pi$
$631$	−4.72173	+	8.17827i	−0.187969	+	0.325572i	0.756604	+	0.653873i	$0.226857\pi$
$632$	−22.6228	+	39.1838i	−0.899885	+	1.55865i
$633$	8.94341			0.355469
$634$	14.3422	−	24.8415i	0.569603	−	0.986581i
$635$	53.0038			2.10339
$636$	31.6873			1.25648
$637$	23.6595	−	8.78788i	0.937425	−	0.348188i
$638$	−12.0417			−0.476735
$639$	1.07199			0.0424075
$640$	−15.4829	+	26.8172i	−0.612015	+	1.06004i
$641$	7.51229			0.296718			0.148359	−	0.988934i	$-0.452601\pi$
$641$	7.51229			0.296718			0.148359	+	0.988934i	$0.452601\pi$
$642$	−2.40815	+	4.17105i	−0.0950423	+	0.164618i
$643$	−16.5029	+	28.5839i	−0.650811	+	1.12724i	0.332115	+	0.943239i	$0.392238\pi$
$643$	−16.5029	+	28.5839i	−0.650811	+	1.12724i	−0.982926	+	0.183999i	$0.941096\pi$
$644$	26.0914	−	15.5112i	1.02815	−	0.611226i
$645$	25.4903			1.00368
$646$	1.90201	+	3.29437i	0.0748335	+	0.129615i
$647$	6.47566	−	11.2162i	0.254584	−	0.440953i	−0.710198	−	0.704002i	$-0.751395\pi$
$647$	6.47566	−	11.2162i	0.254584	−	0.440953i	0.964783	+	0.263049i	$0.0847280\pi$
$648$	3.19646	−	5.53643i	0.125569	−	0.217492i
$649$	−0.0193552	+	0.0335242i	−0.000759759	+	0.00131594i
$650$	−5.20727	+	26.5765i	−0.204246	+	1.04242i
$651$	−20.2042	+	12.0113i	−0.791866	+	0.470759i
$652$	−37.2438	−	64.5082i	−1.45858	−	2.52633i
$653$	−27.1119			−1.06097			−0.530486	−	0.847694i	$-0.677991\pi$
$653$	−27.1119			−1.06097			−0.530486	+	0.847694i	$0.677991\pi$
$654$	25.0338			0.978900
$655$	−31.8945	−	55.2428i	−1.24622	−	2.15852i
$656$	39.7417	+	68.8346i	1.55165	+	2.68754i
$657$	0.729382	−	1.26333i	0.0284559	−	0.0492871i
$658$	−0.767630	−	60.1482i	−0.0299253	−	2.34482i
$659$	23.4945	−	40.6936i	0.915214	−	1.58520i	0.108626	−	0.994083i	$-0.465355\pi$
$659$	23.4945	−	40.6936i	0.915214	−	1.58520i	0.806588	−	0.591114i	$-0.201312\pi$
$660$	6.74710			0.262630
$661$	3.48947	−	6.04395i	0.135725	−	0.235082i	−0.790149	−	0.612914i	$-0.789997\pi$
$661$	3.48947	−	6.04395i	0.135725	−	0.235082i	0.925874	+	0.377832i	$0.123330\pi$
$662$	4.70106	+	8.14248i	0.182712	+	0.316466i
$663$	−1.38454	+	0.474415i	−0.0537709	+	0.0184248i
$664$	−2.87100			−0.111417
$665$	−23.5509	+	14.0008i	−0.913264	+	0.542929i
$666$	−11.4205	−	19.7809i	−0.442536	−	0.766495i
$667$	11.3130	+	19.5947i	0.438041	+	0.758709i
$668$	−25.8641	−	44.7979i	−1.00071	−	1.73328i
$669$	9.26920			0.358368
$670$	28.6191	+	49.5696i	1.10565	+	1.91504i
$671$	−5.17863			−0.199919
$672$	0.196487	+	15.3959i	0.00757966	+	0.593910i
$673$	−21.7362	−	37.6482i	−0.837868	−	1.45123i	−0.891674	−	0.452679i	$-0.850468\pi$
$673$	−21.7362	−	37.6482i	−0.837868	−	1.45123i	0.0538056	−	0.998551i	$-0.482865\pi$
$674$	−81.3822			−3.13473
$675$	−1.47234	−	2.55018i	−0.0566706	−	0.0981563i
$676$	7.97919	+	58.0359i	0.306892	+	2.23215i
$677$	−9.16375	+	15.8721i	−0.352192	+	0.610014i	−0.986633	−	0.162957i	$-0.947897\pi$
$677$	−9.16375	+	15.8721i	−0.352192	+	0.610014i	0.634441	+	0.772971i	$0.281230\pi$
$678$	9.00479	+	15.5968i	0.345827	+	0.598990i
$679$	−0.00568037	−	0.445089i	−0.000217993	−	0.0170810i
$680$	3.65718	−	6.33443i	0.140247	−	0.242914i
$681$	−8.41663	+	14.5780i	−0.322526	+	0.558631i
$682$	−12.0375			−0.460939
$683$	−11.2452			−0.430287			−0.215143	−	0.976582i	$-0.569022\pi$
$683$	−11.2452			−0.430287			−0.215143	+	0.976582i	$0.569022\pi$
$684$	−8.27801	+	14.3379i	−0.316518	+	0.548225i
$685$	12.0481	−	20.8680i	0.460336	−	0.797325i
$686$	−1.80815	−	47.2058i	−0.0690356	−	1.80233i
$687$	0.853294	+	1.47795i	0.0325552	+	0.0563873i
$688$	−32.9821	+	57.1267i	−1.25743	+	2.17793i
$689$	4.87494	−	24.8804i	0.185721	−	0.947867i
$690$	−9.15211	−	15.8519i	−0.348415	−	0.603473i
$691$	−11.1748			−0.425111			−0.212556	−	0.977149i	$-0.568179\pi$
$691$	−11.1748			−0.425111			−0.212556	+	0.977149i	$0.568179\pi$
$692$	38.8753	+	67.3339i	1.47782	+	2.55965i
$693$	−1.20807	+	0.718188i	−0.0458907	+	0.0272817i
$694$	65.0061			2.46760
$695$	−9.78575	−	16.9494i	−0.371195	−	0.642928i
$696$	−56.8147			−2.15356
$697$	2.21163	+	3.83065i	0.0837714	+	0.145096i
$698$	−2.38924	−	4.13828i	−0.0904339	−	0.156636i
$699$	−12.0571	−	20.8834i	−0.456040	−	0.789884i
$700$	30.6261	+	17.1647i	1.15756	+	0.648763i
$701$	−33.0766			−1.24929			−0.624643	−	0.780910i	$-0.714756\pi$
$701$	−33.0766			−1.24929			−0.624643	+	0.780910i	$0.714756\pi$
$702$	−6.93190	−	6.04406i	−0.261628	−	0.228118i
$703$	16.4496	+	28.4915i	0.620409	+	1.07458i
$704$	−0.0680003	+	0.117780i	−0.00256286	+	0.00443900i
$705$	−25.1235			−0.946207
$706$	−16.6764	+	28.8844i	−0.627625	+	1.08708i
$707$	−0.122513	−	9.59958i	−0.00460757	−	0.361029i
$708$	−0.164195	+	0.284394i	−0.00617082	+	0.0106882i
$709$	−17.0209	−	29.4811i	−0.639235	−	1.10719i	−0.985601	−	0.169087i	$-0.945918\pi$
$709$	−17.0209	−	29.4811i	−0.639235	−	1.10719i	0.346366	−	0.938099i	$-0.387415\pi$
$710$	3.85361	+	6.67465i	0.144624	+	0.250495i
$711$	−7.07744			−0.265425
$712$	5.89983			0.221106
$713$	11.3090	+	19.5878i	0.423527	+	0.733570i
$714$	0.0349582	+	2.73917i	0.00130828	+	0.102511i
$715$	1.03801	−	5.29772i	0.0388193	−	0.198123i
$716$	−53.7736	+	93.1387i	−2.00962	+	3.48076i
$717$	10.3786	−	17.9763i	0.387597	−	0.671337i
$718$	4.93085	−	8.54049i	0.184018	−	0.318728i
$719$	1.53311	+	2.65542i	0.0571753	+	0.0990304i	0.893196	−	0.449667i	$-0.148457\pi$
$719$	1.53311	+	2.65542i	0.0571753	+	0.0990304i	−0.836021	+	0.548697i	$0.815124\pi$
$720$	20.5594			0.766205
$721$	−0.302452	−	23.6988i	−0.0112639	−	0.882591i
$722$	−7.01697	+	12.1537i	−0.261145	+	0.452316i
$723$	10.0094	−	17.3368i	0.372253	−	0.644761i
$724$	75.8995			2.82078
$725$	−13.0849	+	22.6638i	−0.485962	+	0.841711i
$726$	27.3384			1.01462
$727$	13.3001			0.493274			0.246637	−	0.969108i	$-0.420674\pi$
$727$	13.3001			0.493274			0.246637	+	0.969108i	$0.420674\pi$
$728$	59.9914	+	10.9614i	2.22343	+	0.406256i
$729$	1.00000			0.0370370
$730$	10.4879			0.388176
$731$	−1.83546	+	3.17911i	−0.0678869	+	0.117584i
$732$	−43.9315			−1.62375
$733$	−16.2567	+	28.1575i	−0.600457	+	1.04002i	0.392295	+	0.919839i	$0.371681\pi$
$733$	−16.2567	+	28.1575i	−0.600457	+	1.04002i	−0.992752	+	0.120182i	$0.961652\pi$
$734$	24.9497	−	43.2142i	0.920911	−	1.59506i
$735$	−19.7240	+	0.503530i	−0.727531	+	0.0185730i
$736$	14.8162			0.546133
$737$	−2.11451	−	3.66243i	−0.0778888	−	0.134907i
$738$	−13.8976	+	24.0714i	−0.511578	+	0.886080i
$739$	7.89026	−	13.6663i	0.290248	−	0.502724i	−0.683620	−	0.729838i	$-0.739596\pi$
$739$	7.89026	−	13.6663i	0.290248	−	0.502724i	0.973868	+	0.227114i	$0.0729288\pi$
$740$	56.8692	−	98.5004i	2.09055	−	3.62095i
$741$	9.98439	+	8.70559i	0.366786	+	0.319808i
$742$	−41.3967	−	23.2011i	−1.51972	−	0.851739i
$743$	5.52954	+	9.57744i	0.202859	+	0.351362i	0.949448	−	0.313923i	$-0.101643\pi$
$743$	5.52954	+	9.57744i	0.202859	+	0.351362i	−0.746589	+	0.665285i	$0.768310\pi$
$744$	−56.7949			−2.08220
$745$	−35.2539			−1.29160
$746$	21.6236	+	37.4531i	0.791695	+	1.37126i
$747$	−0.224546	−	0.388924i	−0.00821569	−	0.0142300i
$748$	−0.485834	+	0.841488i	−0.0177638	+	0.0307679i
$749$	4.29418	−	2.55286i	0.156906	−	0.0932794i
$750$	−7.38844	+	12.7972i	−0.269788	+	0.467286i
$751$	7.91533			0.288834			0.144417	−	0.989517i	$-0.453869\pi$
$751$	7.91533			0.288834			0.144417	+	0.989517i	$0.453869\pi$
$752$	32.5076	−	56.3048i	1.18543	−	2.05322i
$753$	10.4342	+	18.0725i	0.380242	+	0.658599i
$754$	−15.7157	+	80.2084i	−0.572330	+	2.92102i
$755$	22.3432			0.813151
$756$	−10.2483	+	6.09255i	−0.372727	+	0.221584i
$757$	−20.8429	−	36.1010i	−0.757549	−	1.31211i	−0.944097	−	0.329668i	$-0.893063\pi$
$757$	−20.8429	−	36.1010i	−0.757549	−	1.31211i	0.186548	−	0.982446i	$-0.440270\pi$
$758$	−43.3995	−	75.1702i	−1.57634	−	2.73031i
$759$	0.676200	+	1.17121i	0.0245445	+	0.0425123i
$760$	−66.2025			−2.40142
$761$	−3.32578	−	5.76042i	−0.120559	−	0.208815i	0.799429	−	0.600761i	$-0.205135\pi$
$761$	−3.32578	−	5.76042i	−0.120559	−	0.208815i	−0.919988	+	0.391946i	$0.871802\pi$
$762$	−47.9662			−1.73763
$763$	−22.6513	−	12.6951i	−0.820032	−	0.459594i
$764$	−9.58131	−	16.5953i	−0.346640	−	0.600397i
$765$	1.14414			0.0413663
$766$	−26.4619	−	45.8333i	−0.956106	−	1.65602i
$767$	0.198041	+	0.172676i	0.00715084	+	0.00623496i
$768$	14.2674	−	24.7118i	0.514830	−	0.891712i
$769$	14.1496	+	24.5078i	0.510248	+	0.883775i	0.999930	+	0.0118740i	$0.00377971\pi$
$769$	14.1496	+	24.5078i	0.510248	+	0.883775i	−0.489682	+	0.871901i	$0.662887\pi$
$770$	−8.81448	−	4.94015i	−0.317652	−	0.178031i
$771$	4.62089	−	8.00361i	0.166417	−	0.288243i
$772$	3.94907	−	6.83999i	0.142130	−	0.246177i
$773$	−10.9216			−0.392823			−0.196412	−	0.980522i	$-0.562929\pi$
$773$	−10.9216			−0.392823			−0.196412	+	0.980522i	$0.562929\pi$
$774$	−23.0676			−0.829148
$775$	−13.0803	+	22.6558i	−0.469860	+	0.813821i
$776$	0.537778	−	0.931458i	0.0193051	−	0.0334374i
$777$	0.302338	+	23.6899i	0.0108463	+	0.849869i
$778$	19.3969	+	33.5965i	0.695414	+	1.20449i
$779$	20.0175	−	34.6713i	0.717201	−	1.24223i
$780$	8.80566	−	44.9417i	0.315293	−	1.60917i
$781$	−0.284722	−	0.493154i	−0.0101882	−	0.0176464i
$782$	2.63604			0.0942646
$783$	−4.44357	−	7.69648i	−0.158800	−	0.275050i
$784$	24.3926	−	44.8553i	0.871165	−	1.60198i
$785$	31.3900			1.12036
$786$	28.8632	+	49.9925i	1.02951	+	1.78317i
$787$	8.32927			0.296906			0.148453	−	0.988919i	$-0.452571\pi$
$787$	8.32927			0.296906			0.148453	+	0.988919i	$0.452571\pi$
$788$	−14.8329	−	25.6913i	−0.528398	−	0.915213i
$789$	0.0930831	+	0.161225i	0.00331385	+	0.00573975i
$790$	−25.4420	−	44.0669i	−0.905186	−	1.56783i
$791$	−0.238385	−	18.6789i	−0.00847601	−	0.664144i
$792$	−3.39593			−0.120669
$793$	−6.75865	+	34.4943i	−0.240007	+	1.22493i
$794$	−17.8730	−	30.9570i	−0.634291	−	1.09862i
$795$	−9.91002	+	17.1646i	−0.351472	+	0.608767i
$796$	−20.3849			−0.722525
$797$	11.6400	−	20.1610i	0.412308	−	0.714139i	−0.582833	−	0.812592i	$-0.698056\pi$
$797$	11.6400	−	20.1610i	0.412308	−	0.714139i	0.995142	+	0.0984525i	$0.0313893\pi$
$798$	21.3126	−	12.6702i	0.754457	−	0.448519i
$799$	1.80905	−	3.13337i	0.0639996	−	0.110851i
$800$	8.56842	+	14.8409i	0.302940	+	0.524707i
$801$	0.461435	+	0.799229i	0.0163040	+	0.0282394i
$802$	−35.5111			−1.25394
$803$	−0.774897			−0.0273455
$804$	−17.9378	−	31.0692i	−0.632618	−	1.09573i
$805$	0.242286	+	18.9845i	0.00853944	+	0.669114i
$806$	−15.7102	+	80.1803i	−0.553367	+	2.82423i
$807$	6.39082	−	11.0692i	0.224967	−	0.389655i
$808$	11.5987	−	20.0895i	0.408039	−	0.706745i
$809$	1.69607	−	2.93767i	0.0596305	−	0.103283i	−0.834669	−	0.550752i	$-0.814341\pi$
$809$	1.69607	−	2.93767i	0.0596305	−	0.103283i	0.894300	+	0.447469i	$0.147674\pi$
$810$	3.59481	+	6.22639i	0.126309	+	0.218773i
$811$	−11.0351			−0.387496			−0.193748	−	0.981051i	$-0.562064\pi$
$811$	−11.0351			−0.387496			−0.193748	+	0.981051i	$0.562064\pi$
$812$	92.4302	+	51.8033i	3.24366	+	1.81794i
$813$	1.62095	−	2.80757i	0.0568492	−	0.0984658i
$814$	−6.06659	+	10.5076i	−0.212634	+	0.368293i
$815$	46.5911			1.63201
$816$	−1.48041	+	2.56414i	−0.0518246	+	0.0897629i
$817$	33.2255			1.16241
$818$	−45.8267			−1.60229
$819$	3.20712	+	8.98412i	0.112066	+	0.313931i
$820$	−138.408			−4.83342
$821$	24.1736			0.843664			0.421832	−	0.906674i	$-0.361387\pi$
$821$	24.1736			0.843664			0.421832	+	0.906674i	$0.361387\pi$
$822$	−10.9031	+	18.8847i	−0.380288	+	0.658678i
$823$	5.98234			0.208531			0.104266	−	0.994549i	$-0.466751\pi$
$823$	5.98234			0.208531			0.104266	+	0.994549i	$0.466751\pi$
$824$	28.6340	−	49.5956i	0.997514	−	1.72774i
$825$	−0.782111	+	1.35466i	−0.0272296	+	0.0471631i
$826$	0.422736	−	0.251313i	0.0147089	−	0.00874431i
$827$	11.9530			0.415647			0.207824	−	0.978166i	$-0.433362\pi$
$827$	11.9530			0.415647			0.207824	+	0.978166i	$0.433362\pi$
$828$	5.73635	+	9.93565i	0.199352	+	0.345288i
$829$	−19.3535	+	33.5212i	−0.672174	+	1.16424i	0.305113	+	0.952316i	$0.401306\pi$
$829$	−19.3535	+	33.5212i	−0.672174	+	1.16424i	−0.977286	+	0.211923i	$0.932027\pi$
$830$	1.61440	−	2.79622i	0.0560365	−	0.0970581i
$831$	−11.9399	+	20.6806i	−0.414192	+	0.717401i
$832$	0.695772	+	0.606658i	0.0241216	+	0.0210321i
$833$	1.35745	−	2.49621i	0.0470329	−	0.0864884i
$834$	8.85569	+	15.3385i	0.306648	+	0.531129i
$835$	32.3553			1.11970
$836$	8.79458			0.304167
$837$	−4.44201	−	7.69379i	−0.153538	−	0.265936i
$838$	−17.9684	−	31.1222i	−0.620708	−	1.07510i
$839$	−6.50996	+	11.2756i	−0.224749	+	0.389276i	−0.956244	−	0.292570i	$-0.905489\pi$
$839$	−6.50996	+	11.2756i	−0.224749	+	0.389276i	0.731495	+	0.681847i	$0.238823\pi$
$840$	−41.5882	−	23.3085i	−1.43493	−	0.804218i
$841$	−24.9906	+	43.2849i	−0.861744	+	1.49258i
$842$	−11.2818			−0.388797
$843$	1.09310	−	1.89330i	0.0376483	−	0.0652087i
$844$	−20.1508	−	34.9023i	−0.693620	−	1.20139i
$845$	−33.9328	−	13.8281i	−1.16732	−	0.475702i
$846$	22.7357			0.781671
$847$	−24.7366	−	13.8638i	−0.849958	−	0.476366i
$848$	−25.6453	−	44.4190i	−0.880664	−	1.52536i
$849$	−8.57724	−	14.8562i	−0.294370	−	0.509864i
$850$	1.52446	+	2.64044i	0.0522885	+	0.0905663i
$851$	22.7979			0.781502
$852$	−2.41536	−	4.18353i	−0.0827490	−	0.143325i
$853$	−28.3961			−0.972265			−0.486133	−	0.873885i	$-0.661593\pi$
$853$	−28.3961			−0.972265			−0.486133	+	0.873885i	$0.661593\pi$
$854$	57.3925	+	32.1661i	1.96393	+	1.10070i
$855$	−5.17779	−	8.96820i	−0.177077	−	0.306706i
$856$	12.0711			0.412582
$857$	−9.71017	−	16.8185i	−0.331693	−	0.574509i	0.651151	−	0.758948i	$-0.274286\pi$
$857$	−9.71017	−	16.8185i	−0.331693	−	0.574509i	−0.982844	+	0.184439i	$0.940953\pi$
$858$	−0.939355	+	4.79421i	−0.0320690	+	0.163672i
$859$	3.02708	−	5.24306i	0.103283	−	0.178891i	−0.809753	−	0.586771i	$-0.800399\pi$
$859$	3.02708	−	5.24306i	0.103283	−	0.178891i	0.913035	+	0.407881i	$0.133732\pi$
$860$	−57.4333	−	99.4775i	−1.95846	−	3.39215i
$861$	24.7820	−	14.7327i	0.844567	−	0.502089i
$862$	8.21895	−	14.2356i	0.279939	−	0.484868i
$863$	8.90178	−	15.4183i	0.303020	−	0.524846i	−0.673798	−	0.738915i	$-0.735338\pi$
$863$	8.90178	−	15.4183i	0.303020	−	0.524846i	0.976819	+	0.214069i	$0.0686717\pi$
$864$	−5.81958			−0.197986
$865$	−48.6320			−1.65354
$866$	26.6096	−	46.0891i	0.904229	−	1.56617i
$867$	8.41762	−	14.5797i	0.285877	−	0.495154i
$868$	92.3979	+	51.7852i	3.13619	+	1.75770i
$869$	1.87977	+	3.25586i	0.0637669	+	0.110447i
$870$	31.9475	−	55.3347i	1.08312	−	1.87602i
$871$	−27.1547	+	9.30464i	−0.920102	+	0.315276i
$872$	−31.3711	−	54.3363i	−1.06236	−	1.84006i
$873$	0.168242			0.00569412
$874$	−11.9294	−	20.6624i	−0.403519	−	0.698915i
$875$	13.1749	−	7.83240i	0.445394	−	0.264784i
$876$	−6.57362			−0.222102
$877$	−21.6047	−	37.4204i	−0.729538	−	1.26360i	−0.957079	−	0.289828i	$-0.906402\pi$
$877$	−21.6047	−	37.4204i	−0.729538	−	1.26360i	0.227541	−	0.973769i	$-0.426931\pi$
$878$	13.4653			0.454432
$879$	−1.83891	−	3.18509i	−0.0620249	−	0.107430i
$880$	−5.46059	−	9.45803i	−0.184077	−	0.318830i
$881$	−8.85000	−	15.3287i	−0.298164	−	0.516435i	0.677552	−	0.735475i	$-0.263041\pi$
$881$	−8.85000	−	15.3287i	−0.298164	−	0.516435i	−0.975716	+	0.219040i	$0.929708\pi$
$882$	17.8494	−	0.455673i	0.601020	−	0.0153433i
$883$	−15.1305			−0.509181			−0.254591	−	0.967049i	$-0.581941\pi$
$883$	−15.1305			−0.509181			−0.254591	+	0.967049i	$0.581941\pi$
$884$	4.97100	+	4.33431i	0.167193	+	0.145779i
$885$	−0.102702	−	0.177885i	−0.00345228	−	0.00597953i
$886$	−30.5204	+	52.8628i	−1.02535	+	1.77596i
$887$	15.8009			0.530542			0.265271	−	0.964174i	$-0.414538\pi$
$887$	15.8009			0.530542			0.265271	+	0.964174i	$0.414538\pi$
$888$	−28.6232	+	49.5769i	−0.960532	+	1.66369i
$889$	43.4011	+	24.3245i	1.45563	+	0.815818i
$890$	−3.31754	+	5.74614i	−0.111204	+	0.192611i
$891$	−0.265601	−	0.460034i	−0.00889795	−	0.0154117i
$892$	−20.8849	−	36.1737i	−0.699278	−	1.21118i
$893$	−32.7475			−1.09585
$894$	31.9033			1.06701
$895$	−33.6347	−	58.2571i	−1.12429	−	1.94732i
$896$	−24.9848	+	14.8533i	−0.834684	+	0.496214i
$897$	8.68383	−	2.97554i	0.289945	−	0.0993504i
$898$	−32.3860	+	56.0943i	−1.08074	+	1.87189i
$899$	−39.4767	+	68.3757i	−1.31662	+	2.28046i
$900$	−6.63482	+	11.4918i	−0.221161	+	0.383062i
$901$	−1.42717	−	2.47193i	−0.0475458	−	0.0823518i
$902$	14.7649			0.491616
$903$	20.8722	+	11.6980i	0.694584	+	0.389285i
$904$	22.5687	−	39.0901i	0.750623	−	1.30012i
$905$	−23.7371	+	41.1138i	−0.789047	+	1.36667i
$906$	−20.2196			−0.671752
$907$	−6.65877	+	11.5333i	−0.221101	+	0.382958i	−0.955143	−	0.296146i	$-0.904298\pi$
$907$	−6.65877	+	11.5333i	−0.221101	+	0.382958i	0.734042	+	0.679104i	$0.237632\pi$
$908$	75.8556			2.51736
$909$	3.62859			0.120353
$910$	−44.4096	+	52.2649i	−1.47216	+	1.73257i
$911$	11.6199			0.384986			0.192493	−	0.981298i	$-0.438343\pi$
$911$	11.6199			0.384986			0.192493	+	0.981298i	$0.438343\pi$
$912$	26.7984			0.887384
$913$	−0.119279	+	0.206597i	−0.00394755	+	0.00683736i
$914$	5.72843			0.189480
$915$	13.7393	−	23.7972i	0.454207	−	0.786710i
$916$	3.84520	−	6.66008i	0.127049	−	0.220055i
$917$	−0.764100	−	59.8716i	−0.0252328	−	1.97713i
$918$	−1.03539			−0.0341731
$919$	−5.18900	−	8.98762i	−0.171169	−	0.296474i	0.767660	−	0.640858i	$-0.221421\pi$
$919$	−5.18900	−	8.98762i	−0.171169	−	0.296474i	−0.938829	+	0.344384i	$0.888088\pi$
$920$	−22.9379	+	39.7296i	−0.756240	+	1.30985i
$921$	−7.30071	+	12.6452i	−0.240566	+	0.416673i
$922$	23.8929	−	41.3837i	0.786870	−	1.36290i
$923$	−3.65644	+	1.25289i	−0.120353	+	0.0412393i
$924$	5.52473	+	3.09638i	0.181750	+	0.101863i
$925$	13.1843	+	22.8360i	0.433499	+	0.750842i
$926$	−6.42392			−0.211103
$927$	8.95805			0.294221
$928$	25.8597	+	44.7903i	0.848885	+	1.47031i
$929$	−15.5736	−	26.9742i	−0.510952	−	0.884994i	−0.999919	−	0.0126925i	$-0.995960\pi$
$929$	−15.5736	−	26.9742i	−0.510952	−	0.884994i	0.488968	−	0.872302i	$-0.337374\pi$
$930$	31.9363	−	55.3154i	1.04723	−	1.81386i
$931$	−25.7095	+	0.656331i	−0.842593	+	0.0215104i
$932$	−54.3326	+	94.1069i	−1.77973	+	3.08257i
$933$	6.07629			0.198929
$934$	−2.52121	+	4.36686i	−0.0824964	+	0.142888i
$935$	−0.303883	−	0.526341i	−0.00993803	−	0.0172132i
$936$	−4.43204	+	22.6199i	−0.144866	+	0.739354i
$937$	−6.77667			−0.221384			−0.110692	−	0.993855i	$-0.535307\pi$
$937$	−6.77667			−0.221384			−0.110692	+	0.993855i	$0.535307\pi$
$938$	0.685630	+	53.7230i	0.0223866	+	1.75412i
$939$	−1.61084	−	2.79006i	−0.0525678	−	0.0910501i
$940$	56.6070	+	98.0462i	1.84632	+	3.19792i
$941$	23.2912	+	40.3415i	0.759271	+	1.31510i	0.943223	+	0.332160i	$0.107777\pi$
$941$	23.2912	+	40.3415i	0.759271	+	1.31510i	−0.183952	+	0.982935i	$0.558889\pi$
$942$	−28.4066			−0.925537
$943$	−13.8714	−	24.0259i	−0.451714	−	0.782392i
$944$	0.531547			0.0173004
$945$	−0.0951659	−	7.45679i	−0.00309575	−	0.242570i
$946$	6.12677	+	10.6119i	0.199198	+	0.345022i
$947$	16.5742			0.538590			0.269295	−	0.963058i	$-0.413209\pi$
$947$	16.5742			0.538590			0.269295	+	0.963058i	$0.413209\pi$
$948$	15.9465	+	27.6202i	0.517919	+	0.897062i
$949$	−1.01132	+	5.16150i	−0.0328289	+	0.167549i
$950$	13.7979	−	23.8987i	0.447663	−	0.775375i
$951$	−5.62276	−	9.73891i	−0.182331	−	0.315806i
$952$	5.90161	−	3.50847i	0.191272	−	0.113710i
$953$	18.4415	−	31.9415i	0.597377	−	1.03469i	−0.395829	−	0.918324i	$-0.629543\pi$
$953$	18.4415	−	31.9415i	0.597377	−	1.03469i	0.993207	−	0.116364i	$-0.0371239\pi$
$954$	8.96815	−	15.5333i	0.290355	−	0.502909i
$955$	11.9860			0.387857
$956$	−93.5383			−3.02524
$957$	−2.36043	+	4.08838i	−0.0763018	+	0.132159i
$958$	21.9825	−	38.0748i	0.710222	−	1.23014i
$959$	19.4421	−	11.5582i	0.627819	−	0.373234i
$960$	−0.360820	−	0.624958i	−0.0116454	−	0.0201704i
$961$	−23.9629	+	41.5050i	−0.772998	+	1.33887i
$962$	62.0728	+	54.1225i	2.00131	+	1.74498i
$963$	0.944099	+	1.63523i	0.0304232	+	0.0526944i
$964$	−90.2105			−2.90548
$965$	2.47010	+	4.27833i	0.0795152	+	0.137724i
$966$	−0.219258	−	17.1801i	−0.00705452	−	0.552762i
$967$	28.5940			0.919521			0.459761	−	0.888043i	$-0.347935\pi$
$967$	28.5940			0.919521			0.459761	+	0.888043i	$0.347935\pi$
$968$	−34.2591	−	59.3385i	−1.10113	−	1.90721i
$969$	1.49133			0.0479086
$970$	0.604796	+	1.04754i	0.0194188	+	0.0336344i
$971$	18.1825	+	31.4930i	0.583504	+	1.01066i	0.995060	+	0.0992742i	$0.0316521\pi$
$971$	18.1825	+	31.4930i	0.583504	+	1.01066i	−0.411556	+	0.911384i	$0.635015\pi$
$972$	−2.25315	−	3.90257i	−0.0722698	−	0.125175i
$973$	−0.234438	−	18.3696i	−0.00751575	−	0.588902i
$974$	−64.5242			−2.06749
$975$	8.00248	+	6.97752i	0.256285	+	0.223460i
$976$	35.5548	+	61.5827i	1.13808	+	1.97122i
$977$	27.7844	−	48.1239i	0.888900	−	1.53962i	0.0477230	−	0.998861i	$-0.484804\pi$
$977$	27.7844	−	48.1239i	0.888900	−	1.53962i	0.841177	−	0.540760i	$-0.181863\pi$
$978$	−42.1630			−1.34822
$979$	0.245115	−	0.424551i	0.00783390	−	0.0135687i
$980$	46.4062	+	75.8397i	1.48239	+	2.42261i
$981$	4.90716	−	8.49945i	0.156674	−	0.271367i
$982$	−44.9927	−	77.9296i	−1.43577	−	2.48683i
$983$	24.8625	+	43.0631i	0.792991	+	1.37350i	0.924107	+	0.382133i	$0.124810\pi$
$983$	24.8625	+	43.0631i	0.792991	+	1.37350i	−0.131117	+	0.991367i	$0.541856\pi$
$984$	69.6631			2.22078
$985$	18.5555			0.591228
$986$	4.60084	+	7.96889i	0.146521	+	0.253781i
$987$	−20.5719	−	11.5297i	−0.654811	−	0.366994i
$988$	11.4778	−	58.5797i	0.365159	−	1.86367i
$989$	11.5120	−	19.9394i	0.366061	−	0.634037i
$990$	1.90956	−	3.30746i	0.0606899	−	0.105118i
$991$	12.8980	−	22.3401i	0.409720	−	0.709655i	−0.585139	−	0.810933i	$-0.698960\pi$
$991$	12.8980	−	22.3401i	0.409720	−	0.709655i	0.994858	+	0.101278i	$0.0322932\pi$
$992$	25.8506	+	44.7746i	0.820758	+	1.42160i
$993$	3.68603			0.116973
$994$	0.0923215	+	7.23391i	0.00292826	+	0.229446i
$995$	6.37527	−	11.0423i	0.202110	−	0.350064i
$996$	−1.01187	+	1.75261i	−0.0320623	+	0.0555335i
$997$	39.4448			1.24923			0.624615	−	0.780933i	$-0.285256\pi$
$997$	39.4448			1.24923			0.624615	+	0.780933i	$0.285256\pi$
$998$	14.5658	−	25.2287i	0.461072	−	0.798600i
$999$	−8.95466			−0.283313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.c.16.2	yes	20
3.2	odd	2		819.2.s.f.289.9		20
7.4	even	3		273.2.j.c.172.9	yes	20
13.9	even	3		273.2.j.c.100.9	✓	20
21.11	odd	6		819.2.n.f.172.2		20
39.35	odd	6		819.2.n.f.100.2		20
91.74	even	3	inner	273.2.l.c.256.2	yes	20
273.74	odd	6		819.2.s.f.802.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.9	✓	20	13.9	even	3
273.2.j.c.172.9	yes	20	7.4	even	3
273.2.l.c.16.2	yes	20	1.1	even	1	trivial
273.2.l.c.256.2	yes	20	91.74	even	3	inner
819.2.n.f.100.2		20	39.35	odd	6
819.2.n.f.172.2		20	21.11	odd	6
819.2.s.f.289.9		20	3.2	odd	2
819.2.s.f.802.9		20	273.74	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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.55074 q^{2} +(-0.500000 + 0.866025i) q^{3} +4.50630 q^{4} +(-1.40932 + 2.44101i) q^{5} +(1.27537 - 2.20901i) q^{6} +(-2.27422 + 1.35201i) q^{7} -6.39292 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-2.55074 q^{2} +(-0.500000 + 0.866025i) q^{3} +4.50630 q^{4} +(-1.40932 + 2.44101i) q^{5} +(1.27537 - 2.20901i) q^{6} +(-2.27422 + 1.35201i) q^{7} -6.39292 q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.59481 - 6.22639i) q^{10} +(-0.265601 + 0.460034i) q^{11} +(-2.25315 + 3.90257i) q^{12} +(2.71760 + 2.36953i) q^{13} +(5.80095 - 3.44863i) q^{14} +(-1.40932 - 2.44101i) q^{15} +7.29411 q^{16} +0.405918 q^{17} +(1.27537 + 2.20901i) q^{18} +(-1.83699 - 3.18176i) q^{19} +(-6.35080 + 10.9999i) q^{20} +(-0.0337632 - 2.64554i) q^{21} +(0.677479 - 1.17343i) q^{22} -2.54593 q^{23} +(3.19646 - 5.53643i) q^{24} +(-1.47234 - 2.55018i) q^{25} +(-6.93190 - 6.04406i) q^{26} +1.00000 q^{27} +(-10.2483 + 6.09255i) q^{28} +(-4.44357 - 7.69648i) q^{29} +(3.59481 + 6.22639i) q^{30} +(-4.44201 - 7.69379i) q^{31} -5.81958 q^{32} +(-0.265601 - 0.460034i) q^{33} -1.03539 q^{34} +(-0.0951659 - 7.45679i) q^{35} +(-2.25315 - 3.90257i) q^{36} -8.95466 q^{37} +(4.68569 + 8.11585i) q^{38} +(-3.41087 + 1.16874i) q^{39} +(9.00965 - 15.6052i) q^{40} +(5.44846 + 9.43700i) q^{41} +(0.0861212 + 6.74809i) q^{42} +(-4.52174 + 7.83189i) q^{43} +(-1.19687 + 2.07305i) q^{44} +2.81863 q^{45} +6.49401 q^{46} +(4.45669 - 7.71921i) q^{47} +(-3.64706 + 6.31689i) q^{48} +(3.34415 - 6.14953i) q^{49} +(3.75558 + 6.50485i) q^{50} +(-0.202959 + 0.351536i) q^{51} +(12.2463 + 10.6778i) q^{52} +(-3.51589 - 6.08971i) q^{53} -2.55074 q^{54} +(-0.748630 - 1.29667i) q^{55} +(14.5389 - 8.64328i) q^{56} +3.67398 q^{57} +(11.3344 + 19.6318i) q^{58} +0.0728735 q^{59} +(-6.35080 - 10.9999i) q^{60} +(4.87445 + 8.44280i) q^{61} +(11.3304 + 19.6249i) q^{62} +(2.30798 + 1.29353i) q^{63} +0.256025 q^{64} +(-9.61399 + 3.29426i) q^{65} +(0.677479 + 1.17343i) q^{66} +(-3.98061 + 6.89462i) q^{67} +1.82919 q^{68} +(1.27296 - 2.20484i) q^{69} +(0.242744 + 19.0204i) q^{70} +(-0.535997 + 0.928375i) q^{71} +(3.19646 + 5.53643i) q^{72} +(0.729382 + 1.26333i) q^{73} +22.8410 q^{74} +2.94469 q^{75} +(-8.27801 - 14.3379i) q^{76} +(-0.0179350 - 1.40531i) q^{77} +(8.70026 - 2.98117i) q^{78} +(3.53872 - 6.12924i) q^{79} +(-10.2797 + 17.8050i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-13.8976 - 24.0714i) q^{82} +0.449091 q^{83} +(-0.152147 - 11.9216i) q^{84} +(-0.572068 + 0.990850i) q^{85} +(11.5338 - 19.9771i) q^{86} +8.88713 q^{87} +(1.69796 - 2.94096i) q^{88} -0.922870 q^{89} -7.18961 q^{90} +(-9.38403 - 1.71461i) q^{91} -11.4727 q^{92} +8.88402 q^{93} +(-11.3679 + 19.6897i) q^{94} +10.3556 q^{95} +(2.90979 - 5.03990i) q^{96} +(-0.0841208 + 0.145702i) q^{97} +(-8.53007 + 15.6859i) q^{98} +0.531201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9	\( 20 q - 10 q^{3} + 32 q^{4} + 3 q^{7} - 12 q^{8} - 10 q^{9} - 4 q^{10} - 8 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} + 40 q^{16} + 7 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} + 28 q^{23} + 6 q^{24} - 32 q^{25} + 13 q^{26} + 20 q^{27} - 23 q^{28} - 9 q^{29} - 4 q^{30} - 9 q^{31} - 34 q^{32} - 8 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} - 36 q^{37} + 22 q^{38} + 4 q^{39} - 9 q^{40} - q^{41} + 3 q^{42} - 11 q^{43} + 8 q^{44} + 20 q^{46} + 13 q^{47} - 20 q^{48} - 3 q^{49} + 5 q^{50} - 44 q^{52} - 6 q^{53} - 19 q^{55} - 23 q^{56} - 14 q^{57} + 30 q^{59} + 12 q^{60} + 22 q^{62} + 6 q^{63} + 72 q^{64} - 6 q^{65} - 9 q^{66} - 22 q^{67} - 78 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} + 6 q^{72} + 6 q^{74} + 64 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} + 48 q^{80} - 10 q^{81} - 13 q^{82} + 40 q^{83} + 10 q^{84} - 16 q^{85} + 4 q^{86} + 18 q^{87} - 12 q^{88} - 4 q^{89} + 8 q^{90} + 30 q^{91} + 66 q^{92} + 18 q^{93} - 44 q^{94} + 72 q^{95} + 17 q^{96} + 21 q^{97} - 76 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 10 * q^3 + 32 * q^4 + 3 * q^7 - 12 * q^8 - 10 * q^9 - 4 * q^10 - 8 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 + 40 * q^16 + 7 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 + 28 * q^23 + 6 * q^24 - 32 * q^25 + 13 * q^26 + 20 * q^27 - 23 * q^28 - 9 * q^29 - 4 * q^30 - 9 * q^31 - 34 * q^32 - 8 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 - 36 * q^37 + 22 * q^38 + 4 * q^39 - 9 * q^40 - q^41 + 3 * q^42 - 11 * q^43 + 8 * q^44 + 20 * q^46 + 13 * q^47 - 20 * q^48 - 3 * q^49 + 5 * q^50 - 44 * q^52 - 6 * q^53 - 19 * q^55 - 23 * q^56 - 14 * q^57 + 30 * q^59 + 12 * q^60 + 22 * q^62 + 6 * q^63 + 72 * q^64 - 6 * q^65 - 9 * q^66 - 22 * q^67 - 78 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 + 6 * q^72 + 6 * q^74 + 64 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 + 48 * q^80 - 10 * q^81 - 13 * q^82 + 40 * q^83 + 10 * q^84 - 16 * q^85 + 4 * q^86 + 18 * q^87 - 12 * q^88 - 4 * q^89 + 8 * q^90 + 30 * q^91 + 66 * q^92 + 18 * q^93 - 44 * q^94 + 72 * q^95 + 17 * q^96 + 21 * q^97 - 76 * q^98 + 16 * q^99

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