LMFDB - Embedded newform 273.2.j.c.172.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(100,273)]

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, 4]))

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

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

chi := DirichletCharacter("273.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.j (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			172.9
Root			$-1.27537 - 2.20901i$ of defining polynomial
Character	$\chi$	$=$	273.172
Dual form			273.2.j.c.100.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.27537 - 2.20901i) q^{2} +1.00000 q^{3} +(-2.25315 - 3.90257i) q^{4} +(-1.40932 - 2.44101i) q^{5} +(1.27537 - 2.20901i) q^{6} +(-0.0337632 + 2.64554i) q^{7} -6.39292 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.27537 - 2.20901i) q^{2} +1.00000 q^{3} +(-2.25315 - 3.90257i) q^{4} +(-1.40932 - 2.44101i) q^{5} +(1.27537 - 2.20901i) q^{6} +(-0.0337632 + 2.64554i) q^{7} -6.39292 q^{8} +1.00000 q^{9} -7.18961 q^{10} +0.531201 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} +(-3.64706 + 6.31689i) q^{16} +(-0.202959 - 0.351536i) q^{17} +(1.27537 - 2.20901i) q^{18} +3.67398 q^{19} +(-6.35080 + 10.9999i) q^{20} +(-0.0337632 + 2.64554i) q^{21} +(0.677479 - 1.17343i) q^{22} +(1.27296 - 2.20484i) q^{23} -6.39292 q^{24} +(-1.47234 + 2.55018i) q^{25} +(8.70026 - 2.98117i) q^{26} +1.00000 q^{27} +(10.4005 - 5.82902i) q^{28} +(-4.44357 - 7.69648i) q^{29} -7.18961 q^{30} +(-4.44201 + 7.69379i) q^{31} +(2.90979 + 5.03990i) q^{32} +0.531201 q^{33} -1.03539 q^{34} +(6.50536 - 3.64598i) q^{35} +(-2.25315 - 3.90257i) q^{36} +(4.47733 - 7.75496i) q^{37} +(4.68569 - 8.11585i) q^{38} +(2.71760 + 2.36953i) q^{39} +(9.00965 + 15.6052i) q^{40} +(5.44846 + 9.43700i) q^{41} +(5.80095 + 3.44863i) q^{42} +(-4.52174 + 7.83189i) q^{43} +(-1.19687 - 2.07305i) q^{44} +(-1.40932 - 2.44101i) q^{45} +(-3.24701 - 5.62398i) q^{46} +(4.45669 + 7.71921i) q^{47} +(-3.64706 + 6.31689i) q^{48} +(-6.99772 - 0.178643i) q^{49} +(3.75558 + 6.50485i) q^{50} +(-0.202959 - 0.351536i) q^{51} +(3.12409 - 15.9445i) q^{52} +(-3.51589 + 6.08971i) q^{53} +(1.27537 - 2.20901i) q^{54} +(-0.748630 - 1.29667i) q^{55} +(0.215845 - 16.9127i) q^{56} +3.67398 q^{57} -22.6688 q^{58} +(-0.0364367 - 0.0631103i) q^{59} +(-6.35080 + 10.9999i) q^{60} -9.74891 q^{61} +(11.3304 + 19.6249i) q^{62} +(-0.0337632 + 2.64554i) q^{63} +0.256025 q^{64} +(1.95408 - 9.97309i) q^{65} +(0.677479 - 1.17343i) q^{66} +7.96122 q^{67} +(-0.914594 + 1.58412i) q^{68} +(1.27296 - 2.20484i) q^{69} +(0.242744 - 19.0204i) q^{70} +(-0.535997 + 0.928375i) q^{71} -6.39292 q^{72} +(0.729382 - 1.26333i) q^{73} +(-11.4205 - 19.7809i) q^{74} +(-1.47234 + 2.55018i) 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} +20.5594 q^{80} +1.00000 q^{81} +27.7952 q^{82} +0.449091 q^{83} +(10.4005 - 5.82902i) q^{84} +(-0.572068 + 0.990850i) q^{85} +(11.5338 + 19.9771i) q^{86} +(-4.44357 - 7.69648i) q^{87} -3.39593 q^{88} +(0.461435 - 0.799229i) q^{89} -7.18961 q^{90} +(-6.36043 + 7.10950i) q^{91} -11.4727 q^{92} +(-4.44201 + 7.69379i) q^{93} +22.7357 q^{94} +(-5.17779 - 8.96820i) q^{95} +(2.90979 + 5.03990i) q^{96} +(-0.0841208 + 0.145702i) q^{97} +(-9.31932 + 15.2302i) q^{98} +0.531201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9}+O(q^{10}) $ 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9	$ 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25} + 4 q^{26} + 20 q^{27} + 13 q^{28} - 9 q^{29} + 8 q^{30} - 9 q^{31} + 17 q^{32} + 16 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} + 18 q^{37} + 22 q^{38} - 5 q^{39} - 9 q^{40} - q^{41} - 9 q^{42} - 11 q^{43} + 8 q^{44} - 10 q^{46} + 13 q^{47} - 20 q^{48} - 21 q^{49} + 5 q^{50} - 2 q^{52} - 6 q^{53} - 19 q^{55} - 5 q^{56} - 14 q^{57} - 15 q^{59} + 12 q^{60} + 22 q^{62} - 9 q^{63} + 72 q^{64} - 27 q^{65} - 9 q^{66} + 44 q^{67} + 39 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} - 12 q^{72} - 3 q^{74} - 32 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} - 96 q^{80} + 20 q^{81} + 26 q^{82} + 40 q^{83} + 13 q^{84} - 16 q^{85} + 4 q^{86} - 9 q^{87} + 24 q^{88} + 2 q^{89} + 8 q^{90} + 9 q^{91} + 66 q^{92} - 9 q^{93} + 88 q^{94} - 36 q^{95} + 17 q^{96} + 21 q^{97} - 79 q^{98} + 16 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.27537	−	2.20901i	0.901824	−	1.56201i	0.0767000	−	0.997054i	$-0.475562\pi$
$2$	1.27537	−	2.20901i	0.901824	−	1.56201i	0.825124	−	0.564951i	$-0.191105\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−2.25315	−	3.90257i	−1.12657	−	1.95128i
$5$	−1.40932	−	2.44101i	−0.630265	−	1.09165i	−0.987497	−	0.157636i	$-0.949613\pi$
$5$	−1.40932	−	2.44101i	−0.630265	−	1.09165i	0.357232	−	0.934016i	$-0.383721\pi$
$6$	1.27537	−	2.20901i	0.520668	−	0.901824i
$7$	−0.0337632	+	2.64554i	−0.0127613	+	0.999919i
$7$	−0.0337632	+	2.64554i	−0.0127613	+	0.999919i
$8$	−6.39292			−2.26024
$9$	1.00000			0.333333
$10$	−7.18961			−2.27355
$11$	0.531201			0.160163			0.0800816	−	0.996788i	$-0.474482\pi$
$11$	0.531201			0.160163			0.0800816	+	0.996788i	$0.474482\pi$
$12$	−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
$16$	−3.64706	+	6.31689i	−0.911764	+	1.57922i
$17$	−0.202959	−	0.351536i	−0.0492248	−	0.0852599i	0.840363	−	0.542024i	$-0.182342\pi$
$17$	−0.202959	−	0.351536i	−0.0492248	−	0.0852599i	−0.889588	+	0.456764i	$0.849008\pi$
$18$	1.27537	−	2.20901i	0.300608	−	0.520668i
$19$	3.67398			0.842868			0.421434	−	0.906859i	$-0.361527\pi$
$19$	3.67398			0.842868			0.421434	+	0.906859i	$0.361527\pi$
$20$	−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
$23$	1.27296	−	2.20484i	0.265431	−	0.459740i	−0.702245	−	0.711935i	$-0.747819\pi$
$23$	1.27296	−	2.20484i	0.265431	−	0.459740i	0.967677	+	0.252195i	$0.0811523\pi$
$24$	−6.39292			−1.30495
$25$	−1.47234	+	2.55018i	−0.294469	+	0.510035i
$26$	8.70026	−	2.98117i	1.70626	−	0.584655i
$27$	1.00000			0.192450
$28$	10.4005	−	5.82902i	1.96550	−	1.10158i
$29$	−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	$-0.475576\pi$
$30$	−7.18961			−1.31264
$31$	−4.44201	+	7.69379i	−0.797809	+	1.38185i	0.123231	+	0.992378i	$0.460674\pi$
$31$	−4.44201	+	7.69379i	−0.797809	+	1.38185i	−0.921040	+	0.389468i	$0.872659\pi$
$32$	2.90979	+	5.03990i	0.514383	+	0.890937i
$33$	0.531201			0.0924702
$34$	−1.03539			−0.177569
$35$	6.50536	−	3.64598i	1.09961	−	0.616283i
$36$	−2.25315	−	3.90257i	−0.375525	−	0.650428i
$37$	4.47733	−	7.75496i	0.736068	−	1.27491i	−0.218185	−	0.975908i	$-0.570013\pi$
$37$	4.47733	−	7.75496i	0.736068	−	1.27491i	0.954253	−	0.299000i	$-0.0966532\pi$
$38$	4.68569	−	8.11585i	0.760119	−	1.31656i
$39$	2.71760	+	2.36953i	0.435164	+	0.379428i
$40$	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	$0.509387\pi$
$42$	5.80095	+	3.44863i	0.895106	+	0.532135i
$43$	−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
$45$	−1.40932	−	2.44101i	−0.210088	−	0.363884i
$46$	−3.24701	−	5.62398i	−0.478745	−	0.829210i
$47$	4.45669	+	7.71921i	0.650074	+	1.12596i	0.983104	+	0.183046i	$0.0585957\pi$
$47$	4.45669	+	7.71921i	0.650074	+	1.12596i	−0.333030	+	0.942916i	$0.608071\pi$
$48$	−3.64706	+	6.31689i	−0.526407	+	0.911764i
$49$	−6.99772	−	0.178643i	−0.999674	−	0.0255205i
$50$	3.75558	+	6.50485i	0.531119	+	0.919924i
$51$	−0.202959	−	0.351536i	−0.0284200	−	0.0492248i
$52$	3.12409	−	15.9445i	0.433233	−	2.21111i
$53$	−3.51589	+	6.08971i	−0.482945	+	0.836486i	−0.999808	−	0.0195824i	$-0.993766\pi$
$53$	−3.51589	+	6.08971i	−0.482945	+	0.836486i	0.516863	+	0.856068i	$0.327100\pi$
$54$	1.27537	−	2.20901i	0.173556	−	0.300608i
$55$	−0.748630	−	1.29667i	−0.100945	−	0.174842i
$56$	0.215845	−	16.9127i	0.0288435	−	2.26005i
$57$	3.67398			0.486630
$58$	−22.6688			−2.97656
$59$	−0.0364367	−	0.0631103i	−0.00474366	−	0.00821626i	0.863644	−	0.504103i	$-0.168177\pi$
$59$	−0.0364367	−	0.0631103i	−0.00474366	−	0.00821626i	−0.868387	+	0.495886i	$0.834843\pi$
$60$	−6.35080	+	10.9999i	−0.819884	+	1.42008i
$61$	−9.74891			−1.24822			−0.624110	−	0.781337i	$-0.714538\pi$
$61$	−9.74891			−1.24822			−0.624110	+	0.781337i	$0.714538\pi$
$62$	11.3304	+	19.6249i	1.43897	+	2.49236i
$63$	−0.0337632	+	2.64554i	−0.00425376	+	0.333306i
$64$	0.256025			0.0320031
$65$	1.95408	−	9.97309i	0.242374	−	1.23701i
$66$	0.677479	−	1.17343i	0.0833919	−	0.144439i
$67$	7.96122			0.972618			0.486309	−	0.873787i	$-0.338343\pi$
$67$	7.96122			0.972618			0.486309	+	0.873787i	$0.338343\pi$
$68$	−0.914594	+	1.58412i	−0.110911	+	0.192103i
$69$	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	$0.186928\pi$
$72$	−6.39292			−0.753413
$73$	0.729382	−	1.26333i	0.0853677	−	0.147861i	−0.820180	−	0.572105i	$-0.806127\pi$
$73$	0.729382	−	1.26333i	0.0853677	−	0.147861i	0.905548	+	0.424244i	$0.139460\pi$
$74$	−11.4205	−	19.7809i	−1.32761	−	2.29949i
$75$	−1.47234	+	2.55018i	−0.170012	+	0.294469i
$76$	−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	0.993496	−	0.113866i	$-0.0363235\pi$
$79$	3.53872	+	6.12924i	0.398137	+	0.689594i	−0.595359	+	0.803460i	$0.702990\pi$
$80$	20.5594			2.29861
$81$	1.00000			0.111111
$82$	27.7952			3.06947
$83$	0.449091			0.0492942			0.0246471	−	0.999696i	$-0.492154\pi$
$83$	0.449091			0.0492942			0.0246471	+	0.999696i	$0.492154\pi$
$84$	10.4005	−	5.82902i	1.13478	−	0.635998i
$85$	−0.572068	+	0.990850i	−0.0620494	+	0.107473i
$86$	11.5338	+	19.9771i	1.24372	+	2.15419i
$87$	−4.44357	−	7.69648i	−0.476400	−	0.825150i
$88$	−3.39593			−0.362007
$89$	0.461435	−	0.799229i	0.0489120	−	0.0847181i	−0.840533	−	0.541761i	$-0.817758\pi$
$89$	0.461435	−	0.799229i	0.0489120	−	0.0847181i	0.889445	+	0.457043i	$0.151091\pi$
$90$	−7.18961			−0.757852
$91$	−6.36043	+	7.10950i	−0.666754	+	0.745278i
$92$	−11.4727			−1.19611
$93$	−4.44201	+	7.69379i	−0.460615	+	0.797809i
$94$	22.7357			2.34501
$95$	−5.17779	−	8.96820i	−0.531231	−	0.920118i
$96$	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	$0.169385\pi$
$98$	−9.31932	+	15.2302i	−0.941394	+	1.53848i
$99$	0.531201			0.0533877
$100$	13.2696			1.32696
$101$	3.62859			0.361059			0.180529	−	0.983570i	$-0.442219\pi$
$101$	3.62859			0.361059			0.180529	+	0.983570i	$0.442219\pi$
$102$	−1.03539			−0.102519
$103$	−4.47902	−	7.75790i	−0.441331	−	0.764408i	0.556457	−	0.830876i	$-0.312160\pi$
$103$	−4.47902	−	7.75790i	−0.441331	−	0.764408i	−0.997789	+	0.0664681i	$0.978827\pi$
$104$	−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
$107$	0.944099	−	1.63523i	0.0912695	−	0.158083i	−0.816776	−	0.576955i	$-0.804241\pi$
$107$	0.944099	−	1.63523i	0.0912695	−	0.158083i	0.908046	+	0.418871i	$0.137574\pi$
$108$	−2.25315	−	3.90257i	−0.216809	−	0.375525i
$109$	4.90716	−	8.49945i	0.470021	−	0.814100i	−0.529391	−	0.848378i	$-0.677580\pi$
$109$	4.90716	−	8.49945i	0.470021	−	0.814100i	0.999412	+	0.0342776i	$0.0109130\pi$
$110$	−3.81913			−0.364140
$111$	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	$0.274423\pi$
$114$	4.68569	−	8.11585i	0.438855	−	0.760119i
$115$	−7.17603			−0.669169
$116$	−20.0240	+	34.6826i	−1.85918	+	3.22020i
$117$	2.71760	+	2.36953i	0.251242	+	0.219063i
$118$	−0.185882			−0.0171118
$119$	0.936853	−	0.525067i	0.0858812	−	0.0481328i
$120$	9.00965	+	15.6052i	0.822465	+	1.42455i
$121$	−10.7178			−0.974348
$122$	−12.4335	+	21.5354i	−1.12567	+	1.94973i
$123$	5.44846	+	9.43700i	0.491271	+	0.850906i
$124$	40.0340			3.59516
$125$	−5.79316			−0.518156
$126$	5.80095	+	3.44863i	0.516790	+	0.307228i
$127$	−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	$-0.480810\pi$
$128$	−5.49305	+	9.51424i	−0.485522	+	0.840948i
$129$	−4.52174	+	7.83189i	−0.398117	+	0.689559i
$130$	−19.5385	−	17.0360i	−1.71364	−	1.49415i
$131$	−11.3156	−	19.5992i	−0.988647	−	1.71239i	−0.624450	−	0.781065i	$-0.714677\pi$
$131$	−11.3156	−	19.5992i	−0.988647	−	1.71239i	−0.364197	−	0.931322i	$-0.618657\pi$
$132$	−1.19687	−	2.07305i	−0.104175	−	0.180436i
$133$	−0.124045	+	9.71964i	−0.0107561	+	0.842799i
$134$	10.1535	−	17.5864i	0.877131	−	1.51924i
$135$	−1.40932	−	2.44101i	−0.121295	−	0.210088i
$136$	1.29750	+	2.24734i	0.111260	+	0.192708i
$137$	4.27446	+	7.40359i	0.365192	+	0.632531i	0.988807	−	0.149201i	$-0.0476700\pi$
$137$	4.27446	+	7.40359i	0.365192	+	0.632531i	−0.623615	+	0.781732i	$0.714337\pi$
$138$	−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	$0.261811\pi$
$140$	−28.8862	−	17.1727i	−2.44133	−	1.45135i
$141$	4.45669	+	7.71921i	0.375321	+	0.650074i
$142$	1.36719	+	2.36805i	0.114732	+	0.198722i
$143$	1.44359	+	1.25870i	0.120719	+	0.105257i
$144$	−3.64706	+	6.31689i	−0.303921	+	0.526407i
$145$	−12.5248	+	21.6936i	−1.04013	+	1.80155i
$146$	−1.86047	−	3.22242i	−0.153973	−	0.266690i
$147$	−6.99772	−	0.178643i	−0.577162	−	0.0147342i
$148$	−40.3523			−3.31694
$149$	−12.5075			−1.02465			−0.512325	−	0.858792i	$-0.671216\pi$
$149$	−12.5075			−1.02465			−0.512325	+	0.858792i	$0.671216\pi$
$150$	3.75558	+	6.50485i	0.306641	+	0.531119i
$151$	−3.96347	+	6.86494i	−0.322543	+	0.558661i	−0.981012	−	0.193947i	$-0.937871\pi$
$151$	−3.96347	+	6.86494i	−0.322543	+	0.558661i	0.658469	+	0.752608i	$0.271204\pi$
$152$	−23.4874			−1.90508
$153$	−0.202959	−	0.351536i	−0.0164083	−	0.0284200i
$154$	3.08147	+	1.83191i	0.248312	+	0.147620i
$155$	25.0408			2.01133
$156$	3.12409	−	15.9445i	0.250127	−	1.27658i
$157$	−5.56829	+	9.64457i	−0.444398	+	0.769720i	−0.998010	−	0.0630545i	$-0.979916\pi$
$157$	−5.56829	+	9.64457i	−0.444398	+	0.769720i	0.553612	+	0.832775i	$0.313249\pi$
$158$	18.0527			1.43620
$159$	−3.51589	+	6.08971i	−0.278829	+	0.482945i
$160$	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
$163$	16.5297			1.29470			0.647352	−	0.762191i	$-0.275876\pi$
$163$	16.5297			1.29470			0.647352	+	0.762191i	$0.275876\pi$
$164$	24.5524	−	42.5259i	1.91722	−	3.32072i
$165$	−0.748630	−	1.29667i	−0.0582808	−	0.100945i
$166$	0.572758	−	0.992047i	0.0444547	−	0.0769978i
$167$	−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
$171$	3.67398			0.280956
$172$	40.7526			3.10736
$173$	−17.2538			−1.31178			−0.655889	−	0.754857i	$-0.727706\pi$
$173$	−17.2538			−1.31178			−0.655889	+	0.754857i	$0.727706\pi$
$174$	−22.6688			−1.71852
$175$	−6.69687	−	3.98124i	−0.506236	−	0.300954i
$176$	−1.93732	+	3.35554i	−0.146031	+	0.252933i
$177$	−0.0364367	−	0.0631103i	−0.00273875	−	0.00474366i
$178$	−1.17700	−	2.03863i	−0.0882201	−	0.152802i
$179$	23.8660			1.78383			0.891914	−	0.452204i	$-0.149362\pi$
$179$	23.8660			1.78383			0.891914	+	0.452204i	$0.149362\pi$
$180$	−6.35080	+	10.9999i	−0.473360	+	0.819884i
$181$	16.8430			1.25193			0.625964	−	0.779852i	$-0.284706\pi$
$181$	16.8430			1.25193			0.625964	+	0.779852i	$0.284706\pi$
$182$	7.59304	+	23.1175i	0.562834	+	1.71358i
$183$	−9.74891			−0.720660
$184$	−8.13796	+	14.0954i	−0.599938	+	1.03912i
$185$	−25.2399			−1.85567
$186$	11.3304	+	19.6249i	0.830788	+	1.43897i
$187$	−0.107812	−	0.186736i	−0.00788401	−	0.0136555i
$188$	20.0831	−	34.7850i	1.46471	−	2.53696i
$189$	−0.0337632	+	2.64554i	−0.00245591	+	0.192434i
$190$	−26.4145			−1.91631
$191$	4.25241			0.307694			0.153847	−	0.988095i	$-0.450834\pi$
$191$	4.25241			0.307694			0.153847	+	0.988095i	$0.450834\pi$
$192$	0.256025			0.0184770
$193$	−1.75269			−0.126161			−0.0630807	−	0.998008i	$-0.520093\pi$
$193$	−1.75269			−0.126161			−0.0630807	+	0.998008i	$0.520093\pi$
$194$	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	$0.908684\pi$
$198$	0.677479	−	1.17343i	0.0481463	−	0.0833919i
$199$	2.26183	+	3.91760i	0.160337	+	0.277712i	0.934989	−	0.354675i	$-0.115409\pi$
$199$	2.26183	+	3.91760i	0.160337	+	0.277712i	−0.774653	+	0.632387i	$0.782075\pi$
$200$	9.41258	−	16.3031i	0.665570	−	1.15280i
$201$	7.96122			0.561541
$202$	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
$205$	15.3572	−	26.5994i	1.07259	−	1.85779i
$206$	−22.8497			−1.59201
$207$	1.27296	−	2.20484i	0.0884771	−	0.153247i
$208$	−24.8793	+	8.52496i	−1.72507	+	0.591099i
$209$	1.95162			0.134996
$210$	0.242744	−	19.0204i	0.0167509	−	1.31253i
$211$	−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	$0.932941\pi$
$212$	31.6873			2.17629
$213$	−0.535997	+	0.928375i	−0.0367259	+	0.0636112i
$214$	−2.40815	−	4.17105i	−0.164618	−	0.285127i
$215$	25.4903			1.73842
$216$	−6.39292			−0.434983
$217$	−20.2042	−	12.0113i	−1.37155	−	0.815378i
$218$	−12.5169	−	21.6799i	−0.847752	−	1.46835i
$219$	0.729382	−	1.26333i	0.0492871	−	0.0853677i
$220$	−3.37355	+	5.84316i	−0.227445	+	0.393946i
$221$	0.281412	−	1.43625i	0.0189298	−	0.0966127i
$222$	−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	$0.933782\pi$
$224$	−13.4315	+	7.52779i	−0.897429	+	0.502971i
$225$	−1.47234	+	2.55018i	−0.0981563	+	0.170012i
$226$	9.00479	+	15.5968i	0.598990	+	1.03748i
$227$	−8.41663	−	14.5780i	−0.558631	−	0.967578i	−0.997611	−	0.0690807i	$-0.977993\pi$
$227$	−8.41663	−	14.5780i	−0.558631	−	0.967578i	0.438980	−	0.898497i	$-0.355340\pi$
$228$	−8.27801	−	14.3379i	−0.548225	−	0.949553i
$229$	0.853294	+	1.47795i	0.0563873	+	0.0976656i	0.892841	−	0.450372i	$-0.148709\pi$
$229$	0.853294	+	1.47795i	0.0563873	+	0.0976656i	−0.836454	+	0.548037i	$0.815375\pi$
$230$	−9.15211	+	15.8519i	−0.603473	+	1.04525i
$231$	−0.0179350	+	1.40531i	−0.00118004	+	0.0924627i
$232$	28.4074	+	49.2030i	1.86504	+	3.23034i
$233$	−12.0571	−	20.8834i	−0.789884	−	1.36812i	−0.926038	−	0.377431i	$-0.876808\pi$
$233$	−12.0571	−	20.8834i	−0.789884	−	1.36812i	0.136154	−	0.990688i	$-0.456526\pi$
$234$	8.70026	−	2.98117i	0.568754	−	0.194885i
$235$	12.5618	−	21.7576i	0.819439	−	1.41931i
$236$	−0.164195	+	0.284394i	−0.0106882	+	0.0185125i
$237$	3.53872	+	6.12924i	0.229865	+	0.398137i
$238$	0.0349582	−	2.73917i	0.00226600	−	0.177554i
$239$	−20.7572			−1.34267			−0.671337	−	0.741152i	$-0.734280\pi$
$239$	−20.7572			−1.34267			−0.671337	+	0.741152i	$0.734280\pi$
$240$	20.5594			1.32711
$241$	10.0094	+	17.3368i	0.644761	+	1.11676i	0.984357	+	0.176187i	$0.0563764\pi$
$241$	10.0094	+	17.3368i	0.644761	+	1.11676i	−0.339596	+	0.940572i	$0.610290\pi$
$242$	−13.6692	+	23.6758i	−0.878690	+	1.52194i
$243$	1.00000			0.0641500
$244$	21.9657	+	38.0458i	1.40621	+	2.43563i
$245$	9.42593	+	17.3333i	0.602201	+	1.10738i
$246$	27.7952			1.77216
$247$	9.98439	+	8.70559i	0.635292	+	0.553923i
$248$	28.3974	−	49.1858i	1.80324	−	3.12330i
$249$	0.449091			0.0284600
$250$	−7.38844	+	12.7972i	−0.467286	+	0.809363i
$251$	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
$254$	−47.9662			−3.00967
$255$	−0.572068	+	0.990850i	−0.0358243	+	0.0620494i
$256$	14.2674	+	24.7118i	0.891712	+	1.54449i
$257$	4.62089	−	8.00361i	0.288243	−	0.499251i	−0.685147	−	0.728404i	$-0.740262\pi$
$257$	4.62089	−	8.00361i	0.288243	−	0.499251i	0.973390	+	0.229153i	$0.0735956\pi$
$258$	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
$262$	−57.7263			−3.56634
$263$	−0.186166			−0.0114795			−0.00573975	−	0.999984i	$-0.501827\pi$
$263$	−0.186166			−0.0114795			−0.00573975	+	0.999984i	$0.501827\pi$
$264$	−3.39593			−0.209005
$265$	19.8200			1.21753
$266$	21.3126	+	12.6702i	1.30676	+	0.776858i
$267$	0.461435	−	0.799229i	0.0282394	−	0.0489120i
$268$	−17.9378	−	31.0692i	−1.09573	−	1.89785i
$269$	6.39082	+	11.0692i	0.389655	+	0.674902i	0.992403	−	0.123029i	$-0.0392609\pi$
$269$	6.39082	+	11.0692i	0.389655	+	0.674902i	−0.602748	+	0.797932i	$0.705928\pi$
$270$	−7.18961			−0.437546
$271$	1.62095	−	2.80757i	0.0984658	−	0.170548i	−0.812584	−	0.582844i	$-0.801940\pi$
$271$	1.62095	−	2.80757i	0.0984658	−	0.170548i	0.911050	+	0.412296i	$0.135273\pi$
$272$	2.96082			0.179526
$273$	−6.36043	+	7.10950i	−0.384950	+	0.430287i
$274$	21.8061			1.31736
$275$	−0.782111	+	1.35466i	−0.0471631	+	0.0816888i
$276$	−11.4727			−0.690576
$277$	−11.9399	−	20.6806i	−0.717401	−	1.24258i	−0.962026	−	0.272957i	$-0.911998\pi$
$277$	−11.9399	−	20.6806i	−0.717401	−	1.24258i	0.244625	−	0.969618i	$-0.421335\pi$
$278$	8.85569	+	15.3385i	0.531129	+	0.919943i
$279$	−4.44201	+	7.69379i	−0.265936	+	0.460615i
$280$	−41.5882	+	23.3085i	−2.48537	+	1.39295i
$281$	−2.18620			−0.130417			−0.0652087	−	0.997872i	$-0.520771\pi$
$281$	−2.18620			−0.130417			−0.0652087	+	0.997872i	$0.520771\pi$
$282$	22.7357			1.35389
$283$	17.1545			1.01973			0.509864	−	0.860255i	$-0.329696\pi$
$283$	17.1545			1.01973			0.509864	+	0.860255i	$0.329696\pi$
$284$	4.83073			0.286651
$285$	−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
$289$	8.41762	−	14.5797i	0.495154	−	0.857632i
$290$	31.9475	+	55.3347i	1.87602	+	3.24937i
$291$	−0.0841208	+	0.145702i	−0.00493125	+	0.00854117i
$292$	−6.57362			−0.384692
$293$	−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
$296$	−28.6232	+	49.5769i	−1.66369	+	2.88160i
$297$	0.531201			0.0308234
$298$	−15.9517	+	27.6291i	−0.924055	+	1.60051i
$299$	8.68383	−	2.97554i	0.502199	−	0.172080i
$300$	13.2696			0.766123
$301$	−20.5669	−	12.2269i	−1.18545	−	0.704745i
$302$	10.1098	+	17.5107i	0.581754	+	1.00763i
$303$	3.62859			0.208457
$304$	−13.3992	+	23.2081i	−0.768497	+	1.33108i
$305$	13.7393	+	23.7972i	0.786710	+	1.36262i
$306$	−1.03539			−0.0591896
$307$	14.6014			0.833347			0.416673	−	0.909056i	$-0.363196\pi$
$307$	14.6014			0.833347			0.416673	+	0.909056i	$0.363196\pi$
$308$	5.52473	−	3.09638i	0.314801	−	0.176433i
$309$	−4.47902	−	7.75790i	−0.254803	−	0.441331i
$310$	31.9363	−	55.3154i	1.81386	−	3.14170i
$311$	−3.03815	+	5.26223i	−0.172278	+	0.298393i	−0.939216	−	0.343328i	$-0.888446\pi$
$311$	−3.03815	+	5.26223i	−0.172278	+	0.298393i	0.766938	+	0.641721i	$0.221779\pi$
$312$	−17.3734	−	15.1482i	−0.983574	−	0.857598i
$313$	−1.61084	−	2.79006i	−0.0910501	−	0.157703i	0.816903	−	0.576775i	$-0.195689\pi$
$313$	−1.61084	−	2.79006i	−0.0910501	−	0.157703i	−0.907953	+	0.419071i	$0.862356\pi$
$314$	14.2033	+	24.6008i	0.801538	+	1.38831i
$315$	6.50536	−	3.64598i	0.366535	−	0.205428i
$316$	15.9465	−	27.6202i	0.897062	−	1.55376i
$317$	−5.62276	−	9.73891i	−0.315806	−	0.546992i	0.663803	−	0.747908i	$-0.268941\pi$
$317$	−5.62276	−	9.73891i	−0.315806	−	0.546992i	−0.979608	+	0.200916i	$0.935608\pi$
$318$	8.96815	+	15.5333i	0.502909	+	0.871064i
$319$	−2.36043	−	4.08838i	−0.132159	−	0.228905i
$320$	−0.360820	−	0.624958i	−0.0201704	−	0.0349362i
$321$	0.944099	−	1.63523i	0.0526944	−	0.0912695i
$322$	14.9881	−	8.40018i	0.835252	−	0.468124i
$323$	−0.745667	−	1.29153i	−0.0414900	−	0.0718629i
$324$	−2.25315	−	3.90257i	−0.125175	−	0.216809i
$325$	−10.0440	+	3.44159i	−0.557138	+	0.190905i
$326$	21.0815	−	36.5142i	1.16760	−	2.02233i
$327$	4.90716	−	8.49945i	0.271367	−	0.470021i
$328$	−34.8315	−	60.3300i	−1.92325	−	3.33117i
$329$	−20.5719	+	11.5297i	−1.13417	+	0.635653i
$330$	−3.81913			−0.210236
$331$	3.68603			0.202603			0.101301	−	0.994856i	$-0.467699\pi$
$331$	3.68603			0.202603			0.101301	+	0.994856i	$0.467699\pi$
$332$	−1.01187	−	1.75261i	−0.0555335	−	0.0961869i
$333$	4.47733	−	7.75496i	0.245356	−	0.424969i
$334$	−29.2802			−1.60214
$335$	−11.2199	−	19.4334i	−0.613008	−	1.06176i
$336$	−16.5884	−	9.86170i	−0.904972	−	0.538000i
$337$	31.9053			1.73799			0.868996	−	0.494819i	$-0.164766\pi$
$337$	31.9053			1.73799			0.868996	+	0.494819i	$0.164766\pi$
$338$	30.7078	+	12.5139i	1.67028	+	0.680665i
$339$	−3.53026	+	6.11459i	−0.191737	+	0.332099i
$340$	5.15581			0.279613
$341$	−2.35960	+	4.08695i	−0.127780	+	0.221321i
$342$	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
$345$	−7.17603			−0.386345
$346$	−22.0050	+	38.1137i	−1.18299	+	2.04901i
$347$	12.7426	+	22.0708i	0.684057	+	1.18482i	0.973732	+	0.227696i	$0.0731193\pi$
$347$	12.7426	+	22.0708i	0.684057	+	1.18482i	−0.289675	+	0.957125i	$0.593547\pi$
$348$	−20.0240	+	34.6826i	−1.07340	+	1.85918i
$349$	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
$353$	−13.0757			−0.695950			−0.347975	−	0.937504i	$-0.613131\pi$
$353$	−13.0757			−0.695950			−0.347975	+	0.937504i	$0.613131\pi$
$354$	−0.185882			−0.00987950
$355$	3.02156			0.160368
$356$	−4.15873			−0.220412
$357$	0.936853	−	0.525067i	0.0495835	−	0.0277895i
$358$	30.4380	−	52.7202i	1.60870	−	2.78635i
$359$	−1.93310	−	3.34823i	−0.102025	−	0.176713i	0.810494	−	0.585747i	$-0.199199\pi$
$359$	−1.93310	−	3.34823i	−0.102025	−	0.176713i	−0.912519	+	0.409034i	$0.865866\pi$
$360$	9.00965	+	15.6052i	0.474850	+	0.822465i
$361$	−5.50190			−0.289574
$362$	21.4811	−	37.2063i	1.12902	−	1.95552i
$363$	−10.7178			−0.562540
$364$	42.0763	+	8.80323i	2.20540	+	0.461415i
$365$	−4.11172			−0.215217
$366$	−12.4335	+	21.5354i	−0.649909	+	1.12567i
$367$	19.5627			1.02116			0.510582	−	0.859829i	$-0.329430\pi$
$367$	19.5627			1.02116			0.510582	+	0.859829i	$0.329430\pi$
$368$	9.28514	+	16.0823i	0.484022	+	0.838350i
$369$	5.44846	+	9.43700i	0.283635	+	0.491271i
$370$	−32.1903	+	55.7552i	−1.67349	+	2.89857i
$371$	−15.9918	−	9.50703i	−0.830255	−	0.493581i
$372$	40.0340			2.07567
$373$	16.9547			0.877881			0.438941	−	0.898516i	$-0.355354\pi$
$373$	16.9547			0.877881			0.438941	+	0.898516i	$0.355354\pi$
$374$	−0.550002			−0.0284400
$375$	−5.79316			−0.299158
$376$	−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	$0.494868\pi$
$380$	−23.3327	+	40.4134i	−1.19694	+	2.07316i
$381$	−9.40239	−	16.2854i	−0.481699	−	0.834327i
$382$	5.42341	−	9.39361i	0.277486	−	0.480619i
$383$	−20.7483			−1.06019			−0.530095	−	0.847938i	$-0.677844\pi$
$383$	−20.7483			−1.06019			−0.530095	+	0.847938i	$0.677844\pi$
$384$	−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
$387$	−4.52174	+	7.83189i	−0.229853	+	0.398117i
$388$	0.758147			0.0384891
$389$	−7.60442	+	13.1712i	−0.385559	+	0.667808i	−0.991847	−	0.127437i	$-0.959325\pi$
$389$	−7.60442	+	13.1712i	−0.385559	+	0.667808i	0.606287	+	0.795246i	$0.292658\pi$
$390$	−19.5385	−	17.0360i	−0.989369	−	0.862651i
$391$	−1.03344			−0.0522633
$392$	44.7359	+	1.14205i	2.25950	+	0.0576824i
$393$	−11.3156	−	19.5992i	−0.570796	−	0.988647i
$394$	−16.7920			−0.845968
$395$	9.97435	−	17.2761i	0.501864	−	0.869254i
$396$	−1.19687	−	2.07305i	−0.0601452	−	0.104175i
$397$	−14.0140			−0.703342			−0.351671	−	0.936124i	$-0.614386\pi$
$397$	−14.0140			−0.703342			−0.351671	+	0.936124i	$0.614386\pi$
$398$	11.5387			0.578383
$399$	−0.124045	+	9.71964i	−0.00621002	+	0.486590i
$400$	−10.7395	−	18.6013i	−0.536973	−	0.930064i
$401$	−6.96093	+	12.0567i	−0.347612	+	0.602082i	−0.985825	−	0.167778i	$-0.946341\pi$
$401$	−6.96093	+	12.0567i	−0.347612	+	0.602082i	0.638213	+	0.769860i	$0.279674\pi$
$402$	10.1535	−	17.5864i	0.506412	−	0.877131i
$403$	−30.3023	+	10.3832i	−1.50946	+	0.517222i
$404$	−8.17576	−	14.1608i	−0.406759	−	0.704528i
$405$	−1.40932	−	2.44101i	−0.0700295	−	0.121295i
$406$	0.765370	−	59.9711i	0.0379847	−	2.97632i
$407$	2.37836	−	4.11944i	0.117891	−	0.204193i
$408$	1.29750	+	2.24734i	0.0642359	+	0.111260i
$409$	−8.98300	−	15.5590i	−0.444181	−	0.769344i	0.553814	−	0.832641i	$-0.313172\pi$
$409$	−8.98300	−	15.5590i	−0.444181	−	0.769344i	−0.997995	+	0.0632966i	$0.979839\pi$
$410$	−39.1723	−	67.8484i	−1.93458	−	3.35079i
$411$	4.27446	+	7.40359i	0.210844	+	0.365192i
$412$	−20.1838	+	34.9594i	−0.994385	+	1.72232i
$413$	0.168191	−	0.0942639i	0.00827613	−	0.00463842i
$414$	−3.24701	−	5.62398i	−0.159582	−	0.276403i
$415$	−0.632912	−	1.09624i	−0.0310684	−	0.0538121i
$416$	−4.03455	+	20.5912i	−0.197810	+	1.00957i
$417$	−3.47181	+	6.01335i	−0.170015	+	0.294475i
$418$	2.48904	−	4.31115i	0.121743	−	0.210865i
$419$	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	$0.721504\pi$
$420$	−28.8862	−	17.1727i	−1.40950	−	0.837940i
$421$	4.42295			0.215562			0.107781	−	0.994175i	$-0.465626\pi$
$421$	4.42295			0.215562			0.107781	+	0.994175i	$0.465626\pi$
$422$	−22.8124			−1.11049
$423$	4.45669	+	7.71921i	0.216691	+	0.375321i
$424$	22.4768	−	38.9310i	1.09157	−	1.89066i
$425$	1.19530			0.0579808
$426$	1.36719	+	2.36805i	0.0662407	+	0.114732i
$427$	0.329154	−	25.7911i	0.0159289	−	1.24812i
$428$	−8.50878			−0.411287
$429$	1.44359	+	1.25870i	0.0696972	+	0.0607704i
$430$	32.5096	−	56.3082i	1.56775	−	2.71542i
$431$	6.44436			0.310414			0.155207	−	0.987882i	$-0.450396\pi$
$431$	6.44436			0.310414			0.155207	+	0.987882i	$0.450396\pi$
$432$	−3.64706	+	6.31689i	−0.175469	+	0.303921i
$433$	−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
$436$	−44.2263			−2.11805
$437$	4.67684	−	8.10052i	0.223724	−	0.387501i
$438$	−1.86047	−	3.22242i	−0.0888965	−	0.153973i
$439$	2.63948	−	4.57172i	0.125976	−	0.218196i	−0.796138	−	0.605115i	$-0.793127\pi$
$439$	2.63948	−	4.57172i	0.125976	−	0.218196i	0.922114	+	0.386919i	$0.126461\pi$
$440$	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	0.996716	+	0.0809788i	$0.0258046\pi$
$443$	11.9653	+	20.7245i	0.568488	+	0.984649i	−0.428228	+	0.903671i	$0.640862\pi$
$444$	−40.3523			−1.91504
$445$	−2.60123			−0.123310
$446$	−23.6434			−1.11955
$447$	−12.5075			−0.591582
$448$	−0.00864420	+	0.677323i	−0.000408400	+	0.0320005i
$449$	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
$451$	2.89423	+	5.01295i	0.136284	+	0.236050i
$452$	31.8168			1.49654
$453$	−3.96347	+	6.86494i	−0.186220	+	0.322543i
$454$	−42.9373			−2.01515
$455$	26.3182	+	5.50631i	1.23382	+	0.258140i
$456$	−23.4874			−1.09990
$457$	1.12289	−	1.94491i	0.0525267	−	0.0909790i	−0.838567	−	0.544799i	$-0.816606\pi$
$457$	1.12289	−	1.94491i	0.0525267	−	0.0909790i	0.891093	+	0.453820i	$0.149939\pi$
$458$	4.35307			0.203406
$459$	−0.202959	−	0.351536i	−0.00947333	−	0.0164083i
$460$	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	$0.310366\pi$
$462$	3.08147	+	1.83191i	0.143363	+	0.0852283i
$463$	2.51845			0.117042			0.0585212	−	0.998286i	$-0.481361\pi$
$463$	2.51845			0.117042			0.0585212	+	0.998286i	$0.481361\pi$
$464$	64.8238			3.00937
$465$	25.0408			1.16124
$466$	−61.5089			−2.84935
$467$	0.988420	+	1.71199i	0.0457386	+	0.0792216i	0.887988	−	0.459866i	$-0.152103\pi$
$467$	0.988420	+	1.71199i	0.0457386	+	0.0792216i	−0.842250	+	0.539088i	$0.818769\pi$
$468$	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
$471$	−5.56829	+	9.64457i	−0.256573	+	0.444398i
$472$	0.232937	+	0.403459i	0.0107218	+	0.0185707i
$473$	−2.40195	+	4.16031i	−0.110442	+	0.191291i
$474$	18.0527			0.829190
$475$	−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
$478$	−26.4732	+	45.8529i	−1.21086	+	2.09726i
$479$	17.2361			0.787539			0.393769	−	0.919209i	$-0.371171\pi$
$479$	17.2361			0.787539			0.393769	+	0.919209i	$0.371171\pi$
$480$	8.20162	−	14.2056i	0.374351	−	0.648395i
$481$	30.5432	−	10.4657i	1.39265	−	0.477195i
$482$	51.0627			2.32584
$483$	5.79000	+	3.44211i	0.263454	+	0.156622i
$484$	24.1488	+	41.8270i	1.09767	+	1.90123i
$485$	0.474211			0.0215328
$486$	1.27537	−	2.20901i	0.0578521	−	0.100203i
$487$	−12.6481	−	21.9072i	−0.573141	−	0.992709i	−0.996241	−	0.0866257i	$-0.972392\pi$
$487$	−12.6481	−	21.9072i	−0.573141	−	0.992709i	0.423100	−	0.906083i	$-0.360942\pi$
$488$	62.3240			2.82127
$489$	16.5297			0.747498
$490$	50.3109	+	1.28438i	2.27281	+	0.0580222i
$491$	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	$0.540258\pi$
$492$	24.5524	−	42.5259i	1.10691	−	1.91722i
$493$	−1.80373	+	3.12414i	−0.0812357	+	0.140704i
$494$	31.9645	−	10.9527i	1.43815	−	0.492787i
$495$	−0.748630	−	1.29667i	−0.0336484	−	0.0582808i
$496$	−32.4005	−	56.1194i	−1.45483	−	2.51983i
$497$	−2.43795	−	1.44935i	−0.109357	−	0.0650120i
$498$	0.572758	−	0.992047i	0.0256659	−	0.0444547i
$499$	−5.71040	−	9.89071i	−0.255633	−	0.442769i	0.709434	−	0.704771i	$-0.248950\pi$
$499$	−5.71040	−	9.89071i	−0.255633	−	0.442769i	−0.965067	+	0.262002i	$0.915617\pi$
$500$	13.0529	+	22.6082i	0.583742	+	1.01107i
$501$	−5.73954	−	9.94117i	−0.256424	−	0.444139i
$502$	−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	$0.0731249\pi$
$504$	0.215845	−	16.9127i	0.00961451	−	0.753352i
$505$	−5.11384	−	8.85743i	−0.227563	−	0.394150i
$506$	−1.72481	−	2.98746i	−0.0766773	−	0.132809i
$507$	1.77068	+	12.8788i	0.0786385	+	0.571970i
$508$	−42.3699	+	73.3869i	−1.87986	+	3.25602i
$509$	−18.9035	+	32.7419i	−0.837884	+	1.45126i	0.0537772	+	0.998553i	$0.482874\pi$
$509$	−18.9035	+	32.7419i	−0.837884	+	1.45126i	−0.891661	+	0.452704i	$0.850459\pi$
$510$	1.45920	+	2.52741i	0.0646144	+	0.111915i
$511$	3.31755	+	1.97226i	0.146760	+	0.0872476i
$512$	50.8127			2.24563
$513$	3.67398			0.162210
$514$	−11.7867	−	20.4152i	−0.519889	−	0.900474i
$515$	−12.6247	+	21.8667i	−0.556312	+	0.963560i
$516$	40.7526			1.79403
$517$	2.36740	+	4.10045i	0.104118	+	0.180338i
$518$	52.7167	−	29.5455i	2.31624	−	1.29816i
$519$	−17.2538			−0.757356
$520$	−12.4923	+	63.7572i	−0.547823	+	2.79594i
$521$	3.83608	−	6.64429i	0.168062	−	0.291092i	−0.769676	−	0.638434i	$-0.779582\pi$
$521$	3.83608	−	6.64429i	0.168062	−	0.291092i	0.937738	+	0.347342i	$0.112916\pi$
$522$	−22.6688			−0.992187
$523$	−18.2990	+	31.6949i	−0.800161	+	1.38592i	0.119349	+	0.992852i	$0.461919\pi$
$523$	−18.2990	+	31.6949i	−0.800161	+	1.38592i	−0.919510	+	0.393067i	$0.871414\pi$
$524$	−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
$527$	3.60619			0.157088
$528$	−1.93732	+	3.35554i	−0.0843110	+	0.146031i
$529$	8.25913	+	14.3052i	0.359092	+	0.621966i
$530$	25.2779	−	43.7826i	1.09800	−	1.90180i
$531$	−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
$535$	−5.32213			−0.230096
$536$	−50.8955			−2.19835
$537$	23.8660			1.02989
$538$	32.6027			1.40560
$539$	−3.71720	−	0.0948955i	−0.160111	−	0.00408744i
$540$	−6.35080	+	10.9999i	−0.273295	+	0.473360i
$541$	7.93930	+	13.7513i	0.341337	+	0.591214i	0.984681	−	0.174364i	$-0.0557868\pi$
$541$	7.93930	+	13.7513i	0.341337	+	0.591214i	−0.643344	+	0.765577i	$0.722453\pi$
$542$	−4.13463	−	7.16139i	−0.177598	−	0.307608i
$543$	16.8430			0.722801
$544$	1.18114	−	2.04579i	0.0506408	−	0.0877125i
$545$	−27.6630			−1.18495
$546$	7.59304	+	23.1175i	0.324952	+	0.989338i
$547$	−22.5218			−0.962962			−0.481481	−	0.876456i	$-0.659901\pi$
$547$	−22.5218			−0.962962			−0.481481	+	0.876456i	$0.659901\pi$
$548$	19.2620	−	33.3627i	0.822832	−	1.42519i
$549$	−9.74891			−0.416073
$550$	1.99497	+	3.45538i	0.0850656	+	0.147338i
$551$	−16.3256	−	28.2767i	−0.695492	−	1.20463i
$552$	−8.13796	+	14.0954i	−0.346374	+	0.599938i
$553$	−16.3346	+	9.15487i	−0.694618	+	0.389305i
$554$	−60.9114			−2.58788
$555$	−25.2399			−1.07137
$556$	31.2900			1.32699
$557$	0.272732			0.0115560			0.00577802	−	0.999983i	$-0.498161\pi$
$557$	0.272732			0.0115560			0.00577802	+	0.999983i	$0.498161\pi$
$558$	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
$562$	−2.78821	+	4.82933i	−0.117614	+	0.203713i
$563$	−1.54443	−	2.67504i	−0.0650901	−	0.112739i	0.831644	−	0.555309i	$-0.187400\pi$
$563$	−1.54443	−	2.67504i	−0.0650901	−	0.112739i	−0.896734	+	0.442570i	$0.854067\pi$
$564$	20.0831	−	34.7850i	0.845653	−	1.46471i
$565$	19.9010			0.837242
$566$	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
$569$	−12.2929	+	21.2918i	−0.515343	+	0.892600i	0.484498	+	0.874792i	$0.339002\pi$
$569$	−12.2929	+	21.2918i	−0.515343	+	0.892600i	−0.999841	+	0.0178082i	$0.994331\pi$
$570$	−26.4145			−1.10638
$571$	14.4509	−	25.0297i	0.604751	−	1.04746i	−0.387339	−	0.921937i	$-0.626606\pi$
$571$	14.4509	−	25.0297i	0.604751	−	1.04746i	0.992091	−	0.125523i	$-0.0400609\pi$
$572$	1.65952	−	8.46974i	0.0693880	−	0.354137i
$573$	4.25241			0.177647
$574$	−0.938455	+	73.5333i	−0.0391704	+	3.06922i
$575$	3.74848	+	6.49256i	0.156323	+	0.270759i
$576$	0.256025			0.0106677
$577$	−2.80534	+	4.85899i	−0.116788	+	0.202283i	−0.918493	−	0.395437i	$-0.870593\pi$
$577$	−2.80534	+	4.85899i	−0.116788	+	0.202283i	0.801705	+	0.597720i	$0.203926\pi$
$578$	−21.4712	−	37.1892i	−0.893083	−	1.54687i
$579$	−1.75269			−0.0728394
$580$	112.881			4.68712
$581$	−0.0151627	+	1.18809i	−0.000629056	+	0.0492902i
$582$	0.214571	+	0.371647i	0.00889424	+	0.0154053i
$583$	−1.86765	+	3.23486i	−0.0773500	+	0.133974i
$584$	−4.66288	+	8.07635i	−0.192951	+	0.334202i
$585$	1.95408	−	9.97309i	0.0807913	−	0.412337i
$586$	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	$-0.395396\pi$
$588$	15.0697	+	27.7116i	0.621465	+	1.14281i
$589$	−16.3198	+	28.2668i	−0.672448	+	1.16471i
$590$	0.261966	+	0.453738i	0.0107850	+	0.0186801i
$591$	−3.29158	−	5.70119i	−0.135398	−	0.234516i
$592$	32.6582	+	56.5656i	1.34224	+	2.32483i
$593$	6.97018	+	12.0727i	0.286231	+	0.495766i	0.972907	−	0.231197i	$-0.0742643\pi$
$593$	6.97018	+	12.0727i	0.286231	+	0.495766i	−0.686676	+	0.726963i	$0.740931\pi$
$594$	0.677479	−	1.17343i	0.0277973	−	0.0481463i
$595$	−2.60201	−	1.54688i	−0.106672	−	0.0634159i
$596$	28.1811	+	48.8112i	1.15434	+	1.99938i
$597$	2.26183	+	3.91760i	0.0925705	+	0.160337i
$598$	4.50212	−	22.9776i	0.184105	−	0.939623i
$599$	2.84098	−	4.92072i	0.116079	−	0.201055i	−0.802131	−	0.597148i	$-0.796301\pi$
$599$	2.84098	−	4.92072i	0.116079	−	0.201055i	0.918211	+	0.396092i	$0.129634\pi$
$600$	9.41258	−	16.3031i	0.384267	−	0.665570i
$601$	−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	$-0.380117\pi$
$602$	−53.2397	+	29.8386i	−2.16989	+	1.21613i
$603$	7.96122			0.324206
$604$	35.7212			1.45347
$605$	15.1048	+	26.1623i	0.614098	+	1.06365i
$606$	4.62781	−	8.01560i	0.187992	−	0.325611i
$607$	−19.4551			−0.789660			−0.394830	−	0.918754i	$-0.629196\pi$
$607$	−19.4551			−0.789660			−0.394830	+	0.918754i	$0.629196\pi$
$608$	10.6905	+	18.5165i	0.433557	+	0.750942i
$609$	20.5113	−	11.4958i	0.831162	−	0.465832i
$610$	70.0908			2.83790
$611$	−6.17939	+	31.5379i	−0.249992	+	1.27589i
$612$	−0.914594	+	1.58412i	−0.0369703	+	0.0640344i
$613$	45.9561			1.85615			0.928075	−	0.372393i	$-0.121463\pi$
$613$	45.9561			1.85615			0.928075	+	0.372393i	$0.121463\pi$
$614$	18.6222	−	32.2547i	0.751532	−	1.30169i
$615$	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	$0.154997\pi$
$618$	−22.8497			−0.919149
$619$	9.04766	−	15.6710i	0.363656	−	0.629871i	−0.624903	−	0.780702i	$-0.714862\pi$
$619$	9.04766	−	15.6710i	0.363656	−	0.629871i	0.988560	+	0.150831i	$0.0481949\pi$
$620$	−56.4206	−	97.7234i	−2.26591	−	3.92467i
$621$	1.27296	−	2.20484i	0.0510823	−	0.0884771i
$622$	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
$626$	−8.21768			−0.328445
$627$	1.95162			0.0779402
$628$	50.1848			2.00259
$629$	−3.63486			−0.144931
$630$	0.242744	−	19.0204i	0.00967115	−	0.757790i
$631$	−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
$633$	−4.47171	−	7.74522i	−0.177734	−	0.307845i
$634$	−28.6845			−1.13921
$635$	−26.5019	+	45.9026i	−1.05170	+	1.82159i
$636$	31.6873			1.25648
$637$	−18.5937	−	17.0668i	−0.736709	−	0.676210i
$638$	−12.0417			−0.476735
$639$	−0.535997	+	0.928375i	−0.0212037	+	0.0367259i
$640$	30.9658			1.22403
$641$	−3.75614	−	6.50583i	−0.148359	−	0.256965i	0.782262	−	0.622949i	$-0.214066\pi$
$641$	−3.75614	−	6.50583i	−0.148359	−	0.256965i	−0.930621	+	0.365984i	$0.880732\pi$
$642$	−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	$0.941096\pi$
$644$	0.387355	−	30.3514i	0.0152639	−	1.19601i
$645$	25.4903			1.00368
$646$	−3.80401			−0.149667
$647$	−12.9513			−0.509169			−0.254584	−	0.967051i	$-0.581939\pi$
$647$	−12.9513			−0.509169			−0.254584	+	0.967051i	$0.581939\pi$
$648$	−6.39292			−0.251138
$649$	−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
$653$	13.5560	−	23.4796i	0.530486	−	0.918829i	−0.468881	−	0.883261i	$-0.655343\pi$
$653$	13.5560	−	23.4796i	0.530486	−	0.918829i	0.999367	−	0.0355676i	$-0.0113239\pi$
$654$	−12.5169	−	21.6799i	−0.489450	−	0.847752i
$655$	−31.8945	+	55.2428i	−1.24622	+	2.15852i
$656$	−79.4833			−3.10330
$657$	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	$-0.201312\pi$
$660$	−3.37355	+	5.84316i	−0.131315	+	0.227445i
$661$	−6.97895			−0.271450			−0.135725	−	0.990747i	$-0.543336\pi$
$661$	−6.97895			−0.271450			−0.135725	+	0.990747i	$0.543336\pi$
$662$	4.70106	−	8.14248i	0.182712	−	0.316466i
$663$	0.281412	−	1.43625i	0.0109291	−	0.0557793i
$664$	−2.87100			−0.111417
$665$	23.9005	−	13.3952i	0.926823	−	0.519445i
$666$	−11.4205	−	19.7809i	−0.442536	−	0.766495i
$667$	−22.6260			−0.876082
$668$	−25.8641	+	44.7979i	−1.00071	+	1.73328i
$669$	−4.63460	−	8.02737i	−0.179184	−	0.310356i
$670$	−57.2381			−2.21130
$671$	−5.17863			−0.199919
$672$	−13.4315	+	7.52779i	−0.518131	+	0.290391i
$673$	−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	$-0.482865\pi$
$674$	40.6911	−	70.4791i	1.56736	−	2.71475i
$675$	−1.47234	+	2.55018i	−0.0566706	+	0.0981563i
$676$	46.2710	−	35.9281i	1.77965	−	1.38185i
$677$	−9.16375	−	15.8721i	−0.352192	−	0.610014i	0.634441	−	0.772971i	$-0.281230\pi$
$677$	−9.16375	−	15.8721i	−0.352192	−	0.610014i	−0.986633	+	0.162957i	$0.947897\pi$
$678$	9.00479	+	15.5968i	0.345827	+	0.598990i
$679$	−0.382618	−	0.227464i	−0.0146835	−	0.00872927i
$680$	3.65718	−	6.33443i	0.140247	−	0.242914i
$681$	−8.41663	−	14.5780i	−0.322526	−	0.558631i
$682$	6.01874	+	10.4248i	0.230469	+	0.399185i
$683$	5.62262	+	9.73866i	0.215143	+	0.372639i	0.953317	−	0.301972i	$-0.0976448\pi$
$683$	5.62262	+	9.73866i	0.215143	+	0.372639i	−0.738173	+	0.674611i	$0.764311\pi$
$684$	−8.27801	−	14.3379i	−0.316518	−	0.548225i
$685$	12.0481	−	20.8680i	0.460336	−	0.797325i
$686$	−39.9774	−	25.1688i	−1.52634	−	0.960950i
$687$	0.853294	+	1.47795i	0.0325552	+	0.0563873i
$688$	−32.9821	−	57.1267i	−1.25743	−	2.17793i
$689$	−23.9845	+	8.21837i	−0.913737	+	0.313095i
$690$	−9.15211	+	15.8519i	−0.348415	+	0.603473i
$691$	5.58742	−	9.67770i	0.212556	−	0.368157i	−0.739958	−	0.672653i	$-0.765155\pi$
$691$	5.58742	−	9.67770i	0.212556	−	0.368157i	0.952514	+	0.304496i	$0.0984880\pi$
$692$	38.8753	+	67.3339i	1.47782	+	2.55965i
$693$	−0.0179350	+	1.40531i	−0.000681295	+	0.0533834i
$694$	65.0061			2.46760
$695$	19.5715			0.742389
$696$	28.4074	+	49.2030i	1.07678	+	1.86504i
$697$	2.21163	−	3.83065i	0.0837714	−	0.145096i
$698$	4.77847			0.180868
$699$	−12.0571	−	20.8834i	−0.456040	−	0.789884i
$700$	−0.448025	+	35.1053i	−0.0169338	+	1.32686i
$701$	−33.0766			−1.24929			−0.624643	−	0.780910i	$-0.714756\pi$
$701$	−33.0766			−1.24929			−0.624643	+	0.780910i	$0.714756\pi$
$702$	8.70026	−	2.98117i	0.328370	−	0.112517i
$703$	16.4496	−	28.4915i	0.620409	−	1.07458i
$704$	0.136001			0.00512572
$705$	12.5618	−	21.7576i	0.473103	−	0.819439i
$706$	−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
$709$	34.0419			1.27847			0.639235	−	0.769012i	$-0.279251\pi$
$709$	34.0419			1.27847			0.639235	+	0.769012i	$0.279251\pi$
$710$	3.85361	−	6.67465i	0.144624	−	0.250495i
$711$	3.53872	+	6.12924i	0.132712	+	0.229865i
$712$	−2.94992	+	5.10941i	−0.110553	+	0.191483i
$713$	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
$717$	−20.7572			−0.775193
$718$	−9.86171			−0.368036
$719$	−3.06621			−0.114351			−0.0571753	−	0.998364i	$-0.518209\pi$
$719$	−3.06621			−0.114351			−0.0571753	+	0.998364i	$0.518209\pi$
$720$	20.5594			0.766205
$721$	20.6750	−	11.5875i	0.769978	−	0.431540i
$722$	−7.01697	+	12.1537i	−0.261145	+	0.452316i
$723$	10.0094	+	17.3368i	0.372253	+	0.644761i
$724$	−37.9497	−	65.7309i	−1.41039	−	2.44287i
$725$	26.1698			0.971924
$726$	−13.6692	+	23.6758i	−0.507312	+	0.878690i
$727$	13.3001			0.493274			0.246637	−	0.969108i	$-0.420674\pi$
$727$	13.3001			0.493274			0.246637	+	0.969108i	$0.420674\pi$
$728$	40.6617	−	45.4505i	1.50702	−	1.68451i
$729$	1.00000			0.0370370
$730$	−5.24397	+	9.08282i	−0.194088	+	0.336170i
$731$	3.67092			0.135774
$732$	21.9657	+	38.0458i	0.811877	+	1.40621i
$733$	−16.2567	−	28.1575i	−0.600457	−	1.04002i	−0.992752	−	0.120182i	$-0.961652\pi$
$733$	−16.2567	−	28.1575i	−0.600457	−	1.04002i	0.392295	−	0.919839i	$-0.371681\pi$
$734$	24.9497	−	43.2142i	0.920911	−	1.59506i
$735$	9.42593	+	17.3333i	0.347681	+	0.639347i
$736$	14.8162			0.546133
$737$	4.22901			0.155778
$738$	27.7952			1.02316
$739$	−15.7805			−0.580496			−0.290248	−	0.956951i	$-0.593738\pi$
$739$	−15.7805			−0.580496			−0.290248	+	0.956951i	$0.593738\pi$
$740$	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	$0.768310\pi$
$744$	28.3974	−	49.1858i	1.04110	−	1.80324i
$745$	17.6270	+	30.5308i	0.645802	+	1.11856i
$746$	21.6236	−	37.4531i	0.791695	−	1.37126i
$747$	0.449091			0.0164314
$748$	−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
$751$	−3.95766	+	6.85487i	−0.144417	+	0.250138i	−0.929155	−	0.369689i	$-0.879464\pi$
$751$	−3.95766	+	6.85487i	−0.144417	+	0.250138i	0.784738	+	0.619827i	$0.212797\pi$
$752$	−65.0152			−2.37086
$753$	10.4342	−	18.0725i	0.380242	−	0.658599i
$754$	−61.6047	−	53.7144i	−2.24351	−	1.95616i
$755$	22.3432			0.813151
$756$	10.4005	−	5.82902i	0.378261	−	0.211999i
$757$	−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	$-0.440270\pi$
$758$	86.7991			3.15268
$759$	0.676200	−	1.17121i	0.0245445	−	0.0425123i
$760$	33.1012	+	57.3330i	1.20071	+	2.07969i
$761$	6.65156			0.241119			0.120559	−	0.992706i	$-0.461531\pi$
$761$	6.65156			0.241119			0.120559	+	0.992706i	$0.461531\pi$
$762$	−47.9662			−1.73763
$763$	22.3199	+	13.2690i	0.808036	+	0.480372i
$764$	−9.58131	−	16.5953i	−0.346640	−	0.600397i
$765$	−0.572068	+	0.990850i	−0.0206831	+	0.0358243i
$766$	−26.4619	+	45.8333i	−0.956106	+	1.65602i
$767$	0.0505212	−	0.257846i	0.00182421	−	0.00931029i
$768$	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	$0.662887\pi$
$770$	0.128946	−	10.1036i	0.00464689	−	0.364110i
$771$	4.62089	−	8.00361i	0.166417	−	0.288243i
$772$	3.94907	+	6.83999i	0.142130	+	0.246177i
$773$	5.46081	+	9.45840i	0.196412	+	0.340195i	0.947362	−	0.320163i	$-0.103738\pi$
$773$	5.46081	+	9.45840i	0.196412	+	0.340195i	−0.750951	+	0.660358i	$0.770404\pi$
$774$	11.5338	+	19.9771i	0.414574	+	0.718064i
$775$	−13.0803	−	22.6558i	−0.469860	−	0.813821i
$776$	0.537778	−	0.931458i	0.0193051	−	0.0334374i
$777$	20.3649	+	12.1068i	0.730585	+	0.434328i
$778$	19.3969	+	33.5965i	0.695414	+	1.20449i
$779$	20.0175	+	34.6713i	0.717201	+	1.24223i
$780$	−43.3235	+	14.8449i	−1.55123	+	0.531533i
$781$	−0.284722	+	0.493154i	−0.0101882	+	0.0176464i
$782$	−1.31802	+	2.28288i	−0.0471323	+	0.0816355i
$783$	−4.44357	−	7.69648i	−0.158800	−	0.275050i
$784$	26.6496	−	43.5523i	0.951770	−	1.55544i
$785$	31.3900			1.12036
$786$	−57.7263			−2.05903
$787$	−4.16463	−	7.21336i	−0.148453	−	0.257128i	0.782203	−	0.623024i	$-0.214096\pi$
$787$	−4.16463	−	7.21336i	−0.148453	−	0.257128i	−0.930656	+	0.365896i	$0.880763\pi$
$788$	−14.8329	+	25.6913i	−0.528398	+	0.915213i
$789$	−0.186166			−0.00662769
$790$	−25.4420	−	44.0669i	−0.905186	−	1.56783i
$791$	−16.0572	−	9.54588i	−0.570927	−	0.339412i
$792$	−3.39593			−0.120669
$793$	−26.4936	−	23.1003i	−0.940816	−	0.820316i
$794$	−17.8730	+	30.9570i	−0.634291	+	1.09862i
$795$	19.8200			0.702944
$796$	10.1925	−	17.6539i	0.361263	−	0.625725i
$797$	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
$800$	−17.1368			−0.605879
$801$	0.461435	−	0.799229i	0.0163040	−	0.0282394i
$802$	17.7555	+	30.7535i	0.626970	+	1.08594i
$803$	0.387448	−	0.671080i	0.0136728	−	0.0236819i
$804$	−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
$808$	−23.1973			−0.816079
$809$	−3.39213			−0.119261			−0.0596305	−	0.998221i	$-0.518992\pi$
$809$	−3.39213			−0.119261			−0.0596305	+	0.998221i	$0.518992\pi$
$810$	−7.18961			−0.252617
$811$	−11.0351			−0.387496			−0.193748	−	0.981051i	$-0.562064\pi$
$811$	−11.0351			−0.387496			−0.193748	+	0.981051i	$0.562064\pi$
$812$	−91.0781	−	54.1453i	−3.19621	−	1.90013i
$813$	1.62095	−	2.80757i	0.0568492	−	0.0984658i
$814$	−6.06659	−	10.5076i	−0.212634	−	0.368293i
$815$	−23.2955	−	40.3491i	−0.816007	−	1.41337i
$816$	2.96082			0.103649
$817$	−16.6128	+	28.7742i	−0.581207	+	1.00668i
$818$	−45.8267			−1.60229
$819$	−6.36043	+	7.10950i	−0.222251	+	0.248426i
$820$	−138.408			−4.83342
$821$	−12.0868	+	20.9349i	−0.421832	+	0.730634i	−0.996119	−	0.0880198i	$-0.971946\pi$
$821$	−12.0868	+	20.9349i	−0.421832	+	0.730634i	0.574287	+	0.818654i	$0.305279\pi$
$822$	21.8061			0.760576
$823$	−2.99117	−	5.18086i	−0.104266	−	0.180594i	0.809172	−	0.587571i	$-0.199916\pi$
$823$	−2.99117	−	5.18086i	−0.104266	−	0.180594i	−0.913438	+	0.406978i	$0.866583\pi$
$824$	28.6340	+	49.5956i	0.997514	+	1.72774i
$825$	−0.782111	+	1.35466i	−0.0272296	+	0.0471631i
$826$	0.00627595	−	0.491757i	0.000218368	−	0.0171104i
$827$	11.9530			0.415647			0.207824	−	0.978166i	$-0.433362\pi$
$827$	11.9530			0.415647			0.207824	+	0.978166i	$0.433362\pi$
$828$	−11.4727			−0.398704
$829$	38.7069			1.34435			0.672174	−	0.740393i	$-0.265361\pi$
$829$	38.7069			1.34435			0.672174	+	0.740393i	$0.265361\pi$
$830$	−3.22879			−0.112073
$831$	−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
$835$	−16.1777	+	28.0205i	−0.559851	+	0.969690i
$836$	−4.39729	−	7.61633i	−0.152083	−	0.263416i
$837$	−4.44201	+	7.69379i	−0.153538	+	0.265936i
$838$	35.9368			1.24142
$839$	−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
$842$	5.64091	−	9.77035i	0.194399	−	0.336708i
$843$	−2.18620			−0.0752966
$844$	−20.1508	+	34.9023i	−0.693620	+	1.20139i
$845$	28.9419	−	22.4726i	0.995632	−	0.773081i
$846$	22.7357			0.781671
$847$	0.361868	−	28.3544i	0.0124339	−	0.974268i
$848$	−25.6453	−	44.4190i	−0.880664	−	1.52536i
$849$	17.1545			0.588740
$850$	1.52446	−	2.64044i	0.0522885	−	0.0905663i
$851$	−11.3990	−	19.7436i	−0.390751	−	0.676801i
$852$	4.83073			0.165498
$853$	−28.3961			−0.972265			−0.486133	−	0.873885i	$-0.661593\pi$
$853$	−28.3961			−0.972265			−0.486133	+	0.873885i	$0.661593\pi$
$854$	−56.5529	−	33.6203i	−1.93520	−	1.15046i
$855$	−5.17779	−	8.96820i	−0.177077	−	0.306706i
$856$	−6.03555	+	10.4539i	−0.206291	+	0.357306i
$857$	−9.71017	+	16.8185i	−0.331693	+	0.574509i	−0.982844	−	0.184439i	$-0.940953\pi$
$857$	−9.71017	+	16.8185i	−0.331693	+	0.574509i	0.651151	+	0.758948i	$0.274286\pi$
$858$	4.62159	−	1.58360i	0.157778	−	0.0540632i
$859$	3.02708	+	5.24306i	0.103283	+	0.178891i	0.913035	−	0.407881i	$-0.133732\pi$
$859$	3.02708	+	5.24306i	0.103283	+	0.178891i	−0.809753	+	0.586771i	$0.800399\pi$
$860$	−57.4333	−	99.4775i	−1.95846	−	3.39215i
$861$	−25.1499	+	14.0955i	−0.857106	+	0.480372i
$862$	8.21895	−	14.2356i	0.279939	−	0.484868i
$863$	8.90178	+	15.4183i	0.303020	+	0.524846i	0.976819	−	0.214069i	$-0.0686717\pi$
$863$	8.90178	+	15.4183i	0.303020	+	0.524846i	−0.673798	+	0.738915i	$0.735338\pi$
$864$	2.90979	+	5.03990i	0.0989930	+	0.171461i
$865$	24.3160	+	42.1165i	0.826769	+	1.43201i
$866$	26.6096	+	46.0891i	0.904229	+	1.56617i
$867$	8.41762	−	14.5797i	0.285877	−	0.495154i
$868$	−1.35168	+	105.911i	−0.0458789	+	3.59487i
$869$	1.87977	+	3.25586i	0.0637669	+	0.110447i
$870$	31.9475	+	55.3347i	1.08312	+	1.87602i
$871$	21.6354	+	18.8643i	0.733088	+	0.639194i
$872$	−31.3711	+	54.3363i	−1.06236	+	1.84006i
$873$	−0.0841208	+	0.145702i	−0.00284706	+	0.00493125i
$874$	−11.9294	−	20.6624i	−0.403519	−	0.698915i
$875$	0.195596	−	15.3260i	0.00661234	−	0.518114i
$876$	−6.57362			−0.222102
$877$	43.2093			1.45908			0.729538	−	0.683941i	$-0.239735\pi$
$877$	43.2093			1.45908			0.729538	+	0.683941i	$0.239735\pi$
$878$	−6.73265	−	11.6613i	−0.227216	−	0.393549i
$879$	−1.83891	+	3.18509i	−0.0620249	+	0.107430i
$880$	10.9212			0.368153
$881$	−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	$0.929708\pi$
$882$	−9.31932	+	15.2302i	−0.313798	+	0.512827i
$883$	−15.1305			−0.509181			−0.254591	−	0.967049i	$-0.581941\pi$
$883$	−15.1305			−0.509181			−0.254591	+	0.967049i	$0.581941\pi$
$884$	−6.23913	+	2.13786i	−0.209845	+	0.0719039i
$885$	−0.102702	+	0.177885i	−0.00345228	+	0.00597953i
$886$	61.0407			2.05070
$887$	−7.90045	+	13.6840i	−0.265271	+	0.459463i	−0.967635	−	0.252355i	$-0.918795\pi$
$887$	−7.90045	+	13.6840i	−0.265271	+	0.459463i	0.702363	+	0.711819i	$0.252128\pi$
$888$	−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
$891$	0.531201			0.0177959
$892$	−20.8849	+	36.1737i	−0.699278	+	1.21118i
$893$	16.3738	+	28.3602i	0.547927	+	0.949037i
$894$	−15.9517	+	27.6291i	−0.533503	+	0.924055i
$895$	−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
$899$	78.9535			2.63325
$900$	13.2696			0.442321
$901$	2.85433			0.0950916
$902$	14.7649			0.491616
$903$	−20.5669	−	12.2269i	−0.684423	−	0.406884i
$904$	22.5687	−	39.0901i	0.750623	−	1.30012i
$905$	−23.7371	−	41.1138i	−0.789047	−	1.36667i
$906$	10.1098	+	17.5107i	0.335876	+	0.581754i
$907$	13.3175			0.442202			0.221101	−	0.975251i	$-0.429035\pi$
$907$	13.3175			0.442202			0.221101	+	0.975251i	$0.429035\pi$
$908$	−37.9278	+	65.6929i	−1.25868	+	2.18010i
$909$	3.62859			0.120353
$910$	45.7290	−	51.1145i	1.51590	−	1.69443i
$911$	11.6199			0.384986			0.192493	−	0.981298i	$-0.438343\pi$
$911$	11.6199			0.384986			0.192493	+	0.981298i	$0.438343\pi$
$912$	−13.3992	+	23.2081i	−0.443692	+	0.768497i
$913$	0.238558			0.00789511
$914$	−2.86421	−	4.96096i	−0.0947398	−	0.164094i
$915$	13.7393	+	23.7972i	0.454207	+	0.786710i
$916$	3.84520	−	6.66008i	0.127049	−	0.220055i
$917$	52.2323	−	29.2740i	1.72486	−	0.966714i
$918$	−1.03539			−0.0341731
$919$	10.3780			0.342339			0.171169	−	0.985242i	$-0.445245\pi$
$919$	10.3780			0.342339			0.171169	+	0.985242i	$0.445245\pi$
$920$	45.8758			1.51248
$921$	14.6014			0.481133
$922$	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
$926$	3.21196	−	5.56328i	0.105552	−	0.182821i
$927$	−4.47902	−	7.75790i	−0.147110	−	0.254803i
$928$	25.8597	−	44.7903i	0.848885	−	1.47031i
$929$	31.1471			1.02190			0.510952	−	0.859609i	$-0.329293\pi$
$929$	31.1471			1.02190			0.510952	+	0.859609i	$0.329293\pi$
$930$	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
$933$	−3.03815	+	5.26223i	−0.0994645	+	0.172278i
$934$	5.04241			0.164993
$935$	−0.303883	+	0.526341i	−0.00993803	+	0.0172132i
$936$	−17.3734	−	15.1482i	−0.567867	−	0.495135i
$937$	−6.77667			−0.221384			−0.110692	−	0.993855i	$-0.535307\pi$
$937$	−6.77667			−0.221384			−0.110692	+	0.993855i	$0.535307\pi$
$938$	46.1827	+	27.4553i	1.50792	+	0.896447i
$939$	−1.61084	−	2.79006i	−0.0525678	−	0.0910501i
$940$	−113.214			−3.69263
$941$	23.2912	−	40.3415i	0.759271	−	1.31510i	−0.183952	−	0.982935i	$-0.558889\pi$
$941$	23.2912	−	40.3415i	0.759271	−	1.31510i	0.943223	−	0.332160i	$-0.107777\pi$
$942$	14.2033	+	24.6008i	0.462768	+	0.801538i
$943$	27.7427			0.903428
$944$	0.531547			0.0173004
$945$	6.50536	−	3.64598i	0.211619	−	0.118604i
$946$	6.12677	+	10.6119i	0.199198	+	0.345022i
$947$	−8.28711	+	14.3537i	−0.269295	+	0.466432i	−0.968680	−	0.248313i	$-0.920124\pi$
$947$	−8.28711	+	14.3537i	−0.269295	+	0.466432i	0.699385	+	0.714745i	$0.253457\pi$
$948$	15.9465	−	27.6202i	0.517919	−	0.897062i
$949$	4.97565	−	1.70492i	0.161517	−	0.0553441i
$950$	13.7979	+	23.8987i	0.447663	+	0.775375i
$951$	−5.62276	−	9.73891i	−0.182331	−	0.315806i
$952$	−5.98923	+	3.35671i	−0.194112	+	0.108792i
$953$	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
$955$	−5.99299	−	10.3802i	−0.193929	−	0.335894i
$956$	46.7691	+	81.0065i	1.51262	+	2.61994i
$957$	−2.36043	−	4.08838i	−0.0763018	−	0.132159i
$958$	21.9825	−	38.0748i	0.710222	−	1.23014i
$959$	−19.7308	+	11.0583i	−0.637140	+	0.357090i
$960$	−0.360820	−	0.624958i	−0.0116454	−	0.0201704i
$961$	−23.9629	−	41.5050i	−0.772998	−	1.33887i
$962$	15.8351	−	80.8178i	0.510543	−	2.60567i
$963$	0.944099	−	1.63523i	0.0304232	−	0.0526944i
$964$	45.1052	−	78.1246i	1.45274	−	2.51622i
$965$	2.47010	+	4.27833i	0.0795152	+	0.137724i
$966$	14.9881	−	8.40018i	0.482233	−	0.270272i
$967$	28.5940			0.919521			0.459761	−	0.888043i	$-0.347935\pi$
$967$	28.5940			0.919521			0.459761	+	0.888043i	$0.347935\pi$
$968$	68.5182			2.20226
$969$	−0.745667	−	1.29153i	−0.0239543	−	0.0414900i
$970$	0.604796	−	1.04754i	0.0194188	−	0.0336344i
$971$	−36.3650			−1.16701			−0.583504	−	0.812110i	$-0.698319\pi$
$971$	−36.3650			−1.16701			−0.583504	+	0.812110i	$0.698319\pi$
$972$	−2.25315	−	3.90257i	−0.0722698	−	0.125175i
$973$	−15.7913	−	9.38782i	−0.506246	−	0.300960i
$974$	−64.5242			−2.06749
$975$	−10.0440	+	3.44159i	−0.321664	+	0.110219i
$976$	35.5548	−	61.5827i	1.13808	−	1.97122i
$977$	−55.5687			−1.77780			−0.888900	−	0.458101i	$-0.848530\pi$
$977$	−55.5687			−1.77780			−0.888900	+	0.458101i	$0.848530\pi$
$978$	21.0815	−	36.5142i	0.674112	−	1.16760i
$979$	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
$982$	89.9854			2.87155
$983$	24.8625	−	43.0631i	0.792991	−	1.37350i	−0.131117	−	0.991367i	$-0.541856\pi$
$983$	24.8625	−	43.0631i	0.792991	−	1.37350i	0.924107	−	0.382133i	$-0.124810\pi$
$984$	−34.8315	−	60.3300i	−1.11039	−	1.92325i
$985$	−9.27777	+	16.0696i	−0.295614	+	0.512019i
$986$	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
$990$	−3.81913			−0.121380
$991$	−25.7961			−0.819439			−0.409720	−	0.912212i	$-0.634373\pi$
$991$	−25.7961			−0.819439			−0.409720	+	0.912212i	$0.634373\pi$
$992$	−51.7013			−1.64152
$993$	3.68603			0.116973
$994$	−6.31091	+	3.53700i	−0.200170	+	0.112187i
$995$	6.37527	−	11.0423i	0.202110	−	0.350064i
$996$	−1.01187	−	1.75261i	−0.0320623	−	0.0555335i
$997$	−19.7224	−	34.1602i	−0.624615	−	1.08186i	−0.988615	−	0.150465i	$-0.951923\pi$
$997$	−19.7224	−	34.1602i	−0.624615	−	1.08186i	0.364001	−	0.931399i	$-0.381411\pi$
$998$	−29.1316			−0.922144
$999$	4.47733	−	7.75496i	0.141656	−	0.245356i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.c.100.9	✓	20	91.9	even	3	inner
273.2.j.c.172.9	yes	20	1.1	even	1	trivial
273.2.l.c.16.2	yes	20	7.2	even	3
273.2.l.c.256.2	yes	20	13.9	even	3
819.2.n.f.100.2		20	273.191	odd	6
819.2.n.f.172.2		20	3.2	odd	2
819.2.s.f.289.9		20	21.2	odd	6
819.2.s.f.802.9		20	39.35	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.27537 - 2.20901i) q^{2} +1.00000 q^{3} +(-2.25315 - 3.90257i) q^{4} +(-1.40932 - 2.44101i) q^{5} +(1.27537 - 2.20901i) q^{6} +(-0.0337632 + 2.64554i) q^{7} -6.39292 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.27537 - 2.20901i) q^{2} +1.00000 q^{3} +(-2.25315 - 3.90257i) q^{4} +(-1.40932 - 2.44101i) q^{5} +(1.27537 - 2.20901i) q^{6} +(-0.0337632 + 2.64554i) q^{7} -6.39292 q^{8} +1.00000 q^{9} -7.18961 q^{10} +0.531201 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} +(-3.64706 + 6.31689i) q^{16} +(-0.202959 - 0.351536i) q^{17} +(1.27537 - 2.20901i) q^{18} +3.67398 q^{19} +(-6.35080 + 10.9999i) q^{20} +(-0.0337632 + 2.64554i) q^{21} +(0.677479 - 1.17343i) q^{22} +(1.27296 - 2.20484i) q^{23} -6.39292 q^{24} +(-1.47234 + 2.55018i) q^{25} +(8.70026 - 2.98117i) q^{26} +1.00000 q^{27} +(10.4005 - 5.82902i) q^{28} +(-4.44357 - 7.69648i) q^{29} -7.18961 q^{30} +(-4.44201 + 7.69379i) q^{31} +(2.90979 + 5.03990i) q^{32} +0.531201 q^{33} -1.03539 q^{34} +(6.50536 - 3.64598i) q^{35} +(-2.25315 - 3.90257i) q^{36} +(4.47733 - 7.75496i) q^{37} +(4.68569 - 8.11585i) q^{38} +(2.71760 + 2.36953i) q^{39} +(9.00965 + 15.6052i) q^{40} +(5.44846 + 9.43700i) q^{41} +(5.80095 + 3.44863i) q^{42} +(-4.52174 + 7.83189i) q^{43} +(-1.19687 - 2.07305i) q^{44} +(-1.40932 - 2.44101i) q^{45} +(-3.24701 - 5.62398i) q^{46} +(4.45669 + 7.71921i) q^{47} +(-3.64706 + 6.31689i) q^{48} +(-6.99772 - 0.178643i) q^{49} +(3.75558 + 6.50485i) q^{50} +(-0.202959 - 0.351536i) q^{51} +(3.12409 - 15.9445i) q^{52} +(-3.51589 + 6.08971i) q^{53} +(1.27537 - 2.20901i) q^{54} +(-0.748630 - 1.29667i) q^{55} +(0.215845 - 16.9127i) q^{56} +3.67398 q^{57} -22.6688 q^{58} +(-0.0364367 - 0.0631103i) q^{59} +(-6.35080 + 10.9999i) q^{60} -9.74891 q^{61} +(11.3304 + 19.6249i) q^{62} +(-0.0337632 + 2.64554i) q^{63} +0.256025 q^{64} +(1.95408 - 9.97309i) q^{65} +(0.677479 - 1.17343i) q^{66} +7.96122 q^{67} +(-0.914594 + 1.58412i) q^{68} +(1.27296 - 2.20484i) q^{69} +(0.242744 - 19.0204i) q^{70} +(-0.535997 + 0.928375i) q^{71} -6.39292 q^{72} +(0.729382 - 1.26333i) q^{73} +(-11.4205 - 19.7809i) q^{74} +(-1.47234 + 2.55018i) 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} +20.5594 q^{80} +1.00000 q^{81} +27.7952 q^{82} +0.449091 q^{83} +(10.4005 - 5.82902i) q^{84} +(-0.572068 + 0.990850i) q^{85} +(11.5338 + 19.9771i) q^{86} +(-4.44357 - 7.69648i) q^{87} -3.39593 q^{88} +(0.461435 - 0.799229i) q^{89} -7.18961 q^{90} +(-6.36043 + 7.10950i) q^{91} -11.4727 q^{92} +(-4.44201 + 7.69379i) q^{93} +22.7357 q^{94} +(-5.17779 - 8.96820i) q^{95} +(2.90979 + 5.03990i) q^{96} +(-0.0841208 + 0.145702i) q^{97} +(-9.31932 + 15.2302i) q^{98} +0.531201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9	\( 20 q + 20 q^{3} - 16 q^{4} - 9 q^{7} - 12 q^{8} + 20 q^{9} + 8 q^{10} + 16 q^{11} - 16 q^{12} - 5 q^{13} - 9 q^{14} - 20 q^{16} - 14 q^{19} + 12 q^{20} - 9 q^{21} - 9 q^{22} - 14 q^{23} - 12 q^{24} - 32 q^{25} + 4 q^{26} + 20 q^{27} + 13 q^{28} - 9 q^{29} + 8 q^{30} - 9 q^{31} + 17 q^{32} + 16 q^{33} + 12 q^{34} + 10 q^{35} - 16 q^{36} + 18 q^{37} + 22 q^{38} - 5 q^{39} - 9 q^{40} - q^{41} - 9 q^{42} - 11 q^{43} + 8 q^{44} - 10 q^{46} + 13 q^{47} - 20 q^{48} - 21 q^{49} + 5 q^{50} - 2 q^{52} - 6 q^{53} - 19 q^{55} - 5 q^{56} - 14 q^{57} - 15 q^{59} + 12 q^{60} + 22 q^{62} - 9 q^{63} + 72 q^{64} - 27 q^{65} - 9 q^{66} + 44 q^{67} + 39 q^{68} - 14 q^{69} + 30 q^{70} - 11 q^{71} - 12 q^{72} - 3 q^{74} - 32 q^{75} + 6 q^{76} + 56 q^{77} + 4 q^{78} - 36 q^{79} - 96 q^{80} + 20 q^{81} + 26 q^{82} + 40 q^{83} + 13 q^{84} - 16 q^{85} + 4 q^{86} - 9 q^{87} + 24 q^{88} + 2 q^{89} + 8 q^{90} + 9 q^{91} + 66 q^{92} - 9 q^{93} + 88 q^{94} - 36 q^{95} + 17 q^{96} + 21 q^{97} - 79 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 - 16 * q^4 - 9 * q^7 - 12 * q^8 + 20 * q^9 + 8 * q^10 + 16 * q^11 - 16 * q^12 - 5 * q^13 - 9 * q^14 - 20 * q^16 - 14 * q^19 + 12 * q^20 - 9 * q^21 - 9 * q^22 - 14 * q^23 - 12 * q^24 - 32 * q^25 + 4 * q^26 + 20 * q^27 + 13 * q^28 - 9 * q^29 + 8 * q^30 - 9 * q^31 + 17 * q^32 + 16 * q^33 + 12 * q^34 + 10 * q^35 - 16 * q^36 + 18 * q^37 + 22 * q^38 - 5 * q^39 - 9 * q^40 - q^41 - 9 * q^42 - 11 * q^43 + 8 * q^44 - 10 * q^46 + 13 * q^47 - 20 * q^48 - 21 * q^49 + 5 * q^50 - 2 * q^52 - 6 * q^53 - 19 * q^55 - 5 * q^56 - 14 * q^57 - 15 * q^59 + 12 * q^60 + 22 * q^62 - 9 * q^63 + 72 * q^64 - 27 * q^65 - 9 * q^66 + 44 * q^67 + 39 * q^68 - 14 * q^69 + 30 * q^70 - 11 * q^71 - 12 * q^72 - 3 * q^74 - 32 * q^75 + 6 * q^76 + 56 * q^77 + 4 * q^78 - 36 * q^79 - 96 * q^80 + 20 * q^81 + 26 * q^82 + 40 * q^83 + 13 * q^84 - 16 * q^85 + 4 * q^86 - 9 * q^87 + 24 * q^88 + 2 * q^89 + 8 * q^90 + 9 * q^91 + 66 * q^92 - 9 * q^93 + 88 * q^94 - 36 * q^95 + 17 * q^96 + 21 * q^97 - 79 * q^98 + 16 * q^99

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