LMFDB - Embedded newform 731.2.e.b.307.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.2
Character	$\chi$	$=$	731.307
Dual form			731.2.e.b.681.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46945 q^{2} +(-0.974328 + 1.68758i) q^{3} +4.09816 q^{4} +(0.310056 - 0.537033i) q^{5} +(2.40605 - 4.16740i) q^{6} +(1.71828 + 2.97615i) q^{7} -5.18130 q^{8} +(-0.398628 - 0.690445i) q^{9} +O(q^{10})$	\(q-2.46945 q^{2} +(-0.974328 + 1.68758i) q^{3} +4.09816 q^{4} +(0.310056 - 0.537033i) q^{5} +(2.40605 - 4.16740i) q^{6} +(1.71828 + 2.97615i) q^{7} -5.18130 q^{8} +(-0.398628 - 0.690445i) q^{9} +(-0.765666 + 1.32617i) q^{10} -2.95612 q^{11} +(-3.99295 + 6.91600i) q^{12} +(-1.14443 - 1.98222i) q^{13} +(-4.24320 - 7.34943i) q^{14} +(0.604192 + 1.04649i) q^{15} +4.59861 q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.984391 + 1.70502i) q^{18} +(-2.42850 + 4.20629i) q^{19} +(1.27066 - 2.20085i) q^{20} -6.69667 q^{21} +7.29997 q^{22} +(3.68550 - 6.38348i) q^{23} +(5.04828 - 8.74388i) q^{24} +(2.30773 + 3.99711i) q^{25} +(2.82611 + 4.89497i) q^{26} -4.29239 q^{27} +(7.04179 + 12.1967i) q^{28} +(3.44925 + 5.97427i) q^{29} +(-1.49202 - 2.58425i) q^{30} +(-5.53245 + 9.58249i) q^{31} -0.993417 q^{32} +(2.88023 - 4.98870i) q^{33} +(1.23472 + 2.13860i) q^{34} +2.13105 q^{35} +(-1.63364 - 2.82955i) q^{36} +(0.429936 - 0.744671i) q^{37} +(5.99705 - 10.3872i) q^{38} +4.46021 q^{39} +(-1.60649 + 2.78253i) q^{40} -5.79291 q^{41} +16.5371 q^{42} +(6.55727 + 0.0472157i) q^{43} -12.1147 q^{44} -0.494388 q^{45} +(-9.10115 + 15.7637i) q^{46} -5.71839 q^{47} +(-4.48055 + 7.76054i) q^{48} +(-2.40497 + 4.16553i) q^{49} +(-5.69882 - 9.87064i) q^{50} +1.94866 q^{51} +(-4.69007 - 8.12344i) q^{52} +(3.11208 - 5.39028i) q^{53} +10.5998 q^{54} +(-0.916562 + 1.58753i) q^{55} +(-8.90292 - 15.4203i) q^{56} +(-4.73231 - 8.19660i) q^{57} +(-8.51773 - 14.7531i) q^{58} -11.7305 q^{59} +(2.47608 + 4.28869i) q^{60} +(-6.30175 - 10.9149i) q^{61} +(13.6621 - 23.6634i) q^{62} +(1.36991 - 2.37275i) q^{63} -6.74402 q^{64} -1.41935 q^{65} +(-7.11257 + 12.3193i) q^{66} +(0.635603 - 1.10090i) q^{67} +(-2.04908 - 3.54911i) q^{68} +(7.18177 + 12.4392i) q^{69} -5.26252 q^{70} +(4.93126 + 8.54119i) q^{71} +(2.06541 + 3.57740i) q^{72} +(-4.08201 - 7.07025i) q^{73} +(-1.06170 + 1.83893i) q^{74} -8.99394 q^{75} +(-9.95239 + 17.2380i) q^{76} +(-5.07944 - 8.79785i) q^{77} -11.0142 q^{78} +(-1.76498 - 3.05704i) q^{79} +(1.42583 - 2.46960i) q^{80} +(5.37808 - 9.31510i) q^{81} +14.3053 q^{82} +(-6.89469 + 11.9420i) q^{83} -27.4440 q^{84} -0.620112 q^{85} +(-16.1928 - 0.116597i) q^{86} -13.4428 q^{87} +15.3165 q^{88} +(-0.194218 + 0.336395i) q^{89} +1.22087 q^{90} +(3.93291 - 6.81200i) q^{91} +(15.1038 - 26.1605i) q^{92} +(-10.7808 - 18.6730i) q^{93} +14.1213 q^{94} +(1.50594 + 2.60837i) q^{95} +(0.967914 - 1.67648i) q^{96} -1.94205 q^{97} +(5.93894 - 10.2865i) q^{98} +(1.17839 + 2.04104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) $ 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.46945			−1.74616			−0.873081	−	0.487575i	$-0.837881\pi$
$2$	−2.46945			−1.74616			−0.873081	+	0.487575i	$0.837881\pi$
$3$	−0.974328	+	1.68758i	−0.562528	+	0.974328i	0.434747	+	0.900553i	$0.356838\pi$
$3$	−0.974328	+	1.68758i	−0.562528	+	0.974328i	−0.997275	+	0.0737747i	$0.976495\pi$
$4$	4.09816			2.04908
$5$	0.310056	−	0.537033i	0.138661	−	0.240168i	−0.788329	−	0.615254i	$-0.789053\pi$
$5$	0.310056	−	0.537033i	0.138661	−	0.240168i	0.926990	+	0.375086i	$0.122387\pi$
$6$	2.40605	−	4.16740i	0.982265	−	1.70133i
$7$	1.71828	+	2.97615i	0.649449	+	1.12488i	0.983255	+	0.182236i	$0.0583336\pi$
$7$	1.71828	+	2.97615i	0.649449	+	1.12488i	−0.333806	+	0.942642i	$0.608333\pi$
$8$	−5.18130			−1.83187
$9$	−0.398628	−	0.690445i	−0.132876	−	0.230148i
$10$	−0.765666	+	1.32617i	−0.242125	+	0.419373i
$11$	−2.95612			−0.891303			−0.445652	−	0.895206i	$-0.647028\pi$
$11$	−2.95612			−0.891303			−0.445652	+	0.895206i	$0.647028\pi$
$12$	−3.99295	+	6.91600i	−1.15267	+	1.99648i
$13$	−1.14443	−	1.98222i	−0.317409	−	0.549768i	0.662538	−	0.749028i	$-0.269479\pi$
$13$	−1.14443	−	1.98222i	−0.317409	−	0.549768i	−0.979947	+	0.199261i	$0.936146\pi$
$14$	−4.24320	−	7.34943i	−1.13404	−	1.96422i
$15$	0.604192	+	1.04649i	0.156002	+	0.270203i
$16$	4.59861			1.14965
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$	0.984391	+	1.70502i	0.232023	+	0.401876i
$19$	−2.42850	+	4.20629i	−0.557136	+	0.964988i	0.440598	+	0.897705i	$0.354767\pi$
$19$	−2.42850	+	4.20629i	−0.557136	+	0.964988i	−0.997734	+	0.0672835i	$0.978567\pi$
$20$	1.27066	−	2.20085i	0.284128	−	0.492124i
$21$	−6.69667			−1.46133
$22$	7.29997			1.55636
$23$	3.68550	−	6.38348i	0.768481	−	1.33105i	−0.169906	−	0.985460i	$-0.554346\pi$
$23$	3.68550	−	6.38348i	0.768481	−	1.33105i	0.938387	−	0.345587i	$-0.112320\pi$
$24$	5.04828	−	8.74388i	1.03048	−	1.78484i
$25$	2.30773	+	3.99711i	0.461546	+	0.799421i
$26$	2.82611	+	4.89497i	0.554247	+	0.959983i
$27$	−4.29239			−0.826070
$28$	7.04179	+	12.1967i	1.33077	+	2.30497i
$29$	3.44925	+	5.97427i	0.640509	+	1.10939i	0.985319	+	0.170722i	$0.0546099\pi$
$29$	3.44925	+	5.97427i	0.640509	+	1.10939i	−0.344810	+	0.938672i	$0.612057\pi$
$30$	−1.49202	−	2.58425i	−0.272404	−	0.471818i
$31$	−5.53245	+	9.58249i	−0.993658	+	1.72107i	−0.399451	+	0.916755i	$0.630799\pi$
$31$	−5.53245	+	9.58249i	−0.993658	+	1.72107i	−0.594207	+	0.804312i	$0.702534\pi$
$32$	−0.993417			−0.175613
$33$	2.88023	−	4.98870i	0.501383	−	0.868421i
$34$	1.23472	+	2.13860i	0.211753	+	0.366767i
$35$	2.13105			0.360213
$36$	−1.63364	−	2.82955i	−0.272274	−	0.471592i
$37$	0.429936	−	0.744671i	0.0706811	−	0.122423i	−0.828519	−	0.559961i	$-0.810816\pi$
$37$	0.429936	−	0.744671i	0.0706811	−	0.122423i	0.899200	+	0.437538i	$0.144149\pi$
$38$	5.99705	−	10.3872i	0.972850	−	1.68503i
$39$	4.46021			0.714205
$40$	−1.60649	+	2.78253i	−0.254009	+	0.439956i
$41$	−5.79291			−0.904700			−0.452350	−	0.891840i	$-0.649414\pi$
$41$	−5.79291			−0.904700			−0.452350	+	0.891840i	$0.649414\pi$
$42$	16.5371			2.55172
$43$	6.55727	+	0.0472157i	0.999974	+	0.00720033i
$43$	6.55727	+	0.0472157i	0.999974	+	0.00720033i
$44$	−12.1147			−1.82635
$45$	−0.494388			−0.0736991
$46$	−9.10115	+	15.7637i	−1.34189	+	2.32422i
$47$	−5.71839			−0.834113			−0.417057	−	0.908881i	$-0.636938\pi$
$47$	−5.71839			−0.834113			−0.417057	+	0.908881i	$0.636938\pi$
$48$	−4.48055	+	7.76054i	−0.646712	+	1.12014i
$49$	−2.40497	+	4.16553i	−0.343567	+	0.595075i
$50$	−5.69882	−	9.87064i	−0.805934	−	1.39592i
$51$	1.94866			0.272866
$52$	−4.69007	−	8.12344i	−0.650396	−	1.12652i
$53$	3.11208	−	5.39028i	0.427477	−	0.740411i	−0.569171	−	0.822219i	$-0.692736\pi$
$53$	3.11208	−	5.39028i	0.427477	−	0.740411i	0.996648	+	0.0818075i	$0.0260693\pi$
$54$	10.5998			1.44245
$55$	−0.916562	+	1.58753i	−0.123589	+	0.214063i
$56$	−8.90292	−	15.4203i	−1.18970	−	2.06062i
$57$	−4.73231	−	8.19660i	−0.626810	−	1.08567i
$58$	−8.51773	−	14.7531i	−1.11843	−	1.93718i
$59$	−11.7305			−1.52718			−0.763588	−	0.645704i	$-0.776564\pi$
$59$	−11.7305			−1.52718			−0.763588	+	0.645704i	$0.776564\pi$
$60$	2.47608	+	4.28869i	0.319660	+	0.553668i
$61$	−6.30175	−	10.9149i	−0.806856	−	1.39752i	−0.915031	−	0.403384i	$-0.867834\pi$
$61$	−6.30175	−	10.9149i	−0.806856	−	1.39752i	0.108175	−	0.994132i	$-0.465499\pi$
$62$	13.6621	−	23.6634i	1.73509	−	3.00526i
$63$	1.36991	−	2.37275i	0.172592	−	0.298939i
$64$	−6.74402			−0.843003
$65$	−1.41935			−0.176049
$66$	−7.11257	+	12.3193i	−0.875496	+	1.51640i
$67$	0.635603	−	1.10090i	0.0776513	−	0.134496i	−0.824585	−	0.565738i	$-0.808591\pi$
$67$	0.635603	−	1.10090i	0.0776513	−	0.134496i	0.902236	+	0.431242i	$0.141925\pi$
$68$	−2.04908	−	3.54911i	−0.248488	−	0.430393i
$69$	7.18177	+	12.4392i	0.864584	+	1.49750i
$70$	−5.26252			−0.628991
$71$	4.93126	+	8.54119i	0.585233	+	1.01365i	0.994846	+	0.101394i	$0.0323302\pi$
$71$	4.93126	+	8.54119i	0.585233	+	1.01365i	−0.409614	+	0.912259i	$0.634337\pi$
$72$	2.06541	+	3.57740i	0.243411	+	0.421600i
$73$	−4.08201	−	7.07025i	−0.477763	−	0.827510i	0.521912	−	0.852999i	$-0.325219\pi$
$73$	−4.08201	−	7.07025i	−0.477763	−	0.827510i	−0.999675	+	0.0254896i	$0.991886\pi$
$74$	−1.06170	+	1.83893i	−0.123421	+	0.213771i
$75$	−8.99394			−1.03853
$76$	−9.95239	+	17.2380i	−1.14162	+	1.97734i
$77$	−5.07944	−	8.79785i	−0.578856	−	1.00261i
$78$	−11.0142			−1.24712
$79$	−1.76498	−	3.05704i	−0.198576	−	0.343944i	0.749491	−	0.662015i	$-0.230298\pi$
$79$	−1.76498	−	3.05704i	−0.198576	−	0.343944i	−0.948067	+	0.318071i	$0.896965\pi$
$80$	1.42583	−	2.46960i	0.159412	−	0.276110i
$81$	5.37808	−	9.31510i	0.597564	−	1.03501i
$82$	14.3053			1.57975
$83$	−6.89469	+	11.9420i	−0.756791	+	1.31080i	0.187688	+	0.982229i	$0.439901\pi$
$83$	−6.89469	+	11.9420i	−0.756791	+	1.31080i	−0.944479	+	0.328572i	$0.893433\pi$
$84$	−27.4440			−2.99439
$85$	−0.620112			−0.0672606
$86$	−16.1928	−	0.116597i	−1.74612	−	0.0125729i
$87$	−13.4428			−1.44122
$88$	15.3165			1.63275
$89$	−0.194218	+	0.336395i	−0.0205870	+	0.0356578i	−0.876135	−	0.482065i	$-0.839887\pi$
$89$	−0.194218	+	0.336395i	−0.0205870	+	0.0356578i	0.855548	+	0.517723i	$0.173220\pi$
$90$	1.22087			0.128690
$91$	3.93291	−	6.81200i	0.412281	−	0.714092i
$92$	15.1038	−	26.1605i	1.57468	−	2.72742i
$93$	−10.7808	−	18.6730i	−1.11792	−	1.93630i
$94$	14.1213			1.45650
$95$	1.50594	+	2.60837i	0.154506	+	0.267613i
$96$	0.967914	−	1.67648i	0.0987873	−	0.171105i
$97$	−1.94205			−0.197185			−0.0985924	−	0.995128i	$-0.531434\pi$
$97$	−1.94205			−0.197185			−0.0985924	+	0.995128i	$0.531434\pi$
$98$	5.93894	−	10.2865i	0.599923	−	1.03910i
$99$	1.17839	+	2.04104i	0.118433	+	0.205132i
$100$	9.45745	+	16.3808i	0.945745	+	1.63808i
$101$	−6.42395	−	11.1266i	−0.639207	−	1.10714i	−0.985607	−	0.169052i	$-0.945929\pi$
$101$	−6.42395	−	11.1266i	−0.639207	−	1.10714i	0.346400	−	0.938087i	$-0.387404\pi$
$102$	−4.81210			−0.476469
$103$	6.79179	+	11.7637i	0.669214	+	1.15911i	0.978124	+	0.208022i	$0.0667026\pi$
$103$	6.79179	+	11.7637i	0.669214	+	1.15911i	−0.308910	+	0.951091i	$0.599964\pi$
$104$	5.92965	+	10.2704i	0.581450	+	1.00710i
$105$	−2.07634	+	3.59633i	−0.202630	+	0.350966i
$106$	−7.68511	+	13.3110i	−0.746443	+	1.29288i
$107$	−6.03484			−0.583410			−0.291705	−	0.956508i	$-0.594223\pi$
$107$	−6.03484			−0.583410			−0.291705	+	0.956508i	$0.594223\pi$
$108$	−17.5909			−1.69268
$109$	−2.36350	+	4.09371i	−0.226382	+	0.392106i	−0.956733	−	0.290966i	$-0.906023\pi$
$109$	−2.36350	+	4.09371i	−0.226382	+	0.392106i	0.730351	+	0.683072i	$0.239357\pi$
$110$	2.26340	−	3.92033i	0.215807	−	0.373788i
$111$	0.837797	+	1.45111i	0.0795202	+	0.137733i
$112$	7.90169	+	13.6861i	0.746640	+	1.29322i
$113$	−7.94490			−0.747393			−0.373697	−	0.927551i	$-0.621910\pi$
$113$	−7.94490			−0.747393			−0.373697	+	0.927551i	$0.621910\pi$
$114$	11.6862	+	20.2411i	1.09451	+	1.89575i
$115$	−2.28542	−	3.95847i	−0.213117	−	0.369129i
$116$	14.1356	+	24.4835i	1.31245	+	2.27324i
$117$	−0.912407	+	1.58033i	−0.0843520	+	0.146102i
$118$	28.9677			2.66670
$119$	1.71828	−	2.97615i	0.157514	−	0.272823i
$120$	−3.13050	−	5.42218i	−0.285774	−	0.494975i
$121$	−2.26136			−0.205578
$122$	15.5618	+	26.9539i	1.40890	+	2.44029i
$123$	5.64419	−	9.77602i	0.508920	−	0.881474i
$124$	−22.6729	+	39.2706i	−2.03609	+	3.52660i
$125$	5.96266			0.533317
$126$	−3.38292	+	5.85939i	−0.301374	+	0.521996i
$127$	6.62615			0.587976			0.293988	−	0.955809i	$-0.405017\pi$
$127$	6.62615			0.587976			0.293988	+	0.955809i	$0.405017\pi$
$128$	18.6408			1.64763
$129$	−6.46861	+	11.0199i	−0.569529	+	0.970252i
$130$	3.50501			0.307410
$131$	−16.1454			−1.41063			−0.705315	−	0.708894i	$-0.749195\pi$
$131$	−16.1454			−1.41063			−0.705315	+	0.708894i	$0.749195\pi$
$132$	11.8036	−	20.4445i	1.02738	−	1.77947i
$133$	−16.6914			−1.44733
$134$	−1.56959	+	2.71861i	−0.135592	+	0.234852i
$135$	−1.33088	+	2.30515i	−0.114544	+	0.198396i
$136$	2.59065	+	4.48713i	0.222146	+	0.384769i
$137$	6.62439			0.565960			0.282980	−	0.959126i	$-0.408677\pi$
$137$	6.62439			0.565960			0.282980	+	0.959126i	$0.408677\pi$
$138$	−17.7350	−	30.7179i	−1.50970	−	2.61488i
$139$	4.17242	−	7.22684i	0.353900	−	0.612973i	−0.633029	−	0.774128i	$-0.718189\pi$
$139$	4.17242	−	7.22684i	0.353900	−	0.612973i	0.986929	+	0.161155i	$0.0515220\pi$
$140$	8.73339			0.738106
$141$	5.57159	−	9.65027i	0.469212	−	0.812699i
$142$	−12.1775	−	21.0920i	−1.02191	−	1.77000i
$143$	3.38308	+	5.85966i	0.282907	+	0.490010i
$144$	−1.83314	−	3.17508i	−0.152761	−	0.264590i
$145$	4.27784			0.355255
$146$	10.0803	+	17.4596i	0.834251	+	1.44497i
$147$	−4.68645	−	8.11718i	−0.386532	−	0.669493i
$148$	1.76195	−	3.05178i	0.144831	−	0.250855i
$149$	−0.407180	+	0.705256i	−0.0333575	+	0.0577769i	−0.882222	−	0.470833i	$-0.843953\pi$
$149$	−0.407180	+	0.705256i	−0.0333575	+	0.0577769i	0.848865	+	0.528610i	$0.177287\pi$
$150$	22.2101			1.81344
$151$	−4.56194			−0.371245			−0.185623	−	0.982621i	$-0.559430\pi$
$151$	−4.56194			−0.371245			−0.185623	+	0.982621i	$0.559430\pi$
$152$	12.5828	−	21.7940i	1.02060	−	1.76773i
$153$	−0.398628	+	0.690445i	−0.0322272	+	0.0558191i
$154$	12.5434	+	21.7258i	1.01078	+	1.75071i
$155$	3.43074	+	5.94222i	0.275564	+	0.477290i
$156$	18.2787			1.46346
$157$	−0.319392	−	0.553203i	−0.0254902	−	0.0441504i	0.852999	−	0.521913i	$-0.174781\pi$
$157$	−0.319392	−	0.553203i	−0.0254902	−	0.0441504i	−0.878489	+	0.477762i	$0.841448\pi$
$158$	4.35853	+	7.54919i	0.346746	+	0.600581i
$159$	6.06437	+	10.5038i	0.480935	+	0.833005i
$160$	−0.308015	+	0.533498i	−0.0243507	+	0.0421767i
$161$	25.3309			1.99635
$162$	−13.2809	+	23.0031i	−1.04344	+	1.80730i
$163$	−2.07330	−	3.59106i	−0.162393	−	0.281274i	0.773333	−	0.634000i	$-0.218588\pi$
$163$	−2.07330	−	3.59106i	−0.162393	−	0.281274i	−0.935727	+	0.352726i	$0.885255\pi$
$164$	−23.7403			−1.85380
$165$	−1.78606	−	3.09355i	−0.139045	−	0.240833i
$166$	17.0261	−	29.4900i	1.32148	−	2.28887i
$167$	8.90521	−	15.4243i	0.689106	−	1.19357i	−0.283022	−	0.959113i	$-0.591337\pi$
$167$	8.90521	−	15.4243i	0.689106	−	1.19357i	0.972128	−	0.234452i	$-0.0753297\pi$
$168$	34.6974			2.67696
$169$	3.88055	−	6.72131i	0.298504	−	0.517024i
$170$	1.53133			0.117448
$171$	3.87228			0.296120
$172$	26.8727	+	0.193498i	2.04903	+	0.0147541i
$173$	−23.1331			−1.75878			−0.879390	−	0.476101i	$-0.842050\pi$
$173$	−23.1331			−1.75878			−0.879390	+	0.476101i	$0.842050\pi$
$174$	33.1962			2.51660
$175$	−7.93065	+	13.7363i	−0.599501	+	1.03837i
$176$	−13.5940			−1.02469
$177$	11.4293	−	19.7961i	0.859079	−	1.48797i
$178$	0.479610	−	0.830709i	0.0359483	−	0.0622643i
$179$	1.86564	+	3.23139i	0.139445	+	0.241525i	0.927287	−	0.374352i	$-0.122135\pi$
$179$	1.86564	+	3.23139i	0.139445	+	0.241525i	−0.787842	+	0.615878i	$0.788802\pi$
$180$	−2.02608			−0.151015
$181$	7.58844	+	13.1436i	0.564044	+	0.976953i	0.997138	+	0.0756043i	$0.0240886\pi$
$181$	7.58844	+	13.1436i	0.564044	+	0.976953i	−0.433094	+	0.901349i	$0.642578\pi$
$182$	−9.71211	+	16.8219i	−0.719909	+	1.24692i
$183$	24.5599			1.81552
$184$	−19.0957	+	33.0747i	−1.40775	+	2.43830i
$185$	−0.266609	−	0.461780i	−0.0196015	−	0.0339507i
$186$	26.6227	+	46.1119i	1.95207	+	3.38109i
$187$	1.47806	+	2.56007i	0.108086	+	0.187211i
$188$	−23.4349			−1.70917
$189$	−7.37552	−	12.7748i	−0.536490	−	0.929228i
$190$	−3.71884	−	6.44122i	−0.269793	−	0.467295i
$191$	8.58483	−	14.8694i	0.621176	−	1.07591i	−0.368091	−	0.929790i	$-0.619988\pi$
$191$	8.58483	−	14.8694i	0.621176	−	1.07591i	0.989267	−	0.146119i	$-0.0466783\pi$
$192$	6.57089	−	11.3811i	0.474213	−	0.821361i
$193$	−6.97413			−0.502009			−0.251004	−	0.967986i	$-0.580761\pi$
$193$	−6.97413			−0.502009			−0.251004	+	0.967986i	$0.580761\pi$
$194$	4.79578			0.344317
$195$	1.38291	−	2.39528i	0.0990326	−	0.171529i
$196$	−9.85595	+	17.0710i	−0.703996	+	1.21936i
$197$	7.56676	+	13.1060i	0.539109	+	0.933765i	0.998952	+	0.0457645i	$0.0145724\pi$
$197$	7.56676	+	13.1060i	0.539109	+	0.933765i	−0.459843	+	0.888000i	$0.652094\pi$
$198$	−2.90998	−	5.04023i	−0.206803	−	0.358193i
$199$	−4.41500			−0.312971			−0.156485	−	0.987680i	$-0.550016\pi$
$199$	−4.41500			−0.312971			−0.156485	+	0.987680i	$0.550016\pi$
$200$	−11.9570	−	20.7102i	−0.845490	−	1.46443i
$201$	1.23857	+	2.14527i	0.0873621	+	0.151316i
$202$	15.8636	+	27.4765i	1.11616	+	1.93324i
$203$	−11.8535	+	20.5309i	−0.831955	+	1.44099i
$204$	7.98590			0.559125
$205$	−1.79613	+	3.11098i	−0.125447	+	0.217280i
$206$	−16.7719	−	29.0499i	−1.16856	−	2.02400i
$207$	−5.87658			−0.408451
$208$	−5.26280	−	9.11543i	−0.364909	−	0.632041i
$209$	7.17894	−	12.4343i	0.496577	−	0.860097i
$210$	5.12741	−	8.88094i	0.353825	−	0.612843i
$211$	7.43401			0.511779			0.255889	−	0.966706i	$-0.417632\pi$
$211$	7.43401			0.511779			0.255889	+	0.966706i	$0.417632\pi$
$212$	12.7538	−	22.0902i	0.875934	−	1.51716i
$213$	−19.2186			−1.31684
$214$	14.9027			1.01873
$215$	2.05848	−	3.50683i	0.140387	−	0.239164i
$216$	22.2401			1.51325
$217$	−38.0252			−2.58132
$218$	5.83654	−	10.1092i	0.395300	−	0.684680i
$219$	15.9089			1.07502
$220$	−3.75622	+	6.50597i	−0.253244	+	0.438632i
$221$	−1.14443	+	1.98222i	−0.0769829	+	0.133338i
$222$	−2.06890	−	3.58343i	−0.138855	−	0.240504i
$223$	22.0399			1.47590			0.737950	−	0.674856i	$-0.235794\pi$
$223$	22.0399			1.47590			0.737950	+	0.674856i	$0.235794\pi$
$224$	−1.70697	−	2.95656i	−0.114052	−	0.197543i
$225$	1.83985	−	3.18672i	0.122657	−	0.212448i
$226$	19.6195			1.30507
$227$	−6.56679	+	11.3740i	−0.435853	+	0.754920i	−0.997365	−	0.0725491i	$-0.976887\pi$
$227$	−6.56679	+	11.3740i	−0.435853	+	0.754920i	0.561512	+	0.827469i	$0.310220\pi$
$228$	−19.3938	−	33.5910i	−1.28438	−	2.22462i
$229$	−5.06810	−	8.77820i	−0.334909	−	0.580080i	0.648558	−	0.761165i	$-0.275372\pi$
$229$	−5.06810	−	8.77820i	−0.334909	−	0.580080i	−0.983467	+	0.181085i	$0.942039\pi$
$230$	5.64373	+	9.77523i	0.372137	+	0.644560i
$231$	19.7961			1.30249
$232$	−17.8716	−	30.9545i	−1.17333	−	2.03226i
$233$	3.00268	+	5.20079i	0.196712	+	0.340715i	0.947460	−	0.319873i	$-0.103640\pi$
$233$	3.00268	+	5.20079i	0.196712	+	0.340715i	−0.750749	+	0.660588i	$0.770307\pi$
$234$	2.25314	−	3.90255i	0.147292	−	0.255118i
$235$	−1.77302	+	3.07096i	−0.115659	+	0.200328i
$236$	−48.0733			−3.12931
$237$	6.87868			0.446818
$238$	−4.24320	+	7.34943i	−0.275046	+	0.476393i
$239$	1.71141	−	2.96425i	0.110702	−	0.191741i	−0.805352	−	0.592798i	$-0.798023\pi$
$239$	1.71141	−	2.96425i	0.110702	−	0.191741i	0.916053	+	0.401056i	$0.131357\pi$
$240$	2.77844	+	4.81240i	0.179348	+	0.310639i
$241$	10.1983	+	17.6639i	0.656928	+	1.13783i	0.981407	+	0.191940i	$0.0614780\pi$
$241$	10.1983	+	17.6639i	0.656928	+	1.13783i	−0.324478	+	0.945893i	$0.605189\pi$
$242$	5.58431			0.358973
$243$	4.04143	+	6.99997i	0.259258	+	0.449048i
$244$	−25.8256	−	44.7312i	−1.65331	−	2.86362i
$245$	1.49135	+	2.58309i	0.0952788	+	0.165028i
$246$	−13.9380	+	24.1414i	−0.888656	+	1.53920i
$247$	11.1170			0.707359
$248$	28.6653	−	49.6497i	1.82025	−	3.15276i
$249$	−13.4354	−	23.2708i	−0.851432	−	1.47472i
$250$	−14.7245			−0.931257
$251$	−5.25794	−	9.10702i	−0.331878	−	0.574830i	0.651002	−	0.759076i	$-0.274349\pi$
$251$	−5.25794	−	9.10702i	−0.331878	−	0.574830i	−0.982880	+	0.184246i	$0.941016\pi$
$252$	5.61411	−	9.72393i	0.353656	−	0.612550i
$253$	−10.8948	+	18.8703i	−0.684949	+	1.18637i
$254$	−16.3629			−1.02670
$255$	0.604192	−	1.04649i	0.0378360	−	0.0655338i
$256$	−32.5445			−2.03403
$257$	5.46300			0.340773			0.170386	−	0.985377i	$-0.445498\pi$
$257$	5.46300			0.340773			0.170386	+	0.985377i	$0.445498\pi$
$258$	15.9739	−	27.2132i	0.994490	−	1.69422i
$259$	2.95500			0.183615
$260$	−5.81674			−0.360739
$261$	2.74993	−	4.76303i	0.170217	−	0.294824i
$262$	39.8702			2.46319
$263$	−10.1413	+	17.5652i	−0.625339	+	1.08312i	0.363136	+	0.931736i	$0.381706\pi$
$263$	−10.1413	+	17.5652i	−0.625339	+	1.08312i	−0.988475	+	0.151383i	$0.951627\pi$
$264$	−14.9233	+	25.8479i	−0.918467	+	1.59083i
$265$	−1.92984	−	3.34257i	−0.118549	−	0.205333i
$266$	41.2184			2.52726
$267$	−0.378463	−	0.655518i	−0.0231616	−	0.0401170i
$268$	2.60481	−	4.51166i	0.159114	−	0.275593i
$269$	5.46849			0.333420			0.166710	−	0.986006i	$-0.446686\pi$
$269$	5.46849			0.333420			0.166710	+	0.986006i	$0.446686\pi$
$270$	3.28654	−	5.69245i	0.200012	−	0.346431i
$271$	13.7919	+	23.8882i	0.837796	+	1.45111i	0.891733	+	0.452561i	$0.149490\pi$
$271$	13.7919	+	23.8882i	0.837796	+	1.45111i	−0.0539373	+	0.998544i	$0.517177\pi$
$272$	−2.29930	−	3.98251i	−0.139416	−	0.241475i
$273$	7.66389	+	13.2742i	0.463839	+	0.803393i
$274$	−16.3586			−0.988258
$275$	−6.82193	−	11.8159i	−0.411378	−	0.712527i
$276$	29.4321	+	50.9778i	1.77160	+	3.06851i
$277$	−12.1673	+	21.0743i	−0.731059	+	1.26623i	0.225371	+	0.974273i	$0.427640\pi$
$277$	−12.1673	+	21.0743i	−0.731059	+	1.26623i	−0.956431	+	0.291959i	$0.905693\pi$
$278$	−10.3036	+	17.8463i	−0.617966	+	1.07035i
$279$	8.82157			0.528134
$280$	−11.0416			−0.659862
$281$	−10.4988	+	18.1845i	−0.626308	+	1.08480i	0.361979	+	0.932186i	$0.382101\pi$
$281$	−10.4988	+	18.1845i	−0.626308	+	1.08480i	−0.988286	+	0.152611i	$0.951232\pi$
$282$	−13.7587	+	23.8308i	−0.819321	+	1.41910i
$283$	−12.2209	−	21.1672i	−0.726457	−	1.25826i	−0.958372	−	0.285524i	$-0.907833\pi$
$283$	−12.2209	−	21.1672i	−0.726457	−	1.25826i	0.231915	−	0.972736i	$-0.425501\pi$
$284$	20.2091	+	35.0032i	1.19919	+	2.07706i
$285$	−5.86912			−0.347657
$286$	−8.35433	−	14.4701i	−0.494002	−	0.855636i
$287$	−9.95384	−	17.2405i	−0.587556	−	1.01768i
$288$	0.396004	+	0.685900i	0.0233348	+	0.0404170i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−10.5639			−0.620333
$291$	1.89219	−	3.27737i	0.110922	−	0.192123i
$292$	−16.7287	−	28.9750i	−0.978975	−	1.69563i
$293$	−13.6034			−0.794721			−0.397361	−	0.917663i	$-0.630074\pi$
$293$	−13.6034			−0.794721			−0.397361	+	0.917663i	$0.630074\pi$
$294$	11.5729	+	20.0449i	0.674948	+	1.16904i
$295$	−3.63710	+	6.29964i	−0.211760	+	0.366779i
$296$	−2.22763	+	3.85836i	−0.129478	+	0.224263i
$297$	12.6888			0.736279
$298$	1.00551	−	1.74159i	0.0582476	−	0.100888i
$299$	−16.8712			−0.975689
$300$	−36.8586			−2.12803
$301$	11.1267	+	19.5965i	0.641332	+	1.12953i
$302$	11.2655			0.648254
$303$	25.0361			1.43829
$304$	−11.1677	+	19.3431i	−0.640513	+	1.10940i
$305$	−7.81558			−0.447519
$306$	0.984391	−	1.70502i	0.0562739	−	0.0974692i
$307$	5.20324	−	9.01228i	0.296965	−	0.514358i	−0.678475	−	0.734623i	$-0.737359\pi$
$307$	5.20324	−	9.01228i	0.296965	−	0.514358i	0.975440	+	0.220265i	$0.0706923\pi$
$308$	−20.8164	−	36.0550i	−1.18612	−	2.05442i
$309$	−26.4697			−1.50581
$310$	−8.47203	−	14.6740i	−0.481179	−	0.833426i
$311$	−14.8267	+	25.6806i	−0.840746	+	1.45621i	0.0485192	+	0.998822i	$0.484550\pi$
$311$	−14.8267	+	25.6806i	−0.840746	+	1.45621i	−0.889265	+	0.457392i	$0.848784\pi$
$312$	−23.1097			−1.30833
$313$	−16.9121	+	29.2927i	−0.955931	+	1.65572i	−0.223708	+	0.974656i	$0.571816\pi$
$313$	−16.9121	+	29.2927i	−0.955931	+	1.65572i	−0.732223	+	0.681065i	$0.761517\pi$
$314$	0.788721	+	1.36610i	0.0445101	+	0.0770937i
$315$	−0.849497	−	1.47137i	−0.0478638	−	0.0829025i
$316$	−7.23318	−	12.5282i	−0.406898	−	0.704768i
$317$	18.1073			1.01701			0.508504	−	0.861060i	$-0.330199\pi$
$317$	18.1073			1.01701			0.508504	+	0.861060i	$0.330199\pi$
$318$	−14.9756	−	25.9385i	−0.839791	−	1.45456i
$319$	−10.1964	−	17.6607i	−0.570888	−	0.988807i
$320$	−2.09103	+	3.62176i	−0.116892	+	0.202463i
$321$	5.87991	−	10.1843i	0.328185	−	0.568433i
$322$	−62.5533			−3.48596
$323$	4.85700			0.270251
$324$	22.0402	−	38.1748i	1.22446	−	2.12082i
$325$	5.28208	−	9.14884i	0.292997	−	0.507486i
$326$	5.11990	+	8.86793i	0.283565	+	0.491149i
$327$	−4.60565	−	7.97722i	−0.254693	−	0.441141i
$328$	30.0148			1.65729
$329$	−9.82580	−	17.0188i	−0.541714	−	0.938276i
$330$	4.41059	+	7.63936i	0.242795	+	0.420533i
$331$	1.23498	+	2.13905i	0.0678805	+	0.117573i	0.897968	−	0.440060i	$-0.145043\pi$
$331$	1.23498	+	2.13905i	0.0678805	+	0.117573i	−0.830088	+	0.557633i	$0.811710\pi$
$332$	−28.2556	+	48.9401i	−1.55073	+	2.68594i
$333$	−0.685539			−0.0375673
$334$	−21.9909	+	38.0894i	−1.20329	+	2.08416i
$335$	−0.394145	−	0.682680i	−0.0215345	−	0.0372988i
$336$	−30.7953			−1.68002
$337$	−10.5151	−	18.2127i	−0.572795	−	0.992111i	−0.996277	−	0.0862061i	$-0.972526\pi$
$337$	−10.5151	−	18.2127i	−0.572795	−	0.992111i	0.423482	−	0.905905i	$-0.360808\pi$
$338$	−9.58280	+	16.5979i	−0.521236	+	0.902807i
$339$	7.74093	−	13.4077i	0.420430	−	0.728206i
$340$	−2.54132			−0.137822
$341$	16.3546	−	28.3270i	0.885651	−	1.53399i
$342$	−9.56238			−0.517074
$343$	7.52628			0.406381
$344$	−33.9752	−	0.244639i	−1.83182	−	0.0131900i
$345$	8.90701			0.479537
$346$	57.1261			3.07112
$347$	−10.4076	+	18.0265i	−0.558709	+	0.967712i	0.438896	+	0.898538i	$0.355370\pi$
$347$	−10.4076	+	18.0265i	−0.558709	+	0.967712i	−0.997605	+	0.0691738i	$0.977964\pi$
$348$	−55.0907			−2.95317
$349$	14.4758	−	25.0728i	0.774871	−	1.34212i	−0.159995	−	0.987118i	$-0.551148\pi$
$349$	14.4758	−	25.0728i	0.774871	−	1.34212i	0.934867	−	0.354999i	$-0.115519\pi$
$350$	19.5843	−	33.9210i	1.04683	−	1.81316i
$351$	4.91235	+	8.50844i	0.262202	+	0.454147i
$352$	2.93666			0.156524
$353$	12.4260	+	21.5224i	0.661367	+	1.14552i	0.980257	+	0.197729i	$0.0633567\pi$
$353$	12.4260	+	21.5224i	0.661367	+	1.14552i	−0.318890	+	0.947792i	$0.603310\pi$
$354$	−28.2241	+	48.8855i	−1.50009	+	2.59823i
$355$	6.11586			0.324596
$356$	−0.795936	+	1.37860i	−0.0421845	+	0.0730657i
$357$	3.34833	+	5.79948i	0.177213	+	0.306941i
$358$	−4.60711	−	7.97974i	−0.243493	−	0.421742i
$359$	2.64353	+	4.57873i	0.139520	+	0.241656i	0.927315	−	0.374281i	$-0.122111\pi$
$359$	2.64353	+	4.57873i	0.139520	+	0.241656i	−0.787795	+	0.615938i	$0.788777\pi$
$360$	2.56157			0.135007
$361$	−2.29523	−	3.97545i	−0.120801	−	0.209234i
$362$	−18.7392	−	32.4573i	−0.984912	−	1.70592i
$363$	2.20331	−	3.81624i	0.115644	−	0.200301i
$364$	16.1177	−	27.9167i	0.844797	−	1.46323i
$365$	−5.06260			−0.264989
$366$	−60.6493			−3.17019
$367$	−0.367138	+	0.635902i	−0.0191645	+	0.0331938i	−0.875449	−	0.483311i	$-0.839434\pi$
$367$	−0.367138	+	0.635902i	−0.0191645	+	0.0331938i	0.856284	+	0.516505i	$0.172767\pi$
$368$	16.9482	−	29.3551i	0.883485	−	1.53024i
$369$	2.30922	+	3.99968i	0.120213	+	0.208215i
$370$	0.658375	+	1.14034i	0.0342273	+	0.0592834i
$371$	21.3897			1.11050
$372$	−44.1817	−	76.5249i	−2.29071	−	3.96763i
$373$	9.84051	+	17.0443i	0.509522	+	0.882518i	0.999939	+	0.0110304i	$0.00351115\pi$
$373$	9.84051	+	17.0443i	0.509522	+	0.882518i	−0.490417	+	0.871488i	$0.663156\pi$
$374$	−3.64999	−	6.32196i	−0.188736	−	0.326901i
$375$	−5.80959	+	10.0625i	−0.300006	+	0.519625i
$376$	29.6287			1.52798
$377$	7.89486	−	13.6743i	0.406606	−	0.704262i
$378$	18.2134	+	31.5466i	0.936799	+	1.62258i
$379$	−12.8317			−0.659122			−0.329561	−	0.944134i	$-0.606901\pi$
$379$	−12.8317			−0.659122			−0.329561	+	0.944134i	$0.606901\pi$
$380$	6.17159	+	10.6895i	0.316596	+	0.548361i
$381$	−6.45604	+	11.1822i	−0.330753	+	0.572881i
$382$	−21.1998	+	36.7191i	−1.08467	+	1.87871i
$383$	15.3999			0.786898			0.393449	−	0.919346i	$-0.371282\pi$
$383$	15.3999			0.786898			0.393449	+	0.919346i	$0.371282\pi$
$384$	−18.1623	+	31.4580i	−0.926840	+	1.60533i
$385$	−6.29964			−0.321059
$386$	17.2222			0.876589
$387$	−2.58131	−	4.54625i	−0.131216	−	0.231099i
$388$	−7.95882			−0.404048
$389$	11.3476			0.575347			0.287674	−	0.957729i	$-0.407118\pi$
$389$	11.3476			0.575347			0.287674	+	0.957729i	$0.407118\pi$
$390$	−3.41503	+	5.91501i	−0.172927	+	0.299518i
$391$	−7.37101			−0.372768
$392$	12.4609	−	21.5828i	0.629368	−	1.09010i
$393$	15.7309	−	27.2467i	0.793519	−	1.37442i
$394$	−18.6857	−	32.3646i	−0.941372	−	1.63050i
$395$	−2.18897			−0.110139
$396$	4.82924	+	8.36450i	0.242679	+	0.420332i
$397$	10.0543	−	17.4145i	0.504610	−	0.874010i	−0.495376	−	0.868679i	$-0.664970\pi$
$397$	10.0543	−	17.4145i	0.504610	−	0.874010i	0.999986	−	0.00533094i	$-0.00169690\pi$
$398$	10.9026			0.546497
$399$	16.2629	−	28.1681i	0.814161	−	1.41017i
$400$	10.6123	+	18.3811i	0.530617	+	0.919056i
$401$	16.1352	+	27.9471i	0.805756	+	1.39561i	0.915780	+	0.401681i	$0.131574\pi$
$401$	16.1352	+	27.9471i	0.805756	+	1.39561i	−0.110024	+	0.993929i	$0.535093\pi$
$402$	−3.05859	−	5.29763i	−0.152548	−	0.264222i
$403$	25.3261			1.26158
$404$	−26.3264	−	45.5986i	−1.30979	−	2.26862i
$405$	−3.33501	−	5.77641i	−0.165718	−	0.287032i
$406$	29.2717	−	50.7000i	1.45273	−	2.51620i
$407$	−1.27094	+	2.20134i	−0.0629983	+	0.109116i
$408$	−10.0966			−0.499854
$409$	−4.77615			−0.236166			−0.118083	−	0.993004i	$-0.537675\pi$
$409$	−4.77615			−0.236166			−0.118083	+	0.993004i	$0.537675\pi$
$410$	4.43544	−	7.68240i	0.219051	−	0.379407i
$411$	−6.45433	+	11.1792i	−0.318369	+	0.551431i
$412$	27.8338	+	48.2096i	1.37127	+	2.37512i
$413$	−20.1562	−	34.9116i	−0.991822	−	1.71789i
$414$	14.5119			0.713221
$415$	4.27548	+	7.40535i	0.209875	+	0.363514i
$416$	1.13690	+	1.96917i	0.0557411	+	0.0965464i
$417$	8.13060	+	14.0826i	0.398157	+	0.689629i
$418$	−17.7280	+	30.7058i	−0.867104	+	1.50187i
$419$	19.5576			0.955449			0.477725	−	0.878510i	$-0.341462\pi$
$419$	19.5576			0.955449			0.477725	+	0.878510i	$0.341462\pi$
$420$	−8.50919	+	14.7383i	−0.415206	+	0.719157i
$421$	8.59920	+	14.8942i	0.419099	+	0.725901i	0.995849	−	0.0910196i	$-0.0290126\pi$
$421$	8.59920	+	14.8942i	0.419099	+	0.725901i	−0.576750	+	0.816921i	$0.695679\pi$
$422$	−18.3579			−0.893648
$423$	2.27951	+	3.94823i	0.110834	+	0.191970i
$424$	−16.1246	+	27.9286i	−0.783080	+	1.35633i
$425$	2.30773	−	3.99711i	0.111941	−	0.193888i
$426$	47.4594			2.29942
$427$	21.6563	−	37.5099i	1.04802	−	1.81523i
$428$	−24.7318			−1.19546
$429$	−13.1849			−0.636573
$430$	−5.08330	+	8.65992i	−0.245138	+	0.417618i
$431$	7.52143			0.362295			0.181147	−	0.983456i	$-0.442019\pi$
$431$	7.52143			0.362295			0.181147	+	0.983456i	$0.442019\pi$
$432$	−19.7390			−0.949693
$433$	19.6580	−	34.0487i	0.944703	−	1.63627i	0.188359	−	0.982100i	$-0.439683\pi$
$433$	19.6580	−	34.0487i	0.944703	−	1.63627i	0.756344	−	0.654174i	$-0.226983\pi$
$434$	93.9012			4.50740
$435$	−4.16802	+	7.21921i	−0.199841	+	0.346135i
$436$	−9.68602	+	16.7767i	−0.463876	+	0.803457i
$437$	17.9005	+	31.0046i	0.856297	+	1.48315i
$438$	−39.2860			−1.87716
$439$	13.5451	+	23.4607i	0.646470	+	1.11972i	0.983960	+	0.178390i	$0.0570888\pi$
$439$	13.5451	+	23.4607i	0.646470	+	1.11972i	−0.337490	+	0.941329i	$0.609578\pi$
$440$	4.74898	−	8.22548i	0.226399	−	0.392134i
$441$	3.83475			0.182607
$442$	2.82611	−	4.89497i	0.134425	−	0.232830i
$443$	3.08056	+	5.33569i	0.146362	+	0.253507i	0.929880	−	0.367862i	$-0.119910\pi$
$443$	3.08056	+	5.33569i	0.146362	+	0.253507i	−0.783518	+	0.621369i	$0.786577\pi$
$444$	3.43343	+	5.94687i	0.162943	+	0.282226i
$445$	0.120437	+	0.208603i	0.00570925	+	0.00988871i
$446$	−54.4263			−2.57716
$447$	−0.793453	−	1.37430i	−0.0375291	−	0.0650022i
$448$	−11.5881	−	20.0712i	−0.547487	−	0.948276i
$449$	−14.0587	+	24.3504i	−0.663471	+	1.14917i	0.316226	+	0.948684i	$0.397584\pi$
$449$	−14.0587	+	24.3504i	−0.663471	+	1.14917i	−0.979697	+	0.200482i	$0.935749\pi$
$450$	−4.54342	+	7.86943i	−0.214179	+	0.370969i
$451$	17.1245			0.806362
$452$	−32.5595			−1.53147
$453$	4.44482	−	7.69865i	0.208836	−	0.361714i
$454$	16.2163	−	28.0875i	0.761070	−	1.31821i
$455$	−2.43884	−	4.22420i	−0.114335	−	0.198034i
$456$	24.5195	+	42.4690i	1.14823	+	1.98879i
$457$	−15.0493			−0.703975			−0.351988	−	0.936005i	$-0.614494\pi$
$457$	−15.0493			−0.703975			−0.351988	+	0.936005i	$0.614494\pi$
$458$	12.5154	+	21.6773i	0.584806	+	1.01291i
$459$	2.14619	+	3.71732i	0.100176	+	0.173509i
$460$	−9.36604	−	16.2225i	−0.436694	−	0.756376i
$461$	−3.93191	+	6.81028i	−0.183128	+	0.317186i	−0.942944	−	0.332951i	$-0.891955\pi$
$461$	−3.93191	+	6.81028i	−0.183128	+	0.317186i	0.759816	+	0.650138i	$0.225289\pi$
$462$	−48.8855			−2.27436
$463$	15.1232	−	26.1942i	0.702836	−	1.21735i	−0.264631	−	0.964350i	$-0.585250\pi$
$463$	15.1232	−	26.1942i	0.702836	−	1.21735i	0.967467	−	0.252998i	$-0.0814167\pi$
$464$	15.8617	+	27.4733i	0.736362	+	1.27542i
$465$	−13.3707			−0.620050
$466$	−7.41494	−	12.8431i	−0.343491	−	0.594943i
$467$	0.676510	−	1.17175i	0.0313051	−	0.0542221i	−0.849948	−	0.526866i	$-0.823367\pi$
$467$	0.676510	−	1.17175i	0.0313051	−	0.0542221i	0.881254	+	0.472644i	$0.156700\pi$
$468$	−3.73919	+	6.47647i	−0.172844	+	0.299375i
$469$	4.36858			0.201722
$470$	4.37838	−	7.58358i	0.201960	−	0.349804i
$471$	1.24477			0.0573559
$472$	60.7790			2.79758
$473$	−19.3841	−	0.139575i	−0.891280	−	0.00641768i
$474$	−16.9865			−0.780217
$475$	−22.4173			−1.02858
$476$	7.04179	−	12.1967i	0.322760	−	0.559036i
$477$	−4.96225			−0.227206
$478$	−4.22624	+	7.32005i	−0.193303	+	0.334811i
$479$	−6.69593	+	11.5977i	−0.305945	+	0.529912i	−0.977471	−	0.211068i	$-0.932306\pi$
$479$	−6.69593	+	11.5977i	−0.305945	+	0.529912i	0.671526	+	0.740981i	$0.265639\pi$
$480$	−0.600215	−	1.03960i	−0.0273959	−	0.0474512i
$481$	−1.96813			−0.0897391
$482$	−25.1841	−	43.6201i	−1.14710	−	1.98684i
$483$	−24.6806	+	42.7480i	−1.12301	+	1.94510i
$484$	−9.26742			−0.421247
$485$	−0.602143	+	1.04294i	−0.0273419	+	0.0473576i
$486$	−9.98010	−	17.2860i	−0.452707	−	0.784111i
$487$	1.25211	+	2.16871i	0.0567384	+	0.0982737i	0.892999	−	0.450058i	$-0.148597\pi$
$487$	1.25211	+	2.16871i	0.0567384	+	0.0982737i	−0.836261	+	0.548331i	$0.815263\pi$
$488$	32.6512	+	56.5536i	1.47805	+	2.56006i
$489$	8.08030			0.365404
$490$	−3.68281	−	6.37881i	−0.166372	−	0.288165i
$491$	13.8507	+	23.9901i	0.625073	+	1.08266i	0.988527	+	0.151046i	$0.0482643\pi$
$491$	13.8507	+	23.9901i	0.625073	+	1.08266i	−0.363453	+	0.931612i	$0.618402\pi$
$492$	23.1308	−	40.0637i	1.04282	−	1.80621i
$493$	3.44925	−	5.97427i	0.155346	−	0.269068i
$494$	−27.4529			−1.23516
$495$	1.46147			0.0656882
$496$	−25.4416	+	44.0661i	−1.14236	+	1.97863i
$497$	−16.9466	+	29.3523i	−0.760157	+	1.31663i
$498$	33.1779	+	57.4659i	1.48674	+	2.57511i
$499$	4.12421	+	7.14335i	0.184625	+	0.319780i	0.943450	−	0.331514i	$-0.107560\pi$
$499$	4.12421	+	7.14335i	0.184625	+	0.319780i	−0.758825	+	0.651295i	$0.774226\pi$
$500$	24.4360			1.09281
$501$	17.3532	+	30.0566i	0.775283	+	1.34283i
$502$	12.9842	+	22.4893i	0.579513	+	1.00375i
$503$	5.83130	+	10.1001i	0.260005	+	0.450342i	0.966243	−	0.257633i	$-0.0829425\pi$
$503$	5.83130	+	10.1001i	0.260005	+	0.450342i	−0.706238	+	0.707974i	$0.749609\pi$
$504$	−7.09791	+	12.2939i	−0.316166	+	0.547616i
$505$	−7.96713			−0.354533
$506$	26.9041	−	46.5992i	1.19603	−	2.07159i
$507$	7.56185	+	13.0975i	0.335834	+	0.581681i
$508$	27.1550			1.20481
$509$	−6.74989	−	11.6911i	−0.299183	−	0.518201i	0.676766	−	0.736198i	$-0.263381\pi$
$509$	−6.74989	−	11.6911i	−0.299183	−	0.518201i	−0.975949	+	0.217997i	$0.930048\pi$
$510$	−1.49202	+	2.58425i	−0.0660677	+	0.114433i
$511$	14.0281	−	24.2973i	0.620565	−	1.07485i
$512$	43.0852			1.90411
$513$	10.4241	−	18.0550i	0.460234	−	0.797148i
$514$	−13.4906			−0.595044
$515$	8.42333			0.371176
$516$	−26.5094	+	45.1615i	−1.16701	+	1.98812i
$517$	16.9042			0.743448
$518$	−7.29722			−0.320621
$519$	22.5393	−	39.0392i	0.989364	−	1.71363i
$520$	7.35409			0.322498
$521$	15.9122	−	27.5607i	0.697125	−	1.20746i	−0.272334	−	0.962203i	$-0.587796\pi$
$521$	15.9122	−	27.5607i	0.697125	−	1.20746i	0.969459	−	0.245253i	$-0.0788710\pi$
$522$	−6.79081	+	11.7620i	−0.297226	+	0.514810i
$523$	−2.23903	−	3.87811i	−0.0979057	−	0.169578i	0.812912	−	0.582387i	$-0.197881\pi$
$523$	−2.23903	−	3.87811i	−0.0979057	−	0.169578i	−0.910818	+	0.412809i	$0.864548\pi$
$524$	−66.1665			−2.89050
$525$	−15.4541	−	26.7673i	−0.674472	−	1.16822i
$526$	25.0434	−	43.3764i	1.09194	−	1.89130i
$527$	11.0649			0.481995
$528$	13.2450	−	22.9411i	0.576416	−	0.998382i
$529$	−15.6659	−	27.1341i	−0.681125	−	1.17974i
$530$	4.76563	+	8.25431i	0.207006	+	0.358544i
$531$	4.67609	+	8.09923i	0.202925	+	0.351477i
$532$	−68.4039			−2.96569
$533$	6.62959	+	11.4828i	0.287160	+	0.497375i
$534$	0.934595	+	1.61877i	0.0404439	+	0.0700508i
$535$	−1.87114	+	3.24091i	−0.0808964	+	0.140117i
$536$	−3.29325	+	5.70408i	−0.142247	+	0.246379i
$537$	−7.27099			−0.313766
$538$	−13.5041			−0.582204
$539$	7.10937	−	12.3138i	0.306222	−	0.530393i
$540$	−5.45416	+	9.44689i	−0.234710	+	0.406529i
$541$	5.07818	+	8.79566i	0.218328	+	0.378155i	0.954297	−	0.298860i	$-0.0966065\pi$
$541$	5.07818	+	8.79566i	0.218328	+	0.378155i	−0.735969	+	0.677015i	$0.763273\pi$
$542$	−34.0583	−	58.9906i	−1.46293	−	2.53386i
$543$	−29.5745			−1.26916
$544$	0.496709	+	0.860325i	0.0212962	+	0.0368861i
$545$	1.46564	+	2.53856i	0.0627810	+	0.108740i
$546$	−18.9255	−	32.7800i	−0.809939	−	1.40285i
$547$	−6.71516	+	11.6310i	−0.287119	+	0.497305i	−0.973121	−	0.230295i	$-0.926031\pi$
$547$	−6.71516	+	11.6310i	−0.287119	+	0.497305i	0.686002	+	0.727600i	$0.259364\pi$
$548$	27.1478			1.15970
$549$	−5.02411	+	8.70201i	−0.214424	+	0.371393i
$550$	16.8464	+	29.1788i	0.718332	+	1.24419i
$551$	−33.5060			−1.42740
$552$	−37.2109	−	64.4512i	−1.58380	−	2.74322i
$553$	6.06546	−	10.5057i	0.257930	−	0.446747i
$554$	30.0464	−	52.0418i	1.27655	−	2.21105i
$555$	1.03906			0.0441055
$556$	17.0992	−	29.6168i	0.725170	−	1.25603i
$557$	−27.1984			−1.15243			−0.576217	−	0.817297i	$-0.695471\pi$
$557$	−27.1984			−1.15243			−0.576217	+	0.817297i	$0.695471\pi$
$558$	−21.7844			−0.922207
$559$	−7.41076	−	13.0520i	−0.313442	−	0.552039i
$560$	9.79987			0.414120
$561$	−5.76046			−0.243207
$562$	25.9263	−	44.9057i	1.09363	−	1.89423i
$563$	8.12817			0.342562			0.171281	−	0.985222i	$-0.445209\pi$
$563$	8.12817			0.342562			0.171281	+	0.985222i	$0.445209\pi$
$564$	22.8333	−	39.5484i	0.961454	−	1.66529i
$565$	−2.46336	+	4.26667i	−0.103634	+	0.179500i
$566$	30.1788	+	52.2713i	1.26851	+	2.19712i
$567$	36.9641			1.55235
$568$	−25.5503	−	44.2544i	−1.07207	−	1.85688i
$569$	−23.0060	+	39.8476i	−0.964463	+	1.67050i	−0.253411	+	0.967359i	$0.581552\pi$
$569$	−23.0060	+	39.8476i	−0.964463	+	1.67050i	−0.711052	+	0.703140i	$0.751781\pi$
$570$	14.4935			0.607065
$571$	−12.8358	+	22.2323i	−0.537162	+	0.930393i	0.461893	+	0.886936i	$0.347170\pi$
$571$	−12.8358	+	22.2323i	−0.537162	+	0.930393i	−0.999055	+	0.0434568i	$0.986163\pi$
$572$	13.8644	+	24.0139i	0.579700	+	1.00407i
$573$	16.7289	+	28.9753i	0.698859	+	1.21046i
$574$	24.5805	+	42.5746i	1.02597	+	1.77703i
$575$	34.0206			1.41876
$576$	2.68836	+	4.65637i	0.112015	+	0.194016i
$577$	−4.08125	−	7.06894i	−0.169905	−	0.294284i	0.768481	−	0.639872i	$-0.221013\pi$
$577$	−4.08125	−	7.06894i	−0.169905	−	0.294284i	−0.938386	+	0.345588i	$0.887679\pi$
$578$	1.23472	−	2.13860i	0.0513577	−	0.0889541i
$579$	6.79509	−	11.7694i	0.282394	−	0.489121i
$580$	17.5313			0.727946
$581$	−47.3880			−1.96599
$582$	−4.67266	+	8.09328i	−0.193688	+	0.335477i
$583$	−9.19967	+	15.9343i	−0.381011	+	0.659931i
$584$	21.1501	+	36.6330i	0.875197	+	1.51589i
$585$	0.565794	+	0.979984i	0.0233927	+	0.0405174i
$586$	33.5929			1.38771
$587$	−7.91495	−	13.7091i	−0.326685	−	0.565835i	0.655167	−	0.755484i	$-0.272598\pi$
$587$	−7.91495	−	13.7091i	−0.326685	−	0.565835i	−0.981852	+	0.189649i	$0.939265\pi$
$588$	−19.2058	−	33.2655i	−0.792036	−	1.37185i
$589$	−26.8711	−	46.5422i	−1.10721	−	1.91774i
$590$	8.98162	−	15.5566i	0.369767	−	0.640456i
$591$	−29.4900			−1.21306
$592$	1.97711	−	3.42445i	0.0812586	−	0.140744i
$593$	14.2501	+	24.6818i	0.585179	+	1.01356i	0.994853	+	0.101328i	$0.0323093\pi$
$593$	14.2501	+	24.6818i	0.585179	+	1.01356i	−0.409674	+	0.912232i	$0.634357\pi$
$594$	−31.3343			−1.28566
$595$	−1.06553	−	1.84554i	−0.0436823	−	0.0756599i
$596$	−1.66869	+	2.89025i	−0.0683522	+	0.118389i
$597$	4.30165	−	7.45068i	0.176055	−	0.304936i
$598$	41.6626			1.70371
$599$	−8.09204	+	14.0158i	−0.330632	+	0.572671i	−0.982636	−	0.185545i	$-0.940595\pi$
$599$	−8.09204	+	14.0158i	−0.330632	+	0.572671i	0.652004	+	0.758215i	$0.273928\pi$
$600$	46.6003			1.90245
$601$	−14.2229			−0.580165			−0.290083	−	0.957002i	$-0.593683\pi$
$601$	−14.2229			−0.580165			−0.290083	+	0.957002i	$0.593683\pi$
$602$	−27.4768	−	48.3926i	−1.11987	−	1.97233i
$603$	−1.01348			−0.0412720
$604$	−18.6956			−0.760711
$605$	−0.701149	+	1.21442i	−0.0285057	+	0.0493734i
$606$	−61.8253			−2.51148
$607$	−16.6270	+	28.7989i	−0.674870	+	1.16891i	0.301636	+	0.953423i	$0.402467\pi$
$607$	−16.6270	+	28.7989i	−0.674870	+	1.16891i	−0.976507	+	0.215487i	$0.930866\pi$
$608$	2.41251	−	4.17860i	0.0978404	−	0.169464i
$609$	−23.0985	−	40.0077i	−0.935997	−	1.62119i
$610$	19.3001			0.781440
$611$	6.54431	+	11.3351i	0.264755	+	0.458568i
$612$	−1.63364	+	2.82955i	−0.0660361	+	0.114378i
$613$	−22.3602			−0.903120			−0.451560	−	0.892241i	$-0.649132\pi$
$613$	−22.3602			−0.903120			−0.451560	+	0.892241i	$0.649132\pi$
$614$	−12.8491	+	22.2553i	−0.518548	+	0.898152i
$615$	−3.50003	−	6.06223i	−0.141135	−	0.244453i
$616$	26.3181	+	45.5842i	1.06039	+	1.83664i
$617$	−19.3399	−	33.4977i	−0.778596	−	1.34857i	−0.932751	−	0.360521i	$-0.882599\pi$
$617$	−19.3399	−	33.4977i	−0.778596	−	1.34857i	0.154155	−	0.988047i	$-0.450734\pi$
$618$	65.3655			2.62938
$619$	18.5356	+	32.1046i	0.745008	+	1.29039i	0.950191	+	0.311668i	$0.100888\pi$
$619$	18.5356	+	32.1046i	0.745008	+	1.29039i	−0.205183	+	0.978724i	$0.565779\pi$
$620$	14.0597	+	24.3522i	0.564652	+	0.978007i
$621$	−15.8196	+	27.4004i	−0.634819	+	1.09954i
$622$	36.6138	−	63.4169i	1.46808	−	2.54279i
$623$	−1.33488			−0.0534809
$624$	20.5107			0.821087
$625$	−9.68989	+	16.7834i	−0.387596	+	0.671336i
$626$	41.7636	−	72.3367i	1.66921	−	2.89116i
$627$	13.9893	+	24.2301i	0.558678	+	0.967658i
$628$	−1.30892	−	2.26712i	−0.0522316	−	0.0904678i
$629$	−0.859872			−0.0342854
$630$	2.09779	+	3.63347i	0.0835779	+	0.144761i
$631$	−3.96218	−	6.86270i	−0.157732	−	0.273200i	0.776318	−	0.630341i	$-0.217085\pi$
$631$	−3.96218	−	6.86270i	−0.157732	−	0.273200i	−0.934050	+	0.357141i	$0.883752\pi$
$632$	9.14489	+	15.8394i	0.363764	+	0.630058i
$633$	−7.24316	+	12.5455i	−0.287890	+	0.498640i
$634$	−44.7150			−1.77586
$635$	2.05448	−	3.55846i	0.0815294	−	0.141213i
$636$	24.8528	+	43.0462i	0.985476	+	1.70689i
$637$	11.0093			0.436204
$638$	25.1794	+	43.6120i	0.996863	+	1.72662i
$639$	3.93148	−	6.80952i	0.155527	−	0.269380i
$640$	5.77970	−	10.0107i	0.228463	−	0.395709i
$641$	−11.9133			−0.470548			−0.235274	−	0.971929i	$-0.575599\pi$
$641$	−11.9133			−0.470548			−0.235274	+	0.971929i	$0.575599\pi$
$642$	−14.5201	+	25.1496i	−0.573064	+	0.992576i
$643$	5.68112			0.224041			0.112021	−	0.993706i	$-0.464268\pi$
$643$	5.68112			0.224041			0.112021	+	0.993706i	$0.464268\pi$
$644$	103.810			4.09069
$645$	3.91244	+	6.89065i	0.154052	+	0.271319i
$646$	−11.9941			−0.471902
$647$	−2.63127			−0.103446			−0.0517229	−	0.998661i	$-0.516471\pi$
$647$	−2.63127			−0.103446			−0.0517229	+	0.998661i	$0.516471\pi$
$648$	−27.8654	+	48.2643i	−1.09466	+	1.89600i
$649$	34.6766			1.36118
$650$	−13.0438	+	22.5926i	−0.511621	+	0.886153i
$651$	37.0490	−	64.1708i	1.45207	−	2.51505i
$652$	−8.49672	−	14.7168i	−0.332757	−	0.576353i
$653$	47.6438			1.86445			0.932224	−	0.361882i	$-0.117866\pi$
$653$	47.6438			1.86445			0.932224	+	0.361882i	$0.117866\pi$
$654$	11.3734	+	19.6993i	0.444735	+	0.770304i
$655$	−5.00598	+	8.67061i	−0.195600	+	0.338789i
$656$	−26.6393			−1.04009
$657$	−3.25441	+	5.63680i	−0.126967	+	0.219913i
$658$	24.2643	+	42.0269i	0.945920	+	1.63838i
$659$	−1.53235	−	2.65410i	−0.0596918	−	0.103389i	0.834635	−	0.550803i	$-0.185678\pi$
$659$	−1.53235	−	2.65410i	−0.0596918	−	0.103389i	−0.894327	+	0.447414i	$0.852345\pi$
$660$	−7.31958	−	12.6779i	−0.284914	−	0.493486i
$661$	20.2157			0.786300			0.393150	−	0.919474i	$-0.371385\pi$
$661$	20.2157			0.786300			0.393150	+	0.919474i	$0.371385\pi$
$662$	−3.04971	−	5.28226i	−0.118530	−	0.205301i
$663$	−2.23010	−	3.86265i	−0.0866101	−	0.150013i
$664$	35.7234	−	61.8748i	1.38634	−	2.40121i
$665$	−5.17526	+	8.96381i	−0.200688	+	0.347602i
$666$	1.69290			0.0655986
$667$	50.8488			1.96887
$668$	36.4950	−	63.2112i	1.41203	−	2.44571i
$669$	−21.4741	+	37.1942i	−0.830235	+	1.43801i
$670$	0.973320	+	1.68584i	0.0376026	+	0.0651297i
$671$	18.6287	+	32.2659i	0.719154	+	1.24561i
$672$	6.65259			0.256629
$673$	1.79296	+	3.10550i	0.0691135	+	0.119708i	0.898511	−	0.438950i	$-0.144650\pi$
$673$	1.79296	+	3.10550i	0.0691135	+	0.119708i	−0.829398	+	0.558658i	$0.811316\pi$
$674$	25.9665	+	44.9753i	1.00019	+	1.73239i
$675$	−9.90567	−	17.1571i	−0.381270	−	0.660378i
$676$	15.9031	−	27.5450i	0.611658	−	1.05942i
$677$	−3.77227			−0.144980			−0.0724901	−	0.997369i	$-0.523095\pi$
$677$	−3.77227			−0.144980			−0.0724901	+	0.997369i	$0.523095\pi$
$678$	−19.1158	+	33.1096i	−0.734138	+	1.27157i
$679$	−3.33698	−	5.77981i	−0.128061	−	0.221809i
$680$	3.21298			0.123212
$681$	−12.7964	−	22.1640i	−0.490359	−	0.849327i
$682$	−40.3868	+	69.9520i	−1.54649	+	2.67860i
$683$	−18.0210	+	31.2132i	−0.689553	+	1.19434i	0.282429	+	0.959288i	$0.408860\pi$
$683$	−18.0210	+	31.2132i	−0.689553	+	1.19434i	−0.971983	+	0.235053i	$0.924474\pi$
$684$	15.8692			0.606775
$685$	2.05393	−	3.55752i	0.0784767	−	0.135926i
$686$	−18.5857			−0.709607
$687$	19.7519			0.753584
$688$	30.1543	+	0.217127i	1.14962	+	0.00827787i
$689$	−14.2463			−0.542739
$690$	−21.9954			−0.837350
$691$	5.53241	−	9.58241i	0.210463	−	0.364532i	−0.741397	−	0.671067i	$-0.765836\pi$
$691$	5.53241	−	9.58241i	0.210463	−	0.364532i	0.951859	+	0.306535i	$0.0991696\pi$
$692$	−94.8034			−3.60388
$693$	−4.04962	+	7.01414i	−0.153832	+	0.266445i
$694$	25.7010	−	44.5154i	0.975596	−	1.68978i
$695$	−2.58737	−	4.48145i	−0.0981444	−	0.169991i
$696$	69.6511			2.64012
$697$	2.89645	+	5.01681i	0.109711	+	0.190025i
$698$	−35.7472	+	61.9159i	−1.35305	+	2.34355i
$699$	−11.7024			−0.442624
$700$	−32.5011	+	56.2936i	−1.22843	+	2.12770i
$701$	−6.91749	−	11.9814i	−0.261270	−	0.452533i	0.705310	−	0.708899i	$-0.250808\pi$
$701$	−6.91749	−	11.9814i	−0.261270	−	0.452533i	−0.966580	+	0.256366i	$0.917475\pi$
$702$	−12.1308	−	21.0111i	−0.457847	−	0.793014i
$703$	2.08820	+	3.61687i	0.0787580	+	0.136413i
$704$	19.9361			0.751372
$705$	−3.45501	−	5.98425i	−0.130123	−	0.225380i
$706$	−30.6852	−	53.1484i	−1.15485	−	2.00027i
$707$	22.0763	−	38.2372i	0.830264	−	1.43806i
$708$	46.8392	−	81.1278i	1.76032	−	3.04897i
$709$	16.8366			0.632311			0.316155	−	0.948707i	$-0.397608\pi$
$709$	16.8366			0.632311			0.316155	+	0.948707i	$0.397608\pi$
$710$	−15.1028			−0.566798
$711$	−1.40714	+	2.43724i	−0.0527720	+	0.0914038i
$712$	1.00630	−	1.74296i	0.0377127	−	0.0653203i
$713$	40.7798	+	70.6326i	1.52721	+	2.64521i
$714$	−8.26853	−	14.3215i	−0.309442	−	0.535969i
$715$	4.19578			0.156913
$716$	7.64571	+	13.2428i	0.285734	+	0.494905i
$717$	3.33495	+	5.77630i	0.124546	+	0.215720i
$718$	−6.52806	−	11.3069i	−0.243625	−	0.421971i
$719$	23.5523	−	40.7937i	0.878351	−	1.52135i	0.0252008	−	0.999682i	$-0.491977\pi$
$719$	23.5523	−	40.7937i	0.878351	−	1.52135i	0.853150	−	0.521666i	$-0.174689\pi$
$720$	−2.27350			−0.0847283
$721$	−23.3404	+	40.4267i	−0.869241	+	1.50557i
$722$	5.66794	+	9.81716i	0.210939	+	0.365357i
$723$	−39.7458			−1.47816
$724$	31.0986	+	53.8644i	1.15577	+	2.00186i
$725$	−15.9199	+	27.5740i	−0.591249	+	1.02407i
$726$	−5.44095	+	9.42399i	−0.201932	+	0.349757i
$727$	31.8271			1.18040			0.590202	−	0.807256i	$-0.299048\pi$
$727$	31.8271			1.18040			0.590202	+	0.807256i	$0.299048\pi$
$728$	−20.3776	+	35.2950i	−0.755243	+	1.30812i
$729$	16.5177			0.611768
$730$	12.5018			0.462713
$731$	−3.23774	−	5.70237i	−0.119752	−	0.210910i
$732$	100.650			3.72014
$733$	25.3908			0.937829			0.468915	−	0.883243i	$-0.344645\pi$
$733$	25.3908			0.937829			0.468915	+	0.883243i	$0.344645\pi$
$734$	0.906628	−	1.57033i	0.0334643	−	0.0579618i
$735$	−5.81225			−0.214388
$736$	−3.66124	+	6.34146i	−0.134955	+	0.233749i
$737$	−1.87892	+	3.25438i	−0.0692109	+	0.119877i
$738$	−5.70249	−	9.87700i	−0.209911	−	0.363577i
$739$	34.9214			1.28461			0.642303	−	0.766451i	$-0.277979\pi$
$739$	34.9214			1.28461			0.642303	+	0.766451i	$0.277979\pi$
$740$	−1.09261	−	1.89245i	−0.0401650	−	0.0695678i
$741$	−10.8316	+	18.7609i	−0.397909	+	0.689199i
$742$	−52.8206			−1.93911
$743$	−17.4289	+	30.1878i	−0.639406	+	1.10748i	0.346157	+	0.938177i	$0.387486\pi$
$743$	−17.4289	+	30.1878i	−0.639406	+	1.10748i	−0.985563	+	0.169307i	$0.945847\pi$
$744$	55.8588	+	96.7502i	2.04788	+	3.54704i
$745$	0.252497	+	0.437338i	0.00925078	+	0.0160228i
$746$	−24.3006	−	42.0899i	−0.889708	−	1.54102i
$747$	10.9937			0.402238
$748$	6.05733	+	10.4916i	0.221478	+	0.383611i
$749$	−10.3695	−	17.9606i	−0.378895	−	0.656265i
$750$	14.3465	−	24.8488i	0.523859	−	0.907350i
$751$	−22.1111	+	38.2976i	−0.806846	+	1.39750i	0.108192	+	0.994130i	$0.465494\pi$
$751$	−22.1111	+	38.2976i	−0.806846	+	1.39750i	−0.915038	+	0.403368i	$0.867839\pi$
$752$	−26.2966			−0.958940
$753$	20.4918			0.746763
$754$	−19.4959	+	33.7679i	−0.710000	+	1.22976i
$755$	−1.41446	+	2.44991i	−0.0514773	+	0.0891613i
$756$	−30.2261	−	52.3531i	−1.09931	−	1.90406i
$757$	2.45297	+	4.24866i	0.0891546	+	0.154420i	0.907154	−	0.420799i	$-0.138250\pi$
$757$	2.45297	+	4.24866i	0.0891546	+	0.154420i	−0.817999	+	0.575219i	$0.804917\pi$
$758$	31.6873			1.15093
$759$	−21.2302	−	36.7717i	−0.770607	−	1.33473i
$760$	−7.80273	−	13.5147i	−0.283035	−	0.490231i
$761$	21.1588	+	36.6482i	0.767007	+	1.32849i	0.939179	+	0.343428i	$0.111588\pi$
$761$	21.1588	+	36.6482i	0.767007	+	1.32849i	−0.172172	+	0.985067i	$0.555079\pi$
$762$	15.9428	−	27.6138i	0.577548	−	1.00034i
$763$	−16.2446			−0.588095
$764$	35.1820	−	60.9370i	1.27284	−	2.20462i
$765$	0.247194	+	0.428153i	0.00893732	+	0.0154799i
$766$	−38.0292			−1.37405
$767$	13.4247	+	23.2523i	0.484738	+	0.839592i
$768$	31.7090	−	54.9216i	1.14420	−	1.98181i
$769$	20.2123	−	35.0087i	0.728873	−	1.26245i	−0.228486	−	0.973547i	$-0.573378\pi$
$769$	20.2123	−	35.0087i	0.728873	−	1.26245i	0.957360	−	0.288899i	$-0.0932891\pi$
$770$	15.5566			0.560622
$771$	−5.32275	+	9.21928i	−0.191694	+	0.332024i
$772$	−28.5811			−1.02866
$773$	4.81595			0.173218			0.0866089	−	0.996242i	$-0.472397\pi$
$773$	4.81595			0.173218			0.0866089	+	0.996242i	$0.472397\pi$
$774$	6.37441	+	11.2267i	0.229124	+	0.403536i
$775$	−51.0697			−1.83448
$776$	10.0623			0.361216
$777$	−2.87914	+	4.98682i	−0.103289	+	0.178901i
$778$	−28.0223			−1.00465
$779$	14.0681	−	24.3666i	0.504041	−	0.873025i
$780$	5.66741	−	9.81624i	0.202926	−	0.351478i
$781$	−14.5774	−	25.2488i	−0.521620	−	0.903472i
$782$	18.2023			0.650913
$783$	−14.8055	−	25.6439i	−0.529105	−	0.916438i
$784$	−11.0595	+	19.1556i	−0.394982	+	0.684129i
$785$	−0.396117			−0.0141380
$786$	−38.8466	+	67.2843i	−1.38561	+	2.39995i
$787$	−15.0773	−	26.1147i	−0.537449	−	0.930889i	−0.999040	−	0.0437961i	$-0.986055\pi$
$787$	−15.0773	−	26.1147i	−0.537449	−	0.930889i	0.461592	−	0.887092i	$-0.347279\pi$
$788$	31.0098	+	53.7106i	1.10468	+	1.91336i
$789$	−19.7619	−	34.2286i	−0.703542	−	1.21857i
$790$	5.40555			0.192321
$791$	−13.6516	−	23.6452i	−0.485393	−	0.840726i
$792$	−6.10560	−	10.5752i	−0.216953	−	0.375774i
$793$	−14.4239	+	24.9828i	−0.512206	+	0.887167i
$794$	−24.8285	+	43.0042i	−0.881130	+	1.52616i
$795$	7.52117			0.266748
$796$	−18.0934			−0.641302
$797$	−13.0628	+	22.6254i	−0.462707	+	0.801432i	−0.999095	−	0.0425393i	$-0.986455\pi$
$797$	−13.0628	+	22.6254i	−0.462707	+	0.801432i	0.536388	+	0.843972i	$0.319789\pi$
$798$	−40.1602	+	69.5596i	−1.42166	+	2.46238i
$799$	2.85920	+	4.95227i	0.101151	+	0.175199i
$800$	−2.29254	−	3.97079i	−0.0810535	−	0.140389i
$801$	0.309683			0.0109421
$802$	−39.8451	−	69.0138i	−1.40698	−	2.43696i
$803$	12.0669	+	20.9005i	0.425832	+	0.737562i
$804$	5.07587	+	8.79166i	0.179012	+	0.310058i
$805$	7.85400	−	13.6035i	0.276817	−	0.479461i
$806$	−62.5414			−2.20293
$807$	−5.32810	+	9.22854i	−0.187558	+	0.324860i
$808$	33.2844	+	57.6502i	1.17094	+	2.02813i
$809$	25.2109			0.886368			0.443184	−	0.896431i	$-0.353849\pi$
$809$	25.2109			0.886368			0.443184	+	0.896431i	$0.353849\pi$
$810$	8.23562	+	14.2645i	0.289370	+	0.501204i
$811$	−6.79088	+	11.7622i	−0.238460	+	0.413025i	−0.960273	−	0.279064i	$-0.909976\pi$
$811$	−6.79088	+	11.7622i	−0.238460	+	0.413025i	0.721812	+	0.692089i	$0.243309\pi$
$812$	−48.5777	+	84.1391i	−1.70474	+	2.95270i
$813$	−53.7512			−1.88514
$814$	3.13852	−	5.43608i	0.110005	−	0.190535i
$815$	−2.57136			−0.0900707
$816$	8.96110			0.313701
$817$	−16.1229	+	27.4671i	−0.564070	+	0.960952i
$818$	11.7944			0.412383
$819$	−6.27108			−0.219129
$820$	−7.36082	+	12.7493i	−0.257051	+	0.445225i
$821$	−38.9758			−1.36026			−0.680132	−	0.733090i	$-0.738078\pi$
$821$	−38.9758			−1.36026			−0.680132	+	0.733090i	$0.738078\pi$
$822$	15.9386	−	27.6065i	0.555923	−	0.962887i
$823$	10.3899	−	17.9959i	0.362170	−	0.627298i	−0.626147	−	0.779705i	$-0.715369\pi$
$823$	10.3899	−	17.9959i	0.362170	−	0.627298i	0.988318	+	0.152407i	$0.0487025\pi$
$824$	−35.1903	−	60.9513i	−1.22591	−	2.12334i
$825$	26.5872			0.925646
$826$	49.7746	+	86.2122i	1.73188	+	2.99971i
$827$	7.33609	−	12.7065i	0.255101	−	0.441848i	−0.709822	−	0.704381i	$-0.751225\pi$
$827$	7.33609	−	12.7065i	0.255101	−	0.441848i	0.964923	+	0.262533i	$0.0845580\pi$
$828$	−24.0832			−0.836949
$829$	−11.4477	+	19.8280i	−0.397594	+	0.688653i	−0.993429	−	0.114454i	$-0.963488\pi$
$829$	−11.4477	+	19.8280i	−0.397594	+	0.688653i	0.595834	+	0.803107i	$0.296821\pi$
$830$	−10.5581	−	18.2871i	−0.366476	−	0.634755i
$831$	−23.7098	−	41.0665i	−0.822483	−	1.42458i
$832$	7.71808	+	13.3681i	0.267576	+	0.463456i
$833$	4.80994			0.166654
$834$	−20.0781	−	34.7763i	−0.695247	−	1.20420i
$835$	−5.52223	−	9.56477i	−0.191104	−	0.331003i
$836$	29.4204	−	50.9577i	1.01753	−	1.76241i
$837$	23.7474	−	41.1318i	0.820832	−	1.42172i
$838$	−48.2963			−1.66837
$839$	−27.6166			−0.953431			−0.476715	−	0.879058i	$-0.658173\pi$
$839$	−27.6166			−0.953431			−0.476715	+	0.879058i	$0.658173\pi$
$840$	10.7581	−	18.6337i	0.371191	−	0.642922i
$841$	−9.29461	+	16.0987i	−0.320504	+	0.555129i
$842$	−21.2353	−	36.7805i	−0.731815	−	1.26754i
$843$	−20.4586	−	35.4353i	−0.704632	−	1.22046i
$844$	30.4658			1.04868
$845$	−2.40637	−	4.16796i	−0.0827818	−	0.143382i
$846$	−5.62913	−	9.74995i	−0.193534	−	0.335210i
$847$	−3.88565	−	6.73014i	−0.133513	−	0.231250i
$848$	14.3112	−	24.7878i	0.491449	−	0.851215i
$849$	47.6286			1.63461
$850$	−5.69882	+	9.87064i	−0.195468	+	0.338560i
$851$	−3.16906	−	5.48898i	−0.108634	−	0.188160i
$852$	−78.7611			−2.69831
$853$	3.70337	+	6.41443i	0.126801	+	0.219626i	0.922436	−	0.386151i	$-0.126196\pi$
$853$	3.70337	+	6.41443i	0.126801	+	0.219626i	−0.795634	+	0.605777i	$0.792862\pi$
$854$	−53.4791	+	92.6286i	−1.83002	+	3.16968i
$855$	1.20062	−	2.07954i	0.0410604	−	0.0711187i
$856$	31.2683			1.06873
$857$	12.9285	−	22.3927i	0.441628	−	0.764922i	−0.556183	−	0.831060i	$-0.687735\pi$
$857$	12.9285	−	22.3927i	0.441628	−	0.764922i	0.997810	+	0.0661384i	$0.0210679\pi$
$858$	32.5594			1.11156
$859$	−56.5919			−1.93089			−0.965445	−	0.260607i	$-0.916077\pi$
$859$	−56.5919			−1.93089			−0.965445	+	0.260607i	$0.916077\pi$
$860$	8.43597	−	14.3715i	0.287664	−	0.490066i
$861$	38.7932			1.32207
$862$	−18.5738			−0.632625
$863$	10.8759	−	18.8375i	0.370219	−	0.641238i	−0.619380	−	0.785091i	$-0.712616\pi$
$863$	10.8759	−	18.8375i	0.370219	−	0.641238i	0.989599	+	0.143854i	$0.0459494\pi$
$864$	4.26413			0.145069
$865$	−7.17257	+	12.4233i	−0.243875	+	0.422403i
$866$	−48.5444	+	84.0813i	−1.64960	+	2.85720i
$867$	−0.974328	−	1.68758i	−0.0330899	−	0.0573134i
$868$	−155.833			−5.28933
$869$	5.21750	+	9.03697i	0.176991	+	0.306558i
$870$	10.2927	−	17.8275i	0.348955	−	0.604407i
$871$	−2.90962			−0.0985888
$872$	12.2460	−	21.2107i	0.414702	−	0.718285i
$873$	0.774154	+	1.34087i	0.0262012	+	0.0453817i
$874$	−44.2043	−	76.5641i	−1.49523	−	2.58982i
$875$	10.2455	+	17.7458i	0.346362	+	0.599916i
$876$	65.1971			2.20280
$877$	−26.1236	−	45.2474i	−0.882132	−	1.52790i	−0.848966	−	0.528447i	$-0.822775\pi$
$877$	−26.1236	−	45.2474i	−0.882132	−	1.52790i	−0.0331652	−	0.999450i	$-0.510559\pi$
$878$	−33.4488	−	57.9350i	−1.12884	−	1.95521i
$879$	13.2542	−	22.9570i	0.447053	−	0.774319i
$880$	−4.21491	+	7.30044i	−0.142085	+	0.246098i
$881$	51.7912			1.74489			0.872446	−	0.488711i	$-0.162533\pi$
$881$	51.7912			1.74489			0.872446	+	0.488711i	$0.162533\pi$
$882$	−9.46972			−0.318862
$883$	21.8638	−	37.8691i	0.735774	−	1.27440i	−0.218609	−	0.975813i	$-0.570152\pi$
$883$	21.8638	−	37.8691i	0.735774	−	1.27440i	0.954383	−	0.298586i	$-0.0965148\pi$
$884$	−4.69007	+	8.12344i	−0.157744	+	0.273221i
$885$	−7.08745	−	12.2758i	−0.238242	−	0.412647i
$886$	−7.60729	−	13.1762i	−0.255572	−	0.442663i
$887$	13.8481			0.464973			0.232487	−	0.972600i	$-0.425314\pi$
$887$	13.8481			0.464973			0.232487	+	0.972600i	$0.425314\pi$
$888$	−4.34088	−	7.51862i	−0.145670	−	0.252308i
$889$	11.3856	+	19.7204i	0.381860	+	0.661401i
$890$	−0.297412	−	0.515133i	−0.00996927	−	0.0172673i
$891$	−15.8982	+	27.5365i	−0.532611	+	0.922509i
$892$	90.3230			3.02424
$893$	13.8871	−	24.0532i	0.464715	−	0.804909i
$894$	1.95939	+	3.39376i	0.0655318	+	0.113504i
$895$	2.31382			0.0773423
$896$	32.0302	+	55.4779i	1.07005	+	1.85339i
$897$	16.4381	−	28.4716i	0.548853	−	0.950641i
$898$	34.7172	−	60.1320i	1.15853	−	2.00663i
$899$	−76.3312			−2.54579
$900$	7.54002	−	13.0597i	0.251334	−	0.435323i
$901$	−6.22415			−0.207357
$902$	−42.2881			−1.40804
$903$	−43.9119	−	0.316188i	−1.46129	−	0.0105221i
$904$	41.1649			1.36912
$905$	9.41136			0.312844
$906$	−10.9762	+	19.0114i	−0.364661	+	0.631612i
$907$	−26.9863			−0.896066			−0.448033	−	0.894017i	$-0.647875\pi$
$907$	−26.9863			−0.896066			−0.448033	+	0.894017i	$0.647875\pi$
$908$	−26.9118	+	46.6125i	−0.893098	+	1.54689i
$909$	−5.12154	+	8.87076i	−0.169871	+	0.294225i
$910$	6.02259	+	10.4314i	0.199647	+	0.345799i
$911$	36.7573			1.21782			0.608912	−	0.793238i	$-0.291606\pi$
$911$	36.7573			1.21782			0.608912	+	0.793238i	$0.291606\pi$
$912$	−21.7620	−	37.6929i	−0.720613	−	1.24814i
$913$	20.3815	−	35.3018i	0.674530	−	1.16832i
$914$	37.1634			1.22925
$915$	7.61493	−	13.1895i	0.251742	−	0.436030i
$916$	−20.7699	−	35.9745i	−0.686256	−	1.18863i
$917$	−27.7423	−	48.0511i	−0.916132	−	1.58679i
$918$	−5.29991	−	9.17971i	−0.174923	−	0.302976i
$919$	−24.0211			−0.792384			−0.396192	−	0.918168i	$-0.629669\pi$
$919$	−24.0211			−0.792384			−0.396192	+	0.918168i	$0.629669\pi$
$920$	11.8415	+	20.5100i	0.390401	+	0.676195i
$921$	10.1393	+	17.5618i	0.334102	+	0.578682i
$922$	9.70965	−	16.8176i	0.319770	−	0.553858i
$923$	11.2870	−	19.5496i	0.371516	−	0.643484i
$924$	81.1278			2.66891
$925$	3.96871			0.130490
$926$	−37.3460	+	64.6852i	−1.22727	+	2.12569i
$927$	5.41480	−	9.37870i	0.177845	−	0.308037i
$928$	−3.42654	−	5.93494i	−0.112482	−	0.194824i
$929$	14.1901	+	24.5779i	0.465561	+	0.806375i	0.999227	−	0.0393203i	$-0.0125193\pi$
$929$	14.1901	+	24.5779i	0.465561	+	0.806375i	−0.533666	+	0.845696i	$0.679186\pi$
$930$	33.0181			1.08271
$931$	−11.6809	−	20.2320i	−0.382827	−	0.663076i
$932$	12.3055	+	21.3137i	0.403078	+	0.698152i
$933$	−28.8922	−	50.0427i	−0.945887	−	1.63832i
$934$	−1.67060	+	2.89357i	−0.0546638	+	0.0946805i
$935$	1.83312			0.0599496
$936$	4.72745	−	8.18818i	0.154522	−	0.267639i
$937$	5.12075	+	8.86941i	0.167288	+	0.289751i	0.937465	−	0.348079i	$-0.113166\pi$
$937$	5.12075	+	8.86941i	0.167288	+	0.289751i	−0.770178	+	0.637830i	$0.779832\pi$
$938$	−10.7880			−0.352240
$939$	−32.9559	−	57.0814i	−1.07548	−	1.86278i
$940$	−7.26613	+	12.5853i	−0.236995	+	0.410487i
$941$	−10.0070	+	17.3326i	−0.326218	+	0.565026i	−0.981758	−	0.190134i	$-0.939108\pi$
$941$	−10.0070	+	17.3326i	−0.326218	+	0.565026i	0.655540	+	0.755160i	$0.272441\pi$
$942$	−3.07389			−0.100153
$943$	−21.3498	+	36.9789i	−0.695245	+	1.20420i
$944$	−53.9438			−1.75572
$945$	−9.14730			−0.297562
$946$	47.8679	+	0.344674i	1.55632	+	0.0112063i
$947$	19.9649			0.648773			0.324387	−	0.945925i	$-0.394842\pi$
$947$	19.9649			0.648773			0.324387	+	0.945925i	$0.394842\pi$
$948$	28.1899			0.915567
$949$	−9.34317	+	16.1828i	−0.303292	+	0.525317i
$950$	55.3583			1.79606
$951$	−17.6424	+	30.5576i	−0.572095	+	0.990898i
$952$	−8.90292	+	15.4203i	−0.288545	+	0.499775i
$953$	12.3766	+	21.4369i	0.400917	+	0.694409i	0.993837	−	0.110853i	$-0.0353581\pi$
$953$	12.3766	+	21.4369i	0.400917	+	0.694409i	−0.592920	+	0.805262i	$0.702025\pi$
$954$	12.2540			0.396738
$955$	−5.32355	−	9.22067i	−0.172266	−	0.298374i
$956$	7.01364	−	12.1480i	0.226837	−	0.392894i
$957$	39.7385			1.28456
$958$	16.5352	−	28.6399i	0.534230	−	0.925313i
$959$	11.3826	+	19.7152i	0.367562	+	0.636636i
$960$	−4.07469	−	7.05756i	−0.131510	−	0.227782i
$961$	−45.7161	−	79.1826i	−1.47471	−	2.55428i
$962$	4.86020			0.156699
$963$	2.40566	+	4.16672i	0.0775213	+	0.134271i
$964$	41.7942	+	72.3896i	1.34610	+	2.33151i
$965$	−2.16237	+	3.74534i	−0.0696092	+	0.120567i
$966$	60.9474	−	105.564i	1.96095	−	3.39646i
$967$	−1.00999			−0.0324791			−0.0162396	−	0.999868i	$-0.505169\pi$
$967$	−1.00999			−0.0324791			−0.0162396	+	0.999868i	$0.505169\pi$
$968$	11.7168			0.376592
$969$	−4.73231	+	8.19660i	−0.152024	+	0.263313i
$970$	1.48696	−	2.57549i	0.0477434	−	0.0826940i
$971$	−3.44768	−	5.97155i	−0.110641	−	0.191636i	0.805388	−	0.592748i	$-0.201957\pi$
$971$	−3.44768	−	5.97155i	−0.110641	−	0.191636i	−0.916029	+	0.401112i	$0.868624\pi$
$972$	16.5625	+	28.6870i	0.531241	+	0.920136i
$973$	28.6775			0.919359
$974$	−3.09201	−	5.35552i	−0.0990743	−	0.171602i
$975$	10.2930	+	17.8279i	0.329639	+	0.570951i
$976$	−28.9793	−	50.1936i	−0.927604	−	1.60666i
$977$	21.5476	−	37.3215i	0.689367	−	1.19402i	−0.282675	−	0.959216i	$-0.591222\pi$
$977$	21.5476	−	37.3215i	0.689367	−	1.19402i	0.972043	−	0.234804i	$-0.0754447\pi$
$978$	−19.9539			−0.638054
$979$	0.574131	−	0.994424i	0.0183493	−	0.0317819i
$980$	6.11179	+	10.5859i	0.195234	+	0.338155i
$981$	3.76864			0.120323
$982$	−34.2035	−	59.2423i	−1.09148	−	1.89050i
$983$	−5.33726	+	9.24441i	−0.170232	+	0.294851i	−0.938501	−	0.345277i	$-0.887785\pi$
$983$	−5.33726	+	9.24441i	−0.170232	+	0.294851i	0.768269	+	0.640127i	$0.221118\pi$
$984$	−29.2442	+	50.6525i	−0.932272	+	1.61474i
$985$	9.38448			0.299014
$986$	−8.51773	+	14.7531i	−0.271260	+	0.469836i
$987$	38.2942			1.21892
$988$	45.5593			1.44944
$989$	24.4682	−	41.6842i	0.778045	−	1.32548i
$990$	−3.60902			−0.114702
$991$	−43.4788			−1.38115			−0.690575	−	0.723260i	$-0.742643\pi$
$991$	−43.4788			−1.38115			−0.690575	+	0.723260i	$0.742643\pi$
$992$	5.49604	−	9.51941i	0.174499	−	0.302242i
$993$	−4.81309			−0.152739
$994$	41.8486	−	72.4839i	1.32736	−	2.29905i
$995$	−1.36890	+	2.37100i	−0.0433969	+	0.0751657i
$996$	−55.0604	−	95.3673i	−1.74465	−	3.02183i
$997$	17.3003			0.547907			0.273953	−	0.961743i	$-0.411669\pi$
$997$	17.3003			0.547907			0.273953	+	0.961743i	$0.411669\pi$
$998$	−10.1845	−	17.6401i	−0.322385	−	0.558388i
$999$	−1.84545	+	3.19642i	−0.0583875	+	0.101130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.b.307.2	✓	58
43.36	even	3	inner	731.2.e.b.681.2	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.b.307.2	✓	58	1.1	even	1	trivial
731.2.e.b.681.2	yes	58	43.36	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.46945 q^{2} +(-0.974328 + 1.68758i) q^{3} +4.09816 q^{4} +(0.310056 - 0.537033i) q^{5} +(2.40605 - 4.16740i) q^{6} +(1.71828 + 2.97615i) q^{7} -5.18130 q^{8} +(-0.398628 - 0.690445i) q^{9} +O(q^{10})\)	\(q-2.46945 q^{2} +(-0.974328 + 1.68758i) q^{3} +4.09816 q^{4} +(0.310056 - 0.537033i) q^{5} +(2.40605 - 4.16740i) q^{6} +(1.71828 + 2.97615i) q^{7} -5.18130 q^{8} +(-0.398628 - 0.690445i) q^{9} +(-0.765666 + 1.32617i) q^{10} -2.95612 q^{11} +(-3.99295 + 6.91600i) q^{12} +(-1.14443 - 1.98222i) q^{13} +(-4.24320 - 7.34943i) q^{14} +(0.604192 + 1.04649i) q^{15} +4.59861 q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.984391 + 1.70502i) q^{18} +(-2.42850 + 4.20629i) q^{19} +(1.27066 - 2.20085i) q^{20} -6.69667 q^{21} +7.29997 q^{22} +(3.68550 - 6.38348i) q^{23} +(5.04828 - 8.74388i) q^{24} +(2.30773 + 3.99711i) q^{25} +(2.82611 + 4.89497i) q^{26} -4.29239 q^{27} +(7.04179 + 12.1967i) q^{28} +(3.44925 + 5.97427i) q^{29} +(-1.49202 - 2.58425i) q^{30} +(-5.53245 + 9.58249i) q^{31} -0.993417 q^{32} +(2.88023 - 4.98870i) q^{33} +(1.23472 + 2.13860i) q^{34} +2.13105 q^{35} +(-1.63364 - 2.82955i) q^{36} +(0.429936 - 0.744671i) q^{37} +(5.99705 - 10.3872i) q^{38} +4.46021 q^{39} +(-1.60649 + 2.78253i) q^{40} -5.79291 q^{41} +16.5371 q^{42} +(6.55727 + 0.0472157i) q^{43} -12.1147 q^{44} -0.494388 q^{45} +(-9.10115 + 15.7637i) q^{46} -5.71839 q^{47} +(-4.48055 + 7.76054i) q^{48} +(-2.40497 + 4.16553i) q^{49} +(-5.69882 - 9.87064i) q^{50} +1.94866 q^{51} +(-4.69007 - 8.12344i) q^{52} +(3.11208 - 5.39028i) q^{53} +10.5998 q^{54} +(-0.916562 + 1.58753i) q^{55} +(-8.90292 - 15.4203i) q^{56} +(-4.73231 - 8.19660i) q^{57} +(-8.51773 - 14.7531i) q^{58} -11.7305 q^{59} +(2.47608 + 4.28869i) q^{60} +(-6.30175 - 10.9149i) q^{61} +(13.6621 - 23.6634i) q^{62} +(1.36991 - 2.37275i) q^{63} -6.74402 q^{64} -1.41935 q^{65} +(-7.11257 + 12.3193i) q^{66} +(0.635603 - 1.10090i) q^{67} +(-2.04908 - 3.54911i) q^{68} +(7.18177 + 12.4392i) q^{69} -5.26252 q^{70} +(4.93126 + 8.54119i) q^{71} +(2.06541 + 3.57740i) q^{72} +(-4.08201 - 7.07025i) q^{73} +(-1.06170 + 1.83893i) q^{74} -8.99394 q^{75} +(-9.95239 + 17.2380i) q^{76} +(-5.07944 - 8.79785i) q^{77} -11.0142 q^{78} +(-1.76498 - 3.05704i) q^{79} +(1.42583 - 2.46960i) q^{80} +(5.37808 - 9.31510i) q^{81} +14.3053 q^{82} +(-6.89469 + 11.9420i) q^{83} -27.4440 q^{84} -0.620112 q^{85} +(-16.1928 - 0.116597i) q^{86} -13.4428 q^{87} +15.3165 q^{88} +(-0.194218 + 0.336395i) q^{89} +1.22087 q^{90} +(3.93291 - 6.81200i) q^{91} +(15.1038 - 26.1605i) q^{92} +(-10.7808 - 18.6730i) q^{93} +14.1213 q^{94} +(1.50594 + 2.60837i) q^{95} +(0.967914 - 1.67648i) q^{96} -1.94205 q^{97} +(5.93894 - 10.2865i) q^{98} +(1.17839 + 2.04104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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