LMFDB - Embedded newform 273.3.bo.c.160.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,3,Mod(160,273)]

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, 3, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("273.160");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.43871121704$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			160.12
Character	$\chi$	$=$	273.160
Dual form			273.3.bo.c.244.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15840 + 0.668803i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.10541 - 1.91462i) q^{4} -3.82472 q^{5} +(-1.15840 - 2.00641i) q^{6} +(-0.0208330 + 6.99997i) q^{7} -8.30761i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.15840 + 0.668803i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.10541 - 1.91462i) q^{4} -3.82472 q^{5} +(-1.15840 - 2.00641i) q^{6} +(-0.0208330 + 6.99997i) q^{7} -8.30761i q^{8} +(1.50000 + 2.59808i) q^{9} +(-4.43056 - 2.55798i) q^{10} +(17.0475 + 9.84240i) q^{11} +3.82924i q^{12} +(-11.9140 + 5.20156i) q^{13} +(-4.70573 + 8.09483i) q^{14} +(5.73708 + 3.31231i) q^{15} +(1.13453 - 1.96506i) q^{16} +(-26.1168 + 15.0786i) q^{17} +4.01282i q^{18} +(7.26429 + 12.5821i) q^{19} +(4.22787 + 7.32289i) q^{20} +(6.09340 - 10.4819i) q^{21} +(13.1652 + 22.8029i) q^{22} +(-15.4983 + 26.8438i) q^{23} +(-7.19461 + 12.4614i) q^{24} -10.3715 q^{25} +(-17.2800 - 1.94264i) q^{26} -5.19615i q^{27} +(13.4253 - 7.69792i) q^{28} +(10.7930 - 18.6941i) q^{29} +(4.43056 + 7.67395i) q^{30} +37.6446 q^{31} +(-26.1499 + 15.0977i) q^{32} +(-17.0475 - 29.5272i) q^{33} -40.3383 q^{34} +(0.0796803 - 26.7729i) q^{35} +(3.31622 - 5.74386i) q^{36} +(38.6187 + 22.2965i) q^{37} +19.4335i q^{38} +(22.3757 + 2.51551i) q^{39} +31.7743i q^{40} +(6.08738 - 10.5436i) q^{41} +(14.0689 - 8.06696i) q^{42} +(-5.34090 - 9.25071i) q^{43} -43.5194i q^{44} +(-5.73708 - 9.93692i) q^{45} +(-35.9064 + 20.7306i) q^{46} -8.11860 q^{47} +(-3.40359 + 1.96506i) q^{48} +(-48.9991 - 0.291660i) q^{49} +(-12.0143 - 6.93648i) q^{50} +52.2336 q^{51} +(23.1288 + 17.0610i) q^{52} -87.4106 q^{53} +(3.47520 - 6.01922i) q^{54} +(-65.2021 - 37.6444i) q^{55} +(58.1530 + 0.173072i) q^{56} -25.1642i q^{57} +(25.0053 - 14.4368i) q^{58} +(-24.5578 - 42.5353i) q^{59} -14.6458i q^{60} +(63.5991 - 36.7190i) q^{61} +(43.6075 + 25.1768i) q^{62} +(-18.2177 + 10.4458i) q^{63} -49.4657 q^{64} +(45.5678 - 19.8945i) q^{65} -45.6057i q^{66} +(-29.5071 - 17.0360i) q^{67} +(57.7394 + 33.3359i) q^{68} +(46.4948 - 26.8438i) q^{69} +(17.9981 - 30.9605i) q^{70} +(-101.606 + 58.6620i) q^{71} +(21.5838 - 12.4614i) q^{72} -34.1267 q^{73} +(29.8239 + 51.6566i) q^{74} +(15.5572 + 8.98198i) q^{75} +(16.0600 - 27.8167i) q^{76} +(-69.2516 + 119.127i) q^{77} +(24.2376 + 17.8789i) q^{78} +109.869 q^{79} +(-4.33926 + 7.51582i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(14.1032 - 8.14251i) q^{82} -10.6149 q^{83} +(-26.8046 - 0.0797744i) q^{84} +(99.8896 - 57.6713i) q^{85} -14.2880i q^{86} +(-32.3791 + 18.6941i) q^{87} +(81.7669 - 141.624i) q^{88} +(-24.7394 + 42.8499i) q^{89} -15.3479i q^{90} +(-36.1625 - 83.5061i) q^{91} +68.5275 q^{92} +(-56.4668 - 32.6011i) q^{93} +(-9.40459 - 5.42974i) q^{94} +(-27.7839 - 48.1231i) q^{95} +52.2999 q^{96} +(71.6120 + 124.036i) q^{97} +(-56.5655 - 33.1086i) q^{98} +59.0544i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9}+O(q^{10}) $ 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9	$ 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9} + 42 q^{11} - 36 q^{13} + 16 q^{14} + 6 q^{15} - 96 q^{16} - 12 q^{17} + 12 q^{19} - 10 q^{20} - 18 q^{22} + 24 q^{23} + 264 q^{25} + 114 q^{26} - 104 q^{28} + 76 q^{29} - 160 q^{31} - 42 q^{33} - 192 q^{34} - 100 q^{35} - 132 q^{36} + 6 q^{37} + 60 q^{39} + 200 q^{41} + 18 q^{42} + 48 q^{43} - 6 q^{45} + 396 q^{46} + 56 q^{47} + 288 q^{48} - 154 q^{49} - 102 q^{50} + 24 q^{51} - 360 q^{52} + 76 q^{53} + 192 q^{55} - 132 q^{56} - 162 q^{58} + 128 q^{59} - 120 q^{61} + 24 q^{62} - 30 q^{63} - 484 q^{64} - 284 q^{65} - 144 q^{67} + 234 q^{68} - 72 q^{69} + 300 q^{70} - 96 q^{71} + 728 q^{73} - 144 q^{74} - 396 q^{75} - 516 q^{76} - 160 q^{77} - 144 q^{78} + 68 q^{79} - 58 q^{80} - 162 q^{81} + 72 q^{82} + 368 q^{83} + 108 q^{84} - 324 q^{85} - 228 q^{87} + 186 q^{88} + 92 q^{89} + 176 q^{91} - 1044 q^{92} + 240 q^{93} - 336 q^{94} - 2 q^{95} - 72 q^{97} + 234 q^{98}+O(q^{100}) $ 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9 + 42 * q^11 - 36 * q^13 + 16 * q^14 + 6 * q^15 - 96 * q^16 - 12 * q^17 + 12 * q^19 - 10 * q^20 - 18 * q^22 + 24 * q^23 + 264 * q^25 + 114 * q^26 - 104 * q^28 + 76 * q^29 - 160 * q^31 - 42 * q^33 - 192 * q^34 - 100 * q^35 - 132 * q^36 + 6 * q^37 + 60 * q^39 + 200 * q^41 + 18 * q^42 + 48 * q^43 - 6 * q^45 + 396 * q^46 + 56 * q^47 + 288 * q^48 - 154 * q^49 - 102 * q^50 + 24 * q^51 - 360 * q^52 + 76 * q^53 + 192 * q^55 - 132 * q^56 - 162 * q^58 + 128 * q^59 - 120 * q^61 + 24 * q^62 - 30 * q^63 - 484 * q^64 - 284 * q^65 - 144 * q^67 + 234 * q^68 - 72 * q^69 + 300 * q^70 - 96 * q^71 + 728 * q^73 - 144 * q^74 - 396 * q^75 - 516 * q^76 - 160 * q^77 - 144 * q^78 + 68 * q^79 - 58 * q^80 - 162 * q^81 + 72 * q^82 + 368 * q^83 + 108 * q^84 - 324 * q^85 - 228 * q^87 + 186 * q^88 + 92 * q^89 + 176 * q^91 - 1044 * q^92 + 240 * q^93 - 336 * q^94 - 2 * q^95 - 72 * q^97 + 234 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.15840	+	0.668803i	0.579200	+	0.334401i	0.760815	−	0.648968i	$-0.224799\pi$
$2$	1.15840	+	0.668803i	0.579200	+	0.334401i	−0.181615	+	0.983370i	$0.558133\pi$
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	−1.10541	−	1.91462i	−0.276352	−	0.478655i
$5$	−3.82472			−0.764945			−0.382472	−	0.923967i	$-0.624927\pi$
$5$	−3.82472			−0.764945			−0.382472	+	0.923967i	$0.624927\pi$
$6$	−1.15840	−	2.00641i	−0.193067	−	0.334401i
$7$	−0.0208330	+	6.99997i	−0.00297614	+	0.999996i
$7$	−0.0208330	+	6.99997i	−0.00297614	+	0.999996i
$8$		−	8.30761i		−	1.03845i
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−4.43056	−	2.55798i	−0.443056	−	0.255798i
$11$	17.0475	+	9.84240i	1.54978	+	0.894763i	0.998158	+	0.0606665i	$0.0193226\pi$
$11$	17.0475	+	9.84240i	1.54978	+	0.894763i	0.551618	+	0.834097i	$0.314011\pi$
$12$			3.82924i			0.319103i
$13$	−11.9140	+	5.20156i	−0.916463	+	0.400120i
$13$	−11.9140	+	5.20156i	−0.916463	+	0.400120i
$14$	−4.70573	+	8.09483i	−0.336124	+	0.578202i
$15$	5.73708	+	3.31231i	0.382472	+	0.220820i
$16$	1.13453	−	1.96506i	0.0709081	−	0.122816i
$17$	−26.1168	+	15.0786i	−1.53628	+	0.886974i	−0.537232	+	0.843434i	$0.680530\pi$
$17$	−26.1168	+	15.0786i	−1.53628	+	0.886974i	−0.999052	+	0.0435393i	$0.986137\pi$
$18$			4.01282i			0.222934i
$19$	7.26429	+	12.5821i	0.382331	+	0.662217i	0.991395	−	0.130904i	$-0.0417880\pi$
$19$	7.26429	+	12.5821i	0.382331	+	0.662217i	−0.609064	+	0.793121i	$0.708455\pi$
$20$	4.22787	+	7.32289i	0.211394	+	0.366145i
$21$	6.09340	−	10.4819i	0.290162	−	0.499139i
$22$	13.1652	+	22.8029i	0.598420	+	1.03649i
$23$	−15.4983	+	26.8438i	−0.673838	+	1.16712i	0.302970	+	0.953000i	$0.402022\pi$
$23$	−15.4983	+	26.8438i	−0.673838	+	1.16712i	−0.976807	+	0.214121i	$0.931311\pi$
$24$	−7.19461	+	12.4614i	−0.299775	+	0.519226i
$25$	−10.3715			−0.414860
$26$	−17.2800	−	1.94264i	−0.664616	−	0.0747170i
$27$		−	5.19615i		−	0.192450i
$28$	13.4253	−	7.69792i	0.479475	−	0.274926i
$29$	10.7930	−	18.6941i	0.372174	−	0.644624i	−0.617726	−	0.786394i	$-0.711946\pi$
$29$	10.7930	−	18.6941i	0.372174	−	0.644624i	0.989900	+	0.141769i	$0.0452792\pi$
$30$	4.43056	+	7.67395i	0.147685	+	0.255798i
$31$	37.6446			1.21434			0.607170	−	0.794572i	$-0.292305\pi$
$31$	37.6446			1.21434			0.607170	+	0.794572i	$0.292305\pi$
$32$	−26.1499	+	15.0977i	−0.817186	+	0.471802i
$33$	−17.0475	−	29.5272i	−0.516592	−	0.894763i
$34$	−40.3383			−1.18642
$35$	0.0796803	−	26.7729i	0.00227658	−	0.764941i
$36$	3.31622	−	5.74386i	0.0921172	−	0.159552i
$37$	38.6187	+	22.2965i	1.04375	+	0.602608i	0.920893	−	0.389816i	$-0.127461\pi$
$37$	38.6187	+	22.2965i	1.04375	+	0.602608i	0.122856	+	0.992425i	$0.460795\pi$
$38$			19.4335i			0.511408i
$39$	22.3757	+	2.51551i	0.573736	+	0.0645002i
$40$			31.7743i			0.794358i
$41$	6.08738	−	10.5436i	0.148473	−	0.257162i	−0.782191	−	0.623039i	$-0.785898\pi$
$41$	6.08738	−	10.5436i	0.148473	−	0.257162i	0.930663	+	0.365877i	$0.119231\pi$
$42$	14.0689	−	8.06696i	0.334974	−	0.192071i
$43$	−5.34090	−	9.25071i	−0.124207	−	0.215133i	0.797216	−	0.603695i	$-0.206305\pi$
$43$	−5.34090	−	9.25071i	−0.124207	−	0.215133i	−0.921423	+	0.388562i	$0.872972\pi$
$44$		−	43.5194i		−	0.989077i
$45$	−5.73708	−	9.93692i	−0.127491	−	0.220820i
$46$	−35.9064	+	20.7306i	−0.780573	+	0.450664i
$47$	−8.11860			−0.172736			−0.0863681	−	0.996263i	$-0.527526\pi$
$47$	−8.11860			−0.172736			−0.0863681	+	0.996263i	$0.527526\pi$
$48$	−3.40359	+	1.96506i	−0.0709081	+	0.0409388i
$49$	−48.9991	−	0.291660i	−0.999982	−	0.00595225i
$50$	−12.0143	−	6.93648i	−0.240287	−	0.138730i
$51$	52.2336			1.02419
$52$	23.1288	+	17.0610i	0.444785	+	0.328096i
$53$	−87.4106			−1.64926			−0.824628	−	0.565675i	$-0.808616\pi$
$53$	−87.4106			−1.64926			−0.824628	+	0.565675i	$0.808616\pi$
$54$	3.47520	−	6.01922i	0.0643556	−	0.111467i
$55$	−65.2021	−	37.6444i	−1.18549	−	0.684444i
$56$	58.1530	+	0.173072i	1.03845	+	0.00309057i
$57$		−	25.1642i		−	0.441478i
$58$	25.0053	−	14.4368i	0.431126	−	0.248911i
$59$	−24.5578	−	42.5353i	−0.416234	−	0.720938i	0.579323	−	0.815098i	$-0.303317\pi$
$59$	−24.5578	−	42.5353i	−0.416234	−	0.720938i	−0.995557	+	0.0941599i	$0.969984\pi$
$60$		−	14.6458i		−	0.244096i
$61$	63.5991	−	36.7190i	1.04261	−	0.601950i	0.122037	−	0.992526i	$-0.461057\pi$
$61$	63.5991	−	36.7190i	1.04261	−	0.601950i	0.920571	+	0.390575i	$0.127724\pi$
$62$	43.6075	+	25.1768i	0.703346	+	0.406077i
$63$	−18.2177	+	10.4458i	−0.289170	+	0.165807i
$64$	−49.4657			−0.772901
$65$	45.5678	−	19.8945i	0.701043	−	0.306069i
$66$		−	45.6057i		−	0.690996i
$67$	−29.5071	−	17.0360i	−0.440405	−	0.254268i	0.263364	−	0.964696i	$-0.415168\pi$
$67$	−29.5071	−	17.0360i	−0.440405	−	0.254268i	−0.703769	+	0.710428i	$0.748501\pi$
$68$	57.7394	+	33.3359i	0.849109	+	0.490233i
$69$	46.4948	−	26.8438i	0.673838	−	0.389040i
$70$	17.9981	−	30.9605i	0.257116	−	0.442293i
$71$	−101.606	+	58.6620i	−1.43106	+	0.826226i	−0.997202	−	0.0747535i	$-0.976183\pi$
$71$	−101.606	+	58.6620i	−1.43106	+	0.826226i	−0.433863	+	0.900979i	$0.642850\pi$
$72$	21.5838	−	12.4614i	0.299775	−	0.173075i
$73$	−34.1267			−0.467489			−0.233745	−	0.972298i	$-0.575098\pi$
$73$	−34.1267			−0.467489			−0.233745	+	0.972298i	$0.575098\pi$
$74$	29.8239	+	51.6566i	0.403026	+	0.698062i
$75$	15.5572	+	8.98198i	0.207430	+	0.119760i
$76$	16.0600	−	27.8167i	0.211316	−	0.366009i
$77$	−69.2516	+	119.127i	−0.899372	+	1.54711i
$78$	24.2376	+	17.8789i	0.310739	+	0.229217i
$79$	109.869			1.39074			0.695372	−	0.718650i	$-0.255240\pi$
$79$	109.869			1.39074			0.695372	+	0.718650i	$0.255240\pi$
$80$	−4.33926	+	7.51582i	−0.0542407	+	0.0939477i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	14.1032	−	8.14251i	0.171991	−	0.0992989i
$83$	−10.6149			−0.127890			−0.0639451	−	0.997953i	$-0.520368\pi$
$83$	−10.6149			−0.127890			−0.0639451	+	0.997953i	$0.520368\pi$
$84$	−26.8046	−	0.0797744i	−0.319102	−	0.000949695i
$85$	99.8896	−	57.6713i	1.17517	−	0.678486i
$86$		−	14.2880i		−	0.166140i
$87$	−32.3791	+	18.6941i	−0.372174	+	0.214875i
$88$	81.7669	−	141.624i	0.929169	−	1.60937i
$89$	−24.7394	+	42.8499i	−0.277971	+	0.481460i	−0.970880	−	0.239565i	$-0.922995\pi$
$89$	−24.7394	+	42.8499i	−0.277971	+	0.481460i	0.692909	+	0.721025i	$0.256329\pi$
$90$		−	15.3479i		−	0.170532i
$91$	−36.1625	−	83.5061i	−0.397390	−	0.917650i
$92$	68.5275			0.744864
$93$	−56.4668	−	32.6011i	−0.607170	−	0.350550i
$94$	−9.40459	−	5.42974i	−0.100049	−	0.0577632i
$95$	−27.7839	−	48.1231i	−0.292462	−	0.506559i
$96$	52.2999			0.544791
$97$	71.6120	+	124.036i	0.738268	+	1.27872i	0.953274	+	0.302106i	$0.0976896\pi$
$97$	71.6120	+	124.036i	0.738268	+	1.27872i	−0.215006	+	0.976613i	$0.568977\pi$
$98$	−56.5655	−	33.1086i	−0.577199	−	0.337843i
$99$			59.0544i			0.596509i
$100$	11.4647	+	19.8575i	0.114647	+	0.198575i
$101$	−14.3208	−	8.26813i	−0.141790	−	0.0818627i	0.427427	−	0.904050i	$-0.359420\pi$
$101$	−14.3208	−	8.26813i	−0.141790	−	0.0818627i	−0.569217	+	0.822187i	$0.692754\pi$
$102$	60.5075	+	34.9340i	0.593210	+	0.342490i
$103$		−	105.428i		−	1.02358i	−0.859111	−	0.511789i	$-0.828983\pi$
$103$		−	105.428i		−	1.02358i	0.859111	−	0.511789i	$-0.171017\pi$
$104$	43.2125	+	98.9771i	0.415505	+	0.951703i
$105$	−23.3056	+	40.0904i	−0.221958	+	0.381813i
$106$	−101.256	−	58.4604i	−0.955249	−	0.551513i
$107$	−43.2822	+	74.9669i	−0.404506	+	0.700626i	−0.994264	−	0.106955i	$-0.965890\pi$
$107$	−43.2822	+	74.9669i	−0.404506	+	0.700626i	0.589757	+	0.807580i	$0.299223\pi$
$108$	−9.94866	+	5.74386i	−0.0921172	+	0.0531839i
$109$			110.226i			1.01125i	0.862754	+	0.505623i	$0.168737\pi$
$109$			110.226i			1.01125i	−0.862754	+	0.505623i	$0.831263\pi$
$110$	−50.3534	−	87.2147i	−0.457758	−	0.792860i
$111$	−38.6187	−	66.8895i	−0.347916	−	0.602608i
$112$	13.7317	+	7.98261i	0.122605	+	0.0712733i
$113$	−23.0652	−	39.9501i	−0.204117	−	0.353541i	0.745734	−	0.666244i	$-0.232099\pi$
$113$	−23.0652	−	39.9501i	−0.204117	−	0.353541i	−0.949851	+	0.312703i	$0.898766\pi$
$114$	16.8299	−	29.1503i	0.147631	−	0.255704i
$115$	59.2766	−	102.670i	0.515448	−	0.892783i
$116$	−47.7228			−0.411403
$117$	−31.3851	−	23.1512i	−0.268248	−	0.197873i
$118$		−	65.6972i		−	0.556756i
$119$	−105.005	−	183.131i	−0.882398	−	1.53892i
$120$	27.5174	−	47.6615i	0.229311	−	0.397179i
$121$	133.246	+	230.788i	1.10120	+	1.90734i
$122$	98.2309			0.805172
$123$	−18.2621	+	10.5436i	−0.148473	+	0.0857207i
$124$	−41.6125	−	72.0750i	−0.335585	−	0.581250i
$125$	135.286			1.08229
$126$	−28.0896	−	0.0835988i	−0.222933	−	0.000663482i
$127$	11.7503	−	20.3521i	0.0925220	−	0.160253i	−0.816050	−	0.577982i	$-0.803840\pi$
$127$	11.7503	−	20.3521i	0.0925220	−	0.160253i	0.908572	+	0.417729i	$0.137174\pi$
$128$	47.2987	+	27.3079i	0.369521	+	0.213343i
$129$			18.5014i			0.143422i
$130$	66.0913	+	7.43007i	0.508394	+	0.0571544i
$131$			142.023i			1.08415i	0.840331	+	0.542073i	$0.182360\pi$
$131$			142.023i			1.08415i	−0.840331	+	0.542073i	$0.817640\pi$
$132$	−37.6889	+	65.2791i	−0.285522	+	0.494539i
$133$	−88.2258	+	50.5877i	−0.663352	+	0.380359i
$134$	−22.7874	−	39.4689i	−0.170055	−	0.294544i
$135$			19.8738i			0.147214i
$136$	125.267	+	216.969i	0.921080	+	1.59536i
$137$	72.4418	−	41.8243i	0.528772	−	0.305287i	−0.211744	−	0.977325i	$-0.567914\pi$
$137$	72.4418	−	41.8243i	0.528772	−	0.305287i	0.740516	+	0.672038i	$0.234581\pi$
$138$	71.8128			0.520382
$139$	−40.7108	+	23.5044i	−0.292883	+	0.169096i	−0.639241	−	0.769006i	$-0.720752\pi$
$139$	−40.7108	+	23.5044i	−0.292883	+	0.169096i	0.346358	+	0.938102i	$0.387418\pi$
$140$	−51.3481	+	29.4424i	−0.366772	+	0.210303i
$141$	12.1779	+	7.03091i	0.0863681	+	0.0498646i
$142$	−156.933			−1.10516
$143$	−254.300	−	28.5888i	−1.77832	−	0.199922i
$144$	6.80717			0.0472720
$145$	−41.2804	+	71.4997i	−0.284692	+	0.493102i
$146$	−39.5324	−	22.8240i	−0.270770	−	0.156329i
$147$	73.2461	+	42.8720i	0.498273	+	0.291646i
$148$		−	98.5868i		−	0.666127i
$149$	16.3315	−	9.42899i	0.109607	−	0.0632818i	−0.444194	−	0.895931i	$-0.646510\pi$
$149$	16.3315	−	9.42899i	0.109607	−	0.0632818i	0.553801	+	0.832649i	$0.313177\pi$
$150$	12.0143	+	20.8094i	0.0800956	+	0.138730i
$151$		−	79.1120i		−	0.523921i	−0.965079	−	0.261960i	$-0.915631\pi$
$151$		−	79.1120i		−	0.523921i	0.965079	−	0.261960i	$-0.0843690\pi$
$152$	104.527	−	60.3489i	0.687680	−	0.397032i
$153$	−78.3505	−	45.2357i	−0.512095	−	0.295658i
$154$	−159.894	+	91.6812i	−1.03827	+	0.595333i
$155$	−143.980			−0.928903
$156$	−19.9180	−	45.6216i	−0.127680	−	0.292446i
$157$		−	156.869i		−	0.999167i	−0.866266	−	0.499584i	$-0.833486\pi$
$157$		−	156.869i		−	0.999167i	0.866266	−	0.499584i	$-0.166514\pi$
$158$	127.272	+	73.4805i	0.805519	+	0.465066i
$159$	131.116	+	75.6998i	0.824628	+	0.476099i
$160$	100.016	−	57.7444i	0.625102	−	0.360903i
$161$	−187.583	−	109.047i	−1.16511	−	0.677308i
$162$	−10.4256	+	6.01922i	−0.0643556	+	0.0371557i
$163$	126.967	−	73.3045i	0.778939	−	0.449721i	−0.0571151	−	0.998368i	$-0.518190\pi$
$163$	126.967	−	73.3045i	0.778939	−	0.449721i	0.836054	+	0.548647i	$0.184857\pi$
$164$	−26.9161			−0.164123
$165$	65.2021	+	112.933i	0.395164	+	0.684444i
$166$	−12.2963	−	7.09927i	−0.0740741	−	0.0427667i
$167$	2.72006	−	4.71128i	0.0162878	−	0.0282113i	−0.857767	−	0.514039i	$-0.828149\pi$
$167$	2.72006	−	4.71128i	0.0162878	−	0.0282113i	0.874054	+	0.485828i	$0.161482\pi$
$168$	−87.0797	−	50.6216i	−0.518331	−	0.301319i
$169$	114.888	−	123.943i	0.679808	−	0.733390i
$170$	154.283			0.907546
$171$	−21.7929	+	37.7464i	−0.127444	+	0.220739i
$172$	−11.8077	+	20.4516i	−0.0686495	+	0.118905i
$173$	29.3548	−	16.9480i	0.169681	−	0.0979654i	−0.412754	−	0.910842i	$-0.635433\pi$
$173$	29.3548	−	16.9480i	0.169681	−	0.0979654i	0.582435	+	0.812877i	$0.302100\pi$
$174$	−50.0106			−0.287417
$175$	0.216069	−	72.6001i	0.00123468	−	0.414858i
$176$	38.6818	−	22.3330i	0.219783	−	0.126892i
$177$			85.0707i			0.480625i
$178$	−57.3163	+	33.0916i	−0.322002	+	0.185908i
$179$	−20.6175	+	35.7106i	−0.115182	+	0.199501i	−0.917852	−	0.396922i	$-0.870078\pi$
$179$	−20.6175	+	35.7106i	−0.115182	+	0.199501i	0.802671	+	0.596423i	$0.203412\pi$
$180$	−12.6836	+	21.9687i	−0.0704645	+	0.122048i
$181$			37.8270i			0.208989i	0.994525	+	0.104495i	$0.0333225\pi$
$181$			37.8270i			0.208989i	−0.994525	+	0.104495i	$0.966678\pi$
$182$	13.9584	−	120.919i	0.0766947	−	0.664391i
$183$	−127.198			−0.695072
$184$	223.008	+	128.754i	1.21200	+	0.699748i
$185$	−147.706	−	85.2780i	−0.798410	−	0.460962i
$186$	−43.6075	−	75.5303i	−0.234449	−	0.406077i
$187$	−593.637			−3.17453
$188$	8.97435	+	15.5440i	0.0477359	+	0.0826810i
$189$	36.3729	+	0.108251i	0.192449	+	0.000572758i
$190$		−	74.3278i		−	0.391199i
$191$	127.874	+	221.485i	0.669498	+	1.15960i	0.978045	+	0.208396i	$0.0668242\pi$
$191$	127.874	+	221.485i	0.669498	+	1.15960i	−0.308546	+	0.951209i	$0.599843\pi$
$192$	74.1985	+	42.8385i	0.386451	+	0.223117i
$193$	−105.674	−	61.0110i	−0.547535	−	0.316119i	0.200592	−	0.979675i	$-0.435713\pi$
$193$	−105.674	−	61.0110i	−0.547535	−	0.316119i	−0.748127	+	0.663556i	$0.769047\pi$
$194$			191.577i			0.987512i
$195$	−85.5809	−	9.62112i	−0.438876	−	0.0493391i
$196$	53.6055	+	94.1371i	0.273498	+	0.480291i
$197$	86.8951	+	50.1689i	0.441092	+	0.254664i	0.704061	−	0.710140i	$-0.251368\pi$
$197$	86.8951	+	50.1689i	0.441092	+	0.254664i	−0.262969	+	0.964804i	$0.584702\pi$
$198$	−39.4957	+	68.4086i	−0.199473	+	0.345498i
$199$	89.2433	−	51.5247i	0.448459	−	0.258918i	−0.258720	−	0.965952i	$-0.583301\pi$
$199$	89.2433	−	51.5247i	0.448459	−	0.258918i	0.707179	+	0.707034i	$0.249967\pi$
$200$			86.1624i			0.430812i
$201$	29.5071	+	51.1079i	0.146802	+	0.254268i
$202$	−11.0595	−	19.1556i	−0.0547500	−	0.0948298i
$203$	130.633	+	75.9404i	0.643514	+	0.374091i
$204$	−57.7394	−	100.008i	−0.283036	−	0.490233i
$205$	−23.2825	+	40.3265i	−0.113573	+	0.196715i
$206$	70.5108	−	122.128i	0.342286	−	0.592856i
$207$	−92.9896			−0.449225
$208$	−3.29542	+	29.3131i	−0.0158434	+	0.140928i
$209$			285.992i			1.36838i
$210$	−53.8097	+	30.8539i	−0.256237	+	0.146923i
$211$	−204.813	+	354.747i	−0.970678	+	1.68126i	−0.277161	+	0.960823i	$0.589394\pi$
$211$	−204.813	+	354.747i	−0.970678	+	1.68126i	−0.693517	+	0.720440i	$0.743940\pi$
$212$	96.6242	+	167.358i	0.455774	+	0.789425i
$213$	203.211			0.954043
$214$	−100.276	+	57.8945i	−0.468580	+	0.270535i
$215$	20.4275	+	35.3814i	0.0950114	+	0.164565i
$216$	−43.1676			−0.199850
$217$	−0.784247	+	263.511i	−0.00361404	+	1.21434i
$218$	−73.7193	+	127.686i	−0.338162	+	0.585714i
$219$	51.1901	+	29.5546i	0.233745	+	0.134953i
$220$			166.450i			0.756589i
$221$	232.724	−	315.494i	1.05305	−	1.42758i
$222$		−	103.313i		−	0.465374i
$223$	72.8981	−	126.263i	0.326897	−	0.566202i	−0.654997	−	0.755631i	$-0.727330\pi$
$223$	72.8981	−	126.263i	0.326897	−	0.566202i	0.981894	+	0.189429i	$0.0606636\pi$
$224$	−105.138	−	183.363i	−0.469368	−	0.818586i
$225$	−15.5572	−	26.9459i	−0.0691433	−	0.119760i
$226$		−	61.7043i		−	0.273028i
$227$	58.6525	+	101.589i	0.258381	+	0.447529i	0.965808	−	0.259257i	$-0.0834776\pi$
$227$	58.6525	+	101.589i	0.258381	+	0.447529i	−0.707427	+	0.706786i	$0.750144\pi$
$228$	−48.1800	+	27.8167i	−0.211316	+	0.122003i
$229$	−2.99627			−0.0130841			−0.00654207	−	0.999979i	$-0.502082\pi$
$229$	−2.99627			−0.0130841			−0.00654207	+	0.999979i	$0.502082\pi$
$230$	137.332	−	79.2886i	0.597095	−	0.344733i
$231$	207.045	−	118.717i	0.896297	−	0.513927i
$232$	−155.303	−	89.6644i	−0.669411	−	0.386485i
$233$	271.418			1.16489			0.582443	−	0.812872i	$-0.302097\pi$
$233$	271.418			1.16489			0.582443	+	0.812872i	$0.302097\pi$
$234$	−20.8729	−	47.8088i	−0.0892004	−	0.204311i
$235$	31.0514			0.132134
$236$	−54.2927	+	94.0377i	−0.230054	+	0.398465i
$237$	−164.803	−	95.1491i	−0.695372	−	0.401473i
$238$	0.840366	−	282.367i	0.00353095	−	1.18642i
$239$		−	125.573i		−	0.525408i	−0.964876	−	0.262704i	$-0.915386\pi$
$239$		−	125.573i		−	0.525408i	0.964876	−	0.262704i	$-0.0846143\pi$
$240$	13.0178	−	7.51582i	0.0542407	−	0.0313159i
$241$	205.384	+	355.736i	0.852216	+	1.47608i	0.879204	+	0.476446i	$0.158075\pi$
$241$	205.384	+	355.736i	0.852216	+	1.47608i	−0.0269876	+	0.999636i	$0.508591\pi$
$242$			356.460i			1.47298i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$	−140.606	−	81.1787i	−0.576253	−	0.332700i
$245$	187.408	+	1.11552i	0.764931	+	0.00455314i
$246$	−28.2065			−0.114660
$247$	−151.994	−	112.118i	−0.615358	−	0.453919i
$248$		−	312.737i		−	1.26103i
$249$	15.9223	+	9.19277i	0.0639451	+	0.0369187i
$250$	156.715	+	90.4797i	0.626862	+	0.361919i
$251$	−183.064	+	105.692i	−0.729338	+	0.421083i	−0.818180	−	0.574962i	$-0.805017\pi$
$251$	−183.064	+	105.692i	−0.729338	+	0.421083i	0.0888421	+	0.996046i	$0.471683\pi$
$252$	40.1378	+	23.3331i	0.159277	+	0.0925916i
$253$	−528.414	+	305.080i	−2.08859	+	1.20585i
$254$	27.2231	−	15.7173i	0.107177	−	0.0618790i
$255$	−199.779			−0.783448
$256$	135.459	+	234.621i	0.529135	+	0.916489i
$257$	−334.897	−	193.353i	−1.30310	−	0.752346i	−0.322167	−	0.946683i	$-0.604411\pi$
$257$	−334.897	−	193.353i	−1.30310	−	0.752346i	−0.980935	+	0.194336i	$0.937745\pi$
$258$	−12.3738	+	21.4320i	−0.0479604	+	0.0830699i
$259$	−156.879	+	269.865i	−0.605712	+	1.04195i
$260$	−88.4614	−	65.2535i	−0.340236	−	0.250975i
$261$	64.7583			0.248116
$262$	−94.9855	+	164.520i	−0.362540	+	0.627938i
$263$	198.479	−	343.777i	0.754675	−	1.30714i	−0.190861	−	0.981617i	$-0.561128\pi$
$263$	198.479	−	343.777i	0.754675	−	1.30714i	0.945536	−	0.325518i	$-0.105539\pi$
$264$	−245.301	+	141.624i	−0.929169	+	0.536456i
$265$	334.321			1.26159
$266$	−136.034	−	0.404857i	−0.511406	−	0.00152202i
$267$	74.2183	−	42.8499i	0.277971	−	0.160487i
$268$			75.3266i			0.281069i
$269$	226.448	−	130.740i	0.841814	−	0.486021i	−0.0160666	−	0.999871i	$-0.505114\pi$
$269$	226.448	−	130.740i	0.841814	−	0.486021i	0.857880	+	0.513850i	$0.171781\pi$
$270$	−13.2917	+	23.0219i	−0.0492284	+	0.0852661i
$271$	105.788	−	183.229i	0.390360	−	0.676123i	−0.602137	−	0.798393i	$-0.705684\pi$
$271$	105.788	−	183.229i	0.390360	−	0.676123i	0.992497	+	0.122270i	$0.0390173\pi$
$272$			68.4282i			0.251574i
$273$	−18.0746	+	156.577i	−0.0662074	+	0.573542i
$274$	111.889			0.408353
$275$	−176.808	−	102.080i	−0.642940	−	0.371201i
$276$	−102.791	−	59.3466i	−0.372432	−	0.215024i
$277$	35.5865	+	61.6376i	0.128471	+	0.222518i	0.923084	−	0.384597i	$-0.125660\pi$
$277$	35.5865	+	61.6376i	0.128471	+	0.222518i	−0.794613	+	0.607116i	$0.792326\pi$
$278$	−62.8791			−0.226184
$279$	56.4668	+	97.8034i	0.202390	+	0.350550i
$280$	−222.419	−	0.661953i	−0.794355	−	0.00236412i
$281$		−	205.793i		−	0.732360i	−0.930544	−	0.366180i	$-0.880665\pi$
$281$		−	205.793i		−	0.732360i	0.930544	−	0.366180i	$-0.119335\pi$
$282$	9.40459	+	16.2892i	0.0333496	+	0.0577632i
$283$	389.178	+	224.692i	1.37519	+	0.793965i	0.991576	−	0.129529i	$-0.0413465\pi$
$283$	389.178	+	224.692i	1.37519	+	0.793965i	0.383612	+	0.923494i	$0.374680\pi$
$284$	224.631	+	129.691i	0.790954	+	0.456657i
$285$			96.2463i			0.337706i
$286$	−275.461	−	203.194i	−0.963152	−	0.710469i
$287$	73.6784	+	42.8311i	0.256719	+	0.149237i
$288$	−78.4498	−	45.2930i	−0.272395	−	0.157267i
$289$	310.226	−	537.327i	1.07345	−	1.85926i
$290$	−95.6384	+	55.2169i	−0.329788	+	0.190403i
$291$		−	248.071i		−	0.852479i
$292$	37.7239	+	65.3397i	0.129191	+	0.223766i
$293$	−9.82283	−	17.0136i	−0.0335250	−	0.0580671i	0.848776	−	0.528752i	$-0.177340\pi$
$293$	−9.82283	−	17.0136i	−0.0335250	−	0.0580671i	−0.882301	+	0.470685i	$0.844007\pi$
$294$	56.1754	+	98.6501i	0.191073	+	0.335545i
$295$	93.9267	+	162.686i	0.318396	+	0.551478i
$296$	185.231	−	320.829i	0.625780	−	1.08388i
$297$	51.1426	−	88.5816i	0.172197	−	0.298254i
$298$	25.2245			0.0846460
$299$	45.0171	−	400.432i	0.150559	−	1.33924i
$300$		−	39.7149i		−	0.132383i
$301$	64.8659	−	37.1934i	0.215501	−	0.123566i
$302$	52.9103	−	91.6434i	0.175200	−	0.303455i
$303$	14.3208	+	24.8044i	0.0472635	+	0.0818627i
$304$	32.9662			0.108441
$305$	−243.249	+	140.440i	−0.797538	+	0.460459i
$306$	−60.5075	−	104.802i	−0.197737	−	0.342490i
$307$	323.275			1.05301			0.526506	−	0.850171i	$-0.323502\pi$
$307$	323.275			1.05301			0.526506	+	0.850171i	$0.323502\pi$
$308$	304.634	+	0.906637i	0.989073	+	0.00294363i
$309$	−91.3038	+	158.143i	−0.295481	+	0.511789i
$310$	−166.786	−	96.2942i	−0.538021	−	0.310626i
$311$		−	389.084i		−	1.25108i	−0.780194	−	0.625538i	$-0.784880\pi$
$311$		−	389.084i		−	1.25108i	0.780194	−	0.625538i	$-0.215120\pi$
$312$	20.8979	−	185.889i	0.0669803	−	0.595797i
$313$		−	317.270i		−	1.01364i	−0.862051	−	0.506821i	$-0.830821\pi$
$313$		−	317.270i		−	1.01364i	0.862051	−	0.506821i	$-0.169179\pi$
$314$	104.915	−	181.717i	0.334123	−	0.578718i
$315$	69.6777	−	39.9524i	0.221199	−	0.126833i
$316$	−121.450	−	210.357i	−0.384334	−	0.665686i
$317$			95.6599i			0.301766i	0.988552	+	0.150883i	$0.0482117\pi$
$317$			95.6599i			0.301766i	−0.988552	+	0.150883i	$0.951788\pi$
$318$	101.256	+	175.381i	0.318416	+	0.551513i
$319$	367.990	−	212.459i	1.15357	−	0.666015i
$320$	189.193			0.591227
$321$	129.847	−	74.9669i	0.404506	−	0.233542i
$322$	−144.365	−	251.775i	−0.448339	−	0.781911i
$323$	−379.440	−	219.070i	−1.17474	−	0.678235i
$324$	19.8973			0.0614115
$325$	123.566	−	53.9479i	0.380204	−	0.165994i
$326$	196.105			0.601549
$327$	95.4584	−	165.339i	0.291922	−	0.505623i
$328$	−87.5926	−	50.5716i	−0.267051	−	0.154182i
$329$	0.169134	−	56.8299i	0.000514086	−	0.172735i
$330$			174.429i			0.528574i
$331$	−394.217	+	227.601i	−1.19099	+	0.687618i	−0.958531	−	0.284989i	$-0.908010\pi$
$331$	−394.217	+	227.601i	−1.19099	+	0.687618i	−0.232458	+	0.972606i	$0.574677\pi$
$332$	11.7338	+	20.3235i	0.0353427	+	0.0612153i
$333$			133.779i			0.401739i
$334$	6.30183	−	3.63836i	0.0188678	−	0.0108933i
$335$	112.857	+	65.1578i	0.336886	+	0.194501i
$336$	−13.6845	−	23.8659i	−0.0407276	−	0.0710296i
$337$	88.8537			0.263661			0.131830	−	0.991272i	$-0.457915\pi$
$337$	88.8537			0.263661			0.131830	+	0.991272i	$0.457915\pi$
$338$	215.979	−	66.7383i	0.638992	−	0.197451i
$339$			79.9002i			0.235694i
$340$	−220.837	−	127.500i	−0.649521	−	0.375001i
$341$	641.747	+	370.513i	1.88196	+	1.08655i
$342$	−50.4897	+	29.1503i	−0.147631	+	0.0852347i
$343$	3.06241	−	342.986i	0.00892830	−	0.999960i
$344$	−76.8513	+	44.3701i	−0.223405	+	0.128983i
$345$	−177.830	+	102.670i	−0.515448	+	0.297594i
$346$	45.3395			0.131039
$347$	−67.9209	−	117.642i	−0.195737	−	0.339027i	0.751405	−	0.659842i	$-0.229377\pi$
$347$	−67.9209	−	117.642i	−0.195737	−	0.339027i	−0.947142	+	0.320815i	$0.896043\pi$
$348$	71.5842	+	41.3291i	0.205702	+	0.118762i
$349$	−306.048	+	530.091i	−0.876928	+	1.51888i	−0.0222339	+	0.999753i	$0.507078\pi$
$349$	−306.048	+	530.091i	−0.876928	+	1.51888i	−0.854694	+	0.519132i	$0.826255\pi$
$350$	48.8055	−	83.9555i	0.139444	−	0.239873i
$351$	27.0281	+	61.9071i	0.0770031	+	0.176373i
$352$	−594.389			−1.68861
$353$	−45.2732	+	78.4154i	−0.128253	+	0.222140i	−0.923000	−	0.384801i	$-0.874270\pi$
$353$	−45.2732	+	78.4154i	−0.128253	+	0.222140i	0.794747	+	0.606941i	$0.207603\pi$
$354$	−56.8955	+	98.5459i	−0.160722	+	0.278378i
$355$	388.613	−	224.366i	1.09469	−	0.632017i
$356$	109.388			0.307271
$357$	−1.08818	+	365.634i	−0.00304813	+	1.02418i
$358$	−47.7667	+	27.5781i	−0.133427	+	0.0770338i
$359$		−	76.0290i		−	0.211780i	−0.994378	−	0.105890i	$-0.966231\pi$
$359$		−	76.0290i		−	0.211780i	0.994378	−	0.105890i	$-0.0337691\pi$
$360$	−82.5521	+	47.6615i	−0.229311	+	0.132393i
$361$	74.9601	−	129.835i	0.207646	−	0.359653i
$362$	−25.2988	+	43.8188i	−0.0698862	+	0.121047i
$363$		−	461.576i		−	1.27156i
$364$	−119.908	+	161.546i	−0.329418	+	0.443807i
$365$	130.525			0.357603
$366$	−147.346	−	85.0705i	−0.402586	−	0.232433i
$367$	−147.789	−	85.3261i	−0.402695	−	0.232496i	0.284951	−	0.958542i	$-0.408023\pi$
$367$	−147.789	−	85.3261i	−0.402695	−	0.232496i	−0.687646	+	0.726046i	$0.741356\pi$
$368$	35.1665	+	60.9101i	0.0955610	+	0.165517i
$369$	36.5243			0.0989818
$370$	−114.068	−	197.572i	−0.308293	−	0.533978i
$371$	1.82102	−	611.871i	0.00490841	−	1.64925i
$372$			144.150i			0.387500i
$373$	298.145	+	516.403i	0.799317	+	1.38446i	0.920061	+	0.391774i	$0.128139\pi$
$373$	298.145	+	516.403i	0.799317	+	1.38446i	−0.120744	+	0.992684i	$0.538528\pi$
$374$	−687.669	−	397.026i	−1.83869	−	1.06157i
$375$	−202.929	−	117.161i	−0.541145	−	0.312430i
$376$			67.4462i			0.179378i
$377$	−31.3501	+	278.862i	−0.0831567	+	0.739688i
$378$	42.0620	+	24.4517i	0.111275	+	0.0646870i
$379$	−300.931	−	173.742i	−0.794013	−	0.458423i	0.0473606	−	0.998878i	$-0.484919\pi$
$379$	−300.931	−	173.742i	−0.794013	−	0.458423i	−0.841373	+	0.540454i	$0.818252\pi$
$380$	−61.4250	+	106.391i	−0.161645	+	0.279977i
$381$	−35.2509	+	20.3521i	−0.0925220	+	0.0534176i
$382$			342.090i			0.895524i
$383$	8.40205	+	14.5528i	0.0219375	+	0.0379968i	0.876786	−	0.480881i	$-0.159683\pi$
$383$	8.40205	+	14.5528i	0.0219375	+	0.0379968i	−0.854848	+	0.518878i	$0.826350\pi$
$384$	−47.2987	−	81.9238i	−0.123174	−	0.213343i
$385$	264.868	−	455.628i	0.687970	−	1.18345i
$386$	−81.6087	−	141.350i	−0.211421	−	0.366193i
$387$	16.0227	−	27.7521i	0.0414023	−	0.0717109i
$388$	158.321	−	274.220i	0.408043	−	0.706752i
$389$	−182.798			−0.469918			−0.234959	−	0.972005i	$-0.575496\pi$
$389$	−182.798			−0.469918			−0.234959	+	0.972005i	$0.575496\pi$
$390$	−92.7023	−	68.3818i	−0.237698	−	0.175338i
$391$		−	934.766i		−	2.39071i
$392$	−2.42300	+	407.066i	−0.00618112	+	1.03843i
$393$	122.996	−	213.035i	0.312966	−	0.542073i
$394$	67.1062	+	116.231i	0.170320	+	0.295003i
$395$	−420.217			−1.06384
$396$	113.067	−	65.2791i	0.285522	−	0.164846i
$397$	309.470	+	536.017i	0.779520	+	1.35017i	0.932219	+	0.361896i	$0.117870\pi$
$397$	309.470	+	536.017i	0.779520	+	1.35017i	−0.152698	+	0.988273i	$0.548796\pi$
$398$	137.839			0.346330
$399$	176.149	+	0.524245i	0.441476	+	0.00131390i
$400$	−11.7668	+	20.3806i	−0.0294169	+	0.0509516i
$401$	−340.674	−	196.688i	−0.849562	−	0.490495i	0.0109412	−	0.999940i	$-0.496517\pi$
$401$	−340.674	−	196.688i	−0.849562	−	0.490495i	−0.860503	+	0.509445i	$0.829851\pi$
$402$			78.9378i			0.196363i
$403$	−448.498	+	195.810i	−1.11290	+	0.485882i
$404$			36.5586i			0.0904915i
$405$	17.2113	−	29.8108i	0.0424969	−	0.0736068i
$406$	100.536	+	175.337i	0.247627	+	0.431865i
$407$	438.902	+	760.201i	1.07838	+	1.86782i
$408$		−	433.937i		−	1.06357i
$409$	100.963	+	174.873i	0.246853	+	0.427562i	0.962651	−	0.270745i	$-0.0872702\pi$
$409$	100.963	+	174.873i	0.246853	+	0.427562i	−0.715798	+	0.698307i	$0.753937\pi$
$410$	−53.9410	+	31.1428i	−0.131563	+	0.0759581i
$411$	−144.884			−0.352515
$412$	−201.855	+	116.541i	−0.489940	+	0.282867i
$413$	298.258	−	171.018i	0.722174	−	0.414086i
$414$	−107.719	−	62.1917i	−0.260191	−	0.150221i
$415$	40.5990			0.0978290
$416$	233.019	−	315.894i	0.560143	−	0.759362i
$417$	81.4215			0.195255
$418$	−191.272	+	331.293i	−0.457589	+	0.792568i
$419$	496.995	+	286.940i	1.18614	+	0.684821i	0.957428	−	0.288672i	$-0.0932137\pi$
$419$	496.995	+	286.940i	1.18614	+	0.684821i	0.228717	+	0.973493i	$0.426547\pi$
$420$	102.520	+	0.305115i	0.244095	+	0.000726464i
$421$		−	408.681i		−	0.970738i	−0.874309	−	0.485369i	$-0.838685\pi$
$421$		−	408.681i		−	0.970738i	0.874309	−	0.485369i	$-0.161315\pi$
$422$	−474.511	+	273.959i	−1.12443	+	0.649192i
$423$	−12.1779	−	21.0927i	−0.0287894	−	0.0498646i
$424$			726.173i			1.71267i
$425$	270.871	−	156.387i	0.637342	−	0.367970i
$426$	235.400	+	135.908i	0.552582	+	0.319033i
$427$	255.707	+	445.957i	0.598845	+	1.04440i
$428$	191.378			0.447144
$429$	356.692	+	263.114i	0.831450	+	0.613319i
$430$			54.6477i			0.127088i
$431$	−683.249	−	394.474i	−1.58527	−	0.915253i	−0.994072	−	0.108723i	$-0.965324\pi$
$431$	−683.249	−	394.474i	−1.58527	−	0.915253i	−0.591193	−	0.806530i	$-0.701343\pi$
$432$	−10.2108	−	5.89519i	−0.0236360	−	0.0136463i
$433$	−606.449	+	350.133i	−1.40057	+	0.808622i	−0.994451	−	0.105196i	$-0.966453\pi$
$433$	−606.449	+	350.133i	−1.40057	+	0.808622i	−0.406123	+	0.913818i	$0.633120\pi$
$434$	−177.145	+	304.726i	−0.408169	+	0.702135i
$435$	123.841	−	71.4997i	0.284692	−	0.164367i
$436$	211.041	−	121.844i	0.484038	−	0.279460i
$437$	−450.336			−1.03052
$438$	39.5324	+	68.4721i	0.0902566	+	0.156329i
$439$	−17.5163	−	10.1130i	−0.0399003	−	0.0230365i	0.479917	−	0.877314i	$-0.340667\pi$
$439$	−17.5163	−	10.1130i	−0.0399003	−	0.0230365i	−0.519817	+	0.854277i	$0.674000\pi$
$440$	−312.736	+	541.674i	−0.710763	+	1.23108i
$441$	−72.7409	−	127.741i	−0.164945	−	0.289662i
$442$	480.591	−	209.822i	1.08731	−	0.474710i
$443$	671.812			1.51651			0.758253	−	0.651960i	$-0.226053\pi$
$443$	671.812			1.51651			0.758253	+	0.651960i	$0.226053\pi$
$444$	−85.3787	+	147.880i	−0.192294	+	0.333064i
$445$	94.6215	−	163.889i	0.212632	−	0.368290i
$446$	168.890	−	97.5088i	0.378678	−	0.218630i
$447$	−32.6630			−0.0730715
$448$	1.03052	−	346.258i	0.00230026	−	0.772898i
$449$	123.316	−	71.1968i	0.274647	−	0.158567i	−0.356351	−	0.934352i	$-0.615979\pi$
$449$	123.316	−	71.1968i	0.274647	−	0.158567i	0.630997	+	0.775785i	$0.282646\pi$
$450$		−	41.6189i		−	0.0924864i
$451$	207.550	−	119.829i	0.460199	−	0.265696i
$452$	−50.9928	+	88.3222i	−0.112816	+	0.195403i
$453$	−68.5130	+	118.668i	−0.151243	+	0.261960i
$454$			156.908i			0.345612i
$455$	138.312	+	319.388i	0.303982	+	0.701951i
$456$	−209.055			−0.458454
$457$	225.588	+	130.243i	0.493628	+	0.284996i	0.726078	−	0.687612i	$-0.241341\pi$
$457$	225.588	+	130.243i	0.493628	+	0.284996i	−0.232450	+	0.972608i	$0.574674\pi$
$458$	−3.47088	−	2.00391i	−0.00757834	−	0.00437535i
$459$	78.3505	+	135.707i	0.170698	+	0.295658i
$460$	−262.099			−0.569780
$461$	376.482	+	652.086i	0.816663	+	1.41450i	0.908127	+	0.418694i	$0.137512\pi$
$461$	376.482	+	652.086i	0.816663	+	1.41450i	−0.0914641	+	0.995808i	$0.529155\pi$
$462$	319.239	+	0.950102i	0.690993	+	0.00205650i
$463$			846.440i			1.82816i	0.405529	+	0.914082i	$0.367087\pi$
$463$			846.440i			1.82816i	−0.405529	+	0.914082i	$0.632913\pi$
$464$	−24.4900	−	42.4180i	−0.0527803	−	0.0914181i
$465$	215.970	+	124.690i	0.464452	+	0.268151i
$466$	314.411	+	181.525i	0.674702	+	0.389539i
$467$			381.507i			0.816931i	0.912774	+	0.408465i	$0.133936\pi$
$467$			381.507i			0.816931i	−0.912774	+	0.408465i	$0.866064\pi$
$468$	−9.63248	+	85.6819i	−0.0205822	+	0.183081i
$469$	119.866	−	206.194i	0.255578	−	0.439646i
$470$	35.9699	+	20.7673i	0.0765318	+	0.0441856i
$471$	−135.853	+	235.304i	−0.288435	+	0.499584i
$472$	−353.367	+	204.017i	−0.748659	+	0.432239i
$473$		−	210.269i		−	0.444543i
$474$	−127.272	−	220.441i	−0.268506	−	0.465066i
$475$	−75.3416	−	130.495i	−0.158614	−	0.274727i
$476$	−234.553	+	403.480i	−0.492758	+	0.847646i
$477$	−131.116	−	227.099i	−0.274876	−	0.476099i
$478$	83.9833	−	145.463i	0.175697	−	0.304317i
$479$	−250.921	+	434.608i	−0.523844	+	0.907324i	0.475771	+	0.879569i	$0.342169\pi$
$479$	−250.921	+	434.608i	−0.523844	+	0.907324i	−0.999615	+	0.0277551i	$0.991164\pi$
$480$	−200.033			−0.416735
$481$	−576.080	−	64.7637i	−1.19767	−	0.134644i
$482$			549.446i			1.13993i
$483$	186.937	+	326.021i	0.387033	+	0.674992i
$484$	294.581	−	510.229i	0.608639	−	1.05419i
$485$	−273.896	−	474.402i	−0.564734	−	0.978149i
$486$	20.8512			0.0429037
$487$	735.427	−	424.599i	1.51012	−	0.871867i	0.510187	−	0.860063i	$-0.329576\pi$
$487$	735.427	−	424.599i	1.51012	−	0.871867i	0.999930	−	0.0118034i	$-0.00375722\pi$
$488$	−305.047	−	528.357i	−0.625096	−	1.08270i
$489$	−253.934			−0.519293
$490$	216.347	+	126.631i	0.441525	+	0.258431i
$491$	−267.529	+	463.374i	−0.544866	+	0.943735i	0.453749	+	0.891129i	$0.350086\pi$
$491$	−267.529	+	463.374i	−0.544866	+	0.943735i	−0.998615	+	0.0526061i	$0.983247\pi$
$492$	40.3742	+	23.3100i	0.0820613	+	0.0473781i
$493$			650.974i			1.32043i
$494$	−101.084	−	231.531i	−0.204624	−	0.468687i
$495$		−	225.867i		−	0.456296i
$496$	42.7088	−	73.9739i	0.0861065	−	0.149141i
$497$	−408.516	−	712.458i	−0.821963	−	1.43352i
$498$	12.2963	+	21.2978i	0.0246914	+	0.0427667i
$499$			85.8710i			0.172086i	0.996291	+	0.0860431i	$0.0274223\pi$
$499$			85.8710i			0.172086i	−0.996291	+	0.0860431i	$0.972578\pi$
$500$	−149.546	−	259.022i	−0.299092	−	0.518043i
$501$	−8.16018	+	4.71128i	−0.0162878	+	0.00940375i
$502$	−282.748			−0.563243
$503$	374.333	−	216.121i	0.744201	−	0.429665i	−0.0793936	−	0.996843i	$-0.525298\pi$
$503$	374.333	−	216.121i	0.744201	−	0.429665i	0.823595	+	0.567179i	$0.191965\pi$
$504$	86.7799	+	151.346i	0.172182	+	0.300289i
$505$	54.7732	+	31.6233i	0.108462	+	0.0626204i
$506$	−816.154			−1.61295
$507$	−279.669	+	86.4187i	−0.551616	+	0.170451i
$508$	−51.9554			−0.102274
$509$	−345.130	+	597.783i	−0.678055	+	1.17443i	0.297511	+	0.954719i	$0.403844\pi$
$509$	−345.130	+	597.783i	−0.678055	+	1.17443i	−0.975566	+	0.219708i	$0.929490\pi$
$510$	−231.424	−	133.613i	−0.453773	−	0.261986i
$511$	0.710960	−	238.886i	0.00139131	−	0.467487i
$512$			143.917i			0.281088i
$513$	65.3786	−	37.7464i	0.127444	−	0.0735797i
$514$	−258.630	−	447.960i	−0.503171	−	0.871518i
$515$			403.235i			0.782980i
$516$	35.4232	−	20.4516i	0.0686495	−	0.0396348i
$517$	−138.402	−	79.9065i	−0.267702	−	0.154558i
$518$	−362.216	+	207.690i	−0.699258	+	0.400947i
$519$	−58.7096			−0.113121
$520$	−165.276	−	378.560i	−0.317838	−	0.728000i
$521$			794.321i			1.52461i	0.647219	+	0.762304i	$0.275932\pi$
$521$			794.321i			1.52461i	−0.647219	+	0.762304i	$0.724068\pi$
$522$	75.0160	+	43.3105i	0.143709	+	0.0829703i
$523$	−636.199	−	367.310i	−1.21644	−	0.702313i	−0.252286	−	0.967653i	$-0.581182\pi$
$523$	−636.199	−	367.310i	−1.21644	−	0.702313i	−0.964155	+	0.265340i	$0.914516\pi$
$524$	271.920	−	156.993i	0.518932	−	0.299606i
$525$	−63.1977	+	108.713i	−0.120377	+	0.207073i
$526$	459.837	−	265.487i	0.874215	−	0.504728i
$527$	−983.156	+	567.626i	−1.86557	+	1.07709i
$528$	−77.3637			−0.146522
$529$	−215.892	−	373.937i	−0.408114	−	0.706874i
$530$	387.278	+	223.595i	0.730713	+	0.421877i
$531$	73.6734	−	127.606i	0.138745	−	0.240313i
$532$	194.382	+	112.999i	0.365379	+	0.212404i
$533$	−17.6817	+	157.281i	−0.0331740	+	0.295086i
$534$	114.633			0.214668
$535$	165.542	−	286.728i	0.309425	−	0.535940i
$536$	−141.528	+	245.134i	−0.264045	+	0.457340i
$537$	61.8526	−	35.7106i	0.115182	−	0.0665002i
$538$	349.756			0.650105
$539$	−832.444	−	487.241i	−1.54442	−	0.903972i
$540$	38.0509	−	21.9687i	0.0704645	−	0.0406827i
$541$		−	402.701i		−	0.744364i	−0.928160	−	0.372182i	$-0.878610\pi$
$541$		−	402.701i		−	0.744364i	0.928160	−	0.372182i	$-0.121390\pi$
$542$	245.089	−	141.502i	0.452193	−	0.261074i
$543$	32.7592	−	56.7406i	0.0603300	−	0.104495i
$544$	455.302	−	788.607i	0.836953	−	1.44964i
$545$		−	421.583i		−	0.773547i
$546$	−125.657	+	169.290i	−0.230140	+	0.310055i
$547$	611.662			1.11821			0.559106	−	0.829096i	$-0.311144\pi$
$547$	611.662			1.11821			0.559106	+	0.829096i	$0.311144\pi$
$548$	−160.155	−	92.4657i	−0.292254	−	0.168733i
$549$	190.797	+	110.157i	0.347536	+	0.200650i
$550$	−136.543	−	236.500i	−0.248260	−	0.430000i
$551$	313.615			0.569175
$552$	−223.008	−	386.261i	−0.404000	−	0.699748i
$553$	−2.28889	+	769.078i	−0.00413904	+	1.39074i
$554$			95.2013i			0.171844i
$555$	147.706	+	255.834i	0.266137	+	0.460962i
$556$	90.0039	+	51.9638i	0.161877	+	0.0934600i
$557$	24.4780	+	14.1324i	0.0439462	+	0.0253724i	0.521812	−	0.853060i	$-0.325256\pi$
$557$	24.4780	+	14.1324i	0.0439462	+	0.0253724i	−0.477866	+	0.878433i	$0.658590\pi$
$558$			151.061i			0.270718i
$559$	111.750	+	82.4321i	0.199910	+	0.147463i
$560$	−52.5201	−	30.5313i	−0.0937859	−	0.0545201i
$561$	890.455	+	514.104i	1.58726	+	0.916407i
$562$	137.635	−	238.391i	0.244902	−	0.424183i
$563$	89.1434	−	51.4670i	0.158336	−	0.0914156i	−0.418738	−	0.908107i	$-0.637528\pi$
$563$	89.1434	−	51.4670i	0.158336	−	0.0914156i	0.577075	+	0.816691i	$0.304194\pi$
$564$		−	31.0881i		−	0.0551207i
$565$	88.2180	+	152.798i	0.156138	+	0.270439i
$566$	300.549	+	520.567i	0.531006	+	0.919729i
$567$	−54.4656	−	31.6622i	−0.0960593	−	0.0558417i
$568$	487.341	+	844.100i	0.857995	+	1.48609i
$569$	−340.096	+	589.064i	−0.597708	+	1.03526i	0.395450	+	0.918487i	$0.370589\pi$
$569$	−340.096	+	589.064i	−0.597708	+	1.03526i	−0.993159	+	0.116774i	$0.962745\pi$
$570$	−64.3697	+	111.492i	−0.112929	+	0.195599i
$571$	−53.7356			−0.0941078			−0.0470539	−	0.998892i	$-0.514983\pi$
$571$	−53.7356			−0.0941078			−0.0470539	+	0.998892i	$0.514983\pi$
$572$	226.369	+	518.491i	0.395749	+	0.906453i
$573$		−	442.969i		−	0.773070i
$574$	56.7035	+	98.8919i	0.0987866	+	0.172285i
$575$	160.740	−	278.410i	0.279548	−	0.484192i
$576$	−74.1985	−	128.516i	−0.128817	−	0.223117i
$577$	−274.801			−0.476259			−0.238129	−	0.971233i	$-0.576534\pi$
$577$	−274.801			−0.476259			−0.238129	+	0.971233i	$0.576534\pi$
$578$	718.731	−	414.959i	1.24348	−	0.717923i
$579$	105.674	+	183.033i	0.182512	+	0.316119i
$580$	182.526			0.314701
$581$	0.221140	−	74.3039i	0.000380619	−	0.127890i
$582$	165.911	−	287.366i	0.285070	−	0.493756i
$583$	−1490.13	−	860.330i	−2.55598	−	1.47569i
$584$			283.512i			0.485465i
$585$	120.039	+	88.5469i	0.205195	+	0.151362i
$586$		−	26.2781i		−	0.0448433i
$587$	−127.728	+	221.231i	−0.217595	+	0.376885i	−0.954072	−	0.299577i	$-0.903154\pi$
$587$	−127.728	+	221.231i	−0.217595	+	0.376885i	0.736477	+	0.676462i	$0.236488\pi$
$588$	1.11684	−	187.629i	0.00189938	−	0.319098i
$589$	273.461	+	473.649i	0.464280	+	0.804157i
$590$			251.274i			0.425888i
$591$	−86.8951	−	150.507i	−0.147031	−	0.254664i
$592$	87.6280	−	50.5921i	0.148020	−	0.0854596i
$593$	376.355			0.634662			0.317331	−	0.948315i	$-0.397213\pi$
$593$	376.355			0.634662			0.317331	+	0.948315i	$0.397213\pi$
$594$	118.487	−	68.4086i	0.199473	−	0.115166i
$595$	401.616	+	700.426i	0.674985	+	1.17719i
$596$	−36.1058	−	20.8457i	−0.0605803	−	0.0349760i
$597$	−178.487			−0.298973
$598$	319.958	−	433.753i	0.535047	−	0.725340i
$599$	−46.3874			−0.0774414			−0.0387207	−	0.999250i	$-0.512328\pi$
$599$	−46.3874			−0.0774414			−0.0387207	+	0.999250i	$0.512328\pi$
$600$	74.6188	−	129.244i	0.124365	−	0.215406i
$601$	−264.199	−	152.535i	−0.439599	−	0.253803i	0.263828	−	0.964570i	$-0.415015\pi$
$601$	−264.199	−	152.535i	−0.439599	−	0.253803i	−0.703428	+	0.710767i	$0.748348\pi$
$602$	100.016	+	0.297662i	0.166139	+	0.000494455i
$603$		−	102.216i		−	0.169512i
$604$	−151.469	+	87.4509i	−0.250777	+	0.144786i
$605$	−509.628	−	882.701i	−0.842360	−	1.45901i
$606$			38.3112i			0.0632198i
$607$	−323.271	+	186.640i	−0.532571	+	0.307480i	−0.742063	−	0.670330i	$-0.766152\pi$
$607$	−323.271	+	186.640i	−0.532571	+	0.307480i	0.209492	+	0.977810i	$0.432819\pi$
$608$	−379.922	−	219.348i	−0.624871	−	0.360770i
$609$	−130.184	−	227.042i	−0.213766	−	0.372812i
$610$	−375.706			−0.615912
$611$	96.7251	−	42.2294i	0.158306	−	0.0691151i
$612$			200.015i			0.326822i
$613$	−230.798	−	133.251i	−0.376506	−	0.217376i	0.299791	−	0.954005i	$-0.403083\pi$
$613$	−230.798	−	133.251i	−0.376506	−	0.217376i	−0.676297	+	0.736629i	$0.736416\pi$
$614$	374.482	+	216.207i	0.609905	+	0.352129i
$615$	69.8476	−	40.3265i	0.113573	−	0.0655716i
$616$	989.663	+	575.316i	1.60660	+	0.933954i
$617$	−208.680	+	120.482i	−0.338218	+	0.195270i	−0.659484	−	0.751719i	$-0.729225\pi$
$617$	−208.680	+	120.482i	−0.338218	+	0.195270i	0.321266	+	0.946989i	$0.395892\pi$
$618$	−211.533	+	122.128i	−0.342286	+	0.197619i
$619$	−168.160			−0.271664			−0.135832	−	0.990732i	$-0.543371\pi$
$619$	−168.160			−0.271664			−0.135832	+	0.990732i	$0.543371\pi$
$620$	159.156	+	275.667i	0.256704	+	0.444624i
$621$	139.484	+	80.5313i	0.224613	+	0.129680i
$622$	260.221	−	450.715i	0.418361	−	0.724623i
$623$	−299.433	−	174.068i	−0.480631	−	0.279403i
$624$	30.3290	−	41.1157i	0.0486042	−	0.0658906i
$625$	−258.145			−0.413032
$626$	212.191	−	367.525i	0.338963	−	0.587101i
$627$	247.677	−	428.988i	0.395018	−	0.684192i
$628$	−300.345	+	173.404i	−0.478256	+	0.276121i
$629$	−1344.80			−2.13799
$630$	107.435	+	0.319742i	0.170532	+	0.000507527i
$631$	670.561	−	387.149i	1.06270	−	0.613548i	0.136519	−	0.990637i	$-0.456409\pi$
$631$	670.561	−	387.149i	1.06270	−	0.613548i	0.926177	+	0.377090i	$0.123075\pi$
$632$		−	912.747i		−	1.44422i
$633$	614.439	−	354.747i	0.970678	−	0.560421i
$634$	−63.9776	+	110.812i	−0.100911	+	0.174783i
$635$	−44.9416	+	77.8412i	−0.0707742	+	0.122585i
$636$		−	334.716i		−	0.526283i
$637$	585.294	−	251.397i	0.918828	−	0.394658i
$638$	568.372			0.890865
$639$	−304.817	−	175.986i	−0.477022	−	0.275409i
$640$	−180.904	−	104.445i	−0.282663	−	0.163196i
$641$	−283.575	−	491.166i	−0.442395	−	0.766250i	0.555472	−	0.831535i	$-0.312538\pi$
$641$	−283.575	−	491.166i	−0.442395	−	0.766250i	−0.997867	+	0.0652852i	$0.979204\pi$
$642$	200.552			0.312387
$643$	−10.8122	−	18.7272i	−0.0168152	−	0.0291247i	0.857495	−	0.514492i	$-0.172019\pi$
$643$	−10.8122	−	18.7272i	−0.0168152	−	0.0291247i	−0.874311	+	0.485367i	$0.838686\pi$
$644$	−1.42763	+	479.690i	−0.00221682	+	0.744861i
$645$		−	70.7628i		−	0.109710i
$646$	−293.029	−	507.542i	−0.453606	−	0.785668i
$647$	−40.0140	−	23.1021i	−0.0618455	−	0.0357065i	0.468758	−	0.883326i	$-0.344701\pi$
$647$	−40.0140	−	23.1021i	−0.0618455	−	0.0357065i	−0.530604	+	0.847620i	$0.678035\pi$
$648$	64.7514	+	37.3843i	0.0999251	+	0.0576918i
$649$		−	966.830i		−	1.48972i
$650$	179.220	+	20.1481i	0.275722	+	0.0309971i
$651$	229.383	−	394.587i	0.352355	−	0.606124i
$652$	−280.700	−	162.062i	−0.430522	−	0.248562i
$653$	170.336	−	295.031i	0.260852	−	0.451808i	−0.705617	−	0.708594i	$-0.749330\pi$
$653$	170.336	−	295.031i	0.260852	−	0.451808i	0.966468	+	0.256785i	$0.0826633\pi$
$654$	221.158	−	127.686i	0.338162	−	0.195238i
$655$		−	543.199i		−	0.829312i
$656$	−13.8126	−	23.9241i	−0.0210558	−	0.0364697i
$657$	−51.1901	−	88.6638i	−0.0779149	−	0.134953i
$658$	38.2039	−	65.7187i	0.0580607	−	0.0998764i
$659$	−7.11372	−	12.3213i	−0.0107947	−	0.0186970i	0.860578	−	0.509319i	$-0.170103\pi$
$659$	−7.11372	−	12.3213i	−0.0107947	−	0.0186970i	−0.871372	+	0.490622i	$0.836769\pi$
$660$	144.150	−	249.674i	0.218408	−	0.378295i
$661$	124.100	−	214.948i	0.187746	−	0.325186i	−0.756752	−	0.653702i	$-0.773215\pi$
$661$	124.100	−	214.948i	0.187746	−	0.325186i	0.944498	+	0.328516i	$0.106548\pi$
$662$	−608.882			−0.919761
$663$	−622.313	+	271.696i	−0.938631	+	0.409798i
$664$			88.1844i			0.132808i
$665$	337.439	−	193.484i	0.507427	−	0.290953i
$666$	−89.4718	+	154.970i	−0.134342	+	0.232687i
$667$	334.547	+	579.452i	0.501569	+	0.868744i
$668$	−12.0271			−0.0180046
$669$	−218.694	+	126.263i	−0.326897	+	0.188734i
$670$	87.1554	+	150.958i	0.130083	+	0.225310i
$671$	1445.61			2.15441
$672$	−1.08956	+	366.098i	−0.00162137	+	0.544788i
$673$	−558.514	+	967.375i	−0.829888	+	1.43741i	0.0682383	+	0.997669i	$0.478262\pi$
$673$	−558.514	+	967.375i	−0.829888	+	1.43741i	−0.898126	+	0.439738i	$0.855071\pi$
$674$	102.928	+	59.4256i	0.152712	+	0.0881686i
$675$			53.8919i			0.0798398i
$676$	−364.301	−	82.9589i	−0.538907	−	0.122720i
$677$			136.217i			0.201207i	0.994927	+	0.100604i	$0.0320774\pi$
$677$			136.217i			0.201207i	−0.994927	+	0.100604i	$0.967923\pi$
$678$	−53.4375	+	92.5564i	−0.0788163	+	0.136514i
$679$	−869.738	+	498.698i	−1.28091	+	0.734460i
$680$	−479.111	−	829.844i	−0.704575	−	1.22036i
$681$		−	203.178i		−	0.298353i
$682$	495.600	+	858.404i	0.726686	+	1.25866i
$683$	−358.144	+	206.774i	−0.524368	+	0.302744i	−0.738720	−	0.674012i	$-0.764569\pi$
$683$	−358.144	+	206.774i	−0.524368	+	0.302744i	0.214352	+	0.976757i	$0.431236\pi$
$684$	96.3599			0.140877
$685$	−277.070	+	159.966i	−0.404482	+	0.233528i
$686$	232.938	−	395.267i	0.339559	−	0.576191i
$687$	4.49440	+	2.59484i	0.00654207	+	0.00377707i
$688$	−24.2376			−0.0352291
$689$	1041.41	−	454.671i	1.51148	−	0.659900i
$690$	−274.664			−0.398064
$691$	20.1736	−	34.9417i	0.0291948	−	0.0505669i	−0.851059	−	0.525070i	$-0.824039\pi$
$691$	20.1736	−	34.9417i	0.0291948	−	0.0505669i	0.880254	+	0.474503i	$0.157372\pi$
$692$	−64.8980	−	37.4689i	−0.0937832	−	0.0541458i
$693$	−413.379	−	1.23028i	−0.596506	−	0.00177529i
$694$		−	181.703i		−	0.261819i
$695$	155.707	−	89.8977i	0.224039	−	0.129349i
$696$	155.303	+	268.993i	0.223137	+	0.386485i
$697$			367.155i			0.526765i
$698$	−709.052	+	409.371i	−1.01583	+	0.586492i
$699$	−407.127	−	235.055i	−0.582443	−	0.336273i
$700$	−139.241	+	79.8390i	−0.198915	+	0.114056i
$701$	967.001			1.37946			0.689730	−	0.724067i	$-0.257729\pi$
$701$	967.001			1.37946			0.689730	+	0.724067i	$0.257729\pi$
$702$	−10.0943	+	89.7896i	−0.0143793	+	0.127905i
$703$			647.873i			0.921584i
$704$	−843.268	−	486.861i	−1.19782	−	0.691564i
$705$	−46.5771	−	26.8913i	−0.0660668	−	0.0381437i
$706$	−104.889	+	60.5576i	−0.148568	+	0.0857757i
$707$	58.1750	−	100.073i	0.0822843	−	0.141546i
$708$	162.878	−	94.0377i	0.230054	−	0.132822i
$709$	382.482	−	220.826i	0.539466	−	0.311461i	−0.205396	−	0.978679i	$-0.565848\pi$
$709$	382.482	−	220.826i	0.539466	−	0.311461i	0.744863	+	0.667218i	$0.232515\pi$
$710$	600.226			0.845389
$711$	164.803	+	285.447i	0.231791	+	0.401473i
$712$	355.981	+	205.526i	0.499973	+	0.288660i
$713$	−583.425	+	1010.52i	−0.818268	+	1.41728i
$714$	−245.797	+	422.823i	−0.344254	+	0.592188i
$715$	972.629	+	109.344i	1.36032	+	0.152929i
$716$	91.1630			0.127323
$717$	−108.749	+	188.359i	−0.151672	+	0.262704i
$718$	50.8484	−	88.0719i	0.0708194	−	0.122663i
$719$	359.396	−	207.498i	0.499856	−	0.288592i	−0.228798	−	0.973474i	$-0.573480\pi$
$719$	359.396	−	207.498i	0.499856	−	0.288592i	0.728654	+	0.684882i	$0.240146\pi$
$720$	−26.0356			−0.0361605
$721$	737.996	+	2.19639i	1.02357	+	0.00304631i
$722$	173.668	−	100.267i	0.240537	−	0.138874i
$723$		−	711.471i		−	0.984054i
$724$	72.4244	−	41.8142i	0.100034	−	0.0577545i
$725$	−111.940	+	193.886i	−0.154400	+	0.267429i
$726$	308.703	−	534.690i	0.425211	−	0.736488i
$727$		−	1178.69i		−	1.62131i	−0.585522	−	0.810657i	$-0.699110\pi$
$727$		−	1178.69i		−	1.62131i	0.585522	−	0.810657i	$-0.300890\pi$
$728$	−693.737	+	300.424i	−0.952935	+	0.412671i
$729$	−27.0000			−0.0370370
$730$	151.200	+	87.2956i	0.207124	+	0.119583i
$731$	278.975	+	161.066i	0.381634	+	0.220337i
$732$	140.606	+	243.536i	0.192084	+	0.332700i
$733$	929.387			1.26792			0.633961	−	0.773365i	$-0.281428\pi$
$733$	929.387			1.26792			0.633961	+	0.773365i	$0.281428\pi$
$734$	−114.133	−	197.684i	−0.155494	−	0.269324i
$735$	−280.146	−	163.973i	−0.381151	−	0.223093i
$736$		−	935.951i		−	1.27167i
$737$	−335.349	−	580.842i	−0.455019	−	0.788117i
$738$	42.3097	+	24.4275i	0.0573302	+	0.0330996i
$739$	−38.0538	−	21.9704i	−0.0514937	−	0.0297299i	0.474032	−	0.880508i	$-0.342798\pi$
$739$	−38.0538	−	21.9704i	−0.0514937	−	0.0297299i	−0.525526	+	0.850778i	$0.676131\pi$
$740$			377.067i			0.509550i
$741$	130.893	+	299.807i	0.176644	+	0.404598i
$742$	411.331	−	707.574i	0.554354	−	0.953604i
$743$	572.684	+	330.639i	0.770773	+	0.445006i	0.833150	−	0.553047i	$-0.186535\pi$
$743$	572.684	+	330.639i	0.770773	+	0.445006i	−0.0623774	+	0.998053i	$0.519868\pi$
$744$	−270.838	+	469.105i	−0.364029	+	0.630517i
$745$	−62.4634	+	36.0633i	−0.0838435	+	0.0484071i
$746$			797.601i			1.06917i
$747$	−15.9223	−	27.5783i	−0.0213150	−	0.0369187i
$748$	656.210	+	1136.59i	0.877286	+	1.51950i
$749$	−523.865	−	304.536i	−0.699419	−	0.406590i
$750$	−156.715	−	271.439i	−0.208954	−	0.361919i
$751$	−57.4475	+	99.5019i	−0.0764946	+	0.132493i	−0.901735	−	0.432289i	$-0.857706\pi$
$751$	−57.4475	+	99.5019i	−0.0764946	+	0.132493i	0.825241	+	0.564781i	$0.191039\pi$
$752$	−9.21079	+	15.9535i	−0.0122484	+	0.0212148i
$753$	366.128			0.486225
$754$	−222.820	+	302.067i	−0.295517	+	0.400620i
$755$			302.582i			0.400770i
$756$	−39.9996	−	69.7599i	−0.0529095	−	0.0922751i
$757$	−295.481	+	511.788i	−0.390332	+	0.676074i	−0.992493	−	0.122300i	$-0.960973\pi$
$757$	−295.481	+	511.788i	−0.390332	+	0.676074i	0.602162	+	0.798374i	$0.294306\pi$
$758$	−232.399	−	402.527i	−0.306595	−	0.531038i
$759$	1056.83			1.39240
$760$	−399.788	+	230.818i	−0.526037	+	0.303708i
$761$	−747.466	−	1294.65i	−0.982215	−	1.70125i	−0.653711	−	0.756744i	$-0.726789\pi$
$761$	−747.466	−	1294.65i	−0.982215	−	1.70125i	−0.328504	−	0.944502i	$-0.606545\pi$
$762$	−54.4462			−0.0714517
$763$	−771.578	−	2.29633i	−1.01124	−	0.00300961i
$764$	282.706	−	489.661i	0.370034	−	0.640917i
$765$	299.669	+	173.014i	0.391724	+	0.226162i
$766$			22.4772i			0.0293437i
$767$	513.832	+	379.028i	0.669924	+	0.494170i
$768$		−	469.242i		−	0.610993i
$769$	371.953	−	644.241i	0.483684	−	0.837765i	−0.516141	−	0.856504i	$-0.672632\pi$
$769$	371.953	−	644.241i	0.483684	−	0.837765i	0.999824	+	0.0187391i	$0.00596519\pi$
$770$	611.549	−	350.655i	0.794219	−	0.455397i
$771$	334.897	+	580.059i	0.434367	+	0.752346i
$772$			269.768i			0.349440i
$773$	−424.960	−	736.052i	−0.549754	−	0.952202i	−0.998291	−	0.0584379i	$-0.981388\pi$
$773$	−424.960	−	736.052i	−0.549754	−	0.952202i	0.448537	−	0.893764i	$-0.351945\pi$
$774$	37.1214	−	21.4320i	0.0479604	−	0.0276900i
$775$	−390.430			−0.503781
$776$	1030.44	−	594.925i	1.32789	−	0.766656i
$777$	469.029	−	268.936i	0.603641	−	0.346121i
$778$	−211.753	−	122.256i	−0.272176	−	0.157141i
$779$	176.882			0.227063
$780$	76.1809	+	174.490i	0.0976678	+	0.223705i
$781$	−2309.50			−2.95711
$782$	625.174	−	1082.83i	0.799455	−	1.38470i
$783$	−97.1374	−	56.0823i	−0.124058	−	0.0716249i
$784$	−56.1641	+	95.9554i	−0.0716378	+	0.122392i
$785$			599.982i			0.764308i
$786$	284.956	−	164.520i	0.362540	−	0.209313i
$787$	−209.639	−	363.105i	−0.266377	−	0.461378i	0.701547	−	0.712624i	$-0.252493\pi$
$787$	−209.639	−	363.105i	−0.266377	−	0.461378i	−0.967923	+	0.251245i	$0.919160\pi$
$788$		−	221.828i		−	0.281508i
$789$	−595.438	+	343.777i	−0.754675	+	0.435712i
$790$	−486.780	−	281.043i	−0.616177	−	0.355750i
$791$	280.130	−	160.623i	0.354147	−	0.203064i
$792$	490.601			0.619446
$793$	−566.725	+	768.285i	−0.714660	+	0.968833i
$794$			827.896i			1.04269i
$795$	−501.482	−	289.531i	−0.630795	−	0.364190i
$796$	−197.300	−	113.911i	−0.247865	−	0.143105i
$797$	−432.423	+	249.660i	−0.542563	+	0.313249i	−0.746117	−	0.665815i	$-0.768084\pi$
$797$	−432.423	+	249.660i	−0.542563	+	0.313249i	0.203554	+	0.979064i	$0.434751\pi$
$798$	203.700	+	118.416i	0.255264	+	0.148391i
$799$	212.032	−	122.417i	0.265372	−	0.153212i
$800$	271.214	−	156.585i	0.339018	−	0.195732i
$801$	−148.437			−0.185314
$802$	−263.091	−	455.688i	−0.328044	−	0.568189i
$803$	−581.776	−	335.889i	−0.724503	−	0.418292i
$804$	65.2348	−	112.990i	0.0811378	−	0.140535i
$805$	717.452	+	417.073i	0.891245	+	0.518103i
$806$	−650.499	−	73.1299i	−0.807070	−	0.0907319i
$807$	−452.896			−0.561209
$808$	−68.6885	+	118.972i	−0.0850105	+	0.147242i
$809$	127.734	−	221.241i	0.157891	−	0.273475i	−0.776217	−	0.630466i	$-0.782864\pi$
$809$	127.734	−	221.241i	0.157891	−	0.273475i	0.934108	+	0.356991i	$0.116197\pi$
$810$	39.8750	−	23.0219i	0.0492284	−	0.0284220i
$811$	−1376.19			−1.69691			−0.848455	−	0.529267i	$-0.822467\pi$
$811$	−1376.19			−1.69691			−0.848455	+	0.529267i	$0.822467\pi$
$812$	0.994207	−	334.058i	0.00122439	−	0.411402i
$813$	−317.363	+	183.229i	−0.390360	+	0.225374i
$814$			1174.16i			1.44245i
$815$	−485.614	+	280.369i	−0.595845	+	0.344011i
$816$	59.2606	−	102.642i	0.0726233	−	0.125787i
$817$	77.5957	−	134.400i	0.0949763	−	0.164504i
$818$			270.097i			0.330192i
$819$	162.711	−	219.212i	0.198671	−	0.267658i
$820$	102.947			0.125545
$821$	−111.842	−	64.5723i	−0.136227	−	0.0786508i	0.430338	−	0.902668i	$-0.358395\pi$
$821$	−111.842	−	64.5723i	−0.136227	−	0.0786508i	−0.566565	+	0.824017i	$0.691728\pi$
$822$	−167.833	−	96.8985i	−0.204177	−	0.117881i
$823$	−283.207	−	490.528i	−0.344115	−	0.596025i	0.641078	−	0.767476i	$-0.278488\pi$
$823$	−283.207	−	490.528i	−0.344115	−	0.596025i	−0.985193	+	0.171451i	$0.945154\pi$
$824$	−875.859			−1.06294
$825$	176.808	+	306.241i	0.214313	+	0.371201i
$826$	459.879	+	1.36867i	0.556754	+	0.00165698i
$827$		−	575.200i		−	0.695526i	−0.937583	−	0.347763i	$-0.886941\pi$
$827$		−	575.200i		−	0.695526i	0.937583	−	0.347763i	$-0.113059\pi$
$828$	102.791	+	178.040i	0.124144	+	0.215024i
$829$	−683.959	−	394.884i	−0.825041	−	0.476338i	0.0271107	−	0.999632i	$-0.491369\pi$
$829$	−683.959	−	394.884i	−0.825041	−	0.476338i	−0.852152	+	0.523295i	$0.824703\pi$
$830$	47.0299	+	27.1527i	0.0566625	+	0.0327141i
$831$		−	123.275i		−	0.148346i
$832$	589.335	−	257.299i	0.708336	−	0.309253i
$833$	1284.10	−	731.219i	1.54154	−	0.877814i
$834$	94.3187	+	54.4549i	0.113092	+	0.0652937i
$835$	−10.4035	+	18.0193i	−0.0124592	+	0.0215800i
$836$	547.566	−	316.138i	0.654984	−	0.378155i
$837$		−	195.607i		−	0.233700i
$838$	383.812	+	664.783i	0.458010	+	0.793297i
$839$	561.910	+	973.256i	0.669738	+	1.16002i	0.977977	+	0.208711i	$0.0669267\pi$
$839$	561.910	+	973.256i	0.669738	+	1.16002i	−0.308240	+	0.951309i	$0.599740\pi$
$840$	333.056	+	193.614i	0.396495	+	0.230492i
$841$	187.520	+	324.795i	0.222973	+	0.386201i
$842$	273.327	−	473.416i	0.324616	−	0.562252i
$843$	−178.222	+	308.690i	−0.211414	+	0.366180i
$844$	905.607			1.07299
$845$	−439.413	+	474.047i	−0.520016	+	0.561003i
$846$		−	32.5784i		−	0.0385088i
$847$	−1618.29	+	927.907i	−1.91061	+	1.09552i
$848$	−99.1698	+	171.767i	−0.116946	+	0.202556i
$849$	−389.178	−	674.076i	−0.458396	−	0.793965i
$850$	418.369			0.492198
$851$	−1197.05	+	691.114i	−1.40663	+	0.812120i
$852$	−224.631	−	389.072i	−0.263651	−	0.456657i
$853$	740.889			0.868569			0.434285	−	0.900776i	$-0.357001\pi$
$853$	740.889			0.868569			0.434285	+	0.900776i	$0.357001\pi$
$854$	−2.04644	+	687.614i	−0.00239630	+	0.805168i
$855$	83.3517	−	144.369i	0.0974874	−	0.168853i
$856$	622.796	+	359.572i	0.727566	+	0.420060i
$857$			216.662i			0.252815i	0.991978	+	0.126407i	$0.0403446\pi$
$857$			216.662i			0.252815i	−0.991978	+	0.126407i	$0.959655\pi$
$858$	237.221	+	543.348i	0.276481	+	0.633272i
$859$			1464.68i			1.70510i	0.522648	+	0.852549i	$0.324944\pi$
$859$			1464.68i			1.70510i	−0.522648	+	0.852549i	$0.675056\pi$
$860$	45.1613	−	78.2216i	0.0525131	−	0.0909554i
$861$	−73.4248	−	128.054i	−0.0852785	−	0.148727i
$862$	−527.651	−	913.918i	−0.612124	−	1.06023i
$863$			761.209i			0.882050i	0.897495	+	0.441025i	$0.145385\pi$
$863$			761.209i			0.882050i	−0.897495	+	0.441025i	$0.854615\pi$
$864$	78.4498	+	135.879i	0.0907984	+	0.157267i
$865$	−112.274	+	64.8214i	−0.129797	+	0.0749381i
$866$	−936.680			−1.08162
$867$	−930.677	+	537.327i	−1.07345	+	0.619754i
$868$	505.390	−	289.785i	0.582246	−	0.333854i
$869$	1872.99	+	1081.37i	2.15534	+	1.24439i
$870$	191.277			0.219858
$871$	440.162	+	49.4836i	0.505353	+	0.0568124i
$872$	915.714			1.05013
$873$	−214.836	+	372.107i	−0.246089	+	0.426239i
$874$	−521.669	−	301.186i	−0.596875	−	0.344606i
$875$	−2.81841	+	946.999i	−0.00322104	+	1.08228i
$876$		−	130.679i		−	0.149177i
$877$	−371.500	+	214.485i	−0.423603	+	0.244567i	−0.696618	−	0.717443i	$-0.745313\pi$
$877$	−371.500	+	214.485i	−0.423603	+	0.244567i	0.273015	+	0.962010i	$0.411979\pi$
$878$	−13.5272	−	23.4298i	−0.0154069	−	0.0266855i
$879$			34.0273i			0.0387114i
$880$	−147.947	+	85.4174i	−0.168122	+	0.0970653i
$881$	618.727	+	357.222i	0.702301	+	0.405474i	0.808204	−	0.588903i	$-0.200440\pi$
$881$	618.727	+	357.222i	0.702301	+	0.405474i	−0.105903	+	0.994376i	$0.533773\pi$
$882$	1.17038	−	196.624i	0.00132696	−	0.222930i
$883$	14.2009			0.0160826			0.00804129	−	0.999968i	$-0.497440\pi$
$883$	14.2009			0.0160826			0.00804129	+	0.999968i	$0.497440\pi$
$884$	−861.307	−	96.8292i	−0.974329	−	0.109535i
$885$		−	325.372i		−	0.367652i
$886$	778.227	+	449.310i	0.878360	+	0.507122i
$887$	346.521	+	200.064i	0.390667	+	0.225552i	0.682449	−	0.730933i	$-0.260915\pi$
$887$	346.521	+	200.064i	0.390667	+	0.225552i	−0.291782	+	0.956485i	$0.594248\pi$
$888$	−555.692	+	320.829i	−0.625780	+	0.361294i
$889$	142.219	+	82.6757i	0.159977	+	0.0929985i
$890$	219.219	−	126.566i	0.246313	−	0.142209i
$891$	−153.428	+	88.5816i	−0.172197	+	0.0994182i
$892$	−322.328			−0.361354
$893$	−58.9759	−	102.149i	−0.0660424	−	0.114389i
$894$	−37.8368	−	21.8451i	−0.0423230	−	0.0244352i
$895$	78.8563	−	136.583i	0.0881076	−	0.152607i
$896$	−192.140	+	330.521i	−0.214442	+	0.368885i
$897$	−414.310	+	561.663i	−0.461884	+	0.626157i
$898$	190.466			0.212101
$899$	406.299	−	703.731i	0.451946	−	0.782793i
$900$	−34.3941	+	59.5724i	−0.0382157	+	0.0661916i
$901$	2282.89	−	1318.03i	2.53373	−	1.46285i
$902$	320.567			0.355396
$903$	−129.509	−	0.385439i	−0.143421	−	0.000426843i
$904$	−331.890	+	191.617i	−0.367135	+	0.211965i
$905$		−	144.678i		−	0.159865i
$906$	−158.731	+	91.6434i	−0.175200	+	0.101152i
$907$	−91.6901	+	158.812i	−0.101092	+	0.175096i	−0.912135	−	0.409891i	$-0.865567\pi$
$907$	−91.6901	+	158.812i	−0.101092	+	0.175096i	0.811043	+	0.584987i	$0.198900\pi$
$908$	129.670	−	224.595i	0.142808	−	0.247351i
$909$		−	49.6088i		−	0.0545751i
$910$	−53.3871	+	462.482i	−0.0586672	+	0.508222i
$911$	−1477.27			−1.62160			−0.810798	−	0.585327i	$-0.800966\pi$
$911$	−1477.27			−1.62160			−0.810798	+	0.585327i	$0.800966\pi$
$912$	−49.4493	−	28.5496i	−0.0542207	−	0.0313043i
$913$	−180.958	−	104.476i	−0.198201	−	0.114432i
$914$	174.214	+	301.747i	0.190606	+	0.330139i
$915$	486.498			0.531692
$916$	3.31209	+	5.73672i	0.00361582	+	0.00626279i
$917$	−994.158	−	2.95876i	−1.08414	−	0.00322657i
$918$			209.604i			0.228327i
$919$	−645.751	−	1118.47i	−0.702667	−	1.21705i	−0.967527	−	0.252768i	$-0.918659\pi$
$919$	−645.751	−	1118.47i	−0.702667	−	1.21705i	0.264860	−	0.964287i	$-0.414674\pi$
$920$	−852.943	−	492.447i	−0.927112	−	0.535268i
$921$	−484.912	−	279.964i	−0.526506	−	0.303979i
$922$			1007.17i			1.09237i
$923$	905.397	−	1227.41i	0.980928	−	1.32980i
$924$	−456.166	−	265.181i	−0.493687	−	0.286993i
$925$	−400.534	−	231.248i	−0.433009	−	0.249998i
$926$	−566.101	+	980.516i	−0.611340	+	1.05887i
$927$	273.911	−	158.143i	0.295481	−	0.170596i
$928$			651.800i			0.702370i
$929$	771.911	+	1336.99i	0.830906	+	1.43917i	0.897321	+	0.441379i	$0.145511\pi$
$929$	771.911	+	1336.99i	0.830906	+	1.43917i	−0.0664151	+	0.997792i	$0.521156\pi$
$930$	166.786	+	288.883i	0.179340	+	0.310626i
$931$	−352.274	−	618.632i	−0.378383	−	0.664481i
$932$	−300.028	−	519.663i	−0.321918	−	0.557578i
$933$	−336.957	+	583.627i	−0.361154	+	0.625538i
$934$	−255.153	+	441.937i	−0.273183	+	0.473166i
$935$	2270.50			2.42834
$936$	−192.331	+	260.735i	−0.205482	+	0.278563i
$937$		−	412.429i		−	0.440159i	−0.975482	−	0.220080i	$-0.929368\pi$
$937$		−	412.429i		−	0.440159i	0.975482	−	0.220080i	$-0.0706318\pi$
$938$	276.756	−	158.689i	0.295049	−	0.169178i
$939$	−274.764	+	475.905i	−0.292613	+	0.506821i
$940$	−34.3244	−	59.4516i	−0.0365153	−	0.0632464i
$941$	−169.051			−0.179650			−0.0898252	−	0.995958i	$-0.528631\pi$
$941$	−169.051			−0.179650			−0.0898252	+	0.995958i	$0.528631\pi$
$942$	−314.744	+	181.717i	−0.334123	+	0.192906i
$943$	188.688	+	326.816i	0.200093	+	0.346571i
$944$	−111.446			−0.118057
$945$	−139.116	−	0.414031i	−0.147213	−	0.000438128i
$946$	140.628	−	243.576i	0.148656	−	0.257479i
$947$	243.015	+	140.305i	0.256616	+	0.148157i	0.622790	−	0.782389i	$-0.285999\pi$
$947$	243.015	+	140.305i	0.256616	+	0.148157i	−0.366174	+	0.930546i	$0.619332\pi$
$948$			420.714i			0.443791i
$949$	406.586	−	177.512i	0.428436	−	0.187052i
$950$		−	201.555i		−	0.212163i
$951$	82.8439	−	143.490i	0.0871124	−	0.150883i
$952$	−1521.38	+	872.344i	−1.59809	+	0.916328i
$953$	−96.5493	−	167.228i	−0.101311	−	0.175476i	0.810914	−	0.585165i	$-0.198970\pi$
$953$	−96.5493	−	167.228i	−0.101311	−	0.175476i	−0.912225	+	0.409690i	$0.865637\pi$
$954$		−	350.762i		−	0.367676i
$955$	−489.083	−	847.117i	−0.512129	−	0.887033i
$956$	−240.424	+	138.809i	−0.251489	+	0.145197i
$957$	−735.979			−0.769048
$958$	−581.334	+	335.634i	−0.606821	+	0.350348i
$959$	291.260	+	507.962i	0.303712	+	0.529679i
$960$	−283.789	−	163.846i	−0.295613	−	0.170672i
$961$	456.113			0.474623
$962$	−624.017	−	460.306i	−0.648667	−	0.478489i
$963$	−259.693			−0.269671
$964$	454.066	−	786.465i	0.471023	−	0.815835i
$965$	404.174	+	233.350i	0.418834	+	0.241814i
$966$	−1.49607	+	502.687i	−0.00154873	+	0.520380i
$967$		−	499.335i		−	0.516375i	−0.966095	−	0.258188i	$-0.916875\pi$
$967$		−	499.335i		−	0.516375i	0.966095	−	0.258188i	$-0.0831253\pi$
$968$	1917.30	−	1106.95i	1.98068	−	1.14355i
$969$	379.440	+	657.210i	0.391579	+	0.678235i
$970$		−	732.730i		−	0.755392i
$971$	−554.917	+	320.381i	−0.571490	+	0.329950i	−0.757744	−	0.652552i	$-0.773699\pi$
$971$	−554.917	+	320.381i	−0.571490	+	0.329950i	0.186254	+	0.982502i	$0.440365\pi$
$972$	−29.8460	−	17.2316i	−0.0307057	−	0.0177280i
$973$	−163.682	−	285.464i	−0.168224	−	0.293385i
$974$	1135.89			1.16621
$975$	−232.070	−	26.0896i	−0.238020	−	0.0267585i
$976$		−	166.635i		−	0.170732i
$977$	1178.64	+	680.488i	1.20639	+	0.696508i	0.961968	−	0.273162i	$-0.0880695\pi$
$977$	1178.64	+	680.488i	1.20639	+	0.696508i	0.244419	+	0.969670i	$0.421403\pi$
$978$	−294.157	−	169.832i	−0.300774	−	0.173652i
$979$	−843.493	+	486.991i	−0.861586	+	0.497437i
$980$	−205.026	−	360.048i	−0.209211	−	0.367396i
$981$	−286.375	+	165.339i	−0.291922	+	0.168541i
$982$	−619.812	+	357.848i	−0.631173	+	0.364408i
$983$	−1177.67			−1.19803			−0.599017	−	0.800736i	$-0.704442\pi$
$983$	−1177.67			−1.19803			−0.599017	+	0.800736i	$0.704442\pi$
$984$	87.5926	+	151.715i	0.0890168	+	0.154182i
$985$	−332.350	−	191.882i	−0.337411	−	0.194804i
$986$	−435.373	+	754.088i	−0.441555	+	0.764795i
$987$	−49.4699	+	85.0984i	−0.0501215	+	0.0862193i
$988$	−46.6488	+	414.946i	−0.0472153	+	0.419986i
$989$	331.099			0.334781
$990$	151.060	−	261.644i	0.152586	−	0.264287i
$991$	−23.7546	+	41.1441i	−0.0239703	+	0.0415178i	−0.877762	−	0.479097i	$-0.840964\pi$
$991$	−23.7546	+	41.1441i	−0.0239703	+	0.0415178i	0.853791	+	0.520615i	$0.174297\pi$
$992$	−984.403	+	568.345i	−0.992342	+	0.572929i
$993$	788.434			0.793992
$994$	3.26938	−	1098.53i	0.00328912	−	1.10516i
$995$	−341.331	+	197.068i	−0.343046	+	0.198058i
$996$		−	40.6470i		−	0.0408102i
$997$	−940.549	+	543.026i	−0.943380	+	0.544660i	−0.891018	−	0.453968i	$-0.850008\pi$
$997$	−940.549	+	543.026i	−0.943380	+	0.544660i	−0.0523614	+	0.998628i	$0.516675\pi$
$998$	−57.4308	+	99.4730i	−0.0575459	+	0.0996723i
$999$	115.856	−	200.669i	0.115972	−	0.200869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.3.bo.c.160.12	✓	36
7.6	odd	2		273.3.bo.d.160.12	yes	36
13.10	even	6		273.3.bo.d.244.12	yes	36
91.62	odd	6	inner	273.3.bo.c.244.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.3.bo.c.160.12	✓	36	1.1	even	1	trivial
273.3.bo.c.244.12	yes	36	91.62	odd	6	inner
273.3.bo.d.160.12	yes	36	7.6	odd	2
273.3.bo.d.244.12	yes	36	13.10	even	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	273.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15840 + 0.668803i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.10541 - 1.91462i) q^{4} -3.82472 q^{5} +(-1.15840 - 2.00641i) q^{6} +(-0.0208330 + 6.99997i) q^{7} -8.30761i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.15840 + 0.668803i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.10541 - 1.91462i) q^{4} -3.82472 q^{5} +(-1.15840 - 2.00641i) q^{6} +(-0.0208330 + 6.99997i) q^{7} -8.30761i q^{8} +(1.50000 + 2.59808i) q^{9} +(-4.43056 - 2.55798i) q^{10} +(17.0475 + 9.84240i) q^{11} +3.82924i q^{12} +(-11.9140 + 5.20156i) q^{13} +(-4.70573 + 8.09483i) q^{14} +(5.73708 + 3.31231i) q^{15} +(1.13453 - 1.96506i) q^{16} +(-26.1168 + 15.0786i) q^{17} +4.01282i q^{18} +(7.26429 + 12.5821i) q^{19} +(4.22787 + 7.32289i) q^{20} +(6.09340 - 10.4819i) q^{21} +(13.1652 + 22.8029i) q^{22} +(-15.4983 + 26.8438i) q^{23} +(-7.19461 + 12.4614i) q^{24} -10.3715 q^{25} +(-17.2800 - 1.94264i) q^{26} -5.19615i q^{27} +(13.4253 - 7.69792i) q^{28} +(10.7930 - 18.6941i) q^{29} +(4.43056 + 7.67395i) q^{30} +37.6446 q^{31} +(-26.1499 + 15.0977i) q^{32} +(-17.0475 - 29.5272i) q^{33} -40.3383 q^{34} +(0.0796803 - 26.7729i) q^{35} +(3.31622 - 5.74386i) q^{36} +(38.6187 + 22.2965i) q^{37} +19.4335i q^{38} +(22.3757 + 2.51551i) q^{39} +31.7743i q^{40} +(6.08738 - 10.5436i) q^{41} +(14.0689 - 8.06696i) q^{42} +(-5.34090 - 9.25071i) q^{43} -43.5194i q^{44} +(-5.73708 - 9.93692i) q^{45} +(-35.9064 + 20.7306i) q^{46} -8.11860 q^{47} +(-3.40359 + 1.96506i) q^{48} +(-48.9991 - 0.291660i) q^{49} +(-12.0143 - 6.93648i) q^{50} +52.2336 q^{51} +(23.1288 + 17.0610i) q^{52} -87.4106 q^{53} +(3.47520 - 6.01922i) q^{54} +(-65.2021 - 37.6444i) q^{55} +(58.1530 + 0.173072i) q^{56} -25.1642i q^{57} +(25.0053 - 14.4368i) q^{58} +(-24.5578 - 42.5353i) q^{59} -14.6458i q^{60} +(63.5991 - 36.7190i) q^{61} +(43.6075 + 25.1768i) q^{62} +(-18.2177 + 10.4458i) q^{63} -49.4657 q^{64} +(45.5678 - 19.8945i) q^{65} -45.6057i q^{66} +(-29.5071 - 17.0360i) q^{67} +(57.7394 + 33.3359i) q^{68} +(46.4948 - 26.8438i) q^{69} +(17.9981 - 30.9605i) q^{70} +(-101.606 + 58.6620i) q^{71} +(21.5838 - 12.4614i) q^{72} -34.1267 q^{73} +(29.8239 + 51.6566i) q^{74} +(15.5572 + 8.98198i) q^{75} +(16.0600 - 27.8167i) q^{76} +(-69.2516 + 119.127i) q^{77} +(24.2376 + 17.8789i) q^{78} +109.869 q^{79} +(-4.33926 + 7.51582i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(14.1032 - 8.14251i) q^{82} -10.6149 q^{83} +(-26.8046 - 0.0797744i) q^{84} +(99.8896 - 57.6713i) q^{85} -14.2880i q^{86} +(-32.3791 + 18.6941i) q^{87} +(81.7669 - 141.624i) q^{88} +(-24.7394 + 42.8499i) q^{89} -15.3479i q^{90} +(-36.1625 - 83.5061i) q^{91} +68.5275 q^{92} +(-56.4668 - 32.6011i) q^{93} +(-9.40459 - 5.42974i) q^{94} +(-27.7839 - 48.1231i) q^{95} +52.2999 q^{96} +(71.6120 + 124.036i) q^{97} +(-56.5655 - 33.1086i) q^{98} +59.0544i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9}+O(q^{10}) \) 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9	\( 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9} + 42 q^{11} - 36 q^{13} + 16 q^{14} + 6 q^{15} - 96 q^{16} - 12 q^{17} + 12 q^{19} - 10 q^{20} - 18 q^{22} + 24 q^{23} + 264 q^{25} + 114 q^{26} - 104 q^{28} + 76 q^{29} - 160 q^{31} - 42 q^{33} - 192 q^{34} - 100 q^{35} - 132 q^{36} + 6 q^{37} + 60 q^{39} + 200 q^{41} + 18 q^{42} + 48 q^{43} - 6 q^{45} + 396 q^{46} + 56 q^{47} + 288 q^{48} - 154 q^{49} - 102 q^{50} + 24 q^{51} - 360 q^{52} + 76 q^{53} + 192 q^{55} - 132 q^{56} - 162 q^{58} + 128 q^{59} - 120 q^{61} + 24 q^{62} - 30 q^{63} - 484 q^{64} - 284 q^{65} - 144 q^{67} + 234 q^{68} - 72 q^{69} + 300 q^{70} - 96 q^{71} + 728 q^{73} - 144 q^{74} - 396 q^{75} - 516 q^{76} - 160 q^{77} - 144 q^{78} + 68 q^{79} - 58 q^{80} - 162 q^{81} + 72 q^{82} + 368 q^{83} + 108 q^{84} - 324 q^{85} - 228 q^{87} + 186 q^{88} + 92 q^{89} + 176 q^{91} - 1044 q^{92} + 240 q^{93} - 336 q^{94} - 2 q^{95} - 72 q^{97} + 234 q^{98}+O(q^{100}) \) 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9 + 42 * q^11 - 36 * q^13 + 16 * q^14 + 6 * q^15 - 96 * q^16 - 12 * q^17 + 12 * q^19 - 10 * q^20 - 18 * q^22 + 24 * q^23 + 264 * q^25 + 114 * q^26 - 104 * q^28 + 76 * q^29 - 160 * q^31 - 42 * q^33 - 192 * q^34 - 100 * q^35 - 132 * q^36 + 6 * q^37 + 60 * q^39 + 200 * q^41 + 18 * q^42 + 48 * q^43 - 6 * q^45 + 396 * q^46 + 56 * q^47 + 288 * q^48 - 154 * q^49 - 102 * q^50 + 24 * q^51 - 360 * q^52 + 76 * q^53 + 192 * q^55 - 132 * q^56 - 162 * q^58 + 128 * q^59 - 120 * q^61 + 24 * q^62 - 30 * q^63 - 484 * q^64 - 284 * q^65 - 144 * q^67 + 234 * q^68 - 72 * q^69 + 300 * q^70 - 96 * q^71 + 728 * q^73 - 144 * q^74 - 396 * q^75 - 516 * q^76 - 160 * q^77 - 144 * q^78 + 68 * q^79 - 58 * q^80 - 162 * q^81 + 72 * q^82 + 368 * q^83 + 108 * q^84 - 324 * q^85 - 228 * q^87 + 186 * q^88 + 92 * q^89 + 176 * q^91 - 1044 * q^92 + 240 * q^93 - 336 * q^94 - 2 * q^95 - 72 * q^97 + 234 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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