LMFDB - Embedded newform 90.3.h.a.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,3,Mod(11,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("90.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	90.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.45232237924$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 138x^{12} - 1040x^{10} + 5541x^{8} - 26220x^{6} + 99328x^{4} - 202728x^{2} + 181476 $ x^16 - 12x^14 + 138x^12 - 1040x^10 + 5541x^8 - 26220x^6 + 99328x^4 - 202728*x^2 + 181476
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.7
Root			$-1.42311 - 0.410927i$ of defining polynomial
Character	$\chi$	$=$	90.11
Dual form			90.3.h.a.41.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 + 0.707107i) q^{2} +(1.52181 - 2.58536i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(3.69195 - 2.09033i) q^{6} +(-0.496891 + 0.860641i) q^{7} +2.82843i q^{8} +(-4.36821 - 7.86884i) q^{9} +3.16228 q^{10} +(4.31820 + 2.49311i) q^{11} +(5.99979 + 0.0504813i) q^{12} +(-0.710132 - 1.22998i) q^{13} +(-1.21713 + 0.702710i) q^{14} +(0.0564398 - 6.70797i) q^{15} +(-2.00000 + 3.46410i) q^{16} +24.1344i q^{17} +(0.214166 - 12.7261i) q^{18} -27.5702 q^{19} +(3.87298 + 2.23607i) q^{20} +(1.46890 + 2.59437i) q^{21} +(3.52579 + 6.10686i) q^{22} +(-5.23030 + 3.01971i) q^{23} +(7.31251 + 4.30432i) q^{24} +(2.50000 - 4.33013i) q^{25} -2.00856i q^{26} +(-26.9914 - 0.681433i) q^{27} -1.98756 q^{28} +(16.5910 + 9.57883i) q^{29} +(4.81237 - 8.17564i) q^{30} +(-13.6022 - 23.5597i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(13.0171 - 7.37008i) q^{33} +(-17.0656 + 29.5585i) q^{34} +2.22216i q^{35} +(9.26102 - 15.4348i) q^{36} -63.1320 q^{37} +(-33.7664 - 19.4951i) q^{38} +(-4.26064 - 0.0358483i) q^{39} +(3.16228 + 5.47723i) q^{40} +(58.1104 - 33.5501i) q^{41} +(-0.0354737 + 4.21611i) q^{42} +(13.8292 - 23.9528i) q^{43} +9.97245i q^{44} +(-17.2566 - 10.3541i) q^{45} -8.54104 q^{46} +(-5.85337 - 3.37944i) q^{47} +(5.91235 + 10.4424i) q^{48} +(24.0062 + 41.5800i) q^{49} +(6.12372 - 3.53553i) q^{50} +(62.3962 + 36.7279i) q^{51} +(1.42026 - 2.45997i) q^{52} +87.8018i q^{53} +(-32.5757 - 19.9204i) q^{54} +11.1495 q^{55} +(-2.43426 - 1.40542i) q^{56} +(-41.9565 + 71.2790i) q^{57} +(13.5465 + 23.4633i) q^{58} +(89.2923 - 51.5529i) q^{59} +(11.6750 - 6.61021i) q^{60} +(36.0064 - 62.3649i) q^{61} -38.4728i q^{62} +(8.94277 + 0.150497i) q^{63} -8.00000 q^{64} +(-2.75033 - 1.58790i) q^{65} +(21.1540 + 0.177987i) q^{66} +(-9.98403 - 17.2928i) q^{67} +(-41.8020 + 24.1344i) q^{68} +(-0.152439 + 18.1176i) q^{69} +(-1.57131 + 2.72158i) q^{70} -55.1081i q^{71} +(22.2565 - 12.3552i) q^{72} +132.751 q^{73} +(-77.3206 - 44.6411i) q^{74} +(-7.39044 - 13.0530i) q^{75} +(-27.5702 - 47.7530i) q^{76} +(-4.29135 + 2.47761i) q^{77} +(-5.19285 - 3.05663i) q^{78} +(19.7946 - 34.2853i) q^{79} +8.94427i q^{80} +(-42.8374 + 68.7456i) q^{81} +94.8939 q^{82} +(-104.952 - 60.5938i) q^{83} +(-3.02469 + 5.13858i) q^{84} +(26.9831 + 46.7361i) q^{85} +(33.8744 - 19.5574i) q^{86} +(50.0131 - 28.3167i) q^{87} +(-7.05159 + 12.2137i) q^{88} +74.0513i q^{89} +(-13.8135 - 24.8835i) q^{90} +1.41143 q^{91} +(-10.4606 - 6.03943i) q^{92} +(-81.6102 - 0.686656i) q^{93} +(-4.77926 - 8.27791i) q^{94} +(-53.3894 + 30.8244i) q^{95} +(-0.142783 + 16.9700i) q^{96} +(-1.14383 + 1.98117i) q^{97} +67.8998i q^{98} +(0.755106 - 44.8697i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} + 16 q^{4} + 16 q^{6} - 4 q^{7} - 4 q^{9} - 16 q^{12} + 20 q^{13} - 36 q^{14} - 20 q^{15} - 32 q^{16} + 16 q^{18} + 80 q^{19} - 44 q^{21} + 24 q^{22} + 108 q^{23} - 8 q^{24} + 40 q^{25} - 124 q^{27}+ \cdots + 816 q^{99}+O(q^{100}) $ 16 * q - 4 * q^3 + 16 * q^4 + 16 * q^6 - 4 * q^7 - 4 * q^9 - 16 * q^12 + 20 * q^13 - 36 * q^14 - 20 * q^15 - 32 * q^16 + 16 * q^18 + 80 * q^19 - 44 * q^21 + 24 * q^22 + 108 * q^23 - 8 * q^24 + 40 * q^25 - 124 * q^27 - 16 * q^28 - 72 * q^29 + 20 * q^30 - 16 * q^31 - 264 * q^33 - 48 * q^34 + 32 * q^36 - 88 * q^37 - 72 * q^38 - 8 * q^39 + 108 * q^41 + 128 * q^42 + 92 * q^43 - 80 * q^45 + 24 * q^46 + 216 * q^47 - 16 * q^48 - 84 * q^49 + 168 * q^51 - 40 * q^52 + 148 * q^54 - 72 * q^56 + 28 * q^57 + 144 * q^59 + 40 * q^60 - 76 * q^61 - 104 * q^63 - 128 * q^64 + 180 * q^65 + 96 * q^66 + 56 * q^67 + 72 * q^68 - 72 * q^69 + 60 * q^70 + 64 * q^72 + 416 * q^73 - 288 * q^74 + 20 * q^75 + 80 * q^76 - 684 * q^77 + 56 * q^78 + 80 * q^79 + 320 * q^81 - 192 * q^82 + 396 * q^83 + 40 * q^84 - 60 * q^85 - 216 * q^86 + 420 * q^87 - 48 * q^88 - 160 * q^90 - 656 * q^91 + 216 * q^92 - 356 * q^93 - 84 * q^94 - 360 * q^95 - 80 * q^96 - 16 * q^97 + 816 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$2$	1.22474	+	0.707107i	0.612372	+	0.353553i
$3$	1.52181	−	2.58536i	0.507269	−	0.861788i
$3$	1.52181	−	2.58536i	0.507269	−	0.861788i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$	3.69195	−	2.09033i	0.615325	−	0.348389i
$7$	−0.496891	+	0.860641i	−0.0709844	+	0.122949i	−0.899333	−	0.437264i	$-0.855947\pi$
$7$	−0.496891	+	0.860641i	−0.0709844	+	0.122949i	0.828349	+	0.560213i	$0.189281\pi$
$8$			2.82843i			0.353553i
$9$	−4.36821	−	7.86884i	−0.485357	−	0.874316i
$10$	3.16228			0.316228
$11$	4.31820	+	2.49311i	0.392564	+	0.226647i	0.683270	−	0.730166i	$-0.260557\pi$
$11$	4.31820	+	2.49311i	0.392564	+	0.226647i	−0.290707	+	0.956812i	$0.593890\pi$
$12$	5.99979	+	0.0504813i	0.499982	+	0.00420677i
$13$	−0.710132	−	1.22998i	−0.0546255	−	0.0946142i	0.837420	−	0.546561i	$-0.184063\pi$
$13$	−0.710132	−	1.22998i	−0.0546255	−	0.0946142i	−0.892045	+	0.451946i	$0.850730\pi$
$14$	−1.21713	+	0.702710i	−0.0869378	+	0.0501936i
$15$	0.0564398	−	6.70797i	0.00376265	−	0.447198i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$			24.1344i			1.41967i	0.704368	+	0.709835i	$0.251231\pi$
$17$			24.1344i			1.41967i	−0.704368	+	0.709835i	$0.748769\pi$
$18$	0.214166	−	12.7261i	0.0118981	−	0.707007i
$19$	−27.5702			−1.45106			−0.725531	−	0.688189i	$-0.758406\pi$
$19$	−27.5702			−1.45106			−0.725531	+	0.688189i	$0.758406\pi$
$20$	3.87298	+	2.23607i	0.193649	+	0.111803i
$21$	1.46890	+	2.59437i	0.0699475	+	0.123542i
$22$	3.52579	+	6.10686i	0.160263	+	0.277584i
$23$	−5.23030	+	3.01971i	−0.227404	+	0.131292i	−0.609374	−	0.792883i	$-0.708579\pi$
$23$	−5.23030	+	3.01971i	−0.227404	+	0.131292i	0.381970	+	0.924175i	$0.375246\pi$
$24$	7.31251	+	4.30432i	0.304688	+	0.179347i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$		−	2.00856i		−	0.0772522i
$27$	−26.9914	−	0.681433i	−0.999681	−	0.0252382i
$28$	−1.98756			−0.0709844
$29$	16.5910	+	9.57883i	0.572104	+	0.330305i	0.757989	−	0.652267i	$-0.226182\pi$
$29$	16.5910	+	9.57883i	0.572104	+	0.330305i	−0.185885	+	0.982572i	$0.559515\pi$
$30$	4.81237	−	8.17564i	0.160412	−	0.272521i
$31$	−13.6022	−	23.5597i	−0.438780	−	0.759990i	0.558815	−	0.829292i	$-0.311256\pi$
$31$	−13.6022	−	23.5597i	−0.438780	−	0.759990i	−0.997596	+	0.0693023i	$0.977923\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	13.0171	−	7.37008i	0.394457	−	0.223336i
$34$	−17.0656	+	29.5585i	−0.501929	+	0.869367i
$35$			2.22216i			0.0634904i
$36$	9.26102	−	15.4348i	0.257251	−	0.428745i
$37$	−63.1320			−1.70627			−0.853136	−	0.521689i	$-0.825302\pi$
$37$	−63.1320			−1.70627			−0.853136	+	0.521689i	$0.825302\pi$
$38$	−33.7664	−	19.4951i	−0.888591	−	0.513028i
$39$	−4.26064	−	0.0358483i	−0.109247	−	0.000919188i
$40$	3.16228	+	5.47723i	0.0790569	+	0.136931i
$41$	58.1104	−	33.5501i	1.41733	−	0.818294i	0.421264	−	0.906938i	$-0.361587\pi$
$41$	58.1104	−	33.5501i	1.41733	−	0.818294i	0.996063	+	0.0886435i	$0.0282532\pi$
$42$	−0.0354737	+	4.21611i	−0.000844612	+	0.100384i
$43$	13.8292	−	23.9528i	0.321609	−	0.557042i	−0.659212	−	0.751958i	$-0.729110\pi$
$43$	13.8292	−	23.9528i	0.321609	−	0.557042i	0.980820	+	0.194915i	$0.0624431\pi$
$44$			9.97245i			0.226647i
$45$	−17.2566	−	10.3541i	−0.383481	−	0.230092i
$46$	−8.54104			−0.185675
$47$	−5.85337	−	3.37944i	−0.124540	−	0.0719031i	0.436436	−	0.899735i	$-0.356241\pi$
$47$	−5.85337	−	3.37944i	−0.124540	−	0.0719031i	−0.560976	+	0.827832i	$0.689574\pi$
$48$	5.91235	+	10.4424i	0.123174	+	0.217550i
$49$	24.0062	+	41.5800i	0.489922	+	0.848571i
$50$	6.12372	−	3.53553i	0.122474	−	0.0707107i
$51$	62.3962	+	36.7279i	1.22345	+	0.720154i
$52$	1.42026	−	2.45997i	0.0273128	−	0.0473071i
$53$			87.8018i			1.65664i	0.560257	+	0.828319i	$0.310702\pi$
$53$			87.8018i			1.65664i	−0.560257	+	0.828319i	$0.689298\pi$
$54$	−32.5757	−	19.9204i	−0.603254	−	0.368896i
$55$	11.1495			0.202719
$56$	−2.43426	−	1.40542i	−0.0434689	−	0.0250968i
$57$	−41.9565	+	71.2790i	−0.736078	+	1.25051i
$58$	13.5465	+	23.4633i	0.233561	+	0.404539i
$59$	89.2923	−	51.5529i	1.51343	−	0.873778i	0.513552	−	0.858058i	$-0.328329\pi$
$59$	89.2923	−	51.5529i	1.51343	−	0.873778i	0.999876	−	0.0157198i	$-0.00500398\pi$
$60$	11.6750	−	6.61021i	0.194583	−	0.110170i
$61$	36.0064	−	62.3649i	0.590269	−	1.02238i	−0.403927	−	0.914791i	$-0.632355\pi$
$61$	36.0064	−	62.3649i	0.590269	−	1.02238i	0.994196	−	0.107585i	$-0.0343117\pi$
$62$		−	38.4728i		−	0.620529i
$63$	8.94277	+	0.150497i	0.141949	+	0.00238884i
$64$	−8.00000			−0.125000
$65$	−2.75033	−	1.58790i	−0.0423127	−	0.0244293i
$66$	21.1540	+	0.177987i	0.320515	+	0.00269677i
$67$	−9.98403	−	17.2928i	−0.149015	−	0.258102i	0.781848	−	0.623469i	$-0.214277\pi$
$67$	−9.98403	−	17.2928i	−0.149015	−	0.258102i	−0.930864	+	0.365366i	$0.880944\pi$
$68$	−41.8020	+	24.1344i	−0.614735	+	0.354918i
$69$	−0.152439	+	18.1176i	−0.00220926	+	0.262575i
$70$	−1.57131	+	2.72158i	−0.0224473	+	0.0388798i
$71$		−	55.1081i		−	0.776170i	−0.921624	−	0.388085i	$-0.873137\pi$
$71$		−	55.1081i		−	0.776170i	0.921624	−	0.388085i	$-0.126863\pi$
$72$	22.2565	−	12.3552i	0.309117	−	0.171600i
$73$	132.751			1.81851			0.909254	−	0.416241i	$-0.136653\pi$
$73$	132.751			1.81851			0.909254	+	0.416241i	$0.136653\pi$
$74$	−77.3206	−	44.6411i	−1.04487	−	0.603258i
$75$	−7.39044	−	13.0530i	−0.0985392	−	0.174040i
$76$	−27.5702	−	47.7530i	−0.362766	−	0.628328i
$77$	−4.29135	+	2.47761i	−0.0557318	+	0.0321768i
$78$	−5.19285	−	3.05663i	−0.0665750	−	0.0391876i
$79$	19.7946	−	34.2853i	0.250565	−	0.433992i	−0.713116	−	0.701046i	$-0.752717\pi$
$79$	19.7946	−	34.2853i	0.250565	−	0.433992i	0.963682	+	0.267054i	$0.0860502\pi$
$80$			8.94427i			0.111803i
$81$	−42.8374	+	68.7456i	−0.528857	+	0.848711i
$82$	94.8939			1.15724
$83$	−104.952	−	60.5938i	−1.26448	−	0.730046i	−0.290540	−	0.956863i	$-0.593835\pi$
$83$	−104.952	−	60.5938i	−1.26448	−	0.730046i	−0.973937	+	0.226817i	$0.927168\pi$
$84$	−3.02469	+	5.13858i	−0.0360082	+	0.0611735i
$85$	26.9831	+	46.7361i	0.317448	+	0.549836i
$86$	33.8744	−	19.5574i	0.393888	−	0.227412i
$87$	50.0131	−	28.3167i	0.574863	−	0.325479i
$88$	−7.05159	+	12.2137i	−0.0801317	+	0.138792i
$89$			74.0513i			0.832037i	0.909356	+	0.416018i	$0.136575\pi$
$89$			74.0513i			0.832037i	−0.909356	+	0.416018i	$0.863425\pi$
$90$	−13.8135	−	24.8835i	−0.153483	−	0.276483i
$91$	1.41143			0.0155103
$92$	−10.4606	−	6.03943i	−0.113702	−	0.0656460i
$93$	−81.6102	−	0.686656i	−0.877529	−	0.00738339i
$94$	−4.77926	−	8.27791i	−0.0508431	−	0.0880629i
$95$	−53.3894	+	30.8244i	−0.561994	+	0.324467i
$96$	−0.142783	+	16.9700i	−0.00148732	+	0.176770i
$97$	−1.14383	+	1.98117i	−0.0117921	+	0.0204245i	−0.871861	−	0.489753i	$-0.837087\pi$
$97$	−1.14383	+	1.98117i	−0.0117921	+	0.0204245i	0.860069	+	0.510177i	$0.170420\pi$
$98$			67.8998i			0.692855i
$99$	0.755106	−	44.8697i	0.00762734	−	0.453229i
$100$	10.0000			0.100000
$101$	−98.4221	−	56.8240i	−0.974476	−	0.562614i	−0.0738781	−	0.997267i	$-0.523538\pi$
$101$	−98.4221	−	56.8240i	−0.974476	−	0.562614i	−0.900598	+	0.434653i	$0.856871\pi$
$102$	50.4489	+	89.1030i	0.494597	+	0.873559i
$103$	28.3717	+	49.1412i	0.275453	+	0.477099i	0.970249	−	0.242108i	$-0.0778387\pi$
$103$	28.3717	+	49.1412i	0.275453	+	0.477099i	−0.694796	+	0.719207i	$0.744505\pi$
$104$	3.47892	−	2.00856i	0.0334512	−	0.0193130i
$105$	5.74510	+	3.38170i	0.0547153	+	0.0322067i
$106$	−62.0852	+	107.535i	−0.585710	+	1.01448i
$107$		−	93.1862i		−	0.870899i	−0.900213	−	0.435450i	$-0.856589\pi$
$107$		−	93.1862i		−	0.870899i	0.900213	−	0.435450i	$-0.143411\pi$
$108$	−25.8111	−	47.4319i	−0.238992	−	0.439184i
$109$	−21.7553			−0.199590			−0.0997950	−	0.995008i	$-0.531819\pi$
$109$	−21.7553			−0.199590			−0.0997950	+	0.995008i	$0.531819\pi$
$110$	13.6553	+	7.88392i	0.124139	+	0.0716720i
$111$	−96.0747	+	163.219i	−0.865538	+	1.47044i
$112$	−1.98756	−	3.44256i	−0.0177461	−	0.0307372i
$113$	−124.052	+	71.6214i	−1.09780	+	0.633817i	−0.935643	−	0.352947i	$-0.885180\pi$
$113$	−124.052	+	71.6214i	−1.09780	+	0.633817i	−0.162161	+	0.986764i	$0.551846\pi$
$114$	−101.788	+	57.6308i	−0.892875	+	0.505534i
$115$	−6.75229	+	11.6953i	−0.0587155	+	0.101698i
$116$			38.3153i			0.330305i
$117$	−6.57655	+	10.9608i	−0.0562098	+	0.0936816i
$118$	145.814			1.23571
$119$	−20.7710	−	11.9922i	−0.174547	−	0.100775i
$120$	18.9730	+	0.159636i	0.158108	+	0.00133030i
$121$	−48.0688	−	83.2576i	−0.397263	−	0.688079i
$122$	88.1973	−	50.9208i	0.722929	−	0.417383i
$123$	1.69365	−	201.293i	0.0137695	−	1.63653i
$124$	27.2044	−	47.1194i	0.219390	−	0.379995i
$125$		−	11.1803i		−	0.0894427i
$126$	10.8462	+	6.50782i	0.0860809	+	0.0516493i
$127$	−165.052			−1.29962			−0.649811	−	0.760096i	$-0.725152\pi$
$127$	−165.052			−1.29962			−0.649811	+	0.760096i	$0.725152\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	−40.8815	−	72.2050i	−0.316911	−	0.559729i
$130$	−2.24563	−	3.88955i	−0.0172741	−	0.0299196i
$131$	45.4381	−	26.2337i	0.346856	−	0.200257i	−0.316444	−	0.948611i	$-0.602489\pi$
$131$	45.4381	−	26.2337i	0.346856	−	0.200257i	0.663300	+	0.748354i	$0.269156\pi$
$132$	25.7824	+	15.1761i	0.195321	+	0.114971i
$133$	13.6994	−	23.7280i	0.103003	−	0.178406i
$134$		−	28.2391i		−	0.210740i
$135$	−53.0305	+	28.8577i	−0.392818	+	0.213761i
$136$	−68.2624			−0.501929
$137$	104.246	+	60.1866i	0.760921	+	0.439318i	0.829626	−	0.558319i	$-0.188553\pi$
$137$	104.246	+	60.1866i	0.760921	+	0.439318i	−0.0687051	+	0.997637i	$0.521887\pi$
$138$	−12.9978	+	22.0817i	−0.0941870	+	0.160012i
$139$	33.1992	+	57.5027i	0.238843	+	0.413689i	0.960383	−	0.278685i	$-0.0898984\pi$
$139$	33.1992	+	57.5027i	0.238843	+	0.413689i	−0.721539	+	0.692373i	$0.756565\pi$
$140$	−3.84890	+	2.22216i	−0.0274922	+	0.0158726i
$141$	−17.6448	+	9.99023i	−0.125140	+	0.0708527i
$142$	38.9673	−	67.4933i	0.274418	−	0.475305i
$143$		−	7.08176i		−	0.0495228i
$144$	35.9949	+	0.605754i	0.249965	+	0.00420662i
$145$	42.8378			0.295433
$146$	162.586	+	93.8692i	1.11360	+	0.642940i
$147$	144.032	+	1.21186i	0.979810	+	0.00824397i
$148$	−63.1320	−	109.348i	−0.426568	−	0.738837i
$149$	82.8092	−	47.8099i	0.555766	−	0.320872i	−0.195678	−	0.980668i	$-0.562691\pi$
$149$	82.8092	−	47.8099i	0.555766	−	0.320872i	0.751444	+	0.659796i	$0.229357\pi$
$150$	0.178478	−	21.2125i	0.00118985	−	0.141416i
$151$	−135.262	+	234.281i	−0.895776	+	1.55153i	−0.0629346	+	0.998018i	$0.520046\pi$
$151$	−135.262	+	234.281i	−0.895776	+	1.55153i	−0.832841	+	0.553512i	$0.813287\pi$
$152$		−	77.9803i		−	0.513028i
$153$	189.910	−	105.424i	1.24124	−	0.689047i
$154$	−7.00774			−0.0455048
$155$	−52.6810	−	30.4154i	−0.339878	−	0.196229i
$156$	−4.19855	−	7.41549i	−0.0269138	−	0.0475352i
$157$	−18.1726	−	31.4759i	−0.115749	−	0.200483i	0.802330	−	0.596881i	$-0.203594\pi$
$157$	−18.1726	−	31.4759i	−0.115749	−	0.200483i	−0.918079	+	0.396398i	$0.870260\pi$
$158$	48.4868	−	27.9939i	0.306878	−	0.177176i
$159$	227.000	+	133.617i	1.42767	+	0.840360i
$160$	−6.32456	+	10.9545i	−0.0395285	+	0.0684653i
$161$		−	6.00188i		−	0.0372787i
$162$	−101.075	+	53.9052i	−0.623922	+	0.332748i
$163$	93.3260			0.572552			0.286276	−	0.958147i	$-0.407583\pi$
$163$	93.3260			0.572552			0.286276	+	0.958147i	$0.407583\pi$
$164$	116.221	+	67.1001i	0.708664	+	0.409147i
$165$	16.9674	−	28.8256i	0.102833	−	0.174701i
$166$	−85.6926	−	148.424i	−0.516221	−	0.894120i
$167$	49.3009	−	28.4639i	0.295215	−	0.170443i	−0.345076	−	0.938575i	$-0.612147\pi$
$167$	49.3009	−	28.4639i	0.295215	−	0.170443i	0.640291	+	0.768132i	$0.278814\pi$
$168$	−7.33799	+	4.15467i	−0.0436785	+	0.0247302i
$169$	83.4914	−	144.611i	0.494032	−	0.855689i
$170$			76.3197i			0.448939i
$171$	120.432	+	216.945i	0.704283	+	1.26869i
$172$	55.3167			0.321609
$173$	188.482	+	108.820i	1.08949	+	0.629017i	0.933441	−	0.358732i	$-0.116791\pi$
$173$	188.482	+	108.820i	1.08949	+	0.629017i	0.156049	+	0.987749i	$0.450124\pi$
$174$	81.2762	+	0.683845i	0.467105	+	0.00393014i
$175$	2.48446	+	4.30320i	0.0141969	+	0.0245897i
$176$	−17.2728	+	9.97245i	−0.0981409	+	0.0566617i
$177$	2.60246	−	309.307i	0.0147031	−	1.74749i
$178$	−52.3622	+	90.6939i	−0.294169	+	0.509516i
$179$			56.2638i			0.314323i	0.987573	+	0.157161i	$0.0502343\pi$
$179$			56.2638i			0.314323i	−0.987573	+	0.157161i	$0.949766\pi$
$180$	0.677253	−	40.2435i	0.00376252	−	0.223575i
$181$	−130.959			−0.723528			−0.361764	−	0.932270i	$-0.617825\pi$
$181$	−130.959			−0.723528			−0.361764	+	0.932270i	$0.617825\pi$
$182$	1.72865	+	0.998034i	0.00949805	+	0.00548370i
$183$	−106.441	−	187.997i	−0.581646	−	1.02731i
$184$	−8.54104	−	14.7935i	−0.0464187	−	0.0803996i
$185$	−122.255	+	70.5838i	−0.660836	+	0.381534i
$186$	−99.4662	−	58.5481i	−0.534764	−	0.314775i
$187$	−60.1698	+	104.217i	−0.321764	+	0.557311i
$188$		−	13.5178i		−	0.0719031i
$189$	13.9983	−	22.8913i	0.0740648	−	0.121118i
$190$	−87.1846			−0.458866
$191$	−29.4446	−	16.9999i	−0.154160	−	0.0890045i	0.420935	−	0.907091i	$-0.361702\pi$
$191$	−29.4446	−	16.9999i	−0.154160	−	0.0890045i	−0.575096	+	0.818086i	$0.695035\pi$
$192$	−12.1744	+	20.6829i	−0.0634086	+	0.107723i
$193$	91.5542	+	158.577i	0.474374	+	0.821640i	0.999569	−	0.0293415i	$-0.00934104\pi$
$193$	91.5542	+	158.577i	0.474374	+	0.821640i	−0.525195	+	0.850982i	$0.676008\pi$
$194$	−2.80180	+	1.61762i	−0.0144423	+	0.00833825i
$195$	−8.29077	+	4.69412i	−0.0425168	+	0.0240724i
$196$	−48.0124	+	83.1599i	−0.244961	+	0.424285i
$197$			30.9351i			0.157031i	0.996913	+	0.0785154i	$0.0250180\pi$
$197$			30.9351i			0.157031i	−0.996913	+	0.0785154i	$0.974982\pi$
$198$	32.6525	−	54.4200i	0.164911	−	0.274848i
$199$	−332.873			−1.67273			−0.836363	−	0.548176i	$-0.815322\pi$
$199$	−332.873			−1.67273			−0.836363	+	0.548176i	$0.815322\pi$
$200$	12.2474	+	7.07107i	0.0612372	+	0.0353553i
$201$	−59.9021	−	0.504006i	−0.298020	−	0.00250749i
$202$	−80.3613	−	139.190i	−0.397828	−	0.689059i
$203$	−16.4879	+	9.51927i	−0.0812210	+	0.0468930i
$204$	−1.21833	+	144.801i	−0.00597223	+	0.709810i
$205$	75.0202	−	129.939i	0.365952	−	0.633848i
$206$			80.2473i			0.389550i
$207$	46.6087	+	27.9657i	0.225163	+	0.135100i
$208$	5.68105			0.0273128
$209$	−119.054	−	68.7356i	−0.569634	−	0.328878i
$210$	4.64506	+	8.20413i	0.0221193	+	0.0390673i
$211$	80.3859	+	139.232i	0.380976	+	0.659869i	0.991202	−	0.132358i	$-0.0422548\pi$
$211$	80.3859	+	139.232i	0.380976	+	0.659869i	−0.610226	+	0.792227i	$0.708921\pi$
$212$	−152.077	+	87.8018i	−0.717345	+	0.414159i
$213$	−142.474	−	83.8638i	−0.668894	−	0.393727i
$214$	65.8926	−	114.129i	0.307909	−	0.533315i
$215$		−	61.8459i		−	0.287655i
$216$	1.92738	−	76.3432i	0.00892307	−	0.353441i
$217$	27.0352			0.124586
$218$	−26.6447	−	15.3833i	−0.122223	−	0.0705657i
$219$	202.021	−	343.210i	0.922472	−	1.56717i
$220$	11.1495	+	19.3116i	0.0506797	+	0.0877799i
$221$	29.6849	−	17.1386i	0.134321	−	0.0775502i
$222$	−233.080	+	131.967i	−1.04991	+	0.594446i
$223$	−195.701	+	338.964i	−0.877582	+	1.52002i	−0.0235946	+	0.999722i	$0.507511\pi$
$223$	−195.701	+	338.964i	−0.877582	+	1.52002i	−0.853987	+	0.520294i	$0.825822\pi$
$224$		−	5.62168i		−	0.0250968i
$225$	−44.9936	−	0.757192i	−0.199972	−	0.00336530i
$226$	−202.576			−0.896353
$227$	295.054	+	170.350i	1.29980	+	0.750439i	0.980369	−	0.197172i	$-0.0631756\pi$
$227$	295.054	+	170.350i	1.29980	+	0.750439i	0.319429	+	0.947610i	$0.396509\pi$
$228$	−165.415	−	1.39178i	−0.725505	−	0.00610429i
$229$	47.2232	+	81.7931i	0.206215	+	0.357175i	0.950519	−	0.310666i	$-0.100552\pi$
$229$	47.2232	+	81.7931i	0.206215	+	0.357175i	−0.744304	+	0.667841i	$0.767219\pi$
$230$	−16.5397	+	9.54918i	−0.0719116	+	0.0415182i
$231$	−0.125073	+	14.8651i	−0.000541441	+	0.0643513i
$232$	−27.0930	+	46.9265i	−0.116780	+	0.202269i
$233$			117.982i			0.506362i	0.967419	+	0.253181i	$0.0814769\pi$
$233$			117.982i			0.506362i	−0.967419	+	0.253181i	$0.918523\pi$
$234$	−15.8050	+	8.77380i	−0.0675428	+	0.0374949i
$235$	−15.1133			−0.0643121
$236$	178.585	+	103.106i	0.756714	+	0.436889i
$237$	−58.5165	−	103.352i	−0.246905	−	0.436084i
$238$	−16.9595	−	29.3747i	−0.0712583	−	0.123423i
$239$	−319.661	+	184.556i	−1.33749	+	0.772203i	−0.986435	−	0.164151i	$-0.947512\pi$
$239$	−319.661	+	184.556i	−1.33749	+	0.772203i	−0.351059	+	0.936353i	$0.614178\pi$
$240$	23.1242	+	13.6114i	0.0963508	+	0.0567144i
$241$	187.815	−	325.306i	0.779316	−	1.34982i	−0.153020	−	0.988223i	$-0.548900\pi$
$241$	187.815	−	325.306i	0.779316	−	1.34982i	0.932336	−	0.361592i	$-0.117767\pi$
$242$		−	135.959i		−	0.561814i
$243$	112.542	+	215.368i	0.463136	+	0.886287i
$244$	144.026			0.590269
$245$	92.9756	+	53.6795i	0.379492	+	0.219100i
$246$	144.410	−	245.335i	0.587033	−	0.997298i
$247$	19.5785	+	33.9109i	0.0792650	+	0.137291i
$248$	66.6368	−	38.4728i	0.268697	−	0.155132i
$249$	−316.373	+	179.126i	−1.27057	+	0.719382i
$250$	7.90569	−	13.6931i	0.0316228	−	0.0547723i
$251$		−	240.639i		−	0.958722i	−0.877618	−	0.479361i	$-0.840869\pi$
$251$		−	240.639i		−	0.958722i	0.877618	−	0.479361i	$-0.159131\pi$
$252$	8.68211	+	15.6398i	0.0344528	+	0.0620628i
$253$	−30.1140			−0.119028
$254$	−202.146	−	116.709i	−0.795852	−	0.459485i
$255$	161.893	+	1.36214i	0.634873	+	0.00534172i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−108.443	+	62.6094i	−0.421956	+	0.243616i	−0.695914	−	0.718125i	$-0.745000\pi$
$257$	−108.443	+	62.6094i	−0.421956	+	0.243616i	0.273958	+	0.961742i	$0.411667\pi$
$258$	0.987282	−	117.340i	0.00382668	−	0.454807i
$259$	31.3697	−	54.3340i	0.121119	−	0.209784i
$260$		−	6.35161i		−	0.0244293i
$261$	2.90121	−	172.395i	0.0111157	−	0.660516i
$262$	74.2001			0.283207
$263$	−80.7510	−	46.6216i	−0.307038	−	0.177269i	0.338562	−	0.940944i	$-0.390059\pi$
$263$	−80.7510	−	46.6216i	−0.307038	−	0.177269i	−0.645600	+	0.763675i	$0.723393\pi$
$264$	20.8457	+	36.8178i	0.0789611	+	0.139461i
$265$	98.1654	+	170.027i	0.370435	+	0.641613i
$266$	33.5565	−	19.3738i	0.126152	−	0.0728340i
$267$	191.450	+	112.692i	0.717039	+	0.422066i
$268$	19.9681	−	34.5857i	0.0745077	−	0.129051i
$269$		−	76.3366i		−	0.283779i	−0.989882	−	0.141890i	$-0.954682\pi$
$269$		−	76.3366i		−	0.283779i	0.989882	−	0.141890i	$-0.0453178\pi$
$270$	−85.3543	−	2.15488i	−0.316127	−	0.00798103i
$271$	529.738			1.95475			0.977377	−	0.211506i	$-0.0678368\pi$
$271$	529.738			1.95475			0.977377	+	0.211506i	$0.0678368\pi$
$272$	−83.6040	−	48.2688i	−0.307368	−	0.177459i
$273$	2.14793	−	3.64907i	0.00786786	−	0.0133665i
$274$	85.1167	+	147.426i	0.310645	+	0.538053i
$275$	21.5910	−	12.4656i	0.0785127	−	0.0453293i
$276$	−31.5331	+	17.8536i	−0.114250	+	0.0646870i
$277$	42.4806	−	73.5785i	0.153359	−	0.265626i	−0.779101	−	0.626898i	$-0.784324\pi$
$277$	42.4806	−	73.5785i	0.153359	−	0.265626i	0.932460	+	0.361272i	$0.117657\pi$
$278$			93.9016i			0.337775i
$279$	−125.970	+	209.947i	−0.451506	+	0.752499i
$280$	−6.28523			−0.0224473
$281$	−185.539	−	107.121i	−0.660282	−	0.381214i	0.132102	−	0.991236i	$-0.457827\pi$
$281$	−185.539	−	107.121i	−0.660282	−	0.381214i	−0.792384	+	0.610022i	$0.791161\pi$
$282$	−28.6745	−	0.241263i	−0.101683	−	0.000855542i
$283$	−189.079	−	327.494i	−0.668123	−	1.15722i	−0.978428	−	0.206586i	$-0.933765\pi$
$283$	−189.079	−	327.494i	−0.668123	−	1.15722i	0.310305	−	0.950637i	$-0.399569\pi$
$284$	95.4500	−	55.1081i	0.336091	−	0.194042i
$285$	−1.55605	+	184.940i	−0.00545984	+	0.648912i
$286$	5.00756	−	8.67334i	0.0175089	−	0.0303264i
$287$			66.6829i			0.232345i
$288$	43.6562	+	26.1941i	0.151584	+	0.0909519i
$289$	−293.469			−1.01546
$290$	52.4654	+	30.2909i	0.180915	+	0.104451i
$291$	3.38137	+	5.97218i	0.0116198	+	0.0205230i
$292$	132.751	+	229.932i	0.454627	+	0.787437i
$293$	−43.3012	+	25.0000i	−0.147786	+	0.0853242i	−0.572070	−	0.820205i	$-0.693859\pi$
$293$	−43.3012	+	25.0000i	−0.147786	+	0.0853242i	0.424284	+	0.905529i	$0.360526\pi$
$294$	175.546	+	103.330i	0.597094	+	0.351464i
$295$	115.276	−	199.664i	0.390766	−	0.676826i
$296$		−	178.564i		−	0.603258i
$297$	−114.855	−	70.2352i	−0.386718	−	0.236482i
$298$	135.227			0.453781
$299$	7.42840	+	4.28879i	0.0248442	+	0.0143438i
$300$	15.2181	−	25.8536i	0.0507269	−	0.0861788i
$301$	13.7432	+	23.8039i	0.0456584	+	0.0790827i
$302$	−331.323	+	191.290i	−1.09710	+	0.633409i
$303$	−296.690	+	167.982i	−0.979175	+	0.554395i
$304$	55.1404	−	95.5059i	0.181383	−	0.314164i
$305$		−	161.026i		−	0.527953i
$306$	307.137	+	5.16877i	1.00372	+	0.0168914i
$307$	145.083			0.472583			0.236292	−	0.971682i	$-0.424068\pi$
$307$	145.083			0.472583			0.236292	+	0.971682i	$0.424068\pi$
$308$	−8.58270	−	4.95522i	−0.0278659	−	0.0160884i
$309$	170.224	+	1.43224i	0.550887	+	0.00463508i
$310$	−43.0139	−	74.5023i	−0.138755	−	0.240330i
$311$	90.5772	−	52.2947i	0.291245	−	0.168150i	−0.347258	−	0.937770i	$-0.612887\pi$
$311$	90.5772	−	52.2947i	0.291245	−	0.168150i	0.638503	+	0.769619i	$0.279554\pi$
$312$	0.101394	−	12.0509i	0.000324982	−	0.0386247i
$313$	−28.8869	+	50.0335i	−0.0922903	+	0.159852i	−0.908474	−	0.417940i	$-0.862752\pi$
$313$	−28.8869	+	50.0335i	−0.0922903	+	0.159852i	0.816184	+	0.577792i	$0.196085\pi$
$314$		−	51.3999i		−	0.163694i
$315$	17.4859	−	9.70689i	0.0555107	−	0.0308155i
$316$	79.1786			0.250565
$317$	85.1303	+	49.1500i	0.268550	+	0.155047i	0.628228	−	0.778029i	$-0.283780\pi$
$317$	85.1303	+	49.1500i	0.268550	+	0.155047i	−0.359679	+	0.933076i	$0.617114\pi$
$318$	183.535	+	324.160i	0.577154	+	1.01937i
$319$	47.7622	+	82.7266i	0.149725	+	0.259331i
$320$	−15.4919	+	8.94427i	−0.0484123	+	0.0279508i
$321$	−240.920	−	141.811i	−0.750531	−	0.441780i
$322$	4.24397	−	7.35077i	0.0131800	−	0.0228285i
$323$		−	665.390i		−	2.06003i
$324$	−161.908	−	5.45101i	−0.499717	−	0.0168241i
$325$	−7.10132			−0.0218502
$326$	114.301	+	65.9915i	0.350615	+	0.202428i
$327$	−33.1074	+	56.2454i	−0.101246	+	0.172004i
$328$	94.8939	+	164.361i	0.289311	+	0.501101i
$329$	5.81697	−	3.35843i	0.0176808	−	0.0102080i
$330$	41.1636	−	23.3062i	0.124738	−	0.0706250i
$331$	106.537	−	184.528i	0.321865	−	0.557487i	−0.659008	−	0.752136i	$-0.729024\pi$
$331$	106.537	−	184.528i	0.321865	−	0.557487i	0.980873	+	0.194649i	$0.0623569\pi$
$332$		−	242.375i		−	0.730046i
$333$	275.774	+	496.776i	0.828151	+	1.49182i
$334$	80.5081			0.241042
$335$	−38.6680	−	22.3250i	−0.115427	−	0.0666417i
$336$	−11.9250	−	0.100335i	−0.0354910	−	0.000298615i
$337$	−82.5154	−	142.921i	−0.244853	−	0.424097i	0.717237	−	0.696829i	$-0.245406\pi$
$337$	−82.5154	−	142.921i	−0.244853	−	0.424097i	−0.962090	+	0.272731i	$0.912073\pi$
$338$	204.511	−	118.075i	0.605063	−	0.349333i
$339$	−3.61554	+	429.713i	−0.0106653	+	1.26759i
$340$	−53.9661	+	93.4721i	−0.158724	+	0.274918i
$341$		−	135.647i		−	0.397792i
$342$	−5.90460	+	350.861i	−0.0172649	+	1.02591i
$343$	−96.4092			−0.281076
$344$	67.7488	+	39.1148i	0.196944	+	0.113706i
$345$	19.9609	+	35.2551i	0.0578578	+	0.102189i
$346$	153.895	+	266.553i	0.444782	+	0.770385i
$347$	−78.2522	+	45.1789i	−0.225511	+	0.130199i	−0.608499	−	0.793554i	$-0.708228\pi$
$347$	−78.2522	+	45.1789i	−0.225511	+	0.130199i	0.382989	+	0.923753i	$0.374895\pi$
$348$	99.0591	+	58.3085i	0.284653	+	0.167553i
$349$	177.488	−	307.418i	0.508561	−	0.880853i	−0.491390	−	0.870939i	$-0.663511\pi$
$349$	177.488	−	307.418i	0.508561	−	0.880853i	0.999951	−	0.00991327i	$-0.00315554\pi$
$350$			7.02710i			0.0200774i
$351$	18.3293	+	33.6829i	0.0522202	+	0.0959627i
$352$	−28.2064			−0.0801317
$353$	312.718	+	180.548i	0.885887	+	0.511467i	0.872595	−	0.488445i	$-0.162436\pi$
$353$	312.718	+	180.548i	0.885887	+	0.511467i	0.0132919	+	0.999912i	$0.495769\pi$
$354$	221.900	−	376.981i	0.626836	−	1.06492i
$355$	−61.6127	−	106.716i	−0.173557	−	0.300609i
$356$	−128.261	+	74.0513i	−0.360283	+	0.208009i
$357$	−62.6136	+	35.4510i	−0.175388	+	0.0993024i
$358$	−39.7845	+	68.9088i	−0.111130	+	0.192483i
$359$			229.312i			0.638753i	0.947628	+	0.319377i	$0.103473\pi$
$359$			229.312i			0.638753i	−0.947628	+	0.319377i	$0.896527\pi$
$360$	29.2859	−	48.8092i	0.0813498	−	0.135581i
$361$	399.115			1.10558
$362$	−160.391	−	92.6017i	−0.443069	−	0.255806i
$363$	−288.402	−	2.42657i	−0.794497	−	0.00668477i
$364$	1.41143	+	2.44467i	0.00387756	+	0.00671614i
$365$	257.071	−	148.420i	0.704305	−	0.406631i
$366$	2.57054	−	305.514i	0.00702334	−	0.834737i
$367$	−205.787	+	356.434i	−0.560728	+	0.971210i	0.436705	+	0.899605i	$0.356146\pi$
$367$	−205.787	+	356.434i	−0.560728	+	0.971210i	−0.997433	+	0.0716052i	$0.977188\pi$
$368$		−	24.1577i		−	0.0656460i
$369$	−517.839	−	310.708i	−1.40336	−	0.842027i
$370$	−199.641			−0.539570
$371$	−75.5658	−	43.6279i	−0.203681	−	0.117596i
$372$	−80.4209	−	142.040i	−0.216185	−	0.381827i
$373$	−343.514	−	594.984i	−0.920949	−	1.59513i	−0.797950	−	0.602723i	$-0.794082\pi$
$373$	−343.514	−	594.984i	−0.920949	−	1.59513i	−0.122999	−	0.992407i	$-0.539251\pi$
$374$	−147.385	+	85.0929i	−0.394078	+	0.227521i
$375$	−28.9052	−	17.0143i	−0.0770807	−	0.0453715i
$376$	9.55851	−	16.5558i	0.0254216	−	0.0440315i
$377$		−	27.2089i		−	0.0721722i
$378$	33.3309	−	18.1377i	0.0881769	−	0.0479834i
$379$	−154.733			−0.408267			−0.204134	−	0.978943i	$-0.565438\pi$
$379$	−154.733			−0.408267			−0.204134	+	0.978943i	$0.565438\pi$
$380$	−106.779	−	61.6488i	−0.280997	−	0.162234i
$381$	−251.177	+	426.719i	−0.659257	+	1.12000i
$382$	−24.0414	−	41.6410i	−0.0629357	−	0.109008i
$383$	141.268	−	81.5612i	0.368846	−	0.212954i	−0.304108	−	0.952638i	$-0.598358\pi$
$383$	141.268	−	81.5612i	0.368846	−	0.212954i	0.672954	+	0.739684i	$0.265025\pi$
$384$	−29.5356	+	16.7227i	−0.0769157	+	0.0435486i
$385$	−5.54011	+	9.59575i	−0.0143899	+	0.0249240i
$386$			258.954i			0.670866i
$387$	−248.890	−	4.18854i	−0.643126	−	0.0108231i
$388$	−4.57532			−0.0117921
$389$	268.744	+	155.159i	0.690858	+	0.398867i	0.803933	−	0.594719i	$-0.202737\pi$
$389$	268.744	+	155.159i	0.690858	+	0.398867i	−0.113075	+	0.993586i	$0.536070\pi$
$390$	−13.4733	−	0.113362i	−0.0345470	−	0.000290673i
$391$	−72.8790	−	126.230i	−0.186391	−	0.322839i
$392$	−117.606	+	67.8998i	−0.300015	+	0.173214i
$393$	1.32431	−	157.397i	0.00336975	−	0.400500i
$394$	−21.8744	+	37.8876i	−0.0555188	+	0.0961614i
$395$		−	88.5244i		−	0.224112i
$396$	78.4717	−	43.5618i	0.198161	−	0.110005i
$397$	−270.057			−0.680244			−0.340122	−	0.940381i	$-0.610468\pi$
$397$	−270.057			−0.680244			−0.340122	+	0.940381i	$0.610468\pi$
$398$	−407.684	−	235.376i	−1.02433	−	0.591398i
$399$	−40.4978	−	71.5273i	−0.101498	−	0.179266i
$400$	10.0000	+	17.3205i	0.0250000	+	0.0433013i
$401$	−525.394	+	303.336i	−1.31021	+	0.756449i	−0.982130	−	0.188201i	$-0.939734\pi$
$401$	−525.394	+	303.336i	−1.31021	+	0.756449i	−0.328078	+	0.944651i	$0.606401\pi$
$402$	−73.0084	−	42.9744i	−0.181613	−	0.106902i
$403$	−19.3187	+	33.4610i	−0.0479372	+	0.0830297i
$404$		−	227.296i		−	0.562614i
$405$	−6.09442	+	181.019i	−0.0150479	+	0.446960i
$406$	−26.9246			−0.0663167
$407$	−272.617	−	157.395i	−0.669820	−	0.386721i
$408$	−103.882	+	176.483i	−0.254613	+	0.432557i
$409$	332.949	+	576.684i	0.814055	+	1.40998i	0.910004	+	0.414599i	$0.136078\pi$
$409$	332.949	+	576.684i	0.814055	+	1.40998i	−0.0959493	+	0.995386i	$0.530589\pi$
$410$	183.761	−	106.095i	0.448198	−	0.258767i
$411$	314.247	−	177.922i	0.764591	−	0.432901i
$412$	−56.7434	+	98.2825i	−0.137727	+	0.238550i
$413$			102.465i			0.248099i
$414$	37.3091	+	67.2081i	0.0901186	+	0.162338i
$415$	−270.984			−0.652973
$416$	6.95784	+	4.01711i	0.0167256	+	0.00965652i
$417$	199.188	+	1.67594i	0.477670	+	0.00401904i
$418$	−97.2068	−	168.367i	−0.232552	−	0.402792i
$419$	187.245	−	108.106i	0.446886	−	0.258010i	−0.259628	−	0.965709i	$-0.583600\pi$
$419$	187.245	−	108.106i	0.446886	−	0.258010i	0.706514	+	0.707699i	$0.250267\pi$
$420$	−0.112178	+	13.3325i	−0.000267090	+	0.0317441i
$421$	−157.752	+	273.234i	−0.374708	+	0.649013i	−0.990283	−	0.139065i	$-0.955590\pi$
$421$	−157.752	+	273.234i	−0.374708	+	0.649013i	0.615576	+	0.788078i	$0.288924\pi$
$422$			227.366i			0.538781i
$423$	−1.02356	+	60.8214i	−0.00241975	+	0.143786i
$424$	−248.341			−0.585710
$425$	104.505	+	60.3360i	0.245894	+	0.141967i
$426$	−115.194	−	203.456i	−0.270409	−	0.477597i
$427$	35.7825	+	61.9772i	0.0837999	+	0.145146i
$428$	161.403	−	93.1862i	0.377110	−	0.217725i
$429$	−18.3089	−	10.7771i	−0.0426781	−	0.0251213i
$430$	43.7317	−	75.7455i	0.101702	−	0.176152i
$431$			705.119i			1.63601i	0.575213	+	0.818003i	$0.304919\pi$
$431$			705.119i			1.63601i	−0.575213	+	0.818003i	$0.695081\pi$
$432$	56.3434	−	92.1381i	0.130424	−	0.213283i
$433$	152.735			0.352737			0.176369	−	0.984324i	$-0.443565\pi$
$433$	152.735			0.352737			0.176369	+	0.984324i	$0.443565\pi$
$434$	33.1113	+	19.1168i	0.0762932	+	0.0440479i
$435$	65.1909	−	110.751i	0.149864	−	0.254601i
$436$	−21.7553	−	37.6813i	−0.0498975	−	0.0864250i
$437$	144.200	−	83.2541i	0.329978	−	0.190513i
$438$	490.111	−	277.494i	1.11897	−	0.633548i
$439$	−81.1173	+	140.499i	−0.184778	+	0.320044i	−0.943502	−	0.331368i	$-0.892490\pi$
$439$	−81.1173	+	140.499i	−0.184778	+	0.320044i	0.758724	+	0.651412i	$0.225823\pi$
$440$			31.5357i			0.0716720i
$441$	222.322	−	370.531i	0.504132	−	0.840207i
$442$	48.4753			0.109673
$443$	335.641	+	193.783i	0.757655	+	0.437433i	0.828453	−	0.560058i	$-0.189221\pi$
$443$	335.641	+	193.783i	0.757655	+	0.437433i	−0.0707979	+	0.997491i	$0.522555\pi$
$444$	−378.779	−	3.18698i	−0.853105	−	0.00717789i
$445$	82.7919	+	143.400i	0.186049	+	0.322247i
$446$	−479.367	+	276.763i	−1.07481	+	0.620544i
$447$	2.41350	−	286.849i	0.00539934	−	0.641721i
$448$	3.97513	−	6.88513i	0.00887306	−	0.0153686i
$449$			111.025i			0.247272i	0.992328	+	0.123636i	$0.0394554\pi$
$449$			111.025i			0.247272i	−0.992328	+	0.123636i	$0.960545\pi$
$450$	−54.5703	−	32.7427i	−0.121267	−	0.0727615i
$451$	334.577			0.741855
$452$	−248.104	−	143.243i	−0.548902	−	0.316909i
$453$	399.859	+	706.232i	0.882690	+	1.55901i
$454$	240.911	+	417.269i	0.530640	+	0.919096i
$455$	2.73323	−	1.57803i	0.00600709	−	0.00346820i
$456$	−201.607	−	118.671i	−0.442121	−	0.260243i
$457$	149.400	−	258.768i	0.326914	−	0.566232i	−0.654984	−	0.755643i	$-0.727325\pi$
$457$	149.400	−	258.768i	0.326914	−	0.566232i	0.981898	+	0.189411i	$0.0606579\pi$
$458$			133.567i			0.291632i
$459$	16.4460	−	651.421i	0.0358300	−	1.41922i
$460$	−27.0091			−0.0587155
$461$	−180.036	−	103.944i	−0.390534	−	0.225475i	0.291857	−	0.956462i	$-0.405727\pi$
$461$	−180.036	−	103.944i	−0.390534	−	0.225475i	−0.682392	+	0.730987i	$0.739060\pi$
$462$	−10.6644	+	18.1176i	−0.0230832	+	0.0392155i
$463$	−432.563	−	749.220i	−0.934261	−	1.61819i	−0.775947	−	0.630798i	$-0.782728\pi$
$463$	−432.563	−	749.220i	−0.934261	−	1.61819i	−0.158313	−	0.987389i	$-0.550606\pi$
$464$	−66.3641	+	38.3153i	−0.143026	+	0.0825762i
$465$	−158.805	+	89.9133i	−0.341517	+	0.193362i
$466$	−83.4262	+	144.498i	−0.179026	+	0.310082i
$467$			854.726i			1.83025i	0.403172	+	0.915124i	$0.367908\pi$
$467$			854.726i			1.83025i	−0.403172	+	0.915124i	$0.632092\pi$
$468$	−25.5611	−	0.430165i	−0.0546178	−	0.000919156i
$469$	19.8439			0.0423111
$470$	−18.5100	−	10.6867i	−0.0393829	−	0.0227377i
$471$	−109.032	−	0.917377i	−0.231490	−	0.00194772i
$472$	145.814	+	252.557i	0.308927	+	0.535078i
$473$	119.434	−	68.9554i	0.252504	−	0.145783i
$474$	1.41317	−	167.957i	0.00298136	−	0.354340i
$475$	−68.9255	+	119.382i	−0.145106	+	0.251331i
$476$		−	47.9687i		−	0.100775i
$477$	690.899	−	383.537i	1.44842	−	0.804061i
$478$	−522.004			−1.09206
$479$	263.392	+	152.069i	0.549879	+	0.317473i	0.749073	−	0.662487i	$-0.230499\pi$
$479$	263.392	+	152.069i	0.549879	+	0.317473i	−0.199194	+	0.979960i	$0.563832\pi$
$480$	18.6965	+	33.0218i	0.0389510	+	0.0687955i
$481$	44.8321	+	77.6514i	0.0932060	+	0.161437i
$482$	460.051	−	265.611i	0.954464	−	0.551060i
$483$	−15.5170	−	9.13369i	−0.0321264	−	0.0189103i
$484$	96.1375	−	166.515i	0.198631	−	0.344039i
$485$			5.11537i			0.0105472i
$486$	−14.4526	+	343.350i	−0.0297379	+	0.706481i
$487$	907.378			1.86320			0.931600	−	0.363486i	$-0.118413\pi$
$487$	907.378			1.86320			0.931600	+	0.363486i	$0.118413\pi$
$488$	176.395	+	101.842i	0.361465	+	0.208692i
$489$	142.024	−	241.282i	0.290438	−	0.493419i
$490$	75.9143	+	131.487i	0.154927	+	0.268342i
$491$	56.6785	−	32.7234i	0.115435	−	0.0666464i	−0.441171	−	0.897423i	$-0.645437\pi$
$491$	56.6785	−	32.7234i	0.115435	−	0.0666464i	0.556606	+	0.830777i	$0.312103\pi$
$492$	350.344	−	198.360i	0.712081	−	0.403170i
$493$	−231.179	+	400.414i	−0.468924	+	0.812200i
$494$			55.3763i			0.112098i
$495$	−48.7036	−	87.7340i	−0.0983911	−	0.177240i
$496$	108.818			0.219390
$497$	47.4282	+	27.3827i	0.0954291	+	0.0550960i
$498$	−514.138	−	4.32587i	−1.03240	−	0.00868649i
$499$	−358.642	−	621.186i	−0.718721	−	1.24486i	−0.961507	−	0.274782i	$-0.911394\pi$
$499$	−358.642	−	621.186i	−0.718721	−	1.24486i	0.242785	−	0.970080i	$-0.421939\pi$
$500$	19.3649	−	11.1803i	0.0387298	−	0.0223607i
$501$	1.43689	−	170.777i	0.00286805	−	0.340873i
$502$	170.158	−	294.722i	0.338959	−	0.587095i
$503$		−	623.374i		−	1.23931i	−0.784873	−	0.619657i	$-0.787272\pi$
$503$		−	623.374i		−	1.23931i	0.784873	−	0.619657i	$-0.212728\pi$
$504$	−0.425669	+	25.2940i	−0.000844582	+	0.0501865i
$505$	−254.125			−0.503217
$506$	−36.8819	−	21.2938i	−0.0728892	−	0.0420826i
$507$	−246.815	−	435.926i	−0.486815	−	0.859815i
$508$	−165.052	−	285.878i	−0.324905	−	0.562753i
$509$	577.161	−	333.224i	1.13391	−	0.654664i	0.188996	−	0.981978i	$-0.439477\pi$
$509$	577.161	−	333.224i	1.13391	−	0.654664i	0.944916	+	0.327313i	$0.106143\pi$
$510$	197.314	+	116.144i	0.386890	+	0.227733i
$511$	−65.9628	+	114.251i	−0.129086	+	0.223583i
$512$		−	22.6274i		−	0.0441942i
$513$	744.158	+	18.7872i	1.45060	+	0.0366223i
$514$	−177.086			−0.344526
$515$	109.883	+	63.4411i	0.213365	+	0.123187i
$516$	84.1813	−	143.014i	0.163142	−	0.277158i
$517$	−16.8507	−	29.1862i	−0.0325932	−	0.0564530i
$518$	76.8399	−	44.3635i	0.148340	−	0.0856439i
$519$	568.172	−	321.691i	1.09474	−	0.619828i
$520$	4.49127	−	7.77910i	0.00863705	−	0.0149598i
$521$			896.544i			1.72081i	0.509608	+	0.860407i	$0.329790\pi$
$521$			896.544i			1.72081i	−0.509608	+	0.860407i	$0.670210\pi$
$522$	125.455	−	209.088i	0.240335	−	0.400552i
$523$	354.070			0.676999			0.338499	−	0.940967i	$-0.390081\pi$
$523$	354.070			0.676999			0.338499	+	0.940967i	$0.390081\pi$
$524$	90.8762	+	52.4674i	0.173428	+	0.100129i
$525$	14.9062	+	0.125418i	0.0283928	+	0.000238892i
$526$	−65.9329	−	114.199i	−0.125348	−	0.217109i
$527$	568.599	−	328.281i	1.07893	−	0.622923i
$528$	−0.503422	+	59.8326i	−0.000953451	+	0.113319i
$529$	−246.263	+	426.539i	−0.465525	+	0.806313i
$530$			277.654i			0.523875i
$531$	−795.710	−	477.433i	−1.49851	−	0.899120i
$532$	54.7975			0.103003
$533$	−82.5321	−	47.6500i	−0.154845	−	0.0893995i
$534$	154.792	+	273.394i	0.289872	+	0.511973i
$535$	−104.185	−	180.454i	−0.194739	−	0.337298i
$536$	48.9116	−	28.2391i	0.0912529	−	0.0526849i
$537$	145.462	+	85.6226i	0.270880	+	0.159446i
$538$	53.9781	−	93.4928i	0.100331	−	0.173779i
$539$			239.401i			0.444157i
$540$	−103.014	−	62.9938i	−0.190766	−	0.116655i
$541$	−392.737			−0.725947			−0.362974	−	0.931799i	$-0.618238\pi$
$541$	−392.737			−0.725947			−0.362974	+	0.931799i	$0.618238\pi$
$542$	648.794	+	374.581i	1.19704	+	0.691110i
$543$	−199.294	+	338.576i	−0.367023	+	0.623528i
$544$	−68.2624	−	118.234i	−0.125482	−	0.217342i
$545$	−42.1290	+	24.3232i	−0.0773009	+	0.0446297i
$546$	5.21094	−	2.95036i	0.00954385	−	0.00540360i
$547$	−135.528	+	234.742i	−0.247767	+	0.429145i	−0.962906	−	0.269837i	$-0.913030\pi$
$547$	−135.528	+	234.742i	−0.247767	+	0.429145i	0.715139	+	0.698982i	$0.246363\pi$
$548$			240.746i			0.439318i
$549$	−648.024	−	10.9055i	−1.18037	−	0.0198643i
$550$	35.2579			0.0641054
$551$	−457.418	−	264.090i	−0.830159	−	0.479293i
$552$	−51.2444	−	0.431163i	−0.0928341	−	0.000781092i
$553$	19.6716	+	34.0722i	0.0355725	+	0.0616133i
$554$	104.056	−	60.0766i	0.187826	−	0.108442i
$555$	−3.56316	+	423.488i	−0.00642010	+	0.763041i
$556$	−66.3984	+	115.005i	−0.119422	+	0.206844i
$557$		−	122.363i		−	0.219682i	−0.993949	−	0.109841i	$-0.964966\pi$
$557$		−	122.363i		−	0.219682i	0.993949	−	0.109841i	$-0.0350342\pi$
$558$	−302.736	+	168.057i	−0.542538	+	0.301178i
$559$	−39.2821			−0.0702722
$560$	−7.69780	−	4.44433i	−0.0137461	−	0.00793630i
$561$	177.872	+	314.159i	0.317063	+	0.559998i
$562$	−151.492	−	262.392i	−0.269559	−	0.466890i
$563$	45.8232	−	26.4560i	0.0813911	−	0.0469911i	−0.458752	−	0.888564i	$-0.651703\pi$
$563$	45.8232	−	26.4560i	0.0813911	−	0.0469911i	0.540143	+	0.841573i	$0.318370\pi$
$564$	−34.9484	−	20.5714i	−0.0619652	−	0.0364742i
$565$	−160.150	+	277.388i	−0.283452	+	0.490953i
$566$		−	534.796i		−	0.944869i
$567$	−37.8797	−	71.0267i	−0.0668072	−	0.125268i
$568$	155.869			0.274418
$569$	−631.466	−	364.577i	−1.10978	−	0.640733i	−0.171009	−	0.985269i	$-0.554703\pi$
$569$	−631.466	−	364.577i	−1.10978	−	0.640733i	−0.938773	+	0.344536i	$0.888036\pi$
$570$	−132.678	+	225.404i	−0.232768	+	0.395445i
$571$	198.741	+	344.229i	0.348057	+	0.602853i	0.985904	−	0.167310i	$-0.0535081\pi$
$571$	198.741	+	344.229i	0.348057	+	0.602853i	−0.637847	+	0.770163i	$0.720175\pi$
$572$	12.2660	−	7.08176i	0.0214440	−	0.0123807i
$573$	−88.7598	+	50.2546i	−0.154904	+	0.0877043i
$574$	−47.1520	+	81.6696i	−0.0821463	+	0.142282i
$575$			30.1971i			0.0525168i
$576$	34.9457	+	62.9508i	0.0606696	+	0.109290i
$577$	−82.2138			−0.142485			−0.0712425	−	0.997459i	$-0.522696\pi$
$577$	−82.2138			−0.142485			−0.0712425	+	0.997459i	$0.522696\pi$
$578$	−359.425	−	207.514i	−0.621842	−	0.359021i
$579$	549.306	+	4.62177i	0.948715	+	0.00798234i
$580$	42.8378	+	74.1973i	0.0738584	+	0.127926i
$581$	104.299	−	60.2171i	0.179516	−	0.103644i
$582$	−0.0816596	+	9.70538i	−0.000140309	+	0.0166759i
$583$	−218.900	+	379.146i	−0.375471	+	0.650335i
$584$			375.477i			0.642940i
$585$	−0.480939	+	28.5782i	−0.000822118	+	0.0488516i
$586$	−70.7106			−0.120667
$587$	−745.966	−	430.684i	−1.27081	−	0.733703i	−0.295671	−	0.955290i	$-0.595543\pi$
$587$	−745.966	−	430.684i	−1.27081	−	0.733703i	−0.975141	+	0.221587i	$0.928876\pi$
$588$	141.933	+	250.683i	0.241383	+	0.426331i
$589$	375.015	+	649.545i	0.636698	+	1.10279i
$590$	282.367	−	163.025i	0.478588	−	0.276313i
$591$	79.9784	+	47.0772i	0.135327	+	0.0796568i
$592$	126.264	−	218.696i	0.213284	−	0.369419i
$593$			377.445i			0.636500i	0.948007	+	0.318250i	$0.103095\pi$
$593$			377.445i			0.636500i	−0.948007	+	0.318250i	$0.896905\pi$
$594$	−91.0047	−	167.235i	−0.153207	−	0.281541i
$595$	−53.6306			−0.0901355
$596$	165.618	+	95.6198i	0.277883	+	0.160436i
$597$	−506.567	+	860.597i	−0.848522	+	1.44154i
$598$	6.06527	+	10.5053i	0.0101426	+	0.0175675i
$599$	−268.405	+	154.964i	−0.448089	+	0.258704i	−0.707023	−	0.707191i	$-0.749962\pi$
$599$	−268.405	+	154.964i	−0.448089	+	0.258704i	0.258934	+	0.965895i	$0.416629\pi$
$600$	36.9195	−	20.9033i	0.0615325	−	0.0348389i
$601$	−208.891	+	361.810i	−0.347573	+	0.602014i	−0.985818	−	0.167820i	$-0.946327\pi$
$601$	−208.891	+	361.810i	−0.347573	+	0.602014i	0.638245	+	0.769833i	$0.279661\pi$
$602$			38.8716i			0.0645708i
$603$	−92.4624	+	154.102i	−0.153337	+	0.255558i
$604$	−541.049			−0.895776
$605$	−186.170	−	107.485i	−0.307718	−	0.177661i
$606$	−482.151	−	4.05674i	−0.795628	−	0.00669429i
$607$	−428.083	−	741.461i	−0.705244	−	1.22152i	−0.966603	−	0.256277i	$-0.917504\pi$
$607$	−428.083	−	741.461i	−0.705244	−	1.22152i	0.261360	−	0.965241i	$-0.415829\pi$
$608$	135.066	−	77.9803i	0.222148	−	0.128257i
$609$	−0.480545	+	57.1136i	−0.000789072	+	0.0937826i
$610$	113.862	−	197.215i	0.186659	−	0.323304i
$611$			9.59940i			0.0157110i
$612$	372.510	+	223.509i	0.608676	+	0.365211i
$613$	−1022.92			−1.66870			−0.834352	−	0.551231i	$-0.814158\pi$
$613$	−1022.92			−1.66870			−0.834352	+	0.551231i	$0.814158\pi$
$614$	177.690	+	102.589i	0.289397	+	0.167083i
$615$	−221.773	−	391.696i	−0.360607	−	0.636905i
$616$	−7.00774	−	12.1378i	−0.0113762	−	0.0197042i
$617$	−507.463	+	292.984i	−0.822468	+	0.474852i	−0.851267	−	0.524733i	$-0.824165\pi$
$617$	−507.463	+	292.984i	−0.822468	+	0.474852i	0.0287987	+	0.999585i	$0.490832\pi$
$618$	207.468	+	122.121i	0.335710	+	0.197607i
$619$	455.788	−	789.447i	0.736329	−	1.27536i	−0.217809	−	0.975991i	$-0.569891\pi$
$619$	455.788	−	789.447i	0.736329	−	1.27536i	0.954138	−	0.299367i	$-0.0967756\pi$
$620$		−	121.662i		−	0.196229i
$621$	143.231	−	77.9422i	0.230645	−	0.125511i
$622$	147.912			0.237800
$623$	−63.7315	−	36.7954i	−0.102298	−	0.0590617i
$624$	8.64546	−	14.6876i	0.0138549	−	0.0235378i
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−70.7581	+	40.8522i	−0.113032	+	0.0652591i
$627$	−358.883	+	203.194i	−0.572381	+	0.324074i
$628$	36.3452	−	62.9518i	0.0578746	−	0.100242i
$629$		−	1523.65i		−	2.42234i
$630$	28.2795	+	0.475913i	0.0448882	+	0.000755417i
$631$	463.111			0.733932			0.366966	−	0.930234i	$-0.380396\pi$
$631$	463.111			0.733932			0.366966	+	0.930234i	$0.380396\pi$
$632$	96.9736	+	55.9877i	0.153439	+	0.0885882i
$633$	482.298	+	4.05798i	0.761924	+	0.00641071i
$634$	69.5086	+	120.392i	0.109635	+	0.189893i
$635$	−319.622	+	184.534i	−0.503341	+	0.290604i
$636$	−4.43234	+	526.792i	−0.00696910	+	0.828289i
$637$	34.0951	−	59.0545i	0.0535245	−	0.0927072i
$638$			135.092i			0.211743i
$639$	−433.637	+	240.724i	−0.678618	+	0.376720i
$640$	−25.2982			−0.0395285
$641$	−512.450	−	295.863i	−0.799454	−	0.461565i	0.0438265	−	0.999039i	$-0.486045\pi$
$641$	−512.450	−	295.863i	−0.799454	−	0.461565i	−0.843280	+	0.537474i	$0.819378\pi$
$642$	−194.790	−	344.039i	−0.303411	−	0.535886i
$643$	373.551	+	647.010i	0.580950	+	1.00624i	0.995367	+	0.0961484i	$0.0306523\pi$
$643$	373.551	+	647.010i	0.580950	+	1.00624i	−0.414417	+	0.910087i	$0.636014\pi$
$644$	10.3956	−	6.00188i	0.0161422	−	0.00931969i
$645$	−159.894	−	94.1175i	−0.247898	−	0.145919i
$646$	470.502	−	814.933i	0.728331	−	1.26151i
$647$			86.2103i			0.133246i	0.997778	+	0.0666231i	$0.0212225\pi$
$647$			86.2103i			0.133246i	−0.997778	+	0.0666231i	$0.978777\pi$
$648$	−194.442	−	121.163i	−0.300065	−	0.186979i
$649$	514.109			0.792156
$650$	−8.69730	−	5.02139i	−0.0133805	−	0.00772522i
$651$	41.1424	−	69.8959i	0.0631987	−	0.107367i
$652$	93.3260	+	161.645i	0.143138	+	0.247922i
$653$	−148.564	+	85.7737i	−0.227511	+	0.131353i	−0.609423	−	0.792845i	$-0.708599\pi$
$653$	−148.564	+	85.7737i	−0.227511	+	0.131353i	0.381913	+	0.924198i	$0.375266\pi$
$654$	−80.3196	+	45.4758i	−0.122813	+	0.0695349i
$655$	58.6603	−	101.603i	0.0895578	−	0.155119i
$656$			268.401i			0.409147i
$657$	−579.885	−	1044.60i	−0.882626	−	1.58995i
$658$	9.49908			0.0144363
$659$	81.6071	+	47.1159i	0.123835	+	0.0714960i	0.560638	−	0.828061i	$-0.310556\pi$
$659$	81.6071	+	47.1159i	0.123835	+	0.0714960i	−0.436803	+	0.899557i	$0.643889\pi$
$660$	66.8949	+	0.562843i	0.101356	+	0.000852792i
$661$	−422.390	−	731.602i	−0.639017	−	1.10681i	−0.985649	−	0.168809i	$-0.946008\pi$
$661$	−422.390	−	731.602i	−0.639017	−	1.10681i	0.346631	−	0.938001i	$-0.387325\pi$
$662$	260.962	−	150.667i	0.394203	−	0.227593i
$663$	0.865178	−	102.828i	0.00130494	−	0.155095i
$664$	171.385	−	296.848i	0.258110	−	0.447060i
$665$		−	61.2655i		−	0.0921286i
$666$	−13.5208	+	803.426i	−0.0203014	+	1.20635i
$667$	−115.701			−0.173465
$668$	98.6019	+	56.9278i	0.147608	+	0.0852213i
$669$	578.526	+	1021.79i	0.864762	+	1.52735i
$670$	−31.5723	−	54.6848i	−0.0471228	−	0.0816191i
$671$	310.966	−	179.536i	0.463436	−	0.267565i
$672$	−14.5341	−	8.55511i	−0.0216281	−	0.0127308i
$673$	352.145	−	609.933i	0.523247	−	0.906290i	−0.476387	−	0.879235i	$-0.658054\pi$
$673$	352.145	−	609.933i	0.523247	−	0.906290i	0.999634	−	0.0270541i	$-0.00861264\pi$
$674$		−	233.389i		−	0.346274i
$675$	−70.4292	+	115.173i	−0.104340	+	0.170626i
$676$	333.966			0.494032
$677$	−1107.53	−	639.435i	−1.63594	−	0.944513i	−0.982210	−	0.187788i	$-0.939868\pi$
$677$	−1107.53	−	639.435i	−1.63594	−	0.944513i	−0.653734	−	0.756724i	$-0.726799\pi$
$678$	−308.281	+	523.732i	−0.454692	+	0.772466i
$679$	−1.13672	−	1.96886i	−0.00167411	−	0.00289964i
$680$	−132.190	+	76.3197i	−0.194396	+	0.112235i
$681$	889.431	−	503.583i	1.30607	−	0.739476i
$682$	95.9170	−	166.133i	0.140641	−	0.243597i
$683$		−	571.914i		−	0.837356i	−0.908135	−	0.418678i	$-0.862494\pi$
$683$		−	571.914i		−	0.837356i	0.908135	−	0.418678i	$-0.137506\pi$
$684$	−255.328	+	425.541i	−0.373287	+	0.622135i
$685$	269.163			0.392938
$686$	−118.077	−	68.1716i	−0.172123	−	0.0993755i
$687$	283.329	+	2.38389i	0.412415	+	0.00347000i
$688$	55.3167	+	95.8113i	0.0804022	+	0.139261i
$689$	107.995	−	62.3508i	0.156741	−	0.0904947i
$690$	−0.482054	+	57.2930i	−0.000698630	+	0.0830334i
$691$	−310.061	+	537.041i	−0.448713	+	0.777194i	−0.998303	−	0.0582407i	$-0.981451\pi$
$691$	−310.061	+	537.041i	−0.448713	+	0.777194i	0.549589	+	0.835435i	$0.314784\pi$
$692$			435.280i			0.629017i
$693$	38.2415	+	22.9452i	0.0551825	+	0.0331100i
$694$	−127.785			−0.184129
$695$	128.580	+	74.2357i	0.185007	+	0.106814i
$696$	80.0918	+	141.458i	0.115074	+	0.203245i
$697$	809.711	+	1402.46i	1.16171	+	2.01214i
$698$	434.754	−	251.005i	0.622857	−	0.359607i
$699$	305.027	+	179.546i	0.436377	+	0.256862i
$700$	−4.96891	+	8.60641i	−0.00709844	+	0.0122949i
$701$		−	66.6004i		−	0.0950077i	−0.998871	−	0.0475038i	$-0.984873\pi$
$701$		−	66.6004i		−	0.0950077i	0.998871	−	0.0475038i	$-0.0151266\pi$
$702$	−1.36870	+	54.2137i	−0.00194971	+	0.0772276i
$703$	1740.56			2.47591
$704$	−34.5456	−	19.9449i	−0.0490704	−	0.0283308i
$705$	−22.9996	+	39.0735i	−0.0326235	+	0.0554234i
$706$	255.333	+	442.250i	0.361662	+	0.626417i
$707$	97.8101	−	56.4707i	0.138345	−	0.0798737i
$708$	538.337	−	304.799i	0.760363	−	0.430507i
$709$	105.287	−	182.363i	0.148501	−	0.257211i	−0.782173	−	0.623062i	$-0.785889\pi$
$709$	105.287	−	182.363i	0.148501	−	0.257211i	0.930674	+	0.365851i	$0.119222\pi$
$710$		−	174.267i		−	0.245447i
$711$	−356.253	−	5.99534i	−0.501059	−	0.00843226i
$712$	−209.449			−0.294169
$713$	142.287	+	82.1495i	0.199561	+	0.115217i
$714$	−101.753	−	0.856136i	−0.142512	−	0.00119907i
$715$	−7.91764	−	13.7138i	−0.0110736	−	0.0191801i
$716$	−97.4518	+	56.2638i	−0.136106	+	0.0785807i
$717$	−9.31664	+	1107.30i	−0.0129939	+	1.54435i
$718$	−162.148	+	280.849i	−0.225833	+	0.391155i
$719$			900.163i			1.25197i	0.779837	+	0.625983i	$0.215302\pi$
$719$			900.163i			1.25197i	−0.779837	+	0.625983i	$0.784698\pi$
$720$	70.3811	−	39.0705i	0.0977515	−	0.0542646i
$721$	−56.3906			−0.0782116
$722$	488.814	+	282.217i	0.677028	+	0.390882i
$723$	−555.215	−	980.623i	−0.767932	−	1.35632i
$724$	−130.959	−	226.827i	−0.180882	−	0.313297i
$725$	82.9551	−	47.8942i	0.114421	−	0.0660609i
$726$	−351.504	−	206.903i	−0.484165	−	0.284991i
$727$	377.607	−	654.034i	0.519404	−	0.899635i	−0.480341	−	0.877082i	$-0.659487\pi$
$727$	377.607	−	654.034i	0.519404	−	0.899635i	0.999746	−	0.0225530i	$-0.00717944\pi$
$728$			3.99213i			0.00548370i
$729$	728.071	+	36.7856i	0.998726	+	0.0504604i
$730$	419.796			0.575063
$731$	578.087	+	333.759i	0.790817	+	0.456578i
$732$	219.179	−	372.359i	0.299425	−	0.508687i
$733$	63.0608	+	109.224i	0.0860311	+	0.149010i	0.905830	−	0.423641i	$-0.139248\pi$
$733$	63.0608	+	109.224i	0.0860311	+	0.149010i	−0.819799	+	0.572651i	$0.805915\pi$
$734$	−504.074	+	291.027i	−0.686749	+	0.396495i
$735$	280.272	−	158.686i	0.381322	−	0.215899i
$736$	17.0821	−	29.5870i	0.0232094	−	0.0401998i
$737$		−	99.5653i		−	0.135095i
$738$	−414.517	−	746.706i	−0.561676	−	1.01180i
$739$	503.837			0.681782			0.340891	−	0.940103i	$-0.389271\pi$
$739$	503.837			0.681782			0.340891	+	0.940103i	$0.389271\pi$
$740$	−244.509	−	141.168i	−0.330418	−	0.190767i
$741$	117.467	+	0.988346i	0.158524	+	0.00133380i
$742$	−61.6992	−	106.866i	−0.0831526	−	0.144024i
$743$	−634.502	+	366.330i	−0.853973	+	0.493042i	−0.861989	−	0.506926i	$-0.830782\pi$
$743$	−634.502	+	366.330i	−0.853973	+	0.493042i	0.00801616	+	0.999968i	$0.497448\pi$
$744$	1.94216	−	230.829i	0.00261042	−	0.310254i
$745$	106.906	−	185.167i	0.143498	−	0.248546i
$746$		−	971.604i		−	1.30242i
$747$	−18.3525	+	1090.53i	−0.0245682	+	1.45989i
$748$	−240.679			−0.321764
$749$	80.1999	+	46.3034i	0.107076	+	0.0618203i
$750$	−23.3706	−	41.2773i	−0.0311608	−	0.0550364i
$751$	58.1082	+	100.646i	0.0773744	+	0.134016i	0.902116	−	0.431493i	$-0.142013\pi$
$751$	58.1082	+	100.646i	0.0773744	+	0.134016i	−0.824742	+	0.565509i	$0.808680\pi$
$752$	23.4135	−	13.5178i	0.0311349	−	0.0179758i
$753$	−622.140	−	366.206i	−0.826215	−	0.486329i
$754$	19.2396	−	33.3240i	0.0255167	−	0.0441963i
$755$			604.911i			0.801206i
$756$	53.6471	+	1.35439i	0.0709618	+	0.00179152i
$757$	−644.638			−0.851570			−0.425785	−	0.904824i	$-0.640002\pi$
$757$	−644.638			−0.851570			−0.425785	+	0.904824i	$0.640002\pi$
$758$	−189.509	−	109.413i	−0.250012	−	0.144344i
$759$	−45.8276	+	77.8556i	−0.0603789	+	0.102576i
$760$	−87.1846	−	151.008i	−0.114717	−	0.198695i
$761$	917.597	−	529.775i	1.20578	−	0.696156i	0.243943	−	0.969789i	$-0.421559\pi$
$761$	917.597	−	529.775i	1.20578	−	0.696156i	0.961834	+	0.273634i	$0.0882256\pi$
$762$	−609.364	+	345.013i	−0.799690	+	0.452773i
$763$	10.8100	−	18.7235i	0.0141678	−	0.0245393i
$764$		−	67.9994i		−	0.0890045i
$765$	249.891	−	416.479i	0.326655	−	0.544417i
$766$	230.690			0.301162
$767$	−126.819	−	73.2187i	−0.165344	−	0.0954612i
$768$	−47.9983	−	0.403850i	−0.0624978	−	0.000525846i
$769$	347.756	+	602.331i	0.452219	+	0.783266i	0.998524	−	0.0543206i	$-0.0172993\pi$
$769$	347.756	+	602.331i	0.452219	+	0.783266i	−0.546305	+	0.837586i	$0.683966\pi$
$770$	−13.5704	+	7.83490i	−0.0176239	+	0.0101752i
$771$	−3.16060	+	375.643i	−0.00409935	+	0.487216i
$772$	−183.108	+	317.153i	−0.237187	+	0.410820i
$773$		−	931.046i		−	1.20446i	−0.798323	−	0.602229i	$-0.794279\pi$
$773$		−	931.046i		−	1.20446i	0.798323	−	0.602229i	$-0.205721\pi$
$774$	−301.865	−	181.122i	−0.390006	−	0.234007i
$775$	−136.022			−0.175512
$776$	−5.60360	−	3.23524i	−0.00722114	−	0.00416913i
$777$	−92.7345	−	163.788i	−0.119349	−	0.210795i
$778$	219.428	+	380.061i	0.282042	+	0.488510i
$779$	−1602.12	+	924.982i	−2.05663	+	1.18740i
$780$	−16.4212	−	9.66592i	−0.0210529	−	0.0123922i
$781$	137.391	−	237.968i	0.175916	−	0.304696i
$782$		−	206.133i		−	0.263597i
$783$	−441.288	−	269.852i	−0.563586	−	0.344638i
$784$	−192.050			−0.244961
$785$	−70.3823	−	40.6352i	−0.0896589	−	0.0517646i
$786$	112.918	−	191.834i	0.143662	−	0.244064i
$787$	214.800	+	372.045i	0.272936	+	0.472738i	0.969612	−	0.244647i	$-0.0786721\pi$
$787$	214.800	+	372.045i	0.272936	+	0.472738i	−0.696677	+	0.717385i	$0.745339\pi$
$788$	−53.5811	+	30.9351i	−0.0679964	+	0.0392577i
$789$	−243.421	+	137.822i	−0.308519	+	0.174679i
$790$	62.5962	−	108.420i	0.0792357	−	0.137240i
$791$		−	142.352i		−	0.179965i
$792$	126.911	+	2.13576i	0.160241	+	0.00269667i
$793$	−102.277			−0.128975
$794$	−330.751	−	190.959i	−0.416563	−	0.240503i
$795$	588.971	+	4.95551i	0.740845	+	0.00623335i
$796$	−332.873	−	576.552i	−0.418182	−	0.724312i
$797$	528.635	−	305.208i	0.663281	−	0.382945i	−0.130245	−	0.991482i	$-0.541576\pi$
$797$	528.635	−	305.208i	0.663281	−	0.382945i	0.793526	+	0.608536i	$0.208243\pi$
$798$	0.978016	−	116.239i	0.00122558	−	0.145663i
$799$	81.5608	−	141.268i	0.102079	−	0.176805i
$800$			28.2843i			0.0353553i
$801$	582.698	−	323.472i	0.727463	−	0.403835i
$802$	−857.964			−1.06978
$803$	573.246	+	330.964i	0.713880	+	0.412159i
$804$	−59.0291	−	104.257i	−0.0734193	−	0.129673i
$805$	−6.71030	−	11.6226i	−0.00833578	−	0.0144380i
$806$	−47.3209	+	27.3208i	−0.0587108	+	0.0338967i
$807$	−197.358	−	116.169i	−0.244557	−	0.143952i
$808$	160.723	−	278.380i	0.198914	−	0.344529i
$809$		−	304.324i		−	0.376173i	−0.982152	−	0.188087i	$-0.939771\pi$
$809$		−	304.324i		−	0.376173i	0.982152	−	0.188087i	$-0.0602286\pi$
$810$	−135.464	+	217.393i	−0.167239	+	0.268386i
$811$	−639.398			−0.788407			−0.394204	−	0.919023i	$-0.628980\pi$
$811$	−639.398			−0.788407			−0.394204	+	0.919023i	$0.628980\pi$
$812$	−32.9757	−	19.0385i	−0.0406105	−	0.0234465i
$813$	806.159	−	1369.57i	0.991585	−	1.68458i
$814$	−222.591	−	385.538i	−0.273453	−	0.473634i
$815$	180.725	−	104.342i	0.221749	−	0.128027i
$816$	−252.021	+	142.691i	−0.308850	+	0.174866i
$817$	−381.273	+	660.384i	−0.466674	+	0.808303i
$818$			941.721i			1.15125i
$819$	−6.16544	−	11.1063i	−0.00752801	−	0.0135609i
$820$	300.081			0.365952
$821$	1153.10	+	665.742i	1.40451	+	0.810892i	0.994851	−	0.101349i	$-0.0323158\pi$
$821$	1153.10	+	665.742i	1.40451	+	0.810892i	0.409655	+	0.912241i	$0.365649\pi$
$822$	510.682	+	4.29680i	0.621268	+	0.00522725i
$823$	445.511	+	771.647i	0.541325	+	0.937603i	0.998828	+	0.0483950i	$0.0154106\pi$
$823$	445.511	+	771.647i	0.541325	+	0.937603i	−0.457503	+	0.889208i	$0.651256\pi$
$824$	−138.992	+	80.2473i	−0.168680	+	0.0973875i
$825$	0.629277	−	74.7907i	0.000762761	−	0.0906555i
$826$	−72.4535	+	125.493i	−0.0877161	+	0.151929i
$827$			494.513i			0.597960i	0.954259	+	0.298980i	$0.0966465\pi$
$827$			494.513i			0.597960i	−0.954259	+	0.298980i	$0.903354\pi$
$828$	−1.82920	+	108.694i	−0.00220918	+	0.131273i
$829$	−752.153			−0.907302			−0.453651	−	0.891179i	$-0.649879\pi$
$829$	−752.153			−0.907302			−0.453651	+	0.891179i	$0.649879\pi$
$830$	−331.886	−	191.615i	−0.399863	−	0.230861i
$831$	−125.580	−	221.800i	−0.151119	−	0.266907i
$832$	5.68105	+	9.83988i	0.00682819	+	0.0118268i
$833$	−1003.51	+	579.375i	−1.20469	+	0.695528i
$834$	242.770	+	142.900i	0.291091	+	0.171343i
$835$	63.6472	−	110.240i	0.0762242	−	0.132024i
$836$		−	274.942i		−	0.328878i
$837$	351.088	+	645.178i	0.419460	+	0.770822i
$838$	305.770			0.364881
$839$	438.301	+	253.053i	0.522409	+	0.301613i	0.737920	−	0.674888i	$-0.235808\pi$
$839$	438.301	+	253.053i	0.522409	+	0.301613i	−0.215511	+	0.976502i	$0.569142\pi$
$840$	−9.56490	+	16.2496i	−0.0113868	+	0.0193448i
$841$	−236.992	−	410.482i	−0.281798	−	0.488088i
$842$	−386.412	+	223.095i	−0.458921	+	0.264958i
$843$	−559.302	+	316.669i	−0.663466	+	0.375645i
$844$	−160.772	+	278.465i	−0.190488	+	0.329935i
$845$		−	373.385i		−	0.441876i
$846$	−44.2608	+	73.7669i	−0.0523177	+	0.0871949i
$847$	95.5398			0.112798
$848$	−304.154	−	175.604i	−0.358673	−	0.207080i
$849$	−1134.43	−	9.54494i	−1.33620	−	0.0112426i
$850$	85.3280	+	147.792i	0.100386	+	0.173873i
$851$	330.199	−	190.641i	0.388013	−	0.224020i
$852$	2.78192	−	330.637i	0.00326517	−	0.388071i
$853$	−11.0040	+	19.0595i	−0.0129004	+	0.0223441i	−0.872404	−	0.488786i	$-0.837440\pi$
$853$	−11.0040	+	19.0595i	−0.0129004	+	0.0223441i	0.859503	+	0.511130i	$0.170773\pi$
$854$			101.208i			0.118511i
$855$	475.769	+	285.466i	0.556455	+	0.333878i
$856$	263.570			0.307909
$857$	106.086	+	61.2491i	0.123788	+	0.0714691i	0.560615	−	0.828076i	$-0.310565\pi$
$857$	106.086	+	61.2491i	0.123788	+	0.0714691i	−0.436827	+	0.899545i	$0.643898\pi$
$858$	−14.8032	−	26.1455i	−0.0172532	−	0.0304726i
$859$	−705.014	−	1221.12i	−0.820738	−	1.42156i	−0.905134	−	0.425127i	$-0.860229\pi$
$859$	−705.014	−	1221.12i	−0.820738	−	1.42156i	0.0843962	−	0.996432i	$-0.473104\pi$
$860$	107.120	−	61.8459i	0.124558	−	0.0719139i
$861$	172.400	+	101.478i	0.200232	+	0.117861i
$862$	−498.594	+	863.591i	−0.578416	+	1.00185i
$863$			674.484i			0.781557i	0.920485	+	0.390778i	$0.127794\pi$
$863$			674.484i			0.781557i	−0.920485	+	0.390778i	$0.872206\pi$
$864$	134.158	−	73.0049i	0.155275	−	0.0844964i
$865$	486.658			0.562610
$866$	187.062	+	108.000i	0.216007	+	0.124711i
$867$	−446.603	+	758.724i	−0.515113	+	0.875115i
$868$	27.0352	+	46.8264i	0.0311466	+	0.0539475i
$869$	170.954	−	98.7006i	0.196725	−	0.113580i
$870$	158.155	−	89.5453i	0.181788	−	0.102926i
$871$	−14.1800	+	24.5604i	−0.0162801	+	0.0281979i
$872$		−	61.5333i		−	0.0705657i
$873$	20.5860	+	0.346440i	0.0235808	+	0.000396838i
$874$	235.478			0.269426
$875$	9.62226	+	5.55541i	0.0109969	+	0.00634904i
$876$	796.478	+	6.70144i	0.909222	+	0.00765005i
$877$	−685.352	−	1187.06i	−0.781473	−	1.35355i	−0.931084	−	0.364805i	$-0.881136\pi$
$877$	−685.352	−	1187.06i	−0.781473	−	1.35355i	0.149611	−	0.988745i	$-0.452198\pi$
$878$	−198.696	+	114.717i	−0.226305	+	0.130657i
$879$	−1.26203	+	149.995i	−0.00143576	+	0.170642i
$880$	−22.2991	+	38.6231i	−0.0253399	+	0.0438899i
$881$		−	629.262i		−	0.714259i	−0.934055	−	0.357130i	$-0.883755\pi$
$881$		−	629.262i		−	0.714259i	0.934055	−	0.357130i	$-0.116245\pi$
$882$	534.293	−	296.601i	0.605774	−	0.336282i
$883$	−537.868			−0.609137			−0.304569	−	0.952490i	$-0.598512\pi$
$883$	−537.868			−0.609137			−0.304569	+	0.952490i	$0.598512\pi$
$884$	59.3699	+	34.2772i	0.0671605	+	0.0387751i
$885$	−340.776	−	601.879i	−0.385057	−	0.680090i
$886$	274.050	+	474.669i	0.309312	+	0.535743i
$887$	465.175	−	268.569i	0.524437	−	0.302784i	−0.214311	−	0.976765i	$-0.568751\pi$
$887$	465.175	−	268.569i	0.524437	−	0.302784i	0.738748	+	0.673982i	$0.235417\pi$
$888$	−461.654	−	271.740i	−0.519880	−	0.306014i
$889$	82.0128	−	142.050i	0.0922529	−	0.159787i
$890$			234.171i			0.263113i
$891$	−356.371	+	190.059i	−0.399967	+	0.213309i
$892$	−782.803			−0.877582
$893$	161.378	+	93.1719i	0.180715	+	0.104336i
$894$	205.789	−	349.611i	0.230189	−	0.391063i
$895$	62.9049	+	108.954i	0.0702848	+	0.121737i
$896$	9.73704	−	5.62168i	0.0108672	−	0.00627420i
$897$	22.3927	−	12.6784i	0.0249640	−	0.0141342i
$898$	−78.5065	+	135.977i	−0.0874237	+	0.151422i
$899$		−	521.172i		−	0.579725i
$900$	−43.6821	−	78.6884i	−0.0485357	−	0.0874316i
$901$	−2119.04			−2.35188
$902$	409.771	+	236.581i	0.454291	+	0.262285i
$903$	82.4562	+	0.693773i	0.0913136	+	0.000768298i
$904$	−202.576	−	350.872i	−0.224088	−	0.388132i
$905$	−253.600	+	146.416i	−0.280221	+	0.161786i
$906$	−9.65654	+	1147.70i	−0.0106584	+	1.26677i
$907$	−249.443	+	432.047i	−0.275019	+	0.476347i	−0.970140	−	0.242546i	$-0.922018\pi$
$907$	−249.443	+	432.047i	−0.275019	+	0.476347i	0.695121	+	0.718893i	$0.255351\pi$
$908$			681.398i			0.750439i
$909$	−17.2107	+	1022.69i	−0.0189336	+	1.12507i
$910$	4.46334			0.00490477
$911$	980.687	+	566.200i	1.07650	+	0.621515i	0.929949	−	0.367689i	$-0.119851\pi$
$911$	980.687	+	566.200i	1.07650	+	0.621515i	0.146547	+	0.989204i	$0.453184\pi$
$912$	−163.005	−	287.899i	−0.178733	−	0.315679i
$913$	−302.135	−	523.312i	−0.330925	−	0.573179i
$914$	365.953	−	211.283i	0.400386	−	0.231163i
$915$	−416.310	−	245.050i	−0.454983	−	0.267814i
$916$	−94.4465	+	163.586i	−0.103108	+	0.178587i
$917$			52.1412i			0.0568606i
$918$	480.766	−	786.196i	0.523711	−	0.856422i
$919$	−20.1454			−0.0219210			−0.0109605	−	0.999940i	$-0.503489\pi$
$919$	−20.1454			−0.0219210			−0.0109605	+	0.999940i	$0.503489\pi$
$920$	−33.0793	−	19.0984i	−0.0359558	−	0.0207591i
$921$	220.788	−	375.092i	0.239727	−	0.407266i
$922$	−146.999	−	254.610i	−0.159435	−	0.276149i
$923$	−67.7821	+	39.1340i	−0.0734367	+	0.0423987i
$924$	−25.8723	+	14.6485i	−0.0280003	+	0.0158534i
$925$	−157.830	+	273.370i	−0.170627	+	0.295535i
$926$		−	1223.47i		−	1.32124i
$927$	262.751	−	437.912i	0.283442	−	0.472397i
$928$	−108.372			−0.116780
$929$	−260.470	−	150.382i	−0.280377	−	0.161876i	0.353217	−	0.935541i	$-0.385088\pi$
$929$	−260.470	−	150.382i	−0.280377	−	0.161876i	−0.633594	+	0.773666i	$0.718421\pi$
$930$	−258.074	−	2.17140i	−0.277499	−	0.00233483i
$931$	−661.855	−	1146.37i	−0.710908	−	1.23133i
$932$	−204.352	+	117.982i	−0.219261	+	0.126591i
$933$	2.63990	−	313.757i	0.00282948	−	0.336289i
$934$	−604.382	+	1046.82i	−0.647090	+	1.12079i
$935$			269.087i			0.287794i
$936$	−31.0017	−	18.6013i	−0.0331215	−	0.0198732i
$937$	310.906			0.331810			0.165905	−	0.986142i	$-0.446945\pi$
$937$	310.906			0.331810			0.165905	+	0.986142i	$0.446945\pi$
$938$	24.3037	+	14.0318i	0.0259102	+	0.0149592i
$939$	85.3947	+	150.824i	0.0909421	+	0.160622i
$940$	−15.1133	−	26.1771i	−0.0160780	−	0.0278479i
$941$	1259.21	−	727.005i	1.33816	−	0.772588i	0.351627	−	0.936140i	$-0.385629\pi$
$941$	1259.21	−	727.005i	1.33816	−	0.772588i	0.986535	+	0.163553i	$0.0522953\pi$
$942$	−132.888	−	78.2207i	−0.141070	−	0.0830369i
$943$	−202.623	+	350.954i	−0.214871	+	0.372167i
$944$			412.423i			0.436889i
$945$	1.51426	−	59.9793i	0.00160239	−	0.0634702i
$946$	195.035			0.206168
$947$	165.289	+	95.4294i	0.174539	+	0.100770i	0.584724	−	0.811232i	$-0.301203\pi$
$947$	165.289	+	95.4294i	0.174539	+	0.100770i	−0.410185	+	0.912002i	$0.634536\pi$
$948$	120.494	−	204.705i	0.127104	−	0.215934i
$949$	−94.2708	−	163.282i	−0.0993370	−	0.172057i
$950$	−168.832	+	97.4753i	−0.177718	+	0.102606i
$951$	256.623	−	145.296i	0.269845	−	0.152782i
$952$	33.9190	−	58.7494i	0.0356292	−	0.0617115i
$953$			808.807i			0.848695i	0.905499	+	0.424348i	$0.139497\pi$
$953$			808.807i			0.848695i	−0.905499	+	0.424348i	$0.860503\pi$
$954$	1117.38	+	18.8042i	1.17125	+	0.0197109i
$955$	−76.0257			−0.0796081
$956$	−639.322	−	369.113i	−0.668747	−	0.386101i
$957$	286.563	+	2.41110i	0.299439	+	0.00251943i
$958$	215.059	+	372.493i	0.224487	+	0.388823i
$959$	−103.598	+	59.8124i	−0.108027	+	0.0623695i
$960$	−0.451518	+	53.6637i	−0.000470331	+	0.0558997i
$961$	110.461	−	191.324i	0.114944	−	0.199088i
$962$			126.804i			0.131813i
$963$	−733.268	+	407.057i	−0.761441	+	0.422697i
$964$	751.261			0.779316
$965$	354.588	+	204.721i	0.367449	+	0.212147i
$966$	−12.5459	−	22.1586i	−0.0129875	−	0.0229386i
$967$	−213.781	−	370.279i	−0.221076	−	0.382915i	0.734059	−	0.679086i	$-0.237624\pi$
$967$	−213.781	−	370.279i	−0.221076	−	0.382915i	−0.955135	+	0.296171i	$0.904290\pi$
$968$	235.488	−	135.959i	0.243273	−	0.140454i
$969$	−1720.27	−	1012.59i	−1.77531	−	1.04499i
$970$	−3.61711	+	6.26502i	−0.00372898	+	0.00645878i
$971$			932.208i			0.960050i	0.877255	+	0.480025i	$0.159372\pi$
$971$			932.208i			0.960050i	−0.877255	+	0.480025i	$0.840628\pi$
$972$	−260.486	+	410.296i	−0.267990	+	0.422116i
$973$	−65.9856			−0.0678166
$974$	1111.31	+	641.613i	1.14097	+	0.658741i
$975$	−10.8068	+	18.3595i	−0.0110839	+	0.0188302i
$976$	144.026	+	249.460i	0.147567	+	0.255594i
$977$	−176.167	+	101.710i	−0.180315	+	0.104105i	−0.587440	−	0.809267i	$-0.699864\pi$
$977$	−176.167	+	101.710i	−0.180315	+	0.104105i	0.407126	+	0.913372i	$0.366531\pi$
$978$	344.555	−	195.082i	0.352306	−	0.199471i
$979$	−184.618	+	319.768i	−0.188578	+	0.326627i
$980$			214.718i			0.219100i
$981$	95.0318	+	171.189i	0.0968724	+	0.174505i
$982$	92.5557			0.0942522
$983$	1241.90	+	717.012i	1.26338	+	0.729412i	0.973727	−	0.227719i	$-0.0731269\pi$
$983$	1241.90	+	717.012i	1.26338	+	0.729412i	0.289653	+	0.957132i	$0.406460\pi$
$984$	569.343	+	4.79037i	0.578601	+	0.00486826i
$985$	34.5865	+	59.9055i	0.0351132	+	0.0608178i
$986$	−566.271	+	326.937i	−0.574312	+	0.331579i
$987$	0.169538	−	20.1499i	0.000171771	−	0.0204153i
$988$	−39.1569	+	67.8218i	−0.0396325	+	0.0686455i
$989$			167.041i			0.168898i
$990$	2.38786	−	141.890i	0.00241198	−	0.143324i
$991$	−983.596			−0.992528			−0.496264	−	0.868172i	$-0.665295\pi$
$991$	−983.596			−0.992528			−0.496264	+	0.868172i	$0.665295\pi$
$992$	133.274	+	76.9456i	0.134348	+	0.0775661i
$993$	−314.943	−	556.254i	−0.317163	−	0.560175i
$994$	38.7250	+	67.0737i	0.0389588	+	0.0674785i
$995$	−644.605	+	372.163i	−0.647844	+	0.374033i
$996$	−626.629	−	368.848i	−0.629145	−	0.370330i
$997$	495.586	−	858.379i	0.497077	−	0.860962i	−0.502917	−	0.864334i	$-0.667740\pi$
$997$	495.586	−	858.379i	0.497077	−	0.860962i	0.999994	+	0.00337211i	$0.00107338\pi$
$998$		−	1014.39i		−	1.01643i
$999$	1704.02	+	43.0202i	1.70573	+	0.0430633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.3.h.a.11.7	✓	16
3.2	odd	2		270.3.h.a.251.1		16
4.3	odd	2		720.3.bs.d.641.2		16
5.2	odd	4		450.3.k.c.299.6		32
5.3	odd	4		450.3.k.c.299.11		32
5.4	even	2		450.3.i.g.101.2		16
9.2	odd	6		810.3.d.c.161.11		16
9.4	even	3		270.3.h.a.71.1		16
9.5	odd	6	inner	90.3.h.a.41.7	yes	16
9.7	even	3		810.3.d.c.161.7		16
12.11	even	2		2160.3.bs.d.1601.3		16
15.2	even	4		1350.3.k.b.899.11		32
15.8	even	4		1350.3.k.b.899.6		32
15.14	odd	2		1350.3.i.g.251.7		16
36.23	even	6		720.3.bs.d.401.2		16
36.31	odd	6		2160.3.bs.d.881.3		16
45.4	even	6		1350.3.i.g.1151.7		16
45.13	odd	12		1350.3.k.b.449.11		32
45.14	odd	6		450.3.i.g.401.2		16
45.22	odd	12		1350.3.k.b.449.6		32
45.23	even	12		450.3.k.c.149.6		32
45.32	even	12		450.3.k.c.149.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.h.a.11.7	✓	16	1.1	even	1	trivial
90.3.h.a.41.7	yes	16	9.5	odd	6	inner
270.3.h.a.71.1		16	9.4	even	3
270.3.h.a.251.1		16	3.2	odd	2
450.3.i.g.101.2		16	5.4	even	2
450.3.i.g.401.2		16	45.14	odd	6
450.3.k.c.149.6		32	45.23	even	12
450.3.k.c.149.11		32	45.32	even	12
450.3.k.c.299.6		32	5.2	odd	4
450.3.k.c.299.11		32	5.3	odd	4
720.3.bs.d.401.2		16	36.23	even	6
720.3.bs.d.641.2		16	4.3	odd	2
810.3.d.c.161.7		16	9.7	even	3
810.3.d.c.161.11		16	9.2	odd	6
1350.3.i.g.251.7		16	15.14	odd	2
1350.3.i.g.1151.7		16	45.4	even	6
1350.3.k.b.449.6		32	45.22	odd	12
1350.3.k.b.449.11		32	45.13	odd	12
1350.3.k.b.899.6		32	15.8	even	4
1350.3.k.b.899.11		32	15.2	even	4
2160.3.bs.d.881.3		16	36.31	odd	6
2160.3.bs.d.1601.3		16	12.11	even	2

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:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	90.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.52181 - 2.58536i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(3.69195 - 2.09033i) q^{6} +(-0.496891 + 0.860641i) q^{7} +2.82843i q^{8} +(-4.36821 - 7.86884i) q^{9} +3.16228 q^{10} +(4.31820 + 2.49311i) q^{11} +(5.99979 + 0.0504813i) q^{12} +(-0.710132 - 1.22998i) q^{13} +(-1.21713 + 0.702710i) q^{14} +(0.0564398 - 6.70797i) q^{15} +(-2.00000 + 3.46410i) q^{16} +24.1344i q^{17} +(0.214166 - 12.7261i) q^{18} -27.5702 q^{19} +(3.87298 + 2.23607i) q^{20} +(1.46890 + 2.59437i) q^{21} +(3.52579 + 6.10686i) q^{22} +(-5.23030 + 3.01971i) q^{23} +(7.31251 + 4.30432i) q^{24} +(2.50000 - 4.33013i) q^{25} -2.00856i q^{26} +(-26.9914 - 0.681433i) q^{27} -1.98756 q^{28} +(16.5910 + 9.57883i) q^{29} +(4.81237 - 8.17564i) q^{30} +(-13.6022 - 23.5597i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(13.0171 - 7.37008i) q^{33} +(-17.0656 + 29.5585i) q^{34} +2.22216i q^{35} +(9.26102 - 15.4348i) q^{36} -63.1320 q^{37} +(-33.7664 - 19.4951i) q^{38} +(-4.26064 - 0.0358483i) q^{39} +(3.16228 + 5.47723i) q^{40} +(58.1104 - 33.5501i) q^{41} +(-0.0354737 + 4.21611i) q^{42} +(13.8292 - 23.9528i) q^{43} +9.97245i q^{44} +(-17.2566 - 10.3541i) q^{45} -8.54104 q^{46} +(-5.85337 - 3.37944i) q^{47} +(5.91235 + 10.4424i) q^{48} +(24.0062 + 41.5800i) q^{49} +(6.12372 - 3.53553i) q^{50} +(62.3962 + 36.7279i) q^{51} +(1.42026 - 2.45997i) q^{52} +87.8018i q^{53} +(-32.5757 - 19.9204i) q^{54} +11.1495 q^{55} +(-2.43426 - 1.40542i) q^{56} +(-41.9565 + 71.2790i) q^{57} +(13.5465 + 23.4633i) q^{58} +(89.2923 - 51.5529i) q^{59} +(11.6750 - 6.61021i) q^{60} +(36.0064 - 62.3649i) q^{61} -38.4728i q^{62} +(8.94277 + 0.150497i) q^{63} -8.00000 q^{64} +(-2.75033 - 1.58790i) q^{65} +(21.1540 + 0.177987i) q^{66} +(-9.98403 - 17.2928i) q^{67} +(-41.8020 + 24.1344i) q^{68} +(-0.152439 + 18.1176i) q^{69} +(-1.57131 + 2.72158i) q^{70} -55.1081i q^{71} +(22.2565 - 12.3552i) q^{72} +132.751 q^{73} +(-77.3206 - 44.6411i) q^{74} +(-7.39044 - 13.0530i) q^{75} +(-27.5702 - 47.7530i) q^{76} +(-4.29135 + 2.47761i) q^{77} +(-5.19285 - 3.05663i) q^{78} +(19.7946 - 34.2853i) q^{79} +8.94427i q^{80} +(-42.8374 + 68.7456i) q^{81} +94.8939 q^{82} +(-104.952 - 60.5938i) q^{83} +(-3.02469 + 5.13858i) q^{84} +(26.9831 + 46.7361i) q^{85} +(33.8744 - 19.5574i) q^{86} +(50.0131 - 28.3167i) q^{87} +(-7.05159 + 12.2137i) q^{88} +74.0513i q^{89} +(-13.8135 - 24.8835i) q^{90} +1.41143 q^{91} +(-10.4606 - 6.03943i) q^{92} +(-81.6102 - 0.686656i) q^{93} +(-4.77926 - 8.27791i) q^{94} +(-53.3894 + 30.8244i) q^{95} +(-0.142783 + 16.9700i) q^{96} +(-1.14383 + 1.98117i) q^{97} +67.8998i q^{98} +(0.755106 - 44.8697i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} + 16 q^{4} + 16 q^{6} - 4 q^{7} - 4 q^{9} - 16 q^{12} + 20 q^{13} - 36 q^{14} - 20 q^{15} - 32 q^{16} + 16 q^{18} + 80 q^{19} - 44 q^{21} + 24 q^{22} + 108 q^{23} - 8 q^{24} + 40 q^{25} - 124 q^{27}+ \cdots + 816 q^{99}+O(q^{100}) \) 16 * q - 4 * q^3 + 16 * q^4 + 16 * q^6 - 4 * q^7 - 4 * q^9 - 16 * q^12 + 20 * q^13 - 36 * q^14 - 20 * q^15 - 32 * q^16 + 16 * q^18 + 80 * q^19 - 44 * q^21 + 24 * q^22 + 108 * q^23 - 8 * q^24 + 40 * q^25 - 124 * q^27 - 16 * q^28 - 72 * q^29 + 20 * q^30 - 16 * q^31 - 264 * q^33 - 48 * q^34 + 32 * q^36 - 88 * q^37 - 72 * q^38 - 8 * q^39 + 108 * q^41 + 128 * q^42 + 92 * q^43 - 80 * q^45 + 24 * q^46 + 216 * q^47 - 16 * q^48 - 84 * q^49 + 168 * q^51 - 40 * q^52 + 148 * q^54 - 72 * q^56 + 28 * q^57 + 144 * q^59 + 40 * q^60 - 76 * q^61 - 104 * q^63 - 128 * q^64 + 180 * q^65 + 96 * q^66 + 56 * q^67 + 72 * q^68 - 72 * q^69 + 60 * q^70 + 64 * q^72 + 416 * q^73 - 288 * q^74 + 20 * q^75 + 80 * q^76 - 684 * q^77 + 56 * q^78 + 80 * q^79 + 320 * q^81 - 192 * q^82 + 396 * q^83 + 40 * q^84 - 60 * q^85 - 216 * q^86 + 420 * q^87 - 48 * q^88 - 160 * q^90 - 656 * q^91 + 216 * q^92 - 356 * q^93 - 84 * q^94 - 360 * q^95 - 80 * q^96 - 16 * q^97 + 816 * q^99

Introduction

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