LMFDB - Embedded newform 117.3.v.a.95.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(95,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("117.95");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.v (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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			95.11
Character	$\chi$	$=$	117.95
Dual form			117.3.v.a.101.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.647795 q^{2} +(-2.17539 - 2.06583i) q^{3} -3.58036 q^{4} +(-1.12097 + 1.94158i) q^{5} +(1.40921 + 1.33823i) q^{6} +(6.66709 + 3.84925i) q^{7} +4.91052 q^{8} +(0.464681 + 8.98800i) q^{9} +(0.726158 - 1.25774i) q^{10} +5.74159 q^{11} +(7.78870 + 7.39642i) q^{12} +(11.8946 + 5.24585i) q^{13} +(-4.31890 - 2.49352i) q^{14} +(6.44952 - 1.90796i) q^{15} +11.1404 q^{16} +(-19.0666 + 11.0081i) q^{17} +(-0.301018 - 5.82238i) q^{18} +(-4.39605 + 2.53806i) q^{19} +(4.01348 - 6.95155i) q^{20} +(-6.55166 - 22.1467i) q^{21} -3.71937 q^{22} +(-19.9049 + 11.4921i) q^{23} +(-10.6823 - 10.1443i) q^{24} +(9.98685 + 17.2977i) q^{25} +(-7.70525 - 3.39823i) q^{26} +(17.5568 - 20.5124i) q^{27} +(-23.8706 - 13.7817i) q^{28} +25.8169i q^{29} +(-4.17796 + 1.23597i) q^{30} +(32.0171 + 18.4851i) q^{31} -26.8588 q^{32} +(-12.4902 - 11.8611i) q^{33} +(12.3513 - 7.13100i) q^{34} +(-14.9472 + 8.62977i) q^{35} +(-1.66373 - 32.1803i) q^{36} +(20.4567 + 11.8107i) q^{37} +(2.84774 - 1.64414i) q^{38} +(-15.0384 - 35.9840i) q^{39} +(-5.50454 + 9.53414i) q^{40} +(-32.2626 - 55.8805i) q^{41} +(4.24413 + 14.3465i) q^{42} +(15.7842 - 27.3390i) q^{43} -20.5570 q^{44} +(-17.9718 - 9.17305i) q^{45} +(12.8943 - 7.44454i) q^{46} +(30.2047 + 52.3161i) q^{47} +(-24.2349 - 23.0143i) q^{48} +(5.13339 + 8.89129i) q^{49} +(-6.46943 - 11.2054i) q^{50} +(64.2184 + 15.4414i) q^{51} +(-42.5869 - 18.7820i) q^{52} -43.4874i q^{53} +(-11.3732 + 13.2878i) q^{54} +(-6.43614 + 11.1477i) q^{55} +(32.7389 + 18.9018i) q^{56} +(14.8063 + 3.56022i) q^{57} -16.7240i q^{58} +57.8296 q^{59} +(-23.0916 + 6.83119i) q^{60} +(-29.4548 + 51.0172i) q^{61} +(-20.7405 - 11.9745i) q^{62} +(-31.4989 + 61.7124i) q^{63} -27.1628 q^{64} +(-23.5187 + 17.2138i) q^{65} +(8.09109 + 7.68359i) q^{66} +(-59.3116 + 34.2436i) q^{67} +(68.2654 - 39.4131i) q^{68} +(67.0419 + 16.1204i) q^{69} +(9.68272 - 5.59032i) q^{70} +(16.3288 + 28.2823i) q^{71} +(2.28183 + 44.1357i) q^{72} -83.5918i q^{73} +(-13.2518 - 7.65091i) q^{74} +(14.0089 - 58.2606i) q^{75} +(15.7395 - 9.08718i) q^{76} +(38.2797 + 22.1008i) q^{77} +(9.74178 + 23.3102i) q^{78} +(46.0359 + 79.7366i) q^{79} +(-12.4881 + 21.6300i) q^{80} +(-80.5681 + 8.35311i) q^{81} +(20.8996 + 36.1991i) q^{82} +(21.6284 + 37.4615i) q^{83} +(23.4573 + 79.2932i) q^{84} -49.3591i q^{85} +(-10.2249 + 17.7101i) q^{86} +(53.3333 - 56.1618i) q^{87} +28.1942 q^{88} +(-61.5015 + 106.524i) q^{89} +(11.6420 + 5.94226i) q^{90} +(59.1097 + 80.7597i) q^{91} +(71.2669 - 41.1460i) q^{92} +(-31.4628 - 106.354i) q^{93} +(-19.5665 - 33.8901i) q^{94} -11.3804i q^{95} +(58.4285 + 55.4857i) q^{96} +(-116.849 - 67.4631i) q^{97} +(-3.32538 - 5.75973i) q^{98} +(2.66801 + 51.6053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 6 q^{2} - q^{3} + 94 q^{4} - 12 q^{6} - 3 q^{7} - 78 q^{8} + q^{9} + 2 q^{10} - 6 q^{11} + 13 q^{12} - 6 q^{13} - 6 q^{14} + 27 q^{15} + 150 q^{16} + 12 q^{18} + 15 q^{19} - 3 q^{20} - 69 q^{21}+ \cdots - 522 q^{99}+O(q^{100}) $ 52 * q - 6 * q^2 - q^3 + 94 * q^4 - 12 * q^6 - 3 * q^7 - 78 * q^8 + q^9 + 2 * q^10 - 6 * q^11 + 13 * q^12 - 6 * q^13 - 6 * q^14 + 27 * q^15 + 150 * q^16 + 12 * q^18 + 15 * q^19 - 3 * q^20 - 69 * q^21 - 34 * q^22 + 69 * q^23 - 78 * q^24 - 92 * q^25 - 12 * q^26 + 14 * q^27 - 18 * q^28 - 84 * q^30 + 48 * q^31 - 318 * q^32 - 99 * q^33 - 12 * q^34 + 78 * q^35 + 26 * q^36 + 27 * q^37 - 36 * q^38 + 37 * q^39 - 44 * q^40 + 33 * q^41 - 153 * q^42 - 31 * q^43 - 120 * q^44 + 87 * q^45 - 6 * q^46 + 153 * q^47 - 19 * q^48 + 73 * q^49 + 216 * q^50 - 63 * q^51 - 100 * q^52 - 339 * q^54 + 23 * q^55 - 174 * q^56 + 171 * q^57 - 6 * q^59 + 207 * q^60 - 6 * q^61 - 201 * q^62 + 189 * q^63 + 270 * q^64 - 66 * q^65 + 48 * q^66 - 108 * q^67 - 216 * q^68 - 201 * q^69 - 159 * q^70 + 432 * q^71 - 294 * q^72 - 81 * q^74 - 2 * q^75 + 141 * q^76 + 138 * q^77 + 456 * q^78 + 9 * q^79 + 84 * q^80 + 505 * q^81 - 85 * q^82 + 135 * q^83 - 201 * q^84 + 306 * q^86 + 348 * q^87 - 290 * q^88 + 441 * q^89 + 543 * q^90 - 138 * q^91 + 864 * q^92 + 474 * q^93 - 181 * q^94 - 747 * q^96 - 60 * q^97 - 147 * q^98 - 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.647795			−0.323897			−0.161949	−	0.986799i	$-0.551778\pi$
$2$	−0.647795			−0.323897			−0.161949	+	0.986799i	$0.551778\pi$
$3$	−2.17539	−	2.06583i	−0.725131	−	0.688610i
$3$	−2.17539	−	2.06583i	−0.725131	−	0.688610i
$4$	−3.58036			−0.895091
$5$	−1.12097	+	1.94158i	−0.224194	+	0.388315i	−0.956077	−	0.293115i	$-0.905308\pi$
$5$	−1.12097	+	1.94158i	−0.224194	+	0.388315i	0.731883	+	0.681430i	$0.238642\pi$
$6$	1.40921	+	1.33823i	0.234868	+	0.223039i
$7$	6.66709	+	3.84925i	0.952441	+	0.549892i	0.893838	−	0.448389i	$-0.148002\pi$
$7$	6.66709	+	3.84925i	0.952441	+	0.549892i	0.0586029	+	0.998281i	$0.481335\pi$
$8$	4.91052			0.613815
$9$	0.464681	+	8.98800i	0.0516313	+	0.998666i
$10$	0.726158	−	1.25774i	0.0726158	−	0.125774i
$11$	5.74159			0.521962			0.260981	−	0.965344i	$-0.415954\pi$
$11$	5.74159			0.521962			0.260981	+	0.965344i	$0.415954\pi$
$12$	7.78870	+	7.39642i	0.649058	+	0.616369i
$13$	11.8946	+	5.24585i	0.914968	+	0.403527i
$13$	11.8946	+	5.24585i	0.914968	+	0.403527i
$14$	−4.31890	−	2.49352i	−0.308493	−	0.178109i
$15$	6.44952	−	1.90796i	0.429968	−	0.127197i
$16$	11.1404			0.696278
$17$	−19.0666	+	11.0081i	−1.12157	+	0.647537i	−0.941800	−	0.336173i	$-0.890867\pi$
$17$	−19.0666	+	11.0081i	−1.12157	+	0.647537i	−0.179766	+	0.983709i	$0.557534\pi$
$18$	−0.301018	−	5.82238i	−0.0167232	−	0.323465i
$19$	−4.39605	+	2.53806i	−0.231371	+	0.133582i	−0.611204	−	0.791473i	$-0.709315\pi$
$19$	−4.39605	+	2.53806i	−0.231371	+	0.133582i	0.379833	+	0.925055i	$0.375981\pi$
$20$	4.01348	−	6.95155i	0.200674	−	0.347577i
$21$	−6.55166	−	22.1467i	−0.311984	−	1.05461i
$22$	−3.71937			−0.169062
$23$	−19.9049	+	11.4921i	−0.865432	+	0.499658i	−0.865828	−	0.500342i	$-0.833208\pi$
$23$	−19.9049	+	11.4921i	−0.865432	+	0.499658i	0.000395309		1.00000i	$0.499874\pi$
$24$	−10.6823	−	10.1443i	−0.445096	−	0.422679i
$25$	9.98685	+	17.2977i	0.399474	+	0.691910i
$26$	−7.70525	−	3.39823i	−0.296356	−	0.130701i
$27$	17.5568	−	20.5124i	0.650253	−	0.759718i
$28$	−23.8706	−	13.7817i	−0.852521	−	0.492203i
$29$			25.8169i			0.890236i	0.895472	+	0.445118i	$0.146838\pi$
$29$			25.8169i			0.890236i	−0.895472	+	0.445118i	$0.853162\pi$
$30$	−4.17796	+	1.23597i	−0.139265	+	0.0411989i
$31$	32.0171	+	18.4851i	1.03281	+	0.596294i	0.917789	−	0.397069i	$-0.129973\pi$
$31$	32.0171	+	18.4851i	1.03281	+	0.596294i	0.115022	+	0.993363i	$0.463306\pi$
$32$	−26.8588			−0.839337
$33$	−12.4902	−	11.8611i	−0.378491	−	0.359429i
$34$	12.3513	−	7.13100i	0.363272	−	0.209735i
$35$	−14.9472	+	8.62977i	−0.427063	+	0.246565i
$36$	−1.66373	−	32.1803i	−0.0462147	−	0.893897i
$37$	20.4567	+	11.8107i	0.552885	+	0.319208i	0.750285	−	0.661115i	$-0.229916\pi$
$37$	20.4567	+	11.8107i	0.552885	+	0.319208i	−0.197400	+	0.980323i	$0.563250\pi$
$38$	2.84774	−	1.64414i	0.0749405	−	0.0432669i
$39$	−15.0384	−	35.9840i	−0.385599	−	0.922666i
$40$	−5.50454	+	9.53414i	−0.137614	+	0.238354i
$41$	−32.2626	−	55.8805i	−0.786894	−	1.36294i	−0.927861	−	0.372926i	$-0.878355\pi$
$41$	−32.2626	−	55.8805i	−0.786894	−	1.36294i	0.140967	−	0.990014i	$-0.454979\pi$
$42$	4.24413	+	14.3465i	0.101051	+	0.341584i
$43$	15.7842	−	27.3390i	0.367074	−	0.635791i	−0.622032	−	0.782992i	$-0.713693\pi$
$43$	15.7842	−	27.3390i	0.367074	−	0.635791i	0.989107	+	0.147200i	$0.0470261\pi$
$44$	−20.5570			−0.467204
$45$	−17.9718	−	9.17305i	−0.399373	−	0.203846i
$46$	12.8943	−	7.44454i	0.280311	−	0.161838i
$47$	30.2047	+	52.3161i	0.642654	+	1.11311i	0.984838	+	0.173476i	$0.0554999\pi$
$47$	30.2047	+	52.3161i	0.642654	+	1.11311i	−0.342184	+	0.939633i	$0.611167\pi$
$48$	−24.2349	−	23.0143i	−0.504893	−	0.479464i
$49$	5.13339	+	8.89129i	0.104763	+	0.181455i
$50$	−6.46943	−	11.2054i	−0.129389	−	0.224108i
$51$	64.2184	+	15.4414i	1.25918	+	0.302773i
$52$	−42.5869	−	18.7820i	−0.818979	−	0.361193i
$53$		−	43.4874i		−	0.820516i	−0.911969	−	0.410258i	$-0.865439\pi$
$53$		−	43.4874i		−	0.820516i	0.911969	−	0.410258i	$-0.134561\pi$
$54$	−11.3732	+	13.2878i	−0.210615	+	0.246071i
$55$	−6.43614	+	11.1477i	−0.117021	+	0.202686i
$56$	32.7389	+	18.9018i	0.584622	+	0.337532i
$57$	14.8063	+	3.56022i	0.259760	+	0.0624599i
$58$		−	16.7240i		−	0.288345i
$59$	57.8296			0.980163			0.490081	−	0.871677i	$-0.336967\pi$
$59$	57.8296			0.980163			0.490081	+	0.871677i	$0.336967\pi$
$60$	−23.0916	+	6.83119i	−0.384860	+	0.113853i
$61$	−29.4548	+	51.0172i	−0.482866	+	0.836348i	−0.999806	−	0.0196733i	$-0.993737\pi$
$61$	−29.4548	+	51.0172i	−0.482866	+	0.836348i	0.516941	+	0.856021i	$0.327071\pi$
$62$	−20.7405	−	11.9745i	−0.334525	−	0.193138i
$63$	−31.4989	+	61.7124i	−0.499983	+	0.979563i
$64$	−27.1628			−0.424419
$65$	−23.5187	+	17.2138i	−0.361826	+	0.264828i
$66$	8.09109	+	7.68359i	0.122592	+	0.116418i
$67$	−59.3116	+	34.2436i	−0.885248	+	0.511098i	−0.872385	−	0.488819i	$-0.837428\pi$
$67$	−59.3116	+	34.2436i	−0.885248	+	0.511098i	−0.0128627	+	0.999917i	$0.504094\pi$
$68$	68.2654	−	39.4131i	1.00390	−	0.579604i
$69$	67.0419	+	16.1204i	0.971622	+	0.233628i
$70$	9.68272	−	5.59032i	0.138325	−	0.0798617i
$71$	16.3288	+	28.2823i	0.229983	+	0.398343i	0.957803	−	0.287426i	$-0.0927995\pi$
$71$	16.3288	+	28.2823i	0.229983	+	0.398343i	−0.727819	+	0.685769i	$0.759466\pi$
$72$	2.28183	+	44.1357i	0.0316920	+	0.612996i
$73$		−	83.5918i		−	1.14509i	−0.819872	−	0.572547i	$-0.805955\pi$
$73$		−	83.5918i		−	1.14509i	0.819872	−	0.572547i	$-0.194045\pi$
$74$	−13.2518	−	7.65091i	−0.179078	−	0.103391i
$75$	14.0089	−	58.2606i	0.186785	−	0.776808i
$76$	15.7395	−	9.08718i	0.207098	−	0.119568i
$77$	38.2797	+	22.1008i	0.497138	+	0.287023i
$78$	9.74178	+	23.3102i	0.124895	+	0.298849i
$79$	46.0359	+	79.7366i	0.582733	+	1.00932i	0.995154	+	0.0983302i	$0.0313501\pi$
$79$	46.0359	+	79.7366i	0.582733	+	1.00932i	−0.412420	+	0.910994i	$0.635317\pi$
$80$	−12.4881	+	21.6300i	−0.156101	+	0.270375i
$81$	−80.5681	+	8.35311i	−0.994668	+	0.103125i
$82$	20.8996	+	36.1991i	0.254873	+	0.441453i
$83$	21.6284	+	37.4615i	0.260583	+	0.451344i	0.966397	−	0.257054i	$-0.0827518\pi$
$83$	21.6284	+	37.4615i	0.260583	+	0.451344i	−0.705814	+	0.708397i	$0.749418\pi$
$84$	23.4573	+	79.2932i	0.279254	+	0.943967i
$85$		−	49.3591i		−	0.580695i
$86$	−10.2249	+	17.7101i	−0.118894	+	0.205931i
$87$	53.3333	−	56.1618i	0.613026	−	0.645538i
$88$	28.1942			0.320388
$89$	−61.5015	+	106.524i	−0.691028	+	1.19690i	0.280474	+	0.959862i	$0.409508\pi$
$89$	−61.5015	+	106.524i	−0.691028	+	1.19690i	−0.971501	+	0.237034i	$0.923825\pi$
$90$	11.6420	+	5.94226i	0.129356	+	0.0660251i
$91$	59.1097	+	80.7597i	0.649557	+	0.887469i
$92$	71.2669	−	41.1460i	0.774640	−	0.447239i
$93$	−31.4628	−	106.354i	−0.338310	−	1.14360i
$94$	−19.5665	−	33.8901i	−0.208154	−	0.360533i
$95$		−	11.3804i		−	0.119793i
$96$	58.4285	+	55.4857i	0.608630	+	0.577976i
$97$	−116.849	−	67.4631i	−1.20463	−	0.695496i	−0.243052	−	0.970013i	$-0.578148\pi$
$97$	−116.849	−	67.4631i	−1.20463	−	0.695496i	−0.961582	+	0.274518i	$0.911482\pi$
$98$	−3.32538	−	5.75973i	−0.0339325	−	0.0587727i
$99$	2.66801	+	51.6053i	0.0269496	+	0.521266i
$100$	−35.7566	−	61.9322i	−0.357566	−	0.619322i
$101$		−	79.0091i		−	0.782269i	−0.920334	−	0.391134i	$-0.872083\pi$
$101$		−	79.0091i		−	0.782269i	0.920334	−	0.391134i	$-0.127917\pi$
$102$	−41.6003	−	10.0029i	−0.407846	−	0.0980674i
$103$	52.8097	−	91.4690i	0.512715	−	0.888049i	−0.487176	−	0.873304i	$-0.661973\pi$
$103$	52.8097	−	91.4690i	0.512715	−	0.888049i	0.999891	−	0.0147449i	$-0.00469363\pi$
$104$	58.4086	+	25.7598i	0.561621	+	0.247691i
$105$	50.3437	+	12.1052i	0.479464	+	0.115288i
$106$			28.1709i			0.265763i
$107$	53.3219	+	30.7854i	0.498335	+	0.287714i	0.728026	−	0.685550i	$-0.240438\pi$
$107$	53.3219	+	30.7854i	0.498335	+	0.287714i	−0.229691	+	0.973264i	$0.573771\pi$
$108$	−62.8598	+	73.4418i	−0.582035	+	0.680017i
$109$			100.959i			0.926232i	0.886298	+	0.463116i	$0.153269\pi$
$109$			100.959i			0.926232i	−0.886298	+	0.463116i	$0.846731\pi$
$110$	4.16930	−	7.22144i	0.0379027	−	0.0656494i
$111$	−20.1025	−	67.9531i	−0.181104	−	0.612190i
$112$	74.2743	+	42.8823i	0.663164	+	0.382878i
$113$		−	160.154i		−	1.41730i	−0.705562	−	0.708648i	$-0.749305\pi$
$113$		−	160.154i		−	1.41730i	0.705562	−	0.708648i	$-0.250695\pi$
$114$	−9.59147	−	2.30629i	−0.0841357	−	0.0202306i
$115$		−	51.5293i		−	0.448081i
$116$		−	92.4337i		−	0.796842i
$117$	−41.6224	+	109.346i	−0.355747	+	0.934582i
$118$	−37.4617			−0.317472
$119$	−169.492			−1.42430
$120$	31.6705	−	9.36907i	0.263921	−	0.0780756i
$121$	−88.0342			−0.727555
$122$	19.0807	−	33.0487i	0.156399	−	0.270891i
$123$	−45.2558	+	188.211i	−0.367933	+	1.53017i
$124$	−114.633	−	66.1834i	−0.924459	−	0.533737i
$125$	−100.828			−0.806626
$126$	20.4048	−	39.9770i	0.161943	−	0.317278i
$127$	71.9227	−	124.574i	0.566320	−	0.980896i	−0.430605	−	0.902540i	$-0.641700\pi$
$127$	71.9227	−	124.574i	0.566320	−	0.980896i	0.996925	−	0.0783553i	$-0.0249669\pi$
$128$	125.031			0.976805
$129$	−90.8147	+	26.8657i	−0.703990	+	0.208261i
$130$	15.2353	−	11.1510i	0.117194	−	0.0857770i
$131$	−13.9215	−	8.03755i	−0.106271	−	0.0613554i	0.445923	−	0.895071i	$-0.352876\pi$
$131$	−13.9215	−	8.03755i	−0.106271	−	0.0613554i	−0.552193	+	0.833716i	$0.686209\pi$
$132$	44.7195	+	42.4672i	0.338784	+	0.321721i
$133$	−39.0785			−0.293823
$134$	38.4217	−	22.1828i	0.286729	−	0.165543i
$135$	20.1457	+	57.0817i	0.149227	+	0.422827i
$136$	−93.6270	+	54.0556i	−0.688434	+	0.397467i
$137$	77.7377	−	134.646i	0.567429	−	0.982815i	−0.429391	−	0.903119i	$-0.641272\pi$
$137$	77.7377	−	134.646i	0.567429	−	0.982815i	0.996819	−	0.0796963i	$-0.0253950\pi$
$138$	−43.4294	−	10.4427i	−0.314706	−	0.0756716i
$139$	−107.342			−0.772244			−0.386122	−	0.922448i	$-0.626186\pi$
$139$	−107.342			−0.772244			−0.386122	+	0.922448i	$0.626186\pi$
$140$	53.5164	−	30.8977i	0.382260	−	0.220698i
$141$	42.3691	−	176.206i	0.300490	−	1.24969i
$142$	−10.5777	−	18.3212i	−0.0744910	−	0.129022i
$143$	68.2938	+	30.1195i	0.477579	+	0.210626i
$144$	5.17676	+	100.130i	0.0359497	+	0.695349i
$145$	−50.1254	−	28.9399i	−0.345692	−	0.199586i
$146$			54.1503i			0.370893i
$147$	7.20076	−	29.9468i	0.0489848	−	0.203720i
$148$	−73.2425	−	42.2866i	−0.494882	−	0.285720i
$149$	59.6060			0.400040			0.200020	−	0.979792i	$-0.435899\pi$
$149$	59.6060			0.400040			0.200020	+	0.979792i	$0.435899\pi$
$150$	−9.07487	+	37.7409i	−0.0604991	+	0.251606i
$151$	35.0194	−	20.2185i	0.231917	−	0.133897i	−0.379539	−	0.925176i	$-0.623917\pi$
$151$	35.0194	−	20.2185i	0.231917	−	0.133897i	0.611456	+	0.791278i	$0.290584\pi$
$152$	−21.5869	+	12.4632i	−0.142019	+	0.0819947i
$153$	−107.801	−	166.255i	−0.704581	−	1.08664i
$154$	−24.7974	−	14.3168i	−0.161022	−	0.0929660i
$155$	−71.7805	+	41.4425i	−0.463100	+	0.267371i
$156$	53.8428	+	128.836i	0.345146	+	0.825870i
$157$	73.7338	−	127.711i	0.469642	−	0.813444i	−0.529756	−	0.848150i	$-0.677716\pi$
$157$	73.7338	−	127.711i	0.469642	−	0.813444i	0.999398	+	0.0347066i	$0.0110497\pi$
$158$	−29.8218	−	51.6529i	−0.188746	−	0.326917i
$159$	−89.8376	+	94.6022i	−0.565016	+	0.594982i
$160$	30.1079	−	52.1484i	0.188174	−	0.325927i
$161$	−176.944			−1.09903
$162$	52.1916	−	5.41110i	0.322170	−	0.0334018i
$163$	14.1821	−	8.18805i	0.0870069	−	0.0502334i	−0.455865	−	0.890049i	$-0.650670\pi$
$163$	14.1821	−	8.18805i	0.0870069	−	0.0502334i	0.542872	+	0.839815i	$0.317337\pi$
$164$	115.512	+	200.073i	0.704341	+	1.21995i
$165$	37.0305	−	10.9547i	0.224427	−	0.0663922i
$166$	−14.0108	−	24.2674i	−0.0844022	−	0.146189i
$167$	−124.666	−	215.929i	−0.746505	−	1.29299i	−0.949488	−	0.313803i	$-0.898397\pi$
$167$	−124.666	−	215.929i	−0.746505	−	1.29299i	0.202983	−	0.979182i	$-0.434936\pi$
$168$	−32.1720	−	108.752i	−0.191500	−	0.647332i
$169$	113.962	+	124.794i	0.674333	+	0.738428i
$170$			31.9745i			0.188086i
$171$	−24.8548	−	38.3323i	−0.145350	−	0.224165i
$172$	−56.5131	+	97.8836i	−0.328565	+	0.569091i
$173$	192.419	+	111.093i	1.11225	+	0.642158i	0.939411	−	0.342793i	$-0.111373\pi$
$173$	192.419	+	111.093i	1.11225	+	0.642158i	0.172839	+	0.984950i	$0.444706\pi$
$174$	−34.5490	+	36.3813i	−0.198557	+	0.209088i
$175$			153.767i			0.878671i
$176$	63.9638			0.363431
$177$	−125.802	−	119.466i	−0.710747	−	0.674950i
$178$	39.8403	−	69.0055i	0.223822	−	0.387671i
$179$	229.322	+	132.399i	1.28113	+	0.739660i	0.977055	−	0.212989i	$-0.0683198\pi$
$179$	229.322	+	132.399i	1.28113	+	0.739660i	0.304074	+	0.952649i	$0.401653\pi$
$180$	64.3455	+	32.8429i	0.357475	+	0.182460i
$181$	257.354			1.42185			0.710923	−	0.703270i	$-0.248277\pi$
$181$	257.354			1.42185			0.710923	+	0.703270i	$0.248277\pi$
$182$	−38.2909	−	52.3157i	−0.210390	−	0.287449i
$183$	169.469	−	50.1339i	0.926059	−	0.273956i
$184$	−97.7436	+	56.4323i	−0.531215	+	0.306697i
$185$	−45.8627	+	26.4789i	−0.247907	+	0.143129i
$186$	20.3814	+	68.8958i	0.109578	+	0.370408i
$187$	−109.473	+	63.2041i	−0.585415	+	0.337990i
$188$	−108.144	−	187.311i	−0.575233	−	0.996333i
$189$	196.010	−	69.1774i	1.03709	−	0.366018i
$190$			7.37213i			0.0388007i
$191$	−111.916	−	64.6149i	−0.585949	−	0.338298i	0.177545	−	0.984113i	$-0.443185\pi$
$191$	−111.916	−	64.6149i	−0.585949	−	0.338298i	−0.763494	+	0.645815i	$0.776518\pi$
$192$	59.0898	+	56.1137i	0.307759	+	0.292259i
$193$	7.42324	−	4.28581i	0.0384624	−	0.0222063i	−0.480646	−	0.876915i	$-0.659598\pi$
$193$	7.42324	−	4.28581i	0.0384624	−	0.0222063i	0.519108	+	0.854709i	$0.326264\pi$
$194$	75.6944	+	43.7022i	0.390178	+	0.225269i
$195$	86.7232	+	11.1388i	0.444734	+	0.0571220i
$196$	−18.3794	−	31.8340i	−0.0937724	−	0.162419i
$197$	−106.452	+	184.381i	−0.540367	+	0.935943i	0.458516	+	0.888686i	$0.348381\pi$
$197$	−106.452	+	184.381i	−0.540367	+	0.935943i	−0.998883	+	0.0472568i	$0.984952\pi$
$198$	−1.72832	−	33.4297i	−0.00872889	−	0.168837i
$199$	−117.959	−	204.310i	−0.592756	−	1.02668i	−0.993859	−	0.110651i	$-0.964706\pi$
$199$	−117.959	−	204.310i	−0.592756	−	1.02668i	0.401103	−	0.916033i	$-0.368627\pi$
$200$	49.0406	+	84.9409i	0.245203	+	0.424704i
$201$	199.768	+	48.0345i	0.993869	+	0.238978i
$202$			51.1817i			0.253375i
$203$	−99.3754	+	172.123i	−0.489534	+	0.847898i
$204$	−229.925	−	55.2859i	−1.12708	−	0.271009i
$205$	144.662			0.705667
$206$	−34.2098	+	59.2531i	−0.166067	+	0.287637i
$207$	−112.541	−	173.565i	−0.543675	−	0.838480i
$208$	132.511	+	58.4410i	0.637072	+	0.280967i
$209$	−25.2403	+	14.5725i	−0.120767	+	0.0697248i
$210$	−32.6124	−	7.84171i	−0.155297	−	0.0373415i
$211$	150.448	+	260.583i	0.713022	+	1.23499i	0.963718	+	0.266924i	$0.0860073\pi$
$211$	150.448	+	260.583i	0.713022	+	1.23499i	−0.250696	+	0.968066i	$0.580659\pi$
$212$			155.701i			0.734436i
$213$	22.9049	−	95.2579i	0.107535	−	0.447220i
$214$	−34.5416	−	19.9426i	−0.161409	−	0.0931898i
$215$	35.3872	+	61.2924i	0.164592	+	0.285081i
$216$	86.2131	−	100.726i	0.399135	−	0.466326i
$217$	142.307	+	246.484i	0.655795	+	1.13587i
$218$		−	65.4009i		−	0.300004i
$219$	−172.687	+	181.845i	−0.788523	+	0.830343i
$220$	23.0437	−	39.9129i	0.104744	−	0.181422i
$221$	−284.536	+	30.9164i	−1.28750	+	0.139893i
$222$	13.0223	+	44.0196i	0.0586591	+	0.198287i
$223$			26.8891i			0.120579i	0.998181	+	0.0602895i	$0.0192024\pi$
$223$			26.8891i			0.120579i	−0.998181	+	0.0602895i	$0.980798\pi$
$224$	−179.070	−	103.386i	−0.799419	−	0.461545i
$225$	−150.831	+	97.7998i	−0.670361	+	0.434666i
$226$			103.747i			0.459058i
$227$	169.916	−	294.303i	0.748529	−	1.29649i	−0.199999	−	0.979796i	$-0.564094\pi$
$227$	169.916	−	294.303i	0.748529	−	1.29649i	0.948528	−	0.316693i	$-0.102573\pi$
$228$	−53.0121	−	12.7469i	−0.232509	−	0.0559073i
$229$	26.7265	+	15.4306i	0.116710	+	0.0673824i	0.557218	−	0.830366i	$-0.311869\pi$
$229$	26.7265	+	15.4306i	0.116710	+	0.0673824i	−0.440509	+	0.897748i	$0.645202\pi$
$230$			33.3804i			0.145132i
$231$	−37.6169	−	127.157i	−0.162844	−	0.550464i
$232$			126.774i			0.546440i
$233$			38.5905i			0.165624i	0.996565	+	0.0828122i	$0.0263902\pi$
$233$			38.5905i			0.165624i	−0.996565	+	0.0828122i	$0.973610\pi$
$234$	26.9628	−	70.8338i	0.115226	−	0.302709i
$235$	−135.434			−0.576316
$236$	−207.051			−0.877334
$237$	64.5760	−	268.561i	0.272473	−	1.13317i
$238$	109.796			0.461327
$239$	−8.76046	+	15.1736i	−0.0366546	+	0.0634877i	−0.883771	−	0.467920i	$-0.845003\pi$
$239$	−8.76046	+	15.1736i	−0.0366546	+	0.0634877i	0.847116	+	0.531408i	$0.178337\pi$
$240$	71.8505	−	21.2555i	0.299377	−	0.0885646i
$241$	144.406	+	83.3729i	0.599196	+	0.345946i	0.768725	−	0.639579i	$-0.220891\pi$
$241$	144.406	+	83.3729i	0.599196	+	0.345946i	−0.169529	+	0.985525i	$0.554225\pi$
$242$	57.0281			0.235653
$243$	192.524	+	148.269i	0.792278	+	0.610160i
$244$	105.459	−	182.660i	0.432208	−	0.748607i
$245$	−23.0175			−0.0939489
$246$	29.3165	−	121.922i	0.119173	−	0.495619i
$247$	−65.6035	+	7.12817i	−0.265601	+	0.0288590i
$248$	157.221	+	90.7714i	0.633954	+	0.366014i
$249$	30.3388	−	126.174i	0.121843	−	0.506724i
$250$	65.3160			0.261264
$251$	323.798	−	186.945i	1.29003	−	0.744800i	0.311372	−	0.950288i	$-0.399212\pi$
$251$	323.798	−	186.945i	1.29003	−	0.744800i	0.978660	+	0.205488i	$0.0658783\pi$
$252$	112.778	−	220.953i	0.447530	−	0.876797i
$253$	−114.286	+	65.9830i	−0.451723	+	0.260802i
$254$	−46.5911	+	80.6982i	−0.183430	+	0.317709i
$255$	−101.968	+	107.375i	−0.399873	+	0.421080i
$256$	27.6567			0.108034
$257$	−404.597	+	233.594i	−1.57431	+	0.908926i	−0.578674	+	0.815559i	$0.696430\pi$
$257$	−404.597	+	233.594i	−1.57431	+	0.908926i	−0.995632	+	0.0933669i	$0.970237\pi$
$258$	58.8293	−	17.4034i	0.228020	−	0.0674552i
$259$	90.9246	+	157.486i	0.351060	+	0.608054i
$260$	84.2054	−	61.6317i	0.323867	−	0.237045i
$261$	−232.042	+	11.9966i	−0.889049	+	0.0459640i
$262$	9.01824	+	5.20668i	0.0344208	+	0.0198728i
$263$			421.902i			1.60419i	0.597197	+	0.802094i	$0.296281\pi$
$263$			421.902i			1.60419i	−0.597197	+	0.802094i	$0.703719\pi$
$264$	−61.3334	−	58.2444i	−0.232324	−	0.220623i
$265$	84.4340	+	48.7480i	0.318619	+	0.183955i
$266$	25.3148			0.0951685
$267$	353.850	−	104.679i	1.32528	−	0.392057i
$268$	212.357	−	122.604i	0.792377	−	0.457479i
$269$	49.9835	−	28.8580i	0.185812	−	0.107279i	−0.404208	−	0.914667i	$-0.632453\pi$
$269$	49.9835	−	28.8580i	0.185812	−	0.107279i	0.590021	+	0.807388i	$0.299120\pi$
$270$	−13.0503	−	36.9772i	−0.0483344	−	0.136953i
$271$	−108.778	−	62.8029i	−0.401394	−	0.231745i	0.285691	−	0.958322i	$-0.407777\pi$
$271$	−108.778	−	62.8029i	−0.401394	−	0.231745i	−0.687085	+	0.726577i	$0.741110\pi$
$272$	−212.411	+	122.635i	−0.780921	+	0.450865i
$273$	38.2490	−	297.795i	0.140106	−	1.09082i
$274$	−50.3581	+	87.2227i	−0.183789	+	0.318331i
$275$	57.3404	+	99.3165i	0.208510	+	0.361151i
$276$	−240.034	−	57.7167i	−0.869689	−	0.209119i
$277$	133.746	−	231.654i	0.482836	−	0.836296i	−0.516970	−	0.856004i	$-0.672940\pi$
$277$	133.746	−	231.654i	0.482836	−	0.836296i	0.999806	+	0.0197072i	$0.00627339\pi$
$278$	69.5355			0.250128
$279$	−151.266	+	296.360i	−0.542173	+	1.06222i
$280$	−73.3985	+	42.3767i	−0.262138	+	0.151345i
$281$	−156.646	−	271.319i	−0.557460	−	0.965550i	−0.997708	−	0.0676730i	$-0.978443\pi$
$281$	−156.646	−	271.319i	−0.557460	−	0.965550i	0.440247	−	0.897877i	$-0.354891\pi$
$282$	−27.4465	+	114.145i	−0.0973279	+	0.404771i
$283$	−112.665	−	195.141i	−0.398109	−	0.689544i	0.595384	−	0.803441i	$-0.297000\pi$
$283$	−112.665	−	195.141i	−0.398109	−	0.689544i	−0.993493	+	0.113897i	$0.963667\pi$
$284$	−58.4631	−	101.261i	−0.205856	−	0.356553i
$285$	−23.5099	+	24.7568i	−0.0824908	+	0.0868658i
$286$	−44.2403	−	19.5112i	−0.154686	−	0.0682211i
$287$		−	496.747i		−	1.73083i
$288$	−12.4808	−	241.407i	−0.0433360	−	0.838218i
$289$	97.8575	−	169.494i	0.338607	−	0.586485i
$290$	32.4710	+	18.7471i	0.111969	+	0.0646452i
$291$	114.826	+	388.150i	0.394592	+	1.33385i
$292$			299.289i			1.02496i
$293$	−129.915			−0.443397			−0.221698	−	0.975115i	$-0.571160\pi$
$293$	−129.915			−0.443397			−0.221698	+	0.975115i	$0.571160\pi$
$294$	−4.66461	+	19.3994i	−0.0158660	+	0.0659842i
$295$	−64.8252	+	112.281i	−0.219747	+	0.380612i
$296$	100.453	+	57.9966i	0.339369	+	0.195935i
$297$	100.804	−	117.774i	0.339407	−	0.396544i
$298$	−38.6124			−0.129572
$299$	−297.047	+	32.2758i	−0.993468	+	0.107946i
$300$	−50.1568	+	208.594i	−0.167189	+	0.695313i
$301$	210.469	−	121.515i	0.699234	−	0.403703i
$302$	−22.6854	+	13.0974i	−0.0751172	+	0.0433690i
$303$	−163.220	+	171.876i	−0.538678	+	0.567248i
$304$	−48.9739	+	28.2751i	−0.161098	+	0.0930103i
$305$	−66.0359	−	114.377i	−0.216511	−	0.375008i
$306$	69.8328	+	107.699i	0.228212	+	0.351959i
$307$		−	204.231i		−	0.665247i	−0.943060	−	0.332623i	$-0.892066\pi$
$307$		−	204.231i		−	0.665247i	0.943060	−	0.332623i	$-0.107934\pi$
$308$	−137.055	−	79.1288i	−0.444984	−	0.256912i
$309$	−303.841	+	89.8853i	−0.983305	+	0.290891i
$310$	46.4990	−	26.8462i	0.149997	−	0.0866007i
$311$	190.711	+	110.107i	0.613218	+	0.354042i	0.774224	−	0.632912i	$-0.218140\pi$
$311$	190.711	+	110.107i	0.613218	+	0.354042i	−0.161006	+	0.986954i	$0.551474\pi$
$312$	−73.8462	−	176.700i	−0.236687	−	0.566346i
$313$	−188.296	−	326.139i	−0.601586	−	1.04198i	−0.992581	−	0.121585i	$-0.961202\pi$
$313$	−188.296	−	326.139i	−0.601586	−	1.04198i	0.390995	−	0.920393i	$-0.372131\pi$
$314$	−47.7643	+	82.7303i	−0.152116	+	0.263472i
$315$	−84.5101	−	130.335i	−0.268286	−	0.413763i
$316$	−164.825	−	285.486i	−0.521599	−	0.903436i
$317$	−184.898	−	320.252i	−0.583273	−	1.01026i	−0.995088	−	0.0989912i	$-0.968438\pi$
$317$	−184.898	−	320.252i	−0.583273	−	1.01026i	0.411815	−	0.911267i	$-0.364895\pi$
$318$	58.1963	−	61.2828i	0.183007	−	0.192713i
$319$			148.230i			0.464670i
$320$	30.4487	−	52.7386i	0.0951521	−	0.164808i
$321$	−52.3987	−	177.124i	−0.163236	−	0.551789i
$322$	114.623			0.355973
$323$	55.8786	−	96.7845i	0.172999	−	0.299642i
$324$	288.463	−	29.9072i	0.890318	−	0.0923060i
$325$	28.0482	+	258.139i	0.0863021	+	0.794274i
$326$	−9.18710	+	5.30417i	−0.0281813	+	0.0162705i
$327$	208.565	−	219.626i	0.637813	−	0.671640i
$328$	−158.426	−	274.402i	−0.483007	−	0.836593i
$329$			465.062i			1.41356i
$330$	−23.9881	+	7.09640i	−0.0726913	+	0.0215043i
$331$	−530.242	−	306.135i	−1.60194	−	0.924879i	−0.991099	−	0.133124i	$-0.957499\pi$
$331$	−530.242	−	306.135i	−1.60194	−	0.924879i	−0.610839	−	0.791755i	$-0.709168\pi$
$332$	−77.4376	−	134.126i	−0.233246	−	0.403993i
$333$	−96.6487	+	189.353i	−0.290236	+	0.568628i
$334$	80.7582	+	139.877i	0.241791	+	0.418794i
$335$		−	153.544i		−	0.458340i
$336$	−72.9883	−	246.724i	−0.217227	−	0.734298i
$337$	−145.011	+	251.166i	−0.430300	+	0.745301i	−0.996899	−	0.0786925i	$-0.974925\pi$
$337$	−145.011	+	251.166i	−0.430300	+	0.745301i	0.566599	+	0.823994i	$0.308259\pi$
$338$	−73.8241	−	80.8411i	−0.218414	−	0.239175i
$339$	−330.852	+	348.399i	−0.975965	+	1.02773i
$340$			176.723i			0.519775i
$341$	183.829	+	106.134i	0.539088	+	0.311243i
$342$	16.1008	+	24.8314i	0.0470785	+	0.0726066i
$343$		−	298.187i		−	0.869351i
$344$	77.5086	−	134.249i	0.225316	−	0.390258i
$345$	−106.451	+	112.097i	−0.308553	+	0.324917i
$346$	−124.648	−	71.9656i	−0.360255	−	0.207993i
$347$			201.861i			0.581731i	0.956764	+	0.290865i	$0.0939432\pi$
$347$			201.861i			0.581731i	−0.956764	+	0.290865i	$0.906057\pi$
$348$	−190.952	+	201.080i	−0.548714	+	0.577815i
$349$			246.453i			0.706170i	0.935591	+	0.353085i	$0.114867\pi$
$349$			246.453i			0.706170i	−0.935591	+	0.353085i	$0.885133\pi$
$350$		−	99.6097i		−	0.284599i
$351$	316.436	−	151.886i	0.901527	−	0.432724i
$352$	−154.212			−0.438102
$353$	474.422			1.34397			0.671986	−	0.740564i	$-0.265442\pi$
$353$	474.422			1.34397			0.671986	+	0.740564i	$0.265442\pi$
$354$	81.4940	+	77.3896i	0.230209	+	0.218615i
$355$	−73.2164			−0.206244
$356$	220.198	−	381.393i	0.618533	−	1.07133i
$357$	368.712	+	350.142i	1.03281	+	0.980789i
$358$	−148.554	−	85.7674i	−0.414954	−	0.239574i
$359$	604.660			1.68429			0.842145	−	0.539251i	$-0.181293\pi$
$359$	604.660			1.68429			0.842145	+	0.539251i	$0.181293\pi$
$360$	−88.2507	−	45.0444i	−0.245141	−	0.125123i
$361$	−167.616	+	290.320i	−0.464312	+	0.804211i
$362$	−166.713			−0.460532
$363$	191.509	+	181.864i	0.527573	+	0.501002i
$364$	−211.634	−	289.149i	−0.581412	−	0.794365i
$365$	162.300	+	93.7039i	0.444657	+	0.256723i
$366$	−109.781	+	32.4765i	−0.299948	+	0.0887335i
$367$	255.113			0.695130			0.347565	−	0.937656i	$-0.387009\pi$
$367$	255.113			0.695130			0.347565	+	0.937656i	$0.387009\pi$
$368$	−221.750	+	128.027i	−0.602581	+	0.347900i
$369$	487.262	−	315.943i	1.32049	−	0.856215i
$370$	29.7096	−	17.1529i	0.0802963	−	0.0463591i
$371$	167.394	−	289.934i	0.451196	−	0.781494i
$372$	112.648	+	380.787i	0.302818	+	1.02362i
$373$	540.794			1.44985			0.724925	−	0.688828i	$-0.241875\pi$
$373$	540.794			1.44985			0.724925	+	0.688828i	$0.241875\pi$
$374$	70.9158	−	40.9433i	0.189614	−	0.109474i
$375$	219.341	+	208.294i	0.584910	+	0.555451i
$376$	148.321	+	256.899i	0.394470	+	0.683243i
$377$	−135.431	+	307.081i	−0.359234	+	0.814538i
$378$	−126.974	+	44.8128i	−0.335911	+	0.118552i
$379$	398.751	+	230.219i	1.05211	+	0.607438i	0.923241	−	0.384223i	$-0.125530\pi$
$379$	398.751	+	230.219i	1.05211	+	0.607438i	0.128874	+	0.991661i	$0.458864\pi$
$380$			40.7458i			0.107226i
$381$	−413.809	+	122.417i	−1.08611	+	0.321304i
$382$	72.4988	+	41.8572i	0.189787	+	0.109574i
$383$	305.536			0.797744			0.398872	−	0.917007i	$-0.369402\pi$
$383$	305.536			0.797744			0.398872	+	0.917007i	$0.369402\pi$
$384$	−271.992	−	258.293i	−0.708312	−	0.672638i
$385$	−85.8207	+	49.5486i	−0.222911	+	0.128698i
$386$	−4.80873	+	2.77632i	−0.0124579	+	0.00719255i
$387$	253.058	+	129.164i	0.653896	+	0.333758i
$388$	418.363	+	241.542i	1.07826	+	0.622531i
$389$	−457.448	+	264.108i	−1.17596	+	0.678940i	−0.955076	−	0.296360i	$-0.904227\pi$
$389$	−457.448	+	264.108i	−1.17596	+	0.678940i	−0.220883	+	0.975300i	$0.570894\pi$
$390$	−56.1788	−	7.21565i	−0.144048	−	0.0185017i
$391$	253.013	−	438.232i	0.647093	−	1.12080i
$392$	25.2076	+	43.6608i	0.0643051	+	0.111380i
$393$	13.6804	+	46.2442i	0.0348102	+	0.117670i
$394$	68.9592	−	119.441i	0.175023	−	0.303149i
$395$	−206.420			−0.522581
$396$	−9.55244	−	184.766i	−0.0241223	−	0.466580i
$397$	−309.236	+	178.537i	−0.778932	+	0.449717i	−0.836052	−	0.548651i	$-0.815142\pi$
$397$	−309.236	+	178.537i	−0.778932	+	0.449717i	0.0571197	+	0.998367i	$0.481808\pi$
$398$	76.4129	+	132.351i	0.191992	+	0.332540i
$399$	85.0111	+	80.7295i	0.213060	+	0.202330i
$400$	111.258	+	192.704i	0.278145	+	0.481761i
$401$	210.006	+	363.741i	0.523706	+	0.907086i	0.999619	+	0.0275933i	$0.00878435\pi$
$401$	210.006	+	363.741i	0.523706	+	0.907086i	−0.475913	+	0.879492i	$0.657882\pi$
$402$	−129.408	−	31.1165i	−0.321911	−	0.0774042i
$403$	283.860	+	387.830i	0.704368	+	0.962356i
$404$			282.881i			0.700201i
$405$	74.0962	−	165.793i	0.182954	−	0.409365i
$406$	64.3749	−	111.501i	0.158559	−	0.274632i
$407$	117.454	+	67.8121i	0.288585	+	0.166615i
$408$	315.345	+	75.8254i	0.772905	+	0.185847i
$409$		−	467.696i		−	1.14351i	−0.820424	−	0.571756i	$-0.806262\pi$
$409$		−	467.696i		−	1.14351i	0.820424	−	0.571756i	$-0.193738\pi$
$410$	−93.7111			−0.228564
$411$	−447.265	+	132.314i	−1.08824	+	0.321933i
$412$	−189.078	+	327.492i	−0.458926	+	0.794884i
$413$	385.555	+	222.600i	0.933548	+	0.538984i
$414$	72.9032	+	112.435i	0.176095	+	0.271581i
$415$	−96.9792			−0.233685
$416$	−319.474	−	140.897i	−0.767967	−	0.338695i
$417$	233.511	+	221.750i	0.559978	+	0.531775i
$418$	16.3505	−	9.43998i	0.0391161	−	0.0225837i
$419$	550.949	−	318.091i	1.31492	−	0.759167i	0.332009	−	0.943276i	$-0.392273\pi$
$419$	550.949	−	318.091i	1.31492	−	0.759167i	0.982906	+	0.184110i	$0.0589401\pi$
$420$	−180.249	−	43.3412i	−0.429164	−	0.103193i
$421$	−327.040	+	188.817i	−0.776817	+	0.448495i	−0.835301	−	0.549793i	$-0.814707\pi$
$421$	−327.040	+	188.817i	−0.776817	+	0.448495i	0.0584843	+	0.998288i	$0.481373\pi$
$422$	−97.4591	−	168.804i	−0.230946	−	0.400010i
$423$	−456.181	+	295.790i	−1.07844	+	0.699268i
$424$		−	213.545i		−	0.503645i
$425$	−380.831	−	219.873i	−0.896074	−	0.517348i
$426$	−14.8377	+	61.7075i	−0.0348303	+	0.144853i
$427$	−392.756	+	226.758i	−0.919802	+	0.531048i
$428$	−190.912	−	110.223i	−0.446055	−	0.257530i
$429$	−86.3441	−	206.605i	−0.201268	−	0.481597i
$430$	−22.9236	−	39.7049i	−0.0533108	−	0.0923370i
$431$	80.2210	−	138.947i	0.186128	−	0.322382i	−0.757828	−	0.652454i	$-0.773740\pi$
$431$	80.2210	−	138.947i	0.186128	−	0.322382i	0.943956	+	0.330072i	$0.107073\pi$
$432$	195.591	−	228.517i	0.452756	−	0.528975i
$433$	−145.742	−	252.433i	−0.336587	−	0.582986i	0.647201	−	0.762319i	$-0.275939\pi$
$433$	−145.742	−	252.433i	−0.336587	−	0.582986i	−0.983788	+	0.179333i	$0.942606\pi$
$434$	−92.1860	−	159.671i	−0.212410	−	0.367905i
$435$	49.2575	+	166.506i	0.113236	+	0.382773i
$436$		−	361.471i		−	0.829062i
$437$	58.3354	−	101.040i	0.133491	−	0.231213i
$438$	111.865	−	117.798i	0.255401	−	0.268946i
$439$	−502.680			−1.14506			−0.572528	−	0.819885i	$-0.694037\pi$
$439$	−502.680			−1.14506			−0.572528	+	0.819885i	$0.694037\pi$
$440$	−31.6048	+	54.7411i	−0.0718291	+	0.124412i
$441$	−77.5295	+	50.2705i	−0.175804	+	0.113992i
$442$	184.321	−	20.0275i	0.417016	−	0.0453111i
$443$	646.203	−	373.086i	1.45870	−	0.842180i	0.459750	−	0.888048i	$-0.347939\pi$
$443$	646.203	−	373.086i	1.45870	−	0.842180i	0.998947	+	0.0458685i	$0.0146055\pi$
$444$	71.9744	+	243.297i	0.162104	+	0.547965i
$445$	−137.883	−	238.820i	−0.309848	−	0.536673i
$446$		−	17.4186i		−	0.0390552i
$447$	−129.667	−	123.136i	−0.290082	−	0.275472i
$448$	−181.097	−	104.556i	−0.404234	−	0.233385i
$449$	155.690	+	269.663i	0.346749	+	0.600586i	0.985670	−	0.168686i	$-0.0539524\pi$
$449$	155.690	+	269.663i	0.346749	+	0.600586i	−0.638921	+	0.769272i	$0.720619\pi$
$450$	97.7077	−	63.3541i	0.217128	−	0.140787i
$451$	−185.239	−	320.843i	−0.410729	−	0.711403i
$452$			573.411i			1.26861i
$453$	−117.949	−	28.3611i	−0.260373	−	0.0626072i
$454$	−110.071	+	190.648i	−0.242446	+	0.419929i
$455$	−223.061	+	24.2368i	−0.490245	+	0.0532677i
$456$	72.7068	+	17.4825i	0.159445	+	0.0383388i
$457$		−	320.928i		−	0.702249i	−0.936329	−	0.351124i	$-0.885799\pi$
$457$		−	320.928i		−	0.702249i	0.936329	−	0.351124i	$-0.114201\pi$
$458$	−17.3133	−	9.99584i	−0.0378020	−	0.0218250i
$459$	−108.946	+	584.370i	−0.237356	+	1.27314i
$460$			184.494i			0.401073i
$461$	424.984	−	736.094i	0.921874	−	1.59673i	0.125362	−	0.992111i	$-0.459991\pi$
$461$	424.984	−	736.094i	0.921874	−	1.59673i	0.796512	−	0.604622i	$-0.206676\pi$
$462$	24.3680	+	82.3718i	0.0527446	+	0.178294i
$463$	−623.614	−	360.044i	−1.34690	−	0.777632i	−0.359089	−	0.933303i	$-0.616913\pi$
$463$	−623.614	−	360.044i	−1.34690	−	0.777632i	−0.987809	+	0.155672i	$0.950246\pi$
$464$			287.611i			0.619852i
$465$	241.764	+	58.1326i	0.519923	+	0.125016i
$466$		−	24.9987i		−	0.0536453i
$467$		−	343.897i		−	0.736397i	−0.929747	−	0.368199i	$-0.879975\pi$
$467$		−	343.897i		−	0.736397i	0.929747	−	0.368199i	$-0.120025\pi$
$468$	149.023	−	391.499i	0.318426	−	0.836536i
$469$	−527.248			−1.12420
$470$	87.7336			0.186667
$471$	−424.229	+	125.499i	−0.900698	+	0.266453i
$472$	283.973			0.601638
$473$	90.6263	−	156.969i	0.191599	−	0.331859i
$474$	−41.8320	+	173.972i	−0.0882531	+	0.367030i
$475$	−87.8054	−	50.6945i	−0.184854	−	0.106725i
$476$	606.842			1.27488
$477$	390.864	−	20.2078i	0.819422	−	0.0423643i
$478$	5.67498	−	9.82935i	0.0118723	−	0.0205635i
$479$	−77.8918			−0.162613			−0.0813067	−	0.996689i	$-0.525909\pi$
$479$	−77.8918			−0.162613			−0.0813067	+	0.996689i	$0.525909\pi$
$480$	−173.226	+	51.2455i	−0.360888	+	0.106761i
$481$	181.367	+	247.796i	0.377063	+	0.515169i
$482$	−93.5455	−	54.0085i	−0.194078	−	0.112051i
$483$	384.923	+	365.537i	0.796942	+	0.756805i
$484$	315.194			0.651228
$485$	261.969	−	151.248i	0.540143	−	0.311852i
$486$	−124.716	−	96.0478i	−0.256617	−	0.197629i
$487$	−668.979	+	386.235i	−1.37367	+	0.793090i	−0.991388	−	0.130954i	$-0.958196\pi$
$487$	−668.979	+	386.235i	−1.37367	+	0.793090i	−0.382284	+	0.924045i	$0.624863\pi$
$488$	−144.638	+	250.521i	−0.296390	+	0.513363i
$489$	−47.7668	−	11.4856i	−0.0976827	−	0.0234880i
$490$	14.9106			0.0304298
$491$	−173.404	+	100.115i	−0.353166	+	0.203900i	−0.666079	−	0.745881i	$-0.732029\pi$
$491$	−173.404	+	100.115i	−0.353166	+	0.203900i	0.312913	+	0.949782i	$0.398695\pi$
$492$	162.032	−	673.865i	0.329334	−	1.36964i
$493$	−284.195	−	492.240i	−0.576461	−	0.998459i
$494$	42.4976	−	4.61759i	0.0860275	−	0.00934735i
$495$	−103.186	−	52.6679i	−0.208457	−	0.106400i
$496$	356.685	+	205.932i	0.719123	+	0.415186i
$497$			251.415i			0.505864i
$498$	−19.6533	+	81.7350i	−0.0394645	+	0.164126i
$499$	−150.607	−	86.9531i	−0.301818	−	0.174255i	0.341441	−	0.939903i	$-0.389085\pi$
$499$	−150.607	−	86.9531i	−0.301818	−	0.174255i	−0.643259	+	0.765648i	$0.722418\pi$
$500$	361.002			0.722004
$501$	−174.873	+	727.269i	−0.349049	+	1.45164i
$502$	−209.754	+	121.102i	−0.417838	+	0.241239i
$503$	200.679	−	115.862i	0.398965	−	0.230342i	−0.287073	−	0.957909i	$-0.592682\pi$
$503$	200.679	−	115.862i	0.398965	−	0.230342i	0.686037	+	0.727567i	$0.259349\pi$
$504$	−154.676	+	303.040i	−0.306897	+	0.601270i
$505$	153.402	+	88.5668i	0.303767	+	0.175380i
$506$	74.0338	−	42.7434i	0.146312	−	0.0844732i
$507$	9.89123	−	506.904i	0.0195093	−	0.999810i
$508$	−257.509	+	446.019i	−0.506908	+	0.877991i
$509$	−231.172	−	400.401i	−0.454168	−	0.786643i	0.544472	−	0.838779i	$-0.316730\pi$
$509$	−231.172	−	400.401i	−0.454168	−	0.786643i	−0.998640	+	0.0521366i	$0.983397\pi$
$510$	66.0540	−	69.5572i	0.129518	−	0.136387i
$511$	321.766	−	557.314i	0.629678	−	1.09063i
$512$	−518.040			−1.01180
$513$	−25.1190	+	134.734i	−0.0489648	+	0.262639i
$514$	262.095	−	151.321i	0.509913	−	0.294399i
$515$	118.396	+	205.068i	0.229895	+	0.398190i
$516$	325.149	−	96.1889i	0.630135	−	0.186413i
$517$	173.423	+	300.377i	0.335441	+	0.581001i
$518$	−58.9004	−	102.019i	−0.113707	−	0.196947i
$519$	−189.088	−	639.177i	−0.364331	−	1.23156i
$520$	−115.489	+	84.5287i	−0.222094	+	0.162555i
$521$			287.109i			0.551073i	0.961291	+	0.275537i	$0.0888556\pi$
$521$			287.109i			0.551073i	−0.961291	+	0.275537i	$0.911144\pi$
$522$	150.315	−	7.77134i	0.287961	−	0.0148876i
$523$	168.686	−	292.173i	0.322536	−	0.558648i	−0.658475	−	0.752603i	$-0.728798\pi$
$523$	168.686	−	292.173i	0.322536	−	0.558648i	0.981011	+	0.193954i	$0.0621314\pi$
$524$	49.8438	+	28.7774i	0.0951218	+	0.0549186i
$525$	317.658	−	334.505i	0.605062	−	0.637152i
$526$		−	273.306i		−	0.519592i
$527$	−813.945			−1.54449
$528$	−139.146	−	132.138i	−0.263535	−	0.250262i
$529$	−0.362121	+	0.627212i	−0.000684539	+	0.00118566i
$530$	−54.6959	−	31.5787i	−0.103200	−	0.0595824i
$531$	26.8723	+	519.772i	0.0506070	+	0.978856i
$532$	139.915			0.262998
$533$	−90.6100	−	833.921i	−0.170000	−	1.56458i
$534$	−229.222	+	67.8107i	−0.429255	+	0.126986i
$535$	−119.544	+	69.0190i	−0.223447	+	0.129007i
$536$	−291.251	+	168.154i	−0.543378	+	0.313720i
$537$	−225.351	−	761.761i	−0.419649	−	1.41855i
$538$	−32.3790	+	18.6940i	−0.0601841	+	0.0347473i
$539$	29.4738	+	51.0501i	0.0546823	+	0.0947126i
$540$	−72.1289	−	204.373i	−0.133572	−	0.378469i
$541$		−	360.339i		−	0.666061i	−0.942916	−	0.333030i	$-0.891929\pi$
$541$		−	360.339i		−	0.666061i	0.942916	−	0.333030i	$-0.108071\pi$
$542$	70.4657	+	40.6834i	0.130011	+	0.0750616i
$543$	−559.847	−	531.650i	−1.03103	−	0.979098i
$544$	512.106	−	295.665i	0.941372	−	0.543501i
$545$	−196.020	−	113.172i	−0.359670	−	0.207656i
$546$	−24.7775	+	192.910i	−0.0453800	+	0.353315i
$547$	−70.4259	−	121.981i	−0.128749	−	0.223000i	0.794443	−	0.607339i	$-0.207763\pi$
$547$	−70.4259	−	121.981i	−0.128749	−	0.223000i	−0.923192	+	0.384338i	$0.874430\pi$
$548$	−278.329	+	482.080i	−0.507900	+	0.879709i
$549$	−472.230	−	241.033i	−0.860163	−	0.439040i
$550$	−37.1448	−	64.3367i	−0.0675360	−	0.116976i
$551$	−65.5247	−	113.492i	−0.118920	−	0.205975i
$552$	329.210	+	79.1593i	0.596396	+	0.143405i
$553$			708.815i			1.28176i
$554$	−86.6397	+	150.064i	−0.156389	+	0.270874i
$555$	154.470	+	37.1427i	0.278325	+	0.0669238i
$556$	384.323			0.691228
$557$	113.068	−	195.839i	0.202994	−	0.351596i	−0.746498	−	0.665388i	$-0.768266\pi$
$557$	113.068	−	195.839i	0.202994	−	0.351596i	0.949492	+	0.313792i	$0.101599\pi$
$558$	97.9895	−	191.980i	0.175608	−	0.344050i
$559$	331.163	−	242.385i	0.592420	−	0.433605i
$560$	−166.518	+	96.1395i	−0.297354	+	0.171678i
$561$	368.715	+	88.6583i	0.657246	+	0.158036i
$562$	101.475	+	175.759i	0.180560	+	0.312739i
$563$		−	300.947i		−	0.534541i	−0.963622	−	0.267271i	$-0.913878\pi$
$563$		−	300.947i		−	0.534541i	0.963622	−	0.267271i	$-0.0861217\pi$
$564$	−151.697	+	630.881i	−0.268966	+	1.11858i
$565$	310.952	+	179.528i	0.550358	+	0.317749i
$566$	72.9836	+	126.411i	0.128946	+	0.223341i
$567$	−569.308	−	254.436i	−1.00407	−	0.448740i
$568$	80.1830	+	138.881i	0.141167	+	0.244509i
$569$			742.301i			1.30457i	0.757973	+	0.652286i	$0.226190\pi$
$569$			742.301i			1.30457i	−0.757973	+	0.652286i	$0.773810\pi$
$570$	15.2296	−	16.0373i	0.0267186	−	0.0281356i
$571$	−89.6525	+	155.283i	−0.157010	+	0.271949i	−0.933789	−	0.357824i	$-0.883519\pi$
$571$	−89.6525	+	155.283i	−0.157010	+	0.271949i	0.776779	+	0.629773i	$0.216852\pi$
$572$	−244.516	−	107.839i	−0.427476	−	0.188529i
$573$	109.979	+	371.763i	0.191935	+	0.648801i
$574$			321.790i			0.560610i
$575$	−397.576	−	229.540i	−0.691436	−	0.399201i
$576$	−12.6220	−	244.139i	−0.0219133	−	0.423853i
$577$			617.248i			1.06975i	0.844930	+	0.534877i	$0.179642\pi$
$577$			617.248i			1.06975i	−0.844930	+	0.534877i	$0.820358\pi$
$578$	−63.3915	+	109.797i	−0.109674	+	0.189961i
$579$	−25.0022	−	6.01184i	−0.0431818	−	0.0103831i
$580$	179.467	+	103.615i	0.309426	+	0.178647i
$581$			333.012i			0.573171i
$582$	−74.3839	−	251.441i	−0.127807	−	0.432030i
$583$		−	249.686i		−	0.428279i
$584$		−	410.479i		−	0.702875i
$585$	−165.646	−	203.387i	−0.283156	−	0.347670i
$586$	84.1584			0.143615
$587$	130.136			0.221696			0.110848	−	0.993837i	$-0.464643\pi$
$587$	130.136			0.221696			0.110848	+	0.993837i	$0.464643\pi$
$588$	−25.7813	+	107.220i	−0.0438458	+	0.182347i
$589$	−187.665			−0.318617
$590$	41.9934	−	72.7348i	0.0711753	−	0.123279i
$591$	612.475	−	181.188i	1.03634	−	0.306579i
$592$	227.897	+	131.576i	0.384961	+	0.222257i
$593$	−1124.97			−1.89708			−0.948542	−	0.316652i	$-0.897441\pi$
$593$	−1124.97			−1.89708			−0.948542	+	0.316652i	$0.897441\pi$
$594$	−65.3003	+	76.2931i	−0.109933	+	0.128440i
$595$	189.995	−	329.081i	0.319320	−	0.553078i
$596$	−213.411			−0.358072
$597$	−165.464	+	688.137i	−0.277159	+	1.15266i
$598$	192.425	−	20.9081i	0.321782	−	0.0349633i
$599$	148.057	+	85.4805i	0.247173	+	0.142705i	0.618469	−	0.785809i	$-0.287753\pi$
$599$	148.057	+	85.4805i	0.247173	+	0.142705i	−0.371296	+	0.928514i	$0.621087\pi$
$600$	68.7908	−	286.090i	0.114651	−	0.476816i
$601$	446.842			0.743497			0.371749	−	0.928333i	$-0.378758\pi$
$601$	446.842			0.743497			0.371749	+	0.928333i	$0.378758\pi$
$602$	−136.341	+	78.7164i	−0.226480	+	0.130758i
$603$	−335.342	−	517.180i	−0.556123	−	0.857678i
$604$	−125.382	+	72.3895i	−0.207587	+	0.119850i
$605$	98.6836	−	170.925i	0.163113	−	0.282521i
$606$	105.733	−	111.340i	0.174476	−	0.183730i
$607$	272.164			0.448375			0.224187	−	0.974546i	$-0.428027\pi$
$607$	272.164			0.448375			0.224187	+	0.974546i	$0.428027\pi$
$608$	118.073	−	68.1692i	0.194198	−	0.112120i
$609$	571.758	−	169.143i	0.938848	−	0.277739i
$610$	42.7777	+	74.0931i	0.0701273	+	0.121464i
$611$	84.8303	+	780.728i	0.138838	+	1.27779i
$612$	385.966	+	595.255i	0.630664	+	0.972639i
$613$	799.594	+	461.646i	1.30440	+	0.753093i	0.981155	−	0.193224i	$-0.0618943\pi$
$613$	799.594	+	461.646i	1.30440	+	0.753093i	0.323241	+	0.946317i	$0.395228\pi$
$614$			132.300i			0.215472i
$615$	−314.696	−	298.847i	−0.511701	−	0.485930i
$616$	187.973	+	108.526i	0.305151	+	0.176179i
$617$	−139.569			−0.226205			−0.113103	−	0.993583i	$-0.536079\pi$
$617$	−139.569			−0.226205			−0.113103	+	0.993583i	$0.536079\pi$
$618$	196.827	−	58.2272i	0.318490	−	0.0942188i
$619$	752.471	−	434.439i	1.21562	−	0.701840i	0.251644	−	0.967820i	$-0.419029\pi$
$619$	752.471	−	434.439i	1.21562	−	0.701840i	0.963979	+	0.265979i	$0.0856953\pi$
$620$	257.000	−	148.379i	0.414516	−	0.239321i
$621$	−113.737	+	610.063i	−0.183151	+	0.982388i
$622$	−123.542	−	71.3267i	−0.198620	−	0.114673i
$623$	−820.072	+	473.469i	−1.31633	+	0.759982i
$624$	−167.534	−	400.878i	−0.268484	−	0.642432i
$625$	−136.646	+	236.678i	−0.218633	+	0.378684i
$626$	121.977	+	211.271i	0.194852	+	0.337494i
$627$	85.0119	+	20.4413i	0.135585	+	0.0326017i
$628$	−263.994	+	457.250i	−0.420372	+	0.728106i
$629$	−520.054			−0.826796
$630$	54.7452	+	84.4305i	0.0868971	+	0.134017i
$631$	−583.132	+	336.671i	−0.924139	+	0.533552i	−0.884953	−	0.465680i	$-0.845810\pi$
$631$	−583.132	+	336.671i	−0.924139	+	0.533552i	−0.0391857	+	0.999232i	$0.512476\pi$
$632$	226.060	+	391.548i	0.357690	+	0.619538i
$633$	211.037	−	877.670i	0.333392	−	1.38652i
$634$	119.776	+	207.457i	0.188921	+	0.327220i
$635$	161.246	+	279.287i	0.253931	+	0.439822i
$636$	321.651	−	338.710i	0.505741	−	0.532563i
$637$	14.4172	+	132.687i	0.0226329	+	0.208300i
$638$		−	96.0224i		−	0.150505i
$639$	−246.614	+	159.906i	−0.385937	+	0.250244i
$640$	−140.156	+	242.757i	−0.218994	+	0.379308i
$641$	908.387	+	524.458i	1.41714	+	0.818187i	0.996047	−	0.0888301i	$-0.0283128\pi$
$641$	908.387	+	524.458i	1.41714	+	0.818187i	0.421094	+	0.907017i	$0.361646\pi$
$642$	33.9436	+	114.740i	0.0528716	+	0.178723i
$643$			445.890i			0.693452i	0.937966	+	0.346726i	$0.112707\pi$
$643$			445.890i			0.693452i	−0.937966	+	0.346726i	$0.887293\pi$
$644$	633.524			0.983733
$645$	49.6387	−	206.439i	0.0769593	−	0.320061i
$646$	−36.1978	+	62.6965i	−0.0560338	+	0.0970534i
$647$	−794.602	−	458.764i	−1.22813	−	0.709063i	−0.261494	−	0.965205i	$-0.584215\pi$
$647$	−794.602	−	458.764i	−1.22813	−	0.709063i	−0.966639	+	0.256143i	$0.917548\pi$
$648$	−395.631	+	41.0181i	−0.610542	+	0.0632995i
$649$	332.034			0.511608
$650$	−18.1695	−	167.221i	−0.0279530	−	0.257263i
$651$	199.619	−	830.182i	0.306634	−	1.27524i
$652$	−50.7771	+	29.3162i	−0.0778790	+	0.0449635i
$653$	87.8939	−	50.7455i	0.134600	−	0.0777114i	−0.431188	−	0.902262i	$-0.641905\pi$
$653$	87.8939	−	50.7455i	0.134600	−	0.0777114i	0.565788	+	0.824551i	$0.308572\pi$
$654$	−135.107	+	142.273i	−0.206586	+	0.217542i
$655$	31.2110	−	18.0197i	0.0476504	−	0.0275110i
$656$	−359.420	−	622.534i	−0.547897	−	0.948985i
$657$	751.323	−	38.8436i	1.14357	−	0.0591226i
$658$		−	301.264i		−	0.457849i
$659$	291.018	+	168.019i	0.441605	+	0.254961i	0.704278	−	0.709924i	$-0.251271\pi$
$659$	291.018	+	168.019i	0.441605	+	0.254961i	−0.262673	+	0.964885i	$0.584604\pi$
$660$	−132.582	+	39.2218i	−0.200883	+	0.0594270i
$661$	−296.691	+	171.295i	−0.448852	+	0.259145i	−0.707345	−	0.706868i	$-0.750107\pi$
$661$	−296.691	+	171.295i	−0.448852	+	0.259145i	0.258493	+	0.966013i	$0.416774\pi$
$662$	343.488	+	198.313i	0.518863	+	0.299566i
$663$	682.847	+	520.549i	1.02994	+	0.785142i
$664$	106.207	+	183.955i	0.159950	+	0.277041i
$665$	43.8058	−	75.8738i	0.0658733	−	0.114096i
$666$	62.6085	−	122.662i	0.0940067	−	0.184177i
$667$	−296.691	−	513.883i	−0.444813	−	0.770439i
$668$	446.351	+	773.102i	0.668190	+	1.15734i
$669$	55.5484	−	58.4944i	0.0830319	−	0.0874356i
$670$			99.4650i			0.148455i
$671$	−169.117	+	292.920i	−0.252038	+	0.436542i
$672$	175.970	+	594.834i	0.261859	+	0.885169i
$673$	681.482			1.01260			0.506301	−	0.862357i	$-0.331012\pi$
$673$	681.482			1.01260			0.506301	+	0.862357i	$0.331012\pi$
$674$	93.9373	−	162.704i	0.139373	−	0.241401i
$675$	530.155	+	98.8390i	0.785415	+	0.146428i
$676$	−408.026	−	446.809i	−0.603589	−	0.660960i
$677$	326.456	−	188.480i	0.482210	−	0.278404i	−0.239127	−	0.970988i	$-0.576861\pi$
$677$	326.456	−	188.480i	0.482210	−	0.278404i	0.721337	+	0.692584i	$0.243528\pi$
$678$	214.324	−	225.691i	0.316112	−	0.332878i
$679$	−519.364	−	899.565i	−0.764895	−	1.32484i
$680$		−	242.379i		−	0.356439i
$681$	−977.615	+	289.208i	−1.43556	+	0.424681i
$682$	−119.084	−	68.7529i	−0.174609	−	0.100811i
$683$	119.127	+	206.334i	0.174418	+	0.302100i	0.939960	−	0.341286i	$-0.110862\pi$
$683$	119.127	+	206.334i	0.174418	+	0.302100i	−0.765542	+	0.643386i	$0.777529\pi$
$684$	88.9893	+	137.243i	0.130101	+	0.200648i
$685$	174.283	+	301.867i	0.254428	+	0.440682i
$686$			193.164i			0.281580i
$687$	−26.2638	−	88.7801i	−0.0382297	−	0.129229i
$688$	175.843	−	304.569i	0.255586	−	0.442687i
$689$	228.128	−	517.264i	0.331100	−	0.750746i
$690$	68.9583	−	72.6155i	0.0999395	−	0.105240i
$691$			479.627i			0.694106i	0.937846	+	0.347053i	$0.112818\pi$
$691$			479.627i			0.694106i	−0.937846	+	0.347053i	$0.887182\pi$
$692$	−688.930	−	397.754i	−0.995564	−	0.574789i
$693$	−180.854	+	354.327i	−0.260972	+	0.511295i
$694$		−	130.764i		−	0.188421i
$695$	120.327	−	208.412i	0.173132	−	0.299874i
$696$	261.894	−	275.784i	0.376284	−	0.396241i
$697$	1230.28	+	710.302i	1.76511	+	1.01909i
$698$		−	159.651i		−	0.228726i
$699$	79.7215	−	83.9496i	0.114051	−	0.120100i
$700$		−	550.543i		−	0.786490i
$701$			776.513i			1.10772i	0.832609	+	0.553861i	$0.186846\pi$
$701$			776.513i			1.10772i	−0.832609	+	0.553861i	$0.813154\pi$
$702$	−204.985	+	98.3909i	−0.292002	+	0.140158i
$703$	−119.905			−0.170562
$704$	−155.957			−0.221531
$705$	294.623	+	279.784i	0.417905	+	0.396857i
$706$	−307.328			−0.435309
$707$	304.126	−	526.761i	0.430163	−	0.745065i
$708$	450.417	+	427.732i	0.636183	+	0.604142i
$709$	−296.950	−	171.444i	−0.418829	−	0.241811i	0.275747	−	0.961230i	$-0.411075\pi$
$709$	−296.950	−	171.444i	−0.418829	−	0.241811i	−0.694576	+	0.719419i	$0.744408\pi$
$710$	47.4292			0.0668017
$711$	−695.280	+	450.823i	−0.977890	+	0.634069i
$712$	−302.004	+	523.086i	−0.424163	+	0.734672i
$713$	−849.732			−1.19177
$714$	−238.849	−	226.820i	−0.334523	−	0.317675i
$715$	−135.034	+	98.8345i	−0.188859	+	0.138230i
$716$	−821.056	−	474.037i	−1.14673	−	0.662062i
$717$	50.4035	−	14.9108i	0.0702977	−	0.0207962i
$718$	−391.696			−0.545537
$719$	762.050	−	439.970i	1.05987	−	0.611919i	0.134477	−	0.990917i	$-0.457065\pi$
$719$	762.050	−	439.970i	1.05987	−	0.611919i	0.925397	+	0.378998i	$0.123731\pi$
$720$	−200.213	−	102.192i	−0.278074	−	0.141933i
$721$	704.173	−	406.555i	0.976662	−	0.563876i
$722$	108.581	−	188.068i	0.150389	−	0.260482i
$723$	−141.906	−	479.688i	−0.196274	−	0.663468i
$724$	−921.421			−1.27268
$725$	−446.573	+	257.829i	−0.615963	+	0.355626i
$726$	−124.059	−	117.810i	−0.170880	−	0.162273i
$727$	160.422	+	277.859i	0.220663	+	0.382199i	0.955009	−	0.296575i	$-0.0958446\pi$
$727$	160.422	+	277.859i	0.220663	+	0.382199i	−0.734347	+	0.678775i	$0.762511\pi$
$728$	290.259	+	396.572i	0.398708	+	0.544742i
$729$	−112.516	−	720.265i	−0.154343	−	0.988017i
$730$	−105.137	−	60.7009i	−0.144023	−	0.0831519i
$731$			695.017i			0.950776i
$732$	−606.760	+	179.498i	−0.828907	+	0.245215i
$733$	−737.401	−	425.739i	−1.00600	−	0.580817i	−0.0959847	−	0.995383i	$-0.530600\pi$
$733$	−737.401	−	425.739i	−1.00600	−	0.580817i	−0.910019	+	0.414566i	$0.863933\pi$
$734$	−165.261			−0.225151
$735$	50.0721	+	47.5502i	0.0681253	+	0.0646942i
$736$	534.623	−	308.665i	0.726390	−	0.419381i
$737$	−340.543	+	196.612i	−0.462066	+	0.266774i
$738$	−315.646	+	204.666i	−0.427704	+	0.277326i
$739$	−213.656	−	123.354i	−0.289115	−	0.166921i	0.348428	−	0.937336i	$-0.386716\pi$
$739$	−213.656	−	123.354i	−0.289115	−	0.166921i	−0.637543	+	0.770415i	$0.720049\pi$
$740$	164.205	−	94.8039i	0.221899	−	0.128113i
$741$	157.439	+	120.019i	0.212468	+	0.161969i
$742$	−108.437	+	187.818i	−0.146141	+	0.253124i
$743$	−619.175	−	1072.44i	−0.833344	−	1.44339i	−0.895372	−	0.445320i	$-0.853090\pi$
$743$	−619.175	−	1072.44i	−0.833344	−	1.44339i	0.0620274	−	0.998074i	$-0.480243\pi$
$744$	−154.499	−	522.255i	−0.207659	−	0.701956i
$745$	−66.8165	+	115.730i	−0.0896866	+	0.155342i
$746$	−350.323			−0.469602
$747$	−326.654	+	211.804i	−0.437287	+	0.283539i
$748$	391.952	−	226.293i	0.524000	−	0.302531i
$749$	237.001	+	410.498i	0.316423	+	0.548061i
$750$	−142.088	−	134.932i	−0.189451	−	0.179909i
$751$	−26.4038	−	45.7327i	−0.0351581	−	0.0608957i	0.847911	−	0.530139i	$-0.177860\pi$
$751$	−26.4038	−	45.7327i	−0.0351581	−	0.0608957i	−0.883069	+	0.469243i	$0.844527\pi$
$752$	336.494	+	582.825i	0.447465	+	0.775033i
$753$	−1090.58	−	262.233i	−1.44832	−	0.348251i
$754$	87.7316	−	198.925i	0.116355	−	0.263827i
$755$			90.6572i			0.120076i
$756$	−701.787	+	247.680i	−0.928290	+	0.327619i
$757$	−58.9017	+	102.021i	−0.0778094	+	0.134770i	−0.902305	−	0.431099i	$-0.858126\pi$
$757$	−58.9017	+	102.021i	−0.0778094	+	0.134770i	0.824495	+	0.565869i	$0.191459\pi$
$758$	−258.309	−	149.135i	−0.340777	−	0.196748i
$759$	384.927	+	92.5564i	0.507150	+	0.121945i
$760$		−	55.8834i		−	0.0735308i
$761$	−138.383			−0.181844			−0.0909221	−	0.995858i	$-0.528981\pi$
$761$	−138.383			−0.181844			−0.0909221	+	0.995858i	$0.528981\pi$
$762$	268.063	−	79.3010i	0.351789	−	0.104070i
$763$	−388.617	+	673.105i	−0.509328	+	0.882182i
$764$	400.701	+	231.345i	0.524478	+	0.302807i
$765$	443.639	−	22.9362i	0.579920	−	0.0299820i
$766$	−197.924			−0.258387
$767$	687.859	+	303.365i	0.896818	+	0.395522i
$768$	−60.1643	−	57.1341i	−0.0783389	−	0.0743934i
$769$	748.249	−	432.002i	0.973015	−	0.561771i	0.0728610	−	0.997342i	$-0.476787\pi$
$769$	748.249	−	432.002i	0.973015	−	0.561771i	0.900154	+	0.435572i	$0.143454\pi$
$770$	55.5942	−	32.0973i	0.0722002	−	0.0416848i
$771$	1362.72	+	327.669i	1.76747	+	0.424993i
$772$	−26.5779	+	15.3448i	−0.0344273	+	0.0198766i
$773$	615.563	+	1066.19i	0.796329	+	1.37928i	0.921992	+	0.387210i	$0.126561\pi$
$773$	615.563	+	1066.19i	0.796329	+	1.37928i	−0.125662	+	0.992073i	$0.540106\pi$
$774$	−163.929	−	83.6720i	−0.211795	−	0.108103i
$775$			738.432i			0.952816i
$776$	−573.791	−	331.279i	−0.739422	−	0.426905i
$777$	127.543	−	530.429i	0.164148	−	0.682663i
$778$	296.332	−	171.088i	0.380890	−	0.219907i
$779$	283.656	+	163.769i	0.364129	+	0.210230i
$780$	−310.500	−	39.8809i	−0.398078	−	0.0511294i
$781$	93.7533	+	162.386i	0.120043	+	0.207920i
$782$	−163.901	+	283.884i	−0.209592	+	0.363023i
$783$	529.565	+	453.262i	0.676329	+	0.578878i
$784$	57.1882	+	99.0529i	0.0729441	+	0.126343i
$785$	165.307	+	286.320i	0.210582	+	0.364738i
$786$	−8.86210	−	29.9568i	−0.0112749	−	0.0381129i
$787$		−	1009.74i		−	1.28303i	−0.767112	−	0.641514i	$-0.778307\pi$
$787$		−	1009.74i		−	1.28303i	0.767112	−	0.641514i	$-0.221693\pi$
$788$	381.138	−	660.150i	0.483677	−	0.837754i
$789$	871.577	−	917.802i	1.10466	−	1.16325i
$790$	133.717			0.169263
$791$	616.474	−	1067.76i	0.779360	−	1.34989i
$792$	13.1013	+	253.409i	0.0165420	+	0.319961i
$793$	−617.981	+	452.313i	−0.779295	+	0.570382i
$794$	200.321	−	115.656i	0.252294	−	0.145662i
$795$	−82.9721	−	280.473i	−0.104367	−	0.352796i
$796$	422.334	+	731.504i	0.530571	+	0.918975i
$797$			44.1657i			0.0554150i	0.999616	+	0.0277075i	$0.00882070\pi$
$797$			44.1657i			0.0554150i	−0.999616	+	0.0277075i	$0.991179\pi$
$798$	−55.0697	−	52.2962i	−0.0690097	−	0.0655340i
$799$	−1151.80	−	664.994i	−1.44156	−	0.832283i
$800$	−268.235	−	464.596i	−0.335294	−	0.580745i
$801$	−986.013	−	503.275i	−1.23098	−	0.628309i
$802$	−136.041	−	235.630i	−0.169627	−	0.293803i
$803$		−	479.950i		−	0.597696i
$804$	−715.240	−	171.981i	−0.889602	−	0.213907i
$805$	198.349	−	343.550i	0.246396	−	0.426771i
$806$	−183.883	−	251.234i	−0.228143	−	0.311705i
$807$	−168.350	−	40.4800i	−0.208612	−	0.0501611i
$808$		−	387.976i		−	0.480168i
$809$	−197.784	−	114.191i	−0.244480	−	0.141150i	0.372754	−	0.927930i	$-0.378413\pi$
$809$	−197.784	−	114.191i	−0.244480	−	0.141150i	−0.617234	+	0.786780i	$0.711747\pi$
$810$	−47.9991	+	107.400i	−0.0592582	+	0.132592i
$811$			773.624i			0.953914i	0.878927	+	0.476957i	$0.158260\pi$
$811$			773.624i			0.953914i	−0.878927	+	0.476957i	$0.841740\pi$
$812$	355.800	−	616.264i	0.438177	−	0.758945i
$813$	106.894	+	361.338i	0.131482	+	0.444450i
$814$	−76.0861	−	43.9283i	−0.0934719	−	0.0539660i
$815$			36.7142i			0.0450481i
$816$	715.421	+	172.024i	0.876741	+	0.210814i
$817$			160.245i			0.196138i
$818$			302.971i			0.370380i
$819$	−698.401	+	568.805i	−0.852748	+	0.694512i
$820$	−517.942			−0.631636
$821$	273.786			0.333478			0.166739	−	0.986001i	$-0.446676\pi$
$821$	273.786			0.333478			0.166739	+	0.986001i	$0.446676\pi$
$822$	289.736	−	85.7126i	0.352477	−	0.104273i
$823$	−69.6082			−0.0845786			−0.0422893	−	0.999105i	$-0.513465\pi$
$823$	−69.6082			−0.0845786			−0.0422893	+	0.999105i	$0.513465\pi$
$824$	259.323	−	449.160i	0.314712	−	0.545097i
$825$	80.4331	−	334.508i	0.0974947	−	0.405464i
$826$	−249.761	−	144.199i	−0.302374	−	0.174575i
$827$	−871.937			−1.05434			−0.527168	−	0.849761i	$-0.676746\pi$
$827$	−871.937			−1.05434			−0.527168	+	0.849761i	$0.676746\pi$
$828$	402.936	+	621.427i	0.486638	+	0.750516i
$829$	648.756	−	1123.68i	0.782577	−	1.35546i	−0.147860	−	0.989008i	$-0.547238\pi$
$829$	648.756	−	1123.68i	0.782577	−	1.35546i	0.930436	−	0.366454i	$-0.119428\pi$
$830$	62.8226			0.0756899
$831$	−769.508	+	227.643i	−0.926002	+	0.273939i
$832$	−323.090	−	142.492i	−0.388329	−	0.171264i
$833$	−195.753	−	113.018i	−0.234997	−	0.135676i
$834$	−151.267	−	143.649i	−0.181375	−	0.172241i
$835$	558.989			0.669448
$836$	90.3694	−	52.1748i	0.108097	−	0.0624100i
$837$	941.293	−	332.208i	1.12460	−	0.396904i
$838$	−356.902	+	206.057i	−0.425897	+	0.245892i
$839$	224.125	−	388.196i	0.267134	−	0.462689i	−0.700987	−	0.713174i	$-0.747257\pi$
$839$	224.125	−	388.196i	0.267134	−	0.462689i	0.968120	+	0.250485i	$0.0805901\pi$
$840$	247.214	+	59.4430i	0.294302	+	0.0707655i
$841$	174.490			0.207479
$842$	211.855	−	122.314i	0.251609	−	0.145266i
$843$	−219.733	+	913.832i	−0.260656	+	1.08402i
$844$	−538.657	−	932.981i	−0.638219	−	1.10543i
$845$	−370.046	+	81.3757i	−0.437924	+	0.0963026i
$846$	295.512	−	191.611i	0.349305	−	0.226491i
$847$	−586.932	−	338.865i	−0.692954	−	0.400077i
$848$		−	484.469i		−	0.571307i
$849$	−158.038	+	657.255i	−0.186146	+	0.774152i
$850$	246.700	+	142.433i	0.290236	+	0.167568i
$851$	−542.920			−0.637979
$852$	−82.0080	+	341.058i	−0.0962535	+	0.400302i
$853$	−1255.68	+	724.966i	−1.47207	+	0.849901i	−0.999507	−	0.0313950i	$-0.990005\pi$
$853$	−1255.68	+	724.966i	−1.47207	+	0.849901i	−0.472565	+	0.881296i	$0.656672\pi$
$854$	254.425	−	146.892i	0.297921	−	0.172005i
$855$	102.287	−	5.28824i	0.119633	−	0.00618507i
$856$	261.838	+	151.172i	0.305885	+	0.176603i
$857$	322.314	−	186.088i	0.376096	−	0.217139i	−0.300022	−	0.953932i	$-0.596994\pi$
$857$	322.314	−	186.088i	0.376096	−	0.217139i	0.676118	+	0.736793i	$0.263661\pi$
$858$	55.9333	+	133.838i	0.0651903	+	0.155988i
$859$	248.161	−	429.828i	0.288896	−	0.500382i	−0.684651	−	0.728871i	$-0.740045\pi$
$859$	248.161	−	429.828i	0.288896	−	0.500382i	0.973546	+	0.228489i	$0.0733786\pi$
$860$	−126.699	−	219.449i	−0.147324	−	0.255173i
$861$	−1026.20	+	1080.62i	−1.19187	+	1.25508i
$862$	−51.9667	+	90.0090i	−0.0602862	+	0.104419i
$863$	486.822			0.564105			0.282052	−	0.959399i	$-0.408985\pi$
$863$	486.822			0.564105			0.282052	+	0.959399i	$0.408985\pi$
$864$	−471.555	+	550.938i	−0.545781	+	0.637660i
$865$	−431.392	+	249.064i	−0.498719	+	0.287936i
$866$	94.4110	+	163.525i	0.109020	+	0.188828i
$867$	−563.025	+	166.560i	−0.649394	+	0.192110i
$868$	−509.512	−	882.501i	−0.586995	−	1.01671i
$869$	264.319	+	457.814i	0.304165	+	0.526829i
$870$	−31.9088	−	107.862i	−0.0366767	−	0.123979i
$871$	−885.123	+	96.1735i	−1.01622	+	0.110417i
$872$			495.763i			0.568535i
$873$	552.060	−	1081.59i	0.632371	−	1.23894i
$874$	−37.7894	+	65.4531i	−0.0432373	+	0.0748891i
$875$	−672.231	−	388.113i	−0.768264	−	0.443558i
$876$	618.281	−	651.072i	0.705800	−	0.743233i
$877$			836.834i			0.954201i	0.878849	+	0.477101i	$0.158312\pi$
$877$			836.834i			0.954201i	−0.878849	+	0.477101i	$0.841688\pi$
$878$	325.633			0.370880
$879$	282.617	+	268.383i	0.321521	+	0.305328i
$880$	−71.7015	+	124.191i	−0.0814789	+	0.141126i
$881$	4.35223	+	2.51276i	0.00494010	+	0.00285217i	0.502468	−	0.864596i	$-0.332425\pi$
$881$	4.35223	+	2.51276i	0.00494010	+	0.00285217i	−0.497528	+	0.867448i	$0.665759\pi$
$882$	50.2232	−	32.5649i	0.0569424	−	0.0369217i
$883$	1499.62			1.69833			0.849164	−	0.528129i	$-0.177106\pi$
$883$	1499.62			1.69833			0.849164	+	0.528129i	$0.177106\pi$
$884$	1018.74	−	110.692i	1.15242	−	0.125217i
$885$	372.973	−	110.337i	0.421439	−	0.124674i
$886$	−418.607	+	241.683i	−0.472468	+	0.272780i
$887$	1069.94	−	617.733i	1.20625	−	0.696429i	0.244313	−	0.969696i	$-0.421438\pi$
$887$	1069.94	−	617.733i	1.20625	−	0.696429i	0.961938	+	0.273267i	$0.0881043\pi$
$888$	−98.7139	−	333.685i	−0.111164	−	0.375771i
$889$	959.030	−	553.696i	1.07877	−	0.622830i
$890$	89.3196	+	154.706i	0.100359	+	0.173827i
$891$	−462.589	+	47.9601i	−0.519179	+	0.0538273i
$892$		−	96.2728i		−	0.107929i
$893$	−265.563	−	153.323i	−0.297383	−	0.171694i
$894$	83.9973	+	79.7668i	0.0939567	+	0.0892246i
$895$	−514.126	+	296.831i	−0.574442	+	0.331654i
$896$	833.593	+	481.275i	0.930350	+	0.537138i
$897$	712.871	+	543.436i	0.794727	+	0.605838i
$898$	−100.855	−	174.686i	−0.112311	−	0.194528i
$899$	−477.227	+	826.582i	−0.530842	+	0.919446i
$900$	540.031	−	350.159i	0.600034	−	0.389065i
$901$	478.714	+	829.157i	0.531314	+	0.920263i
$902$	119.997	+	207.840i	0.133034	+	0.230422i
$903$	−708.882	−	170.452i	−0.785030	−	0.188762i
$904$		−	786.441i		−	0.869957i
$905$	−288.486	+	499.673i	−0.318769	+	0.552125i
$906$	76.4068	+	18.3722i	0.0843342	+	0.0202783i
$907$	−731.998			−0.807053			−0.403527	−	0.914968i	$-0.632216\pi$
$907$	−731.998			−0.807053			−0.403527	+	0.914968i	$0.632216\pi$
$908$	−608.361	+	1053.71i	−0.670001	+	1.16048i
$909$	710.134	−	36.7141i	0.781225	−	0.0403895i
$910$	144.498	−	15.7005i	0.158789	−	0.0172533i
$911$	−790.210	+	456.228i	−0.867410	+	0.500799i	−0.866487	−	0.499200i	$-0.833627\pi$
$911$	−790.210	+	456.228i	−0.867410	+	0.500799i	−0.000922988		1.00000i	$0.500294\pi$
$912$	164.949	+	39.6624i	0.180865	+	0.0434894i
$913$	124.181	+	215.089i	0.136015	+	0.235584i
$914$			207.895i			0.227456i
$915$	−92.6305	+	385.235i	−0.101236	+	0.421022i
$916$	−95.6907	−	55.2470i	−0.104466	−	0.0603134i
$917$	−61.8770	−	107.174i	−0.0674777	−	0.116875i
$918$	70.5749	−	378.551i	0.0768790	−	0.412365i
$919$	−535.461	−	927.445i	−0.582656	−	1.00919i	−0.995163	−	0.0982351i	$-0.968680\pi$
$919$	−535.461	−	927.445i	−0.582656	−	1.00919i	0.412508	−	0.910954i	$-0.364653\pi$
$920$		−	253.035i		−	0.275039i
$921$	−421.906	+	444.283i	−0.458096	+	0.482391i
$922$	−275.302	+	476.838i	−0.298593	+	0.517178i
$923$	45.8597	+	422.065i	0.0496855	+	0.457275i
$924$	134.682	+	455.269i	0.145760	+	0.492715i
$925$			471.807i			0.510062i
$926$	403.974	+	233.234i	0.436257	+	0.251873i
$927$	846.663	+	432.149i	0.913336	+	0.466180i
$928$		−	693.409i		−	0.747208i
$929$	−112.026	+	194.034i	−0.120587	+	0.208864i	−0.919999	−	0.391920i	$-0.871811\pi$
$929$	−112.026	+	194.034i	−0.120587	+	0.208864i	0.799412	+	0.600783i	$0.205144\pi$
$930$	−156.613	−	37.6580i	−0.168401	−	0.0404925i
$931$	−45.1332	−	26.0577i	−0.0484782	−	0.0279889i
$932$		−	138.168i		−	0.148249i
$933$	−187.409	−	633.503i	−0.200867	−	0.678996i
$934$			222.775i			0.238517i
$935$		−	283.399i		−	0.303101i
$936$	−204.388	+	536.946i	−0.218363	+	0.573660i
$937$	1048.51			1.11901			0.559505	−	0.828827i	$-0.310991\pi$
$937$	1048.51			1.11901			0.559505	+	0.828827i	$0.310991\pi$
$938$	341.548			0.364124
$939$	−264.129	+	1098.47i	−0.281288	+	1.16983i
$940$	484.904			0.515855
$941$	651.843	−	1129.03i	0.692713	−	1.19981i	−0.278232	−	0.960514i	$-0.589749\pi$
$941$	651.843	−	1129.03i	0.692713	−	1.19981i	0.970946	−	0.239301i	$-0.0769182\pi$
$942$	274.813	−	81.2979i	0.291734	−	0.0863035i
$943$	1284.37	+	741.533i	1.36201	+	0.786355i
$944$	644.247			0.682465
$945$	−85.4081	+	458.114i	−0.0903790	+	0.484777i
$946$	−58.7072	+	101.684i	−0.0620584	+	0.107488i
$947$	−107.675			−0.113702			−0.0568508	−	0.998383i	$-0.518106\pi$
$947$	−107.675			−0.113702			−0.0568508	+	0.998383i	$0.518106\pi$
$948$	−231.206	+	961.546i	−0.243888	+	1.01429i
$949$	438.510	−	994.290i	0.462076	−	1.04772i
$950$	56.8799	+	32.8396i	0.0598736	+	0.0345680i
$951$	−259.361	+	1078.64i	−0.272725	+	1.13422i
$952$	−832.293			−0.874257
$953$	−113.357	+	65.4469i	−0.118948	+	0.0686747i	−0.558294	−	0.829643i	$-0.688544\pi$
$953$	−113.357	+	65.4469i	−0.118948	+	0.0686747i	0.439346	+	0.898318i	$0.355210\pi$
$954$	−253.200	+	13.0905i	−0.265409	+	0.0137217i
$955$	250.910	−	144.863i	0.262733	−	0.151689i
$956$	31.3656	−	54.3268i	0.0328092	−	0.0568272i
$957$	306.218	−	322.458i	0.319977	−	0.336947i
$958$	50.4579			0.0526700
$959$	1036.57	−	598.463i	1.08088	−	0.624049i
$960$	−175.187	+	51.8255i	−0.182486	+	0.0539849i
$961$	202.898	+	351.430i	0.211132	+	0.365692i
$962$	−117.489	−	160.521i	−0.122130	−	0.166862i
$963$	−251.921	+	493.562i	−0.261601	+	0.512526i
$964$	−517.026	−	298.505i	−0.536334	−	0.309653i
$965$			19.2170i			0.0199140i
$966$	−249.351	−	236.793i	−0.258127	−	0.245127i
$967$	298.306	+	172.227i	0.308486	+	0.178105i	0.646249	−	0.763127i	$-0.276337\pi$
$967$	298.306	+	172.227i	0.308486	+	0.178105i	−0.337763	+	0.941231i	$0.609670\pi$
$968$	−432.293			−0.446584
$969$	−321.498	+	95.1088i	−0.331784	+	0.0981515i
$970$	−169.702	+	97.9777i	−0.174951	+	0.101008i
$971$	−114.391	+	66.0437i	−0.117808	+	0.0680162i	−0.557746	−	0.830012i	$-0.688334\pi$
$971$	−114.391	+	66.0437i	−0.117808	+	0.0680162i	0.439938	+	0.898028i	$0.355000\pi$
$972$	−689.304	−	530.856i	−0.709161	−	0.546148i
$973$	−715.658	−	413.185i	−0.735517	−	0.424651i
$974$	433.361	−	250.201i	0.444929	−	0.256880i
$975$	472.256	−	619.497i	0.484365	−	0.635381i
$976$	−328.140	+	568.354i	−0.336209	+	0.582330i
$977$	−637.455	−	1104.10i	−0.652461	−	1.13010i	−0.982524	−	0.186137i	$-0.940403\pi$
$977$	−637.455	−	1104.10i	−0.652461	−	1.13010i	0.330062	−	0.943959i	$-0.392930\pi$
$978$	30.9431	+	7.44033i	0.0316392	+	0.00760770i
$979$	−353.116	+	611.615i	−0.360691	+	0.624734i
$980$	82.4109			0.0840928
$981$	−907.422	+	46.9139i	−0.924997	+	0.0478226i
$982$	112.330	−	64.8540i	0.114389	−	0.0660428i
$983$	−205.750	−	356.369i	−0.209308	−	0.362532i	0.742189	−	0.670191i	$-0.233788\pi$
$983$	−205.750	−	356.369i	−0.209308	−	0.362532i	−0.951497	+	0.307659i	$0.900454\pi$
$984$	−222.229	+	924.215i	−0.225843	+	0.939243i
$985$	−238.660	−	413.370i	−0.242294	−	0.419665i
$986$	184.100	+	318.871i	0.186714	+	0.323398i
$987$	960.739	−	1011.69i	0.973393	−	1.02502i
$988$	234.884	−	25.5214i	0.237737	−	0.0258314i
$989$			725.576i			0.733646i
$990$	66.8436	+	34.1180i	0.0675188	+	0.0344626i
$991$	631.685	−	1094.11i	0.637422	−	1.10405i	−0.348575	−	0.937281i	$-0.613334\pi$
$991$	631.685	−	1094.11i	0.637422	−	1.10405i	0.985997	−	0.166766i	$-0.0533324\pi$
$992$	−859.941	−	496.487i	−0.866876	−	0.500491i
$993$	521.061	+	1761.35i	0.524734	+	1.77377i
$994$		−	162.865i		−	0.163848i
$995$	528.912			0.531569
$996$	−108.624	+	451.750i	−0.109060	+	0.453564i
$997$	572.391	−	991.410i	0.574113	−	0.994393i	−0.422024	−	0.906585i	$-0.638680\pi$
$997$	572.391	−	991.410i	0.574113	−	0.994393i	0.996137	−	0.0878088i	$-0.0279864\pi$
$998$	97.5626	+	56.3278i	0.0977581	+	0.0564407i
$999$	601.421	−	212.258i	0.602023	−	0.212471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.v.a.95.11	yes	52
3.2	odd	2		351.3.v.a.17.16		52
9.2	odd	6		117.3.m.a.56.11	yes	52
9.7	even	3		351.3.m.a.251.16		52
13.10	even	6		117.3.m.a.23.11	✓	52
39.23	odd	6		351.3.m.a.179.16		52
117.88	even	6		351.3.v.a.62.16		52
117.101	odd	6	inner	117.3.v.a.101.11	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.m.a.23.11	✓	52	13.10	even	6
117.3.m.a.56.11	yes	52	9.2	odd	6
117.3.v.a.95.11	yes	52	1.1	even	1	trivial
117.3.v.a.101.11	yes	52	117.101	odd	6	inner
351.3.m.a.179.16		52	39.23	odd	6
351.3.m.a.251.16		52	9.7	even	3
351.3.v.a.17.16		52	3.2	odd	2
351.3.v.a.62.16		52	117.88	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.647795 q^{2} +(-2.17539 - 2.06583i) q^{3} -3.58036 q^{4} +(-1.12097 + 1.94158i) q^{5} +(1.40921 + 1.33823i) q^{6} +(6.66709 + 3.84925i) q^{7} +4.91052 q^{8} +(0.464681 + 8.98800i) q^{9} +(0.726158 - 1.25774i) q^{10} +5.74159 q^{11} +(7.78870 + 7.39642i) q^{12} +(11.8946 + 5.24585i) q^{13} +(-4.31890 - 2.49352i) q^{14} +(6.44952 - 1.90796i) q^{15} +11.1404 q^{16} +(-19.0666 + 11.0081i) q^{17} +(-0.301018 - 5.82238i) q^{18} +(-4.39605 + 2.53806i) q^{19} +(4.01348 - 6.95155i) q^{20} +(-6.55166 - 22.1467i) q^{21} -3.71937 q^{22} +(-19.9049 + 11.4921i) q^{23} +(-10.6823 - 10.1443i) q^{24} +(9.98685 + 17.2977i) q^{25} +(-7.70525 - 3.39823i) q^{26} +(17.5568 - 20.5124i) q^{27} +(-23.8706 - 13.7817i) q^{28} +25.8169i q^{29} +(-4.17796 + 1.23597i) q^{30} +(32.0171 + 18.4851i) q^{31} -26.8588 q^{32} +(-12.4902 - 11.8611i) q^{33} +(12.3513 - 7.13100i) q^{34} +(-14.9472 + 8.62977i) q^{35} +(-1.66373 - 32.1803i) q^{36} +(20.4567 + 11.8107i) q^{37} +(2.84774 - 1.64414i) q^{38} +(-15.0384 - 35.9840i) q^{39} +(-5.50454 + 9.53414i) q^{40} +(-32.2626 - 55.8805i) q^{41} +(4.24413 + 14.3465i) q^{42} +(15.7842 - 27.3390i) q^{43} -20.5570 q^{44} +(-17.9718 - 9.17305i) q^{45} +(12.8943 - 7.44454i) q^{46} +(30.2047 + 52.3161i) q^{47} +(-24.2349 - 23.0143i) q^{48} +(5.13339 + 8.89129i) q^{49} +(-6.46943 - 11.2054i) q^{50} +(64.2184 + 15.4414i) q^{51} +(-42.5869 - 18.7820i) q^{52} -43.4874i q^{53} +(-11.3732 + 13.2878i) q^{54} +(-6.43614 + 11.1477i) q^{55} +(32.7389 + 18.9018i) q^{56} +(14.8063 + 3.56022i) q^{57} -16.7240i q^{58} +57.8296 q^{59} +(-23.0916 + 6.83119i) q^{60} +(-29.4548 + 51.0172i) q^{61} +(-20.7405 - 11.9745i) q^{62} +(-31.4989 + 61.7124i) q^{63} -27.1628 q^{64} +(-23.5187 + 17.2138i) q^{65} +(8.09109 + 7.68359i) q^{66} +(-59.3116 + 34.2436i) q^{67} +(68.2654 - 39.4131i) q^{68} +(67.0419 + 16.1204i) q^{69} +(9.68272 - 5.59032i) q^{70} +(16.3288 + 28.2823i) q^{71} +(2.28183 + 44.1357i) q^{72} -83.5918i q^{73} +(-13.2518 - 7.65091i) q^{74} +(14.0089 - 58.2606i) q^{75} +(15.7395 - 9.08718i) q^{76} +(38.2797 + 22.1008i) q^{77} +(9.74178 + 23.3102i) q^{78} +(46.0359 + 79.7366i) q^{79} +(-12.4881 + 21.6300i) q^{80} +(-80.5681 + 8.35311i) q^{81} +(20.8996 + 36.1991i) q^{82} +(21.6284 + 37.4615i) q^{83} +(23.4573 + 79.2932i) q^{84} -49.3591i q^{85} +(-10.2249 + 17.7101i) q^{86} +(53.3333 - 56.1618i) q^{87} +28.1942 q^{88} +(-61.5015 + 106.524i) q^{89} +(11.6420 + 5.94226i) q^{90} +(59.1097 + 80.7597i) q^{91} +(71.2669 - 41.1460i) q^{92} +(-31.4628 - 106.354i) q^{93} +(-19.5665 - 33.8901i) q^{94} -11.3804i q^{95} +(58.4285 + 55.4857i) q^{96} +(-116.849 - 67.4631i) q^{97} +(-3.32538 - 5.75973i) q^{98} +(2.66801 + 51.6053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 6 q^{2} - q^{3} + 94 q^{4} - 12 q^{6} - 3 q^{7} - 78 q^{8} + q^{9} + 2 q^{10} - 6 q^{11} + 13 q^{12} - 6 q^{13} - 6 q^{14} + 27 q^{15} + 150 q^{16} + 12 q^{18} + 15 q^{19} - 3 q^{20} - 69 q^{21}+ \cdots - 522 q^{99}+O(q^{100}) \) 52 * q - 6 * q^2 - q^3 + 94 * q^4 - 12 * q^6 - 3 * q^7 - 78 * q^8 + q^9 + 2 * q^10 - 6 * q^11 + 13 * q^12 - 6 * q^13 - 6 * q^14 + 27 * q^15 + 150 * q^16 + 12 * q^18 + 15 * q^19 - 3 * q^20 - 69 * q^21 - 34 * q^22 + 69 * q^23 - 78 * q^24 - 92 * q^25 - 12 * q^26 + 14 * q^27 - 18 * q^28 - 84 * q^30 + 48 * q^31 - 318 * q^32 - 99 * q^33 - 12 * q^34 + 78 * q^35 + 26 * q^36 + 27 * q^37 - 36 * q^38 + 37 * q^39 - 44 * q^40 + 33 * q^41 - 153 * q^42 - 31 * q^43 - 120 * q^44 + 87 * q^45 - 6 * q^46 + 153 * q^47 - 19 * q^48 + 73 * q^49 + 216 * q^50 - 63 * q^51 - 100 * q^52 - 339 * q^54 + 23 * q^55 - 174 * q^56 + 171 * q^57 - 6 * q^59 + 207 * q^60 - 6 * q^61 - 201 * q^62 + 189 * q^63 + 270 * q^64 - 66 * q^65 + 48 * q^66 - 108 * q^67 - 216 * q^68 - 201 * q^69 - 159 * q^70 + 432 * q^71 - 294 * q^72 - 81 * q^74 - 2 * q^75 + 141 * q^76 + 138 * q^77 + 456 * q^78 + 9 * q^79 + 84 * q^80 + 505 * q^81 - 85 * q^82 + 135 * q^83 - 201 * q^84 + 306 * q^86 + 348 * q^87 - 290 * q^88 + 441 * q^89 + 543 * q^90 - 138 * q^91 + 864 * q^92 + 474 * q^93 - 181 * q^94 - 747 * q^96 - 60 * q^97 - 147 * q^98 - 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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