LMFDB - Embedded newform 108.3.j.a.103.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [108,3,Mod(7,108)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(108, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 16])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("108.7"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.j (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.12
Character	$\chi$	$=$	108.103
Dual form			108.3.j.a.43.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08010 - 1.68327i) q^{2} +(0.579627 - 2.94347i) q^{3} +(-1.66676 + 3.63619i) q^{4} +(9.22169 - 3.35642i) q^{5} +(-5.58070 + 2.20358i) q^{6} +(4.51251 - 0.795677i) q^{7} +(7.92095 - 1.12185i) q^{8} +(-8.32807 - 3.41223i) q^{9} +(-15.6101 - 11.8973i) q^{10} +(-2.67518 + 7.34999i) q^{11} +(9.73694 + 7.01371i) q^{12} +(-5.33182 - 4.47393i) q^{13} +(-6.21330 - 6.73633i) q^{14} +(-4.53440 - 29.0893i) q^{15} +(-10.4438 - 12.1213i) q^{16} +(-7.51307 + 13.0130i) q^{17} +(3.25147 + 17.7039i) q^{18} +(-18.4333 + 10.6425i) q^{19} +(-3.16578 + 39.1262i) q^{20} +(0.273516 - 13.7436i) q^{21} +(15.2614 - 3.43570i) q^{22} +(16.6774 + 2.94067i) q^{23} +(1.28905 - 23.9654i) q^{24} +(54.6229 - 45.8341i) q^{25} +(-1.77190 + 13.8072i) q^{26} +(-14.8710 + 22.5356i) q^{27} +(-4.62805 + 17.7346i) q^{28} +(14.8391 - 12.4515i) q^{29} +(-44.0673 + 39.0519i) q^{30} +(-14.8493 - 2.61834i) q^{31} +(-9.12307 + 30.6720i) q^{32} +(20.0839 + 12.1346i) q^{33} +(30.0192 - 1.40889i) q^{34} +(38.9423 - 22.4834i) q^{35} +(26.2884 - 24.5951i) q^{36} +(-14.9619 + 25.9148i) q^{37} +(37.8239 + 19.5332i) q^{38} +(-16.2594 + 13.1009i) q^{39} +(69.2791 - 36.9314i) q^{40} +(29.3512 + 24.6286i) q^{41} +(-23.4296 + 14.3841i) q^{42} +(-14.2890 + 39.2588i) q^{43} +(-22.2671 - 21.9782i) q^{44} +(-88.2517 - 3.51404i) q^{45} +(-13.0633 - 31.2487i) q^{46} +(60.2645 - 10.6263i) q^{47} +(-41.7324 + 23.7152i) q^{48} +(-26.3153 + 9.57799i) q^{49} +(-136.149 - 42.4394i) q^{50} +(33.9487 + 29.6572i) q^{51} +(25.1550 - 11.9306i) q^{52} -24.8870 q^{53} +(53.9956 + 0.691048i) q^{54} +76.7584i q^{55} +(34.8507 - 11.3649i) q^{56} +(20.6414 + 60.4265i) q^{57} +(-36.9868 - 11.5293i) q^{58} +(-31.1472 - 85.5763i) q^{59} +(113.332 + 31.9970i) q^{60} +(4.84636 + 27.4850i) q^{61} +(11.6314 + 27.8234i) q^{62} +(-40.2955 - 8.77126i) q^{63} +(61.4829 - 17.7723i) q^{64} +(-64.1848 - 23.3614i) q^{65} +(-1.26695 - 46.9131i) q^{66} +(25.2305 - 30.0686i) q^{67} +(-34.7953 - 49.0086i) q^{68} +(18.3225 - 47.3850i) q^{69} +(-79.9071 - 41.2659i) q^{70} +(34.2911 + 19.7980i) q^{71} +(-69.7942 - 17.6852i) q^{72} +(-41.3131 - 71.5564i) q^{73} +(59.7818 - 2.80573i) q^{74} +(-103.250 - 187.348i) q^{75} +(-7.97413 - 84.7654i) q^{76} +(-6.22354 + 35.2955i) q^{77} +(39.6140 + 13.2186i) q^{78} +(10.3986 + 12.3926i) q^{79} +(-136.994 - 76.7255i) q^{80} +(57.7134 + 56.8346i) q^{81} +(9.75418 - 76.0073i) q^{82} +(55.6540 + 66.3258i) q^{83} +(49.5186 + 23.9019i) q^{84} +(-25.6060 + 145.219i) q^{85} +(81.5166 - 18.3512i) q^{86} +(-28.0494 - 50.8956i) q^{87} +(-12.9443 + 61.2201i) q^{88} +(-5.93712 - 10.2834i) q^{89} +(89.4057 + 152.347i) q^{90} +(-27.6197 - 15.9462i) q^{91} +(-38.4901 + 55.7408i) q^{92} +(-16.3141 + 42.1909i) q^{93} +(-82.9785 - 89.9637i) q^{94} +(-134.265 + 160.011i) q^{95} +(84.9941 + 44.6318i) q^{96} +(47.7745 + 17.3885i) q^{97} +(44.5455 + 33.9505i) q^{98} +(47.3589 - 52.0829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	−1.08010	−	1.68327i	−0.540051	−	0.841633i
$2$	−1.08010	−	1.68327i	−0.540051	−	0.841633i
$3$	0.579627	−	2.94347i	0.193209	−	0.981158i
$3$	0.579627	−	2.94347i	0.193209	−	0.981158i
$4$	−1.66676	+	3.63619i	−0.416691	+	0.909048i
$5$	9.22169	−	3.35642i	1.84434	−	0.671284i	0.856426	−	0.516270i	$-0.172680\pi$
$5$	9.22169	−	3.35642i	1.84434	−	0.671284i	0.987912	−	0.155014i	$-0.0495422\pi$
$6$	−5.58070	+	2.20358i	−0.930117	+	0.367264i
$7$	4.51251	−	0.795677i	0.644644	−	0.113668i	0.158238	−	0.987401i	$-0.449419\pi$
$7$	4.51251	−	0.795677i	0.644644	−	0.113668i	0.486406	+	0.873733i	$0.338308\pi$
$8$	7.92095	−	1.12185i	0.990119	−	0.140232i
$9$	−8.32807	−	3.41223i	−0.925341	−	0.379137i
$10$	−15.6101	−	11.8973i	−1.56101	−	1.18973i
$11$	−2.67518	+	7.34999i	−0.243198	+	0.668181i	0.756698	+	0.653765i	$0.226811\pi$
$11$	−2.67518	+	7.34999i	−0.243198	+	0.668181i	−0.999896	+	0.0144166i	$0.995411\pi$
$12$	9.73694	+	7.01371i	0.811411	+	0.584475i
$13$	−5.33182	−	4.47393i	−0.410140	−	0.344149i	0.414257	−	0.910160i	$-0.364041\pi$
$13$	−5.33182	−	4.47393i	−0.410140	−	0.344149i	−0.824397	+	0.566011i	$0.808486\pi$
$14$	−6.21330	−	6.73633i	−0.443807	−	0.481167i
$15$	−4.53440	−	29.0893i	−0.302293	−	1.93928i
$16$	−10.4438	−	12.1213i	−0.652738	−	0.757584i
$17$	−7.51307	+	13.0130i	−0.441945	+	0.765471i	−0.997834	−	0.0657853i	$-0.979045\pi$
$17$	−7.51307	+	13.0130i	−0.441945	+	0.765471i	0.555889	+	0.831257i	$0.312378\pi$
$18$	3.25147	+	17.7039i	0.180637	+	0.983550i
$19$	−18.4333	+	10.6425i	−0.970173	+	0.560129i	−0.899289	−	0.437355i	$-0.855915\pi$
$19$	−18.4333	+	10.6425i	−0.970173	+	0.560129i	−0.0708838	+	0.997485i	$0.522582\pi$
$20$	−3.16578	+	39.1262i	−0.158289	+	1.95631i
$21$	0.273516	−	13.7436i	0.0130246	−	0.654459i
$22$	15.2614	−	3.43570i	0.693702	−	0.156168i
$23$	16.6774	+	2.94067i	0.725104	+	0.127855i	0.524005	−	0.851715i	$-0.324437\pi$
$23$	16.6774	+	2.94067i	0.725104	+	0.127855i	0.201099	+	0.979571i	$0.435549\pi$
$24$	1.28905	−	23.9654i	0.0537104	−	0.998557i
$25$	54.6229	−	45.8341i	2.18492	−	1.83336i
$26$	−1.77190	+	13.8072i	−0.0681501	+	0.531045i
$27$	−14.8710	+	22.5356i	−0.550777	+	0.834653i
$28$	−4.62805	+	17.7346i	−0.165287	+	0.633377i
$29$	14.8391	−	12.4515i	0.511692	−	0.429361i	−0.350032	−	0.936738i	$-0.613829\pi$
$29$	14.8391	−	12.4515i	0.511692	−	0.429361i	0.861724	+	0.507377i	$0.169385\pi$
$30$	−44.0673	+	39.0519i	−1.46891	+	1.30173i
$31$	−14.8493	−	2.61834i	−0.479011	−	0.0844625i	−0.0710708	−	0.997471i	$-0.522642\pi$
$31$	−14.8493	−	2.61834i	−0.479011	−	0.0844625i	−0.407940	+	0.913009i	$0.633753\pi$
$32$	−9.12307	+	30.6720i	−0.285096	+	0.958499i
$33$	20.0839	+	12.1346i	0.608603	+	0.367714i
$34$	30.0192	−	1.40889i	0.882918	−	0.0414379i
$35$	38.9423	−	22.4834i	1.11264	−	0.642382i
$36$	26.2884	−	24.5951i	0.730234	−	0.683197i
$37$	−14.9619	+	25.9148i	−0.404376	+	0.700399i	−0.994249	−	0.107097i	$-0.965844\pi$
$37$	−14.9619	+	25.9148i	−0.404376	+	0.700399i	0.589873	+	0.807496i	$0.299178\pi$
$38$	37.8239	+	19.5332i	0.995365	+	0.514031i
$39$	−16.2594	+	13.1009i	−0.416907	+	0.335920i
$40$	69.2791	−	36.9314i	1.73198	−	0.923285i
$41$	29.3512	+	24.6286i	0.715884	+	0.600698i	0.926243	−	0.376926i	$-0.123019\pi$
$41$	29.3512	+	24.6286i	0.715884	+	0.600698i	−0.210360	+	0.977624i	$0.567463\pi$
$42$	−23.4296	+	14.3841i	−0.557848	+	0.342479i
$43$	−14.2890	+	39.2588i	−0.332303	+	0.912995i	0.655208	+	0.755448i	$0.272581\pi$
$43$	−14.2890	+	39.2588i	−0.332303	+	0.912995i	−0.987511	+	0.157547i	$0.949641\pi$
$44$	−22.2671	−	21.9782i	−0.506071	−	0.499504i
$45$	−88.2517	−	3.51404i	−1.96115	−	0.0780897i
$46$	−13.0633	−	31.2487i	−0.283986	−	0.679320i
$47$	60.2645	−	10.6263i	1.28222	−	0.226090i	0.509299	−	0.860589i	$-0.329905\pi$
$47$	60.2645	−	10.6263i	1.28222	−	0.226090i	0.772924	+	0.634499i	$0.218794\pi$
$48$	−41.7324	+	23.7152i	−0.869424	+	0.494067i
$49$	−26.3153	+	9.57799i	−0.537047	+	0.195469i
$50$	−136.149	−	42.4394i	−2.72298	−	0.848788i
$51$	33.9487	+	29.6572i	0.665660	+	0.581514i
$52$	25.1550	−	11.9306i	0.483749	−	0.229434i
$53$	−24.8870			−0.469565			−0.234783	−	0.972048i	$-0.575438\pi$
$53$	−24.8870			−0.469565			−0.234783	+	0.972048i	$0.575438\pi$
$54$	53.9956	+	0.691048i	0.999918	+	0.0127972i
$55$			76.7584i			1.39561i
$56$	34.8507	−	11.3649i	0.622334	−	0.202944i
$57$	20.6414	+	60.4265i	0.362129	+	1.06011i
$58$	−36.9868	−	11.5293i	−0.637703	−	0.198780i
$59$	−31.1472	−	85.5763i	−0.527919	−	1.45045i	−0.861516	−	0.507730i	$-0.830485\pi$
$59$	−31.1472	−	85.5763i	−0.527919	−	1.45045i	0.333598	−	0.942716i	$-0.391737\pi$
$60$	113.332	+	31.9970i	1.88887	+	0.533283i
$61$	4.84636	+	27.4850i	0.0794484	+	0.450575i	0.998417	+	0.0562438i	$0.0179124\pi$
$61$	4.84636	+	27.4850i	0.0794484	+	0.450575i	−0.918969	+	0.394331i	$0.870976\pi$
$62$	11.6314	+	27.8234i	0.187604	+	0.448765i
$63$	−40.2955	−	8.77126i	−0.639611	−	0.139226i
$64$	61.4829	−	17.7723i	0.960670	−	0.277692i
$65$	−64.1848	−	23.3614i	−0.987459	−	0.359406i
$66$	−1.26695	−	46.9131i	−0.0191962	−	0.710804i
$67$	25.2305	−	30.0686i	0.376575	−	0.448785i	−0.544155	−	0.838985i	$-0.683150\pi$
$67$	25.2305	−	30.0686i	0.376575	−	0.448785i	0.920730	+	0.390200i	$0.127594\pi$
$68$	−34.7953	−	49.0086i	−0.511696	−	0.720714i
$69$	18.3225	−	47.3850i	0.265543	−	0.686739i
$70$	−79.9071	−	41.2659i	−1.14153	−	0.589513i
$71$	34.2911	+	19.7980i	0.482973	+	0.278845i	0.721655	−	0.692253i	$-0.243382\pi$
$71$	34.2911	+	19.7980i	0.482973	+	0.278845i	−0.238682	+	0.971098i	$0.576715\pi$
$72$	−69.7942	−	17.6852i	−0.969364	−	0.245628i
$73$	−41.3131	−	71.5564i	−0.565933	−	0.980225i	−0.996962	−	0.0778868i	$-0.975183\pi$
$73$	−41.3131	−	71.5564i	−0.565933	−	0.980225i	0.431029	−	0.902338i	$-0.358151\pi$
$74$	59.7818	−	2.80573i	0.807862	−	0.0379153i
$75$	−103.250	−	187.348i	−1.37667	−	2.49797i
$76$	−7.97413	−	84.7654i	−0.104923	−	1.11533i
$77$	−6.22354	+	35.2955i	−0.0808252	+	0.458383i
$78$	39.6140	+	13.2186i	0.507872	+	0.169469i
$79$	10.3986	+	12.3926i	0.131628	+	0.156869i	0.827833	−	0.560975i	$-0.189574\pi$
$79$	10.3986	+	12.3926i	0.131628	+	0.156869i	−0.696204	+	0.717844i	$0.745129\pi$
$80$	−136.994	−	76.7255i	−1.71242	−	0.959069i
$81$	57.7134	+	56.8346i	0.712511	+	0.701661i
$82$	9.75418	−	76.0073i	0.118953	−	0.926918i
$83$	55.6540	+	66.3258i	0.670530	+	0.799106i	0.988856	−	0.148875i	$-0.0475652\pi$
$83$	55.6540	+	66.3258i	0.670530	+	0.799106i	−0.318326	+	0.947981i	$0.603121\pi$
$84$	49.5186	+	23.9019i	0.589508	+	0.284547i
$85$	−25.6060	+	145.219i	−0.301247	+	1.70846i
$86$	81.5166	−	18.3512i	0.947867	−	0.213387i
$87$	−28.0494	−	50.8956i	−0.322407	−	0.585007i
$88$	−12.9443	+	61.2201i	−0.147095	+	0.695683i
$89$	−5.93712	−	10.2834i	−0.0667092	−	0.115544i	0.830742	−	0.556658i	$-0.187917\pi$
$89$	−5.93712	−	10.2834i	−0.0667092	−	0.115544i	−0.897451	+	0.441114i	$0.854583\pi$
$90$	89.4057	+	152.347i	0.993397	+	1.69274i
$91$	−27.6197	−	15.9462i	−0.303513	−	0.175233i
$92$	−38.4901	+	55.7408i	−0.418371	+	0.605878i
$93$	−16.3141	+	42.1909i	−0.175420	+	0.453666i
$94$	−82.9785	−	89.9637i	−0.882750	−	0.957060i
$95$	−134.265	+	160.011i	−1.41332	+	1.68433i
$96$	84.9941	+	44.6318i	0.885356	+	0.464915i
$97$	47.7745	+	17.3885i	0.492521	+	0.179263i	0.576327	−	0.817219i	$-0.304486\pi$
$97$	47.7745	+	17.3885i	0.492521	+	0.179263i	−0.0838064	+	0.996482i	$0.526708\pi$
$98$	44.5455	+	33.9505i	0.454546	+	0.346433i
$99$	47.3589	−	52.0829i	0.478373	−	0.526090i
$100$	75.6180	+	275.014i	0.756180	+	2.75014i
$101$	0.442867	+	2.51162i	0.00438482	+	0.0248676i	0.986922	−	0.161201i	$-0.0515366\pi$
$101$	0.442867	+	2.51162i	0.00438482	+	0.0248676i	−0.982537	+	0.186068i	$0.940425\pi$
$102$	13.2529	−	89.1774i	0.129931	−	0.874288i
$103$	20.9977	+	57.6906i	0.203861	+	0.560103i	0.998922	−	0.0464265i	$-0.0147833\pi$
$103$	20.9977	+	57.6906i	0.203861	+	0.560103i	−0.795061	+	0.606530i	$0.792561\pi$
$104$	−47.2522	−	29.4563i	−0.454348	−	0.283233i
$105$	−43.6071	−	127.658i	−0.415306	−	1.21579i
$106$	26.8804	+	41.8914i	0.253589	+	0.395201i
$107$		−	122.605i		−	1.14584i	−0.819612	−	0.572919i	$-0.805811\pi$
$107$		−	122.605i		−	1.14584i	0.819612	−	0.572919i	$-0.194189\pi$
$108$	−57.1575	−	91.6353i	−0.529236	−	0.848475i
$109$	−37.9855			−0.348491			−0.174245	−	0.984702i	$-0.555749\pi$
$109$	−37.9855			−0.348491			−0.174245	+	0.984702i	$0.555749\pi$
$110$	129.205	−	82.9068i	1.17459	−	0.753698i
$111$	67.6071	+	59.0608i	0.609073	+	0.532079i
$112$	−56.7724	−	46.3878i	−0.506896	−	0.414176i
$113$	−102.206	+	37.2000i	−0.904480	+	0.329204i	−0.752047	−	0.659110i	$-0.770933\pi$
$113$	−102.206	+	37.2000i	−0.904480	+	0.329204i	−0.152433	+	0.988314i	$0.548711\pi$
$114$	79.4191	−	100.012i	0.696659	−	0.877295i
$115$	163.664	−	28.8584i	1.42316	−	0.250942i
$116$	20.5427	+	74.7113i	0.177092	+	0.644063i
$117$	29.1377	+	55.4526i	0.249040	+	0.473954i
$118$	−110.405	+	144.860i	−0.935639	+	1.22763i
$119$	−23.5486	+	64.6993i	−0.197888	+	0.543692i
$120$	−68.5506	−	225.328i	−0.571255	−	1.87773i
$121$	45.8256	+	38.4522i	0.378724	+	0.317787i
$122$	41.0301	−	37.8443i	0.336312	−	0.310199i
$123$	89.5064	−	72.1191i	0.727694	−	0.586335i
$124$	34.2711	−	49.6309i	0.276380	−	0.400249i
$125$	227.208	−	393.536i	1.81766	−	3.14829i
$126$	28.7588	+	77.3018i	0.228245	+	0.613507i
$127$	−159.542	+	92.1119i	−1.25624	+	0.725290i	−0.972341	−	0.233564i	$-0.924961\pi$
$127$	−159.542	+	92.1119i	−1.25624	+	0.725290i	−0.283898	+	0.958854i	$0.591628\pi$
$128$	−96.3232	−	84.2962i	−0.752525	−	0.658564i
$129$	107.275	+	64.8148i	0.831588	+	0.502441i
$130$	30.0027	+	133.273i	0.230790	+	1.02517i
$131$	198.290	+	34.9638i	1.51366	+	0.266900i	0.867939	−	0.496671i	$-0.165445\pi$
$131$	198.290	+	34.9638i	1.51366	+	0.266900i	0.645724	+	0.763571i	$0.276556\pi$
$132$	−77.5987	+	52.8035i	−0.587869	+	0.400026i
$133$	−74.7123	+	62.6911i	−0.561747	+	0.471362i
$134$	−77.8649	−	9.99257i	−0.581082	−	0.0745714i
$135$	−61.4965	+	257.730i	−0.455530	+	1.90911i
$136$	−44.9119	+	111.504i	−0.330235	+	0.819882i
$137$	−88.9077	+	74.6024i	−0.648961	+	0.544543i	−0.906756	−	0.421657i	$-0.861449\pi$
$137$	−88.9077	+	74.6024i	−0.648961	+	0.544543i	0.257794	+	0.966200i	$0.417004\pi$
$138$	−99.5516	+	20.3390i	−0.721388	+	0.147384i
$139$	−163.809	−	28.8839i	−1.17848	−	0.207798i	−0.450105	−	0.892975i	$-0.648614\pi$
$139$	−163.809	−	28.8839i	−1.17848	−	0.207798i	−0.728376	+	0.685177i	$0.759725\pi$
$140$	16.8462	+	179.076i	0.120330	+	1.27912i
$141$	3.65280	−	183.546i	0.0259064	−	1.30175i
$142$	−3.71261	−	79.1048i	−0.0261452	−	0.557076i
$143$	47.1469	−	27.2203i	0.329699	−	0.190352i
$144$	45.6159	+	136.584i	0.316777	+	0.948500i
$145$	95.0490	−	164.630i	0.655510	−	1.13538i
$146$	−75.8261	+	146.829i	−0.519357	+	1.00568i
$147$	12.9395	+	83.0101i	0.0880238	+	0.564695i
$148$	−69.2931	−	97.5981i	−0.468197	−	0.659447i
$149$	69.6965	+	58.4823i	0.467762	+	0.392499i	0.845977	−	0.533219i	$-0.179018\pi$
$149$	69.6965	+	58.4823i	0.467762	+	0.392499i	−0.378216	+	0.925718i	$0.623462\pi$
$150$	−203.835	+	376.152i	−1.35890	+	2.50768i
$151$	−8.83574	+	24.2760i	−0.0585148	+	0.160768i	−0.965506	−	0.260382i	$-0.916151\pi$
$151$	−8.83574	+	24.2760i	−0.0585148	+	0.160768i	0.906991	+	0.421151i	$0.138374\pi$
$152$	−134.070	+	104.978i	−0.882038	+	0.690643i
$153$	106.973	−	82.7369i	0.699168	−	0.540764i
$154$	66.1337	−	27.6468i	0.429440	−	0.179525i
$155$	−145.724	+	25.6951i	−0.940156	+	0.165775i
$156$	−20.5368	−	80.9582i	−0.131646	−	0.518963i
$157$	−11.4347	+	4.16190i	−0.0728326	+	0.0265089i	−0.378180	−	0.925732i	$-0.623450\pi$
$157$	−11.4347	+	4.16190i	−0.0728326	+	0.0265089i	0.305347	+	0.952241i	$0.401228\pi$
$158$	9.62848	−	30.8890i	0.0609397	−	0.195500i
$159$	−14.4251	+	73.2541i	−0.0907242	+	0.460718i
$160$	18.8179	+	313.468i	0.117612	+	1.95918i
$161$	77.5967			0.481967
$162$	33.3314	−	158.534i	0.205749	−	0.978605i
$163$		−	187.452i		−	1.15001i	−0.818148	−	0.575007i	$-0.804999\pi$
$163$		−	187.452i		−	1.15001i	0.818148	−	0.575007i	$-0.195001\pi$
$164$	−138.476	+	65.6767i	−0.844365	+	0.400468i
$165$	225.936	+	44.4912i	1.36931	+	0.269644i
$166$	51.5320	−	165.319i	0.310434	−	0.995897i
$167$	−71.8589	−	197.431i	−0.430293	−	1.18222i	−0.945634	−	0.325234i	$-0.894557\pi$
$167$	−71.8589	−	197.431i	−0.430293	−	1.18222i	0.515341	−	0.856985i	$-0.327665\pi$
$168$	−13.2518	−	109.170i	−0.0788799	−	0.649819i
$169$	−20.9343	−	118.724i	−0.123871	−	0.702509i
$170$	272.099	−	113.749i	1.60058	−	0.669115i
$171$	189.828	−	25.7325i	1.11011	−	0.150482i
$172$	−118.936	−	117.393i	−0.691489	−	0.682516i
$173$	−158.665	−	57.7495i	−0.917141	−	0.333812i	−0.160040	−	0.987110i	$-0.551162\pi$
$173$	−158.665	−	57.7495i	−0.917141	−	0.333812i	−0.757100	+	0.653298i	$0.773385\pi$
$174$	−55.3746	+	102.187i	−0.318245	+	0.587281i
$175$	210.017	−	250.289i	1.20010	−	1.43022i
$176$	117.031	−	44.3351i	0.664948	−	0.251904i
$177$	−269.945	+	42.0787i	−1.52511	+	0.237733i
$178$	−10.8970	+	21.1008i	−0.0612190	+	0.118544i
$179$	−273.877	−	158.123i	−1.53004	−	0.883370i	−0.999359	−	0.0357989i	$-0.988602\pi$
$179$	−273.877	−	158.123i	−1.53004	−	0.883370i	−0.530682	−	0.847571i	$-0.678064\pi$
$180$	159.872	−	315.043i	0.888180	−	1.75024i
$181$	−78.2492	−	135.532i	−0.432316	−	0.748793i	0.564757	−	0.825258i	$-0.308970\pi$
$181$	−78.2492	−	135.532i	−0.432316	−	0.748793i	−0.997072	+	0.0764647i	$0.975637\pi$
$182$	2.99032	+	63.7148i	0.0164303	+	0.350081i
$183$	83.7106	+	1.66595i	0.457435	+	0.00910354i
$184$	135.400	+	4.58336i	0.735868	+	0.0249096i
$185$	−50.9931	+	289.196i	−0.275638	+	1.56322i
$186$	88.6394	−	18.1096i	0.476556	−	0.0973633i
$187$	−75.5468	−	90.0331i	−0.403993	−	0.481461i
$188$	−61.8075	+	236.845i	−0.328763	+	1.25981i
$189$	−49.1743	+	113.525i	−0.260182	+	0.600659i
$190$	414.362	+	53.1759i	2.18085	+	0.279873i
$191$	−53.6600	−	63.9495i	−0.280942	−	0.334814i	0.607057	−	0.794658i	$-0.292350\pi$
$191$	−53.6600	−	63.9495i	−0.280942	−	0.334814i	−0.888000	+	0.459844i	$0.847905\pi$
$192$	−16.6751	−	191.275i	−0.0868494	−	0.996221i
$193$	−11.5935	+	65.7498i	−0.0600698	+	0.340673i	−1.00000		0.000694602i	$-0.999779\pi$
$193$	−11.5935	+	65.7498i	−0.0600698	+	0.340673i	0.939930	+	0.341367i	$0.110890\pi$
$194$	−22.3318	−	99.1985i	−0.115113	−	0.511332i
$195$	−105.967	+	175.385i	−0.543419	+	0.899412i
$196$	9.03397	−	111.652i	0.0460917	−	0.569652i
$197$	138.831	+	240.462i	0.704725	+	1.22062i	0.966791	+	0.255570i	$0.0822631\pi$
$197$	138.831	+	240.462i	0.704725	+	1.22062i	−0.262065	+	0.965050i	$0.584404\pi$
$198$	−138.822	−	23.4628i	−0.701120	−	0.118499i
$199$	62.7025	+	36.2013i	0.315088	+	0.181916i	0.649201	−	0.760617i	$-0.275103\pi$
$199$	62.7025	+	36.2013i	0.315088	+	0.181916i	−0.334113	+	0.942533i	$0.608437\pi$
$200$	381.246	−	424.328i	1.90623	−	2.12164i
$201$	−73.8818	−	91.6940i	−0.367571	−	0.456189i
$202$	3.74939	−	3.45827i	0.0185613	−	0.0171201i
$203$	57.0541	−	67.9944i	0.281054	−	0.334948i
$204$	−164.424	+	74.0124i	−0.805999	+	0.362806i
$205$	353.332	+	128.602i	1.72357	+	0.627328i
$206$	74.4290	−	97.6564i	0.361306	−	0.474060i
$207$	−128.856	−	81.3972i	−0.622494	−	0.393223i
$208$	1.45445	+	111.354i	0.00699255	+	0.535354i
$209$	−28.9097	−	163.955i	−0.138324	−	0.784473i
$210$	−167.781	+	211.286i	−0.798959	+	1.00612i
$211$	0.151632	+	0.416605i	0.000718634	+	0.00197443i	0.940051	−	0.341033i	$-0.110777\pi$
$211$	0.151632	+	0.416605i	0.000718634	+	0.00197443i	−0.939333	+	0.343007i	$0.888554\pi$
$212$	41.4807	−	90.4938i	0.195664	−	0.426858i
$213$	78.1508	−	89.4594i	0.366905	−	0.419997i
$214$	−206.376	+	132.425i	−0.964374	+	0.618810i
$215$			409.992i			1.90694i
$216$	−92.5106	+	195.187i	−0.428290	+	0.903641i
$217$	−69.0911			−0.318392
$218$	41.0282	+	63.9397i	0.188203	+	0.293301i
$219$	−234.571	+	80.1280i	−1.07110	+	0.365881i
$220$	−279.108	−	127.938i	−1.26867	−	0.581536i
$221$	98.2777	−	35.7702i	0.444695	−	0.161856i
$222$	26.3925	−	177.592i	0.118885	−	0.799965i
$223$	25.9540	−	4.57639i	0.116386	−	0.0205219i	−0.115152	−	0.993348i	$-0.536735\pi$
$223$	25.9540	−	4.57639i	0.116386	−	0.0205219i	0.231538	+	0.972826i	$0.425624\pi$
$224$	−16.7630	+	145.666i	−0.0748347	+	0.650297i
$225$	−611.299	+	195.323i	−2.71689	+	0.868103i
$226$	173.011	+	131.860i	0.765534	+	0.583453i
$227$	−5.75679	+	15.8167i	−0.0253603	+	0.0696769i	−0.951727	−	0.306947i	$-0.900693\pi$
$227$	−5.75679	+	15.8167i	−0.0253603	+	0.0696769i	0.926366	+	0.376623i	$0.122915\pi$
$228$	−254.127	−	25.6607i	−1.11459	−	0.112547i
$229$	−196.606	−	164.972i	−0.858542	−	0.720403i	0.103111	−	0.994670i	$-0.467120\pi$
$229$	−196.606	−	164.972i	−0.858542	−	0.720403i	−0.961654	+	0.274267i	$0.911565\pi$
$230$	−225.350	−	244.320i	−0.979782	−	1.06226i
$231$	100.284	+	38.7770i	0.434130	+	0.167866i
$232$	103.571	−	115.275i	0.446426	−	0.496873i
$233$	8.54082	−	14.7931i	0.0366559	−	0.0634899i	−0.847115	−	0.531409i	$-0.821663\pi$
$233$	8.54082	−	14.7931i	0.0366559	−	0.0634899i	0.883771	+	0.467919i	$0.154996\pi$
$234$	61.8698	−	108.941i	0.264401	−	0.465559i
$235$	520.074	−	300.265i	2.21308	−	1.27772i
$236$	363.087	+	29.3781i	1.53850	+	0.124483i
$237$	42.5047	−	23.4250i	0.179345	−	0.0988398i
$238$	134.341	−	30.2432i	0.564458	−	0.127072i
$239$	−304.381	−	53.6706i	−1.27356	−	0.224563i	−0.504318	−	0.863518i	$-0.668256\pi$
$239$	−304.381	−	53.6706i	−1.27356	−	0.224563i	−0.769244	+	0.638955i	$0.779367\pi$
$240$	−305.245	+	358.766i	−1.27185	+	1.49486i
$241$	203.062	−	170.389i	0.842580	−	0.707009i	−0.115563	−	0.993300i	$-0.536867\pi$
$241$	203.062	−	170.389i	0.842580	−	0.707009i	0.958143	+	0.286292i	$0.0924226\pi$
$242$	15.2290	−	118.669i	0.0629299	−	0.490367i
$243$	200.743	−	136.935i	0.826104	−	0.563518i
$244$	−108.019	−	28.1888i	−0.442699	−	0.115528i
$245$	−210.524	+	176.651i	−0.859281	+	0.721023i
$246$	−218.072	−	72.7670i	−0.886470	−	0.295801i
$247$	145.897	+	25.7255i	0.590675	+	0.104152i
$248$	−120.558	−	4.08096i	−0.486122	−	0.0164555i
$249$	227.487	−	125.372i	0.913601	−	0.503501i
$250$	−907.833	+	42.6072i	−3.63133	+	0.170429i
$251$	−184.422	+	106.476i	−0.734748	+	0.424207i	−0.820156	−	0.572139i	$-0.806114\pi$
$251$	−184.422	+	106.476i	−0.734748	+	0.424207i	0.0854089	+	0.996346i	$0.472780\pi$
$252$	99.0570	−	131.903i	0.393084	−	0.523423i
$253$	−66.2289	+	114.712i	−0.261774	+	0.453407i
$254$	327.371	+	169.062i	1.28886	+	0.665599i
$255$	412.606	+	159.543i	1.61806	+	0.625661i
$256$	−37.8540	+	253.186i	−0.147867	+	0.989007i
$257$	345.413	+	289.836i	1.34402	+	1.12776i	0.980574	+	0.196149i	$0.0628435\pi$
$257$	345.413	+	289.836i	1.34402	+	1.12776i	0.363444	+	0.931616i	$0.381601\pi$
$258$	−6.76721	−	250.579i	−0.0262295	−	0.971235i
$259$	−46.8959	+	128.845i	−0.181065	+	0.497472i
$260$	191.927	−	194.451i	0.738182	−	0.747887i
$261$	−166.068	+	53.0622i	−0.636276	+	0.203304i
$262$	−155.320	−	371.539i	−0.592823	−	1.41809i
$263$	−19.1179	+	3.37100i	−0.0726916	+	0.0128175i	−0.209876	−	0.977728i	$-0.567306\pi$
$263$	−19.1179	+	3.37100i	−0.0726916	+	0.0128175i	0.137184	+	0.990546i	$0.456195\pi$
$264$	172.697	+	73.5861i	0.654154	+	0.278735i
$265$	−229.500	+	83.5311i	−0.866037	+	0.315212i
$266$	186.223	+	58.0480i	0.700085	+	0.218225i
$267$	−33.7102	+	11.5152i	−0.126255	+	0.0431282i
$268$	67.2819	+	141.860i	0.251052	+	0.529330i
$269$	−421.021			−1.56513			−0.782567	−	0.622567i	$-0.786090\pi$
$269$	−421.021			−1.56513			−0.782567	+	0.622567i	$0.786090\pi$
$270$	500.250	−	174.859i	1.85278	−	0.647627i
$271$			213.999i			0.789665i	0.918753	+	0.394833i	$0.129197\pi$
$271$			213.999i			0.789665i	−0.918753	+	0.394833i	$0.870803\pi$
$272$	236.200	−	44.8369i	0.868383	−	0.164841i
$273$	−62.9464	+	72.0550i	−0.230573	+	0.263938i
$274$	221.605	+	69.0771i	0.808777	+	0.252106i
$275$	190.754	+	524.092i	0.693651	+	1.90579i
$276$	141.762	+	145.603i	0.513629	+	0.527549i
$277$	−19.4010	−	110.028i	−0.0700396	−	0.397214i	−0.999593	−	0.0285268i	$-0.990918\pi$
$277$	−19.4010	−	110.028i	−0.0700396	−	0.397214i	0.929553	−	0.368687i	$-0.120193\pi$
$278$	128.311	+	306.931i	0.461550	+	1.10407i
$279$	114.732	+	72.4750i	0.411225	+	0.259767i
$280$	283.237	−	221.777i	1.01156	−	0.792061i
$281$	47.4594	+	17.2738i	0.168895	+	0.0614727i	0.425084	−	0.905154i	$-0.360245\pi$
$281$	47.4594	+	17.2738i	0.168895	+	0.0614727i	−0.256189	+	0.966627i	$0.582467\pi$
$282$	−312.902	+	192.100i	−1.10958	+	0.681205i
$283$	−323.295	+	385.288i	−1.14238	+	1.36144i	−0.219847	+	0.975534i	$0.570556\pi$
$283$	−323.295	+	385.288i	−1.14238	+	1.36144i	−0.922538	+	0.385907i	$0.873889\pi$
$284$	−129.144	+	91.6905i	−0.454733	+	0.322854i
$285$	393.165	+	487.953i	1.37953	+	1.71212i
$286$	−96.7424	−	49.9601i	−0.338260	−	0.174686i
$287$	152.044	+	87.7827i	0.529770	+	0.305863i
$288$	180.637	−	224.308i	0.627213	−	0.778848i
$289$	31.6076	+	54.7461i	0.109369	+	0.189433i
$290$	−379.778	+	17.8241i	−1.30958	+	0.0614622i
$291$	78.8739	−	130.544i	0.271044	−	0.448605i
$292$	329.052	−	30.9549i	1.12689	−	0.106010i
$293$	19.6082	−	111.204i	0.0669222	−	0.379535i	−0.932890	−	0.360161i	$-0.882722\pi$
$293$	19.6082	−	111.204i	0.0669222	−	0.379535i	0.999812	−	0.0193737i	$-0.00616722\pi$
$294$	125.752	−	111.440i	0.427728	−	0.379047i
$295$	−574.460	−	684.615i	−1.94732	−	2.32073i
$296$	−89.4399	+	222.055i	−0.302162	+	0.750184i
$297$	−125.854	−	169.588i	−0.423751	−	0.571005i
$298$	23.1620	−	180.485i	0.0777247	−	0.605653i
$299$	−75.7645	−	90.2927i	−0.253393	−	0.301982i
$300$	853.326	−	63.1743i	2.84442	−	0.210581i
$301$	−33.2421	+	188.525i	−0.110439	+	0.626329i
$302$	50.4064	−	11.3476i	0.166909	−	0.0375750i
$303$	7.64959	+	0.152237i	0.0252462	+	0.000502431i
$304$	321.514	+	112.288i	1.05761	+	0.369370i
$305$	136.943	+	237.192i	0.448993	+	0.777679i
$306$	−254.810	−	90.6992i	−0.832711	−	0.296403i
$307$	−268.474	−	155.003i	−0.874507	−	0.504897i	−0.00566388	−	0.999984i	$-0.501803\pi$
$307$	−268.474	−	155.003i	−0.874507	−	0.504897i	−0.868843	+	0.495087i	$0.835136\pi$
$308$	−117.968	−	81.4592i	−0.383013	−	0.264478i
$309$	181.982	−	28.3671i	0.588937	−	0.0918028i
$310$	200.649	+	217.539i	0.647253	+	0.701739i
$311$	275.480	−	328.304i	0.885786	−	1.05564i	−0.112292	−	0.993675i	$-0.535819\pi$
$311$	275.480	−	328.304i	0.885786	−	1.05564i	0.998078	−	0.0619638i	$-0.0197363\pi$
$312$	−114.092	+	122.012i	−0.365681	+	0.391064i
$313$	56.7914	+	20.6704i	0.181442	+	0.0660395i	0.431144	−	0.902283i	$-0.358110\pi$
$313$	56.7914	+	20.6704i	0.181442	+	0.0660395i	−0.249701	+	0.968323i	$0.580332\pi$
$314$	19.3562	+	14.7524i	0.0616440	+	0.0469821i
$315$	−401.033	+	54.3627i	−1.27312	+	0.172580i
$316$	−62.3940	+	17.1559i	−0.197449	+	0.0542909i
$317$	−56.8344	−	322.324i	−0.179288	−	1.01680i	−0.933077	−	0.359678i	$-0.882887\pi$
$317$	−56.8344	−	322.324i	−0.179288	−	1.01680i	0.753788	−	0.657117i	$-0.228224\pi$
$318$	138.887	−	54.8405i	0.436751	−	0.172454i
$319$	51.8210	+	142.377i	0.162448	+	0.446323i
$320$	507.325	−	370.253i	1.58539	−	1.15704i
$321$	−360.883	−	71.0649i	−1.12425	−	0.221386i
$322$	−83.8123	−	130.616i	−0.260287	−	0.405639i
$323$		−	319.830i		−	0.990186i
$324$	−302.856	+	115.127i	−0.934741	+	0.355331i
$325$	−496.298			−1.52707
$326$	−315.532	+	202.467i	−0.967890	+	0.621066i
$327$	−22.0174	+	111.809i	−0.0673315	+	0.341925i
$328$	260.119	+	162.154i	0.793047	+	0.494373i
$329$	263.489	−	95.9021i	0.800878	−	0.291496i
$330$	−169.143	−	428.366i	−0.512556	−	1.29808i
$331$	270.454	−	47.6883i	0.817081	−	0.144073i	0.250539	−	0.968107i	$-0.419392\pi$
$331$	270.454	−	47.6883i	0.817081	−	0.144073i	0.566542	+	0.824033i	$0.308281\pi$
$332$	−333.935	+	91.8192i	−1.00583	+	0.276564i
$333$	213.031	−	164.766i	0.639732	−	0.494794i
$334$	−254.713	+	334.203i	−0.762614	+	1.00061i
$335$	131.745	−	361.967i	0.393270	−	1.08050i
$336$	−169.448	+	140.220i	−0.504309	+	0.417323i
$337$	439.240	+	368.567i	1.30338	+	1.09367i	0.989550	+	0.144191i	$0.0460581\pi$
$337$	439.240	+	368.567i	1.30338	+	1.09367i	0.313834	+	0.949478i	$0.398386\pi$
$338$	−177.233	+	163.472i	−0.524358	+	0.483645i
$339$	50.2558	+	322.403i	0.148247	+	0.951043i
$340$	−485.365	−	335.154i	−1.42754	−	0.985747i
$341$	58.9694	−	102.138i	0.172931	−	0.299525i
$342$	−248.348	−	291.737i	−0.726164	−	0.853033i
$343$	−305.570	+	176.421i	−0.890876	+	0.514347i
$344$	−69.1401	+	326.997i	−0.200989	+	0.950573i
$345$	9.92014	−	498.467i	0.0287540	−	1.44483i
$346$	74.1670	+	329.451i	0.214355	+	0.952171i
$347$	18.5984	+	3.27941i	0.0535978	+	0.00945074i	0.200383	−	0.979718i	$-0.435781\pi$
$347$	18.5984	+	3.27941i	0.0535978	+	0.00945074i	−0.146785	+	0.989168i	$0.546893\pi$
$348$	231.818	−	17.1622i	0.666143	−	0.0493166i
$349$	39.3809	−	33.0445i	0.112839	−	0.0946834i	−0.584622	−	0.811306i	$-0.698757\pi$
$349$	39.3809	−	33.0445i	0.112839	−	0.0946834i	0.697462	+	0.716622i	$0.254313\pi$
$350$	−648.142	−	83.1774i	−1.85183	−	0.237650i
$351$	180.112	−	53.6242i	0.513140	−	0.152776i
$352$	−201.033	−	149.107i	−0.571116	−	0.423601i
$353$	192.526	−	161.549i	0.545400	−	0.457645i	−0.327980	−	0.944685i	$-0.606368\pi$
$353$	192.526	−	161.549i	0.545400	−	0.457645i	0.873380	+	0.487040i	$0.161923\pi$
$354$	362.398	+	408.940i	1.02372	+	1.15520i
$355$	382.672	+	67.4754i	1.07795	+	0.190072i
$356$	47.2881	−	4.44853i	0.132832	−	0.0124959i
$357$	176.791	+	106.816i	0.495213	+	0.299205i
$358$	29.6520	+	631.797i	0.0828269	+	1.76480i
$359$	32.9975	−	19.0511i	0.0919150	−	0.0530671i	−0.453338	−	0.891339i	$-0.649767\pi$
$359$	32.9975	−	19.0511i	0.0919150	−	0.0530671i	0.545253	+	0.838272i	$0.316434\pi$
$360$	−702.980	+	71.1709i	−1.95272	+	0.197697i
$361$	46.0239	−	79.7157i	0.127490	−	0.220819i
$362$	−143.618	+	278.102i	−0.396736	+	0.768237i
$363$	139.745	−	112.598i	0.384972	−	0.310188i
$364$	104.019	−	73.8520i	0.285767	−	0.202890i
$365$	−621.150	−	521.207i	−1.70178	−	1.42796i
$366$	−87.6116	−	142.706i	−0.239376	−	0.389908i
$367$	−111.793	+	307.148i	−0.304612	+	0.836915i	0.689071	+	0.724694i	$0.258019\pi$
$367$	−111.793	+	307.148i	−0.304612	+	0.836915i	−0.993683	+	0.112222i	$0.964203\pi$
$368$	−138.530	−	232.864i	−0.376441	−	0.632783i
$369$	−160.400	−	305.262i	−0.434690	−	0.827268i
$370$	541.872	−	226.526i	1.46452	−	0.612233i
$371$	−112.303	+	19.8020i	−0.302702	+	0.0533746i
$372$	−126.223	−	129.643i	−0.339308	−	0.348504i
$373$	168.707	−	61.4042i	0.452297	−	0.164623i	−0.105819	−	0.994385i	$-0.533747\pi$
$373$	168.707	−	61.4042i	0.452297	−	0.164623i	0.558116	+	0.829763i	$0.311524\pi$
$374$	−69.9515	+	224.410i	−0.187036	+	0.600027i
$375$	−1026.67	−	896.885i	−2.73778	−	2.39169i
$376$	465.431	−	151.778i	1.23785	−	0.403665i
$377$	−134.826			−0.357629
$378$	244.205	−	39.8447i	0.646046	−	0.105409i
$379$		−	361.411i		−	0.953590i	−0.879014	−	0.476795i	$-0.841798\pi$
$379$		−	361.411i		−	0.953590i	0.879014	−	0.476795i	$-0.158202\pi$
$380$	−358.043	−	754.916i	−0.942219	−	1.98662i
$381$	178.654	+	522.999i	0.468908	+	1.37270i
$382$	−49.6857	+	159.396i	−0.130067	+	0.417267i
$383$	119.450	+	328.187i	0.311880	+	0.856884i	0.992277	+	0.124040i	$0.0395853\pi$
$383$	119.450	+	328.187i	0.311880	+	0.856884i	−0.680397	+	0.732844i	$0.738193\pi$
$384$	−303.955	+	234.664i	−0.791549	+	0.611105i
$385$	61.0749	+	346.373i	0.158636	+	0.899669i
$386$	123.197	−	51.5016i	0.319162	−	0.133424i
$387$	252.960	−	278.192i	0.653644	−	0.718843i
$388$	−142.857	+	144.735i	−0.368187	+	0.373028i
$389$	−0.536764	−	0.195366i	−0.00137986	−	0.000502227i	0.341330	−	0.939943i	$-0.389123\pi$
$389$	−0.536764	−	0.195366i	−0.00137986	−	0.000502227i	−0.342710	+	0.939441i	$0.611345\pi$
$390$	409.675	−	11.0638i	1.05045	−	0.0283688i
$391$	−163.565	+	194.930i	−0.418326	+	0.498541i
$392$	−197.697	+	105.389i	−0.504330	+	0.268849i
$393$	217.849	−	563.395i	0.554324	−	1.43357i
$394$	254.810	−	493.413i	0.646726	−	1.25232i
$395$	137.488	+	79.3787i	0.348071	+	0.200959i
$396$	110.447	+	259.016i	0.278907	+	0.654081i
$397$	−8.92090	−	15.4515i	−0.0224708	−	0.0389206i	0.854571	−	0.519334i	$-0.173820\pi$
$397$	−8.92090	−	15.4515i	−0.0224708	−	0.0389206i	−0.877042	+	0.480413i	$0.840487\pi$
$398$	−6.78865	−	144.646i	−0.0170569	−	0.363432i
$399$	141.224	+	256.251i	0.353946	+	0.642234i
$400$	−1126.04	−	183.421i	−2.81510	−	0.458553i
$401$	67.6511	−	383.668i	0.168706	−	0.956779i	−0.776455	−	0.630173i	$-0.782984\pi$
$401$	67.6511	−	383.668i	0.168706	−	0.956779i	0.945161	−	0.326606i	$-0.105905\pi$
$402$	−74.5455	+	223.401i	−0.185436	+	0.555725i
$403$	67.4598	+	80.3954i	0.167394	+	0.199492i
$404$	−9.87090	−	2.57593i	−0.0244329	−	0.00637607i
$405$	722.975	+	330.400i	1.78512	+	0.815803i
$406$	−176.077	−	22.5963i	−0.433687	−	0.0556559i
$407$	−150.448	−	179.296i	−0.369650	−	0.440532i
$408$	302.177	+	196.828i	0.740629	+	0.482421i
$409$	84.5691	−	479.615i	0.206770	−	1.17265i	−0.687859	−	0.725844i	$-0.741449\pi$
$409$	84.5691	−	479.615i	0.206770	−	1.17265i	0.894629	−	0.446809i	$-0.147440\pi$
$410$	−165.162	−	733.655i	−0.402835	−	1.78940i
$411$	168.057	+	304.939i	0.408898	+	0.741944i
$412$	−244.772	−	19.8050i	−0.594108	−	0.0480704i
$413$	−208.643	−	361.380i	−0.505189	−	0.875013i
$414$	2.16457	+	304.816i	0.00522844	+	0.736271i
$415$	735.841	+	424.838i	1.77311	+	1.02371i
$416$	185.867	−	122.722i	0.446795	−	0.295004i
$417$	−179.967	+	465.425i	−0.431576	+	1.11613i
$418$	−244.754	+	225.751i	−0.585536	+	0.540073i
$419$	358.205	−	426.892i	0.854905	−	1.01884i	−0.144664	−	0.989481i	$-0.546210\pi$
$419$	358.205	−	426.892i	0.854905	−	1.01884i	0.999569	−	0.0293551i	$-0.00934536\pi$
$420$	536.870	+	54.2109i	1.27826	+	0.129074i
$421$	−693.894	−	252.557i	−1.64821	−	0.599898i	−0.659760	−	0.751476i	$-0.729342\pi$
$421$	−693.894	−	252.557i	−1.64821	−	0.599898i	−0.988445	+	0.151579i	$0.951564\pi$
$422$	0.537479	−	0.705212i	0.00127365	−	0.00167112i
$423$	−538.146	−	117.140i	−1.27221	−	0.276927i
$424$	−197.128	+	27.9195i	−0.464925	+	0.0658479i
$425$	186.054	+	1055.16i	0.437773	+	2.48274i
$426$	−234.995	−	34.9233i	−0.551631	−	0.0819795i
$427$	43.7384	+	120.170i	0.102432	+	0.281429i
$428$	445.814	+	204.353i	1.04162	+	0.477460i
$429$	−52.7946	−	154.553i	−0.123064	−	0.360264i
$430$	690.126	−	442.833i	1.60494	−	1.02984i
$431$			623.656i			1.44700i	0.690326	+	0.723499i	$0.257467\pi$
$431$			623.656i			1.44700i	−0.690326	+	0.723499i	$0.742533\pi$
$432$	428.472	−	55.1013i	0.991832	−	0.127549i
$433$	533.046			1.23105			0.615527	−	0.788116i	$-0.288943\pi$
$433$	533.046			1.23105			0.615527	+	0.788116i	$0.288943\pi$
$434$	74.6253	+	116.299i	0.171948	+	0.267969i
$435$	−429.490	−	375.198i	−0.987333	−	0.862524i
$436$	63.3128	−	138.123i	0.145213	−	0.316795i
$437$	−338.715	+	123.282i	−0.775092	+	0.282110i
$438$	388.237	+	308.298i	0.886385	+	0.703877i
$439$	491.828	−	86.7226i	1.12034	−	0.197546i	0.417349	−	0.908746i	$-0.362959\pi$
$439$	491.828	−	86.7226i	1.12034	−	0.197546i	0.702989	+	0.711201i	$0.251848\pi$
$440$	86.1116	+	607.999i	0.195708	+	1.38182i
$441$	251.838	+	10.0278i	0.571061	+	0.0227387i
$442$	−166.360	−	126.792i	−0.376381	−	0.286860i
$443$	−3.57129	+	9.81203i	−0.00806159	+	0.0221490i	−0.943658	−	0.330922i	$-0.892640\pi$
$443$	−3.57129	+	9.81203i	−0.00806159	+	0.0221490i	0.935597	+	0.353071i	$0.114863\pi$
$444$	−327.442	+	147.392i	−0.737481	+	0.331964i
$445$	−89.2656	−	74.9028i	−0.200597	−	0.168321i
$446$	−35.7362	−	38.7445i	−0.0801260	−	0.0868710i
$447$	212.539	−	171.252i	0.475479	−	0.383114i
$448$	263.301	−	129.118i	0.587725	−	0.288210i
$449$	182.013	−	315.257i	0.405375	−	0.702131i	−0.588990	−	0.808140i	$-0.700474\pi$
$449$	182.013	−	315.257i	0.405375	−	0.702131i	0.994365	+	0.106010i	$0.0338075\pi$
$450$	989.046	+	818.010i	2.19788	+	1.81780i
$451$	−259.540	+	149.845i	−0.575476	+	0.332251i
$452$	35.0871	−	433.645i	0.0776263	−	0.959392i
$453$	66.3343	+	40.0788i	0.146433	+	0.0884741i
$454$	32.8416	−	7.39338i	0.0723382	−	0.0162850i
$455$	−308.223	−	54.3480i	−0.677412	−	0.119446i
$456$	231.289	+	455.479i	0.507213	+	0.998857i
$457$	−193.083	+	162.016i	−0.422502	+	0.354521i	−0.829114	−	0.559080i	$-0.811155\pi$
$457$	−193.083	+	162.016i	−0.422502	+	0.354521i	0.406612	+	0.913601i	$0.366710\pi$
$458$	−65.3374	+	509.127i	−0.142658	+	1.11163i
$459$	−181.530	−	362.828i	−0.395489	−	0.790475i
$460$	−167.854	+	643.214i	−0.364901	+	1.39829i
$461$	210.415	−	176.559i	0.456432	−	0.382992i	−0.385384	−	0.922756i	$-0.625931\pi$
$461$	210.415	−	176.559i	0.456432	−	0.382992i	0.841816	+	0.539764i	$0.181487\pi$
$462$	−43.0448	−	210.688i	−0.0931705	−	0.456034i
$463$	23.3623	+	4.11941i	0.0504586	+	0.00889720i	0.198820	−	0.980036i	$-0.436289\pi$
$463$	23.3623	+	4.11941i	0.0504586	+	0.00889720i	−0.148362	+	0.988933i	$0.547400\pi$
$464$	−305.905	−	49.8289i	−0.659277	−	0.107390i
$465$	−8.83276	+	443.829i	−0.0189952	+	0.954470i
$466$	−34.1257	+	1.60162i	−0.0732312	+	0.00343695i
$467$	−7.22269	+	4.17002i	−0.0154661	+	0.00892939i	−0.507713	−	0.861526i	$-0.669509\pi$
$467$	−7.22269	+	4.17002i	−0.0154661	+	0.00892939i	0.492247	+	0.870456i	$0.336176\pi$
$468$	−250.202	+	13.5239i	−0.534620	+	0.0288973i
$469$	89.9281	−	155.760i	0.191744	−	0.332111i
$470$	−1067.16	−	551.106i	−2.27055	−	1.17257i
$471$	5.62256	+	36.0701i	0.0119375	+	0.0765820i
$472$	−342.719	−	642.903i	−0.726101	−	1.36208i
$473$	−250.326	−	210.049i	−0.529231	−	0.444077i
$474$	−85.3399	−	46.2452i	−0.180042	−	0.0975638i
$475$	−519.092	+	1426.19i	−1.09283	+	3.00251i
$476$	−196.009	−	193.466i	−0.411784	−	0.406441i
$477$	207.260	+	84.9201i	0.434508	+	0.178029i
$478$	238.421	+	570.324i	0.498788	+	1.19315i
$479$	464.091	−	81.8317i	0.968874	−	0.170839i	0.333251	−	0.942838i	$-0.391854\pi$
$479$	464.091	−	81.8317i	0.968874	−	0.170839i	0.635623	+	0.772000i	$0.280743\pi$
$480$	933.593	+	126.305i	1.94498	+	0.263135i
$481$	195.715	−	71.2345i	0.406892	−	0.148097i
$482$	−506.137	−	157.769i	−1.05008	−	0.327322i
$483$	44.9771	−	228.404i	0.0931203	−	0.472886i
$484$	−216.200	+	102.540i	−0.446694	+	0.211859i
$485$	498.925			1.02871
$486$	−447.321	−	190.000i	−0.920413	−	0.390947i
$487$			218.971i			0.449633i	0.974401	+	0.224817i	$0.0721783\pi$
$487$			218.971i			0.449633i	−0.974401	+	0.224817i	$0.927822\pi$
$488$	69.2219	+	212.271i	0.141848	+	0.434981i
$489$	−551.761	−	108.652i	−1.12835	−	0.222193i
$490$	524.737	+	163.567i	1.07089	+	0.333810i
$491$	41.7305	+	114.654i	0.0849908	+	0.233510i	0.974906	−	0.222615i	$-0.0714592\pi$
$491$	41.7305	+	114.654i	0.0849908	+	0.233510i	−0.889916	+	0.456125i	$0.849237\pi$
$492$	113.053	+	445.668i	0.229783	+	0.905829i
$493$	50.5441	+	286.650i	0.102523	+	0.581439i
$494$	−114.280	−	273.369i	−0.231337	−	0.553378i
$495$	261.917	−	639.249i	0.529126	−	1.29141i
$496$	123.346	+	207.339i	0.248681	+	0.418023i
$497$	170.491	+	62.0538i	0.343041	+	0.124857i
$498$	−456.743	−	247.506i	−0.917154	−	0.497001i
$499$	18.9123	−	22.5388i	0.0379004	−	0.0451680i	−0.746761	−	0.665092i	$-0.768392\pi$
$499$	18.9123	−	22.5388i	0.0379004	−	0.0451680i	0.784662	+	0.619924i	$0.212837\pi$
$500$	1052.27	+	1482.10i	2.10454	+	2.96421i
$501$	−622.783	+	97.0786i	−1.24308	+	0.193770i
$502$	378.421	+	195.426i	0.753827	+	0.389294i
$503$	−100.859	−	58.2311i	−0.200515	−	0.115768i	0.396381	−	0.918086i	$-0.370266\pi$
$503$	−100.859	−	58.2311i	−0.200515	−	0.115768i	−0.596896	+	0.802319i	$0.703599\pi$
$504$	−329.019	−	24.2712i	−0.652815	−	0.0481570i
$505$	12.5140	+	21.6750i	0.0247803	+	0.0429207i
$506$	264.624	−	12.4196i	0.522973	−	0.0245446i
$507$	−361.595	−	7.19621i	−0.713205	−	0.0141937i
$508$	−69.0171	−	733.656i	−0.135861	−	1.44420i
$509$	−10.6160	+	60.2066i	−0.0208567	+	0.118284i	−0.993459	−	0.114193i	$-0.963572\pi$
$509$	−10.6160	+	60.2066i	−0.0208567	+	0.118284i	0.972602	+	0.232477i	$0.0746830\pi$
$510$	−177.103	−	866.849i	−0.347260	−	1.69970i
$511$	−243.361	−	290.027i	−0.476246	−	0.567567i
$512$	467.065	−	209.748i	0.912236	−	0.409664i
$513$	34.2865	−	573.669i	0.0668352	−	1.11826i
$514$	114.790	−	894.473i	0.223326	−	1.74022i
$515$	387.268	+	461.528i	0.751977	+	0.896171i
$516$	−414.481	+	282.041i	−0.803258	+	0.546592i
$517$	−83.1153	+	471.371i	−0.160765	+	0.911742i
$518$	267.533	−	60.2278i	0.516473	−	0.116270i
$519$	−261.951	+	433.554i	−0.504722	+	0.835364i
$520$	−534.613	−	113.038i	−1.02810	−	0.217381i
$521$	364.846	+	631.931i	0.700280	+	1.21292i	0.968368	+	0.249526i	$0.0802747\pi$
$521$	364.846	+	631.931i	0.700280	+	1.21292i	−0.268089	+	0.963394i	$0.586392\pi$
$522$	268.688	+	222.224i	0.514728	+	0.425716i
$523$	−318.052	−	183.627i	−0.608130	−	0.351104i	0.164103	−	0.986443i	$-0.447527\pi$
$523$	−318.052	−	183.627i	−0.608130	−	0.351104i	−0.772233	+	0.635339i	$0.780860\pi$
$524$	−457.637	+	662.744i	−0.873354	+	1.26478i
$525$	−614.986	−	763.254i	−1.17140	−	1.45382i
$526$	26.3236	+	28.5395i	0.0500448	+	0.0542576i
$527$	145.636	−	173.563i	0.276350	−	0.329341i
$528$	−62.6650	−	370.175i	−0.118684	−	0.701089i
$529$	−227.610	−	82.8431i	−0.430264	−	0.156603i
$530$	388.488	+	296.087i	0.732996	+	0.558655i
$531$	−32.6099	+	818.966i	−0.0614122	+	1.54231i
$532$	−103.429	−	376.160i	−0.194416	−	0.707067i
$533$	−46.3089	−	262.631i	−0.0868835	−	0.492741i
$534$	55.7936	+	44.3056i	0.104482	+	0.0829692i
$535$	−411.513	−	1130.62i	−0.769182	−	2.11331i
$536$	166.117	−	266.477i	0.309920	−	0.497158i
$537$	−624.178	+	714.498i	−1.16234	+	1.33054i
$538$	454.745	+	708.690i	0.845251	+	1.31727i
$539$		−	219.040i		−	0.406383i
$540$	−834.655	−	653.188i	−1.54566	−	1.20961i
$541$	504.486			0.932507			0.466254	−	0.884651i	$-0.345603\pi$
$541$	504.486			0.932507			0.466254	+	0.884651i	$0.345603\pi$
$542$	360.218	−	231.141i	0.664608	−	0.426459i
$543$	−444.289	+	151.767i	−0.818211	+	0.279497i
$544$	−330.592	−	349.159i	−0.607707	−	0.641837i
$545$	−350.291	+	127.495i	−0.642735	+	0.233936i
$546$	189.276	+	28.1289i	0.346660	+	0.0515181i
$547$	−74.2886	+	13.0991i	−0.135811	+	0.0239472i	−0.241140	−	0.970490i	$-0.577521\pi$
$547$	−74.2886	+	13.0991i	−0.135811	+	0.0239472i	0.105329	+	0.994437i	$0.466410\pi$
$548$	−123.081	−	447.630i	−0.224600	−	0.816843i
$549$	53.4245	−	245.434i	0.0973125	−	0.447057i
$550$	676.152	−	887.162i	1.22937	−	1.61302i
$551$	−141.019	+	387.445i	−0.255932	+	0.703168i
$552$	91.9723	−	395.889i	0.166617	−	0.717190i
$553$	56.7845	+	47.6478i	0.102684	+	0.0861624i
$554$	−164.252	+	151.499i	−0.296484	+	0.273463i
$555$	821.685	+	317.723i	1.48051	+	0.572473i
$556$	378.058	−	547.498i	0.679961	−	0.984709i
$557$	−366.474	+	634.751i	−0.657942	+	1.13959i	0.323206	+	0.946329i	$0.395239\pi$
$557$	−366.474	+	634.751i	−0.657942	+	1.13959i	−0.981148	+	0.193260i	$0.938094\pi$
$558$	−1.92731	−	271.404i	−0.00345396	−	0.486388i
$559$	251.828	−	145.393i	0.450497	−	0.260095i
$560$	−679.234	−	237.221i	−1.21292	−	0.423610i
$561$	−308.799	+	170.184i	−0.550444	+	0.303359i
$562$	−22.1846	−	98.5443i	−0.0394743	−	0.175346i
$563$	329.585	+	58.1147i	0.585408	+	0.103223i	0.458505	−	0.888692i	$-0.348385\pi$
$563$	329.585	+	58.1147i	0.585408	+	0.103223i	0.126903	+	0.991915i	$0.459496\pi$
$564$	661.321	+	319.210i	1.17255	+	0.565975i
$565$	−817.655	+	686.094i	−1.44718	+	1.21433i
$566$	997.733	+	128.041i	1.76278	+	0.226221i
$567$	305.654	+	210.545i	0.539072	+	0.371332i
$568$	293.828	+	118.349i	0.517303	+	0.208361i
$569$	−115.616	+	97.0135i	−0.203192	+	0.170498i	−0.738705	−	0.674028i	$-0.764563\pi$
$569$	−115.616	+	97.0135i	−0.203192	+	0.170498i	0.535513	+	0.844527i	$0.320118\pi$
$570$	396.697	−	1188.84i	0.695959	−	2.08568i
$571$	−538.586	−	94.9673i	−0.943234	−	0.166318i	−0.319176	−	0.947696i	$-0.603406\pi$
$571$	−538.586	−	94.9673i	−0.943234	−	0.166318i	−0.624058	+	0.781378i	$0.714517\pi$
$572$	20.3955	+	216.805i	0.0356565	+	0.379030i
$573$	−219.336	+	120.880i	−0.382786	+	0.210960i
$574$	−16.4614	−	350.745i	−0.0286785	−	0.611053i
$575$	1045.75	−	603.764i	1.81870	−	1.05002i
$576$	−572.677	−	61.7851i	−0.994230	−	0.107266i
$577$	−177.054	+	306.667i	−0.306853	+	0.531485i	−0.977672	−	0.210136i	$-0.932609\pi$
$577$	−177.054	+	306.667i	−0.306853	+	0.531485i	0.670819	+	0.741621i	$0.265943\pi$
$578$	58.0127	−	112.335i	0.100368	−	0.194352i
$579$	186.813	+	72.2354i	0.322648	+	0.124759i
$580$	440.201	+	620.015i	0.758967	+	1.06899i
$581$	303.913	+	255.013i	0.523086	+	0.438921i
$582$	−304.932	+	8.23510i	−0.523938	+	0.0141497i
$583$	66.5771	−	182.919i	0.114197	−	0.313755i
$584$	−407.515	−	520.447i	−0.697799	−	0.891177i
$585$	454.821	+	413.568i	0.777472	+	0.706955i
$586$	−208.364	+	87.1054i	−0.355570	+	0.148644i
$587$	729.661	−	128.659i	1.24303	−	0.219180i	0.486818	−	0.873503i	$-0.338157\pi$
$587$	729.661	−	128.659i	1.24303	−	0.219180i	0.756215	+	0.654323i	$0.227046\pi$
$588$	−323.408	−	91.3076i	−0.550013	−	0.155285i
$589$	301.587	−	109.769i	0.512033	−	0.186365i
$590$	−531.913	+	1706.42i	−0.901548	+	2.89224i
$591$	788.264	−	269.267i	1.33378	−	0.455612i
$592$	470.381	−	89.2904i	0.794562	−	0.150828i
$593$	−912.777			−1.53925			−0.769626	−	0.638495i	$-0.779557\pi$
$593$	−912.777			−1.53925			−0.769626	+	0.638495i	$0.779557\pi$
$594$	−149.527	+	395.018i	−0.251729	+	0.665014i
$595$			675.676i			1.13559i
$596$	−328.821	+	155.954i	−0.551712	+	0.261668i
$597$	142.902	−	163.580i	0.239366	−	0.274003i
$598$	−70.1531	+	225.057i	−0.117313	+	0.376350i
$599$	−241.563	−	663.689i	−0.403277	−	1.10799i	−0.960657	−	0.277737i	$-0.910416\pi$
$599$	−241.563	−	663.689i	−0.403277	−	1.10799i	0.557380	−	0.830257i	$-0.311807\pi$
$600$	−1028.02	−	1368.14i	−1.71336	−	2.28023i
$601$	−113.073	−	641.270i	−0.188142	−	1.06701i	−0.921852	−	0.387543i	$-0.873324\pi$
$601$	−113.073	−	641.270i	−0.188142	−	1.06701i	0.733710	−	0.679463i	$-0.237787\pi$
$602$	353.242	−	147.671i	0.586781	−	0.245301i
$603$	−312.723	+	164.321i	−0.518611	+	0.272505i
$604$	−73.5451	−	72.5908i	−0.121763	−	0.120183i
$605$	551.651	+	200.785i	0.911820	+	0.331875i
$606$	−8.00608	−	13.0407i	−0.0132113	−	0.0215193i
$607$	−260.988	+	311.033i	−0.429963	+	0.512410i	−0.936912	−	0.349566i	$-0.886329\pi$
$607$	−260.988	+	311.033i	−0.429963	+	0.512410i	0.506948	+	0.861976i	$0.330773\pi$
$608$	−158.257	−	662.477i	−0.260291	−	1.08960i
$609$	−167.070	−	207.348i	−0.274334	−	0.340474i
$610$	251.345	−	486.703i	0.412041	−	0.797874i
$611$	−368.861	−	212.962i	−0.603700	−	0.348546i
$612$	122.549	+	526.876i	0.200244	+	0.860909i
$613$	453.001	+	784.621i	0.738990	+	1.27997i	0.952950	+	0.303126i	$0.0980303\pi$
$613$	453.001	+	784.621i	0.738990	+	1.27997i	−0.213960	+	0.976842i	$0.568636\pi$
$614$	29.0670	+	619.332i	0.0473404	+	1.00868i
$615$	583.338	−	965.482i	0.948517	−	1.56989i
$616$	−9.70006	+	286.556i	−0.0157469	+	0.465188i
$617$	−70.9099	+	402.150i	−0.114927	+	0.651783i	0.871859	+	0.489756i	$0.162914\pi$
$617$	−70.9099	+	402.150i	−0.114927	+	0.651783i	−0.986786	+	0.162027i	$0.948197\pi$
$618$	−244.308	−	275.684i	−0.395320	−	0.446091i
$619$	−327.110	−	389.834i	−0.528448	−	0.629780i	0.434108	−	0.900861i	$-0.357064\pi$
$619$	−327.110	−	389.834i	−0.528448	−	0.629780i	−0.962557	+	0.271080i	$0.912619\pi$
$620$	149.455	−	572.709i	0.241057	−	0.923724i
$621$	−314.279	+	332.105i	−0.506085	+	0.534790i
$622$	−850.168	−	109.104i	−1.36683	−	0.175408i
$623$	−34.9735	−	41.6798i	−0.0561373	−	0.0669018i
$624$	328.610	+	60.2624i	0.526618	+	0.0965744i
$625$	464.820	−	2636.13i	0.743712	−	4.21780i
$626$	−26.5467	−	117.921i	−0.0424069	−	0.188372i
$627$	−499.354	−	9.93778i	−0.796417	−	0.0158497i
$628$	3.92550	−	48.5157i	0.00625080	−	0.0772543i
$629$	−224.819	−	389.399i	−0.357424	−	0.619076i
$630$	524.663	+	616.327i	0.832798	+	0.978297i
$631$	−1083.33	−	625.458i	−1.71684	−	0.991218i	−0.924540	−	0.381086i	$-0.875550\pi$
$631$	−1083.33	−	625.458i	−1.71684	−	0.991218i	−0.792300	−	0.610132i	$-0.791116\pi$
$632$	96.2698	+	86.4956i	0.152326	+	0.136860i
$633$	1.31415	−	0.204849i	0.00207607	−	0.000323616i
$634$	−481.170	+	443.810i	−0.758943	+	0.700016i
$635$	−1162.08	+	1384.92i	−1.83005	+	2.18097i
$636$	−242.323	−	174.550i	−0.381011	−	0.274449i
$637$	183.160	+	66.6648i	0.287535	+	0.104654i
$638$	183.686	−	241.010i	0.287909	−	0.377758i
$639$	−218.023	−	281.888i	−0.341194	−	0.441139i
$640$	−1171.20	−	454.052i	−1.82999	−	0.709456i
$641$	−5.31127	−	30.1217i	−0.00828592	−	0.0469918i	0.980384	−	0.197095i	$-0.0631506\pi$
$641$	−5.31127	−	30.1217i	−0.00828592	−	0.0469918i	−0.988670	+	0.150103i	$0.952040\pi$
$642$	270.169	+	684.220i	0.420825	+	1.06576i
$643$	249.775	+	686.251i	0.388453	+	1.06726i	0.967698	+	0.252112i	$0.0811250\pi$
$643$	249.775	+	686.251i	0.388453	+	1.06726i	−0.579246	+	0.815153i	$0.696653\pi$
$644$	−129.335	+	282.157i	−0.200831	+	0.438131i
$645$	1206.80	+	237.643i	1.87101	+	0.368438i
$646$	−538.359	+	345.449i	−0.833373	+	0.534750i
$647$		−	1180.60i		−	1.82472i	−0.409385	−	0.912362i	$-0.634257\pi$
$647$		−	1180.60i		−	1.82472i	0.409385	−	0.912362i	$-0.365743\pi$
$648$	520.905	+	385.438i	0.803865	+	0.594811i
$649$	712.309			1.09755
$650$	536.052	+	835.401i	0.824696	+	1.28523i
$651$	−40.0470	+	203.368i	−0.0615162	+	0.312393i
$652$	681.613	+	312.439i	1.04542	+	0.479200i
$653$	878.642	−	319.800i	1.34555	−	0.489739i	0.433992	−	0.900917i	$-0.357105\pi$
$653$	878.642	−	319.800i	1.34555	−	0.489739i	0.911555	+	0.411178i	$0.134882\pi$
$654$	211.986	−	83.7042i	0.324137	−	0.127988i
$655$	1945.92	−	343.118i	2.97087	−	0.523845i
$656$	−8.00662	−	612.993i	−0.0122052	−	0.934440i
$657$	99.8914	+	736.896i	0.152042	+	1.12161i
$658$	−446.023	−	339.938i	−0.677847	−	0.516622i
$659$	−90.2708	+	248.017i	−0.136982	+	0.376354i	−0.989149	−	0.146915i	$-0.953065\pi$
$659$	−90.2708	+	248.017i	−0.136982	+	0.376354i	0.852168	+	0.523269i	$0.175288\pi$
$660$	−538.361	+	747.391i	−0.815698	+	1.13241i
$661$	−857.449	−	719.486i	−1.29720	−	1.08848i	−0.990621	−	0.136635i	$-0.956371\pi$
$661$	−857.449	−	719.486i	−1.29720	−	1.08848i	−0.306579	−	0.951845i	$-0.599184\pi$
$662$	−372.389	−	403.737i	−0.562522	−	0.609875i
$663$	−48.3241	−	310.011i	−0.0728871	−	0.467588i
$664$	515.240	+	462.928i	0.775964	+	0.697181i
$665$	−478.556	+	828.884i	−0.719634	+	1.24644i
$666$	−507.440	−	180.623i	−0.761922	−	0.271206i
$667$	284.093	−	164.021i	0.425926	−	0.245908i
$668$	837.667	+	67.7773i	1.25399	+	0.101463i
$669$	1.57315	−	79.0475i	0.00235149	−	0.118158i
$670$	−751.586	+	169.199i	−1.12177	+	0.252536i
$671$	−214.980	−	37.9067i	−0.320387	−	0.0564929i
$672$	419.049	+	133.773i	0.623585	+	0.199068i
$673$	155.205	−	130.232i	0.230616	−	0.193510i	−0.520156	−	0.854071i	$-0.674126\pi$
$673$	155.205	−	130.232i	0.230616	−	0.193510i	0.750772	+	0.660561i	$0.229682\pi$
$674$	145.971	−	1137.45i	0.216574	−	1.68761i
$675$	220.603	+	1912.56i	0.326819	+	2.83342i
$676$	466.596	+	121.764i	0.690231	+	0.180124i
$677$	945.200	−	793.117i	1.39616	−	1.17152i	0.433387	−	0.901208i	$-0.357318\pi$
$677$	945.200	−	793.117i	1.39616	−	1.17152i	0.962773	−	0.270310i	$-0.0871260\pi$
$678$	488.409	−	432.822i	0.720367	−	0.638381i
$679$	229.418	+	40.4526i	0.337877	+	0.0595768i
$680$	−39.9098	+	1179.00i	−0.0586908	+	1.73382i
$681$	43.2191	+	26.1127i	0.0634642	+	0.0383447i
$682$	−235.618	+	11.0582i	−0.345481	+	0.0162144i
$683$	−831.903	+	480.300i	−1.21801	+	0.703220i	−0.964493	−	0.264110i	$-0.914922\pi$
$683$	−831.903	+	480.300i	−1.21801	+	0.703220i	−0.253521	+	0.967330i	$0.581589\pi$
$684$	−222.830	+	733.142i	−0.325775	+	1.07184i
$685$	−569.482	+	986.372i	−0.831361	+	1.43996i
$686$	627.011	+	323.803i	0.914010	+	0.472017i
$687$	−599.549	+	483.083i	−0.872707	+	0.703177i
$688$	625.101	−	236.809i	0.908577	−	0.344199i
$689$	132.693	+	111.343i	0.192588	+	0.161600i
$690$	−849.767	+	521.697i	−1.23155	+	0.756082i
$691$	229.573	−	630.745i	0.332232	−	0.912801i	−0.655298	−	0.755371i	$-0.727457\pi$
$691$	229.573	−	630.745i	0.332232	−	0.912801i	0.987530	−	0.157430i	$-0.0503209\pi$
$692$	474.446	−	480.683i	0.685615	−	0.694629i
$693$	172.266	−	272.707i	0.248581	−	0.393516i
$694$	−14.5681	−	34.8482i	−0.0209915	−	0.0502135i
$695$	−1607.54	+	283.453i	−2.31301	+	0.407846i
$696$	−279.275	−	371.674i	−0.401258	−	0.534015i
$697$	−541.010	+	196.912i	−0.776198	+	0.282513i
$698$	−98.1581	−	30.5971i	−0.140628	−	0.0438354i
$699$	−38.5927	−	33.7142i	−0.0552113	−	0.0482320i
$700$	560.049	+	1180.83i	0.800070	+	1.68691i
$701$	−83.2481			−0.118756			−0.0593781	−	0.998236i	$-0.518912\pi$
$701$	−83.2481			−0.118756			−0.0593781	+	0.998236i	$0.518912\pi$
$702$	−284.803	−	245.257i	−0.405703	−	0.349369i
$703$		−	636.925i		−	0.906011i
$704$	−33.8516	+	499.443i	−0.0480847	+	0.709436i
$705$	−582.373	−	1704.87i	−0.826061	−	2.41825i
$706$	−479.877	−	149.584i	−0.679712	−	0.211875i
$707$	3.99688	+	10.9813i	0.00565330	+	0.0155323i
$708$	296.928	−	1051.71i	0.419390	−	1.48546i
$709$	−158.003	−	896.078i	−0.222853	−	1.26386i	−0.866748	−	0.498747i	$-0.833794\pi$
$709$	−158.003	−	896.078i	−0.222853	−	1.26386i	0.643895	−	0.765114i	$-0.277317\pi$
$710$	−299.745	−	717.019i	−0.422177	−	1.00989i
$711$	−44.3141	−	138.689i	−0.0623265	−	0.195062i
$712$	−58.5640	−	74.7936i	−0.0822529	−	0.105047i
$713$	−239.948	−	87.3341i	−0.336534	−	0.122488i
$714$	−11.1525	−	412.959i	−0.0156197	−	0.578374i
$715$	343.412	−	409.262i	0.480296	−	0.572395i
$716$	1031.46	−	732.317i	1.44058	−	1.02279i
$717$	−334.406	+	864.829i	−0.466395	+	1.20618i
$718$	−67.7087	−	34.9664i	−0.0943018	−	0.0486997i
$719$	826.808	+	477.358i	1.14994	+	0.663919i	0.948873	−	0.315658i	$-0.102225\pi$
$719$	826.808	+	477.358i	1.14994	+	0.663919i	0.201069	+	0.979577i	$0.435558\pi$
$720$	879.089	+	1106.43i	1.22096	+	1.53671i
$721$	140.655	+	243.622i	0.195084	+	0.337895i
$722$	−183.893	+	8.63062i	−0.254700	+	0.0119538i
$723$	−383.836	−	696.469i	−0.530893	−	0.963304i
$724$	623.242	−	58.6301i	0.860831	−	0.0809809i
$725$	239.852	−	1360.27i	0.330831	−	1.87623i
$726$	−340.471	−	113.610i	−0.468969	−	0.156487i
$727$	713.696	+	850.550i	0.981700	+	1.16994i	0.985452	+	0.169951i	$0.0543611\pi$
$727$	713.696	+	850.550i	0.981700	+	1.16994i	−0.00375251	+	0.999993i	$0.501194\pi$
$728$	−236.664	−	95.3241i	−0.325087	−	0.130940i
$729$	−286.708	−	670.253i	−0.393290	−	0.919415i
$730$	−206.424	+	1608.52i	−0.282773	+	2.20345i
$731$	−403.521	−	480.897i	−0.552012	−	0.657862i
$732$	−145.583	+	301.611i	−0.198884	+	0.412037i
$733$	−229.498	+	1301.55i	−0.313094	+	1.77565i	0.269618	+	0.962967i	$0.413103\pi$
$733$	−229.498	+	1301.55i	−0.313094	+	1.77565i	−0.582712	+	0.812678i	$0.698009\pi$
$734$	637.759	−	143.574i	0.868881	−	0.195605i
$735$	397.941	+	722.063i	0.541416	+	0.982399i
$736$	−242.345	+	484.700i	−0.329274	+	0.658560i
$737$	153.508	+	265.883i	0.208287	+	0.360764i
$738$	−340.588	+	599.710i	−0.461501	+	0.812615i
$739$	1070.82	+	618.236i	1.44901	+	0.836585i	0.998422	−	0.0561488i	$-0.0178821\pi$
$739$	1070.82	+	618.236i	1.44901	+	0.836585i	0.450585	+	0.892734i	$0.351215\pi$
$740$	−966.580	−	667.442i	−1.30619	−	0.901949i
$741$	160.288	−	414.532i	0.216313	−	0.559422i
$742$	154.630	+	167.647i	0.208396	+	0.225939i
$743$	−213.265	+	254.159i	−0.287032	+	0.342071i	−0.890223	−	0.455526i	$-0.849451\pi$
$743$	−213.265	+	254.159i	−0.287032	+	0.342071i	0.603191	+	0.797597i	$0.293896\pi$
$744$	−81.8909	+	352.494i	−0.110068	+	0.473783i
$745$	839.011	+	305.375i	1.12619	+	0.409899i
$746$	−285.580	−	217.655i	−0.382815	−	0.291763i
$747$	−237.171	−	742.270i	−0.317498	−	0.993668i
$748$	453.296	−	124.639i	0.606011	−	0.166629i
$749$	−97.5536	−	553.254i	−0.130245	−	0.738657i
$750$	−400.791	+	2696.88i	−0.534388	+	3.59584i
$751$	−339.987	−	934.108i	−0.452713	−	1.24382i	−0.930807	−	0.365510i	$-0.880895\pi$
$751$	−339.987	−	934.108i	−0.452713	−	1.24382i	0.478095	−	0.878308i	$-0.341328\pi$
$752$	−758.195	−	619.508i	−1.00824	−	0.823814i
$753$	206.513	+	604.556i	0.274254	+	0.802864i
$754$	145.626	+	226.948i	0.193138	+	0.300992i
$755$			253.522i			0.335791i
$756$	−330.836	−	368.026i	−0.437613	−	0.486807i
$757$	260.196			0.343720			0.171860	−	0.985121i	$-0.445022\pi$
$757$	260.196			0.343720			0.171860	+	0.985121i	$0.445022\pi$
$758$	−608.350	+	390.360i	−0.802573	+	0.514987i
$759$	299.263	+	261.433i	0.394286	+	0.344444i
$760$	−884.001	+	1418.07i	−1.16316	+	1.86588i
$761$	−274.656	+	99.9667i	−0.360915	+	0.131362i	−0.516112	−	0.856521i	$-0.672621\pi$
$761$	−274.656	+	99.9667i	−0.360915	+	0.131362i	0.155197	+	0.987884i	$0.450399\pi$
$762$	687.382	−	865.614i	0.902077	−	1.13598i
$763$	−171.410	+	30.2242i	−0.224653	+	0.0396123i
$764$	321.971	−	88.5295i	0.421428	−	0.115876i
$765$	708.769	−	1122.02i	0.926496	−	1.46669i
$766$	423.407	−	555.541i	0.552751	−	0.725250i
$767$	−216.791	+	595.628i	−0.282648	+	0.776569i
$768$	723.305	+	258.175i	0.941803	+	0.336166i
$769$	163.739	+	137.394i	0.212925	+	0.178665i	0.743012	−	0.669278i	$-0.233396\pi$
$769$	163.739	+	137.394i	0.212925	+	0.178665i	−0.530087	+	0.847943i	$0.677841\pi$
$770$	517.070	−	476.923i	0.671520	−	0.619380i
$771$	1053.33	−	848.716i	1.36619	−	1.10080i
$772$	−219.756	−	151.745i	−0.284657	−	0.196562i
$773$	−365.228	+	632.593i	−0.472481	+	0.818361i	−0.999504	−	0.0314897i	$-0.989975\pi$
$773$	−365.228	+	632.593i	−0.472481	+	0.818361i	0.527023	+	0.849851i	$0.323308\pi$
$774$	−741.494	−	125.323i	−0.958003	−	0.161916i
$775$	−931.123	+	537.584i	−1.20145	+	0.693657i
$776$	397.927	+	84.1374i	0.512792	+	0.108425i
$777$	352.071	+	212.719i	0.453116	+	0.273770i
$778$	0.250907	+	1.11453i	0.000322502	+	0.00143256i
$779$	−803.148	−	141.617i	−1.03100	−	0.181793i
$780$	−461.114	−	677.642i	−0.591172	−	0.868771i
$781$	−237.250	+	199.076i	−0.303777	+	0.254899i
$782$	504.785	+	64.7802i	0.645506	+	0.0828391i
$783$	59.9298	+	519.573i	0.0765387	+	0.663567i
$784$	390.930	+	218.946i	0.498635	+	0.279268i
$785$	−91.4783	+	76.7594i	−0.116533	+	0.0977827i
$786$	−1183.64	+	241.825i	−1.50591	+	0.307666i
$787$	1246.33	+	219.761i	1.58364	+	0.279239i	0.895068	−	0.445929i	$-0.147127\pi$
$787$	1246.33	+	219.761i	1.58364	+	0.279239i	0.688573	+	0.725167i	$0.258238\pi$
$788$	−1105.76	+	104.023i	−1.40325	+	0.132008i
$789$	−1.15879	+	58.2270i	−0.00146868	+	0.0737984i
$790$	−14.8855	−	317.166i	−0.0188424	−	0.401475i
$791$	−431.607	+	249.189i	−0.545648	+	0.315030i
$792$	316.698	−	465.676i	0.399872	−	0.587974i
$793$	97.1263	−	168.228i	0.122480	−	0.212141i
$794$	−16.3734	+	31.7054i	−0.0206214	+	0.0399312i
$795$	112.847	+	723.943i	0.141946	+	0.910621i
$796$	−236.145	+	167.659i	−0.296665	+	0.210627i
$797$	−233.897	−	196.263i	−0.293472	−	0.246252i	0.484149	−	0.874985i	$-0.339129\pi$
$797$	−233.897	−	196.263i	−0.293472	−	0.246252i	−0.777621	+	0.628734i	$0.783574\pi$
$798$	278.802	−	514.495i	0.349376	−	0.644731i
$799$	−314.491	+	864.058i	−0.393606	+	1.08142i
$800$	907.492	+	2093.54i	1.13436	+	2.61692i
$801$	14.3554	+	105.900i	0.0179219	+	0.132209i
$802$	−718.885	+	300.526i	−0.896366	+	0.374720i
$803$	636.459	−	112.225i	0.792601	−	0.139757i
$804$	456.560	−	115.816i	0.567861	−	0.144050i
$805$	715.572	−	260.447i	0.888910	−	0.323537i
$806$	62.4634	−	200.388i	0.0774980	−	0.248620i
$807$	−244.035	+	1239.26i	−0.302398	+	1.53564i
$808$	6.32560	+	19.3976i	0.00782871	+	0.0240069i
$809$	63.8675			0.0789462			0.0394731	−	0.999221i	$-0.487432\pi$
$809$	63.8675			0.0789462			0.0394731	+	0.999221i	$0.487432\pi$
$810$	−224.735	−	1573.83i	−0.277451	−	1.94299i
$811$		−	856.788i		−	1.05646i	−0.849102	−	0.528229i	$-0.822856\pi$
$811$		−	856.788i		−	1.05646i	0.849102	−	0.528229i	$-0.177144\pi$
$812$	152.145	+	320.790i	0.187371	+	0.395062i
$813$	629.901	+	124.040i	0.774786	+	0.152570i
$814$	−139.305	+	446.901i	−0.171136	+	0.549019i
$815$	−629.169	−	1728.63i	−0.771986	−	2.12102i
$816$	4.93180	−	721.238i	0.00604388	−	0.883870i
$817$	−154.416	−	875.739i	−0.189004	−	1.07190i
$818$	−898.663	+	375.681i	−1.09861	+	0.459267i
$819$	175.606	+	227.046i	0.214416	+	0.277224i
$820$	−1056.54	+	1070.43i	−1.28847	+	1.30541i
$821$	630.914	+	229.634i	0.768470	+	0.279700i	0.696356	−	0.717696i	$-0.254803\pi$
$821$	630.914	+	229.634i	0.768470	+	0.279700i	0.0721137	+	0.997396i	$0.477026\pi$
$822$	331.775	−	612.249i	0.403619	−	0.744829i
$823$	806.094	−	960.665i	0.979458	−	1.16727i	−0.00644958	−	0.999979i	$-0.502053\pi$
$823$	806.094	−	960.665i	0.979458	−	1.16727i	0.985907	−	0.167293i	$-0.0535026\pi$
$824$	231.042	+	433.408i	0.280391	+	0.525981i
$825$	1653.22	−	257.701i	2.00390	−	0.312365i
$826$	−382.943	+	741.529i	−0.463612	+	0.897735i
$827$	228.269	+	131.791i	0.276020	+	0.159360i	0.631620	−	0.775278i	$-0.282390\pi$
$827$	228.269	+	131.791i	0.276020	+	0.159360i	−0.355600	+	0.934638i	$0.615724\pi$
$828$	510.749	−	332.876i	0.616846	−	0.402024i
$829$	252.751	+	437.777i	0.304886	+	0.528078i	0.977236	−	0.212155i	$-0.0680483\pi$
$829$	252.751	+	437.777i	0.304886	+	0.528078i	−0.672350	+	0.740234i	$0.734715\pi$
$830$	−79.6677	−	1697.48i	−0.0959852	−	2.04516i
$831$	−335.111	−	6.66913i	−0.403262	−	0.00802543i
$832$	−407.328	−	180.312i	−0.489577	−	0.216721i
$833$	73.0702	−	414.402i	0.0877193	−	0.497481i
$834$	977.817	−	199.774i	1.17244	−	0.239537i
$835$	−1325.32	−	1579.46i	−1.58721	−	1.89156i
$836$	644.357	+	168.153i	0.770762	+	0.201140i
$837$	279.830	−	295.702i	0.334325	−	0.353287i
$838$	−1105.47	−	141.867i	−1.31918	−	0.169293i
$839$	810.051	+	965.381i	0.965495	+	1.15063i	0.988549	+	0.150898i	$0.0482166\pi$
$839$	810.051	+	965.381i	0.965495	+	1.15063i	−0.0230539	+	0.999734i	$0.507339\pi$
$840$	−488.623	−	962.249i	−0.581694	−	1.14553i
$841$	−80.8790	+	458.687i	−0.0961700	+	0.545407i
$842$	324.356	+	1440.80i	0.385221	+	1.71116i
$843$	78.3538	−	129.683i	0.0929463	−	0.153835i
$844$	−1.76759	−	0.143019i	−0.00209430	−	0.000169454i
$845$	−591.537	−	1024.57i	−0.700044	−	1.21251i
$846$	384.074	+	1032.37i	0.453988	+	1.22029i
$847$	237.384	+	137.054i	0.280264	+	0.161811i
$848$	259.915	+	301.663i	0.306503	+	0.355735i
$849$	946.694	+	1174.93i	1.11507	+	1.38390i
$850$	1575.16	−	1452.86i	1.85313	−	1.70925i
$851$	−325.732	+	388.193i	−0.382764	+	0.456160i
$852$	195.033	+	433.279i	0.228912	+	0.508543i
$853$	−410.158	−	149.285i	−0.480842	−	0.175012i	0.0902154	−	0.995922i	$-0.471244\pi$
$853$	−410.158	−	149.285i	−0.480842	−	0.175012i	−0.571057	+	0.820910i	$0.693467\pi$
$854$	155.037	−	203.419i	0.181542	−	0.238196i
$855$	1664.17	−	874.440i	1.94639	−	1.02274i
$856$	−137.544	−	971.145i	−0.160683	−	1.13452i
$857$	25.9873	+	147.381i	0.0303236	+	0.171974i	0.996208	−	0.0869982i	$-0.0277274\pi$
$857$	25.9873	+	147.381i	0.0303236	+	0.171974i	−0.965885	+	0.258972i	$0.916616\pi$
$858$	−203.131	+	255.801i	−0.236749	+	0.298136i
$859$	−245.695	−	675.042i	−0.286025	−	0.785846i	−0.996613	−	0.0822378i	$-0.973793\pi$
$859$	−245.695	−	675.042i	−0.286025	−	0.785846i	0.710588	−	0.703608i	$-0.248429\pi$
$860$	−1490.81	−	683.360i	−1.73350	−	0.794605i
$861$	346.515	−	396.656i	0.402456	−	0.460693i
$862$	1049.78	−	673.611i	1.21784	−	0.781452i
$863$			564.987i			0.654678i	0.944907	+	0.327339i	$0.106152\pi$
$863$			564.987i			0.654678i	−0.944907	+	0.327339i	$0.893848\pi$
$864$	−555.543	−	661.716i	−0.642989	−	0.765875i
$865$	−1656.99			−1.91560
$866$	−575.744	−	897.258i	−0.664831	−	1.03609i
$867$	179.464	−	61.3040i	0.206994	−	0.0707082i
$868$	115.158	−	251.228i	0.132671	−	0.289434i
$869$	−118.904	+	43.2775i	−0.136828	+	0.0498015i
$870$	−167.665	+	1128.20i	−0.192718	+	1.29678i
$871$	−269.050	+	47.4407i	−0.308897	+	0.0544669i
$872$	−300.881	+	42.6141i	−0.345047	+	0.0488694i
$873$	−338.536	−	307.830i	−0.387784	−	0.352612i
$874$	573.363	+	436.990i	0.656022	+	0.499989i
$875$	712.151	−	1956.62i	0.813886	−	2.23613i
$876$	99.6125	−	986.498i	0.113713	−	1.12614i
$877$	−466.664	−	391.577i	−0.532113	−	0.446496i	0.336717	−	0.941606i	$-0.390683\pi$
$877$	−466.664	−	391.577i	−0.532113	−	0.446496i	−0.868830	+	0.495110i	$0.835128\pi$
$878$	−677.202	−	734.208i	−0.771300	−	0.836228i
$879$	−315.960	−	122.173i	−0.359454	−	0.138991i
$880$	930.415	−	801.649i	1.05729	−	0.910965i
$881$	−215.603	+	373.436i	−0.244726	+	0.423877i	−0.962054	−	0.272858i	$-0.912031\pi$
$881$	−215.603	+	373.436i	−0.244726	+	0.423877i	0.717329	+	0.696735i	$0.245365\pi$
$882$	−255.131	−	434.741i	−0.289264	−	0.492904i
$883$	19.1924	−	11.0808i	0.0217355	−	0.0125490i	−0.489093	−	0.872232i	$-0.662672\pi$
$883$	19.1924	−	11.0808i	0.0217355	−	0.0125490i	0.510828	+	0.859683i	$0.329339\pi$
$884$	−33.7384	+	416.977i	−0.0381656	+	0.471693i
$885$	−2348.12	+	1294.09i	−2.65324	+	1.46224i
$886$	20.3736	−	4.58656i	0.0229950	−	0.00517671i
$887$	1621.95	+	285.993i	1.82858	+	0.322428i	0.978816	−	0.204740i	$-0.0656349\pi$
$887$	1621.95	+	285.993i	1.82858	+	0.322428i	0.849761	+	0.527168i	$0.176746\pi$
$888$	601.770	+	391.973i	0.677669	+	0.441411i
$889$	−646.645	+	542.600i	−0.727385	+	0.610348i
$890$	−29.6653	+	231.160i	−0.0333318	+	0.259731i
$891$	−572.127	+	272.150i	−0.642118	+	0.305444i
$892$	−26.6185	+	102.001i	−0.0298414	+	0.114351i
$893$	−997.783	+	837.239i	−1.11734	+	0.937558i
$894$	−517.826	−	172.790i	−0.579224	−	0.193278i
$895$	−3056.34	−	538.915i	−3.41491	−	0.602140i
$896$	−501.732	−	303.745i	−0.559968	−	0.339001i
$897$	−309.689	+	170.675i	−0.345250	+	0.190273i
$898$	−727.253	+	34.1321i	−0.809859	+	0.0380090i
$899$	−252.952	+	146.042i	−0.281371	+	0.162450i
$900$	308.659	−	2548.36i	0.342954	−	2.83151i
$901$	186.977	−	323.854i	0.207522	−	0.359439i
$902$	532.559	+	275.026i	0.590420	+	0.304907i
$903$	535.650	+	207.121i	0.593190	+	0.229370i
$904$	−767.838	+	409.320i	−0.849378	+	0.452788i
$905$	−1176.49	−	987.193i	−1.29999	−	1.09082i
$906$	−4.18456	−	154.947i	−0.00461872	−	0.171024i
$907$	−212.408	+	583.586i	−0.234188	+	0.643425i	0.765812	+	0.643064i	$0.222337\pi$
$907$	−212.408	+	583.586i	−0.234188	+	0.643425i	−1.00000		0.000360886i	$0.999885\pi$
$908$	−47.9172	−	47.2954i	−0.0527723	−	0.0520875i
$909$	4.88201	−	22.4281i	0.00537075	−	0.0246734i
$910$	241.430	+	577.522i	0.265307	+	0.634639i
$911$	−935.459	+	164.947i	−1.02685	+	0.181061i	−0.661606	−	0.749851i	$-0.730125\pi$
$911$	−935.459	+	164.947i	−1.02685	+	0.181061i	−0.365242	+	0.930913i	$0.619014\pi$
$912$	516.876	−	881.284i	0.566750	−	0.966320i
$913$	−636.378	+	231.623i	−0.697019	+	0.253694i
$914$	481.266	+	150.017i	0.526549	+	0.164132i
$915$	777.545	−	265.605i	0.849775	−	0.290279i
$916$	927.567	−	439.929i	1.01263	−	0.480271i
$917$	922.604			1.00611
$918$	−414.665	+	697.453i	−0.451705	+	0.759753i
$919$			1119.44i			1.21811i	0.793128	+	0.609055i	$0.208451\pi$
$919$			1119.44i			1.21811i	−0.793128	+	0.609055i	$0.791549\pi$
$920$	1264.00	−	412.192i	1.37391	−	0.448035i
$921$	−611.863	+	700.401i	−0.664346	+	0.760479i
$922$	−524.466	−	163.483i	−0.568835	−	0.177313i
$923$	−94.2592	−	258.975i	−0.102123	−	0.280580i
$924$	−308.150	+	300.020i	−0.333496	+	0.324697i
$925$	370.517	+	2101.30i	0.400558	+	2.27168i
$926$	−18.2996	−	43.7743i	−0.0197620	−	0.0472725i
$927$	21.9837	−	552.100i	0.0237149	−	0.595578i
$928$	246.533	+	568.739i	0.265660	+	0.612865i
$929$	1350.81	+	491.654i	1.45404	+	0.529229i	0.943718	−	0.330752i	$-0.107302\pi$
$929$	1350.81	+	491.654i	1.45404	+	0.529229i	0.510326	+	0.859981i	$0.329525\pi$
$930$	756.622	−	464.512i	0.813572	−	0.499475i
$931$	383.144	−	456.614i	0.411541	−	0.490455i
$932$	39.5552	+	55.7127i	0.0424412	+	0.0597776i
$933$	−806.678	−	1001.16i	−0.864607	−	1.07305i
$934$	14.8205	+	7.65366i	0.0158678	+	0.00819450i
$935$	−998.858	−	576.691i	−1.06830	−	0.616782i
$936$	293.008	+	406.549i	0.313043	+	0.434347i
$937$	−164.072	−	284.182i	−0.175104	−	0.303289i	0.765093	−	0.643920i	$-0.222693\pi$
$937$	−164.072	−	284.182i	−0.175104	−	0.303289i	−0.940197	+	0.340630i	$0.889360\pi$
$938$	−359.317	+	16.8638i	−0.383067	+	0.0179784i
$939$	93.7604	−	155.183i	0.0998514	−	0.165264i
$940$	224.981	+	2391.56i	0.239342	+	2.54421i
$941$	−116.085	+	658.349i	−0.123363	+	0.699627i	0.858904	+	0.512137i	$0.171146\pi$
$941$	−116.085	+	658.349i	−0.123363	+	0.699627i	−0.982267	+	0.187489i	$0.939965\pi$
$942$	54.6426	−	48.4236i	0.0580070	−	0.0514051i
$943$	417.077	+	497.053i	0.442288	+	0.527098i
$944$	−712.004	+	1271.29i	−0.754242	+	1.34670i
$945$	−72.4339	+	1211.94i	−0.0766496	+	1.28247i
$946$	−83.1899	+	648.239i	−0.0879386	+	0.685242i
$947$	−245.016	−	291.999i	−0.258729	−	0.308341i	0.621006	−	0.783806i	$-0.286724\pi$
$947$	−245.016	−	291.999i	−0.258729	−	0.308341i	−0.879735	+	0.475465i	$0.842280\pi$
$948$	14.3327	+	193.599i	0.0151189	+	0.204219i
$949$	−99.8642	+	566.358i	−0.105231	+	0.596795i
$950$	2961.33	−	666.664i	3.11719	−	0.701752i
$951$	−981.695	−	19.5370i	−1.03228	−	0.0205436i
$952$	−113.944	+	538.898i	−0.119689	+	0.566069i
$953$	−813.401	−	1408.85i	−0.853517	−	1.47833i	−0.878014	−	0.478634i	$-0.841132\pi$
$953$	−813.401	−	1408.85i	−0.853517	−	1.47833i	0.0244977	−	0.999700i	$-0.492201\pi$
$954$	−80.9191	−	440.596i	−0.0848209	−	0.461841i
$955$	−709.477	−	409.617i	−0.742908	−	0.428918i
$956$	702.488	−	1017.33i	0.734820	−	1.06416i
$957$	449.119	−	70.0081i	0.469299	−	0.0731537i
$958$	−639.009	−	692.801i	−0.667024	−	0.723174i
$959$	−341.837	+	407.386i	−0.356452	+	0.424803i
$960$	−795.770	−	1707.91i	−0.828927	−	1.77907i
$961$	−689.398	−	250.920i	−0.717375	−	0.261103i
$962$	−331.299	−	252.500i	−0.344385	−	0.262474i
$963$	−418.355	+	1021.06i	−0.434429	+	1.06029i
$964$	281.112	+	1022.37i	0.291610	+	1.06055i
$965$	113.773	+	645.237i	0.117899	+	0.668640i
$966$	−433.044	+	170.991i	−0.448286	+	0.177009i
$967$	620.108	+	1703.73i	0.641270	+	1.76188i	0.647699	+	0.761896i	$0.275731\pi$
$967$	620.108	+	1703.73i	0.641270	+	1.76188i	−0.00642855	+	0.999979i	$0.502046\pi$
$968$	406.120	+	253.169i	0.419545	+	0.261538i
$969$	−941.411	−	185.382i	−0.971528	−	0.191313i
$970$	−538.889	−	839.822i	−0.555556	−	0.865796i
$971$			284.479i			0.292976i	0.989212	+	0.146488i	$0.0467969\pi$
$971$			284.479i			0.292976i	−0.989212	+	0.146488i	$0.953203\pi$
$972$	163.331	+	958.179i	0.168036	+	0.985781i
$973$	−762.171			−0.783321
$974$	368.587	−	236.511i	0.378426	−	0.242825i
$975$	−287.668	+	1460.84i	−0.295044	+	1.49830i
$976$	282.541	−	345.793i	0.289489	−	0.354296i
$977$	−558.491	+	203.274i	−0.571638	+	0.208059i	−0.611635	−	0.791140i	$-0.709488\pi$
$977$	−558.491	+	203.274i	−0.571638	+	0.208059i	0.0399961	+	0.999200i	$0.487265\pi$
$978$	413.067	+	1046.12i	0.422359	+	1.06965i
$979$	91.4657	−	16.1279i	0.0934276	−	0.0164738i
$980$	−291.442	−	1059.94i	−0.297390	−	1.08157i
$981$	316.346	+	129.615i	0.322473	+	0.132126i
$982$	147.919	−	194.081i	0.150630	−	0.197638i
$983$	−258.620	+	710.553i	−0.263093	+	0.722841i	0.735862	+	0.677131i	$0.236777\pi$
$983$	−258.620	+	710.553i	−0.263093	+	0.722841i	−0.998955	+	0.0457097i	$0.985445\pi$
$984$	628.068	−	671.665i	0.638281	−	0.682587i
$985$	2087.35	+	1751.49i	2.11913	+	1.77816i
$986$	427.915	−	394.690i	0.433990	−	0.400294i
$987$	−129.560	−	831.160i	−0.131267	−	0.842107i
$988$	−336.718	+	487.630i	−0.340808	+	0.493553i
$989$	−353.751	+	612.715i	−0.357686	+	0.619530i
$990$	−1358.92	+	249.577i	−1.37265	+	0.252098i
$991$	1351.75	−	780.435i	1.36403	−	0.787522i	0.373871	−	0.927481i	$-0.378030\pi$
$991$	1351.75	−	780.435i	1.36403	−	0.787522i	0.990157	+	0.139958i	$0.0446969\pi$
$992$	215.781	−	431.571i	0.217521	−	0.435051i
$993$	16.3930	−	823.714i	0.0165085	−	0.829521i
$994$	−79.6950	−	354.007i	−0.0801761	−	0.356144i
$995$	699.730	+	123.381i	0.703246	+	0.124001i
$996$	76.7094	+	1036.15i	0.0770174	+	1.04031i
$997$	1068.15	−	896.280i	1.07136	−	0.898977i	0.0761844	−	0.997094i	$-0.475726\pi$
$997$	1068.15	−	896.280i	1.07136	−	0.898977i	0.995175	+	0.0981166i	$0.0312818\pi$
$998$	−58.3660	−	7.49023i	−0.0584830	−	0.00750524i
$999$	−361.507	−	722.553i	−0.361869	−	0.723277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.j.a.103.12	yes	204
3.2	odd	2		324.3.j.a.199.23		204
4.3	odd	2	inner	108.3.j.a.103.27	yes	204
12.11	even	2		324.3.j.a.199.8		204
27.11	odd	18		324.3.j.a.127.8		204
27.16	even	9	inner	108.3.j.a.43.27	yes	204
108.11	even	18		324.3.j.a.127.23		204
108.43	odd	18	inner	108.3.j.a.43.12	✓	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.43.12	✓	204	108.43	odd	18	inner
108.3.j.a.43.27	yes	204	27.16	even	9	inner
108.3.j.a.103.12	yes	204	1.1	even	1	trivial
108.3.j.a.103.27	yes	204	4.3	odd	2	inner
324.3.j.a.127.8		204	27.11	odd	18
324.3.j.a.127.23		204	108.11	even	18
324.3.j.a.199.8		204	12.11	even	2
324.3.j.a.199.23		204	3.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08010 - 1.68327i) q^{2} +(0.579627 - 2.94347i) q^{3} +(-1.66676 + 3.63619i) q^{4} +(9.22169 - 3.35642i) q^{5} +(-5.58070 + 2.20358i) q^{6} +(4.51251 - 0.795677i) q^{7} +(7.92095 - 1.12185i) q^{8} +(-8.32807 - 3.41223i) q^{9} +(-15.6101 - 11.8973i) q^{10} +(-2.67518 + 7.34999i) q^{11} +(9.73694 + 7.01371i) q^{12} +(-5.33182 - 4.47393i) q^{13} +(-6.21330 - 6.73633i) q^{14} +(-4.53440 - 29.0893i) q^{15} +(-10.4438 - 12.1213i) q^{16} +(-7.51307 + 13.0130i) q^{17} +(3.25147 + 17.7039i) q^{18} +(-18.4333 + 10.6425i) q^{19} +(-3.16578 + 39.1262i) q^{20} +(0.273516 - 13.7436i) q^{21} +(15.2614 - 3.43570i) q^{22} +(16.6774 + 2.94067i) q^{23} +(1.28905 - 23.9654i) q^{24} +(54.6229 - 45.8341i) q^{25} +(-1.77190 + 13.8072i) q^{26} +(-14.8710 + 22.5356i) q^{27} +(-4.62805 + 17.7346i) q^{28} +(14.8391 - 12.4515i) q^{29} +(-44.0673 + 39.0519i) q^{30} +(-14.8493 - 2.61834i) q^{31} +(-9.12307 + 30.6720i) q^{32} +(20.0839 + 12.1346i) q^{33} +(30.0192 - 1.40889i) q^{34} +(38.9423 - 22.4834i) q^{35} +(26.2884 - 24.5951i) q^{36} +(-14.9619 + 25.9148i) q^{37} +(37.8239 + 19.5332i) q^{38} +(-16.2594 + 13.1009i) q^{39} +(69.2791 - 36.9314i) q^{40} +(29.3512 + 24.6286i) q^{41} +(-23.4296 + 14.3841i) q^{42} +(-14.2890 + 39.2588i) q^{43} +(-22.2671 - 21.9782i) q^{44} +(-88.2517 - 3.51404i) q^{45} +(-13.0633 - 31.2487i) q^{46} +(60.2645 - 10.6263i) q^{47} +(-41.7324 + 23.7152i) q^{48} +(-26.3153 + 9.57799i) q^{49} +(-136.149 - 42.4394i) q^{50} +(33.9487 + 29.6572i) q^{51} +(25.1550 - 11.9306i) q^{52} -24.8870 q^{53} +(53.9956 + 0.691048i) q^{54} +76.7584i q^{55} +(34.8507 - 11.3649i) q^{56} +(20.6414 + 60.4265i) q^{57} +(-36.9868 - 11.5293i) q^{58} +(-31.1472 - 85.5763i) q^{59} +(113.332 + 31.9970i) q^{60} +(4.84636 + 27.4850i) q^{61} +(11.6314 + 27.8234i) q^{62} +(-40.2955 - 8.77126i) q^{63} +(61.4829 - 17.7723i) q^{64} +(-64.1848 - 23.3614i) q^{65} +(-1.26695 - 46.9131i) q^{66} +(25.2305 - 30.0686i) q^{67} +(-34.7953 - 49.0086i) q^{68} +(18.3225 - 47.3850i) q^{69} +(-79.9071 - 41.2659i) q^{70} +(34.2911 + 19.7980i) q^{71} +(-69.7942 - 17.6852i) q^{72} +(-41.3131 - 71.5564i) q^{73} +(59.7818 - 2.80573i) q^{74} +(-103.250 - 187.348i) q^{75} +(-7.97413 - 84.7654i) q^{76} +(-6.22354 + 35.2955i) q^{77} +(39.6140 + 13.2186i) q^{78} +(10.3986 + 12.3926i) q^{79} +(-136.994 - 76.7255i) q^{80} +(57.7134 + 56.8346i) q^{81} +(9.75418 - 76.0073i) q^{82} +(55.6540 + 66.3258i) q^{83} +(49.5186 + 23.9019i) q^{84} +(-25.6060 + 145.219i) q^{85} +(81.5166 - 18.3512i) q^{86} +(-28.0494 - 50.8956i) q^{87} +(-12.9443 + 61.2201i) q^{88} +(-5.93712 - 10.2834i) q^{89} +(89.4057 + 152.347i) q^{90} +(-27.6197 - 15.9462i) q^{91} +(-38.4901 + 55.7408i) q^{92} +(-16.3141 + 42.1909i) q^{93} +(-82.9785 - 89.9637i) q^{94} +(-134.265 + 160.011i) q^{95} +(84.9941 + 44.6318i) q^{96} +(47.7745 + 17.3885i) q^{97} +(44.5455 + 33.9505i) q^{98} +(47.3589 - 52.0829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25}+ \cdots + 510 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 39 * q^12 - 12 * q^13 + 39 * q^14 - 6 * q^16 - 6 * q^17 - 27 * q^18 - 69 * q^20 - 12 * q^21 - 6 * q^22 - 138 * q^24 - 12 * q^25 - 174 * q^26 - 12 * q^28 + 60 * q^29 - 153 * q^30 - 96 * q^32 + 48 * q^33 + 6 * q^34 + 24 * q^36 - 6 * q^37 + 72 * q^38 + 69 * q^40 - 192 * q^41 - 126 * q^42 - 219 * q^44 - 132 * q^45 - 3 * q^46 - 219 * q^48 - 12 * q^49 - 165 * q^50 + 21 * q^52 - 24 * q^53 + 78 * q^54 + 99 * q^56 - 150 * q^57 - 141 * q^58 + 210 * q^60 - 12 * q^61 + 294 * q^62 - 3 * q^64 - 156 * q^65 + 393 * q^66 + 375 * q^68 - 60 * q^69 - 165 * q^70 + 228 * q^72 - 6 * q^73 + 447 * q^74 - 54 * q^76 + 132 * q^77 + 750 * q^78 + 798 * q^80 + 228 * q^81 - 12 * q^82 + 762 * q^84 + 138 * q^85 + 606 * q^86 - 198 * q^88 - 114 * q^89 + 894 * q^90 + 723 * q^92 - 1020 * q^93 - 357 * q^94 + 474 * q^96 + 168 * q^97 + 510 * q^98

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