LMFDB - Embedded newform 31.3.f.a.23.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,3,Mod(15,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.15"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	31.f (of order $10$, degree $4$, 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:	$0.844688819517$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 20 x^{18} - 33 x^{17} + 250 x^{16} - 510 x^{15} + 2908 x^{14} - 6447 x^{13} + \cdots + 731025 $ x^20 - 2x^19 + 20x^18 - 33x^17 + 250x^16 - 510x^15 + 2908x^14 - 6447x^13 + 39842x^12 - 79034x^11 + 199542x^10 - 173039x^9 + 688988x^8 - 636120x^7 + 3401146x^6 - 2156427x^5 + 7116556x^4 - 6139950x^3 + 6454710x^2 - 3116475*x + 731025
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.1
Root			$2.39225 - 1.73807i$ of defining polynomial
Character	$\chi$	$=$	31.23
Dual form			31.3.f.a.27.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.913758 + 2.81226i) q^{2} +(5.20635 - 1.69165i) q^{3} +(-3.83778 - 2.78831i) q^{4} -5.21585 q^{5} +16.1874i q^{6} +(-5.08304 - 3.69304i) q^{7} +(1.77924 - 1.29269i) q^{8} +(16.9633 - 12.3246i) q^{9} +(4.76602 - 14.6683i) q^{10} +(-3.31109 + 4.55732i) q^{11} +(-24.6977 - 8.02475i) q^{12} +(6.36975 - 2.06966i) q^{13} +(15.0305 - 10.9203i) q^{14} +(-27.1556 + 8.82338i) q^{15} +(-3.85401 - 11.8614i) q^{16} +(13.9543 + 19.2065i) q^{17} +(19.1595 + 58.9669i) q^{18} +(-1.04359 + 3.21183i) q^{19} +(20.0173 + 14.5434i) q^{20} +(-32.7114 - 10.6286i) q^{21} +(-9.79083 - 13.4759i) q^{22} +(-5.24664 - 7.22139i) q^{23} +(7.07657 - 9.74007i) q^{24} +2.20508 q^{25} +19.8046i q^{26} +(38.5088 - 53.0029i) q^{27} +(9.21022 + 28.3461i) q^{28} +(-18.6515 - 6.06023i) q^{29} -84.4309i q^{30} +(16.9290 + 25.9694i) q^{31} +45.6760 q^{32} +(-9.52932 + 29.3282i) q^{33} +(-66.7644 + 21.6931i) q^{34} +(26.5124 + 19.2624i) q^{35} -99.4660 q^{36} +7.37919i q^{37} +(-8.07892 - 5.86968i) q^{38} +(29.6621 - 21.5507i) q^{39} +(-9.28025 + 6.74249i) q^{40} +(-8.96363 + 27.5872i) q^{41} +(59.7807 - 82.2810i) q^{42} +(10.2018 + 3.31478i) q^{43} +(25.4144 - 8.25765i) q^{44} +(-88.4781 + 64.2831i) q^{45} +(25.1026 - 8.15632i) q^{46} +(-22.3601 - 68.8174i) q^{47} +(-40.1306 - 55.2351i) q^{48} +(-2.94313 - 9.05803i) q^{49} +(-2.01491 + 6.20127i) q^{50} +(105.142 + 76.3899i) q^{51} +(-30.2165 - 9.81794i) q^{52} +(7.30390 + 10.0530i) q^{53} +(113.870 + 156.729i) q^{54} +(17.2701 - 23.7703i) q^{55} -13.8179 q^{56} +18.4873i q^{57} +(34.0859 - 46.9152i) q^{58} +(-24.3552 - 74.9577i) q^{59} +(128.819 + 41.8559i) q^{60} +61.8106i q^{61} +(-88.5016 + 23.8791i) q^{62} -131.740 q^{63} +(-26.3208 + 81.0072i) q^{64} +(-33.2237 + 10.7950i) q^{65} +(-73.7711 - 53.5978i) q^{66} +63.5225 q^{67} -112.619i q^{68} +(-39.5319 - 28.7216i) q^{69} +(-78.3966 + 56.9585i) q^{70} +(20.4625 - 14.8669i) q^{71} +(14.2499 - 43.8567i) q^{72} +(73.0291 - 100.516i) q^{73} +(-20.7522 - 6.74279i) q^{74} +(11.4804 - 3.73022i) q^{75} +(12.9606 - 9.41645i) q^{76} +(33.6608 - 10.9370i) q^{77} +(33.5023 + 103.110i) q^{78} +(40.3121 + 55.4848i) q^{79} +(20.1019 + 61.8673i) q^{80} +(52.5139 - 161.621i) q^{81} +(-69.3918 - 50.4161i) q^{82} +(-14.4260 - 4.68729i) q^{83} +(95.9033 + 132.000i) q^{84} +(-72.7836 - 100.178i) q^{85} +(-18.6440 + 25.6613i) q^{86} -107.358 q^{87} +12.3888i q^{88} +(-91.9646 + 126.578i) q^{89} +(-99.9331 - 307.562i) q^{90} +(-40.0210 - 13.0036i) q^{91} +42.3433i q^{92} +(132.070 + 106.568i) q^{93} +213.964 q^{94} +(5.44320 - 16.7524i) q^{95} +(237.806 - 77.2677i) q^{96} +(-75.4306 - 54.8035i) q^{97} +28.1628 q^{98} +118.115i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9} + 12 q^{10} - 10 q^{11} + 90 q^{12} + 10 q^{13} - 85 q^{15} - 103 q^{16} + 35 q^{17} + 6 q^{18} + 47 q^{19} - 125 q^{20} - 125 q^{21}+ \cdots - 1000 q^{98}+O(q^{100}) $ 20 * q - 3 * q^2 - 5 * q^3 - 11 * q^4 - 14 * q^5 - q^7 - 19 * q^8 + 2 * q^9 + 12 * q^10 - 10 * q^11 + 90 * q^12 + 10 * q^13 - 85 * q^15 - 103 * q^16 + 35 * q^17 + 6 * q^18 + 47 * q^19 - 125 * q^20 - 125 * q^21 + 150 * q^22 + 75 * q^23 + 195 * q^24 + 82 * q^25 + 25 * q^27 + 88 * q^28 + 5 * q^29 + 73 * q^31 + 226 * q^32 - 206 * q^33 - 265 * q^34 - 50 * q^35 - 520 * q^36 + 8 * q^38 + 91 * q^39 - 466 * q^40 - 98 * q^41 + 245 * q^43 + 380 * q^44 - 162 * q^45 - 445 * q^46 - 187 * q^47 + 570 * q^48 + 328 * q^49 - 44 * q^50 + 185 * q^51 - 15 * q^52 + 25 * q^53 + 920 * q^54 + 190 * q^55 + 64 * q^56 - 85 * q^58 - 173 * q^59 + 275 * q^60 - 40 * q^62 + 252 * q^63 - 469 * q^64 - 345 * q^65 - 564 * q^66 + 76 * q^67 - 197 * q^69 - 11 * q^70 - 467 * q^71 - 982 * q^72 - 15 * q^73 + 45 * q^74 - 175 * q^75 + 55 * q^76 - 320 * q^77 - 91 * q^78 + 500 * q^79 + 1030 * q^80 + 117 * q^81 + 178 * q^82 - 50 * q^83 + 65 * q^84 + 20 * q^85 + 1125 * q^86 - 366 * q^87 + 55 * q^89 + 444 * q^90 + 300 * q^91 + 502 * q^93 + 62 * q^94 - 559 * q^95 - 10 * q^96 - 405 * q^97 - 1000 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.913758	+	2.81226i	−0.456879	+	1.40613i	0.412036	+	0.911168i	$0.364818\pi$
$2$	−0.913758	+	2.81226i	−0.456879	+	1.40613i	−0.868915	+	0.494962i	$0.835182\pi$
$3$	5.20635	−	1.69165i	1.73545	−	0.563882i	0.741232	−	0.671249i	$-0.234242\pi$
$3$	5.20635	−	1.69165i	1.73545	−	0.563882i	0.994220	+	0.107366i	$0.0342418\pi$
$4$	−3.83778	−	2.78831i	−0.959444	−	0.697077i
$5$	−5.21585			−1.04317			−0.521585	−	0.853199i	$-0.674659\pi$
$5$	−5.21585			−1.04317			−0.521585	+	0.853199i	$0.674659\pi$
$6$			16.1874i			2.69790i
$7$	−5.08304	−	3.69304i	−0.726148	−	0.527577i	0.162194	−	0.986759i	$-0.448143\pi$
$7$	−5.08304	−	3.69304i	−0.726148	−	0.527577i	−0.888343	+	0.459181i	$0.848143\pi$
$8$	1.77924	−	1.29269i	0.222405	−	0.161587i
$9$	16.9633	−	12.3246i	1.88481	−	1.36940i
$10$	4.76602	−	14.6683i	0.476602	−	1.46683i
$11$	−3.31109	+	4.55732i	−0.301008	+	0.414302i	−0.932551	−	0.361039i	$-0.882422\pi$
$11$	−3.31109	+	4.55732i	−0.301008	+	0.414302i	0.631543	+	0.775341i	$0.282422\pi$
$12$	−24.6977	−	8.02475i	−2.05814	−	0.668730i
$13$	6.36975	−	2.06966i	0.489981	−	0.159204i	−0.0535979	−	0.998563i	$-0.517069\pi$
$13$	6.36975	−	2.06966i	0.489981	−	0.159204i	0.543579	+	0.839358i	$0.317069\pi$
$14$	15.0305	−	10.9203i	1.07360	−	0.780019i
$15$	−27.1556	+	8.82338i	−1.81037	+	0.588225i
$16$	−3.85401	−	11.8614i	−0.240875	−	0.741338i
$17$	13.9543	+	19.2065i	0.820842	+	1.12979i	0.989559	+	0.144127i	$0.0460375\pi$
$17$	13.9543	+	19.2065i	0.820842	+	1.12979i	−0.168717	+	0.985664i	$0.553962\pi$
$18$	19.1595	+	58.9669i	1.06442	+	3.27594i
$19$	−1.04359	+	3.21183i	−0.0549257	+	0.169044i	−0.974756	−	0.223272i	$-0.928326\pi$
$19$	−1.04359	+	3.21183i	−0.0549257	+	0.169044i	0.919830	+	0.392316i	$0.128326\pi$
$20$	20.0173	+	14.5434i	1.00086	+	0.727170i
$21$	−32.7114	−	10.6286i	−1.55769	−	0.506123i
$22$	−9.79083	−	13.4759i	−0.445038	−	0.612542i
$23$	−5.24664	−	7.22139i	−0.228115	−	0.313973i	0.679582	−	0.733599i	$-0.262161\pi$
$23$	−5.24664	−	7.22139i	−0.228115	−	0.313973i	−0.907697	+	0.419626i	$0.862161\pi$
$24$	7.07657	−	9.74007i	0.294857	−	0.405836i
$25$	2.20508			0.0882034
$26$			19.8046i			0.761714i
$27$	38.5088	−	53.0029i	1.42625	−	1.96307i
$28$	9.21022	+	28.3461i	0.328936	+	1.01236i
$29$	−18.6515	−	6.06023i	−0.643154	−	0.208973i	−0.0307608	−	0.999527i	$-0.509793\pi$
$29$	−18.6515	−	6.06023i	−0.643154	−	0.208973i	−0.612393	+	0.790553i	$0.709793\pi$
$30$		−	84.4309i		−	2.81436i
$31$	16.9290	+	25.9694i	0.546098	+	0.837721i
$31$	16.9290	+	25.9694i	0.546098	+	0.837721i
$32$	45.6760			1.42738
$33$	−9.52932	+	29.3282i	−0.288767	+	0.888734i
$34$	−66.7644	+	21.6931i	−1.96366	+	0.638031i
$35$	26.5124	+	19.2624i	0.757496	+	0.550353i
$36$	−99.4660			−2.76295
$37$			7.37919i			0.199438i	0.995016	+	0.0997188i	$0.0317943\pi$
$37$			7.37919i			0.199438i	−0.995016	+	0.0997188i	$0.968206\pi$
$38$	−8.07892	−	5.86968i	−0.212603	−	0.154465i
$39$	29.6621	−	21.5507i	0.760566	−	0.552583i
$40$	−9.28025	+	6.74249i	−0.232006	+	0.168562i
$41$	−8.96363	+	27.5872i	−0.218625	+	0.672859i	0.780251	+	0.625466i	$0.215091\pi$
$41$	−8.96363	+	27.5872i	−0.218625	+	0.672859i	−0.998876	+	0.0473927i	$0.984909\pi$
$42$	59.7807	−	82.2810i	1.42335	−	1.95907i
$43$	10.2018	+	3.31478i	0.237252	+	0.0770879i	0.425230	−	0.905085i	$-0.360193\pi$
$43$	10.2018	+	3.31478i	0.237252	+	0.0770879i	−0.187978	+	0.982173i	$0.560193\pi$
$44$	25.4144	−	8.25765i	0.577601	−	0.187674i
$45$	−88.4781	+	64.2831i	−1.96618	+	1.42851i
$46$	25.1026	−	8.15632i	0.545708	−	0.177311i
$47$	−22.3601	−	68.8174i	−0.475747	−	1.46420i	−0.844947	−	0.534850i	$-0.820368\pi$
$47$	−22.3601	−	68.8174i	−0.475747	−	1.46420i	0.369200	−	0.929350i	$-0.379632\pi$
$48$	−40.1306	−	55.2351i	−0.836055	−	1.15073i
$49$	−2.94313	−	9.05803i	−0.0600639	−	0.184858i
$50$	−2.01491	+	6.20127i	−0.0402983	+	0.124025i
$51$	105.142	+	76.3899i	2.06160	+	1.49784i
$52$	−30.2165	−	9.81794i	−0.581087	−	0.188807i
$53$	7.30390	+	10.0530i	0.137809	+	0.189678i	0.872344	−	0.488893i	$-0.162599\pi$
$53$	7.30390	+	10.0530i	0.137809	+	0.189678i	−0.734534	+	0.678572i	$0.762599\pi$
$54$	113.870	+	156.729i	2.10870	+	2.90238i
$55$	17.2701	−	23.7703i	0.314002	−	0.432187i
$56$	−13.8179			−0.246748
$57$			18.4873i			0.324339i
$58$	34.0859	−	46.9152i	0.587687	−	0.808882i
$59$	−24.3552	−	74.9577i	−0.412801	−	1.27047i	−0.914203	−	0.405255i	$-0.867183\pi$
$59$	−24.3552	−	74.9577i	−0.412801	−	1.27047i	0.501403	−	0.865214i	$-0.332817\pi$
$60$	128.819	+	41.8559i	2.14699	+	0.697598i
$61$			61.8106i			1.01329i	0.862155	+	0.506644i	$0.169114\pi$
$61$			61.8106i			1.01329i	−0.862155	+	0.506644i	$0.830886\pi$
$62$	−88.5016	+	23.8791i	−1.42745	+	0.385147i
$63$	−131.740			−2.09112
$64$	−26.3208	+	81.0072i	−0.411263	+	1.26574i
$65$	−33.2237	+	10.7950i	−0.511133	+	0.166077i
$66$	−73.7711	−	53.5978i	−1.11774	−	0.812088i
$67$	63.5225			0.948097			0.474049	−	0.880499i	$-0.342792\pi$
$67$	63.5225			0.948097			0.474049	+	0.880499i	$0.342792\pi$
$68$		−	112.619i		−	1.65616i
$69$	−39.5319	−	28.7216i	−0.572926	−	0.416255i
$70$	−78.3966	+	56.9585i	−1.11995	+	0.813692i
$71$	20.4625	−	14.8669i	0.288204	−	0.209392i	−0.434284	−	0.900776i	$-0.642999\pi$
$71$	20.4625	−	14.8669i	0.288204	−	0.209392i	0.722488	+	0.691384i	$0.242999\pi$
$72$	14.2499	−	43.8567i	0.197915	−	0.609121i
$73$	73.0291	−	100.516i	1.00040	−	1.37693i	0.0753179	−	0.997160i	$-0.476003\pi$
$73$	73.0291	−	100.516i	1.00040	−	1.37693i	0.925081	−	0.379771i	$-0.123997\pi$
$74$	−20.7522	−	6.74279i	−0.280435	−	0.0911188i
$75$	11.4804	−	3.73022i	0.153073	−	0.0497363i
$76$	12.9606	−	9.41645i	0.170535	−	0.123901i
$77$	33.6608	−	10.9370i	0.437153	−	0.142040i
$78$	33.5023	+	103.110i	0.429517	+	1.32192i
$79$	40.3121	+	55.4848i	0.510280	+	0.702340i	0.983966	−	0.178354i	$-0.0570771\pi$
$79$	40.3121	+	55.4848i	0.510280	+	0.702340i	−0.473687	+	0.880693i	$0.657077\pi$
$80$	20.1019	+	61.8673i	0.251274	+	0.773342i
$81$	52.5139	−	161.621i	0.648319	−	1.99532i
$82$	−69.3918	−	50.4161i	−0.846241	−	0.614830i
$83$	−14.4260	−	4.68729i	−0.173807	−	0.0564734i	0.220821	−	0.975314i	$-0.429126\pi$
$83$	−14.4260	−	4.68729i	−0.173807	−	0.0564734i	−0.394628	+	0.918841i	$0.629126\pi$
$84$	95.9033	+	132.000i	1.14171	+	1.57142i
$85$	−72.7836	−	100.178i	−0.856277	−	1.17856i
$86$	−18.6440	+	25.6613i	−0.216791	+	0.298387i
$87$	−107.358			−1.23400
$88$			12.3888i			0.140782i
$89$	−91.9646	+	126.578i	−1.03331	+	1.42223i	−0.130877	+	0.991399i	$0.541779\pi$
$89$	−91.9646	+	126.578i	−1.03331	+	1.42223i	−0.902433	+	0.430831i	$0.858221\pi$
$90$	−99.9331	−	307.562i	−1.11037	−	3.41736i
$91$	−40.0210	−	13.0036i	−0.439791	−	0.142897i
$92$			42.3433i			0.460253i
$93$	132.070	+	106.568i	1.42010	+	1.14589i
$94$	213.964			2.27621
$95$	5.44320	−	16.7524i	0.0572968	−	0.176342i
$96$	237.806	−	77.2677i	2.47714	−	0.804872i
$97$	−75.4306	−	54.8035i	−0.777635	−	0.564985i	0.126633	−	0.991950i	$-0.459583\pi$
$97$	−75.4306	−	54.8035i	−0.777635	−	0.564985i	−0.904268	+	0.426965i	$0.859583\pi$
$98$	28.1628			0.287376
$99$			118.115i			1.19308i
$100$	−8.46262	−	6.14845i	−0.0846262	−	0.0614845i
$101$	−37.2606	+	27.0714i	−0.368917	+	0.268034i	−0.756762	−	0.653691i	$-0.773220\pi$
$101$	−37.2606	+	27.0714i	−0.368917	+	0.268034i	0.387845	+	0.921725i	$0.373220\pi$
$102$	−310.902	+	225.884i	−3.04806	+	2.21455i
$103$	20.3131	−	62.5174i	0.197215	−	0.606965i	−0.802729	−	0.596344i	$-0.796619\pi$
$103$	20.3131	−	62.5174i	0.197215	−	0.606965i	0.999944	−	0.0106204i	$-0.00338064\pi$
$104$	8.65788	−	11.9166i	0.0832489	−	0.114582i
$105$	170.618	+	55.4371i	1.62493	+	0.527972i
$106$	−34.9455	+	11.3545i	−0.329674	+	0.107118i
$107$	73.7625	−	53.5916i	0.689370	−	0.500856i	−0.187083	−	0.982344i	$-0.559903\pi$
$107$	73.7625	−	53.5916i	0.689370	−	0.500856i	0.876453	+	0.481488i	$0.159903\pi$
$108$	−295.577	+	96.0387i	−2.73682	+	0.889247i
$109$	15.8725	+	48.8504i	0.145619	+	0.448169i	0.997090	−	0.0762323i	$-0.0242891\pi$
$109$	15.8725	+	48.8504i	0.145619	+	0.448169i	−0.851471	+	0.524402i	$0.824289\pi$
$110$	51.0675	+	70.2884i	0.464250	+	0.638985i
$111$	12.4830	+	38.4187i	0.112459	+	0.346114i
$112$	−24.2146	+	74.5250i	−0.216202	+	0.665402i
$113$	−70.6470	−	51.3280i	−0.625194	−	0.454230i	0.229538	−	0.973300i	$-0.426279\pi$
$113$	−70.6470	−	51.3280i	−0.625194	−	0.454230i	−0.854732	+	0.519069i	$0.826279\pi$
$114$	−51.9912	−	16.8929i	−0.456063	−	0.148184i
$115$	27.3657	+	37.6657i	0.237963	+	0.327527i
$116$	54.6824	+	75.2638i	0.471400	+	0.648826i
$117$	82.5444	−	113.613i	0.705508	−	0.971048i
$118$	233.055			1.97504
$119$		−	149.161i		−	1.25345i
$120$	−36.9103	+	50.8027i	−0.307586	+	0.423356i
$121$	27.5852	+	84.8985i	0.227977	+	0.701640i
$122$	−173.827	−	56.4800i	−1.42482	−	0.462951i
$123$			158.792i			1.29099i
$124$	7.44074	−	146.868i	0.0600060	−	1.18442i
$125$	118.895			0.951159
$126$	120.379	−	370.488i	0.955387	−	2.94038i
$127$	34.4876	−	11.2057i	0.271556	−	0.0882338i	−0.170074	−	0.985431i	$-0.554401\pi$
$127$	34.4876	−	11.2057i	0.271556	−	0.0882338i	0.441630	+	0.897198i	$0.354401\pi$
$128$	−55.9515	−	40.6511i	−0.437121	−	0.317587i
$129$	58.7219			0.455208
$130$		−	103.298i		−	0.794597i
$131$	−147.918	−	107.469i	−1.12915	−	0.820373i	−0.143577	−	0.989639i	$-0.545860\pi$
$131$	−147.918	−	107.469i	−1.12915	−	0.820373i	−0.985570	+	0.169266i	$0.945860\pi$
$132$	118.347	−	85.9845i	0.896572	−	0.651398i
$133$	17.1660	−	12.4719i	0.129068	−	0.0937733i
$134$	−58.0442	+	178.642i	−0.433166	+	1.33315i
$135$	−200.856	+	276.455i	−1.48782	+	2.04781i
$136$	49.6561	+	16.1343i	0.365119	+	0.118634i
$137$	119.519	−	38.8342i	0.872404	−	0.283461i	0.161604	−	0.986856i	$-0.448333\pi$
$137$	119.519	−	38.8342i	0.872404	−	0.283461i	0.710800	+	0.703394i	$0.248333\pi$
$138$	116.895	−	84.9294i	0.847067	−	0.615430i
$139$	−236.072	+	76.7046i	−1.69836	+	0.551832i	−0.988329	−	0.152336i	$-0.951321\pi$
$139$	−236.072	+	76.7046i	−1.69836	+	0.551832i	−0.710034	+	0.704167i	$0.751321\pi$
$140$	−48.0391	−	147.849i	−0.343137	−	1.05607i
$141$	−232.829	−	320.462i	−1.65127	−	2.27278i
$142$	23.1117	+	71.1305i	0.162758	+	0.500919i
$143$	−11.6587	+	35.8818i	−0.0815295	+	0.250922i
$144$	−211.563	−	153.710i	−1.46919	−	1.06743i
$145$	97.2832	+	31.6092i	0.670919	+	0.217995i
$146$	215.946	+	297.224i	1.47908	+	2.03578i
$147$	−30.6460	−	42.1806i	−0.208476	−	0.286943i
$148$	20.5754	−	28.3197i	0.139023	−	0.191349i
$149$	−196.177			−1.31662			−0.658310	−	0.752747i	$-0.728729\pi$
$149$	−196.177			−1.31662			−0.658310	+	0.752747i	$0.728729\pi$
$150$			35.6945i			0.237963i
$151$	4.51948	−	6.22054i	0.0299304	−	0.0411956i	−0.793790	−	0.608193i	$-0.791895\pi$
$151$	4.51948	−	6.22054i	0.0299304	−	0.0411956i	0.823720	+	0.566997i	$0.191895\pi$
$152$	2.29512	+	7.06366i	0.0150995	+	0.0464715i
$153$	473.423	+	153.824i	3.09427	+	1.00539i
$154$			104.657i			0.679588i
$155$	−88.2993	−	135.452i	−0.569673	−	0.873886i
$156$	−173.926			−1.11491
$157$	−85.2127	+	262.258i	−0.542756	+	1.67043i	0.183509	+	0.983018i	$0.441254\pi$
$157$	−85.2127	+	262.258i	−0.542756	+	1.67043i	−0.726266	+	0.687414i	$0.758746\pi$
$158$	−192.873	+	62.6683i	−1.22072	+	0.396635i
$159$	55.0327	+	39.9836i	0.346118	+	0.251469i
$160$	−238.239			−1.48900
$161$			56.0826i			0.348339i
$162$	406.535	+	295.365i	2.50948	+	1.82324i
$163$	−117.611	+	85.4491i	−0.721538	+	0.524228i	−0.886875	−	0.462009i	$-0.847129\pi$
$163$	−117.611	+	85.4491i	−0.721538	+	0.524228i	0.165338	+	0.986237i	$0.447129\pi$
$164$	111.322	−	80.8802i	0.678793	−	0.493172i
$165$	49.7035	−	152.972i	0.301233	−	0.927101i
$166$	26.3638	−	36.2866i	0.158818	−	0.218594i
$167$	271.725	+	88.2887i	1.62709	+	0.528675i	0.973601	−	0.228257i	$-0.0733026\pi$
$167$	271.725	+	88.2887i	1.62709	+	0.528675i	0.653494	+	0.756932i	$0.273303\pi$
$168$	−71.9410	+	23.3750i	−0.428220	+	0.139137i
$169$	−100.434	+	72.9693i	−0.594282	+	0.431771i
$170$	348.233	−	113.148i	2.04843	−	0.665575i
$171$	21.8817	+	67.3451i	0.127963	+	0.393831i
$172$	−29.9098	−	41.1673i	−0.173894	−	0.239345i
$173$	−44.4941	−	136.939i	−0.257191	−	0.791553i	−0.993390	−	0.114788i	$-0.963381\pi$
$173$	−44.4941	−	136.939i	−0.257191	−	0.791553i	0.736199	−	0.676765i	$-0.236619\pi$
$174$	98.0992	−	301.918i	0.563788	−	1.73516i
$175$	−11.2085	−	8.14347i	−0.0640487	−	0.0465341i
$176$	66.8172	+	21.7102i	0.379643	+	0.123354i
$177$	−253.604	−	349.056i	−1.43279	−	1.97207i
$178$	−271.938	−	374.290i	−1.52774	−	2.10275i
$179$	120.316	−	165.601i	0.672157	−	0.925144i	−0.327650	−	0.944799i	$-0.606257\pi$
$179$	120.316	−	165.601i	0.672157	−	0.925144i	0.999807	+	0.0196549i	$0.00625676\pi$
$180$	518.800			2.88222
$181$			124.758i			0.689272i	0.938736	+	0.344636i	$0.111998\pi$
$181$			124.758i			0.689272i	−0.938736	+	0.344636i	$0.888002\pi$
$182$	73.1391	−	100.667i	0.401863	−	0.553117i
$183$	104.562	+	321.808i	0.571376	+	1.75851i
$184$	−18.6701	−	6.06627i	−0.101468	−	0.0329689i
$185$		−	38.4887i		−	0.208047i
$186$	−420.376	+	274.037i	−2.26008	+	1.47331i
$187$	−133.734			−0.715155
$188$	−106.071	+	326.453i	−0.564207	+	1.73645i
$189$	−391.484	+	127.201i	−2.07134	+	0.673020i
$190$	42.1384	+	30.6154i	0.221781	+	0.161133i
$191$	95.7014			0.501055			0.250527	−	0.968110i	$-0.419396\pi$
$191$	95.7014			0.501055			0.250527	+	0.968110i	$0.419396\pi$
$192$			466.278i			2.42853i
$193$	100.339	+	72.9004i	0.519890	+	0.377722i	0.816563	−	0.577257i	$-0.195877\pi$
$193$	100.339	+	72.9004i	0.519890	+	0.377722i	−0.296672	+	0.954979i	$0.595877\pi$
$194$	223.047	−	162.053i	1.14973	−	0.835326i
$195$	−154.713	+	112.405i	−0.793399	+	0.576438i
$196$	−13.9615	+	42.9690i	−0.0712321	+	0.219230i
$197$	−90.5460	+	124.626i	−0.459624	+	0.632618i	−0.974431	−	0.224688i	$-0.927864\pi$
$197$	−90.5460	+	124.626i	−0.459624	+	0.632618i	0.514807	+	0.857306i	$0.327864\pi$
$198$	−332.170	−	107.929i	−1.67763	−	0.545093i
$199$	262.101	−	85.1617i	1.31709	−	0.427948i	0.435595	−	0.900143i	$-0.356538\pi$
$199$	262.101	−	85.1617i	1.31709	−	0.427948i	0.881494	+	0.472194i	$0.156538\pi$
$200$	3.92337	−	2.85050i	0.0196169	−	0.0142525i
$201$	330.721	−	107.458i	1.64538	−	0.534615i
$202$	−42.0846	−	129.523i	−0.208340	−	0.641204i
$203$	72.4254	+	99.6850i	0.356775	+	0.491059i
$204$	−190.512	−	586.334i	−0.933881	−	2.87419i
$205$	46.7529	−	143.891i	0.228063	−	0.701906i
$206$	157.254	+	114.251i	0.763367	+	0.554619i
$207$	−178.001	−	57.8360i	−0.859907	−	0.279401i
$208$	−49.0981	−	67.5778i	−0.236049	−	0.324893i
$209$	−11.1819	−	15.3906i	−0.0535021	−	0.0736394i
$210$	−311.807	+	429.165i	−1.48479	+	2.04364i
$211$	10.5159			0.0498383			0.0249191	−	0.999689i	$-0.492067\pi$
$211$	10.5159			0.0498383			0.0249191	+	0.999689i	$0.492067\pi$
$212$		−	58.9465i		−	0.278049i
$213$	81.3854	−	112.017i	0.382091	−	0.525903i
$214$	83.3124	+	256.409i	0.389310	+	1.19817i
$215$	−53.2113	−	17.2894i	−0.247494	−	0.0804158i
$216$		−	144.085i		−	0.667060i
$217$	9.85508	−	194.523i	0.0454151	−	0.896419i
$218$	−151.884			−0.696714
$219$	210.178	−	646.861i	0.959716	−	2.95370i
$220$	−132.558	+	43.0706i	−0.602536	+	0.195776i
$221$	128.636	+	93.4597i	0.582065	+	0.422895i
$222$	−119.450			−0.538062
$223$		−	266.065i		−	1.19312i	−0.802570	−	0.596558i	$-0.796534\pi$
$223$		−	266.065i		−	1.19312i	0.802570	−	0.596558i	$-0.203466\pi$
$224$	−232.173	−	168.684i	−1.03649	−	0.753051i
$225$	37.4055	−	27.1767i	0.166247	−	0.120785i
$226$	208.902	−	151.776i	0.924345	−	0.671576i
$227$	−3.84060	+	11.8202i	−0.0169189	+	0.0520712i	−0.959160	−	0.282866i	$-0.908715\pi$
$227$	−3.84060	+	11.8202i	−0.0169189	+	0.0520712i	0.942241	+	0.334937i	$0.108715\pi$
$228$	51.5484	−	70.9502i	0.226089	−	0.311185i
$229$	−261.591	−	84.9962i	−1.14232	−	0.371163i	−0.324075	−	0.946031i	$-0.605053\pi$
$229$	−261.591	−	84.9962i	−1.14232	−	0.371163i	−0.818246	+	0.574869i	$0.805053\pi$
$230$	−130.931	+	42.5421i	−0.569266	+	0.184966i
$231$	156.748	−	113.884i	0.678564	−	0.493006i
$232$	−41.0194	+	13.3280i	−0.176808	+	0.0574484i
$233$	61.3553	+	188.832i	0.263327	+	0.810438i	0.992074	+	0.125655i	$0.0401032\pi$
$233$	61.3553	+	188.832i	0.263327	+	0.810438i	−0.728747	+	0.684783i	$0.759897\pi$
$234$	244.082	+	335.951i	1.04309	+	1.43569i
$235$	116.627	+	358.941i	0.496285	+	1.52741i
$236$	−115.535	+	355.581i	−0.489556	+	1.50670i
$237$	303.740	+	220.680i	1.28160	+	0.931139i
$238$	419.479	+	136.297i	1.76252	+	0.572677i
$239$	129.225	+	177.863i	0.540689	+	0.744195i	0.988712	−	0.149827i	$-0.0478718\pi$
$239$	129.225	+	177.863i	0.540689	+	0.744195i	−0.448023	+	0.894022i	$0.647872\pi$
$240$	209.315	+	288.098i	0.872148	+	1.20041i
$241$	79.4670	−	109.377i	0.329739	−	0.453846i	−0.611671	−	0.791112i	$-0.709502\pi$
$241$	79.4670	−	109.377i	0.329739	−	0.453846i	0.941409	+	0.337266i	$0.109502\pi$
$242$	−263.963			−1.09075
$243$		−	340.655i		−	1.40187i
$244$	172.347	−	237.215i	0.706340	−	0.972194i
$245$	15.3509	+	47.2453i	0.0626569	+	0.192838i
$246$	−446.565	−	145.098i	−1.81530	−	0.589828i
$247$			22.6185i			0.0915727i
$248$	63.6912	+	24.3217i	0.256819	+	0.0980713i
$249$	−83.0362			−0.333479
$250$	−108.641	+	334.363i	−0.434565	+	1.33745i
$251$	−78.1627	+	25.3966i	−0.311405	+	0.101182i	−0.460550	−	0.887634i	$-0.652348\pi$
$251$	−78.1627	+	25.3966i	−0.311405	+	0.101182i	0.149145	+	0.988815i	$0.452348\pi$
$252$	505.590	+	367.332i	2.00631	+	1.45767i
$253$	50.2823			0.198744
$254$			107.227i			0.422155i
$255$	−548.403	−	398.438i	−2.15060	−	1.56250i
$256$	−110.188	+	80.0560i	−0.430421	+	0.312719i
$257$	−82.5128	+	59.9490i	−0.321061	+	0.233265i	−0.736628	−	0.676298i	$-0.763583\pi$
$257$	−82.5128	+	59.9490i	−0.321061	+	0.233265i	0.415567	+	0.909563i	$0.363583\pi$
$258$	−53.6576	+	165.141i	−0.207975	+	0.640082i
$259$	27.2517	−	37.5087i	0.105219	−	0.144821i
$260$	157.605	+	51.2089i	0.606172	+	0.196957i
$261$	−391.080	+	127.070i	−1.49839	+	0.486857i
$262$	437.392	−	317.784i	1.66943	−	1.21292i
$263$	−166.458	+	54.0855i	−0.632921	+	0.205648i	−0.607868	−	0.794038i	$-0.707975\pi$
$263$	−166.458	+	54.0855i	−0.632921	+	0.205648i	−0.0250522	+	0.999686i	$0.507975\pi$
$264$	20.9575	+	64.5004i	0.0793843	+	0.244320i
$265$	−38.0960	−	52.4347i	−0.143759	−	0.197867i
$266$	19.3885	+	59.6716i	0.0728890	+	0.224329i
$267$	−264.674	+	814.584i	−0.991290	+	3.05088i
$268$	−243.785	−	177.120i	−0.909646	−	0.660897i
$269$	184.972	+	60.1011i	0.687629	+	0.223424i	0.631932	−	0.775024i	$-0.282262\pi$
$269$	184.972	+	60.1011i	0.687629	+	0.223424i	0.0556964	+	0.998448i	$0.482262\pi$
$270$	−593.929	−	817.473i	−2.19974	−	3.02768i
$271$	−54.2554	−	74.6762i	−0.200204	−	0.275558i	0.697096	−	0.716978i	$-0.254475\pi$
$271$	−54.2554	−	74.6762i	−0.200204	−	0.275558i	−0.897301	+	0.441420i	$0.854475\pi$
$272$	174.036	−	239.540i	0.639837	−	0.880661i
$273$	−230.361			−0.843814
$274$			371.605i			1.35622i
$275$	−7.30123	+	10.0493i	−0.0265499	+	0.0365428i
$276$	71.6299	+	220.454i	0.259529	+	0.798747i
$277$	−14.0177	−	4.55461i	−0.0506053	−	0.0164426i	0.283605	−	0.958941i	$-0.408470\pi$
$277$	−14.0177	−	4.55461i	−0.0506053	−	0.0164426i	−0.334210	+	0.942499i	$0.608470\pi$
$278$		−	733.986i		−	2.64024i
$279$	607.233	+	231.883i	2.17646	+	0.831123i
$280$	72.0722			0.257401
$281$	31.0701	−	95.6241i	0.110570	−	0.340299i	−0.880427	−	0.474181i	$-0.842744\pi$
$281$	31.0701	−	95.6241i	0.110570	−	0.340299i	0.990997	+	0.133882i	$0.0427443\pi$
$282$	1113.97	−	361.952i	3.95026	−	1.28352i
$283$	−150.671	−	109.469i	−0.532408	−	0.386817i	0.288850	−	0.957374i	$-0.406727\pi$
$283$	−150.671	−	109.469i	−0.532408	−	0.386817i	−0.821258	+	0.570558i	$0.806727\pi$
$284$	−119.984			−0.422478
$285$		−	96.4271i		−	0.338341i
$286$	−90.2557	−	65.5746i	−0.315579	−	0.229282i
$287$	147.443	−	107.124i	0.513739	−	0.373254i
$288$	774.817	−	562.937i	2.69034	−	1.95464i
$289$	−84.8595	+	261.171i	−0.293631	+	0.903704i
$290$	−177.787	+	244.702i	−0.613058	+	0.843801i
$291$	−485.427	−	157.725i	−1.66813	−	0.542009i
$292$	−560.539	+	182.130i	−1.91965	+	0.623733i
$293$	−259.380	+	188.451i	−0.885257	+	0.643177i	−0.934637	−	0.355603i	$-0.884275\pi$
$293$	−259.380	+	188.451i	−0.885257	+	0.643177i	0.0493799	+	0.998780i	$0.484275\pi$
$294$	146.626	−	47.6416i	0.498727	−	0.162046i
$295$	127.033	+	390.968i	0.430621	+	1.32532i
$296$	9.53903	+	13.1293i	0.0322265	+	0.0443559i
$297$	114.045	+	350.994i	0.383990	+	1.18180i
$298$	179.258	−	551.699i	0.601537	−	1.85134i
$299$	−48.3656	−	35.1397i	−0.161758	−	0.117524i
$300$	−54.4604	−	17.6953i	−0.181535	−	0.0589842i
$301$	−39.6147	−	54.5250i	−0.131610	−	0.181146i
$302$	13.3640	+	18.3940i	0.0442518	+	0.0609074i
$303$	−148.197	+	203.975i	−0.489098	+	0.673185i
$304$	42.1189			0.138549
$305$		−	322.395i		−	1.05703i
$306$	−865.187	+	1190.83i	−2.82741	+	3.89160i
$307$	−153.090	−	471.163i	−0.498665	−	1.53473i	−0.811167	−	0.584815i	$-0.801167\pi$
$307$	−153.090	−	471.163i	−0.498665	−	1.53473i	0.312502	−	0.949917i	$-0.398833\pi$
$308$	−159.678	−	51.8826i	−0.518436	−	0.168450i
$309$		−	359.850i		−	1.16456i
$310$	461.611	−	124.550i	1.48907	−	0.401773i
$311$	321.930			1.03514			0.517572	−	0.855640i	$-0.326836\pi$
$311$	321.930			1.03514			0.517572	+	0.855640i	$0.326836\pi$
$312$	24.9174	−	76.6879i	0.0798635	−	0.245795i
$313$	−78.3120	+	25.4451i	−0.250198	+	0.0812943i	−0.431431	−	0.902146i	$-0.641991\pi$
$313$	−78.3120	+	25.4451i	−0.250198	+	0.0812943i	0.181233	+	0.983440i	$0.441991\pi$
$314$	−659.673	−	479.280i	−2.10087	−	1.52637i
$315$	687.137			2.18139
$316$		−	325.341i		−	1.02956i
$317$	433.663	+	315.075i	1.36802	+	0.993927i	0.997889	+	0.0649488i	$0.0206884\pi$
$317$	433.663	+	315.075i	1.36802	+	0.993927i	0.370135	+	0.928978i	$0.379312\pi$
$318$	−162.731	+	118.231i	−0.511732	+	0.371795i
$319$	89.3751	−	64.9348i	0.280173	−	0.203557i
$320$	137.285	−	422.521i	0.429017	−	1.32038i
$321$	293.376	−	403.797i	0.913943	−	1.25794i
$322$	−157.719	−	51.2460i	−0.489810	−	0.159149i
$323$	−76.2505	+	24.7753i	−0.236070	+	0.0767037i
$324$	−652.186	+	473.841i	−2.01292	+	1.46247i
$325$	14.0458	−	4.56377i	0.0432180	−	0.0140424i
$326$	−132.837	−	408.831i	−0.407476	−	1.25408i
$327$	165.275	+	227.482i	0.505430	+	0.695664i
$328$	19.7134	+	60.6715i	0.0601017	+	0.184974i
$329$	−140.488	+	432.378i	−0.427016	+	1.31422i
$330$	384.779	+	279.558i	1.16600	+	0.847146i
$331$	13.6662	+	4.44042i	0.0412876	+	0.0134152i	0.329588	−	0.944125i	$-0.393090\pi$
$331$	13.6662	+	4.44042i	0.0412876	+	0.0134152i	−0.288300	+	0.957540i	$0.593090\pi$
$332$	42.2942	+	58.2129i	0.127392	+	0.175340i
$333$	90.9453	+	125.175i	0.273109	+	0.375902i
$334$	−496.582	+	683.486i	−1.48677	+	2.04636i
$335$	−331.324			−0.989027
$336$			428.966i			1.27669i
$337$	377.588	−	519.705i	1.12044	−	1.54215i	0.315372	−	0.948968i	$-0.397871\pi$
$337$	377.588	−	519.705i	1.12044	−	1.54215i	0.805067	−	0.593184i	$-0.202129\pi$
$338$	−113.436	−	349.122i	−0.335611	−	1.03290i
$339$	−454.642	−	147.722i	−1.34113	−	0.435759i
$340$			587.404i			1.72766i
$341$	−174.404	−	8.83581i	−0.511449	−	0.0259115i
$342$	−209.386			−0.612241
$343$	−113.627	+	349.709i	−0.331275	+	1.01956i
$344$	22.4365	−	7.29007i	0.0652224	−	0.0211921i
$345$	206.193	+	149.808i	0.597660	+	0.434225i
$346$	425.764			1.23053
$347$			145.682i			0.419832i	0.977719	+	0.209916i	$0.0673191\pi$
$347$			145.682i			0.419832i	−0.977719	+	0.209916i	$0.932681\pi$
$348$	412.016	+	299.347i	1.18395	+	0.860192i
$349$	−376.007	+	273.185i	−1.07738	+	0.782765i	−0.977225	−	0.212207i	$-0.931935\pi$
$349$	−376.007	+	273.185i	−1.07738	+	0.782765i	−0.100158	+	0.994972i	$0.531935\pi$
$350$	33.1434	−	24.0801i	0.0946955	−	0.0688003i
$351$	135.594	−	417.315i	0.386308	−	1.18893i
$352$	−151.237	+	208.160i	−0.429652	+	0.591365i
$353$	265.392	+	86.2310i	0.751818	+	0.244281i	0.659763	−	0.751473i	$-0.270656\pi$
$353$	265.392	+	86.2310i	0.751818	+	0.244281i	0.0920548	+	0.995754i	$0.470656\pi$
$354$	1213.37	−	394.247i	3.42759	−	1.11369i
$355$	−106.729	+	77.5433i	−0.300646	+	0.218432i
$356$	705.879	−	229.354i	1.98281	−	0.644253i
$357$	−252.328	−	776.585i	−0.706801	−	2.17531i
$358$	355.773	+	489.679i	0.993778	+	1.36782i
$359$	−161.666	−	497.557i	−0.450323	−	1.38595i	−0.876539	−	0.481330i	$-0.840154\pi$
$359$	−161.666	−	497.557i	−0.450323	−	1.38595i	0.426216	−	0.904621i	$-0.359846\pi$
$360$	−74.3254	+	228.750i	−0.206459	+	0.635417i
$361$	282.828	+	205.487i	0.783458	+	0.569216i
$362$	−350.852	−	113.999i	−0.969205	−	0.314914i
$363$	287.236	+	395.347i	0.791285	+	1.08911i
$364$	117.334	+	161.496i	0.322345	+	0.443670i
$365$	−380.909	+	524.276i	−1.04359	+	1.43637i
$366$	−1000.55			−2.73375
$367$		−	330.694i		−	0.901074i	−0.892758	−	0.450537i	$-0.851233\pi$
$367$		−	330.694i		−	0.901074i	0.892758	−	0.450537i	$-0.148767\pi$
$368$	−65.4352	+	90.0639i	−0.177813	+	0.244739i
$369$	187.948	+	578.443i	0.509343	+	1.56760i
$370$	108.240	+	35.1694i	0.292541	+	0.0950524i
$371$		−	78.0731i		−	0.210440i
$372$	−209.710	−	777.234i	−0.563735	−	2.08934i
$373$	−65.8984			−0.176671			−0.0883356	−	0.996091i	$-0.528155\pi$
$373$	−65.8984			−0.176671			−0.0883356	+	0.996091i	$0.528155\pi$
$374$	122.201	−	376.095i	0.326739	−	1.00560i
$375$	619.009	−	201.128i	1.65069	−	0.536342i
$376$	−128.744	−	93.5378i	−0.342404	−	0.248771i
$377$	−131.348			−0.348403
$378$		−	1217.18i		−	3.22006i
$379$	402.911	+	292.732i	1.06309	+	0.772381i	0.974658	−	0.223702i	$-0.0718141\pi$
$379$	402.911	+	292.732i	1.06309	+	0.772381i	0.0884330	+	0.996082i	$0.471814\pi$
$380$	−67.6007	+	49.1148i	−0.177897	+	0.129249i
$381$	160.599	−	116.682i	0.421518	−	0.306251i
$382$	−87.4480	+	269.137i	−0.228921	+	0.704548i
$383$	−154.922	+	213.231i	−0.404495	+	0.556739i	−0.961865	−	0.273525i	$-0.911810\pi$
$383$	−154.922	+	213.231i	−0.404495	+	0.556739i	0.557370	+	0.830264i	$0.311810\pi$
$384$	−360.071	−	116.994i	−0.937684	−	0.304672i
$385$	−175.569	+	57.0460i	−0.456025	+	0.148171i
$386$	−296.700	+	215.565i	−0.768654	+	0.558460i
$387$	213.910	−	69.5037i	0.552740	−	0.179596i
$388$	136.677	+	420.647i	0.352259	+	1.08414i
$389$	−416.464	−	573.214i	−1.07060	−	1.47356i	−0.869465	−	0.493995i	$-0.835536\pi$
$389$	−416.464	−	573.214i	−1.07060	−	1.47356i	−0.201137	−	0.979563i	$-0.564464\pi$
$390$	−174.743	−	537.804i	−0.448059	−	1.37898i
$391$	65.4840	−	201.539i	0.167478	−	0.515445i
$392$	−16.9458	−	12.3118i	−0.0432291	−	0.0314078i
$393$	−951.914	−	309.296i	−2.42217	−	0.787012i
$394$	−267.743	−	368.516i	−0.679550	−	0.935321i
$395$	−210.262	−	289.401i	−0.532308	−	0.732660i
$396$	329.341	−	453.299i	0.831669	−	1.14469i
$397$	439.070			1.10597			0.552985	−	0.833191i	$-0.313489\pi$
$397$	439.070			1.10597			0.552985	+	0.833191i	$0.313489\pi$
$398$			814.912i			2.04752i
$399$	68.2745	−	93.9718i	0.171114	−	0.235518i
$400$	−8.49841	−	26.1554i	−0.0212460	−	0.0653885i
$401$	380.052	+	123.486i	0.947762	+	0.307946i	0.741806	−	0.670615i	$-0.233970\pi$
$401$	380.052	+	123.486i	0.947762	+	0.307946i	0.205956	+	0.978561i	$0.433970\pi$
$402$			1028.26i			2.55787i
$403$	161.581	+	130.381i	0.400946	+	0.323526i
$404$	218.481			0.540795
$405$	−273.904	+	842.991i	−0.676307	+	2.08146i
$406$	−346.519	+	112.591i	−0.853496	+	0.277318i
$407$	−33.6293	−	24.4331i	−0.0826274	−	0.0600323i
$408$	285.821			0.700541
$409$		−	225.799i		−	0.552075i	−0.961147	−	0.276037i	$-0.910979\pi$
$409$		−	225.799i		−	0.552075i	0.961147	−	0.276037i	$-0.0890214\pi$
$410$	361.937	+	262.963i	0.882773	+	0.641372i
$411$	556.567	−	404.369i	1.35418	−	0.983867i
$412$	−252.275	+	183.288i	−0.612317	+	0.444875i
$413$	−153.023	+	470.958i	−0.370517	+	1.14033i
$414$	325.299	−	447.736i	0.785747	−	1.08149i
$415$	75.2439	+	24.4482i	0.181311	+	0.0589114i
$416$	290.945	−	94.5338i	0.699387	−	0.227245i
$417$	−1099.32	+	798.703i	−2.63626	+	1.91535i
$418$	53.5000	−	17.3832i	0.127991	−	0.0415866i
$419$	136.617	+	420.465i	0.326056	+	1.00350i	0.970962	+	0.239234i	$0.0768964\pi$
$419$	136.617	+	420.465i	0.326056	+	1.00350i	−0.644906	+	0.764262i	$0.723104\pi$
$420$	−500.217	−	688.490i	−1.19099	−	1.63926i
$421$	−134.613	−	414.296i	−0.319745	−	0.984075i	−0.973757	−	0.227590i	$-0.926915\pi$
$421$	−134.613	−	414.296i	−0.319745	−	0.984075i	0.654012	−	0.756485i	$-0.273085\pi$
$422$	−9.60896	+	29.5733i	−0.0227701	+	0.0700790i
$423$	−1227.45	−	891.792i	−2.90176	−	2.10825i
$424$	25.9908	+	8.44491i	0.0612990	+	0.0199172i
$425$	30.7704	+	42.3519i	0.0724010	+	0.0996514i
$426$	240.655	+	331.234i	0.564919	+	0.777544i
$427$	228.269	−	314.186i	0.534588	−	0.735798i
$428$	−432.514			−1.01055
$429$			206.536i			0.481436i
$430$	97.2445	−	133.846i	0.226150	−	0.311269i
$431$	−79.0915	−	243.419i	−0.183507	−	0.564776i	0.816413	−	0.577469i	$-0.195960\pi$
$431$	−79.0915	−	243.419i	−0.183507	−	0.564776i	−0.999919	+	0.0126929i	$0.995960\pi$
$432$	−777.102	−	252.496i	−1.79885	−	0.584481i
$433$		−	135.443i		−	0.312801i	−0.987694	−	0.156400i	$-0.950011\pi$
$433$		−	135.443i		−	0.312801i	0.987694	−	0.156400i	$-0.0499890\pi$
$434$	538.043	+	205.462i	1.23973	+	0.473414i
$435$	559.963			1.28727
$436$	75.2951	−	231.734i	0.172695	−	0.531501i
$437$	28.6692	−	9.31520i	0.0656046	−	0.0213162i
$438$	1627.09	+	1182.15i	3.71481	+	2.69897i
$439$	−285.701			−0.650800			−0.325400	−	0.945576i	$-0.605499\pi$
$439$	−285.701			−0.650800			−0.325400	+	0.945576i	$0.605499\pi$
$440$		−	64.6181i		−	0.146859i
$441$	−161.562	−	117.381i	−0.366353	−	0.266171i
$442$	−380.375	+	276.359i	−0.860578	+	0.625246i
$443$	389.073	−	282.678i	0.878269	−	0.638100i	−0.0545242	−	0.998512i	$-0.517364\pi$
$443$	389.073	−	282.678i	0.878269	−	0.638100i	0.932793	+	0.360413i	$0.117364\pi$
$444$	59.2162	−	182.249i	0.133370	−	0.410470i
$445$	479.674	−	660.214i	1.07792	−	1.48363i
$446$	748.244	+	243.119i	1.67768	+	0.545110i
$447$	−1021.36	+	331.861i	−2.28493	+	0.742419i
$448$	432.953	−	314.558i	0.966412	−	0.702139i
$449$	141.577	−	46.0012i	0.315316	−	0.102452i	−0.147083	−	0.989124i	$-0.546989\pi$
$449$	141.577	−	46.0012i	0.315316	−	0.102452i	0.462400	+	0.886672i	$0.346989\pi$
$450$	42.2483	+	130.027i	0.0938851	+	0.288949i
$451$	−96.0444	−	132.194i	−0.212959	−	0.293113i
$452$	128.009	+	393.971i	0.283206	+	0.871617i
$453$	13.0071	−	40.0317i	0.0287132	−	0.0883702i
$454$	−29.7320	−	21.6015i	−0.0654889	−	0.0475805i
$455$	208.744	+	67.8249i	0.458777	+	0.149066i
$456$	23.8985	+	32.8934i	0.0524089	+	0.0721346i
$457$	59.9116	+	82.4613i	0.131098	+	0.180440i	0.869519	−	0.493899i	$-0.164429\pi$
$457$	59.9116	+	82.4613i	0.131098	+	0.180440i	−0.738422	+	0.674339i	$0.764429\pi$
$458$	478.063	−	657.997i	1.04380	−	1.43667i
$459$	1555.36			3.38859
$460$		−	220.856i		−	0.480122i
$461$	141.932	−	195.352i	0.307878	−	0.423757i	−0.626840	−	0.779148i	$-0.715652\pi$
$461$	141.932	−	195.352i	0.307878	−	0.423757i	0.934718	+	0.355391i	$0.115652\pi$
$462$	177.042	+	544.879i	0.383208	+	1.17939i
$463$	408.512	+	132.734i	0.882315	+	0.286681i	0.714918	−	0.699208i	$-0.246464\pi$
$463$	408.512	+	132.734i	0.882315	+	0.286681i	0.167397	+	0.985890i	$0.446464\pi$
$464$			244.589i			0.527131i
$465$	−688.855	−	555.841i	−1.48141	−	1.19536i
$466$	−587.109			−1.25989
$467$	175.611	−	540.474i	0.376040	−	1.15733i	−0.566735	−	0.823900i	$-0.691794\pi$
$467$	175.611	−	540.474i	0.376040	−	1.15733i	0.942775	−	0.333431i	$-0.108206\pi$
$468$	−633.574	+	205.861i	−1.35379	+	0.439873i
$469$	−322.887	−	234.591i	−0.688459	−	0.500195i
$470$	−1116.00			−2.37448
$471$			1509.56i			3.20500i
$472$	−140.231	−	101.884i	−0.297100	−	0.215856i
$473$	−48.8857	+	35.5176i	−0.103352	+	0.0750900i
$474$	−898.154	+	652.547i	−1.89484	+	1.37668i
$475$	−2.30120	+	7.08236i	−0.00484463	+	0.0149102i
$476$	−415.907	+	572.447i	−0.873754	+	1.20262i
$477$	247.796	+	80.5140i	0.519489	+	0.168792i
$478$	−618.276	+	200.890i	−1.29346	+	0.420272i
$479$	401.431	−	291.657i	0.838061	−	0.608887i	−0.0837673	−	0.996485i	$-0.526695\pi$
$479$	401.431	−	291.657i	0.838061	−	0.608887i	0.921828	+	0.387598i	$0.126695\pi$
$480$	−1240.36	+	403.017i	−2.58408	+	0.839618i
$481$	15.2724	+	47.0036i	0.0317513	+	0.0977206i
$482$	234.983	+	323.426i	0.487516	+	0.671008i
$483$	94.8720	+	291.986i	0.196422	+	0.604526i
$484$	130.857	−	402.737i	0.270366	−	0.832102i
$485$	393.435	+	285.847i	0.811206	+	0.589375i
$486$	958.011	+	311.277i	1.97122	+	0.640487i
$487$	−155.153	−	213.550i	−0.318590	−	0.438501i	0.619446	−	0.785039i	$-0.287357\pi$
$487$	−155.153	−	213.550i	−0.318590	−	0.438501i	−0.938036	+	0.346538i	$0.887357\pi$
$488$	79.9022	+	109.976i	0.163734	+	0.225361i
$489$	−467.773	+	643.834i	−0.956591	+	1.31663i
$490$	−146.893			−0.299782
$491$			482.796i			0.983290i	0.870796	+	0.491645i	$0.163604\pi$
$491$			482.796i			0.983290i	−0.870796	+	0.491645i	$0.836396\pi$
$492$	442.761	−	609.409i	0.899921	−	1.23864i
$493$	−143.873	−	442.795i	−0.291831	−	0.898164i
$494$	−63.6089	−	20.6678i	−0.128763	−	0.0418376i
$495$		−	616.070i		−	1.24459i
$496$	242.789	−	300.888i	0.489493	−	0.606630i
$497$	−158.915			−0.319749
$498$	75.8750	−	233.519i	0.152359	−	0.468914i
$499$	−319.557	+	103.830i	−0.640394	+	0.208077i	−0.611174	−	0.791496i	$-0.709302\pi$
$499$	−319.557	+	103.830i	−0.640394	+	0.208077i	−0.0292203	+	0.999573i	$0.509302\pi$
$500$	−456.292	−	331.515i	−0.912584	−	0.663031i
$501$	1564.05			3.12185
$502$		−	243.020i		−	0.484104i
$503$	10.4474	+	7.59051i	0.0207703	+	0.0150905i	0.598122	−	0.801405i	$-0.295914\pi$
$503$	10.4474	+	7.59051i	0.0207703	+	0.0150905i	−0.577352	+	0.816496i	$0.695914\pi$
$504$	−234.398	+	170.300i	−0.465074	+	0.337896i
$505$	194.346	−	141.200i	0.384843	−	0.279605i
$506$	−45.9458	+	141.407i	−0.0908020	+	0.279460i
$507$	−399.455	+	549.802i	−0.787879	+	1.08442i
$508$	−163.601	−	53.1570i	−0.322048	−	0.104640i
$509$	387.512	−	125.910i	0.761320	−	0.247368i	0.0974751	−	0.995238i	$-0.468923\pi$
$509$	387.512	−	125.910i	0.761320	−	0.247368i	0.663845	+	0.747870i	$0.268923\pi$
$510$	1621.62	−	1178.17i	3.17964	−	2.31015i
$511$	−742.419	+	241.227i	−1.45288	+	0.472068i
$512$	−209.940	−	646.128i	−0.410038	−	1.26197i
$513$	130.049	+	178.997i	0.253507	+	0.348922i
$514$	−93.1955	−	286.826i	−0.181314	−	0.558028i
$515$	−105.950	+	326.081i	−0.205728	+	0.633167i
$516$	−225.361	−	163.735i	−0.436747	−	0.317315i
$517$	387.659	+	125.958i	0.749824	+	0.243633i
$518$	80.5827	+	110.913i	0.155565	+	0.214117i
$519$	−463.304	−	637.683i	−0.892686	−	1.22868i
$520$	−45.1582	+	62.1549i	−0.0868427	+	0.119529i
$521$	248.737			0.477423			0.238711	−	0.971091i	$-0.423275\pi$
$521$	248.737			0.477423			0.238711	+	0.971091i	$0.423275\pi$
$522$		−	1215.93i		−	2.32937i
$523$	−480.687	+	661.609i	−0.919095	+	1.26503i	0.0448683	+	0.998993i	$0.485713\pi$
$523$	−480.687	+	661.609i	−0.919095	+	1.26503i	−0.963964	+	0.266033i	$0.914287\pi$
$524$	268.021	+	824.883i	0.511490	+	1.57420i
$525$	−72.1314	−	23.4369i	−0.137393	−	0.0446418i
$526$		−	517.544i		−	0.983925i
$527$	−262.547	+	687.531i	−0.498191	+	1.30461i
$528$	384.600			0.728410
$529$	138.849	−	427.333i	0.262474	−	0.807813i
$530$	182.270	−	59.2232i	0.343906	−	0.111742i
$531$	−1336.97	−	971.363i	−2.51783	−	1.82931i
$532$	−100.655			−0.189201
$533$			194.275i			0.364494i
$534$	−2048.97	−	1488.67i	−3.83703	−	2.78776i
$535$	−384.734	+	279.526i	−0.719130	+	0.522478i
$536$	113.022	−	82.1151i	0.210862	−	0.153200i
$537$	346.270	−	1065.71i	0.644823	−	1.98456i
$538$	−338.040	+	465.271i	−0.628326	+	0.864817i
$539$	51.0253	+	16.5791i	0.0946666	+	0.0307591i
$540$	1541.68	−	500.923i	2.85497	−	0.927636i
$541$	513.683	−	373.212i	0.949506	−	0.689856i	−0.00118419	−	0.999999i	$-0.500377\pi$
$541$	513.683	−	373.212i	0.949506	−	0.689856i	0.950690	+	0.310143i	$0.100377\pi$
$542$	259.585	−	84.3443i	0.478939	−	0.155617i
$543$	211.047	+	649.535i	0.388668	+	1.19620i
$544$	637.378	+	877.275i	1.17165	+	1.61264i
$545$	−82.7884	−	254.797i	−0.151905	−	0.467517i
$546$	210.494	−	647.835i	0.385521	−	1.18651i
$547$	511.421	+	371.569i	0.934957	+	0.679286i	0.947201	−	0.320639i	$-0.103898\pi$
$547$	511.421	+	371.569i	0.934957	+	0.679286i	−0.0122447	+	0.999925i	$0.503898\pi$
$548$	−566.970	−	184.220i	−1.03462	−	0.336168i
$549$	761.789	+	1048.51i	1.38759	+	1.90986i
$550$	−21.5896	−	29.7155i	−0.0392538	−	0.0540283i
$551$	38.9289	−	53.5810i	0.0706514	−	0.0972432i
$552$	−107.465			−0.194683
$553$		−	430.906i		−	0.779215i
$554$	25.6175	−	35.2595i	0.0462410	−	0.0636452i
$555$	−65.1094	−	200.386i	−0.117314	−	0.361056i
$556$	1119.87	+	363.868i	2.01415	+	0.654438i
$557$		−	46.8846i		−	0.0841734i	−0.999114	−	0.0420867i	$-0.986599\pi$
$557$		−	46.8846i		−	0.0841734i	0.999114	−	0.0420867i	$-0.0134006\pi$
$558$	−1206.98	+	1495.81i	−2.16305	+	2.68067i
$559$	71.8437			0.128522
$560$	126.300	−	388.711i	0.225536	−	0.694127i
$561$	−696.267	+	226.231i	−1.24112	+	0.403263i
$562$	240.529	+	174.755i	0.427987	+	0.310951i
$563$	−807.800			−1.43481			−0.717407	−	0.696655i	$-0.754671\pi$
$563$	−807.800			−1.43481			−0.717407	+	0.696655i	$0.754671\pi$
$564$			1879.06i			3.33167i
$565$	368.484	+	267.719i	0.652184	+	0.473839i
$566$	445.533	−	323.699i	0.787160	−	0.571905i
$567$	−863.803	+	627.590i	−1.52346	+	1.10686i
$568$	17.1894	−	52.9034i	0.0302630	−	0.0931398i
$569$	−145.543	+	200.323i	−0.255788	+	0.352061i	−0.917528	−	0.397672i	$-0.869818\pi$
$569$	−145.543	+	200.323i	−0.255788	+	0.352061i	0.661740	+	0.749733i	$0.269818\pi$
$570$	271.178	+	88.1111i	0.475751	+	0.154581i
$571$	−903.094	+	293.433i	−1.58160	+	0.513893i	−0.962468	−	0.271394i	$-0.912515\pi$
$571$	−903.094	+	293.433i	−1.58160	+	0.513893i	−0.619132	+	0.785287i	$0.712515\pi$
$572$	144.793	−	105.198i	0.253135	−	0.183913i
$573$	498.256	−	161.893i	0.869556	−	0.282536i
$574$	166.532	+	512.534i	0.290126	+	0.892916i
$575$	−11.5693	−	15.9238i	−0.0201205	−	0.0276935i
$576$	551.890	+	1698.54i	0.958142	+	2.94886i
$577$	10.8420	−	33.3682i	0.0187903	−	0.0578306i	−0.941222	−	0.337789i	$-0.890321\pi$
$577$	10.8420	−	33.3682i	0.0187903	−	0.0578306i	0.960012	+	0.279959i	$0.0903208\pi$
$578$	−656.938	−	477.294i	−1.13657	−	0.825767i
$579$	645.721	+	209.808i	1.11524	+	0.362362i
$580$	−285.215	−	392.565i	−0.491750	−	0.676836i
$581$	56.0176	+	77.1016i	0.0964158	+	0.132705i
$582$	887.125	−	1221.02i	1.52427	−	2.09798i
$583$	−69.9984			−0.120066
$584$		−	273.246i		−	0.467887i
$585$	−430.539	+	592.586i	−0.735965	+	1.01297i
$586$	−292.962	−	901.643i	−0.499934	−	1.53864i
$587$	−220.922	−	71.7818i	−0.376357	−	0.122286i	0.114729	−	0.993397i	$-0.463400\pi$
$587$	−220.922	−	71.7818i	−0.376357	−	0.122286i	−0.491086	+	0.871111i	$0.663400\pi$
$588$			247.330i			0.420629i
$589$	−101.076	+	27.2719i	−0.171606	+	0.0463021i
$590$	−1215.58			−2.06031
$591$	−260.591	+	802.018i	−0.440933	+	1.35705i
$592$	87.5276	−	28.4394i	0.147851	−	0.0480396i
$593$	143.431	+	104.208i	0.241873	+	0.175731i	0.702117	−	0.712061i	$-0.252238\pi$
$593$	143.431	+	104.208i	0.241873	+	0.175731i	−0.460244	+	0.887792i	$0.652238\pi$
$594$	−1091.30			−1.83720
$595$			778.001i			1.30757i
$596$	752.881	+	547.000i	1.26322	+	0.917786i
$597$	1220.53	−	886.764i	2.04443	−	1.48537i
$598$	143.016	−	103.907i	0.239158	−	0.173758i
$599$	173.180	−	532.995i	0.289116	−	0.889807i	−0.696019	−	0.718024i	$-0.745047\pi$
$599$	173.180	−	532.995i	0.289116	−	0.889807i	0.985135	−	0.171784i	$-0.0549530\pi$
$600$	15.6044	−	21.4777i	0.0260074	−	0.0357961i
$601$	−966.674	−	314.091i	−1.60844	−	0.522614i	−0.639266	−	0.768985i	$-0.720762\pi$
$601$	−966.674	−	314.091i	−1.60844	−	0.522614i	−0.969176	+	0.246371i	$0.920762\pi$
$602$	189.537	−	61.5842i	0.314845	−	0.102299i
$603$	1077.55	−	782.887i	1.78699	−	1.29832i
$604$	−34.6895	+	11.2713i	−0.0574330	+	0.0186611i
$605$	−143.880	−	442.818i	−0.237818	−	0.731930i
$606$	−438.215	−	603.151i	−0.723127	−	0.995299i
$607$	96.6970	+	297.603i	0.159303	+	0.490285i	0.998571	−	0.0534329i	$-0.0170163\pi$
$607$	96.6970	+	297.603i	0.159303	+	0.490285i	−0.839268	+	0.543717i	$0.817016\pi$
$608$	−47.6670	+	146.704i	−0.0783996	+	0.241289i
$609$	545.704	+	396.477i	0.896066	+	0.651030i
$610$	906.658	+	294.591i	1.48632	+	0.482936i
$611$	−284.857	−	392.072i	−0.466214	−	0.641689i
$612$	−1387.98	−	1910.39i	−2.26794	−	3.12155i
$613$	32.4139	−	44.6139i	0.0528775	−	0.0727797i	−0.781759	−	0.623580i	$-0.785677\pi$
$613$	32.4139	−	44.6139i	0.0528775	−	0.0727797i	0.834637	+	0.550801i	$0.185677\pi$
$614$	1464.92			2.38586
$615$		−	828.236i		−	1.34672i
$616$	45.7523	−	62.9727i	0.0742733	−	0.102228i
$617$	−34.9324	−	107.511i	−0.0566165	−	0.174248i	0.918749	−	0.394841i	$-0.129200\pi$
$617$	−34.9324	−	107.511i	−0.0566165	−	0.174248i	−0.975366	+	0.220594i	$0.929200\pi$
$618$	1011.99	+	328.816i	1.63753	+	0.532065i
$619$			451.076i			0.728717i	0.931259	+	0.364359i	$0.118712\pi$
$619$			451.076i			0.728717i	−0.931259	+	0.364359i	$0.881288\pi$
$620$	−38.8098	+	766.041i	−0.0625964	+	1.23555i
$621$	−584.796			−0.941701
$622$	−294.166	+	905.349i	−0.472935	+	1.45555i
$623$	934.919	−	303.774i	1.50067	−	0.487598i
$624$	−369.940	−	268.777i	−0.592853	−	0.430733i
$625$	−675.265			−1.08042
$626$		−	243.484i		−	0.388952i
$627$	−84.2527	−	61.2132i	−0.134374	−	0.0976287i
$628$	1058.28	−	768.887i	1.68516	−	1.22434i
$629$	−141.728	+	102.972i	−0.225323	+	0.163707i
$630$	−627.877	+	1932.41i	−0.996631	+	3.06731i
$631$	183.378	−	252.399i	0.290616	−	0.399998i	−0.638598	−	0.769540i	$-0.720485\pi$
$631$	183.378	−	252.399i	0.290616	−	0.399998i	0.929214	+	0.369542i	$0.120485\pi$
$632$	143.450	+	46.6097i	0.226978	+	0.0737495i
$633$	54.7494	−	17.7891i	0.0864919	−	0.0281029i
$634$	−1282.34	+	931.671i	−2.02261	+	1.46951i
$635$	−179.882	+	58.4472i	−0.283279	+	0.0920429i
$636$	−99.7166	−	306.896i	−0.156787	−	0.482541i
$637$	−37.4940	−	51.6061i	−0.0588603	−	0.0810143i
$638$	100.946	+	310.680i	0.158223	+	0.486960i
$639$	163.884	−	504.382i	0.256469	−	0.789330i
$640$	291.834	+	212.030i	0.455991	+	0.331297i
$641$	34.3584	+	11.1637i	0.0536012	+	0.0174161i	0.335695	−	0.941971i	$-0.391029\pi$
$641$	34.3584	+	11.1637i	0.0536012	+	0.0174161i	−0.282094	+	0.959387i	$0.591029\pi$
$642$	867.508	+	1194.02i	1.35126	+	1.85985i
$643$	−148.338	−	204.170i	−0.230697	−	0.317527i	0.677938	−	0.735120i	$-0.262874\pi$
$643$	−148.338	−	204.170i	−0.230697	−	0.317527i	−0.908634	+	0.417592i	$0.862874\pi$
$644$	156.376	−	215.233i	0.242819	−	0.334212i
$645$	−306.284			−0.474859
$646$		−	237.075i		−	0.366989i
$647$	−114.418	+	157.483i	−0.176844	+	0.243405i	−0.888233	−	0.459394i	$-0.848067\pi$
$647$	−114.418	+	157.483i	−0.176844	+	0.243405i	0.711389	+	0.702799i	$0.248067\pi$
$648$	−115.492	−	355.447i	−0.178228	−	0.548529i
$649$	422.249	+	137.197i	0.650614	+	0.211397i
$650$			43.6707i			0.0671857i
$651$	−277.755	−	1029.43i	−0.426659	−	1.58130i
$652$	689.622			1.05770
$653$	3.50040	−	10.7731i	0.00536049	−	0.0164979i	−0.948340	−	0.317254i	$-0.897239\pi$
$653$	3.50040	−	10.7731i	0.00536049	−	0.0164979i	0.953701	+	0.300756i	$0.0972391\pi$
$654$	−790.760	+	256.934i	−1.20911	+	0.392865i
$655$	771.519	+	560.542i	1.17789	+	0.855789i
$656$	361.769			0.551477
$657$		−	2605.13i		−	3.96520i
$658$	−1087.59	−	790.178i	−1.65287	−	1.20088i
$659$	−97.3577	+	70.7345i	−0.147736	+	0.107336i	−0.659198	−	0.751970i	$-0.729104\pi$
$659$	−97.3577	+	70.7345i	−0.147736	+	0.107336i	0.511462	+	0.859306i	$0.329104\pi$
$660$	−617.283	+	448.482i	−0.935277	+	0.679518i
$661$	−371.810	+	1144.31i	−0.562496	+	1.73119i	0.112779	+	0.993620i	$0.464025\pi$
$661$	−371.810	+	1144.31i	−0.562496	+	1.73119i	−0.675275	+	0.737566i	$0.735975\pi$
$662$	−24.9752	+	34.3754i	−0.0377269	+	0.0519266i
$663$	827.827	+	268.977i	1.24861	+	0.405697i
$664$	−31.7266	+	10.3086i	−0.0477810	+	0.0155250i
$665$	−89.5355	+	65.0513i	−0.134640	+	0.0978215i
$666$	−435.128	+	141.382i	−0.653345	+	0.212285i
$667$	54.0943	+	166.485i	0.0811010	+	0.249603i
$668$	−796.643	−	1096.48i	−1.19258	−	1.64144i
$669$	−450.088	−	1385.23i	−0.672777	−	2.07060i
$670$	302.750	−	931.768i	0.451866	−	1.39070i
$671$	−281.691	−	204.660i	−0.419808	−	0.305008i
$672$	−1494.13	−	485.472i	−2.22340	−	0.722428i
$673$	632.418	+	870.448i	0.939699	+	1.29339i	0.955954	+	0.293517i	$0.0948258\pi$
$673$	632.418	+	870.448i	0.939699	+	1.29339i	−0.0162545	+	0.999868i	$0.505174\pi$
$674$	1116.52	+	1536.76i	1.65656	+	2.28006i
$675$	84.9152	−	116.876i	0.125800	−	0.173149i
$676$	588.903			0.871158
$677$			294.316i			0.434736i	0.976090	+	0.217368i	$0.0697471\pi$
$677$			294.316i			0.434736i	−0.976090	+	0.217368i	$0.930253\pi$
$678$	830.866	−	1143.59i	1.22547	−	1.68671i
$679$	181.025	+	557.137i	0.266605	+	0.820526i
$680$	−258.999	−	84.1539i	−0.380881	−	0.123756i
$681$			68.0369i			0.0999073i
$682$	184.212	−	482.396i	0.270105	−	0.707326i
$683$	−1037.16			−1.51853			−0.759264	−	0.650782i	$-0.774441\pi$
$683$	−1037.16			−1.51853			−0.759264	+	0.650782i	$0.774441\pi$
$684$	103.802	−	319.468i	0.151757	−	0.467059i
$685$	−623.395	+	202.553i	−0.910066	+	0.295698i
$686$	−879.645	−	639.100i	−1.28228	−	0.931632i
$687$	−1505.72			−2.19173
$688$		−	133.783i		−	0.194453i
$689$	67.3302	+	48.9182i	0.0977216	+	0.0709989i
$690$	−609.708	+	442.979i	−0.883635	+	0.641998i
$691$	−634.771	+	461.188i	−0.918627	+	0.667422i	−0.943182	−	0.332277i	$-0.892183\pi$
$691$	−634.771	+	461.188i	−0.918627	+	0.667422i	0.0245548	+	0.999698i	$0.492183\pi$
$692$	−211.069	+	649.603i	−0.305013	+	0.938733i
$693$	436.204	−	600.383i	0.629442	−	0.866353i
$694$	−409.695	−	133.118i	−0.590338	−	0.191813i
$695$	1231.32	−	400.080i	1.77168	−	0.575654i
$696$	−191.015	+	138.781i	−0.274448	+	0.199398i
$697$	−654.934	+	212.801i	−0.939647	+	0.305310i
$698$	−424.687	−	1307.05i	−0.608434	−	1.87257i
$699$	638.875	+	879.336i	0.913984	+	1.25799i
$700$	20.3093	+	62.5056i	0.0290133	+	0.0892937i
$701$	−210.137	+	646.736i	−0.299768	+	0.922591i	0.681810	+	0.731529i	$0.261193\pi$
$701$	−210.137	+	646.736i	−0.299768	+	0.922591i	−0.981578	+	0.191062i	$0.938807\pi$
$702$	1049.70	+	762.650i	1.49530	+	1.08640i
$703$	−23.7007	−	7.70083i	−0.0337137	−	0.0109542i
$704$	−282.025	−	388.174i	−0.400604	−	0.551384i
$705$	1214.40	+	1671.48i	1.72256	+	2.37090i
$706$	−485.008	+	667.556i	−0.686980	+	0.945547i
$707$	289.373			0.409297
$708$			2046.72i			2.89085i
$709$	429.911	−	591.722i	0.606363	−	0.834587i	−0.389909	−	0.920853i	$-0.627494\pi$
$709$	429.911	−	591.722i	0.606363	−	0.834587i	0.996272	+	0.0862665i	$0.0274937\pi$
$710$	−120.547	−	371.006i	−0.169785	−	0.522543i
$711$	1367.65	+	444.377i	1.92356	+	0.625003i
$712$			344.095i			0.483280i
$713$	98.7142	−	258.503i	0.138449	−	0.362557i
$714$	2414.52			3.38169
$715$	60.8101	−	187.154i	0.0850491	−	0.261754i
$716$	−923.492	+	300.061i	−1.28979	+	0.419079i
$717$	973.670	+	707.413i	1.35798	+	0.986629i
$718$	1546.98			2.15457
$719$		−	919.406i		−	1.27873i	−0.768904	−	0.639364i	$-0.779198\pi$
$719$		−	919.406i		−	1.27873i	0.768904	−	0.639364i	$-0.220802\pi$
$720$	1103.48	+	801.727i	1.53262	+	1.11351i
$721$	−334.132	+	242.761i	−0.463428	+	0.336700i
$722$	−836.319	+	607.621i	−1.15834	+	0.841581i
$723$	228.706	−	703.885i	0.316329	−	0.973562i
$724$	347.864	−	478.794i	0.480475	−	0.661318i
$725$	−41.1280	−	13.3633i	−0.0567283	−	0.0184322i
$726$	−1374.28	+	446.532i	−1.89295	+	0.615057i
$727$	184.984	−	134.399i	0.254449	−	0.184868i	−0.453247	−	0.891385i	$-0.649735\pi$
$727$	184.984	−	134.399i	0.254449	−	0.184868i	0.707696	+	0.706517i	$0.249735\pi$
$728$	−88.0167	+	28.5984i	−0.120902	+	0.0392834i
$729$	−103.644	−	318.982i	−0.142172	−	0.437562i
$730$	−1126.34	−	1550.28i	−1.54293	−	2.12366i
$731$	78.6945	+	242.197i	0.107653	+	0.331323i
$732$	496.015	−	1526.58i	0.677616	−	2.08549i
$733$	−94.7309	−	68.8261i	−0.129237	−	0.0938964i	0.521289	−	0.853380i	$-0.325451\pi$
$733$	−94.7309	−	68.8261i	−0.129237	−	0.0938964i	−0.650526	+	0.759484i	$0.725451\pi$
$734$	929.997	+	302.174i	1.26703	+	0.411682i
$735$	159.845	+	220.007i	0.217476	+	0.299330i
$736$	−239.646	−	329.844i	−0.325606	−	0.448158i
$737$	−210.329	+	289.493i	−0.285385	+	0.392799i
$738$	−1798.47			−2.43695
$739$		−	942.715i		−	1.27566i	−0.770176	−	0.637832i	$-0.779832\pi$
$739$		−	942.715i		−	1.27566i	0.770176	−	0.637832i	$-0.220168\pi$
$740$	−107.318	+	147.711i	−0.145025	+	0.199610i
$741$	38.2624	+	117.760i	0.0516362	+	0.158920i
$742$	219.562	+	71.3399i	0.295905	+	0.0961455i
$743$		−	759.232i		−	1.02185i	−0.859626	−	0.510923i	$-0.829304\pi$
$743$		−	759.232i		−	1.02185i	0.859626	−	0.510923i	$-0.170696\pi$
$744$	372.743	+	18.8842i	0.500998	+	0.0253820i
$745$	1023.23			1.37346
$746$	60.2152	−	185.323i	0.0807174	−	0.248423i
$747$	−302.482	+	98.2823i	−0.404929	+	0.131569i
$748$	513.241	+	372.891i	0.686151	+	0.498518i
$749$	−572.854			−0.764825
$750$			1924.60i			2.56613i
$751$	326.330	+	237.093i	0.434527	+	0.315703i	0.783457	−	0.621446i	$-0.213455\pi$
$751$	326.330	+	237.093i	0.434527	+	0.315703i	−0.348929	+	0.937149i	$0.613455\pi$
$752$	−730.095	+	530.445i	−0.970871	+	0.705379i
$753$	−363.981	+	264.447i	−0.483374	+	0.351192i
$754$	120.020	−	369.384i	0.159178	−	0.489899i
$755$	−23.5729	+	32.4454i	−0.0312224	+	0.0429740i
$756$	1857.10	+	603.409i	2.45648	+	0.798160i
$757$	766.011	−	248.892i	1.01190	−	0.328787i	0.244291	−	0.969702i	$-0.421445\pi$
$757$	766.011	−	248.892i	1.01190	−	0.328787i	0.767612	+	0.640915i	$0.221445\pi$
$758$	−1191.40	+	865.604i	−1.57177	+	1.14196i
$759$	261.787	−	85.0599i	0.344911	−	0.112068i
$760$	−11.9710	−	36.8430i	−0.0157513	−	0.0484776i
$761$	−182.899	−	251.739i	−0.240340	−	0.330800i	0.671759	−	0.740770i	$-0.265539\pi$
$761$	−182.899	−	251.739i	−0.240340	−	0.330800i	−0.912099	+	0.409970i	$0.865539\pi$
$762$	181.391	+	558.263i	0.238046	+	0.732629i
$763$	99.7264	−	306.926i	0.130703	−	0.402263i
$764$	−367.281	−	266.845i	−0.480734	−	0.349274i
$765$	−2469.30	−	802.324i	−3.22784	−	1.04879i
$766$	−458.100	−	630.521i	−0.598042	−	0.823135i
$767$	−310.274	−	427.055i	−0.404529	−	0.556786i
$768$	−438.250	+	603.199i	−0.570637	+	0.785415i
$769$	−1316.21			−1.71159			−0.855794	−	0.517316i	$-0.826931\pi$
$769$	−1316.21			−1.71159			−0.855794	+	0.517316i	$0.826931\pi$
$770$		−	545.873i		−	0.708926i
$771$	−328.178	+	451.699i	−0.425653	+	0.585861i
$772$	−181.809	−	559.551i	−0.235504	−	0.724807i
$773$	−621.647	−	201.985i	−0.804200	−	0.261300i	−0.122061	−	0.992523i	$-0.538950\pi$
$773$	−621.647	−	201.985i	−0.804200	−	0.261300i	−0.682139	+	0.731222i	$0.738950\pi$
$774$			665.080i			0.859277i
$775$	37.3299	+	57.2646i	0.0481677	+	0.0738898i
$776$	−205.053			−0.264244
$777$	78.4303	−	241.384i	0.100940	−	0.310661i
$778$	1992.57	−	647.426i	2.56115	−	0.832167i
$779$	−79.2512	−	57.5794i	−0.101735	−	0.0739145i
$780$	907.174			1.16304
$781$			142.480i			0.182432i
$782$	506.943	+	368.316i	0.648265	+	0.470992i
$783$	−1039.46	+	755.209i	−1.32753	+	0.964507i
$784$	−96.0982	+	69.8194i	−0.122574	+	0.0890554i
$785$	444.457	−	1367.90i	0.566187	−	1.74254i
$786$	1739.64	−	2394.41i	2.21328	−	3.04632i
$787$	−519.575	−	168.820i	−0.660197	−	0.214511i	−0.0402920	−	0.999188i	$-0.512829\pi$
$787$	−519.575	−	168.820i	−0.660197	−	0.214511i	−0.619905	+	0.784677i	$0.712829\pi$
$788$	694.990	−	225.816i	0.881967	−	0.286568i
$789$	−775.146	+	563.177i	−0.982442	+	0.713786i
$790$	1006.00	−	326.868i	1.27341	−	0.413758i
$791$	169.545	+	521.805i	0.214342	+	0.659677i
$792$	152.686	+	210.155i	0.192786	+	0.265347i
$793$	127.927	+	393.718i	0.161320	+	0.496492i
$794$	−401.204	+	1234.78i	−0.505295	+	1.55514i
$795$	−287.042	−	208.548i	−0.361060	−	0.262325i
$796$	−1243.34	−	403.986i	−1.56199	−	0.507520i
$797$	−272.719	−	375.365i	−0.342182	−	0.470973i	0.602895	−	0.797820i	$-0.294014\pi$
$797$	−272.719	−	375.365i	−0.342182	−	0.470973i	−0.945077	+	0.326848i	$0.894014\pi$
$798$	201.887	+	277.873i	0.252991	+	0.348212i
$799$	1009.72	−	1389.76i	1.26373	−	1.73937i
$800$	100.719			0.125899
$801$			3280.61i			4.09565i
$802$	−694.552	+	955.969i	−0.866025	+	1.19198i
$803$	216.278	+	665.634i	0.269337	+	0.828934i
$804$	−1568.86	−	509.753i	−1.95131	−	0.634021i
$805$		−	292.519i		−	0.363377i
$806$	−514.312	+	335.272i	−0.638104	+	0.415970i
$807$	1064.70			1.31933
$808$	−31.3005	+	96.3330i	−0.0387382	+	0.119224i
$809$	244.661	−	79.4951i	0.302424	−	0.0982634i	−0.153874	−	0.988090i	$-0.549175\pi$
$809$	244.661	−	79.4951i	0.302424	−	0.0982634i	0.456298	+	0.889827i	$0.349175\pi$
$810$	−2120.43	−	1540.58i	−2.61781	−	1.90195i
$811$	1305.17			1.60933			0.804666	−	0.593728i	$-0.202345\pi$
$811$	1305.17			1.60933			0.804666	+	0.593728i	$0.202345\pi$
$812$		−	584.513i		−	0.719844i
$813$	−408.799	−	297.010i	−0.502827	−	0.365326i
$814$	99.4414	−	72.2484i	0.122164	−	0.0887573i
$815$	613.439	−	445.690i	0.752686	−	0.546859i
$816$	500.875	−	1541.54i	0.613818	−	1.88914i
$817$	−21.2930	+	29.3074i	−0.0260625	+	0.0358719i
$818$	635.004	+	206.325i	0.776289	+	0.252232i
$819$	−839.153	+	272.657i	−1.02461	+	0.332915i
$820$	−580.639	+	421.859i	−0.708096	+	0.514462i
$821$	−1015.78	+	330.047i	−1.23725	+	0.402007i	−0.853335	−	0.521362i	$-0.825424\pi$
$821$	−1015.78	+	330.047i	−1.23725	+	0.402007i	−0.383914	+	0.923369i	$0.625424\pi$
$822$	628.624	+	1934.71i	0.764749	+	2.35366i
$823$	230.119	+	316.732i	0.279610	+	0.384850i	0.925605	−	0.378492i	$-0.123557\pi$
$823$	230.119	+	316.732i	0.279610	+	0.384850i	−0.645995	+	0.763342i	$0.723557\pi$
$824$	−44.6739	−	137.492i	−0.0542158	−	0.166859i
$825$	−21.0129	+	64.6712i	−0.0254702	+	0.0783893i
$826$	−1184.63	−	860.683i	−1.43417	−	1.04199i
$827$	431.848	+	140.316i	0.522186	+	0.169669i	0.558237	−	0.829681i	$-0.311478\pi$
$827$	431.848	+	140.316i	0.522186	+	0.169669i	−0.0360511	+	0.999350i	$0.511478\pi$
$828$	521.863	+	718.283i	0.630269	+	0.867491i
$829$	629.022	+	865.774i	0.758772	+	1.04436i	0.997315	+	0.0732281i	$0.0233301\pi$
$829$	629.022	+	865.774i	0.758772	+	1.04436i	−0.238543	+	0.971132i	$0.576670\pi$
$830$	−137.509	+	189.265i	−0.165674	+	0.228031i
$831$	−80.6857			−0.0970947
$832$			570.471i			0.685662i
$833$	132.903	−	182.926i	0.159548	−	0.219599i
$834$	−1241.65	−	3821.39i	−1.48878	−	4.58201i
$835$	−1417.28	−	460.501i	−1.69734	−	0.551498i
$836$			90.2445i			0.107948i
$837$	2028.37	+	102.763i	2.42338	+	0.122775i
$838$	−1307.29			−1.56001
$839$	−286.883	+	882.936i	−0.341935	+	1.05237i	0.621270	+	0.783597i	$0.286617\pi$
$839$	−286.883	+	882.936i	−0.341935	+	1.05237i	−0.963204	+	0.268770i	$0.913383\pi$
$840$	375.233	−	121.921i	0.446706	−	0.145144i
$841$	−369.232	−	268.263i	−0.439040	−	0.318981i
$842$	1288.11			1.52982
$843$		−	550.412i		−	0.652921i
$844$	−40.3576	−	29.3215i	−0.0478170	−	0.0347411i
$845$	523.847	−	380.597i	0.619937	−	0.450410i
$846$	3629.54	−	2637.01i	4.29023	−	3.11704i
$847$	173.317	−	533.415i	0.204625	−	0.629770i
$848$	91.0929	−	125.379i	0.107421	−	0.147852i
$849$	−969.632	−	315.052i	−1.14209	−	0.371087i
$850$	−147.221	+	47.8350i	−0.173201	+	0.0562765i
$851$	53.2880	−	38.7160i	0.0626181	−	0.0454947i
$852$	−624.678	+	202.970i	−0.733190	+	0.238228i
$853$	90.7019	+	279.152i	0.106333	+	0.327259i	0.990041	−	0.140780i	$-0.0449609\pi$
$853$	90.7019	+	279.152i	0.106333	+	0.327259i	−0.883708	+	0.468038i	$0.844961\pi$
$854$	674.988	+	929.042i	0.790385	+	1.08787i
$855$	−114.132	−	351.262i	−0.133488	−	0.410833i
$856$	61.9637	−	190.705i	0.0723875	−	0.222786i
$857$	633.842	+	460.513i	0.739605	+	0.537355i	0.892587	−	0.450874i	$-0.148888\pi$
$857$	633.842	+	460.513i	0.739605	+	0.537355i	−0.152982	+	0.988229i	$0.548888\pi$
$858$	−580.832	−	188.724i	−0.676961	−	0.219958i
$859$	50.7728	+	69.8827i	0.0591069	+	0.0813536i	0.837547	−	0.546365i	$-0.183989\pi$
$859$	50.7728	+	69.8827i	0.0591069	+	0.0813536i	−0.778440	+	0.627719i	$0.783989\pi$
$860$	156.005	+	214.722i	0.181401	+	0.249677i
$861$	586.426	−	807.146i	0.681099	−	0.937452i
$862$	756.826			0.877989
$863$			104.362i			0.120930i	0.998170	+	0.0604648i	$0.0192583\pi$
$863$			104.362i			0.120930i	−0.998170	+	0.0604648i	$0.980742\pi$
$864$	1758.93	−	2420.96i	2.03580	−	2.80204i
$865$	232.074	+	714.252i	0.268294	+	0.825724i
$866$	380.900	+	123.762i	0.439839	+	0.142912i
$867$			1503.30i			1.73391i
$868$	−580.211	+	719.056i	−0.668446	+	0.828406i
$869$	−386.339			−0.444579
$870$	−511.671	+	1574.76i	−0.588127	+	1.81007i
$871$	404.623	−	131.470i	0.464550	−	0.150941i
$872$	91.3896	+	66.3984i	0.104805	+	0.0761450i
$873$	−1954.98			−2.23938
$874$			89.1371i			0.101988i
$875$	−604.347	−	439.084i	−0.690682	−	0.501810i
$876$	−2610.26	+	1896.47i	−2.97975	+	2.16492i
$877$	385.885	−	280.362i	0.440006	−	0.319683i	−0.345631	−	0.938370i	$-0.612335\pi$
$877$	385.885	−	280.362i	0.440006	−	0.319683i	0.785637	+	0.618687i	$0.212335\pi$
$878$	261.062	−	803.466i	0.297337	−	0.915110i
$879$	−1031.63	+	1419.92i	−1.17364	+	1.61538i
$880$	−348.509	−	113.237i	−0.396032	−	0.128679i
$881$	132.919	−	43.1879i	0.150872	−	0.0490214i	−0.232607	−	0.972571i	$-0.574726\pi$
$881$	132.919	−	43.1879i	0.150872	−	0.0490214i	0.383480	+	0.923549i	$0.374726\pi$
$882$	477.735	−	347.095i	0.541649	−	0.393531i
$883$	−1251.19	+	406.536i	−1.41698	+	0.460403i	−0.914640	−	0.404269i	$-0.867526\pi$
$883$	−1251.19	+	406.536i	−1.41698	+	0.460403i	−0.502336	+	0.864672i	$0.667526\pi$
$884$	−233.083	−	717.355i	−0.263668	−	0.811488i
$885$	1322.76	+	1820.62i	1.49464	+	2.05720i
$886$	439.445	+	1352.47i	0.495988	+	1.52649i
$887$	−188.419	+	579.895i	−0.212423	+	0.653771i	0.786903	+	0.617076i	$0.211683\pi$
$887$	−188.419	+	579.895i	−0.212423	+	0.653771i	−0.999327	+	0.0366948i	$0.988317\pi$
$888$	71.8738	+	52.2194i	0.0809390	+	0.0588056i
$889$	−216.685	−	70.4052i	−0.243740	−	0.0791959i
$890$	1418.39	+	1952.24i	1.59369	+	2.19353i
$891$	562.681	+	774.464i	0.631517	+	0.869208i
$892$	−741.871	+	1021.10i	−0.831694	+	1.14473i
$893$	244.365			0.273645
$894$		−	3175.58i		−	3.55211i
$895$	−627.550	+	863.749i	−0.701173	+	0.965083i
$896$	134.277	+	413.262i	0.149863	+	0.461230i
$897$	−311.252	−	101.132i	−0.346993	−	0.112745i
$898$			440.185i			0.490184i
$899$	−158.371	−	586.961i	−0.176163	−	0.652904i
$900$	−219.331			−0.243701
$901$	−91.1608	+	280.564i	−0.101177	+	0.311392i
$902$	459.525	−	149.309i	0.509451	−	0.165531i
$903$	−298.485	−	216.862i	−0.330549	−	0.240158i
$904$	−192.049			−0.212444
$905$		−	650.720i		−	0.719028i
$906$	100.694	+	73.1586i	0.111141	+	0.0807490i
$907$	1126.58	−	818.508i	1.24209	−	0.902435i	0.244359	−	0.969685i	$-0.421423\pi$
$907$	1126.58	−	818.508i	1.24209	−	0.902435i	0.997736	+	0.0672504i	$0.0214226\pi$
$908$	47.6976	−	34.6543i	0.0525304	−	0.0381656i
$909$	−298.420	+	918.441i	−0.328294	+	1.01039i
$910$	−381.482	+	525.065i	−0.419211	+	0.576995i
$911$	994.153	+	323.020i	1.09128	+	0.354577i	0.798740	−	0.601677i	$-0.205501\pi$
$911$	994.153	+	323.020i	1.09128	+	0.354577i	0.292537	+	0.956254i	$0.405501\pi$
$912$	219.286	−	71.2503i	0.240445	−	0.0781253i
$913$	69.1273	−	50.2239i	0.0757144	−	0.0550098i
$914$	−286.647	+	93.1373i	−0.313618	+	0.101901i
$915$	−545.378	−	1678.50i	−0.596042	−	1.83443i
$916$	766.934	+	1055.59i	0.837264	+	1.15239i
$917$	354.987	+	1092.54i	0.387117	+	1.19143i
$918$	−1421.22	+	4374.08i	−1.54818	+	4.76479i
$919$	−94.1551	−	68.4077i	−0.102454	−	0.0744371i	0.535379	−	0.844612i	$-0.320169\pi$
$919$	−94.1551	−	68.4077i	−0.102454	−	0.0744371i	−0.637833	+	0.770175i	$0.720169\pi$
$920$	97.3803	+	31.6408i	0.105848	+	0.0343921i
$921$	−1594.08	−	2194.07i	−1.73082	−	2.38226i
$922$	419.689	+	577.653i	0.455194	+	0.626521i
$923$	99.5716	−	137.048i	0.107878	−	0.148482i
$924$	−919.109			−0.994707
$925$			16.2717i			0.0175911i
$926$	−746.562	+	1027.55i	−0.806222	+	1.10967i
$927$	−425.921	−	1310.85i	−0.459462	−	1.41408i
$928$	−851.925	−	276.807i	−0.918023	−	0.298284i
$929$			16.8619i			0.0181506i	0.999959	+	0.00907531i	$0.00288880\pi$
$929$			16.8619i			0.0181506i	−0.999959	+	0.00907531i	$0.997111\pi$
$930$	2192.62	−	1429.33i	2.35765	−	1.53692i
$931$	32.1643			0.0345481
$932$	291.054	−	895.773i	0.312290	−	0.961130i
$933$	1676.08	−	544.591i	1.79644	−	0.583699i
$934$	1359.49	+	987.724i	1.45555	+	1.05752i
$935$	697.536			0.746028
$936$		−	308.849i		−	0.329967i
$937$	−229.398	−	166.668i	−0.244822	−	0.177874i	0.458607	−	0.888639i	$-0.348349\pi$
$937$	−229.398	−	166.668i	−0.244822	−	0.177874i	−0.703429	+	0.710766i	$0.748349\pi$
$938$	954.772	−	693.683i	1.01788	−	0.739534i
$939$	−364.676	+	264.952i	−0.388366	+	0.282164i
$940$	553.250	−	1702.73i	0.588563	−	1.81141i
$941$	631.597	−	869.318i	0.671197	−	0.923824i	−0.328590	−	0.944473i	$-0.606573\pi$
$941$	631.597	−	869.318i	0.671197	−	0.923824i	0.999787	+	0.0206491i	$0.00657328\pi$
$942$	−4245.26	−	1379.37i	−4.50665	−	1.46430i
$943$	246.247	−	80.0105i	0.261131	−	0.0848467i
$944$	−795.239	+	577.775i	−0.842414	+	0.612050i
$945$	2041.92	−	663.460i	2.16076	−	0.702074i
$946$	−55.2148	−	169.934i	−0.0583666	−	0.179634i
$947$	69.0430	+	95.0295i	0.0729071	+	0.100348i	0.843913	−	0.536480i	$-0.180246\pi$
$947$	69.0430	+	95.0295i	0.0729071	+	0.100348i	−0.771006	+	0.636828i	$0.780246\pi$
$948$	−550.362	−	1693.84i	−0.580551	−	1.78675i
$949$	257.144	−	791.407i	0.270963	−	0.833937i
$950$	−17.8147	−	12.9431i	−0.0187523	−	0.0136244i
$951$	2790.80	+	906.786i	2.93460	+	0.953508i
$952$	−192.819	−	265.393i	−0.202541	−	0.278774i
$953$	−326.856	−	449.879i	−0.342976	−	0.472066i	0.602332	−	0.798246i	$-0.294238\pi$
$953$	−326.856	−	449.879i	−0.342976	−	0.472066i	−0.945308	+	0.326180i	$0.894238\pi$
$954$	−452.852	+	623.297i	−0.474688	+	0.653352i
$955$	−499.164			−0.522685
$956$		−	1042.91i		−	1.09091i
$957$	355.472	−	489.265i	0.371444	−	0.511248i
$958$	453.403	+	1395.43i	0.473281	+	1.45661i
$959$	−750.938	−	243.995i	−0.783043	−	0.254426i
$960$		−	2432.03i		−	2.53337i
$961$	−387.816	+	879.272i	−0.403554	+	0.914956i
$962$	−146.142			−0.151914
$963$	590.763	−	1818.18i	0.613461	−	1.88804i
$964$	−609.953	+	198.186i	−0.632731	+	0.205587i
$965$	−523.352	−	380.238i	−0.542334	−	0.394029i
$966$	−907.831			−0.939783
$967$			441.345i			0.456406i	0.973614	+	0.228203i	$0.0732850\pi$
$967$			441.345i			0.456406i	−0.973614	+	0.228203i	$0.926715\pi$
$968$	158.828	+	115.396i	0.164079	+	0.119210i
$969$	−355.076	+	257.978i	−0.366436	+	0.266231i
$970$	−1163.38	+	845.245i	−1.19936	+	0.871387i
$971$	−86.3666	+	265.809i	−0.0889461	+	0.273748i	−0.985629	−	0.168926i	$-0.945970\pi$
$971$	−86.3666	+	265.809i	−0.0889461	+	0.273748i	0.896683	+	0.442674i	$0.145970\pi$
$972$	−949.852	+	1307.36i	−0.977213	+	1.34502i
$973$	1483.24	+	481.933i	1.52440	+	0.495307i
$974$	742.331	−	241.198i	0.762147	−	0.247636i
$975$	65.4073	−	47.5212i	0.0670844	−	0.0487397i
$976$	733.161	−	238.219i	0.751190	−	0.244076i
$977$	369.006	+	1135.68i	0.377693	+	1.16242i	0.941644	+	0.336611i	$0.109281\pi$
$977$	369.006	+	1135.68i	0.377693	+	1.16242i	−0.563951	+	0.825808i	$0.690719\pi$
$978$	−1383.20	−	1903.81i	−1.41431	−	1.94663i
$979$	−272.356	−	838.225i	−0.278198	−	0.856205i
$980$	72.8210	−	224.120i	0.0743072	−	0.228694i
$981$	871.310	+	633.044i	0.888186	+	0.645305i
$982$	−1357.75	−	441.158i	−1.38263	−	0.449245i
$983$	−724.460	−	997.133i	−0.736989	−	1.01438i	−0.998786	−	0.0492549i	$-0.984315\pi$
$983$	−724.460	−	997.133i	−0.736989	−	1.01438i	0.261798	−	0.965123i	$-0.415685\pi$
$984$	205.270	+	282.529i	0.208607	+	0.287123i
$985$	472.274	−	650.029i	0.479466	−	0.659928i
$986$	1376.72			1.39627
$987$			2488.77i			2.52155i
$988$	63.0672	−	86.8046i	0.0638332	−	0.0878589i
$989$	−29.5881	−	91.0629i	−0.0299172	−	0.0920757i
$990$	1732.55	+	562.939i	1.75005	+	0.568625i
$991$		−	875.612i		−	0.883564i	−0.897122	−	0.441782i	$-0.854346\pi$
$991$		−	875.612i		−	0.883564i	0.897122	−	0.441782i	$-0.145654\pi$
$992$	773.251	+	1186.18i	0.779487	+	1.19574i
$993$	78.6628			0.0792173
$994$	145.210	−	446.911i	0.146087	−	0.449609i
$995$	−1367.08	+	444.191i	−1.37395	+	0.446423i
$996$	318.674	+	231.530i	0.319954	+	0.232460i
$997$	−1277.59			−1.28144			−0.640719	−	0.767776i	$-0.721363\pi$
$997$	−1277.59			−1.28144			−0.640719	+	0.767776i	$0.721363\pi$
$998$		−	993.552i		−	0.995543i
$999$	391.118	+	284.164i	0.391510	+	0.284449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.3.f.a.23.1	✓	20
3.2	odd	2		279.3.v.a.271.5		20
31.27	odd	10	inner	31.3.f.a.27.1	yes	20
93.89	even	10		279.3.v.a.244.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.3.f.a.23.1	✓	20	1.1	even	1	trivial
31.3.f.a.27.1	yes	20	31.27	odd	10	inner
279.3.v.a.244.5		20	93.89	even	10
279.3.v.a.271.5		20	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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	31.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913758 + 2.81226i) q^{2} +(5.20635 - 1.69165i) q^{3} +(-3.83778 - 2.78831i) q^{4} -5.21585 q^{5} +16.1874i q^{6} +(-5.08304 - 3.69304i) q^{7} +(1.77924 - 1.29269i) q^{8} +(16.9633 - 12.3246i) q^{9} +(4.76602 - 14.6683i) q^{10} +(-3.31109 + 4.55732i) q^{11} +(-24.6977 - 8.02475i) q^{12} +(6.36975 - 2.06966i) q^{13} +(15.0305 - 10.9203i) q^{14} +(-27.1556 + 8.82338i) q^{15} +(-3.85401 - 11.8614i) q^{16} +(13.9543 + 19.2065i) q^{17} +(19.1595 + 58.9669i) q^{18} +(-1.04359 + 3.21183i) q^{19} +(20.0173 + 14.5434i) q^{20} +(-32.7114 - 10.6286i) q^{21} +(-9.79083 - 13.4759i) q^{22} +(-5.24664 - 7.22139i) q^{23} +(7.07657 - 9.74007i) q^{24} +2.20508 q^{25} +19.8046i q^{26} +(38.5088 - 53.0029i) q^{27} +(9.21022 + 28.3461i) q^{28} +(-18.6515 - 6.06023i) q^{29} -84.4309i q^{30} +(16.9290 + 25.9694i) q^{31} +45.6760 q^{32} +(-9.52932 + 29.3282i) q^{33} +(-66.7644 + 21.6931i) q^{34} +(26.5124 + 19.2624i) q^{35} -99.4660 q^{36} +7.37919i q^{37} +(-8.07892 - 5.86968i) q^{38} +(29.6621 - 21.5507i) q^{39} +(-9.28025 + 6.74249i) q^{40} +(-8.96363 + 27.5872i) q^{41} +(59.7807 - 82.2810i) q^{42} +(10.2018 + 3.31478i) q^{43} +(25.4144 - 8.25765i) q^{44} +(-88.4781 + 64.2831i) q^{45} +(25.1026 - 8.15632i) q^{46} +(-22.3601 - 68.8174i) q^{47} +(-40.1306 - 55.2351i) q^{48} +(-2.94313 - 9.05803i) q^{49} +(-2.01491 + 6.20127i) q^{50} +(105.142 + 76.3899i) q^{51} +(-30.2165 - 9.81794i) q^{52} +(7.30390 + 10.0530i) q^{53} +(113.870 + 156.729i) q^{54} +(17.2701 - 23.7703i) q^{55} -13.8179 q^{56} +18.4873i q^{57} +(34.0859 - 46.9152i) q^{58} +(-24.3552 - 74.9577i) q^{59} +(128.819 + 41.8559i) q^{60} +61.8106i q^{61} +(-88.5016 + 23.8791i) q^{62} -131.740 q^{63} +(-26.3208 + 81.0072i) q^{64} +(-33.2237 + 10.7950i) q^{65} +(-73.7711 - 53.5978i) q^{66} +63.5225 q^{67} -112.619i q^{68} +(-39.5319 - 28.7216i) q^{69} +(-78.3966 + 56.9585i) q^{70} +(20.4625 - 14.8669i) q^{71} +(14.2499 - 43.8567i) q^{72} +(73.0291 - 100.516i) q^{73} +(-20.7522 - 6.74279i) q^{74} +(11.4804 - 3.73022i) q^{75} +(12.9606 - 9.41645i) q^{76} +(33.6608 - 10.9370i) q^{77} +(33.5023 + 103.110i) q^{78} +(40.3121 + 55.4848i) q^{79} +(20.1019 + 61.8673i) q^{80} +(52.5139 - 161.621i) q^{81} +(-69.3918 - 50.4161i) q^{82} +(-14.4260 - 4.68729i) q^{83} +(95.9033 + 132.000i) q^{84} +(-72.7836 - 100.178i) q^{85} +(-18.6440 + 25.6613i) q^{86} -107.358 q^{87} +12.3888i q^{88} +(-91.9646 + 126.578i) q^{89} +(-99.9331 - 307.562i) q^{90} +(-40.0210 - 13.0036i) q^{91} +42.3433i q^{92} +(132.070 + 106.568i) q^{93} +213.964 q^{94} +(5.44320 - 16.7524i) q^{95} +(237.806 - 77.2677i) q^{96} +(-75.4306 - 54.8035i) q^{97} +28.1628 q^{98} +118.115i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9} + 12 q^{10} - 10 q^{11} + 90 q^{12} + 10 q^{13} - 85 q^{15} - 103 q^{16} + 35 q^{17} + 6 q^{18} + 47 q^{19} - 125 q^{20} - 125 q^{21}+ \cdots - 1000 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 5 * q^3 - 11 * q^4 - 14 * q^5 - q^7 - 19 * q^8 + 2 * q^9 + 12 * q^10 - 10 * q^11 + 90 * q^12 + 10 * q^13 - 85 * q^15 - 103 * q^16 + 35 * q^17 + 6 * q^18 + 47 * q^19 - 125 * q^20 - 125 * q^21 + 150 * q^22 + 75 * q^23 + 195 * q^24 + 82 * q^25 + 25 * q^27 + 88 * q^28 + 5 * q^29 + 73 * q^31 + 226 * q^32 - 206 * q^33 - 265 * q^34 - 50 * q^35 - 520 * q^36 + 8 * q^38 + 91 * q^39 - 466 * q^40 - 98 * q^41 + 245 * q^43 + 380 * q^44 - 162 * q^45 - 445 * q^46 - 187 * q^47 + 570 * q^48 + 328 * q^49 - 44 * q^50 + 185 * q^51 - 15 * q^52 + 25 * q^53 + 920 * q^54 + 190 * q^55 + 64 * q^56 - 85 * q^58 - 173 * q^59 + 275 * q^60 - 40 * q^62 + 252 * q^63 - 469 * q^64 - 345 * q^65 - 564 * q^66 + 76 * q^67 - 197 * q^69 - 11 * q^70 - 467 * q^71 - 982 * q^72 - 15 * q^73 + 45 * q^74 - 175 * q^75 + 55 * q^76 - 320 * q^77 - 91 * q^78 + 500 * q^79 + 1030 * q^80 + 117 * q^81 + 178 * q^82 - 50 * q^83 + 65 * q^84 + 20 * q^85 + 1125 * q^86 - 366 * q^87 + 55 * q^89 + 444 * q^90 + 300 * q^91 + 502 * q^93 + 62 * q^94 - 559 * q^95 - 10 * q^96 - 405 * q^97 - 1000 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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