LMFDB - Embedded newform 431.3.f.a.101.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [431,3,Mod(47,431)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(431, base_ring=CyclotomicField(86))

chi = DirichletCharacter(H, H._module([63]))

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

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

chi := DirichletCharacter("431.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 431 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	431.f (of order $86$, degree $42$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7438993939$
Analytic rank:	$0$
Dimension:	$2982$
Relative dimension:	$71$ over $\Q(\zeta_{86})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{86}]$

Embedding invariants

Embedding label			101.11
Character	$\chi$	$=$	431.101
Dual form			431.3.f.a.367.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35584 + 2.63713i) q^{2} +(0.459232 + 4.17365i) q^{3} +(-2.78870 - 3.89789i) q^{4} +(3.04268 + 1.42635i) q^{5} +(-11.6291 - 4.44775i) q^{6} +(-2.23823 - 10.0478i) q^{7} +(2.32564 - 0.342263i) q^{8} +(-8.42376 + 1.87647i) q^{9} +(-7.88685 + 6.09003i) q^{10} +(-12.0732 + 6.77581i) q^{11} +(14.9878 - 13.4291i) q^{12} +(-1.72895 + 0.888915i) q^{13} +(29.5319 + 7.72065i) q^{14} +(-4.55578 + 13.3541i) q^{15} +(3.93933 - 11.5471i) q^{16} +(-11.4138 - 20.3372i) q^{17} +(6.47278 - 24.7587i) q^{18} +(13.5062 - 6.33143i) q^{19} +(-2.92537 - 15.8377i) q^{20} +(40.9080 - 13.9559i) q^{21} +(-1.49933 - 41.0255i) q^{22} +(-17.9680 - 18.6367i) q^{23} +(2.49649 + 9.54921i) q^{24} +(-8.76840 - 10.5363i) q^{25} -5.76469i q^{26} +(0.501302 + 1.46944i) q^{27} +(-32.9233 + 36.7446i) q^{28} +(-15.6681 + 21.9001i) q^{29} +(-29.0395 - 30.1202i) q^{30} +(-16.3620 - 42.7800i) q^{31} +(31.6363 + 32.8136i) q^{32} +(-33.8243 - 47.2777i) q^{33} +(69.1069 - 2.52561i) q^{34} +(7.52139 - 33.7646i) q^{35} +(30.8056 + 27.6020i) q^{36} +(26.0010 + 6.79754i) q^{37} +(-1.61542 + 44.2019i) q^{38} +(-4.50401 - 6.80781i) q^{39} +(7.56435 + 2.27577i) q^{40} +(-24.1312 + 70.7343i) q^{41} +(-18.6613 + 126.801i) q^{42} +(10.1486 - 13.1429i) q^{43} +(60.0799 + 28.1643i) q^{44} +(-28.3073 - 6.30572i) q^{45} +(73.5091 - 22.1156i) q^{46} +(-1.29151 + 17.6458i) q^{47} +(50.0027 + 11.1386i) q^{48} +(-51.5809 + 24.1801i) q^{49} +(39.6742 - 8.83781i) q^{50} +(79.6386 - 56.9765i) q^{51} +(8.28642 + 4.26034i) q^{52} +(-93.4333 + 6.83844i) q^{53} +(-4.55477 - 0.670324i) q^{54} +(-46.3996 + 3.39601i) q^{55} +(-8.64429 - 22.6014i) q^{56} +(32.6276 + 53.4624i) q^{57} +(-36.5097 - 71.0119i) q^{58} +(-7.11134 + 13.8316i) q^{59} +(64.7575 - 19.4826i) q^{60} +(-19.1560 - 45.0777i) q^{61} +(135.001 + 14.8543i) q^{62} +(37.7087 + 80.4400i) q^{63} +(-82.6944 + 24.8790i) q^{64} +(-6.52854 + 0.238595i) q^{65} +(170.537 - 25.0979i) q^{66} +(-47.2322 - 12.3481i) q^{67} +(-47.4424 + 101.204i) q^{68} +(69.5315 - 83.5508i) q^{69} +(78.8438 + 65.6143i) q^{70} +(1.34066 - 18.3174i) q^{71} +(-18.9484 + 7.24713i) q^{72} +(51.4427 + 77.7558i) q^{73} +(-53.1791 + 59.3515i) q^{74} +(39.9482 - 41.4349i) q^{75} +(-62.3439 - 34.9891i) q^{76} +(95.1044 + 106.143i) q^{77} +(24.0598 - 2.64733i) q^{78} +(-15.7712 + 52.4214i) q^{79} +(28.4563 - 29.5153i) q^{80} +(-76.2308 + 35.7355i) q^{81} +(-153.817 - 159.542i) q^{82} +(2.15796 - 0.237444i) q^{83} +(-168.478 - 120.536i) q^{84} +(-5.72053 - 78.1594i) q^{85} +(20.8995 + 44.5828i) q^{86} +(-98.5984 - 55.3361i) q^{87} +(-25.7588 + 19.8903i) q^{88} +(-98.5875 + 18.2100i) q^{89} +(55.0092 - 66.1004i) q^{90} +(12.8014 + 15.3825i) q^{91} +(-22.5363 + 122.010i) q^{92} +(171.035 - 87.9351i) q^{93} +(-44.7832 - 27.3308i) q^{94} +50.1258 q^{95} +(-122.424 + 147.108i) q^{96} +(9.56619 - 2.87804i) q^{97} +(6.16939 - 168.810i) q^{98} +(88.9872 - 79.7329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2982 q - 43 q^{2} - 41 q^{3} - 187 q^{4} - 41 q^{5} - 33 q^{6} - 43 q^{7} - 37 q^{8} - 252 q^{9} - 23 q^{10} + 187 q^{11} + 19 q^{12} - 43 q^{13} - 43 q^{14} - 71 q^{15} - 359 q^{16} - 43 q^{17} - 93 q^{18}+ \cdots - 609 q^{99}+O(q^{100}) $ 2982 * q - 43 * q^2 - 41 * q^3 - 187 * q^4 - 41 * q^5 - 33 * q^6 - 43 * q^7 - 37 * q^8 - 252 * q^9 - 23 * q^10 + 187 * q^11 + 19 * q^12 - 43 * q^13 - 43 * q^14 - 71 * q^15 - 359 * q^16 - 43 * q^17 - 93 * q^18 - 55 * q^19 + 9 * q^20 - 172 * q^21 - 47 * q^22 + 45 * q^23 + 17 * q^24 - 436 * q^25 + 37 * q^27 - 43 * q^28 - 93 * q^29 - 911 * q^30 - 43 * q^31 + 181 * q^32 + 733 * q^33 - 43 * q^34 - 43 * q^35 - 521 * q^36 - 43 * q^37 + 691 * q^38 - 43 * q^39 + 199 * q^40 + 456 * q^41 - 43 * q^42 - 43 * q^43 - 161 * q^44 - 3 * q^45 - 279 * q^46 - 43 * q^47 + 271 * q^48 + 362 * q^49 - 21 * q^50 - 43 * q^51 - 2107 * q^52 + 53 * q^53 - 2864 * q^54 + 111 * q^55 - 1978 * q^56 + 11 * q^57 - 349 * q^58 + 59 * q^59 + 29 * q^60 - 1433 * q^61 - 43 * q^62 - 2451 * q^63 - 801 * q^64 - 43 * q^65 - 253 * q^66 + 3053 * q^67 - 43 * q^68 + 25 * q^69 - 1978 * q^70 + 2021 * q^71 - 63 * q^72 - 43 * q^73 - 43 * q^74 - 401 * q^75 - 225 * q^76 + 645 * q^77 + 344 * q^78 + 3397 * q^79 + 227 * q^80 - 1054 * q^81 - 845 * q^82 - 43 * q^83 + 6106 * q^84 - 43 * q^85 - 43 * q^86 - 1021 * q^87 + 6277 * q^88 - 43 * q^89 - 815 * q^90 - 147 * q^91 - 239 * q^92 + 2193 * q^93 - 43 * q^94 - 70 * q^95 + 129 * q^96 + 125 * q^97 + 643 * q^98 - 609 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/431\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{37}{86}\right)$

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 $

$2$	−1.35584	+	2.63713i	−0.677920	+	1.31856i	0.257929	+	0.966164i	$0.416960\pi$
$2$	−1.35584	+	2.63713i	−0.677920	+	1.31856i	−0.935850	+	0.352400i	$0.885366\pi$
$3$	0.459232	+	4.17365i	0.153077	+	1.39122i	0.786586	+	0.617481i	$0.211847\pi$
$3$	0.459232	+	4.17365i	0.153077	+	1.39122i	−0.633509	+	0.773735i	$0.718386\pi$
$4$	−2.78870	−	3.89789i	−0.697175	−	0.974472i
$5$	3.04268	+	1.42635i	0.608536	+	0.285270i	0.704041	−	0.710159i	$-0.251377\pi$
$5$	3.04268	+	1.42635i	0.608536	+	0.285270i	−0.0955056	+	0.995429i	$0.530447\pi$
$6$	−11.6291	−	4.44775i	−1.93818	−	0.741291i
$7$	−2.23823	−	10.0478i	−0.319748	−	1.43539i	−0.821414	−	0.570333i	$-0.806814\pi$
$7$	−2.23823	−	10.0478i	−0.319748	−	1.43539i	0.501666	−	0.865062i	$-0.332721\pi$
$8$	2.32564	−	0.342263i	0.290704	−	0.0427828i
$9$	−8.42376	+	1.87647i	−0.935974	+	0.208497i
$10$	−7.88685	+	6.09003i	−0.788685	+	0.609003i
$11$	−12.0732	+	6.77581i	−1.09756	+	0.615983i	−0.929139	−	0.369731i	$-0.879450\pi$
$11$	−12.0732	+	6.77581i	−1.09756	+	0.615983i	−0.168426	+	0.985714i	$0.553868\pi$
$12$	14.9878	−	13.4291i	1.24898	−	1.11909i
$13$	−1.72895	+	0.888915i	−0.132996	+	0.0683781i	−0.522460	−	0.852664i	$-0.674986\pi$
$13$	−1.72895	+	0.888915i	−0.132996	+	0.0683781i	0.389464	+	0.921042i	$0.372660\pi$
$14$	29.5319	+	7.72065i	2.10942	+	0.551475i
$15$	−4.55578	+	13.3541i	−0.303719	+	0.890273i
$16$	3.93933	−	11.5471i	0.246208	−	0.721695i
$17$	−11.4138	−	20.3372i	−0.671398	−	1.19630i	−0.970273	−	0.242011i	$-0.922193\pi$
$17$	−11.4138	−	20.3372i	−0.671398	−	1.19630i	0.298875	−	0.954292i	$-0.403388\pi$
$18$	6.47278	−	24.7587i	0.359599	−	1.37548i
$19$	13.5062	−	6.33143i	0.710851	−	0.333233i	−0.0349619	−	0.999389i	$-0.511131\pi$
$19$	13.5062	−	6.33143i	0.710851	−	0.333233i	0.745813	+	0.666155i	$0.232061\pi$
$20$	−2.92537	−	15.8377i	−0.146268	−	0.791884i
$21$	40.9080	−	13.9559i	1.94800	−	0.664565i
$22$	−1.49933	−	41.0255i	−0.0681516	−	1.86480i
$23$	−17.9680	−	18.6367i	−0.781219	−	0.810291i	0.204469	−	0.978873i	$-0.434453\pi$
$23$	−17.9680	−	18.6367i	−0.781219	−	0.810291i	−0.985688	+	0.168582i	$0.946081\pi$
$24$	2.49649	+	9.54921i	0.104020	+	0.397884i
$25$	−8.76840	−	10.5363i	−0.350736	−	0.421453i
$26$		−	5.76469i		−	0.221719i
$27$	0.501302	+	1.46944i	0.0185667	+	0.0544236i
$28$	−32.9233	+	36.7446i	−1.17583	+	1.31231i
$29$	−15.6681	+	21.9001i	−0.540281	+	0.755174i	−0.990465	−	0.137761i	$-0.956009\pi$
$29$	−15.6681	+	21.9001i	−0.540281	+	0.755174i	0.450185	+	0.892936i	$0.351358\pi$
$30$	−29.0395	−	30.1202i	−0.967984	−	1.00401i
$31$	−16.3620	−	42.7800i	−0.527806	−	1.38000i	−0.893415	−	0.449233i	$-0.851697\pi$
$31$	−16.3620	−	42.7800i	−0.527806	−	1.38000i	0.365609	−	0.930768i	$-0.380861\pi$
$32$	31.6363	+	32.8136i	0.988635	+	1.02543i
$33$	−33.8243	−	47.2777i	−1.02498	−	1.43266i
$34$	69.1069	−	2.52561i	2.03256	−	0.0742826i
$35$	7.52139	−	33.7646i	0.214897	−	0.964703i
$36$	30.8056	+	27.6020i	0.855712	+	0.766721i
$37$	26.0010	+	6.79754i	0.702729	+	0.183717i	0.587028	−	0.809567i	$-0.300298\pi$
$37$	26.0010	+	6.79754i	0.702729	+	0.183717i	0.115701	+	0.993284i	$0.463089\pi$
$38$	−1.61542	+	44.2019i	−0.0425111	+	1.16321i
$39$	−4.50401	−	6.80781i	−0.115487	−	0.174559i
$40$	7.56435	+	2.27577i	0.189109	+	0.0568943i
$41$	−24.1312	+	70.7343i	−0.588566	+	1.72523i	0.0951342	+	0.995464i	$0.469672\pi$
$41$	−24.1312	+	70.7343i	−0.588566	+	1.72523i	−0.683700	+	0.729763i	$0.739630\pi$
$42$	−18.6613	+	126.801i	−0.444317	+	3.01908i
$43$	10.1486	−	13.1429i	0.236014	−	0.305648i	−0.658596	−	0.752497i	$-0.728849\pi$
$43$	10.1486	−	13.1429i	0.236014	−	0.305648i	0.894609	+	0.446849i	$0.147454\pi$
$44$	60.0799	+	28.1643i	1.36545	+	0.640098i
$45$	−28.3073	−	6.30572i	−0.629051	−	0.140127i
$46$	73.5091	−	22.1156i	1.59802	−	0.480774i
$47$	−1.29151	+	17.6458i	−0.0274789	+	0.375443i	0.965767	+	0.259412i	$0.0835288\pi$
$47$	−1.29151	+	17.6458i	−0.0274789	+	0.375443i	−0.993246	+	0.116031i	$0.962983\pi$
$48$	50.0027	+	11.1386i	1.04172	+	0.232054i
$49$	−51.5809	+	24.1801i	−1.05267	+	0.493472i
$50$	39.6742	−	8.83781i	0.793484	−	0.176756i
$51$	79.6386	−	56.9765i	1.56154	−	1.11719i
$52$	8.28642	+	4.26034i	0.159354	+	0.0819296i
$53$	−93.4333	+	6.83844i	−1.76289	+	0.129027i	−0.915598	−	0.402096i	$-0.868282\pi$
$53$	−93.4333	+	6.83844i	−1.76289	+	0.129027i	−0.847295	+	0.531123i	$0.821770\pi$
$54$	−4.55477	−	0.670324i	−0.0843477	−	0.0124134i
$55$	−46.3996	+	3.39601i	−0.843628	+	0.0617456i
$56$	−8.64429	−	22.6014i	−0.154362	−	0.403596i
$57$	32.6276	+	53.4624i	0.572415	+	0.937937i
$58$	−36.5097	−	71.0119i	−0.629478	−	1.22434i
$59$	−7.11134	+	13.8316i	−0.120531	+	0.234435i	−0.941849	−	0.336036i	$-0.890914\pi$
$59$	−7.11134	+	13.8316i	−0.120531	+	0.234435i	0.821318	+	0.570471i	$0.193239\pi$
$60$	64.7575	−	19.4826i	1.07929	−	0.324710i
$61$	−19.1560	−	45.0777i	−0.314032	−	0.738979i	−0.999936	−	0.0112871i	$-0.996407\pi$
$61$	−19.1560	−	45.0777i	−0.314032	−	0.738979i	0.685904	−	0.727692i	$-0.259407\pi$
$62$	135.001	+	14.8543i	2.17743	+	0.239585i
$63$	37.7087	+	80.4400i	0.598551	+	1.27682i
$64$	−82.6944	+	24.8790i	−1.29210	+	0.388735i
$65$	−6.52854	+	0.238595i	−0.100439	+	0.00367069i
$66$	170.537	−	25.0979i	2.58390	−	0.380271i
$67$	−47.2322	−	12.3481i	−0.704958	−	0.184300i	−0.116929	−	0.993140i	$-0.537305\pi$
$67$	−47.2322	−	12.3481i	−0.704958	−	0.184300i	−0.588029	+	0.808840i	$0.700096\pi$
$68$	−47.4424	+	101.204i	−0.697682	+	1.48829i
$69$	69.5315	−	83.5508i	1.00770	−	1.21088i
$70$	78.8438	+	65.6143i	1.12634	+	0.937347i
$71$	1.34066	−	18.3174i	0.0188825	−	0.257991i	−0.979514	−	0.201378i	$-0.935458\pi$
$71$	1.34066	−	18.3174i	0.0188825	−	0.257991i	0.998396	−	0.0566135i	$-0.0180303\pi$
$72$	−18.9484	+	7.24713i	−0.263172	+	0.100655i
$73$	51.4427	+	77.7558i	0.704695	+	1.06515i	0.994156	+	0.107958i	$0.0344311\pi$
$73$	51.4427	+	77.7558i	0.704695	+	1.06515i	−0.289461	+	0.957190i	$0.593476\pi$
$74$	−53.1791	+	59.3515i	−0.718637	+	0.802047i
$75$	39.9482	−	41.4349i	0.532643	−	0.552465i
$76$	−62.3439	−	34.9891i	−0.820314	−	0.460383i
$77$	95.1044	+	106.143i	1.23512	+	1.37848i
$78$	24.0598	−	2.64733i	0.308459	−	0.0339401i
$79$	−15.7712	+	52.4214i	−0.199636	+	0.663561i	0.798470	+	0.602035i	$0.205643\pi$
$79$	−15.7712	+	52.4214i	−0.199636	+	0.663561i	−0.998105	+	0.0615263i	$0.980403\pi$
$80$	28.4563	−	29.5153i	0.355704	−	0.368941i
$81$	−76.2308	+	35.7355i	−0.941120	+	0.441179i
$82$	−153.817	−	159.542i	−1.87582	−	1.94563i
$83$	2.15796	−	0.237444i	0.0259996	−	0.00286077i	−0.0963621	−	0.995346i	$-0.530721\pi$
$83$	2.15796	−	0.237444i	0.0259996	−	0.00286077i	0.122362	+	0.992486i	$0.460953\pi$
$84$	−168.478	−	120.536i	−2.00570	−	1.43495i
$85$	−5.72053	−	78.1594i	−0.0673004	−	0.919523i
$86$	20.8995	+	44.5828i	0.243018	+	0.518404i
$87$	−98.5984	−	55.3361i	−1.13332	−	0.636047i
$88$	−25.7588	+	19.8903i	−0.292713	+	0.226026i
$89$	−98.5875	+	18.2100i	−1.10772	+	0.204607i	−0.703949	−	0.710251i	$-0.748582\pi$
$89$	−98.5875	+	18.2100i	−1.10772	+	0.204607i	−0.403776	+	0.914858i	$0.632302\pi$
$90$	55.0092	−	66.1004i	0.611213	−	0.734449i
$91$	12.8014	+	15.3825i	0.140675	+	0.169038i
$92$	−22.5363	+	122.010i	−0.244960	+	1.32619i
$93$	171.035	−	87.9351i	1.83908	−	0.945539i
$94$	−44.7832	−	27.3308i	−0.476417	−	0.290753i
$95$	50.1258			0.527640
$96$	−122.424	+	147.108i	−1.27525	+	1.53237i
$97$	9.56619	−	2.87804i	0.0986205	−	0.0296705i	−0.238407	−	0.971165i	$-0.576625\pi$
$97$	9.56619	−	2.87804i	0.0986205	−	0.0296705i	0.337027	+	0.941495i	$0.390579\pi$
$98$	6.16939	−	168.810i	0.0629529	−	1.72255i
$99$	88.9872	−	79.7329i	0.898861	−	0.805383i
$100$	−16.6170	+	63.5609i	−0.166170	+	0.635609i
$101$	40.5271	−	134.706i	0.401259	−	1.33373i	−0.486605	−	0.873622i	$-0.661765\pi$
$101$	40.5271	−	134.706i	0.401259	−	1.33373i	0.887864	−	0.460105i	$-0.152188\pi$
$102$	42.2771	+	287.268i	0.414481	+	2.81635i
$103$	184.249	+	34.0326i	1.78883	+	0.330413i	0.969904	−	0.243487i	$-0.0782914\pi$
$103$	184.249	+	34.0326i	1.78883	+	0.330413i	0.818925	+	0.573901i	$0.194570\pi$
$104$	−3.71667	+	2.65905i	−0.0357372	+	0.0255678i
$105$	144.376	+	15.8858i	1.37501	+	0.151294i
$106$	108.647	−	255.667i	1.02497	−	2.41196i
$107$	−37.5653	+	66.9341i	−0.351077	+	0.625553i	−0.989566	−	0.144078i	$-0.953978\pi$
$107$	−37.5653	+	66.9341i	−0.351077	+	0.625553i	0.638489	+	0.769631i	$0.279560\pi$
$108$	4.32972	−	6.05184i	0.0400900	−	0.0560355i
$109$	−158.481	+	88.9438i	−1.45395	+	0.815999i	−0.997285	−	0.0736381i	$-0.976539\pi$
$109$	−158.481	+	88.9438i	−1.45395	+	0.815999i	−0.456669	+	0.889637i	$0.650958\pi$
$110$	53.9547	−	126.966i	0.490497	−	1.15424i
$111$	−16.4301	+	111.641i	−0.148019	+	1.00577i
$112$	−124.840	−	13.7363i	−1.11464	−	0.122645i
$113$	−5.94463	+	19.7591i	−0.0526074	+	0.174859i	−0.979905	−	0.199466i	$-0.936079\pi$
$113$	−5.94463	+	19.7591i	−0.0526074	+	0.174859i	0.927297	+	0.374326i	$0.122126\pi$
$114$	−185.225	+	13.5567i	−1.62478	+	0.118919i
$115$	−28.0885	−	82.3342i	−0.244248	−	0.715949i
$116$	129.058			1.11257
$117$	12.8962	−	10.7323i	0.110224	−	0.0917294i
$118$	−26.8340	−	37.5070i	−0.227406	−	0.317856i
$119$	−178.796	+	160.202i	−1.50249	+	1.34624i
$120$	−6.02449	+	32.6160i	−0.0502041	+	0.271800i
$121$	36.8169	−	60.3268i	0.304272	−	0.498569i
$122$	144.848	+	10.6015i	1.18728	+	0.0868976i
$123$	−306.302	−	68.2317i	−2.49026	−	0.554729i
$124$	−121.123	+	183.078i	−0.976800	+	1.47643i
$125$	−32.8999	−	125.844i	−0.263200	−	1.00675i
$126$	−263.257	−	9.62111i	−2.08934	−	0.0763580i
$127$	168.617	−	18.5531i	1.32769	−	0.146088i	0.582441	−	0.812873i	$-0.302098\pi$
$127$	168.617	−	18.5531i	1.32769	−	0.146088i	0.745250	+	0.666786i	$0.232330\pi$
$128$	13.3948	−	72.5180i	0.104647	−	0.566547i
$129$	59.5143	+	36.3210i	0.461351	+	0.281558i
$130$	8.22246	−	17.5401i	0.0632497	−	0.134924i
$131$	13.9861	−	95.0338i	0.106764	−	0.725449i	−0.867070	−	0.498187i	$-0.833999\pi$
$131$	13.9861	−	95.0338i	0.106764	−	0.725449i	0.973834	−	0.227262i	$-0.0729774\pi$
$132$	−89.9573	+	263.686i	−0.681495	+	1.99762i
$133$	−93.8467	−	121.536i	−0.705614	−	0.913801i
$134$	96.6029	−	107.815i	0.720917	−	0.804591i
$135$	−0.570628	+	5.18605i	−0.00422687	+	0.0384152i
$136$	−33.5049	−	43.3903i	−0.246360	−	0.319046i
$137$	−12.9739	−	177.262i	−0.0946999	−	1.29388i	−0.806388	−	0.591386i	$-0.798581\pi$
$137$	−12.9739	−	177.262i	−0.0946999	−	1.29388i	0.711689	−	0.702495i	$-0.247931\pi$
$138$	126.060	+	296.645i	0.913482	+	2.14960i
$139$	−156.281	−	59.7722i	−1.12432	−	0.430016i	−0.276879	−	0.960905i	$-0.589300\pi$
$139$	−156.281	−	59.7722i	−1.12432	−	0.430016i	−0.847442	+	0.530889i	$0.821858\pi$
$140$	−152.586	+	64.8418i	−1.08990	+	0.463156i
$141$	−74.2406	+	2.71323i	−0.526529	+	0.0192427i
$142$	46.4876	+	28.3709i	0.327377	+	0.199795i
$143$	14.8509	−	22.4471i	0.103852	−	0.156973i
$144$	−11.5161	+	104.662i	−0.0799731	+	0.726821i
$145$	−78.9103	+	44.2866i	−0.544209	+	0.305425i
$146$	−274.800	+	30.2366i	−1.88219	+	0.207100i
$147$	−124.607	−	204.176i	−0.847666	−	1.38895i
$148$	−46.0128	−	120.305i	−0.310897	−	0.812873i
$149$	97.4385	+	45.6773i	0.653949	+	0.306559i	0.722789	−	0.691069i	$-0.242860\pi$
$149$	97.4385	+	45.6773i	0.653949	+	0.306559i	−0.0688396	+	0.997628i	$0.521930\pi$
$150$	55.1056	+	161.528i	0.367370	+	1.07685i
$151$	−221.177	−	16.1880i	−1.46475	−	0.107206i	−0.682824	−	0.730583i	$-0.739249\pi$
$151$	−221.177	−	16.1880i	−1.46475	−	0.107206i	−0.781921	+	0.623377i	$0.785760\pi$
$152$	29.2434	−	19.3473i	0.192391	−	0.127285i
$153$	134.309	+	149.898i	0.877836	+	0.979724i
$154$	−408.859	+	106.890i	−2.65493	+	0.694089i
$155$	11.2350	−	153.504i	0.0724841	−	0.990347i
$156$	−13.9758	+	36.5411i	−0.0895883	+	0.234238i
$157$	48.6906	−	114.579i	0.310131	−	0.729800i	−0.689852	−	0.723951i	$-0.742324\pi$
$157$	48.6906	−	114.579i	0.310131	−	0.729800i	0.999983	−	0.00584912i	$-0.00186184\pi$
$158$	−116.858	−	112.666i	−0.739611	−	0.713074i
$159$	−71.4488	−	386.817i	−0.449363	−	2.43281i
$160$	49.4555	+	144.966i	0.309097	+	0.906036i
$161$	−147.040	+	222.252i	−0.913294	+	1.38045i
$162$	9.11766	−	249.482i	0.0562819	−	1.54001i
$163$	−2.55356	+	0.976654i	−0.0156660	+	0.00599174i	−0.365051	−	0.930987i	$-0.618949\pi$
$163$	−2.55356	+	0.976654i	−0.0156660	+	0.00599174i	0.349385	+	0.936979i	$0.386390\pi$
$164$	343.009	−	103.196i	2.09152	−	0.629245i
$165$	−35.4819	−	192.096i	−0.215042	−	1.16422i
$166$	−2.29969	+	6.01276i	−0.0138535	+	0.0362215i
$167$	177.064	−	170.711i	1.06026	−	1.02222i	0.0605541	−	0.998165i	$-0.480713\pi$
$167$	177.064	−	170.711i	1.06026	−	1.02222i	0.999711	−	0.0240587i	$-0.00765886\pi$
$168$	90.3604	−	46.4575i	0.537860	−	0.276533i
$169$	−96.1351	+	134.372i	−0.568846	+	0.795102i
$170$	213.873	+	90.8860i	1.25807	+	0.534623i
$171$	−101.892	+	78.6785i	−0.595860	+	0.460108i
$172$	−79.5308	−	2.90657i	−0.462389	−	0.0168986i
$173$	104.513	+	171.251i	0.604120	+	0.989887i	0.997511	+	0.0705162i	$0.0224647\pi$
$173$	104.513	+	171.251i	0.604120	+	0.989887i	−0.393391	+	0.919371i	$0.628698\pi$
$174$	279.612	−	184.990i	1.60697	−	1.06316i
$175$	−86.2408	+	111.686i	−0.492805	+	0.638204i
$176$	30.6808	+	166.103i	0.174323	+	0.943767i
$177$	−60.9941	−	23.3283i	−0.344600	−	0.131798i
$178$	85.6467	−	284.678i	0.481162	−	1.59931i
$179$	−5.09048	−	2.85692i	−0.0284385	−	0.0159604i	0.475134	−	0.879914i	$-0.342400\pi$
$179$	−5.09048	−	2.85692i	−0.0284385	−	0.0159604i	−0.503572	+	0.863953i	$0.667981\pi$
$180$	54.3616	+	127.923i	0.302009	+	0.710686i
$181$	26.5921	−	119.376i	0.146918	−	0.659536i	−0.845223	−	0.534413i	$-0.820533\pi$
$181$	26.5921	−	119.376i	0.146918	−	0.659536i	0.992141	−	0.125123i	$-0.0399325\pi$
$182$	−57.9222	+	12.9027i	−0.318254	+	0.0708941i
$183$	179.341	−	100.651i	0.980008	−	0.550007i
$184$	−48.1657	−	37.1924i	−0.261770	−	0.202132i
$185$	69.4169	+	57.7692i	0.375226	+	0.312266i
$186$			570.267i			3.06595i
$187$	275.602	+	168.197i	1.47381	+	0.899450i
$188$	72.3831	−	44.1748i	0.385016	−	0.234972i
$189$	13.6425	−	8.32590i	0.0721826	−	0.0440524i
$190$	−67.9626	+	132.188i	−0.357698	+	0.695726i
$191$	121.959	−	157.942i	0.638527	−	0.826921i	−0.355657	−	0.934617i	$-0.615743\pi$
$191$	121.959	−	157.942i	0.638527	−	0.826921i	0.994184	+	0.107696i	$0.0343473\pi$
$192$	−141.812	−	333.712i	−0.738605	−	1.73808i
$193$	−141.125	+	36.8948i	−0.731216	+	0.191165i	−0.599786	−	0.800161i	$-0.704748\pi$
$193$	−141.125	+	36.8948i	−0.731216	+	0.191165i	−0.131430	+	0.991325i	$0.541957\pi$
$194$	−5.38048	+	29.1294i	−0.0277344	+	0.150152i
$195$	−3.99393	−	27.1383i	−0.0204817	−	0.139171i
$196$	238.095	+	133.625i	1.21477	+	0.681762i
$197$	−130.349	+	29.0366i	−0.661672	+	0.147394i	−0.535396	−	0.844601i	$-0.679837\pi$
$197$	−130.349	+	29.0366i	−0.661672	+	0.147394i	−0.126276	+	0.991995i	$0.540303\pi$
$198$	89.6133	+	342.776i	0.452592	+	1.73119i
$199$	15.9141	+	8.18199i	0.0799702	+	0.0411155i	0.496765	−	0.867885i	$-0.334521\pi$
$199$	15.9141	+	8.18199i	0.0799702	+	0.0411155i	−0.416795	+	0.909001i	$0.636847\pi$
$200$	−23.9983	−	21.5026i	−0.119992	−	0.107513i
$201$	29.8462	−	202.801i	0.148488	−	1.00896i
$202$	300.290	+	289.516i	1.48658	+	1.43325i
$203$	255.116	+	108.412i	1.25673	+	0.534051i
$204$	−444.176	−	151.532i	−2.17733	−	0.742803i
$205$	−174.315	+	180.802i	−0.850319	+	0.881962i
$206$	−339.561	+	439.746i	−1.64835	+	2.13469i
$207$	186.330	+	123.275i	0.900143	+	0.595529i
$208$	3.45350	+	23.4661i	0.0166034	+	0.112818i
$209$	−120.162	+	167.956i	−0.574939	+	0.803617i
$210$	−237.643	+	359.198i	−1.13164	+	1.71047i
$211$	−14.9294	+	12.4243i	−0.0707555	+	0.0588832i	−0.674373	−	0.738391i	$-0.735586\pi$
$211$	−14.9294	+	12.4243i	−0.0707555	+	0.0588832i	0.603617	+	0.797274i	$0.293725\pi$
$212$	287.213	+	345.122i	1.35478	+	1.62794i
$213$	77.0660	−	2.81649i	0.361812	−	0.0132229i
$214$	−125.581	−	189.816i	−0.586829	−	0.886992i
$215$	49.6252	−	25.5141i	0.230815	−	0.118670i
$216$	1.66878	+	3.24580i	0.00772583	+	0.0150268i
$217$	−393.222	+	260.153i	−1.81208	+	1.19886i
$218$	−19.6813	−	538.528i	−0.0902811	−	2.47031i
$219$	−300.901	+	250.412i	−1.37398	+	1.14343i
$220$	142.632	+	171.390i	0.648326	+	0.779045i
$221$	37.8118	+	25.0161i	0.171094	+	0.113195i
$222$	−272.134	−	194.695i	−1.22583	−	0.877004i
$223$	331.190	−	48.7411i	1.48516	−	0.218570i	0.646368	−	0.763026i	$-0.276287\pi$
$223$	331.190	−	48.7411i	1.48516	−	0.218570i	0.838790	+	0.544456i	$0.183264\pi$
$224$	258.894	−	391.319i	1.15578	−	1.74696i
$225$	93.6341	+	72.3019i	0.416152	+	0.321342i
$226$	−44.0473	−	42.4670i	−0.194900	−	0.187907i
$227$	122.561	−	359.255i	0.539916	−	1.58262i	−0.249248	−	0.968440i	$-0.580183\pi$
$227$	122.561	−	359.255i	0.539916	−	1.58262i	0.789164	−	0.614183i	$-0.210514\pi$
$228$	117.402	−	276.270i	0.514920	−	1.21171i
$229$	33.5380	−	34.7861i	0.146454	−	0.151904i	−0.642659	−	0.766153i	$-0.722169\pi$
$229$	33.5380	−	34.7861i	0.146454	−	0.151904i	0.789113	+	0.614248i	$0.210541\pi$
$230$	255.209	+	37.5590i	1.10961	+	0.163300i
$231$	−399.328	+	445.677i	−1.72869	+	1.92934i
$232$	−28.9428	+	56.2942i	−0.124754	+	0.242647i
$233$	−101.554	+	26.5496i	−0.435852	+	0.113947i	−0.464359	−	0.885647i	$-0.653715\pi$
$233$	−101.554	+	26.5496i	−0.435852	+	0.113947i	0.0285072	+	0.999594i	$0.490925\pi$
$234$	10.8173	+	48.5604i	0.0462277	+	0.207523i
$235$	−29.0988	+	51.8484i	−0.123824	+	0.220632i
$236$	73.7456	−	10.8531i	0.312481	−	0.0459877i
$237$	−226.031	−	41.7500i	−0.953717	−	0.176160i
$238$	−180.054	−	688.717i	−0.756530	−	2.89377i
$239$	−80.0053	+	33.9986i	−0.334750	+	0.142253i	−0.551958	−	0.833872i	$-0.686119\pi$
$239$	−80.0053	+	33.9986i	−0.334750	+	0.142253i	0.217208	+	0.976125i	$0.430305\pi$
$240$	136.255	+	105.212i	0.567727	+	0.438385i
$241$	23.2187	+	11.9376i	0.0963433	+	0.0495335i	0.504743	−	0.863270i	$-0.331587\pi$
$241$	23.2187	+	11.9376i	0.0963433	+	0.0495335i	−0.408399	+	0.912803i	$0.633913\pi$
$242$	109.172	+	178.884i	0.451122	+	0.739192i
$243$	−176.876	−	289.822i	−0.727884	−	1.19268i
$244$	−122.288	+	200.376i	−0.501179	+	0.821213i
$245$	−191.433			−0.781360
$246$	595.232	−	715.246i	2.41964	−	2.90750i
$247$	−17.7234	+	22.9526i	−0.0717547	+	0.0929254i
$248$	−52.6940	−	93.8907i	−0.212476	−	0.378591i
$249$	1.98201	+	8.89754i	0.00795989	+	0.0357331i
$250$	376.474	+	83.8631i	1.50590	+	0.335453i
$251$	−63.5551	+	27.0080i	−0.253208	+	0.107602i	−0.513990	−	0.857796i	$-0.671833\pi$
$251$	−63.5551	+	27.0080i	−0.253208	+	0.107602i	0.260783	+	0.965397i	$0.416019\pi$
$252$	208.388	−	371.307i	0.826936	−	1.47344i
$253$	343.211	+	103.257i	1.35656	+	0.408129i
$254$	−179.690	+	469.819i	−0.707443	+	1.84968i
$255$	323.583	−	59.7688i	1.26895	−	0.234387i
$256$	−100.323	−	77.4671i	−0.391888	−	0.302606i
$257$	−234.551	−	354.525i	−0.912651	−	1.37947i	−0.925170	−	0.379552i	$-0.876078\pi$
$257$	−234.551	−	354.525i	−0.912651	−	1.37947i	0.0125195	−	0.999922i	$-0.496015\pi$
$258$	−176.475	+	107.701i	−0.684012	+	0.417446i
$259$	10.1038	−	276.466i	0.0390110	−	1.06744i
$260$	19.1362	+	24.7822i	0.0736007	+	0.0953160i
$261$	90.8899	−	213.882i	0.348237	−	0.819470i
$262$	231.653	+	165.734i	0.884173	+	0.632572i
$263$	208.577	+	405.685i	0.793069	+	1.54253i	0.839344	+	0.543601i	$0.182940\pi$
$263$	208.577	+	405.685i	0.793069	+	1.54253i	−0.0462744	+	0.998929i	$0.514735\pi$
$264$	−94.8443	−	98.3738i	−0.359259	−	0.372628i
$265$	−294.041	−	112.461i	−1.10959	−	0.424382i
$266$	447.746	−	82.7029i	1.68326	−	0.310913i
$267$	−121.277	−	403.107i	−0.454220	−	1.50976i
$268$	83.5849	+	218.541i	0.311884	+	0.815452i
$269$	−151.373	−	5.53216i	−0.562727	−	0.0205656i	−0.246319	−	0.969189i	$-0.579221\pi$
$269$	−151.373	−	5.53216i	−0.562727	−	0.0205656i	−0.316408	+	0.948623i	$0.602477\pi$
$270$	−12.9026	−	8.53628i	−0.0477874	−	0.0316158i
$271$	−412.493	+	140.723i	−1.52211	+	0.519273i	−0.952996	−	0.302984i	$-0.902017\pi$
$271$	−412.493	+	140.723i	−1.52211	+	0.519273i	−0.569117	+	0.822256i	$0.692715\pi$
$272$	−279.798	+	51.6813i	−1.02867	+	0.190005i
$273$	−58.3223	+	60.4927i	−0.213635	+	0.221585i
$274$	485.052	+	206.125i	1.77026	+	0.752281i
$275$	177.255	+	67.7943i	0.644564	+	0.246525i
$276$	−519.574	−	38.0279i	−1.88252	−	0.137782i
$277$	46.9729	+	179.674i	0.169577	+	0.648642i	0.996293	+	0.0860224i	$0.0274157\pi$
$277$	46.9729	+	179.674i	0.169577	+	0.648642i	−0.826716	+	0.562619i	$0.809794\pi$
$278$	369.519	−	331.090i	1.32920	−	1.19097i
$279$	218.105	+	329.666i	0.781738	+	1.18160i
$280$	5.93564	−	81.0985i	0.0211987	−	0.289637i
$281$	377.452	−	128.769i	1.34325	−	0.458252i	0.444130	−	0.895962i	$-0.353513\pi$
$281$	377.452	−	128.769i	1.34325	−	0.458252i	0.899116	+	0.437711i	$0.144211\pi$
$282$	93.5033	−	199.461i	0.331572	−	0.707307i
$283$	288.842	−	110.473i	1.02064	−	0.390363i	0.211126	−	0.977459i	$-0.432287\pi$
$283$	288.842	−	110.473i	1.02064	−	0.390363i	0.809518	+	0.587096i	$0.199729\pi$
$284$	−75.1378	+	45.8560i	−0.264570	+	0.161465i
$285$	23.0194	+	209.207i	0.0807697	+	0.734061i
$286$	39.0605	+	69.5983i	0.136575	+	0.243351i
$287$	764.733	+	84.1446i	2.66457	+	0.293187i
$288$	−328.071	−	217.050i	−1.13913	−	0.753644i
$289$	−132.774	+	217.559i	−0.459426	+	0.752798i
$290$	−9.79962	−	268.142i	−0.0337918	−	0.924627i
$291$	16.4050	+	38.6042i	0.0563746	+	0.132661i
$292$	159.625	−	417.356i	0.546661	−	1.42930i
$293$	265.454	−	112.806i	0.905985	−	0.385002i	0.112543	−	0.993647i	$-0.464101\pi$
$293$	265.454	−	112.806i	0.905985	−	0.385002i	0.793443	+	0.608645i	$0.208287\pi$
$294$	707.385	−	51.7739i	2.40607	−	0.176102i
$295$	−41.3663	+	31.9420i	−0.140225	+	0.108278i
$296$	62.7953	+	6.90945i	0.212146	+	0.0233427i
$297$	−16.0089	−	14.3441i	−0.0539022	−	0.0482966i
$298$	−252.568	+	195.026i	−0.847543	+	0.654451i
$299$	47.6323	+	16.2499i	0.159305	+	0.0543474i
$300$	−272.912	−	40.1643i	−0.909707	−	0.133881i
$301$	−154.771	−	72.5538i	−0.514191	−	0.241043i
$302$	342.570	−	561.322i	1.13434	−	1.85868i
$303$	580.829	+	107.285i	1.91693	+	0.354074i
$304$	−19.9045	−	180.899i	−0.0654755	−	0.595062i
$305$	6.01115	−	164.480i	0.0197087	−	0.539279i
$306$	−577.401	+	150.952i	−1.88693	+	0.493308i
$307$	−241.016	−	159.455i	−0.785068	−	0.519396i	0.0942975	−	0.995544i	$-0.469940\pi$
$307$	−241.016	−	159.455i	−0.785068	−	0.519396i	−0.879365	+	0.476148i	$0.842033\pi$
$308$	148.515	−	666.707i	0.482193	−	2.16463i
$309$	−57.4269	+	784.621i	−0.185847	+	2.53923i
$310$	389.576	+	237.755i	1.25670	+	0.766951i
$311$	46.5265	+	8.59389i	0.149603	+	0.0276331i	0.255912	−	0.966700i	$-0.417624\pi$
$311$	46.5265	+	8.59389i	0.149603	+	0.0276331i	−0.106309	+	0.994333i	$0.533903\pi$
$312$	−12.8047	−	14.2909i	−0.0410408	−	0.0458043i
$313$	−420.531	+	300.864i	−1.34355	+	0.961228i	−0.343796	+	0.939044i	$0.611713\pi$
$313$	−420.531	+	300.864i	−1.34355	+	0.961228i	−0.999754	+	0.0221837i	$0.992938\pi$
$314$	236.142	+	283.754i	0.752043	+	0.903674i
$315$			298.539i			0.947742i
$316$	248.314	−	84.7129i	0.785803	−	0.268079i
$317$	−4.72067	−	64.4984i	−0.0148917	−	0.203465i	−0.999576	−	0.0291179i	$-0.990730\pi$
$317$	−4.72067	−	64.4984i	−0.0148917	−	0.203465i	0.984684	−	0.174347i	$-0.0557814\pi$
$318$	1116.96	+	336.043i	3.51245	+	1.05674i
$319$	40.7741	−	370.568i	0.127819	−	1.16166i
$320$	−287.099	−	42.2522i	−0.897183	−	0.132038i
$321$	−296.611	−	126.046i	−0.924021	−	0.392666i
$322$	−386.743	−	689.102i	−1.20106	−	2.14007i
$323$	−282.920	−	202.412i	−0.875912	−	0.626661i
$324$	351.878	+	197.483i	1.08604	+	0.609517i
$325$	24.5260	+	10.4224i	0.0754648	+	0.0320690i
$326$	0.886660	−	8.05825i	0.00271981	−	0.0247186i
$327$	−444.000	−	620.598i	−1.35780	−	1.89785i
$328$	−31.9107	+	172.761i	−0.0972886	+	0.526712i
$329$	180.192	−	26.5187i	0.547695	−	0.0806041i
$330$	554.689	+	166.881i	1.68088	+	0.505700i
$331$	473.448	+	123.776i	1.43036	+	0.373944i	0.885521	−	0.464598i	$-0.153801\pi$
$331$	473.448	+	123.776i	1.43036	+	0.373944i	0.544836	+	0.838543i	$0.316592\pi$
$332$	−6.94344	−	7.74935i	−0.0209140	−	0.0233414i
$333$	−231.781	−	8.47077i	−0.696040	−	0.0254378i
$334$	210.117	+	698.398i	0.629092	+	2.09101i
$335$	−126.100	−	104.941i	−0.376417	−	0.313257i
$336$		−	527.346i		−	1.56948i
$337$	−135.021	+	221.240i	−0.400655	+	0.656498i	−0.988283	−	0.152633i	$-0.951225\pi$
$337$	−135.021	+	221.240i	−0.400655	+	0.656498i	0.587628	+	0.809131i	$0.300062\pi$
$338$	−224.013	−	435.708i	−0.662760	−	1.28908i
$339$	−85.1976	−	15.7368i	−0.251320	−	0.0464212i
$340$	−288.704	+	240.261i	−0.849129	+	0.706651i
$341$	487.411	+	405.627i	1.42936	+	1.18952i
$342$	−69.3358	−	375.378i	−0.202736	−	1.09760i
$343$	50.1253	+	64.9144i	0.146138	+	0.189255i
$344$	19.1036	−	34.0390i	0.0555338	−	0.0989506i
$345$	330.735	−	155.042i	0.958651	−	0.449397i
$346$	−593.312	+	43.4248i	−1.71477	+	0.125505i
$347$	−263.885	+	368.843i	−0.760474	+	1.06295i	0.235373	+	0.971905i	$0.424369\pi$
$347$	−263.885	+	368.843i	−0.760474	+	1.06295i	−0.995847	+	0.0910430i	$0.970980\pi$
$348$	59.2674	+	538.642i	0.170309	+	1.54782i
$349$	−357.167	+	344.352i	−1.02340	+	0.986682i	−0.999915	−	0.0130417i	$-0.995849\pi$
$349$	−357.167	+	344.352i	−1.02340	+	0.986682i	−0.0234859	+	0.999724i	$0.507476\pi$
$350$	−177.600	−	378.856i	−0.507430	−	1.08245i
$351$	−2.17293	−	2.09497i	−0.00619068	−	0.00596857i
$352$	−604.291	−	181.804i	−1.71674	−	0.516489i
$353$	16.3190	+	148.312i	0.0462294	+	0.420147i	0.994663	+	0.103173i	$0.0328995\pi$
$353$	16.3190	+	148.312i	0.0462294	+	0.420147i	−0.948434	+	0.316974i	$0.897333\pi$
$354$	144.218	−	129.220i	0.407395	−	0.365028i
$355$	30.2062	−	53.8217i	0.0850879	−	0.151610i
$356$	345.912	+	333.501i	0.971662	+	0.936800i
$357$	−750.736	−	672.663i	−2.10290	−	1.88421i
$358$	14.4359	−	9.55073i	0.0403239	−	0.0266780i
$359$	−1.75742	−	4.59496i	−0.00489533	−	0.0127993i	0.931547	−	0.363622i	$-0.118460\pi$
$359$	−1.75742	−	4.59496i	−0.00489533	−	0.0127993i	−0.936442	+	0.350823i	$0.885902\pi$
$360$	−67.9907	−	4.97628i	−0.188863	−	0.0138230i
$361$	−88.5923	+	106.455i	−0.245408	+	0.294889i
$362$	278.755	+	231.982i	0.770042	+	0.640834i
$363$	268.690	+	125.957i	0.740194	+	0.346989i
$364$	24.2599	−	92.7956i	0.0666482	−	0.254933i
$365$	45.6168	+	309.961i	0.124978	+	0.849208i
$366$	22.2719	+	609.413i	0.0608521	+	1.66506i
$367$	18.7261	+	62.2429i	0.0510248	+	0.169599i	0.979351	−	0.202168i	$-0.0647986\pi$
$367$	18.7261	+	62.2429i	0.0510248	+	0.169599i	−0.928326	+	0.371767i	$0.878752\pi$
$368$	−285.982	+	134.063i	−0.777125	+	0.364301i
$369$	70.5444	−	641.131i	0.191177	−	1.73748i
$370$	−246.463	+	104.735i	−0.666116	+	0.283069i
$371$	277.837	+	923.490i	0.748886	+	2.48919i
$372$	−819.726	−	421.450i	−2.20356	−	1.13293i
$373$	−517.679	+	266.157i	−1.38788	+	0.713558i	−0.979910	−	0.199438i	$-0.936088\pi$
$373$	−517.679	+	266.157i	−1.38788	+	0.713558i	−0.407969	+	0.912996i	$0.633763\pi$
$374$	−817.229	+	498.748i	−2.18510	+	1.33355i
$375$	510.120	−	195.104i	1.36032	−	0.520278i
$376$	3.03593	+	41.4798i	0.00807428	+	0.110319i
$377$	7.62217	−	51.7918i	0.0202180	−	0.137379i
$378$	3.45940	+	47.2656i	0.00915185	+	0.125041i
$379$	203.970	−	396.725i	0.538180	−	1.04677i	−0.449936	−	0.893061i	$-0.648553\pi$
$379$	203.970	−	396.725i	0.538180	−	1.04677i	0.988116	−	0.153707i	$-0.0491212\pi$
$380$	−139.786	−	195.385i	−0.367857	−	0.514170i
$381$	154.868	+	695.227i	0.406479	+	1.82474i
$382$	251.156	+	535.765i	0.657477	+	1.40253i
$383$	−32.9258	+	147.809i	−0.0859682	+	0.385924i	−0.999796	−	0.0201771i	$-0.993577\pi$
$383$	−32.9258	+	147.809i	−0.0859682	+	0.385924i	0.913828	+	0.406101i	$0.133112\pi$
$384$	308.816	+	22.6024i	0.804208	+	0.0588604i
$385$	137.975	+	458.611i	0.358378	+	1.19120i
$386$	94.0462	−	422.187i	0.243643	−	1.09375i
$387$	−60.8271	+	129.756i	−0.157176	+	0.335287i
$388$	−37.8955	−	29.2620i	−0.0976688	−	0.0754174i
$389$	11.5881	+	1.70541i	0.0297894	+	0.00438408i	0.160479	−	0.987039i	$-0.448696\pi$
$389$	11.5881	+	1.70541i	0.0297894	+	0.00438408i	−0.130690	+	0.991423i	$0.541719\pi$
$390$	76.9822	+	26.2627i	0.197390	+	0.0673402i
$391$	−173.934	+	578.134i	−0.444845	+	1.47860i
$392$	−111.682	+	73.8883i	−0.284904	+	0.188491i
$393$	403.061	+	14.7304i	1.02560	+	0.0374820i
$394$	100.160	−	383.117i	0.254213	−	0.972378i
$395$	−122.758	+	137.006i	−0.310780	+	0.346851i
$396$	−558.949	−	124.511i	−1.41149	−	0.314422i
$397$	12.5580	+	343.618i	0.0316322	+	0.865536i	0.916581	+	0.399848i	$0.130937\pi$
$397$	12.5580	+	343.618i	0.0316322	+	0.865536i	−0.884949	+	0.465688i	$0.845807\pi$
$398$	−43.1539	+	30.8740i	−0.108427	+	0.0775728i
$399$	464.149	−	447.496i	1.16328	−	1.12154i
$400$	−156.206	+	59.7437i	−0.390515	+	0.149359i
$401$	256.275	−	247.081i	0.639091	−	0.616161i	−0.302408	−	0.953179i	$-0.597790\pi$
$401$	256.275	−	247.081i	0.639091	−	0.616161i	0.941498	+	0.337018i	$0.109418\pi$
$402$	494.346	+	353.674i	1.22972	+	0.879787i
$403$	66.3169	+	59.4202i	0.164558	+	0.147445i
$404$	−638.089	+	217.686i	−1.57943	+	0.538826i
$405$	−282.917			−0.698560
$406$	−631.793	+	525.782i	−1.55614	+	1.29503i
$407$	−359.974	+	94.1095i	−0.884457	+	0.231227i
$408$	165.709	−	159.764i	0.406150	−	0.391578i
$409$	−297.214	+	10.8621i	−0.726686	+	0.0265577i	−0.397365	−	0.917661i	$-0.630075\pi$
$409$	−297.214	+	10.8621i	−0.726686	+	0.0265577i	−0.329320	+	0.944218i	$0.606820\pi$
$410$	−240.455	−	704.831i	−0.586475	−	1.71910i
$411$	733.870	−	135.553i	1.78557	−	0.329812i
$412$	−381.161	−	813.090i	−0.925148	−	1.97352i
$413$	154.894	+	40.4946i	0.375046	+	0.0980498i
$414$	−577.724	+	324.234i	−1.39547	+	0.783175i
$415$	6.90467	+	2.35555i	0.0166378	+	0.00567601i
$416$	−83.8662	−	28.6112i	−0.201601	−	0.0687768i
$417$	177.699	−	679.709i	0.426137	−	1.63000i
$418$	−280.001	−	544.605i	−0.669858	−	1.30288i
$419$	−212.017	−	236.625i	−0.506007	−	0.564737i	0.436165	−	0.899867i	$-0.356336\pi$
$419$	−212.017	−	236.625i	−0.506007	−	0.564737i	−0.942172	+	0.335129i	$0.891220\pi$
$420$	−340.699	−	607.061i	−0.811189	−	1.44538i
$421$	−127.376	−	164.957i	−0.302555	−	0.391822i	0.615590	−	0.788067i	$-0.288918\pi$
$421$	−127.376	−	164.957i	−0.302555	−	0.391822i	−0.918145	+	0.396245i	$0.870313\pi$
$422$	−12.5227	−	56.2162i	−0.0296746	−	0.133214i
$423$	−22.2326	−	151.068i	−0.0525592	−	0.357134i
$424$	−214.951	+	47.8824i	−0.506961	+	0.112930i
$425$	−114.199	+	298.584i	−0.268703	+	0.702550i
$426$	−97.0618	+	207.052i	−0.227845	+	0.486037i
$427$	−410.055	+	293.369i	−0.960315	+	0.687047i
$428$	365.660	−	40.2340i	0.854346	−	0.0940048i
$429$	100.506	+	51.6738i	0.234280	+	0.120452i
$430$			165.461i			0.384793i
$431$	−95.9461	+	420.185i	−0.222613	+	0.974907i
$431$	−95.9461	+	420.185i	−0.222613	+	0.974907i
$432$	18.9425			0.0438485
$433$	−19.3865	+	37.7070i	−0.0447726	+	0.0870832i	−0.910662	−	0.413152i	$-0.864428\pi$
$433$	−19.3865	+	37.7070i	−0.0447726	+	0.0870832i	0.865889	+	0.500236i	$0.166753\pi$
$434$	−152.911	−	1389.70i	−0.352329	−	3.20208i
$435$	−221.075	−	309.006i	−0.508218	−	0.710358i
$436$	788.649	+	369.704i	1.80883	+	0.847944i
$437$	−360.676	−	137.947i	−0.825346	−	0.315668i
$438$	−252.394	−	1133.03i	−0.576242	−	2.58683i
$439$	687.554	−	101.187i	1.56618	−	0.230494i	0.694109	−	0.719870i	$-0.255798\pi$
$439$	687.554	−	101.187i	1.56618	−	0.230494i	0.872073	+	0.489375i	$0.162775\pi$
$440$	−106.746	+	23.7787i	−0.242605	+	0.0540425i
$441$	389.132	−	300.478i	0.882384	−	0.681355i
$442$	−117.237	+	65.7968i	−0.265243	+	0.148862i
$443$	167.925	−	150.462i	0.379064	−	0.339643i	−0.455817	−	0.890074i	$-0.650653\pi$
$443$	167.925	−	150.462i	0.379064	−	0.339643i	0.834881	+	0.550431i	$0.185537\pi$
$444$	480.981	−	247.289i	1.08329	−	0.556958i
$445$	−325.944	−	85.2129i	−0.732458	−	0.191490i
$446$	−320.505	+	939.476i	−0.718620	+	2.10645i
$447$	−145.894	+	427.650i	−0.326385	+	0.956712i
$448$	435.068	+	775.208i	0.971134	+	1.73038i
$449$	−57.6525	+	220.524i	−0.128402	+	0.491145i	0.871597	+	0.490222i	$0.163084\pi$
$449$	−57.6525	+	220.524i	−0.128402	+	0.491145i	−1.00000		0.000922617i	$0.999706\pi$
$450$	−317.622	+	148.895i	−0.705827	+	0.330878i
$451$	−187.942	−	1017.50i	−0.416722	−	2.25609i
$452$	93.5967	−	31.9307i	0.207072	−	0.0706432i
$453$	−34.0082	−	930.547i	−0.0750732	−	2.05419i
$454$	781.229	+	810.302i	1.72077	+	1.78481i
$455$	17.0098	+	65.0632i	0.0373841	+	0.142996i
$456$	94.1782	+	113.167i	0.206531	+	0.248173i
$457$		−	116.791i		−	0.255560i	−0.991803	−	0.127780i	$-0.959215\pi$
$457$		−	116.791i		−	0.255560i	0.991803	−	0.127780i	$-0.0407852\pi$
$458$	46.2631	+	135.608i	0.101011	+	0.296088i
$459$	24.1624	−	26.9669i	0.0526414	−	0.0587513i
$460$	−242.599	+	339.091i	−0.527389	+	0.737155i
$461$	−86.2415	−	89.4509i	−0.187075	−	0.194037i	0.619799	−	0.784761i	$-0.287214\pi$
$461$	−86.2415	−	89.4509i	−0.187075	−	0.194037i	−0.806874	+	0.590724i	$0.798842\pi$
$462$	−633.881	−	1657.35i	−1.37204	−	3.58733i
$463$	185.619	+	192.526i	0.400905	+	0.415824i	0.889679	−	0.456586i	$-0.150928\pi$
$463$	185.619	+	192.526i	0.400905	+	0.415824i	−0.488775	+	0.872410i	$0.662556\pi$
$464$	191.161	+	267.194i	0.411984	+	0.575848i
$465$	645.830	−	23.6028i	1.38888	−	0.0507587i
$466$	67.6758	−	303.807i	0.145227	−	0.651945i
$467$	−472.462	−	423.328i	−1.01170	−	0.906484i	−0.0160667	−	0.999871i	$-0.505114\pi$
$467$	−472.462	−	423.328i	−1.01170	−	0.906484i	−0.995630	+	0.0933868i	$0.970231\pi$
$468$	−77.7972	−	20.3389i	−0.166233	−	0.0434591i
$469$	−18.3542	+	502.216i	−0.0391347	+	1.07082i
$470$	−97.2777	−	147.035i	−0.206974	−	0.312841i
$471$	500.571	+	150.599i	1.06278	+	0.319744i
$472$	−11.8043	+	34.6013i	−0.0250092	+	0.0733078i
$473$	−33.4725	+	227.442i	−0.0707663	+	0.480849i
$474$	416.562	−	539.466i	0.878823	−	1.13811i
$475$	−185.138	−	86.7890i	−0.389764	−	0.182714i
$476$	1123.06	+	250.172i	2.35937	+	0.525572i
$477$	774.228	−	232.930i	1.62312	−	0.488324i
$478$	18.8159	−	257.081i	0.0393638	−	0.537826i
$479$	−326.286	−	72.6832i	−0.681181	−	0.151740i	−0.136827	−	0.990595i	$-0.543690\pi$
$479$	−326.286	−	72.6832i	−0.681181	−	0.151740i	−0.544354	+	0.838855i	$0.683225\pi$
$480$	−582.325	+	272.983i	−1.21318	+	0.568714i
$481$	−50.9968	+	11.3600i	−0.106022	+	0.0236175i
$482$	−62.9618	+	45.0453i	−0.130626	+	0.0934550i
$483$	−995.126	−	511.630i	−2.06030	−	1.05927i
$484$	−337.819	+	24.7251i	−0.697972	+	0.0510850i
$485$	33.2119	+	4.88778i	0.0684782	+	0.0100779i
$486$	1004.11	−	73.4916i	2.06608	−	0.151217i
$487$	−233.238	−	609.824i	−0.478928	−	1.25220i	−0.932560	−	0.361016i	$-0.882430\pi$
$487$	−233.238	−	609.824i	−0.478928	−	1.25220i	0.453632	−	0.891189i	$-0.350128\pi$
$488$	−59.9782	−	98.2780i	−0.122906	−	0.201389i
$489$	−5.24889	−	10.2092i	−0.0107339	−	0.0208776i
$490$	259.553	−	504.834i	0.529700	−	1.03027i
$491$	−694.018	+	208.799i	−1.41348	+	0.425252i	−0.901139	−	0.433531i	$-0.857267\pi$
$491$	−694.018	+	208.799i	−1.41348	+	0.425252i	−0.512339	+	0.858783i	$0.671221\pi$
$492$	588.225	+	1384.21i	1.19558	+	2.81343i
$493$	624.217	+	68.6835i	1.26616	+	0.139317i
$494$	−36.4987	−	77.8589i	−0.0738841	−	0.157609i
$495$	384.486	−	115.675i	0.776740	−	0.233686i
$496$	−558.441	+	20.4090i	−1.12589	+	0.0411472i
$497$	−187.049	+	27.5280i	−0.376357	+	0.0553883i
$498$	−26.1512	−	6.83683i	−0.0525125	−	0.0137286i
$499$	85.4030	−	182.181i	0.171148	−	0.365092i	−0.801282	−	0.598287i	$-0.795848\pi$
$499$	85.4030	−	182.181i	0.171148	−	0.365092i	0.972430	+	0.233195i	$0.0749180\pi$
$500$	−398.778	+	479.182i	−0.797556	+	0.958363i
$501$	793.803	+	660.608i	1.58444	+	1.31858i
$502$	14.9471	−	204.221i	0.0297751	−	0.406816i
$503$	−718.418	+	274.772i	−1.42827	+	0.546266i	−0.944377	−	0.328864i	$-0.893334\pi$
$503$	−718.418	+	274.772i	−1.42827	+	0.546266i	−0.483889	+	0.875129i	$0.660776\pi$
$504$	115.228	+	174.168i	0.228628	+	0.345571i
$505$	315.449	−	352.063i	0.624652	−	0.697154i
$506$	−737.640	+	765.090i	−1.45779	+	1.51204i
$507$	−604.971	−	339.526i	−1.19324	−	0.669676i
$508$	−542.539	−	605.510i	−1.06799	−	1.19195i
$509$	−113.903	+	12.5328i	−0.223777	+	0.0246225i	−0.220565	−	0.975372i	$-0.570790\pi$
$509$	−113.903	+	12.5328i	−0.223777	+	0.0246225i	−0.00321244	+	0.999995i	$0.501023\pi$
$510$	−281.109	+	934.366i	−0.551194	+	1.83209i
$511$	666.131	−	690.920i	1.30358	−	1.35209i
$512$	607.401	−	284.738i	1.18633	−	0.556129i
$513$	16.0743	+	16.6725i	0.0313339	+	0.0325000i
$514$	1252.94	−	137.863i	2.43763	−	0.268215i
$515$	512.069	+	366.354i	0.994309	+	0.711367i
$516$	−24.3921	−	333.268i	−0.0472715	−	0.645869i
$517$	−103.972	−	221.793i	−0.201107	−	0.429000i
$518$	715.377	+	401.489i	1.38104	+	0.775075i
$519$	−666.744	+	514.843i	−1.28467	+	0.991990i
$520$	−15.1014	+	2.78936i	−0.0290411	+	0.00536416i
$521$	−400.825	+	481.641i	−0.769338	+	0.924456i	−0.998806	−	0.0488607i	$-0.984441\pi$
$521$	−400.825	+	481.641i	−0.769338	+	0.924456i	0.229468	+	0.973316i	$0.426301\pi$
$522$	440.801	+	529.678i	0.844447	+	1.01471i
$523$	10.8141	−	58.5465i	0.0206770	−	0.111944i	−0.971433	−	0.237314i	$-0.923733\pi$
$523$	10.8141	−	58.5465i	0.0206770	−	0.111944i	0.992110	+	0.125371i	$0.0400120\pi$
$524$	−409.434	+	210.505i	−0.781363	+	0.401726i
$525$	−505.741	−	308.649i	−0.963316	−	0.587903i
$526$	−1352.64			−2.57156
$527$	−683.272	+	821.037i	−1.29653	+	1.55795i
$528$	−679.166	+	204.331i	−1.28630	+	0.386990i
$529$	−5.15605	+	141.082i	−0.00974679	+	0.266696i
$530$	695.248	−	622.945i	1.31179	−	1.17537i
$531$	33.9495	−	129.859i	0.0639350	−	0.244555i
$532$	−212.022	+	704.730i	−0.398537	+	1.32468i
$533$	−21.1551	−	143.747i	−0.0396907	−	0.269694i
$534$	1227.48	+	226.726i	2.29864	+	0.424581i
$535$	−209.770	+	150.078i	−0.392094	+	0.280519i
$536$	−114.071	−	12.5514i	−0.212819	−	0.0234168i
$537$	9.58606	−	22.5579i	0.0178511	−	0.0420072i
$538$	219.827	−	391.690i	0.408601	−	0.728049i
$539$	458.907	−	641.434i	0.851404	−	1.19004i
$540$	21.8060	−	12.2381i	0.0403814	−	0.0226632i
$541$	18.5000	−	43.5341i	0.0341959	−	0.0804696i	−0.902368	−	0.430966i	$-0.858173\pi$
$541$	18.5000	−	43.5341i	0.0341959	−	0.0804696i	0.936564	+	0.350496i	$0.113987\pi$
$542$	188.170	−	1278.59i	0.347177	−	2.35903i
$543$	510.446	+	56.1650i	0.940047	+	0.103435i
$544$	306.247	−	1017.92i	0.562953	−	1.87118i
$545$	−609.072	+	44.5783i	−1.11756	+	0.0817950i
$546$	−80.4512	−	235.822i	−0.147346	−	0.431908i
$547$	−359.695			−0.657578			−0.328789	−	0.944403i	$-0.606641\pi$
$547$	−359.695			−0.657578			−0.328789	+	0.944403i	$0.606641\pi$
$548$	−654.766	+	544.901i	−1.19483	+	0.994344i
$549$	245.952	+	343.778i	0.448000	+	0.626190i
$550$	−419.112	+	375.526i	−0.762021	+	0.682774i
$551$	−72.9579	+	394.988i	−0.132410	+	0.716856i
$552$	133.109	−	218.107i	0.241139	−	0.395121i
$553$	562.017	+	41.1343i	1.01631	+	0.0743840i
$554$	−537.510	−	119.736i	−0.970235	−	0.216129i
$555$	−209.230	+	316.251i	−0.376991	+	0.569822i
$556$	202.834	+	775.851i	0.364809	+	1.39542i
$557$	776.113	+	28.3641i	1.39338	+	0.0509231i	0.722874	−	0.690980i	$-0.242821\pi$
$557$	776.113	+	28.3641i	1.39338	+	0.0509231i	0.670507	+	0.741903i	$0.266077\pi$
$558$	−1165.09	+	128.196i	−2.08797	+	0.229742i
$559$	−5.86353	+	31.7446i	−0.0104893	+	0.0567882i
$560$	−360.255	−	219.860i	−0.643312	−	0.392608i
$561$	−575.431	+	1227.51i	−1.02572	+	2.18807i
$562$	−172.185	+	1169.98i	−0.306379	+	2.08181i
$563$	317.942	−	931.963i	0.564728	−	1.65535i	−0.176657	−	0.984272i	$-0.556528\pi$
$563$	317.942	−	931.963i	0.564728	−	1.65535i	0.741385	−	0.671080i	$-0.234169\pi$
$564$	217.611	+	281.815i	0.385834	+	0.499672i
$565$	−46.2710	+	51.6415i	−0.0818956	+	0.0914009i
$566$	−100.293	+	911.497i	−0.177196	+	1.61042i
$567$	529.684	+	685.964i	0.934187	+	1.20981i
$568$	−3.15147	−	43.0584i	−0.00554836	−	0.0758071i
$569$	182.285	+	428.952i	0.320360	+	0.753870i	0.999797	+	0.0201361i	$0.00640995\pi$
$569$	182.285	+	428.952i	0.320360	+	0.753870i	−0.679437	+	0.733733i	$0.737776\pi$
$570$	−582.917	−	222.947i	−1.02266	−	0.391135i
$571$	339.166	−	144.130i	0.593987	−	0.252417i	−0.0731881	−	0.997318i	$-0.523317\pi$
$571$	339.166	−	144.130i	0.593987	−	0.252417i	0.667175	+	0.744901i	$0.267503\pi$
$572$	−128.911	+	4.71123i	−0.225369	+	0.00823642i
$573$	715.201	+	436.481i	1.24817	+	0.761747i
$574$	−1258.76	+	1902.61i	−2.19295	+	3.31465i
$575$	−38.8115	+	352.731i	−0.0674982	+	0.613446i
$576$	649.913	−	364.749i	1.12832	−	0.633244i
$577$	631.778	−	69.5154i	1.09494	−	0.120477i	0.456181	−	0.889887i	$-0.349217\pi$
$577$	631.778	−	69.5154i	1.09494	−	0.120477i	0.638755	+	0.769410i	$0.279450\pi$
$578$	−393.709	−	645.117i	−0.681158	−	1.11612i
$579$	−218.795	−	572.062i	−0.377884	−	0.988016i
$580$	392.681	+	184.081i	0.677037	+	0.317382i
$581$	−7.21581	−	21.1513i	−0.0124196	−	0.0364049i
$582$	−124.047	−	9.07906i	−0.213139	−	0.0155998i
$583$	1081.70	−	715.648i	1.85541	−	1.22753i
$584$	146.250	+	163.225i	0.250428	+	0.279494i
$585$	54.5472	−	14.2605i	0.0932431	−	0.0243769i
$586$	−62.4302	+	852.982i	−0.106536	+	1.45560i
$587$	324.293	−	847.897i	0.552459	−	1.44446i	−0.316030	−	0.948749i	$-0.602350\pi$
$587$	324.293	−	847.897i	0.552459	−	1.44446i	0.868488	−	0.495710i	$-0.165092\pi$
$588$	−448.364	+	1055.09i	−0.762525	+	1.79437i
$589$	−491.847	−	474.200i	−0.835054	−	0.805093i
$590$	−28.1490	−	152.396i	−0.0477102	−	0.258299i
$591$	−181.049	−	530.698i	−0.306343	−	0.897966i
$592$	180.918	−	273.458i	0.305605	−	0.461923i
$593$	−7.75119	+	212.092i	−0.0130711	+	0.357659i	0.976666	+	0.214762i	$0.0688976\pi$
$593$	−7.75119	+	212.092i	−0.0130711	+	0.357659i	−0.989738	+	0.142897i	$0.954358\pi$
$594$	59.5327	−	22.7693i	0.100223	−	0.0383322i
$595$	−772.524	+	232.418i	−1.29836	+	0.390618i
$596$	−93.6817	−	507.184i	−0.157184	−	0.850981i
$597$	−26.8405	+	70.1772i	−0.0449590	+	0.117550i
$598$	−107.435	+	103.580i	−0.179657	+	0.173211i
$599$	−145.259	+	74.6830i	−0.242503	+	0.124679i	−0.574224	−	0.818698i	$-0.694696\pi$
$599$	−145.259	+	74.6830i	−0.242503	+	0.124679i	0.331721	+	0.943377i	$0.392371\pi$
$600$	78.7234	−	110.035i	0.131206	−	0.183392i
$601$	123.598	+	52.5235i	0.205654	+	0.0873935i	0.491483	−	0.870887i	$-0.336455\pi$
$601$	123.598	+	52.5235i	0.205654	+	0.0873935i	−0.285829	+	0.958281i	$0.592269\pi$
$602$	401.179	−	309.780i	0.666410	−	0.514585i
$603$	421.044	+	15.3876i	0.698248	+	0.0255185i
$604$	553.696	+	907.265i	0.916715	+	1.50210i
$605$	198.069	−	131.041i	0.327387	−	0.216597i
$606$	−1070.43	+	1386.26i	−1.76639	+	2.28756i
$607$	174.028	+	942.171i	0.286701	+	1.55218i	0.747251	+	0.664542i	$0.231373\pi$
$607$	174.028	+	942.171i	0.286701	+	1.55218i	−0.460549	+	0.887634i	$0.652348\pi$
$608$	635.043	+	242.883i	1.04448	+	0.399479i
$609$	−335.318	+	1114.55i	−0.550604	+	1.83013i
$610$	425.605	+	238.861i	0.697713	+	0.391575i
$611$	−13.4527	−	31.6568i	−0.0220175	−	0.0518115i
$612$	209.737	−	941.541i	0.342708	−	1.53847i
$613$	50.2766	−	11.1996i	0.0820173	−	0.0182701i	−0.176230	−	0.984349i	$-0.556390\pi$
$613$	50.2766	−	11.1996i	0.0820173	−	0.0182701i	0.258247	+	0.966079i	$0.416855\pi$
$614$	747.281	−	419.394i	1.21707	−	0.683053i
$615$	−834.656	−	644.501i	−1.35716	−	1.04797i
$616$	257.507	+	214.299i	0.418031	+	0.347888i
$617$		−	280.276i		−	0.454256i	−0.973865	−	0.227128i	$-0.927066\pi$
$617$		−	280.276i		−	0.454256i	0.973865	−	0.227128i	$-0.0729336\pi$
$618$	−1991.28	−	1215.26i	−3.22214	−	1.96644i
$619$	−98.5518	+	60.1453i	−0.159211	+	0.0971653i	−0.598276	−	0.801290i	$-0.704147\pi$
$619$	−98.5518	+	60.1453i	−0.159211	+	0.0971653i	0.439064	+	0.898456i	$0.355310\pi$
$620$	−629.672	+	384.283i	−1.01560	+	0.619811i
$621$	18.3780	−	35.7455i	0.0295942	−	0.0575612i
$622$	−85.7457	+	111.044i	−0.137855	+	0.178528i
$623$	403.632	+	949.825i	0.647884	+	1.52460i
$624$	−96.3534	+	25.1901i	−0.154413	+	0.0403687i
$625$	17.1483	−	92.8394i	0.0274373	−	0.148543i
$626$	−223.244	−	1516.92i	−0.356620	−	2.42319i
$627$	−756.172	−	424.384i	−1.20602	−	0.676849i
$628$	−582.398	+	129.735i	−0.927386	+	0.206584i
$629$	−158.526	−	606.371i	−0.252029	−	0.964024i
$630$	−787.285	−	404.771i	−1.24966	−	0.642494i
$631$	−780.960	−	699.743i	−1.23765	−	1.10894i	−0.990143	−	0.140058i	$-0.955271\pi$
$631$	−780.960	−	699.743i	−1.23765	−	1.10894i	−0.247511	−	0.968885i	$-0.579613\pi$
$632$	−18.7363	+	127.311i	−0.0296460	+	0.201441i
$633$	−58.7109	−	56.6044i	−0.0927503	−	0.0894225i
$634$	176.491	+	75.0005i	0.278377	+	0.118297i
$635$	539.510	+	184.055i	0.849621	+	0.289851i
$636$	−1308.52	+	1357.22i	−2.05742	+	2.13399i
$637$	67.6867	−	87.6572i	0.106259	−	0.137609i
$638$	921.953	+	609.958i	1.44507	+	0.956047i
$639$	23.0787	+	156.817i	0.0361169	+	0.245410i
$640$	144.192	−	201.543i	0.225300	−	0.314911i
$641$	−290.059	+	438.424i	−0.452510	+	0.683969i	−0.986912	−	0.161261i	$-0.948444\pi$
$641$	−290.059	+	438.424i	−0.452510	+	0.683969i	0.534402	+	0.845230i	$0.320537\pi$
$642$	734.556	−	611.302i	1.14417	−	0.952184i
$643$	−21.4030	−	25.7184i	−0.0332861	−	0.0399974i	0.751744	−	0.659455i	$-0.229213\pi$
$643$	−21.4030	−	25.7184i	−0.0332861	−	0.0399974i	−0.785030	+	0.619458i	$0.787353\pi$
$644$	1276.36	−	46.6465i	1.98193	−	0.0724325i
$645$	129.276	+	195.401i	0.200428	+	0.302948i
$646$	917.379	−	471.657i	1.42009	−	0.730119i
$647$	139.316	+	270.971i	0.215326	+	0.418811i	0.972000	−	0.234981i	$-0.0755027\pi$
$647$	139.316	+	270.971i	0.215326	+	0.418811i	−0.756674	+	0.653792i	$0.773177\pi$
$648$	−165.054	+	109.199i	−0.254713	+	0.168517i
$649$	−7.86396	−	215.177i	−0.0121170	−	0.331552i
$650$	−60.7387	+	50.5471i	−0.0934442	+	0.0777648i
$651$	−1266.37	−	1521.70i	−1.94526	−	2.33748i
$652$	10.9280	+	7.22990i	0.0167607	+	0.0110888i
$653$	793.032	+	567.366i	1.21444	+	0.868860i	0.994301	−	0.106607i	$-0.0339987\pi$
$653$	793.032	+	567.366i	1.21444	+	0.868860i	0.220143	+	0.975468i	$0.429348\pi$
$654$	2238.59	−	329.452i	3.42292	−	0.503749i
$655$	178.107	−	269.208i	0.271918	−	0.411005i
$656$	721.717	+	557.292i	1.10018	+	0.849530i
$657$	−579.248	−	558.465i	−0.881656	−	0.850023i
$658$	−174.378	+	511.144i	−0.265012	+	0.776814i
$659$	−276.092	+	649.699i	−0.418956	+	0.985886i	0.567725	+	0.823218i	$0.307824\pi$
$659$	−276.092	+	649.699i	−0.418956	+	0.985886i	−0.986681	+	0.162667i	$0.947990\pi$
$660$	−649.820	+	674.002i	−0.984576	+	1.02122i
$661$	796.663	+	117.245i	1.20524	+	0.177374i	0.718094	−	0.695946i	$-0.245015\pi$
$661$	796.663	+	117.245i	1.20524	+	0.177374i	0.487146	+	0.873321i	$0.338038\pi$
$662$	−968.332	+	1080.72i	−1.46274	+	1.63251i
$663$	−87.0439	+	169.302i	−0.131288	+	0.255357i
$664$	4.93737	−	1.29080i	0.00743580	−	0.00194397i
$665$	−112.193	−	503.652i	−0.168712	−	0.757371i
$666$	336.597	−	599.752i	0.505401	−	0.900528i
$667$	689.670	−	101.498i	1.03399	−	0.152172i
$668$	−1159.19	−	214.114i	−1.73532	−	0.320530i
$669$	355.521	+	1359.89i	0.531422	+	2.03272i
$670$	447.714	−	190.258i	0.668229	−	0.283967i
$671$	536.712	+	414.435i	0.799869	+	0.617639i
$672$	1752.12	+	900.827i	2.60732	+	1.34052i
$673$	491.411	+	805.208i	0.730180	+	1.19645i	0.973983	+	0.226621i	$0.0727678\pi$
$673$	491.411	+	805.208i	0.730180	+	1.19645i	−0.243803	+	0.969825i	$0.578395\pi$
$674$	−400.371	−	656.033i	−0.594022	−	0.973343i
$675$	11.0869	−	18.1665i	0.0164250	−	0.0269133i
$676$	791.860			1.17139
$677$	200.285	−	240.667i	0.295841	−	0.355490i	−0.599893	−	0.800080i	$-0.704790\pi$
$677$	200.285	−	240.667i	0.295841	−	0.355490i	0.895734	+	0.444590i	$0.146651\pi$
$678$	157.014	−	203.340i	0.231584	−	0.299912i
$679$	−50.3292	−	89.6771i	−0.0741225	−	0.132072i
$680$	−40.0549	−	179.812i	−0.0589043	−	0.264430i
$681$	1555.69	+	346.545i	2.28442	+	0.508876i
$682$	−1730.54	+	735.400i	−2.53745	+	1.07830i
$683$	304.114	−	541.873i	0.445262	−	0.793372i	−0.553971	−	0.832536i	$-0.686888\pi$
$683$	304.114	−	541.873i	0.445262	−	0.793372i	0.999233	+	0.0391638i	$0.0124694\pi$
$684$	590.826	+	177.753i	0.863781	+	0.259873i
$685$	213.362	−	557.856i	0.311477	−	0.814388i
$686$	−239.149	+	44.1731i	−0.348614	+	0.0643923i
$687$	160.587	+	124.001i	0.233750	+	0.180496i
$688$	−111.784	−	168.961i	−0.162476	−	0.245583i
$689$	155.463	−	94.8776i	0.225635	−	0.137703i
$690$	−39.5579	+	1082.40i	−0.0573303	+	1.56870i
$691$	201.732	+	261.251i	0.291942	+	0.378077i	0.914561	−	0.404447i	$-0.132536\pi$
$691$	201.732	+	261.251i	0.291942	+	0.378077i	−0.622619	+	0.782525i	$0.713931\pi$
$692$	376.061	−	884.945i	0.543441	−	1.27882i
$693$	−1000.31	−	715.661i	−1.44345	−	1.03270i
$694$	−614.901	−	1195.99i	−0.886024	−	1.72333i
$695$	−390.255	−	404.778i	−0.561519	−	0.582415i
$696$	−248.244	−	94.9451i	−0.356672	−	0.136415i
$697$	1713.96	−	316.585i	2.45906	−	0.454211i
$698$	−423.839	−	1408.78i	−0.607219	−	2.01831i
$699$	−157.445	−	411.656i	−0.225244	−	0.588922i
$700$	675.838	+	24.6995i	0.965483	+	0.0352849i
$701$	−867.887	−	574.189i	−1.23807	−	0.819099i	−0.249283	−	0.968431i	$-0.580195\pi$
$701$	−867.887	−	574.189i	−1.23807	−	0.819099i	−0.988787	+	0.149331i	$0.952288\pi$
$702$	8.47084	−	2.88985i	0.0120667	−	0.00411660i
$703$	394.212	−	72.8146i	0.560756	−	0.103577i
$704$	829.811	−	860.691i	1.17871	−	1.22257i
$705$	−229.760	−	97.6375i	−0.325901	−	0.138493i
$706$	−413.244	−	158.052i	−0.585331	−	0.223870i
$707$	−1444.21	−	105.702i	−2.04273	−	0.149508i
$708$	79.1633	+	302.804i	0.111813	+	0.427689i
$709$	285.752	−	256.035i	0.403036	−	0.361122i	−0.440909	−	0.897552i	$-0.645344\pi$
$709$	285.752	−	256.035i	0.403036	−	0.361122i	0.843945	+	0.536430i	$0.180228\pi$
$710$	100.980	+	152.631i	0.142225	+	0.214973i
$711$	34.4859	−	471.179i	0.0485033	−	0.662699i
$712$	−223.046	+	76.0927i	−0.313267	+	0.106872i
$713$	−503.286	+	1073.61i	−0.705871	+	1.50576i
$714$	2791.78	−	1067.76i	3.91005	−	1.49547i
$715$	77.2038	−	47.1168i	0.107977	−	0.0658976i
$716$	3.05989	+	27.8092i	0.00427358	+	0.0388397i
$717$	−178.639	−	318.301i	−0.249148	−	0.443934i
$718$	14.5003	+	1.59548i	0.0201954	+	0.00222212i
$719$	−1120.60	−	741.381i	−1.55855	−	1.03113i	−0.975850	−	0.218442i	$-0.929903\pi$
$719$	−1120.60	−	741.381i	−1.55855	−	1.03113i	−0.582702	−	0.812686i	$-0.698004\pi$
$720$	−184.325	+	302.028i	−0.256007	+	0.419483i
$721$	−70.4420	−	1927.47i	−0.0977004	−	2.67332i
$722$	−160.618	−	377.965i	−0.222462	−	0.523497i
$723$	−39.1604	+	102.389i	−0.0541638	+	0.141617i
$724$	−539.472	+	229.251i	−0.745127	+	0.316645i
$725$	368.131	−	26.9437i	0.507767	−	0.0371637i
$726$	−696.466	+	537.793i	−0.959319	+	0.740762i
$727$	1360.38	+	149.685i	1.87123	+	0.205894i	0.972547	−	0.232706i	$-0.0747581\pi$
$727$	1360.38	+	149.685i	1.87123	+	0.205894i	0.898682	+	0.438600i	$0.144526\pi$
$728$	35.0362	+	31.3926i	0.0481267	+	0.0431217i
$729$	528.654	−	408.214i	0.725178	−	0.559964i
$730$	−879.256	−	299.960i	−1.20446	−	0.410905i
$731$	−383.122	−	56.3839i	−0.524107	−	0.0771326i
$732$	−892.457	−	418.367i	−1.21920	−	0.571539i
$733$	122.439	−	200.624i	0.167038	−	0.273703i	−0.759032	−	0.651053i	$-0.774328\pi$
$733$	122.439	−	200.624i	0.167038	−	0.273703i	0.926071	+	0.377350i	$0.123165\pi$
$734$	−189.532	−	35.0083i	−0.258218	−	0.0476953i
$735$	−87.9123	−	798.975i	−0.119609	−	1.08704i
$736$	43.0953	−	1179.19i	0.0585533	−	1.60216i
$737$	653.913	−	170.955i	0.887263	−	0.231961i
$738$	1595.10	+	1055.31i	2.16138	+	1.42995i
$739$	−125.281	+	562.405i	−0.169528	+	0.761036i	0.814085	+	0.580745i	$0.197239\pi$
$739$	−125.281	+	562.405i	−0.169528	+	0.761036i	−0.983613	+	0.180291i	$0.942296\pi$
$740$	31.5949	−	431.680i	0.0426958	−	0.583352i
$741$	−103.935	−	63.4307i	−0.140263	−	0.0856015i
$742$	−2812.06	−	519.414i	−3.78984	−	0.700019i
$743$	426.119	+	475.577i	0.573512	+	0.640077i	0.959259	−	0.282527i	$-0.0911727\pi$
$743$	426.119	+	475.577i	0.573512	+	0.640077i	−0.385748	+	0.922604i	$0.626056\pi$
$744$	367.668	−	263.044i	0.494177	−	0.353554i
$745$	231.322	+	277.962i	0.310500	+	0.373104i
$746$		−	1726.05i		−	2.31374i
$747$	−17.7326	+	6.04953i	−0.0237384	+	0.00809843i
$748$	−112.956	−	1543.32i	−0.151011	−	2.06326i
$749$	756.618	+	227.632i	1.01017	+	0.303915i
$750$	−177.126	+	1609.78i	−0.236169	+	2.14638i
$751$	−194.755	−	28.6621i	−0.259328	−	0.0381652i	0.0146812	−	0.999892i	$-0.495327\pi$
$751$	−194.755	−	28.6621i	−0.259328	−	0.0381652i	−0.274009	+	0.961727i	$0.588350\pi$
$752$	198.671	+	84.4259i	0.264190	+	0.112269i
$753$	−141.908	−	252.854i	−0.188457	−	0.335795i
$754$	126.247	+	90.3220i	0.167436	+	0.119790i
$755$	−649.880	−	364.730i	−0.860768	−	0.483086i
$756$	−70.4983	−	29.9585i	−0.0932518	−	0.0396277i
$757$	159.498	−	1449.57i	0.210697	−	1.91488i	−0.161753	−	0.986831i	$-0.551715\pi$
$757$	159.498	−	1449.57i	0.210697	−	1.91488i	0.372450	−	0.928052i	$-0.378518\pi$
$758$	769.663	+	1075.79i	1.01539	+	1.41925i
$759$	−273.344	+	1479.86i	−0.360137	+	1.94975i
$760$	116.574	−	17.1562i	0.153387	−	0.0225739i
$761$	336.652	+	101.284i	0.442381	+	0.133093i	0.501499	−	0.865158i	$-0.332782\pi$
$761$	336.652	+	101.284i	0.442381	+	0.133093i	−0.0591176	+	0.998251i	$0.518829\pi$
$762$	−2043.38	−	534.209i	−2.68160	−	0.701062i
$763$	1248.40	+	1393.30i	1.63618	+	1.82608i
$764$	−955.746	−	34.9291i	−1.25098	−	0.0457187i
$765$	194.853	+	647.662i	0.254709	+	0.846617i
$766$	−345.148	−	287.235i	−0.450585	−	0.374980i
$767$		−	30.2356i		−	0.0394206i
$768$	277.249	−	454.290i	0.361001	−	0.591523i
$769$	−106.593	−	207.324i	−0.138612	−	0.269602i	0.809760	−	0.586761i	$-0.199597\pi$
$769$	−106.593	−	207.324i	−0.138612	−	0.269602i	−0.948373	+	0.317158i	$0.897271\pi$
$770$	−1396.49	−	257.944i	−1.81362	−	0.334993i
$771$	1371.95	−	1141.74i	1.77944	−	1.48086i
$772$	537.366	+	447.200i	0.696070	+	0.579274i
$773$	−15.9090	−	86.1298i	−0.0205808	−	0.111423i	0.971496	−	0.237056i	$-0.0761826\pi$
$773$	−15.9090	−	86.1298i	−0.0205808	−	0.111423i	−0.992077	+	0.125634i	$0.959904\pi$
$774$	−259.711	−	336.337i	−0.335544	−	0.434544i
$775$	−307.276	+	547.508i	−0.396486	+	0.706462i
$776$	21.2624	−	9.96742i	0.0274000	−	0.0128446i
$777$	1158.51	−	84.7921i	1.49101	−	0.109128i
$778$	−20.2089	+	28.2469i	−0.0259755	+	0.0363071i
$779$	121.930	+	1108.14i	0.156521	+	1.42251i
$780$	−94.6441	+	91.2484i	−0.121339	+	0.116985i
$781$	107.929	+	230.234i	0.138194	+	0.294793i
$782$	−1288.78	−	1242.54i	−1.64806	−	1.58893i
$783$	−40.0352	−	12.0448i	−0.0511305	−	0.0153829i
$784$	76.0166	+	690.864i	0.0969600	+	0.881204i
$785$	311.579	−	279.176i	0.396916	−	0.355638i
$786$	−585.332	+	1042.95i	−0.744697	+	1.32691i
$787$	−366.347	−	353.203i	−0.465499	−	0.448797i	0.424049	−	0.905639i	$-0.360608\pi$
$787$	−366.347	−	353.203i	−0.465499	−	0.448797i	−0.889548	+	0.456842i	$0.848980\pi$
$788$	476.687	+	427.113i	0.604932	+	0.542022i
$789$	−1597.40	+	1056.83i	−2.02459	+	1.33946i
$790$	−194.862	−	509.487i	−0.246661	−	0.644920i
$791$	211.840	+	15.5047i	0.267813	+	0.0196014i
$792$	179.662	−	215.887i	0.226846	−	0.272584i
$793$	73.1899	+	60.9091i	0.0922950	+	0.0768085i
$794$	−923.190	−	432.774i	−1.16271	−	0.545055i
$795$	334.341	−	1278.87i	0.420555	−	1.60864i
$796$	−12.4871	−	84.8484i	−0.0156873	−	0.106593i
$797$	−30.4100	−	832.092i	−0.0381556	−	1.04403i	−0.871232	−	0.490872i	$-0.836678\pi$
$797$	−30.4100	−	832.092i	−0.0381556	−	1.04403i	0.833076	−	0.553158i	$-0.186578\pi$
$798$	550.792	+	1830.75i	0.690215	+	2.29418i
$799$	373.607	−	175.140i	0.467593	−	0.219199i
$800$	68.3354	−	621.054i	0.0854192	−	0.776318i
$801$	796.307	−	338.394i	0.994141	−	0.422464i
$802$	304.114	+	1010.83i	0.379195	+	1.26039i
$803$	−1147.94	−	590.195i	−1.42956	−	0.734988i
$804$	−873.729	+	449.215i	−1.08673	+	0.558725i
$805$	−764.405	+	466.510i	−0.949572	+	0.579515i
$806$	−246.614	+	94.3217i	−0.305972	+	0.117024i
$807$	−46.4263	−	634.320i	−0.0575294	−	0.786022i
$808$	48.1464	−	327.149i	0.0595871	−	0.404887i
$809$	−53.0990	−	725.489i	−0.0656353	−	0.896773i	−0.923672	−	0.383184i	$-0.874827\pi$
$809$	−53.0990	−	725.489i	−0.0656353	−	0.896773i	0.858037	−	0.513588i	$-0.171684\pi$
$810$	383.590	−	746.088i	0.473568	−	0.921096i
$811$	156.334	+	218.515i	0.192767	+	0.269439i	0.898438	−	0.439101i	$-0.144703\pi$
$811$	156.334	+	218.515i	0.192767	+	0.269439i	−0.705670	+	0.708540i	$0.749354\pi$
$812$	−288.862	−	1296.74i	−0.355741	−	1.59697i
$813$	−776.758	−	1656.97i	−0.955422	−	2.03810i
$814$	239.888	−	1076.89i	0.294703	−	1.32297i
$815$	−9.16271	−	0.670624i	−0.0112426	−	0.000822852i
$816$	−344.192	−	1144.05i	−0.421804	−	1.40202i
$817$	53.8554	−	241.765i	0.0659185	−	0.295918i
$818$	374.331	−	798.520i	0.457617	−	0.976185i
$819$	−136.701	−	105.557i	−0.166912	−	0.128885i
$820$	1190.86	+	175.258i	1.45227	+	0.213730i
$821$	1386.42	+	472.982i	1.68870	+	0.576104i	0.990219	−	0.139524i	$-0.0445571\pi$
$821$	1386.42	+	472.982i	1.68870	+	0.576104i	0.698481	+	0.715628i	$0.253859\pi$
$822$	−637.541	+	2119.10i	−0.775598	+	2.57798i
$823$	−416.014	+	275.233i	−0.505485	+	0.334426i	−0.778563	−	0.627566i	$-0.784051\pi$
$823$	−416.014	+	275.233i	−0.505485	+	0.334426i	0.273078	+	0.961992i	$0.411958\pi$
$824$	440.145	+	16.0857i	0.534157	+	0.0195215i
$825$	−201.548	+	770.933i	−0.244301	+	0.934465i
$826$	−316.801	+	353.571i	−0.383536	+	0.428052i
$827$	−745.190	−	165.998i	−0.901076	−	0.200723i	−0.257656	−	0.966237i	$-0.582950\pi$
$827$	−745.190	−	165.998i	−0.901076	−	0.200723i	−0.643420	+	0.765513i	$0.722485\pi$
$828$	−39.1071	−	1070.07i	−0.0472308	−	1.29235i
$829$	−845.629	+	604.996i	−1.02006	+	0.729790i	−0.963253	−	0.268595i	$-0.913441\pi$
$829$	−845.629	+	604.996i	−1.02006	+	0.729790i	−0.0568065	+	0.998385i	$0.518092\pi$
$830$	−15.5735	+	15.0147i	−0.0187633	+	0.0180901i
$831$	−728.324	+	278.560i	−0.876443	+	0.335211i
$832$	120.859	−	116.523i	0.145263	−	0.140052i
$833$	1080.49	+	773.022i	1.29710	+	0.927997i
$834$	1551.55	+	1390.19i	1.86037	+	1.66690i
$835$	782.243	−	266.864i	0.936818	−	0.319598i
$836$	989.770			1.18394
$837$	54.6602	−	45.4886i	0.0653049	−	0.0543472i
$838$	911.471	−	238.290i	1.08767	−	0.284355i
$839$	1052.64	−	1014.87i	1.25463	−	1.20962i	0.286812	−	0.957987i	$-0.407405\pi$
$839$	1052.64	−	1014.87i	1.25463	−	1.20962i	0.967823	−	0.251633i	$-0.0809675\pi$
$840$	341.202	−	12.4697i	0.406193	−	0.0148449i
$841$	37.4207	+	109.689i	0.0444955	+	0.130427i
$842$	607.713	−	112.250i	0.721750	−	0.133314i
$843$	710.774	+	1516.22i	0.843148	+	1.79860i
$844$	90.0624	+	23.5454i	0.106709	+	0.0278974i
$845$	−484.170	+	271.729i	−0.572982	+	0.321573i
$846$	428.529	+	146.194i	0.506535	+	0.172806i
$847$	−688.555	−	234.902i	−0.812933	−	0.277334i
$848$	−289.100	+	1105.82i	−0.340920	+	1.30404i
$849$	593.720	+	1154.79i	0.699317	+	1.36018i
$850$	−632.568	−	705.988i	−0.744198	−	0.830574i
$851$	−340.502	−	606.710i	−0.400120	−	0.712938i
$852$	−225.892	−	292.540i	−0.265132	−	0.343357i
$853$	−56.6199	−	254.175i	−0.0663774	−	0.297978i	0.931449	−	0.363871i	$-0.118545\pi$
$853$	−56.6199	−	254.175i	−0.0663774	−	0.297978i	−0.997827	+	0.0658934i	$0.979010\pi$
$854$	−217.682	−	1479.13i	−0.254897	−	1.73200i
$855$	−422.248	+	94.0597i	−0.493857	+	0.110011i
$856$	−64.4540	+	168.522i	−0.0752968	+	0.196871i
$857$	−199.836	+	426.288i	−0.233181	+	0.497419i	−0.987211	−	0.159421i	$-0.949037\pi$
$857$	−199.836	+	426.288i	−0.233181	+	0.497419i	0.754030	+	0.656840i	$0.228107\pi$
$858$	−272.541	+	194.986i	−0.317647	+	0.227257i
$859$	−82.0061	+	9.02323i	−0.0954669	+	0.0105043i	−0.156978	−	0.987602i	$-0.550175\pi$
$859$	−82.0061	+	9.02323i	−0.0954669	+	0.0105043i	0.0615116	+	0.998106i	$0.480408\pi$
$860$	−237.841	−	122.282i	−0.276559	−	0.142189i
$861$			3230.37i			3.75188i
$862$	−977.993	−	822.726i	−1.13456	−	0.954438i
$863$	−752.798			−0.872303			−0.436152	−	0.899873i	$-0.643659\pi$
$863$	−752.798			−0.872303			−0.436152	+	0.899873i	$0.643659\pi$
$864$	−32.3582	+	62.9371i	−0.0374516	+	0.0728439i
$865$	73.7355	+	670.132i	0.0852433	+	0.774719i
$866$	−73.1532	−	102.249i	−0.0844725	−	0.118071i
$867$	−968.988	−	454.243i	−1.11763	−	0.523925i
$868$	2110.62	+	807.246i	2.43160	+	0.930006i
$869$	−164.788	−	739.757i	−0.189629	−	0.851274i
$870$	1114.63	−	164.040i	1.28118	−	0.188551i
$871$	92.6386	−	20.6361i	0.106359	−	0.0236924i
$872$	−338.127	+	261.093i	−0.387760	+	0.299419i
$873$	−75.1827	+	42.1946i	−0.0861200	+	0.0483329i
$874$	852.803	−	764.115i	0.975747	−	0.874274i
$875$	−1190.81	+	612.239i	−1.36093	+	0.699702i
$876$	1815.20	+	474.556i	2.07215	+	0.541730i
$877$	−255.236	+	748.157i	−0.291033	+	0.853086i	0.699356	+	0.714774i	$0.253470\pi$
$877$	−255.236	+	748.157i	−0.291033	+	0.853086i	−0.990389	+	0.138313i	$0.955832\pi$
$878$	−665.371	+	1950.36i	−0.757825	+	2.22137i
$879$	592.716	+	1056.11i	0.674307	+	1.20149i
$880$	−143.569	+	549.159i	−0.163147	+	0.624045i
$881$	−1405.89	+	659.052i	−1.59578	+	0.748073i	−0.998542	−	0.0539878i	$-0.982807\pi$
$881$	−1405.89	+	659.052i	−1.59578	+	0.748073i	−0.597243	+	0.802061i	$0.703737\pi$
$882$	264.797	+	1433.59i	0.300224	+	1.62538i
$883$	1175.72	−	401.099i	1.33150	−	0.454246i	0.436259	−	0.899821i	$-0.356303\pi$
$883$	1175.72	−	401.099i	1.33150	−	0.454246i	0.895244	+	0.445575i	$0.147001\pi$
$884$	−7.93600	−	217.149i	−0.00897738	−	0.245643i
$885$	−152.311	−	157.979i	−0.172103	−	0.178508i
$886$	169.107	+	646.842i	0.190865	+	0.730070i
$887$	503.138	+	604.584i	0.567236	+	0.681605i	0.972583	−	0.232558i	$-0.0747096\pi$
$887$	503.138	+	604.584i	0.567236	+	0.681605i	−0.405346	+	0.914163i	$0.632849\pi$
$888$			265.259i			0.298715i
$889$	−563.821	−	1652.69i	−0.634219	−	1.85905i
$890$	666.645	−	744.020i	0.749040	−	0.835978i
$891$	678.213	−	947.968i	0.761181	−	1.06394i
$892$	−1113.58	−	1155.02i	−1.24841	−	1.29486i
$893$	94.2800	+	246.505i	0.105577	+	0.276041i
$894$	−929.959	−	964.567i	−1.04022	−	1.07893i
$895$	−11.4137	−	15.9535i	−0.0127528	−	0.0178251i
$896$	−758.624	+	27.7250i	−0.846679	+	0.0309431i
$897$	−45.9470	+	206.263i	−0.0512230	+	0.229947i
$898$	−503.382	−	451.032i	−0.560559	−	0.502263i
$899$	1193.25	+	311.956i	1.32730	+	0.347003i
$900$	20.7073	−	566.604i	0.0230081	−	0.629560i
$901$	1205.50	+	1822.12i	1.33796	+	2.02233i
$902$	2938.09	+	883.940i	3.25731	+	0.979978i
$903$	231.738	−	679.280i	0.256631	−	0.752248i
$904$	−7.06224	+	47.9871i	−0.00781222	+	0.0530831i
$905$	251.183	−	325.293i	0.277551	−	0.359440i
$906$	2500.08	+	1171.99i	2.75947	+	1.29359i
$907$	−113.780	−	25.3455i	−0.125446	−	0.0279443i	0.154258	−	0.988031i	$-0.450701\pi$
$907$	−113.780	−	25.3455i	−0.125446	−	0.0279443i	−0.279704	+	0.960086i	$0.590236\pi$
$908$	−1742.12	+	524.127i	−1.91864	+	0.577232i
$909$	−88.6179	+	1210.78i	−0.0974894	+	1.33199i
$910$	−194.643	−	43.3585i	−0.213893	−	0.0476467i
$911$	−1131.03	+	530.205i	−1.24153	+	0.582003i	−0.929764	−	0.368157i	$-0.879989\pi$
$911$	−1131.03	+	530.205i	−1.24153	+	0.582003i	−0.311762	+	0.950160i	$0.600919\pi$
$912$	745.868	−	166.149i	0.817838	−	0.182181i
$913$	−24.4447	+	17.4887i	−0.0267740	+	0.0191552i
$914$	307.993	+	158.350i	0.336972	+	0.173249i
$915$	689.242	−	50.4460i	0.753270	−	0.0551323i
$916$	−229.120	−	33.7194i	−0.250131	−	0.0368116i
$917$	−986.181	+	72.1792i	−1.07544	+	0.0787123i
$918$	38.3547	+	100.282i	0.0417807	+	0.109240i
$919$	−438.727	−	718.882i	−0.477396	−	0.782244i	0.520014	−	0.854158i	$-0.325927\pi$
$919$	−438.727	−	718.882i	−0.477396	−	0.782244i	−0.997411	+	0.0719138i	$0.977089\pi$
$920$	−93.5035	−	181.866i	−0.101634	−	0.197680i
$921$	554.825	−	1079.14i	0.602416	−	1.17171i
$922$	352.823	−	106.149i	0.382671	−	0.115129i
$923$	13.9647	+	32.8616i	0.0151296	+	0.0356030i
$924$	2850.80	+	313.678i	3.08529	+	0.339478i
$925$	−156.366	−	333.558i	−0.169044	−	0.360604i
$926$	−759.386	+	228.465i	−0.820071	+	0.246723i
$927$	−1615.93	+	59.0566i	−1.74319	+	0.0637072i
$928$	−1214.30	+	178.708i	−1.30852	+	0.192574i
$929$	−954.366	−	249.504i	−1.02730	−	0.268573i	−0.299310	−	0.954156i	$-0.596757\pi$
$929$	−954.366	−	249.504i	−1.02730	−	0.268573i	−0.727994	+	0.685583i	$0.759547\pi$
$930$	−813.399	+	1735.14i	−0.874623	+	1.86574i
$931$	−543.565	+	653.162i	−0.583851	+	0.701570i
$932$	386.690	+	321.806i	0.414903	+	0.345285i
$933$	−14.5014	+	198.132i	−0.0155428	+	0.212360i
$934$	1756.95	−	671.978i	1.88111	−	0.719462i
$935$	598.659	+	904.874i	0.640277	+	0.967780i
$936$	26.3187	−	29.3734i	0.0281183	−	0.0313818i
$937$	377.881	−	391.944i	0.403288	−	0.418296i	−0.487208	−	0.873286i	$-0.661985\pi$
$937$	377.881	−	391.944i	0.403288	−	0.418296i	0.890497	+	0.454989i	$0.150357\pi$
$938$	−1299.52	−	729.327i	−1.38542	−	0.777534i
$939$	−1448.82	−	1616.98i	−1.54294	−	1.72203i
$940$	283.247	−	31.1660i	0.301327	−	0.0331554i
$941$	−203.224	+	675.489i	−0.215966	+	0.717842i	0.779809	+	0.626018i	$0.215316\pi$
$941$	−203.224	+	675.489i	−0.215966	+	0.717842i	−0.995775	+	0.0918241i	$0.970730\pi$
$942$	−1075.84	+	1115.88i	−1.14209	+	1.18459i
$943$	1751.84	−	821.231i	1.85774	−	0.870870i
$944$	131.702	+	136.603i	0.139515	+	0.144706i
$945$	53.3854	−	5.87407i	0.0564925	−	0.00621594i
$946$	−554.409	−	396.646i	−0.586056	−	0.419287i
$947$	39.7191	+	542.681i	0.0419420	+	0.573052i	0.976259	+	0.216608i	$0.0694994\pi$
$947$	39.7191	+	542.681i	0.0419420	+	0.573052i	−0.934317	+	0.356444i	$0.883989\pi$
$948$	467.596	+	997.472i	0.493244	+	1.05219i
$949$	−158.060	−	88.7077i	−0.166554	−	0.0934749i
$950$	479.891	−	370.560i	0.505148	−	0.390063i
$951$	267.026	−	49.3221i	0.280784	−	0.0518634i
$952$	−360.984	+	433.767i	−0.379185	+	0.455638i
$953$	−289.715	−	348.129i	−0.304003	−	0.365298i	0.594630	−	0.804000i	$-0.297299\pi$
$953$	−289.715	−	348.129i	−0.304003	−	0.365298i	−0.898632	+	0.438702i	$0.855438\pi$
$954$	−435.462	+	2357.55i	−0.456459	+	2.47123i
$955$	596.361	−	306.611i	0.624462	−	0.321058i
$956$	355.633	+	217.040i	0.372001	+	0.227029i
$957$	1565.35			1.63568
$958$	634.066	−	761.910i	0.661865	−	0.795313i
$959$	−1752.05	+	527.112i	−1.82695	+	0.549647i
$960$	44.5008	−	1217.65i	0.0463550	−	1.26839i
$961$	−846.691	+	758.638i	−0.881052	+	0.789426i
$962$	39.1857	−	149.887i	0.0407336	−	0.155808i
$963$	190.841	−	634.327i	0.198173	−	0.658699i
$964$	−18.2187	−	123.794i	−0.0188991	−	0.128417i
$965$	−482.022	−	89.0340i	−0.499505	−	0.0922632i
$966$	2698.47	−	1930.59i	2.79344	−	1.99854i
$967$	−1019.39	−	112.165i	−1.05418	−	0.115992i	−0.434360	−	0.900739i	$-0.643025\pi$
$967$	−1019.39	−	112.165i	−1.05418	−	0.115992i	−0.619816	+	0.784747i	$0.712793\pi$
$968$	64.9752	−	152.899i	0.0671231	−	0.157954i
$969$	714.869	−	1273.76i	0.737739	−	1.31451i
$970$	−57.9198	+	80.9570i	−0.0597111	+	0.0834608i
$971$	57.7172	−	32.3924i	0.0594409	−	0.0333599i	−0.459413	−	0.888223i	$-0.651940\pi$
$971$	57.7172	−	32.3924i	0.0594409	−	0.0333599i	0.518854	+	0.854863i	$0.326359\pi$
$972$	−636.440	+	1497.67i	−0.654774	+	1.54081i
$973$	−250.785	+	1704.05i	−0.257744	+	1.75134i
$974$	1924.42	+	211.746i	1.97579	+	0.217398i
$975$	−32.2365	+	107.149i	−0.0330630	+	0.109897i
$976$	−595.979	+	43.6201i	−0.610635	+	0.0446927i
$977$	298.676	+	875.491i	0.305707	+	0.896101i	0.986520	+	0.163643i	$0.0523246\pi$
$977$	298.676	+	875.491i	0.305707	+	0.896101i	−0.680812	+	0.732458i	$0.738373\pi$
$978$	34.0395			0.0348052
$979$	1066.88	−	887.864i	1.08976	−	0.906909i
$980$	533.850	+	746.186i	0.544745	+	0.761414i
$981$	1168.11	−	1046.63i	1.19073	−	1.06690i
$982$	390.348	−	2113.31i	0.397503	−	2.15205i
$983$	320.130	−	524.552i	0.325666	−	0.533624i	−0.647989	−	0.761650i	$-0.724390\pi$
$983$	320.130	−	524.552i	0.325666	−	0.533624i	0.973655	+	0.228026i	$0.0732270\pi$
$984$	−735.700	−	53.8463i	−0.747663	−	0.0547219i
$985$	−438.028	−	97.5748i	−0.444698	−	0.0990607i
$986$	−1027.47	+	1553.02i	−1.04206	+	1.57507i
$987$	193.430	+	739.879i	0.195977	+	0.749624i
$988$	138.892	+	5.07600i	0.140579	+	0.00513765i
$989$	−427.290	+	47.0153i	−0.432042	+	0.0475382i
$990$	−216.253	+	1170.78i	−0.218438	+	1.18260i
$991$	−1048.06	−	639.620i	−1.05758	−	0.645429i	−0.119845	−	0.992793i	$-0.538240\pi$
$991$	−1048.06	−	639.620i	−1.05758	−	0.645429i	−0.937730	+	0.347364i	$0.887077\pi$
$992$	886.136	−	1890.30i	0.893282	−	1.90554i
$993$	−299.173	+	2032.85i	−0.301282	+	2.04718i
$994$	181.014	−	530.597i	0.182107	−	0.533800i
$995$	36.7510	+	47.5942i	0.0369357	+	0.0478334i
$996$	29.1544	−	32.5382i	0.0292715	−	0.0326689i
$997$	−62.5501	+	568.475i	−0.0627383	+	0.570186i	0.920870	+	0.389869i	$0.127480\pi$
$997$	−62.5501	+	568.475i	−0.0627383	+	0.570186i	−0.983609	+	0.180317i	$0.942288\pi$
$998$	364.642	+	472.227i	0.365373	+	0.473173i
$999$	3.04578	+	41.6144i	0.00304883	+	0.0416560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	431.3.f.a.101.11	✓	2982
431.367	odd	86	inner	431.3.f.a.367.11	yes	2982

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
431.3.f.a.101.11	✓	2982	1.1	even	1	trivial
431.3.f.a.367.11	yes	2982	431.367	odd	86	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 431 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	431.f (of order \(86\), degree \(42\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35584 + 2.63713i) q^{2} +(0.459232 + 4.17365i) q^{3} +(-2.78870 - 3.89789i) q^{4} +(3.04268 + 1.42635i) q^{5} +(-11.6291 - 4.44775i) q^{6} +(-2.23823 - 10.0478i) q^{7} +(2.32564 - 0.342263i) q^{8} +(-8.42376 + 1.87647i) q^{9} +(-7.88685 + 6.09003i) q^{10} +(-12.0732 + 6.77581i) q^{11} +(14.9878 - 13.4291i) q^{12} +(-1.72895 + 0.888915i) q^{13} +(29.5319 + 7.72065i) q^{14} +(-4.55578 + 13.3541i) q^{15} +(3.93933 - 11.5471i) q^{16} +(-11.4138 - 20.3372i) q^{17} +(6.47278 - 24.7587i) q^{18} +(13.5062 - 6.33143i) q^{19} +(-2.92537 - 15.8377i) q^{20} +(40.9080 - 13.9559i) q^{21} +(-1.49933 - 41.0255i) q^{22} +(-17.9680 - 18.6367i) q^{23} +(2.49649 + 9.54921i) q^{24} +(-8.76840 - 10.5363i) q^{25} -5.76469i q^{26} +(0.501302 + 1.46944i) q^{27} +(-32.9233 + 36.7446i) q^{28} +(-15.6681 + 21.9001i) q^{29} +(-29.0395 - 30.1202i) q^{30} +(-16.3620 - 42.7800i) q^{31} +(31.6363 + 32.8136i) q^{32} +(-33.8243 - 47.2777i) q^{33} +(69.1069 - 2.52561i) q^{34} +(7.52139 - 33.7646i) q^{35} +(30.8056 + 27.6020i) q^{36} +(26.0010 + 6.79754i) q^{37} +(-1.61542 + 44.2019i) q^{38} +(-4.50401 - 6.80781i) q^{39} +(7.56435 + 2.27577i) q^{40} +(-24.1312 + 70.7343i) q^{41} +(-18.6613 + 126.801i) q^{42} +(10.1486 - 13.1429i) q^{43} +(60.0799 + 28.1643i) q^{44} +(-28.3073 - 6.30572i) q^{45} +(73.5091 - 22.1156i) q^{46} +(-1.29151 + 17.6458i) q^{47} +(50.0027 + 11.1386i) q^{48} +(-51.5809 + 24.1801i) q^{49} +(39.6742 - 8.83781i) q^{50} +(79.6386 - 56.9765i) q^{51} +(8.28642 + 4.26034i) q^{52} +(-93.4333 + 6.83844i) q^{53} +(-4.55477 - 0.670324i) q^{54} +(-46.3996 + 3.39601i) q^{55} +(-8.64429 - 22.6014i) q^{56} +(32.6276 + 53.4624i) q^{57} +(-36.5097 - 71.0119i) q^{58} +(-7.11134 + 13.8316i) q^{59} +(64.7575 - 19.4826i) q^{60} +(-19.1560 - 45.0777i) q^{61} +(135.001 + 14.8543i) q^{62} +(37.7087 + 80.4400i) q^{63} +(-82.6944 + 24.8790i) q^{64} +(-6.52854 + 0.238595i) q^{65} +(170.537 - 25.0979i) q^{66} +(-47.2322 - 12.3481i) q^{67} +(-47.4424 + 101.204i) q^{68} +(69.5315 - 83.5508i) q^{69} +(78.8438 + 65.6143i) q^{70} +(1.34066 - 18.3174i) q^{71} +(-18.9484 + 7.24713i) q^{72} +(51.4427 + 77.7558i) q^{73} +(-53.1791 + 59.3515i) q^{74} +(39.9482 - 41.4349i) q^{75} +(-62.3439 - 34.9891i) q^{76} +(95.1044 + 106.143i) q^{77} +(24.0598 - 2.64733i) q^{78} +(-15.7712 + 52.4214i) q^{79} +(28.4563 - 29.5153i) q^{80} +(-76.2308 + 35.7355i) q^{81} +(-153.817 - 159.542i) q^{82} +(2.15796 - 0.237444i) q^{83} +(-168.478 - 120.536i) q^{84} +(-5.72053 - 78.1594i) q^{85} +(20.8995 + 44.5828i) q^{86} +(-98.5984 - 55.3361i) q^{87} +(-25.7588 + 19.8903i) q^{88} +(-98.5875 + 18.2100i) q^{89} +(55.0092 - 66.1004i) q^{90} +(12.8014 + 15.3825i) q^{91} +(-22.5363 + 122.010i) q^{92} +(171.035 - 87.9351i) q^{93} +(-44.7832 - 27.3308i) q^{94} +50.1258 q^{95} +(-122.424 + 147.108i) q^{96} +(9.56619 - 2.87804i) q^{97} +(6.16939 - 168.810i) q^{98} +(88.9872 - 79.7329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2982 q - 43 q^{2} - 41 q^{3} - 187 q^{4} - 41 q^{5} - 33 q^{6} - 43 q^{7} - 37 q^{8} - 252 q^{9} - 23 q^{10} + 187 q^{11} + 19 q^{12} - 43 q^{13} - 43 q^{14} - 71 q^{15} - 359 q^{16} - 43 q^{17} - 93 q^{18}+ \cdots - 609 q^{99}+O(q^{100}) \) 2982 * q - 43 * q^2 - 41 * q^3 - 187 * q^4 - 41 * q^5 - 33 * q^6 - 43 * q^7 - 37 * q^8 - 252 * q^9 - 23 * q^10 + 187 * q^11 + 19 * q^12 - 43 * q^13 - 43 * q^14 - 71 * q^15 - 359 * q^16 - 43 * q^17 - 93 * q^18 - 55 * q^19 + 9 * q^20 - 172 * q^21 - 47 * q^22 + 45 * q^23 + 17 * q^24 - 436 * q^25 + 37 * q^27 - 43 * q^28 - 93 * q^29 - 911 * q^30 - 43 * q^31 + 181 * q^32 + 733 * q^33 - 43 * q^34 - 43 * q^35 - 521 * q^36 - 43 * q^37 + 691 * q^38 - 43 * q^39 + 199 * q^40 + 456 * q^41 - 43 * q^42 - 43 * q^43 - 161 * q^44 - 3 * q^45 - 279 * q^46 - 43 * q^47 + 271 * q^48 + 362 * q^49 - 21 * q^50 - 43 * q^51 - 2107 * q^52 + 53 * q^53 - 2864 * q^54 + 111 * q^55 - 1978 * q^56 + 11 * q^57 - 349 * q^58 + 59 * q^59 + 29 * q^60 - 1433 * q^61 - 43 * q^62 - 2451 * q^63 - 801 * q^64 - 43 * q^65 - 253 * q^66 + 3053 * q^67 - 43 * q^68 + 25 * q^69 - 1978 * q^70 + 2021 * q^71 - 63 * q^72 - 43 * q^73 - 43 * q^74 - 401 * q^75 - 225 * q^76 + 645 * q^77 + 344 * q^78 + 3397 * q^79 + 227 * q^80 - 1054 * q^81 - 845 * q^82 - 43 * q^83 + 6106 * q^84 - 43 * q^85 - 43 * q^86 - 1021 * q^87 + 6277 * q^88 - 43 * q^89 - 815 * q^90 - 147 * q^91 - 239 * q^92 + 2193 * q^93 - 43 * q^94 - 70 * q^95 + 129 * q^96 + 125 * q^97 + 643 * q^98 - 609 * q^99

Introduction

L-functions

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