LMFDB - Embedded newform 230.4.l.a.53.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			53.25
Character	$\chi$	$=$	230.53
Dual form			230.4.l.a.217.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.142678 + 1.99490i) q^{2} +(-3.01257 - 0.655343i) q^{3} +(-3.95929 + 0.569259i) q^{4} +(-10.2092 - 4.55770i) q^{5} +(0.877520 - 6.10328i) q^{6} +(21.4100 + 11.6907i) q^{7} +(-1.70052 - 7.81717i) q^{8} +(-15.9140 - 7.26768i) q^{9} +(7.63554 - 21.0166i) q^{10} +(-0.215840 + 0.187026i) q^{11} +(12.3007 + 0.879761i) q^{12} +(-20.6934 - 37.8971i) q^{13} +(-20.2672 + 44.3789i) q^{14} +(27.7690 + 20.4209i) q^{15} +(15.3519 - 4.50772i) q^{16} +(72.2806 - 54.1086i) q^{17} +(12.2277 - 32.7838i) q^{18} +(11.1253 + 77.3785i) q^{19} +(43.0156 + 12.2336i) q^{20} +(-56.8376 - 49.2500i) q^{21} +(-0.403895 - 0.403895i) q^{22} +(43.0286 + 101.565i) q^{23} +24.6642i q^{24} +(83.4548 + 93.0607i) q^{25} +(72.6486 - 46.6884i) q^{26} +(109.817 + 82.2083i) q^{27} +(-91.4234 - 34.0992i) q^{28} +(221.034 + 31.7799i) q^{29} +(-36.7757 + 58.3100i) q^{30} +(248.450 + 159.669i) q^{31} +(11.1829 + 29.9824i) q^{32} +(0.772799 - 0.421980i) q^{33} +(118.254 + 136.473i) q^{34} +(-165.296 - 216.933i) q^{35} +(67.1452 + 19.7156i) q^{36} +(-89.2359 + 33.2833i) q^{37} +(-152.775 + 33.2342i) q^{38} +(37.5046 + 127.729i) q^{39} +(-18.2674 + 87.5574i) q^{40} +(-108.856 - 238.361i) q^{41} +(90.1396 - 120.412i) q^{42} +(29.2007 - 134.233i) q^{43} +(0.748106 - 0.863360i) q^{44} +(129.345 + 146.728i) q^{45} +(-196.474 + 100.329i) q^{46} +(-348.756 + 348.756i) q^{47} +(-49.2027 + 3.51904i) q^{48} +(136.275 + 212.048i) q^{49} +(-173.740 + 179.762i) q^{50} +(-253.210 + 115.637i) q^{51} +(103.504 + 138.266i) q^{52} +(313.428 - 574.000i) q^{53} +(-148.329 + 230.805i) q^{54} +(3.05596 - 0.925653i) q^{55} +(54.9804 - 187.246i) q^{56} +(17.1937 - 240.399i) q^{57} +(-31.8611 + 445.476i) q^{58} +(144.941 - 493.625i) q^{59} +(-121.570 - 65.0444i) q^{60} +(233.297 - 363.017i) q^{61} +(-283.076 + 518.415i) q^{62} +(-255.754 - 341.647i) q^{63} +(-58.2164 + 26.5866i) q^{64} +(38.5389 + 481.213i) q^{65} +(0.952071 + 1.48145i) q^{66} +(970.128 - 69.3849i) q^{67} +(-255.378 + 255.378i) q^{68} +(-63.0661 - 334.171i) q^{69} +(409.177 - 360.701i) q^{70} +(284.951 - 328.851i) q^{71} +(-29.7506 + 136.761i) q^{72} +(-689.590 + 921.184i) q^{73} +(-79.1290 - 173.268i) q^{74} +(-190.426 - 335.043i) q^{75} +(-88.0969 - 300.030i) q^{76} +(-6.80761 + 1.48091i) q^{77} +(-249.456 + 93.0422i) q^{78} +(602.728 + 176.977i) q^{79} +(-177.275 - 23.9491i) q^{80} +(32.3754 + 37.3631i) q^{81} +(459.976 - 251.166i) q^{82} +(372.104 + 997.649i) q^{83} +(253.072 + 162.640i) q^{84} +(-984.536 + 222.971i) q^{85} +(271.949 + 39.1003i) q^{86} +(-645.053 - 240.592i) q^{87} +(1.82906 + 1.36922i) q^{88} +(280.614 - 180.339i) q^{89} +(-274.254 + 278.966i) q^{90} -1053.30i q^{91} +(-228.179 - 377.632i) q^{92} +(-643.833 - 643.833i) q^{93} +(-745.496 - 645.976i) q^{94} +(239.087 - 840.677i) q^{95} +(-14.0403 - 97.6525i) q^{96} +(190.616 - 511.060i) q^{97} +(-403.572 + 302.110i) q^{98} +(4.79412 - 1.40768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) $ 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.142678	+	1.99490i	0.0504444	+	0.705305i
$2$	0.142678	+	1.99490i	0.0504444	+	0.705305i
$3$	−3.01257	−	0.655343i	−0.579768	−	0.126121i	−0.0868882	−	0.996218i	$-0.527692\pi$
$3$	−3.01257	−	0.655343i	−0.579768	−	0.126121i	−0.492880	+	0.870097i	$0.664056\pi$
$4$	−3.95929	+	0.569259i	−0.494911	+	0.0711574i
$5$	−10.2092	−	4.55770i	−0.913137	−	0.407653i
$5$	−10.2092	−	4.55770i	−0.913137	−	0.407653i
$6$	0.877520	−	6.10328i	0.0597076	−	0.415276i
$7$	21.4100	+	11.6907i	1.15603	+	0.631241i	0.938659	−	0.344848i	$-0.112069\pi$
$7$	21.4100	+	11.6907i	1.15603	+	0.631241i	0.217373	+	0.976089i	$0.430251\pi$
$8$	−1.70052	−	7.81717i	−0.0751532	−	0.345474i
$9$	−15.9140	−	7.26768i	−0.589407	−	0.269173i
$10$	7.63554	−	21.0166i	0.241457	−	0.664604i
$11$	−0.215840	+	0.187026i	−0.00591620	+	0.00512642i	−0.657814	−	0.753181i	$-0.728519\pi$
$11$	−0.215840	+	0.187026i	−0.00591620	+	0.00512642i	0.651898	+	0.758307i	$0.273973\pi$
$12$	12.3007	+	0.879761i	0.295908	+	0.0211638i
$13$	−20.6934	−	37.8971i	−0.441486	−	0.808521i	0.558291	−	0.829645i	$-0.311457\pi$
$13$	−20.6934	−	37.8971i	−0.441486	−	0.808521i	−0.999777	+	0.0211243i	$0.993275\pi$
$14$	−20.2672	+	44.3789i	−0.386902	+	0.847198i
$15$	27.7690	+	20.4209i	0.477994	+	0.351510i
$16$	15.3519	−	4.50772i	0.239873	−	0.0704331i
$17$	72.2806	−	54.1086i	1.03121	−	0.771956i	0.0571804	−	0.998364i	$-0.481789\pi$
$17$	72.2806	−	54.1086i	1.03121	−	0.771956i	0.974033	+	0.226407i	$0.0726981\pi$
$18$	12.2277	−	32.7838i	0.160117	−	0.429290i
$19$	11.1253	+	77.3785i	0.134333	+	0.934308i	0.939814	+	0.341686i	$0.110998\pi$
$19$	11.1253	+	77.3785i	0.134333	+	0.934308i	−0.805481	+	0.592622i	$0.798093\pi$
$20$	43.0156	+	12.2336i	0.480929	+	0.136775i
$21$	−56.8376	−	49.2500i	−0.590618	−	0.511773i
$22$	−0.403895	−	0.403895i	−0.00391413	−	0.00391413i
$23$	43.0286	+	101.565i	0.390090	+	0.920777i
$23$	43.0286	+	101.565i	0.390090	+	0.920777i
$24$			24.6642i			0.209773i
$25$	83.4548	+	93.0607i	0.667638	+	0.744486i
$26$	72.6486	−	46.6884i	0.547983	−	0.352168i
$27$	109.817	+	82.2083i	0.782755	+	0.585963i
$28$	−91.4234	−	34.0992i	−0.617050	−	0.230148i
$29$	221.034	+	31.7799i	1.41535	+	0.203496i	0.807176	−	0.590311i	$-0.200995\pi$
$29$	221.034	+	31.7799i	1.41535	+	0.203496i	0.608170	+	0.793807i	$0.291904\pi$
$30$	−36.7757	+	58.3100i	−0.223810	+	0.354864i
$31$	248.450	+	159.669i	1.43945	+	0.925078i	0.999636	+	0.0269883i	$0.00859169\pi$
$31$	248.450	+	159.669i	1.43945	+	0.925078i	0.439813	+	0.898089i	$0.355045\pi$
$32$	11.1829	+	29.9824i	0.0617771	+	0.165631i
$33$	0.772799	−	0.421980i	0.00407657	−	0.00222598i
$34$	118.254	+	136.473i	0.596484	+	0.688379i
$35$	−165.296	−	216.933i	−0.798288	−	1.04767i
$36$	67.1452	+	19.7156i	0.310858	+	0.0912760i
$37$	−89.2359	+	33.2833i	−0.396494	+	0.147885i	−0.539799	−	0.841794i	$-0.681500\pi$
$37$	−89.2359	+	33.2833i	−0.396494	+	0.147885i	0.143305	+	0.989679i	$0.454227\pi$
$38$	−152.775	+	33.2342i	−0.652196	+	0.141876i
$39$	37.5046	+	127.729i	0.153988	+	0.524435i
$40$	−18.2674	+	87.5574i	−0.0722082	+	0.346101i
$41$	−108.856	−	238.361i	−0.414645	−	0.907946i	−0.995573	−	0.0939908i	$-0.970038\pi$
$41$	−108.856	−	238.361i	−0.414645	−	0.907946i	0.580928	−	0.813955i	$-0.302690\pi$
$42$	90.1396	−	120.412i	0.331163	−	0.442382i
$43$	29.2007	−	134.233i	0.103560	−	0.476055i	−0.895933	−	0.444190i	$-0.853492\pi$
$43$	29.2007	−	134.233i	0.103560	−	0.476055i	0.999492	−	0.0318655i	$-0.0101448\pi$
$44$	0.748106	−	0.863360i	0.00256321	−	0.00295810i
$45$	129.345	+	146.728i	0.428480	+	0.486065i
$46$	−196.474	+	100.329i	−0.629751	+	0.321581i
$47$	−348.756	+	348.756i	−1.08237	+	1.08237i	−0.0860808	+	0.996288i	$0.527434\pi$
$47$	−348.756	+	348.756i	−1.08237	+	1.08237i	−0.996288	+	0.0860808i	$0.972566\pi$
$48$	−49.2027	+	3.51904i	−0.147954	+	0.0105819i
$49$	136.275	+	212.048i	0.397303	+	0.618216i
$50$	−173.740	+	179.762i	−0.491411	+	0.508444i
$51$	−253.210	+	115.637i	−0.695225	+	0.317498i
$52$	103.504	+	138.266i	0.276028	+	0.368731i
$53$	313.428	−	574.000i	0.812314	−	1.48764i	−0.0597305	−	0.998215i	$-0.519024\pi$
$53$	313.428	−	574.000i	0.812314	−	1.48764i	0.872044	−	0.489427i	$-0.162794\pi$
$54$	−148.329	+	230.805i	−0.373797	+	0.581639i
$55$	3.05596	−	0.925653i	0.00749210	−	0.00226936i
$56$	54.9804	−	187.246i	0.131198	−	0.446818i
$57$	17.1937	−	240.399i	0.0399536	−	0.558624i
$58$	−31.8611	+	445.476i	−0.0721305	+	1.00852i
$59$	144.941	−	493.625i	0.319826	−	1.08923i	−0.630038	−	0.776565i	$-0.716961\pi$
$59$	144.941	−	493.625i	0.319826	−	1.08923i	0.949864	−	0.312664i	$-0.101221\pi$
$60$	−121.570	−	65.0444i	−0.261577	−	0.139953i
$61$	233.297	−	363.017i	0.489682	−	0.761960i	−0.505200	−	0.863002i	$-0.668581\pi$
$61$	233.297	−	363.017i	0.489682	−	0.761960i	0.994882	+	0.101042i	$0.0322177\pi$
$62$	−283.076	+	518.415i	−0.579850	+	1.06192i
$63$	−255.754	−	341.647i	−0.511460	−	0.683231i
$64$	−58.2164	+	26.5866i	−0.113704	+	0.0519269i
$65$	38.5389	+	481.213i	0.0735410	+	0.918263i
$66$	0.952071	+	1.48145i	0.00177563	+	0.00276294i
$67$	970.128	−	69.3849i	1.76896	−	0.126518i	0.851499	−	0.524356i	$-0.175694\pi$
$67$	970.128	−	69.3849i	1.76896	−	0.126518i	0.917456	+	0.397838i	$0.130239\pi$
$68$	−255.378	+	255.378i	−0.455428	+	0.455428i
$69$	−63.0661	−	334.171i	−0.110033	−	0.583036i
$70$	409.177	−	360.701i	0.698657	−	0.615886i
$71$	284.951	−	328.851i	0.476302	−	0.549682i	−0.465852	−	0.884863i	$-0.654252\pi$
$71$	284.951	−	328.851i	0.476302	−	0.549682i	0.942154	+	0.335181i	$0.108797\pi$
$72$	−29.7506	+	136.761i	−0.0486964	+	0.223854i
$73$	−689.590	+	921.184i	−1.10562	+	1.47694i	−0.243730	+	0.969843i	$0.578371\pi$
$73$	−689.590	+	921.184i	−1.10562	+	1.47694i	−0.861891	+	0.507094i	$0.830720\pi$
$74$	−79.1290	−	173.268i	−0.124305	−	0.272190i
$75$	−190.426	−	335.043i	−0.293180	−	0.515833i
$76$	−88.0969	−	300.030i	−0.132966	−	0.452840i
$77$	−6.80761	+	1.48091i	−0.0100753	+	0.00219175i
$78$	−249.456	+	93.0422i	−0.362119	+	0.135063i
$79$	602.728	+	176.977i	0.858383	+	0.252044i	0.681167	−	0.732128i	$-0.261473\pi$
$79$	602.728	+	176.977i	0.858383	+	0.252044i	0.177216	+	0.984172i	$0.443291\pi$
$80$	−177.275	−	23.9491i	−0.247749	−	0.0334699i
$81$	32.3754	+	37.3631i	0.0444106	+	0.0512526i
$82$	459.976	−	251.166i	0.619462	−	0.338252i
$83$	372.104	+	997.649i	0.492093	+	1.31935i	0.911405	+	0.411510i	$0.134998\pi$
$83$	372.104	+	997.649i	0.492093	+	1.31935i	−0.419313	+	0.907842i	$0.637729\pi$
$84$	253.072	+	162.640i	0.328720	+	0.211255i
$85$	−984.536	+	222.971i	−1.25633	+	0.284525i
$86$	271.949	+	39.1003i	0.340988	+	0.0490267i
$87$	−645.053	−	240.592i	−0.794908	−	0.296485i
$88$	1.82906	+	1.36922i	0.00221566	+	0.00165862i
$89$	280.614	−	180.339i	0.334213	−	0.214786i	−0.362761	−	0.931882i	$-0.618166\pi$
$89$	280.614	−	180.339i	0.334213	−	0.214786i	0.696974	+	0.717097i	$0.254529\pi$
$90$	−274.254	+	278.966i	−0.321210	+	0.326729i
$91$		−	1053.30i		−	1.21336i
$92$	−228.179	−	377.632i	−0.258580	−	0.427944i
$93$	−643.833	−	643.833i	−0.717875	−	0.717875i
$94$	−745.496	−	645.976i	−0.818000	−	0.708801i
$95$	239.087	−	840.677i	0.258209	−	0.907912i
$96$	−14.0403	−	97.6525i	−0.0149269	−	0.103819i
$97$	190.616	−	511.060i	0.199527	−	0.534952i	−0.798196	−	0.602397i	$-0.794212\pi$
$97$	190.616	−	511.060i	0.199527	−	0.534952i	0.997723	+	0.0674458i	$0.0214850\pi$
$98$	−403.572	+	302.110i	−0.415989	+	0.311405i
$99$	4.79412	−	1.40768i	0.00486694	−	0.00142906i
$100$	−383.397	−	320.947i	−0.383397	−	0.320947i
$101$	−13.9212	+	30.4833i	−0.0137150	+	0.0300317i	−0.916366	−	0.400343i	$-0.868891\pi$
$101$	−13.9212	+	30.4833i	−0.0137150	+	0.0300317i	0.902651	+	0.430374i	$0.141618\pi$
$102$	−266.812	−	488.630i	−0.259003	−	0.474329i
$103$	−1452.77	−	103.904i	−1.38976	−	0.0993978i	−0.643702	−	0.765276i	$-0.722603\pi$
$103$	−1452.77	−	103.904i	−1.38976	−	0.0993978i	−0.746061	+	0.665878i	$0.768057\pi$
$104$	−261.059	+	226.209i	−0.246144	+	0.213285i
$105$	355.798	+	761.851i	0.330689	+	0.708086i
$106$	1189.79	+	543.361i	1.09022	+	0.497886i
$107$	−397.832	−	1828.81i	−0.359438	−	1.65231i	−0.701526	−	0.712644i	$-0.747498\pi$
$107$	−397.832	−	1828.81i	−0.359438	−	1.65231i	0.342088	−	0.939668i	$-0.388866\pi$
$108$	−481.596	−	262.972i	−0.429089	−	0.234300i
$109$	−69.2253	+	481.472i	−0.0608310	+	0.423089i	0.936536	+	0.350571i	$0.114013\pi$
$109$	−69.2253	+	481.472i	−0.0608310	+	0.423089i	−0.997367	+	0.0725178i	$0.976897\pi$
$110$	2.28261	+	5.96428i	0.00197853	+	0.00516974i
$111$	290.641	−	41.7879i	0.248526	−	0.0357327i
$112$	381.383	+	82.9647i	0.321761	+	0.0699949i
$113$	−38.7127	−	541.274i	−0.0322282	−	0.450609i	−0.987787	−	0.155809i	$-0.950202\pi$
$113$	−38.7127	−	541.274i	−0.0322282	−	0.450609i	0.955559	−	0.294800i	$-0.0952530\pi$
$114$	482.026			0.396016
$115$	23.6185	−	1233.01i	0.0191516	−	0.999817i
$116$	−893.229			−0.714950
$117$	53.8905	+	753.487i	0.0425827	+	0.595384i
$118$	1005.41	+	218.714i	0.784372	+	0.170630i
$119$	2180.10	−	313.451i	1.67941	−	0.241462i
$120$	112.412	−	251.801i	0.0855146	−	0.191552i
$121$	−189.409	+	1317.37i	−0.142306	+	0.989761i
$122$	757.470	+	413.610i	0.562116	+	0.306939i
$123$	171.727	+	789.417i	0.125887	+	0.578694i
$124$	−1074.58	−	490.743i	−0.778225	−	0.355403i
$125$	−427.862	−	1330.44i	−0.306153	−	0.951982i
$126$	645.063	−	558.951i	0.456086	−	0.395201i
$127$	221.749	+	15.8598i	0.154938	+	0.0110814i	0.148592	−	0.988899i	$-0.452526\pi$
$127$	221.749	+	15.8598i	0.154938	+	0.0110814i	0.00634509	+	0.999980i	$0.497980\pi$
$128$	−61.3439	−	112.343i	−0.0423600	−	0.0775766i
$129$	−175.938	+	385.250i	−0.120081	+	0.262941i
$130$	−954.475	+	145.540i	−0.643946	+	0.0981901i
$131$	1034.90	−	303.875i	0.690229	−	0.202669i	0.0822370	−	0.996613i	$-0.473794\pi$
$131$	1034.90	−	303.875i	0.690229	−	0.202669i	0.607992	+	0.793943i	$0.291975\pi$
$132$	−2.81951	+	2.11066i	−0.00185915	+	0.00139174i
$133$	−666.419	+	1786.74i	−0.434480	+	1.16489i
$134$	276.833	+	1925.41i	0.178468	+	1.24127i
$135$	−746.465	−	1339.79i	−0.475893	−	0.854157i
$136$	−545.891	−	473.017i	−0.344189	−	0.298242i
$137$	605.092	+	605.092i	0.377347	+	0.377347i	0.870144	−	0.492797i	$-0.164026\pi$
$137$	605.092	+	605.092i	0.377347	+	0.377347i	−0.492797	+	0.870144i	$0.664026\pi$
$138$	657.641	−	173.490i	0.405668	−	0.107018i
$139$		−	676.623i		−	0.412881i	−0.978459	−	0.206440i	$-0.933812\pi$
$139$		−	676.623i		−	0.412881i	0.978459	−	0.206440i	$-0.0661880\pi$
$140$	777.944	+	764.805i	0.469631	+	0.461699i
$141$	1279.21	−	822.096i	0.764033	−	0.491014i
$142$	696.683	+	521.530i	0.411720	+	0.308210i
$143$	11.5542	+	4.30950i	0.00675673	+	0.00252013i
$144$	−277.070	−	39.8367i	−0.160342	−	0.0230537i
$145$	−2111.73	−	1331.85i	−1.20945	−	0.762789i
$146$	−1936.06	−	1244.23i	−1.09746	−	0.705297i
$147$	−271.573	−	728.115i	−0.152374	−	0.408530i
$148$	334.364	−	182.576i	0.185706	−	0.101403i
$149$	1494.35	+	1724.57i	0.821623	+	0.948203i	0.999356	−	0.0358754i	$-0.0114220\pi$
$149$	1494.35	+	1724.57i	0.821623	+	0.948203i	−0.177733	+	0.984079i	$0.556877\pi$
$150$	641.209	−	427.685i	0.349030	−	0.232802i
$151$	785.417	+	230.619i	0.423287	+	0.124288i	0.486437	−	0.873716i	$-0.338296\pi$
$151$	785.417	+	230.619i	0.423287	+	0.124288i	−0.0631498	+	0.998004i	$0.520115\pi$
$152$	585.962	−	218.553i	0.312683	−	0.116625i
$153$	−1543.52	+	335.771i	−0.815594	+	0.177422i
$154$	−3.92556	−	13.3692i	−0.00205410	−	0.00699561i
$155$	−1808.75	−	2762.45i	−0.937303	−	1.43152i
$156$	−221.202	−	484.365i	−0.113528	−	0.248591i
$157$	−2065.82	+	2759.61i	−1.05013	+	1.40281i	−0.139191	+	0.990266i	$0.544450\pi$
$157$	−2065.82	+	2759.61i	−1.05013	+	1.40281i	−0.910938	+	0.412543i	$0.864641\pi$
$158$	−267.056	+	1227.64i	−0.134467	+	0.618136i
$159$	−1320.39	+	1523.81i	−0.658577	+	0.760038i
$160$	22.4829	−	357.064i	0.0111089	−	0.176427i
$161$	−266.135	+	2677.55i	−0.130275	+	1.31069i
$162$	−69.9166	+	69.9166i	−0.0339085	+	0.0339085i
$163$	−3702.89	+	264.836i	−1.77934	+	0.127261i	−0.921927	−	0.387364i	$-0.873386\pi$
$163$	−3702.89	+	264.836i	−1.77934	+	0.127261i	−0.857415	+	0.514625i	$0.827931\pi$
$164$	566.681	+	881.773i	0.269819	+	0.419847i
$165$	−9.81290	+	0.785887i	−0.00462990	+	0.000370795i
$166$	−1937.12	+	884.654i	−0.905722	+	0.413629i
$167$	1491.07	+	1991.83i	0.690911	+	0.922950i	0.999602	−	0.0282129i	$-0.00898163\pi$
$167$	1491.07	+	1991.83i	0.690911	+	0.922950i	−0.308690	+	0.951163i	$0.599891\pi$
$168$	−288.343	+	528.060i	−0.132417	+	0.242504i
$169$	179.813	−	279.794i	0.0818446	−	0.127353i
$170$	−585.278	−	1932.24i	−0.264052	−	0.871743i
$171$	385.313	−	1312.26i	0.172314	−	0.586846i
$172$	−39.2002	+	548.091i	−0.0173778	+	0.242974i
$173$	245.475	−	3432.18i	0.107879	−	1.50835i	−0.598849	−	0.800862i	$-0.704375\pi$
$173$	245.475	−	3432.18i	0.107879	−	1.50835i	0.706728	−	0.707486i	$-0.250171\pi$
$174$	387.924	−	1321.15i	0.169014	−	0.575608i
$175$	698.817	+	2968.08i	0.301861	+	1.28209i
$176$	−2.47049	+	3.84415i	−0.00105807	+	0.00164639i
$177$	−760.139	+	1392.09i	−0.322800	+	0.591163i
$178$	399.797	+	534.067i	0.168349	+	0.224888i
$179$	1760.22	−	803.863i	0.734998	−	0.335662i	−0.0125040	−	0.999922i	$-0.503980\pi$
$179$	1760.22	−	803.863i	0.734998	−	0.335662i	0.747502	+	0.664259i	$0.231253\pi$
$180$	−595.640	−	507.308i	−0.246647	−	0.210069i
$181$	793.617	+	1234.89i	0.325907	+	0.507120i	0.965085	−	0.261938i	$-0.0843617\pi$
$181$	793.617	+	1234.89i	0.325907	+	0.507120i	−0.639178	+	0.769059i	$0.720725\pi$
$182$	2101.23	−	150.283i	0.855789	−	0.0612072i
$183$	−940.723	+	940.723i	−0.380001	+	0.380001i
$184$	720.784	−	509.076i	0.288787	−	0.203965i
$185$	1062.72	+	66.9154i	0.422339	+	0.0265931i
$186$	1192.52	−	1376.25i	0.470108	−	0.542534i
$187$	−5.48131	+	25.1972i	−0.00214349	+	0.00985348i
$188$	1182.29	−	1579.36i	0.458657	−	0.612695i
$189$	1390.12	+	3043.93i	0.535005	+	1.17150i
$190$	1711.18	+	357.010i	0.653380	+	0.136317i
$191$	502.296	+	1710.66i	0.190287	+	0.648059i	0.998267	+	0.0588484i	$0.0187429\pi$
$191$	502.296	+	1710.66i	0.190287	+	0.648059i	−0.807980	+	0.589210i	$0.799439\pi$
$192$	192.804	−	41.9420i	0.0724711	−	0.0157651i
$193$	816.531	−	304.550i	0.304535	−	0.113586i	−0.192551	−	0.981287i	$-0.561676\pi$
$193$	816.531	−	304.550i	0.304535	−	0.113586i	0.497086	+	0.867701i	$0.334403\pi$
$194$	1046.71	+	307.343i	0.387369	+	0.113742i
$195$	199.259	−	1474.94i	0.0731754	−	0.541655i
$196$	−660.262	−	761.983i	−0.240620	−	0.277691i
$197$	−762.172	+	416.177i	−0.275647	+	0.150515i	−0.611127	−	0.791533i	$-0.709283\pi$
$197$	−762.172	+	416.177i	−0.275647	+	0.150515i	0.335480	+	0.942047i	$0.391102\pi$
$198$	3.49221	+	9.36297i	0.00125344	+	0.00336059i
$199$	245.057	+	157.489i	0.0872947	+	0.0561009i	0.583560	−	0.812070i	$-0.301659\pi$
$199$	245.057	+	157.489i	0.0872947	+	0.0561009i	−0.496265	+	0.868171i	$0.665296\pi$
$200$	585.555	−	810.632i	0.207025	−	0.286602i
$201$	−2968.04	−	426.740i	−1.04154	−	0.149751i
$202$	−62.7974	−	23.4222i	−0.0218733	−	0.00815833i
$203$	4360.81	+	3264.46i	1.50773	+	1.12867i
$204$	936.702	−	601.982i	0.321482	−	0.206604i
$205$	24.9512	+	2929.61i	0.00850081	+	0.998110i
$206$		−	2912.96i		−	0.985221i
$207$	53.3888	−	1929.03i	0.0179265	−	0.647714i
$208$	−488.512	−	488.512i	−0.162847	−	0.162847i
$209$	−16.8731	−	14.6206i	−0.00558439	−	0.00483890i
$210$	−1469.06	+	818.483i	−0.482736	+	0.268956i
$211$	470.499	+	3272.39i	0.153509	+	1.06768i	0.910278	+	0.413998i	$0.135868\pi$
$211$	470.499	+	3272.39i	0.153509	+	1.06768i	−0.756769	+	0.653683i	$0.773223\pi$
$212$	−914.195	+	2451.05i	−0.296166	+	0.794052i
$213$	−1073.94	+	803.944i	−0.345471	+	0.258617i
$214$	3591.53	−	1054.57i	1.14725	−	0.336864i
$215$	−909.910	+	1237.32i	−0.288629	+	0.392487i
$216$	455.890	−	998.259i	0.143608	−	0.314458i
$217$	3452.66	+	6323.08i	1.08010	+	1.97806i
$218$	−970.368	−	69.4021i	−0.301475	−	0.0215619i
$219$	2681.13	−	2323.21i	0.827277	−	0.716840i
$220$	−11.5725	+	5.40456i	−0.00354644	+	0.00165625i
$221$	−3546.29	−	1619.54i	−1.07941	−	0.492949i
$222$	124.831	+	573.839i	0.0377392	+	0.173484i
$223$	2687.16	+	1467.30i	0.806931	+	0.440618i	0.829075	−	0.559137i	$-0.188867\pi$
$223$	2687.16	+	1467.30i	0.806931	+	0.440618i	−0.0221440	+	0.999755i	$0.507049\pi$
$224$	−111.092	+	772.659i	−0.0331367	+	0.230471i
$225$	−651.763	−	2087.49i	−0.193115	−	0.618516i
$226$	1074.27	−	154.456i	0.316191	−	0.0454614i
$227$	−3637.19	−	791.222i	−1.06347	−	0.231345i	−0.353401	−	0.935472i	$-0.614975\pi$
$227$	−3637.19	−	791.222i	−1.06347	−	0.231345i	−0.710074	+	0.704127i	$0.751338\pi$
$228$	68.7746	+	961.595i	0.0199768	+	0.279312i
$229$	2302.79			0.664508			0.332254	−	0.943190i	$-0.392191\pi$
$229$	2302.79			0.664508			0.332254	+	0.943190i	$0.392191\pi$
$230$	2463.11	−	128.807i	0.706142	−	0.0369275i
$231$	21.4789			0.00611778
$232$	−127.444	−	1781.91i	−0.0360652	−	0.504258i
$233$	1790.21	+	389.437i	0.503351	+	0.109497i	0.457069	−	0.889431i	$-0.348899\pi$
$233$	1790.21	+	389.437i	0.503351	+	0.109497i	0.0462819	+	0.998928i	$0.485263\pi$
$234$	−1495.45	+	215.013i	−0.417779	+	0.0600676i
$235$	5150.04	−	1970.99i	1.42958	−	0.547120i
$236$	−292.864	+	2036.91i	−0.0807788	+	0.561829i
$237$	−1699.78	−	928.149i	−0.465875	−	0.254387i
$238$	936.357	+	4304.36i	0.255021	+	1.17231i
$239$	−1722.32	−	786.559i	−0.466142	−	0.212880i	0.168476	−	0.985706i	$-0.446115\pi$
$239$	−1722.32	−	786.559i	−0.466142	−	0.212880i	−0.634618	+	0.772826i	$0.718843\pi$
$240$	518.358	+	188.324i	0.139416	+	0.0506512i
$241$	3070.53	−	2660.63i	0.820705	−	0.711145i	−0.139566	−	0.990213i	$-0.544571\pi$
$241$	3070.53	−	2660.63i	0.820705	−	0.711145i	0.960271	+	0.279068i	$0.0900253\pi$
$242$	−2655.05	−	189.893i	−0.705262	−	0.0504413i
$243$	−1848.11	−	3384.55i	−0.487885	−	0.893494i
$244$	−717.038	+	1570.09i	−0.188130	+	0.411947i
$245$	−424.805	−	2785.94i	−0.110775	−	0.726477i
$246$	−1550.31	+	455.212i	−0.401805	+	0.117981i
$247$	2702.20	−	2022.84i	0.696101	−	0.521095i
$248$	825.666	−	2213.70i	0.211411	−	0.566814i
$249$	−467.184	−	3249.34i	−0.118902	−	0.826981i
$250$	2593.05	−	1043.37i	0.655994	−	0.263954i
$251$	214.047	+	185.473i	0.0538267	+	0.0466411i	0.681359	−	0.731950i	$-0.261389\pi$
$251$	214.047	+	185.473i	0.0538267	+	0.0466411i	−0.627532	+	0.778591i	$0.715935\pi$
$252$	1207.09	+	1207.09i	0.301744	+	0.301744i
$253$	−28.2827	−	13.8744i	−0.00702814	−	0.00344773i
$254$			444.632i			0.109837i
$255$	3112.10	−	26.5055i	0.764264	−	0.00650917i
$256$	215.361	−	138.404i	0.0525783	−	0.0337901i
$257$	4053.24	+	3034.22i	0.983791	+	0.736456i	0.964697	−	0.263361i	$-0.0848311\pi$
$257$	4053.24	+	3034.22i	0.983791	+	0.736456i	0.0190934	+	0.999818i	$0.493922\pi$
$258$	−793.640	−	296.012i	−0.191511	−	0.0714299i
$259$	−2299.65	−	330.639i	−0.551711	−	0.0793241i
$260$	−426.522	−	1883.32i	−0.101737	−	0.449225i
$261$	−3286.57	−	2112.15i	−0.779439	−	0.500915i
$262$	753.860	+	2021.18i	0.177762	+	0.476598i
$263$	−2705.25	+	1477.18i	−0.634270	+	0.346338i	−0.764004	−	0.645211i	$-0.776769\pi$
$263$	−2705.25	+	1477.18i	−0.634270	+	0.346338i	0.129734	+	0.991549i	$0.458588\pi$
$264$	−4.61285	−	5.32352i	−0.00107538	−	0.00124106i
$265$	−5815.96	+	4431.56i	−1.34820	+	1.02728i
$266$	−3659.45	−	1074.51i	−0.843517	−	0.247679i
$267$	−963.551	+	359.386i	−0.220855	+	0.0823748i
$268$	−3801.52	+	826.969i	−0.866472	+	0.188489i
$269$	−965.604	−	3288.55i	−0.218862	−	0.745376i	−0.993586	−	0.113077i	$-0.963929\pi$
$269$	−965.604	−	3288.55i	−0.218862	−	0.745376i	0.774724	−	0.632300i	$-0.217889\pi$
$270$	2566.26	−	1680.29i	0.578435	−	0.378737i
$271$	2373.22	+	5196.63i	0.531967	+	1.16484i	0.964707	+	0.263326i	$0.0848195\pi$
$271$	2373.22	+	5196.63i	0.531967	+	1.16484i	−0.432740	+	0.901519i	$0.642453\pi$
$272$	865.737	−	1156.49i	0.192989	−	0.257803i
$273$	−690.273	+	3173.13i	−0.153030	+	0.703468i
$274$	−1120.77	+	1293.43i	−0.247110	+	0.285180i
$275$	−35.4177	−	4.47799i	−0.00776643	−	0.000981937i
$276$	439.927	+	1287.18i	0.0959437	+	0.280721i
$277$	2184.22	−	2184.22i	0.473780	−	0.473780i	−0.429355	−	0.903136i	$-0.641259\pi$
$277$	2184.22	−	2184.22i	0.473780	−	0.473780i	0.903136	+	0.429355i	$0.141259\pi$
$278$	1349.80	−	96.5395i	0.291207	−	0.0208275i
$279$	−2793.41	−	4346.62i	−0.599415	−	0.932708i
$280$	−1414.72	+	1661.05i	−0.301948	+	0.354523i
$281$	−892.762	+	407.711i	−0.189529	+	0.0865551i	−0.507919	−	0.861405i	$-0.669585\pi$
$281$	−892.762	+	407.711i	−0.189529	+	0.0865551i	0.318390	+	0.947960i	$0.396858\pi$
$282$	1822.52	+	2434.60i	0.384856	+	0.514107i
$283$	−166.995	+	305.828i	−0.0350770	+	0.0642387i	−0.894630	−	0.446809i	$-0.852561\pi$
$283$	−166.995	+	305.828i	−0.0350770	+	0.0642387i	0.859553	+	0.511047i	$0.170742\pi$
$284$	−941.001	+	1464.23i	−0.196613	+	0.305936i
$285$	−1271.20	+	2375.91i	−0.264208	+	0.493813i
$286$	−6.94851	+	23.6644i	−0.00143662	+	0.00489269i
$287$	456.015	−	6375.92i	0.0937899	−	1.31135i
$288$	39.9385	−	558.413i	0.00817152	−	0.114253i
$289$	912.595	−	3108.01i	0.185751	−	0.632610i
$290$	2355.62	−	4402.74i	0.476989	−	0.891509i
$291$	−909.162	+	1414.68i	−0.183148	+	0.284984i
$292$	2205.89	−	4039.79i	0.442089	−	0.809625i
$293$	−3457.23	−	4618.32i	−0.689329	−	0.920836i	0.310226	−	0.950663i	$-0.399595\pi$
$293$	−3457.23	−	4618.32i	−0.689329	−	0.920836i	−0.999555	+	0.0298267i	$0.990504\pi$
$294$	1413.77	−	645.648i	0.280452	−	0.128078i
$295$	−3729.53	+	4378.91i	−0.736072	+	0.864236i
$296$	411.929	+	640.974i	0.0808881	+	0.125864i
$297$	−39.0781	+	2.79492i	−0.00763482	+	0.000546053i
$298$	−3227.14	+	3227.14i	−0.627326	+	0.627326i
$299$	2958.63	−	3732.39i	0.572248	−	0.721906i
$300$	944.678	+	1218.13i	0.181803	+	0.234429i
$301$	2194.47	−	2532.56i	0.420224	−	0.484964i
$302$	−348.001	+	1599.74i	−0.0663087	+	0.304816i
$303$	61.9156	−	82.7096i	0.0117391	−	0.0156817i
$304$	519.596	+	1137.76i	0.0980292	+	0.214654i
$305$	−4036.29	+	2642.81i	−0.757762	+	0.496153i
$306$	−890.058	−	3031.26i	−0.166279	−	0.566293i
$307$	−5968.35	+	1298.34i	−1.10955	+	0.241368i	−0.729759	−	0.683704i	$-0.760368\pi$
$307$	−5968.35	+	1298.34i	−1.10955	+	0.241368i	−0.379791	+	0.925072i	$0.624004\pi$
$308$	26.1103	−	9.73863i	0.00483042	−	0.00180166i
$309$	4308.47	+	1265.08i	0.793205	+	0.232906i
$310$	5252.75	−	4002.42i	0.962375	−	0.733297i
$311$	−1040.75	−	1201.09i	−0.189761	−	0.218996i	0.652895	−	0.757449i	$-0.273554\pi$
$311$	−1040.75	−	1201.09i	−0.189761	−	0.218996i	−0.842655	+	0.538453i	$0.819009\pi$
$312$	934.701	−	510.386i	0.169606	−	0.0926118i
$313$	−1948.53	−	5224.22i	−0.351877	−	0.943419i	−0.985485	−	0.169765i	$-0.945699\pi$
$313$	−1948.53	−	5224.22i	−0.351877	−	0.943419i	0.633607	−	0.773655i	$-0.281573\pi$
$314$	−5799.91	−	3727.37i	−1.04238	−	0.669898i
$315$	1053.91	+	4653.59i	0.188512	+	0.832381i
$316$	−2487.12	−	357.594i	−0.442758	−	0.0636589i
$317$	1338.05	+	499.067i	0.237074	+	0.0884239i	0.465193	−	0.885209i	$-0.345985\pi$
$317$	1338.05	+	499.067i	0.237074	+	0.0884239i	−0.228119	+	0.973633i	$0.573258\pi$
$318$	−3228.25	−	2416.64i	−0.569280	−	0.426158i
$319$	−53.6517	+	34.4799i	−0.00941667	+	0.00605173i
$320$	715.516	−	6.09398i	0.124995	−	0.00106457i
$321$			5770.11i			1.00329i
$322$	−5379.43	−	148.884i	−0.931007	−	0.0257670i
$323$	4990.99	+	4990.99i	0.859771	+	0.859771i
$324$	−149.453	−	129.501i	−0.0256263	−	0.0222053i
$325$	1799.77	−	5088.44i	0.307180	−	0.868479i
$326$	−1056.64	−	7349.13i	−0.179516	−	1.24856i
$327$	524.075	−	1405.10i	0.0886282	−	0.237622i
$328$	−1678.20	+	1256.28i	−0.282509	+	0.211484i
$329$	−11544.1	+	3389.65i	−1.93449	+	0.568017i
$330$	−2.96786	−	19.4637i	−0.000495076	−	0.00324679i
$331$	206.472	−	452.111i	0.0342863	−	0.0750764i	−0.891714	−	0.452599i	$-0.850497\pi$
$331$	206.472	−	452.111i	0.0342863	−	0.0750764i	0.926000	+	0.377523i	$0.123224\pi$
$332$	−2041.19	−	3738.15i	−0.337424	−	0.617945i
$333$	1661.99	+	118.868i	0.273503	+	0.0195613i
$334$	−3760.77	+	3258.73i	−0.616109	+	0.533861i
$335$	−10220.4	−	3713.19i	−1.66687	−	0.605591i
$336$	−1094.57	−	499.873i	−0.177719	−	0.0811617i
$337$	2131.58	+	9798.74i	0.344554	+	1.58389i	0.744674	+	0.667428i	$0.232605\pi$
$337$	2131.58	+	9798.74i	0.344554	+	1.58389i	−0.400120	+	0.916463i	$0.631032\pi$
$338$	583.817	+	318.788i	0.0939511	+	0.0513012i
$339$	−238.096	+	1655.99i	−0.0381463	+	0.265314i
$340$	3771.13	−	1443.26i	0.601525	−	0.230212i
$341$	−83.4877	+	12.0037i	−0.0132584	+	0.00190627i
$342$	2672.80	+	581.432i	0.422598	+	0.0919306i
$343$	−158.254	−	2212.68i	−0.0249123	−	0.348319i
$344$	−1098.98			−0.172247
$345$	−879.198	+	3699.05i	−0.137201	+	0.577247i
$346$	6881.90			1.06929
$347$	−221.630	−	3098.79i	−0.0342873	−	0.479399i	−0.985366	−	0.170451i	$-0.945478\pi$
$347$	−221.630	−	3098.79i	−0.0342873	−	0.479399i	0.951079	−	0.308948i	$-0.0999770\pi$
$348$	2690.91	+	585.371i	0.414505	+	0.0901701i
$349$	−6522.72	+	937.826i	−1.00044	+	0.143841i	−0.623024	−	0.782203i	$-0.714096\pi$
$349$	−6522.72	+	937.826i	−1.00044	+	0.143841i	−0.377415	+	0.926044i	$0.623187\pi$
$350$	−5821.33	+	1817.55i	−0.889037	+	0.277578i
$351$	842.963	−	5862.93i	0.128188	−	0.891568i
$352$	−8.02121	−	4.37991i	−0.00121458	−	0.000663210i
$353$	−323.663	−	1487.85i	−0.0488012	−	0.224336i	0.946287	−	0.323328i	$-0.104802\pi$
$353$	−323.663	−	1487.85i	−0.0488012	−	0.224336i	−0.995088	+	0.0989923i	$0.968438\pi$
$354$	−2885.54	−	1317.78i	−0.433234	−	0.197851i
$355$	−4407.92	+	2058.58i	−0.659009	+	0.307769i
$356$	−1008.37	+	873.757i	−0.150122	+	0.130082i
$357$	−6773.11	−	484.422i	−1.00412	−	0.0718161i
$358$	1854.78	+	3396.77i	0.273821	+	0.501466i
$359$	−1126.01	+	2465.62i	−0.165539	+	0.362480i	−0.974163	−	0.225846i	$-0.927485\pi$
$359$	−1126.01	+	2465.62i	−0.165539	+	0.362480i	0.808624	+	0.588326i	$0.200213\pi$
$360$	927.046	−	1260.63i	0.135721	−	0.184558i
$361$	717.504	−	210.678i	0.104608	−	0.0307156i
$362$	−2350.26	+	1759.38i	−0.341234	+	0.255445i
$363$	1433.94	−	3844.54i	0.207334	−	0.555884i
$364$	599.600	+	4170.31i	0.0863395	+	0.600505i
$365$	11238.6	−	6261.59i	1.61166	−	0.897936i
$366$	−2010.87	−	1742.43i	−0.287186	−	0.248848i
$367$	3439.06	+	3439.06i	0.489148	+	0.489148i	0.908037	−	0.418889i	$-0.137581\pi$
$367$	3439.06	+	3439.06i	0.489148	+	0.489148i	−0.418889	+	0.908037i	$0.637581\pi$
$368$	1118.40	+	1365.26i	0.158425	+	0.193394i
$369$			4584.41i			0.646761i
$370$	18.1374	+	2129.57i	0.00254843	+	0.299220i
$371$	13421.0	−	8625.14i	1.87812	−	1.20699i
$372$	2915.63	+	2182.61i	0.406366	+	0.304202i
$373$	−3133.38	−	1168.69i	−0.434961	−	0.162232i	0.122439	−	0.992476i	$-0.460928\pi$
$373$	−3133.38	−	1168.69i	−0.434961	−	0.162232i	−0.557400	+	0.830244i	$0.688201\pi$
$374$	−51.0480	−	7.33960i	−0.00705784	−	0.00101476i
$375$	417.070	+	4288.42i	0.0574330	+	0.590542i
$376$	3319.36	+	2133.22i	0.455273	+	0.292586i
$377$	−3369.58	−	9034.19i	−0.460324	−	1.23418i
$378$	−5874.01	+	3207.45i	−0.799276	+	0.436438i
$379$	−3391.04	−	3913.46i	−0.459593	−	0.530399i	0.477894	−	0.878417i	$-0.341400\pi$
$379$	−3391.04	−	3913.46i	−0.459593	−	0.530399i	−0.937488	+	0.348018i	$0.886855\pi$
$380$	−468.051	+	3464.58i	−0.0631856	+	0.467709i
$381$	−657.641	−	193.101i	−0.0884303	−	0.0259655i
$382$	−3340.94	+	1246.11i	−0.447480	+	0.166901i
$383$	1539.58	−	334.916i	0.205402	−	0.0446825i	−0.108687	−	0.994076i	$-0.534665\pi$
$383$	1539.58	−	334.916i	0.205402	−	0.0446825i	0.314089	+	0.949394i	$0.398301\pi$
$384$	111.179	+	378.642i	0.0147750	+	0.0503189i
$385$	76.2497	+	15.9082i	0.0100936	+	0.00210586i
$386$	724.050	+	1585.45i	0.0954745	+	0.209060i
$387$	−1440.26	+	1923.97i	−0.189180	+	0.252715i
$388$	−463.776	+	2131.94i	−0.0606821	+	0.278951i
$389$	5829.56	−	6727.67i	0.759821	−	0.876880i	−0.235661	−	0.971835i	$-0.575725\pi$
$389$	5829.56	−	6727.67i	0.759821	−	0.876880i	0.995482	+	0.0949553i	$0.0302708\pi$
$390$	2970.80	+	187.060i	0.385723	+	0.0242875i
$391$	8605.69	+	5013.00i	1.11307	+	0.648384i
$392$	1425.88	−	1425.88i	0.183719	−	0.183719i
$393$	−3316.86	+	237.226i	−0.425734	+	0.0304491i
$394$	−938.979	−	1461.08i	−0.120064	−	0.186823i
$395$	−5346.75	−	4553.84i	−0.681074	−	0.580073i
$396$	−18.1800	+	8.30251i	−0.00230701	+	0.00105358i
$397$	1256.08	+	1677.93i	0.158794	+	0.212123i	0.872881	−	0.487933i	$-0.162249\pi$
$397$	1256.08	+	1677.93i	0.158794	+	0.212123i	−0.714087	+	0.700057i	$0.753158\pi$
$398$	−279.210	+	511.336i	−0.0351647	+	0.0643994i
$399$	3178.56	−	4945.93i	0.398814	−	0.620567i
$400$	1700.68	+	1052.47i	0.212585	+	0.131558i
$401$	−3693.15	+	12577.7i	−0.459917	+	1.56633i	0.324366	+	0.945932i	$0.394849\pi$
$401$	−3693.15	+	12577.7i	−0.459917	+	1.56633i	−0.784283	+	0.620403i	$0.786969\pi$
$402$	427.830	−	5981.85i	0.0530802	−	0.742158i
$403$	909.726	−	12719.6i	0.112448	−	1.57223i
$404$	37.7653	−	128.617i	0.00465073	−	0.0158389i
$405$	−160.236	−	529.004i	−0.0196597	−	0.0649048i
$406$	−5890.10	+	9165.17i	−0.720002	+	1.12034i
$407$	13.0358	−	23.8733i	0.00158762	−	0.00290751i
$408$	1334.54	+	1782.74i	0.161936	+	0.216321i
$409$	5654.80	−	2582.46i	0.683648	−	0.312211i	−0.0431445	−	0.999069i	$-0.513738\pi$
$409$	5654.80	−	2582.46i	0.683648	−	0.312211i	0.726792	+	0.686857i	$0.241010\pi$
$410$	−5840.72	+	467.767i	−0.703543	+	0.0563447i
$411$	−1426.34	−	2219.42i	−0.171182	−	0.266365i
$412$	5811.08	−	415.616i	0.694882	−	0.0496989i
$413$	8874.04	−	8874.04i	1.05729	−	1.05729i
$414$	3855.85	−	168.725i	0.457740	−	0.0200299i
$415$	748.108	−	11881.1i	0.0884896	−	1.40535i
$416$	904.835	−	1044.24i	0.106642	−	0.123072i
$417$	−443.421	+	2038.37i	−0.0520729	+	0.239375i
$418$	26.7593	−	35.7463i	0.00313120	−	0.00418280i
$419$	3059.47	+	6699.30i	0.356718	+	0.781103i	0.999882	+	0.0153743i	$0.00489400\pi$
$419$	3059.47	+	6699.30i	0.356718	+	0.781103i	−0.643164	+	0.765728i	$0.722379\pi$
$420$	−1842.40	−	2813.85i	−0.214047	−	0.326909i
$421$	3539.40	+	12054.1i	0.409739	+	1.39544i	0.863514	+	0.504326i	$0.168259\pi$
$421$	3539.40	+	12054.1i	0.409739	+	1.39544i	−0.453775	+	0.891116i	$0.649923\pi$
$422$	−6460.98	+	1405.50i	−0.745297	+	0.162129i
$423$	8084.75	−	3015.46i	0.929301	−	0.346611i
$424$	−5020.05	−	1474.02i	−0.574989	−	0.168832i
$425$	11067.5	+	2210.87i	1.26319	+	0.252336i
$426$	−1757.02	−	2027.71i	−0.199831	−	0.230617i
$427$	9238.83	−	5044.78i	1.04707	−	0.571743i
$428$	2616.20	+	7014.30i	0.295464	+	0.792170i
$429$	−31.9837	−	20.5546i	−0.00359950	−	0.00231326i
$430$	−2598.17	−	1638.64i	−0.291383	−	0.183773i
$431$	−3573.12	−	513.738i	−0.399330	−	0.0574150i	−0.0602758	−	0.998182i	$-0.519198\pi$
$431$	−3573.12	−	513.738i	−0.399330	−	0.0574150i	−0.339054	+	0.940767i	$0.610107\pi$
$432$	2056.48	+	767.026i	0.229033	+	0.0854249i
$433$	−2815.17	−	2107.41i	−0.312445	−	0.233893i	0.431534	−	0.902097i	$-0.357973\pi$
$433$	−2815.17	−	2107.41i	−0.312445	−	0.233893i	−0.743978	+	0.668204i	$0.767063\pi$
$434$	−12121.3	+	7789.90i	−1.34065	+	0.861583i
$435$	5488.92	+	5396.21i	0.604996	+	0.594778i
$436$		−	1945.69i		−	0.213720i
$437$	−7380.28	+	4459.44i	−0.807887	+	0.488155i
$438$	5017.12	+	5017.12i	0.547322	+	0.547322i
$439$	−3372.24	−	2922.06i	−0.366625	−	0.317682i	0.451992	−	0.892022i	$-0.350713\pi$
$439$	−3372.24	−	2922.06i	−0.366625	−	0.317682i	−0.818617	+	0.574340i	$0.805259\pi$
$440$	−12.4327	−	22.3149i	−0.00134706	−	0.00241777i
$441$	−627.582	−	4364.93i	−0.0677662	−	0.471324i
$442$	2724.84	−	7305.58i	0.293230	−	0.786179i
$443$	−2114.18	+	1582.65i	−0.226744	+	0.169739i	−0.706610	−	0.707603i	$-0.749776\pi$
$443$	−2114.18	+	1582.65i	−0.226744	+	0.169739i	0.479866	+	0.877342i	$0.340685\pi$
$444$	−1126.94	+	330.900i	−0.120456	+	0.0353690i
$445$	−3686.77	+	562.166i	−0.392741	+	0.0598858i
$446$	−2543.73	+	5569.98i	−0.270065	+	0.591359i
$447$	−3371.64	−	6174.69i	−0.356763	−	0.653362i
$448$	−1557.23	−	111.375i	−0.164224	−	0.0117455i
$449$	−4000.78	+	3466.69i	−0.420509	+	0.364373i	−0.839262	−	0.543727i	$-0.817013\pi$
$449$	−4000.78	+	3466.69i	−0.420509	+	0.364373i	0.418753	+	0.908100i	$0.362467\pi$
$450$	4071.35	−	1598.04i	0.426501	−	0.167406i
$451$	68.0753	+	31.0890i	0.00710763	+	0.00324595i
$452$	461.400	+	2121.02i	0.0480143	+	0.220718i
$453$	−2214.99	−	1209.47i	−0.229733	−	0.125444i
$454$	1059.46	−	7368.74i	0.109522	−	0.761744i
$455$	−4800.62	+	10753.3i	−0.494630	+	1.10796i
$456$	−1908.48	+	274.398i	−0.195993	+	0.0281795i
$457$	−11484.0	−	2498.19i	−1.17549	−	0.255712i	−0.417930	−	0.908479i	$-0.637244\pi$
$457$	−11484.0	−	2498.19i	−1.17549	−	0.255712i	−0.757558	+	0.652768i	$0.773608\pi$
$458$	328.558	+	4593.84i	0.0335207	+	0.468681i
$459$	12385.8			1.25952
$460$	608.391	+	4895.29i	0.0616660	+	0.496183i
$461$	7479.92			0.755693			0.377846	−	0.925868i	$-0.376665\pi$
$461$	7479.92			0.755693			0.377846	+	0.925868i	$0.376665\pi$
$462$	3.06457	+	42.8483i	0.000308608	+	0.00431490i
$463$	10673.2	+	2321.80i	1.07132	+	0.233052i	0.713442	−	0.700714i	$-0.247135\pi$
$463$	10673.2	+	2321.80i	1.07132	+	0.233052i	0.357883	+	0.933767i	$0.383499\pi$
$464$	3536.55	−	508.479i	0.353836	−	0.0508740i
$465$	3638.61	+	9507.41i	0.362874	+	0.948163i
$466$	−521.465	+	3626.87i	−0.0518378	+	0.360540i
$467$	−12700.6	−	6935.03i	−1.25848	−	0.687184i	−0.295139	−	0.955454i	$-0.595366\pi$
$467$	−12700.6	−	6935.03i	−1.25848	−	0.687184i	−0.963344	+	0.268271i	$0.913548\pi$
$468$	−642.297	−	2952.59i	−0.0634406	−	0.291632i
$469$	21581.6	+	9855.99i	2.12483	+	0.970378i
$470$	4666.74	+	9992.63i	0.458001	+	0.980692i
$471$	8031.91	−	6959.69i	0.785755	−	0.680861i
$472$	−4105.23	−	293.612i	−0.400336	−	0.0286326i
$473$	18.8025	+	34.4342i	0.00182778	+	0.00334733i
$474$	1609.05	−	3523.32i	0.155920	−	0.341417i
$475$	−6272.44	+	7492.94i	−0.605893	+	0.723789i
$476$	−8453.20	+	2482.08i	−0.813974	+	0.239004i
$477$	−9159.54	+	6856.74i	−0.879217	+	0.658173i
$478$	1323.37	−	3548.10i	0.126631	−	0.339511i
$479$	−803.997	−	5591.92i	−0.0766922	−	0.533406i	−0.991560	−	0.129652i	$-0.958614\pi$
$479$	−803.997	−	5591.92i	−0.0766922	−	0.533406i	0.914867	−	0.403754i	$-0.132295\pi$
$480$	−301.731	+	1060.94i	−0.0286918	+	0.100886i
$481$	3107.93	+	2693.04i	0.294615	+	0.255285i
$482$	5745.79	+	5745.79i	0.542974	+	0.542974i
$483$	2556.46	−	7891.89i	0.240835	−	0.743465i
$484$		−	5323.67i		−	0.499969i
$485$	−4275.29	+	4348.74i	−0.400270	+	0.407146i
$486$	6488.17	−	4169.70i	0.605575	−	0.389179i
$487$	−946.010	−	708.174i	−0.0880242	−	0.0658941i	0.554359	−	0.832278i	$-0.312963\pi$
$487$	−946.010	−	708.174i	−0.0880242	−	0.0658941i	−0.642383	+	0.766383i	$0.722054\pi$
$488$	−3234.49	−	1206.40i	−0.300038	−	0.111908i
$489$	11328.8	+	1628.83i	1.04766	+	0.150630i
$490$	5497.07	−	1244.94i	0.506800	−	0.114777i
$491$	−3345.49	−	2150.02i	−0.307495	−	0.197615i	0.377788	−	0.925892i	$-0.376685\pi$
$491$	−3345.49	−	2150.02i	−0.307495	−	0.197615i	−0.685283	+	0.728277i	$0.740321\pi$
$492$	−1129.30	−	3027.77i	−0.103481	−	0.277444i
$493$	17696.1	−	9662.77i	1.61661	−	0.882737i
$494$	4420.92	+	5102.02i	0.402645	+	0.464677i
$495$	−55.3599	−	7.47889i	−0.00502675	−	0.000679093i
$496$	4533.92	+	1331.28i	0.410441	+	0.120516i
$497$	9945.32	−	3709.41i	0.897603	−	0.334788i
$498$	6415.46	−	1395.60i	0.577276	−	0.125579i
$499$	1818.64	+	6193.71i	0.163153	+	0.555649i	0.999967	+	0.00816069i	$0.00259766\pi$
$499$	1818.64	+	6193.71i	0.163153	+	0.555649i	−0.836814	+	0.547488i	$0.815584\pi$
$500$	2451.39	+	5024.01i	0.219259	+	0.449361i
$501$	−3186.60	−	6977.68i	−0.284165	−	0.622235i
$502$	−339.460	+	453.466i	−0.0301810	+	0.0403171i
$503$	2107.09	−	9686.12i	0.186780	−	0.858614i	−0.784398	−	0.620258i	$-0.787028\pi$
$503$	2107.09	−	9686.12i	0.186780	−	0.858614i	0.971178	−	0.238356i	$-0.0766085\pi$
$504$	−2235.80	+	2580.25i	−0.197600	+	0.228043i
$505$	281.058	−	247.760i	0.0247662	−	0.0218321i
$506$	23.6428	−	58.4009i	0.00207717	−	0.00513090i
$507$	−725.058	+	725.058i	−0.0635127	+	0.0635127i
$508$	−886.997	+	63.4393i	−0.0774688	+	0.00554068i
$509$	−11046.9	−	17189.4i	−0.961977	−	1.49687i	−0.865118	−	0.501568i	$-0.832757\pi$
$509$	−11046.9	−	17189.4i	−0.961977	−	1.49687i	−0.0968591	−	0.995298i	$-0.530880\pi$
$510$	496.906	+	6204.57i	0.0431438	+	0.538711i
$511$	−25533.4	+	11660.7i	−2.21044	+	1.00947i
$512$	306.830	+	409.877i	0.0264846	+	0.0353793i
$513$	−5139.40	+	9412.10i	−0.442320	+	0.810048i
$514$	−5474.66	+	8518.74i	−0.469800	+	0.731023i
$515$	14358.0	+	7682.06i	1.22852	+	0.657305i
$516$	477.281	−	1625.47i	0.0407192	−	0.138677i
$517$	10.0489	−	140.502i	0.000854837	−	0.0119522i
$518$	331.484	−	4634.75i	0.0281169	−	0.393126i
$519$	−2988.77	+	10178.8i	−0.252779	+	0.860887i
$520$	3696.19	−	1119.58i	0.311709	−	0.0944169i
$521$	6960.66	−	10831.0i	0.585321	−	0.910777i	−0.414679	−	0.909968i	$-0.636106\pi$
$521$	6960.66	−	10831.0i	0.585321	−	0.910777i	1.00000		0.000809106i	$-0.000257546\pi$
$522$	3744.61	−	6857.75i	0.313980	−	0.575011i
$523$	357.371	+	477.392i	0.0298791	+	0.0399138i	0.815232	−	0.579135i	$-0.196609\pi$
$523$	357.371	+	477.392i	0.0298791	+	0.0399138i	−0.785353	+	0.619048i	$0.787519\pi$
$524$	−3924.50	+	1792.26i	−0.327180	+	0.149418i
$525$	−160.121	−	9399.50i	−0.0133110	−	0.781386i
$526$	−3332.81	−	5185.96i	−0.276269	−	0.429883i
$527$	26597.6	−	1902.30i	2.19850	−	0.157240i
$528$	9.96175	−	9.96175i	0.000821079	−	0.000821079i
$529$	−8464.09	+	8740.43i	−0.695659	+	0.718372i
$530$	−9670.36	−	10970.0i	−0.792554	−	0.899069i
$531$	−5894.10	+	6802.15i	−0.481699	+	0.555910i
$532$	1621.43	−	7453.57i	0.132139	−	0.607431i
$533$	−6780.61	+	9057.83i	−0.551033	+	0.736094i
$534$	−854.419	−	1870.92i	−0.0692403	−	0.151615i
$535$	−4273.60	+	20483.8i	−0.345353	+	1.65531i
$536$	−2192.12	−	7465.67i	−0.176651	−	0.601619i
$537$	−5829.57	+	1268.15i	−0.468463	+	0.101908i
$538$	6422.56	−	2395.49i	0.514677	−	0.191965i
$539$	−69.0722	−	20.2814i	−0.00551976	−	0.00162075i
$540$	3718.16	+	4879.70i	0.296304	+	0.388868i
$541$	−7936.33	−	9159.01i	−0.630701	−	0.727868i	0.347001	−	0.937865i	$-0.387200\pi$
$541$	−7936.33	−	9159.01i	−0.630701	−	0.727868i	−0.977702	+	0.209997i	$0.932655\pi$
$542$	−10028.2	+	5475.80i	−0.794736	+	0.433959i
$543$	−1581.54	−	4240.28i	−0.124992	−	0.335116i
$544$	2430.61	+	1562.06i	0.191565	+	0.123111i
$545$	2901.14	−	4599.93i	0.228020	−	0.361540i
$546$	−6428.58	−	924.290i	−0.503879	−	0.0724468i
$547$	16725.6	+	6238.33i	1.30738	+	0.487627i	0.904049	−	0.427429i	$-0.140581\pi$
$547$	16725.6	+	6238.33i	1.30738	+	0.487627i	0.403328	+	0.915055i	$0.367853\pi$
$548$	−2740.19	−	2051.28i	−0.213604	−	0.159902i
$549$	−6350.97	+	4081.52i	−0.493721	+	0.317295i
$550$	3.87981	−	71.2938i	0.000300792	−	0.00552723i
$551$			17456.9i			1.34970i
$552$	−2505.03	+	1061.26i	−0.193154	+	0.0818304i
$553$	10835.4	+	10835.4i	0.833217	+	0.833217i
$554$	4668.95	+	4045.67i	0.358059	+	0.310260i
$555$	−3157.66	−	898.034i	−0.241505	−	0.0686836i
$556$	385.174	+	2678.94i	0.0293795	+	0.204339i
$557$	−3516.67	+	9428.57i	−0.267516	+	0.717237i	0.731844	+	0.681472i	$0.238660\pi$
$557$	−3516.67	+	9428.57i	−0.267516	+	0.717237i	−0.999360	+	0.0357658i	$0.988613\pi$
$558$	8272.54	−	6192.75i	0.627607	−	0.469821i
$559$	−5691.32	+	1671.12i	−0.430621	+	0.126442i
$560$	−3515.48	−	2585.23i	−0.265279	−	0.195082i
$561$	33.0256	−	72.3160i	0.00248546	−	0.00544240i
$562$	−940.722	−	1722.80i	−0.0706084	−	0.129310i
$563$	795.416	+	56.8893i	0.0595432	+	0.00425861i	0.101079	−	0.994878i	$-0.467771\pi$
$563$	795.416	+	56.8893i	0.0595432	+	0.00425861i	−0.0415358	+	0.999137i	$0.513225\pi$
$564$	−4596.76	+	3983.11i	−0.343189	+	0.297375i
$565$	−2071.74	+	5702.41i	−0.154263	+	0.424606i
$566$	−633.923	−	289.503i	−0.0470774	−	0.0214995i
$567$	256.353	+	1178.44i	0.0189874	+	0.0872834i
$568$	−3055.25	−	1668.29i	−0.225696	−	0.123240i
$569$	−316.241	+	2199.50i	−0.0232996	+	0.162053i	−0.998149	−	0.0608109i	$-0.980631\pi$
$569$	−316.241	+	2199.50i	−0.0232996	+	0.162053i	0.974850	+	0.222864i	$0.0715404\pi$
$570$	−4921.09	−	2196.93i	−0.361617	−	0.161437i
$571$	8079.05	−	1161.59i	0.592115	−	0.0851333i	0.160258	−	0.987075i	$-0.448768\pi$
$571$	8079.05	−	1161.59i	0.592115	−	0.0851333i	0.431857	+	0.901942i	$0.357858\pi$
$572$	−48.1997	−	10.4852i	−0.00352331	−	0.000766448i
$573$	−392.128	−	5482.66i	−0.0285888	−	0.399723i
$574$	12784.4			0.929636
$575$	−5860.82	+	12480.4i	−0.425066	+	0.905162i
$576$	1119.68			0.0809953
$577$	−1899.23	−	26554.7i	−0.137029	−	1.91592i	−0.346409	−	0.938084i	$-0.612599\pi$
$577$	−1899.23	−	26554.7i	−0.137029	−	1.91592i	0.209379	−	0.977834i	$-0.432856\pi$
$578$	6330.40	+	1377.09i	0.455553	+	0.0990995i
$579$	−2659.44	+	382.369i	−0.190885	+	0.0274451i
$580$	9119.13	+	4071.07i	0.652847	+	0.291451i
$581$	−3696.52	+	25709.8i	−0.263954	+	1.83584i
$582$	−2951.88	−	1611.85i	−0.210239	−	0.114799i
$583$	39.7029	+	182.512i	0.00282046	+	0.0129654i
$584$	8373.72	+	3824.15i	0.593334	+	0.270966i
$585$	2883.99	−	7938.10i	0.203826	−	0.561026i
$586$	8719.83	−	7555.78i	0.614698	−	0.532639i
$587$	−11877.9	−	849.527i	−0.835188	−	0.0597338i	−0.352808	−	0.935696i	$-0.614773\pi$
$587$	−11877.9	−	849.527i	−0.835188	−	0.0597338i	−0.482380	+	0.875962i	$0.660228\pi$
$588$	1489.72	+	2728.22i	0.104481	+	0.191343i
$589$	−9590.86	+	21001.1i	−0.670941	+	1.46916i
$590$	−9267.62	−	6815.27i	−0.646681	−	0.475560i
$591$	2568.83	−	754.277i	0.178795	−	0.0524988i
$592$	−1219.91	+	913.212i	−0.0846924	+	0.0633999i
$593$	−140.815	+	377.539i	−0.00975137	+	0.0261444i	−0.941734	−	0.336358i	$-0.890805\pi$
$593$	−140.815	+	377.539i	−0.00975137	+	0.0261444i	0.931983	+	0.362502i	$0.118078\pi$
$594$	−11.1512	−	77.5583i	−0.000770268	−	0.00535733i
$595$	−23685.6	−	6736.15i	−1.63196	−	0.464127i
$596$	−6898.28	−	5977.39i	−0.474102	−	0.410811i
$597$	−635.041	−	635.041i	−0.0435352	−	0.0435352i
$598$	7867.90	+	5369.66i	0.538031	+	0.367193i
$599$		−	23242.3i		−	1.58540i	−0.609614	−	0.792698i	$-0.708676\pi$
$599$		−	23242.3i		−	1.58540i	0.609614	−	0.792698i	$-0.291324\pi$
$600$	−2295.27	+	2058.34i	−0.156173	+	0.140052i
$601$	−13166.3	+	8461.45i	−0.893617	+	0.574293i	−0.904891	−	0.425644i	$-0.860048\pi$
$601$	−13166.3	+	8461.45i	−0.893617	+	0.574293i	0.0112741	+	0.999936i	$0.496411\pi$
$602$	5365.31	+	4016.42i	0.363246	+	0.271922i
$603$	−15942.9	−	5946.38i	−1.07669	−	0.401585i
$604$	−3240.97	−	465.982i	−0.218333	−	0.0313916i
$605$	7937.90	−	12586.0i	0.533424	−	0.845776i
$606$	173.832	+	111.715i	0.0116525	+	0.00748863i
$607$	−8319.07	−	22304.3i	−0.556278	−	1.49144i	−0.845393	−	0.534144i	$-0.820634\pi$
$607$	−8319.07	−	22304.3i	−0.556278	−	1.49144i	0.289115	−	0.957294i	$-0.406639\pi$
$608$	−2195.58	+	1198.88i	−0.146451	+	0.0799686i
$609$	−10997.9	−	12692.2i	−0.731785	−	0.844524i
$610$	−5848.04	−	7674.94i	−0.388164	−	0.509425i
$611$	20433.8	+	5999.91i	1.35297	+	0.397267i
$612$	5920.08	−	2208.08i	0.391021	−	0.145843i
$613$	14585.3	−	3172.84i	0.961002	−	0.209053i	0.295411	−	0.955370i	$-0.404543\pi$
$613$	14585.3	−	3172.84i	0.961002	−	0.209053i	0.665591	+	0.746317i	$0.268180\pi$
$614$	−3441.61	−	11721.0i	−0.226209	−	0.770396i
$615$	1844.73	−	8841.98i	0.120954	−	0.579745i
$616$	23.1530	+	50.6980i	0.00151438	+	0.00331604i
$617$	−12815.0	+	17118.8i	−0.836160	+	1.11698i	0.155467	+	0.987841i	$0.450312\pi$
$617$	−12815.0	+	17118.8i	−0.836160	+	1.11698i	−0.991627	+	0.129137i	$0.958779\pi$
$618$	−1908.99	+	8775.48i	−0.124257	+	0.571200i
$619$	−10138.8	+	11700.9i	−0.658344	+	0.759769i	−0.982506	−	0.186232i	$-0.940372\pi$
$619$	−10138.8	+	11700.9i	−0.658344	+	0.759769i	0.324162	+	0.946002i	$0.394918\pi$
$620$	8733.89	+	9907.68i	0.565745	+	0.641778i
$621$	−3624.24	+	14691.0i	−0.234196	+	0.949321i
$622$	2247.57	−	2247.57i	0.144886	−	0.144886i
$623$	8116.24	−	580.485i	0.521943	−	0.0373301i
$624$	1151.53	+	1791.82i	0.0738753	+	0.114952i
$625$	−1695.61	+	15532.7i	−0.108519	+	0.994094i
$626$	10143.8	−	4632.52i	0.647648	−	0.295771i
$627$	41.2498	+	55.1033i	0.00262737	+	0.00350975i
$628$	6608.23	−	12102.1i	0.419900	−	0.768989i
$629$	−4649.11	+	7234.16i	−0.294710	+	0.458577i
$630$	−9133.10	+	2766.42i	−0.577573	+	0.174948i
$631$	888.178	−	3024.86i	0.0560345	−	0.190836i	−0.926719	−	0.375754i	$-0.877384\pi$
$631$	888.178	−	3024.86i	0.0560345	−	0.190836i	0.982754	+	0.184918i	$0.0592019\pi$
$632$	358.507	−	5012.59i	0.0225643	−	0.315490i
$633$	727.132	−	10166.6i	0.0456570	−	0.638368i
$634$	−804.679	+	2740.49i	−0.0504068	+	0.171670i
$635$	−2191.59	−	1172.58i	−0.136962	−	0.0732796i
$636$	4360.35	−	6784.84i	0.271854	−	0.423014i
$637$	5216.02	−	9552.42i	0.324437	−	0.594161i
$638$	−76.4389	−	102.110i	−0.00474333	−	0.00633635i
$639$	−6924.69	+	3162.40i	−0.428696	+	0.195779i
$640$	114.246	+	1426.52i	0.00705617	+	0.0881062i
$641$	15572.2	+	24230.8i	0.959539	+	1.49307i	0.867573	+	0.497310i	$0.165679\pi$
$641$	15572.2	+	24230.8i	0.959539	+	1.49307i	0.0919662	+	0.995762i	$0.470685\pi$
$642$	−11510.8	+	823.271i	−0.707626	+	0.0506104i
$643$	−13643.2	+	13643.2i	−0.836758	+	0.836758i	−0.988431	−	0.151673i	$-0.951534\pi$
$643$	−13643.2	+	13643.2i	−0.836758	+	0.836758i	0.151673	+	0.988431i	$0.451534\pi$
$644$	−470.519	−	10752.7i	−0.0287905	−	0.657944i
$645$	3552.04	−	3131.22i	0.216839	−	0.191150i
$646$	−9244.44	+	10668.6i	−0.563030	+	0.649771i
$647$	4481.56	−	20601.4i	0.272316	−	1.25182i	−0.614212	−	0.789141i	$-0.710526\pi$
$647$	4481.56	−	20601.4i	0.272316	−	1.25182i	0.886528	−	0.462675i	$-0.153110\pi$
$648$	237.019	−	316.621i	0.0143688	−	0.0191945i
$649$	61.0367	+	133.652i	0.00369168	+	0.00808366i
$650$	10407.7	+	2864.36i	0.628038	+	0.172845i
$651$	−6257.58	−	21311.4i	−0.376734	−	1.28304i
$652$	14510.0	−	3156.47i	0.871560	−	0.189596i
$653$	−15464.8	+	5768.07i	−0.926775	+	0.345669i	−0.767120	−	0.641504i	$-0.778311\pi$
$653$	−15464.8	+	5768.07i	−0.926775	+	0.345669i	−0.159655	+	0.987173i	$0.551038\pi$
$654$	2877.82	+	845.003i	0.172066	+	0.0505233i
$655$	−11950.5	−	1614.46i	−0.712892	−	0.0963088i
$656$	−2745.61	−	3168.60i	−0.163412	−	0.188587i
$657$	17669.0	−	9648.00i	1.04921	−	0.572914i
$658$	−8409.13	−	22545.7i	−0.498210	−	1.33575i
$659$	9460.38	+	6079.82i	0.559217	+	0.359387i	0.789513	−	0.613734i	$-0.210333\pi$
$659$	9460.38	+	6079.82i	0.559217	+	0.359387i	−0.230296	+	0.973121i	$0.573969\pi$
$660$	38.4047	−	8.69763i	0.00226500	−	0.000512962i
$661$	4201.00	+	604.013i	0.247201	+	0.0355422i	0.264802	−	0.964303i	$-0.414694\pi$
$661$	4201.00	+	604.013i	0.247201	+	0.0355422i	−0.0176003	+	0.999845i	$0.505603\pi$
$662$	931.378	+	347.386i	0.0546813	+	0.0203951i
$663$	9622.08	+	7203.00i	0.563636	+	0.421933i
$664$	7166.02	−	4605.32i	0.418819	−	0.269158i
$665$	14947.0	−	15203.8i	0.871609	−	0.886583i
$666$			3332.47i			0.193890i
$667$	6283.04	+	23816.9i	0.364738	+	1.38260i
$668$	−7037.43	−	7037.43i	−0.407614	−	0.407614i
$669$	−7133.66	−	6181.36i	−0.412262	−	0.357227i
$670$	5949.22	−	20918.6i	0.343042	−	1.20620i
$671$	17.5390	+	121.986i	0.00100907	+	0.00701822i
$672$	841.028	−	2254.88i	0.0482788	−	0.129440i
$673$	22366.4	−	16743.3i	1.28107	−	0.959000i	0.281075	−	0.959686i	$-0.409309\pi$
$673$	22366.4	−	16743.3i	1.28107	−	0.959000i	1.00000		0.000685670i	$0.000218256\pi$
$674$	−19243.4	+	5650.37i	−1.09975	+	0.322914i
$675$	1514.42	+	17080.4i	0.0863557	+	0.973961i
$676$	−552.654	+	1210.14i	−0.0314437	+	0.0688521i
$677$	−15559.3	−	28494.8i	−0.883300	−	1.61764i	−0.782425	−	0.622744i	$-0.786018\pi$
$677$	−15559.3	−	28494.8i	−0.883300	−	1.61764i	−0.100875	−	0.994899i	$-0.532164\pi$
$678$	−3337.52	−	238.704i	−0.189051	−	0.0135212i
$679$	10055.8	−	8713.36i	0.568342	−	0.492472i
$680$	3417.23	+	7317.13i	0.192713	+	0.412646i
$681$	10438.8	+	4767.22i	0.587392	+	0.268253i
$682$	−35.8582	−	164.837i	−0.00201331	−	0.00925506i
$683$	−12885.0	−	7035.74i	−0.721860	−	0.394165i	0.0759200	−	0.997114i	$-0.475811\pi$
$683$	−12885.0	−	7035.74i	−0.721860	−	0.394165i	−0.797780	+	0.602948i	$0.793992\pi$
$684$	−778.551	+	5414.94i	−0.0435214	+	0.302698i
$685$	−3419.67	−	8935.32i	−0.190743	−	0.498396i
$686$	4391.51	−	631.403i	0.244415	−	0.0351415i
$687$	−6937.29	−	1509.12i	−0.385261	−	0.0838084i
$688$	−156.801	−	2192.36i	−0.00868892	−	0.121487i
$689$	−28238.8			−1.56141
$690$	−7504.69	−	1226.14i	−0.414056	−	0.0676499i
$691$	4688.60			0.258123			0.129061	−	0.991637i	$-0.458804\pi$
$691$	4688.60			0.258123			0.129061	+	0.991637i	$0.458804\pi$
$692$	981.899	+	13728.7i	0.0539396	+	0.754174i
$693$	119.099	+	25.9084i	0.00652843	+	0.00142017i
$694$	6150.16	−	884.260i	0.336393	−	0.0483661i
$695$	−3083.85	+	6907.77i	−0.168312	+	0.377017i
$696$	−783.825	+	5451.63i	−0.0426880	+	0.296901i
$697$	−20765.6	−	11338.9i	−1.12848	−	0.616198i
$698$	−2801.52	−	12878.4i	−0.151919	−	0.698359i
$699$	−5137.92	−	2346.41i	−0.278017	−	0.126966i
$700$	−4456.42	−	11353.7i	−0.240624	−	0.613040i
$701$	20634.8	−	17880.1i	1.11179	−	0.963371i	0.112249	−	0.993680i	$-0.464195\pi$
$701$	20634.8	−	17880.1i	1.11179	−	0.963371i	0.999541	+	0.0303091i	$0.00964916\pi$
$702$	11816.3	+	845.116i	0.635294	+	0.0454371i
$703$	−3568.19	−	6534.65i	−0.191432	−	0.350582i
$704$	7.59305	−	16.6265i	0.000406497	−	0.000890104i
$705$	−16806.5	+	2562.69i	−0.897830	+	0.136903i
$706$	2921.95	−	857.961i	0.155763	−	0.0457362i
$707$	−654.426	+	489.897i	−0.0348122	+	0.0260601i
$708$	2217.15	−	5944.40i	0.117691	−	0.315543i
$709$	−4591.31	−	31933.3i	−0.243202	−	1.69151i	−0.635844	−	0.771817i	$-0.719348\pi$
$709$	−4591.31	−	31933.3i	−0.243202	−	1.69151i	0.392642	−	0.919691i	$-0.371561\pi$
$710$	−4735.58	−	8499.66i	−0.250314	−	0.449277i
$711$	−8305.60	−	7196.84i	−0.438093	−	0.379610i
$712$	−1886.93	−	1886.93i	−0.0993200	−	0.0993200i
$713$	−5526.42	+	32104.3i	−0.290275	+	1.68627i
$714$		−	13580.8i		−	0.711834i
$715$	−98.3178	−	96.6572i	−0.00514248	−	0.00505563i
$716$	−6511.59	+	4184.74i	−0.339874	+	0.218423i
$717$	4673.15	+	3498.27i	0.243406	+	0.182211i
$718$	−5079.33	−	1894.49i	−0.264009	−	0.0984704i
$719$	−5980.16	−	859.818i	−0.310184	−	0.0445978i	−0.0145351	−	0.999894i	$-0.504627\pi$
$719$	−5980.16	−	859.818i	−0.310184	−	0.0445978i	−0.295649	+	0.955297i	$0.595536\pi$
$720$	2647.10	+	1669.50i	0.137016	+	0.0864149i
$721$	−29889.1	−	19208.5i	−1.54387	−	0.992183i
$722$	522.655	+	1401.29i	0.0269407	+	0.0722309i
$723$	−10993.8	+	6003.06i	−0.565509	+	0.308791i
$724$	−3845.13	−	4437.52i	−0.197380	−	0.227789i
$725$	15488.9	+	23221.8i	0.793439	+	1.18957i
$726$	7874.08	+	2312.04i	0.402527	+	0.118193i
$727$	−15848.9	+	5911.34i	−0.808534	+	0.301568i	−0.719528	−	0.694464i	$-0.755642\pi$
$727$	−15848.9	+	5911.34i	−0.808534	+	0.301568i	−0.0890060	+	0.996031i	$0.528369\pi$
$728$	−8233.82	+	1791.16i	−0.419184	+	0.0911878i
$729$	2973.43	+	10126.6i	0.151066	+	0.514482i
$730$	14094.8	+	21526.6i	0.714618	+	1.09142i
$731$	−5152.53	−	11282.5i	−0.260702	−	0.570858i
$732$	3189.07	−	4260.11i	0.161027	−	0.215107i
$733$	471.652	−	2168.15i	0.0237665	−	0.109253i	−0.963735	−	0.266859i	$-0.914014\pi$
$733$	471.652	−	2168.15i	0.0237665	−	0.109253i	0.987502	+	0.157606i	$0.0503777\pi$
$734$	−6369.91	+	7351.27i	−0.320324	+	0.369673i
$735$	−545.993	+	8671.21i	−0.0274003	+	0.435160i
$736$	−2563.99	+	2425.89i	−0.128410	+	0.121494i
$737$	−196.416	+	196.416i	−0.00981691	+	0.00981691i
$738$	−9145.45	+	654.096i	−0.456164	+	0.0326255i
$739$	10194.9	+	15863.5i	0.507476	+	0.789648i	0.996585	−	0.0825747i	$-0.0263143\pi$
$739$	10194.9	+	15863.5i	0.507476	+	0.789648i	−0.489109	+	0.872223i	$0.662678\pi$
$740$	−4245.71	+	340.026i	−0.210913	+	0.0168914i
$741$	−9466.21	+	4323.08i	−0.469298	+	0.214321i
$742$	19121.2	+	25543.0i	0.946040	+	1.26376i
$743$	−3550.89	+	6502.96i	−0.175329	+	0.321091i	−0.950535	−	0.310618i	$-0.899464\pi$
$743$	−3550.89	+	6502.96i	−0.175329	+	0.321091i	0.775206	+	0.631708i	$0.217646\pi$
$744$	−3938.11	+	6127.81i	−0.194056	+	0.301958i
$745$	−7396.00	−	24417.2i	−0.363716	−	1.20078i
$746$	1884.36	−	6417.54i	0.0924817	−	0.314964i
$747$	1328.93	−	18580.9i	0.0650911	−	0.910093i
$748$	7.35835	−	102.883i	0.000359690	−	0.00502912i
$749$	12862.5	−	43805.7i	0.627485	−	2.13702i
$750$	−8495.48	+	1443.88i	−0.413615	+	0.0702973i
$751$	−2035.16	+	3166.77i	−0.0988868	+	0.153871i	−0.887172	−	0.461440i	$-0.847333\pi$
$751$	−2035.16	+	3166.77i	−0.0988868	+	0.153871i	0.788285	+	0.615311i	$0.210969\pi$
$752$	−3781.97	+	6926.16i	−0.183397	+	0.335866i
$753$	−523.281	−	699.022i	−0.0253246	−	0.0338297i
$754$	17541.6	−	8010.97i	0.847250	−	0.386926i
$755$	−6967.37	−	5934.13i	−0.335853	−	0.286046i
$756$	−7236.65	−	11260.4i	−0.348141	−	0.541718i
$757$	25589.2	−	1830.17i	1.22860	−	0.0878715i	0.558098	−	0.829775i	$-0.311531\pi$
$757$	25589.2	−	1830.17i	1.22860	−	0.0878715i	0.670507	+	0.741903i	$0.266077\pi$
$758$	7323.16	−	7323.16i	0.350909	−	0.350909i
$759$	76.1110	+	60.3325i	0.00363986	+	0.00288528i
$760$	−6978.29	−	439.396i	−0.333065	−	0.0209718i
$761$	3060.06	−	3531.50i	0.145765	−	0.168222i	−0.678172	−	0.734903i	$-0.737228\pi$
$761$	3060.06	−	3531.50i	0.145765	−	0.168222i	0.823937	+	0.566682i	$0.191773\pi$
$762$	291.386	−	1339.48i	0.0138528	−	0.0636802i
$763$	−7110.89	+	9499.03i	−0.337394	+	0.450705i
$764$	−2962.54	−	6487.07i	−0.140289	−	0.307191i
$765$	17288.4	+	3606.93i	0.817076	+	0.170469i
$766$	887.789	+	3023.53i	0.0418762	+	0.142617i
$767$	−21706.3	+	4721.91i	−1.02186	+	0.222293i
$768$	−739.491	+	275.816i	−0.0347449	+	0.0129592i
$769$	−19575.7	−	5747.95i	−0.917970	−	0.269540i	−0.211578	−	0.977361i	$-0.567860\pi$
$769$	−19575.7	−	5747.95i	−0.917970	−	0.269540i	−0.706392	+	0.707821i	$0.749678\pi$
$770$	−20.8562	+	154.381i	−0.000976110	+	0.00722531i
$771$	−10222.2	−	11797.0i	−0.477488	−	0.551051i
$772$	−3059.51	+	1670.62i	−0.142635	+	0.0778846i
$773$	10292.1	+	27594.2i	0.478889	+	1.28395i	0.921898	+	0.387434i	$0.126638\pi$
$773$	10292.1	+	27594.2i	0.478889	+	1.28395i	−0.443008	+	0.896517i	$0.646089\pi$
$774$	−4043.62	−	2598.68i	−0.187784	−	0.120682i
$775$	5875.41	+	36446.1i	0.272324	+	1.68927i
$776$	−4319.19	−	621.006i	−0.199807	−	0.0287279i
$777$	6711.16	+	2503.13i	0.309860	+	0.115572i
$778$	14252.8	+	10669.5i	0.656797	+	0.491672i
$779$	17233.0	−	11075.0i	0.792600	−	0.509373i
$780$	50.7024	+	5953.14i	0.00232748	+	0.273278i
$781$			124.273i			0.00569375i
$782$	−8772.61	+	17882.8i	−0.401161	+	0.817758i
$783$	21660.8	+	21660.8i	0.988627	+	0.988627i
$784$	3047.93	+	2641.05i	0.138845	+	0.120310i
$785$	33667.8	−	18758.0i	1.53077	−	0.852868i
$786$	−946.488	−	6582.97i	−0.0429518	−	0.298736i
$787$	−5383.65	+	14434.1i	−0.243846	+	0.653775i	−1.00000		0.000618168i	$-0.999803\pi$
$787$	−5383.65	+	14434.1i	−0.243846	+	0.653775i	0.756154	+	0.654393i	$0.227076\pi$
$788$	2780.74	−	2081.64i	0.125710	−	0.0941057i
$789$	9117.81	−	2677.23i	0.411410	−	0.120801i
$790$	8321.62	−	11316.0i	0.374772	−	0.509627i
$791$	5499.06	−	12041.3i	0.247186	−	0.541262i
$792$	−19.1566	−	35.0827i	−0.000859470	−	0.00157400i
$793$	−18585.0	−	1329.23i	−0.832248	−	0.0595236i
$794$	−3168.10	+	2745.17i	−0.141601	+	0.122698i
$795$	20425.2	−	9538.92i	0.911202	−	0.425548i
$796$	−1059.90	−	484.041i	−0.0471951	−	0.0215533i
$797$	6549.07	+	30105.6i	0.291066	+	1.33801i	0.857747	+	0.514072i	$0.171864\pi$
$797$	6549.07	+	30105.6i	0.291066	+	1.33801i	−0.566681	+	0.823938i	$0.691773\pi$
$798$	10320.2	+	5635.24i	0.457807	+	0.249982i
$799$	−6337.61	+	44079.0i	−0.280611	+	1.95169i
$800$	−1856.92	+	3542.86i	−0.0820651	+	0.156574i
$801$	−5776.33	+	830.511i	−0.254802	+	0.0366350i
$802$	−25618.2	−	5572.91i	−1.12794	−	0.245369i
$803$	−23.4447	−	327.800i	−0.00103032	−	0.0144057i
$804$	11994.3			0.526126
$805$	14920.5	−	26122.7i	0.653265	−	1.14373i
$806$	25504.2			1.11458
$807$	753.819	+	10539.8i	0.0328819	+	0.459749i
$808$	261.966	+	56.9873i	0.0114059	+	0.00248120i
$809$	7857.37	−	1129.72i	0.341471	−	0.0490962i	0.0305540	−	0.999533i	$-0.490273\pi$
$809$	7857.37	−	1129.72i	0.341471	−	0.0490962i	0.310917	+	0.950437i	$0.399364\pi$
$810$	1032.45	−	395.133i	0.0447859	−	0.0171402i
$811$	−6299.08	+	43811.0i	−0.272738	+	1.89693i	0.146750	+	0.989174i	$0.453119\pi$
$811$	−6299.08	+	43811.0i	−0.272738	+	1.89693i	−0.419488	+	0.907761i	$0.637790\pi$
$812$	−19124.0	−	10442.5i	−0.826505	−	0.451306i
$813$	−3743.91	−	17210.5i	−0.161506	−	0.742432i
$814$	49.4849	+	22.5990i	0.00213077	+	0.000973090i
$815$	39010.5	+	14172.9i	1.67666	+	0.609147i
$816$	−3365.99	+	2916.65i	−0.144403	+	0.125126i
$817$	10711.6	+	766.112i	0.458694	+	0.0328064i
$818$	5958.58	+	10912.3i	0.254691	+	0.466431i
$819$	−7655.03	+	16762.2i	−0.326604	+	0.715163i
$820$	−1766.49	−	11584.9i	−0.0752301	−	0.493370i
$821$	12133.4	−	3562.70i	0.515786	−	0.151448i	−0.0134722	−	0.999909i	$-0.504288\pi$
$821$	12133.4	−	3562.70i	0.515786	−	0.151448i	0.529258	+	0.848461i	$0.322470\pi$
$822$	4224.03	−	3162.07i	0.179233	−	0.134172i
$823$	7550.69	−	20244.2i	0.319806	−	0.857434i	−0.673209	−	0.739452i	$-0.735085\pi$
$823$	7550.69	−	20244.2i	0.319806	−	0.857434i	0.993016	−	0.117982i	$-0.0376426\pi$
$824$	1658.23	+	11533.2i	0.0701058	+	0.487597i
$825$	103.763	+	36.7010i	0.00437889	+	0.00154880i
$826$	18969.0	+	16436.7i	0.799050	+	0.692381i
$827$	11854.5	+	11854.5i	0.498455	+	0.498455i	0.910957	−	0.412502i	$-0.135345\pi$
$827$	11854.5	+	11854.5i	0.498455	+	0.498455i	−0.412502	+	0.910957i	$0.635345\pi$
$828$	886.736	+	7667.97i	0.0372177	+	0.321836i
$829$		−	35317.3i		−	1.47964i	−0.672805	−	0.739820i	$-0.734911\pi$
$829$		−	35317.3i		−	1.47964i	0.672805	−	0.739820i	$-0.265089\pi$
$830$	23808.4	−	202.774i	0.995665	−	0.00847999i
$831$	−8011.52	+	5148.69i	−0.334436	+	0.214929i
$832$	2212.25	+	1656.07i	0.0921827	+	0.0690071i
$833$	21323.7	+	7953.31i	0.886940	+	0.330811i
$834$	−4129.62	−	593.750i	−0.171459	−	0.0246521i
$835$	−6144.40	−	27130.8i	−0.254654	−	1.12443i
$836$	75.1284	+	48.2821i	0.00310810	+	0.00199745i
$837$	14158.0	+	37959.1i	0.584674	+	1.56757i
$838$	−12927.9	+	7059.19i	−0.532921	+	0.290997i
$839$	−3854.19	−	4447.97i	−0.158595	−	0.183029i	0.670891	−	0.741556i	$-0.265912\pi$
$839$	−3854.19	−	4447.97i	−0.158595	−	0.183029i	−0.829486	+	0.558528i	$0.811366\pi$
$840$	5350.48	−	4076.88i	0.219773	−	0.167459i
$841$	24445.1	+	7177.72i	1.00230	+	0.294302i
$842$	−23541.8	+	8780.63i	−0.963543	+	0.359383i
$843$	2956.69	−	643.189i	0.120799	−	0.0262783i
$844$	−3725.68	−	12688.5i	−0.151947	−	0.517483i
$845$	−3110.96	+	2036.93i	−0.126651	+	0.0829262i
$846$	7169.07	+	15698.1i	0.291345	+	0.637956i
$847$	−19456.3	+	25990.6i	−0.789288	+	1.05437i
$848$	2224.28	−	10224.8i	0.0900731	−	0.414059i
$849$	703.504	−	811.887i	0.0284384	−	0.0328197i
$850$	−2831.37	+	22394.1i	−0.114253	+	0.903662i
$851$	−7220.12	−	7631.16i	−0.290837	−	0.307394i
$852$	3794.40	−	3794.40i	0.152575	−	0.152575i
$853$	−4885.32	+	349.405i	−0.196096	+	0.0140251i	−0.169042	−	0.985609i	$-0.554067\pi$
$853$	−4885.32	+	349.405i	−0.196096	+	0.0140251i	−0.0270545	+	0.999634i	$0.508613\pi$
$854$	11382.0	+	17710.8i	0.456072	+	0.709661i
$855$	−9914.60	+	11640.9i	−0.396576	+	0.465627i
$856$	−13619.6	+	6219.85i	−0.543817	+	0.248353i
$857$	4568.53	+	6102.84i	0.182098	+	0.243254i	0.882297	−	0.470694i	$-0.155996\pi$
$857$	4568.53	+	6102.84i	0.182098	+	0.243254i	−0.700199	+	0.713948i	$0.746905\pi$
$858$	36.4412	−	66.7370i	0.00144998	−	0.00265544i
$859$	8242.56	−	12825.7i	0.327395	−	0.509437i	−0.638067	−	0.769981i	$-0.720266\pi$
$859$	8242.56	−	12825.7i	0.327395	−	0.509437i	0.965462	+	0.260544i	$0.0839019\pi$
$860$	2898.23	−	5416.89i	0.114917	−	0.214784i
$861$	−5552.19	+	18909.0i	−0.219766	+	0.748453i
$862$	515.050	−	7201.34i	0.0203511	−	0.284546i
$863$	−2717.95	+	38001.9i	−0.107207	+	1.49896i	0.604571	+	0.796551i	$0.293345\pi$
$863$	−2717.95	+	38001.9i	−0.107207	+	1.49896i	−0.711778	+	0.702404i	$0.752110\pi$
$864$	−1236.73	+	4211.91i	−0.0486972	+	0.165847i
$865$	−18149.0	+	33921.0i	−0.713391	+	1.33335i
$866$	3802.42	−	5916.68i	0.149205	−	0.232167i
$867$	−4786.07	+	8765.03i	−0.187478	+	0.343340i
$868$	−17269.6	−	23069.4i	−0.675307	−	0.902105i
$869$	−163.192	+	74.5274i	−0.00637045	+	0.00290928i
$870$	−9981.77	+	11719.8i	−0.388981	+	0.456710i
$871$	−22704.7	−	35329.2i	−0.883261	−	1.37438i
$872$	3881.47	−	277.608i	0.150738	−	0.0107810i
$873$	−6747.67	+	6747.67i	−0.261597	+	0.261597i
$874$	−9949.15	−	14086.7i	−0.385052	−	0.545182i
$875$	6393.26	−	33486.7i	0.247008	−	1.29378i
$876$	−9292.83	+	10724.5i	−0.358420	+	0.413638i
$877$	336.688	−	1547.73i	0.0129637	−	0.0595930i	−0.970211	−	0.242263i	$-0.922110\pi$
$877$	336.688	−	1547.73i	0.0129637	−	0.0595930i	0.983174	+	0.182670i	$0.0584740\pi$
$878$	5348.09	−	7144.21i	0.205569	−	0.274608i
$879$	7388.54	+	16178.7i	0.283515	+	0.620811i
$880$	42.7422	−	27.9859i	0.00163732	−	0.00107205i
$881$	−6663.81	−	22694.9i	−0.254835	−	0.867888i	−0.983174	−	0.182671i	$-0.941526\pi$
$881$	−6663.81	−	22694.9i	−0.254835	−	0.867888i	0.728339	−	0.685217i	$-0.240293\pi$
$882$	8618.08	−	1874.75i	0.329009	−	0.0715715i
$883$	−22008.2	+	8208.62i	−0.838770	+	0.312845i	−0.731887	−	0.681427i	$-0.761360\pi$
$883$	−22008.2	+	8208.62i	−0.838770	+	0.312845i	−0.106883	+	0.994272i	$0.534087\pi$
$884$	14962.7	+	4393.45i	0.569288	+	0.167158i
$885$	14105.1	−	10747.6i	0.535750	−	0.408223i
$886$	−3458.89	−	3991.77i	−0.131155	−	0.151361i
$887$	−5248.18	+	2865.72i	−0.198666	+	0.108480i	−0.575503	−	0.817800i	$-0.695194\pi$
$887$	−5248.18	+	2865.72i	−0.198666	+	0.108480i	0.376837	+	0.926280i	$0.377012\pi$
$888$	−820.904	−	2200.93i	−0.0310222	−	0.0831738i
$889$	4562.24	+	2931.97i	0.172118	+	0.110613i
$890$	−1647.49	−	7274.54i	−0.0620494	−	0.273981i
$891$	−13.9758	−	2.00942i	−0.000525484	−	7.55533e-5i
$892$	−11474.5	−	4279.77i	−0.430712	−	0.160647i
$893$	−30866.3	−	23106.2i	−1.15666	−	0.865868i
$894$	11836.9	−	7607.09i	0.442823	−	0.284585i
$895$	−21634.1	+	184.256i	−0.807988	+	0.00688156i
$896$		−	3122.42i		−	0.116420i
$897$	−11359.1	+	9305.16i	−0.422819	+	0.346366i
$898$	−7486.55	−	7486.55i	−0.278206	−	0.278206i
$899$	49841.6	+	43188.0i	1.84907	+	1.60223i
$900$	3768.84	+	7893.95i	0.139587	+	0.292368i
$901$	−8403.59	−	58448.2i	−0.310726	−	2.16115i
$902$	−52.3066	+	140.239i	−0.00193084	+	0.00517679i
$903$	−8270.69	+	6191.36i	−0.304797	+	0.228168i
$904$	−4165.41	+	1223.07i	−0.153251	+	0.0449987i
$905$	−2473.91	−	16224.3i	−0.0908681	−	0.595927i
$906$	2096.75	−	4591.25i	0.0768874	−	0.168360i
$907$	−5253.11	−	9620.36i	−0.192312	−	0.352193i	0.763676	−	0.645600i	$-0.223393\pi$
$907$	−5253.11	−	9620.36i	−0.192312	−	0.352193i	−0.955988	+	0.293407i	$0.905211\pi$
$908$	14851.1	+	1062.17i	0.542787	+	0.0388209i
$909$	443.085	−	383.935i	0.0161674	−	0.0140092i
$910$	−22136.8	−	8042.51i	−0.806404	−	0.292974i
$911$	−24909.5	−	11375.8i	−0.905916	−	0.413718i	−0.0927097	−	0.995693i	$-0.529553\pi$
$911$	−24909.5	−	11375.8i	−0.905916	−	0.413718i	−0.813207	+	0.581975i	$0.802280\pi$
$912$	−819.695	−	3768.08i	−0.0297619	−	0.136813i
$913$	−266.902	−	145.739i	−0.00967486	−	0.00528288i
$914$	3345.13	−	23265.9i	0.121058	−	0.841977i
$915$	13891.5	−	5316.48i	0.501902	−	0.192085i
$916$	−9117.39	+	1310.88i	−0.328872	+	0.0472847i
$917$	25709.8	+	5592.83i	0.925860	+	0.201408i
$918$	1767.19	+	24708.6i	0.0635360	+	0.888349i
$919$	32583.1			1.16955			0.584776	−	0.811195i	$-0.301183\pi$
$919$	32583.1			1.16955			0.584776	+	0.811195i	$0.301183\pi$
$920$	−9678.83	+	1912.13i	−0.346850	+	0.0685230i
$921$	18830.9			0.673724
$922$	1067.22	+	14921.7i	0.0381205	+	0.532994i
$923$	−18359.1	−	3993.78i	−0.654710	−	0.142423i
$924$	−85.0410	+	12.2271i	−0.00302775	+	0.000435325i
$925$	−10544.5	−	5526.71i	−0.374813	−	0.196451i
$926$	−3108.94	+	21623.2i	−0.110331	+	0.767367i
$927$	22364.2	+	12211.8i	0.792381	+	0.432673i
$928$	1518.96	+	6982.52i	0.0537308	+	0.246996i
$929$	−51345.1	−	23448.5i	−1.81333	−	0.828118i	−0.940200	−	0.340622i	$-0.889362\pi$
$929$	−51345.1	−	23448.5i	−1.81333	−	0.828118i	−0.873125	−	0.487496i	$-0.837910\pi$
$930$	−18447.2	+	8615.19i	−0.650439	+	0.303767i
$931$	−14891.8	+	12903.9i	−0.524233	+	0.454250i
$932$	−7309.66	−	522.797i	−0.256905	−	0.0183742i
$933$	2348.20	+	4300.41i	0.0823973	+	0.150899i
$934$	12022.6	−	26325.9i	0.421191	−	0.922279i
$935$	170.801	−	232.260i	0.00597410	−	0.00812377i
$936$	5798.50	−	1702.59i	0.202489	−	0.0594562i
$937$	−7480.12	+	5599.55i	−0.260795	+	0.195229i	−0.721672	−	0.692235i	$-0.756626\pi$
$937$	−7480.12	+	5599.55i	−0.260795	+	0.195229i	0.460877	+	0.887464i	$0.347535\pi$
$938$	−16582.5	+	44459.5i	−0.577227	+	1.54760i
$939$	2446.42	+	17015.3i	0.0850224	+	0.591344i
$940$	−19268.5	+	10735.4i	−0.668584	+	0.372501i
$941$	−16762.1	−	14524.5i	−0.580690	−	0.503171i	0.314260	−	0.949337i	$-0.398244\pi$
$941$	−16762.1	−	14524.5i	−0.580690	−	0.503171i	−0.894950	+	0.446166i	$0.852789\pi$
$942$	15029.9	+	15029.9i	0.519852	+	0.519852i
$943$	19525.4	−	21312.3i	0.674266	−	0.735976i
$944$		−	8231.43i		−	0.283803i
$945$	−318.632	−	37411.7i	−0.0109684	−	1.28783i
$946$	−66.0102	+	42.4222i	−0.00226869	+	0.00145800i
$947$	9161.80	+	6858.43i	0.314381	+	0.235342i	0.744802	−	0.667286i	$-0.232544\pi$
$947$	9161.80	+	6858.43i	0.314381	+	0.235342i	−0.430421	+	0.902628i	$0.641635\pi$
$948$	7258.26	+	2707.19i	0.248668	+	0.0927484i
$949$	49180.2	+	7071.04i	1.68225	+	0.241871i
$950$	−15842.6	−	11443.8i	−0.541056	−	0.390828i
$951$	−3703.90	−	2380.35i	−0.126296	−	0.0811653i
$952$	−6157.60	−	16509.2i	−0.209631	−	0.562044i
$953$	29641.9	−	16185.7i	1.00755	−	0.550165i	0.111336	−	0.993783i	$-0.464487\pi$
$953$	29641.9	−	16185.7i	1.00755	−	0.550165i	0.896216	+	0.443618i	$0.146305\pi$
$954$	−14985.4	−	17294.1i	−0.508565	−	0.586915i
$955$	2668.66	−	19753.8i	0.0904248	−	0.669337i
$956$	7266.93	+	2133.76i	0.245847	+	0.0721871i
$957$	184.225	−	68.7125i	0.00622274	−	0.00232096i
$958$	11040.6	−	2401.74i	0.372345	−	0.0809988i
$959$	5881.05	+	20029.0i	0.198028	+	0.674421i
$960$	−2159.53	−	450.550i	−0.0726027	−	0.0151473i
$961$	23857.5	+	52240.7i	0.800829	+	1.75357i
$962$	−4928.92	+	6584.27i	−0.165192	+	0.220671i
$963$	−6960.07	+	31994.9i	−0.232902	+	1.07064i
$964$	−10642.5	+	12282.1i	−0.355573	+	0.410353i
$965$	−9724.16	−	612.293i	−0.324385	−	0.0204253i
$966$	16108.3	+	3973.90i	0.536518	+	0.132358i
$967$	4342.17	−	4342.17i	0.144400	−	0.144400i	−0.631211	−	0.775611i	$-0.717442\pi$
$967$	4342.17	−	4342.17i	0.144400	−	0.144400i	0.775611	+	0.631211i	$0.217442\pi$
$968$	10620.2	−	759.573i	0.352631	−	0.0252207i
$969$	−11764.9	−	18306.5i	−0.390033	−	0.606903i
$970$	−9285.31	−	7908.32i	−0.307354	−	0.261774i
$971$	9189.51	−	4196.71i	0.303713	−	0.138701i	−0.257729	−	0.966217i	$-0.582974\pi$
$971$	9189.51	−	4196.71i	0.303713	−	0.138701i	0.561442	+	0.827516i	$0.310247\pi$
$972$	9243.86	+	12348.4i	0.305038	+	0.407483i
$973$	7910.23	−	14486.5i	0.260627	−	0.477303i
$974$	1277.76	−	1988.24i	0.0420351	−	0.0654079i
$975$	−8756.61	+	14149.8i	−0.287626	+	0.464775i
$976$	1945.17	−	6624.63i	0.0637944	−	0.217264i
$977$	−1514.87	+	21180.6i	−0.0496058	+	0.693580i	0.910423	+	0.413679i	$0.135756\pi$
$977$	−1514.87	+	21180.6i	−0.0496058	+	0.693580i	−0.960029	+	0.279901i	$0.909698\pi$
$978$	−1632.99	+	22832.2i	−0.0533919	+	0.746516i
$979$	−26.8394	+	91.4066i	−0.000876191	+	0.00298403i
$980$	3267.84	+	10788.5i	0.106518	+	0.351659i
$981$	4600.84	−	7159.04i	0.149738	−	0.232997i
$982$	3811.75	−	6980.70i	0.123867	−	0.226846i
$983$	−1402.00	−	1872.86i	−0.0454902	−	0.0607679i	0.777219	−	0.629230i	$-0.216630\pi$
$983$	−1402.00	−	1872.86i	−0.0454902	−	0.0607679i	−0.822710	+	0.568462i	$0.807539\pi$
$984$	5878.98	−	2684.84i	0.190463	−	0.0869813i
$985$	9677.96	−	775.080i	0.313061	−	0.0250722i
$986$	21801.2	+	33923.3i	0.704148	+	1.09568i
$987$	36998.7	−	2646.20i	1.19319	−	0.0853389i
$988$	−9547.26	+	9547.26i	−0.307428	+	0.307428i
$989$	14889.9	−	2810.09i	0.478738	−	0.0903494i
$990$	7.02102	−	111.505i	0.000225397	−	0.00357965i
$991$	18379.3	−	21210.9i	0.589141	−	0.679905i	−0.380403	−	0.924821i	$-0.624215\pi$
$991$	18379.3	−	21210.9i	0.589141	−	0.679905i	0.969544	+	0.244915i	$0.0787602\pi$
$992$	−2008.88	+	9234.68i	−0.0642964	+	0.295566i
$993$	−918.300	+	1226.70i	−0.0293468	+	0.0392027i
$994$	8818.90	+	19310.7i	0.281407	+	0.616195i
$995$	−1784.05	−	2724.73i	−0.0568423	−	0.0868137i
$996$	3699.43	+	12599.1i	0.117692	+	0.400821i
$997$	2752.84	−	598.845i	0.0874458	−	0.0190227i	−0.168629	−	0.985680i	$-0.553934\pi$
$997$	2752.84	−	598.845i	0.0874458	−	0.0190227i	0.256075	+	0.966657i	$0.417570\pi$
$998$	−12096.4	+	4511.72i	−0.383672	+	0.143102i
$999$	−12535.8	−	3680.85i	−0.397013	−	0.116573i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.l.a.53.25	yes	720
5.2	odd	4	inner	230.4.l.a.7.7	✓	720
23.10	odd	22	inner	230.4.l.a.33.7	yes	720
115.102	even	44	inner	230.4.l.a.217.25	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.l.a.7.7	✓	720	5.2	odd	4	inner
230.4.l.a.33.7	yes	720	23.10	odd	22	inner
230.4.l.a.53.25	yes	720	1.1	even	1	trivial
230.4.l.a.217.25	yes	720	115.102	even	44	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142678 + 1.99490i) q^{2} +(-3.01257 - 0.655343i) q^{3} +(-3.95929 + 0.569259i) q^{4} +(-10.2092 - 4.55770i) q^{5} +(0.877520 - 6.10328i) q^{6} +(21.4100 + 11.6907i) q^{7} +(-1.70052 - 7.81717i) q^{8} +(-15.9140 - 7.26768i) q^{9} +(7.63554 - 21.0166i) q^{10} +(-0.215840 + 0.187026i) q^{11} +(12.3007 + 0.879761i) q^{12} +(-20.6934 - 37.8971i) q^{13} +(-20.2672 + 44.3789i) q^{14} +(27.7690 + 20.4209i) q^{15} +(15.3519 - 4.50772i) q^{16} +(72.2806 - 54.1086i) q^{17} +(12.2277 - 32.7838i) q^{18} +(11.1253 + 77.3785i) q^{19} +(43.0156 + 12.2336i) q^{20} +(-56.8376 - 49.2500i) q^{21} +(-0.403895 - 0.403895i) q^{22} +(43.0286 + 101.565i) q^{23} +24.6642i q^{24} +(83.4548 + 93.0607i) q^{25} +(72.6486 - 46.6884i) q^{26} +(109.817 + 82.2083i) q^{27} +(-91.4234 - 34.0992i) q^{28} +(221.034 + 31.7799i) q^{29} +(-36.7757 + 58.3100i) q^{30} +(248.450 + 159.669i) q^{31} +(11.1829 + 29.9824i) q^{32} +(0.772799 - 0.421980i) q^{33} +(118.254 + 136.473i) q^{34} +(-165.296 - 216.933i) q^{35} +(67.1452 + 19.7156i) q^{36} +(-89.2359 + 33.2833i) q^{37} +(-152.775 + 33.2342i) q^{38} +(37.5046 + 127.729i) q^{39} +(-18.2674 + 87.5574i) q^{40} +(-108.856 - 238.361i) q^{41} +(90.1396 - 120.412i) q^{42} +(29.2007 - 134.233i) q^{43} +(0.748106 - 0.863360i) q^{44} +(129.345 + 146.728i) q^{45} +(-196.474 + 100.329i) q^{46} +(-348.756 + 348.756i) q^{47} +(-49.2027 + 3.51904i) q^{48} +(136.275 + 212.048i) q^{49} +(-173.740 + 179.762i) q^{50} +(-253.210 + 115.637i) q^{51} +(103.504 + 138.266i) q^{52} +(313.428 - 574.000i) q^{53} +(-148.329 + 230.805i) q^{54} +(3.05596 - 0.925653i) q^{55} +(54.9804 - 187.246i) q^{56} +(17.1937 - 240.399i) q^{57} +(-31.8611 + 445.476i) q^{58} +(144.941 - 493.625i) q^{59} +(-121.570 - 65.0444i) q^{60} +(233.297 - 363.017i) q^{61} +(-283.076 + 518.415i) q^{62} +(-255.754 - 341.647i) q^{63} +(-58.2164 + 26.5866i) q^{64} +(38.5389 + 481.213i) q^{65} +(0.952071 + 1.48145i) q^{66} +(970.128 - 69.3849i) q^{67} +(-255.378 + 255.378i) q^{68} +(-63.0661 - 334.171i) q^{69} +(409.177 - 360.701i) q^{70} +(284.951 - 328.851i) q^{71} +(-29.7506 + 136.761i) q^{72} +(-689.590 + 921.184i) q^{73} +(-79.1290 - 173.268i) q^{74} +(-190.426 - 335.043i) q^{75} +(-88.0969 - 300.030i) q^{76} +(-6.80761 + 1.48091i) q^{77} +(-249.456 + 93.0422i) q^{78} +(602.728 + 176.977i) q^{79} +(-177.275 - 23.9491i) q^{80} +(32.3754 + 37.3631i) q^{81} +(459.976 - 251.166i) q^{82} +(372.104 + 997.649i) q^{83} +(253.072 + 162.640i) q^{84} +(-984.536 + 222.971i) q^{85} +(271.949 + 39.1003i) q^{86} +(-645.053 - 240.592i) q^{87} +(1.82906 + 1.36922i) q^{88} +(280.614 - 180.339i) q^{89} +(-274.254 + 278.966i) q^{90} -1053.30i q^{91} +(-228.179 - 377.632i) q^{92} +(-643.833 - 643.833i) q^{93} +(-745.496 - 645.976i) q^{94} +(239.087 - 840.677i) q^{95} +(-14.0403 - 97.6525i) q^{96} +(190.616 - 511.060i) q^{97} +(-403.572 + 302.110i) q^{98} +(4.79412 - 1.40768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{3} + 16 q^{6} + 64 q^{12} - 192 q^{13} + 1152 q^{16} + 144 q^{18} + 1660 q^{23} - 880 q^{25} - 304 q^{26} - 728 q^{27} - 352 q^{28} - 608 q^{31} - 3872 q^{33} - 688 q^{35} - 2816 q^{36} - 2376 q^{37}+ \cdots + 14352 q^{98}+O(q^{100}) \) 720 * q + 16 * q^3 + 16 * q^6 + 64 * q^12 - 192 * q^13 + 1152 * q^16 + 144 * q^18 + 1660 * q^23 - 880 * q^25 - 304 * q^26 - 728 * q^27 - 352 * q^28 - 608 * q^31 - 3872 * q^33 - 688 * q^35 - 2816 * q^36 - 2376 * q^37 + 2208 * q^41 + 256 * q^46 + 3640 * q^47 - 256 * q^48 - 272 * q^50 - 768 * q^52 + 2360 * q^55 - 3872 * q^56 - 7656 * q^57 + 2112 * q^61 + 1376 * q^62 + 10912 * q^66 + 1104 * q^70 + 22752 * q^71 - 128 * q^72 + 1296 * q^73 - 5396 * q^75 + 752 * q^77 - 6000 * q^78 - 3928 * q^81 - 80 * q^82 + 3060 * q^85 - 10472 * q^86 - 6760 * q^87 - 1104 * q^92 + 5288 * q^93 + 9392 * q^95 - 256 * q^96 + 25344 * q^97 + 14352 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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