LMFDB - Embedded newform 21.4.g.a.17.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [21,4,Mod(5,21)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(21, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("21.5"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$N$	$=$	$21 = 3 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	21.g (of order $6$ , degree $2$ , 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:	$1.23904011012$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441$ x^12 - x^11 - 29x^9 + 6x^8 - 49x^7 + 1564x^6 - 441x^5 + 486x^4 - 21141x^3 - 59049x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$3^{3}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.3
Root			$-2.23014 - 2.00661i$ of defining polynomial
Character	$\chi$	$=$	21.17
Dual form			21.4.g.a.5.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65310 + 0.954416i) q^{2} +(-3.47555 + 3.86271i) q^{3} +(-2.17818 + 3.77272i) q^{4} +(0.623706 + 1.08029i) q^{5} +(2.05878 - 9.70256i) q^{6} +(10.0808 + 15.5363i) q^{7} -23.5862i q^{8} +(-2.84113 - 26.8501i) q^{9} +(-2.06209 - 1.19055i) q^{10} +(35.2392 + 20.3453i) q^{11} +(-7.00257 - 21.5260i) q^{12} +19.5973i q^{13} +(-31.4927 - 16.0617i) q^{14} +(-6.34057 - 1.34540i) q^{15} +(5.08559 + 8.80850i) q^{16} +(-52.3592 + 90.6889i) q^{17} +(30.3228 + 41.6742i) q^{18} +(35.0345 - 20.2272i) q^{19} -5.43418 q^{20} +(-95.0487 - 15.0578i) q^{21} -77.6716 q^{22} +(69.6324 - 40.2023i) q^{23} +(91.1068 + 81.9750i) q^{24} +(61.7220 - 106.906i) q^{25} +(-18.7040 - 32.3962i) q^{26} +(113.589 + 82.3444i) q^{27} +(-80.5720 + 4.19132i) q^{28} -211.712i q^{29} +(11.7656 - 3.82746i) q^{30} +(-86.6242 - 50.0125i) q^{31} +(146.596 + 84.6373i) q^{32} +(-201.064 + 65.4076i) q^{33} -199.890i q^{34} +(-10.4962 + 20.5803i) q^{35} +(107.486 + 47.7656i) q^{36} +(94.9875 + 164.523i) q^{37} +(-38.6103 + 66.8750i) q^{38} +(-75.6987 - 68.1113i) q^{39} +(25.4799 - 14.7109i) q^{40} -186.753 q^{41} +(171.496 - 65.8241i) q^{42} +158.618 q^{43} +(-153.515 + 88.6317i) q^{44} +(27.2339 - 19.8158i) q^{45} +(-76.7393 + 132.916i) q^{46} +(179.034 + 310.097i) q^{47} +(-51.6999 - 10.9702i) q^{48} +(-139.753 + 313.238i) q^{49} +235.634i q^{50} +(-168.328 - 517.442i) q^{51} +(-73.9351 - 42.6865i) q^{52} +(-366.460 - 211.576i) q^{53} +(-266.364 - 27.7123i) q^{54} +50.7580i q^{55} +(366.442 - 237.769i) q^{56} +(-43.6323 + 205.629i) q^{57} +(202.061 + 349.980i) q^{58} +(312.781 - 541.753i) q^{59} +(18.8867 - 20.9907i) q^{60} +(699.575 - 403.900i) q^{61} +190.931 q^{62} +(388.510 - 314.812i) q^{63} -404.486 q^{64} +(-21.1708 + 12.2229i) q^{65} +(269.952 - 300.023i) q^{66} +(-149.272 + 258.547i) q^{67} +(-228.096 - 395.074i) q^{68} +(-86.7208 + 408.695i) q^{69} +(-2.29089 - 44.0390i) q^{70} +455.386i q^{71} +(-633.292 + 67.0114i) q^{72} +(-434.467 - 250.840i) q^{73} +(-314.047 - 181.315i) q^{74} +(198.428 + 609.970i) q^{75} +176.234i q^{76} +(39.1491 + 752.584i) q^{77} +(190.144 + 40.3465i) q^{78} +(30.9561 + 53.6176i) q^{79} +(-6.34382 + 10.9878i) q^{80} +(-712.856 + 152.569i) q^{81} +(308.720 - 178.240i) q^{82} -73.1180 q^{83} +(263.842 - 325.794i) q^{84} -130.627 q^{85} +(-262.211 + 151.388i) q^{86} +(817.783 + 735.816i) q^{87} +(479.870 - 831.158i) q^{88} +(57.3723 + 99.3717i) q^{89} +(-26.1077 + 58.7498i) q^{90} +(-304.469 + 197.557i) q^{91} +350.271i q^{92} +(494.251 - 160.784i) q^{93} +(-591.922 - 341.746i) q^{94} +(43.7025 + 25.2316i) q^{95} +(-836.432 + 272.098i) q^{96} -1416.51i q^{97} +(-67.9336 - 651.195i) q^{98} +(446.156 - 1003.98i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 3 q^{3} + 14 q^{4} - 56 q^{7} - 3 q^{9} + 30 q^{10} - 192 q^{12} + 6 q^{15} + 134 q^{16} + 66 q^{18} + 300 q^{19} + 357 q^{21} - 268 q^{22} + 414 q^{24} - 42 q^{25} - 602 q^{28} - 822 q^{30} - 930 q^{31}+ \cdots - 3354 q^{99}+O(q^{100})$ 12 * q - 3 * q^3 + 14 * q^4 - 56 * q^7 - 3 * q^9 + 30 * q^10 - 192 * q^12 + 6 * q^15 + 134 * q^16 + 66 * q^18 + 300 * q^19 + 357 * q^21 - 268 * q^22 + 414 * q^24 - 42 * q^25 - 602 * q^28 - 822 * q^30 - 930 * q^31 - 855 * q^33 + 852 * q^36 + 764 * q^37 - 426 * q^39 + 2298 * q^40 + 966 * q^42 - 1012 * q^43 + 2367 * q^45 + 608 * q^46 - 336 * q^49 - 1341 * q^51 - 3000 * q^52 - 4158 * q^54 + 270 * q^57 + 2870 * q^58 - 918 * q^60 + 2358 * q^61 + 1071 * q^63 - 548 * q^64 + 2934 * q^66 + 792 * q^67 - 4242 * q^70 - 2712 * q^72 - 2904 * q^73 - 2418 * q^75 + 4296 * q^78 + 1674 * q^79 + 837 * q^81 + 5040 * q^82 + 3864 * q^84 + 348 * q^85 + 1638 * q^87 - 554 * q^88 - 1218 * q^91 - 1479 * q^93 - 1356 * q^94 - 4410 * q^96 - 3354 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$ .

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.65310	+	0.954416i	−0.584458	+	0.337437i	−0.762903	−	0.646513i	$-0.776227\pi$
$2$	−1.65310	+	0.954416i	−0.584458	+	0.337437i	0.178445	+	0.983950i	$0.442893\pi$
$3$	−3.47555	+	3.86271i	−0.668870	+	0.743380i
$3$	−3.47555	+	3.86271i	−0.668870	+	0.743380i
$4$	−2.17818	+	3.77272i	−0.272273	+	0.471590i
$5$	0.623706	+	1.08029i	0.0557859	+	0.0966240i	0.892570	−	0.450909i	$-0.148900\pi$
$5$	0.623706	+	1.08029i	0.0557859	+	0.0966240i	−0.836784	+	0.547533i	$0.815567\pi$
$6$	2.05878	−	9.70256i	0.140082	−	0.660175i
$7$	10.0808	+	15.5363i	0.544314	+	0.838881i
$7$	10.0808	+	15.5363i	0.544314	+	0.838881i
$8$		−	23.5862i		−	1.04237i
$9$	−2.84113	−	26.8501i	−0.105227	−	0.994448i
$10$	−2.06209	−	1.19055i	−0.0652090	−	0.0376484i
$11$	35.2392	+	20.3453i	0.965910	+	0.557668i	0.897987	−	0.440022i	$-0.145029\pi$
$11$	35.2392	+	20.3453i	0.965910	+	0.557668i	0.0679230	+	0.997691i	$0.478363\pi$
$12$	−7.00257	−	21.5260i	−0.168456	−	0.517834i
$13$			19.5973i			0.418101i	0.977905	+	0.209050i	$0.0670373\pi$
$13$			19.5973i			0.418101i	−0.977905	+	0.209050i	$0.932963\pi$
$14$	−31.4927	−	16.0617i	−0.601198	−	0.306619i
$15$	−6.34057	−	1.34540i	−0.109142	−	0.0231588i
$16$	5.08559	+	8.80850i	0.0794623	+	0.137633i
$17$	−52.3592	+	90.6889i	−0.746999	+	1.29384i	0.202256	+	0.979333i	$0.435173\pi$
$17$	−52.3592	+	90.6889i	−0.746999	+	1.29384i	−0.949255	+	0.314507i	$0.898161\pi$
$18$	30.3228	+	41.6742i	0.397064	+	0.545706i
$19$	35.0345	−	20.2272i	0.423025	−	0.244234i	−0.273346	−	0.961916i	$-0.588130\pi$
$19$	35.0345	−	20.2272i	0.423025	−	0.244234i	0.696371	+	0.717682i	$0.254797\pi$
$20$	−5.43418			−0.0607559
$21$	−95.0487	−	15.0578i	−0.987683	−	0.156470i
$22$	−77.6716			−0.752711
$23$	69.6324	−	40.2023i	0.631276	−	0.364467i	−0.149970	−	0.988691i	$-0.547918\pi$
$23$	69.6324	−	40.2023i	0.631276	−	0.364467i	0.781246	+	0.624223i	$0.214584\pi$
$24$	91.1068	+	81.9750i	0.774879	+	0.697212i
$25$	61.7220	−	106.906i	0.493776	−	0.855245i
$26$	−18.7040	−	32.3962i	−0.141083	−	0.244362i
$27$	113.589	+	82.3444i	0.809636	+	0.586933i
$28$	−80.5720	+	4.19132i	−0.543810	+	0.0282888i
$29$		−	211.712i		−	1.35565i	−0.735222	−	0.677827i	$-0.762922\pi$
$29$		−	211.712i		−	1.35565i	0.735222	−	0.677827i	$-0.237078\pi$
$30$	11.7656	−	3.82746i	0.0716034	−	0.0232932i
$31$	−86.6242	−	50.0125i	−0.501876	−	0.289758i	0.227612	−	0.973752i	$-0.426908\pi$
$31$	−86.6242	−	50.0125i	−0.501876	−	0.289758i	−0.729488	+	0.683994i	$0.760242\pi$
$32$	146.596	+	84.6373i	0.809837	+	0.467560i
$33$	−201.064	+	65.4076i	−1.06063	+	0.345030i
$34$		−	199.890i		−	1.00826i
$35$	−10.4962	+	20.5803i	−0.0506910	+	0.0993916i
$36$	107.486	+	47.7656i	0.497622	+	0.221137i
$37$	94.9875	+	164.523i	0.422050	+	0.731012i	0.996140	−	0.0877801i	$-0.0279773\pi$
$37$	94.9875	+	164.523i	0.422050	+	0.731012i	−0.574090	+	0.818792i	$0.694644\pi$
$38$	−38.6103	+	66.8750i	−0.164827	+	0.285488i
$39$	−75.6987	−	68.1113i	−0.310808	−	0.279655i
$40$	25.4799	−	14.7109i	0.100718	−	0.0581497i
$41$	−186.753			−0.711362			−0.355681	−	0.934607i	$-0.615751\pi$
$41$	−186.753			−0.711362			−0.355681	+	0.934607i	$0.615751\pi$
$42$	171.496	−	65.8241i	0.630058	−	0.241830i
$43$	158.618			0.562536			0.281268	−	0.959629i	$-0.409245\pi$
$43$	158.618			0.562536			0.281268	+	0.959629i	$0.409245\pi$
$44$	−153.515	+	88.6317i	−0.525982	+	0.303676i
$45$	27.2339	−	19.8158i	0.0902174	−	0.0656437i
$46$	−76.7393	+	132.916i	−0.245969	+	0.426032i
$47$	179.034	+	310.097i	0.555635	+	0.962388i	0.997854	+	0.0654808i	$0.0208581\pi$
$47$	179.034	+	310.097i	0.555635	+	0.962388i	−0.442219	+	0.896907i	$0.645809\pi$
$48$	−51.6999	−	10.9702i	−0.155463	−	0.0329877i
$49$	−139.753	+	313.238i	−0.407444	+	0.913230i
$50$			235.634i			0.666473i
$51$	−168.328	−	517.442i	−0.462170	−	1.42071i
$52$	−73.9351	−	42.6865i	−0.197172	−	0.113837i
$53$	−366.460	−	211.576i	−0.949758	−	0.548343i	−0.0567521	−	0.998388i	$-0.518074\pi$
$53$	−366.460	−	211.576i	−0.949758	−	0.548343i	−0.893006	+	0.450045i	$0.851408\pi$
$54$	−266.364	−	27.7123i	−0.671251	−	0.0698364i
$55$			50.7580i			0.124440i
$56$	366.442	−	237.769i	0.874427	−	0.567379i
$57$	−43.6323	+	205.629i	−0.101390	+	0.477829i
$58$	202.061	+	349.980i	0.457447	+	0.792322i
$59$	312.781	−	541.753i	0.690180	−	1.19543i	−0.281599	−	0.959532i	$-0.590865\pi$
$59$	312.781	−	541.753i	0.690180	−	1.19543i	0.971779	−	0.235895i	$-0.0758020\pi$
$60$	18.8867	−	20.9907i	0.0406378	−	0.0451647i
$61$	699.575	−	403.900i	1.46838	−	0.847772i	0.469011	−	0.883192i	$-0.344611\pi$
$61$	699.575	−	403.900i	1.46838	−	0.847772i	0.999372	+	0.0354209i	$0.0112772\pi$
$62$	190.931			0.391101
$63$	388.510	−	314.812i	0.776948	−	0.629565i
$64$	−404.486			−0.790012
$65$	−21.1708	+	12.2229i	−0.0403986	+	0.0233241i
$66$	269.952	−	300.023i	0.503466	−	0.559550i
$67$	−149.272	+	258.547i	−0.272187	+	0.471441i	−0.969421	−	0.245402i	$-0.921080\pi$
$67$	−149.272	+	258.547i	−0.272187	+	0.471441i	0.697235	+	0.716843i	$0.254413\pi$
$68$	−228.096	−	395.074i	−0.406775	−	0.704555i
$69$	−86.7208	+	408.695i	−0.151304	+	0.713059i
$70$	−2.29089	−	44.0390i	−0.00391162	−	0.0751952i
$71$			455.386i			0.761189i	0.924742	+	0.380594i	$0.124281\pi$
$71$			455.386i			0.761189i	−0.924742	+	0.380594i	$0.875719\pi$
$72$	−633.292	+	67.0114i	−1.03659	+	0.109686i
$73$	−434.467	−	250.840i	−0.696582	−	0.402172i	0.109491	−	0.993988i	$-0.465078\pi$
$73$	−434.467	−	250.840i	−0.696582	−	0.402172i	−0.806073	+	0.591816i	$0.798411\pi$
$74$	−314.047	−	181.315i	−0.493341	−	0.284831i
$75$	198.428	+	609.970i	0.305500	+	0.939110i
$76$			176.234i			0.265993i
$77$	39.1491	+	752.584i	0.0579410	+	1.11383i
$78$	190.144	+	40.3465i	0.276020	+	0.0585685i
$79$	30.9561	+	53.6176i	0.0440865	+	0.0763601i	0.887227	−	0.461334i	$-0.152629\pi$
$79$	30.9561	+	53.6176i	0.0440865	+	0.0763601i	−0.843140	+	0.537694i	$0.819296\pi$
$80$	−6.34382	+	10.9878i	−0.00886576	+	0.0153559i
$81$	−712.856	+	152.569i	−0.977855	+	0.209285i
$82$	308.720	−	178.240i	0.415761	−	0.240040i
$83$	−73.1180			−0.0966957			−0.0483478	−	0.998831i	$-0.515396\pi$
$83$	−73.1180			−0.0966957			−0.0483478	+	0.998831i	$0.515396\pi$
$84$	263.842	−	325.794i	0.342709	−	0.423179i
$85$	−130.627			−0.166688
$86$	−262.211	+	151.388i	−0.328779	+	0.189820i
$87$	817.783	+	735.816i	1.00777	+	0.906755i
$88$	479.870	−	831.158i	0.581298	−	1.00684i
$89$	57.3723	+	99.3717i	0.0683309	+	0.118353i	0.898167	−	0.439655i	$-0.144899\pi$
$89$	57.3723	+	99.3717i	0.0683309	+	0.118353i	−0.829836	+	0.558008i	$0.811566\pi$
$90$	−26.1077	+	58.7498i	−0.0305777	+	0.0688086i
$91$	−304.469	+	197.557i	−0.350737	+	0.227578i
$92$			350.271i			0.396938i
$93$	494.251	−	160.784i	0.551090	−	0.179274i
$94$	−591.922	−	341.746i	−0.649490	−	0.374983i
$95$	43.7025	+	25.2316i	0.0471977	+	0.0272496i
$96$	−836.432	+	272.098i	−0.889250	+	0.289280i
$97$		−	1416.51i		−	1.48273i	−0.671101	−	0.741366i	$-0.734178\pi$
$97$		−	1416.51i		−	1.48273i	0.671101	−	0.741366i	$-0.265822\pi$
$98$	−67.9336	−	651.195i	−0.0700238	−	0.671231i
$99$	446.156	−	1003.98i	0.452933	−	1.01923i
$100$	268.883	+	465.720i	0.268883	+	0.465720i
$101$	120.406	−	208.549i	0.118622	−	0.205459i	−0.800600	−	0.599199i	$-0.795486\pi$
$101$	120.406	−	208.549i	0.118622	−	0.205459i	0.919222	+	0.393740i	$0.128819\pi$
$102$	772.117	+	694.727i	0.749520	+	0.674394i
$103$	−960.453	+	554.518i	−0.918799	+	0.530469i	−0.883252	−	0.468899i	$-0.844651\pi$
$103$	−960.453	+	554.518i	−0.918799	+	0.530469i	−0.0355471	+	0.999368i	$0.511317\pi$
$104$	462.226			0.435817
$105$	−43.0157	−	112.072i	−0.0399800	−	0.104163i
$106$	807.725			0.740124
$107$	924.644	−	533.843i	0.835408	−	0.482323i	−0.0202926	−	0.999794i	$-0.506460\pi$
$107$	924.644	−	533.843i	0.835408	−	0.482323i	0.855701	+	0.517471i	$0.173126\pi$
$108$	−558.079	+	249.178i	−0.497233	+	0.222011i
$109$	−5.04376	+	8.73604i	−0.00443215	+	0.00767671i	−0.868233	−	0.496157i	$-0.834744\pi$
$109$	−5.04376	+	8.73604i	−0.00443215	+	0.00767671i	0.863801	+	0.503833i	$0.168077\pi$
$110$	−48.4442	−	83.9079i	−0.0419907	−	0.0727300i
$111$	−965.640	−	204.899i	−0.825716	−	0.175208i
$112$	−85.5845	+	167.808i	−0.0722051	+	0.141575i
$113$		−	884.294i		−	0.736171i	−0.929792	−	0.368086i	$-0.880013\pi$
$113$		−	884.294i		−	0.736171i	0.929792	−	0.368086i	$-0.119987\pi$
$114$	−124.127	−	381.568i	−0.101979	−	0.313484i
$115$	86.8602	+	50.1487i	0.0704326	+	0.0406643i
$116$	798.731	+	461.148i	0.639313	+	0.369108i
$117$	526.189	−	55.6784i	0.415780	−	0.0439954i
$118$			1194.09i			0.931569i
$119$	−1936.79	+	100.751i	−1.49198	+	0.0776122i
$120$	−31.7330	+	149.550i	−0.0241401	+	0.113767i
$121$	162.366	+	281.226i	0.121988	+	0.211289i
$122$	−770.976	+	1335.37i	−0.572139	+	0.990973i
$123$	649.067	−	721.372i	0.475808	−	0.528812i
$124$	377.366	−	217.873i	0.273294	−	0.157787i
$125$	309.912			0.221755
$126$	−341.783	+	891.215i	−0.241655	+	0.630125i
$127$	−840.132			−0.587005			−0.293503	−	0.955958i	$-0.594821\pi$
$127$	−840.132			−0.587005			−0.293503	+	0.955958i	$0.594821\pi$
$128$	−504.115	+	291.051i	−0.348108	+	0.200980i
$129$	−551.285	+	612.697i	−0.376263	+	0.418178i
$130$	23.3315	−	40.4114i	0.0157408	−	0.0272639i
$131$	−258.951	−	448.517i	−0.172707	−	0.299138i	0.766658	−	0.642056i	$-0.221918\pi$
$131$	−258.951	−	448.517i	−0.172707	−	0.299138i	−0.939366	+	0.342918i	$0.888585\pi$
$132$	191.189	−	901.027i	0.126067	−	0.594124i
$133$	667.434	+	340.400i	0.435142	+	0.221928i
$134$		−	569.871i		−	0.367383i
$135$	−18.1098	+	174.067i	−0.0115455	+	0.110973i
$136$	2139.01	+	1234.96i	1.34866	+	0.778651i
$137$	950.957	+	549.035i	0.593034	+	0.342389i	0.766296	−	0.642487i	$-0.222097\pi$
$137$	950.957	+	549.035i	0.593034	+	0.342389i	−0.173262	+	0.984876i	$0.555431\pi$
$138$	−246.707	−	758.380i	−0.152182	−	0.467808i
$139$			828.268i			0.505416i	0.967543	+	0.252708i	$0.0813212\pi$
$139$			828.268i			0.505416i	−0.967543	+	0.252708i	$0.918679\pi$
$140$	−54.7811	−	84.4270i	−0.0330703	−	0.0509670i
$141$	−1820.06	−	386.197i	−1.08707	−	0.230664i
$142$	−434.628	−	752.797i	−0.256853	−	0.444883i
$143$	−398.714	+	690.592i	−0.233162	+	0.403848i
$144$	222.060	−	161.575i	0.128507	−	0.0935039i
$145$	228.710	−	132.046i	0.130989	−	0.0756264i
$146$	957.621			0.542830
$147$	−724.230	−	1628.50i	−0.406350	−	0.913717i
$148$	−827.601			−0.459651
$149$	773.007	−	446.296i	0.425015	−	0.245382i	−0.272206	−	0.962239i	$-0.587753\pi$
$149$	773.007	−	446.296i	0.425015	−	0.245382i	0.697221	+	0.716857i	$0.254420\pi$
$150$	−910.186	−	818.956i	−0.495442	−	0.445783i
$151$	−712.518	+	1234.12i	−0.383999	+	0.665106i	−0.991630	−	0.129113i	$-0.958787\pi$
$151$	−712.518	+	1234.12i	−0.383999	+	0.665106i	0.607630	+	0.794220i	$0.292120\pi$
$152$	−477.083	−	826.332i	−0.254583	−	0.440950i
$153$	2583.76	+	1148.19i	1.36526	+	0.606705i
$154$	−782.996	−	1206.73i	−0.409712	−	0.631436i
$155$		−	124.772i		−	0.0646577i
$156$	421.851	−	137.231i	0.216507	−	0.0704314i
$157$	−244.872	−	141.377i	−0.124477	−	0.0718670i	0.436468	−	0.899720i	$-0.356229\pi$
$157$	−244.872	−	141.377i	−0.124477	−	0.0718670i	−0.560946	+	0.827853i	$0.689562\pi$
$158$	−102.347	−	59.0900i	−0.0515334	−	0.0297528i
$159$	2090.91	−	680.189i	1.04289	−	0.339261i
$160$			211.155i			0.104333i
$161$	1326.55	+	676.557i	0.649358	+	0.331181i
$162$	1032.81	−	932.572i	0.500894	−	0.452283i
$163$	−1158.07	−	2005.83i	−0.556484	−	0.963858i	−0.997786	−	0.0664997i	$-0.978817\pi$
$163$	−1158.07	−	2005.83i	−0.556484	−	0.963858i	0.441303	−	0.897358i	$-0.354516\pi$
$164$	406.781	−	704.565i	0.193685	−	0.335471i
$165$	−196.064	−	176.412i	−0.0925063	−	0.0832342i
$166$	120.871	−	69.7849i	0.0565145	−	0.0326287i
$167$	−2344.70			−1.08646			−0.543229	−	0.839585i	$-0.682798\pi$
$167$	−2344.70			−1.08646			−0.543229	+	0.839585i	$0.682798\pi$
$168$	−355.155	+	2241.84i	−0.163100	+	1.02953i
$169$	1812.95			0.825192
$170$	215.939	−	124.672i	0.0974221	−	0.0562467i
$171$	−642.640	−	883.213i	−0.287391	−	0.394977i
$172$	−345.499	+	598.423i	−0.153163	+	0.265287i
$173$	516.901	+	895.298i	0.227163	+	0.393458i	0.956966	−	0.290199i	$-0.0937216\pi$
$173$	516.901	+	895.298i	0.227163	+	0.393458i	−0.729803	+	0.683657i	$0.760388\pi$
$174$	−2054.15	−	435.869i	−0.894969	−	0.189903i
$175$	2283.13	−	118.767i	0.986218	−	0.0513026i
$176$			413.872i			0.177255i
$177$	1005.55	+	3091.07i	0.427016	+	1.31265i
$178$	−189.684	−	109.514i	−0.0798730	−	0.0461147i
$179$	−125.472	−	72.4412i	−0.0523922	−	0.0302486i	0.473575	−	0.880753i	$-0.342963\pi$
$179$	−125.472	−	72.4412i	−0.0523922	−	0.0302486i	−0.525967	+	0.850505i	$0.676297\pi$
$180$	15.4392	+	145.908i	0.00639316	+	0.0604186i
$181$		−	2057.17i		−	0.844797i	−0.906410	−	0.422398i	$-0.861188\pi$
$181$		−	2057.17i		−	0.844797i	0.906410	−	0.422398i	$-0.138812\pi$
$182$	314.766	−	617.171i	0.128198	−	0.251361i
$183$	−871.257	+	4106.03i	−0.351941	+	1.65862i
$184$	−948.219	−	1642.36i	−0.379911	−	0.658025i
$185$	−118.489	+	205.228i	−0.0470889	+	0.0815604i
$186$	−663.589	+	737.511i	−0.261595	+	0.290736i
$187$	−3690.19	+	2130.53i	−1.44307	+	0.833155i
$188$	−1559.88			−0.605137
$189$	−134.257	+	2594.85i	−0.0516706	+	0.998664i
$190$	−96.3259			−0.0367801
$191$	−2553.66	+	1474.36i	−0.967417	+	0.558538i	−0.898448	−	0.439080i	$-0.855304\pi$
$191$	−2553.66	+	1474.36i	−0.967417	+	0.558538i	−0.0689690	+	0.997619i	$0.521971\pi$
$192$	1405.81	−	1562.41i	0.528415	−	0.587279i
$193$	1135.40	−	1966.57i	0.423460	−	0.733455i	−0.572815	−	0.819685i	$-0.694149\pi$
$193$	1135.40	−	1966.57i	0.423460	−	0.733455i	0.996275	+	0.0862300i	$0.0274820\pi$
$194$	1351.94	+	2341.63i	0.500329	+	0.866594i
$195$	26.3662	−	124.258i	0.00968270	−	0.0456323i
$196$	−877.352	−	1209.54i	−0.319735	−	0.440794i
$197$		−	495.849i		−	0.179329i	−0.995972	−	0.0896645i	$-0.971421\pi$
$197$		−	495.849i		−	0.179329i	0.995972	−	0.0896645i	$-0.0285795\pi$
$198$	220.675	+	2085.49i	0.0792055	+	0.748532i
$199$	727.207	+	419.853i	0.259047	+	0.149561i	0.623900	−	0.781504i	$-0.285547\pi$
$199$	727.207	+	419.853i	0.259047	+	0.149561i	−0.364853	+	0.931065i	$0.618881\pi$
$200$	−2521.50	−	1455.79i	−0.891484	−	0.514699i
$201$	−479.890	−	1475.19i	−0.168402	−	0.517670i
$202$			459.668i			0.160109i
$203$	3289.22	−	2134.24i	1.13723	−	0.737902i
$204$	2318.81	+	492.028i	0.795831	+	0.168867i
$205$	−116.479	−	201.747i	−0.0396840	−	0.0687347i
$206$	1058.48	−	1833.34i	0.357999	−	0.620073i
$207$	−1277.27	−	1755.42i	−0.428871	−	0.589420i
$208$	−172.623	+	99.6638i	−0.0575444	+	0.0332233i
$209$	1646.12			0.544805
$210$	178.072	+	144.211i	0.0585150	+	0.0473880i
$211$	4001.71			1.30564			0.652818	−	0.757514i	$-0.273586\pi$
$211$	4001.71			1.30564			0.652818	+	0.757514i	$0.273586\pi$
$212$	1596.43	−	921.701i	0.517186	−	0.298598i
$213$	−1759.03	−	1582.72i	−0.565852	−	0.509136i
$214$	−1019.02	+	1764.99i	−0.325507	+	0.563795i
$215$	98.9311	+	171.354i	0.0313816	+	0.0543545i
$216$	1942.19	−	2679.13i	0.611803	−	0.843943i
$217$	−96.2355	−	1849.99i	−0.0301055	−	0.578734i
$218$		−	19.2554i		−	0.00598228i
$219$	2478.93	−	806.416i	0.764889	−	0.248825i
$220$	−191.496	−	110.560i	−0.0586848	−	0.0338817i
$221$	−1777.26	−	1026.10i	−0.540955	−	0.312321i
$222$	1791.85	−	582.905i	0.541718	−	0.176225i
$223$			3040.54i			0.913047i	0.889711	+	0.456523i	$0.150905\pi$
$223$			3040.54i			0.913047i	−0.889711	+	0.456523i	$0.849095\pi$
$224$	162.862	+	3130.78i	0.0485788	+	0.933856i
$225$	−3045.79	−	1353.51i	−0.902455	−	0.401040i
$226$	843.984	+	1461.82i	0.248411	+	0.430261i
$227$	2198.24	−	3807.46i	0.642741	−	1.11326i	−0.342078	−	0.939672i	$-0.611131\pi$
$227$	2198.24	−	3807.46i	0.642741	−	1.11326i	0.984818	−	0.173588i	$-0.0555360\pi$
$228$	−680.742	−	612.510i	−0.197734	−	0.177914i
$229$	−1717.81	+	991.778i	−0.495703	+	0.286194i	−0.726937	−	0.686704i	$-0.759057\pi$
$229$	−1717.81	+	991.778i	−0.495703	+	0.286194i	0.231234	+	0.972898i	$0.425724\pi$
$230$	−191.451			−0.0548865
$231$	−3043.08	−	2464.42i	−0.866754	−	0.701935i
$232$	−4993.49			−1.41310
$233$	−3787.78	+	2186.87i	−1.06500	+	0.614879i	−0.926812	−	0.375526i	$-0.877462\pi$
$233$	−3787.78	+	2186.87i	−1.06500	+	0.614879i	−0.138191	+	0.990406i	$0.544129\pi$
$234$	−816.701	+	594.245i	−0.228160	+	0.166013i
$235$	−223.329	+	386.818i	−0.0619932	+	0.107375i
$236$	1362.59	+	2360.07i	0.375834	+	0.650964i
$237$	−314.699	−	66.7758i	−0.0862527	−	0.0183019i
$238$	3105.55	−	2015.06i	0.845810	−	0.548810i
$239$			3826.41i			1.03561i	0.855500	+	0.517803i	$0.173250\pi$
$239$			3826.41i			1.03561i	−0.855500	+	0.517803i	$0.826750\pi$
$240$	−20.3946	−	62.6931i	−0.00548526	−	0.0168618i
$241$	2979.03	+	1719.94i	0.796250	+	0.459715i	0.842158	−	0.539231i	$-0.181285\pi$
$241$	2979.03	+	1719.94i	0.796250	+	0.459715i	−0.0459083	+	0.998946i	$0.514618\pi$
$242$	−536.813	−	309.929i	−0.142594	−	0.0823264i
$243$	1888.24	−	3283.82i	0.498479	−	0.866902i
$244$			3519.07i			0.923300i
$245$	−425.553	+	44.3943i	−0.110970	+	0.0115765i
$246$	−384.483	+	1811.98i	−0.0996493	+	0.469624i
$247$	396.398	+	686.582i	0.102114	+	0.176867i
$248$	−1179.61	+	2043.14i	−0.302036	+	0.523142i
$249$	254.125	−	282.434i	0.0646768	−	0.0718816i
$250$	−512.314	+	295.785i	−0.129606	+	0.0748282i
$251$	−2046.61			−0.514664			−0.257332	−	0.966323i	$-0.582843\pi$
$251$	−2046.61			−0.514664			−0.257332	+	0.966323i	$0.582843\pi$
$252$	341.453	+	2151.46i	0.0853552	+	0.537814i
$253$	3271.72			0.813008
$254$	1388.82	−	801.835i	0.343080	−	0.198077i
$255$	454.000	−	504.575i	0.111493	−	0.123913i
$256$	2173.51	−	3764.63i	0.530642	−	0.919099i
$257$	−3025.57	−	5240.44i	−0.734357	−	1.27194i	−0.955005	−	0.296590i	$-0.904150\pi$
$257$	−3025.57	−	5240.44i	−0.734357	−	1.27194i	0.220648	−	0.975354i	$-0.429183\pi$
$258$	326.560	−	1539.00i	0.0788014	−	0.371372i
$259$	−1598.53	+	3134.29i	−0.383505	+	0.751950i
$260$		−	106.495i		−	0.0254021i
$261$	−5684.49	+	601.501i	−1.34813	+	0.142651i
$262$	856.143	+	494.294i	0.201880	+	0.116556i
$263$	5433.69	+	3137.14i	1.27398	+	0.735530i	0.975734	−	0.218960i	$-0.0702665\pi$
$263$	5433.69	+	3137.14i	1.27398	+	0.735530i	0.298242	+	0.954490i	$0.403600\pi$
$264$	1542.72	+	4742.33i	0.359650	+	1.10557i
$265$		−	527.844i		−	0.122359i
$266$	−1428.22	+	74.2951i	−0.329209	+	0.0171253i
$267$	−583.245	−	123.758i	−0.133685	−	0.0283666i
$268$	−650.284	−	1126.32i	−0.148218	−	0.256721i
$269$	−1668.18	+	2889.37i	−0.378106	+	0.654899i	−0.990787	−	0.135432i	$-0.956758\pi$
$269$	−1668.18	+	2889.37i	−0.378106	+	0.654899i	0.612681	+	0.790331i	$0.290091\pi$
$270$	−136.195	−	305.034i	−0.0306985	−	0.0687548i
$271$	2462.26	−	1421.59i	0.551925	−	0.318654i	−0.197973	−	0.980207i	$-0.563436\pi$
$271$	2462.26	−	1421.59i	0.551925	−	0.318654i	0.749898	+	0.661553i	$0.230103\pi$
$272$	−1065.11			−0.237433
$273$	295.091	−	1862.70i	0.0654202	−	0.412951i
$274$	−2096.03			−0.462138
$275$	4350.06	−	2511.51i	0.953886	−	0.550726i
$276$	−1353.00	−	1217.39i	−0.295076	−	0.265500i
$277$	−3174.17	+	5497.82i	−0.688510	+	1.19253i	0.283809	+	0.958881i	$0.408402\pi$
$277$	−3174.17	+	5497.82i	−0.688510	+	1.19253i	−0.972320	+	0.233654i	$0.924932\pi$
$278$	−790.512	−	1369.21i	−0.170546	−	0.295394i
$279$	−1096.73	+	2467.96i	−0.235339	+	0.529580i
$280$	485.411	+	247.566i	0.103603	+	0.0528390i
$281$		−	3735.88i		−	0.793110i	−0.918011	−	0.396555i	$-0.870206\pi$
$281$		−	3735.88i		−	0.793110i	0.918011	−	0.396555i	$-0.129794\pi$
$282$	3377.32	−	1098.67i	0.713179	−	0.232003i
$283$	−4777.96	−	2758.56i	−1.00361	−	0.579432i	−0.0942927	−	0.995545i	$-0.530059\pi$
$283$	−4777.96	−	2758.56i	−1.00361	−	0.579432i	−0.909313	+	0.416112i	$0.863392\pi$
$284$	−1718.05	−	991.914i	−0.358969	−	0.207251i
$285$	−249.353	+	81.1164i	−0.0518259	+	0.0168594i
$286$		−	1522.15i		−	0.314709i
$287$	−1882.62	−	2901.44i	−0.387205	−	0.596748i
$288$	1856.02	−	4176.59i	0.379747	−	0.854541i
$289$	−3026.48	−	5242.01i	−0.616014	−	1.06697i
$290$	−252.054	+	436.570i	−0.0510383	+	0.0884008i
$291$	5471.58	+	4923.16i	1.10223	+	0.991755i
$292$	1892.70	−	1092.75i	0.379321	−	0.219001i
$293$	7574.50			1.51026			0.755131	−	0.655574i	$-0.227573\pi$
$293$	7574.50			1.51026			0.755131	+	0.655574i	$0.227573\pi$
$294$	2751.49	+	2000.85i	0.545816	+	0.396912i
$295$	780.333			0.154009
$296$	3880.48	−	2240.40i	0.761988	−	0.439934i
$297$	2327.45	+	5212.75i	0.454721	+	1.01843i
$298$	−851.904	+	1475.54i	−0.165602	+	0.286831i
$299$	787.855	+	1364.61i	0.152384	+	0.263937i
$300$	−2733.46	−	580.012i	−0.526055	−	0.111623i
$301$	1599.01	+	2464.34i	0.306196	+	0.471901i
$302$		−	2720.15i		−	0.518302i
$303$	387.088	+	1189.91i	0.0733915	+	0.225606i
$304$	356.343	+	205.735i	0.0672291	+	0.0388148i
$305$	872.657	+	503.829i	0.163830	+	0.0945874i
$306$	−5367.06	+	567.912i	−1.00266	+	0.106096i
$307$		−	10635.6i		−	1.97723i	−0.150480	−	0.988613i	$-0.548082\pi$
$307$		−	10635.6i		−	1.97723i	0.150480	−	0.988613i	$-0.451918\pi$
$308$	−2924.57	−	1491.57i	−0.541047	−	0.275941i
$309$	1196.16	−	5637.21i	0.220217	−	1.03783i
$310$	119.085	+	206.261i	0.0218179	+	0.0377897i
$311$	−2885.59	+	4997.99i	−0.526132	+	0.911287i	0.473405	+	0.880845i	$0.343025\pi$
$311$	−2885.59	+	4997.99i	−0.526132	+	0.911287i	−0.999537	+	0.0304419i	$0.990309\pi$
$312$	−1606.49	+	1785.45i	−0.291505	+	0.323978i
$313$	−2030.41	+	1172.26i	−0.366664	+	0.211694i	−0.672000	−	0.740551i	$-0.734565\pi$
$313$	−2030.41	+	1172.26i	−0.366664	+	0.211694i	0.305336	+	0.952245i	$0.401231\pi$
$314$	539.730			0.0970023
$315$	582.404	+	223.354i	0.104174	+	0.0399509i
$316$	−269.712			−0.0480142
$317$	−6852.10	+	3956.06i	−1.21405	+	0.700929i	−0.963638	−	0.267211i	$-0.913898\pi$
$317$	−6852.10	+	3956.06i	−1.21405	+	0.700929i	−0.250407	+	0.968141i	$0.580565\pi$
$318$	−2807.29	+	3120.01i	−0.495047	+	0.550193i
$319$	4307.36	−	7460.56i	0.756005	−	1.30944i
$320$	−252.280	−	436.962i	−0.0440715	−	0.0763341i
$321$	−1151.56	+	5427.03i	−0.200230	+	0.943637i
$322$	−2838.63	+	147.664i	−0.491275	+	0.0255559i
$323$			4236.32i			0.729769i
$324$	977.130	−	3021.73i	0.167546	−	0.518129i
$325$	2095.06	+	1209.58i	0.357579	+	0.206448i
$326$	3828.79	+	2210.55i	0.650482	+	0.375556i
$327$	−16.2150	−	49.8451i	−0.00274218	−	0.00842949i
$328$			4404.78i			0.741505i
$329$	−3012.94	+	5907.57i	−0.504889	+	0.989953i
$330$	492.482	+	104.500i	0.0821523	+	0.0174319i
$331$	2440.02	+	4226.23i	0.405182	+	0.701797i	0.994343	−	0.106220i	$-0.0338747\pi$
$331$	2440.02	+	4226.23i	0.405182	+	0.701797i	−0.589160	+	0.808016i	$0.700541\pi$
$332$	159.264	−	275.854i	0.0263276	−	0.0456007i
$333$	4147.59	−	3017.86i	0.682543	−	0.496629i
$334$	3876.02	−	2237.82i	0.634989	−	0.366611i
$335$	−372.407			−0.0607367
$336$	−350.743	−	913.814i	−0.0569482	−	0.148371i
$337$	−4136.39			−0.668616			−0.334308	−	0.942464i	$-0.608503\pi$
$337$	−4136.39			−0.668616			−0.334308	+	0.942464i	$0.608503\pi$
$338$	−2996.97	+	1730.30i	−0.482290	+	0.278450i
$339$	3415.77	+	3073.41i	0.547255	+	0.492403i
$340$	284.529	−	492.819i	0.0453846	−	0.0786085i
$341$	−2035.04	−	3524.80i	−0.323178	−	0.559761i
$342$	1905.30	+	846.691i	0.301248	+	0.133871i
$343$	−6275.39	+	986.454i	−0.987869	+	0.155287i
$344$		−	3741.20i		−	0.586373i
$345$	−495.597	+	161.222i	−0.0773393	+	0.0251591i
$346$	−1708.97	−	986.676i	−0.265535	−	0.153306i
$347$	2009.83	+	1160.38i	0.310933	+	0.179517i	0.647344	−	0.762198i	$-0.275880\pi$
$347$	2009.83	+	1160.38i	0.310933	+	0.179517i	−0.336411	+	0.941715i	$0.609213\pi$
$348$	−4557.31	+	1482.53i	−0.702004	+	0.228368i
$349$		−	226.795i		−	0.0347853i	−0.999849	−	0.0173926i	$-0.994463\pi$
$349$		−	226.795i		−	0.0347853i	0.999849	−	0.0173926i	$-0.00553653\pi$
$350$	−3660.88	+	2375.39i	−0.559092	+	0.362771i
$351$	−1613.73	+	2226.03i	−0.245397	+	0.338509i
$352$	3443.95	+	5965.10i	0.521486	+	0.903241i
$353$	742.854	−	1286.66i	0.112006	−	0.194000i	−0.804573	−	0.593854i	$-0.797606\pi$
$353$	742.854	−	1286.66i	0.112006	−	0.194000i	0.916579	+	0.399854i	$0.130939\pi$
$354$	−4612.44	−	4150.13i	−0.692509	−	0.623098i
$355$	−491.949	+	284.027i	−0.0735491	+	0.0424636i
$356$	−499.869			−0.0744185
$357$	6342.25	−	7831.45i	0.940245	−	1.16102i
$358$	276.556			0.0408280
$359$	9419.94	−	5438.60i	1.38486	−	0.799550i	0.392131	−	0.919909i	$-0.371738\pi$
$359$	9419.94	−	5438.60i	1.38486	−	0.799550i	0.992730	+	0.120359i	$0.0384045\pi$
$360$	−467.380	−	642.344i	−0.0684252	−	0.0940402i
$361$	−2611.22	+	4522.77i	−0.380700	+	0.659392i
$362$	1963.39	+	3400.70i	0.285066	+	0.493748i
$363$	−1650.61	−	350.241i	−0.238662	−	0.0506416i
$364$	−82.1386	−	1578.99i	−0.0118276	−	0.227367i
$365$		−	625.800i		−	0.0897421i
$366$	−2478.59	−	7619.21i	−0.353983	−	1.08815i
$367$	−3299.69	−	1905.08i	−0.469325	−	0.270965i	0.246632	−	0.969109i	$-0.420676\pi$
$367$	−3299.69	−	1905.08i	−0.469325	−	0.270965i	−0.715957	+	0.698144i	$0.754009\pi$
$368$	708.243	+	408.904i	0.100325	+	0.0579229i
$369$	530.587	+	5014.32i	0.0748544	+	0.707413i
$370$		−	452.349i		−	0.0635581i
$371$	−407.121	−	7826.30i	−0.0569721	−	1.09521i
$372$	−469.976	+	2214.89i	−0.0655030	+	0.308700i
$373$	4869.55	+	8434.30i	0.675967	+	1.17081i	0.976185	+	0.216938i	$0.0696070\pi$
$373$	4869.55	+	8434.30i	0.675967	+	1.17081i	−0.300219	+	0.953870i	$0.597060\pi$
$374$	4066.83	−	7043.95i	0.562274	−	0.973888i
$375$	−1077.11	+	1197.10i	−0.148325	+	0.164848i
$376$	7314.00	−	4222.74i	1.00317	−	0.579179i
$377$	4148.98			0.566800
$378$	−2254.63	−	4417.67i	−0.306787	−	0.601113i
$379$	320.171			0.0433933			0.0216967	−	0.999765i	$-0.493093\pi$
$379$	320.171			0.0433933			0.0216967	+	0.999765i	$0.493093\pi$
$380$	−190.384	+	109.918i	−0.0257013	+	0.0148386i
$381$	2919.92	−	3245.19i	0.392630	−	0.436368i
$382$	2814.30	−	4874.51i	0.376943	−	0.652884i
$383$	−2185.13	−	3784.75i	−0.291527	−	0.504939i	0.682644	−	0.730751i	$-0.260830\pi$
$383$	−2185.13	−	3784.75i	−0.291527	−	0.504939i	−0.974171	+	0.225812i	$0.927497\pi$
$384$	627.829	−	2958.81i	0.0834343	−	0.393206i
$385$	−788.592	+	511.683i	−0.104391	+	0.0677346i
$386$			4334.57i			0.571564i
$387$	−450.654	−	4258.92i	−0.0591939	−	0.559413i
$388$	5344.11	+	3085.42i	0.699242	+	0.403708i
$389$	−11877.4	−	6857.42i	−1.54809	−	0.893791i	−0.998288	−	0.0584981i	$-0.981369\pi$
$389$	−11877.4	−	6857.42i	−1.54809	−	0.893791i	−0.549805	−	0.835293i	$-0.685298\pi$
$390$	75.0078	+	230.575i	0.00973889	+	0.0299375i
$391$			8419.84i			1.08903i
$392$	7388.10	+	3296.25i	0.951927	+	0.424709i
$393$	2632.49	+	558.587i	0.337892	+	0.0716971i
$394$	473.246	+	819.687i	0.0605122	+	0.104810i
$395$	−38.6150	+	66.8832i	−0.00491882	+	0.00851964i
$396$	2815.93	+	3870.07i	0.357337	+	0.491107i
$397$	−2181.61	+	1259.55i	−0.275798	+	0.159232i	−0.631520	−	0.775360i	$-0.717568\pi$
$397$	−2181.61	+	1259.55i	−0.275798	+	0.159232i	0.355722	+	0.934592i	$0.384235\pi$
$398$	−1602.86			−0.201869
$399$	−3634.57	+	1395.03i	−0.456030	+	0.175035i
$400$	1255.57			0.156946
$401$	−2268.96	+	1309.98i	−0.282560	+	0.163136i	−0.634582	−	0.772856i	$-0.718828\pi$
$401$	−2268.96	+	1309.98i	−0.282560	+	0.163136i	0.352022	+	0.935992i	$0.385494\pi$
$402$	2201.25	+	1980.61i	0.273105	+	0.245731i
$403$	980.109	−	1697.60i	0.121148	−	0.209835i
$404$	524.530	+	908.513i	0.0645950	+	0.111882i
$405$	−609.431	−	674.933i	−0.0747725	−	0.0828091i
$406$	−3400.45	+	6667.38i	−0.415669	+	0.815016i
$407$			7730.22i			0.941456i
$408$	−12204.5	+	3970.22i	−1.48091	+	0.481753i
$409$	−12058.7	−	6962.09i	−1.45786	−	0.841694i	−0.458952	−	0.888461i	$-0.651775\pi$
$409$	−12058.7	−	6962.09i	−1.45786	−	0.841694i	−0.998906	+	0.0467669i	$0.985108\pi$
$410$	385.101	+	222.338i	0.0463872	+	0.0267817i
$411$	−5425.86	+	1765.08i	−0.651187	+	0.211836i
$412$		−	4831.36i		−	0.577729i
$413$	11569.9	−	601.863i	1.37850	−	0.0717088i
$414$	3786.85	+	1682.83i	0.449549	+	0.199774i
$415$	−45.6041	−	78.9886i	−0.00539426	−	0.00934313i
$416$	−1658.66	+	2872.89i	−0.195487	+	0.338593i
$417$	−3199.36	−	2878.69i	−0.375716	−	0.338057i
$418$	−2721.19	+	1571.08i	−0.318416	+	0.183837i
$419$	−15171.1			−1.76887			−0.884433	−	0.466666i	$-0.845455\pi$
$419$	−15171.1			−1.76887			−0.884433	+	0.466666i	$0.845455\pi$
$420$	516.512	+	81.8265i	0.0600076	+	0.00950648i
$421$	−1052.53			−0.121846			−0.0609228	−	0.998142i	$-0.519404\pi$
$421$	−1052.53			−0.121846			−0.0609228	+	0.998142i	$0.519404\pi$
$422$	−6615.22	+	3819.30i	−0.763090	+	0.440570i
$423$	7817.47	−	5688.11i	0.898577	−	0.653819i
$424$	−4990.27	+	8643.40i	−0.571578	+	0.990002i
$425$	6463.43	+	11195.0i	0.737700	+	1.27773i
$426$	4418.41	+	937.541i	0.502518	+	0.106629i
$427$	13327.4	+	6797.16i	1.51044	+	0.770345i
$428$			4651.23i			0.525294i
$429$	−1281.81	−	3940.30i	−0.144258	−	0.443449i
$430$	−327.085	−	188.843i	−0.0366824	−	0.0211786i
$431$	−6923.58	−	3997.33i	−0.773776	−	0.446740i	0.0604442	−	0.998172i	$-0.480748\pi$
$431$	−6923.58	−	3997.33i	−0.773776	−	0.446740i	−0.834220	+	0.551432i	$0.814082\pi$
$432$	−147.665	+	1419.32i	−0.0164456	+	0.158072i
$433$		−	12889.4i		−	1.43055i	−0.698845	−	0.715273i	$-0.746303\pi$
$433$		−	12889.4i		−	1.43055i	0.698845	−	0.715273i	$-0.253697\pi$
$434$	1924.74	+	2966.36i	0.212882	+	0.328087i
$435$	−284.838	+	1342.38i	−0.0313953	+	0.147959i
$436$	−21.9724	−	38.0574i	−0.00241351	−	0.00418032i
$437$	1626.36	−	2816.94i	0.178030	−	0.308358i
$438$	−3328.26	+	3699.02i	−0.363083	+	0.403529i
$439$	12456.7	−	7191.89i	1.35427	−	0.781891i	0.365430	−	0.930839i	$-0.380922\pi$
$439$	12456.7	−	7191.89i	1.35427	−	0.781891i	0.988845	+	0.148948i	$0.0475888\pi$
$440$	1197.19			0.129713
$441$	8807.53	+	2862.44i	0.951034	+	0.309085i
$442$	3917.30			0.421554
$443$	−3432.16	+	1981.56i	−0.368097	+	0.212521i	−0.672627	−	0.739982i	$-0.734834\pi$
$443$	−3432.16	+	1981.56i	−0.368097	+	0.212521i	0.304530	+	0.952503i	$0.401501\pi$
$444$	2876.37	−	3196.79i	0.307447	−	0.341695i
$445$	−71.5668	+	123.957i	−0.00762380	+	0.0132048i
$446$	−2901.94	−	5026.30i	−0.308096	−	0.533637i
$447$	−962.710	+	4537.03i	−0.101867	+	0.480076i
$448$	−4077.56	−	6284.22i	−0.430015	−	0.662726i
$449$		−	13479.1i		−	1.41675i	−0.705838	−	0.708373i	$-0.749430\pi$
$449$		−	13479.1i		−	1.41675i	0.705838	−	0.708373i	$-0.250570\pi$
$450$	6326.79	−	669.465i	0.662773	−	0.0701308i
$451$	−6581.00	−	3799.54i	−0.687112	−	0.396704i
$452$	3336.19	+	1926.15i	0.347171	+	0.200439i
$453$	−2290.65	−	7041.49i	−0.237581	−	0.730327i
$454$			8392.13i			0.867538i
$455$	−403.318	−	205.698i	−0.0415557	−	0.0211940i
$456$	4850.01	+	1029.12i	0.498076	+	0.105686i
$457$	−1989.79	−	3446.42i	−0.203673	−	0.352772i	0.746036	−	0.665905i	$-0.231955\pi$
$457$	−1989.79	−	3446.42i	−0.203673	−	0.352772i	−0.949709	+	0.313134i	$0.898621\pi$
$458$	1893.14	−	3279.01i	0.193145	−	0.334537i
$459$	−13415.1	+	5989.74i	−1.36419	+	0.609101i
$460$	−378.395	+	218.466i	−0.0383538	+	0.0221436i
$461$	9053.72			0.914694			0.457347	−	0.889288i	$-0.348800\pi$
$461$	9053.72			0.914694			0.457347	+	0.889288i	$0.348800\pi$
$462$	7382.59	+	1169.56i	0.743440	+	0.117777i
$463$	−5736.10			−0.575764			−0.287882	−	0.957666i	$-0.592951\pi$
$463$	−5736.10			−0.575764			−0.287882	+	0.957666i	$0.592951\pi$
$464$	1864.87	−	1076.68i	0.186582	−	0.107723i
$465$	481.960	+	433.652i	0.0480653	+	0.0432476i
$466$	4174.37	−	7230.23i	0.414966	−	0.718742i
$467$	6196.30	+	10732.3i	0.613984	+	1.06345i	0.990562	+	0.137067i	$0.0437675\pi$
$467$	6196.30	+	10732.3i	0.613984	+	1.06345i	−0.376578	+	0.926385i	$0.622899\pi$
$468$	−936.077	+	2106.44i	−0.0924576	+	0.208056i
$469$	−5521.65	+	287.234i	−0.543638	+	0.0282798i
$470$		−	852.596i		−	0.0836752i
$471$	1397.17	−	454.509i	0.136684	−	0.0444643i
$472$	−12777.9	−	7377.32i	−1.24608	−	0.719425i
$473$	5589.57	+	3227.14i	0.543359	+	0.313709i
$474$	583.959	−	189.967i	0.0565868	−	0.0184081i
$475$		−	4993.85i		−	0.482387i
$476$	3838.58	−	7526.44i	0.369624	−	0.724735i
$477$	−4639.67	+	10440.6i	−0.445359	+	1.00219i
$478$	−3651.98	−	6325.42i	−0.349452	−	0.605268i
$479$	4133.87	−	7160.07i	0.394324	−	0.682989i	−0.598691	−	0.800980i	$-0.704312\pi$
$479$	4133.87	−	7160.07i	0.394324	−	0.682989i	0.993015	+	0.117991i	$0.0376455\pi$
$480$	−815.632	−	733.880i	−0.0775590	−	0.0697851i
$481$	−3224.21	+	1861.50i	−0.305637	+	0.176460i
$482$	−6566.17			−0.620499
$483$	−7223.82	+	2772.67i	−0.680529	+	0.261202i
$484$	−1414.65			−0.132856
$485$	1530.24	−	883.487i	0.143268	−	0.0827156i
$486$	12.6949	+	7230.63i	0.00118488	+	0.674873i
$487$	−470.075	+	814.194i	−0.0437395	+	0.0757590i	−0.887066	−	0.461642i	$-0.847260\pi$
$487$	−470.075	+	814.194i	−0.0437395	+	0.0757590i	0.843327	+	0.537401i	$0.180594\pi$
$488$	−9526.46	−	16500.3i	−0.883694	−	1.53060i
$489$	11772.9	+	2498.08i	1.08873	+	0.231017i
$490$	661.109	−	479.542i	0.0609507	−	0.0442112i
$491$			1057.30i			0.0971801i	0.998819	+	0.0485900i	$0.0154728\pi$
$491$			1057.30i			0.0971801i	−0.998819	+	0.0485900i	$0.984527\pi$
$492$	1307.75	+	4020.03i	0.119833	+	0.368368i
$493$	19199.9	+	11085.1i	1.75400	+	1.01267i
$494$	−1310.57	−	756.658i	−0.119363	−	0.0689142i
$495$	1362.86	−	144.210i	0.123749	−	0.0130944i
$496$		−	1017.37i		−	0.0920995i
$497$	−7075.02	+	4590.68i	−0.638547	+	0.414326i
$498$	−150.534	+	709.431i	−0.0135454	+	0.0638361i
$499$	3086.65	+	5346.23i	0.276909	+	0.479620i	0.970615	−	0.240638i	$-0.0773568\pi$
$499$	3086.65	+	5346.23i	0.276909	+	0.479620i	−0.693706	+	0.720258i	$0.744023\pi$
$500$	−675.044	+	1169.21i	−0.0603778	+	0.104577i
$501$	8149.12	−	9056.91i	0.726699	−	0.807651i
$502$	3383.24	−	1953.31i	0.300800	−	0.173667i
$503$	−4284.28			−0.379775			−0.189887	−	0.981806i	$-0.560812\pi$
$503$	−4284.28			−0.379775			−0.189887	+	0.981806i	$0.560812\pi$
$504$	−7425.23	−	9163.49i	−0.656242	−	0.809869i
$505$	300.390			0.0264697
$506$	−5408.46	+	3122.58i	−0.475169	+	0.274339i
$507$	−6300.98	+	7002.89i	−0.551946	+	0.613431i
$508$	1829.96	−	3169.58i	0.159826	−	0.276826i
$509$	7550.52	+	13077.9i	0.657507	+	1.13884i	0.981259	+	0.192693i	$0.0617223\pi$
$509$	7550.52	+	13077.9i	0.657507	+	1.13884i	−0.323752	+	0.946142i	$0.604944\pi$
$510$	−268.932	+	1267.42i	−0.0233500	+	0.110043i
$511$	−482.673	−	9278.68i	−0.0417851	−	0.803258i
$512$			3640.92i			0.314272i
$513$	5645.13	+	587.315i	0.485845	+	0.0505470i
$514$	10003.1	+	5775.30i	0.858401	+	0.495598i
$515$	−1198.08	−	691.712i	−0.102512	−	0.0591854i
$516$	−1110.74	−	3414.41i	−0.0947624	−	0.291301i
$517$			14570.1i			1.23944i
$518$	−348.892	−	6706.94i	−0.0295935	−	0.568892i
$519$	−5254.79	−	1115.01i	−0.444431	−	0.0943037i
$520$	288.293	+	499.338i	0.0243125	+	0.0421104i
$521$	−6894.00	+	11940.8i	−0.579715	+	1.00410i	0.415796	+	0.909458i	$0.363503\pi$
$521$	−6894.00	+	11940.8i	−0.579715	+	1.00410i	−0.995512	+	0.0946385i	$0.969830\pi$
$522$	8822.93	−	6419.71i	0.739788	−	0.538281i
$523$	−832.513	+	480.652i	−0.0696047	+	0.0401863i	−0.534398	−	0.845233i	$-0.679462\pi$
$523$	−832.513	+	480.652i	−0.0696047	+	0.0401863i	0.464794	+	0.885419i	$0.346128\pi$
$524$	2256.17			0.188094
$525$	−7476.36	+	9231.85i	−0.621514	+	0.767449i
$526$	−11976.5			−0.992780
$527$	9071.15	−	5237.23i	0.749802	−	0.432898i
$528$	−1598.67	−	1438.43i	−0.131767	−	0.118560i
$529$	−2851.06	+	4938.17i	−0.234327	+	0.405866i
$530$	503.783	+	872.577i	0.0412885	+	0.0715138i
$531$	−15434.8	−	6859.02i	−1.26142	−	0.560557i
$532$	−2738.03	+	1776.59i	−0.223136	+	0.144784i
$533$		−	3659.84i		−	0.297421i
$534$	1082.28	−	352.073i	0.0877054	−	0.0285313i
$535$	1153.41	+	665.922i	0.0932080	+	0.0538137i
$536$	6098.14	+	3520.76i	0.491417	+	0.283720i
$537$	715.903	−	232.889i	0.0575298	−	0.0187149i
$538$		−	6368.54i		−	0.510348i
$539$	−11297.7	+	8194.92i	−0.902834	+	0.654880i
$540$	−617.261	−	447.474i	−0.0491902	−	0.0356596i
$541$	597.846	+	1035.50i	0.0475109	+	0.0822913i	0.888803	−	0.458290i	$-0.151538\pi$
$541$	597.846	+	1035.50i	0.0475109	+	0.0822913i	−0.841292	+	0.540581i	$0.818204\pi$
$542$	−2713.57	+	4700.04i	−0.215051	+	0.372480i
$543$	7946.26	+	7149.79i	0.628005	+	0.565059i
$544$	−15351.3	+	8863.09i	−1.20989	+	0.698533i
$545$	−12.5833			−0.000989006
$546$	1289.97	+	3360.86i	0.101109	+	0.263428i
$547$	18601.8			1.45403			0.727014	−	0.686622i	$-0.240907\pi$
$547$	18601.8			1.45403			0.727014	+	0.686622i	$0.240907\pi$
$548$	−4142.71	+	2391.80i	−0.322934	+	0.186446i
$549$	−12832.3	−	17636.1i	−0.997578	−	1.37102i
$550$	−4794.05	+	8303.53i	−0.371671	+	0.643753i
$551$	−4282.34	−	7417.24i	−0.331096	−	0.573475i
$552$	9639.56	+	2045.41i	0.743274	+	0.157715i
$553$	−520.955	+	1021.45i	−0.0400601	+	0.0785473i
$554$		−	12117.9i		−	0.929315i
$555$	−380.925	−	1170.97i	−0.0291340	−	0.0895582i
$556$	−3124.83	−	1804.12i	−0.238349	−	0.137611i
$557$	5908.09	+	3411.04i	0.449432	+	0.259480i	0.707590	−	0.706623i	$-0.249782\pi$
$557$	5908.09	+	3411.04i	0.449432	+	0.259480i	−0.258158	+	0.966103i	$0.583116\pi$
$558$	−542.458	−	5126.51i	−0.0411543	−	0.388929i
$559$			3108.49i			0.235197i
$560$	−234.661	+	12.2070i	−0.0177076	+	0.000921141i
$561$	4595.80	−	21658.9i	0.345873	−	1.63002i
$562$	3565.58	+	6175.77i	0.267624	+	0.463539i
$563$	−5679.80	+	9837.71i	−0.425178	+	0.736430i	−0.996437	−	0.0843399i	$-0.973122\pi$
$563$	−5679.80	+	9837.71i	−0.425178	+	0.736430i	0.571259	+	0.820770i	$0.306455\pi$
$564$	5421.43	−	6025.36i	0.404758	−	0.449847i
$565$	955.293	−	551.539i	0.0711318	−	0.0410680i
$566$	10531.2			0.782087
$567$	−9556.55	−	9537.12i	−0.707826	−	0.706387i
$568$	10740.8			0.793443
$569$	18467.2	−	10662.1i	1.36061	−	0.785549i	0.370905	−	0.928671i	$-0.379047\pi$
$569$	18467.2	−	10662.1i	1.36061	−	0.785549i	0.989705	+	0.143122i	$0.0457141\pi$
$570$	334.785	−	372.079i	0.0246011	−	0.0273416i
$571$	7384.00	−	12789.5i	0.541175	−	0.937343i	−0.457662	−	0.889126i	$-0.651313\pi$
$571$	7384.00	−	12789.5i	0.541175	−	0.937343i	0.998837	−	0.0482163i	$-0.0153537\pi$
$572$	−1736.94	−	3008.47i	−0.126967	−	0.219913i
$573$	3180.36	−	14988.3i	0.231870	−	1.09275i
$574$	5881.34	+	2999.56i	0.427670	+	0.218117i
$575$		−	9925.45i		−	0.719861i
$576$	1149.20	+	10860.5i	0.0831305	+	0.785626i
$577$	16718.5	+	9652.44i	1.20624	+	0.696424i	0.961936	−	0.273275i	$-0.0881068\pi$
$577$	16718.5	+	9652.44i	1.20624	+	0.696424i	0.244305	+	0.969698i	$0.421440\pi$
$578$	10006.1	+	5777.04i	0.720069	+	0.415732i
$579$	3650.16	+	11220.6i	0.261996	+	0.805377i
$580$			1150.48i			0.0823640i
$581$	−737.091	−	1135.98i	−0.0526328	−	0.0811162i
$582$	−13743.8	−	2916.29i	−0.978863	−	0.207705i
$583$	−8609.17	−	14911.5i	−0.611587	−	1.05930i
$584$	−5916.35	+	10247.4i	−0.419213	+	0.726099i
$585$	388.336	+	533.710i	0.0274457	+	0.0377200i
$586$	−12521.4	+	7229.22i	−0.882684	+	0.509618i
$587$	4397.46			0.309204			0.154602	−	0.987977i	$-0.450590\pi$
$587$	4397.46			0.309204			0.154602	+	0.987977i	$0.450590\pi$
$588$	7721.38	+	814.854i	0.541538	+	0.0571497i
$589$	−4046.45			−0.283075
$590$	−1289.97	+	744.762i	−0.0900119	+	0.0519684i
$591$	1915.32	+	1723.35i	0.133310	+	0.119948i
$592$	−966.135	+	1673.40i	−0.0670742	+	0.116176i
$593$	−10970.1	−	19000.8i	−0.759677	−	1.31580i	−0.943015	−	0.332749i	$-0.892024\pi$
$593$	−10970.1	−	19000.8i	−0.759677	−	1.31580i	0.183339	−	0.983050i	$-0.441309\pi$
$594$	−8822.62	−	6395.82i	−0.609422	−	0.441791i
$595$	−1316.83	−	2029.46i	−0.0907307	−	0.139832i
$596$			3888.46i			0.267244i
$597$	−4149.21	+	1349.77i	−0.284449	+	0.0925335i
$598$	−2604.80	−	1503.88i	−0.178124	−	0.102840i
$599$	−4765.07	−	2751.12i	−0.325034	−	0.187659i	0.328600	−	0.944469i	$-0.393423\pi$
$599$	−4765.07	−	2751.12i	−0.325034	−	0.187659i	−0.653634	+	0.756810i	$0.726757\pi$
$600$	14386.9	−	4680.17i	0.978903	−	0.318445i
$601$		−	5814.58i		−	0.394645i	−0.980339	−	0.197322i	$-0.936775\pi$
$601$		−	5814.58i		−	0.394645i	0.980339	−	0.197322i	$-0.0632246\pi$
$602$	−4995.31	−	2547.68i	−0.338196	−	0.172484i
$603$	7366.11	+	3273.41i	0.497465	+	0.221067i
$604$	−3103.99	−	5376.27i	−0.209105	−	0.362181i
$605$	−202.537	+	350.804i	−0.0136104	+	0.0235739i
$606$	−1775.56	−	1597.60i	−0.119022	−	0.107092i
$607$	−11510.7	+	6645.69i	−0.769693	+	0.444382i	−0.832765	−	0.553627i	$-0.813244\pi$
$607$	−11510.7	+	6645.69i	−0.769693	+	0.444382i	0.0630721	+	0.998009i	$0.479910\pi$
$608$	6847.90			0.456775
$609$	−3187.91	+	20123.0i	−0.212119	+	1.33896i
$610$	−1923.45			−0.127669
$611$	−6077.05	+	3508.59i	−0.402375	+	0.232311i
$612$	−9959.72	+	7246.85i	−0.657839	+	0.478655i
$613$	−9797.17	+	16969.2i	−0.645520	+	1.11807i	0.338661	+	0.940909i	$0.390026\pi$
$613$	−9797.17	+	16969.2i	−0.645520	+	1.11807i	−0.984181	+	0.177166i	$0.943307\pi$
$614$	10150.8	+	17581.7i	0.667189	+	1.15561i
$615$	1184.12	+	251.257i	0.0776394	+	0.0164743i
$616$	17750.6	−	923.379i	1.16103	−	0.0603961i
$617$			348.388i			0.0227319i	0.999935	+	0.0113660i	$0.00361797\pi$
$617$			348.388i			0.0227319i	−0.999935	+	0.0113660i	$0.996382\pi$
$618$	3402.88	+	10460.5i	0.221495	+	0.680878i
$619$	5867.68	+	3387.71i	0.381005	+	0.219973i	0.678255	−	0.734826i	$-0.262736\pi$
$619$	5867.68	+	3387.71i	0.381005	+	0.219973i	−0.297251	+	0.954799i	$0.596070\pi$
$620$	470.731	+	271.777i	0.0304920	+	0.0176045i
$621$	11219.9	+	1167.31i	0.725022	+	0.0754307i
$622$		−	11016.2i		−	0.710145i
$623$	−965.508	+	1893.10i	−0.0620903	+	0.121742i
$624$	214.986	−	1013.18i	0.0137922	−	0.0649994i
$625$	−7521.95	−	13028.4i	−0.481405	−	0.833818i
$626$	2237.65	−	3875.72i	0.142866	−	0.247452i
$627$	−5721.16	+	6358.48i	−0.364404	+	0.404997i
$628$	1066.75	−	615.890i	0.0677836	−	0.0391349i
$629$	−19893.9			−1.26108
$630$	−1175.94	+	186.631i	−0.0743662	+	0.0118025i
$631$	−7326.82			−0.462244			−0.231122	−	0.972925i	$-0.574240\pi$
$631$	−7326.82			−0.462244			−0.231122	+	0.972925i	$0.574240\pi$
$632$	1264.64	−	730.138i	0.0795957	−	0.0459546i
$633$	−13908.2	+	15457.5i	−0.873301	+	0.970584i
$634$	7551.46	−	13079.5i	0.473039	−	0.819327i
$635$	−523.995	−	907.586i	−0.0327466	−	0.0567188i
$636$	−1988.21	+	9369.98i	−0.123959	+	0.584189i
$637$	−6138.62	−	2738.79i	−0.381822	−	0.170353i
$638$			16444.0i			1.02042i
$639$	12227.2	−	1293.81i	0.756963	−	0.0800975i
$640$	−628.838	−	363.060i	−0.0388391	−	0.0224238i
$641$	−2433.38	−	1404.91i	−0.149942	−	0.0865689i	0.423152	−	0.906059i	$-0.360924\pi$
$641$	−2433.38	−	1404.91i	−0.149942	−	0.0865689i	−0.573094	+	0.819490i	$0.694257\pi$
$642$	−3276.01	−	10070.5i	−0.201392	−	0.619081i
$643$			27485.5i			1.68573i	0.538128	+	0.842863i	$0.319132\pi$
$643$			27485.5i			1.68573i	−0.538128	+	0.842863i	$0.680868\pi$
$644$	−5441.92	+	3531.03i	−0.332984	+	0.216059i
$645$	−1005.73	−	213.405i	−0.0613962	−	0.0130276i
$646$	−4043.21	−	7003.05i	−0.246251	−	0.426519i
$647$	14659.9	−	25391.7i	0.890790	−	1.54289i	0.0518595	−	0.998654i	$-0.483485\pi$
$647$	14659.9	−	25391.7i	0.890790	−	1.54289i	0.838930	−	0.544239i	$-0.183181\pi$
$648$	3598.53	+	16813.6i	0.218153	+	1.01929i
$649$	22044.3	−	12727.3i	1.33330	−	0.769783i
$650$	−4617.78			−0.278653
$651$	7480.44	+	6057.99i	0.450356	+	0.364718i
$652$	10089.9			0.606061
$653$	−14500.6	+	8371.91i	−0.868992	+	0.501713i	−0.867013	−	0.498285i	$-0.833963\pi$
$653$	−14500.6	+	8371.91i	−0.868992	+	0.501713i	−0.00197863	+	0.999998i	$0.500630\pi$
$654$	74.3780	+	66.9229i	0.00444711	+	0.00400137i
$655$	323.019	−	559.485i	0.0192693	−	0.0333754i
$656$	−949.747	−	1645.01i	−0.0565265	−	0.0979068i
$657$	−5500.69	+	12378.1i	−0.326640	+	0.735034i
$658$	−657.599	−	12641.4i	−0.0389603	−	0.748954i
$659$			9520.47i			0.562769i	0.959595	+	0.281385i	$0.0907937\pi$
$659$			9520.47i			0.562769i	−0.959595	+	0.281385i	$0.909206\pi$
$660$	1092.62	−	355.437i	0.0644394	−	0.0209626i
$661$	−20217.5	−	11672.6i	−1.18966	−	0.686853i	−0.231434	−	0.972851i	$-0.574342\pi$
$661$	−20217.5	−	11672.6i	−1.18966	−	0.686853i	−0.958230	+	0.285998i	$0.907675\pi$
$662$	−8067.16	−	4657.58i	−0.473624	−	0.273447i
$663$	10140.5	−	3298.77i	0.594002	−	0.193233i
$664$			1724.58i			0.100793i
$665$	48.5515	+	933.331i	0.00283120	+	0.0544256i
$666$	−3976.08	+	8947.34i	−0.231337	+	0.520574i
$667$	−8511.31	−	14742.0i	−0.494092	−	0.855792i
$668$	5107.19	−	8845.91i	0.295813	−	0.512363i
$669$	−11744.7	−	10567.5i	−0.678740	−	0.610709i
$670$	615.625	−	355.431i	0.0354980	−	0.0204948i
$671$	32869.9			1.89110
$672$	−12659.3	−	10252.1i	−0.726703	−	0.588516i
$673$	−12283.5			−0.703559			−0.351780	−	0.936083i	$-0.614423\pi$
$673$	−12283.5			−0.703559			−0.351780	+	0.936083i	$0.614423\pi$
$674$	6837.85	−	3947.84i	0.390778	−	0.225616i
$675$	15814.0	−	7060.82i	0.901750	−	0.402624i
$676$	−3948.93	+	6839.74i	−0.224677	+	0.389152i
$677$	−6495.88	−	11251.2i	−0.368769	−	0.638727i	0.620604	−	0.784124i	$-0.286887\pi$
$677$	−6495.88	−	11251.2i	−0.368769	−	0.638727i	−0.989373	+	0.145397i	$0.953554\pi$
$678$	−8579.91	−	1820.57i	−0.486002	−	0.103125i
$679$	22007.4	−	14279.6i	1.24384	−	0.807072i
$680$			3081.00i			0.173751i
$681$	7067.05	+	21724.2i	0.397665	+	1.22243i
$682$	6728.24	+	3884.55i	0.377768	+	0.218104i
$683$	7366.62	+	4253.12i	0.412703	+	0.238274i	0.691950	−	0.721945i	$-0.256752\pi$
$683$	7366.62	+	4253.12i	0.412703	+	0.238274i	−0.279248	+	0.960219i	$0.590085\pi$
$684$	4731.90	−	500.703i	0.264516	−	0.0279896i
$685$			1369.74i			0.0764018i
$686$	9432.34	−	7620.03i	0.524968	−	0.424102i
$687$	2139.38	−	10082.4i	0.118810	−	0.559923i
$688$	806.667	+	1397.19i	0.0447004	+	0.0774234i
$689$	4146.31	−	7181.62i	0.229263	−	0.397095i
$690$	665.397	−	739.520i	0.0367119	−	0.0408015i
$691$	−22372.0	+	12916.5i	−1.23165	+	0.711093i	−0.967374	−	0.253354i	$-0.918466\pi$
$691$	−22372.0	+	12916.5i	−1.23165	+	0.711093i	−0.264276	+	0.964447i	$0.585133\pi$
$692$	−4503.61			−0.247401
$693$	20095.7	−	3189.34i	1.10155	−	0.174824i
$694$	−4429.93			−0.242303
$695$	−894.770	+	516.595i	−0.0488353	+	0.0281951i
$696$	17355.1	−	19288.4i	0.945177	−	1.05047i
$697$	9778.22	−	16936.4i	0.531387	−	0.920389i
$698$	216.457	+	374.914i	0.0117378	+	0.0203305i
$699$	4717.33	−	22231.7i	0.255259	−	1.20298i
$700$	−4524.99	+	8872.30i	−0.244327	+	0.479059i
$701$			22607.8i			1.21810i	0.793134	+	0.609048i	$0.208448\pi$
$701$			22607.8i			1.21810i	−0.793134	+	0.609048i	$0.791552\pi$
$702$	543.086	−	5220.01i	0.0291987	−	0.280650i
$703$	6655.69	+	3842.67i	0.357076	+	0.206158i
$704$	−14253.8	−	8229.41i	−0.763080	−	0.440565i
$705$	−717.975	−	2207.06i	−0.0383553	−	0.117905i
$706$			2835.96i			0.151180i
$707$	4453.86	−	231.688i	0.236923	−	0.0123246i
$708$	−13852.0	−	2939.26i	−0.735298	−	0.156023i
$709$	5472.41	+	9478.50i	0.289874	+	0.502077i	0.973779	−	0.227494i	$-0.0730532\pi$
$709$	5472.41	+	9478.50i	0.289874	+	0.502077i	−0.683905	+	0.729571i	$0.739720\pi$
$710$	542.159	−	939.048i	0.0286576	−	0.0496364i
$711$	1351.69	−	983.509i	0.0712971	−	0.0518769i
$712$	2343.80	−	1353.19i	0.123368	−	0.0712263i
$713$	−8042.46			−0.422430
$714$	−3009.89	+	18999.3i	−0.157762	+	0.995841i
$715$	−994.720			−0.0520285
$716$	546.601	−	315.580i	0.0285299	−	0.0164718i
$717$	−14780.3	−	13298.9i	−0.769849	−	0.692685i
$718$	−10381.4	+	17981.1i	−0.539595	+	0.934607i
$719$	12885.3	+	22317.9i	0.668344	+	1.15761i	0.978367	+	0.206877i	$0.0663299\pi$
$719$	12885.3	+	22317.9i	0.668344	+	1.15761i	−0.310023	+	0.950729i	$0.600337\pi$
$720$	313.048	+	139.114i	0.0162036	+	0.00720068i
$721$	−18297.3	−	9331.88i	−0.945116	−	0.482021i
$722$		−	9968.76i		−	0.513849i
$723$	−16997.4	+	5529.40i	−0.874330	+	0.284427i
$724$	7761.13	+	4480.89i	0.398398	+	0.230015i
$725$	−22633.2	−	13067.3i	−1.15942	−	0.669389i
$726$	3062.89	−	996.381i	0.156576	−	0.0509355i
$727$			15593.1i			0.795485i	0.917497	+	0.397742i	$0.130206\pi$
$727$			15593.1i			0.795485i	−0.917497	+	0.397742i	$0.869794\pi$
$728$	4659.63	+	7181.28i	0.237221	+	0.365599i
$729$	6121.81	+	18706.8i	0.311020	+	0.950403i
$730$	597.273	+	1034.51i	0.0302823	+	0.0524505i
$731$	−8305.13	+	14384.9i	−0.420214	+	0.727832i
$732$	−13593.2	−	12230.7i	−0.686363	−	0.617568i
$733$	692.858	−	400.022i	0.0349131	−	0.0201571i	−0.482442	−	0.875928i	$-0.660250\pi$
$733$	692.858	−	400.022i	0.0349131	−	0.0201571i	0.517355	+	0.855771i	$0.326917\pi$
$734$	7272.94			0.365734
$735$	1307.55	−	1798.08i	0.0656185	−	0.0902358i
$736$	13610.4			0.681641
$737$	−10520.5	+	6073.99i	−0.525815	+	0.303580i
$738$	−5662.86	−	7782.76i	−0.282456	−	0.388194i
$739$	454.445	−	787.122i	0.0226211	−	0.0391810i	−0.854493	−	0.519463i	$-0.826132\pi$
$739$	454.445	−	787.122i	0.0226211	−	0.0391810i	0.877114	+	0.480282i	$0.159466\pi$
$740$	−516.179	−	894.048i	−0.0256421	−	0.0444133i
$741$	−4029.77	−	855.076i	−0.199781	−	0.0423914i
$742$	8142.55	+	12549.1i	0.402860	+	0.620877i
$743$			8109.00i			0.400391i	0.979756	+	0.200195i	$0.0641577\pi$
$743$			8109.00i			0.400391i	−0.979756	+	0.200195i	$0.935842\pi$
$744$	−3792.28	−	11657.5i	−0.186870	−	0.574442i
$745$	964.258	+	556.715i	0.0474197	+	0.0273778i
$746$	−16099.7	−	9295.14i	−0.790148	−	0.456192i
$747$	207.737	+	1963.22i	0.0101750	+	0.0961588i
$748$		−	18562.8i		−	0.907382i
$749$	17615.1	+	8983.95i	0.859337	+	0.438273i
$750$	638.041	−	3006.94i	0.0310639	−	0.146397i
$751$	10382.2	+	17982.5i	0.504463	+	0.873756i	0.999987	+	0.00516122i	$0.00164288\pi$
$751$	10382.2	+	17982.5i	0.504463	+	0.873756i	−0.495524	+	0.868594i	$0.665024\pi$
$752$	−1820.99	+	3154.05i	−0.0883041	+	0.152947i
$753$	7113.09	−	7905.46i	0.344243	−	0.382591i
$754$	−6858.67	+	3959.85i	−0.331271	+	0.191259i
$755$	−1777.61			−0.0856870
$756$	−9497.21	−	6158.57i	−0.456892	−	0.296276i
$757$	23295.6			1.11848			0.559242	−	0.829005i	$-0.311092\pi$
$757$	23295.6			1.11848			0.559242	+	0.829005i	$0.311092\pi$
$758$	−529.273	+	305.576i	−0.0253616	+	0.0146425i
$759$	−11371.0	+	12637.7i	−0.543796	+	0.604374i
$760$	595.119	−	1030.78i	0.0284042	−	0.0491976i
$761$	5014.38	+	8685.16i	0.238858	+	0.413715i	0.960387	−	0.278670i	$-0.0898935\pi$
$761$	5014.38	+	8685.16i	0.238858	+	0.413715i	−0.721529	+	0.692385i	$0.756560\pi$
$762$	−1729.65	+	8151.43i	−0.0822290	+	0.387526i
$763$	−186.571	+	9.70535i	−0.00885233	+	0.000460494i
$764$		−	12845.7i		−	0.608299i
$765$	371.128	+	3507.35i	0.0175401	+	0.165763i
$766$	7224.45	+	4171.04i	0.340770	+	0.196744i
$767$	10616.9	+	6129.66i	0.499809	+	0.288565i
$768$	6987.55	+	21479.8i	0.328309	+	1.00923i
$769$		−	13500.3i		−	0.633074i	−0.948580	−	0.316537i	$-0.897480\pi$
$769$		−	13500.3i		−	0.633074i	0.948580	−	0.316537i	$-0.102520\pi$
$770$	815.259	−	1598.51i	0.0381557	−	0.0748132i
$771$	30757.8	+	6526.49i	1.43673	+	0.304858i
$772$	4946.21	+	8567.09i	0.230593	+	0.399399i
$773$	11644.9	−	20169.5i	0.541833	−	0.938482i	−0.456966	−	0.889484i	$-0.651064\pi$
$773$	11644.9	−	20169.5i	0.541833	−	0.938482i	0.998799	−	0.0489979i	$-0.0156028\pi$
$774$	4809.75	+	6610.29i	0.223363	+	0.306979i
$775$	−10693.2	+	6173.74i	−0.495629	+	0.286151i
$776$	−33410.2			−1.54556
$777$	−6551.10	−	17068.0i	−0.302470	−	0.788046i
$778$	26179.3			1.20639
$779$	−6542.79	+	3777.48i	−0.300924	+	0.173739i
$780$	411.360	+	370.129i	0.0188834	+	0.0169907i
$781$	−9264.99	+	16047.4i	−0.424491	+	0.735240i
$782$	−8036.02	−	13918.8i	−0.367478	−	0.636490i
$783$	17433.3	−	24048.1i	0.795677	−	1.09759i
$784$	−3469.88	+	361.983i	−0.158067	+	0.0164898i
$785$		−	352.711i		−	0.0160367i
$786$	−4884.88	+	1589.09i	−0.221677	+	0.0721132i
$787$	−20635.4	−	11913.8i	−0.934653	−	0.539622i	−0.0463726	−	0.998924i	$-0.514766\pi$
$787$	−20635.4	−	11913.8i	−0.934653	−	0.539622i	−0.888280	+	0.459302i	$0.848099\pi$
$788$	1870.70	+	1080.05i	0.0845698	+	0.0488264i
$789$	−31002.9	+	10085.5i	−1.39890	+	0.455074i
$790$		−	147.419i		−	0.00663916i
$791$	13738.7	−	8914.42i	0.617560	−	0.400709i
$792$	−23680.1	−	10523.1i	−1.06242	−	0.472125i
$793$	7915.34	+	13709.8i	0.354454	+	0.613932i
$794$	2404.27	−	4164.32i	0.107461	−	0.186129i
$795$	2038.91	+	1834.55i	0.0909594	+	0.0818424i
$796$	−3167.98	+	1829.03i	−0.141063	+	0.0814426i
$797$	−12609.3			−0.560406			−0.280203	−	0.959941i	$-0.590402\pi$
$797$	−12609.3			−0.560406			−0.280203	+	0.959941i	$0.590402\pi$
$798$	4676.85	−	5775.00i	0.207467	−	0.256182i
$799$	−37496.4			−1.66023
$800$	18096.4	−	10448.0i	0.799756	−	0.461739i
$801$	2505.14	−	1822.78i	0.110505	−	0.0804054i
$802$	2500.54	−	4331.06i	0.110096	−	0.190692i
$803$	−10206.8	−	17678.8i	−0.448557	−	0.776924i
$804$	6610.76	+	1402.74i	0.289980	+	0.0615307i
$805$	96.4977	+	1855.03i	0.00422497	+	0.0812188i
$806$			3741.73i			0.163519i
$807$	−5362.97	−	16485.8i	−0.233935	−	0.719118i
$808$	−4918.87	−	2839.91i	−0.214165	−	0.123648i
$809$	30281.4	+	17483.0i	1.31599	+	0.759789i	0.983082	−	0.183169i	$-0.0586354\pi$
$809$	30281.4	+	17483.0i	1.31599	+	0.759789i	0.332912	+	0.942958i	$0.391969\pi$
$810$	1651.61	+	534.079i	0.0716442	+	0.0231674i
$811$			5691.42i			0.246428i	0.992380	+	0.123214i	$0.0393201\pi$
$811$			5691.42i			0.246428i	−0.992380	+	0.123214i	$0.960680\pi$
$812$	887.354	+	17058.1i	0.0383498	+	0.737218i
$813$	−3066.52	+	14451.8i	−0.132285	+	0.623428i
$814$	−7377.84	−	12778.8i	−0.317682	−	0.550241i
$815$	1444.59	−	2502.10i	0.0620879	−	0.107539i
$816$	3701.84	−	4114.22i	0.158812	−	0.176503i
$817$	5557.12	−	3208.40i	0.237967	−	0.137390i
$818$	26578.9			1.13607
$819$	6169.47	+	7613.75i	0.263222	+	0.324842i
$820$	1014.85			0.0432195
$821$	10487.0	−	6054.70i	0.445798	−	0.257382i	−0.260256	−	0.965540i	$-0.583807\pi$
$821$	10487.0	−	6054.70i	0.445798	−	0.257382i	0.706054	+	0.708158i	$0.250474\pi$
$822$	7284.86	−	8096.37i	0.309110	−	0.343544i
$823$	15861.0	−	27472.0i	0.671784	−	1.16356i	−0.305614	−	0.952155i	$-0.598862\pi$
$823$	15861.0	−	27472.0i	0.671784	−	1.16356i	0.977398	−	0.211408i	$-0.0678049\pi$
$824$	13079.0	+	22653.5i	0.552946	+	0.957731i
$825$	−5417.61	+	25531.9i	−0.228627	+	1.07746i
$826$	−18551.8	+	12037.5i	−0.781476	+	0.507066i
$827$		−	36401.9i		−	1.53061i	−0.643666	−	0.765307i	$-0.722587\pi$
$827$		−	36401.9i		−	1.53061i	0.643666	−	0.765307i	$-0.277413\pi$
$828$	9404.82	−	995.165i	0.394735	−	0.0417686i
$829$	27287.8	+	15754.6i	1.14324	+	0.660049i	0.947230	−	0.320554i	$-0.103869\pi$
$829$	27287.8	+	15754.6i	1.14324	+	0.660049i	0.196007	+	0.980602i	$0.437202\pi$
$830$	150.776	+	87.0505i	0.00630543	+	0.00364044i
$831$	−10204.5	−	31368.9i	−0.425983	−	1.30948i
$832$		−	7926.83i		−	0.330305i
$833$	−21089.8	−	29075.0i	−0.877214	−	1.20935i
$834$	8036.32	+	1705.22i	0.333663	+	0.0707998i
$835$	−1462.40	−	2532.96i	−0.0606090	−	0.104978i
$836$	−3585.54	+	6210.34i	−0.148336	+	0.256925i
$837$	−5721.28	−	12813.9i	−0.236268	−	0.529166i
$838$	25079.2	−	14479.5i	1.03383	−	0.596881i
$839$	−13781.4			−0.567090			−0.283545	−	0.958959i	$-0.591510\pi$
$839$	−13781.4			−0.567090			−0.283545	+	0.958959i	$0.591510\pi$
$840$	−2643.35	+	1014.58i	−0.108576	+	0.0416741i
$841$	−20433.0			−0.837796
$842$	1739.93	−	1004.55i	0.0712136	−	0.0411152i
$843$	14430.6	+	12984.2i	0.589582	+	0.530487i
$844$	−8716.46	+	15097.4i	−0.355489	+	0.615726i
$845$	1130.74	+	1958.51i	0.0460341	+	0.0797334i
$846$	−7494.20	+	16864.1i	−0.304558	+	0.685343i
$847$	−2732.43	+	5357.56i	−0.110847	+	0.217341i
$848$		−	4303.95i		−	0.174290i
$849$	27261.6	−	8868.40i	1.10202	−	0.358496i
$850$	−21369.3	−	12337.6i	−0.862309	−	0.497854i
$851$	13228.4	+	7637.43i	0.532860	+	0.307647i
$852$	9802.63	−	3188.87i	0.394170	−	0.128227i
$853$		−	11376.3i		−	0.456645i	−0.973586	−	0.228322i	$-0.926676\pi$
$853$		−	11376.3i		−	0.456645i	0.973586	−	0.228322i	$-0.0733240\pi$
$854$	−28518.8	+	1483.54i	−1.14273	+	0.0594444i
$855$	553.308	−	1245.10i	0.0221318	−	0.0498030i
$856$	−12591.3	−	21808.8i	−0.502761	−	0.870807i
$857$	−21559.6	+	37342.3i	−0.859349	+	1.48844i	0.0132022	+	0.999913i	$0.495797\pi$
$857$	−21559.6	+	37342.3i	−0.859349	+	1.48844i	−0.872551	+	0.488523i	$0.837536\pi$
$858$	5879.65	+	5290.32i	0.233948	+	0.210499i
$859$	32325.9	−	18663.4i	1.28399	−	0.741311i	0.306413	−	0.951899i	$-0.400871\pi$
$859$	32325.9	−	18663.4i	1.28399	−	0.741311i	0.977575	+	0.210588i	$0.0675378\pi$
$860$	−861.960			−0.0341774
$861$	17750.6	+	2812.07i	0.702600	+	0.111307i
$862$	15260.5			0.602986
$863$	−30262.7	+	17472.2i	−1.19369	+	0.689176i	−0.959141	−	0.282929i	$-0.908694\pi$
$863$	−30262.7	+	17472.2i	−1.19369	+	0.689176i	−0.234547	+	0.972105i	$0.575361\pi$
$864$	9682.26	+	21685.2i	0.381247	+	0.853873i
$865$	−644.788	+	1116.80i	−0.0253450	+	0.0438988i
$866$	12301.9	+	21307.5i	0.482719	+	0.836093i
$867$	30767.1	+	6528.45i	1.20520	+	0.255730i
$868$	7189.11	+	3666.54i	0.281122	+	0.143376i
$869$			2519.25i			0.0983426i
$870$	−810.319	−	2490.93i	−0.0315775	−	0.0970694i
$871$	−5066.82	−	2925.33i	−0.197110	−	0.113801i
$872$	206.050	+	118.963i	0.00800200	+	0.00461995i
$873$	−38033.5	+	4024.49i	−1.47450	+	0.156023i
$874$			6208.89i			0.240296i
$875$	3124.17	+	4814.88i	0.120704	+	0.186026i
$876$	−2357.18	+	11108.8i	−0.0909152	+	0.428462i
$877$	−2054.59	−	3558.66i	−0.0791092	−	0.137021i	0.823757	−	0.566944i	$-0.191874\pi$
$877$	−2054.59	−	3558.66i	−0.0791092	−	0.137021i	−0.902866	+	0.429922i	$0.858541\pi$
$878$	−13728.1	+	23777.8i	−0.527678	+	0.913964i
$879$	−26325.5	+	29258.1i	−1.01017	+	1.12270i
$880$	−447.102	+	258.134i	−0.0171271	+	0.00988831i
$881$	15697.6			0.600301			0.300151	−	0.953892i	$-0.402963\pi$
$881$	15697.6			0.600301			0.300151	+	0.953892i	$0.402963\pi$
$882$	−17291.6	+	3674.15i	−0.660136	+	0.140267i
$883$	−44102.6			−1.68083			−0.840413	−	0.541946i	$-0.817688\pi$
$883$	−44102.6			−1.68083			−0.840413	+	0.541946i	$0.817688\pi$
$884$	7742.37	−	4470.06i	0.294575	−	0.170073i
$885$	−2712.09	+	3014.20i	−0.103012	+	0.114487i
$886$	3782.46	−	6551.42i	0.143425	−	0.248419i
$887$	−14164.5	−	24533.5i	−0.536185	−	0.928699i	−0.999105	−	0.0422991i	$-0.986532\pi$
$887$	−14164.5	−	24533.5i	−0.536185	−	0.928699i	0.462920	−	0.886400i	$-0.346802\pi$
$888$	−4832.79	+	22775.8i	−0.182633	+	0.860704i
$889$	−8469.24	−	13052.5i	−0.319515	−	0.492428i
$890$		−	273.218i		−	0.0102902i
$891$	−28224.5	−	9126.89i	−1.06123	−	0.343168i
$892$	−11471.1	−	6622.84i	−0.430584	−	0.248598i
$893$	12544.8	+	7242.73i	0.470095	+	0.271409i
$894$	−2738.76	−	8418.97i	−0.102458	−	0.314958i
$895$		−	180.728i		−	0.00674979i
$896$	−9603.75	−	4898.04i	−0.358079	−	0.182625i
$897$	−8009.31	−	1699.49i	−0.298131	−	0.0632602i
$898$	12864.7	+	22282.3i	0.478062	+	0.828028i
$899$	−10588.3	+	18339.4i	−0.392812	+	0.680370i
$900$	11740.7	−	8542.72i	0.434840	−	0.316397i
$901$	38375.1	−	22155.9i	1.41894	−	0.819223i
$902$	14505.4			0.535450
$903$	−15076.5	−	2388.43i	−0.555607	−	0.0880201i
$904$	−20857.1			−0.767365
$905$	2222.34	−	1283.07i	0.0816277	−	0.0471278i
$906$	10507.2	+	9454.03i	0.385295	+	0.346677i
$907$	−7102.79	+	12302.4i	−0.260027	+	0.450380i	−0.966249	−	0.257611i	$-0.917065\pi$
$907$	−7102.79	+	12302.4i	−0.260027	+	0.450380i	0.706222	+	0.707991i	$0.250398\pi$
$908$	9576.32	+	16586.7i	0.350002	+	0.606220i
$909$	−5941.64	−	2640.39i	−0.216800	−	0.0963434i
$910$	863.045	−	44.8952i	0.0314392	−	0.00163545i
$911$		−	17955.9i		−	0.653025i	−0.945193	−	0.326512i	$-0.894127\pi$
$911$		−	17955.9i		−	0.653025i	0.945193	−	0.326512i	$-0.105873\pi$
$912$	−2033.18	+	661.410i	−0.0738216	+	0.0240148i
$913$	−2576.62	−	1487.61i	−0.0933993	−	0.0539241i
$914$	6578.63	+	3798.17i	0.238076	+	0.137453i
$915$	−4979.11	+	1619.74i	−0.179895	+	0.0585214i
$916$		−	8641.09i		−	0.311692i
$917$	4357.84	−	8544.57i	0.156934	−	0.307706i
$918$	16459.8	−	22705.2i	0.591781	−	0.816323i
$919$	21121.3	+	36583.1i	0.758135	+	1.31313i	0.943800	+	0.330516i	$0.107223\pi$
$919$	21121.3	+	36583.1i	0.758135	+	1.31313i	−0.185665	+	0.982613i	$0.559444\pi$
$920$	1182.82	−	2048.70i	0.0423874	−	0.0734171i
$921$	41082.5	+	36964.7i	1.46983	+	1.32251i
$922$	−14966.7	+	8641.01i	−0.534600	+	0.308651i
$923$	−8924.34			−0.318254
$924$	15926.0	−	6112.75i	0.567019	−	0.217635i
$925$	23451.3			0.833593
$926$	9482.32	−	5474.62i	0.336510	−	0.194284i
$927$	17617.6	+	24212.8i	0.624206	+	0.857878i
$928$	17918.7	−	31036.2i	0.633849	−	1.09786i
$929$	−22338.1	−	38690.6i	−0.788900	−	1.36641i	−0.926642	−	0.375946i	$-0.877318\pi$
$929$	−22338.1	−	38690.6i	−0.788900	−	1.36641i	0.137742	−	0.990468i	$-0.456016\pi$
$930$	−1210.61	−	256.879i	−0.0426854	−	0.00905741i
$931$	1439.74	+	13801.0i	0.0506826	+	0.485831i
$932$		−	19053.6i		−	0.669660i
$933$	−9276.80	−	28517.0i	−0.325519	−	1.00065i
$934$	−20486.2	−	11827.7i	−0.717696	−	0.414362i
$935$	−4603.19	−	2657.65i	−0.161006	−	0.0929566i
$936$	−1313.24	−	12410.8i	−0.0458597	−	0.433398i
$937$		−	15309.3i		−	0.533761i	−0.963730	−	0.266880i	$-0.914007\pi$
$937$		−	15309.3i		−	0.533761i	0.963730	−	0.266880i	$-0.0859929\pi$
$938$	8853.68	−	5744.78i	0.308191	−	0.199972i
$939$	2528.70	−	11917.2i	0.0878817	−	0.414166i
$940$	−972.904	−	1685.12i	−0.0337581	−	0.0584708i
$941$	21192.2	−	36706.0i	0.734162	−	1.27161i	−0.220928	−	0.975290i	$-0.570909\pi$
$941$	21192.2	−	36706.0i	0.734162	−	1.27161i	0.955090	−	0.296316i	$-0.0957582\pi$
$942$	−1875.86	+	2084.82i	−0.0648819	+	0.0721096i
$943$	−13004.0	+	7507.87i	−0.449066	+	0.259268i
$944$	6362.70			0.219373
$945$	−2886.93	+	1473.39i	−0.0993775	+	0.0507188i
$946$	−12320.1			−0.423427
$947$	10648.1	−	6147.69i	0.365383	−	0.210954i	−0.306057	−	0.952013i	$-0.599010\pi$
$947$	10648.1	−	6147.69i	0.365383	−	0.210954i	0.671439	+	0.741060i	$0.265676\pi$
$948$	937.398	−	1041.82i	0.0321153	−	0.0356928i
$949$	4915.78	−	8514.37i	0.168148	−	0.291242i
$950$	4766.21	+	8255.32i	0.162775	+	0.281935i
$951$	8533.67	−	40217.2i	0.290981	−	1.37133i
$952$	2376.34	+	45681.6i	0.0809008	+	1.55520i
$953$			1322.78i			0.0449621i	0.999747	+	0.0224811i	$0.00715655\pi$
$953$			1322.78i			0.0449621i	−0.999747	+	0.0224811i	$0.992843\pi$
$954$	−2294.85	−	21687.5i	−0.0778810	−	0.736015i
$955$	−3185.47	−	1839.13i	−0.107936	−	0.0623171i
$956$	−14436.0	−	8334.62i	−0.488382	−	0.281967i
$957$	13847.6	+	42567.6i	0.467742	+	1.43784i
$958$			15781.7i			0.532238i
$959$	1056.47	+	20309.1i	0.0355737	+	0.683852i
$960$	2564.67	+	544.197i	0.0862234	+	0.0182957i
$961$	−9893.00	−	17135.2i	−0.332080	−	0.575180i
$962$	3553.29	−	6154.47i	0.119088	−	0.206266i
$963$	−16960.8	−	23310.1i	−0.567553	−	0.780017i
$964$	−12977.7	+	7492.70i	−0.433594	+	0.250336i
$965$	2832.62			0.0944925
$966$	9295.40	−	11478.0i	0.309601	−	0.382297i
$967$	36887.2			1.22669			0.613346	−	0.789814i	$-0.289823\pi$
$967$	36887.2			1.22669			0.613346	+	0.789814i	$0.289823\pi$
$968$	6633.06	−	3829.60i	0.220242	−	0.127157i
$969$	−16363.7	−	14723.5i	−0.542495	−	0.488120i
$970$	−1686.43	+	2920.98i	−0.0558226	+	0.0966875i
$971$	3409.79	+	5905.93i	0.112693	+	0.195191i	0.916855	−	0.399220i	$-0.130719\pi$
$971$	3409.79	+	5905.93i	0.112693	+	0.195191i	−0.804162	+	0.594410i	$0.797386\pi$
$972$	8276.02	+	14276.5i	0.273100	+	0.471111i
$973$	−12868.2	+	8349.64i	−0.423984	+	0.275105i
$974$		−	1794.59i		−	0.0590373i
$975$	−11953.8	+	3888.65i	−0.392643	+	0.127730i
$976$	7115.50	+	4108.14i	0.233362	+	0.134732i
$977$	42700.8	+	24653.3i	1.39828	+	0.807298i	0.994213	−	0.107431i	$-0.0342624\pi$
$977$	42700.8	+	24653.3i	1.39828	+	0.807298i	0.404068	+	0.914729i	$0.367596\pi$
$978$	−21845.9	+	7106.65i	−0.714269	+	0.232357i
$979$			4669.03i			0.152424i
$980$	759.444	−	1702.19i	0.0247546	−	0.0554842i
$981$	248.894	+	110.605i	0.00810047	+	0.00359975i
$982$	−1009.11	−	1747.82i	−0.0327921	−	0.0567977i
$983$	−9765.55	+	16914.4i	−0.316859	+	0.548816i	−0.979831	−	0.199828i	$-0.935962\pi$
$983$	−9765.55	+	16914.4i	−0.316859	+	0.548816i	0.662972	+	0.748644i	$0.269295\pi$
$984$	−17014.4	−	15309.0i	−0.551220	−	0.495970i
$985$	535.661	−	309.264i	0.0173275	−	0.0100040i
$986$	−42319.1			−1.36685
$987$	−12347.6	−	32170.1i	−0.398206	−	1.03747i
$988$	−3453.71			−0.111212
$989$	11045.0	−	6376.81i	0.355116	−	0.205026i
$990$	−2115.30	+	1539.13i	−0.0679077	+	0.0494107i
$991$	−9285.39	+	16082.8i	−0.297639	+	0.515526i	−0.975595	−	0.219576i	$-0.929533\pi$
$991$	−9285.39	+	16082.8i	−0.297639	+	0.515526i	0.677956	+	0.735102i	$0.262866\pi$
$992$	−8465.85	−	14663.3i	−0.270959	−	0.469314i
$993$	−24805.1	−	5263.39i	−0.792716	−	0.168206i
$994$	7314.27	−	14341.3i	0.233395	−	0.457625i
$995$			1047.46i			0.0333735i
$996$	512.014	+	1573.94i	0.0162889	+	0.0500723i
$997$	19389.3	+	11194.4i	0.615913	+	0.355598i	0.775276	−	0.631622i	$-0.217611\pi$
$997$	19389.3	+	11194.4i	0.615913	+	0.355598i	−0.159363	+	0.987220i	$0.550944\pi$
$998$	−10205.1	−	5891.89i	−0.323683	−	0.186878i
$999$	−2758.05	+	26509.7i	−0.0873481	+	0.839569i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.4.g.a.17.3	yes	12
3.2	odd	2	inner	21.4.g.a.17.4	yes	12
4.3	odd	2		336.4.bc.d.17.5		12
7.2	even	3		147.4.g.d.68.4		12
7.3	odd	6		147.4.c.a.146.5		12
7.4	even	3		147.4.c.a.146.6		12
7.5	odd	6	inner	21.4.g.a.5.4	yes	12
7.6	odd	2		147.4.g.d.80.3		12
12.11	even	2		336.4.bc.d.17.3		12
21.2	odd	6		147.4.g.d.68.3		12
21.5	even	6	inner	21.4.g.a.5.3	✓	12
21.11	odd	6		147.4.c.a.146.7		12
21.17	even	6		147.4.c.a.146.8		12
21.20	even	2		147.4.g.d.80.4		12
28.19	even	6		336.4.bc.d.257.3		12
84.47	odd	6		336.4.bc.d.257.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.3	✓	12	21.5	even	6	inner
21.4.g.a.5.4	yes	12	7.5	odd	6	inner
21.4.g.a.17.3	yes	12	1.1	even	1	trivial
21.4.g.a.17.4	yes	12	3.2	odd	2	inner
147.4.c.a.146.5		12	7.3	odd	6
147.4.c.a.146.6		12	7.4	even	3
147.4.c.a.146.7		12	21.11	odd	6
147.4.c.a.146.8		12	21.17	even	6
147.4.g.d.68.3		12	21.2	odd	6
147.4.g.d.68.4		12	7.2	even	3
147.4.g.d.80.3		12	7.6	odd	2
147.4.g.d.80.4		12	21.20	even	2
336.4.bc.d.17.3		12	12.11	even	2
336.4.bc.d.17.5		12	4.3	odd	2
336.4.bc.d.257.3		12	28.19	even	6
336.4.bc.d.257.5		12	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	21.4.g.a.17.3

Level	$21$
Weight	$4$
Character	21.17
Analytic conductor	$1.239$
Analytic rank	$0$
Dimension	$12$
Inner twists	$4$