LMFDB - Embedded newform 84.4.o.a.31.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,4,Mod(19,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("84.19");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	84.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.95616044048$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.10
Character	$\chi$	$=$	84.31
Dual form			84.4.o.a.19.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.12158 + 1.87053i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(1.00225 + 7.93697i) q^{4} +(18.9410 - 10.9356i) q^{5} +(-8.04215 + 2.70625i) q^{6} +(2.66595 + 18.3274i) q^{7} +(-12.7200 + 18.7137i) q^{8} +(-4.50000 - 7.79423i) q^{9} +(60.6402 + 12.2289i) q^{10} +(-24.0267 - 13.8718i) q^{11} +(-22.1242 - 9.30155i) q^{12} +35.4983i q^{13} +(-28.6258 + 43.8698i) q^{14} +65.6135i q^{15} +(-61.9910 + 15.9096i) q^{16} +(5.22169 + 3.01475i) q^{17} +(5.03220 - 24.9535i) q^{18} +(-39.2181 - 67.9277i) q^{19} +(105.779 + 139.374i) q^{20} +(-51.6148 - 20.5647i) q^{21} +(-25.0270 - 74.3727i) q^{22} +(163.382 - 94.3288i) q^{23} +(-29.5396 - 61.1180i) q^{24} +(176.674 - 306.008i) q^{25} +(-66.4007 + 75.3127i) q^{26} +27.0000 q^{27} +(-142.792 + 39.5281i) q^{28} -47.8979 q^{29} +(-122.732 + 139.205i) q^{30} +(-37.1324 + 64.3151i) q^{31} +(-161.279 - 82.2024i) q^{32} +(72.0800 - 41.6154i) q^{33} +(5.43910 + 16.1634i) q^{34} +(250.916 + 317.985i) q^{35} +(57.3525 - 43.5281i) q^{36} +(-35.1090 - 60.8106i) q^{37} +(43.8562 - 217.473i) q^{38} +(-92.2274 - 53.2475i) q^{39} +(-36.2839 + 493.556i) q^{40} -70.5559i q^{41} +(-71.0384 - 140.177i) q^{42} -380.755i q^{43} +(86.0194 - 204.602i) q^{44} +(-170.469 - 98.4203i) q^{45} +(523.074 + 105.485i) q^{46} +(17.9041 + 31.0107i) q^{47} +(51.6522 - 184.922i) q^{48} +(-328.785 + 97.7197i) q^{49} +(947.227 - 318.749i) q^{50} +(-15.6651 + 9.04424i) q^{51} +(-281.749 + 35.5780i) q^{52} +(-153.731 + 266.270i) q^{53} +(57.2828 + 50.5043i) q^{54} -606.785 q^{55} +(-376.884 - 183.234i) q^{56} +235.308 q^{57} +(-101.619 - 89.5943i) q^{58} +(57.3388 - 99.3137i) q^{59} +(-520.773 + 65.7608i) q^{60} +(-75.2261 + 43.4318i) q^{61} +(-199.083 + 66.9929i) q^{62} +(130.851 - 103.252i) q^{63} +(-188.404 - 476.076i) q^{64} +(388.195 + 672.374i) q^{65} +(230.767 + 46.5371i) q^{66} +(-521.631 - 301.164i) q^{67} +(-18.6945 + 44.4659i) q^{68} +565.973i q^{69} +(-62.4596 + 1143.98i) q^{70} +325.107i q^{71} +(203.099 + 14.9309i) q^{72} +(395.235 + 228.189i) q^{73} +(39.2612 - 194.687i) q^{74} +(530.022 + 918.025i) q^{75} +(499.834 - 379.353i) q^{76} +(190.180 - 477.327i) q^{77} +(-96.0673 - 285.483i) q^{78} +(49.4204 - 28.5329i) q^{79} +(-1000.19 + 979.251i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(131.977 - 149.690i) q^{82} +635.785 q^{83} +(111.491 - 430.276i) q^{84} +131.872 q^{85} +(712.213 - 807.804i) q^{86} +(71.8468 - 124.442i) q^{87} +(565.211 - 273.178i) q^{88} +(-1029.36 + 594.302i) q^{89} +(-177.566 - 527.674i) q^{90} +(-650.591 + 94.6368i) q^{91} +(912.434 + 1202.22i) q^{92} +(-111.397 - 192.945i) q^{93} +(-20.0215 + 99.2820i) q^{94} +(-1485.66 - 857.745i) q^{95} +(455.486 - 295.710i) q^{96} +1388.42i q^{97} +(-880.334 - 407.682i) q^{98} +249.692i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} - 36 q^{3} - 5 q^{4} + 6 q^{6} + 10 q^{7} - 76 q^{8} - 108 q^{9} - 19 q^{10} + 6 q^{11} - 15 q^{12} - 62 q^{14} - 89 q^{16} - 9 q^{18} + 42 q^{19} - 134 q^{20} - 60 q^{21} + 14 q^{22} - 21 q^{24}+ \cdots + 7795 q^{98}+O(q^{100}) $ 24 * q - q^2 - 36 * q^3 - 5 * q^4 + 6 * q^6 + 10 * q^7 - 76 * q^8 - 108 * q^9 - 19 * q^10 + 6 * q^11 - 15 * q^12 - 62 * q^14 - 89 * q^16 - 9 * q^18 + 42 * q^19 - 134 * q^20 - 60 * q^21 + 14 * q^22 - 21 * q^24 + 342 * q^25 - 516 * q^26 + 648 * q^27 + 37 * q^28 + 400 * q^29 - 111 * q^30 + 78 * q^31 - 591 * q^32 - 18 * q^33 + 580 * q^34 + 84 * q^35 + 90 * q^36 - 134 * q^37 + 280 * q^38 + 162 * q^39 + 899 * q^40 - 303 * q^42 + 1091 * q^44 + 468 * q^46 - 140 * q^47 - 258 * q^48 + 268 * q^49 + 1246 * q^50 - 1108 * q^52 - 572 * q^53 - 27 * q^54 - 424 * q^55 - 1709 * q^56 - 252 * q^57 - 2145 * q^58 - 302 * q^59 + 21 * q^60 - 300 * q^61 + 2448 * q^62 + 90 * q^63 - 1646 * q^64 + 140 * q^65 + 1005 * q^66 - 2310 * q^67 + 3934 * q^68 + 2625 * q^70 + 747 * q^72 - 486 * q^73 - 2516 * q^74 + 1026 * q^75 - 2540 * q^76 - 968 * q^77 + 846 * q^78 - 1326 * q^79 - 3045 * q^80 - 972 * q^81 - 4298 * q^82 - 668 * q^83 - 1410 * q^84 + 1824 * q^85 - 5214 * q^86 - 600 * q^87 + 4619 * q^88 + 504 * q^90 - 2114 * q^91 - 476 * q^92 + 234 * q^93 + 4424 * q^94 + 1992 * q^95 + 2097 * q^96 + 7795 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	2.12158	+	1.87053i	0.750094	+	0.661332i
$2$	2.12158	+	1.87053i	0.750094	+	0.661332i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$3$	−1.50000	+	2.59808i	−0.288675	+	0.500000i
$4$	1.00225	+	7.93697i	0.125281	+	0.992121i
$5$	18.9410	−	10.9356i	1.69413	−	0.978109i	0.743019	−	0.669270i	$-0.233393\pi$
$5$	18.9410	−	10.9356i	1.69413	−	0.978109i	0.951115	−	0.308838i	$-0.0999402\pi$
$6$	−8.04215	+	2.70625i	−0.547199	+	0.184137i
$7$	2.66595	+	18.3274i	0.143948	+	0.989585i
$7$	2.66595	+	18.3274i	0.143948	+	0.989585i
$8$	−12.7200	+	18.7137i	−0.562149	+	0.827036i
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	60.6402	+	12.2289i	1.91761	+	0.386711i
$11$	−24.0267	−	13.8718i	−0.658574	−	0.380228i	0.133160	−	0.991095i	$-0.457488\pi$
$11$	−24.0267	−	13.8718i	−0.658574	−	0.380228i	−0.791733	+	0.610867i	$0.790821\pi$
$12$	−22.1242	−	9.30155i	−0.532226	−	0.223760i
$13$			35.4983i			0.757344i	0.925531	+	0.378672i	$0.123619\pi$
$13$			35.4983i			0.757344i	−0.925531	+	0.378672i	$0.876381\pi$
$14$	−28.6258	+	43.8698i	−0.546470	+	0.837479i
$15$			65.6135i			1.12942i
$16$	−61.9910	+	15.9096i	−0.968610	+	0.248587i
$17$	5.22169	+	3.01475i	0.0744968	+	0.0430108i	0.536786	−	0.843719i	$-0.319638\pi$
$17$	5.22169	+	3.01475i	0.0744968	+	0.0430108i	−0.462289	+	0.886729i	$0.652972\pi$
$18$	5.03220	−	24.9535i	0.0658944	−	0.326755i
$19$	−39.2181	−	67.9277i	−0.473539	−	0.820194i	0.526002	−	0.850483i	$-0.323690\pi$
$19$	−39.2181	−	67.9277i	−0.473539	−	0.820194i	−0.999541	+	0.0302895i	$0.990357\pi$
$20$	105.779	+	139.374i	1.18264	+	1.55825i
$21$	−51.6148	−	20.5647i	−0.536347	−	0.213695i
$22$	−25.0270	−	74.3727i	−0.242535	−	0.720742i
$23$	163.382	−	94.3288i	1.48120	−	0.855171i	0.481426	−	0.876487i	$-0.340119\pi$
$23$	163.382	−	94.3288i	1.48120	−	0.855171i	0.999773	+	0.0213161i	$0.00678564\pi$
$24$	−29.5396	−	61.1180i	−0.251239	−	0.519819i
$25$	176.674	−	306.008i	1.41339	−	2.44807i
$26$	−66.4007	+	75.3127i	−0.500855	+	0.568079i
$27$	27.0000			0.192450
$28$	−142.792	+	39.5281i	−0.963755	+	0.266790i
$29$	−47.8979			−0.306704			−0.153352	−	0.988172i	$-0.549007\pi$
$29$	−47.8979			−0.306704			−0.153352	+	0.988172i	$0.549007\pi$
$30$	−122.732	+	139.205i	−0.746923	+	0.847172i
$31$	−37.1324	+	64.3151i	−0.215134	+	0.372624i	−0.953314	−	0.301980i	$-0.902352\pi$
$31$	−37.1324	+	64.3151i	−0.215134	+	0.372624i	0.738180	+	0.674604i	$0.235686\pi$
$32$	−161.279	−	82.2024i	−0.890946	−	0.454109i
$33$	72.0800	−	41.6154i	0.380228	−	0.219525i
$34$	5.43910	+	16.1634i	0.0274352	+	0.0815292i
$35$	250.916	+	317.985i	1.21179	+	1.53569i
$36$	57.3525	−	43.5281i	0.265521	−	0.201519i
$37$	−35.1090	−	60.8106i	−0.155997	−	0.270195i	0.777425	−	0.628976i	$-0.216526\pi$
$37$	−35.1090	−	60.8106i	−0.155997	−	0.270195i	−0.933422	+	0.358781i	$0.883192\pi$
$38$	43.8562	−	217.473i	0.187222	−	0.928388i
$39$	−92.2274	−	53.2475i	−0.378672	−	0.218626i
$40$	−36.2839	+	493.556i	−0.143425	+	1.95095i
$41$		−	70.5559i		−	0.268756i	−0.990930	−	0.134378i	$-0.957096\pi$
$41$		−	70.5559i		−	0.268756i	0.990930	−	0.134378i	$-0.0429036\pi$
$42$	−71.0384	−	140.177i	−0.260987	−	0.514994i
$43$		−	380.755i		−	1.35034i	−0.737662	−	0.675170i	$-0.764070\pi$
$43$		−	380.755i		−	1.35034i	0.737662	−	0.675170i	$-0.235930\pi$
$44$	86.0194	−	204.602i	0.294725	−	0.701020i
$45$	−170.469	−	98.4203i	−0.564711	−	0.326036i
$46$	523.074	+	105.485i	1.67659	+	0.338106i
$47$	17.9041	+	31.0107i	0.0555654	+	0.0962421i	0.892470	−	0.451106i	$-0.148971\pi$
$47$	17.9041	+	31.0107i	0.0555654	+	0.0962421i	−0.836905	+	0.547349i	$0.815637\pi$
$48$	51.6522	−	184.922i	0.155320	−	0.556066i
$49$	−328.785	+	97.7197i	−0.958558	+	0.284897i
$50$	947.227	−	318.749i	2.67916	−	0.901558i
$51$	−15.6651	+	9.04424i	−0.0430108	+	0.0248323i
$52$	−281.749	+	35.5780i	−0.751377	+	0.0948805i
$53$	−153.731	+	266.270i	−0.398425	+	0.690093i	−0.993532	−	0.113554i	$-0.963777\pi$
$53$	−153.731	+	266.270i	−0.398425	+	0.690093i	0.595106	+	0.803647i	$0.297110\pi$
$54$	57.2828	+	50.5043i	0.144356	+	0.127273i
$55$	−606.785			−1.48762
$56$	−376.884	−	183.234i	−0.899343	−	0.437245i
$57$	235.308			0.546796
$58$	−101.619	−	89.5943i	−0.230056	−	0.202833i
$59$	57.3388	−	99.3137i	0.126523	−	0.219145i	−0.795804	−	0.605554i	$-0.792952\pi$
$59$	57.3388	−	99.3137i	0.126523	−	0.219145i	0.922327	+	0.386409i	$0.126285\pi$
$60$	−520.773	+	65.7608i	−1.12052	+	0.141495i
$61$	−75.2261	+	43.4318i	−0.157897	+	0.0911618i	−0.576867	−	0.816838i	$-0.695725\pi$
$61$	−75.2261	+	43.4318i	−0.157897	+	0.0911618i	0.418970	+	0.908000i	$0.362391\pi$
$62$	−199.083	+	66.9929i	−0.407799	+	0.137227i
$63$	130.851	−	103.252i	0.261677	−	0.206485i
$64$	−188.404	−	476.076i	−0.367977	−	0.929835i
$65$	388.195	+	672.374i	0.740764	+	1.28304i
$66$	230.767	+	46.5371i	0.430385	+	0.0867927i
$67$	−521.631	−	301.164i	−0.951155	−	0.549150i	−0.0577158	−	0.998333i	$-0.518382\pi$
$67$	−521.631	−	301.164i	−0.951155	−	0.549150i	−0.893440	+	0.449183i	$0.851715\pi$
$68$	−18.6945	+	44.4659i	−0.0333389	+	0.0792983i
$69$			565.973i			0.987466i
$70$	−62.4596	+	1143.98i	−0.106648	+	1.95331i
$71$			325.107i			0.543424i	0.962379	+	0.271712i	$0.0875898\pi$
$71$			325.107i			0.543424i	−0.962379	+	0.271712i	$0.912410\pi$
$72$	203.099	+	14.9309i	0.332436	+	0.0244391i
$73$	395.235	+	228.189i	0.633682	+	0.365856i	0.782177	−	0.623057i	$-0.214109\pi$
$73$	395.235	+	228.189i	0.633682	+	0.365856i	−0.148495	+	0.988913i	$0.547443\pi$
$74$	39.2612	−	194.687i	0.0616760	−	0.305837i
$75$	530.022	+	918.025i	0.816023	+	1.41339i
$76$	499.834	−	379.353i	0.754406	−	0.572563i
$77$	190.180	−	477.327i	0.281468	−	0.706448i
$78$	−96.0673	−	285.483i	−0.139455	−	0.414418i
$79$	49.4204	−	28.5329i	0.0703827	−	0.0406355i	−0.464396	−	0.885628i	$-0.653728\pi$
$79$	49.4204	−	28.5329i	0.0703827	−	0.0406355i	0.534778	+	0.844992i	$0.320395\pi$
$80$	−1000.19	+	979.251i	−1.39781	+	1.36855i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	131.977	−	149.690i	0.177737	−	0.201592i
$83$	635.785			0.840801			0.420400	−	0.907339i	$-0.361890\pi$
$83$	635.785			0.840801			0.420400	+	0.907339i	$0.361890\pi$
$84$	111.491	−	430.276i	0.144817	−	0.558893i
$85$	131.872			0.168277
$86$	712.213	−	807.804i	0.893022	−	1.01288i
$87$	71.8468	−	124.442i	0.0885377	−	0.153352i
$88$	565.211	−	273.178i	0.684679	−	0.330919i
$89$	−1029.36	+	594.302i	−1.22598	+	0.707819i	−0.966186	−	0.257846i	$-0.916987\pi$
$89$	−1029.36	+	594.302i	−1.22598	+	0.707819i	−0.259792	+	0.965665i	$0.583654\pi$
$90$	−177.566	−	527.674i	−0.207968	−	0.618019i
$91$	−650.591	+	94.6368i	−0.749456	+	0.109018i
$92$	912.434	+	1202.22i	1.03400	+	1.36239i
$93$	−111.397	−	192.945i	−0.124208	−	0.215134i
$94$	−20.0215	+	99.2820i	−0.0219687	+	0.108938i
$95$	−1485.66	−	857.745i	−1.60448	−	0.926345i
$96$	455.486	−	295.710i	0.484248	−	0.314383i
$97$			1388.42i			1.45333i	0.686993	+	0.726664i	$0.258930\pi$
$97$			1388.42i			1.45333i	−0.686993	+	0.726664i	$0.741070\pi$
$98$	−880.334	−	407.682i	−0.907420	−	0.420225i
$99$			249.692i			0.253485i
$100$	2605.85	+	1095.56i	2.60585	+	1.09556i
$101$	979.341	+	565.423i	0.964832	+	0.557046i	0.897657	−	0.440695i	$-0.145268\pi$
$101$	979.341	+	565.423i	0.964832	+	0.557046i	0.0671752	+	0.997741i	$0.478601\pi$
$102$	−50.1523	−	10.1139i	−0.0486845	−	0.00981785i
$103$	352.212	+	610.049i	0.336937	+	0.583591i	0.983855	−	0.178968i	$-0.0572759\pi$
$103$	352.212	+	610.049i	0.336937	+	0.583591i	−0.646918	+	0.762559i	$0.723943\pi$
$104$	−664.305	−	451.538i	−0.626350	−	0.425740i
$105$	−1202.52	+	174.922i	−1.11766	+	0.162578i
$106$	−824.218	+	277.356i	−0.755237	+	0.254143i
$107$	−697.961	+	402.968i	−0.630602	+	0.364078i	−0.780985	−	0.624550i	$-0.785283\pi$
$107$	−697.961	+	402.968i	−0.630602	+	0.364078i	0.150383	+	0.988628i	$0.451949\pi$
$108$	27.0606	+	214.298i	0.0241103	+	0.190934i
$109$	760.770	−	1317.69i	0.668518	−	1.15791i	−0.309800	−	0.950802i	$-0.600262\pi$
$109$	760.770	−	1317.69i	0.668518	−	1.15791i	0.978318	−	0.207106i	$-0.0664045\pi$
$110$	−1287.35	−	1135.01i	−1.11585	−	0.983807i
$111$	210.654			0.180130
$112$	−456.846	−	1093.72i	−0.385427	−	0.922738i
$113$	−1791.92			−1.49177			−0.745884	−	0.666076i	$-0.767973\pi$
$113$	−1791.92			−1.49177			−0.745884	+	0.666076i	$0.767973\pi$
$114$	499.227	+	440.151i	0.410148	+	0.361613i
$115$	2063.08	−	3573.36i	1.67290	−	2.89755i
$116$	−48.0054	−	380.164i	−0.0384241	−	0.304287i
$117$	276.682	−	159.743i	0.218626	−	0.126224i
$118$	307.418	−	103.449i	0.239832	−	0.0807052i
$119$	−41.3316	+	103.737i	−0.0318392	+	0.0799123i
$120$	−1227.87	−	834.603i	−0.934073	−	0.634904i
$121$	−280.646	−	486.094i	−0.210854	−	0.365210i
$122$	−240.839	−	48.5683i	−0.178726	−	0.0360423i
$123$	183.310	+	105.834i	0.134378	+	0.0775831i
$124$	−547.683	−	230.259i	−0.396640	−	0.166757i
$125$		−	4994.24i		−	3.57359i
$126$	470.748	+	25.7022i	0.332838	+	0.0181725i
$127$			1196.41i			0.835938i	0.908461	+	0.417969i	$0.137258\pi$
$127$			1196.41i			0.835938i	−0.908461	+	0.417969i	$0.862742\pi$
$128$	490.798	−	1362.45i	0.338912	−	0.940818i
$129$	989.230	+	571.132i	0.675170	+	0.389809i
$130$	−434.105	+	2152.63i	−0.292873	+	1.45229i
$131$	1267.97	+	2196.19i	0.845672	+	1.46475i	0.885036	+	0.465522i	$0.154133\pi$
$131$	1267.97	+	2196.19i	0.845672	+	1.46475i	−0.0393642	+	0.999225i	$0.512533\pi$
$132$	402.542	+	530.388i	0.265430	+	0.349730i
$133$	1140.38	−	899.856i	0.743487	−	0.586672i
$134$	−543.349	−	1614.67i	−0.350285	−	1.04094i
$135$	511.407	−	295.261i	0.326036	−	0.188237i
$136$	−122.837	+	59.3696i	−0.0774498	+	0.0374331i
$137$	122.386	−	211.978i	0.0763221	−	0.132194i	−0.825338	−	0.564638i	$-0.809016\pi$
$137$	122.386	−	211.978i	0.0763221	−	0.132194i	0.901660	+	0.432445i	$0.142349\pi$
$138$	−1058.67	+	1200.76i	−0.653043	+	0.740692i
$139$	−2011.00			−1.22713			−0.613563	−	0.789646i	$-0.710264\pi$
$139$	−2011.00			−1.22713			−0.613563	+	0.789646i	$0.710264\pi$
$140$	−2272.36	+	2310.21i	−1.37178	+	1.39463i
$141$	−107.424			−0.0641614
$142$	−608.122	+	689.742i	−0.359383	+	0.407619i
$143$	492.426	−	852.907i	0.287963	−	0.498767i
$144$	402.962	+	411.579i	0.233196	+	0.238182i
$145$	−907.233	+	523.791i	−0.519597	+	0.299990i
$146$	411.691	+	1223.42i	0.233368	+	0.693501i
$147$	239.295	−	1000.79i	0.134263	−	0.561522i
$148$	447.464	−	339.606i	0.248522	−	0.188618i
$149$	297.256	+	514.863i	0.163437	+	0.283082i	0.936099	−	0.351736i	$-0.114408\pi$
$149$	297.256	+	514.863i	0.163437	+	0.283082i	−0.772662	+	0.634818i	$0.781075\pi$
$150$	−592.706	+	2939.09i	−0.322628	+	1.59984i
$151$	−362.398	−	209.231i	−0.195308	−	0.112761i	0.399157	−	0.916883i	$-0.369303\pi$
$151$	−362.398	−	209.231i	−0.195308	−	0.112761i	−0.594465	+	0.804121i	$0.702636\pi$
$152$	1770.03	+	130.124i	0.944529	+	0.0694374i
$153$		−	54.2654i		−	0.0286738i
$154$	1296.34	−	656.953i	0.678323	−	0.343758i
$155$			1624.26i			0.841699i
$156$	330.189	−	785.373i	0.169464	−	0.403078i
$157$	−1160.85	−	670.215i	−0.590099	−	0.340694i	0.175038	−	0.984562i	$-0.443995\pi$
$157$	−1160.85	−	670.215i	−0.590099	−	0.340694i	−0.765137	+	0.643868i	$0.777329\pi$
$158$	158.221	+	31.9074i	0.0796671	+	0.0160659i
$159$	−461.192	−	798.809i	−0.230031	−	0.398425i
$160$	−3953.71	+	206.680i	−1.95355	+	0.102122i
$161$	2164.37	+	2742.89i	1.05948	+	1.34267i
$162$	−217.138	+	73.0687i	−0.105309	+	0.0354371i
$163$	−1129.55	+	652.144i	−0.542778	+	0.313373i	−0.746204	−	0.665717i	$-0.768126\pi$
$163$	−1129.55	+	652.144i	−0.542778	+	0.313373i	0.203426	+	0.979090i	$0.434792\pi$
$164$	560.000	−	70.7143i	0.266638	−	0.0336699i
$165$	910.177	−	1576.47i	0.429438	−	0.743808i
$166$	1348.87	+	1189.25i	0.630679	+	0.556048i
$167$	898.752			0.416452			0.208226	−	0.978081i	$-0.433231\pi$
$167$	898.752			0.416452			0.208226	+	0.978081i	$0.433231\pi$
$168$	1041.38	−	704.321i	0.478240	−	0.323450i
$169$	936.868			0.426430
$170$	279.778	+	246.670i	0.126223	+	0.111287i
$171$	−352.963	+	611.349i	−0.157846	+	0.273398i
$172$	3022.04	−	381.610i	1.33970	−	0.169171i
$173$	−218.339	+	126.058i	−0.0959540	+	0.0553990i	−0.547209	−	0.836996i	$-0.684310\pi$
$173$	−218.339	+	126.058i	−0.0959540	+	0.0553990i	0.451255	+	0.892395i	$0.350976\pi$
$174$	385.202	−	129.623i	0.167828	−	0.0564754i
$175$	6079.34	+	2422.17i	2.62603	+	1.04628i
$176$	1710.13	+	477.673i	0.732420	+	0.204579i
$177$	172.016	+	297.941i	0.0730482	+	0.126523i
$178$	−3295.53	−	664.587i	−1.38770	−	0.279848i
$179$	−2320.95	−	1340.00i	−0.969138	−	0.559532i	−0.0701648	−	0.997535i	$-0.522353\pi$
$179$	−2320.95	−	1340.00i	−0.969138	−	0.559532i	−0.898973	+	0.438003i	$0.855686\pi$
$180$	610.307	−	1451.65i	0.252720	−	0.601108i
$181$			7.76418i			0.00318843i	0.999999	+	0.00159422i	$0.000507455\pi$
$181$			7.76418i			0.00318843i	−0.999999	+	0.00159422i	$0.999493\pi$
$182$	−1557.31	−	1016.17i	−0.634259	−	0.413866i
$183$		−	260.591i		−	0.105265i
$184$	−312.980	+	4257.35i	−0.125398	+	1.70574i
$185$	−1330.00	−	767.875i	−0.528559	−	0.305164i
$186$	124.572	−	617.721i	0.0491077	−	0.243514i
$187$	−83.6399	−	144.869i	−0.0327078	−	0.0566515i
$188$	−228.187	+	173.184i	−0.0885226	+	0.0671849i
$189$	71.9806	+	494.839i	0.0277028	+	0.190446i
$190$	−1547.51	−	4598.75i	−0.590886	−	1.75594i
$191$	1010.06	−	583.156i	0.382644	−	0.220920i	−0.296324	−	0.955088i	$-0.595761\pi$
$191$	1010.06	−	583.156i	0.382644	−	0.220920i	0.678968	+	0.734168i	$0.262427\pi$
$192$	1519.49	+	224.625i	0.571143	+	0.0844318i
$193$	−1292.42	+	2238.54i	−0.482024	+	0.834890i	−0.999787	−	0.0206338i	$-0.993432\pi$
$193$	−1292.42	+	2238.54i	−0.482024	+	0.834890i	0.517763	+	0.855524i	$0.326765\pi$
$194$	−2597.08	+	2945.65i	−0.961132	+	1.09013i
$195$	−2329.17			−0.855361
$196$	−1105.12	−	2511.62i	−0.402741	−	0.915314i
$197$	3257.36			1.17806			0.589029	−	0.808112i	$-0.299510\pi$
$197$	3257.36			1.17806			0.589029	+	0.808112i	$0.299510\pi$
$198$	−467.057	+	529.744i	−0.167638	+	0.190138i
$199$	−1638.08	+	2837.23i	−0.583519	+	1.01068i	0.411540	+	0.911392i	$0.364991\pi$
$199$	−1638.08	+	2837.23i	−0.583519	+	1.01068i	−0.995058	+	0.0992920i	$0.968342\pi$
$200$	3479.26	+	7198.64i	1.23010	+	2.54511i
$201$	1564.89	−	903.492i	0.549150	−	0.317052i
$202$	1020.12	+	3031.48i	0.355322	+	1.05591i
$203$	−127.693	−	877.842i	−0.0441493	−	0.303510i
$204$	−87.4841	−	115.269i	−0.0300251	−	0.0395609i
$205$	−771.570	−	1336.40i	−0.262872	−	0.455308i
$206$	−393.866	+	1953.09i	−0.133213	+	0.660575i
$207$	−1470.44	−	848.960i	−0.493733	−	0.285057i
$208$	−564.764	−	2200.58i	−0.188266	−	0.733570i
$209$			2176.10i			0.720211i
$210$	−2878.45	−	1878.24i	−0.945867	−	0.617195i
$211$			3782.63i			1.23416i	0.786901	+	0.617079i	$0.211684\pi$
$211$			3782.63i			1.23416i	−0.786901	+	0.617079i	$0.788316\pi$
$212$	−2267.45	−	953.289i	−0.734571	−	0.308831i
$213$	−844.653	−	487.660i	−0.271712	−	0.156873i
$214$	−2234.55	−	450.625i	−0.713787	−	0.143944i
$215$	−4163.78	−	7211.88i	−1.32078	−	2.28766i
$216$	−343.440	+	505.270i	−0.108186	+	0.159163i
$217$	−1277.72	−	509.078i	−0.399711	−	0.159256i
$218$	4078.82	−	1372.55i	1.26721	−	0.426427i
$219$	−1185.71	+	684.567i	−0.365856	+	0.211227i
$220$	−608.147	−	4816.03i	−0.186369	−	1.47590i
$221$	−107.018	+	185.361i	−0.0325739	+	0.0564197i
$222$	446.920	+	394.034i	0.135114	+	0.119125i
$223$	−1227.51			−0.368611			−0.184306	−	0.982869i	$-0.559004\pi$
$223$	−1227.51			−0.368611			−0.184306	+	0.982869i	$0.559004\pi$
$224$	1076.59	−	3174.96i	0.321129	−	0.947035i
$225$	−3180.13			−0.942262
$226$	−3801.71	−	3351.84i	−1.11897	−	0.986554i
$227$	2834.70	−	4909.84i	0.828834	−	1.43558i	−0.0701187	−	0.997539i	$-0.522338\pi$
$227$	2834.70	−	4909.84i	0.828834	−	1.43558i	0.898953	−	0.438045i	$-0.144329\pi$
$228$	235.837	+	1867.64i	0.0685030	+	0.542488i
$229$	−1040.17	+	600.540i	−0.300157	+	0.173296i	−0.642514	−	0.766274i	$-0.722108\pi$
$229$	−1040.17	+	600.540i	−0.300157	+	0.173296i	0.342356	+	0.939570i	$0.388775\pi$
$230$	11061.1	−	3722.14i	3.17107	−	1.06709i
$231$	954.863	+	1210.09i	0.271971	+	0.344668i
$232$	609.260	−	896.345i	0.172413	−	0.253655i
$233$	−305.990	−	529.990i	−0.0860345	−	0.149016i	0.819797	−	0.572654i	$-0.194086\pi$
$233$	−305.990	−	529.990i	−0.0860345	−	0.149016i	−0.905832	+	0.423638i	$0.860753\pi$
$234$	885.808	+	178.635i	0.247466	+	0.0499047i
$235$	678.241	+	391.583i	0.188271	+	0.108698i
$236$	845.717	+	355.559i	0.233269	+	0.0980718i
$237$			171.197i			0.0469218i
$238$	−281.732	+	142.775i	−0.0767309	+	0.0388854i
$239$			5119.48i			1.38557i	0.721144	+	0.692785i	$0.243617\pi$
$239$			5119.48i			1.38557i	−0.721144	+	0.692785i	$0.756383\pi$
$240$	−1043.88	−	4067.45i	−0.280760	−	1.09397i
$241$	3921.35	+	2263.99i	1.04812	+	0.605131i	0.922122	−	0.386899i	$-0.126454\pi$
$241$	3921.35	+	2263.99i	1.04812	+	0.605131i	0.125996	+	0.992031i	$0.459787\pi$
$242$	313.837	−	1556.25i	0.0833646	−	0.413386i
$243$	−121.500	−	210.444i	−0.0320750	−	0.0555556i
$244$	−420.112	−	553.538i	−0.110225	−	0.145232i
$245$	−5158.90	+	5446.37i	−1.34527	+	1.42023i
$246$	190.942	+	567.421i	0.0494878	+	0.147063i
$247$	2411.32	−	1392.18i	0.621169	−	0.358632i
$248$	−731.250	−	1512.97i	−0.187236	−	0.387394i
$249$	−953.677	+	1651.82i	−0.242718	+	0.420400i
$250$	9341.87	−	10595.7i	2.36333	−	2.68053i
$251$	5530.10			1.39066			0.695332	−	0.718689i	$-0.255257\pi$
$251$	5530.10			1.39066			0.695332	+	0.718689i	$0.255257\pi$
$252$	950.655	+	935.076i	0.237641	+	0.233747i
$253$	−5234.04			−1.30064
$254$	−2237.92	+	2538.28i	−0.552832	+	0.627031i
$255$	−197.808	+	342.614i	−0.0485773	+	0.0841384i
$256$	3589.77	−	1972.50i	0.876409	−	0.481568i
$257$	2203.37	−	1272.12i	0.534797	−	0.308765i	−0.208171	−	0.978092i	$-0.566751\pi$
$257$	2203.37	−	1272.12i	0.534797	−	0.308765i	0.742967	+	0.669328i	$0.233418\pi$
$258$	1030.42	+	3062.09i	0.248647	+	0.738905i
$259$	1020.90	−	805.574i	0.244925	−	0.193266i
$260$	−4947.54	+	3754.98i	−1.18013	+	0.895668i
$261$	215.540	+	373.327i	0.0511173	+	0.0885377i
$262$	−1417.93	+	7031.17i	−0.334351	+	1.65797i
$263$	167.915	+	96.9458i	0.0393692	+	0.0227298i	0.519555	−	0.854437i	$-0.326098\pi$
$263$	167.915	+	96.9458i	0.0393692	+	0.0227298i	−0.480186	+	0.877167i	$0.659431\pi$
$264$	−138.079	+	1878.23i	−0.0321900	+	0.437867i
$265$			6724.54i			1.55881i
$266$	4102.63	+	223.998i	0.945670	+	0.0516323i
$267$		−	3565.81i		−	0.817319i
$268$	1867.53	−	4442.01i	0.425662	−	1.01246i
$269$	−2652.80	−	1531.60i	−0.601279	−	0.347149i	0.168265	−	0.985742i	$-0.446183\pi$
$269$	−2652.80	−	1531.60i	−0.601279	−	0.347149i	−0.769545	+	0.638593i	$0.779517\pi$
$270$	1637.29	+	330.180i	0.369045	+	0.0744227i
$271$	−984.326	−	1704.90i	−0.220640	−	0.382160i	0.734362	−	0.678758i	$-0.237481\pi$
$271$	−984.326	−	1704.90i	−0.220640	−	0.382160i	−0.955003	+	0.296597i	$0.904148\pi$
$272$	−371.661	−	103.812i	−0.0828503	−	0.0231417i
$273$	730.014	−	1832.24i	0.161840	−	0.406199i
$274$	656.163	−	220.804i	0.144673	−	0.0486834i
$275$	−8489.77	+	4901.57i	−1.86165	+	1.07482i
$276$	−4492.11	+	567.244i	−0.979686	+	0.123710i
$277$	1053.95	−	1825.49i	0.228612	−	0.395968i	−0.728785	−	0.684743i	$-0.759915\pi$
$277$	1053.95	−	1825.49i	0.228612	−	0.395968i	0.957397	+	0.288775i	$0.0932478\pi$
$278$	−4266.50	−	3761.62i	−0.920459	−	0.811537i
$279$	668.382			0.143423
$280$	−9142.32	+	650.806i	−1.95128	+	0.138904i
$281$	5847.13			1.24132			0.620659	−	0.784080i	$-0.286865\pi$
$281$	5847.13			1.24132			0.620659	+	0.784080i	$0.286865\pi$
$282$	−227.910	−	200.940i	−0.0481271	−	0.0424320i
$283$	−154.903	+	268.300i	−0.0325372	+	0.0563561i	−0.881835	−	0.471557i	$-0.843692\pi$
$283$	−154.903	+	268.300i	−0.0325372	+	0.0563561i	0.849298	+	0.527913i	$0.177025\pi$
$284$	−2580.36	+	325.837i	−0.539142	+	0.0680805i
$285$	4456.97	−	2573.24i	0.926345	−	0.534826i
$286$	2640.11	−	888.417i	0.545849	−	0.183683i
$287$	1293.10	−	188.098i	0.265957	−	0.0386868i
$288$	85.0489	+	1626.95i	0.0174012	+	0.332879i
$289$	−2438.32	−	4223.30i	−0.496300	−	0.859617i
$290$	−2904.54	−	585.738i	−0.588139	−	0.118606i
$291$	−3607.22	−	2082.63i	−0.726664	−	0.419540i
$292$	−1415.01	+	3365.67i	−0.283586	+	0.674524i
$293$			1344.08i			0.267993i	0.990982	+	0.133997i	$0.0427812\pi$
$293$			1344.08i			0.267993i	−0.990982	+	0.133997i	$0.957219\pi$
$294$	2379.69	−	1675.65i	0.472062	−	0.332401i
$295$		−	2508.13i		−	0.495014i
$296$	1584.58	+	116.491i	0.311154	+	0.0228746i
$297$	−648.720	−	374.539i	−0.126743	−	0.0731748i
$298$	−332.412	+	1648.35i	−0.0646177	+	0.320424i
$299$	3348.52	+	5799.80i	0.647658	+	1.12178i
$300$	−6755.13	+	5126.86i	−1.30002	+	0.986664i
$301$	6978.24	−	1015.07i	1.33628	−	0.194378i
$302$	−377.487	−	1121.78i	−0.0719269	−	0.213745i
$303$	−2938.02	+	1696.27i	−0.557046	+	0.321611i
$304$	3511.87	+	3586.96i	0.662564	+	0.676732i
$305$	−949.904	+	1645.28i	−0.178332	+	0.308881i
$306$	101.505	−	115.129i	0.0189629	−	0.0215081i
$307$	7970.56			1.48177			0.740886	−	0.671631i	$-0.234406\pi$
$307$	7970.56			1.48177			0.740886	+	0.671631i	$0.234406\pi$
$308$	3979.14	+	1031.05i	0.736144	+	0.190746i
$309$	−2113.27			−0.389061
$310$	−3038.22	+	3446.00i	−0.556643	+	0.631353i
$311$	561.232	−	972.083i	0.102330	−	0.177240i	−0.810314	−	0.585995i	$-0.800704\pi$
$311$	561.232	−	972.083i	0.102330	−	0.177240i	0.912644	+	0.408755i	$0.134037\pi$
$312$	2169.59	−	1048.61i	0.393682	−	0.190275i
$313$	−2962.75	+	1710.55i	−0.535031	+	0.308900i	−0.743063	−	0.669222i	$-0.766628\pi$
$313$	−2962.75	+	1710.55i	−0.535031	+	0.308900i	0.208032	+	0.978122i	$0.433294\pi$
$314$	−1209.18	−	3593.31i	−0.217318	−	0.645804i
$315$	1349.32	−	3386.63i	0.241352	−	0.605762i
$316$	275.996	+	363.652i	0.0491329	+	0.0647373i
$317$	−4751.20	−	8229.32i	−0.841811	−	1.45806i	−0.888362	−	0.459144i	$-0.848156\pi$
$317$	−4751.20	−	8229.32i	−0.841811	−	1.45806i	0.0465508	−	0.998916i	$-0.485177\pi$
$318$	515.736	−	2557.41i	0.0909466	−	0.450983i
$319$	1150.83	+	664.429i	0.201987	+	0.116617i
$320$	−8774.72	−	6957.03i	−1.53288	−	1.21534i
$321$		−	2417.81i		−	0.420401i
$322$	−538.768	+	9867.80i	−0.0932434	+	1.70780i
$323$		−	472.930i		−	0.0814691i
$324$	−597.354	−	251.142i	−0.102427	−	0.0430627i
$325$	10862.8	+	6271.64i	1.85403	+	1.07042i
$326$	−3616.28	−	729.270i	−0.614378	−	0.123897i
$327$	2282.31	+	3953.07i	0.385969	+	0.668518i
$328$	1320.36	+	897.470i	0.222271	+	0.151081i
$329$	−520.614	+	410.807i	−0.0872413	+	0.0688406i
$330$	4879.86	−	1642.11i	0.814022	−	0.273925i
$331$	−8047.03	+	4645.96i	−1.33627	+	0.771495i	−0.986252	−	0.165248i	$-0.947157\pi$
$331$	−8047.03	+	4645.96i	−1.33627	+	0.771495i	−0.350017	+	0.936743i	$0.613824\pi$
$332$	637.212	+	5046.20i	0.105336	+	0.834176i
$333$	−315.981	+	547.295i	−0.0519990	+	0.0900649i
$334$	1906.78	+	1681.14i	0.312378	+	0.275413i
$335$	−13173.6			−2.14851
$336$	3526.83	+	453.657i	0.572632	+	0.0736578i
$337$	−5870.33			−0.948894			−0.474447	−	0.880284i	$-0.657352\pi$
$337$	−5870.33			−0.948894			−0.474447	+	0.880284i	$0.657352\pi$
$338$	1987.64	+	1752.44i	0.319863	+	0.282012i
$339$	2687.88	−	4655.55i	0.430636	−	0.745884i
$340$	132.168	+	1046.66i	0.0210818	+	0.166951i
$341$	1784.33	−	1030.19i	0.283364	−	0.163600i
$342$	−1892.39	+	636.803i	−0.299206	+	0.100685i
$343$	−2667.47	−	5765.26i	−0.419912	−	0.907565i
$344$	7125.33	+	4843.20i	1.11678	+	0.759092i
$345$	6189.25	+	10720.1i	0.965849	+	1.67290i
$346$	−699.021	−	140.967i	−0.108612	−	0.0219029i
$347$	4471.43	+	2581.58i	0.691755	+	0.399385i	0.804269	−	0.594265i	$-0.202557\pi$
$347$	4471.43	+	2581.58i	0.691755	+	0.399385i	−0.112514	+	0.993650i	$0.535890\pi$
$348$	1059.70	+	445.524i	0.163236	+	0.0686282i
$349$		−	8061.50i		−	1.23645i	−0.786000	−	0.618227i	$-0.787851\pi$
$349$		−	8061.50i		−	1.23645i	0.786000	−	0.618227i	$-0.212149\pi$
$350$	8367.09	+	16510.4i	1.27783	+	2.52148i
$351$			958.455i			0.145751i
$352$	2734.69	+	4212.27i	0.414089	+	0.637826i
$353$	−5232.02	−	3020.71i	−0.788873	−	0.455456i	0.0506924	−	0.998714i	$-0.483857\pi$
$353$	−5232.02	−	3020.71i	−0.788873	−	0.455456i	−0.839566	+	0.543258i	$0.817191\pi$
$354$	−192.360	+	953.868i	−0.0288808	+	0.143213i
$355$	3555.24	+	6157.85i	0.531528	+	0.920633i
$356$	−5748.63	−	7574.37i	−0.855833	−	1.12764i
$357$	−207.519	−	262.988i	−0.0307650	−	0.0389883i
$358$	−2417.58	−	7184.32i	−0.356908	−	1.06062i
$359$	6193.16	−	3575.62i	0.910480	−	0.525666i	0.0298946	−	0.999553i	$-0.490483\pi$
$359$	6193.16	−	3575.62i	0.910480	−	0.525666i	0.880586	+	0.473887i	$0.157149\pi$
$360$	4010.17	−	1938.20i	0.587096	−	0.283756i
$361$	353.386	−	612.082i	0.0515215	−	0.0892378i
$362$	−14.5231	+	16.4724i	−0.00210861	+	0.00239162i
$363$	1683.88			0.243473
$364$	−1403.18	−	5068.88i	−0.202051	−	0.729894i
$365$	9981.53			1.43139
$366$	487.443	−	552.866i	0.0696148	−	0.0789583i
$367$	−4243.79	+	7350.47i	−0.603608	+	1.04548i	0.388661	+	0.921381i	$0.372938\pi$
$367$	−4243.79	+	7350.47i	−0.603608	+	1.04548i	−0.992270	+	0.124100i	$0.960396\pi$
$368$	−8627.50	+	8446.89i	−1.22212	+	1.19653i
$369$	−549.929	+	317.502i	−0.0775831	+	0.0447926i
$370$	−1385.37	−	4116.91i	−0.194654	−	0.578454i
$371$	−5289.86	−	2107.62i	−0.740258	−	0.294939i
$372$	1419.75	−	1077.53i	0.197879	−	0.150182i
$373$	−4300.88	−	7449.35i	−0.597028	−	1.03408i	−0.993257	−	0.115931i	$-0.963015\pi$
$373$	−4300.88	−	7449.35i	−0.597028	−	1.03408i	0.396230	−	0.918151i	$-0.370318\pi$
$374$	93.5316	−	463.802i	0.0129316	−	0.0641246i
$375$	12975.4	+	7491.36i	1.78679	+	1.03161i
$376$	−808.064	−	59.4051i	−0.110832	−	0.00814783i
$377$		−	1700.29i		−	0.232280i
$378$	−772.898	+	1184.49i	−0.105168	+	0.161173i
$379$		−	7459.51i		−	1.01100i	−0.862826	−	0.505501i	$-0.831308\pi$
$379$		−	7459.51i		−	1.01100i	0.862826	−	0.505501i	$-0.168692\pi$
$380$	5318.90	−	12651.3i	0.718037	−	1.70789i
$381$	−3108.36	−	1794.61i	−0.417969	−	0.241314i
$382$	3233.73	+	652.123i	0.433120	+	0.0873443i
$383$	−2643.57	−	4578.79i	−0.352689	−	0.610876i	0.634030	−	0.773308i	$-0.281399\pi$
$383$	−2643.57	−	4578.79i	−0.352689	−	0.610876i	−0.986720	+	0.162432i	$0.948066\pi$
$384$	2803.55	+	3318.80i	0.372573	+	0.441047i
$385$	−1617.66	−	11120.8i	−0.214139	−	1.47212i
$386$	−6929.24	+	2331.74i	−0.913703	+	0.307468i
$387$	−2967.69	+	1713.40i	−0.389809	+	0.225057i
$388$	−11019.9	+	1391.54i	−1.44188	+	0.182074i
$389$	5883.95	−	10191.3i	0.766910	−	1.32833i	−0.172321	−	0.985041i	$-0.555127\pi$
$389$	5883.95	−	10191.3i	0.766910	−	1.32833i	0.939231	−	0.343286i	$-0.111540\pi$
$390$	−4941.53	−	4356.78i	−0.641601	−	0.565677i
$391$	1137.51			0.147126
$392$	2353.45	−	7395.78i	0.303232	−	0.952917i
$393$	−7607.82			−0.976498
$394$	6910.77	+	6092.99i	0.883654	+	0.779088i
$395$	624.048	−	1080.88i	0.0794918	−	0.137684i
$396$	−1981.80	+	250.253i	−0.251488	+	0.0317568i
$397$	−2040.52	+	1178.09i	−0.257961	+	0.148934i	−0.623404	−	0.781900i	$-0.714251\pi$
$397$	−2040.52	+	1178.09i	−0.257961	+	0.148934i	0.365443	+	0.930834i	$0.380918\pi$
$398$	−8782.44	+	2955.36i	−1.10609	+	0.372208i
$399$	627.320	+	4312.59i	0.0787100	+	0.541101i
$400$	−6083.74	+	21780.6i	−0.760467	+	2.72257i
$401$	2294.83	+	3974.76i	0.285781	+	0.494988i	0.972798	−	0.231654i	$-0.0744136\pi$
$401$	2294.83	+	3974.76i	0.285781	+	0.494988i	−0.687017	+	0.726641i	$0.741080\pi$
$402$	5010.06	+	1010.34i	0.621590	+	0.125352i
$403$	−2283.08	−	1318.14i	−0.282204	−	0.162931i
$404$	−3506.20	+	8339.69i	−0.431782	+	1.02702i
$405$			1771.56i			0.217357i
$406$	1371.12	−	2101.27i	0.167604	−	0.256858i
$407$			1948.10i			0.237257i
$408$	30.0085	−	408.194i	0.00364128	−	0.0495309i
$409$	3386.93	+	1955.45i	0.409470	+	0.236407i	0.690562	−	0.723273i	$-0.257363\pi$
$409$	3386.93	+	1955.45i	0.409470	+	0.236407i	−0.281092	+	0.959681i	$0.590697\pi$
$410$	862.820	−	4278.53i	0.103931	−	0.515369i
$411$	367.157	+	635.935i	0.0440646	+	0.0763221i
$412$	−4488.94	+	3406.91i	−0.536782	+	0.407395i
$413$	1973.02	+	786.104i	0.235075	+	0.0936602i
$414$	−1531.66	−	4551.64i	−0.181829	−	0.540341i
$415$	12042.4	−	6952.68i	1.42443	−	0.822394i
$416$	2918.05	−	5725.12i	0.343916	−	0.674753i
$417$	3016.49	−	5224.72i	0.354241	−	0.613563i
$418$	−4070.46	+	4616.78i	−0.476298	+	0.540225i
$419$	9514.72			1.10937			0.554683	−	0.832062i	$-0.312839\pi$
$419$	9514.72			1.10937			0.554683	+	0.832062i	$0.312839\pi$
$420$	−2593.58	−	9369.08i	−0.301318	−	1.08849i
$421$	4910.22			0.568431			0.284216	−	0.958760i	$-0.408267\pi$
$421$	4910.22			0.568431			0.284216	+	0.958760i	$0.408267\pi$
$422$	−7075.52	+	8025.18i	−0.816187	+	0.925733i
$423$	161.136	−	279.097i	0.0185218	−	0.0320807i
$424$	−3027.43	−	6263.81i	−0.346757	−	0.717447i
$425$	1845.07	−	1065.25i	0.210587	−	0.121582i
$426$	−879.820	−	2614.56i	−0.100064	−	0.297361i
$427$	−996.540	−	1262.91i	−0.112941	−	0.143130i
$428$	−3897.87	−	5135.82i	−0.440212	−	0.580022i
$429$	1477.28	+	2558.72i	0.166256	+	0.287963i
$430$	4656.21	−	23089.1i	0.522192	−	2.58943i
$431$	1288.55	+	743.946i	0.144008	+	0.0831430i	0.570273	−	0.821455i	$-0.306838\pi$
$431$	1288.55	+	743.946i	0.144008	+	0.0831430i	−0.426265	+	0.904598i	$0.640171\pi$
$432$	−1673.76	+	429.559i	−0.186409	+	0.0478406i
$433$			5878.76i			0.652460i	0.945290	+	0.326230i	$0.105778\pi$
$433$			5878.76i			0.652460i	−0.945290	+	0.326230i	$0.894222\pi$
$434$	−1758.55	−	3470.06i	−0.194500	−	0.383798i
$435$		−	3142.75i		−	0.346398i
$436$	11221.0	+	4717.56i	1.23254	+	0.518188i
$437$	−12815.1	−	7398.79i	−1.40281	−	0.809913i
$438$	−3796.08	−	765.528i	−0.414118	−	0.0835122i
$439$	−7141.81	−	12370.0i	−0.776446	−	1.34484i	−0.933978	−	0.357330i	$-0.883687\pi$
$439$	−7141.81	−	12370.0i	−0.776446	−	1.34484i	0.157532	−	0.987514i	$-0.449646\pi$
$440$	7718.29	−	11355.2i	0.836262	−	1.23031i
$441$	2241.18	+	2122.89i	0.242002	+	0.229229i
$442$	−573.773	+	193.079i	−0.0617456	+	0.0207779i
$443$	11798.8	−	6812.03i	1.26541	−	0.730586i	0.291295	−	0.956633i	$-0.405914\pi$
$443$	11798.8	−	6812.03i	1.26541	−	0.730586i	0.974116	+	0.226048i	$0.0725805\pi$
$444$	211.127	+	1671.96i	0.0225668	+	0.178711i
$445$	−12998.1	+	22513.3i	−1.38465	+	2.39828i
$446$	−2604.27	−	2296.10i	−0.276493	−	0.243774i
$447$	−1783.54			−0.188721
$448$	8222.94	−	4722.15i	0.867182	−	0.497992i
$449$	−17244.3			−1.81250			−0.906248	−	0.422747i	$-0.861066\pi$
$449$	−17244.3			−1.81250			−0.906248	+	0.422747i	$0.861066\pi$
$450$	−6746.92	−	5948.53i	−0.706784	−	0.623148i
$451$	−978.737	+	1695.22i	−0.102188	+	0.176995i
$452$	−1795.95	−	14222.4i	−0.186890	−	1.48001i
$453$	1087.20	−	627.693i	0.112761	−	0.0651028i
$454$	15198.0	−	5114.26i	1.57110	−	0.528687i
$455$	−11287.9	+	8907.11i	−1.16305	+	0.917740i
$456$	−2993.12	+	4403.49i	−0.307381	+	0.452220i
$457$	1750.60	+	3032.13i	0.179190	+	0.310366i	0.941603	−	0.336724i	$-0.109319\pi$
$457$	1750.60	+	3032.13i	0.179190	+	0.310366i	−0.762413	+	0.647090i	$0.775986\pi$
$458$	−3330.12	−	671.563i	−0.339752	−	0.0685154i
$459$	140.986	+	81.3981i	0.0143369	+	0.00827743i
$460$	30429.4	+	12793.2i	3.08430	+	1.29671i
$461$			9216.59i			0.931148i	0.885009	+	0.465574i	$0.154152\pi$
$461$			9216.59i			0.931148i	−0.885009	+	0.465574i	$0.845848\pi$
$462$	−237.690	+	4353.41i	−0.0239358	+	0.438396i
$463$		−	5526.20i		−	0.554696i	−0.960770	−	0.277348i	$-0.910544\pi$
$463$		−	5526.20i		−	0.554696i	0.960770	−	0.277348i	$-0.0894555\pi$
$464$	2969.24	−	762.035i	0.297076	−	0.0762426i
$465$	−4219.94	−	2436.38i	−0.420850	−	0.242978i
$466$	342.178	−	1696.78i	0.0340152	−	0.168673i
$467$	−625.113	−	1082.73i	−0.0619418	−	0.107286i	0.833392	−	0.552683i	$-0.186396\pi$
$467$	−625.113	−	1082.73i	−0.0619418	−	0.107286i	−0.895333	+	0.445397i	$0.853063\pi$
$468$	1545.18	+	2035.92i	0.152619	+	0.201090i
$469$	4128.90	−	10363.0i	0.406514	−	1.02030i
$470$	706.479	+	2099.45i	0.0693350	+	0.206043i
$471$	3482.54	−	2010.64i	0.340694	−	0.196700i
$472$	1129.18	+	2336.29i	0.110116	+	0.227831i
$473$	−5281.76	+	9148.27i	−0.513436	+	0.889298i
$474$	−320.230	+	363.210i	−0.0310309	+	0.0351957i
$475$	−27715.3			−2.67719
$476$	−864.782	−	224.078i	−0.0832715	−	0.0215769i
$477$	2767.15			0.265617
$478$	−9576.13	+	10861.4i	−0.916322	+	1.03931i
$479$	−8609.57	+	14912.2i	−0.821255	+	1.42246i	0.0834930	+	0.996508i	$0.473392\pi$
$479$	−8609.57	+	14912.2i	−0.821255	+	1.42246i	−0.904748	+	0.425947i	$0.859941\pi$
$480$	5393.59	−	10582.1i	0.512880	−	1.00625i
$481$	2158.68	−	1246.31i	0.204630	−	0.118143i
$482$	4084.62	+	12138.3i	0.385994	+	1.14706i
$483$	−10372.8	+	1508.86i	−0.977182	+	0.142143i
$484$	3576.84	−	2714.67i	0.335916	−	0.254946i
$485$	15183.2	+	26298.1i	1.42151	+	2.46213i
$486$	135.869	−	673.744i	0.0126814	−	0.0628841i
$487$	−12544.4	−	7242.51i	−1.16723	−	0.673900i	−0.214203	−	0.976789i	$-0.568716\pi$
$487$	−12544.4	−	7242.51i	−1.16723	−	0.673900i	−0.953026	+	0.302889i	$0.902049\pi$
$488$	144.105	−	1960.21i	0.0133675	−	0.181833i
$489$		−	3912.86i		−	0.361852i
$490$	−21132.6	+	1905.07i	−1.94832	+	0.175637i
$491$			11944.3i			1.09784i	0.835875	+	0.548920i	$0.184961\pi$
$491$			11944.3i			1.09784i	−0.835875	+	0.548920i	$0.815039\pi$
$492$	−656.279	+	1560.99i	−0.0601369	+	0.143039i
$493$	−250.108	−	144.400i	−0.0228485	−	0.0131916i
$494$	7719.93	+	1556.82i	0.703109	+	0.141791i
$495$	2730.53	+	4729.42i	0.247936	+	0.429438i
$496$	1278.65	−	4577.72i	0.115752	−	0.414407i
$497$	−5958.36	+	866.719i	−0.537764	+	0.0782246i
$498$	−5113.08	+	1720.59i	−0.460085	+	0.154822i
$499$	12792.5	−	7385.73i	1.14763	−	0.662586i	0.199324	−	0.979934i	$-0.436125\pi$
$499$	12792.5	−	7385.73i	1.14763	−	0.662586i	0.948309	+	0.317347i	$0.102792\pi$
$500$	39639.1	−	5005.45i	3.54543	−	0.447701i
$501$	−1348.13	+	2335.03i	−0.120219	+	0.208226i
$502$	11732.6	+	10344.2i	1.04313	+	0.919690i
$503$	9486.10			0.840883			0.420442	−	0.907320i	$-0.361875\pi$
$503$	9486.10			0.840883			0.420442	+	0.907320i	$0.361875\pi$
$504$	267.807	+	3762.07i	0.0236688	+	0.332492i
$505$	24732.9			2.17941
$506$	−11104.5	−	9790.43i	−0.975600	−	0.860153i
$507$	−1405.30	+	2434.05i	−0.123100	+	0.213215i
$508$	−9495.86	+	1199.09i	−0.829351	+	0.104727i
$509$	−13442.5	+	7761.05i	−1.17059	+	0.675840i	−0.953819	−	0.300383i	$-0.902886\pi$
$509$	−13442.5	+	7761.05i	−1.17059	+	0.675840i	−0.216770	+	0.976223i	$0.569552\pi$
$510$	−1060.53	+	356.878i	−0.0920809	+	0.0309859i
$511$	−3128.43	+	7851.96i	−0.270829	+	0.679747i
$512$	11305.6	+	2529.94i	0.975865	+	0.218376i
$513$	−1058.89	−	1834.05i	−0.0911326	−	0.157846i
$514$	7054.18	+	1422.57i	0.605343	+	0.122075i
$515$	13342.5	+	7703.29i	1.14163	+	0.659121i
$516$	−3541.61	+	8423.91i	−0.302152	+	0.718686i
$517$		−	993.446i		−	0.0845100i
$518$	3672.77	+	200.528i	0.311530	+	0.0170091i
$519$		−	756.350i		−	0.0639693i
$520$	−17520.4	−	1288.02i	−1.47754	−	0.108622i
$521$	18793.1	+	10850.2i	1.58031	+	0.912393i	0.994813	+	0.101720i	$0.0324346\pi$
$521$	18793.1	+	10850.2i	1.58031	+	0.912393i	0.585499	+	0.810673i	$0.300899\pi$
$522$	−241.031	+	1195.22i	−0.0202101	+	0.100217i
$523$	−3963.59	−	6865.14i	−0.331388	−	0.573980i	0.651396	−	0.758738i	$-0.274183\pi$
$523$	−3963.59	−	6865.14i	−0.331388	−	0.573980i	−0.982784	+	0.184757i	$0.940850\pi$
$524$	−16160.3	+	12265.0i	−1.34726	+	1.02251i
$525$	−15412.0	+	12161.3i	−1.28121	+	1.01098i
$526$	174.906	+	519.769i	0.0144986	+	0.0430855i
$527$	−387.787	+	223.889i	−0.0320537	+	0.0185062i
$528$	−3806.23	+	3726.54i	−0.313721	+	0.307153i
$529$	11712.4	−	20286.4i	0.962633	−	1.66733i
$530$	−12578.5	+	14266.7i	−1.03089	+	1.16926i
$531$	−1032.10			−0.0843488
$532$	8285.08	+	8149.31i	0.675195	+	0.664130i
$533$	2504.62			0.203540
$534$	6669.95	−	7565.17i	0.540519	−	0.613065i
$535$	−8813.38	+	15265.2i	−0.712216	+	1.23359i
$536$	12271.0	−	5930.85i	0.988858	−	0.477936i
$537$	6962.84	−	4020.00i	0.559532	−	0.323046i
$538$	−2763.25	−	8211.55i	−0.221435	−	0.658039i
$539$	9255.16	+	2212.97i	0.739607	+	0.176845i
$540$	2856.03	+	3763.10i	0.227600	+	0.299885i
$541$	2899.98	+	5022.92i	0.230462	+	0.399172i	0.957944	−	0.286955i	$-0.0926429\pi$
$541$	2899.98	+	5022.92i	0.230462	+	0.399172i	−0.727482	+	0.686127i	$0.759310\pi$
$542$	1100.74	−	5458.31i	0.0872339	−	0.432573i
$543$	−20.1719	−	11.6463i	−0.00159422	−	0.000920422i
$544$	−594.327	−	915.449i	−0.0468411	−	0.0721499i
$545$		−	33277.8i		−	2.61553i
$546$	4976.05	−	2521.74i	0.390028	−	0.197657i
$547$		−	783.787i		−	0.0612656i	−0.999531	−	0.0306328i	$-0.990248\pi$
$547$		−	783.787i		−	0.0612656i	0.999531	−	0.0306328i	$-0.00975225\pi$
$548$	1805.13	+	758.918i	0.140714	+	0.0591594i
$549$	677.035	+	390.886i	0.0526323	+	0.0303873i
$550$	−27180.3	−	5481.26i	−2.10722	−	0.424949i
$551$	1878.46	+	3253.59i	0.145236	+	0.251556i
$552$	−10591.4	−	7199.17i	−0.816670	−	0.555103i
$553$	654.686	+	829.680i	0.0503437	+	0.0638003i
$554$	5650.68	−	1901.50i	0.433347	−	0.145825i
$555$	3990.00	−	2303.63i	0.305164	−	0.176186i
$556$	−2015.51	−	15961.2i	−0.153735	−	1.21746i
$557$	−1362.77	+	2360.39i	−0.103667	+	0.179556i	−0.913193	−	0.407528i	$-0.866391\pi$
$557$	−1362.77	+	2360.39i	−0.103667	+	0.179556i	0.809526	+	0.587084i	$0.199724\pi$
$558$	1418.03	+	1250.23i	0.107581	+	0.0948502i
$559$	13516.2			1.02267
$560$	−20613.6	−	15720.2i	−1.55550	−	1.18625i
$561$	501.839			0.0377677
$562$	12405.2	+	10937.2i	0.931105	+	0.820923i
$563$	−5546.33	+	9606.53i	−0.415187	+	0.719124i	−0.995448	−	0.0953060i	$-0.969617\pi$
$563$	−5546.33	+	9606.53i	−0.415187	+	0.719124i	0.580261	+	0.814430i	$0.302950\pi$
$564$	−107.666	−	852.624i	−0.00803819	−	0.0636559i
$565$	−33940.8	+	19595.7i	−2.52725	+	1.45911i
$566$	−830.502	+	279.470i	−0.0616760	+	0.0207544i
$567$	−1393.60	−	555.248i	−0.103220	−	0.0411256i
$568$	−6083.95	−	4135.35i	−0.449431	−	0.305485i
$569$	2361.17	+	4089.67i	0.173964	+	0.301315i	0.939802	−	0.341719i	$-0.111009\pi$
$569$	2361.17	+	4089.67i	0.173964	+	0.301315i	−0.765838	+	0.643033i	$0.777676\pi$
$570$	14269.2	+	2877.56i	1.04854	+	0.211452i
$571$	−4054.83	−	2341.06i	−0.297179	−	0.171577i	0.343996	−	0.938971i	$-0.388219\pi$
$571$	−4054.83	−	2341.06i	−0.297179	−	0.171577i	−0.641175	+	0.767395i	$0.721553\pi$
$572$	7263.03	+	3053.55i	0.530913	+	0.223208i
$573$			3498.94i			0.255096i
$574$	3095.28	+	2019.72i	0.225077	+	0.146867i
$575$		−	66661.8i		−	4.83477i
$576$	−2862.82	+	3610.80i	−0.207091	+	0.261198i
$577$	−11844.4	−	6838.39i	−0.854576	−	0.493389i	0.00761647	−	0.999971i	$-0.497576\pi$
$577$	−11844.4	−	6838.39i	−0.854576	−	0.493389i	−0.862192	+	0.506582i	$0.830909\pi$
$578$	2726.69	−	13521.0i	0.196221	−	0.973012i
$579$	−3877.27	−	6715.63i	−0.278297	−	0.482024i
$580$	−5066.58	−	6675.71i	−0.362722	−	0.477921i
$581$	1694.97	+	11652.3i	0.121031	+	0.832044i
$582$	−3757.41	−	11165.9i	−0.267611	−	0.795260i
$583$	7387.27	−	4265.04i	0.524785	−	0.302985i
$584$	−9297.64	+	4493.75i	−0.658800	+	0.318412i
$585$	3493.76	−	6051.36i	0.246921	−	0.427680i
$586$	−2514.14	+	2851.58i	−0.177233	+	0.201020i
$587$	−2955.48			−0.207812			−0.103906	−	0.994587i	$-0.533134\pi$
$587$	−2955.48			−0.207812			−0.103906	+	0.994587i	$0.533134\pi$
$588$	8183.07	+	896.240i	0.573918	+	0.0628577i
$589$	5825.04			0.407498
$590$	4691.53	−	5321.21i	0.327368	−	0.371307i
$591$	−4886.05	+	8462.88i	−0.340076	+	0.589029i
$592$	3143.91	+	3211.14i	0.218267	+	0.222934i
$593$	17844.8	−	10302.7i	1.23575	−	0.713461i	0.267527	−	0.963550i	$-0.413793\pi$
$593$	17844.8	−	10302.7i	1.23575	−	0.713461i	0.968223	+	0.250090i	$0.0804601\pi$
$594$	−675.729	−	2008.06i	−0.0466759	−	0.138707i
$595$	351.564	+	2416.87i	0.0242231	+	0.166524i
$596$	−3788.53	+	2875.33i	−0.260376	+	0.197615i
$597$	−4914.23	−	8511.70i	−0.336895	−	0.583519i
$598$	−3744.53	+	18568.3i	−0.256062	+	1.26975i
$599$	−2175.54	−	1256.05i	−0.148397	−	0.0856773i	0.423963	−	0.905680i	$-0.360639\pi$
$599$	−2175.54	−	1256.05i	−0.148397	−	0.0856773i	−0.572360	+	0.820002i	$0.693972\pi$
$600$	−23921.5	−	1758.60i	−1.62765	−	0.119657i
$601$			18171.8i			1.23335i	0.787219	+	0.616674i	$0.211520\pi$
$601$			18171.8i			1.23335i	−0.787219	+	0.616674i	$0.788480\pi$
$602$	16703.7	+	10899.4i	1.13088	+	0.737920i
$603$			5420.95i			0.366100i
$604$	1297.45	−	3086.05i	0.0874046	−	0.207896i
$605$	−10631.4	−	6138.07i	−0.714429	−	0.412476i
$606$	−9406.18	−	1896.88i	−0.630528	−	0.127154i
$607$	8152.74	+	14121.0i	0.545156	+	0.944237i	0.998597	+	0.0529513i	$0.0168628\pi$
$607$	8152.74	+	14121.0i	0.545156	+	0.944237i	−0.453441	+	0.891286i	$0.649804\pi$
$608$	741.212	+	14179.1i	0.0494410	+	0.945787i
$609$	2472.24	+	985.006i	0.164500	+	0.0655410i
$610$	−5092.85	+	1713.78i	−0.338039	+	0.113753i
$611$	−1100.83	+	635.564i	−0.0728884	+	0.0420821i
$612$	430.703	−	54.3873i	0.0284479	−	0.00359228i
$613$	−4504.39	+	7801.84i	−0.296787	+	0.514051i	−0.975399	−	0.220446i	$-0.929249\pi$
$613$	−4504.39	+	7801.84i	−0.296787	+	0.514051i	0.678612	+	0.734497i	$0.262582\pi$
$614$	16910.2	+	14909.2i	1.11147	+	0.979943i
$615$	4629.42			0.303539
$616$	6513.47	+	9630.56i	0.426031	+	0.629913i
$617$	−8044.33			−0.524883			−0.262441	−	0.964948i	$-0.584528\pi$
$617$	−8044.33			−0.524883			−0.262441	+	0.964948i	$0.584528\pi$
$618$	−4483.48	−	3952.93i	−0.291832	−	0.257298i
$619$	3126.98	−	5416.09i	0.203043	−	0.351682i	−0.746464	−	0.665426i	$-0.768250\pi$
$619$	3126.98	−	5416.09i	0.203043	−	0.351682i	0.949508	+	0.313744i	$0.101583\pi$
$620$	−12891.7	+	1627.90i	−0.835068	+	0.105449i
$621$	4411.32	−	2546.88i	0.285057	−	0.164578i
$622$	3009.01	−	1012.56i	0.193972	−	0.0652729i
$623$	−13636.2	−	17281.1i	−0.876924	−	1.11132i
$624$	6564.42	+	1833.57i	0.421133	+	0.117631i
$625$	−32530.7	−	56344.8i	−2.08196	−	3.60607i
$626$	−9485.36	−	1912.84i	−0.605609	−	0.122129i
$627$	−5653.68	−	3264.15i	−0.360105	−	0.207907i
$628$	4156.02	−	9885.32i	0.264082	−	0.628132i
$629$		−	423.379i		−	0.0268382i
$630$	9197.50	−	4661.08i	0.581646	−	0.294765i
$631$			23910.4i			1.50849i	0.656592	+	0.754246i	$0.271998\pi$
$631$			23910.4i			1.50849i	−0.656592	+	0.754246i	$0.728002\pi$
$632$	−94.6713	+	1287.78i	−0.00595858	+	0.0810522i
$633$	−9827.57	−	5673.95i	−0.617079	−	0.356271i
$634$	5313.11	−	26346.5i	0.332824	−	1.65040i
$635$	13083.4	+	22661.2i	0.817638	+	1.41619i
$636$	5877.89	−	4461.07i	0.366468	−	0.278134i
$637$	−3468.89	−	11671.3i	−0.215765	−	0.725958i
$638$	1198.74	+	3562.30i	0.0743865	+	0.221054i
$639$	2533.96	−	1462.98i	0.156873	−	0.0905707i
$640$	−5603.00	−	31173.3i	−0.346059	−	1.92536i
$641$	4478.50	−	7756.98i	0.275959	−	0.477976i	−0.694417	−	0.719573i	$-0.744338\pi$
$641$	4478.50	−	7756.98i	0.275959	−	0.477976i	0.970377	+	0.241597i	$0.0776711\pi$
$642$	4522.58	−	5129.58i	0.278025	−	0.315340i
$643$	12297.7			0.754238			0.377119	−	0.926165i	$-0.376915\pi$
$643$	12297.7			0.754238			0.377119	+	0.926165i	$0.376915\pi$
$644$	−19601.0	+	19927.6i	−1.19936	+	1.21934i
$645$	24982.7			1.52510
$646$	884.629	−	1003.36i	0.0538781	−	0.0611095i
$647$	11422.9	−	19785.0i	0.694094	−	1.20221i	−0.276391	−	0.961045i	$-0.589138\pi$
$647$	11422.9	−	19785.0i	0.694094	−	1.20221i	0.970485	−	0.241161i	$-0.0775283\pi$
$648$	−797.569	−	1650.19i	−0.0483511	−	0.100039i
$649$	−2755.32	+	1590.78i	−0.166650	+	0.0962153i
$650$	11315.1	+	33625.0i	0.682790	+	2.02905i
$651$	3239.20	−	2556.00i	0.195014	−	0.153882i
$652$	−6308.13	−	8311.57i	−0.378904	−	0.499242i
$653$	−1429.28	−	2475.59i	−0.0856541	−	0.148357i	0.820016	−	0.572341i	$-0.193965\pi$
$653$	−1429.28	−	2475.59i	−0.0856541	−	0.148357i	−0.905670	+	0.423984i	$0.860631\pi$
$654$	−2552.23	+	12655.9i	−0.152599	+	0.756705i
$655$	48033.2	+	27732.0i	2.86536	+	1.65432i
$656$	1122.52	+	4373.83i	0.0668092	+	0.260319i
$657$		−	4107.40i		−	0.243904i
$658$	−1872.95	−	102.261i	−0.110966	−	0.00605857i
$659$			8605.92i			0.508709i	0.967111	+	0.254354i	$0.0818629\pi$
$659$			8605.92i			0.508709i	−0.967111	+	0.254354i	$0.918137\pi$
$660$	13424.6	+	5644.04i	0.791748	+	0.332870i
$661$	19147.7	+	11054.9i	1.12672	+	0.650509i	0.943107	−	0.332490i	$-0.107889\pi$
$661$	19147.7	+	11054.9i	1.12672	+	0.650509i	0.183608	+	0.982999i	$0.441222\pi$
$662$	−25762.9	−	5195.41i	−1.51254	−	0.305023i
$663$	−321.055	−	556.084i	−0.0188066	−	0.0325739i
$664$	−8087.17	+	11897.9i	−0.472655	+	0.695372i
$665$	11759.5	−	29514.9i	0.685737	−	1.72111i
$666$	−1694.11	+	570.082i	−0.0985668	+	0.0331685i
$667$	−7825.66	+	4518.15i	−0.454289	+	0.262284i
$668$	900.770	+	7133.37i	0.0521734	+	0.413171i
$669$	1841.27	−	3189.17i	0.106409	−	0.184306i
$670$	−27949.0	−	24641.6i	−1.61159	−	1.42088i
$671$	2409.91			0.138649
$672$	6633.90	+	7559.51i	0.380816	+	0.433950i
$673$	31596.4			1.80974			0.904868	−	0.425693i	$-0.139970\pi$
$673$	31596.4			1.80974			0.904868	+	0.425693i	$0.139970\pi$
$674$	−12454.4	−	10980.6i	−0.711760	−	0.627534i
$675$	4770.20	−	8262.23i	0.272008	−	0.471131i
$676$	938.971	+	7435.89i	0.0534235	+	0.423071i
$677$	22985.5	−	13270.7i	1.30488	−	0.753375i	0.323646	−	0.946178i	$-0.395091\pi$
$677$	22985.5	−	13270.7i	1.30488	−	0.753375i	0.981237	+	0.192804i	$0.0617581\pi$
$678$	14410.9	−	4849.38i	0.816294	−	0.274689i
$679$	−25446.1	+	3701.46i	−1.43819	+	0.209203i
$680$	−1677.41	+	2467.81i	−0.0945967	+	0.139171i
$681$	8504.09	+	14729.5i	0.478528	+	0.828834i
$682$	5712.60	+	1152.02i	0.320743	+	0.0646820i
$683$	−7794.67	−	4500.25i	−0.436683	−	0.252119i	0.265506	−	0.964109i	$-0.414461\pi$
$683$	−7794.67	−	4500.25i	−0.436683	−	0.252119i	−0.702190	+	0.711990i	$0.747794\pi$
$684$	−5206.02	−	2188.73i	−0.291019	−	0.122351i
$685$		−	5353.44i		−	0.298605i
$686$	5124.81	−	17221.1i	0.285228	−	0.958460i
$687$		−	3603.24i		−	0.200105i
$688$	6057.65	+	23603.4i	0.335677	+	1.30795i
$689$	−9452.13	−	5457.19i	−0.522638	−	0.301745i
$690$	−6921.22	+	34320.7i	−0.381864	+	1.89358i
$691$	−15055.8	−	26077.3i	−0.828868	−	1.43564i	−0.898927	−	0.438099i	$-0.855652\pi$
$691$	−15055.8	−	26077.3i	−0.828868	−	1.43564i	0.0700585	−	0.997543i	$-0.477681\pi$
$692$	−1219.35	−	1606.61i	−0.0669837	−	0.0882575i
$693$	−4576.21	+	665.667i	−0.250845	+	0.0364886i
$694$	4657.60	+	13841.0i	0.254755	+	0.757056i
$695$	−38090.2	+	21991.4i	−2.07891	+	1.20026i
$696$	1414.88	+	2927.42i	0.0770561	+	0.159431i
$697$	212.708	−	368.421i	0.0115594	−	0.0200214i
$698$	15079.3	−	17103.2i	0.817706	−	0.927456i
$699$	1835.94			0.0993441
$700$	−13131.7	+	50679.1i	−0.709045	+	2.73642i
$701$	−19891.8			−1.07176			−0.535879	−	0.844295i	$-0.680020\pi$
$701$	−19891.8			−1.07176			−0.535879	+	0.844295i	$0.680020\pi$
$702$	−1792.82	+	2033.44i	−0.0963897	+	0.109327i
$703$	−2753.82	+	4769.75i	−0.147741	+	0.255895i
$704$	−2077.30	+	14052.0i	−0.111209	+	0.752280i
$705$	−2034.72	+	1174.75i	−0.108698	+	0.0627568i
$706$	−5449.85	−	16195.3i	−0.290521	−	0.863342i
$707$	−7751.84	+	19456.1i	−0.412359	+	1.03497i
$708$	−2192.35	+	1663.90i	−0.116375	+	0.0883236i
$709$	11180.4	+	19365.1i	0.592229	+	1.02577i	0.993932	+	0.110001i	$0.0350853\pi$
$709$	11180.4	+	19365.1i	0.592229	+	1.02577i	−0.401702	+	0.915770i	$0.631581\pi$
$710$	−3975.70	+	19714.6i	−0.210148	+	1.04208i
$711$	−444.784	−	256.796i	−0.0234609	−	0.0135452i
$712$	1971.87	−	26822.6i	0.103791	−	1.41183i
$713$			14010.6i			0.735907i
$714$	51.6570	−	946.123i	0.00270758	−	0.0495907i
$715$		−	21539.9i		−	1.12664i
$716$	8309.38	−	19764.3i	0.433710	−	1.03160i
$717$	−13300.8	−	7679.21i	−0.692785	−	0.399980i
$718$	19827.6	+	3998.50i	1.03058	+	0.207831i
$719$	−140.787	−	243.850i	−0.00730244	−	0.0126482i	0.862351	−	0.506311i	$-0.168991\pi$
$719$	−140.787	−	243.850i	−0.00730244	−	0.0126482i	−0.869654	+	0.493663i	$0.835658\pi$
$720$	12133.4	+	3389.08i	0.628033	+	0.175422i
$721$	−10241.6	+	8081.48i	−0.529012	+	0.417434i
$722$	1894.66	−	637.566i	0.0976617	−	0.0328639i
$723$	−11764.1	+	6791.98i	−0.605131	+	0.349373i
$724$	−61.6240	+	7.78161i	−0.00316331	+	0.000399449i
$725$	−8462.31	+	14657.1i	−0.433493	+	0.750831i
$726$	3572.49	+	3149.74i	0.182628	+	0.161016i
$727$	29088.8			1.48396			0.741982	−	0.670419i	$-0.233886\pi$
$727$	29088.8			1.48396			0.741982	+	0.670419i	$0.233886\pi$
$728$	6504.51	−	13378.7i	0.331144	−	0.681112i
$729$	729.000			0.0370370
$730$	21176.7	+	18670.7i	1.07368	+	0.946623i
$731$	1147.88	−	1988.19i	0.0580791	−	0.100596i
$732$	2068.30	−	261.176i	0.104435	−	0.0131876i
$733$	2513.56	−	1451.20i	0.126658	−	0.0731260i	−0.435332	−	0.900270i	$-0.643369\pi$
$733$	2513.56	−	1451.20i	0.126658	−	0.0731260i	0.561990	+	0.827144i	$0.310036\pi$
$734$	−22752.8	+	7656.50i	−1.14417	+	0.385023i
$735$	−6411.73	−	21572.8i	−0.321769	−	1.08262i
$736$	−34104.1	+	1782.79i	−1.70801	+	0.0892861i
$737$	8355.37	+	14471.9i	0.417604	+	0.723311i
$738$	−1760.62	−	355.051i	−0.0878173	−	0.0177095i
$739$	−3736.78	−	2157.43i	−0.186008	−	0.107392i	0.404105	−	0.914713i	$-0.367583\pi$
$739$	−3736.78	−	2157.43i	−0.186008	−	0.107392i	−0.590112	+	0.807321i	$0.700917\pi$
$740$	4761.62	−	11325.8i	0.236541	−	0.562626i
$741$			8353.06i			0.414112i
$742$	−7280.52	−	14366.3i	−0.360211	−	0.710788i
$743$			11294.3i			0.557670i	0.960339	+	0.278835i	$0.0899482\pi$
$743$			11294.3i			0.557670i	−0.960339	+	0.278835i	$0.910052\pi$
$744$	5027.69	+	369.612i	0.247747	+	0.0182132i
$745$	11260.7	+	6501.34i	0.553770	+	0.319719i
$746$	4809.53	−	23849.3i	0.236045	−	1.17049i
$747$	−2861.03	−	4955.45i	−0.140133	−	0.242718i
$748$	1065.99	−	809.041i	0.0521075	−	0.0395474i
$749$	−9246.07	−	11717.5i	−0.451060	−	0.571626i
$750$	13515.6	+	40164.5i	0.658029	+	1.95546i
$751$	1961.45	−	1132.44i	0.0953053	−	0.0550245i	−0.451590	−	0.892226i	$-0.649143\pi$
$751$	1961.45	−	1132.44i	0.0953053	−	0.0550245i	0.546895	+	0.837201i	$0.315810\pi$
$752$	−1603.26	−	1637.54i	−0.0777458	−	0.0794082i
$753$	−8295.14	+	14367.6i	−0.401450	+	0.695332i
$754$	3180.45	−	3607.32i	0.153614	−	0.174232i
$755$	−9152.25			−0.441171
$756$	−3855.38	+	1067.26i	−0.185475	+	0.0513437i
$757$	−35826.9			−1.72015			−0.860074	−	0.510169i	$-0.829583\pi$
$757$	−35826.9			−1.72015			−0.860074	+	0.510169i	$0.829583\pi$
$758$	13953.2	−	15826.0i	0.668607	−	0.758346i
$759$	7851.06	−	13598.4i	0.375462	−	0.650319i
$760$	34949.1	−	16891.6i	1.66808	−	0.806216i
$761$	2124.15	−	1226.38i	0.101183	−	0.0584182i	−0.448554	−	0.893755i	$-0.648061\pi$
$761$	2124.15	−	1226.38i	0.101183	−	0.0584182i	0.549738	+	0.835337i	$0.314728\pi$
$762$	−3237.78	−	9621.70i	−0.153927	−	0.457424i
$763$	26178.0	+	10430.0i	1.24208	+	0.494878i
$764$	5640.81	+	7432.32i	0.267117	+	0.351953i
$765$	−593.424	−	1027.84i	−0.0280461	−	0.0485773i
$766$	2956.21	−	14659.2i	0.139442	−	0.691458i
$767$	3525.47	+	2035.43i	0.165968	+	0.0958216i
$768$	−259.944	+	12285.3i	−0.0122134	+	0.577221i
$769$			42464.7i			1.99131i	0.0931282	+	0.995654i	$0.470313\pi$
$769$			42464.7i			1.99131i	−0.0931282	+	0.995654i	$0.529687\pi$
$770$	17369.7	−	26619.5i	0.812937	−	1.24585i
$771$			7632.71i			0.356531i
$772$	−19062.6	−	8014.36i	−0.888701	−	0.373631i
$773$	9746.10	+	5626.91i	0.453484	+	0.261819i	0.709300	−	0.704906i	$-0.249011\pi$
$773$	9746.10	+	5626.91i	0.453484	+	0.261819i	−0.255817	+	0.966725i	$0.582344\pi$
$774$	−9501.17	−	1916.03i	−0.441231	−	0.0889798i
$775$	13120.6	+	22725.6i	0.608139	+	1.05333i
$776$	−25982.5	−	17660.7i	−1.20195	−	0.816987i
$777$	561.593	+	3860.74i	0.0259293	+	0.178254i
$778$	31546.4	−	10615.6i	1.45372	−	0.489188i
$779$	−4792.70	+	2767.07i	−0.220432	+	0.127266i
$780$	−2334.40	−	18486.6i	−0.107160	−	0.848622i
$781$	4509.82	−	7811.23i	0.206625	−	0.357885i
$782$	2413.32	+	2127.74i	0.110358	+	0.0972992i
$783$	−1293.24			−0.0590252
$784$	18827.1	−	11288.6i	0.857647	−	0.514239i
$785$	−29316.8			−1.33294
$786$	−16140.6	−	14230.6i	−0.732465	−	0.645789i
$787$	−65.7626	+	113.904i	−0.00297863	+	0.00515914i	−0.867511	−	0.497418i	$-0.834281\pi$
$787$	−65.7626	+	113.904i	−0.00297863	+	0.00515914i	0.864532	+	0.502577i	$0.167615\pi$
$788$	3264.68	+	25853.6i	0.147588	+	1.16878i
$789$	−503.745	+	290.837i	−0.0227298	+	0.0131231i
$790$	3345.79	−	1125.89i	0.150681	−	0.0507053i
$791$	−4777.17	−	32841.2i	−0.214737	−	1.47623i
$792$	−4672.66	−	3176.08i	−0.209641	−	0.142496i
$793$	−1541.76	−	2670.40i	−0.0690408	−	0.119582i
$794$	−6532.79	−	1317.42i	−0.291990	−	0.0588836i
$795$	−17470.9	−	10086.8i	−0.779407	−	0.449991i
$796$	−24160.8	−	10157.8i	−1.07582	−	0.452302i
$797$			613.321i			0.0272584i	0.999907	+	0.0136292i	$0.00433844\pi$
$797$			613.321i			0.0272584i	−0.999907	+	0.0136292i	$0.995662\pi$
$798$	−6735.90	+	10322.9i	−0.298807	+	0.457930i
$799$			215.905i			0.00955965i
$800$	−53648.4	+	34829.6i	−2.37095	+	1.53926i
$801$	9264.25	+	5348.72i	0.408659	+	0.235940i
$802$	−2566.23	+	12725.3i	−0.112988	+	0.560283i
$803$	−6330.79	−	10965.2i	−0.278217	−	0.481887i
$804$	8739.40	+	11515.0i	0.383352	+	0.505103i
$805$	70990.4	+	28284.5i	3.10818	+	1.23838i
$806$	−2378.14	−	7067.11i	−0.103928	−	0.308844i
$807$	7958.40	−	4594.79i	0.347149	−	0.200426i
$808$	−23038.3	+	11134.9i	−1.00308	+	0.484808i
$809$	−388.962	+	673.701i	−0.0169038	+	0.0292782i	−0.874354	−	0.485289i	$-0.838714\pi$
$809$	−388.962	+	673.701i	−0.0169038	+	0.0292782i	0.857450	+	0.514568i	$0.172048\pi$
$810$	−3313.76	+	3758.53i	−0.143745	+	0.163038i
$811$	−31760.2			−1.37516			−0.687579	−	0.726110i	$-0.741326\pi$
$811$	−31760.2			−1.37516			−0.687579	+	0.726110i	$0.741326\pi$
$812$	6839.43	−	1893.31i	0.295587	−	0.0818253i
$813$	5905.96			0.254774
$814$	−3643.98	+	4133.06i	−0.156906	+	0.177965i
$815$	−14263.1	+	24704.5i	−0.613026	+	1.06179i
$816$	827.204	−	809.886i	0.0354877	−	0.0347447i
$817$	−25863.8	+	14932.5i	−1.10754	+	0.639438i
$818$	3527.95	+	10484.0i	0.150797	+	0.448123i
$819$	3665.28	+	4644.99i	0.156380	+	0.198180i
$820$	9833.66	−	7463.33i	0.418788	−	0.317842i
$821$	1140.77	+	1975.87i	0.0484935	+	0.0839933i	0.889253	−	0.457415i	$-0.151225\pi$
$821$	1140.77	+	1975.87i	0.0484935	+	0.0839933i	−0.840760	+	0.541408i	$0.817891\pi$
$822$	−410.579	+	2035.97i	−0.0174217	+	0.0863900i
$823$	23061.4	+	13314.5i	0.976755	+	0.563930i	0.901289	−	0.433219i	$-0.142622\pi$
$823$	23061.4	+	13314.5i	0.976755	+	0.563930i	0.0754662	+	0.997148i	$0.475956\pi$
$824$	−15896.4	−	1168.63i	−0.672060	−	0.0494067i
$825$		−	29409.4i		−	1.24110i
$826$	2715.50	+	5358.38i	0.114388	+	0.225716i
$827$			9465.42i			0.397999i	0.980000	+	0.198999i	$0.0637692\pi$
$827$			9465.42i			0.397999i	−0.980000	+	0.198999i	$0.936231\pi$
$828$	5264.42	−	12521.7i	0.220956	−	0.525555i
$829$	−10765.0	−	6215.15i	−0.451004	−	0.260387i	0.257250	−	0.966345i	$-0.417184\pi$
$829$	−10765.0	−	6215.15i	−0.451004	−	0.260387i	−0.708254	+	0.705958i	$0.750517\pi$
$830$	38554.1	+	7774.94i	1.61233	+	0.325147i
$831$	3161.85	+	5476.48i	0.131989	+	0.228612i
$832$	16899.9	−	6688.03i	0.704205	−	0.278685i
$833$	−2011.42	−	480.942i	−0.0836632	−	0.0200044i
$834$	16172.7	−	5442.25i	0.671482	−	0.225959i
$835$	17023.3	−	9828.38i	0.705526	−	0.407335i
$836$	−17271.6	+	2180.99i	−0.714536	+	0.0902285i
$837$	−1002.57	+	1736.51i	−0.0414026	+	0.0717115i
$838$	20186.3	+	17797.6i	0.832129	+	0.733659i
$839$	−25569.1			−1.05214			−0.526068	−	0.850442i	$-0.676334\pi$
$839$	−25569.1			−1.05214			−0.526068	+	0.850442i	$0.676334\pi$
$840$	12022.6	−	24728.7i	0.493834	−	1.01574i
$841$	−22094.8			−0.905933
$842$	10417.5	+	9184.71i	0.426377	+	0.375922i
$843$	−8770.69	+	15191.3i	−0.358338	+	0.620659i
$844$	−30022.6	+	3791.13i	−1.22443	+	0.154616i
$845$	17745.2	−	10245.2i	0.722430	−	0.417095i
$846$	863.923	−	290.717i	0.0351091	−	0.0118145i
$847$	8160.64	−	6439.42i	0.331054	−	0.261229i
$848$	5293.69	−	18952.1i	0.214370	−	0.767474i
$849$	−464.709	−	804.899i	−0.0187854	−	0.0325372i
$850$	5907.07	+	1191.24i	0.238366	+	0.0480695i
$851$	−11472.4	−	6623.58i	−0.462125	−	0.266808i
$852$	3024.00	−	7192.74i	0.121597	−	0.289224i
$853$		−	23892.7i		−	0.959051i	−0.877528	−	0.479525i	$-0.840809\pi$
$853$		−	23892.7i		−	0.959051i	0.877528	−	0.479525i	$-0.159191\pi$
$854$	248.065	−	4543.43i	0.00993982	−	0.182053i
$855$			15439.4i			0.617563i
$856$	1337.03	−	18187.2i	0.0533866	−	0.726197i
$857$	9057.42	+	5229.30i	0.361022	+	0.208436i	0.669529	−	0.742786i	$-0.266496\pi$
$857$	9057.42	+	5229.30i	0.361022	+	0.208436i	−0.308507	+	0.951222i	$0.599829\pi$
$858$	−1651.99	+	8191.83i	−0.0657319	+	0.325949i
$859$	−14936.3	−	25870.4i	−0.593272	−	1.02758i	−0.993788	−	0.111287i	$-0.964503\pi$
$859$	−14936.3	−	25870.4i	−0.593272	−	1.02758i	0.400517	−	0.916289i	$-0.368831\pi$
$860$	53067.3	−	40275.9i	2.10416	−	1.59697i
$861$	−1450.96	+	3641.73i	−0.0574317	+	0.144146i
$862$	1342.20	+	3988.62i	0.0530343	+	0.157602i
$863$	13656.5	−	7884.58i	0.538670	−	0.311001i	−0.205870	−	0.978579i	$-0.566002\pi$
$863$	13656.5	−	7884.58i	0.538670	−	0.311001i	0.744540	+	0.667578i	$0.232669\pi$
$864$	−4354.52	−	2219.47i	−0.171463	−	0.0873932i
$865$	−2757.04	+	4775.34i	−0.108373	+	0.187707i
$866$	−10996.4	+	12472.3i	−0.431493	+	0.489406i
$867$	14629.9			0.573078
$868$	2759.95	−	10651.5i	0.107925	−	0.416514i
$869$	−1583.21			−0.0618029
$870$	5878.60	−	6667.60i	0.229084	−	0.259831i
$871$	10690.8	−	18517.0i	0.415895	−	0.720352i
$872$	14981.9	+	30997.8i	0.581824	+	1.20381i
$873$	10821.7	−	6247.89i	0.419540	−	0.242221i
$874$	−13348.6	−	39668.1i	−0.516618	−	1.53523i
$875$	91531.3	−	13314.4i	3.53637	−	0.514410i
$876$	−6621.76	−	8724.81i	−0.255398	−	0.336511i
$877$	−12652.5	−	21914.8i	−0.487166	−	0.843797i	0.512725	−	0.858553i	$-0.328636\pi$
$877$	−12652.5	−	21914.8i	−0.487166	−	0.843797i	−0.999891	+	0.0147561i	$0.995303\pi$
$878$	7986.44	−	39602.9i	0.306981	−	1.52225i
$879$	−3492.03	−	2016.12i	−0.133997	−	0.0773630i
$880$	37615.2	−	9653.70i	1.44092	−	0.369802i
$881$			9954.76i			0.380686i	0.981718	+	0.190343i	$0.0609600\pi$
$881$			9954.76i			0.380686i	−0.981718	+	0.190343i	$0.939040\pi$
$882$	783.936	+	8696.09i	0.0299280	+	0.331987i
$883$			52248.7i			1.99129i	0.0932311	+	0.995644i	$0.470280\pi$
$883$			52248.7i			1.99129i	−0.0932311	+	0.995644i	$0.529720\pi$
$884$	−1578.47	−	663.625i	−0.0600561	−	0.0252490i
$885$	6516.32	+	3762.20i	0.247507	+	0.142898i
$886$	37774.2	+	7617.66i	1.43234	+	0.288849i
$887$	−19978.8	−	34604.3i	−0.756282	−	1.30992i	−0.944734	−	0.327837i	$-0.893680\pi$
$887$	−19978.8	−	34604.3i	−0.756282	−	1.30992i	0.188452	−	0.982082i	$-0.439653\pi$
$888$	−2679.52	+	3942.11i	−0.101260	+	0.148974i
$889$	−21927.0	+	3189.56i	−0.827231	+	0.120331i
$890$	−69688.3	+	23450.7i	−2.62467	+	0.883222i
$891$	1946.16	−	1123.62i	0.0731748	−	0.0422475i
$892$	−1230.27	−	9742.73i	−0.0461799	−	0.365707i
$893$	1404.33	−	2432.36i	0.0526248	−	0.0911488i
$894$	−3783.93	−	3336.16i	−0.141559	−	0.124807i
$895$	−58614.7			−2.18913
$896$	26278.6	+	5362.81i	0.979805	+	0.199954i
$897$	−20091.1			−0.747851
$898$	−36585.3	−	32256.0i	−1.35954	−	1.19866i
$899$	1778.56	−	3080.56i	0.0659825	−	0.114285i
$900$	−3187.27	−	25240.6i	−0.118047	−	0.934838i
$901$	−1605.47	+	926.918i	−0.0593629	+	0.0342732i
$902$	−5247.44	+	1765.80i	−0.193703	+	0.0651827i
$903$	−7830.12	+	19652.6i	−0.288560	+	0.724250i
$904$	22793.2	−	33533.5i	0.838596	−	1.23375i
$905$	84.9058	+	147.061i	0.00311864	+	0.00540163i
$906$	3480.69	+	701.927i	0.127636	+	0.0257395i
$907$	−21439.2	−	12377.9i	−0.784870	−	0.453145i	0.0532833	−	0.998579i	$-0.483031\pi$
$907$	−21439.2	−	12377.9i	−0.784870	−	0.453145i	−0.838153	+	0.545434i	$0.816365\pi$
$908$	41810.3	+	17578.0i	1.52811	+	0.642454i
$909$		−	10177.6i		−	0.371364i
$910$	−40609.3	−	2217.21i	−1.47933	−	0.0807691i
$911$		−	20356.9i		−	0.740346i	−0.928963	−	0.370173i	$-0.879298\pi$
$911$		−	20356.9i		−	0.740346i	0.928963	−	0.370173i	$-0.120702\pi$
$912$	−14587.0	+	3743.66i	−0.529632	+	0.135926i
$913$	−15275.8	−	8819.48i	−0.553729	−	0.319696i
$914$	−1957.64	+	9707.49i	−0.0708457	+	0.351308i
$915$	−2849.71	−	4935.85i	−0.102960	−	0.178332i
$916$	−5808.97	−	7653.87i	−0.209535	−	0.276082i
$917$	−36870.0	+	29093.5i	−1.32776	+	1.04771i
$918$	146.856	+	436.411i	0.00527991	+	0.0156903i
$919$	−40244.8	+	23235.3i	−1.44456	+	0.834018i	−0.998149	−	0.0608093i	$-0.980632\pi$
$919$	−40244.8	+	23235.3i	−1.44456	+	0.834018i	−0.446412	+	0.894827i	$0.647299\pi$
$920$	40628.4	+	84061.0i	1.45596	+	3.01240i
$921$	−11955.8	+	20708.1i	−0.427751	+	0.740886i
$922$	−17239.9	+	19553.8i	−0.615798	+	0.698448i
$923$	−11540.8			−0.411559
$924$	−8647.46	+	8791.53i	−0.307879	+	0.313009i
$925$	−24811.4			−0.881939
$926$	10336.9	−	11724.3i	0.366838	−	0.416074i
$927$	3169.91	−	5490.44i	0.112312	−	0.194530i
$928$	7724.90	+	3937.32i	0.273257	+	0.139277i
$929$	−5274.68	+	3045.34i	−0.186283	+	0.107550i	−0.590241	−	0.807227i	$-0.700967\pi$
$929$	−5274.68	+	3045.34i	−0.186283	+	0.107550i	0.403959	+	0.914777i	$0.367634\pi$
$930$	−4395.64	−	13062.5i	−0.154988	−	0.460577i
$931$	19532.2	+	18501.3i	0.687586	+	0.651293i
$932$	3899.84	−	2959.81i	0.137064	−	0.104026i
$933$	1683.70	+	2916.25i	0.0590801	+	0.102330i
$934$	699.043	−	3466.39i	0.0244897	−	0.121439i
$935$	−3168.44	−	1829.30i	−0.110823	−	0.0639835i
$936$	−530.021	+	7209.67i	−0.0185088	+	0.251768i
$937$		−	28766.7i		−	1.00295i	−0.865172	−	0.501476i	$-0.832791\pi$
$937$		−	28766.7i		−	1.00295i	0.865172	−	0.501476i	$-0.167209\pi$
$938$	28144.1	−	14262.8i	0.979679	−	0.496479i
$939$		−	10263.3i		−	0.356687i
$940$	−2428.22	+	5775.64i	−0.0842550	+	0.200405i
$941$	27658.4	+	15968.6i	0.958169	+	0.553199i	0.895609	−	0.444842i	$-0.146740\pi$
$941$	27658.4	+	15968.6i	0.958169	+	0.553199i	0.0625601	+	0.998041i	$0.480073\pi$
$942$	11149.5	+	2248.43i	0.385636	+	0.0777685i
$943$	−6655.46	−	11527.6i	−0.229832	−	0.398081i
$944$	−1974.45	+	7068.79i	−0.0680750	+	0.243718i
$945$	6774.74	+	8585.59i	0.233209	+	0.295544i
$946$	−28317.8	+	9529.16i	−0.973246	+	0.327505i
$947$	31110.8	−	17961.8i	1.06755	−	0.616347i	0.140035	−	0.990147i	$-0.455278\pi$
$947$	31110.8	−	17961.8i	1.06755	−	0.616347i	0.927510	+	0.373799i	$0.121945\pi$
$948$	−1358.79	+	171.582i	−0.0465521	+	0.00587839i
$949$	−8100.34	+	14030.2i	−0.277079	+	0.479915i
$950$	−58800.3	−	51842.2i	−2.00814	−	1.77051i
$951$	28507.2			0.972040
$952$	−1415.57	−	2093.00i	−0.0481920	−	0.0712548i
$953$	31203.6			1.06063			0.530317	−	0.847800i	$-0.322073\pi$
$953$	31203.6			1.06063			0.530317	+	0.847800i	$0.322073\pi$
$954$	5870.75	+	5176.04i	0.199238	+	0.175661i
$955$	12754.3	−	22091.1i	0.432167	−	0.748535i
$956$	−40633.1	+	5130.97i	−1.37465	+	0.173585i
$957$	−3452.48	+	1993.29i	−0.116617	+	0.0673290i
$958$	−46159.6	+	15533.1i	−1.55673	+	0.523853i
$959$	4211.28	+	1677.89i	0.141803	+	0.0564982i
$960$	31237.0	−	12361.9i	1.05018	−	0.415601i
$961$	12137.9	+	21023.4i	0.407434	+	0.705697i
$962$	6911.07	+	1393.71i	0.231624	+	0.0467099i
$963$	6281.65	+	3626.71i	0.210201	+	0.121359i
$964$	−14039.1	+	33392.7i	−0.469055	+	1.11567i
$965$			56533.6i			1.88589i
$966$	−24829.1	−	16201.5i	−0.826982	−	0.539620i
$967$		−	10111.4i		−	0.336259i	−0.985765	−	0.168129i	$-0.946227\pi$
$967$		−	10111.4i		−	0.336259i	0.985765	−	0.168129i	$-0.0537726\pi$
$968$	12666.4	+	931.176i	0.420573	+	0.0309185i
$969$	1228.71	+	709.395i	0.0407346	+	0.0235181i
$970$	−16978.8	+	84194.2i	−0.562019	+	2.78692i
$971$	12065.8	+	20898.6i	0.398774	+	0.690698i	0.993575	−	0.113176i	$-0.0361023\pi$
$971$	12065.8	+	20898.6i	0.398774	+	0.690698i	−0.594801	+	0.803873i	$0.702769\pi$
$972$	1548.52	−	1175.26i	0.0510995	−	0.0387823i
$973$	−5361.21	−	36856.3i	−0.176642	−	1.21435i
$974$	−13066.7	−	38830.2i	−0.429860	−	1.27741i
$975$	−32588.4	+	18814.9i	−1.07042	+	0.618010i
$976$	3972.36	−	3889.20i	0.130279	−	0.127551i
$977$	22579.5	−	39108.8i	0.739387	−	1.28066i	−0.213385	−	0.976968i	$-0.568449\pi$
$977$	22579.5	−	39108.8i	0.739387	−	1.28066i	0.952772	−	0.303687i	$-0.0982178\pi$
$978$	7319.12	−	8301.47i	0.239304	−	0.271423i
$979$	32976.1			1.07653
$980$	−48398.2	−	35487.4i	−1.57757	−	1.15674i
$981$	−13693.9			−0.445679
$982$	−22342.2	+	25340.9i	−0.726037	+	0.823483i
$983$	−7512.92	+	13012.8i	−0.243769	+	0.422220i	−0.961785	−	0.273807i	$-0.911717\pi$
$983$	−7512.92	+	13012.8i	−0.243769	+	0.422220i	0.718016	+	0.696027i	$0.245051\pi$
$984$	−4312.24	+	2084.19i	−0.139704	+	0.0675220i
$985$	61697.7	−	35621.2i	1.99579	−	1.15227i
$986$	−260.521	−	774.190i	−0.00841448	−	0.0250053i
$987$	−286.388	−	1968.81i	−0.00923589	−	0.0634932i
$988$	13466.4	+	17743.3i	0.433627	+	0.571345i
$989$	−35916.2	−	62208.6i	−1.15477	−	2.00012i
$990$	−3053.46	+	15141.4i	−0.0980256	+	0.486086i
$991$	−21895.0	−	12641.1i	−0.701834	−	0.405204i	0.106196	−	0.994345i	$-0.466133\pi$
$991$	−21895.0	−	12641.1i	−0.701834	−	0.405204i	−0.808030	+	0.589141i	$0.799466\pi$
$992$	11275.5	−	7320.28i	0.360885	−	0.234293i
$993$		−	27875.7i		−	0.890846i
$994$	−14262.4	−	9306.46i	−0.455106	−	0.296965i
$995$			71653.3i			2.28298i
$996$	−14066.2	−	5913.78i	−0.447496	−	0.188138i
$997$	15618.4	+	9017.31i	0.496129	+	0.286440i	0.727114	−	0.686517i	$-0.240861\pi$
$997$	15618.4	+	9017.31i	0.496129	+	0.286440i	−0.230985	+	0.972957i	$0.574195\pi$
$998$	40955.5	+	8259.21i	1.29902	+	0.261965i
$999$	−947.943	−	1641.89i	−0.0300216	−	0.0519990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.4.o.a.31.10	yes	24
4.3	odd	2		84.4.o.b.31.7	yes	24
7.5	odd	6		84.4.o.b.19.7	yes	24
28.19	even	6	inner	84.4.o.a.19.10	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.4.o.a.19.10	✓	24	28.19	even	6	inner
84.4.o.a.31.10	yes	24	1.1	even	1	trivial
84.4.o.b.19.7	yes	24	7.5	odd	6
84.4.o.b.31.7	yes	24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	84.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.12158 + 1.87053i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(1.00225 + 7.93697i) q^{4} +(18.9410 - 10.9356i) q^{5} +(-8.04215 + 2.70625i) q^{6} +(2.66595 + 18.3274i) q^{7} +(-12.7200 + 18.7137i) q^{8} +(-4.50000 - 7.79423i) q^{9} +(60.6402 + 12.2289i) q^{10} +(-24.0267 - 13.8718i) q^{11} +(-22.1242 - 9.30155i) q^{12} +35.4983i q^{13} +(-28.6258 + 43.8698i) q^{14} +65.6135i q^{15} +(-61.9910 + 15.9096i) q^{16} +(5.22169 + 3.01475i) q^{17} +(5.03220 - 24.9535i) q^{18} +(-39.2181 - 67.9277i) q^{19} +(105.779 + 139.374i) q^{20} +(-51.6148 - 20.5647i) q^{21} +(-25.0270 - 74.3727i) q^{22} +(163.382 - 94.3288i) q^{23} +(-29.5396 - 61.1180i) q^{24} +(176.674 - 306.008i) q^{25} +(-66.4007 + 75.3127i) q^{26} +27.0000 q^{27} +(-142.792 + 39.5281i) q^{28} -47.8979 q^{29} +(-122.732 + 139.205i) q^{30} +(-37.1324 + 64.3151i) q^{31} +(-161.279 - 82.2024i) q^{32} +(72.0800 - 41.6154i) q^{33} +(5.43910 + 16.1634i) q^{34} +(250.916 + 317.985i) q^{35} +(57.3525 - 43.5281i) q^{36} +(-35.1090 - 60.8106i) q^{37} +(43.8562 - 217.473i) q^{38} +(-92.2274 - 53.2475i) q^{39} +(-36.2839 + 493.556i) q^{40} -70.5559i q^{41} +(-71.0384 - 140.177i) q^{42} -380.755i q^{43} +(86.0194 - 204.602i) q^{44} +(-170.469 - 98.4203i) q^{45} +(523.074 + 105.485i) q^{46} +(17.9041 + 31.0107i) q^{47} +(51.6522 - 184.922i) q^{48} +(-328.785 + 97.7197i) q^{49} +(947.227 - 318.749i) q^{50} +(-15.6651 + 9.04424i) q^{51} +(-281.749 + 35.5780i) q^{52} +(-153.731 + 266.270i) q^{53} +(57.2828 + 50.5043i) q^{54} -606.785 q^{55} +(-376.884 - 183.234i) q^{56} +235.308 q^{57} +(-101.619 - 89.5943i) q^{58} +(57.3388 - 99.3137i) q^{59} +(-520.773 + 65.7608i) q^{60} +(-75.2261 + 43.4318i) q^{61} +(-199.083 + 66.9929i) q^{62} +(130.851 - 103.252i) q^{63} +(-188.404 - 476.076i) q^{64} +(388.195 + 672.374i) q^{65} +(230.767 + 46.5371i) q^{66} +(-521.631 - 301.164i) q^{67} +(-18.6945 + 44.4659i) q^{68} +565.973i q^{69} +(-62.4596 + 1143.98i) q^{70} +325.107i q^{71} +(203.099 + 14.9309i) q^{72} +(395.235 + 228.189i) q^{73} +(39.2612 - 194.687i) q^{74} +(530.022 + 918.025i) q^{75} +(499.834 - 379.353i) q^{76} +(190.180 - 477.327i) q^{77} +(-96.0673 - 285.483i) q^{78} +(49.4204 - 28.5329i) q^{79} +(-1000.19 + 979.251i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(131.977 - 149.690i) q^{82} +635.785 q^{83} +(111.491 - 430.276i) q^{84} +131.872 q^{85} +(712.213 - 807.804i) q^{86} +(71.8468 - 124.442i) q^{87} +(565.211 - 273.178i) q^{88} +(-1029.36 + 594.302i) q^{89} +(-177.566 - 527.674i) q^{90} +(-650.591 + 94.6368i) q^{91} +(912.434 + 1202.22i) q^{92} +(-111.397 - 192.945i) q^{93} +(-20.0215 + 99.2820i) q^{94} +(-1485.66 - 857.745i) q^{95} +(455.486 - 295.710i) q^{96} +1388.42i q^{97} +(-880.334 - 407.682i) q^{98} +249.692i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} - 36 q^{3} - 5 q^{4} + 6 q^{6} + 10 q^{7} - 76 q^{8} - 108 q^{9} - 19 q^{10} + 6 q^{11} - 15 q^{12} - 62 q^{14} - 89 q^{16} - 9 q^{18} + 42 q^{19} - 134 q^{20} - 60 q^{21} + 14 q^{22} - 21 q^{24}+ \cdots + 7795 q^{98}+O(q^{100}) \) 24 * q - q^2 - 36 * q^3 - 5 * q^4 + 6 * q^6 + 10 * q^7 - 76 * q^8 - 108 * q^9 - 19 * q^10 + 6 * q^11 - 15 * q^12 - 62 * q^14 - 89 * q^16 - 9 * q^18 + 42 * q^19 - 134 * q^20 - 60 * q^21 + 14 * q^22 - 21 * q^24 + 342 * q^25 - 516 * q^26 + 648 * q^27 + 37 * q^28 + 400 * q^29 - 111 * q^30 + 78 * q^31 - 591 * q^32 - 18 * q^33 + 580 * q^34 + 84 * q^35 + 90 * q^36 - 134 * q^37 + 280 * q^38 + 162 * q^39 + 899 * q^40 - 303 * q^42 + 1091 * q^44 + 468 * q^46 - 140 * q^47 - 258 * q^48 + 268 * q^49 + 1246 * q^50 - 1108 * q^52 - 572 * q^53 - 27 * q^54 - 424 * q^55 - 1709 * q^56 - 252 * q^57 - 2145 * q^58 - 302 * q^59 + 21 * q^60 - 300 * q^61 + 2448 * q^62 + 90 * q^63 - 1646 * q^64 + 140 * q^65 + 1005 * q^66 - 2310 * q^67 + 3934 * q^68 + 2625 * q^70 + 747 * q^72 - 486 * q^73 - 2516 * q^74 + 1026 * q^75 - 2540 * q^76 - 968 * q^77 + 846 * q^78 - 1326 * q^79 - 3045 * q^80 - 972 * q^81 - 4298 * q^82 - 668 * q^83 - 1410 * q^84 + 1824 * q^85 - 5214 * q^86 - 600 * q^87 + 4619 * q^88 + 504 * q^90 - 2114 * q^91 - 476 * q^92 + 234 * q^93 + 4424 * q^94 + 1992 * q^95 + 2097 * q^96 + 7795 * q^98

Introduction

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