LMFDB - Embedded newform 120.4.b.b.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(11,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("120.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.b (of order $2$, degree $1$, 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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	120.11
Dual form			120.4.b.b.11.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35014 - 2.48538i) q^{2} +(-0.403912 + 5.18043i) q^{3} +(-4.35424 - 6.71123i) q^{4} -5.00000 q^{5} +(12.3300 + 7.99819i) q^{6} +23.0707i q^{7} +(-22.5588 + 1.76083i) q^{8} +(-26.6737 - 4.18488i) q^{9} +O(q^{10})$	\(q+(1.35014 - 2.48538i) q^{2} +(-0.403912 + 5.18043i) q^{3} +(-4.35424 - 6.71123i) q^{4} -5.00000 q^{5} +(12.3300 + 7.99819i) q^{6} +23.0707i q^{7} +(-22.5588 + 1.76083i) q^{8} +(-26.6737 - 4.18488i) q^{9} +(-6.75071 + 12.4269i) q^{10} +56.7258i q^{11} +(36.5258 - 19.8461i) q^{12} -55.8943i q^{13} +(57.3396 + 31.1488i) q^{14} +(2.01956 - 25.9021i) q^{15} +(-26.0812 + 58.4446i) q^{16} +118.393i q^{17} +(-46.4143 + 60.6442i) q^{18} -69.8100 q^{19} +(21.7712 + 33.5562i) q^{20} +(-119.516 - 9.31856i) q^{21} +(140.985 + 76.5878i) q^{22} +49.8352 q^{23} +(-0.0100821 - 117.576i) q^{24} +25.0000 q^{25} +(-138.919 - 75.4652i) q^{26} +(32.4533 - 136.491i) q^{27} +(154.833 - 100.456i) q^{28} +15.0035 q^{29} +(-61.6500 - 39.9909i) q^{30} +3.06167i q^{31} +(110.044 + 143.730i) q^{32} +(-293.864 - 22.9122i) q^{33} +(294.251 + 159.847i) q^{34} -115.354i q^{35} +(88.0580 + 197.235i) q^{36} -346.935i q^{37} +(-94.2534 + 173.505i) q^{38} +(289.557 + 22.5764i) q^{39} +(112.794 - 8.80416i) q^{40} +80.0429i q^{41} +(-184.524 + 284.462i) q^{42} +115.914 q^{43} +(380.700 - 246.997i) q^{44} +(133.369 + 20.9244i) q^{45} +(67.2846 - 123.859i) q^{46} +45.7407 q^{47} +(-292.234 - 158.718i) q^{48} -189.259 q^{49} +(33.7535 - 62.1345i) q^{50} +(-613.325 - 47.8203i) q^{51} +(-375.120 + 243.377i) q^{52} -660.112 q^{53} +(-295.415 - 264.941i) q^{54} -283.629i q^{55} +(-40.6237 - 520.448i) q^{56} +(28.1971 - 361.646i) q^{57} +(20.2568 - 37.2893i) q^{58} -406.553i q^{59} +(-182.629 + 99.2304i) q^{60} +845.957i q^{61} +(7.60943 + 4.13369i) q^{62} +(96.5483 - 615.382i) q^{63} +(505.799 - 79.4445i) q^{64} +279.472i q^{65} +(-453.703 + 699.429i) q^{66} -106.153 q^{67} +(794.561 - 515.510i) q^{68} +(-20.1291 + 258.168i) q^{69} +(-286.698 - 155.744i) q^{70} +726.584 q^{71} +(609.096 + 47.4380i) q^{72} +427.133 q^{73} +(-862.266 - 468.411i) q^{74} +(-10.0978 + 129.511i) q^{75} +(303.969 + 468.511i) q^{76} -1308.71 q^{77} +(447.053 - 689.177i) q^{78} +673.524i q^{79} +(130.406 - 292.223i) q^{80} +(693.974 + 223.253i) q^{81} +(198.937 + 108.069i) q^{82} +490.554i q^{83} +(457.864 + 842.677i) q^{84} -591.964i q^{85} +(156.500 - 288.090i) q^{86} +(-6.06008 + 77.7244i) q^{87} +(-99.8845 - 1279.67i) q^{88} +1277.64i q^{89} +(232.071 - 303.221i) q^{90} +1289.52 q^{91} +(-216.994 - 334.456i) q^{92} +(-15.8608 - 1.23665i) q^{93} +(61.7564 - 113.683i) q^{94} +349.050 q^{95} +(-789.032 + 512.019i) q^{96} +762.377 q^{97} +(-255.527 + 470.381i) q^{98} +(237.391 - 1513.09i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) $ 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	$ 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 q^{96} + 792 q^{97} - 4851 q^{98} - 1328 q^{99}+O(q^{100}) $ 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * q^96 + 792 * q^97 - 4851 * q^98 - 1328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	1.35014	−	2.48538i	0.477347	−	0.878715i
$2$	1.35014	−	2.48538i	0.477347	−	0.878715i
$3$	−0.403912	+	5.18043i	−0.0777330	+	0.996974i
$3$	−0.403912	+	5.18043i	−0.0777330	+	0.996974i
$4$	−4.35424	−	6.71123i	−0.544280	−	0.838904i
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	12.3300	+	7.99819i	0.838950	+	0.544208i
$7$			23.0707i			1.24570i	0.782340	+	0.622852i	$0.214026\pi$
$7$			23.0707i			1.24570i	−0.782340	+	0.622852i	$0.785974\pi$
$8$	−22.5588	+	1.76083i	−0.996968	+	0.0778185i
$9$	−26.6737	−	4.18488i	−0.987915	−	0.154996i
$10$	−6.75071	+	12.4269i	−0.213476	+	0.392973i
$11$			56.7258i			1.55486i	0.628969	+	0.777430i	$0.283477\pi$
$11$			56.7258i			1.55486i	−0.628969	+	0.777430i	$0.716523\pi$
$12$	36.5258	−	19.8461i	0.878674	−	0.477422i
$13$		−	55.8943i		−	1.19248i	−0.802805	−	0.596242i	$-0.796660\pi$
$13$		−	55.8943i		−	1.19248i	0.802805	−	0.596242i	$-0.203340\pi$
$14$	57.3396	+	31.1488i	1.09462	+	0.594633i
$15$	2.01956	−	25.9021i	0.0347632	−	0.445860i
$16$	−26.0812	+	58.4446i	−0.407519	+	0.913197i
$17$			118.393i			1.68909i	0.535488	+	0.844543i	$0.320128\pi$
$17$			118.393i			1.68909i	−0.535488	+	0.844543i	$0.679872\pi$
$18$	−46.4143	+	60.6442i	−0.607775	+	0.794109i
$19$	−69.8100			−0.842922			−0.421461	−	0.906847i	$-0.638483\pi$
$19$	−69.8100			−0.842922			−0.421461	+	0.906847i	$0.638483\pi$
$20$	21.7712	+	33.5562i	0.243409	+	0.375169i
$21$	−119.516	−	9.31856i	−1.24193	−	0.0968322i
$22$	140.985	+	76.5878i	1.36628	+	0.742208i
$23$	49.8352			0.451798			0.225899	−	0.974151i	$-0.427468\pi$
$23$	49.8352			0.451798			0.225899	+	0.974151i	$0.427468\pi$
$24$	−0.0100821	−	117.576i	−8.57502e−5	−	1.00000i
$25$	25.0000			0.200000
$26$	−138.919	−	75.4652i	−1.04785	−	0.569229i
$27$	32.4533	−	136.491i	0.231320	−	0.972878i
$28$	154.833	−	100.456i	1.04503	−	0.678011i
$29$	15.0035			0.0960715			0.0480357	−	0.998846i	$-0.484704\pi$
$29$	15.0035			0.0960715			0.0480357	+	0.998846i	$0.484704\pi$
$30$	−61.6500	−	39.9909i	−0.375190	−	0.243377i
$31$			3.06167i			0.0177385i	0.999961	+	0.00886924i	$0.00282320\pi$
$31$			3.06167i			0.0177385i	−0.999961	+	0.00886924i	$0.997177\pi$
$32$	110.044	+	143.730i	0.607911	+	0.794005i
$33$	−293.864	−	22.9122i	−1.55016	−	0.120864i
$34$	294.251	+	159.847i	1.48422	+	0.806280i
$35$		−	115.354i		−	0.557095i
$36$	88.0580	+	197.235i	0.407676	+	0.913127i
$37$		−	346.935i		−	1.54151i	−0.637133	−	0.770754i	$-0.719880\pi$
$37$		−	346.935i		−	1.54151i	0.637133	−	0.770754i	$-0.280120\pi$
$38$	−94.2534	+	173.505i	−0.402366	+	0.740688i
$39$	289.557	+	22.5764i	1.18888	+	0.0926954i
$40$	112.794	−	8.80416i	0.445857	−	0.0348015i
$41$			80.0429i			0.304893i	0.988312	+	0.152446i	$0.0487151\pi$
$41$			80.0429i			0.304893i	−0.988312	+	0.152446i	$0.951285\pi$
$42$	−184.524	+	284.462i	−0.677921	+	1.04508i
$43$	115.914			0.411086			0.205543	−	0.978648i	$-0.434104\pi$
$43$	115.914			0.411086			0.205543	+	0.978648i	$0.434104\pi$
$44$	380.700	−	246.997i	1.30438	−	0.846279i
$45$	133.369	+	20.9244i	0.441809	+	0.0693161i
$46$	67.2846	−	123.859i	0.215665	−	0.397002i
$47$	45.7407			0.141957			0.0709783	−	0.997478i	$-0.477388\pi$
$47$	45.7407			0.141957			0.0709783	+	0.997478i	$0.477388\pi$
$48$	−292.234	−	158.718i	−0.878756	−	0.477272i
$49$	−189.259			−0.551776
$50$	33.7535	−	62.1345i	0.0954694	−	0.175743i
$51$	−613.325	−	47.8203i	−1.68397	−	0.131298i
$52$	−375.120	+	243.377i	−1.00038	+	0.649045i
$53$	−660.112			−1.71082			−0.855409	−	0.517953i	$-0.826694\pi$
$53$	−660.112			−1.71082			−0.855409	+	0.517953i	$0.826694\pi$
$54$	−295.415	−	264.941i	−0.744462	−	0.667665i
$55$		−	283.629i		−	0.695355i
$56$	−40.6237	−	520.448i	−0.0969387	−	1.24193i
$57$	28.1971	−	361.646i	0.0655228	−	0.840371i
$58$	20.2568	−	37.2893i	0.0458594	−	0.0844194i
$59$		−	406.553i		−	0.897097i	−0.893758	−	0.448549i	$-0.851941\pi$
$59$		−	406.553i		−	0.897097i	0.893758	−	0.448549i	$-0.148059\pi$
$60$	−182.629	+	99.2304i	−0.392955	+	0.213510i
$61$			845.957i			1.77563i	0.460196	+	0.887817i	$0.347779\pi$
$61$			845.957i			1.77563i	−0.460196	+	0.887817i	$0.652221\pi$
$62$	7.60943	+	4.13369i	0.0155871	+	0.00846741i
$63$	96.5483	−	615.382i	0.193078	−	1.23065i
$64$	505.799	−	79.4445i	0.987889	−	0.155165i
$65$			279.472i			0.533295i
$66$	−453.703	+	699.429i	−0.846167	+	1.30445i
$67$	−106.153			−0.193563			−0.0967814	−	0.995306i	$-0.530855\pi$
$67$	−106.153			−0.193563			−0.0967814	+	0.995306i	$0.530855\pi$
$68$	794.561	−	515.510i	1.41698	−	0.919335i
$69$	−20.1291	+	258.168i	−0.0351196	+	0.450431i
$70$	−286.698	−	155.744i	−0.489528	−	0.265928i
$71$	726.584			1.21450			0.607251	−	0.794510i	$-0.292272\pi$
$71$	726.584			1.21450			0.607251	+	0.794510i	$0.292272\pi$
$72$	609.096	+	47.4380i	0.996981	+	0.0776475i
$73$	427.133			0.684825			0.342412	−	0.939550i	$-0.388756\pi$
$73$	427.133			0.684825			0.342412	+	0.939550i	$0.388756\pi$
$74$	−862.266	−	468.411i	−1.35455	−	0.735834i
$75$	−10.0978	+	129.511i	−0.0155466	+	0.199395i
$76$	303.969	+	468.511i	0.458785	+	0.707130i
$77$	−1308.71			−1.93689
$78$	447.053	−	689.177i	0.648959	−	1.00044i
$79$			673.524i			0.959208i	0.877485	+	0.479604i	$0.159220\pi$
$79$			673.524i			0.959208i	−0.877485	+	0.479604i	$0.840780\pi$
$80$	130.406	−	292.223i	0.182248	−	0.408394i
$81$	693.974	+	223.253i	0.951953	+	0.306245i
$82$	198.937	+	108.069i	0.267914	+	0.145540i
$83$			490.554i			0.648738i	0.945931	+	0.324369i	$0.105152\pi$
$83$			490.554i			0.648738i	−0.945931	+	0.324369i	$0.894848\pi$
$84$	457.864	+	842.677i	0.594727	+	1.09457i
$85$		−	591.964i		−	0.755382i
$86$	156.500	−	288.090i	0.196230	−	0.361227i
$87$	−6.06008	+	77.7244i	−0.00746792	+	0.0957808i
$88$	−99.8845	−	1279.67i	−0.120997	−	1.55014i
$89$			1277.64i			1.52168i	0.648940	+	0.760840i	$0.275213\pi$
$89$			1277.64i			1.52168i	−0.648940	+	0.760840i	$0.724787\pi$
$90$	232.071	−	303.221i	0.271805	−	0.355136i
$91$	1289.52			1.48548
$92$	−216.994	−	334.456i	−0.245905	−	0.379015i
$93$	−15.8608	−	1.23665i	−0.0176848	−	0.00137887i
$94$	61.7564	−	113.683i	0.0677626	−	0.124739i
$95$	349.050			0.376966
$96$	−789.032	+	512.019i	−0.838857	+	0.544352i
$97$	762.377			0.798017			0.399008	−	0.916947i	$-0.369354\pi$
$97$	762.377			0.798017			0.399008	+	0.916947i	$0.369354\pi$
$98$	−255.527	+	470.381i	−0.263389	+	0.484854i
$99$	237.391	−	1513.09i	0.240996	−	1.53607i
$100$	−108.856	−	167.781i	−0.108856	−	0.167781i
$101$	1107.78			1.09137			0.545685	−	0.837990i	$-0.316270\pi$
$101$	1107.78			1.09137			0.545685	+	0.837990i	$0.316270\pi$
$102$	−946.927	+	1459.78i	−0.919213	+	1.41706i
$103$		−	182.440i		−	0.174527i	−0.996185	−	0.0872636i	$-0.972188\pi$
$103$		−	182.440i		−	0.174527i	0.996185	−	0.0872636i	$-0.0278122\pi$
$104$	98.4205	+	1260.91i	0.0927973	+	1.18887i
$105$	597.582	+	46.5928i	0.555410	+	0.0433047i
$106$	−891.244	+	1640.63i	−0.816654	+	1.50332i
$107$		−	66.4766i		−	0.0600611i	−0.999549	−	0.0300305i	$-0.990440\pi$
$107$		−	66.4766i		−	0.0600611i	0.999549	−	0.0300305i	$-0.00956046\pi$
$108$	−1057.33	+	376.512i	−0.942054	+	0.335462i
$109$			368.204i			0.323556i	0.986827	+	0.161778i	$0.0517228\pi$
$109$			368.204i			0.323556i	−0.986827	+	0.161778i	$0.948277\pi$
$110$	−704.926	−	382.939i	−0.611018	−	0.331925i
$111$	1797.27	+	140.131i	1.53684	+	0.119826i
$112$	−1348.36	−	601.713i	−1.13757	−	0.507648i
$113$		−	64.5415i		−	0.0537306i	−0.999639	−	0.0268653i	$-0.991447\pi$
$113$		−	64.5415i		−	0.0537306i	0.999639	−	0.0268653i	$-0.00855252\pi$
$114$	−860.758	−	558.354i	−0.707170	−	0.458725i
$115$	−249.176			−0.202050
$116$	−65.3286	−	100.692i	−0.0522898	−	0.0805947i
$117$	−233.911	+	1490.91i	−0.184830	+	1.17807i
$118$	−1010.44	−	548.904i	−0.788293	−	0.428227i
$119$	−2731.41			−2.10410
$120$	0.0504106	+	587.878i	3.83487e−5	+	0.447214i
$121$	−1886.81			−1.41759
$122$	2102.53	+	1142.16i	1.56028	+	0.847594i
$123$	−414.656	−	32.3303i	−0.303970	−	0.0237002i
$124$	20.5476	−	13.3313i	0.0148809	−	0.00965469i
$125$	−125.000			−0.0894427
$126$	−1399.11	−	1070.81i	−0.989224	−	0.757108i
$127$			1297.38i			0.906485i	0.891387	+	0.453242i	$0.149733\pi$
$127$			1297.38i			0.906485i	−0.891387	+	0.453242i	$0.850267\pi$
$128$	485.450	−	1364.36i	0.335220	−	0.942140i
$129$	−46.8190	+	600.483i	−0.0319549	+	0.409842i
$130$	694.594	+	377.326i	0.468615	+	0.254567i
$131$			2198.91i			1.46656i	0.679926	+	0.733280i	$0.262012\pi$
$131$			2198.91i			1.46656i	−0.679926	+	0.733280i	$0.737988\pi$
$132$	1125.78	+	2071.95i	0.742325	+	1.36622i
$133$		−	1610.57i		−	1.05003i
$134$	−143.322	+	263.832i	−0.0923967	+	0.170087i
$135$	−162.267	+	682.455i	−0.103450	+	0.435084i
$136$	−208.470	−	2670.80i	−0.131442	−	1.68396i
$137$		−	1285.88i		−	0.801902i	−0.916100	−	0.400951i	$-0.868680\pi$
$137$		−	1285.88i		−	0.801902i	0.916100	−	0.400951i	$-0.131320\pi$
$138$	614.468	+	398.591i	0.379036	+	0.245872i
$139$	1176.79			0.718089			0.359045	−	0.933320i	$-0.383103\pi$
$139$	1176.79			0.718089			0.359045	+	0.933320i	$0.383103\pi$
$140$	−774.165	+	502.278i	−0.467349	+	0.303216i
$141$	−18.4752	+	236.956i	−0.0110347	+	0.141527i
$142$	980.991	−	1805.84i	0.579739	−	1.06720i
$143$	3170.65			1.85415
$144$	940.267	−	1449.79i	0.544136	−	0.838997i
$145$	−75.0173			−0.0429645
$146$	576.690	−	1061.59i	0.326899	−	0.601765i
$147$	76.4442	−	980.444i	0.0428912	−	0.550107i
$148$	−2328.36	+	1510.64i	−1.29318	+	0.839011i
$149$	−1866.85			−1.02643			−0.513216	−	0.858259i	$-0.671546\pi$
$149$	−1866.85			−1.02643			−0.513216	+	0.858259i	$0.671546\pi$
$150$	308.250	+	199.955i	0.167790	+	0.108842i
$151$			2362.77i			1.27337i	0.771123	+	0.636686i	$0.219695\pi$
$151$			2362.77i			1.27337i	−0.771123	+	0.636686i	$0.780305\pi$
$152$	1574.83	−	122.924i	0.840366	−	0.0655949i
$153$	495.459	−	3157.97i	0.261801	−	1.66867i
$154$	−1766.94	+	3252.63i	−0.924571	+	1.70198i
$155$		−	15.3084i		−	0.00793289i
$156$	−1109.28	−	2041.58i	−0.569319	−	1.04781i
$157$		−	1036.07i		−	0.526672i	−0.964704	−	0.263336i	$-0.915177\pi$
$157$		−	1036.07i		−	0.526672i	0.964704	−	0.263336i	$-0.0848227\pi$
$158$	1673.96	+	909.353i	0.842870	+	0.457875i
$159$	266.627	−	3419.66i	0.132987	−	1.70564i
$160$	−550.219	−	718.651i	−0.271866	−	0.355090i
$161$			1149.74i			0.562807i
$162$	1491.83	−	1423.37i	0.723514	−	0.690310i
$163$	2431.22			1.16827			0.584135	−	0.811657i	$-0.301434\pi$
$163$	2431.22			1.16827			0.584135	+	0.811657i	$0.301434\pi$
$164$	537.186	−	348.526i	0.255776	−	0.165947i
$165$	1469.32	+	114.561i	0.693251	+	0.0540520i
$166$	1219.21	+	662.317i	0.570056	+	0.309673i
$167$	−2901.17			−1.34431			−0.672154	−	0.740411i	$-0.734631\pi$
$167$	−2901.17			−1.34431			−0.672154	+	0.740411i	$0.734631\pi$
$168$	2712.55	−	0.232602i	1.24570	−	0.000106819i
$169$	−927.177			−0.422019
$170$	−1471.26	−	799.234i	−0.663765	−	0.360579i
$171$	1862.09	+	292.147i	0.832735	+	0.130649i
$172$	−504.716	−	777.924i	−0.223746	−	0.344861i
$173$	486.086			0.213621			0.106811	−	0.994279i	$-0.465936\pi$
$173$	486.086			0.213621			0.106811	+	0.994279i	$0.465936\pi$
$174$	184.993	+	120.000i	0.0805992	+	0.0522828i
$175$			576.769i			0.249141i
$176$	−3315.31	−	1479.48i	−1.41989	−	0.633635i
$177$	2106.12	+	164.212i	0.894383	+	0.0697341i
$178$	3175.42	+	1724.99i	1.33712	+	0.726369i
$179$		−	544.294i		−	0.227276i	−0.993522	−	0.113638i	$-0.963750\pi$
$179$		−	544.294i		−	0.227276i	0.993522	−	0.113638i	$-0.0362504\pi$
$180$	−440.290	−	986.177i	−0.182318	−	0.408363i
$181$		−	3410.15i		−	1.40041i	−0.713940	−	0.700206i	$-0.753091\pi$
$181$		−	3410.15i		−	1.40041i	0.713940	−	0.700206i	$-0.246909\pi$
$182$	1741.04	−	3204.96i	0.709090	−	1.30531i
$183$	−4382.42	−	341.693i	−1.77026	−	0.138025i
$184$	−1124.22	+	87.7514i	−0.450428	+	0.0351583i
$185$			1734.68i			0.689383i
$186$	−24.4878	+	37.7505i	−0.00965342	+	0.0148817i
$187$	−6715.92			−2.62629
$188$	−199.166	−	306.976i	−0.0772641	−	0.119088i
$189$	3148.95	+	748.722i	1.21192	+	0.288156i
$190$	471.267	−	867.523i	0.179944	−	0.331246i
$191$	−608.308			−0.230448			−0.115224	−	0.993340i	$-0.536759\pi$
$191$	−608.308			−0.230448			−0.115224	+	0.993340i	$0.536759\pi$
$192$	207.258	+	2652.34i	0.0779040	+	0.996961i
$193$	−4043.90			−1.50822			−0.754110	−	0.656748i	$-0.771931\pi$
$193$	−4043.90			−1.50822			−0.754110	+	0.656748i	$0.771931\pi$
$194$	1029.32	−	1894.80i	0.380931	−	0.701229i
$195$	−1447.78	−	112.882i	−0.531682	−	0.0414546i
$196$	824.080	+	1270.16i	0.300321	+	0.462887i
$197$	1811.04			0.654982			0.327491	−	0.944854i	$-0.393797\pi$
$197$	1811.04			0.654982			0.327491	+	0.944854i	$0.393797\pi$
$198$	−3440.09	−	2632.89i	−1.23473	−	0.945005i
$199$		−	598.762i		−	0.213292i	−0.994297	−	0.106646i	$-0.965989\pi$
$199$		−	598.762i		−	0.213292i	0.994297	−	0.106646i	$-0.0340112\pi$
$200$	−563.970	+	44.0208i	−0.199394	+	0.0155637i
$201$	42.8767	−	549.921i	0.0150462	−	0.192977i
$202$	1495.66	−	2753.26i	0.520962	−	0.959003i
$203$			346.141i			0.119677i
$204$	2349.63	+	4324.39i	0.806407	+	1.48416i
$205$		−	400.214i		−	0.136352i
$206$	−453.432	−	246.319i	−0.153360	−	0.0833100i
$207$	−1329.29	−	208.554i	−0.446338	−	0.0700267i
$208$	3266.72	+	1457.79i	1.08897	+	0.485960i
$209$		−	3960.03i		−	1.31063i
$210$	922.621	−	1422.31i	0.303176	−	0.467375i
$211$	−3248.67			−1.05994			−0.529970	−	0.848016i	$-0.677797\pi$
$211$	−3248.67			−1.05994			−0.529970	+	0.848016i	$0.677797\pi$
$212$	2874.28	+	4430.16i	0.931163	+	1.43521i
$213$	−293.476	+	3764.02i	−0.0944069	+	1.21083i
$214$	−165.220	−	89.7528i	−0.0527766	−	0.0286700i
$215$	−579.569			−0.183843
$216$	−491.771	+	3136.22i	−0.154911	+	0.987928i
$217$	−70.6351			−0.0220969
$218$	915.127	+	497.127i	0.284313	+	0.154448i
$219$	−172.525	+	2212.73i	−0.0532335	+	0.682752i
$220$	−1903.50	+	1234.99i	−0.583336	+	0.378467i
$221$	6617.48			2.01421
$222$	2774.85	−	4277.71i	0.838900	−	1.29325i
$223$		−	1247.65i		−	0.374658i	−0.982297	−	0.187329i	$-0.940017\pi$
$223$		−	1247.65i		−	0.374658i	0.982297	−	0.187329i	$-0.0599831\pi$
$224$	−3315.96	+	2538.79i	−0.989094	+	0.757277i
$225$	−666.843	−	104.622i	−0.197583	−	0.0309991i
$226$	−160.410	−	87.1402i	−0.0472139	−	0.0256481i
$227$			302.882i			0.0885593i	0.999019	+	0.0442797i	$0.0140993\pi$
$227$			302.882i			0.0885593i	−0.999019	+	0.0442797i	$0.985901\pi$
$228$	−2549.87	+	1385.45i	−0.740654	+	0.402430i
$229$		−	364.029i		−	0.105047i	−0.998620	−	0.0525234i	$-0.983274\pi$
$229$		−	364.029i		−	0.105047i	0.998620	−	0.0525234i	$-0.0167264\pi$
$230$	−336.423	+	619.297i	−0.0964481	+	0.177545i
$231$	528.602	−	6779.66i	0.150561	−	1.93103i
$232$	−338.460	+	26.4186i	−0.0957801	+	0.00747614i
$233$			269.866i			0.0758776i	0.999280	+	0.0379388i	$0.0120792\pi$
$233$			269.866i			0.0758776i	−0.999280	+	0.0379388i	$0.987921\pi$
$234$	3389.66	+	2594.30i	0.946963	+	0.724763i
$235$	−228.703			−0.0634849
$236$	−2728.47	+	1770.23i	−0.752578	+	0.488272i
$237$	−3489.15	−	272.045i	−0.956306	−	0.0745621i
$238$	−3687.79	+	6788.59i	−1.00439	+	1.84890i
$239$	−1873.71			−0.507114			−0.253557	−	0.967320i	$-0.581601\pi$
$239$	−1873.71			−0.507114			−0.253557	+	0.967320i	$0.581601\pi$
$240$	1461.17	+	793.592i	0.392992	+	0.213442i
$241$	2033.30			0.543471			0.271735	−	0.962372i	$-0.412402\pi$
$241$	2033.30			0.543471			0.271735	+	0.962372i	$0.412402\pi$
$242$	−2547.46	+	4689.45i	−0.676682	+	1.24566i
$243$	−1436.85	+	3504.91i	−0.379316	+	0.925267i
$244$	5677.41	−	3683.50i	1.48959	−	0.966442i
$245$	946.296			0.246762
$246$	−640.198	+	986.929i	−0.165925	+	0.255790i
$247$			3901.98i			1.00517i
$248$	−5.39109	−	69.0677i	−0.00138038	−	0.0176847i
$249$	−2541.28	−	198.141i	−0.646775	−	0.0504284i
$250$	−168.768	+	310.673i	−0.0426952	+	0.0785946i
$251$			1243.39i			0.312677i	0.987704	+	0.156339i	$0.0499691\pi$
$251$			1243.39i			0.312677i	−0.987704	+	0.156339i	$0.950031\pi$
$252$	−4550.37	+	2031.56i	−1.13748	+	0.507843i
$253$			2826.94i			0.702483i
$254$	3224.48	+	1751.64i	0.796542	+	0.432708i
$255$	3066.63	+	239.101i	0.753096	+	0.0587181i
$256$	−2735.54	−	3048.61i	−0.667856	−	0.744290i
$257$		−	4979.23i		−	1.20855i	−0.796778	−	0.604273i	$-0.793464\pi$
$257$		−	4979.23i		−	1.20855i	0.796778	−	0.604273i	$-0.206536\pi$
$258$	1429.22	+	927.100i	0.344880	+	0.223716i
$259$	8004.05			1.92026
$260$	1875.60	−	1216.89i	0.447383	−	0.290262i
$261$	−400.198	−	62.7877i	−0.0949105	−	0.0148907i
$262$	5465.12	+	2968.84i	1.28869	+	0.700058i
$263$	−4190.72			−0.982552			−0.491276	−	0.871004i	$-0.663469\pi$
$263$	−4190.72			−0.982552			−0.491276	+	0.871004i	$0.663469\pi$
$264$	6669.56	−	0.571916i	1.55486	−	0.000133330i
$265$	3300.56			0.765101
$266$	−4002.88	−	2174.50i	−0.922678	−	0.501229i
$267$	−6618.72	−	516.055i	−1.51708	−	0.118285i
$268$	462.218	+	712.421i	0.105352	+	0.162381i
$269$	−979.655			−0.222047			−0.111023	−	0.993818i	$-0.535413\pi$
$269$	−979.655			−0.222047			−0.111023	+	0.993818i	$0.535413\pi$
$270$	1477.08	+	1324.70i	0.332934	+	0.298589i
$271$		−	1787.50i		−	0.400675i	−0.979727	−	0.200337i	$-0.935796\pi$
$271$		−	1787.50i		−	0.400675i	0.979727	−	0.200337i	$-0.0642038\pi$
$272$	−6919.41	−	3087.83i	−1.54247	−	0.688335i
$273$	−520.855	+	6680.29i	−0.115471	+	1.48099i
$274$	−3195.91	−	1736.13i	−0.704643	−	0.382785i
$275$			1418.14i			0.310972i
$276$	1820.27	−	989.033i	0.396983	−	0.215699i
$277$		−	8206.02i		−	1.77997i	−0.455990	−	0.889985i	$-0.650715\pi$
$277$		−	8206.02i		−	1.77997i	0.455990	−	0.889985i	$-0.349285\pi$
$278$	1588.84	−	2924.78i	0.342778	−	0.630996i
$279$	12.8127	−	81.6662i	0.00274939	−	0.0175241i
$280$	203.118	+	2602.24i	0.0433523	+	0.555406i
$281$			2233.49i			0.474159i	0.971490	+	0.237080i	$0.0761902\pi$
$281$			2233.49i			0.474159i	−0.971490	+	0.237080i	$0.923810\pi$
$282$	563.983	+	365.843i	0.119095	+	0.0772539i
$283$	4233.88			0.889321			0.444661	−	0.895699i	$-0.353324\pi$
$283$	4233.88			0.889321			0.444661	+	0.895699i	$0.353324\pi$
$284$	−3163.72	−	4876.27i	−0.661029	−	1.01885i
$285$	−140.986	+	1808.23i	−0.0293027	+	0.375826i
$286$	4280.82	−	7880.27i	0.885071	−	1.62927i
$287$	−1846.65			−0.379806
$288$	−2333.78	−	4294.34i	−0.477498	−	0.878633i
$289$	−9103.84			−1.85301
$290$	−101.284	+	186.447i	−0.0205090	+	0.0377535i
$291$	−307.933	+	3949.44i	−0.0620322	+	0.795602i
$292$	−1859.84	−	2866.59i	−0.372736	−	0.574502i
$293$	2687.50			0.535855			0.267928	−	0.963439i	$-0.413661\pi$
$293$	2687.50			0.535855			0.267928	+	0.963439i	$0.413661\pi$
$294$	−2333.57	−	1513.73i	−0.462913	−	0.300281i
$295$			2032.77i			0.401194i
$296$	610.894	+	7826.44i	0.119958	+	1.53683i
$297$	7742.55	+	1840.94i	1.51269	+	0.359671i
$298$	−2520.51	+	4639.84i	−0.489965	+	0.901942i
$299$		−	2785.51i		−	0.538762i
$300$	913.145	−	496.152i	0.175735	−	0.0954845i
$301$			2674.22i			0.512091i
$302$	5872.38	+	3190.07i	1.11893	+	0.607841i
$303$	−447.447	+	5738.78i	−0.0848354	+	1.08807i
$304$	1820.73	−	4080.02i	0.343507	−	0.769754i
$305$		−	4229.79i		−	0.794088i
$306$	−7179.83	−	5495.11i	−1.34132	−	1.02658i
$307$	7863.18			1.46181			0.730904	−	0.682480i	$-0.239098\pi$
$307$	7863.18			1.46181			0.730904	+	0.682480i	$0.239098\pi$
$308$	5698.42	+	8783.02i	1.05421	+	1.62487i
$309$	945.115	+	73.6896i	0.173999	+	0.0135665i
$310$	−38.0471	−	20.6685i	−0.00697075	−	0.00378674i
$311$	6208.54			1.13201			0.566003	−	0.824403i	$-0.308489\pi$
$311$	6208.54			1.13201			0.566003	+	0.824403i	$0.308489\pi$
$312$	−6571.80	+	0.563534i	−1.19248	+	0.000102256i
$313$	824.384			0.148872			0.0744360	−	0.997226i	$-0.476284\pi$
$313$	824.384			0.148872			0.0744360	+	0.997226i	$0.476284\pi$
$314$	−2575.03	−	1398.84i	−0.462794	−	0.251405i
$315$	−482.742	+	3076.91i	−0.0863473	+	0.550363i
$316$	4520.18	−	2932.69i	0.804683	−	0.522077i
$317$	−2961.21			−0.524662			−0.262331	−	0.964978i	$-0.584491\pi$
$317$	−2961.21			−0.524662			−0.262331	+	0.964978i	$0.584491\pi$
$318$	−8139.18	−	5279.70i	−1.43529	−	0.931040i
$319$			851.083i			0.149378i
$320$	−2528.99	+	397.222i	−0.441797	+	0.0693919i
$321$	344.377	+	26.8507i	0.0598794	+	0.00466873i
$322$	2857.53	+	1552.31i	0.494546	+	0.268654i
$323$		−	8265.00i		−	1.42377i
$324$	−1523.43	−	5629.51i	−0.261219	−	0.965280i
$325$		−	1397.36i		−	0.238497i
$326$	3282.49	−	6042.51i	0.557670	−	1.02658i
$327$	−1907.46	−	148.722i	−0.322576	−	0.0251509i
$328$	−140.942	−	1805.67i	−0.0237263	−	0.303968i
$329$			1055.27i			0.176836i
$330$	2268.52	−	3497.14i	0.378417	−	0.583368i
$331$	2915.41			0.484125			0.242062	−	0.970261i	$-0.422176\pi$
$331$	2915.41			0.484125			0.242062	+	0.970261i	$0.422176\pi$
$332$	3292.22	−	2135.99i	0.544229	−	0.353095i
$333$	−1451.88	+	9254.04i	−0.238927	+	1.52288i
$334$	−3916.99	+	7210.52i	−0.641702	+	1.18126i
$335$	530.767			0.0865639
$336$	3661.75	−	6742.05i	0.594539	−	1.09467i
$337$	8797.92			1.42212			0.711058	−	0.703133i	$-0.248216\pi$
$337$	8797.92			1.42212			0.711058	+	0.703133i	$0.248216\pi$
$338$	−1251.82	+	2304.39i	−0.201450	+	0.370835i
$339$	334.353	+	26.0691i	0.0535680	+	0.00417664i
$340$	−3972.80	+	2577.55i	−0.633693	+	0.411139i
$341$	−173.676			−0.0275809
$342$	3240.18	−	4233.57i	0.512307	−	0.669372i
$343$			3546.91i			0.558354i
$344$	−2614.87	+	204.105i	−0.409839	+	0.0319901i
$345$	100.645	−	1290.84i	0.0157060	−	0.201439i
$346$	656.285	−	1208.11i	0.101971	−	0.187712i
$347$			2351.18i			0.363741i	0.983322	+	0.181871i	$0.0582152\pi$
$347$			2351.18i			0.363741i	−0.983322	+	0.181871i	$0.941785\pi$
$348$	548.013	−	297.760i	0.0844155	−	0.0458667i
$349$			7041.61i			1.08003i	0.841657	+	0.540013i	$0.181581\pi$
$349$			7041.61i			1.08003i	−0.841657	+	0.540013i	$0.818419\pi$
$350$	1433.49	+	778.719i	0.218924	+	0.118927i
$351$	−7629.07	−	1813.96i	−1.16014	−	0.275846i
$352$	−8153.21	+	6242.31i	−1.23457	+	0.945217i
$353$		−	64.5832i		−	0.00973772i	−0.999988	−	0.00486886i	$-0.998450\pi$
$353$		−	64.5832i		−	0.00973772i	0.999988	−	0.00486886i	$-0.00154981\pi$
$354$	3251.69	−	5012.80i	0.488207	−	0.752620i
$355$	−3632.92			−0.543142
$356$	8574.53	−	5563.15i	1.27654	−	0.828220i
$357$	1103.25	−	14149.9i	0.163558	−	2.09773i
$358$	−1352.78	−	734.874i	−0.199711	−	0.108490i
$359$	5803.46			0.853189			0.426594	−	0.904443i	$-0.359713\pi$
$359$	5803.46			0.853189			0.426594	+	0.904443i	$0.359713\pi$
$360$	−3045.48	−	237.190i	−0.445863	−	0.0347250i
$361$	−1985.56			−0.289483
$362$	−8475.53	−	4604.19i	−1.23056	−	0.668483i
$363$	762.107	−	9774.50i	0.110193	−	1.41330i
$364$	−5614.89	−	8654.29i	−0.808518	−	1.24618i
$365$	−2135.67			−0.306263
$366$	−6766.13	+	10430.7i	−0.966314	+	1.48967i
$367$			7945.70i			1.13014i	0.825042	+	0.565071i	$0.191151\pi$
$367$			7945.70i			1.13014i	−0.825042	+	0.565071i	$0.808849\pi$
$368$	−1299.76	+	2912.60i	−0.184116	+	0.412581i
$369$	334.970	−	2135.04i	0.0472570	−	0.301208i
$370$	4311.33	+	2342.06i	0.605771	+	0.329075i
$371$		−	15229.3i		−	2.13117i
$372$	60.7622	+	111.830i	0.00846875	+	0.0155863i
$373$		−	10813.1i		−	1.50102i	−0.660859	−	0.750510i	$-0.729808\pi$
$373$		−	10813.1i		−	1.50102i	0.660859	−	0.750510i	$-0.270192\pi$
$374$	−9067.44	+	16691.6i	−1.25365	+	2.30776i
$375$	50.4891	−	647.554i	0.00695265	−	0.0891721i
$376$	−1031.85	+	80.5416i	−0.141526	+	0.0110469i
$377$		−	838.608i		−	0.114564i
$378$	6112.38	−	6815.46i	0.831712	−	0.927379i
$379$	6083.95			0.824569			0.412284	−	0.911055i	$-0.364731\pi$
$379$	6083.95			0.824569			0.412284	+	0.911055i	$0.364731\pi$
$380$	−1519.85	−	2342.56i	−0.205175	−	0.316238i
$381$	−6720.97	−	524.027i	−0.903742	−	0.0704638i
$382$	−821.301	+	1511.88i	−0.110004	+	0.202498i
$383$	11051.1			1.47437			0.737186	−	0.675690i	$-0.236154\pi$
$383$	11051.1			1.47437			0.737186	+	0.675690i	$0.236154\pi$
$384$	6871.91	+	3065.92i	0.913232	+	0.407441i
$385$	6543.53			0.866205
$386$	−5459.84	+	10050.6i	−0.719944	+	1.32530i
$387$	−3091.85	−	485.085i	−0.406118	−	0.0637164i
$388$	−3319.57	−	5116.48i	−0.434344	−	0.669459i
$389$	−9599.68			−1.25122			−0.625608	−	0.780137i	$-0.715149\pi$
$389$	−9599.68			−1.25122			−0.625608	+	0.780137i	$0.715149\pi$
$390$	−2235.27	+	3445.89i	−0.290223	+	0.447408i
$391$			5900.13i			0.763126i
$392$	4269.46	−	333.254i	0.550103	−	0.0429384i
$393$	−11391.3	−	888.166i	−1.46212	−	0.114000i
$394$	2445.16	−	4501.13i	0.312653	−	0.575542i
$395$		−	3367.62i		−	0.428971i
$396$	−11188.3	+	4995.16i	−1.41978	+	0.633879i
$397$			8847.87i			1.11854i	0.828984	+	0.559272i	$0.188919\pi$
$397$			8847.87i			1.11854i	−0.828984	+	0.559272i	$0.811081\pi$
$398$	−1488.15	−	808.413i	−0.187423	−	0.101814i
$399$	8343.44	+	650.529i	1.04685	+	0.0816220i
$400$	−652.031	+	1461.11i	−0.0815038	+	0.182639i
$401$			4547.23i			0.566279i	0.959079	+	0.283139i	$0.0913759\pi$
$401$			4547.23i			0.566279i	−0.959079	+	0.283139i	$0.908624\pi$
$402$	−1308.87	−	849.036i	−0.162390	−	0.105338i
$403$	171.130			0.0211529
$404$	−4823.54	−	7434.58i	−0.594011	−	0.915554i
$405$	−3469.87	−	1116.26i	−0.425726	−	0.136957i
$406$	860.292	+	467.339i	0.105162	+	0.0571272i
$407$	19680.2			2.39683
$408$	13920.1	−	1.19365i	1.68909	−	0.000144839i
$409$	−7023.13			−0.849074			−0.424537	−	0.905411i	$-0.639563\pi$
$409$	−7023.13			−0.849074			−0.424537	+	0.905411i	$0.639563\pi$
$410$	−994.685	−	540.346i	−0.119815	−	0.0650873i
$411$	6661.44	+	519.385i	0.799475	+	0.0623342i
$412$	−1224.39	+	794.385i	−0.146412	+	0.0949916i
$413$	9379.49			1.11752
$414$	−2313.07	+	3022.21i	−0.274592	+	0.358777i
$415$		−	2452.77i		−	0.290125i
$416$	8033.71	−	6150.82i	0.946839	−	0.724925i
$417$	−475.322	+	6096.30i	−0.0558192	+	0.715916i
$418$	−9842.18	−	5346.60i	−1.15167	−	0.625623i
$419$			16871.1i			1.96709i	0.180671	+	0.983544i	$0.442173\pi$
$419$			16871.1i			1.96709i	−0.180671	+	0.983544i	$0.557827\pi$
$420$	−2289.32	−	4213.39i	−0.265970	−	0.489505i
$421$			5069.42i			0.586861i	0.955980	+	0.293430i	$0.0947969\pi$
$421$			5069.42i			0.586861i	−0.955980	+	0.293430i	$0.905203\pi$
$422$	−4386.16	+	8074.18i	−0.505959	+	0.931386i
$423$	−1220.07	−	191.419i	−0.140241	−	0.0220027i
$424$	14891.3	−	1162.35i	1.70563	−	0.133133i
$425$			2959.82i			0.337817i
$426$	8958.79	+	5811.36i	1.01891	+	0.660942i
$427$	−19516.9			−2.21191
$428$	−446.140	+	289.455i	−0.0503855	+	0.0326900i
$429$	−1280.66	+	16425.3i	−0.144128	+	1.84854i
$430$	−782.499	+	1440.45i	−0.0877569	+	0.161546i
$431$	−8496.29			−0.949540			−0.474770	−	0.880110i	$-0.657469\pi$
$431$	−8496.29			−0.949540			−0.474770	+	0.880110i	$0.657469\pi$
$432$	7130.73	+	5456.57i	0.794161	+	0.607707i
$433$	12464.3			1.38336			0.691679	−	0.722205i	$-0.256871\pi$
$433$	12464.3			1.38336			0.691679	+	0.722205i	$0.256871\pi$
$434$	−95.3674	+	175.555i	−0.0105479	+	0.0194169i
$435$	30.3004	−	388.622i	0.00333976	−	0.0428345i
$436$	2471.10	−	1603.25i	0.271432	−	0.176105i
$437$	−3479.00			−0.380831
$438$	5266.56	+	3416.29i	0.574534	+	0.372687i
$439$		−	14679.2i		−	1.59590i	−0.602723	−	0.797951i	$-0.705917\pi$
$439$		−	14679.2i		−	1.59590i	0.602723	−	0.797951i	$-0.294083\pi$
$440$	499.422	+	6398.33i	0.0541114	+	0.693246i
$441$	5048.25	+	792.027i	0.545108	+	0.0855229i
$442$	8934.54	−	16447.0i	0.961476	−	1.76991i
$443$			9927.80i			1.06475i	0.846509	+	0.532375i	$0.178700\pi$
$443$			9927.80i			1.06475i	−0.846509	+	0.532375i	$0.821300\pi$
$444$	−6885.30	−	12672.1i	−0.735950	−	1.35448i
$445$		−	6388.20i		−	0.680516i
$446$	−3100.88	−	1684.50i	−0.329218	−	0.178842i
$447$	754.045	−	9671.10i	0.0797877	−	1.02333i
$448$	1832.84	+	11669.2i	0.193290	+	1.23062i
$449$		−	8136.48i		−	0.855199i	−0.903968	−	0.427599i	$-0.859359\pi$
$449$		−	8136.48i		−	0.855199i	0.903968	−	0.427599i	$-0.140641\pi$
$450$	−1160.36	+	1516.10i	−0.121555	+	0.158822i
$451$	−4540.49			−0.474065
$452$	−433.153	+	281.029i	−0.0450748	+	0.0292445i
$453$	−12240.2	−	954.351i	−1.26952	−	0.0989831i
$454$	752.776	+	408.933i	0.0778184	+	0.0422735i
$455$	−6447.62			−0.664328
$456$	0.703834	+	8207.95i	7.22808e−5	+	0.842922i
$457$	9697.93			0.992670			0.496335	−	0.868131i	$-0.334679\pi$
$457$	9697.93			0.992670			0.496335	+	0.868131i	$0.334679\pi$
$458$	−904.751	−	491.491i	−0.0923062	−	0.0501438i
$459$	16159.5	+	3842.24i	1.64327	+	0.390720i
$460$	1084.97	+	1672.28i	0.109972	+	0.169501i
$461$	−12155.1			−1.22802			−0.614011	−	0.789297i	$-0.710445\pi$
$461$	−12155.1			−1.22802			−0.614011	+	0.789297i	$0.710445\pi$
$462$	−16136.3	−	10467.3i	−1.62496	−	1.05407i
$463$		−	19333.9i		−	1.94065i	−0.241807	−	0.970324i	$-0.577740\pi$
$463$		−	19333.9i		−	1.94065i	0.241807	−	0.970324i	$-0.422260\pi$
$464$	−391.309	+	876.871i	−0.0391510	+	0.0877321i
$465$	79.3039	+	6.18324i	0.00790889	+	0.000616647i
$466$	670.719	+	364.357i	0.0666748	+	0.0362199i
$467$		−	2499.66i		−	0.247688i	−0.992302	−	0.123844i	$-0.960478\pi$
$467$		−	2499.66i		−	0.247688i	0.992302	−	0.123844i	$-0.0395223\pi$
$468$	11024.3	−	4921.94i	1.08889	−	0.486147i
$469$		−	2449.04i		−	0.241122i
$470$	−308.782	+	568.415i	−0.0303043	+	0.0557852i
$471$	5367.29	+	418.482i	0.525078	+	0.0409398i
$472$	715.872	+	9171.36i	0.0698108	+	0.894377i
$473$			6575.29i			0.639180i
$474$	−5386.98	+	8304.56i	−0.522008	+	0.804728i
$475$	−1745.25			−0.168584
$476$	11893.2	+	18331.1i	1.14522	+	1.76514i
$477$	17607.6	+	2762.49i	1.69014	+	0.265169i
$478$	−2529.77	+	4656.88i	−0.242069	+	0.445609i
$479$	−4179.14			−0.398643			−0.199321	−	0.979934i	$-0.563874\pi$
$479$	−4179.14			−0.398643			−0.199321	+	0.979934i	$0.563874\pi$
$480$	3945.16	−	2560.10i	0.375148	−	0.243441i
$481$	−19391.7			−1.83822
$482$	2745.24	−	5053.53i	0.259424	−	0.477556i
$483$	−5956.12	−	464.392i	−0.561104	−	0.0437486i
$484$	8215.63	+	12662.8i	0.771565	+	1.18922i
$485$	−3811.88			−0.356884
$486$	6771.08	+	8303.24i	0.631980	+	0.774984i
$487$		−	890.371i		−	0.0828472i	−0.999142	−	0.0414236i	$-0.986811\pi$
$487$		−	890.371i		−	0.0828472i	0.999142	−	0.0414236i	$-0.0131893\pi$
$488$	−1489.59	−	19083.8i	−0.138177	−	1.77025i
$489$	−982.001	+	12594.8i	−0.0908131	+	1.16473i
$490$	1277.63	−	2351.91i	0.117791	−	0.216833i
$491$		−	12489.8i		−	1.14797i	−0.818865	−	0.573987i	$-0.805396\pi$
$491$		−	12489.8i		−	1.14797i	0.818865	−	0.573987i	$-0.194604\pi$
$492$	1588.54	+	2923.63i	0.145563	+	0.267901i
$493$			1776.30i			0.162273i
$494$	9697.92	+	5268.23i	0.883259	+	0.479816i
$495$	−1186.95	+	7565.43i	−0.107777	+	0.686951i
$496$	−178.938	−	79.8522i	−0.0161987	−	0.00722877i
$497$			16762.8i			1.51291i
$498$	−3923.54	+	6048.53i	−0.353048	+	0.544259i
$499$	−14905.5			−1.33720			−0.668599	−	0.743623i	$-0.733106\pi$
$499$	−14905.5			−1.33720			−0.668599	+	0.743623i	$0.733106\pi$
$500$	544.280	+	838.904i	0.0486819	+	0.0750338i
$501$	1171.82	−	15029.3i	0.104497	−	1.34024i
$502$	3090.29	+	1678.75i	0.274754	+	0.149256i
$503$	−8756.60			−0.776218			−0.388109	−	0.921613i	$-0.626872\pi$
$503$	−8756.60			−0.776218			−0.388109	+	0.921613i	$0.626872\pi$
$504$	−1094.43	+	14052.3i	−0.0967257	+	1.24194i
$505$	−5538.91			−0.488075
$506$	7026.02	+	3816.77i	0.617282	+	0.335328i
$507$	374.498	−	4803.17i	0.0328048	−	0.420742i
$508$	8707.00	−	5649.09i	0.760454	−	0.493381i
$509$	−2581.53			−0.224803			−0.112401	−	0.993663i	$-0.535854\pi$
$509$	−2581.53			−0.224803			−0.112401	+	0.993663i	$0.535854\pi$
$510$	4734.64	−	7298.91i	0.411085	−	0.633728i
$511$			9854.29i			0.853088i
$512$	−11270.3	+	2682.80i	−0.972818	+	0.231570i
$513$	−2265.57	+	9528.44i	−0.194985	+	0.820060i
$514$	−12375.3	−	6722.67i	−1.06197	−	0.576895i
$515$			912.198i			0.0780509i
$516$	4233.84	−	2300.43i	0.361210	−	0.196261i
$517$			2594.67i			0.220723i
$518$	10806.6	−	19893.1i	0.916631	−	1.68736i
$519$	−196.336	+	2518.14i	−0.0166054	+	0.212975i
$520$	−492.102	−	6304.55i	−0.0415002	−	0.531678i
$521$		−	4731.55i		−	0.397876i	−0.980012	−	0.198938i	$-0.936251\pi$
$521$		−	4731.55i		−	0.397876i	0.980012	−	0.198938i	$-0.0637492\pi$
$522$	−696.375	+	909.872i	−0.0583899	+	0.0762912i
$523$	11839.4			0.989867			0.494934	−	0.868931i	$-0.335192\pi$
$523$	11839.4			0.989867			0.494934	+	0.868931i	$0.335192\pi$
$524$	14757.4	−	9574.57i	1.23030	−	0.798219i
$525$	−2987.91	−	232.964i	−0.248387	−	0.0193664i
$526$	−5658.07	+	10415.5i	−0.469018	+	0.863383i
$527$	−362.480			−0.0299618
$528$	9003.43	−	16577.2i	0.742091	−	1.36634i
$529$	−9683.45			−0.795878
$530$	4456.22	−	8203.15i	0.365219	−	0.672306i
$531$	−1701.38	+	10844.3i	−0.139046	+	0.886256i
$532$	−10808.9	+	7012.80i	−0.880875	+	0.571510i
$533$	4473.94			0.363580
$534$	−10218.8	+	15753.3i	−0.828110	+	1.27661i
$535$			332.383i			0.0268601i
$536$	2394.70	−	186.918i	0.192976	−	0.0150628i
$537$	2819.68	+	219.847i	0.226589	+	0.0176669i
$538$	−1322.67	+	2434.82i	−0.105993	+	0.195116i
$539$		−	10735.9i		−	0.857935i
$540$	5286.66	−	1882.56i	0.421299	−	0.150023i
$541$			20325.4i			1.61526i	0.589688	+	0.807631i	$0.299251\pi$
$541$			20325.4i			1.61526i	−0.589688	+	0.807631i	$0.700749\pi$
$542$	−4442.62	−	2413.38i	−0.352079	−	0.191261i
$543$	17666.1	+	1377.40i	1.39618	+	0.108858i
$544$	−17016.6	+	13028.4i	−1.34114	+	1.02681i
$545$		−	1841.02i		−	0.144698i
$546$	15899.8	+	10313.9i	1.24625	+	0.808411i
$547$	−21541.0			−1.68378			−0.841888	−	0.539652i	$-0.818556\pi$
$547$	−21541.0			−1.68378			−0.841888	+	0.539652i	$0.818556\pi$
$548$	−8629.87	+	5599.05i	−0.672718	+	0.436459i
$549$	3540.23	−	22564.8i	0.275216	−	1.75418i
$550$	3524.63	+	1914.69i	0.273256	+	0.148442i
$551$	−1047.39			−0.0809808
$552$	−0.502445	−	5859.40i	−3.87418e−5	−	0.451798i
$553$	−15538.7			−1.19489
$554$	−20395.1	−	11079.3i	−1.56409	−	0.849663i
$555$	−8986.36	−	700.657i	−0.687297	−	0.0535878i
$556$	−5124.04	−	7897.74i	−0.390841	−	0.602408i
$557$	2507.54			0.190750			0.0953750	−	0.995441i	$-0.469595\pi$
$557$	2507.54			0.190750			0.0953750	+	0.995441i	$0.469595\pi$
$558$	−185.673	−	142.105i	−0.0140863	−	0.0107810i
$559$		−	6478.92i		−	0.490213i
$560$	6741.80	+	3008.57i	0.508738	+	0.227027i
$561$	2712.64	−	34791.3i	0.204149	−	2.61834i
$562$	5551.07	+	3015.52i	0.416651	+	0.226338i
$563$		−	848.586i		−	0.0635233i	−0.999495	−	0.0317617i	$-0.989888\pi$
$563$		−	848.586i		−	0.0635233i	0.999495	−	0.0317617i	$-0.0101118\pi$
$564$	1670.71	−	907.773i	0.124734	−	0.0677733i
$565$			322.708i			0.0240290i
$566$	5716.33	−	10522.8i	0.424515	−	0.781460i
$567$	−5150.60	+	16010.5i	−0.381490	+	1.18585i
$568$	−16390.9	+	1279.39i	−1.21082	+	0.0945107i
$569$			1305.66i			0.0961968i	0.998843	+	0.0480984i	$0.0153161\pi$
$569$			1305.66i			0.0961968i	−0.998843	+	0.0480984i	$0.984684\pi$
$570$	4303.79	+	2791.77i	0.316256	+	0.205148i
$571$	−6973.58			−0.511095			−0.255547	−	0.966797i	$-0.582256\pi$
$571$	−6973.58			−0.511095			−0.255547	+	0.966797i	$0.582256\pi$
$572$	−13805.8	−	21279.0i	−1.00917	−	1.55545i
$573$	245.703	−	3151.30i	0.0179134	−	0.229751i
$574$	−2493.24	+	4589.63i	−0.181299	+	0.333741i
$575$	1245.88			0.0903597
$576$	−13824.0	+	2.37082i	−1.00000	+	0.000171500i
$577$	4879.56			0.352061			0.176030	−	0.984385i	$-0.443674\pi$
$577$	4879.56			0.352061			0.176030	+	0.984385i	$0.443674\pi$
$578$	−12291.5	+	22626.5i	−0.884529	+	1.62827i
$579$	1633.38	−	20949.2i	0.117238	−	1.50366i
$580$	326.643	+	503.458i	0.0233847	+	0.0360431i
$581$	−11317.4			−0.808135
$582$	9400.11	+	6097.63i	0.669496	+	0.434287i
$583$		−	37445.3i		−	2.66008i
$584$	−9635.62	+	752.110i	−0.682748	+	0.0532920i
$585$	1169.56	−	7454.55i	0.0826584	−	0.526851i
$586$	3628.51	−	6679.47i	0.255789	−	0.470864i
$587$			26908.1i			1.89202i	0.324137	+	0.946010i	$0.394926\pi$
$587$			26908.1i			1.89202i	−0.324137	+	0.946010i	$0.605074\pi$
$588$	−6912.84	+	3756.05i	−0.484831	+	0.263430i
$589$		−	213.736i		−	0.0149522i
$590$	5052.20	+	2744.52i	0.352535	+	0.191509i
$591$	−731.502	+	9381.97i	−0.0509137	+	0.653000i
$592$	20276.5	+	9048.49i	1.40770	+	0.628194i
$593$		−	14269.9i		−	0.988184i	−0.869410	−	0.494092i	$-0.835501\pi$
$593$		−	14269.9i		−	0.988184i	0.869410	−	0.494092i	$-0.164499\pi$
$594$	15029.0	−	16757.7i	1.03813	−	1.15753i
$595$	13657.0			0.940982
$596$	8128.72	+	12528.9i	0.558667	+	0.861079i
$597$	3101.85	+	241.847i	0.212647	+	0.0165798i
$598$	−6923.04	−	3760.83i	−0.473419	−	0.257177i
$599$	14472.9			0.987222			0.493611	−	0.869683i	$-0.335677\pi$
$599$	14472.9			0.987222			0.493611	+	0.869683i	$0.335677\pi$
$600$	−0.252053	−	2939.39i	−1.71500e−5	−	0.200000i
$601$	13965.2			0.947841			0.473920	−	0.880568i	$-0.342838\pi$
$601$	13965.2			0.947841			0.473920	+	0.880568i	$0.342838\pi$
$602$	6646.45	+	3610.57i	0.449982	+	0.244445i
$603$	2831.51	+	444.240i	0.191224	+	0.0300014i
$604$	15857.1	−	10288.1i	1.06824	−	0.693071i
$605$	9434.06			0.633965
$606$	13658.9	+	8860.24i	0.915605	+	0.593932i
$607$			23345.5i			1.56106i	0.625116	+	0.780532i	$0.285052\pi$
$607$			23345.5i			1.56106i	−0.625116	+	0.780532i	$0.714948\pi$
$608$	−7682.15	−	10033.8i	−0.512422	−	0.669284i
$609$	−1793.16	−	139.811i	−0.119314	−	0.00930281i
$610$	−10512.6	−	5710.81i	−0.697777	−	0.379056i
$611$		−	2556.64i		−	0.169281i
$612$	−23351.2	+	10425.4i	−1.54235	+	0.688599i
$613$		−	19931.0i		−	1.31322i	−0.754230	−	0.656611i	$-0.771989\pi$
$613$		−	19931.0i		−	1.31322i	0.754230	−	0.656611i	$-0.228011\pi$
$614$	10616.4	−	19543.0i	0.697790	−	1.28451i
$615$	2073.28	+	161.652i	0.135940	+	0.0105991i
$616$	29522.8	−	2304.41i	1.93102	−	0.150726i
$617$		−	24665.8i		−	1.60941i	−0.593675	−	0.804705i	$-0.702323\pi$
$617$		−	24665.8i		−	1.60941i	0.593675	−	0.804705i	$-0.297677\pi$
$618$	1459.19	−	2249.48i	0.0949791	−	0.146420i
$619$	16800.4			1.09090			0.545448	−	0.838145i	$-0.316360\pi$
$619$	16800.4			1.09090			0.545448	+	0.838145i	$0.316360\pi$
$620$	−102.738	+	66.6563i	−0.00665493	+	0.00431771i
$621$	1617.32	−	6802.06i	0.104510	−	0.439544i
$622$	8382.40	−	15430.6i	0.540360	−	0.994710i
$623$	−29476.1			−1.89556
$624$	−8871.46	+	16334.2i	−0.569139	+	1.04790i
$625$	625.000			0.0400000
$626$	1113.03	−	2048.91i	0.0710636	−	0.130816i
$627$	20514.6	+	1599.50i	1.30666	+	0.101879i
$628$	−6953.31	+	4511.30i	−0.441827	+	0.286657i
$629$	41074.6			2.60374
$630$	6995.53	+	5354.06i	0.442395	+	0.338589i
$631$			5407.04i			0.341127i	0.985347	+	0.170563i	$0.0545587\pi$
$631$			5407.04i			0.341127i	−0.985347	+	0.170563i	$0.945441\pi$
$632$	−1185.96	−	15193.9i	−0.0746441	−	0.956299i
$633$	1312.18	−	16829.5i	0.0823924	−	1.05673i
$634$	−3998.05	+	7359.73i	−0.250446	+	0.461028i
$635$		−	6486.88i		−	0.405392i
$636$	−24111.1	+	13100.6i	−1.50325	+	0.816783i
$637$			10578.5i			0.657985i
$638$	2115.26	+	1149.08i	0.131260	+	0.0713050i
$639$	−19380.7	−	3040.67i	−1.19983	−	0.188242i
$640$	−2427.25	+	6821.82i	−0.149915	+	0.421338i
$641$			25127.5i			1.54833i	0.632987	+	0.774163i	$0.281829\pi$
$641$			25127.5i			1.54833i	−0.632987	+	0.774163i	$0.718171\pi$
$642$	531.693	−	819.657i	0.0326857	−	0.0503883i
$643$	9999.39			0.613277			0.306639	−	0.951826i	$-0.400796\pi$
$643$	9999.39			0.613277			0.306639	+	0.951826i	$0.400796\pi$
$644$	7716.14	−	5006.22i	0.472141	−	0.306324i
$645$	234.095	−	3002.41i	0.0142907	−	0.183287i
$646$	−20541.7	−	11158.9i	−1.25109	−	0.679631i
$647$	19198.9			1.16659			0.583296	−	0.812259i	$-0.301763\pi$
$647$	19198.9			1.16659			0.583296	+	0.812259i	$0.301763\pi$
$648$	−16048.3	−	3814.34i	−0.972898	−	0.231237i
$649$	23062.1			1.39486
$650$	−3472.97	−	1886.63i	−0.209571	−	0.113846i
$651$	28.5304	−	365.920i	0.00171766	−	0.0220300i
$652$	−10586.1	−	16316.5i	−0.635865	−	0.980066i
$653$	−24312.9			−1.45703			−0.728513	−	0.685032i	$-0.759788\pi$
$653$	−24312.9			−1.45703			−0.728513	+	0.685032i	$0.759788\pi$
$654$	−2944.97	+	4539.96i	−0.176081	+	0.271447i
$655$		−	10994.5i		−	0.655866i
$656$	−4678.07	−	2087.62i	−0.278427	−	0.124250i
$657$	−11393.2	−	1787.50i	−0.676549	−	0.106145i
$658$	2622.75	+	1424.77i	0.155388	+	0.0844121i
$659$			9172.96i			0.542227i	0.962547	+	0.271114i	$0.0873919\pi$
$659$			9172.96i			0.542227i	−0.962547	+	0.271114i	$0.912608\pi$
$660$	−5628.92	−	10359.8i	−0.331978	−	0.610990i
$661$			1731.59i			0.101893i	0.998701	+	0.0509464i	$0.0162238\pi$
$661$			1731.59i			0.101893i	−0.998701	+	0.0509464i	$0.983776\pi$
$662$	3936.21	−	7245.90i	0.231095	−	0.425408i
$663$	−2672.88	+	34281.4i	−0.156570	+	2.00811i
$664$	−863.782	−	11066.3i	−0.0504838	−	0.646771i
$665$			8052.85i			0.469588i
$666$	21039.6	+	16102.7i	1.22412	+	0.936890i
$667$	747.701			0.0434049
$668$	12632.4	+	19470.4i	0.731680	+	1.12775i
$669$	6463.36	+	503.941i	0.373524	+	0.0291233i
$670$	716.611	−	1319.16i	0.0413210	−	0.0760650i
$671$	−47987.6			−2.76086
$672$	−11812.7	−	18203.6i	−0.678101	−	1.04497i
$673$	6125.28			0.350835			0.175418	−	0.984494i	$-0.443872\pi$
$673$	6125.28			0.350835			0.175418	+	0.984494i	$0.443872\pi$
$674$	11878.4	−	21866.2i	0.678843	−	1.24963i
$675$	811.333	−	3412.27i	0.0462640	−	0.194576i
$676$	4037.15	+	6222.50i	0.229697	+	0.354034i
$677$	−4105.42			−0.233064			−0.116532	−	0.993187i	$-0.537178\pi$
$677$	−4105.42			−0.233064			−0.116532	+	0.993187i	$0.537178\pi$
$678$	516.215	−	795.797i	0.0292406	−	0.0450773i
$679$			17588.6i			0.994092i
$680$	1042.35	+	13354.0i	0.0587827	+	0.753091i
$681$	−1569.06	−	122.338i	−0.0882914	−	0.00688398i
$682$	−234.487	+	431.650i	−0.0131656	+	0.0242357i
$683$			14765.0i			0.827183i	0.910463	+	0.413591i	$0.135726\pi$
$683$			14765.0i			0.827183i	−0.910463	+	0.413591i	$0.864274\pi$
$684$	−6147.33	−	13769.0i	−0.343639	−	0.769695i
$685$			6429.42i			0.358621i
$686$	8815.43	+	4788.83i	0.490634	+	0.266528i
$687$	1885.83	+	147.036i	0.104729	+	0.00816561i
$688$	−3023.17	+	6774.53i	−0.167525	+	0.375402i
$689$			36896.5i			2.04012i
$690$	−3072.34	−	1992.96i	−0.169510	−	0.109957i
$691$	11561.2			0.636479			0.318240	−	0.948010i	$-0.396908\pi$
$691$	11561.2			0.636479			0.318240	+	0.948010i	$0.396908\pi$
$692$	−2116.53	−	3262.24i	−0.116270	−	0.179208i
$693$	34908.0	+	5476.78i	1.91349	+	0.300210i
$694$	5843.59	+	3174.43i	0.319625	+	0.173631i
$695$	−5883.97			−0.321139
$696$	−0.151267	−	1764.04i	−8.23815e−6	−	0.0960715i
$697$	−9476.49			−0.514990
$698$	17501.1	+	9507.17i	0.949034	+	0.515547i
$699$	−1398.02	−	109.002i	−0.0756480	−	0.00589819i
$700$	3870.83	−	2511.39i	0.209005	−	0.135602i
$701$	12297.2			0.662566			0.331283	−	0.943531i	$-0.392518\pi$
$701$	12297.2			0.662566			0.331283	+	0.943531i	$0.392518\pi$
$702$	−14808.7	+	16512.1i	−0.796180	+	0.887760i
$703$			24219.5i			1.29937i
$704$	4506.55	+	28691.8i	0.241260	+	1.53603i
$705$	92.3761	−	1184.78i	0.00493487	−	0.0632929i
$706$	−160.514	−	87.1964i	−0.00855668	−	0.00464827i
$707$			25557.3i			1.35952i
$708$	−8068.49	−	14849.7i	−0.428294	−	0.788256i
$709$			22463.7i			1.18990i	0.803761	+	0.594952i	$0.202829\pi$
$709$			22463.7i			1.18990i	−0.803761	+	0.594952i	$0.797171\pi$
$710$	−4904.96	+	9029.19i	−0.259267	+	0.477267i
$711$	2818.62	−	17965.4i	0.148673	−	0.947616i
$712$	−2249.71	−	28822.0i	−0.118415	−	1.51707i
$713$			152.579i			0.00801421i
$714$	−33678.3	−	21846.3i	−1.76523	−	1.14507i
$715$	−15853.2			−0.829200
$716$	−3652.88	+	2369.99i	−0.190663	+	0.123702i
$717$	756.815	−	9706.63i	0.0394195	−	0.505580i
$718$	7835.49	−	14423.8i	0.407267	−	0.749710i
$719$	−5671.20			−0.294159			−0.147079	−	0.989125i	$-0.546987\pi$
$719$	−5671.20			−0.294159			−0.147079	+	0.989125i	$0.546987\pi$
$720$	−4701.33	+	7248.94i	−0.243345	+	0.375211i
$721$	4209.02			0.217409
$722$	−2680.79	+	4934.87i	−0.138184	+	0.254373i
$723$	−821.276	+	10533.4i	−0.0422456	+	0.541826i
$724$	−22886.3	+	14848.6i	−1.17481	+	0.762216i
$725$	375.086			0.0192143
$726$	−23264.4	−	15091.1i	−1.18929	−	0.771463i
$727$		−	24781.5i		−	1.26423i	−0.774875	−	0.632115i	$-0.782187\pi$
$727$		−	24781.5i		−	1.26423i	0.774875	−	0.632115i	$-0.217813\pi$
$728$	−29090.1	+	2270.63i	−1.48098	+	0.115598i
$729$	−17576.6	−	8859.17i	−0.892982	−	0.450092i
$730$	−2883.45	+	5307.95i	−0.146194	+	0.269118i
$731$			13723.3i			0.694359i
$732$	16788.9	+	30899.3i	0.847728	+	1.56020i
$733$			27354.3i			1.37838i	0.724579	+	0.689192i	$0.242034\pi$
$733$			27354.3i			1.37838i	−0.724579	+	0.689192i	$0.757966\pi$
$734$	19748.1	+	10727.8i	0.993072	+	0.539470i
$735$	−382.221	+	4902.22i	−0.0191815	+	0.246015i
$736$	5484.05	+	7162.83i	0.274653	+	0.358730i
$737$		−	6021.64i		−	0.300963i
$738$	−4854.13	−	3715.13i	−0.242118	−	0.185306i
$739$	−13412.9			−0.667659			−0.333829	−	0.942634i	$-0.608341\pi$
$739$	−13412.9			−0.667659			−0.333829	+	0.942634i	$0.608341\pi$
$740$	11641.8	−	7553.19i	0.578326	−	0.375217i
$741$	−20214.0	−	1576.06i	−1.00213	−	0.0781350i
$742$	−37850.5	−	20561.7i	−1.87269	−	1.01731i
$743$	26521.0			1.30951			0.654753	−	0.755843i	$-0.272773\pi$
$743$	26521.0			1.30951			0.654753	+	0.755843i	$0.272773\pi$
$744$	359.978	−	0.0308682i	0.0177385	−	1.52108e-6i
$745$	9334.26			0.459035
$746$	−26874.6	−	14599.2i	−1.31897	−	0.716507i
$747$	2052.91	−	13084.9i	0.100552	−	0.640898i
$748$	29242.7	+	45072.1i	1.42944	+	2.20321i
$749$	1533.67			0.0748183
$750$	−1541.25	−	999.774i	−0.0750380	−	0.0486754i
$751$		−	31691.2i		−	1.53985i	−0.638134	−	0.769925i	$-0.720294\pi$
$751$		−	31691.2i		−	1.53985i	0.638134	−	0.769925i	$-0.279706\pi$
$752$	−1192.97	+	2673.29i	−0.0578501	+	0.129634i
$753$	−6441.29	−	502.220i	−0.311731	−	0.0243053i
$754$	−2084.26	−	1132.24i	−0.100669	−	0.0546867i
$755$		−	11813.8i		−	0.569470i
$756$	−8686.42	−	24393.4i	−0.417886	−	1.17352i
$757$		−	24304.8i		−	1.16694i	−0.812134	−	0.583470i	$-0.801694\pi$
$757$		−	24304.8i		−	1.16694i	0.812134	−	0.583470i	$-0.198306\pi$
$758$	8214.19	−	15120.9i	0.393605	−	0.724561i
$759$	−14644.8	−	1141.84i	−0.700358	−	0.0546061i
$760$	−7874.15	+	614.618i	−0.375823	+	0.0293349i
$761$		−	2995.25i		−	0.142678i	−0.997452	−	0.0713388i	$-0.977273\pi$
$761$		−	2995.25i		−	0.142678i	0.997452	−	0.0713388i	$-0.0227272\pi$
$762$	−10376.7	+	15996.7i	−0.493316	+	0.760496i
$763$	−8494.74			−0.403054
$764$	2648.72	+	4082.49i	0.125428	+	0.193324i
$765$	−2477.30	+	15789.9i	−0.117081	+	0.746253i
$766$	14920.5	−	27466.2i	0.703787	−	1.29555i
$767$	−22724.0			−1.06977
$768$	16898.0	−	12939.9i	0.793953	−	0.607980i
$769$	35379.0			1.65904			0.829518	−	0.558480i	$-0.188615\pi$
$769$	35379.0			1.65904			0.829518	+	0.558480i	$0.188615\pi$
$770$	8834.69	−	16263.2i	0.413481	−	0.761148i
$771$	25794.6	+	2011.17i	1.20489	+	0.0939438i
$772$	17608.1	+	27139.6i	0.820894	+	1.26525i
$773$	−18639.0			−0.867270			−0.433635	−	0.901089i	$-0.642769\pi$
$773$	−18639.0			−0.867270			−0.433635	+	0.901089i	$0.642769\pi$
$774$	−5380.05	+	7029.49i	−0.249848	+	0.326447i
$775$			76.5418i			0.00354770i
$776$	−17198.3	+	1342.42i	−0.795597	+	0.0621004i
$777$	−3232.94	+	41464.4i	−0.149268	+	1.91445i
$778$	−12960.9	+	23858.9i	−0.597264	+	1.09946i
$779$		−	5587.79i		−	0.257001i
$780$	5546.42	+	10207.9i	0.254607	+	0.468593i
$781$			41216.0i			1.88838i
$782$	14664.1	+	7966.00i	0.670570	+	0.364276i
$783$	486.912	−	2047.84i	0.0222233	−	0.0934658i
$784$	4936.11	−	11061.2i	0.224859	−	0.503880i
$785$			5180.35i			0.235535i
$786$	−17587.3	+	27112.5i	−0.798114	+	1.23037i
$787$	43015.8			1.94835			0.974173	−	0.225802i	$-0.0725002\pi$
$787$	43015.8			1.94835			0.974173	+	0.225802i	$0.0725002\pi$
$788$	−7885.71	−	12154.3i	−0.356493	−	0.549467i
$789$	1692.69	−	21709.8i	0.0763767	−	0.979579i
$790$	−8369.82	−	4546.77i	−0.376943	−	0.204768i
$791$	1489.02			0.0669324
$792$	−2690.96	+	34551.4i	−0.120731	+	1.55017i
$793$	47284.2			2.11742
$794$	21990.3	+	11945.9i	0.982881	+	0.533934i
$795$	−1333.14	+	17098.3i	−0.0594736	+	0.762786i
$796$	−4018.43	+	2607.15i	−0.178932	+	0.116091i
$797$	35362.4			1.57164			0.785822	−	0.618452i	$-0.212240\pi$
$797$	35362.4			1.57164			0.785822	+	0.618452i	$0.212240\pi$
$798$	12881.6	−	19858.3i	0.571435	−	0.880924i
$799$			5415.36i			0.239777i
$800$	2751.09	+	3593.26i	0.121582	+	0.158801i
$801$	5346.77	−	34079.4i	0.235854	−	1.50329i
$802$	11301.6	+	6139.40i	0.497597	+	0.270311i
$803$			24229.5i			1.06481i
$804$	−3877.34	+	2106.73i	−0.170079	+	0.0924112i
$805$		−	5748.68i		−	0.251695i
$806$	231.050	−	425.324i	0.0100973	−	0.0185873i
$807$	395.695	−	5075.04i	0.0172604	−	0.221375i
$808$	−24990.2	+	1950.62i	−1.08806	+	0.0849288i
$809$		−	39925.8i		−	1.73513i	−0.497326	−	0.867564i	$-0.665685\pi$
$809$		−	39925.8i		−	1.73513i	0.497326	−	0.867564i	$-0.334315\pi$
$810$	−7459.15	+	7116.83i	−0.323565	+	0.308716i
$811$	−37954.1			−1.64334			−0.821670	−	0.569964i	$-0.806957\pi$
$811$	−37954.1			−1.64334			−0.821670	+	0.569964i	$0.806957\pi$
$812$	2323.03	−	1507.18i	0.100397	−	0.0651375i
$813$	9260.01	+	721.993i	0.399462	+	0.0311456i
$814$	26571.0	−	48912.7i	1.14412	−	2.10613i
$815$	−12156.1			−0.522466
$816$	18791.1	−	34598.3i	0.806153	−	1.48429i
$817$	−8091.94			−0.346513
$818$	−9482.22	+	17455.2i	−0.405303	+	0.746094i
$819$	−34396.4	−	5396.50i	−1.46753	−	0.230243i
$820$	−2685.93	+	1742.63i	−0.114386	+	0.0742137i
$821$	22806.7			0.969498			0.484749	−	0.874653i	$-0.338911\pi$
$821$	22806.7			0.969498			0.484749	+	0.874653i	$0.338911\pi$
$822$	10284.7	−	15855.0i	0.436401	−	0.672756i
$823$			12201.6i			0.516792i	0.966039	+	0.258396i	$0.0831939\pi$
$823$			12201.6i			0.516792i	−0.966039	+	0.258396i	$0.916806\pi$
$824$	321.245	+	4115.62i	0.0135814	+	0.173998i
$825$	−7346.60	−	572.806i	−0.310031	−	0.0241728i
$826$	12663.6	−	23311.6i	0.533443	−	0.981979i
$827$		−	20473.8i		−	0.860875i	−0.902620	−	0.430438i	$-0.858359\pi$
$827$		−	20473.8i		−	0.860875i	0.902620	−	0.430438i	$-0.141641\pi$
$828$	4388.39	+	9829.27i	0.184187	+	0.412549i
$829$			4092.58i			0.171461i	0.996318	+	0.0857306i	$0.0273224\pi$
$829$			4092.58i			0.171461i	−0.996318	+	0.0857306i	$0.972678\pi$
$830$	−6096.06	−	3311.58i	−0.254937	−	0.138490i
$831$	42510.7	+	3314.51i	1.77458	+	0.138362i
$832$	−4440.50	−	28271.3i	−0.185032	−	1.17804i
$833$		−	22406.9i		−	0.931997i
$834$	14509.9	+	9412.22i	0.602441	+	0.390790i
$835$	14505.9			0.601193
$836$	−26576.7	+	17242.9i	−1.09949	+	0.713347i
$837$	417.891	+	99.3615i	0.0172574	+	0.00410327i
$838$	41931.2	+	22778.4i	1.72851	+	0.938983i
$839$	4781.01			0.196733			0.0983664	−	0.995150i	$-0.468638\pi$
$839$	4781.01			0.196733			0.0983664	+	0.995150i	$0.468638\pi$
$840$	−13562.8	+	1.16301i	−0.557095	+	4.77711e-5i
$841$	−24163.9			−0.990770
$842$	12599.4	+	6844.43i	0.515683	+	0.280136i
$843$	−11570.4	−	902.133i	−0.472724	−	0.0368578i
$844$	14145.5	+	21802.6i	0.576904	+	0.889188i
$845$	4635.88			0.188733
$846$	−2123.02	+	2773.90i	−0.0862777	+	0.112729i
$847$		−	43530.2i		−	1.76590i
$848$	17216.5	−	38580.0i	0.697191	−	1.56231i
$849$	−1710.12	+	21933.3i	−0.0691296	+	0.886630i
$850$	7356.28	+	3996.17i	0.296845	+	0.161256i
$851$		−	17289.6i		−	0.696450i
$852$	26539.1	−	14419.8i	1.06715	−	0.579831i
$853$		−	14703.4i		−	0.590194i	−0.955467	−	0.295097i	$-0.904648\pi$
$853$		−	14703.4i		−	0.590194i	0.955467	−	0.295097i	$-0.0953520\pi$
$854$	−26350.5	+	48506.8i	−1.05585	+	1.94364i
$855$	−9310.46	−	1460.73i	−0.372411	−	0.0584281i
$856$	117.054	+	1499.63i	0.00467386	+	0.0598790i
$857$		−	30204.4i		−	1.20392i	−0.798525	−	0.601962i	$-0.794386\pi$
$857$		−	30204.4i		−	1.20392i	0.798525	−	0.601962i	$-0.205614\pi$
$858$	39094.1	+	25359.4i	1.55554	+	1.00904i
$859$	8234.73			0.327084			0.163542	−	0.986536i	$-0.447708\pi$
$859$	8234.73			0.327084			0.163542	+	0.986536i	$0.447708\pi$
$860$	2523.58	+	3889.62i	0.100062	+	0.154227i
$861$	745.884	−	9566.43i	0.0295234	−	0.378656i
$862$	−11471.2	+	21116.5i	−0.453260	+	0.834375i
$863$	17940.1			0.707633			0.353817	−	0.935315i	$-0.384884\pi$
$863$	17940.1			0.707633			0.353817	+	0.935315i	$0.384884\pi$
$864$	23189.2	−	10355.4i	0.913092	−	0.407754i
$865$	−2430.43			−0.0955342
$866$	16828.5	−	30978.4i	0.660342	−	1.21558i
$867$	3677.15	−	47161.8i	0.144040	−	1.84740i
$868$	307.562	+	474.048i	0.0120269	+	0.0185372i
$869$	−38206.2			−1.49143
$870$	−924.964	−	600.002i	−0.0360451	−	0.0233816i
$871$			5933.38i			0.230821i
$872$	−648.345	−	8306.24i	−0.0251786	−	0.322574i
$873$	−20335.4	−	3190.45i	−0.788373	−	0.123689i
$874$	−4697.14	+	8646.63i	−0.181788	+	0.334642i
$875$		−	2883.84i		−	0.111419i
$876$	15601.4	−	8476.92i	0.601737	−	0.326951i
$877$			15368.6i			0.591746i	0.955227	+	0.295873i	$0.0956105\pi$
$877$			15368.6i			0.591746i	−0.955227	+	0.295873i	$0.904390\pi$
$878$	−36483.4	−	19819.0i	−1.40234	−	0.761799i
$879$	−1085.52	+	13922.4i	−0.0416536	+	0.534234i
$880$	16576.6	+	7397.39i	0.634995	+	0.283370i
$881$		−	14488.9i		−	0.554081i	−0.960858	−	0.277040i	$-0.910646\pi$
$881$		−	14488.9i		−	0.554081i	0.960858	−	0.277040i	$-0.0893536\pi$
$882$	8784.34	−	11477.5i	0.335356	−	0.438171i
$883$	−49860.8			−1.90028			−0.950140	−	0.311822i	$-0.899061\pi$
$883$	−49860.8			−1.90028			−0.950140	+	0.311822i	$0.899061\pi$
$884$	−28814.1	−	44411.4i	−1.09629	−	1.68973i
$885$	−10530.6	−	821.060i	−0.399980	−	0.0311860i
$886$	24674.4	+	13403.9i	0.935611	+	0.508255i
$887$	−29934.2			−1.13314			−0.566569	−	0.824015i	$-0.691729\pi$
$887$	−29934.2			−1.13314			−0.566569	+	0.824015i	$0.691729\pi$
$888$	−40791.1	+	3.49784i	−1.54151	+	0.000132185i
$889$	−29931.5			−1.12921
$890$	−15877.1	−	8624.97i	−0.597980	−	0.324842i
$891$	−12664.2	+	39366.2i	−0.476168	+	1.48015i
$892$	−8373.26	+	5432.56i	−0.314302	+	0.203919i
$893$	−3193.16			−0.119658
$894$	−23018.3	−	14931.4i	−0.861126	−	0.558593i
$895$			2721.47i			0.101641i
$896$	31476.9	+	11199.7i	1.17363	+	0.417584i
$897$	14430.1	+	1125.10i	0.537132	+	0.0418796i
$898$	−20222.3	−	10985.4i	−0.751476	−	0.408227i
$899$			45.9357i			0.00170416i
$900$	2201.45	+	4930.88i	0.0815352	+	0.182625i
$901$		−	78152.4i		−	2.88972i
$902$	−6130.31	+	11284.9i	−0.226294	+	0.416568i
$903$	−13853.6	−	1080.15i	−0.510541	−	0.0398063i
$904$	113.647	+	1455.98i	0.00418123	+	0.0535677i
$905$			17050.8i			0.626284i
$906$	−18897.9	+	29132.9i	−0.692979	+	1.06830i
$907$	2336.23			0.0855273			0.0427636	−	0.999085i	$-0.486384\pi$
$907$	2336.23			0.0855273			0.0427636	+	0.999085i	$0.486384\pi$
$908$	2032.71	−	1318.82i	0.0742927	−	0.0482010i
$909$	−29548.6	−	4635.93i	−1.07818	−	0.169158i
$910$	−8705.20	+	16024.8i	−0.317115	+	0.583755i
$911$	35814.8			1.30252			0.651261	−	0.758854i	$-0.274240\pi$
$911$	35814.8			1.30252			0.651261	+	0.758854i	$0.274240\pi$
$912$	20400.8	+	11080.1i	0.740723	+	0.402303i
$913$	−27827.0			−1.00870
$914$	13093.6	−	24103.1i	0.473848	−	0.872274i
$915$	21912.1	+	1708.46i	0.791685	+	0.0617268i
$916$	−2443.08	+	1585.07i	−0.0881242	+	0.0571749i
$917$	−50730.4			−1.82690
$918$	31367.1	−	34975.0i	1.12774	−	1.25746i
$919$			22895.7i			0.821829i	0.911674	+	0.410914i	$0.134790\pi$
$919$			22895.7i			0.821829i	−0.911674	+	0.410914i	$0.865210\pi$
$920$	5621.11	−	438.757i	0.201438	−	0.0157232i
$921$	−3176.04	+	40734.6i	−0.113631	+	1.45739i
$922$	−16411.1	+	30210.0i	−0.586193	+	1.07908i
$923$		−	40611.9i		−	1.44828i
$924$	−47801.5	+	25972.7i	−1.70190	+	0.924716i
$925$		−	8673.38i		−	0.308301i
$926$	−48052.0	−	26103.4i	−1.70528	−	0.926363i
$927$	−763.488	+	4866.34i	−0.0270509	+	0.172418i
$928$	1651.04	+	2156.45i	0.0584029	+	0.0762812i
$929$			11843.1i			0.418254i	0.977888	+	0.209127i	$0.0670622\pi$
$929$			11843.1i			0.418254i	−0.977888	+	0.209127i	$0.932938\pi$
$930$	122.439	−	188.752i	0.00431714	−	0.00665530i
$931$	13212.2			0.465104
$932$	1811.13	−	1175.06i	0.0636540	−	0.0412986i
$933$	−2507.71	+	32162.9i	−0.0879942	+	1.12858i
$934$	−6212.60	−	3374.89i	−0.217647	−	0.118233i
$935$	33579.6			1.17451
$936$	2651.51	−	34045.0i	0.0925934	−	1.18888i
$937$	−45489.6			−1.58600			−0.792999	−	0.609224i	$-0.791481\pi$
$937$	−45489.6			−1.58600			−0.792999	+	0.609224i	$0.791481\pi$
$938$	−6086.80	−	3306.55i	−0.211877	−	0.115099i
$939$	−332.979	+	4270.66i	−0.0115723	+	0.148421i
$940$	995.829	+	1534.88i	0.0345536	+	0.0532578i
$941$	14504.9			0.502492			0.251246	−	0.967923i	$-0.419160\pi$
$941$	14504.9			0.502492			0.251246	+	0.967923i	$0.419160\pi$
$942$	8286.69	−	12774.8i	0.286619	−	0.441852i
$943$			3988.95i			0.137750i
$944$	23760.8	+	10603.4i	0.819226	+	0.365584i
$945$	−15744.7	−	3743.61i	−0.541986	−	0.128867i
$946$	16342.1	+	8877.58i	0.561657	+	0.305111i
$947$			2304.38i			0.0790730i	0.999218	+	0.0395365i	$0.0125881\pi$
$947$			2304.38i			0.0790730i	−0.999218	+	0.0395365i	$0.987412\pi$
$948$	13366.8	+	24601.0i	0.457947	+	0.842831i
$949$		−	23874.3i		−	0.816643i
$950$	−2356.33	+	4337.61i	−0.0804733	+	0.148138i
$951$	1196.07	−	15340.3i	0.0407836	−	0.523075i
$952$	61617.3	−	4809.55i	2.09772	−	0.163738i
$953$			33511.7i			1.13909i	0.821962	+	0.569543i	$0.192880\pi$
$953$			33511.7i			1.13909i	−0.821962	+	0.569543i	$0.807120\pi$
$954$	30638.6	−	40031.9i	1.03979	−	1.35858i
$955$	3041.54			0.103060
$956$	8158.58	+	12574.9i	0.276012	+	0.425420i
$957$	−4408.97	−	343.763i	−0.148926	−	0.0116116i
$958$	−5642.43	+	10386.8i	−0.190291	+	0.350293i
$959$	29666.3			0.998932
$960$	−1036.29	−	13261.7i	−0.0348397	−	0.445854i
$961$	29781.6			0.999685
$962$	−26181.5	+	48195.8i	−0.877471	+	1.61527i
$963$	−278.197	+	1773.18i	−0.00930920	+	0.0593353i
$964$	−8853.48	−	13646.0i	−0.295800	−	0.455920i
$965$	20219.5			0.674497
$966$	−9195.80	+	14176.2i	−0.306284	+	0.472167i
$967$		−	26105.1i		−	0.868132i	−0.900881	−	0.434066i	$-0.857078\pi$
$967$		−	26105.1i		−	0.868132i	0.900881	−	0.434066i	$-0.142922\pi$
$968$	42564.2	−	3322.36i	1.41329	−	0.110315i
$969$	42816.2	+	3338.34i	1.41946	+	0.110674i
$970$	−5146.58	+	9473.98i	−0.170357	+	0.313599i
$971$		−	55315.6i		−	1.82818i	−0.405512	−	0.914090i	$-0.632907\pi$
$971$		−	55315.6i		−	1.82818i	0.405512	−	0.914090i	$-0.367093\pi$
$972$	29778.6	−	5618.17i	0.982664	−	0.185394i
$973$			27149.5i			0.894526i
$974$	−2212.91	−	1202.13i	−0.0727991	−	0.0395469i
$975$	7238.92	+	564.410i	0.237775	+	0.0185391i
$976$	−49441.6	−	22063.6i	−1.62150	−	0.723605i
$977$			5010.13i			0.164062i	0.996630	+	0.0820308i	$0.0261406\pi$
$977$			5010.13i			0.164062i	−0.996630	+	0.0820308i	$0.973859\pi$
$978$	29977.0	+	19445.4i	0.980120	+	0.635781i
$979$	−72475.1			−2.36600
$980$	−4120.40	−	6350.81i	−0.134307	−	0.207009i
$981$	1540.89	−	9821.37i	0.0501497	−	0.319645i
$982$	−31041.8	−	16862.9i	−1.00874	−	0.547982i
$983$	14082.5			0.456929			0.228464	−	0.973552i	$-0.426630\pi$
$983$	14082.5			0.456929			0.228464	+	0.973552i	$0.426630\pi$
$984$	9411.08	−	0.807002i	0.304893	−	2.61446e-5i
$985$	−9055.21			−0.292917
$986$	4414.78	+	2398.26i	0.142592	+	0.0774605i
$987$	−5466.76	−	426.237i	−0.176301	−	0.0137460i
$988$	26187.1	−	16990.2i	0.843242	−	0.547094i
$989$	5776.59			0.185728
$990$	17200.4	+	13164.4i	0.552187	+	0.422619i
$991$			11971.0i			0.383724i	0.981422	+	0.191862i	$0.0614526\pi$
$991$			11971.0i			0.383724i	−0.981422	+	0.191862i	$0.938547\pi$
$992$	−440.055	+	336.918i	−0.0140844	+	0.0107834i
$993$	−1177.57	+	15103.1i	−0.0376325	+	0.482660i
$994$	41662.0	+	22632.2i	1.32942	+	0.722183i
$995$			2993.81i			0.0953871i
$996$	9735.57	+	17917.9i	0.309722	+	0.570029i
$997$			35759.1i			1.13591i	0.823060	+	0.567955i	$0.192265\pi$
$997$			35759.1i			1.13591i	−0.823060	+	0.567955i	$0.807735\pi$
$998$	−20124.5	+	37045.9i	−0.638308	+	1.17502i
$999$	−47353.5	−	11259.2i	−1.49970	−	0.356582i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.b.b.11.15	yes	24
3.2	odd	2		120.4.b.a.11.10	yes	24
4.3	odd	2		480.4.b.a.431.11		24
8.3	odd	2		120.4.b.a.11.9	✓	24
8.5	even	2		480.4.b.b.431.11		24
12.11	even	2		480.4.b.b.431.12		24
24.5	odd	2		480.4.b.a.431.12		24
24.11	even	2	inner	120.4.b.b.11.16	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.b.a.11.9	✓	24	8.3	odd	2
120.4.b.a.11.10	yes	24	3.2	odd	2
120.4.b.b.11.15	yes	24	1.1	even	1	trivial
120.4.b.b.11.16	yes	24	24.11	even	2	inner
480.4.b.a.431.11		24	4.3	odd	2
480.4.b.a.431.12		24	24.5	odd	2
480.4.b.b.431.11		24	8.5	even	2
480.4.b.b.431.12		24	12.11	even	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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35014 - 2.48538i) q^{2} +(-0.403912 + 5.18043i) q^{3} +(-4.35424 - 6.71123i) q^{4} -5.00000 q^{5} +(12.3300 + 7.99819i) q^{6} +23.0707i q^{7} +(-22.5588 + 1.76083i) q^{8} +(-26.6737 - 4.18488i) q^{9} +O(q^{10})\)	\(q+(1.35014 - 2.48538i) q^{2} +(-0.403912 + 5.18043i) q^{3} +(-4.35424 - 6.71123i) q^{4} -5.00000 q^{5} +(12.3300 + 7.99819i) q^{6} +23.0707i q^{7} +(-22.5588 + 1.76083i) q^{8} +(-26.6737 - 4.18488i) q^{9} +(-6.75071 + 12.4269i) q^{10} +56.7258i q^{11} +(36.5258 - 19.8461i) q^{12} -55.8943i q^{13} +(57.3396 + 31.1488i) q^{14} +(2.01956 - 25.9021i) q^{15} +(-26.0812 + 58.4446i) q^{16} +118.393i q^{17} +(-46.4143 + 60.6442i) q^{18} -69.8100 q^{19} +(21.7712 + 33.5562i) q^{20} +(-119.516 - 9.31856i) q^{21} +(140.985 + 76.5878i) q^{22} +49.8352 q^{23} +(-0.0100821 - 117.576i) q^{24} +25.0000 q^{25} +(-138.919 - 75.4652i) q^{26} +(32.4533 - 136.491i) q^{27} +(154.833 - 100.456i) q^{28} +15.0035 q^{29} +(-61.6500 - 39.9909i) q^{30} +3.06167i q^{31} +(110.044 + 143.730i) q^{32} +(-293.864 - 22.9122i) q^{33} +(294.251 + 159.847i) q^{34} -115.354i q^{35} +(88.0580 + 197.235i) q^{36} -346.935i q^{37} +(-94.2534 + 173.505i) q^{38} +(289.557 + 22.5764i) q^{39} +(112.794 - 8.80416i) q^{40} +80.0429i q^{41} +(-184.524 + 284.462i) q^{42} +115.914 q^{43} +(380.700 - 246.997i) q^{44} +(133.369 + 20.9244i) q^{45} +(67.2846 - 123.859i) q^{46} +45.7407 q^{47} +(-292.234 - 158.718i) q^{48} -189.259 q^{49} +(33.7535 - 62.1345i) q^{50} +(-613.325 - 47.8203i) q^{51} +(-375.120 + 243.377i) q^{52} -660.112 q^{53} +(-295.415 - 264.941i) q^{54} -283.629i q^{55} +(-40.6237 - 520.448i) q^{56} +(28.1971 - 361.646i) q^{57} +(20.2568 - 37.2893i) q^{58} -406.553i q^{59} +(-182.629 + 99.2304i) q^{60} +845.957i q^{61} +(7.60943 + 4.13369i) q^{62} +(96.5483 - 615.382i) q^{63} +(505.799 - 79.4445i) q^{64} +279.472i q^{65} +(-453.703 + 699.429i) q^{66} -106.153 q^{67} +(794.561 - 515.510i) q^{68} +(-20.1291 + 258.168i) q^{69} +(-286.698 - 155.744i) q^{70} +726.584 q^{71} +(609.096 + 47.4380i) q^{72} +427.133 q^{73} +(-862.266 - 468.411i) q^{74} +(-10.0978 + 129.511i) q^{75} +(303.969 + 468.511i) q^{76} -1308.71 q^{77} +(447.053 - 689.177i) q^{78} +673.524i q^{79} +(130.406 - 292.223i) q^{80} +(693.974 + 223.253i) q^{81} +(198.937 + 108.069i) q^{82} +490.554i q^{83} +(457.864 + 842.677i) q^{84} -591.964i q^{85} +(156.500 - 288.090i) q^{86} +(-6.06008 + 77.7244i) q^{87} +(-99.8845 - 1279.67i) q^{88} +1277.64i q^{89} +(232.071 - 303.221i) q^{90} +1289.52 q^{91} +(-216.994 - 334.456i) q^{92} +(-15.8608 - 1.23665i) q^{93} +(61.7564 - 113.683i) q^{94} +349.050 q^{95} +(-789.032 + 512.019i) q^{96} +762.377 q^{97} +(-255.527 + 470.381i) q^{98} +(237.391 - 1513.09i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8}+O(q^{10}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8	\( 24 q + 3 q^{2} - 3 q^{4} - 120 q^{5} + 11 q^{6} - 21 q^{8} - 15 q^{10} - 33 q^{12} + 54 q^{14} + 153 q^{16} + 59 q^{18} + 12 q^{19} + 15 q^{20} + 4 q^{21} - 102 q^{22} - 228 q^{23} - 27 q^{24} + 600 q^{25} - 336 q^{26} + 132 q^{27} - 186 q^{28} - 55 q^{30} - 177 q^{32} + 116 q^{33} + 408 q^{34} + 641 q^{36} - 312 q^{38} + 656 q^{39} + 105 q^{40} - 1042 q^{42} + 450 q^{44} - 1104 q^{46} + 924 q^{47} - 717 q^{48} - 816 q^{49} + 75 q^{50} - 700 q^{51} - 1548 q^{52} - 528 q^{53} + 987 q^{54} + 390 q^{56} - 172 q^{57} + 1410 q^{58} + 165 q^{60} + 978 q^{62} - 476 q^{63} + 1137 q^{64} - 582 q^{66} + 1632 q^{67} + 1608 q^{68} - 980 q^{69} - 270 q^{70} - 216 q^{71} - 589 q^{72} - 216 q^{73} - 768 q^{74} - 1812 q^{76} - 324 q^{78} - 765 q^{80} + 152 q^{81} + 2244 q^{82} - 134 q^{84} + 2808 q^{86} - 252 q^{87} + 2622 q^{88} - 295 q^{90} - 1800 q^{91} + 1836 q^{92} - 1968 q^{94} - 60 q^{95} + 1445 q^{96} + 792 q^{97} - 4851 q^{98} - 1328 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 3 * q^4 - 120 * q^5 + 11 * q^6 - 21 * q^8 - 15 * q^10 - 33 * q^12 + 54 * q^14 + 153 * q^16 + 59 * q^18 + 12 * q^19 + 15 * q^20 + 4 * q^21 - 102 * q^22 - 228 * q^23 - 27 * q^24 + 600 * q^25 - 336 * q^26 + 132 * q^27 - 186 * q^28 - 55 * q^30 - 177 * q^32 + 116 * q^33 + 408 * q^34 + 641 * q^36 - 312 * q^38 + 656 * q^39 + 105 * q^40 - 1042 * q^42 + 450 * q^44 - 1104 * q^46 + 924 * q^47 - 717 * q^48 - 816 * q^49 + 75 * q^50 - 700 * q^51 - 1548 * q^52 - 528 * q^53 + 987 * q^54 + 390 * q^56 - 172 * q^57 + 1410 * q^58 + 165 * q^60 + 978 * q^62 - 476 * q^63 + 1137 * q^64 - 582 * q^66 + 1632 * q^67 + 1608 * q^68 - 980 * q^69 - 270 * q^70 - 216 * q^71 - 589 * q^72 - 216 * q^73 - 768 * q^74 - 1812 * q^76 - 324 * q^78 - 765 * q^80 + 152 * q^81 + 2244 * q^82 - 134 * q^84 + 2808 * q^86 - 252 * q^87 + 2622 * q^88 - 295 * q^90 - 1800 * q^91 + 1836 * q^92 - 1968 * q^94 - 60 * q^95 + 1445 * q^96 + 792 * q^97 - 4851 * q^98 - 1328 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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