LMFDB - Embedded newform 105.4.i.c.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(16,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("105.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.i (of order $3$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.646154928.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 11x^{4} - 8x^{3} + 121x^{2} - 44x + 16 $ x^6 + 11x^4 - 8x^3 + 121x^2 - 44x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$1.55859 - 2.69955i$ of defining polynomial
Character	$\chi$	$=$	105.16
Dual form			105.4.i.c.46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05859 + 3.56558i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.47557 - 7.75191i) q^{4} +(-2.50000 + 4.33013i) q^{5} -12.3515 q^{6} +(-9.40914 - 15.9521i) q^{7} +3.91601 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-2.05859 + 3.56558i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.47557 - 7.75191i) q^{4} +(-2.50000 + 4.33013i) q^{5} -12.3515 q^{6} +(-9.40914 - 15.9521i) q^{7} +3.91601 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-10.2929 - 17.8279i) q^{10} +(-7.99313 - 13.8445i) q^{11} +(13.4267 - 23.2557i) q^{12} -79.5076 q^{13} +(76.2479 - 0.710343i) q^{14} -15.0000 q^{15} +(27.7431 - 48.0525i) q^{16} +(34.7362 + 60.1649i) q^{17} +(-18.5273 - 32.0902i) q^{18} +(20.6015 - 35.6828i) q^{19} +44.7557 q^{20} +(27.3309 - 48.3738i) q^{21} +65.8183 q^{22} +(5.63966 - 9.76818i) q^{23} +(5.87401 + 10.1741i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(163.673 - 283.491i) q^{26} -27.0000 q^{27} +(-81.5477 + 144.333i) q^{28} +16.1213 q^{29} +(30.8788 - 53.4837i) q^{30} +(-35.5888 - 61.6416i) q^{31} +(129.887 + 224.971i) q^{32} +(23.9794 - 41.5335i) q^{33} -286.030 q^{34} +(92.5973 - 0.862658i) q^{35} +80.5603 q^{36} +(-178.238 + 308.717i) q^{37} +(84.8200 + 146.913i) q^{38} +(-119.261 - 206.567i) q^{39} +(-9.79002 + 16.9568i) q^{40} -426.478 q^{41} +(116.217 + 197.032i) q^{42} -346.164 q^{43} +(-71.5477 + 123.924i) q^{44} +(-22.5000 - 38.9711i) q^{45} +(23.2195 + 40.2173i) q^{46} +(-70.1765 + 121.549i) q^{47} +166.459 q^{48} +(-165.936 + 300.190i) q^{49} +102.929 q^{50} +(-104.209 + 180.495i) q^{51} +(355.842 + 616.336i) q^{52} +(-171.325 - 296.743i) q^{53} +(55.5819 - 96.2706i) q^{54} +79.9313 q^{55} +(-36.8463 - 62.4684i) q^{56} +123.609 q^{57} +(-33.1871 + 57.4817i) q^{58} +(384.259 + 665.557i) q^{59} +(67.1335 + 116.279i) q^{60} +(292.896 - 507.311i) q^{61} +293.051 q^{62} +(166.675 - 1.55278i) q^{63} -625.648 q^{64} +(198.769 - 344.278i) q^{65} +(98.7274 + 171.001i) q^{66} +(91.8419 + 159.075i) q^{67} +(310.929 - 538.545i) q^{68} +33.8380 q^{69} +(-187.544 + 331.939i) q^{70} -881.259 q^{71} +(-17.6220 + 30.5223i) q^{72} +(6.04661 + 10.4730i) q^{73} +(-733.836 - 1271.04i) q^{74} +(37.5000 - 64.9519i) q^{75} -368.814 q^{76} +(-145.640 + 257.772i) q^{77} +982.041 q^{78} +(591.821 - 1025.06i) q^{79} +(138.716 + 240.262i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(877.942 - 1520.64i) q^{82} -245.258 q^{83} +(-497.311 + 4.63306i) q^{84} -347.362 q^{85} +(712.610 - 1234.28i) q^{86} +(24.1819 + 41.8843i) q^{87} +(-31.3012 - 54.2153i) q^{88} +(-443.596 + 768.331i) q^{89} +185.273 q^{90} +(748.099 + 1268.31i) q^{91} -100.963 q^{92} +(106.766 - 184.925i) q^{93} +(-288.929 - 500.439i) q^{94} +(103.008 + 178.414i) q^{95} +(-389.662 + 674.914i) q^{96} +1371.47 q^{97} +(-728.759 - 1209.63i) q^{98} +143.876 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9	\( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9} - 15 q^{10} + q^{11} + 3 q^{12} - 158 q^{13} + 161 q^{14} - 90 q^{15} + 79 q^{16} + 72 q^{17} - 27 q^{18} + 29 q^{19} + 10 q^{20} - 39 q^{21} + 286 q^{22} + 63 q^{23} + 27 q^{24} - 75 q^{25} + 339 q^{26} - 162 q^{27} - 195 q^{28} + 440 q^{29} + 45 q^{30} - 136 q^{31} + 155 q^{32} - 3 q^{33} - 440 q^{34} - 55 q^{35} + 18 q^{36} - 43 q^{37} + 21 q^{38} - 237 q^{39} - 45 q^{40} - 1198 q^{41} - 42 q^{42} + 340 q^{43} - 135 q^{44} - 135 q^{45} - 265 q^{46} + 3 q^{47} + 474 q^{48} - 192 q^{49} + 150 q^{50} - 216 q^{51} + 701 q^{52} - 331 q^{53} + 81 q^{54} - 10 q^{55} - 1176 q^{56} + 174 q^{57} + 472 q^{58} + 1520 q^{59} + 15 q^{60} + 1160 q^{61} - 1496 q^{62} - 99 q^{63} + 34 q^{64} + 395 q^{65} + 429 q^{66} - 806 q^{67} + 684 q^{68} + 378 q^{69} - 875 q^{70} - 812 q^{71} - 81 q^{72} + 1192 q^{73} - 959 q^{74} + 225 q^{75} - 1182 q^{76} - 1309 q^{77} + 2034 q^{78} + 2590 q^{79} + 395 q^{80} - 243 q^{81} + 1191 q^{82} - 1016 q^{83} - 1629 q^{84} - 720 q^{85} + 742 q^{86} + 660 q^{87} + 749 q^{88} - 42 q^{89} + 270 q^{90} + 1346 q^{91} - 422 q^{92} + 408 q^{93} + 1167 q^{94} + 145 q^{95} - 465 q^{96} - 2040 q^{97} - 4053 q^{98} - 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9 - 15 * q^10 + q^11 + 3 * q^12 - 158 * q^13 + 161 * q^14 - 90 * q^15 + 79 * q^16 + 72 * q^17 - 27 * q^18 + 29 * q^19 + 10 * q^20 - 39 * q^21 + 286 * q^22 + 63 * q^23 + 27 * q^24 - 75 * q^25 + 339 * q^26 - 162 * q^27 - 195 * q^28 + 440 * q^29 + 45 * q^30 - 136 * q^31 + 155 * q^32 - 3 * q^33 - 440 * q^34 - 55 * q^35 + 18 * q^36 - 43 * q^37 + 21 * q^38 - 237 * q^39 - 45 * q^40 - 1198 * q^41 - 42 * q^42 + 340 * q^43 - 135 * q^44 - 135 * q^45 - 265 * q^46 + 3 * q^47 + 474 * q^48 - 192 * q^49 + 150 * q^50 - 216 * q^51 + 701 * q^52 - 331 * q^53 + 81 * q^54 - 10 * q^55 - 1176 * q^56 + 174 * q^57 + 472 * q^58 + 1520 * q^59 + 15 * q^60 + 1160 * q^61 - 1496 * q^62 - 99 * q^63 + 34 * q^64 + 395 * q^65 + 429 * q^66 - 806 * q^67 + 684 * q^68 + 378 * q^69 - 875 * q^70 - 812 * q^71 - 81 * q^72 + 1192 * q^73 - 959 * q^74 + 225 * q^75 - 1182 * q^76 - 1309 * q^77 + 2034 * q^78 + 2590 * q^79 + 395 * q^80 - 243 * q^81 + 1191 * q^82 - 1016 * q^83 - 1629 * q^84 - 720 * q^85 + 742 * q^86 + 660 * q^87 + 749 * q^88 - 42 * q^89 + 270 * q^90 + 1346 * q^91 - 422 * q^92 + 408 * q^93 + 1167 * q^94 + 145 * q^95 - 465 * q^96 - 2040 * q^97 - 4053 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−2.05859	+	3.56558i	−0.727821	+	1.26062i	0.229982	+	0.973195i	$0.426133\pi$
$2$	−2.05859	+	3.56558i	−0.727821	+	1.26062i	−0.957802	+	0.287428i	$0.907200\pi$
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$	−4.47557	−	7.75191i	−0.559446	−	0.968989i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$5$	−2.50000	+	4.33013i	−0.223607	+	0.387298i
$6$	−12.3515			−0.840415
$7$	−9.40914	−	15.9521i	−0.508046	−	0.861330i
$7$	−9.40914	−	15.9521i	−0.508046	−	0.861330i
$8$	3.91601			0.173065
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	−10.2929	−	17.8279i	−0.325491	−	0.563768i
$11$	−7.99313	−	13.8445i	−0.219093	−	0.379480i	0.735438	−	0.677592i	$-0.236976\pi$
$11$	−7.99313	−	13.8445i	−0.219093	−	0.379480i	−0.954531	+	0.298112i	$0.903643\pi$
$12$	13.4267	−	23.2557i	0.322996	−	0.559446i
$13$	−79.5076			−1.69627			−0.848133	−	0.529784i	$-0.822273\pi$
$13$	−79.5076			−1.69627			−0.848133	+	0.529784i	$0.822273\pi$
$14$	76.2479	−	0.710343i	1.45558	−	0.0135605i
$15$	−15.0000			−0.258199
$16$	27.7431	−	48.0525i	0.433486	−	0.750820i
$17$	34.7362	+	60.1649i	0.495575	+	0.858361i	0.999987	−	0.00510194i	$-0.00162401\pi$
$17$	34.7362	+	60.1649i	0.495575	+	0.858361i	−0.504412	+	0.863463i	$0.668291\pi$
$18$	−18.5273	−	32.0902i	−0.242607	−	0.420208i
$19$	20.6015	−	35.6828i	0.248753	−	0.430853i	−0.714427	−	0.699710i	$-0.753313\pi$
$19$	20.6015	−	35.6828i	0.248753	−	0.430853i	0.963180	+	0.268857i	$0.0866459\pi$
$20$	44.7557			0.500384
$21$	27.3309	−	48.3738i	0.284005	−	0.502668i
$22$	65.8183			0.637841
$23$	5.63966	−	9.76818i	0.0511283	−	0.0885568i	−0.839329	−	0.543624i	$-0.817052\pi$
$23$	5.63966	−	9.76818i	0.0511283	−	0.0885568i	0.890457	+	0.455068i	$0.150385\pi$
$24$	5.87401	+	10.1741i	0.0499595	+	0.0865324i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	163.673	−	283.491i	1.23458	−	2.13835i
$27$	−27.0000			−0.192450
$28$	−81.5477	+	144.333i	−0.550395	+	0.974159i
$29$	16.1213			0.103229			0.0516146	−	0.998667i	$-0.483563\pi$
$29$	16.1213			0.103229			0.0516146	+	0.998667i	$0.483563\pi$
$30$	30.8788	−	53.4837i	0.187923	−	0.325491i
$31$	−35.5888	−	61.6416i	−0.206192	−	0.357134i	0.744320	−	0.667823i	$-0.232774\pi$
$31$	−35.5888	−	61.6416i	−0.206192	−	0.357134i	−0.950512	+	0.310689i	$0.899440\pi$
$32$	129.887	+	224.971i	0.717533	+	1.24280i
$33$	23.9794	−	41.5335i	0.126493	−	0.219093i
$34$	−286.030			−1.44276
$35$	92.5973	−	0.862658i	0.447194	−	0.00416617i
$36$	80.5603			0.372964
$37$	−178.238	+	308.717i	−0.791948	+	1.37169i	0.132811	+	0.991141i	$0.457600\pi$
$37$	−178.238	+	308.717i	−0.791948	+	1.37169i	−0.924759	+	0.380553i	$0.875734\pi$
$38$	84.8200	+	146.913i	0.362095	+	0.627168i
$39$	−119.261	−	206.567i	−0.489670	−	0.848133i
$40$	−9.79002	+	16.9568i	−0.0386985	+	0.0670277i
$41$	−426.478			−1.62450			−0.812251	−	0.583307i	$-0.801758\pi$
$41$	−426.478			−1.62450			−0.812251	+	0.583307i	$0.801758\pi$
$42$	116.217	+	197.032i	0.426970	+	0.723875i
$43$	−346.164			−1.22766			−0.613832	−	0.789436i	$-0.710373\pi$
$43$	−346.164			−1.22766			−0.613832	+	0.789436i	$0.710373\pi$
$44$	−71.5477	+	123.924i	−0.245141	+	0.424597i
$45$	−22.5000	−	38.9711i	−0.0745356	−	0.129099i
$46$	23.2195	+	40.2173i	0.0744245	+	0.128907i
$47$	−70.1765	+	121.549i	−0.217793	+	0.377229i	−0.954133	−	0.299383i	$-0.903219\pi$
$47$	−70.1765	+	121.549i	−0.217793	+	0.377229i	0.736340	+	0.676612i	$0.236553\pi$
$48$	166.459			0.500547
$49$	−165.936	+	300.190i	−0.483778	+	0.875191i
$50$	102.929			0.291128
$51$	−104.209	+	180.495i	−0.286120	+	0.495575i
$52$	355.842	+	616.336i	0.948969	+	1.64366i
$53$	−171.325	−	296.743i	−0.444024	−	0.769072i	0.553960	−	0.832543i	$-0.313116\pi$
$53$	−171.325	−	296.743i	−0.444024	−	0.769072i	−0.997984	+	0.0634715i	$0.979783\pi$
$54$	55.5819	−	96.2706i	0.140069	−	0.242607i
$55$	79.9313			0.195963
$56$	−36.8463	−	62.4684i	−0.0879249	−	0.149066i
$57$	123.609			0.287235
$58$	−33.1871	+	57.4817i	−0.0751324	+	0.130133i
$59$	384.259	+	665.557i	0.847903	+	1.46861i	0.883076	+	0.469231i	$0.155469\pi$
$59$	384.259	+	665.557i	0.847903	+	1.46861i	−0.0351723	+	0.999381i	$0.511198\pi$
$60$	67.1335	+	116.279i	0.144448	+	0.250192i
$61$	292.896	−	507.311i	0.614779	−	1.06483i	−0.375645	−	0.926764i	$-0.622579\pi$
$61$	292.896	−	507.311i	0.614779	−	1.06483i	0.990423	−	0.138064i	$-0.0440880\pi$
$62$	293.051			0.600282
$63$	166.675	−	1.55278i	0.333319	−	0.00310528i
$64$	−625.648			−1.22197
$65$	198.769	−	344.278i	0.379296	−	0.656961i
$66$	98.7274	+	171.001i	0.184129	+	0.318921i
$67$	91.8419	+	159.075i	0.167467	+	0.290061i	0.937529	−	0.347908i	$-0.113108\pi$
$67$	91.8419	+	159.075i	0.167467	+	0.290061i	−0.770062	+	0.637969i	$0.779775\pi$
$68$	310.929	−	538.545i	0.554495	−	0.960414i
$69$	33.8380			0.0590379
$70$	−187.544	+	331.939i	−0.320225	+	0.566775i
$71$	−881.259			−1.47305			−0.736523	−	0.676413i	$-0.763533\pi$
$71$	−881.259			−1.47305			−0.736523	+	0.676413i	$0.763533\pi$
$72$	−17.6220	+	30.5223i	−0.0288441	+	0.0499595i
$73$	6.04661	+	10.4730i	0.00969455	+	0.0167914i	0.870832	−	0.491581i	$-0.163581\pi$
$73$	6.04661	+	10.4730i	0.00969455	+	0.0167914i	−0.861137	+	0.508372i	$0.830247\pi$
$74$	−733.836	−	1271.04i	−1.15279	−	1.99670i
$75$	37.5000	−	64.9519i	0.0577350	−	0.100000i
$76$	−368.814			−0.556656
$77$	−145.640	+	257.772i	−0.215548	+	0.381504i
$78$	982.041			1.42557
$79$	591.821	−	1025.06i	0.842848	−	1.45986i	−0.0446282	−	0.999004i	$-0.514210\pi$
$79$	591.821	−	1025.06i	0.842848	−	1.45986i	0.887477	−	0.460853i	$-0.152456\pi$
$80$	138.716	+	240.262i	0.193861	+	0.335777i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	877.942	−	1520.64i	1.18235	−	2.04789i
$83$	−245.258			−0.324344			−0.162172	−	0.986763i	$-0.551850\pi$
$83$	−245.258			−0.324344			−0.162172	+	0.986763i	$0.551850\pi$
$84$	−497.311	+	4.63306i	−0.645965	+	0.00601796i
$85$	−347.362			−0.443256
$86$	712.610	−	1234.28i	0.893520	−	1.54762i
$87$	24.1819	+	41.8843i	0.0297997	+	0.0516146i
$88$	−31.3012	−	54.2153i	−0.0379173	−	0.0656746i
$89$	−443.596	+	768.331i	−0.528327	+	0.915089i	0.471128	+	0.882065i	$0.343847\pi$
$89$	−443.596	+	768.331i	−0.528327	+	0.915089i	−0.999455	+	0.0330240i	$0.989486\pi$
$90$	185.273			0.216994
$91$	748.099	+	1268.31i	0.861781	+	1.46104i
$92$	−100.963			−0.114414
$93$	106.766	−	184.925i	0.119045	−	0.206192i
$94$	−288.929	−	500.439i	−0.317029	−	0.549111i
$95$	103.008	+	178.414i	0.111246	+	0.192683i
$96$	−389.662	+	674.914i	−0.414268	+	0.717533i
$97$	1371.47			1.43558			0.717790	−	0.696259i	$-0.245154\pi$
$97$	1371.47			1.43558			0.717790	+	0.696259i	$0.245154\pi$
$98$	−728.759	−	1209.63i	−0.751181	−	1.24684i
$99$	143.876			0.146062
$100$	−111.889	+	193.798i	−0.111889	+	0.193798i
$101$	466.653	+	808.267i	0.459740	+	0.796293i	0.998947	−	0.0458803i	$-0.0146093\pi$
$101$	466.653	+	808.267i	0.459740	+	0.796293i	−0.539207	+	0.842173i	$0.681276\pi$
$102$	−429.046	−	743.129i	−0.416489	−	0.721380i
$103$	−702.631	+	1216.99i	−0.672158	+	1.16421i	0.305133	+	0.952310i	$0.401299\pi$
$103$	−702.631	+	1216.99i	−0.672158	+	1.16421i	−0.977291	+	0.211902i	$0.932034\pi$
$104$	−311.353			−0.293564
$105$	141.137	+	239.281i	0.131177	+	0.222394i
$106$	1410.75			1.29268
$107$	−97.7332	+	169.279i	−0.0883012	+	0.152942i	−0.906793	−	0.421576i	$-0.861477\pi$
$107$	−97.7332	+	169.279i	−0.0883012	+	0.152942i	0.818492	+	0.574518i	$0.194810\pi$
$108$	120.840	+	209.302i	0.107665	+	0.186482i
$109$	−509.439	−	882.374i	−0.447664	−	0.775377i	0.550569	−	0.834789i	$-0.314411\pi$
$109$	−509.439	−	882.374i	−0.447664	−	0.775377i	−0.998234	+	0.0594125i	$0.981077\pi$
$110$	−164.546	+	285.002i	−0.142626	+	0.247035i
$111$	−1069.43			−0.914463
$112$	−1027.57	+	9.57312i	−0.866935	+	0.00807656i
$113$	120.447			0.100272			0.0501360	−	0.998742i	$-0.484035\pi$
$113$	120.447			0.100272			0.0501360	+	0.998742i	$0.484035\pi$
$114$	−254.460	+	440.738i	−0.209056	+	0.362095i
$115$	28.1983	+	48.8409i	0.0228653	+	0.0396038i
$116$	−72.1520	−	124.971i	−0.0577512	−	0.100028i
$117$	357.784	−	619.701i	0.282711	−	0.489670i
$118$	−3164.13			−2.46849
$119$	632.916	−	1120.21i	0.487557	−	0.862941i
$120$	−58.7401			−0.0446851
$121$	537.720	−	931.358i	0.403997	−	0.699743i
$122$	1205.90	+	2088.69i	0.894898	+	1.55001i
$123$	−639.716	−	1108.02i	−0.468954	−	0.812251i
$124$	−318.560	+	551.763i	−0.230706	+	0.399595i
$125$	125.000			0.0894427
$126$	−337.579	+	597.490i	−0.238682	+	0.422449i
$127$	388.485			0.271437			0.135718	−	0.990747i	$-0.456666\pi$
$127$	388.485			0.271437			0.135718	+	0.990747i	$0.456666\pi$
$128$	248.853	−	431.027i	0.171842	−	0.297638i
$129$	−519.247	−	899.362i	−0.354396	−	0.613832i
$130$	818.367	+	1417.45i	0.552120	+	0.956299i
$131$	−1098.66	+	1902.93i	−0.732748	+	1.26916i	0.222957	+	0.974828i	$0.428429\pi$
$131$	−1098.66	+	1902.93i	−0.732748	+	1.26916i	−0.955705	+	0.294328i	$0.904904\pi$
$132$	−429.286			−0.283065
$133$	−763.057	+	7.10882i	−0.497485	+	0.00463468i
$134$	−756.259			−0.487543
$135$	67.5000	−	116.913i	0.0430331	−	0.0745356i
$136$	136.027	+	235.606i	0.0857666	+	0.148552i
$137$	305.701	+	529.490i	0.190641	+	0.330200i	0.945463	−	0.325730i	$-0.105610\pi$
$137$	305.701	+	529.490i	0.190641	+	0.330200i	−0.754822	+	0.655930i	$0.772277\pi$
$138$	−69.6584	+	120.652i	−0.0429690	+	0.0744245i
$139$	1729.63			1.05544			0.527718	−	0.849420i	$-0.323048\pi$
$139$	1729.63			1.05544			0.527718	+	0.849420i	$0.323048\pi$
$140$	−421.113	−	713.945i	−0.254218	−	0.430996i
$141$	−421.059			−0.251486
$142$	1814.15	−	3142.20i	1.07211	−	1.85695i
$143$	635.515	+	1100.74i	0.371639	+	0.643698i
$144$	249.688	+	432.472i	0.144495	+	0.250273i
$145$	−40.3032	+	69.8072i	−0.0230828	+	0.0399805i
$146$	−49.7899			−0.0282236
$147$	−1028.82	+	19.1711i	−0.577250	+	0.0107565i
$148$	3190.86			1.77221
$149$	−64.0566	+	110.949i	−0.0352196	+	0.0610022i	−0.883098	−	0.469189i	$-0.844546\pi$
$149$	−64.0566	+	110.949i	−0.0352196	+	0.0610022i	0.847878	+	0.530191i	$0.177880\pi$
$150$	154.394	+	267.418i	0.0840415	+	0.145564i
$151$	1020.62	+	1767.77i	0.550047	+	0.952709i	0.998271	+	0.0587874i	$0.0187234\pi$
$151$	1020.62	+	1767.77i	0.550047	+	0.952709i	−0.448224	+	0.893921i	$0.647943\pi$
$152$	80.6757	−	139.734i	0.0430504	−	0.0745655i
$153$	−625.252			−0.330383
$154$	−619.294	−	1049.94i	−0.324053	−	0.549392i
$155$	355.888			0.184423
$156$	−1067.53	+	1849.01i	−0.547888	+	0.948969i
$157$	−1310.82	−	2270.41i	−0.666338	−	1.15413i	−0.978921	−	0.204241i	$-0.934527\pi$
$157$	−1310.82	−	2270.41i	−0.666338	−	1.15413i	0.312583	−	0.949891i	$-0.398806\pi$
$158$	2436.63	+	4220.37i	1.22689	+	2.12503i
$159$	513.974	−	890.230i	0.256357	−	0.444024i
$160$	−1298.87			−0.641781
$161$	−208.887	+	1.94604i	−0.102252	+	0.000952605i
$162$	333.491			0.161738
$163$	−387.823	+	671.729i	−0.186360	+	0.322785i	−0.944034	−	0.329848i	$-0.893002\pi$
$163$	−387.823	+	671.729i	−0.186360	+	0.322785i	0.757674	+	0.652633i	$0.226336\pi$
$164$	1908.73	+	3306.02i	0.908822	+	1.57413i
$165$	119.897	+	207.668i	0.0565695	+	0.0979813i
$166$	504.884	−	874.485i	0.236064	−	0.408875i
$167$	2591.61			1.20087			0.600434	−	0.799674i	$-0.294994\pi$
$167$	2591.61			1.20087			0.600434	+	0.799674i	$0.294994\pi$
$168$	107.028	−	189.432i	0.0491512	−	0.0869941i
$169$	4124.46			1.87731
$170$	715.076	−	1238.55i	0.322611	−	0.558778i
$171$	185.414	+	321.146i	0.0829177	+	0.143618i
$172$	1549.28	+	2683.44i	0.686812	+	1.18959i
$173$	302.068	−	523.198i	0.132750	−	0.229931i	−0.791985	−	0.610540i	$-0.790952\pi$
$173$	302.068	−	523.198i	0.132750	−	0.229931i	0.924736	+	0.380609i	$0.124286\pi$
$174$	−199.123			−0.0867554
$175$	−227.758	+	403.115i	−0.0983821	+	0.174129i
$176$	−887.018			−0.379895
$177$	−1152.78	+	1996.67i	−0.489537	+	0.847903i
$178$	−1826.36	−	3163.35i	−0.769055	−	1.33204i
$179$	−1467.30	−	2541.44i	−0.612688	−	1.06121i	−0.990785	−	0.135441i	$-0.956755\pi$
$179$	−1467.30	−	2541.44i	−0.612688	−	1.06121i	0.378097	−	0.925766i	$-0.376578\pi$
$180$	−201.401	+	348.836i	−0.0833973	+	0.144448i
$181$	−3400.10			−1.39628			−0.698141	−	0.715960i	$-0.745989\pi$
$181$	−3400.10			−1.39628			−0.698141	+	0.715960i	$0.745989\pi$
$182$	−6062.29	+	56.4777i	−2.46905	+	0.0230022i
$183$	1757.38			0.709885
$184$	22.0850	−	38.2523i	0.00884851	−	0.0153261i
$185$	−891.188	−	1543.58i	−0.354170	−	0.613441i
$186$	439.576	+	761.368i	0.173286	+	0.300141i
$187$	555.303	−	961.813i	0.217154	−	0.376122i
$188$	1256.32			0.487375
$189$	254.047	+	430.705i	0.0977735	+	0.165763i
$190$	−848.200			−0.323868
$191$	1750.06	−	3031.19i	0.662984	−	1.14832i	−0.316844	−	0.948478i	$-0.602623\pi$
$191$	1750.06	−	3031.19i	0.662984	−	1.14832i	0.979828	−	0.199844i	$-0.0640436\pi$
$192$	−938.472	−	1625.48i	−0.352752	−	0.610984i
$193$	−1588.61	−	2751.56i	−0.592492	−	1.02623i	−0.993896	−	0.110324i	$-0.964811\pi$
$193$	−1588.61	−	2751.56i	−0.592492	−	1.02623i	0.401404	−	0.915901i	$-0.368522\pi$
$194$	−2823.28	+	4890.07i	−1.04485	+	1.80973i
$195$	1192.61			0.437974
$196$	3069.71	−	57.2012i	1.11870	−	0.0208459i
$197$	−5271.00			−1.90631			−0.953156	−	0.302479i	$-0.902186\pi$
$197$	−5271.00			−1.90631			−0.953156	+	0.302479i	$0.902186\pi$
$198$	−296.182	+	513.003i	−0.106307	+	0.184129i
$199$	2166.08	+	3751.76i	0.771605	+	1.33646i	0.936683	+	0.350179i	$0.113879\pi$
$199$	2166.08	+	3751.76i	0.771605	+	1.33646i	−0.165078	+	0.986281i	$0.552788\pi$
$200$	−48.9501	−	84.7841i	−0.0173065	−	0.0299757i
$201$	−275.526	+	477.225i	−0.0966870	+	0.167467i
$202$	−3842.59			−1.33843
$203$	−151.688	−	257.168i	−0.0524452	−	0.0889145i
$204$	1865.57			0.640276
$205$	1066.19	−	1846.70i	0.363250	−	0.629167i
$206$	−2892.86	−	5010.57i	−0.978421	−	1.69468i
$207$	50.7570	+	87.9136i	0.0170428	+	0.0295189i
$208$	−2205.79	+	3820.54i	−0.735307	+	1.27359i
$209$	−658.682			−0.218000
$210$	−1143.72	+	10.6551i	−0.375829	+	0.00350131i
$211$	524.642			0.171175			0.0855874	−	0.996331i	$-0.472723\pi$
$211$	524.642			0.171175			0.0855874	+	0.996331i	$0.472723\pi$
$212$	−1533.55	+	2656.19i	−0.496815	+	0.860509i
$213$	−1321.89	−	2289.58i	−0.425232	−	0.736523i
$214$	−402.385	−	696.951i	−0.128535	−	0.222629i
$215$	865.411	−	1498.94i	0.274514	−	0.475473i
$216$	−105.732			−0.0333063
$217$	−648.450	+	1147.71i	−0.202856	+	0.359040i
$218$	4194.90			1.30328
$219$	−18.1398	+	31.4191i	−0.00559715	+	0.00969455i
$220$	−357.738	−	619.621i	−0.109631	−	0.189886i
$221$	−2761.80	−	4783.57i	−0.840627	−	1.45601i
$222$	2201.51	−	3813.12i	0.665565	−	1.15279i
$223$	4731.48			1.42082			0.710411	−	0.703787i	$-0.248509\pi$
$223$	4731.48			1.42082			0.710411	+	0.703787i	$0.248509\pi$
$224$	2366.63	−	4188.76i	0.705924	−	1.24943i
$225$	225.000			0.0666667
$226$	−247.952	+	429.465i	−0.0729800	+	0.126405i
$227$	186.087	+	322.312i	0.0544098	+	0.0942406i	0.891947	−	0.452139i	$-0.149339\pi$
$227$	186.087	+	322.312i	0.0544098	+	0.0942406i	−0.837538	+	0.546380i	$0.816006\pi$
$228$	−553.221	−	958.206i	−0.160693	−	0.278328i
$229$	−1155.39	+	2001.19i	−0.333407	+	0.577477i	−0.983177	−	0.182653i	$-0.941531\pi$
$229$	−1155.39	+	2001.19i	−0.333407	+	0.577477i	0.649771	+	0.760130i	$0.274865\pi$
$230$	−232.195			−0.0665673
$231$	−888.171	+	8.27441i	−0.252976	+	0.00235678i
$232$	63.1311			0.0178654
$233$	−113.130	+	195.947i	−0.0318086	+	0.0550940i	−0.881491	−	0.472200i	$-0.843460\pi$
$233$	−113.130	+	195.947i	−0.0318086	+	0.0550940i	0.849683	+	0.527294i	$0.176793\pi$
$234$	1473.06	+	2551.42i	0.411526	+	0.712783i
$235$	−350.882	−	607.746i	−0.0974002	−	0.168702i
$236$	3439.56	−	5957.49i	0.948713	−	1.64322i
$237$	3550.92			0.973238
$238$	2691.30	+	4562.77i	0.732988	+	1.24269i
$239$	−729.570			−0.197456			−0.0987279	−	0.995114i	$-0.531477\pi$
$239$	−729.570			−0.197456			−0.0987279	+	0.995114i	$0.531477\pi$
$240$	−416.147	+	720.787i	−0.111926	+	0.193861i
$241$	669.850	+	1160.21i	0.179041	+	0.310108i	0.941552	−	0.336867i	$-0.109367\pi$
$241$	669.850	+	1160.21i	0.179041	+	0.310108i	−0.762511	+	0.646975i	$0.776034\pi$
$242$	2213.89	+	3834.56i	0.588074	+	1.01857i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−5243.51			−1.37574
$245$	−885.022	−	1469.00i	−0.230784	−	0.383065i
$246$	5267.65			1.36526
$247$	−1637.98	+	2837.06i	−0.421951	+	0.730841i
$248$	−139.366	−	241.389i	−0.0356845	−	0.0618074i
$249$	−367.886	−	637.198i	−0.0936299	−	0.162172i
$250$	−257.324	+	445.697i	−0.0650983	+	0.112754i
$251$	6429.19			1.61676			0.808381	−	0.588660i	$-0.200344\pi$
$251$	6429.19			1.61676			0.808381	+	0.588660i	$0.200344\pi$
$252$	−758.003	−	1285.10i	−0.189483	−	0.321245i
$253$	−180.314			−0.0448074
$254$	−799.730	+	1385.17i	−0.197557	+	0.342179i
$255$	−521.044	−	902.474i	−0.127957	−	0.221628i
$256$	−1478.02	−	2560.00i	−0.360845	−	0.625001i
$257$	938.643	−	1625.78i	0.227825	−	0.394604i	−0.729338	−	0.684153i	$-0.760172\pi$
$257$	938.643	−	1625.78i	0.227825	−	0.394604i	0.957163	+	0.289549i	$0.0935054\pi$
$258$	4275.66			1.03175
$259$	6601.73	−	61.5032i	1.58383	−	0.0147553i
$260$	−3558.42			−0.848784
$261$	−72.5458	+	125.653i	−0.0172049	+	0.0297997i
$262$	−4523.36	−	7834.68i	−1.06662	−	1.84744i
$263$	−3735.90	−	6470.77i	−0.875915	−	1.51713i	−0.855785	−	0.517331i	$-0.826925\pi$
$263$	−3735.90	−	6470.77i	−0.875915	−	1.51713i	−0.0201295	−	0.999797i	$-0.506408\pi$
$264$	93.9036	−	162.646i	0.0218915	−	0.0379173i
$265$	1713.25			0.397147
$266$	1545.47	−	2735.37i	0.356237	−	0.630514i
$267$	−2661.58			−0.610059
$268$	822.090	−	1423.90i	0.187377	−	0.324547i
$269$	1625.68	+	2815.76i	0.368473	+	0.638214i	0.989327	−	0.145712i	$-0.0465473\pi$
$269$	1625.68	+	2815.76i	0.368473	+	0.638214i	−0.620854	+	0.783926i	$0.713214\pi$
$270$	277.909	+	481.353i	0.0626408	+	0.108497i
$271$	−1032.99	+	1789.19i	−0.231549	+	0.401054i	−0.958264	−	0.285885i	$-0.907713\pi$
$271$	−1032.99	+	1789.19i	−0.231549	+	0.401054i	0.726715	+	0.686939i	$0.241046\pi$
$272$	3854.77			0.859300
$273$	−2173.02	+	3846.08i	−0.481747	+	0.852657i
$274$	−2517.25			−0.555009
$275$	−199.828	+	346.113i	−0.0438186	+	0.0758960i
$276$	−151.444	−	262.309i	−0.0330285	−	0.0572071i
$277$	1105.16	+	1914.20i	0.239722	+	0.415210i	0.960634	−	0.277816i	$-0.0896105\pi$
$277$	1105.16	+	1914.20i	0.239722	+	0.415210i	−0.720913	+	0.693026i	$0.756277\pi$
$278$	−3560.60	+	6167.15i	−0.768168	+	1.33051i
$279$	640.598			0.137461
$280$	362.612	−	3.37818i	0.0773936	−	0.000721017i
$281$	−41.6488			−0.00884184			−0.00442092	−	0.999990i	$-0.501407\pi$
$281$	−41.6488			−0.00884184			−0.00442092	+	0.999990i	$0.501407\pi$
$282$	866.787	−	1501.32i	0.183037	−	0.317029i
$283$	258.425	+	447.605i	0.0542818	+	0.0940189i	0.891889	−	0.452253i	$-0.149380\pi$
$283$	258.425	+	447.605i	0.0542818	+	0.0940189i	−0.837608	+	0.546272i	$0.816046\pi$
$284$	3944.14	+	6831.44i	0.824090	+	1.42736i
$285$	−309.023	+	535.243i	−0.0642278	+	0.111246i
$286$	−5233.06			−1.08195
$287$	4012.79	+	6803.19i	0.825322	+	1.39923i
$288$	−2337.97			−0.478355
$289$	43.2869	−	74.9751i	0.00881068	−	0.0152605i
$290$	−165.936	−	287.409i	−0.0336002	−	0.0581973i
$291$	2057.20	+	3563.17i	0.414416	+	0.717790i
$292$	54.1240	−	93.7456i	0.0108472	−	0.0187878i
$293$	−4607.40			−0.918660			−0.459330	−	0.888266i	$-0.651910\pi$
$293$	−4607.40			−0.918660			−0.459330	+	0.888266i	$0.651910\pi$
$294$	2049.56	−	3707.81i	0.406575	−	0.735523i
$295$	−3842.59			−0.758388
$296$	−697.980	+	1208.94i	−0.137058	+	0.237392i
$297$	215.815	+	373.802i	0.0421644	+	0.0730309i
$298$	−263.732	−	456.798i	−0.0512671	−	0.0887973i
$299$	−448.396	+	776.645i	−0.0867271	+	0.150216i
$300$	−671.335			−0.129199
$301$	3257.11	+	5522.03i	0.623710	+	1.05742i
$302$	−8404.16			−1.60134
$303$	−1399.96	+	2424.80i	−0.265431	+	0.459740i
$304$	−1143.10	−	1979.91i	−0.215662	−	0.373538i
$305$	1464.48	+	2536.55i	0.274937	+	0.476206i
$306$	1287.14	−	2229.39i	0.240460	−	0.416489i
$307$	−2429.76			−0.451707			−0.225853	−	0.974161i	$-0.572517\pi$
$307$	−2429.76			−0.451707			−0.225853	+	0.974161i	$0.572517\pi$
$308$	2650.05	−	24.6885i	0.490261	−	0.00456739i
$309$	−4215.79			−0.776141
$310$	−732.627	+	1268.95i	−0.134227	+	0.232488i
$311$	1871.05	+	3240.75i	0.341149	+	0.590887i	0.984646	−	0.174561i	$-0.0558506\pi$
$311$	1871.05	+	3240.75i	0.341149	+	0.590887i	−0.643497	+	0.765448i	$0.722517\pi$
$312$	−467.029	−	808.918i	−0.0847446	−	0.146782i
$313$	1880.61	−	3257.32i	0.339612	−	0.588225i	−0.644748	−	0.764396i	$-0.723038\pi$
$313$	1880.61	−	3257.32i	0.339612	−	0.588225i	0.984360	+	0.176170i	$0.0563709\pi$
$314$	10793.8			1.93990
$315$	−409.964	+	725.606i	−0.0733297	+	0.129788i
$316$	−10594.9			−1.88611
$317$	1287.78	−	2230.50i	0.228167	−	0.395197i	−0.729098	−	0.684409i	$-0.760060\pi$
$317$	1287.78	−	2230.50i	0.228167	−	0.395197i	0.957265	+	0.289212i	$0.0933934\pi$
$318$	2116.12	+	3665.23i	0.373164	+	0.646340i
$319$	−128.860	−	223.191i	−0.0226168	−	0.0391734i
$320$	1564.12	−	2709.14i	0.273241	−	0.473267i
$321$	−586.399			−0.101961
$322$	423.073	−	748.809i	0.0732204	−	0.129595i
$323$	2862.48			0.493103
$324$	−362.521	+	627.905i	−0.0621607	+	0.107665i
$325$	993.845	+	1721.39i	0.169627	+	0.293802i
$326$	−1596.74	−	2765.63i	−0.271273	−	0.469859i
$327$	1528.32	−	2647.12i	0.258459	−	0.447664i
$328$	−1670.09			−0.281144
$329$	2599.26	−	24.2153i	0.435568	−	0.00405785i
$330$	−987.274			−0.164690
$331$	−5219.73	+	9040.83i	−0.866774	+	1.50130i	−0.00149822	+	0.999999i	$0.500477\pi$
$331$	−5219.73	+	9040.83i	−0.866774	+	1.50130i	−0.865275	+	0.501297i	$0.832856\pi$
$332$	1097.67	+	1901.22i	0.181453	+	0.314285i
$333$	−1604.14	−	2778.45i	−0.263983	−	0.457232i
$334$	−5335.06	+	9240.60i	−0.874017	+	1.51384i
$335$	−918.419			−0.149787
$336$	−1566.23	−	2655.36i	−0.254301	−	0.431136i
$337$	−11248.3			−1.81820			−0.909099	−	0.416579i	$-0.863229\pi$
$337$	−11248.3			−1.81820			−0.909099	+	0.416579i	$0.863229\pi$
$338$	−8490.57	+	14706.1i	−1.36635	+	2.36659i
$339$	180.671	+	312.931i	0.0289460	+	0.0501360i
$340$	1554.64	+	2692.72i	0.247978	+	0.429510i
$341$	−568.932	+	985.420i	−0.0903502	+	0.156491i
$342$	−1526.76			−0.241397
$343$	6349.97	−	177.514i	0.999609	−	0.0279443i
$344$	−1355.58			−0.212466
$345$	−84.5949	+	146.523i	−0.0132013	+	0.0228653i
$346$	1243.67	+	2154.10i	0.193237	+	0.334697i
$347$	182.062	+	315.341i	0.0281660	+	0.0487849i	0.879765	−	0.475409i	$-0.157700\pi$
$347$	182.062	+	315.341i	0.0281660	+	0.0487849i	−0.851599	+	0.524194i	$0.824367\pi$
$348$	216.456	−	374.913i	0.0333427	−	0.0577512i
$349$	−8924.17			−1.36877			−0.684383	−	0.729122i	$-0.739929\pi$
$349$	−8924.17			−1.36877			−0.684383	+	0.729122i	$0.739929\pi$
$350$	−968.478	−	1641.94i	−0.147907	−	0.250758i
$351$	2146.71			0.326446
$352$	2076.41	−	3596.45i	0.314413	−	0.544578i
$353$	−2526.23	−	4375.56i	−0.380900	−	0.659739i	0.610291	−	0.792177i	$-0.291053\pi$
$353$	−2526.23	−	4375.56i	−0.380900	−	0.659739i	−0.991191	+	0.132439i	$0.957719\pi$
$354$	−4746.19	−	8220.64i	−0.712591	−	1.23424i
$355$	2203.15	−	3815.96i	0.329383	−	0.570508i
$356$	7941.38			1.18228
$357$	3859.78	−	35.9586i	0.572216	−	0.00533090i
$358$	12082.3			1.78371
$359$	−992.667	+	1719.35i	−0.145936	+	0.252768i	−0.929722	−	0.368263i	$-0.879953\pi$
$359$	−992.667	+	1719.35i	−0.145936	+	0.252768i	0.783786	+	0.621031i	$0.213286\pi$
$360$	−88.1102	−	152.611i	−0.0128995	−	0.0223426i
$361$	2580.66	+	4469.83i	0.376244	+	0.651673i
$362$	6999.40	−	12123.3i	1.01624	−	1.76018i
$363$	3226.32			0.466495
$364$	6483.66	−	11475.6i	0.933616	−	1.65243i
$365$	−60.4661			−0.00867107
$366$	−3617.71	+	6266.07i	−0.516669	+	0.894898i
$367$	−4426.76	−	7667.38i	−0.629633	−	1.09056i	−0.987625	−	0.156831i	$-0.949872\pi$
$367$	−4426.76	−	7667.38i	−0.629633	−	1.09056i	0.357993	−	0.933724i	$-0.383461\pi$
$368$	−312.924	−	541.999i	−0.0443268	−	0.0767763i
$369$	1919.15	−	3324.06i	0.270750	−	0.468954i
$370$	7338.36			1.03109
$371$	−3121.64	+	5525.08i	−0.436840	+	0.773175i
$372$	−1911.36			−0.266397
$373$	4361.57	−	7554.46i	0.605452	−	1.04867i	−0.386528	−	0.922278i	$-0.626326\pi$
$373$	4361.57	−	7554.46i	0.605452	−	1.04867i	0.991980	−	0.126396i	$-0.0403409\pi$
$374$	2286.28	+	3959.95i	0.316098	+	0.547498i
$375$	187.500	+	324.760i	0.0258199	+	0.0447214i
$376$	−274.812	+	475.988i	−0.0376924	+	0.0652851i
$377$	−1281.77			−0.175104
$378$	−2058.69	+	19.1793i	−0.280126	+	0.00260972i
$379$	−4239.97			−0.574651			−0.287325	−	0.957833i	$-0.592766\pi$
$379$	−4239.97			−0.574651			−0.287325	+	0.957833i	$0.592766\pi$
$380$	922.035	−	1597.01i	0.124472	−	0.215592i
$381$	582.727	+	1009.31i	0.0783570	+	0.135718i
$382$	7205.31	+	12480.0i	0.965067	+	1.67155i
$383$	6627.61	−	11479.4i	0.884217	−	1.53151i	0.0376075	−	0.999293i	$-0.488026\pi$
$383$	6627.61	−	11479.4i	0.884217	−	1.53151i	0.846609	−	0.532215i	$-0.178640\pi$
$384$	1493.12			0.198426
$385$	−752.086	−	1275.07i	−0.0995580	−	0.168788i
$386$	13081.2			1.72491
$387$	1557.74	−	2698.09i	0.204611	−	0.354396i
$388$	−6138.09	−	10631.5i	−0.803130	−	1.39106i
$389$	−1787.34	−	3095.76i	−0.232961	−	0.403500i	0.725717	−	0.687993i	$-0.241508\pi$
$389$	−1787.34	−	3095.76i	−0.232961	−	0.403500i	−0.958678	+	0.284493i	$0.908175\pi$
$390$	−2455.10	+	4252.36i	−0.318766	+	0.552120i
$391$	783.603			0.101352
$392$	−649.807	+	1175.55i	−0.0837250	+	0.151465i
$393$	−6591.93			−0.846104
$394$	10850.8	−	18794.2i	1.38745	−	2.40314i
$395$	2959.10	+	5125.32i	0.376933	+	0.652868i
$396$	−643.929	−	1115.32i	−0.0817138	−	0.141532i
$397$	732.897	−	1269.42i	0.0926526	−	0.160479i	−0.815974	−	0.578089i	$-0.803799\pi$
$397$	732.897	−	1269.42i	0.0926526	−	0.160479i	0.908626	+	0.417610i	$0.137132\pi$
$398$	−17836.3			−2.24636
$399$	−1163.06	−	1971.82i	−0.145929	−	0.247404i
$400$	−1387.16			−0.173394
$401$	−4921.48	+	8524.26i	−0.612886	+	1.06155i	0.377866	+	0.925860i	$0.376658\pi$
$401$	−4921.48	+	8524.26i	−0.612886	+	1.06155i	−0.990752	+	0.135689i	$0.956675\pi$
$402$	−1134.39	−	1964.82i	−0.140742	−	0.243772i
$403$	2829.58	+	4900.98i	0.349755	+	0.605794i
$404$	4177.08	−	7234.91i	0.514400	−	0.890966i
$405$	405.000			0.0496904
$406$	1229.21	−	11.4516i	0.150258	−	0.00139984i
$407$	5698.71			0.694041
$408$	−408.082	+	706.819i	−0.0495174	+	0.0857666i
$409$	846.229	+	1465.71i	0.102306	+	0.177200i	0.912635	−	0.408776i	$-0.134044\pi$
$409$	846.229	+	1465.71i	0.102306	+	0.177200i	−0.810328	+	0.585976i	$0.800711\pi$
$410$	4389.71	+	7603.20i	0.528762	+	0.915842i
$411$	−917.103	+	1588.47i	−0.110067	+	0.190641i
$412$	12578.7			1.50415
$413$	7001.44	−	12392.0i	0.834185	−	1.47645i
$414$	−417.951			−0.0496163
$415$	613.144	−	1062.00i	0.0725254	−	0.125618i
$416$	−10327.0	−	17886.9i	−1.21713	−	2.10812i
$417$	2594.45	+	4493.72i	0.304678	+	0.527718i
$418$	1355.96	−	2348.58i	0.158665	−	0.274816i
$419$	−7849.48			−0.915209			−0.457604	−	0.889156i	$-0.651292\pi$
$419$	−7849.48			−0.915209			−0.457604	+	0.889156i	$0.651292\pi$
$420$	1223.21	−	2165.00i	0.142111	−	0.251527i
$421$	−14050.7			−1.62658			−0.813289	−	0.581860i	$-0.802325\pi$
$421$	−14050.7			−1.62658			−0.813289	+	0.581860i	$0.802325\pi$
$422$	−1080.02	+	1870.65i	−0.124585	+	0.215787i
$423$	−631.588	−	1093.94i	−0.0725978	−	0.125743i
$424$	−670.909	−	1162.05i	−0.0768449	−	0.133099i
$425$	868.406	−	1504.12i	0.0991150	−	0.171672i
$426$	10884.9			1.23797
$427$	−10848.6	+	101.068i	−1.22950	+	0.0114543i
$428$	1749.65			0.197599
$429$	−1906.55	+	3302.23i	−0.214566	+	0.371639i
$430$	3563.05	+	6171.38i	0.399594	+	0.692118i
$431$	−7337.26	−	12708.5i	−0.820008	−	1.42030i	−0.905675	−	0.423972i	$-0.860636\pi$
$431$	−7337.26	−	12708.5i	−0.820008	−	1.42030i	0.0856676	−	0.996324i	$-0.472698\pi$
$432$	−749.064	+	1297.42i	−0.0834244	+	0.144495i
$433$	3566.95			0.395881			0.197941	−	0.980214i	$-0.436575\pi$
$433$	3566.95			0.395881			0.197941	+	0.980214i	$0.436575\pi$
$434$	−2757.36	−	4674.76i	−0.304971	−	0.517041i
$435$	−241.819			−0.0266537
$436$	−4560.06	+	7898.25i	−0.500888	+	0.867563i
$437$	−232.371	−	402.478i	−0.0254366	−	0.0440576i
$438$	−74.6849	−	129.358i	−0.00814744	−	0.0141118i
$439$	−3411.71	+	5909.25i	−0.370916	+	0.642445i	−0.989707	−	0.143111i	$-0.954289\pi$
$439$	−3411.71	+	5909.25i	−0.370916	+	0.642445i	0.618791	+	0.785556i	$0.287623\pi$
$440$	313.012			0.0339142
$441$	−1593.04	−	2644.20i	−0.172016	−	0.285520i
$442$	22741.6			2.44730
$443$	−8078.12	+	13991.7i	−0.866372	+	1.50060i	−0.000693841		1.00000i	$0.500221\pi$
$443$	−8078.12	+	13991.7i	−0.866372	+	1.50060i	−0.865678	+	0.500601i	$0.833112\pi$
$444$	4786.29	+	8290.10i	0.511593	+	0.886105i
$445$	−2217.98	−	3841.65i	−0.236275	−	0.409240i
$446$	−9740.17	+	16870.5i	−1.03410	+	1.79112i
$447$	−384.340			−0.0406681
$448$	5886.81	+	9980.37i	0.620816	+	1.05252i
$449$	−16762.3			−1.76183			−0.880917	−	0.473271i	$-0.843073\pi$
$449$	−16762.3			−1.76183			−0.880917	+	0.473271i	$0.843073\pi$
$450$	−463.182	+	802.255i	−0.0485214	+	0.0840415i
$451$	3408.89	+	5904.38i	0.355917	+	0.616466i
$452$	−539.071	−	933.698i	−0.0560968	−	0.0971625i
$453$	−3061.87	+	5303.31i	−0.317570	+	0.550047i
$454$	−1532.31			−0.158402
$455$	−7362.19	+	68.5879i	−0.758560	+	0.00706692i
$456$	484.054			0.0497103
$457$	8292.83	−	14363.6i	0.848845	−	1.47024i	−0.0333945	−	0.999442i	$-0.510632\pi$
$457$	8292.83	−	14363.6i	0.848845	−	1.47024i	0.882240	−	0.470801i	$-0.156035\pi$
$458$	−4756.93	−	8239.24i	−0.485320	−	0.840600i
$459$	−937.879	−	1624.45i	−0.0953735	−	0.165192i
$460$	252.407	−	437.182i	0.0255838	−	0.0443124i
$461$	3423.02			0.345826			0.172913	−	0.984937i	$-0.444682\pi$
$461$	3423.02			0.345826			0.172913	+	0.984937i	$0.444682\pi$
$462$	1798.88	−	3183.88i	0.181150	−	0.320622i
$463$	−5522.24			−0.554299			−0.277149	−	0.960827i	$-0.589390\pi$
$463$	−5522.24			−0.554299			−0.277149	+	0.960827i	$0.589390\pi$
$464$	447.255	−	774.668i	0.0447485	−	0.0775066i
$465$	533.832	+	924.624i	0.0532384	+	0.0922117i
$466$	−465.776	−	806.748i	−0.0463019	−	0.0801972i
$467$	−6623.90	+	11472.9i	−0.656354	+	1.13684i	0.325198	+	0.945646i	$0.394569\pi$
$467$	−6623.90	+	11472.9i	−0.656354	+	1.13684i	−0.981552	+	0.191193i	$0.938764\pi$
$468$	−6405.15			−0.632646
$469$	1673.42	−	2961.83i	0.164757	−	0.291609i
$470$	2889.29			0.283559
$471$	3932.47	−	6811.24i	0.384710	−	0.666338i
$472$	1504.76	+	2606.33i	0.146742	+	0.254165i
$473$	2766.94	+	4792.48i	0.268973	+	0.465874i
$474$	−7309.89	+	12661.1i	−0.708343	+	1.22689i
$475$	−1030.08			−0.0995012
$476$	−11516.5	+	107.290i	−1.10894	+	0.0103312i
$477$	3083.85			0.296016
$478$	1501.88	−	2601.34i	0.143712	−	0.248917i
$479$	−8601.56	−	14898.3i	−0.820491	−	1.42113i	−0.905317	−	0.424736i	$-0.860367\pi$
$479$	−8601.56	−	14898.3i	−0.820491	−	1.42113i	0.0848259	−	0.996396i	$-0.472967\pi$
$480$	−1948.31	−	3374.57i	−0.185266	−	0.320890i
$481$	14171.2	−	24545.3i	1.34335	−	2.32676i
$482$	−5515.78			−0.521239
$483$	−318.386	−	539.785i	−0.0299940	−	0.0508511i
$484$	−9626.41			−0.904058
$485$	−3428.67	+	5938.62i	−0.321006	+	0.555998i
$486$	500.237	+	866.436i	0.0466897	+	0.0808690i
$487$	4437.00	+	7685.11i	0.412853	+	0.715083i	0.995200	−	0.0978573i	$-0.0311989\pi$
$487$	4437.00	+	7685.11i	0.412853	+	0.715083i	−0.582347	+	0.812940i	$0.697866\pi$
$488$	1146.98	−	1986.63i	0.106397	−	0.184284i
$489$	−2326.94			−0.215190
$490$	7059.73	−	131.552i	0.650870	−	0.0121284i
$491$	19527.2			1.79480			0.897402	−	0.441215i	$-0.145452\pi$
$491$	19527.2			1.79480			0.897402	+	0.441215i	$0.145452\pi$
$492$	−5726.19	+	9918.05i	−0.524709	+	0.908822i
$493$	559.993	+	969.937i	0.0511579	+	0.0886080i
$494$	−6743.84	−	11680.7i	−0.614210	−	1.06384i
$495$	−359.691	+	623.003i	−0.0326604	+	0.0565695i
$496$	−3949.38			−0.357525
$497$	8291.89	+	14057.9i	0.748375	+	1.26878i
$498$	3029.31			0.272583
$499$	−353.163	+	611.695i	−0.0316828	+	0.0548762i	−0.881432	−	0.472311i	$-0.843420\pi$
$499$	−353.163	+	611.695i	−0.0316828	+	0.0548762i	0.849749	+	0.527187i	$0.176753\pi$
$500$	−559.446	−	968.989i	−0.0500384	−	0.0866690i
$501$	3887.42	+	6733.21i	0.346661	+	0.600434i
$502$	−13235.1	+	22923.8i	−1.17671	+	2.03813i
$503$	−6512.70			−0.577310			−0.288655	−	0.957433i	$-0.593208\pi$
$503$	−6512.70			−0.577310			−0.288655	+	0.957433i	$0.593208\pi$
$504$	652.701	−	6.08072i	0.0576858	−	0.000537414i
$505$	−4666.53			−0.411204
$506$	371.193	−	642.925i	0.0326117	−	0.0564852i
$507$	6186.69	+	10715.7i	0.541934	+	0.938657i
$508$	−1738.69	−	3011.50i	−0.151854	−	0.263019i
$509$	−10499.1	+	18185.0i	−0.914271	+	1.58356i	−0.106305	+	0.994334i	$0.533902\pi$
$509$	−10499.1	+	18185.0i	−0.914271	+	1.58356i	−0.807965	+	0.589230i	$0.799431\pi$
$510$	4290.46			0.372519
$511$	110.173	−	194.998i	0.00953770	−	0.0168810i
$512$	16152.2			1.39420
$513$	−556.241	+	963.437i	−0.0478726	+	0.0829177i
$514$	3864.56	+	6693.61i	0.331631	+	0.574402i
$515$	−3513.16	−	6084.96i	−0.300598	−	0.520652i
$516$	−4647.85	+	8050.31i	−0.396531	+	0.686812i
$517$	2243.72			0.190868
$518$	−13370.9	+	23665.6i	−1.13414	+	2.00735i
$519$	1812.41			0.153287
$520$	778.381	−	1348.20i	0.0656429	−	0.113697i
$521$	49.4432	+	85.6382i	0.00415767	+	0.00720130i	0.868097	−	0.496395i	$-0.165343\pi$
$521$	49.4432	+	85.6382i	0.00415767	+	0.00720130i	−0.863939	+	0.503596i	$0.832010\pi$
$522$	−298.684	−	517.336i	−0.0250441	−	0.0433777i
$523$	5228.24	−	9055.57i	0.437122	−	0.757118i	−0.560344	−	0.828260i	$-0.689331\pi$
$523$	5228.24	−	9055.57i	0.437122	−	0.757118i	0.997466	+	0.0711422i	$0.0226644\pi$
$524$	19668.4			1.63973
$525$	−1388.96	+	12.9399i	−0.115465	+	0.00107570i
$526$	30762.7			2.55004
$527$	2472.44	−	4282.40i	0.204367	−	0.353974i
$528$	−1330.53	−	2304.54i	−0.109666	−	0.189947i
$529$	6019.89	+	10426.8i	0.494772	+	0.856970i
$530$	−3526.87	+	6108.72i	−0.289052	+	0.500653i
$531$	−6916.67			−0.565269
$532$	3470.22	+	5883.34i	0.282807	+	0.479464i
$533$	33908.2			2.75559
$534$	5479.09	−	9490.06i	0.444014	−	0.769055i
$535$	−488.666	−	846.394i	−0.0394895	−	0.0683978i
$536$	359.654	+	622.939i	0.0289826	+	0.0501994i
$537$	4401.90	−	7624.32i	0.353736	−	0.612688i
$538$	−13386.4			−1.07273
$539$	5482.34	−	102.158i	0.438110	−	0.00816377i
$540$	−1208.40			−0.0962989
$541$	8747.30	−	15150.8i	0.695149	−	1.20403i	−0.274981	−	0.961450i	$-0.588672\pi$
$541$	8747.30	−	15150.8i	0.695149	−	1.20403i	0.970130	−	0.242584i	$-0.0779950\pi$
$542$	−4253.00	−	7366.41i	−0.337052	−	0.583791i
$543$	−5100.14	−	8833.71i	−0.403072	−	0.698141i
$544$	−9023.59	+	15629.3i	−0.711183	+	1.23180i
$545$	5094.39			0.400403
$546$	−9240.16	−	15665.6i	−0.724254	−	1.22788i
$547$	−8263.77			−0.645947			−0.322974	−	0.946408i	$-0.604683\pi$
$547$	−8263.77			−0.645947			−0.322974	+	0.946408i	$0.604683\pi$
$548$	2736.37	−	4739.53i	0.213307	−	0.369458i
$549$	2636.06	+	4565.80i	0.204926	+	0.354943i
$550$	−822.729	−	1425.01i	−0.0637841	−	0.110477i
$551$	332.123	−	575.254i	0.0256786	−	0.0444766i
$552$	132.510			0.0102174
$553$	−21920.4	+	204.215i	−1.68562	+	0.0157037i
$554$	−9100.31			−0.697897
$555$	2673.56	−	4630.75i	0.204480	−	0.354170i
$556$	−7741.10	−	13408.0i	−0.590460	−	1.02271i
$557$	976.741	+	1691.77i	0.0743014	+	0.128694i	0.900782	−	0.434271i	$-0.142994\pi$
$557$	976.741	+	1691.77i	0.0743014	+	0.128694i	−0.826481	+	0.562965i	$0.809661\pi$
$558$	−1318.73	+	2284.10i	−0.100047	+	0.173286i
$559$	27522.7			2.08244
$560$	2527.48	−	4473.46i	0.190724	−	0.337568i
$561$	3331.82			0.250748
$562$	85.7377	−	148.502i	0.00643528	−	0.0111462i
$563$	4309.36	+	7464.04i	0.322590	+	0.558742i	0.981022	−	0.193899i	$-0.0621133\pi$
$563$	4309.36	+	7464.04i	0.322590	+	0.558742i	−0.658432	+	0.752640i	$0.728780\pi$
$564$	1884.48	+	3264.01i	0.140693	+	0.243687i
$565$	−301.118	+	521.552i	−0.0224215	+	0.0388352i
$566$	−2127.96			−0.158030
$567$	−737.935	+	1306.09i	−0.0546567	+	0.0967384i
$568$	−3451.02			−0.254932
$569$	−2902.29	+	5026.91i	−0.213832	+	0.370368i	−0.952911	−	0.303251i	$-0.901928\pi$
$569$	−2902.29	+	5026.91i	−0.213832	+	0.370368i	0.739079	+	0.673619i	$0.235261\pi$
$570$	−1272.30	−	2203.69i	−0.0934926	−	0.161934i
$571$	−93.6069	−	162.132i	−0.00686047	−	0.0118827i	0.862575	−	0.505930i	$-0.168850\pi$
$571$	−93.6069	−	162.132i	−0.00686047	−	0.0118827i	−0.869435	+	0.494047i	$0.835517\pi$
$572$	5688.58	−	9852.92i	0.415825	−	0.720229i
$573$	10500.4			0.765548
$574$	−32518.0	+	302.945i	−2.36459	+	0.0220291i
$575$	−281.983			−0.0204513
$576$	2815.42	−	4876.44i	0.203661	−	0.352752i
$577$	−2594.93	−	4494.54i	−0.187224	−	0.324281i	0.757100	−	0.653299i	$-0.226616\pi$
$577$	−2594.93	−	4494.54i	−0.187224	−	0.324281i	−0.944324	+	0.329018i	$0.893282\pi$
$578$	178.220	+	308.685i	0.0128252	+	0.0222139i
$579$	4765.84	−	8254.68i	0.342075	−	0.592492i
$580$	721.520			0.0516543
$581$	2307.66	+	3912.36i	0.164781	+	0.279367i
$582$	−16939.7			−1.20648
$583$	−2738.84	+	4743.82i	−0.194565	+	0.336996i
$584$	23.6786	+	41.0125i	0.00167779	+	0.00290601i
$585$	1788.92	+	3098.50i	0.126432	+	0.218987i
$586$	9484.74	−	16428.1i	0.668620	−	1.15808i
$587$	−5908.43			−0.415446			−0.207723	−	0.978188i	$-0.566605\pi$
$587$	−5908.43			−0.415446			−0.207723	+	0.978188i	$0.566605\pi$
$588$	4753.18	+	7889.53i	0.333363	+	0.553331i
$589$	−2932.73			−0.205163
$590$	7910.32	−	13701.1i	0.551970	−	0.956041i
$591$	−7906.51	−	13694.5i	−0.550305	−	0.953156i
$592$	9889.73	+	17129.5i	0.686597	+	1.18922i
$593$	9059.64	−	15691.8i	0.627377	−	1.08665i	−0.360699	−	0.932682i	$-0.617462\pi$
$593$	9059.64	−	15691.8i	0.627377	−	1.08665i	0.988076	−	0.153967i	$-0.0492050\pi$
$594$	−1777.09			−0.122753
$595$	3268.38	+	5541.14i	0.225194	+	0.381790i
$596$	1146.76			0.0788139
$597$	−6498.24	+	11255.3i	−0.445486	+	0.771605i
$598$	−1846.13	−	3197.58i	−0.126244	−	0.218660i
$599$	2871.93	+	4974.34i	0.195900	+	0.339309i	0.947195	−	0.320658i	$-0.103904\pi$
$599$	2871.93	+	4974.34i	0.195900	+	0.339309i	−0.751295	+	0.659966i	$0.770571\pi$
$600$	146.850	−	254.352i	0.00999190	−	0.0173065i
$601$	−24830.0			−1.68525			−0.842627	−	0.538497i	$-0.818992\pi$
$601$	−24830.0			−1.68525			−0.842627	+	0.538497i	$0.818992\pi$
$602$	−26394.3	+	245.895i	−1.78696	+	0.0166478i
$603$	−1653.15			−0.111645
$604$	9135.73	−	15823.5i	0.615443	−	1.06598i
$605$	2688.60	+	4656.79i	0.180673	+	0.312934i
$606$	−5763.88	−	9983.33i	−0.386372	−	0.669217i
$607$	−11511.3	+	19938.2i	−0.769738	+	1.33322i	0.167967	+	0.985793i	$0.446280\pi$
$607$	−11511.3	+	19938.2i	−0.769738	+	1.33322i	−0.937705	+	0.347432i	$0.887054\pi$
$608$	10703.5			0.713954
$609$	440.610	−	779.847i	0.0293176	−	0.0518900i
$610$	−12059.0			−0.800421
$611$	5579.56	−	9664.09i	0.369435	−	0.639881i
$612$	2798.36	+	4846.90i	0.184832	+	0.320138i
$613$	−2136.59	−	3700.68i	−0.140777	−	0.243832i	0.787013	−	0.616937i	$-0.211627\pi$
$613$	−2136.59	−	3700.68i	−0.140777	−	0.243832i	−0.927789	+	0.373105i	$0.878293\pi$
$614$	5001.88	−	8663.51i	0.328761	−	0.569432i
$615$	6397.16			0.419445
$616$	−570.327	+	1009.44i	−0.0373038	+	0.0660250i
$617$	23745.5			1.54936			0.774682	−	0.632351i	$-0.217910\pi$
$617$	23745.5			1.54936			0.774682	+	0.632351i	$0.217910\pi$
$618$	8678.57	−	15031.7i	0.564892	−	0.978421i
$619$	3640.83	+	6306.11i	0.236409	+	0.409473i	0.959681	−	0.281090i	$-0.0906960\pi$
$619$	3640.83	+	6306.11i	0.236409	+	0.409473i	−0.723272	+	0.690563i	$0.757363\pi$
$620$	−1592.80	−	2758.81i	−0.103175	−	0.178704i
$621$	−152.271	+	263.741i	−0.00983965	+	0.0170428i
$622$	−15406.9			−0.993181
$623$	16430.3	−	153.069i	1.05661	−	0.00984361i
$624$	−13234.7			−0.849060
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	7742.82	+	13411.0i	0.494354	+	0.856245i
$627$	−988.023	−	1711.31i	−0.0629312	−	0.109000i
$628$	−11733.4	+	20322.8i	−0.745561	+	1.29135i
$629$	−24765.2			−1.56988
$630$	−1743.26	−	2955.48i	−0.110243	−	0.186904i
$631$	−18200.0			−1.14823			−0.574114	−	0.818775i	$-0.694653\pi$
$631$	−18200.0			−1.14823			−0.574114	+	0.818775i	$0.694653\pi$
$632$	2317.58	−	4014.16i	0.145867	−	0.252650i
$633$	786.964	+	1363.06i	0.0494139	+	0.0855874i
$634$	5302.02	+	9183.37i	0.332130	+	0.575265i
$635$	−971.212	+	1682.19i	−0.0606951	+	0.105127i
$636$	−9201.31			−0.573673
$637$	13193.2	−	23867.4i	0.820616	−	1.48456i
$638$	1061.08			0.0658439
$639$	3965.67	−	6868.73i	0.245508	−	0.425232i
$640$	1244.27	+	2155.13i	0.0768499	+	0.133108i
$641$	15365.3	+	26613.5i	0.946790	+	1.63989i	0.752128	+	0.659017i	$0.229028\pi$
$641$	15365.3	+	26613.5i	0.946790	+	1.63989i	0.194662	+	0.980870i	$0.437639\pi$
$642$	1207.15	−	2090.85i	0.0742096	−	0.128535i
$643$	−3865.33			−0.237067			−0.118533	−	0.992950i	$-0.537819\pi$
$643$	−3865.33			−0.237067			−0.118533	+	0.992950i	$0.537819\pi$
$644$	949.974	+	1610.56i	0.0581276	+	0.0985483i
$645$	5192.47			0.316982
$646$	−5892.66	+	10206.4i	−0.358891	+	0.621617i
$647$	11498.3	+	19915.6i	0.698676	+	1.21014i	0.968926	+	0.247353i	$0.0795606\pi$
$647$	11498.3	+	19915.6i	0.698676	+	1.21014i	−0.270249	+	0.962790i	$0.587106\pi$
$648$	−158.598	−	274.700i	−0.00961471	−	0.0166532i
$649$	6142.87	−	10639.8i	0.371539	−	0.643525i
$650$	−8183.67			−0.493831
$651$	−3954.51	+	36.8412i	−0.238079	+	0.00221800i
$652$	6942.92			0.417033
$653$	−6665.49	+	11545.0i	−0.399450	+	0.691867i	−0.993658	−	0.112444i	$-0.964132\pi$
$653$	−6665.49	+	11545.0i	−0.399450	+	0.691867i	0.594208	+	0.804311i	$0.297466\pi$
$654$	6292.35	+	10898.7i	0.376224	+	0.651638i
$655$	−5493.28	−	9514.63i	−0.327695	−	0.567584i
$656$	−11831.8	+	20493.3i	−0.704199	+	1.21971i
$657$	−108.839			−0.00646303
$658$	−5264.46	+	9317.72i	−0.311900	+	0.552040i
$659$	4095.99			0.242120			0.121060	−	0.992645i	$-0.461371\pi$
$659$	4095.99			0.242120			0.121060	+	0.992645i	$0.461371\pi$
$660$	1073.21	−	1858.86i	0.0632952	−	0.109631i
$661$	6188.36	+	10718.5i	0.364144	+	0.630716i	0.988638	−	0.150313i	$-0.0480283\pi$
$661$	6188.36	+	10718.5i	0.364144	+	0.630716i	−0.624494	+	0.781029i	$0.714695\pi$
$662$	−21490.5	−	37222.7i	−1.26171	−	2.18535i
$663$	8285.39	−	14350.7i	0.485336	−	0.840627i
$664$	−960.431			−0.0561325
$665$	1876.86	−	3321.91i	0.109446	−	0.193711i
$666$	13209.0			0.768529
$667$	90.9186	−	157.476i	0.00527794	−	0.00914165i
$668$	−11598.9	−	20090.0i	−0.671821	−	1.16363i
$669$	7097.22	+	12292.8i	0.410156	+	0.710411i
$670$	1890.65	−	3274.70i	0.109018	−	0.188825i
$671$	−9364.63			−0.538774
$672$	14432.7	−	134.458i	0.828499	−	0.00771849i
$673$	5293.58			0.303199			0.151599	−	0.988442i	$-0.451558\pi$
$673$	5293.58			0.303199			0.151599	+	0.988442i	$0.451558\pi$
$674$	23155.6	−	40106.6i	1.32332	−	2.29206i
$675$	337.500	+	584.567i	0.0192450	+	0.0333333i
$676$	−18459.3	−	31972.5i	−1.05026	−	1.81910i
$677$	9415.09	−	16307.4i	0.534492	−	0.925768i	−0.464696	−	0.885470i	$-0.653836\pi$
$677$	9415.09	−	16307.4i	0.534492	−	0.925768i	0.999188	−	0.0402970i	$-0.0128304\pi$
$678$	−1487.71			−0.0842701
$679$	−12904.3	−	21877.7i	−0.729341	−	1.23651i
$680$	−1360.27			−0.0767120
$681$	−558.261	+	966.937i	−0.0314135	+	0.0544098i
$682$	−2342.39	−	4057.15i	−0.131517	−	0.227795i
$683$	−4865.65	−	8427.55i	−0.272590	−	0.472140i	0.696934	−	0.717135i	$-0.254547\pi$
$683$	−4865.65	−	8427.55i	−0.272590	−	0.472140i	−0.969524	+	0.244995i	$0.921214\pi$
$684$	1659.66	−	2874.62i	0.0927760	−	0.160693i
$685$	−3057.01			−0.170514
$686$	−12439.0	+	23006.7i	−0.692309	+	1.28047i
$687$	−6932.32			−0.384985
$688$	−9603.68	+	16634.1i	−0.532176	+	0.921755i
$689$	13621.6	+	23593.3i	0.753182	+	1.30455i
$690$	−348.292	−	603.260i	−0.0192163	−	0.0332836i
$691$	3059.35	−	5298.94i	0.168427	−	0.291724i	−0.769440	−	0.638719i	$-0.779465\pi$
$691$	3059.35	−	5298.94i	0.168427	−	0.291724i	0.937867	+	0.346995i	$0.112798\pi$
$692$	−5407.71			−0.297067
$693$	−1353.75	−	2295.12i	−0.0742062	−	0.125807i
$694$	−1499.16			−0.0819992
$695$	−4324.08	+	7489.53i	−0.236003	+	0.408769i
$696$	94.6967	+	164.020i	0.00515728	+	0.00893268i
$697$	−14814.2	−	25659.0i	−0.805063	−	1.39441i
$698$	18371.2	−	31819.8i	0.996217	−	1.72550i
$699$	−678.780			−0.0367294
$700$	4144.26	−	38.6089i	0.223769	−	0.00208468i
$701$	−4457.41			−0.240163			−0.120081	−	0.992764i	$-0.538316\pi$
$701$	−4457.41			−0.240163			−0.120081	+	0.992764i	$0.538316\pi$
$702$	−4419.18	+	7654.25i	−0.237594	+	0.411526i
$703$	7343.93	+	12720.1i	0.393999	+	0.682427i
$704$	5000.89	+	8661.79i	0.267725	+	0.463713i
$705$	1052.65	−	1823.24i	0.0562340	−	0.0974002i
$706$	20801.9			1.10891
$707$	8502.71	−	15049.2i	0.452302	−	0.800541i
$708$	20637.4			1.09548
$709$	2387.66	−	4135.55i	0.126474	−	0.219060i	−0.795834	−	0.605515i	$-0.792967\pi$
$709$	2387.66	−	4135.55i	0.126474	−	0.219060i	0.922308	+	0.386455i	$0.126300\pi$
$710$	9070.75	+	15711.0i	0.479463	+	0.830455i
$711$	5326.39	+	9225.57i	0.280949	+	0.486619i
$712$	−1737.13	+	3008.79i	−0.0914348	+	0.158370i
$713$	−802.835			−0.0421689
$714$	−7817.48	+	13836.4i	−0.409750	+	0.725228i
$715$	−6355.15			−0.332404
$716$	−13134.0	+	22748.8i	−0.685532	+	1.18738i
$717$	−1094.35	−	1895.48i	−0.0570006	−	0.0987279i
$718$	−4086.99	−	7078.87i	−0.212430	−	0.367940i
$719$	14208.0	−	24609.1i	0.736955	−	1.27644i	−0.216905	−	0.976193i	$-0.569596\pi$
$719$	14208.0	−	24609.1i	0.736955	−	1.27644i	0.953860	−	0.300251i	$-0.0970705\pi$
$720$	−2496.88			−0.129241
$721$	26024.7	−	242.452i	1.34426	−	0.0125234i
$722$	−21250.0			−1.09535
$723$	−2009.55	+	3480.64i	−0.103369	+	0.179041i
$724$	15217.4	+	26357.2i	0.781145	+	1.35298i
$725$	−201.516	−	349.036i	−0.0103229	−	0.0178798i
$726$	−6641.66	+	11503.7i	−0.339525	+	0.588074i
$727$	−19780.0			−1.00908			−0.504538	−	0.863389i	$-0.668337\pi$
$727$	−19780.0			−1.00908			−0.504538	+	0.863389i	$0.668337\pi$
$728$	2929.56	+	4966.71i	0.149144	+	0.252855i
$729$	729.000			0.0370370
$730$	124.475	−	215.597i	0.00631098	−	0.0109309i
$731$	−12024.5	−	20827.0i	−0.608400	−	1.05378i
$732$	−7865.26	−	13623.0i	−0.397143	−	0.687871i
$733$	−1286.55	+	2228.37i	−0.0648292	+	0.112288i	−0.896618	−	0.442804i	$-0.853984\pi$
$733$	−1286.55	+	2228.37i	−0.0648292	+	0.112288i	0.831789	+	0.555092i	$0.187317\pi$
$734$	36451.5			1.83304
$735$	2489.04	−	4502.86i	0.124911	−	0.225973i
$736$	2930.08			0.146745
$737$	1468.21	−	2543.01i	0.0733816	−	0.127101i
$738$	7901.48	+	13685.8i	0.394116	+	0.682628i
$739$	11503.5	+	19924.7i	0.572618	+	0.991803i	0.996296	+	0.0859904i	$0.0274054\pi$
$739$	11503.5	+	19924.7i	0.572618	+	0.991803i	−0.423678	+	0.905813i	$0.639261\pi$
$740$	−7977.15	+	13816.8i	−0.396278	+	0.686374i
$741$	−9827.86			−0.487227
$742$	−13273.9	−	22504.3i	−0.656741	−	1.11342i
$743$	−25357.8			−1.25207			−0.626034	−	0.779796i	$-0.715323\pi$
$743$	−25357.8			−1.25207			−0.626034	+	0.779796i	$0.715323\pi$
$744$	418.098	−	724.167i	0.0206025	−	0.0356845i
$745$	−320.283	−	554.746i	−0.0157507	−	0.0272810i
$746$	17957.4	+	31103.1i	0.881321	+	1.52649i
$747$	1103.66	−	1911.59i	0.0540573	−	0.0936299i
$748$	−9941.19			−0.485944
$749$	3619.93	−	33.7241i	0.176595	−	0.00164520i
$750$	−1543.94			−0.0751690
$751$	5985.59	−	10367.3i	0.290835	−	0.503741i	−0.683172	−	0.730257i	$-0.739400\pi$
$751$	5985.59	−	10367.3i	0.290835	−	0.503741i	0.974007	+	0.226516i	$0.0727335\pi$
$752$	3893.83	+	6744.31i	0.188821	+	0.327047i
$753$	9643.79	+	16703.5i	0.466719	+	0.808381i
$754$	2638.63	−	4570.24i	0.127444	−	0.220740i
$755$	−10206.2			−0.491977
$756$	2201.79	−	3897.00i	0.105924	−	0.187477i
$757$	34224.9			1.64323			0.821615	−	0.570043i	$-0.193074\pi$
$757$	34224.9			1.64323			0.821615	+	0.570043i	$0.193074\pi$
$758$	8728.35	−	15118.0i	0.418243	−	0.724418i
$759$	−270.471	−	468.470i	−0.0129348	−	0.0224037i
$760$	403.378	+	698.672i	0.0192527	+	0.0333467i
$761$	−5738.44	+	9939.27i	−0.273349	+	0.473454i	−0.969717	−	0.244231i	$-0.921465\pi$
$761$	−5738.44	+	9939.27i	−0.273349	+	0.473454i	0.696369	+	0.717684i	$0.254798\pi$
$762$	−4798.38			−0.228119
$763$	−9282.29	+	16429.0i	−0.440421	+	0.779514i
$764$	−31330.1			−1.48362
$765$	1563.13	−	2707.42i	0.0738760	−	0.127957i
$766$	27287.0	+	47262.5i	1.28710	+	2.22933i
$767$	−30551.5	−	52916.8i	−1.43827	−	2.49115i
$768$	4434.06	−	7680.01i	0.208334	−	0.360845i
$769$	8739.36			0.409817			0.204908	−	0.978781i	$-0.434310\pi$
$769$	8739.36			0.409817			0.204908	+	0.978781i	$0.434310\pi$
$770$	6094.59	−	56.7787i	0.285239	−	0.00265735i
$771$	5631.86			0.263069
$772$	−14219.9	+	24629.6i	−0.662934	+	1.14824i
$773$	3316.05	+	5743.57i	0.154295	+	0.267247i	0.932802	−	0.360389i	$-0.117356\pi$
$773$	3316.05	+	5743.57i	0.154295	+	0.267247i	−0.778507	+	0.627636i	$0.784023\pi$
$774$	6413.49	+	11108.5i	0.297840	+	0.515874i
$775$	−889.720	+	1541.04i	−0.0412383	+	0.0714268i
$776$	5370.68			0.248448
$777$	10062.4	+	17059.5i	0.464589	+	0.787654i
$778$	14717.6			0.678215
$779$	−8786.08	+	15217.9i	−0.404100	+	0.699922i
$780$	−5337.63	−	9245.04i	−0.245023	−	0.424392i
$781$	7044.02	+	12200.6i	0.322734	+	0.558991i
$782$	−1613.12	+	2794.00i	−0.0737658	+	0.127766i
$783$	−435.275			−0.0198665
$784$	9821.31	+	16301.8i	0.447399	+	0.742613i
$785$	13108.2			0.595991
$786$	13570.1	−	23504.1i	0.615812	−	1.06662i
$787$	4084.40	+	7074.38i	0.184998	+	0.320425i	0.943576	−	0.331157i	$-0.107439\pi$
$787$	4084.40	+	7074.38i	0.184998	+	0.320425i	−0.758578	+	0.651582i	$0.774106\pi$
$788$	23590.7	+	40860.4i	1.06648	+	1.84720i
$789$	11207.7	−	19412.3i	0.505710	−	0.875915i
$790$	−24366.3			−1.09736
$791$	−1133.31	−	1921.38i	−0.0509428	−	0.0863673i
$792$	563.421			0.0252782
$793$	−23287.5	+	40335.1i	−1.04283	+	1.80623i
$794$	3017.47	+	5226.41i	0.134869	+	0.233600i
$795$	2569.87	+	4451.15i	0.114646	+	0.198574i
$796$	19388.9	−	33582.5i	0.863343	−	1.49535i
$797$	−25149.4			−1.11774			−0.558870	−	0.829255i	$-0.688765\pi$
$797$	−25149.4			−1.11774			−0.558870	+	0.829255i	$0.688765\pi$
$798$	9424.92	−	87.8048i	0.418094	−	0.00389506i
$799$	−9750.67			−0.431732
$800$	3247.18	−	5624.29i	0.143507	−	0.248561i
$801$	−3992.36	−	6914.98i	−0.176109	−	0.305030i
$802$	−20262.6	−	35095.9i	−0.892142	−	1.54524i
$803$	96.6627	−	167.425i	0.00424801	−	0.00735777i
$804$	4932.54			0.216365
$805$	513.791	−	909.372i	0.0224953	−	0.0398151i
$806$	−23299.8			−1.01824
$807$	−4877.03	+	8447.27i	−0.212738	+	0.368473i
$808$	1827.42	+	3165.18i	0.0795648	+	0.137810i
$809$	−4411.76	−	7641.39i	−0.191730	−	0.332085i	0.754094	−	0.656767i	$-0.228076\pi$
$809$	−4411.76	−	7641.39i	−0.191730	−	0.332085i	−0.945823	+	0.324681i	$0.894743\pi$
$810$	−833.728	+	1444.06i	−0.0361657	+	0.0626408i
$811$	−4573.00			−0.198002			−0.0990012	−	0.995087i	$-0.531565\pi$
$811$	−4573.00			−0.198002			−0.0990012	+	0.995087i	$0.531565\pi$
$812$	−1314.65	+	2326.84i	−0.0568169	+	0.100562i
$813$	−6197.94			−0.267369
$814$	−11731.3	+	20319.2i	−0.505137	+	0.874923i
$815$	−1939.12	−	3358.65i	−0.0833427	−	0.144354i
$816$	5782.15	+	10015.0i	0.248058	+	0.429650i
$817$	−7131.51	+	12352.1i	−0.305385	+	0.528943i
$818$	−6968.15			−0.297843
$819$	−13251.9	+	123.458i	−0.565397	+	0.00526737i
$820$	−19087.3			−0.812875
$821$	−515.068	+	892.123i	−0.0218952	+	0.0379236i	−0.876765	−	0.480918i	$-0.840303\pi$
$821$	−515.068	+	892.123i	−0.0218952	+	0.0379236i	0.854870	+	0.518842i	$0.173637\pi$
$822$	−3775.87	−	6540.01i	−0.160217	−	0.277505i
$823$	−7813.30	−	13533.0i	−0.330929	−	0.573186i	0.651765	−	0.758421i	$-0.274029\pi$
$823$	−7813.30	−	13533.0i	−0.330929	−	0.573186i	−0.982694	+	0.185235i	$0.940695\pi$
$824$	−2751.51	+	4765.76i	−0.116327	+	0.201484i
$825$	−1198.97			−0.0505973
$826$	29771.7	+	50474.3i	1.25411	+	2.12618i
$827$	−28523.7			−1.19936			−0.599678	−	0.800242i	$-0.704705\pi$
$827$	−28523.7			−1.19936			−0.599678	+	0.800242i	$0.704705\pi$
$828$	454.333	−	786.927i	0.0190690	−	0.0330285i
$829$	951.668	+	1648.34i	0.0398707	+	0.0690581i	0.885272	−	0.465073i	$-0.153972\pi$
$829$	951.668	+	1648.34i	0.0398707	+	0.0690581i	−0.845401	+	0.534131i	$0.820639\pi$
$830$	2524.42	+	4372.43i	0.105571	+	0.182854i
$831$	−3315.49	+	5742.60i	−0.138403	+	0.239722i
$832$	49743.8			2.07278
$833$	−23824.9	+	443.956i	−0.990978	+	0.0184660i
$834$	−21363.6			−0.887005
$835$	−6479.03	+	11222.0i	−0.268522	+	0.465094i
$836$	2947.98	+	5106.05i	0.121959	+	0.211240i
$837$	960.898	+	1664.32i	0.0396816	+	0.0687305i
$838$	16158.9	−	27988.0i	0.666108	−	1.15373i
$839$	6072.08			0.249859			0.124929	−	0.992166i	$-0.460130\pi$
$839$	6072.08			0.249859			0.124929	+	0.992166i	$0.460130\pi$
$840$	552.695	+	937.026i	0.0227021	+	0.0384886i
$841$	−24129.1			−0.989344
$842$	28924.6	−	50098.9i	1.18386	−	2.05050i
$843$	−62.4732	−	108.207i	−0.00255242	−	0.00442092i
$844$	−2348.07	−	4066.98i	−0.0957631	−	0.165867i
$845$	−10311.2	+	17859.4i	−0.419780	+	0.727081i
$846$	5200.72			0.211353
$847$	−19916.5	+	185.547i	−0.807958	+	0.00752713i
$848$	−19012.3			−0.769913
$849$	−775.274	+	1342.81i	−0.0313396	+	0.0542818i
$850$	3575.38	+	6192.74i	0.144276	+	0.249893i
$851$	2010.40	+	3482.12i	0.0809819	+	0.140265i
$852$	−11832.4	+	20494.3i	−0.475788	+	0.824090i
$853$	−17591.5			−0.706123			−0.353062	−	0.935600i	$-0.614859\pi$
$853$	−17591.5			−0.706123			−0.353062	+	0.935600i	$0.614859\pi$
$854$	21972.3	−	38889.4i	0.880419	−	1.55828i
$855$	−1854.14			−0.0741638
$856$	−382.724	+	662.898i	−0.0152818	+	0.0264689i
$857$	1085.18	+	1879.58i	0.0432543	+	0.0749187i	0.886842	−	0.462073i	$-0.152894\pi$
$857$	1085.18	+	1879.58i	0.0432543	+	0.0749187i	−0.843588	+	0.536991i	$0.819561\pi$
$858$	−7849.58	−	13595.9i	−0.312331	−	0.540974i
$859$	2586.25	−	4479.52i	0.102726	−	0.177927i	−0.810081	−	0.586318i	$-0.800577\pi$
$859$	2586.25	−	4479.52i	0.102726	−	0.177927i	0.912807	+	0.408391i	$0.133910\pi$
$860$	−15492.8			−0.614304
$861$	−11656.0	+	20630.3i	−0.461366	+	0.816585i
$862$	60417.6			2.38728
$863$	4336.18	−	7510.49i	0.171037	−	0.296246i	−0.767745	−	0.640755i	$-0.778621\pi$
$863$	4336.18	−	7510.49i	0.171037	−	0.296246i	0.938783	+	0.344509i	$0.111955\pi$
$864$	−3506.96	−	6074.23i	−0.138089	−	0.239178i
$865$	1510.34	+	2615.99i	0.0593678	+	0.102828i
$866$	−7342.88	+	12718.2i	−0.288131	+	0.499057i
$867$	259.721			0.0101737
$868$	11799.1	−	109.923i	0.461392	−	0.00429844i
$869$	−18922.0			−0.738648
$870$	497.807	−	862.226i	0.0193991	−	0.0336002i
$871$	−7302.13	−	12647.7i	−0.284068	−	0.492020i
$872$	−1994.97	−	3455.38i	−0.0774749	−	0.134190i
$873$	−6171.60	+	10689.5i	−0.239263	+	0.414416i
$874$	1913.42			0.0740533
$875$	−1176.14	−	1994.01i	−0.0454410	−	0.0770397i
$876$	324.744			0.0125252
$877$	−14467.0	+	25057.6i	−0.557032	+	0.964808i	0.440710	+	0.897649i	$0.354727\pi$
$877$	−14467.0	+	25057.6i	−0.557032	+	0.964808i	−0.997742	+	0.0671582i	$0.978607\pi$
$878$	−14046.6	−	24329.4i	−0.539920	−	0.935169i
$879$	−6911.10	−	11970.4i	−0.265194	−	0.459330i
$880$	2217.54	−	3840.90i	0.0849470	−	0.147133i
$881$	−7738.54			−0.295934			−0.147967	−	0.988992i	$-0.547273\pi$
$881$	−7738.54			−0.295934			−0.147967	+	0.988992i	$0.547273\pi$
$882$	12707.5	−	236.793i	0.485130	−	0.00903995i
$883$	11134.4			0.424353			0.212177	−	0.977231i	$-0.431945\pi$
$883$	11134.4			0.424353			0.212177	+	0.977231i	$0.431945\pi$
$884$	−24721.2	+	42818.4i	−0.940571	+	1.62912i
$885$	−5763.89	−	9983.35i	−0.218928	−	0.379194i
$886$	−33259.0	−	57606.3i	−1.26113	−	2.18434i
$887$	2277.54	−	3944.82i	0.0862146	−	0.149328i	−0.819694	−	0.572802i	$-0.805856\pi$
$887$	2277.54	−	3944.82i	0.0862146	−	0.149328i	0.905908	+	0.423474i	$0.139190\pi$
$888$	−4187.88			−0.158261
$889$	−3655.31	−	6197.13i	−0.137902	−	0.233796i
$890$	18263.6			0.687863
$891$	−647.444	+	1121.41i	−0.0243436	+	0.0421644i
$892$	−21176.1	−	36678.0i	−0.794874	−	1.37676i
$893$	2891.48	+	5008.19i	0.108354	+	0.187674i
$894$	791.197	−	1370.39i	0.0295991	−	0.0512671i
$895$	14673.0			0.548005
$896$	−9217.25	+	85.8701i	−0.343668	+	0.00320169i
$897$	−2690.38			−0.100144
$898$	34506.7	−	59767.4i	1.28230	−	2.22101i
$899$	−573.738	−	993.743i	−0.0212850	−	0.0368667i
$900$	−1007.00	−	1744.18i	−0.0372964	−	0.0645993i
$901$	11902.4	−	20615.5i	0.440094	−	0.762266i
$902$	−28070.0			−1.03617
$903$	−9461.00	+	16745.3i	−0.348663	+	0.617107i
$904$	471.673			0.0173536
$905$	8500.24	−	14722.8i	0.312218	−	0.540778i
$906$	−12606.2	−	21834.7i	−0.462267	−	0.800671i
$907$	−5053.40	−	8752.75i	−0.185000	−	0.320430i	0.758576	−	0.651584i	$-0.225895\pi$
$907$	−5053.40	−	8752.75i	−0.185000	−	0.320430i	−0.943577	+	0.331154i	$0.892562\pi$
$908$	1665.69	−	2885.06i	0.0608787	−	0.105445i
$909$	−8399.76			−0.306493
$910$	14911.2	−	26391.7i	0.543187	−	0.961401i
$911$	17944.2			0.652598			0.326299	−	0.945267i	$-0.394198\pi$
$911$	17944.2			0.652598			0.326299	+	0.945267i	$0.394198\pi$
$912$	3429.30	−	5939.72i	0.124513	−	0.215662i
$913$	1960.38	+	3395.47i	0.0710613	+	0.123082i
$914$	34143.0	+	59137.5i	1.23561	+	2.14015i
$915$	−4393.44	+	7609.66i	−0.158735	+	0.274937i
$916$	20684.1			0.746092
$917$	40693.0	−	379.105i	1.46543	−	0.0136523i
$918$	7722.82			0.277659
$919$	22060.0	−	38209.0i	0.791829	−	1.37149i	−0.133005	−	0.991115i	$-0.542463\pi$
$919$	22060.0	−	38209.0i	0.791829	−	1.37149i	0.924833	−	0.380372i	$-0.124204\pi$
$920$	110.425	+	191.261i	0.00395717	+	0.00685403i
$921$	−3644.64	−	6312.71i	−0.130396	−	0.225853i
$922$	−7046.59	+	12205.1i	−0.251700	+	0.435957i
$923$	70066.8			2.49867
$924$	4039.21	+	6847.99i	0.143810	+	0.243812i
$925$	8911.88			0.316779
$926$	11368.0	−	19690.0i	0.403430	−	0.698761i
$927$	−6323.68	−	10952.9i	−0.224053	−	0.388071i
$928$	2093.95	+	3626.83i	0.0740704	+	0.128294i
$929$	1140.21	−	1974.90i	0.0402682	−	0.0697465i	−0.845189	−	0.534468i	$-0.820512\pi$
$929$	1140.21	−	1974.90i	0.0402682	−	0.0697465i	0.885457	+	0.464721i	$0.153845\pi$
$930$	−4395.76			−0.154992
$931$	7293.12	+	12105.4i	0.256737	+	0.426144i
$932$	2025.29			0.0711807
$933$	−5613.14	+	9722.24i	−0.196962	+	0.341149i
$934$	−27271.8	−	47236.1i	−0.955416	−	1.65483i
$935$	2776.51	+	4809.06i	0.0971142	+	0.168207i
$936$	1401.09	−	2426.75i	0.0489273	−	0.0847446i
$937$	28971.8			1.01010			0.505051	−	0.863089i	$-0.331474\pi$
$937$	28971.8			1.01010			0.505051	+	0.863089i	$0.331474\pi$
$938$	7115.75	+	12063.9i	0.247695	+	0.419936i
$939$	11283.7			0.392150
$940$	−3140.80	+	5440.02i	−0.108980	+	0.188759i
$941$	−21849.6	−	37844.5i	−0.756934	−	1.31105i	−0.944407	−	0.328779i	$-0.893363\pi$
$941$	−21849.6	−	37844.5i	−0.756934	−	1.31105i	0.187473	−	0.982270i	$-0.439970\pi$
$942$	16190.7	+	28043.1i	0.560001	+	0.969949i
$943$	−2405.19	+	4165.91i	−0.0830581	+	0.143861i
$944$	42642.2			1.47022
$945$	−2500.13	+	23.2918i	−0.0860626	+	0.000801779i
$946$	−22784.0			−0.783055
$947$	−4013.32	+	6951.27i	−0.137714	+	0.238528i	−0.926631	−	0.375972i	$-0.877309\pi$
$947$	−4013.32	+	6951.27i	−0.137714	+	0.238528i	0.788917	+	0.614500i	$0.210642\pi$
$948$	−15892.4	−	27526.5i	−0.544474	−	0.943057i
$949$	−480.751	−	832.686i	−0.0164445	−	0.0284827i
$950$	2120.50	−	3672.81i	0.0724191	−	0.125434i
$951$	7726.68			0.263465
$952$	2478.50	−	4386.77i	0.0843790	−	0.149345i
$953$	−9323.40			−0.316909			−0.158455	−	0.987366i	$-0.550651\pi$
$953$	−9323.40			−0.316909			−0.158455	+	0.987366i	$0.550651\pi$
$954$	−6348.37	+	10995.7i	−0.215447	+	0.373164i
$955$	8750.30	+	15156.0i	0.296495	+	0.513545i
$956$	3265.24	+	5655.56i	0.110466	+	0.191333i
$957$	386.579	−	669.574i	0.0130578	−	0.0226168i
$958$	70828.3			2.38868
$959$	5570.06	−	9858.60i	0.187556	−	0.331961i
$960$	9384.72			0.315511
$961$	12362.4	−	21412.3i	0.414970	−	0.718749i
$962$	58345.5	+	101057.i	1.95544	+	3.38693i
$963$	−879.599	−	1523.51i	−0.0294337	−	0.0509807i
$964$	5995.92	−	10385.2i	0.200327	−	0.346977i
$965$	15886.1			0.529941
$966$	2580.07	−	24.0366i	0.0859343	−	0.000800584i
$967$	10623.3			0.353281			0.176640	−	0.984275i	$-0.443477\pi$
$967$	10623.3			0.353281			0.176640	+	0.984275i	$0.443477\pi$
$968$	2105.72	−	3647.21i	0.0699176	−	0.121101i
$969$	4293.71	+	7436.93i	0.142347	+	0.246552i
$970$	−14116.4	−	24450.4i	−0.467269	−	0.809334i
$971$	−14286.5	+	24745.0i	−0.472169	+	0.817820i	−0.999493	−	0.0318441i	$-0.989862\pi$
$971$	−14286.5	+	24745.0i	−0.472169	+	0.817820i	0.527324	+	0.849664i	$0.323195\pi$
$972$	−2175.13			−0.0717770
$973$	−16274.4	−	27591.2i	−0.536210	−	0.909079i
$974$	−36535.8			−1.20193
$975$	−2981.54	+	5164.17i	−0.0979339	+	0.169627i
$976$	−16251.7	−	28148.8i	−0.532996	−	0.923176i
$977$	−9050.20	−	15675.4i	−0.296358	−	0.513307i	0.678942	−	0.734192i	$-0.262439\pi$
$977$	−9050.20	−	15675.4i	−0.296358	−	0.513307i	−0.975300	+	0.220885i	$0.929105\pi$
$978$	4790.21	−	8296.89i	0.156620	−	0.271273i
$979$	14182.9			0.463010
$980$	−7426.58	+	13435.2i	−0.242075	+	0.437931i
$981$	9169.90			0.298443
$982$	−40198.4	+	69625.6i	−1.30630	+	2.26257i
$983$	−3451.45	−	5978.09i	−0.111988	−	0.193969i	0.804584	−	0.593839i	$-0.202389\pi$
$983$	−3451.45	−	5978.09i	−0.111988	−	0.193969i	−0.916572	+	0.399870i	$0.869055\pi$
$984$	−2505.14	−	4339.02i	−0.0811594	−	0.140572i
$985$	13177.5	−	22824.1i	0.426264	−	0.738311i
$986$	−4611.18			−0.148935
$987$	3961.80	+	6716.75i	0.127767	+	0.216613i
$988$	29323.5			0.944236
$989$	−1952.25	+	3381.40i	−0.0627684	+	0.108718i
$990$	−1480.91	−	2565.01i	−0.0475419	−	0.0823449i
$991$	18924.5	+	32778.1i	0.606615	+	1.05069i	0.991794	+	0.127846i	$0.0408062\pi$
$991$	18924.5	+	32778.1i	0.606615	+	1.05069i	−0.385179	+	0.922842i	$0.625860\pi$
$992$	9245.07	−	16012.9i	0.295898	−	0.512511i
$993$	−31318.4			−1.00086
$994$	−67194.1	+	625.996i	−2.14413	+	0.0199752i
$995$	−21660.8			−0.690145
$996$	−3293.00	+	5703.65i	−0.104762	+	0.181453i
$997$	−2045.10	−	3542.21i	−0.0649637	−	0.112520i	0.831714	−	0.555204i	$-0.187360\pi$
$997$	−2045.10	−	3542.21i	−0.0649637	−	0.112520i	−0.896678	+	0.442684i	$0.854026\pi$
$998$	−1454.03	−	2518.46i	−0.0461188	−	0.0798802i
$999$	4812.42	−	8335.35i	0.152411	−	0.263983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.i.c.16.1	✓	6
3.2	odd	2		315.4.j.e.226.3		6
7.2	even	3		735.4.a.r.1.3		3
7.4	even	3	inner	105.4.i.c.46.1	yes	6
7.5	odd	6		735.4.a.s.1.3		3
21.2	odd	6		2205.4.a.bi.1.1		3
21.5	even	6		2205.4.a.bj.1.1		3
21.11	odd	6		315.4.j.e.46.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.i.c.16.1	✓	6	1.1	even	1	trivial
105.4.i.c.46.1	yes	6	7.4	even	3	inner
315.4.j.e.46.3		6	21.11	odd	6
315.4.j.e.226.3		6	3.2	odd	2
735.4.a.r.1.3		3	7.2	even	3
735.4.a.s.1.3		3	7.5	odd	6
2205.4.a.bi.1.1		3	21.2	odd	6
2205.4.a.bj.1.1		3	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.05859 + 3.56558i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.47557 - 7.75191i) q^{4} +(-2.50000 + 4.33013i) q^{5} -12.3515 q^{6} +(-9.40914 - 15.9521i) q^{7} +3.91601 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-2.05859 + 3.56558i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-4.47557 - 7.75191i) q^{4} +(-2.50000 + 4.33013i) q^{5} -12.3515 q^{6} +(-9.40914 - 15.9521i) q^{7} +3.91601 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-10.2929 - 17.8279i) q^{10} +(-7.99313 - 13.8445i) q^{11} +(13.4267 - 23.2557i) q^{12} -79.5076 q^{13} +(76.2479 - 0.710343i) q^{14} -15.0000 q^{15} +(27.7431 - 48.0525i) q^{16} +(34.7362 + 60.1649i) q^{17} +(-18.5273 - 32.0902i) q^{18} +(20.6015 - 35.6828i) q^{19} +44.7557 q^{20} +(27.3309 - 48.3738i) q^{21} +65.8183 q^{22} +(5.63966 - 9.76818i) q^{23} +(5.87401 + 10.1741i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(163.673 - 283.491i) q^{26} -27.0000 q^{27} +(-81.5477 + 144.333i) q^{28} +16.1213 q^{29} +(30.8788 - 53.4837i) q^{30} +(-35.5888 - 61.6416i) q^{31} +(129.887 + 224.971i) q^{32} +(23.9794 - 41.5335i) q^{33} -286.030 q^{34} +(92.5973 - 0.862658i) q^{35} +80.5603 q^{36} +(-178.238 + 308.717i) q^{37} +(84.8200 + 146.913i) q^{38} +(-119.261 - 206.567i) q^{39} +(-9.79002 + 16.9568i) q^{40} -426.478 q^{41} +(116.217 + 197.032i) q^{42} -346.164 q^{43} +(-71.5477 + 123.924i) q^{44} +(-22.5000 - 38.9711i) q^{45} +(23.2195 + 40.2173i) q^{46} +(-70.1765 + 121.549i) q^{47} +166.459 q^{48} +(-165.936 + 300.190i) q^{49} +102.929 q^{50} +(-104.209 + 180.495i) q^{51} +(355.842 + 616.336i) q^{52} +(-171.325 - 296.743i) q^{53} +(55.5819 - 96.2706i) q^{54} +79.9313 q^{55} +(-36.8463 - 62.4684i) q^{56} +123.609 q^{57} +(-33.1871 + 57.4817i) q^{58} +(384.259 + 665.557i) q^{59} +(67.1335 + 116.279i) q^{60} +(292.896 - 507.311i) q^{61} +293.051 q^{62} +(166.675 - 1.55278i) q^{63} -625.648 q^{64} +(198.769 - 344.278i) q^{65} +(98.7274 + 171.001i) q^{66} +(91.8419 + 159.075i) q^{67} +(310.929 - 538.545i) q^{68} +33.8380 q^{69} +(-187.544 + 331.939i) q^{70} -881.259 q^{71} +(-17.6220 + 30.5223i) q^{72} +(6.04661 + 10.4730i) q^{73} +(-733.836 - 1271.04i) q^{74} +(37.5000 - 64.9519i) q^{75} -368.814 q^{76} +(-145.640 + 257.772i) q^{77} +982.041 q^{78} +(591.821 - 1025.06i) q^{79} +(138.716 + 240.262i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(877.942 - 1520.64i) q^{82} -245.258 q^{83} +(-497.311 + 4.63306i) q^{84} -347.362 q^{85} +(712.610 - 1234.28i) q^{86} +(24.1819 + 41.8843i) q^{87} +(-31.3012 - 54.2153i) q^{88} +(-443.596 + 768.331i) q^{89} +185.273 q^{90} +(748.099 + 1268.31i) q^{91} -100.963 q^{92} +(106.766 - 184.925i) q^{93} +(-288.929 - 500.439i) q^{94} +(103.008 + 178.414i) q^{95} +(-389.662 + 674.914i) q^{96} +1371.47 q^{97} +(-728.759 - 1209.63i) q^{98} +143.876 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9	\( 6 q - 3 q^{2} + 9 q^{3} - q^{4} - 15 q^{5} - 18 q^{6} - 2 q^{7} + 18 q^{8} - 27 q^{9} - 15 q^{10} + q^{11} + 3 q^{12} - 158 q^{13} + 161 q^{14} - 90 q^{15} + 79 q^{16} + 72 q^{17} - 27 q^{18} + 29 q^{19} + 10 q^{20} - 39 q^{21} + 286 q^{22} + 63 q^{23} + 27 q^{24} - 75 q^{25} + 339 q^{26} - 162 q^{27} - 195 q^{28} + 440 q^{29} + 45 q^{30} - 136 q^{31} + 155 q^{32} - 3 q^{33} - 440 q^{34} - 55 q^{35} + 18 q^{36} - 43 q^{37} + 21 q^{38} - 237 q^{39} - 45 q^{40} - 1198 q^{41} - 42 q^{42} + 340 q^{43} - 135 q^{44} - 135 q^{45} - 265 q^{46} + 3 q^{47} + 474 q^{48} - 192 q^{49} + 150 q^{50} - 216 q^{51} + 701 q^{52} - 331 q^{53} + 81 q^{54} - 10 q^{55} - 1176 q^{56} + 174 q^{57} + 472 q^{58} + 1520 q^{59} + 15 q^{60} + 1160 q^{61} - 1496 q^{62} - 99 q^{63} + 34 q^{64} + 395 q^{65} + 429 q^{66} - 806 q^{67} + 684 q^{68} + 378 q^{69} - 875 q^{70} - 812 q^{71} - 81 q^{72} + 1192 q^{73} - 959 q^{74} + 225 q^{75} - 1182 q^{76} - 1309 q^{77} + 2034 q^{78} + 2590 q^{79} + 395 q^{80} - 243 q^{81} + 1191 q^{82} - 1016 q^{83} - 1629 q^{84} - 720 q^{85} + 742 q^{86} + 660 q^{87} + 749 q^{88} - 42 q^{89} + 270 q^{90} + 1346 q^{91} - 422 q^{92} + 408 q^{93} + 1167 q^{94} + 145 q^{95} - 465 q^{96} - 2040 q^{97} - 4053 q^{98} - 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 9 * q^3 - q^4 - 15 * q^5 - 18 * q^6 - 2 * q^7 + 18 * q^8 - 27 * q^9 - 15 * q^10 + q^11 + 3 * q^12 - 158 * q^13 + 161 * q^14 - 90 * q^15 + 79 * q^16 + 72 * q^17 - 27 * q^18 + 29 * q^19 + 10 * q^20 - 39 * q^21 + 286 * q^22 + 63 * q^23 + 27 * q^24 - 75 * q^25 + 339 * q^26 - 162 * q^27 - 195 * q^28 + 440 * q^29 + 45 * q^30 - 136 * q^31 + 155 * q^32 - 3 * q^33 - 440 * q^34 - 55 * q^35 + 18 * q^36 - 43 * q^37 + 21 * q^38 - 237 * q^39 - 45 * q^40 - 1198 * q^41 - 42 * q^42 + 340 * q^43 - 135 * q^44 - 135 * q^45 - 265 * q^46 + 3 * q^47 + 474 * q^48 - 192 * q^49 + 150 * q^50 - 216 * q^51 + 701 * q^52 - 331 * q^53 + 81 * q^54 - 10 * q^55 - 1176 * q^56 + 174 * q^57 + 472 * q^58 + 1520 * q^59 + 15 * q^60 + 1160 * q^61 - 1496 * q^62 - 99 * q^63 + 34 * q^64 + 395 * q^65 + 429 * q^66 - 806 * q^67 + 684 * q^68 + 378 * q^69 - 875 * q^70 - 812 * q^71 - 81 * q^72 + 1192 * q^73 - 959 * q^74 + 225 * q^75 - 1182 * q^76 - 1309 * q^77 + 2034 * q^78 + 2590 * q^79 + 395 * q^80 - 243 * q^81 + 1191 * q^82 - 1016 * q^83 - 1629 * q^84 - 720 * q^85 + 742 * q^86 + 660 * q^87 + 749 * q^88 - 42 * q^89 + 270 * q^90 + 1346 * q^91 - 422 * q^92 + 408 * q^93 + 1167 * q^94 + 145 * q^95 - 465 * q^96 - 2040 * q^97 - 4053 * q^98 - 18 * q^99

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