LMFDB - Embedded newform 165.4.p.a.41.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,4,Mod(41,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("165.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	165.p (of order $10$, degree $4$, 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:	$9.73531515095$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.10
Character	$\chi$	$=$	165.41
Dual form			165.4.p.a.161.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.84801 + 2.06920i) q^{2} +(4.14644 - 3.13162i) q^{3} +(1.35744 - 4.17778i) q^{4} +(2.93893 - 4.04508i) q^{5} +(-5.32916 + 17.4987i) q^{6} +(-7.01306 - 2.27868i) q^{7} +(-3.92409 - 12.0771i) q^{8} +(7.38594 - 25.9701i) q^{9} +17.6017i q^{10} +(-35.7314 - 7.36645i) q^{11} +(-7.45466 - 21.5739i) q^{12} +(24.2515 + 33.3793i) q^{13} +(24.6883 - 8.02173i) q^{14} +(-0.481578 - 25.9763i) q^{15} +(64.5965 + 46.9321i) q^{16} +(-92.0548 - 66.8817i) q^{17} +(32.7022 + 89.2463i) q^{18} +(-149.209 + 48.4809i) q^{19} +(-12.9101 - 17.7692i) q^{20} +(-36.2152 + 12.5138i) q^{21} +(117.006 - 52.9558i) q^{22} +46.5502i q^{23} +(-54.0919 - 37.7883i) q^{24} +(-7.72542 - 23.7764i) q^{25} +(-138.137 - 44.8834i) q^{26} +(-50.7032 - 130.814i) q^{27} +(-19.0397 + 26.2059i) q^{28} +(50.6416 - 155.859i) q^{29} +(55.1218 + 72.9844i) q^{30} +(32.9018 - 23.9045i) q^{31} -179.495 q^{32} +(-171.227 + 81.3526i) q^{33} +400.565 q^{34} +(-29.8283 + 21.6716i) q^{35} +(-98.4716 - 66.1098i) q^{36} +(86.4104 - 265.944i) q^{37} +(324.632 - 446.818i) q^{38} +(205.088 + 62.4588i) q^{39} +(-60.3856 - 19.6205i) q^{40} +(-153.451 - 472.274i) q^{41} +(77.2478 - 110.576i) q^{42} +75.0666i q^{43} +(-79.2788 + 139.279i) q^{44} +(-83.3447 - 106.201i) q^{45} +(-96.3217 - 132.576i) q^{46} +(-21.1101 + 6.85909i) q^{47} +(414.819 - 7.69039i) q^{48} +(-233.502 - 169.649i) q^{49} +(71.2003 + 51.7301i) q^{50} +(-591.148 + 10.9594i) q^{51} +(172.371 - 56.0068i) q^{52} +(428.794 + 590.184i) q^{53} +(415.083 + 267.644i) q^{54} +(-134.810 + 122.887i) q^{55} +93.6394i q^{56} +(-466.862 + 668.289i) q^{57} +(178.275 + 548.675i) q^{58} +(-530.742 - 172.449i) q^{59} +(-109.177 - 33.2494i) q^{60} +(-103.934 + 143.053i) q^{61} +(-44.2414 + 136.161i) q^{62} +(-110.976 + 165.300i) q^{63} +(-5.56867 + 4.04588i) q^{64} +206.295 q^{65} +(319.322 - 585.997i) q^{66} +250.246 q^{67} +(-404.377 + 293.797i) q^{68} +(145.777 + 193.018i) q^{69} +(40.1087 - 123.442i) q^{70} +(182.830 - 251.644i) q^{71} +(-342.628 + 12.7084i) q^{72} +(334.651 + 108.735i) q^{73} +(304.194 + 936.213i) q^{74} +(-106.492 - 74.3944i) q^{75} +689.173i q^{76} +(233.801 + 133.082i) q^{77} +(-713.334 + 246.486i) q^{78} +(479.922 + 660.556i) q^{79} +(379.689 - 123.368i) q^{80} +(-619.896 - 383.628i) q^{81} +(1414.26 + 1027.52i) q^{82} +(643.162 + 467.285i) q^{83} +(3.11988 + 168.286i) q^{84} +(-541.085 + 175.809i) q^{85} +(-155.328 - 213.791i) q^{86} +(-278.108 - 804.849i) q^{87} +(51.2480 + 460.439i) q^{88} -706.692i q^{89} +(457.118 + 130.005i) q^{90} +(-94.0162 - 289.352i) q^{91} +(194.476 + 63.1892i) q^{92} +(61.5654 - 202.155i) q^{93} +(45.9290 - 63.2159i) q^{94} +(-242.405 + 746.045i) q^{95} +(-744.265 + 562.109i) q^{96} +(-171.572 + 124.654i) q^{97} +1016.06 q^{98} +(-455.218 + 873.542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 4 q^{3} - 192 q^{4} - 100 q^{6} + 108 q^{9} + 48 q^{12} - 60 q^{15} - 1248 q^{16} - 460 q^{18} + 900 q^{19} + 888 q^{22} + 1200 q^{24} + 1200 q^{25} + 568 q^{27} - 1680 q^{28} - 576 q^{31} - 1402 q^{33}+ \cdots - 736 q^{99}+O(q^{100}) $ 192 * q + 4 * q^3 - 192 * q^4 - 100 * q^6 + 108 * q^9 + 48 * q^12 - 60 * q^15 - 1248 * q^16 - 460 * q^18 + 900 * q^19 + 888 * q^22 + 1200 * q^24 + 1200 * q^25 + 568 * q^27 - 1680 * q^28 - 576 * q^31 - 1402 * q^33 + 264 * q^34 - 2364 * q^36 + 24 * q^37 + 1220 * q^39 + 4438 * q^42 - 360 * q^46 + 1946 * q^48 + 1848 * q^49 + 930 * q^51 + 840 * q^55 - 4170 * q^57 + 4320 * q^58 - 830 * q^60 - 1560 * q^61 - 7900 * q^63 - 11700 * q^64 - 4214 * q^66 + 168 * q^67 - 4992 * q^69 - 1620 * q^70 + 6720 * q^72 - 360 * q^73 + 150 * q^75 + 13972 * q^78 + 4740 * q^79 + 916 * q^81 + 6420 * q^82 + 6880 * q^84 + 2868 * q^88 + 8736 * q^91 - 5696 * q^93 - 840 * q^94 - 12470 * q^96 - 7356 * q^97 - 736 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

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 $

$2$	−2.84801	+	2.06920i	−1.00692	+	0.731574i	−0.963562	−	0.267486i	$-0.913807\pi$
$2$	−2.84801	+	2.06920i	−1.00692	+	0.731574i	−0.0433629	+	0.999059i	$0.513807\pi$
$3$	4.14644	−	3.13162i	0.797983	−	0.602680i
$3$	4.14644	−	3.13162i	0.797983	−	0.602680i
$4$	1.35744	−	4.17778i	0.169680	−	0.522223i
$5$	2.93893	−	4.04508i	0.262866	−	0.361803i
$5$	2.93893	−	4.04508i	0.262866	−	0.361803i
$6$	−5.32916	+	17.4987i	−0.362604	+	1.19064i
$7$	−7.01306	−	2.27868i	−0.378670	−	0.123037i	0.113497	−	0.993538i	$-0.463795\pi$
$7$	−7.01306	−	2.27868i	−0.378670	−	0.123037i	−0.492166	+	0.870501i	$0.663795\pi$
$8$	−3.92409	−	12.0771i	−0.173422	−	0.533738i
$9$	7.38594	−	25.9701i	0.273553	−	0.961857i
$10$			17.6017i			0.556614i
$11$	−35.7314	−	7.36645i	−0.979403	−	0.201915i
$11$	−35.7314	−	7.36645i	−0.979403	−	0.201915i
$12$	−7.45466	−	21.5739i	−0.179331	−	0.518988i
$13$	24.2515	+	33.3793i	0.517396	+	0.712134i	0.985145	−	0.171727i	$-0.0549348\pi$
$13$	24.2515	+	33.3793i	0.517396	+	0.712134i	−0.467749	+	0.883861i	$0.654935\pi$
$14$	24.6883	−	8.02173i	0.471303	−	0.153136i
$15$	−0.481578	−	25.9763i	−0.00828952	−	0.447137i
$16$	64.5965	+	46.9321i	1.00932	+	0.733315i
$17$	−92.0548	−	66.8817i	−1.31333	−	0.954189i	−0.999990	−	0.00454698i	$-0.998553\pi$
$17$	−92.0548	−	66.8817i	−1.31333	−	0.954189i	−0.313338	−	0.949642i	$-0.601447\pi$
$18$	32.7022	+	89.2463i	0.428222	+	1.16864i
$19$	−149.209	+	48.4809i	−1.80163	+	0.585384i	−0.999924	−	0.0123402i	$-0.996072\pi$
$19$	−149.209	+	48.4809i	−1.80163	+	0.585384i	−0.801702	+	0.597724i	$0.796072\pi$
$20$	−12.9101	−	17.7692i	−0.144339	−	0.198665i
$21$	−36.2152	+	12.5138i	−0.376324	+	0.130035i
$22$	117.006	−	52.9558i	1.13390	−	0.513192i
$23$			46.5502i			0.422017i	0.977484	+	0.211008i	$0.0676747\pi$
$23$			46.5502i			0.422017i	−0.977484	+	0.211008i	$0.932325\pi$
$24$	−54.0919	−	37.7883i	−0.460061	−	0.321396i
$25$	−7.72542	−	23.7764i	−0.0618034	−	0.190211i
$26$	−138.137	−	44.8834i	−1.04196	−	0.338552i
$27$	−50.7032	−	130.814i	−0.361401	−	0.932410i
$28$	−19.0397	+	26.2059i	−0.128506	+	0.176873i
$29$	50.6416	−	155.859i	0.324272	−	0.998008i	−0.647496	−	0.762069i	$-0.724184\pi$
$29$	50.6416	−	155.859i	0.324272	−	0.998008i	0.971768	−	0.235939i	$-0.0758164\pi$
$30$	55.1218	+	72.9844i	0.335460	+	0.444169i
$31$	32.9018	−	23.9045i	0.190624	−	0.138496i	−0.488380	−	0.872631i	$-0.662412\pi$
$31$	32.9018	−	23.9045i	0.190624	−	0.138496i	0.679004	+	0.734135i	$0.262412\pi$
$32$	−179.495			−0.991578
$33$	−171.227	+	81.3526i	−0.903237	+	0.429142i
$34$	400.565			2.02048
$35$	−29.8283	+	21.6716i	−0.144055	+	0.104662i
$36$	−98.4716	−	66.1098i	−0.455887	−	0.306064i
$37$	86.4104	−	265.944i	0.383940	−	1.18165i	−0.553306	−	0.832978i	$-0.686634\pi$
$37$	86.4104	−	265.944i	0.383940	−	1.18165i	0.937246	−	0.348668i	$-0.113366\pi$
$38$	324.632	−	446.818i	1.38585	−	1.90746i
$39$	205.088	+	62.4588i	0.842062	+	0.256447i
$40$	−60.3856	−	19.6205i	−0.238695	−	0.0775567i
$41$	−153.451	−	472.274i	−0.584513	−	1.79895i	−0.601218	−	0.799085i	$-0.705318\pi$
$41$	−153.451	−	472.274i	−0.584513	−	1.79895i	0.0167054	−	0.999860i	$-0.494682\pi$
$42$	77.2478	−	110.576i	0.283800	−	0.406244i
$43$			75.0666i			0.266222i	0.991101	+	0.133111i	$0.0424967\pi$
$43$			75.0666i			0.266222i	−0.991101	+	0.133111i	$0.957503\pi$
$44$	−79.2788	+	139.279i	−0.271630	+	0.477205i
$45$	−83.3447	−	106.201i	−0.276095	−	0.351812i
$46$	−96.3217	−	132.576i	−0.308736	−	0.424939i
$47$	−21.1101	+	6.85909i	−0.0655155	+	0.0212873i	−0.341591	−	0.939849i	$-0.610966\pi$
$47$	−21.1101	+	6.85909i	−0.0655155	+	0.0212873i	0.276076	+	0.961136i	$0.410966\pi$
$48$	414.819	−	7.69039i	1.24738	−	0.0231252i
$49$	−233.502	−	169.649i	−0.680764	−	0.494604i
$50$	71.2003	+	51.7301i	0.201385	+	0.146315i
$51$	−591.148	+	10.9594i	−1.62308	+	0.0300906i
$52$	172.371	−	56.0068i	0.459684	−	0.149361i
$53$	428.794	+	590.184i	1.11131	+	1.52959i	0.819474	+	0.573116i	$0.194266\pi$
$53$	428.794	+	590.184i	1.11131	+	1.52959i	0.291835	+	0.956469i	$0.405734\pi$
$54$	415.083	+	267.644i	1.04603	+	0.674475i
$55$	−134.810	+	122.887i	−0.330505	+	0.301275i
$56$			93.6394i			0.223448i
$57$	−466.862	+	668.289i	−1.08487	+	1.55293i
$58$	178.275	+	548.675i	0.403598	+	1.24215i
$59$	−530.742	−	172.449i	−1.17113	−	0.380524i	−0.342067	−	0.939676i	$-0.611127\pi$
$59$	−530.742	−	172.449i	−1.17113	−	0.380524i	−0.829065	+	0.559152i	$0.811127\pi$
$60$	−109.177	−	33.2494i	−0.234912	−	0.0715414i
$61$	−103.934	+	143.053i	−0.218154	+	0.300263i	−0.904042	−	0.427444i	$-0.859414\pi$
$61$	−103.934	+	143.053i	−0.218154	+	0.300263i	0.685888	+	0.727707i	$0.259414\pi$
$62$	−44.2414	+	136.161i	−0.0906236	+	0.278911i
$63$	−110.976	+	165.300i	−0.221931	+	0.330569i
$64$	−5.56867	+	4.04588i	−0.0108763	+	0.00790211i
$65$	206.295			0.393658
$66$	319.322	−	585.997i	0.595543	−	1.09290i
$67$	250.246			0.456305			0.228152	−	0.973625i	$-0.426732\pi$
$67$	250.246			0.456305			0.228152	+	0.973625i	$0.426732\pi$
$68$	−404.377	+	293.797i	−0.721145	+	0.523942i
$69$	145.777	+	193.018i	0.254341	+	0.336762i
$70$	40.1087	−	123.442i	0.0684843	−	0.210773i
$71$	182.830	−	251.644i	0.305605	−	0.420629i	−0.628399	−	0.777891i	$-0.716290\pi$
$71$	182.830	−	251.644i	0.305605	−	0.420629i	0.934004	+	0.357262i	$0.116290\pi$
$72$	−342.628	+	12.7084i	−0.560820	+	0.0208014i
$73$	334.651	+	108.735i	0.536547	+	0.174335i	0.564742	−	0.825268i	$-0.308976\pi$
$73$	334.651	+	108.735i	0.536547	+	0.174335i	−0.0281945	+	0.999602i	$0.508976\pi$
$74$	304.194	+	936.213i	0.477863	+	1.47071i
$75$	−106.492	−	74.3944i	−0.163955	−	0.114538i
$76$			689.173i			1.04018i
$77$	233.801	+	133.082i	0.346027	+	0.196962i
$78$	−713.334	+	246.486i	−1.03550	+	0.357808i
$79$	479.922	+	660.556i	0.683487	+	0.940739i	0.999969	−	0.00785944i	$-0.00250176\pi$
$79$	479.922	+	660.556i	0.683487	+	0.940739i	−0.316482	+	0.948598i	$0.602502\pi$
$80$	379.689	−	123.368i	0.530631	−	0.172413i
$81$	−619.896	−	383.628i	−0.850337	−	0.526238i
$82$	1414.26	+	1027.52i	1.90462	+	1.38379i
$83$	643.162	+	467.285i	0.850557	+	0.617966i	0.925300	−	0.379237i	$-0.123814\pi$
$83$	643.162	+	467.285i	0.850557	+	0.617966i	−0.0747426	+	0.997203i	$0.523814\pi$
$84$	3.11988	+	168.286i	0.00405246	+	0.218589i
$85$	−541.085	+	175.809i	−0.690457	+	0.224343i
$86$	−155.328	−	213.791i	−0.194761	−	0.268066i
$87$	−278.108	−	804.849i	−0.342716	−	0.991826i
$88$	51.2480	+	460.439i	0.0620801	+	0.557762i
$89$		−	706.692i		−	0.841676i	−0.907136	−	0.420838i	$-0.861736\pi$
$89$		−	706.692i		−	0.841676i	0.907136	−	0.420838i	$-0.138264\pi$
$90$	457.118	+	130.005i	0.535383	+	0.152264i
$91$	−94.0162	−	289.352i	−0.108303	−	0.333323i
$92$	194.476	+	63.1892i	0.220387	+	0.0716080i
$93$	61.5654	−	202.155i	0.0686455	−	0.225403i
$94$	45.9290	−	63.2159i	0.0503960	−	0.0693641i
$95$	−242.405	+	746.045i	−0.261792	+	0.805712i
$96$	−744.265	+	562.109i	−0.791262	+	0.597605i
$97$	−171.572	+	124.654i	−0.179593	+	0.130482i	−0.673950	−	0.738777i	$-0.735404\pi$
$97$	−171.572	+	124.654i	−0.179593	+	0.130482i	0.494357	+	0.869259i	$0.335404\pi$
$98$	1016.06			1.04732
$99$	−455.218	+	873.542i	−0.462133	+	0.886811i
$100$	−109.819			−0.109819
$101$	−1511.09	+	1097.87i	−1.48870	+	1.08161i	−0.514084	+	0.857740i	$0.671868\pi$
$101$	−1511.09	+	1097.87i	−1.48870	+	1.08161i	−0.974620	+	0.223866i	$0.928132\pi$
$102$	1660.92	−	1254.42i	1.61231	−	1.21770i
$103$	386.256	−	1188.77i	0.369504	−	1.13722i	−0.577608	−	0.816314i	$-0.696014\pi$
$103$	386.256	−	1188.77i	0.369504	−	1.13722i	0.947112	−	0.320902i	$-0.103986\pi$
$104$	307.960	−	423.871i	0.290365	−	0.399654i
$105$	−55.8144	+	183.271i	−0.0518755	+	0.170337i
$106$	−2442.42	−	793.591i	−2.23801	−	0.727173i
$107$	505.479	+	1555.70i	0.456696	+	1.40557i	0.869133	+	0.494579i	$0.164678\pi$
$107$	505.479	+	1555.70i	0.456696	+	1.40557i	−0.412437	+	0.910986i	$0.635322\pi$
$108$	−615.337	+	34.2548i	−0.548249	+	0.0305201i
$109$		−	587.144i		−	0.515947i	−0.966152	−	0.257973i	$-0.916945\pi$
$109$		−	587.144i		−	0.515947i	0.966152	−	0.257973i	$-0.0830547\pi$
$110$	129.662	−	628.934i	0.112389	−	0.545150i
$111$	−474.539	−	1373.33i	−0.405777	−	1.17433i
$112$	−346.076	−	476.333i	−0.291974	−	0.401868i
$113$	−405.507	+	131.757i	−0.337583	+	0.109687i	−0.472903	−	0.881115i	$-0.656794\pi$
$113$	−405.507	+	131.757i	−0.337583	+	0.109687i	0.135320	+	0.990802i	$0.456794\pi$
$114$	−53.1948	−	2869.33i	−0.0437031	−	2.35734i
$115$	188.299	+	136.808i	0.152687	+	0.110934i
$116$	−582.400	−	423.139i	−0.466160	−	0.338685i
$117$	1045.98	−	383.276i	0.826506	−	0.302854i
$118$	1868.39	−	607.078i	1.45762	−	0.473610i
$119$	493.184	+	678.810i	0.379917	+	0.522911i
$120$	−311.829	+	107.750i	−0.237216	+	0.0819678i
$121$	1222.47	+	526.428i	0.918460	+	0.395513i
$122$		−	622.476i		−	0.461937i
$123$	−2115.26	−	1477.70i	−1.55062	−	1.08325i
$124$	−55.2057	−	169.906i	−0.0399808	−	0.123048i
$125$	−118.882	−	38.6271i	−0.0850651	−	0.0276393i
$126$	−25.9788	−	700.408i	−0.0183681	−	0.495217i
$127$	1139.92	−	1568.97i	0.796472	−	1.09625i	−0.196800	−	0.980444i	$-0.563055\pi$
$127$	1139.92	−	1568.97i	0.796472	−	1.09625i	0.993272	−	0.115806i	$-0.0369451\pi$
$128$	451.224	−	1388.72i	0.311585	−	0.958961i
$129$	235.080	+	311.259i	0.160447	+	0.212441i
$130$	−587.531	+	426.867i	−0.396384	+	0.287990i
$131$	2218.59			1.47969			0.739844	−	0.672779i	$-0.234899\pi$
$131$	2218.59			1.47969			0.739844	+	0.672779i	$0.234899\pi$
$132$	107.442	+	825.781i	0.0708458	+	0.544508i
$133$	1156.88			0.754245
$134$	−712.704	+	517.810i	−0.459464	+	0.333820i
$135$	−678.165	−	179.353i	−0.432349	−	0.114342i
$136$	−446.507	+	1374.21i	−0.281527	+	0.866451i
$137$	208.434	−	286.885i	0.129983	−	0.178907i	−0.739065	−	0.673634i	$-0.764732\pi$
$137$	208.434	−	286.885i	0.129983	−	0.178907i	0.869048	+	0.494728i	$0.164732\pi$
$138$	−814.568	−	248.074i	−0.502468	−	0.153025i
$139$	−1578.70	−	512.952i	−0.963338	−	0.313007i	−0.215214	−	0.976567i	$-0.569045\pi$
$139$	−1578.70	−	512.952i	−0.963338	−	0.313007i	−0.748124	+	0.663559i	$0.769045\pi$
$140$	50.0487	+	154.034i	0.0302135	+	0.0929876i
$141$	−66.0518	+	94.5497i	−0.0394508	+	0.0564718i
$142$			1095.00i			0.647114i
$143$	−620.652	−	1371.34i	−0.362948	−	0.801936i
$144$	1695.94	−	1330.94i	0.981447	−	0.770222i
$145$	−481.630	−	662.907i	−0.275843	−	0.379665i
$146$	−1178.09	+	382.783i	−0.667801	+	0.216982i
$147$	−1499.48	+	27.7990i	−0.841326	+	0.0155975i
$148$	−993.759	−	722.008i	−0.551936	−	0.401005i
$149$	−1212.69	−	881.071i	−0.666762	−	0.484431i	0.202178	−	0.979349i	$-0.435198\pi$
$149$	−1212.69	−	881.071i	−0.666762	−	0.484431i	−0.868940	+	0.494918i	$0.835198\pi$
$150$	457.227	−	8.47658i	0.248883	−	0.00461407i
$151$	1625.16	−	528.046i	0.875851	−	0.284581i	0.163618	−	0.986524i	$-0.447684\pi$
$151$	1625.16	−	528.046i	0.875851	−	0.284581i	0.712234	+	0.701943i	$0.247684\pi$
$152$	1171.02	+	1611.77i	0.624883	+	0.860078i
$153$	−2416.84	+	1896.69i	−1.27706	+	1.00221i
$154$	−941.242	+	104.762i	−0.492516	+	0.0548181i
$155$		−	203.344i		−	0.105374i
$156$	539.335	−	772.030i	0.276804	−	0.396230i
$157$	555.579	+	1709.90i	0.282421	+	0.869202i	0.987160	+	0.159735i	$0.0510641\pi$
$157$	555.579	+	1709.90i	0.282421	+	0.869202i	−0.704739	+	0.709467i	$0.748936\pi$
$158$	−2733.65	−	888.217i	−1.37644	−	0.447232i
$159$	3626.20	+	1104.34i	1.80866	+	0.550819i
$160$	−527.522	+	726.072i	−0.260652	+	0.358756i
$161$	106.073	−	326.459i	0.0519238	−	0.159805i
$162$	2559.27	−	190.114i	1.24121	−	0.0922021i
$163$	606.553	−	440.686i	0.291466	−	0.211762i	−0.432437	−	0.901664i	$-0.642346\pi$
$163$	606.553	−	440.686i	0.291466	−	0.211762i	0.723903	+	0.689902i	$0.242346\pi$
$164$	−2181.36			−1.03863
$165$	−174.146	+	931.718i	−0.0821650	+	0.439601i
$166$	−2798.64			−1.30853
$167$	−1387.99	+	1008.43i	−0.643148	+	0.467274i	−0.860930	−	0.508723i	$-0.830118\pi$
$167$	−1387.99	+	1008.43i	−0.643148	+	0.467274i	0.217782	+	0.975997i	$0.430118\pi$
$168$	293.243	+	388.270i	0.134668	+	0.178308i
$169$	152.868	−	470.480i	0.0695804	−	0.214146i
$170$	1177.23	−	1620.32i	0.531115	−	0.731017i
$171$	157.008	+	4233.06i	0.0702147	+	1.89304i
$172$	313.612	+	101.899i	0.139027	+	0.0451727i
$173$	−269.333	−	828.923i	−0.118364	−	0.364288i	0.874269	−	0.485441i	$-0.161341\pi$
$173$	−269.333	−	828.923i	−0.118364	−	0.364288i	−0.992634	+	0.121153i	$0.961341\pi$
$174$	2457.45	+	1716.76i	1.07068	+	0.747972i
$175$			184.349i			0.0796314i
$176$	−1962.40	−	2152.80i	−0.840464	−	0.922008i
$177$	−2740.74	+	947.034i	−1.16388	+	0.402166i
$178$	1462.29	+	2012.67i	0.615748	+	0.847504i
$179$	−279.272	+	90.7410i	−0.116613	+	0.0378899i	−0.366742	−	0.930323i	$-0.619527\pi$
$179$	−279.272	+	90.7410i	−0.116613	+	0.0378899i	0.250129	+	0.968212i	$0.419527\pi$
$180$	−556.821	+	204.034i	−0.230572	+	0.0844877i
$181$	−655.509	−	476.255i	−0.269191	−	0.195579i	0.444998	−	0.895532i	$-0.353204\pi$
$181$	−655.509	−	476.255i	−0.269191	−	0.195579i	−0.714189	+	0.699953i	$0.753204\pi$
$182$	866.488	+	629.540i	0.352903	+	0.256399i
$183$	17.0308	+	918.640i	0.00687952	+	0.371081i
$184$	562.192	−	182.667i	0.225246	−	0.0731870i
$185$	−821.812	−	1131.13i	−0.326599	−	0.449525i
$186$	242.960	+	703.130i	0.0957779	+	0.277183i
$187$	2796.57	+	3067.90i	1.09361	+	1.19972i
$188$			97.5043i			0.0378257i
$189$	57.5021	+	1032.94i	0.0221305	+	0.397541i
$190$	−853.347	−	2626.33i	−0.325833	−	1.00281i
$191$	2607.42	+	847.203i	0.987782	+	0.320950i	0.757973	−	0.652286i	$-0.226190\pi$
$191$	2607.42	+	847.203i	0.987782	+	0.320950i	0.229809	+	0.973236i	$0.426190\pi$
$192$	−10.4200	+	34.2150i	−0.00391667	+	0.0128607i
$193$	−129.948	+	178.859i	−0.0484658	+	0.0667074i	−0.832562	−	0.553932i	$-0.813127\pi$
$193$	−129.948	+	178.859i	−0.0484658	+	0.0667074i	0.784096	+	0.620639i	$0.213127\pi$
$194$	230.704	−	710.034i	0.0853793	−	0.262771i
$195$	855.391	−	646.038i	0.314132	−	0.237250i
$196$	−1025.72	+	745.232i	−0.373806	+	0.271586i
$197$	−2898.23			−1.04817			−0.524087	−	0.851665i	$-0.675593\pi$
$197$	−2898.23			−1.04817			−0.524087	+	0.851665i	$0.675593\pi$
$198$	−511.069	−	3429.80i	−0.183435	−	1.23104i
$199$	−2456.33			−0.874998			−0.437499	−	0.899219i	$-0.644136\pi$
$199$	−2456.33			−0.874998			−0.437499	+	0.899219i	$0.644136\pi$
$200$	−256.835	+	186.602i	−0.0908050	+	0.0659737i
$201$	1037.63	−	783.675i	0.364123	−	0.275006i
$202$	2031.89	−	6253.50i	0.707738	−	2.17819i
$203$	−710.305	+	977.651i	−0.245584	+	0.338018i
$204$	−756.664	+	2484.56i	−0.259692	+	0.852717i
$205$	−2361.37	−	767.255i	−0.804513	−	0.261402i
$206$	1359.75	+	4184.88i	0.459895	+	1.41541i
$207$	1208.91	+	343.817i	0.405920	+	0.115444i
$208$			3294.36i			1.09819i
$209$	5688.58	−	633.152i	1.88272	−	0.209551i
$210$	−220.264	−	637.449i	−0.0723794	−	0.209467i
$211$	−933.403	−	1284.72i	−0.304541	−	0.419165i	0.629128	−	0.777302i	$-0.283412\pi$
$211$	−933.403	−	1284.72i	−0.304541	−	0.419165i	−0.933669	+	0.358137i	$0.883412\pi$
$212$	3047.72	−	990.265i	0.987351	−	0.320810i
$213$	−29.9589	−	1615.98i	−0.00963732	−	0.519837i
$214$	−4658.68	−	3384.73i	−1.48813	−	1.08119i
$215$	303.651	+	220.615i	0.0963201	+	0.0699807i
$216$	−1380.89	+	1125.67i	−0.434988	+	0.354594i
$217$	−285.213	+	92.6714i	−0.0892237	+	0.0289905i
$218$	1214.92	+	1672.19i	0.377453	+	0.519520i
$219$	1728.13	−	597.137i	0.533224	−	0.184250i
$220$	330.399	+	730.019i	0.101252	+	0.223718i
$221$		−	4694.70i		−	1.42896i
$222$	4193.18	+	2929.33i	1.26769	+	0.885603i
$223$	−284.921	−	876.897i	−0.0855593	−	0.263325i	0.899119	−	0.437704i	$-0.144208\pi$
$223$	−284.921	−	876.897i	−0.0855593	−	0.263325i	−0.984679	+	0.174379i	$0.944208\pi$
$224$	1258.81	+	409.012i	0.375481	+	0.122001i
$225$	−674.536	+	25.0192i	−0.199863	+	0.00741310i
$226$	882.256	−	1214.32i	0.259676	−	0.357414i
$227$	484.314	−	1490.56i	0.141608	−	0.435825i	−0.854951	−	0.518709i	$-0.826413\pi$
$227$	484.314	−	1490.56i	0.141608	−	0.435825i	0.996559	+	0.0828836i	$0.0264130\pi$
$228$	2158.23	+	2857.61i	0.626895	+	0.830044i
$229$	729.252	−	529.833i	0.210438	−	0.152892i	−0.477574	−	0.878592i	$-0.658484\pi$
$229$	729.252	−	529.833i	0.210438	−	0.152892i	0.688012	+	0.725699i	$0.258484\pi$
$230$	−819.362			−0.234900
$231$	1386.20	−	180.359i	0.394829	−	0.0513711i
$232$	−2081.05			−0.588911
$233$	2877.87	−	2090.89i	0.809165	−	0.587893i	−0.104424	−	0.994533i	$-0.533300\pi$
$233$	2877.87	−	2090.89i	0.809165	−	0.587893i	0.913588	+	0.406640i	$0.133300\pi$
$234$	−2185.90	+	3255.93i	−0.610670	+	0.909601i
$235$	−34.2955	+	105.551i	−0.00951996	+	0.0292994i
$236$	−1440.91	+	1983.24i	−0.397436	+	0.547024i
$237$	4058.58	+	1236.02i	1.11238	+	0.338770i
$238$	−2809.19	−	912.761i	−0.765095	−	0.248595i
$239$	403.631	+	1242.25i	0.109242	+	0.336211i	0.990703	−	0.136046i	$-0.0434395\pi$
$239$	403.631	+	1242.25i	0.109242	+	0.336211i	−0.881461	+	0.472257i	$0.843439\pi$
$240$	1188.01	−	1700.58i	0.319525	−	0.457383i
$241$		−	903.011i		−	0.241361i	−0.992691	−	0.120681i	$-0.961492\pi$
$241$		−	903.011i		−	0.241361i	0.992691	−	0.120681i	$-0.0385077\pi$
$242$	−4570.90	+	1030.27i	−1.21417	+	0.273669i
$243$	−3771.74	+	350.588i	−0.995708	+	0.0925524i
$244$	456.558	+	628.399i	0.119788	+	0.164873i
$245$	−1372.49	+	445.949i	−0.357899	+	0.116288i
$246$	9081.95	−	168.371i	2.35384	−	0.0436381i
$247$	−5236.79	−	3804.75i	−1.34903	−	0.980124i
$248$	−417.808	−	303.555i	−0.106979	−	0.0777249i
$249$	4130.19	−	76.5701i	1.05117	−	0.0194877i
$250$	418.505	−	135.981i	0.105874	−	0.0344007i
$251$	1574.28	+	2166.81i	0.395887	+	0.544891i	0.959706	−	0.281007i	$-0.0906685\pi$
$251$	1574.28	+	2166.81i	0.395887	+	0.544891i	−0.563819	+	0.825898i	$0.690668\pi$
$252$	539.944	+	688.018i	0.134973	+	0.171988i
$253$	342.910	−	1663.30i	0.0852117	−	0.413324i
$254$			6827.19i			1.68652i
$255$	−1693.01	+	2423.45i	−0.415766	+	0.595147i
$256$	1571.44	+	4836.40i	0.383653	+	1.18076i
$257$	−2195.28	−	713.289i	−0.532832	−	0.173128i	0.0302291	−	0.999543i	$-0.490376\pi$
$257$	−2195.28	−	713.289i	−0.532832	−	0.173128i	−0.563061	+	0.826415i	$0.690376\pi$
$258$	−1313.57	−	400.043i	−0.316974	−	0.0965332i
$259$	−1212.00	+	1668.18i	−0.290773	+	0.400215i
$260$	280.034	−	861.856i	0.0667961	−	0.205577i
$261$	−3673.64	−	2466.33i	−0.871235	−	0.584912i
$262$	−6318.57	+	4590.71i	−1.48993	+	1.08250i
$263$	603.972			0.141606			0.0708032	−	0.997490i	$-0.477444\pi$
$263$	603.972			0.141606			0.0708032	+	0.997490i	$0.477444\pi$
$264$	1654.42	+	1748.70i	0.385691	+	0.407670i
$265$	3647.54			0.845534
$266$	−3294.82	+	2393.83i	−0.759468	+	0.551786i
$267$	−2213.09	−	2930.26i	−0.507261	−	0.671643i
$268$	339.695	−	1045.47i	0.0774260	−	0.238293i
$269$	2466.43	−	3394.75i	0.559037	−	0.769448i	−0.432167	−	0.901794i	$-0.642251\pi$
$269$	2466.43	−	3394.75i	0.559037	−	0.769448i	0.991204	+	0.132345i	$0.0422508\pi$
$270$	2302.54	−	892.462i	0.518993	−	0.201161i
$271$	−36.3705	−	11.8175i	−0.00815258	−	0.00264893i	0.304938	−	0.952372i	$-0.401364\pi$
$271$	−36.3705	−	11.8175i	−0.00815258	−	0.00264893i	−0.313090	+	0.949723i	$0.601364\pi$
$272$	−2807.52	−	8640.66i	−0.625849	−	1.92617i
$273$	−1295.97	−	905.359i	−0.287311	−	0.200714i
$274$			1248.34i			0.275238i
$275$	100.893	+	906.474i	0.0221238	+	0.198773i
$276$	1004.27	−	347.016i	0.219021	−	0.0756807i
$277$	−779.471	−	1072.85i	−0.169075	−	0.232712i	0.716068	−	0.698030i	$-0.245940\pi$
$277$	−779.471	−	1072.85i	−0.169075	−	0.232712i	−0.885144	+	0.465318i	$0.845940\pi$
$278$	5557.57	−	1805.77i	1.19900	−	0.389578i
$279$	−377.794	−	1031.02i	−0.0810678	−	0.221239i
$280$	378.779	+	275.199i	0.0808442	+	0.0587368i
$281$	1517.15	+	1102.27i	0.322083	+	0.234007i	0.737064	−	0.675823i	$-0.236212\pi$
$281$	1517.15	+	1102.27i	0.322083	+	0.234007i	−0.414981	+	0.909830i	$0.636212\pi$
$282$	−7.52602	−	405.953i	−0.00158925	−	0.0857240i
$283$	5434.58	−	1765.80i	1.14153	−	0.370905i	0.323582	−	0.946200i	$-0.395113\pi$
$283$	5434.58	−	1765.80i	1.14153	−	0.370905i	0.817946	+	0.575295i	$0.195113\pi$
$284$	−803.133	−	1105.42i	−0.167807	−	0.230966i
$285$	1331.21	+	3852.55i	0.276681	+	0.800721i
$286$	4605.20	+	2621.33i	0.952137	+	0.541966i
$287$			3661.75i			0.753123i
$288$	−1325.74	+	4661.51i	−0.271249	+	0.953756i
$289$	2482.72	+	7641.03i	0.505337	+	1.55527i
$290$	2743.38	+	891.377i	0.555505	+	0.180495i
$291$	−321.043	+	1054.17i	−0.0646731	+	0.212359i
$292$	908.540	−	1250.50i	0.182083	−	0.250616i
$293$	2518.73	−	7751.86i	0.502205	−	1.54563i	−0.303215	−	0.952922i	$-0.598060\pi$
$293$	2518.73	−	7751.86i	0.502205	−	1.54563i	0.805420	−	0.592705i	$-0.201940\pi$
$294$	4213.02	−	3181.90i	0.835742	−	0.631198i
$295$	−2257.38	+	1640.08i	−0.445525	+	0.323693i
$296$	−3550.92			−0.697274
$297$	848.066	+	5047.66i	0.165689	+	0.986178i
$298$	5276.88			1.02578
$299$	−1553.81	+	1128.91i	−0.300532	+	0.218350i
$300$	−455.360	+	343.913i	−0.0876341	+	0.0661860i
$301$	171.053	−	526.447i	0.0327553	−	0.100810i
$302$	−3535.84	+	4866.66i	−0.673724	+	0.927301i
$303$	−2827.53	+	9284.41i	−0.536097	+	1.76032i
$304$	−11913.7	−	3871.00i	−2.24769	−	0.730319i
$305$	273.206	+	840.842i	0.0512910	+	0.157857i
$306$	2958.55	−	10402.7i	0.552709	−	1.94341i
$307$		−	5744.47i		−	1.06793i	−0.845507	−	0.533964i	$-0.820702\pi$
$307$		−	5744.47i		−	1.06793i	0.845507	−	0.533964i	$-0.179298\pi$
$308$	873.359	−	796.118i	0.161572	−	0.147283i
$309$	−2121.20	−	6138.78i	−0.390520	−	1.13017i
$310$	420.760	+	579.127i	0.0770890	+	0.106104i
$311$	−9859.93	+	3203.69i	−1.79777	+	0.584130i	−0.999827	−	0.0186065i	$-0.994077\pi$
$311$	−9859.93	+	3203.69i	−1.79777	+	0.584130i	−0.797940	+	0.602736i	$0.794077\pi$
$312$	−50.4630	−	2721.97i	−0.00915674	−	0.493914i
$313$	−6034.10	−	4384.03i	−1.08967	−	0.791694i	−0.110329	−	0.993895i	$-0.535191\pi$
$313$	−6034.10	−	4384.03i	−1.08967	−	0.791694i	−0.979344	+	0.202201i	$0.935191\pi$
$314$	−5120.42	−	3720.20i	−0.920262	−	0.668609i
$315$	342.503	+	934.711i	0.0612630	+	0.167190i
$316$	3411.13	−	1108.34i	0.607250	−	0.197307i
$317$	−354.171	−	487.474i	−0.0627514	−	0.0863699i	0.776488	−	0.630132i	$-0.216999\pi$
$317$	−354.171	−	487.474i	−0.0627514	−	0.0863699i	−0.839239	+	0.543762i	$0.816999\pi$
$318$	−12612.6	+	4358.15i	−2.22415	+	0.768532i
$319$	−2957.62	+	5196.01i	−0.519107	+	0.911976i
$320$			34.4163i			0.00601228i
$321$	6967.81	+	4867.67i	1.21154	+	0.846376i
$322$	373.413	+	1149.25i	0.0646257	+	0.198898i
$323$	16977.9	+	5516.45i	2.92469	+	0.950290i
$324$	−2444.19	+	2069.04i	−0.419099	+	0.354773i
$325$	606.286	−	834.482i	0.103479	−	0.142427i
$326$	−815.601	+	2510.16i	−0.138564	+	0.426457i
$327$	−1838.71	−	2434.56i	−0.310951	−	0.411717i
$328$	−5101.55	+	3706.49i	−0.858799	+	0.623954i
$329$	163.676			0.0274279
$330$	−1431.94	−	3013.89i	−0.238866	−	0.502755i
$331$	−436.163			−0.0724281			−0.0362141	−	0.999344i	$-0.511530\pi$
$331$	−436.163			−0.0724281			−0.0362141	+	0.999344i	$0.511530\pi$
$332$	2825.27	−	2052.68i	0.467039	−	0.339323i
$333$	−6268.38	−	4208.34i	−1.03155	−	0.692539i
$334$	1866.36	−	5744.05i	0.305756	−	0.941020i
$335$	735.454	−	1012.27i	0.119947	−	0.165093i
$336$	−2926.68	−	891.308i	−0.475189	−	0.144717i
$337$	904.399	+	293.857i	0.146189	+	0.0474997i	0.381198	−	0.924494i	$-0.375512\pi$
$337$	904.399	+	293.857i	0.146189	+	0.0474997i	−0.235008	+	0.971993i	$0.575512\pi$
$338$	538.148	+	1656.25i	0.0866017	+	0.266533i
$339$	−1268.80	+	1816.22i	−0.203279	+	0.290983i
$340$			2499.18i			0.398639i
$341$	−1351.72	+	611.774i	−0.214662	+	0.0971538i
$342$	−9206.21	−	11730.9i	−1.45560	−	1.85478i
$343$	2737.66	+	3768.06i	0.430961	+	0.593167i
$344$	906.589	−	294.569i	0.142093	−	0.0461688i
$345$	1209.20	−	22.4175i	0.188699	−	0.00349832i
$346$	2482.27	+	1803.48i	0.385688	+	0.280218i
$347$	−6836.89	−	4967.29i	−1.05771	−	0.768468i	−0.0840427	−	0.996462i	$-0.526783\pi$
$347$	−6836.89	−	4967.29i	−1.05771	−	0.768468i	−0.973662	+	0.227994i	$0.926783\pi$
$348$	−3740.00	+	69.3363i	−0.576106	+	0.0106805i
$349$	7271.80	−	2362.75i	1.11533	−	0.362393i	0.307347	−	0.951598i	$-0.400559\pi$
$349$	7271.80	−	2362.75i	1.11533	−	0.362393i	0.807984	+	0.589205i	$0.200559\pi$
$350$	−381.456	−	525.029i	−0.0582562	−	0.0801828i
$351$	3136.83	−	4864.85i	0.477014	−	0.739791i
$352$	6413.61	+	1322.24i	0.971155	+	0.200215i
$353$			4644.45i			0.700281i	0.936697	+	0.350141i	$0.113866\pi$
$353$			4644.45i			0.700281i	−0.936697	+	0.350141i	$0.886134\pi$
$354$	5846.04	−	8368.30i	0.877722	−	1.25641i
$355$	−480.597	−	1479.13i	−0.0718520	−	0.221138i
$356$	−2952.40	−	959.294i	−0.439542	−	0.142816i
$357$	4170.73	+	1270.18i	0.618315	+	0.188305i
$358$	607.609	−	836.302i	0.0897015	−	0.123464i
$359$	10.3225	−	31.7693i	0.00151755	−	0.00467053i	−0.950295	−	0.311351i	$-0.899218\pi$
$359$	10.3225	−	31.7693i	0.00151755	−	0.00467053i	0.951812	+	0.306681i	$0.0992184\pi$
$360$	−955.551	+	1423.31i	−0.139894	+	0.208375i
$361$	14363.9	−	10436.0i	2.09416	−	1.52150i
$362$	2852.37			0.414135
$363$	6717.47	−	1645.51i	0.971284	−	0.237925i
$364$	−1336.47			−0.192446
$365$	1423.36	−	1034.13i	0.204115	−	0.148298i
$366$	−1949.36	−	2581.06i	−0.278400	−	0.368618i
$367$	−3418.59	+	10521.3i	−0.486237	+	1.49648i	0.343943	+	0.938990i	$0.388237\pi$
$367$	−3418.59	+	10521.3i	−0.486237	+	1.49648i	−0.830181	+	0.557495i	$0.811763\pi$
$368$	−2184.70	+	3006.98i	−0.309471	+	0.425950i
$369$	−13398.4	+	496.960i	−1.89022	+	0.0701103i
$370$	4681.06	+	1520.97i	0.657721	+	0.213707i
$371$	−1662.32	−	5116.08i	−0.232623	−	0.715940i
$372$	−760.986	−	531.620i	−0.106063	−	0.0740947i
$373$			67.5562i			0.00937781i	0.999989	+	0.00468891i	$0.00149253\pi$
$373$			67.5562i			0.00937781i	−0.999989	+	0.00468891i	$0.998507\pi$
$374$	−14312.8	−	2950.75i	−1.97887	−	0.407966i
$375$	−613.903	+	212.128i	−0.0845381	+	0.0292113i
$376$	165.676	+	228.034i	0.0227237	+	0.0312764i
$377$	6430.58	−	2089.42i	0.878492	−	0.285440i
$378$	−2301.13	−	2822.84i	−0.313115	−	0.384104i
$379$	−393.932	−	286.208i	−0.0533903	−	0.0387903i	0.560770	−	0.827972i	$-0.310505\pi$
$379$	−393.932	−	286.208i	−0.0533903	−	0.0387903i	−0.614160	+	0.789181i	$0.710505\pi$
$380$	2787.76	+	2025.43i	0.376340	+	0.273427i
$381$	−186.790	−	10075.5i	−0.0251169	−	1.35481i
$382$	−9179.00	+	2982.44i	−1.22942	+	0.399463i
$383$	−3880.77	−	5341.42i	−0.517749	−	0.712621i	0.467453	−	0.884018i	$-0.345172\pi$
$383$	−3880.77	−	5341.42i	−0.517749	−	0.712621i	−0.985202	+	0.171397i	$0.945172\pi$
$384$	−2477.98	−	7171.32i	−0.329307	−	0.953020i
$385$	1225.45	−	554.627i	0.162220	−	0.0734192i
$386$		−	778.282i		−	0.102626i
$387$	1949.49	+	554.438i	0.256068	+	0.0728260i
$388$	287.879	+	886.001i	0.0376672	+	0.115928i
$389$	2034.30	+	660.986i	0.265150	+	0.0861524i	0.438575	−	0.898695i	$-0.355483\pi$
$389$	2034.30	+	660.986i	0.265150	+	0.0861524i	−0.173425	+	0.984847i	$0.555483\pi$
$390$	−1099.38	+	3609.90i	−0.142742	+	0.468704i
$391$	3113.36	−	4285.17i	0.402683	−	0.554246i
$392$	−1132.59	+	3485.75i	−0.145930	+	0.449125i
$393$	9199.25	−	6947.77i	1.18077	−	0.891778i
$394$	8254.19	−	5997.02i	1.05543	−	0.766816i
$395$	4082.46			0.520028
$396$	3031.53	+	3087.59i	0.384698	+	0.391811i
$397$	−3989.00			−0.504288			−0.252144	−	0.967690i	$-0.581136\pi$
$397$	−3989.00			−0.504288			−0.252144	+	0.967690i	$0.581136\pi$
$398$	6995.66	−	5082.64i	0.881057	−	0.640125i
$399$	4796.95	−	3622.92i	0.601875	−	0.454569i
$400$	616.842	−	1898.44i	0.0771053	−	0.237306i
$401$	−5446.20	+	7496.05i	−0.678230	+	0.933504i	−0.999911	−	0.0133445i	$-0.995752\pi$
$401$	−5446.20	+	7496.05i	−0.678230	+	0.933504i	0.321681	+	0.946848i	$0.395752\pi$
$402$	−1333.60	+	4378.98i	−0.165458	+	0.543293i
$403$	1595.83	+	518.517i	0.197256	+	0.0640923i
$404$	2535.45	+	7803.30i	0.312236	+	0.960962i
$405$	−3373.63	+	1380.08i	−0.413919	+	0.169325i
$406$		−	4254.13i		−	0.520022i
$407$	−5046.63	+	8866.02i	−0.614625	+	1.07978i
$408$	2452.08	+	7096.36i	0.297539	+	0.861084i
$409$	−1426.91	−	1963.97i	−0.172508	−	0.237437i	0.714005	−	0.700141i	$-0.246879\pi$
$409$	−1426.91	−	1963.97i	−0.172508	−	0.237437i	−0.886513	+	0.462703i	$0.846879\pi$
$410$	8312.82	−	2701.00i	1.00132	−	0.325348i
$411$	−34.1544	−	1842.29i	−0.00409905	−	0.221103i
$412$	−4442.11	−	3227.38i	−0.531182	−	0.385927i
$413$	3329.17	+	2418.79i	0.396654	+	0.288186i
$414$	−4154.43	+	1522.29i	−0.493186	+	0.180717i
$415$	3780.41	−	1228.33i	0.447164	−	0.145292i
$416$	−4353.01	−	5991.41i	−0.513038	−	0.706137i
$417$	−8152.37	+	2816.97i	−0.957370	+	0.330810i
$418$	−14891.0	+	13574.1i	−1.74245	+	1.58835i
$419$			10373.5i			1.20949i	0.796418	+	0.604747i	$0.206726\pi$
$419$			10373.5i			1.20949i	−0.796418	+	0.604747i	$0.793274\pi$
$420$	689.900	+	481.960i	0.0801516	+	0.0559934i
$421$	−2727.35	−	8393.91i	−0.315731	−	0.971720i	−0.975453	−	0.220210i	$-0.929326\pi$
$421$	−2727.35	−	8393.91i	−0.315731	−	0.971720i	0.659722	−	0.751510i	$-0.270674\pi$
$422$	5316.69	+	1727.50i	0.613300	+	0.199273i
$423$	22.2136	+	598.894i	0.00255333	+	0.0688397i
$424$	5445.10	−	7494.53i	0.623673	−	0.858412i
$425$	−879.045	+	2705.42i	−0.100329	+	0.308782i
$426$	3429.12	+	4540.35i	0.390003	+	0.516386i
$427$	1054.87	−	766.405i	0.119552	−	0.0868593i
$428$	7185.55			0.811511
$429$	−6868.00	−	3742.52i	−0.772937	−	0.421190i
$430$	−1321.30			−0.148183
$431$	−5972.74	+	4339.45i	−0.667510	+	0.484974i	−0.869191	−	0.494477i	$-0.835360\pi$
$431$	−5972.74	+	4339.45i	−0.667510	+	0.484974i	0.201681	+	0.979451i	$0.435360\pi$
$432$	2864.11	−	10829.7i	0.318980	−	1.20612i
$433$	2396.19	−	7374.72i	0.265944	−	0.818491i	−0.725531	−	0.688190i	$-0.758406\pi$
$433$	2396.19	−	7374.72i	0.265944	−	0.818491i	0.991474	−	0.130301i	$-0.0415943\pi$
$434$	620.535	−	854.093i	0.0686328	−	0.0944649i
$435$	−4073.02	−	1240.42i	−0.448934	−	0.136721i
$436$	−2452.96	−	797.015i	−0.269439	−	0.0875461i
$437$	−2256.80	−	6945.70i	−0.247042	−	0.760316i
$438$	−3686.13	+	5276.50i	−0.402123	+	0.575619i
$439$			10519.7i			1.14369i	0.820363	+	0.571843i	$0.193771\pi$
$439$			10519.7i			1.14369i	−0.820363	+	0.571843i	$0.806229\pi$
$440$	2013.13	+	1145.90i	0.218119	+	0.124155i
$441$	−6130.45	+	4811.06i	−0.661964	+	0.519497i
$442$	9714.29	+	13370.6i	1.04539	+	1.43885i
$443$	−5993.33	+	1947.35i	−0.642781	+	0.208852i	−0.612228	−	0.790681i	$-0.709727\pi$
$443$	−5993.33	+	1947.35i	−0.642781	+	0.208852i	−0.0305524	+	0.999533i	$0.509727\pi$
$444$	−6381.61	+	118.310i	−0.682113	+	0.0126458i
$445$	−2858.63	−	2076.91i	−0.304521	−	0.221248i
$446$	2625.94	+	1907.85i	0.278793	+	0.202555i
$447$	−7787.53	+	144.374i	−0.824021	+	0.0152766i
$448$	48.2727	−	15.6848i	0.00509079	−	0.00165410i
$449$	−5441.07	−	7488.99i	−0.571893	−	0.787143i	0.420885	−	0.907114i	$-0.361720\pi$
$449$	−5441.07	−	7488.99i	−0.571893	−	0.787143i	−0.992777	+	0.119971i	$0.961720\pi$
$450$	1869.32	−	1467.01i	0.195823	−	0.153679i
$451$	2004.04	+	18005.4i	0.209239	+	1.87991i
$452$			1872.97i			0.194905i
$453$	5084.98	−	7278.89i	0.527403	−	0.754949i
$454$	1704.95	+	5247.29i	0.176249	+	0.542440i
$455$	−1446.76	−	470.081i	−0.149066	−	0.0484346i
$456$	9903.02	+	3015.93i	1.01700	+	0.309723i
$457$	3555.38	−	4893.56i	0.363925	−	0.500900i	−0.587312	−	0.809361i	$-0.699814\pi$
$457$	3555.38	−	4893.56i	0.363925	−	0.500900i	0.951237	+	0.308461i	$0.0998139\pi$
$458$	−980.589	+	3017.94i	−0.100043	+	0.307902i
$459$	−4081.57	+	15433.1i	−0.415057	+	1.56941i
$460$	827.158	−	600.965i	0.0838401	−	0.0609134i
$461$	8452.11			0.853913			0.426956	−	0.904272i	$-0.359586\pi$
$461$	8452.11			0.853913			0.426956	+	0.904272i	$0.359586\pi$
$462$	−3574.73	+	3382.00i	−0.359981	+	0.340573i
$463$	15503.0			1.55613			0.778064	−	0.628185i	$-0.216202\pi$
$463$	15503.0			1.55613			0.778064	+	0.628185i	$0.216202\pi$
$464$	10586.1	−	7691.22i	1.05915	−	0.769517i
$465$	−636.796	−	843.155i	−0.0635069	−	0.0840868i
$466$	−3869.72	+	11909.8i	−0.384681	+	1.18393i
$467$	1836.32	−	2527.48i	0.181959	−	0.250445i	−0.708288	−	0.705924i	$-0.750532\pi$
$467$	1836.32	−	2527.48i	0.181959	−	0.250445i	0.890246	+	0.455479i	$0.150532\pi$
$468$	−181.381	−	4890.17i	−0.0179153	−	0.483009i
$469$	−1754.99	−	570.231i	−0.172789	−	0.0561425i
$470$	−120.732	−	371.574i	−0.0118488	−	0.0364669i
$471$	7658.42	+	5350.13i	0.749218	+	0.523399i
$472$			7086.54i			0.691069i
$473$	552.975	−	2682.24i	0.0537544	−	0.260739i
$474$	−14116.5	+	4877.81i	−1.36791	+	0.472669i
$475$	2305.41	+	3173.12i	0.222693	+	0.306511i
$476$	3505.39	−	1138.97i	0.337540	−	0.109673i
$477$	18494.2	−	6776.77i	1.77524	−	0.650497i
$478$	−3720.01	−	2702.75i	−0.355961	−	0.258621i
$479$	−10536.9	−	7655.53i	−1.00510	−	0.730251i	−0.0419274	−	0.999121i	$-0.513350\pi$
$479$	−10536.9	−	7655.53i	−1.00510	−	0.730251i	−0.963176	+	0.268870i	$0.913350\pi$
$480$	86.4407	+	4662.61i	0.00821971	+	0.443371i
$481$	10972.6	−	3565.21i	1.04014	−	0.337962i
$482$	1868.51	+	2571.79i	0.176573	+	0.243033i
$483$	−582.520	−	1685.82i	−0.0548770	−	0.158815i
$484$	3858.74	−	4392.62i	0.362391	−	0.412530i
$485$			1060.37i			0.0992764i
$486$	10016.5	−	8802.97i	0.934894	−	0.821627i
$487$	−1753.73	−	5397.41i	−0.163180	−	0.502218i	0.835717	−	0.549160i	$-0.185052\pi$
$487$	−1753.73	−	5397.41i	−0.163180	−	0.502218i	−0.998898	+	0.0469423i	$0.985052\pi$
$488$	2135.51	+	693.869i	0.198094	+	0.0643647i
$489$	1134.97	−	3726.77i	0.104960	−	0.344643i
$490$	2986.11	−	4110.03i	0.275304	−	0.378923i
$491$	1782.30	−	5485.35i	0.163817	−	0.504176i	−0.835131	−	0.550052i	$-0.814608\pi$
$491$	1782.30	−	5485.35i	0.163817	−	0.504176i	0.998947	+	0.0458761i	$0.0146079\pi$
$492$	−9044.87	+	6831.18i	−0.828809	+	0.625962i
$493$	−15085.9	+	10960.5i	−1.37816	+	1.00129i
$494$	22787.3			2.07540
$495$	2195.70	+	4408.67i	0.199372	+	0.400313i
$496$	3247.23			0.293962
$497$	−1855.62	+	1348.18i	−0.167476	+	0.121679i
$498$	−11604.4	+	8764.28i	−1.04419	+	0.788628i
$499$	−5231.09	+	16099.6i	−0.469290	+	1.44433i	0.384216	+	0.923243i	$0.374472\pi$
$499$	−5231.09	+	16099.6i	−0.469290	+	1.44433i	−0.853506	+	0.521083i	$0.825528\pi$
$500$	−322.751	+	444.229i	−0.0288678	+	0.0397331i
$501$	−2597.18	+	8528.05i	−0.231604	+	0.760489i
$502$	−8967.13	−	2913.60i	−0.797256	−	0.259044i
$503$	1275.95	+	3926.98i	0.113105	+	0.348102i	0.991547	−	0.129747i	$-0.0414165\pi$
$503$	1275.95	+	3926.98i	0.113105	+	0.348102i	−0.878442	+	0.477849i	$0.841416\pi$
$504$	2431.83	+	691.614i	0.214925	+	0.0611249i
$505$			9339.05i			0.822935i
$506$	2465.10	+	5446.66i	0.216575	+	0.478525i
$507$	−839.504	−	2429.54i	−0.0735379	−	0.212820i
$508$	−5007.44	−	6892.15i	−0.437341	−	0.601948i
$509$	−13703.6	+	4452.56i	−1.19332	+	0.387733i	−0.837299	−	0.546745i	$-0.815867\pi$
$509$	−13703.6	+	4452.56i	−1.19332	+	0.387733i	−0.356021	+	0.934478i	$0.615867\pi$
$510$	−192.903	−	10405.2i	−0.0167488	−	0.903432i
$511$	−2099.16	−	1525.13i	−0.181725	−	0.132031i
$512$	−5032.44	−	3656.28i	−0.434384	−	0.315599i
$513$	13907.3	+	17060.4i	1.19693	+	1.46830i
$514$	7728.12	−	2511.02i	0.663177	−	0.215479i
$515$	−3673.51	−	5056.15i	−0.314319	−	0.432623i
$516$	1619.48	−	559.596i	0.138166	−	0.0477419i
$517$	804.822	−	89.5785i	0.0684643	−	0.00762023i
$518$		−	7258.88i		−	0.615708i
$519$	−3712.64	−	2593.63i	−0.314002	−	0.219360i
$520$	−809.522	−	2491.45i	−0.0682690	−	0.210110i
$521$	−8247.81	−	2679.87i	−0.693557	−	0.225350i	−0.0590356	−	0.998256i	$-0.518803\pi$
$521$	−8247.81	−	2679.87i	−0.693557	−	0.225350i	−0.634521	+	0.772906i	$0.718803\pi$
$522$	15565.9	−	577.355i	1.30517	−	0.0484102i
$523$	593.256	−	816.547i	0.0496009	−	0.0682698i	−0.783496	−	0.621397i	$-0.786566\pi$
$523$	593.256	−	816.547i	0.0496009	−	0.0682698i	0.833097	+	0.553127i	$0.186566\pi$
$524$	3011.61	−	9268.78i	0.251074	−	0.772726i
$525$	577.311	+	764.393i	0.0479923	+	0.0635445i
$526$	−1720.12	+	1249.74i	−0.142587	+	0.103596i
$527$	−4627.55			−0.382503
$528$	−14878.7	−	2780.96i	−1.22635	−	0.229215i
$529$	10000.1			0.821902
$530$	−10388.2	+	7547.50i	−0.851389	+	0.618570i
$531$	−8398.55	+	12509.8i	−0.686376	+	1.02237i
$532$	1570.41	−	4833.21i	0.127981	−	0.393884i
$533$	12042.7	−	16575.4i	0.978666	−	1.34702i
$534$	12366.2	+	3766.08i	1.00213	+	0.305195i
$535$	7778.52	+	2527.39i	0.628588	+	0.204241i
$536$	−981.989	−	3022.25i	−0.0791333	−	0.243547i
$537$	−873.819	+	1250.83i	−0.0702199	+	0.100516i
$538$			14771.8i			1.18375i
$539$	7093.65	+	7781.89i	0.566874	+	0.621874i
$540$	−1669.87	+	2589.76i	−0.133073	+	0.206381i
$541$	−2246.04	−	3091.41i	−0.178493	−	0.245675i	0.710391	−	0.703808i	$-0.248518\pi$
$541$	−2246.04	−	3091.41i	−0.178493	−	0.245675i	−0.888884	+	0.458133i	$0.848518\pi$
$542$	128.036	−	41.6016i	0.0101469	−	0.00329694i
$543$	−4209.48	+	78.0400i	−0.332681	+	0.00616762i
$544$	16523.4	+	12004.9i	1.30227	+	0.946153i
$545$	−2375.05	−	1725.57i	−0.186671	−	0.135625i
$546$	5564.32	−	103.158i	0.436137	−	0.00808560i
$547$	−15048.5	+	4889.54i	−1.17628	+	0.382197i	−0.830984	−	0.556297i	$-0.812222\pi$
$547$	−15048.5	+	4889.54i	−1.17628	+	0.382197i	−0.345297	+	0.938494i	$0.612222\pi$
$548$	−915.604	−	1260.22i	−0.0713735	−	0.0982372i
$549$	2947.45	+	3755.75i	0.229133	+	0.291970i
$550$	−2163.02	−	2372.88i	−0.167694	−	0.183964i
$551$			25710.7i			1.98786i
$552$	1759.05	−	2517.99i	0.135634	−	0.194154i
$553$	−1860.53	−	5726.11i	−0.143070	−	0.440324i
$554$	4439.89	+	1442.61i	0.340492	+	0.110633i
$555$	−6949.85	−	2116.55i	−0.531540	−	0.161879i
$556$	−4286.00	+	5899.18i	−0.326919	+	0.449966i
$557$	−1811.19	+	5574.28i	−0.137779	+	0.424039i	−0.996012	−	0.0892209i	$-0.971562\pi$
$557$	−1811.19	+	5574.28i	−0.137779	+	0.424039i	0.858233	+	0.513260i	$0.171562\pi$
$558$	3209.35	+	2154.63i	0.243482	+	0.163464i
$559$	−2505.67	+	1820.48i	−0.189586	+	0.137742i
$560$	−2943.90			−0.222147
$561$	21203.3	+	3963.07i	1.59573	+	0.298255i
$562$	−6601.68			−0.495507
$563$	−7231.77	+	5254.19i	−0.541355	+	0.393317i	−0.824588	−	0.565734i	$-0.808593\pi$
$563$	−7231.77	+	5254.19i	−0.541355	+	0.393317i	0.283233	+	0.959051i	$0.408593\pi$
$564$	305.346	+	404.296i	0.0227968	+	0.0301843i
$565$	−658.786	+	2027.53i	−0.0490537	+	0.150972i
$566$	−11824.0	+	16274.3i	−0.878089	+	1.20859i
$567$	3473.20	+	4102.95i	0.257250	+	0.303894i
$568$	−3756.58	−	1220.59i	−0.277504	−	0.0901667i
$569$	−6519.67	−	20065.5i	−0.480350	−	1.47836i	−0.838605	−	0.544740i	$-0.816628\pi$
$569$	−6519.67	−	20065.5i	−0.480350	−	1.47836i	0.358255	−	0.933624i	$-0.383372\pi$
$570$	−11763.0	−	8217.57i	−0.864383	−	0.603853i
$571$		−	25304.4i		−	1.85457i	−0.374360	−	0.927283i	$-0.622138\pi$
$571$		−	25304.4i		−	1.85457i	0.374360	−	0.927283i	$-0.377862\pi$
$572$	−6571.64	+	731.439i	−0.480374	+	0.0534668i
$573$	13464.6	−	4652.57i	0.981663	−	0.339204i
$574$	−7576.91	−	10428.7i	−0.550965	−	0.758338i
$575$	1106.80	−	359.620i	0.0802723	−	0.0260821i
$576$	63.9421	+	174.502i	0.00462544	+	0.0126231i
$577$	7572.50	+	5501.75i	0.546356	+	0.396951i	0.826440	−	0.563025i	$-0.190362\pi$
$577$	7572.50	+	5501.75i	0.546356	+	0.396951i	−0.280084	+	0.959975i	$0.590362\pi$
$578$	−22881.7	−	16624.5i	−1.64663	−	1.19635i
$579$	21.2936	+	1148.58i	0.00152838	+	0.0824407i
$580$	−3423.26	+	1112.29i	−0.245075	+	0.0796296i
$581$	−3445.74	−	4742.66i	−0.246047	−	0.338655i
$582$	−1266.96	−	3666.59i	−0.0902354	−	0.261143i
$583$	−10973.9	−	24246.8i	−0.779572	−	1.72247i
$584$		−	4468.31i		−	0.316609i
$585$	1523.68	−	5357.51i	0.107686	−	0.378643i
$586$	8866.79	+	27289.2i	0.625058	+	1.92373i
$587$	9946.26	+	3231.73i	0.699363	+	0.227237i	0.637053	−	0.770820i	$-0.280153\pi$
$587$	9946.26	+	3231.73i	0.699363	+	0.227237i	0.0623099	+	0.998057i	$0.480153\pi$
$588$	−1919.32	+	6302.23i	−0.134611	+	0.442006i
$589$	−3750.33	+	5161.88i	−0.262359	+	0.361106i
$590$	3035.39	−	9341.96i	0.211805	−	0.651869i
$591$	−12017.3	+	9076.15i	−0.836425	+	0.631714i
$592$	18063.1	−	13123.6i	1.25404	−	0.911112i
$593$	−17109.1			−1.18480			−0.592400	−	0.805644i	$-0.701819\pi$
$593$	−17109.1			−1.18480			−0.592400	+	0.805644i	$0.701819\pi$
$594$	−12859.9	−	12621.0i	−0.888299	−	0.871793i
$595$	4195.27			0.289058
$596$	−5327.08	+	3870.35i	−0.366117	+	0.266000i
$597$	−10185.0	+	7692.29i	−0.698233	+	0.527344i
$598$	2089.33	−	6430.30i	0.142875	−	0.439723i
$599$	3004.19	−	4134.91i	0.204921	−	0.282050i	−0.694170	−	0.719811i	$-0.744228\pi$
$599$	3004.19	−	4134.91i	0.204921	−	0.282050i	0.899091	+	0.437761i	$0.144228\pi$
$600$	−480.587	+	1578.04i	−0.0326998	+	0.107372i
$601$	−12779.6	−	4152.33i	−0.867370	−	0.281826i	−0.158667	−	0.987332i	$-0.550720\pi$
$601$	−12779.6	−	4152.33i	−0.867370	−	0.281826i	−0.708703	+	0.705507i	$0.750720\pi$
$602$	602.164	+	1853.27i	0.0407681	+	0.125471i
$603$	1848.30	−	6498.92i	0.124824	−	0.438900i
$604$		−	7506.35i		−	0.505677i
$605$	5722.20	−	3397.86i	0.384530	−	0.228335i
$606$	−11158.5	−	32292.9i	−0.747991	−	2.16470i
$607$	−3273.58	−	4505.70i	−0.218897	−	0.301286i	0.685419	−	0.728149i	$-0.259619\pi$
$607$	−3273.58	−	4505.70i	−0.218897	−	0.301286i	−0.904317	+	0.426862i	$0.859619\pi$
$608$	26782.2	−	8702.08i	1.78645	−	0.580454i
$609$	116.392	+	6278.17i	0.00774456	+	0.417741i
$610$	−2517.97	−	1829.41i	−0.167130	−	0.121427i
$611$	−740.903	−	538.297i	−0.0490568	−	0.0356419i
$612$	4643.24	+	12671.7i	0.306686	+	0.836964i
$613$	20229.5	−	6572.97i	1.33289	−	0.433083i	0.445989	−	0.895038i	$-0.352852\pi$
$613$	20229.5	−	6572.97i	1.33289	−	0.433083i	0.886903	+	0.461955i	$0.152852\pi$
$614$	11886.5	+	16360.3i	0.781268	+	1.07532i
$615$	−12194.0	+	4213.53i	−0.799529	+	0.276270i
$616$	689.790	−	3345.87i	0.0451176	−	0.218846i
$617$		−	617.697i		−	0.0403040i	−0.999797	−	0.0201520i	$-0.993585\pi$
$617$		−	617.697i		−	0.0403040i	0.999797	−	0.0201520i	$-0.00641501\pi$
$618$	18743.6	+	13094.1i	1.22003	+	0.852304i
$619$	2524.46	+	7769.47i	0.163920	+	0.504494i	0.998955	−	0.0457030i	$-0.0145528\pi$
$619$	2524.46	+	7769.47i	0.163920	+	0.504494i	−0.835035	+	0.550197i	$0.814553\pi$
$620$	−849.528	−	276.028i	−0.0550288	−	0.0178799i
$621$	6089.39	−	2360.24i	0.393493	−	0.152517i
$622$	21452.1	−	29526.3i	1.38288	−	1.90337i
$623$	−1610.33	+	4956.07i	−0.103558	+	0.318717i
$624$	10316.7	+	13659.9i	0.661855	+	0.876333i
$625$	−505.636	+	367.366i	−0.0323607	+	0.0235114i
$626$	26256.7			1.67640
$627$	21604.6	−	20439.8i	1.37608	−	1.30189i
$628$	7897.75			0.501838
$629$	−25741.3	+	18702.1i	−1.63175	+	1.18554i
$630$	−2909.56	−	1953.36i	−0.183999	−	0.123530i
$631$	4321.35	−	13299.7i	0.272631	−	0.839072i	−0.717206	−	0.696862i	$-0.754579\pi$
$631$	4321.35	−	13299.7i	0.272631	−	0.839072i	0.989836	−	0.142210i	$-0.0454209\pi$
$632$	6094.36	−	8388.16i	0.383577	−	0.527948i
$633$	−7893.55	−	2403.95i	−0.495641	−	0.150945i
$634$	2017.37	+	655.482i	0.126372	+	0.0410607i
$635$	−2996.47	−	9222.18i	−0.187262	−	0.576333i
$636$	9536.07	−	13650.4i	0.594544	−	0.851058i
$637$		−	11908.4i		−	0.740702i
$638$	−2328.24	−	20918.2i	−0.144477	−	1.29806i
$639$	−5184.86	−	6606.75i	−0.320986	−	0.409013i
$640$	−4291.39	−	5906.59i	−0.265050	−	0.364810i
$641$	16953.3	−	5508.46i	1.04464	−	0.339424i	0.264078	−	0.964501i	$-0.414932\pi$
$641$	16953.3	−	5508.46i	1.04464	−	0.339424i	0.780563	+	0.625077i	$0.214932\pi$
$642$	−29916.6	+	554.627i	−1.83912	+	0.0340956i
$643$	−25005.5	−	18167.6i	−1.53363	−	1.11424i	−0.954180	−	0.299234i	$-0.903269\pi$
$643$	−25005.5	−	18167.6i	−1.53363	−	1.11424i	−0.579446	−	0.815010i	$-0.696731\pi$
$644$	−1219.89	−	886.300i	−0.0746433	−	0.0542315i
$645$	1949.95	−	36.1504i	0.119038	−	0.00220686i
$646$	−59767.9	+	19419.8i	−3.64015	+	1.18276i
$647$	−3686.26	−	5073.70i	−0.223990	−	0.308296i	0.682200	−	0.731165i	$-0.261023\pi$
$647$	−3686.26	−	5073.70i	−0.223990	−	0.308296i	−0.906191	+	0.422869i	$0.861023\pi$
$648$	−2200.59	+	8991.95i	−0.133406	+	0.545119i
$649$	17693.9	+	10071.5i	1.07018	+	0.609156i
$650$			3631.14i			0.219116i
$651$	−892.408	+	1277.44i	−0.0537269	+	0.0769073i
$652$	−1017.73	−	3132.25i	−0.0611310	−	0.188142i
$653$	−17334.8	−	5632.43i	−1.03884	−	0.337541i	−0.260563	−	0.965457i	$-0.583908\pi$
$653$	−17334.8	−	5632.43i	−1.03884	−	0.337541i	−0.778281	+	0.627916i	$0.783908\pi$
$654$	10274.3	+	3128.99i	0.614305	+	0.187084i
$655$	6520.27	−	8974.38i	0.388959	−	0.535356i
$656$	12252.4	−	37709.0i	0.729232	−	2.24435i
$657$	5295.57	−	7887.83i	0.314459	−	0.468392i
$658$	−466.152	+	338.679i	−0.0276178	+	0.0200655i
$659$	−1114.71			−0.0658920			−0.0329460	−	0.999457i	$-0.510489\pi$
$659$	−1114.71			−0.0658920			−0.0329460	+	0.999457i	$0.510489\pi$
$660$	3656.12	+	1992.30i	0.215628	+	0.117500i
$661$	−32411.6			−1.90721			−0.953604	−	0.301063i	$-0.902659\pi$
$661$	−32411.6			−1.90721			−0.953604	+	0.301063i	$0.902659\pi$
$662$	1242.20	−	902.510i	0.0729297	−	0.0529865i
$663$	−14702.0	−	19466.3i	−0.861205	−	1.14028i
$664$	3119.62	−	9601.22i	0.182327	−	0.561144i
$665$	3400.00	−	4679.70i	0.198265	−	0.272889i
$666$	26560.3	−	985.149i	1.54533	−	0.0573180i
$667$	7255.25	+	2357.37i	0.421176	+	0.136848i
$668$	2328.89	+	7167.60i	0.134892	+	0.415154i
$669$	−3927.51	−	2743.74i	−0.226975	−	0.158564i
$670$			4404.75i			0.253986i
$671$	4767.50	−	4345.85i	0.274288	−	0.250029i
$672$	6500.44	−	2246.16i	0.373155	−	0.128940i
$673$	−13154.0	−	18105.0i	−0.753419	−	1.03699i	−0.997733	−	0.0672958i	$-0.978563\pi$
$673$	−13154.0	−	18105.0i	−0.753419	−	1.03699i	0.244314	−	0.969696i	$-0.421437\pi$
$674$	−3183.79	+	1034.48i	−0.181951	+	0.0591195i
$675$	−2718.57	+	2216.13i	−0.155019	+	0.126369i
$676$	−1758.05	−	1277.30i	−0.100026	−	0.0726729i
$677$	15428.3	+	11209.3i	0.875859	+	0.636348i	0.932153	−	0.362066i	$-0.117928\pi$
$677$	15428.3	+	11209.3i	0.875859	+	0.636348i	−0.0562940	+	0.998414i	$0.517928\pi$
$678$	−144.568	−	7798.00i	−0.00818895	−	0.441712i
$679$	1487.29	−	483.251i	0.0840604	−	0.0273129i
$680$	4246.53	+	5844.85i	0.239481	+	0.329617i
$681$	−2659.70	−	7697.22i	−0.149662	−	0.433125i
$682$	2583.83	−	4539.32i	0.145073	−	0.254868i
$683$			12473.4i			0.698802i	0.936973	+	0.349401i	$0.113615\pi$
$683$			12473.4i			0.698802i	−0.936973	+	0.349401i	$0.886385\pi$
$684$	17897.9	+	5090.19i	1.00050	+	0.284544i
$685$	−547.901	−	1686.27i	−0.0305609	−	0.0940568i
$686$	−15593.8	−	5066.72i	−0.867890	−	0.281995i
$687$	1364.57	−	4480.66i	0.0757809	−	0.248832i
$688$	−3523.04	+	4849.05i	−0.195225	+	0.268704i
$689$	−9301.04	+	28625.6i	−0.514283	+	1.58280i
$690$	−3397.43	+	2565.93i	−0.187447	+	0.141570i
$691$	−5044.80	+	3665.26i	−0.277733	+	0.201785i	−0.717928	−	0.696118i	$-0.754909\pi$
$691$	−5044.80	+	3665.26i	−0.277733	+	0.201785i	0.440195	+	0.897902i	$0.354909\pi$
$692$	−3828.66			−0.210324
$693$	5183.00	−	5088.91i	0.284106	−	0.278949i
$694$	29749.9			1.62722
$695$	−6714.63	+	4878.47i	−0.366476	+	0.266260i
$696$	−8628.93	+	6517.04i	−0.469941	+	0.354925i
$697$	−17460.6	+	53738.1i	−0.948876	+	2.92034i
$698$	−15821.2	+	21776.0i	−0.857937	+	1.18085i
$699$	5385.03	−	17682.1i	0.291388	−	0.956796i
$700$	770.171	+	250.244i	0.0415853	+	0.0135119i
$701$	−367.373	−	1130.66i	−0.0197938	−	0.0609192i	0.940672	−	0.339318i	$-0.110196\pi$
$701$	−367.373	−	1130.66i	−0.0197938	−	0.0609192i	−0.960466	+	0.278399i	$0.910196\pi$
$702$	1132.62	+	20345.9i	0.0608948	+	1.09388i
$703$			43870.5i			2.35364i
$704$	228.781	−	103.544i	0.0122479	−	0.00554325i
$705$	188.340	+	545.060i	0.0100614	+	0.0291179i
$706$	−9610.32	−	13227.5i	−0.512307	−	0.705131i
$707$	13099.1	−	4256.14i	0.696805	−	0.226406i
$708$	236.109	+	12735.7i	0.0125332	+	0.676043i
$709$	−9475.27	−	6884.19i	−0.501906	−	0.364656i	0.307839	−	0.951439i	$-0.400394\pi$
$709$	−9475.27	−	6884.19i	−0.501906	−	0.364656i	−0.809744	+	0.586783i	$0.800394\pi$
$710$	4429.36	+	3218.12i	0.234128	+	0.170104i
$711$	20699.4	−	7584.82i	1.09183	−	0.400074i
$712$	−8534.80	+	2773.12i	−0.449235	+	0.145965i
$713$	1112.76	+	1531.58i	0.0584477	+	0.0804464i
$714$	−14506.6	+	5012.60i	−0.760356	+	0.262734i
$715$	−7371.22	−	1519.66i	−0.385550	−	0.0794856i
$716$			1289.91i			0.0673273i
$717$	5563.88	+	3886.89i	0.289801	+	0.202453i
$718$	36.3386	+	111.839i	0.00188878	+	0.00581307i
$719$	5201.77	+	1690.16i	0.269810	+	0.0876665i	0.440797	−	0.897607i	$-0.354696\pi$
$719$	5201.77	+	1690.16i	0.269810	+	0.0876665i	−0.170987	+	0.985273i	$0.554696\pi$
$720$	−399.536	−	10771.8i	−0.0206803	−	0.557556i
$721$	−5417.67	+	7456.78i	−0.279840	+	0.385167i
$722$	−19314.4	+	59443.5i	−0.995577	+	3.06407i
$723$	−2827.89	−	3744.28i	−0.145464	−	0.192602i
$724$	−2879.51	+	2092.08i	−0.147812	+	0.107392i
$725$	−4096.99			−0.209874
$726$	−15726.6	+	18586.2i	−0.803950	+	0.950138i
$727$	23944.2			1.22151			0.610757	−	0.791818i	$-0.290865\pi$
$727$	23944.2			1.22151			0.610757	+	0.791818i	$0.290865\pi$
$728$	−3125.61	+	2270.89i	−0.159125	+	0.115611i
$729$	−14541.4	+	13265.3i	−0.738778	+	0.673949i
$730$	−1913.92	+	5890.43i	−0.0970372	+	0.298650i
$731$	5020.59	−	6910.25i	0.254026	−	0.349637i
$732$	3861.00	+	1175.85i	0.194954	+	0.0593726i
$733$	7613.90	+	2473.91i	0.383664	+	0.124660i	0.494498	−	0.869179i	$-0.335352\pi$
$733$	7613.90	+	2473.91i	0.383664	+	0.124660i	−0.110833	+	0.993839i	$0.535352\pi$
$734$	−12034.6	−	37038.7i	−0.605184	−	1.86257i
$735$	−4294.41	+	6147.22i	−0.215513	+	0.308495i
$736$		−	8355.52i		−	0.418463i
$737$	−8941.65	−	1843.43i	−0.446906	−	0.0921349i
$738$	37130.5	−	29139.3i	1.85202	−	1.45343i
$739$	−1849.64	−	2545.80i	−0.0920703	−	0.126724i	0.760497	−	0.649342i	$-0.224955\pi$
$739$	−1849.64	−	2545.80i	−0.0920703	−	0.126724i	−0.852567	+	0.522618i	$0.824955\pi$
$740$	−5841.17	+	1897.91i	−0.290170	+	0.0942818i
$741$	−33629.1	+	623.454i	−1.66720	+	0.0309084i
$742$	15320.5	+	11131.0i	0.757997	+	0.550717i
$743$	20087.6	+	14594.5i	0.991845	+	0.720618i	0.960324	−	0.278885i	$-0.0899650\pi$
$743$	20087.6	+	14594.5i	0.991845	+	0.720618i	0.0315207	+	0.999503i	$0.489965\pi$
$744$	−2683.03	+	49.7411i	−0.132211	+	0.00245107i
$745$	−7128.02	+	2316.03i	−0.350537	+	0.113897i
$746$	−139.787	−	192.401i	−0.00686056	−	0.00944275i
$747$	16885.8	−	13251.7i	0.827067	−	0.649067i
$748$	16613.2	−	7518.96i	0.812084	−	0.367541i
$749$		−	12062.1i		−	0.588436i
$750$	1309.47	−	1874.43i	0.0637533	−	0.0912595i
$751$	2769.71	+	8524.30i	0.134578	+	0.414189i	0.995524	−	0.0945072i	$-0.0301275\pi$
$751$	2769.71	+	8524.30i	0.134578	+	0.414189i	−0.860946	+	0.508697i	$0.830128\pi$
$752$	−1685.55	−	547.669i	−0.0817364	−	0.0265578i
$753$	13313.3	+	4054.50i	0.644306	+	0.196221i
$754$	−13990.9	+	19256.9i	−0.675756	+	0.930098i
$755$	2640.23	−	8125.79i	0.127269	−	0.391692i
$756$	4393.45	+	1161.93i	0.211360	+	0.0558980i
$757$	−2469.24	+	1794.01i	−0.118555	+	0.0861353i	−0.645483	−	0.763775i	$-0.723344\pi$
$757$	−2469.24	+	1794.01i	−0.118555	+	0.0861353i	0.526928	+	0.849910i	$0.323344\pi$
$758$	1714.15			0.0821380
$759$	−3786.98	−	7970.65i	−0.181105	−	0.381181i
$760$	9961.29			0.475440
$761$	−29468.5	+	21410.1i	−1.40372	+	1.01986i	−0.409522	+	0.912300i	$0.634305\pi$
$761$	−29468.5	+	21410.1i	−1.40372	+	1.01986i	−0.994198	+	0.107563i	$0.965695\pi$
$762$	21380.1	+	28308.5i	1.01643	+	1.34581i
$763$	−1337.92	+	4117.68i	−0.0634807	+	0.195374i
$764$	7078.85	−	9743.21i	0.335215	−	0.461383i
$765$	569.368	+	15350.6i	0.0269092	+	0.725491i
$766$	22105.0	+	7182.34i	1.04267	+	0.338784i
$767$	−7115.07	−	21897.9i	−0.334955	−	1.03088i
$768$	21661.7	+	15132.7i	1.01777	+	0.711008i
$769$		−	35765.7i		−	1.67717i	−0.544770	−	0.838586i	$-0.683383\pi$
$769$		−	35765.7i		−	1.67717i	0.544770	−	0.838586i	$-0.316617\pi$
$770$	−2342.47	+	4115.29i	−0.109632	+	0.192604i
$771$	−11336.3	+	3917.16i	−0.529531	+	0.182974i
$772$	570.835	+	785.687i	0.0266124	+	0.0366289i
$773$	28148.3	−	9145.93i	1.30973	−	0.425558i	0.430775	−	0.902459i	$-0.358240\pi$
$773$	28148.3	−	9145.93i	1.30973	−	0.425558i	0.878957	+	0.476901i	$0.158240\pi$
$774$	−6699.42	+	2454.85i	−0.311118	+	0.114002i
$775$	−822.545	−	597.614i	−0.0381247	−	0.0276993i
$776$	2178.73	+	1582.94i	0.100788	+	0.0732271i
$777$	198.601	+	10712.5i	0.00916960	+	0.494608i
$778$	−7161.44	+	2326.89i	−0.330013	+	0.107228i
$779$	45792.5	+	63028.0i	2.10615	+	2.89886i
$780$	−1537.86	−	4450.60i	−0.0705951	−	0.204304i
$781$	−8386.51	+	7644.79i	−0.384242	+	0.350259i
$782$			18646.4i			0.852677i
$783$	−22956.1	+	1277.93i	−1.04775	+	0.0583263i
$784$	−7121.43	−	21917.5i	−0.324409	−	0.998429i
$785$	8549.49	+	2777.90i	0.388719	+	0.126302i
$786$	−11823.2	+	38822.5i	−0.536540	+	1.76177i
$787$	−7897.10	+	10869.4i	−0.357689	+	0.492317i	−0.949503	−	0.313758i	$-0.898412\pi$
$787$	−7897.10	+	10869.4i	−0.357689	+	0.492317i	0.591814	+	0.806075i	$0.298412\pi$
$788$	−3934.18	+	12108.2i	−0.177855	+	0.547380i
$789$	2504.33	−	1891.41i	0.113000	−	0.0853434i
$790$	−11626.9	+	8447.44i	−0.523629	+	0.380439i
$791$	3144.08			0.141328
$792$	12336.2	+	2069.86i	0.553469	+	0.0928653i
$793$	−7295.54			−0.326699
$794$	11360.7	−	8254.05i	0.507780	−	0.368924i
$795$	15124.3	−	11422.7i	0.674722	−	0.509586i
$796$	−3334.33	+	10262.0i	−0.148470	+	0.456944i
$797$	15380.3	−	21169.2i	0.683563	−	0.940844i	−0.316407	−	0.948624i	$-0.602476\pi$
$797$	15380.3	−	21169.2i	0.683563	−	0.940844i	0.999970	+	0.00777970i	$0.00247638\pi$
$798$	−6165.23	+	20244.0i	−0.273492	+	0.898032i
$799$	2402.04	+	780.469i	0.106355	+	0.0345570i
$800$	1386.67	+	4267.74i	0.0612829	+	0.188609i
$801$	−18352.9	−	5219.58i	−0.809572	−	0.230243i
$802$		−	32618.1i		−	1.43614i
$803$	−11156.6	−	6350.44i	−0.490295	−	0.279081i
$804$	−1865.50	−	5398.78i	−0.0818296	−	0.236816i
$805$	−1008.81	−	1388.51i	−0.0441690	−	0.0607934i
$806$	−5617.87	+	1825.36i	−0.245510	+	0.0797710i
$807$	−404.154	−	21800.1i	−0.0176294	−	0.950927i
$808$	19188.8	+	13941.5i	0.835469	+	0.607004i
$809$	3745.12	+	2720.99i	0.162758	+	0.118251i	0.666183	−	0.745788i	$-0.267927\pi$
$809$	3745.12	+	2720.99i	0.162758	+	0.118251i	−0.503425	+	0.864039i	$0.667927\pi$
$810$	6752.49	−	10911.2i	0.292912	−	0.473310i
$811$	−4025.53	+	1307.97i	−0.174298	+	0.0566327i	−0.394866	−	0.918739i	$-0.629209\pi$
$811$	−4025.53	+	1307.97i	−0.174298	+	0.0566327i	0.220568	+	0.975372i	$0.429209\pi$
$812$	3120.21	+	4294.60i	0.134850	+	0.185605i
$813$	−187.816	+	64.8980i	−0.00810208	+	0.00279960i
$814$	−3972.72	−	35693.1i	−0.171061	−	1.53691i
$815$		−	3748.70i		−	0.161118i
$816$	−38700.5	−	27035.9i	−1.66028	−	1.15986i
$817$	−3639.30	−	11200.6i	−0.155842	−	0.479633i
$818$	8127.69	+	2640.85i	0.347406	+	0.112879i
$819$	−8208.91	+	304.477i	−0.350235	+	0.0129906i
$820$	−6410.85	+	8823.78i	−0.273020	+	0.375780i
$821$	5805.86	−	17868.6i	0.246804	−	0.759584i	−0.748531	−	0.663100i	$-0.769240\pi$
$821$	5805.86	−	17868.6i	0.246804	−	0.759584i	0.995335	−	0.0964839i	$-0.0307596\pi$
$822$	3909.33	+	5176.18i	0.165880	+	0.219635i
$823$	−22733.3	+	16516.7i	−0.962861	+	0.699559i	−0.953813	−	0.300400i	$-0.902880\pi$
$823$	−22733.3	+	16516.7i	−0.962861	+	0.699559i	−0.00904726	+	0.999959i	$0.502880\pi$
$824$	−15872.7			−0.671056
$825$	3257.08	+	3442.68i	0.137451	+	0.145284i
$826$	−14486.5			−0.610229
$827$	6502.25	−	4724.16i	0.273404	−	0.198640i	−0.442631	−	0.896704i	$-0.645955\pi$
$827$	6502.25	−	4724.16i	0.273404	−	0.198640i	0.716036	+	0.698064i	$0.245955\pi$
$828$	3077.42	−	4583.87i	0.129164	−	0.192392i
$829$	−3966.73	+	12208.4i	−0.166189	+	0.511476i	−0.999122	−	0.0418974i	$-0.986660\pi$
$829$	−3966.73	+	12208.4i	−0.166189	+	0.511476i	0.832933	+	0.553373i	$0.186660\pi$
$830$	−8225.00	+	11320.7i	−0.343969	+	0.473432i
$831$	−6591.79	−	2007.50i	−0.275170	−	0.0838020i
$832$	−270.097	−	87.7598i	−0.0112547	−	0.00365688i
$833$	10148.6	+	31234.1i	0.422121	+	1.29916i
$834$	17389.2	−	24891.7i	0.721988	−	1.03349i
$835$			8578.23i			0.355523i
$836$	5076.76	−	24625.1i	0.210028	−	1.01875i
$837$	−4795.26	−	3091.96i	−0.198027	−	0.127687i
$838$	−21464.8	−	29543.8i	−0.884834	−	1.21787i
$839$	3624.22	−	1177.58i	0.149132	−	0.0484559i	−0.233500	−	0.972357i	$-0.575018\pi$
$839$	3624.22	−	1177.58i	0.149132	−	0.0484559i	0.382632	+	0.923901i	$0.375018\pi$
$840$	2432.40	−	45.0946i	0.0999118	−	0.00185228i
$841$	−1996.24	−	1450.36i	−0.0818502	−	0.0594676i
$842$	25136.2	+	18262.5i	1.02880	+	0.747469i
$843$	9742.66	−	180.620i	0.398049	−	0.00737947i
$844$	−6634.32	+	2155.62i	−0.270572	+	0.0879141i
$845$	−1453.86	−	2001.07i	−0.0591886	−	0.0814662i
$846$	−1302.50	−	1659.69i	−0.0529323	−	0.0674485i
$847$	−7373.70	−	6477.49i	−0.299130	−	0.262774i
$848$			58248.1i			2.35878i
$849$	17004.4	−	24340.8i	0.687383	−	0.983952i
$850$	−3094.54	−	9524.00i	−0.124873	−	0.384318i
$851$	12379.7	+	4022.42i	0.498674	+	0.162029i
$852$	−6791.89	−	2068.44i	−0.273106	−	0.0831733i
$853$	1250.86	−	1721.66i	0.0502093	−	0.0691071i	−0.783174	−	0.621802i	$-0.786401\pi$
$853$	1250.86	−	1721.66i	0.0502093	−	0.0691071i	0.833383	+	0.552695i	$0.186401\pi$
$854$	−1418.42	+	4365.46i	−0.0568355	+	0.174922i
$855$	17584.5	+	11805.5i	0.703365	+	0.472211i
$856$	16804.9	−	12209.5i	0.671003	−	0.487512i
$857$	34039.8			1.35680			0.678399	−	0.734694i	$-0.262674\pi$
$857$	34039.8			1.35680			0.678399	+	0.734694i	$0.262674\pi$
$858$	27304.2	−	3552.54i	1.08642	−	0.141354i
$859$	−9548.06			−0.379250			−0.189625	−	0.981857i	$-0.560727\pi$
$859$	−9548.06			−0.379250			−0.189625	+	0.981857i	$0.560727\pi$
$860$	1333.87	−	969.115i	0.0528891	−	0.0384262i
$861$	11467.2	+	15183.2i	0.453892	+	0.600979i
$862$	8031.24	−	24717.6i	0.317338	−	0.976665i
$863$	15807.4	−	21757.0i	0.623512	−	0.858191i	−0.374091	−	0.927392i	$-0.622045\pi$
$863$	15807.4	−	21757.0i	0.623512	−	0.858191i	0.997603	+	0.0692015i	$0.0220451\pi$
$864$	9100.96	+	23480.4i	0.358358	+	0.924558i
$865$	−4144.61	−	1346.67i	−0.162915	−	0.0529342i
$866$	8435.41	+	25961.5i	0.331001	+	1.01872i
$867$	34223.3	+	23908.2i	1.34058	+	0.936521i
$868$			1317.35i			0.0515137i
$869$	−12282.4	−	27137.9i	−0.479459	−	1.05937i
$870$	14166.7	−	4895.16i	0.552064	−	0.190760i
$871$	6068.83	+	8353.02i	0.236090	+	0.324950i
$872$	−7091.01	+	2304.01i	−0.275381	+	0.0894766i
$873$	1970.07	+	5376.44i	0.0763766	+	0.208436i
$874$	20799.5	+	15111.7i	0.804980	+	0.584852i
$875$	745.708	+	541.789i	0.0288109	+	0.0209324i
$876$	−148.875	−	8030.32i	−0.00574203	−	0.309725i
$877$	7247.43	−	2354.83i	0.279052	−	0.0906694i	−0.166148	−	0.986101i	$-0.553133\pi$
$877$	7247.43	−	2354.83i	0.279052	−	0.0906694i	0.445199	+	0.895432i	$0.353133\pi$
$878$	−21767.4	−	29960.3i	−0.836691	−	1.15161i
$879$	−13832.1	−	40030.4i	−0.530768	−	1.53605i
$880$	−14475.6	+	1611.17i	−0.554515	+	0.0617187i
$881$		−	34117.0i		−	1.30469i	−0.757923	−	0.652344i	$-0.773786\pi$
$881$		−	34117.0i		−	1.30469i	0.757923	−	0.652344i	$-0.226214\pi$
$882$	7504.53	−	26387.1i	0.286497	−	1.00737i
$883$	−1111.30	−	3420.24i	−0.0423537	−	0.130351i	0.927644	−	0.373466i	$-0.121831\pi$
$883$	−1111.30	−	3420.24i	−0.0423537	−	0.130351i	−0.969997	+	0.243115i	$0.921831\pi$
$884$	−19613.4	−	6372.79i	−0.746235	−	0.242466i
$885$	−4223.98	+	13869.8i	−0.160438	+	0.526810i
$886$	13039.6	−	17947.5i	0.494441	−	0.680540i
$887$	11622.5	−	35770.5i	0.439962	−	1.35407i	−0.447953	−	0.894057i	$-0.647847\pi$
$887$	11622.5	−	35770.5i	0.439962	−	1.35407i	0.887915	−	0.460008i	$-0.152153\pi$
$888$	−14723.7	+	11120.1i	−0.556413	+	0.420233i
$889$	−11569.5	+	8405.77i	−0.436479	+	0.317121i
$890$	12439.0			0.468489
$891$	19323.8	+	18274.0i	0.726567	+	0.687095i
$892$	−4050.25			−0.152032
$893$	2817.28	−	2046.88i	0.105573	−	0.0767034i
$894$	21880.2	−	16525.2i	0.818551	−	0.618215i
$895$	−453.705	+	1396.36i	−0.0169449	+	0.0521510i
$896$	−6328.92	+	8711.01i	−0.235976	+	0.324793i
$897$	−2907.47	+	9546.90i	−0.108225	+	0.355364i
$898$	30992.5	+	10070.1i	1.15171	+	0.374212i
$899$	−2059.53	−	6338.59i	−0.0764063	−	0.235155i
$900$	−811.120	+	2852.03i	−0.0300415	+	0.105631i
$901$		−	83007.8i		−	3.06924i
$902$	−42964.4	−	47132.9i	−1.58598	−	1.73986i
$903$	−939.370	−	2718.55i	−0.0346182	−	0.100186i
$904$	3182.49	+	4380.33i	0.117089	+	0.161159i
$905$	−3852.98	+	1251.91i	−0.141522	+	0.0459833i
$906$	579.389	+	31252.2i	0.0212460	+	1.14601i
$907$	26705.0	+	19402.3i	0.977647	+	0.710302i	0.957182	−	0.289488i	$-0.0934852\pi$
$907$	26705.0	+	19402.3i	0.977647	+	0.710302i	0.0204655	+	0.999791i	$0.493485\pi$
$908$	−5569.83	−	4046.72i	−0.203570	−	0.147902i
$909$	17351.0	+	47352.0i	0.633111	+	1.72780i
$910$	5093.09	−	1654.84i	0.185532	−	0.0602830i
$911$	−21579.2	−	29701.2i	−0.784798	−	1.08018i	−0.994736	−	0.102467i	$-0.967327\pi$
$911$	−21579.2	−	29701.2i	−0.784798	−	1.08018i	0.209939	−	0.977715i	$-0.432673\pi$
$912$	−61521.9	+	21258.3i	−2.23377	+	0.771856i
$913$	−19538.9	−	21434.6i	−0.708261	−	0.776978i
$914$			21293.7i			0.770606i
$915$	3766.03	+	2630.93i	0.136067	+	0.0950554i
$916$	−1223.61	−	3765.87i	−0.0441366	−	0.135838i
$917$	−15559.1	−	5055.46i	−0.560313	−	0.182057i
$918$	−20309.9	−	52399.4i	−0.730205	−	1.88392i
$919$	−3276.42	+	4509.60i	−0.117605	+	0.161869i	−0.863761	−	0.503902i	$-0.831897\pi$
$919$	−3276.42	+	4509.60i	−0.117605	+	0.161869i	0.746156	+	0.665771i	$0.231897\pi$
$920$	913.336	−	2810.96i	0.0327302	−	0.100733i
$921$	−17989.5	−	23819.1i	−0.643619	−	0.852188i
$922$	−24071.7	+	17489.1i	−0.859826	+	0.624700i
$923$	12833.6			0.457663
$924$	1128.19	−	6036.08i	0.0401676	−	0.214905i
$925$	−6990.75			−0.248491
$926$	−44152.9	+	32078.9i	−1.56690	+	1.13842i
$927$	−28019.7	−	18811.3i	−0.992760	−	0.666499i
$928$	−9089.90	+	27975.8i	−0.321542	+	0.989603i
$929$	−19893.0	+	27380.4i	−0.702549	+	0.966976i	0.297376	+	0.954760i	$0.403888\pi$
$929$	−19893.0	+	27380.4i	−0.702549	+	0.966976i	−0.999925	+	0.0122153i	$0.996112\pi$
$930$	3558.26	+	1083.66i	0.125462	+	0.0382091i
$931$	43065.4	+	13992.8i	1.51602	+	0.492583i
$932$	−4828.75	−	14861.4i	−0.169711	−	0.522318i
$933$	−30850.9	+	44161.4i	−1.08254	+	1.54960i
$934$			10998.0i			0.385295i
$935$	20628.8	−	2296.03i	0.721534	−	0.0803084i
$936$	−8733.41	−	11128.5i	−0.304979	−	0.388616i
$937$	18507.4	+	25473.3i	0.645262	+	0.888127i	0.998883	−	0.0472618i	$-0.0150495\pi$
$937$	18507.4	+	25473.3i	0.645262	+	0.888127i	−0.353620	+	0.935389i	$0.615050\pi$
$938$	6178.16	−	2007.41i	0.215058	−	0.0698765i
$939$	−38749.2	+	718.376i	−1.34668	+	0.0249663i
$940$	394.413	+	286.558i	0.0136855	+	0.00994307i
$941$	22298.0	+	16200.5i	0.772470	+	0.561232i	0.902710	−	0.430250i	$-0.141575\pi$
$941$	22298.0	+	16200.5i	0.772470	+	0.561232i	−0.130240	+	0.991483i	$0.541575\pi$
$942$	−32881.8	+	609.600i	−1.13731	+	0.0210847i
$943$	21984.4	−	7143.17i	0.759185	−	0.246674i
$944$	−26190.7	−	36048.5i	−0.903004	−	1.24288i
$945$	4347.32	+	2803.13i	0.149649	+	0.0964931i
$946$	3975.22	+	8783.27i	0.136623	+	0.301870i
$947$		−	23364.4i		−	0.801734i	−0.916136	−	0.400867i	$-0.868709\pi$
$947$		−	23364.4i		−	0.801734i	0.916136	−	0.400867i	$-0.131291\pi$
$948$	10673.1	−	15278.0i	0.365662	−	0.523425i
$949$	4486.29	+	13807.4i	0.153458	+	0.472294i
$950$	−13131.7	−	4266.73i	−0.448471	−	0.145717i
$951$	−2995.13	−	912.155i	−0.102128	−	0.0311027i
$952$	6262.76	−	8619.95i	0.213211	−	0.293460i
$953$	−9961.58	+	30658.6i	−0.338602	+	1.04211i	0.626319	+	0.779567i	$0.284561\pi$
$953$	−9961.58	+	30658.6i	−0.338602	+	1.04211i	−0.964921	+	0.262542i	$0.915439\pi$
$954$	−38649.2	+	57568.6i	−1.31165	+	1.95372i
$955$	11090.0	−	8057.37i	0.375775	−	0.273016i
$956$	5737.75			0.194113
$957$	4008.30	+	30807.1i	0.135392	+	1.04060i
$958$	45850.2			1.54630
$959$	−2115.48	+	1536.99i	−0.0712329	+	0.0517538i
$960$	107.779	+	142.705i	0.00362348	+	0.00479770i
$961$	−8694.82	+	26759.9i	−0.291861	+	0.898255i
$962$	−23872.9	+	32858.3i	−0.800098	+	1.10124i
$963$	44135.3	−	1637.02i	1.47688	−	0.0547791i
$964$	−3772.58	−	1225.79i	−0.126044	−	0.0409543i
$965$	341.590	+	1051.31i	0.0113950	+	0.0350702i
$966$	5147.34	+	3595.90i	0.171442	+	0.119768i
$967$		−	25825.1i		−	0.858821i	−0.903109	−	0.429411i	$-0.858721\pi$
$967$		−	25825.1i		−	0.858821i	0.903109	−	0.429411i	$-0.141279\pi$
$968$	1560.64	−	16829.7i	0.0518192	−	0.558808i
$969$	87673.3	−	30294.6i	2.90658	−	1.00434i
$970$	−2194.13	−	3019.96i	−0.0726280	−	0.0999639i
$971$	6674.76	−	2168.76i	0.220601	−	0.0716775i	−0.196631	−	0.980477i	$-0.563000\pi$
$971$	6674.76	−	2168.76i	0.220601	−	0.0716775i	0.417232	+	0.908800i	$0.363000\pi$
$972$	−3655.24	+	16233.4i	−0.120619	+	0.535686i
$973$	9902.70	+	7194.73i	0.326275	+	0.237053i
$974$	16163.0	+	11743.1i	0.531720	+	0.386317i
$975$	−99.3472	−	5358.79i	−0.00326324	−	0.176019i
$976$	−13427.5	+	4362.87i	−0.440374	+	0.143086i
$977$	27710.6	+	38140.4i	0.907411	+	1.24894i	0.968043	+	0.250784i	$0.0806885\pi$
$977$	27710.6	+	38140.4i	0.907411	+	1.24894i	−0.0606316	+	0.998160i	$0.519311\pi$
$978$	4479.03	+	12962.4i	0.146445	+	0.423815i
$979$	−5205.81	+	25251.1i	−0.169947	+	0.824340i
$980$			6339.32i			0.206635i
$981$	−15248.2	−	4336.61i	−0.496267	−	0.141139i
$982$	6274.29	+	19310.3i	0.203891	+	0.627511i
$983$	−35615.0	−	11572.0i	−1.15559	−	0.375473i	−0.332342	−	0.943159i	$-0.607839\pi$
$983$	−35615.0	−	11572.0i	−1.15559	−	0.375473i	−0.823245	+	0.567686i	$0.807839\pi$
$984$	−9545.95	+	31344.9i	−0.309262	+	1.01549i
$985$	−8517.68	+	11723.6i	−0.275529	+	0.379233i
$986$	20285.2	−	62431.6i	0.655186	−	2.01646i
$987$	678.674	−	512.572i	0.0218870	−	0.0165302i
$988$	−23004.1	+	16713.4i	−0.740746	+	0.538184i
$989$	−3494.37			−0.112350
$990$	−15375.8	−	8012.61i	−0.493612	−	0.257230i
$991$	32095.4			1.02880			0.514402	−	0.857549i	$-0.328014\pi$
$991$	32095.4			1.02880			0.514402	+	0.857549i	$0.328014\pi$
$992$	−5905.70	+	4290.74i	−0.189018	+	0.137330i
$993$	−1808.53	+	1365.90i	−0.0577964	+	0.0436510i
$994$	2495.15	−	7679.29i	0.0796192	−	0.245043i
$995$	−7218.97	+	9936.06i	−0.230007	+	0.316577i
$996$	5286.61	−	17359.0i	0.168185	−	0.552249i
$997$	12053.3	+	3916.37i	0.382882	+	0.124406i	0.494133	−	0.869387i	$-0.335486\pi$
$997$	12053.3	+	3916.37i	0.382882	+	0.124406i	−0.111251	+	0.993792i	$0.535486\pi$
$998$	−18415.2	−	56676.2i	−0.584091	−	1.79765i
$999$	−39170.4	+	2180.55i	−1.24054	+	0.0690587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.4.p.a.41.10	✓	192
3.2	odd	2	inner	165.4.p.a.41.39	yes	192
11.7	odd	10	inner	165.4.p.a.161.39	yes	192
33.29	even	10	inner	165.4.p.a.161.10	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.p.a.41.10	✓	192	1.1	even	1	trivial
165.4.p.a.41.39	yes	192	3.2	odd	2	inner
165.4.p.a.161.10	yes	192	33.29	even	10	inner
165.4.p.a.161.39	yes	192	11.7	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	165.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.84801 + 2.06920i) q^{2} +(4.14644 - 3.13162i) q^{3} +(1.35744 - 4.17778i) q^{4} +(2.93893 - 4.04508i) q^{5} +(-5.32916 + 17.4987i) q^{6} +(-7.01306 - 2.27868i) q^{7} +(-3.92409 - 12.0771i) q^{8} +(7.38594 - 25.9701i) q^{9} +17.6017i q^{10} +(-35.7314 - 7.36645i) q^{11} +(-7.45466 - 21.5739i) q^{12} +(24.2515 + 33.3793i) q^{13} +(24.6883 - 8.02173i) q^{14} +(-0.481578 - 25.9763i) q^{15} +(64.5965 + 46.9321i) q^{16} +(-92.0548 - 66.8817i) q^{17} +(32.7022 + 89.2463i) q^{18} +(-149.209 + 48.4809i) q^{19} +(-12.9101 - 17.7692i) q^{20} +(-36.2152 + 12.5138i) q^{21} +(117.006 - 52.9558i) q^{22} +46.5502i q^{23} +(-54.0919 - 37.7883i) q^{24} +(-7.72542 - 23.7764i) q^{25} +(-138.137 - 44.8834i) q^{26} +(-50.7032 - 130.814i) q^{27} +(-19.0397 + 26.2059i) q^{28} +(50.6416 - 155.859i) q^{29} +(55.1218 + 72.9844i) q^{30} +(32.9018 - 23.9045i) q^{31} -179.495 q^{32} +(-171.227 + 81.3526i) q^{33} +400.565 q^{34} +(-29.8283 + 21.6716i) q^{35} +(-98.4716 - 66.1098i) q^{36} +(86.4104 - 265.944i) q^{37} +(324.632 - 446.818i) q^{38} +(205.088 + 62.4588i) q^{39} +(-60.3856 - 19.6205i) q^{40} +(-153.451 - 472.274i) q^{41} +(77.2478 - 110.576i) q^{42} +75.0666i q^{43} +(-79.2788 + 139.279i) q^{44} +(-83.3447 - 106.201i) q^{45} +(-96.3217 - 132.576i) q^{46} +(-21.1101 + 6.85909i) q^{47} +(414.819 - 7.69039i) q^{48} +(-233.502 - 169.649i) q^{49} +(71.2003 + 51.7301i) q^{50} +(-591.148 + 10.9594i) q^{51} +(172.371 - 56.0068i) q^{52} +(428.794 + 590.184i) q^{53} +(415.083 + 267.644i) q^{54} +(-134.810 + 122.887i) q^{55} +93.6394i q^{56} +(-466.862 + 668.289i) q^{57} +(178.275 + 548.675i) q^{58} +(-530.742 - 172.449i) q^{59} +(-109.177 - 33.2494i) q^{60} +(-103.934 + 143.053i) q^{61} +(-44.2414 + 136.161i) q^{62} +(-110.976 + 165.300i) q^{63} +(-5.56867 + 4.04588i) q^{64} +206.295 q^{65} +(319.322 - 585.997i) q^{66} +250.246 q^{67} +(-404.377 + 293.797i) q^{68} +(145.777 + 193.018i) q^{69} +(40.1087 - 123.442i) q^{70} +(182.830 - 251.644i) q^{71} +(-342.628 + 12.7084i) q^{72} +(334.651 + 108.735i) q^{73} +(304.194 + 936.213i) q^{74} +(-106.492 - 74.3944i) q^{75} +689.173i q^{76} +(233.801 + 133.082i) q^{77} +(-713.334 + 246.486i) q^{78} +(479.922 + 660.556i) q^{79} +(379.689 - 123.368i) q^{80} +(-619.896 - 383.628i) q^{81} +(1414.26 + 1027.52i) q^{82} +(643.162 + 467.285i) q^{83} +(3.11988 + 168.286i) q^{84} +(-541.085 + 175.809i) q^{85} +(-155.328 - 213.791i) q^{86} +(-278.108 - 804.849i) q^{87} +(51.2480 + 460.439i) q^{88} -706.692i q^{89} +(457.118 + 130.005i) q^{90} +(-94.0162 - 289.352i) q^{91} +(194.476 + 63.1892i) q^{92} +(61.5654 - 202.155i) q^{93} +(45.9290 - 63.2159i) q^{94} +(-242.405 + 746.045i) q^{95} +(-744.265 + 562.109i) q^{96} +(-171.572 + 124.654i) q^{97} +1016.06 q^{98} +(-455.218 + 873.542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 4 q^{3} - 192 q^{4} - 100 q^{6} + 108 q^{9} + 48 q^{12} - 60 q^{15} - 1248 q^{16} - 460 q^{18} + 900 q^{19} + 888 q^{22} + 1200 q^{24} + 1200 q^{25} + 568 q^{27} - 1680 q^{28} - 576 q^{31} - 1402 q^{33}+ \cdots - 736 q^{99}+O(q^{100}) \) 192 * q + 4 * q^3 - 192 * q^4 - 100 * q^6 + 108 * q^9 + 48 * q^12 - 60 * q^15 - 1248 * q^16 - 460 * q^18 + 900 * q^19 + 888 * q^22 + 1200 * q^24 + 1200 * q^25 + 568 * q^27 - 1680 * q^28 - 576 * q^31 - 1402 * q^33 + 264 * q^34 - 2364 * q^36 + 24 * q^37 + 1220 * q^39 + 4438 * q^42 - 360 * q^46 + 1946 * q^48 + 1848 * q^49 + 930 * q^51 + 840 * q^55 - 4170 * q^57 + 4320 * q^58 - 830 * q^60 - 1560 * q^61 - 7900 * q^63 - 11700 * q^64 - 4214 * q^66 + 168 * q^67 - 4992 * q^69 - 1620 * q^70 + 6720 * q^72 - 360 * q^73 + 150 * q^75 + 13972 * q^78 + 4740 * q^79 + 916 * q^81 + 6420 * q^82 + 6880 * q^84 + 2868 * q^88 + 8736 * q^91 - 5696 * q^93 - 840 * q^94 - 12470 * q^96 - 7356 * q^97 - 736 * q^99

Introduction

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